Finite Group Databasebeta

← C2×#10595466 #11918887

Subgroups — C2×#10595466 #11918887

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×#1009C211yesmaximal, characteristic, complemented
2C2×#64298C211yesmaximal, characteristic, complemented
3C2×#64160C211yesmaximal, characteristic, complemented
4C2×C3×#950C211yesmaximal, characteristic, complemented
5#10595466C2116yesmaximal, direct product factor
6C2×#63947C212yesmaximal, complemented
7C2×#63943C212yesmaximal, complemented
8C2×#63932C212yesmaximal, complemented
9C2×D3×#214C212yesmaximal, complemented
10C22×#3716C211yesmaximal, characteristic, complemented
11C2×#63823C211yesmaximal, characteristic, complemented
12C2×#63814C211yesmaximal, characteristic, complemented
13C2×#5836—31nomaximal
14C2×#5770—31nomaximal
15C2×C32×#41C2211yescharacteristic
16C22×#634C2211yescharacteristic, complemented
17C3×#1009—24no—
18C3×#1009C2218yescomplemented
19C2×C3×#239C2212yes—
20C2×C3×D3×D4—22no—
21C2×C3×D3×D4C2212yes—
22C2×C3×#235—21no—
23C2×C3×#235C2211yescharacteristic
24C2×C3×#235C2211yescharacteristic, complemented
25C22×C3×D12—21no—
26C22×C3×D12C2211yescharacteristic
27C2×#3805—22no—
28#64298—24no—
29#64298C2218yescomplemented
30C2×#3795—21no—
31C2×#3795C2212yescomplemented
32C2×D3×Dic6—21no—
33C2×D3×Dic6C2212yescomplemented
34#64160C2218yescomplemented
35C2×#3756C2212yescomplemented
36C2×#3754C2212yescomplemented
37C2×#3748C2211yescharacteristic, complemented
38C3×#950C2218yescomplemented
39C2×C3×#216C2211yescharacteristic, complemented
40C2×C3×#215C2211yescharacteristic, complemented
41C2×C3×#214C2211yescharacteristic, complemented
42C2×C3×#213C2211yescharacteristic, complemented
43C22×C3×C3⋊C8C2211yescharacteristic, complemented
44#63947C22116yescomplemented
45#63943C22116yescomplemented
46#63932C22116yescomplemented
47D3×#214C22116yescomplemented
48C2×#3716C2212yescomplemented
49C2×#3716C2212yescomplemented
50C2×#3716C2218yescomplemented
51C2×#3715C2212yescomplemented
52#63823C2218yescomplemented
53C2×#3713C2212yescomplemented
54C2×#3711C2212yescomplemented
55#63814C2218yescomplemented
56C2×D3×C3⋊C8C2212yescomplemented
57C2×C3×H(5,𝔽2)—31no—
58C2×#1010—31no—
59C2×#1010—31no—
60C2×#1009D311yescharacteristic, complemented
61C2×C3×#135—31no—
62#5836—316no—
63C2×#951—31no—
64C2×#951—31no—
65C2×#951—32no—
66C2×#951—61no—
67C2×#950—32no—
68C2×#950D311yescharacteristic, complemented
69C2×#949—31no—
70C2×#948—31no—
71C22×#214—32no—
72C22×#214—31no—
73C2×#932—31no—
74C2×#932—32no—
75#5770—316no—
76C2×#918—32no—
77C2×#916—32no—
78C2×D3×SD16—32no—
79C2×#911—32no—
80C22×#204—31no—
81C2×#901—31no—
82C23×C3×D3—21no—
83C23×C3×D3—22no—
84C32×#41—22no—
85C32×#41C2314yes—
86C2×C32×Q8C2311yescharacteristic
87C2×C32×D4—21no—
88C2×C32×D4C2311yescharacteristic
89C22×C32×C4—21no—
90C22×C32×C4C2311yescharacteristic
91C22×C3⋊Dic3—21no—
92C2×#634—21no—
93C2×#634—22no—
94C2×#634C2312yes—
95C2×#634C2314yescomplemented
96C2×C3×#67—21no—
97C2×C3×#67—22no—
98C2×C3×#67D412yes—
99C3×#239—24no—
100C3×#239C2318yes—
101C3×D3×D4—216no—
102C3×D3×D4—24no—
103C3×D3×D4C2318yes—
104C3×#235—22no—
105C3×#235—28no—
106C3×#235D414yes—
107C3×#235C2314yes—
108C3×#235C2314yescomplemented
109C2×C3×D12—22no—
110C2×C3×D12—21no—
111C2×C3×D12—22no—
112C2×C3×D12—28no—
113C2×C3×D12D411yescharacteristic
114C2×C3×D12C2311yescharacteristic
115C2×C3×D12C2312yes—
116C2×C3×D12C2314yes—
117C2×C3×C4×D3—21no—
118C2×C3×C4×D3—22no—
119C2×C3×C4×D3C2312yes—
120C2×C3×Dic6D411yescharacteristic
121C2×C3×Dic6C2311yescharacteristic
122C2×#627—22no—
123C2×#625—22no—
124#3805—216no—
125C2×D3×Dic3—22no—
126C2×D3×Dic3—22no—
127#3795—28no—
128#3795—24no—
129#3795C2318yescomplemented
130D3×Dic6—24no—
131D3×Dic6—28no—
132D3×Dic6C2318yescomplemented
133#3756C2318yescomplemented
134#3754C2318yescomplemented
135#3748C2314yescomplemented
136C2×C3⋊(C3⋊C8)C2312yes—
137C3×#216C2314yescomplemented
138C3×#215C2314yescomplemented
139C3×#214C2314yescomplemented
140C3×#213C2314yescomplemented
141C2×C3×C3⋊C8C2311yescharacteristic
142C2×C3×C3⋊C8C2311yescharacteristic
143C2×C3×C3⋊C8C2314yescomplemented
144#3716C2318yescomplemented
145#3716C2318yescomplemented
146#3715C2318yescomplemented
147#3713C2318yescomplemented
148#3711C2318yescomplemented
149D3×C3⋊C8C2318yescomplemented
150C2×#577—91noSylow
151C3×H(5,𝔽2)—38no—
152C3×H(5,𝔽2)—64no—
153C2×C3×#41—21no—
154C2×C3×#41—31no—
155C2×C3×#41—32no—
156C2×C3×#41—31no—
157C2×C3×#41—61no—
158C2×C3×#41C2×D311yescharacteristic
159C2×C3×#41C2×D311yescharacteristic
160C22×C3×D4—32no—
161C22×C3×D4—31no—
162C22×C3×D4—61no—
163C22×C3×D4—62no—
164#1010—38no—
165#1010—38no—
166#1010—64no—
167#1010—64no—
168#1009—24no—
169#1009C2×D318yescomplemented
170C2×#239C2×D312yes—
171C2×D3×Q8—32no—
172C2×D3×Q8—61no—
173C2×#237—32no—
174C2×#237—61no—
175C2×#237—62no—
176C2×#237—62no—
177C2×D3×D4—22no—
178C2×D3×D4C2×D312yes—
179C2×#235—21no—
180C2×#235—32no—
181C2×#235—61no—
182C2×#235C2×D311yescharacteristic
183C2×#235C2×D311yescharacteristic, complemented
184C22×D12—21no—
185C22×D12C2×D311yescharacteristic
186C22×Dic6—31no—
187C22×Dic6—31no—
188C22×Dic6—32no—
189C22×Dic6—61no—
190C22×Dic6—61no—
191C3×#135—38no—
192C2×C3×Q16—31no—
193C2×C3×SD16—31no—
194C2×C3×SD16—31no—
195C2×C3×D8—31no—
196C22×C3×C8—31no—
197#951—38no—
198#951—38no—
199#951—316no—
200#951—68no—
201#950—316no—
202#950C2×D318yescomplemented
203#949—38no—
204#948—38no—
205C2×#216—32no—
206C2×#216—32no—
207C2×#216—62no—
208C2×#216C2×D311yescharacteristic, complemented
209C2×#215—32no—
210C2×#215C2×D311yescharacteristic, complemented
211C2×#214—32no—
212C2×#214—32no—
213C2×#214—32no—
214C2×#214—316no—
215C2×#214—32no—
216C2×#214—32no—
217C2×#214—38no—
218C2×#214—62no—
219C2×#214C2×D311yescharacteristic, complemented
220#932—38no—
221#932—316no—
222C2×#213—32no—
223C2×#213—32no—
224C2×#213C2×D311yescharacteristic, complemented
225C2×#208—31no—
226C2×#208—31no—
227C2×#208—32no—
228C2×#208—61no—
229C22×C3⋊C8—32no—
230C22×C3⋊C8C2×D311yescharacteristic, complemented
231#918—316no—
232#916—316no—
233D3×SD16—316no—
234#911—316no—
235C2×#204—32no—
236C2×#204—32no—
237C2×#204—38no—
238#901—38no—
239C2×ΓL(1,𝔽25)—32no—
240C2×D3×C8—32no—
241C23×C32—21no—
242C23×C32C2×D411yescharacteristic
243C22×C3×D3—22no—
244C22×C3×D3—21no—
245C22×C3×D3—24no—
246C22×C3×D3—28no—
247C22×C3×D3—84no—
248C22×C3×D3—82no—
249C22×C3×D3C2×D412yes—
250C32×Q8—21no—
251C32×Q8C2412yes—
252C32×D4—24no—
253C32×D4—21no—
254C32×D4C2412yes—
255C2×C32×C4—21no—
256C2×C32×C4—24no—
257C2×C32×C4C2×D411yescharacteristic
258C2×C32×C4C2×D412yes—
259C2×C32×C4C2411yescharacteristic
260C2×C32×C4C2412yes—
261C2×C3⋊Dic3—22no—
262C2×C3⋊Dic3—24no—
263#634—22no—
264#634—24no—
265#634C2414yes—
266C3×#67—24no—
267C3×#67—28no—
268C3×#67C2×D418yes—
269C2×C3×Dic3—21no—
270C2×C3×Dic3C2×D412yes—
271C3×D12—28no—
272C3×D12—21no—
273C3×D12—24no—
274C3×D12—22no—
275C3×D12C2×D414yes—
276C3×D12C2412yes—
277C3×D12C2414yes—
278C3×C4×D3—24no—
279C3×C4×D3—28no—
280C3×C4×D3C2×D414yes—
281C3×C4×D3C2414yes—
282C3×Dic6—21no—
283C3×Dic6C2×D414yes—
284C3×Dic6C2412yes—
285#627—28no—
286#625—28no—
287D3×Dic3—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—31no—
300C2×#135—92no—
301C22×SD16—91no—
302C22×SD16—92no—
303C2×#131—91no—
304C24×C3—62no—
305C24×C3—61no—
306C23×D3—21no—
307C23×D3—22no—
308C3×#41—22no—
309C3×#41—22no—
310C3×#41—24no—
311C3×#41—34no—
312C3×#41—34no—
313C3×#41—38no—
314C3×#41—34no—
315C3×#41—42no—
316C3×#41—68no—
317C3×#41—64no—
318C3×#41—62no—
319C3×#41C22×D314yes—
320C3×#41C22×D314yes—
321C2×C3×Q8—21no—
322C2×C3×Q8—31no—
323C2×C3×Q8—31no—
324C2×C3×Q8C22×D311yescharacteristic
325C2×C3×Q8C22×D311yescharacteristic
326C2×C3×D4—21no—
327C2×C3×D4—21no—
328C2×C3×D4—21no—
329C2×C3×D4—32no—
330C2×C3×D4—38no—
331C2×C3×D4—31no—
332C2×C3×D4—31no—
333C2×C3×D4—32no—
334C2×C3×D4—34no—
335C2×C3×D4—41no—
336C2×C3×D4—68no—
337C2×C3×D4—62no—
338C2×C3×D4—64no—
339C2×C3×D4—62no—
340C2×C3×D4—616no—
341C2×C3×D4—61no—
342C2×C3×D4—61no—
343C2×C3×D4—62no—
344C2×C3×D4C22×D311yescharacteristic
345C2×C3×D4C22×D311yescharacteristic
346C22×C3×C4—21no—
347C22×C3×C4—21no—
348C22×C3×C4—21no—
349C22×C3×C4—32no—
350C22×C3×C4—41no—
351C22×C3×C4—62no—
352C22×C3×C4—61no—
353C22×C3×C4C22×D311yescharacteristic
354C22×C3×C4C22×D311yescharacteristic
355C2×#67—21no—
356C2×#67—22no—
357C2×#67—62no—
358C2×#67—62no—
359C2×#67#6712yes—
360C22×Dic3—62no—
361C22×Dic3—61no—
362C22×Dic3—61no—
363C22×Dic3—62no—
364C22×Dic3—121no—
365#239—24no—
366#239C22×D318yes—
367D3×Q8—38no—
368D3×Q8—68no—
369D3×Q8—64no—
370#237—38no—
371#237—68no—
372#237—616no—
373#237—616no—
374#237—64no—
375D3×D4—216no—
376D3×D4—24no—
377D3×D4C22×D318yes—
378#235—22no—
379#235—28no—
380#235—38no—
381#235—64no—
382#235—68no—
383#235#6714yes—
384#235C22×D314yes—
385#235C22×D314yescomplemented
386C2×D12—22no—
387C2×D12—21no—
388C2×D12—22no—
389C2×D12—28no—
390C2×D12#6711yescharacteristic
391C2×D12C22×D312yes—
392C2×D12C22×D314yes—
393C2×D12C22×D311yescharacteristic
394C2×C4×D3—21no—
395C2×C4×D3—22no—
396C2×C4×D3—62no—
397C2×C4×D3—62no—
398C2×C4×D3C22×D312yes—
399C2×Dic6—32no—
400C2×Dic6—34no—
401C2×Dic6—32no—
402C2×Dic6—34no—
403C2×Dic6—38no—
404C2×Dic6—62no—
405C2×Dic6—64no—
406C2×Dic6—64no—
407C2×Dic6—62no—
408C2×Dic6—61no—
409C2×Dic6—62no—
410C2×Dic6—61no—
411C2×Dic6—62no—
412C2×Dic6—62no—
413C2×Dic6—68no—
414C2×Dic6—121no—
415C2×Dic6—122no—
416C2×Dic6#6711yescharacteristic
417C2×Dic6C22×D311yescharacteristic
418C3×Q16—34no—
419C3×SD16—34no—
420C3×SD16—34no—
421C3×D8—34no—
422C2×C3×C8—31no—
423C2×C3×C8—31no—
424C2×C3×C8—34no—
425#216—38no—
426#216—38no—
427#216—68no—
428#216C22×D314yescomplemented
429#215—38no—
430#215C22×D314yescomplemented
431#214—38no—
432#214—38no—
433#214—38no—
434#214—38no—
435#214—38no—
436#214—68no—
437#214C22×D314yescomplemented
438#213—38no—
439#213—38no—
440#213C22×D314yescomplemented
441#208—34no—
442#208—34no—
443#208—38no—
444#208—64no—
445C2×C3⋊C8—32no—
446C2×C3⋊C8—32no—
447C2×C3⋊C8—38no—
448C2×C3⋊C8—62no—
449C2×C3⋊C8C22×D311yescharacteristic
450C2×C3⋊C8C22×D311yescharacteristic
451C2×C3⋊C8C22×D314yescomplemented
452#204—38no—
453#204—38no—
454ΓL(1,𝔽25)—38no—
455D3×C8—38no—
456C22×C32—22no—
457C22×C32—22no—
458C22×C32—42no—
459C22×C32C22×D412yes—
460C22×C32C22×D411yescharacteristic
461C2×C3×D3—24no—
462C2×C3×D3—22no—
463C2×C3×D3—24no—
464C2×C3×D3—42no—
465C2×C3×D3—44no—
466C2×C3×D3—88no—
467C2×C3×D3—84no—
468C2×C3×D3C22×D414yes—
469C32×C4—22no—
470C32×C4C22×D411yescharacteristic
471C32×C4C22×D412yes—
472C32×C4C2511yescharacteristic
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—181no—
486C2×#41—182no—
487C2×#41D3211yescharacteristic
488C22×Q8—92no—
489C22×Q8—91no—
490C22×Q8—181no—
491C22×D4—32no—
492C22×D4—31no—
493C22×D4—61no—
494C22×D4—62no—
495#137—916no—
496#137—98no—
497AGL(1,ℤ/8)—916no—
498AGL(1,ℤ/8)—98no—
499#135—38no—
500#135—916no—
501C2×Q16—31no—
502C2×Q16—92no—
503C2×SD16—31no—
504C2×SD16—31no—
505C2×SD16—92no—
506C2×SD16—92no—
507C2×SD16—98no—
508C2×SD16—916no—
509C2×SD16—92no—
510C2×SD16—92no—
511C2×D8—31no—
512C2×D8—92no—
513#131—98no—
514C2×M16—92no—
515C2×M16—91no—
516C22×C8—31no—
517C22×C8—92no—
518C23×C3—21no—
519C23×C3—21no—
520C23×C3—21no—
521C23×C3—32no—
522C23×C3—41no—
523C23×C3—68no—
524C23×C3—62no—
525C23×C3—61no—
526C23×C3—64no—
527C23×C3—242no—
528C23×C3—244no—
529C23×C3D3×D411yescharacteristic
530C23×C3C2×#6711yescharacteristic
531C22×D3—21no—
532C22×D3—22no—
533C22×D3—24no—
534C22×D3—28no—
535C22×D3—84no—
536C22×D3—82no—
537C22×D3C2×#6712yes—
538C3×Q8—21no—
539C3×Q8—21no—
540C3×Q8—22no—
541C3×Q8—34no—
542C3×Q8—32no—
543C3×Q8—41no—
544C3×Q8—61no—
545C3×Q8C23×D312yes—
546C3×Q8C23×D312yes—
547C3×D4—24no—
548C3×D4—24no—
549C3×D4—21no—
550C3×D4—21no—
551C3×D4—22no—
552C3×D4—38no—
553C3×D4—34no—
554C3×D4—32no—
555C3×D4—34no—
556C3×D4—41no—
557C3×D4—44no—
558C3×D4—68no—
559C3×D4—68no—
560C3×D4—64no—
561C3×D4—62no—
562C3×D4—64no—
563C3×D4—61no—
564C3×D4C23×D312yes—
565C3×D4C23×D312yes—
566C2×C3×C4—21no—
567C2×C3×C4—21no—
568C2×C3×C4—24no—
569C2×C3×C4—24no—
570C2×C3×C4—21no—
571C2×C3×C4—22no—
572C2×C3×C4—21no—
573C2×C3×C4—22no—
574C2×C3×C4—32no—
575C2×C3×C4—34no—
576C2×C3×C4—34no—
577C2×C3×C4—44no—
578C2×C3×C4—41no—
579C2×C3×C4—68no—
580C2×C3×C4—61no—
581C2×C3×C4—64no—
582C2×C3×C4D3×D411yescharacteristic
583C2×C3×C4D3×D412yes—
584C2×C3×C4C2×#6711yescharacteristic
585C2×C3×C4C2×#6712yes—
586C2×C3×C4C23×D311yescharacteristic
587C2×C3×C4C23×D312yes—
588C2×C3×C4C23×D311yescharacteristic
589C2×C3×C4C23×D312yes—
590#67—24no—
591#67—28no—
592#67—68no—
593#67—68no—
594#67C2×#6718yes—
595C2×Dic3—21no—
596C2×Dic3—68no—
597C2×Dic3—62no—
598C2×Dic3—64no—
599C2×Dic3—62no—
600C2×Dic3—64no—
601C2×Dic3—68no—
602C2×Dic3—124no—
603C2×Dic3—122no—
604C2×Dic3C2×#6712yes—
605D12—28no—
606D12—21no—
607D12—24no—
608D12—22no—
609D12C2×#6714yes—
610D12C23×D314yes—
611D12C23×D312yes—
612C4×D3—24no—
613C4×D3—28no—
614C4×D3—68no—
615C4×D3—68no—
616C4×D3C2×#6714yes—
617C4×D3C23×D314yes—
618Dic6—21no—
619Dic6—34no—
620Dic6—34no—
621Dic6—64no—
622Dic6—68no—
623Dic6—62no—
624Dic6—64no—
625Dic6—64no—
626Dic6—62no—
627Dic6—68no—
628Dic6—124no—
629Dic6—122no—
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—42no—
641C2×C32#57712yescomplemented
642C2×C32C23×D411yescharacteristic
643C3×D3—24no—
644C3×D3—42no—
645C3×D3—44no—
646C24—62no—
647C24—61no—
648#41—22no—
649#41—34no—
650#41—34no—
651#41—38no—
652#41—34no—
653#41—68no—
654#41—64no—
655#41—62no—
656#41—98no—
657#41—184no—
658#41—188no—
659#41—1816no—
660#41C2×D3214yes—
661C2×Q8—31no—
662C2×Q8—31no—
663C2×Q8—98no—
664C2×Q8—92no—
665C2×Q8—94no—
666C2×Q8—182no—
667C2×Q8—184no—
668C2×Q8—188no—
669C2×Q8—181no—
670C2×Q8—182no—
671C2×Q8C2×D3211yescharacteristic
672C2×D4—21no—
673C2×D4—32no—
674C2×D4—38no—
675C2×D4—31no—
676C2×D4—32no—
677C2×D4—34no—
678C2×D4—31no—
679C2×D4—68no—
680C2×D4—62no—
681C2×D4—64no—
682C2×D4—62no—
683C2×D4—616no—
684C2×D4—61no—
685C2×D4—61no—
686C2×D4—62no—
687C2×D4—182no—
688C2×D4C2×D3211yescharacteristic
689C22×C4—21no—
690C22×C4—32no—
691C22×C4—62no—
692C22×C4—61no—
693C22×C4—182no—
694C22×C4—182no—
695C22×C4—181no—
696C22×C4C2×D3211yescharacteristic
697Q16—34no—
698Q16—98no—
699SD16—34no—
700SD16—34no—
701SD16—98no—
702SD16—98no—
703SD16—98no—
704SD16—98no—
705D8—34no—
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—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—64no—
727C22×C3—62no—
728C22×C3—82no—
729C22×C3—124no—
730C22×C3—122no—
731C22×C3—244no—
732C22×C3—248no—
733C22×C3C2×D3×D412yes—
734C22×C3C2×D3×D411yescharacteristic
735C22×C3C22×#6712yes—
736C22×C3C22×#6711yescharacteristic
737C2×D3—24no—
738C2×D3—22no—
739C2×D3—24no—
740C2×D3—42no—
741C2×D3—44no—
742C2×D3—88no—
743C2×D3—84no—
744C2×D3C22×#6714yes—
745C3×C4—22no—
746C3×C4—22no—
747C3×C4—22no—
748C3×C4—21no—
749C3×C4—21no—
750C3×C4—34no—
751C3×C4—42no—
752C3×C4—62no—
753C3×C4C2×D3×D411yescharacteristic
754C3×C4C2×D3×D412yes—
755C3×C4C22×#6712yes—
756C3×C4C22×#6711yescharacteristic
757C3×C4C24×D311yescharacteristic
758C3×C4C24×D311yescharacteristic
759Dic3—22no—
760Dic3—64no—
761Dic3—64no—
762Dic3—124no—
763Dic3C22×#6714yes—
764C32C2×#57711yescharacteristic, complemented, Sylow
765C23—21no—
766C23—32no—
767C23—68no—
768C23—61no—
769C23—62no—
770C23—64no—
771C23—242no—
772C23—244no—
773C23D3×#6711yescharacteristic
774Q8—21no—
775Q8—34no—
776Q8—32no—
777Q8—61no—
778Q8—94no—
779Q8—188no—
780Q8—184no—
781Q8—182no—
782Q8C22×D3212yes—
783D4—24no—
784D4—21no—
785D4—38no—
786D4—34no—
787D4—32no—
788D4—34no—
789D4—68no—
790D4—68no—
791D4—64no—
792D4—64no—
793D4—62no—
794D4—61no—
795D4—188no—
796D4C22×D3212yes—
797C2×C4—21no—
798C2×C4—24no—
799C2×C4—32no—
800C2×C4—34no—
801C2×C4—34no—
802C2×C4—68no—
803C2×C4—61no—
804C2×C4—64no—
805C2×C4—188no—
806C2×C4—188no—
807C2×C4—184no—
808C2×C4—182no—
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—42no—
822C2×C3—42no—
823C2×C3—64no—
824C2×C3—82no—
825C2×C3—124no—
826C2×C3—122no—
827C2×C3#577012yescomplemented
828C2×C3#583612yescomplemented
829C2×C3C22×D3×D411yescharacteristic
830C2×C3C23×#6711yescharacteristic
831D3—24no—
832D3—42no—
833D3—44no—
834C22—22no—
835C22—22no—
836C22—34no—
837C22—42no—
838C22—64no—
839C22—62no—
840C22—64no—
841C22—124no—
842C22—122no—
843C22—244no—
844C22—248no—
845C22C2×D3×#6712yes—
846C22C2×D3×#6711yescharacteristic
847C4—22no—
848C4—34no—
849C4—62no—
850C4—184no—
851C4C2×D3×#6712yes—
852C4C2×D3×#6711yescharacteristic
853C4C23×D3211yescharacteristic
854C3—21no—
855C3C2×#577011yescharacteristic, complemented
856C3C2×#583611yescharacteristic, complemented
857C2—22no—
858C2—42no—
859C2—64no—
860C2—124no—
861C2—122no—
862C2#1059546612yesdirect product factor
863C2C22×D3×#6711yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutator, cosocleC32×C4C25
FrattiniC4C23×D32
FittingC2×C32×#41C22
socleC22×C32C22×D4
hypercenterC2×#41D32
hypocenterC32C2×#577
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×#1009C2semidirect
2. C2×#64298C2semidirect
3. C2×#64160C2semidirect
4. C2×C3×#950C2semidirect
5. #10595466C2direct (N × H)
6. C2×#63947C2semidirect
7. C2×#63943C2semidirect
8. C2×#63932C2semidirect
9. C2×D3×#214C2semidirect
10. C22×#3716C2semidirect
11. C2×#63823C2semidirect
12. C2×#63814C2semidirect
16. C22×#634C22semidirect
18. C3×#1009C22semidirect
24. C2×C3×#235C22semidirect
29. #64298C22semidirect
31. C2×#3795C22semidirect
33. C2×D3×Dic6C22semidirect
34. #64160C22semidirect
35. C2×#3756C22semidirect
36. C2×#3754C22semidirect
37. C2×#3748C22semidirect
38. C3×#950C22semidirect
39. C2×C3×#216C22semidirect
40. C2×C3×#215C22semidirect
41. C2×C3×#214C22semidirect
42. C2×C3×#213C22semidirect
43. C22×C3×C3⋊C8C22semidirect
44. #63947C22semidirect
45. #63943C22semidirect
46. #63932C22semidirect
47. D3×#214C22semidirect
48. C2×#3716C22semidirect
49. C2×#3716C22semidirect
50. C2×#3716C22semidirect
51. C2×#3715C22semidirect
52. #63823C22semidirect
53. C2×#3713C22semidirect
54. C2×#3711C22semidirect
55. #63814C22semidirect
56. C2×D3×C3⋊C8C22semidirect
60. C2×#1009D3semidirect
68. C2×#950D3semidirect
95. C2×#634C23semidirect
108. C3×#235C23semidirect
129. #3795C23semidirect
132. D3×Dic6C23semidirect
133. #3756C23semidirect
134. #3754C23semidirect
135. #3748C23semidirect
137. C3×#216C23semidirect
138. C3×#215C23semidirect
139. C3×#214C23semidirect
140. C3×#213C23semidirect
143. C2×C3×C3⋊C8C23semidirect
144. #3716C23semidirect
145. #3716C23semidirect
146. #3715C23semidirect
147. #3713C23semidirect
148. #3711C23semidirect
149. D3×C3⋊C8C23semidirect
169. #1009C2×D3semidirect
183. C2×#235C2×D3semidirect
202. #950C2×D3semidirect
208. C2×#216C2×D3semidirect
210. C2×#215C2×D3semidirect
219. C2×#214C2×D3semidirect
224. C2×#213C2×D3semidirect
230. C22×C3⋊C8C2×D3semidirect
385. #235C22×D3semidirect
428. #216C22×D3semidirect
430. #215C22×D3semidirect
437. #214C22×D3semidirect
440. #213C22×D3semidirect
451. C2×C3⋊C8C22×D3semidirect
641. C2×C32#577semidirect
764. C32C2×#577semidirect
827. C2×C3#5770semidirect
828. C2×C3#5836semidirect
855. C3C2×#5770semidirect
856. C3C2×#5836semidirect
862. C2#10595466direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×#10092
C2×#642982
C2×#641602
C2×C3×#9502
#105954662
C2×#639472
C2×#639432
C2×#639322
C2×D3×#2142
C22×#37162
C2×#638232
C2×#638142
C2×#58363
C2×#57703