Finite Group Databasebeta

← #11910059

Subgroups — #11910059

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#10595975C211yesmaximal, characteristic, complemented
2C3×#5514C211yesmaximal, characteristic, complemented
3C3×#5513C211yesmaximal, characteristic, complemented
4#10595031C212yesmaximal, complemented
5#10594984C211yesmaximal, characteristic, complemented
6#10594961C212yesmaximal, complemented
7#10594957C212yesmaximal, complemented
8#10594934C211yesmaximal, characteristic, complemented
9#10594933C212yesmaximal, complemented
10#10594919C211yesmaximal, characteristic, complemented
11#10594916C211yesmaximal, characteristic, complemented
12#10594575C211yesmaximal, characteristic, complemented
13#10594571C212yesmaximal, complemented
14#10594566C211yesmaximal, characteristic, complemented
15#10594525C211yesmaximal, characteristic, complemented
16#10594501C211yesmaximal, characteristic, complemented
17#10594473C212yesmaximal, complemented
18#10594471C212yesmaximal, complemented
19#10594453C211yesmaximal, characteristic, complemented
20#10594441C212yesmaximal, complemented
21#10594358C211yesmaximal, characteristic, complemented
22#10594357C211yesmaximal, characteristic, complemented
23#10594324C211yesmaximal, characteristic, complemented
24#86891—31nomaximal
25#86843—31nomaximal
26C2×#3828C2211yescharacteristic
27C2×#3795C2211yescharacteristic
28C2×D3×Dic6C2211yescharacteristic
29C2×C32×C4⋊C4C2211yescharacteristic
30C4×#638C2212yes—
31C4×#638C2212yes—
32#64135C2211yescharacteristic
33#64102C2211yescharacteristic
34#64102C2211yescharacteristic
35#64101C2212yes—
36C4⋊C4×C3⋊D3C2212yes—
37#64096C2211yescharacteristic
38#64096C2211yescharacteristic
39C3×#930C2211yescharacteristic
40C3×#930C2212yes—
41C3×#929C2212yes—
42C3×C4×#67C2211yescharacteristic
43C3×C4×#67C2211yescharacteristic
44C3×C4×#67C2212yes—
45C3×#926C2212yes—
46C3×#924C2211yescharacteristic
47C3×#898C2212yes—
48C3×#898C2212yes—
49C3×#897C2211yescharacteristic
50C3×#895C2211yescharacteristic
51C3×#894C2212yes—
52C3×#893C2211yescharacteristic
53C3×#892C2211yescharacteristic
54C3×#892C2211yescharacteristic
55C3×#890C2211yescharacteristic
56C3×#890C2211yescharacteristic
57C3×#889C2212yes—
58C3×#887C2211yescharacteristic
59#63979C2212yes—
60#63971C2212yes—
61#63971C2212yes—
62#63970C2211yescharacteristic
63#63969C2212yes—
64#63969C2211yescharacteristic
65#63959C2211yescharacteristic
66#63959C2212yes—
67#63956C2211yescharacteristic
68#63953C2212yes—
69#63919C2212yes—
70#63919C2211yescharacteristic
71C4×#627C2211yescharacteristic
72C4×#627C2212yes—
73#63916C2212yes—
74#63915C2212yes—
75#63912C2212yes—
76#63912C2212yes—
77#63911C2211yescharacteristic
78#63909C2211yescharacteristic
79#63909C2211yescharacteristic
80C4×#626C2212yes—
81#63902C2212yes—
82C4×#625C2211yescharacteristic
83#63899C2212yes—
84#63898C2211yescharacteristic
85#63898C2212yes—
86#63893C2211yescharacteristic
87#63893C2212yes—
88#63891C2211yescharacteristic
89#63890C2212yes—
90#63890C2212yes—
91#63886C2212yes—
92#63885C2212yes—
93#63881C2212yes—
94#63881C2212yes—
95#63881C2212yes—
96#63879C2212yes—
97#63878C2212yes—
98#63877C2212yes—
99#63877C2212yes—
100C4×D3×Dic3C2212yes—
101C4×D3×Dic3C2211yescharacteristic
102#63874C2212yes—
103#63865C2212yes—
104#63864C2211yescharacteristic
105#63863C2211yescharacteristic
106#63861C2211yescharacteristic
107#63861C2212yes—
108#63855C2211yescharacteristic
109#63853C2212yes—
110#63853C2212yes—
111#63852C2212yes—
112#63852C2212yes—
113#63852C2212yes—
114#63850C2212yes—
115#63849C2212yes—
116#63848C2212yes—
117#63847C2212yes—
118#63847C2212yes—
119#63845C2211yescharacteristic
120#63844C2211yescharacteristic
121#63844C2211yescharacteristic
122#63843C2211yescharacteristic
123#63838C2212yes—
124#63837C2212yes—
125C3×#553—31no—
126C3×#552—31no—
127#5710—32no—
128#5710—32no—
129#5709—32no—
130#5708—32no—
131#5697—31no—
132#5693—32no—
133#5691—31no—
134#5691—32no—
135#5685—31no—
136#5685—31no—
137#5664—32no—
138#5663—32no—
139#5661—32no—
140#5649—32no—
141#5643—31no—
142#5633—31no—
143#5633—31no—
144#5624—31no—
145#5619—31no—
146#5616—32no—
147#5615—32no—
148#5603—31no—
149#5599—31no—
150#5598—31no—
151#5585—31no—
152#5572—31no—
153#5559—32no—
154#5559—31no—
155#5557—31no—
156#5553—31no—
157#5552—31no—
158#5538—31no—
159#5538—32no—
160C4×#237—31no—
161#5532—32no—
162#5532—31no—
163#5532—31no—
164#5528—32no—
165#5522—31no—
166#5516—31no—
167#5514D311yescharacteristic, complemented
168#5513D311yescharacteristic, complemented
169#5504—31no—
170#5504—31no—
171#5504—61no—
172C22×C32×C4C2311yescharacteristic
173C22×C32×C4C2312yes—
174C2×#638C2312yes—
175#3828—24no—
176C2×C4⋊(C3⋊D3)C2311yescharacteristic
177C2×C4×C3⋊D3C2312yes—
178C2×C4×C3⋊D3C2312yes—
179C2×C4×C3⋊D3C2312yes—
180C2×#634C2311yescharacteristic
181C2×C3×#67C2311yescharacteristic
182C2×C3×#67C2312yes—
183C2×C3×#67C2311yescharacteristic
184C2×C3×D12C2311yescharacteristic
185C2×C3×D12C2312yes—
186C2×C3×C4×D3C2311yescharacteristic
187C2×C3×C4×D3C2311yescharacteristic
188C2×C3×C4×D3C2312yes—
189C2×C3×Dic6C2311yescharacteristic
190C2×#627C2312yes—
191C2×#627C2312yes—
192C2×#627C2311yescharacteristic
193C2×#626C2312yes—
194C2×#626C2312yes—
195C2×#626C2312yes—
196C2×#626C2312yes—
197C2×#625C2312yes—
198C2×#625C2311yescharacteristic
199C2×D3×Dic3C2312yes—
200C2×D3×Dic3C2312yes—
201C2×D3×Dic3C2311yescharacteristic
202C2×D3×Dic3C2312yes—
203C2×D3×Dic3C2311yescharacteristic
204#3795—24no—
205D3×Dic6—24no—
206C32×C4⋊C4C2311yescharacteristic
207C32×C4⋊C4C2312yes—
208C32×C4⋊C4C2311yescharacteristic
209#3757C2311yescharacteristic
210#3757C2311yescharacteristic
211#3752C2312yes—
212#3752C2312yes—
213C4⋊(C3⋊Dic3)C2311yescharacteristic
214C4⋊(C3⋊Dic3)C2311yescharacteristic
215#3750C2312yes—
216#3750C2312yes—
217C4×C3⋊Dic3C2312yes—
218C4×C3⋊Dic3C2311yescharacteristic
219C4×C3⋊Dic3C2312yes—
220C4×C3⋊Dic3C2311yescharacteristic
221C3×#217C2312yes—
222C3×#217C2311yescharacteristic
223C3×#217C2311yescharacteristic
224C3×(C2×D3)⋊C4C2312yes—
225C3×(C2×D3)⋊C4C2312yes—
226C3×(C2×D3)⋊C4C2312yes—
227C3×(C2×D3)⋊C4C2311yescharacteristic
228C3×(C2×D3)⋊C4C2312yes—
229C3×(C2×D3)⋊C4C2312yes—
230C3×(C2×D3)⋊C4C2312yes—
231C3×(C2×D3)⋊C4C2311yescharacteristic
232C3×C4⋊Dic3C2312yes—
233C3×C4⋊Dic3C2311yescharacteristic
234C3×C4⋊Dic3C2311yescharacteristic
235C3×C4⋊Dic3C2312yes—
236C3×C4⋊Dic3C2312yes—
237C3×Dic3⋊C4C2312yes—
238C3×Dic3⋊C4C2311yescharacteristic
239C3×Dic3⋊C4C2312yes—
240C3×Dic3⋊C4C2312yes—
241C3×Dic3⋊C4C2312yes—
242C3×Dic3⋊C4C2311yescharacteristic
243C3×C4×Dic3C2311yescharacteristic
244C3×C4×Dic3C2312yes—
245C3×C4×Dic3C2312yes—
246C3×C4×Dic3C2311yescharacteristic
247C3×C4×Dic3C2312yes—
248#3724C2311yescharacteristic
249#3724C2312yes—
250#3724C2312yes—
251#3724C2311yescharacteristic
252#3724C2312yes—
253Dic3⋊Dic3C2311yescharacteristic
254Dic3⋊Dic3C2312yes—
255Dic3⋊Dic3C2311yescharacteristic
256Dic3⋊Dic3C2311yescharacteristic
257Dic3⋊Dic3C2311yescharacteristic
258#3722C2312yes—
259#3722C2312yes—
260#3722C2312yes—
261#3722C2312yes—
262(C2×D3)⋊Dic3C2312yes—
263(C2×D3)⋊Dic3C2311yescharacteristic
264(C2×D3)⋊Dic3C2311yescharacteristic
265(C2×D3)⋊Dic3C2312yes—
266(C2×D3)⋊Dic3C2312yes—
267(C2×D3)⋊Dic3C2311yescharacteristic
268(C2×D3)⋊Dic3C2311yescharacteristic
269Dic32C2312yes—
270Dic32C2312yes—
271Dic32C2312yes—
272Dic32C2311yescharacteristic
273Dic32C2311yescharacteristic
274#3524—91noSylow
275C2×D3×Q8—31no—
276C2×#237—31no—
277C2×#235—31no—
278C2×#235—31no—
279C2×#235—31no—
280C2×#235—61no—
281C22×Dic6—31no—
282C3×#126—32no—
283C3×#126—32no—
284C3×#125—32no—
285C3×#125—31no—
286C3×#125—31no—
287C3×#123—32no—
288C3×#123—32no—
289C3×C22⋊Q8—31no—
290C3×C22⋊Q8—31no—
291C3×#121—31no—
292C3×#121—32no—
293C3×#121—31no—
294C3×C4×Q8—31no—
295C3×C4×D4—31no—
296C3×C4×D4—32no—
297C3×C4×D4—31no—
298C3×C4×D4—31no—
299C3×#117—32no—
300C3×#117—31no—
301C3×#117—31no—
302C2×C3×C4⋊C4—21no—
303C2×C3×C4⋊C4C2×D311yescharacteristic
304C2×C3×C4⋊C4C2×D311yescharacteristic
305#947—31no—
306#947—31no—
307Q8×Dic3—31no—
308#940—32no—
309#940—32no—
310#940—31no—
311#939—31no—
312#939—32no—
313#939—32no—
314#939—32no—
315#939—32no—
316#938—31no—
317#938—32no—
318#936—31no—
319#936—31no—
320#936—32no—
321#935—31no—
322#935—32no—
323D4×Dic3—32no—
324D4×Dic3—31no—
325#930—31no—
326#930—31no—
327#930C2×D311yescharacteristic
328#930C2×D312yes—
329#929—32no—
330#929C2×D312yes—
331C4×#67—32no—
332C4×#67—32no—
333C4×#67—32no—
334C4×#67—32no—
335C4×#67—31no—
336C4×#67—31no—
337C4×#67—32no—
338C4×#67—32no—
339C4×#67—62no—
340C4×#67—62no—
341C4×#67C2×D311yescharacteristic
342C4×#67C2×D312yes—
343C4×#67C2×D311yescharacteristic
344#926—31no—
345#926—31no—
346#926—31no—
347#926—61no—
348#926C2×D312yes—
349#924C2×D311yescharacteristic
350C2×C4×Dic3—32no—
351C2×C4×Dic3—31no—
352#898—32no—
353#898—31no—
354#898—32no—
355#898—32no—
356#898C2×D312yes—
357#898C2×D312yes—
358#897—32no—
359#897—31no—
360#897C2×D311yescharacteristic
361#896—32no—
362#896—32no—
363#896—32no—
364#895—32no—
365#895—32no—
366#895—31no—
367#895—31no—
368#895C2×D311yescharacteristic
369#894—32no—
370#894—32no—
371#894—32no—
372#894—32no—
373#894—32no—
374#894C2×D312yes—
375#893—32no—
376#893—31no—
377#893—31no—
378#893—31no—
379#893—31no—
380#893—31no—
381#893—32no—
382#893—32no—
383#893—32no—
384#893—61no—
385#893—61no—
386#893C2×D311yescharacteristic
387#892—32no—
388#892—32no—
389#892—32no—
390#892—32no—
391#892—32no—
392#892—62no—
393#892C2×D311yescharacteristic
394#892C2×D311yescharacteristic
395D3×C4⋊C4—32no—
396D3×C4⋊C4—32no—
397D3×C4⋊C4—62no—
398#890—31no—
399#890C2×D311yescharacteristic
400#890C2×D311yescharacteristic
401#889—32no—
402#889—32no—
403#889—32no—
404#889—32no—
405#889—31no—
406#889C2×D312yes—
407#888—31no—
408#888—32no—
409#888—32no—
410#888—31no—
411#887—31no—
412#887—31no—
413#887—31no—
414#887—31no—
415#887—31no—
416#887—32no—
417#887—32no—
418#887—31no—
419#887—32no—
420#887—31no—
421#887—61no—
422#887—61no—
423#887C2×D311yescharacteristic
424#886—31no—
425#886—32no—
426#886—32no—
427#885—32no—
428#885—31no—
429#885—32no—
430#885—32no—
431#885—32no—
432#885—32no—
433#885—32no—
434#885—32no—
435#885—32no—
436#884—32no—
437#884—32no—
438#884—32no—
439#884—32no—
440#884—32no—
441#884—32no—
442#884—32no—
443#883—32no—
444#883—31no—
445#883—31no—
446#883—32no—
447#883—32no—
448#67⋊C4—32no—
449#67⋊C4—32no—
450#67⋊C4—32no—
451#67⋊C4—32no—
452#67⋊C4—32no—
453#67⋊C4—32no—
454#879—31no—
455#879—31no—
456#879—31no—
457#879—32no—
458#878—32no—
459#878—32no—
460#878—31no—
461#877—32no—
462#877—32no—
463#877—32no—
464#875—31no—
465#875—32no—
466#875—32no—
467#875—32no—
468#874—31no—
469C4×D12—32no—
470#872—31no—
471#872—32no—
472#872—32no—
473#872—32no—
474#872—32no—
475C42×D3—32no—
476C42×D3—31no—
477C4×Dic6—31no—
478C4×Dic6—31no—
479C4×Dic6—32no—
480C4×Dic6—31no—
481C4×Dic6—31no—
482C4×Dic6—32no—
483C4×Dic6—32no—
484C23×C32C2411yescharacteristic
485C22×C3⋊D3C2412yes—
486C22×C3×D3C2411yescharacteristic
487C22×C3×D3C2412yes—
488C22×C3×D3C2411yescharacteristic
489C2×C32×C4—22no—
490C2×C32×C4—42no—
491C2×C32×C4C2412yes—
492C2×C32×C4C2411yescharacteristic
493C2×C32×C4C2412yes—
494C2×C32×C4C2411yescharacteristic
495#638—24no—
496C2×C3⋊Dic3C2411yescharacteristic
497C2×C3⋊Dic3C2411yescharacteristic
498C2×C3⋊Dic3C2411yescharacteristic
499C2×C3⋊Dic3C2411yescharacteristic
500C2×C3⋊Dic3C2412yes—
501C4⋊(C3⋊D3)—22no—
502C4×C3⋊D3—24no—
503C4×C3⋊D3—42no—
504C4×C3⋊D3—42no—
505#634#4114yes—
506C3×#67—41no—
507C3×#67—41no—
508C3×#67—42no—
509C2×C3×Dic3C2411yescharacteristic
510C2×C3×Dic3C2411yescharacteristic
511C2×C3×Dic3C2411yescharacteristic
512C2×C3×Dic3C2412yes—
513C2×C3×Dic3C2412yes—
514C2×C3×Dic3C2412yes—
515C2×C3×Dic3C2411yescharacteristic
516C2×C3×Dic3C2411yescharacteristic
517C2×C3×Dic3C2411yescharacteristic
518C3×D12—22no—
519C3×D12—42no—
520C3×C4×D3—22no—
521C3×C4×D3—22no—
522C3×C4×D3—42no—
523C3×Dic6—22no—
524#627—24no—
525#627—42no—
526#627—41no—
527#626—42no—
528#626—42no—
529#626—42no—
530#626—42no—
531#625—24no—
532#625—41no—
533D3×Dic3—24no—
534D3×Dic3—24no—
535D3×Dic3—42no—
536D3×Dic3—41no—
537D3×Dic3—41no—
538#559—91no—
539#559—92no—
540#557—91no—
541#555—91no—
542#555—92no—
543#553—31no—
544#553—92no—
545#552—31no—
546#552—92no—
547#550—91no—
548#548—91no—
549#548—91no—
550#542—91no—
551#542—92no—
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×D4—32no—
563C2×C3×D4—31no—
564C2×C3×D4—31no—
565C2×C3×D4—31no—
566C2×C3×D4—32no—
567C22×C3×C4—21no—
568C22×C3×C4—22no—
569C22×C3×C4—31no—
570C22×C3×C4—31no—
571C22×C3×C4—32no—
572C22×C3×C4C22×D311yescharacteristic
573C22×C3×C4C22×D311yescharacteristic
574C22×C3×C4C22×D312yes—
575C22×C3×C4C22×D312yes—
576C2×#67—32no—
577C2×#67—32no—
578C2×#67—32no—
579C2×#67—32no—
580C2×#67—31no—
581C2×#67—31no—
582C2×#67—32no—
583C2×#67—32no—
584C2×#67—32no—
585C2×#67—32no—
586C2×#67—62no—
587C2×#67C22×D312yes—
588C2×#67C22×D311yescharacteristic
589C2×#67C22×D311yescharacteristic
590C22×Dic3—32no—
591C22×Dic3—32no—
592C22×Dic3—31no—
593C22×Dic3—32no—
594C22×Dic3—31no—
595D3×Q8—64no—
596#237—64no—
597#235—64no—
598#235—64no—
599#235—64no—
600#235—68no—
601C2×D12—31no—
602C2×D12—31no—
603C2×D12—32no—
604C2×D12—32no—
605C2×D12—32no—
606C2×D12—32no—
607C2×D12—61no—
608C2×D12C22×D311yescharacteristic
609C2×D12C22×D312yes—
610C2×C4×D3—32no—
611C2×C4×D3—32no—
612C2×C4×D3—32no—
613C2×C4×D3—32no—
614C2×C4×D3—31no—
615C2×C4×D3—32no—
616C2×C4×D3—31no—
617C2×C4×D3—32no—
618C2×C4×D3—32no—
619C2×C4×D3—32no—
620C2×C4×D3—32no—
621C2×C4×D3—62no—
622C2×C4×D3—62no—
623C2×C4×D3—62no—
624C2×C4×D3C22×D311yescharacteristic
625C2×C4×D3C22×D311yescharacteristic
626C2×C4×D3C22×D312yes—
627C2×Dic6—31no—
628C2×Dic6—31no—
629C2×Dic6—32no—
630C2×Dic6—32no—
631C2×Dic6—31no—
632C2×Dic6—31no—
633C2×Dic6—32no—
634C2×Dic6—32no—
635C2×Dic6—61no—
636C2×Dic6—64no—
637C2×Dic6C22×D311yescharacteristic
638C3×C4⋊C4—21no—
639C3×C4⋊C4—21no—
640C3×C4⋊C4—22no—
641C3×C4⋊C4—31no—
642C3×C4⋊C4—31no—
643C3×C4⋊C4—32no—
644C3×C4⋊C4—32no—
645C3×C4⋊C4—32no—
646C3×C4⋊C4—32no—
647C3×C4⋊C4—32no—
648C3×C4⋊C4—31no—
649C3×C4⋊C4—31no—
650C3×C4⋊C4—32no—
651C3×C4⋊C4—32no—
652C3×C4⋊C4C22×D311yescharacteristic
653C3×C4⋊C4C22×D311yescharacteristic
654C3×C4⋊C4C22×D311yescharacteristic
655C3×C4⋊C4C22×D311yescharacteristic
656C3×C4⋊C4C22×D312yes—
657C3×C4⋊C4C22×D312yes—
658C3×C22⋊C4—31no—
659C3×C22⋊C4—31no—
660C3×C22⋊C4—32no—
661C3×C22⋊C4—32no—
662C3×C22⋊C4—32no—
663C3×C22⋊C4—32no—
664C3×C22⋊C4—32no—
665C3×C22⋊C4—31no—
666C3×C22⋊C4—31no—
667C3×C22⋊C4—32no—
668C3×C22⋊C4—32no—
669C3×C42—31no—
670C3×C42—31no—
671C3×C42—32no—
672C3×C42—32no—
673C3×C42—32no—
674#217—31no—
675#217—31no—
676#217—31no—
677#217—31no—
678#217—31no—
679#217—31no—
680#217—32no—
681#217—32no—
682#217—31no—
683#217—32no—
684#217—31no—
685#217—61no—
686#217—61no—
687#217C22×D311yescharacteristic
688#217C22×D311yescharacteristic
689#217C22×D312yes—
690(C2×D3)⋊C4—31no—
691(C2×D3)⋊C4—32no—
692(C2×D3)⋊C4—31no—
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—32no—
699(C2×D3)⋊C4—32no—
700(C2×D3)⋊C4—32no—
701(C2×D3)⋊C4—32no—
702(C2×D3)⋊C4—32no—
703(C2×D3)⋊C4—32no—
704(C2×D3)⋊C4—32no—
705(C2×D3)⋊C4—32no—
706(C2×D3)⋊C4—32no—
707(C2×D3)⋊C4—32no—
708(C2×D3)⋊C4—32no—
709(C2×D3)⋊C4—62no—
710(C2×D3)⋊C4—62no—
711(C2×D3)⋊C4C22×D312yes—
712(C2×D3)⋊C4C22×D312yes—
713(C2×D3)⋊C4C22×D312yes—
714(C2×D3)⋊C4C22×D311yescharacteristic
715(C2×D3)⋊C4C22×D312yes—
716(C2×D3)⋊C4C22×D312yes—
717(C2×D3)⋊C4C22×D312yes—
718(C2×D3)⋊C4C22×D311yescharacteristic
719C4⋊Dic3—31no—
720C4⋊Dic3—31no—
721C4⋊Dic3—31no—
722C4⋊Dic3—31no—
723C4⋊Dic3—31no—
724C4⋊Dic3—31no—
725C4⋊Dic3—31no—
726C4⋊Dic3—31no—
727C4⋊Dic3—32no—
728C4⋊Dic3—61no—
729C4⋊Dic3—61no—
730C4⋊Dic3C22×D311yescharacteristic
731C4⋊Dic3C22×D311yescharacteristic
732C4⋊Dic3C22×D312yes—
733C4⋊Dic3C22×D312yes—
734C4⋊Dic3C22×D312yes—
735Dic3⋊C4—32no—
736Dic3⋊C4—32no—
737Dic3⋊C4—32no—
738Dic3⋊C4—32no—
739Dic3⋊C4—31no—
740Dic3⋊C4—32no—
741Dic3⋊C4—32no—
742Dic3⋊C4—32no—
743Dic3⋊C4—32no—
744Dic3⋊C4—31no—
745Dic3⋊C4—31no—
746Dic3⋊C4—31no—
747Dic3⋊C4—31no—
748Dic3⋊C4—31no—
749Dic3⋊C4—31no—
750Dic3⋊C4—32no—
751Dic3⋊C4—32no—
752Dic3⋊C4—32no—
753Dic3⋊C4—31no—
754Dic3⋊C4—62no—
755Dic3⋊C4—62no—
756Dic3⋊C4C22×D312yes—
757Dic3⋊C4C22×D312yes—
758Dic3⋊C4C22×D311yescharacteristic
759Dic3⋊C4C22×D311yescharacteristic
760Dic3⋊C4C22×D312yes—
761Dic3⋊C4C22×D312yes—
762C4×Dic3—32no—
763C4×Dic3—32no—
764C4×Dic3—31no—
765C4×Dic3—31no—
766C4×Dic3—31no—
767C4×Dic3—31no—
768C4×Dic3—32no—
769C4×Dic3—32no—
770C4×Dic3—32no—
771C4×Dic3—32no—
772C4×Dic3—32no—
773C4×Dic3—32no—
774C4×Dic3—31no—
775C4×Dic3—31no—
776C4×Dic3—31no—
777C4×Dic3—32no—
778C4×Dic3—31no—
779C4×Dic3—32no—
780C4×Dic3—62no—
781C4×Dic3—62no—
782C4×Dic3—61no—
783C4×Dic3—61no—
784C4×Dic3C22×D312yes—
785C4×Dic3C22×D312yes—
786C4×Dic3C22×D311yescharacteristic
787C4×Dic3C22×D311yescharacteristic
788C4×Dic3C22×D312yes—
789C22×C32—21no—
790C22×C32—21no—
791C22×C32—21no—
792C22×C32C2511yescharacteristic
793C2×C3⋊D3—22no—
794C2×C3⋊D3—22no—
795C2×C3⋊D3—22no—
796C2×C3×D3—21no—
797C2×C3×D3—22no—
798C2×C3×D3—21no—
799C2×C3×D3—21no—
800C2×C3×D3—21no—
801C2×C3×D3—22no—
802C2×C3×D3—21no—
803C2×C3×D3—21no—
804C2×C3×D3—22no—
805C32×C4—21no—
806C32×C4—22no—
807C32×C4—22no—
808C32×C4C2×#4112yes—
809C3⋊Dic3—21no—
810C3⋊Dic3—21no—
811C3⋊Dic3—21no—
812C3⋊Dic3—21no—
813C3⋊Dic3C2×#4114yes—
814C3×Dic3—21no—
815C3×Dic3—22no—
816C3×Dic3—21no—
817C3×Dic3—22no—
818C3×Dic3—21no—
819C3×Dic3—21no—
820C3×Dic3—21no—
821C3×Dic3—21no—
822C3×Dic3—22no—
823C2×#41—91no—
824C2×#41—91no—
825C22×Q8—91no—
826C4⋊Q8—91no—
827C4⋊Q8—92no—
828#127—91no—
829#127—92no—
830#126—32no—
831#126—32no—
832#126—91no—
833#126—91no—
834#126—92no—
835#126—92no—
836#125—32no—
837#125—31no—
838#125—31no—
839#125—91no—
840#125—92no—
841#125—92no—
842#124—92no—
843#124—92no—
844#124—92no—
845#124—91no—
846#124—92no—
847#124—92no—
848#124—91no—
849#124—92no—
850#124—91no—
851#123—32no—
852#123—32no—
853#123—91no—
854#123—92no—
855#123—92no—
856#123—92no—
857#123—92no—
858#123—92no—
859#123—91no—
860#123—92no—
861C22⋊Q8—31no—
862C22⋊Q8—31no—
863C22⋊Q8—91no—
864C22⋊Q8—92no—
865C22⋊Q8—92no—
866C22⋊Q8—92no—
867#121—32no—
868#121—31no—
869#121—31no—
870#121—92no—
871#121—92no—
872#121—92no—
873#121—92no—
874#121—92no—
875#121—91no—
876#121—91no—
877#121—92no—
878#121—92no—
879#121—91no—
880C4×Q8—31no—
881C4×Q8—92no—
882C4×Q8—91no—
883C4×Q8—91no—
884C4×Q8—91no—
885C4×Q8—92no—
886C4×Q8—92no—
887C4×Q8—91no—
888C4×Q8—91no—
889C4×Q8—91no—
890C4×D4—31no—
891C4×D4—31no—
892C4×D4—32no—
893C4×D4—31no—
894C4×D4—92no—
895C4×D4—92no—
896C4×D4—92no—
897C4×D4—92no—
898C4×D4—92no—
899C4×D4—92no—
900C4×D4—91no—
901C4×D4—92no—
902C4×D4—91no—
903C4×D4—92no—
904C4×D4—92no—
905C4×D4—91no—
906C4×D4—91no—
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—91no—
917#117—92no—
918C2×C4⋊C4—92no—
919C2×C4⋊C4D3211yescharacteristic
920C2×C42—92no—
921C2×C42—91no—
922C23×C3—21no—
923C23×C3—31no—
924C23×C3—32no—
925C23×C3—31no—
926C23×C3C23×D311yescharacteristic
927C23×C3C23×D311yescharacteristic
928C22×D3—32no—
929C22×D3—32no—
930C22×D3—62no—
931C22×D3C23×D311yescharacteristic
932C22×D3C23×D312yes—
933C22×D3C23×D311yescharacteristic
934C3×Q8—62no—
935C3×D4—62no—
936C3×D4—122no—
937C3×D4—121no—
938C3×D4—121no—
939C3×D4—122no—
940C2×C3×C4—24no—
941C2×C3×C4—22no—
942C2×C3×C4—22no—
943C2×C3×C4—21no—
944C2×C3×C4—21no—
945C2×C3×C4—22no—
946C2×C3×C4—22no—
947C2×C3×C4—31no—
948C2×C3×C4—32no—
949C2×C3×C4—31no—
950C2×C3×C4—31no—
951C2×C3×C4—31no—
952C2×C3×C4—32no—
953C2×C3×C4—32no—
954C2×C3×C4—31no—
955C2×C3×C4—31no—
956C2×C3×C4—42no—
957C2×C3×C4—42no—
958C2×C3×C4—62no—
959C2×C3×C4—62no—
960C2×C3×C4—82no—
961C2×C3×C4—122no—
962C2×C3×C4C23×D312yes—
963C2×C3×C4C23×D312yes—
964C2×C3×C4C23×D312yes—
965C2×C3×C4C23×D312yes—
966C2×C3×C4C23×D311yescharacteristic
967C2×C3×C4C23×D311yescharacteristic
968C2×C3×C4C23×D311yescharacteristic
969C2×C3×C4C23×D311yescharacteristic
970#67—41no—
971#67—42no—
972#67—41no—
973#67—64no—
974#67—64no—
975#67—64no—
976#67—64no—
977#67—68no—
978#67—122no—
979#67—122no—
980#67—122no—
981#67—122no—
982#67—121no—
983#67—121no—
984C2×Dic3—32no—
985C2×Dic3—32no—
986C2×Dic3—31no—
987C2×Dic3—31no—
988C2×Dic3—31no—
989C2×Dic3—31no—
990C2×Dic3—31no—
991C2×Dic3—31no—
992C2×Dic3—31no—
993C2×Dic3—31no—
994C2×Dic3—62no—
995C2×Dic3—61no—
996C2×Dic3—61no—
997C2×Dic3—61no—
998C2×Dic3—61no—
999C2×Dic3—64no—
1000C2×Dic3—64no—
1001C2×Dic3—121no—
1002C2×Dic3—121no—
1003C2×Dic3—122no—
1004C2×Dic3C23×D311yescharacteristic
1005C2×Dic3C23×D311yescharacteristic
1006C2×Dic3C23×D312yes—
1007C2×Dic3C23×D311yescharacteristic
1008C2×Dic3C23×D311yescharacteristic
1009C2×Dic3C23×D312yes—
1010C2×Dic3C23×D312yes—
1011C2×Dic3C23×D311yescharacteristic
1012C2×Dic3C23×D311yescharacteristic
1013D12—22no—
1014D12—42no—
1015D12—64no—
1016D12—62no—
1017D12—62no—
1018D12—122no—
1019D12—122no—
1020D12—122no—
1021D12—122no—
1022C4×D3—22no—
1023C4×D3—22no—
1024C4×D3—42no—
1025C4×D3—64no—
1026C4×D3—64no—
1027C4×D3—64no—
1028C4×D3—64no—
1029C4×D3—68no—
1030C4×D3—122no—
1031C4×D3—122no—
1032C4×D3—122no—
1033C4×D3—122no—
1034C4×D3—121no—
1035C4×D3—122no—
1036C4×D3—121no—
1037C4×D3—242no—
1038C4×D3—242no—
1039Dic6—22no—
1040Dic6—34no—
1041Dic6—34no—
1042Dic6—64no—
1043Dic6—64no—
1044Dic6—64no—
1045Dic6—121no—
1046Dic6—122no—
1047Dic6—122no—
1048Dic6—121no—
1049C2×C32—41no—
1050C2×C32C22×#4111yescharacteristic
1051C2×C32#58511yescharacteristic
1052C2×C32#58511yescharacteristic
1053C3⋊D3—42no—
1054C3×D3—41no—
1055C3×D3—41no—
1056C3×D3—42no—
1057#41—184no—
1058#41—184no—
1059C2×Q8—31no—
1060C2×Q8—92no—
1061C2×Q8—91no—
1062C2×Q8—92no—
1063C2×Q8—91no—
1064C2×Q8—184no—
1065C2×D4—31no—
1066C2×D4—32no—
1067C2×D4—31no—
1068C2×D4—31no—
1069C2×D4—32no—
1070C2×D4—92no—
1071C2×D4—92no—
1072C2×D4—92no—
1073C2×D4—92no—
1074C2×D4—92no—
1075C2×D4—92no—
1076C2×D4—91no—
1077C2×D4—91no—
1078C22×C4—31no—
1079C22×C4—31no—
1080C22×C4—32no—
1081C22×C4—92no—
1082C22×C4—92no—
1083C22×C4—91no—
1084C22×C4—92no—
1085C22×C4—91no—
1086C22×C4—92no—
1087C22×C4—92no—
1088C22×C4—92no—
1089C22×C4C2×D3211yescharacteristic
1090C22×C4C2×D3212yes—
1091C4⋊C4—32no—
1092C4⋊C4—31no—
1093C4⋊C4—31no—
1094C4⋊C4—32no—
1095C4⋊C4—32no—
1096C4⋊C4—32no—
1097C4⋊C4—31no—
1098C4⋊C4—32no—
1099C4⋊C4—31no—
1100C4⋊C4—32no—
1101C4⋊C4—32no—
1102C4⋊C4—91no—
1103C4⋊C4—92no—
1104C4⋊C4—92no—
1105C4⋊C4—91no—
1106C4⋊C4—92no—
1107C4⋊C4—91no—
1108C4⋊C4—92no—
1109C4⋊C4—91no—
1110C4⋊C4—91no—
1111C4⋊C4—91no—
1112C4⋊C4—91no—
1113C4⋊C4—92no—
1114C4⋊C4—92no—
1115C4⋊C4—91no—
1116C4⋊C4C2×D3212yes—
1117C4⋊C4C2×D3211yescharacteristic
1118C4⋊C4C2×D3211yescharacteristic
1119C22⋊C4—31no—
1120C22⋊C4—32no—
1121C22⋊C4—31no—
1122C22⋊C4—32no—
1123C22⋊C4—32no—
1124C22⋊C4—32no—
1125C22⋊C4—31no—
1126C22⋊C4—32no—
1127C22⋊C4—31no—
1128C22⋊C4—32no—
1129C22⋊C4—32no—
1130C22⋊C4—92no—
1131C22⋊C4—92no—
1132C22⋊C4—92no—
1133C22⋊C4—92no—
1134C22⋊C4—91no—
1135C22⋊C4—91no—
1136C22⋊C4—92no—
1137C22⋊C4—91no—
1138C22⋊C4—92no—
1139C22⋊C4—91no—
1140C22⋊C4—92no—
1141C22⋊C4—91no—
1142C22⋊C4—91no—
1143C22⋊C4—92no—
1144C22⋊C4—92no—
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—
1158C42—91no—
1159C22×C3—22no—
1160C22×C3—21no—
1161C22×C3—21no—
1162C22×C3—21no—
1163C22×C3—21no—
1164C22×C3—21no—
1165C22×C3—21no—
1166C22×C3—21no—
1167C22×C3—41no—
1168C22×C3—41no—
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—22no—
1184C2×D3—21no—
1185C2×D3—21no—
1186C2×D3—22no—
1187C2×D3—21no—
1188C2×D3—21no—
1189C2×D3—64no—
1190C2×D3—62no—
1191C2×D3—62no—
1192C2×D3—62no—
1193C2×D3—62no—
1194C2×D3—62no—
1195C2×D3—62no—
1196C2×D3—122no—
1197C2×D3—122no—
1198C3×C4—22no—
1199C3×C4—21no—
1200C3×C4—21no—
1201C3×C4—22no—
1202C3×C4—22no—
1203C3×C4—22no—
1204C3×C4—22no—
1205C3×C4—22no—
1206C3×C4—42no—
1207C3×C4—42no—
1208C3×C4—61no—
1209C3×C4—62no—
1210C3×C4—61no—
1211C3×C4—62no—
1212C3×C4—61no—
1213C3×C4—61no—
1214C3×C4—61no—
1215C3×C4—61no—
1216C3×C4—62no—
1217C3×C4D3×#4112yes—
1218C3×C4D3×#4112yes—
1219Dic3—22no—
1220Dic3—21no—
1221Dic3—21no—
1222Dic3—21no—
1223Dic3—22no—
1224Dic3—21no—
1225Dic3—21no—
1226Dic3—22no—
1227Dic3—21no—
1228Dic3—34no—
1229Dic3—34no—
1230Dic3—64no—
1231Dic3—61no—
1232Dic3—61no—
1233Dic3—61no—
1234Dic3—61no—
1235Dic3—61no—
1236Dic3—61no—
1237Dic3—61no—
1238Dic3—61no—
1239Dic3—121no—
1240Dic3—121no—
1241Dic3—121no—
1242Dic3—121no—
1243C32#352411yescharacteristic, complemented, Sylow
1244C23—31no—
1245C23—31no—
1246C23—32no—
1247C23—92no—
1248C23C22×D3211yescharacteristic
1249Q8—62no—
1250Q8—94no—
1251Q8—184no—
1252Q8—361no—
1253Q8—362no—
1254D4—62no—
1255D4—122no—
1256D4—121no—
1257D4—121no—
1258D4—122no—
1259D4—184no—
1260D4—184no—
1261D4—182no—
1262D4—362no—
1263D4—362no—
1264D4—362no—
1265D4—362no—
1266D4—361no—
1267C2×C4—22no—
1268C2×C4—31no—
1269C2×C4—31no—
1270C2×C4—31no—
1271C2×C4—31no—
1272C2×C4—32no—
1273C2×C4—31no—
1274C2×C4—32no—
1275C2×C4—32no—
1276C2×C4—31no—
1277C2×C4—42no—
1278C2×C4—62no—
1279C2×C4—62no—
1280C2×C4—92no—
1281C2×C4—91no—
1282C2×C4—91no—
1283C2×C4—91no—
1284C2×C4—91no—
1285C2×C4—122no—
1286C2×C4—184no—
1287C2×C4—184no—
1288C2×C4—184no—
1289C2×C4—362no—
1290C2×C4—362no—
1291C2×C4—361no—
1292C2×C4—361no—
1293C2×C4—362no—
1294C2×C4C22×D3212yes—
1295C2×C4C22×D3212yes—
1296C2×C4C22×D3211yescharacteristic
1297C2×C4C22×D3211yescharacteristic
1298C2×C3—21no—
1299C2×C3—21no—
1300C2×C3—21no—
1301C2×C3—42no—
1302C2×C3—41no—
1303C2×C3—41no—
1304C2×C3—121no—
1305C2×C3—122no—
1306C2×C3—121no—
1307C2×C3C2×D3×#4111yescharacteristic
1308C2×C3C2×D3×#4111yescharacteristic
1309C2×C3#596411yescharacteristic
1310C2×C3#596411yescharacteristic
1311C2×C3#596611yescharacteristic
1312C2×C3#596811yescharacteristic
1313D3—41no—
1314D3—41no—
1315D3—42no—
1316D3—124no—
1317D3—122no—
1318D3—122no—
1319C22—21no—
1320C22—21no—
1321C22—21no—
1322C22—61no—
1323C22—61no—
1324C22—62no—
1325C22—62no—
1326C22—61no—
1327C22—61no—
1328C22—62no—
1329C22—61no—
1330C22—61no—
1331C22—182no—
1332C22—182no—
1333C22—182no—
1334C22C23×D3211yescharacteristic
1335C4—21no—
1336C4—22no—
1337C4—22no—
1338C4—61no—
1339C4—61no—
1340C4—62no—
1341C4—61no—
1342C4—61no—
1343C4—61no—
1344C4—62no—
1345C4—62no—
1346C4—61no—
1347C4—94no—
1348C4—181no—
1349C4—181no—
1350C4—181no—
1351C4—181no—
1352C4#6430612yes—
1353C3—21no—
1354C3#8684311yescharacteristic, complemented
1355C3#8689111yescharacteristic, complemented
1356C2—41no—
1357C2—121no—
1358C2—121no—
1359C2—122no—
1360C2—362no—
1361C2C2×#6430611yescharacteristic
1362C2#1059667811yescharacteristic
1363C2#1059668811yescharacteristic
subgroupG/H
center, FrattiniC22C23×D32
commutator, socle, cosocleC22×C32C25
FittingC2×C32×C4⋊C4C22
hypercenterC2×C4⋊C4D32
hypocenterC32#3524
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
1. #10595975C2semidirect
2. C3×#5514C2semidirect
3. C3×#5513C2semidirect
4. #10595031C2semidirect
5. #10594984C2semidirect
6. #10594961C2semidirect
7. #10594957C2semidirect
8. #10594934C2semidirect
9. #10594933C2semidirect
10. #10594919C2semidirect
11. #10594916C2semidirect
12. #10594575C2semidirect
13. #10594571C2semidirect
14. #10594566C2semidirect
15. #10594525C2semidirect
16. #10594501C2semidirect
17. #10594473C2semidirect
18. #10594471C2semidirect
19. #10594453C2semidirect
20. #10594441C2semidirect
21. #10594358C2semidirect
22. #10594357C2semidirect
23. #10594324C2semidirect
167. #5514D3semidirect
168. #5513D3semidirect
1243. C32#3524semidirect
1354. C3#86843semidirect
1355. C3#86891semidirect

Maximal subgroups

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

subgroupindex
#105959752
C3×#55142
C3×#55132
#105950312
#105949842
#105949612
#105949572
#105949342
#105949332
#105949192
#105949162
#105945752
#105945712
#105945662
#105945252
#105945012
#105944732
#105944712
#105944532
#105944412
#105943582
#105943572
#105943242
#868913
#868433