Finite Group Databasebeta

← #14771887

Subgroups — #14771887

Order 2816.

1126 conjugacy classes of subgroups.

The subgroup lattice has 698 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×(C22⋊D11)⋊C8C211yesmaximal, characteristic
2C22×#66871C211yesmaximal, characteristic, complemented
3C2×D11×#107C211yesmaximal, characteristic, complemented
4C4⋊C4×C22⋊D11C211yesmaximal, characteristic
5#13071512C211yesmaximal, characteristic
6#13069373C211yesmaximal, characteristic, complemented
7#13069371C211yesmaximal, characteristic, complemented
8#13068806C211yesmaximal, characteristic, complemented
9#13068805C211yesmaximal, characteristic, complemented
10#13068802C211yesmaximal, characteristic, complemented
11#13068774C211yesmaximal, characteristic, complemented
12#13068644C211yesmaximal, characteristic, complemented
13#13068643C211yesmaximal, characteristic, complemented
14#13068508C211yesmaximal, characteristic, complemented
15C11×#1852C211yesmaximal, characteristic, complemented
16C22×C11×C4⋊C4C2211yescharacteristic
17C2×C4×C22⋊D11—21no—
18C2×C4×C22⋊D11C2211yescharacteristic
19C22×C4⋊Dic11C2211yescharacteristic
20C23×C11⋊C8C2211yescharacteristic
21C22×C8×D11C2211yescharacteristic
22C2×C4⋊C4×D11C2211yescharacteristic
23C2×C4⋊C4×D11C2211yescharacteristic
24C2×(C22⋊D11)⋊C4—21no—
25C2×C11×#107C2211yescharacteristic
26C2×C11×#107C2211yescharacteristic
27C2×C11×C22⋊C8C2211yescharacteristic
28C11×#380C2211yescharacteristic
29#10622825C2211yescharacteristic
30#10622823—21no—
31C2×(C2×D11)⋊C8C2211yescharacteristic
32C2×#66882C2211yescharacteristic
33C2×#66882C2211yescharacteristic
34C2×Dic11⋊C8C2211yescharacteristic
35C2×C8×Dic11C2211yescharacteristic
36#10622602—21no—
37#10622600C2211yescharacteristic
38#10622600C2211yescharacteristic
39#10622589C2211yescharacteristic
40#10622589C2211yescharacteristic
41C4⋊C4×Dic11C2211yescharacteristic
42C4⋊C4×Dic11C2211yescharacteristic
43#10622585—21no—
44C2×#66871—24no—
45C2×#66871C2211yescharacteristic
46C2×#66871C2211yescharacteristic
47C2×#66871C2211yescharacteristic
48C2×#66871C2211yescharacteristic
49C2×#66871C2211yescharacteristic
50C2×#66871C2211yescharacteristic
51#10622559—21no—
52D11×#107—24no—
53(C22⋊D11)⋊C8C418yescomplemented
54#10622281—21no—
55#10622260—21no—
56C11×#340C2211yescharacteristic
57C11×#340C2211yescharacteristic
58#10622189C2211yescharacteristic
59#10622189C2211yescharacteristic
60#10622167C2211yescharacteristic
61#10622167C2211yescharacteristic
62C23×C4×C11—21no—
63C23×C4×C11C2311yescharacteristic
64C22×C22⋊D11D411yescharacteristic
65C23×Dic11—21no—
66C22×C4×D11—21no—
67C22×C4×D11—21no—
68C22×C4×D11C2311yescharacteristic
69C22×C8×C11C2311yescharacteristic
70C22×C8×C11C2311yescharacteristic
71C2×C11×C4⋊C4—22no—
72C2×C11×C4⋊C4—21no—
73C2×C11×C4⋊C4—41no—
74C2×C11×C4⋊C4C2311yescharacteristic
75C2×C11×C4⋊C4C2311yescharacteristic
76C2×C11×C4⋊C4C2311yescharacteristic
77C2×C11×C4⋊C4C2311yescharacteristic
78C2×C11×C22⋊C4—21no—
79C2×C22⋊Dic11—21no—
80C2×C22⋊Dic11D411yescharacteristic
81C4×C22⋊D11—44no—
82C4×C22⋊D11C2×C414yes—
83C4×C22⋊D11Q814yes—
84C2×(C2×D11)⋊C4—21no—
85C2×(C2×D11)⋊C4—21no—
86C2×(C2×D11)⋊C4D411yescharacteristic
87C2×C4⋊Dic11—22no—
88C2×C4⋊Dic11—21no—
89C2×C4⋊Dic11—41no—
90C2×C4⋊Dic11C2311yescharacteristic
91C2×C4⋊Dic11C2311yescharacteristic
92C2×C4⋊Dic11C2311yescharacteristic
93C2×C4⋊Dic11C2311yescharacteristic
94C2×Dic11⋊C4—21no—
95C2×Dic11⋊C4—21no—
96C2×Dic11⋊C4—21no—
97C2×Dic11⋊C4—21no—
98C2×Dic11⋊C4—21no—
99C2×Dic11⋊C4—21no—
100C2×Dic11⋊C4D411yescharacteristic
101C2×C4×Dic11—21no—
102C2×C4×Dic11—21no—
103C2×C4×Dic11C2311yescharacteristic
104C22×C11⋊C8—22no—
105C22×C11⋊C8—22no—
106C22×C11⋊C8C2×C414yescomplemented
107C22×C11⋊C8C2311yescharacteristic
108C22×C11⋊C8C2311yescharacteristic
109C2×C8×D11—22no—
110C2×C8×D11—22no—
111C2×C8×D11C2×C414yescomplemented
112C4⋊C4×D11—22no—
113C4⋊C4×D11—22no—
114C4⋊C4×D11—41no—
115C4⋊C4×D11—41no—
116(C22⋊D11)⋊C4—44no—
117C11×#107—22no—
118C11×#107—41no—
119C11×C22⋊C8C2×C414yescomplemented
120C11×#95—21no—
121C11⋊#95—21no—
122C11⋊#95—21no—
123C11⋊#95—21no—
124C11⋊#95—21no—
125C11⋊#95—21no—
126(C2×D11)⋊C8C2×C414yescomplemented
127#66882—22no—
128#66882—41no—
129Dic11⋊C8C2×C414yescomplemented
130C8×Dic11C2×C414yescomplemented
131#66871—22no—
132#66871—22no—
133#66871—22no—
134#66871—22no—
135#66871—22no—
136#66871D414yescomplemented
137D4×#107—111nomaximal, Sylow
138C24×C11C2×D411yescharacteristic
139C23×D11C2×D411yescharacteristic
140C22×C4×C11—21no—
141C22×C4×C11—21no—
142C22×C4×C11—21no—
143C22×C4×C11—21no—
144C22×C4×C11—21no—
145C22×C4×C11—21no—
146C22×C4×C11—21no—
147C22×C4×C11—21no—
148C22×C4×C11—42no—
149C22×C4×C11—42no—
150C22×C4×C11—81no—
151C22×C4×C11C22×C412yes—
152C22×C4×C11C2×D411yescharacteristic
153C22×C4×C11C2×Q812yes—
154C22×C4×C11C2411yescharacteristic
155C2×C22⋊D11C4⋊C414yes—
156C2×C22⋊D11D814yes—
157C2×C22⋊D11Q1614yes—
158C22×Dic11—21no—
159C22×Dic11—21no—
160C22×Dic11—21no—
161C22×Dic11—21no—
162C22×Dic11—42no—
163C22×Dic11—42no—
164C22×Dic11—81no—
165C22×Dic11C2×D411yescharacteristic
166C22×Dic11C2×D411yescharacteristic
167C22×Dic11C2×D411yescharacteristic
168C2×C4×D11—21no—
169C2×C4×D11—21no—
170C2×C4×D11—21no—
171C2×C4×D11—21no—
172C2×C4×D11—42no—
173C2×C4×D11—42no—
174C2×C4×D11—42no—
175C2×C4×D11—42no—
176C2×C4×D11—81no—
177C2×C4×D11—81no—
178C2×C4×D11C22×C412yes—
179C2×C4×D11C2×Q812yes—
180C2×C8×C11—21no—
181C2×C8×C11—21no—
182C2×C8×C11—21no—
183C2×C8×C11—21no—
184C2×C8×C11C22×C412yes—
185C2×C8×C11C22×C412yes—
186C11×C4⋊C4—21no—
187C11×C4⋊C4—21no—
188C11×C4⋊C4—21no—
189C11×C4⋊C4—21no—
190C11×C4⋊C4—21no—
191C11×C4⋊C4—21no—
192C11×C4⋊C4—21no—
193C11×C4⋊C4—42no—
194C11×C4⋊C4C2×D412yes—
195C11×C22⋊C4—42no—
196C22⋊Dic11—42no—
197C22⋊Dic11C4⋊C414yes—
198(C2×D11)⋊C4—42no—
199(C2×D11)⋊C4—42no—
200(C2×D11)⋊C4C4⋊C414yes—
201C4⋊Dic11—21no—
202C4⋊Dic11—21no—
203C4⋊Dic11—21no—
204C4⋊Dic11—21no—
205C4⋊Dic11—21no—
206C4⋊Dic11—21no—
207C4⋊Dic11—21no—
208C4⋊Dic11—42no—
209C4⋊Dic11C2×D412yes—
210Dic11⋊C4—42no—
211Dic11⋊C4—42no—
212Dic11⋊C4—42no—
213Dic11⋊C4—42no—
214Dic11⋊C4—81no—
215Dic11⋊C4—81no—
216Dic11⋊C4C4⋊C414yes—
217C4×Dic11—42no—
218C4×Dic11—42no—
219C4×Dic11C22×C412yes—
220C4×Dic11C2×Q812yes—
221C2×C11⋊C8—28no—
222C2×C11⋊C8—21no—
223C2×C11⋊C8—21no—
224C2×C11⋊C8C22×C412yes—
225C2×C11⋊C8C22×C412yes—
226C2×C11⋊C8C2×D412yes—
227C2×C11⋊C8#4112yes—
228C8×D11—28no—
229C2×C8×D4—111no—
230C22×#107—111no—
231C22×#107—111no—
232D4×C4⋊C4—111no—
233D4×C4⋊C4—111no—
234#1947—111no—
235#1947—111no—
236#1852—111no—
237#1852—111no—
238#1852—111no—
239#1852D1111yescharacteristic, complemented
240#1845—111no—
241#1808—111no—
242#1808—111no—
243C4×#107—111no—
244C23×C11—21no—
245C23×C11—21no—
246C23×C11—21no—
247C23×C11—21no—
248C23×C11C2×C4⋊C412yes—
249C23×C11C2×D812yes—
250C23×C11C2×Q1612yes—
251C23×C11C22×D411yescharacteristic
252C22×D11—21no—
253C22×D11—21no—
254C22×D11—21no—
255C22×D11—21no—
256C22×D11C2×C4⋊C412yes—
257C22×D11C2×D812yes—
258C22×D11C2×Q1612yes—
259C2×C4×C11—21no—
260C2×C4×C11—21no—
261C2×C4×C11—22no—
262C2×C4×C11—22no—
263C2×C4×C11—22no—
264C2×C4×C11—22no—
265C2×C4×C11—22no—
266C2×C4×C11—41no—
267C2×C4×C11—41no—
268C2×C4×C11—41no—
269C2×C4×C11—41no—
270C2×C4×C11—41no—
271C2×C4×C11—41no—
272C2×C4×C11—41no—
273C2×C4×C11—41no—
274C2×C4×C11—41no—
275C2×C4×C11—41no—
276C2×C4×C11—41no—
277C2×C4×C11—84no—
278C2×C4×C11C2×C4⋊C412yes—
279C2×C4×C11C23×C411yescharacteristic
280C2×C4×C11C22×D411yescharacteristic
281C2×C4×C11C22×Q811yescharacteristic
282C2×C4×C11C2×#4111yescharacteristic
283C2×C4×C11H(5,𝔽2)11yescharacteristic
284C2×C4×C112−1+411yescharacteristic
285C22⋊D11#107116yescomplemented
286C2×Dic11—21no—
287C2×Dic11—21no—
288C2×Dic11—21no—
289C2×Dic11—21no—
290C2×Dic11—22no—
291C2×Dic11—41no—
292C2×Dic11—41no—
293C2×Dic11—41no—
294C2×Dic11—41no—
295C2×Dic11—41no—
296C2×Dic11—41no—
297C2×Dic11—41no—
298C2×Dic11—41no—
299C2×Dic11—41no—
300C2×Dic11—41no—
301C2×Dic11—41no—
302C2×Dic11—84no—
303C2×Dic11C2×C4⋊C412yes—
304C2×Dic11C2×C4⋊C412yes—
305C2×Dic11C2×C4⋊C412yes—
306C2×Dic11C2×D812yes—
307C2×Dic11C2×Q1612yes—
308C4×D11—22no—
309C4×D11—22no—
310C4×D11—22no—
311C4×D11—22no—
312C4×D11—84no—
313C4×D11—84no—
314C8×C11—22no—
315C8×C11—22no—
316C11⋊C8—22no—
317C11⋊C8C4×D414yescomplemented
318C23×C8—111no—
319C23×C8—111no—
320C2×C4×D4—111no—
321C2×C4×D4—221no—
322C2×C4×D4—221no—
323C22×C4⋊C4—111no—
324C22×C4⋊C4—111no—
325C22×C4⋊C4—111no—
326C22×C4⋊C4C2×D1111yescharacteristic
327C8×D4—118no—
328C2×#107—111no—
329C2×#107—111no—
330C2×#107—111no—
331C2×#107—111no—
332C2×#107—111no—
333C2×#107—111no—
334C2×#107—111no—
335C2×#107—111no—
336C2×#107—224no—
337C2×#107—224no—
338C2×#107C2×D1111yescharacteristic
339C2×#107C2×D1111yescharacteristic
340C2×C4⋊C8—111no—
341C2×C22⋊C8—111no—
342C2×C22⋊C8C2×D1111yescharacteristic
343C2×C4×C8—111no—
344#389—221no—
345#389—221no—
346#385—221no—
347#385—221no—
348#385—221no—
349#385—221no—
350#384—111no—
351#384—111no—
352#380—111no—
353#380—111no—
354#380—111no—
355#380C2×D1111yescharacteristic
356C4×C4⋊C4—111no—
357C4×C4⋊C4—111no—
358#340—111no—
359#340—111no—
360#340—111no—
361#340—111no—
362#340C2×D1111yescharacteristic
363#340C2×D1111yescharacteristic
364C22×C11—22no—
365C22×C11—22no—
366C22×C11—22no—
367C22×C11—22no—
368C22×C11—22no—
369C22×C11—22no—
370C22×C11C2×#10714yescomplemented
371C22×C11C22×C4⋊C411yescharacteristic
372C22×C11D4211yescharacteristic
373C22×C11#54711yescharacteristic
374C22×C11C22×D811yescharacteristic
375C22×C11C22×Q1611yescharacteristic
376C22×C11#57611yescharacteristic
377C22×C11#57811yescharacteristic
378C2×D11—22no—
379C2×D11—22no—
380C2×D11—22no—
381C2×D11—22no—
382C2×D11—22no—
383C2×D11—22no—
384C2×D11C2×#10714yescomplemented
385C4×C11—22no—
386C4×C11—42no—
387C4×C11—81no—
388C4×C11—81no—
389C4×C11—81no—
390C4×C11C2×C4×D411yescharacteristic
391C4×C11#52011yescharacteristic
392C4×C11D4×Q811yescharacteristic
393C4×C11#55411yescharacteristic
394Dic11—22no—
395Dic11—22no—
396Dic11—42no—
397Dic11—81no—
398Dic11—81no—
399Dic11—81no—
400Dic11C2×#10714yescomplemented
401C22×D4—111no—
402C23×C4—21no—
403C23×C4—111no—
404C23×C4—221no—
405C23×C4—221no—
406C23×C4—221no—
407C23×C4C22×D1111yescharacteristic
408C22×C8—111no—
409C22×C8—114no—
410C22×C8—111no—
411C22×C8—114no—
412C22×C8—222no—
413C22×C8—222no—
414C22×C8—222no—
415C22×C8—222no—
416C22×C8C22×D1111yescharacteristic
417C22×C8C22×D1111yescharacteristic
418C4×D4—114no—
419C4×D4—114no—
420C4×D4—444no—
421C4×D4—444no—
422C2×C4⋊C4—22no—
423C2×C4⋊C4—21no—
424C2×C4⋊C4—41no—
425C2×C4⋊C4—111no—
426C2×C4⋊C4—111no—
427C2×C4⋊C4—111no—
428C2×C4⋊C4—111no—
429C2×C4⋊C4—111no—
430C2×C4⋊C4—222no—
431C2×C4⋊C4—222no—
432C2×C4⋊C4—222no—
433C2×C4⋊C4—221no—
434C2×C4⋊C4—221no—
435C2×C4⋊C4—221no—
436C2×C4⋊C4—221no—
437C2×C4⋊C4—221no—
438C2×C4⋊C4—221no—
439C2×C4⋊C4—221no—
440C2×C4⋊C4—441no—
441C2×C4⋊C4—441no—
442C2×C4⋊C4—441no—
443C2×C4⋊C4C22×D1111yescharacteristic
444C2×C4⋊C4C22×D1111yescharacteristic
445C2×C4⋊C4C22×D1111yescharacteristic
446C2×C4⋊C4C22×D1111yescharacteristic
447C2×C22⋊C4—21no—
448C2×C22⋊C4—111no—
449C2×C22⋊C4—111no—
450C2×C22⋊C4—221no—
451C2×C22⋊C4—221no—
452C2×C22⋊C4—221no—
453C2×C42—111no—
454C2×C42—221no—
455C2×C42—221no—
456#107—22no—
457#107—41no—
458#107—114no—
459#107—222no—
460#107—222no—
461#107—222no—
462#107—222no—
463#107—222no—
464#107—222no—
465#107—441no—
466C4⋊C8—114no—
467C22⋊C8—114no—
468C22⋊C8C4×D1114yescomplemented
469C4×C8—114no—
470#95—21no—
471#95—221no—
472#95—221no—
473#95—221no—
474#95—221no—
475#95—221no—
476C2×C11—24no—
477C2×C11D4×C4⋊C411yescharacteristic
478C2×C11C22×#10711yescharacteristic
479C2×C11#291311yescharacteristic
480C2×C11D4×D811yescharacteristic
481C2×C11D4×Q1611yescharacteristic
482C2×C11#333411yescharacteristic
483C2×C11#333811yescharacteristic
484D11—24no—
485C24—111no—
486C24D4×D1111yescharacteristic
487C2×D4—114no—
488C2×D4—114no—
489C2×D4—114no—
490C22×C4—21no—
491C22×C4—21no—
492C22×C4—21no—
493C22×C4—21no—
494C22×C4—21no—
495C22×C4—21no—
496C22×C4—21no—
497C22×C4—21no—
498C22×C4—42no—
499C22×C4—42no—
500C22×C4—81no—
501C22×C4—111no—
502C22×C4—111no—
503C22×C4—111no—
504C22×C4—112no—
505C22×C4—112no—
506C22×C4—221no—
507C22×C4—221no—
508C22×C4—221no—
509C22×C4—221no—
510C22×C4—221no—
511C22×C4—221no—
512C22×C4—221no—
513C22×C4—221no—
514C22×C4—442no—
515C22×C4—442no—
516C22×C4—442no—
517C22×C4—442no—
518C22×C4—442no—
519C22×C4—442no—
520C22×C4—881no—
521C22×C4—881no—
522C22×C4—881no—
523C22×C4C2×C4×D1112yes—
524C22×C4D4×D1111yescharacteristic
525C22×C4Q8×D1112yes—
526C22×C4C23×D1111yescharacteristic
527C2×C8—21no—
528C2×C8—21no—
529C2×C8—21no—
530C2×C8—21no—
531C2×C8—112no—
532C2×C8—112no—
533C2×C8—112no—
534C2×C8—112no—
535C2×C8—228no—
536C2×C8—228no—
537C2×C8—221no—
538C2×C8—221no—
539C2×C8C2×C4×D1112yes—
540C2×C8C2×C4×D1112yes—
541C4⋊C4—21no—
542C4⋊C4—21no—
543C4⋊C4—21no—
544C4⋊C4—21no—
545C4⋊C4—21no—
546C4⋊C4—21no—
547C4⋊C4—21no—
548C4⋊C4—42no—
549C4⋊C4—114no—
550C4⋊C4—112no—
551C4⋊C4—221no—
552C4⋊C4—221no—
553C4⋊C4—221no—
554C4⋊C4—221no—
555C4⋊C4—221no—
556C4⋊C4—221no—
557C4⋊C4—221no—
558C4⋊C4—442no—
559C4⋊C4—442no—
560C4⋊C4—442no—
561C4⋊C4—442no—
562C4⋊C4—442no—
563C4⋊C4—881no—
564C4⋊C4—881no—
565C4⋊C4D4×D1112yes—
566C22⋊C4—42no—
567C22⋊C4—114no—
568C22⋊C4—114no—
569C22⋊C4—442no—
570C22⋊C4—442no—
571C22⋊C4—442no—
572C42—112no—
573C42—112no—
574C42—442no—
575C42—442no—
576C11D4×#10711yescharacteristic, complemented, Sylow
577C23—21no—
578C23—21no—
579C23—21no—
580C23—21no—
581C23—112no—
582C23—112no—
583C23—112no—
584C23—221no—
585C23—221no—
586C23—221no—
587C23—221no—
588C23C4⋊C4×D1112yes—
589C23D8×D1112yes—
590C23Q16×D1112yes—
591C23C2×D4×D1111yescharacteristic
592D4—1116no—
593C2×C4—21no—
594C2×C4—21no—
595C2×C4—22no—
596C2×C4—22no—
597C2×C4—22no—
598C2×C4—22no—
599C2×C4—22no—
600C2×C4—41no—
601C2×C4—41no—
602C2×C4—41no—
603C2×C4—41no—
604C2×C4—41no—
605C2×C4—41no—
606C2×C4—41no—
607C2×C4—41no—
608C2×C4—41no—
609C2×C4—41no—
610C2×C4—41no—
611C2×C4—84no—
612C2×C4—112no—
613C2×C4—112no—
614C2×C4—112no—
615C2×C4—112no—
616C2×C4—112no—
617C2×C4—221no—
618C2×C4—221no—
619C2×C4—221no—
620C2×C4—221no—
621C2×C4—222no—
622C2×C4—222no—
623C2×C4—222no—
624C2×C4—222no—
625C2×C4—222no—
626C2×C4—441no—
627C2×C4—441no—
628C2×C4—441no—
629C2×C4—441no—
630C2×C4—441no—
631C2×C4—441no—
632C2×C4—441no—
633C2×C4—441no—
634C2×C4—441no—
635C2×C4—441no—
636C2×C4—441no—
637C2×C4—884no—
638C2×C4—884no—
639C2×C4—884no—
640C2×C4C4⋊C4×D1112yes—
641C2×C4C22×C4×D1111yescharacteristic
642C2×C4C2×D4×D1111yescharacteristic
643C2×C4#6703711yescharacteristic
644C2×C4C2×Q8×D1111yescharacteristic
645C2×C4#41×D1111yescharacteristic
646C2×C4#6704311yescharacteristic
647C8—22no—
648C8—22no—
649C8—114no—
650C8—222no—
651C22—22no—
652C22—22no—
653C22—22no—
654C22—22no—
655C22—22no—
656C22—22no—
657C22—114no—
658C22—222no—
659C22—222no—
660C22—222no—
661C22—222no—
662C22—222no—
663C22—222no—
664C22D11×#10714yescomplemented
665C22C2×C4⋊C4×D1111yescharacteristic
666C22#1062312111yescharacteristic
667C22#1062318611yescharacteristic
668C22C2×D8×D1111yescharacteristic
669C22C2×Q16×D1111yescharacteristic
670C22#1062330511yescharacteristic
671C22#1062331011yescharacteristic
672C4—22no—
673C4—42no—
674C4—81no—
675C4—81no—
676C4—81no—
677C4—114no—
678C4—222no—
679C4—222no—
680C4—442no—
681C4—881no—
682C4—881no—
683C4—881no—
684C4C4×D4×D1111yescharacteristic
685C4#1062307711yescharacteristic
686C4#1062316311yescharacteristic
687C4#1062316711yescharacteristic
688C2—24no—
689C2—224no—
690C2#1307151411yescharacteristic
691C2C2×D11×#10711yescharacteristic
692C2#1307721511yescharacteristic
693C2#1308028611yescharacteristic
694C2#1308036111yescharacteristic
695C2#1308095811yescharacteristic
696C2#1308100311yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1852C2
socleC23×C11C22×D4
prime radicalC22×C22⋊D11D4
cosocleC22×C4×C11C24
hypercenter#1852D11
hypocenterC11D4×#107
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1852

Complements

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

NH ≅ G/Ntype
2. C22×#66871C2semidirect
3. C2×D11×#107C2semidirect
6. #13069373C2semidirect
7. #13069371C2semidirect
8. #13068806C2semidirect
9. #13068805C2semidirect
10. #13068802C2semidirect
11. #13068774C2semidirect
12. #13068644C2semidirect
13. #13068643C2semidirect
14. #13068508C2semidirect
15. C11×#1852C2semidirect
53. (C22⋊D11)⋊C8C4semidirect
106. C22×C11⋊C8C2×C4semidirect
111. C2×C8×D11C2×C4semidirect
119. C11×C22⋊C8C2×C4semidirect
126. (C2×D11)⋊C8C2×C4semidirect
129. Dic11⋊C8C2×C4semidirect
130. C8×Dic11C2×C4semidirect
136. #66871D4semidirect
239. #1852D11semidirect
285. C22⋊D11#107semidirect
317. C11⋊C8C4×D4semidirect
370. C22×C11C2×#107semidirect
384. C2×D11C2×#107semidirect
400. Dic11C2×#107semidirect
468. C22⋊C8C4×D11semidirect
576. C11D4×#107semidirect
664. C22D11×#107semidirect

Maximal subgroups

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

subgroupindex
C2×(C22⋊D11)⋊C82
C22×#668712
C2×D11×#1072
C4⋊C4×C22⋊D112
#130715122
#130693732
#130693712
#130688062
#130688052
#130688022
#130687742
#130686442
#130686432
#130685082
C11×#18522
D4×#10711