Finite Group Databasebeta

← #33994619

Subgroups — #33994619

Order 18688.

7242 conjugacy classes of subgroups.

The subgroup lattice has 1534 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#22624229C214yesmaximal, complemented
2#22624210C214yesmaximal, complemented
3#22624172C214yesmaximal, complemented
4#22624147C214yesmaximal, complemented
5#22624130C218yesmaximal, complemented
6#22623981C214yesmaximal, complemented
7#22623973C214yesmaximal, complemented
8#22623767C214yesmaximal, complemented
9#22623726C214yesmaximal, complemented
10#22623680C212yesmaximal, complemented
11#22623673C212yesmaximal, complemented
12#22623637C212yesmaximal, complemented
13#22623632C214yesmaximal, complemented
14#22623614C214yesmaximal, complemented
15#22623609C212yesmaximal, complemented
16#22623604C212yesmaximal, complemented
17#22623582C211yesmaximal, characteristic, complemented
18#525×D73C212yesmaximal, complemented
19C22×#14556567C211yesmaximal, characteristic, complemented
20C73×#3486C211yesmaximal, characteristic, complemented
21C2×#14556639C2211yescharacteristic, complemented
22C2×#41×D73C2212yescomplemented
23C23×C4×D73C2211yescharacteristic
24#17989338C2218yescomplemented
25#17989336C2218yescomplemented
26#17989333C2218yescomplemented
27#17989331C2218yescomplemented
28#17989310C2214yescomplemented
29#17989308C2214yescomplemented
30#17989298C2218yescomplemented
31#17989297C2214yescomplemented
32#17989296C2218yescomplemented
33#17989295C2214yescomplemented
34#17989295C2214yescomplemented
35#17989294C2214yescomplemented
36#17989291C2218yescomplemented
37#17989291C2218yescomplemented
38#17989289C2214yescomplemented
39#17989286C2218yescomplemented
40#17989283C2214yescomplemented
41#17989280C2218yescomplemented
42#17989279C2214yescomplemented
43#17989279C2214yescomplemented
44#17989278C2214yescomplemented
45#17989278C2214yescomplemented
46#17989277C2214yescomplemented
47#17989274C2218yescomplemented
48#17989271C2214yescomplemented
49#17989270C2218yescomplemented
50#17989267C2218yescomplemented
51#17989266C2218yescomplemented
52#17989264C2218yescomplemented
53#17989264C2218yescomplemented
54#17989261C2218yescomplemented
55#17989260C2218yescomplemented
56#17989252C2214yescomplemented
57Q8×C22⋊D73C2214yescomplemented
58Q8×C22⋊D73C2214yescomplemented
59Q8×C22⋊D73C2214yescomplemented
60#17989248C2214yescomplemented
61#17989248C2214yescomplemented
62#17989248C2214yescomplemented
63#17989245C2214yescomplemented
64#17989241C2214yescomplemented
65#17989240C2214yescomplemented
66#17989237C2214yescomplemented
67#17989236C2218yescomplemented
68#17989236C2214yescomplemented
69#17989235C2218yescomplemented
70#17989232C2218yescomplemented
71#17989230C2214yescomplemented
72#17989229C2218yescomplemented
73#17989226C2218yescomplemented
74#17989225C2218yescomplemented
75#17989225C2214yescomplemented
76#17989216C2214yescomplemented
77#17989215C2212yescomplemented
78#17989214C2218yescomplemented
79#17989212C2214yes—
80#17989212C2218yescomplemented
81#17989211C2218yescomplemented
82#17989209C2214yescomplemented
83#17989206C2214yescomplemented
84#17989201C2218yescomplemented
85#17989198C2214yescomplemented
86#17989195C2214yescomplemented
87#17989186C2214yescomplemented
88#17989186C2218yescomplemented
89#17989183C2218yescomplemented
90#17989183C2218yescomplemented
91#17989182C2214yescomplemented
92#17989181C2218yescomplemented
93#17989179C2218yescomplemented
94#17989177C2214yescomplemented
95#17989174C2214yescomplemented
96#17989171C2218yescomplemented
97#17989170C2218yescomplemented
98#17989167C2214yescomplemented
99#17989165C2212yescomplemented
100#17989165C2214yescomplemented
101#17989164C2214yescomplemented
102#17989161C2212yescomplemented
103#17989161C2214yescomplemented
104#17989161C2214yescomplemented
105#17989160C2214yescomplemented
106#17989145C2214yes—
107#17989142C2214yescomplemented
108#17989141C2214yescomplemented
109#17989124C2214yescomplemented
110#17989116C2214yescomplemented
111#17989100C2212yes—
112#17989100C2212yescomplemented
113#17989100C2214yescomplemented
114#17989099C2212yes—
115#17989098C2214yescomplemented
116#17989098C2212yescomplemented
117#17989097C2212yes—
118#17989097C2212yescomplemented
119#17989096C2214yes—
120#17989096C2214yescomplemented
121#17989095C2214yes—
122#17989094C2212yes—
123#17989094C2214yescomplemented
124#17989093C2218yescomplemented
125#17989093C2214yescomplemented
126#123×D73C2214yescomplemented
127C2×#14556567C2214yes—
128C2×#14556567C2212yescomplemented
129C2×#14556567C2212yescomplemented
130C2×#14556567C2214yescomplemented
131C2×#14556567C2214yescomplemented
132C2×#14556567C2214yescomplemented
133C2×#14556567C2214yescomplemented
134C2×#14556567C2214yescomplemented
135C22⋊Q8×D73C2212yes—
136C22⋊Q8×D73C2212yescomplemented
137C22⋊Q8×D73C2214yescomplemented
138#121×D73C2212yes—
139#121×D73C2212yescomplemented
140#120×D73C2214yes—
141#17989070C2212yescomplemented
142#17989067C2212yescomplemented
143#17989066C2218yescomplemented
144#17989065C2211yescharacteristic, complemented
145#17989059C2218yes—
146C4×D4×D73C2214yes—
147C4×D4×D73C2214yescomplemented
148#117×D73C2212yescomplemented
149C22×C4⋊Dic73C2211yescharacteristic, complemented
150C22×#11924007C2212yescomplemented
151C22×#11924005C2212yes—
152C2×2−1+4×C73C2211yescharacteristic, complemented
153C23×Q8×C73C2211yescharacteristic, complemented
154D4×Q8×C73C2214yescomplemented
155D4×Q8×C73C2214yescomplemented
156#548×C73C2214yescomplemented
157#548×C73C2214yescomplemented
158#536×C73C2212yescomplemented
159#536×C73C2214yescomplemented
160#525×C73C2214yescomplemented
161#525×C73C2212yescomplemented
162#519×C73C2211yescharacteristic, complemented
163C24×D73C2311yescharacteristic
164#14556639—44no—
165C2×#11924029C2312yes—
166C2×#11924029C2314yescomplemented
167C2×#11924028C2312yes—
168C2×#11924028C2314yes—
169C2×#11924028C2314yes—
170C2×#11924027C2314yes—
171C2×#11924027C2312yes—
172C2×#11924027C2318yes—
173#41×D73—48no—
174C2×Q8×D73C2312yes—
175C2×Q8×D73C2314yescomplemented
176C2×D4×D73C2314yes—
177C2×D4×D73C2314yes—
178C2×D4×D73C2312yes—
179C2×D4×D73C2314yes—
180C23×Dic73C2311yescharacteristic
181C23×Dic73C2312yes—
182C22×C4×D73—44no—
183C22×C4×D73C2312yes—
184C22×C4×D73C2312yes—
185C22×C4×D73C2312yes—
186C22×C4×D73C2312yes—
187C22×C4×D73C2312yes—
188C22×C4×D73C2312yes—
189C22×C4×D73C2314yes—
190#14556591C2314yescomplemented
191#14556590C2314yescomplemented
192#14556590C2318yescomplemented
193#14556589C2314yescomplemented
194#14556589C2318yescomplemented
195#14556589C2318yescomplemented
196#14556586C2318yes—
197#14556586C2318yes—
198#14556586C2318yes—
199#14556586C2318yescomplemented
200#14556586C2318yescomplemented
201#14556585C2318yes—
202#14556585C2318yescomplemented
203#14556584C2318yescomplemented
204#14556584C2318yescomplemented
205#14556584C2318yescomplemented
206#14556583C2318yescomplemented
207#14556583C2314yescomplemented
208#14556582C2314yescomplemented
209#14556582C2318yescomplemented
210#14556582C2318yescomplemented
211#14556581C2318yescomplemented
212#14556581C2318yescomplemented
213#14556581C2318yescomplemented
214#14556581C2318yescomplemented
215#14556581C2318yescomplemented
216#14556580C2318yes—
217#14556580C2314yescomplemented
218#14556580C2318yescomplemented
219#14556579C2318yes—
220#14556577C2318yes—
221#14556577C2318yes—
222#14556576C2318yes—
223#14556576C2318yes—
224#14556576C2318yes—
225#14556576C2314yes—
226#14556576C2314yes—
227#14556576C2318yescomplemented
228#14556575C2318yes—
229#14556575C2318yes—
230#14556575C2314yes—
231#14556575C2318yescomplemented
232#14556574C2314yes—
233#14556574C2318yes—
234#14556574C2318yes—
235#14556574C2318yescomplemented
236#14556573C2318yes—
237#14556573C2314yes—
238#14556573C2314yes—
239#14556573C2318yescomplemented
240#14556573C2318yescomplemented
241#14556572C2318yes—
242#14556572C2314yes—
243#14556572C2318yescomplemented
244#14556571C2312yes—
245#14556571C2318yes—
246#14556571C2312yes—
247#14556571C2318yescomplemented
248#14556570C2314yes—
249#14556570C2314yes—
250#14556570C2312yes—
251#14556570C2312yes—
252#14556570C2314yescomplemented
253#14556570C2318yescomplemented
254#14556569C2318yes—
255#14556569C2318yes—
256#14556569C2314yes—
257#14556569C2314yes—
258#14556569C2318yescomplemented
259#14556569C2318yescomplemented
260#14556568C2318yes—
261#14556568C2314yes—
262#14556568C2318yes—
263#14556568C2314yes—
264#14556568C2318yescomplemented
265#14556568C2318yescomplemented
266#14556568C2318yescomplemented
267#14556567C2314yes—
268#14556567C2312yes—
269#14556567C2314yes—
270#14556567C2314yes—
271#14556567C2312yes—
272#14556567C2314yes—
273#14556567C2318yes—
274#14556567C2318yes—
275#14556567C2318yes—
276#14556567C2314yes—
277#14556567C2314yes—
278#14556567C2314yes—
279#14556567C2314yes—
280#14556567C2318yes—
281#14556567C2318yes—
282#14556567C2314yescomplemented
283#14556567C2314yescomplemented
284#14556567C2314yescomplemented
285#14556567C2318yescomplemented
286#14556567C2318yescomplemented
287#14556567C2318yescomplemented
288#14556566C2312yes—
289#14556566C2312yes—
290#14556566C2318yes—
291#14556565C2314yes—
292#14556565C2314yes—
293#14556565C2318yes—
294#14556565C2312yes—
295#14556565C2312yes—
296#14556565C2314yescomplemented
297#14556564C2318yes—
298#14556564C2314yes—
299#14556564C2314yes—
300#14556564C2318yescomplemented
301#14556563C2318yes—
302#14556563C2314yes—
303#14556563C2318yes—
304#14556563C2318yes—
305#14556563C2314yes—
306#14556563C2318yescomplemented
307#14556562C2312yes—
308#14556562C2312yes—
309#14556562C2314yescomplemented
310#14556561C2318yes—
311#14556561C2314yes—
312#14556561C2314yes—
313#14556561C2314yes—
314#14556560C2314yes—
315#14556559C2318yes—
316#14556559C2314yes—
317#14556559C2314yes—
318#14556559C2314yes—
319Q8×Dic73C2314yescomplemented
320Q8×Dic73C2314yescomplemented
321Q8×Dic73C2314yescomplemented
322C4×Dic146C2314yescomplemented
323C4×Dic146C2318yescomplemented
324#14556556C2318yescomplemented
325C4×D292C2318yes—
326C4×D292C2314yes—
327C4×D292C2314yes—
328C4×D292C2314yescomplemented
329D4×Dic73C2318yes—
330D4×Dic73C2318yes—
331D4×Dic73C2314yes—
332D4×Dic73C2314yes—
333D4×Dic73C2314yescomplemented
334#14556553C2314yes—
335#14556553C2318yes—
336#14556553C2314yes—
337C4×C22⋊D73C2318yes—
338C4×C22⋊D73C2318yes—
339C4×C22⋊D73C2318yes—
340C4×C22⋊D73C2314yes—
341C4×C22⋊D73C2314yes—
342C4×C22⋊D73C2314yes—
343C4×C22⋊D73C2314yes—
344C4×C22⋊D73C2318yescomplemented
345#14556551C2318yes—
346#14556551C2318yes—
347#14556551C2318yes—
348#14556551C2314yes—
349#14556551C2314yes—
350#14556551C2314yes—
351#14556551C2314yes—
352#14556551C2318yescomplemented
353#14556550C2312yes—
354#14556550C2314yes—
355#14556550C2314yescomplemented
356#14556549C2318yes—
357#14556549C2312yes—
358#14556549C2312yes—
359#14556549C2314yescomplemented
360#14556548C2318yes—
361#14556548C2314yes—
362#14556548C2318yescomplemented
363#14556547C2318yes—
364#14556547C2314yes—
365#14556547C2318yescomplemented
366C2×C4⋊Dic73C2312yes—
367C2×C4⋊Dic73C2312yes—
368C2×C4⋊Dic73C2314yes—
369C2×C4⋊Dic73C2314yes—
370C2×C4⋊Dic73C2314yescomplemented
371C2×#11924007C2314yes—
372C2×#11924007C2314yes—
373C2×#11924007C2314yes—
374C2×#11924007C2314yes—
375C2×#11924007C2318yes—
376C2×#11924007C2318yescomplemented
377C4⋊C4×D73C2314yes—
378C4⋊C4×D73C2312yes—
379C4⋊C4×D73C2314yes—
380C4⋊C4×D73C2312yes—
381C4⋊C4×D73C2314yescomplemented
382C4⋊C4×D73C2318yescomplemented
383C2×#11924005C2314yes—
384C2×#11924005C2314yes—
385C2×#11924005C2318yes—
386C2×#11924005C2314yes—
387C2×#11924005C2318yes—
388C2×#11924005C2314yes—
389C22⋊C4×D73C2314yes—
390C22⋊C4×D73C2314yes—
391C22⋊C4×D73C2318yes—
392C22⋊C4×D73C2314yes—
393C22⋊C4×D73C2314yes—
394C22⋊C4×D73C2314yes—
395C42×D73C2314yes—
3962−1+4×C73—44no—
397C2×#41×C73C2312yes—
398C2×#41×C73C2314yes—
399C2×#41×C73C2314yescomplemented
400C22×Q8×C73—44no—
401C22×Q8×C73C2311yescharacteristic
402C22×Q8×C73C2311yescharacteristic
403C22×Q8×C73C2312yes—
404C22×Q8×C73C2314yes—
405C22×Q8×C73C2314yes—
406C22×Q8×C73C2314yescomplemented
407C23×C4×C73C2311yescharacteristic
408C23×C4×C73C2312yes—
409C4⋊Q8×C73C2314yescomplemented
410C4⋊Q8×C73C2318yescomplemented
411#124×C73C2318yescomplemented
412#124×C73C2314yescomplemented
413#123×C73C2314yes—
414#123×C73C2318yes—
415C22⋊Q8×C73C2314yes—
416C22⋊Q8×C73C2314yes—
417C22⋊Q8×C73C2312yes—
418C22⋊Q8×C73C2312yes—
419C22⋊Q8×C73C2314yescomplemented
420C22⋊Q8×C73C2314yescomplemented
421C22⋊Q8×C73C2318yescomplemented
422C22⋊Q8×C73C2318yescomplemented
423#121×C73C2314yes—
424#121×C73C2314yes—
425#121×C73C2312yes—
426#121×C73C2312yes—
427#120×C73C2314yes—
428C4×Q8×C73C2314yescomplemented
429C4×Q8×C73C2314yescomplemented
430C4×D4×C73C2318yes—
431C4×D4×C73C2318yes—
432C4×D4×C73C2314yes—
433C4×D4×C73C2314yes—
434#117×C73C2312yes—
435#117×C73C2314yes—
436C23×D73—24no—
437C23×D73—42no—
438C23×D73—42no—
439C23×D73C2412yes—
440C23×D73C2412yes—
441C23×D73C2414yes—
442C23×D73C2411yescharacteristic
443C23×D73C2411yescharacteristic
444#11924029—44no—
445#11924029—48no—
446#11924028—28no—
447#11924028—48no—
448#11924028—48no—
449#11924027—44no—
450#11924027—48no—
451#11924027—416no—
452C2×Dic146C2412yes—
453C2×Dic146C2418yes—
454C2×Dic146C2414yes—
455C2×Dic146C2414yes—
456Q8×D73—44no—
457Q8×D73—48no—
458C2×D292C2414yes—
459C2×D292C2412yes—
460C2×D292C2414yes—
461C2×D292C2414yes—
462C2×D292C2414yes—
463C2×C22⋊D73C2414yes—
464C2×C22⋊D73C2414yes—
465C2×C22⋊D73C2414yes—
466C2×C22⋊D73C2414yes—
467C2×C22⋊D73C2414yes—
468C2×C22⋊D73C2418yes—
469C2×C22⋊D73C2414yes—
470C2×C22⋊D73C2414yes—
471D4×D73—216no—
472D4×D73—44no—
473D4×D73—48no—
474D4×D73—48no—
475C22×Dic73—42no—
476C22×Dic73—44no—
477C22×Dic73C2414yes—
478C22×Dic73C2412yes—
479C22×Dic73C2414yes—
480C22×Dic73C2414yes—
481C22×Dic73C2418yes—
482C22×Dic73C2411yescharacteristic
483C22×Dic73C2412yes—
484C22×Dic73C2411yescharacteristic
485C22×Dic73C2414yes—
486C2×C4×D73—28no—
487C2×C4×D73—44no—
488C2×C4×D73—44no—
489C2×C4×D73—44no—
490C2×C4×D73—44no—
491C2×C4×D73—48no—
492C2×C4×D73—44no—
493C2×C4×D73C2412yes—
494C2×C4×D73C2414yes—
495C2×C4×D73C2412yes—
496C2×C4×D73C2414yes—
497C2×C4×D73C2412yes—
498C2×C4×D73C2412yes—
499C2×C4×D73C2414yes—
500C2×C4×D73C2412yes—
501C2×C4×D73C2414yes—
502C2×C4×D73C2412yes—
503C2×C4×D73C2418yes—
504C2×C4×D73C2418yes—
505C2×C4×D73C2414yes—
506C2×C4×D73C2412yes—
507C2×C4×D73C2412yes—
508C4⋊Dic73C2414yes—
509C4⋊Dic73C2412yes—
510C4⋊Dic73C2412yes—
511C4⋊Dic73C2414yes—
512C4⋊Dic73C2414yes—
513C4⋊Dic73C2414yes—
514C4⋊Dic73C2418yes—
515C4⋊Dic73C2418yes—
516C4⋊Dic73C2418yes—
517C4⋊Dic73C2414yes—
518C4⋊Dic73C2414yes—
519#11924007C2414yes—
520#11924007C2414yes—
521#11924007C2414yes—
522#11924007C2414yes—
523#11924007C2414yes—
524#11924007C2414yes—
525#11924007C2418yes—
526#11924007C2418yes—
527#11924007C2418yes—
528#11924007C2418yes—
529#11924007C2418yes—
530#11924007C2418yes—
531#11924007C2418yes—
532#11924007C2418yes—
533#11924007C2418yes—
534#11924007C2418yes—
535C22⋊Dic73C2414yes—
536C22⋊Dic73C2414yes—
537C22⋊Dic73C2414yes—
538C22⋊Dic73C2414yes—
539C22⋊Dic73C2414yes—
540C22⋊Dic73C2418yes—
541C22⋊Dic73C2418yes—
542#11924005C2414yes—
543#11924005C2418yes—
544#11924005C2414yes—
545#11924005C2414yes—
546#11924005C2414yes—
547#11924005C2414yes—
548#11924005C2414yes—
549#11924005C2414yes—
550#11924005C2414yes—
551#11924005C2414yes—
552#11924005C2414yes—
553#11924005C2418yes—
554#11924005C2418yes—
555#11924005C2418yes—
556#11924005C2418yes—
557#11924005C2418yes—
558#11924005C2418yes—
559#11924005C2418yes—
560C4×Dic73C2414yes—
561C4×Dic73C2414yes—
562C4×Dic73C2414yes—
563C4×Dic73C2418yes—
564C4×Dic73C2418yes—
565C4×Dic73C2418yes—
566C24×C73C2411yescharacteristic
567#41×C73—28no—
568#41×C73—48no—
569#41×C73—48no—
570C2×Q8×C73—24no—
571C2×Q8×C73—24no—
572C2×Q8×C73—44no—
573C2×Q8×C73—48no—
574C2×Q8×C73—48no—
575C2×Q8×C73—48no—
576C2×Q8×C73C2414yes—
577C2×Q8×C73C2412yes—
578C2×Q8×C73C2414yes—
579C2×Q8×C73C2414yes—
580C2×Q8×C73C2418yes—
581C2×D4×C73C2414yes—
582C2×D4×C73C2414yes—
583C2×D4×C73C2414yes—
584C2×D4×C73C2412yes—
585C2×D4×C73C2414yes—
586C22×C4×C73—24no—
587C22×C4×C73—44no—
588C22×C4×C73C2412yes—
589C22×C4×C73C2412yes—
590C22×C4×C73C2412yes—
591C22×C4×C73C2414yes—
592C22×C4×C73C2412yes—
593C22×C4×C73C2411yescharacteristic
594C22×C4×C73C2414yes—
595C22×C4×C73C2414yes—
596C22×C4×C73C2418yes—
597C22×C4×C73C2411yescharacteristic
598C4⋊C4×C73C2412yes—
599C4⋊C4×C73C2412yes—
600C4⋊C4×C73C2414yes—
601C4⋊C4×C73C2414yes—
602C4⋊C4×C73C2414yes—
603C4⋊C4×C73C2414yes—
604C4⋊C4×C73C2418yes—
605C4⋊C4×C73C2418yes—
606C22⋊C4×C73C2414yes—
607C22⋊C4×C73C2414yes—
608C22⋊C4×C73C2414yes—
609C22⋊C4×C73C2418yes—
610C22⋊C4×C73C2414yes—
611C22⋊C4×C73C2414yes—
612C22⋊C4×C73C2418yes—
613C42×C73C2414yes—
614C42×C73C2418yes—
615C23×C73—22no—
616C23×C73—22no—
617C23×C73—22no—
618C23×C73C2514yes—
619C23×C73C2511yescharacteristic
620C23×C73C2511yescharacteristic
621C23×C73C2511yescharacteristic
622C22×D73—24no—
623C22×D73—22no—
624C22×D73—24no—
625C22×D73—24no—
626C22×D73—24no—
627C22×D73—28no—
628C22×D73—41no—
629C22×D73—42no—
630C22×D73—41no—
631C22×D73—41no—
632C22×D73—42no—
633C22×D73—41no—
634C22×D73—44no—
635C22×D73—44no—
636C22×D73—416no—
637C22×D732−1+414yescomplemented
638C22×D73C2512yes—
639C22×D73C2514yes—
640C22×D73C2512yes—
641Q8×C73—28no—
642Q8×C73—28no—
643Q8×C73—24no—
644Q8×C73—48no—
645Q8×C73—44no—
646D4×C73—28no—
647D4×C73—28no—
648D4×C73—28no—
649D4×C73—24no—
650D4×C73—44no—
651C2×C4×C73—22no—
652C2×C4×C73—24no—
653C2×C4×C73—24no—
654C2×C4×C73—24no—
655C2×C4×C73—24no—
656C2×C4×C73—28no—
657C2×C4×C73—44no—
658C2×C4×C73—44no—
659C2×C4×C73—48no—
660C2×C4×C73H(5,𝔽2)14yes—
661C2×C4×C73C2514yes—
662C2×C4×C73C2514yes—
663C2×C4×C73C2514yes—
664C2×C4×C73C2514yes—
665C2×C4×C73C2512yes—
666C2×C4×C73C2514yes—
667C2×C4×C73C2512yes—
668C22⋊D73—28no—
669C22⋊D73—28no—
670C22⋊D73—28no—
671C22⋊D73—28no—
672C22⋊D73—44no—
673C22⋊D73—44no—
674C22⋊D73—44no—
675C22⋊D73—48no—
676C2×Dic73—24no—
677C2×Dic73—28no—
678C2×Dic73—41no—
679C2×Dic73—42no—
680C2×Dic73—41no—
681C2×Dic73—44no—
682C2×Dic73—44no—
683C2×Dic73—44no—
684C2×Dic73—48no—
685C2×Dic73C2514yes—
686C2×Dic73C2514yes—
687C2×Dic73C2512yes—
688C2×Dic73C2518yes—
689C2×Dic73C2514yes—
690C2×Dic73C2512yes—
691D292—28no—
692D292—24no—
693D292—44no—
694D292—44no—
695D292—44no—
696C4×D73—28no—
697C4×D73—24no—
698C4×D73—24no—
699C4×D73—24no—
700C4×D73—24no—
701C4×D73—28no—
702C4×D73—42no—
703C4×D73—42no—
704C4×D73—42no—
705C4×D73—42no—
706C4×D73—44no—
707C4×D73—44no—
708C4×D73—44no—
709C4×D73—48no—
710C4×D73—48no—
711Dic146—24no—
712Dic146—44no—
713Dic146—44no—
714Dic146—48no—
715C22×C73—28no—
716C22×C73—21no—
717C22×C73—21no—
718C22×C73—21no—
719C22×C73—21no—
720C22×C73—21no—
721C22×C73—21no—
722C22×C73—24no—
723C22×C73—24no—
724C22×C73—24no—
725C22×C73C2×H(5,𝔽2)12yes—
726C22×C73C2×2−1+412yes—
727C22×C73#58512yes—
728C22×C73C2611yescharacteristic
729C2×D73—22no—
730C2×D73—22no—
731C2×D73—22no—
732C2×D73—24no—
733C2×D73—24no—
734C2×D73—22no—
735C2×D73—24no—
736C2×D73—22no—
737C2×D73—44no—
738C2×D73—48no—
739C2×D73—48no—
740C2×D73—44no—
741C2×D73—88no—
742C2×D73C2×2−1+414yes—
743C4×C73—24no—
744C4×C73—24no—
745C4×C73—22no—
746C4×C73—24no—
747C4×C73—24no—
748C4×C73—24no—
749C4×C73C2×H(5,𝔽2)14yes—
750Dic73—24no—
751Dic73—22no—
752Dic73—22no—
753Dic73—24no—
754Dic73—24no—
755Dic73—28no—
756#62819—731nomaximal, Sylow
757C2×C73—22no—
758C2×C73—22no—
759C2×C73—22no—
760C2×C73—44no—
761C2×C73C22×H(5,𝔽2)11yescharacteristic
762C2×C73C22×2−1+411yescharacteristic
763C2×C73C2×#58511yescharacteristic
764D73—24no—
765D73—42no—
766D73—44no—
767#3541—734no—
768#3541—734no—
769#3538—734no—
770#3536—734no—
771#3535—738no—
772#3520—734no—
773#3520—734no—
774#3505—734no—
775#3501—734no—
776#3495—732no—
777#3495—732no—
778#3492—734no—
779#3492—732no—
780#3490—734no—
781#3489—732no—
782#3489—732no—
783#3486—731no—
784#3486D7311yescharacteristic, complemented
785C2×#525—732no—
786C22×C22⋊Q8—731no—
787C73#6281911yescharacteristic, complemented, Sylow
788C2×2−1+4—731no—
789C2×2−1+4C2×D7311yescharacteristic, complemented
790C22×#41—732no—
791C23×Q8C2×D7311yescharacteristic, complemented
792C24×C4—731no—
793#563—738no—
794#563—738no—
795#562—738no—
796#562—738no—
797#556—734no—
798#556—734no—
799#554—738no—
800#554—738no—
801#554—734no—
802#554—734no—
803#554—738no—
804#554—734no—
805#554—734no—
806#554—738no—
807#553—738no—
808#553—734no—
809#553—734no—
810#553—738no—
811#552—738no—
812#552—734no—
813#552—734no—
814#552—734no—
815#552—734no—
816#552—734no—
817#552—734no—
818#552—738no—
819#551—738no—
820#551—738no—
821#551—738no—
822#551—738no—
823#551—738no—
824#551—738no—
825D4×Q8—734no—
826D4×Q8—734no—
827D4×Q8—734no—
828D4×Q8—734no—
829D4×Q8C2×D7314yescomplemented
830D4×Q8C2×D7314yescomplemented
831#548—734no—
832#548—734no—
833#548—734no—
834#548—734no—
835#548C2×D7314yescomplemented
836#548C2×D7314yescomplemented
837#547—738no—
838#547—734no—
839#547—734no—
840#547—738no—
841#547—734no—
842#547—734no—
843#546—738no—
844#546—734no—
845#546—734no—
846#546—738no—
847#546—738no—
848#546—738no—
849#544—738no—
850#544—734no—
851#544—732no—
852#543—734no—
853#543—738no—
854#542—738no—
855#542—738no—
856#542—734no—
857#542—734no—
858#541—734no—
859#541—734no—
860#539—738no—
861#539—734no—
862#539—738no—
863#539—738no—
864#539—738no—
865#539—734no—
866#539—738no—
867#538—738no—
868#538—734no—
869#538—734no—
870#538—738no—
871#537—732no—
872#537—734no—
873#537—734no—
874#537—734no—
875#536—732no—
876#536—734no—
877#536—734no—
878#536—734no—
879#536C2×D7312yescomplemented
880#536C2×D7314yescomplemented
881#534—734no—
882#533—734no—
883#533—734no—
884#529—734no—
885#529—734no—
886#525—732no—
887#525—734no—
888#525—732no—
889#525—734no—
890#525—734no—
891#525—732no—
892#525—732no—
893#525—734no—
894#525—732no—
895#525—732no—
896#525—734no—
897#525—738no—
898#525—734no—
899#525—734no—
900#525—732no—
901#525C2×D7312yescomplemented
902#525C2×D7314yescomplemented
903C2×#123—734no—
904C2×C22⋊Q8—732no—
905C2×C22⋊Q8—732no—
906C2×C22⋊Q8—734no—
907C2×C22⋊Q8—734no—
908C2×C22⋊Q8—734no—
909C2×C22⋊Q8—734no—
910C2×C22⋊Q8—734no—
911C2×C22⋊Q8—734no—
912C2×C22⋊Q8—732no—
913C2×C22⋊Q8—732no—
914C2×C22⋊Q8—734no—
915C2×#121—732no—
916C2×#121—732no—
917C2×#120—734no—
918#520—732no—
919#520—738no—
920#520—732no—
921#519—731no—
922#519C2×D7311yescharacteristic, complemented
923#518—738no—
924C2×C4×D4—734no—
925C2×C4×D4—734no—
926C2×#117—732no—
927C22×C4⋊C4—732no—
928C22×C4⋊C4—731no—
929C22×C22⋊C4—732no—
930C25—731no—
9312−1+4—44no—
9322−1+4—2924no—
933C2×#41—2928no—
934C2×#41—732no—
935C2×#41—734no—
936C2×#41—738no—
937C2×#41—734no—
938C2×#41—732no—
939C2×#41—734no—
940C2×#41—734no—
941C2×#41—732no—
942C2×#41C22×D7312yes—
943C2×#41C22×D7314yes—
944C2×#41C22×D7314yescomplemented
945C22×Q8—44no—
946C22×Q8—732no—
947C22×Q8—734no—
948C22×Q8C22×D7311yescharacteristic
949C22×Q8C22×D7311yescharacteristic
950C22×Q8C22×D7312yes—
951C22×Q8C22×D7314yes—
952C22×Q8C22×D7314yes—
953C22×Q8C22×D7314yescomplemented
954C22×D4—734no—
955C22×D4—734no—
956C22×D4—732no—
957C22×D4—734no—
958C23×C4—2924no—
959C23×C4—732no—
960C23×C4—731no—
961C23×C4—732no—
962C23×C4—732no—
963C23×C4—734no—
964C23×C4—732no—
965C23×C4—732no—
966C23×C4—732no—
967C23×C4—732no—
968C23×C4C22×D7311yescharacteristic
969C23×C4C22×D7312yes—
970C4⋊Q8—734no—
971C4⋊Q8—738no—
972C4⋊Q8—738no—
973C4⋊Q8—734no—
974C4⋊Q8—738no—
975C4⋊Q8—734no—
976C4⋊Q8C22×D7314yescomplemented
977C4⋊Q8C22×D7318yescomplemented
978#126—738no—
979#126—738no—
980#126—738no—
981#126—738no—
982#126—738no—
983#126—738no—
984#126—738no—
985#126—738no—
986#126—738no—
987#126—738no—
988#125—734no—
989#125—738no—
990#125—738no—
991#125—738no—
992#125—738no—
993#125—738no—
994#125—738no—
995#125—738no—
996#125—734no—
997#125—738no—
998#124—734no—
999#124—738no—
1000#124—738no—
1001#124—738no—
1002#124—738no—
1003#124—738no—
1004#124C22×D7314yescomplemented
1005#124C22×D7318yescomplemented
1006#123—734no—
1007#123—738no—
1008#123—738no—
1009#123—734no—
1010#123—738no—
1011#123—738no—
1012#123—738no—
1013#123—734no—
1014#123—734no—
1015#123—738no—
1016#123—738no—
1017#123—738no—
1018#123—738no—
1019#123—734no—
1020#123—734no—
1021#123—734no—
1022#123—738no—
1023#123—738no—
1024#123—738no—
1025#123—738no—
1026#123—738no—
1027#123—738no—
1028#123C22×D7314yes—
1029#123C22×D7318yes—
1030C22⋊Q8—734no—
1031C22⋊Q8—734no—
1032C22⋊Q8—732no—
1033C22⋊Q8—734no—
1034C22⋊Q8—734no—
1035C22⋊Q8—738no—
1036C22⋊Q8—738no—
1037C22⋊Q8—734no—
1038C22⋊Q8—734no—
1039C22⋊Q8—734no—
1040C22⋊Q8—734no—
1041C22⋊Q8—738no—
1042C22⋊Q8—738no—
1043C22⋊Q8—732no—
1044C22⋊Q8—734no—
1045C22⋊Q8—734no—
1046C22⋊Q8—738no—
1047C22⋊Q8—738no—
1048C22⋊Q8—734no—
1049C22⋊Q8—738no—
1050C22⋊Q8—738no—
1051C22⋊Q8—732no—
1052C22⋊Q8—732no—
1053C22⋊Q8—734no—
1054C22⋊Q8—734no—
1055C22⋊Q8—734no—
1056C22⋊Q8—738no—
1057C22⋊Q8—732no—
1058C22⋊Q8—732no—
1059C22⋊Q8—734no—
1060C22⋊Q8—734no—
1061C22⋊Q8—738no—
1062C22⋊Q8—738no—
1063C22⋊Q8—738no—
1064C22⋊Q8—738no—
1065C22⋊Q8—738no—
1066C22⋊Q8—738no—
1067C22⋊Q8—734no—
1068C22⋊Q8—734no—
1069C22⋊Q8—738no—
1070C22⋊Q8—738no—
1071C22⋊Q8—738no—
1072C22⋊Q8—738no—
1073C22⋊Q8—738no—
1074C22⋊Q8C22×D7312yes—
1075C22⋊Q8C22×D7312yes—
1076C22⋊Q8C22×D7314yes—
1077C22⋊Q8C22×D7314yes—
1078C22⋊Q8C22×D7314yescomplemented
1079C22⋊Q8C22×D7314yescomplemented
1080C22⋊Q8C22×D7318yescomplemented
1081C22⋊Q8C22×D7318yescomplemented
1082#121—732no—
1083#121—734no—
1084#121—732no—
1085#121—734no—
1086#121—738no—
1087#121—734no—
1088#121—738no—
1089#121—738no—
1090#121—738no—
1091#121—732no—
1092#121—732no—
1093#121—734no—
1094#121—734no—
1095#121—734no—
1096#121—738no—
1097#121—732no—
1098#121—732no—
1099#121—738no—
1100#121—734no—
1101#121—734no—
1102#121—738no—
1103#121—738no—
1104#121C22×D7312yes—
1105#121C22×D7312yes—
1106#121C22×D7314yes—
1107#121C22×D7314yes—
1108#120—734no—
1109#120—734no—
1110#120—734no—
1111#120—734no—
1112#120—738no—
1113#120—734no—
1114#120—734no—
1115#120—734no—
1116#120—738no—
1117#120C22×D7314yes—
1118C4×Q8—734no—
1119C4×Q8—734no—
1120C4×Q8—734no—
1121C4×Q8—738no—
1122C4×Q8—734no—
1123C4×Q8—738no—
1124C4×Q8C22×D7314yescomplemented
1125C4×Q8C22×D7314yescomplemented
1126C4×D4—734no—
1127C4×D4—734no—
1128C4×D4—738no—
1129C4×D4—738no—
1130C4×D4—734no—
1131C4×D4—734no—
1132C4×D4—734no—
1133C4×D4—734no—
1134C4×D4—734no—
1135C4×D4—738no—
1136C4×D4—738no—
1137C4×D4—738no—
1138C4×D4—738no—
1139C4×D4—734no—
1140C4×D4—734no—
1141C4×D4—738no—
1142C4×D4—734no—
1143C4×D4—734no—
1144C4×D4—734no—
1145C4×D4—734no—
1146C4×D4—738no—
1147C4×D4—738no—
1148C4×D4—738no—
1149C4×D4—738no—
1150C4×D4—734no—
1151C4×D4—734no—
1152C4×D4—738no—
1153C4×D4—734no—
1154C4×D4C22×D7314yes—
1155C4×D4C22×D7314yes—
1156C4×D4C22×D7318yes—
1157C4×D4C22×D7318yes—
1158#117—732no—
1159#117—734no—
1160#117—734no—
1161#117—732no—
1162#117—732no—
1163#117—738no—
1164#117—734no—
1165#117—734no—
1166#117—738no—
1167#117—738no—
1168#117—734no—
1169#117—738no—
1170#117—738no—
1171#117C22×D7312yes—
1172#117C22×D7314yes—
1173C2×C4⋊C4—732no—
1174C2×C4⋊C4—734no—
1175C2×C4⋊C4—734no—
1176C2×C4⋊C4—732no—
1177C2×C4⋊C4—734no—
1178C2×C4⋊C4—734no—
1179C2×C4⋊C4—734no—
1180C2×C4⋊C4—738no—
1181C2×C4⋊C4—734no—
1182C2×C4⋊C4—734no—
1183C2×C4⋊C4—738no—
1184C2×C4⋊C4—732no—
1185C2×C4⋊C4—732no—
1186C2×C4⋊C4—734no—
1187C2×C4⋊C4—734no—
1188C2×C4⋊C4—734no—
1189C2×C4⋊C4—738no—
1190C2×C22⋊C4—734no—
1191C2×C22⋊C4—734no—
1192C2×C22⋊C4—734no—
1193C2×C22⋊C4—734no—
1194C2×C22⋊C4—738no—
1195C2×C22⋊C4—738no—
1196C2×C22⋊C4—734no—
1197C2×C22⋊C4—734no—
1198C2×C22⋊C4—734no—
1199C2×C22⋊C4—734no—
1200C2×C22⋊C4—734no—
1201C2×C22⋊C4—738no—
1202C2×C42—734no—
1203C24—2922no—
1204C24—2922no—
1205C24—731no—
1206C24—734no—
1207C24—731no—
1208C24—732no—
1209C24—732no—
1210C24—1464no—
1211C24C23×D7311yescharacteristic
1212#41—28no—
1213#41—48no—
1214#41—48no—
1215#41—2928no—
1216#41—2928no—
1217#41—2924no—
1218#41—2928no—
1219#41—29216no—
1220#41—2924no—
1221#41—2928no—
1222#41—1468no—
1223C2×Q8—24no—
1224C2×Q8—24no—
1225C2×Q8—44no—
1226C2×Q8—48no—
1227C2×Q8—48no—
1228C2×Q8—48no—
1229C2×Q8—2924no—
1230C2×Q8—2928no—
1231C2×Q8—738no—
1232C2×Q8—734no—
1233C2×Q8—734no—
1234C2×Q8—732no—
1235C2×Q8C23×D7312yes—
1236C2×Q8C23×D7314yes—
1237C2×Q8C23×D7314yes—
1238C2×Q8C23×D7318yes—
1239C2×Q8C23×D7314yes—
1240C2×D4—2928no—
1241C2×D4—2928no—
1242C2×D4—2924no—
1243C2×D4—738no—
1244C2×D4—734no—
1245C2×D4—734no—
1246C2×D4—734no—
1247C2×D4—734no—
1248C2×D4—734no—
1249C2×D4—734no—
1250C2×D4—734no—
1251C2×D4—734no—
1252C2×D4—734no—
1253C2×D4—734no—
1254C2×D4—734no—
1255C2×D4—732no—
1256C2×D4—14616no—
1257C2×D4C23×D7314yes—
1258C2×D4C23×D7314yes—
1259C2×D4C23×D7312yes—
1260C2×D4C23×D7314yes—
1261C2×D4C23×D7314yes—
1262C22×C4—24no—
1263C22×C4—44no—
1264C22×C4—2924no—
1265C22×C4—2924no—
1266C22×C4—2924no—
1267C22×C4—2924no—
1268C22×C4—2924no—
1269C22×C4—2928no—
1270C22×C4—2922no—
1271C22×C4—2924no—
1272C22×C4—734no—
1273C22×C4—734no—
1274C22×C4—738no—
1275C22×C4—731no—
1276C22×C4—732no—
1277C22×C4—731no—
1278C22×C4—734no—
1279C22×C4—734no—
1280C22×C4—732no—
1281C22×C4—734no—
1282C22×C4—732no—
1283C22×C4—738no—
1284C22×C4—738no—
1285C22×C4—734no—
1286C22×C4—732no—
1287C22×C4—732no—
1288C22×C4—734no—
1289C22×C4—732no—
1290C22×C4—732no—
1291C22×C4—734no—
1292C22×C4—732no—
1293C22×C4—734no—
1294C22×C4—732no—
1295C22×C4—732no—
1296C22×C4—1468no—
1297C22×C4C23×D7312yes—
1298C22×C4C23×D7312yes—
1299C22×C4C23×D7312yes—
1300C22×C4C23×D7312yes—
1301C22×C4C23×D7311yescharacteristic
1302C22×C4C23×D7314yes—
1303C22×C4C23×D7314yes—
1304C22×C4C23×D7314yes—
1305C22×C4C23×D7318yes—
1306C22×C4C23×D7311yescharacteristic
1307C4⋊C4—738no—
1308C4⋊C4—738no—
1309C4⋊C4—734no—
1310C4⋊C4—738no—
1311C4⋊C4—738no—
1312C4⋊C4—738no—
1313C4⋊C4—734no—
1314C4⋊C4—734no—
1315C4⋊C4—734no—
1316C4⋊C4—734no—
1317C4⋊C4—734no—
1318C4⋊C4—738no—
1319C4⋊C4—738no—
1320C4⋊C4—738no—
1321C4⋊C4—738no—
1322C4⋊C4—738no—
1323C4⋊C4—734no—
1324C4⋊C4—734no—
1325C4⋊C4—732no—
1326C4⋊C4—734no—
1327C4⋊C4—738no—
1328C4⋊C4—732no—
1329C4⋊C4—734no—
1330C4⋊C4—738no—
1331C4⋊C4—738no—
1332C4⋊C4—734no—
1333C4⋊C4—734no—
1334C4⋊C4C23×D7312yes—
1335C4⋊C4C23×D7312yes—
1336C4⋊C4C23×D7314yes—
1337C4⋊C4C23×D7314yes—
1338C4⋊C4C23×D7318yes—
1339C4⋊C4C23×D7318yes—
1340C4⋊C4C23×D7314yes—
1341C4⋊C4C23×D7314yes—
1342C22⋊C4—734no—
1343C22⋊C4—734no—
1344C22⋊C4—734no—
1345C22⋊C4—734no—
1346C22⋊C4—734no—
1347C22⋊C4—738no—
1348C22⋊C4—738no—
1349C22⋊C4—738no—
1350C22⋊C4—738no—
1351C22⋊C4—734no—
1352C22⋊C4—734no—
1353C22⋊C4—738no—
1354C22⋊C4—738no—
1355C22⋊C4—734no—
1356C22⋊C4—734no—
1357C22⋊C4—734no—
1358C22⋊C4—734no—
1359C22⋊C4—734no—
1360C22⋊C4—734no—
1361C22⋊C4—738no—
1362C22⋊C4—738no—
1363C22⋊C4—734no—
1364C22⋊C4—734no—
1365C22⋊C4—738no—
1366C22⋊C4—738no—
1367C22⋊C4C23×D7314yes—
1368C22⋊C4C23×D7314yes—
1369C22⋊C4C23×D7314yes—
1370C22⋊C4C23×D7318yes—
1371C22⋊C4C23×D7314yes—
1372C22⋊C4C23×D7314yes—
1373C22⋊C4C23×D7318yes—
1374C42—734no—
1375C42—734no—
1376C42—734no—
1377C42—738no—
1378C42—738no—
1379C42—738no—
1380C42C23×D7314yes—
1381C42C23×D7318yes—
1382C23—22no—
1383C23—22no—
1384C23—22no—
1385C23—29216no—
1386C23—2921no—
1387C23—2922no—
1388C23—2921no—
1389C23—2921no—
1390C23—2922no—
1391C23—2921no—
1392C23—2924no—
1393C23—2924no—
1394C23—734no—
1395C23—732no—
1396C23—732no—
1397C23—734no—
1398C23—1464no—
1399C23—1464no—
1400C23—1468no—
1401C23—1464no—
1402C23—1462no—
1403C23—1464no—
1404C23C24×D7314yes—
1405C23C24×D7311yescharacteristic
1406C23C24×D7311yescharacteristic
1407C23C24×D7311yescharacteristic
1408Q8—28no—
1409Q8—28no—
1410Q8—24no—
1411Q8—48no—
1412Q8—44no—
1413Q8—2924no—
1414Q8—2924no—
1415Q8—2928no—
1416Q8—1464no—
1417D4—28no—
1418D4—28no—
1419D4—28no—
1420D4—24no—
1421D4—44no—
1422D4—2924no—
1423D4—2924no—
1424D4—2924no—
1425D4—2924no—
1426D4—2924no—
1427D4—2924no—
1428D4—2928no—
1429D4—1468no—
1430D4—1468no—
1431D4—1468no—
1432D4—1468no—
1433D4—1468no—
1434D4—1464no—
1435C2×C4—22no—
1436C2×C4—24no—
1437C2×C4—24no—
1438C2×C4—24no—
1439C2×C4—24no—
1440C2×C4—28no—
1441C2×C4—44no—
1442C2×C4—44no—
1443C2×C4—48no—
1444C2×C4—2922no—
1445C2×C4—2922no—
1446C2×C4—2922no—
1447C2×C4—2922no—
1448C2×C4—2924no—
1449C2×C4—2924no—
1450C2×C4—2924no—
1451C2×C4—2928no—
1452C2×C4—2928no—
1453C2×C4—2921no—
1454C2×C4—2922no—
1455C2×C4—2921no—
1456C2×C4—2924no—
1457C2×C4—2924no—
1458C2×C4—2924no—
1459C2×C4—2928no—
1460C2×C4—734no—
1461C2×C4—734no—
1462C2×C4—732no—
1463C2×C4—738no—
1464C2×C4—734no—
1465C2×C4—732no—
1466C2×C4—1468no—
1467C2×C4—1464no—
1468C2×C4—1468no—
1469C2×C4—1464no—
1470C2×C4—1464no—
1471C2×C4—1464no—
1472C2×C4—1464no—
1473C2×C4—1468no—
1474C2×C4#1455663614yes—
1475C2×C4C24×D7314yes—
1476C2×C4C24×D7314yes—
1477C2×C4C24×D7314yes—
1478C2×C4C24×D7314yes—
1479C2×C4C24×D7314yes—
1480C2×C4C24×D7312yes—
1481C2×C4C24×D7312yes—
1482C22—28no—
1483C22—21no—
1484C22—21no—
1485C22—21no—
1486C22—21no—
1487C22—21no—
1488C22—21no—
1489C22—24no—
1490C22—24no—
1491C22—24no—
1492C22—2924no—
1493C22—2928no—
1494C22—2928no—
1495C22—2924no—
1496C22—5848no—
1497C22—734no—
1498C22—1464no—
1499C22—1462no—
1500C22—1464no—
1501C22—1462no—
1502C22—1464no—
1503C22—1462no—
1504C22—1462no—
1505C22—1462no—
1506C22C2×#1455663612yes—
1507C222−1+4×D7312yes—
1508C22#1798942412yes—
1509C22C25×D7311yescharacteristic
1510C4—22no—
1511C4—24no—
1512C4—24no—
1513C4—24no—
1514C4—24no—
1515C4—24no—
1516C4—1462no—
1517C4—1462no—
1518C4—1464no—
1519C4—1464no—
1520C4—1468no—
1521C4—1464no—
1522C4C2×#1455663614yes—
1523C2—22no—
1524C2—22no—
1525C2—22no—
1526C2—44no—
1527C2—2922no—
1528C2—2924no—
1529C2—1464no—
1530C2C22×#1455663611yescharacteristic
1531C2C2×2−1+4×D7311yescharacteristic
1532C2C2×#1798942411yescharacteristic
subgroupG/H
center, FrattiniC22C25×D73
commutator, socle, cosocleC22×C73C26
FittingC73×#3486C2
hypercenter#3486D73
hypocenterC73#62819
LCSG ▷ C22×C73 ▷ C73
UCSC1 ◁ C22 ◁ #3486

Complements

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

NH ≅ G/Ntype
1. #22624229C2semidirect
2. #22624210C2semidirect
3. #22624172C2semidirect
4. #22624147C2semidirect
5. #22624130C2semidirect
6. #22623981C2semidirect
7. #22623973C2semidirect
8. #22623767C2semidirect
9. #22623726C2semidirect
10. #22623680C2semidirect
11. #22623673C2semidirect
12. #22623637C2semidirect
13. #22623632C2semidirect
14. #22623614C2semidirect
15. #22623609C2semidirect
16. #22623604C2semidirect
17. #22623582C2semidirect
18. #525×D73C2semidirect
19. C22×#14556567C2semidirect
20. C73×#3486C2semidirect
21. C2×#14556639C22semidirect
22. C2×#41×D73C22semidirect
24. #17989338C22semidirect
25. #17989336C22semidirect
26. #17989333C22semidirect
27. #17989331C22semidirect
28. #17989310C22semidirect
29. #17989308C22semidirect
30. #17989298C22semidirect
31. #17989297C22semidirect
32. #17989296C22semidirect
33. #17989295C22semidirect
34. #17989295C22semidirect
35. #17989294C22semidirect
36. #17989291C22semidirect
37. #17989291C22semidirect
38. #17989289C22semidirect
39. #17989286C22semidirect
40. #17989283C22semidirect
41. #17989280C22semidirect
42. #17989279C22semidirect
43. #17989279C22semidirect
44. #17989278C22semidirect
45. #17989278C22semidirect
46. #17989277C22semidirect
47. #17989274C22semidirect
48. #17989271C22semidirect
49. #17989270C22semidirect
50. #17989267C22semidirect
51. #17989266C22semidirect
52. #17989264C22semidirect
53. #17989264C22semidirect
54. #17989261C22semidirect
55. #17989260C22semidirect
56. #17989252C22semidirect
57. Q8×C22⋊D73C22semidirect
58. Q8×C22⋊D73C22semidirect
59. Q8×C22⋊D73C22semidirect
60. #17989248C22semidirect
61. #17989248C22semidirect
62. #17989248C22semidirect
63. #17989245C22semidirect
64. #17989241C22semidirect
65. #17989240C22semidirect
66. #17989237C22semidirect
67. #17989236C22semidirect
68. #17989236C22semidirect
69. #17989235C22semidirect
70. #17989232C22semidirect
71. #17989230C22semidirect
72. #17989229C22semidirect
73. #17989226C22semidirect
74. #17989225C22semidirect
75. #17989225C22semidirect
76. #17989216C22semidirect
77. #17989215C22semidirect
78. #17989214C22semidirect
80. #17989212C22semidirect
81. #17989211C22semidirect
82. #17989209C22semidirect
83. #17989206C22semidirect
84. #17989201C22semidirect
85. #17989198C22semidirect
86. #17989195C22semidirect
87. #17989186C22semidirect
88. #17989186C22semidirect
89. #17989183C22semidirect
90. #17989183C22semidirect
91. #17989182C22semidirect
92. #17989181C22semidirect
93. #17989179C22semidirect
94. #17989177C22semidirect
95. #17989174C22semidirect
96. #17989171C22semidirect
97. #17989170C22semidirect
98. #17989167C22semidirect
99. #17989165C22semidirect
100. #17989165C22semidirect
101. #17989164C22semidirect
102. #17989161C22semidirect
103. #17989161C22semidirect
104. #17989161C22semidirect
105. #17989160C22semidirect
107. #17989142C22semidirect
108. #17989141C22semidirect
109. #17989124C22semidirect
110. #17989116C22semidirect
112. #17989100C22semidirect
113. #17989100C22semidirect
115. #17989098C22semidirect
116. #17989098C22semidirect
118. #17989097C22semidirect
120. #17989096C22semidirect
123. #17989094C22semidirect
124. #17989093C22semidirect
125. #17989093C22semidirect
126. #123×D73C22semidirect
128. C2×#14556567C22semidirect
129. C2×#14556567C22semidirect
130. C2×#14556567C22semidirect
131. C2×#14556567C22semidirect
132. C2×#14556567C22semidirect
133. C2×#14556567C22semidirect
134. C2×#14556567C22semidirect
136. C22⋊Q8×D73C22semidirect
137. C22⋊Q8×D73C22semidirect
139. #121×D73C22semidirect
141. #17989070C22semidirect
142. #17989067C22semidirect
143. #17989066C22semidirect
144. #17989065C22semidirect
147. C4×D4×D73C22semidirect
148. #117×D73C22semidirect
149. C22×C4⋊Dic73C22semidirect
150. C22×#11924007C22semidirect
152. C2×2−1+4×C73C22semidirect
153. C23×Q8×C73C22semidirect
154. D4×Q8×C73C22semidirect
155. D4×Q8×C73C22semidirect
156. #548×C73C22semidirect
157. #548×C73C22semidirect
158. #536×C73C22semidirect
159. #536×C73C22semidirect
160. #525×C73C22semidirect
161. #525×C73C22semidirect
162. #519×C73C22semidirect
166. C2×#11924029C23semidirect
175. C2×Q8×D73C23semidirect
190. #14556591C23semidirect
191. #14556590C23semidirect
192. #14556590C23semidirect
193. #14556589C23semidirect
194. #14556589C23semidirect
195. #14556589C23semidirect
199. #14556586C23semidirect
200. #14556586C23semidirect
202. #14556585C23semidirect
203. #14556584C23semidirect
204. #14556584C23semidirect
205. #14556584C23semidirect
206. #14556583C23semidirect
207. #14556583C23semidirect
208. #14556582C23semidirect
209. #14556582C23semidirect
210. #14556582C23semidirect
211. #14556581C23semidirect
212. #14556581C23semidirect
213. #14556581C23semidirect
214. #14556581C23semidirect
215. #14556581C23semidirect
217. #14556580C23semidirect
218. #14556580C23semidirect
227. #14556576C23semidirect
231. #14556575C23semidirect
235. #14556574C23semidirect
239. #14556573C23semidirect
240. #14556573C23semidirect
243. #14556572C23semidirect
247. #14556571C23semidirect
252. #14556570C23semidirect
253. #14556570C23semidirect
258. #14556569C23semidirect
259. #14556569C23semidirect
264. #14556568C23semidirect
265. #14556568C23semidirect
266. #14556568C23semidirect
282. #14556567C23semidirect
283. #14556567C23semidirect
284. #14556567C23semidirect
285. #14556567C23semidirect
286. #14556567C23semidirect
287. #14556567C23semidirect
296. #14556565C23semidirect
300. #14556564C23semidirect
306. #14556563C23semidirect
309. #14556562C23semidirect
319. Q8×Dic73C23semidirect
320. Q8×Dic73C23semidirect
321. Q8×Dic73C23semidirect
322. C4×Dic146C23semidirect
323. C4×Dic146C23semidirect
324. #14556556C23semidirect
328. C4×D292C23semidirect
333. D4×Dic73C23semidirect
344. C4×C22⋊D73C23semidirect
352. #14556551C23semidirect
355. #14556550C23semidirect
359. #14556549C23semidirect
362. #14556548C23semidirect
365. #14556547C23semidirect
370. C2×C4⋊Dic73C23semidirect
376. C2×#11924007C23semidirect
381. C4⋊C4×D73C23semidirect
382. C4⋊C4×D73C23semidirect
399. C2×#41×C73C23semidirect
406. C22×Q8×C73C23semidirect
409. C4⋊Q8×C73C23semidirect
410. C4⋊Q8×C73C23semidirect
411. #124×C73C23semidirect
412. #124×C73C23semidirect
419. C22⋊Q8×C73C23semidirect
420. C22⋊Q8×C73C23semidirect
421. C22⋊Q8×C73C23semidirect
422. C22⋊Q8×C73C23semidirect
428. C4×Q8×C73C23semidirect
429. C4×Q8×C73C23semidirect
637. C22×D732−1+4semidirect
784. #3486D73semidirect
787. C73#62819semidirect
789. C2×2−1+4C2×D73semidirect
791. C23×Q8C2×D73semidirect
829. D4×Q8C2×D73semidirect
830. D4×Q8C2×D73semidirect
835. #548C2×D73semidirect
836. #548C2×D73semidirect
879. #536C2×D73semidirect
880. #536C2×D73semidirect
901. #525C2×D73semidirect
902. #525C2×D73semidirect
922. #519C2×D73semidirect
944. C2×#41C22×D73semidirect
953. C22×Q8C22×D73semidirect
976. C4⋊Q8C22×D73semidirect
977. C4⋊Q8C22×D73semidirect
1004. #124C22×D73semidirect
1005. #124C22×D73semidirect
1078. C22⋊Q8C22×D73semidirect
1079. C22⋊Q8C22×D73semidirect
1080. C22⋊Q8C22×D73semidirect
1081. C22⋊Q8C22×D73semidirect
1124. C4×Q8C22×D73semidirect
1125. C4×Q8C22×D73semidirect

Maximal subgroups

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

subgroupindex
#226242292
#226242102
#226241722
#226241472
#226241302
#226239812
#226239732
#226237672
#226237262
#226236802
#226236732
#226236372
#226236322
#226236142
#226236092
#226236042
#226235822
#525×D732
C22×#145565672
C73×#34862
#6281973