Finite Group Databasebeta

← #11903533

Subgroups — #11903533

Order 1152.

2477 conjugacy classes of subgroups.

The subgroup lattice has 877 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64102C211yesmaximal, characteristic, complemented
2C3×#5513C212yesmaximal, complemented
3#10595018C212yesmaximal, complemented
4#10594969C212yesmaximal, complemented
5#10594966C214yesmaximal, complemented
6#10594920C212yesmaximal, complemented
7C4×#3805C211yesmaximal, characteristic, complemented
8#10594810C211yesmaximal, characteristic, complemented
9#10594575C211yesmaximal, characteristic, complemented
10#10594530C211yesmaximal, characteristic, complemented
11#10594484C211yesmaximal, characteristic, complemented
12#10594476C212yesmaximal, complemented
13#10594475C212yesmaximal, complemented
14#10594465C214yesmaximal, complemented
15#10594453C212yesmaximal, complemented
16#10594362C212yesmaximal, complemented
17#10594350C211yesmaximal, characteristic, complemented
18#86826—32nomaximal
19C22×C4⋊(C3⋊D3)C2211yescharacteristic
20C22×C4×C3⋊D3C2212yes—
21C2×#3805C2211yescharacteristic
22C2×#3799C2212yes—
23C2×C32×C4⋊C4C2211yescharacteristic
24C2×#3752C2212yes—
25C2×C4×C3⋊Dic3C2211yescharacteristic
26#64102C2211yescharacteristic
27#64102C2211yescharacteristic
28#64102C2211yescharacteristic
29#64102C2212yes—
30#64102C2212yes—
31#64102C2211yescharacteristic
32C3×#929C2214yes—
33C3×C4×#67C2212yes—
34C3×#926C2214yes—
35C3×#924C2212yes—
36C3×#898C2214yescomplemented
37C3×#897C2212yescomplemented
38C3×#892C2212yescomplemented
39C3×#890C2212yescomplemented
40C3×#889C2214yescomplemented
41C3×#887C2212yescomplemented
42#63982C2212yes—
43#63981C2214yes—
44#63974C2214yes—
45#67⋊Dic3C2212yes—
46#63957C2211yescharacteristic
47#63957C2212yes—
48#63919C2211yescharacteristic, complemented
49C4×#627C2211yescharacteristic, complemented
50#63912C2212yescomplemented
51#63912C2212yescomplemented
52#63910C2214yes—
53#63909C2212yes—
54#63902C2211yescharacteristic, complemented
55C4×#625C2211yescharacteristic, complemented
56#63900C2212yescomplemented
57#63900C2212yescomplemented
58#63897C2214yes—
59#63895C2214yescomplemented
60#63894C2212yes—
61#63890C2214yescomplemented
62C4×#624C2214yescomplemented
63#63881C2214yescomplemented
64#63881C2214yescomplemented
65#63880C2214yescomplemented
66#63878C2212yescomplemented
67C4×D3×Dic3C2212yescomplemented
68#63874C2212yescomplemented
69#63874C2212yescomplemented
70#63873C2211yescharacteristic, complemented
71#63870C2212yescomplemented
72#63868C2214yescomplemented
73#63865C2212yescomplemented
74#63865C2212yescomplemented
75#63864C2212yes—
76#63854C2214yescomplemented
77#63852C2214yescomplemented
78#63849C2214yescomplemented
79#63848C2214yescomplemented
80#63843C2212yescomplemented
81#63838C2211yescharacteristic, complemented
82#63838C2212yescomplemented
83#63836C2214yescomplemented
84C3×#552—32no—
85#5709—34no—
86#5706—34no—
87#5693—34no—
88#5691—34no—
89#5691—32no—
90#5690—32no—
91#5658—34no—
92#5656—34no—
93#5631—32no—
94#5630—32no—
95#5624—32no—
96#5622—32no—
97C4×#239—32no—
98#5568—32no—
99#5550—32no—
100C4×#237—32no—
101#5532—32no—
102#5527—34no—
103#5522—32no—
104D3×#117—34no—
105#5513D312yescomplemented
106C2×#893—32no—
107C2×#893—61no—
108C23×C3⋊D3C2312yes—
109C22×C32×C4C2311yescharacteristic
110C22×C32×C4C2312yes—
111C22×C3⋊Dic3C2311yescharacteristic
112C22×C3⋊Dic3C2311yescharacteristic
113C2×C4⋊(C3⋊D3)—24no—
114C2×C4⋊(C3⋊D3)C2311yescharacteristic
115C2×C4⋊(C3⋊D3)C2312yes—
116C2×C4⋊(C3⋊D3)C2311yescharacteristic
117C2×C4×C3⋊D3—28no—
118C2×C4×C3⋊D3C2312yes—
119C2×C4×C3⋊D3C2312yes—
120C2×C4×C3⋊D3C2312yes—
121C2×C4×C3⋊D3C2312yes—
122C2×C3×#67C2312yes—
123C2×C3×C4×D3C2312yes—
124C2×C3×Dic6C2312yes—
125C2×#627C2311yescharacteristic
126C2×#627C2312yes—
127C2×#626C2314yes—
128C2×#626C2314yes—
129C2×#625C2311yescharacteristic
130C2×#624C2314yes—
131C2×#624C2314yes—
132#3805—24no—
133C2×D3×Dic3C2312yes—
134C2×D3×Dic3C2312yes—
135#3799—28no—
136C32×C4⋊C4C2311yescharacteristic
137C32×C4⋊C4C2312yes—
138C32×C4⋊C4C2311yescharacteristic
139#3752C2312yes—
140#3752C2312yes—
141#3752C2312yes—
142#3752C2312yes—
143C4×C3⋊Dic3C2311yescharacteristic
144C4×C3⋊Dic3C2311yescharacteristic
145C4×C3⋊Dic3C2311yescharacteristic
146C4×C3⋊Dic3C2311yescharacteristic
147C3×#217C2314yes—
148C3×#217C2312yes—
149C3×(C2×D3)⋊C4C2314yes—
150C3×(C2×D3)⋊C4C2314yes—
151C3×(C2×D3)⋊C4C2312yes—
152C3×C4⋊Dic3C2314yes—
153C3×C4⋊Dic3C2312yes—
154C3×C4⋊Dic3C2314yes—
155C3×Dic3⋊C4C2314yes—
156C3×Dic3⋊C4C2312yes—
157C3×Dic3⋊C4C2314yes—
158C3×Dic3⋊C4C2314yes—
159C3×C4×Dic3C2312yes—
160C3×C4×Dic3C2314yes—
161C3×C4×Dic3C2314yes—
162#3724C2312yes—
163#3724C2311yescharacteristic
164#3724C2312yes—
165#3724C2312yes—
166#3724C2311yescharacteristic
167Dic3⋊Dic3C2314yes—
168Dic3⋊Dic3C2312yes—
169#3722C2314yes—
170#3722C2314yes—
171#3722C2314yes—
172#3722C2314yes—
173(C2×D3)⋊Dic3C2312yes—
174Dic32C2312yes—
175Dic32C2314yes—
176Dic32C2312yes—
177#3475—91noSylow
178C2×#239—32no—
179C2×#237—32no—
180C2×#235—32no—
181C22×D12—32no—
182C22×D12—61no—
183C22×C4×D3—34no—
184C22×C4×D3—62no—
185C3×#126—34no—
186C3×#125—34no—
187C3×#125—32no—
188C3×#123—34no—
189C3×C22⋊Q8—32no—
190C3×C22⋊Q8—32no—
191C3×C4×Q8—32no—
192C3×C4×D4—32no—
193C3×#117—34no—
194C3×#117—32no—
195C2×C3×C4⋊C4—21no—
196C2×C3×C4⋊C4C2×D312yes—
197#947—32no—
198Q8×Dic3—32no—
199#944—32no—
200#937—34no—
201D4×Dic3—32no—
202#930—32no—
203#929C2×D314yes—
204C4×#67—32no—
205C4×#67C2×D312yes—
206C2×(C2×D3)⋊C4—34no—
207C2×(C2×D3)⋊C4—62no—
208#926C2×D314yes—
209#924C2×D312yes—
210C2×C4×Dic3—32no—
211C2×C4×Dic3—32no—
212C2×C4×Dic3—61no—
213#898—34no—
214#898—34no—
215#898—34no—
216#898C2×D314yescomplemented
217#897—34no—
218#897C2×D312yescomplemented
219#896—34no—
220#896—34no—
221#896—34no—
222#895—32no—
223#895—34no—
224#894—34no—
225#894—34no—
226#894—34no—
227#894—34no—
228#893—32no—
229#893—34no—
230#893—32no—
231#893—34no—
232#893—32no—
233#893—32no—
234#893—34no—
235#893—34no—
236#893—32no—
237#893—61no—
238#893—61no—
239#893—62no—
240#893—61no—
241#893—62no—
242#893—61no—
243#892—32no—
244#892—34no—
245#892—34no—
246#892—34no—
247#892C2×D312yescomplemented
248D3×C4⋊C4—34no—
249D3×C4⋊C4—34no—
250#890C2×D312yescomplemented
251#889—34no—
252#889C2×D314yescomplemented
253#888—32no—
254#887—32no—
255#887—34no—
256#887—32no—
257#887C2×D312yescomplemented
258#886—34no—
259#885—34no—
260#884—34no—
261#884—34no—
262#884—34no—
263#883—34no—
264#882—34no—
265#67⋊C4—32no—
266#67⋊C4—32no—
267#67⋊C4—34no—
268#67⋊C4—34no—
269#67⋊C4—34no—
270D3×C22⋊C4—34no—
271D3×C22⋊C4—34no—
272#878—34no—
273#877—34no—
274#877—32no—
275#877—32no—
276#876—34no—
277#875—32no—
278#875—34no—
279C4×D12—34no—
280C4×D12—32no—
281#872—34no—
282#872—34no—
283#872—34no—
284C42×D3—32no—
285C42×D3—34no—
286C42×D3—34no—
287C4×Dic6—32no—
288C23×C32C2411yescharacteristic
289C22×C3⋊D3—24no—
290C22×C3⋊D3—24no—
291C22×C3⋊D3—42no—
292C22×C3⋊D3C2412yes—
293C22×C3⋊D3C2412yes—
294C22×C3×D3C2412yes—
295C2×C32×C4—22no—
296C2×C32×C4—24no—
297C2×C32×C4C2412yes—
298C2×C32×C4C2411yescharacteristic
299C2×C32×C4C2412yes—
300C2×C32×C4C2411yescharacteristic
301C2×C3⋊Dic3—41no—
302C2×C3⋊Dic3#4114yescomplemented
303C2×C3⋊Dic3C2411yescharacteristic
304C2×C3⋊Dic3C2411yescharacteristic
305C2×C3⋊Dic3C2411yescharacteristic
306C2×C3⋊Dic3C2411yescharacteristic
307C4⋊(C3⋊D3)—24no—
308C4⋊(C3⋊D3)—22no—
309C4⋊(C3⋊D3)#4114yescomplemented
310C4×C3⋊D3—24no—
311C4×C3⋊D3—24no—
312C4×C3⋊D3—24no—
313C4×C3⋊D3—24no—
314C3×#67—24no—
315C2×C3×Dic3C2412yes—
316C2×C3×Dic3C2412yes—
317C2×C3×Dic3C2414yes—
318C2×C3×Dic3C2412yes—
319C2×C3×Dic3C2414yes—
320C3×C4×D3—24no—
321C3×Dic6—24no—
322#627—22no—
323#627—42no—
324#626—28no—
325#626—44no—
326#625—22no—
327#624—28no—
328#624—44no—
329D3×Dic3—24no—
330D3×Dic3—42no—
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—92no—
342#529—94no—
343#525—92no—
344C4×#41—92no—
345C4×#41—91no—
346C2×C4×D4—91no—
347C2×#117—92no—
348C23×D3—34no—
349C23×D3—62no—
350C2×C3×Q8—32no—
351C2×C3×D4—32no—
352C22×C3×C4—21no—
353C22×C3×C4—22no—
354C22×C3×C4—32no—
355C22×C3×C4C22×D312yes—
356C22×C3×C4C22×D314yes—
357C2×#67—32no—
358C2×#67—34no—
359C2×#67—34no—
360C2×#67C22×D312yes—
361C22×Dic3—32no—
362C22×Dic3—32no—
363C22×Dic3—32no—
364C22×Dic3—32no—
365C22×Dic3—61no—
366C22×Dic3—61no—
367#239—68no—
368#237—68no—
369#235—68no—
370C2×D12—32no—
371C2×D12—34no—
372C2×D12—32no—
373C2×D12—34no—
374C2×D12—34no—
375C2×D12—61no—
376C2×D12—62no—
377C2×D12—61no—
378C2×D12—68no—
379C2×D12—68no—
380C2×C4×D3—32no—
381C2×C4×D3—34no—
382C2×C4×D3—34no—
383C2×C4×D3—34no—
384C2×C4×D3—34no—
385C2×C4×D3—34no—
386C2×C4×D3—34no—
387C2×C4×D3—32no—
388C2×C4×D3—34no—
389C2×C4×D3—34no—
390C2×C4×D3—62no—
391C2×C4×D3—62no—
392C2×C4×D3—62no—
393C2×C4×D3—62no—
394C2×C4×D3—616no—
395C2×C4×D3—128no—
396C2×C4×D3C22×D312yes—
397C2×Dic6—32no—
398C2×Dic6—34no—
399C2×Dic6C22×D312yes—
400C3×C4⋊C4—21no—
401C3×C4⋊C4—21no—
402C3×C4⋊C4—22no—
403C3×C4⋊C4—32no—
404C3×C4⋊C4—34no—
405C3×C4⋊C4—32no—
406C3×C4⋊C4—34no—
407C3×C4⋊C4—34no—
408C3×C4⋊C4—34no—
409C3×C4⋊C4—34no—
410C3×C4⋊C4C22×D312yes—
411C3×C4⋊C4C22×D314yes—
412C3×C4⋊C4C22×D312yes—
413C3×C22⋊C4—34no—
414C3×C22⋊C4—32no—
415C3×C22⋊C4—32no—
416C3×C22⋊C4—34no—
417C3×C22⋊C4—34no—
418C3×C42—32no—
419C3×C42—34no—
420C3×C42—34no—
421#217—32no—
422#217C22×D314yes—
423#217C22×D312yes—
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—34no—
436(C2×D3)⋊C4—34no—
437(C2×D3)⋊C4—62no—
438(C2×D3)⋊C4—62no—
439(C2×D3)⋊C4—62no—
440(C2×D3)⋊C4—62no—
441(C2×D3)⋊C4C22×D314yes—
442(C2×D3)⋊C4C22×D312yes—
443(C2×D3)⋊C4C22×D314yes—
444C4⋊Dic3—32no—
445C4⋊Dic3—34no—
446C4⋊Dic3C22×D312yes—
447C4⋊Dic3C22×D314yes—
448C4⋊Dic3C22×D314yes—
449Dic3⋊C4—32no—
450Dic3⋊C4—32no—
451Dic3⋊C4—32no—
452Dic3⋊C4—34no—
453Dic3⋊C4—34no—
454Dic3⋊C4—34no—
455Dic3⋊C4—34no—
456Dic3⋊C4C22×D314yes—
457Dic3⋊C4C22×D312yes—
458Dic3⋊C4C22×D314yes—
459Dic3⋊C4C22×D314yes—
460C4×Dic3—32no—
461C4×Dic3—32no—
462C4×Dic3—32no—
463C4×Dic3—32no—
464C4×Dic3—32no—
465C4×Dic3—32no—
466C4×Dic3—34no—
467C4×Dic3—34no—
468C4×Dic3—32no—
469C4×Dic3—32no—
470C4×Dic3—61no—
471C4×Dic3—61no—
472C4×Dic3—61no—
473C4×Dic3—61no—
474C4×Dic3C22×D312yes—
475C4×Dic3C22×D314yes—
476C4×Dic3C22×D314yes—
477C22×C32—21no—
478C22×C32—21no—
479C22×C32C2×#4112yes—
480C22×C32C2511yescharacteristic
481C2×C3⋊D3—22no—
482C2×C3⋊D3—22no—
483C2×C3⋊D3—22no—
484C2×C3⋊D3—22no—
485C2×C3⋊D3—22no—
486C2×C3⋊D3—48no—
487C2×C3⋊D3C2×#4114yes—
488C2×C3×D3—22no—
489C2×C3×D3—22no—
490C2×C3×D3—22no—
491C32×C4—21no—
492C32×C4—22no—
493C32×C4—22no—
494C32×C4C2×#4112yes—
495C3⋊Dic3—21no—
496C3⋊Dic3—21no—
497C3⋊Dic3C2×#4112yes—
498C3⋊Dic3C2×#4112yes—
499C3×Dic3—22no—
500C3×Dic3—22no—
501C3×Dic3—24no—
502C3×Dic3—22no—
503C3×Dic3—24no—
504C2×#41—92no—
505C2×#41—91no—
506C22×D4—91no—
507C23×C4—92no—
508C4⋊Q8—91no—
509C4⋊Q8—91no—
510#126—34no—
511#126—94no—
512#126—94no—
513#125—34no—
514#125—32no—
515#125—92no—
516#124—94no—
517#124—92no—
518#123—34no—
519#123—94no—
520#123—94no—
521#123—94no—
522C22⋊Q8—32no—
523C22⋊Q8—32no—
524C22⋊Q8—92no—
525C22⋊Q8—92no—
526C22⋊Q8—92no—
527C22⋊Q8—94no—
528#121—92no—
529#121—92no—
530#121—94no—
531#121—92no—
532#120—94no—
533C4×Q8—32no—
534C4×Q8—91no—
535C4×Q8—91no—
536C4×Q8—92no—
537C4×Q8—92no—
538C4×D4—32no—
539C4×D4—94no—
540C4×D4—92no—
541C4×D4—91no—
542C4×D4—94no—
543C4×D4—94no—
544C4×D4—92no—
545C4×D4—91no—
546C4×D4—91no—
547C4×D4—91no—
548C4×D4—92no—
549C4×D4—91no—
550C4×D4—92no—
551C4×D4—91no—
552#117—34no—
553#117—32no—
554#117—92no—
555#117—92no—
556#117—94no—
557#117—91no—
558#117—92no—
559#117—92no—
560#117—94no—
561C2×C4⋊C4—92no—
562C2×C4⋊C4—92no—
563C2×C4⋊C4D3211yescharacteristic
564C2×C22⋊C4—94no—
565C2×C22⋊C4—92no—
566C2×C42—94no—
567C2×C42—92no—
568C2×C42—91no—
569C23×C3—21no—
570C23×C3—32no—
571C23×C3C23×D312yes—
572C22×D3—34no—
573C22×D3—34no—
574C22×D3—62no—
575C22×D3—62no—
576C22×D3—68no—
577C22×D3—68no—
578C22×D3—68no—
579C22×D3—124no—
580C22×D3—124no—
581C22×D3—124no—
582C22×D3C23×D312yes—
583C3×Q8—64no—
584C3×D4—64no—
585C2×C3×C4—24no—
586C2×C3×C4—28no—
587C2×C3×C4—24no—
588C2×C3×C4—21no—
589C2×C3×C4—21no—
590C2×C3×C4—22no—
591C2×C3×C4—22no—
592C2×C3×C4—32no—
593C2×C3×C4—34no—
594C2×C3×C4—32no—
595C2×C3×C4—34no—
596C2×C3×C4—32no—
597C2×C3×C4—44no—
598C2×C3×C4—64no—
599C2×C3×C4C23×D312yes—
600C2×C3×C4C23×D314yes—
601C2×C3×C4C23×D314yes—
602C2×C3×C4C23×D312yes—
603#67—24no—
604#67—68no—
605#67—64no—
606#67—124no—
607C2×Dic3—38no—
608C2×Dic3—32no—
609C2×Dic3—32no—
610C2×Dic3—32no—
611C2×Dic3—32no—
612C2×Dic3—64no—
613C2×Dic3—61no—
614C2×Dic3—61no—
615C2×Dic3—61no—
616C2×Dic3—61no—
617C2×Dic3—64no—
618C2×Dic3—122no—
619C2×Dic3—122no—
620C2×Dic3—122no—
621C2×Dic3C23×D312yes—
622C2×Dic3C23×D312yes—
623C2×Dic3C23×D314yes—
624C2×Dic3C23×D312yes—
625C2×Dic3C23×D314yes—
626D12—38no—
627D12—64no—
628D12—68no—
629D12—68no—
630D12—64no—
631D12—68no—
632D12—64no—
633D12—124no—
634C4×D3—24no—
635C4×D3—68no—
636C4×D3—68no—
637C4×D3—68no—
638C4×D3—68no—
639C4×D3—68no—
640C4×D3—68no—
641C4×D3—64no—
642C4×D3—124no—
643C4×D3—124no—
644C4×D3—124no—
645C4×D3—124no—
646C4×D3—124no—
647C4×D3—124no—
648C4×D3—122no—
649Dic6—24no—
650Dic6—64no—
651Dic6—124no—
652C2×C32—22no—
653C2×C32C22×#4111yescharacteristic
654C2×C32C22×#4111yescharacteristic
655C2×C32#58511yescharacteristic
656C3⋊D3—24no—
657C3⋊D3—42no—
658C3×D3—42no—
659C24—92no—
660#41—188no—
661#41—184no—
662C2×Q8—32no—
663C2×Q8—91no—
664C2×Q8—92no—
665C2×D4—32no—
666C2×D4—94no—
667C2×D4—94no—
668C2×D4—91no—
669C2×D4—91no—
670C2×D4—92no—
671C2×D4—91no—
672C2×D4—184no—
673C22×C4—32no—
674C22×C4—94no—
675C22×C4—94no—
676C22×C4—92no—
677C22×C4—92no—
678C22×C4—91no—
679C22×C4—91no—
680C22×C4—92no—
681C22×C4—92no—
682C22×C4—92no—
683C22×C4—92no—
684C22×C4—188no—
685C22×C4C2×D3211yescharacteristic
686C22×C4C2×D3212yes—
687C4⋊C4—34no—
688C4⋊C4—34no—
689C4⋊C4—32no—
690C4⋊C4—32no—
691C4⋊C4—34no—
692C4⋊C4—34no—
693C4⋊C4—34no—
694C4⋊C4—91no—
695C4⋊C4—91no—
696C4⋊C4—92no—
697C4⋊C4—92no—
698C4⋊C4—92no—
699C4⋊C4—94no—
700C4⋊C4—92no—
701C4⋊C4C2×D3211yescharacteristic
702C4⋊C4C2×D3211yescharacteristic
703C4⋊C4C2×D3212yes—
704C22⋊C4—32no—
705C22⋊C4—34no—
706C22⋊C4—34no—
707C22⋊C4—32no—
708C22⋊C4—34no—
709C22⋊C4—94no—
710C22⋊C4—94no—
711C22⋊C4—94no—
712C22⋊C4—94no—
713C22⋊C4—92no—
714C22⋊C4—92no—
715C22⋊C4—92no—
716C22⋊C4—92no—
717C22⋊C4—92no—
718C42—34no—
719C42—34no—
720C42—32no—
721C42—92no—
722C42—94no—
723C42—92no—
724C42—91no—
725C42—91no—
726C42—91no—
727C42—91no—
728C22×C3—22no—
729C22×C3—22no—
730C22×C3—22no—
731C22×C3—22no—
732C22×C3—22no—
733C22×C3—21no—
734C22×C3—62no—
735C22×C3—62no—
736C22×C3—62no—
737C22×C3D3×#4114yes—
738C22×C3C24×D312yes—
739C2×D3—22no—
740C2×D3—22no—
741C2×D3—22no—
742C2×D3—38no—
743C2×D3—64no—
744C2×D3—64no—
745C2×D3—64no—
746C2×D3—64no—
747C2×D3—64no—
748C2×D3—64no—
749C2×D3—64no—
750C2×D3—122no—
751C2×D3—122no—
752C2×D3—122no—
753C2×D3—122no—
754C2×D3—1216no—
755C2×D3—1216no—
756C3×C4—22no—
757C3×C4—24no—
758C3×C4—24no—
759C3×C4—22no—
760C3×C4—22no—
761C3×C4—42no—
762C3×C4—42no—
763C3×C4—62no—
764C3×C4—62no—
765C3×C4—64no—
766C3×C4—64no—
767C3×C4—62no—
768C3×C4D3×#4114yes—
769Dic3—24no—
770Dic3—22no—
771Dic3—22no—
772Dic3—24no—
773Dic3—22no—
774Dic3—34no—
775Dic3—34no—
776Dic3—62no—
777Dic3—62no—
778Dic3—62no—
779Dic3—62no—
780Dic3—121no—
781Dic3—121no—
782C32#347511yescharacteristic, complemented, Sylow
783C23—32no—
784C23—92no—
785C23—92no—
786C23—184no—
787C23—184no—
788C23—362no—
789C23C22×D3211yescharacteristic
790Q8—64no—
791Q8—182no—
792Q8—362no—
793D4—64no—
794D4—94no—
795D4—184no—
796D4—188no—
797D4—182no—
798D4—182no—
799D4—364no—
800C2×C4—24no—
801C2×C4—22no—
802C2×C4—32no—
803C2×C4—32no—
804C2×C4—34no—
805C2×C4—34no—
806C2×C4—32no—
807C2×C4—64no—
808C2×C4—94no—
809C2×C4—91no—
810C2×C4—91no—
811C2×C4—91no—
812C2×C4—91no—
813C2×C4—184no—
814C2×C4—184no—
815C2×C4—184no—
816C2×C4—184no—
817C2×C4—188no—
818C2×C4—184no—
819C2×C4—364no—
820C2×C4—362no—
821C2×C4—361no—
822C2×C4C22×D3212yes—
823C2×C4C22×D3211yescharacteristic
824C2×C4C22×D3212yes—
825C2×C4C22×D3211yescharacteristic
826C2×C3—24no—
827C2×C3—24no—
828C2×C3—21no—
829C2×C3—21no—
830C2×C3—21no—
831C2×C3—122no—
832C2×C3C2×D3×#4112yes—
833C2×C3C2×D3×#4112yes—
834C2×C3#596812yes—
835D3—42no—
836D3—68no—
837D3—124no—
838D3—124no—
839D3—124no—
840C22—21no—
841C22—21no—
842C22—62no—
843C22—62no—
844C22—62no—
845C22—94no—
846C22—182no—
847C22—182no—
848C22—182no—
849C22—182no—
850C22—182no—
851C22—368no—
852C22#6431212yes—
853C22C23×D3211yescharacteristic
854C4—21no—
855C4—22no—
856C4—22no—
857C4—62no—
858C4—64no—
859C4—62no—
860C4—62no—
861C4—64no—
862C4—92no—
863C4—92no—
864C4—181no—
865C4—181no—
866C4#6430612yes—
867C3—21no—
868C3#8682612yescomplemented
869C2—22no—
870C2—122no—
871C2—184no—
872C2—362no—
873C2C2×#6430611yescharacteristic
874C2C2×#6431211yescharacteristic
875C2#1059668911yescharacteristic
subgroupG/H
center, FrattiniC22C23×D32
commutator, socle, cosocleC22×C32C25
FittingC2×C32×C4⋊C4C22
hypercenterC2×C4⋊C4D32
hypocenterC32#3475
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
1. C2×#64102C2semidirect
2. C3×#5513C2semidirect
3. #10595018C2semidirect
4. #10594969C2semidirect
5. #10594966C2semidirect
6. #10594920C2semidirect
7. C4×#3805C2semidirect
8. #10594810C2semidirect
9. #10594575C2semidirect
10. #10594530C2semidirect
11. #10594484C2semidirect
12. #10594476C2semidirect
13. #10594475C2semidirect
14. #10594465C2semidirect
15. #10594453C2semidirect
16. #10594362C2semidirect
17. #10594350C2semidirect
36. C3×#898C22semidirect
37. C3×#897C22semidirect
38. C3×#892C22semidirect
39. C3×#890C22semidirect
40. C3×#889C22semidirect
41. C3×#887C22semidirect
48. #63919C22semidirect
49. C4×#627C22semidirect
50. #63912C22semidirect
51. #63912C22semidirect
54. #63902C22semidirect
55. C4×#625C22semidirect
56. #63900C22semidirect
57. #63900C22semidirect
59. #63895C22semidirect
61. #63890C22semidirect
62. C4×#624C22semidirect
63. #63881C22semidirect
64. #63881C22semidirect
65. #63880C22semidirect
66. #63878C22semidirect
67. C4×D3×Dic3C22semidirect
68. #63874C22semidirect
69. #63874C22semidirect
70. #63873C22semidirect
71. #63870C22semidirect
72. #63868C22semidirect
73. #63865C22semidirect
74. #63865C22semidirect
76. #63854C22semidirect
77. #63852C22semidirect
78. #63849C22semidirect
79. #63848C22semidirect
80. #63843C22semidirect
81. #63838C22semidirect
82. #63838C22semidirect
83. #63836C22semidirect
105. #5513D3semidirect
216. #898C2×D3semidirect
218. #897C2×D3semidirect
247. #892C2×D3semidirect
250. #890C2×D3semidirect
252. #889C2×D3semidirect
257. #887C2×D3semidirect
302. C2×C3⋊Dic3#41semidirect
309. C4⋊(C3⋊D3)#41semidirect
782. C32#3475semidirect
868. C3#86826semidirect

Maximal subgroups

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

subgroupindex
C2×#641022
C3×#55132
#105950182
#105949692
#105949662
#105949202
C4×#38052
#105948102
#105945752
#105945302
#105944842
#105944762
#105944752
#105944652
#105944532
#105943622
#105943502
#868263