Finite Group Databasebeta

← #11901781

Subgroups — #11901781

Order 1152.

2235 conjugacy classes of subgroups.

The subgroup lattice has 1216 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10596067C211yesmaximal, characteristic, complemented
2C3×#5617C211yesmaximal, characteristic, complemented
3C3×#5602C211yesmaximal, characteristic, complemented
4#10595251C212yesmaximal, complemented
5#10595202C212yesmaximal, complemented
6#10595190C212yesmaximal, complemented
7#10595160C212yesmaximal, complemented
8#10595127C212yesmaximal, complemented
9#10595123C212yesmaximal, complemented
10#10595038C211yesmaximal, characteristic, complemented
11#10594980C211yesmaximal, characteristic, complemented
12C2×#63878C211yesmaximal, characteristic, complemented
13#10594810C211yesmaximal, characteristic, complemented
14#10594479C212yesmaximal, complemented
15#10594465C212yesmaximal, complemented
16#10594230C212yesmaximal, complemented
17#10594159C212yesmaximal, complemented
18#10594144C212yesmaximal, complemented
19#10594137C212yesmaximal, complemented
20#86427—31nomaximal
21#86387—31nomaximal
22C2×#3830C2212yes—
23C22×D3×Dic3C2211yescharacteristic
24C32×#121C2211yescharacteristic
25#64149C2211yescharacteristic, complemented
26#64148C2212yes—
27D4×C3⋊Dic3C2211yescharacteristic, complemented
28#64139C2211yescharacteristic
29C2×C4×C3⋊Dic3C2211yescharacteristic
30#64102C2211yescharacteristic, complemented
31#64097C2211yescharacteristic, complemented
32#64094C2212yescomplemented
33#64090C2212yescomplemented
34C3×#939C2212yes—
35C3×#937C2212yes—
36C3×#935C2212yes—
37C3×#935C2212yescomplemented
38C3×D4×Dic3C2212yes—
39C3×D4×Dic3C2212yes—
40C2×C3×(C2×D3)⋊C4C2211yescharacteristic
41C3×#924C2211yescharacteristic
42C3×#924C2211yescharacteristic
43C2×C3×Dic3⋊C4C2211yescharacteristic
44C3×#898C2212yes—
45C3×#889C2212yescomplemented
46C3×#886C2212yes—
47C3×#885C2212yes—
48C3×#879C2212yescomplemented
49C3×#878C2212yescomplemented
50#63982C2212yes—
51#63978C2212yes—
52#63977C2212yes—
53#63975C2212yescomplemented
54#67⋊Dic3C2212yes—
55#67⋊Dic3C2212yes—
56#63971C2212yes—
57#63971C2212yes—
58#63966C2212yes—
59#63966C2212yescomplemented
60C2×Dic3⋊Dic3C2211yescharacteristic
61#63964C2212yescomplemented
62#63961C2212yes—
63C2×(C2×D3)⋊Dic3C2211yescharacteristic
64#63959C2212yes—
65#63958C2212yes—
66#63957C2212yes—
67#63957C2212yescomplemented
68#63956C2212yescomplemented
69C2×Dic32C2211yescharacteristic
70C2×Dic32C2212yescomplemented
71#63952C2212yes—
72#63952C2212yes—
73#63952C2212yescomplemented
74#63952C2212yescomplemented
75#63919C2211yescharacteristic, complemented
76#63910C2212yes—
77#63907C2212yes—
78#63897C2212yescomplemented
79#63896C2212yes—
80#63896C2212yes—
81#63895C2212yescomplemented
82#63888C2212yescomplemented
83C4×#624C2212yescomplemented
84#63881C2212yes—
85#63881C2212yes—
86#63878C2212yes—
87#63878C2212yes—
88#63878C2212yes—
89#63878C2212yes—
90#63873C2211yescharacteristic, complemented
91#63870C2212yescomplemented
92#63868C2212yescomplemented
93#63867C2212yescomplemented
94#63861C2212yes—
95#63859C2212yes—
96#63858C2212yes—
97#63854C2212yes—
98#63854C2212yes—
99#63852C2212yes—
100#63849C2212yescomplemented
101#63848C2212yescomplemented
102#63846C2212yescomplemented
103#63845C2212yescomplemented
104#63844C2212yescomplemented
105#63844C2212yescomplemented
106#63843C2211yescharacteristic, complemented
107#63843C2211yescharacteristic, complemented
108#63838C2212yescomplemented
109C3×#539—31no—
110C3×#538—31no—
111#5710—32no—
112#5706—32no—
113#5706—32no—
114#5701—32no—
115#5696—32no—
116#5691—32no—
117#5680—32no—
118#5669—32no—
119#5665—32no—
120#5663—32no—
121#5662—32no—
122#5656—32no—
123#5649—32no—
124#5649—32no—
125#5645—31no—
126#5644—31no—
127#5640—32no—
128#5624—32no—
129#5622—31no—
130#5622—31no—
131#5617D311yescharacteristic, complemented
132#5615—32no—
133#5602D311yescharacteristic, complemented
134#5600—32no—
135#5596—31no—
136#5596—31no—
137#5596—61no—
138#5593—32no—
139#5586—32no—
140#5564—32no—
141#5560—32no—
142C4×#237—32no—
143C4×#237—32no—
144#5515—31no—
145C2×#892—31no—
146#5494—31no—
147C2×#877—31no—
148C23×C3×D3C2311yescharacteristic
149C2×C32×D4C2312yes—
150C2×C32×D4C2311yescharacteristic
151C22×C32×C4C2311yescharacteristic
152C2×#638C2312yes—
153C2×#638C2312yes—
154C2×#638C2312yes—
155C22×C3⋊Dic3C2312yes—
156C22×C3⋊Dic3C2311yescharacteristic
157C22×C3⋊Dic3C2311yescharacteristic
158#3830—28no—
159C2×C4⋊(C3⋊D3)C2311yescharacteristic
160C2×C4×C3⋊D3C2312yes—
161C2×#634C2312yes—
162C2×C3×#67C2312yes—
163C2×C3×#67C2312yes—
164C22×C3×Dic3C2311yescharacteristic
165C22×C3×Dic3C2312yes—
166C22×C3×Dic3C2312yes—
167C22×C3×Dic3C2311yescharacteristic
168C22×C3×Dic3C2311yescharacteristic
169C2×C3×Dic6C2311yescharacteristic
170C2×C3×Dic6C2311yescharacteristic
171C2×#627C2312yes—
172C2×#626C2312yes—
173C2×#626C2312yes—
174C2×#624C2312yes—
175C2×#624C2312yes—
176C2×D3×Dic3—24no—
177C2×D3×Dic3C2312yes—
178C2×D3×Dic3C2312yes—
179C32×C4⋊C4C2311yescharacteristic
180C32×C22⋊C4C2312yes—
181#3757C2312yes—
182#3752C2312yes—
183#3752C2312yes—
184C4⋊(C3⋊Dic3)C2311yescharacteristic
185#3750C2312yes—
186C4×C3⋊Dic3C2311yescharacteristic
187C4×C3⋊Dic3C2311yescharacteristic
188C4×C3⋊Dic3C2311yescharacteristic
189C4×C3⋊Dic3C2311yescharacteristic
190C3×#217C2312yes—
191C3×#217C2312yes—
192C3×#217C2312yes—
193C3×#217C2312yes—
194C3×#217C2312yes—
195C3×#217C2312yes—
196C3×(C2×D3)⋊C4C2312yes—
197C3×(C2×D3)⋊C4C2312yes—
198C3×(C2×D3)⋊C4C2312yes—
199C3×(C2×D3)⋊C4C2312yes—
200C3×C4⋊Dic3C2312yes—
201C3×C4⋊Dic3C2311yescharacteristic
202C3×C4⋊Dic3C2311yescharacteristic
203C3×C4⋊Dic3C2312yes—
204C3×Dic3⋊C4C2312yes—
205C3×Dic3⋊C4C2312yes—
206C3×Dic3⋊C4C2312yes—
207C3×Dic3⋊C4C2312yes—
208C3×Dic3⋊C4C2312yes—
209C3×Dic3⋊C4C2312yes—
210C3×C4×Dic3C2312yes—
211C3×C4×Dic3C2312yes—
212#3724C2312yes—
213#3724C2312yes—
214#3724C2312yes—
215#3724C2312yes—
216#3724C2312yes—
217Dic3⋊Dic3C2312yes—
218Dic3⋊Dic3C2312yes—
219Dic3⋊Dic3C2312yes—
220Dic3⋊Dic3C2312yes—
221Dic3⋊Dic3C2312yes—
222Dic3⋊Dic3C2312yes—
223#3722C2312yes—
224#3722C2312yes—
225#3722C2312yes—
226#3722C2312yes—
227(C2×D3)⋊Dic3C2312yes—
228(C2×D3)⋊Dic3C2312yes—
229(C2×D3)⋊Dic3C2312yes—
230(C2×D3)⋊Dic3C2312yes—
231Dic32C2312yes—
232Dic32C2312yes—
233Dic32C2312yes—
234Dic32C2312yes—
235Dic32C2312yes—
236Dic32C2312yes—
237#3455—91noSylow
238C23×Dic3—31no—
239C2×#237—32no—
240C2×#237—32no—
241C2×#237—62no—
242C22×C4×D3—31no—
243C3×#126—32no—
244C3×#126—32no—
245C3×#125—32no—
246C3×#124—32no—
247C3×#123—32no—
248C3×#123—32no—
249C3×#123—32no—
250C3×C22⋊Q8—31no—
251C3×C22⋊Q8—31no—
252C3×C22⋊Q8—32no—
253C3×#121—21no—
254C3×#121—32no—
255C3×#121C2×D311yescharacteristic
256C3×#121C2×D311yescharacteristic
257C3×#120—32no—
258C3×C4×D4—32no—
259C3×C4×D4—32no—
260C2×C3×C4⋊C4—31no—
261C2×C3×C22⋊C4—31no—
262#953—32no—
263C2×#217—31no—
264#947—32no—
265#946—32no—
266Q8×Dic3—31no—
267Q8×Dic3—31no—
268#944—31no—
269#944—31no—
270#940—31no—
271#940—31no—
272#940—61no—
273#939—32no—
274#939—32no—
275#939—32no—
276#939—32no—
277#939—32no—
278#939—62no—
279#939C2×D312yes—
280#938—32no—
281#937C2×D312yes—
282#936—32no—
283#935—32no—
284#935C2×D312yes—
285#935C2×D312yescomplemented
286D4×Dic3—31no—
287D4×Dic3—31no—
288D4×Dic3—32no—
289D4×Dic3—32no—
290D4×Dic3—61no—
291D4×Dic3C2×D312yes—
292D4×Dic3C2×D312yes—
293#930—31no—
294#930—31no—
295#930—32no—
296#930—61no—
297#929—32no—
298#929—32no—
299#929—32no—
300C4×#67—32no—
301C4×#67—32no—
302C4×#67—32no—
303C4×#67—32no—
304C2×(C2×D3)⋊C4—31no—
305C2×(C2×D3)⋊C4C2×D311yescharacteristic
306C2×C4⋊Dic3—31no—
307#924—32no—
308#924C2×D311yescharacteristic
309#924C2×D311yescharacteristic
310C2×Dic3⋊C4—31no—
311C2×Dic3⋊C4C2×D311yescharacteristic
312C2×C4×Dic3—31no—
313C2×C4×Dic3—31no—
314C2×C4×Dic3—32no—
315C2×C4×Dic3—32no—
316C2×C4×Dic3—31no—
317C2×C4×Dic3—31no—
318C2×C4×Dic3—61no—
319#898—32no—
320#898—32no—
321#898—32no—
322#898—32no—
323#898—32no—
324#898C2×D312yes—
325#897—32no—
326#896—32no—
327#896—32no—
328#896—32no—
329#896—32no—
330#895—32no—
331#894—32no—
332#894—32no—
333#894—32no—
334#894—32no—
335#893—31no—
336#893—31no—
337#893—32no—
338#893—32no—
339#893—61no—
340#892—32no—
341#892—32no—
342#892—32no—
343#892—32no—
344#892—32no—
345#892—32no—
346#890—32no—
347#890—32no—
348#889—32no—
349#889—32no—
350#889—32no—
351#889—32no—
352#889—32no—
353#889C2×D312yescomplemented
354#888—31no—
355#888—31no—
356#888—31no—
357#888—31no—
358#888—61no—
359#887—31no—
360#887—31no—
361#887—32no—
362#887—32no—
363#887—32no—
364#887—32no—
365#886—32no—
366#886—32no—
367#886C2×D312yes—
368#885—32no—
369#885—32no—
370#885—32no—
371#885—32no—
372#885—32no—
373#885—62no—
374#885C2×D312yes—
375#884—32no—
376#884—32no—
377#884—32no—
378#884—32no—
379#883—32no—
380#883—32no—
381#883—32no—
382#883—32no—
383#882—32no—
384#67⋊C4—32no—
385#67⋊C4—32no—
386#67⋊C4—32no—
387#67⋊C4—32no—
388#67⋊C4—32no—
389#67⋊C4—32no—
390#67⋊C4—32no—
391#67⋊C4—32no—
392#67⋊C4—32no—
393#67⋊C4—32no—
394#67⋊C4—62no—
395#879—32no—
396#879—32no—
397#879—32no—
398#879—32no—
399#879—32no—
400#879C2×D312yescomplemented
401#878—32no—
402#878—32no—
403#878—32no—
404#878—32no—
405#878—32no—
406#878C2×D312yescomplemented
407#877—32no—
408#877—32no—
409#877—32no—
410#877—32no—
411#877—32no—
412#877—32no—
413#877—32no—
414#877—32no—
415#876—32no—
416#876—32no—
417#875—32no—
418C42×D3—32no—
419C42×D3—32no—
420#870—32no—
421C4×Dic6—32no—
422C4×Dic6—32no—
423C23×C32C2412yes—
424C23×C32C2411yescharacteristic
425C22×C3⋊D3C2412yes—
426C22×C3×D3—22no—
427C22×C3×D3—41no—
428C22×C3×D3—41no—
429C22×C3×D3C2412yes—
430C32×D4—24no—
431C32×D4—41no—
432C2×C32×C4—41no—
433C2×C32×C4C2412yes—
434C2×C32×C4C2411yescharacteristic
435C2×C32×C4C2411yescharacteristic
436#638—24no—
437#638—24no—
438#638—42no—
439C2×C3⋊Dic3—24no—
440C2×C3⋊Dic3—41no—
441C2×C3⋊Dic3#4114yes—
442C2×C3⋊Dic3C2412yes—
443C2×C3⋊Dic3C2411yescharacteristic
444C2×C3⋊Dic3C2411yescharacteristic
445C2×C3⋊Dic3C2411yescharacteristic
446C2×C3⋊Dic3C2411yescharacteristic
447C4⋊(C3⋊D3)—41no—
448C4×C3⋊D3—24no—
449#634—24no—
450C3×#67—42no—
451C3×#67—42no—
452C2×C3×Dic3—22no—
453C2×C3×Dic3—41no—
454C2×C3×Dic3—41no—
455C2×C3×Dic3—42no—
456C2×C3×Dic3—42no—
457C2×C3×Dic3C2412yes—
458C2×C3×Dic3C2412yes—
459C2×C3×Dic3C2412yes—
460C2×C3×Dic3C2412yes—
461C2×C3×Dic3C2412yes—
462C2×C3×Dic3C2412yes—
463C2×C3×Dic3C2412yes—
464C3×Dic6—41no—
465C3×Dic6—41no—
466#627—42no—
467#626—42no—
468#626—42no—
469#624—42no—
470#624—42no—
471D3×Dic3—24no—
472D3×Dic3—24no—
473#542—92no—
474#542—92no—
475#541—92no—
476#540—92no—
477#539—31no—
478#539—91no—
479#539—92no—
480#538—31no—
481#538—91no—
482#538—92no—
483#533—91no—
484#532—91no—
485#529—92no—
486#529—92no—
487#529—92no—
488#529—92no—
489#525—92no—
490C4×#41—92no—
491C2×#117—91no—
492C24×C3—31no—
493C23×D3C22×D311yescharacteristic
494C2×C3×Q8—31no—
495C2×C3×Q8—31no—
496C2×C3×D4—21no—
497C2×C3×D4—22no—
498C2×C3×D4—32no—
499C2×C3×D4—32no—
500C2×C3×D4C22×D312yes—
501C2×C3×D4C22×D312yes—
502C2×C3×D4C22×D311yescharacteristic
503C2×C3×D4C22×D311yescharacteristic
504C22×C3×C4—21no—
505C22×C3×C4—31no—
506C22×C3×C4—31no—
507C22×C3×C4—32no—
508C22×C3×C4—31no—
509C22×C3×C4—32no—
510C22×C3×C4C22×D311yescharacteristic
511C22×C3×C4C22×D311yescharacteristic
512C2×#67—32no—
513C2×#67—32no—
514C2×#67—32no—
515C2×#67—32no—
516C2×#67—32no—
517C2×#67—32no—
518C2×#67—32no—
519C2×#67—32no—
520C2×#67—62no—
521C2×#67—62no—
522C2×#67—62no—
523C2×#67C22×D312yes—
524C2×#67C22×D312yes—
525C22×Dic3—31no—
526C22×Dic3—31no—
527C22×Dic3—32no—
528C22×Dic3—32no—
529C22×Dic3—31no—
530C22×Dic3—31no—
531C22×Dic3—32no—
532C22×Dic3—32no—
533C22×Dic3—61no—
534C22×Dic3—62no—
535C22×Dic3—61no—
536C22×Dic3—64no—
537C22×Dic3C22×D311yescharacteristic
538C22×Dic3C22×D312yes—
539C22×Dic3C22×D312yes—
540C22×Dic3C22×D311yescharacteristic
541C22×Dic3C22×D311yescharacteristic
542#237—68no—
543#237—68no—
544#237—128no—
545C2×D12—32no—
546C2×D12—32no—
547C2×D12—31no—
548C2×D12—31no—
549C2×D12—61no—
550C2×C4×D3—32no—
551C2×C4×D3—32no—
552C2×C4×D3—32no—
553C2×C4×D3—32no—
554C2×C4×D3—32no—
555C2×C4×D3—32no—
556C2×C4×D3—32no—
557C2×C4×D3—32no—
558C2×C4×D3—62no—
559C2×C4×D3—64no—
560C2×Dic6—32no—
561C2×Dic6—32no—
562C2×Dic6—32no—
563C2×Dic6—32no—
564C2×Dic6—62no—
565C2×Dic6C22×D311yescharacteristic
566C2×Dic6C22×D311yescharacteristic
567C3×C4⋊C4—21no—
568C3×C4⋊C4—31no—
569C3×C4⋊C4—31no—
570C3×C4⋊C4—32no—
571C3×C4⋊C4—32no—
572C3×C4⋊C4—32no—
573C3×C4⋊C4—32no—
574C3×C4⋊C4—32no—
575C3×C4⋊C4—32no—
576C3×C4⋊C4—32no—
577C3×C4⋊C4—32no—
578C3×C4⋊C4C22×D311yescharacteristic
579C3×C4⋊C4C22×D311yescharacteristic
580C3×C22⋊C4—22no—
581C3×C22⋊C4—32no—
582C3×C22⋊C4—32no—
583C3×C22⋊C4—32no—
584C3×C22⋊C4—32no—
585C3×C22⋊C4—32no—
586C3×C22⋊C4—32no—
587C3×C22⋊C4—32no—
588C3×C22⋊C4—32no—
589C3×C22⋊C4—32no—
590C3×C22⋊C4—32no—
591C3×C22⋊C4C22×D312yes—
592C3×C22⋊C4C22×D312yes—
593C3×C42—32no—
594C3×C42—32no—
595#217—32no—
596#217—32no—
597#217—32no—
598#217—32no—
599#217—32no—
600#217—32no—
601#217—62no—
602#217C22×D312yes—
603#217C22×D312yes—
604#217C22×D312yes—
605#217C22×D312yes—
606#217C22×D312yes—
607#217C22×D312yes—
608(C2×D3)⋊C4—32no—
609(C2×D3)⋊C4—32no—
610(C2×D3)⋊C4—32no—
611(C2×D3)⋊C4—32no—
612(C2×D3)⋊C4—32no—
613(C2×D3)⋊C4—32no—
614(C2×D3)⋊C4—32no—
615(C2×D3)⋊C4—32no—
616(C2×D3)⋊C4—32no—
617(C2×D3)⋊C4—32no—
618(C2×D3)⋊C4—32no—
619(C2×D3)⋊C4—32no—
620(C2×D3)⋊C4—32no—
621(C2×D3)⋊C4—32no—
622(C2×D3)⋊C4—32no—
623(C2×D3)⋊C4—32no—
624(C2×D3)⋊C4—62no—
625(C2×D3)⋊C4—62no—
626(C2×D3)⋊C4C22×D312yes—
627(C2×D3)⋊C4C22×D312yes—
628(C2×D3)⋊C4C22×D312yes—
629(C2×D3)⋊C4C22×D312yes—
630C4⋊Dic3—31no—
631C4⋊Dic3—31no—
632C4⋊Dic3—32no—
633C4⋊Dic3—32no—
634C4⋊Dic3—32no—
635C4⋊Dic3—32no—
636C4⋊Dic3—32no—
637C4⋊Dic3—32no—
638C4⋊Dic3—61no—
639C4⋊Dic3C22×D312yes—
640C4⋊Dic3C22×D312yes—
641C4⋊Dic3C22×D311yescharacteristic
642C4⋊Dic3C22×D311yescharacteristic
643Dic3⋊C4—32no—
644Dic3⋊C4—32no—
645Dic3⋊C4—32no—
646Dic3⋊C4—32no—
647Dic3⋊C4—32no—
648Dic3⋊C4—32no—
649Dic3⋊C4—32no—
650Dic3⋊C4—32no—
651Dic3⋊C4—32no—
652Dic3⋊C4—32no—
653Dic3⋊C4—32no—
654Dic3⋊C4—32no—
655Dic3⋊C4—32no—
656Dic3⋊C4—32no—
657Dic3⋊C4—32no—
658Dic3⋊C4—32no—
659Dic3⋊C4—32no—
660Dic3⋊C4—32no—
661Dic3⋊C4—62no—
662Dic3⋊C4C22×D312yes—
663Dic3⋊C4C22×D312yes—
664Dic3⋊C4C22×D312yes—
665Dic3⋊C4C22×D312yes—
666Dic3⋊C4C22×D312yes—
667Dic3⋊C4C22×D312yes—
668C4×Dic3—31no—
669C4×Dic3—31no—
670C4×Dic3—31no—
671C4×Dic3—31no—
672C4×Dic3—31no—
673C4×Dic3—31no—
674C4×Dic3—31no—
675C4×Dic3—31no—
676C4×Dic3—32no—
677C4×Dic3—32no—
678C4×Dic3—32no—
679C4×Dic3—32no—
680C4×Dic3—32no—
681C4×Dic3—32no—
682C4×Dic3—32no—
683C4×Dic3—32no—
684C4×Dic3—32no—
685C4×Dic3—32no—
686C4×Dic3—32no—
687C4×Dic3—32no—
688C4×Dic3—61no—
689C4×Dic3—61no—
690C4×Dic3—61no—
691C4×Dic3—61no—
692C4×Dic3C22×D312yes—
693C4×Dic3C22×D312yes—
694C22×C32—21no—
695C22×C32—21no—
696C22×C32—22no—
697C22×C32—22no—
698C22×C32—22no—
699C22×C32C2×#4112yes—
700C22×C32C2511yescharacteristic
701C2×C3⋊D3—22no—
702C2×C3⋊D3—22no—
703C2×C3⋊D3—22no—
704C2×C3×D3—22no—
705C2×C3×D3—22no—
706C2×C3×D3—22no—
707C2×C3×D3—44no—
708C32×C4—21no—
709C32×C4—22no—
710C32×C4—21no—
711C3⋊Dic3—21no—
712C3⋊Dic3—22no—
713C3⋊Dic3—21no—
714C3⋊Dic3C2×#4112yes—
715C3⋊Dic3C2×#4112yes—
716C3×Dic3—22no—
717C3×Dic3—22no—
718C3×Dic3—22no—
719C3×Dic3—22no—
720C3×Dic3—22no—
721C3×Dic3—22no—
722C3×Dic3—22no—
723C2×#41—92no—
724C23×C4—91no—
725C4⋊Q8—91no—
726C4⋊Q8—91no—
727C4⋊Q8—91no—
728#127—91no—
729#126—32no—
730#126—32no—
731#126—92no—
732#126—92no—
733#126—92no—
734#126—92no—
735#126—92no—
736#126—92no—
737#125—32no—
738#125—92no—
739#125—92no—
740#125—92no—
741#125—92no—
742#124—32no—
743#124—92no—
744#124—92no—
745#124—92no—
746#124—92no—
747#123—32no—
748#123—32no—
749#123—32no—
750#123—92no—
751#123—92no—
752#123—92no—
753#123—92no—
754#123—92no—
755#123—92no—
756#123—92no—
757C22⋊Q8—31no—
758C22⋊Q8—31no—
759C22⋊Q8—32no—
760C22⋊Q8—92no—
761C22⋊Q8—92no—
762C22⋊Q8—92no—
763C22⋊Q8—92no—
764C22⋊Q8—92no—
765C22⋊Q8—92no—
766#121—32no—
767#121—92no—
768#121—92no—
769#121—92no—
770#121—92no—
771#121—92no—
772#121—92no—
773#121—91no—
774#121D3211yescharacteristic
775#120—32no—
776#120—92no—
777C4×Q8—92no—
778C4×Q8—92no—
779C4×Q8—92no—
780C4×Q8—91no—
781C4×Q8—91no—
782C4×D4—32no—
783C4×D4—32no—
784C4×D4—92no—
785C4×D4—92no—
786C4×D4—92no—
787C4×D4—92no—
788C4×D4—92no—
789C4×D4—92no—
790C4×D4—92no—
791C4×D4—92no—
792C4×D4—91no—
793C4×D4—91no—
794C4×D4—92no—
795#117—92no—
796#117—92no—
797#117—92no—
798#117—92no—
799#117—92no—
800#117—92no—
801#117—92no—
802C2×C4⋊C4—31no—
803C2×C4⋊C4—91no—
804C2×C22⋊C4—31no—
805C2×C22⋊C4—91no—
806C2×C42—92no—
807C2×C42—91no—
808C2×C42—92no—
809C2×C42—91no—
810C23×C3—21no—
811C23×C3—22no—
812C23×C3—32no—
813C23×C3—62no—
814C23×C3—121no—
815C23×C3—121no—
816C23×C3C23×D312yes—
817C23×C3C23×D312yes—
818C23×C3C23×D311yescharacteristic
819C23×C3C23×D311yescharacteristic
820C22×D3—22no—
821C22×D3—32no—
822C22×D3—32no—
823C22×D3—41no—
824C22×D3—41no—
825C22×D3—62no—
826C22×D3C23×D312yes—
827C3×Q8—121no—
828C3×Q8—121no—
829C3×D4—24no—
830C3×D4—24no—
831C3×D4—44no—
832C3×D4—41no—
833C3×D4—41no—
834C3×D4—42no—
835C3×D4—122no—
836C3×D4—122no—
837C2×C3×C4—21no—
838C2×C3×C4—21no—
839C2×C3×C4—22no—
840C2×C3×C4—32no—
841C2×C3×C4—32no—
842C2×C3×C4—32no—
843C2×C3×C4—32no—
844C2×C3×C4—32no—
845C2×C3×C4—32no—
846C2×C3×C4—32no—
847C2×C3×C4—41no—
848C2×C3×C4—41no—
849C2×C3×C4—42no—
850C2×C3×C4—62no—
851C2×C3×C4—121no—
852C2×C3×C4—122no—
853C2×C3×C4—122no—
854C2×C3×C4—121no—
855C2×C3×C4C23×D311yescharacteristic
856C2×C3×C4C23×D311yescharacteristic
857C2×C3×C4C23×D311yescharacteristic
858C2×C3×C4C23×D311yescharacteristic
859C2×C3×C4C23×D312yes—
860C2×C3×C4C23×D312yes—
861#67—42no—
862#67—42no—
863#67—64no—
864#67—64no—
865#67—64no—
866#67—64no—
867#67—124no—
868#67—124no—
869#67—122no—
870#67—122no—
871#67—122no—
872#67—122no—
873#67—124no—
874C2×Dic3—22no—
875C2×Dic3—34no—
876C2×Dic3—34no—
877C2×Dic3—31no—
878C2×Dic3—31no—
879C2×Dic3—31no—
880C2×Dic3—31no—
881C2×Dic3—31no—
882C2×Dic3—32no—
883C2×Dic3—31no—
884C2×Dic3—31no—
885C2×Dic3—32no—
886C2×Dic3—31no—
887C2×Dic3—42no—
888C2×Dic3—42no—
889C2×Dic3—41no—
890C2×Dic3—41no—
891C2×Dic3—64no—
892C2×Dic3—61no—
893C2×Dic3—61no—
894C2×Dic3—61no—
895C2×Dic3—61no—
896C2×Dic3—62no—
897C2×Dic3—64no—
898C2×Dic3—64no—
899C2×Dic3—64no—
900C2×Dic3—64no—
901C2×Dic3—124no—
902C2×Dic3—121no—
903C2×Dic3—121no—
904C2×Dic3—122no—
905C2×Dic3C23×D312yes—
906C2×Dic3C23×D312yes—
907C2×Dic3C23×D312yes—
908C2×Dic3C23×D312yes—
909C2×Dic3C23×D312yes—
910C2×Dic3C23×D312yes—
911C2×Dic3C23×D312yes—
912D12—121no—
913D12—121no—
914D12—122no—
915D12—122no—
916D12—122no—
917C4×D3—64no—
918C4×D3—64no—
919C4×D3—64no—
920C4×D3—64no—
921C4×D3—124no—
922C4×D3—122no—
923C4×D3—122no—
924C4×D3—122no—
925C4×D3—122no—
926Dic6—41no—
927Dic6—41no—
928Dic6—64no—
929Dic6—64no—
930Dic6—124no—
931Dic6—122no—
932Dic6—122no—
933C2×C32—22no—
934C2×C32—42no—
935C2×C32C22×#4111yescharacteristic
936C2×C32#58511yescharacteristic
937C2×C32#58511yescharacteristic
938C3⋊D3—42no—
939C3×D3—42no—
940C24—31no—
941#41—188no—
942C2×Q8—31no—
943C2×Q8—31no—
944C2×Q8—92no—
945C2×Q8—92no—
946C2×D4—32no—
947C2×D4—32no—
948C2×D4—92no—
949C2×D4—92no—
950C2×D4—92no—
951C2×D4—92no—
952C2×D4—92no—
953C2×D4—91no—
954C2×D4C2×D3212yes—
955C2×D4C2×D3211yescharacteristic
956C22×C4—31no—
957C22×C4—31no—
958C22×C4—31no—
959C22×C4—32no—
960C22×C4—32no—
961C22×C4—92no—
962C22×C4—92no—
963C22×C4—92no—
964C22×C4—92no—
965C22×C4—91no—
966C22×C4—92no—
967C22×C4—91no—
968C22×C4—92no—
969C22×C4—184no—
970C22×C4C2×D3211yescharacteristic
971C4⋊C4—32no—
972C4⋊C4—32no—
973C4⋊C4—32no—
974C4⋊C4—32no—
975C4⋊C4—32no—
976C4⋊C4—32no—
977C4⋊C4—32no—
978C4⋊C4—32no—
979C4⋊C4—31no—
980C4⋊C4—31no—
981C4⋊C4—92no—
982C4⋊C4—92no—
983C4⋊C4—92no—
984C4⋊C4—92no—
985C4⋊C4—92no—
986C4⋊C4—92no—
987C4⋊C4—92no—
988C4⋊C4—92no—
989C4⋊C4—92no—
990C4⋊C4—92no—
991C4⋊C4—92no—
992C4⋊C4—92no—
993C4⋊C4—91no—
994C4⋊C4C2×D3211yescharacteristic
995C22⋊C4—32no—
996C22⋊C4—32no—
997C22⋊C4—32no—
998C22⋊C4—32no—
999C22⋊C4—32no—
1000C22⋊C4—32no—
1001C22⋊C4—32no—
1002C22⋊C4—32no—
1003C22⋊C4—32no—
1004C22⋊C4—32no—
1005C22⋊C4—92no—
1006C22⋊C4—92no—
1007C22⋊C4—92no—
1008C22⋊C4—92no—
1009C22⋊C4—92no—
1010C22⋊C4—92no—
1011C22⋊C4—92no—
1012C22⋊C4—92no—
1013C22⋊C4—92no—
1014C22⋊C4—92no—
1015C22⋊C4—92no—
1016C22⋊C4C2×D3212yes—
1017C42—32no—
1018C42—32no—
1019C42—92no—
1020C42—92no—
1021C42—92no—
1022C42—92no—
1023C42—92no—
1024C42—92no—
1025C42—91no—
1026C42—91no—
1027C42—91no—
1028C42—91no—
1029C22×C3—21no—
1030C22×C3—21no—
1031C22×C3—21no—
1032C22×C3—21no—
1033C22×C3—22no—
1034C22×C3—22no—
1035C22×C3—22no—
1036C22×C3—22no—
1037C22×C3—22no—
1038C22×C3—22no—
1039C22×C3—22no—
1040C22×C3—21no—
1041C22×C3—41no—
1042C22×C3—41no—
1043C22×C3—42no—
1044C22×C3—42no—
1045C22×C3—42no—
1046C22×C3—62no—
1047C22×C3—62no—
1048C22×C3—62no—
1049C22×C3—124no—
1050C22×C3D3×#4112yes—
1051C22×C3D3×#4112yes—
1052C22×C3C24×D311yescharacteristic
1053C22×C3C24×D311yescharacteristic
1054C2×D3—22no—
1055C2×D3—22no—
1056C2×D3—22no—
1057C2×D3—44no—
1058C2×D3—62no—
1059C2×D3—62no—
1060C2×D3—62no—
1061C2×D3—62no—
1062C2×D3—62no—
1063C2×D3—62no—
1064C2×D3—122no—
1065C2×D3—122no—
1066C2×D3—122no—
1067C3×C4—22no—
1068C3×C4—22no—
1069C3×C4—22no—
1070C3×C4—21no—
1071C3×C4—21no—
1072C3×C4—21no—
1073C3×C4—21no—
1074C3×C4—42no—
1075C3×C4—41no—
1076C3×C4—62no—
1077C3×C4—62no—
1078C3×C4—62no—
1079C3×C4—62no—
1080C3×C4—62no—
1081C3×C4—62no—
1082C3×C4—62no—
1083Dic3—22no—
1084Dic3—22no—
1085Dic3—22no—
1086Dic3—22no—
1087Dic3—22no—
1088Dic3—22no—
1089Dic3—22no—
1090Dic3—32no—
1091Dic3—32no—
1092Dic3—32no—
1093Dic3—32no—
1094Dic3—62no—
1095Dic3—62no—
1096Dic3—62no—
1097Dic3—62no—
1098Dic3—62no—
1099Dic3—61no—
1100Dic3—61no—
1101Dic3—61no—
1102Dic3—61no—
1103Dic3—122no—
1104Dic3—121no—
1105C32#345511yescharacteristic, complemented, Sylow
1106C23—32no—
1107C23—62no—
1108C23—92no—
1109C23—121no—
1110C23—121no—
1111C23C22×D3212yes—
1112C23C22×D3211yescharacteristic
1113Q8—121no—
1114Q8—121no—
1115Q8—184no—
1116Q8—362no—
1117D4—24no—
1118D4—41no—
1119D4—122no—
1120D4—122no—
1121D4—184no—
1122D4—184no—
1123D4—361no—
1124D4—362no—
1125D4—362no—
1126D4—362no—
1127C2×C4—32no—
1128C2×C4—32no—
1129C2×C4—32no—
1130C2×C4—32no—
1131C2×C4—32no—
1132C2×C4—32no—
1133C2×C4—32no—
1134C2×C4—41no—
1135C2×C4—62no—
1136C2×C4—94no—
1137C2×C4—91no—
1138C2×C4—91no—
1139C2×C4—91no—
1140C2×C4—92no—
1141C2×C4—91no—
1142C2×C4—121no—
1143C2×C4—122no—
1144C2×C4—121no—
1145C2×C4—122no—
1146C2×C4—184no—
1147C2×C4—184no—
1148C2×C4—184no—
1149C2×C4—184no—
1150C2×C4—362no—
1151C2×C4—362no—
1152C2×C4—361no—
1153C2×C4C22×D3212yes—
1154C2×C4C22×D3211yescharacteristic
1155C2×C4C22×D3211yescharacteristic
1156C2×C3—22no—
1157C2×C3—22no—
1158C2×C3—21no—
1159C2×C3—21no—
1160C2×C3—21no—
1161C2×C3—42no—
1162C2×C3—42no—
1163C2×C3—42no—
1164C2×C3—82no—
1165C2×C3—122no—
1166C2×C3C2×D3×#4111yescharacteristic
1167C2×C3C2×D3×#4111yescharacteristic
1168C2×C3#596611yescharacteristic
1169C2×C3#596611yescharacteristic
1170C2×C3#596611yescharacteristic
1171C2×C3#596811yescharacteristic
1172D3—42no—
1173D3—122no—
1174D3—122no—
1175D3—242no—
1176C22—21no—
1177C22—21no—
1178C22—22no—
1179C22—22no—
1180C22—22no—
1181C22—62no—
1182C22—62no—
1183C22—62no—
1184C22—124no—
1185C22—182no—
1186C22—182no—
1187C22—182no—
1188C22#6431212yes—
1189C22C23×D3211yescharacteristic
1190C4—22no—
1191C4—21no—
1192C4—21no—
1193C4—62no—
1194C4—62no—
1195C4—62no—
1196C4—62no—
1197C4—62no—
1198C4—62no—
1199C4—62no—
1200C4—92no—
1201C4—92no—
1202C4—182no—
1203C4—181no—
1204C4—181no—
1205C3—21no—
1206C3#8638711yescharacteristic, complemented
1207C3#8642711yescharacteristic, complemented
1208C2—22no—
1209C2—42no—
1210C2—122no—
1211C2—362no—
1212C2C2×#6431211yescharacteristic
1213C2#1059667911yescharacteristic
1214C2#1059669811yescharacteristic
subgroupG/H
center, FrattiniC22C23×D32
commutator, socle, cosocleC22×C32C25
FittingC32×#121C22
hypercenter#121D32
hypocenterC32#3455
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ #121

Complements

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

NH ≅ G/Ntype
1. #10596067C2semidirect
2. C3×#5617C2semidirect
3. C3×#5602C2semidirect
4. #10595251C2semidirect
5. #10595202C2semidirect
6. #10595190C2semidirect
7. #10595160C2semidirect
8. #10595127C2semidirect
9. #10595123C2semidirect
10. #10595038C2semidirect
11. #10594980C2semidirect
12. C2×#63878C2semidirect
13. #10594810C2semidirect
14. #10594479C2semidirect
15. #10594465C2semidirect
16. #10594230C2semidirect
17. #10594159C2semidirect
18. #10594144C2semidirect
19. #10594137C2semidirect
25. #64149C22semidirect
27. D4×C3⋊Dic3C22semidirect
30. #64102C22semidirect
31. #64097C22semidirect
32. #64094C22semidirect
33. #64090C22semidirect
37. C3×#935C22semidirect
45. C3×#889C22semidirect
48. C3×#879C22semidirect
49. C3×#878C22semidirect
53. #63975C22semidirect
59. #63966C22semidirect
61. #63964C22semidirect
67. #63957C22semidirect
68. #63956C22semidirect
70. C2×Dic32C22semidirect
73. #63952C22semidirect
74. #63952C22semidirect
75. #63919C22semidirect
78. #63897C22semidirect
81. #63895C22semidirect
82. #63888C22semidirect
83. C4×#624C22semidirect
90. #63873C22semidirect
91. #63870C22semidirect
92. #63868C22semidirect
93. #63867C22semidirect
100. #63849C22semidirect
101. #63848C22semidirect
102. #63846C22semidirect
103. #63845C22semidirect
104. #63844C22semidirect
105. #63844C22semidirect
106. #63843C22semidirect
107. #63843C22semidirect
108. #63838C22semidirect
131. #5617D3semidirect
133. #5602D3semidirect
285. #935C2×D3semidirect
353. #889C2×D3semidirect
400. #879C2×D3semidirect
406. #878C2×D3semidirect
1105. C32#3455semidirect
1206. C3#86387semidirect
1207. C3#86427semidirect

Maximal subgroups

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

subgroupindex
#105960672
C3×#56172
C3×#56022
#105952512
#105952022
#105951902
#105951602
#105951272
#105951232
#105950382
#105949802
C2×#638782
#105948102
#105944792
#105944652
#105942302
#105941592
#105941442
#105941372
#864273
#863873