Finite Group Databasebeta

← #11910739

Subgroups — #11910739

Order 1152.

2293 conjugacy classes of subgroups.

The subgroup lattice has 1288 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10596124C211yesmaximal, characteristic, complemented
2C3×#5664C211yesmaximal, characteristic, complemented
3C3×#5651C211yesmaximal, characteristic, complemented
4#10595266C211yesmaximal, characteristic, complemented
5#10595208C211yesmaximal, characteristic, complemented
6#10595169C211yesmaximal, characteristic, complemented
7#10595168C211yesmaximal, characteristic, complemented
8#10595018C212yesmaximal, complemented
9#10594936C212yesmaximal, complemented
10#10594467C212yesmaximal, complemented
11#10594372C212yesmaximal, complemented
12#10594352C212yesmaximal, complemented
13#10594349C212yesmaximal, complemented
14#10594178C212yesmaximal, complemented
15#10594162C212yesmaximal, complemented
16#10594162C212yesmaximal, complemented
17#10594153C212yesmaximal, complemented
18#10594097C212yesmaximal, complemented
19#10594066C212yesmaximal, complemented
20#87128—31nomaximal
21#87065—31nomaximal
22C2×D4×C3⋊D3C2211yescharacteristic
23C22×C4⋊(C3⋊D3)C2211yescharacteristic
24C22×#624C2211yescharacteristic, complemented
25C2×#3799C2212yes—
26C2×#3796C2211yescharacteristic, complemented
27C32×#123C2211yescharacteristic
28#64146C2211yescharacteristic
29#64138C2211yescharacteristic
30#64104C2212yes—
31#64103C2212yes—
32#64093C2212yes—
33#64091C2212yes—
34#64091C2211yescharacteristic
35C22⋊C4×C3⋊D3C2211yescharacteristic
36C3×#940C2211yescharacteristic
37C3×#936C2211yescharacteristic
38C3×#935C2211yescharacteristic
39C3×#935C2211yescharacteristic
40C3×C4×#67C2212yescomplemented
41C3×#924C2212yescomplemented
42C3×#894C2212yescomplemented
43C3×#889C2212yescomplemented
44C3×#888C2212yescomplemented
45C3×#887C2212yescomplemented
46C3×#885C2212yescomplemented
47C3×#885C2212yescomplemented
48C3×#67⋊C4C2212yescomplemented
49C3×#879C2212yescomplemented
50C3×#879C2212yescomplemented
51C3×#878C2212yescomplemented
52#63981C2212yes—
53#63981C2212yescomplemented
54#63981C2212yescomplemented
55#63978C2212yescomplemented
56#63975C2212yes—
57#63975C2212yescomplemented
58#63974C2212yes—
59#63974C2211yescharacteristic, complemented
60#63974C2212yescomplemented
61#63971C2212yes—
62#63971C2212yescomplemented
63#63971C2212yescomplemented
64#63969C2212yescomplemented
65#63966C2211yescharacteristic, complemented
66#63966C2211yescharacteristic, complemented
67#63956C2212yescomplemented
68#63952C2212yescomplemented
69#63911C2211yescharacteristic, complemented
70#63910C2212yes—
71#63910C2212yescomplemented
72#63910C2212yescomplemented
73#63910C2212yescomplemented
74#63909C2212yescomplemented
75#63904C2212yescomplemented
76#63897C2212yes—
77#63897C2212yescomplemented
78#63897C2212yescomplemented
79#63894C2212yes—
80#63894C2212yescomplemented
81#63890C2212yescomplemented
82#63890C2212yescomplemented
83#63888C2212yescomplemented
84#63888C2212yescomplemented
85#63888C2212yescomplemented
86#63888C2212yescomplemented
87#63887C2212yescomplemented
88#63886C2212yescomplemented
89#63883C2212yescomplemented
90#63881C2212yescomplemented
91#63880C2212yescomplemented
92#63880C2212yescomplemented
93D3×Dic3⋊C4C2212yescomplemented
94#63874C2211yescharacteristic, complemented
95#63874C2212yescomplemented
96#63871C2212yescomplemented
97#63868C2212yescomplemented
98#63868C2212yescomplemented
99#63868C2212yescomplemented
100#63867C2212yescomplemented
101#63864C2211yescharacteristic, complemented
102#63864C2212yescomplemented
103#63864C2212yescomplemented
104#63854C2212yescomplemented
105#63853C2212yescomplemented
106#63847C2212yescomplemented
107#63836C2212yescomplemented
108#63836C2212yescomplemented
109C3×#563—31no—
110C3×#559—31no—
111#5733—32no—
112#5726—32no—
113#5720—31no—
114#5715—31no—
115#5709—32no—
116#5705—32no—
117#5704—32no—
118#5704—32no—
119#5697—32no—
120#5693—32no—
121#5684—32no—
122#5679—31no—
123#5679—32no—
124#5678—32no—
125#5678—32no—
126#5674—31no—
127#5666—31no—
128#5664D311yescharacteristic, complemented
129#5663—32no—
130#5659—31no—
131#5655—32no—
132#5653—31no—
133#5653—31no—
134#5653—61no—
135D3×#123—31no—
136D3×#123—31no—
137#5651D311yescharacteristic, complemented
138#5647—32no—
139#5638—32no—
140#5630—32no—
141#5627—32no—
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×D4C2311yescharacteristic
152C22×C32×C4C2311yescharacteristic
153C2×#638C2312yes—
154C2×#638C2311yescharacteristic
155C2×#638C2311yescharacteristic
156D4×C3⋊D3—42no—
157C2×C4⋊(C3⋊D3)—42no—
158C2×C4⋊(C3⋊D3)C2312yes—
159C2×C4⋊(C3⋊D3)C2312yes—
160C2×C4⋊(C3⋊D3)C2312yes—
161C2×C4⋊(C3⋊D3)C2311yescharacteristic
162C2×C4×C3⋊D3C2311yescharacteristic
163C2×C4×C3⋊D3C2312yes—
164C2×C3×#67C2312yes—
165C2×C3×#67C2312yes—
166C22×C3×Dic3C2311yescharacteristic
167C22×C3×Dic3C2311yescharacteristic
168C2×C3×D12C2311yescharacteristic
169C2×C3×C4×D3C2312yes—
170C2×C3×Dic6C2312yes—
171C2×C3×Dic6C2312yes—
172C2×C3×Dic6C2311yescharacteristic
173C2×#626C2312yes—
174C2×#626C2312yes—
175C2×#626C2312yes—
176C2×#626C2312yes—
177C2×#626C2312yes—
178C2×#624—42no—
179C2×#624C2312yes—
180C2×#624C2312yes—
181C2×#624C2312yes—
182C2×#624C2312yes—
183C2×#624C2312yes—
184C2×D3×Dic3C2312yes—
185C2×D3×Dic3C2312yes—
186#3799—44no—
187#3796—42no—
188C32×C4⋊C4C2312yes—
189C32×C22⋊C4C2312yes—
190C32×C22⋊C4C2311yescharacteristic
191#3757C2311yescharacteristic
192#3752C2312yes—
193#3752C2312yes—
194#3752C2312yes—
195#3752C2312yes—
196#3750C2312yes—
197C3×#217C2312yes—
198C3×#217C2311yescharacteristic
199C3×#217C2312yes—
200C3×#217C2312yes—
201C3×#217C2311yescharacteristic
202C3×#217C2312yes—
203C3×(C2×D3)⋊C4C2312yes—
204C3×(C2×D3)⋊C4C2312yes—
205C3×(C2×D3)⋊C4C2312yes—
206C3×C4⋊Dic3C2312yes—
207C3×C4⋊Dic3C2312yes—
208C3×Dic3⋊C4C2312yes—
209C3×Dic3⋊C4C2312yes—
210C3×Dic3⋊C4C2312yes—
211C3×Dic3⋊C4C2312yes—
212C3×Dic3⋊C4C2312yes—
213C3×Dic3⋊C4C2312yes—
214C3×Dic3⋊C4C2312yes—
215C3×C4×Dic3C2312yes—
216C3×C4×Dic3C2312yes—
217C3×C4×Dic3C2312yes—
218C3×C4×Dic3C2311yescharacteristic
219C3×C4×Dic3C2311yescharacteristic
220#3724C2312yes—
221#3724C2312yes—
222#3724C2312yes—
223Dic3⋊Dic3C2312yes—
224Dic3⋊Dic3C2312yes—
225Dic3⋊Dic3C2312yes—
226Dic3⋊Dic3C2312yes—
227Dic3⋊Dic3C2312yes—
228#3722C2312yes—
229#3722C2312yes—
230#3722C2312yes—
231#3722C2312yes—
232#3722C2312yes—
233#3722C2312yes—
234#3722C2312yes—
235#3722C2312yes—
236#3722C2312yes—
237#3722C2312yes—
238(C2×D3)⋊Dic3C2312yes—
239Dic32C2312yes—
240#3533—91noSylow
241C2×#239—31no—
242C2×#239—32no—
243C2×#237—31no—
244C2×D3×D4—31no—
245C2×D3×D4—31no—
246C2×D3×D4—61no—
247C2×#235—32no—
248C22×D12—31no—
249C22×D12—31no—
250C22×D12—61no—
251C22×C4×D3—31no—
252C22×C4×D3—31no—
253C3×C4⋊Q8—32no—
254C3×#127—31no—
255C3×#126—32no—
256C3×#126—32no—
257C3×#125—32no—
258C3×#124—31no—
259C3×#124—32no—
260C3×#124—32no—
261C3×#123—21no—
262C3×#123—31no—
263C3×#123—31no—
264C3×#123—32no—
265C3×#123C2×D311yescharacteristic
266C3×#123C2×D311yescharacteristic
267C3×C22⋊Q8—32no—
268C3×C22⋊Q8—32no—
269C3×C4×Q8—32no—
270C3×C4×D4—32no—
271C3×C4×D4—32no—
272#947—32no—
273#947—31no—
274#947—32no—
275#946—32no—
276#946—32no—
277#946—32no—
278#946—32no—
279#946—32no—
280#946—32no—
281#940—31no—
282#940C2×D311yescharacteristic
283#939—32no—
284#939—32no—
285#939—32no—
286#939—32no—
287#939—32no—
288#937—31no—
289#937—31no—
290#937—32no—
291#937—32no—
292#937—32no—
293#937—61no—
294#936C2×D311yescharacteristic
295#935—32no—
296#935C2×D311yescharacteristic
297#935C2×D311yescharacteristic
298#930—32no—
299#930—32no—
300#929—31no—
301#929—31no—
302#929—31no—
303#929—31no—
304#929—61no—
305C4×#67—32no—
306C4×#67—32no—
307C4×#67C2×D312yescomplemented
308#924C2×D312yescomplemented
309C2×Dic3⋊C4—32no—
310#898—32no—
311#898—32no—
312#898—32no—
313#897—32no—
314#896—32no—
315#896—32no—
316#896—32no—
317#896—32no—
318#895—32no—
319#895—32no—
320#895—32no—
321#895—32no—
322#895—32no—
323#895—32no—
324#895—32no—
325#895—32no—
326#895—62no—
327#894—32no—
328#894—32no—
329#894—32no—
330#894—32no—
331#894—32no—
332#894—32no—
333#894—32no—
334#894—32no—
335#894—32no—
336#894—32no—
337#894—32no—
338#894—32no—
339#894—62no—
340#894C2×D312yescomplemented
341#893—32no—
342#893—32no—
343#893—32no—
344#893—32no—
345#892—32no—
346#892—32no—
347D3×C4⋊C4—32no—
348D3×C4⋊C4—32no—
349D3×C4⋊C4—32no—
350#889—32no—
351#889—32no—
352#889—32no—
353#889C2×D312yescomplemented
354#888C2×D312yescomplemented
355#887C2×D312yescomplemented
356#886—31no—
357#886—31no—
358#886—32no—
359#886—32no—
360#885C2×D312yescomplemented
361#885C2×D312yescomplemented
362#884—32no—
363#884—32no—
364#884—32no—
365#884—32no—
366#884—32no—
367#884—32no—
368#884—32no—
369#884—32no—
370#884—32no—
371#884—62no—
372#883—32no—
373#883—32no—
374#883—32no—
375#883—32no—
376#883—32no—
377#883—32no—
378#883—32no—
379#882—32no—
380#882—32no—
381#882—32no—
382#882—31no—
383#882—32no—
384#882—31no—
385#882—32no—
386#882—62no—
387#882—61no—
388#67⋊C4—32no—
389#67⋊C4—32no—
390#67⋊C4—32no—
391#67⋊C4—32no—
392#67⋊C4C2×D312yescomplemented
393D3×C22⋊C4—31no—
394D3×C22⋊C4—31no—
395D3×C22⋊C4—31no—
396D3×C22⋊C4—32no—
397D3×C22⋊C4—31no—
398D3×C22⋊C4—32no—
399D3×C22⋊C4—32no—
400D3×C22⋊C4—32no—
401D3×C22⋊C4—61no—
402#879—32no—
403#879—32no—
404#879C2×D312yescomplemented
405#879C2×D312yescomplemented
406#878—32no—
407#878C2×D312yescomplemented
408#876—32no—
409#876—32no—
410#876—32no—
411#875—32no—
412#875—32no—
413#875—31no—
414#874—31no—
415C4×D12—32no—
416C4×D12—32no—
417C4×D12—32no—
418C4×D12—32no—
419#872—32no—
420#872—32no—
421#872—31no—
422#872—32no—
423#872—32no—
424#872—31no—
425#870—32no—
426C23×C32C2411yescharacteristic
427C23×C32C2411yescharacteristic
428C22×C3⋊D3—22no—
429C22×C3⋊D3—22no—
430C22×C3⋊D3—41no—
431C22×C3⋊D3—42no—
432C22×C3⋊D3—42no—
433C22×C3⋊D3—42no—
434C22×C3⋊D3C2411yescharacteristic
435C22×C3⋊D3C2411yescharacteristic
436C22×C3⋊D3C2412yes—
437C22×C3⋊D3C2411yescharacteristic
438C22×C3×D3C2412yes—
439C32×D4—41no—
440C2×C32×C4—41no—
441C2×C32×C4C2411yescharacteristic
442C2×C32×C4C2412yes—
443C2×C32×C4C2412yes—
444#638—41no—
445#638—41no—
446#638—42no—
447C2×C3⋊Dic3C2412yes—
448C2×C3⋊Dic3C2411yescharacteristic
449C4⋊(C3⋊D3)—24no—
450C4⋊(C3⋊D3)—42no—
451C4⋊(C3⋊D3)—41no—
452C4⋊(C3⋊D3)—42no—
453C4×C3⋊D3—22no—
454C4×C3⋊D3—42no—
455C3×#67—42no—
456C3×#67—42no—
457C2×C3×Dic3—41no—
458C2×C3×Dic3—41no—
459C2×C3×Dic3C2412yes—
460C2×C3×Dic3C2412yes—
461C2×C3×Dic3C2412yes—
462C2×C3×Dic3C2412yes—
463C2×C3×Dic3C2412yes—
464C2×C3×Dic3C2412yes—
465C2×C3×Dic3C2412yes—
466C3×D12—41no—
467C3×C4×D3—42no—
468C3×Dic6—41no—
469C3×Dic6—42no—
470C3×Dic6—42no—
471#626—24no—
472#626—42no—
473#626—42no—
474#626—42no—
475#626—42no—
476#624—24no—
477#624—42no—
478#624—42no—
479#624—42no—
480#624—42no—
481D3×Dic3—42no—
482D3×Dic3—42no—
483#563—31no—
484#562—92no—
485#560—91no—
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—
502C23×D3—31no—
503C23×D3—31no—
504C23×D3—31no—
505C23×D3—31no—
506C23×D3—31no—
507C23×D3—31no—
508C23×D3—61no—
509C23×D3—61no—
510C23×D3—61no—
511C2×C3×Q8—32no—
512C2×C3×Q8—32no—
513C2×C3×Q8—31no—
514C2×C3×D4—21no—
515C2×C3×D4—32no—
516C2×C3×D4—32no—
517C2×C3×D4—31no—
518C2×C3×D4C22×D311yescharacteristic
519C2×C3×D4C22×D311yescharacteristic
520C22×C3×C4—21no—
521C22×C3×C4—31no—
522C22×C3×C4—31no—
523C22×C3×C4—32no—
524C22×C3×C4C22×D311yescharacteristic
525C22×C3×C4C22×D311yescharacteristic
526C2×#67—32no—
527C2×#67—31no—
528C2×#67—31no—
529C2×#67—32no—
530C2×#67—31no—
531C2×#67—31no—
532C2×#67—32no—
533C2×#67—32no—
534C2×#67—32no—
535C2×#67—32no—
536C2×#67—32no—
537C2×#67—61no—
538C2×#67—61no—
539C2×#67—62no—
540C2×#67C22×D312yes—
541C2×#67C22×D312yes—
542C22×Dic3—32no—
543C22×Dic3—32no—
544C22×Dic3C22×D311yescharacteristic
545C22×Dic3C22×D311yescharacteristic
546#239—124no—
547#239—122no—
548#237—122no—
549D3×D4—122no—
550D3×D4—122no—
551D3×D4—124no—
552#235—124no—
553C2×D12—32no—
554C2×D12—32no—
555C2×D12—32no—
556C2×D12—32no—
557C2×D12—32no—
558C2×D12—32no—
559C2×D12—32no—
560C2×D12—32no—
561C2×D12—31no—
562C2×D12—32no—
563C2×D12—32no—
564C2×D12—31no—
565C2×D12—32no—
566C2×D12—62no—
567C2×D12—62no—
568C2×D12—61no—
569C2×D12—62no—
570C2×D12—122no—
571C2×D12—122no—
572C2×D12—124no—
573C2×D12C22×D311yescharacteristic
574C2×C4×D3—31no—
575C2×C4×D3—31no—
576C2×C4×D3—32no—
577C2×C4×D3—32no—
578C2×C4×D3—32no—
579C2×C4×D3—32no—
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—62no—
592C2×C4×D3—122no—
593C2×C4×D3—122no—
594C2×C4×D3C22×D312yes—
595C2×Dic6C22×D312yes—
596C2×Dic6C22×D312yes—
597C2×Dic6C22×D311yescharacteristic
598C3×C4⋊C4—22no—
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×C4⋊C4—32no—
606C3×C4⋊C4—32no—
607C3×C4⋊C4—32no—
608C3×C4⋊C4C22×D312yes—
609C3×C4⋊C4C22×D312yes—
610C3×C22⋊C4—21no—
611C3×C22⋊C4—22no—
612C3×C22⋊C4—32no—
613C3×C22⋊C4—32no—
614C3×C22⋊C4—32no—
615C3×C22⋊C4—31no—
616C3×C22⋊C4—31no—
617C3×C22⋊C4—32no—
618C3×C22⋊C4—32no—
619C3×C22⋊C4—32no—
620C3×C22⋊C4—32no—
621C3×C22⋊C4C22×D312yes—
622C3×C22⋊C4C22×D311yescharacteristic
623C3×C22⋊C4C22×D311yescharacteristic
624C3×C22⋊C4C22×D312yes—
625C3×C42—32no—
626C3×C42—31no—
627C3×C42—32no—
628C3×C42—32no—
629C3×C42—31no—
630#217—31no—
631#217—31no—
632#217—32no—
633#217—61no—
634#217C22×D312yes—
635#217C22×D312yes—
636#217C22×D312yes—
637#217C22×D311yescharacteristic
638#217C22×D312yes—
639#217C22×D311yescharacteristic
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—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—32no—
664(C2×D3)⋊C4—32no—
665(C2×D3)⋊C4—32no—
666(C2×D3)⋊C4—32no—
667(C2×D3)⋊C4—32no—
668(C2×D3)⋊C4—32no—
669(C2×D3)⋊C4—62no—
670(C2×D3)⋊C4—62no—
671(C2×D3)⋊C4—62no—
672(C2×D3)⋊C4—62no—
673(C2×D3)⋊C4C22×D312yes—
674(C2×D3)⋊C4C22×D312yes—
675(C2×D3)⋊C4C22×D312yes—
676C4⋊Dic3—32no—
677C4⋊Dic3—32no—
678C4⋊Dic3—32no—
679C4⋊Dic3—32no—
680C4⋊Dic3—32no—
681C4⋊Dic3C22×D312yes—
682C4⋊Dic3C22×D312yes—
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—
702Dic3⋊C4C22×D312yes—
703Dic3⋊C4C22×D312yes—
704C4×Dic3—32no—
705C4×Dic3—32no—
706C4×Dic3C22×D312yes—
707C4×Dic3C22×D312yes—
708C4×Dic3C22×D311yescharacteristic
709C4×Dic3C22×D311yescharacteristic
710C4×Dic3C22×D312yes—
711C22×C32—21no—
712C22×C32—21no—
713C22×C32—22no—
714C22×C32—22no—
715C22×C32C2511yescharacteristic
716C2×C3⋊D3—21no—
717C2×C3⋊D3—22no—
718C2×C3⋊D3—21no—
719C2×C3⋊D3—22no—
720C2×C3⋊D3—22no—
721C2×C3⋊D3—22no—
722C2×C3⋊D3—22no—
723C2×C3⋊D3—22no—
724C2×C3⋊D3—44no—
725C2×C3⋊D3—82no—
726C2×C3⋊D3—82no—
727C2×C3⋊D3H(5,𝔽2)12yes—
728C2×C3×D3—22no—
729C2×C3×D3—22no—
730C2×C3×D3—22no—
731C32×C4—22no—
732C32×C4—21no—
733C32×C4—22no—
734C3⋊Dic3—21no—
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—32no—
749#127—31no—
750#127—91no—
751#126—32no—
752#126—32no—
753#126—92no—
754#126—92no—
755#126—92no—
756#126—92no—
757#125—32no—
758#125—92no—
759#125—92no—
760#124—31no—
761#124—32no—
762#124—32no—
763#124—91no—
764#124—92no—
765#124—92no—
766#123—31no—
767#123—31no—
768#123—32no—
769#123—92no—
770#123—92no—
771#123—92no—
772#123—92no—
773#123—92no—
774#123—92no—
775#123—91no—
776#123—91no—
777#123—92no—
778#123—92no—
779#123—92no—
780#123—92no—
781#123—91no—
782#123—92no—
783#123D3211yescharacteristic
784C22⋊Q8—32no—
785C22⋊Q8—32no—
786C22⋊Q8—92no—
787C22⋊Q8—92no—
788C22⋊Q8—92no—
789C22⋊Q8—92no—
790C22⋊Q8—92no—
791C22⋊Q8—92no—
792#121—92no—
793#121—92no—
794#121—92no—
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—92no—
805#120—92no—
806#120—92no—
807#120—91no—
808#120—92no—
809#120—91no—
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—91no—
821#117—92no—
822#117—92no—
823#117—92no—
824C2×C4⋊C4—92no—
825C2×C4⋊C4—92no—
826C2×C22⋊C4—91no—
827C2×C22⋊C4—92no—
828C2×C22⋊C4—92no—
829C2×C22⋊C4—91no—
830C23×C3—21no—
831C23×C3—21no—
832C23×C3—32no—
833C23×C3C23×D311yescharacteristic
834C23×C3C23×D311yescharacteristic
835C23×C3C23×D311yescharacteristic
836C23×C3C23×D311yescharacteristic
837C22×D3—31no—
838C22×D3—31no—
839C22×D3—31no—
840C22×D3—32no—
841C22×D3—31no—
842C22×D3—31no—
843C22×D3—32no—
844C22×D3—31no—
845C22×D3—61no—
846C22×D3—61no—
847C22×D3—62no—
848C22×D3—61no—
849C22×D3—62no—
850C22×D3—62no—
851C22×D3—62no—
852C22×D3—62no—
853C22×D3—64no—
854C22×D3—122no—
855C22×D3—122no—
856C22×D3—122no—
857C22×D3—121no—
858C22×D3—121no—
859C22×D3—122no—
860C22×D3—122no—
861C22×D3—122no—
862C22×D3—122no—
863C22×D3—122no—
864C22×D3—242no—
865C22×D3—242no—
866C22×D3—242no—
867C22×D3C23×D312yes—
868C3×Q8—122no—
869C3×Q8—121no—
870C3×Q8—122no—
871C3×D4—41no—
872C3×D4—41no—
873C3×D4—42no—
874C3×D4—121no—
875C3×D4—122no—
876C3×D4—122no—
877C2×C3×C4—22no—
878C2×C3×C4—22no—
879C2×C3×C4—21no—
880C2×C3×C4—32no—
881C2×C3×C4—32no—
882C2×C3×C4—32no—
883C2×C3×C4—32no—
884C2×C3×C4—32no—
885C2×C3×C4—32no—
886C2×C3×C4—32no—
887C2×C3×C4—41no—
888C2×C3×C4—41no—
889C2×C3×C4—42no—
890C2×C3×C4—122no—
891C2×C3×C4—121no—
892C2×C3×C4—121no—
893C2×C3×C4C23×D312yes—
894C2×C3×C4C23×D312yes—
895C2×C3×C4C23×D311yescharacteristic
896C2×C3×C4C23×D311yescharacteristic
897C2×C3×C4C23×D312yes—
898C2×C3×C4C23×D312yes—
899#67—42no—
900#67—42no—
901#67—64no—
902#67—122no—
903#67—122no—
904#67—122no—
905#67—122no—
906#67—121no—
907#67—121no—
908#67—121no—
909#67—121no—
910#67—122no—
911#67—122no—
912#67—122no—
913#67—122no—
914#67—242no—
915C2×Dic3—32no—
916C2×Dic3—32no—
917C2×Dic3—31no—
918C2×Dic3—31no—
919C2×Dic3—41no—
920C2×Dic3—41no—
921C2×Dic3—61no—
922C2×Dic3—62no—
923C2×Dic3—122no—
924C2×Dic3—122no—
925C2×Dic3C23×D312yes—
926C2×Dic3C23×D312yes—
927C2×Dic3C23×D312yes—
928C2×Dic3C23×D312yes—
929C2×Dic3C23×D312yes—
930C2×Dic3C23×D312yes—
931C2×Dic3C23×D312yes—
932D12—41no—
933D12—64no—
934D12—64no—
935D12—64no—
936D12—124no—
937D12—122no—
938D12—122no—
939D12—122no—
940D12—122no—
941D12—121no—
942D12—121no—
943D12—124no—
944D12—122no—
945D12—122no—
946D12—122no—
947D12—122no—
948D12—122no—
949D12—242no—
950C4×D3—42no—
951C4×D3—64no—
952C4×D3—64no—
953C4×D3—62no—
954C4×D3—62no—
955C4×D3—122no—
956C4×D3—122no—
957C4×D3—122no—
958C4×D3—122no—
959C4×D3—122no—
960C4×D3—122no—
961C4×D3—122no—
962C4×D3—122no—
963C4×D3—122no—
964C4×D3—122no—
965C4×D3—122no—
966C4×D3—122no—
967C4×D3—122no—
968C4×D3—242no—
969Dic6—42no—
970Dic6—42no—
971Dic6—41no—
972C2×C32—41no—
973C2×C32—41no—
974C2×C32C2×H(5,𝔽2)11yescharacteristic
975C2×C32#58512yes—
976C3⋊D3—22no—
977C3⋊D3—41no—
978C3⋊D3—41no—
979C3⋊D3—42no—
980C3×D3—42no—
981C24—91no—
982C24—91no—
983C24—91no—
984#41—364no—
985#41—362no—
986C2×Q8—32no—
987C2×Q8—32no—
988C2×Q8—31no—
989C2×D4—32no—
990C2×D4—32no—
991C2×D4—31no—
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—92no—
1001C2×D4—92no—
1002C2×D4—92no—
1003C2×D4—91no—
1004C2×D4—362no—
1005C2×D4—362no—
1006C2×D4C2×D3211yescharacteristic
1007C22×C4—31no—
1008C22×C4—31no—
1009C22×C4—32no—
1010C22×C4—92no—
1011C22×C4—92no—
1012C22×C4—92no—
1013C22×C4—92no—
1014C22×C4—92no—
1015C22×C4—92no—
1016C22×C4—92no—
1017C22×C4—91no—
1018C22×C4—92no—
1019C22×C4—362no—
1020C22×C4C2×D3211yescharacteristic
1021C4⋊C4—32no—
1022C4⋊C4—32no—
1023C4⋊C4—32no—
1024C4⋊C4—32no—
1025C4⋊C4—32no—
1026C4⋊C4—32no—
1027C4⋊C4—32no—
1028C4⋊C4—32no—
1029C4⋊C4—32no—
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⋊C4C2×D3212yes—
1040C22⋊C4—32no—
1041C22⋊C4—32no—
1042C22⋊C4—32no—
1043C22⋊C4—31no—
1044C22⋊C4—31no—
1045C22⋊C4—32no—
1046C22⋊C4—32no—
1047C22⋊C4—32no—
1048C22⋊C4—32no—
1049C22⋊C4—92no—
1050C22⋊C4—92no—
1051C22⋊C4—92no—
1052C22⋊C4—92no—
1053C22⋊C4—92no—
1054C22⋊C4—92no—
1055C22⋊C4—92no—
1056C22⋊C4—92no—
1057C22⋊C4—92no—
1058C22⋊C4—92no—
1059C22⋊C4—92no—
1060C22⋊C4—91no—
1061C22⋊C4—92no—
1062C22⋊C4—92no—
1063C22⋊C4—92no—
1064C22⋊C4—92no—
1065C22⋊C4C2×D3211yescharacteristic
1066C22⋊C4C2×D3212yes—
1067C42—31no—
1068C42—32no—
1069C42—32no—
1070C42—31no—
1071C42—32no—
1072C42—92no—
1073C22×C3—22no—
1074C22×C3—22no—
1075C22×C3—22no—
1076C22×C3—21no—
1077C22×C3—21no—
1078C22×C3—21no—
1079C22×C3—21no—
1080C22×C3—22no—
1081C22×C3—22no—
1082C22×C3—21no—
1083C22×C3—42no—
1084C22×C3—41no—
1085C22×C3—42no—
1086C22×C3—62no—
1087C22×C3—62no—
1088C22×C3—62no—
1089C22×C3C24×D311yescharacteristic
1090C22×C3C24×D311yescharacteristic
1091C2×D3—22no—
1092C2×D3—22no—
1093C2×D3—22no—
1094C2×D3—32no—
1095C2×D3—32no—
1096C2×D3—62no—
1097C2×D3—62no—
1098C2×D3—62no—
1099C2×D3—62no—
1100C2×D3—62no—
1101C2×D3—62no—
1102C2×D3—62no—
1103C2×D3—62no—
1104C2×D3—61no—
1105C2×D3—61no—
1106C2×D3—62no—
1107C2×D3—62no—
1108C2×D3—61no—
1109C2×D3—61no—
1110C2×D3—62no—
1111C2×D3—62no—
1112C2×D3—62no—
1113C2×D3—62no—
1114C2×D3—122no—
1115C2×D3—122no—
1116C2×D3—122no—
1117C2×D3—121no—
1118C2×D3—122no—
1119C2×D3—122no—
1120C2×D3—122no—
1121C2×D3—124no—
1122C2×D3—124no—
1123C2×D3—244no—
1124C2×D3—242no—
1125C2×D3—242no—
1126C2×D3—244no—
1127C2×D3—242no—
1128C2×D3—242no—
1129C2×D3—244no—
1130C3×C4—22no—
1131C3×C4—21no—
1132C3×C4—22no—
1133C3×C4—22no—
1134C3×C4—21no—
1135C3×C4—22no—
1136C3×C4—41no—
1137C3×C4—42no—
1138C3×C4—42no—
1139C3×C4—62no—
1140C3×C4—62no—
1141C3×C4—62no—
1142C3×C4—62no—
1143C3×C4—62no—
1144C3×C4—62no—
1145C3×C4—62no—
1146Dic3—22no—
1147Dic3—22no—
1148Dic3—22no—
1149Dic3—22no—
1150Dic3—22no—
1151Dic3—22no—
1152Dic3—22no—
1153Dic3—62no—
1154Dic3—61no—
1155Dic3—61no—
1156Dic3—62no—
1157Dic3—121no—
1158Dic3—122no—
1159C32#353311yescharacteristic, complemented, Sylow
1160C23—32no—
1161C23—91no—
1162C23—91no—
1163C23—92no—
1164C23—91no—
1165C23—182no—
1166C23—182no—
1167C23—362no—
1168C23—361no—
1169C23—362no—
1170C23—362no—
1171C23C22×D3211yescharacteristic
1172C23C22×D3211yescharacteristic
1173Q8—122no—
1174Q8—121no—
1175Q8—122no—
1176D4—41no—
1177D4—121no—
1178D4—122no—
1179D4—122no—
1180D4—184no—
1181D4—184no—
1182D4—362no—
1183D4—361no—
1184D4—362no—
1185D4—362no—
1186D4—362no—
1187D4—362no—
1188D4—362no—
1189D4—361no—
1190D4—361no—
1191D4—362no—
1192C2×C4—32no—
1193C2×C4—32no—
1194C2×C4—32no—
1195C2×C4—32no—
1196C2×C4—32no—
1197C2×C4—32no—
1198C2×C4—32no—
1199C2×C4—41no—
1200C2×C4—92no—
1201C2×C4—91no—
1202C2×C4—122no—
1203C2×C4—121no—
1204C2×C4—121no—
1205C2×C4—182no—
1206C2×C4—184no—
1207C2×C4—362no—
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×C4C22×D3212yes—
1217C2×C3—21no—
1218C2×C3—22no—
1219C2×C3—42no—
1220C2×C3—41no—
1221C2×C3—41no—
1222C2×C3—41no—
1223C2×C3—41no—
1224C2×C3—81no—
1225C2×C3—122no—
1226C2×C3#596412yes—
1227C2×C3D3×H(5,𝔽2)11yescharacteristic
1228C2×C3D3×H(5,𝔽2)11yescharacteristic
1229C2×C3#596812yes—
1230D3—42no—
1231D3—62no—
1232D3—62no—
1233D3—122no—
1234D3—122no—
1235D3—121no—
1236D3—121no—
1237D3—122no—
1238D3—121no—
1239D3—121no—
1240D3—122no—
1241D3—241no—
1242D3—242no—
1243C22—21no—
1244C22—21no—
1245C22—22no—
1246C22—22no—
1247C22—62no—
1248C22—62no—
1249C22—62no—
1250C22—92no—
1251C22—182no—
1252C22—181no—
1253C22—182no—
1254C22—181no—
1255C22—182no—
1256C22—182no—
1257C22—182no—
1258C22—182no—
1259C22—364no—
1260C22—722no—
1261C22—722no—
1262C22C23×D3211yescharacteristic
1263C4—22no—
1264C4—21no—
1265C4—22no—
1266C4—62no—
1267C4—62no—
1268C4—62no—
1269C4—62no—
1270C4—62no—
1271C4—62no—
1272C4—62no—
1273C4—181no—
1274C4—182no—
1275C3—21no—
1276C3#8706511yescharacteristic, complemented
1277C3#8712811yescharacteristic, complemented
1278C2—41no—
1279C2—41no—
1280C2—122no—
1281C2—182no—
1282C2—361no—
1283C2—361no—
1284C2—362no—
1285C2#1059667511yescharacteristic
1286C2#1059669712yes—
subgroupG/H
center, FrattiniC22C23×D32
commutator, socle, cosocleC22×C32C25
FittingC32×#123C22
hypercenter#123D32
hypocenterC32#3533
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ #123

Complements

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

NH ≅ G/Ntype
1. #10596124C2semidirect
2. C3×#5664C2semidirect
3. C3×#5651C2semidirect
4. #10595266C2semidirect
5. #10595208C2semidirect
6. #10595169C2semidirect
7. #10595168C2semidirect
8. #10595018C2semidirect
9. #10594936C2semidirect
10. #10594467C2semidirect
11. #10594372C2semidirect
12. #10594352C2semidirect
13. #10594349C2semidirect
14. #10594178C2semidirect
15. #10594162C2semidirect
16. #10594162C2semidirect
17. #10594153C2semidirect
18. #10594097C2semidirect
19. #10594066C2semidirect
24. C22×#624C22semidirect
26. C2×#3796C22semidirect
40. C3×C4×#67C22semidirect
41. C3×#924C22semidirect
42. C3×#894C22semidirect
43. C3×#889C22semidirect
44. C3×#888C22semidirect
45. C3×#887C22semidirect
46. C3×#885C22semidirect
47. C3×#885C22semidirect
48. C3×#67⋊C4C22semidirect
49. C3×#879C22semidirect
50. C3×#879C22semidirect
51. C3×#878C22semidirect
53. #63981C22semidirect
54. #63981C22semidirect
55. #63978C22semidirect
57. #63975C22semidirect
59. #63974C22semidirect
60. #63974C22semidirect
62. #63971C22semidirect
63. #63971C22semidirect
64. #63969C22semidirect
65. #63966C22semidirect
66. #63966C22semidirect
67. #63956C22semidirect
68. #63952C22semidirect
69. #63911C22semidirect
71. #63910C22semidirect
72. #63910C22semidirect
73. #63910C22semidirect
74. #63909C22semidirect
75. #63904C22semidirect
77. #63897C22semidirect
78. #63897C22semidirect
80. #63894C22semidirect
81. #63890C22semidirect
82. #63890C22semidirect
83. #63888C22semidirect
84. #63888C22semidirect
85. #63888C22semidirect
86. #63888C22semidirect
87. #63887C22semidirect
88. #63886C22semidirect
89. #63883C22semidirect
90. #63881C22semidirect
91. #63880C22semidirect
92. #63880C22semidirect
93. D3×Dic3⋊C4C22semidirect
94. #63874C22semidirect
95. #63874C22semidirect
96. #63871C22semidirect
97. #63868C22semidirect
98. #63868C22semidirect
99. #63868C22semidirect
100. #63867C22semidirect
101. #63864C22semidirect
102. #63864C22semidirect
103. #63864C22semidirect
104. #63854C22semidirect
105. #63853C22semidirect
106. #63847C22semidirect
107. #63836C22semidirect
108. #63836C22semidirect
128. #5664D3semidirect
137. #5651D3semidirect
307. C4×#67C2×D3semidirect
308. #924C2×D3semidirect
340. #894C2×D3semidirect
353. #889C2×D3semidirect
354. #888C2×D3semidirect
355. #887C2×D3semidirect
360. #885C2×D3semidirect
361. #885C2×D3semidirect
392. #67⋊C4C2×D3semidirect
404. #879C2×D3semidirect
405. #879C2×D3semidirect
407. #878C2×D3semidirect
1159. C32#3533semidirect
1276. C3#87065semidirect
1277. C3#87128semidirect

Maximal subgroups

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

subgroupindex
#105961242
C3×#56642
C3×#56512
#105952662
#105952082
#105951692
#105951682
#105950182
#105949362
#105944672
#105943722
#105943522
#105943492
#105941782
#105941622
#105941532
#105940972
#105940662
#871283
#870653