Finite Group Databasebeta

← #10957204

Subgroups — #10957204

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×#5555C211yesmaximal, characteristic
2C2×#5546C212yesmaximal, complemented
3C3×C42×D4C211yesmaximal, characteristic, complemented
4D4×C4⋊Dic3C211yesmaximal, characteristic, complemented
5#82330C212yesmaximal, complemented
6C4×#930C212yesmaximal, complemented
7C2×#4928C212yesmaximal, complemented
8#73773C212yesmaximal, complemented
9C4⋊C4×D12C211yesmaximal, characteristic, complemented
10#73762C212yesmaximal, complemented
11#73650C211yesmaximal, characteristic, complemented
12#73467C212yesmaximal, complemented
13#73464C214yesmaximal, complemented
14#73456C212yesmaximal, complemented
15#73446C214yesmaximal, complemented
16C4×#869C211yesmaximal, characteristic, complemented
17#73299C211yesmaximal, characteristic, complemented
18#34308—31nomaximal, Sylow
19C22×#237C2212yes—
20C2×C3×C4×D4C2211yescharacteristic
21C2×C3×C4×D4C2211yescharacteristic
22C2×C3×C4×D4C2211yescharacteristic
23C22×C3×C42C2212yes—
24C2×D4×Dic3C2212yes—
25C2×#930C2212yes—
26C2×C4×#67C2214yes—
27C22×C4⋊Dic3C2212yes—
28C22×C4⋊Dic3C2212yes—
29C22×Dic3⋊C4C2214yes—
30#5555C4116yescomplemented
31#5546—216no—
32C2×#897C2212yes—
33C2×D3×C4⋊C4C2212yes—
34C2×#887C2212yes—
35C2×#886C2214yes—
36C2×#67⋊C4C2214yes—
37C2×#877C2214yes—
38C2×C4×D12C2212yes—
39C2×C4×D12C2211yescharacteristic
40C2×#872C2212yes—
41C2×#869C2211yescharacteristic
42C2×C4×Dic6C2212yes—
43C3×C4×C4⋊C4C2211yescharacteristic
44C3×C4×C4⋊C4C2211yescharacteristic
45C3×C4×C4⋊C4C2211yescharacteristic
46C3×C4×C22⋊C4C2212yes—
47C3×C4×C22⋊C4C2212yes—
48C3×C4×C22⋊C4C2212yes—
49C3×C43C2211yescharacteristic
50#5213C2214yes—
51#5212C2212yes—
52C2×C3⋊#95C2214yes—
53#4987C2212yes—
54#4984C2212yes—
55#4973C2212yes—
56#4958C2214yes—
57#4950C2214yes—
58#4943C2214yes—
59#4940C2214yes—
60#4940C2212yes—
61#4940C2212yes—
62#4939C2211yescharacteristic
63#4939C2211yescharacteristic
64C4×(C2×D3)⋊C4C2212yes—
65C4×(C2×D3)⋊C4C2214yes—
66#4935C2211yescharacteristic
67C4×C4⋊Dic3C2211yescharacteristic
68C4×C4⋊Dic3C2212yes—
69C4×C4⋊Dic3C2212yes—
70C4×C4⋊Dic3C2212yes—
71#4929C2212yes—
72#4928C2214yes—
73#4928C2212yes—
74#4928C2214yes—
75#4928C2211yescharacteristic
76#4928C2211yescharacteristic
77#4928C2212yes—
78#4928C2212yes—
79#4928C2212yes—
80#4670C2214yes—
81#4668C2214yes—
82#4668C2214yes—
83#4653C2214yes—
84#4653C2214yes—
85#4653C2214yes—
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⋊Q8—31no—
99C4×#121—32no—
100#2293—31no—
101C2×#389—32no—
102C42×D4D311yescharacteristic, complemented
103C22×C3×D4C2311yescharacteristic
104C23×C3×C4C2312yes—
105C23×C3×C4C2312yes—
106C23×C3×C4C2312yes—
107C22×#67C2314yes—
108C23×Dic3C2314yes—
109C23×Dic3C2314yes—
110C2×#237—28no—
111C2×#237—28no—
112C2×#237C2×C4116yescomplemented
113C22×D12C2311yescharacteristic
114C22×C4×D3C2312yes—
115C22×C4×D3C2314yes—
116C22×Dic6C2312yes—
117C3×C4×D4—24no—
118C3×C4×D4C2×C418yescomplemented
119C3×C4×D4D418yescomplemented
120C2×C3×C4⋊C4C2311yescharacteristic
121C2×C3×C4⋊C4C2311yescharacteristic
122C2×C3×C4⋊C4C2311yescharacteristic
123C2×C3×C22⋊C4C2312yes—
124C2×C3×C22⋊C4C2312yes—
125C2×C3×C22⋊C4C2312yes—
126C2×C3×C42—44no—
127C2×C3×C42C2311yescharacteristic
128C2×C3×C42C2312yes—
129C2×C3×C42C2311yescharacteristic
130C2×C3×C42C2311yescharacteristic
131C2×C3×C42C2311yescharacteristic
132C2×C3×C42C2312yes—
133C2×C3×C42C2311yescharacteristic
134C2×C3×C42C2312yes—
135C2×C3×C42C2311yescharacteristic
136C2×C3×C42C2311yescharacteristic
137C2×#217C2314yes—
138D4×Dic3—28no—
139#930C2×C4116yescomplemented
140C4×#67—216no—
141C2×(C2×D3)⋊C4C2312yes—
142C2×(C2×D3)⋊C4C2312yes—
143C2×(C2×D3)⋊C4C2312yes—
144C2×(C2×D3)⋊C4C2312yes—
145C2×(C2×D3)⋊C4C2314yes—
146C2×(C2×D3)⋊C4C2312yes—
147C2×(C2×D3)⋊C4C2314yes—
148C2×C4⋊Dic3—44no—
149C2×C4⋊Dic3C2×C4116yescomplemented
150C2×C4⋊Dic3C2311yescharacteristic
151C2×C4⋊Dic3C2312yes—
152C2×C4⋊Dic3C2311yescharacteristic
153C2×C4⋊Dic3C2312yes—
154C2×C4⋊Dic3C2312yes—
155C2×C4⋊Dic3C2314yes—
156C2×C4⋊Dic3C2314yes—
157C2×C4⋊Dic3C2312yes—
158C2×C4⋊Dic3C2311yescharacteristic
159C2×C4⋊Dic3C2312yes—
160C2×Dic3⋊C4—216no—
161C2×Dic3⋊C4C2312yes—
162C2×Dic3⋊C4C2314yes—
163C2×Dic3⋊C4C2314yes—
164C2×Dic3⋊C4C2314yes—
165C2×Dic3⋊C4C2312yes—
166C2×C4×Dic3C2314yes—
167C2×C4×Dic3C2314yes—
168C2×C4×Dic3C2312yes—
169#897C2×C4116yescomplemented
170D3×C4⋊C4—28no—
171#887—28no—
172#886C2×C4132yescomplemented
173#67⋊C4—216no—
174#877—216no—
175C4×D12—44no—
176C4×D12C2×C418yescomplemented
177#872—28no—
178#869C2×C418yescomplemented
179C4×Dic6—28no—
180C3×#95C2312yes—
181C3×#95C2312yes—
182C3×#95C2312yes—
183C3⋊#95C2312yes—
184C3⋊#95C2312yes—
185C3⋊#95C2314yes—
186C3⋊#95C2314yes—
187C3⋊#95C2314yes—
188C3⋊#95C2314yes—
189C3⋊#95C2314yes—
190C3⋊#95C2312yes—
191C3⋊#95C2314yes—
192C22×#41—32no—
193#547—316no—
194C2×C4⋊Q8—31no—
195C2×#123—34no—
196C2×C22⋊Q8—32no—
197C2×#121—32no—
198#520—616no—
199C2×C4×Q8—32no—
200C2×C4×Q8—32no—
201C2×C4×D4—32no—
202C2×C4×D4—34no—
203C2×C4×D4—34no—
204C2×C4×D4—31no—
205C2×C4×D4—32no—
206C2×C4×D4C2×D311yescharacteristic
207C2×C4×D4C2×D311yescharacteristic
208C2×C4×D4C2×D311yescharacteristic
209C2×#117—34no—
210C2×#117—32no—
211C22×C4⋊C4—32no—
212C22×C4⋊C4—34no—
213C22×C4⋊C4—32no—
214C22×C4⋊C4—32no—
215C22×C42C2×D312yes—
216#391—32no—
217#391—32no—
218#390—31no—
219#390—31no—
220#389—32no—
221#389—32no—
222#389—32no—
223#389—34no—
224#389—31no—
225#389—32no—
226#389—34no—
227#389—32no—
228#389—31no—
229#388—32no—
230#388—34no—
231#388—32no—
232#388—34no—
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#384—31no—
242#381—34no—
243#380—32no—
244#380—32no—
245C4×C4⋊C4—32no—
246C4×C4⋊C4—32no—
247C4×C4⋊C4—32no—
248C4×C4⋊C4—31no—
249C4×C4⋊C4C2×D311yescharacteristic
250C4×C4⋊C4C2×D311yescharacteristic
251C4×C4⋊C4C2×D311yescharacteristic
252C4×C22⋊C4—32no—
253C4×C22⋊C4—34no—
254C4×C22⋊C4C2×D312yes—
255C4×C22⋊C4C2×D312yes—
256C4×C22⋊C4C2×D312yes—
257C2×#95—34no—
258C43C2×D311yescharacteristic
259C24×C3C2412yes—
260C23×D3C2412yes—
261C2×C3×D4C22×C414yes—
262C2×C3×D4C2×D414yes—
263C2×C3×D4#4114yes—
264C22×C3×C4—24no—
265C22×C3×C4—24no—
266C22×C3×C4—24no—
267C22×C3×C4—24no—
268C22×C3×C4—42no—
269C22×C3×C4—42no—
270C22×C3×C4—42no—
271C22×C3×C4C22×C418yes—
272C22×C3×C4C2×D418yes—
273C22×C3×C4C2411yescharacteristic
274C22×C3×C4C2412yes—
275C22×C3×C4C2411yescharacteristic
276C22×C3×C4C2412yes—
277C22×C3×C4C2411yescharacteristic
278C22×C3×C4C2412yes—
279C22×C3×C4C2411yescharacteristic
280C22×C3×C4C2411yescharacteristic
281C22×C3×C4C2411yescharacteristic
282C22×C3×C4C2411yescharacteristic
283C2×#67—28no—
284C2×#67—28no—
285C2×#67C22×C4116yes—
286C22×Dic3—28no—
287C22×Dic3—28no—
288C22×Dic3—28no—
289C22×Dic3—44no—
290C22×Dic3—44no—
291C22×Dic3C22×C4116yes—
292C22×Dic3C2412yes—
293C22×Dic3C2412yes—
294C22×Dic3C2414yes—
295C22×Dic3C2414yes—
296C22×Dic3C2412yes—
297#237—264no—
298C2×D12—22no—
299C2×D12—22no—
300C2×D12C22×C414yes—
301C2×C4×D3—24no—
302C2×C4×D3—24no—
303C2×C4×D3—28no—
304C2×C4×D3—44no—
305C2×C4×D3—44no—
306C2×C4×D3C22×C418yes—
307C2×Dic6—24no—
308C2×Dic6—24no—
309C2×Dic6C22×C418yes—
310C3×C4⋊C4—22no—
311C3×C4⋊C4C22×C414yes—
312C3×C4⋊C4C2×D414yes—
313C3×C22⋊C4—24no—
314C3×C22⋊C4C22×C418yes—
315C3×C22⋊C4C2×D418yes—
316C3×C42—22no—
317C3×C42—24no—
318C3×C42—22no—
319C3×C42—22no—
320C3×C42—22no—
321C3×C42—42no—
322C3×C42—42no—
323C3×C42—41no—
324C3×C42C22×C414yes—
325C3×C42C2×D414yes—
326#217—28no—
327(C2×D3)⋊C4—24no—
328(C2×D3)⋊C4—24no—
329(C2×D3)⋊C4—24no—
330(C2×D3)⋊C4—44no—
331(C2×D3)⋊C4—42no—
332(C2×D3)⋊C4C22×C418yes—
333(C2×D3)⋊C4C22×C4116yes—
334C4⋊Dic3—24no—
335C4⋊Dic3—24no—
336C4⋊Dic3—22no—
337C4⋊Dic3—22no—
338C4⋊Dic3—44no—
339C4⋊Dic3—42no—
340C4⋊Dic3C22×C418yes—
341C4⋊Dic3C22×C418yes—
342C4⋊Dic3C22×C414yes—
343C4⋊Dic3C22×C4116yes—
344Dic3⋊C4—28no—
345Dic3⋊C4—24no—
346Dic3⋊C4—24no—
347Dic3⋊C4—28no—
348Dic3⋊C4—28no—
349C4×Dic3—28no—
350C4×Dic3—24no—
351C4×Dic3—28no—
352C2×#41—316no—
353C2×#41—68no—
354C2×#41—68no—
355C22×Q8—32no—
356C22×D4—34no—
357C22×D4—31no—
358C22×D4C22×D311yescharacteristic
359C23×C4—34no—
360C23×C4—32no—
361C23×C4—34no—
362C23×C4—34no—
363C23×C4C22×D312yes—
364C23×C4C22×D312yes—
365C23×C4C22×D312yes—
366C4⋊Q8—38no—
367#123—332no—
368C22⋊Q8—316no—
369#121—316no—
370C4×Q8—68no—
371C4×Q8—68no—
372C4×D4—24no—
373C4×D4—38no—
374C4×D4—68no—
375C4×D4—616no—
376C4×D4—616no—
377C4×D4—124no—
378C4×D4C4×D318yescomplemented
379C4×D4D1218yescomplemented
380#117—616no—
381#117—68no—
382C2×C4⋊C4—316no—
383C2×C4⋊C4—31no—
384C2×C4⋊C4—32no—
385C2×C4⋊C4—34no—
386C2×C4⋊C4—32no—
387C2×C4⋊C4—34no—
388C2×C4⋊C4—32no—
389C2×C4⋊C4—31no—
390C2×C4⋊C4—32no—
391C2×C4⋊C4—34no—
392C2×C4⋊C4—34no—
393C2×C4⋊C4—32no—
394C2×C4⋊C4—32no—
395C2×C4⋊C4—31no—
396C2×C4⋊C4—34no—
397C2×C4⋊C4—32no—
398C2×C4⋊C4—616no—
399C2×C4⋊C4—68no—
400C2×C4⋊C4—124no—
401C2×C4⋊C4C22×D311yescharacteristic
402C2×C4⋊C4C22×D311yescharacteristic
403C2×C4⋊C4C22×D311yescharacteristic
404C2×C22⋊C4—32no—
405C2×C22⋊C4—34no—
406C2×C22⋊C4—34no—
407C2×C22⋊C4—32no—
408C2×C22⋊C4—32no—
409C2×C22⋊C4—32no—
410C2×C22⋊C4—34no—
411C2×C22⋊C4—32no—
412C2×C22⋊C4C22×D312yes—
413C2×C22⋊C4C22×D312yes—
414C2×C22⋊C4C22×D312yes—
415C2×C42—34no—
416C2×C42—32no—
417C2×C42—34no—
418C2×C42—44no—
419C2×C42C22×D312yes—
420C2×C42C22×D311yescharacteristic
421C2×C42C22×D311yescharacteristic
422C2×C42C22×D311yescharacteristic
423C2×C42C22×D311yescharacteristic
424C2×C42C22×D311yescharacteristic
425C2×C42C22×D312yes—
426C2×C42C22×D312yes—
427C2×C42C22×D311yescharacteristic
428C2×C42C22×D311yescharacteristic
429#95—32no—
430#95—34no—
431#95—34no—
432#95—34no—
433#95—34no—
434#95—32no—
435#95—34no—
436#95—34no—
437#95—32no—
438#95C22×D312yes—
439#95C22×D312yes—
440#95C22×D312yes—
441C23×C3—22no—
442C23×C3—22no—
443C23×C3—22no—
444C23×C3—22no—
445C23×C3C23×C414yes—
446C23×C3C22×D414yes—
447C23×C3C2×#4114yes—
448C23×C3C2511yescharacteristic
449C22×D3—22no—
450C22×D3—22no—
451C22×D3—22no—
452C22×D3—22no—
453C22×D3—22no—
454C22×D3—22no—
455C22×D3C23×C414yes—
456C3×D4C4×D4116yescomplemented
457C2×C3×C4—21no—
458C2×C3×C4—22no—
459C2×C3×C4—21no—
460C2×C3×C4—21no—
461C2×C3×C4—22no—
462C2×C3×C4—21no—
463C2×C3×C4—21no—
464C2×C3×C4—21no—
465C2×C3×C4—22no—
466C2×C3×C4—21no—
467C2×C3×C4—21no—
468C2×C3×C4—22no—
469C2×C3×C4—216no—
470C2×C3×C4—21no—
471C2×C3×C4—22no—
472C2×C3×C4—22no—
473C2×C3×C4—21no—
474C2×C3×C4—22no—
475C2×C3×C4—21no—
476C2×C3×C4—48no—
477C2×C3×C4—48no—
478C2×C3×C4C23×C412yes—
479C2×C3×C4C23×C414yes—
480C2×C3×C4C23×C412yes—
481C2×C3×C4C23×C412yes—
482C2×C3×C4C22×D412yes—
483C2×C3×C4C22×D414yes—
484C2×C3×C4C22×D412yes—
485C2×C3×C4C22×D412yes—
486C2×C3×C4C2×#4112yes—
487C2×C3×C4H(5,𝔽2)12yes—
488C2×C3×C42−1+412yes—
489C2×C3×C42−1+412yes—
490#67—232no—
491C2×Dic3—232no—
492C2×Dic3—24no—
493C2×Dic3—22no—
494C2×Dic3—24no—
495C2×Dic3—22no—
496C2×Dic3—22no—
497C2×Dic3—22no—
498C2×Dic3—24no—
499C2×Dic3—22no—
500C2×Dic3—24no—
501C2×Dic3—22no—
502C2×Dic3—22no—
503C2×Dic3—24no—
504C2×Dic3—22no—
505C2×Dic3—88no—
506C2×Dic3C23×C418yes—
507C2×Dic3C23×C414yes—
508D12—28no—
509C4×D3—216no—
510C4×D3—88no—
511Dic6—216no—
512C24—32no—
513C24C23×D312yes—
514#41—664no—
515C2×Q8—38no—
516C2×Q8—64no—
517C2×Q8—64no—
518C2×D4—316no—
519C2×D4—34no—
520C2×D4—68no—
521C2×D4—68no—
522C2×D4—62no—
523C2×D4—62no—
524C2×D4C2×C4×D314yes—
525C2×D4C2×D1214yes—
526C2×D4#23514yes—
527C22×C4—24no—
528C22×C4—24no—
529C22×C4—24no—
530C22×C4—24no—
531C22×C4—316no—
532C22×C4—34no—
533C22×C4—32no—
534C22×C4—38no—
535C22×C4—32no—
536C22×C4—34no—
537C22×C4—32no—
538C22×C4—42no—
539C22×C4—42no—
540C22×C4—42no—
541C22×C4—68no—
542C22×C4—68no—
543C22×C4—64no—
544C22×C4—64no—
545C22×C4—68no—
546C22×C4—68no—
547C22×C4—124no—
548C22×C4—124no—
549C22×C4—124no—
550C22×C4—124no—
551C22×C4C2×C4×D318yes—
552C22×C4C2×D1218yes—
553C22×C4C23×D311yescharacteristic
554C22×C4C23×D312yes—
555C22×C4C23×D311yescharacteristic
556C22×C4C23×D312yes—
557C22×C4C23×D311yescharacteristic
558C22×C4C23×D312yes—
559C22×C4C23×D311yescharacteristic
560C22×C4C23×D311yescharacteristic
561C22×C4C23×D311yescharacteristic
562C22×C4C23×D311yescharacteristic
563C4⋊C4—22no—
564C4⋊C4—34no—
565C4⋊C4—38no—
566C4⋊C4—316no—
567C4⋊C4—38no—
568C4⋊C4—68no—
569C4⋊C4—64no—
570C4⋊C4—68no—
571C4⋊C4—68no—
572C4⋊C4—64no—
573C4⋊C4—64no—
574C4⋊C4—62no—
575C4⋊C4—64no—
576C4⋊C4—62no—
577C4⋊C4—124no—
578C4⋊C4—122no—
579C4⋊C4C2×C4×D314yes—
580C4⋊C4C2×D1214yes—
581C22⋊C4—24no—
582C22⋊C4—38no—
583C22⋊C4—316no—
584C22⋊C4—68no—
585C22⋊C4—64no—
586C22⋊C4—64no—
587C22⋊C4—64no—
588C22⋊C4—124no—
589C22⋊C4—122no—
590C22⋊C4C2×C4×D318yes—
591C22⋊C4C2×D1218yes—
592C42—22no—
593C42—22no—
594C42—24no—
595C42—22no—
596C42—22no—
597C42—42no—
598C42—42no—
599C42—41no—
600C42—68no—
601C42—68no—
602C42—64no—
603C42C2×C4×D314yes—
604C42C2×D1214yes—
605C22×C3—24no—
606C22×C3—24no—
607C22×C3—24no—
608C22×C3—24no—
609C22×C3—24no—
610C22×C3—24no—
611C22×C3C2×C4×D418yes—
612C22×C3C24×C411yescharacteristic
613C22×C3C23×D411yescharacteristic
614C22×C3C22×#4111yescharacteristic
615C22×C3C2×H(5,𝔽2)11yescharacteristic
616C22×C3C2×2−1+411yescharacteristic
617C22×C3C2×2−1+411yescharacteristic
618C22×C3#58511yescharacteristic
619C2×D3—24no—
620C2×D3—24no—
621C2×D3—24no—
622C2×D3—42no—
623C2×D3—42no—
624C2×D3—42no—
625C2×D3—42no—
626C3×C4—24no—
627C3×C4—22no—
628C3×C4—24no—
629C3×C4—22no—
630C3×C4—22no—
631C3×C4—22no—
632C3×C4—41no—
633C3×C4—42no—
634C3×C4C2×C4×D414yes—
635C3×C4#52014yescomplemented
636Dic3—28no—
637Dic3—24no—
638Dic3—44no—
639Dic3—42no—
640Dic3—42no—
641C23—22no—
642C23—22no—
643C23—22no—
644C23—22no—
645C23—34no—
646C23—62no—
647C23—62no—
648C23—62no—
649C23—62no—
650C23—62no—
651C23—62no—
652C23C22×C4×D314yes—
653C23C22×D1214yes—
654C23C2×#23514yes—
655C23C24×D311yescharacteristic
656Q8—616no—
657D4—632no—
658D4—68no—
659D4C4×D12116yescomplemented
660C2×C4—21no—
661C2×C4—21no—
662C2×C4—21no—
663C2×C4—22no—
664C2×C4—22no—
665C2×C4—21no—
666C2×C4—21no—
667C2×C4—21no—
668C2×C4—22no—
669C2×C4—21no—
670C2×C4—21no—
671C2×C4—22no—
672C2×C4—216no—
673C2×C4—21no—
674C2×C4—22no—
675C2×C4—22no—
676C2×C4—21no—
677C2×C4—22no—
678C2×C4—21no—
679C2×C4—34no—
680C2×C4—38no—
681C2×C4—48no—
682C2×C4—48no—
683C2×C4—64no—
684C2×C4—62no—
685C2×C4—62no—
686C2×C4—64no—
687C2×C4—632no—
688C2×C4—616no—
689C2×C4—62no—
690C2×C4—64no—
691C2×C4—62no—
692C2×C4—64no—
693C2×C4—62no—
694C2×C4—62no—
695C2×C4—62no—
696C2×C4—62no—
697C2×C4—64no—
698C2×C4—248no—
699C2×C4—248no—
700C2×C4C22×C4×D312yes—
701C2×C4C22×C4×D314yes—
702C2×C4C22×C4×D312yes—
703C2×C4C22×C4×D312yes—
704C2×C4C22×D1212yes—
705C2×C4C22×D1214yes—
706C2×C4C22×D1212yes—
707C2×C4C22×D1212yes—
708C2×C4C2×#23512yes—
709C2×C4#100412yes—
710C2×C4#101012yes—
711C2×C4#101012yes—
712C2×C3—28no—
713C2×C3C22×C4×D411yescharacteristic
714C2×C3C2×#52011yescharacteristic
715C2×C3C4×2−1+411yescharacteristic
716C2×C3#349611yescharacteristic
717C2×C3#349911yescharacteristic
718C2×C3#351511yescharacteristic
719C2×C3#352011yescharacteristic
720D3—44no—
721C22—24no—
722C22—24no—
723C22—24no—
724C22—24no—
725C22—24no—
726C22—24no—
727C22—64no—
728C22—64no—
729C22—64no—
730C22—122no—
731C22—122no—
732C22—122no—
733C22—122no—
734C22C2×C4×D1218yes—
735C22C23×C4×D311yescharacteristic
736C22C23×D1211yescharacteristic
737C22C22×#23511yescharacteristic
738C22C2×#100411yescharacteristic
739C22C2×#101011yescharacteristic
740C22C2×#101011yescharacteristic
741C22#596411yescharacteristic
742C4—22no—
743C4—22no—
744C4—24no—
745C4—22no—
746C4—22no—
747C4—24no—
748C4—42no—
749C4—41no—
750C4—64no—
751C4—68no—
752C4—124no—
753C4—122no—
754C4—122no—
755C4C2×C4×D1214yes—
756C4#554614yescomplemented
757C3#3430811yescharacteristic, complemented, Sylow
758C2—28no—
759C2—124no—
760C2C22×C4×D1211yescharacteristic
761C2C2×#554611yescharacteristic
762C2#8576711yescharacteristic
763C2#8578611yescharacteristic
764C2C4×#101011yescharacteristic
765C2#8582711yescharacteristic
766C2#8583111yescharacteristic
subgroupG/H
center, FrattiniC23C24×D3
commutatorC22×C3C24×C4
FittingC3×C42×D4C2
socle, cosocleC23×C3C25
prime radicalC2×#5555C2
hypercenterC42×D4D3
hypocenterC3#34308
LCSG ▷ C22×C3 ▷ C3
UCSC1 ◁ C23 ◁ C42×D4

Complements

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

NH ≅ G/Ntype
2. C2×#5546C2semidirect
3. C3×C42×D4C2semidirect
4. D4×C4⋊Dic3C2semidirect
5. #82330C2semidirect
6. C4×#930C2semidirect
7. C2×#4928C2semidirect
8. #73773C2semidirect
9. C4⋊C4×D12C2semidirect
10. #73762C2semidirect
11. #73650C2semidirect
12. #73467C2semidirect
13. #73464C2semidirect
14. #73456C2semidirect
15. #73446C2semidirect
16. C4×#869C2semidirect
17. #73299C2semidirect
30. #5555C4semidirect
102. C42×D4D3semidirect
112. C2×#237C2×C4semidirect
118. C3×C4×D4C2×C4semidirect
119. C3×C4×D4D4semidirect
139. #930C2×C4semidirect
149. C2×C4⋊Dic3C2×C4semidirect
169. #897C2×C4semidirect
172. #886C2×C4semidirect
176. C4×D12C2×C4semidirect
178. #869C2×C4semidirect
378. C4×D4C4×D3semidirect
379. C4×D4D12semidirect
456. C3×D4C4×D4semidirect
635. C3×C4#520semidirect
659. D4C4×D12semidirect
756. C4#5546semidirect
757. C3#34308semidirect

Maximal subgroups

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

subgroupindex
C2×#55552
C2×#55462
C3×C42×D42
D4×C4⋊Dic32
#823302
C4×#9302
C2×#49282
#737732
C4⋊C4×D122
#737622
#736502
#734672
#734642
#734562
#734462
C4×#8692
#732992
#343083