Finite Group Databasebeta

← #14770130

Subgroups — #14770130

Order 2816.

1122 conjugacy classes of subgroups.

The subgroup lattice has 710 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623072C211yesmaximal, characteristic
2C2×#10622624C211yesmaximal, characteristic
3#13069584C211yesmaximal, characteristic, complemented
4#13069573C211yesmaximal, characteristic, complemented
5#13069047C211yesmaximal, characteristic, complemented
6#13069037C211yesmaximal, characteristic, complemented
7#13068928C211yesmaximal, characteristic, complemented
8#13068928C211yesmaximal, characteristic, complemented
9#13068708C211yesmaximal, characteristic, complemented
10#13068704C211yesmaximal, characteristic, complemented
11#13068618C211yesmaximal, characteristic, complemented
12#13068449C211yesmaximal, characteristic, complemented
13#13068337C211yesmaximal, characteristic, complemented
14#13068332C211yesmaximal, characteristic, complemented
15C11×#2354C211yesmaximal, characteristic
16C2×C4×D4×C11C2211yescharacteristic
17C2×C11×#117C2211yescharacteristic
18C2×C11×#117C2211yescharacteristic
19C2×#66988—21no—
20C2×#66979C2211yescharacteristic
21C22×C4⋊Dic11C2211yescharacteristic
22C2×#66977C2211yescharacteristic
23C2×#66977C2211yescharacteristic
24C22×#4318C2211yescharacteristic
25C23×C11⋊C8C2211yescharacteristic
26#10623072—24no—
27#10623072C418yescomplemented
28C2×#66942—21no—
29C2×#66932—21no—
30C2×#66930—21no—
31C2×#66923C2211yescharacteristic
32C2×C4×Dic22C2211yescharacteristic
33C11×#390—21no—
34C11×#388—21no—
35C11×#388—21no—
36C11×#384C2211yescharacteristic
37C11×#380C2211yescharacteristic
38C11×#380C2211yescharacteristic
39C4×C11×C4⋊C4—21no—
40C4×C11×C4⋊C4C2211yescharacteristic
41C2×C22⋊(C11⋊C8)C2211yescharacteristic
42C2×C22⋊(C11⋊C8)C2211yescharacteristic
43#10622624—24no—
44C2×#66874C2211yescharacteristic
45C2×#66874C2211yescharacteristic
46C2×#66874C2211yescharacteristic
47C2×#66874C2211yescharacteristic
48C2×C4⋊(C11⋊C8)C2211yescharacteristic
49C2×#66867C2211yescharacteristic
50#10622167C2211yescharacteristic
51#10622167C2211yescharacteristic
52#10622167C2211yescharacteristic
53#10622167C2211yescharacteristic
54#10622167C2211yescharacteristic
55#10622167C2211yescharacteristic
56#10622167C2211yescharacteristic
57#10622167C2211yescharacteristic
58#10622167C2211yescharacteristic
59#10622167C2211yescharacteristic
60#10622167C2211yescharacteristic
61#10622167C2211yescharacteristic
62C22×D4×C11D411yescharacteristic
63C23×C4×C11C2311yescharacteristic
64C23×C4×C11C2311yescharacteristic
65C23×Dic11—21no—
66C22×Dic22C2311yescharacteristic
67C4×D4×C11C2×C414yes—
68C4×D4×C11D414yes—
69C11×#117—22no—
70C11×#117—22no—
71C11×#117—41no—
72C11×#117—41no—
73C2×C11×C4⋊C4—21no—
74C2×C11×C4⋊C4—21no—
75C2×C11×C4⋊C4D411yescharacteristic
76C2×C11×C4⋊C4C2311yescharacteristic
77C2×C11×C4⋊C4C2311yescharacteristic
78C2×C11×C4⋊C4C2311yescharacteristic
79C2×C11×C4⋊C4C2311yescharacteristic
80C2×C11×C22⋊C4—21no—
81C2×C11×C22⋊C4—21no—
82C2×C11×C22⋊C4—21no—
83C2×C11×C22⋊C4—21no—
84C2×C11×C22⋊C4D411yescharacteristic
85C2×C11×C22⋊C4D411yescharacteristic
86C2×C42×C11—21no—
87C2×C42×C11—21no—
88C2×C42×C11—21no—
89C2×C42×C11C2311yescharacteristic
90C2×C22⋊Dic11—21no—
91C2×C22⋊Dic11—21no—
92C2×C22⋊Dic11—21no—
93#66988—28no—
94#66979—22no—
95#66979C2×C414yes—
96C2×C4⋊Dic11—21no—
97C2×C4⋊Dic11—22no—
98C2×C4⋊Dic11C2×C414yes—
99C2×C4⋊Dic11C2311yescharacteristic
100C2×C4⋊Dic11C2311yescharacteristic
101C2×C4⋊Dic11C2311yescharacteristic
102#66977—22no—
103#66977—22no—
104#66977C2×C414yes—
105#66977C2×C414yes—
106C2×Dic11⋊C4—21no—
107C2×Dic11⋊C4—21no—
108C2×Dic11⋊C4—21no—
109C2×Dic11⋊C4—21no—
110C2×Dic11⋊C4—21no—
111C2×C4×Dic11—21no—
112C2×C4×Dic11—21no—
113C2×#4318—22no—
114C2×#4318—22no—
115C2×#4318—41no—
116C22×C11⋊C8—22no—
117C22×C11⋊C8—22no—
118C22×C11⋊C8—41no—
119C22×C11⋊C8C2311yescharacteristic
120C22×C11⋊C8C2311yescharacteristic
121C22×C11⋊C8C2311yescharacteristic
122C22×C11⋊C8C2311yescharacteristic
123#66942—28no—
124#66932—28no—
125#66930—28no—
126#66923—22no—
127#66923C2×C414yes—
128C4×Dic22—22no—
129C4×Dic22C2×C414yes—
130C11×#95—21no—
131C11×#95—21no—
132C11×#95—21no—
133C22⋊(C11⋊C8)—22no—
134C22⋊(C11⋊C8)—22no—
135#66874—22no—
136#66874—22no—
137#66874—41no—
138#66874—41no—
139C4⋊(C11⋊C8)—22no—
140#66867—22no—
141#22496—111nomaximal, Sylow
142C24×C11C2×D411yescharacteristic
143C24×C11C2×D411yescharacteristic
144C2×D4×C11—41no—
145C2×D4×C11—41no—
146C2×D4×C11C22⋊C414yes—
147C22×C4×C11—21no—
148C22×C4×C11—21no—
149C22×C4×C11—21no—
150C22×C4×C11—21no—
151C22×C4×C11—21no—
152C22×C4×C11—21no—
153C22×C4×C11—21no—
154C22×C4×C11—21no—
155C22×C4×C11—21no—
156C22×C4×C11—21no—
157C22×C4×C11—21no—
158C22×C4×C11—21no—
159C22×C4×C11C22×C412yes—
160C22×C4×C11C22×C412yes—
161C22×C4×C11C2×D411yescharacteristic
162C22×C4×C11C2×D411yescharacteristic
163C22×C4×C11C2×D411yescharacteristic
164C22×C4×C11C2×D411yescharacteristic
165C22×C4×C11C2×D412yes—
166C22×C4×C11C2×D412yes—
167C22×C4×C11C2411yescharacteristic
168C22×Dic11—24no—
169C22×Dic11—21no—
170C22×Dic11—21no—
171C22×Dic11—21no—
172C22×Dic11—21no—
173C22×Dic11—42no—
174C22×Dic11—42no—
175C2×Dic22—21no—
176C2×Dic22—21no—
177C2×Dic22—21no—
178C2×Dic22—21no—
179C2×Dic22—21no—
180C2×Dic22C22×C412yes—
181C11×C4⋊C4—21no—
182C11×C4⋊C4—21no—
183C11×C4⋊C4—21no—
184C11×C4⋊C4—21no—
185C11×C4⋊C4—21no—
186C11×C4⋊C4—21no—
187C11×C4⋊C4—21no—
188C11×C4⋊C4—42no—
189C11×C4⋊C4—81no—
190C11×C4⋊C4C22⋊C414yes—
191C11×C4⋊C4#4112yes—
192C11×C22⋊C4—42no—
193C11×C22⋊C4—42no—
194C11×C22⋊C4—81no—
195C11×C22⋊C4—81no—
196C11×C22⋊C4C22⋊C414yes—
197C11×C22⋊C4C22⋊C414yes—
198C42×C11—42no—
199C42×C11—42no—
200C42×C11—42no—
201C42×C11C22×C412yes—
202C42×C11C2×D412yes—
203C22⋊Dic11—24no—
204C22⋊Dic11—24no—
205C22⋊Dic11—24no—
206C4⋊Dic11—24no—
207C4⋊Dic11—21no—
208C4⋊Dic11—21no—
209C4⋊Dic11—21no—
210C4⋊Dic11C22×C412yes—
211C4⋊Dic11C22×C412yes—
212C4⋊Dic11C22×C412yes—
213Dic11⋊C4—24no—
214Dic11⋊C4—24no—
215Dic11⋊C4—24no—
216Dic11⋊C4—24no—
217Dic11⋊C4—24no—
218C4×Dic11—24no—
219C4×Dic11—24no—
220#4318—44no—
221C2×C11⋊C8—21no—
222C2×C11⋊C8—21no—
223C2×C11⋊C8—21no—
224C2×C11⋊C8—21no—
225C2×C11⋊C8—21no—
226C2×C11⋊C8—21no—
227C2×C11⋊C8—21no—
228C2×C11⋊C8—21no—
229C2×C11⋊C8—21no—
230C2×C11⋊C8—21no—
231C2×C11⋊C8—21no—
232C2×C11⋊C8—44no—
233C2×C11⋊C8#4112yes—
234C2×#552—111no—
235C2×#435—111no—
236#2354D1111yescharacteristic
237#1992—111no—
238#1989—111no—
239#1894—111no—
240#1892—111no—
241#1873—111no—
242#1873—111no—
243#1825—111no—
244#1824—111no—
245#1803—111no—
246#1763—111no—
247#1736—111no—
248#1735—111no—
249C23×C11—21no—
250C23×C11—21no—
251C23×C11—21no—
252C23×C11—21no—
253C23×C11—21no—
254C23×C11—21no—
255C23×C11—21no—
256C23×C11—21no—
257C23×C11—21no—
258C23×C11—21no—
259C23×C11—21no—
260C23×C11—21no—
261C23×C11C2×C22⋊C412yes—
262C23×C11C2×C22⋊C412yes—
263C23×C11C22×D411yescharacteristic
264D4×C11—44no—
265C2×C4×C11—21no—
266C2×C4×C11—21no—
267C2×C4×C11—21no—
268C2×C4×C11—21no—
269C2×C4×C11—21no—
270C2×C4×C11—21no—
271C2×C4×C11—21no—
272C2×C4×C11—21no—
273C2×C4×C11—22no—
274C2×C4×C11—22no—
275C2×C4×C11—22no—
276C2×C4×C11—22no—
277C2×C4×C11—22no—
278C2×C4×C11—22no—
279C2×C4×C11—22no—
280C2×C4×C11—22no—
281C2×C4×C11—22no—
282C2×C4×C11—41no—
283C2×C4×C11—41no—
284C2×C4×C11—41no—
285C2×C4×C11—41no—
286C2×C4×C11—41no—
287C2×C4×C11—41no—
288C2×C4×C11—41no—
289C2×C4×C11—41no—
290C2×C4×C11—41no—
291C2×C4×C11—41no—
292C2×C4×C11—41no—
293C2×C4×C11C2×C22⋊C412yes—
294C2×C4×C11C2×C22⋊C412yes—
295C2×C4×C11C2×C22⋊C412yes—
296C2×C4×C11C2×C22⋊C412yes—
297C2×C4×C11C23×C411yescharacteristic
298C2×C4×C11C22×D411yescharacteristic
299C2×C4×C11C2×#4111yescharacteristic
300C2×C4×C11C2×#4111yescharacteristic
301C2×C4×C11H(5,𝔽2)11yescharacteristic
302C2×C4×C112−1+411yescharacteristic
303C2×Dic11—22no—
304C2×Dic11—22no—
305C2×Dic11—22no—
306C2×Dic11—22no—
307C2×Dic11—48no—
308C2×Dic11—41no—
309C2×Dic11—41no—
310C2×Dic11—41no—
311C2×Dic11—41no—
312C2×Dic11—41no—
313C2×Dic11—41no—
314C2×Dic11—41no—
315C2×Dic11—41no—
316Dic22—22no—
317Dic22—22no—
318Dic22—41no—
319Dic22—41no—
320C11⋊C8—22no—
321C11⋊C8—41no—
322C11⋊C8—41no—
323C11⋊C8—41no—
324C22×M16—111no—
325C23×C8—111no—
326#552—118no—
327#552—224no—
328C2×#126—221no—
329C2×#125—111no—
330C2×#125—221no—
331C2×#123—221no—
332C2×C22⋊Q8—111no—
333C2×C22⋊Q8—111no—
334C2×C4×Q8—111no—
335C2×C4×D4C2×D1111yescharacteristic
336C2×#117—111no—
337C2×#117—221no—
338C2×#117C2×D1111yescharacteristic
339C2×#117C2×D1111yescharacteristic
340C22×C4⋊C4—111no—
341#435—224no—
342C2×C4⋊C8—111no—
343C2×#103—111no—
344C2×#103—111no—
345C2×#103—111no—
346C2×#103—111no—
347C2×C22⋊C8—111no—
348C2×C22⋊C8—111no—
349C2×#97—111no—
350#390—21no—
351#388—21no—
352#388—21no—
353#384C2×D1111yescharacteristic
354#380C2×D1111yescharacteristic
355#380C2×D1111yescharacteristic
356C4×C4⋊C4—21no—
357C4×C4⋊C4C2×D1111yescharacteristic
358#340—111no—
359#340—111no—
360#340—111no—
361#340—111no—
362#340—111no—
363#340—111no—
364#340—111no—
365#340—111no—
366#340—111no—
367#340—111no—
368#340—111no—
369#340—111no—
370C22×C11—22no—
371C22×C11—22no—
372C22×C11—22no—
373C22×C11—22no—
374C22×C11—22no—
375C22×C11—22no—
376C22×C11—41no—
377C22×C11—41no—
378C22×C11—41no—
379C22×C11—41no—
380C22×C11—41no—
381C22×C11—41no—
382C22×C11—41no—
383C22×C11—41no—
384C22×C11C22×C22⋊C411yescharacteristic
385C22×C11#54611yescharacteristic
386C22×C11#54711yescharacteristic
387C22×C11#57511yescharacteristic
388C22×C11#57511yescharacteristic
389C22×C11#57711yescharacteristic
390C22×C11#57811yescharacteristic
391C4×C11—22no—
392C4×C11—22no—
393C4×C11—22no—
394C4×C11—22no—
395C4×C11—42no—
396C4×C11—81no—
397C4×C11—81no—
398C4×C11—81no—
399C4×C11C4×#4111yescharacteristic
400C4×C11#52011yescharacteristic
401C4×C11#54611yescharacteristic
402C4×C11#54711yescharacteristic
403Dic11—42no—
404Dic11—42no—
405Dic11—42no—
406Dic11—42no—
407C22×Q8—111no—
408C22×D4C22⋊D1111yescharacteristic
409C23×C4—221no—
410C23×C4C22×D1111yescharacteristic
411C23×C4C22×D1111yescharacteristic
412C2×M16—222no—
413C2×M16—222no—
414C2×M16—441no—
415C22×C8—111no—
416C22×C8—111no—
417C22×C8—111no—
418C22×C8—111no—
419C22×C8—222no—
420C22×C8—222no—
421C22×C8—441no—
422#126—228no—
423#125—114no—
424#125—228no—
425#125—222no—
426#123—228no—
427C22⋊Q8—114no—
428C22⋊Q8—114no—
429C22⋊Q8—222no—
430C22⋊Q8—222no—
431C4×Q8—114no—
432C4×Q8—222no—
433C4×D4C4×D1114yes—
434C4×D4D4414yes—
435#117—22no—
436#117—22no—
437#117—41no—
438#117—41no—
439#117—114no—
440#117—222no—
441#117—228no—
442C2×C4⋊C4—21no—
443C2×C4⋊C4—21no—
444C2×C4⋊C4—114no—
445C2×C4⋊C4—111no—
446C2×C4⋊C4—111no—
447C2×C4⋊C4—111no—
448C2×C4⋊C4—222no—
449C2×C4⋊C4—221no—
450C2×C4⋊C4—221no—
451C2×C4⋊C4—221no—
452C2×C4⋊C4—221no—
453C2×C4⋊C4—221no—
454C2×C4⋊C4—221no—
455C2×C4⋊C4C22⋊D1111yescharacteristic
456C2×C4⋊C4C22×D1111yescharacteristic
457C2×C4⋊C4C22×D1111yescharacteristic
458C2×C4⋊C4C22×D1111yescharacteristic
459C2×C4⋊C4C22×D1111yescharacteristic
460C2×C22⋊C4—21no—
461C2×C22⋊C4—21no—
462C2×C22⋊C4—21no—
463C2×C22⋊C4—21no—
464C2×C22⋊C4—221no—
465C2×C22⋊C4—221no—
466C2×C22⋊C4—221no—
467C2×C22⋊C4C22⋊D1111yescharacteristic
468C2×C22⋊C4C22⋊D1111yescharacteristic
469C2×C42—21no—
470C2×C42—21no—
471C2×C42—21no—
472C2×C42—221no—
473C2×C42—221no—
474C2×C42C22×D1111yescharacteristic
475C4⋊C8—222no—
476#103—222no—
477#103—222no—
478#103—441no—
479#103—441no—
480C22⋊C8—222no—
481C22⋊C8—222no—
482#97—222no—
483#95—21no—
484#95—21no—
485#95—21no—
486C2×C11—42no—
487C2×C11—42no—
488C2×C11#233911yescharacteristic
489C2×C11#289611yescharacteristic
490C2×C11#289811yescharacteristic
491C2×C11#331511yescharacteristic
492C2×C11#331711yescharacteristic
493C2×C11#334811yescharacteristic
494C2×C11#334911yescharacteristic
495C24C2×C22⋊D1111yescharacteristic
496C24C2×C22⋊D1111yescharacteristic
497C2×Q8—112no—
498C2×Q8—221no—
499C2×Q8—221no—
500C2×Q8—221no—
501C2×Q8—221no—
502C2×Q8—221no—
503C2×D4—41no—
504C2×D4—41no—
505C2×D4(C2×D11)⋊C414yes—
506C22×C4—21no—
507C22×C4—21no—
508C22×C4—21no—
509C22×C4—21no—
510C22×C4—21no—
511C22×C4—21no—
512C22×C4—21no—
513C22×C4—21no—
514C22×C4—21no—
515C22×C4—21no—
516C22×C4—21no—
517C22×C4—21no—
518C22×C4—224no—
519C22×C4—221no—
520C22×C4—221no—
521C22×C4—221no—
522C22×C4—221no—
523C22×C4—442no—
524C22×C4—442no—
525C22×C4C2×C4×D1112yes—
526C22×C4C2×C4×D1112yes—
527C22×C4C2×D4412yes—
528C22×C4C2×D4412yes—
529C22×C4C2×C22⋊D1111yescharacteristic
530C22×C4C2×C22⋊D1111yescharacteristic
531C22×C4C2×C22⋊D1111yescharacteristic
532C22×C4C2×C22⋊D1111yescharacteristic
533C22×C4C23×D1111yescharacteristic
534M16—444no—
535C2×C8—112no—
536C2×C8—221no—
537C2×C8—221no—
538C2×C8—221no—
539C2×C8—221no—
540C2×C8—221no—
541C2×C8—221no—
542C2×C8—221no—
543C2×C8—221no—
544C2×C8—221no—
545C2×C8—221no—
546C2×C8—221no—
547C2×C8—444no—
548C4⋊C4—21no—
549C4⋊C4—21no—
550C4⋊C4—21no—
551C4⋊C4—21no—
552C4⋊C4—21no—
553C4⋊C4—21no—
554C4⋊C4—21no—
555C4⋊C4—42no—
556C4⋊C4—81no—
557C4⋊C4—112no—
558C4⋊C4—112no—
559C4⋊C4—112no—
560C4⋊C4—224no—
561C4⋊C4—224no—
562C4⋊C4—224no—
563C4⋊C4—224no—
564C4⋊C4—224no—
565C4⋊C4—224no—
566C4⋊C4—221no—
567C4⋊C4—221no—
568C4⋊C4—221no—
569C4⋊C4(C2×D11)⋊C414yes—
570C4⋊C4#434112yes—
571C22⋊C4—42no—
572C22⋊C4—42no—
573C22⋊C4—81no—
574C22⋊C4—81no—
575C22⋊C4—224no—
576C22⋊C4—224no—
577C22⋊C4—224no—
578C22⋊C4(C2×D11)⋊C414yes—
579C22⋊C4(C2×D11)⋊C414yes—
580C42—42no—
581C42—42no—
582C42—42no—
583C42—224no—
584C42—224no—
585C42C2×C4×D1112yes—
586C42C2×D4412yes—
587C11#2249611yescharacteristic, complemented, Sylow
588C23—21no—
589C23—21no—
590C23—21no—
591C23—21no—
592C23—21no—
593C23—21no—
594C23—21no—
595C23—21no—
596C23—21no—
597C23—21no—
598C23—21no—
599C23—21no—
600C23C2×(C2×D11)⋊C412yes—
601C23C2×(C2×D11)⋊C412yes—
602C23C22×C22⋊D1111yescharacteristic
603Q8—222no—
604Q8—222no—
605Q8—441no—
606Q8—441no—
607D4—44no—
608C2×C4—21no—
609C2×C4—21no—
610C2×C4—21no—
611C2×C4—21no—
612C2×C4—21no—
613C2×C4—21no—
614C2×C4—21no—
615C2×C4—21no—
616C2×C4—22no—
617C2×C4—22no—
618C2×C4—22no—
619C2×C4—22no—
620C2×C4—22no—
621C2×C4—22no—
622C2×C4—22no—
623C2×C4—22no—
624C2×C4—22no—
625C2×C4—41no—
626C2×C4—41no—
627C2×C4—41no—
628C2×C4—41no—
629C2×C4—41no—
630C2×C4—41no—
631C2×C4—41no—
632C2×C4—41no—
633C2×C4—41no—
634C2×C4—41no—
635C2×C4—41no—
636C2×C4—222no—
637C2×C4—222no—
638C2×C4—222no—
639C2×C4—222no—
640C2×C4—448no—
641C2×C4—441no—
642C2×C4—441no—
643C2×C4—441no—
644C2×C4—441no—
645C2×C4—441no—
646C2×C4—441no—
647C2×C4—441no—
648C2×C4—441no—
649C2×C4C2×(C2×D11)⋊C412yes—
650C2×C4C2×(C2×D11)⋊C412yes—
651C2×C4C2×(C2×D11)⋊C412yes—
652C2×C4C2×(C2×D11)⋊C412yes—
653C2×C4C22×C4×D1111yescharacteristic
654C2×C4C22×D4411yescharacteristic
655C2×C4C2×#434111yescharacteristic
656C2×C4#6703711yescharacteristic
657C2×C4#41×D1111yescharacteristic
658C2×C4#6704311yescharacteristic
659C8—222no—
660C8—441no—
661C8—441no—
662C8—441no—
663C22—22no—
664C22—22no—
665C22—22no—
666C22—22no—
667C22—22no—
668C22—22no—
669C22—41no—
670C22—41no—
671C22—41no—
672C22—41no—
673C22—41no—
674C22—41no—
675C22—41no—
676C22—41no—
677C22C22×(C2×D11)⋊C411yescharacteristic
678C22#1062333711yescharacteristic
679C22#1062335311yescharacteristic
680C22#1062335311yescharacteristic
681C22#1062335511yescharacteristic
682C22#1062336711yescharacteristic
683C22#1062336911yescharacteristic
684C4—22no—
685C4—22no—
686C4—22no—
687C4—22no—
688C4—42no—
689C4—81no—
690C4—81no—
691C4—81no—
692C4—442no—
693C4—442no—
694C4—442no—
695C4—442no—
696C4C4×#434111yescharacteristic
697C4#1062307711yescharacteristic
698C4#1062308511yescharacteristic
699C4#1062308611yescharacteristic
700C2—42no—
701C2—42no—
702C2#1307144111yescharacteristic
703C2#1307713311yescharacteristic
704C2#1307714611yescharacteristic
705C2#1308071211yescharacteristic
706C2#1308074211yescharacteristic
707C2#1308113111yescharacteristic
708C2#1308114011yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#2354C2
socleC23×C11C22×D4
prime radicalC22×D4×C11D4
cosocleC22×C4×C11C24
hypercenter#2354D11
hypocenterC11#22496
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ #2354

Complements

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

NH ≅ G/Ntype
3. #13069584C2semidirect
4. #13069573C2semidirect
5. #13069047C2semidirect
6. #13069037C2semidirect
7. #13068928C2semidirect
8. #13068928C2semidirect
9. #13068708C2semidirect
10. #13068704C2semidirect
11. #13068618C2semidirect
12. #13068449C2semidirect
13. #13068337C2semidirect
14. #13068332C2semidirect
27. #10623072C4semidirect
587. C11#22496semidirect

Maximal subgroups

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

subgroupindex
C2×#106230722
C2×#106226242
#130695842
#130695732
#130690472
#130690372
#130689282
#130687082
#130687042
#130686182
#130684492
#130683372
#130683322
C11×#23542
#2249611