Finite Group Databasebeta

← #11903609

Subgroups — #11903609

Order 1152.

2419 conjugacy classes of subgroups.

The subgroup lattice has 875 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×#3832C211yesmaximal, characteristic, complemented
2C3×#5581C212yesmaximal, complemented
3#10595430C212yesmaximal, complemented
4#10595413C211yesmaximal, characteristic, complemented
5#10595407C211yesmaximal, characteristic, complemented
6#10594616C212yesmaximal, complemented
7D3×#892C212yesmaximal, complemented
8#10594575C211yesmaximal, characteristic, complemented
9#10594512C211yesmaximal, characteristic, complemented
10#10594476C212yesmaximal, complemented
11#10594441C214yesmaximal, complemented
12#10594017C214yesmaximal, complemented
13C4×#3802C211yesmaximal, characteristic, complemented
14#10593979C212yesmaximal, complemented
15#10593966C212yesmaximal, complemented
16#10593925C212yesmaximal, complemented
17#10593854C211yesmaximal, characteristic, complemented
18#86827—32nomaximal
19C2×#3832C2211yescharacteristic
20C2×#3802C2211yescharacteristic
21C2×C4×D32C2212yes—
22C2×#3798C2212yes—
23C32×C4×Q8C2211yescharacteristic, complemented
24Q8×C3⋊Dic3C2211yescharacteristic, complemented
25#64102C2212yes—
26#64102C2211yescharacteristic, complemented
27#64101C2211yescharacteristic
28#64101C2212yescomplemented
29C4×C4⋊(C3⋊D3)C2212yes—
30C4×C4⋊(C3⋊D3)C2211yescharacteristic, complemented
31C42×C3⋊D3C2211yescharacteristic
32C42×C3⋊D3C2212yescomplemented
33C3×#946C2212yescomplemented
34C3×#946C2212yescomplemented
35C3×#894C2214yes—
36C3×#892C2212yescomplemented
37C3×D3×C4⋊C4C2212yescomplemented
38C3×#889C2214yescomplemented
39C3×#876C2214yescomplemented
40C3×C4×D12C2212yes—
41C3×#872C2214yescomplemented
42C3×#870C2212yescomplemented
43#63923C2214yes—
44#63921C2212yes—
45D3×(C2×D3)⋊C4C2214yes—
46#63919C2211yescharacteristic, complemented
47#63919C2211yescharacteristic, complemented
48#63915C2212yes—
49#63912C2212yes—
50#63909C2212yescomplemented
51#63909C2212yescomplemented
52#63902C2212yes—
53#63902C2211yescharacteristic
54#63902C2211yescharacteristic
55C4×#625C2211yescharacteristic
56C4×#625C2211yescharacteristic
57#63900C2211yescharacteristic
58#63898C2212yes—
59#63897C2214yes—
60#63893C2214yescomplemented
61D3×C4⋊Dic3C2212yescomplemented
62#63886C2214yes—
63#63881C2214yescomplemented
64#63881C2214yescomplemented
65#63881C2214yescomplemented
66#63878C2214yescomplemented
67C4×D3×Dic3C2214yescomplemented
68#63874C2212yescomplemented
69#63870C2212yescomplemented
70#63865C2212yes—
71#63865C2212yes—
72#63865C2212yescomplemented
73#63861C2214yescomplemented
74#63853C2214yescomplemented
75#63852C2214yescomplemented
76#63850C2214yescomplemented
77#63849C2212yes—
78#63848C2214yescomplemented
79#63841C2212yescomplemented
80#63838C2212yescomplemented
81#63838C2212yescomplemented
82#63838C2212yescomplemented
83#63836C2214yes—
84C3×#552—32no—
85#5706—34no—
86#5705—34no—
87#5695—32no—
88#5693—34no—
89#5691—34no—
90#5688—32no—
91#5654—34no—
92#5649—34no—
93#5641—32no—
94#5635—32no—
95#5627—32no—
96#5627—32no—
97#5581D312yescomplemented
98C4×#239—32no—
99C4×#239—61no—
100#5565—32no—
101C4×D3×D4—32no—
102#5532—32no—
103#5527—34no—
104#5522—34no—
105D3×#117—32no—
106#5507—32no—
107C2×#892—32no—
108C22×D32C2312yes—
109C2×C32×Q8C2311yescharacteristic
110#3832—24no—
111C2×C4⋊(C3⋊D3)C2312yes—
112C2×C4⋊(C3⋊D3)C2311yescharacteristic
113C2×C4×C3⋊D3C2312yes—
114C2×C4×C3⋊D3C2311yescharacteristic
115C2×C4×C3⋊D3C2312yes—
116C2×C4×C3⋊D3C2311yescharacteristic
117C2×C4×C3⋊D3C2312yes—
118C2×C4×C3⋊D3C2311yescharacteristic
119C2×C3×D12C2312yes—
120C2×C3×C4×D3C2314yes—
121C2×C3×C4×D3C2312yes—
122C2×C3×C4×D3C2312yes—
123C2×#627C2312yes—
124C2×#627C2312yes—
125C2×#626C2314yes—
126C2×#626C2314yes—
127C2×#625C2311yescharacteristic
128C2×#625C2311yescharacteristic
129C2×#624C2312yes—
130C2×D3×Dic3C2312yes—
131C2×D3×Dic3C2312yes—
132C2×D3×Dic3C2314yes—
133#3802—24no—
134C4×D32—28no—
135#3798—28no—
136C32×C4⋊C4C2312yes—
137C32×C4⋊C4C2311yescharacteristic
138C32×C42C2311yescharacteristic
139C32×C42C2312yes—
140#3752C2312yes—
141#3752C2312yes—
142#3752C2312yes—
143C4⋊(C3⋊Dic3)C2312yes—
144C4⋊(C3⋊Dic3)C2311yescharacteristic
145C4×C3⋊Dic3C2311yescharacteristic
146C4×C3⋊Dic3C2311yescharacteristic
147C4×C3⋊Dic3C2311yescharacteristic
148C4×C3⋊Dic3C2312yes—
149C4×C3⋊Dic3C2312yes—
150C3×(C2×D3)⋊C4C2314yes—
151C3×(C2×D3)⋊C4C2314yes—
152C3×(C2×D3)⋊C4C2314yes—
153C3×(C2×D3)⋊C4C2312yes—
154C3×(C2×D3)⋊C4C2312yes—
155C3×C4⋊Dic3C2312yes—
156C3×C4⋊Dic3C2312yes—
157C3×C4⋊Dic3C2312yes—
158C3×Dic3⋊C4C2314yes—
159C3×Dic3⋊C4C2314yes—
160C3×Dic3⋊C4C2314yes—
161C3×Dic3⋊C4C2314yes—
162C3×Dic3⋊C4C2314yes—
163C3×C4×Dic3C2314yes—
164#3724C2311yescharacteristic
165#3724C2312yes—
166#3724C2312yes—
167#3724C2311yescharacteristic
168Dic3⋊Dic3C2314yes—
169#3722C2314yes—
170#3722C2314yes—
171#3722C2314yes—
172(C2×D3)⋊Dic3C2314yes—
173(C2×D3)⋊Dic3C2312yes—
174(C2×D3)⋊Dic3C2312yes—
175Dic32C2314yes—
176Dic32C2314yes—
177#3475—91noSylow
178C2×#239—32no—
179C2×#239—61no—
180C2×D3×D4—32no—
181C2×#235—34no—
182C22×C4×D3—32no—
183C22×C4×D3—32no—
184C3×#126—34no—
185C3×#125—34no—
186C3×#125—32no—
187C3×#123—34no—
188C3×C22⋊Q8—32no—
189C3×C22⋊Q8—32no—
190C3×C4×Q8—21no—
191C3×C4×Q8C2×D312yescomplemented
192C3×C4×D4—32no—
193C3×#117—32no—
194C3×#117—34no—
195C2×C3×C4⋊C4—32no—
196#946C2×D312yescomplemented
197#946C2×D312yescomplemented
198Q8×Dic3—32no—
199Q8×Dic3—61no—
200#939—34no—
201D4×Dic3—32no—
202#930—32no—
203#930—32no—
204#929—34no—
205C4×#67—32no—
206C4×#67—32no—
207C2×(C2×D3)⋊C4—34no—
208#926—32no—
209C2×C4⋊Dic3—32no—
210C2×C4×Dic3—34no—
211#898—34no—
212#898—34no—
213#898—34no—
214#897—34no—
215#896—34no—
216#896—34no—
217#896—34no—
218#895—34no—
219#895—32no—
220#895—32no—
221#894—34no—
222#894—34no—
223#894—34no—
224#894—34no—
225#894C2×D314yes—
226#893—32no—
227#893—34no—
228#893—32no—
229#893—34no—
230#893—34no—
231#893—34no—
232#893—62no—
233#893—61no—
234#892—32no—
235#892—34no—
236#892—32no—
237#892—34no—
238#892—32no—
239#892—32no—
240#892—34no—
241#892—61no—
242#892—62no—
243#892C2×D312yescomplemented
244D3×C4⋊C4—32no—
245D3×C4⋊C4—32no—
246D3×C4⋊C4C2×D312yescomplemented
247#889—34no—
248#889C2×D314yescomplemented
249#888—32no—
250#888—32no—
251#887—34no—
252#887—34no—
253#887—34no—
254#885—34no—
255#885—34no—
256#884—34no—
257#883—34no—
258#882—34no—
259#882—34no—
260#67⋊C4—34no—
261#67⋊C4—32no—
262#67⋊C4—32no—
263#67⋊C4—34no—
264#67⋊C4—34no—
265#67⋊C4—34no—
266D3×C22⋊C4—34no—
267D3×C22⋊C4—32no—
268D3×C22⋊C4—32no—
269#879—34no—
270#878—34no—
271#877—34no—
272#876C2×D314yescomplemented
273#875—34no—
274C4×D12—32no—
275C4×D12—34no—
276C4×D12—62no—
277C4×D12—61no—
278C4×D12C2×D312yes—
279#872—34no—
280#872—34no—
281#872C2×D314yescomplemented
282C42×D3—34no—
283C42×D3—32no—
284C42×D3—34no—
285C42×D3—61no—
286C42×D3—62no—
287#870C2×D312yescomplemented
288C22×C3⋊D3C2412yes—
289C22×C3⋊D3C2411yescharacteristic
290C22×C3×D3C2412yes—
291C22×C3×D3C2412yes—
292C2×D32—24no—
293C2×D32—24no—
294C2×D32—42no—
295C32×Q8—22no—
296C2×C32×C4C2412yes—
297C2×C32×C4C2411yescharacteristic
298C2×C32×C4C2412yes—
299C2×C32×C4C2411yescharacteristic
300C2×C32×C4C2411yescharacteristic
301C2×C3⋊Dic3C2412yes—
302C2×C3⋊Dic3C2411yescharacteristic
303C2×C3⋊Dic3C2411yescharacteristic
304C2×C3⋊Dic3C2411yescharacteristic
305C4⋊(C3⋊D3)—24no—
306C4⋊(C3⋊D3)—22no—
307C4×C3⋊D3—24no—
308C4×C3⋊D3—24no—
309C4×C3⋊D3—22no—
310C4×C3⋊D3—42no—
311C4×C3⋊D3—41no—
312C4×C3⋊D3#4114yescomplemented
313C2×C3×Dic3C2412yes—
314C2×C3×Dic3C2414yes—
315C2×C3×Dic3C2414yes—
316C2×C3×Dic3C2412yes—
317C3×D12—24no—
318C3×C4×D3—28no—
319C3×C4×D3—24no—
320C3×C4×D3—24no—
321#627—24no—
322#627—42no—
323#626—28no—
324#626—44no—
325#625—22no—
326#625#4114yescomplemented
327#624—24no—
328D3×Dic3—24no—
329D3×Dic3—24no—
330D3×Dic3—44no—
331#556—91no—
332#555—91no—
333#554—91no—
334#553—92no—
335#552—32no—
336#552—92no—
337#551—94no—
338#547—91no—
339#546—92no—
340#533—91no—
341#529—94no—
342#529—92no—
343#525—92no—
344C4×#41—92no—
345C4×#41—91no—
346C2×C4×D4—91no—
347C2×#117—92no—
348C23×D3—32no—
349C23×D3—32no—
350C2×C3×Q8—21no—
351C2×C3×Q8C22×D312yes—
352C2×C3×D4—32no—
353C22×C3×C4—34no—
354C22×C3×C4—32no—
355C22×C3×C4—32no—
356C2×#67—32no—
357C2×#67—32no—
358C2×#67—34no—
359C2×#67—34no—
360C22×Dic3—32no—
361C22×Dic3—32no—
362C22×Dic3—34no—
363#239—68no—
364#239—68no—
365D3×D4—68no—
366#235—616no—
367C2×D12—34no—
368C2×D12—34no—
369C2×D12—32no—
370C2×D12—34no—
371C2×D12—62no—
372C2×D12—61no—
373C2×D12C22×D312yes—
374C2×C4×D3—32no—
375C2×C4×D3—32no—
376C2×C4×D3—32no—
377C2×C4×D3—34no—
378C2×C4×D3—34no—
379C2×C4×D3—32no—
380C2×C4×D3—32no—
381C2×C4×D3—32no—
382C2×C4×D3—34no—
383C2×C4×D3—32no—
384C2×C4×D3—34no—
385C2×C4×D3—61no—
386C2×C4×D3—62no—
387C2×C4×D3—61no—
388C2×C4×D3—62no—
389C2×C4×D3—61no—
390C2×C4×D3—62no—
391C2×C4×D3—68no—
392C2×C4×D3—68no—
393C2×C4×D3C22×D314yes—
394C2×C4×D3C22×D312yes—
395C2×C4×D3C22×D312yes—
396C2×Dic6—34no—
397C2×Dic6—34no—
398C3×C4⋊C4—21no—
399C3×C4⋊C4—22no—
400C3×C4⋊C4—34no—
401C3×C4⋊C4—34no—
402C3×C4⋊C4—34no—
403C3×C4⋊C4—32no—
404C3×C4⋊C4—32no—
405C3×C4⋊C4—34no—
406C3×C4⋊C4—32no—
407C3×C4⋊C4—34no—
408C3×C4⋊C4C22×D314yes—
409C3×C4⋊C4C22×D312yes—
410C3×C22⋊C4—34no—
411C3×C22⋊C4—34no—
412C3×C22⋊C4—34no—
413C3×C22⋊C4—32no—
414C3×C22⋊C4—32no—
415C3×C42—22no—
416C3×C42—21no—
417C3×C42—34no—
418C3×C42C22×D312yes—
419C3×C42C22×D314yes—
420#217—34no—
421#217—32no—
422#217—32no—
423(C2×D3)⋊C4—32no—
424(C2×D3)⋊C4—32no—
425(C2×D3)⋊C4—34no—
426(C2×D3)⋊C4—34no—
427(C2×D3)⋊C4—34no—
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—34no—
434(C2×D3)⋊C4—34no—
435(C2×D3)⋊C4—62no—
436(C2×D3)⋊C4—62no—
437(C2×D3)⋊C4—62no—
438(C2×D3)⋊C4C22×D312yes—
439(C2×D3)⋊C4C22×D314yes—
440(C2×D3)⋊C4C22×D312yes—
441(C2×D3)⋊C4C22×D314yes—
442(C2×D3)⋊C4C22×D314yes—
443C4⋊Dic3—34no—
444C4⋊Dic3—32no—
445C4⋊Dic3—34no—
446C4⋊Dic3—61no—
447C4⋊Dic3—62no—
448C4⋊Dic3C22×D312yes—
449C4⋊Dic3C22×D312yes—
450C4⋊Dic3C22×D312yes—
451Dic3⋊C4—32no—
452Dic3⋊C4—34no—
453Dic3⋊C4—34no—
454Dic3⋊C4—34no—
455Dic3⋊C4—32no—
456Dic3⋊C4C22×D314yes—
457Dic3⋊C4C22×D314yes—
458Dic3⋊C4C22×D314yes—
459Dic3⋊C4C22×D314yes—
460Dic3⋊C4C22×D314yes—
461C4×Dic3—32no—
462C4×Dic3—34no—
463C4×Dic3—34no—
464C4×Dic3—32no—
465C4×Dic3—32no—
466C4×Dic3—34no—
467C4×Dic3—34no—
468C4×Dic3—34no—
469C4×Dic3—34no—
470C4×Dic3—61no—
471C4×Dic3—62no—
472C4×Dic3—61no—
473C4×Dic3—61no—
474C4×Dic3—62no—
475C4×Dic3C22×D314yes—
476C22×C32C2511yescharacteristic
477C2×C3⋊D3—22no—
478C2×C3⋊D3—21no—
479C2×C3⋊D3—21no—
480C2×C3⋊D3—22no—
481C2×C3⋊D3—22no—
482C2×C3⋊D3C2×#4112yes—
483C2×C3×D3—22no—
484C2×C3×D3—22no—
485C2×C3×D3—22no—
486C2×C3×D3—22no—
487C2×C3×D3—22no—
488C2×C3×D3C2×#4114yes—
489D32—48no—
490C32×C4—22no—
491C32×C4—21no—
492C32×C4—22no—
493C32×C4—21no—
494C32×C4C2×#4112yes—
495C3⋊Dic3—22no—
496C3⋊Dic3—21no—
497C3⋊Dic3C2×#4112yes—
498C3⋊Dic3C2×#4112yes—
499C3×Dic3—22no—
500C3×Dic3—22no—
501C3×Dic3—24no—
502C3×Dic3—24no—
503C2×#41—92no—
504C2×#41—91no—
505C22×D4—91no—
506C23×C4—92no—
507C4⋊Q8—91no—
508C4⋊Q8—91no—
509#126—34no—
510#126—94no—
511#126—94no—
512#125—34no—
513#125—32no—
514#125—92no—
515#124—94no—
516#124—92no—
517#123—34no—
518#123—94no—
519#123—94no—
520#123—94no—
521C22⋊Q8—32no—
522C22⋊Q8—32no—
523C22⋊Q8—94no—
524C22⋊Q8—92no—
525C22⋊Q8—92no—
526C22⋊Q8—92no—
527#121—92no—
528#121—92no—
529#121—92no—
530#121—94no—
531#120—94no—
532C4×Q8—92no—
533C4×Q8—92no—
534C4×Q8—92no—
535C4×Q8—91no—
536C4×Q8D3211yescharacteristic, complemented
537C4×D4—32no—
538C4×D4—91no—
539C4×D4—91no—
540C4×D4—92no—
541C4×D4—94no—
542C4×D4—94no—
543C4×D4—94no—
544C4×D4—92no—
545C4×D4—91no—
546C4×D4—91no—
547C4×D4—92no—
548C4×D4—91no—
549C4×D4—92no—
550C4×D4—91no—
551#117—32no—
552#117—34no—
553#117—92no—
554#117—94no—
555#117—94no—
556#117—92no—
557#117—92no—
558#117—91no—
559#117—92no—
560C2×C4⋊C4—32no—
561C2×C4⋊C4—91no—
562C2×C4⋊C4—92no—
563C2×C22⋊C4—92no—
564C2×C22⋊C4—94no—
565C2×C42—94no—
566C2×C42—91no—
567C2×C42—92no—
568C23×C3—32no—
569C23×C3—32no—
570C22×D3—32no—
571C22×D3—34no—
572C22×D3—61no—
573C22×D3—62no—
574C22×D3—64no—
575C22×D3—64no—
576C22×D3—64no—
577C22×D3—64no—
578C22×D3—122no—
579C22×D3—122no—
580C22×D3C23×D312yes—
581C22×D3C23×D312yes—
582C3×Q8—24no—
583C3×Q8—24no—
584C3×D4—64no—
585C2×C3×C4—22no—
586C2×C3×C4—21no—
587C2×C3×C4—21no—
588C2×C3×C4—22no—
589C2×C3×C4—21no—
590C2×C3×C4—32no—
591C2×C3×C4—34no—
592C2×C3×C4—34no—
593C2×C3×C4—32no—
594C2×C3×C4—68no—
595C2×C3×C4—64no—
596C2×C3×C4—64no—
597C2×C3×C4C23×D314yes—
598C2×C3×C4C23×D314yes—
599C2×C3×C4C23×D312yes—
600C2×C3×C4C23×D312yes—
601C2×C3×C4C23×D312yes—
602#67—38no—
603#67—68no—
604#67—64no—
605#67—124no—
606C2×Dic3—32no—
607C2×Dic3—32no—
608C2×Dic3—34no—
609C2×Dic3—32no—
610C2×Dic3—61no—
611C2×Dic3—61no—
612C2×Dic3—62no—
613C2×Dic3—61no—
614C2×Dic3—64no—
615C2×Dic3—64no—
616C2×Dic3—124no—
617C2×Dic3C23×D312yes—
618C2×Dic3C23×D314yes—
619C2×Dic3C23×D314yes—
620C2×Dic3C23×D312yes—
621D12—24no—
622D12—68no—
623D12—68no—
624D12—64no—
625D12—68no—
626D12—64no—
627D12—124no—
628C4×D3—28no—
629C4×D3—24no—
630C4×D3—24no—
631C4×D3—38no—
632C4×D3—64no—
633C4×D3—64no—
634C4×D3—64no—
635C4×D3—68no—
636C4×D3—64no—
637C4×D3—68no—
638C4×D3—64no—
639C4×D3—64no—
640C4×D3—68no—
641C4×D3—122no—
642C4×D3—124no—
643C4×D3—122no—
644C4×D3—124no—
645C4×D3—124no—
646C4×D3—124no—
647C4×D3—122no—
648Dic6—68no—
649Dic6—124no—
650C2×C32C22×#4111yescharacteristic
651C2×C32C22×#4111yescharacteristic
652C2×C32#58511yescharacteristic
653C3⋊D3—22no—
654C3⋊D3—42no—
655C3×D3—24no—
656C3×D3—42no—
657C24—92no—
658#41—188no—
659#41—184no—
660C2×Q8—92no—
661C2×Q8—92no—
662C2×Q8C2×D3211yescharacteristic
663C2×D4—32no—
664C2×D4—94no—
665C2×D4—94no—
666C2×D4—91no—
667C2×D4—91no—
668C2×D4—92no—
669C2×D4—91no—
670C2×D4—184no—
671C22×C4—34no—
672C22×C4—32no—
673C22×C4—32no—
674C22×C4—92no—
675C22×C4—92no—
676C22×C4—92no—
677C22×C4—94no—
678C22×C4—91no—
679C22×C4—91no—
680C22×C4—92no—
681C22×C4—92no—
682C22×C4—91no—
683C22×C4—92no—
684C22×C4—188no—
685C4⋊C4—32no—
686C4⋊C4—34no—
687C4⋊C4—32no—
688C4⋊C4—32no—
689C4⋊C4—34no—
690C4⋊C4—34no—
691C4⋊C4—34no—
692C4⋊C4—34no—
693C4⋊C4—91no—
694C4⋊C4—94no—
695C4⋊C4—91no—
696C4⋊C4—92no—
697C4⋊C4—92no—
698C4⋊C4—91no—
699C4⋊C4—92no—
700C4⋊C4C2×D3211yescharacteristic
701C4⋊C4C2×D3212yes—
702C22⋊C4—32no—
703C22⋊C4—34no—
704C22⋊C4—32no—
705C22⋊C4—34no—
706C22⋊C4—34no—
707C22⋊C4—94no—
708C22⋊C4—94no—
709C22⋊C4—94no—
710C22⋊C4—94no—
711C22⋊C4—92no—
712C22⋊C4—92no—
713C22⋊C4—92no—
714C22⋊C4—92no—
715C22⋊C4—92no—
716C42—34no—
717C42—94no—
718C42—94no—
719C42—92no—
720C42—91no—
721C42—91no—
722C42—91no—
723C42—92no—
724C42C2×D3212yes—
725C42C2×D3211yescharacteristic
726C22×C3—21no—
727C22×C3—34no—
728C22×C3—62no—
729C22×C3—62no—
730C22×C3—62no—
731C22×C3—62no—
732C22×C3—62no—
733C22×C3C24×D312yes—
734C2×D3—22no—
735C2×D3—22no—
736C2×D3—22no—
737C2×D3—22no—
738C2×D3—22no—
739C2×D3—34no—
740C2×D3—62no—
741C2×D3—62no—
742C2×D3—62no—
743C2×D3—64no—
744C2×D3—64no—
745C2×D3—64no—
746C2×D3—64no—
747C2×D3—121no—
748C2×D3—121no—
749C2×D3—122no—
750C2×D3—122no—
751C2×D3—128no—
752C2×D3—128no—
753C2×D3D3×#4114yes—
754C3×C4—24no—
755C3×C4—22no—
756C3×C4—24no—
757C3×C4—22no—
758C3×C4—24no—
759C3×C4—22no—
760C3×C4—22no—
761C3×C4—42no—
762C3×C4—41no—
763C3×C4—64no—
764C3×C4—62no—
765C3×C4—62no—
766C3×C4—64no—
767C3×C4D3×#4114yes—
768Dic3—24no—
769Dic3—22no—
770Dic3—22no—
771Dic3—24no—
772Dic3—34no—
773Dic3—34no—
774Dic3—62no—
775Dic3—62no—
776Dic3—62no—
777Dic3—64no—
778Dic3—122no—
779Dic3—121no—
780C32#347511yescharacteristic, complemented, Sylow
781C23—32no—
782C23—32no—
783C23—91no—
784C23—92no—
785C23—184no—
786C23—184no—
787C23—362no—
788Q8—22no—
789Q8—184no—
790Q8—362no—
791D4—64no—
792D4—94no—
793D4—184no—
794D4—188no—
795D4—182no—
796D4—182no—
797D4—364no—
798C2×C4—32no—
799C2×C4—34no—
800C2×C4—34no—
801C2×C4—32no—
802C2×C4—68no—
803C2×C4—64no—
804C2×C4—64no—
805C2×C4—91no—
806C2×C4—91no—
807C2×C4—94no—
808C2×C4—92no—
809C2×C4—91no—
810C2×C4—182no—
811C2×C4—184no—
812C2×C4—184no—
813C2×C4—184no—
814C2×C4—184no—
815C2×C4—184no—
816C2×C4—362no—
817C2×C4—361no—
818C2×C4—364no—
819C2×C4C22×D3212yes—
820C2×C4C22×D3211yescharacteristic
821C2×C4C22×D3212yes—
822C2×C4C22×D3211yescharacteristic
823C2×C4C22×D3211yescharacteristic
824C2×C3—21no—
825C2×C3—21no—
826C2×C3—21no—
827C2×C3—64no—
828C2×C3—122no—
829C2×C3C2×D3×#4112yes—
830C2×C3C2×D3×#4112yes—
831C2×C3#596812yes—
832D3—24no—
833D3—42no—
834D3—64no—
835D3—122no—
836D3—124no—
837D3—124no—
838C22—34no—
839C22—62no—
840C22—62no—
841C22—62no—
842C22—62no—
843C22—62no—
844C22—92no—
845C22—181no—
846C22—181no—
847C22—182no—
848C22—182no—
849C22—182no—
850C22—368no—
851C22C23×D3211yescharacteristic
852C4—22no—
853C4—21no—
854C4—22no—
855C4—21no—
856C4—62no—
857C4—62no—
858C4—64no—
859C4—64no—
860C4—92no—
861C4—92no—
862C4—182no—
863C4—181no—
864C4#6430612yes—
865C3—21no—
866C3#8682712yescomplemented
867C2—64no—
868C2—122no—
869C2—182no—
870C2—362no—
871C2C2×#6430611yescharacteristic
872C2#1059668911yescharacteristic
873C2D32×#4111yescharacteristic
subgroupG/H
center, FrattiniC22C23×D32
commutator, socle, cosocleC22×C32C25
FittingC32×C4×Q8C22
hypercenterC4×Q8D32
hypocenterC32#3475
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C4×Q8

Complements

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

NH ≅ G/Ntype
1. C4×#3832C2semidirect
2. C3×#5581C2semidirect
3. #10595430C2semidirect
4. #10595413C2semidirect
5. #10595407C2semidirect
6. #10594616C2semidirect
7. D3×#892C2semidirect
8. #10594575C2semidirect
9. #10594512C2semidirect
10. #10594476C2semidirect
11. #10594441C2semidirect
12. #10594017C2semidirect
13. C4×#3802C2semidirect
14. #10593979C2semidirect
15. #10593966C2semidirect
16. #10593925C2semidirect
17. #10593854C2semidirect
23. C32×C4×Q8C22semidirect
24. Q8×C3⋊Dic3C22semidirect
26. #64102C22semidirect
28. #64101C22semidirect
30. C4×C4⋊(C3⋊D3)C22semidirect
32. C42×C3⋊D3C22semidirect
33. C3×#946C22semidirect
34. C3×#946C22semidirect
36. C3×#892C22semidirect
37. C3×D3×C4⋊C4C22semidirect
38. C3×#889C22semidirect
39. C3×#876C22semidirect
41. C3×#872C22semidirect
42. C3×#870C22semidirect
46. #63919C22semidirect
47. #63919C22semidirect
50. #63909C22semidirect
51. #63909C22semidirect
60. #63893C22semidirect
61. D3×C4⋊Dic3C22semidirect
63. #63881C22semidirect
64. #63881C22semidirect
65. #63881C22semidirect
66. #63878C22semidirect
67. C4×D3×Dic3C22semidirect
68. #63874C22semidirect
69. #63870C22semidirect
72. #63865C22semidirect
73. #63861C22semidirect
74. #63853C22semidirect
75. #63852C22semidirect
76. #63850C22semidirect
78. #63848C22semidirect
79. #63841C22semidirect
80. #63838C22semidirect
81. #63838C22semidirect
82. #63838C22semidirect
97. #5581D3semidirect
191. C3×C4×Q8C2×D3semidirect
196. #946C2×D3semidirect
197. #946C2×D3semidirect
243. #892C2×D3semidirect
246. D3×C4⋊C4C2×D3semidirect
248. #889C2×D3semidirect
272. #876C2×D3semidirect
281. #872C2×D3semidirect
287. #870C2×D3semidirect
312. C4×C3⋊D3#41semidirect
326. #625#41semidirect
536. C4×Q8D32semidirect
780. C32#3475semidirect
866. C3#86827semidirect

Maximal subgroups

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

subgroupindex
C4×#38322
C3×#55812
#105954302
#105954132
#105954072
#105946162
D3×#8922
#105945752
#105945122
#105944762
#105944412
#105940172
C4×#38022
#105939792
#105939662
#105939252
#105938542
#868273