Finite Group Databasebeta

← C2×#79664 #11664948

Subgroups — C2×#79664 #11664948

Order 768.

2266 conjugacy classes of subgroups.

The subgroup lattice has 794 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#5580C211yesmaximal, characteristic, complemented
2C2×#5548C211yesmaximal, characteristic, complemented
3C2×C3×C4×SD16C211yesmaximal, characteristic, complemented
4C2×#5174C211yesmaximal, characteristic, complemented
5C2×#5176C211yesmaximal, characteristic, complemented
6C2×C4×#215C211yesmaximal, characteristic, complemented
7C2×C4×#213C211yesmaximal, characteristic, complemented
8#79664C2116yesmaximal, direct product factor
9C2×#4865C211yesmaximal, characteristic, complemented
10C2×#4856C211yesmaximal, characteristic, complemented
11C2×#4812C211yesmaximal, characteristic, complemented
12C2×#4794C211yesmaximal, characteristic, complemented
13C2×#4782C211yesmaximal, characteristic, complemented
14C2×#4764C211yesmaximal, characteristic, complemented
15C2×C4×D24C211yesmaximal, characteristic, complemented
16C2×C4×ΓL(1,𝔽25)C211yesmaximal, characteristic, complemented
17C2×#3171—31nomaximal, Sylow
18C22×#235—21no—
19C22×C3×SD16C2211yescharacteristic
20C2×C3×C4×Q8C2211yescharacteristic
21C2×C3×C4×D4C2211yescharacteristic
22C2×#947C2211yescharacteristic
23C2×#946C2211yescharacteristic
24C22×#215C2211yescharacteristic
25C2×#940C2211yescharacteristic
26C2×#938C2211yescharacteristic
27C22×#213C2211yescharacteristic
28C2×C4×#67—21no—
29C22×D24C2211yescharacteristic
30C22×ΓL(1,𝔽25)C2211yescharacteristic
31C22×ΓL(1,𝔽25)C2211yescharacteristic
32#5580—24no—
33#5580C2218yescomplemented
34#5548—24no—
35#5548C2218yescomplemented
36C2×#898—21no—
37C2×#895C2211yescharacteristic
38C2×#895C2211yescharacteristic
39C2×#894—21no—
40C2×#890C2211yescharacteristic
41C2×#888C2211yescharacteristic
42C2×#885—21no—
43C2×#884—21no—
44C2×C4×D12—21no—
45C2×C4×D12C2211yescharacteristic
46C2×C4×D12C2211yescharacteristic
47C2×#872—21no—
48C2×C42×D3C2211yescharacteristic
49C3×C4×SD16C2218yescomplemented
50C2×C3×#106C2211yescharacteristic
51C2×C3×#103C2211yescharacteristic
52C2×C3×#102C2211yescharacteristic
53C2×C3×C4×C8C2211yescharacteristic
54C2×#835C2211yescharacteristic
55C2×#832C2211yescharacteristic
56#5176C2218yescomplemented
57#5174C2218yescomplemented
58C2×#821C2211yescharacteristic
59C2×#821C2211yescharacteristic
60C2×#818C2211yescharacteristic
61C2×#815C2211yescharacteristic
62C2×#815C2211yescharacteristic
63C4×#215C2218yescomplemented
64C4×#213C2218yescomplemented
65C2×#809C2211yescharacteristic
66C2×#809C2211yescharacteristic
67C2×#808C2211yescharacteristic
68C2×#807C2211yescharacteristic
69C2×C4×C3⋊C8C2211yescharacteristic
70#4865C2218yescomplemented
71#4856C2218yescomplemented
72#4812C2218yescomplemented
73#4794C2218yescomplemented
74#4782C2218yescomplemented
75#4764C2218yescomplemented
76C4×D24C2218yescomplemented
77C4×ΓL(1,𝔽25)C2218yescomplemented
78C2×#532—31no—
79C2×#529—31no—
80#3171—316no—
81C2×#501—31no—
82C2×#496—31no—
83C2×#490—31no—
84C2×#489—31no—
85C2×#469—31no—
86C2×#469—31no—
87C2×#468—31no—
88C2×#468—31no—
89C2×C4×SD16—31no—
90C2×C4×SD16D311yescharacteristic, complemented
91C2×C4×D8—31no—
92C2×C4×D8—31no—
93C2×C4×M16—31no—
94C22×C3×Q8C2311yescharacteristic
95C22×C3×D4C2311yescharacteristic
96C23×C3×C4—21no—
97C22×#67—21no—
98C22×#67—21no—
99C22×#67—21no—
100C2×#235—28no—
101C2×#235—48no—
102C22×D12—21no—
103C22×D12—21no—
104C22×D12C2311yescharacteristic
105C22×D12C2311yescharacteristic
106C22×C4×D3—21no—
107C22×C4×D3—21no—
108C22×C4×D3D411yescharacteristic
109C22×C4×D3D411yescharacteristic
110C22×C4×D3C2311yescharacteristic
111C22×Dic6—21no—
112C2×C3×SD16—24no—
113C2×C3×SD16C2314yes—
114C22×C3×C8C2311yescharacteristic
115C22×C3×C8C2311yescharacteristic
116C3×C4×Q8—22no—
117C3×C4×Q8C2314yes—
118C3×C4×D4—22no—
119C3×C4×D4C2314yes—
120C2×C3×C4⋊C4—21no—
121C2×C3×C4⋊C4C2311yescharacteristic
122C2×C3×C4⋊C4C2311yescharacteristic
123C2×C3×C22⋊C4—21no—
124C2×C3×C42—21no—
125C2×C3×C42C2311yescharacteristic
126C2×#217—21no—
127#947—22no—
128#947C2314yes—
129#946—22no—
130#946C2314yes—
131C2×#215—24no—
132C2×#215C2314yes—
133#940—22no—
134#940C2314yes—
135#938—22no—
136#938C2314yes—
137C2×#213—24no—
138C2×#213C2314yes—
139C4×#67—28no—
140C2×(C2×D3)⋊C4—21no—
141C2×(C2×D3)⋊C4—21no—
142C2×(C2×D3)⋊C4—21no—
143C2×(C2×D3)⋊C4—21no—
144C2×(C2×D3)⋊C4—21no—
145C2×(C2×D3)⋊C4—21no—
146C2×(C2×D3)⋊C4—21no—
147C2×C4⋊Dic3—21no—
148C2×C4⋊Dic3C2311yescharacteristic
149C2×C4⋊Dic3C2311yescharacteristic
150C2×Dic3⋊C4—21no—
151C2×Dic3⋊C4—21no—
152C2×Dic3⋊C4—21no—
153C2×C4×Dic3D411yescharacteristic
154C2×C4×Dic3D411yescharacteristic
155C2×C4×Dic3C2311yescharacteristic
156C22×C3⋊C8C2311yescharacteristic
157C22×C3⋊C8C2311yescharacteristic
158C2×D24—24no—
159C2×D24C2314yes—
160C2×ΓL(1,𝔽25)—24no—
161C2×ΓL(1,𝔽25)—24no—
162C2×ΓL(1,𝔽25)C2314yes—
163C2×ΓL(1,𝔽25)C2314yes—
164#898—28no—
165#895—22no—
166#895—22no—
167#895C2314yes—
168#895C2314yes—
169#894—28no—
170#890—22no—
171#890C2314yes—
172#888—22no—
173#888C2314yes—
174#885—28no—
175#884—28no—
176C4×D12—28no—
177C4×D12—22no—
178C4×D12—22no—
179C4×D12C2314yes—
180C4×D12C2314yes—
181#872—28no—
182C42×D3D414yes—
183C42×D3C2314yes—
184C3×#106C2314yes—
185C3×#103C2314yes—
186C3×#102C2314yes—
187C3×C4×C8C2314yes—
188#835C2314yes—
189#832C2314yes—
190#821C2314yes—
191#821C2314yes—
192#818C2314yes—
193#815C2314yes—
194#815C2314yes—
195#809C2314yes—
196#809C2314yes—
197#808C2314yes—
198#807C2314yes—
199C4×C3⋊C8C2314yes—
200C22×#41—61no—
201C22×SD16—31no—
202C22×SD16C2×D311yescharacteristic
203C22×D8—31no—
204C22×D8—31no—
205C22×M16—31no—
206C22×M16—31no—
207#532—38no—
208#532—64no—
209C2×C4⋊Q8—31no—
210C2×#127—31no—
211#529—38no—
212#529—64no—
213C2×#126—61no—
214C2×#125—31no—
215C2×#124—31no—
216C2×#124—61no—
217C2×#123—61no—
218C2×C22⋊Q8—31no—
219C2×#121—31no—
220C2×#121—31no—
221C2×#121—31no—
222C2×#121—61no—
223C2×C4×Q8C2×D311yescharacteristic
224C2×C4×D4—31no—
225C2×C4×D4—31no—
226C2×C4×D4—61no—
227C2×C4×D4—61no—
228C2×C4×D4C2×D311yescharacteristic
229C2×#117—61no—
230C22×C42—31no—
231#501—38no—
232#496—38no—
233#490—38no—
234#489—38no—
235#469—38no—
236#469—38no—
237#468—38no—
238#468—38no—
239C4×SD16—38no—
240C4×SD16C2×D318yescomplemented
241C4×D8—38no—
242C4×D8—38no—
243C2×#107—31no—
244C2×#107—31no—
245C2×#106—31no—
246C2×#106C2×D311yescharacteristic
247C2×#103—31no—
248C2×#103C2×D311yescharacteristic
249C2×#102—31no—
250C2×#102—31no—
251C2×#102—31no—
252C2×#102—31no—
253C2×#102—31no—
254C2×#102C2×D311yescharacteristic
255C4×M16—38no—
256C2×#97—31no—
257C2×#97—31no—
258C2×C4×C8—31no—
259C2×C4×C8C2×D311yescharacteristic
260C24×C3—21no—
261C23×D3—21no—
262C23×D3—21no—
263C23×D3C2×D411yescharacteristic
264C2×C3×Q8—21no—
265C2×C3×Q8—22no—
266C2×C3×Q8—22no—
267C2×C3×Q8C2412yes—
268C2×C3×D4—21no—
269C2×C3×D4—22no—
270C2×C3×D4—22no—
271C2×C3×D4C2412yes—
272C22×C3×C4—21no—
273C22×C3×C4—21no—
274C22×C3×C4—21no—
275C22×C3×C4—24no—
276C22×C3×C4—44no—
277C22×C3×C4C2×D411yescharacteristic
278C22×C3×C4C2×D411yescharacteristic
279C22×C3×C4C2411yescharacteristic
280C2×#67—24no—
281C2×#67—24no—
282C2×#67—24no—
283C2×#67—44no—
284C2×#67—44no—
285C2×#67—44no—
286C22×Dic3—21no—
287C22×Dic3—21no—
288C22×Dic3C2×D411yescharacteristic
289C22×Dic3C2×D411yescharacteristic
290C22×Dic3C2×D411yescharacteristic
291#235—432no—
292C2×D12—22no—
293C2×D12—22no—
294C2×D12—22no—
295C2×D12—22no—
296C2×D12—24no—
297C2×D12—24no—
298C2×D12—21no—
299C2×D12—21no—
300C2×D12—44no—
301C2×D12—44no—
302C2×D12C2412yes—
303C2×D12C2412yes—
304C2×C4×D3—24no—
305C2×C4×D3—22no—
306C2×C4×D3—22no—
307C2×C4×D3—24no—
308C2×C4×D3—24no—
309C2×C4×D3—42no—
310C2×C4×D3—44no—
311C2×C4×D3—44no—
312C2×C4×D3C2×D412yes—
313C2×C4×D3C2×D414yes—
314C2×C4×D3C2×D414yes—
315C2×C4×D3C2412yes—
316C2×Dic6—24no—
317C2×Dic6—44no—
318C3×SD16—28no—
319C2×C3×C8—22no—
320C2×C3×C8#4114yescomplemented
321C2×C3×C8C2412yes—
322C2×C3×C8C2412yes—
323C3×C4⋊C4—21no—
324C3×C4⋊C4—21no—
325C3×C4⋊C4—24no—
326C3×C4⋊C4C2412yes—
327C3×C4⋊C4C2412yes—
328C3×C22⋊C4—24no—
329C3×C42—24no—
330C3×C42C2×D412yes—
331C3×C42C2412yes—
332#217—24no—
333#215—28no—
334#213—28no—
335(C2×D3)⋊C4—24no—
336(C2×D3)⋊C4—24no—
337(C2×D3)⋊C4—24no—
338(C2×D3)⋊C4—24no—
339(C2×D3)⋊C4—24no—
340(C2×D3)⋊C4—24no—
341(C2×D3)⋊C4—24no—
342C4⋊Dic3—21no—
343C4⋊Dic3—21no—
344C4⋊Dic3—24no—
345C4⋊Dic3C2412yes—
346C4⋊Dic3C2412yes—
347Dic3⋊C4—24no—
348Dic3⋊C4—24no—
349Dic3⋊C4—24no—
350C4×Dic3C2×D412yes—
351C4×Dic3C2×D414yes—
352C4×Dic3C2×D414yes—
353C4×Dic3C2412yes—
354C2×C3⋊C8—22no—
355C2×C3⋊C8#4114yescomplemented
356C2×C3⋊C8C2412yes—
357C2×C3⋊C8C2412yes—
358D24—28no—
359ΓL(1,𝔽25)—28no—
360ΓL(1,𝔽25)—28no—
361C2×#41—68no—
362C2×#41—128no—
363C22×Q8—61no—
364C22×Q8C22×D311yescharacteristic
365C22×D4—31no—
366C22×D4—31no—
367C22×D4—61no—
368C22×D4—61no—
369C22×D4—61no—
370C22×D4—61no—
371C22×D4—61no—
372C22×D4C22×D311yescharacteristic
373C23×C4—21no—
374C23×C4—31no—
375C23×C4—31no—
376C23×C4—31no—
377C23×C4—61no—
378C23×C4—61no—
379C2×SD16—24no—
380C2×SD16—34no—
381C2×SD16—64no—
382C2×SD16C22×D314yes—
383C2×D8—34no—
384C2×D8—34no—
385C2×D8—64no—
386C2×D8—64no—
387C2×M16—34no—
388C2×M16—34no—
389C2×M16—64no—
390C2×M16—64no—
391C22×C8—31no—
392C22×C8—31no—
393C22×C8C22×D311yescharacteristic
394C22×C8C22×D311yescharacteristic
395C4⋊Q8—34no—
396C4⋊Q8—62no—
397#127—34no—
398#127—62no—
399#126—68no—
400#125—34no—
401#125—62no—
402#124—34no—
403#124—68no—
404#124—62no—
405#123—68no—
406C22⋊Q8—34no—
407C22⋊Q8—62no—
408#121—34no—
409#121—34no—
410#121—34no—
411#121—68no—
412#121—62no—
413#121—62no—
414#121—62no—
415C4×Q8—22no—
416C4×Q8C22×D314yes—
417C4×D4—22no—
418C4×D4—34no—
419C4×D4—34no—
420C4×D4—68no—
421C4×D4—68no—
422C4×D4—62no—
423C4×D4—62no—
424C4×D4C22×D314yes—
425#117—68no—
426C2×C4⋊C4—21no—
427C2×C4⋊C4—31no—
428C2×C4⋊C4—31no—
429C2×C4⋊C4—61no—
430C2×C4⋊C4—61no—
431C2×C4⋊C4—61no—
432C2×C4⋊C4—61no—
433C2×C4⋊C4C22×D311yescharacteristic
434C2×C4⋊C4C22×D311yescharacteristic
435C2×C22⋊C4—21no—
436C2×C22⋊C4—61no—
437C2×C22⋊C4—61no—
438C2×C22⋊C4—61no—
439C2×C22⋊C4—61no—
440C2×C22⋊C4—61no—
441C2×C22⋊C4—61no—
442C2×C22⋊C4—61no—
443C2×C22⋊C4—61no—
444C2×C42—21no—
445C2×C42—31no—
446C2×C42—31no—
447C2×C42—31no—
448C2×C42—34no—
449C2×C42—34no—
450C2×C42C22×D311yescharacteristic
451#107—34no—
452#107—34no—
453#106—34no—
454#106C22×D314yes—
455#103—34no—
456#103C22×D314yes—
457#102—34no—
458#102—34no—
459#102—34no—
460#102—34no—
461#102—34no—
462#102C22×D314yes—
463#97—34no—
464#97—34no—
465C4×C8—34no—
466C4×C8C22×D314yes—
467C23×C3—22no—
468C23×C3—42no—
469C23×C3—42no—
470C23×C3—42no—
471C23×C3C22×D411yescharacteristic
472C22×D3—22no—
473C22×D3—22no—
474C22×D3—22no—
475C22×D3—22no—
476C22×D3—22no—
477C22×D3—42no—
478C22×D3—42no—
479C22×D3—42no—
480C22×D3—42no—
481C22×D3—42no—
482C22×D3—42no—
483C22×D3C22×D412yes—
484C3×Q8—22no—
485C3×Q8—22no—
486C3×Q8—42no—
487C3×D4—22no—
488C3×D4—22no—
489C3×D4—42no—
490C2×C3×C4—22no—
491C2×C3×C4—22no—
492C2×C3×C4—22no—
493C2×C3×C4—22no—
494C2×C3×C4—42no—
495C2×C3×C4—42no—
496C2×C3×C4—42no—
497C2×C3×C4—48no—
498C2×C3×C4AGL(1,ℤ/8)14yes—
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—
506#67—48no—
507#67—48no—
508C2×Dic3—22no—
509C2×Dic3—22no—
510C2×Dic3—22no—
511C2×Dic3—22no—
512C2×Dic3—22no—
513C2×Dic3—42no—
514C2×Dic3—42no—
515C2×Dic3C22×D412yes—
516C2×Dic3C22×D412yes—
517C2×Dic3C22×D412yes—
518D12—22no—
519D12—22no—
520D12—22no—
521D12—22no—
522D12—48no—
523D12—48no—
524D12—42no—
525D12—42no—
526C4×D3—24no—
527C4×D3—28no—
528C4×D3—22no—
529C4×D3—22no—
530C4×D3—44no—
531C4×D3—48no—
532C4×D3—48no—
533Dic6—48no—
534C3×C8—22no—
535C3×C8C2×#4114yescomplemented
536C3⋊C8—22no—
537C3⋊C8C2×#4114yescomplemented
538C24—21no—
539C24—31no—
540C24—61no—
541C24—61no—
542#41—1232no—
543C2×Q8—21no—
544C2×Q8—22no—
545C2×Q8—22no—
546C2×Q8—64no—
547C2×Q8—124no—
548C2×Q8C23×D312yes—
549C2×D4—22no—
550C2×D4—21no—
551C2×D4—22no—
552C2×D4—32no—
553C2×D4—32no—
554C2×D4—64no—
555C2×D4—64no—
556C2×D4—64no—
557C2×D4—64no—
558C2×D4—64no—
559C2×D4—62no—
560C2×D4—62no—
561C2×D4—61no—
562C2×D4—61no—
563C2×D4—62no—
564C2×D4—62no—
565C2×D4—124no—
566C2×D4—124no—
567C2×D4—124no—
568C2×D4—124no—
569C2×D4—124no—
570C2×D4C23×D312yes—
571C22×C4—21no—
572C22×C4—21no—
573C22×C4—21no—
574C22×C4—24no—
575C22×C4—31no—
576C22×C4—31no—
577C22×C4—31no—
578C22×C4—34no—
579C22×C4—32no—
580C22×C4—32no—
581C22×C4—34no—
582C22×C4—44no—
583C22×C4—64no—
584C22×C4—62no—
585C22×C4—62no—
586C22×C4—61no—
587C22×C4—61no—
588C22×C4—64no—
589C22×C4—64no—
590C22×C4—122no—
591C22×C4—124no—
592C22×C4—124no—
593C22×C4D3×D411yescharacteristic
594C22×C4D3×D411yescharacteristic
595C22×C4C23×D311yescharacteristic
596SD16—28no—
597SD16—68no—
598D8—68no—
599D8—68no—
600M16—68no—
601M16—68no—
602C2×C8—22no—
603C2×C8—34no—
604C2×C8—32no—
605C2×C8—32no—
606C2×C8—62no—
607C2×C8#23514yescomplemented
608C2×C8C23×D312yes—
609C2×C8C23×D312yes—
610C4⋊C4—24no—
611C4⋊C4—21no—
612C4⋊C4—21no—
613C4⋊C4—32no—
614C4⋊C4—32no—
615C4⋊C4—64no—
616C4⋊C4—64no—
617C4⋊C4—64no—
618C4⋊C4—64no—
619C4⋊C4—61no—
620C4⋊C4—61no—
621C4⋊C4C23×D312yes—
622C4⋊C4C23×D312yes—
623C22⋊C4—24no—
624C22⋊C4—64no—
625C22⋊C4—64no—
626C22⋊C4—64no—
627C22⋊C4—64no—
628C22⋊C4—64no—
629C22⋊C4—64no—
630C22⋊C4—64no—
631C22⋊C4—64no—
632C42—24no—
633C42—34no—
634C42—34no—
635C42—32no—
636C42—32no—
637C42D3×D412yes—
638C42C23×D312yes—
639C22×C3—42no—
640C22×C3—42no—
641C22×C3—42no—
642C22×C3—84no—
643C22×C3#53212yes—
644C22×C3C2×AGL(1,ℤ/8)12yes—
645C22×C3#57512yes—
646C22×C3C23×D411yescharacteristic
647C2×D3—22no—
648C2×D3—22no—
649C2×D3—22no—
650C2×D3—44no—
651C2×D3—42no—
652C2×D3—42no—
653C2×D3—42no—
654C2×D3—42no—
655C2×D3—42no—
656C2×D3—42no—
657C2×D3—84no—
658C2×D3—84no—
659C3×C4—22no—
660C3×C4—42no—
661C3×C4—42no—
662C3×C4—42no—
663C3×C4#53212yes—
664C3×C4C2×AGL(1,ℤ/8)14yes—
665C3×C4C22×#4111yescharacteristic
666C3×C4C22×#4111yescharacteristic
667Dic3—22no—
668Dic3—22no—
669Dic3—22no—
670Dic3—42no—
671Dic3—42no—
672C23—22no—
673C23—32no—
674C23—42no—
675C23—42no—
676C23—42no—
677C23—62no—
678C23—62no—
679C23—62no—
680C23—62no—
681C23—62no—
682C23—122no—
683C23—122no—
684C23—122no—
685C23—122no—
686C23—122no—
687C23—122no—
688C23C2×D3×D411yescharacteristic
689Q8—22no—
690Q8—22no—
691Q8—42no—
692Q8—128no—
693D4—22no—
694D4—22no—
695D4—42no—
696D4—62no—
697D4—62no—
698D4—62no—
699D4—62no—
700D4—128no—
701D4—128no—
702D4—128no—
703D4—128no—
704D4—128no—
705D4—122no—
706D4—122no—
707C2×C4—22no—
708C2×C4—22no—
709C2×C4—22no—
710C2×C4—22no—
711C2×C4—32no—
712C2×C4—32no—
713C2×C4—32no—
714C2×C4—42no—
715C2×C4—42no—
716C2×C4—42no—
717C2×C4—48no—
718C2×C4—62no—
719C2×C4—62no—
720C2×C4—62no—
721C2×C4—62no—
722C2×C4—62no—
723C2×C4—68no—
724C2×C4—64no—
725C2×C4—62no—
726C2×C4—62no—
727C2×C4—124no—
728C2×C4—122no—
729C2×C4—122no—
730C2×C4—128no—
731C2×C4—128no—
732C2×C4#91414yes—
733C2×C4C2×#23512yes—
734C2×C4C2×D3×D412yes—
735C2×C4C2×D3×D412yes—
736C2×C4C2×D3×D411yescharacteristic
737C2×C4D3×#4112yes—
738C2×C4C24×D311yescharacteristic
739C8—22no—
740C8—34no—
741C8—62no—
742C8C2×#23514yescomplemented
743C2×C3—82no—
744C2×C3#317114yescomplemented
745C2×C3C2×#53211yescharacteristic
746C2×C3C22×AGL(1,ℤ/8)11yescharacteristic
747C2×C3C2×#57511yescharacteristic
748D3—42no—
749D3—82no—
750D3—82no—
751C22—42no—
752C22—42no—
753C22—42no—
754C22—62no—
755C22—62no—
756C22—62no—
757C22—84no—
758C22—124no—
759C22—122no—
760C22—122no—
761C22—122no—
762C22—122no—
763C22—122no—
764C22—122no—
765C22—244no—
766C22—244no—
767C22#554812yes—
768C22C2×#91412yes—
769C22#576812yes—
770C22C22×D3×D411yescharacteristic
771C4—22no—
772C4—42no—
773C4—42no—
774C4—42no—
775C4—62no—
776C4—62no—
777C4—62no—
778C4—122no—
779C4—122no—
780C4#554812yes—
781C4C2×#91414yes—
782C4C22×#23511yescharacteristic
783C4C2×D3×#4111yescharacteristic
784C3C2×#317111yescharacteristic, complemented, Sylow
785C2—82no—
786C2—122no—
787C2—242no—
788C2—242no—
789C2#7966414yesdirect product factor
790C2C2×#554811yescharacteristic
791C2C22×#91411yescharacteristic
792C2C2×#576811yescharacteristic
subgroupG/H
centerC22×C4D3×D4
commutator, cosocleC2×C3×C4C25
FrattiniC2×C4C24×D3
FittingC2×C3×C4×SD16C2
socleC23×C3C22×D4
hypercenterC2×C4×SD16D3
hypocenterC3C2×#3171
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C4 ◁ C2×C42 ◁ C2×C4×SD16

Complements

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

NH ≅ G/Ntype
1. C2×#5580C2semidirect
2. C2×#5548C2semidirect
3. C2×C3×C4×SD16C2semidirect
4. C2×#5174C2semidirect
5. C2×#5176C2semidirect
6. C2×C4×#215C2semidirect
7. C2×C4×#213C2semidirect
8. #79664C2direct (N × H)
9. C2×#4865C2semidirect
10. C2×#4856C2semidirect
11. C2×#4812C2semidirect
12. C2×#4794C2semidirect
13. C2×#4782C2semidirect
14. C2×#4764C2semidirect
15. C2×C4×D24C2semidirect
16. C2×C4×ΓL(1,𝔽25)C2semidirect
33. #5580C22semidirect
35. #5548C22semidirect
49. C3×C4×SD16C22semidirect
56. #5176C22semidirect
57. #5174C22semidirect
63. C4×#215C22semidirect
64. C4×#213C22semidirect
70. #4865C22semidirect
71. #4856C22semidirect
72. #4812C22semidirect
73. #4794C22semidirect
74. #4782C22semidirect
75. #4764C22semidirect
76. C4×D24C22semidirect
77. C4×ΓL(1,𝔽25)C22semidirect
90. C2×C4×SD16D3semidirect
240. C4×SD16C2×D3semidirect
320. C2×C3×C8#41semidirect
355. C2×C3⋊C8#41semidirect
535. C3×C8C2×#41semidirect
537. C3⋊C8C2×#41semidirect
607. C2×C8#235semidirect
742. C8C2×#235semidirect
744. C2×C3#3171semidirect
784. C3C2×#3171semidirect
789. C2#79664direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#55802
C2×#55482
C2×C3×C4×SD162
C2×#51742
C2×#51762
C2×C4×#2152
C2×C4×#2132
#796642
C2×#48652
C2×#48562
C2×#48122
C2×#47942
C2×#47822
C2×#47642
C2×C4×D242
C2×C4×ΓL(1,𝔽25)2
C2×#31713