Finite Group Databasebeta

← #10957200

Subgroups — #10957200

Order 768.

3124 conjugacy classes of subgroups.

The subgroup lattice has 768 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#5726C211yesmaximal, characteristic
2C2×#5574C212yesmaximal, complemented
3C3×C4×C4⋊Q8C211yesmaximal, characteristic, complemented
4#83229C211yesmaximal, characteristic, complemented
5#82488C212yesmaximal, complemented
6#76615C212yesmaximal, complemented
7#76613C212yesmaximal, complemented
8#76196C214yesmaximal, complemented
9D3×#389C212yesmaximal, complemented
10#75964C212yesmaximal, complemented
11#74360C211yesmaximal, characteristic, complemented
12#74360C211yesmaximal, characteristic, complemented
13#73774C212yesmaximal, complemented
14#73772C214yesmaximal, complemented
15#73767C212yesmaximal, complemented
16#73299C211yesmaximal, characteristic, complemented
17C42×D12C211yesmaximal, characteristic, complemented
18#34308—31nomaximal, Sylow
19C22×#239C2212yes—
20C2×C3×C4⋊Q8C2211yescharacteristic
21C2×C3×C4×Q8C2212yes—
22C2×#946C2212yes—
23C2×Q8×Dic3C2212yes—
24#5726C4116yescomplemented
25#5574—216no—
26C2×#895C2212yes—
27C2×#894C2214yes—
28C2×#893C2212yes—
29C2×#893C2214yes—
30C2×#893C2212yes—
31C2×D3×C4⋊C4C2212yes—
32C2×D3×C4⋊C4C2214yes—
33C2×D3×C4⋊C4C2212yes—
34C2×D3×C4⋊C4C2212yes—
35C2×C4×D12C2214yes—
36C2×C4×D12C2211yescharacteristic
37C2×C4×D12C2211yescharacteristic
38C2×C4×D12C2211yescharacteristic
39C2×C4×D12C2211yescharacteristic
40C2×#872C2214yes—
41C2×#872C2212yes—
42C2×C42×D3C2212yes—
43C3×#391C2212yes—
44C3×#389C2212yes—
45C3×#389C2212yes—
46C3×#384C2211yescharacteristic
47C3×C4×C4⋊C4C2212yes—
48C3×C4×C4⋊C4C2212yes—
49C3×C43C2211yescharacteristic
50#5229C2212yes—
51#4990C2214yes—
52#4989C2214yes—
53#4989C2214yes—
54#4987C2212yes—
55#4987C2212yes—
56#4984C2212yes—
57#4980C2214yes—
58#4976C2214yes—
59Dic3×C4⋊C4C2212yes—
60#4972C2212yes—
61#4972C2212yes—
62#4940C2212yes—
63#4940C2214yes—
64#4940C2212yes—
65#4939C2211yescharacteristic
66#4939C2211yescharacteristic
67C4×(C2×D3)⋊C4C2212yes—
68C4×(C2×D3)⋊C4C2212yes—
69C4×(C2×D3)⋊C4C2212yes—
70C4×(C2×D3)⋊C4C2212yes—
71C4×C4⋊Dic3C2211yescharacteristic
72C4×C4⋊Dic3C2211yescharacteristic
73C4×C4⋊Dic3C2211yescharacteristic
74C4×C4⋊Dic3C2211yescharacteristic
75#4933C2214yes—
76#4928C2211yescharacteristic
77#4928C2211yescharacteristic
78#4668C2214yes—
79#4666C2214yes—
80#4665C2214yes—
81#4665C2214yes—
82#4664C2214yes—
83D3×#95C2214yes—
84#4652C2214yes—
85#4647C2214yes—
86C2×#547—31no—
87C2×#520—32no—
88#2365—31no—
89#2361—32no—
90#2360—32no—
91#2359—34no—
92D4×C4⋊C4—31no—
93D4×C4⋊C4—31no—
94#2344—32no—
95#2339—32no—
96#2323—32no—
97#2322—34no—
98C4×C4⋊Q8D311yescharacteristic, complemented
99C4×#121—32no—
100#2293—31no—
101C2×#389—32no—
102C42×D4—31no—
103C22×C3×Q8C2312yes—
104C2×#239—28no—
105C2×#239—28no—
106C2×#239C2×C4116yescomplemented
107C22×D12C2314yes—
108C22×D12C2311yescharacteristic
109C22×D12C2311yescharacteristic
110C22×C4×D3C2312yes—
111C22×C4×D3C2314yes—
112C22×C4×D3C2312yes—
113C22×C4×D3C2312yes—
114C22×C4×D3C2314yes—
115C22×C4×D3C2314yes—
116C22×C4×D3C2312yes—
117C3×C4⋊Q8C2×C418yescomplemented
118C3×C4×Q8—28no—
119C2×C3×C4⋊C4C2312yes—
120C2×C3×C4⋊C4C2312yes—
121C2×C3×C4⋊C4C2314yes—
122C2×C3×C4⋊C4C2312yes—
123C2×C3×C4⋊C4C2312yes—
124C2×C3×C4⋊C4C2312yes—
125C2×C3×C42C2311yescharacteristic
126C2×C3×C42C2311yescharacteristic
127C2×C3×C42C2314yes—
128C2×C3×C42C2311yescharacteristic
129C2×C3×C42C2311yescharacteristic
130C2×C3×C42C2311yescharacteristic
131C2×C3×C42C2311yescharacteristic
132C2×C3×C42C2311yescharacteristic
133#946C2×C4116yescomplemented
134Q8×Dic3—28no—
135C2×(C2×D3)⋊C4C2312yes—
136C2×(C2×D3)⋊C4C2314yes—
137C2×(C2×D3)⋊C4C2312yes—
138C2×(C2×D3)⋊C4C2312yes—
139C2×(C2×D3)⋊C4C2312yes—
140C2×(C2×D3)⋊C4C2312yes—
141C2×(C2×D3)⋊C4C2314yes—
142C2×(C2×D3)⋊C4C2314yes—
143C2×(C2×D3)⋊C4C2312yes—
144C2×(C2×D3)⋊C4C2312yes—
145C2×(C2×D3)⋊C4C2312yes—
146C2×C4⋊Dic3C2314yes—
147C2×C4⋊Dic3C2311yescharacteristic
148C2×C4⋊Dic3C2311yescharacteristic
149C2×C4⋊Dic3C2311yescharacteristic
150C2×C4⋊Dic3C2311yescharacteristic
151C2×C4⋊Dic3C2311yescharacteristic
152C2×C4⋊Dic3C2311yescharacteristic
153C2×Dic3⋊C4C2314yes—
154C2×Dic3⋊C4C2312yes—
155C2×Dic3⋊C4C2312yes—
156C2×Dic3⋊C4C2314yes—
157C2×Dic3⋊C4C2314yes—
158C2×C4×Dic3C2314yes—
159C2×C4×Dic3C2312yes—
160C2×C4×Dic3C2312yes—
161C2×C4×Dic3C2312yes—
162C2×C4×Dic3C2312yes—
163#895C2×C4116yescomplemented
164#894C2×C4132yescomplemented
165#893—28no—
166#893—216no—
167#893—44no—
168D3×C4⋊C4—216no—
169D3×C4⋊C4—28no—
170D3×C4⋊C4—44no—
171D3×C4⋊C4C2×C4116yescomplemented
172C4×D12—24no—
173C4×D12—216no—
174C4×D12C2×C418yescomplemented
175C4×D12C2×C418yescomplemented
176C4×D12D418yescomplemented
177#872—28no—
178#872—216no—
179C42×D3—44no—
180C3×#95C2314yes—
181C3×#95C2314yes—
182C3⋊#95C2312yes—
183C3⋊#95C2312yes—
184C3⋊#95C2312yes—
185C3⋊#95C2314yes—
186C3⋊#95C2314yes—
187C3⋊#95C2314yes—
188C3⋊#95C2314yes—
189C3⋊#95C2312yes—
190C3⋊#95C2312yes—
191C3⋊#95C2312yes—
192C22×#41—32no—
193#547—316no—
194C2×C4⋊Q8C2×D311yescharacteristic
195C2×#123—34no—
196C2×C22⋊Q8—32no—
197C2×#121—32no—
198#520—616no—
199C2×C4×Q8—32no—
200C2×C4×Q8C2×D312yes—
201C2×C4×D4—34no—
202C2×C4×D4—32no—
203C2×C4×D4—32no—
204C2×C4×D4—31no—
205C2×C4×D4—31no—
206C2×C4×D4—31no—
207C2×C4×D4—31no—
208C2×C4×D4—34no—
209C2×#117—32no—
210C2×#117—34no—
211C22×C4⋊C4—32no—
212C22×C4⋊C4—34no—
213C22×C4⋊C4—32no—
214C22×C4⋊C4—32no—
215C22×C42—32no—
216#391—32no—
217#391C2×D312yes—
218#390—31no—
219#390—31no—
220#389—34no—
221#389—32no—
222#389—32no—
223#389—32no—
224#389—31no—
225#389—31no—
226#389—34no—
227#389C2×D312yes—
228#389C2×D312yes—
229#388—34no—
230#388—32no—
231#388—34no—
232#388—32no—
233#387—34no—
234#387—34no—
235#387—34no—
236#386—34no—
237#386—34no—
238#385—34no—
239#385—34no—
240#385—34no—
241#384C2×D311yescharacteristic
242#381—34no—
243#380—32no—
244#380—32no—
245C4×C4⋊C4—32no—
246C4×C4⋊C4—31no—
247C4×C4⋊C4—31no—
248C4×C4⋊C4—31no—
249C4×C4⋊C4—31no—
250C4×C4⋊C4C2×D312yes—
251C4×C4⋊C4C2×D312yes—
252C4×C22⋊C4—32no—
253C4×C22⋊C4—32no—
254C4×C22⋊C4—32no—
255C4×C22⋊C4—32no—
256C4×C22⋊C4—34no—
257C2×#95—34no—
258C43C2×D311yescharacteristic
259C23×D3C2412yes—
260C23×D3C2412yes—
261C2×C3×Q8—24no—
262C2×C3×Q8—24no—
263C2×C3×Q8C22×C418yes—
264C22×C3×C4C2411yescharacteristic
265C22×C3×C4C2414yes—
266C22×C3×C4C2411yescharacteristic
267C22×C3×C4C2414yes—
268C22×C3×C4C2411yescharacteristic
269C22×C3×C4C2411yescharacteristic
270C22×C3×C4C2411yescharacteristic
271C22×C3×C4C2411yescharacteristic
272C22×C3×C4C2411yescharacteristic
273C22×Dic3C2412yes—
274C22×Dic3C2412yes—
275C22×Dic3C2412yes—
276C22×Dic3C2412yes—
277C22×Dic3C2412yes—
278C22×Dic3C2412yes—
279#239—264no—
280C2×D12—28no—
281C2×D12—28no—
282C2×D12—22no—
283C2×D12—22no—
284C2×D12C22×C414yes—
285C2×D12C22×C4116yes—
286C2×D12C22×C414yes—
287C2×D12C2×D414yes—
288C2×D12#4114yes—
289C2×C4×D3—28no—
290C2×C4×D3—28no—
291C2×C4×D3—24no—
292C2×C4×D3—24no—
293C2×C4×D3—24no—
294C2×C4×D3—24no—
295C2×C4×D3—24no—
296C2×C4×D3—24no—
297C2×C4×D3—28no—
298C2×C4×D3—28no—
299C2×C4×D3—42no—
300C2×C4×D3—42no—
301C2×C4×D3—42no—
302C2×C4×D3—44no—
303C2×C4×D3—44no—
304C2×C4×D3—44no—
305C2×C4×D3—44no—
306C2×C4×D3C22×C418yes—
307C2×C4×D3C22×C418yes—
308C2×C4×D3C22×C4116yes—
309C2×C4×D3C2×D418yes—
310C3×C4⋊C4—28no—
311C3×C4⋊C4—24no—
312C3×C4⋊C4—24no—
313C3×C4⋊C4—42no—
314C3×C4⋊C4C22×C418yes—
315C3×C4⋊C4C22×C418yes—
316C3×C42—28no—
317C3×C42—22no—
318C3×C42—22no—
319C3×C42—22no—
320C3×C42—22no—
321C3×C42—41no—
322C3×C42C22×C414yes—
323C3×C42C2×D414yes—
324(C2×D3)⋊C4—28no—
325(C2×D3)⋊C4—24no—
326(C2×D3)⋊C4—24no—
327(C2×D3)⋊C4—24no—
328(C2×D3)⋊C4—24no—
329(C2×D3)⋊C4—44no—
330(C2×D3)⋊C4—42no—
331(C2×D3)⋊C4C22×C418yes—
332(C2×D3)⋊C4C22×C418yes—
333(C2×D3)⋊C4C22×C4116yes—
334(C2×D3)⋊C4C2×D418yes—
335C4⋊Dic3—22no—
336C4⋊Dic3—22no—
337C4⋊Dic3—22no—
338C4⋊Dic3—28no—
339C4⋊Dic3C22×C414yes—
340C4⋊Dic3C22×C414yes—
341C4⋊Dic3C2×D414yes—
342Dic3⋊C4—24no—
343Dic3⋊C4—24no—
344Dic3⋊C4—28no—
345Dic3⋊C4—44no—
346Dic3⋊C4C22×C4116yes—
347C4×Dic3—24no—
348C4×Dic3—24no—
349C4×Dic3—28no—
350C4×Dic3—42no—
351C4×Dic3—42no—
352C2×#41—316no—
353C2×#41—68no—
354C2×#41—68no—
355C22×Q8C22×D312yes—
356C22×D4—31no—
357C22×D4—31no—
358C22×D4—34no—
359C23×C4—34no—
360C23×C4—32no—
361C23×C4—32no—
362C23×C4—32no—
363C23×C4—32no—
364C23×C4—34no—
365C23×C4—34no—
366C4⋊Q8C4×D318yescomplemented
367#123—332no—
368C22⋊Q8—316no—
369#121—316no—
370C4×Q8—28no—
371C4×Q8—68no—
372C4×D4—38no—
373C4×D4—38no—
374C4×D4—38no—
375C4×D4—616no—
376C4×D4—64no—
377C4×D4—616no—
378C4×D4—68no—
379C4×D4—124no—
380#117—616no—
381#117—68no—
382C2×C4⋊C4—31no—
383C2×C4⋊C4—31no—
384C2×C4⋊C4—34no—
385C2×C4⋊C4—31no—
386C2×C4⋊C4—316no—
387C2×C4⋊C4—34no—
388C2×C4⋊C4—32no—
389C2×C4⋊C4—31no—
390C2×C4⋊C4—34no—
391C2×C4⋊C4—32no—
392C2×C4⋊C4—31no—
393C2×C4⋊C4—31no—
394C2×C4⋊C4—34no—
395C2×C4⋊C4—68no—
396C2×C4⋊C4—616no—
397C2×C4⋊C4—124no—
398C2×C4⋊C4C22×D312yes—
399C2×C4⋊C4C22×D314yes—
400C2×C4⋊C4C22×D312yes—
401C2×C4⋊C4C22×D312yes—
402C2×C4⋊C4C22×D312yes—
403C2×C4⋊C4C22×D312yes—
404C2×C22⋊C4—32no—
405C2×C22⋊C4—32no—
406C2×C22⋊C4—32no—
407C2×C22⋊C4—34no—
408C2×C22⋊C4—34no—
409C2×C22⋊C4—32no—
410C2×C22⋊C4—32no—
411C2×C22⋊C4—32no—
412C2×C22⋊C4—32no—
413C2×C22⋊C4—34no—
414C2×C22⋊C4—32no—
415C2×C42—34no—
416C2×C42—32no—
417C2×C42—32no—
418C2×C42—32no—
419C2×C42—32no—
420C2×C42—124no—
421C2×C42C22×D314yes—
422C2×C42C22×D311yescharacteristic
423C2×C42C22×D311yescharacteristic
424C2×C42C22×D311yescharacteristic
425C2×C42C22×D311yescharacteristic
426C2×C42C22×D311yescharacteristic
427C2×C42C22×D311yescharacteristic
428C2×C42C22×D311yescharacteristic
429#95—32no—
430#95—34no—
431#95—34no—
432#95—32no—
433#95—32no—
434#95—32no—
435#95—34no—
436#95—32no—
437#95—34no—
438#95—32no—
439#95C22×D314yes—
440#95C22×D314yes—
441C23×C3C2511yescharacteristic
442C22×D3—22no—
443C22×D3—22no—
444C22×D3—22no—
445C22×D3—22no—
446C22×D3—22no—
447C22×D3—22no—
448C22×D3—22no—
449C22×D3—22no—
450C22×D3—22no—
451C22×D3—22no—
452C22×D3C23×C414yes—
453C22×D3C23×C414yes—
454C22×D3C22×D414yes—
455C22×D3C2×#4114yes—
456C3×Q8—216no—
457C2×C3×C4—24no—
458C2×C3×C4—21no—
459C2×C3×C4—24no—
460C2×C3×C4—21no—
461C2×C3×C4—21no—
462C2×C3×C4—21no—
463C2×C3×C4—21no—
464C2×C3×C4—21no—
465C2×C3×C4—21no—
466C2×C3×C4—21no—
467C2×C3×C4—24no—
468C2×C3×C4—21no—
469C2×C3×C4—24no—
470C2×C3×C4—21no—
471C2×C3×C4—21no—
472C2×C3×C4—24no—
473C2×C3×C4C23×C418yes—
474C2×C3×C4C23×C412yes—
475C2×C3×C4C23×C412yes—
476C2×C3×C4C23×C412yes—
477C2×C3×C4C22×D412yes—
478C2×C3×C4C22×D412yes—
479C2×C3×C4C22×D412yes—
480C2×C3×C4C2×#4112yes—
481C2×C3×C4H(5,𝔽2)12yes—
482C2×C3×C42−1+412yes—
483C2×C3×C42−1+412yes—
484C2×Dic3—22no—
485C2×Dic3—22no—
486C2×Dic3—22no—
487C2×Dic3—22no—
488C2×Dic3—22no—
489C2×Dic3—22no—
490C2×Dic3—22no—
491C2×Dic3—22no—
492C2×Dic3—22no—
493C2×Dic3—22no—
494C2×Dic3—22no—
495C2×Dic3—22no—
496C2×Dic3—22no—
497C2×Dic3—22no—
498C2×Dic3—22no—
499C2×Dic3C23×C414yes—
500C2×Dic3C23×C414yes—
501C2×Dic3C22×D414yes—
502D12—232no—
503D12—28no—
504D12C4×D4116yescomplemented
505C4×D3—232no—
506C4×D3—216no—
507C4×D3—216no—
508C4×D3—48no—
509C4×D3—48no—
510C4×D3—88no—
511C4×D3—88no—
512C24—32no—
513C24—32no—
514#41—664no—
515C2×Q8—24no—
516C2×Q8—24no—
517C2×Q8C2×C4×D318yes—
518C2×D4—34no—
519C2×D4—34no—
520C2×D4—316no—
521C2×D4—34no—
522C2×D4—34no—
523C2×D4—68no—
524C2×D4—68no—
525C2×D4—62no—
526C2×D4—62no—
527C22×C4—32no—
528C22×C4—32no—
529C22×C4—32no—
530C22×C4—38no—
531C22×C4—316no—
532C22×C4—38no—
533C22×C4—38no—
534C22×C4—32no—
535C22×C4—32no—
536C22×C4—32no—
537C22×C4—68no—
538C22×C4—68no—
539C22×C4—68no—
540C22×C4—64no—
541C22×C4—68no—
542C22×C4—64no—
543C22×C4—64no—
544C22×C4—64no—
545C22×C4—64no—
546C22×C4—64no—
547C22×C4—122no—
548C22×C4—122no—
549C22×C4—122no—
550C22×C4—124no—
551C22×C4—124no—
552C22×C4—124no—
553C22×C4—124no—
554C22×C4C23×D311yescharacteristic
555C22×C4C23×D314yes—
556C22×C4C23×D311yescharacteristic
557C22×C4C23×D314yes—
558C22×C4C23×D311yescharacteristic
559C22×C4C23×D311yescharacteristic
560C22×C4C23×D311yescharacteristic
561C22×C4C23×D311yescharacteristic
562C22×C4C23×D311yescharacteristic
563C4⋊C4—28no—
564C4⋊C4—24no—
565C4⋊C4—24no—
566C4⋊C4—34no—
567C4⋊C4—316no—
568C4⋊C4—34no—
569C4⋊C4—34no—
570C4⋊C4—42no—
571C4⋊C4—68no—
572C4⋊C4—68no—
573C4⋊C4—64no—
574C4⋊C4—64no—
575C4⋊C4—62no—
576C4⋊C4—62no—
577C4⋊C4—62no—
578C4⋊C4—124no—
579C4⋊C4C2×C4×D318yes—
580C4⋊C4C2×C4×D318yes—
581C22⋊C4—38no—
582C22⋊C4—38no—
583C22⋊C4—316no—
584C22⋊C4—38no—
585C22⋊C4—68no—
586C22⋊C4—64no—
587C22⋊C4—64no—
588C22⋊C4—64no—
589C22⋊C4—64no—
590C22⋊C4—124no—
591C22⋊C4—122no—
592C42—28no—
593C42—22no—
594C42—22no—
595C42—22no—
596C42—22no—
597C42—41no—
598C42—68no—
599C42—64no—
600C42—64no—
601C42—122no—
602C42—122no—
603C42C2×C4×D314yes—
604C42D3×D414yes—
605C22×C3C24×C411yescharacteristic
606C22×C3C23×D411yescharacteristic
607C22×C3C22×#4111yescharacteristic
608C22×C3C2×H(5,𝔽2)11yescharacteristic
609C22×C3C2×2−1+411yescharacteristic
610C22×C3C2×2−1+411yescharacteristic
611C22×C3#58511yescharacteristic
612C2×D3—24no—
613C2×D3—24no—
614C2×D3—24no—
615C2×D3—24no—
616C2×D3—24no—
617C2×D3—24no—
618C2×D3—24no—
619C2×D3—24no—
620C2×D3—24no—
621C2×D3—42no—
622C2×D3—42no—
623C2×D3—42no—
624C2×D3—42no—
625C2×D3C2×C4×D418yes—
626C3×C4—28no—
627C3×C4—22no—
628C3×C4—22no—
629C3×C4—22no—
630C3×C4—22no—
631C3×C4—44no—
632C3×C4—41no—
633C3×C4C2×C4×D414yes—
634C3×C4#52014yescomplemented
635Dic3—24no—
636Dic3—24no—
637Dic3—24no—
638Dic3—42no—
639Dic3—42no—
640Dic3—42no—
641C23—34no—
642C23—34no—
643C23—34no—
644C23—34no—
645C23—62no—
646C23—62no—
647C23—62no—
648C23—62no—
649C23—62no—
650C23—62no—
651C23—62no—
652C23—62no—
653C23—62no—
654C23—62no—
655C23C24×D311yescharacteristic
656Q8—216no—
657D4—316no—
658D4—632no—
659D4—68no—
660C2×C4—24no—
661C2×C4—21no—
662C2×C4—21no—
663C2×C4—21no—
664C2×C4—21no—
665C2×C4—24no—
666C2×C4—21no—
667C2×C4—21no—
668C2×C4—21no—
669C2×C4—21no—
670C2×C4—24no—
671C2×C4—21no—
672C2×C4—21no—
673C2×C4—24no—
674C2×C4—21no—
675C2×C4—24no—
676C2×C4—34no—
677C2×C4—34no—
678C2×C4—34no—
679C2×C4—632no—
680C2×C4—62no—
681C2×C4—62no—
682C2×C4—62no—
683C2×C4—62no—
684C2×C4—62no—
685C2×C4—62no—
686C2×C4—616no—
687C2×C4—616no—
688C2×C4—62no—
689C2×C4—62no—
690C2×C4—62no—
691C2×C4—62no—
692C2×C4—62no—
693C2×C4—62no—
694C2×C4—62no—
695C2×C4—62no—
696C2×C4—62no—
697C2×C4—128no—
698C2×C4—128no—
699C2×C4—248no—
700C2×C4—248no—
701C2×C4C22×C4×D312yes—
702C2×C4C22×C4×D318yes—
703C2×C4C22×C4×D312yes—
704C2×C4C22×C4×D312yes—
705C2×C4C2×D3×D412yes—
706C2×C4C2×D3×D412yes—
707C2×C4C2×D3×D412yes—
708C2×C4#100712yes—
709C2×C4#100712yes—
710C2×C4D3×#4112yes—
711C2×C4#100912yes—
712C2×C3C22×C4×D411yescharacteristic
713C2×C3C2×#52011yescharacteristic
714C2×C3C4×2−1+411yescharacteristic
715C2×C3#349611yescharacteristic
716C2×C3#349911yescharacteristic
717C2×C3#351511yescharacteristic
718C2×C3#352011yescharacteristic
719D3—28no—
720D3—44no—
721C22—38no—
722C22—64no—
723C22—64no—
724C22—64no—
725C22—64no—
726C22—64no—
727C22—64no—
728C22—64no—
729C22—64no—
730C22—64no—
731C22—122no—
732C22—122no—
733C22—122no—
734C22—122no—
735C22C23×C4×D311yescharacteristic
736C22C22×D3×D411yescharacteristic
737C22C2×#100711yescharacteristic
738C22C2×#100711yescharacteristic
739C22C2×D3×#4111yescharacteristic
740C22C2×#100911yescharacteristic
741C22#596411yescharacteristic
742C4—28no—
743C4—22no—
744C4—22no—
745C4—22no—
746C4—22no—
747C4—41no—
748C4—44no—
749C4—64no—
750C4—64no—
751C4—64no—
752C4—122no—
753C4—122no—
754C4—122no—
755C4C4×D3×D414yes—
756C4#557414yescomplemented
757C3#3430811yescharacteristic, complemented, Sylow
758C2—68no—
759C2—124no—
760C2C2×C4×D3×D411yescharacteristic
761C2C2×#557411yescharacteristic
762C2C4×#100711yescharacteristic
763C2#8621411yescharacteristic
764C2#8624111yescharacteristic
765C2#8628411yescharacteristic
766C2#8628511yescharacteristic
subgroupG/H
center, FrattiniC23C24×D3
commutatorC22×C3C24×C4
FittingC3×C4×C4⋊Q8C2
socle, cosocleC23×C3C25
prime radicalC2×#5726C2
hypercenterC4×C4⋊Q8D3
hypocenterC3#34308
LCSG ▷ C22×C3 ▷ C3
UCSC1 ◁ C23 ◁ C4×C4⋊Q8

Complements

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

NH ≅ G/Ntype
2. C2×#5574C2semidirect
3. C3×C4×C4⋊Q8C2semidirect
4. #83229C2semidirect
5. #82488C2semidirect
6. #76615C2semidirect
7. #76613C2semidirect
8. #76196C2semidirect
9. D3×#389C2semidirect
10. #75964C2semidirect
11. #74360C2semidirect
12. #74360C2semidirect
13. #73774C2semidirect
14. #73772C2semidirect
15. #73767C2semidirect
16. #73299C2semidirect
17. C42×D12C2semidirect
24. #5726C4semidirect
98. C4×C4⋊Q8D3semidirect
106. C2×#239C2×C4semidirect
117. C3×C4⋊Q8C2×C4semidirect
133. #946C2×C4semidirect
163. #895C2×C4semidirect
164. #894C2×C4semidirect
171. D3×C4⋊C4C2×C4semidirect
174. C4×D12C2×C4semidirect
175. C4×D12C2×C4semidirect
176. C4×D12D4semidirect
366. C4⋊Q8C4×D3semidirect
504. D12C4×D4semidirect
634. C3×C4#520semidirect
756. C4#5574semidirect
757. C3#34308semidirect

Maximal subgroups

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

subgroupindex
C2×#57262
C2×#55742
C3×C4×C4⋊Q82
#832292
#824882
#766152
#766132
#761962
D3×#3892
#759642
#743602
#737742
#737722
#737672
#732992
C42×D122
#343083