Finite Group Databasebeta

← #11910010

Subgroups — #11910010

Order 1152.

2177 conjugacy classes of subgroups.

The subgroup lattice has 1363 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10596071C211yesmaximal, characteristic, complemented
2C3×#5616C211yesmaximal, characteristic, complemented
3C3×#5599C211yesmaximal, characteristic, complemented
4#10595222C211yesmaximal, characteristic, complemented
5#10595217C211yesmaximal, characteristic, complemented
6#10595201C212yesmaximal, complemented
7#10595199C212yesmaximal, complemented
8#10595198C211yesmaximal, characteristic, complemented
9#10595189C212yesmaximal, complemented
10#10595188C212yesmaximal, complemented
11#10595157C211yesmaximal, characteristic, complemented
12#10595033C211yesmaximal, characteristic, complemented
13#10594958C211yesmaximal, characteristic, complemented
14#10594939C211yesmaximal, characteristic, complemented
15#10594899C211yesmaximal, characteristic, complemented
16#10594494C211yesmaximal, characteristic, complemented
17#10594433C211yesmaximal, characteristic, complemented
18#10594357C211yesmaximal, characteristic, complemented
19#10594317C211yesmaximal, characteristic, complemented
20#10594136C212yesmaximal, complemented
21#10594087C212yesmaximal, complemented
22#10594086C212yesmaximal, complemented
23#10594039C212yesmaximal, complemented
24#86965—31nomaximal
25#86777—31nomaximal
26C2×C3×#237C2211yescharacteristic
27C2×C3×#235C2211yescharacteristic
28C2×D3×Dic6C2211yescharacteristic
29C32×#121C2211yescharacteristic
30#64145C2211yescharacteristic
31#64144C2212yes—
32D4×C3⋊Dic3C2212yes—
33D4×C3⋊Dic3C2211yescharacteristic
34#64133C2211yescharacteristic
35C2×C4×C3⋊Dic3C2211yescharacteristic
36#64099C2211yescharacteristic
37#64096C2211yescharacteristic
38#64088C2212yes—
39#64086C2212yes—
40C3×#940C2212yes—
41C3×#940C2211yescharacteristic
42C3×#939C2212yes—
43C3×#939C2212yes—
44C3×#938C2211yescharacteristic
45C3×#936C2212yes—
46C3×D4×Dic3C2211yescharacteristic
47C3×C4×#67C2211yescharacteristic
48C3×C4×#67C2211yescharacteristic
49C3×#926C2211yescharacteristic
50C3×#895C2211yescharacteristic
51C3×#892C2211yescharacteristic
52C3×#888C2211yescharacteristic
53C3×#887C2211yescharacteristic
54C3×#885C2212yes—
55C3×#884C2212yes—
56C3×#67⋊C4C2212yes—
57C3×#877C2212yes—
58#63982C2211yescharacteristic
59#63980C2212yes—
60#63980C2211yescharacteristic
61#67⋊Dic3C2212yes—
62#67⋊Dic3C2212yes—
63#67⋊Dic3C2212yes—
64Dic3×#67C2212yes—
65Dic3×#67C2212yes—
66Dic3×#67C2212yes—
67#63970C2212yes—
68#63970C2212yes—
69#63970C2212yes—
70#63969C2212yes—
71#63969C2212yes—
72#63969C2212yes—
73C2×Dic3⋊Dic3C2212yes—
74#63964C2212yes—
75#63962C2211yescharacteristic
76#63962C2211yescharacteristic
77#63962C2212yes—
78#63961C2212yes—
79#63959C2212yes—
80#63959C2212yes—
81#63959C2212yes—
82#63956C2212yes—
83#63955C2212yes—
84C4×#627C2211yescharacteristic
85C4×#627C2212yes—
86#63915C2211yescharacteristic
87#63908C2211yescharacteristic
88C4×#625C2211yescharacteristic
89#63898C2211yescharacteristic
90#63898C2211yescharacteristic
91Dic3×D12C2212yes—
92#63891C2212yes—
93D3×C4⋊Dic3C2211yescharacteristic
94#63887C2212yes—
95#63885C2212yes—
96#63884C2212yes—
97#63879C2212yes—
98#63878C2212yes—
99#63877C2212yes—
100#63877C2212yes—
101C4×D3×Dic3C2212yes—
102#63870C2211yescharacteristic
103#63869C2211yescharacteristic
104#63867C2212yes—
105#63867C2212yes—
106#63863C2212yes—
107#63862C2211yescharacteristic
108#63862C2211yescharacteristic
109#63862C2212yes—
110#63860C2211yescharacteristic
111#63859C2212yes—
112#63857C2211yescharacteristic
113#63855C2211yescharacteristic
114#63855C2212yes—
115#63855C2211yescharacteristic
116#63851C2212yes—
117#63845C2212yes—
118#63844C2211yescharacteristic
119#63843C2211yescharacteristic
120#63843C2211yescharacteristic
121Dic3×Dic6C2212yes—
122Dic3×Dic6C2211yescharacteristic
123#63839C2212yes—
124#63837C2212yes—
125C3×#555—31no—
126C3×#550—31no—
127#5831—31no—
128#5831—31no—
129#5827—31no—
130Dic3×#41—31no—
131#5733—31no—
132#5721—31no—
133#5719—32no—
134#5719—31no—
135#5713—32no—
136#5713—31no—
137#5681—32no—
138#5680—32no—
139#5670—32no—
140#5669—32no—
141#5619—31no—
142#5618—32no—
143#5618—31no—
144#5616—32no—
145#5616D311yescharacteristic, complemented
146#5615—32no—
147#5603—32no—
148#5603—31no—
149#5601—32no—
150#5600—31no—
151#5600—31no—
152#5600—32no—
153#5600—61no—
154#5599D311yescharacteristic, complemented
155#5598—31no—
156#5572—31no—
157#5569—31no—
158#5559—31no—
159#5552—31no—
160#5546—31no—
161#5541—31no—
162#5541—32no—
163#5538—31no—
164#5538—31no—
165#5538—32no—
166#5531—32no—
167#5530—31no—
168#5529—31no—
169#5528—32no—
170#5522—31no—
171#5516—31no—
172C2×C32×D4C2311yescharacteristic
173C2×C32×D4C2312yes—
174C22×C32×C4C2311yescharacteristic
175C22×C3⋊Dic3C2312yes—
176C22×C3⋊Dic3C2311yescharacteristic
177C22×C3⋊Dic3C2311yescharacteristic
178C2×#634C2311yescharacteristic
179C2×C3×#67C2312yes—
180C2×C3×#67C2312yes—
181C2×C3×#67C2312yes—
182C2×C3×#67C2312yes—
183C2×C3×#67C2312yes—
184C2×C3×#67C2311yescharacteristic
185C2×C3×#67C2311yescharacteristic
186C22×C3×Dic3C2312yes—
187C22×C3×Dic3C2312yes—
188C3×#237—24no—
189C3×#235—24no—
190C2×C3×D12C2311yescharacteristic
191C2×C3×D12C2312yes—
192C2×C3×C4×D3C2312yes—
193C2×C3×C4×D3C2311yescharacteristic
194C2×C3×C4×D3C2311yescharacteristic
195C2×C3×Dic6C2312yes—
196C2×C3×Dic6C2311yescharacteristic
197C2×#627C2312yes—
198C2×#627C2311yescharacteristic
199C2×#625C2312yes—
200C2×#625C2311yescharacteristic
201C2×D3×Dic3C2312yes—
202C2×D3×Dic3C2312yes—
203C2×D3×Dic3C2312yes—
204C2×D3×Dic3C2312yes—
205D3×Dic6—24no—
206C32×C4⋊C4C2311yescharacteristic
207C32×C22⋊C4C2312yes—
208#3757C2312yes—
209#3757C2312yes—
210#3757C2312yes—
211#3757C2312yes—
212C4⋊(C3⋊Dic3)C2312yes—
213C4⋊(C3⋊Dic3)C2311yescharacteristic
214#3750C2312yes—
215#3750C2312yes—
216#3750C2312yes—
217C4×C3⋊Dic3C2311yescharacteristic
218C4×C3⋊Dic3C2312yes—
219C4×C3⋊Dic3C2311yescharacteristic
220C4×C3⋊Dic3C2311yescharacteristic
221C4×C3⋊Dic3C2311yescharacteristic
222C3×#217C2312yes—
223C3×#217C2312yes—
224C3×#217C2312yes—
225C3×#217C2311yescharacteristic
226C3×#217C2311yescharacteristic
227C3×(C2×D3)⋊C4C2312yes—
228C3×(C2×D3)⋊C4C2311yescharacteristic
229C3×(C2×D3)⋊C4C2311yescharacteristic
230C3×(C2×D3)⋊C4C2312yes—
231C3×C4⋊Dic3C2311yescharacteristic
232C3×C4⋊Dic3C2311yescharacteristic
233C3×Dic3⋊C4C2311yescharacteristic
234C3×Dic3⋊C4C2312yes—
235C3×Dic3⋊C4C2311yescharacteristic
236C3×Dic3⋊C4C2312yes—
237C3×C4×Dic3C2312yes—
238C3×C4×Dic3C2312yes—
239C3×C4×Dic3C2312yes—
240C3×C4×Dic3C2311yescharacteristic
241C3×C4×Dic3C2311yescharacteristic
242#3724C2312yes—
243#3724C2312yes—
244#3724C2311yescharacteristic
245#3724C2311yescharacteristic
246Dic3⋊Dic3C2311yescharacteristic
247Dic3⋊Dic3C2312yes—
248Dic3⋊Dic3C2311yescharacteristic
249Dic3⋊Dic3C2312yes—
250Dic3⋊Dic3C2312yes—
251Dic3⋊Dic3C2312yes—
252Dic3⋊Dic3C2311yescharacteristic
253Dic3⋊Dic3C2311yescharacteristic
254Dic3⋊Dic3C2311yescharacteristic
255Dic3⋊Dic3C2311yescharacteristic
256Dic3⋊Dic3C2312yes—
257Dic3⋊Dic3C2312yes—
258(C2×D3)⋊Dic3C2312yes—
259(C2×D3)⋊Dic3C2312yes—
260(C2×D3)⋊Dic3C2312yes—
261(C2×D3)⋊Dic3C2312yes—
262(C2×D3)⋊Dic3C2311yescharacteristic
263(C2×D3)⋊Dic3C2311yescharacteristic
264(C2×D3)⋊Dic3C2311yescharacteristic
265(C2×D3)⋊Dic3C2311yescharacteristic
266(C2×D3)⋊Dic3C2312yes—
267(C2×D3)⋊Dic3C2312yes—
268(C2×D3)⋊Dic3C2311yescharacteristic
269(C2×D3)⋊Dic3C2311yescharacteristic
270Dic32C2312yes—
271Dic32C2312yes—
272Dic32C2312yes—
273Dic32C2312yes—
274#3524—91noSylow
275C2×C3×#41—31no—
276C2×C3×#41—31no—
277C2×D3×Q8—31no—
278C2×#237C2×D311yescharacteristic
279C2×#235C2×D311yescharacteristic
280C22×Dic6—31no—
281C3×C4⋊Q8—31no—
282C3×#127—32no—
283C3×#127—31no—
284C3×#124—32no—
285C3×#124—32no—
286C3×#121—21no—
287C3×#121—31no—
288C3×#121—32no—
289C3×#121—32no—
290C3×#121—31no—
291C3×#121—32no—
292C3×#121C2×D311yescharacteristic
293C3×#121C2×D311yescharacteristic
294C3×C4×Q8—31no—
295C3×C4×D4—31no—
296C3×C4×D4—31no—
297C3×C4×D4—31no—
298C3×C4×D4—32no—
299C3×#117—31no—
300C3×#117—31no—
301C3×#117—32no—
302#947—32no—
303#946—32no—
304Q8×Dic3—31no—
305Q8×Dic3—31no—
306Q8×Dic3—32no—
307Q8×Dic3—31no—
308#944—32no—
309#940C2×D312yes—
310#940C2×D311yescharacteristic
311#939—32no—
312#939—32no—
313#939—32no—
314#939—31no—
315#939—32no—
316#939—31no—
317#939—32no—
318#939—32no—
319#939C2×D312yes—
320#939C2×D312yes—
321#938—32no—
322#938—32no—
323#938—32no—
324#938—31no—
325#938C2×D311yescharacteristic
326#936—31no—
327#936—31no—
328#936—32no—
329#936—32no—
330#936—32no—
331#936—32no—
332#936—31no—
333#936—61no—
334#936C2×D312yes—
335#935—32no—
336#935—32no—
337#935—32no—
338#935—31no—
339#935—32no—
340#935—32no—
341#935—32no—
342#935—32no—
343#935—31no—
344#935—32no—
345#935—62no—
346D4×Dic3—32no—
347D4×Dic3—32no—
348D4×Dic3—31no—
349D4×Dic3—31no—
350D4×Dic3—32no—
351D4×Dic3—32no—
352D4×Dic3—32no—
353D4×Dic3—32no—
354D4×Dic3—32no—
355D4×Dic3—32no—
356D4×Dic3—31no—
357D4×Dic3—31no—
358D4×Dic3—32no—
359D4×Dic3—61no—
360D4×Dic3—62no—
361D4×Dic3C2×D311yescharacteristic
362#930—31no—
363#929—32no—
364C4×#67—32no—
365C4×#67—32no—
366C4×#67—32no—
367C4×#67—31no—
368C4×#67—31no—
369C4×#67—32no—
370C4×#67C2×D311yescharacteristic
371C4×#67C2×D311yescharacteristic
372#926—32no—
373#926—31no—
374#926—31no—
375#926—32no—
376#926C2×D311yescharacteristic
377C2×C4⋊Dic3—32no—
378C2×C4⋊Dic3—31no—
379#924—31no—
380#924—31no—
381#924—32no—
382#924—31no—
383#924—32no—
384#924—61no—
385C2×Dic3⋊C4—32no—
386C2×C4×Dic3—31no—
387C2×C4×Dic3—31no—
388C2×C4×Dic3—32no—
389C2×C4×Dic3—61no—
390#898—32no—
391#898—31no—
392#898—31no—
393#897—31no—
394#896—32no—
395#895C2×D311yescharacteristic
396#894—32no—
397#893—31no—
398#893—31no—
399#892—32no—
400#892C2×D311yescharacteristic
401D3×C4⋊C4—31no—
402#890—31no—
403#890—31no—
404#890—32no—
405#890—31no—
406#890—61no—
407#889—32no—
408#889—31no—
409#889—31no—
410#889—32no—
411#889—32no—
412#888—32no—
413#888C2×D311yescharacteristic
414#887—31no—
415#887—31no—
416#887—31no—
417#887—31no—
418#887—32no—
419#887—31no—
420#887—61no—
421#887C2×D311yescharacteristic
422#886—31no—
423#886—32no—
424#886—31no—
425#886—32no—
426#885—32no—
427#885—32no—
428#885—32no—
429#885—31no—
430#885—31no—
431#885C2×D312yes—
432#884—32no—
433#884C2×D312yes—
434#883—32no—
435#883—32no—
436#883—32no—
437#883—32no—
438#67⋊C4—32no—
439#67⋊C4—32no—
440#67⋊C4—32no—
441#67⋊C4—32no—
442#67⋊C4C2×D312yes—
443#879—32no—
444#879—32no—
445#879—32no—
446#879—32no—
447#879—31no—
448#879—31no—
449#879—32no—
450#879—32no—
451#879—62no—
452#878—32no—
453#878—32no—
454#878—31no—
455#878—31no—
456#877—32no—
457#877—32no—
458#877—32no—
459#877—32no—
460#877—32no—
461#877—32no—
462#877—62no—
463#877C2×D312yes—
464#876—32no—
465#875—31no—
466C4×D12—32no—
467#872—32no—
468#872—31no—
469#872—31no—
470#872—32no—
471#872—32no—
472C42×D3—32no—
473#870—31no—
474#870—32no—
475#870—32no—
476C4×Dic6—32no—
477C4×Dic6—31no—
478C4×Dic6—31no—
479C4×Dic6—32no—
480C4×Dic6—32no—
481C4×Dic6—31no—
482C4×Dic6—32no—
483C4×Dic6—31no—
484C23×C32C2411yescharacteristic
485C23×C32C2412yes—
486C22×C3×D3C2412yes—
487C22×C3×D3C2411yescharacteristic
488C22×C3×D3C2411yescharacteristic
489C32×D4—22no—
490C32×D4—42no—
491C2×C32×C4—22no—
492C2×C32×C4C2411yescharacteristic
493C2×C32×C4C2412yes—
494C2×C32×C4C2411yescharacteristic
495C2×C3⋊Dic3—41no—
496C2×C3⋊Dic3—42no—
497C2×C3⋊Dic3—41no—
498C2×C3⋊Dic3C2411yescharacteristic
499C2×C3⋊Dic3C2411yescharacteristic
500C2×C3⋊Dic3C2412yes—
501C2×C3⋊Dic3C2412yes—
502C2×C3⋊Dic3C2411yescharacteristic
503C2×C3⋊Dic3C2411yescharacteristic
504#634—22no—
505C3×#67—24no—
506C3×#67—24no—
507C3×#67—42no—
508C3×#67—42no—
509C3×#67—41no—
510C3×#67—41no—
511C3×#67—42no—
512C2×C3×Dic3—24no—
513C2×C3×Dic3—42no—
514C2×C3×Dic3C2411yescharacteristic
515C2×C3×Dic3C2411yescharacteristic
516C2×C3×Dic3C2412yes—
517C2×C3×Dic3C2412yes—
518C2×C3×Dic3C2411yescharacteristic
519C2×C3×Dic3C2411yescharacteristic
520C2×C3×Dic3C2411yescharacteristic
521C2×C3×Dic3C2411yescharacteristic
522C2×C3×Dic3C2412yes—
523C3×D12—22no—
524C3×D12—42no—
525C3×C4×D3—22no—
526C3×C4×D3—22no—
527C3×C4×D3—24no—
528C3×Dic6—42no—
529C3×Dic6#4114yes—
530#627—24no—
531#627—41no—
532#625—42no—
533#625—41no—
534D3×Dic3—24no—
535D3×Dic3—42no—
536D3×Dic3—42no—
537D3×Dic3—42no—
538#559—91no—
539#559—92no—
540#557—91no—
541#555—31no—
542#555—92no—
543#553—91no—
544#553—92no—
545#552—91no—
546#552—92no—
547#550—31no—
548#548—91no—
549#548—91no—
550#542—92no—
551#542—91no—
552#540—92no—
553#540—91no—
554#529—92no—
555#529—91no—
556#529—92no—
557#529—91no—
558#520—91no—
559#519—91no—
560C4×#41—91no—
561C3×#41—64no—
562C3×#41—64no—
563C2×C3×Q8—31no—
564C2×C3×Q8—32no—
565C2×C3×D4—22no—
566C2×C3×D4—21no—
567C2×C3×D4—32no—
568C2×C3×D4—32no—
569C2×C3×D4—32no—
570C2×C3×D4—32no—
571C2×C3×D4—32no—
572C2×C3×D4—31no—
573C2×C3×D4—31no—
574C2×C3×D4—31no—
575C2×C3×D4—32no—
576C2×C3×D4C22×D311yescharacteristic
577C2×C3×D4C22×D311yescharacteristic
578C2×C3×D4C22×D312yes—
579C2×C3×D4C22×D312yes—
580C22×C3×C4—21no—
581C22×C3×C4—32no—
582C22×C3×C4—32no—
583C22×C3×C4—32no—
584C22×C3×C4—31no—
585C22×C3×C4—31no—
586C22×C3×C4C22×D311yescharacteristic
587C22×C3×C4C22×D311yescharacteristic
588C2×#67—32no—
589C2×#67—31no—
590C2×#67—31no—
591C2×#67—32no—
592C2×#67C22×D312yes—
593C2×#67C22×D312yes—
594C2×#67C22×D312yes—
595C2×#67C22×D311yescharacteristic
596C2×#67C22×D312yes—
597C2×#67C22×D312yes—
598C2×#67C22×D311yescharacteristic
599C22×Dic3—32no—
600C22×Dic3—32no—
601C22×Dic3—31no—
602C22×Dic3—31no—
603C22×Dic3—31no—
604C22×Dic3—31no—
605C22×Dic3—32no—
606C22×Dic3—32no—
607C22×Dic3—32no—
608C22×Dic3—32no—
609C22×Dic3—62no—
610C22×Dic3—61no—
611C22×Dic3—61no—
612C22×Dic3C22×D312yes—
613C22×Dic3C22×D312yes—
614D3×Q8—64no—
615#237—24no—
616#235—24no—
617C2×D12C22×D311yescharacteristic
618C2×D12C22×D312yes—
619C2×C4×D3—32no—
620C2×C4×D3—32no—
621C2×C4×D3—32no—
622C2×C4×D3—32no—
623C2×C4×D3C22×D312yes—
624C2×C4×D3C22×D311yescharacteristic
625C2×C4×D3C22×D311yescharacteristic
626C2×Dic6—31no—
627C2×Dic6—31no—
628C2×Dic6—32no—
629C2×Dic6—32no—
630C2×Dic6—31no—
631C2×Dic6—31no—
632C2×Dic6—61no—
633C2×Dic6—64no—
634C2×Dic6C22×D312yes—
635C2×Dic6C22×D311yescharacteristic
636C3×C4⋊C4—21no—
637C3×C4⋊C4—31no—
638C3×C4⋊C4—32no—
639C3×C4⋊C4—31no—
640C3×C4⋊C4—31no—
641C3×C4⋊C4—32no—
642C3×C4⋊C4—31no—
643C3×C4⋊C4C22×D311yescharacteristic
644C3×C4⋊C4C22×D311yescharacteristic
645C3×C22⋊C4—22no—
646C3×C22⋊C4—32no—
647C3×C22⋊C4—31no—
648C3×C22⋊C4—32no—
649C3×C22⋊C4—31no—
650C3×C22⋊C4—32no—
651C3×C22⋊C4—31no—
652C3×C22⋊C4—32no—
653C3×C22⋊C4—32no—
654C3×C22⋊C4—31no—
655C3×C22⋊C4C22×D312yes—
656C3×C22⋊C4C22×D312yes—
657C3×C42—32no—
658C3×C42—31no—
659C3×C42—31no—
660C3×C42—32no—
661C3×C42—32no—
662#217—32no—
663#217—32no—
664#217—32no—
665#217—32no—
666#217—32no—
667#217—32no—
668#217—32no—
669#217—32no—
670#217—31no—
671#217—31no—
672#217—32no—
673#217—32no—
674#217—31no—
675#217—32no—
676#217—32no—
677#217—31no—
678#217—32no—
679#217—32no—
680#217—31no—
681#217—31no—
682#217—62no—
683#217—62no—
684#217—62no—
685#217—62no—
686#217C22×D312yes—
687#217C22×D311yescharacteristic
688#217C22×D311yescharacteristic
689#217C22×D312yes—
690#217C22×D312yes—
691(C2×D3)⋊C4—31no—
692(C2×D3)⋊C4—32no—
693(C2×D3)⋊C4—31no—
694(C2×D3)⋊C4—32no—
695(C2×D3)⋊C4—32no—
696(C2×D3)⋊C4—31no—
697(C2×D3)⋊C4—31no—
698(C2×D3)⋊C4—31no—
699(C2×D3)⋊C4—32no—
700(C2×D3)⋊C4—32no—
701(C2×D3)⋊C4—32no—
702(C2×D3)⋊C4—31no—
703(C2×D3)⋊C4C22×D311yescharacteristic
704(C2×D3)⋊C4C22×D312yes—
705(C2×D3)⋊C4C22×D312yes—
706(C2×D3)⋊C4C22×D311yescharacteristic
707C4⋊Dic3—32no—
708C4⋊Dic3—31no—
709C4⋊Dic3—31no—
710C4⋊Dic3—32no—
711C4⋊Dic3—31no—
712C4⋊Dic3—31no—
713C4⋊Dic3—31no—
714C4⋊Dic3—31no—
715C4⋊Dic3—32no—
716C4⋊Dic3—32no—
717C4⋊Dic3—32no—
718C4⋊Dic3—32no—
719C4⋊Dic3—32no—
720C4⋊Dic3—31no—
721C4⋊Dic3—31no—
722C4⋊Dic3—32no—
723C4⋊Dic3—62no—
724C4⋊Dic3—61no—
725C4⋊Dic3C22×D311yescharacteristic
726C4⋊Dic3C22×D311yescharacteristic
727Dic3⋊C4—32no—
728Dic3⋊C4—32no—
729Dic3⋊C4—32no—
730Dic3⋊C4—32no—
731Dic3⋊C4—32no—
732Dic3⋊C4—32no—
733Dic3⋊C4—31no—
734Dic3⋊C4—31no—
735Dic3⋊C4—32no—
736Dic3⋊C4—32no—
737Dic3⋊C4—31no—
738Dic3⋊C4—32no—
739Dic3⋊C4—32no—
740Dic3⋊C4—31no—
741Dic3⋊C4—32no—
742Dic3⋊C4—31no—
743Dic3⋊C4—32no—
744Dic3⋊C4—32no—
745Dic3⋊C4—31no—
746Dic3⋊C4—31no—
747Dic3⋊C4—32no—
748Dic3⋊C4—32no—
749Dic3⋊C4—31no—
750Dic3⋊C4—31no—
751Dic3⋊C4—32no—
752Dic3⋊C4—31no—
753Dic3⋊C4—62no—
754Dic3⋊C4—62no—
755Dic3⋊C4—62no—
756Dic3⋊C4C22×D312yes—
757Dic3⋊C4C22×D311yescharacteristic
758Dic3⋊C4C22×D312yes—
759Dic3⋊C4C22×D311yescharacteristic
760C4×Dic3—32no—
761C4×Dic3—32no—
762C4×Dic3—31no—
763C4×Dic3—31no—
764C4×Dic3—31no—
765C4×Dic3—31no—
766C4×Dic3—31no—
767C4×Dic3—31no—
768C4×Dic3—31no—
769C4×Dic3—31no—
770C4×Dic3—32no—
771C4×Dic3—32no—
772C4×Dic3—32no—
773C4×Dic3—32no—
774C4×Dic3—32no—
775C4×Dic3—32no—
776C4×Dic3—32no—
777C4×Dic3—32no—
778C4×Dic3—61no—
779C4×Dic3—62no—
780C4×Dic3—61no—
781C4×Dic3—61no—
782C4×Dic3—61no—
783C4×Dic3C22×D312yes—
784C4×Dic3C22×D312yes—
785C4×Dic3C22×D311yescharacteristic
786C4×Dic3C22×D311yescharacteristic
787C4×Dic3C22×D312yes—
788C22×C32—21no—
789C22×C32—22no—
790C22×C32—21no—
791C22×C32—22no—
792C22×C32—21no—
793C22×C32—22no—
794C22×C32C2511yescharacteristic
795C2×C3×D3—21no—
796C2×C3×D3—22no—
797C2×C3×D3—21no—
798C2×C3×D3—21no—
799C2×C3×D3—22no—
800C2×C3×D3—22no—
801C2×C3×D3—21no—
802C2×C3×D3—21no—
803C2×C3×D3—21no—
804C32×C4—21no—
805C32×C4—22no—
806C32×C4C2×#4112yes—
807C3⋊Dic3—21no—
808C3⋊Dic3—22no—
809C3⋊Dic3—21no—
810C3⋊Dic3—21no—
811C3⋊Dic3—22no—
812C3⋊Dic3—21no—
813C3×Dic3—21no—
814C3×Dic3—21no—
815C3×Dic3—22no—
816C3×Dic3—22no—
817C3×Dic3—21no—
818C3×Dic3—21no—
819C3×Dic3—21no—
820C3×Dic3—21no—
821C3×Dic3C2×#4114yes—
822C2×#41—31no—
823C2×#41—31no—
824C22×Q8—91no—
825C4⋊Q8—31no—
826C4⋊Q8—92no—
827#127—32no—
828#127—31no—
829#126—92no—
830#126—92no—
831#126—91no—
832#126—91no—
833#126—92no—
834#126—92no—
835#125—92no—
836#125—92no—
837#125—91no—
838#125—91no—
839#125—92no—
840#125—91no—
841#124—32no—
842#124—32no—
843#124—91no—
844#124—91no—
845#124—92no—
846#124—92no—
847#124—92no—
848#124—92no—
849#124—91no—
850#123—92no—
851#123—92no—
852#123—91no—
853#123—92no—
854#123—91no—
855#123—92no—
856#123—92no—
857#123—92no—
858#123—92no—
859#123—92no—
860C22⋊Q8—91no—
861C22⋊Q8—92no—
862C22⋊Q8—92no—
863C22⋊Q8—92no—
864C22⋊Q8—91no—
865C22⋊Q8—91no—
866#121—31no—
867#121—32no—
868#121—32no—
869#121—31no—
870#121—32no—
871#121—92no—
872#121—91no—
873#121—92no—
874#121—91no—
875#121—92no—
876#121—92no—
877#121—92no—
878#121D3211yescharacteristic
879C4×Q8—31no—
880C4×Q8—92no—
881C4×Q8—91no—
882C4×Q8—92no—
883C4×Q8—91no—
884C4×Q8—91no—
885C4×Q8—92no—
886C4×Q8—91no—
887C4×Q8—91no—
888C4×Q8—91no—
889C4×D4—31no—
890C4×D4—31no—
891C4×D4—31no—
892C4×D4—32no—
893C4×D4—92no—
894C4×D4—92no—
895C4×D4—92no—
896C4×D4—92no—
897C4×D4—92no—
898C4×D4—91no—
899C4×D4—91no—
900C4×D4—91no—
901C4×D4—92no—
902C4×D4—92no—
903C4×D4—92no—
904C4×D4—91no—
905C4×D4—92no—
906#117—31no—
907#117—31no—
908#117—32no—
909#117—92no—
910#117—92no—
911#117—92no—
912#117—91no—
913#117—91no—
914#117—92no—
915#117—92no—
916#117—92no—
917C2×C4⋊C4—91no—
918C2×C4⋊C4—92no—
919C2×C42—92no—
920C2×C42—91no—
921C23×C3—21no—
922C23×C3—22no—
923C23×C3—31no—
924C23×C3—32no—
925C23×C3—31no—
926C23×C3C23×D312yes—
927C23×C3C23×D312yes—
928C23×C3C23×D311yescharacteristic
929C23×C3C23×D311yescharacteristic
930C22×D3C23×D312yes—
931C22×D3C23×D311yescharacteristic
932C22×D3C23×D311yescharacteristic
933C3×Q8—34no—
934C3×Q8—122no—
935C3×D4—22no—
936C3×D4—22no—
937C3×D4—42no—
938C3×D4—42no—
939C3×D4—42no—
940C3×D4—44no—
941C3×D4—64no—
942C3×D4—64no—
943C3×D4—62no—
944C3×D4—122no—
945C3×D4—121no—
946C3×D4—122no—
947C3×D4—121no—
948C3×D4—122no—
949C3×D4—122no—
950C2×C3×C4—22no—
951C2×C3×C4—22no—
952C2×C3×C4—21no—
953C2×C3×C4—21no—
954C2×C3×C4—22no—
955C2×C3×C4—32no—
956C2×C3×C4—31no—
957C2×C3×C4—32no—
958C2×C3×C4—31no—
959C2×C3×C4—32no—
960C2×C3×C4—31no—
961C2×C3×C4—31no—
962C2×C3×C4—31no—
963C2×C3×C4—31no—
964C2×C3×C4—42no—
965C2×C3×C4—64no—
966C2×C3×C4—64no—
967C2×C3×C4—62no—
968C2×C3×C4—62no—
969C2×C3×C4—122no—
970C2×C3×C4C23×D311yescharacteristic
971C2×C3×C4C23×D311yescharacteristic
972C2×C3×C4C23×D312yes—
973C2×C3×C4C23×D312yes—
974C2×C3×C4C23×D311yescharacteristic
975C2×C3×C4C23×D311yescharacteristic
976#67—24no—
977#67—24no—
978#67—41no—
979#67—41no—
980#67—42no—
981#67—42no—
982#67—42no—
983#67—122no—
984#67—122no—
985#67—121no—
986#67—121no—
987C2×Dic3—24no—
988C2×Dic3—31no—
989C2×Dic3—31no—
990C2×Dic3—31no—
991C2×Dic3—31no—
992C2×Dic3—31no—
993C2×Dic3—31no—
994C2×Dic3—31no—
995C2×Dic3—31no—
996C2×Dic3—32no—
997C2×Dic3—32no—
998C2×Dic3—32no—
999C2×Dic3—32no—
1000C2×Dic3—42no—
1001C2×Dic3—61no—
1002C2×Dic3—61no—
1003C2×Dic3—61no—
1004C2×Dic3—61no—
1005C2×Dic3—62no—
1006C2×Dic3—62no—
1007C2×Dic3—64no—
1008C2×Dic3—122no—
1009C2×Dic3—122no—
1010C2×Dic3—122no—
1011C2×Dic3—121no—
1012C2×Dic3—122no—
1013C2×Dic3—121no—
1014C2×Dic3—122no—
1015C2×Dic3—121no—
1016C2×Dic3—121no—
1017C2×Dic3—122no—
1018C2×Dic3—124no—
1019C2×Dic3—122no—
1020C2×Dic3C23×D312yes—
1021C2×Dic3C23×D311yescharacteristic
1022C2×Dic3C23×D311yescharacteristic
1023C2×Dic3C23×D312yes—
1024C2×Dic3C23×D311yescharacteristic
1025C2×Dic3C23×D311yescharacteristic
1026C2×Dic3C23×D311yescharacteristic
1027C2×Dic3C23×D311yescharacteristic
1028C2×Dic3C23×D312yes—
1029D12—22no—
1030D12—42no—
1031C4×D3—22no—
1032C4×D3—22no—
1033C4×D3—24no—
1034C4×D3—64no—
1035C4×D3—122no—
1036C4×D3—122no—
1037C4×D3—122no—
1038Dic6—42no—
1039Dic6—64no—
1040Dic6—62no—
1041Dic6—62no—
1042Dic6—64no—
1043Dic6—122no—
1044Dic6—121no—
1045Dic6—121no—
1046Dic6#23714yes—
1047C2×C32—41no—
1048C2×C32—42no—
1049C2×C32C22×#4111yescharacteristic
1050C2×C32#58511yescharacteristic
1051C2×C32#58511yescharacteristic
1052C3×D3—41no—
1053C3×D3—42no—
1054C3×D3—41no—
1055#41—64no—
1056#41—64no—
1057C2×Q8—31no—
1058C2×Q8—32no—
1059C2×Q8—92no—
1060C2×Q8—91no—
1061C2×Q8—91no—
1062C2×Q8—184no—
1063C2×D4—32no—
1064C2×D4—32no—
1065C2×D4—31no—
1066C2×D4—31no—
1067C2×D4—32no—
1068C2×D4—32no—
1069C2×D4—32no—
1070C2×D4—31no—
1071C2×D4—32no—
1072C2×D4—92no—
1073C2×D4—91no—
1074C2×D4C2×D3211yescharacteristic
1075C2×D4C2×D3212yes—
1076C22×C4—32no—
1077C22×C4—32no—
1078C22×C4—32no—
1079C22×C4—31no—
1080C22×C4—31no—
1081C22×C4—92no—
1082C22×C4—92no—
1083C22×C4—92no—
1084C22×C4—92no—
1085C22×C4—91no—
1086C22×C4—91no—
1087C22×C4—92no—
1088C22×C4C2×D3211yescharacteristic
1089C4⋊C4—31no—
1090C4⋊C4—31no—
1091C4⋊C4—31no—
1092C4⋊C4—32no—
1093C4⋊C4—32no—
1094C4⋊C4—31no—
1095C4⋊C4—92no—
1096C4⋊C4—91no—
1097C4⋊C4—92no—
1098C4⋊C4—92no—
1099C4⋊C4—91no—
1100C4⋊C4—92no—
1101C4⋊C4—91no—
1102C4⋊C4—92no—
1103C4⋊C4—91no—
1104C4⋊C4—92no—
1105C4⋊C4—91no—
1106C4⋊C4—91no—
1107C4⋊C4—92no—
1108C4⋊C4—91no—
1109C4⋊C4—91no—
1110C4⋊C4—92no—
1111C4⋊C4—91no—
1112C4⋊C4—92no—
1113C4⋊C4—92no—
1114C4⋊C4—92no—
1115C4⋊C4—92no—
1116C4⋊C4C2×D3211yescharacteristic
1117C22⋊C4—32no—
1118C22⋊C4—32no—
1119C22⋊C4—32no—
1120C22⋊C4—31no—
1121C22⋊C4—31no—
1122C22⋊C4—32no—
1123C22⋊C4—31no—
1124C22⋊C4—31no—
1125C22⋊C4—32no—
1126C22⋊C4—91no—
1127C22⋊C4—91no—
1128C22⋊C4—91no—
1129C22⋊C4—92no—
1130C22⋊C4—92no—
1131C22⋊C4—91no—
1132C22⋊C4—92no—
1133C22⋊C4—91no—
1134C22⋊C4—91no—
1135C22⋊C4—92no—
1136C22⋊C4—92no—
1137C22⋊C4—92no—
1138C22⋊C4—92no—
1139C22⋊C4—92no—
1140C22⋊C4—92no—
1141C22⋊C4—92no—
1142C22⋊C4C2×D3212yes—
1143C42—32no—
1144C42—32no—
1145C42—31no—
1146C42—32no—
1147C42—31no—
1148C42—92no—
1149C42—92no—
1150C42—92no—
1151C42—92no—
1152C42—91no—
1153C42—91no—
1154C42—91no—
1155C42—91no—
1156C42—92no—
1157C22×C3—22no—
1158C22×C3—22no—
1159C22×C3—21no—
1160C22×C3—21no—
1161C22×C3—22no—
1162C22×C3—22no—
1163C22×C3—22no—
1164C22×C3—21no—
1165C22×C3—21no—
1166C22×C3—21no—
1167C22×C3—21no—
1168C22×C3—22no—
1169C22×C3—22no—
1170C22×C3—21no—
1171C22×C3—41no—
1172C22×C3—41no—
1173C22×C3—42no—
1174C22×C3—42no—
1175C22×C3—42no—
1176C22×C3—61no—
1177C22×C3—62no—
1178C22×C3—61no—
1179C22×C3—61no—
1180C22×C3—62no—
1181C22×C3—61no—
1182C22×C3—62no—
1183C22×C3—61no—
1184C22×C3—61no—
1185C22×C3C24×D311yescharacteristic
1186C22×C3C24×D311yescharacteristic
1187C2×D3—22no—
1188C2×D3—21no—
1189C2×D3—21no—
1190C2×D3—21no—
1191C2×D3—22no—
1192C2×D3—21no—
1193C2×D3—22no—
1194C2×D3—21no—
1195C2×D3—21no—
1196C3×C4—21no—
1197C3×C4—21no—
1198C3×C4—22no—
1199C3×C4—22no—
1200C3×C4—22no—
1201C3×C4—34no—
1202C3×C4—41no—
1203C3×C4—42no—
1204C3×C4—61no—
1205C3×C4—61no—
1206C3×C4—62no—
1207C3×C4—61no—
1208C3×C4—61no—
1209C3×C4—61no—
1210C3×C4—61no—
1211C3×C4—62no—
1212C3×C4C2×#23712yes—
1213C3×C4D3×#4112yes—
1214Dic3—21no—
1215Dic3—21no—
1216Dic3—21no—
1217Dic3—22no—
1218Dic3—21no—
1219Dic3—21no—
1220Dic3—22no—
1221Dic3—21no—
1222Dic3—62no—
1223Dic3—62no—
1224Dic3—62no—
1225Dic3—61no—
1226Dic3—62no—
1227Dic3—61no—
1228Dic3—61no—
1229Dic3—61no—
1230Dic3—62no—
1231Dic3—61no—
1232Dic3—61no—
1233Dic3—61no—
1234Dic3—61no—
1235Dic3—122no—
1236Dic3—121no—
1237Dic3—121no—
1238Dic3—121no—
1239Dic3—122no—
1240Dic3C2×#23714yes—
1241C32#352411yescharacteristic, complemented, Sylow
1242C23—31no—
1243C23—32no—
1244C23—31no—
1245C23C22×D3211yescharacteristic
1246C23C22×D3212yes—
1247Q8—34no—
1248Q8—122no—
1249Q8—184no—
1250Q8—182no—
1251Q8—361no—
1252D4—22no—
1253D4—42no—
1254D4—64no—
1255D4—64no—
1256D4—62no—
1257D4—122no—
1258D4—122no—
1259D4—122no—
1260D4—121no—
1261D4—122no—
1262D4—121no—
1263D4—361no—
1264D4—362no—
1265C2×C4—22no—
1266C2×C4—32no—
1267C2×C4—31no—
1268C2×C4—32no—
1269C2×C4—31no—
1270C2×C4—31no—
1271C2×C4—31no—
1272C2×C4—32no—
1273C2×C4—31no—
1274C2×C4—31no—
1275C2×C4—64no—
1276C2×C4—64no—
1277C2×C4—62no—
1278C2×C4—62no—
1279C2×C4—91no—
1280C2×C4—91no—
1281C2×C4—91no—
1282C2×C4—92no—
1283C2×C4—91no—
1284C2×C4—92no—
1285C2×C4—122no—
1286C2×C4—184no—
1287C2×C4—362no—
1288C2×C4—362no—
1289C2×C4—362no—
1290C2×C4—361no—
1291C2×C4—361no—
1292C2×C4—362no—
1293C2×C4C22×D3211yescharacteristic
1294C2×C4C22×D3212yes—
1295C2×C4C22×D3211yescharacteristic
1296C2×C3—21no—
1297C2×C3—21no—
1298C2×C3—21no—
1299C2×C3—42no—
1300C2×C3—41no—
1301C2×C3—42no—
1302C2×C3—41no—
1303C2×C3—42no—
1304C2×C3—82no—
1305C2×C3—121no—
1306C2×C3—122no—
1307C2×C3—121no—
1308C2×C3C22×#23711yescharacteristic
1309C2×C3C2×D3×#4111yescharacteristic
1310C2×C3#596411yescharacteristic
1311C2×C3#596411yescharacteristic
1312C2×C3#596611yescharacteristic
1313C2×C3#596611yescharacteristic
1314D3—41no—
1315D3—42no—
1316D3—41no—
1317C22—21no—
1318C22—22no—
1319C22—21no—
1320C22—22no—
1321C22—22no—
1322C22—21no—
1323C22—61no—
1324C22—62no—
1325C22—61no—
1326C22—62no—
1327C22—61no—
1328C22—61no—
1329C22—61no—
1330C22—62no—
1331C22—61no—
1332C22C23×D3211yescharacteristic
1333C4—21no—
1334C4—22no—
1335C4—34no—
1336C4—61no—
1337C4—61no—
1338C4—62no—
1339C4—61no—
1340C4—61no—
1341C4—61no—
1342C4—62no—
1343C4—61no—
1344C4—182no—
1345C4—181no—
1346C4—181no—
1347C4—181no—
1348C4—181no—
1349C4—182no—
1350C4D3×#23712yes—
1351C3—21no—
1352C3#8677711yescharacteristic, complemented
1353C3#8696511yescharacteristic, complemented
1354C2—41no—
1355C2—42no—
1356C2—121no—
1357C2—122no—
1358C2—121no—
1359C2C2×D3×#23711yescharacteristic
1360C2#1059667911yescharacteristic
1361C2#1059669511yescharacteristic
subgroupG/H
center, FrattiniC22C23×D32
commutator, socle, cosocleC22×C32C25
FittingC32×#121C22
hypercenter#121D32
hypocenterC32#3524
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ #121

Complements

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

NH ≅ G/Ntype
1. #10596071C2semidirect
2. C3×#5616C2semidirect
3. C3×#5599C2semidirect
4. #10595222C2semidirect
5. #10595217C2semidirect
6. #10595201C2semidirect
7. #10595199C2semidirect
8. #10595198C2semidirect
9. #10595189C2semidirect
10. #10595188C2semidirect
11. #10595157C2semidirect
12. #10595033C2semidirect
13. #10594958C2semidirect
14. #10594939C2semidirect
15. #10594899C2semidirect
16. #10594494C2semidirect
17. #10594433C2semidirect
18. #10594357C2semidirect
19. #10594317C2semidirect
20. #10594136C2semidirect
21. #10594087C2semidirect
22. #10594086C2semidirect
23. #10594039C2semidirect
145. #5616D3semidirect
154. #5599D3semidirect
1241. C32#3524semidirect
1352. C3#86777semidirect
1353. C3#86965semidirect

Maximal subgroups

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

subgroupindex
#105960712
C3×#56162
C3×#55992
#105952222
#105952172
#105952012
#105951992
#105951982
#105951892
#105951882
#105951572
#105950332
#105949582
#105949392
#105948992
#105944942
#105944332
#105943572
#105943172
#105941362
#105940872
#105940862
#105940392
#869653
#867773