Finite Group Databasebeta

← #11903085

Subgroups — #11903085

Order 1152.

2409 conjugacy classes of subgroups.

The subgroup lattice has 885 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3⋊D3×C22⋊Q8C211yesmaximal, characteristic, complemented
2C3×#5639C212yesmaximal, complemented
3#10595429C211yesmaximal, characteristic, complemented
4#10595379C212yesmaximal, complemented
5Q8×#624C211yesmaximal, characteristic, complemented
6C4×#3811C211yesmaximal, characteristic
7#10594969C211yesmaximal, characteristic, complemented
8#10594939C212yesmaximal, complemented
9#10594602C212yesmaximal, complemented
10D32×C4⋊C4C211yesmaximal, characteristic, complemented
11#10594553C212yesmaximal, complemented
12#10594482C211yesmaximal, characteristic, complemented
13#10594408C214yesmaximal, complemented
14#10594399C212yesmaximal, complemented
15#10594260C212yesmaximal
16#10594154C212yesmaximal, complemented
17#10594116C214yesmaximal, complemented
18D3×#552—32nomaximal
19C2×Q8×C3⋊D3C2211yescharacteristic
20C22×C4×C3⋊D3C2211yescharacteristic
21C2×#3811C2211yescharacteristic
22C2×C4×D32C2212yes—
23C2×C4×D32C2211yescharacteristic
24C32×C22⋊Q8C2211yescharacteristic, complemented
25#64155C2211yescharacteristic, complemented
26#64133C2211yescharacteristic, complemented
27#64106C2211yescharacteristic, complemented
28#64105C2212yescomplemented
29C4⋊C4×C3⋊D3C2211yescharacteristic
30C4⋊C4×C3⋊D3C2212yes—
31C22⋊C4×C3⋊D3C2212yes—
32#64087C2212yescomplemented
33C3×#946C2212yescomplemented
34C3×Q8×Dic3C2212yescomplemented
35C3×C4×#67C2212yes—
36C3×#926C2212yescomplemented
37C3×#892C2214yescomplemented
38C3×D3×C4⋊C4C2212yescomplemented
39C3×#890C2212yescomplemented
40C3×#889C2214yescomplemented
41C3×#883C2214yes—
42C3×#879C2214yescomplemented
43#63974C2211yescharacteristic
44#63974C2212yes—
45#67⋊Dic3C2212yes—
46#63969C2214yes—
47#63957C2212yescomplemented
48#63956C2214yescomplemented
49#63921C2211yescharacteristic
50#63921C2212yes—
51C4×#626C2212yes—
52#63900C2211yescharacteristic
53#63900C2212yes—
54#63900C2212yes—
55#63900C2211yescharacteristic
56#63896C2214yescomplemented
57#63890C2214yes—
58D3×C4⋊Dic3C2212yescomplemented
59#63883C2212yes—
60#63883C2211yescharacteristic
61#63883C2212yes—
62#63883C2212yes—
63C4×#624C2212yes—
64C4×#624C2212yes—
65C4×#624C2211yescharacteristic
66#63881C2212yes—
67#63877C2214yescomplemented
68#63877C2214yescomplemented
69D3×Dic3⋊C4C2214yescomplemented
70#63874C2212yescomplemented
71#63869C2212yescomplemented
72#63868C2214yescomplemented
73#63867C2214yescomplemented
74#63857C2212yescomplemented
75#63850C2214yes—
76#63849C2212yescomplemented
77#63848C2214yescomplemented
78#63847C2214yescomplemented
79#63846C2214yescomplemented
80#63845C2214yescomplemented
81#63844C2214yescomplemented
82#63844C2212yescomplemented
83#63841C2214yescomplemented
84C3×#552—32no—
85#5708—34no—
86D3×#126—34no—
87#5694—32no—
88#5693—34no—
89D3×#125—32no—
90D3×#125—34no—
91D3×#123—34no—
92#5650—34no—
93#5642—32no—
94#5639D312yescomplemented
95D3×C22⋊Q8—32no—
96D3×C22⋊Q8—32no—
97D3×C22⋊Q8—61no—
98#5581—32no—
99C4×D3×Q8—32no—
100C4×D3×D4—32no—
101#5541—32no—
102#5531—34no—
103#5529—32no—
104D3×#117—32no—
105D3×#117—34no—
106#5513—32no—
107C2×D3×C4⋊C4—32no—
108C23×C3⋊D3C2311yescharacteristic
109C22×D32C2311yescharacteristic
110C2×C32×Q8C2311yescharacteristic
111C22×C32×C4C2311yescharacteristic
112C22×C3⋊Dic3C2311yescharacteristic
113Q8×C3⋊D3—24no—
114C2×C4×C3⋊D3—24no—
115C2×C4×C3⋊D3C2312yes—
116C2×C4×C3⋊D3C2312yes—
117C2×C4×C3⋊D3C2311yescharacteristic
118C2×C4×C3⋊D3C2311yescharacteristic
119C2×C4×C3⋊D3C2311yescharacteristic
120C2×C4×C3⋊D3C2311yescharacteristic
121C2×#634C2312yes—
122C2×#634C2311yescharacteristic
123C2×C3×#67C2312yes—
124C2×C3×C4×D3C2314yes—
125C2×C3×C4×D3C2312yes—
126#3811—24no—
127C2×#626C2312yes—
128C2×#624C2312yes—
129C2×#624C2311yescharacteristic
130C2×#624C2311yescharacteristic
131C2×#624C2311yescharacteristic
132C2×#624C2312yes—
133C2×D3×Dic3C2312yes—
134C2×D3×Dic3C2314yes—
135C4×D32—28no—
136C4×D32—24no—
137C32×C4⋊C4C2312yes—
138C32×C4⋊C4C2311yescharacteristic
139C32×C22⋊C4C2312yes—
140#3757C2312yes—
141#3752C2312yes—
142#3752C2312yes—
143C4⋊(C3⋊Dic3)C2312yes—
144C4⋊(C3⋊Dic3)C2311yescharacteristic
145#3750C2312yes—
146#3750C2312yes—
147#3750C2312yes—
148C3×#217C2312yes—
149C3×#217C2314yes—
150C3×(C2×D3)⋊C4C2314yes—
151C3×(C2×D3)⋊C4C2312yes—
152C3×C4⋊Dic3C2314yes—
153C3×C4⋊Dic3C2314yes—
154C3×C4⋊Dic3C2312yes—
155C3×C4⋊Dic3C2312yes—
156C3×Dic3⋊C4C2314yes—
157C3×Dic3⋊C4C2314yes—
158C3×Dic3⋊C4C2314yes—
159C3×Dic3⋊C4C2312yes—
160C3×C4×Dic3C2314yes—
161C3×C4×Dic3C2314yes—
162C3×C4×Dic3C2312yes—
163#3724C2314yes—
164#3724C2312yes—
165#3724C2312yes—
166#3724C2314yes—
167Dic3⋊Dic3C2312yes—
168Dic3⋊Dic3C2314yes—
169Dic3⋊Dic3C2314yes—
170Dic3⋊Dic3C2314yes—
171#3722C2312yes—
172#3722C2314yes—
173(C2×D3)⋊Dic3C2312yes—
174(C2×D3)⋊Dic3C2314yes—
175Dic32C2314yes—
176Dic32C2314yes—
177Dic32C2312yes—
178C2×#552—91noSylow
179C2×D3×Q8—32no—
180C2×D3×Q8—61no—
181C2×D3×D4—32no—
182C22×C4×D3—32no—
183C22×C4×D3—34no—
184C22×C4×D3—32no—
185C22×C4×D3—61no—
186C3×#126—34no—
187C3×#125—34no—
188C3×#125—32no—
189C3×#123—34no—
190C3×C22⋊Q8—21no—
191C3×C22⋊Q8—32no—
192C3×C22⋊Q8C2×D312yescomplemented
193C3×C4×Q8—32no—
194C3×C4×D4—32no—
195C3×#117—32no—
196C3×#117—34no—
197C2×C3×C4⋊C4—32no—
198#946—32no—
199#946—61no—
200#946C2×D312yescomplemented
201Q8×Dic3C2×D312yescomplemented
202#935—34no—
203D4×Dic3—32no—
204#929—34no—
205C4×#67—32no—
206C4×#67C2×D312yes—
207#926—34no—
208#926C2×D312yescomplemented
209C2×C4⋊Dic3—32no—
210#924—32no—
211#924—32no—
212#924—61no—
213C2×Dic3⋊C4—34no—
214#898—34no—
215#898—34no—
216#898—34no—
217#897—32no—
218#897—32no—
219#897—61no—
220#896—34no—
221#896—34no—
222#896—62no—
223#894—34no—
224#894—34no—
225#893—32no—
226#892—34no—
227#892—32no—
228#892—32no—
229#892C2×D314yescomplemented
230D3×C4⋊C4—34no—
231D3×C4⋊C4—32no—
232D3×C4⋊C4—32no—
233D3×C4⋊C4—34no—
234D3×C4⋊C4—34no—
235D3×C4⋊C4—34no—
236D3×C4⋊C4—32no—
237D3×C4⋊C4—32no—
238D3×C4⋊C4—34no—
239D3×C4⋊C4—32no—
240D3×C4⋊C4—34no—
241D3×C4⋊C4—34no—
242D3×C4⋊C4—61no—
243D3×C4⋊C4—62no—
244D3×C4⋊C4C2×D312yescomplemented
245#890—34no—
246#890—34no—
247#890—32no—
248#890C2×D312yescomplemented
249#889—34no—
250#889—34no—
251#889—34no—
252#889—34no—
253#889—34no—
254#889C2×D314yescomplemented
255#887—34no—
256#887—32no—
257#886—34no—
258#883—34no—
259#883C2×D314yes—
260#67⋊C4—32no—
261#67⋊C4—32no—
262D3×C22⋊C4—34no—
263D3×C22⋊C4—34no—
264D3×C22⋊C4—32no—
265D3×C22⋊C4—34no—
266D3×C22⋊C4—32no—
267D3×C22⋊C4—62no—
268#879—34no—
269#879—34no—
270#879C2×D314yescomplemented
271#878—34no—
272#878—34no—
273#878—62no—
274#877—34no—
275#877—34no—
276#877—34no—
277#876—34no—
278C4×D12—32no—
279#872—34no—
280#872—34no—
281#872—34no—
282C42×D3—34no—
283C42×D3—32no—
284C42×D3—34no—
285#870—32no—
286#870—34no—
287C4×Dic6—32no—
288C4×Dic6—34no—
289C23×C32C2411yescharacteristic
290C22×C3⋊D3—22no—
291C22×C3⋊D3—22no—
292C22×C3⋊D3—22no—
293C22×C3⋊D3C2411yescharacteristic
294C22×C3⋊D3C2411yescharacteristic
295C22×C3×D3C2412yes—
296C2×D32—22no—
297C2×D32—22no—
298C2×D32#4114yes—
299C32×Q8—22no—
300C2×C32×C4—22no—
301C2×C32×C4C2411yescharacteristic
302C2×C32×C4C2412yes—
303C2×C32×C4C2412yes—
304C2×C32×C4C2411yescharacteristic
305C2×C3⋊Dic3—22no—
306C2×C3⋊Dic3C2411yescharacteristic
307C2×C3⋊Dic3C2412yes—
308C2×C3⋊Dic3C2412yes—
309C2×C3⋊Dic3C2411yescharacteristic
310C4×C3⋊D3—24no—
311C4×C3⋊D3—22no—
312C4×C3⋊D3—24no—
313C4×C3⋊D3—22no—
314C4×C3⋊D3—22no—
315C4×C3⋊D3#4114yes—
316#634—22no—
317#634—24no—
318C3×#67—24no—
319C2×C3×Dic3C2412yes—
320C2×C3×Dic3C2414yes—
321C2×C3×Dic3C2414yes—
322C2×C3×Dic3C2412yes—
323C2×C3×Dic3C2412yes—
324C3×C4×D3—28no—
325C3×C4×D3—24no—
326#626—24no—
327#624—24no—
328#624—22no—
329#624—22no—
330#624—22no—
331#624—24no—
332D3×Dic3—28no—
333D3×Dic3—24no—
334#552—32no—
335#552—92no—
336#552—92no—
337#552—94no—
338#552—92no—
339#552—94no—
340C2×#126—92no—
341C2×#125—92no—
342C2×#125—91no—
343C2×#123—92no—
344C2×C22⋊Q8—91no—
345C2×C22⋊Q8—91no—
346C2×C4×Q8—91no—
347C2×C4×D4—91no—
348C2×#117—91no—
349C2×#117—92no—
350C22×C4⋊C4—91no—
351C23×D3—32no—
352C23×D3—32no—
353C23×D3—61no—
354C2×C3×Q8—21no—
355C2×C3×Q8C22×D312yes—
356C2×C3×D4—32no—
357C22×C3×C4—21no—
358C22×C3×C4—34no—
359C22×C3×C4—32no—
360C22×C3×C4C22×D312yes—
361C2×#67—32no—
362C2×#67C22×D312yes—
363C22×Dic3—32no—
364C22×Dic3—34no—
365C22×Dic3—32no—
366C22×Dic3—61no—
367D3×Q8—68no—
368D3×Q8—124no—
369D3×D4—68no—
370C2×D12—32no—
371C2×C4×D3—32no—
372C2×C4×D3—34no—
373C2×C4×D3—32no—
374C2×C4×D3—32no—
375C2×C4×D3—34no—
376C2×C4×D3—32no—
377C2×C4×D3—32no—
378C2×C4×D3—34no—
379C2×C4×D3—32no—
380C2×C4×D3—34no—
381C2×C4×D3—34no—
382C2×C4×D3—32no—
383C2×C4×D3—32no—
384C2×C4×D3—61no—
385C2×C4×D3—62no—
386C2×C4×D3—62no—
387C2×C4×D3—61no—
388C2×C4×D3—61no—
389C2×C4×D3—61no—
390C2×C4×D3—68no—
391C2×C4×D3—616no—
392C2×C4×D3—68no—
393C2×C4×D3—124no—
394C2×C4×D3C22×D312yes—
395C2×C4×D3C22×D314yes—
396C2×Dic6—34no—
397C2×Dic6—32no—
398C2×Dic6—62no—
399C2×Dic6—61no—
400C3×C4⋊C4—22no—
401C3×C4⋊C4—21no—
402C3×C4⋊C4—34no—
403C3×C4⋊C4—32no—
404C3×C4⋊C4—32no—
405C3×C4⋊C4—34no—
406C3×C4⋊C4—34no—
407C3×C4⋊C4—34no—
408C3×C4⋊C4—32no—
409C3×C4⋊C4—34no—
410C3×C4⋊C4C22×D314yes—
411C3×C4⋊C4C22×D312yes—
412C3×C22⋊C4—22no—
413C3×C22⋊C4—34no—
414C3×C22⋊C4—32no—
415C3×C22⋊C4—32no—
416C3×C22⋊C4—34no—
417C3×C22⋊C4C22×D314yes—
418C3×C42—32no—
419C3×C42—34no—
420C3×C42—34no—
421#217—34no—
422#217—32no—
423#217—34no—
424#217—62no—
425#217C22×D314yes—
426#217C22×D312yes—
427(C2×D3)⋊C4—32no—
428(C2×D3)⋊C4—34no—
429(C2×D3)⋊C4—34no—
430(C2×D3)⋊C4—34no—
431(C2×D3)⋊C4—34no—
432(C2×D3)⋊C4—34no—
433(C2×D3)⋊C4—32no—
434(C2×D3)⋊C4—32no—
435(C2×D3)⋊C4—62no—
436(C2×D3)⋊C4—62no—
437(C2×D3)⋊C4C22×D312yes—
438(C2×D3)⋊C4C22×D314yes—
439C4⋊Dic3—32no—
440C4⋊Dic3—34no—
441C4⋊Dic3—34no—
442C4⋊Dic3—34no—
443C4⋊Dic3—32no—
444C4⋊Dic3—34no—
445C4⋊Dic3—62no—
446C4⋊Dic3—61no—
447C4⋊Dic3C22×D314yes—
448C4⋊Dic3C22×D312yes—
449C4⋊Dic3C22×D312yes—
450C4⋊Dic3C22×D314yes—
451Dic3⋊C4—34no—
452Dic3⋊C4—34no—
453Dic3⋊C4—34no—
454Dic3⋊C4—34no—
455Dic3⋊C4—34no—
456Dic3⋊C4—34no—
457Dic3⋊C4—34no—
458Dic3⋊C4—34no—
459Dic3⋊C4—34no—
460Dic3⋊C4—34no—
461Dic3⋊C4—34no—
462Dic3⋊C4—34no—
463Dic3⋊C4—32no—
464Dic3⋊C4—62no—
465Dic3⋊C4—62no—
466Dic3⋊C4—62no—
467Dic3⋊C4C22×D312yes—
468Dic3⋊C4C22×D314yes—
469Dic3⋊C4C22×D314yes—
470Dic3⋊C4C22×D314yes—
471C4×Dic3—34no—
472C4×Dic3—32no—
473C4×Dic3—34no—
474C4×Dic3—34no—
475C4×Dic3—34no—
476C4×Dic3—32no—
477C4×Dic3C22×D314yes—
478C4×Dic3C22×D314yes—
479C4×Dic3C22×D312yes—
480C22×C32—21no—
481C22×C32—21no—
482C22×C32—21no—
483C22×C32C2511yescharacteristic
484C2×C3⋊D3—21no—
485C2×C3⋊D3—21no—
486C2×C3⋊D3—21no—
487C2×C3⋊D3—44no—
488C2×C3⋊D3C2×#4112yes—
489C2×C3⋊D3C2×#4112yes—
490C2×C3⋊D32−1+412yes—
491C2×C3×D3—22no—
492C2×C3×D3—22no—
493C2×C3×D3C2×#4114yes—
494D32—28no—
495C32×C4—22no—
496C32×C4—22no—
497C32×C4—21no—
498C32×C4C2×#4112yes—
499C3⋊Dic3—22no—
500C3⋊Dic3—22no—
501C3⋊Dic3—21no—
502C3⋊Dic3C2×#4112yes—
503C3×Dic3—24no—
504C3×Dic3—22no—
505C3×Dic3—22no—
506C3×Dic3—22no—
507C3×Dic3—24no—
508C22×Q8—91no—
509C22×D4—91no—
510C23×C4—92no—
511C23×C4—91no—
512C23×C4—91no—
513#126—34no—
514#126—94no—
515#126—94no—
516#126—94no—
517#125—34no—
518#125—32no—
519#125—94no—
520#125—92no—
521#125—94no—
522#125—94no—
523#125—94no—
524#123—34no—
525#123—94no—
526#123—94no—
527#123—94no—
528C22⋊Q8—32no—
529C22⋊Q8—94no—
530C22⋊Q8—92no—
531C22⋊Q8—91no—
532C22⋊Q8—91no—
533C22⋊Q8—92no—
534C22⋊Q8—91no—
535C22⋊Q8—92no—
536C22⋊Q8D3211yescharacteristic, complemented
537C4×Q8—32no—
538C4×Q8—94no—
539C4×Q8—92no—
540C4×D4—32no—
541C4×D4—92no—
542C4×D4—92no—
543C4×D4—92no—
544#117—32no—
545#117—34no—
546#117—92no—
547#117—94no—
548#117—94no—
549#117—92no—
550#117—92no—
551#117—94no—
552C2×C4⋊C4—32no—
553C2×C4⋊C4—91no—
554C2×C4⋊C4—92no—
555C2×C4⋊C4—91no—
556C2×C4⋊C4—92no—
557C2×C4⋊C4—91no—
558C2×C4⋊C4—92no—
559C2×C4⋊C4—92no—
560C2×C4⋊C4—92no—
561C2×C4⋊C4—94no—
562C2×C4⋊C4—92no—
563C2×C4⋊C4—91no—
564C2×C4⋊C4—92no—
565C2×C22⋊C4—91no—
566C2×C22⋊C4—92no—
567C2×C22⋊C4—92no—
568C2×C22⋊C4—91no—
569C2×C22⋊C4—92no—
570C2×C42—92no—
571C2×C42—92no—
572C2×C42—91no—
573C23×C3—21no—
574C23×C3—32no—
575C23×C3C23×D312yes—
576C22×D3—32no—
577C22×D3—38no—
578C22×D3—32no—
579C22×D3—61no—
580C22×D3—61no—
581C22×D3—64no—
582C22×D3—64no—
583C22×D3—64no—
584C22×D3—64no—
585C22×D3—64no—
586C22×D3—64no—
587C22×D3—122no—
588C22×D3—122no—
589C22×D3C23×D312yes—
590C3×Q8—24no—
591C3×Q8—42no—
592C3×D4—64no—
593C2×C3×C4—24no—
594C2×C3×C4—21no—
595C2×C3×C4—21no—
596C2×C3×C4—22no—
597C2×C3×C4—22no—
598C2×C3×C4—32no—
599C2×C3×C4—34no—
600C2×C3×C4—32no—
601C2×C3×C4—34no—
602C2×C3×C4—32no—
603C2×C3×C4—42no—
604C2×C3×C4—68no—
605C2×C3×C4—64no—
606C2×C3×C4C23×D312yes—
607C2×C3×C4C23×D314yes—
608C2×C3×C4C23×D314yes—
609C2×C3×C4C23×D312yes—
610#67—24no—
611#67—64no—
612C2×Dic3—32no—
613C2×Dic3—32no—
614C2×Dic3—34no—
615C2×Dic3—34no—
616C2×Dic3—61no—
617C2×Dic3—62no—
618C2×Dic3—61no—
619C2×Dic3—62no—
620C2×Dic3—64no—
621C2×Dic3—68no—
622C2×Dic3—64no—
623C2×Dic3—122no—
624C2×Dic3C23×D312yes—
625C2×Dic3C23×D314yes—
626C2×Dic3C23×D314yes—
627C2×Dic3C23×D312yes—
628C2×Dic3C23×D312yes—
629D12—64no—
630C4×D3—28no—
631C4×D3—24no—
632C4×D3—38no—
633C4×D3—64no—
634C4×D3—64no—
635C4×D3—68no—
636C4×D3—64no—
637C4×D3—68no—
638C4×D3—64no—
639C4×D3—64no—
640C4×D3—64no—
641C4×D3—68no—
642C4×D3—64no—
643C4×D3—68no—
644C4×D3—68no—
645C4×D3—64no—
646C4×D3—122no—
647C4×D3—122no—
648C4×D3—124no—
649C4×D3—122no—
650C4×D3—124no—
651Dic6—68no—
652Dic6—64no—
653Dic6—124no—
654Dic6—122no—
655C2×C32—41no—
656C2×C32C22×#4111yescharacteristic
657C2×C32C22×#4111yescharacteristic
658C2×C32C2×2−1+411yescharacteristic
659C3⋊D3—41no—
660C3⋊D3#55214yescomplemented
661C3×D3—24no—
662C24—91no—
663C24—91no—
664C2×Q8—92no—
665C2×Q8—91no—
666C2×Q8—184no—
667C2×Q8C2×D3211yescharacteristic
668C2×D4—32no—
669C2×D4—92no—
670C2×D4—184no—
671C22×C4—34no—
672C22×C4—32no—
673C22×C4—91no—
674C22×C4—92no—
675C22×C4—92no—
676C22×C4—91no—
677C22×C4—91no—
678C22×C4—94no—
679C22×C4—92no—
680C22×C4—91no—
681C22×C4—91no—
682C22×C4—91no—
683C22×C4—92no—
684C22×C4—92no—
685C22×C4—91no—
686C22×C4—91no—
687C22×C4—184no—
688C22×C4—184no—
689C22×C4—188no—
690C22×C4C2×D3211yescharacteristic
691C4⋊C4—32no—
692C4⋊C4—34no—
693C4⋊C4—32no—
694C4⋊C4—34no—
695C4⋊C4—32no—
696C4⋊C4—34no—
697C4⋊C4—34no—
698C4⋊C4—34no—
699C4⋊C4—92no—
700C4⋊C4—94no—
701C4⋊C4—92no—
702C4⋊C4—94no—
703C4⋊C4—92no—
704C4⋊C4—94no—
705C4⋊C4—94no—
706C4⋊C4—94no—
707C4⋊C4—92no—
708C4⋊C4—91no—
709C4⋊C4—92no—
710C4⋊C4—92no—
711C4⋊C4—92no—
712C4⋊C4C2×D3211yescharacteristic
713C4⋊C4C2×D3212yes—
714C22⋊C4—34no—
715C22⋊C4—32no—
716C22⋊C4—32no—
717C22⋊C4—34no—
718C22⋊C4—94no—
719C22⋊C4—92no—
720C22⋊C4—92no—
721C22⋊C4—94no—
722C22⋊C4—92no—
723C22⋊C4—92no—
724C22⋊C4—92no—
725C22⋊C4C2×D3212yes—
726C42—34no—
727C42—34no—
728C42—32no—
729C42—94no—
730C42—94no—
731C42—92no—
732C22×C3—22no—
733C22×C3—22no—
734C22×C3—22no—
735C22×C3—22no—
736C22×C3—21no—
737C22×C3—34no—
738C22×C3—41no—
739C22×C3—41no—
740C22×C3—62no—
741C22×C3—62no—
742C22×C3C24×D312yes—
743C2×D3—22no—
744C2×D3—22no—
745C2×D3—34no—
746C2×D3—34no—
747C2×D3—34no—
748C2×D3—62no—
749C2×D3—62no—
750C2×D3—62no—
751C2×D3—616no—
752C2×D3—62no—
753C2×D3—62no—
754C2×D3—62no—
755C2×D3—62no—
756C2×D3—121no—
757C2×D3—121no—
758C2×D3—128no—
759C2×D3—128no—
760C2×D3D3×#4114yes—
761C3×C4—24no—
762C3×C4—24no—
763C3×C4—22no—
764C3×C4—22no—
765C3×C4—42no—
766C3×C4—41no—
767C3×C4—42no—
768C3×C4—62no—
769C3×C4—64no—
770C3×C4—62no—
771C3×C4—62no—
772C3×C4—64no—
773C3×C4D3×#4114yes—
774Dic3—22no—
775Dic3—24no—
776Dic3—22no—
777Dic3—22no—
778Dic3—24no—
779Dic3—34no—
780Dic3—62no—
781Dic3—64no—
782Dic3—62no—
783Dic3—64no—
784Dic3—122no—
785Dic3—121no—
786Dic3—122no—
787C32C2×#55211yescharacteristic, complemented, Sylow
788C23—32no—
789C23—94no—
790C23—91no—
791C23—91no—
792C23—182no—
793C23—182no—
794C23—182no—
795C23—182no—
796C23—182no—
797C23C22×D3211yescharacteristic
798Q8—22no—
799Q8—184no—
800Q8—182no—
801D4—64no—
802D4—184no—
803C2×C4—22no—
804C2×C4—32no—
805C2×C4—34no—
806C2×C4—34no—
807C2×C4—32no—
808C2×C4—32no—
809C2×C4—68no—
810C2×C4—64no—
811C2×C4—91no—
812C2×C4—94no—
813C2×C4—91no—
814C2×C4—92no—
815C2×C4—92no—
816C2×C4—182no—
817C2×C4—182no—
818C2×C4—184no—
819C2×C4—184no—
820C2×C4—182no—
821C2×C4—184no—
822C2×C4—182no—
823C2×C4—182no—
824C2×C4—184no—
825C2×C4—184no—
826C2×C4—188no—
827C2×C4—182no—
828C2×C4—182no—
829C2×C4C22×D3211yescharacteristic
830C2×C4C22×D3212yes—
831C2×C4C22×D3212yes—
832C2×C4C22×D3211yescharacteristic
833C2×C3—21no—
834C2×C3—21no—
835C2×C3—21no—
836C2×C3—42no—
837C2×C3—42no—
838C2×C3—64no—
839C2×C3C2×D3×#4112yes—
840C2×C3C2×D3×#4112yes—
841C2×C3D3×2−1+412yes—
842D3—24no—
843D3—38no—
844D3—64no—
845D3—122no—
846D3—122no—
847C22—21no—
848C22—21no—
849C22—21no—
850C22—34no—
851C22—62no—
852C22—62no—
853C22—92no—
854C22—92no—
855C22—92no—
856C22—188no—
857C22—181no—
858C22—181no—
859C22—181no—
860C22—364no—
861C22C23×D3211yescharacteristic
862C4—21no—
863C4—22no—
864C4—22no—
865C4—62no—
866C4—62no—
867C4—64no—
868C4—64no—
869C4—62no—
870C4—92no—
871C4—181no—
872C4—182no—
873C4—182no—
874C4#6431212yes—
875C3—21no—
876C3D3×#55212yescomplemented
877C2—41no—
878C2—64no—
879C2—94no—
880C2—361no—
881C2C2×#6431211yescharacteristic
882C2#1059668711yescharacteristic
883C2D32×#4111yescharacteristic
subgroupG/H
center, FrattiniC22C23×D32
commutator, socle, cosocleC22×C32C25
FittingC32×C22⋊Q8C22
prime radicalC2×#3811C22
hypercenterC22⋊Q8D32
hypocenterC32C2×#552
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22⋊Q8

Complements

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

NH ≅ G/Ntype
1. C3⋊D3×C22⋊Q8C2semidirect
2. C3×#5639C2semidirect
3. #10595429C2semidirect
4. #10595379C2semidirect
5. Q8×#624C2semidirect
7. #10594969C2semidirect
8. #10594939C2semidirect
9. #10594602C2semidirect
10. D32×C4⋊C4C2semidirect
11. #10594553C2semidirect
12. #10594482C2semidirect
13. #10594408C2semidirect
14. #10594399C2semidirect
16. #10594154C2semidirect
17. #10594116C2semidirect
24. C32×C22⋊Q8C22semidirect
25. #64155C22semidirect
26. #64133C22semidirect
27. #64106C22semidirect
28. #64105C22semidirect
32. #64087C22semidirect
33. C3×#946C22semidirect
34. C3×Q8×Dic3C22semidirect
36. C3×#926C22semidirect
37. C3×#892C22semidirect
38. C3×D3×C4⋊C4C22semidirect
39. C3×#890C22semidirect
40. C3×#889C22semidirect
42. C3×#879C22semidirect
47. #63957C22semidirect
48. #63956C22semidirect
56. #63896C22semidirect
58. D3×C4⋊Dic3C22semidirect
67. #63877C22semidirect
68. #63877C22semidirect
69. D3×Dic3⋊C4C22semidirect
70. #63874C22semidirect
71. #63869C22semidirect
72. #63868C22semidirect
73. #63867C22semidirect
74. #63857C22semidirect
76. #63849C22semidirect
77. #63848C22semidirect
78. #63847C22semidirect
79. #63846C22semidirect
80. #63845C22semidirect
81. #63844C22semidirect
82. #63844C22semidirect
83. #63841C22semidirect
94. #5639D3semidirect
192. C3×C22⋊Q8C2×D3semidirect
200. #946C2×D3semidirect
201. Q8×Dic3C2×D3semidirect
208. #926C2×D3semidirect
229. #892C2×D3semidirect
244. D3×C4⋊C4C2×D3semidirect
248. #890C2×D3semidirect
254. #889C2×D3semidirect
270. #879C2×D3semidirect
536. C22⋊Q8D32semidirect
660. C3⋊D3#552semidirect
787. C32C2×#552semidirect
876. C3D3×#552semidirect

Maximal subgroups

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

subgroupindex
C3⋊D3×C22⋊Q82
C3×#56392
#105954292
#105953792
Q8×#6242
C4×#38112
#105949692
#105949392
#105946022
D32×C4⋊C42
#105945532
#105944822
#105944082
#105943992
#105942602
#105941542
#105941162
D3×#5523