Finite Group Databasebeta

← C2×#10595460 #11918768

Subgroups — C2×#10595460 #11918768

Order 1152.

3413 conjugacy classes of subgroups.

The subgroup lattice has 865 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#41×C3⋊D3C211yesmaximal, characteristic, complemented
2C2×#64306C211yesmaximal, characteristic, complemented
3C2×C3×#950C212yesmaximal, complemented
4#10595460C2116yesmaximal, direct product factor
5C2×#63951C212yesmaximal, complemented
6C2×#63945C211yesmaximal, characteristic, complemented
7C2×#63941C211yesmaximal, characteristic, complemented
8C2×#63937C212yesmaximal, complemented
9C2×#63931C211yesmaximal, characteristic, complemented
10C2×#63927C211yesmaximal, characteristic, complemented
11C2×#63829C212yesmaximal, complemented
12C22×#3712C211yesmaximal, characteristic, complemented
13C2×#5768—32nomaximal
14C2×C32×#41C2211yescharacteristic, complemented
15#41×C3⋊D3—24no—
16#41×C3⋊D3C2218yescomplemented
17C2×#3832C2211yescharacteristic
18C2×Q8×C3⋊D3C2211yescharacteristic, complemented
19C2×#3830—21no—
20C2×#3830C2211yescharacteristic
21C2×D4×C3⋊D3—21no—
22C2×D4×C3⋊D3C2211yescharacteristic, complemented
23C2×#3828—21no—
24C2×#3828C2211yescharacteristic, complemented
25C22×C4×C3⋊D3—21no—
26C22×C4×C3⋊D3C2211yescharacteristic
27C2×C3×#235C2212yescomplemented
28C2×#3811—21no—
29C2×#3805—21no—
30#64306—24no—
31#64306C2218yescomplemented
32C2×#3802C2211yescharacteristic, complemented
33C2×C4×D32—21no—
34C2×#3798—21no—
35C2×#3797C2211yescharacteristic, complemented
36C2×#3796C2212yes—
37C3×#950C22116yescomplemented
38C2×C3×#216C2212yescomplemented
39C2×C3×#215C2212yescomplemented
40C2×C3×#214C2212yescomplemented
41C2×C3×#213C2212yescomplemented
42C22×C3×C3⋊C8C2212yescomplemented
43#63951C22116yescomplemented
44#63945C2218yescomplemented
45#63941C2218yescomplemented
46#63937C22116yescomplemented
47#63931C2218yescomplemented
48#63927C2218yescomplemented
49C2×#3719C2212yescomplemented
50C2×#3717C2212yescomplemented
51#63829C22116yescomplemented
52C2×#3716C2212yescomplemented
53C2×#3714C2212yescomplemented
54C2×#3712C2211yescharacteristic, complemented
55C2×#3712C2212yescomplemented
56C2×#3712C2211yescharacteristic, complemented
57C2×#3712C2218yescomplemented
58C2×D3×#41—32no—
59C2×D3×#41—32no—
60C2×D3×#41—61no—
61C2×C3×#135—32no—
62C2×#950—32no—
63C2×#950D312yescomplemented
64#5768—332no—
65C2×#918—32no—
66C2×#918—32no—
67C2×#915—32no—
68C2×#915—32no—
69C2×#914—32no—
70C2×#914—32no—
71C2×#911—32no—
72C2×#911—32no—
73C2×#904—32no—
74C22×ΓL(1,𝔽25)—32no—
75C23×C3⋊D3—21no—
76C23×C3⋊D3D411yescharacteristic
77C22×D32—21no—
78C32×#41—22no—
79C32×#41C2314yescomplemented
80C2×C32×Q8C2311yescharacteristic
81C2×C32×D4—21no—
82C2×C32×D4C2311yescharacteristic
83C22×C32×C4—21no—
84C22×C32×C4C2311yescharacteristic
85C2×#638—21no—
86C2×#638—21no—
87C2×#638—21no—
88C22×C3⋊Dic3—21no—
89C22×C3⋊Dic3D411yescharacteristic
90#3832—22no—
91#3832C2314yes—
92Q8×C3⋊D3—22no—
93Q8×C3⋊D3C2314yescomplemented
94#3830—28no—
95#3830—22no—
96#3830C2314yes—
97D4×C3⋊D3—28no—
98D4×C3⋊D3—22no—
99D4×C3⋊D3C2314yescomplemented
100#3828—22no—
101#3828—28no—
102#3828C2314yescomplemented
103C2×C4⋊(C3⋊D3)—21no—
104C2×C4⋊(C3⋊D3)C2311yescharacteristic
105C2×C4×C3⋊D3—21no—
106C2×C4×C3⋊D3—21no—
107C2×C4×C3⋊D3—21no—
108C2×C4×C3⋊D3—28no—
109C2×C4×C3⋊D3D411yescharacteristic
110C2×C4×C3⋊D3D411yescharacteristic
111C2×C4×C3⋊D3D414yes—
112C2×C4×C3⋊D3C2311yescharacteristic
113C2×C4×C3⋊D3C2311yescharacteristic
114C2×C4×C3⋊D3C2314yes—
115C2×#634—21no—
116C2×#634C2311yescharacteristic
117C2×C3×#67—22no—
118C3×#235—24no—
119C3×#235C2318yescomplemented
120C2×C3×D12C2312yes—
121C2×C3×C4×D3—22no—
122C2×C3×Dic6C2312yes—
123#3811—28no—
124C2×#627—21no—
125C2×#626—22no—
126C2×#625—21no—
127C2×#624—21no—
128#3805—28no—
129C2×D3×Dic3—22no—
130#3802—22no—
131#3802C2314yescomplemented
132C4×D32—28no—
133#3798—28no—
134#3797—22no—
135#3797C2314yescomplemented
136#3796—24no—
137#3796C2318yes—
138C3×#216C2318yescomplemented
139C3×#215C2318yescomplemented
140C3×#214C2318yescomplemented
141C3×#213C2318yescomplemented
142C2×C3×C3⋊C8C2312yes—
143C2×C3×C3⋊C8C2312yes—
144C2×C3×C3⋊C8C2318yescomplemented
145#3719C2318yescomplemented
146#3717C2318yescomplemented
147#3716C2318yescomplemented
148#3714C2318yescomplemented
149#3712C2314yescomplemented
150#3712C2314yescomplemented
151#3712C2318yescomplemented
152C2×#575—91noSylow
153C2×C3×#41—21no—
154C2×C3×#41—32no—
155C2×C3×#41C2×D312yescomplemented
156D3×#41—316no—
157D3×#41—316no—
158D3×#41—68no—
159D3×#41—68no—
160D3×#41—68no—
161D3×#41—68no—
162C2×#239—32no—
163C2×#239—32no—
164C2×#239—61no—
165C2×D3×Q8—32no—
166C2×D3×Q8—32no—
167C2×D3×Q8—61no—
168C2×#237—32no—
169C2×#237—32no—
170C2×#237—61no—
171C2×#237—62no—
172C2×#237—62no—
173C2×#237—62no—
174C2×D3×D4—32no—
175C2×D3×D4—32no—
176C2×D3×D4—61no—
177C2×D3×D4—62no—
178C2×D3×D4—62no—
179C2×D3×D4—62no—
180C2×#235—32no—
181C2×#235—61no—
182C2×#235—62no—
183C2×#235—62no—
184C2×#235—62no—
185C2×#235C2×D312yescomplemented
186C22×C4×D3—32no—
187C22×C4×D3—61no—
188C22×C4×D3—62no—
189C22×C4×D3—62no—
190C22×C4×D3—62no—
191C3×#135—316no—
192C2×C3×Q16—32no—
193C2×C3×SD16—32no—
194C2×C3×SD16—32no—
195C2×C3×D8—32no—
196C22×C3×C8—32no—
197#950—316no—
198#950C2×D3116yescomplemented
199C2×#216—32no—
200C2×#216C2×D312yescomplemented
201C2×#215—32no—
202C2×#215C2×D312yescomplemented
203C2×#214—32no—
204C2×#214C2×D312yescomplemented
205C2×#213—32no—
206C2×#213C2×D312yescomplemented
207C22×C3⋊C8C2×D312yescomplemented
208#918—316no—
209#918—316no—
210#915—316no—
211#915—316no—
212#914—316no—
213#914—316no—
214#911—316no—
215#911—316no—
216C2×Dic12—32no—
217#904—316no—
218C2×D24—32no—
219C2×#204—32no—
220C2×#204—32no—
221C2×ΓL(1,𝔽25)—32no—
222C2×ΓL(1,𝔽25)—32no—
223C2×ΓL(1,𝔽25)—32no—
224C2×ΓL(1,𝔽25)—32no—
225C2×ΓL(1,𝔽25)—316no—
226C23×C32—21no—
227C23×C32C2×D411yescharacteristic
228C22×C3⋊D3—21no—
229C22×C3⋊D3—24no—
230C22×C3⋊D3—42no—
231C22×C3⋊D3—44no—
232C22×C3⋊D3C2×D411yescharacteristic
233C22×C3⋊D3C2×D411yescharacteristic
234C22×C3⋊D3C2×D414yes—
235C22×C3×D3—22no—
236C2×D32—24no—
237C2×D32—44no—
238C32×Q8—21no—
239C32×Q8C2412yes—
240C32×D4—24no—
241C32×D4—21no—
242C32×D4C2412yes—
243C2×C32×C4—21no—
244C2×C32×C4—24no—
245C2×C32×C4C2×D411yescharacteristic
246C2×C32×C4C2×D412yes—
247C2×C32×C4C2411yescharacteristic
248C2×C32×C4C2412yes—
249#638—24no—
250#638—24no—
251#638—24no—
252C2×C3⋊Dic3—21no—
253C2×C3⋊Dic3—24no—
254C2×C3⋊Dic3C2×D411yescharacteristic
255C2×C3⋊Dic3C2×D414yes—
256C2×C3⋊Dic3C2×D411yescharacteristic
257C4⋊(C3⋊D3)—24no—
258C4⋊(C3⋊D3)—21no—
259C4⋊(C3⋊D3)C2412yes—
260C4×C3⋊D3—24no—
261C4×C3⋊D3—24no—
262C4×C3⋊D3—24no—
263C4×C3⋊D3C2×D412yes—
264C4×C3⋊D3C2×D412yes—
265C4×C3⋊D3C2×D414yes—
266C4×C3⋊D3C2×D414yes—
267C4×C3⋊D3C2412yes—
268C4×C3⋊D3C2412yes—
269#634—21no—
270#634—24no—
271#634C2412yes—
272C3×#67—28no—
273C2×C3×Dic3—22no—
274C3×D12—22no—
275C3×D12C2414yes—
276C3×C4×D3—28no—
277C3×Dic6—22no—
278C3×Dic6C2414yes—
279#627—24no—
280#626—28no—
281#625—24no—
282#624—24no—
283D3×Dic3—28no—
284C3×C3⋊C8C2414yes—
285C3×C3⋊C8C2414yes—
286C22×#41—91no—
287C22×#41—91no—
288#575—916no—
289C2×#137—91no—
290C2×#137—92no—
291C2×#137—91no—
292C2×AGL(1,ℤ/8)—91no—
293C2×AGL(1,ℤ/8)—92no—
294C2×AGL(1,ℤ/8)—91no—
295C2×#135—32no—
296C2×#135—92no—
297C22×M16—91no—
298C23×D3—32no—
299C23×D3—61no—
300C23×D3—62no—
301C23×D3—62no—
302C23×D3—62no—
303C3×#41—24no—
304C3×#41—24no—
305C3×#41—24no—
306C3×#41—38no—
307C3×#41—64no—
308C3×#41C22×D318yescomplemented
309C2×C3×Q8—21no—
310C2×C3×Q8—32no—
311C2×C3×Q8C22×D312yes—
312C2×C3×D4—22no—
313C2×C3×D4—22no—
314C2×C3×D4—21no—
315C2×C3×D4—32no—
316C2×C3×D4—62no—
317C2×C3×D4C22×D312yes—
318C22×C3×C4—22no—
319C22×C3×C4—22no—
320C22×C3×C4—21no—
321C22×C3×C4—62no—
322C22×C3×C4C22×D312yes—
323C2×#67—22no—
324C2×#67—62no—
325C2×#67—62no—
326C2×#67—62no—
327C2×#67—62no—
328C2×#67—62no—
329C2×#67—62no—
330C2×#67—62no—
331C2×#67—62no—
332C22×Dic3—32no—
333C22×Dic3—61no—
334C22×Dic3—62no—
335C22×Dic3—62no—
336C22×Dic3—62no—
337#239—38no—
338#239—38no—
339#239—64no—
340#239—64no—
341#239—64no—
342#239—64no—
343D3×Q8—38no—
344D3×Q8—38no—
345D3×Q8—64no—
346D3×Q8—64no—
347D3×Q8—64no—
348D3×Q8—64no—
349#237—38no—
350#237—38no—
351#237—64no—
352#237—64no—
353#237—64no—
354#237—616no—
355#237—616no—
356#237—64no—
357#237—616no—
358D3×D4—38no—
359D3×D4—38no—
360D3×D4—64no—
361D3×D4—64no—
362D3×D4—64no—
363D3×D4—616no—
364D3×D4—616no—
365D3×D4—64no—
366D3×D4—616no—
367#235—24no—
368#235—38no—
369#235—64no—
370#235—616no—
371#235—616no—
372#235—616no—
373#235—64no—
374#235—64no—
375#235C22×D318yescomplemented
376C2×D12—32no—
377C2×D12—61no—
378C2×D12—62no—
379C2×D12—62no—
380C2×D12—62no—
381C2×D12C22×D312yes—
382C2×C4×D3—22no—
383C2×C4×D3—32no—
384C2×C4×D3—32no—
385C2×C4×D3—38no—
386C2×C4×D3—32no—
387C2×C4×D3—32no—
388C2×C4×D3—38no—
389C2×C4×D3—61no—
390C2×C4×D3—61no—
391C2×C4×D3—61no—
392C2×C4×D3—61no—
393C2×C4×D3—64no—
394C2×C4×D3—64no—
395C2×C4×D3—616no—
396C2×C4×D3—616no—
397C2×C4×D3—62no—
398C2×C4×D3—62no—
399C2×C4×D3—62no—
400C2×C4×D3—62no—
401C2×C4×D3—62no—
402C2×C4×D3—62no—
403C2×C4×D3—62no—
404C2×C4×D3—616no—
405C2×C4×D3—62no—
406C2×Dic6—32no—
407C2×Dic6—61no—
408C2×Dic6—62no—
409C2×Dic6—62no—
410C2×Dic6—62no—
411C2×Dic6C22×D312yes—
412C3×Q16—38no—
413C3×SD16—38no—
414C3×SD16—38no—
415C3×D8—38no—
416C2×C3×C8—32no—
417C2×C3×C8—32no—
418C2×C3×C8—38no—
419#216—38no—
420#216C22×D318yescomplemented
421#215—38no—
422#215C22×D318yescomplemented
423#214—38no—
424#214C22×D318yescomplemented
425#213—38no—
426#213C22×D318yescomplemented
427C2×C3⋊C8C22×D312yes—
428C2×C3⋊C8C22×D312yes—
429C2×C3⋊C8C22×D318yescomplemented
430Dic12—38no—
431D24—38no—
432#204—38no—
433#204—38no—
434ΓL(1,𝔽25)—38no—
435ΓL(1,𝔽25)—38no—
436ΓL(1,𝔽25)—38no—
437ΓL(1,𝔽25)—38no—
438C22×C32—22no—
439C22×C32—22no—
440C22×C32—42no—
441C22×C32C22×D412yes—
442C22×C32C22×D411yescharacteristic
443C2×C3⋊D3—22no—
444C2×C3⋊D3—22no—
445C2×C3⋊D3—22no—
446C2×C3⋊D3—44no—
447C2×C3⋊D3—48no—
448C2×C3⋊D3—42no—
449C2×C3⋊D3C22×D412yes—
450C2×C3⋊D3C22×D412yes—
451C2×C3×D3—24no—
452C2×C3×D3—44no—
453D32—48no—
454C32×C4—22no—
455C32×C4C22×D411yescharacteristic
456C32×C4C22×D412yes—
457C32×C4C2511yescharacteristic
458C3⋊Dic3—22no—
459C3⋊Dic3C22×D412yes—
460C3⋊Dic3C22×D412yes—
461C3×Dic3—24no—
462C2×#41—32no—
463C2×#41—92no—
464C2×#41—98no—
465C2×#41—98no—
466C2×#41—91no—
467C2×#41—91no—
468C2×#41—91no—
469C2×#41—181no—
470C2×#41—181no—
471C2×#41—181no—
472C2×#41—181no—
473C2×#41—184no—
474C2×#41—184no—
475C2×#41D3211yescharacteristic, complemented
476C22×Q8—91no—
477C22×Q8—91no—
478C22×D4—91no—
479C22×D4—91no—
480C22×D4—181no—
481C22×D4—181no—
482C23×C4—91no—
483C23×C4—181no—
484C23×C4—181no—
485#137—98no—
486#137—916no—
487#137—98no—
488AGL(1,ℤ/8)—98no—
489AGL(1,ℤ/8)—916no—
490AGL(1,ℤ/8)—98no—
491#135—316no—
492#135—916no—
493C2×Q16—32no—
494C2×Q16—92no—
495C2×SD16—32no—
496C2×SD16—32no—
497C2×SD16—92no—
498C2×SD16—92no—
499C2×D8—32no—
500C2×D8—92no—
501C2×M16—91no—
502C2×M16—92no—
503C2×M16—91no—
504C2×M16—98no—
505C22×C8—32no—
506C23×C3—22no—
507C23×C3—22no—
508C23×C3—21no—
509C23×C3—62no—
510C23×C3D3×D412yes—
511C22×D3—22no—
512C22×D3—32no—
513C22×D3—32no—
514C22×D3—38no—
515C22×D3—61no—
516C22×D3—61no—
517C22×D3—64no—
518C22×D3—68no—
519C22×D3—68no—
520C22×D3—62no—
521C22×D3—68no—
522C22×D3—62no—
523C22×D3—128no—
524C22×D3—124no—
525C22×D3—124no—
526C22×D3—128no—
527C22×D3—128no—
528C3×Q8—22no—
529C3×Q8—22no—
530C3×Q8—22no—
531C3×Q8—34no—
532C3×Q8—62no—
533C3×Q8C23×D314yes—
534C3×D4—28no—
535C3×D4—22no—
536C3×D4—28no—
537C3×D4—22no—
538C3×D4—22no—
539C3×D4—34no—
540C3×D4—68no—
541C3×D4—62no—
542C3×D4C23×D314yes—
543C2×C3×C4—22no—
544C2×C3×C4—28no—
545C2×C3×C4—22no—
546C2×C3×C4—28no—
547C2×C3×C4—21no—
548C2×C3×C4—22no—
549C2×C3×C4—22no—
550C2×C3×C4—21no—
551C2×C3×C4—62no—
552C2×C3×C4—68no—
553C2×C3×C4D3×D414yes—
554C2×C3×C4D3×D412yes—
555C2×C3×C4C23×D312yes—
556C2×C3×C4C23×D314yes—
557#67—28no—
558#67—68no—
559#67—68no—
560#67—68no—
561#67—68no—
562#67—68no—
563#67—68no—
564#67—68no—
565#67—68no—
566C2×Dic3—22no—
567C2×Dic3—32no—
568C2×Dic3—32no—
569C2×Dic3—38no—
570C2×Dic3—61no—
571C2×Dic3—61no—
572C2×Dic3—64no—
573C2×Dic3—68no—
574C2×Dic3—68no—
575C2×Dic3—62no—
576C2×Dic3—68no—
577C2×Dic3—62no—
578D12—22no—
579D12—34no—
580D12—62no—
581D12—68no—
582D12—68no—
583D12—62no—
584D12—68no—
585D12—62no—
586D12C23×D314yes—
587C4×D3—28no—
588C4×D3—38no—
589C4×D3—38no—
590C4×D3—34no—
591C4×D3—34no—
592C4×D3—34no—
593C4×D3—34no—
594C4×D3—64no—
595C4×D3—64no—
596C4×D3—62no—
597C4×D3—62no—
598C4×D3—62no—
599C4×D3—62no—
600C4×D3—68no—
601C4×D3—68no—
602C4×D3—68no—
603C4×D3—68no—
604C4×D3—68no—
605C4×D3—68no—
606C4×D3—68no—
607C4×D3—68no—
608Dic6—22no—
609Dic6—34no—
610Dic6—62no—
611Dic6—68no—
612Dic6—68no—
613Dic6—68no—
614Dic6—62no—
615Dic6—62no—
616Dic6C23×D314yes—
617C3×C8—34no—
618C3×C8—34no—
619C3⋊C8C23×D314yes—
620C3⋊C8C23×D314yes—
621C2×C32—22no—
622C2×C32—42no—
623C2×C32#57512yescomplemented
624C2×C32C23×D411yescharacteristic
625C3⋊D3—22no—
626C3⋊D3—22no—
627C3⋊D3—42no—
628C3×D3—44no—
629C24—91no—
630C24—181no—
631C24—181no—
632#41—22no—
633#41—38no—
634#41—64no—
635#41—98no—
636#41—94no—
637#41—94no—
638#41—94no—
639#41—188no—
640#41—188no—
641#41—188no—
642#41—182no—
643#41—188no—
644#41—184no—
645#41—182no—
646#41—182no—
647#41C2×D3214yescomplemented
648C2×Q8—32no—
649C2×Q8—94no—
650C2×Q8—94no—
651C2×Q8—91no—
652C2×Q8—181no—
653C2×Q8—181no—
654C2×Q8—182no—
655C2×Q8—182no—
656C2×Q8C2×D3211yescharacteristic
657C2×D4—21no—
658C2×D4—32no—
659C2×D4—62no—
660C2×D4—94no—
661C2×D4—94no—
662C2×D4—91no—
663C2×D4—181no—
664C2×D4—182no—
665C2×D4—182no—
666C2×D4—182no—
667C2×D4—181no—
668C2×D4—181no—
669C2×D4—188no—
670C2×D4—188no—
671C2×D4—181no—
672C2×D4—181no—
673C2×D4C2×D3211yescharacteristic
674C22×C4—21no—
675C22×C4—62no—
676C22×C4—91no—
677C22×C4—91no—
678C22×C4—91no—
679C22×C4—94no—
680C22×C4—94no—
681C22×C4—91no—
682C22×C4—91no—
683C22×C4—181no—
684C22×C4—188no—
685C22×C4—181no—
686C22×C4—188no—
687C22×C4—181no—
688C22×C4—182no—
689C22×C4—181no—
690C22×C4—181no—
691C22×C4C2×D3211yescharacteristic
692Q16—38no—
693Q16—98no—
694SD16—38no—
695SD16—38no—
696SD16—98no—
697SD16—98no—
698D8—38no—
699D8—98no—
700M16—94no—
701M16—98no—
702M16—94no—
703C2×C8—32no—
704C2×C8—32no—
705C2×C8—38no—
706C22×C3—24no—
707C22×C3—24no—
708C22×C3—24no—
709C22×C3—21no—
710C22×C3—22no—
711C22×C3—42no—
712C22×C3—44no—
713C22×C3—44no—
714C22×C3—64no—
715C22×C3—124no—
716C22×C3C2×D3×D414yes—
717C22×C3C2×D3×D412yes—
718C2×D3—24no—
719C2×D3—34no—
720C2×D3—34no—
721C2×D3—44no—
722C2×D3—62no—
723C2×D3—62no—
724C2×D3—64no—
725C2×D3—64no—
726C2×D3—64no—
727C2×D3—64no—
728C2×D3—64no—
729C2×D3—122no—
730C2×D3—1216no—
731C2×D3—128no—
732C2×D3—128no—
733C2×D3—1216no—
734C2×D3—1216no—
735C2×D3—124no—
736C2×D3—124no—
737C3×C4—24no—
738C3×C4—24no—
739C3×C4—21no—
740C3×C4—22no—
741C3×C4—21no—
742C3×C4—64no—
743C3×C4C2×D3×D412yes—
744C3×C4C2×D3×D414yes—
745C3×C4C24×D312yes—
746Dic3—24no—
747Dic3—34no—
748Dic3—34no—
749Dic3—62no—
750Dic3—62no—
751Dic3—64no—
752Dic3—64no—
753C32C2×#57511yescharacteristic, complemented, Sylow
754C23—21no—
755C23—62no—
756C23—91no—
757C23—91no—
758C23—94no—
759C23—184no—
760C23—184no—
761C23—181no—
762C23—362no—
763C23—364no—
764C23—364no—
765C23#381111yescharacteristic
766Q8—21no—
767Q8—34no—
768Q8—62no—
769Q8—92no—
770Q8—184no—
771Q8—184no—
772Q8—181no—
773Q8C22×D3212yes—
774D4—24no—
775D4—21no—
776D4—34no—
777D4—68no—
778D4—62no—
779D4—92no—
780D4—184no—
781D4—188no—
782D4—184no—
783D4—184no—
784D4—184no—
785D4—184no—
786D4—181no—
787D4C22×D3212yes—
788C2×C4—21no—
789C2×C4—24no—
790C2×C4—62no—
791C2×C4—68no—
792C2×C4—91no—
793C2×C4—91no—
794C2×C4—94no—
795C2×C4—94no—
796C2×C4—94no—
797C2×C4—92no—
798C2×C4—92no—
799C2×C4—92no—
800C2×C4—92no—
801C2×C4—184no—
802C2×C4—184no—
803C2×C4—184no—
804C2×C4—188no—
805C2×C4—184no—
806C2×C4—181no—
807C2×C4—184no—
808C2×C4#381112yes—
809C2×C4#381111yescharacteristic
810C2×C4C22×D3211yescharacteristic
811C2×C4C22×D3212yes—
812C8—34no—
813C8—34no—
814C2×C3—24no—
815C2×C3—21no—
816C2×C3—22no—
817C2×C3—42no—
818C2×C3—44no—
819C2×C3—44no—
820C2×C3—124no—
821C2×C3#576814yescomplemented
822C2×C3C22×D3×D412yes—
823D3—44no—
824D3—64no—
825D3—64no—
826D3—64no—
827D3—122no—
828D3—124no—
829D3—124no—
830C22—22no—
831C22—22no—
832C22—42no—
833C22—64no—
834C22—92no—
835C22—92no—
836C22—124no—
837C22—182no—
838C22—182no—
839C22—182no—
840C22—364no—
841C22—368no—
842C22—368no—
843C22—362no—
844C22C2×#381112yes—
845C22C2×#381111yescharacteristic
846C4—22no—
847C4—64no—
848C4—92no—
849C4—92no—
850C4—182no—
851C4C2×#381112yes—
852C4C2×#381111yescharacteristic
853C4C23×D3211yescharacteristic
854C3—21no—
855C3C2×#576812yescomplemented
856C2—22no—
857C2—42no—
858C2—124no—
859C2—182no—
860C2—182no—
861C2—362no—
862C2#1059546012yesdirect product factor
863C2C22×#381111yescharacteristic
subgroupG/H
centerC2×C4#3811
commutator, cosocleC32×C4C25
FrattiniC4C23×D32
FittingC2×C32×#41C22
socleC22×C32C22×D4
hypercenterC2×#41D32
hypocenterC32C2×#575
LCSG ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C2×#41

Complements

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

NH ≅ G/Ntype
1. C2×#41×C3⋊D3C2semidirect
2. C2×#64306C2semidirect
3. C2×C3×#950C2semidirect
4. #10595460C2direct (N × H)
5. C2×#63951C2semidirect
6. C2×#63945C2semidirect
7. C2×#63941C2semidirect
8. C2×#63937C2semidirect
9. C2×#63931C2semidirect
10. C2×#63927C2semidirect
11. C2×#63829C2semidirect
12. C22×#3712C2semidirect
14. C2×C32×#41C22semidirect
16. #41×C3⋊D3C22semidirect
18. C2×Q8×C3⋊D3C22semidirect
22. C2×D4×C3⋊D3C22semidirect
24. C2×#3828C22semidirect
27. C2×C3×#235C22semidirect
31. #64306C22semidirect
32. C2×#3802C22semidirect
35. C2×#3797C22semidirect
37. C3×#950C22semidirect
38. C2×C3×#216C22semidirect
39. C2×C3×#215C22semidirect
40. C2×C3×#214C22semidirect
41. C2×C3×#213C22semidirect
42. C22×C3×C3⋊C8C22semidirect
43. #63951C22semidirect
44. #63945C22semidirect
45. #63941C22semidirect
46. #63937C22semidirect
47. #63931C22semidirect
48. #63927C22semidirect
49. C2×#3719C22semidirect
50. C2×#3717C22semidirect
51. #63829C22semidirect
52. C2×#3716C22semidirect
53. C2×#3714C22semidirect
54. C2×#3712C22semidirect
55. C2×#3712C22semidirect
56. C2×#3712C22semidirect
57. C2×#3712C22semidirect
63. C2×#950D3semidirect
79. C32×#41C23semidirect
93. Q8×C3⋊D3C23semidirect
99. D4×C3⋊D3C23semidirect
102. #3828C23semidirect
119. C3×#235C23semidirect
131. #3802C23semidirect
135. #3797C23semidirect
138. C3×#216C23semidirect
139. C3×#215C23semidirect
140. C3×#214C23semidirect
141. C3×#213C23semidirect
144. C2×C3×C3⋊C8C23semidirect
145. #3719C23semidirect
146. #3717C23semidirect
147. #3716C23semidirect
148. #3714C23semidirect
149. #3712C23semidirect
150. #3712C23semidirect
151. #3712C23semidirect
155. C2×C3×#41C2×D3semidirect
185. C2×#235C2×D3semidirect
198. #950C2×D3semidirect
200. C2×#216C2×D3semidirect
202. C2×#215C2×D3semidirect
204. C2×#214C2×D3semidirect
206. C2×#213C2×D3semidirect
207. C22×C3⋊C8C2×D3semidirect
308. C3×#41C22×D3semidirect
375. #235C22×D3semidirect
420. #216C22×D3semidirect
422. #215C22×D3semidirect
424. #214C22×D3semidirect
426. #213C22×D3semidirect
429. C2×C3⋊C8C22×D3semidirect
475. C2×#41D32semidirect
623. C2×C32#575semidirect
647. #41C2×D32semidirect
753. C32C2×#575semidirect
821. C2×C3#5768semidirect
855. C3C2×#5768semidirect
862. C2#10595460direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#41×C3⋊D32
C2×#643062
C2×C3×#9502
#105954602
C2×#639512
C2×#639452
C2×#639412
C2×#639372
C2×#639312
C2×#639272
C2×#638292
C22×#37122
C2×#57683