Finite Group Databasebeta

← #33993812

Subgroups — #33993812

Order 18688.

7270 conjugacy classes of subgroups.

The subgroup lattice has 1816 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#22624353C214yesmaximal, complemented
2#22624342C211yesmaximal, characteristic, complemented
3#22624336C211yesmaximal, characteristic, complemented
4#22624331C211yesmaximal, characteristic, complemented
5#22624329C211yesmaximal, characteristic, complemented
6#22624322C212yesmaximal, complemented
7#22624314C212yesmaximal, complemented
8#22624305C212yesmaximal, complemented
9#22624297C212yesmaximal, complemented
10#22624283C214yesmaximal, complemented
11#22624271C212yesmaximal, complemented
12#22624261C212yesmaximal, complemented
13#22624247C214yesmaximal, complemented
14#22624239C214yesmaximal, complemented
15#22624070C214yesmaximal, complemented
16#22623557C212yesmaximal, complemented
17#22623541C212yesmaximal, complemented
18#22623498C212yesmaximal, complemented
19#22623495C212yesmaximal, complemented
20#41×D292C212yesmaximal, complemented
21#22623417C212yesmaximal, complemented
22#22623352C214yesmaximal, complemented
23#22623347C214yesmaximal, complemented
24#22623261C214yesmaximal, complemented
25#22623227C211yesmaximal, characteristic, complemented
26C2×#17989137C211yesmaximal, characteristic, complemented
27C73×#3444C211yesmaximal, characteristic, complemented
28C22×#11924028C2212yescomplemented
29C2×#41×D73C2214yescomplemented
30#17989341C2214yescomplemented
31#17989339C2218yescomplemented
32#17989335C2214yescomplemented
33#17989334C2218yescomplemented
34#17989333C2218yescomplemented
35#17989331C2214yescomplemented
36#17989329C2214yescomplemented
37#17989328C2218yescomplemented
38#17989327C2218yescomplemented
39#17989325C2218yescomplemented
40#17989322C2212yescomplemented
41Q8×Dic146C2212yescomplemented
42#17989311C2212yescomplemented
43#17989310C2212yescomplemented
44#17989303C2212yescomplemented
45#17989302C2212yescomplemented
46#17989302C2212yescomplemented
47#17989302C2214yescomplemented
48#17989300C2218yescomplemented
49#17989300C2214yescomplemented
50#17989298C2212yescomplemented
51#17989297C2212yescomplemented
52#17989297C2212yescomplemented
53#17989294C2212yescomplemented
54#17989290C2214yescomplemented
55#17989287C2214yescomplemented
56#17989283C2214yescomplemented
57#17989281C2214yescomplemented
58#17989279C2214yescomplemented
59#17989278C2214yescomplemented
60#17989277C2214yescomplemented
61#17989275C2214yescomplemented
62#17989266C2218yescomplemented
63#17989264C2218yescomplemented
64#17989261C2218yescomplemented
65#17989259C2212yescomplemented
66#17989259C2212yescomplemented
67#17989258C2212yescomplemented
68#17989258C2214yescomplemented
69#17989257C2212yescomplemented
70#17989256C2214yescomplemented
71Q8×D292C2212yescomplemented
72#17989252C2212yescomplemented
73#17989249C2214yescomplemented
74#17989245C2214yescomplemented
75#17989242C2212yescomplemented
76#17989241C2214yescomplemented
77#17989241C2212yescomplemented
78#17989240C2212yescomplemented
79#17989240C2212yescomplemented
80#17989237C2214yescomplemented
81#17989233C2214yescomplemented
82#17989233C2214yescomplemented
83#17989232C2218yescomplemented
84#17989232C2214yescomplemented
85#17989230C2214yescomplemented
86#17989228C2214yescomplemented
87#17989226C2218yescomplemented
88#17989225C2214yescomplemented
89D4×D292C2212yescomplemented
90D4×D292C2214yescomplemented
91D4×D292C2212yescomplemented
92#17989222C2212yescomplemented
93#17989221C2214yescomplemented
94#17989217C2214yescomplemented
95#17989215C2214yescomplemented
96#17989210C2214yescomplemented
97#17989209C2218yescomplemented
98#17989208C2214yescomplemented
99#17989208C2214yescomplemented
100#17989206C2214yescomplemented
101#17989203C2218yescomplemented
102#17989193C2214yescomplemented
103#17989192C2214yescomplemented
104#17989192C2214yescomplemented
105#17989190C2214yescomplemented
106#17989189C2218yescomplemented
107#17989188C2218yescomplemented
108#17989176C2218yescomplemented
109#17989173C2218yescomplemented
110#17989170C2218yescomplemented
111#17989170C2218yescomplemented
112#17989167C2214yescomplemented
113#17989167C2214yescomplemented
114#17989167C2214yescomplemented
115#17989166C2214yescomplemented
116#17989166C2214yescomplemented
117#17989165C2214yescomplemented
118#17989160C2214yescomplemented
119#17989160C2214yescomplemented
120#17989159C2218yescomplemented
121#17989156C2214yescomplemented
122#17989155C2214yescomplemented
123#17989153C2214yescomplemented
124#17989153C2214yescomplemented
125#17989153C2214yescomplemented
126#17989152C2218yescomplemented
127#17989151C2214yescomplemented
128#17989148C2218yescomplemented
129#17989147C2218yescomplemented
130#17989144C2211yescharacteristic, complemented
131#17989144C2211yescharacteristic, complemented
132#17989144C2211yescharacteristic, complemented
133#17989137C2211yescharacteristic
134#17989137C2211yescharacteristic
135#17989137C2211yescharacteristic
136#17989137C2212yescomplemented
137#17989137C2211yescharacteristic, complemented
138#17989137C2212yescomplemented
139#17989137C2211yescharacteristic, complemented
140#17989137C2214yescomplemented
141#17989137C2212yescomplemented
142#17989137C2211yescharacteristic, complemented
143#17989137C2211yescharacteristic, complemented
144#17989137C2212yescomplemented
145#17989137C2212yescomplemented
146#17989137C2212yescomplemented
147#17989134C2218yescomplemented
148#17989134C2218yescomplemented
149#17989134C2214yescomplemented
150C2×#14556591C2211yescharacteristic, complemented
151C2×#14556588C2211yescharacteristic
152#17989124C2214yescomplemented
153#17989124C2218yescomplemented
154#17989121C2212yescomplemented
155#17989121C2214yescomplemented
156#17989121C2212yescomplemented
157#17989121C2212yescomplemented
158#17989121C2212yescomplemented
159#17989121C2212yescomplemented
160#17989121C2212yescomplemented
161#17989115C2218yescomplemented
162C2×#14556579C2212yescomplemented
163#17989099C2214yescomplemented
164#17989099C2218yescomplemented
165#17989098C2212yescomplemented
166#17989098C2212yescomplemented
167#17989098C2212yescomplemented
168#17989096C2218yescomplemented
169#17989096C2218yescomplemented
170#17989096C2218yescomplemented
171#17989094C2214yescomplemented
172C2×#14556565C2212yescomplemented
173C2×#14556565C2212yescomplemented
174C4×#11924029C2214yescomplemented
175C4×#11924028C2214yescomplemented
176C4×#11924028C2212yescomplemented
177C4×#11924028C2212yescomplemented
178C4×#11924028C2212yescomplemented
179C2×C4×D292C2212yescomplemented
180C2×C4×D292C2212yescomplemented
181C2×C4×D292C2214yescomplemented
182C4×D4×D73C2214yescomplemented
183#117×D73C2214yescomplemented
184#533×C73C2211yescharacteristic, complemented
185#533×C73C2211yescharacteristic, complemented
186#533×C73C2211yescharacteristic, complemented
187#532×C73C2211yescharacteristic
188#532×C73C2211yescharacteristic, complemented
189#532×C73C2211yescharacteristic, complemented
190#529×C73C2212yescomplemented
191#529×C73C2212yescomplemented
192#529×C73C2212yescomplemented
193#529×C73C2212yescomplemented
194#529×C73C2212yescomplemented
195#529×C73C2212yescomplemented
196#525×C73C2212yescomplemented
197#525×C73C2212yescomplemented
198#525×C73C2212yescomplemented
199C4×#41×C73C2212yescomplemented
200C4×#41×C73C2212yescomplemented
201C4×#41×C73C2212yescomplemented
202C22×C42×C73C2211yescharacteristic, complemented
203C2×#11924029C2314yes—
204C2×#11924029C2314yes—
205C2×#11924028—48no—
206C2×#11924028C2312yes—
207C2×#11924028C2312yes—
208C2×#11924028C2318yes—
209C2×#11924028C2314yes—
210C2×#11924028C2312yes—
211C2×#11924028C2312yes—
212C2×#11924028C2314yes—
213C2×#11924028C2312yes—
214C2×#11924028C2312yes—
215C2×#11924028C2312yes—
216C2×#11924028C2314yes—
217C2×#11924027C2318yes—
218C2×#11924027C2314yes—
219#41×D73—416no—
220C22×Dic146C2312yes—
221C2×Q8×D73C2314yes—
222C22×D292C2312yes—
223C22×D292C2312yes—
224C22×D292C2312yes—
225C22×D292C2314yes—
226C22×C22⋊D73C2314yes—
227C2×D4×D73C2318yes—
228C2×D4×D73C2314yes—
229C2×D4×D73C2314yes—
230C22×C4×D73C2314yes—
231C22×C4×D73C2318yes—
232#14556591C2311yescharacteristic
233#14556591C2311yescharacteristic
234#14556591C2312yes—
235#14556591C2312yes—
236#14556591C2312yes—
237#14556591C2311yescharacteristic
238#14556591C2311yescharacteristic
239#14556591C2311yescharacteristic
240#14556591C2314yes—
241#14556590C2318yes—
242#14556590C2318yes—
243#14556590C2314yes—
244#14556588C2311yescharacteristic
245#14556588C2312yes—
246#14556588C2312yes—
247#14556588C2311yescharacteristic
248#14556588C2312yes—
249#14556588C2311yescharacteristic
250#14556588C2314yes—
251#14556587C2318yes—
252#14556587C2318yes—
253#14556587C2314yes—
254#14556586C2318yes—
255#14556586C2318yes—
256#14556586C2318yes—
257#14556586C2318yes—
258#14556585C2314yes—
259#14556585C2314yes—
260#14556585C2318yes—
261#14556584C2318yes—
262#14556583C2312yes—
263#14556583C2312yes—
264#14556583C2312yes—
265#14556583C2314yes—
266#14556582C2318yes—
267#14556582C2314yes—
268#14556581C2318yes—
269#14556580C2318yes—
270#14556580C2314yes—
271#14556579C2312yes—
272#14556579C2312yes—
273#14556579C2312yes—
274#14556579C2314yes—
275#14556579C2312yes—
276#14556579C2312yes—
277#14556579C2314yes—
278#14556579C2314yes—
279#14556579C2312yes—
280#14556579C2312yes—
281#14556579C2318yes—
282#14556577C2318yes—
283#14556577C2318yes—
284#14556577C2318yes—
285#14556577C2318yes—
286#14556577C2318yes—
287#14556577C2318yes—
288#14556576C2318yes—
289#14556576C2318yes—
290#14556576C2318yes—
291#14556576C2318yes—
292#14556576C2318yes—
293#14556576C2318yes—
294#14556576C2318yes—
295#14556575C2318yes—
296#14556575C2318yes—
297#14556575C2318yes—
298#14556574C2314yes—
299#14556574C2314yes—
300#14556574C2314yes—
301#14556574C2318yes—
302#14556573C2318yes—
303#14556573C2318yes—
304#14556573C2318yes—
305#14556573C2318yes—
306#14556572C2318yes—
307#14556571C2314yes—
308#14556571C2314yes—
309#14556571C2318yes—
310#14556571C2318yes—
311#14556570C2312yes—
312#14556570C2312yes—
313#14556570C2312yes—
314#14556570C2312yes—
315#14556570C2312yes—
316#14556570C2312yes—
317#14556570C2314yes—
318#14556569C2318yes—
319#14556569C2318yes—
320#14556569C2318yes—
321#14556569C2318yes—
322#14556568C2318yes—
323#14556568C2318yes—
324#14556568C2318yes—
325#14556567C2318yes—
326#14556567C2314yes—
327#14556567C2314yes—
328#14556567C2314yes—
329#14556566C2314yes—
330#14556566C2318yes—
331#14556566C2318yes—
332#14556566C2318yes—
333#14556566C2314yes—
334#14556566C2314yes—
335#14556566C2314yes—
336#14556566C2318yes—
337#14556566C2318yes—
338#14556565C2312yes—
339#14556565C2312yes—
340#14556565C2312yes—
341#14556565C2312yes—
342#14556565C2312yes—
343#14556565C2312yes—
344#14556565C2314yes—
345#14556565C2312yes—
346#14556565C2312yes—
347#14556565C2312yes—
348#14556565C2312yes—
349#14556565C2312yes—
350#14556565C2312yes—
351#14556565C2314yes—
352#14556565C2314yes—
353#14556565C2312yes—
354#14556565C2312yes—
355#14556565C2314yes—
356#14556565C2314yes—
357#14556565C2314yes—
358#14556565C2314yes—
359#14556565C2318yes—
360#14556564C2318yes—
361#14556564C2318yes—
362#14556564C2318yes—
363#14556564C2318yes—
364#14556564C2318yes—
365#14556564C2318yes—
366#14556564C2318yes—
367#14556564C2318yes—
368#14556564C2318yes—
369#14556563C2318yes—
370#14556563C2318yes—
371#14556563C2318yes—
372#14556562C2318yes—
373#14556562C2318yes—
374#14556562C2314yes—
375#14556562C2314yes—
376#14556562C2314yes—
377#14556561C2318yes—
378#14556561C2318yes—
379#14556561C2318yes—
380#14556561C2318yes—
381#14556561C2318yes—
382#14556561C2318yes—
383#14556560C2314yes—
384#14556559C2318yes—
385#14556559C2318yes—
386#14556559C2318yes—
387#14556559C2318yes—
388Q8×Dic73C2314yes—
389C4×Dic146C2312yes—
390C4×Dic146C2312yes—
391C4×Dic146C2312yes—
392C4×Dic146C2312yes—
393C4×Dic146C2312yes—
394C4×Dic146C2312yes—
395C4×Dic146C2314yes—
396C4×D292C2312yes—
397C4×D292C2312yes—
398C4×D292C2312yes—
399C4×D292C2312yes—
400C4×D292C2312yes—
401C4×D292C2312yes—
402C4×D292C2312yes—
403C4×D292C2318yes—
404C4×D292C2312yes—
405C4×D292C2314yes—
406C4×D292C2318yes—
407C4×D292C2312yes—
408C4×D292C2312yes—
409C4×D292C2312yes—
410C4×D292C2312yes—
411C4×D292C2314yes—
412C4×D292C2314yes—
413C4×D292C2312yes—
414C4×D292C2312yes—
415C4×D292C2314yes—
416C4×D292C2318yes—
417C4×D292C2314yes—
418C4×D292C2314yes—
419C4×D292C2314yes—
420D4×Dic73C2314yes—
421#14556553C2318yes—
422#14556553C2314yes—
423#14556553C2314yes—
424C4×C22⋊D73C2314yes—
425C4×C22⋊D73C2314yes—
426C4×C22⋊D73C2318yes—
427C4×C22⋊D73C2314yes—
428C4×C22⋊D73C2314yes—
429C4×C22⋊D73C2314yes—
430C4×C22⋊D73C2314yes—
431C4×C22⋊D73C2318yes—
432C4×C22⋊D73C2318yes—
433#14556551C2318yes—
434#14556550C2312yes—
435#14556550C2312yes—
436#14556550C2312yes—
437#14556550C2314yes—
438#14556549C2314yes—
439#14556549C2314yes—
440#14556549C2314yes—
441#14556549C2318yes—
442#14556548C2314yes—
443#14556548C2314yes—
444#14556548C2314yes—
445#14556548C2318yes—
446#14556548C2318yes—
447#14556547C2318yes—
448C2×C4⋊Dic73C2312yes—
449C2×C4⋊Dic73C2312yes—
450C2×C4⋊Dic73C2314yes—
451C4⋊C4×D73C2314yes—
452C4⋊C4×D73C2314yes—
453C4⋊C4×D73C2314yes—
454C2×#11924005C2318yes—
455C2×#11924005C2314yes—
456C2×#11924005C2314yes—
457C22⋊C4×D73C2318yes—
458C22⋊C4×D73C2318yes—
459C42×D73C2318yes—
460C42×D73C2314yes—
461C2×#41×C73C2312yes—
462C2×#41×C73C2312yes—
463C2×#41×C73C2312yes—
464C23×C4×C73C2311yescharacteristic
465C23×C4×C73C2311yescharacteristic
466C23×C4×C73C2311yescharacteristic
467C4⋊Q8×C73C2311yescharacteristic
468C4⋊Q8×C73C2311yescharacteristic
469C4⋊Q8×C73C2311yescharacteristic
470#127×C73C2311yescharacteristic
471#126×C73C2314yes—
472#126×C73C2314yes—
473#125×C73C2312yes—
474#125×C73C2312yes—
475#125×C73C2312yes—
476#124×C73C2312yes—
477#124×C73C2312yes—
478#124×C73C2312yes—
479#123×C73C2314yes—
480#123×C73C2314yes—
481#123×C73C2314yes—
482C22⋊Q8×C73C2312yes—
483C22⋊Q8×C73C2312yes—
484C22⋊Q8×C73C2312yes—
485C22⋊Q8×C73C2312yes—
486C22⋊Q8×C73C2312yes—
487C22⋊Q8×C73C2312yes—
488#121×C73C2312yes—
489#121×C73C2312yes—
490#121×C73C2312yes—
491#121×C73C2312yes—
492#121×C73C2312yes—
493#121×C73C2312yes—
494#120×C73C2314yes—
495C4×Q8×C73C2312yes—
496C4×Q8×C73C2312yes—
497C4×Q8×C73C2312yes—
498C4×Q8×C73C2312yes—
499C4×Q8×C73C2312yes—
500C4×Q8×C73C2312yes—
501C4×D4×C73C2314yes—
502C4×D4×C73C2314yes—
503C4×D4×C73C2312yes—
504C4×D4×C73C2312yes—
505C4×D4×C73C2314yes—
506C4×D4×C73C2314yes—
507C4×D4×C73C2312yes—
508C4×D4×C73C2312yes—
509C4×D4×C73C2314yes—
510C4×D4×C73C2312yes—
511C4×D4×C73C2314yes—
512C4×D4×C73C2312yes—
513#117×C73C2314yes—
514#117×C73C2312yes—
515#117×C73C2314yes—
516#117×C73C2312yes—
517#117×C73C2312yes—
518#117×C73C2314yes—
519C2×C42×C73C2311yescharacteristic
520C2×C42×C73C2311yescharacteristic
521C2×C42×C73C2311yescharacteristic
522C2×C42×C73C2311yescharacteristic
523C2×C42×C73C2311yescharacteristic
524C2×C42×C73C2311yescharacteristic
525C2×C42×C73C2314yes—
526C2×C42×C73C2311yescharacteristic
527C2×C42×C73C2311yescharacteristic
528C2×C42×C73C2311yescharacteristic
529C2×C42×C73C2311yescharacteristic
530C2×C42×C73C2311yescharacteristic
531C2×C42×C73C2311yescharacteristic
532C23×D73C2414yes—
533C23×D73C2418yes—
534#11924029—48no—
535#11924029—48no—
536#11924028—28no—
537#11924028—44no—
538#11924028—48no—
539#11924028—416no—
540#11924028—44no—
541#11924028—48no—
542#11924028—44no—
543#11924028—48no—
544#11924028—44no—
545#11924028—44no—
546#11924028—44no—
547#11924027—48no—
548#11924027—416no—
549C2×Dic146—44no—
550C2×Dic146C2412yes—
551C2×Dic146C2412yes—
552C2×Dic146C2412yes—
553C2×Dic146C2412yes—
554C2×Dic146C2414yes—
555C2×Dic146C2418yes—
556C2×Dic146C2412yes—
557Q8×D73—48no—
558C2×D292—44no—
559C2×D292—48no—
560C2×D292—44no—
561C2×D292—44no—
562C2×D292C2412yes—
563C2×D292C2412yes—
564C2×D292C2412yes—
565C2×D292C2412yes—
566C2×D292C2412yes—
567C2×D292C2412yes—
568C2×D292C2418yes—
569C2×D292C2412yes—
570C2×D292C2418yes—
571C2×D292C2414yes—
572C2×D292C2414yes—
573C2×D292C2412yes—
574C2×D292C2414yes—
575C2×D292C2418yes—
576C2×D292C2412yes—
577C2×C22⋊D73—48no—
578C2×C22⋊D73C2414yes—
579C2×C22⋊D73C2418yes—
580C2×C22⋊D73C2414yes—
581C2×C22⋊D73C2414yes—
582C2×C22⋊D73C2418yes—
583C2×C22⋊D73C2414yes—
584C2×C22⋊D73C2414yes—
585C2×C22⋊D73C2418yes—
586C2×C22⋊D73C2418yes—
587C2×C22⋊D73C2414yes—
588C2×C22⋊D73C2414yes—
589D4×D73—48no—
590D4×D73—48no—
591D4×D73—416no—
592C22×Dic73C2414yes—
593C22×Dic73C2418yes—
594C2×C4×D73—216no—
595C2×C4×D73—416no—
596C2×C4×D73C2414yes—
597C2×C4×D73C2414yes—
598C2×C4×D73C2414yes—
599C2×C4×D73C2414yes—
600C2×C4×D73C2414yes—
601C2×C4×D73C2414yes—
602C2×C4×D73C2414yes—
603C2×C4×D73C2418yes—
604C2×C4×D73C2418yes—
605C2×C4×D73C2418yes—
606C2×C4×D73C2418yes—
607C4⋊Dic73C2412yes—
608C4⋊Dic73C2412yes—
609C4⋊Dic73C2412yes—
610C4⋊Dic73C2412yes—
611C4⋊Dic73C2412yes—
612C4⋊Dic73C2412yes—
613C4⋊Dic73C2412yes—
614C4⋊Dic73C2418yes—
615C4⋊Dic73C2414yes—
616C4⋊Dic73C2414yes—
617C4⋊Dic73C2418yes—
618C4⋊Dic73C2412yes—
619C4⋊Dic73C2412yes—
620C4⋊Dic73C2412yes—
621#11924007C2418yes—
622#11924007C2418yes—
623#11924007C2418yes—
624#11924007C2414yes—
625#11924007C2414yes—
626#11924007C2418yes—
627#11924007C2414yes—
628#11924007C2414yes—
629#11924007C2414yes—
630#11924007C2414yes—
631C22⋊Dic73C2414yes—
632C22⋊Dic73C2418yes—
633C22⋊Dic73C2418yes—
634C22⋊Dic73C2414yes—
635C22⋊Dic73C2414yes—
636#11924005C2414yes—
637#11924005C2418yes—
638#11924005C2418yes—
639#11924005C2418yes—
640#11924005C2414yes—
641#11924005C2414yes—
642#11924005C2414yes—
643#11924005C2414yes—
644#11924005C2414yes—
645#11924005C2418yes—
646#11924005C2418yes—
647#11924005C2414yes—
648#11924005C2414yes—
649#11924005C2414yes—
650#11924005C2414yes—
651#11924005C2418yes—
652#11924005C2414yes—
653#11924005C2414yes—
654#11924005C2414yes—
655#11924005C2414yes—
656#11924005C2418yes—
657#11924005C2418yes—
658C4×Dic73C2414yes—
659C4×Dic73C2418yes—
660C4×Dic73C2418yes—
661C4×Dic73C2414yes—
662C4×Dic73C2414yes—
663C24×C73C2411yescharacteristic
664#41×C73—28no—
665#41×C73—44no—
666#41×C73—44no—
667C2×Q8×C73C2412yes—
668C2×Q8×C73C2412yes—
669C2×Q8×C73C2412yes—
670C2×D4×C73C2414yes—
671C2×D4×C73C2412yes—
672C2×D4×C73C2412yes—
673C2×D4×C73C2414yes—
674C2×D4×C73C2414yes—
675C2×D4×C73C2412yes—
676C22×C4×C73—24no—
677C22×C4×C73—42no—
678C22×C4×C73—42no—
679C22×C4×C73C2411yescharacteristic
680C22×C4×C73C2411yescharacteristic
681C22×C4×C73C2411yescharacteristic
682C22×C4×C73C2411yescharacteristic
683C22×C4×C73C2411yescharacteristic
684C22×C4×C73C2411yescharacteristic
685C22×C4×C73C2411yescharacteristic
686C22×C4×C73C2411yescharacteristic
687C22×C4×C73C2411yescharacteristic
688C22×C4×C73C2411yescharacteristic
689C22×C4×C73C2411yescharacteristic
690C22×C4×C73C2414yes—
691C22×C4×C73C2414yes—
692C22×C4×C73C2411yescharacteristic
693C22×C4×C73C2411yescharacteristic
694C22×C4×C73C2411yescharacteristic
695C22×C4×C73C2411yescharacteristic
696C22×C4×C73C2411yescharacteristic
697C22×C4×C73C2411yescharacteristic
698C22×C4×C73C2414yes—
699C22×C4×C73C2411yescharacteristic
700C4⋊C4×C73C2412yes—
701C4⋊C4×C73C2412yes—
702C4⋊C4×C73C2412yes—
703C4⋊C4×C73C2412yes—
704C4⋊C4×C73C2412yes—
705C4⋊C4×C73C2412yes—
706C4⋊C4×C73C2414yes—
707C4⋊C4×C73C2414yes—
708C4⋊C4×C73C2414yes—
709C4⋊C4×C73C2414yes—
710C4⋊C4×C73C2414yes—
711C4⋊C4×C73C2414yes—
712C22⋊C4×C73C2414yes—
713C22⋊C4×C73C2414yes—
714C22⋊C4×C73C2414yes—
715C22⋊C4×C73C2414yes—
716C22⋊C4×C73C2414yes—
717C22⋊C4×C73C2414yes—
718C22⋊C4×C73C2414yes—
719C22⋊C4×C73C2414yes—
720C22⋊C4×C73C2414yes—
721C42×C73C2411yescharacteristic
722C42×C73C2411yescharacteristic
723C42×C73C2411yescharacteristic
724C42×C73C2411yescharacteristic
725C42×C73C2411yescharacteristic
726C42×C73C2411yescharacteristic
727C42×C73C2411yescharacteristic
728C42×C73C2411yescharacteristic
729C42×C73C2411yescharacteristic
730C42×C73C2411yescharacteristic
731C42×C73C2411yescharacteristic
732C42×C73C2411yescharacteristic
733C42×C73C2411yescharacteristic
734C42×C73C2411yescharacteristic
735C42×C73C2411yescharacteristic
736C42×C73C2411yescharacteristic
737C42×C73C2414yes—
738C42×C73C2414yes—
739C42×C73C2414yes—
740C23×C73—22no—
741C23×C73—41no—
742C23×C73—41no—
743C23×C73C2514yes—
744C23×C73C2511yescharacteristic
745C23×C73C2511yescharacteristic
746C23×C73C2511yescharacteristic
747C22×D73—28no—
748C22×D73—48no—
749C22×D73—48no—
750C22×D73—44no—
751C22×D73—44no—
752C22×D73—48no—
753C22×D73C2514yes—
754C22×D73C2514yes—
755C22×D73C2514yes—
756Q8×C73—24no—
757Q8×C73—24no—
758Q8×C73—42no—
759D4×C73—28no—
760D4×C73—24no—
761D4×C73—24no—
762D4×C73—44no—
763D4×C73—44no—
764D4×C73—42no—
765C2×C4×C73—22no—
766C2×C4×C73—22no—
767C2×C4×C73—22no—
768C2×C4×C73—22no—
769C2×C4×C73—22no—
770C2×C4×C73—28no—
771C2×C4×C73—22no—
772C2×C4×C73—22no—
773C2×C4×C73—22no—
774C2×C4×C73—22no—
775C2×C4×C73—22no—
776C2×C4×C73—22no—
777C2×C4×C73—28no—
778C2×C4×C73—41no—
779C2×C4×C73—41no—
780C2×C4×C73—41no—
781C2×C4×C73—41no—
782C2×C4×C73—41no—
783C2×C4×C73—41no—
784C2×C4×C73—44no—
785C2×C4×C73H(5,𝔽2)14yes—
786C2×C4×C73C2511yescharacteristic
787C2×C4×C73C2511yescharacteristic
788C2×C4×C73C2511yescharacteristic
789C2×C4×C73C2511yescharacteristic
790C2×C4×C73C2511yescharacteristic
791C2×C4×C73C2511yescharacteristic
792C2×C4×C73C2511yescharacteristic
793C2×C4×C73C2511yescharacteristic
794C2×C4×C73C2514yes—
795C2×C4×C73C2514yes—
796C2×C4×C73C2514yes—
797C2×C4×C73C2511yescharacteristic
798C2×C4×C73C2511yescharacteristic
799C2×C4×C73C2511yescharacteristic
800C2×C4×C73C2511yescharacteristic
801C22⋊D73—28no—
802C22⋊D73—48no—
803C22⋊D73—48no—
804C22⋊D73—48no—
805C22⋊D73—44no—
806C22⋊D73—44no—
807C22⋊D73—44no—
808C22⋊D73—44no—
809C22⋊D73—48no—
810C22⋊D73—44no—
811C22⋊D73—44no—
812C2×Dic73—28no—
813C2×Dic73—48no—
814C2×Dic73C2514yes—
815C2×Dic73C2514yes—
816C2×Dic73C2514yes—
817C2×Dic73C2514yes—
818C2×Dic73C2514yes—
819D292—24no—
820D292—24no—
821D292—24no—
822D292—24no—
823D292—24no—
824D292—24no—
825D292—48no—
826D292—48no—
827D292—44no—
828D292—44no—
829D292—42no—
830D292—44no—
831D292—42no—
832D292—42no—
833D292—48no—
834C4×D73—28no—
835C4×D73—28no—
836C4×D73—28no—
837C4×D73—28no—
838C4×D73—28no—
839C4×D73—28no—
840C4×D73—48no—
841C4×D73—48no—
842C4×D73—44no—
843C4×D73—48no—
844C4×D73—48no—
845Dic146—24no—
846Dic146—24no—
847Dic146—48no—
848Dic146—42no—
849Dic146—44no—
850Dic146—42no—
851Dic146—42no—
852C22×C73—21no—
853C22×C73—21no—
854C22×C73—24no—
855C22×C73—21no—
856C22×C73—21no—
857C22×C73—21no—
858C22×C73—21no—
859C22×C73—24no—
860C22×C73—24no—
861C22×C73—21no—
862C22×C73—21no—
863C22×C73—44no—
864C22×C73C2×H(5,𝔽2)12yes—
865C22×C73C2611yescharacteristic
866C2×D73—24no—
867C2×D73—24no—
868C2×D73—24no—
869C2×D73—24no—
870C2×D73—24no—
871C2×D73—24no—
872C2×D73—24no—
873C2×D73—24no—
874C2×D73—24no—
875C2×D73—88no—
876C2×D73—816no—
877C4×C73—21no—
878C4×C73—21no—
879C4×C73—24no—
880C4×C73—21no—
881C4×C73—21no—
882C4×C73—24no—
883C4×C73—24no—
884C4×C73—21no—
885C4×C73—21no—
886C4×C73—21no—
887C4×C73—21no—
888C4×C73C2×H(5,𝔽2)12yes—
889C4×C73C2×H(5,𝔽2)12yes—
890C4×C73#58512yes—
891C4×C73#58512yes—
892Dic73—24no—
893Dic73—24no—
894Dic73—24no—
895Dic73—24no—
896Dic73—24no—
897#62759—731nomaximal, Sylow
898C2×C73—22no—
899C2×C73—44no—
900C2×C73—41no—
901C2×C73—41no—
902C2×C73C22×H(5,𝔽2)11yescharacteristic
903C2×C73C2×#58511yescharacteristic
904C2×C73C2×#58511yescharacteristic
905D73—44no—
906D73—44no—
907D73—44no—
908#3551—734no—
909#3550—731no—
910#3549—731no—
911#3548—731no—
912#3548—731no—
913#3547—732no—
914#3547—732no—
915#3546—732no—
916#3546—732no—
917#3545—734no—
918#3544—732no—
919#3543—732no—
920#3542—734no—
921#3542—734no—
922#3529—734no—
923#3483—732no—
924#3481—732no—
925#3475—732no—
926#3475—732no—
927D4×#41—732no—
928D4×#41—732no—
929#3460—734no—
930#3460—734no—
931#3449—734no—
932#3444—731no—
933#3444D7311yescharacteristic, complemented
934C2×#532—731no—
935C73#6275911yescharacteristic, complemented, Sylow
936C22×#41—734no—
937C22×#41—732no—
938#563—738no—
939#563—734no—
940#562—734no—
941#562—734no—
942#562—738no—
943#562—738no—
944H(3,𝔽4)—734no—
945#560—738no—
946#560—738no—
947#560—738no—
948#559—732no—
949Q82—732no—
950#556—732no—
951#556—732no—
952#555—732no—
953#555—732no—
954#555—734no—
955#555—732no—
956#555—734no—
957#555—738no—
958#554—732no—
959#554—732no—
960#554—732no—
961#554—732no—
962#553—734no—
963#553—734no—
964#553—734no—
965#553—734no—
966#552—734no—
967#552—734no—
968#552—734no—
969#552—734no—
970#551—738no—
971#551—738no—
972#551—738no—
973#550—734no—
974#550—732no—
975#550—732no—
976#550—732no—
977#550—734no—
978#550—732no—
979D4×Q8—732no—
980D4×Q8—732no—
981#548—734no—
982#548—734no—
983#547—732no—
984#547—732no—
985#547—734no—
986#547—734no—
987#547—732no—
988#547—732no—
989#546—734no—
990#546—734no—
991#546—734no—
992#546—738no—
993#546—738no—
994#546—734no—
995#546—734no—
996#546—734no—
997D42—732no—
998D42—734no—
999D42—734no—
1000D42—732no—
1001D42—732no—
1002#544—734no—
1003#544—734no—
1004#542—738no—
1005#542—734no—
1006#542—734no—
1007#542—738no—
1008#542—734no—
1009#542—734no—
1010#540—734no—
1011#540—738no—
1012#540—734no—
1013#540—738no—
1014#540—734no—
1015#540—734no—
1016#538—738no—
1017#538—738no—
1018#538—738no—
1019#538—738no—
1020#537—734no—
1021#537—734no—
1022#537—734no—
1023#537—734no—
1024#537—734no—
1025#537—734no—
1026#536—738no—
1027#536—734no—
1028#536—734no—
1029#535—734no—
1030#535—734no—
1031#535—734no—
1032#535—734no—
1033#535—734no—
1034#535—738no—
1035#535—734no—
1036#534—738no—
1037#534—738no—
1038#533—731no—
1039#533—731no—
1040#533—731no—
1041#533C2×D7311yescharacteristic, complemented
1042#533C2×D7311yescharacteristic, complemented
1043#533C2×D7311yescharacteristic, complemented
1044#532—738no—
1045#532—738no—
1046#532—734no—
1047#532—731no—
1048#532—731no—
1049#532—731no—
1050#532—732no—
1051#532—732no—
1052#532—731no—
1053#532—732no—
1054#532—732no—
1055#532—732no—
1056#532—731no—
1057#532—732no—
1058#532—731no—
1059#532—731no—
1060#532—734no—
1061#532C2×D7311yescharacteristic
1062#532C2×D7311yescharacteristic, complemented
1063#532C2×D7311yescharacteristic, complemented
1064C2×C4⋊Q8—731no—
1065C2×#127—731no—
1066#529—734no—
1067#529—738no—
1068#529—738no—
1069#529—732no—
1070#529—732no—
1071#529—732no—
1072#529—732no—
1073#529—732no—
1074#529—732no—
1075#529—734no—
1076#529C2×D7312yescomplemented
1077#529C2×D7312yescomplemented
1078#529C2×D7312yescomplemented
1079#529C2×D7312yescomplemented
1080#529C2×D7312yescomplemented
1081#529C2×D7312yescomplemented
1082C2×#124—732no—
1083#525—734no—
1084#525—732no—
1085#525—732no—
1086#525—732no—
1087#525—738no—
1088#525—738no—
1089#525—738no—
1090#525—734no—
1091#525—738no—
1092#525C2×D7312yescomplemented
1093#525C2×D7312yescomplemented
1094#525C2×D7312yescomplemented
1095C2×#121—732no—
1096C2×#121—732no—
1097C4×#41—734no—
1098C4×#41—732no—
1099C4×#41—732no—
1100C4×#41—732no—
1101C4×#41—734no—
1102C4×#41C2×D7312yescomplemented
1103C4×#41C2×D7312yescomplemented
1104C4×#41C2×D7312yescomplemented
1105C2×C4×D4—734no—
1106C2×C4×D4—732no—
1107C2×C4×D4—732no—
1108C2×C4×D4—734no—
1109C2×#117—734no—
1110C22×C42C2×D7311yescharacteristic, complemented
1111C2×#41—2928no—
1112C2×#41—29216no—
1113C2×#41—734no—
1114C2×#41—734no—
1115C2×#41—738no—
1116C2×#41—734no—
1117C2×#41—732no—
1118C2×#41—732no—
1119C2×#41—734no—
1120C2×#41—732no—
1121C2×#41—738no—
1122C2×#41—734no—
1123C2×#41—732no—
1124C2×#41—732no—
1125C2×#41—734no—
1126C2×#41—732no—
1127C2×#41—732no—
1128C2×#41C22×D7312yes—
1129C2×#41C22×D7312yes—
1130C2×#41C22×D7312yes—
1131C22×Q8—734no—
1132C22×Q8—732no—
1133C22×D4—734no—
1134C22×D4—734no—
1135C22×D4—738no—
1136C22×D4—734no—
1137C22×D4—732no—
1138C22×D4—732no—
1139C22×D4—734no—
1140C22×D4—732no—
1141C23×C4—738no—
1142C23×C4—734no—
1143C23×C4C22×D7311yescharacteristic
1144C23×C4C22×D7311yescharacteristic
1145C23×C4C22×D7311yescharacteristic
1146C4⋊Q8—738no—
1147C4⋊Q8—738no—
1148C4⋊Q8—734no—
1149C4⋊Q8—732no—
1150C4⋊Q8—732no—
1151C4⋊Q8—731no—
1152C4⋊Q8—731no—
1153C4⋊Q8—732no—
1154C4⋊Q8—731no—
1155C4⋊Q8—731no—
1156C4⋊Q8—731no—
1157C4⋊Q8—734no—
1158C4⋊Q8C22×D7311yescharacteristic
1159C4⋊Q8C22×D7311yescharacteristic
1160C4⋊Q8C22×D7311yescharacteristic
1161#127—738no—
1162#127—738no—
1163#127—734no—
1164#127—732no—
1165#127—732no—
1166#127—731no—
1167#127—731no—
1168#127—732no—
1169#127—731no—
1170#127—734no—
1171#127C22×D7311yescharacteristic
1172#126—738no—
1173#126—738no—
1174#126—738no—
1175#126—738no—
1176#126—738no—
1177#126—734no—
1178#126—734no—
1179#126—738no—
1180#126C22×D7314yes—
1181#126C22×D7314yes—
1182#125—738no—
1183#125—738no—
1184#125—734no—
1185#125—732no—
1186#125—732no—
1187#125—732no—
1188#125—734no—
1189#125C22×D7312yes—
1190#125C22×D7312yes—
1191#125C22×D7312yes—
1192#124—734no—
1193#124—738no—
1194#124—738no—
1195#124—738no—
1196#124—738no—
1197#124—738no—
1198#124—738no—
1199#124—738no—
1200#124—734no—
1201#124—734no—
1202#124—732no—
1203#124—732no—
1204#124—732no—
1205#124—732no—
1206#124—732no—
1207#124—732no—
1208#124—732no—
1209#124—734no—
1210#124—738no—
1211#124C22×D7312yes—
1212#124C22×D7312yes—
1213#124C22×D7312yes—
1214#123—738no—
1215#123—734no—
1216#123—734no—
1217#123—734no—
1218#123—738no—
1219#123—738no—
1220#123—738no—
1221#123—738no—
1222#123—738no—
1223#123—738no—
1224#123—738no—
1225#123—738no—
1226#123—738no—
1227#123—738no—
1228#123—738no—
1229#123—738no—
1230#123—738no—
1231#123—738no—
1232#123—738no—
1233#123C22×D7314yes—
1234#123C22×D7314yes—
1235#123C22×D7314yes—
1236C22⋊Q8—734no—
1237C22⋊Q8—734no—
1238C22⋊Q8—734no—
1239C22⋊Q8—738no—
1240C22⋊Q8—732no—
1241C22⋊Q8—732no—
1242C22⋊Q8—732no—
1243C22⋊Q8—732no—
1244C22⋊Q8—732no—
1245C22⋊Q8—732no—
1246C22⋊Q8—734no—
1247C22⋊Q8—738no—
1248C22⋊Q8—734no—
1249C22⋊Q8—734no—
1250C22⋊Q8—738no—
1251C22⋊Q8—738no—
1252C22⋊Q8—738no—
1253C22⋊Q8—738no—
1254C22⋊Q8—738no—
1255C22⋊Q8—738no—
1256C22⋊Q8—738no—
1257C22⋊Q8—738no—
1258C22⋊Q8C22×D7312yes—
1259C22⋊Q8C22×D7312yes—
1260C22⋊Q8C22×D7312yes—
1261C22⋊Q8C22×D7312yes—
1262C22⋊Q8C22×D7312yes—
1263C22⋊Q8C22×D7312yes—
1264#121—738no—
1265#121—734no—
1266#121—734no—
1267#121—738no—
1268#121—738no—
1269#121—738no—
1270#121—738no—
1271#121—734no—
1272#121—732no—
1273#121—732no—
1274#121—732no—
1275#121—732no—
1276#121—734no—
1277#121—734no—
1278#121—732no—
1279#121—732no—
1280#121—732no—
1281#121—732no—
1282#121—734no—
1283#121—734no—
1284#121—732no—
1285#121—732no—
1286#121—732no—
1287#121—732no—
1288#121—732no—
1289#121—732no—
1290#121—734no—
1291#121—734no—
1292#121—734no—
1293#121—738no—
1294#121—734no—
1295#121—734no—
1296#121—738no—
1297#121—738no—
1298#121—734no—
1299#121—738no—
1300#121—738no—
1301#121—738no—
1302#121—734no—
1303#121—738no—
1304#121—738no—
1305#121—738no—
1306#121—738no—
1307#121—738no—
1308#121—738no—
1309#121—738no—
1310#121—738no—
1311#121—738no—
1312#121C22×D7312yes—
1313#121C22×D7312yes—
1314#121C22×D7312yes—
1315#121C22×D7312yes—
1316#121C22×D7312yes—
1317#121C22×D7312yes—
1318#120—734no—
1319#120—738no—
1320#120—738no—
1321#120—738no—
1322#120—738no—
1323#120—738no—
1324#120—738no—
1325#120—738no—
1326#120—738no—
1327#120—738no—
1328#120—738no—
1329#120C22×D7314yes—
1330C4×Q8—734no—
1331C4×Q8—732no—
1332C4×Q8—732no—
1333C4×Q8—732no—
1334C4×Q8—732no—
1335C4×Q8—732no—
1336C4×Q8—732no—
1337C4×Q8—734no—
1338C4×Q8C22×D7312yes—
1339C4×Q8C22×D7312yes—
1340C4×Q8C22×D7312yes—
1341C4×Q8C22×D7312yes—
1342C4×Q8C22×D7312yes—
1343C4×Q8C22×D7312yes—
1344C4×D4—734no—
1345C4×D4—738no—
1346C4×D4—738no—
1347C4×D4—734no—
1348C4×D4—734no—
1349C4×D4—734no—
1350C4×D4—734no—
1351C4×D4—734no—
1352C4×D4—734no—
1353C4×D4—738no—
1354C4×D4—734no—
1355C4×D4—738no—
1356C4×D4—734no—
1357C4×D4—738no—
1358C4×D4—732no—
1359C4×D4—732no—
1360C4×D4—732no—
1361C4×D4—732no—
1362C4×D4—732no—
1363C4×D4—738no—
1364C4×D4—734no—
1365C4×D4—734no—
1366C4×D4—732no—
1367C4×D4—732no—
1368C4×D4—734no—
1369C4×D4—734no—
1370C4×D4—732no—
1371C4×D4—732no—
1372C4×D4—734no—
1373C4×D4—734no—
1374C4×D4—738no—
1375C4×D4—732no—
1376C4×D4—738no—
1377C4×D4—732no—
1378C4×D4—732no—
1379C4×D4—732no—
1380C4×D4—732no—
1381C4×D4—734no—
1382C4×D4C22×D7312yes—
1383C4×D4C22×D7312yes—
1384C4×D4C22×D7314yes—
1385C4×D4C22×D7314yes—
1386C4×D4C22×D7314yes—
1387C4×D4C22×D7314yes—
1388C4×D4C22×D7314yes—
1389C4×D4C22×D7314yes—
1390C4×D4C22×D7312yes—
1391C4×D4C22×D7312yes—
1392C4×D4C22×D7312yes—
1393C4×D4C22×D7312yes—
1394#117—732no—
1395#117—732no—
1396#117—732no—
1397#117—734no—
1398#117—734no—
1399#117—734no—
1400#117—734no—
1401#117—738no—
1402#117—738no—
1403#117—738no—
1404#117—734no—
1405#117—734no—
1406#117—734no—
1407#117—738no—
1408#117C22×D7312yes—
1409#117C22×D7314yes—
1410#117C22×D7312yes—
1411#117C22×D7312yes—
1412#117C22×D7314yes—
1413#117C22×D7314yes—
1414C2×C4⋊C4—732no—
1415C2×C4⋊C4—732no—
1416C2×C4⋊C4—734no—
1417C2×C4⋊C4—734no—
1418C2×C4⋊C4—734no—
1419C2×C4⋊C4—734no—
1420C2×C22⋊C4—734no—
1421C2×C22⋊C4—734no—
1422C2×C22⋊C4—738no—
1423C2×C22⋊C4—738no—
1424C2×C22⋊C4—738no—
1425C2×C42—738no—
1426C2×C42—734no—
1427C2×C42C22×D7311yescharacteristic
1428C2×C42C22×D7311yescharacteristic
1429C2×C42C22×D7314yes—
1430C2×C42C22×D7311yescharacteristic
1431C2×C42C22×D7311yescharacteristic
1432C2×C42C22×D7311yescharacteristic
1433C2×C42C22×D7311yescharacteristic
1434C2×C42C22×D7311yescharacteristic
1435C2×C42C22×D7311yescharacteristic
1436C2×C42C22×D7311yescharacteristic
1437C2×C42C22×D7311yescharacteristic
1438C2×C42C22×D7311yescharacteristic
1439C2×C42C22×D7311yescharacteristic
1440C24—738no—
1441C24—734no—
1442C24C23×D7311yescharacteristic
1443#41—28no—
1444#41—44no—
1445#41—44no—
1446#41—2924no—
1447#41—2928no—
1448#41—2924no—
1449#41—2928no—
1450#41—2924no—
1451#41—2928no—
1452#41—2924no—
1453#41—2924no—
1454#41—29216no—
1455#41—2924no—
1456#41—2928no—
1457#41—29216no—
1458#41—2928no—
1459#41—2928no—
1460#41—1468no—
1461C2×Q8—2924no—
1462C2×Q8—2928no—
1463C2×Q8—732no—
1464C2×Q8—732no—
1465C2×Q8—738no—
1466C2×Q8—734no—
1467C2×Q8—732no—
1468C2×Q8—732no—
1469C2×Q8—732no—
1470C2×Q8C23×D7312yes—
1471C2×Q8C23×D7312yes—
1472C2×Q8C23×D7312yes—
1473C2×D4—2924no—
1474C2×D4—2924no—
1475C2×D4—2924no—
1476C2×D4—2928no—
1477C2×D4—29216no—
1478C2×D4—2928no—
1479C2×D4—2928no—
1480C2×D4—2928no—
1481C2×D4—738no—
1482C2×D4—734no—
1483C2×D4—734no—
1484C2×D4—738no—
1485C2×D4—734no—
1486C2×D4—734no—
1487C2×D4—738no—
1488C2×D4—738no—
1489C2×D4—734no—
1490C2×D4—734no—
1491C2×D4—734no—
1492C2×D4—732no—
1493C2×D4—738no—
1494C2×D4—738no—
1495C2×D4—734no—
1496C2×D4—734no—
1497C2×D4—732no—
1498C2×D4—734no—
1499C2×D4—738no—
1500C2×D4—732no—
1501C2×D4—732no—
1502C2×D4—732no—
1503C2×D4—732no—
1504C2×D4—732no—
1505C2×D4—732no—
1506C2×D4—732no—
1507C2×D4C23×D7312yes—
1508C2×D4C23×D7314yes—
1509C2×D4C23×D7312yes—
1510C2×D4C23×D7312yes—
1511C2×D4C23×D7314yes—
1512C2×D4C23×D7314yes—
1513C22×C4—24no—
1514C22×C4—42no—
1515C22×C4—42no—
1516C22×C4—29216no—
1517C22×C4—738no—
1518C22×C4—734no—
1519C22×C4—738no—
1520C22×C4—738no—
1521C22×C4—738no—
1522C22×C4—738no—
1523C22×C4—734no—
1524C22×C4—734no—
1525C22×C4—734no—
1526C22×C4—734no—
1527C22×C4—734no—
1528C22×C4—734no—
1529C22×C4—734no—
1530C22×C4—14616no—
1531C22×C4C23×D7311yescharacteristic
1532C22×C4C23×D7311yescharacteristic
1533C22×C4C23×D7311yescharacteristic
1534C22×C4C23×D7311yescharacteristic
1535C22×C4C23×D7311yescharacteristic
1536C22×C4C23×D7311yescharacteristic
1537C22×C4C23×D7311yescharacteristic
1538C22×C4C23×D7311yescharacteristic
1539C22×C4C23×D7311yescharacteristic
1540C22×C4C23×D7314yes—
1541C22×C4C23×D7311yescharacteristic
1542C22×C4C23×D7311yescharacteristic
1543C22×C4C23×D7314yes—
1544C22×C4C23×D7311yescharacteristic
1545C22×C4C23×D7311yescharacteristic
1546C22×C4C23×D7311yescharacteristic
1547C22×C4C23×D7311yescharacteristic
1548C22×C4C23×D7311yescharacteristic
1549C22×C4C23×D7311yescharacteristic
1550C22×C4C23×D7314yes—
1551C22×C4C23×D7311yescharacteristic
1552C4⋊C4—738no—
1553C4⋊C4—738no—
1554C4⋊C4—738no—
1555C4⋊C4—734no—
1556C4⋊C4—734no—
1557C4⋊C4—734no—
1558C4⋊C4—738no—
1559C4⋊C4—734no—
1560C4⋊C4—734no—
1561C4⋊C4—734no—
1562C4⋊C4—732no—
1563C4⋊C4—732no—
1564C4⋊C4—732no—
1565C4⋊C4—732no—
1566C4⋊C4—732no—
1567C4⋊C4—732no—
1568C4⋊C4—732no—
1569C4⋊C4—734no—
1570C4⋊C4—734no—
1571C4⋊C4—738no—
1572C4⋊C4—732no—
1573C4⋊C4—738no—
1574C4⋊C4—732no—
1575C4⋊C4—732no—
1576C4⋊C4C23×D7312yes—
1577C4⋊C4C23×D7312yes—
1578C4⋊C4C23×D7312yes—
1579C4⋊C4C23×D7312yes—
1580C4⋊C4C23×D7314yes—
1581C4⋊C4C23×D7314yes—
1582C4⋊C4C23×D7314yes—
1583C4⋊C4C23×D7314yes—
1584C4⋊C4C23×D7314yes—
1585C4⋊C4C23×D7314yes—
1586C4⋊C4C23×D7312yes—
1587C4⋊C4C23×D7312yes—
1588C22⋊C4—734no—
1589C22⋊C4—738no—
1590C22⋊C4—738no—
1591C22⋊C4—734no—
1592C22⋊C4—734no—
1593C22⋊C4—734no—
1594C22⋊C4—734no—
1595C22⋊C4—734no—
1596C22⋊C4—734no—
1597C22⋊C4—734no—
1598C22⋊C4—738no—
1599C22⋊C4—738no—
1600C22⋊C4—738no—
1601C22⋊C4—738no—
1602C22⋊C4—734no—
1603C22⋊C4—734no—
1604C22⋊C4—738no—
1605C22⋊C4—734no—
1606C22⋊C4—734no—
1607C22⋊C4—734no—
1608C22⋊C4—734no—
1609C22⋊C4—734no—
1610C22⋊C4—738no—
1611C22⋊C4—734no—
1612C22⋊C4—734no—
1613C22⋊C4—738no—
1614C22⋊C4—738no—
1615C22⋊C4C23×D7314yes—
1616C22⋊C4C23×D7314yes—
1617C22⋊C4C23×D7314yes—
1618C22⋊C4C23×D7314yes—
1619C22⋊C4C23×D7314yes—
1620C22⋊C4C23×D7314yes—
1621C22⋊C4C23×D7314yes—
1622C22⋊C4C23×D7314yes—
1623C22⋊C4C23×D7314yes—
1624C42—738no—
1625C42—734no—
1626C42—734no—
1627C42—738no—
1628C42—734no—
1629C42C23×D7311yescharacteristic
1630C42C23×D7311yescharacteristic
1631C42C23×D7311yescharacteristic
1632C42C23×D7311yescharacteristic
1633C42C23×D7311yescharacteristic
1634C42C23×D7311yescharacteristic
1635C42C23×D7311yescharacteristic
1636C42C23×D7311yescharacteristic
1637C42C23×D7311yescharacteristic
1638C42C23×D7311yescharacteristic
1639C42C23×D7311yescharacteristic
1640C42C23×D7311yescharacteristic
1641C42C23×D7314yes—
1642C42C23×D7314yes—
1643C42C23×D7311yescharacteristic
1644C42C23×D7314yes—
1645C42C23×D7311yescharacteristic
1646C42C23×D7311yescharacteristic
1647C42C23×D7311yescharacteristic
1648C23—22no—
1649C23—41no—
1650C23—41no—
1651C23—2928no—
1652C23—2924no—
1653C23—2924no—
1654C23—2928no—
1655C23—2928no—
1656C23—734no—
1657C23—734no—
1658C23—734no—
1659C23—1468no—
1660C23C24×D7314yes—
1661C23C24×D7311yescharacteristic
1662C23C24×D7311yescharacteristic
1663C23C24×D7311yescharacteristic
1664Q8—24no—
1665Q8—24no—
1666Q8—42no—
1667Q8—2922no—
1668Q8—2924no—
1669Q8—2922no—
1670Q8—2928no—
1671Q8—2922no—
1672Q8—1464no—
1673Q8—1464no—
1674D4—28no—
1675D4—24no—
1676D4—24no—
1677D4—42no—
1678D4—44no—
1679D4—44no—
1680D4—2922no—
1681D4—2924no—
1682D4—2922no—
1683D4—2928no—
1684D4—2924no—
1685D4—2924no—
1686D4—2928no—
1687D4—2922no—
1688D4—2928no—
1689D4—2924no—
1690D4—2924no—
1691D4—2928no—
1692D4—2924no—
1693D4—2924no—
1694D4—2928no—
1695D4—2928no—
1696D4—2924no—
1697D4—2928no—
1698D4—2924no—
1699D4—1468no—
1700D4—1464no—
1701D4—1464no—
1702D4—1464no—
1703D4—1464no—
1704D4—1464no—
1705D4—1464no—
1706C2×C4—22no—
1707C2×C4—22no—
1708C2×C4—22no—
1709C2×C4—22no—
1710C2×C4—22no—
1711C2×C4—28no—
1712C2×C4—22no—
1713C2×C4—22no—
1714C2×C4—22no—
1715C2×C4—22no—
1716C2×C4—22no—
1717C2×C4—22no—
1718C2×C4—28no—
1719C2×C4—41no—
1720C2×C4—41no—
1721C2×C4—41no—
1722C2×C4—41no—
1723C2×C4—41no—
1724C2×C4—41no—
1725C2×C4—44no—
1726C2×C4—2928no—
1727C2×C4—2928no—
1728C2×C4—2924no—
1729C2×C4—2928no—
1730C2×C4—2928no—
1731C2×C4—2928no—
1732C2×C4—734no—
1733C2×C4—734no—
1734C2×C4—734no—
1735C2×C4—734no—
1736C2×C4—734no—
1737C2×C4—1468no—
1738C2×C4—1468no—
1739C2×C4—1468no—
1740C2×C4—1468no—
1741C2×C4—1468no—
1742C2×C4—1468no—
1743C2×C4—1468no—
1744C2×C4#1455663714yes—
1745C2×C4C24×D7311yescharacteristic
1746C2×C4C24×D7314yes—
1747C2×C4C24×D7314yes—
1748C2×C4C24×D7311yescharacteristic
1749C2×C4C24×D7311yescharacteristic
1750C2×C4C24×D7311yescharacteristic
1751C2×C4C24×D7311yescharacteristic
1752C2×C4C24×D7311yescharacteristic
1753C2×C4C24×D7311yescharacteristic
1754C2×C4C24×D7311yescharacteristic
1755C2×C4C24×D7314yes—
1756C2×C4C24×D7311yescharacteristic
1757C2×C4C24×D7311yescharacteristic
1758C2×C4C24×D7311yescharacteristic
1759C2×C4C24×D7311yescharacteristic
1760C22—21no—
1761C22—21no—
1762C22—21no—
1763C22—21no—
1764C22—24no—
1765C22—21no—
1766C22—21no—
1767C22—21no—
1768C22—21no—
1769C22—24no—
1770C22—24no—
1771C22—44no—
1772C22—5848no—
1773C22—58416no—
1774C22—1464no—
1775C22—1464no—
1776C22—1464no—
1777C22—1464no—
1778C22—1464no—
1779C22—1464no—
1780C22—1464no—
1781C22—1464no—
1782C22—1464no—
1783C22C2×#1455663712yes—
1784C22C25×D7311yescharacteristic
1785C4—21no—
1786C4—21no—
1787C4—24no—
1788C4—21no—
1789C4—21no—
1790C4—21no—
1791C4—21no—
1792C4—21no—
1793C4—21no—
1794C4—24no—
1795C4—24no—
1796C4—1464no—
1797C4—1464no—
1798C4—1464no—
1799C4—1464no—
1800C4—1464no—
1801C4C2×#1455663712yes—
1802C4C2×#1455663712yes—
1803C4#1798942312yes—
1804C4#1798942312yes—
1805C2—22no—
1806C2—41no—
1807C2—41no—
1808C2—44no—
1809C2—2924no—
1810C2—2924no—
1811C2—2924no—
1812C2C22×#1455663711yescharacteristic
1813C2C2×#1798942311yescharacteristic
1814C2C2×#1798942311yescharacteristic
subgroupG/H
centerC2×C4C24×D73
commutator, socle, cosocleC22×C73C26
FrattiniC22C25×D73
FittingC73×#3444C2
hypercenter#3444D73
hypocenterC73#62759
LCSG ▷ C22×C73 ▷ C73
UCSC1 ◁ C2×C4 ◁ #3444

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. #22624353C2semidirect
2. #22624342C2semidirect
3. #22624336C2semidirect
4. #22624331C2semidirect
5. #22624329C2semidirect
6. #22624322C2semidirect
7. #22624314C2semidirect
8. #22624305C2semidirect
9. #22624297C2semidirect
10. #22624283C2semidirect
11. #22624271C2semidirect
12. #22624261C2semidirect
13. #22624247C2semidirect
14. #22624239C2semidirect
15. #22624070C2semidirect
16. #22623557C2semidirect
17. #22623541C2semidirect
18. #22623498C2semidirect
19. #22623495C2semidirect
20. #41×D292C2semidirect
21. #22623417C2semidirect
22. #22623352C2semidirect
23. #22623347C2semidirect
24. #22623261C2semidirect
25. #22623227C2semidirect
26. C2×#17989137C2semidirect
27. C73×#3444C2semidirect
28. C22×#11924028C22semidirect
29. C2×#41×D73C22semidirect
30. #17989341C22semidirect
31. #17989339C22semidirect
32. #17989335C22semidirect
33. #17989334C22semidirect
34. #17989333C22semidirect
35. #17989331C22semidirect
36. #17989329C22semidirect
37. #17989328C22semidirect
38. #17989327C22semidirect
39. #17989325C22semidirect
40. #17989322C22semidirect
41. Q8×Dic146C22semidirect
42. #17989311C22semidirect
43. #17989310C22semidirect
44. #17989303C22semidirect
45. #17989302C22semidirect
46. #17989302C22semidirect
47. #17989302C22semidirect
48. #17989300C22semidirect
49. #17989300C22semidirect
50. #17989298C22semidirect
51. #17989297C22semidirect
52. #17989297C22semidirect
53. #17989294C22semidirect
54. #17989290C22semidirect
55. #17989287C22semidirect
56. #17989283C22semidirect
57. #17989281C22semidirect
58. #17989279C22semidirect
59. #17989278C22semidirect
60. #17989277C22semidirect
61. #17989275C22semidirect
62. #17989266C22semidirect
63. #17989264C22semidirect
64. #17989261C22semidirect
65. #17989259C22semidirect
66. #17989259C22semidirect
67. #17989258C22semidirect
68. #17989258C22semidirect
69. #17989257C22semidirect
70. #17989256C22semidirect
71. Q8×D292C22semidirect
72. #17989252C22semidirect
73. #17989249C22semidirect
74. #17989245C22semidirect
75. #17989242C22semidirect
76. #17989241C22semidirect
77. #17989241C22semidirect
78. #17989240C22semidirect
79. #17989240C22semidirect
80. #17989237C22semidirect
81. #17989233C22semidirect
82. #17989233C22semidirect
83. #17989232C22semidirect
84. #17989232C22semidirect
85. #17989230C22semidirect
86. #17989228C22semidirect
87. #17989226C22semidirect
88. #17989225C22semidirect
89. D4×D292C22semidirect
90. D4×D292C22semidirect
91. D4×D292C22semidirect
92. #17989222C22semidirect
93. #17989221C22semidirect
94. #17989217C22semidirect
95. #17989215C22semidirect
96. #17989210C22semidirect
97. #17989209C22semidirect
98. #17989208C22semidirect
99. #17989208C22semidirect
100. #17989206C22semidirect
101. #17989203C22semidirect
102. #17989193C22semidirect
103. #17989192C22semidirect
104. #17989192C22semidirect
105. #17989190C22semidirect
106. #17989189C22semidirect
107. #17989188C22semidirect
108. #17989176C22semidirect
109. #17989173C22semidirect
110. #17989170C22semidirect
111. #17989170C22semidirect
112. #17989167C22semidirect
113. #17989167C22semidirect
114. #17989167C22semidirect
115. #17989166C22semidirect
116. #17989166C22semidirect
117. #17989165C22semidirect
118. #17989160C22semidirect
119. #17989160C22semidirect
120. #17989159C22semidirect
121. #17989156C22semidirect
122. #17989155C22semidirect
123. #17989153C22semidirect
124. #17989153C22semidirect
125. #17989153C22semidirect
126. #17989152C22semidirect
127. #17989151C22semidirect
128. #17989148C22semidirect
129. #17989147C22semidirect
130. #17989144C22semidirect
131. #17989144C22semidirect
132. #17989144C22semidirect
136. #17989137C22semidirect
137. #17989137C22semidirect
138. #17989137C22semidirect
139. #17989137C22semidirect
140. #17989137C22semidirect
141. #17989137C22semidirect
142. #17989137C22semidirect
143. #17989137C22semidirect
144. #17989137C22semidirect
145. #17989137C22semidirect
146. #17989137C22semidirect
147. #17989134C22semidirect
148. #17989134C22semidirect
149. #17989134C22semidirect
150. C2×#14556591C22semidirect
152. #17989124C22semidirect
153. #17989124C22semidirect
154. #17989121C22semidirect
155. #17989121C22semidirect
156. #17989121C22semidirect
157. #17989121C22semidirect
158. #17989121C22semidirect
159. #17989121C22semidirect
160. #17989121C22semidirect
161. #17989115C22semidirect
162. C2×#14556579C22semidirect
163. #17989099C22semidirect
164. #17989099C22semidirect
165. #17989098C22semidirect
166. #17989098C22semidirect
167. #17989098C22semidirect
168. #17989096C22semidirect
169. #17989096C22semidirect
170. #17989096C22semidirect
171. #17989094C22semidirect
172. C2×#14556565C22semidirect
173. C2×#14556565C22semidirect
174. C4×#11924029C22semidirect
175. C4×#11924028C22semidirect
176. C4×#11924028C22semidirect
177. C4×#11924028C22semidirect
178. C4×#11924028C22semidirect
179. C2×C4×D292C22semidirect
180. C2×C4×D292C22semidirect
181. C2×C4×D292C22semidirect
182. C4×D4×D73C22semidirect
183. #117×D73C22semidirect
184. #533×C73C22semidirect
185. #533×C73C22semidirect
186. #533×C73C22semidirect
188. #532×C73C22semidirect
189. #532×C73C22semidirect
190. #529×C73C22semidirect
191. #529×C73C22semidirect
192. #529×C73C22semidirect
193. #529×C73C22semidirect
194. #529×C73C22semidirect
195. #529×C73C22semidirect
196. #525×C73C22semidirect
197. #525×C73C22semidirect
198. #525×C73C22semidirect
199. C4×#41×C73C22semidirect
200. C4×#41×C73C22semidirect
201. C4×#41×C73C22semidirect
202. C22×C42×C73C22semidirect
933. #3444D73semidirect
935. C73#62759semidirect
1041. #533C2×D73semidirect
1042. #533C2×D73semidirect
1043. #533C2×D73semidirect
1062. #532C2×D73semidirect
1063. #532C2×D73semidirect
1076. #529C2×D73semidirect
1077. #529C2×D73semidirect
1078. #529C2×D73semidirect
1079. #529C2×D73semidirect
1080. #529C2×D73semidirect
1081. #529C2×D73semidirect
1092. #525C2×D73semidirect
1093. #525C2×D73semidirect
1094. #525C2×D73semidirect
1102. C4×#41C2×D73semidirect
1103. C4×#41C2×D73semidirect
1104. C4×#41C2×D73semidirect
1110. C22×C42C2×D73semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#226243532
#226243422
#226243362
#226243312
#226243292
#226243222
#226243142
#226243052
#226242972
#226242832
#226242712
#226242612
#226242472
#226242392
#226240702
#226235572
#226235412
#226234982
#226234952
#41×D2922
#226234172
#226233522
#226233472
#226232612
#226232272
C2×#179891372
C73×#34442
#6275973