Finite Group Databasebeta

← C2×#10595105 #11918880

Subgroups — C2×#10595105 #11918880

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×C3×#1004C211yesmaximal, characteristic, complemented
2C2×#64297C211yesmaximal, characteristic, complemented
3C2×#64141C211yesmaximal, characteristic, complemented
4C22×C3×#214C211yesmaximal, characteristic, complemented
5C2×#63935C212yesmaximal, complemented
6C2×#63934C212yesmaximal, complemented
7#10595105C2116yesmaximal, direct product factor
8C2×#63929C212yesmaximal, complemented
9C2×D3×#214C212yesmaximal, complemented
10C2×#63829C211yesmaximal, characteristic, complemented
11C2×#63827C211yesmaximal, characteristic, complemented
12C2×#63814C211yesmaximal, characteristic, complemented
13C2×#5836—31nomaximal
14C2×#5762—31nomaximal
15C22×C32×D4C2211yescharacteristic
16C2×#3828C2211yescharacteristic, complemented
17C22×C3×#67—22no—
18C3×#1004—24no—
19C3×#1004C2218yescomplemented
20C2×C3×#237—21no—
21C2×C3×#237C2212yes—
22C2×C3×D3×D4—21no—
23C2×C3×D3×D4C2212yes—
24C2×C3×#235C2211yescharacteristic
25C2×C3×#235C2211yescharacteristic
26C22×C3×Dic6C2211yescharacteristic, complemented
27C2×#3804—22no—
28C2×#3799C2212yescomplemented
29C2×#3797—21no—
30#64297—24no—
31#64297C2218yescomplemented
32C2×#3796—21no—
33C2×D3×Dic6C2212yescomplemented
34C2×#3754C2212yescomplemented
35#64141C2218yescomplemented
36C2×#3753C2212yescomplemented
37C2×#3748C2211yescharacteristic, complemented
38C2×C3×#214C2212yescomplemented
39C2×C3×#214C2212yescomplemented
40C2×C3×#214C2218yescomplemented
41C22×C3×C3⋊C8C2211yescharacteristic, complemented
42#63935C22116yescomplemented
43#63934C22116yescomplemented
44#63929C22116yescomplemented
45D3×#214C22116yescomplemented
46C2×#3719C2211yescharacteristic, complemented
47C2×#3718C2212yescomplemented
48C2×#3717C2211yescharacteristic, complemented
49#63829C2218yescomplemented
50C2×#3716C2211yescharacteristic, complemented
51#63827C2218yescomplemented
52C2×#3715C2212yescomplemented
53C2×#3714C2211yescharacteristic, complemented
54C2×#3711C2212yescomplemented
55#63814C2218yescomplemented
56C2×D3×C3⋊C8C2212yescomplemented
57C2×C3×H(5,𝔽2)—31no—
58C2×#1010—31no—
59C2×#1007—31no—
60C2×#1004D311yescharacteristic, complemented
61C22×C3×SD16—31no—
62#5836—316no—
63C2×#951—31no—
64C2×#951—32no—
65C2×#950—32no—
66C2×#950—31no—
67C2×#948—31no—
68C2×#942—31no—
69C22×#214—32no—
70C22×#214D311yescharacteristic, complemented
71C2×#932—31no—
72C2×#932—31no—
73C2×#932—32no—
74C2×#932—61no—
75#5762—316no—
76C2×#916—32no—
77C2×#915—32no—
78C2×#914—32no—
79C2×D3×SD16—32no—
80C2×#904—31no—
81C2×#901—31no—
82C24×C32—21no—
83C23×C3×D3—22no—
84C2×C32×D4—21no—
85C2×C32×D4—22no—
86C2×C32×D4C2312yes—
87C2×C32×D4C2314yes—
88C22×C32×C4C2311yescharacteristic
89C2×#638—21no—
90#3828—22no—
91#3828C2314yescomplemented
92C2×C4⋊(C3⋊D3)C2311yescharacteristic
93C2×C4×C3⋊D3—21no—
94C2×#634C2311yescharacteristic
95C2×C3×#67—21no—
96C2×C3×#67—22no—
97C2×C3×#67—216no—
98C2×C3×#67—22no—
99C2×C3×#67D412yes—
100C22×C3×Dic3—21no—
101C22×C3×Dic3—22no—
102C3×#237—24no—
103C3×#237—28no—
104C3×#237C2318yes—
105C3×D3×D4—28no—
106C3×D3×D4—24no—
107C3×D3×D4C2318yes—
108C3×#235—22no—
109C3×#235D414yes—
110C3×#235C2314yes—
111C3×#235C2314yes—
112C2×C3×D12D411yescharacteristic
113C2×C3×D12C2311yescharacteristic
114C2×C3×C4×D3—21no—
115C2×C3×C4×D3C2312yes—
116C2×C3×Dic6—21no—
117C2×C3×Dic6—22no—
118C2×C3×Dic6D411yescharacteristic
119C2×C3×Dic6C2312yes—
120C2×C3×Dic6C2311yescharacteristic
121C2×C3×Dic6C2314yescomplemented
122C2×#627—22no—
123C2×#626—22no—
124C2×#624—22no—
125#3804—216no—
126C2×D3×Dic3—22no—
127#3799—24no—
128#3799C2318yescomplemented
129#3797—28no—
130#3796—28no—
131D3×Dic6—24no—
132D3×Dic6C2318yescomplemented
133#3754C2318yescomplemented
134#3753C2318yescomplemented
135#3748C2314yescomplemented
136C2×C3⋊(C3⋊C8)C2312yes—
137C3×#214C2318yescomplemented
138C3×#214C2318yescomplemented
139C2×C3×C3⋊C8C2311yescharacteristic
140C2×C3×C3⋊C8C2311yescharacteristic
141C2×C3×C3⋊C8C2314yescomplemented
142#3719C2314yescomplemented
143#3718C2318yescomplemented
144#3717C2314yescomplemented
145#3716C2314yescomplemented
146#3715C2318yescomplemented
147#3714C2314yescomplemented
148#3711C2318yescomplemented
149D3×C3⋊C8C2318yescomplemented
150C2×#577—91noSylow
151C3×H(5,𝔽2)—38no—
152C3×H(5,𝔽2)—64no—
153C2×C3×#41—31no—
154C2×C3×#41—32no—
155C2×C3×#41—31no—
156C2×C3×#41—61no—
157C22×C3×Q8—31no—
158C22×C3×D4—21no—
159C22×C3×D4—32no—
160C22×C3×D4—61no—
161C22×C3×D4—62no—
162C22×C3×D4C2×D311yescharacteristic
163C22×C3×D4C2×D311yescharacteristic
164C22×#67—22no—
165#1010—38no—
166#1010—64no—
167#1007—38no—
168#1007—64no—
169C2×#239—32no—
170C2×#239—61no—
171C2×D3×Q8—32no—
172C2×D3×Q8—61no—
173C2×D3×Q8—61no—
174#1004—24no—
175#1004C2×D318yescomplemented
176C2×#237—21no—
177C2×#237—61no—
178C2×#237—62no—
179C2×#237C2×D312yes—
180C2×D3×D4—21no—
181C2×D3×D4C2×D312yes—
182C2×#235—31no—
183C2×#235—31no—
184C2×#235—32no—
185C2×#235—61no—
186C2×#235—62no—
187C2×#235C2×D311yescharacteristic
188C2×#235C2×D311yescharacteristic
189C22×Dic6—32no—
190C22×Dic6C2×D311yescharacteristic, complemented
191C2×C3×SD16—32no—
192C2×C3×SD16—32no—
193C2×C3×SD16—38no—
194C22×C3×C8—31no—
195#951—38no—
196#951—316no—
197#950—316no—
198#950—38no—
199#948—38no—
200C2×#216—32no—
201C2×#216—32no—
202C2×#216—31no—
203#942—38no—
204C2×#215—32no—
205C2×#215—31no—
206C2×#214—32no—
207C2×#214—32no—
208C2×#214—32no—
209C2×#214—316no—
210C2×#214—31no—
211C2×#214—62no—
212C2×#214C2×D312yescomplemented
213C2×#214C2×D312yescomplemented
214C2×#214C2×D318yescomplemented
215#932—38no—
216#932—38no—
217#932—316no—
218#932—68no—
219C2×#213—32no—
220C2×#213—32no—
221C2×#213—31no—
222C2×#213—62no—
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×C32—22no—
242C23×C32—24no—
243C23×C32—82no—
244C23×C32C2×D411yescharacteristic
245C22×C3⋊D3—21no—
246C22×C3×D3—21no—
247C22×C3×D3—28no—
248C22×C3×D3—84no—
249C22×C3×D3C2×D412yes—
250C32×D4—22no—
251C32×D4—24no—
252C32×D4C2414yes—
253C2×C32×C4C2×D411yescharacteristic
254C2×C32×C4C2×D412yes—
255C2×C32×C4C2411yescharacteristic
256C2×C32×C4C2412yes—
257#638—24no—
258C2×C3⋊Dic3—21no—
259C4⋊(C3⋊D3)—21no—
260C4⋊(C3⋊D3)C2412yes—
261C4×C3⋊D3—24no—
262#634—21no—
263#634C2412yes—
264C3×#67—24no—
265C3×#67—28no—
266C3×#67—28no—
267C3×#67C2×D418yes—
268C2×C3×Dic3—22no—
269C2×C3×Dic3—24no—
270C2×C3×Dic3—21no—
271C2×C3×Dic3—28no—
272C2×C3×Dic3C2×D412yes—
273C3×D12—21no—
274C3×D12C2×D414yes—
275C3×D12C2412yes—
276C3×C4×D3—24no—
277C3×C4×D3C2×D414yes—
278C3×C4×D3C2414yes—
279C3×Dic6—22no—
280C3×Dic6—24no—
281C3×Dic6—21no—
282C3×Dic6C2×D414yes—
283C3×Dic6C2414yes—
284C3×Dic6C2412yes—
285#627—28no—
286#626—28no—
287#624—28no—
288D3×Dic3—28no—
289C3⋊(C3⋊C8)C2414yes—
290C3×C3⋊C8C2412yes—
291C3×C3⋊C8C2412yes—
292C2×2−1+4—91no—
293C2×H(5,𝔽2)—31no—
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—21no—
305C24×C3—21no—
306C24×C3—41no—
307C24×C3—62no—
308C23×D3—22no—
309C3×#41—34no—
310C3×#41—34no—
311C3×#41—38no—
312C3×#41—34no—
313C3×#41—64no—
314C3×#41—68no—
315C3×#41—62no—
316C2×C3×Q8—31no—
317C2×C3×Q8—31no—
318C2×C3×Q8—32no—
319C2×C3×Q8—34no—
320C2×C3×Q8—61no—
321C2×C3×Q8—62no—
322C2×C3×D4—21no—
323C2×C3×D4—22no—
324C2×C3×D4—21no—
325C2×C3×D4—22no—
326C2×C3×D4—22no—
327C2×C3×D4—24no—
328C2×C3×D4—32no—
329C2×C3×D4—38no—
330C2×C3×D4—31no—
331C2×C3×D4—31no—
332C2×C3×D4—41no—
333C2×C3×D4—42no—
334C2×C3×D4—64no—
335C2×C3×D4—62no—
336C2×C3×D4—68no—
337C2×C3×D4—616no—
338C2×C3×D4—62no—
339C2×C3×D4—61no—
340C2×C3×D4C22×D312yes—
341C2×C3×D4C22×D312yes—
342C2×C3×D4C22×D314yes—
343C2×C3×D4C22×D314yes—
344C22×C3×C4—21no—
345C22×C3×C4—32no—
346C22×C3×C4—62no—
347C22×C3×C4—61no—
348C22×C3×C4—61no—
349C22×C3×C4C22×D311yescharacteristic
350C22×C3×C4C22×D311yescharacteristic
351C2×#67—21no—
352C2×#67—22no—
353C2×#67—216no—
354C2×#67—22no—
355C2×#67—62no—
356C2×#67—61no—
357C2×#67—61no—
358C2×#67—121no—
359C2×#67#6712yes—
360C22×Dic3—21no—
361C22×Dic3—22no—
362C22×Dic3—62no—
363#239—38no—
364#239—68no—
365#239—64no—
366D3×Q8—38no—
367D3×Q8—68no—
368D3×Q8—64no—
369D3×Q8—68no—
370#237—24no—
371#237—28no—
372#237—68no—
373#237—616no—
374#237C22×D318yes—
375D3×D4—28no—
376D3×D4—24no—
377D3×D4C22×D318yes—
378#235—22no—
379#235—34no—
380#235—34no—
381#235—38no—
382#235—64no—
383#235—64no—
384#235—62no—
385#235—62no—
386#235—616no—
387#235—122no—
388#235#6714yes—
389#235C22×D314yes—
390#235C22×D314yes—
391C2×D12—31no—
392C2×D12—31no—
393C2×D12—61no—
394C2×D12—62no—
395C2×D12#6711yescharacteristic
396C2×D12C22×D311yescharacteristic
397C2×C4×D3—21no—
398C2×C4×D3—62no—
399C2×C4×D3—62no—
400C2×C4×D3—61no—
401C2×C4×D3—61no—
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×Dic6#6711yescharacteristic
415C2×Dic6C22×D311yescharacteristic
416C2×Dic6C22×D312yes—
417C2×Dic6C22×D314yescomplemented
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#215—38no—
427#215—34no—
428#214—38no—
429#214—38no—
430#214—38no—
431#214—34no—
432#214—68no—
433#214C22×D318yescomplemented
434#214C22×D318yescomplemented
435#213—38no—
436#213—38no—
437#213—34no—
438#213—68no—
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×C32—24no—
458C22×C32—44no—
459C22×C32—84no—
460C22×C32C22×D412yes—
461C22×C32C22×D411yescharacteristic
462C2×C3⋊D3—22no—
463C2×C3⋊D3—42no—
464C2×C3×D3—24no—
465C2×C3×D3—22no—
466C2×C3×D3—42no—
467C2×C3×D3—88no—
468C2×C3×D3C22×D414yes—
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)—38no—
479H(5,𝔽2)—64no—
480C2×#41—31no—
481C2×#41—32no—
482C2×#41—31no—
483C2×#41—61no—
484C2×#41—92no—
485C2×#41—91no—
486C2×#41—182no—
487C2×#41—181no—
488C22×Q8—31no—
489C22×Q8—92no—
490C22×Q8—181no—
491C22×D4—32no—
492C22×D4—61no—
493C22×D4—62no—
494C22×D4D3211yescharacteristic
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—22no—
519C23×C3—22no—
520C23×C3—24no—
521C23×C3—24no—
522C23×C3—21no—
523C23×C3—32no—
524C23×C3—42no—
525C23×C3—44no—
526C23×C3—68no—
527C23×C3—61no—
528C23×C3—82no—
529C23×C3—82no—
530C23×C3—84no—
531C23×C3—244no—
532C23×C3D3×D411yescharacteristic
533C23×C3C2×#6711yescharacteristic
534C22×D3—21no—
535C22×D3—28no—
536C22×D3—61no—
537C22×D3—61no—
538C22×D3—84no—
539C22×D3—121no—
540C22×D3C2×#6712yes—
541C3×Q8—34no—
542C3×Q8—32no—
543C3×Q8—34no—
544C3×Q8—61no—
545C3×Q8—62no—
546C3×Q8—64no—
547C3×D4—22no—
548C3×D4—24no—
549C3×D4—22no—
550C3×D4—24no—
551C3×D4—24no—
552C3×D4—38no—
553C3×D4—34no—
554C3×D4—32no—
555C3×D4—42no—
556C3×D4—44no—
557C3×D4—68no—
558C3×D4—68no—
559C3×D4—64no—
560C3×D4—61no—
561C3×D4C23×D314yes—
562C3×D4C23×D314yes—
563C2×C3×C4—21no—
564C2×C3×C4—22no—
565C2×C3×C4—21no—
566C2×C3×C4—22no—
567C2×C3×C4—32no—
568C2×C3×C4—34no—
569C2×C3×C4—34no—
570C2×C3×C4—68no—
571C2×C3×C4—61no—
572C2×C3×C4—62no—
573C2×C3×C4—64no—
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—24no—
584#67—28no—
585#67—28no—
586#67—68no—
587#67—64no—
588#67—64no—
589#67—124no—
590#67C2×#6718yes—
591C2×Dic3—22no—
592C2×Dic3—24no—
593C2×Dic3—21no—
594C2×Dic3—28no—
595C2×Dic3—68no—
596C2×Dic3—61no—
597C2×Dic3—61no—
598C2×Dic3—121no—
599C2×Dic3C2×#6712yes—
600D12—21no—
601D12—32no—
602D12—32no—
603D12—62no—
604D12—68no—
605D12—61no—
606D12—61no—
607D12—121no—
608D12C2×#6714yes—
609D12C23×D312yes—
610C4×D3—24no—
611C4×D3—68no—
612C4×D3—68no—
613C4×D3—64no—
614C4×D3—64no—
615C4×D3—68no—
616C4×D3—124no—
617C4×D3C2×#6714yes—
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×#6714yes—
631Dic6C23×D312yes—
632Dic6C23×D314yes—
633C3×C8—32no—
634C3×C8—32no—
635C3⋊C8—34no—
636C3⋊C8—34no—
637C3⋊C8—64no—
638C3⋊C8C23×D312yes—
639C3⋊C8C23×D312yes—
640C2×C32—22no—
641C2×C32—44no—
642C2×C32#57712yescomplemented
643C2×C32C23×D411yescharacteristic
644C3⋊D3—42no—
645C3×D3—24no—
646C3×D3—42no—
647C24—21no—
648C24—62no—
649#41—34no—
650#41—34no—
651#41—38no—
652#41—34no—
653#41—64no—
654#41—68no—
655#41—62no—
656#41—98no—
657#41—94no—
658#41—184no—
659#41—1816no—
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—21no—
674C2×D4—22no—
675C2×D4—32no—
676C2×D4—38no—
677C2×D4—31no—
678C2×D4—31no—
679C2×D4—64no—
680C2×D4—62no—
681C2×D4—68no—
682C2×D4—616no—
683C2×D4—62no—
684C2×D4—61no—
685C2×D4—91no—
686C2×D4—182no—
687C2×D4—181no—
688C2×D4C2×D3212yes—
689C2×D4C2×D3214yes—
690C22×C4—32no—
691C22×C4—62no—
692C22×C4—61no—
693C22×C4—61no—
694C22×C4—182no—
695C22×C4—182no—
696C22×C4—181no—
697C22×C4C2×D3211yescharacteristic
698Q16—94no—
699Q16—98no—
700SD16—38no—
701SD16—38no—
702SD16—94no—
703SD16—94no—
704SD16—98no—
705SD16—98no—
706D8—94no—
707D8—98no—
708M16—98no—
709M16—94no—
710C2×C8—31no—
711C2×C8—31no—
712C2×C8—34no—
713C2×C8—98no—
714C2×C8—92no—
715C22×C3—22no—
716C22×C3—22no—
717C22×C3—24no—
718C22×C3—24no—
719C22×C3—22no—
720C22×C3—21no—
721C22×C3—34no—
722C22×C3—42no—
723C22×C3—44no—
724C22×C3—44no—
725C22×C3—44no—
726C22×C3—64no—
727C22×C3—62no—
728C22×C3—84no—
729C22×C3—84no—
730C22×C3—84no—
731C22×C3—88no—
732C22×C3—122no—
733C22×C3—248no—
734C22×C3C2×D3×D412yes—
735C22×C3C2×D3×D411yescharacteristic
736C22×C3C22×#6712yes—
737C22×C3C22×#6711yescharacteristic
738C2×D3—24no—
739C2×D3—22no—
740C2×D3—42no—
741C2×D3—62no—
742C2×D3—62no—
743C2×D3—88no—
744C2×D3—122no—
745C2×D3—122no—
746C2×D3—122no—
747C2×D3—242no—
748C2×D3C22×#6714yes—
749C3×C4—21no—
750C3×C4—22no—
751C3×C4—21no—
752C3×C4—34no—
753C3×C4—62no—
754C3×C4—64no—
755C3×C4C2×D3×D411yescharacteristic
756C3×C4C2×D3×D412yes—
757C3×C4C22×#6711yescharacteristic
758C3×C4C22×#6712yes—
759C3×C4C24×D311yescharacteristic
760C3×C4C24×D311yescharacteristic
761Dic3—24no—
762Dic3—22no—
763Dic3—62no—
764Dic3—62no—
765Dic3—122no—
766Dic3C22×#6714yes—
767C32C2×#57711yescharacteristic, complemented, Sylow
768C23—22no—
769C23—24no—
770C23—32no—
771C23—68no—
772C23—61no—
773C23—82no—
774C23—181no—
775C23—244no—
776C23D3×#6711yescharacteristic
777Q8—34no—
778Q8—34no—
779Q8—32no—
780Q8—62no—
781Q8—64no—
782Q8—61no—
783Q8—92no—
784Q8—188no—
785Q8—181no—
786D4—22no—
787D4—24no—
788D4—38no—
789D4—34no—
790D4—32no—
791D4—68no—
792D4—68no—
793D4—64no—
794D4—61no—
795D4—92no—
796D4—188no—
797D4—184no—
798D4—181no—
799D4C22×D3214yes—
800C2×C4—32no—
801C2×C4—34no—
802C2×C4—34no—
803C2×C4—68no—
804C2×C4—64no—
805C2×C4—61no—
806C2×C4—62no—
807C2×C4—64no—
808C2×C4—188no—
809C2×C4—188no—
810C2×C4—181no—
811C2×C4—184no—
812C2×C4D3×#6712yes—
813C2×C4D3×#6711yescharacteristic
814C2×C4C22×D3212yes—
815C2×C4C22×D3211yescharacteristic
816C8—32no—
817C8—32no—
818C8—94no—
819C2×C3—22no—
820C2×C3—22no—
821C2×C3—22no—
822C2×C3—21no—
823C2×C3—42no—
824C2×C3—44no—
825C2×C3—44no—
826C2×C3—64no—
827C2×C3—84no—
828C2×C3—122no—
829C2×C3#576212yescomplemented
830C2×C3#583612yescomplemented
831C2×C3C22×D3×D411yescharacteristic
832C2×C3C23×#6711yescharacteristic
833D3—24no—
834D3—42no—
835D3—122no—
836D3—122no—
837D3—242no—
838C22—22no—
839C22—24no—
840C22—34no—
841C22—44no—
842C22—64no—
843C22—62no—
844C22—84no—
845C22—122no—
846C22—182no—
847C22—248no—
848C22—362no—
849C22C2×D3×#6712yes—
850C22C2×D3×#6711yescharacteristic
851C4—34no—
852C4—62no—
853C4—64no—
854C4—182no—
855C4C2×D3×#6711yescharacteristic
856C4C2×D3×#6712yes—
857C4C23×D3211yescharacteristic
858C3—21no—
859C3C2×#576211yescharacteristic, complemented
860C3C2×#583611yescharacteristic, complemented
861C2—22no—
862C2—44no—
863C2—64no—
864C2—122no—
865C2—362no—
866C2#1059510512yesdirect product factor
867C2C22×D3×#6711yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutator, cosocleC32×C4C25
FrattiniC4C23×D32
FittingC22×C32×D4C22
socleC22×C32C22×D4
hypercenterC22×D4D32
hypocenterC32C2×#577
LCSG ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×D4

Complements

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

NH ≅ G/Ntype
1. C2×C3×#1004C2semidirect
2. C2×#64297C2semidirect
3. C2×#64141C2semidirect
4. C22×C3×#214C2semidirect
5. C2×#63935C2semidirect
6. C2×#63934C2semidirect
7. #10595105C2direct (N × H)
8. C2×#63929C2semidirect
9. C2×D3×#214C2semidirect
10. C2×#63829C2semidirect
11. C2×#63827C2semidirect
12. C2×#63814C2semidirect
16. C2×#3828C22semidirect
19. C3×#1004C22semidirect
26. C22×C3×Dic6C22semidirect
28. C2×#3799C22semidirect
31. #64297C22semidirect
33. C2×D3×Dic6C22semidirect
34. C2×#3754C22semidirect
35. #64141C22semidirect
36. C2×#3753C22semidirect
37. C2×#3748C22semidirect
38. C2×C3×#214C22semidirect
39. C2×C3×#214C22semidirect
40. C2×C3×#214C22semidirect
41. C22×C3×C3⋊C8C22semidirect
42. #63935C22semidirect
43. #63934C22semidirect
44. #63929C22semidirect
45. D3×#214C22semidirect
46. C2×#3719C22semidirect
47. C2×#3718C22semidirect
48. C2×#3717C22semidirect
49. #63829C22semidirect
50. C2×#3716C22semidirect
51. #63827C22semidirect
52. C2×#3715C22semidirect
53. C2×#3714C22semidirect
54. C2×#3711C22semidirect
55. #63814C22semidirect
56. C2×D3×C3⋊C8C22semidirect
60. C2×#1004D3semidirect
70. C22×#214D3semidirect
91. #3828C23semidirect
121. C2×C3×Dic6C23semidirect
128. #3799C23semidirect
132. D3×Dic6C23semidirect
133. #3754C23semidirect
134. #3753C23semidirect
135. #3748C23semidirect
137. C3×#214C23semidirect
138. C3×#214C23semidirect
141. C2×C3×C3⋊C8C23semidirect
142. #3719C23semidirect
143. #3718C23semidirect
144. #3717C23semidirect
145. #3716C23semidirect
146. #3715C23semidirect
147. #3714C23semidirect
148. #3711C23semidirect
149. D3×C3⋊C8C23semidirect
175. #1004C2×D3semidirect
190. C22×Dic6C2×D3semidirect
212. C2×#214C2×D3semidirect
213. C2×#214C2×D3semidirect
214. C2×#214C2×D3semidirect
228. C22×C3⋊C8C2×D3semidirect
417. C2×Dic6C22×D3semidirect
433. #214C22×D3semidirect
434. #214C22×D3semidirect
449. C2×C3⋊C8C22×D3semidirect
642. C2×C32#577semidirect
767. C32C2×#577semidirect
829. C2×C3#5762semidirect
830. C2×C3#5836semidirect
859. C3C2×#5762semidirect
860. C3C2×#5836semidirect
866. C2#10595105direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×#10042
C2×#642972
C2×#641412
C22×C3×#2142
C2×#639352
C2×#639342
#105951052
C2×#639292
C2×D3×#2142
C2×#638292
C2×#638272
C2×#638142
C2×#58363
C2×#57623