Finite Group Databasebeta

← C2×#13081091 #15632341

Subgroups — C2×#13081091 #15632341

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×#10623089C211yesmaximal, characteristic, complemented
2C2×#10623082C211yesmaximal, characteristic, complemented
3#13081091C2116yesmaximal, direct product factor
4C2×#10622315C211yesmaximal, characteristic, complemented
5C2×#10622390C211yesmaximal, characteristic, complemented
6C2×#10622390C211yesmaximal, characteristic, complemented
7C2×#10622397C211yesmaximal, characteristic, complemented
8C2×#10622387C211yesmaximal, characteristic, complemented
9C2×#10622622C211yesmaximal, characteristic, complemented
10C2×#10622621C211yesmaximal, characteristic, complemented
11C2×#10622772C211yesmaximal, characteristic, complemented
12C2×#10622770C211yesmaximal, characteristic, complemented
13C2×#10622319C211yesmaximal, characteristic, complemented
14C2×#10622474C211yesmaximal, characteristic, complemented
15C2×D11×#106C211yesmaximal, characteristic, complemented
16C2×C11×#442C211yesmaximal, characteristic, complemented
17C22×#4339—21no—
18C22×C11×D8C2211yescharacteristic
19C2×C4×D4×C11C2211yescharacteristic
20C2×C4×D4×C11C2211yescharacteristic
21C2×#66991C2211yescharacteristic
22C2×#66991C2211yescharacteristic
23C2×#66991C2211yescharacteristic
24C2×#66991C2211yescharacteristic
25C2×#66982—21no—
26C2×C4×C22⋊D11—21no—
27C2×#66977—21no—
28C22×#4313C2211yescharacteristic
29C22×C8×D11C2211yescharacteristic
30#10623089—24no—
31#10623089C2218yescomplemented
32#10623082—24no—
33#10623082C2218yescomplemented
34C2×#66945C2211yescharacteristic
35C2×C4⋊C4×D11C2211yescharacteristic
36C2×C4⋊C4×D11C2211yescharacteristic
37C2×C4⋊C4×D11C2211yescharacteristic
38C2×#66937—21no—
39C2×#66936—21no—
40C2×#66936—21no—
41C2×#66932—21no—
42C2×C4×D44C2211yescharacteristic
43C2×#66923C2211yescharacteristic
44C2×#66922C2211yescharacteristic
45C11×#442C2218yescomplemented
46C2×C11×#106C2211yescharacteristic
47C2×C11×#102C2211yescharacteristic
48C2×C11×#102C2211yescharacteristic
49C2×C11×#97C2211yescharacteristic
50C2×#66896C2211yescharacteristic
51C2×#66896C2211yescharacteristic
52C2×#66896C2211yescharacteristic
53C2×#66896C2211yescharacteristic
54#10622772C2218yescomplemented
55#10622770C2218yescomplemented
56C2×(C2×D11)⋊C8C2211yescharacteristic
57C2×(C2×D11)⋊C8C2211yescharacteristic
58C2×#66882C2211yescharacteristic
59C2×#66882C2211yescharacteristic
60C2×#66881C2211yescharacteristic
61C2×#66881C2211yescharacteristic
62#10622622C2218yescomplemented
63#10622621C2218yescomplemented
64C2×#66872C2211yescharacteristic
65C2×#66872C2211yescharacteristic
66C2×#66872C2211yescharacteristic
67C2×#66871C2211yescharacteristic
68C2×C4⋊(C11⋊C8)C2211yescharacteristic
69#10622474C2218yescomplemented
70D11×#106C2218yescomplemented
71#10622397C2218yescomplemented
72#10622390C2218yescomplemented
73#10622390C2218yescomplemented
74#10622387C2218yescomplemented
75#10622319C2218yescomplemented
76#10622315C2218yescomplemented
77C22×D4×C11C2311yescharacteristic
78C22×D4×C11C2311yescharacteristic
79C23×C4×C11—21no—
80C23×C4×C11—21no—
81C22×C22⋊D11—21no—
82C22×C22⋊D11—21no—
83C22×C22⋊D11—21no—
84C22×C22⋊D11—21no—
85C2×#4339—28no—
86C2×#4339—48no—
87C22×D44D411yescharacteristic
88C22×C4×D11—21no—
89C22×C4×D11—21no—
90C22×C4×D11—21no—
91C22×C4×D11C2311yescharacteristic
92C22×C4×D11C2311yescharacteristic
93C22×Dic22—21no—
94C2×C11×D8—24no—
95C2×C11×D8C2314yes—
96C22×C8×C11C2311yescharacteristic
97C22×C8×C11C2311yescharacteristic
98C4×D4×C11—22no—
99C4×D4×C11—22no—
100C4×D4×C11C2314yes—
101C4×D4×C11C2314yes—
102C2×C11×C4⋊C4C2311yescharacteristic
103C2×C11×C4⋊C4C2311yescharacteristic
104C2×C11×C22⋊C4—21no—
105C2×C11×C22⋊C4—21no—
106C2×C42×C11C2311yescharacteristic
107C2×C22⋊Dic11—21no—
108C2×C22⋊Dic11—21no—
109C2×C22⋊Dic11—21no—
110C2×C22⋊Dic11—21no—
111#66991—22no—
112#66991—22no—
113#66991—22no—
114#66991—22no—
115#66991C2314yes—
116#66991C2314yes—
117#66991C2314yes—
118#66991C2314yes—
119#66982—28no—
120C4×C22⋊D11—28no—
121C2×(C2×D11)⋊C4—21no—
122C2×(C2×D11)⋊C4D411yescharacteristic
123C2×(C2×D11)⋊C4D411yescharacteristic
124C2×C4⋊Dic11—21no—
125C2×C4⋊Dic11D411yescharacteristic
126C2×C4⋊Dic11C2311yescharacteristic
127C2×C4⋊Dic11C2311yescharacteristic
128C2×C4⋊Dic11C2311yescharacteristic
129C2×C4⋊Dic11C2311yescharacteristic
130#66977—28no—
131C2×Dic11⋊C4—21no—
132C2×Dic11⋊C4—21no—
133C2×Dic11⋊C4—21no—
134C2×Dic11⋊C4—21no—
135C2×Dic11⋊C4—21no—
136C2×C4×Dic11—21no—
137C22×C11⋊C8C2311yescharacteristic
138C22×C11⋊C8C2311yescharacteristic
139C2×#4313—24no—
140C2×#4313C2314yes—
141C2×C8×D11—24no—
142C2×C8×D11C2314yes—
143#66945—22no—
144#66945C2314yes—
145C4⋊C4×D11—22no—
146C4⋊C4×D11—22no—
147C4⋊C4×D11—22no—
148C4⋊C4×D11C2314yes—
149C4⋊C4×D11C2314yes—
150C4⋊C4×D11C2314yes—
151#66937—28no—
152#66936—28no—
153#66936—28no—
154#66932—28no—
155C4×D44D414yes—
156C4×D44C2314yes—
157#66923—22no—
158#66923C2314yes—
159#66922—22no—
160#66922C2314yes—
161C11×#106C2314yes—
162C11×#102C2314yes—
163C11×#102C2314yes—
164C11×#97C2314yes—
165#66896C2314yes—
166#66896C2314yes—
167#66896C2314yes—
168#66896C2314yes—
169(C2×D11)⋊C8C2314yes—
170(C2×D11)⋊C8C2314yes—
171#66882C2314yes—
172#66882C2314yes—
173#66881C2314yes—
174#66881C2314yes—
175#66872C2314yes—
176#66872C2314yes—
177#66872C2314yes—
178#66871C2314yes—
179C4⋊(C11⋊C8)C2314yes—
180C2×#3345—111nomaximal, Sylow
181C24×C11—21no—
182C24×C11—21no—
183C23×D11C2×D411yescharacteristic
184C23×D11C2×D411yescharacteristic
185C2×D4×C11—21no—
186C2×D4×C11—21no—
187C2×D4×C11—22no—
188C2×D4×C11—22no—
189C2×D4×C11—22no—
190C2×D4×C11—22no—
191C2×D4×C11C2412yes—
192C2×D4×C11C2412yes—
193C22×C4×C11—21no—
194C22×C4×C11—21no—
195C22×C4×C11—24no—
196C22×C4×C11—24no—
197C22×C4×C11—44no—
198C22×C4×C11—82no—
199C22×C4×C11C2×D411yescharacteristic
200C22×C4×C11C2×D411yescharacteristic
201C22×C4×C11C2411yescharacteristic
202C2×C22⋊D11—24no—
203C2×C22⋊D11—24no—
204C2×C22⋊D11—24no—
205C2×C22⋊D11—24no—
206C2×C22⋊D11—44no—
207C2×C22⋊D11—44no—
208C2×C22⋊D11—44no—
209C2×C22⋊D11—82no—
210C22×Dic11—21no—
211C22×Dic11—21no—
212C22×Dic11—21no—
213C22×Dic11—21no—
214C22×Dic11C2×D411yescharacteristic
215C22×Dic11C2×D411yescharacteristic
216#4339—432no—
217C2×D44—24no—
218C2×D44C2×D414yes—
219C2×C4×D11—24no—
220C2×C4×D11—24no—
221C2×C4×D11—24no—
222C2×C4×D11—22no—
223C2×C4×D11—22no—
224C2×C4×D11—22no—
225C2×C4×D11—22no—
226C2×C4×D11—44no—
227C2×C4×D11—44no—
228C2×C4×D11—82no—
229C2×C4×D11C2×D412yes—
230C2×C4×D11C2×D412yes—
231C2×C4×D11C2412yes—
232C2×C4×D11C2412yes—
233C2×Dic22—24no—
234C2×Dic22—44no—
235C11×D8—28no—
236C2×C8×C11—22no—
237C2×C8×C11#4114yescomplemented
238C2×C8×C11C2412yes—
239C2×C8×C11C2412yes—
240C11×C4⋊C4—21no—
241C11×C4⋊C4—21no—
242C11×C4⋊C4C2412yes—
243C11×C4⋊C4C2412yes—
244C11×C22⋊C4—24no—
245C11×C22⋊C4—24no—
246C42×C11C2×D412yes—
247C42×C11C2412yes—
248C22⋊Dic11—24no—
249C22⋊Dic11—24no—
250C22⋊Dic11—24no—
251C22⋊Dic11—24no—
252(C2×D11)⋊C4—24no—
253(C2×D11)⋊C4C2×D414yes—
254(C2×D11)⋊C4C2×D414yes—
255C4⋊Dic11—21no—
256C4⋊Dic11—21no—
257C4⋊Dic11—24no—
258C4⋊Dic11—21no—
259C4⋊Dic11—21no—
260C4⋊Dic11C2×D414yes—
261C4⋊Dic11C2412yes—
262C4⋊Dic11C2412yes—
263C4⋊Dic11C2412yes—
264C4⋊Dic11C2412yes—
265Dic11⋊C4—24no—
266Dic11⋊C4—24no—
267Dic11⋊C4—24no—
268Dic11⋊C4—24no—
269Dic11⋊C4—24no—
270C4×Dic11—24no—
271C2×C11⋊C8—22no—
272C2×C11⋊C8—22no—
273C2×C11⋊C8C2412yes—
274C2×C11⋊C8C2412yes—
275#4313—28no—
276C8×D11—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×#466—111no—
289C2×#442D1111yescharacteristic, complemented
290C2×#435—111no—
291C2×#428—111no—
292C22×#106—111no—
293C23×C11—22no—
294C23×C11—22no—
295C23×C11—42no—
296C23×C11—42no—
297C23×C11—42no—
298C23×C11—42no—
299C23×C11—42no—
300C23×C11—42no—
301C23×C11C22×D411yescharacteristic
302C22×D11—22no—
303C22×D11—22no—
304C22×D11—22no—
305C22×D11—22no—
306C22×D11—22no—
307C22×D11AGL(1,ℤ/8)14yes—
308C22×D11C22×D412yes—
309C22×D11C22×D412yes—
310D4×C11—22no—
311D4×C11—22no—
312D4×C11—22no—
313D4×C11—22no—
314D4×C11—42no—
315D4×C11—42no—
316C2×C4×C11—22no—
317C2×C4×C11—22no—
318C2×C4×C11—22no—
319C2×C4×C11—22no—
320C2×C4×C11—48no—
321C2×C4×C11—42no—
322C2×C4×C11—42no—
323C2×C4×C11—84no—
324C2×C4×C11C22×D412yes—
325C2×C4×C11C22×D412yes—
326C2×C4×C11C22×D411yescharacteristic
327C2×C4×C11C2×#4112yes—
328C2×C4×C112−1+412yes—
329C2×C4×C11C2511yescharacteristic
330C22⋊D11—48no—
331C22⋊D11—48no—
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—42no—
341C2×Dic11—42no—
342C2×Dic11—42no—
343C2×Dic11—42no—
344C2×Dic11C22×D412yes—
345C2×Dic11C22×D412yes—
346D44—28no—
347C4×D11—24no—
348C4×D11—24no—
349C4×D11—22no—
350C4×D11—22no—
351C4×D11—22no—
352C4×D11—22no—
353C4×D11—48no—
354C4×D11—48no—
355C4×D11—84no—
356Dic22—48no—
357C8×C11—22no—
358C8×C11C2×#4114yescomplemented
359C11⋊C8—22no—
360C11⋊C8—22no—
361C22×#41—221no—
362C22×D8C2×D1111yescharacteristic
363C22×M16—111no—
364C23×C8—111no—
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—111no—
379C2×#121—111no—
380C2×#121—221no—
381C2×C4×D4—111no—
382C2×C4×D4—221no—
383C2×C4×D4C2×D1111yescharacteristic
384C2×C4×D4C2×D1111yescharacteristic
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#466—118no—
398#442C2×D1118yescomplemented
399#435—118no—
400#428—118no—
401C2×#107—111no—
402C2×#107—111no—
403C2×#107—111no—
404C2×#106—111no—
405C2×#106—111no—
406C2×#106—111no—
407C2×#106—111no—
408C2×#106—111no—
409C2×#106—118no—
410C2×#106C2×D1111yescharacteristic
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×#97C2×D1111yescharacteristic
421C22×C11—42no—
422C22×C11—42no—
423C22×C11—42no—
424C22×C11—42no—
425C22×C11—42no—
426C22×C11—42no—
427C22×C11—84no—
428C22×C11—84no—
429C22×C11#54712yes—
430C22×C11C2×AGL(1,ℤ/8)12yes—
431C22×C11#57712yes—
432C22×C11C23×D411yescharacteristic
433C2×D11—28no—
434C2×D11—22no—
435C2×D11—22no—
436C2×D11—22no—
437C2×D11—22no—
438C2×D11—22no—
439C2×D11—44no—
440C2×D11C2×AGL(1,ℤ/8)14yes—
441C4×C11—22no—
442C4×C11—22no—
443C4×C11—42no—
444C4×C11—42no—
445C4×C11#54712yes—
446C4×C11C22×#4111yescharacteristic
447C4×C11C2×2−1+411yescharacteristic
448Dic11—22no—
449Dic11—22no—
450Dic11—42no—
451Dic11—42no—
452Dic11—42no—
453Dic11—42no—
454C2×#41—228no—
455C2×#41—448no—
456C22×Q8—221no—
457C22×D4—111no—
458C22×D4—221no—
459C22×D4—221no—
460C22×D4—221no—
461C22×D4—221no—
462C22×D4C22×D1111yescharacteristic
463C22×D4C22×D1111yescharacteristic
464C23×C4—21no—
465C23×C4—21no—
466C23×C4—111no—
467C23×C4—111no—
468C23×C4—221no—
469C23×C4—221no—
470C23×C4—221no—
471C2×D8—24no—
472C2×D8C22×D1114yes—
473C2×M16—114no—
474C2×M16—224no—
475C22×C8—111no—
476C22×C8—111no—
477C22×C8—114no—
478C22×C8—224no—
479C22×C8C22×D1111yescharacteristic
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—114no—
491#121—114no—
492#121—114no—
493#121—114no—
494#121—228no—
495#121—222no—
496#121—222no—
497#121—222no—
498#121—222no—
499C4×D4—22no—
500C4×D4—22no—
501C4×D4—114no—
502C4×D4—114no—
503C4×D4—228no—
504C4×D4C22×D1114yes—
505C4×D4C22×D1114yes—
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—222no—
518C2×C4⋊C4—222no—
519C2×C4⋊C4—221no—
520C2×C4⋊C4—221no—
521C2×C4⋊C4—221no—
522C2×C4⋊C4—221no—
523C2×C4⋊C4—221no—
524C2×C4⋊C4—221no—
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—221no—
537C2×C42C22×D1111yescharacteristic
538#107—114no—
539#107—114no—
540#107—114no—
541#106—114no—
542#106—114no—
543#106—114no—
544#106—114no—
545#106—114no—
546#106C22×D1114yes—
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#97C22×D1114yes—
557C2×C11—82no—
558C2×C11—82no—
559C2×C11#334514yescomplemented
560C2×C11C2×#54711yescharacteristic
561C2×C11C22×AGL(1,ℤ/8)11yescharacteristic
562C2×C11C2×#57711yescharacteristic
563D11—24no—
564D11—42no—
565C24—21no—
566C24—21no—
567C24—111no—
568C24—111no—
569#41—4432no—
570C2×Q8—224no—
571C2×Q8—444no—
572C2×D4—22no—
573C2×D4—22no—
574C2×D4—21no—
575C2×D4—21no—
576C2×D4—22no—
577C2×D4—22no—
578C2×D4—114no—
579C2×D4—224no—
580C2×D4—224no—
581C2×D4—224no—
582C2×D4—224no—
583C2×D4—224no—
584C2×D4—444no—
585C2×D4—444no—
586C2×D4—444no—
587C2×D4—882no—
588C2×D4C23×D1112yes—
589C2×D4C23×D1112yes—
590C22×C4—21no—
591C22×C4—21no—
592C22×C4—24no—
593C22×C4—24no—
594C22×C4—44no—
595C22×C4—82no—
596C22×C4—111no—
597C22×C4—111no—
598C22×C4—112no—
599C22×C4—112no—
600C22×C4—112no—
601C22×C4—112no—
602C22×C4—224no—
603C22×C4—224no—
604C22×C4—224no—
605C22×C4—222no—
606C22×C4—222no—
607C22×C4—222no—
608C22×C4—222no—
609C22×C4—221no—
610C22×C4—221no—
611C22×C4—221no—
612C22×C4—221no—
613C22×C4—444no—
614C22×C4—444no—
615C22×C4—882no—
616C22×C4D4×D1111yescharacteristic
617C22×C4D4×D1111yescharacteristic
618C22×C4C23×D1111yescharacteristic
619D8—28no—
620M16—228no—
621C2×C8—22no—
622C2×C8—112no—
623C2×C8—112no—
624C2×C8—222no—
625C2×C8—222no—
626C2×C8—228no—
627C2×C8#433914yescomplemented
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—221no—
641C4⋊C4—221no—
642C4⋊C4—221no—
643C4⋊C4—221no—
644C4⋊C4—224no—
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—224no—
659C42D4×D1112yes—
660C42C23×D1112yes—
661C11C2×#334511yescharacteristic, complemented, Sylow
662C23—22no—
663C23—22no—
664C23—42no—
665C23—42no—
666C23—42no—
667C23—42no—
668C23—42no—
669C23—42no—
670C23—114no—
671C23—112no—
672C23—112no—
673C23—222no—
674C23—222no—
675C23—222no—
676C23—222no—
677C23—222no—
678C23C2×D4×D1111yescharacteristic
679Q8—448no—
680D4—22no—
681D4—22no—
682D4—22no—
683D4—22no—
684D4—42no—
685D4—42no—
686D4—228no—
687D4—448no—
688D4—448no—
689D4—448no—
690D4—884no—
691C2×C4—22no—
692C2×C4—22no—
693C2×C4—22no—
694C2×C4—22no—
695C2×C4—48no—
696C2×C4—42no—
697C2×C4—42no—
698C2×C4—84no—
699C2×C4—112no—
700C2×C4—112no—
701C2×C4—222no—
702C2×C4—222no—
703C2×C4—224no—
704C2×C4—224no—
705C2×C4—222no—
706C2×C4—222no—
707C2×C4—222no—
708C2×C4—222no—
709C2×C4—222no—
710C2×C4—222no—
711C2×C4—222no—
712C2×C4—222no—
713C2×C4—448no—
714C2×C4—448no—
715C2×C4—442no—
716C2×C4—442no—
717C2×C4—442no—
718C2×C4—442no—
719C2×C4—884no—
720C2×C4C2×#433912yes—
721C2×C4C2×D4×D1112yes—
722C2×C4C2×D4×D1112yes—
723C2×C4C2×D4×D1111yescharacteristic
724C2×C4#6704312yes—
725C2×C4C24×D1111yescharacteristic
726C8—22no—
727C8—222no—
728C8—222no—
729C8C2×#433914yescomplemented
730C22—42no—
731C22—42no—
732C22—42no—
733C22—42no—
734C22—42no—
735C22—42no—
736C22—84no—
737C22—84no—
738C22—114no—
739C22—228no—
740C22—222no—
741C22—222no—
742C22—222no—
743C22—222no—
744C22—222no—
745C22—444no—
746C22#1062308212yes—
747C22D11×AGL(1,ℤ/8)12yes—
748C22#1062330612yes—
749C22C22×D4×D1111yescharacteristic
750C4—22no—
751C4—22no—
752C4—42no—
753C4—42no—
754C4—222no—
755C4—222no—
756C4—442no—
757C4—442no—
758C4—442no—
759C4—442no—
760C4#1062308212yes—
761C4C22×#433911yescharacteristic
762C4C2×#6704311yescharacteristic
763C2—82no—
764C2—82no—
765C2—224no—
766C2—442no—
767C2#1308109114yesdirect product factor
768C2C2×#1062308211yescharacteristic
769C2C2×D11×AGL(1,ℤ/8)11yescharacteristic
770C2C2×#1062330611yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#442C2
socleC23×C11C22×D4
hypercenterC2×#442D11
hypocenterC11C2×#3345
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#442

Complements

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

NH ≅ G/Ntype
1. C2×#10623089C2semidirect
2. C2×#10623082C2semidirect
3. #13081091C2direct (N × H)
4. C2×#10622315C2semidirect
5. C2×#10622390C2semidirect
6. C2×#10622390C2semidirect
7. C2×#10622397C2semidirect
8. C2×#10622387C2semidirect
9. C2×#10622622C2semidirect
10. C2×#10622621C2semidirect
11. C2×#10622772C2semidirect
12. C2×#10622770C2semidirect
13. C2×#10622319C2semidirect
14. C2×#10622474C2semidirect
15. C2×D11×#106C2semidirect
16. C2×C11×#442C2semidirect
31. #10623089C22semidirect
33. #10623082C22semidirect
45. C11×#442C22semidirect
54. #10622772C22semidirect
55. #10622770C22semidirect
62. #10622622C22semidirect
63. #10622621C22semidirect
69. #10622474C22semidirect
70. D11×#106C22semidirect
71. #10622397C22semidirect
72. #10622390C22semidirect
73. #10622390C22semidirect
74. #10622387C22semidirect
75. #10622319C22semidirect
76. #10622315C22semidirect
237. C2×C8×C11#41semidirect
289. C2×#442D11semidirect
358. C8×C11C2×#41semidirect
398. #442C2×D11semidirect
559. C2×C11#3345semidirect
627. C2×C8#4339semidirect
661. C11C2×#3345semidirect
729. C8C2×#4339semidirect
767. C2#13081091direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106230892
C2×#106230822
#130810912
C2×#106223152
C2×#106223902
C2×#106223972
C2×#106223872
C2×#106226222
C2×#106226212
C2×#106227722
C2×#106227702
C2×#106223192
C2×#106224742
C2×D11×#1062
C2×C11×#4422
C2×#334511