Finite Group Databasebeta

← C2×#13079718 #15625161

Subgroups — C2×#13079718 #15625161

Order 2816.

2086 conjugacy classes of subgroups.

The subgroup lattice has 810 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623213C211yesmaximal, characteristic, complemented
2C2×#10623206C211yesmaximal, characteristic, complemented
3#13079718C2116yesmaximal, direct product factor
4C2×#10622673C211yesmaximal, characteristic, complemented
5C2×#10622668C211yesmaximal, characteristic, complemented
6C2×#10622294C211yesmaximal, characteristic, complemented
7C2×#10622779C211yesmaximal, characteristic, complemented
8C2×#10622795C211yesmaximal, characteristic, complemented
9C2×#10622766C211yesmaximal, characteristic, complemented
10C2×#10622775C211yesmaximal, characteristic, complemented
11C2×#10622786C211yesmaximal, characteristic, complemented
12C2×#10622771C211yesmaximal, characteristic
13C2×#10622799C211yesmaximal, characteristic, complemented
14C2×#10622783C211yesmaximal, characteristic, complemented
15C2×#10622303C211yesmaximal, characteristic, complemented
16C2×C11×#495C211yesmaximal, characteristic, complemented
17C22×Q8×D11C2211yescharacteristic
18C22×#4341C2211yescharacteristic
19C22×C11×Q16C2211yescharacteristic
20C22×C11×SD16C2211yescharacteristic
21C22×C11×SD16C2211yescharacteristic
22C22×C11×D8C2211yescharacteristic
23C2×C11×#124C2211yescharacteristic
24C2×C11×#124C2211yescharacteristic
25C2×#66999C2211yescharacteristic
26C2×Q8×Dic11C2211yescharacteristic
27C2×#66997C2211yescharacteristic
28C22×#4326C2211yescharacteristic
29C22×#4326C2211yescharacteristic
30C2×#66991C2211yescharacteristic
31C2×#66989C2211yescharacteristic
32C2×D4×Dic11C2211yescharacteristic
33C22×#4324C2211yescharacteristic
34C22×#4324C2211yescharacteristic
35#10623213—24no—
36#10623213C2218yescomplemented
37#10623206—24no—
38#10623206C2218yescomplemented
39C2×#66939—21no—
40C2×#66938—21no—
41C2×#66936—21no—
42C2×#66936—21no—
43C2×#66932—21no—
44C2×#66931—21no—
45C2×#66931—21no—
46C2×#66931—21no—
47C2×#66925C2211yescharacteristic
48C2×#66922C2211yescharacteristic
49C2×#66922C2211yescharacteristic
50C11×#495C2218yescomplemented
51C2×C4×C8×C11C2211yescharacteristic
52C2×#66899C2211yescharacteristic
53C2×#66899C2211yescharacteristic
54C2×#66896C2211yescharacteristic
55C2×#66896C2211yescharacteristic
56#10622799C2218yescomplemented
57#10622795C2218yescomplemented
58#10622786C2218yescomplemented
59#10622783C2218yescomplemented
60#10622779C2218yescomplemented
61#10622775C2218yescomplemented
62#10622771C2218yes—
63#10622766C2218yescomplemented
64C2×(C2×D11)⋊C8C2211yescharacteristic
65C2×(C2×D11)⋊C8C2211yescharacteristic
66C2×#66880C2211yescharacteristic
67C2×#66880C2211yescharacteristic
68C2×#66880C2211yescharacteristic
69C2×#66880C2211yescharacteristic
70C2×Dic11⋊C8C2211yescharacteristic
71C2×Dic11⋊C8C2211yescharacteristic
72#10622673C2218yescomplemented
73#10622668C2218yescomplemented
74C2×#66867C2211yescharacteristic
75#10622303C2218yescomplemented
76#10622294C2218yescomplemented
77C22×Q8×C11C2311yescharacteristic
78C22×Q8×C11C2311yescharacteristic
79C22×D4×C11C2311yescharacteristic
80C22×D4×C11C2311yescharacteristic
81C22×C22⋊D11—21no—
82C22×C22⋊D11—21no—
83C23×Dic11—21no—
84C23×Dic11—21no—
85C2×Q8×D11—22no—
86C2×Q8×D11—42no—
87C2×Q8×D11—42no—
88C2×Q8×D11C2314yes—
89C2×#4341—22no—
90C2×#4341—42no—
91C2×#4341—42no—
92C2×#4341C2314yes—
93C22×C4×D11—21no—
94C22×C4×D11C2311yescharacteristic
95C22×Dic22—21no—
96C22×Dic22—21no—
97C22×Dic22C2311yescharacteristic
98C22×Dic22C2311yescharacteristic
99C2×C11×Q16—42no—
100C2×C11×Q16C2314yes—
101C2×C11×SD16—42no—
102C2×C11×SD16—42no—
103C2×C11×SD16C2314yes—
104C2×C11×SD16C2314yes—
105C2×C11×D8—42no—
106C2×C11×D8C2314yes—
107C22×C8×C11C2311yescharacteristic
108C22×C8×C11C2311yescharacteristic
109C11×#124—22no—
110C11×#124—22no—
111C11×#124C2314yes—
112C11×#124C2314yes—
113C2×C11×C22⋊C4—21no—
114C2×C11×C22⋊C4—21no—
115C2×C11×C22⋊C4—21no—
116C2×C11×C22⋊C4—21no—
117C2×C42×C11C2311yescharacteristic
118C2×C22⋊Dic11—21no—
119C2×C22⋊Dic11—21no—
120C2×C22⋊Dic11—21no—
121C2×C22⋊Dic11—21no—
122#66999—22no—
123#66999C2314yes—
124Q8×Dic11—22no—
125Q8×Dic11C2314yes—
126#66997—22no—
127#66997C2314yes—
128C2×#4326—42no—
129C2×#4326—42no—
130C2×#4326C2314yes—
131C2×#4326C2314yes—
132#66991—22no—
133#66991C2314yes—
134#66989—22no—
135#66989C2314yes—
136D4×Dic11—22no—
137D4×Dic11C2314yes—
138C2×#4324—42no—
139C2×#4324—42no—
140C2×#4324C2314yes—
141C2×#4324C2314yes—
142C2×(C2×D11)⋊C4—21no—
143C2×(C2×D11)⋊C4D411yescharacteristic
144C2×(C2×D11)⋊C4D411yescharacteristic
145C2×C4⋊Dic11—21no—
146C2×C4⋊Dic11—21no—
147C2×C4⋊Dic11—21no—
148C2×C4⋊Dic11—21no—
149C2×C4⋊Dic11C2311yescharacteristic
150C2×C4⋊Dic11C2311yescharacteristic
151C2×Dic11⋊C4—21no—
152C2×Dic11⋊C4—21no—
153C2×Dic11⋊C4—21no—
154C2×Dic11⋊C4D411yescharacteristic
155C2×Dic11⋊C4D411yescharacteristic
156C2×C4×Dic11—21no—
157C2×C4×Dic11C2311yescharacteristic
158C22×C11⋊C8C2311yescharacteristic
159C22×C11⋊C8C2311yescharacteristic
160#66939—28no—
161#66938—28no—
162#66936—28no—
163#66936—28no—
164#66932—28no—
165#66931—28no—
166#66931—28no—
167#66931—28no—
168#66925D414yes—
169#66925C2314yes—
170#66922—22no—
171#66922—22no—
172#66922C2314yes—
173#66922C2314yes—
174C4×C8×C11C2314yes—
175#66899C2314yes—
176#66899C2314yes—
177#66896C2314yes—
178#66896C2314yes—
179(C2×D11)⋊C8C2314yes—
180(C2×D11)⋊C8C2314yes—
181#66880C2314yes—
182#66880C2314yes—
183#66880C2314yes—
184#66880C2314yes—
185Dic11⋊C8C2314yes—
186Dic11⋊C8C2314yes—
187#66867C2314yes—
188C2×#3225—111nomaximal, Sylow
189C24×C11—21no—
190C24×C11—21no—
191C23×D11C2×D411yescharacteristic
192C2×Q8×C11—21no—
193C2×Q8×C11—21no—
194C2×Q8×C11—22no—
195C2×Q8×C11—22no—
196C2×Q8×C11—22no—
197C2×Q8×C11—22no—
198C2×Q8×C11C2412yes—
199C2×Q8×C11C2412yes—
200C2×D4×C11—21no—
201C2×D4×C11—21no—
202C2×D4×C11—22no—
203C2×D4×C11—22no—
204C2×D4×C11—22no—
205C2×D4×C11—22no—
206C2×D4×C11C2412yes—
207C2×D4×C11C2412yes—
208C22×C4×C11—21no—
209C22×C4×C11—21no—
210C22×C4×C11C2×D411yescharacteristic
211C22×C4×C11C2×D411yescharacteristic
212C22×C4×C11C2411yescharacteristic
213C2×C22⋊D11—24no—
214C2×C22⋊D11—24no—
215C2×C22⋊D11—44no—
216C2×C22⋊D11—82no—
217C22×Dic11—24no—
218C22×Dic11—24no—
219C22×Dic11—21no—
220C22×Dic11—21no—
221C22×Dic11—21no—
222C22×Dic11—21no—
223C22×Dic11—44no—
224C22×Dic11—82no—
225C22×Dic11C2×D411yescharacteristic
226C22×Dic11C2×D411yescharacteristic
227C22×Dic11C2×D411yescharacteristic
228Q8×D11—44no—
229Q8×D11—44no—
230Q8×D11—48no—
231#4341—44no—
232#4341—44no—
233#4341—48no—
234C2×C4×D11—24no—
235C2×C4×D11—22no—
236C2×C4×D11—22no—
237C2×C4×D11—44no—
238C2×C4×D11C2×D412yes—
239C2×C4×D11C2412yes—
240C2×Dic22—24no—
241C2×Dic22—21no—
242C2×Dic22—21no—
243C2×Dic22—24no—
244C2×Dic22—22no—
245C2×Dic22—22no—
246C2×Dic22—22no—
247C2×Dic22—22no—
248C2×Dic22—44no—
249C2×Dic22—82no—
250C2×Dic22C2412yes—
251C2×Dic22C2412yes—
252C11×Q16—44no—
253C11×SD16—44no—
254C11×SD16—44no—
255C11×D8—44no—
256C2×C8×C11—22no—
257C2×C8×C11—22no—
258C2×C8×C11C2412yes—
259C2×C8×C11C2412yes—
260C11×C22⋊C4—24no—
261C11×C22⋊C4—24no—
262C11×C22⋊C4—24no—
263C11×C22⋊C4—24no—
264C42×C11C2×D412yes—
265C42×C11C2412yes—
266C22⋊Dic11—24no—
267C22⋊Dic11—24no—
268C22⋊Dic11—24no—
269C22⋊Dic11—24no—
270#4326—44no—
271#4326—44no—
272#4324—44no—
273#4324—44no—
274(C2×D11)⋊C4—24no—
275(C2×D11)⋊C4C2×D414yes—
276(C2×D11)⋊C4C2×D414yes—
277C4⋊Dic11—24no—
278C4⋊Dic11—21no—
279C4⋊Dic11—21no—
280C4⋊Dic11—24no—
281C4⋊Dic11—24no—
282C4⋊Dic11—24no—
283C4⋊Dic11C2412yes—
284C4⋊Dic11C2412yes—
285Dic11⋊C4—24no—
286Dic11⋊C4—24no—
287Dic11⋊C4—24no—
288Dic11⋊C4C2×D414yes—
289Dic11⋊C4C2×D414yes—
290C4×Dic11—24no—
291C4×Dic11C2×D412yes—
292C4×Dic11C2412yes—
293C2×C11⋊C8—22no—
294C2×C11⋊C8—22no—
295C2×C11⋊C8C2412yes—
296C2×C11⋊C8C2412yes—
297C2×#542—111no—
298C2×#536—111no—
299#3225—1116no—
300C2×#497—111no—
301C2×#495D1111yescharacteristic, complemented
302C2×#489—111no—
303C2×#487—111no—
304C2×#464—111no—
305C2×#462—111no—
306C2×#463—111no—
307C2×#461—111no—
308C2×#452—111no—
309C2×#449—111no—
310C2×#451—111no—
311C2×#448—111no—
312C2×#433—111no—
313C23×C11—22no—
314C23×C11—22no—
315C23×C11—42no—
316C23×C11—42no—
317C23×C11—42no—
318C23×C11—42no—
319C23×C11—42no—
320C23×C11—42no—
321C23×C11C22×D411yescharacteristic
322C22×D11—22no—
323C22×D11—22no—
324C22×D11—22no—
325C22×D11C22×D412yes—
326Q8×C11—22no—
327Q8×C11—22no—
328Q8×C11—22no—
329Q8×C11—22no—
330Q8×C11—42no—
331Q8×C11—42no—
332D4×C11—22no—
333D4×C11—22no—
334D4×C11—22no—
335D4×C11—22no—
336D4×C11—42no—
337D4×C11—42no—
338C2×C4×C11—22no—
339C2×C4×C11—22no—
340C2×C4×C11—22no—
341C2×C4×C11—22no—
342C2×C4×C11—42no—
343C2×C4×C11—42no—
344C2×C4×C11C22×D412yes—
345C2×C4×C11C22×D412yes—
346C2×C4×C11C22×D411yescharacteristic
347C2×C4×C11H(5,𝔽2)12yes—
348C2×C4×C11H(5,𝔽2)12yes—
349C2×C4×C11C2511yescharacteristic
350C22⋊D11—48no—
351C22⋊D11—84no—
352C2×Dic11—22no—
353C2×Dic11—22no—
354C2×Dic11—22no—
355C2×Dic11—22no—
356C2×Dic11—22no—
357C2×Dic11—22no—
358C2×Dic11—22no—
359C2×Dic11—48no—
360C2×Dic11—42no—
361C2×Dic11—42no—
362C2×Dic11—42no—
363C2×Dic11—42no—
364C2×Dic11—84no—
365C2×Dic11C22×D412yes—
366C2×Dic11C22×D412yes—
367C2×Dic11C22×D412yes—
368C4×D11—24no—
369C4×D11—22no—
370C4×D11—22no—
371C4×D11—48no—
372Dic22—22no—
373Dic22—22no—
374Dic22—22no—
375Dic22—22no—
376Dic22—48no—
377Dic22—42no—
378Dic22—42no—
379Dic22—84no—
380C8×C11—22no—
381C8×C11—22no—
382C11⋊C8—22no—
383C11⋊C8—22no—
384C22×#41—111no—
385C23×Q8—111no—
386C22×Q16—111no—
387C22×Q16—111no—
388C22×Q16C2×D1111yescharacteristic
389C22×SD16—111no—
390C22×SD16—111no—
391C22×SD16C2×D1111yescharacteristic
392C22×SD16C2×D1111yescharacteristic
393C22×D8C2×D1111yescharacteristic
394#542—118no—
395#542—224no—
396#536—118no—
397#536—224no—
398C2×C4⋊Q8—111no—
399C2×C4⋊Q8—111no—
400C2×C4⋊Q8—111no—
401C2×#126—221no—
402C2×#124—111no—
403C2×#124—221no—
404C2×#124C2×D1111yescharacteristic
405C2×#124C2×D1111yescharacteristic
406C2×#123—221no—
407C2×#123—221no—
408C2×#123—221no—
409C2×C22⋊Q8—111no—
410C2×C22⋊Q8—221no—
411C2×C22⋊Q8—221no—
412C2×C22⋊Q8—221no—
413C2×#121—111no—
414C2×C4×Q8—111no—
415C2×C4×D4—111no—
416C2×#117—111no—
417#497—118no—
418#495C2×D1118yescomplemented
419#489—118no—
420#487—118no—
421#464—118no—
422#463—118no—
423#462—118no—
424#461—118no—
425#452—118no—
426#451—118no—
427#449—118no—
428#448—118no—
429#433—118no—
430C2×C4⋊C8—111no—
431C2×C4⋊C8—111no—
432C2×#103—111no—
433C2×#103—111no—
434C2×#103—111no—
435C2×#103—111no—
436C2×#103—111no—
437C2×#103—111no—
438C2×#102—111no—
439C2×#102—111no—
440C2×C22⋊C8—111no—
441C2×C22⋊C8—111no—
442C2×#97—111no—
443C2×C4×C8C2×D1111yescharacteristic
444C22×C11—42no—
445C22×C11—42no—
446C22×C11—42no—
447C22×C11—42no—
448C22×C11—42no—
449C22×C11—42no—
450C22×C11—84no—
451C22×C11—84no—
452C22×C11#53512yes—
453C22×C11#57712yes—
454C22×C11#57812yes—
455C22×C11C23×D411yescharacteristic
456C2×D11—22no—
457C2×D11—22no—
458C2×D11—22no—
459C2×D11—44no—
460C4×C11—22no—
461C4×C11—22no—
462C4×C11—42no—
463C4×C11—42no—
464C4×C11#53512yes—
465C4×C11C2×H(5,𝔽2)11yescharacteristic
466C4×C11C2×H(5,𝔽2)11yescharacteristic
467Dic11—22no—
468Dic11—22no—
469Dic11—22no—
470Dic11—42no—
471Dic11—42no—
472Dic11—42no—
473Dic11—42no—
474C2×#41—114no—
475C2×#41—222no—
476C2×#41—442no—
477C2×#41—442no—
478C22×Q8—114no—
479C22×Q8—111no—
480C22×Q8—111no—
481C22×Q8—221no—
482C22×Q8—222no—
483C22×Q8—221no—
484C22×Q8—442no—
485C22×Q8—442no—
486C22×Q8C22×D1111yescharacteristic
487C22×Q8C22×D1111yescharacteristic
488C22×D4—221no—
489C22×D4—221no—
490C22×D4C22×D1111yescharacteristic
491C22×D4C22×D1111yescharacteristic
492C23×C4—111no—
493C23×C4—221no—
494C23×C4—221no—
495C23×C4—221no—
496C2×Q16—42no—
497C2×Q16—114no—
498C2×Q16—114no—
499C2×Q16—442no—
500C2×Q16—442no—
501C2×Q16C22×D1114yes—
502C2×SD16—42no—
503C2×SD16—42no—
504C2×SD16—114no—
505C2×SD16—114no—
506C2×SD16—442no—
507C2×SD16—442no—
508C2×SD16C22×D1114yes—
509C2×SD16C22×D1114yes—
510C2×D8—42no—
511C2×D8C22×D1114yes—
512C22×C8—111no—
513C22×C8—111no—
514C22×C8C22×D1111yescharacteristic
515C22×C8C22×D1111yescharacteristic
516C4⋊Q8—114no—
517C4⋊Q8—114no—
518C4⋊Q8—114no—
519C4⋊Q8—222no—
520C4⋊Q8—222no—
521C4⋊Q8—222no—
522#126—228no—
523#124—22no—
524#124—22no—
525#124—114no—
526#124—222no—
527#124—228no—
528#124C22×D1114yes—
529#124C22×D1114yes—
530#123—228no—
531#123—228no—
532#123—228no—
533C22⋊Q8—114no—
534C22⋊Q8—228no—
535C22⋊Q8—228no—
536C22⋊Q8—228no—
537C22⋊Q8—222no—
538#121—114no—
539#121—222no—
540C4×Q8—114no—
541C4×Q8—222no—
542C4×D4—114no—
543C4×D4—222no—
544#117—114no—
545#117—114no—
546C2×C4⋊C4—111no—
547C2×C4⋊C4—111no—
548C2×C4⋊C4—111no—
549C2×C4⋊C4—111no—
550C2×C4⋊C4—221no—
551C2×C4⋊C4—221no—
552C2×C4⋊C4—221no—
553C2×C4⋊C4—221no—
554C2×C4⋊C4—221no—
555C2×C4⋊C4—221no—
556C2×C4⋊C4—221no—
557C2×C22⋊C4—21no—
558C2×C22⋊C4—21no—
559C2×C22⋊C4—21no—
560C2×C22⋊C4—21no—
561C2×C22⋊C4—111no—
562C2×C22⋊C4—111no—
563C2×C22⋊C4—221no—
564C2×C22⋊C4—221no—
565C2×C22⋊C4—221no—
566C2×C22⋊C4—221no—
567C2×C22⋊C4—221no—
568C2×C42—111no—
569C2×C42—221no—
570C2×C42C22×D1111yescharacteristic
571C4⋊C8—114no—
572C4⋊C8—114no—
573#103—114no—
574#103—114no—
575#103—114no—
576#103—114no—
577#103—114no—
578#103—114no—
579#102—114no—
580#102—114no—
581C22⋊C8—114no—
582C22⋊C8—114no—
583#97—114no—
584C4×C8C22×D1114yes—
585C2×C11—82no—
586C2×C11—82no—
587C2×C11#322514yescomplemented
588C2×C11C2×#53511yescharacteristic
589C2×C11C2×#57711yescharacteristic
590C2×C11C2×#57811yescharacteristic
591D11—42no—
592C24—21no—
593C24—21no—
594C24—111no—
595#41—444no—
596#41—444no—
597#41—448no—
598C2×Q8—21no—
599C2×Q8—21no—
600C2×Q8—22no—
601C2×Q8—22no—
602C2×Q8—22no—
603C2×Q8—22no—
604C2×Q8—112no—
605C2×Q8—112no—
606C2×Q8—224no—
607C2×Q8—221no—
608C2×Q8—221no—
609C2×Q8—224no—
610C2×Q8—222no—
611C2×Q8—222no—
612C2×Q8—222no—
613C2×Q8—222no—
614C2×Q8—444no—
615C2×Q8—444no—
616C2×Q8—444no—
617C2×Q8—448no—
618C2×Q8—882no—
619C2×Q8C23×D1112yes—
620C2×Q8C23×D1112yes—
621C2×D4—21no—
622C2×D4—21no—
623C2×D4—22no—
624C2×D4—22no—
625C2×D4—22no—
626C2×D4—22no—
627C2×D4—224no—
628C2×D4—224no—
629C2×D4—444no—
630C2×D4—882no—
631C2×D4C23×D1112yes—
632C2×D4C23×D1112yes—
633C22×C4—21no—
634C22×C4—21no—
635C22×C4—111no—
636C22×C4—111no—
637C22×C4—111no—
638C22×C4—112no—
639C22×C4—112no—
640C22×C4—224no—
641C22×C4—224no—
642C22×C4—224no—
643C22×C4—222no—
644C22×C4—222no—
645C22×C4—221no—
646C22×C4—221no—
647C22×C4—221no—
648C22×C4—221no—
649C22×C4—444no—
650C22×C4—444no—
651C22×C4—882no—
652C22×C4D4×D1111yescharacteristic
653C22×C4D4×D1111yescharacteristic
654C22×C4C23×D1111yescharacteristic
655Q16—44no—
656Q16—444no—
657Q16—444no—
658SD16—44no—
659SD16—44no—
660SD16—444no—
661SD16—444no—
662D8—44no—
663C2×C8—22no—
664C2×C8—22no—
665C2×C8—112no—
666C2×C8—112no—
667C2×C8—222no—
668C2×C8—222no—
669C2×C8C23×D1112yes—
670C2×C8C23×D1112yes—
671C4⋊C4—114no—
672C4⋊C4—114no—
673C4⋊C4—112no—
674C4⋊C4—112no—
675C4⋊C4—224no—
676C4⋊C4—224no—
677C4⋊C4—224no—
678C4⋊C4—224no—
679C4⋊C4—221no—
680C4⋊C4—221no—
681C4⋊C4—224no—
682C4⋊C4—224no—
683C4⋊C4—224no—
684C22⋊C4—24no—
685C22⋊C4—24no—
686C22⋊C4—24no—
687C22⋊C4—24no—
688C22⋊C4—114no—
689C22⋊C4—114no—
690C22⋊C4—224no—
691C22⋊C4—224no—
692C22⋊C4—224no—
693C22⋊C4—224no—
694C22⋊C4—224no—
695C42—112no—
696C42—112no—
697C42—224no—
698C42D4×D1112yes—
699C42C23×D1112yes—
700C11C2×#322511yescharacteristic, complemented, Sylow
701C23—22no—
702C23—22no—
703C23—42no—
704C23—42no—
705C23—42no—
706C23—42no—
707C23—42no—
708C23—42no—
709C23—112no—
710C23—222no—
711C23—222no—
712C23—222no—
713C23C2×D4×D1111yescharacteristic
714Q8—22no—
715Q8—22no—
716Q8—22no—
717Q8—22no—
718Q8—42no—
719Q8—42no—
720Q8—222no—
721Q8—222no—
722Q8—222no—
723Q8—222no—
724Q8—448no—
725Q8—442no—
726Q8—442no—
727Q8—884no—
728D4—22no—
729D4—22no—
730D4—22no—
731D4—22no—
732D4—42no—
733D4—42no—
734D4—448no—
735D4—884no—
736C2×C4—22no—
737C2×C4—22no—
738C2×C4—22no—
739C2×C4—22no—
740C2×C4—42no—
741C2×C4—42no—
742C2×C4—112no—
743C2×C4—112no—
744C2×C4—112no—
745C2×C4—222no—
746C2×C4—222no—
747C2×C4—222no—
748C2×C4—224no—
749C2×C4—222no—
750C2×C4—222no—
751C2×C4—222no—
752C2×C4—222no—
753C2×C4—222no—
754C2×C4—222no—
755C2×C4—448no—
756C2×C4—448no—
757C2×C4—442no—
758C2×C4—442no—
759C2×C4—442no—
760C2×C4—442no—
761C2×C4—884no—
762C2×C4C2×D4×D1112yes—
763C2×C4C2×D4×D1112yes—
764C2×C4C2×D4×D1111yescharacteristic
765C2×C4#6703712yes—
766C2×C4#6703712yes—
767C2×C4C24×D1111yescharacteristic
768C8—22no—
769C8—22no—
770C8—222no—
771C8—222no—
772C22—42no—
773C22—42no—
774C22—42no—
775C22—42no—
776C22—42no—
777C22—42no—
778C22—84no—
779C22—84no—
780C22—222no—
781C22—222no—
782C22—222no—
783C22—444no—
784C22#1062324612yes—
785C22#1062330112yes—
786C22#1062330212yes—
787C22C22×D4×D1111yescharacteristic
788C4—22no—
789C4—22no—
790C4—42no—
791C4—42no—
792C4—222no—
793C4—222no—
794C4—222no—
795C4—442no—
796C4—442no—
797C4—442no—
798C4—442no—
799C4#1062324612yes—
800C4C2×#6703711yescharacteristic
801C4C2×#6703711yescharacteristic
802C2—82no—
803C2—82no—
804C2—442no—
805C2#1307971814yesdirect product factor
806C2C2×#1062324611yescharacteristic
807C2C2×#1062330111yescharacteristic
808C2C2×#1062330211yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#495C2
socleC23×C11C22×D4
prime radicalC2×#10622771C2
hypercenterC2×#495D11
hypocenterC11C2×#3225
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#495

Complements

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

NH ≅ G/Ntype
1. C2×#10623213C2semidirect
2. C2×#10623206C2semidirect
3. #13079718C2direct (N × H)
4. C2×#10622673C2semidirect
5. C2×#10622668C2semidirect
6. C2×#10622294C2semidirect
7. C2×#10622779C2semidirect
8. C2×#10622795C2semidirect
9. C2×#10622766C2semidirect
10. C2×#10622775C2semidirect
11. C2×#10622786C2semidirect
13. C2×#10622799C2semidirect
14. C2×#10622783C2semidirect
15. C2×#10622303C2semidirect
16. C2×C11×#495C2semidirect
36. #10623213C22semidirect
38. #10623206C22semidirect
50. C11×#495C22semidirect
56. #10622799C22semidirect
57. #10622795C22semidirect
58. #10622786C22semidirect
59. #10622783C22semidirect
60. #10622779C22semidirect
61. #10622775C22semidirect
63. #10622766C22semidirect
72. #10622673C22semidirect
73. #10622668C22semidirect
75. #10622303C22semidirect
76. #10622294C22semidirect
301. C2×#495D11semidirect
418. #495C2×D11semidirect
587. C2×C11#3225semidirect
700. C11C2×#3225semidirect
805. C2#13079718direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106232132
C2×#106232062
#130797182
C2×#106226732
C2×#106226682
C2×#106222942
C2×#106227792
C2×#106227952
C2×#106227662
C2×#106227752
C2×#106227862
C2×#106227712
C2×#106227992
C2×#106227832
C2×#106223032
C2×C11×#4952
C2×#322511