Finite Group Databasebeta

← #11910065

Subgroups — #11910065

Order 1152.

2207 conjugacy classes of subgroups.

The subgroup lattice has 1365 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10596017C211yesmaximal, characteristic, complemented
2C3×#5563C211yesmaximal, characteristic, complemented
3C3×#5559C211yesmaximal, characteristic, complemented
4#10595217C211yesmaximal, characteristic, complemented
5#10595173C211yesmaximal, characteristic, complemented
6#10595164C211yesmaximal, characteristic, complemented
7#10595161C211yesmaximal, characteristic, complemented
8#10595031C212yesmaximal, complemented
9#10594962C212yesmaximal, complemented
10#10594960C212yesmaximal, complemented
11#10594933C212yesmaximal, complemented
12#10594583C211yesmaximal, characteristic, complemented
13#10594358C211yesmaximal, characteristic, complemented
14#10594357C211yesmaximal, characteristic, complemented
15#10594337C211yesmaximal, characteristic, complemented
16#10594224C212yesmaximal, complemented
17#10594219C212yesmaximal, complemented
18#10594150C212yesmaximal, complemented
19#10594111C212yesmaximal, complemented
20#10593955C211yesmaximal, characteristic, complemented
21#10593911C211yesmaximal, characteristic, complemented
22#10593905C211yesmaximal, characteristic, complemented
23#10593864C211yesmaximal, characteristic, complemented
24#87056—31nomaximal
25#86965—31nomaximal
26C2×#3830C2211yescharacteristic
27C2×#3795C2211yescharacteristic
28C2×D3×Dic6C2211yescharacteristic
29C32×C4×D4C2211yescharacteristic
30D4×C3⋊Dic3C2211yescharacteristic
31C4×#638C2212yes—
32C2×#3750C2212yes—
33C4⋊C4×C3⋊D3C2211yescharacteristic
34#64096C2211yescharacteristic
35#64090C2212yes—
36#64086C2212yes—
37#64081C2211yescharacteristic
38C4×#634C2211yescharacteristic
39C3×#940C2211yescharacteristic
40C3×#938C2211yescharacteristic
41C3×#938C2211yescharacteristic
42C3×#936C2211yescharacteristic
43C3×#930C2212yes—
44C3×#929C2212yes—
45C3×C4×#67C2212yes—
46C3×#926C2212yes—
47C3×#893C2211yescharacteristic
48C3×#892C2211yescharacteristic
49C3×#892C2211yescharacteristic
50C3×#887C2211yescharacteristic
51C3×#885C2212yes—
52C3×#885C2212yes—
53C3×#885C2212yes—
54C3×#883C2212yes—
55C3×#875C2211yescharacteristic
56C3×C4×D12C2211yescharacteristic
57C3×#869C2211yescharacteristic
58C3×C4×Dic6C2211yescharacteristic
59#63982C2212yes—
60#63980C2212yes—
61#63980C2212yes—
62#63979C2212yes—
63#67⋊Dic3C2212yes—
64#67⋊Dic3C2212yes—
65#67⋊Dic3C2212yes—
66#63971C2212yes—
67#63971C2212yes—
68#63970C2212yes—
69#63969C2212yes—
70#63969C2212yes—
71#63962C2212yes—
72#63957C2212yes—
73#63956C2212yes—
74#63953C2212yes—
75C4×#627C2212yes—
76#63916C2211yescharacteristic
77#63915C2212yes—
78#63912C2212yes—
79#63908C2211yescharacteristic
80#63907C2211yescharacteristic
81#63907C2212yes—
82#63905C2212yes—
83C4×#626C2211yescharacteristic
84C4×#626C2212yes—
85C4×#626C2211yescharacteristic
86#63902C2212yes—
87#63902C2212yes—
88#63899C2212yes—
89#63898C2211yescharacteristic
90#63890C2212yes—
91#63890C2211yescharacteristic
92#63887C2212yes—
93#63887C2211yescharacteristic
94#63886C2211yescharacteristic
95#63885C2212yes—
96#63884C2211yescharacteristic
97#63879C2212yes—
98#63878C2212yes—
99#63877C2212yes—
100#63877C2212yes—
101C4×D3×Dic3C2212yes—
102C4×D3×Dic3C2211yescharacteristic
103#63874C2212yes—
104#63873C2212yes—
105#63871C2211yescharacteristic
106#63869C2211yescharacteristic
107#63869C2211yescharacteristic
108#63867C2212yes—
109#63859C2212yes—
110#63859C2212yes—
111#63858C2211yescharacteristic
112#63858C2212yes—
113#63856C2211yescharacteristic
114#63855C2211yescharacteristic
115#63853C2212yes—
116#63848C2211yescharacteristic
117#63847C2212yes—
118#63847C2212yes—
119#63846C2211yescharacteristic
120#63844C2211yescharacteristic
121#63844C2211yescharacteristic
122#63843C2211yescharacteristic
123#63843C2212yes—
124#63837C2212yes—
125C3×#559—31no—
126C3×#555—31no—
127#5733—31no—
128#5721—31no—
129#5719—31no—
130#5718—31no—
131#5682—31no—
132#5681—32no—
133#5680—31no—
134#5680—32no—
135#5677—31no—
136#5677—31no—
137#5670—32no—
138#5670—32no—
139#5669—32no—
140#5669—32no—
141#5664—32no—
142#5663—32no—
143#5650—32no—
144#5649—32no—
145#5619—31no—
146#5615—32no—
147#5601—32no—
148#5600—31no—
149#5599—31no—
150#5598—31no—
151#5581—31no—
152#5580—31no—
153#5572—31no—
154#5567—31no—
155#5563D311yescharacteristic, complemented
156#5559D311yescharacteristic, complemented
157#5558—31no—
158#5552—31no—
159#5546—31no—
160#5546—31no—
161#5546—61no—
162#5540—32no—
163#5538—32no—
164#5538—31no—
165C4×#237—31no—
166#5531—32no—
167#5530—31no—
168#5529—31no—
169#5528—32no—
170#5522—31no—
171#5516—31no—
172C2×C32×D4C2311yescharacteristic
173C22×C32×C4C2312yes—
174C2×#638C2312yes—
175C22×C3⋊Dic3C2312yes—
176C22×C3⋊Dic3C2312yes—
177#3830—24no—
178C2×C4×C3⋊D3C2311yescharacteristic
179C2×C4×C3⋊D3C2312yes—
180C2×#634C2311yescharacteristic
181C2×C3×#67C2312yes—
182C2×C3×#67C2312yes—
183C2×C3×#67C2312yes—
184C2×C3×#67C2312yes—
185C2×C3×D12C2311yescharacteristic
186C2×C3×D12C2311yescharacteristic
187C2×C3×C4×D3C2311yescharacteristic
188C2×C3×C4×D3C2311yescharacteristic
189C2×C3×C4×D3C2312yes—
190C2×C3×Dic6C2311yescharacteristic
191C2×C3×Dic6C2312yes—
192C2×C3×Dic6C2311yescharacteristic
193C2×#627C2312yes—
194C2×#626C2311yescharacteristic
195C2×#626C2311yescharacteristic
196C2×#626C2312yes—
197C2×#625C2312yes—
198C2×#625C2312yes—
199C2×D3×Dic3C2312yes—
200C2×D3×Dic3C2312yes—
201C2×D3×Dic3C2311yescharacteristic
202C2×D3×Dic3C2311yescharacteristic
203C2×D3×Dic3C2312yes—
204#3795—24no—
205D3×Dic6—24no—
206C32×C4⋊C4C2311yescharacteristic
207C32×C22⋊C4C2312yes—
208C32×C42C2311yescharacteristic
209#3757C2312yes—
210#3752C2311yescharacteristic
211#3752C2311yescharacteristic
212C4⋊(C3⋊Dic3)C2311yescharacteristic
213#3750C2312yes—
214#3750C2311yescharacteristic
215#3750C2311yescharacteristic
216#3750C2312yes—
217#3750C2312yes—
218C4×C3⋊Dic3C2312yes—
219C4×C3⋊Dic3C2311yescharacteristic
220C4×C3⋊Dic3C2312yes—
221C3×#217C2312yes—
222C3×#217C2312yes—
223C3×#217C2312yes—
224C3×#217C2312yes—
225C3×(C2×D3)⋊C4C2312yes—
226C3×(C2×D3)⋊C4C2311yescharacteristic
227C3×(C2×D3)⋊C4C2311yescharacteristic
228C3×(C2×D3)⋊C4C2312yes—
229C3×(C2×D3)⋊C4C2312yes—
230C3×(C2×D3)⋊C4C2312yes—
231C3×(C2×D3)⋊C4C2312yes—
232C3×C4⋊Dic3C2311yescharacteristic
233C3×C4⋊Dic3C2311yescharacteristic
234C3×C4⋊Dic3C2311yescharacteristic
235C3×C4⋊Dic3C2311yescharacteristic
236C3×C4⋊Dic3C2312yes—
237C3×Dic3⋊C4C2312yes—
238C3×Dic3⋊C4C2311yescharacteristic
239C3×Dic3⋊C4C2311yescharacteristic
240C3×C4×Dic3C2312yes—
241C3×C4×Dic3C2312yes—
242C3×C4×Dic3C2312yes—
243C3×C4×Dic3C2311yescharacteristic
244C3×C4×Dic3C2311yescharacteristic
245#3724C2312yes—
246#3724C2312yes—
247#3724C2312yes—
248#3724C2312yes—
249#3724C2312yes—
250Dic3⋊Dic3C2311yescharacteristic
251Dic3⋊Dic3C2312yes—
252Dic3⋊Dic3C2312yes—
253Dic3⋊Dic3C2312yes—
254Dic3⋊Dic3C2311yescharacteristic
255Dic3⋊Dic3C2311yescharacteristic
256Dic3⋊Dic3C2311yescharacteristic
257Dic3⋊Dic3C2312yes—
258#3722C2311yescharacteristic
259#3722C2311yescharacteristic
260#3722C2312yes—
261(C2×D3)⋊Dic3C2312yes—
262(C2×D3)⋊Dic3C2311yescharacteristic
263(C2×D3)⋊Dic3C2311yescharacteristic
264(C2×D3)⋊Dic3C2312yes—
265(C2×D3)⋊Dic3C2312yes—
266(C2×D3)⋊Dic3C2311yescharacteristic
267(C2×D3)⋊Dic3C2311yescharacteristic
268(C2×D3)⋊Dic3C2312yes—
269Dic32C2312yes—
270Dic32C2312yes—
271Dic32C2312yes—
272Dic32C2311yescharacteristic
273Dic32C2311yescharacteristic
274#3524—91noSylow
275C2×D3×Q8—31no—
276C2×#237—31no—
277C2×#237—31no—
278C2×#237—31no—
279C2×#237—61no—
280C2×#235—31no—
281C22×Dic6—31no—
282C3×C4⋊Q8—31no—
283C3×#127—31no—
284C3×#124—31no—
285C3×#124—32no—
286C3×#124—32no—
287C3×#124—32no—
288C3×#124—31no—
289C3×#123—32no—
290C3×#123—32no—
291C3×#121—31no—
292C3×#121—31no—
293C3×#121—32no—
294C3×C4×Q8—31no—
295C3×C4×Q8—31no—
296C3×C4×D4—21no—
297C3×C4×D4—32no—
298C3×C4×D4—31no—
299C3×C4×D4—31no—
300C3×C4×D4C2×D311yescharacteristic
301C3×C4×D4C2×D311yescharacteristic
302C3×#117—32no—
303C3×#117—31no—
304C3×#117—31no—
305#947—31no—
306#947—32no—
307#946—31no—
308#946—31no—
309#946—32no—
310#946—31no—
311Q8×Dic3—32no—
312Q8×Dic3—31no—
313#944—32no—
314#944—32no—
315#940—32no—
316#940—32no—
317#940C2×D311yescharacteristic
318#939—32no—
319#939—32no—
320#939—32no—
321#939—32no—
322#939—32no—
323#939—32no—
324#939—32no—
325#939—32no—
326#939—31no—
327#938—32no—
328#938—31no—
329#938—31no—
330#938C2×D311yescharacteristic
331#938C2×D311yescharacteristic
332#936C2×D311yescharacteristic
333#935—32no—
334#935—32no—
335#935—32no—
336#935—31no—
337D4×Dic3—31no—
338D4×Dic3—31no—
339D4×Dic3—32no—
340D4×Dic3—32no—
341D4×Dic3—32no—
342D4×Dic3—31no—
343D4×Dic3—61no—
344#930—31no—
345#930C2×D312yes—
346#929—32no—
347#929C2×D312yes—
348C4×#67—32no—
349C4×#67—32no—
350C4×#67—32no—
351C4×#67—32no—
352C4×#67—31no—
353C4×#67—31no—
354C4×#67—62no—
355C4×#67C2×D312yes—
356#926—31no—
357#926C2×D312yes—
358#924—31no—
359C2×Dic3⋊C4—32no—
360C2×Dic3⋊C4—32no—
361C2×Dic3⋊C4—62no—
362C2×C4×Dic3—32no—
363C2×C4×Dic3—31no—
364#898—31no—
365#898—32no—
366#898—31no—
367#898—31no—
368#897—31no—
369#896—32no—
370#895—31no—
371#895—31no—
372#894—31no—
373#894—32no—
374#894—31no—
375#894—32no—
376#893—31no—
377#893C2×D311yescharacteristic
378#892—32no—
379#892C2×D311yescharacteristic
380#892C2×D311yescharacteristic
381D3×C4⋊C4—31no—
382D3×C4⋊C4—31no—
383D3×C4⋊C4—61no—
384#890—31no—
385#890—31no—
386#890—31no—
387#889—32no—
388#889—32no—
389#889—32no—
390#889—32no—
391#889—31no—
392#889—32no—
393#887—32no—
394#887—31no—
395#887—31no—
396#887—31no—
397#887—32no—
398#887—31no—
399#887—31no—
400#887—61no—
401#887C2×D311yescharacteristic
402#886—32no—
403#886—32no—
404#886—31no—
405#885—32no—
406#885—31no—
407#885—32no—
408#885—32no—
409#885—32no—
410#885—32no—
411#885C2×D312yes—
412#885C2×D312yes—
413#885C2×D312yes—
414#884—32no—
415#884—32no—
416#884—32no—
417#884—32no—
418#884—32no—
419#883—32no—
420#883—32no—
421#883—32no—
422#883—32no—
423#883C2×D312yes—
424#67⋊C4—32no—
425#67⋊C4—32no—
426#67⋊C4—32no—
427#67⋊C4—32no—
428#67⋊C4—32no—
429#67⋊C4—32no—
430#67⋊C4—32no—
431#67⋊C4—32no—
432#67⋊C4—32no—
433#67⋊C4—32no—
434#67⋊C4—62no—
435#879—32no—
436#879—32no—
437#879—32no—
438#879—31no—
439#879—32no—
440#879—32no—
441#878—32no—
442#878—31no—
443#878—32no—
444#878—32no—
445#878—32no—
446#877—32no—
447#877—32no—
448#877—32no—
449#877—32no—
450#877—32no—
451#877—32no—
452#877—32no—
453#877—62no—
454#876—32no—
455#876—32no—
456#875C2×D311yescharacteristic
457C4×D12—31no—
458C4×D12—32no—
459C4×D12—31no—
460C4×D12C2×D311yescharacteristic
461#872—31no—
462#872—31no—
463#872—31no—
464#872—32no—
465#872—32no—
466#872—32no—
467#872—32no—
468#872—61no—
469C42×D3—32no—
470C42×D3—31no—
471#870—31no—
472#870—31no—
473#870—32no—
474#869C2×D311yescharacteristic
475C4×Dic6—31no—
476C4×Dic6—31no—
477C4×Dic6—31no—
478C4×Dic6—31no—
479C4×Dic6—32no—
480C4×Dic6—32no—
481C4×Dic6—32no—
482C4×Dic6—61no—
483C4×Dic6C2×D311yescharacteristic
484C23×C32C2412yes—
485C22×C3⋊D3C2411yescharacteristic
486C22×C3×D3C2411yescharacteristic
487C22×C3×D3C2412yes—
488C22×C3×D3C2411yescharacteristic
489C32×D4—22no—
490C2×C32×C4—42no—
491C2×C32×C4C2412yes—
492C2×C32×C4C2411yescharacteristic
493C2×C32×C4C2411yescharacteristic
494C2×C32×C4C2411yescharacteristic
495#638—24no—
496C2×C3⋊Dic3—24no—
497C2×C3⋊Dic3—42no—
498C2×C3⋊Dic3C2411yescharacteristic
499C2×C3⋊Dic3C2411yescharacteristic
500C2×C3⋊Dic3C2411yescharacteristic
501C2×C3⋊Dic3C2412yes—
502C2×C3⋊Dic3C2412yes—
503C4×C3⋊D3—22no—
504C4×C3⋊D3—42no—
505#634#4114yes—
506C3×#67—42no—
507C3×#67—42no—
508C3×#67—42no—
509C3×#67—42no—
510C2×C3×Dic3C2411yescharacteristic
511C2×C3×Dic3C2411yescharacteristic
512C2×C3×Dic3C2412yes—
513C2×C3×Dic3C2411yescharacteristic
514C2×C3×Dic3C2412yes—
515C2×C3×Dic3C2412yes—
516C2×C3×Dic3C2411yescharacteristic
517C2×C3×Dic3C2411yescharacteristic
518C2×C3×Dic3C2411yescharacteristic
519C3×D12—22no—
520C3×D12—41no—
521C3×C4×D3—22no—
522C3×C4×D3—22no—
523C3×C4×D3—42no—
524C3×Dic6—22no—
525C3×Dic6—41no—
526C3×Dic6—42no—
527#627—24no—
528#626—41no—
529#626—42no—
530#626—41no—
531#625—24no—
532#625—42no—
533D3×Dic3—24no—
534D3×Dic3—24no—
535D3×Dic3—41no—
536D3×Dic3—42no—
537D3×Dic3—41no—
538#559—31no—
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—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—91no—
561C2×C3×Q8—31no—
562C2×C3×Q8—31no—
563C2×C3×Q8—32no—
564C2×C3×D4—21no—
565C2×C3×D4—32no—
566C2×C3×D4—32no—
567C2×C3×D4—32no—
568C2×C3×D4—32no—
569C2×C3×D4—31no—
570C2×C3×D4—31no—
571C2×C3×D4C22×D311yescharacteristic
572C2×C3×D4C22×D311yescharacteristic
573C22×C3×C4—22no—
574C22×C3×C4—31no—
575C22×C3×C4—31no—
576C22×C3×C4—32no—
577C22×C3×C4C22×D312yes—
578C22×C3×C4C22×D312yes—
579C2×#67—32no—
580C2×#67—32no—
581C2×#67—32no—
582C2×#67—32no—
583C2×#67—32no—
584C2×#67—32no—
585C2×#67—31no—
586C2×#67—31no—
587C2×#67—32no—
588C2×#67—62no—
589C2×#67C22×D312yes—
590C2×#67C22×D312yes—
591C2×#67C22×D312yes—
592C2×#67C22×D312yes—
593C22×Dic3—32no—
594C22×Dic3—32no—
595C22×Dic3—32no—
596C22×Dic3—32no—
597C22×Dic3—32no—
598C22×Dic3—32no—
599C22×Dic3—31no—
600C22×Dic3—32no—
601C22×Dic3—31no—
602C22×Dic3—62no—
603C22×Dic3—62no—
604D3×Q8—64no—
605#237—64no—
606#237—64no—
607#237—64no—
608#237—68no—
609#235—64no—
610C2×D12—31no—
611C2×D12—32no—
612C2×D12—31no—
613C2×D12C22×D311yescharacteristic
614C2×D12C22×D311yescharacteristic
615C2×C4×D3—32no—
616C2×C4×D3—32no—
617C2×C4×D3—31no—
618C2×C4×D3—31no—
619C2×C4×D3—31no—
620C2×C4×D3—31no—
621C2×C4×D3—32no—
622C2×C4×D3—32no—
623C2×C4×D3—32no—
624C2×C4×D3—61no—
625C2×C4×D3—62no—
626C2×C4×D3C22×D311yescharacteristic
627C2×C4×D3C22×D311yescharacteristic
628C2×C4×D3C22×D312yes—
629C2×Dic6—31no—
630C2×Dic6—31no—
631C2×Dic6—32no—
632C2×Dic6—32no—
633C2×Dic6—61no—
634C2×Dic6—64no—
635C2×Dic6C22×D311yescharacteristic
636C2×Dic6C22×D311yescharacteristic
637C2×Dic6C22×D312yes—
638C3×C4⋊C4—21no—
639C3×C4⋊C4—31no—
640C3×C4⋊C4—31no—
641C3×C4⋊C4—32no—
642C3×C4⋊C4—31no—
643C3×C4⋊C4—31no—
644C3×C4⋊C4—31no—
645C3×C4⋊C4—32no—
646C3×C4⋊C4—31no—
647C3×C4⋊C4C22×D311yescharacteristic
648C3×C4⋊C4C22×D311yescharacteristic
649C3×C22⋊C4—22no—
650C3×C22⋊C4—32no—
651C3×C22⋊C4—32no—
652C3×C22⋊C4—32no—
653C3×C22⋊C4—32no—
654C3×C22⋊C4—32no—
655C3×C22⋊C4—32no—
656C3×C22⋊C4—32no—
657C3×C22⋊C4—32no—
658C3×C22⋊C4—31no—
659C3×C22⋊C4—32no—
660C3×C22⋊C4—31no—
661C3×C22⋊C4C22×D312yes—
662C3×C22⋊C4C22×D312yes—
663C3×C42—21no—
664C3×C42—32no—
665C3×C42—31no—
666C3×C42—31no—
667C3×C42—32no—
668C3×C42—32no—
669C3×C42C22×D311yescharacteristic
670C3×C42C22×D311yescharacteristic
671#217—32no—
672#217—32no—
673#217—31no—
674#217—31no—
675#217—32no—
676#217—31no—
677#217—32no—
678#217—32no—
679#217—31no—
680#217—32no—
681#217—62no—
682#217C22×D312yes—
683#217C22×D312yes—
684#217C22×D312yes—
685#217C22×D312yes—
686(C2×D3)⋊C4—31no—
687(C2×D3)⋊C4—32no—
688(C2×D3)⋊C4—31no—
689(C2×D3)⋊C4—31no—
690(C2×D3)⋊C4—32no—
691(C2×D3)⋊C4—31no—
692(C2×D3)⋊C4—32no—
693(C2×D3)⋊C4—32no—
694(C2×D3)⋊C4—31no—
695(C2×D3)⋊C4—31no—
696(C2×D3)⋊C4—31no—
697(C2×D3)⋊C4—31no—
698(C2×D3)⋊C4—31no—
699(C2×D3)⋊C4—31no—
700(C2×D3)⋊C4—32no—
701(C2×D3)⋊C4—32no—
702(C2×D3)⋊C4—31no—
703(C2×D3)⋊C4—31no—
704(C2×D3)⋊C4—61no—
705(C2×D3)⋊C4—61no—
706(C2×D3)⋊C4C22×D312yes—
707(C2×D3)⋊C4C22×D312yes—
708(C2×D3)⋊C4C22×D311yescharacteristic
709(C2×D3)⋊C4C22×D311yescharacteristic
710(C2×D3)⋊C4C22×D312yes—
711(C2×D3)⋊C4C22×D312yes—
712(C2×D3)⋊C4C22×D312yes—
713C4⋊Dic3—31no—
714C4⋊Dic3—31no—
715C4⋊Dic3—31no—
716C4⋊Dic3—31no—
717C4⋊Dic3—32no—
718C4⋊Dic3—32no—
719C4⋊Dic3—32no—
720C4⋊Dic3—31no—
721C4⋊Dic3—32no—
722C4⋊Dic3—31no—
723C4⋊Dic3—61no—
724C4⋊Dic3C22×D311yescharacteristic
725C4⋊Dic3C22×D311yescharacteristic
726C4⋊Dic3C22×D311yescharacteristic
727C4⋊Dic3C22×D312yes—
728C4⋊Dic3C22×D311yescharacteristic
729Dic3⋊C4—32no—
730Dic3⋊C4—32no—
731Dic3⋊C4—32no—
732Dic3⋊C4—32no—
733Dic3⋊C4—31no—
734Dic3⋊C4—31no—
735Dic3⋊C4—32no—
736Dic3⋊C4—31no—
737Dic3⋊C4—31no—
738Dic3⋊C4—32no—
739Dic3⋊C4—32no—
740Dic3⋊C4—31no—
741Dic3⋊C4—32no—
742Dic3⋊C4—32no—
743Dic3⋊C4—32no—
744Dic3⋊C4—31no—
745Dic3⋊C4—32no—
746Dic3⋊C4—32no—
747Dic3⋊C4—32no—
748Dic3⋊C4—32no—
749Dic3⋊C4—32no—
750Dic3⋊C4—32no—
751Dic3⋊C4—32no—
752Dic3⋊C4—32no—
753Dic3⋊C4—31no—
754Dic3⋊C4—31no—
755Dic3⋊C4—32no—
756Dic3⋊C4—32no—
757Dic3⋊C4—62no—
758Dic3⋊C4—61no—
759Dic3⋊C4—61no—
760Dic3⋊C4—62no—
761Dic3⋊C4—62no—
762Dic3⋊C4C22×D312yes—
763Dic3⋊C4C22×D311yescharacteristic
764Dic3⋊C4C22×D311yescharacteristic
765C4×Dic3—32no—
766C4×Dic3—32no—
767C4×Dic3—32no—
768C4×Dic3—32no—
769C4×Dic3—31no—
770C4×Dic3—31no—
771C4×Dic3—32no—
772C4×Dic3—32no—
773C4×Dic3—32no—
774C4×Dic3—32no—
775C4×Dic3—31no—
776C4×Dic3—31no—
777C4×Dic3—31no—
778C4×Dic3—32no—
779C4×Dic3—31no—
780C4×Dic3—32no—
781C4×Dic3—62no—
782C4×Dic3—61no—
783C4×Dic3—62no—
784C4×Dic3C22×D312yes—
785C4×Dic3C22×D312yes—
786C4×Dic3C22×D311yescharacteristic
787C4×Dic3C22×D311yescharacteristic
788C4×Dic3C22×D312yes—
789C22×C32—22no—
790C22×C32—22no—
791C22×C32—22no—
792C22×C32C2511yescharacteristic
793C2×C3⋊D3—21no—
794C2×C3⋊D3—21no—
795C2×C3⋊D3—21no—
796C2×C3×D3—21no—
797C2×C3×D3—22no—
798C2×C3×D3—21no—
799C2×C3×D3—21no—
800C2×C3×D3—22no—
801C2×C3×D3—21no—
802C2×C3×D3—21no—
803C2×C3×D3—22no—
804C2×C3×D3—21no—
805C32×C4—21no—
806C32×C4—22no—
807C32×C4—21no—
808C32×C4C2×#4112yes—
809C3⋊Dic3—21no—
810C3⋊Dic3—21no—
811C3⋊Dic3—21no—
812C3⋊Dic3—22no—
813C3⋊Dic3C2×#4114yes—
814C3×Dic3—21no—
815C3×Dic3—22no—
816C3×Dic3—21no—
817C3×Dic3—21no—
818C3×Dic3—22no—
819C3×Dic3—21no—
820C3×Dic3—22no—
821C3×Dic3—21no—
822C3×Dic3—21no—
823C2×#41—91no—
824C2×#41—91no—
825C22×Q8—91no—
826C4⋊Q8—31no—
827C4⋊Q8—92no—
828#127—31no—
829#127—92no—
830#126—92no—
831#126—92no—
832#126—92no—
833#126—91no—
834#126—92no—
835#126—91no—
836#125—92no—
837#125—91no—
838#125—91no—
839#125—91no—
840#125—92no—
841#125—92no—
842#124—31no—
843#124—32no—
844#124—32no—
845#124—32no—
846#124—31no—
847#124—92no—
848#124—92no—
849#124—91no—
850#124—92no—
851#123—32no—
852#123—32no—
853#123—92no—
854#123—91no—
855#123—92no—
856#123—92no—
857#123—92no—
858#123—92no—
859#123—92no—
860#123—91no—
861C22⋊Q8—92no—
862C22⋊Q8—92no—
863C22⋊Q8—91no—
864C22⋊Q8—92no—
865C22⋊Q8—91no—
866C22⋊Q8—91no—
867#121—31no—
868#121—31no—
869#121—32no—
870#121—92no—
871#121—92no—
872#121—92no—
873#121—92no—
874#121—91no—
875#121—91no—
876#121—91no—
877#121—92no—
878#121—92no—
879#121—92no—
880C4×Q8—31no—
881C4×Q8—31no—
882C4×Q8—92no—
883C4×Q8—91no—
884C4×Q8—91no—
885C4×Q8—92no—
886C4×Q8—91no—
887C4×Q8—92no—
888C4×Q8—91no—
889C4×Q8—91no—
890C4×D4—32no—
891C4×D4—31no—
892C4×D4—31no—
893C4×D4—91no—
894C4×D4—91no—
895C4×D4—92no—
896C4×D4—92no—
897C4×D4—92no—
898C4×D4—92no—
899C4×D4—92no—
900C4×D4—92no—
901C4×D4—92no—
902C4×D4—91no—
903C4×D4—91no—
904C4×D4—92no—
905C4×D4—92no—
906C4×D4D3211yescharacteristic
907#117—32no—
908#117—31no—
909#117—31no—
910#117—92no—
911#117—92no—
912#117—92no—
913#117—91no—
914#117—92no—
915#117—92no—
916#117—92no—
917#117—91no—
918C2×C4⋊C4—92no—
919C2×C4⋊C4—91no—
920C2×C42—92no—
921C2×C42—91no—
922C23×C3—22no—
923C23×C3—31no—
924C23×C3—32no—
925C23×C3—31no—
926C23×C3C23×D312yes—
927C23×C3C23×D312yes—
928C22×D3—31no—
929C22×D3—31no—
930C22×D3—61no—
931C22×D3C23×D311yescharacteristic
932C22×D3C23×D311yescharacteristic
933C22×D3C23×D312yes—
934C3×Q8—62no—
935C3×Q8—122no—
936C3×Q8—121no—
937C3×D4—24no—
938C3×D4—22no—
939C3×D4—22no—
940C3×D4—62no—
941C3×D4—121no—
942C3×D4—122no—
943C3×D4—122no—
944C3×D4—122no—
945C3×D4—122no—
946C2×C3×C4—21no—
947C2×C3×C4—21no—
948C2×C3×C4—22no—
949C2×C3×C4—21no—
950C2×C3×C4—31no—
951C2×C3×C4—32no—
952C2×C3×C4—31no—
953C2×C3×C4—31no—
954C2×C3×C4—31no—
955C2×C3×C4—32no—
956C2×C3×C4—32no—
957C2×C3×C4—31no—
958C2×C3×C4—31no—
959C2×C3×C4—42no—
960C2×C3×C4—42no—
961C2×C3×C4—62no—
962C2×C3×C4—62no—
963C2×C3×C4—82no—
964C2×C3×C4—122no—
965C2×C3×C4C23×D311yescharacteristic
966C2×C3×C4C23×D311yescharacteristic
967C2×C3×C4C23×D312yes—
968C2×C3×C4C23×D312yes—
969C2×C3×C4C23×D311yescharacteristic
970C2×C3×C4C23×D311yescharacteristic
971C2×C3×C4C23×D311yescharacteristic
972C2×C3×C4C23×D311yescharacteristic
973#67—42no—
974#67—42no—
975#67—42no—
976#67—42no—
977#67—64no—
978#67—64no—
979#67—64no—
980#67—64no—
981#67—68no—
982#67—121no—
983#67—122no—
984#67—121no—
985#67—122no—
986#67—122no—
987C2×Dic3—32no—
988C2×Dic3—32no—
989C2×Dic3—31no—
990C2×Dic3—31no—
991C2×Dic3—31no—
992C2×Dic3—31no—
993C2×Dic3—32no—
994C2×Dic3—32no—
995C2×Dic3—31no—
996C2×Dic3—31no—
997C2×Dic3—62no—
998C2×Dic3—61no—
999C2×Dic3—61no—
1000C2×Dic3—61no—
1001C2×Dic3—62no—
1002C2×Dic3—64no—
1003C2×Dic3—64no—
1004C2×Dic3—64no—
1005C2×Dic3—64no—
1006C2×Dic3—68no—
1007C2×Dic3—121no—
1008C2×Dic3—122no—
1009C2×Dic3—121no—
1010C2×Dic3—122no—
1011C2×Dic3—122no—
1012C2×Dic3—242no—
1013C2×Dic3C23×D311yescharacteristic
1014C2×Dic3C23×D311yescharacteristic
1015C2×Dic3C23×D312yes—
1016C2×Dic3C23×D311yescharacteristic
1017C2×Dic3C23×D311yescharacteristic
1018C2×Dic3C23×D312yes—
1019C2×Dic3C23×D312yes—
1020C2×Dic3C23×D311yescharacteristic
1021C2×Dic3C23×D311yescharacteristic
1022D12—22no—
1023D12—41no—
1024D12—121no—
1025D12—122no—
1026D12—121no—
1027C4×D3—22no—
1028C4×D3—22no—
1029C4×D3—42no—
1030C4×D3—64no—
1031C4×D3—64no—
1032C4×D3—64no—
1033C4×D3—62no—
1034C4×D3—62no—
1035C4×D3—122no—
1036C4×D3—122no—
1037C4×D3—122no—
1038C4×D3—121no—
1039C4×D3—121no—
1040C4×D3—242no—
1041Dic6—22no—
1042Dic6—34no—
1043Dic6—34no—
1044Dic6—41no—
1045Dic6—42no—
1046Dic6—64no—
1047Dic6—64no—
1048Dic6—64no—
1049C2×C32—42no—
1050C2×C32C22×#4111yescharacteristic
1051C2×C32#58511yescharacteristic
1052C2×C32#58511yescharacteristic
1053C3⋊D3—41no—
1054C3×D3—42no—
1055C3×D3—41no—
1056C3×D3—41no—
1057#41—184no—
1058#41—184no—
1059C2×Q8—31no—
1060C2×Q8—31no—
1061C2×Q8—32no—
1062C2×Q8—92no—
1063C2×Q8—91no—
1064C2×Q8—184no—
1065C2×D4—32no—
1066C2×D4—32no—
1067C2×D4—32no—
1068C2×D4—32no—
1069C2×D4—31no—
1070C2×D4—31no—
1071C2×D4—91no—
1072C2×D4—92no—
1073C2×D4—91no—
1074C2×D4—92no—
1075C2×D4—92no—
1076C2×D4—92no—
1077C2×D4C2×D3211yescharacteristic
1078C22×C4—31no—
1079C22×C4—31no—
1080C22×C4—32no—
1081C22×C4—92no—
1082C22×C4—92no—
1083C22×C4—91no—
1084C22×C4—91no—
1085C22×C4—92no—
1086C22×C4—92no—
1087C22×C4—92no—
1088C22×C4—91no—
1089C22×C4—92no—
1090C22×C4C2×D3212yes—
1091C4⋊C4—31no—
1092C4⋊C4—31no—
1093C4⋊C4—31no—
1094C4⋊C4—32no—
1095C4⋊C4—32no—
1096C4⋊C4—31no—
1097C4⋊C4—31no—
1098C4⋊C4—31no—
1099C4⋊C4—92no—
1100C4⋊C4—92no—
1101C4⋊C4—92no—
1102C4⋊C4—91no—
1103C4⋊C4—92no—
1104C4⋊C4—91no—
1105C4⋊C4—92no—
1106C4⋊C4—92no—
1107C4⋊C4—91no—
1108C4⋊C4—92no—
1109C4⋊C4—91no—
1110C4⋊C4—92no—
1111C4⋊C4—92no—
1112C4⋊C4—91no—
1113C4⋊C4—92no—
1114C4⋊C4—92no—
1115C4⋊C4—92no—
1116C4⋊C4—91no—
1117C4⋊C4—91no—
1118C4⋊C4C2×D3211yescharacteristic
1119C22⋊C4—32no—
1120C22⋊C4—32no—
1121C22⋊C4—32no—
1122C22⋊C4—32no—
1123C22⋊C4—32no—
1124C22⋊C4—32no—
1125C22⋊C4—32no—
1126C22⋊C4—31no—
1127C22⋊C4—32no—
1128C22⋊C4—31no—
1129C22⋊C4—32no—
1130C22⋊C4—91no—
1131C22⋊C4—92no—
1132C22⋊C4—91no—
1133C22⋊C4—91no—
1134C22⋊C4—91no—
1135C22⋊C4—92no—
1136C22⋊C4—91no—
1137C22⋊C4—91no—
1138C22⋊C4—92no—
1139C22⋊C4—92no—
1140C22⋊C4—92no—
1141C22⋊C4—92no—
1142C22⋊C4—91no—
1143C22⋊C4—91no—
1144C22⋊C4C2×D3212yes—
1145C42—32no—
1146C42—31no—
1147C42—32no—
1148C42—32no—
1149C42—31no—
1150C42—91no—
1151C42—91no—
1152C42—92no—
1153C42—92no—
1154C42—92no—
1155C42—92no—
1156C42—91no—
1157C42—92no—
1158C42C2×D3211yescharacteristic
1159C22×C3—24no—
1160C22×C3—22no—
1161C22×C3—22no—
1162C22×C3—22no—
1163C22×C3—22no—
1164C22×C3—22no—
1165C22×C3—22no—
1166C22×C3—21no—
1167C22×C3—42no—
1168C22×C3—42no—
1169C22×C3—61no—
1170C22×C3—62no—
1171C22×C3—61no—
1172C22×C3—61no—
1173C22×C3—62no—
1174C22×C3—61no—
1175C22×C3—61no—
1176C22×C3—62no—
1177C22×C3—61no—
1178C22×C3C24×D311yescharacteristic
1179C22×C3C24×D311yescharacteristic
1180C2×D3—21no—
1181C2×D3—21no—
1182C2×D3—22no—
1183C2×D3—21no—
1184C2×D3—22no—
1185C2×D3—21no—
1186C2×D3—22no—
1187C2×D3—21no—
1188C2×D3—21no—
1189C2×D3—62no—
1190C2×D3—61no—
1191C2×D3—61no—
1192C2×D3—61no—
1193C2×D3—61no—
1194C2×D3—61no—
1195C2×D3—61no—
1196C2×D3—121no—
1197C2×D3—121no—
1198C3×C4—21no—
1199C3×C4—22no—
1200C3×C4—21no—
1201C3×C4—21no—
1202C3×C4—22no—
1203C3×C4—21no—
1204C3×C4—22no—
1205C3×C4—42no—
1206C3×C4—41no—
1207C3×C4—41no—
1208C3×C4—61no—
1209C3×C4—62no—
1210C3×C4—61no—
1211C3×C4—61no—
1212C3×C4—62no—
1213C3×C4—61no—
1214C3×C4—62no—
1215C3×C4—61no—
1216C3×C4—61no—
1217C3×C4D3×#4112yes—
1218C3×C4D3×#4112yes—
1219Dic3—22no—
1220Dic3—21no—
1221Dic3—21no—
1222Dic3—21no—
1223Dic3—21no—
1224Dic3—22no—
1225Dic3—22no—
1226Dic3—21no—
1227Dic3—21no—
1228Dic3—34no—
1229Dic3—34no—
1230Dic3—64no—
1231Dic3—62no—
1232Dic3—61no—
1233Dic3—61no—
1234Dic3—61no—
1235Dic3—61no—
1236Dic3—62no—
1237Dic3—61no—
1238Dic3—62no—
1239Dic3—61no—
1240Dic3—122no—
1241Dic3—121no—
1242Dic3—121no—
1243C32#352411yescharacteristic, complemented, Sylow
1244C23—31no—
1245C23—31no—
1246C23—32no—
1247C23—91no—
1248C23C22×D3212yes—
1249Q8—62no—
1250Q8—94no—
1251Q8—122no—
1252Q8—121no—
1253Q8—184no—
1254D4—22no—
1255D4—62no—
1256D4—121no—
1257D4—122no—
1258D4—122no—
1259D4—122no—
1260D4—122no—
1261D4—184no—
1262D4—184no—
1263D4—361no—
1264D4—361no—
1265D4—362no—
1266D4—362no—
1267C2×C4—31no—
1268C2×C4—31no—
1269C2×C4—31no—
1270C2×C4—31no—
1271C2×C4—32no—
1272C2×C4—31no—
1273C2×C4—32no—
1274C2×C4—31no—
1275C2×C4—32no—
1276C2×C4—42no—
1277C2×C4—62no—
1278C2×C4—62no—
1279C2×C4—92no—
1280C2×C4—91no—
1281C2×C4—91no—
1282C2×C4—92no—
1283C2×C4—91no—
1284C2×C4—122no—
1285C2×C4—184no—
1286C2×C4—184no—
1287C2×C4—184no—
1288C2×C4—182no—
1289C2×C4—362no—
1290C2×C4—361no—
1291C2×C4—362no—
1292C2×C4—361no—
1293C2×C4—362no—
1294C2×C4C22×D3212yes—
1295C2×C4C22×D3211yescharacteristic
1296C2×C4C22×D3211yescharacteristic
1297C2×C4C22×D3211yescharacteristic
1298C2×C3—21no—
1299C2×C3—21no—
1300C2×C3—21no—
1301C2×C3—44no—
1302C2×C3—42no—
1303C2×C3—42no—
1304C2×C3—121no—
1305C2×C3—121no—
1306C2×C3—122no—
1307C2×C3C2×D3×#4111yescharacteristic
1308C2×C3C2×D3×#4111yescharacteristic
1309C2×C3#596411yescharacteristic
1310C2×C3#596411yescharacteristic
1311C2×C3#596611yescharacteristic
1312C2×C3#596611yescharacteristic
1313D3—42no—
1314D3—41no—
1315D3—41no—
1316D3—122no—
1317D3—121no—
1318D3—121no—
1319C22—22no—
1320C22—22no—
1321C22—22no—
1322C22—61no—
1323C22—61no—
1324C22—62no—
1325C22—62no—
1326C22—61no—
1327C22—61no—
1328C22—61no—
1329C22—62no—
1330C22—61no—
1331C22—181no—
1332C22—181no—
1333C22—181no—
1334C22C23×D3211yescharacteristic
1335C4—21no—
1336C4—22no—
1337C4—21no—
1338C4—61no—
1339C4—61no—
1340C4—62no—
1341C4—61no—
1342C4—61no—
1343C4—62no—
1344C4—61no—
1345C4—61no—
1346C4—62no—
1347C4—94no—
1348C4—181no—
1349C4—181no—
1350C4—182no—
1351C4—181no—
1352C4#6430612yes—
1353C3—21no—
1354C3#8696511yescharacteristic, complemented
1355C3#8705611yescharacteristic, complemented
1356C2—42no—
1357C2—121no—
1358C2—121no—
1359C2—122no—
1360C2—361no—
1361C2C2×#6430611yescharacteristic
1362C2#1059667811yescharacteristic
1363C2#1059669611yescharacteristic
subgroupG/H
center, FrattiniC22C23×D32
commutator, socle, cosocleC22×C32C25
FittingC32×C4×D4C22
hypercenterC4×D4D32
hypocenterC32#3524
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C4×D4

Complements

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

NH ≅ G/Ntype
1. #10596017C2semidirect
2. C3×#5563C2semidirect
3. C3×#5559C2semidirect
4. #10595217C2semidirect
5. #10595173C2semidirect
6. #10595164C2semidirect
7. #10595161C2semidirect
8. #10595031C2semidirect
9. #10594962C2semidirect
10. #10594960C2semidirect
11. #10594933C2semidirect
12. #10594583C2semidirect
13. #10594358C2semidirect
14. #10594357C2semidirect
15. #10594337C2semidirect
16. #10594224C2semidirect
17. #10594219C2semidirect
18. #10594150C2semidirect
19. #10594111C2semidirect
20. #10593955C2semidirect
21. #10593911C2semidirect
22. #10593905C2semidirect
23. #10593864C2semidirect
155. #5563D3semidirect
156. #5559D3semidirect
1243. C32#3524semidirect
1354. C3#86965semidirect
1355. C3#87056semidirect

Maximal subgroups

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

subgroupindex
#105960172
C3×#55632
C3×#55592
#105952172
#105951732
#105951642
#105951612
#105950312
#105949622
#105949602
#105949332
#105945832
#105943582
#105943572
#105943372
#105942242
#105942192
#105941502
#105941112
#105939552
#105939112
#105939052
#105938642
#870563
#869653