Finite Group Databasebeta

← #11910466

Subgroups — #11910466

Order 1152.

1970 conjugacy classes of subgroups.

The subgroup lattice has 1136 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10596155C211yesmaximal, characteristic, complemented
2C3×#5680C211yesmaximal, characteristic, complemented
3C3×#5672C211yesmaximal, characteristic, complemented
4#10595374C212yesmaximal, complemented
5#10595345C212yesmaximal, complemented
6#10595263C212yesmaximal, complemented
7#10595116C212yesmaximal, complemented
8#10594251C212yesmaximal, complemented
9#10594216C212yesmaximal, complemented
10#10594107C212yesmaximal, complemented
11#10594106C212yesmaximal, complemented
12#10594044C212yesmaximal, complemented
13#10594043C212yesmaximal, complemented
14#10594036C212yesmaximal, complemented
15#10594029C212yesmaximal, complemented
16#10593976C211yesmaximal, characteristic, complemented
17#10593874C211yesmaximal, characteristic, complemented
18#10593868C211yesmaximal, characteristic, complemented
19#10593857C211yesmaximal, characteristic, complemented
20#87116—31nomaximal
21#86132—31nomaximal
22C32×#124C2211yescharacteristic
23#64155C2212yes—
24#64148C2212yes—
25#64095C2212yes—
26#64093C2212yes—
27#64092C2212yes—
28#64087C2212yes—
29#64084C2211yescharacteristic
30#64079C2211yescharacteristic
31C3×#946C2211yescharacteristic
32C3×Q8×Dic3C2211yescharacteristic
33C3×#944C2212yes—
34C3×#938C2211yescharacteristic
35C3×#935C2212yes—
36C3×D4×Dic3C2211yescharacteristic
37C3×#883C2212yes—
38C3×#67⋊C4C2212yes—
39C3×#879C2212yes—
40C3×#879C2212yes—
41C3×#879C2212yes—
42C3×#878C2212yes—
43C3×#878C2212yes—
44C3×#877C2212yes—
45C3×C42×D3C2211yescharacteristic
46C3×#870C2211yescharacteristic
47C3×#870C2211yescharacteristic
48C3×#870C2211yescharacteristic
49#63982C2212yes—
50#63982C2212yes—
51#63978C2212yes—
52#63975C2212yes—
53#63966C2212yes—
54#63964C2212yes—
55#63962C2212yes—
56#63959C2212yes—
57#63958C2212yes—
58#63956C2212yes—
59#63955C2212yes—
60C2×Dic32C2212yes—
61#63953C2212yes—
62#63953C2212yes—
63#63952C2212yes—
64#63952C2212yes—
65#63918C2212yes—
66#63918C2211yescharacteristic
67#63918C2211yescharacteristic
68#63909C2211yescharacteristic
69#63907C2212yes—
70#63904C2212yes—
71#63897C2212yes—
72#63895C2212yes—
73#63895C2212yes—
74#63895C2212yes—
75#63894C2211yescharacteristic
76C4×#624C2212yes—
77#63871C2212yes—
78#63868C2212yes—
79#63868C2212yes—
80#63865C2212yes—
81#63861C2212yes—
82#63859C2212yes—
83#63857C2211yescharacteristic
84#63853C2212yes—
85#63851C2212yes—
86#63851C2212yes—
87#63850C2212yes—
88#63848C2212yes—
89#63848C2212yes—
90#63847C2212yes—
91#63847C2212yes—
92#63846C2212yes—
93#63846C2212yes—
94#63846C2212yes—
95#63845C2212yes—
96#63845C2212yes—
97#63845C2212yes—
98#63844C2211yescharacteristic
99Dic3×Dic6C2212yes—
100#63841C2211yescharacteristic
101#63841C2211yescharacteristic
102#63840C2212yes—
103#63839C2212yes—
104#63837C2212yes—
105#63837C2212yes—
106#63837C2212yes—
107#63836C2212yes—
108#63836C2212yes—
109C3×#563—31no—
110C3×#529—31no—
111#5735—32no—
112#5728—32no—
113#5712—32no—
114#5712—32no—
115#5712—32no—
116#5712—32no—
117#5706—32no—
118#5706—32no—
119#5699—31no—
120#5699—31no—
121#5691—31no—
122#5688—31no—
123C3⋊#564—31no—
124C3⋊#564—31no—
125#5684—31no—
126#5684—31no—
127#5684—61no—
128#5680D311yescharacteristic, complemented
129#5672D311yescharacteristic, complemented
130#5667—32no—
131#5667—32no—
132#5651—32no—
133#5649—32no—
134#5647—32no—
135#5646—32no—
136#5646—32no—
137#5624—32no—
138#5622—32no—
139#5621—32no—
140#5578—32no—
141#5557—32no—
142#5538—32no—
143#5538—32no—
144#5528—32no—
145#5517—32no—
146#5479—31no—
147#5470—31no—
148C2×C32×Q8C2311yescharacteristic
149C2×C32×D4C2311yescharacteristic
150C2×#638C2312yes—
151C2×#638C2312yes—
152C22×C3⋊Dic3C2312yes—
153C2×C4⋊(C3⋊D3)C2311yescharacteristic
154C2×C4×C3⋊D3C2312yes—
155C2×#634C2311yescharacteristic
156C2×C3×#67C2312yes—
157C22×C3×Dic3C2312yes—
158C22×C3×Dic3C2312yes—
159C2×C3×C4×D3C2311yescharacteristic
160C2×C3×C4×D3C2311yescharacteristic
161C2×C3×C4×D3C2311yescharacteristic
162C2×C3×Dic6C2312yes—
163C2×#627C2312yes—
164C2×#627C2312yes—
165C2×#627C2312yes—
166C2×#626C2312yes—
167C2×#624C2312yes—
168C2×#624C2312yes—
169C32×C22⋊C4C2312yes—
170C32×C22⋊C4C2312yes—
171C32×C42C2311yescharacteristic
172#3757C2312yes—
173#3752C2312yes—
174#3752C2312yes—
175#3752C2312yes—
176C4⋊(C3⋊Dic3)C2311yescharacteristic
177C4⋊(C3⋊Dic3)C2311yescharacteristic
178C4⋊(C3⋊Dic3)C2312yes—
179#3750C2312yes—
180#3750C2312yes—
181#3750C2312yes—
182C3×#217C2312yes—
183C3×#217C2312yes—
184C3×#217C2312yes—
185C3×#217C2312yes—
186C3×#217C2312yes—
187C3×(C2×D3)⋊C4C2312yes—
188C3×C4⋊Dic3C2311yescharacteristic
189C3×C4⋊Dic3C2311yescharacteristic
190C3×C4⋊Dic3C2311yescharacteristic
191C3×C4⋊Dic3C2311yescharacteristic
192C3×C4⋊Dic3C2312yes—
193C3×C4⋊Dic3C2311yescharacteristic
194C3×C4⋊Dic3C2311yescharacteristic
195C3×Dic3⋊C4C2312yes—
196C3×Dic3⋊C4C2312yes—
197C3×Dic3⋊C4C2312yes—
198C3×Dic3⋊C4C2312yes—
199C3×Dic3⋊C4C2312yes—
200C3×Dic3⋊C4C2312yes—
201C3×Dic3⋊C4C2312yes—
202C3×Dic3⋊C4C2312yes—
203C3×Dic3⋊C4C2312yes—
204C3×C4×Dic3C2311yescharacteristic
205C3×C4×Dic3C2312yes—
206C3×C4×Dic3C2312yes—
207C3×C4×Dic3C2311yescharacteristic
208C3×C4×Dic3C2311yescharacteristic
209#3724C2312yes—
210#3724C2312yes—
211#3724C2312yes—
212Dic3⋊Dic3C2312yes—
213Dic3⋊Dic3C2312yes—
214Dic3⋊Dic3C2312yes—
215Dic3⋊Dic3C2312yes—
216Dic3⋊Dic3C2312yes—
217Dic3⋊Dic3C2312yes—
218Dic3⋊Dic3C2312yes—
219Dic3⋊Dic3C2312yes—
220Dic3⋊Dic3C2312yes—
221#3722C2312yes—
222#3722C2312yes—
223#3722C2312yes—
224#3722C2312yes—
225#3722C2312yes—
226(C2×D3)⋊Dic3C2312yes—
227(C2×D3)⋊Dic3C2312yes—
228(C2×D3)⋊Dic3C2312yes—
229Dic32C2312yes—
230Dic32C2312yes—
231Dic32C2312yes—
232Dic32C2312yes—
233Dic32C2312yes—
234Dic32C2312yes—
235#3531—91noSylow
236C3×C4⋊Q8—32no—
237C3×#126—32no—
238C3×#126—32no—
239C3×#126—32no—
240C3×#125—31no—
241C3×#125—31no—
242C3×#125—31no—
243C3×#124—21no—
244C3×#124C2×D311yescharacteristic
245C3×#124C2×D311yescharacteristic
246C3×#123—32no—
247C3×#123—32no—
248C3×C22⋊Q8—31no—
249C3×C22⋊Q8—32no—
250C3×C22⋊Q8—32no—
251C3×#121—31no—
252C3×C4×Q8—31no—
253C3×C4×D4—31no—
254C3×C4×D4—32no—
255C3×#117—32no—
256C2×C3×C42—31no—
257#947—32no—
258#946—32no—
259#946—32no—
260#946—32no—
261#946—62no—
262#946C2×D311yescharacteristic
263Q8×Dic3—32no—
264Q8×Dic3C2×D311yescharacteristic
265#944—32no—
266#944C2×D312yes—
267#939—32no—
268#939—32no—
269#939—32no—
270#939—62no—
271#938—32no—
272#938C2×D311yescharacteristic
273#936—32no—
274#935—32no—
275#935C2×D312yes—
276D4×Dic3C2×D311yescharacteristic
277#930—32no—
278#930—31no—
279#929—32no—
280#929—32no—
281C4×#67—32no—
282C4×#67—32no—
283C4×#67—32no—
284#926—32no—
285#926—31no—
286#926—31no—
287#924—32no—
288#924—31no—
289#924—32no—
290#924—32no—
291C2×C4×Dic3—32no—
292C2×C4×Dic3—32no—
293#898—32no—
294#898—32no—
295#898—32no—
296#898—32no—
297#898—32no—
298#898—32no—
299#898—32no—
300#897—31no—
301#897—32no—
302#897—32no—
303#897—32no—
304#897—32no—
305#896—32no—
306#896—32no—
307#896—32no—
308#896—32no—
309#896—32no—
310#896—32no—
311#896—32no—
312#895—31no—
313#894—32no—
314#894—32no—
315#894—32no—
316#894—32no—
317#893—32no—
318#893—31no—
319#892—31no—
320#892—31no—
321#892—32no—
322#892—32no—
323#890—32no—
324#890—32no—
325#890—32no—
326#890—32no—
327#890—32no—
328#890—32no—
329#889—32no—
330#889—32no—
331#889—32no—
332#889—32no—
333#889—32no—
334#889—32no—
335#889—32no—
336#889—32no—
337#889—32no—
338#889—32no—
339#888—32no—
340#888—32no—
341#888—32no—
342#888—31no—
343#888—32no—
344#888—31no—
345#887—32no—
346#887—32no—
347#887—31no—
348#887—32no—
349#886—32no—
350#886—32no—
351#886—32no—
352#886—32no—
353#886—62no—
354#885—32no—
355#885—32no—
356#885—32no—
357#885—32no—
358#885—32no—
359#885—32no—
360#884—32no—
361#884—32no—
362#884—32no—
363#884—62no—
364#883—32no—
365#883—32no—
366#883—32no—
367#883—32no—
368#883—32no—
369#883—62no—
370#883C2×D312yes—
371#67⋊C4—32no—
372#67⋊C4—32no—
373#67⋊C4C2×D312yes—
374#879—32no—
375#879—32no—
376#879—32no—
377#879—32no—
378#879C2×D312yes—
379#879C2×D312yes—
380#879C2×D312yes—
381#878—32no—
382#878—32no—
383#878—32no—
384#878—32no—
385#878—32no—
386#878—32no—
387#878—32no—
388#878—62no—
389#878C2×D312yes—
390#878C2×D312yes—
391#877—32no—
392#877C2×D312yes—
393#876—32no—
394#876—32no—
395#876—32no—
396#875—31no—
397#875—31no—
398#875—61no—
399C4×D12—31no—
400#872—32no—
401#872—32no—
402C42×D3—32no—
403C42×D3—32no—
404C42×D3C2×D311yescharacteristic
405#870—31no—
406#870—31no—
407#870—61no—
408#870C2×D311yescharacteristic
409#870C2×D311yescharacteristic
410#870C2×D311yescharacteristic
411#869—31no—
412#869—31no—
413#869—32no—
414C4×Dic6—32no—
415C4×Dic6—31no—
416C4×Dic6—32no—
417C4×Dic6—32no—
418C4×Dic6—32no—
419C23×C32C2412yes—
420C22×C3⋊D3C2412yes—
421C22×C3×D3C2411yescharacteristic
422C32×Q8—41no—
423C32×D4—41no—
424C2×C32×C4C2412yes—
425C2×C32×C4C2411yescharacteristic
426C2×C32×C4C2411yescharacteristic
427C2×C32×C4C2411yescharacteristic
428#638—42no—
429#638—42no—
430C2×C3⋊Dic3—42no—
431C2×C3⋊Dic3C2412yes—
432C2×C3⋊Dic3C2412yes—
433C2×C3⋊Dic3C2412yes—
434C4⋊(C3⋊D3)—41no—
435C4×C3⋊D3—42no—
436#634—41no—
437C3×#67—42no—
438C2×C3×Dic3—24no—
439C2×C3×Dic3—42no—
440C2×C3×Dic3C2412yes—
441C2×C3×Dic3C2412yes—
442C2×C3×Dic3C2412yes—
443C2×C3×Dic3C2412yes—
444C2×C3×Dic3C2412yes—
445C2×C3×Dic3C2412yes—
446C2×C3×Dic3C2411yescharacteristic
447C2×C3×Dic3C2411yescharacteristic
448C2×C3×Dic3C2411yescharacteristic
449C3×C4×D3—22no—
450C3×C4×D3—41no—
451C3×C4×D3—41no—
452C3×Dic6—42no—
453#627—42no—
454#627—42no—
455#627—42no—
456#626—42no—
457#624—24no—
458#624—42no—
459#564—91no—
460#563—31no—
461#563—92no—
462#563—92no—
463#563—92no—
464#563—91no—
465#563—92no—
466#562—92no—
467#562—92no—
468#562—91no—
469#533—91no—
470#533—92no—
471#533—92no—
472#529—31no—
473#529—91no—
474#529—92no—
475#529—92no—
476#529—92no—
477#529—92no—
478C2×C3×Q8—21no—
479C2×C3×Q8—32no—
480C2×C3×Q8C22×D311yescharacteristic
481C2×C3×Q8C22×D311yescharacteristic
482C2×C3×D4—21no—
483C2×C3×D4—32no—
484C2×C3×D4C22×D311yescharacteristic
485C2×C3×D4C22×D311yescharacteristic
486C22×C3×C4—32no—
487C22×C3×C4—32no—
488C22×C3×C4—31no—
489C22×C3×C4—31no—
490C22×C3×C4—31no—
491C2×#67—32no—
492C2×#67—32no—
493C2×#67—32no—
494C2×#67—32no—
495C2×#67—32no—
496C2×#67—62no—
497C2×#67—62no—
498C2×#67C22×D312yes—
499C22×Dic3—32no—
500C22×Dic3—32no—
501C22×Dic3—62no—
502C22×Dic3C22×D312yes—
503C22×Dic3C22×D312yes—
504C2×D12—32no—
505C2×D12—31no—
506C2×D12—31no—
507C2×D12—61no—
508C2×C4×D3—32no—
509C2×C4×D3—32no—
510C2×C4×D3—32no—
511C2×C4×D3—32no—
512C2×C4×D3—32no—
513C2×C4×D3—32no—
514C2×C4×D3—62no—
515C2×C4×D3C22×D311yescharacteristic
516C2×C4×D3C22×D311yescharacteristic
517C2×C4×D3C22×D311yescharacteristic
518C2×Dic6—31no—
519C2×Dic6—31no—
520C2×Dic6—32no—
521C2×Dic6—32no—
522C2×Dic6—32no—
523C2×Dic6—32no—
524C2×Dic6—32no—
525C2×Dic6—32no—
526C2×Dic6—61no—
527C2×Dic6C22×D312yes—
528C3×C4⋊C4—32no—
529C3×C4⋊C4—31no—
530C3×C4⋊C4—32no—
531C3×C4⋊C4—32no—
532C3×C4⋊C4—32no—
533C3×C4⋊C4—32no—
534C3×C4⋊C4—32no—
535C3×C4⋊C4—31no—
536C3×C4⋊C4—31no—
537C3×C4⋊C4—31no—
538C3×C4⋊C4—31no—
539C3×C4⋊C4—31no—
540C3×C4⋊C4—32no—
541C3×C4⋊C4—32no—
542C3×C4⋊C4—32no—
543C3×C4⋊C4—32no—
544C3×C22⋊C4—22no—
545C3×C22⋊C4—22no—
546C3×C22⋊C4—32no—
547C3×C22⋊C4—32no—
548C3×C22⋊C4—32no—
549C3×C22⋊C4—32no—
550C3×C22⋊C4—32no—
551C3×C22⋊C4—32no—
552C3×C22⋊C4C22×D312yes—
553C3×C22⋊C4C22×D312yes—
554C3×C22⋊C4C22×D312yes—
555C3×C22⋊C4C22×D312yes—
556C3×C42—21no—
557C3×C42—31no—
558C3×C42—32no—
559C3×C42—31no—
560C3×C42—31no—
561C3×C42—32no—
562C3×C42C22×D311yescharacteristic
563C3×C42C22×D311yescharacteristic
564#217—32no—
565#217—32no—
566#217—32no—
567#217—32no—
568#217—32no—
569#217—62no—
570#217C22×D312yes—
571#217C22×D312yes—
572#217C22×D312yes—
573#217C22×D312yes—
574#217C22×D312yes—
575(C2×D3)⋊C4—32no—
576(C2×D3)⋊C4—32no—
577(C2×D3)⋊C4—32no—
578(C2×D3)⋊C4—32no—
579(C2×D3)⋊C4—32no—
580(C2×D3)⋊C4—32no—
581(C2×D3)⋊C4—32no—
582(C2×D3)⋊C4—32no—
583(C2×D3)⋊C4—32no—
584(C2×D3)⋊C4—32no—
585(C2×D3)⋊C4—32no—
586(C2×D3)⋊C4—32no—
587(C2×D3)⋊C4—32no—
588(C2×D3)⋊C4—32no—
589(C2×D3)⋊C4—32no—
590(C2×D3)⋊C4—32no—
591(C2×D3)⋊C4—32no—
592(C2×D3)⋊C4—32no—
593(C2×D3)⋊C4—32no—
594(C2×D3)⋊C4—62no—
595(C2×D3)⋊C4—62no—
596(C2×D3)⋊C4—62no—
597(C2×D3)⋊C4C22×D312yes—
598C4⋊Dic3—32no—
599C4⋊Dic3—31no—
600C4⋊Dic3—31no—
601C4⋊Dic3—32no—
602C4⋊Dic3—31no—
603C4⋊Dic3—31no—
604C4⋊Dic3—32no—
605C4⋊Dic3—32no—
606C4⋊Dic3—32no—
607C4⋊Dic3—32no—
608C4⋊Dic3—32no—
609C4⋊Dic3—32no—
610C4⋊Dic3—32no—
611C4⋊Dic3—32no—
612C4⋊Dic3—32no—
613C4⋊Dic3—61no—
614C4⋊Dic3—61no—
615C4⋊Dic3—62no—
616C4⋊Dic3C22×D311yescharacteristic
617C4⋊Dic3C22×D311yescharacteristic
618C4⋊Dic3C22×D311yescharacteristic
619C4⋊Dic3C22×D312yes—
620C4⋊Dic3C22×D311yescharacteristic
621C4⋊Dic3C22×D311yescharacteristic
622C4⋊Dic3C22×D311yescharacteristic
623Dic3⋊C4—32no—
624Dic3⋊C4—32no—
625Dic3⋊C4—32no—
626Dic3⋊C4—32no—
627Dic3⋊C4—32no—
628Dic3⋊C4—32no—
629Dic3⋊C4—32no—
630Dic3⋊C4—32no—
631Dic3⋊C4—32no—
632Dic3⋊C4—32no—
633Dic3⋊C4—32no—
634Dic3⋊C4—32no—
635Dic3⋊C4—32no—
636Dic3⋊C4—32no—
637Dic3⋊C4—32no—
638Dic3⋊C4—32no—
639Dic3⋊C4—32no—
640Dic3⋊C4—32no—
641Dic3⋊C4—32no—
642Dic3⋊C4—32no—
643Dic3⋊C4—32no—
644Dic3⋊C4—62no—
645Dic3⋊C4—62no—
646Dic3⋊C4—62no—
647Dic3⋊C4C22×D312yes—
648Dic3⋊C4C22×D312yes—
649Dic3⋊C4C22×D312yes—
650Dic3⋊C4C22×D312yes—
651Dic3⋊C4C22×D312yes—
652Dic3⋊C4C22×D312yes—
653Dic3⋊C4C22×D312yes—
654Dic3⋊C4C22×D312yes—
655Dic3⋊C4C22×D312yes—
656C4×Dic3—32no—
657C4×Dic3—32no—
658C4×Dic3—32no—
659C4×Dic3—32no—
660C4×Dic3—32no—
661C4×Dic3—32no—
662C4×Dic3—32no—
663C4×Dic3—32no—
664C4×Dic3—32no—
665C4×Dic3—32no—
666C4×Dic3—32no—
667C4×Dic3—32no—
668C4×Dic3C22×D312yes—
669C4×Dic3C22×D312yes—
670C4×Dic3C22×D311yescharacteristic
671C4×Dic3C22×D311yescharacteristic
672C4×Dic3C22×D311yescharacteristic
673C22×C32—22no—
674C22×C32—22no—
675C22×C32—22no—
676C22×C32C2511yescharacteristic
677C2×C3⋊D3—22no—
678C2×C3⋊D3—22no—
679C2×C3⋊D3—22no—
680C2×C3×D3—21no—
681C2×C3×D3—21no—
682C2×C3×D3—21no—
683C32×C4—21no—
684C32×C4—22no—
685C32×C4—21no—
686C32×C4—21no—
687C3⋊Dic3—22no—
688C3⋊Dic3—22no—
689C3⋊Dic3—22no—
690C3×Dic3—22no—
691C3×Dic3—22no—
692C3×Dic3—22no—
693C3×Dic3—22no—
694C3×Dic3—22no—
695C3×Dic3—21no—
696C3×Dic3—21no—
697C3×Dic3—22no—
698C3×Dic32−1+412yes—
699C4⋊Q8—32no—
700C4⋊Q8—91no—
701C4⋊Q8—91no—
702C4⋊Q8—92no—
703C4⋊Q8—92no—
704C4⋊Q8—92no—
705#126—32no—
706#126—32no—
707#126—32no—
708#126—92no—
709#126—92no—
710#126—92no—
711#126—92no—
712#126—92no—
713#126—92no—
714#126—92no—
715#125—31no—
716#125—31no—
717#125—31no—
718#125—92no—
719#125—92no—
720#125—92no—
721#125—92no—
722#125—92no—
723#125—92no—
724#125—92no—
725#125—92no—
726#125—91no—
727#124—92no—
728#124—92no—
729#124—92no—
730#124—92no—
731#124—91no—
732#124D3211yescharacteristic
733#123—32no—
734#123—32no—
735#123—92no—
736#123—92no—
737#123—92no—
738#123—92no—
739#123—92no—
740#123—92no—
741#123—92no—
742#123—92no—
743C22⋊Q8—31no—
744C22⋊Q8—32no—
745C22⋊Q8—32no—
746C22⋊Q8—92no—
747C22⋊Q8—92no—
748C22⋊Q8—92no—
749C22⋊Q8—92no—
750C22⋊Q8—92no—
751C22⋊Q8—92no—
752C22⋊Q8—92no—
753C22⋊Q8—91no—
754C22⋊Q8—92no—
755C22⋊Q8—92no—
756C22⋊Q8—92no—
757C22⋊Q8—92no—
758C22⋊Q8—92no—
759#121—31no—
760#121—92no—
761#121—91no—
762#121—92no—
763#121—92no—
764#121—92no—
765C4×Q8—31no—
766C4×Q8—91no—
767C4×Q8—92no—
768C4×Q8—92no—
769C4×Q8—92no—
770C4×Q8—92no—
771C4×D4—31no—
772C4×D4—32no—
773C4×D4—91no—
774C4×D4—92no—
775C4×D4—92no—
776C4×D4—92no—
777#117—32no—
778#117—92no—
779#117—92no—
780#117—92no—
781#117—91no—
782#117—91no—
783C2×C42—31no—
784C2×C42—92no—
785C2×C42—92no—
786C23×C3—22no—
787C23×C3—31no—
788C23×C3C23×D312yes—
789C23×C3C23×D312yes—
790C22×D3—32no—
791C22×D3—32no—
792C22×D3—62no—
793C22×D3C23×D311yescharacteristic
794C3×Q8—41no—
795C3×Q8—41no—
796C3×Q8—81no—
797C3×Q8—122no—
798C3×D4—41no—
799C3×D4—41no—
800C3×D4—81no—
801C3×D4—122no—
802C2×C3×C4—21no—
803C2×C3×C4—21no—
804C2×C3×C4—22no—
805C2×C3×C4—21no—
806C2×C3×C4—31no—
807C2×C3×C4—32no—
808C2×C3×C4—32no—
809C2×C3×C4—32no—
810C2×C3×C4—32no—
811C2×C3×C4—32no—
812C2×C3×C4—32no—
813C2×C3×C4—31no—
814C2×C3×C4—31no—
815C2×C3×C4—62no—
816C2×C3×C4—64no—
817C2×C3×C4—121no—
818C2×C3×C4—121no—
819C2×C3×C4—122no—
820C2×C3×C4C23×D311yescharacteristic
821C2×C3×C4C23×D311yescharacteristic
822C2×C3×C4C23×D312yes—
823C2×C3×C4C23×D312yes—
824C2×C3×C4C23×D311yescharacteristic
825C2×C3×C4C23×D311yescharacteristic
826C2×C3×C4C23×D311yescharacteristic
827C2×C3×C4C23×D311yescharacteristic
828#67—42no—
829#67—122no—
830#67—122no—
831#67—122no—
832#67—122no—
833#67—122no—
834#67—242no—
835#67—242no—
836C2×Dic3—24no—
837C2×Dic3—32no—
838C2×Dic3—32no—
839C2×Dic3—32no—
840C2×Dic3—32no—
841C2×Dic3—32no—
842C2×Dic3—32no—
843C2×Dic3—42no—
844C2×Dic3—62no—
845C2×Dic3—62no—
846C2×Dic3—62no—
847C2×Dic3—122no—
848C2×Dic3—122no—
849C2×Dic3—242no—
850C2×Dic3C23×D312yes—
851C2×Dic3C23×D312yes—
852C2×Dic3C23×D312yes—
853C2×Dic3C23×D312yes—
854C2×Dic3C23×D312yes—
855C2×Dic3C23×D312yes—
856C2×Dic3C23×D311yescharacteristic
857C2×Dic3C23×D311yescharacteristic
858C2×Dic3C23×D311yescharacteristic
859D12—121no—
860D12—121no—
861D12—122no—
862D12—241no—
863C4×D3—22no—
864C4×D3—41no—
865C4×D3—41no—
866C4×D3—64no—
867C4×D3—64no—
868C4×D3—122no—
869C4×D3—122no—
870C4×D3—122no—
871C4×D3—122no—
872C4×D3—242no—
873Dic6—42no—
874Dic6—122no—
875Dic6—122no—
876Dic6—122no—
877Dic6—122no—
878Dic6—122no—
879Dic6—122no—
880Dic6—121no—
881Dic6—121no—
882Dic6—241no—
883C2×C32—42no—
884C2×C32C2×2−1+411yescharacteristic
885C2×C32#58511yescharacteristic
886C2×C32#58511yescharacteristic
887C3⋊D3—42no—
888C3×D3—41no—
889C2×Q8—32no—
890C2×Q8—92no—
891C2×Q8—92no—
892C2×Q8—92no—
893C2×Q8—91no—
894C2×Q8C2×D3211yescharacteristic
895C2×D4—32no—
896C2×D4—92no—
897C2×D4—92no—
898C2×D4—92no—
899C2×D4—91no—
900C2×D4C2×D3211yescharacteristic
901C22×C4—32no—
902C22×C4—32no—
903C22×C4—31no—
904C22×C4—31no—
905C22×C4—31no—
906C22×C4—92no—
907C22×C4—92no—
908C22×C4—92no—
909C22×C4—92no—
910C4⋊C4—32no—
911C4⋊C4—32no—
912C4⋊C4—31no—
913C4⋊C4—32no—
914C4⋊C4—31no—
915C4⋊C4—32no—
916C4⋊C4—31no—
917C4⋊C4—32no—
918C4⋊C4—32no—
919C4⋊C4—31no—
920C4⋊C4—31no—
921C4⋊C4—32no—
922C4⋊C4—31no—
923C4⋊C4—32no—
924C4⋊C4—32no—
925C4⋊C4—32no—
926C4⋊C4—92no—
927C4⋊C4—92no—
928C4⋊C4—92no—
929C4⋊C4—92no—
930C4⋊C4—92no—
931C4⋊C4—92no—
932C4⋊C4—92no—
933C4⋊C4—92no—
934C4⋊C4—92no—
935C4⋊C4—92no—
936C4⋊C4—92no—
937C4⋊C4—92no—
938C4⋊C4—91no—
939C4⋊C4—91no—
940C4⋊C4—92no—
941C4⋊C4—92no—
942C4⋊C4—92no—
943C4⋊C4—92no—
944C22⋊C4—32no—
945C22⋊C4—32no—
946C22⋊C4—32no—
947C22⋊C4—32no—
948C22⋊C4—32no—
949C22⋊C4—32no—
950C22⋊C4—92no—
951C22⋊C4—92no—
952C22⋊C4—92no—
953C22⋊C4—92no—
954C22⋊C4—92no—
955C22⋊C4—92no—
956C22⋊C4—92no—
957C22⋊C4—92no—
958C22⋊C4—92no—
959C22⋊C4—92no—
960C22⋊C4—92no—
961C22⋊C4—92no—
962C22⋊C4C2×D3212yes—
963C22⋊C4C2×D3212yes—
964C42—31no—
965C42—31no—
966C42—31no—
967C42—32no—
968C42—32no—
969C42—92no—
970C42—92no—
971C42—92no—
972C42—92no—
973C42—92no—
974C42—92no—
975C42C2×D3211yescharacteristic
976C22×C3—22no—
977C22×C3—22no—
978C22×C3—22no—
979C22×C3—22no—
980C22×C3—22no—
981C22×C3—22no—
982C22×C3—21no—
983C22×C3—42no—
984C22×C3—42no—
985C22×C3—42no—
986C22×C3—61no—
987C22×C3—61no—
988C22×C3—61no—
989C22×C3C24×D311yescharacteristic
990C22×C3C24×D311yescharacteristic
991C2×D3—21no—
992C2×D3—21no—
993C2×D3—21no—
994C2×D3—62no—
995C2×D3—62no—
996C2×D3—62no—
997C2×D3—62no—
998C2×D3—62no—
999C2×D3—62no—
1000C2×D3—122no—
1001C2×D3—122no—
1002C2×D3—122no—
1003C3×C4—21no—
1004C3×C4—21no—
1005C3×C4—21no—
1006C3×C4—22no—
1007C3×C4—22no—
1008C3×C4—21no—
1009C3×C4—21no—
1010C3×C4—21no—
1011C3×C4—32no—
1012C3×C4—41no—
1013C3×C4—42no—
1014C3×C4—41no—
1015C3×C4—41no—
1016C3×C4—62no—
1017C3×C4—62no—
1018C3×C4—62no—
1019C3×C4—62no—
1020C3×C4—61no—
1021C3×C4—62no—
1022C3×C4—61no—
1023C3×C4—62no—
1024Dic3—22no—
1025Dic3—21no—
1026Dic3—21no—
1027Dic3—22no—
1028Dic3—22no—
1029Dic3—22no—
1030Dic3—22no—
1031Dic3—22no—
1032Dic3—62no—
1033Dic3—62no—
1034Dic3—62no—
1035Dic3—62no—
1036Dic3—62no—
1037Dic3—62no—
1038Dic3—122no—
1039Dic3—122no—
1040Dic3—122no—
1041Dic3#101012yes—
1042C32#353111yescharacteristic, complemented, Sylow
1043C23—31no—
1044C23—92no—
1045C23C22×D3212yes—
1046Q8—41no—
1047Q8—122no—
1048Q8—361no—
1049Q8—362no—
1050Q8—362no—
1051Q8—362no—
1052D4—41no—
1053D4—122no—
1054D4—361no—
1055D4—362no—
1056D4—362no—
1057D4—362no—
1058C2×C4—31no—
1059C2×C4—31no—
1060C2×C4—31no—
1061C2×C4—32no—
1062C2×C4—32no—
1063C2×C4—32no—
1064C2×C4—32no—
1065C2×C4—32no—
1066C2×C4—32no—
1067C2×C4—62no—
1068C2×C4—64no—
1069C2×C4—92no—
1070C2×C4—92no—
1071C2×C4—92no—
1072C2×C4—121no—
1073C2×C4—121no—
1074C2×C4—122no—
1075C2×C4—184no—
1076C2×C4—362no—
1077C2×C4—362no—
1078C2×C4—362no—
1079C2×C4C22×D3212yes—
1080C2×C4C22×D3211yescharacteristic
1081C2×C4C22×D3211yescharacteristic
1082C2×C4C22×D3211yescharacteristic
1083C2×C3—21no—
1084C2×C3—21no—
1085C2×C3—21no—
1086C2×C3—42no—
1087C2×C3—42no—
1088C2×C3—82no—
1089C2×C3—121no—
1090C2×C3C2×#101011yescharacteristic
1091C2×C3#596411yescharacteristic
1092C2×C3#596411yescharacteristic
1093C2×C3#596611yescharacteristic
1094C2×C3D3×2−1+411yescharacteristic
1095C2×C3#596811yescharacteristic
1096D3—41no—
1097D3—122no—
1098D3—122no—
1099D3—242no—
1100C22—22no—
1101C22—22no—
1102C22—22no—
1103C22—61no—
1104C22—61no—
1105C22—61no—
1106C22—182no—
1107C22—182no—
1108C22—182no—
1109C22C23×D3211yescharacteristic
1110C4—21no—
1111C4—22no—
1112C4—21no—
1113C4—21no—
1114C4—32no—
1115C4—62no—
1116C4—62no—
1117C4—61no—
1118C4—62no—
1119C4—62no—
1120C4—61no—
1121C4—62no—
1122C4—62no—
1123C4—182no—
1124C4—182no—
1125C4—182no—
1126C3—21no—
1127C3#8613211yescharacteristic, complemented
1128C3#8711611yescharacteristic, complemented
1129C2—42no—
1130C2—121no—
1131C2—362no—
1132C2#1059667811yescharacteristic
1133C2D3×#101011yescharacteristic
1134C2#1059669711yescharacteristic
subgroupG/H
center, FrattiniC22C23×D32
commutator, socle, cosocleC22×C32C25
FittingC32×#124C22
hypercenter#124D32
hypocenterC32#3531
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ #124

Complements

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

NH ≅ G/Ntype
1. #10596155C2semidirect
2. C3×#5680C2semidirect
3. C3×#5672C2semidirect
4. #10595374C2semidirect
5. #10595345C2semidirect
6. #10595263C2semidirect
7. #10595116C2semidirect
8. #10594251C2semidirect
9. #10594216C2semidirect
10. #10594107C2semidirect
11. #10594106C2semidirect
12. #10594044C2semidirect
13. #10594043C2semidirect
14. #10594036C2semidirect
15. #10594029C2semidirect
16. #10593976C2semidirect
17. #10593874C2semidirect
18. #10593868C2semidirect
19. #10593857C2semidirect
128. #5680D3semidirect
129. #5672D3semidirect
1042. C32#3531semidirect
1127. C3#86132semidirect
1128. C3#87116semidirect

Maximal subgroups

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

subgroupindex
#105961552
C3×#56802
C3×#56722
#105953742
#105953452
#105952632
#105951162
#105942512
#105942162
#105941072
#105941062
#105940442
#105940432
#105940362
#105940292
#105939762
#105938742
#105938682
#105938572
#871163
#861323