Finite Group Databasebeta

← C2×#13078721 #15621949

Subgroups — C2×#13078721 #15621949

Order 2816.

2182 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×#10623088C211yesmaximal, characteristic, complemented
2C2×C4×#4341C211yesmaximal, characteristic, complemented
3#13078721C2116yesmaximal, direct product factor
4C2×#10622480C211yesmaximal, characteristic, complemented
5C2×#10622392C211yesmaximal, characteristic, complemented
6C2×#10622470C211yesmaximal, characteristic, complemented
7C2×#10622376C211yesmaximal, characteristic, complemented
8C2×#10622380C211yesmaximal, characteristic, complemented
9C2×#10622766C211yesmaximal, characteristic, complemented
10C2×#10622396C211yesmaximal, characteristic, complemented
11C2×#10622771C211yesmaximal, characteristic
12C2×#10622329C211yesmaximal, characteristic, complemented
13C2×#10622631C211yesmaximal, characteristic, complemented
14C2×#10622631C211yesmaximal, characteristic, complemented
15C2×#10622318C211yesmaximal, characteristic, complemented
16C2×C11×#442C211yesmaximal, characteristic, complemented
17C22×#4341C2211yescharacteristic
18C22×C11×D8C2211yescharacteristic
19C2×C4×D4×C11C2211yescharacteristic
20C2×C4×D4×C11C2211yescharacteristic
21C2×#66991C2211yescharacteristic
22C2×#66989C2211yescharacteristic
23C2×D4×Dic11C2211yescharacteristic
24C22×#4324C2211yescharacteristic
25C22×#4324C2211yescharacteristic
26C2×C4×C22⋊D11—21no—
27C2×C4×C22⋊D11—21no—
28C2×#66979—21no—
29C22×C4×Dic11—21no—
30C22×Dic44C2211yescharacteristic
31#10623088—24no—
32#10623088C2218yescomplemented
33C4×#4341—24no—
34C4×#4341C2218yescomplemented
35C2×#66950C2211yescharacteristic
36C2×#66945C2211yescharacteristic
37C2×#66943C2211yescharacteristic
38C2×#66940C2211yescharacteristic
39C2×#66936—21no—
40C2×(C22⋊D11)⋊C4—21no—
41C2×#66932—21no—
42C2×#66930—21no—
43C2×C42×D11C2211yescharacteristic
44C2×C4×Dic22C2211yescharacteristic
45C2×C4×Dic22C2211yescharacteristic
46C11×#442C2218yescomplemented
47C2×C11×#106C2211yescharacteristic
48C2×C11×#102C2211yescharacteristic
49C2×C11×#102C2211yescharacteristic
50C2×C11×#97C2211yescharacteristic
51C2×#66896C2211yescharacteristic
52C2×#66896C2211yescharacteristic
53#10622771C2218yes—
54#10622766C2218yescomplemented
55C2×(C2×D11)⋊C8C2211yescharacteristic
56C2×(C2×D11)⋊C8C2211yescharacteristic
57C2×#66881C2211yescharacteristic
58C2×#66880C2211yescharacteristic
59C2×#66880C2211yescharacteristic
60C2×Dic11⋊C8C2211yescharacteristic
61C2×Dic11⋊C8C2211yescharacteristic
62#10622631C2218yescomplemented
63#10622631C2218yescomplemented
64C2×#66874C2211yescharacteristic
65C2×#66874C2211yescharacteristic
66C2×#66871C2211yescharacteristic
67C2×#66871C2211yescharacteristic
68C2×#66867C2211yescharacteristic
69#10622480C2218yescomplemented
70#10622470C2218yescomplemented
71#10622396C2218yescomplemented
72#10622392C2218yescomplemented
73#10622380C2218yescomplemented
74#10622376C2218yescomplemented
75#10622329C2218yescomplemented
76#10622318C2218yescomplemented
77C22×D4×C11C2311yescharacteristic
78C22×D4×C11C2311yescharacteristic
79C23×C4×C11—21no—
80C23×C4×C11—21no—
81C22×C22⋊D11—21no—
82C22×C22⋊D11—21no—
83C23×Dic11—21no—
84C23×Dic11—21no—
85C2×#4341—24no—
86C2×#4341—22no—
87C2×#4341—24no—
88C2×#4341C2314yes—
89C22×C4×D11D411yescharacteristic
90C22×C4×D11D411yescharacteristic
91C22×C4×D11C2311yescharacteristic
92C22×Dic22C2311yescharacteristic
93C22×Dic22C2311yescharacteristic
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#66991C2314yes—
113#66989—22no—
114#66989C2314yes—
115D4×Dic11—22no—
116D4×Dic11C2314yes—
117C2×#4324—24no—
118C2×#4324—24no—
119C2×#4324C2314yes—
120C2×#4324C2314yes—
121C4×C22⋊D11—28no—
122C4×C22⋊D11—28no—
123C2×(C2×D11)⋊C4—21no—
124C2×(C2×D11)⋊C4—21no—
125#66979—28no—
126C2×C4⋊Dic11—21no—
127C2×C4⋊Dic11—21no—
128C2×C4⋊Dic11C2311yescharacteristic
129C2×C4⋊Dic11C2311yescharacteristic
130C2×Dic11⋊C4—21no—
131C2×Dic11⋊C4—21no—
132C2×Dic11⋊C4—21no—
133C2×Dic11⋊C4—21no—
134C2×C4×Dic11—21no—
135C2×C4×Dic11—21no—
136C2×C4×Dic11—21no—
137C2×C4×Dic11—21no—
138C2×C4×Dic11—28no—
139C2×C4×Dic11D411yescharacteristic
140C2×C4×Dic11D411yescharacteristic
141C2×C4×Dic11C2311yescharacteristic
142C22×C11⋊C8C2311yescharacteristic
143C22×C11⋊C8C2311yescharacteristic
144C2×Dic44—24no—
145C2×Dic44C2314yes—
146#66950—22no—
147#66950C2314yes—
148#66945—22no—
149#66945C2314yes—
150#66943—22no—
151#66943C2314yes—
152#66940—22no—
153#66940C2314yes—
154#66936—28no—
155(C22⋊D11)⋊C4—28no—
156#66932—28no—
157#66930—28no—
158C42×D11D414yes—
159C42×D11C2314yes—
160C4×Dic22—22no—
161C4×Dic22—22no—
162C4×Dic22C2314yes—
163C4×Dic22C2314yes—
164C11×#106C2314yes—
165C11×#102C2314yes—
166C11×#102C2314yes—
167C11×#97C2314yes—
168#66896C2314yes—
169#66896C2314yes—
170(C2×D11)⋊C8C2314yes—
171(C2×D11)⋊C8C2314yes—
172#66881C2314yes—
173#66880C2314yes—
174#66880C2314yes—
175Dic11⋊C8C2314yes—
176Dic11⋊C8C2314yes—
177#66874C2314yes—
178#66874C2314yes—
179#66871C2314yes—
180#66871C2314yes—
181#66867C2314yes—
182C2×#3111—111nomaximal, Sylow
183C24×C11—21no—
184C24×C11—21no—
185C23×D11C2×D411yescharacteristic
186C2×D4×C11—21no—
187C2×D4×C11—21no—
188C2×D4×C11—22no—
189C2×D4×C11—22no—
190C2×D4×C11—22no—
191C2×D4×C11#4114yes—
192C2×D4×C11C2412yes—
193C2×D4×C11C2412yes—
194C22×C4×C11—21no—
195C22×C4×C11—21no—
196C22×C4×C11—24no—
197C22×C4×C11—24no—
198C22×C4×C11—44no—
199C22×C4×C11—44no—
200C22×C4×C11C2×D411yescharacteristic
201C22×C4×C11C2×D411yescharacteristic
202C22×C4×C11C2411yescharacteristic
203C2×C22⋊D11—28no—
204C2×C22⋊D11—24no—
205C2×C22⋊D11—24no—
206C2×C22⋊D11—44no—
207C22×Dic11—28no—
208C22×Dic11—24no—
209C22×Dic11—24no—
210C22×Dic11—21no—
211C22×Dic11—21no—
212C22×Dic11—21no—
213C22×Dic11—21no—
214C22×Dic11—44no—
215C22×Dic11C2×D411yescharacteristic
216C22×Dic11C2×D411yescharacteristic
217C22×Dic11C2×D411yescharacteristic
218#4341—216no—
219#4341—28no—
220#4341—28no—
221C2×C4×D11—22no—
222C2×C4×D11—22no—
223C2×C4×D11—42no—
224C2×C4×D11—42no—
225C2×C4×D11C2×D412yes—
226C2×C4×D11C2×D414yes—
227C2×C4×D11C2×D414yes—
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—
237C11×D8—28no—
238C2×C8×C11—22no—
239C2×C8×C11—22no—
240C2×C8×C11C2412yes—
241C2×C8×C11C2412yes—
242C11×C4⋊C4—21no—
243C11×C4⋊C4—21no—
244C11×C4⋊C4C2412yes—
245C11×C4⋊C4C2412yes—
246C11×C22⋊C4—24no—
247C11×C22⋊C4—24no—
248C42×C11C2×D412yes—
249C42×C11C2412yes—
250C22⋊Dic11—24no—
251C22⋊Dic11—24no—
252C22⋊Dic11—24no—
253C22⋊Dic11—24no—
254#4324—28no—
255#4324—28no—
256(C2×D11)⋊C4—24no—
257(C2×D11)⋊C4—24no—
258C4⋊Dic11—24no—
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—
268C4×Dic11—24no—
269C4×Dic11—24no—
270C4×Dic11—24no—
271C4×Dic11—24no—
272C4×Dic11C2×D412yes—
273C4×Dic11C2×D414yes—
274C4×Dic11C2×D414yes—
275C4×Dic11C2412yes—
276C2×C11⋊C8—22no—
277C2×C11⋊C8—22no—
278C2×C11⋊C8C2412yes—
279C2×C11⋊C8C2412yes—
280Dic44—28no—
281C2×#529—111no—
282C2×C4×#41—111no—
283#3111—1116no—
284C2×#485—111no—
285C2×#482—111no—
286C2×#479—111no—
287C2×#478—111no—
288C2×#464—111no—
289C2×#463—111no—
290C2×#452—111no—
291C2×#449—111no—
292C2×#442D1111yescharacteristic, complemented
293C2×#441—111no—
294C2×#440—111no—
295C2×#440—111no—
296C2×#432—111no—
297C23×C11—24no—
298C23×C11—22no—
299C23×C11—22no—
300C23×C11—42no—
301C23×C11—42no—
302C23×C11—42no—
303C23×C11—42no—
304C23×C11—42no—
305C23×C11C22×D411yescharacteristic
306C22×D11—22no—
307C22×D11—22no—
308C22×D11—22no—
309C22×D11C22×D412yes—
310D4×C11—24no—
311D4×C11—22no—
312D4×C11—22no—
313D4×C11—22no—
314D4×C11—42no—
315D4×C11C2×#4114yes—
316C2×C4×C11—22no—
317C2×C4×C11—22no—
318C2×C4×C11—22no—
319C2×C4×C11—22no—
320C2×C4×C11—48no—
321C2×C4×C11—48no—
322C2×C4×C11—42no—
323C2×C4×C11—42no—
324C2×C4×C11C22×D412yes—
325C2×C4×C11C22×D412yes—
326C2×C4×C11C22×D411yescharacteristic
327C2×C4×C11C2×#4112yes—
328C2×C4×C11C2×#4112yes—
329C2×C4×C11C2511yescharacteristic
330C22⋊D11—216no—
331C22⋊D11—48no—
332C2×Dic11—216no—
333C2×Dic11—24no—
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—42no—
345C2×Dic11C22×D412yes—
346C2×Dic11C22×D412yes—
347C2×Dic11C22×D412yes—
348C4×D11—24no—
349C4×D11—22no—
350C4×D11—22no—
351C4×D11—44no—
352C4×D11—44no—
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×D8C2×D1111yescharacteristic
368#529—118no—
369#529—224no—
370C2×#126—221no—
371C2×#125—111no—
372C2×#124—111no—
373C2×#123—221no—
374C2×C22⋊Q8—111no—
375C2×#121—111no—
376C4×#41—118no—
377C4×#41—224no—
378C2×C4×Q8—111no—
379C2×C4×Q8—111no—
380C2×C4×Q8—111no—
381C2×C4×D4—111no—
382C2×C4×D4—221no—
383C2×C4×D4—221no—
384C2×C4×D4—221no—
385C2×C4×D4C2×D1111yescharacteristic
386C2×C4×D4C2×D1111yescharacteristic
387C2×#117—111no—
388C2×#117—221no—
389C2×#117—221no—
390C22×C42—111no—
391C22×C42—221no—
392#485—118no—
393#482—118no—
394#479—118no—
395#478—118no—
396#464—118no—
397#463—118no—
398#452—118no—
399#449—118no—
400#442C2×D1118yescomplemented
401#441—118no—
402#440—118no—
403#440—118no—
404#432—118no—
405C2×#107—111no—
406C2×#107—111no—
407C2×#106—111no—
408C2×#106C2×D1111yescharacteristic
409C2×C4⋊C8—111no—
410C2×C4⋊C8—111no—
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×#97C2×D1111yescharacteristic
423C22×C11—24no—
424C22×C11—48no—
425C22×C11—42no—
426C22×C11—42no—
427C22×C11—42no—
428C22×C11—42no—
429C22×C11—42no—
430C22×C11—84no—
431C22×C11#52512yes—
432C22×C11#57512yes—
433C22×C11#57512yes—
434C22×C11C23×D411yescharacteristic
435C2×D11—22no—
436C2×D11—22no—
437C2×D11—22no—
438C2×D11—44no—
439C4×C11—22no—
440C4×C11—22no—
441C4×C11—42no—
442C4×C11—42no—
443C4×C11#52512yes—
444C4×C11C22×#4111yescharacteristic
445C4×C11C22×#4111yescharacteristic
446Dic11—24no—
447Dic11—22no—
448Dic11—22no—
449Dic11—22no—
450Dic11—42no—
451Dic11—42no—
452Dic11—42no—
453C2×#41—114no—
454C2×#41—222no—
455C2×#41—224no—
456C2×#41—224no—
457C22×Q8—111no—
458C22×Q8—111no—
459C22×D4—221no—
460C22×D4—221no—
461C22×D4C22×D1111yescharacteristic
462C22×D4C22×D1111yescharacteristic
463C23×C4—21no—
464C23×C4—21no—
465C23×C4—111no—
466C23×C4—111no—
467C23×C4—111no—
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—24no—
477C2×D8C22×D1114yes—
478C22×C8—111no—
479C22×C8—111no—
480C22×C8C22×D1111yescharacteristic
481C22×C8C22×D1111yescharacteristic
482#126—228no—
483#125—114no—
484#125—222no—
485#124—114no—
486#124—222no—
487#123—228no—
488C22⋊Q8—114no—
489C22⋊Q8—222no—
490#121—114no—
491#121—222no—
492C4×Q8—114no—
493C4×Q8—114no—
494C4×Q8—114no—
495C4×Q8—222no—
496C4×Q8—222no—
497C4×Q8—222no—
498C4×D4—22no—
499C4×D4—22no—
500C4×D4—114no—
501C4×D4—222no—
502C4×D4—228no—
503C4×D4—228no—
504C4×D4—228no—
505C4×D4C22×D1114yes—
506C4×D4C22×D1114yes—
507#117—114no—
508#117—228no—
509#117—228no—
510#117—222no—
511C2×C4⋊C4—111no—
512C2×C4⋊C4—111no—
513C2×C4⋊C4—221no—
514C2×C4⋊C4—221no—
515C2×C4⋊C4—221no—
516C2×C4⋊C4—221no—
517C2×C4⋊C4—221no—
518C2×C4⋊C4—221no—
519C2×C4⋊C4C22×D1111yescharacteristic
520C2×C4⋊C4C22×D1111yescharacteristic
521C2×C22⋊C4—21no—
522C2×C22⋊C4—21no—
523C2×C22⋊C4—221no—
524C2×C22⋊C4—221no—
525C2×C22⋊C4—221no—
526C2×C22⋊C4—221no—
527C2×C22⋊C4—221no—
528C2×C22⋊C4—221no—
529C2×C42—111no—
530C2×C42—111no—
531C2×C42—111no—
532C2×C42—114no—
533C2×C42—114no—
534C2×C42—228no—
535C2×C42—221no—
536C2×C42—221no—
537C2×C42—221no—
538C2×C42—221no—
539C2×C42C22×D1111yescharacteristic
540#107—114no—
541#107—114no—
542#106—114no—
543#106C22×D1114yes—
544C4⋊C8—114no—
545C4⋊C8—114no—
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—
557#97C22×D1114yes—
558C2×C11—44no—
559C2×C11—82no—
560C2×C11#311114yescomplemented
561C2×C11C2×#52511yescharacteristic
562C2×C11C2×#57511yescharacteristic
563C2×C11C2×#57511yescharacteristic
564D11—42no—
565C24—21no—
566C24—21no—
567C24—111no—
568#41—228no—
569#41—2216no—
570#41—228no—
571C2×Q8—114no—
572C2×Q8—112no—
573C2×Q8—112no—
574C2×Q8—222no—
575C2×Q8—221no—
576C2×Q8—221no—
577C2×Q8—222no—
578C2×Q8—222no—
579C2×D4—22no—
580C2×D4—21no—
581C2×D4—21no—
582C2×D4—22no—
583C2×D4—22no—
584C2×D4—224no—
585C2×D4—228no—
586C2×D4—224no—
587C2×D4—444no—
588C2×D4#433914yes—
589C2×D4C23×D1112yes—
590C2×D4C23×D1112yes—
591C22×C4—21no—
592C22×C4—21no—
593C22×C4—24no—
594C22×C4—24no—
595C22×C4—44no—
596C22×C4—44no—
597C22×C4—111no—
598C22×C4—111no—
599C22×C4—111no—
600C22×C4—112no—
601C22×C4—112no—
602C22×C4—114no—
603C22×C4—114no—
604C22×C4—224no—
605C22×C4—224no—
606C22×C4—228no—
607C22×C4—221no—
608C22×C4—222no—
609C22×C4—222no—
610C22×C4—221no—
611C22×C4—221no—
612C22×C4—221no—
613C22×C4—442no—
614C22×C4—442no—
615C22×C4—444no—
616C22×C4D4×D1111yescharacteristic
617C22×C4D4×D1111yescharacteristic
618C22×C4C23×D1111yescharacteristic
619Q16—228no—
620SD16—228no—
621SD16—228no—
622D8—28no—
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—21no—
632C4⋊C4—21no—
633C4⋊C4—112no—
634C4⋊C4—112no—
635C4⋊C4—224no—
636C4⋊C4—224no—
637C4⋊C4—224no—
638C4⋊C4—224no—
639C4⋊C4—221no—
640C4⋊C4—221no—
641C4⋊C4—224no—
642C4⋊C4—224no—
643C4⋊C4C23×D1112yes—
644C4⋊C4C23×D1112yes—
645C22⋊C4—24no—
646C22⋊C4—24no—
647C22⋊C4—224no—
648C22⋊C4—224no—
649C22⋊C4—224no—
650C22⋊C4—224no—
651C22⋊C4—224no—
652C22⋊C4—224no—
653C42—114no—
654C42—114no—
655C42—112no—
656C42—112no—
657C42—224no—
658C42—224no—
659C42—224no—
660C42—224no—
661C42D4×D1112yes—
662C42C23×D1112yes—
663C11C2×#311111yescharacteristic, complemented, Sylow
664C23—24no—
665C23—22no—
666C23—22no—
667C23—42no—
668C23—42no—
669C23—42no—
670C23—42no—
671C23—42no—
672C23—112no—
673C23—222no—
674C23—222no—
675C23—222no—
676C23C2×D4×D1111yescharacteristic
677Q8—114no—
678Q8—224no—
679Q8—222no—
680Q8—222no—
681Q8—222no—
682Q8—442no—
683D4—24no—
684D4—22no—
685D4—22no—
686D4—22no—
687D4—42no—
688D4—2216no—
689D4—448no—
690D4C2×#433914yes—
691C2×C4—22no—
692C2×C4—22no—
693C2×C4—22no—
694C2×C4—22no—
695C2×C4—48no—
696C2×C4—48no—
697C2×C4—42no—
698C2×C4—42no—
699C2×C4—112no—
700C2×C4—112no—
701C2×C4—112no—
702C2×C4—2216no—
703C2×C4—222no—
704C2×C4—222no—
705C2×C4—222no—
706C2×C4—224no—
707C2×C4—222no—
708C2×C4—224no—
709C2×C4—222no—
710C2×C4—222no—
711C2×C4—222no—
712C2×C4—222no—
713C2×C4—222no—
714C2×C4—444no—
715C2×C4—444no—
716C2×C4—448no—
717C2×C4—442no—
718C2×C4—442no—
719C2×C4—442no—
720C2×C4C2×#433912yes—
721C2×C4C2×D4×D1112yes—
722C2×C4C2×D4×D1112yes—
723C2×C4C2×D4×D1111yescharacteristic
724C2×C4#41×D1112yes—
725C2×C4C24×D1111yescharacteristic
726C8—22no—
727C8—22no—
728C8—222no—
729C8—222no—
730C22—24no—
731C22—48no—
732C22—42no—
733C22—42no—
734C22—42no—
735C22—42no—
736C22—42no—
737C22—84no—
738C22—222no—
739C22—222no—
740C22—222no—
741C22—444no—
742C22#1062307812yes—
743C22#1062330412yes—
744C22#1062330412yes—
745C22C22×D4×D1111yescharacteristic
746C4—22no—
747C4—22no—
748C4—42no—
749C4—42no—
750C4—222no—
751C4—224no—
752C4—222no—
753C4—222no—
754C4—442no—
755C4—442no—
756C4—442no—
757C4#1062307812yes—
758C4C22×#433911yescharacteristic
759C4C2×#41×D1111yescharacteristic
760C2—44no—
761C2—82no—
762C2—442no—
763C2#1307872114yesdirect product factor
764C2C2×#1062307811yescharacteristic
765C2C2×#1062330411yescharacteristic
766C2C2×#1062330411yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#442C2
socleC23×C11C22×D4
prime radicalC2×#10622771C2
hypercenterC2×#442D11
hypocenterC11C2×#3111
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×#10623088C2semidirect
2. C2×C4×#4341C2semidirect
3. #13078721C2direct (N × H)
4. C2×#10622480C2semidirect
5. C2×#10622392C2semidirect
6. C2×#10622470C2semidirect
7. C2×#10622376C2semidirect
8. C2×#10622380C2semidirect
9. C2×#10622766C2semidirect
10. C2×#10622396C2semidirect
12. C2×#10622329C2semidirect
13. C2×#10622631C2semidirect
14. C2×#10622631C2semidirect
15. C2×#10622318C2semidirect
16. C2×C11×#442C2semidirect
32. #10623088C22semidirect
34. C4×#4341C22semidirect
46. C11×#442C22semidirect
54. #10622766C22semidirect
62. #10622631C22semidirect
63. #10622631C22semidirect
69. #10622480C22semidirect
70. #10622470C22semidirect
71. #10622396C22semidirect
72. #10622392C22semidirect
73. #10622380C22semidirect
74. #10622376C22semidirect
75. #10622329C22semidirect
76. #10622318C22semidirect
292. C2×#442D11semidirect
400. #442C2×D11semidirect
560. C2×C11#3111semidirect
663. C11C2×#3111semidirect
763. C2#13078721direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106230882
C2×C4×#43412
#130787212
C2×#106224802
C2×#106223922
C2×#106224702
C2×#106223762
C2×#106223802
C2×#106227662
C2×#106223962
C2×#106227712
C2×#106223292
C2×#106226312
C2×#106223182
C2×C11×#4422
C2×#311111