Finite Group Databasebeta

← C2×#13081166 #15632421

Subgroups — C2×#13081166 #15632421

Order 2816.

1898 conjugacy classes of subgroups.

The subgroup lattice has 736 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623115C211yesmaximal, characteristic, complemented
2C2×#10623089C211yesmaximal, characteristic
3#13081166C2116yesmaximal, direct product factor
4C2×#10622315C211yesmaximal, characteristic, complemented
5C2×#10622427C211yesmaximal, characteristic, complemented
6C2×#10622392C211yesmaximal, characteristic, complemented
7C2×#10622397C211yesmaximal, characteristic, complemented
8C2×#10622418C211yesmaximal, characteristic, complemented
9C2×#10622635C211yesmaximal, characteristic, complemented
10C2×#10622621C211yesmaximal, characteristic, complemented
11C2×#10622787C211yesmaximal, characteristic, complemented
12C2×#10622784C211yesmaximal, characteristic, complemented
13C2×#10622319C211yesmaximal, characteristic, complemented
14C2×#10622494C211yesmaximal, characteristic, complemented
15C2×#10622493C211yesmaximal, characteristic, complemented
16C2×C11×#440C211yesmaximal, characteristic, complemented
17C22×C11×SD16C2211yescharacteristic
18C2×C4×Q8×C11C2211yescharacteristic
19C2×C4×D4×C11C2211yescharacteristic
20C2×#66999C2211yescharacteristic
21C2×#66999C2211yescharacteristic
22C2×#66991C2211yescharacteristic
23C2×#66991C2211yescharacteristic
24C2×#66982—21no—
25C2×C4×C22⋊D11—21no—
26C22×#4313C2211yescharacteristic
27C22×C8×D11C2211yescharacteristic
28#10623115—24no—
29#10623115C2218yescomplemented
30#10623089—24no—
31#10623089C2218yes—
32C2×#66951—21no—
33C2×#66951—21no—
34C2×#66945C2211yescharacteristic
35C2×#66945C2211yescharacteristic
36C2×#66945C2211yescharacteristic
37C2×C4⋊C4×D11C2211yescharacteristic
38C2×#66937—21no—
39C2×#66932—21no—
40C2×#66928—21no—
41C2×C4×D44C2211yescharacteristic
42C2×#66923C2211yescharacteristic
43C2×#66922C2211yescharacteristic
44C2×C4×Dic22—21no—
45C11×#440C2218yescomplemented
46C2×C11×#107C2211yescharacteristic
47C2×C11×#103C2211yescharacteristic
48C2×C11×#102C2211yescharacteristic
49C2×C11×#97C2211yescharacteristic
50C2×#66899C2211yescharacteristic
51C2×#66899C2211yescharacteristic
52C2×#66896C2211yescharacteristic
53C2×#66896C2211yescharacteristic
54#10622787C2218yescomplemented
55#10622784C2218yescomplemented
56C2×(C2×D11)⋊C8C2211yescharacteristic
57C2×(C2×D11)⋊C8C2211yescharacteristic
58C2×#66882C2211yescharacteristic
59C2×#66882C2211yescharacteristic
60C2×#66881C2211yescharacteristic
61C2×#66881C2211yescharacteristic
62#10622635C2218yescomplemented
63#10622621C2218yescomplemented
64C2×#66872C2211yescharacteristic
65C2×#66872C2211yescharacteristic
66C2×#66872C2211yescharacteristic
67C2×#66871C2211yescharacteristic
68C2×C4⋊(C11⋊C8)C2211yescharacteristic
69#10622494C2218yescomplemented
70#10622493C2218yescomplemented
71#10622427C2218yescomplemented
72#10622418C2218yescomplemented
73#10622397C2218yescomplemented
74#10622392C2218yescomplemented
75#10622319C2218yescomplemented
76#10622315C2218yescomplemented
77C22×Q8×C11C2311yescharacteristic
78C22×D4×C11C2311yescharacteristic
79C23×C4×C11—21no—
80C22×C22⋊D11—21no—
81C22×C22⋊D11—21no—
82C22×D44D411yescharacteristic
83C22×C4×D11—21no—
84C22×C4×D11C2311yescharacteristic
85C22×C4×D11C2311yescharacteristic
86C22×Dic22—21no—
87C2×C11×SD16—24no—
88C2×C11×SD16C2314yes—
89C22×C8×C11C2311yescharacteristic
90C22×C8×C11C2311yescharacteristic
91C4×Q8×C11—22no—
92C4×Q8×C11C2314yes—
93C4×D4×C11—22no—
94C4×D4×C11C2314yes—
95C2×C11×C4⋊C4—21no—
96C2×C11×C4⋊C4C2311yescharacteristic
97C2×C11×C4⋊C4C2311yescharacteristic
98C2×C11×C22⋊C4—21no—
99C2×C42×C11—21no—
100C2×C42×C11C2311yescharacteristic
101C2×C22⋊Dic11—21no—
102C2×C22⋊Dic11—21no—
103#66999—22no—
104#66999—22no—
105#66999C2314yes—
106#66999C2314yes—
107#66991—22no—
108#66991—22no—
109#66991C2314yes—
110#66991C2314yes—
111#66982—28no—
112C4×C22⋊D11—28no—
113C2×(C2×D11)⋊C4—21no—
114C2×(C2×D11)⋊C4—21no—
115C2×(C2×D11)⋊C4—21no—
116C2×(C2×D11)⋊C4—21no—
117C2×(C2×D11)⋊C4—21no—
118C2×(C2×D11)⋊C4D411yescharacteristic
119C2×(C2×D11)⋊C4D411yescharacteristic
120C2×C4⋊Dic11—21no—
121C2×C4⋊Dic11D411yescharacteristic
122C2×C4⋊Dic11C2311yescharacteristic
123C2×C4⋊Dic11C2311yescharacteristic
124C2×C4⋊Dic11C2311yescharacteristic
125C2×C4⋊Dic11C2311yescharacteristic
126C2×Dic11⋊C4—21no—
127C2×Dic11⋊C4—21no—
128C2×Dic11⋊C4—21no—
129C2×Dic11⋊C4—21no—
130C2×Dic11⋊C4—21no—
131C2×C4×Dic11—21no—
132C2×C4×Dic11—21no—
133C2×C4×Dic11—21no—
134C22×C11⋊C8C2311yescharacteristic
135C22×C11⋊C8C2311yescharacteristic
136C2×#4313—24no—
137C2×#4313C2314yes—
138C2×C8×D11—24no—
139C2×C8×D11C2314yes—
140#66951—28no—
141#66951—28no—
142#66945—22no—
143#66945—22no—
144#66945—22no—
145#66945C2314yes—
146#66945C2314yes—
147#66945C2314yes—
148C4⋊C4×D11—22no—
149C4⋊C4×D11C2314yes—
150#66937—28no—
151#66932—28no—
152#66928—28no—
153C4×D44D414yes—
154C4×D44C2314yes—
155#66923—22no—
156#66923C2314yes—
157#66922—22no—
158#66922C2314yes—
159C4×Dic22—28no—
160C11×#107C2314yes—
161C11×#103C2314yes—
162C11×#102C2314yes—
163C11×#97C2314yes—
164#66899C2314yes—
165#66899C2314yes—
166#66896C2314yes—
167#66896C2314yes—
168(C2×D11)⋊C8C2314yes—
169(C2×D11)⋊C8C2314yes—
170#66882C2314yes—
171#66882C2314yes—
172#66881C2314yes—
173#66881C2314yes—
174#66872C2314yes—
175#66872C2314yes—
176#66872C2314yes—
177#66871C2314yes—
178C4⋊(C11⋊C8)C2314yes—
179C2×#3350—111nomaximal, Sylow
180C24×C11—21no—
181C23×D11C2×D411yescharacteristic
182C23×D11C2×D411yescharacteristic
183C2×Q8×C11—21no—
184C2×Q8×C11—22no—
185C2×Q8×C11—22no—
186C2×Q8×C11C2412yes—
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×Dic11—21no—
207C22×Dic11C2×D411yescharacteristic
208C22×Dic11C2×D411yescharacteristic
209C2×D44—42no—
210C2×D44C2×D414yes—
211C2×C4×D11—24no—
212C2×C4×D11—22no—
213C2×C4×D11—22no—
214C2×C4×D11—22no—
215C2×C4×D11—22no—
216C2×C4×D11—82no—
217C2×C4×D11C2×D412yes—
218C2×C4×D11C2×D412yes—
219C2×C4×D11C2412yes—
220C2×C4×D11C2412yes—
221C2×Dic22—24no—
222C2×Dic22—44no—
223C11×SD16—28no—
224C2×C8×C11—22no—
225C2×C8×C11#4114yes—
226C2×C8×C11C2412yes—
227C2×C8×C11C2412yes—
228C11×C4⋊C4—21no—
229C11×C4⋊C4—21no—
230C11×C4⋊C4—24no—
231C11×C4⋊C4C2412yes—
232C11×C4⋊C4C2412yes—
233C11×C22⋊C4—24no—
234C42×C11—24no—
235C42×C11C2×D412yes—
236C42×C11C2412yes—
237C22⋊Dic11—24no—
238C22⋊Dic11—24no—
239(C2×D11)⋊C4—24no—
240(C2×D11)⋊C4—24no—
241(C2×D11)⋊C4—24no—
242(C2×D11)⋊C4—24no—
243(C2×D11)⋊C4—24no—
244(C2×D11)⋊C4C2×D414yes—
245(C2×D11)⋊C4C2×D414yes—
246C4⋊Dic11—21no—
247C4⋊Dic11—21no—
248C4⋊Dic11—24no—
249C4⋊Dic11—21no—
250C4⋊Dic11—21no—
251C4⋊Dic11C2×D414yes—
252C4⋊Dic11C2412yes—
253C4⋊Dic11C2412yes—
254C4⋊Dic11C2412yes—
255C4⋊Dic11C2412yes—
256Dic11⋊C4—24no—
257Dic11⋊C4—24no—
258Dic11⋊C4—24no—
259Dic11⋊C4—24no—
260Dic11⋊C4—24no—
261C4×Dic11—24no—
262C4×Dic11—24no—
263C4×Dic11—24no—
264C2×C11⋊C8—22no—
265C2×C11⋊C8—22no—
266C2×C11⋊C8C2412yes—
267C2×C11⋊C8C2412yes—
268#4313—28no—
269C8×D11—28no—
270C2×#556—111no—
271C2×#553—111no—
272#3350—1116no—
273C2×#501—111no—
274C2×#485—111no—
275C2×#482—111no—
276C2×#482—111no—
277C2×#483—111no—
278C2×#479—111no—
279C2×#476—111no—
280C2×#468—111no—
281C2×#465—111no—
282C2×#440D1111yescharacteristic, complemented
283C2×#435—111no—
284C2×#428—111no—
285C2×#427—111no—
286C23×C11—22no—
287C23×C11—42no—
288C23×C11—42no—
289C23×C11—42no—
290C23×C11C22×D411yescharacteristic
291C22×D11—22no—
292C22×D11—22no—
293C22×D11—22no—
294C22×D11—22no—
295C22×D11—22no—
296C22×D11—22no—
297C22×D11C22×D412yes—
298C22×D11C22×D412yes—
299Q8×C11—22no—
300Q8×C11—22no—
301Q8×C11—42no—
302D4×C11—22no—
303D4×C11—22no—
304D4×C11—42no—
305C2×C4×C11—22no—
306C2×C4×C11—22no—
307C2×C4×C11—22no—
308C2×C4×C11—22no—
309C2×C4×C11—22no—
310C2×C4×C11—42no—
311C2×C4×C11—42no—
312C2×C4×C11—42no—
313C2×C4×C11—84no—
314C2×C4×C11C22×D412yes—
315C2×C4×C11C22×D412yes—
316C2×C4×C11C22×D411yescharacteristic
317C2×C4×C11C2×#4112yes—
318C2×C4×C112−1+412yes—
319C2×C4×C11C2511yescharacteristic
320C22⋊D11—48no—
321C22⋊D11—84no—
322C2×Dic11—22no—
323C2×Dic11—22no—
324C2×Dic11—22no—
325C2×Dic11—22no—
326C2×Dic11—22no—
327C2×Dic11—22no—
328C2×Dic11—42no—
329C2×Dic11—42no—
330C2×Dic11—42no—
331C2×Dic11—42no—
332C2×Dic11C22×D412yes—
333C2×Dic11C22×D412yes—
334D44—44no—
335C4×D11—24no—
336C4×D11—24no—
337C4×D11—22no—
338C4×D11—22no—
339C4×D11—22no—
340C4×D11—22no—
341C4×D11—84no—
342Dic22—48no—
343C8×C11—22no—
344C8×C11C2×#4114yes—
345C11⋊C8—22no—
346C11⋊C8—22no—
347C22×SD16C2×D1111yescharacteristic
348C22×M16—111no—
349C23×C8—111no—
350#556—118no—
351#556—224no—
352#553—118no—
353#553—224no—
354C2×C4⋊Q8—111no—
355C2×#126—221no—
356C2×#126—221no—
357C2×#126—221no—
358C2×#125—111no—
359C2×#124—221no—
360C2×#123—221no—
361C2×C22⋊Q8—111no—
362C2×C22⋊Q8—111no—
363C2×#121—111no—
364C2×#121—111no—
365C2×#121—221no—
366C2×C4×Q8—221no—
367C2×C4×Q8C2×D1111yescharacteristic
368C2×C4×D4—111no—
369C2×C4×D4—221no—
370C2×C4×D4C2×D1111yescharacteristic
371C2×#117—111no—
372C2×#117—111no—
373C2×#117—111no—
374C22×C4⋊C4—111no—
375#501—118no—
376#485—118no—
377#483—118no—
378#482—118no—
379#482—118no—
380#479—118no—
381#476—118no—
382#468—118no—
383#465—118no—
384#440C2×D1118yescomplemented
385#435—118no—
386#428—118no—
387#427—118no—
388C2×#107—111no—
389C2×#107—111no—
390C2×#107—111no—
391C2×#107C2×D1111yescharacteristic
392C2×#106—111no—
393C2×#106—111no—
394C2×#106—111no—
395C2×#106—111no—
396C2×#106—111no—
397C2×C4⋊C8—111no—
398C2×#103—111no—
399C2×#103—111no—
400C2×#103C2×D1111yescharacteristic
401C2×#102—111no—
402C2×#102—111no—
403C2×#102C2×D1111yescharacteristic
404C2×C22⋊C8—111no—
405C2×C22⋊C8—111no—
406C2×#97C2×D1111yescharacteristic
407C22×C11—42no—
408C22×C11—42no—
409C22×C11—42no—
410C22×C11—84no—
411C22×C11#54712yes—
412C22×C11#57512yes—
413C22×C11#57712yes—
414C22×C11C23×D411yescharacteristic
415C2×D11—22no—
416C2×D11—22no—
417C2×D11—22no—
418C2×D11—22no—
419C2×D11—22no—
420C2×D11—22no—
421C2×D11—44no—
422C2×D11—44no—
423C4×C11—22no—
424C4×C11—22no—
425C4×C11—42no—
426C4×C11—42no—
427C4×C11—42no—
428C4×C11#54712yes—
429C4×C11C22×#4111yescharacteristic
430C4×C11C2×2−1+411yescharacteristic
431Dic11—22no—
432Dic11—22no—
433Dic11—42no—
434Dic11—42no—
435Dic11—42no—
436Dic11—42no—
437C22×Q8—221no—
438C22×Q8C22×D1111yescharacteristic
439C22×D4—111no—
440C22×D4—221no—
441C22×D4—221no—
442C22×D4C22×D1111yescharacteristic
443C23×C4—21no—
444C23×C4—111no—
445C23×C4—111no—
446C23×C4—221no—
447C2×SD16—24no—
448C2×SD16C22×D1114yes—
449C2×M16—114no—
450C2×M16—224no—
451C22×C8—111no—
452C22×C8—111no—
453C22×C8—114no—
454C22×C8—224no—
455C22×C8C22×D1111yescharacteristic
456C22×C8C22×D1111yescharacteristic
457C4⋊Q8—114no—
458C4⋊Q8—222no—
459#126—228no—
460#126—228no—
461#126—228no—
462#125—114no—
463#125—222no—
464#124—228no—
465#123—228no—
466C22⋊Q8—114no—
467C22⋊Q8—114no—
468C22⋊Q8—222no—
469C22⋊Q8—222no—
470#121—114no—
471#121—114no—
472#121—228no—
473#121—222no—
474#121—222no—
475C4×Q8—22no—
476C4×Q8—228no—
477C4×Q8C22×D1114yes—
478C4×D4—22no—
479C4×D4—114no—
480C4×D4—114no—
481C4×D4—228no—
482C4×D4C22×D1114yes—
483#117—114no—
484#117—114no—
485#117—114no—
486#117—222no—
487#117—222no—
488#117—222no—
489C2×C4⋊C4—21no—
490C2×C4⋊C4—111no—
491C2×C4⋊C4—111no—
492C2×C4⋊C4—111no—
493C2×C4⋊C4—111no—
494C2×C4⋊C4—111no—
495C2×C4⋊C4—114no—
496C2×C4⋊C4—222no—
497C2×C4⋊C4—221no—
498C2×C4⋊C4—221no—
499C2×C4⋊C4—221no—
500C2×C4⋊C4—221no—
501C2×C4⋊C4—221no—
502C2×C4⋊C4—221no—
503C2×C4⋊C4C22×D1111yescharacteristic
504C2×C4⋊C4C22×D1111yescharacteristic
505C2×C22⋊C4—21no—
506C2×C22⋊C4—111no—
507C2×C22⋊C4—111no—
508C2×C22⋊C4—221no—
509C2×C22⋊C4—221no—
510C2×C22⋊C4—221no—
511C2×C22⋊C4—221no—
512C2×C22⋊C4—221no—
513C2×C22⋊C4—221no—
514C2×C22⋊C4—221no—
515C2×C42—21no—
516C2×C42—221no—
517C2×C42—221no—
518C2×C42—221no—
519C2×C42C22×D1111yescharacteristic
520#107—114no—
521#107—114no—
522#107—114no—
523#107C22×D1114yes—
524#106—114no—
525#106—114no—
526#106—114no—
527#106—114no—
528#106—114no—
529C4⋊C8—114no—
530#103—114no—
531#103—114no—
532#103C22×D1114yes—
533#102—114no—
534#102—114no—
535#102C22×D1114yes—
536C22⋊C8—114no—
537C22⋊C8—114no—
538#97C22×D1114yes—
539C2×C11—82no—
540C2×C11#335014yescomplemented
541C2×C11C2×#54711yescharacteristic
542C2×C11C2×#57511yescharacteristic
543C2×C11C2×#57711yescharacteristic
544D11—42no—
545D11—42no—
546C24—21no—
547C24—111no—
548C24—111no—
549C2×Q8—21no—
550C2×Q8—22no—
551C2×Q8—22no—
552C2×Q8—224no—
553C2×Q8—444no—
554C2×Q8C23×D1112yes—
555C2×D4—22no—
556C2×D4—21no—
557C2×D4—22no—
558C2×D4—114no—
559C2×D4—224no—
560C2×D4—224no—
561C2×D4—442no—
562C2×D4—444no—
563C2×D4—882no—
564C2×D4C23×D1112yes—
565C22×C4—21no—
566C22×C4—21no—
567C22×C4—21no—
568C22×C4—24no—
569C22×C4—82no—
570C22×C4—111no—
571C22×C4—111no—
572C22×C4—112no—
573C22×C4—112no—
574C22×C4—112no—
575C22×C4—112no—
576C22×C4—224no—
577C22×C4—222no—
578C22×C4—222no—
579C22×C4—222no—
580C22×C4—222no—
581C22×C4—221no—
582C22×C4—221no—
583C22×C4—221no—
584C22×C4—221no—
585C22×C4—882no—
586C22×C4D4×D1111yescharacteristic
587C22×C4D4×D1111yescharacteristic
588C22×C4C23×D1111yescharacteristic
589SD16—28no—
590M16—228no—
591C2×C8—22no—
592C2×C8—112no—
593C2×C8—112no—
594C2×C8—222no—
595C2×C8—222no—
596C2×C8—228no—
597C2×C8#433914yes—
598C2×C8C23×D1112yes—
599C2×C8C23×D1112yes—
600C4⋊C4—24no—
601C4⋊C4—21no—
602C4⋊C4—21no—
603C4⋊C4—114no—
604C4⋊C4—112no—
605C4⋊C4—112no—
606C4⋊C4—112no—
607C4⋊C4—112no—
608C4⋊C4—224no—
609C4⋊C4—224no—
610C4⋊C4—224no—
611C4⋊C4—221no—
612C4⋊C4—221no—
613C4⋊C4—221no—
614C4⋊C4—221no—
615C4⋊C4—224no—
616C4⋊C4—224no—
617C4⋊C4—224no—
618C4⋊C4C23×D1112yes—
619C4⋊C4C23×D1112yes—
620C22⋊C4—24no—
621C22⋊C4—114no—
622C22⋊C4—114no—
623C22⋊C4—224no—
624C22⋊C4—224no—
625C22⋊C4—224no—
626C22⋊C4—224no—
627C22⋊C4—224no—
628C22⋊C4—224no—
629C22⋊C4—224no—
630C42—24no—
631C42—224no—
632C42—224no—
633C42—224no—
634C42D4×D1112yes—
635C42C23×D1112yes—
636C11C2×#335011yescharacteristic, complemented, Sylow
637C23—22no—
638C23—42no—
639C23—42no—
640C23—42no—
641C23—112no—
642C23—112no—
643C23—222no—
644C23—222no—
645C23—222no—
646C23—222no—
647C23—222no—
648C23—222no—
649C23C2×D4×D1111yescharacteristic
650Q8—22no—
651Q8—22no—
652Q8—42no—
653Q8—448no—
654D4—22no—
655D4—22no—
656D4—42no—
657D4—444no—
658D4—448no—
659D4—884no—
660C2×C4—22no—
661C2×C4—22no—
662C2×C4—22no—
663C2×C4—22no—
664C2×C4—22no—
665C2×C4—42no—
666C2×C4—42no—
667C2×C4—42no—
668C2×C4—84no—
669C2×C4—112no—
670C2×C4—112no—
671C2×C4—222no—
672C2×C4—222no—
673C2×C4—224no—
674C2×C4—224no—
675C2×C4—222no—
676C2×C4—222no—
677C2×C4—222no—
678C2×C4—222no—
679C2×C4—222no—
680C2×C4—222no—
681C2×C4—222no—
682C2×C4—222no—
683C2×C4—442no—
684C2×C4—442no—
685C2×C4—442no—
686C2×C4—442no—
687C2×C4—884no—
688C2×C4C2×#433912yes—
689C2×C4C2×D4×D1112yes—
690C2×C4C2×D4×D1112yes—
691C2×C4C2×D4×D1111yescharacteristic
692C2×C4#6704312yes—
693C2×C4C24×D1111yescharacteristic
694C8—22no—
695C8—222no—
696C8—222no—
697C8C2×#433914yes—
698C22—42no—
699C22—42no—
700C22—42no—
701C22—84no—
702C22—222no—
703C22—222no—
704C22—222no—
705C22—222no—
706C22—222no—
707C22—222no—
708C22—444no—
709C22—444no—
710C22#1062308212yes—
711C22#1062330612yes—
712C22#1062330812yes—
713C22C22×D4×D1111yescharacteristic
714C4—22no—
715C4—22no—
716C4—42no—
717C4—42no—
718C4—42no—
719C4—222no—
720C4—222no—
721C4—442no—
722C4—442no—
723C4—442no—
724C4—442no—
725C4#1062308212yes—
726C4C22×#433911yescharacteristic
727C4C2×#6704311yescharacteristic
728C2—82no—
729C2—442no—
730C2—442no—
731C2#1308116614yesdirect product factor
732C2C2×#1062308211yescharacteristic
733C2C2×#1062330811yescharacteristic
734C2C2×#1062330611yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#440C2
socleC23×C11C22×D4
prime radicalC2×#10623089C2
hypercenterC2×#440D11
hypocenterC11C2×#3350
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#440

Complements

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

NH ≅ G/Ntype
1. C2×#10623115C2semidirect
3. #13081166C2direct (N × H)
4. C2×#10622315C2semidirect
5. C2×#10622427C2semidirect
6. C2×#10622392C2semidirect
7. C2×#10622397C2semidirect
8. C2×#10622418C2semidirect
9. C2×#10622635C2semidirect
10. C2×#10622621C2semidirect
11. C2×#10622787C2semidirect
12. C2×#10622784C2semidirect
13. C2×#10622319C2semidirect
14. C2×#10622494C2semidirect
15. C2×#10622493C2semidirect
16. C2×C11×#440C2semidirect
29. #10623115C22semidirect
45. C11×#440C22semidirect
54. #10622787C22semidirect
55. #10622784C22semidirect
62. #10622635C22semidirect
63. #10622621C22semidirect
69. #10622494C22semidirect
70. #10622493C22semidirect
71. #10622427C22semidirect
72. #10622418C22semidirect
73. #10622397C22semidirect
74. #10622392C22semidirect
75. #10622319C22semidirect
76. #10622315C22semidirect
282. C2×#440D11semidirect
384. #440C2×D11semidirect
540. C2×C11#3350semidirect
636. C11C2×#3350semidirect
731. C2#13081166direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106231152
C2×#106230892
#130811662
C2×#106223152
C2×#106224272
C2×#106223922
C2×#106223972
C2×#106224182
C2×#106226352
C2×#106226212
C2×#106227872
C2×#106227842
C2×#106223192
C2×#106224942
C2×#106224932
C2×C11×#4402
C2×#335011