Finite Group Databasebeta

← C2×#80632 #11664896

Subgroups — C2×#80632 #11664896

Order 768.

2286 conjugacy classes of subgroups.

The subgroup lattice has 778 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#5622C211yesmaximal, characteristic, complemented
2C2×#5596C211yesmaximal, characteristic
3C2×C3×#465C211yesmaximal, characteristic, complemented
4C2×#5175C211yesmaximal, characteristic, complemented
5C2×Dic3×SD16C211yesmaximal, characteristic, complemented
6C2×#5114C211yesmaximal, characteristic, complemented
7C22×C8×Dic3C211yesmaximal, characteristic, complemented
8C2×#5048C211yesmaximal, characteristic, complemented
9C2×#5041C211yesmaximal, characteristic, complemented
10#80632C2116yesmaximal, direct product factor
11C2×#4855C211yesmaximal, characteristic, complemented
12C2×#4852C211yesmaximal, characteristic, complemented
13C2×#4792C211yesmaximal, characteristic, complemented
14C2×#4788C211yesmaximal, characteristic, complemented
15C2×#4760C211yesmaximal, characteristic, complemented
16C2×#4758C211yesmaximal, characteristic, complemented
17C2×#3167—31nomaximal, Sylow
18C22×#237—21no—
19C22×C3×SD16C2211yescharacteristic
20C23×C3×C8C2211yescharacteristic
21C2×C3×C22⋊Q8C2211yescharacteristic
22C2×C3×#121C2211yescharacteristic
23C2×Q8×Dic3C2211yescharacteristic
24C2×#944C2211yescharacteristic
25C22×#215C2211yescharacteristic
26C2×#940C2211yescharacteristic
27C2×#939—21no—
28C2×D4×Dic3C2211yescharacteristic
29C22×#214C2211yescharacteristic
30C2×#930C2211yescharacteristic
31C2×#924C2211yescharacteristic
32C22×C4×Dic3C2211yescharacteristic
33C23×C3⋊C8C2211yescharacteristic
34C22×#204C2211yescharacteristic
35#5622—24no—
36#5622C2218yescomplemented
37#5596—24no—
38#5596C2218yes—
39C2×#893C2211yescharacteristic
40C2×#889—21no—
41C2×#888C2211yescharacteristic
42C2×#888C2211yescharacteristic
43C2×#887—21no—
44C2×#887C2211yescharacteristic
45C2×#885—21no—
46C2×#67⋊C4—21no—
47C2×#878—21no—
48C2×#877—21no—
49C3×#465C2218yescomplemented
50C2×C3×#106C2211yescharacteristic
51C2×C3×#103C2211yescharacteristic
52C2×C3×#102C2211yescharacteristic
53C2×#835C2211yescharacteristic
54C2×#832C2211yescharacteristic
55#5175C2218yescomplemented
56Dic3×SD16C2218yescomplemented
57#5114C2218yescomplemented
58C2×#821C2211yescharacteristic
59C2×#817C2211yescharacteristic
60C2×#816C2211yescharacteristic
61C2×C8×Dic3C2211yescharacteristic
62C2×C8×Dic3C2211yescharacteristic
63C2×C8×Dic3C2211yescharacteristic
64C2×C8×Dic3C2211yescharacteristic
65C2×C8×Dic3C2218yescomplemented
66#5048C2218yescomplemented
67#5041C2218yescomplemented
68C2×#810C2211yescharacteristic
69C2×#809C2211yescharacteristic
70C2×#808C2211yescharacteristic
71C2×#808C2211yescharacteristic
72#4855C2218yescomplemented
73#4852C2218yescomplemented
74#4792C2218yescomplemented
75#4788C2218yescomplemented
76#4760C2218yescomplemented
77#4758C2218yescomplemented
78C2×#533—31no—
79C2×#532—31no—
80#3167—316no—
81C2×#498—31no—
82C2×#492—31no—
83C2×#487—31no—
84C2×#486—31no—
85C2×#465—31no—
86C2×#465—31no—
87C2×#465—31no—
88C2×#465D311yescharacteristic, complemented
89C2×C4×SD16—31no—
90C2×C4×SD16—31no—
91C2×C4×SD16—31no—
92C2×C4×SD16—31no—
93C22×C4×C8—31no—
94C22×C3×Q8C2311yescharacteristic
95C22×C3×D4—21no—
96C22×C3×D4C2311yescharacteristic
97C23×C3×C4C2311yescharacteristic
98C22×#67—21no—
99C22×#67—21no—
100C22×#67—21no—
101C23×Dic3—21no—
102C23×Dic3D411yescharacteristic
103C23×Dic3D411yescharacteristic
104C2×#237—28no—
105C2×#237—48no—
106C22×D12C2311yescharacteristic
107C22×C4×D3—21no—
108C22×Dic6—21no—
109C22×Dic6—21no—
110C22×Dic6C2311yescharacteristic
111C2×C3×SD16—24no—
112C2×C3×SD16C2314yes—
113C22×C3×C8—24no—
114C22×C3×C8C2311yescharacteristic
115C22×C3×C8C2314yes—
116C22×C3×C8C2311yescharacteristic
117C3×C22⋊Q8—22no—
118C3×C22⋊Q8C2314yes—
119C3×#121—22no—
120C3×#121C2314yes—
121C2×C3×C4⋊C4—21no—
122C2×C3×C4⋊C4C2311yescharacteristic
123C2×C3×C4⋊C4C2311yescharacteristic
124C2×C3×C22⋊C4—21no—
125C2×C3×C22⋊C4—21no—
126C2×#217—21no—
127C2×#217—21no—
128Q8×Dic3—22no—
129Q8×Dic3C2314yes—
130#944—22no—
131#944C2314yes—
132C2×#215—24no—
133C2×#215C2314yes—
134#940—22no—
135#940C2314yes—
136#939—28no—
137D4×Dic3—22no—
138D4×Dic3C2314yes—
139C2×#214—24no—
140C2×#214C2314yes—
141#930—22no—
142#930C2314yes—
143C2×(C2×D3)⋊C4—21no—
144C2×(C2×D3)⋊C4—21no—
145C2×C4⋊Dic3—21no—
146C2×C4⋊Dic3C2311yescharacteristic
147C2×C4⋊Dic3C2311yescharacteristic
148#924—22no—
149#924C2314yes—
150C2×Dic3⋊C4—21no—
151C2×Dic3⋊C4—21no—
152C2×Dic3⋊C4—21no—
153C2×Dic3⋊C4—21no—
154C2×Dic3⋊C4—21no—
155C2×Dic3⋊C4—21no—
156C2×C4×Dic3—21no—
157C2×C4×Dic3—21no—
158C2×C4×Dic3D411yescharacteristic
159C2×C4×Dic3D411yescharacteristic
160C2×C4×Dic3D414yes—
161C2×C4×Dic3C2311yescharacteristic
162C2×C4×Dic3C2311yescharacteristic
163C2×C4×Dic3C2314yes—
164C22×C3⋊C8—24no—
165C22×C3⋊C8C2311yescharacteristic
166C22×C3⋊C8C2314yes—
167C22×C3⋊C8C2311yescharacteristic
168C2×#204—24no—
169C2×#204C2314yes—
170#893—22no—
171#893C2314yes—
172#889—28no—
173#888—22no—
174#888—22no—
175#888C2314yes—
176#888C2314yes—
177#887—28no—
178#887—22no—
179#887C2314yes—
180#885—28no—
181#67⋊C4—28no—
182#878—28no—
183#877—28no—
184C3×#106C2314yes—
185C3×#103C2314yes—
186C3×#102C2314yes—
187#835C2314yes—
188#832C2314yes—
189#821C2314yes—
190#817C2314yes—
191#816C2314yes—
192C8×Dic3C2314yes—
193C8×Dic3C2314yes—
194C8×Dic3C2314yes—
195C8×Dic3C2314yes—
196#810C2314yes—
197#809C2314yes—
198#808C2314yes—
199#808C2314yes—
200C22×#41—61no—
201C22×SD16—31no—
202C22×SD16—31no—
203C22×SD16—31no—
204C22×SD16C2×D311yescharacteristic
205C23×C8—31no—
206C23×C8C2×D311yescharacteristic
207#533—38no—
208#533—64no—
209#532—38no—
210#532—64no—
211C2×C4⋊Q8—31no—
212C2×C4⋊Q8—31no—
213C2×C4⋊Q8—31no—
214C2×#127—31no—
215C2×#125—61no—
216C2×#124—61no—
217C2×C22⋊Q8—31no—
218C2×C22⋊Q8—61no—
219C2×C22⋊Q8C2×D311yescharacteristic
220C2×#121—31no—
221C2×#121—61no—
222C2×#121C2×D311yescharacteristic
223C2×C4×Q8—31no—
224C2×C4×Q8—31no—
225C2×C4×Q8—61no—
226C2×C4×D4—31no—
227C2×C4×D4—31no—
228C2×C4×D4—61no—
229C2×#117—61no—
230C22×C42—31no—
231#498—38no—
232#492—38no—
233#487—38no—
234#486—38no—
235#465—38no—
236#465—38no—
237#465—38no—
238#465C2×D318yescomplemented
239C4×SD16—38no—
240C4×SD16—38no—
241C4×SD16—38no—
242C4×SD16—38no—
243C2×#106—31no—
244C2×#106—31no—
245C2×#106—31no—
246C2×#106C2×D311yescharacteristic
247C2×#103—31no—
248C2×#103—31no—
249C2×#103—31no—
250C2×#103C2×D311yescharacteristic
251C2×#102—31no—
252C2×#102—31no—
253C2×#102—31no—
254C2×#102C2×D311yescharacteristic
255C2×C4×C8—31no—
256C2×C4×C8—31no—
257C2×C4×C8—38no—
258C2×C4×C8—31no—
259C2×C4×C8—31no—
260C24×C3—21no—
261C24×C3C2×D411yescharacteristic
262C23×D3—21no—
263C2×C3×Q8—21no—
264C2×C3×Q8—22no—
265C2×C3×Q8—22no—
266C2×C3×Q8C2412yes—
267C2×C3×D4—24no—
268C2×C3×D4—21no—
269C2×C3×D4—22no—
270C2×C3×D4—22no—
271C2×C3×D4—44no—
272C2×C3×D4C2412yes—
273C22×C3×C4—22no—
274C22×C3×C4—22no—
275C22×C3×C4—21no—
276C22×C3×C4—21no—
277C22×C3×C4—21no—
278C22×C3×C4C2×D411yescharacteristic
279C22×C3×C4C2×D412yes—
280C22×C3×C4C2412yes—
281C22×C3×C4C2411yescharacteristic
282C2×#67—24no—
283C2×#67—24no—
284C2×#67—24no—
285C2×#67—44no—
286C2×#67—44no—
287C2×#67—44no—
288C22×Dic3—24no—
289C22×Dic3—21no—
290C22×Dic3—21no—
291C22×Dic3—21no—
292C22×Dic3—24no—
293C22×Dic3—44no—
294C22×Dic3SD1618yescomplemented
295C22×Dic3C2×D414yes—
296C22×Dic3C2×D411yescharacteristic
297C22×Dic3C2×D411yescharacteristic
298C22×Dic3C2×D411yescharacteristic
299C22×Dic3C2×D414yes—
300C22×Dic3C2×D411yescharacteristic
301#237—432no—
302C2×D12—22no—
303C2×D12—22no—
304C2×D12—21no—
305C2×D12C2412yes—
306C2×C4×D3—24no—
307C2×C4×D3—44no—
308C2×Dic6—22no—
309C2×Dic6—22no—
310C2×Dic6—21no—
311C2×Dic6—24no—
312C2×Dic6—24no—
313C2×Dic6—44no—
314C2×Dic6—44no—
315C2×Dic6C2412yes—
316C3×SD16—28no—
317C2×C3×C8—22no—
318C2×C3×C8—28no—
319C2×C3×C8#4114yescomplemented
320C2×C3×C8C2412yes—
321C2×C3×C8C2412yes—
322C3×C4⋊C4—21no—
323C3×C4⋊C4—24no—
324C3×C4⋊C4—21no—
325C3×C4⋊C4C2412yes—
326C3×C4⋊C4C2412yes—
327C3×C22⋊C4—24no—
328C3×C22⋊C4—24no—
329#217—24no—
330#217—24no—
331#215—28no—
332#214—28no—
333(C2×D3)⋊C4—24no—
334(C2×D3)⋊C4—24no—
335C4⋊Dic3—21no—
336C4⋊Dic3—21no—
337C4⋊Dic3—24no—
338C4⋊Dic3C2412yes—
339C4⋊Dic3C2412yes—
340Dic3⋊C4—24no—
341Dic3⋊C4—24no—
342Dic3⋊C4—24no—
343Dic3⋊C4—24no—
344Dic3⋊C4—24no—
345Dic3⋊C4—24no—
346C4×Dic3—24no—
347C4×Dic3—24no—
348C4×Dic3C2×D414yes—
349C4×Dic3C2×D414yes—
350C4×Dic3C2×D412yes—
351C4×Dic3C2×D412yes—
352C4×Dic3C2412yes—
353C4×Dic3C2412yes—
354C2×C3⋊C8—22no—
355C2×C3⋊C8—28no—
356C2×C3⋊C8#4114yescomplemented
357C2×C3⋊C8C2412yes—
358C2×C3⋊C8C2412yes—
359#204—28no—
360C2×#41—68no—
361C2×#41—128no—
362C22×Q8—31no—
363C22×Q8—61no—
364C22×Q8—61no—
365C22×Q8C22×D311yescharacteristic
366C22×D4—21no—
367C22×D4—31no—
368C22×D4—61no—
369C22×D4—61no—
370C22×D4—61no—
371C22×D4C22×D311yescharacteristic
372C23×C4—31no—
373C23×C4—31no—
374C23×C4—61no—
375C23×C4—61no—
376C23×C4C22×D311yescharacteristic
377C2×SD16—24no—
378C2×SD16—34no—
379C2×SD16—34no—
380C2×SD16—34no—
381C2×SD16—64no—
382C2×SD16—64no—
383C2×SD16—64no—
384C2×SD16C22×D314yes—
385C22×C8—24no—
386C22×C8—31no—
387C22×C8—31no—
388C22×C8—34no—
389C22×C8—64no—
390C22×C8C22×D311yescharacteristic
391C22×C8C22×D314yes—
392C22×C8C22×D311yescharacteristic
393C4⋊Q8—34no—
394C4⋊Q8—34no—
395C4⋊Q8—34no—
396C4⋊Q8—62no—
397C4⋊Q8—62no—
398C4⋊Q8—62no—
399#127—34no—
400#127—62no—
401#125—68no—
402#124—68no—
403C22⋊Q8—22no—
404C22⋊Q8—34no—
405C22⋊Q8—68no—
406C22⋊Q8—62no—
407C22⋊Q8C22×D314yes—
408#121—22no—
409#121—34no—
410#121—68no—
411#121—62no—
412#121C22×D314yes—
413C4×Q8—34no—
414C4×Q8—34no—
415C4×Q8—62no—
416C4×Q8—68no—
417C4×Q8—62no—
418C4×D4—34no—
419C4×D4—34no—
420C4×D4—68no—
421C4×D4—62no—
422C4×D4—62no—
423#117—68no—
424C2×C4⋊C4—21no—
425C2×C4⋊C4—31no—
426C2×C4⋊C4—31no—
427C2×C4⋊C4—61no—
428C2×C4⋊C4—61no—
429C2×C4⋊C4—61no—
430C2×C4⋊C4—61no—
431C2×C4⋊C4—61no—
432C2×C4⋊C4—61no—
433C2×C4⋊C4—61no—
434C2×C4⋊C4C22×D311yescharacteristic
435C2×C4⋊C4C22×D311yescharacteristic
436C2×C22⋊C4—21no—
437C2×C22⋊C4—21no—
438C2×C22⋊C4—61no—
439C2×C22⋊C4—61no—
440C2×C22⋊C4—61no—
441C2×C22⋊C4—61no—
442C2×C42—31no—
443C2×C42—31no—
444C2×C42—34no—
445C2×C42—31no—
446C2×C42—31no—
447C2×C42—34no—
448C2×C42—61no—
449C2×C42—61no—
450#106—34no—
451#106—34no—
452#106—34no—
453#106C22×D314yes—
454#103—34no—
455#103—34no—
456#103—34no—
457#103C22×D314yes—
458#102—34no—
459#102—34no—
460#102—34no—
461#102C22×D314yes—
462C4×C8—34no—
463C4×C8—34no—
464C4×C8—34no—
465C4×C8—34no—
466C23×C3—22no—
467C23×C3—22no—
468C23×C3—22no—
469C23×C3—42no—
470C23×C3—42no—
471C23×C3—42no—
472C23×C3C2×SD1614yes—
473C23×C3C22×D412yes—
474C23×C3C22×D411yescharacteristic
475C22×D3—22no—
476C22×D3—42no—
477C22×D3—42no—
478C22×D3—42no—
479C3×Q8—22no—
480C3×Q8—22no—
481C3×Q8—42no—
482C3×D4—22no—
483C3×D4—22no—
484C3×D4—48no—
485C3×D4—42no—
486C2×C3×C4—22no—
487C2×C3×C4—24no—
488C2×C3×C4—22no—
489C2×C3×C4—22no—
490C2×C3×C4—22no—
491C2×C3×C4—22no—
492C2×C3×C4—22no—
493C2×C3×C4—42no—
494C2×C3×C4—42no—
495C2×C3×C4—42no—
496C2×C3×C4C22×D412yes—
497C2×C3×C4C22×D411yescharacteristic
498C2×C3×C4C2×#4112yes—
499C2×C3×C4C2×#4112yes—
500C2×C3×C4C2511yescharacteristic
501#67—48no—
502#67—48no—
503#67—48no—
504C2×Dic3—22no—
505C2×Dic3—28no—
506C2×Dic3—22no—
507C2×Dic3—22no—
508C2×Dic3—22no—
509C2×Dic3—42no—
510C2×Dic3—42no—
511C2×Dic3—42no—
512C2×Dic3—48no—
513C2×Dic3C2×SD1614yes—
514C2×Dic3C2×SD1614yes—
515C2×Dic3C2×SD16116yescomplemented
516C2×Dic3#13514yes—
517C2×Dic3C22×D412yes—
518C2×Dic3C22×D412yes—
519C2×Dic3C22×D412yes—
520C2×Dic3C22×D412yes—
521D12—22no—
522D12—22no—
523D12—42no—
524C4×D3—48no—
525Dic6—22no—
526Dic6—22no—
527Dic6—42no—
528Dic6—48no—
529Dic6—48no—
530C3×C8—22no—
531C3×C8C2×#4114yescomplemented
532C3⋊C8—22no—
533C3⋊C8C2×#4114yescomplemented
534C24—21no—
535C24—61no—
536C24D3×D411yescharacteristic
537#41—1232no—
538C2×Q8—21no—
539C2×Q8—22no—
540C2×Q8—22no—
541C2×Q8—32no—
542C2×Q8—64no—
543C2×Q8—64no—
544C2×Q8—61no—
545C2×Q8—62no—
546C2×Q8—62no—
547C2×Q8—124no—
548C2×Q8—124no—
549C2×Q8C23×D312yes—
550C2×D4—24no—
551C2×D4—21no—
552C2×D4—22no—
553C2×D4—22no—
554C2×D4—32no—
555C2×D4—44no—
556C2×D4—64no—
557C2×D4—64no—
558C2×D4—64no—
559C2×D4—61no—
560C2×D4—62no—
561C2×D4—62no—
562C2×D4—124no—
563C2×D4—124no—
564C2×D4—124no—
565C2×D4C23×D312yes—
566C22×C4—22no—
567C22×C4—22no—
568C22×C4—21no—
569C22×C4—21no—
570C22×C4—21no—
571C22×C4—38no—
572C22×C4—34no—
573C22×C4—31no—
574C22×C4—31no—
575C22×C4—31no—
576C22×C4—34no—
577C22×C4—31no—
578C22×C4—64no—
579C22×C4—64no—
580C22×C4—64no—
581C22×C4—61no—
582C22×C4—61no—
583C22×C4—61no—
584C22×C4—124no—
585C22×C4—124no—
586C22×C4D3×D412yes—
587C22×C4D3×D411yescharacteristic
588C22×C4C23×D312yes—
589C22×C4C23×D311yescharacteristic
590SD16—28no—
591SD16—68no—
592SD16—68no—
593SD16—68no—
594C2×C8—22no—
595C2×C8—28no—
596C2×C8—34no—
597C2×C8—32no—
598C2×C8—32no—
599C2×C8—68no—
600C2×C8—62no—
601C2×C8#23714yescomplemented
602C2×C8C23×D312yes—
603C2×C8C23×D312yes—
604C4⋊C4—24no—
605C4⋊C4—21no—
606C4⋊C4—21no—
607C4⋊C4—32no—
608C4⋊C4—32no—
609C4⋊C4—64no—
610C4⋊C4—64no—
611C4⋊C4—64no—
612C4⋊C4—64no—
613C4⋊C4—64no—
614C4⋊C4—64no—
615C4⋊C4—61no—
616C4⋊C4—61no—
617C4⋊C4—64no—
618C4⋊C4C23×D312yes—
619C4⋊C4C23×D312yes—
620C22⋊C4—24no—
621C22⋊C4—24no—
622C22⋊C4—64no—
623C22⋊C4—64no—
624C22⋊C4—64no—
625C22⋊C4—64no—
626C42—34no—
627C42—32no—
628C42—34no—
629C42—32no—
630C42—32no—
631C42—32no—
632C42—64no—
633C42—64no—
634C22×C3—28no—
635C22×C3—22no—
636C22×C3—22no—
637C22×C3—42no—
638C22×C3—42no—
639C22×C3—42no—
640C22×C3—84no—
641C22×C3#53212yes—
642C22×C3C22×SD1614yes—
643C22×C3C22×SD1612yes—
644C22×C3C2×#13512yes—
645C22×C3C23×D411yescharacteristic
646C2×D3—42no—
647C2×D3—42no—
648C2×D3—42no—
649C2×D3—84no—
650C3×C4—22no—
651C3×C4—42no—
652C3×C4—42no—
653C3×C4—42no—
654C3×C4#53212yes—
655C3×C4C22×#4111yescharacteristic
656C3×C4C22×#4111yescharacteristic
657Dic3—22no—
658Dic3—42no—
659Dic3—42no—
660Dic3—42no—
661Dic3C22×SD1614yes—
662Dic3C22×SD1614yes—
663Dic3C2×#13514yes—
664C23—22no—
665C23—22no—
666C23—22no—
667C23—42no—
668C23—42no—
669C23—42no—
670C23—62no—
671C23—122no—
672C23—122no—
673C23—122no—
674C23D3×SD1614yes—
675C23C2×D3×D412yes—
676C23C2×D3×D411yescharacteristic
677Q8—22no—
678Q8—22no—
679Q8—42no—
680Q8—62no—
681Q8—62no—
682Q8—128no—
683Q8—128no—
684Q8—122no—
685D4—22no—
686D4—22no—
687D4—48no—
688D4—42no—
689D4—62no—
690D4—62no—
691D4—128no—
692D4—128no—
693D4—128no—
694D4—122no—
695C2×C4—22no—
696C2×C4—22no—
697C2×C4—22no—
698C2×C4—24no—
699C2×C4—22no—
700C2×C4—22no—
701C2×C4—22no—
702C2×C4—32no—
703C2×C4—32no—
704C2×C4—32no—
705C2×C4—34no—
706C2×C4—34no—
707C2×C4—316no—
708C2×C4—34no—
709C2×C4—32no—
710C2×C4—42no—
711C2×C4—42no—
712C2×C4—42no—
713C2×C4—68no—
714C2×C4—62no—
715C2×C4—62no—
716C2×C4—62no—
717C2×C4—62no—
718C2×C4—128no—
719C2×C4—128no—
720C2×C4—122no—
721C2×C4—122no—
722C2×C4—122no—
723C2×C4C2×D3×D412yes—
724C2×C4C2×D3×D411yescharacteristic
725C2×C4C2×#23712yes—
726C2×C4D3×#4112yes—
727C2×C4C24×D311yescharacteristic
728C8—22no—
729C8—34no—
730C8—62no—
731C8C2×#23714yescomplemented
732C2×C3—24no—
733C2×C3—82no—
734C2×C3#316714yescomplemented
735C2×C3C2×#53211yescharacteristic
736C2×C3C23×SD1611yescharacteristic
737C2×C3C22×#13511yescharacteristic
738D3—82no—
739C22—22no—
740C22—22no—
741C22—28no—
742C22—42no—
743C22—42no—
744C22—42no—
745C22—84no—
746C22—122no—
747C22—122no—
748C22—122no—
749C22—244no—
750C22#559612yes—
751C22C2×D3×SD1614yes—
752C22C2×D3×SD1612yes—
753C22D3×#13512yes—
754C22C22×D3×D411yescharacteristic
755C4—22no—
756C4—34no—
757C4—34no—
758C4—34no—
759C4—42no—
760C4—42no—
761C4—42no—
762C4—62no—
763C4—122no—
764C4—122no—
765C4—122no—
766C4#559612yes—
767C4C22×#23711yescharacteristic
768C4C2×D3×#4111yescharacteristic
769C3C2×#316711yescharacteristic, complemented, Sylow
770C2—24no—
771C2—82no—
772C2—242no—
773C2#8063214yesdirect product factor
774C2C2×#559611yescharacteristic
775C2C22×D3×SD1611yescharacteristic
776C2C2×D3×#13511yescharacteristic
subgroupG/H
centerC23C2×D3×D4
commutator, cosocleC2×C3×C4C25
FrattiniC2×C4C24×D3
FittingC2×C3×#465C2
socleC23×C3C22×D4
prime radicalC2×#5596C2
hypercenterC2×#465D3
hypocenterC3C2×#3167
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#465

Complements

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

NH ≅ G/Ntype
1. C2×#5622C2semidirect
3. C2×C3×#465C2semidirect
4. C2×#5175C2semidirect
5. C2×Dic3×SD16C2semidirect
6. C2×#5114C2semidirect
7. C22×C8×Dic3C2semidirect
8. C2×#5048C2semidirect
9. C2×#5041C2semidirect
10. #80632C2direct (N × H)
11. C2×#4855C2semidirect
12. C2×#4852C2semidirect
13. C2×#4792C2semidirect
14. C2×#4788C2semidirect
15. C2×#4760C2semidirect
16. C2×#4758C2semidirect
36. #5622C22semidirect
49. C3×#465C22semidirect
55. #5175C22semidirect
56. Dic3×SD16C22semidirect
57. #5114C22semidirect
65. C2×C8×Dic3C22semidirect
66. #5048C22semidirect
67. #5041C22semidirect
72. #4855C22semidirect
73. #4852C22semidirect
74. #4792C22semidirect
75. #4788C22semidirect
76. #4760C22semidirect
77. #4758C22semidirect
88. C2×#465D3semidirect
238. #465C2×D3semidirect
294. C22×Dic3SD16semidirect
319. C2×C3×C8#41semidirect
356. C2×C3⋊C8#41semidirect
515. C2×Dic3C2×SD16semidirect
531. C3×C8C2×#41semidirect
533. C3⋊C8C2×#41semidirect
601. C2×C8#237semidirect
731. C8C2×#237semidirect
734. C2×C3#3167semidirect
769. C3C2×#3167semidirect
773. C2#80632direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#56222
C2×#55962
C2×C3×#4652
C2×#51752
C2×Dic3×SD162
C2×#51142
C22×C8×Dic32
C2×#50482
C2×#50412
#806322
C2×#48552
C2×#48522
C2×#47922
C2×#47882
C2×#47602
C2×#47582
C2×#31673