Finite Group Databasebeta

← C2×#10595465 #11918944

Subgroups — C2×#10595465 #11918944

Order 1152.

2949 conjugacy classes of subgroups.

The subgroup lattice has 854 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#1010C211yesmaximal, characteristic, complemented
2C2×#64297C211yesmaximal, characteristic, complemented
3C2×#64159C211yesmaximal, characteristic, complemented
4C2×C3×#951C211yesmaximal, characteristic, complemented
5#10595465C2116yesmaximal, direct product factor
6C2×#63948C212yesmaximal, complemented
7C2×D3×#216C212yesmaximal, complemented
8C2×#63935C212yesmaximal, complemented
9C2×#63929C212yesmaximal, complemented
10C22×#3718C211yesmaximal, characteristic, complemented
11C2×#63833C211yesmaximal, characteristic, complemented
12C2×#63815C211yesmaximal, characteristic, complemented
13C2×#5838—31nomaximal
14C2×#5779—31nomaximal
15C2×C32×#41C2211yescharacteristic
16C2×#3828C2211yescharacteristic
17C3×#1010—24no—
18C3×#1010C2218yescomplemented
19C2×C3×D3×Q8C2212yes—
20C2×C3×#237—22no—
21C2×C3×#237C2212yes—
22C2×C3×#235—21no—
23C2×C3×#235C2211yescharacteristic
24C22×C3×Dic6—21no—
25C22×C3×Dic6C2211yescharacteristic
26C22×C3×Dic6C2211yescharacteristic
27C2×#3804—22no—
28C2×#3799C2212yes—
29C2×#3797—21no—
30#64297—24no—
31#64297C2218yescomplemented
32C2×#3796—21no—
33C2×D3×Dic6C2212yes—
34#64159C2218yescomplemented
35C2×#3756C2211yescharacteristic
36C2×#3755C2211yescharacteristic
37C2×#3754C2211yescharacteristic
38C2×#3753C2211yescharacteristic
39C22×C3⋊(C3⋊C8)C2211yescharacteristic
40C3×#951C2218yescomplemented
41C2×C3×#216C2212yes—
42C2×C3×#214C2212yes—
43C2×C3×#208C2211yescharacteristic
44#63948C22116yescomplemented
45D3×#216C22116yescomplemented
46#63935C22116yescomplemented
47#63929C22116yescomplemented
48C2×#3719C2212yes—
49C2×#3718C2212yes—
50C2×#3718C2212yes—
51C2×#3718C2218yescomplemented
52#63833C2218yescomplemented
53C2×#3717C2212yes—
54C2×#3711C2212yes—
55#63815C2218yescomplemented
56C2×D3×C3⋊C8C2212yes—
57C2×C3×2−1+4—31no—
58C2×#1010—31no—
59C2×#1010D311yescharacteristic, complemented
60C2×#1007—31no—
61C2×C3×#137—31no—
62#5838—316no—
63C2×#951—32no—
64C2×#951D311yescharacteristic, complemented
65C2×#950—31no—
66C2×#950—31no—
67C2×#950—32no—
68C2×#950—61no—
69C2×#948—31no—
70C22×#216—31no—
71C22×#216—31no—
72C22×#216—32no—
73C2×#942—32no—
74C2×#942—31no—
75#5779—316no—
76C2×#918—32no—
77C2×D3×Q16—32no—
78C2×#916—32no—
79C2×#915—32no—
80C2×#909—31no—
81C2×#907—31no—
82C32×#41—22no—
83C32×#41C2314yes—
84C2×C32×Q8C2311yescharacteristic
85C2×C32×D4—21no—
86C2×C32×D4C2311yescharacteristic
87C22×C32×C4—21no—
88C22×C32×C4C2311yescharacteristic
89C2×#638—21no—
90#3828—22no—
91#3828C2314yes—
92C2×C4⋊(C3⋊D3)C2311yescharacteristic
93C2×C4×C3⋊D3—21no—
94C2×#634C2311yescharacteristic
95C2×C3×#67—22no—
96C2×C3×#67D412yes—
97C22×C3×Dic3—21no—
98C22×C3×Dic3—21no—
99C22×C3×Dic3—22no—
100C3×D3×Q8—24no—
101C3×D3×Q8C2318yes—
102C3×#237—216no—
103C3×#237—24no—
104C3×#237C2318yes—
105C3×#235—28no—
106C3×#235D414yes—
107C3×#235C2314yes—
108C2×C3×D12D411yescharacteristic
109C2×C3×C4×D3—22no—
110C2×C3×C4×D3C2312yes—
111C2×C3×Dic6—21no—
112C2×C3×Dic6—22no—
113C2×C3×Dic6—21no—
114C2×C3×Dic6—22no—
115C2×C3×Dic6—22no—
116C2×C3×Dic6—28no—
117C2×C3×Dic6D411yescharacteristic
118C2×C3×Dic6C2312yes—
119C2×C3×Dic6C2314yes—
120C2×C3×Dic6C2312yes—
121C2×C3×Dic6C2314yes—
122C2×#627—22no—
123C2×#626—22no—
124C2×#624—22no—
125#3804—216no—
126C2×D3×Dic3—22no—
127#3799—24no—
128#3799C2318yes—
129#3797—28no—
130#3796—28no—
131D3×Dic6—24no—
132D3×Dic6C2318yes—
133#3756C2314yes—
134#3755C2314yes—
135#3754C2314yes—
136#3753C2314yes—
137C2×C3⋊(C3⋊C8)C2311yescharacteristic
138C2×C3⋊(C3⋊C8)C2314yes—
139C2×C3⋊(C3⋊C8)C2311yescharacteristic
140C3×#216C2318yes—
141C3×#214C2318yes—
142C3×#208C2314yes—
143C2×C3×C3⋊C8C2312yes—
144#3719C2318yes—
145#3718C2318yes—
146#3718C2318yes—
147#3717C2318yes—
148#3711C2318yes—
149D3×C3⋊C8C2318yes—
150C2×#578—91noSylow
151C3×2−1+4—38no—
152C3×2−1+4—64no—
153C2×C3×#41—21no—
154C2×C3×#41—31no—
155C2×C3×#41—32no—
156C2×C3×#41—61no—
157C2×C3×#41—62no—
158C2×C3×#41C2×D311yescharacteristic
159C2×C3×#41C2×D311yescharacteristic
160C22×C3×Q8—32no—
161C22×C3×Q8—31no—
162C22×C3×Q8—31no—
163C22×C3×Q8—61no—
164#1010—24no—
165#1010—38no—
166#1010—64no—
167#1010C2×D318yescomplemented
168#1007—38no—
169#1007—64no—
170C2×#239—32no—
171C2×#239—61no—
172C2×D3×Q8—32no—
173C2×D3×Q8—61no—
174C2×D3×Q8—61no—
175C2×D3×Q8C2×D312yes—
176C2×#237—22no—
177C2×#237—61no—
178C2×#237—62no—
179C2×#237C2×D312yes—
180C2×#235—21no—
181C2×#235—31no—
182C2×#235—31no—
183C2×#235—32no—
184C2×#235—61no—
185C2×#235—62no—
186C2×#235C2×D311yescharacteristic
187C22×Dic6—21no—
188C22×Dic6—32no—
189C22×Dic6C2×D311yescharacteristic
190C22×Dic6C2×D311yescharacteristic
191C3×#137—38no—
192C2×C3×Q16—32no—
193C2×C3×SD16—32no—
194C2×C3×M16—31no—
195#951—316no—
196#951C2×D318yescomplemented
197#950—38no—
198#950—38no—
199#950—316no—
200#950—68no—
201#948—38no—
202C2×#216—31no—
203C2×#216—31no—
204C2×#216—32no—
205C2×#216—32no—
206C2×#216—32no—
207C2×#216—32no—
208C2×#216—38no—
209C2×#216—38no—
210C2×#216—316no—
211C2×#216—32no—
212C2×#216—61no—
213C2×#216C2×D312yes—
214#942—316no—
215#942—38no—
216C2×#215—31no—
217C2×#215—31no—
218C2×#215—32no—
219C2×#215—61no—
220C2×#214—31no—
221C2×#214—31no—
222C2×#214—61no—
223C2×#214C2×D312yes—
224C2×#213—31no—
225C2×#213—31no—
226C2×#213—61no—
227C2×#208—32no—
228C2×#208C2×D311yescharacteristic
229C22×C3⋊C8—31no—
230C22×C3⋊C8—31no—
231C22×C3⋊C8—32no—
232C22×C3⋊C8—61no—
233#918—316no—
234D3×Q16—316no—
235#916—316no—
236#915—316no—
237#909—38no—
238#907—38no—
239C2×Dic12—32no—
240C2×#204—32no—
241C2×ΓL(1,𝔽25)—32no—
242C2×D3×C8—32no—
243C23×C32—21no—
244C23×C32C2×D411yescharacteristic
245C22×C3⋊D3—21no—
246C22×C3×D3C2×D412yes—
247C32×Q8—21no—
248C32×Q8C2412yes—
249C32×D4—24no—
250C32×D4—21no—
251C32×D4C2412yes—
252C2×C32×C4—21no—
253C2×C32×C4—24no—
254C2×C32×C4C2×D411yescharacteristic
255C2×C32×C4C2×D412yes—
256C2×C32×C4C2411yescharacteristic
257C2×C32×C4C2412yes—
258#638—24no—
259C2×C3⋊Dic3—21no—
260C4⋊(C3⋊D3)—21no—
261C4⋊(C3⋊D3)C2412yes—
262C4×C3⋊D3—24no—
263#634—21no—
264#634C2412yes—
265C3×#67—28no—
266C3×#67C2×D418yes—
267C2×C3×Dic3—22no—
268C2×C3×Dic3—24no—
269C2×C3×Dic3—22no—
270C2×C3×Dic3—24no—
271C2×C3×Dic3—28no—
272C2×C3×Dic3C2×D412yes—
273C3×D12C2×D414yes—
274C3×C4×D3—28no—
275C3×C4×D3C2×D414yes—
276C3×C4×D3C2414yes—
277C3×Dic6—22no—
278C3×Dic6—24no—
279C3×Dic6—24no—
280C3×Dic6—22no—
281C3×Dic6—28no—
282C3×Dic6C2×D414yes—
283C3×Dic6C2414yes—
284C3×Dic6C2414yes—
285#627—28no—
286#626—28no—
287#624—28no—
288D3×Dic3—28no—
289C3⋊(C3⋊C8)C2412yes—
290C3⋊(C3⋊C8)C2412yes—
291C3×C3⋊C8C2414yes—
292C2×2−1+4—31no—
293C2×2−1+4—91no—
294#578—916no—
295C2×#137—31no—
296C2×#137—91no—
297C2×#137—92no—
298C2×#137—92no—
299C2×#135—92no—
300C2×#135—91no—
301C22×Q16—92no—
302C22×Q16—91no—
303C2×#131—91no—
304C3×#41—22no—
305C3×#41—22no—
306C3×#41—24no—
307C3×#41—34no—
308C3×#41—34no—
309C3×#41—38no—
310C3×#41—42no—
311C3×#41—68no—
312C3×#41—64no—
313C3×#41—616no—
314C3×#41C22×D314yes—
315C3×#41C22×D314yes—
316C2×C3×Q8—21no—
317C2×C3×Q8—31no—
318C2×C3×Q8—38no—
319C2×C3×Q8—32no—
320C2×C3×Q8—34no—
321C2×C3×Q8—32no—
322C2×C3×Q8—34no—
323C2×C3×Q8—62no—
324C2×C3×Q8—68no—
325C2×C3×Q8—64no—
326C2×C3×Q8—61no—
327C2×C3×Q8—62no—
328C2×C3×Q8—61no—
329C2×C3×Q8—62no—
330C2×C3×Q8C22×D311yescharacteristic
331C2×C3×Q8C22×D311yescharacteristic
332C2×C3×D4—21no—
333C2×C3×D4—21no—
334C2×C3×D4—21no—
335C2×C3×D4—32no—
336C2×C3×D4—31no—
337C2×C3×D4—41no—
338C2×C3×D4—62no—
339C2×C3×D4C22×D311yescharacteristic
340C2×C3×D4C22×D311yescharacteristic
341C22×C3×C4—21no—
342C22×C3×C4—21no—
343C22×C3×C4—21no—
344C22×C3×C4—32no—
345C22×C3×C4—41no—
346C22×C3×C4—62no—
347C22×C3×C4—62no—
348C22×C3×C4—61no—
349C22×C3×C4—61no—
350C22×C3×C4C22×D311yescharacteristic
351C22×C3×C4C22×D311yescharacteristic
352C2×#67—22no—
353C2×#67—62no—
354C2×#67—61no—
355C2×#67—61no—
356C2×#67—121no—
357C2×#67#6712yes—
358C22×Dic3—21no—
359C22×Dic3—21no—
360C22×Dic3—22no—
361C22×Dic3—62no—
362#239—38no—
363#239—68no—
364#239—64no—
365D3×Q8—24no—
366D3×Q8—38no—
367D3×Q8—68no—
368D3×Q8—64no—
369D3×Q8—68no—
370D3×Q8C22×D318yes—
371#237—216no—
372#237—24no—
373#237—68no—
374#237—616no—
375#237C22×D318yes—
376#235—28no—
377#235—34no—
378#235—34no—
379#235—38no—
380#235—64no—
381#235—64no—
382#235—62no—
383#235—62no—
384#235—616no—
385#235—122no—
386#235#6714yes—
387#235C22×D314yes—
388C2×D12—31no—
389C2×D12—31no—
390C2×D12—61no—
391C2×D12—62no—
392C2×D12#6711yescharacteristic
393C2×C4×D3—22no—
394C2×C4×D3—62no—
395C2×C4×D3—62no—
396C2×C4×D3—61no—
397C2×C4×D3—61no—
398C2×C4×D3—62no—
399C2×C4×D3—121no—
400C2×C4×D3C22×D312yes—
401C2×Dic6—21no—
402C2×Dic6—22no—
403C2×Dic6—21no—
404C2×Dic6—22no—
405C2×Dic6—22no—
406C2×Dic6—28no—
407C2×Dic6—31no—
408C2×Dic6—31no—
409C2×Dic6—38no—
410C2×Dic6—61no—
411C2×Dic6—64no—
412C2×Dic6—62no—
413C2×Dic6—62no—
414C2×Dic6#6711yescharacteristic
415C2×Dic6C22×D312yes—
416C2×Dic6C22×D314yes—
417C2×Dic6C22×D312yes—
418C2×Dic6C22×D314yes—
419C3×Q16—38no—
420C3×SD16—38no—
421C3×M16—34no—
422C2×C3×C8—32no—
423#216—34no—
424#216—34no—
425#216—38no—
426#216—38no—
427#216—38no—
428#216—38no—
429#216—38no—
430#216—64no—
431#216C22×D318yes—
432#215—34no—
433#215—34no—
434#215—38no—
435#215—64no—
436#214—34no—
437#214—34no—
438#214—64no—
439#214C22×D318yes—
440#213—34no—
441#213—34no—
442#213—64no—
443#208—38no—
444#208C22×D314yes—
445C2×C3⋊C8—31no—
446C2×C3⋊C8—31no—
447C2×C3⋊C8—34no—
448C2×C3⋊C8—31no—
449C2×C3⋊C8—31no—
450C2×C3⋊C8—34no—
451C2×C3⋊C8—38no—
452C2×C3⋊C8—61no—
453C2×C3⋊C8—61no—
454C2×C3⋊C8—64no—
455C2×C3⋊C8C22×D312yes—
456Dic12—38no—
457#204—38no—
458ΓL(1,𝔽25)—38no—
459D3×C8—38no—
460C22×C32—22no—
461C22×C32—22no—
462C22×C32—42no—
463C22×C32C22×D412yes—
464C22×C32C22×D411yescharacteristic
465C2×C3⋊D3—22no—
466C2×C3⋊D3—42no—
467C2×C3×D3—24no—
468C2×C3×D3C22×D414yes—
469C32×C4—22no—
470C32×C4C22×D412yes—
471C32×C4C22×D411yescharacteristic
472C32×C4C2511yescharacteristic
473C3⋊Dic3—22no—
474C3×Dic3—24no—
475C3×Dic3—24no—
476C3×Dic3C22×D414yes—
4772−1+4—38no—
4782−1+4—64no—
4792−1+4—98no—
4802−1+4—184no—
481C2×#41—31no—
482C2×#41—32no—
483C2×#41—61no—
484C2×#41—62no—
485C2×#41—92no—
486C2×#41—91no—
487C2×#41—182no—
488C2×#41—181no—
489C2×#41D3211yescharacteristic
490C22×Q8—32no—
491C22×Q8—31no—
492C22×Q8—31no—
493C22×Q8—61no—
494C22×Q8—92no—
495C22×Q8—181no—
496#137—38no—
497#137—98no—
498#137—916no—
499#137—916no—
500#135—916no—
501#135—98no—
502C2×Q16—32no—
503C2×Q16—92no—
504C2×Q16—916no—
505C2×Q16—92no—
506C2×Q16—92no—
507C2×Q16—98no—
508C2×Q16—91no—
509C2×SD16—32no—
510C2×SD16—92no—
511C2×SD16—91no—
512C2×SD16—91no—
513C2×D8—91no—
514#131—98no—
515C2×M16—31no—
516C2×M16—92no—
517C22×C8—92no—
518C22×C8—91no—
519C23×C3—21no—
520C23×C3—21no—
521C23×C3—21no—
522C23×C3—32no—
523C23×C3—41no—
524C23×C3D3×D411yescharacteristic
525C23×C3C2×#6711yescharacteristic
526C22×D3—61no—
527C22×D3—61no—
528C22×D3—121no—
529C22×D3C2×#6712yes—
530C3×Q8—21no—
531C3×Q8—21no—
532C3×Q8—22no—
533C3×Q8—34no—
534C3×Q8—34no—
535C3×Q8—34no—
536C3×Q8—41no—
537C3×Q8—68no—
538C3×Q8—62no—
539C3×Q8—64no—
540C3×Q8—62no—
541C3×Q8—64no—
542C3×Q8C23×D312yes—
543C3×Q8C23×D312yes—
544C3×D4—24no—
545C3×D4—24no—
546C3×D4—21no—
547C3×D4—21no—
548C3×D4—22no—
549C3×D4—38no—
550C3×D4—34no—
551C3×D4—41no—
552C3×D4—44no—
553C3×D4—68no—
554C3×D4C23×D312yes—
555C3×D4C23×D312yes—
556C2×C3×C4—21no—
557C2×C3×C4—21no—
558C2×C3×C4—24no—
559C2×C3×C4—24no—
560C2×C3×C4—21no—
561C2×C3×C4—22no—
562C2×C3×C4—21no—
563C2×C3×C4—22no—
564C2×C3×C4—32no—
565C2×C3×C4—34no—
566C2×C3×C4—34no—
567C2×C3×C4—44no—
568C2×C3×C4—41no—
569C2×C3×C4—68no—
570C2×C3×C4—68no—
571C2×C3×C4—62no—
572C2×C3×C4—64no—
573C2×C3×C4—62no—
574C2×C3×C4—64no—
575C2×C3×C4D3×D411yescharacteristic
576C2×C3×C4D3×D412yes—
577C2×C3×C4C2×#6711yescharacteristic
578C2×C3×C4C2×#6712yes—
579C2×C3×C4C23×D311yescharacteristic
580C2×C3×C4C23×D312yes—
581C2×C3×C4C23×D311yescharacteristic
582C2×C3×C4C23×D312yes—
583#67—28no—
584#67—68no—
585#67—64no—
586#67—64no—
587#67—124no—
588#67C2×#6718yes—
589C2×Dic3—22no—
590C2×Dic3—24no—
591C2×Dic3—22no—
592C2×Dic3—24no—
593C2×Dic3—28no—
594C2×Dic3—68no—
595C2×Dic3—61no—
596C2×Dic3—61no—
597C2×Dic3—121no—
598C2×Dic3C2×#6712yes—
599D12—32no—
600D12—32no—
601D12—62no—
602D12—68no—
603D12—61no—
604D12—61no—
605D12—121no—
606D12C2×#6714yes—
607C4×D3—28no—
608C4×D3—68no—
609C4×D3—68no—
610C4×D3—64no—
611C4×D3—64no—
612C4×D3—68no—
613C4×D3—124no—
614C4×D3C2×#6714yes—
615C4×D3C23×D314yes—
616Dic6—22no—
617Dic6—24no—
618Dic6—24no—
619Dic6—22no—
620Dic6—28no—
621Dic6—32no—
622Dic6—32no—
623Dic6—62no—
624Dic6—68no—
625Dic6—61no—
626Dic6—61no—
627Dic6—68no—
628Dic6—121no—
629Dic6C2×#6714yes—
630Dic6C23×D314yes—
631Dic6C23×D314yes—
632C3×C8—34no—
633C3⋊C8—32no—
634C3⋊C8—32no—
635C3⋊C8—32no—
636C3⋊C8—32no—
637C3⋊C8—62no—
638C3⋊C8—62no—
639C3⋊C8C23×D314yes—
640C2×C32—22no—
641C2×C32—42no—
642C2×C32#57812yescomplemented
643C2×C32C23×D411yescharacteristic
644C3⋊D3—42no—
645C3×D3—24no—
646#41—22no—
647#41—34no—
648#41—34no—
649#41—38no—
650#41—68no—
651#41—64no—
652#41—616no—
653#41—98no—
654#41—94no—
655#41—184no—
656#41—1816no—
657#41—188no—
658#41—182no—
659#41C2×D3214yes—
660C2×Q8—31no—
661C2×Q8—38no—
662C2×Q8—32no—
663C2×Q8—32no—
664C2×Q8—34no—
665C2×Q8—34no—
666C2×Q8—62no—
667C2×Q8—68no—
668C2×Q8—64no—
669C2×Q8—61no—
670C2×Q8—61no—
671C2×Q8—62no—
672C2×Q8—62no—
673C2×Q8—98no—
674C2×Q8—91no—
675C2×Q8—182no—
676C2×Q8—184no—
677C2×Q8—188no—
678C2×Q8C2×D3211yescharacteristic
679C2×D4—21no—
680C2×D4—32no—
681C2×D4—31no—
682C2×D4—62no—
683C2×D4—91no—
684C2×D4—182no—
685C2×D4—181no—
686C2×D4C2×D3211yescharacteristic
687C22×C4—21no—
688C22×C4—32no—
689C22×C4—62no—
690C22×C4—62no—
691C22×C4—61no—
692C22×C4—61no—
693C22×C4—182no—
694C22×C4—182no—
695C22×C4—181no—
696C22×C4C2×D3211yescharacteristic
697Q16—38no—
698Q16—98no—
699Q16—98no—
700Q16—98no—
701Q16—94no—
702SD16—38no—
703SD16—98no—
704SD16—94no—
705SD16—94no—
706D8—94no—
707M16—34no—
708M16—98no—
709C2×C8—32no—
710C2×C8—98no—
711C2×C8—91no—
712C2×C8—91no—
713C2×C8—94no—
714C22×C3—22no—
715C22×C3—22no—
716C22×C3—22no—
717C22×C3—22no—
718C22×C3—22no—
719C22×C3—21no—
720C22×C3—34no—
721C22×C3—42no—
722C22×C3—42no—
723C22×C3—42no—
724C22×C3—42no—
725C22×C3—64no—
726C22×C3—82no—
727C22×C3C2×D3×D412yes—
728C22×C3C2×D3×D411yescharacteristic
729C22×C3C22×#6712yes—
730C22×C3C22×#6711yescharacteristic
731C2×D3—24no—
732C2×D3—62no—
733C2×D3—62no—
734C2×D3—122no—
735C2×D3—122no—
736C2×D3—122no—
737C2×D3—242no—
738C2×D3C22×#6714yes—
739C3×C4—22no—
740C3×C4—22no—
741C3×C4—21no—
742C3×C4—22no—
743C3×C4—21no—
744C3×C4—34no—
745C3×C4—42no—
746C3×C4—64no—
747C3×C4—64no—
748C3×C4C2×D3×D411yescharacteristic
749C3×C4C2×D3×D412yes—
750C3×C4C22×#6711yescharacteristic
751C3×C4C22×#6712yes—
752C3×C4C24×D311yescharacteristic
753C3×C4C24×D311yescharacteristic
754Dic3—24no—
755Dic3—24no—
756Dic3—62no—
757Dic3—62no—
758Dic3—122no—
759Dic3C22×#6714yes—
760C32C2×#57811yescharacteristic, complemented, Sylow
761C23—21no—
762C23—32no—
763C23—181no—
764C23D3×#6711yescharacteristic
765Q8—21no—
766Q8—34no—
767Q8—34no—
768Q8—34no—
769Q8—68no—
770Q8—64no—
771Q8—62no—
772Q8—64no—
773Q8—62no—
774Q8—92no—
775Q8—188no—
776Q8—181no—
777Q8C22×D3212yes—
778D4—24no—
779D4—21no—
780D4—38no—
781D4—34no—
782D4—68no—
783D4—92no—
784D4—188no—
785D4—184no—
786D4—181no—
787D4C22×D3212yes—
788C2×C4—21no—
789C2×C4—24no—
790C2×C4—32no—
791C2×C4—34no—
792C2×C4—34no—
793C2×C4—68no—
794C2×C4—68no—
795C2×C4—64no—
796C2×C4—64no—
797C2×C4—62no—
798C2×C4—62no—
799C2×C4—188no—
800C2×C4—188no—
801C2×C4—181no—
802C2×C4—184no—
803C2×C4D3×#6712yes—
804C2×C4D3×#6711yescharacteristic
805C2×C4C22×D3212yes—
806C2×C4C22×D3211yescharacteristic
807C8—34no—
808C8—92no—
809C8—92no—
810C2×C3—22no—
811C2×C3—22no—
812C2×C3—21no—
813C2×C3—22no—
814C2×C3—42no—
815C2×C3—42no—
816C2×C3—42no—
817C2×C3—64no—
818C2×C3—82no—
819C2×C3#577912yescomplemented
820C2×C3#583812yescomplemented
821C2×C3C22×D3×D411yescharacteristic
822C2×C3C23×#6711yescharacteristic
823D3—24no—
824D3—122no—
825D3—122no—
826D3—242no—
827C22—22no—
828C22—22no—
829C22—34no—
830C22—42no—
831C22—64no—
832C22—182no—
833C22—362no—
834C22C2×D3×#6712yes—
835C22C2×D3×#6711yescharacteristic
836C4—22no—
837C4—34no—
838C4—64no—
839C4—64no—
840C4—182no—
841C4C2×D3×#6712yes—
842C4C2×D3×#6711yescharacteristic
843C4C23×D3211yescharacteristic
844C3—21no—
845C3C2×#577911yescharacteristic, complemented
846C3C2×#583811yescharacteristic, complemented
847C2—22no—
848C2—42no—
849C2—64no—
850C2—362no—
851C2#1059546512yesdirect product factor
852C2C22×D3×#6711yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutator, cosocleC32×C4C25
FrattiniC4C23×D32
FittingC2×C32×#41C22
socleC22×C32C22×D4
hypercenterC2×#41D32
hypocenterC32C2×#578
LCSG ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#41

Complements

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

NH ≅ G/Ntype
1. C2×C3×#1010C2semidirect
2. C2×#64297C2semidirect
3. C2×#64159C2semidirect
4. C2×C3×#951C2semidirect
5. #10595465C2direct (N × H)
6. C2×#63948C2semidirect
7. C2×D3×#216C2semidirect
8. C2×#63935C2semidirect
9. C2×#63929C2semidirect
10. C22×#3718C2semidirect
11. C2×#63833C2semidirect
12. C2×#63815C2semidirect
18. C3×#1010C22semidirect
31. #64297C22semidirect
34. #64159C22semidirect
40. C3×#951C22semidirect
44. #63948C22semidirect
45. D3×#216C22semidirect
46. #63935C22semidirect
47. #63929C22semidirect
51. C2×#3718C22semidirect
52. #63833C22semidirect
55. #63815C22semidirect
59. C2×#1010D3semidirect
64. C2×#951D3semidirect
167. #1010C2×D3semidirect
196. #951C2×D3semidirect
642. C2×C32#578semidirect
760. C32C2×#578semidirect
819. C2×C3#5779semidirect
820. C2×C3#5838semidirect
845. C3C2×#5779semidirect
846. C3C2×#5838semidirect
851. C2#10595465direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×#10102
C2×#642972
C2×#641592
C2×C3×#9512
#105954652
C2×#639482
C2×D3×#2162
C2×#639352
C2×#639292
C22×#37182
C2×#638332
C2×#638152
C2×#58383
C2×#57793