Finite Group Databasebeta

← C2×#13078883 #15622093

Subgroups — C2×#13078883 #15622093

Order 2816.

2134 conjugacy classes of subgroups.

The subgroup lattice has 768 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623264C211yesmaximal, characteristic, complemented
2C2×#10623077C211yesmaximal, characteristic, complemented
3#13078883C2116yesmaximal, direct product factor
4C2×#10622497C211yesmaximal, characteristic, complemented
5C2×#10622495C211yesmaximal, characteristic, complemented
6C2×#10622704C211yesmaximal, characteristic, complemented
7C2×#10622458C211yesmaximal, characteristic, complemented
8C2×#10622629C211yesmaximal, characteristic, complemented
9C2×#10622396C211yesmaximal, characteristic, complemented
10C2×#10622394C211yesmaximal, characteristic
11C2×#10622502C211yesmaximal, characteristic, complemented
12C2×#10622370C211yesmaximal, characteristic, complemented
13C2×#10622486C211yesmaximal, characteristic, complemented
14C2×#10622369C211yesmaximal, characteristic, complemented
15C2×#10622453C211yesmaximal, characteristic, complemented
16C2×C11×#474C211yesmaximal, characteristic, complemented
17C22×#4341C2211yescharacteristic
18C2×C11×C4⋊Q8C2211yescharacteristic
19C2×C4×D4×C11C2211yescharacteristic
20C2×#67000—21no—
21C2×#66999—21no—
22C2×D4×Dic11C2211yescharacteristic
23C22×#4324C2211yescharacteristic
24C22×#4323C2211yescharacteristic
25C2×C4×C22⋊D11—21no—
26C22×Dic11⋊C4—21no—
27C22×Dic44C2211yescharacteristic
28C22×#4314C2211yescharacteristic
29#10623264—24no—
30#10623264C2218yescomplemented
31#10623077—24no—
32#10623077C2218yescomplemented
33C2×#66951—21no—
34C2×#66950C2211yescharacteristic
35C2×#66948C2211yescharacteristic
36C2×#66947—21no—
37C2×#66946C2211yescharacteristic
38C2×C4⋊C4×D11C2211yescharacteristic
39C2×#66940C2211yescharacteristic
40C2×#66940C2211yescharacteristic
41C2×(C22⋊D11)⋊C4—21no—
42C2×#66930—21no—
43C2×#66928C2211yescharacteristic
44C2×#66925C2211yescharacteristic
45C2×C4×Dic22C2211yescharacteristic
46C11×#474C2218yescomplemented
47C2×C11×#107C2211yescharacteristic
48C2×C11×#107C2211yescharacteristic
49C2×C11×C4⋊C8C2211yescharacteristic
50C2×C11×#102C2211yescharacteristic
51C2×C11×#102C2211yescharacteristic
52C2×#66885C2211yescharacteristic
53C2×(C2×D11)⋊C8C2211yescharacteristic
54C2×(C2×D11)⋊C8C2211yescharacteristic
55C2×#66880C2211yescharacteristic
56C2×#66879C2211yescharacteristic
57C2×C8×Dic11C2211yescharacteristic
58#10622704C2218yescomplemented
59#10622629C2218yescomplemented
60C2×#66874C2211yescharacteristic
61C2×#66874C2211yescharacteristic
62C2×#66874C2211yescharacteristic
63C2×#66873C2211yescharacteristic
64C2×#66871C2211yescharacteristic
65C2×#66871C2211yescharacteristic
66C2×C4⋊(C11⋊C8)C2211yescharacteristic
67#10622502C2218yescomplemented
68#10622497C2218yescomplemented
69#10622495C2218yescomplemented
70#10622486C2218yescomplemented
71#10622458C2218yescomplemented
72#10622453C2218yescomplemented
73#10622396C2218yescomplemented
74#10622394C2218yes—
75#10622370C2218yescomplemented
76#10622369C2218yescomplemented
77C22×Q8×C11—21no—
78C22×D4×C11C2311yescharacteristic
79C23×C4×C11—21no—
80C22×C22⋊D11—21no—
81C23×Dic11—21no—
82C23×Dic11—21no—
83C2×#4341—24no—
84C2×#4341—22no—
85C2×#4341—24no—
86C2×#4341C2314yes—
87C22×D44—21no—
88C22×D44C2311yescharacteristic
89C22×C4×D11—21no—
90C22×C4×D11—21no—
91C22×C4×D11C2311yescharacteristic
92C22×Dic22C2311yescharacteristic
93C22×Dic22C2311yescharacteristic
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—
107#67000—28no—
108#66999—28no—
109D4×Dic11—22no—
110D4×Dic11C2314yes—
111C2×#4324—24no—
112C2×#4324C2314yes—
113C2×#4323—24no—
114C2×#4323C2314yes—
115C4×C22⋊D11—28no—
116C2×(C2×D11)⋊C4—21no—
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⋊Dic11—21no—
124C2×C4⋊Dic11C2311yescharacteristic
125C2×Dic11⋊C4—21no—
126C2×Dic11⋊C4—21no—
127C2×Dic11⋊C4—21no—
128C2×Dic11⋊C4—21no—
129C2×Dic11⋊C4—28no—
130C2×Dic11⋊C4D411yescharacteristic
131C2×Dic11⋊C4D411yescharacteristic
132C2×C4×Dic11—21no—
133C2×C4×Dic11—21no—
134C2×C4×Dic11—21no—
135C2×C4×Dic11C2311yescharacteristic
136C22×C11⋊C8C2311yescharacteristic
137C22×C11⋊C8C2311yescharacteristic
138C2×Dic44—24no—
139C2×Dic44C2314yes—
140C2×#4314—24no—
141C2×#4314C2314yes—
142#66951—28no—
143#66950—22no—
144#66950C2314yes—
145#66948—22no—
146#66948C2314yes—
147#66947—28no—
148#66946—22no—
149#66946C2314yes—
150C4⋊C4×D11—22no—
151C4⋊C4×D11C2314yes—
152#66940—22no—
153#66940—22no—
154#66940C2314yes—
155#66940C2314yes—
156(C22⋊D11)⋊C4—28no—
157#66930—28no—
158#66928—22no—
159#66928C2314yes—
160#66925D414yes—
161#66925C2314yes—
162C4×Dic22—22no—
163C4×Dic22C2314yes—
164C11×#107C2314yes—
165C11×#107C2314yes—
166C11×C4⋊C8C2314yes—
167C11×#102C2314yes—
168C11×#102C2314yes—
169#66885C2314yes—
170(C2×D11)⋊C8C2314yes—
171(C2×D11)⋊C8C2314yes—
172#66880C2314yes—
173#66879C2314yes—
174C8×Dic11C2314yes—
175#66874C2314yes—
176#66874C2314yes—
177#66874C2314yes—
178#66873C2314yes—
179#66871C2314yes—
180#66871C2314yes—
181C4⋊(C11⋊C8)C2314yes—
182C2×#3124—111nomaximal, Sylow
183C24×C11—21no—
184C23×D11—21no—
185C23×D11C2×D411yescharacteristic
186C2×Q8×C11—24no—
187C2×Q8×C11—82no—
188C2×D4×C11—21no—
189C2×D4×C11—22no—
190C2×D4×C11#4114yes—
191C2×D4×C11C2412yes—
192C22×C4×C11—21no—
193C22×C4×C11—21no—
194C22×C4×C11—21no—
195C22×C4×C11—24no—
196C22×C4×C11—82no—
197C22×C4×C11C2×D411yescharacteristic
198C22×C4×C11C2×D411yescharacteristic
199C22×C4×C11C2411yescharacteristic
200C2×C22⋊D11—28no—
201C2×C22⋊D11—24no—
202C22×Dic11—28no—
203C22×Dic11—24no—
204C22×Dic11—24no—
205C22×Dic11—21no—
206C22×Dic11—21no—
207C22×Dic11—21no—
208C22×Dic11—82no—
209C22×Dic11C2×D411yescharacteristic
210C22×Dic11C2×D411yescharacteristic
211C22×Dic11C2×D411yescharacteristic
212#4341—216no—
213#4341—28no—
214#4341—28no—
215C2×D44—24no—
216C2×D44—21no—
217C2×D44—22no—
218C2×D44—22no—
219C2×D44—82no—
220C2×D44C2412yes—
221C2×C4×D11—24no—
222C2×C4×D11—24no—
223C2×C4×D11—22no—
224C2×C4×D11—22no—
225C2×C4×D11—82no—
226C2×C4×D11—82no—
227C2×C4×D11C2×D412yes—
228C2×C4×D11C2412yes—
229C2×Dic22—21no—
230C2×Dic22—21no—
231C2×Dic22—22no—
232C2×Dic22—22no—
233C2×Dic22—22no—
234C2×Dic22#4114yes—
235C2×Dic22C2412yes—
236C2×Dic22C2412yes—
237C2×C8×C11—22no—
238C2×C8×C11—22no—
239C2×C8×C11C2412yes—
240C2×C8×C11C2412yes—
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×C22⋊C4—24no—
249C42×C11C2×D412yes—
250C42×C11C2412yes—
251C22⋊Dic11—24no—
252#4324—28no—
253#4323—28no—
254(C2×D11)⋊C4—24no—
255(C2×D11)⋊C4—24no—
256(C2×D11)⋊C4—24no—
257(C2×D11)⋊C4—24no—
258(C2×D11)⋊C4—24no—
259(C2×D11)⋊C4C2×D414yes—
260(C2×D11)⋊C4C2×D414yes—
261C4⋊Dic11—24no—
262C4⋊Dic11—21no—
263C4⋊Dic11C2412yes—
264Dic11⋊C4—24no—
265Dic11⋊C4—24no—
266Dic11⋊C4—24no—
267Dic11⋊C4—24no—
268Dic11⋊C4C2×D414yes—
269Dic11⋊C4C2×D414yes—
270C4×Dic11—24no—
271C4×Dic11—24no—
272C4×Dic11—24no—
273C4×Dic11C2×D412yes—
274C4×Dic11C2412yes—
275C2×C11⋊C8—22no—
276C2×C11⋊C8—22no—
277C2×C11⋊C8C2412yes—
278C2×C11⋊C8C2412yes—
279Dic44—28no—
280#4314—28no—
281C2×#542—111no—
282C2×#520—111no—
283#3124—1116no—
284C2×#484—111no—
285C2×#480—111no—
286C2×#477—111no—
287C2×#474D1111yescharacteristic, complemented
288C2×#464—111no—
289C2×#463—111no—
290C2×#452—111no—
291C2×#449—111no—
292C2×#440—111no—
293C2×#440—111no—
294C2×C4×Q16—111no—
295C2×C4×D8—111no—
296C2×#433—111no—
297C23×C11—24no—
298C23×C11—22no—
299C23×C11—42no—
300C23×C11—42no—
301C23×C11C22×D411yescharacteristic
302C22×D11—22no—
303C22×D11—22no—
304C22×D11—22no—
305C22×D11—22no—
306C22×D11—42no—
307C22×D11—42no—
308C22×D11—42no—
309C22×D11C22×D412yes—
310Q8×C11—84no—
311D4×C11—24no—
312D4×C11—22no—
313D4×C11C2×#4114yes—
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×C11C2×#4112yes—
328C2×C4×C11C2511yescharacteristic
329C22⋊D11—216no—
330C2×Dic11—216no—
331C2×Dic11—24no—
332C2×Dic11—22no—
333C2×Dic11—22no—
334C2×Dic11—22no—
335C2×Dic11—22no—
336C2×Dic11—22no—
337C2×Dic11—22no—
338C2×Dic11—42no—
339C2×Dic11—42no—
340C2×Dic11—84no—
341C2×Dic11C22×D412yes—
342C2×Dic11C22×D412yes—
343C2×Dic11C22×D412yes—
344D44—22no—
345D44—22no—
346D44—42no—
347D44—84no—
348C4×D11—24no—
349C4×D11—22no—
350C4×D11—22no—
351C4×D11—84no—
352C4×D11—84no—
353Dic22—24no—
354Dic22—22no—
355Dic22—22no—
356Dic22—22no—
357Dic22—42no—
358Dic22C2×#4114yes—
359C8×C11—22no—
360C8×C11—22no—
361C11⋊C8—22no—
362C11⋊C8—22no—
363C22×#41—111no—
364C22×Q16—111no—
365C22×SD16—111no—
366C22×SD16—111no—
367C22×D8—111no—
368#542—118no—
369#542—224no—
370C2×C4⋊Q8C2×D1111yescharacteristic
371C2×#126—221no—
372C2×#124—111no—
373C2×#124—221no—
374C2×#123—221no—
375C2×C22⋊Q8—111no—
376C2×C22⋊Q8—221no—
377C2×#121—111no—
378#520—118no—
379#520—224no—
380C2×C4×Q8—111no—
381C2×C4×Q8—111no—
382C2×C4×Q8—111no—
383C2×C4×D4—111no—
384C2×C4×D4—111no—
385C2×C4×D4—221no—
386C2×C4×D4—221no—
387C2×C4×D4C2×D1111yescharacteristic
388C2×#117—111no—
389C2×#117—221no—
390C22×C4⋊C4—111no—
391C22×C4⋊C4—221no—
392#484—118no—
393#480—118no—
394#477—118no—
395#474C2×D1118yescomplemented
396#464—118no—
397#463—118no—
398#452—118no—
399#449—118no—
400#440—118no—
401#440—118no—
402C4×Q16—118no—
403C4×D8—118no—
404#433—118no—
405C2×#107—111no—
406C2×#107—111no—
407C2×#107C2×D1111yescharacteristic
408C2×#107C2×D1111yescharacteristic
409C2×C4⋊C8—111no—
410C2×C4⋊C8C2×D1111yescharacteristic
411C2×#103—111no—
412C2×#103—111no—
413C2×#103—111no—
414C2×#103—111no—
415C2×#102—111no—
416C2×#102—111no—
417C2×#102C2×D1111yescharacteristic
418C2×#102C2×D1111yescharacteristic
419C2×C22⋊C8—111no—
420C2×C22⋊C8—111no—
421C2×#97—111no—
422C2×C4×C8—111no—
423C22×C11—24no—
424C22×C11—48no—
425C22×C11—42no—
426C22×C11—42no—
427C22×C11#52512yes—
428C22×C11#57612yes—
429C22×C11#57812yes—
430C22×C11C23×D411yescharacteristic
431C2×D11—22no—
432C2×D11—22no—
433C2×D11—22no—
434C2×D11—44no—
435C2×D11—42no—
436C2×D11—42no—
437C2×D11—42no—
438C2×D11—84no—
439C4×C11—22no—
440C4×C11—22no—
441C4×C11—42no—
442C4×C11—42no—
443C4×C11—42no—
444C4×C11#52512yes—
445C4×C11C22×#4111yescharacteristic
446C4×C11C22×#4111yescharacteristic
447Dic11—24no—
448Dic11—22no—
449Dic11—22no—
450Dic11—22no—
451Dic11—42no—
452Dic11—42no—
453C2×#41—114no—
454C2×#41—222no—
455C2×#41—224no—
456C2×#41—224no—
457C22×Q8—21no—
458C22×Q8—111no—
459C22×Q8—111no—
460C22×D4—111no—
461C22×D4—221no—
462C22×D4—221no—
463C22×D4C22×D1111yescharacteristic
464C23×C4—21no—
465C23×C4—111no—
466C23×C4—221no—
467C23×C4—221no—
468C23×C4—221no—
469C23×C4—221no—
470C2×Q16—114no—
471C2×Q16—224no—
472C2×SD16—114no—
473C2×SD16—114no—
474C2×SD16—224no—
475C2×SD16—224no—
476C2×D8—114no—
477C2×D8—224no—
478C22×C8—111no—
479C22×C8—111no—
480C22×C8C22×D1111yescharacteristic
481C22×C8C22×D1111yescharacteristic
482C4⋊Q8—22no—
483C4⋊Q8C22×D1114yes—
484#126—228no—
485#124—114no—
486#124—228no—
487#124—222no—
488#123—228no—
489C22⋊Q8—114no—
490C22⋊Q8—222no—
491C22⋊Q8—228no—
492#121—114no—
493#121—222no—
494C4×Q8—114no—
495C4×Q8—114no—
496C4×Q8—114no—
497C4×Q8—222no—
498C4×Q8—222no—
499C4×Q8—222no—
500C4×D4—22no—
501C4×D4—114no—
502C4×D4—114no—
503C4×D4—222no—
504C4×D4—222no—
505C4×D4—228no—
506C4×D4—228no—
507C4×D4C22×D1114yes—
508#117—114no—
509#117—114no—
510#117—228no—
511C2×C4⋊C4—21no—
512C2×C4⋊C4—111no—
513C2×C4⋊C4—111no—
514C2×C4⋊C4—111no—
515C2×C4⋊C4—114no—
516C2×C4⋊C4—222no—
517C2×C4⋊C4—228no—
518C2×C4⋊C4—221no—
519C2×C4⋊C4—221no—
520C2×C4⋊C4—221no—
521C2×C4⋊C4—221no—
522C2×C4⋊C4—221no—
523C2×C4⋊C4C22×D1111yescharacteristic
524C2×C4⋊C4C22×D1111yescharacteristic
525C2×C4⋊C4C22×D1111yescharacteristic
526C2×C22⋊C4—21no—
527C2×C22⋊C4—111no—
528C2×C22⋊C4—111no—
529C2×C22⋊C4—221no—
530C2×C22⋊C4—221no—
531C2×C22⋊C4—221no—
532C2×C22⋊C4—221no—
533C2×C22⋊C4—221no—
534C2×C22⋊C4—221no—
535C2×C42—111no—
536C2×C42—221no—
537C2×C42—221no—
538C2×C42—221no—
539C2×C42C22×D1111yescharacteristic
540#107—114no—
541#107—114no—
542#107C22×D1114yes—
543#107C22×D1114yes—
544C4⋊C8—114no—
545C4⋊C8C22×D1114yes—
546#103—114no—
547#103—114no—
548#103—114no—
549#103—114no—
550#102—114no—
551#102—114no—
552#102C22×D1114yes—
553#102C22×D1114yes—
554C22⋊C8—114no—
555C22⋊C8—114no—
556#97—114no—
557C4×C8—114no—
558C2×C11—44no—
559C2×C11#312414yescomplemented
560C2×C11C2×#52511yescharacteristic
561C2×C11C2×#57611yescharacteristic
562C2×C11C2×#57811yescharacteristic
563D11—42no—
564D11—82no—
565C24—21no—
566C24—111no—
567C24—221no—
568#41—228no—
569#41—2216no—
570#41—228no—
571C2×Q8—24no—
572C2×Q8—82no—
573C2×Q8—114no—
574C2×Q8—112no—
575C2×Q8—112no—
576C2×Q8—221no—
577C2×Q8—221no—
578C2×Q8—222no—
579C2×Q8—222no—
580C2×Q8—222no—
581C2×D4—21no—
582C2×D4—22no—
583C2×D4—112no—
584C2×D4—224no—
585C2×D4—224no—
586C2×D4—228no—
587C2×D4—221no—
588C2×D4—222no—
589C2×D4—222no—
590C2×D4—882no—
591C2×D4#434314yes—
592C2×D4C23×D1112yes—
593C22×C4—21no—
594C22×C4—21no—
595C22×C4—21no—
596C22×C4—24no—
597C22×C4—82no—
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—228no—
608C22×C4—221no—
609C22×C4—222no—
610C22×C4—222no—
611C22×C4—221no—
612C22×C4—221no—
613C22×C4—882no—
614C22×C4—882no—
615C22×C4—882no—
616C22×C4D4×D1111yescharacteristic
617C22×C4D4×D1111yescharacteristic
618C22×C4C23×D1111yescharacteristic
619Q16—228no—
620SD16—228no—
621SD16—228no—
622D8—228no—
623C2×C8—22no—
624C2×C8—22no—
625C2×C8—112no—
626C2×C8—112no—
627C2×C8—222no—
628C2×C8—222no—
629C2×C8C23×D1112yes—
630C2×C8C23×D1112yes—
631C4⋊C4—24no—
632C4⋊C4—21no—
633C4⋊C4—21no—
634C4⋊C4—21no—
635C4⋊C4—114no—
636C4⋊C4—114no—
637C4⋊C4—112no—
638C4⋊C4—224no—
639C4⋊C4—224no—
640C4⋊C4—224no—
641C4⋊C4—224no—
642C4⋊C4—221no—
643C4⋊C4—224no—
644C4⋊C4C23×D1112yes—
645C4⋊C4C23×D1112yes—
646C4⋊C4C23×D1112yes—
647C22⋊C4—24no—
648C22⋊C4—114no—
649C22⋊C4—114no—
650C22⋊C4—224no—
651C22⋊C4—224no—
652C22⋊C4—224no—
653C22⋊C4—224no—
654C22⋊C4—224no—
655C22⋊C4—224no—
656C42—112no—
657C42—112no—
658C42—224no—
659C42—224no—
660C42—224no—
661C42D4×D1112yes—
662C42C23×D1112yes—
663C11C2×#312411yescharacteristic, complemented, Sylow
664C23—24no—
665C23—22no—
666C23—42no—
667C23—42no—
668C23—112no—
669C23—222no—
670C23—222no—
671C23—222no—
672C23—222no—
673C23—442no—
674C23—442no—
675C23—442no—
676C23C2×D4×D1111yescharacteristic
677Q8—84no—
678Q8—114no—
679Q8—224no—
680Q8—222no—
681Q8—222no—
682Q8—222no—
683Q8—442no—
684D4—24no—
685D4—22no—
686D4—2216no—
687D4—222no—
688D4—222no—
689D4—442no—
690D4—884no—
691D4C2×#434314yes—
692C2×C4—22no—
693C2×C4—22no—
694C2×C4—22no—
695C2×C4—22no—
696C2×C4—22no—
697C2×C4—42no—
698C2×C4—42no—
699C2×C4—42no—
700C2×C4—84no—
701C2×C4—112no—
702C2×C4—112no—
703C2×C4—112no—
704C2×C4—2216no—
705C2×C4—222no—
706C2×C4—222no—
707C2×C4—222no—
708C2×C4—224no—
709C2×C4—222no—
710C2×C4—224no—
711C2×C4—222no—
712C2×C4—222no—
713C2×C4—222no—
714C2×C4—222no—
715C2×C4—442no—
716C2×C4—442no—
717C2×C4—884no—
718C2×C4—884no—
719C2×C4—884no—
720C2×C4C2×D4×D1112yes—
721C2×C4C2×D4×D1112yes—
722C2×C4C2×D4×D1111yescharacteristic
723C2×C4C2×#434312yes—
724C2×C4#41×D1112yes—
725C2×C4C24×D1111yescharacteristic
726C8—22no—
727C8—22no—
728C8—222no—
729C8—222no—
730C22—24no—
731C22—48no—
732C22—42no—
733C22—42no—
734C22—222no—
735C22—222no—
736C22—222no—
737C22—444no—
738C22—442no—
739C22—442no—
740C22—442no—
741C22—884no—
742C22#1062315812yes—
743C22#1062328812yes—
744C22#1062331012yes—
745C22C22×D4×D1111yescharacteristic
746C4—22no—
747C4—22no—
748C4—42no—
749C4—42no—
750C4—42no—
751C4—222no—
752C4—224no—
753C4—222no—
754C4—222no—
755C4—442no—
756C4—442no—
757C4#1062315812yes—
758C4C22×#434311yescharacteristic
759C4C2×#41×D1111yescharacteristic
760C2—44no—
761C2—442no—
762C2—882no—
763C2#1307888314yesdirect product factor
764C2C2×#1062315811yescharacteristic
765C2C2×#1062328811yescharacteristic
766C2C2×#1062331011yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#474C2
socleC23×C11C22×D4
prime radicalC2×#10622394C2
hypercenterC2×#474D11
hypocenterC11C2×#3124
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#474

Complements

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

NH ≅ G/Ntype
1. C2×#10623264C2semidirect
2. C2×#10623077C2semidirect
3. #13078883C2direct (N × H)
4. C2×#10622497C2semidirect
5. C2×#10622495C2semidirect
6. C2×#10622704C2semidirect
7. C2×#10622458C2semidirect
8. C2×#10622629C2semidirect
9. C2×#10622396C2semidirect
11. C2×#10622502C2semidirect
12. C2×#10622370C2semidirect
13. C2×#10622486C2semidirect
14. C2×#10622369C2semidirect
15. C2×#10622453C2semidirect
16. C2×C11×#474C2semidirect
30. #10623264C22semidirect
32. #10623077C22semidirect
46. C11×#474C22semidirect
58. #10622704C22semidirect
59. #10622629C22semidirect
67. #10622502C22semidirect
68. #10622497C22semidirect
69. #10622495C22semidirect
70. #10622486C22semidirect
71. #10622458C22semidirect
72. #10622453C22semidirect
73. #10622396C22semidirect
75. #10622370C22semidirect
76. #10622369C22semidirect
287. C2×#474D11semidirect
395. #474C2×D11semidirect
559. C2×C11#3124semidirect
663. C11C2×#3124semidirect
763. C2#13078883direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106232642
C2×#106230772
#130788832
C2×#106224972
C2×#106224952
C2×#106227042
C2×#106224582
C2×#106226292
C2×#106223962
C2×#106223942
C2×#106225022
C2×#106223702
C2×#106224862
C2×#106223692
C2×#106224532
C2×C11×#4742
C2×#312411