Finite Group Databasebeta

← C2×#13079509 #15624471

Subgroups — C2×#13079509 #15624471

Order 2816.

2122 conjugacy classes of subgroups.

The subgroup lattice has 816 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623347C211yesmaximal, characteristic
2C2×#10623159C211yesmaximal, characteristic
3#13079509C2116yesmaximal, direct product factor
4C2×#10622336C211yesmaximal, characteristic, complemented
5C2×#10622427C211yesmaximal, characteristic, complemented
6C2×#10622428C211yesmaximal, characteristic, complemented
7C2×#10622658C211yesmaximal, characteristic, complemented
8C2×#10622429C211yesmaximal, characteristic, complemented
9C2×#10622802C211yesmaximal, characteristic, complemented
10C2×#10622426C211yesmaximal, characteristic, complemented
11C2×#10622801C211yesmaximal, characteristic, complemented
12C2×#10622841C211yesmaximal, characteristic, complemented
13C2×#10622799C211yesmaximal, characteristic, complemented
14C2×#10622799C211yesmaximal, characteristic, complemented
15C2×#10622340C211yesmaximal, characteristic
16C2×C11×#451C211yesmaximal, characteristic, complemented
17C23×Q8×C11C2211yescharacteristic
18C22×Q8×D11C2211yescharacteristic
19C22×#4339C2211yescharacteristic
20C22×C11×Q16C2211yescharacteristic
21C22×C11×Q16C2211yescharacteristic
22C2×C11×C22⋊Q8C2211yescharacteristic
23#10623347—24no—
24#10623347C2218yes—
25C2×#67000—21no—
26C2×#66999C2211yescharacteristic
27C2×#66999C2211yescharacteristic
28C2×#66999C2211yescharacteristic
29C2×#66999C2211yescharacteristic
30C2×#66999C2211yescharacteristic
31C2×#66997—21no—
32C22×#4326C2211yescharacteristic
33C22×#4326C2211yescharacteristic
34C2×#66982—21no—
35C2×#66982—21no—
36C2×#66979C2211yescharacteristic
37C2×#66977C2211yescharacteristic
38C22×#4313C2211yescharacteristic
39C22×C8×D11C2211yescharacteristic
40#10623159—24no—
41#10623159C2218yes—
42C2×#66950C2211yescharacteristic
43C2×#66947—21no—
44C2×#66945C2211yescharacteristic
45C2×#66941—21no—
46C2×#66938—21no—
47C2×#66936—21no—
48C11×#451C2218yescomplemented
49C2×C11×#103C2211yescharacteristic
50C2×C11×#103C2211yescharacteristic
51C2×C11×C22⋊C8C2211yescharacteristic
52#10622841C2218yescomplemented
53C2×#66899C2211yescharacteristic
54C2×#66899C2211yescharacteristic
55C2×#66899C2211yescharacteristic
56C2×#66899C2211yescharacteristic
57C2×C22⋊(C11⋊C8)C2211yescharacteristic
58#10622802C2218yescomplemented
59#10622801C2218yescomplemented
60#10622799C2218yescomplemented
61#10622799C2218yescomplemented
62C2×(C2×D11)⋊C8C2211yescharacteristic
63C2×(C2×D11)⋊C8C2211yescharacteristic
64C2×#66882C2211yescharacteristic
65C2×#66881C2211yescharacteristic
66C2×#66880C2211yescharacteristic
67C2×#66880C2211yescharacteristic
68#10622658C2218yescomplemented
69C2×#66872C2211yescharacteristic
70C2×#66871C2211yescharacteristic
71#10622429C2218yescomplemented
72#10622428C2218yescomplemented
73#10622427C2218yescomplemented
74#10622426C2218yescomplemented
75#10622340C2218yes—
76#10622336C2218yescomplemented
77C22×Q8×C11—21no—
78C22×Q8×C11—22no—
79C22×Q8×C11—42no—
80C22×Q8×C11—42no—
81C22×Q8×C11C2311yescharacteristic
82C22×Q8×C11C2311yescharacteristic
83C22×Q8×C11C2311yescharacteristic
84C22×Q8×C11C2314yes—
85C23×C4×C11—21no—
86C23×C4×C11C2311yescharacteristic
87C22×C22⋊D11D411yescharacteristic
88C22×C22⋊D11D411yescharacteristic
89C2×Q8×D11—22no—
90C2×Q8×D11—42no—
91C2×Q8×D11—42no—
92C2×Q8×D11C2314yes—
93C2×#4339—42no—
94C2×#4339—42no—
95C2×#4339D414yes—
96C2×#4339C2314yes—
97C22×D44D411yescharacteristic
98C22×C4×D11—21no—
99C22×C4×D11C2311yescharacteristic
100C22×C4×D11C2311yescharacteristic
101C22×Dic22—21no—
102C22×Dic22D411yescharacteristic
103C22×Dic22C2311yescharacteristic
104C2×C11×Q16—42no—
105C2×C11×Q16—42no—
106C2×C11×Q16C2314yes—
107C2×C11×Q16C2314yes—
108C22×C8×C11C2311yescharacteristic
109C22×C8×C11C2311yescharacteristic
110C11×C22⋊Q8—22no—
111C11×C22⋊Q8C2314yes—
112C2×C11×C4⋊C4—21no—
113C2×C11×C4⋊C4C2311yescharacteristic
114C2×C11×C22⋊C4—21no—
115C2×C22⋊Dic11—21no—
116C2×C22⋊Dic11—21no—
117#67000—28no—
118#66999—22no—
119#66999—22no—
120#66999—22no—
121#66999—22no—
122#66999—22no—
123#66999C2314yes—
124#66999C2314yes—
125#66999C2314yes—
126#66999C2314yes—
127#66999C2314yes—
128#66997—28no—
129C2×#4326—42no—
130C2×#4326—42no—
131C2×#4326C2314yes—
132C2×#4326C2314yes—
133#66982—28no—
134#66982—28no—
135C2×(C2×D11)⋊C4—21no—
136C2×(C2×D11)⋊C4—21no—
137C2×(C2×D11)⋊C4—21no—
138C2×(C2×D11)⋊C4—21no—
139C2×(C2×D11)⋊C4—21no—
140C2×(C2×D11)⋊C4—21no—
141C2×(C2×D11)⋊C4—21no—
142#66979—22no—
143#66979C2314yes—
144C2×C4⋊Dic11—21no—
145C2×C4⋊Dic11C2311yescharacteristic
146C2×C4⋊Dic11C2311yescharacteristic
147C2×C4⋊Dic11C2311yescharacteristic
148#66977—22no—
149#66977C2314yes—
150C2×Dic11⋊C4—21no—
151C2×Dic11⋊C4—21no—
152C2×Dic11⋊C4—21no—
153C2×Dic11⋊C4—21no—
154C2×Dic11⋊C4—21no—
155C2×Dic11⋊C4—21no—
156C2×C4×Dic11—21no—
157C2×C4×Dic11—21no—
158C22×C11⋊C8C2311yescharacteristic
159C22×C11⋊C8C2311yescharacteristic
160C2×#4313—42no—
161C2×#4313C2314yes—
162C2×C8×D11—42no—
163C2×C8×D11C2314yes—
164#66950—22no—
165#66950C2314yes—
166#66947—28no—
167#66945—22no—
168#66945C2314yes—
169#66941—28no—
170#66938—28no—
171#66936—28no—
172C11×#103C2314yes—
173C11×#103C2314yes—
174C11×C22⋊C8C2314yes—
175#66899C2314yes—
176#66899C2314yes—
177#66899C2314yes—
178#66899C2314yes—
179C22⋊(C11⋊C8)C2314yes—
180(C2×D11)⋊C8C2314yes—
181(C2×D11)⋊C8C2314yes—
182#66882C2314yes—
183#66881C2314yes—
184#66880C2314yes—
185#66880C2314yes—
186#66872C2314yes—
187#66871C2314yes—
188C2×#3202—111nomaximal, Sylow
189C24×C11C2×D411yescharacteristic
190C23×D11C2×D411yescharacteristic
191C23×D11C2×D411yescharacteristic
192C2×Q8×C11—24no—
193C2×Q8×C11—21no—
194C2×Q8×C11—21no—
195C2×Q8×C11—21no—
196C2×Q8×C11—22no—
197C2×Q8×C11—22no—
198C2×Q8×C11—22no—
199C2×Q8×C11—22no—
200C2×Q8×C11—22no—
201C2×Q8×C11—22no—
202C2×Q8×C11—44no—
203C2×Q8×C11—44no—
204C2×Q8×C11—44no—
205C2×Q8×C11—48no—
206C2×Q8×C11C2412yes—
207C2×Q8×C11C2412yes—
208C2×Q8×C11C2412yes—
209C22×C4×C11—22no—
210C22×C4×C11—22no—
211C22×C4×C11—21no—
212C22×C4×C11—21no—
213C22×C4×C11—21no—
214C22×C4×C11—21no—
215C22×C4×C11—24no—
216C22×C4×C11—44no—
217C22×C4×C11C2×D411yescharacteristic
218C22×C4×C11C2×D412yes—
219C22×C4×C11C2412yes—
220C22×C4×C11C2411yescharacteristic
221C2×C22⋊D11—42no—
222C2×C22⋊D11—42no—
223C2×C22⋊D11C2×D414yes—
224C2×C22⋊D11C2×D414yes—
225C22×Dic11—21no—
226C22×Dic11—21no—
227C22×Dic11—21no—
228C22×Dic11—21no—
229C22×Dic11C2×D411yescharacteristic
230C22×Dic11C2×D411yescharacteristic
231Q8×D11—44no—
232Q8×D11—44no—
233Q8×D11—48no—
234#4339—48no—
235#4339—44no—
236#4339—44no—
237C2×D44—42no—
238C2×D44C2×D414yes—
239C2×C4×D11—24no—
240C2×C4×D11—22no—
241C2×C4×D11—22no—
242C2×C4×D11—22no—
243C2×C4×D11—22no—
244C2×C4×D11—44no—
245C2×C4×D11C2×D412yes—
246C2×C4×D11C2×D412yes—
247C2×C4×D11C2412yes—
248C2×C4×D11C2412yes—
249C2×Dic22—24no—
250C2×Dic22—21no—
251C2×Dic22—22no—
252C2×Dic22—22no—
253C2×Dic22—42no—
254C2×Dic22—44no—
255C2×Dic22C2×D414yes—
256C2×Dic22C2412yes—
257C11×Q16—44no—
258C11×Q16—44no—
259C2×C8×C11—22no—
260C2×C8×C11—22no—
261C2×C8×C11C2412yes—
262C2×C8×C11C2412yes—
263C11×C4⋊C4—24no—
264C11×C4⋊C4—21no—
265C11×C4⋊C4C2412yes—
266C11×C22⋊C4—24no—
267C22⋊Dic11—24no—
268C22⋊Dic11—24no—
269#4326—44no—
270#4326—44no—
271(C2×D11)⋊C4—24no—
272(C2×D11)⋊C4—24no—
273(C2×D11)⋊C4—24no—
274(C2×D11)⋊C4—24no—
275(C2×D11)⋊C4—24no—
276(C2×D11)⋊C4—24no—
277(C2×D11)⋊C4—24no—
278C4⋊Dic11—24no—
279C4⋊Dic11—21no—
280C4⋊Dic11—21no—
281C4⋊Dic11—21no—
282C4⋊Dic11C2412yes—
283C4⋊Dic11C2412yes—
284C4⋊Dic11C2412yes—
285Dic11⋊C4—24no—
286Dic11⋊C4—24no—
287Dic11⋊C4—24no—
288Dic11⋊C4—24no—
289Dic11⋊C4—24no—
290Dic11⋊C4—24no—
291C4×Dic11—24no—
292C4×Dic11—24no—
293C2×C11⋊C8—22no—
294C2×C11⋊C8—22no—
295C2×C11⋊C8C2412yes—
296C2×C11⋊C8C2412yes—
297#4313—44no—
298C8×D11—44no—
299C2×#536—111no—
300C2×#536—111no—
301#3202—1116no—
302C2×#485—111no—
303C2×#485—111no—
304C2×#485—111no—
305C2×#485—111no—
306C2×#470—111no—
307C2×#470—111no—
308C2×#467—111no—
309C2×#467—111no—
310C2×#451—111no—
311C2×#451—111no—
312C2×#451—111no—
313C2×#451D1111yescharacteristic, complemented
314C2×#408—111no—
315C23×C11—22no—
316C23×C11—22no—
317C23×C11—22no—
318C23×C11C22×D412yes—
319C23×C11C22×D411yescharacteristic
320C22×D11—22no—
321C22×D11—22no—
322C22×D11—22no—
323C22×D11—22no—
324C22×D11—22no—
325C22×D11—22no—
326C22×D11C22×D412yes—
327C22×D11C22×D412yes—
328Q8×C11—22no—
329Q8×C11—22no—
330Q8×C11—22no—
331Q8×C11—22no—
332Q8×C11—22no—
333Q8×C11—22no—
334Q8×C11—48no—
335Q8×C11—42no—
336Q8×C11—42no—
337Q8×C11—42no—
338C2×C4×C11—22no—
339C2×C4×C11—24no—
340C2×C4×C11—22no—
341C2×C4×C11—22no—
342C2×C4×C11—22no—
343C2×C4×C11—22no—
344C2×C4×C11—22no—
345C2×C4×C11—22no—
346C2×C4×C11—48no—
347C2×C4×C11—42no—
348C2×C4×C11—42no—
349C2×C4×C11—42no—
350C2×C4×C11—42no—
351C2×C4×C11C22×D412yes—
352C2×C4×C11C22×D411yescharacteristic
353C2×C4×C11H(5,𝔽2)12yes—
354C2×C4×C11H(5,𝔽2)12yes—
355C2×C4×C11C2511yescharacteristic
356C22⋊D11—44no—
357C22⋊D11—44no—
358C2×Dic11—22no—
359C2×Dic11—22no—
360C2×Dic11—22no—
361C2×Dic11—22no—
362C2×Dic11—22no—
363C2×Dic11—22no—
364C2×Dic11—42no—
365C2×Dic11—42no—
366C2×Dic11—42no—
367C2×Dic11—42no—
368C2×Dic11C22×D412yes—
369C2×Dic11C22×D412yes—
370D44—44no—
371C4×D11—24no—
372C4×D11—24no—
373C4×D11—22no—
374C4×D11—22no—
375C4×D11—22no—
376C4×D11—22no—
377C4×D11—48no—
378Dic22—22no—
379Dic22—22no—
380Dic22—44no—
381Dic22—48no—
382Dic22—42no—
383C8×C11—22no—
384C8×C11—22no—
385C11⋊C8—22no—
386C11⋊C8—22no—
387C22×#41—111no—
388C23×Q8—111no—
389C23×Q8C2×D1111yescharacteristic
390C22×Q16—111no—
391C22×Q16—111no—
392C22×Q16C2×D1111yescharacteristic
393C22×Q16C2×D1111yescharacteristic
394C22×M16—111no—
395C23×C8—111no—
396#536—118no—
397#536—118no—
398#536—224no—
399#536—224no—
400C2×C4⋊Q8—221no—
401C2×C4⋊Q8—221no—
402C2×#124—221no—
403C2×#124—221no—
404C2×#123—221no—
405C2×#123—221no—
406C2×#123—221no—
407C2×#123—221no—
408C2×C22⋊Q8—111no—
409C2×C22⋊Q8—111no—
410C2×C22⋊Q8—111no—
411C2×C22⋊Q8—111no—
412C2×C22⋊Q8—111no—
413C2×C22⋊Q8—111no—
414C2×C22⋊Q8—111no—
415C2×C22⋊Q8C2×D1111yescharacteristic
416C2×#117—111no—
417C2×#117—111no—
418#485—118no—
419#485—118no—
420#485—118no—
421#485—118no—
422#470—118no—
423#470—118no—
424#467—118no—
425#467—118no—
426#451—118no—
427#451—118no—
428#451—118no—
429#451C2×D1118yescomplemented
430C2×#107—111no—
431C2×#107—111no—
432C2×#106—111no—
433C2×#106—111no—
434C2×#103—111no—
435C2×#103—111no—
436C2×#103—111no—
437C2×#103—111no—
438C2×#103—111no—
439C2×#103—111no—
440C2×#103C2×D1111yescharacteristic
441C2×#103C2×D1111yescharacteristic
442#408—118no—
443C2×C22⋊C8—111no—
444C2×C22⋊C8—111no—
445C2×C22⋊C8—111no—
446C2×C22⋊C8C2×D1111yescharacteristic
447C22×C11—22no—
448C22×C11—22no—
449C22×C11—22no—
450C22×C11—44no—
451C22×C11#53412yes—
452C22×C11#57812yes—
453C22×C11#57812yes—
454C22×C11C23×D411yescharacteristic
455C2×D11—22no—
456C2×D11—22no—
457C2×D11—22no—
458C2×D11—22no—
459C2×D11—22no—
460C2×D11—22no—
461C2×D11—44no—
462C2×D11—44no—
463C4×C11—22no—
464C4×C11—42no—
465C4×C11—42no—
466C4×C11—42no—
467C4×C11—42no—
468C4×C11#53412yes—
469C4×C11C2×H(5,𝔽2)11yescharacteristic
470C4×C11C2×H(5,𝔽2)11yescharacteristic
471Dic11—22no—
472Dic11—22no—
473Dic11—42no—
474Dic11—42no—
475Dic11—42no—
476Dic11—42no—
477C2×#41—114no—
478C2×#41—114no—
479C2×#41—442no—
480C2×#41—442no—
481C22×Q8—21no—
482C22×Q8—22no—
483C22×Q8—42no—
484C22×Q8—42no—
485C22×Q8—111no—
486C22×Q8—114no—
487C22×Q8—111no—
488C22×Q8—221no—
489C22×Q8—222no—
490C22×Q8—442no—
491C22×Q8—442no—
492C22×Q8C22×D1111yescharacteristic
493C22×Q8C22×D1111yescharacteristic
494C22×Q8C22×D1111yescharacteristic
495C22×Q8C22×D1114yes—
496C22×D4—111no—
497C22×D4—111no—
498C22×D4—111no—
499C23×C4—21no—
500C23×C4—111no—
501C23×C4—111no—
502C23×C4—221no—
503C23×C4C22×D1111yescharacteristic
504C2×Q16—42no—
505C2×Q16—42no—
506C2×Q16—114no—
507C2×Q16—114no—
508C2×Q16—442no—
509C2×Q16—442no—
510C2×Q16C22×D1114yes—
511C2×Q16C22×D1114yes—
512C2×M16—114no—
513C2×M16—442no—
514C22×C8—111no—
515C22×C8—111no—
516C22×C8—114no—
517C22×C8—442no—
518C22×C8C22×D1111yescharacteristic
519C22×C8C22×D1111yescharacteristic
520C4⋊Q8—228no—
521C4⋊Q8—228no—
522#124—228no—
523#124—228no—
524#123—228no—
525#123—228no—
526#123—228no—
527#123—228no—
528C22⋊Q8—22no—
529C22⋊Q8—114no—
530C22⋊Q8—114no—
531C22⋊Q8—114no—
532C22⋊Q8—114no—
533C22⋊Q8—114no—
534C22⋊Q8—114no—
535C22⋊Q8—114no—
536C22⋊Q8—222no—
537C22⋊Q8—222no—
538C22⋊Q8—222no—
539C22⋊Q8—222no—
540C22⋊Q8—222no—
541C22⋊Q8—222no—
542C22⋊Q8—222no—
543C22⋊Q8C22×D1114yes—
544#117—114no—
545#117—114no—
546#117—222no—
547#117—222no—
548C2×C4⋊C4—21no—
549C2×C4⋊C4—111no—
550C2×C4⋊C4—111no—
551C2×C4⋊C4—111no—
552C2×C4⋊C4—221no—
553C2×C4⋊C4—221no—
554C2×C4⋊C4—221no—
555C2×C4⋊C4—221no—
556C2×C4⋊C4—221no—
557C2×C4⋊C4—221no—
558C2×C4⋊C4—221no—
559C2×C4⋊C4C22×D1111yescharacteristic
560C2×C22⋊C4—21no—
561C2×C22⋊C4—221no—
562C2×C22⋊C4—221no—
563C2×C22⋊C4—221no—
564C2×C22⋊C4—221no—
565C2×C22⋊C4—221no—
566C2×C22⋊C4—221no—
567C2×C22⋊C4—221no—
568C2×C22⋊C4—221no—
569C2×C22⋊C4—221no—
570C2×C42—221no—
571C2×C42—221no—
572#107—114no—
573#107—114no—
574#106—114no—
575#106—114no—
576#103—114no—
577#103—114no—
578#103—114no—
579#103—114no—
580#103—114no—
581#103—114no—
582#103C22×D1114yes—
583#103C22×D1114yes—
584C22⋊C8—114no—
585C22⋊C8—114no—
586C22⋊C8—114no—
587C22⋊C8C22×D1114yes—
588C2×C11—42no—
589C2×C11#320214yescomplemented
590C2×C11C2×#53411yescharacteristic
591C2×C11C2×#57811yescharacteristic
592C2×C11C2×#57811yescharacteristic
593D11—42no—
594D11—42no—
595C24—111no—
596C24—111no—
597C24D4×D1111yescharacteristic
598#41—448no—
599#41—444no—
600#41—444no—
601C2×Q8—21no—
602C2×Q8—21no—
603C2×Q8—21no—
604C2×Q8—24no—
605C2×Q8—22no—
606C2×Q8—22no—
607C2×Q8—22no—
608C2×Q8—22no—
609C2×Q8—22no—
610C2×Q8—22no—
611C2×Q8—44no—
612C2×Q8—44no—
613C2×Q8—44no—
614C2×Q8—48no—
615C2×Q8—114no—
616C2×Q8—112no—
617C2×Q8—224no—
618C2×Q8—221no—
619C2×Q8—222no—
620C2×Q8—222no—
621C2×Q8—442no—
622C2×Q8—444no—
623C2×Q8—444no—
624C2×Q8—444no—
625C2×Q8—448no—
626C2×Q8C23×D1112yes—
627C2×Q8C23×D1112yes—
628C2×Q8C23×D1112yes—
629C2×D4—114no—
630C2×D4—114no—
631C2×D4—114no—
632C2×D4—442no—
633C2×D4—442no—
634C2×D4—442no—
635C22×C4—22no—
636C22×C4—22no—
637C22×C4—24no—
638C22×C4—21no—
639C22×C4—21no—
640C22×C4—21no—
641C22×C4—21no—
642C22×C4—44no—
643C22×C4—111no—
644C22×C4—111no—
645C22×C4—112no—
646C22×C4—112no—
647C22×C4—112no—
648C22×C4—112no—
649C22×C4—224no—
650C22×C4—222no—
651C22×C4—222no—
652C22×C4—222no—
653C22×C4—222no—
654C22×C4—221no—
655C22×C4—221no—
656C22×C4—221no—
657C22×C4—221no—
658C22×C4—444no—
659C22×C4D4×D1112yes—
660C22×C4D4×D1111yescharacteristic
661C22×C4C23×D1112yes—
662C22×C4C23×D1111yescharacteristic
663Q16—44no—
664Q16—44no—
665Q16—444no—
666Q16—444no—
667M16—444no—
668C2×C8—22no—
669C2×C8—22no—
670C2×C8—112no—
671C2×C8—112no—
672C2×C8—222no—
673C2×C8—222no—
674C2×C8—444no—
675C2×C8C23×D1112yes—
676C2×C8C23×D1112yes—
677C4⋊C4—24no—
678C4⋊C4—21no—
679C4⋊C4—112no—
680C4⋊C4—112no—
681C4⋊C4—112no—
682C4⋊C4—224no—
683C4⋊C4—224no—
684C4⋊C4—224no—
685C4⋊C4—224no—
686C4⋊C4—224no—
687C4⋊C4—224no—
688C4⋊C4—221no—
689C4⋊C4—221no—
690C4⋊C4—221no—
691C4⋊C4—224no—
692C4⋊C4C23×D1112yes—
693C22⋊C4—24no—
694C22⋊C4—224no—
695C22⋊C4—224no—
696C22⋊C4—224no—
697C22⋊C4—224no—
698C22⋊C4—224no—
699C22⋊C4—224no—
700C22⋊C4—224no—
701C22⋊C4—224no—
702C22⋊C4—224no—
703C42—224no—
704C42—224no—
705C11C2×#320211yescharacteristic, complemented, Sylow
706C23—22no—
707C23—22no—
708C23—22no—
709C23—112no—
710C23—112no—
711C23—222no—
712C23—222no—
713C23—222no—
714C23—222no—
715C23—222no—
716C23—222no—
717C23C2×D4×D1112yes—
718C23C2×D4×D1111yescharacteristic
719Q8—22no—
720Q8—22no—
721Q8—22no—
722Q8—22no—
723Q8—22no—
724Q8—22no—
725Q8—48no—
726Q8—42no—
727Q8—42no—
728Q8—42no—
729Q8—222no—
730Q8—222no—
731Q8—444no—
732Q8—448no—
733Q8—442no—
734D4—444no—
735D4—444no—
736D4—444no—
737C2×C4—22no—
738C2×C4—24no—
739C2×C4—22no—
740C2×C4—22no—
741C2×C4—22no—
742C2×C4—22no—
743C2×C4—22no—
744C2×C4—22no—
745C2×C4—48no—
746C2×C4—42no—
747C2×C4—42no—
748C2×C4—42no—
749C2×C4—42no—
750C2×C4—112no—
751C2×C4—112no—
752C2×C4—222no—
753C2×C4—222no—
754C2×C4—224no—
755C2×C4—224no—
756C2×C4—222no—
757C2×C4—222no—
758C2×C4—222no—
759C2×C4—222no—
760C2×C4—222no—
761C2×C4—222no—
762C2×C4—222no—
763C2×C4—222no—
764C2×C4—448no—
765C2×C4—442no—
766C2×C4—442no—
767C2×C4—442no—
768C2×C4—442no—
769C2×C4C2×D4×D1112yes—
770C2×C4C2×D4×D1111yescharacteristic
771C2×C4#6703712yes—
772C2×C4#6703712yes—
773C2×C4C24×D1111yescharacteristic
774C8—22no—
775C8—22no—
776C8—222no—
777C8—222no—
778C22—22no—
779C22—22no—
780C22—22no—
781C22—44no—
782C22—222no—
783C22—222no—
784C22—222no—
785C22—222no—
786C22—222no—
787C22—222no—
788C22—444no—
789C22—444no—
790C22#1062312012yes—
791C22#1062329712yes—
792C22#1062331012yes—
793C22C22×D4×D1111yescharacteristic
794C4—22no—
795C4—42no—
796C4—42no—
797C4—42no—
798C4—42no—
799C4—222no—
800C4—222no—
801C4—442no—
802C4—442no—
803C4—442no—
804C4—442no—
805C4#1062312012yes—
806C4C2×#6703711yescharacteristic
807C4C2×#6703711yescharacteristic
808C2—42no—
809C2—442no—
810C2—442no—
811C2#1307950914yesdirect product factor
812C2C2×#1062312011yescharacteristic
813C2C2×#1062329711yescharacteristic
814C2C2×#1062331011yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#451C2
socleC23×C11C22×D4
prime radicalC22×#4339C22
hypercenterC2×#451D11
hypocenterC11C2×#3202
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#451

Complements

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

NH ≅ G/Ntype
3. #13079509C2direct (N × H)
4. C2×#10622336C2semidirect
5. C2×#10622427C2semidirect
6. C2×#10622428C2semidirect
7. C2×#10622658C2semidirect
8. C2×#10622429C2semidirect
9. C2×#10622802C2semidirect
10. C2×#10622426C2semidirect
11. C2×#10622801C2semidirect
12. C2×#10622841C2semidirect
13. C2×#10622799C2semidirect
14. C2×#10622799C2semidirect
16. C2×C11×#451C2semidirect
48. C11×#451C22semidirect
52. #10622841C22semidirect
58. #10622802C22semidirect
59. #10622801C22semidirect
60. #10622799C22semidirect
61. #10622799C22semidirect
68. #10622658C22semidirect
71. #10622429C22semidirect
72. #10622428C22semidirect
73. #10622427C22semidirect
74. #10622426C22semidirect
76. #10622336C22semidirect
313. C2×#451D11semidirect
429. #451C2×D11semidirect
589. C2×C11#3202semidirect
705. C11C2×#3202semidirect
811. C2#13079509direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106233472
C2×#106231592
#130795092
C2×#106223362
C2×#106224272
C2×#106224282
C2×#106226582
C2×#106224292
C2×#106228022
C2×#106224262
C2×#106228012
C2×#106228412
C2×#106227992
C2×#106223402
C2×C11×#4512
C2×#320211