Finite Group Databasebeta

← #11910043

Subgroups — #11910043

Order 1152.

2167 conjugacy classes of subgroups.

The subgroup lattice has 1361 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10596000C211yesmaximal, characteristic, complemented
2C3×#5532C211yesmaximal, characteristic, complemented
3C3×#5522C211yesmaximal, characteristic, complemented
4#10595006C211yesmaximal, characteristic, complemented
5#10594949C211yesmaximal, characteristic, complemented
6#10594899C211yesmaximal, characteristic, complemented
7#10594839C211yesmaximal, characteristic, complemented
8#10594583C211yesmaximal, characteristic, complemented
9#10594582C211yesmaximal, characteristic, complemented
10#10594496C211yesmaximal, characteristic, complemented
11#10594382C211yesmaximal, characteristic, complemented
12#10594361C211yesmaximal, characteristic, complemented
13#10594357C211yesmaximal, characteristic, complemented
14#10594341C211yesmaximal, characteristic, complemented
15#10594317C211yesmaximal, characteristic, complemented
16#10594200C212yesmaximal, complemented
17#10594101C212yesmaximal, complemented
18#10594100C212yesmaximal, complemented
19#10594096C212yesmaximal, complemented
20#10593973C212yesmaximal, complemented
21#10593930C212yesmaximal, complemented
22#10593921C212yesmaximal, complemented
23#10593915C212yesmaximal, complemented
24#86965—31nomaximal
25#85855—31nomaximal
26C2×C3×#235C2211yescharacteristic
27C2×#3796C2211yescharacteristic
28C2×D3×Dic6C2211yescharacteristic
29C32×#117C2211yescharacteristic
30C4×#638C2211yescharacteristic
31#64133C2211yescharacteristic
32#64106C2211yescharacteristic
33C4⋊C4×C3⋊D3C2211yescharacteristic
34#64099C2211yescharacteristic
35#64096C2211yescharacteristic
36#64092C2212yes—
37#64088C2212yes—
38#64081C2212yes—
39#64079C2212yes—
40C3×#930C2211yescharacteristic
41C3×C4×#67C2211yescharacteristic
42C2×C3×C4×Dic3C2211yescharacteristic
43C3×#895C2211yescharacteristic
44C3×#893C2211yescharacteristic
45C3×#893C2211yescharacteristic
46C3×#893C2211yescharacteristic
47C3×#892C2211yescharacteristic
48C3×#888C2211yescharacteristic
49C3×#887C2211yescharacteristic
50C3×#887C2211yescharacteristic
51C3×#885C2212yes—
52C3×#884C2212yes—
53C3×#67⋊C4C2212yes—
54C3×#67⋊C4C2212yes—
55C3×#875C2212yes—
56C3×#872C2212yes—
57C3×#872C2212yes—
58C3×C42×D3C2212yes—
59#63979C2212yes—
60#63978C2211yescharacteristic
61Dic3×#67C2212yes—
62#63970C2212yes—
63#63970C2212yes—
64#63966C2211yescharacteristic
65#63964C2211yescharacteristic
66#63961C2211yescharacteristic
67#63961C2212yes—
68#63959C2212yes—
69C4×#627C2211yescharacteristic
70C4×#627C2212yes—
71#63916C2211yescharacteristic
72#63915C2212yes—
73#63914C2211yescharacteristic
74#63912C2212yes—
75#63908C2211yescharacteristic
76#63908C2212yes—
77#63907C2212yes—
78#63906C2212yes—
79#63905C2212yes—
80#63905C2212yes—
81#63905C2212yes—
82#63905C2212yes—
83C4×#626C2211yescharacteristic
84C4×#626C2212yes—
85C4×#626C2212yes—
86C4×#625C2212yes—
87#63893C2212yes—
88Dic3×D12C2212yes—
89Dic3×D12C2211yescharacteristic
90#63891C2212yes—
91#63886C2212yes—
92#63885C2212yes—
93#63881C2212yes—
94#63879C2212yes—
95#63879C2212yes—
96#63878C2212yes—
97#63877C2212yes—
98#63877C2212yes—
99#63877C2212yes—
100D3×Dic3⋊C4C2212yes—
101#63874C2211yescharacteristic
102#63869C2211yescharacteristic
103#63868C2211yescharacteristic
104#63867C2212yes—
105#63867C2211yescharacteristic
106#63861C2212yes—
107#63860C2211yescharacteristic
108#63860C2211yescharacteristic
109#63859C2212yes—
110#63859C2211yescharacteristic
111#63859C2212yes—
112#63856C2212yes—
113#63855C2211yescharacteristic
114#63852C2211yescharacteristic
115#63852C2212yes—
116#63851C2212yes—
117#63850C2212yes—
118#63845C2212yes—
119#63844C2211yescharacteristic
120#63843C2211yescharacteristic
121Dic3×Dic6C2211yescharacteristic
122Dic3×Dic6C2212yes—
123#63839C2212yes—
124#63837C2212yes—
125C3×#555—31no—
126C3×C4×#41—31no—
127#5834—31no—
128#5831—31no—
129#5733—31no—
130#5721—31no—
131#5681—32no—
132#5680—32no—
133#5670—32no—
134#5669—32no—
135#5619—31no—
136#5615—32no—
137#5601—32no—
138#5600—31no—
139#5599—31no—
140#5598—31no—
141#5576—31no—
142#5574—31no—
143#5572—31no—
144#5569—31no—
145#5562—31no—
146#5562—32no—
147#5561—31no—
148#5561—32no—
149#5559—31no—
150#5559—31no—
151#5559—32no—
152#5558—31no—
153#5558—32no—
154#5552—31no—
155#5546—31no—
156#5538—31no—
157#5532—32no—
158#5532D311yescharacteristic, complemented
159#5531—32no—
160#5530—31no—
161#5529—31no—
162#5529—31no—
163#5529—32no—
164#5529—61no—
165#5528—32no—
166#5522D311yescharacteristic, complemented
167#5516—31no—
168#5479—31no—
169#5479—31no—
170#5479—32no—
171#5479—32no—
172C22×C32×C4C2311yescharacteristic
173C2×#638C2311yescharacteristic
174C2×C4×C3⋊D3C2311yescharacteristic
175C2×C4×C3⋊D3C2312yes—
176C2×#634C2311yescharacteristic
177C2×C3×#67C2312yes—
178C2×C3×#67C2311yescharacteristic
179C2×C3×#67C2312yes—
180C22×C3×Dic3C2311yescharacteristic
181C22×C3×Dic3C2311yescharacteristic
182C3×#235—24no—
183C2×C3×D12C2311yescharacteristic
184C2×C3×D12C2311yescharacteristic
185C2×C3×D12C2312yes—
186C2×C3×C4×D3C2311yescharacteristic
187C2×C3×C4×D3C2312yes—
188C2×C3×C4×D3C2312yes—
189C2×C3×C4×D3C2312yes—
190C2×C3×C4×D3C2312yes—
191C2×C3×Dic6C2312yes—
192C2×C3×Dic6C2311yescharacteristic
193C2×#627C2312yes—
194C2×#627C2311yescharacteristic
195C2×#626C2312yes—
196C2×#626C2312yes—
197C2×#626C2311yescharacteristic
198C2×#625C2312yes—
199C2×#625C2312yes—
200C2×#625C2312yes—
201C2×D3×Dic3C2312yes—
202C2×D3×Dic3C2312yes—
203C2×D3×Dic3C2312yes—
204#3796—24no—
205D3×Dic6—24no—
206C32×C4⋊C4C2311yescharacteristic
207C32×C4⋊C4C2311yescharacteristic
208C32×C22⋊C4C2312yes—
209C32×C42C2312yes—
210#3757C2311yescharacteristic
211#3757C2312yes—
212#3752C2311yescharacteristic
213#3752C2312yes—
214C4⋊(C3⋊Dic3)C2312yes—
215C4⋊(C3⋊Dic3)C2312yes—
216C4⋊(C3⋊Dic3)C2311yescharacteristic
217#3750C2311yescharacteristic
218#3750C2312yes—
219#3750C2312yes—
220#3750C2312yes—
221#3750C2312yes—
222C4×C3⋊Dic3C2312yes—
223C4×C3⋊Dic3C2311yescharacteristic
224C3×#217C2311yescharacteristic
225C3×(C2×D3)⋊C4C2312yes—
226C3×(C2×D3)⋊C4C2312yes—
227C3×(C2×D3)⋊C4C2312yes—
228C3×(C2×D3)⋊C4C2312yes—
229C3×(C2×D3)⋊C4C2312yes—
230C3×(C2×D3)⋊C4C2311yescharacteristic
231C3×(C2×D3)⋊C4C2312yes—
232C3×C4⋊Dic3C2311yescharacteristic
233C3×Dic3⋊C4C2312yes—
234C3×Dic3⋊C4C2312yes—
235C3×Dic3⋊C4C2312yes—
236C3×Dic3⋊C4C2311yescharacteristic
237C3×C4×Dic3C2312yes—
238C3×C4×Dic3C2312yes—
239C3×C4×Dic3C2312yes—
240C3×C4×Dic3C2311yescharacteristic
241C3×C4×Dic3C2311yescharacteristic
242C3×C4×Dic3C2311yescharacteristic
243C3×C4×Dic3C2311yescharacteristic
244C3×C4×Dic3C2311yescharacteristic
245#3724C2312yes—
246#3724C2312yes—
247#3724C2311yescharacteristic
248#3724C2311yescharacteristic
249#3724C2311yescharacteristic
250Dic3⋊Dic3C2311yescharacteristic
251Dic3⋊Dic3C2312yes—
252Dic3⋊Dic3C2311yescharacteristic
253Dic3⋊Dic3C2312yes—
254Dic3⋊Dic3C2312yes—
255Dic3⋊Dic3C2311yescharacteristic
256Dic3⋊Dic3C2311yescharacteristic
257Dic3⋊Dic3C2311yescharacteristic
258#3722C2311yescharacteristic
259#3722C2311yescharacteristic
260#3722C2311yescharacteristic
261(C2×D3)⋊Dic3C2312yes—
262(C2×D3)⋊Dic3C2312yes—
263(C2×D3)⋊Dic3C2311yescharacteristic
264(C2×D3)⋊Dic3C2312yes—
265(C2×D3)⋊Dic3C2311yescharacteristic
266(C2×D3)⋊Dic3C2312yes—
267(C2×D3)⋊Dic3C2312yes—
268(C2×D3)⋊Dic3C2312yes—
269(C2×D3)⋊Dic3C2311yescharacteristic
270(C2×D3)⋊Dic3C2312yes—
271Dic32C2312yes—
272Dic32C2312yes—
273Dic32C2312yes—
274#3524—91noSylow
275C2×C3×#41—31no—
276C2×#239—31no—
277C2×D3×Q8—31no—
278C2×#237—31no—
279C2×#235C2×D311yescharacteristic
280C22×Dic6—31no—
281C3×C4⋊Q8—31no—
282C3×#124—32no—
283C3×#124—32no—
284C3×#121—31no—
285C3×#121—31no—
286C3×#121—32no—
287C3×C4×Q8—31no—
288C3×C4×Q8—31no—
289C3×C4×D4—31no—
290C3×C4×D4—31no—
291C3×C4×D4—31no—
292C3×C4×D4—31no—
293C3×C4×D4—32no—
294C3×C4×D4—32no—
295C3×#117—21no—
296C3×#117—31no—
297C3×#117—32no—
298C3×#117—32no—
299C3×#117C2×D311yescharacteristic
300C3×#117C2×D311yescharacteristic
301C2×C3×C42—31no—
302C2×C3×C42—32no—
303#947—32no—
304#946—32no—
305Q8×Dic3—31no—
306Q8×Dic3—32no—
307Q8×Dic3—31no—
308#944—32no—
309#940—32no—
310#940—32no—
311#940—31no—
312#940—31no—
313#939—32no—
314#939—32no—
315#939—31no—
316#939—32no—
317#939—32no—
318#938—32no—
319#938—32no—
320#938—32no—
321#938—31no—
322#938—31no—
323#936—32no—
324#936—31no—
325#936—31no—
326#935—32no—
327#935—31no—
328D4×Dic3—32no—
329D4×Dic3—32no—
330D4×Dic3—31no—
331#930—31no—
332#930—32no—
333#930—31no—
334#930—32no—
335#930C2×D311yescharacteristic
336#929—31no—
337#929—32no—
338#929—31no—
339#929—32no—
340#929—32no—
341#929—32no—
342#929—32no—
343#929—32no—
344C4×#67—31no—
345C4×#67—31no—
346C4×#67—32no—
347C4×#67—32no—
348C4×#67—32no—
349C4×#67—32no—
350C4×#67—32no—
351C4×#67—32no—
352C4×#67—32no—
353C4×#67—31no—
354C4×#67—61no—
355C4×#67C2×D311yescharacteristic
356#926—31no—
357#924—31no—
358#924—31no—
359#924—32no—
360#924—31no—
361#924—32no—
362#924—61no—
363C2×Dic3⋊C4—32no—
364C2×C4×Dic3C2×D311yescharacteristic
365#898—32no—
366#898—31no—
367#897—31no—
368#897—31no—
369#897—32no—
370#897—61no—
371#896—32no—
372#895—31no—
373#895—32no—
374#895C2×D311yescharacteristic
375#894—32no—
376#893—32no—
377#893C2×D311yescharacteristic
378#893C2×D311yescharacteristic
379#893C2×D311yescharacteristic
380#892—32no—
381#892C2×D311yescharacteristic
382D3×C4⋊C4—32no—
383D3×C4⋊C4—31no—
384D3×C4⋊C4—31no—
385D3×C4⋊C4—61no—
386#890—31no—
387#890—31no—
388#890—32no—
389#890—31no—
390#890—61no—
391#889—32no—
392#889—32no—
393#889—31no—
394#888—32no—
395#888C2×D311yescharacteristic
396#887—31no—
397#887—31no—
398#887—31no—
399#887—32no—
400#887—31no—
401#887—61no—
402#887C2×D311yescharacteristic
403#887C2×D311yescharacteristic
404#886—31no—
405#886—32no—
406#885—32no—
407#885—32no—
408#885—32no—
409#885—32no—
410#885—31no—
411#885—32no—
412#885C2×D312yes—
413#884—32no—
414#884—32no—
415#884—32no—
416#884—32no—
417#884C2×D312yes—
418#883—32no—
419#883—32no—
420#883—32no—
421#883—32no—
422#883—32no—
423#883—32no—
424#883—32no—
425#883—62no—
426#67⋊C4—32no—
427#67⋊C4—32no—
428#67⋊C4—32no—
429#67⋊C4C2×D312yes—
430#67⋊C4C2×D312yes—
431#879—32no—
432#879—32no—
433#879—32no—
434#879—31no—
435#879—32no—
436#879—32no—
437#879—62no—
438#878—31no—
439#878—32no—
440#877—32no—
441#877—32no—
442#877—32no—
443#877—32no—
444#876—32no—
445#876—31no—
446#876—32no—
447#876—31no—
448#875—31no—
449#875—31no—
450#875—31no—
451#875—32no—
452#875C2×D312yes—
453C4×D12—32no—
454C4×D12—31no—
455C4×D12—32no—
456C4×D12—31no—
457C4×D12—32no—
458#872—31no—
459#872—32no—
460#872—32no—
461#872—32no—
462#872—32no—
463#872—32no—
464#872—31no—
465#872—31no—
466#872—62no—
467#872C2×D312yes—
468#872C2×D312yes—
469C42×D3C2×D312yes—
470#870—32no—
471#870—32no—
472#870—31no—
473#870—31no—
474#870—32no—
475#870—62no—
476C4×Dic6—31no—
477C4×Dic6—32no—
478C4×Dic6—31no—
479C4×Dic6—32no—
480C4×Dic6—32no—
481C4×Dic6—31no—
482C4×Dic6—31no—
483C4×Dic6—32no—
484C23×C32C2411yescharacteristic
485C22×C3⋊D3C2411yescharacteristic
486C22×C3×D3C2412yes—
487C22×C3×D3C2411yescharacteristic
488C22×C3×D3C2412yes—
489C2×C32×C4—22no—
490C2×C32×C4C2412yes—
491C2×C32×C4C2411yescharacteristic
492C2×C32×C4C2412yes—
493C2×C32×C4C2411yescharacteristic
494#638—41no—
495C2×C3⋊Dic3C2411yescharacteristic
496C2×C3⋊Dic3C2412yes—
497C2×C3⋊Dic3C2412yes—
498C2×C3⋊Dic3C2411yescharacteristic
499C2×C3⋊Dic3C2411yescharacteristic
500C4×C3⋊D3—22no—
501C4×C3⋊D3—42no—
502#634—22no—
503C3×#67—24no—
504C3×#67—42no—
505C3×#67—41no—
506C2×C3×Dic3—41no—
507C2×C3×Dic3—41no—
508C2×C3×Dic3C2411yescharacteristic
509C2×C3×Dic3C2411yescharacteristic
510C2×C3×Dic3C2412yes—
511C2×C3×Dic3C2411yescharacteristic
512C2×C3×Dic3C2411yescharacteristic
513C2×C3×Dic3C2411yescharacteristic
514C2×C3×Dic3C2411yescharacteristic
515C2×C3×Dic3C2411yescharacteristic
516C2×C3×Dic3C2412yes—
517C3×D12—22no—
518C3×D12—22no—
519C3×D12—42no—
520C3×C4×D3—22no—
521C3×C4×D3—24no—
522C3×C4×D3—42no—
523C3×C4×D3—42no—
524C3×C4×D3—42no—
525C3×Dic6—42no—
526C3×Dic6#4114yes—
527#627—24no—
528#627—41no—
529#626—24no—
530#626—41no—
531#626—42no—
532#625—42no—
533#625—42no—
534#625—42no—
535D3×Dic3—24no—
536D3×Dic3—24no—
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—92no—
546#552—91no—
547#550—91no—
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—91no—
557#529—92no—
558#520—91no—
559#519—91no—
560C4×#41—31no—
561C3×#41—64no—
562C2×C3×Q8—31no—
563C2×C3×Q8—32no—
564C2×C3×D4—32no—
565C2×C3×D4—32no—
566C2×C3×D4—31no—
567C2×C3×D4—31no—
568C2×C3×D4—31no—
569C2×C3×D4—32no—
570C22×C3×C4—21no—
571C22×C3×C4—31no—
572C22×C3×C4—31no—
573C22×C3×C4—32no—
574C22×C3×C4—31no—
575C22×C3×C4—32no—
576C22×C3×C4—32no—
577C22×C3×C4—32no—
578C22×C3×C4C22×D311yescharacteristic
579C22×C3×C4C22×D311yescharacteristic
580C2×#67—31no—
581C2×#67—31no—
582C2×#67—32no—
583C2×#67—32no—
584C2×#67—32no—
585C2×#67—32no—
586C2×#67—32no—
587C2×#67—32no—
588C2×#67—32no—
589C2×#67—31no—
590C2×#67—32no—
591C2×#67—61no—
592C2×#67C22×D312yes—
593C2×#67C22×D311yescharacteristic
594C2×#67C22×D312yes—
595C22×Dic3—32no—
596C22×Dic3—32no—
597C22×Dic3—32no—
598C22×Dic3C22×D311yescharacteristic
599C22×Dic3C22×D311yescharacteristic
600#239—64no—
601D3×Q8—64no—
602#237—64no—
603#235—24no—
604C2×D12—32no—
605C2×D12—31no—
606C2×D12—32no—
607C2×D12C22×D311yescharacteristic
608C2×D12C22×D311yescharacteristic
609C2×D12C22×D312yes—
610C2×C4×D3—32no—
611C2×C4×D3—32no—
612C2×C4×D3—31no—
613C2×C4×D3—31no—
614C2×C4×D3—32no—
615C2×C4×D3—32no—
616C2×C4×D3—32no—
617C2×C4×D3—62no—
618C2×C4×D3—61no—
619C2×C4×D3C22×D312yes—
620C2×C4×D3C22×D311yescharacteristic
621C2×C4×D3C22×D312yes—
622C2×C4×D3C22×D312yes—
623C2×C4×D3C22×D312yes—
624C2×Dic6—31no—
625C2×Dic6—31no—
626C2×Dic6—32no—
627C2×Dic6—32no—
628C2×Dic6—31no—
629C2×Dic6—31no—
630C2×Dic6—61no—
631C2×Dic6—64no—
632C2×Dic6C22×D312yes—
633C2×Dic6C22×D311yescharacteristic
634C3×C4⋊C4—21no—
635C3×C4⋊C4—21no—
636C3×C4⋊C4—31no—
637C3×C4⋊C4—32no—
638C3×C4⋊C4—32no—
639C3×C4⋊C4—32no—
640C3×C4⋊C4—31no—
641C3×C4⋊C4C22×D311yescharacteristic
642C3×C4⋊C4C22×D311yescharacteristic
643C3×C4⋊C4C22×D311yescharacteristic
644C3×C4⋊C4C22×D311yescharacteristic
645C3×C22⋊C4—22no—
646C3×C22⋊C4—31no—
647C3×C22⋊C4—32no—
648C3×C22⋊C4—32no—
649C3×C22⋊C4—32no—
650C3×C22⋊C4—32no—
651C3×C22⋊C4—31no—
652C3×C22⋊C4—32no—
653C3×C22⋊C4—32no—
654C3×C22⋊C4C22×D312yes—
655C3×C22⋊C4C22×D312yes—
656C3×C42—22no—
657C3×C42—31no—
658C3×C42—32no—
659C3×C42—32no—
660C3×C42—31no—
661C3×C42—32no—
662C3×C42—31no—
663C3×C42—31no—
664C3×C42—31no—
665C3×C42C22×D312yes—
666C3×C42C22×D312yes—
667#217—31no—
668#217—31no—
669#217—32no—
670#217—32no—
671#217—31no—
672#217—31no—
673#217—32no—
674#217—32no—
675#217—32no—
676#217—31no—
677#217—32no—
678#217—32no—
679#217—32no—
680#217—32no—
681#217—61no—
682#217—62no—
683#217C22×D311yescharacteristic
684(C2×D3)⋊C4—31no—
685(C2×D3)⋊C4—32no—
686(C2×D3)⋊C4—32no—
687(C2×D3)⋊C4—31no—
688(C2×D3)⋊C4—31no—
689(C2×D3)⋊C4—32no—
690(C2×D3)⋊C4—32no—
691(C2×D3)⋊C4—32no—
692(C2×D3)⋊C4—32no—
693(C2×D3)⋊C4—32no—
694(C2×D3)⋊C4—31no—
695(C2×D3)⋊C4—31no—
696(C2×D3)⋊C4—32no—
697(C2×D3)⋊C4—32no—
698(C2×D3)⋊C4—31no—
699(C2×D3)⋊C4—31no—
700(C2×D3)⋊C4—31no—
701(C2×D3)⋊C4—31no—
702(C2×D3)⋊C4—31no—
703(C2×D3)⋊C4—31no—
704(C2×D3)⋊C4—61no—
705(C2×D3)⋊C4—62no—
706(C2×D3)⋊C4C22×D312yes—
707(C2×D3)⋊C4C22×D312yes—
708(C2×D3)⋊C4C22×D312yes—
709(C2×D3)⋊C4C22×D312yes—
710(C2×D3)⋊C4C22×D312yes—
711(C2×D3)⋊C4C22×D312yes—
712(C2×D3)⋊C4C22×D311yescharacteristic
713C4⋊Dic3—32no—
714C4⋊Dic3—31no—
715C4⋊Dic3—32no—
716C4⋊Dic3—31no—
717C4⋊Dic3—32no—
718C4⋊Dic3—32no—
719C4⋊Dic3—31no—
720C4⋊Dic3—31no—
721C4⋊Dic3—31no—
722C4⋊Dic3—32no—
723C4⋊Dic3—31no—
724C4⋊Dic3—31no—
725C4⋊Dic3—32no—
726C4⋊Dic3—32no—
727C4⋊Dic3—62no—
728C4⋊Dic3—62no—
729C4⋊Dic3—61no—
730C4⋊Dic3C22×D311yescharacteristic
731Dic3⋊C4—32no—
732Dic3⋊C4—31no—
733Dic3⋊C4—31no—
734Dic3⋊C4—32no—
735Dic3⋊C4—32no—
736Dic3⋊C4—32no—
737Dic3⋊C4—32no—
738Dic3⋊C4—32no—
739Dic3⋊C4—32no—
740Dic3⋊C4—32no—
741Dic3⋊C4—31no—
742Dic3⋊C4—31no—
743Dic3⋊C4—32no—
744Dic3⋊C4—32no—
745Dic3⋊C4—31no—
746Dic3⋊C4—32no—
747Dic3⋊C4—32no—
748Dic3⋊C4—31no—
749Dic3⋊C4—32no—
750Dic3⋊C4—31no—
751Dic3⋊C4—31no—
752Dic3⋊C4—32no—
753Dic3⋊C4—31no—
754Dic3⋊C4—31no—
755Dic3⋊C4—31no—
756Dic3⋊C4—31no—
757Dic3⋊C4—31no—
758Dic3⋊C4—32no—
759Dic3⋊C4—61no—
760Dic3⋊C4—62no—
761Dic3⋊C4—62no—
762Dic3⋊C4—62no—
763Dic3⋊C4—62no—
764Dic3⋊C4C22×D312yes—
765Dic3⋊C4C22×D311yescharacteristic
766Dic3⋊C4C22×D312yes—
767Dic3⋊C4C22×D312yes—
768C4×Dic3—32no—
769C4×Dic3—32no—
770C4×Dic3—31no—
771C4×Dic3—31no—
772C4×Dic3—32no—
773C4×Dic3—32no—
774C4×Dic3—32no—
775C4×Dic3—32no—
776C4×Dic3—32no—
777C4×Dic3—32no—
778C4×Dic3—62no—
779C4×Dic3—61no—
780C4×Dic3C22×D312yes—
781C4×Dic3C22×D311yescharacteristic
782C4×Dic3C22×D312yes—
783C4×Dic3C22×D311yescharacteristic
784C4×Dic3C22×D311yescharacteristic
785C4×Dic3C22×D312yes—
786C4×Dic3C22×D311yescharacteristic
787C4×Dic3C22×D311yescharacteristic
788C22×C32—21no—
789C22×C32—21no—
790C22×C32—21no—
791C22×C32C2511yescharacteristic
792C2×C3⋊D3—21no—
793C2×C3⋊D3—21no—
794C2×C3⋊D3—21no—
795C2×C3×D3—21no—
796C2×C3×D3—22no—
797C2×C3×D3—22no—
798C2×C3×D3—22no—
799C2×C3×D3—22no—
800C2×C3×D3—21no—
801C2×C3×D3—22no—
802C2×C3×D3—22no—
803C2×C3×D3—21no—
804C32×C4—21no—
805C32×C4—22no—
806C32×C4—22no—
807C32×C4C2×#4112yes—
808C3⋊Dic3—21no—
809C3⋊Dic3—22no—
810C3⋊Dic3—22no—
811C3⋊Dic3—21no—
812C3⋊Dic3—21no—
813C3×Dic3—21no—
814C3×Dic3—21no—
815C3×Dic3—21no—
816C3×Dic3—22no—
817C3×Dic3—21no—
818C3×Dic3—21no—
819C3×Dic3—21no—
820C3×Dic3—21no—
821C3×Dic3C2×#4114yes—
822C2×#41—31no—
823C2×#41—91no—
824C22×Q8—91no—
825C4⋊Q8—31no—
826C4⋊Q8—92no—
827#127—92no—
828#127—91no—
829#126—92no—
830#126—91no—
831#126—92no—
832#126—91no—
833#126—92no—
834#126—92no—
835#125—91no—
836#125—92no—
837#125—91no—
838#125—92no—
839#125—91no—
840#125—92no—
841#124—32no—
842#124—32no—
843#124—92no—
844#124—91no—
845#124—91no—
846#124—91no—
847#124—92no—
848#124—92no—
849#124—92no—
850#123—92no—
851#123—92no—
852#123—92no—
853#123—92no—
854#123—91no—
855#123—92no—
856#123—92no—
857#123—92no—
858#123—91no—
859#123—92no—
860C22⋊Q8—92no—
861C22⋊Q8—91no—
862C22⋊Q8—92no—
863C22⋊Q8—92no—
864C22⋊Q8—91no—
865C22⋊Q8—91no—
866#121—31no—
867#121—31no—
868#121—32no—
869#121—92no—
870#121—92no—
871#121—92no—
872#121—92no—
873#121—91no—
874#121—92no—
875#121—91no—
876#121—91no—
877#121—92no—
878#121—92no—
879C4×Q8—31no—
880C4×Q8—31no—
881C4×Q8—92no—
882C4×Q8—91no—
883C4×Q8—91no—
884C4×Q8—92no—
885C4×Q8—91no—
886C4×Q8—92no—
887C4×Q8—91no—
888C4×Q8—91no—
889C4×D4—31no—
890C4×D4—31no—
891C4×D4—31no—
892C4×D4—31no—
893C4×D4—32no—
894C4×D4—32no—
895C4×D4—92no—
896C4×D4—91no—
897C4×D4—92no—
898C4×D4—91no—
899C4×D4—92no—
900C4×D4—92no—
901C4×D4—92no—
902C4×D4—92no—
903C4×D4—92no—
904C4×D4—92no—
905C4×D4—91no—
906#117—31no—
907#117—32no—
908#117—32no—
909#117—91no—
910#117—92no—
911#117—92no—
912#117—92no—
913#117—91no—
914#117—92no—
915#117—92no—
916#117D3211yescharacteristic
917C2×C4⋊C4—92no—
918C2×C4⋊C4—91no—
919C2×C42—31no—
920C2×C42—32no—
921C23×C3—21no—
922C23×C3—32no—
923C23×C3—31no—
924C23×C3—32no—
925C23×C3C23×D311yescharacteristic
926C23×C3C23×D311yescharacteristic
927C22×D3—31no—
928C22×D3—31no—
929C22×D3—61no—
930C22×D3C23×D312yes—
931C22×D3C23×D311yescharacteristic
932C22×D3C23×D312yes—
933C3×Q8—34no—
934C3×Q8—122no—
935C3×D4—64no—
936C3×D4—62no—
937C3×D4—62no—
938C3×D4—122no—
939C3×D4—122no—
940C3×D4—121no—
941C2×C3×C4—22no—
942C2×C3×C4—22no—
943C2×C3×C4—21no—
944C2×C3×C4—22no—
945C2×C3×C4—21no—
946C2×C3×C4—22no—
947C2×C3×C4—32no—
948C2×C3×C4—32no—
949C2×C3×C4—31no—
950C2×C3×C4—31no—
951C2×C3×C4—31no—
952C2×C3×C4—31no—
953C2×C3×C4—31no—
954C2×C3×C4—31no—
955C2×C3×C4—31no—
956C2×C3×C4—42no—
957C2×C3×C4—64no—
958C2×C3×C4—62no—
959C2×C3×C4—122no—
960C2×C3×C4—122no—
961C2×C3×C4—122no—
962C2×C3×C4—121no—
963C2×C3×C4—121no—
964C2×C3×C4C23×D312yes—
965C2×C3×C4C23×D312yes—
966C2×C3×C4C23×D311yescharacteristic
967C2×C3×C4C23×D312yes—
968C2×C3×C4C23×D311yescharacteristic
969C2×C3×C4C23×D312yes—
970C2×C3×C4C23×D311yescharacteristic
971C2×C3×C4C23×D311yescharacteristic
972#67—24no—
973#67—41no—
974#67—42no—
975#67—64no—
976#67—121no—
977#67—122no—
978#67—122no—
979#67—122no—
980#67—122no—
981#67—122no—
982#67—122no—
983#67—122no—
984#67—121no—
985#67—121no—
986#67—122no—
987C2×Dic3—31no—
988C2×Dic3—31no—
989C2×Dic3—31no—
990C2×Dic3—31no—
991C2×Dic3—32no—
992C2×Dic3—32no—
993C2×Dic3—32no—
994C2×Dic3—32no—
995C2×Dic3—31no—
996C2×Dic3—31no—
997C2×Dic3—41no—
998C2×Dic3—41no—
999C2×Dic3—61no—
1000C2×Dic3—61no—
1001C2×Dic3—62no—
1002C2×Dic3—62no—
1003C2×Dic3—61no—
1004C2×Dic3—64no—
1005C2×Dic3—64no—
1006C2×Dic3—122no—
1007C2×Dic3C23×D311yescharacteristic
1008C2×Dic3C23×D312yes—
1009C2×Dic3C23×D311yescharacteristic
1010C2×Dic3C23×D311yescharacteristic
1011C2×Dic3C23×D311yescharacteristic
1012C2×Dic3C23×D311yescharacteristic
1013C2×Dic3C23×D311yescharacteristic
1014C2×Dic3C23×D311yescharacteristic
1015C2×Dic3C23×D312yes—
1016D12—22no—
1017D12—22no—
1018D12—42no—
1019D12—64no—
1020D12—122no—
1021D12—121no—
1022C4×D3—22no—
1023C4×D3—24no—
1024C4×D3—42no—
1025C4×D3—42no—
1026C4×D3—42no—
1027C4×D3—64no—
1028C4×D3—64no—
1029C4×D3—62no—
1030C4×D3—62no—
1031C4×D3—122no—
1032C4×D3—122no—
1033C4×D3—122no—
1034C4×D3—122no—
1035C4×D3—124no—
1036Dic6—42no—
1037Dic6—64no—
1038Dic6—62no—
1039Dic6—62no—
1040Dic6—64no—
1041Dic6—122no—
1042Dic6—121no—
1043Dic6—121no—
1044Dic6#23514yes—
1045C2×C32—41no—
1046C2×C32C22×#4111yescharacteristic
1047C2×C32#58511yescharacteristic
1048C2×C32#58511yescharacteristic
1049C3⋊D3—41no—
1050C3×D3—42no—
1051C3×D3—41no—
1052C3×D3—42no—
1053#41—64no—
1054#41—184no—
1055C2×Q8—31no—
1056C2×Q8—32no—
1057C2×Q8—92no—
1058C2×Q8—91no—
1059C2×Q8—91no—
1060C2×Q8—184no—
1061C2×D4—32no—
1062C2×D4—31no—
1063C2×D4—32no—
1064C2×D4—31no—
1065C2×D4—31no—
1066C2×D4—32no—
1067C2×D4—92no—
1068C2×D4—91no—
1069C2×D4—92no—
1070C2×D4—92no—
1071C2×D4—92no—
1072C2×D4—92no—
1073C2×D4—91no—
1074C22×C4—31no—
1075C22×C4—31no—
1076C22×C4—32no—
1077C22×C4—31no—
1078C22×C4—32no—
1079C22×C4—32no—
1080C22×C4—32no—
1081C22×C4—92no—
1082C22×C4—92no—
1083C22×C4—92no—
1084C22×C4—91no—
1085C22×C4—92no—
1086C22×C4C2×D3211yescharacteristic
1087C4⋊C4—32no—
1088C4⋊C4—31no—
1089C4⋊C4—32no—
1090C4⋊C4—31no—
1091C4⋊C4—32no—
1092C4⋊C4—91no—
1093C4⋊C4—92no—
1094C4⋊C4—91no—
1095C4⋊C4—92no—
1096C4⋊C4—92no—
1097C4⋊C4—91no—
1098C4⋊C4—91no—
1099C4⋊C4—92no—
1100C4⋊C4—91no—
1101C4⋊C4—92no—
1102C4⋊C4—91no—
1103C4⋊C4—91no—
1104C4⋊C4—91no—
1105C4⋊C4—92no—
1106C4⋊C4—91no—
1107C4⋊C4—92no—
1108C4⋊C4—92no—
1109C4⋊C4—92no—
1110C4⋊C4—91no—
1111C4⋊C4—92no—
1112C4⋊C4—92no—
1113C4⋊C4C2×D3211yescharacteristic
1114C4⋊C4C2×D3211yescharacteristic
1115C22⋊C4—31no—
1116C22⋊C4—32no—
1117C22⋊C4—32no—
1118C22⋊C4—32no—
1119C22⋊C4—32no—
1120C22⋊C4—32no—
1121C22⋊C4—32no—
1122C22⋊C4—31no—
1123C22⋊C4—91no—
1124C22⋊C4—91no—
1125C22⋊C4—91no—
1126C22⋊C4—91no—
1127C22⋊C4—91no—
1128C22⋊C4—92no—
1129C22⋊C4—92no—
1130C22⋊C4—91no—
1131C22⋊C4—92no—
1132C22⋊C4—92no—
1133C22⋊C4—92no—
1134C22⋊C4—92no—
1135C22⋊C4—92no—
1136C22⋊C4—91no—
1137C22⋊C4—92no—
1138C22⋊C4—91no—
1139C22⋊C4—92no—
1140C22⋊C4C2×D3212yes—
1141C42—31no—
1142C42—31no—
1143C42—32no—
1144C42—31no—
1145C42—32no—
1146C42—31no—
1147C42—32no—
1148C42—31no—
1149C42—92no—
1150C42—92no—
1151C42—92no—
1152C42—92no—
1153C42—91no—
1154C42C2×D3212yes—
1155C22×C3—21no—
1156C22×C3—21no—
1157C22×C3—21no—
1158C22×C3—21no—
1159C22×C3—21no—
1160C22×C3—21no—
1161C22×C3—21no—
1162C22×C3—41no—
1163C22×C3—41no—
1164C22×C3—41no—
1165C22×C3—61no—
1166C22×C3—62no—
1167C22×C3—62no—
1168C22×C3—62no—
1169C22×C3—62no—
1170C22×C3—61no—
1171C22×C3—61no—
1172C22×C3—62no—
1173C22×C3—62no—
1174C22×C3C24×D311yescharacteristic
1175C22×C3C24×D311yescharacteristic
1176C2×D3—22no—
1177C2×D3—21no—
1178C2×D3—22no—
1179C2×D3—22no—
1180C2×D3—22no—
1181C2×D3—22no—
1182C2×D3—21no—
1183C2×D3—21no—
1184C2×D3—22no—
1185C2×D3—62no—
1186C2×D3—61no—
1187C2×D3—61no—
1188C2×D3—61no—
1189C2×D3—61no—
1190C2×D3—61no—
1191C2×D3—61no—
1192C2×D3—121no—
1193C2×D3—121no—
1194C3×C4—21no—
1195C3×C4—21no—
1196C3×C4—22no—
1197C3×C4—22no—
1198C3×C4—22no—
1199C3×C4—22no—
1200C3×C4—22no—
1201C3×C4—34no—
1202C3×C4—42no—
1203C3×C4—41no—
1204C3×C4—42no—
1205C3×C4—61no—
1206C3×C4—61no—
1207C3×C4—61no—
1208C3×C4—62no—
1209C3×C4—61no—
1210C3×C4—61no—
1211C3×C4—61no—
1212C3×C4—61no—
1213C3×C4C2×#23512yes—
1214C3×C4D3×#4112yes—
1215Dic3—21no—
1216Dic3—21no—
1217Dic3—21no—
1218Dic3—21no—
1219Dic3—21no—
1220Dic3—21no—
1221Dic3—21no—
1222Dic3—22no—
1223Dic3—62no—
1224Dic3—61no—
1225Dic3—62no—
1226Dic3—61no—
1227Dic3—61no—
1228Dic3—62no—
1229Dic3—62no—
1230Dic3—61no—
1231Dic3—61no—
1232Dic3—61no—
1233Dic3—122no—
1234Dic3—121no—
1235Dic3—122no—
1236Dic3—121no—
1237Dic3—121no—
1238Dic3C2×#23514yes—
1239C32#352411yescharacteristic, complemented, Sylow
1240C23—31no—
1241C23—32no—
1242C23—32no—
1243C23—91no—
1244C23C22×D3211yescharacteristic
1245Q8—34no—
1246Q8—122no—
1247Q8—184no—
1248Q8—182no—
1249Q8—361no—
1250D4—64no—
1251D4—62no—
1252D4—62no—
1253D4—122no—
1254D4—121no—
1255D4—122no—
1256D4—184no—
1257D4—361no—
1258D4—362no—
1259D4—361no—
1260D4—362no—
1261D4—362no—
1262D4—362no—
1263C2×C4—22no—
1264C2×C4—32no—
1265C2×C4—31no—
1266C2×C4—31no—
1267C2×C4—31no—
1268C2×C4—31no—
1269C2×C4—31no—
1270C2×C4—31no—
1271C2×C4—32no—
1272C2×C4—31no—
1273C2×C4—64no—
1274C2×C4—62no—
1275C2×C4—91no—
1276C2×C4—91no—
1277C2×C4—92no—
1278C2×C4—92no—
1279C2×C4—91no—
1280C2×C4—122no—
1281C2×C4—122no—
1282C2×C4—122no—
1283C2×C4—121no—
1284C2×C4—121no—
1285C2×C4—184no—
1286C2×C4—184no—
1287C2×C4—182no—
1288C2×C4—362no—
1289C2×C4—362no—
1290C2×C4C22×D3212yes—
1291C2×C4C22×D3211yescharacteristic
1292C2×C4C22×D3212yes—
1293C2×C4C22×D3211yescharacteristic
1294C2×C3—21no—
1295C2×C3—21no—
1296C2×C3—21no—
1297C2×C3—41no—
1298C2×C3—41no—
1299C2×C3—81no—
1300C2×C3—121no—
1301C2×C3—122no—
1302C2×C3—122no—
1303C2×C3C22×#23511yescharacteristic
1304C2×C3C2×D3×#4111yescharacteristic
1305C2×C3#596411yescharacteristic
1306C2×C3#596411yescharacteristic
1307C2×C3#596411yescharacteristic
1308C2×C3#596611yescharacteristic
1309D3—42no—
1310D3—41no—
1311D3—42no—
1312D3—122no—
1313D3—121no—
1314D3—121no—
1315C22—21no—
1316C22—21no—
1317C22—21no—
1318C22—61no—
1319C22—62no—
1320C22—62no—
1321C22—62no—
1322C22—62no—
1323C22—61no—
1324C22—62no—
1325C22—61no—
1326C22—62no—
1327C22—181no—
1328C22—181no—
1329C22—181no—
1330C22C23×D3211yescharacteristic
1331C4—21no—
1332C4—22no—
1333C4—22no—
1334C4—34no—
1335C4—61no—
1336C4—61no—
1337C4—61no—
1338C4—61no—
1339C4—61no—
1340C4—61no—
1341C4—62no—
1342C4—61no—
1343C4—181no—
1344C4—182no—
1345C4—182no—
1346C4—181no—
1347C4—181no—
1348C4D3×#23512yes—
1349C3—21no—
1350C3#8585511yescharacteristic, complemented
1351C3#8696511yescharacteristic, complemented
1352C2—41no—
1353C2—121no—
1354C2—122no—
1355C2—122no—
1356C2—361no—
1357C2C2×D3×#23511yescharacteristic
1358C2#1059669511yescharacteristic
1359C2#1059669611yescharacteristic
subgroupG/H
center, FrattiniC22C23×D32
commutator, socle, cosocleC22×C32C25
FittingC32×#117C22
hypercenter#117D32
hypocenterC32#3524
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ #117

Complements

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

NH ≅ G/Ntype
1. #10596000C2semidirect
2. C3×#5532C2semidirect
3. C3×#5522C2semidirect
4. #10595006C2semidirect
5. #10594949C2semidirect
6. #10594899C2semidirect
7. #10594839C2semidirect
8. #10594583C2semidirect
9. #10594582C2semidirect
10. #10594496C2semidirect
11. #10594382C2semidirect
12. #10594361C2semidirect
13. #10594357C2semidirect
14. #10594341C2semidirect
15. #10594317C2semidirect
16. #10594200C2semidirect
17. #10594101C2semidirect
18. #10594100C2semidirect
19. #10594096C2semidirect
20. #10593973C2semidirect
21. #10593930C2semidirect
22. #10593921C2semidirect
23. #10593915C2semidirect
158. #5532D3semidirect
166. #5522D3semidirect
1239. C32#3524semidirect
1350. C3#85855semidirect
1351. C3#86965semidirect

Maximal subgroups

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

subgroupindex
#105960002
C3×#55322
C3×#55222
#105950062
#105949492
#105948992
#105948392
#105945832
#105945822
#105944962
#105943822
#105943612
#105943572
#105943412
#105943172
#105942002
#105941012
#105941002
#105940962
#105939732
#105939302
#105939212
#105939152
#869653
#858553