Finite Group Databasebeta

← C2×#81681 #11664432

Subgroups — C2×#81681 #11664432

Order 768.

2070 conjugacy classes of subgroups.

The subgroup lattice has 754 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#5729C211yesmaximal, characteristic, complemented
2C2×#5675C211yesmaximal, characteristic
3C2×C3×#489C211yesmaximal, characteristic, complemented
4C2×#5093C211yesmaximal, characteristic, complemented
5C2×#5056C211yesmaximal, characteristic, complemented
6#81681C2116yesmaximal, direct product factor
7C2×#4802C211yesmaximal, characteristic, complemented
8C2×D3×#103C211yesmaximal, characteristic, complemented
9C2×#4797C211yesmaximal, characteristic, complemented
10C2×#4792C211yesmaximal, characteristic, complemented
11C2×#4771C211yesmaximal, characteristic
12C2×#4772C211yesmaximal, characteristic
13C2×#4765C211yesmaximal, characteristic, complemented
14C2×#4768C211yesmaximal, characteristic, complemented
15C2×#4703C211yesmaximal, characteristic, complemented
16C2×#4708C211yesmaximal, characteristic, complemented
17C2×#3137—31nomaximal, Sylow
18C22×D3×Q8C2211yescharacteristic
19C22×#237C2211yescharacteristic
20C2×C3×C4⋊Q8C2211yescharacteristic
21C2×C3×#124C2211yescharacteristic
22C2×#946—21no—
23C2×#944—21no—
24C2×#944C2211yescharacteristic
25C2×#936C2211yescharacteristic
26C22×ΓL(1,𝔽25)C2211yescharacteristic
27C22×D3×C8C2211yescharacteristic
28#5729—24no—
29#5729C2218yescomplemented
30#5675—24no—
31#5675C2218yes—
32C2×#896—21no—
33C2×#892C2211yescharacteristic
34C2×D3×C4⋊C4C2211yescharacteristic
35C2×#890C2211yescharacteristic
36C2×#889—21no—
37C2×#888C2211yescharacteristic
38C2×#883—21no—
39C2×#883—21no—
40C2×#878—21no—
41C2×#878—21no—
42C2×#872C2211yescharacteristic
43C2×#870C2211yescharacteristic
44C2×#869C2211yescharacteristic
45C3×#489C2218yescomplemented
46C2×C3×#103C2211yescharacteristic
47C2×C3×#103C2211yescharacteristic
48C2×C3×#102C2211yescharacteristic
49C2×C3×#102C2211yescharacteristic
50C2×C3×#97C2211yescharacteristic
51C2×#835C2211yescharacteristic
52C2×#835C2211yescharacteristic
53C2×#832C2211yescharacteristic
54C2×#832C2211yescharacteristic
55C2×#816C2211yescharacteristic
56C2×#816C2211yescharacteristic
57C2×#816C2211yescharacteristic
58C2×#816C2211yescharacteristic
59C2×#815C2211yescharacteristic
60C2×C8×Dic3C2211yescharacteristic
61#5093C2218yescomplemented
62#5056C2218yescomplemented
63C2×#810C2211yescharacteristic
64C2×#810C2211yescharacteristic
65C2×#810C2211yescharacteristic
66C2×#810C2211yescharacteristic
67C2×C4×C3⋊C8C2211yescharacteristic
68#4802C2218yescomplemented
69D3×#103C2218yescomplemented
70#4797C2218yescomplemented
71#4792C2218yescomplemented
72#4772C2218yes—
73#4771C2218yes—
74#4768C2218yescomplemented
75#4765C2218yescomplemented
76#4708C2218yescomplemented
77#4703C2218yescomplemented
78C2×#544—31no—
79C2×#536—31no—
80#3137—316no—
81C2×#491—31no—
82C2×#491—31no—
83C2×#489—31no—
84C2×#489D311yescharacteristic, complemented
85C2×#488—31no—
86C2×#488—31no—
87C2×#487—31no—
88C2×#487—31no—
89C2×#417—31no—
90C2×#419—31no—
91C2×#416—31no—
92C22×#103—31no—
93C2×#405—31no—
94C22×C3×Q8—21no—
95C22×C3×Q8C2311yescharacteristic
96C22×C3×D4C2311yescharacteristic
97C22×#67—21no—
98C23×Dic3—21no—
99C2×D3×Q8—22no—
100C2×D3×Q8—24no—
101C2×D3×Q8—24no—
102C2×D3×Q8C2314yes—
103C2×#237—22no—
104C2×#237—24no—
105C2×#237—24no—
106C2×#237C2314yes—
107C22×C4×D3—21no—
108C22×C4×D3—21no—
109C22×C4×D3C2311yescharacteristic
110C22×Dic6—21no—
111C22×Dic6—21no—
112C22×Dic6C2311yescharacteristic
113C22×Dic6C2311yescharacteristic
114C22×C3×C8C2311yescharacteristic
115C22×C3×C8C2311yescharacteristic
116C3×C4⋊Q8—22no—
117C3×C4⋊Q8C2314yes—
118C3×#124—22no—
119C3×#124C2314yes—
120C2×C3×C4⋊C4—21no—
121C2×C3×C4⋊C4C2311yescharacteristic
122C2×C3×C4⋊C4C2311yescharacteristic
123C2×C3×C22⋊C4—21no—
124C2×C3×C22⋊C4—21no—
125C2×C3×C42C2311yescharacteristic
126C2×#217—21no—
127C2×#217—21no—
128#946—28no—
129#944—28no—
130#944—22no—
131#944C2314yes—
132#936—22no—
133#936C2314yes—
134C2×(C2×D3)⋊C4—21no—
135C2×(C2×D3)⋊C4D411yescharacteristic
136C2×(C2×D3)⋊C4D411yescharacteristic
137C2×C4⋊Dic3—21no—
138C2×C4⋊Dic3—21no—
139C2×C4⋊Dic3—21no—
140C2×C4⋊Dic3C2311yescharacteristic
141C2×C4⋊Dic3C2311yescharacteristic
142C2×Dic3⋊C4—21no—
143C2×Dic3⋊C4—21no—
144C2×Dic3⋊C4—21no—
145C2×Dic3⋊C4—21no—
146C2×Dic3⋊C4—21no—
147C2×Dic3⋊C4—21no—
148C2×Dic3⋊C4—21no—
149C2×Dic3⋊C4D411yescharacteristic
150C2×Dic3⋊C4D411yescharacteristic
151C2×C4×Dic3—21no—
152C2×C4×Dic3C2311yescharacteristic
153C22×C3⋊C8C2311yescharacteristic
154C22×C3⋊C8C2311yescharacteristic
155C2×ΓL(1,𝔽25)—24no—
156C2×ΓL(1,𝔽25)C2314yes—
157C2×D3×C8—24no—
158C2×D3×C8C2314yes—
159#896—28no—
160#892—22no—
161#892C2314yes—
162D3×C4⋊C4—22no—
163D3×C4⋊C4C2314yes—
164#890—22no—
165#890C2314yes—
166#889—28no—
167#888—22no—
168#888C2314yes—
169#883—28no—
170#883—28no—
171#878—28no—
172#878—28no—
173#872D414yes—
174#872C2314yes—
175#870—22no—
176#870C2314yes—
177#869—22no—
178#869C2314yes—
179C3×#103C2314yes—
180C3×#103C2314yes—
181C3×#102C2314yes—
182C3×#102C2314yes—
183C3×#97C2314yes—
184#835C2314yes—
185#835C2314yes—
186#832C2314yes—
187#832C2314yes—
188#816C2314yes—
189#816C2314yes—
190#816C2314yes—
191#816C2314yes—
192#815C2314yes—
193C8×Dic3C2314yes—
194#810C2314yes—
195#810C2314yes—
196#810C2314yes—
197#810C2314yes—
198C4×C3⋊C8C2314yes—
199C22×#41—31no—
200C23×Q8—31no—
201C22×M16—31no—
202C23×C8—31no—
203#544—38no—
204#544—64no—
205#536—38no—
206#536—64no—
207C2×C4⋊Q8—31no—
208C2×C4⋊Q8—31no—
209C2×C4⋊Q8—31no—
210C2×C4⋊Q8—61no—
211C2×C4⋊Q8C2×D311yescharacteristic
212C2×#125—31no—
213C2×#125—31no—
214C2×#125—61no—
215C2×#124—31no—
216C2×#124C2×D311yescharacteristic
217C2×#123—61no—
218C2×#123—61no—
219C2×C22⋊Q8—61no—
220C2×C22⋊Q8—61no—
221C2×C22⋊Q8—61no—
222C2×C22⋊Q8—61no—
223C2×#117—31no—
224C2×#117—31no—
225C22×C4⋊C4—31no—
226#491—38no—
227#491—38no—
228#489—38no—
229#489C2×D318yescomplemented
230#488—38no—
231#488—38no—
232#487—38no—
233#487—38no—
234#419—38no—
235#417—38no—
236#416—38no—
237C2×#103—31no—
238C2×#103—31no—
239C2×#103—31no—
240C2×#103—31no—
241C2×#103—31no—
242C2×#103—31no—
243C2×#103—31no—
244C2×#103—31no—
245C2×#103—31no—
246C2×#103—31no—
247C2×#103—38no—
248C2×#103C2×D311yescharacteristic
249C2×#103C2×D311yescharacteristic
250C2×#102—31no—
251C2×#102—31no—
252C2×#102C2×D311yescharacteristic
253C2×#102C2×D311yescharacteristic
254#405—38no—
255C2×#97—31no—
256C2×#97C2×D311yescharacteristic
257C2×C4×C8—31no—
258C2×C4×C8—31no—
259C24×C3—21no—
260C23×D3C2×D411yescharacteristic
261C2×C3×Q8—21no—
262C2×C3×Q8—24no—
263C2×C3×Q8—22no—
264C2×C3×Q8—22no—
265C2×C3×Q8—82no—
266C2×C3×Q8C2412yes—
267C2×C3×D4—21no—
268C2×C3×D4—22no—
269C2×C3×D4—22no—
270C2×C3×D4C2412yes—
271C22×C3×C4—21no—
272C22×C3×C4—21no—
273C22×C3×C4—21no—
274C22×C3×C4C2×D411yescharacteristic
275C22×C3×C4C2×D411yescharacteristic
276C22×C3×C4C2411yescharacteristic
277C2×#67—24no—
278C2×#67—44no—
279C22×Dic3—21no—
280C22×Dic3—21no—
281C22×Dic3—21no—
282C22×Dic3—21no—
283C22×Dic3—24no—
284C22×Dic3—44no—
285C22×Dic3C2×D411yescharacteristic
286C22×Dic3C2×D411yescharacteristic
287C22×Dic3C2×D411yescharacteristic
288D3×Q8—28no—
289D3×Q8—28no—
290D3×Q8—48no—
291#237—28no—
292#237—28no—
293#237—48no—
294C2×C4×D3—24no—
295C2×C4×D3—24no—
296C2×C4×D3—44no—
297C2×C4×D3—82no—
298C2×C4×D3C2×D412yes—
299C2×C4×D3#4114yes—
300C2×C4×D3#4114yes—
301C2×C4×D3C2412yes—
302C2×Dic6—22no—
303C2×Dic6—22no—
304C2×Dic6—22no—
305C2×Dic6—22no—
306C2×Dic6—21no—
307C2×Dic6—21no—
308C2×Dic6—24no—
309C2×Dic6—24no—
310C2×Dic6—44no—
311C2×Dic6—82no—
312C2×Dic6C2412yes—
313C2×Dic6C2412yes—
314C2×C3×C8—22no—
315C2×C3×C8—22no—
316C2×C3×C8C2412yes—
317C2×C3×C8C2412yes—
318C3×C4⋊C4—21no—
319C3×C4⋊C4—24no—
320C3×C4⋊C4—21no—
321C3×C4⋊C4C2412yes—
322C3×C4⋊C4C2412yes—
323C3×C22⋊C4—24no—
324C3×C22⋊C4—24no—
325C3×C42C2×D412yes—
326C3×C42C2412yes—
327#217—24no—
328#217—24no—
329(C2×D3)⋊C4—24no—
330(C2×D3)⋊C4C2×D414yes—
331(C2×D3)⋊C4C2×D414yes—
332C4⋊Dic3—24no—
333C4⋊Dic3—24no—
334C4⋊Dic3—21no—
335C4⋊Dic3—21no—
336C4⋊Dic3—24no—
337C4⋊Dic3C2412yes—
338C4⋊Dic3C2412yes—
339Dic3⋊C4—24no—
340Dic3⋊C4—24no—
341Dic3⋊C4—24no—
342Dic3⋊C4—24no—
343Dic3⋊C4—24no—
344Dic3⋊C4—24no—
345Dic3⋊C4—24no—
346Dic3⋊C4C2×D414yes—
347Dic3⋊C4C2×D414yes—
348C4×Dic3—24no—
349C4×Dic3C2×D412yes—
350C4×Dic3C2412yes—
351C2×C3⋊C8—22no—
352C2×C3⋊C8—22no—
353C2×C3⋊C8C2412yes—
354C2×C3⋊C8C2412yes—
355ΓL(1,𝔽25)—28no—
356D3×C8—28no—
357C2×#41—34no—
358C2×#41—62no—
359C2×#41—64no—
360C2×#41—64no—
361C22×Q8—21no—
362C22×Q8—34no—
363C22×Q8—31no—
364C22×Q8—31no—
365C22×Q8—61no—
366C22×Q8—61no—
367C22×Q8—62no—
368C22×Q8—64no—
369C22×Q8—64no—
370C22×Q8C22×D311yescharacteristic
371C22×D4—61no—
372C22×D4C22×D311yescharacteristic
373C23×C4—31no—
374C23×C4—61no—
375C23×C4—61no—
376C23×C4—61no—
377C2×M16—34no—
378C2×M16—64no—
379C22×C8—31no—
380C22×C8—31no—
381C22×C8—34no—
382C22×C8—64no—
383C22×C8C22×D311yescharacteristic
384C22×C8C22×D311yescharacteristic
385C4⋊Q8—22no—
386C4⋊Q8—34no—
387C4⋊Q8—34no—
388C4⋊Q8—34no—
389C4⋊Q8—62no—
390C4⋊Q8—62no—
391C4⋊Q8—68no—
392C4⋊Q8—62no—
393C4⋊Q8C22×D314yes—
394#125—34no—
395#125—34no—
396#125—62no—
397#125—68no—
398#125—62no—
399#124—22no—
400#124—34no—
401#124—62no—
402#124C22×D314yes—
403#123—68no—
404#123—68no—
405C22⋊Q8—68no—
406C22⋊Q8—68no—
407C22⋊Q8—68no—
408C22⋊Q8—68no—
409#117—34no—
410#117—34no—
411#117—34no—
412#117—62no—
413C2×C4⋊C4—21no—
414C2×C4⋊C4—31no—
415C2×C4⋊C4—31no—
416C2×C4⋊C4—31no—
417C2×C4⋊C4—31no—
418C2×C4⋊C4—34no—
419C2×C4⋊C4—62no—
420C2×C4⋊C4—61no—
421C2×C4⋊C4—61no—
422C2×C4⋊C4—61no—
423C2×C4⋊C4—61no—
424C2×C4⋊C4—61no—
425C2×C4⋊C4—61no—
426C2×C4⋊C4—61no—
427C2×C4⋊C4—61no—
428C2×C4⋊C4—61no—
429C2×C4⋊C4—61no—
430C2×C4⋊C4C22×D311yescharacteristic
431C2×C4⋊C4C22×D311yescharacteristic
432C2×C22⋊C4—21no—
433C2×C22⋊C4—21no—
434C2×C22⋊C4—31no—
435C2×C22⋊C4—31no—
436C2×C22⋊C4—61no—
437C2×C22⋊C4—61no—
438C2×C22⋊C4—61no—
439C2×C42—31no—
440C2×C42—61no—
441C2×C42C22×D311yescharacteristic
442#103—34no—
443#103—34no—
444#103—34no—
445#103—34no—
446#103—34no—
447#103—34no—
448#103—34no—
449#103—34no—
450#103—34no—
451#103—34no—
452#103C22×D314yes—
453#103C22×D314yes—
454#102—34no—
455#102—34no—
456#102C22×D314yes—
457#102C22×D314yes—
458#97—34no—
459#97C22×D314yes—
460C4×C8—34no—
461C4×C8—34no—
462C23×C3—22no—
463C23×C3—42no—
464C23×C3—42no—
465C23×C3—42no—
466C23×C3C22×D411yescharacteristic
467C22×D3—22no—
468C22×D3—22no—
469C22×D3#12414yes—
470C22×D3C22×D412yes—
471C3×Q8—22no—
472C3×Q8—22no—
473C3×Q8—42no—
474C3×Q8—84no—
475C3×D4—22no—
476C3×D4—22no—
477C3×D4—42no—
478C2×C3×C4—22no—
479C2×C3×C4—22no—
480C2×C3×C4—22no—
481C2×C3×C4—22no—
482C2×C3×C4—22no—
483C2×C3×C4—42no—
484C2×C3×C4—42no—
485C2×C3×C4—42no—
486C2×C3×C4C22×D412yes—
487C2×C3×C4C22×D412yes—
488C2×C3×C4C22×D411yescharacteristic
489C2×C3×C4C2×#4112yes—
490C2×C3×C4C2×#4112yes—
491C2×C3×C4C2511yescharacteristic
492#67—48no—
493C2×Dic3—22no—
494C2×Dic3—22no—
495C2×Dic3—22no—
496C2×Dic3—22no—
497C2×Dic3—22no—
498C2×Dic3—22no—
499C2×Dic3—42no—
500C2×Dic3—42no—
501C2×Dic3—42no—
502C2×Dic3—42no—
503C2×Dic3—48no—
504C2×Dic3#12414yes—
505C2×Dic3C22×D412yes—
506C2×Dic3C22×D412yes—
507C2×Dic3C22×D412yes—
508C4×D3—48no—
509C4×D3—84no—
510C4×D3#12418yes—
511C4×D3C2×#4114yes—
512C4×D3C2×#4114yes—
513Dic6—22no—
514Dic6—22no—
515Dic6—22no—
516Dic6—22no—
517Dic6—42no—
518Dic6—42no—
519Dic6—48no—
520Dic6—84no—
521C3×C8—22no—
522C3×C8—22no—
523C3⋊C8—22no—
524C3⋊C8—22no—
525C24—21no—
526C24—31no—
527#41—68no—
528#41—68no—
529#41—128no—
530C2×Q8—21no—
531C2×Q8—24no—
532C2×Q8—22no—
533C2×Q8—22no—
534C2×Q8—32no—
535C2×Q8—32no—
536C2×Q8—64no—
537C2×Q8—64no—
538C2×Q8—68no—
539C2×Q8—68no—
540C2×Q8—61no—
541C2×Q8—61no—
542C2×Q8—62no—
543C2×Q8—62no—
544C2×Q8—62no—
545C2×Q8—62no—
546C2×Q8—82no—
547C2×Q8—124no—
548C2×Q8—128no—
549C2×Q8—242no—
550C2×Q8C23×D312yes—
551C2×D4—21no—
552C2×D4—22no—
553C2×D4—22no—
554C2×D4—64no—
555C2×D4—124no—
556C2×D4C23×D312yes—
557C22×C4—21no—
558C22×C4—21no—
559C22×C4—21no—
560C22×C4—31no—
561C22×C4—32no—
562C22×C4—34no—
563C22×C4—34no—
564C22×C4—32no—
565C22×C4—31no—
566C22×C4—31no—
567C22×C4—64no—
568C22×C4—64no—
569C22×C4—64no—
570C22×C4—61no—
571C22×C4—61no—
572C22×C4—61no—
573C22×C4—61no—
574C22×C4—124no—
575C22×C4—124no—
576C22×C4—242no—
577C22×C4D3×D411yescharacteristic
578C22×C4D3×D411yescharacteristic
579C22×C4C23×D311yescharacteristic
580M16—68no—
581C2×C8—22no—
582C2×C8—22no—
583C2×C8—32no—
584C2×C8—32no—
585C2×C8—68no—
586C2×C8—62no—
587C2×C8—62no—
588C2×C8C23×D312yes—
589C2×C8C23×D312yes—
590C4⋊C4—24no—
591C4⋊C4—21no—
592C4⋊C4—21no—
593C4⋊C4—34no—
594C4⋊C4—34no—
595C4⋊C4—32no—
596C4⋊C4—32no—
597C4⋊C4—64no—
598C4⋊C4—64no—
599C4⋊C4—64no—
600C4⋊C4—64no—
601C4⋊C4—64no—
602C4⋊C4—64no—
603C4⋊C4—61no—
604C4⋊C4—61no—
605C4⋊C4—64no—
606C4⋊C4—64no—
607C4⋊C4—64no—
608C4⋊C4—64no—
609C4⋊C4C23×D312yes—
610C4⋊C4C23×D312yes—
611C22⋊C4—24no—
612C22⋊C4—24no—
613C22⋊C4—34no—
614C22⋊C4—34no—
615C22⋊C4—64no—
616C22⋊C4—64no—
617C22⋊C4—64no—
618C42—32no—
619C42—32no—
620C42—64no—
621C42D3×D412yes—
622C42C23×D312yes—
623C22×C3—42no—
624C22×C3—42no—
625C22×C3—42no—
626C22×C3—84no—
627C22×C3C2×#12412yes—
628C22×C3#57712yes—
629C22×C3#57812yes—
630C22×C3C23×D411yescharacteristic
631C2×D3—28no—
632C2×D3—22no—
633C2×D3—22no—
634C2×D3C2×#12414yes—
635C3×C4—22no—
636C3×C4—22no—
637C3×C4—42no—
638C3×C4—42no—
639C3×C4—42no—
640C3×C4C2×#12412yes—
641C3×C4C22×#4111yescharacteristic
642C3×C4C22×#4111yescharacteristic
643Dic3—22no—
644Dic3—22no—
645Dic3—42no—
646Dic3—42no—
647Dic3—42no—
648Dic3—42no—
649Dic3C2×#12414yes—
650C23—22no—
651C23—34no—
652C23—32no—
653C23—42no—
654C23—42no—
655C23—42no—
656C23—62no—
657C23—62no—
658C23C2×D3×D411yescharacteristic
659Q8—22no—
660Q8—22no—
661Q8—42no—
662Q8—62no—
663Q8—62no—
664Q8—62no—
665Q8—62no—
666Q8—84no—
667Q8—128no—
668Q8—122no—
669Q8—122no—
670Q8—244no—
671D4—22no—
672D4—22no—
673D4—42no—
674D4—128no—
675C2×C4—22no—
676C2×C4—22no—
677C2×C4—22no—
678C2×C4—22no—
679C2×C4—22no—
680C2×C4—34no—
681C2×C4—32no—
682C2×C4—38no—
683C2×C4—34no—
684C2×C4—34no—
685C2×C4—32no—
686C2×C4—32no—
687C2×C4—42no—
688C2×C4—42no—
689C2×C4—42no—
690C2×C4—62no—
691C2×C4—62no—
692C2×C4—62no—
693C2×C4—62no—
694C2×C4—62no—
695C2×C4—62no—
696C2×C4—128no—
697C2×C4—128no—
698C2×C4—122no—
699C2×C4—122no—
700C2×C4—122no—
701C2×C4—122no—
702C2×C4—244no—
703C2×C4C2×D3×D412yes—
704C2×C4C2×D3×D412yes—
705C2×C4C2×D3×D411yescharacteristic
706C2×C4D3×#4112yes—
707C2×C4D3×#4112yes—
708C2×C4C24×D311yescharacteristic
709C8—22no—
710C8—22no—
711C8—62no—
712C8—62no—
713C2×C3—82no—
714C2×C3#313714yescomplemented
715C2×C3C22×#12411yescharacteristic
716C2×C3C2×#57711yescharacteristic
717C2×C3C2×#57811yescharacteristic
718D3—24no—
719C22—34no—
720C22—42no—
721C22—42no—
722C22—42no—
723C22—68no—
724C22—62no—
725C22—62no—
726C22—84no—
727C22D3×#12412yes—
728C22#577512yes—
729C22#577912yes—
730C22C22×D3×D411yescharacteristic
731C4—22no—
732C4—22no—
733C4—34no—
734C4—42no—
735C4—42no—
736C4—42no—
737C4—62no—
738C4—62no—
739C4—122no—
740C4—122no—
741C4—122no—
742C4—122no—
743C4D3×#12412yes—
744C4C2×D3×#4111yescharacteristic
745C4C2×D3×#4111yescharacteristic
746C3C2×#313711yescharacteristic, complemented, Sylow
747C2—64no—
748C2—82no—
749C2#8168114yesdirect product factor
750C2C2×D3×#12411yescharacteristic
751C2C2×#577511yescharacteristic
752C2C2×#577911yescharacteristic
subgroupG/H
centerC23C2×D3×D4
commutator, cosocleC2×C3×C4C25
FrattiniC2×C4C24×D3
FittingC2×C3×#489C2
socleC23×C3C22×D4
prime radicalC22×#237C22
hypercenterC2×#489D3
hypocenterC3C2×#3137
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#489

Complements

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

NH ≅ G/Ntype
1. C2×#5729C2semidirect
3. C2×C3×#489C2semidirect
4. C2×#5093C2semidirect
5. C2×#5056C2semidirect
6. #81681C2direct (N × H)
7. C2×#4802C2semidirect
8. C2×D3×#103C2semidirect
9. C2×#4797C2semidirect
10. C2×#4792C2semidirect
13. C2×#4765C2semidirect
14. C2×#4768C2semidirect
15. C2×#4703C2semidirect
16. C2×#4708C2semidirect
29. #5729C22semidirect
45. C3×#489C22semidirect
61. #5093C22semidirect
62. #5056C22semidirect
68. #4802C22semidirect
69. D3×#103C22semidirect
70. #4797C22semidirect
71. #4792C22semidirect
74. #4768C22semidirect
75. #4765C22semidirect
76. #4708C22semidirect
77. #4703C22semidirect
84. C2×#489D3semidirect
229. #489C2×D3semidirect
714. C2×C3#3137semidirect
746. C3C2×#3137semidirect
749. C2#81681direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#57292
C2×#56752
C2×C3×#4892
C2×#50932
C2×#50562
#816812
C2×#48022
C2×D3×#1032
C2×#47972
C2×#47922
C2×#47712
C2×#47722
C2×#47652
C2×#47682
C2×#47032
C2×#47082
C2×#31373