Finite Group Databasebeta

← C2×#83134 #11664907

Subgroups — C2×#83134 #11664907

Order 768.

2070 conjugacy classes of subgroups.

The subgroup lattice has 758 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#529C211yesmaximal, characteristic, complemented
2C2×#5479C211yesmaximal, characteristic, complemented
3#83134C2116yesmaximal, direct product factor
4C2×#5065C211yesmaximal, characteristic, complemented
5C2×#5068C211yesmaximal, characteristic, complemented
6C2×#5059C211yesmaximal, characteristic, complemented
7C2×#5056C211yesmaximal, characteristic, complemented
8C2×#5051C211yesmaximal, characteristic, complemented
9C2×#5048C211yesmaximal, characteristic, complemented
10C2×#5038C211yesmaximal, characteristic
11C2×#5041C211yesmaximal, characteristic, complemented
12C2×C4×#216C211yesmaximal, characteristic, complemented
13C2×C4×#215C211yesmaximal, characteristic, complemented
14C2×C4×#214C211yesmaximal, characteristic, complemented
15C2×C4×#213C211yesmaximal, characteristic, complemented
16C22×C4×C3⋊C8C211yesmaximal, characteristic, complemented
17C2×#3168—31nomaximal, Sylow
18C3×#529—24no—
19C3×#529C2218yescomplemented
20C2×C3×#126—21no—
21C2×C3×#125C2211yescharacteristic
22C2×C3×#124C2211yescharacteristic
23C2×C3×#123—21no—
24C2×C3×C22⋊Q8C2211yescharacteristic
25C2×C3×#121C2211yescharacteristic
26C2×C3×C4×Q8C2211yescharacteristic
27C2×C3×C4×D4—21no—
28C2×C3×C4×D4C2211yescharacteristic
29C2×C3×#117—21no—
30C22×C3×C42C2211yescharacteristic
31C22×#216C2211yescharacteristic
32C22×#215C2211yescharacteristic
33C22×#214C2211yescharacteristic
34C22×#213C2211yescharacteristic
35C2×#930C2211yescharacteristic
36C2×#929—21no—
37C2×C4×#67—21no—
38C2×#924C2211yescharacteristic
39C23×C3⋊C8C2211yescharacteristic
40C23×C3⋊C8C2211yescharacteristic
41#5479—24no—
42#5479C2218yescomplemented
43C2×#876—21no—
44C2×#875C2211yescharacteristic
45C2×C4×D12C2211yescharacteristic
46C2×#872—21no—
47C2×#870C2211yescharacteristic
48C2×C4×Dic6C2211yescharacteristic
49C2×#835C2211yescharacteristic
50C2×#835C2211yescharacteristic
51C2×#832C2211yescharacteristic
52C2×#832C2211yescharacteristic
53#5068C2218yescomplemented
54#5065C2218yescomplemented
55#5059C2218yescomplemented
56#5056C2218yescomplemented
57#5051C2218yescomplemented
58#5048C2218yescomplemented
59#5041C2218yescomplemented
60#5038C2218yes—
61C4×#216C2218yescomplemented
62C4×#215C2218yescomplemented
63C4×#214C2218yescomplemented
64C4×#213C2218yescomplemented
65C2×#810C2211yescharacteristic
66C2×#810C2211yescharacteristic
67C2×#809C2211yescharacteristic
68C2×#809C2211yescharacteristic
69C2×#808C2211yescharacteristic
70C2×#808C2211yescharacteristic
71C2×#807C2211yescharacteristic
72C2×#807C2211yescharacteristic
73C2×C4×C3⋊C8C2211yescharacteristic
74C2×C4×C3⋊C8C2211yescharacteristic
75C2×C4×C3⋊C8C2211yescharacteristic
76C2×C4×C3⋊C8C2211yescharacteristic
77C2×C4×C3⋊C8C2218yescomplemented
78C2×#529—31no—
79C2×#529D311yescharacteristic, complemented
80#3168—316no—
81C2×#499—31no—
82C2×#495—31no—
83C2×#488—31no—
84C2×#488—31no—
85C2×#467—31no—
86C2×#466—31no—
87C2×#465—31no—
88C2×#465—31no—
89C2×C4×Q16—31no—
90C2×C4×SD16—31no—
91C2×C4×SD16—31no—
92C2×C4×D8—31no—
93C22×C4×C8—31no—
94C22×C3×Q8C2311yescharacteristic
95C22×C3×D4—21no—
96C22×C3×D4C2311yescharacteristic
97C23×C3×C4—21no—
98C23×C3×C4D411yescharacteristic
99C23×C3×C4D411yescharacteristic
100C23×C3×C4C2311yescharacteristic
101C22×#67—21no—
102C22×D12C2311yescharacteristic
103C22×C4×D3—21no—
104C22×Dic6C2311yescharacteristic
105C3×#126—28no—
106C3×#125—22no—
107C3×#125C2314yes—
108C3×#124—22no—
109C3×#124C2314yes—
110C3×#123—28no—
111C3×C22⋊Q8—22no—
112C3×C22⋊Q8C2314yes—
113C3×#121—22no—
114C3×#121C2314yes—
115C3×C4×Q8—22no—
116C3×C4×Q8C2314yes—
117C3×C4×D4—28no—
118C3×C4×D4—22no—
119C3×C4×D4C2314yes—
120C3×#117—28no—
121C2×C3×C4⋊C4—21no—
122C2×C3×C4⋊C4—21no—
123C2×C3×C4⋊C4—21no—
124C2×C3×C4⋊C4—21no—
125C2×C3×C4⋊C4C2311yescharacteristic
126C2×C3×C4⋊C4C2311yescharacteristic
127C2×C3×C22⋊C4—21no—
128C2×C3×C22⋊C4—21no—
129C2×C3×C22⋊C4—21no—
130C2×C3×C22⋊C4—21no—
131C2×C3×C22⋊C4—21no—
132C2×C3×C42—21no—
133C2×C3×C42D411yescharacteristic
134C2×C3×C42D411yescharacteristic
135C2×C3×C42D414yes—
136C2×C3×C42C2311yescharacteristic
137C2×C3×C42C2311yescharacteristic
138C2×C3×C42C2314yes—
139C2×#217—21no—
140C2×#216—24no—
141C2×#216C2314yes—
142C2×#215—24no—
143C2×#215C2314yes—
144C2×#214—24no—
145C2×#214C2314yes—
146C2×#213—24no—
147C2×#213C2314yes—
148#930—22no—
149#930C2314yes—
150#929—28no—
151C4×#67—28no—
152C2×(C2×D3)⋊C4—21no—
153C2×(C2×D3)⋊C4—21no—
154C2×(C2×D3)⋊C4—21no—
155C2×(C2×D3)⋊C4—21no—
156C2×C4⋊Dic3C2311yescharacteristic
157C2×C4⋊Dic3C2311yescharacteristic
158#924—22no—
159#924C2314yes—
160C2×Dic3⋊C4—21no—
161C2×Dic3⋊C4—21no—
162C2×Dic3⋊C4—21no—
163C2×Dic3⋊C4—21no—
164C2×C4×Dic3—21no—
165C22×C3⋊C8—24no—
166C22×C3⋊C8—24no—
167C22×C3⋊C8C2311yescharacteristic
168C22×C3⋊C8C2311yescharacteristic
169C22×C3⋊C8C2314yes—
170C22×C3⋊C8C2314yes—
171C22×C3⋊C8C2311yescharacteristic
172C22×C3⋊C8C2311yescharacteristic
173#876—28no—
174#875—22no—
175#875C2314yes—
176C4×D12—22no—
177C4×D12C2314yes—
178#872—28no—
179#870—22no—
180#870C2314yes—
181C4×Dic6—22no—
182C4×Dic6C2314yes—
183#835C2314yes—
184#835C2314yes—
185#832C2314yes—
186#832C2314yes—
187#810C2314yes—
188#810C2314yes—
189#809C2314yes—
190#809C2314yes—
191#808C2314yes—
192#808C2314yes—
193#807C2314yes—
194#807C2314yes—
195C4×C3⋊C8C2314yes—
196C4×C3⋊C8C2314yes—
197C4×C3⋊C8C2314yes—
198C4×C3⋊C8C2314yes—
199C22×Q16—31no—
200C22×SD16—31no—
201C22×SD16—31no—
202C22×D8—31no—
203C23×C8—31no—
204C23×C8—31no—
205#529—24no—
206#529—38no—
207#529—64no—
208#529C2×D318yescomplemented
209C2×#126—21no—
210C2×#126—61no—
211C2×#125—31no—
212C2×#125C2×D311yescharacteristic
213C2×#124—31no—
214C2×#124C2×D311yescharacteristic
215C2×#123—21no—
216C2×#123—61no—
217C2×C22⋊Q8—31no—
218C2×C22⋊Q8C2×D311yescharacteristic
219C2×#121—31no—
220C2×#121C2×D311yescharacteristic
221C2×C4×Q8—31no—
222C2×C4×Q8C2×D311yescharacteristic
223C2×C4×D4—21no—
224C2×C4×D4—31no—
225C2×C4×D4—61no—
226C2×C4×D4C2×D311yescharacteristic
227C2×#117—21no—
228C2×#117—61no—
229C22×C42C2×D311yescharacteristic
230#499—38no—
231#495—38no—
232#488—38no—
233#488—38no—
234#467—38no—
235#466—38no—
236#465—38no—
237#465—38no—
238C4×Q16—38no—
239C4×SD16—38no—
240C4×SD16—38no—
241C4×D8—38no—
242C2×#107—31no—
243C2×#107—31no—
244C2×#106—31no—
245C2×#106—31no—
246C2×#103—31no—
247C2×#103—31no—
248C2×#103—31no—
249C2×#103—31no—
250C2×#102—31no—
251C2×#102—31no—
252C2×#102—31no—
253C2×#102—31no—
254C2×C4×C8—31no—
255C2×C4×C8—31no—
256C2×C4×C8—31no—
257C2×C4×C8—31no—
258C2×C4×C8—38no—
259C24×C3—21no—
260C24×C3C2×D411yescharacteristic
261C23×D3—21no—
262C2×C3×Q8—21no—
263C2×C3×Q8—22no—
264C2×C3×Q8—22no—
265C2×C3×Q8C2412yes—
266C2×C3×D4—24no—
267C2×C3×D4—21no—
268C2×C3×D4—22no—
269C2×C3×D4—22no—
270C2×C3×D4—44no—
271C2×C3×D4C2412yes—
272C22×C3×C4—24no—
273C22×C3×C4—24no—
274C22×C3×C4—22no—
275C22×C3×C4—22no—
276C22×C3×C4—21no—
277C22×C3×C4—21no—
278C22×C3×C4—21no—
279C22×C3×C4—24no—
280C22×C3×C4—44no—
281C22×C3×C4C2×D411yescharacteristic
282C22×C3×C4C2×D411yescharacteristic
283C22×C3×C4C2×D411yescharacteristic
284C22×C3×C4C2×D411yescharacteristic
285C22×C3×C4C2×D412yes—
286C22×C3×C4C2×D414yes—
287C22×C3×C4C2×D414yes—
288C22×C3×C4C2×D411yescharacteristic
289C22×C3×C4C2412yes—
290C22×C3×C4C2411yescharacteristic
291C2×#67—24no—
292C2×#67—44no—
293C22×Dic3—21no—
294C22×Dic3—21no—
295C22×Dic3—21no—
296C2×D12—22no—
297C2×D12—22no—
298C2×D12—21no—
299C2×D12C2412yes—
300C2×C4×D3—24no—
301C2×C4×D3—44no—
302C2×Dic6—22no—
303C2×Dic6—22no—
304C2×Dic6—21no—
305C2×Dic6C2412yes—
306C3×C4⋊C4—24no—
307C3×C4⋊C4—24no—
308C3×C4⋊C4—24no—
309C3×C4⋊C4—24no—
310C3×C4⋊C4—21no—
311C3×C4⋊C4—21no—
312C3×C4⋊C4C2412yes—
313C3×C4⋊C4C2412yes—
314C3×C22⋊C4—24no—
315C3×C22⋊C4—24no—
316C3×C22⋊C4—24no—
317C3×C22⋊C4—24no—
318C3×C22⋊C4—24no—
319C3×C42—24no—
320C3×C42C2×D412yes—
321C3×C42C2×D412yes—
322C3×C42C2×D414yes—
323C3×C42C2×D414yes—
324C3×C42C2412yes—
325C3×C42C2412yes—
326#217—24no—
327#216—28no—
328#215—28no—
329#214—28no—
330#213—28no—
331(C2×D3)⋊C4—24no—
332(C2×D3)⋊C4—24no—
333(C2×D3)⋊C4—24no—
334(C2×D3)⋊C4—24no—
335C4⋊Dic3—21no—
336C4⋊Dic3—21no—
337C4⋊Dic3C2412yes—
338C4⋊Dic3C2412yes—
339Dic3⋊C4—24no—
340Dic3⋊C4—24no—
341Dic3⋊C4—24no—
342Dic3⋊C4—24no—
343C4×Dic3—24no—
344C2×C3⋊C8—22no—
345C2×C3⋊C8—22no—
346C2×C3⋊C8—28no—
347C2×C3⋊C8—28no—
348C2×C3⋊C8#4114yes—
349C2×C3⋊C8#4114yes—
350C2×C3⋊C8C2412yes—
351C2×C3⋊C8C2412yes—
352C2×C3⋊C8C2412yes—
353C2×C3⋊C8C2412yes—
354C22×Q8—31no—
355C22×Q8C22×D311yescharacteristic
356C22×D4—21no—
357C22×D4—31no—
358C22×D4—61no—
359C22×D4C22×D311yescharacteristic
360C23×C4—21no—
361C23×C4—61no—
362C23×C4#6711yescharacteristic
363C23×C4#6711yescharacteristic
364C23×C4C22×D311yescharacteristic
365C2×Q16—34no—
366C2×Q16—64no—
367C2×SD16—34no—
368C2×SD16—34no—
369C2×SD16—64no—
370C2×SD16—64no—
371C2×D8—34no—
372C2×D8—64no—
373C22×C8—31no—
374C22×C8—31no—
375C22×C8—31no—
376C22×C8—31no—
377C22×C8—34no—
378C22×C8—34no—
379C22×C8—64no—
380C22×C8—64no—
381#126—28no—
382#126—68no—
383#125—22no—
384#125—34no—
385#125—62no—
386#125C22×D314yes—
387#124—22no—
388#124—34no—
389#124—62no—
390#124C22×D314yes—
391#123—28no—
392#123—68no—
393C22⋊Q8—22no—
394C22⋊Q8—34no—
395C22⋊Q8—62no—
396C22⋊Q8C22×D314yes—
397#121—22no—
398#121—34no—
399#121—62no—
400#121C22×D314yes—
401C4×Q8—22no—
402C4×Q8—34no—
403C4×Q8—62no—
404C4×Q8C22×D314yes—
405C4×D4—28no—
406C4×D4—22no—
407C4×D4—34no—
408C4×D4—68no—
409C4×D4—62no—
410C4×D4C22×D314yes—
411#117—28no—
412#117—68no—
413C2×C4⋊C4—21no—
414C2×C4⋊C4—21no—
415C2×C4⋊C4—21no—
416C2×C4⋊C4—21no—
417C2×C4⋊C4—31no—
418C2×C4⋊C4—31no—
419C2×C4⋊C4—61no—
420C2×C4⋊C4—61no—
421C2×C4⋊C4—61no—
422C2×C4⋊C4—61no—
423C2×C4⋊C4C22×D311yescharacteristic
424C2×C4⋊C4C22×D311yescharacteristic
425C2×C22⋊C4—21no—
426C2×C22⋊C4—21no—
427C2×C22⋊C4—21no—
428C2×C22⋊C4—21no—
429C2×C22⋊C4—21no—
430C2×C22⋊C4—61no—
431C2×C22⋊C4—61no—
432C2×C22⋊C4—61no—
433C2×C22⋊C4—61no—
434C2×C22⋊C4—61no—
435C2×C42—21no—
436C2×C42—61no—
437C2×C42#6711yescharacteristic
438C2×C42#6714yes—
439C2×C42#6711yescharacteristic
440C2×C42C22×D311yescharacteristic
441C2×C42C22×D314yes—
442C2×C42C22×D311yescharacteristic
443#107—34no—
444#107—34no—
445#106—34no—
446#106—34no—
447#103—34no—
448#103—34no—
449#103—34no—
450#103—34no—
451#102—34no—
452#102—34no—
453#102—34no—
454#102—34no—
455C4×C8—34no—
456C4×C8—34no—
457C4×C8—34no—
458C4×C8—34no—
459C23×C3—22no—
460C23×C3—22no—
461C23×C3—22no—
462C23×C3—42no—
463C23×C3—42no—
464C23×C3—42no—
465C23×C3#13514yes—
466C23×C3C22×D412yes—
467C23×C3C22×D411yescharacteristic
468C22×D3—22no—
469C22×D3—42no—
470C22×D3—42no—
471C22×D3—42no—
472C3×Q8—22no—
473C3×Q8—22no—
474C3×Q8—42no—
475C3×D4—22no—
476C3×D4—22no—
477C3×D4—48no—
478C3×D4—42no—
479C2×C3×C4—22no—
480C2×C3×C4—28no—
481C2×C3×C4—22no—
482C2×C3×C4—22no—
483C2×C3×C4—22no—
484C2×C3×C4—24no—
485C2×C3×C4—28no—
486C2×C3×C4—22no—
487C2×C3×C4—22no—
488C2×C3×C4—22no—
489C2×C3×C4—22no—
490C2×C3×C4—22no—
491C2×C3×C4—42no—
492C2×C3×C4—42no—
493C2×C3×C4—42no—
494C2×C3×C4—48no—
495C2×C3×C4#13514yes—
496C2×C3×C4C22×D412yes—
497C2×C3×C4C22×D412yes—
498C2×C3×C4C22×D412yes—
499C2×C3×C4C22×D412yes—
500C2×C3×C4C22×D411yescharacteristic
501C2×C3×C4C22×D412yes—
502C2×C3×C4C2×#4112yes—
503C2×C3×C4C2×#4112yes—
504C2×C3×C4C2511yescharacteristic
505#67—48no—
506C2×Dic3—22no—
507C2×Dic3—22no—
508C2×Dic3—22no—
509C2×Dic3—42no—
510C2×Dic3—42no—
511C2×Dic3—42no—
512D12—22no—
513D12—22no—
514D12—42no—
515C4×D3—48no—
516Dic6—22no—
517Dic6—22no—
518Dic6—42no—
519C3⋊C8—22no—
520C3⋊C8—22no—
521C3⋊C8C2×#4114yes—
522C3⋊C8C2×#4114yes—
523C24—21no—
524C24—61no—
525C24C2×#6711yescharacteristic
526C2×Q8—21no—
527C2×Q8—22no—
528C2×Q8—22no—
529C2×Q8—32no—
530C2×Q8—61no—
531C2×Q8—62no—
532C2×Q8—62no—
533C2×Q8C23×D312yes—
534C2×D4—24no—
535C2×D4—22no—
536C2×D4—22no—
537C2×D4—21no—
538C2×D4—32no—
539C2×D4—44no—
540C2×D4—64no—
541C2×D4—62no—
542C2×D4—62no—
543C2×D4—61no—
544C2×D4—124no—
545C2×D4C23×D312yes—
546C22×C4—24no—
547C22×C4—24no—
548C22×C4—22no—
549C22×C4—22no—
550C22×C4—21no—
551C22×C4—21no—
552C22×C4—21no—
553C22×C4—24no—
554C22×C4—44no—
555C22×C4—61no—
556C22×C4—61no—
557C22×C4—61no—
558C22×C4—64no—
559C22×C4—124no—
560C22×C4C2×#6711yescharacteristic
561C22×C4C2×#6712yes—
562C22×C4C2×#6711yescharacteristic
563C22×C4C2×#6711yescharacteristic
564C22×C4C2×#6711yescharacteristic
565C22×C4C2×#6714yes—
566C22×C4C2×#6714yes—
567C22×C4C2×#6711yescharacteristic
568C22×C4C23×D312yes—
569C22×C4C23×D311yescharacteristic
570Q16—68no—
571SD16—68no—
572SD16—68no—
573D8—68no—
574C2×C8—34no—
575C2×C8—34no—
576C2×C8—32no—
577C2×C8—32no—
578C2×C8—32no—
579C2×C8—32no—
580C2×C8—68no—
581C2×C8—68no—
582C2×C8—62no—
583C2×C8—62no—
584C4⋊C4—24no—
585C4⋊C4—24no—
586C4⋊C4—24no—
587C4⋊C4—24no—
588C4⋊C4—21no—
589C4⋊C4—21no—
590C4⋊C4—32no—
591C4⋊C4—32no—
592C4⋊C4—61no—
593C4⋊C4—61no—
594C4⋊C4—64no—
595C4⋊C4—64no—
596C4⋊C4—64no—
597C4⋊C4—64no—
598C4⋊C4C23×D312yes—
599C4⋊C4C23×D312yes—
600C22⋊C4—24no—
601C22⋊C4—24no—
602C22⋊C4—24no—
603C22⋊C4—24no—
604C22⋊C4—24no—
605C22⋊C4—64no—
606C22⋊C4—64no—
607C22⋊C4—64no—
608C22⋊C4—64no—
609C22⋊C4—64no—
610C42—24no—
611C42—64no—
612C42C2×#6714yes—
613C42C2×#6712yes—
614C42C2×#6712yes—
615C42C2×#6714yes—
616C42C23×D312yes—
617C42C23×D312yes—
618C22×C3—28no—
619C22×C3—22no—
620C22×C3—22no—
621C22×C3—42no—
622C22×C3—42no—
623C22×C3—42no—
624C22×C3—84no—
625C22×C3#53212yes—
626C22×C3C2×#13514yes—
627C22×C3C2×#13512yes—
628C22×C3C2×#13512yes—
629C22×C3C23×D411yescharacteristic
630C2×D3—42no—
631C2×D3—42no—
632C2×D3—42no—
633C2×D3—84no—
634C3×C4—22no—
635C3×C4—22no—
636C3×C4—22no—
637C3×C4—22no—
638C3×C4—42no—
639C3×C4—42no—
640C3×C4—42no—
641C3×C4#53212yes—
642C3×C4C2×#13514yes—
643C3×C4C22×#4111yescharacteristic
644C3×C4C22×#4111yescharacteristic
645Dic3—42no—
646Dic3—42no—
647Dic3—42no—
648C23—22no—
649C23—22no—
650C23—22no—
651C23—42no—
652C23—42no—
653C23—42no—
654C23—62no—
655C23—122no—
656C23—122no—
657C23—122no—
658C23#95014yes—
659C23C22×#6712yes—
660C23C22×#6711yescharacteristic
661Q8—22no—
662Q8—22no—
663Q8—42no—
664Q8—62no—
665Q8—62no—
666Q8—122no—
667D4—22no—
668D4—22no—
669D4—48no—
670D4—42no—
671D4—62no—
672D4—62no—
673D4—128no—
674D4—122no—
675C2×C4—28no—
676C2×C4—22no—
677C2×C4—22no—
678C2×C4—22no—
679C2×C4—22no—
680C2×C4—22no—
681C2×C4—22no—
682C2×C4—28no—
683C2×C4—24no—
684C2×C4—22no—
685C2×C4—22no—
686C2×C4—22no—
687C2×C4—42no—
688C2×C4—42no—
689C2×C4—42no—
690C2×C4—48no—
691C2×C4—62no—
692C2×C4—62no—
693C2×C4—62no—
694C2×C4—122no—
695C2×C4—122no—
696C2×C4—122no—
697C2×C4—128no—
698C2×C4#95014yes—
699C2×C4D3×#4112yes—
700C2×C4D3×#4112yes—
701C2×C4C22×#6712yes—
702C2×C4C22×#6712yes—
703C2×C4C22×#6712yes—
704C2×C4C22×#6712yes—
705C2×C4C22×#6712yes—
706C2×C4C22×#6711yescharacteristic
707C2×C4C24×D311yescharacteristic
708C8—34no—
709C8—34no—
710C8—62no—
711C8—62no—
712C2×C3—24no—
713C2×C3—82no—
714C2×C3#316814yescomplemented
715C2×C3C2×#53211yescharacteristic
716C2×C3C22×#13511yescharacteristic
717C2×C3C22×#13511yescharacteristic
718D3—82no—
719C22—28no—
720C22—22no—
721C22—22no—
722C22—42no—
723C22—42no—
724C22—42no—
725C22—84no—
726C22—122no—
727C22—122no—
728C22—122no—
729C22—244no—
730C22C2×#95014yes—
731C22C2×#95012yes—
732C22C2×#95012yes—
733C22#583212yes—
734C22C23×#6711yescharacteristic
735C4—22no—
736C4—22no—
737C4—22no—
738C4—22no—
739C4—42no—
740C4—42no—
741C4—42no—
742C4—122no—
743C4—122no—
744C4—122no—
745C4C2×#95014yes—
746C4#583212yes—
747C4C2×D3×#4111yescharacteristic
748C4C2×D3×#4111yescharacteristic
749C3C2×#316811yescharacteristic, complemented, Sylow
750C2—24no—
751C2—82no—
752C2—242no—
753C2#8313414yesdirect product factor
754C2C22×#95011yescharacteristic
755C2C22×#95011yescharacteristic
756C2C2×#583211yescharacteristic
subgroupG/H
centerC22×C4C2×#67
commutator, cosocleC2×C3×C4C25
FrattiniC2×C4C24×D3
FittingC2×C3×#529C2
socleC23×C3C22×D4
prime radicalC2×#5038C2
hypercenterC2×#529D3
hypocenterC3C2×#3168
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C4 ◁ C22×C42 ◁ C2×#529

Complements

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

NH ≅ G/Ntype
1. C2×C3×#529C2semidirect
2. C2×#5479C2semidirect
3. #83134C2direct (N × H)
4. C2×#5065C2semidirect
5. C2×#5068C2semidirect
6. C2×#5059C2semidirect
7. C2×#5056C2semidirect
8. C2×#5051C2semidirect
9. C2×#5048C2semidirect
11. C2×#5041C2semidirect
12. C2×C4×#216C2semidirect
13. C2×C4×#215C2semidirect
14. C2×C4×#214C2semidirect
15. C2×C4×#213C2semidirect
16. C22×C4×C3⋊C8C2semidirect
19. C3×#529C22semidirect
42. #5479C22semidirect
53. #5068C22semidirect
54. #5065C22semidirect
55. #5059C22semidirect
56. #5056C22semidirect
57. #5051C22semidirect
58. #5048C22semidirect
59. #5041C22semidirect
61. C4×#216C22semidirect
62. C4×#215C22semidirect
63. C4×#214C22semidirect
64. C4×#213C22semidirect
77. C2×C4×C3⋊C8C22semidirect
79. C2×#529D3semidirect
208. #529C2×D3semidirect
714. C2×C3#3168semidirect
749. C3C2×#3168semidirect
753. C2#83134direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×#5292
C2×#54792
#831342
C2×#50652
C2×#50682
C2×#50592
C2×#50562
C2×#50512
C2×#50482
C2×#50382
C2×#50412
C2×C4×#2162
C2×C4×#2152
C2×C4×#2142
C2×C4×#2132
C22×C4×C3⋊C82
C2×#31683