Finite Group Databasebeta

← #14770217

Subgroups — #14770217

Order 2816.

1154 conjugacy classes of subgroups.

The subgroup lattice has 722 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623166C211yesmaximal, characteristic
2C2×#10622741C211yesmaximal, characteristic
3#13071560C211yesmaximal, characteristic
4#13069575C211yesmaximal, characteristic, complemented
5#13069562C211yesmaximal, characteristic, complemented
6#13069046C211yesmaximal, characteristic, complemented
7#13068929C211yesmaximal, characteristic, complemented
8#13068925C211yesmaximal, characteristic, complemented
9#13068701C211yesmaximal, characteristic, complemented
10#13068700C211yesmaximal, characteristic, complemented
11#13068619C211yesmaximal, characteristic, complemented
12#103×Dic11C211yesmaximal, characteristic, complemented
13#13068336C211yesmaximal, characteristic, complemented
14#13068334C211yesmaximal, characteristic, complemented
15C11×#1894C211yesmaximal, characteristic, complemented
16C22×C11×M16C2211yescharacteristic
17C2×C11×C22⋊Q8C2211yescharacteristic
18C2×#66999C2211yescharacteristic
19C2×Q8×Dic11C2211yescharacteristic
20C2×C4×C22⋊D11C2211yescharacteristic
21C2×#66979C2211yescharacteristic
22C22×C4⋊Dic11C2211yescharacteristic
23C22×#4313C2211yescharacteristic
24#10623166—24no—
25#10623166C418yescomplemented
26C2×#66950—21no—
27C2×#66945C2211yescharacteristic
28C2×C4⋊C4×D11C2211yescharacteristic
29C2×#66942—21no—
30C2×#66941C2211yescharacteristic
31C2×(C22⋊D11)⋊C4—21no—
32C2×#66931—21no—
33C2×C11×#103C2211yescharacteristic
34C2×C11×#103C2211yescharacteristic
35C11×#380C2211yescharacteristic
36C2×#66899C2211yescharacteristic
37C2×#66899C2211yescharacteristic
38C2×C22⋊(C11⋊C8)C2211yescharacteristic
39#10622741—24no—
40C2×(C2×D11)⋊C8C2211yescharacteristic
41C2×Dic11⋊C8C2211yescharacteristic
42C2×C8×Dic11C2211yescharacteristic
43#10622600C2211yescharacteristic
44#10622589C2211yescharacteristic
45C4⋊C4×Dic11C2211yescharacteristic
46#10622570—21no—
47#10622558—21no—
48#10622282—21no—
49#10622262—21no—
50C11×#340C2211yescharacteristic
51C11×#340C2211yescharacteristic
52#10622189C2211yescharacteristic
53#10622189C2211yescharacteristic
54#10622189C2211yescharacteristic
55#10622189C2211yescharacteristic
56#10622167C2211yescharacteristic
57#10622167C2211yescharacteristic
58#10622167C2211yescharacteristic
59#10622167C2211yescharacteristic
60#10622167C2211yescharacteristic
61#10622167C2211yescharacteristic
62C22×Q8×C11C2311yescharacteristic
63C23×C4×C11C2311yescharacteristic
64C22×C22⋊D11D411yescharacteristic
65C23×Dic11—21no—
66C22×C4×D11—21no—
67C22×C4×D11C2311yescharacteristic
68C22×Dic22—21no—
69C2×C11×M16—22no—
70C2×C11×M16—22no—
71C2×C11×M16—41no—
72C22×C8×C11C2311yescharacteristic
73C22×C8×C11C2311yescharacteristic
74C11×C22⋊Q8—22no—
75C11×C22⋊Q8C2×C414yes—
76C2×C11×C4⋊C4—21no—
77C2×C11×C4⋊C4C2311yescharacteristic
78C2×C11×C4⋊C4C2311yescharacteristic
79C2×C11×C4⋊C4C2311yescharacteristic
80C2×C11×C22⋊C4—21no—
81C2×C11×C22⋊C4—21no—
82C2×C22⋊Dic11—21no—
83C2×C22⋊Dic11D411yescharacteristic
84#66999—22no—
85#66999C2×C414yes—
86Q8×Dic11—22no—
87Q8×Dic11C2×C414yes—
88C4×C22⋊D11C2×C414yes—
89C4×C22⋊D11D414yes—
90C2×(C2×D11)⋊C4—21no—
91C2×(C2×D11)⋊C4—21no—
92C2×(C2×D11)⋊C4—21no—
93C2×(C2×D11)⋊C4D411yescharacteristic
94#66979—22no—
95#66979—41no—
96C2×C4⋊Dic11—21no—
97C2×C4⋊Dic11—22no—
98C2×C4⋊Dic11—21no—
99C2×C4⋊Dic11C2×C414yes—
100C2×C4⋊Dic11C2311yescharacteristic
101C2×C4⋊Dic11C2311yescharacteristic
102C2×C4⋊Dic11C2311yescharacteristic
103C2×C4⋊Dic11C2311yescharacteristic
104C2×Dic11⋊C4—21no—
105C2×Dic11⋊C4—21no—
106C2×Dic11⋊C4—21no—
107C2×Dic11⋊C4—21no—
108C2×Dic11⋊C4—21no—
109C2×Dic11⋊C4D411yescharacteristic
110C2×C4×Dic11—21no—
111C2×C4×Dic11—21no—
112C2×C4×Dic11—21no—
113C2×C4×Dic11—21no—
114C2×C4×Dic11C2311yescharacteristic
115C22×C11⋊C8C2311yescharacteristic
116C22×C11⋊C8C2311yescharacteristic
117C2×#4313—22no—
118C2×#4313—22no—
119C2×#4313—41no—
120#66950—28no—
121#66945—22no—
122#66945—41no—
123C4⋊C4×D11—22no—
124C4⋊C4×D11C2×C414yes—
125#66942—28no—
126#66941—22no—
127#66941C2×C414yes—
128(C22⋊D11)⋊C4—28no—
129#66931—28no—
130C11×#103—22no—
131C11×#103—41no—
132C11×#95—21no—
133#66899—22no—
134#66899—41no—
135C11⋊#95—21no—
136C11⋊#95—21no—
137C22⋊(C11⋊C8)—22no—
138(C2×D11)⋊C8—22no—
139Dic11⋊C8—22no—
140C8×Dic11—22no—
141#22502—111nomaximal, Sylow
142C24×C11C2×D411yescharacteristic
143C23×D11C2×D411yescharacteristic
144C2×Q8×C11—21no—
145C2×Q8×C11—21no—
146C2×Q8×C11—21no—
147C2×Q8×C11—21no—
148C2×Q8×C11—21no—
149C2×Q8×C11C22×C412yes—
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×C11C22×C412yes—
159C22×C4×C11C2×D411yescharacteristic
160C22×C4×C11C2×D412yes—
161C22×C4×C11C2411yescharacteristic
162C2×C22⋊D11—22no—
163C2×C22⋊D11—22no—
164C2×C22⋊D11C22⋊C414yes—
165C22×Dic11—24no—
166C22×Dic11—21no—
167C22×Dic11—21no—
168C22×Dic11—21no—
169C22×Dic11—21no—
170C22×Dic11—81no—
171C22×Dic11—81no—
172C22×Dic11C2×D411yescharacteristic
173C22×Dic11C2×D411yescharacteristic
174C22×Dic11C2×D411yescharacteristic
175C2×C4×D11—24no—
176C2×C4×D11—21no—
177C2×C4×D11—21no—
178C2×C4×D11—21no—
179C2×C4×D11—21no—
180C2×C4×D11—81no—
181C2×C4×D11—81no—
182C2×C4×D11C22×C412yes—
183C2×C4×D11C2×D412yes—
184C2×Dic22—24no—
185C2×Dic22—81no—
186C2×Dic22—81no—
187C11×M16—44no—
188C2×C8×C11—21no—
189C2×C8×C11—21no—
190C2×C8×C11—21no—
191C2×C8×C11—21no—
192C2×C8×C11—21no—
193C2×C8×C11#4112yes—
194C11×C4⋊C4—24no—
195C11×C4⋊C4—21no—
196C11×C4⋊C4—21no—
197C11×C4⋊C4—21no—
198C11×C4⋊C4—21no—
199C11×C4⋊C4—21no—
200C11×C4⋊C4C22×C412yes—
201C11×C22⋊C4—24no—
202C11×C22⋊C4—81no—
203C22⋊Dic11—42no—
204C22⋊Dic11C22⋊C414yes—
205(C2×D11)⋊C4—24no—
206(C2×D11)⋊C4—42no—
207(C2×D11)⋊C4—81no—
208(C2×D11)⋊C4C22⋊C414yes—
209C4⋊Dic11—24no—
210C4⋊Dic11—24no—
211C4⋊Dic11—21no—
212C4⋊Dic11—21no—
213C4⋊Dic11—21no—
214C4⋊Dic11—21no—
215C4⋊Dic11—21no—
216C4⋊Dic11C22×C412yes—
217C4⋊Dic11C22×C412yes—
218C4⋊Dic11#4112yes—
219Dic11⋊C4—24no—
220Dic11⋊C4—24no—
221Dic11⋊C4—24no—
222Dic11⋊C4—42no—
223Dic11⋊C4—81no—
224Dic11⋊C4C22⋊C414yes—
225C4×Dic11—24no—
226C4×Dic11—42no—
227C4×Dic11—42no—
228C4×Dic11—42no—
229C4×Dic11C22×C412yes—
230C4×Dic11C2×D412yes—
231C2×C11⋊C8—21no—
232C2×C11⋊C8—21no—
233C2×C11⋊C8—21no—
234C2×C11⋊C8—21no—
235C2×C11⋊C8—21no—
236C2×C11⋊C8—21no—
237#4313—44no—
238C2×#554—111no—
239C2×#436—111no—
240#2354—111no—
241#1990—111no—
242#1987—111no—
243#1894—111no—
244#1894D1111yescharacteristic, complemented
245#1873—111no—
246#1873—111no—
247#1823—111no—
248#1823—111no—
249#1803—111no—
250C4×#103—111no—
251#1736—111no—
252#1736—111no—
253C23×C11—21no—
254C23×C11—21no—
255C23×C11—21no—
256C23×C11—21no—
257C23×C11—21no—
258C23×C11—21no—
259C23×C11C2×C22⋊C412yes—
260C23×C11C22×D411yescharacteristic
261C22×D11—21no—
262C22×D11—21no—
263C22×D11—21no—
264C22×D11—21no—
265C22×D11—21no—
266C22×D11—21no—
267C22×D11C2×C22⋊C412yes—
268Q8×C11—22no—
269Q8×C11—22no—
270Q8×C11—41no—
271Q8×C11—41no—
272C2×C4×C11—21no—
273C2×C4×C11—21no—
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—41no—
281C2×C4×C11—41no—
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×C11C2×C22⋊C412yes—
291C2×C4×C11C23×C411yescharacteristic
292C2×C4×C11C22×D411yescharacteristic
293C2×C4×C11C2×#4111yescharacteristic
294C2×C4×C11C2×#4111yescharacteristic
295C2×C4×C11H(5,𝔽2)11yescharacteristic
296C2×C4×C112−1+411yescharacteristic
297C22⋊D11—28no—
298C2×Dic11—21no—
299C2×Dic11—21no—
300C2×Dic11—21no—
301C2×Dic11—21no—
302C2×Dic11—22no—
303C2×Dic11—22no—
304C2×Dic11—22no—
305C2×Dic11—41no—
306C2×Dic11—41no—
307C2×Dic11—41no—
308C2×Dic11—41no—
309C2×Dic11—41no—
310C2×Dic11—41no—
311C2×Dic11—41no—
312C2×Dic11—41no—
313C2×Dic11—41no—
314C2×Dic11—84no—
315C2×Dic11C2×C22⋊C412yes—
316C2×Dic11C2×C22⋊C412yes—
317C2×Dic11C2×C22⋊C412yes—
318C2×Dic11#13712yes—
319C2×Dic11#13712yes—
320C4×D11—22no—
321C4×D11—22no—
322C4×D11—22no—
323C4×D11—22no—
324C4×D11—84no—
325Dic22—84no—
326C8×C11—22no—
327C8×C11—41no—
328C11⋊C8—41no—
329C11⋊C8—41no—
330C22×M16—111no—
331C22×M16C2×D1111yescharacteristic
332#554—118no—
333#554—224no—
334C2×C4⋊Q8—111no—
335C2×#125—221no—
336C2×C22⋊Q8—111no—
337C2×C22⋊Q8—221no—
338C2×C22⋊Q8—221no—
339C2×C22⋊Q8C2×D1111yescharacteristic
340C2×C4×Q8—111no—
341C2×C4×D4—111no—
342C2×C4×D4—221no—
343C2×#117—111no—
344C2×#117—111no—
345C22×C4⋊C4—111no—
346C22×C4⋊C4—111no—
347#436—224no—
348C2×C4⋊C8—111no—
349C2×#103—111no—
350C2×#103—111no—
351C2×#103C2×D1111yescharacteristic
352C2×#103C2×D1111yescharacteristic
353C2×C22⋊C8—111no—
354C2×C22⋊C8—111no—
355C2×C4×C8—111no—
356#390—221no—
357#388—221no—
358#388—221no—
359#384—111no—
360#380—111no—
361#380C2×D1111yescharacteristic
362C4×C4⋊C4—111no—
363C4×C4⋊C4—221no—
364#340—111no—
365#340—111no—
366#340—111no—
367#340—111no—
368#340—111no—
369#340—111no—
370#340—111no—
371#340—111no—
372#340—111no—
373#340—111no—
374#340C2×D1111yescharacteristic
375#340C2×D1111yescharacteristic
376C22×C11—22no—
377C22×C11—22no—
378C22×C11—22no—
379C22×C11—41no—
380C22×C11—41no—
381C22×C11—41no—
382C22×C11—41no—
383C22×C11C22×C22⋊C411yescharacteristic
384C22×C11#54611yescharacteristic
385C22×C11#54711yescharacteristic
386C22×C11C2×#13711yescharacteristic
387C22×C11C2×#13711yescharacteristic
388C22×C11#57611yescharacteristic
389C22×C11#57711yescharacteristic
390C2×D11—22no—
391C2×D11—22no—
392C2×D11—22no—
393C2×D11—41no—
394C2×D11—41no—
395C2×D11—41no—
396C2×D11—41no—
397C4×C11—22no—
398C4×C11—42no—
399C4×C11—42no—
400C4×C11—81no—
401C4×C11—81no—
402C4×C11C4×#4111yescharacteristic
403C4×C11#52011yescharacteristic
404C4×C11#54611yescharacteristic
405C4×C11#54711yescharacteristic
406Dic11—22no—
407Dic11—22no—
408Dic11—42no—
409Dic11—42no—
410Dic11—42no—
411Dic11—81no—
412Dic11#41914yes—
413C22×Q8—221no—
414C22×Q8C22×D1111yescharacteristic
415C22×D4—111no—
416C23×C4—111no—
417C23×C4—221no—
418C23×C4—221no—
419C23×C4C22×D1111yescharacteristic
420C2×M16—22no—
421C2×M16—22no—
422C2×M16—41no—
423C2×M16—222no—
424C2×M16—222no—
425C2×M16—441no—
426C22×C8—111no—
427C22×C8—111no—
428C22×C8C22×D1111yescharacteristic
429C22×C8C22×D1111yescharacteristic
430C4⋊Q8—114no—
431C4⋊Q8—222no—
432#125—228no—
433C22⋊Q8—22no—
434C22⋊Q8—114no—
435C22⋊Q8—228no—
436C22⋊Q8—228no—
437C22⋊Q8—222no—
438C22⋊Q8C4×D1114yes—
439C4×Q8—114no—
440C4×Q8—222no—
441C4×D4—114no—
442C4×D4—114no—
443C4×D4—228no—
444#117—222no—
445#117—222no—
446#117—441no—
447#117—441no—
448C2×C4⋊C4—21no—
449C2×C4⋊C4—111no—
450C2×C4⋊C4—114no—
451C2×C4⋊C4—111no—
452C2×C4⋊C4—111no—
453C2×C4⋊C4—111no—
454C2×C4⋊C4—114no—
455C2×C4⋊C4—111no—
456C2×C4⋊C4—222no—
457C2×C4⋊C4—221no—
458C2×C4⋊C4—221no—
459C2×C4⋊C4—221no—
460C2×C4⋊C4—221no—
461C2×C4⋊C4—221no—
462C2×C4⋊C4—222no—
463C2×C4⋊C4—221no—
464C2×C4⋊C4—221no—
465C2×C4⋊C4C22×D1111yescharacteristic
466C2×C4⋊C4C22×D1111yescharacteristic
467C2×C4⋊C4C22×D1111yescharacteristic
468C2×C22⋊C4—21no—
469C2×C22⋊C4—21no—
470C2×C22⋊C4—111no—
471C2×C22⋊C4—111no—
472C2×C22⋊C4—221no—
473C2×C22⋊C4—221no—
474C2×C22⋊C4—221no—
475C2×C22⋊C4—221no—
476C2×C42—111no—
477C2×C42—221no—
478C2×C42—221no—
479C2×C42—221no—
480C2×C42—221no—
481C4⋊C8—222no—
482#103—22no—
483#103—41no—
484#103—222no—
485#103—441no—
486C22⋊C8—222no—
487C22⋊C8—222no—
488C4×C8—222no—
489#95—21no—
490#95—221no—
491#95—221no—
492C2×C11—42no—
493C2×C11#233911yescharacteristic
494C2×C11C2×#41911yescharacteristic
495C2×C11#289711yescharacteristic
496C2×C11#333111yescharacteristic
497C2×C11#333311yescharacteristic
498C2×C11#335611yescharacteristic
499C2×C11#335711yescharacteristic
500D11—42no—
501C24—111no—
502C24D4×D1111yescharacteristic
503C2×Q8—21no—
504C2×Q8—21no—
505C2×Q8—21no—
506C2×Q8—21no—
507C2×Q8—21no—
508C2×Q8—224no—
509C2×Q8—881no—
510C2×Q8—881no—
511C2×Q8C2×C4×D1112yes—
512C2×D4—114no—
513C2×D4—222no—
514C2×D4—222no—
515C22×C4—21no—
516C22×C4—21no—
517C22×C4—21no—
518C22×C4—21no—
519C22×C4—21no—
520C22×C4—21no—
521C22×C4—21no—
522C22×C4—21no—
523C22×C4—111no—
524C22×C4—111no—
525C22×C4—111no—
526C22×C4—112no—
527C22×C4—112no—
528C22×C4—224no—
529C22×C4—221no—
530C22×C4—221no—
531C22×C4—221no—
532C22×C4—221no—
533C22×C4—221no—
534C22×C4—221no—
535C22×C4—221no—
536C22×C4—224no—
537C22×C4—221no—
538C22×C4—881no—
539C22×C4—881no—
540C22×C4—881no—
541C22×C4—881no—
542C22×C4C2×C4×D1112yes—
543C22×C4D4×D1111yescharacteristic
544C22×C4D4×D1112yes—
545C22×C4C23×D1111yescharacteristic
546M16—44no—
547M16—444no—
548C2×C8—21no—
549C2×C8—21no—
550C2×C8—21no—
551C2×C8—21no—
552C2×C8—21no—
553C2×C8—221no—
554C2×C8—221no—
555C2×C8—221no—
556C2×C8—221no—
557C2×C8—221no—
558C2×C8—221no—
559C2×C8#434112yes—
560C4⋊C4—24no—
561C4⋊C4—21no—
562C4⋊C4—21no—
563C4⋊C4—21no—
564C4⋊C4—21no—
565C4⋊C4—21no—
566C4⋊C4—114no—
567C4⋊C4—112no—
568C4⋊C4—112no—
569C4⋊C4—112no—
570C4⋊C4—224no—
571C4⋊C4—224no—
572C4⋊C4—224no—
573C4⋊C4—224no—
574C4⋊C4—224no—
575C4⋊C4—221no—
576C4⋊C4—221no—
577C4⋊C4—221no—
578C4⋊C4—221no—
579C4⋊C4—221no—
580C4⋊C4—442no—
581C4⋊C4—881no—
582C4⋊C4C2×C4×D1112yes—
583C22⋊C4—24no—
584C22⋊C4—81no—
585C22⋊C4—114no—
586C22⋊C4—114no—
587C22⋊C4—224no—
588C22⋊C4—442no—
589C22⋊C4—442no—
590C22⋊C4—881no—
591C42—112no—
592C42—112no—
593C42—224no—
594C42—442no—
595C42—442no—
596C42—442no—
597C11#2250211yescharacteristic, complemented, Sylow
598C23—21no—
599C23—21no—
600C23—21no—
601C23—21no—
602C23—21no—
603C23—21no—
604C23—112no—
605C23—221no—
606C23—221no—
607C23—221no—
608C23—221no—
609C23—221no—
610C23—221no—
611C23C22⋊C4×D1112yes—
612C23C2×D4×D1111yescharacteristic
613Q8—22no—
614Q8—22no—
615Q8—41no—
616Q8—41no—
617Q8—884no—
618D4—228no—
619C2×C4—21no—
620C2×C4—21no—
621C2×C4—22no—
622C2×C4—22no—
623C2×C4—22no—
624C2×C4—22no—
625C2×C4—22no—
626C2×C4—22no—
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—41no—
637C2×C4—112no—
638C2×C4—112no—
639C2×C4—112no—
640C2×C4—112no—
641C2×C4—112no—
642C2×C4—221no—
643C2×C4—221no—
644C2×C4—221no—
645C2×C4—221no—
646C2×C4—222no—
647C2×C4—222no—
648C2×C4—222no—
649C2×C4—222no—
650C2×C4—222no—
651C2×C4—222no—
652C2×C4—222no—
653C2×C4—441no—
654C2×C4—441no—
655C2×C4—441no—
656C2×C4—441no—
657C2×C4—441no—
658C2×C4—441no—
659C2×C4—441no—
660C2×C4—441no—
661C2×C4—441no—
662C2×C4—884no—
663C2×C4—884no—
664C2×C4C22⋊C4×D1112yes—
665C2×C4C22×C4×D1111yescharacteristic
666C2×C4C2×D4×D1111yescharacteristic
667C2×C4C2×#434111yescharacteristic
668C2×C4#6703711yescharacteristic
669C2×C4#41×D1111yescharacteristic
670C2×C4#6704311yescharacteristic
671C8—22no—
672C8—41no—
673C8—441no—
674C8—441no—
675C22—22no—
676C22—22no—
677C22—22no—
678C22—41no—
679C22—41no—
680C22—41no—
681C22—41no—
682C22—222no—
683C22—222no—
684C22—222no—
685C22—441no—
686C22—441no—
687C22—441no—
688C22—441no—
689C22C2×C22⋊C4×D1111yescharacteristic
690C22#1062314111yescharacteristic
691C22#1062314211yescharacteristic
692C22#1062330511yescharacteristic
693C22D11×#13711yescharacteristic
694C22D11×#13711yescharacteristic
695C22#1062330911yescharacteristic
696C4—22no—
697C4—42no—
698C4—42no—
699C4—81no—
700C4—81no—
701C4—114no—
702C4—222no—
703C4—222no—
704C4—442no—
705C4—442no—
706C4—442no—
707C4—881no—
708C4C4×#434111yescharacteristic
709C4#1062307711yescharacteristic
710C4#1062312211yescharacteristic
711C4#1062318611yescharacteristic
712C2—42no—
713C2—442no—
714C2#1307144211yescharacteristic
715C2D11×#41911yescharacteristic
716C2#1307714011yescharacteristic
717C2#1308092711yescharacteristic
718C2#1308094911yescharacteristic
719C2#1308122611yescharacteristic
720C2#1308123711yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1894C2
socleC23×C11C22×D4
prime radicalC22×C22⋊D11D4
cosocleC22×C4×C11C24
hypercenter#1894D11
hypocenterC11#22502
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1894

Complements

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

NH ≅ G/Ntype
4. #13069575C2semidirect
5. #13069562C2semidirect
6. #13069046C2semidirect
7. #13068929C2semidirect
8. #13068925C2semidirect
9. #13068701C2semidirect
10. #13068700C2semidirect
11. #13068619C2semidirect
12. #103×Dic11C2semidirect
13. #13068336C2semidirect
14. #13068334C2semidirect
15. C11×#1894C2semidirect
25. #10623166C4semidirect
244. #1894D11semidirect
597. C11#22502semidirect

Maximal subgroups

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

subgroupindex
C2×#106231662
C2×#106227412
#130715602
#130695752
#130695622
#130690462
#130689292
#130689252
#130687012
#130687002
#130686192
#103×Dic112
#130683362
#130683342
C11×#18942
#2250211