Finite Group Databasebeta

← #11910396

Subgroups — #11910396

Order 1152.

2281 conjugacy classes of subgroups.

The subgroup lattice has 1186 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10596127C211yesmaximal, characteristic, complemented
2C3×#5667C212yesmaximal, complemented
3#10595306C211yesmaximal, characteristic, complemented
4#10595264C212yesmaximal, complemented
5#10595165C211yesmaximal, characteristic, complemented
6#10595091C211yesmaximal, characteristic, complemented
7#10594922C212yesmaximal, complemented
8#10594811C211yesmaximal, characteristic, complemented
9#10594615C212yesmaximal, complemented
10#10594585C212yesmaximal, complemented
11#10594453C212yesmaximal, complemented
12#10594339C212yesmaximal, complemented
13#10594311C211yesmaximal, characteristic, complemented
14#10594308C212yesmaximal, complemented
15#10594244C211yesmaximal, characteristic, complemented
16#10594178C212yesmaximal, complemented
17#10594144C212yesmaximal, complemented
18#10594111C212yesmaximal, complemented
19#10594061C212yesmaximal, complemented
20#87093—32nomaximal
21C2×#3830C2211yescharacteristic
22C22×C4×C3⋊D3C2211yescharacteristic, complemented
23C2×#3805C2211yescharacteristic, complemented
24C2×C4×D32C2211yescharacteristic, complemented
25C2×#3796C2212yes—
26C32×#123C2211yescharacteristic, complemented
27#64146C2211yescharacteristic, complemented
28#64138C2211yescharacteristic
29#64105C2212yescomplemented
30#64102C2212yes—
31#64093C2212yes—
32#64091C2211yescharacteristic
33#64090C2212yescomplemented
34#64086C2211yescharacteristic, complemented
35C3×#939C2212yescomplemented
36C3×#938C2212yes—
37C3×#930C2212yes—
38C3×#924C2212yescomplemented
39C3×#897C2212yescomplemented
40C3×#896C2212yescomplemented
41C3×#894C2212yescomplemented
42C3×#890C2212yescomplemented
43C3×#886C2212yescomplemented
44C3×#885C2212yes—
45C3×#885C2212yescomplemented
46C3×#884C2212yescomplemented
47C3×#883C2212yescomplemented
48C3×#878C2212yescomplemented
49#63983C2211yescharacteristic
50#63983C2211yescharacteristic, complemented
51#63981C2212yes—
52#63981C2212yescomplemented
53#63979C2212yes—
54#63979C2211yescharacteristic
55#63978C2212yes—
56#63978C2212yescomplemented
57#63975C2211yescharacteristic
58#63975C2211yescharacteristic, complemented
59#67⋊Dic3C2212yes—
60#67⋊Dic3C2212yescomplemented
61#67⋊Dic3C2212yescomplemented
62#63971C2212yescomplemented
63#63970C2212yes—
64#63966C2212yescomplemented
65#63956C2212yescomplemented
66C2×Dic32C2211yescharacteristic, complemented
67#63953C2211yescharacteristic
68#63923C2212yes—
69#63922C2212yescomplemented
70#63916C2212yes—
71#63913C2211yescharacteristic, complemented
72#63910C2212yes—
73#63909C2212yes—
74#63907C2212yes—
75#63906C2212yes—
76#63906C2212yescomplemented
77#63905C2212yescomplemented
78#63902C2212yescomplemented
79#63890C2212yescomplemented
80#63890C2212yescomplemented
81#63888C2212yescomplemented
82#63887C2212yescomplemented
83#63885C2212yescomplemented
84#63881C2212yes—
85#63881C2212yescomplemented
86#63881C2212yescomplemented
87#63878C2212yescomplemented
88C4×D3×Dic3C2212yescomplemented
89#63871C2212yescomplemented
90#63867C2212yescomplemented
91#63864C2212yes—
92#63858C2212yescomplemented
93#63858C2212yescomplemented
94#63857C2212yescomplemented
95#63853C2212yes—
96#63853C2212yescomplemented
97#63852C2212yes—
98#63850C2212yes—
99#63849C2212yescomplemented
100#63849C2211yescharacteristic, complemented
101#63848C2212yescomplemented
102#63848C2212yescomplemented
103#63848C2212yescomplemented
104#63846C2212yescomplemented
105#63843C2212yescomplemented
106#63840C2211yescharacteristic, complemented
107#63839C2212yescomplemented
108C3×#562—32no—
109#5699—32no—
110#5691—32no—
111#5684—32no—
112#5683—32no—
113#5680—32no—
114#5668—32no—
115#5667—32no—
116#5667D312yescomplemented
117#5666—32no—
118#5666—32no—
119#5656—32no—
120#5656—32no—
121#5656—61no—
122#5649—32no—
123#5649—32no—
124#5647—32no—
125#5647—32no—
126#5646—32no—
127#5646—32no—
128#5627—32no—
129#5627—32no—
130#5624—32no—
131#5624—32no—
132#5620—32no—
133#5620—32no—
134#5620—32no—
135#5620—32no—
136#5606—32no—
137#5606—32no—
138#5596—32no—
139#5596—32no—
140C23×C3⋊D3C2311yescharacteristic
141C22×D32C2311yescharacteristic
142C2×C32×D4C2311yescharacteristic
143C22×C32×C4C2311yescharacteristic
144C2×#638C2312yes—
145C2×#638C2311yescharacteristic
146C2×#638C2311yescharacteristic
147C22×C3⋊Dic3C2311yescharacteristic
148C22×C3⋊Dic3C2311yescharacteristic
149#3830—42no—
150C2×C4⋊(C3⋊D3)C2312yes—
151C2×C4×C3⋊D3—42no—
152C2×C4×C3⋊D3C2312yes—
153C2×C4×C3⋊D3C2311yescharacteristic
154C2×C4×C3⋊D3C2312yes—
155C2×#634C2311yescharacteristic
156C2×C3×#67C2312yes—
157C2×C3×#67C2312yes—
158C2×C3×#67C2312yes—
159C2×C3×#67C2312yes—
160C22×C3×Dic3C2312yes—
161C2×C3×D12C2312yes—
162C2×C3×C4×D3C2312yes—
163C2×C3×C4×D3C2312yes—
164C2×C3×Dic6C2312yes—
165C2×C3×Dic6C2312yes—
166C2×#627C2311yescharacteristic
167C2×#626C2312yes—
168C2×#626C2312yes—
169C2×#626C2312yes—
170C2×#626C2312yes—
171C2×#626C2312yes—
172C2×#625C2311yescharacteristic
173C2×#625C2312yes—
174C2×#624C2311yescharacteristic
175#3805—42no—
176C2×D3×Dic3C2312yes—
177C2×D3×Dic3C2312yes—
178C2×D3×Dic3C2312yes—
179C4×D32—42no—
180#3796—44no—
181C32×C4⋊C4C2312yes—
182C32×C22⋊C4C2312yes—
183C32×C22⋊C4C2311yescharacteristic
184#3757C2311yescharacteristic
185#3752C2312yes—
186#3752C2312yes—
187#3752C2312yes—
188#3750C2312yes—
189#3750C2312yes—
190C4×C3⋊Dic3C2312yes—
191C3×#217C2312yes—
192C3×#217C2312yes—
193C3×#217C2312yes—
194C3×(C2×D3)⋊C4C2312yes—
195C3×(C2×D3)⋊C4C2312yes—
196C3×(C2×D3)⋊C4C2312yes—
197C3×(C2×D3)⋊C4C2312yes—
198C3×(C2×D3)⋊C4C2312yes—
199C3×(C2×D3)⋊C4C2312yes—
200C3×C4⋊Dic3C2312yes—
201C3×C4⋊Dic3C2312yes—
202C3×C4⋊Dic3C2312yes—
203C3×C4⋊Dic3C2312yes—
204C3×Dic3⋊C4C2312yes—
205C3×Dic3⋊C4C2312yes—
206C3×Dic3⋊C4C2312yes—
207C3×Dic3⋊C4C2312yes—
208C3×C4×Dic3C2312yes—
209#3724C2312yes—
210Dic3⋊Dic3C2312yes—
211Dic3⋊Dic3C2312yes—
212Dic3⋊Dic3C2312yes—
213Dic3⋊Dic3C2312yes—
214Dic3⋊Dic3C2312yes—
215Dic3⋊Dic3C2312yes—
216#3722C2312yes—
217#3722C2311yescharacteristic
218#3722C2312yes—
219#3722C2312yes—
220#3722C2312yes—
221#3722C2312yes—
222#3722C2311yescharacteristic
223(C2×D3)⋊Dic3C2312yes—
224(C2×D3)⋊Dic3C2312yes—
225(C2×D3)⋊Dic3C2312yes—
226(C2×D3)⋊Dic3C2312yes—
227Dic32C2312yes—
228Dic32C2311yescharacteristic
229Dic32C2312yes—
230Dic32C2312yes—
231Dic32C2311yescharacteristic
232#3529—91noSylow
233C2×#239—32no—
234C2×#237—32no—
235C2×#237—32no—
236C2×#237—32no—
237C2×#237—61no—
238C22×C4×D3—32no—
239C22×C4×D3—32no—
240C22×C4×D3—61no—
241C3×#125—32no—
242C3×#124—32no—
243C3×#124—32no—
244C3×#123—21no—
245C3×#123—32no—
246C3×#123—32no—
247C3×#123—32no—
248C3×#123C2×D312yescomplemented
249C3×C22⋊Q8—32no—
250C3×C22⋊Q8—32no—
251C3×C22⋊Q8—32no—
252C3×C22⋊Q8—32no—
253C3×#121—32no—
254C3×#121—32no—
255C3×#121—32no—
256C3×#121—32no—
257#947—32no—
258#947—32no—
259#946—32no—
260#946—32no—
261#946—32no—
262Q8×Dic3—32no—
263#944—32no—
264#940—32no—
265#940—32no—
266#940—32no—
267#939—32no—
268#939—32no—
269#939—32no—
270#939—32no—
271#939—32no—
272#939C2×D312yescomplemented
273#938—32no—
274#938—32no—
275#938C2×D312yes—
276#937—32no—
277#937—32no—
278#937—32no—
279#937—32no—
280#937—32no—
281#937—32no—
282#937—61no—
283D4×Dic3—32no—
284D4×Dic3—32no—
285D4×Dic3—32no—
286#930—32no—
287#930—32no—
288#930—32no—
289#930—32no—
290#930—32no—
291#930C2×D312yes—
292#929—32no—
293#929—32no—
294#929—32no—
295#929—32no—
296#929—61no—
297#924—32no—
298#924C2×D312yescomplemented
299C2×C4×Dic3—32no—
300C2×C4×Dic3—32no—
301#898—32no—
302#898—32no—
303#898—32no—
304#898—32no—
305#898—32no—
306#898—32no—
307#898—32no—
308#898—32no—
309#897—32no—
310#897—32no—
311#897C2×D312yescomplemented
312#896—32no—
313#896—32no—
314#896—32no—
315#896—62no—
316#896C2×D312yescomplemented
317#895—32no—
318#895—32no—
319#895—32no—
320#894—32no—
321#894—32no—
322#894—32no—
323#894—32no—
324#894—32no—
325#894C2×D312yescomplemented
326#893—32no—
327#893—32no—
328#893—32no—
329#893—32no—
330#893—32no—
331#893—62no—
332#892—32no—
333#892—32no—
334#892—32no—
335#892—32no—
336#890—32no—
337#890C2×D312yescomplemented
338#889—32no—
339#889—32no—
340#888—32no—
341#888—32no—
342#887—32no—
343#886—32no—
344#886—32no—
345#886—32no—
346#886C2×D312yescomplemented
347#885—32no—
348#885—32no—
349#885—32no—
350#885—32no—
351#885C2×D312yes—
352#885C2×D312yescomplemented
353#884—32no—
354#884—32no—
355#884—32no—
356#884—32no—
357#884—32no—
358#884—32no—
359#884—32no—
360#884—62no—
361#884C2×D312yescomplemented
362#883—32no—
363#883—32no—
364#883—32no—
365#883—32no—
366#883—32no—
367#883C2×D312yescomplemented
368#882—32no—
369#882—32no—
370#882—32no—
371#882—32no—
372#882—32no—
373#882—32no—
374#882—61no—
375#67⋊C4—32no—
376#67⋊C4—32no—
377#67⋊C4—32no—
378#67⋊C4—32no—
379#67⋊C4—32no—
380#67⋊C4—32no—
381#67⋊C4—32no—
382#67⋊C4—32no—
383#67⋊C4—32no—
384#67⋊C4—32no—
385#67⋊C4—62no—
386#879—32no—
387#879—32no—
388#879—32no—
389#879—32no—
390#878—32no—
391#878C2×D312yescomplemented
392#877—32no—
393#877—32no—
394#877—61no—
395#875—32no—
396#875—32no—
397C42×D3—32no—
398#870—32no—
399C23×C32C2411yescharacteristic
400C23×C32C2411yescharacteristic
401C22×C3⋊D3—42no—
402C22×C3⋊D3—41no—
403C22×C3⋊D3C2411yescharacteristic
404C22×C3⋊D3C2412yes—
405C22×C3×D3C2412yes—
406C22×C3×D3C2412yes—
407C2×D32—42no—
408C2×D32—41no—
409C32×D4—41no—
410C2×C32×C4—41no—
411C2×C32×C4C2412yes—
412C2×C32×C4C2412yes—
413C2×C32×C4C2411yescharacteristic
414#638—41no—
415#638—41no—
416#638—42no—
417C2×C3⋊Dic3—22no—
418C2×C3⋊Dic3—22no—
419C2×C3⋊Dic3C2411yescharacteristic
420C2×C3⋊Dic3C2412yes—
421C2×C3⋊Dic3C2411yescharacteristic
422C2×C3⋊Dic3C2411yescharacteristic
423C4⋊(C3⋊D3)—42no—
424C4×C3⋊D3—24no—
425C4×C3⋊D3—22no—
426C4×C3⋊D3—42no—
427#634—41no—
428C3×#67—42no—
429C3×#67—42no—
430C3×#67—42no—
431C3×#67—42no—
432C2×C3×Dic3—42no—
433C2×C3×Dic3C2412yes—
434C2×C3×Dic3C2412yes—
435C2×C3×Dic3C2412yes—
436C2×C3×Dic3C2412yes—
437C2×C3×Dic3C2412yes—
438C2×C3×Dic3C2412yes—
439C3×D12—42no—
440C3×C4×D3—42no—
441C3×C4×D3—42no—
442C3×Dic6—42no—
443C3×Dic6—42no—
444#627—41no—
445#626—42no—
446#626—42no—
447#626—42no—
448#626—42no—
449#626—42no—
450#625—41no—
451#625—42no—
452#624—41no—
453D3×Dic3—24no—
454D3×Dic3—24no—
455D3×Dic3—42no—
456#563—91no—
457#563—92no—
458#562—32no—
459#562—92no—
460#562—92no—
461H(3,𝔽4)—91no—
462#560—91no—
463#560—92no—
464#560—92no—
465#560—91no—
466#532—91no—
467#532—92no—
468#529—92no—
469#529—92no—
470#529—92no—
471#525—91no—
472#525—92no—
473#525—92no—
474#525—91no—
475C23×D3—32no—
476C23×D3—32no—
477C23×D3—61no—
478C2×C3×Q8—32no—
479C2×C3×Q8—32no—
480C2×C3×D4—21no—
481C2×C3×D4—32no—
482C2×C3×D4—32no—
483C2×C3×D4—32no—
484C2×C3×D4—32no—
485C2×C3×D4—32no—
486C2×C3×D4C22×D312yes—
487C22×C3×C4—21no—
488C22×C3×C4—32no—
489C22×C3×C4—32no—
490C22×C3×C4—32no—
491C22×C3×C4C22×D312yes—
492C2×#67—32no—
493C2×#67—32no—
494C2×#67—32no—
495C2×#67—32no—
496C2×#67—32no—
497C2×#67—32no—
498C2×#67—32no—
499C2×#67—32no—
500C2×#67—32no—
501C2×#67—32no—
502C2×#67—32no—
503C2×#67—32no—
504C2×#67—62no—
505C2×#67—61no—
506C2×#67—61no—
507C2×#67C22×D312yes—
508C2×#67C22×D312yes—
509C2×#67C22×D312yes—
510C2×#67C22×D312yes—
511C22×Dic3—32no—
512C22×Dic3—32no—
513C22×Dic3—32no—
514C22×Dic3—32no—
515C22×Dic3—32no—
516C22×Dic3—61no—
517C22×Dic3—61no—
518C22×Dic3C22×D312yes—
519#239—124no—
520#237—124no—
521#237—124no—
522#237—124no—
523#237—124no—
524C2×D12—32no—
525C2×D12—32no—
526C2×D12—32no—
527C2×D12—32no—
528C2×D12—32no—
529C2×D12—32no—
530C2×D12—32no—
531C2×D12—62no—
532C2×D12C22×D312yes—
533C2×C4×D3—32no—
534C2×C4×D3—32no—
535C2×C4×D3—32no—
536C2×C4×D3—32no—
537C2×C4×D3—32no—
538C2×C4×D3—32no—
539C2×C4×D3—32no—
540C2×C4×D3—32no—
541C2×C4×D3—32no—
542C2×C4×D3—62no—
543C2×C4×D3—62no—
544C2×C4×D3—61no—
545C2×C4×D3—124no—
546C2×C4×D3—124no—
547C2×C4×D3—124no—
548C2×C4×D3C22×D312yes—
549C2×C4×D3C22×D312yes—
550C2×Dic6—32no—
551C2×Dic6—32no—
552C2×Dic6—61no—
553C2×Dic6C22×D312yes—
554C2×Dic6C22×D312yes—
555C3×C4⋊C4—22no—
556C3×C4⋊C4—32no—
557C3×C4⋊C4—32no—
558C3×C4⋊C4—32no—
559C3×C4⋊C4—32no—
560C3×C4⋊C4—32no—
561C3×C4⋊C4—32no—
562C3×C4⋊C4—32no—
563C3×C4⋊C4—32no—
564C3×C4⋊C4C22×D312yes—
565C3×C4⋊C4C22×D312yes—
566C3×C22⋊C4—21no—
567C3×C22⋊C4—22no—
568C3×C22⋊C4—32no—
569C3×C22⋊C4—32no—
570C3×C22⋊C4—32no—
571C3×C22⋊C4—32no—
572C3×C22⋊C4—32no—
573C3×C22⋊C4—32no—
574C3×C22⋊C4—32no—
575C3×C22⋊C4—32no—
576C3×C22⋊C4—32no—
577C3×C22⋊C4C22×D312yes—
578C3×C22⋊C4C22×D312yes—
579C3×C22⋊C4C22×D312yes—
580C3×C42—32no—
581#217—32no—
582#217—32no—
583#217—32no—
584#217—32no—
585#217—32no—
586#217—61no—
587#217C22×D312yes—
588#217C22×D312yes—
589#217C22×D312yes—
590(C2×D3)⋊C4—32no—
591(C2×D3)⋊C4—32no—
592(C2×D3)⋊C4—32no—
593(C2×D3)⋊C4—32no—
594(C2×D3)⋊C4—32no—
595(C2×D3)⋊C4—32no—
596(C2×D3)⋊C4—32no—
597(C2×D3)⋊C4—32no—
598(C2×D3)⋊C4—32no—
599(C2×D3)⋊C4—32no—
600(C2×D3)⋊C4—32no—
601(C2×D3)⋊C4—32no—
602(C2×D3)⋊C4—32no—
603(C2×D3)⋊C4—32no—
604(C2×D3)⋊C4—32no—
605(C2×D3)⋊C4—32no—
606(C2×D3)⋊C4—32no—
607(C2×D3)⋊C4—32no—
608(C2×D3)⋊C4—32no—
609(C2×D3)⋊C4—32no—
610(C2×D3)⋊C4—32no—
611(C2×D3)⋊C4—32no—
612(C2×D3)⋊C4—62no—
613(C2×D3)⋊C4—62no—
614(C2×D3)⋊C4—62no—
615(C2×D3)⋊C4C22×D312yes—
616(C2×D3)⋊C4C22×D312yes—
617(C2×D3)⋊C4C22×D312yes—
618(C2×D3)⋊C4C22×D312yes—
619(C2×D3)⋊C4C22×D312yes—
620(C2×D3)⋊C4C22×D312yes—
621C4⋊Dic3—32no—
622C4⋊Dic3—32no—
623C4⋊Dic3—32no—
624C4⋊Dic3—32no—
625C4⋊Dic3—32no—
626C4⋊Dic3—32no—
627C4⋊Dic3C22×D312yes—
628C4⋊Dic3C22×D312yes—
629C4⋊Dic3C22×D312yes—
630C4⋊Dic3C22×D312yes—
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—62no—
644Dic3⋊C4—62no—
645Dic3⋊C4C22×D312yes—
646Dic3⋊C4C22×D312yes—
647Dic3⋊C4C22×D312yes—
648Dic3⋊C4C22×D312yes—
649C4×Dic3—32no—
650C4×Dic3—32no—
651C4×Dic3—32no—
652C4×Dic3—32no—
653C4×Dic3—32no—
654C4×Dic3—32no—
655C4×Dic3—32no—
656C4×Dic3—32no—
657C4×Dic3—32no—
658C4×Dic3—32no—
659C4×Dic3—62no—
660C4×Dic3C22×D312yes—
661C22×C32—21no—
662C22×C32—21no—
663C22×C32—22no—
664C22×C32—22no—
665C22×C32C2511yescharacteristic
666C2×C3⋊D3—22no—
667C2×C3⋊D3—21no—
668C2×C3⋊D3—22no—
669C2×C3⋊D3—22no—
670C2×C3⋊D3—22no—
671C2×C3⋊D3—44no—
672C2×C3×D3—22no—
673C2×C3×D3—22no—
674C2×C3×D3—22no—
675C2×C3×D3—22no—
676C2×C3×D3—22no—
677C2×C3×D3—22no—
678D32—44no—
679C32×C4—22no—
680C32×C4—21no—
681C32×C4—22no—
682C3⋊Dic3—21no—
683C3⋊Dic3—21no—
684C3⋊Dic3—22no—
685C3⋊Dic3H(5,𝔽2)12yes—
686C3×Dic3—22no—
687C3×Dic3—22no—
688C3×Dic3—22no—
689C3×Dic3—22no—
690C3×Dic3—22no—
691C3×Dic3—22no—
692C2×#41—91no—
693C2×#41—92no—
694C2×#41—91no—
695C23×C4—91no—
696C23×C4—91no—
697C4⋊Q8—91no—
698C4⋊Q8—92no—
699#127—91no—
700#127—92no—
701#126—92no—
702#126—92no—
703#126—92no—
704#126—92no—
705#126—92no—
706#126—92no—
707#125—32no—
708#125—92no—
709#125—92no—
710#124—32no—
711#124—32no—
712#124—92no—
713#124—92no—
714#124—91no—
715#124—91no—
716#124—92no—
717#123—32no—
718#123—32no—
719#123—32no—
720#123—91no—
721#123—91no—
722#123—92no—
723#123—92no—
724#123—92no—
725#123—92no—
726#123—92no—
727#123—92no—
728#123—92no—
729#123—91no—
730#123D3211yescharacteristic, complemented
731C22⋊Q8—32no—
732C22⋊Q8—32no—
733C22⋊Q8—32no—
734C22⋊Q8—32no—
735C22⋊Q8—92no—
736C22⋊Q8—92no—
737C22⋊Q8—92no—
738C22⋊Q8—92no—
739C22⋊Q8—92no—
740#121—32no—
741#121—32no—
742#121—32no—
743#121—32no—
744#121—92no—
745#121—92no—
746#121—92no—
747#121—92no—
748#121—92no—
749#121—92no—
750#121—92no—
751#121—92no—
752#121—92no—
753#121—92no—
754#121—92no—
755#120—92no—
756#120—92no—
757#120—92no—
758#120—92no—
759#120—91no—
760#120—91no—
761#120—91no—
762#120—91no—
763C4×Q8—92no—
764C4×D4—92no—
765C4×D4—92no—
766C4×D4—92no—
767C4×D4—92no—
768C4×D4—92no—
769C4×D4—92no—
770C4×D4—92no—
771C4×D4—92no—
772C4×D4—92no—
773#117—92no—
774#117—91no—
775#117—92no—
776#117—91no—
777C2×C42—92no—
778C2×C42—91no—
779C23×C3—21no—
780C23×C3—21no—
781C23×C3—32no—
782C23×C3—32no—
783C23×C3C23×D312yes—
784C23×C3C23×D312yes—
785C22×D3—32no—
786C22×D3—32no—
787C22×D3—32no—
788C22×D3—62no—
789C22×D3—61no—
790C22×D3—122no—
791C22×D3—122no—
792C22×D3—122no—
793C22×D3—122no—
794C22×D3—122no—
795C22×D3—122no—
796C22×D3—124no—
797C22×D3—122no—
798C22×D3C23×D312yes—
799C22×D3C23×D312yes—
800C3×Q8—122no—
801C3×Q8—122no—
802C3×D4—42no—
803C3×D4—42no—
804C3×D4—122no—
805C3×D4—122no—
806C3×D4—122no—
807C3×D4—122no—
808C3×D4—122no—
809C2×C3×C4—22no—
810C2×C3×C4—22no—
811C2×C3×C4—21no—
812C2×C3×C4—32no—
813C2×C3×C4—32no—
814C2×C3×C4—32no—
815C2×C3×C4—32no—
816C2×C3×C4—32no—
817C2×C3×C4—32no—
818C2×C3×C4—42no—
819C2×C3×C4—42no—
820C2×C3×C4—122no—
821C2×C3×C4—122no—
822C2×C3×C4—122no—
823C2×C3×C4C23×D312yes—
824C2×C3×C4C23×D312yes—
825C2×C3×C4C23×D312yes—
826C2×C3×C4C23×D312yes—
827C2×C3×C4C23×D312yes—
828#67—42no—
829#67—42no—
830#67—42no—
831#67—42no—
832#67—122no—
833#67—122no—
834#67—122no—
835#67—122no—
836#67—122no—
837#67—122no—
838#67—122no—
839#67—122no—
840#67—122no—
841#67—122no—
842#67—122no—
843#67—122no—
844#67—122no—
845#67—124no—
846#67—122no—
847C2×Dic3—32no—
848C2×Dic3—32no—
849C2×Dic3—32no—
850C2×Dic3—32no—
851C2×Dic3—32no—
852C2×Dic3—42no—
853C2×Dic3—61no—
854C2×Dic3—61no—
855C2×Dic3—62no—
856C2×Dic3—61no—
857C2×Dic3—64no—
858C2×Dic3—64no—
859C2×Dic3—64no—
860C2×Dic3—64no—
861C2×Dic3—64no—
862C2×Dic3—122no—
863C2×Dic3—122no—
864C2×Dic3C23×D312yes—
865C2×Dic3C23×D312yes—
866C2×Dic3C23×D312yes—
867C2×Dic3C23×D312yes—
868C2×Dic3C23×D312yes—
869C2×Dic3C23×D312yes—
870D12—42no—
871D12—122no—
872D12—122no—
873D12—124no—
874D12—122no—
875D12—122no—
876D12—122no—
877D12—122no—
878D12—122no—
879C4×D3—42no—
880C4×D3—42no—
881C4×D3—64no—
882C4×D3—64no—
883C4×D3—64no—
884C4×D3—64no—
885C4×D3—64no—
886C4×D3—124no—
887C4×D3—122no—
888C4×D3—122no—
889C4×D3—122no—
890C4×D3—122no—
891C4×D3—124no—
892C4×D3—122no—
893Dic6—42no—
894Dic6—42no—
895Dic6—122no—
896Dic6—122no—
897Dic6—122no—
898C2×C32—41no—
899C2×C32—41no—
900C2×C32C2×H(5,𝔽2)11yescharacteristic
901C2×C32#58512yes—
902C3⋊D3—42no—
903C3⋊D3—41no—
904C3×D3—42no—
905C3×D3—42no—
906C24—91no—
907C24—91no—
908#41—362no—
909#41—362no—
910#41—364no—
911C2×Q8—32no—
912C2×Q8—32no—
913C2×Q8—91no—
914C2×Q8—91no—
915C2×D4—32no—
916C2×D4—32no—
917C2×D4—32no—
918C2×D4—32no—
919C2×D4—32no—
920C2×D4—92no—
921C2×D4—92no—
922C2×D4—92no—
923C2×D4—92no—
924C2×D4—92no—
925C2×D4—92no—
926C2×D4—91no—
927C2×D4—92no—
928C2×D4—91no—
929C2×D4—91no—
930C2×D4—92no—
931C2×D4C2×D3211yescharacteristic
932C22×C4—32no—
933C22×C4—32no—
934C22×C4—32no—
935C22×C4—91no—
936C22×C4—92no—
937C22×C4—92no—
938C22×C4—92no—
939C22×C4—91no—
940C22×C4—91no—
941C22×C4—91no—
942C22×C4—92no—
943C22×C4—92no—
944C22×C4—362no—
945C22×C4—362no—
946C22×C4C2×D3211yescharacteristic
947C4⋊C4—32no—
948C4⋊C4—32no—
949C4⋊C4—32no—
950C4⋊C4—32no—
951C4⋊C4—32no—
952C4⋊C4—32no—
953C4⋊C4—32no—
954C4⋊C4—32no—
955C4⋊C4—92no—
956C4⋊C4—92no—
957C4⋊C4—92no—
958C4⋊C4—92no—
959C4⋊C4—92no—
960C4⋊C4—92no—
961C4⋊C4—92no—
962C4⋊C4—92no—
963C4⋊C4—92no—
964C4⋊C4C2×D3212yes—
965C22⋊C4—32no—
966C22⋊C4—32no—
967C22⋊C4—32no—
968C22⋊C4—32no—
969C22⋊C4—32no—
970C22⋊C4—32no—
971C22⋊C4—32no—
972C22⋊C4—32no—
973C22⋊C4—32no—
974C22⋊C4—92no—
975C22⋊C4—91no—
976C22⋊C4—91no—
977C22⋊C4—92no—
978C22⋊C4—92no—
979C22⋊C4—92no—
980C22⋊C4—92no—
981C22⋊C4—92no—
982C22⋊C4—92no—
983C22⋊C4—92no—
984C22⋊C4—92no—
985C22⋊C4—91no—
986C22⋊C4—92no—
987C22⋊C4—92no—
988C22⋊C4—92no—
989C22⋊C4C2×D3211yescharacteristic
990C22⋊C4C2×D3212yes—
991C42—32no—
992C42—92no—
993C42—92no—
994C42—91no—
995C42—92no—
996C42—91no—
997C42—92no—
998C22×C3—22no—
999C22×C3—22no—
1000C22×C3—22no—
1001C22×C3—22no—
1002C22×C3—22no—
1003C22×C3—22no—
1004C22×C3—22no—
1005C22×C3—21no—
1006C22×C3—42no—
1007C22×C3—41no—
1008C22×C3—42no—
1009C22×C3—62no—
1010C22×C3—62no—
1011C22×C3—62no—
1012C22×C3—62no—
1013C22×C3—62no—
1014C22×C3—62no—
1015C22×C3C24×D312yes—
1016C2×D3—22no—
1017C2×D3—22no—
1018C2×D3—22no—
1019C2×D3—22no—
1020C2×D3—22no—
1021C2×D3—22no—
1022C2×D3—64no—
1023C2×D3—62no—
1024C2×D3—62no—
1025C2×D3—62no—
1026C2×D3—62no—
1027C2×D3—62no—
1028C2×D3—62no—
1029C2×D3—62no—
1030C2×D3—62no—
1031C2×D3—62no—
1032C2×D3—122no—
1033C2×D3—122no—
1034C2×D3—121no—
1035C2×D3—122no—
1036C2×D3—128no—
1037C2×D3—128no—
1038C2×D3—128no—
1039C3×C4—22no—
1040C3×C4—22no—
1041C3×C4—22no—
1042C3×C4—22no—
1043C3×C4—22no—
1044C3×C4—41no—
1045C3×C4—42no—
1046C3×C4—42no—
1047C3×C4—62no—
1048C3×C4—62no—
1049C3×C4—62no—
1050C3×C4—62no—
1051C3×C4—62no—
1052C3×C4—62no—
1053Dic3—22no—
1054Dic3—22no—
1055Dic3—22no—
1056Dic3—22no—
1057Dic3—22no—
1058Dic3—22no—
1059Dic3—34no—
1060Dic3—62no—
1061Dic3—62no—
1062Dic3—62no—
1063Dic3—62no—
1064Dic3—62no—
1065Dic3—62no—
1066Dic3—121no—
1067Dic3—122no—
1068C32#352911yescharacteristic, complemented, Sylow
1069C23—32no—
1070C23—32no—
1071C23—92no—
1072C23—91no—
1073C23—361no—
1074C23—362no—
1075C23—361no—
1076C23—362no—
1077C23C22×D3211yescharacteristic
1078C23C22×D3211yescharacteristic
1079Q8—122no—
1080Q8—122no—
1081Q8—361no—
1082Q8—361no—
1083D4—41no—
1084D4—122no—
1085D4—122no—
1086D4—122no—
1087D4—122no—
1088D4—122no—
1089D4—362no—
1090D4—362no—
1091D4—362no—
1092D4—362no—
1093D4—362no—
1094D4—362no—
1095D4—361no—
1096D4—361no—
1097D4—362no—
1098D4—361no—
1099D4—362no—
1100C2×C4—32no—
1101C2×C4—32no—
1102C2×C4—32no—
1103C2×C4—32no—
1104C2×C4—32no—
1105C2×C4—32no—
1106C2×C4—41no—
1107C2×C4—91no—
1108C2×C4—92no—
1109C2×C4—91no—
1110C2×C4—91no—
1111C2×C4—122no—
1112C2×C4—122no—
1113C2×C4—122no—
1114C2×C4—184no—
1115C2×C4—182no—
1116C2×C4—184no—
1117C2×C4—184no—
1118C2×C4—182no—
1119C2×C4—182no—
1120C2×C4—362no—
1121C2×C4—361no—
1122C2×C4—362no—
1123C2×C4C22×D3212yes—
1124C2×C4C22×D3211yescharacteristic
1125C2×C4C22×D3212yes—
1126C2×C3—21no—
1127C2×C3—22no—
1128C2×C3—42no—
1129C2×C3—42no—
1130C2×C3—42no—
1131C2×C3—81no—
1132C2×C3—122no—
1133C2×C3—122no—
1134C2×C3D3×H(5,𝔽2)12yes—
1135C2×C3#596612yes—
1136C2×C3#596812yes—
1137D3—42no—
1138D3—42no—
1139D3—124no—
1140D3—122no—
1141D3—122no—
1142D3—122no—
1143D3—241no—
1144C22—21no—
1145C22—21no—
1146C22—22no—
1147C22—22no—
1148C22—62no—
1149C22—62no—
1150C22—62no—
1151C22—62no—
1152C22—62no—
1153C22—62no—
1154C22—182no—
1155C22—181no—
1156C22—182no—
1157C22—182no—
1158C22—182no—
1159C22—364no—
1160C22—364no—
1161C22C23×D3211yescharacteristic
1162C4—22no—
1163C4—21no—
1164C4—22no—
1165C4—62no—
1166C4—62no—
1167C4—62no—
1168C4—62no—
1169C4—62no—
1170C4—62no—
1171C4—92no—
1172C4—181no—
1173C4—181no—
1174C4—182no—
1175C3—21no—
1176C3#8709312yescomplemented
1177C2—41no—
1178C2—41no—
1179C2—122no—
1180C2—122no—
1181C2—362no—
1182C2—361no—
1183C2#1059667511yescharacteristic
1184C2#1059669812yes—
subgroupG/H
center, FrattiniC22C23×D32
commutator, socle, cosocleC22×C32C25
FittingC32×#123C22
hypercenter#123D32
hypocenterC32#3529
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ #123

Complements

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

NH ≅ G/Ntype
1. #10596127C2semidirect
2. C3×#5667C2semidirect
3. #10595306C2semidirect
4. #10595264C2semidirect
5. #10595165C2semidirect
6. #10595091C2semidirect
7. #10594922C2semidirect
8. #10594811C2semidirect
9. #10594615C2semidirect
10. #10594585C2semidirect
11. #10594453C2semidirect
12. #10594339C2semidirect
13. #10594311C2semidirect
14. #10594308C2semidirect
15. #10594244C2semidirect
16. #10594178C2semidirect
17. #10594144C2semidirect
18. #10594111C2semidirect
19. #10594061C2semidirect
22. C22×C4×C3⋊D3C22semidirect
23. C2×#3805C22semidirect
24. C2×C4×D32C22semidirect
26. C32×#123C22semidirect
27. #64146C22semidirect
29. #64105C22semidirect
33. #64090C22semidirect
34. #64086C22semidirect
35. C3×#939C22semidirect
38. C3×#924C22semidirect
39. C3×#897C22semidirect
40. C3×#896C22semidirect
41. C3×#894C22semidirect
42. C3×#890C22semidirect
43. C3×#886C22semidirect
45. C3×#885C22semidirect
46. C3×#884C22semidirect
47. C3×#883C22semidirect
48. C3×#878C22semidirect
50. #63983C22semidirect
52. #63981C22semidirect
56. #63978C22semidirect
58. #63975C22semidirect
60. #67⋊Dic3C22semidirect
61. #67⋊Dic3C22semidirect
62. #63971C22semidirect
64. #63966C22semidirect
65. #63956C22semidirect
66. C2×Dic32C22semidirect
69. #63922C22semidirect
71. #63913C22semidirect
76. #63906C22semidirect
77. #63905C22semidirect
78. #63902C22semidirect
79. #63890C22semidirect
80. #63890C22semidirect
81. #63888C22semidirect
82. #63887C22semidirect
83. #63885C22semidirect
85. #63881C22semidirect
86. #63881C22semidirect
87. #63878C22semidirect
88. C4×D3×Dic3C22semidirect
89. #63871C22semidirect
90. #63867C22semidirect
92. #63858C22semidirect
93. #63858C22semidirect
94. #63857C22semidirect
96. #63853C22semidirect
99. #63849C22semidirect
100. #63849C22semidirect
101. #63848C22semidirect
102. #63848C22semidirect
103. #63848C22semidirect
104. #63846C22semidirect
105. #63843C22semidirect
106. #63840C22semidirect
107. #63839C22semidirect
116. #5667D3semidirect
248. C3×#123C2×D3semidirect
272. #939C2×D3semidirect
298. #924C2×D3semidirect
311. #897C2×D3semidirect
316. #896C2×D3semidirect
325. #894C2×D3semidirect
337. #890C2×D3semidirect
346. #886C2×D3semidirect
352. #885C2×D3semidirect
361. #884C2×D3semidirect
367. #883C2×D3semidirect
391. #878C2×D3semidirect
730. #123D32semidirect
1068. C32#3529semidirect
1176. C3#87093semidirect

Maximal subgroups

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

subgroupindex
#105961272
C3×#56672
#105953062
#105952642
#105951652
#105950912
#105949222
#105948112
#105946152
#105945852
#105944532
#105943392
#105943112
#105943082
#105942442
#105941782
#105941442
#105941112
#105940612
#870933