Finite Group Databasebeta

← #11903786

Subgroups — #11903786

Order 1152.

2247 conjugacy classes of subgroups.

The subgroup lattice has 1076 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10596049C211yesmaximal, characteristic, complemented
2C3×#5578C212yesmaximal, complemented
3#10595421C211yesmaximal, characteristic, complemented
4#10595372C212yesmaximal, complemented
5#10595370C211yesmaximal, characteristic, complemented
6#10594535C212yesmaximal, complemented
7#10594396C212yesmaximal, complemented
8#10594395C212yesmaximal, complemented
9#10594378C212yesmaximal, complemented
10#10594377C211yesmaximal, characteristic, complemented
11#10594315C211yesmaximal, characteristic, complemented
12#10594314C212yesmaximal, complemented
13#10593966C211yesmaximal, characteristic
14#10593965C212yesmaximal
15#10593935C212yesmaximal, complemented
16#10593926C212yesmaximal, complemented
17#10593926C212yesmaximal, complemented
18C4×#3797C211yesmaximal, characteristic, complemented
19C4×D3×Dic6C212yesmaximal, complemented
20#86277—32nomaximal
21C2×#3798C2211yescharacteristic
22C2×#3797C2211yescharacteristic
23C2×D3×Dic6C2212yes—
24C32×C4×Q8C2211yescharacteristic
25#64155C2211yescharacteristic
26#64153C2211yescharacteristic
27#64106C2211yescharacteristic
28#64105C2212yes—
29#64098C2212yes—
30#64097C2211yescharacteristic
31#64081C2212yes—
32C42×C3⋊D3C2211yescharacteristic
33C4×#634C2212yes—
34C4×#634C2211yescharacteristic
35C3×#946C2212yes—
36C3×#944C2212yes—
37C3×#897C2212yes—
38C3×#896C2212yes—
39C3×#896C2212yes—
40C3×#889C2212yes—
41C3×#889C2212yes—
42C3×#888C2212yes—
43C3×#872C2212yes—
44C3×#872C2212yes—
45C3×C42×D3C2212yes—
46C3×C4×Dic6C2212yes—
47C3×C4×Dic6C2212yes—
48C3×C4×Dic6C2212yes—
49C4×#627C2211yescharacteristic
50C4×#627C2212yes—
51C4×#627C2211yescharacteristic
52C4×#627C2212yes—
53#63904C2212yes—
54#63904C2212yes—
55#63902C2211yescharacteristic
56#63902C2211yescharacteristic
57#63900C2211yescharacteristic
58#63899C2212yes—
59#63899C2212yes—
60#63896C2212yes—
61#63896C2212yes—
62#63895C2212yes—
63#63895C2212yes—
64#63893C2212yes—
65#63893C2212yes—
66D3×C4⋊Dic3C2212yes—
67#63888C2212yes—
68#63888C2212yes—
69#63887C2212yes—
70#63887C2212yes—
71#63883C2212yes—
72C4×#624C2212yes—
73#63881C2212yes—
74#63881C2212yes—
75#63880C2212yes—
76#63880C2212yes—
77#63879C2212yes—
78#63879C2212yes—
79D3×Dic3⋊C4C2212yes—
80D3×Dic3⋊C4C2212yes—
81C4×D3×Dic3C2212yes—
82C4×D3×Dic3C2212yes—
83#63874C2211yescharacteristic
84#63855C2212yes—
85#63847C2212yes—
86#63847C2212yes—
87#63846C2212yes—
88#63846C2212yes—
89#63845C2212yes—
90#63845C2212yes—
91#63844C2212yes—
92#63843C2212yes—
93Dic3×Dic6C2212yes—
94#63840C2212yes—
95#63840C2212yes—
96#63839C2212yes—
97#63839C2212yes—
98#63839C2212yes—
99#63839C2212yes—
100#63838C2211yescharacteristic
101#63838C2211yescharacteristic
102#63838C2211yescharacteristic
103#63838C2211yescharacteristic
104#63837C2212yes—
105#63837C2212yes—
106#63837C2212yes—
107#63837C2212yes—
108C3×#533—32no—
109#5730—32no—
110#5727—32no—
111#5722—32no—
112#5721—32no—
113#5690—32no—
114#5690—32no—
115#5685—32no—
116#5685—32no—
117#5636—32no—
118#5636—32no—
119#5636—32no—
120#5636—32no—
121#5635—32no—
122#5635—32no—
123#5632—32no—
124#5632—32no—
125#5578—32no—
126#5578—32no—
127#5578—32no—
128#5578—32no—
129#5578—32no—
130#5578—61no—
131#5578D312yescomplemented
132C4×D3×Q8—32no—
133C4×D3×Q8—32no—
134#5522—32no—
135#5522—32no—
136#5517—32no—
137#5517—32no—
138C4×#235—32no—
139C2×C4×Dic6—32no—
140C2×C32×Q8C2311yescharacteristic
141C2×C4×C3⋊D3C2311yescharacteristic
142C2×C4×C3⋊D3C2311yescharacteristic
143C2×C4×C3⋊D3C2311yescharacteristic
144C2×#634C2312yes—
145C2×#634C2311yescharacteristic
146C2×C3×C4×D3C2312yes—
147C2×C3×C4×D3C2312yes—
148C2×C3×C4×D3C2312yes—
149C2×C3×Dic6C2312yes—
150C2×C3×Dic6C2312yes—
151C2×C3×Dic6C2312yes—
152C2×#627C2312yes—
153C2×#627C2311yescharacteristic
154C2×#627C2312yes—
155C2×#627C2311yescharacteristic
156C2×#627C2311yescharacteristic
157C2×#626C2312yes—
158C2×#625C2311yescharacteristic
159C2×#624C2312yes—
160C2×#624C2312yes—
161C2×D3×Dic3C2312yes—
162C2×D3×Dic3C2312yes—
163C2×D3×Dic3C2312yes—
164C2×D3×Dic3C2312yes—
165#3798Q818yescomplemented
166#3797—24no—
167D3×Dic6—28no—
168C32×C4⋊C4C2312yes—
169C32×C4⋊C4C2311yescharacteristic
170C32×C42C2311yescharacteristic
171C32×C42C2312yes—
172#3752C2312yes—
173#3752C2312yes—
174C4⋊(C3⋊Dic3)C2311yescharacteristic
175C4⋊(C3⋊Dic3)C2312yes—
176#3750C2312yes—
177#3750C2312yes—
178#3750C2312yes—
179#3750C2312yes—
180#3750C2312yes—
181C4×C3⋊Dic3C2311yescharacteristic
182C4×C3⋊Dic3C2312yes—
183C4×C3⋊Dic3C2311yescharacteristic
184C4×C3⋊Dic3C2311yescharacteristic
185C3×(C2×D3)⋊C4C2312yes—
186C3×(C2×D3)⋊C4C2312yes—
187C3×(C2×D3)⋊C4C2312yes—
188C3×(C2×D3)⋊C4C2312yes—
189C3×C4⋊Dic3C2312yes—
190C3×C4⋊Dic3C2312yes—
191C3×C4⋊Dic3C2312yes—
192C3×Dic3⋊C4C2312yes—
193C3×Dic3⋊C4C2312yes—
194C3×Dic3⋊C4C2312yes—
195C3×Dic3⋊C4C2312yes—
196C3×Dic3⋊C4C2312yes—
197C3×Dic3⋊C4C2312yes—
198C3×Dic3⋊C4C2312yes—
199C3×Dic3⋊C4C2312yes—
200C3×Dic3⋊C4C2312yes—
201C3×Dic3⋊C4C2312yes—
202C3×C4×Dic3C2312yes—
203C3×C4×Dic3C2312yes—
204C3×C4×Dic3C2312yes—
205C3×C4×Dic3C2312yes—
206C3×C4×Dic3C2312yes—
207#3724C2311yescharacteristic
208#3724C2311yescharacteristic
209#3724C2311yescharacteristic
210#3724C2311yescharacteristic
211#3724C2312yes—
212#3724C2312yes—
213Dic3⋊Dic3C2312yes—
214Dic3⋊Dic3C2312yes—
215Dic3⋊Dic3C2312yes—
216Dic3⋊Dic3C2312yes—
217Dic3⋊Dic3C2312yes—
218Dic3⋊Dic3C2312yes—
219Dic3⋊Dic3C2312yes—
220Dic3⋊Dic3C2312yes—
221#3722C2312yes—
222(C2×D3)⋊Dic3C2312yes—
223(C2×D3)⋊Dic3C2312yes—
224Dic32C2312yes—
225Dic32C2312yes—
226Dic32C2312yes—
227Dic32C2312yes—
228Dic32C2312yes—
229Dic32C2312yes—
230Q8×#41—91noSylow
231C2×D3×Q8—32no—
232C2×D3×Q8—32no—
233C2×#235—32no—
234C22×Dic6—32no—
235C3×C4⋊Q8—32no—
236C3×C4⋊Q8—32no—
237C3×#125—32no—
238C3×#125—32no—
239C3×C22⋊Q8—32no—
240C3×C22⋊Q8—32no—
241C3×C22⋊Q8—32no—
242C3×C22⋊Q8—32no—
243C3×C4×Q8—21no—
244C3×C4×Q8—32no—
245C3×C4×Q8—32no—
246C3×C4×Q8—32no—
247C3×C4×Q8C2×D312yes—
248C3×#117—32no—
249C3×#117—32no—
250C2×C3×C42—32no—
251#946—32no—
252#946—32no—
253#946—32no—
254#946—32no—
255#946—32no—
256#946—61no—
257#946C2×D312yes—
258Q8×Dic3—32no—
259Q8×Dic3—32no—
260#944—32no—
261#944—32no—
262#944—32no—
263#944—32no—
264#944—32no—
265#944—61no—
266#944C2×D312yes—
267C4×#67—32no—
268C4×#67—32no—
269C4×#67—32no—
270C4×#67—32no—
271#926—32no—
272C2×C4⋊Dic3—32no—
273C2×Dic3⋊C4—32no—
274C2×Dic3⋊C4—32no—
275C2×C4×Dic3—32no—
276C2×C4×Dic3—32no—
277#897—32no—
278#897—32no—
279#897—32no—
280#897—32no—
281#897—32no—
282#897—61no—
283#897C2×D312yes—
284#896—32no—
285#896—32no—
286#896—32no—
287#896—32no—
288#896—32no—
289#896—32no—
290#896—32no—
291#896—32no—
292#896—32no—
293#896—32no—
294#896—62no—
295#896C2×D312yes—
296#896C2×D312yes—
297#893—32no—
298#893—32no—
299#893—32no—
300#893—32no—
301D3×C4⋊C4—32no—
302D3×C4⋊C4—32no—
303D3×C4⋊C4—32no—
304D3×C4⋊C4—32no—
305D3×C4⋊C4—32no—
306D3×C4⋊C4—32no—
307#890—32no—
308#890—32no—
309#890—32no—
310#890—32no—
311#889—32no—
312#889—32no—
313#889—32no—
314#889—32no—
315#889—32no—
316#889—32no—
317#889—32no—
318#889—32no—
319#889—32no—
320#889—32no—
321#889—62no—
322#889C2×D312yes—
323#889C2×D312yes—
324#888—32no—
325#888—32no—
326#888—32no—
327#888—32no—
328#888—32no—
329#888—32no—
330#888—32no—
331#888—32no—
332#888—32no—
333#888—61no—
334#888C2×D312yes—
335#887—32no—
336#887—32no—
337#887—32no—
338#887—32no—
339#887—32no—
340#887—32no—
341#887—32no—
342#887—32no—
343#887—32no—
344#887—32no—
345#67⋊C4—32no—
346#67⋊C4—32no—
347#67⋊C4—32no—
348#67⋊C4—32no—
349#67⋊C4—32no—
350#67⋊C4—32no—
351#67⋊C4—32no—
352#67⋊C4—32no—
353#878—32no—
354#878—32no—
355#878—32no—
356#878—32no—
357#878—32no—
358#878—32no—
359#878—32no—
360#878—32no—
361C4×D12—32no—
362C4×D12—32no—
363#872—32no—
364#872—32no—
365#872—32no—
366#872—32no—
367#872—62no—
368#872C2×D312yes—
369#872C2×D312yes—
370C42×D3—32no—
371C42×D3—32no—
372C42×D3—32no—
373C42×D3—32no—
374C42×D3—32no—
375C42×D3—61no—
376C42×D3C2×D312yes—
377C4×Dic6—32no—
378C4×Dic6—32no—
379C4×Dic6—32no—
380C4×Dic6—32no—
381C4×Dic6—32no—
382C4×Dic6—32no—
383C4×Dic6—32no—
384C4×Dic6—32no—
385C4×Dic6—32no—
386C4×Dic6—32no—
387C4×Dic6—32no—
388C4×Dic6—32no—
389C4×Dic6—32no—
390C4×Dic6—32no—
391C4×Dic6—32no—
392C4×Dic6—62no—
393C4×Dic6—61no—
394C4×Dic6C2×D312yes—
395C4×Dic6C2×D312yes—
396C4×Dic6C2×D312yes—
397C22×C3⋊D3C2411yescharacteristic
398C22×C3×D3C2412yes—
399C32×Q8—41no—
400C2×C32×C4C2412yes—
401C2×C32×C4C2412yes—
402C2×C32×C4C2411yescharacteristic
403C2×C32×C4C2411yescharacteristic
404C2×C32×C4C2411yescharacteristic
405C2×C3⋊Dic3C2411yescharacteristic
406C2×C3⋊Dic3C2412yes—
407C2×C3⋊Dic3C2412yes—
408C2×C3⋊Dic3C2411yescharacteristic
409C2×C3⋊Dic3C2411yescharacteristic
410C4×C3⋊D3—22no—
411C4×C3⋊D3—41no—
412C4×C3⋊D3C2×Q814yescomplemented
413#634—24no—
414#634—41no—
415C2×C3×Dic3C2412yes—
416C2×C3×Dic3C2412yes—
417C2×C3×Dic3C2412yes—
418C2×C3×Dic3C2412yes—
419C2×C3×Dic3C2412yes—
420C2×C3×Dic3C2412yes—
421C2×C3×Dic3C2412yes—
422C3×C4×D3—24no—
423C3×C4×D3—42no—
424C3×C4×D3C2×Q818yescomplemented
425C3×Dic6—24no—
426C3×Dic6—24no—
427C3×Dic6—42no—
428#627—22no—
429#627—24no—
430#627—42no—
431#627C2×Q814yescomplemented
432#627#4114yescomplemented
433#626C2×Q818yescomplemented
434#625C2×Q814yescomplemented
435#624—24no—
436#624—42no—
437D3×Dic3—24no—
438D3×Dic3—24no—
439D3×Dic3—42no—
440D3×Dic3—42no—
441Q82—91no—
442#557—91no—
443#557—92no—
444#554—92no—
445#554—91no—
446#554—92no—
447#554—92no—
448#554—92no—
449D4×Q8—91no—
450D4×Q8—92no—
451#533—32no—
452#533—92no—
453#533—92no—
454#533—92no—
455#533—91no—
456C4×#41—92no—
457C4×#41—91no—
458C2×C4×Q8—92no—
459C2×C4×Q8—91no—
460C2×C3×Q8—21no—
461C2×C3×Q8—32no—
462C2×C3×Q8—32no—
463C2×C3×Q8—32no—
464C2×C3×Q8C22×D312yes—
465C22×C3×C4—32no—
466C22×C3×C4—32no—
467C22×C3×C4—32no—
468C2×#67—32no—
469C2×#67—32no—
470C22×Dic3—32no—
471C22×Dic3—32no—
472C22×Dic3—32no—
473C22×Dic3—32no—
474D3×Q8—68no—
475D3×Q8—68no—
476#235—316no—
477C2×D12—32no—
478C2×C4×D3—32no—
479C2×C4×D3—32no—
480C2×C4×D3—32no—
481C2×C4×D3—32no—
482C2×C4×D3—32no—
483C2×C4×D3—32no—
484C2×C4×D3—32no—
485C2×C4×D3—32no—
486C2×C4×D3—32no—
487C2×C4×D3—32no—
488C2×C4×D3—32no—
489C2×C4×D3—61no—
490C2×C4×D3—61no—
491C2×C4×D3—61no—
492C2×C4×D3C22×D312yes—
493C2×C4×D3C22×D312yes—
494C2×C4×D3C22×D312yes—
495C2×Dic6—32no—
496C2×Dic6—32no—
497C2×Dic6—32no—
498C2×Dic6—32no—
499C2×Dic6—32no—
500C2×Dic6—32no—
501C2×Dic6—32no—
502C2×Dic6—32no—
503C2×Dic6—32no—
504C2×Dic6—32no—
505C2×Dic6—62no—
506C2×Dic6—61no—
507C2×Dic6—68no—
508C2×Dic6C22×D312yes—
509C2×Dic6C22×D312yes—
510C2×Dic6C22×D312yes—
511C3×C4⋊C4—21no—
512C3×C4⋊C4—22no—
513C3×C4⋊C4—32no—
514C3×C4⋊C4—32no—
515C3×C4⋊C4—32no—
516C3×C4⋊C4—32no—
517C3×C4⋊C4—32no—
518C3×C4⋊C4—32no—
519C3×C4⋊C4—32no—
520C3×C4⋊C4—32no—
521C3×C4⋊C4—32no—
522C3×C4⋊C4—32no—
523C3×C4⋊C4—32no—
524C3×C4⋊C4—32no—
525C3×C4⋊C4—32no—
526C3×C4⋊C4C22×D312yes—
527C3×C4⋊C4C22×D312yes—
528C3×C4⋊C4C22×D312yes—
529C3×C22⋊C4—32no—
530C3×C22⋊C4—32no—
531C3×C22⋊C4—32no—
532C3×C22⋊C4—32no—
533C3×C42—21no—
534C3×C42—22no—
535C3×C42—32no—
536C3×C42—32no—
537C3×C42—32no—
538C3×C42—32no—
539C3×C42—32no—
540C3×C42C22×D312yes—
541C3×C42C22×D312yes—
542C3×C42C22×D312yes—
543#217—32no—
544#217—32no—
545(C2×D3)⋊C4—32no—
546(C2×D3)⋊C4—32no—
547(C2×D3)⋊C4—32no—
548(C2×D3)⋊C4—32no—
549(C2×D3)⋊C4—32no—
550(C2×D3)⋊C4—32no—
551(C2×D3)⋊C4—32no—
552(C2×D3)⋊C4—32no—
553(C2×D3)⋊C4—62no—
554(C2×D3)⋊C4—62no—
555(C2×D3)⋊C4C22×D312yes—
556(C2×D3)⋊C4C22×D312yes—
557(C2×D3)⋊C4C22×D312yes—
558(C2×D3)⋊C4C22×D312yes—
559C4⋊Dic3—32no—
560C4⋊Dic3—32no—
561C4⋊Dic3—32no—
562C4⋊Dic3—32no—
563C4⋊Dic3—32no—
564C4⋊Dic3—32no—
565C4⋊Dic3—32no—
566C4⋊Dic3—32no—
567C4⋊Dic3—32no—
568C4⋊Dic3—32no—
569C4⋊Dic3—32no—
570C4⋊Dic3—61no—
571C4⋊Dic3—62no—
572C4⋊Dic3C22×D312yes—
573C4⋊Dic3C22×D312yes—
574C4⋊Dic3C22×D312yes—
575Dic3⋊C4—32no—
576Dic3⋊C4—32no—
577Dic3⋊C4—32no—
578Dic3⋊C4—32no—
579Dic3⋊C4—32no—
580Dic3⋊C4—32no—
581Dic3⋊C4—32no—
582Dic3⋊C4—32no—
583Dic3⋊C4—32no—
584Dic3⋊C4—32no—
585Dic3⋊C4—32no—
586Dic3⋊C4—32no—
587Dic3⋊C4—32no—
588Dic3⋊C4—32no—
589Dic3⋊C4—32no—
590Dic3⋊C4—32no—
591Dic3⋊C4—32no—
592Dic3⋊C4—32no—
593Dic3⋊C4—32no—
594Dic3⋊C4—32no—
595Dic3⋊C4—32no—
596Dic3⋊C4—32no—
597Dic3⋊C4—32no—
598Dic3⋊C4—32no—
599Dic3⋊C4—32no—
600Dic3⋊C4—32no—
601Dic3⋊C4—62no—
602Dic3⋊C4—62no—
603Dic3⋊C4—62no—
604Dic3⋊C4—62no—
605Dic3⋊C4—62no—
606Dic3⋊C4C22×D312yes—
607Dic3⋊C4C22×D312yes—
608Dic3⋊C4C22×D312yes—
609Dic3⋊C4C22×D312yes—
610Dic3⋊C4C22×D312yes—
611Dic3⋊C4C22×D312yes—
612Dic3⋊C4C22×D312yes—
613Dic3⋊C4C22×D312yes—
614Dic3⋊C4C22×D312yes—
615Dic3⋊C4C22×D312yes—
616C4×Dic3—32no—
617C4×Dic3—32no—
618C4×Dic3—32no—
619C4×Dic3—32no—
620C4×Dic3—32no—
621C4×Dic3—32no—
622C4×Dic3—32no—
623C4×Dic3—32no—
624C4×Dic3—32no—
625C4×Dic3—32no—
626C4×Dic3—32no—
627C4×Dic3—32no—
628C4×Dic3—32no—
629C4×Dic3—32no—
630C4×Dic3—32no—
631C4×Dic3—32no—
632C4×Dic3—32no—
633C4×Dic3—61no—
634C4×Dic3—62no—
635C4×Dic3—61no—
636C4×Dic3—61no—
637C4×Dic3C22×D312yes—
638C4×Dic3C22×D312yes—
639C4×Dic3C22×D312yes—
640C4×Dic3C22×D312yes—
641C4×Dic3C22×D312yes—
642C22×C32C2511yescharacteristic
643C2×C3⋊D3—21no—
644C2×C3⋊D3—21no—
645C2×C3⋊D3C22×Q812yes—
646C2×C3×D3—22no—
647C2×C3×D3—22no—
648C2×C3×D3C22×Q814yes—
649C32×C4—21no—
650C32×C4—21no—
651C32×C4—22no—
652C32×C4—22no—
653C32×C4C22×Q812yes—
654C3⋊Dic3—22no—
655C3⋊Dic3—21no—
656C3⋊Dic3—22no—
657C3⋊Dic3C22×Q812yes—
658C3⋊Dic3C2×#4112yes—
659C3×Dic3—22no—
660C3×Dic3—22no—
661C3×Dic3—22no—
662C3×Dic3—22no—
663C3×Dic3—22no—
664C3×Dic3C22×Q814yes—
665C3×Dic3C2×#4114yes—
666C2×#41—91no—
667C22×Q8—92no—
668C22×Q8—91no—
669C4⋊Q8—32no—
670C4⋊Q8—32no—
671C4⋊Q8—92no—
672C4⋊Q8—92no—
673C4⋊Q8—92no—
674C4⋊Q8—92no—
675C4⋊Q8—92no—
676C4⋊Q8—92no—
677C4⋊Q8—91no—
678C4⋊Q8—91no—
679#125—32no—
680#125—32no—
681#125—92no—
682#125—92no—
683#125—92no—
684#125—92no—
685#125—92no—
686#125—92no—
687#125—92no—
688C22⋊Q8—32no—
689C22⋊Q8—32no—
690C22⋊Q8—32no—
691C22⋊Q8—32no—
692C22⋊Q8—92no—
693C22⋊Q8—92no—
694C22⋊Q8—92no—
695C22⋊Q8—92no—
696C22⋊Q8—92no—
697C22⋊Q8—92no—
698C22⋊Q8—92no—
699C22⋊Q8—92no—
700C22⋊Q8—92no—
701C22⋊Q8—92no—
702C22⋊Q8—92no—
703C22⋊Q8—92no—
704C22⋊Q8—91no—
705C22⋊Q8—92no—
706C22⋊Q8—91no—
707C4×Q8—32no—
708C4×Q8—32no—
709C4×Q8—32no—
710C4×Q8—91no—
711C4×Q8—92no—
712C4×Q8—91no—
713C4×Q8—92no—
714C4×Q8—92no—
715C4×Q8—92no—
716C4×Q8—92no—
717C4×Q8—92no—
718C4×Q8—92no—
719C4×Q8—92no—
720C4×Q8—91no—
721C4×Q8—91no—
722C4×Q8—91no—
723C4×Q8—91no—
724C4×Q8—92no—
725C4×Q8—92no—
726C4×Q8—91no—
727C4×Q8D3211yescharacteristic
728C4×D4—92no—
729C4×D4—92no—
730C4×D4—91no—
731C4×D4—91no—
732C4×D4—92no—
733C4×D4—92no—
734C4×D4—92no—
735C4×D4—92no—
736C4×D4—92no—
737C4×D4—92no—
738#117—32no—
739#117—32no—
740#117—91no—
741#117—92no—
742#117—92no—
743C2×C4⋊C4—92no—
744C2×C4⋊C4—91no—
745C2×C4⋊C4—92no—
746C2×C4⋊C4—92no—
747C2×C4⋊C4—92no—
748C2×C42—32no—
749C2×C42—92no—
750C2×C42—92no—
751C2×C42—92no—
752C2×C42—91no—
753C23×C3—32no—
754C22×D3—32no—
755C22×D3—61no—
756C22×D3C23×D312yes—
757C3×Q8—42no—
758C3×Q8—42no—
759C3×Q8—64no—
760C3×Q8—64no—
761C3×Q8—122no—
762C2×C3×C4—21no—
763C2×C3×C4—21no—
764C2×C3×C4—22no—
765C2×C3×C4—22no—
766C2×C3×C4—21no—
767C2×C3×C4—32no—
768C2×C3×C4—32no—
769C2×C3×C4—38no—
770C2×C3×C4—32no—
771C2×C3×C4—32no—
772C2×C3×C4—32no—
773C2×C3×C4—32no—
774C2×C3×C4—32no—
775C2×C3×C4—64no—
776C2×C3×C4—122no—
777C2×C3×C4C23×D312yes—
778C2×C3×C4C23×D312yes—
779C2×C3×C4C23×D312yes—
780C2×C3×C4C23×D312yes—
781C2×C3×C4C23×D312yes—
782C2×C3×C4C23×D312yes—
783C2×C3×C4C23×D312yes—
784#67—38no—
785#67—38no—
786C2×Dic3—32no—
787C2×Dic3—32no—
788C2×Dic3—32no—
789C2×Dic3—32no—
790C2×Dic3—32no—
791C2×Dic3—32no—
792C2×Dic3—32no—
793C2×Dic3—61no—
794C2×Dic3—61no—
795C2×Dic3—61no—
796C2×Dic3—62no—
797C2×Dic3—62no—
798C2×Dic3—64no—
799C2×Dic3—64no—
800C2×Dic3—122no—
801C2×Dic3—122no—
802C2×Dic3C23×D312yes—
803C2×Dic3C23×D312yes—
804C2×Dic3C23×D312yes—
805C2×Dic3C23×D312yes—
806C2×Dic3C23×D312yes—
807C2×Dic3C23×D312yes—
808C2×Dic3C23×D312yes—
809D12—38no—
810C4×D3—24no—
811C4×D3—38no—
812C4×D3—42no—
813C4×D3—64no—
814C4×D3—64no—
815C4×D3—64no—
816C4×D3—64no—
817C4×D3—64no—
818C4×D3—64no—
819C4×D3—122no—
820C4×D3—122no—
821C4×D3—122no—
822C4×D3—122no—
823C4×D3—122no—
824C4×D3—122no—
825C4×D3—122no—
826C4×D3D3×Q818yescomplemented
827Dic6—24no—
828Dic6—24no—
829Dic6—38no—
830Dic6—38no—
831Dic6—42no—
832Dic6—64no—
833Dic6—64no—
834Dic6—64no—
835Dic6—64no—
836Dic6—64no—
837Dic6—124no—
838Dic6—122no—
839Dic6—122no—
840Dic6—122no—
841Dic6—122no—
842C2×C32C23×Q811yescharacteristic
843C2×C32C22×#4111yescharacteristic
844C2×C32#58511yescharacteristic
845C3⋊D3—22no—
846C3×D3—24no—
847#41—98no—
848C2×Q8—32no—
849C2×Q8—32no—
850C2×Q8—32no—
851C2×Q8—91no—
852C2×Q8—91no—
853C2×Q8—92no—
854C2×Q8—91no—
855C2×Q8—92no—
856C2×Q8—92no—
857C2×Q8—91no—
858C2×Q8—188no—
859C2×Q8—184no—
860C2×Q8C2×D3211yescharacteristic
861C2×D4—92no—
862C2×D4—91no—
863C22×C4—32no—
864C22×C4—32no—
865C22×C4—32no—
866C22×C4—92no—
867C22×C4—92no—
868C22×C4—92no—
869C22×C4—92no—
870C22×C4—92no—
871C22×C4—92no—
872C22×C4—91no—
873C22×C4—91no—
874C22×C4—91no—
875C4⋊C4—32no—
876C4⋊C4—32no—
877C4⋊C4—32no—
878C4⋊C4—32no—
879C4⋊C4—32no—
880C4⋊C4—32no—
881C4⋊C4—32no—
882C4⋊C4—32no—
883C4⋊C4—32no—
884C4⋊C4—32no—
885C4⋊C4—32no—
886C4⋊C4—32no—
887C4⋊C4—32no—
888C4⋊C4—91no—
889C4⋊C4—92no—
890C4⋊C4—92no—
891C4⋊C4—92no—
892C4⋊C4—92no—
893C4⋊C4—91no—
894C4⋊C4—92no—
895C4⋊C4—91no—
896C4⋊C4—91no—
897C4⋊C4—92no—
898C4⋊C4—92no—
899C4⋊C4—92no—
900C4⋊C4—92no—
901C4⋊C4—92no—
902C4⋊C4—92no—
903C4⋊C4—92no—
904C4⋊C4—92no—
905C4⋊C4—92no—
906C4⋊C4—92no—
907C4⋊C4—92no—
908C4⋊C4—91no—
909C4⋊C4C2×D3211yescharacteristic
910C4⋊C4C2×D3212yes—
911C22⋊C4—32no—
912C22⋊C4—32no—
913C22⋊C4—32no—
914C22⋊C4—32no—
915C22⋊C4—92no—
916C22⋊C4—92no—
917C22⋊C4—92no—
918C22⋊C4—92no—
919C22⋊C4—92no—
920C42—32no—
921C42—32no—
922C42—32no—
923C42—32no—
924C42—32no—
925C42—92no—
926C42—92no—
927C42—92no—
928C42—92no—
929C42—92no—
930C42—92no—
931C42—91no—
932C42—91no—
933C42—91no—
934C42—92no—
935C42C2×D3212yes—
936C42C2×D3211yescharacteristic
937C22×C3—21no—
938C22×C3—34no—
939C22×C3—62no—
940C22×C3—62no—
941C22×C3C24×D312yes—
942C2×D3—22no—
943C2×D3—22no—
944C2×D3—34no—
945C2×D3—62no—
946C2×D3—62no—
947C2×D3—62no—
948C2×D3—121no—
949C2×D3—121no—
950C2×D3C2×D3×Q814yes—
951C3×C4—22no—
952C3×C4—22no—
953C3×C4—22no—
954C3×C4—22no—
955C3×C4—22no—
956C3×C4—22no—
957C3×C4—22no—
958C3×C4—22no—
959C3×C4—34no—
960C3×C4—34no—
961C3×C4—42no—
962C3×C4—41no—
963C3×C4—42no—
964C3×C4—62no—
965C3×C4—62no—
966C3×C4—62no—
967C3×C4—62no—
968C3×C4—62no—
969C3×C4C2×D3×Q814yes—
970Dic3—22no—
971Dic3—22no—
972Dic3—22no—
973Dic3—22no—
974Dic3—22no—
975Dic3—34no—
976Dic3—34no—
977Dic3—62no—
978Dic3—62no—
979Dic3—62no—
980Dic3—62no—
981Dic3—62no—
982Dic3—62no—
983Dic3—62no—
984Dic3—122no—
985Dic3—122no—
986Dic3—121no—
987Dic3C2×D3×Q814yes—
988Dic3D3×#4114yes—
989C32Q8×#4111yescharacteristic, complemented, Sylow
990C23—32no—
991C23—91no—
992Q8—41no—
993Q8—64no—
994Q8—64no—
995Q8—94no—
996Q8—94no—
997Q8—122no—
998Q8—184no—
999Q8—184no—
1000Q8—182no—
1001Q8—361no—
1002Q8—362no—
1003D4—98no—
1004D4—94no—
1005C2×C4—32no—
1006C2×C4—32no—
1007C2×C4—38no—
1008C2×C4—32no—
1009C2×C4—32no—
1010C2×C4—32no—
1011C2×C4—32no—
1012C2×C4—32no—
1013C2×C4—64no—
1014C2×C4—91no—
1015C2×C4—91no—
1016C2×C4—94no—
1017C2×C4—91no—
1018C2×C4—92no—
1019C2×C4—92no—
1020C2×C4—122no—
1021C2×C4—182no—
1022C2×C4—184no—
1023C2×C4—184no—
1024C2×C4—184no—
1025C2×C4—361no—
1026C2×C4—362no—
1027C2×C4—362no—
1028C2×C4—362no—
1029C2×C4C22×D3212yes—
1030C2×C4C22×D3212yes—
1031C2×C4C22×D3211yescharacteristic
1032C2×C4C22×D3211yescharacteristic
1033C2×C4C22×D3211yescharacteristic
1034C2×C3—21no—
1035C2×C3—21no—
1036C2×C3—21no—
1037C2×C3—64no—
1038C2×C3C22×D3×Q812yes—
1039C2×C3C2×D3×#4112yes—
1040C2×C3#596412yes—
1041D3—24no—
1042D3—64no—
1043D3—122no—
1044C22—34no—
1045C22—62no—
1046C22—62no—
1047C22—92no—
1048C22—181no—
1049C22—181no—
1050C22C23×D3211yescharacteristic
1051C4—22no—
1052C4—21no—
1053C4—22no—
1054C4—21no—
1055C4—34no—
1056C4—34no—
1057C4—62no—
1058C4—62no—
1059C4—62no—
1060C4—62no—
1061C4—62no—
1062C4—92no—
1063C4—92no—
1064C4—181no—
1065C4—182no—
1066C4—182no—
1067C4D32×Q812yes—
1068C3—21no—
1069C3#8627712yescomplemented
1070C2—64no—
1071C2—182no—
1072C2#1059666911yescharacteristic
1073C2C2×D32×Q811yescharacteristic
1074C2D32×#4111yescharacteristic
subgroupG/H
centerC2×C4C22×D32
commutator, socle, cosocleC22×C32C25
FrattiniC22C23×D32
FittingC32×C4×Q8C22
prime radicalC2×#3798C22
hypercenterC4×Q8D32
hypocenterC32Q8×#41
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ C4×Q8

Complements

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

NH ≅ G/Ntype
1. #10596049C2semidirect
2. C3×#5578C2semidirect
3. #10595421C2semidirect
4. #10595372C2semidirect
5. #10595370C2semidirect
6. #10594535C2semidirect
7. #10594396C2semidirect
8. #10594395C2semidirect
9. #10594378C2semidirect
10. #10594377C2semidirect
11. #10594315C2semidirect
12. #10594314C2semidirect
15. #10593935C2semidirect
16. #10593926C2semidirect
17. #10593926C2semidirect
18. C4×#3797C2semidirect
19. C4×D3×Dic6C2semidirect
131. #5578D3semidirect
165. #3798Q8semidirect
412. C4×C3⋊D3C2×Q8semidirect
424. C3×C4×D3C2×Q8semidirect
431. #627C2×Q8semidirect
432. #627#41semidirect
433. #626C2×Q8semidirect
434. #625C2×Q8semidirect
826. C4×D3D3×Q8semidirect
989. C32Q8×#41semidirect
1069. C3#86277semidirect

Maximal subgroups

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

subgroupindex
#105960492
C3×#55782
#105954212
#105953722
#105953702
#105945352
#105943962
#105943952
#105943782
#105943772
#105943152
#105943142
#105939662
#105939652
#105939352
#105939262
C4×#37972
C4×D3×Dic62
#862773