Finite Group Databasebeta

← #33994615

Subgroups — #33994615

Order 18688.

8042 conjugacy classes of subgroups.

The subgroup lattice has 1612 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#22624248C214yesmaximal, complemented
2#22624241C214yesmaximal, complemented
3#22624167C214yesmaximal, complemented
4#22624159C214yesmaximal, complemented
5#22624119C218yesmaximal, complemented
6#22623964C214yesmaximal, complemented
7#22623956C214yesmaximal, complemented
8#22623771C214yesmaximal, complemented
9#22623689C214yesmaximal, complemented
10#22623669C212yesmaximal, complemented
11#22623667C212yesmaximal, complemented
12#22623640C211yesmaximal, characteristic, complemented
13#22623614C214yesmaximal, complemented
14#22623601C212yesmaximal, complemented
15#22623595C212yesmaximal, complemented
16#22623564C214yesmaximal, complemented
17#22623564C212yesmaximal, complemented
18#525×D73C212yesmaximal, complemented
19C22×#14556566C211yesmaximal, characteristic, complemented
20C73×#3492C211yesmaximal, characteristic, complemented
21C2×#14556637C2212yescomplemented
22C2×#14556637C2214yescomplemented
23C2×#41×D73C2212yescomplemented
24C23×D292C2211yescharacteristic, complemented
25C23×D292C2212yescomplemented
26C23×C4×D73C2211yescharacteristic, complemented
27#17989335C2218yescomplemented
28#17989333C2218yescomplemented
29#17989328C2218yescomplemented
30#17989327C2218yescomplemented
31#17989303C2214yescomplemented
32#17989300C2214yescomplemented
33#17989292C2214yescomplemented
34#17989290C2218yescomplemented
35#17989290C2214yescomplemented
36#17989290C2214yescomplemented
37#17989288C2218yescomplemented
38#17989285C2214yescomplemented
39#17989285C2214yescomplemented
40#17989281C2214yescomplemented
41#17989272C2214yescomplemented
42#17989266C2218yescomplemented
43#17989264C2218yescomplemented
44#17989261C2218yescomplemented
45#17989260C2218yescomplemented
46#17989259C2214yescomplemented
47#17989255C2214yescomplemented
48#17989249C2214yescomplemented
49#17989247C2214yescomplemented
50#17989240C2214yescomplemented
51#17989238C2214yescomplemented
52#17989238C2214yescomplemented
53#17989233C2214yescomplemented
54#17989233C2218yescomplemented
55#17989233C2218yescomplemented
56#17989233C2214yescomplemented
57#17989232C2218yescomplemented
58#17989232C2214yescomplemented
59#17989229C2218yescomplemented
60#17989229C2218yescomplemented
61#17989228C2214yescomplemented
62#17989228C2218yescomplemented
63#17989228C2218yescomplemented
64#17989228C2214yescomplemented
65#17989228C2214yescomplemented
66#17989228C2218yescomplemented
67#17989226C2218yescomplemented
68#17989225C2218yescomplemented
69D4×D292C2218yescomplemented
70D4×D292C2218yescomplemented
71D4×D292C2214yescomplemented
72D4×D292C2214yescomplemented
73D4×D292C2214yescomplemented
74#17989221C2218yescomplemented
75#17989221C2218yescomplemented
76#17989221C2214yescomplemented
77#17989221C2214yescomplemented
78#17989221C2214yescomplemented
79#17989218C2211yescharacteristic, complemented
80#17989212C2214yescomplemented
81#17989211C2214yescomplemented
82#17989209C2214yescomplemented
83#17989193C2218yescomplemented
84#17989193C2214yescomplemented
85#17989189C2218yescomplemented
86#17989188C2214yescomplemented
87#17989185C2218yescomplemented
88#17989184C2214yescomplemented
89#17989177C2214yescomplemented
90#17989177C2218yescomplemented
91#17989176C2218yescomplemented
92#17989176C2218yescomplemented
93#17989174C2214yescomplemented
94#17989170C2218yescomplemented
95#17989168C2211yescharacteristic, complemented
96#17989168C2214yescomplemented
97#17989167C2214yescomplemented
98#17989167C2218yescomplemented
99#17989156C2212yescomplemented
100#17989156C2214yescomplemented
101#17989156C2214yescomplemented
102#17989153C2214yescomplemented
103#17989151C2212yescomplemented
104#17989151C2214yescomplemented
105#17989148C2218yescomplemented
106#17989148C2218yescomplemented
107#17989148C2218yescomplemented
108#17989148C2218yescomplemented
109#17989145C2214yescomplemented
110#17989138C2214yescomplemented
111#17989134C2214yescomplemented
112#17989124C2214yescomplemented
113#17989122C2214yescomplemented
114#17989100C2212yescomplemented
115#17989100C2212yescomplemented
116#17989100C2214yescomplemented
117#17989099C2212yescomplemented
118#17989099C2214yescomplemented
119#17989098C2214yescomplemented
120#17989098C2212yescomplemented
121#17989097C2212yescomplemented
122#17989097C2212yescomplemented
123#17989096C2214yescomplemented
124#17989096C2214yescomplemented
125#17989095C2214yescomplemented
126#17989094C2212yescomplemented
127#17989093C2214yescomplemented
128#123×D73C2214yescomplemented
129C22⋊Q8×D73C2212yescomplemented
130C22⋊Q8×D73C2212yescomplemented
131C2×#14556566C2214yescomplemented
132C2×#14556566C2212yescomplemented
133C2×#14556566C2212yescomplemented
134C2×#14556566C2214yescomplemented
135C2×#14556566C2214yescomplemented
136C2×#14556566C2214yescomplemented
137C2×#14556566C2214yescomplemented
138C2×#14556566C2214yescomplemented
139#121×D73C2212yescomplemented
140#121×D73C2212yescomplemented
141#121×D73C2214yescomplemented
142#120×D73C2218yescomplemented
143#120×D73C2214yescomplemented
144#17989068C2212yescomplemented
145#17989061C2214yescomplemented
146#17989061C2212yescomplemented
147#17989059C2218yescomplemented
148C4×D4×D73C2214yescomplemented
149C4×D4×D73C2214yescomplemented
150#117×D73C2212yescomplemented
151C22×#11924005C2212yescomplemented
152#554×C73C2214yescomplemented
153#553×C73C2214yescomplemented
154#552×C73C2214yescomplemented
155#547×C73C2214yescomplemented
156#544×C73C2211yescharacteristic, complemented
157#539×C73C2214yescomplemented
158#537×C73C2211yescharacteristic, complemented
159#525×C73C2214yescomplemented
160#525×C73C2212yescomplemented
161#520×C73C2212yescomplemented
162C22×C4⋊C4×C73C2211yescharacteristic, complemented
163C24×D73C2311yescharacteristic
164C24×D73C2312yes—
165#14556637—48no—
166#14556637—416no—
167C2×#11924029C2318yescomplemented
168C2×#11924029C2312yescomplemented
169C2×#11924029C2314yescomplemented
170C2×#11924028C2312yes—
171C2×#11924028C2314yes—
172C2×#11924028C2318yescomplemented
173C2×#11924028C2314yescomplemented
174C2×#11924028C2314yescomplemented
175C2×#11924027C2314yes—
176C2×#11924027C2312yescomplemented
177#41×D73—48no—
178C2×Q8×D73C2312yescomplemented
179C22×D292—44no—
180C22×D292—48no—
181C22×D292C2314yes—
182C22×D292C2312yes—
183C22×D292C2312yes—
184C22×D292C2314yes—
185C22×D292C2314yes—
186C22×D292C2314yes—
187C22×D292C2314yes—
188C22×D292C2318yes—
189C22×D292C2314yes—
190C22×D292C2318yescomplemented
191C22×D292C2314yescomplemented
192C2×D4×D73C2314yes—
193C2×D4×D73C2318yes—
194C2×D4×D73C2318yes—
195C2×D4×D73C2318yes—
196C2×D4×D73C2314yes—
197C2×D4×D73C2314yes—
198C2×D4×D73C2318yescomplemented
199C2×D4×D73C2314yescomplemented
200C2×D4×D73C2312yescomplemented
201C23×Dic73C2311yescharacteristic
202C22×C4×D73—44no—
203C22×C4×D73C2312yes—
204C22×C4×D73C2312yes—
205C22×C4×D73C2312yes—
206C22×C4×D73C2312yes—
207C22×C4×D73C2312yes—
208C22×C4×D73C2312yes—
209C22×C4×D73C2314yescomplemented
210#14556590C2314yescomplemented
211#14556588C2314yescomplemented
212#14556588C2318yescomplemented
213#14556587C2314yescomplemented
214#14556587C2318yescomplemented
215#14556586C2318yescomplemented
216#14556586C2318yescomplemented
217#14556586C2318yescomplemented
218#14556586C2318yescomplemented
219#14556585C2318yescomplemented
220#14556582C2314yescomplemented
221#14556581C2318yescomplemented
222#14556580C2314yescomplemented
223#14556580C2318yescomplemented
224#14556580C2318yescomplemented
225#14556579C2314yescomplemented
226#14556579C2318yescomplemented
227#14556579C2318yescomplemented
228#14556577C2318yescomplemented
229#14556577C2318yescomplemented
230#14556576C2318yescomplemented
231#14556576C2318yescomplemented
232#14556576C2318yescomplemented
233#14556576C2318yescomplemented
234#14556576C2318yescomplemented
235#14556576C2318yescomplemented
236#14556576C2318yescomplemented
237#14556576C2318yescomplemented
238#14556576C2318yescomplemented
239#14556576C2314yescomplemented
240#14556576C2318yescomplemented
241#14556576C2314yescomplemented
242#14556575C2314yes—
243#14556575C2318yescomplemented
244#14556574C2314yes—
245#14556574C2318yes—
246#14556574C2318yescomplemented
247#14556573C2318yescomplemented
248#14556573C2314yescomplemented
249#14556573C2314yescomplemented
250#14556572C2314yes—
251#14556571C2312yescomplemented
252#14556571C2312yescomplemented
253#14556571C2314yescomplemented
254#14556571C2318yescomplemented
255#14556570C2314yes—
256#14556570C2314yes—
257#14556570C2312yes—
258#14556570C2312yes—
259#14556569C2318yescomplemented
260#14556569C2318yescomplemented
261#14556569C2318yescomplemented
262#14556569C2314yescomplemented
263#14556569C2314yescomplemented
264#14556568C2314yes—
265#14556568C2314yes—
266#14556567C2312yescomplemented
267#14556567C2312yescomplemented
268#14556567C2318yescomplemented
269#14556566C2314yes—
270#14556566C2314yes—
271#14556566C2318yes—
272#14556566C2314yes—
273#14556566C2314yes—
274#14556566C2318yes—
275#14556566C2314yes—
276#14556566C2314yes—
277#14556566C2318yes—
278#14556566C2314yes—
279#14556566C2314yes—
280#14556566C2318yes—
281#14556566C2312yescomplemented
282#14556566C2318yescomplemented
283#14556566C2318yescomplemented
284#14556566C2318yescomplemented
285#14556566C2318yescomplemented
286#14556566C2318yescomplemented
287#14556566C2318yescomplemented
288#14556566C2312yescomplemented
289#14556566C2314yescomplemented
290#14556566C2318yescomplemented
291#14556566C2314yescomplemented
292#14556566C2314yescomplemented
293#14556566C2318yescomplemented
294#14556566C2318yescomplemented
295#14556565C2314yes—
296#14556565C2314yes—
297#14556565C2312yes—
298#14556565C2312yes—
299#14556565C2314yescomplemented
300#14556565C2314yescomplemented
301#14556565C2318yescomplemented
302#14556565C2318yescomplemented
303#14556565C2318yescomplemented
304#14556564C2318yescomplemented
305#14556564C2314yescomplemented
306#14556564C2318yescomplemented
307#14556564C2318yescomplemented
308#14556564C2318yescomplemented
309#14556564C2318yescomplemented
310#14556564C2318yescomplemented
311#14556564C2318yescomplemented
312#14556564C2314yescomplemented
313#14556563C2314yes—
314#14556563C2314yes—
315#14556563C2318yescomplemented
316#14556562C2312yescomplemented
317#14556562C2312yescomplemented
318#14556561C2314yes—
319#14556561C2318yes—
320#14556561C2318yes—
321#14556561C2318yes—
322#14556561C2314yes—
323#14556561C2314yes—
324#14556561C2318yescomplemented
325#14556561C2318yescomplemented
326#14556561C2318yescomplemented
327#14556561C2318yescomplemented
328#14556561C2318yescomplemented
329#14556561C2318yescomplemented
330#14556561C2318yescomplemented
331#14556560C2314yes—
332#14556559C2314yes—
333#14556559C2318yes—
334#14556559C2318yes—
335#14556559C2318yes—
336#14556559C2314yes—
337#14556559C2314yes—
338#14556559C2318yescomplemented
339#14556556C2314yescomplemented
340C4×D292C2318yescomplemented
341C4×D292C2314yescomplemented
342C4×D292C2314yescomplemented
343C4×D292C2318yescomplemented
344C4×D292C2318yescomplemented
345C4×D292C2314yescomplemented
346C4×D292C2314yescomplemented
347D4×Dic73C2314yes—
348D4×Dic73C2314yes—
349#14556553C2318yescomplemented
350#14556553C2314yescomplemented
351#14556553C2314yescomplemented
352#14556553C2318yescomplemented
353#14556553C2314yescomplemented
354#14556553C2314yescomplemented
355#14556553C2318yescomplemented
356#14556553C2314yescomplemented
357C4×C22⋊D73C2318yes—
358C4×C22⋊D73C2318yes—
359C4×C22⋊D73C2314yes—
360C4×C22⋊D73C2314yes—
361C4×C22⋊D73C2318yescomplemented
362C4×C22⋊D73C2314yescomplemented
363C4×C22⋊D73C2314yescomplemented
364#14556551C2314yes—
365#14556551C2314yes—
366#14556551C2314yescomplemented
367#14556551C2318yescomplemented
368#14556551C2314yescomplemented
369#14556550C2312yes—
370#14556550C2314yes—
371#14556549C2318yescomplemented
372#14556549C2314yescomplemented
373#14556549C2312yescomplemented
374#14556549C2312yescomplemented
375#14556548C2318yescomplemented
376#14556548C2314yescomplemented
377#14556547C2314yes—
378C4⋊C4×D73C2314yescomplemented
379C4⋊C4×D73C2314yescomplemented
380C4⋊C4×D73C2312yescomplemented
381C4⋊C4×D73C2312yescomplemented
382C4⋊C4×D73C2314yescomplemented
383C2×#11924005C2314yes—
384C2×#11924005C2314yes—
385C2×#11924005C2318yes—
386C2×#11924005C2314yes—
387C2×#11924005C2314yes—
388C2×#11924005C2318yescomplemented
389C22⋊C4×D73C2314yes—
390C22⋊C4×D73C2318yes—
391C22⋊C4×D73C2318yes—
392C22⋊C4×D73C2318yes—
393C22⋊C4×D73C2314yes—
394C22⋊C4×D73C2314yes—
395C22⋊C4×D73C2314yescomplemented
396C22⋊C4×D73C2318yescomplemented
397C22⋊C4×D73C2314yescomplemented
398C42×D73C2314yescomplemented
399C2×#41×C73C2312yes—
400C2×#41×C73C2314yes—
401C23×C4×C73C2311yescharacteristic
402C23×C4×C73C2312yes—
403C4⋊Q8×C73C2314yescomplemented
404#126×C73C2318yescomplemented
405#125×C73C2314yescomplemented
406#125×C73C2318yescomplemented
407#123×C73C2318yes—
408#123×C73C2314yes—
409#123×C73C2318yescomplemented
410C22⋊Q8×C73C2314yes—
411C22⋊Q8×C73C2314yes—
412C22⋊Q8×C73C2312yes—
413C22⋊Q8×C73C2312yes—
414C22⋊Q8×C73C2318yescomplemented
415C22⋊Q8×C73C2314yescomplemented
416#121×C73C2314yes—
417#121×C73C2314yes—
418#121×C73C2312yes—
419#121×C73C2312yes—
420#121×C73C2314yescomplemented
421#120×C73C2314yes—
422C4×Q8×C73C2314yescomplemented
423C4×D4×C73C2318yes—
424C4×D4×C73C2318yes—
425C4×D4×C73C2314yes—
426C4×D4×C73C2314yes—
427C4×D4×C73C2314yescomplemented
428#117×C73C2314yes—
429#117×C73C2312yes—
430#117×C73C2314yescomplemented
431C2×C4⋊C4×C73C2311yescharacteristic
432C2×C4⋊C4×C73C2312yes—
433C2×C4⋊C4×C73C2314yes—
434C2×C4⋊C4×C73C2311yescharacteristic
435C2×C4⋊C4×C73C2314yes—
436C2×C4⋊C4×C73C2314yescomplemented
437C23×D73—24no—
438C23×D73—42no—
439C23×D73—42no—
440C23×D73—44no—
441C23×D73—44no—
442C23×D73—44no—
443C23×D73C2412yes—
444C23×D73C2412yes—
445C23×D73C2414yes—
446C23×D73C2414yes—
447C23×D73C2414yes—
448C23×D73C2414yes—
449C23×D73C2411yescharacteristic
450C23×D73C2418yes—
451C23×D73C2411yescharacteristic
452#11924029—416no—
453#11924029—44no—
454#11924029—48no—
455#11924028—28no—
456#11924028—48no—
457#11924028—48no—
458#11924028—416no—
459#11924028—48no—
460#11924027—44no—
461#11924027—48no—
462C2×Dic146C2412yes—
463C2×Dic146C2414yes—
464C2×Dic146C2414yes—
465Q8×D73—44no—
466C2×D292—216no—
467C2×D292—28no—
468C2×D292—48no—
469C2×D292—48no—
470C2×D292—48no—
471C2×D292—48no—
472C2×D292—416no—
473C2×D292—48no—
474C2×D292—416no—
475C2×D292—44no—
476C2×D292—48no—
477C2×D292C2418yes—
478C2×D292C2412yes—
479C2×D292C2414yes—
480C2×D292C2414yes—
481C2×D292C2418yes—
482C2×D292C2414yes—
483C2×D292C2418yes—
484C2×D292C2414yes—
485C2×D292C2414yes—
486C2×D292C2418yes—
487C2×D292C2418yes—
488C2×D292C2418yes—
489C2×D292C2414yes—
490C2×D292C2418yes—
491C2×D292C2418yes—
492C2×C22⋊D73C2414yes—
493C2×C22⋊D73C2414yes—
494C2×C22⋊D73C2414yes—
495C2×C22⋊D73C2414yes—
496C2×C22⋊D73C2418yes—
497C2×C22⋊D73C2414yes—
498C2×C22⋊D73C2414yes—
499C2×C22⋊D73C2418yes—
500C2×C22⋊D73C2418yes—
501C2×C22⋊D73C2414yes—
502D4×D73—216no—
503D4×D73—44no—
504D4×D73—48no—
505D4×D73—416no—
506D4×D73—48no—
507D4×D73—416no—
508D4×D73—48no—
509D4×D73—416no—
510D4×D73—416no—
511C22×Dic73—42no—
512C22×Dic73C2412yes—
513C22×Dic73C2411yescharacteristic
514C22×Dic73C2412yes—
515C22×Dic73C2411yescharacteristic
516C22×Dic73C2414yes—
517C2×C4×D73—28no—
518C2×C4×D73—44no—
519C2×C4×D73—44no—
520C2×C4×D73—44no—
521C2×C4×D73—44no—
522C2×C4×D73—48no—
523C2×C4×D73—44no—
524C2×C4×D73C2412yes—
525C2×C4×D73C2414yes—
526C2×C4×D73C2412yes—
527C2×C4×D73C2414yes—
528C2×C4×D73C2412yes—
529C2×C4×D73C2412yes—
530C2×C4×D73C2414yes—
531C2×C4×D73C2414yes—
532C2×C4×D73C2418yes—
533C2×C4×D73C2418yes—
534C2×C4×D73C2418yes—
535C2×C4×D73C2412yes—
536C2×C4×D73C2412yes—
537C2×C4×D73C2414yes—
538C2×C4×D73C2418yes—
539C2×C4×D73C2412yes—
540C2×C4×D73C2412yes—
541C4⋊Dic73C2412yes—
542C4⋊Dic73C2412yes—
543C4⋊Dic73C2414yes—
544C4⋊Dic73C2414yes—
545C4⋊Dic73C2414yes—
546C4⋊Dic73C2414yes—
547#11924007C2414yes—
548#11924007C2414yes—
549#11924007C2414yes—
550#11924007C2414yes—
551#11924007C2414yes—
552#11924007C2414yes—
553#11924007C2418yes—
554#11924007C2418yes—
555C22⋊Dic73C2414yes—
556C22⋊Dic73C2414yes—
557C22⋊Dic73C2414yes—
558C22⋊Dic73C2414yes—
559C22⋊Dic73C2414yes—
560#11924005C2418yes—
561#11924005C2418yes—
562#11924005C2414yes—
563#11924005C2414yes—
564#11924005C2414yes—
565#11924005C2414yes—
566#11924005C2414yes—
567#11924005C2414yes—
568#11924005C2418yes—
569#11924005C2418yes—
570#11924005C2418yes—
571#11924005C2418yes—
572#11924005C2418yes—
573#11924005C2414yes—
574#11924005C2414yes—
575#11924005C2414yes—
576#11924005C2414yes—
577#11924005C2418yes—
578#11924005C2418yes—
579#11924005C2418yes—
580#11924005C2418yes—
581#11924005C2418yes—
582C4×Dic73C2414yes—
583C4×Dic73C2414yes—
584C4×Dic73C2414yes—
585C4×Dic73C2418yes—
586C24×C73C2411yescharacteristic
587#41×C73—28no—
588#41×C73—48no—
589C2×Q8×C73C2412yes—
590C2×Q8×C73C2414yes—
591C2×D4×C73C2414yes—
592C2×D4×C73C2414yes—
593C2×D4×C73C2414yes—
594C2×D4×C73C2412yes—
595C2×D4×C73C2414yes—
596C22×C4×C73—24no—
597C22×C4×C73—44no—
598C22×C4×C73C2414yes—
599C22×C4×C73C2412yes—
600C22×C4×C73C2412yes—
601C22×C4×C73C2411yescharacteristic
602C22×C4×C73C2414yes—
603C22×C4×C73C2412yes—
604C22×C4×C73C2414yes—
605C22×C4×C73C2412yes—
606C22×C4×C73C2418yes—
607C22×C4×C73C2411yescharacteristic
608C4⋊C4×C73C2414yes—
609C4⋊C4×C73C2414yes—
610C4⋊C4×C73C2418yes—
611C4⋊C4×C73C2412yes—
612C4⋊C4×C73C2418yes—
613C4⋊C4×C73C2412yes—
614C4⋊C4×C73C2414yes—
615C4⋊C4×C73C2414yes—
616C4⋊C4×C73C2414yes—
617C4⋊C4×C73C2418yes—
618C4⋊C4×C73C2414yes—
619C22⋊C4×C73C2414yes—
620C22⋊C4×C73C2414yes—
621C22⋊C4×C73C2418yes—
622C22⋊C4×C73C2414yes—
623C22⋊C4×C73C2418yes—
624C22⋊C4×C73C2414yes—
625C22⋊C4×C73C2414yes—
626C42×C73C2418yes—
627C42×C73C2414yes—
628C23×C73—22no—
629C23×C73—22no—
630C23×C73—22no—
631C23×C73C2514yes—
632C23×C73C2511yescharacteristic
633C23×C73C2511yescharacteristic
634C23×C73C2511yescharacteristic
635C22×D73—24no—
636C22×D73—22no—
637C22×D73—24no—
638C22×D73—28no—
639C22×D73—28no—
640C22×D73—28no—
641C22×D73—24no—
642C22×D73—24no—
643C22×D73—28no—
644C22×D73—41no—
645C22×D73—42no—
646C22×D73—41no—
647C22×D73—41no—
648C22×D73—42no—
649C22×D73—41no—
650C22×D73—44no—
651C22×D73—44no—
652C22×D73—44no—
653C22×D73—44no—
654C22×D73—44no—
655C22×D73—44no—
656C22×D73—44no—
657C22×D73—44no—
658C22×D73—48no—
659C22×D73—48no—
660C22×D73—48no—
661C22×D73—416no—
662C22×D73—816no—
663C22×D73H(5,𝔽2)14yescomplemented
664C22×D73C2518yes—
665C22×D73C2512yes—
666C22×D73C2514yes—
667C22×D73C2512yes—
668Q8×C73—24no—
669Q8×C73—44no—
670D4×C73—28no—
671D4×C73—28no—
672D4×C73—28no—
673D4×C73—24no—
674D4×C73—44no—
675C2×C4×C73—22no—
676C2×C4×C73—28no—
677C2×C4×C73—24no—
678C2×C4×C73—24no—
679C2×C4×C73—28no—
680C2×C4×C73—42no—
681C2×C4×C73—44no—
682C2×C4×C73—42no—
683C2×C4×C73—48no—
684C2×C4×C73H(5,𝔽2)14yescomplemented
685C2×C4×C73C2514yes—
686C2×C4×C73C2514yes—
687C2×C4×C73C2514yes—
688C2×C4×C73C2514yes—
689C2×C4×C73C2512yes—
690C2×C4×C73C2514yes—
691C2×C4×C73C2512yes—
692C22⋊D73—28no—
693C22⋊D73—28no—
694C22⋊D73—28no—
695C22⋊D73—28no—
696C22⋊D73—48no—
697C22⋊D73—48no—
698C22⋊D73—48no—
699C22⋊D73—44no—
700C22⋊D73—44no—
701C22⋊D73—44no—
702C2×Dic73—24no—
703C2×Dic73—41no—
704C2×Dic73—42no—
705C2×Dic73—41no—
706C2×Dic73—44no—
707C2×Dic73C2512yes—
708C2×Dic73C2514yes—
709C2×Dic73C2514yes—
710C2×Dic73C2514yes—
711C2×Dic73C2512yes—
712D292—28no—
713D292—216no—
714D292—216no—
715D292—28no—
716D292—24no—
717D292—28no—
718D292—48no—
719D292—48no—
720D292—48no—
721D292—44no—
722D292—44no—
723D292—48no—
724D292—48no—
725D292—48no—
726D292—44no—
727C4×D73—28no—
728C4×D73—24no—
729C4×D73—24no—
730C4×D73—24no—
731C4×D73—24no—
732C4×D73—28no—
733C4×D73—42no—
734C4×D73—42no—
735C4×D73—42no—
736C4×D73—42no—
737C4×D73—44no—
738C4×D73—44no—
739C4×D73—44no—
740C4×D73—48no—
741C4×D73—48no—
742C4×D73—48no—
743C4×D73—48no—
744Dic146—24no—
745Dic146—44no—
746Dic146—44no—
747C22×C73—28no—
748C22×C73—21no—
749C22×C73—21no—
750C22×C73—21no—
751C22×C73—21no—
752C22×C73—21no—
753C22×C73—21no—
754C22×C73—24no—
755C22×C73—24no—
756C22×C73—24no—
757C22×C73C2×H(5,𝔽2)12yes—
758C22×C73C2×H(5,𝔽2)12yes—
759C22×C73#58512yes—
760C22×C73C2611yescharacteristic
761C2×D73—22no—
762C2×D73—22no—
763C2×D73—22no—
764C2×D73—24no—
765C2×D73—24no—
766C2×D73—28no—
767C2×D73—28no—
768C2×D73—22no—
769C2×D73—28no—
770C2×D73—24no—
771C2×D73—22no—
772C2×D73—44no—
773C2×D73—48no—
774C2×D73—48no—
775C2×D73—44no—
776C2×D73—88no—
777C2×D73—88no—
778C2×D73—88no—
779C2×D73—88no—
780C2×D73—168no—
781C2×D73C2×H(5,𝔽2)14yes—
782C4×C73—24no—
783C4×C73—24no—
784C4×C73—24no—
785C4×C73—22no—
786C4×C73—24no—
787C4×C73—24no—
788C4×C73C2×H(5,𝔽2)14yes—
789Dic73—24no—
790Dic73—22no—
791Dic73—24no—
792Dic73—22no—
793Dic73—24no—
794#62818—731nomaximal, Sylow
795C2×C73—22no—
796C2×C73—22no—
797C2×C73—22no—
798C2×C73—44no—
799C2×C73C22×H(5,𝔽2)11yescharacteristic
800C2×C73C22×H(5,𝔽2)11yescharacteristic
801C2×C73C2×#58511yescharacteristic
802D73—24no—
803D73—42no—
804D73—48no—
805D73—44no—
806#3542—734no—
807#3542—734no—
808#3537—734no—
809#3536—734no—
810#3534—738no—
811#3519—734no—
812#3519—734no—
813#3505—734no—
814#3496—734no—
815#3494—732no—
816#3494—732no—
817#3492—731no—
818#3492D7311yescharacteristic, complemented
819#3490—734no—
820#3488—732no—
821#3488—732no—
822#3484—732no—
823#3484—734no—
824C2×#525—732no—
825C22×#121—731no—
826C73#6281811yescharacteristic, complemented, Sylow
827C2×H(5,𝔽2)—732no—
828C2×H(5,𝔽2)—734no—
829C22×#41—732no—
830C23×D4—731no—
831C23×D4—732no—
832C24×C4—731no—
833#562—738no—
834#562—738no—
835#560—738no—
836#560—738no—
837#555—734no—
838#555—734no—
839#554—734no—
840#554C2×D7314yescomplemented
841#553—738no—
842#553—734no—
843#553—734no—
844#553—738no—
845#553—734no—
846#553—734no—
847#553—734no—
848#553C2×D7314yescomplemented
849#552—734no—
850#552C2×D7314yescomplemented
851#551—738no—
852#551—738no—
853#551—738no—
854#551—738no—
855#550—734no—
856#550—734no—
857#548—734no—
858#548—734no—
859#547—734no—
860#547—734no—
861#547—734no—
862#547C2×D7314yescomplemented
863#546—738no—
864#546—738no—
865#546—738no—
866#546—738no—
867#546—734no—
868#546—738no—
869#546—734no—
870#546—734no—
871#546—738no—
872#546—738no—
873#546—738no—
874#546—738no—
875#546—734no—
876#546—738no—
877#546—734no—
878#546—734no—
879D42—738no—
880D42—734no—
881D42—734no—
882D42—738no—
883D42—734no—
884D42—738no—
885D42—734no—
886D42—738no—
887D42—734no—
888D42—734no—
889#544—731no—
890#544C2×D7311yescharacteristic, complemented
891#543—734no—
892#542—734no—
893#542—734no—
894#540—734no—
895#540—738no—
896#540—738no—
897#540—734no—
898#539—738no—
899#539—734no—
900#539C2×D7314yescomplemented
901#538—738no—
902#538—738no—
903#538—734no—
904#538—738no—
905#538—734no—
906#538—738no—
907#537—734no—
908#537—738no—
909#537—731no—
910#537—734no—
911#537C2×D7311yescharacteristic, complemented
912#535—732no—
913#535—734no—
914#535—734no—
915#535—732no—
916#535—734no—
917#535—734no—
918#534—738no—
919#534—738no—
920#534—738no—
921#534—738no—
922#534—734no—
923#532—734no—
924#532—734no—
925#529—734no—
926#529—734no—
927#525—732no—
928#525—732no—
929#525—734no—
930#525—734no—
931#525—732no—
932#525—732no—
933#525—734no—
934#525—732no—
935#525—732no—
936#525—734no—
937#525—734no—
938#525—734no—
939#525—732no—
940#525—734no—
941#525C2×D7312yescomplemented
942#525C2×D7314yescomplemented
943C2×#123—734no—
944C2×C22⋊Q8—732no—
945C2×C22⋊Q8—732no—
946C2×#121—732no—
947C2×#121—732no—
948C2×#121—734no—
949C2×#121—732no—
950C2×#121—732no—
951C2×#121—734no—
952C2×#121—734no—
953C2×#121—734no—
954C2×#121—734no—
955C2×#121—734no—
956C2×#121—734no—
957C2×#120—734no—
958C2×#120—738no—
959#520—732no—
960#520C2×D7312yescomplemented
961#518—738no—
962#518—732no—
963#518—734no—
964C2×C4×D4—734no—
965C2×C4×D4—734no—
966C2×#117—732no—
967C22×C4⋊C4C2×D7311yescharacteristic, complemented
968C22×C22⋊C4—732no—
969C25—732no—
970C25—731no—
971H(5,𝔽2)—2928no—
972H(5,𝔽2)—29216no—
973C2×#41—2928no—
974C2×#41—732no—
975C2×#41—734no—
976C2×#41—738no—
977C2×#41—734no—
978C2×#41—732no—
979C2×#41—734no—
980C2×#41—734no—
981C2×#41—734no—
982C2×#41—738no—
983C2×#41—732no—
984C2×#41C22×D7312yes—
985C2×#41C22×D7314yes—
986C22×Q8—732no—
987C22×D4—2924no—
988C22×D4—2928no—
989C22×D4—734no—
990C22×D4—738no—
991C22×D4—734no—
992C22×D4—738no—
993C22×D4—738no—
994C22×D4—732no—
995C22×D4—738no—
996C22×D4—734no—
997C22×D4—734no—
998C22×D4—732no—
999C22×D4—734no—
1000C22×D4—734no—
1001C22×D4—734no—
1002C22×D4—734no—
1003C22×D4—738no—
1004C22×D4—734no—
1005C22×D4—738no—
1006C22×D4—734no—
1007C22×D4—734no—
1008C22×D4—732no—
1009C23×C4—2924no—
1010C23×C4—731no—
1011C23×C4—732no—
1012C23×C4—732no—
1013C23×C4—734no—
1014C23×C4—732no—
1015C23×C4—732no—
1016C23×C4—732no—
1017C23×C4—732no—
1018C23×C4C22×D7311yescharacteristic
1019C23×C4C22×D7312yes—
1020C4⋊Q8—734no—
1021C4⋊Q8C22×D7314yescomplemented
1022#127—734no—
1023#127—738no—
1024#127—734no—
1025#127—738no—
1026#126—738no—
1027#126—738no—
1028#126—738no—
1029#126—738no—
1030#126—738no—
1031#126C22×D7318yescomplemented
1032#125—734no—
1033#125—738no—
1034#125C22×D7314yescomplemented
1035#125C22×D7318yescomplemented
1036#124—734no—
1037#124—738no—
1038#124—738no—
1039#124—738no—
1040#124—738no—
1041#124—734no—
1042#124—738no—
1043#124—738no—
1044#123—734no—
1045#123—734no—
1046#123—738no—
1047#123—738no—
1048#123—734no—
1049#123—734no—
1050#123—738no—
1051#123—738no—
1052#123—738no—
1053#123—738no—
1054#123—738no—
1055#123—738no—
1056#123—738no—
1057#123—738no—
1058#123—738no—
1059#123—738no—
1060#123—734no—
1061#123—734no—
1062#123—734no—
1063#123—738no—
1064#123—738no—
1065#123C22×D7314yes—
1066#123C22×D7318yes—
1067#123C22×D7318yescomplemented
1068C22⋊Q8—732no—
1069C22⋊Q8—732no—
1070C22⋊Q8—738no—
1071C22⋊Q8—732no—
1072C22⋊Q8—732no—
1073C22⋊Q8—734no—
1074C22⋊Q8—734no—
1075C22⋊Q8—732no—
1076C22⋊Q8—732no—
1077C22⋊Q8—734no—
1078C22⋊Q8—734no—
1079C22⋊Q8—734no—
1080C22⋊Q8—738no—
1081C22⋊Q8—738no—
1082C22⋊Q8—738no—
1083C22⋊Q8—738no—
1084C22⋊Q8—734no—
1085C22⋊Q8—734no—
1086C22⋊Q8C22×D7312yes—
1087C22⋊Q8C22×D7312yes—
1088C22⋊Q8C22×D7314yes—
1089C22⋊Q8C22×D7314yes—
1090C22⋊Q8C22×D7314yescomplemented
1091C22⋊Q8C22×D7318yescomplemented
1092#121—732no—
1093#121—734no—
1094#121—732no—
1095#121—734no—
1096#121—738no—
1097#121—732no—
1098#121—732no—
1099#121—734no—
1100#121—734no—
1101#121—734no—
1102#121—734no—
1103#121—738no—
1104#121—738no—
1105#121—738no—
1106#121—734no—
1107#121—734no—
1108#121—732no—
1109#121—738no—
1110#121—734no—
1111#121—734no—
1112#121—738no—
1113#121—734no—
1114#121—734no—
1115#121—738no—
1116#121—734no—
1117#121—734no—
1118#121—738no—
1119#121—732no—
1120#121—738no—
1121#121—734no—
1122#121—734no—
1123#121—738no—
1124#121—734no—
1125#121—738no—
1126#121—738no—
1127#121—738no—
1128#121—738no—
1129#121—738no—
1130#121—738no—
1131#121—738no—
1132#121—734no—
1133#121—734no—
1134#121—738no—
1135#121—738no—
1136#121—738no—
1137#121—738no—
1138#121—738no—
1139#121—738no—
1140#121—738no—
1141#121C22×D7312yes—
1142#121C22×D7312yes—
1143#121C22×D7314yes—
1144#121C22×D7314yes—
1145#121C22×D7314yescomplemented
1146#120—734no—
1147#120—734no—
1148#120—734no—
1149#120—734no—
1150#120—738no—
1151#120—738no—
1152#120—738no—
1153#120—738no—
1154#120—734no—
1155#120—734no—
1156#120—734no—
1157#120—738no—
1158#120—738no—
1159#120—738no—
1160#120—738no—
1161#120—738no—
1162#120—738no—
1163#120—738no—
1164#120—738no—
1165#120—738no—
1166#120—738no—
1167#120C22×D7314yes—
1168C4×Q8—734no—
1169C4×Q8C22×D7314yescomplemented
1170C4×D4—734no—
1171C4×D4—734no—
1172C4×D4—734no—
1173C4×D4—734no—
1174C4×D4—734no—
1175C4×D4—734no—
1176C4×D4—738no—
1177C4×D4—738no—
1178C4×D4—738no—
1179C4×D4—734no—
1180C4×D4—734no—
1181C4×D4—738no—
1182C4×D4—738no—
1183C4×D4—734no—
1184C4×D4—738no—
1185C4×D4—734no—
1186C4×D4—734no—
1187C4×D4—734no—
1188C4×D4—734no—
1189C4×D4—734no—
1190C4×D4—734no—
1191C4×D4—738no—
1192C4×D4—734no—
1193C4×D4—734no—
1194C4×D4—738no—
1195C4×D4—738no—
1196C4×D4—738no—
1197C4×D4—734no—
1198C4×D4—734no—
1199C4×D4C22×D7314yes—
1200C4×D4C22×D7314yes—
1201C4×D4C22×D7318yes—
1202C4×D4C22×D7318yes—
1203C4×D4C22×D7314yescomplemented
1204#117—732no—
1205#117—734no—
1206#117—732no—
1207#117—732no—
1208#117—738no—
1209#117—734no—
1210#117—734no—
1211#117—734no—
1212#117—738no—
1213#117C22×D7312yes—
1214#117C22×D7314yes—
1215#117C22×D7314yescomplemented
1216C2×C4⋊C4—732no—
1217C2×C4⋊C4—732no—
1218C2×C4⋊C4—734no—
1219C2×C4⋊C4—734no—
1220C2×C4⋊C4—734no—
1221C2×C4⋊C4C22×D7311yescharacteristic
1222C2×C4⋊C4C22×D7311yescharacteristic
1223C2×C4⋊C4C22×D7312yes—
1224C2×C4⋊C4C22×D7314yes—
1225C2×C4⋊C4C22×D7314yes—
1226C2×C4⋊C4C22×D7314yescomplemented
1227C2×C22⋊C4—734no—
1228C2×C22⋊C4—734no—
1229C2×C22⋊C4—738no—
1230C2×C22⋊C4—734no—
1231C2×C22⋊C4—734no—
1232C2×C22⋊C4—738no—
1233C2×C22⋊C4—734no—
1234C2×C22⋊C4—734no—
1235C2×C22⋊C4—734no—
1236C2×C22⋊C4—734no—
1237C2×C22⋊C4—734no—
1238C2×C22⋊C4—738no—
1239C2×C22⋊C4—738no—
1240C2×C22⋊C4—738no—
1241C2×C22⋊C4—738no—
1242C2×C42—734no—
1243C24—2922no—
1244C24—2922no—
1245C24—2924no—
1246C24—2924no—
1247C24—2924no—
1248C24—738no—
1249C24—731no—
1250C24—734no—
1251C24—734no—
1252C24—734no—
1253C24—734no—
1254C24—731no—
1255C24—732no—
1256C24—732no—
1257C24—1464no—
1258C24C23×D7311yescharacteristic
1259#41—28no—
1260#41—48no—
1261#41—2928no—
1262#41—2928no—
1263#41—2928no—
1264#41—29216no—
1265#41—2924no—
1266#41—2928no—
1267#41—2924no—
1268#41—2928no—
1269#41—29216no—
1270#41—1468no—
1271C2×Q8—2924no—
1272C2×Q8—734no—
1273C2×Q8—734no—
1274C2×Q8—732no—
1275C2×Q8C23×D7312yes—
1276C2×Q8C23×D7314yes—
1277C2×D4—2928no—
1278C2×D4—2924no—
1279C2×D4—2928no—
1280C2×D4—2928no—
1281C2×D4—2928no—
1282C2×D4—2928no—
1283C2×D4—29216no—
1284C2×D4—2928no—
1285C2×D4—29216no—
1286C2×D4—2928no—
1287C2×D4—29216no—
1288C2×D4—2928no—
1289C2×D4—29216no—
1290C2×D4—29216no—
1291C2×D4—29216no—
1292C2×D4—2924no—
1293C2×D4—2928no—
1294C2×D4—738no—
1295C2×D4—734no—
1296C2×D4—734no—
1297C2×D4—734no—
1298C2×D4—738no—
1299C2×D4—738no—
1300C2×D4—734no—
1301C2×D4—734no—
1302C2×D4—734no—
1303C2×D4—734no—
1304C2×D4—738no—
1305C2×D4—734no—
1306C2×D4—734no—
1307C2×D4—738no—
1308C2×D4—738no—
1309C2×D4—738no—
1310C2×D4—734no—
1311C2×D4—738no—
1312C2×D4—738no—
1313C2×D4—734no—
1314C2×D4—738no—
1315C2×D4—738no—
1316C2×D4—734no—
1317C2×D4—734no—
1318C2×D4—732no—
1319C2×D4—14616no—
1320C2×D4—14616no—
1321C2×D4—1468no—
1322C2×D4C23×D7314yes—
1323C2×D4C23×D7314yes—
1324C2×D4C23×D7314yes—
1325C2×D4C23×D7312yes—
1326C2×D4C23×D7314yes—
1327C22×C4—24no—
1328C22×C4—44no—
1329C22×C4—2924no—
1330C22×C4—2924no—
1331C22×C4—2924no—
1332C22×C4—2924no—
1333C22×C4—2924no—
1334C22×C4—2928no—
1335C22×C4—2922no—
1336C22×C4—731no—
1337C22×C4—732no—
1338C22×C4—731no—
1339C22×C4—734no—
1340C22×C4—734no—
1341C22×C4—732no—
1342C22×C4—734no—
1343C22×C4—732no—
1344C22×C4—738no—
1345C22×C4—734no—
1346C22×C4—738no—
1347C22×C4—738no—
1348C22×C4—738no—
1349C22×C4—732no—
1350C22×C4—732no—
1351C22×C4—732no—
1352C22×C4—732no—
1353C22×C4—734no—
1354C22×C4—732no—
1355C22×C4—734no—
1356C22×C4—732no—
1357C22×C4—732no—
1358C22×C4—1468no—
1359C22×C4C23×D7314yes—
1360C22×C4C23×D7312yes—
1361C22×C4C23×D7312yes—
1362C22×C4C23×D7311yescharacteristic
1363C22×C4C23×D7314yes—
1364C22×C4C23×D7312yes—
1365C22×C4C23×D7314yes—
1366C22×C4C23×D7312yes—
1367C22×C4C23×D7318yes—
1368C22×C4C23×D7311yescharacteristic
1369C4⋊C4—734no—
1370C4⋊C4—734no—
1371C4⋊C4—734no—
1372C4⋊C4—734no—
1373C4⋊C4—734no—
1374C4⋊C4—734no—
1375C4⋊C4—738no—
1376C4⋊C4—738no—
1377C4⋊C4—732no—
1378C4⋊C4—732no—
1379C4⋊C4—734no—
1380C4⋊C4—734no—
1381C4⋊C4—734no—
1382C4⋊C4—734no—
1383C4⋊C4C23×D7314yes—
1384C4⋊C4C23×D7312yes—
1385C4⋊C4C23×D7312yes—
1386C4⋊C4C23×D7314yes—
1387C4⋊C4C23×D7314yes—
1388C4⋊C4C23×D7314yes—
1389C4⋊C4C23×D7318yes—
1390C4⋊C4C23×D7318yes—
1391C4⋊C4C23×D7318yes—
1392C4⋊C4C23×D7314yes—
1393C4⋊C4C23×D7314yes—
1394C22⋊C4—734no—
1395C22⋊C4—734no—
1396C22⋊C4—734no—
1397C22⋊C4—734no—
1398C22⋊C4—734no—
1399C22⋊C4—738no—
1400C22⋊C4—738no—
1401C22⋊C4—734no—
1402C22⋊C4—738no—
1403C22⋊C4—738no—
1404C22⋊C4—738no—
1405C22⋊C4—738no—
1406C22⋊C4—734no—
1407C22⋊C4—734no—
1408C22⋊C4—734no—
1409C22⋊C4—734no—
1410C22⋊C4—738no—
1411C22⋊C4—738no—
1412C22⋊C4—738no—
1413C22⋊C4—738no—
1414C22⋊C4—738no—
1415C22⋊C4—734no—
1416C22⋊C4—734no—
1417C22⋊C4—734no—
1418C22⋊C4—734no—
1419C22⋊C4—734no—
1420C22⋊C4—738no—
1421C22⋊C4C23×D7314yes—
1422C22⋊C4C23×D7314yes—
1423C22⋊C4C23×D7314yes—
1424C22⋊C4C23×D7318yes—
1425C22⋊C4C23×D7314yes—
1426C22⋊C4C23×D7314yes—
1427C22⋊C4C23×D7318yes—
1428C42—734no—
1429C42—734no—
1430C42—734no—
1431C42—738no—
1432C42C23×D7314yes—
1433C42C23×D7318yes—
1434C23—22no—
1435C23—22no—
1436C23—22no—
1437C23—29216no—
1438C23—2921no—
1439C23—2922no—
1440C23—2921no—
1441C23—2921no—
1442C23—2922no—
1443C23—2921no—
1444C23—2924no—
1445C23—2924no—
1446C23—2924no—
1447C23—2924no—
1448C23—2924no—
1449C23—2924no—
1450C23—2924no—
1451C23—2924no—
1452C23—2928no—
1453C23—2928no—
1454C23—2928no—
1455C23—58416no—
1456C23—734no—
1457C23—732no—
1458C23—738no—
1459C23—734no—
1460C23—732no—
1461C23—1464no—
1462C23—1464no—
1463C23—1468no—
1464C23—1462no—
1465C23—1464no—
1466C23—1464no—
1467C23—1468no—
1468C23—1468no—
1469C23—1468no—
1470C23C24×D7314yes—
1471C23C24×D7311yescharacteristic
1472C23C24×D7311yescharacteristic
1473C23C24×D7311yescharacteristic
1474Q8—24no—
1475Q8—44no—
1476Q8—2924no—
1477Q8—2924no—
1478Q8—1464no—
1479D4—28no—
1480D4—28no—
1481D4—28no—
1482D4—24no—
1483D4—44no—
1484D4—2928no—
1485D4—2928no—
1486D4—2928no—
1487D4—2924no—
1488D4—2928no—
1489D4—2928no—
1490D4—2924no—
1491D4—2928no—
1492D4—2924no—
1493D4—2928no—
1494D4—2928no—
1495D4—2924no—
1496D4—2924no—
1497D4—2928no—
1498D4—2924no—
1499D4—14616no—
1500D4—14616no—
1501D4—1468no—
1502D4—1468no—
1503D4—1468no—
1504D4—1468no—
1505D4—1468no—
1506D4—1468no—
1507D4—1468no—
1508D4—1464no—
1509C2×C4—28no—
1510C2×C4—22no—
1511C2×C4—24no—
1512C2×C4—24no—
1513C2×C4—28no—
1514C2×C4—42no—
1515C2×C4—44no—
1516C2×C4—42no—
1517C2×C4—48no—
1518C2×C4—2922no—
1519C2×C4—2922no—
1520C2×C4—2922no—
1521C2×C4—2922no—
1522C2×C4—2924no—
1523C2×C4—2924no—
1524C2×C4—2928no—
1525C2×C4—2928no—
1526C2×C4—2928no—
1527C2×C4—2928no—
1528C2×C4—2924no—
1529C2×C4—2921no—
1530C2×C4—2922no—
1531C2×C4—2921no—
1532C2×C4—2924no—
1533C2×C4—734no—
1534C2×C4—732no—
1535C2×C4—734no—
1536C2×C4—734no—
1537C2×C4—732no—
1538C2×C4—1468no—
1539C2×C4—1464no—
1540C2×C4—1464no—
1541C2×C4—1464no—
1542C2×C4—1464no—
1543C2×C4—1464no—
1544C2×C4—1468no—
1545C2×C4#1455663714yescomplemented
1546C2×C4C24×D7314yes—
1547C2×C4C24×D7314yes—
1548C2×C4C24×D7314yes—
1549C2×C4C24×D7314yes—
1550C2×C4C24×D7314yes—
1551C2×C4C24×D7312yes—
1552C2×C4C24×D7312yes—
1553C22—28no—
1554C22—21no—
1555C22—21no—
1556C22—21no—
1557C22—21no—
1558C22—21no—
1559C22—21no—
1560C22—24no—
1561C22—24no—
1562C22—24no—
1563C22—2924no—
1564C22—2928no—
1565C22—2928no—
1566C22—2924no—
1567C22—5848no—
1568C22—5848no—
1569C22—5848no—
1570C22—5848no—
1571C22—734no—
1572C22—11688no—
1573C22—1464no—
1574C22—1468no—
1575C22—1462no—
1576C22—1462no—
1577C22—1464no—
1578C22—1468no—
1579C22—1468no—
1580C22—1462no—
1581C22—1464no—
1582C22—1462no—
1583C22—1462no—
1584C22H(5,𝔽2)×D7312yes—
1585C22C2×#1455663712yes—
1586C22#1798942412yes—
1587C22C25×D7311yescharacteristic
1588C4—24no—
1589C4—24no—
1590C4—24no—
1591C4—22no—
1592C4—24no—
1593C4—24no—
1594C4—1464no—
1595C4—1462no—
1596C4—1462no—
1597C4—1464no—
1598C4—1464no—
1599C4C2×#1455663714yes—
1600C2—22no—
1601C2—22no—
1602C2—22no—
1603C2—44no—
1604C2—2922no—
1605C2—2928no—
1606C2—2924no—
1607C2—1464no—
1608C2C2×H(5,𝔽2)×D7311yescharacteristic
1609C2C22×#1455663711yescharacteristic
1610C2C2×#1798942411yescharacteristic
subgroupG/H
center, FrattiniC22C25×D73
commutator, socle, cosocleC22×C73C26
FittingC73×#3492C2
hypercenter#3492D73
hypocenterC73#62818
LCSG ▷ C22×C73 ▷ C73
UCSC1 ◁ C22 ◁ #3492

Complements

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

NH ≅ G/Ntype
1. #22624248C2semidirect
2. #22624241C2semidirect
3. #22624167C2semidirect
4. #22624159C2semidirect
5. #22624119C2semidirect
6. #22623964C2semidirect
7. #22623956C2semidirect
8. #22623771C2semidirect
9. #22623689C2semidirect
10. #22623669C2semidirect
11. #22623667C2semidirect
12. #22623640C2semidirect
13. #22623614C2semidirect
14. #22623601C2semidirect
15. #22623595C2semidirect
16. #22623564C2semidirect
17. #22623564C2semidirect
18. #525×D73C2semidirect
19. C22×#14556566C2semidirect
20. C73×#3492C2semidirect
21. C2×#14556637C22semidirect
22. C2×#14556637C22semidirect
23. C2×#41×D73C22semidirect
24. C23×D292C22semidirect
25. C23×D292C22semidirect
26. C23×C4×D73C22semidirect
27. #17989335C22semidirect
28. #17989333C22semidirect
29. #17989328C22semidirect
30. #17989327C22semidirect
31. #17989303C22semidirect
32. #17989300C22semidirect
33. #17989292C22semidirect
34. #17989290C22semidirect
35. #17989290C22semidirect
36. #17989290C22semidirect
37. #17989288C22semidirect
38. #17989285C22semidirect
39. #17989285C22semidirect
40. #17989281C22semidirect
41. #17989272C22semidirect
42. #17989266C22semidirect
43. #17989264C22semidirect
44. #17989261C22semidirect
45. #17989260C22semidirect
46. #17989259C22semidirect
47. #17989255C22semidirect
48. #17989249C22semidirect
49. #17989247C22semidirect
50. #17989240C22semidirect
51. #17989238C22semidirect
52. #17989238C22semidirect
53. #17989233C22semidirect
54. #17989233C22semidirect
55. #17989233C22semidirect
56. #17989233C22semidirect
57. #17989232C22semidirect
58. #17989232C22semidirect
59. #17989229C22semidirect
60. #17989229C22semidirect
61. #17989228C22semidirect
62. #17989228C22semidirect
63. #17989228C22semidirect
64. #17989228C22semidirect
65. #17989228C22semidirect
66. #17989228C22semidirect
67. #17989226C22semidirect
68. #17989225C22semidirect
69. D4×D292C22semidirect
70. D4×D292C22semidirect
71. D4×D292C22semidirect
72. D4×D292C22semidirect
73. D4×D292C22semidirect
74. #17989221C22semidirect
75. #17989221C22semidirect
76. #17989221C22semidirect
77. #17989221C22semidirect
78. #17989221C22semidirect
79. #17989218C22semidirect
80. #17989212C22semidirect
81. #17989211C22semidirect
82. #17989209C22semidirect
83. #17989193C22semidirect
84. #17989193C22semidirect
85. #17989189C22semidirect
86. #17989188C22semidirect
87. #17989185C22semidirect
88. #17989184C22semidirect
89. #17989177C22semidirect
90. #17989177C22semidirect
91. #17989176C22semidirect
92. #17989176C22semidirect
93. #17989174C22semidirect
94. #17989170C22semidirect
95. #17989168C22semidirect
96. #17989168C22semidirect
97. #17989167C22semidirect
98. #17989167C22semidirect
99. #17989156C22semidirect
100. #17989156C22semidirect
101. #17989156C22semidirect
102. #17989153C22semidirect
103. #17989151C22semidirect
104. #17989151C22semidirect
105. #17989148C22semidirect
106. #17989148C22semidirect
107. #17989148C22semidirect
108. #17989148C22semidirect
109. #17989145C22semidirect
110. #17989138C22semidirect
111. #17989134C22semidirect
112. #17989124C22semidirect
113. #17989122C22semidirect
114. #17989100C22semidirect
115. #17989100C22semidirect
116. #17989100C22semidirect
117. #17989099C22semidirect
118. #17989099C22semidirect
119. #17989098C22semidirect
120. #17989098C22semidirect
121. #17989097C22semidirect
122. #17989097C22semidirect
123. #17989096C22semidirect
124. #17989096C22semidirect
125. #17989095C22semidirect
126. #17989094C22semidirect
127. #17989093C22semidirect
128. #123×D73C22semidirect
129. C22⋊Q8×D73C22semidirect
130. C22⋊Q8×D73C22semidirect
131. C2×#14556566C22semidirect
132. C2×#14556566C22semidirect
133. C2×#14556566C22semidirect
134. C2×#14556566C22semidirect
135. C2×#14556566C22semidirect
136. C2×#14556566C22semidirect
137. C2×#14556566C22semidirect
138. C2×#14556566C22semidirect
139. #121×D73C22semidirect
140. #121×D73C22semidirect
141. #121×D73C22semidirect
142. #120×D73C22semidirect
143. #120×D73C22semidirect
144. #17989068C22semidirect
145. #17989061C22semidirect
146. #17989061C22semidirect
147. #17989059C22semidirect
148. C4×D4×D73C22semidirect
149. C4×D4×D73C22semidirect
150. #117×D73C22semidirect
151. C22×#11924005C22semidirect
152. #554×C73C22semidirect
153. #553×C73C22semidirect
154. #552×C73C22semidirect
155. #547×C73C22semidirect
156. #544×C73C22semidirect
157. #539×C73C22semidirect
158. #537×C73C22semidirect
159. #525×C73C22semidirect
160. #525×C73C22semidirect
161. #520×C73C22semidirect
162. C22×C4⋊C4×C73C22semidirect
167. C2×#11924029C23semidirect
168. C2×#11924029C23semidirect
169. C2×#11924029C23semidirect
172. C2×#11924028C23semidirect
173. C2×#11924028C23semidirect
174. C2×#11924028C23semidirect
176. C2×#11924027C23semidirect
178. C2×Q8×D73C23semidirect
190. C22×D292C23semidirect
191. C22×D292C23semidirect
198. C2×D4×D73C23semidirect
199. C2×D4×D73C23semidirect
200. C2×D4×D73C23semidirect
209. C22×C4×D73C23semidirect
210. #14556590C23semidirect
211. #14556588C23semidirect
212. #14556588C23semidirect
213. #14556587C23semidirect
214. #14556587C23semidirect
215. #14556586C23semidirect
216. #14556586C23semidirect
217. #14556586C23semidirect
218. #14556586C23semidirect
219. #14556585C23semidirect
220. #14556582C23semidirect
221. #14556581C23semidirect
222. #14556580C23semidirect
223. #14556580C23semidirect
224. #14556580C23semidirect
225. #14556579C23semidirect
226. #14556579C23semidirect
227. #14556579C23semidirect
228. #14556577C23semidirect
229. #14556577C23semidirect
230. #14556576C23semidirect
231. #14556576C23semidirect
232. #14556576C23semidirect
233. #14556576C23semidirect
234. #14556576C23semidirect
235. #14556576C23semidirect
236. #14556576C23semidirect
237. #14556576C23semidirect
238. #14556576C23semidirect
239. #14556576C23semidirect
240. #14556576C23semidirect
241. #14556576C23semidirect
243. #14556575C23semidirect
246. #14556574C23semidirect
247. #14556573C23semidirect
248. #14556573C23semidirect
249. #14556573C23semidirect
251. #14556571C23semidirect
252. #14556571C23semidirect
253. #14556571C23semidirect
254. #14556571C23semidirect
259. #14556569C23semidirect
260. #14556569C23semidirect
261. #14556569C23semidirect
262. #14556569C23semidirect
263. #14556569C23semidirect
266. #14556567C23semidirect
267. #14556567C23semidirect
268. #14556567C23semidirect
281. #14556566C23semidirect
282. #14556566C23semidirect
283. #14556566C23semidirect
284. #14556566C23semidirect
285. #14556566C23semidirect
286. #14556566C23semidirect
287. #14556566C23semidirect
288. #14556566C23semidirect
289. #14556566C23semidirect
290. #14556566C23semidirect
291. #14556566C23semidirect
292. #14556566C23semidirect
293. #14556566C23semidirect
294. #14556566C23semidirect
299. #14556565C23semidirect
300. #14556565C23semidirect
301. #14556565C23semidirect
302. #14556565C23semidirect
303. #14556565C23semidirect
304. #14556564C23semidirect
305. #14556564C23semidirect
306. #14556564C23semidirect
307. #14556564C23semidirect
308. #14556564C23semidirect
309. #14556564C23semidirect
310. #14556564C23semidirect
311. #14556564C23semidirect
312. #14556564C23semidirect
315. #14556563C23semidirect
316. #14556562C23semidirect
317. #14556562C23semidirect
324. #14556561C23semidirect
325. #14556561C23semidirect
326. #14556561C23semidirect
327. #14556561C23semidirect
328. #14556561C23semidirect
329. #14556561C23semidirect
330. #14556561C23semidirect
338. #14556559C23semidirect
339. #14556556C23semidirect
340. C4×D292C23semidirect
341. C4×D292C23semidirect
342. C4×D292C23semidirect
343. C4×D292C23semidirect
344. C4×D292C23semidirect
345. C4×D292C23semidirect
346. C4×D292C23semidirect
349. #14556553C23semidirect
350. #14556553C23semidirect
351. #14556553C23semidirect
352. #14556553C23semidirect
353. #14556553C23semidirect
354. #14556553C23semidirect
355. #14556553C23semidirect
356. #14556553C23semidirect
361. C4×C22⋊D73C23semidirect
362. C4×C22⋊D73C23semidirect
363. C4×C22⋊D73C23semidirect
366. #14556551C23semidirect
367. #14556551C23semidirect
368. #14556551C23semidirect
371. #14556549C23semidirect
372. #14556549C23semidirect
373. #14556549C23semidirect
374. #14556549C23semidirect
375. #14556548C23semidirect
376. #14556548C23semidirect
378. C4⋊C4×D73C23semidirect
379. C4⋊C4×D73C23semidirect
380. C4⋊C4×D73C23semidirect
381. C4⋊C4×D73C23semidirect
382. C4⋊C4×D73C23semidirect
388. C2×#11924005C23semidirect
395. C22⋊C4×D73C23semidirect
396. C22⋊C4×D73C23semidirect
397. C22⋊C4×D73C23semidirect
398. C42×D73C23semidirect
403. C4⋊Q8×C73C23semidirect
404. #126×C73C23semidirect
405. #125×C73C23semidirect
406. #125×C73C23semidirect
409. #123×C73C23semidirect
414. C22⋊Q8×C73C23semidirect
415. C22⋊Q8×C73C23semidirect
420. #121×C73C23semidirect
422. C4×Q8×C73C23semidirect
427. C4×D4×C73C23semidirect
430. #117×C73C23semidirect
436. C2×C4⋊C4×C73C23semidirect
663. C22×D73H(5,𝔽2)semidirect
684. C2×C4×C73H(5,𝔽2)semidirect
818. #3492D73semidirect
826. C73#62818semidirect
840. #554C2×D73semidirect
848. #553C2×D73semidirect
850. #552C2×D73semidirect
862. #547C2×D73semidirect
890. #544C2×D73semidirect
900. #539C2×D73semidirect
911. #537C2×D73semidirect
941. #525C2×D73semidirect
942. #525C2×D73semidirect
960. #520C2×D73semidirect
967. C22×C4⋊C4C2×D73semidirect
1021. C4⋊Q8C22×D73semidirect
1031. #126C22×D73semidirect
1034. #125C22×D73semidirect
1035. #125C22×D73semidirect
1067. #123C22×D73semidirect
1090. C22⋊Q8C22×D73semidirect
1091. C22⋊Q8C22×D73semidirect
1145. #121C22×D73semidirect
1169. C4×Q8C22×D73semidirect
1203. C4×D4C22×D73semidirect
1215. #117C22×D73semidirect
1226. C2×C4⋊C4C22×D73semidirect
1545. C2×C4#14556637semidirect

Maximal subgroups

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

subgroupindex
#226242482
#226242412
#226241672
#226241592
#226241192
#226239642
#226239562
#226237712
#226236892
#226236692
#226236672
#226236402
#226236142
#226236012
#226235952
#226235642
#525×D732
C22×#145565662
C73×#34922
#6281873