Finite Group Databasebeta

← C2×#10595318 #11918877

Subgroups — C2×#10595318 #11918877

Order 1152.

3049 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×C3×#1007C211yesmaximal, characteristic, complemented
2C2×#64307C211yesmaximal, characteristic, complemented
3C2×#64151C211yesmaximal, characteristic, complemented
4C22×C3×#215C211yesmaximal, characteristic, complemented
5C2×#63947C212yesmaximal, complemented
6C2×#63946C212yesmaximal, complemented
7#10595318C2116yesmaximal, direct product factor
8C2×#63939C212yesmaximal, complemented
9C2×D3×#215C212yesmaximal, complemented
10C2×#63829C211yesmaximal, characteristic, complemented
11C2×#63823C211yesmaximal, characteristic, complemented
12C2×#63814C211yesmaximal, characteristic, complemented
13C2×#5837—31nomaximal
14C2×#5762—31nomaximal
15C22×C32×Q8C2211yescharacteristic, complemented
16C2×#3828C2211yescharacteristic
17C3×#1007—24no—
18C3×#1007C2218yescomplemented
19C2×C3×#239—21no—
20C2×C3×#239C2212yescomplemented
21C2×C3×D3×Q8—21no—
22C2×C3×D3×Q8C2212yescomplemented
23C2×C3×#235—22no—
24C2×C3×#235C2211yescharacteristic
25C2×C3×#235C2211yescharacteristic, complemented
26C22×C3×D12C2211yescharacteristic
27C2×D3×#67—22no—
28#64307—24no—
29#64307C2218yescomplemented
30C2×#3802—21no—
31C2×D3×D12C2212yes—
32C2×#3796—21no—
33C2×#3795C2212yes—
34C2×#3756C2212yescomplemented
35#64151C2218yescomplemented
36C2×#3755C2212yescomplemented
37C2×#3748C2211yescharacteristic, complemented
38C2×C3×#215C2212yescomplemented
39C2×C3×#215C2212yescomplemented
40C2×C3×#215C2218yescomplemented
41C22×C3×C3⋊C8C2211yescharacteristic, complemented
42#63947C22116yescomplemented
43#63946C22116yescomplemented
44#63939C22116yescomplemented
45D3×#215C22116yescomplemented
46C2×#3719C2211yescharacteristic, complemented
47C2×#3717C2211yescharacteristic, complemented
48#63829C2218yescomplemented
49C2×#3716C2211yescharacteristic, complemented
50C2×#3715C2212yescomplemented
51C2×#3714C2211yescharacteristic, complemented
52#63823C2218yescomplemented
53C2×#3713C2212yescomplemented
54C2×#3711C2212yescomplemented
55#63814C2218yescomplemented
56C2×D3×C3⋊C8C2212yescomplemented
57C2×C3×2−1+4—31no—
58C2×#1009—31no—
59C2×#1007D311yescharacteristic, complemented
60C2×#1004—31no—
61C22×C3×SD16—31no—
62#5837—316no—
63C2×#950—32no—
64C2×#950—31no—
65C2×#949—31no—
66C2×#949—32no—
67C2×#948—31no—
68C2×#942—31no—
69C2×#942—31no—
70C2×#942—32no—
71C2×#942—61no—
72C22×#215—32no—
73C22×#215D311yescharacteristic, complemented
74C2×#932—31no—
75#5762—316no—
76C2×#916—32no—
77C2×#915—32no—
78C2×#914—32no—
79C2×D3×SD16—32no—
80C2×#904—31no—
81C2×#901—31no—
82C23×C3×D3—21no—
83C22×D32—22no—
84C2×C32×Q8—21no—
85C2×C32×Q8—22no—
86C2×C32×Q8C2312yes—
87C2×C32×Q8C2314yescomplemented
88C22×C32×C4—21no—
89C22×C32×C4C2311yescharacteristic
90C2×#638—21no—
91#3828—22no—
92#3828C2314yes—
93C2×C4⋊(C3⋊D3)C2311yescharacteristic
94C2×C4×C3⋊D3—21no—
95C2×#634C2311yescharacteristic
96C2×C3×#67—21no—
97C2×C3×#67D412yes—
98C3×#239—28no—
99C3×#239—24no—
100C3×#239C2318yescomplemented
101C3×D3×Q8—24no—
102C3×D3×Q8—28no—
103C3×D3×Q8C2318yescomplemented
104C3×#235—22no—
105C3×#235—216no—
106C3×#235D414yes—
107C3×#235C2314yes—
108C3×#235C2314yescomplemented
109C2×C3×D12—22no—
110C2×C3×D12—21no—
111C2×C3×D12—22no—
112C2×C3×D12D411yescharacteristic
113C2×C3×D12C2312yes—
114C2×C3×D12C2314yes—
115C2×C3×D12C2311yescharacteristic
116C2×C3×C4×D3—22no—
117C2×C3×C4×D3—21no—
118C2×C3×C4×D3—22no—
119C2×C3×C4×D3C2312yes—
120C2×C3×Dic6—22no—
121C2×C3×Dic6D411yescharacteristic
122C2×C3×Dic6C2311yescharacteristic
123D3×#67—216no—
124C2×#626—22no—
125C2×#625—22no—
126C2×D3×Dic3—22no—
127#3802—28no—
128D3×D12—24no—
129D3×D12C2318yes—
130#3796—28no—
131#3795—24no—
132#3795C2318yes—
133#3756C2318yescomplemented
134#3755C2318yescomplemented
135#3748C2314yescomplemented
136C2×C3⋊(C3⋊C8)C2312yes—
137C3×#215C2318yescomplemented
138C3×#215C2318yescomplemented
139C2×C3×C3⋊C8C2311yescharacteristic
140C2×C3×C3⋊C8C2311yescharacteristic
141C2×C3×C3⋊C8C2314yescomplemented
142#3719C2314yescomplemented
143#3717C2314yescomplemented
144#3716C2314yescomplemented
145#3715C2318yescomplemented
146#3714C2314yescomplemented
147#3713C2318yescomplemented
148#3711C2318yescomplemented
149D3×C3⋊C8C2318yescomplemented
150C2×#577—91noSylow
151C3×2−1+4—38no—
152C3×2−1+4—64no—
153C2×C3×#41—31no—
154C2×C3×#41—32no—
155C2×C3×#41—31no—
156C2×C3×#41—62no—
157C2×C3×#41—61no—
158C22×C3×Q8—21no—
159C22×C3×Q8—32no—
160C22×C3×Q8—61no—
161C22×C3×Q8C2×D311yescharacteristic, complemented
162C22×C3×Q8C2×D311yescharacteristic, complemented
163C22×C3×D4—31no—
164C22×#67—62no—
165#1009—38no—
166#1009—64no—
167#1007—24no—
168#1007C2×D318yescomplemented
169C2×#239—21no—
170C2×#239—61no—
171C2×#239C2×D312yescomplemented
172C2×D3×Q8—21no—
173C2×D3×Q8C2×D312yescomplemented
174#1004—38no—
175#1004—64no—
176C2×#237—32no—
177C2×#237—61no—
178C2×D3×D4—32no—
179C2×D3×D4—61no—
180C2×D3×D4—62no—
181C2×D3×D4—61no—
182C2×#235—22no—
183C2×#235—31no—
184C2×#235—31no—
185C2×#235—32no—
186C2×#235—61no—
187C2×#235C2×D311yescharacteristic
188C2×#235C2×D311yescharacteristic, complemented
189C22×D12—32no—
190C22×D12C2×D311yescharacteristic
191C2×C3×SD16—32no—
192C2×C3×SD16—32no—
193C2×C3×SD16—38no—
194C22×C3×C8—31no—
195#950—316no—
196#950—38no—
197#949—38no—
198#949—316no—
199#948—38no—
200C2×#216—32no—
201C2×#216—32no—
202C2×#216—31no—
203C2×#216—62no—
204#942—38no—
205#942—38no—
206#942—316no—
207#942—68no—
208C2×#215—32no—
209C2×#215—32no—
210C2×#215—32no—
211C2×#215—316no—
212C2×#215—31no—
213C2×#215—62no—
214C2×#215C2×D312yescomplemented
215C2×#215C2×D312yescomplemented
216C2×#215C2×D318yescomplemented
217C2×#214—32no—
218C2×#214—31no—
219#932—38no—
220C2×#213—32no—
221C2×#213—32no—
222C2×#213—31no—
223C2×#208—31no—
224C2×#208—31no—
225C2×#208—32no—
226C2×#208—61no—
227C22×C3⋊C8—32no—
228C22×C3⋊C8C2×D311yescharacteristic, complemented
229#916—316no—
230#915—316no—
231#914—316no—
232D3×SD16—316no—
233C2×Dic12—31no—
234#904—38no—
235C2×D24—31no—
236C2×#204—31no—
237C2×#204—31no—
238#901—38no—
239C2×ΓL(1,𝔽25)—32no—
240C2×D3×C8—32no—
241C23×C32C2×D411yescharacteristic
242C22×C3⋊D3—21no—
243C22×C3×D3—22no—
244C22×C3×D3—21no—
245C22×C3×D3—24no—
246C22×C3×D3—82no—
247C22×C3×D3C2×D412yes—
248C2×D32—28no—
249C2×D32—84no—
250C32×Q8—22no—
251C32×Q8—24no—
252C32×Q8C2414yes—
253C2×C32×C4—22no—
254C2×C32×C4—24no—
255C2×C32×C4C2×D411yescharacteristic
256C2×C32×C4C2×D412yes—
257C2×C32×C4C2411yescharacteristic
258C2×C32×C4C2412yes—
259#638—24no—
260C2×C3⋊Dic3—21no—
261C4⋊(C3⋊D3)—21no—
262C4⋊(C3⋊D3)C2412yes—
263C4×C3⋊D3—24no—
264#634—21no—
265#634C2412yes—
266C3×#67—24no—
267C3×#67C2×D418yes—
268C2×C3×Dic3—21no—
269C2×C3×Dic3C2×D412yes—
270C3×D12—28no—
271C3×D12—22no—
272C3×D12—24no—
273C3×D12—21no—
274C3×D12C2×D414yes—
275C3×D12C2412yes—
276C3×D12C2414yes—
277C3×C4×D3—28no—
278C3×C4×D3—24no—
279C3×C4×D3—28no—
280C3×C4×D3C2×D414yes—
281C3×C4×D3C2414yes—
282C3×Dic6—21no—
283C3×Dic6—28no—
284C3×Dic6C2×D414yes—
285C3×Dic6C2412yes—
286#626—28no—
287#625—28no—
288D3×Dic3—28no—
289C3⋊(C3⋊C8)C2414yes—
290C3×C3⋊C8C2412yes—
291C3×C3⋊C8C2412yes—
292C2×2−1+4—31no—
293C2×H(5,𝔽2)—91no—
294#577—916no—
295C2×#137—92no—
296C2×#137—91no—
297C2×AGL(1,ℤ/8)—92no—
298C2×AGL(1,ℤ/8)—91no—
299C2×#135—91no—
300C2×#135—92no—
301C22×SD16—31no—
302C22×SD16—92no—
303C2×#131—91no—
304C24×C3—61no—
305C23×D3—21no—
306C23×D3—62no—
307C23×D3—62no—
308C3×#41—34no—
309C3×#41—34no—
310C3×#41—38no—
311C3×#41—34no—
312C3×#41—616no—
313C3×#41—64no—
314C3×#41—68no—
315C3×#41—62no—
316C2×C3×Q8—21no—
317C2×C3×Q8—22no—
318C2×C3×Q8—21no—
319C2×C3×Q8—22no—
320C2×C3×Q8—22no—
321C2×C3×Q8—24no—
322C2×C3×Q8—31no—
323C2×C3×Q8—38no—
324C2×C3×Q8—31no—
325C2×C3×Q8—41no—
326C2×C3×Q8—42no—
327C2×C3×Q8—62no—
328C2×C3×Q8—64no—
329C2×C3×Q8—68no—
330C2×C3×Q8C22×D312yes—
331C2×C3×Q8C22×D312yes—
332C2×C3×Q8C22×D314yescomplemented
333C2×C3×Q8C22×D314yescomplemented
334C2×C3×D4—32no—
335C2×C3×D4—31no—
336C2×C3×D4—31no—
337C2×C3×D4—32no—
338C2×C3×D4—34no—
339C2×C3×D4—62no—
340C2×C3×D4—61no—
341C2×C3×D4—61no—
342C2×C3×D4—62no—
343C22×C3×C4—21no—
344C22×C3×C4—21no—
345C22×C3×C4—21no—
346C22×C3×C4—32no—
347C22×C3×C4—41no—
348C22×C3×C4—62no—
349C22×C3×C4—62no—
350C22×C3×C4—61no—
351C22×C3×C4C22×D311yescharacteristic
352C22×C3×C4C22×D311yescharacteristic
353C2×#67—21no—
354C2×#67—62no—
355C2×#67—61no—
356C2×#67—61no—
357C2×#67—62no—
358C2×#67—616no—
359C2×#67—62no—
360C2×#67—121no—
361C2×#67#6712yes—
362C22×Dic3—62no—
363#239—28no—
364#239—24no—
365#239—68no—
366#239C22×D318yescomplemented
367D3×Q8—24no—
368D3×Q8—28no—
369D3×Q8C22×D318yescomplemented
370#237—38no—
371#237—64no—
372#237—68no—
373D3×D4—38no—
374D3×D4—68no—
375D3×D4—616no—
376D3×D4—68no—
377D3×D4—64no—
378#235—22no—
379#235—216no—
380#235—34no—
381#235—34no—
382#235—38no—
383#235—64no—
384#235—64no—
385#235—62no—
386#235—62no—
387#235—122no—
388#235#6714yes—
389#235C22×D314yes—
390#235C22×D314yescomplemented
391C2×D12—22no—
392C2×D12—21no—
393C2×D12—22no—
394C2×D12—31no—
395C2×D12—31no—
396C2×D12—38no—
397C2×D12—61no—
398C2×D12—64no—
399C2×D12—62no—
400C2×D12#6711yescharacteristic
401C2×D12C22×D311yescharacteristic
402C2×D12C22×D312yes—
403C2×D12C22×D314yes—
404C2×C4×D3—22no—
405C2×C4×D3—21no—
406C2×C4×D3—22no—
407C2×C4×D3—62no—
408C2×C4×D3—61no—
409C2×C4×D3—61no—
410C2×C4×D3—121no—
411C2×C4×D3C22×D312yes—
412C2×Dic6—22no—
413C2×Dic6—31no—
414C2×Dic6—31no—
415C2×Dic6—61no—
416C2×Dic6#6711yescharacteristic
417C2×Dic6C22×D311yescharacteristic
418C3×SD16—38no—
419C3×SD16—38no—
420C2×C3×C8—31no—
421C2×C3×C8—31no—
422C2×C3×C8—34no—
423#216—38no—
424#216—38no—
425#216—34no—
426#216—68no—
427#215—38no—
428#215—38no—
429#215—38no—
430#215—34no—
431#215—68no—
432#215C22×D318yescomplemented
433#215C22×D318yescomplemented
434#214—38no—
435#214—34no—
436#213—38no—
437#213—38no—
438#213—34no—
439#208—34no—
440#208—34no—
441#208—38no—
442#208—64no—
443C2×C3⋊C8—32no—
444C2×C3⋊C8—32no—
445C2×C3⋊C8—38no—
446C2×C3⋊C8—62no—
447C2×C3⋊C8C22×D311yescharacteristic
448C2×C3⋊C8C22×D311yescharacteristic
449C2×C3⋊C8C22×D314yescomplemented
450Dic12—34no—
451D24—34no—
452#204—34no—
453#204—34no—
454ΓL(1,𝔽25)—38no—
455D3×C8—38no—
456C22×C32—22no—
457C22×C32C22×D412yes—
458C22×C32C22×D411yescharacteristic
459C2×C3⋊D3—22no—
460C2×C3⋊D3—42no—
461C2×C3×D3—24no—
462C2×C3×D3—24no—
463C2×C3×D3—22no—
464C2×C3×D3—44no—
465C2×C3×D3—42no—
466C2×C3×D3—84no—
467C2×C3×D3C22×D414yes—
468D32—88no—
469C32×C4—24no—
470C32×C4C22×D411yescharacteristic
471C32×C4C22×D412yes—
472C32×C4C2511yescharacteristic
473C3⋊Dic3—22no—
474C3×Dic3—22no—
475C3×Dic3C22×D414yes—
4762−1+4—38no—
4772−1+4—64no—
478H(5,𝔽2)—98no—
479H(5,𝔽2)—184no—
480C2×#41—31no—
481C2×#41—32no—
482C2×#41—31no—
483C2×#41—62no—
484C2×#41—61no—
485C2×#41—92no—
486C2×#41—91no—
487C2×#41—181no—
488C22×Q8—32no—
489C22×Q8—61no—
490C22×Q8D3211yescharacteristic, complemented
491C22×D4—31no—
492C22×D4—92no—
493C22×D4—181no—
494C22×D4—182no—
495#137—916no—
496#137—98no—
497AGL(1,ℤ/8)—916no—
498AGL(1,ℤ/8)—98no—
499#135—98no—
500#135—916no—
501C2×Q16—91no—
502C2×Q16—92no—
503C2×SD16—32no—
504C2×SD16—32no—
505C2×SD16—38no—
506C2×SD16—91no—
507C2×SD16—91no—
508C2×SD16—916no—
509C2×SD16—92no—
510C2×SD16—92no—
511C2×D8—91no—
512C2×D8—92no—
513#131—98no—
514C2×M16—92no—
515C2×M16—91no—
516C22×C8—31no—
517C22×C8—92no—
518C23×C3—21no—
519C23×C3—32no—
520C23×C3—61no—
521C23×C3—62no—
522C23×C3—64no—
523C23×C3—242no—
524C23×C3D3×D411yescharacteristic
525C23×C3C2×#6711yescharacteristic
526C22×D3—22no—
527C22×D3—21no—
528C22×D3—24no—
529C22×D3—68no—
530C22×D3—61no—
531C22×D3—61no—
532C22×D3—68no—
533C22×D3—82no—
534C22×D3—121no—
535C22×D3—244no—
536C22×D3—244no—
537C22×D3C2×#6712yes—
538C3×Q8—22no—
539C3×Q8—24no—
540C3×Q8—22no—
541C3×Q8—24no—
542C3×Q8—24no—
543C3×Q8—34no—
544C3×Q8—32no—
545C3×Q8—42no—
546C3×Q8—44no—
547C3×Q8—68no—
548C3×Q8—61no—
549C3×Q8C23×D314yes—
550C3×Q8C23×D314yes—
551C3×D4—38no—
552C3×D4—34no—
553C3×D4—32no—
554C3×D4—34no—
555C3×D4—68no—
556C3×D4—64no—
557C3×D4—61no—
558C3×D4—62no—
559C3×D4—64no—
560C2×C3×C4—22no—
561C2×C3×C4—24no—
562C2×C3×C4—22no—
563C2×C3×C4—24no—
564C2×C3×C4—21no—
565C2×C3×C4—22no—
566C2×C3×C4—21no—
567C2×C3×C4—22no—
568C2×C3×C4—32no—
569C2×C3×C4—34no—
570C2×C3×C4—34no—
571C2×C3×C4—44no—
572C2×C3×C4—42no—
573C2×C3×C4—68no—
574C2×C3×C4—68no—
575C2×C3×C4—61no—
576C2×C3×C4—64no—
577C2×C3×C4D3×D411yescharacteristic
578C2×C3×C4D3×D412yes—
579C2×C3×C4C2×#6711yescharacteristic
580C2×C3×C4C2×#6712yes—
581C2×C3×C4C23×D311yescharacteristic
582C2×C3×C4C23×D312yes—
583C2×C3×C4C23×D311yescharacteristic
584C2×C3×C4C23×D312yes—
585#67—24no—
586#67—68no—
587#67—64no—
588#67—64no—
589#67—68no—
590#67—68no—
591#67—124no—
592#67C2×#6718yes—
593C2×Dic3—21no—
594C2×Dic3—61no—
595C2×Dic3—61no—
596C2×Dic3—68no—
597C2×Dic3—121no—
598C2×Dic3C2×#6712yes—
599D12—28no—
600D12—22no—
601D12—24no—
602D12—21no—
603D12—32no—
604D12—32no—
605D12—62no—
606D12—68no—
607D12—61no—
608D12—61no—
609D12—121no—
610D12C2×#6714yes—
611D12C23×D312yes—
612D12C23×D314yes—
613C4×D3—28no—
614C4×D3—24no—
615C4×D3—28no—
616C4×D3—68no—
617C4×D3—64no—
618C4×D3—64no—
619C4×D3—124no—
620C4×D3C2×#6714yes—
621C4×D3C23×D314yes—
622Dic6—21no—
623Dic6—28no—
624Dic6—32no—
625Dic6—32no—
626Dic6—62no—
627Dic6—61no—
628Dic6—61no—
629Dic6—121no—
630Dic6C2×#6714yes—
631Dic6C23×D312yes—
632C3×C8—32no—
633C3×C8—32no—
634C3⋊C8—34no—
635C3⋊C8—34no—
636C3⋊C8—64no—
637C3⋊C8C23×D312yes—
638C3⋊C8C23×D312yes—
639C2×C32—22no—
640C2×C32#57712yescomplemented
641C2×C32C23×D411yescharacteristic
642C3⋊D3—42no—
643C3×D3—24no—
644C3×D3—44no—
645C3×D3—42no—
646C24—61no—
647C24—182no—
648#41—34no—
649#41—34no—
650#41—38no—
651#41—34no—
652#41—616no—
653#41—64no—
654#41—68no—
655#41—62no—
656#41—98no—
657#41—94no—
658#41—184no—
659#41—188no—
660#41—182no—
661C2×Q8—21no—
662C2×Q8—22no—
663C2×Q8—31no—
664C2×Q8—38no—
665C2×Q8—31no—
666C2×Q8—62no—
667C2×Q8—64no—
668C2×Q8—68no—
669C2×Q8—91no—
670C2×Q8C2×D3212yes—
671C2×Q8C2×D3214yescomplemented
672C2×D4—32no—
673C2×D4—31no—
674C2×D4—32no—
675C2×D4—34no—
676C2×D4—31no—
677C2×D4—62no—
678C2×D4—61no—
679C2×D4—61no—
680C2×D4—62no—
681C2×D4—98no—
682C2×D4—91no—
683C2×D4—184no—
684C2×D4—182no—
685C2×D4—188no—
686C2×D4—1816no—
687C2×D4—182no—
688C2×D4—181no—
689C22×C4—21no—
690C22×C4—32no—
691C22×C4—62no—
692C22×C4—62no—
693C22×C4—61no—
694C22×C4—182no—
695C22×C4—181no—
696C22×C4C2×D3211yescharacteristic
697Q16—94no—
698Q16—98no—
699SD16—38no—
700SD16—38no—
701SD16—94no—
702SD16—94no—
703SD16—98no—
704SD16—98no—
705D8—94no—
706D8—98no—
707M16—98no—
708M16—94no—
709C2×C8—31no—
710C2×C8—31no—
711C2×C8—34no—
712C2×C8—98no—
713C2×C8—92no—
714C22×C3—22no—
715C22×C3—22no—
716C22×C3—22no—
717C22×C3—21no—
718C22×C3—34no—
719C22×C3—42no—
720C22×C3—64no—
721C22×C3—62no—
722C22×C3—64no—
723C22×C3—122no—
724C22×C3—124no—
725C22×C3—244no—
726C22×C3C2×D3×D412yes—
727C22×C3C2×D3×D411yescharacteristic
728C22×C3C22×#6712yes—
729C22×C3C22×#6711yescharacteristic
730C2×D3—24no—
731C2×D3—24no—
732C2×D3—22no—
733C2×D3—44no—
734C2×D3—42no—
735C2×D3—62no—
736C2×D3—62no—
737C2×D3—84no—
738C2×D3—122no—
739C2×D3—122no—
740C2×D3—122no—
741C2×D3—242no—
742C2×D3—248no—
743C2×D3—248no—
744C2×D3C22×#6714yes—
745C3×C4—24no—
746C3×C4—24no—
747C3×C4—21no—
748C3×C4—22no—
749C3×C4—21no—
750C3×C4—34no—
751C3×C4—44no—
752C3×C4—62no—
753C3×C4C2×D3×D411yescharacteristic
754C3×C4C2×D3×D412yes—
755C3×C4C22×#6711yescharacteristic
756C3×C4C22×#6712yes—
757C3×C4C24×D311yescharacteristic
758C3×C4C24×D311yescharacteristic
759Dic3—22no—
760Dic3—62no—
761Dic3—62no—
762Dic3—122no—
763Dic3C22×#6714yes—
764C32C2×#57711yescharacteristic, complemented, Sylow
765C23—32no—
766C23—61no—
767C23—62no—
768C23—64no—
769C23—188no—
770C23—181no—
771C23—242no—
772C23—724no—
773C23D3×#6711yescharacteristic
774Q8—22no—
775Q8—24no—
776Q8—34no—
777Q8—32no—
778Q8—68no—
779Q8—61no—
780Q8—92no—
781Q8—181no—
782Q8C22×D3214yes—
783D4—38no—
784D4—34no—
785D4—32no—
786D4—34no—
787D4—68no—
788D4—64no—
789D4—62no—
790D4—64no—
791D4—61no—
792D4—92no—
793D4—188no—
794D4—188no—
795D4—184no—
796D4—181no—
797C2×C4—24no—
798C2×C4—22no—
799C2×C4—32no—
800C2×C4—34no—
801C2×C4—34no—
802C2×C4—68no—
803C2×C4—68no—
804C2×C4—61no—
805C2×C4—64no—
806C2×C4—188no—
807C2×C4—181no—
808C2×C4—184no—
809C2×C4D3×#6712yes—
810C2×C4D3×#6711yescharacteristic
811C2×C4C22×D3212yes—
812C2×C4C22×D3211yescharacteristic
813C8—32no—
814C8—32no—
815C8—94no—
816C2×C3—22no—
817C2×C3—22no—
818C2×C3—21no—
819C2×C3—22no—
820C2×C3—42no—
821C2×C3—64no—
822C2×C3—122no—
823C2×C3—124no—
824C2×C3#576212yescomplemented
825C2×C3#583712yescomplemented
826C2×C3C22×D3×D411yescharacteristic
827C2×C3C23×#6711yescharacteristic
828D3—24no—
829D3—44no—
830D3—42no—
831D3—122no—
832D3—122no—
833D3—242no—
834C22—22no—
835C22—34no—
836C22—64no—
837C22—62no—
838C22—64no—
839C22—124no—
840C22—122no—
841C22—182no—
842C22—244no—
843C22—362no—
844C22—728no—
845C22C2×D3×#6712yes—
846C22C2×D3×#6711yescharacteristic
847C4—24no—
848C4—34no—
849C4—62no—
850C4—182no—
851C4C2×D3×#6711yescharacteristic
852C4C2×D3×#6712yes—
853C4C23×D3211yescharacteristic
854C3—21no—
855C3C2×#576211yescharacteristic, complemented
856C3C2×#583711yescharacteristic, complemented
857C2—22no—
858C2—64no—
859C2—124no—
860C2—122no—
861C2—362no—
862C2#1059531812yesdirect product factor
863C2C22×D3×#6711yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutator, cosocleC32×C4C25
FrattiniC4C23×D32
FittingC22×C32×Q8C22
socleC22×C32C22×D4
hypercenterC22×Q8D32
hypocenterC32C2×#577
LCSG ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×Q8

Complements

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

NH ≅ G/Ntype
1. C2×C3×#1007C2semidirect
2. C2×#64307C2semidirect
3. C2×#64151C2semidirect
4. C22×C3×#215C2semidirect
5. C2×#63947C2semidirect
6. C2×#63946C2semidirect
7. #10595318C2direct (N × H)
8. C2×#63939C2semidirect
9. C2×D3×#215C2semidirect
10. C2×#63829C2semidirect
11. C2×#63823C2semidirect
12. C2×#63814C2semidirect
15. C22×C32×Q8C22semidirect
18. C3×#1007C22semidirect
20. C2×C3×#239C22semidirect
22. C2×C3×D3×Q8C22semidirect
25. C2×C3×#235C22semidirect
29. #64307C22semidirect
34. C2×#3756C22semidirect
35. #64151C22semidirect
36. C2×#3755C22semidirect
37. C2×#3748C22semidirect
38. C2×C3×#215C22semidirect
39. C2×C3×#215C22semidirect
40. C2×C3×#215C22semidirect
41. C22×C3×C3⋊C8C22semidirect
42. #63947C22semidirect
43. #63946C22semidirect
44. #63939C22semidirect
45. D3×#215C22semidirect
46. C2×#3719C22semidirect
47. C2×#3717C22semidirect
48. #63829C22semidirect
49. C2×#3716C22semidirect
50. C2×#3715C22semidirect
51. C2×#3714C22semidirect
52. #63823C22semidirect
53. C2×#3713C22semidirect
54. C2×#3711C22semidirect
55. #63814C22semidirect
56. C2×D3×C3⋊C8C22semidirect
59. C2×#1007D3semidirect
73. C22×#215D3semidirect
87. C2×C32×Q8C23semidirect
100. C3×#239C23semidirect
103. C3×D3×Q8C23semidirect
108. C3×#235C23semidirect
133. #3756C23semidirect
134. #3755C23semidirect
135. #3748C23semidirect
137. C3×#215C23semidirect
138. C3×#215C23semidirect
141. C2×C3×C3⋊C8C23semidirect
142. #3719C23semidirect
143. #3717C23semidirect
144. #3716C23semidirect
145. #3715C23semidirect
146. #3714C23semidirect
147. #3713C23semidirect
148. #3711C23semidirect
149. D3×C3⋊C8C23semidirect
161. C22×C3×Q8C2×D3semidirect
162. C22×C3×Q8C2×D3semidirect
168. #1007C2×D3semidirect
171. C2×#239C2×D3semidirect
173. C2×D3×Q8C2×D3semidirect
188. C2×#235C2×D3semidirect
214. C2×#215C2×D3semidirect
215. C2×#215C2×D3semidirect
216. C2×#215C2×D3semidirect
228. C22×C3⋊C8C2×D3semidirect
332. C2×C3×Q8C22×D3semidirect
333. C2×C3×Q8C22×D3semidirect
366. #239C22×D3semidirect
369. D3×Q8C22×D3semidirect
390. #235C22×D3semidirect
432. #215C22×D3semidirect
433. #215C22×D3semidirect
449. C2×C3⋊C8C22×D3semidirect
490. C22×Q8D32semidirect
640. C2×C32#577semidirect
671. C2×Q8C2×D32semidirect
764. C32C2×#577semidirect
824. C2×C3#5762semidirect
825. C2×C3#5837semidirect
855. C3C2×#5762semidirect
856. C3C2×#5837semidirect
862. C2#10595318direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×#10072
C2×#643072
C2×#641512
C22×C3×#2152
C2×#639472
C2×#639462
#105953182
C2×#639392
C2×D3×#2152
C2×#638292
C2×#638232
C2×#638142
C2×#58373
C2×#57623