Finite Group Databasebeta

← #11910742

Subgroups — #11910742

Order 1152.

2287 conjugacy classes of subgroups.

The subgroup lattice has 1287 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10596186C211yesmaximal, characteristic, complemented
2C3×#5720C211yesmaximal, characteristic, complemented
3C3×#5713C211yesmaximal, characteristic, complemented
4#10595275C211yesmaximal, characteristic, complemented
5#10595251C212yesmaximal, complemented
6#10595242C211yesmaximal, characteristic, complemented
7#10595214C212yesmaximal, complemented
8#10595208C212yesmaximal, complemented
9#10595207C212yesmaximal, complemented
10#10595193C212yesmaximal, complemented
11#10595184C212yesmaximal, complemented
12#10595178C211yesmaximal, characteristic, complemented
13#10595169C211yesmaximal, characteristic, complemented
14#10595162C212yesmaximal, complemented
15#10595138C212yesmaximal, complemented
16#10595135C212yesmaximal, complemented
17#10595127C212yesmaximal, complemented
18#10593936C212yesmaximal, complemented
19#10593933C212yesmaximal, complemented
20#87081—31nomaximal
21#87065—31nomaximal
22C2×#3830C2211yescharacteristic, complemented
23C2×D4×C3⋊D3C2211yescharacteristic
24C22×#626C2211yescharacteristic
25C22×#624C2211yescharacteristic, complemented
26C2×#3804C2212yes—
27C32×#127C2211yescharacteristic
28#64149C2211yescharacteristic, complemented
29#64148C2212yes—
30#64148C2212yescomplemented
31#64146C2212yes—
32#64146C2212yescomplemented
33#64145C2211yescharacteristic
34#64084C2211yescharacteristic, complemented
35#64081C2211yescharacteristic, complemented
36C3×#939C2212yescomplemented
37C3×#939C2212yescomplemented
38C3×#939C2212yescomplemented
39C3×#937C2211yescharacteristic
40C3×#937C2212yescomplemented
41C3×#936C2212yescomplemented
42C3×#936C2212yescomplemented
43C3×#935C2211yescharacteristic
44C3×#935C2211yescharacteristic
45C3×#935C2211yescharacteristic
46C3×#935C2212yescomplemented
47C3×#935C2212yescomplemented
48C3×D4×Dic3C2212yescomplemented
49C3×D4×Dic3C2212yescomplemented
50C3×#876C2212yescomplemented
51C3×C4×Dic6C2212yescomplemented
52#63982C2212yescomplemented
53#63981C2212yes—
54#63978C2212yescomplemented
55#63977C2211yescharacteristic
56#63975C2212yes—
57#63975C2212yescomplemented
58#63975C2212yescomplemented
59#63974C2212yes—
60#63974C2211yescharacteristic
61#63974C2211yescharacteristic, complemented
62#67⋊Dic3C2212yescomplemented
63Dic3×#67C2212yescomplemented
64#63971C2212yescomplemented
65#63971C2212yescomplemented
66#63969C2212yescomplemented
67D3×#217C2212yescomplemented
68#63966C2211yescharacteristic
69#63966C2212yescomplemented
70#63966C2211yescharacteristic, complemented
71#63966C2211yescharacteristic, complemented
72C2×Dic3⋊Dic3C2212yescomplemented
73#63964C2212yescomplemented
74#63964C2212yescomplemented
75#63962C2212yescomplemented
76#63958C2212yes—
77#63958C2212yes—
78#63958C2212yescomplemented
79#63956C2212yescomplemented
80#63956C2212yescomplemented
81#63956C2212yescomplemented
82#63952C2212yescomplemented
83#63952C2212yescomplemented
84#63952C2212yescomplemented
85#63910C2212yes—
86#63907C2212yescomplemented
87#63897C2212yescomplemented
88#63896C2212yescomplemented
89#63895C2212yescomplemented
90#63890C2212yescomplemented
91#63888C2212yescomplemented
92#63888C2212yescomplemented
93#63887C2212yescomplemented
94#63883C2212yescomplemented
95#63880C2212yes—
96#63880C2212yescomplemented
97#63878C2212yescomplemented
98#63870C2212yescomplemented
99#63868C2212yescomplemented
100#63867C2212yescomplemented
101#63859C2212yescomplemented
102#63854C2212yes—
103#63853C2212yes—
104#63852C2212yescomplemented
105#63846C2212yescomplemented
106#63840C2212yescomplemented
107#63836C2212yescomplemented
108#63836C2212yescomplemented
109C3×#560—31no—
110C3×#559—31no—
111#5720D311yescharacteristic, complemented
112#5715—31no—
113#5715—31no—
114#5715—61no—
115#5713D311yescharacteristic, complemented
116#5710—32no—
117#5708—32no—
118#5684—32no—
119#5679—32no—
120#5678—32no—
121#5678—32no—
122#5665—32no—
123#5663—32no—
124#5659—31no—
125#5659—32no—
126#5655—32no—
127#5653—31no—
128D3×#123—31no—
129D3×#123—31no—
130#5651—31no—
131#5651—31no—
132#5621—32no—
133#5618—32no—
134#5615—32no—
135#5613—32no—
136#5611—32no—
137#5606—32no—
138#5593—32no—
139#5591—32no—
140#5589—31no—
141#5587—31no—
142#5582—32no—
143#5581—32no—
144#5564—32no—
145#5550—32no—
146#5547—32no—
147#5540—32no—
148C23×C3⋊D3C2311yescharacteristic
149C23×C3⋊D3C2311yescharacteristic
150C23×C3×D3C2311yescharacteristic
151C2×C32×D4C2312yes—
152C2×C32×D4C2312yes—
153C2×C32×D4C2311yescharacteristic
154C2×C32×D4C2311yescharacteristic
155C2×#638C2312yes—
156C2×#638C2311yescharacteristic
157C2×#638C2311yescharacteristic
158C2×#638C2312yes—
159C2×#638C2312yes—
160C22×C3⋊Dic3C2312yes—
161#3830—42no—
162D4×C3⋊D3—42no—
163C2×C4⋊(C3⋊D3)C2311yescharacteristic
164C2×C4×C3⋊D3C2311yescharacteristic
165C2×#634C2311yescharacteristic
166C2×C3×#67C2312yes—
167C2×C3×#67C2312yes—
168C2×C3×#67C2312yes—
169C22×C3×Dic3C2311yescharacteristic
170C22×C3×Dic3C2311yescharacteristic
171C22×C3×Dic3C2312yes—
172C22×C3×Dic3C2311yescharacteristic
173C22×C3×Dic3C2312yes—
174C2×C3×Dic6C2312yes—
175C2×#627C2312yes—
176C2×#626—42no—
177C2×#626C2312yes—
178C2×#626C2312yes—
179C2×#626C2312yes—
180C2×#624—42no—
181C2×#624C2312yes—
182C2×#624C2312yes—
183C2×#624C2312yes—
184C2×#624C2312yes—
185#3804—44no—
186C2×D3×Dic3C2312yes—
187C2×D3×Dic3C2312yes—
188C32×C42C2311yescharacteristic
189#3757C2312yes—
190#3757C2312yes—
191#3752C2312yes—
192#3752C2312yes—
193#3752C2312yes—
194#3750C2312yes—
195C4×C3⋊Dic3C2311yescharacteristic
196C3×#217C2312yes—
197C3×#217C2312yes—
198C3×#217C2312yes—
199C3×#217C2312yes—
200C3×#217C2312yes—
201C3×#217C2311yescharacteristic
202C3×#217C2311yescharacteristic
203C3×#217C2311yescharacteristic
204C3×#217C2311yescharacteristic
205C3×#217C2312yes—
206C3×#217C2312yes—
207C3×(C2×D3)⋊C4C2312yes—
208C3×(C2×D3)⋊C4C2312yes—
209C3×(C2×D3)⋊C4C2312yes—
210C3×C4⋊Dic3C2312yes—
211C3×Dic3⋊C4C2312yes—
212C3×Dic3⋊C4C2312yes—
213C3×Dic3⋊C4C2312yes—
214C3×Dic3⋊C4C2312yes—
215C3×Dic3⋊C4C2312yes—
216C3×C4×Dic3C2312yes—
217C3×C4×Dic3C2312yes—
218#3724C2312yes—
219#3724C2312yes—
220#3724C2312yes—
221Dic3⋊Dic3C2312yes—
222Dic3⋊Dic3C2312yes—
223Dic3⋊Dic3C2312yes—
224Dic3⋊Dic3C2312yes—
225Dic3⋊Dic3C2312yes—
226Dic3⋊Dic3C2312yes—
227Dic3⋊Dic3C2312yes—
228Dic3⋊Dic3C2312yes—
229Dic3⋊Dic3C2312yes—
230#3722C2312yes—
231#3722C2312yes—
232#3722C2312yes—
233#3722C2312yes—
234#3722C2312yes—
235(C2×D3)⋊Dic3C2312yes—
236(C2×D3)⋊Dic3C2312yes—
237(C2×D3)⋊Dic3C2312yes—
238Dic32C2312yes—
239Dic32C2312yes—
240#3533—91noSylow
241C22×#67—31no—
242C2×#237—31no—
243C2×#237—31no—
244C2×#237—32no—
245C2×#237—61no—
246C2×D3×D4—31no—
247C2×D3×D4—31no—
248C2×D3×D4—61no—
249C2×#235—32no—
250C22×D12—31no—
251C22×C4×D3—31no—
252C22×C4×D3—31no—
253C3×#127—21no—
254C3×#127C2×D311yescharacteristic
255C3×#127C2×D311yescharacteristic
256C3×#126—32no—
257C3×#124—32no—
258C3×#124—32no—
259C3×#123—31no—
260C3×#123—31no—
261C3×#123—32no—
262C3×#123—31no—
263C3×#123—32no—
264C3×#121—32no—
265C3×#121—32no—
266C3×#121—32no—
267C3×#120—31no—
268C3×#120—32no—
269C3×C4×Q8—32no—
270C3×C4×D4—32no—
271C3×C4×D4—32no—
272#953—31no—
273C2×#217—32no—
274#947—32no—
275#946—32no—
276#946—32no—
277#946—32no—
278#940—31no—
279#940—31no—
280#940—61no—
281#939—32no—
282#939—32no—
283#939—32no—
284#939—32no—
285#939—32no—
286#939—32no—
287#939—32no—
288#939—62no—
289#939—62no—
290#939C2×D312yescomplemented
291#939C2×D312yescomplemented
292#939C2×D312yescomplemented
293#938—32no—
294#938—32no—
295#938—32no—
296#937—32no—
297#937—32no—
298#937—32no—
299#937—32no—
300#937—32no—
301#937—62no—
302#937—62no—
303#937C2×D311yescharacteristic
304#937C2×D312yescomplemented
305#936—31no—
306#936—31no—
307#936—61no—
308#936C2×D312yescomplemented
309#936C2×D312yescomplemented
310#935—32no—
311#935—32no—
312#935C2×D311yescharacteristic
313#935C2×D311yescharacteristic
314#935C2×D311yescharacteristic
315#935C2×D312yescomplemented
316#935C2×D312yescomplemented
317D4×Dic3—32no—
318D4×Dic3—32no—
319D4×Dic3C2×D312yescomplemented
320D4×Dic3C2×D312yescomplemented
321#930—32no—
322#929—31no—
323#929—31no—
324#929—31no—
325#929—32no—
326C4×#67—32no—
327C4×#67—32no—
328C4×#67—32no—
329C4×#67—32no—
330C2×C4⋊Dic3—32no—
331#924—32no—
332#924—32no—
333C2×Dic3⋊C4—32no—
334#898—32no—
335#897—32no—
336#896—32no—
337#896—32no—
338#896—32no—
339#896—32no—
340#895—32no—
341#894—32no—
342#894—32no—
343#894—32no—
344#894—32no—
345#894—32no—
346#892—32no—
347#892—32no—
348#892—32no—
349D3×C4⋊C4—32no—
350D3×C4⋊C4—32no—
351#890—32no—
352#889—32no—
353#889—32no—
354#889—32no—
355#889—32no—
356#888—32no—
357#888—32no—
358#886—32no—
359#886—31no—
360#886—31no—
361#886—32no—
362#886—31no—
363#886—32no—
364#885—32no—
365#885—32no—
366#884—32no—
367#884—32no—
368#884—32no—
369#884—32no—
370#884—32no—
371#884—32no—
372#883—32no—
373#883—32no—
374#883—32no—
375#883—32no—
376#883—32no—
377#883—32no—
378#883—32no—
379#883—32no—
380#883—32no—
381#882—31no—
382#882—32no—
383#67⋊C4—32no—
384#67⋊C4—32no—
385#67⋊C4—32no—
386#67⋊C4—32no—
387#67⋊C4—32no—
388#67⋊C4—32no—
389D3×C22⋊C4—32no—
390D3×C22⋊C4—32no—
391D3×C22⋊C4—31no—
392D3×C22⋊C4—32no—
393D3×C22⋊C4—31no—
394D3×C22⋊C4—31no—
395D3×C22⋊C4—31no—
396#879—32no—
397#879—32no—
398#879—32no—
399#879—32no—
400#879—32no—
401#879—32no—
402#879—32no—
403#878—32no—
404#878—32no—
405#878—32no—
406#878—32no—
407#878—32no—
408#878—32no—
409#877—32no—
410#876—32no—
411#876—32no—
412#876C2×D312yescomplemented
413#875—31no—
414#875—31no—
415#875—32no—
416#875—61no—
417C4×D12—32no—
418C4×D12—32no—
419#872—31no—
420#872—31no—
421#872—32no—
422#872—32no—
423#872—61no—
424#870—32no—
425C4×Dic6C2×D312yescomplemented
426C23×C32C2411yescharacteristic
427C23×C32C2411yescharacteristic
428C23×C32C2412yes—
429C22×C3⋊D3—22no—
430C22×C3⋊D3—22no—
431C22×C3⋊D3—42no—
432C22×C3⋊D3—42no—
433C22×C3⋊D3C2411yescharacteristic
434C22×C3⋊D3C2411yescharacteristic
435C22×C3⋊D3C2411yescharacteristic
436C22×C3×D3—42no—
437C22×C3×D3—41no—
438C22×C3×D3C2412yes—
439C32×D4—41no—
440C32×D4—41no—
441C32×D4—42no—
442C32×D4—42no—
443C2×C32×C4C2412yes—
444C2×C32×C4C2411yescharacteristic
445#638—24no—
446#638—41no—
447#638—41no—
448#638—42no—
449#638—42no—
450C2×C3⋊Dic3—42no—
451C2×C3⋊Dic3C2412yes—
452C2×C3⋊Dic3C2412yes—
453C2×C3⋊Dic3C2411yescharacteristic
454C4⋊(C3⋊D3)—41no—
455C4×C3⋊D3—22no—
456#634—41no—
457C3×#67—42no—
458C3×#67—42no—
459C3×#67—42no—
460C2×C3×Dic3—42no—
461C2×C3×Dic3—41no—
462C2×C3×Dic3—41no—
463C2×C3×Dic3—41no—
464C2×C3×Dic3—42no—
465C2×C3×Dic3C2412yes—
466C2×C3×Dic3C2412yes—
467C2×C3×Dic3C2412yes—
468C2×C3×Dic3C2412yes—
469C2×C3×Dic3C2412yes—
470C2×C3×Dic3C2412yes—
471C2×C3×Dic3C2412yes—
472C3×Dic6—42no—
473#627—42no—
474#626—24no—
475#626—42no—
476#626—42no—
477#624—24no—
478#624—42no—
479#624—42no—
480#624—42no—
481D3×Dic3—42no—
482D3×Dic3—42no—
483#563—91no—
484#562—92no—
485#560—31no—
486#559—31no—
487#553—92no—
488#552—92no—
489#551—91no—
490#551—92no—
491#547—92no—
492#546—92no—
493#542—92no—
494#540—92no—
495#539—92no—
496#538—92no—
497#538—92no—
498#535—91no—
499#534—91no—
500#525—92no—
501C2×#123—91no—
502C24×C3—31no—
503C23×D3—31no—
504C23×D3—31no—
505C23×D3—31no—
506C23×D3—31no—
507C23×D3—61no—
508C23×D3—61no—
509C23×D3C22×D311yescharacteristic
510C2×C3×Q8—32no—
511C2×C3×D4—21no—
512C2×C3×D4—21no—
513C2×C3×D4—22no—
514C2×C3×D4—22no—
515C2×C3×D4—32no—
516C2×C3×D4—32no—
517C2×C3×D4—32no—
518C2×C3×D4C22×D312yes—
519C2×C3×D4C22×D312yes—
520C2×C3×D4C22×D311yescharacteristic
521C2×C3×D4C22×D311yescharacteristic
522C2×C3×D4C22×D311yescharacteristic
523C2×C3×D4C22×D312yes—
524C2×C3×D4C22×D312yes—
525C2×C3×D4C22×D311yescharacteristic
526C22×C3×C4—32no—
527C22×C3×C4—31no—
528C22×C3×C4—31no—
529C22×C3×C4—32no—
530C22×C3×C4—31no—
531C2×#67—32no—
532C2×#67—32no—
533C2×#67—32no—
534C2×#67—32no—
535C2×#67—31no—
536C2×#67—31no—
537C2×#67—32no—
538C2×#67—32no—
539C2×#67—31no—
540C2×#67—31no—
541C2×#67—32no—
542C2×#67—32no—
543C2×#67—32no—
544C2×#67—62no—
545C2×#67—61no—
546C2×#67—61no—
547C2×#67—62no—
548C2×#67—62no—
549C2×#67—122no—
550C2×#67C22×D312yes—
551C2×#67C22×D312yes—
552C2×#67C22×D312yes—
553C22×Dic3—32no—
554C22×Dic3—32no—
555C22×Dic3—32no—
556C22×Dic3—32no—
557C22×Dic3—62no—
558C22×Dic3C22×D311yescharacteristic
559C22×Dic3C22×D311yescharacteristic
560C22×Dic3C22×D312yes—
561C22×Dic3C22×D312yes—
562C22×Dic3C22×D311yescharacteristic
563#237—124no—
564#237—122no—
565#237—122no—
566#237—124no—
567D3×D4—122no—
568D3×D4—122no—
569D3×D4—124no—
570#235—124no—
571C2×D12—32no—
572C2×D12—32no—
573C2×D12—32no—
574C2×D12—31no—
575C2×D12—31no—
576C2×D12—61no—
577C2×D12—122no—
578C2×C4×D3—31no—
579C2×C4×D3—31no—
580C2×C4×D3—32no—
581C2×C4×D3—32no—
582C2×C4×D3—32no—
583C2×C4×D3—32no—
584C2×C4×D3—32no—
585C2×C4×D3—32no—
586C2×C4×D3—32no—
587C2×C4×D3—32no—
588C2×C4×D3—32no—
589C2×C4×D3—32no—
590C2×C4×D3—61no—
591C2×C4×D3—122no—
592C2×C4×D3—122no—
593C2×Dic6—31no—
594C2×Dic6—31no—
595C2×Dic6—32no—
596C2×Dic6—32no—
597C2×Dic6—61no—
598C2×Dic6C22×D312yes—
599C3×C4⋊C4—32no—
600C3×C4⋊C4—32no—
601C3×C4⋊C4—32no—
602C3×C4⋊C4—32no—
603C3×C4⋊C4—32no—
604C3×C4⋊C4—32no—
605C3×C22⋊C4—32no—
606C3×C22⋊C4—32no—
607C3×C22⋊C4—32no—
608C3×C22⋊C4—32no—
609C3×C22⋊C4—31no—
610C3×C22⋊C4—31no—
611C3×C22⋊C4—31no—
612C3×C22⋊C4—32no—
613C3×C22⋊C4—31no—
614C3×C22⋊C4—32no—
615C3×C22⋊C4—32no—
616C3×C22⋊C4—32no—
617C3×C22⋊C4—32no—
618C3×C22⋊C4—32no—
619C3×C42—21no—
620C3×C42—32no—
621C3×C42—32no—
622C3×C42C22×D311yescharacteristic
623C3×C42C22×D311yescharacteristic
624#217—32no—
625#217—32no—
626#217—32no—
627#217—32no—
628#217—32no—
629#217—32no—
630#217—32no—
631#217—62no—
632#217—62no—
633#217C22×D312yes—
634#217C22×D312yes—
635#217C22×D311yescharacteristic
636#217C22×D311yescharacteristic
637#217C22×D311yescharacteristic
638#217C22×D312yes—
639#217C22×D312yes—
640#217C22×D312yes—
641#217C22×D311yescharacteristic
642#217C22×D312yes—
643#217C22×D312yes—
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—32no—
650(C2×D3)⋊C4—32no—
651(C2×D3)⋊C4—32no—
652(C2×D3)⋊C4—32no—
653(C2×D3)⋊C4—32no—
654(C2×D3)⋊C4—32no—
655(C2×D3)⋊C4—32no—
656(C2×D3)⋊C4—32no—
657(C2×D3)⋊C4—32no—
658(C2×D3)⋊C4—32no—
659(C2×D3)⋊C4—32no—
660(C2×D3)⋊C4—32no—
661(C2×D3)⋊C4—32no—
662(C2×D3)⋊C4—32no—
663(C2×D3)⋊C4—62no—
664(C2×D3)⋊C4—62no—
665(C2×D3)⋊C4—62no—
666(C2×D3)⋊C4C22×D312yes—
667(C2×D3)⋊C4C22×D312yes—
668(C2×D3)⋊C4C22×D312yes—
669C4⋊Dic3—32no—
670C4⋊Dic3—32no—
671C4⋊Dic3—32no—
672C4⋊Dic3—32no—
673C4⋊Dic3—32no—
674C4⋊Dic3—32no—
675C4⋊Dic3—32no—
676C4⋊Dic3—32no—
677C4⋊Dic3—32no—
678C4⋊Dic3C22×D312yes—
679Dic3⋊C4—32no—
680Dic3⋊C4—32no—
681Dic3⋊C4—32no—
682Dic3⋊C4—32no—
683Dic3⋊C4—32no—
684Dic3⋊C4—32no—
685Dic3⋊C4—32no—
686Dic3⋊C4—32no—
687Dic3⋊C4—32no—
688Dic3⋊C4—32no—
689Dic3⋊C4—32no—
690Dic3⋊C4—32no—
691Dic3⋊C4—32no—
692Dic3⋊C4—32no—
693Dic3⋊C4—32no—
694Dic3⋊C4—32no—
695Dic3⋊C4—32no—
696Dic3⋊C4—62no—
697Dic3⋊C4C22×D312yes—
698Dic3⋊C4C22×D312yes—
699Dic3⋊C4C22×D312yes—
700Dic3⋊C4C22×D312yes—
701Dic3⋊C4C22×D312yes—
702C4×Dic3—31no—
703C4×Dic3—31no—
704C4×Dic3—32no—
705C4×Dic3—32no—
706C4×Dic3—32no—
707C4×Dic3—32no—
708C4×Dic3—61no—
709C4×Dic3C22×D312yes—
710C4×Dic3C22×D312yes—
711C22×C32—21no—
712C22×C32—22no—
713C22×C32—21no—
714C22×C32—22no—
715C22×C32—22no—
716C22×C32—22no—
717C22×C32—22no—
718C22×C32C2511yescharacteristic
719C2×C3⋊D3—22no—
720C2×C3⋊D3—21no—
721C2×C3⋊D3—21no—
722C2×C3⋊D3—22no—
723C2×C3⋊D3—22no—
724C2×C3⋊D3—44no—
725C2×C3⋊D3—82no—
726C2×C3⋊D3H(5,𝔽2)12yes—
727C2×C3×D3—22no—
728C2×C3×D3—22no—
729C2×C3×D3—22no—
730C2×C3×D3—82no—
731C32×C4—21no—
732C32×C4—22no—
733C3⋊Dic3—21no—
734C3⋊Dic3—22no—
735C3⋊Dic3—22no—
736C3×Dic3—22no—
737C3×Dic3—22no—
738C3×Dic3—22no—
739C3×Dic3—22no—
740C3×Dic3—22no—
741C3×Dic3—22no—
742C3×Dic3—22no—
743C2×#41—92no—
744C2×#41—91no—
745C22×D4—91no—
746C22×D4—91no—
747C23×C4—91no—
748C4⋊Q8—92no—
749#127—91no—
750#127D3211yescharacteristic
751#126—32no—
752#126—92no—
753#126—92no—
754#126—92no—
755#126—92no—
756#126—92no—
757#125—92no—
758#125—92no—
759#125—92no—
760#124—32no—
761#124—32no—
762#124—92no—
763#124—92no—
764#124—91no—
765#124—91no—
766#123—31no—
767#123—31no—
768#123—31no—
769#123—32no—
770#123—32no—
771#123—92no—
772#123—92no—
773#123—92no—
774#123—92no—
775#123—92no—
776#123—92no—
777#123—91no—
778#123—91no—
779#123—91no—
780#123—92no—
781#123—92no—
782#123—92no—
783#123—92no—
784C22⋊Q8—92no—
785C22⋊Q8—92no—
786C22⋊Q8—92no—
787C22⋊Q8—92no—
788C22⋊Q8—92no—
789C22⋊Q8—92no—
790C22⋊Q8—92no—
791C22⋊Q8—92no—
792#121—32no—
793#121—32no—
794#121—32no—
795#121—92no—
796#121—92no—
797#121—92no—
798#121—92no—
799#121—92no—
800#121—92no—
801#121—92no—
802#121—92no—
803#121—92no—
804#120—31no—
805#120—32no—
806#120—92no—
807#120—91no—
808#120—92no—
809#120—92no—
810C4×Q8—32no—
811C4×D4—32no—
812C4×D4—32no—
813C4×D4—92no—
814C4×D4—92no—
815C4×D4—92no—
816C4×D4—92no—
817C4×D4—92no—
818C4×D4—92no—
819C4×D4—92no—
820#117—92no—
821#117—92no—
822#117—92no—
823#117—91no—
824C2×C4⋊C4—92no—
825C2×C4⋊C4—92no—
826C2×C22⋊C4—91no—
827C2×C22⋊C4—92no—
828C2×C22⋊C4—91no—
829C2×C22⋊C4—92no—
830C23×C3—21no—
831C23×C3—21no—
832C23×C3—22no—
833C23×C3—32no—
834C23×C3—121no—
835C23×C3—122no—
836C23×C3C23×D311yescharacteristic
837C23×C3C23×D311yescharacteristic
838C23×C3C23×D311yescharacteristic
839C23×C3C23×D311yescharacteristic
840C23×C3C23×D312yes—
841C23×C3C23×D312yes—
842C22×D3—31no—
843C22×D3—31no—
844C22×D3—31no—
845C22×D3—31no—
846C22×D3—31no—
847C22×D3—31no—
848C22×D3—41no—
849C22×D3—42no—
850C22×D3—61no—
851C22×D3—61no—
852C22×D3—61no—
853C22×D3—62no—
854C22×D3—62no—
855C22×D3—62no—
856C22×D3—62no—
857C22×D3—122no—
858C22×D3—122no—
859C22×D3—122no—
860C22×D3—122no—
861C22×D3—122no—
862C22×D3—122no—
863C22×D3—242no—
864C22×D3—242no—
865C22×D3C23×D312yes—
866C3×Q8—122no—
867C3×D4—41no—
868C3×D4—41no—
869C3×D4—41no—
870C3×D4—41no—
871C3×D4—42no—
872C3×D4—42no—
873C3×D4—42no—
874C3×D4—42no—
875C3×D4—42no—
876C3×D4—42no—
877C3×D4—82no—
878C3×D4—82no—
879C3×D4—122no—
880C3×D4—122no—
881C3×D4—122no—
882C2×C3×C4—21no—
883C2×C3×C4—22no—
884C2×C3×C4—32no—
885C2×C3×C4—32no—
886C2×C3×C4—32no—
887C2×C3×C4—32no—
888C2×C3×C4—32no—
889C2×C3×C4—32no—
890C2×C3×C4—32no—
891C2×C3×C4—121no—
892C2×C3×C4—121no—
893C2×C3×C4—121no—
894C2×C3×C4—122no—
895C2×C3×C4—122no—
896C2×C3×C4C23×D311yescharacteristic
897C2×C3×C4C23×D311yescharacteristic
898C2×C3×C4C23×D312yes—
899C2×C3×C4C23×D312yes—
900#67—42no—
901#67—42no—
902#67—42no—
903#67—64no—
904#67—64no—
905#67—64no—
906#67—124no—
907#67—122no—
908#67—122no—
909#67—121no—
910#67—121no—
911#67—121no—
912#67—121no—
913#67—122no—
914#67—122no—
915#67—122no—
916#67—122no—
917#67—122no—
918#67—122no—
919#67—242no—
920#67—242no—
921C2×Dic3—32no—
922C2×Dic3—32no—
923C2×Dic3—32no—
924C2×Dic3—32no—
925C2×Dic3—31no—
926C2×Dic3—31no—
927C2×Dic3—41no—
928C2×Dic3—41no—
929C2×Dic3—42no—
930C2×Dic3—42no—
931C2×Dic3—41no—
932C2×Dic3—61no—
933C2×Dic3—62no—
934C2×Dic3—62no—
935C2×Dic3—122no—
936C2×Dic3—122no—
937C2×Dic3—122no—
938C2×Dic3—122no—
939C2×Dic3—124no—
940C2×Dic3C23×D312yes—
941C2×Dic3C23×D312yes—
942C2×Dic3C23×D312yes—
943C2×Dic3C23×D312yes—
944C2×Dic3C23×D312yes—
945C2×Dic3C23×D312yes—
946C2×Dic3C23×D312yes—
947D12—64no—
948D12—121no—
949D12—121no—
950D12—122no—
951D12—122no—
952D12—122no—
953C4×D3—64no—
954C4×D3—64no—
955C4×D3—62no—
956C4×D3—62no—
957C4×D3—64no—
958C4×D3—122no—
959C4×D3—122no—
960C4×D3—122no—
961C4×D3—122no—
962C4×D3—122no—
963C4×D3—122no—
964C4×D3—122no—
965C4×D3—122no—
966Dic6—42no—
967Dic6—122no—
968Dic6—122no—
969Dic6—121no—
970Dic6—121no—
971Dic6—122no—
972C2×C32—41no—
973C2×C32—41no—
974C2×C32—42no—
975C2×C32C2×H(5,𝔽2)11yescharacteristic
976C2×C32#58512yes—
977C3⋊D3—22no—
978C3⋊D3—41no—
979C3⋊D3—41no—
980C3×D3—42no—
981C24—31no—
982C24—91no—
983C24—91no—
984#41—364no—
985#41—362no—
986C2×Q8—32no—
987C2×Q8—92no—
988C2×Q8—91no—
989C2×D4—32no—
990C2×D4—32no—
991C2×D4—32no—
992C2×D4—92no—
993C2×D4—92no—
994C2×D4—92no—
995C2×D4—92no—
996C2×D4—92no—
997C2×D4—92no—
998C2×D4—91no—
999C2×D4—91no—
1000C2×D4—91no—
1001C2×D4—362no—
1002C2×D4—362no—
1003C2×D4C2×D3212yes—
1004C2×D4C2×D3212yes—
1005C2×D4C2×D3211yescharacteristic
1006C2×D4C2×D3211yescharacteristic
1007C22×C4—32no—
1008C22×C4—32no—
1009C22×C4—31no—
1010C22×C4—31no—
1011C22×C4—31no—
1012C22×C4—92no—
1013C22×C4—92no—
1014C22×C4—92no—
1015C22×C4—92no—
1016C22×C4—92no—
1017C22×C4—92no—
1018C22×C4—92no—
1019C22×C4—91no—
1020C22×C4—362no—
1021C4⋊C4—32no—
1022C4⋊C4—32no—
1023C4⋊C4—32no—
1024C4⋊C4—32no—
1025C4⋊C4—32no—
1026C4⋊C4—32no—
1027C4⋊C4—92no—
1028C4⋊C4—92no—
1029C4⋊C4—92no—
1030C4⋊C4—92no—
1031C4⋊C4—92no—
1032C4⋊C4—92no—
1033C4⋊C4—92no—
1034C4⋊C4—92no—
1035C4⋊C4—92no—
1036C4⋊C4—92no—
1037C4⋊C4—92no—
1038C4⋊C4—92no—
1039C4⋊C4—92no—
1040C22⋊C4—32no—
1041C22⋊C4—32no—
1042C22⋊C4—31no—
1043C22⋊C4—31no—
1044C22⋊C4—31no—
1045C22⋊C4—31no—
1046C22⋊C4—32no—
1047C22⋊C4—32no—
1048C22⋊C4—32no—
1049C22⋊C4—32no—
1050C22⋊C4—32no—
1051C22⋊C4—32no—
1052C22⋊C4—32no—
1053C22⋊C4—32no—
1054C22⋊C4—92no—
1055C22⋊C4—92no—
1056C22⋊C4—92no—
1057C22⋊C4—92no—
1058C22⋊C4—92no—
1059C22⋊C4—92no—
1060C22⋊C4—92no—
1061C22⋊C4—92no—
1062C22⋊C4—92no—
1063C22⋊C4—92no—
1064C22⋊C4—92no—
1065C22⋊C4—92no—
1066C22⋊C4—92no—
1067C42—32no—
1068C42—32no—
1069C42—92no—
1070C42—92no—
1071C42—91no—
1072C42C2×D3211yescharacteristic
1073C22×C3—22no—
1074C22×C3—22no—
1075C22×C3—22no—
1076C22×C3—22no—
1077C22×C3—22no—
1078C22×C3—21no—
1079C22×C3—21no—
1080C22×C3—21no—
1081C22×C3—22no—
1082C22×C3—21no—
1083C22×C3—22no—
1084C22×C3—22no—
1085C22×C3—22no—
1086C22×C3—22no—
1087C22×C3—21no—
1088C22×C3—42no—
1089C22×C3—41no—
1090C22×C3—41no—
1091C22×C3—42no—
1092C22×C3—42no—
1093C22×C3—42no—
1094C22×C3—42no—
1095C22×C3—62no—
1096C22×C3—62no—
1097C22×C3—62no—
1098C22×C3—242no—
1099C22×C3C24×D311yescharacteristic
1100C22×C3C24×D311yescharacteristic
1101C2×D3—22no—
1102C2×D3—22no—
1103C2×D3—22no—
1104C2×D3—32no—
1105C2×D3—32no—
1106C2×D3—62no—
1107C2×D3—62no—
1108C2×D3—62no—
1109C2×D3—62no—
1110C2×D3—62no—
1111C2×D3—61no—
1112C2×D3—61no—
1113C2×D3—61no—
1114C2×D3—61no—
1115C2×D3—62no—
1116C2×D3—62no—
1117C2×D3—82no—
1118C2×D3—122no—
1119C2×D3—121no—
1120C2×D3—121no—
1121C2×D3—122no—
1122C2×D3—122no—
1123C2×D3—124no—
1124C2×D3—124no—
1125C2×D3—244no—
1126C2×D3—242no—
1127C2×D3—242no—
1128C2×D3—244no—
1129C3×C4—22no—
1130C3×C4—22no—
1131C3×C4—21no—
1132C3×C4—21no—
1133C3×C4—22no—
1134C3×C4—42no—
1135C3×C4—62no—
1136C3×C4—62no—
1137C3×C4—62no—
1138C3×C4—62no—
1139C3×C4—62no—
1140C3×C4—62no—
1141C3×C4—62no—
1142Dic3—22no—
1143Dic3—22no—
1144Dic3—22no—
1145Dic3—22no—
1146Dic3—22no—
1147Dic3—22no—
1148Dic3—22no—
1149Dic3—62no—
1150Dic3—62no—
1151Dic3—62no—
1152Dic3—62no—
1153Dic3—61no—
1154Dic3—61no—
1155Dic3—62no—
1156Dic3—122no—
1157Dic3—122no—
1158C32#353311yescharacteristic, complemented, Sylow
1159C23—32no—
1160C23—91no—
1161C23—91no—
1162C23—91no—
1163C23—121no—
1164C23—122no—
1165C23—182no—
1166C23—182no—
1167C23—362no—
1168C23—362no—
1169C23C22×D3211yescharacteristic
1170C23C22×D3211yescharacteristic
1171C23C22×D3212yes—
1172Q8—122no—
1173Q8—361no—
1174Q8—362no—
1175D4—41no—
1176D4—41no—
1177D4—42no—
1178D4—42no—
1179D4—122no—
1180D4—122no—
1181D4—122no—
1182D4—184no—
1183D4—184no—
1184D4—361no—
1185D4—362no—
1186D4—362no—
1187D4—361no—
1188D4—361no—
1189D4—362no—
1190D4—362no—
1191C2×C4—32no—
1192C2×C4—32no—
1193C2×C4—32no—
1194C2×C4—32no—
1195C2×C4—32no—
1196C2×C4—32no—
1197C2×C4—32no—
1198C2×C4—92no—
1199C2×C4—92no—
1200C2×C4—91no—
1201C2×C4—121no—
1202C2×C4—121no—
1203C2×C4—121no—
1204C2×C4—122no—
1205C2×C4—122no—
1206C2×C4—182no—
1207C2×C4—184no—
1208C2×C4—362no—
1209C2×C4—362no—
1210C2×C4—362no—
1211C2×C4—362no—
1212C2×C4—362no—
1213C2×C4—362no—
1214C2×C4C22×D3212yes—
1215C2×C4C22×D3211yescharacteristic
1216C2×C3—21no—
1217C2×C3—22no—
1218C2×C3—41no—
1219C2×C3—41no—
1220C2×C3—42no—
1221C2×C3—41no—
1222C2×C3—41no—
1223C2×C3—42no—
1224C2×C3—81no—
1225C2×C3—81no—
1226C2×C3—82no—
1227C2×C3—122no—
1228C2×C3#596412yes—
1229C2×C3D3×H(5,𝔽2)11yescharacteristic
1230C2×C3D3×H(5,𝔽2)11yescharacteristic
1231C2×C3#596612yes—
1232D3—42no—
1233D3—62no—
1234D3—62no—
1235D3—122no—
1236D3—121no—
1237D3—121no—
1238D3—121no—
1239D3—121no—
1240D3—241no—
1241D3—241no—
1242C22—21no—
1243C22—22no—
1244C22—21no—
1245C22—22no—
1246C22—22no—
1247C22—22no—
1248C22—22no—
1249C22—62no—
1250C22—62no—
1251C22—62no—
1252C22—92no—
1253C22—182no—
1254C22—181no—
1255C22—181no—
1256C22—182no—
1257C22—182no—
1258C22—242no—
1259C22—364no—
1260C22—722no—
1261C22C23×D3211yescharacteristic
1262C4—21no—
1263C4—22no—
1264C4—62no—
1265C4—62no—
1266C4—62no—
1267C4—62no—
1268C4—62no—
1269C4—62no—
1270C4—62no—
1271C4—181no—
1272C4—182no—
1273C4—182no—
1274C3—21no—
1275C3#8706511yescharacteristic, complemented
1276C3#8708111yescharacteristic, complemented
1277C2—41no—
1278C2—41no—
1279C2—42no—
1280C2—122no—
1281C2—182no—
1282C2—361no—
1283C2—361no—
1284C2#1059667511yescharacteristic
1285C2#1059667812yes—
subgroupG/H
center, FrattiniC22C23×D32
commutator, socle, cosocleC22×C32C25
FittingC32×#127C22
hypercenter#127D32
hypocenterC32#3533
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ #127

Complements

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

NH ≅ G/Ntype
1. #10596186C2semidirect
2. C3×#5720C2semidirect
3. C3×#5713C2semidirect
4. #10595275C2semidirect
5. #10595251C2semidirect
6. #10595242C2semidirect
7. #10595214C2semidirect
8. #10595208C2semidirect
9. #10595207C2semidirect
10. #10595193C2semidirect
11. #10595184C2semidirect
12. #10595178C2semidirect
13. #10595169C2semidirect
14. #10595162C2semidirect
15. #10595138C2semidirect
16. #10595135C2semidirect
17. #10595127C2semidirect
18. #10593936C2semidirect
19. #10593933C2semidirect
22. C2×#3830C22semidirect
25. C22×#624C22semidirect
28. #64149C22semidirect
30. #64148C22semidirect
32. #64146C22semidirect
34. #64084C22semidirect
35. #64081C22semidirect
36. C3×#939C22semidirect
37. C3×#939C22semidirect
38. C3×#939C22semidirect
40. C3×#937C22semidirect
41. C3×#936C22semidirect
42. C3×#936C22semidirect
46. C3×#935C22semidirect
47. C3×#935C22semidirect
48. C3×D4×Dic3C22semidirect
49. C3×D4×Dic3C22semidirect
50. C3×#876C22semidirect
51. C3×C4×Dic6C22semidirect
52. #63982C22semidirect
54. #63978C22semidirect
57. #63975C22semidirect
58. #63975C22semidirect
61. #63974C22semidirect
62. #67⋊Dic3C22semidirect
63. Dic3×#67C22semidirect
64. #63971C22semidirect
65. #63971C22semidirect
66. #63969C22semidirect
67. D3×#217C22semidirect
69. #63966C22semidirect
70. #63966C22semidirect
71. #63966C22semidirect
72. C2×Dic3⋊Dic3C22semidirect
73. #63964C22semidirect
74. #63964C22semidirect
75. #63962C22semidirect
78. #63958C22semidirect
79. #63956C22semidirect
80. #63956C22semidirect
81. #63956C22semidirect
82. #63952C22semidirect
83. #63952C22semidirect
84. #63952C22semidirect
86. #63907C22semidirect
87. #63897C22semidirect
88. #63896C22semidirect
89. #63895C22semidirect
90. #63890C22semidirect
91. #63888C22semidirect
92. #63888C22semidirect
93. #63887C22semidirect
94. #63883C22semidirect
96. #63880C22semidirect
97. #63878C22semidirect
98. #63870C22semidirect
99. #63868C22semidirect
100. #63867C22semidirect
101. #63859C22semidirect
104. #63852C22semidirect
105. #63846C22semidirect
106. #63840C22semidirect
107. #63836C22semidirect
108. #63836C22semidirect
111. #5720D3semidirect
115. #5713D3semidirect
290. #939C2×D3semidirect
291. #939C2×D3semidirect
292. #939C2×D3semidirect
304. #937C2×D3semidirect
308. #936C2×D3semidirect
309. #936C2×D3semidirect
315. #935C2×D3semidirect
316. #935C2×D3semidirect
319. D4×Dic3C2×D3semidirect
320. D4×Dic3C2×D3semidirect
412. #876C2×D3semidirect
425. C4×Dic6C2×D3semidirect
1158. C32#3533semidirect
1275. C3#87065semidirect
1276. C3#87081semidirect

Maximal subgroups

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

subgroupindex
#105961862
C3×#57202
C3×#57132
#105952752
#105952512
#105952422
#105952142
#105952082
#105952072
#105951932
#105951842
#105951782
#105951692
#105951622
#105951382
#105951352
#105951272
#105939362
#105939332
#870813
#870653