Finite Group Databasebeta

← C2×#13081092 #15632342

Subgroups — C2×#13081092 #15632342

Order 2816.

2158 conjugacy classes of subgroups.

The subgroup lattice has 772 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623149C211yesmaximal, characteristic, complemented
2C2×#10623142C211yesmaximal, characteristic, complemented
3#13081092C2116yesmaximal, direct product factor
4C2×#10622489C211yesmaximal, characteristic, complemented
5C2×#10622390C211yesmaximal, characteristic, complemented
6C2×#10622647C211yesmaximal, characteristic, complemented
7C2×#10622392C211yesmaximal, characteristic, complemented
8C2×#10622646C211yesmaximal, characteristic, complemented
9C2×#10622376C211yesmaximal, characteristic, complemented
10C2×#10622374C211yesmaximal, characteristic, complemented
11C2×#10622772C211yesmaximal, characteristic, complemented
12C2×#10622765C211yesmaximal, characteristic, complemented
13C2×#10622724C211yesmaximal, characteristic, complemented
14C2×#10622494C211yesmaximal, characteristic, complemented
15C22×#66881C211yesmaximal, characteristic, complemented
16C2×C11×#466C211yesmaximal, characteristic, complemented
17C22×#4341—21no—
18C22×C11×D8C2211yescharacteristic
19C23×C8×C11C2211yescharacteristic
20C2×C11×#121C2211yescharacteristic
21C2×C11×#121C2211yescharacteristic
22C2×#66992—21no—
23C2×#66991C2211yescharacteristic
24C2×#66991C2211yescharacteristic
25C2×#66988—21no—
26C2×D4×Dic11—21no—
27C2×D4×Dic11C2211yescharacteristic
28C2×D4×Dic11C2211yescharacteristic
29C2×C4×C22⋊D11C2211yescharacteristic
30C22×C4⋊Dic11C2211yescharacteristic
31C22×C4⋊Dic11C2211yescharacteristic
32C22×#4313C2211yescharacteristic
33#10623149—24no—
34#10623149C2218yescomplemented
35#10623142—24no—
36#10623142C2218yescomplemented
37C2×#66945C2211yescharacteristic
38C2×C4⋊C4×D11C2211yescharacteristic
39C2×#66943C2211yescharacteristic
40C2×#66941C2211yescharacteristic
41C2×#66939—21no—
42C2×#66936—21no—
43C2×#66932—21no—
44C2×#66931—21no—
45C11×#466C2218yescomplemented
46C2×C11×#107C2211yescharacteristic
47C2×C11×#102C2211yescharacteristic
48C2×C11×#102C2211yescharacteristic
49C2×#66896C2211yescharacteristic
50C2×#66896C2211yescharacteristic
51C2×#66896C2211yescharacteristic
52C2×#66896C2211yescharacteristic
53C2×C22⋊(C11⋊C8)C2211yescharacteristic
54#10622772C2218yescomplemented
55#10622765C2218yescomplemented
56#10622724C2218yescomplemented
57C2×(C2×D11)⋊C8C2211yescharacteristic
58C2×#66881C2211yescharacteristic
59C2×#66881C2211yescharacteristic
60C2×#66881C2211yescharacteristic
61C2×#66881C2211yescharacteristic
62C2×#66881C2218yescomplemented
63C2×#66879C2211yescharacteristic
64C2×Dic11⋊C8C2211yescharacteristic
65#10622647C2218yescomplemented
66#10622646C2218yescomplemented
67C2×#66872C2211yescharacteristic
68C2×#66872C2211yescharacteristic
69C2×#66871C2211yescharacteristic
70C2×#66871C2211yescharacteristic
71#10622494C2218yescomplemented
72#10622489C2218yescomplemented
73#10622392C2218yescomplemented
74#10622390C2218yescomplemented
75#10622376C2218yescomplemented
76#10622374C2218yescomplemented
77C22×D4×C11—21no—
78C22×D4×C11—21no—
79C22×D4×C11C2311yescharacteristic
80C22×D4×C11C2311yescharacteristic
81C23×C4×C11C2311yescharacteristic
82C22×C22⋊D11—21no—
83C22×C22⋊D11—21no—
84C22×C22⋊D11D411yescharacteristic
85C23×Dic11—21no—
86C23×Dic11—21no—
87C23×Dic11—21no—
88C23×Dic11—21no—
89C2×#4341—28no—
90C2×#4341—48no—
91C22×C4×D11—21no—
92C22×C4×D11C2311yescharacteristic
93C22×Dic22—21no—
94C2×C11×D8—24no—
95C2×C11×D8C2314yes—
96C22×C8×C11—24no—
97C22×C8×C11C2311yescharacteristic
98C22×C8×C11C2314yes—
99C22×C8×C11C2311yescharacteristic
100C11×#121—22no—
101C11×#121—22no—
102C11×#121C2314yes—
103C11×#121C2314yes—
104C2×C11×C4⋊C4C2311yescharacteristic
105C2×C11×C4⋊C4C2311yescharacteristic
106C2×C11×C22⋊C4—21no—
107C2×C11×C22⋊C4—21no—
108C2×C22⋊Dic11—21no—
109C2×C22⋊Dic11—21no—
110C2×C22⋊Dic11—21no—
111C2×C22⋊Dic11—21no—
112C2×C22⋊Dic11D411yescharacteristic
113#66992—28no—
114#66991—22no—
115#66991—22no—
116#66991C2314yes—
117#66991C2314yes—
118#66988—28no—
119D4×Dic11—28no—
120D4×Dic11—22no—
121D4×Dic11—22no—
122D4×Dic11C2314yes—
123D4×Dic11C2314yes—
124C4×C22⋊D11D414yes—
125C4×C22⋊D11C2314yes—
126C2×(C2×D11)⋊C4—21no—
127C2×(C2×D11)⋊C4D411yescharacteristic
128C2×C4⋊Dic11—21no—
129C2×C4⋊Dic11—21no—
130C2×C4⋊Dic11—22no—
131C2×C4⋊Dic11—22no—
132C2×C4⋊Dic11—21no—
133C2×C4⋊Dic11C2311yescharacteristic
134C2×C4⋊Dic11C2311yescharacteristic
135C2×C4⋊Dic11C2311yescharacteristic
136C2×C4⋊Dic11C2311yescharacteristic
137C2×C4⋊Dic11C2314yes—
138C2×C4⋊Dic11C2314yes—
139C2×Dic11⋊C4—21no—
140C2×Dic11⋊C4—21no—
141C2×Dic11⋊C4—21no—
142C2×Dic11⋊C4D411yescharacteristic
143C2×C4×Dic11—21no—
144C2×C4×Dic11C2311yescharacteristic
145C22×C11⋊C8C2311yescharacteristic
146C22×C11⋊C8C2311yescharacteristic
147C2×#4313—24no—
148C2×#4313C2314yes—
149#66945—22no—
150#66945C2314yes—
151C4⋊C4×D11—22no—
152C4⋊C4×D11C2314yes—
153#66943—22no—
154#66943C2314yes—
155#66941—22no—
156#66941C2314yes—
157#66939—28no—
158#66936—28no—
159#66932—28no—
160#66931—28no—
161C11×#107C2314yes—
162C11×#102C2314yes—
163C11×#102C2314yes—
164#66896C2314yes—
165#66896C2314yes—
166#66896C2314yes—
167#66896C2314yes—
168C22⋊(C11⋊C8)C2314yes—
169(C2×D11)⋊C8C2314yes—
170#66881C2314yes—
171#66881C2314yes—
172#66881C2314yes—
173#66881C2314yes—
174#66879C2314yes—
175Dic11⋊C8C2314yes—
176#66872C2314yes—
177#66872C2314yes—
178#66871C2314yes—
179#66871C2314yes—
180C2×#3345—111nomaximal, Sylow
181C24×C11—21no—
182C24×C11—21no—
183C24×C11C2×D411yescharacteristic
184C23×D11C2×D411yescharacteristic
185C2×D4×C11—24no—
186C2×D4×C11—24no—
187C2×D4×C11—21no—
188C2×D4×C11—21no—
189C2×D4×C11—22no—
190C2×D4×C11—22no—
191C2×D4×C11—22no—
192C2×D4×C11—22no—
193C2×D4×C11—44no—
194C2×D4×C11—44no—
195C2×D4×C11C2412yes—
196C2×D4×C11C2412yes—
197C22×C4×C11—22no—
198C22×C4×C11—22no—
199C22×C4×C11—21no—
200C22×C4×C11—21no—
201C22×C4×C11C2×D411yescharacteristic
202C22×C4×C11C2×D412yes—
203C22×C4×C11C2412yes—
204C22×C4×C11C2411yescharacteristic
205C2×C22⋊D11—24no—
206C2×C22⋊D11—24no—
207C2×C22⋊D11—24no—
208C2×C22⋊D11—44no—
209C2×C22⋊D11—82no—
210C2×C22⋊D11C2×D414yes—
211C22×Dic11—24no—
212C22×Dic11—24no—
213C22×Dic11—21no—
214C22×Dic11—21no—
215C22×Dic11—21no—
216C22×Dic11—21no—
217C22×Dic11—24no—
218C22×Dic11—24no—
219C22×Dic11—44no—
220C22×Dic11—44no—
221C22×Dic11—82no—
222C22×Dic11—82no—
223C22×Dic11C2×D411yescharacteristic
224C22×Dic11C2×D411yescharacteristic
225C22×Dic11C2×D411yescharacteristic
226#4341—432no—
227C2×C4×D11—24no—
228C2×C4×D11—22no—
229C2×C4×D11—22no—
230C2×C4×D11—44no—
231C2×C4×D11C2×D412yes—
232C2×C4×D11C2412yes—
233C2×Dic22—24no—
234C2×Dic22—44no—
235C11×D8—28no—
236C2×C8×C11—28no—
237C2×C8×C11—22no—
238C2×C8×C11#4114yescomplemented
239C2×C8×C11C2412yes—
240C2×C8×C11C2412yes—
241C11×C4⋊C4—21no—
242C11×C4⋊C4—21no—
243C11×C4⋊C4C2412yes—
244C11×C4⋊C4C2412yes—
245C11×C22⋊C4—24no—
246C11×C22⋊C4—24no—
247C22⋊Dic11—24no—
248C22⋊Dic11—24no—
249C22⋊Dic11—24no—
250C22⋊Dic11—24no—
251C22⋊Dic11C2×D414yes—
252(C2×D11)⋊C4—24no—
253(C2×D11)⋊C4C2×D414yes—
254C4⋊Dic11—24no—
255C4⋊Dic11—24no—
256C4⋊Dic11—24no—
257C4⋊Dic11—21no—
258C4⋊Dic11—21no—
259C4⋊Dic11—21no—
260C4⋊Dic11—21no—
261C4⋊Dic11C2412yes—
262C4⋊Dic11C2412yes—
263C4⋊Dic11C2412yes—
264C4⋊Dic11C2412yes—
265Dic11⋊C4—24no—
266Dic11⋊C4—24no—
267Dic11⋊C4—24no—
268Dic11⋊C4C2×D414yes—
269C4×Dic11—24no—
270C4×Dic11C2×D412yes—
271C4×Dic11C2412yes—
272C2×C11⋊C8—22no—
273C2×C11⋊C8—22no—
274C2×C11⋊C8C2412yes—
275C2×C11⋊C8C2412yes—
276#4313—28no—
277C2×#553—111no—
278C2×#547—111no—
279#3345—1116no—
280C2×#501—111no—
281C2×#481—111no—
282C2×#481—111no—
283C2×#482—111no—
284C2×#480—111no—
285C2×#478—111no—
286C2×#476—111no—
287C2×#469—111no—
288C2×#466D1111yescharacteristic, complemented
289C2×#442—111no—
290C2×#435—111no—
291C2×#428—111no—
292C22×#106—111no—
293C23×C11—22no—
294C23×C11—22no—
295C23×C11—22no—
296C23×C11—22no—
297C23×C11—42no—
298C23×C11—42no—
299C23×C11—42no—
300C23×C11—42no—
301C23×C11—42no—
302C23×C11—42no—
303C23×C11AGL(1,ℤ/8)14yes—
304C23×C11C22×D412yes—
305C23×C11C22×D411yescharacteristic
306C22×D11—22no—
307C22×D11—22no—
308C22×D11—22no—
309C22×D11C22×D412yes—
310D4×C11—22no—
311D4×C11—22no—
312D4×C11—22no—
313D4×C11—22no—
314D4×C11—48no—
315D4×C11—48no—
316D4×C11—42no—
317D4×C11—42no—
318C2×C4×C11—22no—
319C2×C4×C11—24no—
320C2×C4×C11—22no—
321C2×C4×C11—22no—
322C2×C4×C11—22no—
323C2×C4×C11—22no—
324C2×C4×C11—42no—
325C2×C4×C11—42no—
326C2×C4×C11C22×D412yes—
327C2×C4×C11C22×D411yescharacteristic
328C2×C4×C11C2×#4112yes—
329C2×C4×C112−1+412yes—
330C2×C4×C11C2511yescharacteristic
331C22⋊D11—28no—
332C22⋊D11—48no—
333C22⋊D11—84no—
334C2×Dic11—22no—
335C2×Dic11—22no—
336C2×Dic11—22no—
337C2×Dic11—22no—
338C2×Dic11—22no—
339C2×Dic11—22no—
340C2×Dic11—22no—
341C2×Dic11—48no—
342C2×Dic11—42no—
343C2×Dic11—42no—
344C2×Dic11—48no—
345C2×Dic11—42no—
346C2×Dic11—42no—
347C2×Dic11—84no—
348C2×Dic11—84no—
349C2×Dic11C22×D412yes—
350C2×Dic11C22×D412yes—
351C2×Dic11C22×D412yes—
352C4×D11—24no—
353C4×D11—22no—
354C4×D11—22no—
355C4×D11—48no—
356Dic22—48no—
357C8×C11—22no—
358C8×C11C2×#4114yescomplemented
359C11⋊C8—22no—
360C11⋊C8—22no—
361C22×#41—221no—
362C22×D8C2×D1111yescharacteristic
363C22×M16—111no—
364C23×C8C2×D1111yescharacteristic
365#553—118no—
366#553—224no—
367#547—118no—
368#547—224no—
369C2×C4⋊Q8—111no—
370C2×#126—221no—
371C2×#125—111no—
372C2×#123—221no—
373C2×#123—221no—
374C2×#123—221no—
375C2×C22⋊Q8—221no—
376C2×#121—111no—
377C2×#121—111no—
378C2×#121—221no—
379C2×#121C2×D1111yescharacteristic
380C2×#121C2×D1111yescharacteristic
381C2×C4×D4—111no—
382C2×C4×D4—111no—
383C2×C4×D4—111no—
384C2×C4×D4—221no—
385C2×#117—111no—
386C22×C4⋊C4—111no—
387C22×C4⋊C4—111no—
388C22×C4⋊C4—111no—
389#501—118no—
390#482—118no—
391#481—118no—
392#481—118no—
393#480—118no—
394#478—118no—
395#476—118no—
396#469—118no—
397#466C2×D1118yescomplemented
398#442—118no—
399#435—118no—
400#428—118no—
401C2×#107—111no—
402C2×#107—111no—
403C2×#107C2×D1111yescharacteristic
404C2×#106—111no—
405C2×#106—111no—
406C2×#106—118no—
407C2×#106—111no—
408C2×#106—111no—
409C2×#106—111no—
410C2×#106—111no—
411C2×C4⋊C8—111no—
412C2×#102—111no—
413C2×#102—111no—
414C2×#102—111no—
415C2×#102—111no—
416C2×#102C2×D1111yescharacteristic
417C2×#102C2×D1111yescharacteristic
418C2×C22⋊C8—111no—
419C2×C22⋊C8—111no—
420C2×#97—111no—
421C22×C11—28no—
422C22×C11—22no—
423C22×C11—22no—
424C22×C11—42no—
425C22×C11—42no—
426C22×C11—42no—
427C22×C11—42no—
428C22×C11—42no—
429C22×C11—42no—
430C22×C11—84no—
431C22×C11—84no—
432C22×C11#54712yes—
433C22×C11C2×AGL(1,ℤ/8)14yes—
434C22×C11C2×AGL(1,ℤ/8)12yes—
435C22×C11#57712yes—
436C22×C11C23×D411yescharacteristic
437C2×D11—22no—
438C2×D11—22no—
439C2×D11—22no—
440C2×D11—44no—
441C4×C11—22no—
442C4×C11—42no—
443C4×C11—42no—
444C4×C11#54712yes—
445C4×C11C22×#4111yescharacteristic
446C4×C11C2×2−1+411yescharacteristic
447Dic11—22no—
448Dic11—22no—
449Dic11—22no—
450Dic11—42no—
451Dic11—42no—
452Dic11—42no—
453Dic11—42no—
454C2×#41—228no—
455C2×#41—448no—
456C22×Q8—221no—
457C22×D4—21no—
458C22×D4—21no—
459C22×D4—111no—
460C22×D4—221no—
461C22×D4—221no—
462C22×D4C22×D1111yescharacteristic
463C22×D4C22×D1111yescharacteristic
464C23×C4—111no—
465C23×C4—221no—
466C23×C4—221no—
467C23×C4—221no—
468C23×C4—221no—
469C23×C4—221no—
470C23×C4C22×D1111yescharacteristic
471C2×D8—24no—
472C2×D8C22×D1114yes—
473C2×M16—114no—
474C2×M16—224no—
475C22×C8—24no—
476C22×C8—111no—
477C22×C8—111no—
478C22×C8C22×D1111yescharacteristic
479C22×C8C22×D1114yes—
480C22×C8C22×D1111yescharacteristic
481C4⋊Q8—114no—
482C4⋊Q8—222no—
483#126—228no—
484#125—114no—
485#125—222no—
486#123—228no—
487#123—228no—
488#123—228no—
489C22⋊Q8—228no—
490#121—22no—
491#121—22no—
492#121—114no—
493#121—114no—
494#121—222no—
495#121—222no—
496#121—228no—
497#121C22×D1114yes—
498#121C22×D1114yes—
499C4×D4—114no—
500C4×D4—114no—
501C4×D4—114no—
502C4×D4—114no—
503C4×D4—222no—
504C4×D4—222no—
505C4×D4—228no—
506#117—114no—
507#117—222no—
508C2×C4⋊C4—111no—
509C2×C4⋊C4—111no—
510C2×C4⋊C4—111no—
511C2×C4⋊C4—111no—
512C2×C4⋊C4—111no—
513C2×C4⋊C4—114no—
514C2×C4⋊C4—114no—
515C2×C4⋊C4—114no—
516C2×C4⋊C4—222no—
517C2×C4⋊C4—221no—
518C2×C4⋊C4—221no—
519C2×C4⋊C4—221no—
520C2×C4⋊C4—221no—
521C2×C4⋊C4—221no—
522C2×C4⋊C4—221no—
523C2×C4⋊C4—222no—
524C2×C4⋊C4—222no—
525C2×C4⋊C4C22×D1111yescharacteristic
526C2×C4⋊C4C22×D1111yescharacteristic
527C2×C22⋊C4—21no—
528C2×C22⋊C4—21no—
529C2×C22⋊C4—111no—
530C2×C22⋊C4—111no—
531C2×C22⋊C4—221no—
532C2×C22⋊C4—221no—
533C2×C22⋊C4—221no—
534C2×C22⋊C4—221no—
535C2×C22⋊C4—221no—
536C2×C42—111no—
537C2×C42—221no—
538#107—114no—
539#107—114no—
540#107C22×D1114yes—
541#106—114no—
542#106—114no—
543#106—114no—
544#106—114no—
545#106—114no—
546#106—114no—
547C4⋊C8—114no—
548#102—114no—
549#102—114no—
550#102—114no—
551#102—114no—
552#102C22×D1114yes—
553#102C22×D1114yes—
554C22⋊C8—114no—
555C22⋊C8—114no—
556#97—114no—
557C2×C11—24no—
558C2×C11—82no—
559C2×C11—82no—
560C2×C11#334514yescomplemented
561C2×C11C2×#54711yescharacteristic
562C2×C11C22×AGL(1,ℤ/8)11yescharacteristic
563C2×C11C2×#57711yescharacteristic
564D11—42no—
565C24—21no—
566C24—21no—
567C24—111no—
568C24D4×D1111yescharacteristic
569#41—4432no—
570C2×Q8—224no—
571C2×Q8—444no—
572C2×D4—24no—
573C2×D4—24no—
574C2×D4—21no—
575C2×D4—21no—
576C2×D4—22no—
577C2×D4—22no—
578C2×D4—22no—
579C2×D4—22no—
580C2×D4—44no—
581C2×D4—44no—
582C2×D4—114no—
583C2×D4—224no—
584C2×D4—224no—
585C2×D4—224no—
586C2×D4—444no—
587C2×D4—882no—
588C2×D4C23×D1112yes—
589C2×D4C23×D1112yes—
590C22×C4—22no—
591C22×C4—22no—
592C22×C4—21no—
593C22×C4—21no—
594C22×C4—111no—
595C22×C4—111no—
596C22×C4—111no—
597C22×C4—112no—
598C22×C4—112no—
599C22×C4—224no—
600C22×C4—224no—
601C22×C4—224no—
602C22×C4—222no—
603C22×C4—222no—
604C22×C4—224no—
605C22×C4—221no—
606C22×C4—221no—
607C22×C4—221no—
608C22×C4—221no—
609C22×C4—224no—
610C22×C4—444no—
611C22×C4—444no—
612C22×C4—444no—
613C22×C4—882no—
614C22×C4—882no—
615C22×C4D4×D1112yes—
616C22×C4D4×D1111yescharacteristic
617C22×C4C23×D1112yes—
618C22×C4C23×D1111yescharacteristic
619D8—28no—
620M16—228no—
621C2×C8—22no—
622C2×C8—28no—
623C2×C8—112no—
624C2×C8—112no—
625C2×C8—222no—
626C2×C8—222no—
627C2×C8#434114yescomplemented
628C2×C8C23×D1112yes—
629C2×C8C23×D1112yes—
630C4⋊C4—21no—
631C4⋊C4—21no—
632C4⋊C4—114no—
633C4⋊C4—112no—
634C4⋊C4—112no—
635C4⋊C4—112no—
636C4⋊C4—112no—
637C4⋊C4—224no—
638C4⋊C4—224no—
639C4⋊C4—224no—
640C4⋊C4—224no—
641C4⋊C4—221no—
642C4⋊C4—221no—
643C4⋊C4—221no—
644C4⋊C4—221no—
645C4⋊C4—224no—
646C4⋊C4—224no—
647C4⋊C4C23×D1112yes—
648C4⋊C4C23×D1112yes—
649C22⋊C4—24no—
650C22⋊C4—24no—
651C22⋊C4—114no—
652C22⋊C4—114no—
653C22⋊C4—224no—
654C22⋊C4—224no—
655C22⋊C4—224no—
656C22⋊C4—224no—
657C22⋊C4—224no—
658C42—112no—
659C42—112no—
660C42—224no—
661C11C2×#334511yescharacteristic, complemented, Sylow
662C23—22no—
663C23—22no—
664C23—22no—
665C23—22no—
666C23—42no—
667C23—42no—
668C23—42no—
669C23—42no—
670C23—42no—
671C23—42no—
672C23—112no—
673C23—222no—
674C23—222no—
675C23—222no—
676C23#6696414yes—
677C23C2×D4×D1112yes—
678C23C2×D4×D1111yescharacteristic
679Q8—448no—
680D4—22no—
681D4—22no—
682D4—22no—
683D4—22no—
684D4—48no—
685D4—48no—
686D4—42no—
687D4—42no—
688D4—228no—
689D4—448no—
690D4—884no—
691C2×C4—22no—
692C2×C4—24no—
693C2×C4—22no—
694C2×C4—22no—
695C2×C4—22no—
696C2×C4—22no—
697C2×C4—42no—
698C2×C4—42no—
699C2×C4—112no—
700C2×C4—112no—
701C2×C4—112no—
702C2×C4—222no—
703C2×C4—222no—
704C2×C4—222no—
705C2×C4—224no—
706C2×C4—222no—
707C2×C4—222no—
708C2×C4—222no—
709C2×C4—222no—
710C2×C4—222no—
711C2×C4—222no—
712C2×C4—448no—
713C2×C4—448no—
714C2×C4—442no—
715C2×C4—442no—
716C2×C4—448no—
717C2×C4—442no—
718C2×C4—442no—
719C2×C4—884no—
720C2×C4—884no—
721C2×C4C2×D4×D1112yes—
722C2×C4C2×D4×D1111yescharacteristic
723C2×C4C2×#434112yes—
724C2×C4#6704312yes—
725C2×C4C24×D1111yescharacteristic
726C8—22no—
727C8—222no—
728C8—222no—
729C8C2×#434114yescomplemented
730C22—28no—
731C22—22no—
732C22—22no—
733C22—42no—
734C22—42no—
735C22—42no—
736C22—42no—
737C22—42no—
738C22—42no—
739C22—84no—
740C22—84no—
741C22—222no—
742C22—222no—
743C22—222no—
744C22—444no—
745C22#1062314212yes—
746C22C2×#6696414yes—
747C22C2×#6696412yes—
748C22#1062330112yes—
749C22C22×D4×D1111yescharacteristic
750C4—22no—
751C4—42no—
752C4—42no—
753C4—222no—
754C4—222no—
755C4—222no—
756C4—442no—
757C4—442no—
758C4—442no—
759C4—442no—
760C4#1062314212yes—
761C4C22×#434111yescharacteristic
762C4C2×#6704311yescharacteristic
763C2—24no—
764C2—82no—
765C2—82no—
766C2—442no—
767C2#1308109214yesdirect product factor
768C2C2×#1062314211yescharacteristic
769C2C22×#6696411yescharacteristic
770C2C2×#1062330111yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#466C2
socleC23×C11C22×D4
hypercenterC2×#466D11
hypocenterC11C2×#3345
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#466

Complements

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

NH ≅ G/Ntype
1. C2×#10623149C2semidirect
2. C2×#10623142C2semidirect
3. #13081092C2direct (N × H)
4. C2×#10622489C2semidirect
5. C2×#10622390C2semidirect
6. C2×#10622647C2semidirect
7. C2×#10622392C2semidirect
8. C2×#10622646C2semidirect
9. C2×#10622376C2semidirect
10. C2×#10622374C2semidirect
11. C2×#10622772C2semidirect
12. C2×#10622765C2semidirect
13. C2×#10622724C2semidirect
14. C2×#10622494C2semidirect
15. C22×#66881C2semidirect
16. C2×C11×#466C2semidirect
34. #10623149C22semidirect
36. #10623142C22semidirect
45. C11×#466C22semidirect
54. #10622772C22semidirect
55. #10622765C22semidirect
56. #10622724C22semidirect
62. C2×#66881C22semidirect
65. #10622647C22semidirect
66. #10622646C22semidirect
71. #10622494C22semidirect
72. #10622489C22semidirect
73. #10622392C22semidirect
74. #10622390C22semidirect
75. #10622376C22semidirect
76. #10622374C22semidirect
238. C2×C8×C11#41semidirect
288. C2×#466D11semidirect
358. C8×C11C2×#41semidirect
397. #466C2×D11semidirect
560. C2×C11#3345semidirect
627. C2×C8#4341semidirect
661. C11C2×#3345semidirect
729. C8C2×#4341semidirect
767. C2#13081092direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106231492
C2×#106231422
#130810922
C2×#106224892
C2×#106223902
C2×#106226472
C2×#106223922
C2×#106226462
C2×#106223762
C2×#106223742
C2×#106227722
C2×#106227652
C2×#106227242
C2×#106224942
C22×#668812
C2×C11×#4662
C2×#334511