Finite Group Databasebeta

← C2×#13081087 #15632337

Subgroups — C2×#13081087 #15632337

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×#10623061C211yesmaximal, characteristic, complemented
2C2×#10623038C211yesmaximal, characteristic, complemented
3#13081087C2116yesmaximal, direct product factor
4C2×#10622489C211yesmaximal, characteristic, complemented
5C2×#10622476C211yesmaximal, characteristic, complemented
6C2×#10622581C211yesmaximal, characteristic, complemented
7C2×#10622616C211yesmaximal, characteristic, complemented
8C2×#10622495C211yesmaximal, characteristic, complemented
9C2×#10622504C211yesmaximal, characteristic, complemented
10C2×#10622483C211yesmaximal, characteristic, complemented
11C2×#10622748C211yesmaximal, characteristic, complemented
12C2×#10622496C211yesmaximal, characteristic, complemented
13C2×#10622482C211yesmaximal, characteristic, complemented
14C2×#10622740C211yesmaximal, characteristic, complemented
15C2×D11×#106C211yesmaximal, characteristic, complemented
16C2×C11×#428C211yesmaximal, characteristic, complemented
17C22×#4339—21no—
18C22×C11×M16C2211yescharacteristic
19C2×C11×#117C2211yescharacteristic
20C22×C11×C4⋊C4C2211yescharacteristic
21C2×#66983C2211yescharacteristic
22C2×#66983C2211yescharacteristic
23C2×#66982—21no—
24C2×C4×C22⋊D11C2211yescharacteristic
25C22×D88C2211yescharacteristic
26C22×C8×D11C2211yescharacteristic
27#10623061—24no—
28#10623061C2218yescomplemented
29C2×#66949—21no—
30#10623038—24no—
31#10623038C2218yescomplemented
32C2×#66948C2211yescharacteristic
33C2×#66948C2211yescharacteristic
34C2×#66947—21no—
35C2×#66946C2211yescharacteristic
36C2×#66946C2211yescharacteristic
37C2×C4⋊C4×D11C2211yescharacteristic
38C2×C4⋊C4×D11C2211yescharacteristic
39C2×#66943C2211yescharacteristic
40C2×#66941C2211yescharacteristic
41C2×#66937—21no—
42C2×#66936—21no—
43C2×#66929—21no—
44C2×C4×D44—21no—
45C11×#428C2218yescomplemented
46C2×C11×#107C2211yescharacteristic
47C2×C11×#107C2211yescharacteristic
48C2×C11×#106C2211yescharacteristic
49C2×C11×#106C2211yescharacteristic
50C2×C22⋊(C11⋊C8)C2211yescharacteristic
51#10622748C2218yescomplemented
52#10622740C2218yescomplemented
53C2×#66885C2211yescharacteristic
54C2×#66885C2211yescharacteristic
55C2×(C2×D11)⋊C8C2211yescharacteristic
56C2×#66881C2211yescharacteristic
57C2×#66879C2211yescharacteristic
58C2×Dic11⋊C8C2211yescharacteristic
59#10622616C2218yescomplemented
60#10622581C2218yescomplemented
61C2×#66873C2211yescharacteristic
62C2×#66873C2211yescharacteristic
63C2×#66873C2211yescharacteristic
64C2×#66873C2211yescharacteristic
65C2×#66872C2211yescharacteristic
66C2×#66872C2211yescharacteristic
67C2×#66872C2211yescharacteristic
68C2×#66871C2211yescharacteristic
69#10622504C2218yescomplemented
70#10622496C2218yescomplemented
71#10622495C2218yescomplemented
72#10622489C2218yescomplemented
73#10622483C2218yescomplemented
74#10622482C2218yescomplemented
75#10622476C2218yescomplemented
76D11×#106C2218yescomplemented
77C23×C4×C11—21no—
78C23×C4×C11C2311yescharacteristic
79C22×C22⋊D11—21no—
80C22×C22⋊D11—21no—
81C22×C22⋊D11D411yescharacteristic
82C2×#4339—28no—
83C2×#4339—48no—
84C22×D44—21no—
85C22×D44—21no—
86C22×D44C2311yescharacteristic
87C22×D44C2311yescharacteristic
88C22×C4×D11—21no—
89C22×C4×D11—21no—
90C22×C4×D11—21no—
91C22×C4×D11—21no—
92C22×C4×D11C2311yescharacteristic
93C22×Dic22—21no—
94C2×C11×M16—24no—
95C2×C11×M16C2314yes—
96C22×C8×C11C2311yescharacteristic
97C22×C8×C11C2311yescharacteristic
98C11×#117—22no—
99C11×#117C2314yes—
100C2×C11×C4⋊C4—21no—
101C2×C11×C4⋊C4—22no—
102C2×C11×C4⋊C4C2311yescharacteristic
103C2×C11×C4⋊C4C2311yescharacteristic
104C2×C11×C4⋊C4C2311yescharacteristic
105C2×C11×C4⋊C4C2311yescharacteristic
106C2×C11×C4⋊C4C2314yes—
107C2×C11×C22⋊C4—21no—
108C2×C42×C11—21no—
109C2×C22⋊Dic11D411yescharacteristic
110#66983—22no—
111#66983—22no—
112#66983C2314yes—
113#66983C2314yes—
114#66982—28no—
115C4×C22⋊D11D414yes—
116C4×C22⋊D11C2314yes—
117C2×(C2×D11)⋊C4—21no—
118C2×(C2×D11)⋊C4—21no—
119C2×(C2×D11)⋊C4—21no—
120C2×(C2×D11)⋊C4—21no—
121C2×(C2×D11)⋊C4—21no—
122C2×(C2×D11)⋊C4—21no—
123C2×(C2×D11)⋊C4D411yescharacteristic
124C2×C4⋊Dic11—21no—
125C2×C4⋊Dic11C2311yescharacteristic
126C2×C4⋊Dic11C2311yescharacteristic
127C2×Dic11⋊C4—21no—
128C2×Dic11⋊C4—21no—
129C2×Dic11⋊C4—21no—
130C2×Dic11⋊C4—21no—
131C2×Dic11⋊C4D411yescharacteristic
132C2×C4×Dic11C2311yescharacteristic
133C22×C11⋊C8C2311yescharacteristic
134C22×C11⋊C8C2311yescharacteristic
135C2×D88—24no—
136C2×D88C2314yes—
137C2×C8×D11—24no—
138C2×C8×D11C2314yes—
139#66949—28no—
140#66948—22no—
141#66948—22no—
142#66948C2314yes—
143#66948C2314yes—
144#66947—28no—
145#66946—22no—
146#66946—22no—
147#66946C2314yes—
148#66946C2314yes—
149C4⋊C4×D11—22no—
150C4⋊C4×D11—22no—
151C4⋊C4×D11C2314yes—
152C4⋊C4×D11C2314yes—
153#66943—22no—
154#66943C2314yes—
155#66941—22no—
156#66941C2314yes—
157#66937—28no—
158#66936—28no—
159#66929—28no—
160C4×D44—28no—
161C11×#107C2314yes—
162C11×#107C2314yes—
163C11×#106C2314yes—
164C11×#106C2314yes—
165C22⋊(C11⋊C8)C2314yes—
166#66885C2314yes—
167#66885C2314yes—
168(C2×D11)⋊C8C2314yes—
169#66881C2314yes—
170#66879C2314yes—
171Dic11⋊C8C2314yes—
172#66873C2314yes—
173#66873C2314yes—
174#66873C2314yes—
175#66873C2314yes—
176#66872C2314yes—
177#66872C2314yes—
178#66872C2314yes—
179#66871C2314yes—
180C2×#3345—111nomaximal, Sylow
181C24×C11C2×D411yescharacteristic
182C23×D11—21no—
183C23×D11—21no—
184C23×D11C2×D411yescharacteristic
185C22×C4×C11—22no—
186C22×C4×C11—22no—
187C22×C4×C11—21no—
188C22×C4×C11—21no—
189C22×C4×C11—21no—
190C22×C4×C11—21no—
191C22×C4×C11—24no—
192C22×C4×C11—44no—
193C22×C4×C11C2×D411yescharacteristic
194C22×C4×C11C2×D412yes—
195C22×C4×C11C2412yes—
196C22×C4×C11C2411yescharacteristic
197C2×C22⋊D11—24no—
198C2×C22⋊D11—24no—
199C2×C22⋊D11—24no—
200C2×C22⋊D11—44no—
201C2×C22⋊D11—82no—
202C2×C22⋊D11C2×D414yes—
203C22×Dic11—21no—
204C22×Dic11—21no—
205C22×Dic11C2×D411yescharacteristic
206C22×Dic11C2×D411yescharacteristic
207C22×Dic11C2×D411yescharacteristic
208#4339—432no—
209C2×D44—24no—
210C2×D44—24no—
211C2×D44—21no—
212C2×D44—21no—
213C2×D44—22no—
214C2×D44—22no—
215C2×D44—22no—
216C2×D44—22no—
217C2×D44—44no—
218C2×D44—44no—
219C2×D44C2412yes—
220C2×D44C2412yes—
221C2×C4×D11—24no—
222C2×C4×D11—24no—
223C2×C4×D11—24no—
224C2×C4×D11—24no—
225C2×C4×D11—22no—
226C2×C4×D11—22no—
227C2×C4×D11—44no—
228C2×C4×D11—44no—
229C2×C4×D11—82no—
230C2×C4×D11—82no—
231C2×C4×D11C2×D412yes—
232C2×C4×D11C2412yes—
233C2×Dic22—24no—
234C2×Dic22—44no—
235C11×M16—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⋊C4—21no—
243C11×C4⋊C4—21no—
244C11×C4⋊C4—24no—
245C11×C4⋊C4C2412yes—
246C11×C4⋊C4C2412yes—
247C11×C4⋊C4C2412yes—
248C11×C4⋊C4C2412yes—
249C11×C22⋊C4—24no—
250C42×C11—24no—
251C22⋊Dic11C2×D414yes—
252(C2×D11)⋊C4—24no—
253(C2×D11)⋊C4—24no—
254(C2×D11)⋊C4—24no—
255(C2×D11)⋊C4—24no—
256(C2×D11)⋊C4—24no—
257(C2×D11)⋊C4—24no—
258(C2×D11)⋊C4C2×D414yes—
259C4⋊Dic11—24no—
260C4⋊Dic11—21no—
261C4⋊Dic11—21no—
262C4⋊Dic11C2412yes—
263C4⋊Dic11C2412yes—
264Dic11⋊C4—24no—
265Dic11⋊C4—24no—
266Dic11⋊C4—24no—
267Dic11⋊C4—24no—
268Dic11⋊C4C2×D414yes—
269C4×Dic11C2×D412yes—
270C4×Dic11C2412yes—
271C2×C11⋊C8—22no—
272C2×C11⋊C8—22no—
273C2×C11⋊C8C2412yes—
274C2×C11⋊C8C2412yes—
275D88—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×#442—111no—
290C2×#435—111no—
291C2×#428D1111yescharacteristic, complemented
292C22×#106—111no—
293C23×C11—22no—
294C23×C11—22no—
295C23×C11—22no—
296C23×C11C22×D412yes—
297C23×C11C22×D411yescharacteristic
298C22×D11—22no—
299C22×D11—22no—
300C22×D11—22no—
301C22×D11—22no—
302C22×D11—42no—
303C22×D11—42no—
304C22×D11—42no—
305C22×D11—42no—
306C22×D11—42no—
307C22×D11—42no—
308C22×D11AGL(1,ℤ/8)14yes—
309C22×D11C22×D412yes—
310C2×C4×C11—22no—
311C2×C4×C11—24no—
312C2×C4×C11—22no—
313C2×C4×C11—22no—
314C2×C4×C11—22no—
315C2×C4×C11—22no—
316C2×C4×C11—22no—
317C2×C4×C11—22no—
318C2×C4×C11—48no—
319C2×C4×C11—42no—
320C2×C4×C11—42no—
321C2×C4×C11—42no—
322C2×C4×C11—42no—
323C2×C4×C11C22×D412yes—
324C2×C4×C11C22×D411yescharacteristic
325C2×C4×C11C2×#4112yes—
326C2×C4×C112−1+412yes—
327C2×C4×C11C2511yescharacteristic
328C22⋊D11—28no—
329C22⋊D11—48no—
330C22⋊D11—84no—
331C2×Dic11—22no—
332C2×Dic11—22no—
333C2×Dic11—22no—
334C2×Dic11—22no—
335C2×Dic11—22no—
336C2×Dic11—42no—
337C2×Dic11—42no—
338C2×Dic11C22×D412yes—
339C2×Dic11C22×D412yes—
340C2×Dic11C22×D412yes—
341D44—22no—
342D44—22no—
343D44—22no—
344D44—22no—
345D44—48no—
346D44—48no—
347D44—42no—
348D44—42no—
349C4×D11—24no—
350C4×D11—22no—
351C4×D11—22no—
352C4×D11—48no—
353C4×D11—48no—
354C4×D11—84no—
355C4×D11—84no—
356Dic22—48no—
357C8×C11—22no—
358C8×C11C2×#4114yescomplemented
359C11⋊C8—22no—
360C11⋊C8—22no—
361C22×#41—221no—
362C22×D8—111no—
363C22×M16C2×D1111yescharacteristic
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—111no—
383C2×C4×D4—111no—
384C2×C4×D4—221no—
385C2×#117C2×D1111yescharacteristic
386C22×C4⋊C4—111no—
387C22×C4⋊C4—111no—
388C22×C4⋊C4C2×D1111yescharacteristic
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#442—118no—
399#435—118no—
400#428C2×D1118yescomplemented
401C2×#107—111no—
402C2×#107C2×D1111yescharacteristic
403C2×#107C2×D1111yescharacteristic
404C2×#106—111no—
405C2×#106—111no—
406C2×#106—111no—
407C2×#106—111no—
408C2×#106—118no—
409C2×#106C2×D1111yescharacteristic
410C2×#106C2×D1111yescharacteristic
411C2×C4⋊C8—111no—
412C2×#102—111no—
413C2×#102—111no—
414C2×#102—111no—
415C2×#102—111no—
416C2×#102—111no—
417C2×#102—111no—
418C2×C22⋊C8—111no—
419C2×C22⋊C8—111no—
420C2×#97—111no—
421C22×C11—22no—
422C22×C11—22no—
423C22×C11—22no—
424C22×C11—44no—
425C22×C11#54712yes—
426C22×C11C2×AGL(1,ℤ/8)12yes—
427C22×C11#57712yes—
428C22×C11C23×D411yescharacteristic
429C2×D11—28no—
430C2×D11—22no—
431C2×D11—22no—
432C2×D11—42no—
433C2×D11—42no—
434C2×D11—42no—
435C2×D11—42no—
436C2×D11—42no—
437C2×D11—42no—
438C2×D11—84no—
439C2×D11—84no—
440C2×D11C2×AGL(1,ℤ/8)14yes—
441C4×C11—22no—
442C4×C11—42no—
443C4×C11—42no—
444C4×C11—42no—
445C4×C11—42no—
446C4×C11#54712yes—
447C4×C11C22×#4111yescharacteristic
448C4×C11C2×2−1+411yescharacteristic
449Dic11—22no—
450Dic11—22no—
451Dic11—22no—
452Dic11—42no—
453Dic11—42no—
454C2×#41—228no—
455C2×#41—448no—
456C22×Q8—221no—
457C22×D4—111no—
458C22×D4—111no—
459C22×D4—111no—
460C22×D4—221no—
461C22×D4—221no—
462C22×D4—221no—
463C22×D4—221no—
464C23×C4—21no—
465C23×C4—111no—
466C23×C4—221no—
467C23×C4—221no—
468C23×C4—221no—
469C23×C4—221no—
470C23×C4C22×D1111yescharacteristic
471C2×D8—114no—
472C2×D8—224no—
473C2×M16—24no—
474C2×M16C22×D1114yes—
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—114no—
500C4×D4—114no—
501C4×D4—114no—
502C4×D4—114no—
503C4×D4—228no—
504C4×D4—222no—
505C4×D4—222no—
506#117—22no—
507#117C22×D1114yes—
508C2×C4⋊C4—21no—
509C2×C4⋊C4—22no—
510C2×C4⋊C4—111no—
511C2×C4⋊C4—111no—
512C2×C4⋊C4—111no—
513C2×C4⋊C4—114no—
514C2×C4⋊C4—114no—
515C2×C4⋊C4—222no—
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⋊C4C22×D1111yescharacteristic
523C2×C4⋊C4C22×D1111yescharacteristic
524C2×C4⋊C4C22×D1111yescharacteristic
525C2×C4⋊C4C22×D1114yes—
526C2×C4⋊C4C22×D1111yescharacteristic
527C2×C22⋊C4—21no—
528C2×C22⋊C4—111no—
529C2×C22⋊C4—111no—
530C2×C22⋊C4—221no—
531C2×C22⋊C4—221no—
532C2×C22⋊C4—221no—
533C2×C22⋊C4—221no—
534C2×C22⋊C4—221no—
535C2×C22⋊C4—221no—
536C2×C42—21no—
537C2×C42—111no—
538#107—114no—
539#107C22×D1114yes—
540#107C22×D1114yes—
541#106—114no—
542#106—114no—
543#106—114no—
544#106—114no—
545#106C22×D1114yes—
546#106C22×D1114yes—
547C4⋊C8—114no—
548#102—114no—
549#102—114no—
550#102—114no—
551#102—114no—
552#102—114no—
553#102—114no—
554C22⋊C8—114no—
555C22⋊C8—114no—
556#97—114no—
557C2×C11—42no—
558C2×C11#334514yescomplemented
559C2×C11C2×#54711yescharacteristic
560C2×C11C22×AGL(1,ℤ/8)11yescharacteristic
561C2×C11C2×#57711yescharacteristic
562D11—24no—
563D11—82no—
564D11—82no—
565C24—111no—
566C24—221no—
567C24—221no—
568C24D4×D1111yescharacteristic
569#41—4432no—
570C2×Q8—224no—
571C2×Q8—444no—
572C2×D4—114no—
573C2×D4—112no—
574C2×D4—112no—
575C2×D4—224no—
576C2×D4—224no—
577C2×D4—224no—
578C2×D4—224no—
579C2×D4—224no—
580C2×D4—222no—
581C2×D4—222no—
582C2×D4—221no—
583C2×D4—221no—
584C2×D4—222no—
585C2×D4—222no—
586C2×D4—444no—
587C2×D4—444no—
588C2×D4—444no—
589C2×D4—882no—
590C22×C4—22no—
591C22×C4—22no—
592C22×C4—24no—
593C22×C4—21no—
594C22×C4—21no—
595C22×C4—21no—
596C22×C4—21no—
597C22×C4—44no—
598C22×C4—111no—
599C22×C4—111no—
600C22×C4—111no—
601C22×C4—112no—
602C22×C4—112no—
603C22×C4—224no—
604C22×C4—224no—
605C22×C4—224no—
606C22×C4—224no—
607C22×C4—222no—
608C22×C4—222no—
609C22×C4—221no—
610C22×C4—221no—
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—228no—
620M16—28no—
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—24no—
633C4⋊C4—21no—
634C4⋊C4—21no—
635C4⋊C4—114no—
636C4⋊C4—112no—
637C4⋊C4—112no—
638C4⋊C4—224no—
639C4⋊C4—224no—
640C4⋊C4—224no—
641C4⋊C4—224no—
642C4⋊C4—224no—
643C4⋊C4—221no—
644C4⋊C4—221no—
645C4⋊C4C23×D1112yes—
646C4⋊C4C23×D1112yes—
647C4⋊C4C23×D1112yes—
648C4⋊C4C23×D1112yes—
649C22⋊C4—24no—
650C22⋊C4—114no—
651C22⋊C4—114no—
652C22⋊C4—224no—
653C22⋊C4—224no—
654C22⋊C4—224no—
655C22⋊C4—224no—
656C22⋊C4—224no—
657C22⋊C4—224no—
658C42—24no—
659C42—112no—
660C42—112no—
661C11C2×#334511yescharacteristic, complemented, Sylow
662C23—22no—
663C23—22no—
664C23—22no—
665C23—114no—
666C23—112no—
667C23—222no—
668C23—222no—
669C23—222no—
670C23—222no—
671C23—442no—
672C23—442no—
673C23—442no—
674C23—442no—
675C23—442no—
676C23—442no—
677C23C2×D4×D1112yes—
678C23C2×D4×D1111yescharacteristic
679Q8—448no—
680D4—228no—
681D4—222no—
682D4—222no—
683D4—222no—
684D4—222no—
685D4—448no—
686D4—448no—
687D4—448no—
688D4—442no—
689D4—442no—
690D4—884no—
691C2×C4—22no—
692C2×C4—24no—
693C2×C4—22no—
694C2×C4—22no—
695C2×C4—22no—
696C2×C4—22no—
697C2×C4—22no—
698C2×C4—22no—
699C2×C4—48no—
700C2×C4—42no—
701C2×C4—42no—
702C2×C4—42no—
703C2×C4—42no—
704C2×C4—112no—
705C2×C4—112no—
706C2×C4—112no—
707C2×C4—222no—
708C2×C4—222no—
709C2×C4—222no—
710C2×C4—224no—
711C2×C4—222no—
712C2×C4—222no—
713C2×C4—222no—
714C2×C4—222no—
715C2×C4—448no—
716C2×C4—448no—
717C2×C4—442no—
718C2×C4—442no—
719C2×C4—884no—
720C2×C4—884no—
721C2×C4C2×#433912yes—
722C2×C4C2×D4×D1112yes—
723C2×C4C2×D4×D1111yescharacteristic
724C2×C4#6704012yes—
725C2×C4C24×D1111yescharacteristic
726C8—22no—
727C8—222no—
728C8—222no—
729C8C2×#433914yescomplemented
730C22—22no—
731C22—22no—
732C22—22no—
733C22—44no—
734C22—114no—
735C22—222no—
736C22—222no—
737C22—228no—
738C22—442no—
739C22—442no—
740C22—442no—
741C22—442no—
742C22—442no—
743C22—442no—
744C22—884no—
745C22—884no—
746C22#1062303812yes—
747C22D11×AGL(1,ℤ/8)12yes—
748C22#1062330912yes—
749C22C22×D4×D1111yescharacteristic
750C4—22no—
751C4—42no—
752C4—42no—
753C4—42no—
754C4—42no—
755C4—222no—
756C4—222no—
757C4—222no—
758C4—442no—
759C4—442no—
760C4#1062303812yes—
761C4C22×#433911yescharacteristic
762C4C2×#6704011yescharacteristic
763C2—42no—
764C2—224no—
765C2—882no—
766C2—882no—
767C2#1308108714yesdirect product factor
768C2C2×#1062303811yescharacteristic
769C2C2×D11×AGL(1,ℤ/8)11yescharacteristic
770C2C2×#1062330911yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#428C2
socleC23×C11C22×D4
hypercenterC2×#428D11
hypocenterC11C2×#3345
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#428

Complements

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

NH ≅ G/Ntype
1. C2×#10623061C2semidirect
2. C2×#10623038C2semidirect
3. #13081087C2direct (N × H)
4. C2×#10622489C2semidirect
5. C2×#10622476C2semidirect
6. C2×#10622581C2semidirect
7. C2×#10622616C2semidirect
8. C2×#10622495C2semidirect
9. C2×#10622504C2semidirect
10. C2×#10622483C2semidirect
11. C2×#10622748C2semidirect
12. C2×#10622496C2semidirect
13. C2×#10622482C2semidirect
14. C2×#10622740C2semidirect
15. C2×D11×#106C2semidirect
16. C2×C11×#428C2semidirect
28. #10623061C22semidirect
31. #10623038C22semidirect
45. C11×#428C22semidirect
51. #10622748C22semidirect
52. #10622740C22semidirect
59. #10622616C22semidirect
60. #10622581C22semidirect
69. #10622504C22semidirect
70. #10622496C22semidirect
71. #10622495C22semidirect
72. #10622489C22semidirect
73. #10622483C22semidirect
74. #10622482C22semidirect
75. #10622476C22semidirect
76. D11×#106C22semidirect
237. C2×C8×C11#41semidirect
291. C2×#428D11semidirect
358. C8×C11C2×#41semidirect
400. #428C2×D11semidirect
558. C2×C11#3345semidirect
627. C2×C8#4339semidirect
661. C11C2×#3345semidirect
729. C8C2×#4339semidirect
767. C2#13081087direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106230612
C2×#106230382
#130810872
C2×#106224892
C2×#106224762
C2×#106225812
C2×#106226162
C2×#106224952
C2×#106225042
C2×#106224832
C2×#106227482
C2×#106224962
C2×#106224822
C2×#106227402
C2×D11×#1062
C2×C11×#4282
C2×#334511