Finite Group Databasebeta

← #11910058

Subgroups — #11910058

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#10595984C211yesmaximal, characteristic, complemented
2C3×#5514C211yesmaximal, characteristic, complemented
3C3×#5504C211yesmaximal, characteristic, complemented
4#10595030C212yesmaximal, complemented
5#10595026C212yesmaximal, complemented
6#10595006C211yesmaximal, characteristic, complemented
7#10594983C211yesmaximal, characteristic, complemented
8#10594950C212yesmaximal, complemented
9#10594934C212yesmaximal, complemented
10#10594899C211yesmaximal, characteristic, complemented
11#10594836C211yesmaximal, characteristic, complemented
12#10594582C211yesmaximal, characteristic, complemented
13#10594555C211yesmaximal, characteristic, complemented
14#10594548C212yesmaximal, complemented
15#10594544C212yesmaximal, complemented
16#10594543C212yesmaximal, complemented
17#10594496C211yesmaximal, characteristic, complemented
18#10594447C211yesmaximal, characteristic, complemented
19#10594404C212yesmaximal, complemented
20#10594382C211yesmaximal, characteristic, complemented
21#10594360C211yesmaximal, characteristic, complemented
22#10594357C211yesmaximal, characteristic, complemented
23#10594321C211yesmaximal, characteristic, complemented
24#86891—31nomaximal
25#85898—31nomaximal
26C2×C3×#235C2211yescharacteristic
27C2×#3796C2211yescharacteristic
28C2×D3×Dic6C2211yescharacteristic
29C2×C32×C4⋊C4C2211yescharacteristic
30#64138C2212yes—
31C4×#638C2211yescharacteristic
32#64135C2212yes—
33#64133C2211yescharacteristic
34#64107C2212yes—
35#64106C2211yescharacteristic
36#64101C2211yescharacteristic
37#64099C2211yescharacteristic
38#64098C2212yes—
39#64096C2211yescharacteristic
40C3×#930C2212yes—
41C3×#930C2211yescharacteristic
42C3×C4×#67C2212yes—
43C3×C4×#67C2212yes—
44C3×C4×#67C2211yescharacteristic
45C3×C4×#67C2212yes—
46C3×#926C2211yescharacteristic
47C3×#898C2212yes—
48C3×#895C2211yescharacteristic
49C3×#894C2212yes—
50C3×#893C2211yescharacteristic
51C3×#893C2211yescharacteristic
52C3×#893C2211yescharacteristic
53C3×#892C2212yes—
54C3×#892C2211yescharacteristic
55C3×D3×C4⋊C4C2212yes—
56C3×#890C2211yescharacteristic
57C3×#887C2211yescharacteristic
58C3×#887C2211yescharacteristic
59#63979C2212yes—
60#63975C2211yescharacteristic
61#63970C2212yes—
62#63970C2212yes—
63#63969C2212yes—
64#63959C2211yescharacteristic
65#63959C2212yes—
66#63959C2212yes—
67#63958C2211yescharacteristic
68#63956C2211yescharacteristic
69#63918C2211yescharacteristic
70#63918C2212yes—
71C4×#627C2211yescharacteristic
72C4×#627C2212yes—
73#63916C2211yescharacteristic
74#63915C2212yes—
75#63915C2212yes—
76#63914C2211yescharacteristic
77#63908C2211yescharacteristic
78#63908C2212yes—
79#63906C2212yes—
80#63906C2212yes—
81#63905C2212yes—
82#63905C2212yes—
83#63905C2212yes—
84#63904C2212yes—
85#63904C2212yes—
86C4×#626C2211yescharacteristic
87C4×#625C2212yes—
88#63899C2212yes—
89#63895C2211yescharacteristic
90#63893C2212yes—
91Dic3×D12C2211yescharacteristic
92Dic3×D12C2212yes—
93#63891C2212yes—
94#63886C2212yes—
95#63885C2212yes—
96C4×#624C2211yescharacteristic
97#63880C2212yes—
98#63879C2212yes—
99#63879C2212yes—
100#63878C2212yes—
101#63878C2212yes—
102#63877C2212yes—
103C4×D3×Dic3C2212yes—
104#63861C2212yes—
105#63860C2211yescharacteristic
106#63860C2211yescharacteristic
107#63858C2211yescharacteristic
108#63858C2212yes—
109#63855C2211yescharacteristic
110#63855C2212yes—
111#63854C2211yescharacteristic
112#63854C2212yes—
113#63852C2212yes—
114#63852C2212yes—
115#63851C2212yes—
116#63846C2212yes—
117#63846C2211yescharacteristic
118#63845C2212yes—
119#63844C2211yescharacteristic
120#63843C2211yescharacteristic
121Dic3×Dic6C2211yescharacteristic
122#63841C2212yes—
123#63837C2212yes—
124#63837C2212yes—
125C3×#553—31no—
126C3×#520—31no—
127#5834—31no—
128#5831—31no—
129#5710—32no—
130#5708—32no—
131#5691—31no—
132#5685—31no—
133#5661—32no—
134#5649—32no—
135#5619—31no—
136#5616—32no—
137#5615—32no—
138#5603—31no—
139#5599—31no—
140#5598—31no—
141#5576—31no—
142C4×#239—31no—
143#5572—31no—
144#5570—31no—
145#5563—32no—
146#5563—31no—
147#5562—32no—
148#5562—31no—
149#5559—32no—
150#5559—32no—
151#5559—31no—
152#5559—31no—
153#5557—32no—
154#5557—31no—
155#5557—31no—
156#5552—31no—
157#5538—32no—
158C4×#237—31no—
159#5534—31no—
160#5534—32no—
161#5532—31no—
162#5528—31no—
163#5528—32no—
164#5516—31no—
165#5514—32no—
166#5514D311yescharacteristic, complemented
167#5513—31no—
168#5513—31no—
169#5513—32no—
170#5513—61no—
171#5504D311yescharacteristic, complemented
172C22×C32×C4C2311yescharacteristic
173C22×C32×C4C2312yes—
174C2×#638C2311yescharacteristic
175C2×C4×C3⋊D3C2311yescharacteristic
176C2×#634C2311yescharacteristic
177C2×C3×#67C2312yes—
178C2×C3×#67C2311yescharacteristic
179C2×C3×#67C2312yes—
180C3×#235—24no—
181C2×C3×D12C2311yescharacteristic
182C2×C3×D12C2311yescharacteristic
183C2×C3×D12C2312yes—
184C2×C3×C4×D3C2312yes—
185C2×C3×C4×D3C2311yescharacteristic
186C2×C3×C4×D3C2312yes—
187C2×C3×C4×D3C2312yes—
188C2×C3×C4×D3C2312yes—
189C2×C3×Dic6C2311yescharacteristic
190C2×#627C2312yes—
191C2×#627C2312yes—
192C2×#627C2311yescharacteristic
193C2×#626C2312yes—
194C2×#626C2312yes—
195C2×#626C2311yescharacteristic
196C2×#625C2312yes—
197C2×#625C2312yes—
198C2×#625C2312yes—
199C2×#624C2311yescharacteristic
200C2×#624C2311yescharacteristic
201C2×D3×Dic3C2312yes—
202C2×D3×Dic3C2312yes—
203C2×D3×Dic3C2312yes—
204#3796—24no—
205D3×Dic6—24no—
206C32×C4⋊C4C2311yescharacteristic
207C32×C4⋊C4C2311yescharacteristic
208C32×C4⋊C4C2312yes—
209#3757C2312yes—
210#3757C2311yescharacteristic
211#3752C2312yes—
212#3752C2312yes—
213#3752C2311yescharacteristic
214C4⋊(C3⋊Dic3)C2312yes—
215C4⋊(C3⋊Dic3)C2311yescharacteristic
216C4⋊(C3⋊Dic3)C2312yes—
217#3750C2312yes—
218#3750C2312yes—
219#3750C2311yescharacteristic
220#3750C2312yes—
221C4×C3⋊Dic3C2311yescharacteristic
222C4×C3⋊Dic3C2312yes—
223C4×C3⋊Dic3C2312yes—
224C3×#217C2311yescharacteristic
225C3×#217C2311yescharacteristic
226C3×#217C2311yescharacteristic
227C3×(C2×D3)⋊C4C2312yes—
228C3×(C2×D3)⋊C4C2312yes—
229C3×(C2×D3)⋊C4C2312yes—
230C3×(C2×D3)⋊C4C2312yes—
231C3×(C2×D3)⋊C4C2311yescharacteristic
232C3×(C2×D3)⋊C4C2312yes—
233C3×(C2×D3)⋊C4C2312yes—
234C3×C4⋊Dic3C2311yescharacteristic
235C3×C4⋊Dic3C2312yes—
236C3×C4⋊Dic3C2311yescharacteristic
237C3×C4⋊Dic3C2311yescharacteristic
238C3×Dic3⋊C4C2312yes—
239C3×Dic3⋊C4C2312yes—
240C3×Dic3⋊C4C2312yes—
241C3×Dic3⋊C4C2311yescharacteristic
242C3×C4×Dic3C2312yes—
243C3×C4×Dic3C2312yes—
244C3×C4×Dic3C2311yescharacteristic
245C3×C4×Dic3C2311yescharacteristic
246C3×C4×Dic3C2311yescharacteristic
247C3×C4×Dic3C2312yes—
248#3724C2312yes—
249#3724C2311yescharacteristic
250Dic3⋊Dic3C2311yescharacteristic
251Dic3⋊Dic3C2311yescharacteristic
252Dic3⋊Dic3C2312yes—
253Dic3⋊Dic3C2312yes—
254Dic3⋊Dic3C2312yes—
255Dic3⋊Dic3C2311yescharacteristic
256Dic3⋊Dic3C2311yescharacteristic
257Dic3⋊Dic3C2311yescharacteristic
258#3722C2311yescharacteristic
259(C2×D3)⋊Dic3C2312yes—
260(C2×D3)⋊Dic3C2312yes—
261(C2×D3)⋊Dic3C2312yes—
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)⋊Dic3C2312yes—
269Dic32C2312yes—
270Dic32C2312yes—
271Dic32C2312yes—
272Dic32C2311yescharacteristic
273Dic32C2311yescharacteristic
274#3524—91noSylow
275C2×C3×#41—31no—
276C2×#239—31no—
277C2×D3×Q8—31no—
278C2×#237—31no—
279C2×#235C2×D311yescharacteristic
280C22×Dic6—31no—
281C3×#126—32no—
282C3×#125—31no—
283C3×#123—32no—
284C3×#121—31no—
285C3×#121—32no—
286C3×#121—31no—
287C3×C4×Q8—31no—
288C3×C4×Q8—31no—
289C3×C4×D4—32no—
290C3×C4×D4—31no—
291C3×C4×D4—32no—
292C3×C4×D4—32no—
293C3×C4×D4—31no—
294C3×C4×D4—31no—
295C3×C4×D4—31no—
296C3×#117—31no—
297C3×#117—31no—
298C3×#117—32no—
299C2×C3×C4⋊C4—21no—
300C2×C3×C4⋊C4—32no—
301C2×C3×C4⋊C4C2×D311yescharacteristic
302C2×C3×C4⋊C4C2×D311yescharacteristic
303Q8×Dic3—31no—
304Q8×Dic3—31no—
305#940—32no—
306#940—32no—
307#940—31no—
308#940—31no—
309#939—32no—
310#939—32no—
311#939—32no—
312#939—32no—
313#938—32no—
314#938—32no—
315#938—32no—
316#938—31no—
317#938—31no—
318#938—31no—
319#936—32no—
320#936—31no—
321#936—32no—
322#936—31no—
323#936—31no—
324#935—32no—
325D4×Dic3—32no—
326D4×Dic3—31no—
327#930—32no—
328#930—31no—
329#930—32no—
330#930—32no—
331#930C2×D311yescharacteristic
332#930C2×D312yes—
333#929—32no—
334#929—32no—
335#929—32no—
336#929—32no—
337#929—32no—
338#929—62no—
339C4×#67—31no—
340C4×#67—31no—
341C4×#67—32no—
342C4×#67—32no—
343C4×#67—32no—
344C4×#67—32no—
345C4×#67—32no—
346C4×#67—32no—
347C4×#67—31no—
348C4×#67—61no—
349C4×#67C2×D312yes—
350C4×#67C2×D312yes—
351C4×#67C2×D311yescharacteristic
352C4×#67C2×D312yes—
353#926—32no—
354#926—32no—
355#926—32no—
356#926—32no—
357#926—31no—
358#926—62no—
359#926C2×D311yescharacteristic
360#924—31no—
361#924—31no—
362#924—32no—
363#924—61no—
364C2×C4×Dic3—32no—
365#898—32no—
366#898—32no—
367#898—32no—
368#898—32no—
369#898—31no—
370#898—62no—
371#898C2×D312yes—
372#897—31no—
373#897—31no—
374#897—32no—
375#897—31no—
376#897—61no—
377#896—32no—
378#896—32no—
379#896—31no—
380#895—31no—
381#895—32no—
382#895C2×D311yescharacteristic
383#894—32no—
384#894—31no—
385#894C2×D312yes—
386#893—32no—
387#893—32no—
388#893C2×D311yescharacteristic
389#893C2×D311yescharacteristic
390#893C2×D311yescharacteristic
391#892—32no—
392#892—31no—
393#892—31no—
394#892—32no—
395#892—32no—
396#892—61no—
397#892C2×D312yes—
398#892C2×D311yescharacteristic
399D3×C4⋊C4C2×D312yes—
400#890—31no—
401#890—31no—
402#890—31no—
403#890—32no—
404#890—32no—
405#890—61no—
406#890C2×D311yescharacteristic
407#889—32no—
408#889—32no—
409#889—32no—
410#889—32no—
411#889—31no—
412#889—62no—
413#888—32no—
414#888—31no—
415#887—31no—
416#887—31no—
417#887—31no—
418#887—32no—
419#887—31no—
420#887—32no—
421#887—61no—
422#887C2×D311yescharacteristic
423#887C2×D311yescharacteristic
424#886—32no—
425#885—31no—
426#885—32no—
427#885—32no—
428#885—32no—
429#885—32no—
430#885—32no—
431#885—32no—
432#885—32no—
433#885—32no—
434#884—31no—
435#884—32no—
436#884—32no—
437#884—32no—
438#883—32no—
439#883—32no—
440#883—32no—
441#883—32no—
442#883—31no—
443#883—31no—
444#883—32no—
445#883—31no—
446#883—32no—
447#67⋊C4—32no—
448#67⋊C4—32no—
449#67⋊C4—32no—
450#879—31no—
451#879—31no—
452#879—31no—
453#879—32no—
454#879—32no—
455#878—32no—
456#878—32no—
457#877—32no—
458#877—32no—
459#877—32no—
460#875—31no—
461#875—31no—
462#875—32no—
463#875—32no—
464C4×D12—32no—
465C4×D12—31no—
466C4×D12—31no—
467C4×D12—32no—
468#872—32no—
469#872—31no—
470#872—32no—
471C42×D3—32no—
472C42×D3—31no—
473C42×D3—31no—
474#869—31no—
475#869—32no—
476C4×Dic6—31no—
477C4×Dic6—31no—
478C4×Dic6—32no—
479C4×Dic6—32no—
480C4×Dic6—31no—
481C4×Dic6—32no—
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×C4—42no—
491C2×C32×C4C2412yes—
492C2×C32×C4C2412yes—
493C2×C32×C4C2411yescharacteristic
494C2×C32×C4C2411yescharacteristic
495#638—41no—
496C2×C3⋊Dic3C2411yescharacteristic
497C2×C3⋊Dic3C2411yescharacteristic
498C2×C3⋊Dic3C2412yes—
499C2×C3⋊Dic3C2412yes—
500C2×C3⋊Dic3C2411yescharacteristic
501C4×C3⋊D3—22no—
502#634—22no—
503C3×#67—24no—
504C3×#67—41no—
505C3×#67—42no—
506C2×C3×Dic3C2411yescharacteristic
507C2×C3×Dic3C2411yescharacteristic
508C2×C3×Dic3C2412yes—
509C2×C3×Dic3C2411yescharacteristic
510C2×C3×Dic3C2411yescharacteristic
511C2×C3×Dic3C2411yescharacteristic
512C2×C3×Dic3C2411yescharacteristic
513C2×C3×Dic3C2411yescharacteristic
514C2×C3×Dic3C2412yes—
515C3×D12—22no—
516C3×D12—22no—
517C3×D12—42no—
518C3×C4×D3—22no—
519C3×C4×D3—24no—
520C3×C4×D3—42no—
521C3×C4×D3—42no—
522C3×C4×D3—42no—
523C3×Dic6#4114yes—
524#627—24no—
525#627—41no—
526#627—42no—
527#626—24no—
528#626—42no—
529#626—41no—
530#625—42no—
531#625—42no—
532#625—42no—
533#624—41no—
534#624—41no—
535D3×Dic3—24no—
536D3×Dic3—24no—
537D3×Dic3—42no—
538#559—92no—
539#559—91no—
540#557—91no—
541#555—91no—
542#555—92no—
543#553—31no—
544#553—92no—
545#552—92no—
546#552—91no—
547#550—91no—
548#548—91no—
549#548—91no—
550#542—91no—
551#542—92no—
552#540—92no—
553#540—91no—
554#529—91no—
555#529—92no—
556#529—92no—
557#529—91no—
558#520—31no—
559#519—91no—
560C4×#41—91no—
561C3×#41—64no—
562C2×C3×Q8—31no—
563C2×C3×D4—32no—
564C2×C3×D4—32no—
565C2×C3×D4—31no—
566C2×C3×D4—31no—
567C2×C3×D4—31no—
568C2×C3×D4—32no—
569C22×C3×C4—21no—
570C22×C3×C4—22no—
571C22×C3×C4—32no—
572C22×C3×C4—31no—
573C22×C3×C4—32no—
574C22×C3×C4—32no—
575C22×C3×C4—32no—
576C22×C3×C4C22×D311yescharacteristic
577C22×C3×C4C22×D311yescharacteristic
578C22×C3×C4C22×D312yes—
579C22×C3×C4C22×D312yes—
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×D312yes—
594C2×#67C22×D311yescharacteristic
595C22×Dic3—32no—
596C22×Dic3—32no—
597C22×Dic3—32no—
598#239—64no—
599D3×Q8—64no—
600#237—64no—
601#235—24no—
602C2×D12—32no—
603C2×D12—31no—
604C2×D12—32no—
605C2×D12C22×D311yescharacteristic
606C2×D12C22×D311yescharacteristic
607C2×D12C22×D312yes—
608C2×C4×D3—32no—
609C2×C4×D3—32no—
610C2×C4×D3—31no—
611C2×C4×D3—31no—
612C2×C4×D3—32no—
613C2×C4×D3—31no—
614C2×C4×D3—31no—
615C2×C4×D3—31no—
616C2×C4×D3—31no—
617C2×C4×D3—61no—
618C2×C4×D3C22×D311yescharacteristic
619C2×C4×D3C22×D312yes—
620C2×C4×D3C22×D312yes—
621C2×C4×D3C22×D312yes—
622C2×C4×D3C22×D312yes—
623C2×Dic6—31no—
624C2×Dic6—31no—
625C2×Dic6—32no—
626C2×Dic6—32no—
627C2×Dic6—31no—
628C2×Dic6—32no—
629C2×Dic6—31no—
630C2×Dic6—32no—
631C2×Dic6—61no—
632C2×Dic6—64no—
633C2×Dic6C22×D311yescharacteristic
634C3×C4⋊C4—21no—
635C3×C4⋊C4—22no—
636C3×C4⋊C4—21no—
637C3×C4⋊C4—31no—
638C3×C4⋊C4—32no—
639C3×C4⋊C4—32no—
640C3×C4⋊C4—32no—
641C3×C4⋊C4—31no—
642C3×C4⋊C4—32no—
643C3×C4⋊C4—31no—
644C3×C4⋊C4—31no—
645C3×C4⋊C4C22×D311yescharacteristic
646C3×C4⋊C4C22×D311yescharacteristic
647C3×C4⋊C4C22×D311yescharacteristic
648C3×C4⋊C4C22×D312yes—
649C3×C4⋊C4C22×D312yes—
650C3×C4⋊C4C22×D311yescharacteristic
651C3×C22⋊C4—31no—
652C3×C22⋊C4—31no—
653C3×C22⋊C4—31no—
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—32no—
661C3×C42—31no—
662C3×C42—32no—
663C3×C42—32no—
664C3×C42—31no—
665C3×C42—32no—
666C3×C42—31no—
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—32no—
677#217—31no—
678#217—32no—
679#217—32no—
680#217—32no—
681#217—62no—
682#217—61no—
683#217C22×D311yescharacteristic
684#217C22×D311yescharacteristic
685#217C22×D311yescharacteristic
686(C2×D3)⋊C4—31no—
687(C2×D3)⋊C4—32no—
688(C2×D3)⋊C4—32no—
689(C2×D3)⋊C4—31no—
690(C2×D3)⋊C4—31no—
691(C2×D3)⋊C4—32no—
692(C2×D3)⋊C4—32no—
693(C2×D3)⋊C4—32no—
694(C2×D3)⋊C4—32no—
695(C2×D3)⋊C4—32no—
696(C2×D3)⋊C4—32no—
697(C2×D3)⋊C4—32no—
698(C2×D3)⋊C4—32no—
699(C2×D3)⋊C4—31no—
700(C2×D3)⋊C4—32no—
701(C2×D3)⋊C4—31no—
702(C2×D3)⋊C4—31no—
703(C2×D3)⋊C4—31no—
704(C2×D3)⋊C4—62no—
705(C2×D3)⋊C4—62no—
706(C2×D3)⋊C4—61no—
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
713(C2×D3)⋊C4C22×D312yes—
714C4⋊Dic3—31no—
715C4⋊Dic3—31no—
716C4⋊Dic3—32no—
717C4⋊Dic3—32no—
718C4⋊Dic3—32no—
719C4⋊Dic3—32no—
720C4⋊Dic3—31no—
721C4⋊Dic3—31no—
722C4⋊Dic3—31no—
723C4⋊Dic3—32no—
724C4⋊Dic3—31no—
725C4⋊Dic3—32no—
726C4⋊Dic3—32no—
727C4⋊Dic3—31no—
728C4⋊Dic3—62no—
729C4⋊Dic3—61no—
730C4⋊Dic3—62no—
731C4⋊Dic3C22×D311yescharacteristic
732C4⋊Dic3C22×D312yes—
733C4⋊Dic3C22×D311yescharacteristic
734C4⋊Dic3C22×D311yescharacteristic
735Dic3⋊C4—32no—
736Dic3⋊C4—32no—
737Dic3⋊C4—32no—
738Dic3⋊C4—32no—
739Dic3⋊C4—31no—
740Dic3⋊C4—32no—
741Dic3⋊C4—31no—
742Dic3⋊C4—32no—
743Dic3⋊C4—31no—
744Dic3⋊C4—32no—
745Dic3⋊C4—32no—
746Dic3⋊C4—32no—
747Dic3⋊C4—32no—
748Dic3⋊C4—31no—
749Dic3⋊C4—31no—
750Dic3⋊C4—31no—
751Dic3⋊C4—31no—
752Dic3⋊C4—31no—
753Dic3⋊C4—32no—
754Dic3⋊C4—31no—
755Dic3⋊C4—62no—
756Dic3⋊C4—61no—
757Dic3⋊C4—62no—
758Dic3⋊C4—62no—
759Dic3⋊C4C22×D312yes—
760Dic3⋊C4C22×D312yes—
761Dic3⋊C4C22×D312yes—
762Dic3⋊C4C22×D311yescharacteristic
763C4×Dic3—31no—
764C4×Dic3—32no—
765C4×Dic3—32no—
766C4×Dic3—31no—
767C4×Dic3—32no—
768C4×Dic3—32no—
769C4×Dic3—32no—
770C4×Dic3—32no—
771C4×Dic3—32no—
772C4×Dic3—32no—
773C4×Dic3—32no—
774C4×Dic3—32no—
775C4×Dic3—31no—
776C4×Dic3—31no—
777C4×Dic3—31no—
778C4×Dic3—31no—
779C4×Dic3—61no—
780C4×Dic3—62no—
781C4×Dic3—62no—
782C4×Dic3C22×D311yescharacteristic
783C4×Dic3C22×D312yes—
784C4×Dic3C22×D312yes—
785C4×Dic3C22×D311yescharacteristic
786C4×Dic3C22×D311yescharacteristic
787C4×Dic3C22×D312yes—
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—21no—
817C3×Dic3—21no—
818C3×Dic3—22no—
819C3×Dic3—21no—
820C3×Dic3—21no—
821C3×Dic3C2×#4114yes—
822C2×#41—31no—
823C2×#41—91no—
824C22×Q8—91no—
825C4⋊Q8—91no—
826C4⋊Q8—92no—
827#127—92no—
828#127—91no—
829#126—32no—
830#126—91no—
831#126—92no—
832#126—91no—
833#126—92no—
834#126—92no—
835#125—31no—
836#125—91no—
837#125—92no—
838#125—92no—
839#125—92no—
840#125—91no—
841#124—92no—
842#124—92no—
843#124—91no—
844#124—91no—
845#124—92no—
846#124—92no—
847#124—92no—
848#124—91no—
849#124—92no—
850#123—32no—
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—92no—
861C22⋊Q8—92no—
862C22⋊Q8—91no—
863C22⋊Q8—92no—
864C22⋊Q8—91no—
865C22⋊Q8—91no—
866#121—32no—
867#121—31no—
868#121—31no—
869#121—92no—
870#121—92no—
871#121—91no—
872#121—92no—
873#121—91no—
874#121—92no—
875#121—91no—
876#121—92no—
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—92no—
886C4×Q8—91no—
887C4×Q8—91no—
888C4×Q8—91no—
889C4×D4—32no—
890C4×D4—32no—
891C4×D4—31no—
892C4×D4—32no—
893C4×D4—31no—
894C4×D4—31no—
895C4×D4—31no—
896C4×D4—92no—
897C4×D4—91no—
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—31no—
908#117—32no—
909#117—92no—
910#117—91no—
911#117—92no—
912#117—92no—
913#117—92no—
914#117—92no—
915#117—92no—
916#117—91no—
917C2×C4⋊C4—32no—
918C2×C4⋊C4D3211yescharacteristic
919C2×C42—91no—
920C2×C42—92no—
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×D4—64no—
935C3×D4—62no—
936C3×D4—62no—
937C3×D4—122no—
938C3×D4—121no—
939C3×D4—122no—
940C2×C3×C4—22no—
941C2×C3×C4—22no—
942C2×C3×C4—21no—
943C2×C3×C4—22no—
944C2×C3×C4—21no—
945C2×C3×C4—22no—
946C2×C3×C4—32no—
947C2×C3×C4—31no—
948C2×C3×C4—31no—
949C2×C3×C4—32no—
950C2×C3×C4—31no—
951C2×C3×C4—31no—
952C2×C3×C4—31no—
953C2×C3×C4—31no—
954C2×C3×C4—31no—
955C2×C3×C4—42no—
956C2×C3×C4—42no—
957C2×C3×C4—42no—
958C2×C3×C4—44no—
959C2×C3×C4—64no—
960C2×C3×C4—62no—
961C2×C3×C4—122no—
962C2×C3×C4—122no—
963C2×C3×C4—122no—
964C2×C3×C4C23×D312yes—
965C2×C3×C4C23×D312yes—
966C2×C3×C4C23×D312yes—
967C2×C3×C4C23×D311yescharacteristic
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—122no—
977#67—121no—
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—31no—
992C2×Dic3—31no—
993C2×Dic3—32no—
994C2×Dic3—32no—
995C2×Dic3—32no—
996C2×Dic3—32no—
997C2×Dic3—61no—
998C2×Dic3—61no—
999C2×Dic3—61no—
1000C2×Dic3—62no—
1001C2×Dic3—62no—
1002C2×Dic3—64no—
1003C2×Dic3—64no—
1004C2×Dic3—122no—
1005C2×Dic3C23×D311yescharacteristic
1006C2×Dic3C23×D311yescharacteristic
1007C2×Dic3C23×D312yes—
1008C2×Dic3C23×D311yescharacteristic
1009C2×Dic3C23×D311yescharacteristic
1010C2×Dic3C23×D311yescharacteristic
1011C2×Dic3C23×D311yescharacteristic
1012C2×Dic3C23×D311yescharacteristic
1013C2×Dic3C23×D312yes—
1014D12—22no—
1015D12—22no—
1016D12—42no—
1017D12—64no—
1018D12—121no—
1019D12—122no—
1020C4×D3—22no—
1021C4×D3—24no—
1022C4×D3—42no—
1023C4×D3—42no—
1024C4×D3—42no—
1025C4×D3—64no—
1026C4×D3—64no—
1027C4×D3—62no—
1028C4×D3—62no—
1029C4×D3—122no—
1030C4×D3—121no—
1031C4×D3—121no—
1032C4×D3—121no—
1033C4×D3—121no—
1034C4×D3—122no—
1035Dic6—64no—
1036Dic6—62no—
1037Dic6—62no—
1038Dic6—64no—
1039Dic6—122no—
1040Dic6—121no—
1041Dic6—122no—
1042Dic6—122no—
1043Dic6—121no—
1044Dic6#23514yes—
1045C2×C32—41no—
1046C2×C32C22×#4111yescharacteristic
1047C2×C32#58511yescharacteristic
1048C2×C32#58511yescharacteristic
1049C3⋊D3—41no—
1050C3×D3—41no—
1051C3×D3—42no—
1052C3×D3—42no—
1053#41—64no—
1054#41—184no—
1055C2×Q8—31no—
1056C2×Q8—92no—
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—32no—
1075C22×C4—31no—
1076C22×C4—32no—
1077C22×C4—32no—
1078C22×C4—32no—
1079C22×C4—91no—
1080C22×C4—91no—
1081C22×C4—92no—
1082C22×C4—92no—
1083C22×C4—92no—
1084C22×C4—91no—
1085C22×C4C2×D3211yescharacteristic
1086C22×C4C2×D3212yes—
1087C4⋊C4—31no—
1088C4⋊C4—32no—
1089C4⋊C4—32no—
1090C4⋊C4—31no—
1091C4⋊C4—31no—
1092C4⋊C4—32no—
1093C4⋊C4—32no—
1094C4⋊C4—31no—
1095C4⋊C4—91no—
1096C4⋊C4—92no—
1097C4⋊C4—92no—
1098C4⋊C4—92no—
1099C4⋊C4—91no—
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—91no—
1110C4⋊C4—92no—
1111C4⋊C4—92no—
1112C4⋊C4C2×D3212yes—
1113C4⋊C4C2×D3211yescharacteristic
1114C4⋊C4C2×D3211yescharacteristic
1115C22⋊C4—31no—
1116C22⋊C4—31no—
1117C22⋊C4—31no—
1118C22⋊C4—32no—
1119C22⋊C4—32no—
1120C22⋊C4—32no—
1121C22⋊C4—32no—
1122C22⋊C4—31no—
1123C22⋊C4—32no—
1124C22⋊C4—32no—
1125C22⋊C4—91no—
1126C22⋊C4—91no—
1127C22⋊C4—91no—
1128C22⋊C4—92no—
1129C22⋊C4—92no—
1130C22⋊C4—92no—
1131C22⋊C4—92no—
1132C22⋊C4—92no—
1133C22⋊C4—91no—
1134C22⋊C4—92no—
1135C22⋊C4—92no—
1136C22⋊C4—91no—
1137C22⋊C4—92no—
1138C22⋊C4—92no—
1139C22⋊C4—91no—
1140C22⋊C4—92no—
1141C42—32no—
1142C42—31no—
1143C42—31no—
1144C42—32no—
1145C42—32no—
1146C42—31no—
1147C42—91no—
1148C42—91no—
1149C42—92no—
1150C42—92no—
1151C42—92no—
1152C42—92no—
1153C42—92no—
1154C42—91no—
1155C22×C3—22no—
1156C22×C3—21no—
1157C22×C3—21no—
1158C22×C3—21no—
1159C22×C3—21no—
1160C22×C3—21no—
1161C22×C3—21no—
1162C22×C3—21no—
1163C22×C3—41no—
1164C22×C3—41no—
1165C22×C3—61no—
1166C22×C3—62no—
1167C22×C3—62no—
1168C22×C3—62no—
1169C22×C3—62no—
1170C22×C3—62no—
1171C22×C3—61no—
1172C22×C3—62no—
1173C22×C3—61no—
1174C22×C3C24×D311yescharacteristic
1175C22×C3C24×D311yescharacteristic
1176C2×D3—22no—
1177C2×D3—21no—
1178C2×D3—22no—
1179C2×D3—22no—
1180C2×D3—21no—
1181C2×D3—22no—
1182C2×D3—22no—
1183C2×D3—21no—
1184C2×D3—22no—
1185C2×D3—61no—
1186C2×D3—61no—
1187C2×D3—61no—
1188C2×D3—61no—
1189C2×D3—61no—
1190C2×D3—61no—
1191C2×D3—121no—
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—41no—
1203C3×C4—42no—
1204C3×C4—42no—
1205C3×C4—61no—
1206C3×C4—61no—
1207C3×C4—61no—
1208C3×C4—61no—
1209C3×C4—61no—
1210C3×C4—61no—
1211C3×C4—61no—
1212C3×C4—62no—
1213C3×C4C2×#23512yes—
1214C3×C4D3×#4112yes—
1215Dic3—21no—
1216Dic3—21no—
1217Dic3—22no—
1218Dic3—21no—
1219Dic3—21no—
1220Dic3—21no—
1221Dic3—21no—
1222Dic3—21no—
1223Dic3—62no—
1224Dic3—61no—
1225Dic3—62no—
1226Dic3—61no—
1227Dic3—62no—
1228Dic3—61no—
1229Dic3—61no—
1230Dic3—61no—
1231Dic3—62no—
1232Dic3—61no—
1233Dic3—122no—
1234Dic3—121no—
1235Dic3—121no—
1236Dic3—122no—
1237Dic3—121no—
1238Dic3C2×#23514yes—
1239C32#352411yescharacteristic, complemented, Sylow
1240C23—31no—
1241C23—32no—
1242C23—32no—
1243C23—91no—
1244C23C22×D3211yescharacteristic
1245Q8—34no—
1246Q8—184no—
1247Q8—182no—
1248Q8—361no—
1249Q8—362no—
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—32no—
1271C2×C4—31no—
1272C2×C4—31no—
1273C2×C4—42no—
1274C2×C4—64no—
1275C2×C4—62no—
1276C2×C4—91no—
1277C2×C4—91no—
1278C2×C4—91no—
1279C2×C4—92no—
1280C2×C4—92no—
1281C2×C4—122no—
1282C2×C4—122no—
1283C2×C4—122no—
1284C2×C4—184no—
1285C2×C4—184no—
1286C2×C4—182no—
1287C2×C4—361no—
1288C2×C4—361no—
1289C2×C4—362no—
1290C2×C4C22×D3212yes—
1291C2×C4C22×D3212yes—
1292C2×C4C22×D3211yescharacteristic
1293C2×C4C22×D3211yescharacteristic
1294C2×C3—21no—
1295C2×C3—21no—
1296C2×C3—21no—
1297C2×C3—42no—
1298C2×C3—41no—
1299C2×C3—41no—
1300C2×C3—122no—
1301C2×C3—121no—
1302C2×C3—122no—
1303C2×C3C22×#23511yescharacteristic
1304C2×C3C2×D3×#4111yescharacteristic
1305C2×C3#596411yescharacteristic
1306C2×C3#596611yescharacteristic
1307C2×C3#596611yescharacteristic
1308C2×C3#596811yescharacteristic
1309D3—41no—
1310D3—42no—
1311D3—42no—
1312D3—121no—
1313D3—121no—
1314D3—241no—
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—181no—
1346C4—182no—
1347C4—181no—
1348C4D3×#23512yes—
1349C3—21no—
1350C3#8589811yescharacteristic, complemented
1351C3#8689111yescharacteristic, complemented
1352C2—41no—
1353C2—121no—
1354C2—122no—
1355C2—122no—
1356C2—361no—
1357C2C2×D3×#23511yescharacteristic
1358C2#1059667911yescharacteristic
1359C2#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. #10595984C2semidirect
2. C3×#5514C2semidirect
3. C3×#5504C2semidirect
4. #10595030C2semidirect
5. #10595026C2semidirect
6. #10595006C2semidirect
7. #10594983C2semidirect
8. #10594950C2semidirect
9. #10594934C2semidirect
10. #10594899C2semidirect
11. #10594836C2semidirect
12. #10594582C2semidirect
13. #10594555C2semidirect
14. #10594548C2semidirect
15. #10594544C2semidirect
16. #10594543C2semidirect
17. #10594496C2semidirect
18. #10594447C2semidirect
19. #10594404C2semidirect
20. #10594382C2semidirect
21. #10594360C2semidirect
22. #10594357C2semidirect
23. #10594321C2semidirect
166. #5514D3semidirect
171. #5504D3semidirect
1239. C32#3524semidirect
1350. C3#85898semidirect
1351. C3#86891semidirect

Maximal subgroups

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

subgroupindex
#105959842
C3×#55142
C3×#55042
#105950302
#105950262
#105950062
#105949832
#105949502
#105949342
#105948992
#105948362
#105945822
#105945552
#105945482
#105945442
#105945432
#105944962
#105944472
#105944042
#105943822
#105943602
#105943572
#105943212
#868913
#858983