Finite Group Databasebeta

← #11911180

Subgroups — #11911180

Order 1152.

2545 conjugacy classes of subgroups.

The subgroup lattice has 1283 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3⋊D3×#121C211yesmaximal, characteristic, complemented
2C3×#5615C212yesmaximal, complemented
3#10595313C212yesmaximal, complemented
4#10595311C211yesmaximal, characteristic, complemented
5#10595308C212yesmaximal, complemented
6#10595297C212yesmaximal, complemented
7#10595263C212yesmaximal, complemented
8#10595163C212yesmaximal, complemented
9#10595140C211yesmaximal, characteristic, complemented
10#10595085C212yesmaximal, complemented
11#10595079C211yesmaximal, characteristic, complemented
12#10595016C211yesmaximal, characteristic, complemented
13#10594610C211yesmaximal, characteristic, complemented
14#10594572C212yesmaximal, complemented
15#10594483C211yesmaximal, characteristic, complemented
16#10594283C212yesmaximal, complemented
17#10594279C212yesmaximal, complemented
18#10594204C212yesmaximal, complemented
19#10594040C212yesmaximal, complemented
20#86490—32nomaximal
21C2×D4×C3⋊D3C2212yescomplemented
22C2×D4×C3⋊D3C2211yescharacteristic, complemented
23C22×C4×C3⋊D3C2211yescharacteristic, complemented
24C2×#3811C2211yescharacteristic
25C2×#3811C2212yescomplemented
26C2×#3804C2212yescomplemented
27C2×D3×D12C2212yescomplemented
28C2×#3798C2211yescharacteristic, complemented
29C32×#121C2211yescharacteristic, complemented
30#64148C2212yescomplemented
31#64147C2211yescharacteristic, complemented
32#64139C2211yescharacteristic, complemented
33#64104C2211yescharacteristic
34C4⋊C4×C3⋊D3C2211yescharacteristic, complemented
35#64093C2212yescomplemented
36C22⋊C4×C3⋊D3C2212yescomplemented
37C3×#940C2212yescomplemented
38C3×#939C2212yescomplemented
39C3×#939C2212yescomplemented
40C3×#939C2212yescomplemented
41C3×#938C2212yescomplemented
42C3×#935C2212yescomplemented
43C3×#929C2212yescomplemented
44C3×C4×#67C2212yescomplemented
45C3×#894C2212yescomplemented
46C3×#889C2212yescomplemented
47C3×#884C2212yescomplemented
48C3×#883C2212yescomplemented
49C3×#67⋊C4C2212yescomplemented
50C3×#877C2212yescomplemented
51#63983C2212yescomplemented
52#63983C2212yescomplemented
53#63983C2212yescomplemented
54#63982C2211yescharacteristic, complemented
55#63981C2212yes—
56#63981C2212yescomplemented
57#63981C2212yescomplemented
58#63980C2211yescharacteristic, complemented
59#63978C2212yescomplemented
60#63978C2212yescomplemented
61#63975C2212yescomplemented
62#63974C2211yescharacteristic, complemented
63#63971C2212yescomplemented
64#63970C2212yescomplemented
65#63964C2212yescomplemented
66C2×#3722C2212yescomplemented
67#63962C2212yescomplemented
68#63961C2212yescomplemented
69#63959C2212yescomplemented
70#63958C2212yescomplemented
71#63958C2212yescomplemented
72#63953C2212yescomplemented
73#63952C2212yescomplemented
74#63923C2212yescomplemented
75#63922C2212yescomplemented
76#63921C2211yescharacteristic, complemented
77#63921C2211yescharacteristic, complemented
78D3×(C2×D3)⋊C4C2212yescomplemented
79#63916C2212yes—
80#63912C2211yescharacteristic, complemented
81#63910C2212yescomplemented
82#63904C2212yescomplemented
83C4×#626C2212yescomplemented
84C4×#626C2212yescomplemented
85#63897C2212yescomplemented
86#63897C2212yescomplemented
87#63895C2212yescomplemented
88#63894C2212yescomplemented
89#63893C2212yescomplemented
90#63884C2212yescomplemented
91#63883C2211yescharacteristic, complemented
92#63883C2211yescharacteristic, complemented
93#63881C2212yescomplemented
94#63874C2211yescharacteristic, complemented
95#63868C2212yescomplemented
96#63868C2212yescomplemented
97#63865C2212yescomplemented
98#63865C2211yescharacteristic, complemented
99#63861C2212yescomplemented
100#63859C2212yescomplemented
101#63853C2212yescomplemented
102#63853C2212yescomplemented
103#63853C2212yescomplemented
104#63852C2212yescomplemented
105#63851C2212yescomplemented
106#63850C2212yescomplemented
107#63846C2212yescomplemented
108C3×#540—32no—
109#5720—32no—
110#5717—32no—
111#5692—32no—
112#5692—32no—
113#5667—32no—
114#5661—32no—
115#5660—32no—
116#5657—32no—
117#5654—32no—
118#5654—32no—
119#5653—32no—
120D3×#123—32no—
121#5621—32no—
122#5620—32no—
123#5615D312yescomplemented
124#5613—32no—
125#5612—32no—
126#5610—32no—
127#5610—32no—
128#5609—32no—
129#5608—32no—
130#5605—32no—
131#5605—32no—
132D3×#121—32no—
133D3×#121—61no—
134#5560—32no—
135#5556—32no—
136#5550—32no—
137#5547—32no—
138#5530—32no—
139#5527—32no—
140C23×C3⋊D3C2311yescharacteristic
141C23×C3⋊D3C2312yes—
142C22×D32C2311yescharacteristic
143C22×D32C2312yes—
144C2×C32×D4C2312yes—
145C2×C32×D4C2311yescharacteristic
146C22×C32×C4C2311yescharacteristic
147C2×#638C2312yes—
148C2×#638C2312yes—
149C2×#638C2312yes—
150C22×C3⋊Dic3C2311yescharacteristic
151D4×C3⋊D3—42no—
152D4×C3⋊D3—44no—
153C2×C4⋊(C3⋊D3)C2312yes—
154C2×C4⋊(C3⋊D3)C2311yescharacteristic
155C2×C4×C3⋊D3—42no—
156C2×C4×C3⋊D3C2311yescharacteristic
157C2×C4×C3⋊D3C2311yescharacteristic
158C2×C4×C3⋊D3C2312yes—
159C2×C4×C3⋊D3C2311yescharacteristic
160C2×C4×C3⋊D3C2311yescharacteristic
161C2×C3×#67C2312yes—
162C2×C3×#67C2312yes—
163C2×C3×#67C2312yes—
164C2×C3×#67C2312yes—
165C2×C3×#67C2312yes—
166C2×C3×#67C2312yes—
167C22×C3×Dic3C2312yes—
168C22×C3×Dic3C2312yes—
169C2×C3×D12C2312yes—
170C2×C3×C4×D3C2312yes—
171C2×C3×C4×D3C2312yes—
172#3811—42no—
173#3811—44no—
174C2×#627C2311yescharacteristic
175C2×#627C2312yes—
176C2×#626C2312yes—
177C2×#626C2312yes—
178C2×#626C2312yes—
179C2×#626C2312yes—
180C2×#626C2312yes—
181C2×#625C2311yescharacteristic
182C2×#624C2311yescharacteristic
183C2×#624C2311yescharacteristic
184C2×#624C2312yes—
185C2×#624C2311yescharacteristic
186#3804—44no—
187C2×D3×Dic3C2312yes—
188D3×D12—44no—
189#3798—42no—
190C32×C4⋊C4C2311yescharacteristic
191C32×C22⋊C4C2312yes—
192#3757C2312yes—
193#3752C2312yes—
194#3752C2312yes—
195C4⋊(C3⋊Dic3)C2311yescharacteristic
196#3750C2312yes—
197C3×#217C2312yes—
198C3×#217C2312yes—
199C3×#217C2312yes—
200C3×#217C2312yes—
201C3×(C2×D3)⋊C4C2312yes—
202C3×(C2×D3)⋊C4C2312yes—
203C3×(C2×D3)⋊C4C2312yes—
204C3×(C2×D3)⋊C4C2312yes—
205C3×C4⋊Dic3C2312yes—
206C3×Dic3⋊C4C2312yes—
207C3×Dic3⋊C4C2312yes—
208C3×Dic3⋊C4C2312yes—
209C3×Dic3⋊C4C2312yes—
210C3×Dic3⋊C4C2312yes—
211C3×Dic3⋊C4C2312yes—
212C3×C4×Dic3C2312yes—
213C3×C4×Dic3C2312yes—
214#3724C2311yescharacteristic
215#3724C2312yes—
216#3724C2311yescharacteristic
217Dic3⋊Dic3C2312yes—
218Dic3⋊Dic3C2312yes—
219Dic3⋊Dic3C2312yes—
220Dic3⋊Dic3C2312yes—
221#3722C2312yes—
222#3722C2312yes—
223#3722C2312yes—
224#3722C2312yes—
225#3722C2312yes—
226#3722C2312yes—
227#3722C2312yes—
228(C2×D3)⋊Dic3C2312yes—
229(C2×D3)⋊Dic3C2312yes—
230(C2×D3)⋊Dic3C2312yes—
231(C2×D3)⋊Dic3C2312yes—
232(C2×D3)⋊Dic3C2312yes—
233(C2×D3)⋊Dic3C2312yes—
234Dic32C2312yes—
235#3534—91noSylow
236C2×#237—32no—
237C2×D3×D4—32no—
238C2×D3×D4—32no—
239C2×D3×D4—32no—
240C2×D3×D4—32no—
241C2×D3×D4—32no—
242C2×D3×D4—32no—
243C2×D3×D4—32no—
244C2×D3×D4—61no—
245C2×D3×D4—62no—
246C2×#235—32no—
247C2×#235—32no—
248C22×D12—32no—
249C22×C4×D3—32no—
250C22×C4×D3—61no—
251C3×#127—32no—
252C3×#125—32no—
253C3×#123—32no—
254C3×#123—32no—
255C3×#123—32no—
256C3×#123—32no—
257C3×#121—21no—
258C3×#121—32no—
259C3×#121—32no—
260C3×#121—32no—
261C3×#121—32no—
262C3×#121—32no—
263C3×#121C2×D312yescomplemented
264C3×C4×D4—32no—
265C3×C4×D4—32no—
266C3×#117—32no—
267#940C2×D312yescomplemented
268#939—32no—
269#939—32no—
270#939—32no—
271#939—32no—
272#939—32no—
273#939—32no—
274#939—32no—
275#939—62no—
276#939C2×D312yescomplemented
277#939C2×D312yescomplemented
278#939C2×D312yescomplemented
279#938—32no—
280#938—32no—
281#938—32no—
282#938—32no—
283#938—32no—
284#938—61no—
285#938C2×D312yescomplemented
286#937—32no—
287#937—32no—
288#937—32no—
289#937—32no—
290#937—32no—
291#937—32no—
292#937—32no—
293#937—32no—
294#937—32no—
295#937—32no—
296#936—32no—
297#935—32no—
298#935—32no—
299#935—32no—
300#935C2×D312yescomplemented
301#930—32no—
302#930—32no—
303#930—32no—
304#930—61no—
305#929—32no—
306#929—32no—
307#929C2×D312yescomplemented
308C4×#67—32no—
309C4×#67—32no—
310C4×#67—32no—
311C4×#67—32no—
312C4×#67C2×D312yescomplemented
313C2×(C2×D3)⋊C4—32no—
314C2×(C2×D3)⋊C4—32no—
315C2×(C2×D3)⋊C4—32no—
316#924—32no—
317#924—32no—
318#898—32no—
319#898—32no—
320#898—32no—
321#897—32no—
322#897—32no—
323#896—32no—
324#896—32no—
325#896—32no—
326#896—32no—
327#896—32no—
328#895—32no—
329#895—32no—
330#895—32no—
331#895—61no—
332#894—32no—
333#894—32no—
334#894—32no—
335#894—32no—
336#894—32no—
337#894—32no—
338#894—32no—
339#894—32no—
340#894—32no—
341#894C2×D312yescomplemented
342#893—32no—
343#893—32no—
344#893—32no—
345D3×C4⋊C4—32no—
346D3×C4⋊C4—32no—
347D3×C4⋊C4—32no—
348D3×C4⋊C4—61no—
349#890—32no—
350#889—32no—
351#889C2×D312yescomplemented
352#886—32no—
353#885—32no—
354#885—32no—
355#885—32no—
356#885—32no—
357#884—32no—
358#884—32no—
359#884—32no—
360#884—32no—
361#884—32no—
362#884—32no—
363#884—32no—
364#884—62no—
365#884C2×D312yescomplemented
366#883—32no—
367#883—32no—
368#883—32no—
369#883—32no—
370#883—32no—
371#883C2×D312yescomplemented
372#882—32no—
373#882—32no—
374#882—32no—
375#882—32no—
376#882—32no—
377#882—32no—
378#67⋊C4—32no—
379#67⋊C4—32no—
380#67⋊C4C2×D312yescomplemented
381D3×C22⋊C4—32no—
382D3×C22⋊C4—32no—
383D3×C22⋊C4—32no—
384D3×C22⋊C4—32no—
385D3×C22⋊C4—32no—
386D3×C22⋊C4—32no—
387D3×C22⋊C4—62no—
388#879—32no—
389#879—32no—
390#878—32no—
391#878—32no—
392#878—32no—
393#877C2×D312yescomplemented
394#876—32no—
395#876—32no—
396#876—32no—
397#875—32no—
398C4×D12—32no—
399C4×D12—32no—
400C4×D12—32no—
401#872—32no—
402C23×C32C2411yescharacteristic
403C23×C32C2412yes—
404C22×C3⋊D3—22no—
405C22×C3⋊D3—22no—
406C22×C3⋊D3—24no—
407C22×C3⋊D3—41no—
408C22×C3⋊D3—42no—
409C22×C3⋊D3—42no—
410C22×C3⋊D3C2412yes—
411C22×C3⋊D3C2411yescharacteristic
412C22×C3⋊D3C2411yescharacteristic
413C22×C3×D3C2412yes—
414C22×C3×D3C2412yes—
415C2×D32—22no—
416C2×D32—41no—
417C2×D32—42no—
418C2×D32—42no—
419C2×D32—41no—
420C2×D32—42no—
421C32×D4—41no—
422C32×D4—42no—
423C2×C32×C4—41no—
424C2×C32×C4C2411yescharacteristic
425C2×C32×C4C2412yes—
426C2×C32×C4C2411yescharacteristic
427#638—24no—
428#638—42no—
429#638—42no—
430C2×C3⋊Dic3—41no—
431C2×C3⋊Dic3C2412yes—
432C2×C3⋊Dic3C2411yescharacteristic
433C2×C3⋊Dic3C2411yescharacteristic
434C4⋊(C3⋊D3)—24no—
435C4⋊(C3⋊D3)—41no—
436C4×C3⋊D3—22no—
437C4×C3⋊D3—22no—
438C4×C3⋊D3—41no—
439C4×C3⋊D3—41no—
440C4×C3⋊D3—42no—
441C3×#67—42no—
442C3×#67—42no—
443C3×#67—42no—
444C3×#67—42no—
445C3×#67—42no—
446C3×#67—42no—
447C2×C3×Dic3—42no—
448C2×C3×Dic3—42no—
449C2×C3×Dic3C2412yes—
450C2×C3×Dic3C2412yes—
451C2×C3×Dic3C2412yes—
452C2×C3×Dic3C2412yes—
453C2×C3×Dic3C2412yes—
454C2×C3×Dic3C2412yes—
455C3×D12—42no—
456C3×C4×D3—42no—
457C3×C4×D3—42no—
458#627—41no—
459#627—42no—
460#626—24no—
461#626—24no—
462#626—24no—
463#626—42no—
464#626—42no—
465#625—41no—
466#624—22no—
467#624—41no—
468#624—41no—
469#624—42no—
470D3×Dic3—42no—
471#562—92no—
472#560—92no—
473#553—92no—
474#551—92no—
475#546—92no—
476#546—92no—
477#546—92no—
478D42—92no—
479#540—32no—
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—
490C23×D3—32no—
491C23×D3—32no—
492C23×D3—32no—
493C23×D3—32no—
494C23×D3—32no—
495C23×D3—32no—
496C23×D3—61no—
497C23×D3—62no—
498C2×C3×D4—21no—
499C2×C3×D4—22no—
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×D4C22×D312yes—
508C2×C3×D4C22×D312yes—
509C2×C3×D4C22×D312yes—
510C22×C3×C4—21no—
511C22×C3×C4—32no—
512C22×C3×C4—32no—
513C22×C3×C4—32no—
514C22×C3×C4—32no—
515C22×C3×C4C22×D312yes—
516C2×#67—32no—
517C2×#67—32no—
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—62no—
529C2×#67—62no—
530C2×#67—62no—
531C2×#67C22×D312yes—
532C2×#67C22×D312yes—
533C2×#67C22×D312yes—
534C2×#67C22×D312yes—
535C2×#67C22×D312yes—
536C2×#67C22×D312yes—
537C22×Dic3—32no—
538C22×Dic3—32no—
539C22×Dic3—61no—
540C22×Dic3C22×D312yes—
541C22×Dic3C22×D312yes—
542#237—124no—
543D3×D4—124no—
544D3×D4—124no—
545D3×D4—124no—
546D3×D4—124no—
547D3×D4—124no—
548D3×D4—124no—
549D3×D4—124no—
550D3×D4—124no—
551D3×D4—128no—
552#235—124no—
553#235—124no—
554C2×D12—32no—
555C2×D12—32no—
556C2×D12—32no—
557C2×D12—32no—
558C2×D12—32no—
559C2×D12—32no—
560C2×D12—32no—
561C2×D12—32no—
562C2×D12—62no—
563C2×D12—61no—
564C2×D12—124no—
565C2×D12C22×D312yes—
566C2×C4×D3—32no—
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—32no—
576C2×C4×D3—32no—
577C2×C4×D3—32no—
578C2×C4×D3—61no—
579C2×C4×D3—61no—
580C2×C4×D3—62no—
581C2×C4×D3—61no—
582C2×C4×D3—61no—
583C2×C4×D3—124no—
584C2×C4×D3—124no—
585C2×C4×D3C22×D312yes—
586C2×C4×D3C22×D312yes—
587C2×Dic6—32no—
588C2×Dic6—32no—
589C2×Dic6—32no—
590C3×C4⋊C4—21no—
591C3×C4⋊C4—32no—
592C3×C4⋊C4—32no—
593C3×C4⋊C4—32no—
594C3×C4⋊C4—32no—
595C3×C4⋊C4—32no—
596C3×C4⋊C4—32no—
597C3×C4⋊C4—32no—
598C3×C4⋊C4C22×D312yes—
599C3×C22⋊C4—22no—
600C3×C22⋊C4—32no—
601C3×C22⋊C4—32no—
602C3×C22⋊C4—32no—
603C3×C22⋊C4—32no—
604C3×C22⋊C4—32no—
605C3×C22⋊C4—32no—
606C3×C22⋊C4—32no—
607C3×C22⋊C4—32no—
608C3×C22⋊C4C22×D312yes—
609C3×C22⋊C4C22×D312yes—
610C3×C42—32no—
611C3×C42—32no—
612#217—32no—
613#217—32no—
614#217—32no—
615#217—32no—
616#217—32no—
617#217—32no—
618#217—32no—
619#217—32no—
620#217—62no—
621#217C22×D312yes—
622#217C22×D312yes—
623#217C22×D312yes—
624#217C22×D312yes—
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—32no—
641(C2×D3)⋊C4—32no—
642(C2×D3)⋊C4—32no—
643(C2×D3)⋊C4—32no—
644(C2×D3)⋊C4—32no—
645(C2×D3)⋊C4—32no—
646(C2×D3)⋊C4—32no—
647(C2×D3)⋊C4—32no—
648(C2×D3)⋊C4—32no—
649(C2×D3)⋊C4—62no—
650(C2×D3)⋊C4—62no—
651(C2×D3)⋊C4C22×D312yes—
652(C2×D3)⋊C4C22×D312yes—
653(C2×D3)⋊C4C22×D312yes—
654(C2×D3)⋊C4C22×D312yes—
655C4⋊Dic3—32no—
656C4⋊Dic3—32no—
657C4⋊Dic3—32no—
658C4⋊Dic3—32no—
659C4⋊Dic3—32no—
660C4⋊Dic3—61no—
661C4⋊Dic3C22×D312yes—
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⋊C4C22×D312yes—
674Dic3⋊C4C22×D312yes—
675Dic3⋊C4C22×D312yes—
676Dic3⋊C4C22×D312yes—
677Dic3⋊C4C22×D312yes—
678Dic3⋊C4C22×D312yes—
679C4×Dic3—32no—
680C4×Dic3—32no—
681C4×Dic3C22×D312yes—
682C4×Dic3C22×D312yes—
683C22×C32—21no—
684C22×C32—22no—
685C22×C32—21no—
686C22×C32—22no—
687C22×C32—22no—
688C22×C32—21no—
689C22×C32C2511yescharacteristic
690C2×C3⋊D3—21no—
691C2×C3⋊D3—21no—
692C2×C3⋊D3—21no—
693C2×C3⋊D3—21no—
694C2×C3⋊D3—22no—
695C2×C3⋊D3—22no—
696C2×C3⋊D3—22no—
697C2×C3⋊D3—44no—
698C2×C3⋊D3—84no—
699C2×C3⋊D3H(5,𝔽2)12yes—
700C2×C3⋊D3H(5,𝔽2)12yes—
701C2×C3×D3—22no—
702C2×C3×D3—22no—
703C2×C3×D3—22no—
704C2×C3×D3—22no—
705C2×C3×D3—22no—
706C2×C3×D3—22no—
707D32—82no—
708D32—84no—
709C32×C4—21no—
710C32×C4—21no—
711C32×C4—22no—
712C3⋊Dic3—21no—
713C3⋊Dic3—22no—
714C3⋊Dic3—21no—
715C3×Dic3—22no—
716C3×Dic3—22no—
717C3×Dic3—22no—
718C3×Dic3—22no—
719C3×Dic3—22no—
720C3×Dic3—22no—
721C2×#41—91no—
722C2×#41—92no—
723C22×D4—92no—
724C22×D4—91no—
725C22×D4—92no—
726C22×D4—91no—
727C22×D4—92no—
728C23×C4—91no—
729#127—32no—
730#126—92no—
731#126—92no—
732#126—92no—
733#126—92no—
734#125—32no—
735#125—92no—
736#124—92no—
737#124—92no—
738#124—92no—
739#123—32no—
740#123—32no—
741#123—32no—
742#123—32no—
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—
752#123—92no—
753C22⋊Q8—91no—
754C22⋊Q8—92no—
755C22⋊Q8—92no—
756C22⋊Q8—91no—
757C22⋊Q8—92no—
758C22⋊Q8—92no—
759C22⋊Q8—92no—
760#121—32no—
761#121—32no—
762#121—32no—
763#121—32no—
764#121—32no—
765#121—91no—
766#121—92no—
767#121—92no—
768#121—92no—
769#121—92no—
770#121—92no—
771#121—92no—
772#121—92no—
773#121—91no—
774#121—92no—
775#121—91no—
776#121—92no—
777#121—91no—
778#121—91no—
779#121—92no—
780#121D3211yescharacteristic, complemented
781#120—92no—
782#120—92no—
783#120—92no—
784#120—92no—
785#120—92no—
786#120—92no—
787#120—92no—
788#120—92no—
789C4×D4—32no—
790C4×D4—32no—
791C4×D4—92no—
792C4×D4—92no—
793C4×D4—92no—
794C4×D4—92no—
795C4×D4—92no—
796C4×D4—92no—
797#117—32no—
798#117—91no—
799C2×C4⋊C4—91no—
800C2×C4⋊C4—91no—
801C2×C4⋊C4—91no—
802C2×C22⋊C4—91no—
803C2×C22⋊C4—91no—
804C2×C22⋊C4—91no—
805C2×C22⋊C4—92no—
806C2×C22⋊C4—92no—
807C2×C22⋊C4—92no—
808C23×C3—21no—
809C23×C3—22no—
810C23×C3—32no—
811C23×C3—32no—
812C23×C3C23×D312yes—
813C23×C3C23×D312yes—
814C23×C3C23×D312yes—
815C22×D3—32no—
816C22×D3—32no—
817C22×D3—32no—
818C22×D3—32no—
819C22×D3—61no—
820C22×D3—61no—
821C22×D3—62no—
822C22×D3—64no—
823C22×D3—64no—
824C22×D3—64no—
825C22×D3—64no—
826C22×D3—64no—
827C22×D3—64no—
828C22×D3—122no—
829C22×D3—124no—
830C22×D3—122no—
831C22×D3—122no—
832C22×D3—122no—
833C22×D3—122no—
834C22×D3—122no—
835C22×D3—122no—
836C22×D3—122no—
837C22×D3—122no—
838C22×D3—122no—
839C22×D3—122no—
840C22×D3—122no—
841C22×D3—122no—
842C22×D3—122no—
843C22×D3—122no—
844C22×D3—124no—
845C22×D3—124no—
846C22×D3C23×D312yes—
847C22×D3C23×D312yes—
848C3×D4—42no—
849C3×D4—42no—
850C3×D4—42no—
851C3×D4—42no—
852C3×D4—44no—
853C3×D4—122no—
854C3×D4—122no—
855C3×D4—122no—
856C3×D4—122no—
857C3×D4—122no—
858C3×D4—122no—
859C3×D4—122no—
860C2×C3×C4—21no—
861C2×C3×C4—22no—
862C2×C3×C4—21no—
863C2×C3×C4—32no—
864C2×C3×C4—32no—
865C2×C3×C4—32no—
866C2×C3×C4—32no—
867C2×C3×C4—32no—
868C2×C3×C4—32no—
869C2×C3×C4—42no—
870C2×C3×C4—42no—
871C2×C3×C4—122no—
872C2×C3×C4—122no—
873C2×C3×C4—122no—
874C2×C3×C4—122no—
875C2×C3×C4C23×D312yes—
876C2×C3×C4C23×D312yes—
877C2×C3×C4C23×D312yes—
878C2×C3×C4C23×D312yes—
879#67—42no—
880#67—42no—
881#67—42no—
882#67—42no—
883#67—42no—
884#67—42no—
885#67—64no—
886#67—64no—
887#67—64no—
888#67—64no—
889#67—64no—
890#67—124no—
891#67—122no—
892#67—122no—
893#67—122no—
894#67—122no—
895#67—122no—
896#67—122no—
897#67—122no—
898#67—124no—
899#67—124no—
900C2×Dic3—32no—
901C2×Dic3—32no—
902C2×Dic3—32no—
903C2×Dic3—32no—
904C2×Dic3—42no—
905C2×Dic3—42no—
906C2×Dic3—61no—
907C2×Dic3—62no—
908C2×Dic3—61no—
909C2×Dic3—122no—
910C2×Dic3—122no—
911C2×Dic3—122no—
912C2×Dic3C23×D312yes—
913C2×Dic3C23×D312yes—
914C2×Dic3C23×D312yes—
915C2×Dic3C23×D312yes—
916C2×Dic3C23×D312yes—
917C2×Dic3C23×D312yes—
918D12—42no—
919D12—64no—
920D12—64no—
921D12—64no—
922D12—64no—
923D12—64no—
924D12—124no—
925D12—122no—
926D12—122no—
927D12—122no—
928D12—122no—
929C4×D3—42no—
930C4×D3—42no—
931C4×D3—64no—
932C4×D3—64no—
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—
945C4×D3—122no—
946C4×D3—122no—
947C4×D3—124no—
948Dic6—122no—
949Dic6—122no—
950Dic6—122no—
951C2×C32—41no—
952C2×C32—42no—
953C2×C32C2×H(5,𝔽2)11yescharacteristic
954C2×C32C2×H(5,𝔽2)11yescharacteristic
955C2×C32#58511yescharacteristic
956C3⋊D3—22no—
957C3⋊D3—22no—
958C3⋊D3—42no—
959C3×D3—42no—
960C3×D3—42no—
961C24—91no—
962C24—92no—
963C24—91no—
964C24—92no—
965#41—362no—
966#41—364no—
967C2×Q8—92no—
968C2×Q8—91no—
969C2×D4—32no—
970C2×D4—32no—
971C2×D4—32no—
972C2×D4—32no—
973C2×D4—32no—
974C2×D4—32no—
975C2×D4—32no—
976C2×D4—92no—
977C2×D4—92no—
978C2×D4—92no—
979C2×D4—92no—
980C2×D4—92no—
981C2×D4—92no—
982C2×D4—91no—
983C2×D4—92no—
984C2×D4—92no—
985C2×D4—92no—
986C2×D4—91no—
987C2×D4—364no—
988C2×D4—362no—
989C2×D4—364no—
990C2×D4—362no—
991C2×D4—364no—
992C2×D4C2×D3211yescharacteristic
993C2×D4C2×D3212yes—
994C22×C4—32no—
995C22×C4—32no—
996C22×C4—32no—
997C22×C4—32no—
998C22×C4—91no—
999C22×C4—91no—
1000C22×C4—91no—
1001C22×C4—92no—
1002C22×C4—92no—
1003C22×C4—91no—
1004C22×C4—91no—
1005C22×C4—91no—
1006C22×C4—91no—
1007C22×C4—92no—
1008C22×C4—91no—
1009C22×C4—362no—
1010C22×C4C2×D3211yescharacteristic
1011C4⋊C4—32no—
1012C4⋊C4—32no—
1013C4⋊C4—32no—
1014C4⋊C4—32no—
1015C4⋊C4—32no—
1016C4⋊C4—32no—
1017C4⋊C4—32no—
1018C4⋊C4—92no—
1019C4⋊C4—92no—
1020C4⋊C4—91no—
1021C4⋊C4—91no—
1022C4⋊C4—92no—
1023C4⋊C4—92no—
1024C4⋊C4—92no—
1025C4⋊C4—91no—
1026C4⋊C4—92no—
1027C4⋊C4C2×D3211yescharacteristic
1028C22⋊C4—32no—
1029C22⋊C4—32no—
1030C22⋊C4—32no—
1031C22⋊C4—32no—
1032C22⋊C4—32no—
1033C22⋊C4—32no—
1034C22⋊C4—32no—
1035C22⋊C4—32no—
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⋊C4—92no—
1048C22⋊C4—92no—
1049C22⋊C4—92no—
1050C22⋊C4—92no—
1051C22⋊C4—92no—
1052C22⋊C4C2×D3212yes—
1053C42—32no—
1054C42—32no—
1055C42—92no—
1056C22×C3—22no—
1057C22×C3—22no—
1058C22×C3—22no—
1059C22×C3—22no—
1060C22×C3—22no—
1061C22×C3—22no—
1062C22×C3—22no—
1063C22×C3—22no—
1064C22×C3—22no—
1065C22×C3—22no—
1066C22×C3—21no—
1067C22×C3—41no—
1068C22×C3—41no—
1069C22×C3—42no—
1070C22×C3—42no—
1071C22×C3—42no—
1072C22×C3—62no—
1073C22×C3—62no—
1074C22×C3—62no—
1075C22×C3—62no—
1076C22×C3—62no—
1077C22×C3—62no—
1078C22×C3C24×D312yes—
1079C2×D3—22no—
1080C2×D3—22no—
1081C2×D3—22no—
1082C2×D3—22no—
1083C2×D3—22no—
1084C2×D3—22no—
1085C2×D3—34no—
1086C2×D3—34no—
1087C2×D3—62no—
1088C2×D3—62no—
1089C2×D3—62no—
1090C2×D3—62no—
1091C2×D3—62no—
1092C2×D3—62no—
1093C2×D3—62no—
1094C2×D3—62no—
1095C2×D3—62no—
1096C2×D3—62no—
1097C2×D3—62no—
1098C2×D3—62no—
1099C2×D3—62no—
1100C2×D3—62no—
1101C2×D3—121no—
1102C2×D3—121no—
1103C2×D3—122no—
1104C2×D3—122no—
1105C2×D3—122no—
1106C2×D3—128no—
1107C2×D3—128no—
1108C2×D3—244no—
1109C2×D3—244no—
1110C2×D3—244no—
1111C2×D3—244no—
1112C2×D3—244no—
1113C2×D3—248no—
1114C3×C4—22no—
1115C3×C4—22no—
1116C3×C4—22no—
1117C3×C4—22no—
1118C3×C4—22no—
1119C3×C4—41no—
1120C3×C4—42no—
1121C3×C4—62no—
1122C3×C4—62no—
1123C3×C4—62no—
1124C3×C4—62no—
1125C3×C4—62no—
1126C3×C4—62no—
1127Dic3—22no—
1128Dic3—22no—
1129Dic3—22no—
1130Dic3—22no—
1131Dic3—22no—
1132Dic3—22no—
1133Dic3—62no—
1134Dic3—62no—
1135Dic3—62no—
1136Dic3—62no—
1137Dic3—62no—
1138Dic3—121no—
1139Dic3—122no—
1140C32#353411yescharacteristic, complemented, Sylow
1141C23—32no—
1142C23—32no—
1143C23—91no—
1144C23—91no—
1145C23—92no—
1146C23—182no—
1147C23—182no—
1148C23—184no—
1149C23—182no—
1150C23—361no—
1151C23—362no—
1152C23—362no—
1153C23—362no—
1154C23—362no—
1155C23—361no—
1156C23—362no—
1157C23—361no—
1158C23C22×D3211yescharacteristic
1159C23C22×D3212yes—
1160Q8—362no—
1161Q8—361no—
1162D4—41no—
1163D4—42no—
1164D4—122no—
1165D4—122no—
1166D4—122no—
1167D4—122no—
1168D4—122no—
1169D4—122no—
1170D4—122no—
1171D4—184no—
1172D4—184no—
1173D4—184no—
1174D4—184no—
1175D4—184no—
1176D4—361no—
1177D4—362no—
1178D4—362no—
1179D4—362no—
1180D4—362no—
1181D4—361no—
1182C2×C4—32no—
1183C2×C4—32no—
1184C2×C4—32no—
1185C2×C4—32no—
1186C2×C4—32no—
1187C2×C4—32no—
1188C2×C4—41no—
1189C2×C4—92no—
1190C2×C4—91no—
1191C2×C4—91no—
1192C2×C4—122no—
1193C2×C4—122no—
1194C2×C4—122no—
1195C2×C4—122no—
1196C2×C4—182no—
1197C2×C4—182no—
1198C2×C4—182no—
1199C2×C4—361no—
1200C2×C4—361no—
1201C2×C4—362no—
1202C2×C4—362no—
1203C2×C4—361no—
1204C2×C4—361no—
1205C2×C4—362no—
1206C2×C4—361no—
1207C2×C4C22×D3211yescharacteristic
1208C2×C4C22×D3212yes—
1209C2×C4C22×D3211yescharacteristic
1210C2×C3—21no—
1211C2×C3—21no—
1212C2×C3—21no—
1213C2×C3—42no—
1214C2×C3—42no—
1215C2×C3—42no—
1216C2×C3—42no—
1217C2×C3—82no—
1218C2×C3—122no—
1219C2×C3—122no—
1220C2×C3#596412yes—
1221C2×C3D3×H(5,𝔽2)12yes—
1222C2×C3D3×H(5,𝔽2)12yes—
1223D3—42no—
1224D3—42no—
1225D3—64no—
1226D3—64no—
1227D3—64no—
1228D3—122no—
1229D3—122no—
1230D3—122no—
1231D3—242no—
1232C22—21no—
1233C22—22no—
1234C22—21no—
1235C22—22no—
1236C22—22no—
1237C22—21no—
1238C22—62no—
1239C22—62no—
1240C22—62no—
1241C22—62no—
1242C22—62no—
1243C22—62no—
1244C22—92no—
1245C22—92no—
1246C22—181no—
1247C22—181no—
1248C22—181no—
1249C22—181no—
1250C22—182no—
1251C22—182no—
1252C22—182no—
1253C22—364no—
1254C22—724no—
1255C22—722no—
1256C22—724no—
1257C22C23×D3211yescharacteristic
1258C4—21no—
1259C4—21no—
1260C4—22no—
1261C4—62no—
1262C4—62no—
1263C4—62no—
1264C4—62no—
1265C4—62no—
1266C4—62no—
1267C4—181no—
1268C4—181no—
1269C4—182no—
1270C3—21no—
1271C3#8649012yescomplemented
1272C2—41no—
1273C2—42no—
1274C2—122no—
1275C2—122no—
1276C2—182no—
1277C2—182no—
1278C2—362no—
1279C2#1059667511yescharacteristic
1280C2#1059667511yescharacteristic
1281C2#1059669511yescharacteristic
subgroupG/H
center, FrattiniC22C23×D32
commutator, socle, cosocleC22×C32C25
FittingC32×#121C22
hypercenter#121D32
hypocenterC32#3534
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ #121

Complements

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

NH ≅ G/Ntype
1. C3⋊D3×#121C2semidirect
2. C3×#5615C2semidirect
3. #10595313C2semidirect
4. #10595311C2semidirect
5. #10595308C2semidirect
6. #10595297C2semidirect
7. #10595263C2semidirect
8. #10595163C2semidirect
9. #10595140C2semidirect
10. #10595085C2semidirect
11. #10595079C2semidirect
12. #10595016C2semidirect
13. #10594610C2semidirect
14. #10594572C2semidirect
15. #10594483C2semidirect
16. #10594283C2semidirect
17. #10594279C2semidirect
18. #10594204C2semidirect
19. #10594040C2semidirect
21. C2×D4×C3⋊D3C22semidirect
22. C2×D4×C3⋊D3C22semidirect
23. C22×C4×C3⋊D3C22semidirect
25. C2×#3811C22semidirect
26. C2×#3804C22semidirect
27. C2×D3×D12C22semidirect
28. C2×#3798C22semidirect
29. C32×#121C22semidirect
30. #64148C22semidirect
31. #64147C22semidirect
32. #64139C22semidirect
34. C4⋊C4×C3⋊D3C22semidirect
35. #64093C22semidirect
36. C22⋊C4×C3⋊D3C22semidirect
37. C3×#940C22semidirect
38. C3×#939C22semidirect
39. C3×#939C22semidirect
40. C3×#939C22semidirect
41. C3×#938C22semidirect
42. C3×#935C22semidirect
43. C3×#929C22semidirect
44. C3×C4×#67C22semidirect
45. C3×#894C22semidirect
46. C3×#889C22semidirect
47. C3×#884C22semidirect
48. C3×#883C22semidirect
49. C3×#67⋊C4C22semidirect
50. C3×#877C22semidirect
51. #63983C22semidirect
52. #63983C22semidirect
53. #63983C22semidirect
54. #63982C22semidirect
56. #63981C22semidirect
57. #63981C22semidirect
58. #63980C22semidirect
59. #63978C22semidirect
60. #63978C22semidirect
61. #63975C22semidirect
62. #63974C22semidirect
63. #63971C22semidirect
64. #63970C22semidirect
65. #63964C22semidirect
66. C2×#3722C22semidirect
67. #63962C22semidirect
68. #63961C22semidirect
69. #63959C22semidirect
70. #63958C22semidirect
71. #63958C22semidirect
72. #63953C22semidirect
73. #63952C22semidirect
74. #63923C22semidirect
75. #63922C22semidirect
76. #63921C22semidirect
77. #63921C22semidirect
78. D3×(C2×D3)⋊C4C22semidirect
80. #63912C22semidirect
81. #63910C22semidirect
82. #63904C22semidirect
83. C4×#626C22semidirect
84. C4×#626C22semidirect
85. #63897C22semidirect
86. #63897C22semidirect
87. #63895C22semidirect
88. #63894C22semidirect
89. #63893C22semidirect
90. #63884C22semidirect
91. #63883C22semidirect
92. #63883C22semidirect
93. #63881C22semidirect
94. #63874C22semidirect
95. #63868C22semidirect
96. #63868C22semidirect
97. #63865C22semidirect
98. #63865C22semidirect
99. #63861C22semidirect
100. #63859C22semidirect
101. #63853C22semidirect
102. #63853C22semidirect
103. #63853C22semidirect
104. #63852C22semidirect
105. #63851C22semidirect
106. #63850C22semidirect
107. #63846C22semidirect
123. #5615D3semidirect
263. C3×#121C2×D3semidirect
267. #940C2×D3semidirect
276. #939C2×D3semidirect
277. #939C2×D3semidirect
278. #939C2×D3semidirect
285. #938C2×D3semidirect
300. #935C2×D3semidirect
307. #929C2×D3semidirect
312. C4×#67C2×D3semidirect
341. #894C2×D3semidirect
351. #889C2×D3semidirect
365. #884C2×D3semidirect
371. #883C2×D3semidirect
380. #67⋊C4C2×D3semidirect
393. #877C2×D3semidirect
780. #121D32semidirect
1140. C32#3534semidirect
1271. C3#86490semidirect

Maximal subgroups

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

subgroupindex
C3⋊D3×#1212
C3×#56152
#105953132
#105953112
#105953082
#105952972
#105952632
#105951632
#105951402
#105950852
#105950792
#105950162
#105946102
#105945722
#105944832
#105942832
#105942792
#105942042
#105940402
#864903