Finite Group Databasebeta

← C2×#13081093 #15632343

Subgroups — C2×#13081093 #15632343

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×#10623257C211yesmaximal, characteristic, complemented
3#13081093C2116yesmaximal, direct product factor
4C2×#10622693C211yesmaximal, characteristic, complemented
5C2×#10622476C211yesmaximal, characteristic, complemented
6C2×#10622390C211yesmaximal, characteristic, complemented
7C2×#10622479C211yesmaximal, characteristic, complemented
8C2×#10622387C211yesmaximal, characteristic, complemented
9C2×#10622460C211yesmaximal, characteristic, complemented
10C2×#10622395C211yesmaximal, characteristic, complemented
11C2×#10622388C211yesmaximal, characteristic, complemented
12C2×#10622627C211yesmaximal, characteristic, complemented
13C2×#10622449C211yesmaximal, characteristic, complemented
14C2×#10622474C211yesmaximal, characteristic, complemented
15C2×D11×#106C211yesmaximal, characteristic, complemented
16C2×C11×#476C211yesmaximal, characteristic, complemented
17C22×#4343—21no—
18C2×C11×C4⋊Q8C2211yescharacteristic
19C2×C4×D4×C11C2211yescharacteristic
20C2×#66999—21no—
21C2×#66991C2211yescharacteristic
22C2×#66991C2211yescharacteristic
23C22×#4323C2211yescharacteristic
24C2×#66982—21no—
25C2×C4×C22⋊D11—21no—
26C22×#4313C2211yescharacteristic
27C22×C8×D11C2211yescharacteristic
28#10623257—24no—
29#10623257C2218yescomplemented
30#10623089—24no—
31#10623089C2218yescomplemented
32C2×#66948C2211yescharacteristic
33C2×#66948C2211yescharacteristic
34C2×#66947—21no—
35C2×#66947—21no—
36C2×#66945C2211yescharacteristic
37C2×C4⋊C4×D11C2211yescharacteristic
38C2×C4⋊C4×D11C2211yescharacteristic
39C2×C4⋊C4×D11C2211yescharacteristic
40C2×#66937—21no—
41C2×#66932—21no—
42C2×C4×D44C2211yescharacteristic
43C2×C4×D44C2211yescharacteristic
44C2×#66923C2211yescharacteristic
45C11×#476C2218yescomplemented
46C2×C11×#106C2211yescharacteristic
47C2×C11×#106C2211yescharacteristic
48C2×C11×C4⋊C8C2211yescharacteristic
49C2×C11×#102C2211yescharacteristic
50C2×C11×#102C2211yescharacteristic
51C2×#66896C2211yescharacteristic
52C2×#66885C2211yescharacteristic
53C2×#66885C2211yescharacteristic
54C2×(C2×D11)⋊C8C2211yescharacteristic
55C2×(C2×D11)⋊C8C2211yescharacteristic
56C2×#66882C2211yescharacteristic
57C2×#66881C2211yescharacteristic
58#10622693C2218yescomplemented
59#10622627C2218yescomplemented
60C2×#66873C2211yescharacteristic
61C2×#66872C2211yescharacteristic
62C2×#66872C2211yescharacteristic
63C2×#66872C2211yescharacteristic
64C2×#66871C2211yescharacteristic
65C2×#66871C2211yescharacteristic
66C2×#66867C2211yescharacteristic
67#10622479C2218yescomplemented
68#10622476C2218yescomplemented
69#10622474C2218yescomplemented
70D11×#106C2218yescomplemented
71#10622460C2218yescomplemented
72#10622449C2218yescomplemented
73#10622395C2218yescomplemented
74#10622390C2218yescomplemented
75#10622388C2218yescomplemented
76#10622387C2218yescomplemented
77C22×Q8×C11—21no—
78C22×D4×C11C2311yescharacteristic
79C23×C4×C11—21no—
80C22×C22⋊D11—21no—
81C22×C22⋊D11—21no—
82C2×#4343—28no—
83C2×#4343—48no—
84C22×D44—21no—
85C22×D44—21no—
86C22×D44D411yescharacteristic
87C22×D44C2311yescharacteristic
88C22×C4×D11—21no—
89C22×C4×D11—21no—
90C22×C4×D11—21no—
91C22×C4×D11—21no—
92C22×C4×D11C2311yescharacteristic
93C22×C4×D11C2311yescharacteristic
94C22×C8×C11C2311yescharacteristic
95C22×C8×C11C2311yescharacteristic
96C11×C4⋊Q8—22no—
97C11×C4⋊Q8C2314yes—
98C4×D4×C11—22no—
99C4×D4×C11C2314yes—
100C2×C11×C4⋊C4—21no—
101C2×C11×C4⋊C4C2311yescharacteristic
102C2×C11×C4⋊C4C2311yescharacteristic
103C2×C11×C4⋊C4C2311yescharacteristic
104C2×C11×C22⋊C4—21no—
105C2×C42×C11C2311yescharacteristic
106C2×C22⋊Dic11—21no—
107C2×C22⋊Dic11—21no—
108#66999—28no—
109#66991—22no—
110#66991—22no—
111#66991C2314yes—
112#66991C2314yes—
113C2×#4323—24no—
114C2×#4323C2314yes—
115#66982—28no—
116C4×C22⋊D11—28no—
117C2×(C2×D11)⋊C4—21no—
118C2×(C2×D11)⋊C4—21no—
119C2×(C2×D11)⋊C4—21no—
120C2×(C2×D11)⋊C4—21no—
121C2×(C2×D11)⋊C4D411yescharacteristic
122C2×(C2×D11)⋊C4D411yescharacteristic
123C2×C4⋊Dic11D411yescharacteristic
124C2×C4⋊Dic11C2311yescharacteristic
125C2×C4⋊Dic11C2311yescharacteristic
126C2×C4⋊Dic11C2311yescharacteristic
127C2×Dic11⋊C4—21no—
128C2×Dic11⋊C4—21no—
129C2×Dic11⋊C4—21no—
130C2×Dic11⋊C4—21no—
131C2×Dic11⋊C4—21no—
132C2×C4×Dic11—21no—
133C22×C11⋊C8C2311yescharacteristic
134C22×C11⋊C8C2311yescharacteristic
135C2×#4313—24no—
136C2×#4313C2314yes—
137C2×C8×D11—24no—
138C2×C8×D11C2314yes—
139#66948—22no—
140#66948—22no—
141#66948C2314yes—
142#66948C2314yes—
143#66947—28no—
144#66947—28no—
145#66945—22no—
146#66945C2314yes—
147C4⋊C4×D11—22no—
148C4⋊C4×D11—22no—
149C4⋊C4×D11—22no—
150C4⋊C4×D11C2314yes—
151C4⋊C4×D11C2314yes—
152C4⋊C4×D11C2314yes—
153#66937—28no—
154#66932—28no—
155C4×D44—22no—
156C4×D44D414yes—
157C4×D44C2314yes—
158C4×D44C2314yes—
159#66923—22no—
160#66923C2314yes—
161C11×#106C2314yes—
162C11×#106C2314yes—
163C11×C4⋊C8C2314yes—
164C11×#102C2314yes—
165C11×#102C2314yes—
166#66896C2314yes—
167#66885C2314yes—
168#66885C2314yes—
169(C2×D11)⋊C8C2314yes—
170(C2×D11)⋊C8C2314yes—
171#66882C2314yes—
172#66881C2314yes—
173#66873C2314yes—
174#66872C2314yes—
175#66872C2314yes—
176#66872C2314yes—
177#66871C2314yes—
178#66871C2314yes—
179#66867C2314yes—
180C2×#3345—111nomaximal, Sylow
181C24×C11—21no—
182C23×D11—21no—
183C23×D11C2×D411yescharacteristic
184C23×D11C2×D411yescharacteristic
185C2×Q8×C11—24no—
186C2×Q8×C11—44no—
187C2×D4×C11—21no—
188C2×D4×C11—22no—
189C2×D4×C11—22no—
190C2×D4×C11C2412yes—
191C22×C4×C11—21no—
192C22×C4×C11—21no—
193C22×C4×C11—21no—
194C22×C4×C11—24no—
195C22×C4×C11—82no—
196C22×C4×C11C2×D411yescharacteristic
197C22×C4×C11C2×D411yescharacteristic
198C22×C4×C11C2411yescharacteristic
199C2×C22⋊D11—24no—
200C2×C22⋊D11—24no—
201C2×C22⋊D11—44no—
202C2×C22⋊D11—82no—
203C22×Dic11—21no—
204C22×Dic11—21no—
205C22×Dic11—21no—
206C22×Dic11C2×D411yescharacteristic
207C22×Dic11C2×D411yescharacteristic
208#4343—432no—
209C2×D44—24no—
210C2×D44—24no—
211C2×D44—24no—
212C2×D44—21no—
213C2×D44—22no—
214C2×D44—22no—
215C2×D44—44no—
216C2×D44—44no—
217C2×D44C2×D414yes—
218C2×D44C2412yes—
219C2×C4×D11—24no—
220C2×C4×D11—24no—
221C2×C4×D11—24no—
222C2×C4×D11—24no—
223C2×C4×D11—22no—
224C2×C4×D11—22no—
225C2×C4×D11—22no—
226C2×C4×D11—22no—
227C2×C4×D11—44no—
228C2×C4×D11—44no—
229C2×C4×D11—44no—
230C2×C4×D11—82no—
231C2×C4×D11C2×D412yes—
232C2×C4×D11C2×D412yes—
233C2×C4×D11C2412yes—
234C2×C4×D11C2412yes—
235C2×C8×C11—22no—
236C2×C8×C11—22no—
237C2×C8×C11C2412yes—
238C2×C8×C11C2412yes—
239C11×C4⋊C4—21no—
240C11×C4⋊C4—21no—
241C11×C4⋊C4—21no—
242C11×C4⋊C4—24no—
243C11×C4⋊C4C2412yes—
244C11×C4⋊C4C2412yes—
245C11×C4⋊C4C2412yes—
246C11×C22⋊C4—24no—
247C42×C11C2×D412yes—
248C42×C11C2412yes—
249C22⋊Dic11—24no—
250C22⋊Dic11—24no—
251#4323—28no—
252(C2×D11)⋊C4—24no—
253(C2×D11)⋊C4—24no—
254(C2×D11)⋊C4—24no—
255(C2×D11)⋊C4—24no—
256(C2×D11)⋊C4C2×D414yes—
257(C2×D11)⋊C4C2×D414yes—
258C4⋊Dic11—21no—
259C4⋊Dic11—21no—
260C4⋊Dic11—21no—
261C4⋊Dic11C2×D414yes—
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#4114yescomplemented
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×#476D1111yescharacteristic, complemented
287C2×#469—111no—
288C2×#466—111no—
289C2×#442—111no—
290C2×#435—111no—
291C2×#428—111no—
292C22×#106—111no—
293C23×C11—22no—
294C23×C11—42no—
295C23×C11—42no—
296C23×C11—42no—
297C23×C11C22×D411yescharacteristic
298C22×D11—22no—
299C22×D11—22no—
300C22×D11—22no—
301C22×D11—22no—
302C22×D11—22no—
303C22×D11—22no—
304C22×D11—42no—
305C22×D11—42no—
306C22×D11—42no—
307C22×D11AGL(1,ℤ/8)14yes—
308C22×D11C22×D412yes—
309C22×D11C22×D412yes—
310Q8×C11—48no—
311D4×C11—22no—
312D4×C11—22no—
313D4×C11—42no—
314C2×C4×C11—22no—
315C2×C4×C11—22no—
316C2×C4×C11—22no—
317C2×C4×C11—22no—
318C2×C4×C11—22no—
319C2×C4×C11—42no—
320C2×C4×C11—42no—
321C2×C4×C11—42no—
322C2×C4×C11—84no—
323C2×C4×C11C22×D412yes—
324C2×C4×C11C22×D412yes—
325C2×C4×C11C22×D411yescharacteristic
326C2×C4×C11C2×#4112yes—
327C2×C4×C112−1+412yes—
328C2×C4×C11C2511yescharacteristic
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×Dic11—42no—
339C2×Dic11C22×D412yes—
340C2×Dic11C22×D412yes—
341D44—28no—
342D44—22no—
343D44—22no—
344D44—48no—
345D44—48no—
346D44—42no—
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—48no—
356C4×D11—84no—
357C8×C11—22no—
358C8×C11—22no—
359C11⋊C8—22no—
360C11⋊C8C2×#4114yescomplemented
361C22×#41—221no—
362C22×D8—111no—
363C22×M16—111no—
364C23×C8—111no—
365#553—118no—
366#553—224no—
367#547—118no—
368#547—224no—
369C2×C4⋊Q8C2×D1111yescharacteristic
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—221no—
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#476C2×D1118yescomplemented
396#469—118no—
397#466—118no—
398#442—118no—
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—118no—
409C2×#106C2×D1111yescharacteristic
410C2×#106C2×D1111yescharacteristic
411C2×C4⋊C8C2×D1111yescharacteristic
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—42no—
422C22×C11—42no—
423C22×C11—42no—
424C22×C11—84no—
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—22no—
433C2×D11—22no—
434C2×D11—22no—
435C2×D11—44no—
436C2×D11—42no—
437C2×D11—42no—
438C2×D11—42no—
439C2×D11—84no—
440C2×D11C2×AGL(1,ℤ/8)14yes—
441C4×C11—22no—
442C4×C11—22no—
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—42no—
452Dic11—42no—
453Dic11—42no—
454C2×#41—228no—
455C2×#41—448no—
456C22×Q8—21no—
457C22×D4—111no—
458C22×D4—111no—
459C22×D4—221no—
460C22×D4—221no—
461C22×D4—221no—
462C22×D4—221no—
463C22×D4C22×D1111yescharacteristic
464C23×C4—21no—
465C23×C4—111no—
466C23×C4—111no—
467C23×C4—221no—
468C23×C4—221no—
469C23×C4—221no—
470C23×C4—221no—
471C2×D8—114no—
472C2×D8—224no—
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—22no—
482C4⋊Q8C22×D1114yes—
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—114no—
501C4×D4—114no—
502C4×D4—114no—
503C4×D4—228no—
504C4×D4—222no—
505C4×D4C22×D1114yes—
506#117—114no—
507#117—222no—
508C2×C4⋊C4—21no—
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⋊C4C22×D1111yescharacteristic
525C2×C4⋊C4C22×D1111yescharacteristic
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—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#106C22×D1114yes—
546#106C22×D1114yes—
547C4⋊C8C22×D1114yes—
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—82no—
558C2×C11#334514yescomplemented
559C2×C11C2×#54711yescharacteristic
560C2×C11C22×AGL(1,ℤ/8)11yescharacteristic
561C2×C11C2×#57711yescharacteristic
562D11—24no—
563D11—42no—
564D11—82no—
565C24—21no—
566C24—111no—
567C24—111no—
568C24—221no—
569#41—4432no—
570C2×Q8—24no—
571C2×Q8—44no—
572C2×D4—21no—
573C2×D4—22no—
574C2×D4—22no—
575C2×D4—114no—
576C2×D4—112no—
577C2×D4—224no—
578C2×D4—224no—
579C2×D4—224no—
580C2×D4—224no—
581C2×D4—224no—
582C2×D4—221no—
583C2×D4—222no—
584C2×D4—222no—
585C2×D4—444no—
586C2×D4—444no—
587C2×D4—444no—
588C2×D4—882no—
589C2×D4C23×D1112yes—
590C22×C4—21no—
591C22×C4—21no—
592C22×C4—21no—
593C22×C4—24no—
594C22×C4—82no—
595C22×C4—111no—
596C22×C4—111no—
597C22×C4—112no—
598C22×C4—112no—
599C22×C4—112no—
600C22×C4—112no—
601C22×C4—224no—
602C22×C4—224no—
603C22×C4—224no—
604C22×C4—222no—
605C22×C4—222no—
606C22×C4—222no—
607C22×C4—222no—
608C22×C4—221no—
609C22×C4—221no—
610C22×C4—221no—
611C22×C4—224no—
612C22×C4—444no—
613C22×C4—444no—
614C22×C4—444no—
615C22×C4—882no—
616C22×C4D4×D1111yescharacteristic
617C22×C4D4×D1111yescharacteristic
618C22×C4C23×D1111yescharacteristic
619D8—228no—
620M16—228no—
621C2×C8—22no—
622C2×C8—22no—
623C2×C8—114no—
624C2×C8—112no—
625C2×C8—112no—
626C2×C8—228no—
627C2×C8—222no—
628C2×C8C23×D1112yes—
629C2×C8C23×D1112yes—
630C4⋊C4—24no—
631C4⋊C4—21no—
632C4⋊C4—21no—
633C4⋊C4—21no—
634C4⋊C4—114no—
635C4⋊C4—112no—
636C4⋊C4—112no—
637C4⋊C4—112no—
638C4⋊C4—224no—
639C4⋊C4—224no—
640C4⋊C4—224no—
641C4⋊C4—221no—
642C4⋊C4—221no—
643C4⋊C4—221no—
644C4⋊C4—224no—
645C4⋊C4—224no—
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—224no—
659C42D4×D1112yes—
660C42C23×D1112yes—
661C11C2×#334511yescharacteristic, complemented, Sylow
662C23—22no—
663C23—42no—
664C23—42no—
665C23—42no—
666C23—114no—
667C23—112no—
668C23—112no—
669C23—222no—
670C23—222no—
671C23—222no—
672C23—222no—
673C23—222no—
674C23—222no—
675C23—442no—
676C23—442no—
677C23—442no—
678C23C2×D4×D1111yescharacteristic
679Q8—48no—
680D4—22no—
681D4—22no—
682D4—42no—
683D4—228no—
684D4—222no—
685D4—222no—
686D4—448no—
687D4—448no—
688D4—448no—
689D4—442no—
690D4—884no—
691C2×C4—22no—
692C2×C4—22no—
693C2×C4—22no—
694C2×C4—22no—
695C2×C4—22no—
696C2×C4—42no—
697C2×C4—42no—
698C2×C4—42no—
699C2×C4—84no—
700C2×C4—112no—
701C2×C4—112no—
702C2×C4—222no—
703C2×C4—222no—
704C2×C4—224no—
705C2×C4—224no—
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—448no—
716C2×C4—442no—
717C2×C4—442no—
718C2×C4—442no—
719C2×C4—884no—
720C2×C4C2×D4×D1112yes—
721C2×C4C2×D4×D1112yes—
722C2×C4C2×D4×D1111yescharacteristic
723C2×C4#6704012yes—
724C2×C4#41×D1112yes—
725C2×C4C24×D1111yescharacteristic
726C8—22no—
727C8—22no—
728C8—114no—
729C8—222no—
730C22—42no—
731C22—42no—
732C22—42no—
733C22—84no—
734C22—114no—
735C22—228no—
736C22—222no—
737C22—222no—
738C22—222no—
739C22—222no—
740C22—222no—
741C22—444no—
742C22—442no—
743C22—442no—
744C22—442no—
745C22—884no—
746C22#1062316212yes—
747C22#1062329312yes—
748C22D11×AGL(1,ℤ/8)12yes—
749C22C22×D4×D1111yescharacteristic
750C4—22no—
751C4—22no—
752C4—42no—
753C4—42no—
754C4—42no—
755C4—222no—
756C4—222no—
757C4—442no—
758C4—442no—
759C4—442no—
760C4#1062316212yes—
761C4C2×#6704011yescharacteristic
762C4C2×#41×D1111yescharacteristic
763C2—82no—
764C2—224no—
765C2—442no—
766C2—882no—
767C2#1308109314yesdirect product factor
768C2C2×#1062316211yescharacteristic
769C2C2×D11×AGL(1,ℤ/8)11yescharacteristic
770C2C2×#1062329311yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#476C2
socleC23×C11C22×D4
hypercenterC2×#476D11
hypocenterC11C2×#3345
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#476

Complements

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

NH ≅ G/Ntype
1. C2×#10623089C2semidirect
2. C2×#10623257C2semidirect
3. #13081093C2direct (N × H)
4. C2×#10622693C2semidirect
5. C2×#10622476C2semidirect
6. C2×#10622390C2semidirect
7. C2×#10622479C2semidirect
8. C2×#10622387C2semidirect
9. C2×#10622460C2semidirect
10. C2×#10622395C2semidirect
11. C2×#10622388C2semidirect
12. C2×#10622627C2semidirect
13. C2×#10622449C2semidirect
14. C2×#10622474C2semidirect
15. C2×D11×#106C2semidirect
16. C2×C11×#476C2semidirect
29. #10623257C22semidirect
31. #10623089C22semidirect
45. C11×#476C22semidirect
58. #10622693C22semidirect
59. #10622627C22semidirect
67. #10622479C22semidirect
68. #10622476C22semidirect
69. #10622474C22semidirect
70. D11×#106C22semidirect
71. #10622460C22semidirect
72. #10622449C22semidirect
73. #10622395C22semidirect
74. #10622390C22semidirect
75. #10622388C22semidirect
76. #10622387C22semidirect
272. C2×C11⋊C8#41semidirect
286. C2×#476D11semidirect
360. C11⋊C8C2×#41semidirect
395. #476C2×D11semidirect
558. C2×C11#3345semidirect
661. C11C2×#3345semidirect
767. C2#13081093direct (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×#106232572
#130810932
C2×#106226932
C2×#106224762
C2×#106223902
C2×#106224792
C2×#106223872
C2×#106224602
C2×#106223952
C2×#106223882
C2×#106226272
C2×#106224492
C2×#106224742
C2×D11×#1062
C2×C11×#4762
C2×#334511