Finite Group Databasebeta

← #11911012

Subgroups — #11911012

Order 1152.

2503 conjugacy classes of subgroups.

The subgroup lattice has 1276 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64092C211yesmaximal, characteristic, complemented
2C3×#5490C212yesmaximal, complemented
3#10595526C212yesmaximal, complemented
4#10595518C211yesmaximal, characteristic, complemented
5#10595508C211yesmaximal, characteristic, complemented
6#10595081C211yesmaximal, characteristic, complemented
7#10595068C212yesmaximal, complemented
8#10595044C211yesmaximal, characteristic, complemented
9#10595016C211yesmaximal, characteristic, complemented
10#10594994C211yesmaximal, characteristic, complemented
11#10594962C212yesmaximal, complemented
12#10594300C212yesmaximal, complemented
13#10594278C212yesmaximal, complemented
14#10594263C212yesmaximal, complemented
15#10594240C212yesmaximal, complemented
16#10594233C212yesmaximal, complemented
17#10594196C212yesmaximal, complemented
18#10594100C212yesmaximal, complemented
19#10594041C212yesmaximal, complemented
20#86669—32nomaximal
21C22×#638C2211yescharacteristic
22C22×C4×C3⋊D3C2211yescharacteristic, complemented
23C22×C3×#67C2212yescomplemented
24C2×C3×#235C2212yescomplemented
25C2×#3811C2212yescomplemented
26C2×D3×#67C2212yescomplemented
27C2×#3802C2211yescharacteristic, complemented
28C2×#3798C2211yescharacteristic, complemented
29C2×C32×C22⋊C4C2211yescharacteristic, complemented
30C2×#3757C2211yescharacteristic, complemented
31C2×#3752C2211yescharacteristic, complemented
32C2×C4⋊(C3⋊Dic3)C2211yescharacteristic, complemented
33C2×#3750C2211yescharacteristic, complemented
34#64092C2212yescomplemented
35#64092C2212yescomplemented
36#64092C2212yescomplemented
37#64092C2212yescomplemented
38C3×#953C2212yescomplemented
39C3×#930C2212yescomplemented
40C3×#929C2212yescomplemented
41C3×C4×#67C2212yescomplemented
42C3×#885C2212yescomplemented
43C3×#884C2212yescomplemented
44C3×#884C2212yescomplemented
45C3×#883C2212yescomplemented
46C3×#882C2212yescomplemented
47C3×#67⋊C4C2212yescomplemented
48C3×D3×C22⋊C4C2212yescomplemented
49C3×#878C2212yescomplemented
50#63983C2212yes—
51#63982C2211yescharacteristic, complemented
52#63981C2212yescomplemented
53#63980C2211yescharacteristic
54#63980C2211yescharacteristic, complemented
55#63980C2212yescomplemented
56#63980C2212yescomplemented
57#63980C2211yescharacteristic, complemented
58#63979C2212yescomplemented
59#63978C2212yescomplemented
60#63977C2212yescomplemented
61#63976C2212yescomplemented
62#63976C2212yescomplemented
63#67⋊Dic3C2212yescomplemented
64#67⋊Dic3C2212yescomplemented
65#63971C2212yescomplemented
66#63970C2212yescomplemented
67#63969C2212yescomplemented
68#63961C2212yescomplemented
69#63961C2212yescomplemented
70#63959C2212yescomplemented
71#63958C2212yes—
72#63956C2212yescomplemented
73#63952C2212yescomplemented
74#63922C2212yescomplemented
75#63921C2212yescomplemented
76D3×(C2×D3)⋊C4C2212yescomplemented
77#63916C2212yescomplemented
78#63912C2211yescharacteristic, complemented
79#63912C2211yescharacteristic, complemented
80#63912C2211yescharacteristic, complemented
81#63908C2212yescomplemented
82#63908C2212yescomplemented
83#63907C2212yescomplemented
84#63906C2212yescomplemented
85#63905C2212yescomplemented
86#63904C2212yescomplemented
87C4×#626C2212yescomplemented
88#63900C2211yescharacteristic, complemented
89#63893C2212yescomplemented
90#63891C2212yescomplemented
91#63888C2212yescomplemented
92#63886C2212yescomplemented
93#63885C2212yescomplemented
94#63884C2212yescomplemented
95#63879C2212yescomplemented
96#63877C2212yescomplemented
97#63874C2211yescharacteristic, complemented
98#63865C2211yescharacteristic, complemented
99#63861C2212yescomplemented
100#63859C2212yescomplemented
101#63858C2212yescomplemented
102#63856C2212yescomplemented
103#63856C2212yescomplemented
104#63853C2212yescomplemented
105#63850C2212yescomplemented
106#63847C2212yescomplemented
107#63845C2212yescomplemented
108C3×#546—32no—
109#5833—32no—
110#5829—32no—
111#5804—32no—
112D4×#67—32no—
113#5679—32no—
114#5678—32no—
115#5666—32no—
116#5665—32no—
117#5660—32no—
118#5654—32no—
119#5647—32no—
120#5638—32no—
121#5621—32no—
122#5615—32no—
123#5612—32no—
124#5605—32no—
125D3×#121—32no—
126#5601—32no—
127#5595—32no—
128#5593—32no—
129#5590—32no—
130#5589—32no—
131#5562—32no—
132#5556—32no—
133#5547—32no—
134#5540—32no—
135#5494—32no—
136#5490—32no—
137#5490D312yescomplemented
138C2×#883—32no—
139C2×#883—61no—
140C24×C32C2311yescharacteristic
141C23×C3⋊D3C2311yescharacteristic
142C23×C3×D3C2312yes—
143C22×D32C2312yes—
144C22×C32×C4C2311yescharacteristic
145C22×C32×C4C2311yescharacteristic
146C2×#638—42no—
147C2×#638C2312yes—
148C2×#638C2312yes—
149C22×C3⋊Dic3C2311yescharacteristic
150C22×C3⋊Dic3C2311yescharacteristic
151C22×C3⋊Dic3C2311yescharacteristic
152C2×C4×C3⋊D3—42no—
153C2×C4×C3⋊D3C2311yescharacteristic
154C2×C4×C3⋊D3C2311yescharacteristic
155C2×C4×C3⋊D3C2311yescharacteristic
156C2×C4×C3⋊D3C2311yescharacteristic
157C2×C3×#67—44no—
158C2×C3×#67C2312yes—
159C2×C3×#67C2312yes—
160C2×C3×#67C2312yes—
161C2×C3×#67C2312yes—
162C2×C3×#67C2312yes—
163C2×C3×#67C2312yes—
164C2×C3×#67C2312yes—
165C22×C3×Dic3C2312yes—
166C3×#235—44no—
167C2×C3×D12C2312yes—
168C2×C3×D12C2312yes—
169C2×C3×C4×D3C2312yes—
170C2×C3×C4×D3C2312yes—
171C2×C3×C4×D3C2312yes—
172C2×C3×Dic6C2312yes—
173#3811—44no—
174D3×#67—44no—
175C2×#627C2311yescharacteristic
176C2×#626C2312yes—
177C2×#626C2312yes—
178C2×#626C2312yes—
179C2×#626C2312yes—
180C2×#625C2311yescharacteristic
181C2×#625C2311yescharacteristic
182C2×#625C2311yescharacteristic
183C2×#625C2312yes—
184C2×#625C2312yes—
185C2×#624C2312yes—
186C2×D3×Dic3C2312yes—
187C2×D3×Dic3C2312yes—
188#3802—42no—
189#3798—42no—
190C32×C22⋊C4C2312yes—
191C32×C22⋊C4C2312yes—
192#3757C2312yes—
193#3757C2312yes—
194#3752C2312yes—
195#3752C2312yes—
196C4⋊(C3⋊Dic3)C2312yes—
197C4⋊(C3⋊Dic3)C2312yes—
198#3750C2312yes—
199#3750C2312yes—
200C3×#217C2312yes—
201C3×#217C2312yes—
202C3×#217C2312yes—
203C3×(C2×D3)⋊C4C2312yes—
204C3×(C2×D3)⋊C4C2312yes—
205C3×(C2×D3)⋊C4C2312yes—
206C3×(C2×D3)⋊C4C2312yes—
207C3×(C2×D3)⋊C4C2312yes—
208C3×C4⋊Dic3C2312yes—
209C3×Dic3⋊C4C2312yes—
210C3×Dic3⋊C4C2312yes—
211C3×Dic3⋊C4C2312yes—
212C3×C4×Dic3C2312yes—
213#3724C2311yescharacteristic
214#3724C2312yes—
215#3724C2312yes—
216#3724C2311yescharacteristic
217#3724C2311yescharacteristic
218#3724C2311yescharacteristic
219Dic3⋊Dic3C2312yes—
220Dic3⋊Dic3C2312yes—
221Dic3⋊Dic3C2312yes—
222#3722C2312yes—
223#3722C2312yes—
224(C2×D3)⋊Dic3C2312yes—
225(C2×D3)⋊Dic3C2312yes—
226(C2×D3)⋊Dic3C2312yes—
227(C2×D3)⋊Dic3C2312yes—
228(C2×D3)⋊Dic3C2312yes—
229(C2×D3)⋊Dic3C2312yes—
230(C2×D3)⋊Dic3C2312yes—
231(C2×D3)⋊Dic3C2312yes—
232(C2×D3)⋊Dic3C2312yes—
233Dic32C2312yes—
234Dic32C2312yes—
235#3534—91noSylow
236C2×C3×#41—32no—
237C22×C3×D4—32no—
238C22×#67—32no—
239C22×#67—32no—
240C22×#67—61no—
241C22×#67C2×D312yescomplemented
242C2×D3×D4—32no—
243C2×D3×D4—32no—
244C2×D3×D4—32no—
245C2×D3×D4—32no—
246C2×#235—32no—
247C2×#235C2×D312yescomplemented
248C22×C4×D3—32no—
249C22×C4×D3—61no—
250C3×#124—32no—
251C3×#123—32no—
252C3×#123—32no—
253C3×C22⋊Q8—32no—
254C3×#121—32no—
255C3×#121—32no—
256C3×#121—32no—
257C3×#120—32no—
258C3×#120—32no—
259C3×C4×D4—32no—
260C3×C4×D4—32no—
261C2×C3×C22⋊C4—21no—
262C2×C3×C22⋊C4—32no—
263C2×C3×C22⋊C4C2×D312yescomplemented
264#953—32no—
265#953—32no—
266#953—32no—
267#953C2×D312yescomplemented
268C2×#217—32no—
269C2×#217—61no—
270#947—32no—
271#946—32no—
272#946—32no—
273#946—32no—
274#940—32no—
275#940—32no—
276#939—32no—
277#939—32no—
278#939—32no—
279#939—32no—
280#939—32no—
281#939—32no—
282#939—32no—
283#939—32no—
284#939—32no—
285#939—32no—
286#939—32no—
287#939—32no—
288#938—32no—
289#938—32no—
290#938—32no—
291#938—32no—
292#938—32no—
293#937—32no—
294#937—32no—
295#937—32no—
296#937—32no—
297#937—32no—
298#937—32no—
299#936—32no—
300#935—32no—
301#935—32no—
302#935—32no—
303#935—32no—
304D4×Dic3—32no—
305D4×Dic3—32no—
306#930—32no—
307#930—32no—
308#930—32no—
309#930—32no—
310#930C2×D312yescomplemented
311#929—32no—
312#929—32no—
313#929—32no—
314#929—32no—
315#929C2×D312yescomplemented
316C4×#67—32no—
317C4×#67—32no—
318C4×#67—32no—
319C4×#67—32no—
320C4×#67C2×D312yescomplemented
321C2×(C2×D3)⋊C4—32no—
322C2×(C2×D3)⋊C4—32no—
323C2×(C2×D3)⋊C4—61no—
324C2×C4⋊Dic3—32no—
325C2×C4⋊Dic3—61no—
326#924—32no—
327#924—32no—
328C2×Dic3⋊C4—32no—
329C2×Dic3⋊C4—61no—
330#898—32no—
331#898—32no—
332#897—32no—
333#896—32no—
334#896—32no—
335#895—32no—
336#895—32no—
337#894—32no—
338#894—32no—
339#894—32no—
340#893—32no—
341D3×C4⋊C4—32no—
342#890—32no—
343#889—32no—
344#889—32no—
345#889—32no—
346#886—32no—
347#885—32no—
348#885—32no—
349#885C2×D312yescomplemented
350#884—32no—
351#884—32no—
352#884—32no—
353#884—32no—
354#884—32no—
355#884—32no—
356#884—32no—
357#884C2×D312yescomplemented
358#884C2×D312yescomplemented
359#883—32no—
360#883—32no—
361#883—32no—
362#883—32no—
363#883—32no—
364#883—32no—
365#883—32no—
366#883—32no—
367#883—32no—
368#883—32no—
369#883—32no—
370#883—32no—
371#883—62no—
372#883—62no—
373#883—62no—
374#883—62no—
375#883C2×D312yescomplemented
376#882—32no—
377#882—32no—
378#882—32no—
379#882C2×D312yescomplemented
380#67⋊C4—32no—
381#67⋊C4—32no—
382#67⋊C4—32no—
383#67⋊C4—32no—
384#67⋊C4C2×D312yescomplemented
385D3×C22⋊C4—32no—
386D3×C22⋊C4—32no—
387D3×C22⋊C4—32no—
388D3×C22⋊C4C2×D312yescomplemented
389#879—32no—
390#879—32no—
391#879—32no—
392#879—32no—
393#879—32no—
394#878—32no—
395#878—32no—
396#878C2×D312yescomplemented
397#877—32no—
398#876—32no—
399C4×D12—32no—
400#872—32no—
401#872—32no—
402C23×C32—22no—
403C23×C32—41no—
404C23×C32—41no—
405C23×C32C2412yes—
406C23×C32C2411yescharacteristic
407C22×C3⋊D3—22no—
408C22×C3⋊D3—22no—
409C22×C3⋊D3—41no—
410C22×C3⋊D3C2411yescharacteristic
411C22×C3⋊D3C2411yescharacteristic
412C22×C3×D3—42no—
413C22×C3×D3—42no—
414C22×C3×D3—42no—
415C22×C3×D3C2412yes—
416C22×C3×D3C2412yes—
417C22×C3×D3C2412yes—
418C2×D32—24no—
419C2×D32—42no—
420C2×D32—42no—
421C2×C32×C4—22no—
422C2×C32×C4—41no—
423C2×C32×C4C2411yescharacteristic
424C2×C32×C4C2411yescharacteristic
425C2×C32×C4C2412yes—
426#638—24no—
427#638—42no—
428C2×C3⋊Dic3—41no—
429C2×C3⋊Dic3—41no—
430C2×C3⋊Dic3—41no—
431C2×C3⋊Dic3C2412yes—
432C2×C3⋊Dic3C2412yes—
433C2×C3⋊Dic3C2411yescharacteristic
434C2×C3⋊Dic3C2411yescharacteristic
435C4×C3⋊D3—22no—
436C4×C3⋊D3—22no—
437C4×C3⋊D3—41no—
438C4×C3⋊D3—41no—
439C3×#67—24no—
440C3×#67—24no—
441C3×#67—24no—
442C3×#67—42no—
443C3×#67—42no—
444C3×#67—42no—
445C3×#67—42no—
446C2×C3×Dic3—42no—
447C2×C3×Dic3C2412yes—
448C2×C3×Dic3C2412yes—
449C2×C3×Dic3C2412yes—
450C2×C3×Dic3C2412yes—
451C2×C3×Dic3C2412yes—
452C3×D12—42no—
453C3×D12—42no—
454C3×C4×D3—42no—
455C3×C4×D3—42no—
456C3×C4×D3—42no—
457C3×Dic6—42no—
458#627—41no—
459#626—24no—
460#626—42no—
461#626—42no—
462#626—42no—
463#625—41no—
464#625—41no—
465#625—41no—
466#625—42no—
467#625—42no—
468#624—42no—
469D3×Dic3—42no—
470D3×Dic3—42no—
471#562—92no—
472#560—92no—
473#553—92no—
474#551—92no—
475#546—32no—
476#546—92no—
477#546—92no—
478D42—92no—
479#540—92no—
480#539—92no—
481#539—91no—
482#538—92no—
483#538—91no—
484#537—91no—
485#534—92no—
486#534—91no—
487#525—91no—
488C2×#123—91no—
489C2×#121—91no—
490C24×C3—21no—
491C24×C3—32no—
492C24×C3C22×D312yes—
493C23×D3—32no—
494C23×D3—32no—
495C23×D3—32no—
496C23×D3—61no—
497C23×D3C22×D312yes—
498C3×#41—124no—
499C2×C3×Q8—32no—
500C2×C3×D4—32no—
501C2×C3×D4—32no—
502C2×C3×D4—32no—
503C2×C3×D4—32no—
504C2×C3×D4—32no—
505C2×C3×D4—32no—
506C2×C3×D4—32no—
507C2×C3×D4—32no—
508C2×C3×D4—32no—
509C2×C3×D4—124no—
510C22×C3×C4—21no—
511C22×C3×C4—21no—
512C22×C3×C4—32no—
513C22×C3×C4—32no—
514C22×C3×C4—32no—
515C22×C3×C4—32no—
516C22×C3×C4C22×D312yes—
517C22×C3×C4C22×D312yes—
518C2×#67—32no—
519C2×#67—32no—
520C2×#67—32no—
521C2×#67—32no—
522C2×#67—32no—
523C2×#67—32no—
524C2×#67—32no—
525C2×#67—32no—
526C2×#67—32no—
527C2×#67—32no—
528C2×#67—32no—
529C2×#67—32no—
530C2×#67—32no—
531C2×#67—32no—
532C2×#67—32no—
533C2×#67—44no—
534C2×#67—62no—
535C2×#67—62no—
536C2×#67—124no—
537C2×#67—124no—
538C2×#67—124no—
539C2×#67C22×D312yes—
540C2×#67C22×D312yes—
541C2×#67C22×D312yes—
542C2×#67C22×D312yes—
543C2×#67C22×D312yes—
544C2×#67C22×D312yes—
545C2×#67C22×D312yes—
546C22×Dic3—32no—
547C22×Dic3—32no—
548C22×Dic3—32no—
549C22×Dic3—32no—
550C22×Dic3—32no—
551C22×Dic3—61no—
552C22×Dic3—61no—
553C22×Dic3—61no—
554C22×Dic3C22×D312yes—
555D3×D4—124no—
556D3×D4—124no—
557D3×D4—124no—
558D3×D4—124no—
559#235—44no—
560#235—124no—
561C2×D12—32no—
562C2×D12—32no—
563C2×D12—32no—
564C2×D12—32no—
565C2×D12C22×D312yes—
566C2×D12C22×D312yes—
567C2×C4×D3—32no—
568C2×C4×D3—32no—
569C2×C4×D3—32no—
570C2×C4×D3—32no—
571C2×C4×D3—32no—
572C2×C4×D3—32no—
573C2×C4×D3—32no—
574C2×C4×D3—32no—
575C2×C4×D3—61no—
576C2×C4×D3—61no—
577C2×C4×D3—61no—
578C2×C4×D3—61no—
579C2×C4×D3—124no—
580C2×C4×D3—124no—
581C2×C4×D3C22×D312yes—
582C2×C4×D3C22×D312yes—
583C2×C4×D3C22×D312yes—
584C2×Dic6—32no—
585C2×Dic6C22×D312yes—
586C3×C4⋊C4—32no—
587C3×C4⋊C4—32no—
588C3×C4⋊C4—32no—
589C3×C4⋊C4—32no—
590C3×C22⋊C4—22no—
591C3×C22⋊C4—22no—
592C3×C22⋊C4—32no—
593C3×C22⋊C4—32no—
594C3×C22⋊C4—32no—
595C3×C22⋊C4—32no—
596C3×C22⋊C4—32no—
597C3×C22⋊C4—32no—
598C3×C22⋊C4—32no—
599C3×C22⋊C4—32no—
600C3×C22⋊C4C22×D312yes—
601C3×C22⋊C4C22×D312yes—
602C3×C22⋊C4C22×D312yes—
603C3×C22⋊C4C22×D312yes—
604C3×C42—32no—
605#217—32no—
606#217—32no—
607#217—32no—
608#217—32no—
609#217—32no—
610#217—32no—
611#217—32no—
612#217—32no—
613#217—32no—
614#217—32no—
615#217—32no—
616#217—32no—
617#217—32no—
618#217—62no—
619#217—62no—
620#217C22×D312yes—
621#217C22×D312yes—
622#217C22×D312yes—
623(C2×D3)⋊C4—32no—
624(C2×D3)⋊C4—32no—
625(C2×D3)⋊C4—32no—
626(C2×D3)⋊C4—32no—
627(C2×D3)⋊C4—32no—
628(C2×D3)⋊C4—32no—
629(C2×D3)⋊C4—32no—
630(C2×D3)⋊C4—32no—
631(C2×D3)⋊C4—32no—
632(C2×D3)⋊C4—32no—
633(C2×D3)⋊C4—32no—
634(C2×D3)⋊C4—32no—
635(C2×D3)⋊C4—32no—
636(C2×D3)⋊C4—32no—
637(C2×D3)⋊C4—32no—
638(C2×D3)⋊C4—32no—
639(C2×D3)⋊C4—32no—
640(C2×D3)⋊C4—62no—
641(C2×D3)⋊C4—62no—
642(C2×D3)⋊C4C22×D312yes—
643(C2×D3)⋊C4C22×D312yes—
644(C2×D3)⋊C4C22×D312yes—
645(C2×D3)⋊C4C22×D312yes—
646(C2×D3)⋊C4C22×D312yes—
647C4⋊Dic3—32no—
648C4⋊Dic3—32no—
649C4⋊Dic3—32no—
650C4⋊Dic3—32no—
651C4⋊Dic3—32no—
652C4⋊Dic3—32no—
653C4⋊Dic3—32no—
654C4⋊Dic3—62no—
655C4⋊Dic3—62no—
656C4⋊Dic3C22×D312yes—
657Dic3⋊C4—32no—
658Dic3⋊C4—32no—
659Dic3⋊C4—32no—
660Dic3⋊C4—32no—
661Dic3⋊C4—32no—
662Dic3⋊C4—32no—
663Dic3⋊C4—32no—
664Dic3⋊C4—32no—
665Dic3⋊C4—32no—
666Dic3⋊C4—32no—
667Dic3⋊C4—32no—
668Dic3⋊C4—32no—
669Dic3⋊C4—32no—
670Dic3⋊C4—32no—
671Dic3⋊C4—32no—
672Dic3⋊C4—62no—
673Dic3⋊C4—62no—
674Dic3⋊C4C22×D312yes—
675Dic3⋊C4C22×D312yes—
676Dic3⋊C4C22×D312yes—
677C4×Dic3—32no—
678C4×Dic3—32no—
679C4×Dic3—32no—
680C4×Dic3—32no—
681C4×Dic3C22×D312yes—
682C22×C32—21no—
683C22×C32—21no—
684C22×C32—22no—
685C22×C32—22no—
686C22×C32—22no—
687C22×C32—82no—
688C22×C32H(5,𝔽2)12yes—
689C22×C32C2511yescharacteristic
690C2×C3⋊D3—21no—
691C2×C3⋊D3—21no—
692C2×C3⋊D3—21no—
693C2×C3⋊D3—21no—
694C2×C3⋊D3—21no—
695C2×C3⋊D3—44no—
696C2×C3⋊D3H(5,𝔽2)12yes—
697C2×C3×D3—22no—
698C2×C3×D3—22no—
699C2×C3×D3—22no—
700C2×C3×D3—22no—
701C2×C3×D3—22no—
702C2×C3×D3—22no—
703C2×C3×D3—22no—
704C2×C3×D3—22no—
705C2×C3×D3—22no—
706C2×C3×D3—84no—
707D32—84no—
708C32×C4—22no—
709C32×C4—21no—
710C32×C4—21no—
711C3⋊Dic3—22no—
712C3⋊Dic3—21no—
713C3⋊Dic3—21no—
714C3⋊Dic3—22no—
715C3×Dic3—22no—
716C3×Dic3—22no—
717C3×Dic3—22no—
718C3×Dic3—22no—
719C3×Dic3—22no—
720C2×#41—32no—
721C2×#41—91no—
722C22×D4—32no—
723C22×D4—91no—
724C22×D4—92no—
725C22×D4—92no—
726C22×D4—91no—
727C23×C4—91no—
728#127—92no—
729#126—92no—
730#126—92no—
731#126—92no—
732#126—92no—
733#125—92no—
734#125—92no—
735#124—32no—
736#124—92no—
737#124—92no—
738#123—32no—
739#123—32no—
740#123—92no—
741#123—92no—
742#123—92no—
743#123—92no—
744#123—92no—
745#123—92no—
746#123—92no—
747#123—92no—
748#123—92no—
749#123—92no—
750#123—92no—
751#123—92no—
752C22⋊Q8—32no—
753C22⋊Q8—91no—
754C22⋊Q8—92no—
755C22⋊Q8—91no—
756C22⋊Q8—92no—
757C22⋊Q8—92no—
758C22⋊Q8—92no—
759#121—32no—
760#121—32no—
761#121—32no—
762#121—91no—
763#121—91no—
764#121—91no—
765#121—92no—
766#121—92no—
767#121—92no—
768#121—92no—
769#121—92no—
770#121—92no—
771#121—92no—
772#121—92no—
773#121—92no—
774#121—91no—
775#121—91no—
776#121—91no—
777#121—92no—
778#121—92no—
779#121—92no—
780#120—32no—
781#120—32no—
782#120—92no—
783#120—92no—
784#120—92no—
785#120—92no—
786#120—92no—
787#120—92no—
788C4×D4—32no—
789C4×D4—32no—
790C4×D4—92no—
791C4×D4—92no—
792C4×D4—92no—
793C4×D4—92no—
794C4×D4—92no—
795C4×D4—92no—
796#117—91no—
797#117—92no—
798C2×C4⋊C4—91no—
799C2×C4⋊C4—91no—
800C2×C4⋊C4—91no—
801C2×C22⋊C4—32no—
802C2×C22⋊C4—92no—
803C2×C22⋊C4—92no—
804C2×C22⋊C4—91no—
805C2×C22⋊C4—91no—
806C2×C22⋊C4D3211yescharacteristic, complemented
807C23×C3—24no—
808C23×C3—21no—
809C23×C3—22no—
810C23×C3—32no—
811C23×C3—32no—
812C23×C3—32no—
813C23×C3—42no—
814C23×C3—42no—
815C23×C3—42no—
816C23×C3—42no—
817C23×C3—42no—
818C23×C3—122no—
819C23×C3—122no—
820C23×C3—122no—
821C23×C3C23×D312yes—
822C23×C3C23×D312yes—
823C23×C3C23×D312yes—
824C22×D3—32no—
825C22×D3—32no—
826C22×D3—42no—
827C22×D3—42no—
828C22×D3—42no—
829C22×D3—61no—
830C22×D3—61no—
831C22×D3—64no—
832C22×D3—64no—
833C22×D3—64no—
834C22×D3—64no—
835C22×D3—64no—
836C22×D3—122no—
837C22×D3—122no—
838C22×D3—122no—
839C22×D3—122no—
840C22×D3—122no—
841C22×D3—122no—
842C22×D3—122no—
843C22×D3C23×D312yes—
844C22×D3C23×D312yes—
845C22×D3C23×D312yes—
846C3×Q8—122no—
847C3×D4—64no—
848C3×D4—64no—
849C3×D4—64no—
850C3×D4—122no—
851C3×D4—122no—
852C3×D4—122no—
853C3×D4—122no—
854C3×D4—122no—
855C3×D4—122no—
856C2×C3×C4—24no—
857C2×C3×C4—21no—
858C2×C3×C4—21no—
859C2×C3×C4—22no—
860C2×C3×C4—32no—
861C2×C3×C4—32no—
862C2×C3×C4—32no—
863C2×C3×C4—32no—
864C2×C3×C4—32no—
865C2×C3×C4—42no—
866C2×C3×C4—42no—
867C2×C3×C4—42no—
868C2×C3×C4—122no—
869C2×C3×C4—122no—
870C2×C3×C4—122no—
871C2×C3×C4—122no—
872C2×C3×C4C23×D312yes—
873C2×C3×C4C23×D312yes—
874C2×C3×C4C23×D312yes—
875C2×C3×C4C23×D312yes—
876#67—24no—
877#67—24no—
878#67—24no—
879#67—42no—
880#67—42no—
881#67—42no—
882#67—42no—
883#67—64no—
884#67—64no—
885#67—64no—
886#67—124no—
887#67—122no—
888#67—122no—
889#67—122no—
890#67—122no—
891#67—122no—
892#67—122no—
893#67—122no—
894#67—122no—
895#67—122no—
896#67—122no—
897#67—122no—
898#67—122no—
899#67—124no—
900C2×Dic3—32no—
901C2×Dic3—32no—
902C2×Dic3—32no—
903C2×Dic3—32no—
904C2×Dic3—32no—
905C2×Dic3—32no—
906C2×Dic3—42no—
907C2×Dic3—62no—
908C2×Dic3—62no—
909C2×Dic3—61no—
910C2×Dic3—61no—
911C2×Dic3—122no—
912C2×Dic3—122no—
913C2×Dic3—122no—
914C2×Dic3—122no—
915C2×Dic3—122no—
916C2×Dic3—122no—
917C2×Dic3—122no—
918C2×Dic3—122no—
919C2×Dic3C23×D312yes—
920C2×Dic3C23×D312yes—
921C2×Dic3C23×D312yes—
922C2×Dic3C23×D312yes—
923C2×Dic3C23×D312yes—
924D12—42no—
925D12—42no—
926D12—64no—
927D12—122no—
928D12—122no—
929D12—122no—
930C4×D3—42no—
931C4×D3—42no—
932C4×D3—42no—
933C4×D3—64no—
934C4×D3—64no—
935C4×D3—122no—
936C4×D3—122no—
937C4×D3—122no—
938C4×D3—122no—
939C4×D3—122no—
940C4×D3—122no—
941C4×D3—122no—
942C4×D3—122no—
943C4×D3—122no—
944C4×D3—122no—
945Dic6—42no—
946Dic6—122no—
947C2×C32—22no—
948C2×C32—42no—
949C2×C32C2×H(5,𝔽2)11yescharacteristic
950C2×C32C2×H(5,𝔽2)11yescharacteristic
951C2×C32#58511yescharacteristic
952C3⋊D3—22no—
953C3⋊D3—41no—
954C3×D3—42no—
955C3×D3—42no—
956C3×D3—42no—
957C24—32no—
958C24—92no—
959C24—91no—
960C24C2×D3211yescharacteristic
961#41—124no—
962#41—362no—
963C2×Q8—32no—
964C2×Q8—91no—
965C2×D4—32no—
966C2×D4—32no—
967C2×D4—32no—
968C2×D4—32no—
969C2×D4—32no—
970C2×D4—32no—
971C2×D4—32no—
972C2×D4—32no—
973C2×D4—32no—
974C2×D4—92no—
975C2×D4—92no—
976C2×D4—92no—
977C2×D4—92no—
978C2×D4—92no—
979C2×D4—92no—
980C2×D4—91no—
981C2×D4—91no—
982C2×D4—91no—
983C2×D4—92no—
984C2×D4—92no—
985C2×D4—124no—
986C2×D4—362no—
987C2×D4—364no—
988C2×D4—364no—
989C2×D4—362no—
990C22×C4—32no—
991C22×C4—32no—
992C22×C4—32no—
993C22×C4—32no—
994C22×C4—92no—
995C22×C4—92no—
996C22×C4—92no—
997C22×C4—91no—
998C22×C4—91no—
999C22×C4—91no—
1000C22×C4—91no—
1001C22×C4—91no—
1002C22×C4—91no—
1003C22×C4—91no—
1004C22×C4—362no—
1005C22×C4C2×D3211yescharacteristic
1006C22×C4C2×D3211yescharacteristic
1007C4⋊C4—32no—
1008C4⋊C4—32no—
1009C4⋊C4—32no—
1010C4⋊C4—32no—
1011C4⋊C4—91no—
1012C4⋊C4—91no—
1013C4⋊C4—91no—
1014C4⋊C4—92no—
1015C4⋊C4—91no—
1016C4⋊C4—92no—
1017C4⋊C4—92no—
1018C4⋊C4—92no—
1019C4⋊C4—92no—
1020C4⋊C4—92no—
1021C4⋊C4—92no—
1022C4⋊C4—92no—
1023C4⋊C4—92no—
1024C22⋊C4—32no—
1025C22⋊C4—32no—
1026C22⋊C4—32no—
1027C22⋊C4—32no—
1028C22⋊C4—32no—
1029C22⋊C4—32no—
1030C22⋊C4—32no—
1031C22⋊C4—32no—
1032C22⋊C4—92no—
1033C22⋊C4—92no—
1034C22⋊C4—92no—
1035C22⋊C4—92no—
1036C22⋊C4—92no—
1037C22⋊C4—92no—
1038C22⋊C4—92no—
1039C22⋊C4—92no—
1040C22⋊C4—92no—
1041C22⋊C4—92no—
1042C22⋊C4—92no—
1043C22⋊C4—92no—
1044C22⋊C4—92no—
1045C22⋊C4—92no—
1046C22⋊C4—92no—
1047C22⋊C4C2×D3212yes—
1048C22⋊C4C2×D3212yes—
1049C42—32no—
1050C42—92no—
1051C42—92no—
1052C22×C3—22no—
1053C22×C3—22no—
1054C22×C3—22no—
1055C22×C3—22no—
1056C22×C3—22no—
1057C22×C3—22no—
1058C22×C3—22no—
1059C22×C3—22no—
1060C22×C3—22no—
1061C22×C3—22no—
1062C22×C3—22no—
1063C22×C3—21no—
1064C22×C3—42no—
1065C22×C3—42no—
1066C22×C3—42no—
1067C22×C3—62no—
1068C22×C3—62no—
1069C22×C3—62no—
1070C22×C3—62no—
1071C22×C3—62no—
1072C22×C3—62no—
1073C22×C3—62no—
1074C22×C3—62no—
1075C22×C3—62no—
1076C22×C3—84no—
1077C22×C3—84no—
1078C22×C3—244no—
1079C22×C3#100414yes—
1080C22×C3C24×D312yes—
1081C2×D3—22no—
1082C2×D3—22no—
1083C2×D3—22no—
1084C2×D3—22no—
1085C2×D3—22no—
1086C2×D3—22no—
1087C2×D3—22no—
1088C2×D3—22no—
1089C2×D3—22no—
1090C2×D3—34no—
1091C2×D3—62no—
1092C2×D3—62no—
1093C2×D3—62no—
1094C2×D3—62no—
1095C2×D3—62no—
1096C2×D3—62no—
1097C2×D3—62no—
1098C2×D3—84no—
1099C2×D3—121no—
1100C2×D3—121no—
1101C2×D3—121no—
1102C2×D3—121no—
1103C2×D3—128no—
1104C2×D3—128no—
1105C2×D3—244no—
1106C2×D3—244no—
1107C3×C4—22no—
1108C3×C4—22no—
1109C3×C4—22no—
1110C3×C4—22no—
1111C3×C4—41no—
1112C3×C4—41no—
1113C3×C4—42no—
1114C3×C4—62no—
1115C3×C4—62no—
1116C3×C4—62no—
1117C3×C4—62no—
1118C3×C4—62no—
1119Dic3—22no—
1120Dic3—22no—
1121Dic3—22no—
1122Dic3—22no—
1123Dic3—22no—
1124Dic3—62no—
1125Dic3—62no—
1126Dic3—62no—
1127Dic3—62no—
1128Dic3—62no—
1129Dic3—62no—
1130Dic3—121no—
1131Dic3—121no—
1132Dic3—122no—
1133Dic3—122no—
1134C32#353411yescharacteristic, complemented, Sylow
1135C23—22no—
1136C23—32no—
1137C23—32no—
1138C23—32no—
1139C23—41no—
1140C23—41no—
1141C23—91no—
1142C23—91no—
1143C23—122no—
1144C23—122no—
1145C23—122no—
1146C23—182no—
1147C23—184no—
1148C23—182no—
1149C23—361no—
1150C23—362no—
1151C23—362no—
1152C23C22×D3212yes—
1153C23C22×D3211yescharacteristic
1154Q8—122no—
1155Q8—361no—
1156D4—64no—
1157D4—64no—
1158D4—64no—
1159D4—122no—
1160D4—122no—
1161D4—122no—
1162D4—122no—
1163D4—122no—
1164D4—122no—
1165D4—184no—
1166D4—184no—
1167D4—362no—
1168D4—362no—
1169D4—362no—
1170D4—362no—
1171D4—361no—
1172D4—361no—
1173D4—362no—
1174D4—361no—
1175D4—362no—
1176C2×C4—22no—
1177C2×C4—32no—
1178C2×C4—32no—
1179C2×C4—32no—
1180C2×C4—32no—
1181C2×C4—32no—
1182C2×C4—41no—
1183C2×C4—92no—
1184C2×C4—92no—
1185C2×C4—91no—
1186C2×C4—91no—
1187C2×C4—122no—
1188C2×C4—122no—
1189C2×C4—122no—
1190C2×C4—122no—
1191C2×C4—182no—
1192C2×C4—182no—
1193C2×C4—361no—
1194C2×C4—361no—
1195C2×C4—362no—
1196C2×C4—362no—
1197C2×C4—362no—
1198C2×C4—361no—
1199C2×C4—361no—
1200C2×C4—361no—
1201C2×C4C22×D3211yescharacteristic
1202C2×C4C22×D3212yes—
1203C2×C4C22×D3211yescharacteristic
1204C2×C3—24no—
1205C2×C3—24no—
1206C2×C3—21no—
1207C2×C3—21no—
1208C2×C3—21no—
1209C2×C3—42no—
1210C2×C3—42no—
1211C2×C3—82no—
1212C2×C3—122no—
1213C2×C3—122no—
1214C2×C3—122no—
1215C2×C3C2×#100412yes—
1216C2×C3#596412yes—
1217C2×C3D3×H(5,𝔽2)12yes—
1218D3—42no—
1219D3—42no—
1220D3—42no—
1221D3—64no—
1222D3—122no—
1223D3—122no—
1224D3—122no—
1225C22—21no—
1226C22—21no—
1227C22—22no—
1228C22—22no—
1229C22—22no—
1230C22—62no—
1231C22—62no—
1232C22—62no—
1233C22—62no—
1234C22—62no—
1235C22—62no—
1236C22—62no—
1237C22—62no—
1238C22—62no—
1239C22—82no—
1240C22—92no—
1241C22—181no—
1242C22—181no—
1243C22—181no—
1244C22—181no—
1245C22—181no—
1246C22—244no—
1247C22—364no—
1248C22—724no—
1249C22#6431312yes—
1250C22C23×D3211yescharacteristic
1251C4—21no—
1252C4—21no—
1253C4—22no—
1254C4—62no—
1255C4—62no—
1256C4—62no—
1257C4—62no—
1258C4—62no—
1259C4—182no—
1260C4—181no—
1261C4—181no—
1262C4—182no—
1263C3—21no—
1264C3#8666912yescomplemented
1265C2—22no—
1266C2—42no—
1267C2—122no—
1268C2—122no—
1269C2—122no—
1270C2—182no—
1271C2—361no—
1272C2#1059666911yescharacteristic
1273C2#1059667511yescharacteristic
1274C2C2×#6431311yescharacteristic
subgroupG/H
center, FrattiniC22C23×D32
commutator, socle, cosocleC22×C32C25
FittingC2×C32×C22⋊C4C22
hypercenterC2×C22⋊C4D32
hypocenterC32#3534
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C22⋊C4

Complements

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

NH ≅ G/Ntype
1. C2×#64092C2semidirect
2. C3×#5490C2semidirect
3. #10595526C2semidirect
4. #10595518C2semidirect
5. #10595508C2semidirect
6. #10595081C2semidirect
7. #10595068C2semidirect
8. #10595044C2semidirect
9. #10595016C2semidirect
10. #10594994C2semidirect
11. #10594962C2semidirect
12. #10594300C2semidirect
13. #10594278C2semidirect
14. #10594263C2semidirect
15. #10594240C2semidirect
16. #10594233C2semidirect
17. #10594196C2semidirect
18. #10594100C2semidirect
19. #10594041C2semidirect
22. C22×C4×C3⋊D3C22semidirect
23. C22×C3×#67C22semidirect
24. C2×C3×#235C22semidirect
25. C2×#3811C22semidirect
26. C2×D3×#67C22semidirect
27. C2×#3802C22semidirect
28. C2×#3798C22semidirect
29. C2×C32×C22⋊C4C22semidirect
30. C2×#3757C22semidirect
31. C2×#3752C22semidirect
32. C2×C4⋊(C3⋊Dic3)C22semidirect
33. C2×#3750C22semidirect
34. #64092C22semidirect
35. #64092C22semidirect
36. #64092C22semidirect
37. #64092C22semidirect
38. C3×#953C22semidirect
39. C3×#930C22semidirect
40. C3×#929C22semidirect
41. C3×C4×#67C22semidirect
42. C3×#885C22semidirect
43. C3×#884C22semidirect
44. C3×#884C22semidirect
45. C3×#883C22semidirect
46. C3×#882C22semidirect
47. C3×#67⋊C4C22semidirect
48. C3×D3×C22⋊C4C22semidirect
49. C3×#878C22semidirect
51. #63982C22semidirect
52. #63981C22semidirect
54. #63980C22semidirect
55. #63980C22semidirect
56. #63980C22semidirect
57. #63980C22semidirect
58. #63979C22semidirect
59. #63978C22semidirect
60. #63977C22semidirect
61. #63976C22semidirect
62. #63976C22semidirect
63. #67⋊Dic3C22semidirect
64. #67⋊Dic3C22semidirect
65. #63971C22semidirect
66. #63970C22semidirect
67. #63969C22semidirect
68. #63961C22semidirect
69. #63961C22semidirect
70. #63959C22semidirect
72. #63956C22semidirect
73. #63952C22semidirect
74. #63922C22semidirect
75. #63921C22semidirect
76. D3×(C2×D3)⋊C4C22semidirect
77. #63916C22semidirect
78. #63912C22semidirect
79. #63912C22semidirect
80. #63912C22semidirect
81. #63908C22semidirect
82. #63908C22semidirect
83. #63907C22semidirect
84. #63906C22semidirect
85. #63905C22semidirect
86. #63904C22semidirect
87. C4×#626C22semidirect
88. #63900C22semidirect
89. #63893C22semidirect
90. #63891C22semidirect
91. #63888C22semidirect
92. #63886C22semidirect
93. #63885C22semidirect
94. #63884C22semidirect
95. #63879C22semidirect
96. #63877C22semidirect
97. #63874C22semidirect
98. #63865C22semidirect
99. #63861C22semidirect
100. #63859C22semidirect
101. #63858C22semidirect
102. #63856C22semidirect
103. #63856C22semidirect
104. #63853C22semidirect
105. #63850C22semidirect
106. #63847C22semidirect
107. #63845C22semidirect
137. #5490D3semidirect
241. C22×#67C2×D3semidirect
247. C2×#235C2×D3semidirect
263. C2×C3×C22⋊C4C2×D3semidirect
267. #953C2×D3semidirect
310. #930C2×D3semidirect
315. #929C2×D3semidirect
320. C4×#67C2×D3semidirect
349. #885C2×D3semidirect
357. #884C2×D3semidirect
358. #884C2×D3semidirect
375. #883C2×D3semidirect
379. #882C2×D3semidirect
384. #67⋊C4C2×D3semidirect
388. D3×C22⋊C4C2×D3semidirect
396. #878C2×D3semidirect
806. C2×C22⋊C4D32semidirect
1134. C32#3534semidirect
1264. C3#86669semidirect

Maximal subgroups

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

subgroupindex
C2×#640922
C3×#54902
#105955262
#105955182
#105955082
#105950812
#105950682
#105950442
#105950162
#105949942
#105949622
#105943002
#105942782
#105942632
#105942402
#105942332
#105941962
#105941002
#105940412
#866693