Finite Group Databasebeta

← C2×#10594715 #11918890

Subgroups — C2×#10594715 #11918890

Order 1152.

3069 conjugacy classes of subgroups.

The subgroup lattice has 869 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64308C211yesmaximal, characteristic, complemented
2C2×#64297C211yesmaximal, characteristic, complemented
3C2×#64117C211yesmaximal, characteristic, complemented
4C2×C3×#909C211yesmaximal, characteristic, complemented
5C2×C3×#907C211yesmaximal, characteristic, complemented
6C22×#3717C211yesmaximal, characteristic, complemented
7C2×#63829C211yesmaximal, characteristic, complemented
8#10594715C2116yesmaximal, direct product factor
9C2×#63808C212yesmaximal, complemented
10C2×#63801C212yesmaximal, complemented
11C2×#63794C212yesmaximal, complemented
12C2×D3×#204C212yesmaximal, complemented
13C2×#5778—31nomaximal
14C2×#5751—31nomaximal
15C2×#3828C2211yescharacteristic, complemented
16C22×C4⋊(C3⋊D3)C2211yescharacteristic
17C2×C3×#235C2211yescharacteristic
18C2×C3×#235C2211yescharacteristic
19C22×C3×Dic6C2211yescharacteristic, complemented
20C2×#3811—22no—
21C2×#3804—22no—
22#64308—24no—
23#64308C2218yescomplemented
24C2×D3×D12—21no—
25C2×D3×D12C2212yes—
26C2×#3799—21no—
27C2×#3799C2212yes—
28C2×#3799C2212yescomplemented
29C2×#3797—21no—
30#64297—24no—
31#64297C2218yescomplemented
32C2×#3796—21no—
33C2×D3×Dic6C2212yescomplemented
34C2×C32×M16C2211yescharacteristic, complemented
35#64117C2218yescomplemented
36C2×#3745C2212yescomplemented
37C2×#3744C2212yescomplemented
38C22×C3×C3⋊C8C2211yescharacteristic, complemented
39C3×#909C2218yescomplemented
40C3×#907C2218yescomplemented
41C2×C3×Dic12C2212yescomplemented
42C2×C3×#204C2212yescomplemented
43C2×C3×ΓL(1,𝔽25)C2212yescomplemented
44C2×C3×D3×C8C2212yescomplemented
45C2×#3719C2211yescharacteristic, complemented
46C2×#3717C2212yescomplemented
47C2×#3717C2212yescomplemented
48C2×#3717C2211yescharacteristic, complemented
49C2×#3717C2218yescomplemented
50#63829C2218yescomplemented
51C2×#3716C2211yescharacteristic, complemented
52C2×#3714C2211yescharacteristic, complemented
53#63808C22116yescomplemented
54#63801C22116yescomplemented
55#63794C22116yescomplemented
56D3×#204C22116yescomplemented
57C2×#1010—31no—
58C2×#1009—31no—
59C2×#1009—31no—
60C2×#1007—31no—
61C2×C3×#137—31no—
62C2×C3×#131—31no—
63C2×#950—31no—
64C22×#215—31no—
65#5778—316no—
66C2×#919—32no—
67C2×#918—32no—
68C2×#914—32no—
69C2×D3×SD16—32no—
70#5751—316no—
71C2×#909—32no—
72C2×#909D311yescharacteristic, complemented
73C2×#908—31no—
74C2×#908—31no—
75C2×#908—32no—
76C2×#908—61no—
77C2×#907D311yescharacteristic, complemented
78C2×#904—31no—
79C2×#904—32no—
80C22×#204—31no—
81C22×#204—32no—
82C23×C3⋊D3—21no—
83C22×D32—22no—
84C22×C32×C4C2311yescharacteristic
85C2×#638—21no—
86#3828—22no—
87#3828C2314yescomplemented
88C2×C4⋊(C3⋊D3)—21no—
89C2×C4⋊(C3⋊D3)—22no—
90C2×C4⋊(C3⋊D3)C2312yes—
91C2×C4⋊(C3⋊D3)C2311yescharacteristic
92C2×C4⋊(C3⋊D3)C2314yes—
93C2×C4×C3⋊D3—21no—
94C2×#634C2311yescharacteristic
95C2×C3×#67—21no—
96C2×C3×#67D412yes—
97C22×C3×Dic3—21no—
98C3×#235—22no—
99C3×#235D414yes—
100C3×#235C2314yes—
101C3×#235C2314yes—
102C2×C3×D12D411yescharacteristic
103C2×C3×D12C2311yescharacteristic
104C2×C3×C4×D3—21no—
105C2×C3×C4×D3C2312yes—
106C2×C3×Dic6—21no—
107C2×C3×Dic6—22no—
108C2×C3×Dic6D411yescharacteristic
109C2×C3×Dic6C2312yes—
110C2×C3×Dic6C2311yescharacteristic
111C2×C3×Dic6C2314yescomplemented
112#3811—216no—
113C2×#627—22no—
114C2×#626—22no—
115C2×#626—22no—
116C2×#626—22no—
117C2×#624—22no—
118C2×#624—22no—
119#3804—216no—
120C2×D3×Dic3—22no—
121D3×D12—28no—
122D3×D12—24no—
123D3×D12C2318yes—
124#3799—24no—
125#3799—24no—
126#3799—28no—
127#3799C2318yes—
128#3799C2318yescomplemented
129#3797—28no—
130#3796—28no—
131D3×Dic6—24no—
132D3×Dic6C2318yescomplemented
133C32×M16C2314yescomplemented
134C2×C32×C8C2312yes—
135#3745C2318yescomplemented
136#3744C2318yescomplemented
137C2×C3×C3⋊C8C2311yescharacteristic
138C2×C3×C3⋊C8C2311yescharacteristic
139C2×C3×C3⋊C8C2314yescomplemented
140C3×Dic12C2318yescomplemented
141C3×#204C2318yescomplemented
142C3×ΓL(1,𝔽25)C2318yescomplemented
143C3×D3×C8C2318yescomplemented
144#3719C2314yescomplemented
145#3717C2318yescomplemented
146#3717C2318yescomplemented
147#3717C2314yescomplemented
148#3716C2314yescomplemented
149#3714C2314yescomplemented
150C2×#577—91noSylow
151C2×C3×#41—31no—
152C2×C3×#41—31no—
153C22×C3×Q8—31no—
154#1010—38no—
155#1010—64no—
156#1009—38no—
157#1009—38no—
158#1009—64no—
159#1009—64no—
160#1007—38no—
161#1007—64no—
162C2×#239—32no—
163C2×#239—32no—
164C2×#239—61no—
165C2×#239—61no—
166C2×D3×Q8—32no—
167C2×D3×Q8—61no—
168C2×D3×Q8—61no—
169C2×#237—61no—
170C2×#237—62no—
171C2×D3×D4—32no—
172C2×D3×D4—61no—
173C2×D3×D4—62no—
174C2×D3×D4—62no—
175C2×#235—31no—
176C2×#235—31no—
177C2×#235—32no—
178C2×#235—32no—
179C2×#235—61no—
180C2×#235—62no—
181C2×#235—61no—
182C2×#235C2×D311yescharacteristic
183C2×#235C2×D311yescharacteristic
184C22×D12—31no—
185C22×D12—31no—
186C22×D12—32no—
187C22×D12—61no—
188C22×D12—61no—
189C22×Dic6—32no—
190C22×Dic6C2×D311yescharacteristic, complemented
191C3×#137—38no—
192C2×C3×Q16—32no—
193C2×C3×SD16—32no—
194C3×#131—38no—
195C2×C3×M16—21no—
196C2×C3×M16—32no—
197C2×C3×M16C2×D311yescharacteristic, complemented
198C2×C3×M16C2×D311yescharacteristic, complemented
199C22×C3×C8—31no—
200C22×C3×C8—32no—
201#950—38no—
202C2×#216—31no—
203C2×#215—32no—
204C2×#215—32no—
205C2×#215—31no—
206C2×#215—38no—
207C2×#214—31no—
208C2×#213—31no—
209C22×C3⋊C8C2×D311yescharacteristic, complemented
210#919—316no—
211#918—316no—
212#914—316no—
213D3×SD16—316no—
214#909—316no—
215#909C2×D318yescomplemented
216#908—38no—
217#908—38no—
218#908—316no—
219#908—68no—
220#907C2×D318yescomplemented
221C2×Dic12—31no—
222C2×Dic12C2×D312yescomplemented
223#904—38no—
224#904—316no—
225C2×D24—31no—
226C2×D24—32no—
227C2×D24—32no—
228C2×D24—62no—
229C2×#204—31no—
230C2×#204—32no—
231C2×#204—32no—
232C2×#204—31no—
233C2×#204—38no—
234C2×#204—32no—
235C2×#204—32no—
236C2×#204—316no—
237C2×#204—62no—
238C2×#204C2×D312yescomplemented
239C2×ΓL(1,𝔽25)C2×D312yescomplemented
240C2×D3×C8C2×D312yescomplemented
241C23×C32C2×D411yescharacteristic
242C22×C3⋊D3—22no—
243C22×C3⋊D3—21no—
244C22×C3⋊D3—24no—
245C22×C3⋊D3—82no—
246C22×C3×D3—21no—
247C22×C3×D3C2×D412yes—
248C2×D32—28no—
249C2×D32—84no—
250C2×C32×C4C2×D411yescharacteristic
251C2×C32×C4C2×D412yes—
252C2×C32×C4C2411yescharacteristic
253C2×C32×C4C2412yes—
254#638—24no—
255C2×C3⋊Dic3—21no—
256C4⋊(C3⋊D3)—21no—
257C4⋊(C3⋊D3)—24no—
258C4⋊(C3⋊D3)—22no—
259C4⋊(C3⋊D3)C2412yes—
260C4⋊(C3⋊D3)C2414yes—
261C4×C3⋊D3—24no—
262#634—21no—
263#634C2412yes—
264C3×#67—24no—
265C3×#67C2×D418yes—
266C2×C3×Dic3—22no—
267C2×C3×Dic3—24no—
268C2×C3×Dic3—21no—
269C2×C3×Dic3C2×D412yes—
270C3×D12—21no—
271C3×D12C2×D414yes—
272C3×D12C2412yes—
273C3×C4×D3—24no—
274C3×C4×D3C2×D414yes—
275C3×C4×D3C2414yes—
276C3×Dic6—22no—
277C3×Dic6—24no—
278C3×Dic6—21no—
279C3×Dic6C2×D414yes—
280C3×Dic6C2414yes—
281C3×Dic6C2412yes—
282#627—28no—
283#626—28no—
284#626—28no—
285#626—28no—
286#624—28no—
287#624—28no—
288D3×Dic3—28no—
289C32×C8C2414yes—
290C3×C3⋊C8C2412yes—
291C3×C3⋊C8C2412yes—
292C2×2−1+4—91no—
293C2×H(5,𝔽2)—91no—
294#577—916no—
295C2×#137—31no—
296C2×#137—92no—
297C2×AGL(1,ℤ/8)—92no—
298C2×AGL(1,ℤ/8)—91no—
299C2×#135—92no—
300C2×#135—91no—
301C22×SD16—92no—
302C22×SD16—91no—
303C2×#131—31no—
304C23×D3—62no—
305C23×D3—61no—
306C23×D3—61no—
307C23×D3—62no—
308C23×D3—121no—
309C3×#41—34no—
310C3×#41—34no—
311C3×#41—34no—
312C3×#41—62no—
313C2×C3×Q8—31no—
314C2×C3×Q8—32no—
315C2×C3×Q8—34no—
316C2×C3×Q8—31no—
317C2×C3×Q8—61no—
318C2×C3×Q8—62no—
319C2×C3×D4—32no—
320C2×C3×D4—31no—
321C2×C3×D4—31no—
322C2×C3×D4—61no—
323C22×C3×C4—21no—
324C22×C3×C4—32no—
325C22×C3×C4—61no—
326C22×C3×C4—61no—
327C22×C3×C4C22×D311yescharacteristic
328C22×C3×C4C22×D311yescharacteristic
329C2×#67—21no—
330C2×#67—62no—
331C2×#67—62no—
332C2×#67—61no—
333C2×#67—61no—
334C2×#67—62no—
335C2×#67—121no—
336C2×#67D1212yes—
337C22×Dic3—21no—
338C22×Dic3—62no—
339#239—38no—
340#239—38no—
341#239—68no—
342#239—68no—
343#239—64no—
344#239—64no—
345D3×Q8—38no—
346D3×Q8—68no—
347D3×Q8—64no—
348D3×Q8—68no—
349#237—68no—
350#237—616no—
351D3×D4—38no—
352D3×D4—68no—
353D3×D4—616no—
354D3×D4—616no—
355D3×D4—64no—
356#235—22no—
357#235—34no—
358#235—34no—
359#235—38no—
360#235—38no—
361#235—64no—
362#235—64no—
363#235—64no—
364#235—62no—
365#235—62no—
366#235—616no—
367#235—68no—
368#235—122no—
369#235D1214yes—
370#235C22×D314yes—
371#235C22×D314yes—
372C2×D12—32no—
373C2×D12—34no—
374C2×D12—31no—
375C2×D12—32no—
376C2×D12—31no—
377C2×D12—34no—
378C2×D12—38no—
379C2×D12—62no—
380C2×D12—61no—
381C2×D12—64no—
382C2×D12—64no—
383C2×D12—62no—
384C2×D12—62no—
385C2×D12—62no—
386C2×D12—61no—
387C2×D12—62no—
388C2×D12—61no—
389C2×D12—62no—
390C2×D12—68no—
391C2×D12—121no—
392C2×D12—122no—
393C2×D12D1211yescharacteristic
394C2×D12C22×D311yescharacteristic
395C2×C4×D3—21no—
396C2×C4×D3—62no—
397C2×C4×D3—62no—
398C2×C4×D3—62no—
399C2×C4×D3—61no—
400C2×C4×D3—61no—
401C2×C4×D3—62no—
402C2×C4×D3—62no—
403C2×C4×D3—121no—
404C2×C4×D3C22×D312yes—
405C2×Dic6—21no—
406C2×Dic6—22no—
407C2×Dic6—31no—
408C2×Dic6—31no—
409C2×Dic6—38no—
410C2×Dic6—61no—
411C2×Dic6—64no—
412C2×Dic6—62no—
413C2×Dic6—62no—
414C2×Dic6D1211yescharacteristic
415C2×Dic6C22×D312yes—
416C2×Dic6C22×D311yescharacteristic
417C2×Dic6C22×D314yescomplemented
418C3×Q16—38no—
419C3×SD16—38no—
420C3×M16—24no—
421C3×M16—38no—
422C3×M16C22×D314yescomplemented
423C3×M16C22×D314yescomplemented
424C2×C3×C8—22no—
425C2×C3×C8—31no—
426C2×C3×C8—31no—
427C2×C3×C8—34no—
428C2×C3×C8—38no—
429C2×C3×C8C22×D312yes—
430C2×C3×C8C22×D312yes—
431#216—34no—
432#215—38no—
433#215—38no—
434#215—34no—
435#214—34no—
436#213—34no—
437C2×C3⋊C8C22×D311yescharacteristic
438C2×C3⋊C8C22×D311yescharacteristic
439C2×C3⋊C8C22×D314yescomplemented
440Dic12—34no—
441Dic12C22×D318yescomplemented
442D24—34no—
443D24—38no—
444D24—38no—
445D24—68no—
446#204—34no—
447#204—38no—
448#204—38no—
449#204—34no—
450#204—38no—
451#204—38no—
452#204—68no—
453#204C22×D318yescomplemented
454ΓL(1,𝔽25)C22×D318yescomplemented
455D3×C8C22×D318yescomplemented
456C22×C32—22no—
457C22×C32C22×D412yes—
458C22×C32C22×D411yescharacteristic
459C2×C3⋊D3—22no—
460C2×C3⋊D3—24no—
461C2×C3⋊D3—44no—
462C2×C3⋊D3—42no—
463C2×C3⋊D3—84no—
464C2×C3×D3—24no—
465C2×C3×D3—22no—
466C2×C3×D3—42no—
467C2×C3×D3C22×D414yes—
468D32—88no—
469C32×C4C22×D411yescharacteristic
470C32×C4C22×D412yes—
471C32×C4C2511yescharacteristic
472C3⋊Dic3—22no—
473C3×Dic3—24no—
474C3×Dic3—22no—
475C3×Dic3C22×D414yes—
4762−1+4—98no—
4772−1+4—184no—
478H(5,𝔽2)—98no—
479H(5,𝔽2)—184no—
480C2×#41—31no—
481C2×#41—31no—
482C2×#41—92no—
483C2×#41—92no—
484C2×#41—91no—
485C2×#41—182no—
486C2×#41—181no—
487C2×#41—181no—
488C22×Q8—31no—
489C22×Q8—92no—
490C22×Q8—181no—
491C22×D4—92no—
492C22×D4—91no—
493C22×D4—181no—
494C22×D4—182no—
495#137—38no—
496#137—916no—
497AGL(1,ℤ/8)—916no—
498AGL(1,ℤ/8)—98no—
499#135—916no—
500#135—98no—
501C2×Q16—32no—
502C2×Q16—91no—
503C2×SD16—32no—
504C2×SD16—916no—
505C2×SD16—91no—
506C2×SD16—92no—
507C2×SD16—92no—
508C2×SD16—98no—
509C2×SD16—91no—
510C2×SD16—92no—
511C2×D8—91no—
512C2×D8—92no—
513#131—38no—
514C2×M16—32no—
515C2×M16D3211yescharacteristic, complemented
516C22×C8—31no—
517C22×C8—32no—
518C23×C3—21no—
519C23×C3—32no—
520C23×C3—61no—
521C23×C3C2×D1211yescharacteristic
522C23×C3D3×D411yescharacteristic
523C22×D3—21no—
524C22×D3—68no—
525C22×D3—61no—
526C22×D3—62no—
527C22×D3—61no—
528C22×D3—62no—
529C22×D3—64no—
530C22×D3—64no—
531C22×D3—68no—
532C22×D3—121no—
533C22×D3—122no—
534C22×D3—124no—
535C22×D3—244no—
536C22×D3—244no—
537C22×D3—242no—
538C22×D3—242no—
539C22×D3—244no—
540C22×D3C2×D1212yes—
541C3×Q8—34no—
542C3×Q8—34no—
543C3×Q8—32no—
544C3×Q8—62no—
545C3×Q8—64no—
546C3×Q8—61no—
547C3×D4—38no—
548C3×D4—34no—
549C3×D4—32no—
550C3×D4—64no—
551C3×D4—61no—
552C2×C3×C4—21no—
553C2×C3×C4—22no—
554C2×C3×C4—21no—
555C2×C3×C4—22no—
556C2×C3×C4—32no—
557C2×C3×C4—34no—
558C2×C3×C4—34no—
559C2×C3×C4—62no—
560C2×C3×C4—61no—
561C2×C3×C4—64no—
562C2×C3×C4—64no—
563C2×C3×C4C2×D1211yescharacteristic
564C2×C3×C4C2×D1212yes—
565C2×C3×C4D3×D411yescharacteristic
566C2×C3×C4D3×D412yes—
567C2×C3×C4C23×D311yescharacteristic
568C2×C3×C4C23×D312yes—
569C2×C3×C4C23×D311yescharacteristic
570C2×C3×C4C23×D312yes—
571#67—24no—
572#67—68no—
573#67—68no—
574#67—64no—
575#67—64no—
576#67—68no—
577#67—124no—
578#67C2×D1218yes—
579C2×Dic3—22no—
580C2×Dic3—24no—
581C2×Dic3—21no—
582C2×Dic3—68no—
583C2×Dic3—61no—
584C2×Dic3—61no—
585C2×Dic3—121no—
586C2×Dic3C2×D1212yes—
587D12—21no—
588D12—34no—
589D12—32no—
590D12—34no—
591D12—32no—
592D12—64no—
593D12—62no—
594D12—68no—
595D12—68no—
596D12—68no—
597D12—64no—
598D12—62no—
599D12—61no—
600D12—62no—
601D12—64no—
602D12—61no—
603D12—122no—
604D12—124no—
605D12—121no—
606D12C2×D1214yes—
607D12C23×D312yes—
608C4×D3—24no—
609C4×D3—68no—
610C4×D3—68no—
611C4×D3—68no—
612C4×D3—64no—
613C4×D3—64no—
614C4×D3—68no—
615C4×D3—68no—
616C4×D3—124no—
617C4×D3C2×D1214yes—
618C4×D3C23×D314yes—
619Dic6—22no—
620Dic6—24no—
621Dic6—21no—
622Dic6—32no—
623Dic6—32no—
624Dic6—62no—
625Dic6—68no—
626Dic6—61no—
627Dic6—61no—
628Dic6—68no—
629Dic6—121no—
630Dic6C2×D1214yes—
631Dic6C23×D314yes—
632Dic6C23×D312yes—
633C3×C8—24no—
634C3×C8—32no—
635C3×C8—32no—
636C3×C8C23×D314yes—
637C3×C8C23×D314yes—
638C3⋊C8C23×D312yes—
639C3⋊C8C23×D312yes—
640C2×C32—22no—
641C2×C32#57712yescomplemented
642C2×C32C23×D411yescharacteristic
643C3⋊D3—44no—
644C3⋊D3—42no—
645C3×D3—24no—
646C3×D3—42no—
647C24—182no—
648C24—181no—
649#41—34no—
650#41—34no—
651#41—34no—
652#41—62no—
653#41—98no—
654#41—98no—
655#41—94no—
656#41—184no—
657#41—184no—
658#41—1816no—
659#41—188no—
660#41—188no—
661#41—182no—
662C2×Q8—31no—
663C2×Q8—32no—
664C2×Q8—34no—
665C2×Q8—31no—
666C2×Q8—61no—
667C2×Q8—62no—
668C2×Q8—98no—
669C2×Q8—91no—
670C2×Q8—182no—
671C2×Q8—184no—
672C2×Q8—188no—
673C2×D4—32no—
674C2×D4—31no—
675C2×D4—31no—
676C2×D4—61no—
677C2×D4—98no—
678C2×D4—91no—
679C2×D4—92no—
680C2×D4—94no—
681C2×D4—184no—
682C2×D4—182no—
683C2×D4—188no—
684C2×D4—182no—
685C2×D4—182no—
686C2×D4—1816no—
687C2×D4—181no—
688C2×D4—181no—
689C2×D4—182no—
690C22×C4—32no—
691C22×C4—61no—
692C22×C4—61no—
693C22×C4—182no—
694C22×C4—182no—
695C22×C4—182no—
696C22×C4—181no—
697C22×C4C2×D3211yescharacteristic
698Q16—38no—
699Q16—94no—
700SD16—38no—
701SD16—94no—
702SD16—98no—
703SD16—98no—
704SD16—94no—
705SD16—98no—
706D8—94no—
707D8—98no—
708M16—38no—
709M16C2×D3214yescomplemented
710C2×C8—31no—
711C2×C8—31no—
712C2×C8—34no—
713C2×C8—38no—
714C2×C8C2×D3212yes—
715C22×C3—22no—
716C22×C3—22no—
717C22×C3—22no—
718C22×C3—21no—
719C22×C3—34no—
720C22×C3—42no—
721C22×C3—64no—
722C22×C3—62no—
723C22×C3—122no—
724C22×C3C22×D1212yes—
725C22×C3C22×D1211yescharacteristic
726C22×C3C2×D3×D412yes—
727C22×C3C2×D3×D411yescharacteristic
728C2×D3—24no—
729C2×D3—22no—
730C2×D3—42no—
731C2×D3—62no—
732C2×D3—64no—
733C2×D3—62no—
734C2×D3—64no—
735C2×D3—122no—
736C2×D3—124no—
737C2×D3—124no—
738C2×D3—122no—
739C2×D3—124no—
740C2×D3—122no—
741C2×D3—244no—
742C2×D3—242no—
743C2×D3—248no—
744C2×D3—248no—
745C2×D3—244no—
746C2×D3—244no—
747C2×D3—248no—
748C2×D3C22×D1214yes—
749C3×C4—21no—
750C3×C4—22no—
751C3×C4—21no—
752C3×C4—34no—
753C3×C4—64no—
754C3×C4—62no—
755C3×C4C22×D1211yescharacteristic
756C3×C4C22×D1212yes—
757C3×C4C2×D3×D411yescharacteristic
758C3×C4C2×D3×D412yes—
759C3×C4C24×D311yescharacteristic
760C3×C4C24×D311yescharacteristic
761Dic3—24no—
762Dic3—22no—
763Dic3—62no—
764Dic3—62no—
765Dic3—122no—
766Dic3C22×D1214yes—
767C32C2×#57711yescharacteristic, complemented, Sylow
768C23—32no—
769C23—61no—
770C23—188no—
771C23—181no—
772C23—182no—
773C23—184no—
774C23—722no—
775C23—724no—
776C23D3×D1211yescharacteristic
777Q8—34no—
778Q8—34no—
779Q8—32no—
780Q8—62no—
781Q8—64no—
782Q8—61no—
783Q8—92no—
784Q8—188no—
785Q8—181no—
786D4—38no—
787D4—34no—
788D4—32no—
789D4—64no—
790D4—61no—
791D4—92no—
792D4—94no—
793D4—188no—
794D4—188no—
795D4—188no—
796D4—184no—
797D4—182no—
798D4—184no—
799D4—181no—
800C2×C4—32no—
801C2×C4—34no—
802C2×C4—34no—
803C2×C4—64no—
804C2×C4—61no—
805C2×C4—62no—
806C2×C4—64no—
807C2×C4—188no—
808C2×C4—188no—
809C2×C4—188no—
810C2×C4—181no—
811C2×C4—184no—
812C2×C4D3×D1212yes—
813C2×C4D3×D1211yescharacteristic
814C2×C4C22×D3212yes—
815C2×C4C22×D3211yescharacteristic
816C8—32no—
817C8—32no—
818C8C22×D3214yes—
819C2×C3—22no—
820C2×C3—22no—
821C2×C3—21no—
822C2×C3—22no—
823C2×C3—42no—
824C2×C3—64no—
825C2×C3—122no—
826C2×C3#575112yescomplemented
827C2×C3#577812yescomplemented
828C2×C3C23×D1211yescharacteristic
829C2×C3C22×D3×D411yescharacteristic
830D3—24no—
831D3—42no—
832D3—124no—
833D3—122no—
834D3—124no—
835D3—122no—
836D3—244no—
837D3—242no—
838C22—22no—
839C22—34no—
840C22—64no—
841C22—62no—
842C22—122no—
843C22—182no—
844C22—184no—
845C22—364no—
846C22—362no—
847C22—724no—
848C22—728no—
849C22C2×D3×D1212yes—
850C22C2×D3×D1211yescharacteristic
851C4—34no—
852C4—62no—
853C4—64no—
854C4—182no—
855C4C2×D3×D1211yescharacteristic
856C4C2×D3×D1212yes—
857C4C23×D3211yescharacteristic
858C3—21no—
859C3C2×#575111yescharacteristic, complemented
860C3C2×#577811yescharacteristic, complemented
861C2—22no—
862C2—64no—
863C2—122no—
864C2—364no—
865C2—362no—
866C2#1059471512yesdirect product factor
867C2C22×D3×D1211yescharacteristic
subgroupG/H
centerC22C2×D3×D12
commutator, cosocleC32×C4C25
FrattiniC4C23×D32
FittingC2×C32×M16C22
socleC22×C32C22×D4
hypercenterC2×M16D32
hypocenterC32C2×#577
LCSG ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×M16

Complements

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

NH ≅ G/Ntype
1. C2×#64308C2semidirect
2. C2×#64297C2semidirect
3. C2×#64117C2semidirect
4. C2×C3×#909C2semidirect
5. C2×C3×#907C2semidirect
6. C22×#3717C2semidirect
7. C2×#63829C2semidirect
8. #10594715C2direct (N × H)
9. C2×#63808C2semidirect
10. C2×#63801C2semidirect
11. C2×#63794C2semidirect
12. C2×D3×#204C2semidirect
15. C2×#3828C22semidirect
19. C22×C3×Dic6C22semidirect
23. #64308C22semidirect
28. C2×#3799C22semidirect
31. #64297C22semidirect
33. C2×D3×Dic6C22semidirect
34. C2×C32×M16C22semidirect
35. #64117C22semidirect
36. C2×#3745C22semidirect
37. C2×#3744C22semidirect
38. C22×C3×C3⋊C8C22semidirect
39. C3×#909C22semidirect
40. C3×#907C22semidirect
41. C2×C3×Dic12C22semidirect
42. C2×C3×#204C22semidirect
43. C2×C3×ΓL(1,𝔽25)C22semidirect
44. C2×C3×D3×C8C22semidirect
45. C2×#3719C22semidirect
46. C2×#3717C22semidirect
47. C2×#3717C22semidirect
48. C2×#3717C22semidirect
49. C2×#3717C22semidirect
50. #63829C22semidirect
51. C2×#3716C22semidirect
52. C2×#3714C22semidirect
53. #63808C22semidirect
54. #63801C22semidirect
55. #63794C22semidirect
56. D3×#204C22semidirect
72. C2×#909D3semidirect
77. C2×#907D3semidirect
87. #3828C23semidirect
111. C2×C3×Dic6C23semidirect
128. #3799C23semidirect
132. D3×Dic6C23semidirect
133. C32×M16C23semidirect
135. #3745C23semidirect
136. #3744C23semidirect
139. C2×C3×C3⋊C8C23semidirect
140. C3×Dic12C23semidirect
141. C3×#204C23semidirect
142. C3×ΓL(1,𝔽25)C23semidirect
143. C3×D3×C8C23semidirect
144. #3719C23semidirect
145. #3717C23semidirect
146. #3717C23semidirect
147. #3717C23semidirect
148. #3716C23semidirect
149. #3714C23semidirect
190. C22×Dic6C2×D3semidirect
197. C2×C3×M16C2×D3semidirect
198. C2×C3×M16C2×D3semidirect
209. C22×C3⋊C8C2×D3semidirect
215. #909C2×D3semidirect
220. #907C2×D3semidirect
222. C2×Dic12C2×D3semidirect
238. C2×#204C2×D3semidirect
239. C2×ΓL(1,𝔽25)C2×D3semidirect
240. C2×D3×C8C2×D3semidirect
417. C2×Dic6C22×D3semidirect
422. C3×M16C22×D3semidirect
423. C3×M16C22×D3semidirect
439. C2×C3⋊C8C22×D3semidirect
441. Dic12C22×D3semidirect
453. #204C22×D3semidirect
454. ΓL(1,𝔽25)C22×D3semidirect
455. D3×C8C22×D3semidirect
515. C2×M16D32semidirect
641. C2×C32#577semidirect
709. M16C2×D32semidirect
767. C32C2×#577semidirect
826. C2×C3#5751semidirect
827. C2×C3#5778semidirect
859. C3C2×#5751semidirect
860. C3C2×#5778semidirect
866. C2#10594715direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#643082
C2×#642972
C2×#641172
C2×C3×#9092
C2×C3×#9072
C22×#37172
C2×#638292
#105947152
C2×#638082
C2×#638012
C2×#637942
C2×D3×#2042
C2×#57783
C2×#57513