Finite Group Databasebeta

← #14775414

Subgroups — #14775414

Order 2816.

768 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
1#13077343C211yesmaximal, characteristic
2#13077274C211yesmaximal, characteristic, complemented
3#13069370C211yesmaximal, characteristic, complemented
4#13069329C211yesmaximal, characteristic, complemented
5#13069266C211yesmaximal, characteristic, complemented
6#13069217C211yesmaximal, characteristic, complemented
7#13069217C211yesmaximal, characteristic, complemented
8#13069060C211yesmaximal, characteristic
9#13068893C211yesmaximal, characteristic, complemented
10#13068823C211yesmaximal, characteristic, complemented
11#13068502C211yesmaximal, characteristic, complemented
12#13068463C211yesmaximal, characteristic, complemented
13#13068380C211yesmaximal, characteristic, complemented
14C2×#10622170C211yesmaximal, characteristic, complemented
15C11×#3091C211yesmaximal, characteristic
16C11×#525C2211yescharacteristic
17C2×C11×#117C2211yescharacteristic
18C2×#67001C2211yescharacteristic
19C22×C4×Dic11C2211yescharacteristic
20C22×#4318C2211yescharacteristic
21C11×#485C411yescharacteristic, complemented
22C11×#485C411yescharacteristic, complemented
23C11×#484C411yescharacteristic, complemented
24C11×#483C411yescharacteristic, complemented
25C11×#482C411yescharacteristic, complemented
26C11×#482C411yescharacteristic, complemented
27C11×#481C411yescharacteristic, complemented
28C11×#480C411yescharacteristic, complemented
29C11×#427C2211yescharacteristic
30C11×#427C2211yescharacteristic
31C11×#416C2211yescharacteristic
32C11×#416C2211yescharacteristic
33C2×C11×C22⋊C8C2211yescharacteristic
34C2×#66901C2211yescharacteristic
35C2×#66901C2211yescharacteristic
36#10622847C2211yescharacteristic
37#10622820C2211yescharacteristic
38C2×C22⋊(C11⋊C8)C2211yescharacteristic
39C2×#66883C2211yescharacteristic
40C2×#66883C2211yescharacteristic
41C2×#66879C2211yescharacteristic
42C2×#66879C2211yescharacteristic
43#10622625—21no—
44#10622624—21no—
45#10622624—21no—
46D4×C11⋊C8—21no—
47#10622613—21no—
48#10622613—21no—
49#10622612C2211yescharacteristic
50#10622612C2211yescharacteristic
51#10622612C2211yescharacteristic
52#10622610C2211yescharacteristic
53#10622610C2211yescharacteristic
54#10622610C2211yescharacteristic
55#10622539—21no—
56#10622538—21no—
57#10622190C2211yescharacteristic
58#10622190C2211yescharacteristic
59#10622188C2211yescharacteristic
60#10622188C2211yescharacteristic
61#10622170C2211yescharacteristic
62#10622170C2211yescharacteristic
63#10622170C2211yescharacteristic
64#10622170C2211yescharacteristic
65#10622170C2211yescharacteristic
66#10622170C2211yescharacteristic
67C2×C11×#41C2311yescharacteristic
68C23×C4×C11C2311yescharacteristic
69C23×Dic11—21no—
70C22×C8×C11C2311yescharacteristic
71C22×C8×C11C2311yescharacteristic
72C11×#123—21no—
73C11×C22⋊Q8C2×C411yescharacteristic
74C11×C22⋊Q8C2×C411yescharacteristic
75C11×#121C2×C411yescharacteristic
76C11×#121C2×C411yescharacteristic
77C11×#120—21no—
78C4×D4×C11—21no—
79C4×D4×C11—21no—
80C11×#117—21no—
81C11×#117—21no—
82C11×#117C2×C411yescharacteristic
83C11×#117C2×C411yescharacteristic
84C11×#117C2311yescharacteristic
85C11×#117C2311yescharacteristic
86C11×#117C2311yescharacteristic
87C2×C11×C4⋊C4C2×C411yescharacteristic
88C2×C11×C4⋊C4C2×C411yescharacteristic
89C2×C11×C22⋊C4—21no—
90C2×C42×C11—21no—
91#67001—22no—
92#67001—41no—
93C2×C4×Dic11—22no—
94C2×C4×Dic11—21no—
95C2×C4×Dic11—41no—
96C2×C4×Dic11C2311yescharacteristic
97C2×C4×Dic11C2311yescharacteristic
98C2×#4318—21no—
99C2×#4318—21no—
100C2×#4318—22no—
101C2×#4318—41no—
102C2×#4318C2311yescharacteristic
103C2×#4318C2311yescharacteristic
104C2×#4318C2311yescharacteristic
105C2×#4318C2311yescharacteristic
106C22×C11⋊C8—21no—
107C22×C11⋊C8—21no—
108C22×C11⋊C8C2311yescharacteristic
109C22×C11⋊C8C2311yescharacteristic
110C11×#107C2×C411yescharacteristic, complemented
111C11×#107C2×C411yescharacteristic, complemented
112C11×#107C2×C411yescharacteristic, complemented
113C11×#107C2×C411yescharacteristic, complemented
114C11×#106C2×C411yescharacteristic, complemented
115C11×#106C2×C411yescharacteristic, complemented
116C11×#106C2×C411yescharacteristic, complemented
117C11×#106C2×C411yescharacteristic, complemented
118C11×#103C2×C411yescharacteristic, complemented
119C11×#103C2×C411yescharacteristic, complemented
120C11×#103C2×C411yescharacteristic, complemented
121C11×#103C2×C411yescharacteristic, complemented
122C11×#102C2×C411yescharacteristic, complemented
123C11×#102C2×C411yescharacteristic, complemented
124C11×#102C2×C411yescharacteristic, complemented
125C11×#102C2×C411yescharacteristic, complemented
126C11×C22⋊C8C2×C411yescharacteristic
127C11×C22⋊C8C2×C411yescharacteristic
128C11×C22⋊C8C2×C411yescharacteristic
129C11×C22⋊C8C2×C411yescharacteristic
130#66901—22no—
131#66901—41no—
132C22⋊(C11⋊C8)—21no—
133C22⋊(C11⋊C8)—21no—
134C22⋊(C11⋊C8)—21no—
135C22⋊(C11⋊C8)—21no—
136C22⋊(C11⋊C8)D411yescharacteristic
137C22⋊(C11⋊C8)D411yescharacteristic
138C22⋊(C11⋊C8)D411yescharacteristic
139C22⋊(C11⋊C8)D411yescharacteristic
140#66883—22no—
141#66883—41no—
142#66879—22no—
143#66879—41no—
144C4⋊(C11⋊C8)—21no—
145C4⋊(C11⋊C8)—21no—
146C4⋊(C11⋊C8)—21no—
147C4⋊(C11⋊C8)—21no—
148C4⋊(C11⋊C8)—21no—
149C4⋊(C11⋊C8)—21no—
150#66867—21no—
151#66867—21no—
152#66867—21no—
153C4×C11⋊C8—21no—
154C4×C11⋊C8—21no—
155C4×C11⋊C8—21no—
156#22950—111nomaximal, Sylow
157C24×C11#4111yescharacteristic
158C11×#41—21no—
159C11×#41—21no—
160C11×#41—21no—
161C11×#41—21no—
162C2×Q8×C11C22×C411yescharacteristic
163C2×D4×C11—21no—
164C2×D4×C11—21no—
165C2×D4×C11—21no—
166C2×D4×C11C22×C411yescharacteristic
167C22×C4×C11—21no—
168C22×C4×C11—21no—
169C22×C4×C11—21no—
170C22×C4×C11—21no—
171C22×C4×C11—21no—
172C22×C4×C11—21no—
173C22×C4×C11—21no—
174C22×C4×C11C22×C411yescharacteristic
175C22×C4×C11C22×C411yescharacteristic
176C22×C4×C11C2×D411yescharacteristic
177C22×C4×C11C2×D411yescharacteristic
178C22×C4×C11#4111yescharacteristic
179C22×C4×C11C2411yescharacteristic
180C22×Dic11—21no—
181C22×Dic11—21no—
182C22×Dic11—42no—
183C22×Dic11—42no—
184C22×Dic11—42no—
185C2×C8×C11—21no—
186C2×C8×C11—21no—
187C2×C8×C11—21no—
188C2×C8×C11—21no—
189C2×C8×C11C22×C411yescharacteristic
190C2×C8×C11C22×C411yescharacteristic
191C2×C8×C11C22×C411yescharacteristic
192C2×C8×C11C22×C411yescharacteristic
193C11×C4⋊C4—21no—
194C11×C4⋊C4—21no—
195C11×C4⋊C4—21no—
196C11×C4⋊C4—21no—
197C11×C4⋊C4C22×C411yescharacteristic
198C11×C4⋊C4C22×C411yescharacteristic
199C11×C4⋊C4C22×C411yescharacteristic
200C11×C4⋊C4C22×C411yescharacteristic
201C11×C4⋊C4C22×C411yescharacteristic
202C11×C4⋊C4C22×C411yescharacteristic
203C11×C22⋊C4—21no—
204C11×C22⋊C4—21no—
205C11×C22⋊C4—21no—
206C11×C22⋊C4—21no—
207C11×C22⋊C4—21no—
208C11×C22⋊C4—21no—
209C11×C22⋊C4—21no—
210C11×C22⋊C4—21no—
211C11×C22⋊C4—21no—
212C42×C11—21no—
213C42×C11—21no—
214C42×C11—21no—
215C42×C11—21no—
216C42×C11—21no—
217C4×Dic11—21no—
218C4×Dic11—21no—
219C4×Dic11—21no—
220C4×Dic11—42no—
221C4×Dic11#4112yes—
222#4318—21no—
223#4318—21no—
224#4318—21no—
225#4318—21no—
226#4318—21no—
227#4318—21no—
228#4318—21no—
229#4318—42no—
230#4318—42no—
231#4318#4112yes—
232C2×C11⋊C8—21no—
233C2×C11⋊C8—21no—
234C2×C11⋊C8—21no—
235C2×C11⋊C8—21no—
236C2×C11⋊C8—21no—
237C2×C11⋊C8—21no—
238C2×C11⋊C8—21no—
239C2×C11⋊C8—21no—
240C2×C11⋊C8—42no—
241C2×C11⋊C8—42no—
242C2×C11⋊C8C2×D411yescharacteristic
243C2×C11⋊C8C2×D411yescharacteristic
244C2×C11⋊C8C2×D411yescharacteristic
245C2×C11⋊C8C2×D411yescharacteristic
246#3091D1111yescharacteristic
247#2933—111no—
248#2924—111no—
249#1946—111no—
250#1938—111no—
251#1929—111no—
252#1922—111no—
253#1922—111no—
254#1896—111no—
255#1866—111no—
256#1855—111no—
257#1773—111no—
258#1765—111no—
259#1749—111no—
260C2×#339—111no—
261C23×C11—21no—
262C23×C11—21no—
263C23×C11—22no—
264C23×C11—21no—
265C23×C11—41no—
266C23×C11C4×D411yescharacteristic
267C23×C11C4×D411yescharacteristic
268C23×C11C2×#4111yescharacteristic
269Q8×C11—21no—
270Q8×C11—21no—
271D4×C11—21no—
272D4×C11—21no—
273D4×C11—41no—
274D4×C11—41no—
275D4×C11—42no—
276D4×C11—81no—
277C2×C4×C11—21no—
278C2×C4×C11—21no—
279C2×C4×C11—21no—
280C2×C4×C11—21no—
281C2×C4×C11—21no—
282C2×C4×C11—21no—
283C2×C4×C11—21no—
284C2×C4×C11—21no—
285C2×C4×C11—21no—
286C2×C4×C11—21no—
287C2×C4×C11—21no—
288C2×C4×C11—21no—
289C2×C4×C11—21no—
290C2×C4×C11—21no—
291C2×C4×C11—21no—
292C2×C4×C11—21no—
293C2×C4×C11—21no—
294C2×C4×C11—42no—
295C2×C4×C11—41no—
296C2×C4×C11—41no—
297C2×C4×C11—81no—
298C2×C4×C11C4×D411yescharacteristic
299C2×C4×C11C4×D411yescharacteristic
300C2×C4×C11C23×C411yescharacteristic
301C2×C4×C11C22×D411yescharacteristic
302C2×C4×C11C2×#4111yescharacteristic
303C2×C4×C11C2×#4111yescharacteristic
304C2×C4×C11H(5,𝔽2)11yescharacteristic
305C2×C4×C112−1+411yescharacteristic
306C2×Dic11—22no—
307C2×Dic11—22no—
308C2×Dic11—41no—
309C2×Dic11—41no—
310C2×Dic11—41no—
311C2×Dic11—48no—
312C2×Dic11—41no—
313C8×C11—21no—
314C8×C11—21no—
315C8×C11—21no—
316C8×C11—21no—
317C11⋊C8—21no—
318C11⋊C8—21no—
319C11⋊C8—22no—
320C11⋊C8—21no—
321C11⋊C8—21no—
322C11⋊C8—41no—
323C11⋊C8—41no—
324C11⋊C8—41no—
325C2×#131—111no—
326C22×M16—111no—
327#525C2×D1111yescharacteristic
328C2×#117C2×D1111yescharacteristic
329C22×C42—111no—
330#485Dic1111yescharacteristic, complemented
331#485Dic1111yescharacteristic, complemented
332#484Dic1111yescharacteristic, complemented
333#483Dic1111yescharacteristic, complemented
334#482Dic1111yescharacteristic, complemented
335#482Dic1111yescharacteristic, complemented
336#481Dic1111yescharacteristic, complemented
337#480Dic1111yescharacteristic, complemented
338#436—221no—
339#435—221no—
340#435—221no—
341C8×D4—221no—
342#433—221no—
343#433—221no—
344#432—221no—
345#431—221no—
346C2×#108—111no—
347C2×#108—111no—
348#427C2×D1111yescharacteristic
349#427C2×D1111yescharacteristic
350#424—111no—
351#424—111no—
352#424—111no—
353C2×#104—111no—
354C2×#104—111no—
355#416C2×D1111yescharacteristic
356#416C2×D1111yescharacteristic
357#408—111no—
358#407—111no—
359C2×C22⋊C8—111no—
360C2×C22⋊C8C2×D1111yescharacteristic
361#405—111no—
362#405—111no—
363#405—111no—
364C2×#97—111no—
365C2×#97—111no—
366#341—111no—
367#341—111no—
368#339—111no—
369#339—111no—
370#339—111no—
371#339—111no—
372#339—111no—
373#339—111no—
374#336—111no—
375#336—111no—
376C22×C11—21no—
377C22×C11—21no—
378C22×C11—21no—
379C22×C11—21no—
380C22×C11—21no—
381C22×C11—21no—
382C22×C11—21no—
383C22×C11—42no—
384C22×C11—42no—
385C22×C11—41no—
386C22×C11—41no—
387C22×C11—41no—
388C22×C11#44412yes—
389C22×C11C2×C4×D411yescharacteristic
390C22×C11#55111yescharacteristic
391C22×C11#55211yescharacteristic
392C4×C11—21no—
393C4×C11—21no—
394C4×C11—41no—
395C4×C11—41no—
396C4×C11—41no—
397C4×C11—41no—
398C4×C11—41no—
399C4×C11—41no—
400C4×C11—41no—
401C4×C11C4×#4111yescharacteristic
402C4×C11#52011yescharacteristic
403C4×C11#54611yescharacteristic
404C4×C11#54711yescharacteristic
405Dic11—42no—
406Dic11—42no—
407C2×#41C22×D1111yescharacteristic
408C23×C4—221no—
409C23×C4C22×D1111yescharacteristic
410#131—222no—
411#131—441no—
412C2×M16—111no—
413C2×M16—111no—
414C2×M16—111no—
415C2×M16—111no—
416C2×M16—221no—
417C2×M16—221no—
418C2×M16—222no—
419C2×M16—441no—
420C22×C8—111no—
421C22×C8—111no—
422C22×C8—221no—
423C22×C8—221no—
424C22×C8C22×D1111yescharacteristic
425C22×C8C22×D1111yescharacteristic
426#123—21no—
427C22⋊Q8C2×Dic1111yescharacteristic
428C22⋊Q8C2×Dic1111yescharacteristic
429#121C2×Dic1111yescharacteristic
430#121C2×Dic1111yescharacteristic
431#120—21no—
432C4×D4—21no—
433C4×D4—21no—
434#117—21no—
435#117—21no—
436#117C2×Dic1111yescharacteristic
437#117C2×Dic1111yescharacteristic
438#117C22×D1111yescharacteristic
439#117C22×D1111yescharacteristic
440#117C22×D1111yescharacteristic
441C2×C4⋊C4C2×Dic1111yescharacteristic
442C2×C4⋊C4C2×Dic1111yescharacteristic
443C2×C22⋊C4—21no—
444C2×C42—21no—
445C2×C42—111no—
446C2×C42—111no—
447C2×C42—222no—
448C2×C42—221no—
449C2×C42—441no—
450#108—222no—
451#108—441no—
452#107C2×Dic1111yescharacteristic, complemented
453#107C2×Dic1111yescharacteristic, complemented
454#107C2×Dic1111yescharacteristic, complemented
455#107C2×Dic1111yescharacteristic, complemented
456#106C2×Dic1111yescharacteristic, complemented
457#106C2×Dic1111yescharacteristic, complemented
458#106C2×Dic1111yescharacteristic, complemented
459#106C2×Dic1111yescharacteristic, complemented
460C4⋊C8—221no—
461C4⋊C8—221no—
462C4⋊C8—221no—
463C4⋊C8—221no—
464C4⋊C8—221no—
465C4⋊C8—221no—
466#104—222no—
467#104—441no—
468#103C2×Dic1111yescharacteristic, complemented
469#103C2×Dic1111yescharacteristic, complemented
470#103C2×Dic1111yescharacteristic, complemented
471#103C2×Dic1111yescharacteristic, complemented
472#102C2×Dic1111yescharacteristic, complemented
473#102C2×Dic1111yescharacteristic, complemented
474#102C2×Dic1111yescharacteristic, complemented
475#102C2×Dic1111yescharacteristic, complemented
476C22⋊C8—111no—
477C22⋊C8—111no—
478C22⋊C8—111no—
479C22⋊C8—111no—
480C22⋊C8—221no—
481C22⋊C8—221no—
482C22⋊C8—221no—
483C22⋊C8—221no—
484C22⋊C8C2×Dic1111yescharacteristic
485C22⋊C8C2×Dic1111yescharacteristic
486C22⋊C8C2×Dic1111yescharacteristic
487C22⋊C8C2×Dic1111yescharacteristic
488#97—221no—
489#97—221no—
490#97—221no—
491#97—222no—
492#97—441no—
493C4×C8—221no—
494C4×C8—221no—
495C4×C8—221no—
496C2×C11—21no—
497C2×C11—21no—
498C2×C11—22no—
499C2×C11—41no—
500C2×C11—81no—
501C2×C11#235911yescharacteristic
502C2×C11C2×#44411yescharacteristic
503C2×C11#295611yescharacteristic
504C24#434111yescharacteristic
505#41—21no—
506#41—21no—
507#41—21no—
508#41—21no—
509C2×Q8C22×Dic1111yescharacteristic
510C2×D4—21no—
511C2×D4—21no—
512C2×D4—21no—
513C2×D4C22×Dic1111yescharacteristic
514C22×C4—21no—
515C22×C4—21no—
516C22×C4—21no—
517C22×C4—21no—
518C22×C4—21no—
519C22×C4—21no—
520C22×C4—21no—
521C22×C4—221no—
522C22×C4—221no—
523C22×C4—442no—
524C22×C4—442no—
525C22×C4—442no—
526C22×C4D4×D1111yescharacteristic
527C22×C4D4×D1111yescharacteristic
528C22×C4#434111yescharacteristic
529C22×C4C22×Dic1111yescharacteristic
530C22×C4C22×Dic1111yescharacteristic
531C22×C4C23×D1111yescharacteristic
532M16—112no—
533M16—221no—
534M16—221no—
535M16—221no—
536M16—221no—
537M16—221no—
538M16—221no—
539M16—221no—
540M16—442no—
541M16—442no—
542C2×C8—21no—
543C2×C8—21no—
544C2×C8—21no—
545C2×C8—21no—
546C2×C8—111no—
547C2×C8—111no—
548C2×C8—111no—
549C2×C8—111no—
550C2×C8—221no—
551C2×C8—221no—
552C2×C8—221no—
553C2×C8—221no—
554C2×C8—221no—
555C2×C8—221no—
556C2×C8—221no—
557C2×C8—221no—
558C2×C8—442no—
559C2×C8—442no—
560C2×C8C22×Dic1111yescharacteristic
561C2×C8C22×Dic1111yescharacteristic
562C2×C8C22×Dic1111yescharacteristic
563C2×C8C22×Dic1111yescharacteristic
564C4⋊C4—21no—
565C4⋊C4—21no—
566C4⋊C4—21no—
567C4⋊C4—21no—
568C4⋊C4C22×Dic1111yescharacteristic
569C4⋊C4C22×Dic1111yescharacteristic
570C4⋊C4C22×Dic1111yescharacteristic
571C4⋊C4C22×Dic1111yescharacteristic
572C4⋊C4C22×Dic1111yescharacteristic
573C4⋊C4C22×Dic1111yescharacteristic
574C22⋊C4—21no—
575C22⋊C4—21no—
576C22⋊C4—21no—
577C22⋊C4—21no—
578C22⋊C4—21no—
579C22⋊C4—21no—
580C22⋊C4—21no—
581C22⋊C4—21no—
582C22⋊C4—21no—
583C42—21no—
584C42—21no—
585C42—21no—
586C42—21no—
587C42—21no—
588C42—112no—
589C42—221no—
590C42—221no—
591C42—221no—
592C42—442no—
593C11#2295011yescharacteristic, complemented, Sylow
594C23—22no—
595C23—21no—
596C23—21no—
597C23—21no—
598C23—41no—
599C23D4×Dic1111yescharacteristic
600C23D4×Dic1111yescharacteristic
601C23C2×#434111yescharacteristic
602Q8—21no—
603Q8—21no—
604D4—21no—
605D4—21no—
606D4—42no—
607D4—41no—
608D4—41no—
609D4—81no—
610C2×C4—21no—
611C2×C4—21no—
612C2×C4—21no—
613C2×C4—21no—
614C2×C4—21no—
615C2×C4—21no—
616C2×C4—21no—
617C2×C4—21no—
618C2×C4—21no—
619C2×C4—21no—
620C2×C4—21no—
621C2×C4—21no—
622C2×C4—21no—
623C2×C4—21no—
624C2×C4—21no—
625C2×C4—21no—
626C2×C4—21no—
627C2×C4—42no—
628C2×C4—41no—
629C2×C4—41no—
630C2×C4—81no—
631C2×C4—222no—
632C2×C4—222no—
633C2×C4—441no—
634C2×C4—441no—
635C2×C4—441no—
636C2×C4—448no—
637C2×C4—441no—
638C2×C4D4×Dic1111yescharacteristic
639C2×C4D4×Dic1111yescharacteristic
640C2×C4C2×D4×D1111yescharacteristic
641C2×C4#41×D1111yescharacteristic
642C2×C4#41×D1111yescharacteristic
643C2×C4#6704211yescharacteristic
644C2×C4#6704311yescharacteristic
645C2×C4C23×Dic1111yescharacteristic
646C8—21no—
647C8—21no—
648C8—21no—
649C8—21no—
650C8—221no—
651C8—221no—
652C8—222no—
653C8—221no—
654C8—221no—
655C8—441no—
656C8—441no—
657C8—441no—
658C22—21no—
659C22—21no—
660C22—21no—
661C22—21no—
662C22—21no—
663C22—21no—
664C22—21no—
665C22—42no—
666C22—42no—
667C22—41no—
668C22—41no—
669C22—41no—
670C22#1062281012yes—
671C22#1062318111yescharacteristic
672C22#1062318911yescharacteristic
673C22C2×D4×Dic1111yescharacteristic
674C4—21no—
675C4—21no—
676C4—41no—
677C4—41no—
678C4—41no—
679C4—41no—
680C4—41no—
681C4—41no—
682C4—41no—
683C4—442no—
684C4—442no—
685C4#1062318511yescharacteristic
686C4#1062318611yescharacteristic
687C4#41×Dic1111yescharacteristic
688C4#1062335811yescharacteristic
689C2—21no—
690C2—22no—
691C2—21no—
692C2—41no—
693C2—81no—
694C2#1307161211yescharacteristic
695C2C2×#1062281011yescharacteristic
696C2#1307752611yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#3091C2
socleC22×C11C2×C4×D4
prime radicalC11×#525C22
cosocleC22×C4×C11C24
hypercenter#3091D11
hypocenterC11#22950
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ #3091

Complements

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

NH ≅ G/Ntype
2. #13077274C2semidirect
3. #13069370C2semidirect
4. #13069329C2semidirect
5. #13069266C2semidirect
6. #13069217C2semidirect
7. #13069217C2semidirect
9. #13068893C2semidirect
10. #13068823C2semidirect
11. #13068502C2semidirect
12. #13068463C2semidirect
13. #13068380C2semidirect
14. C2×#10622170C2semidirect
21. C11×#485C4semidirect
22. C11×#485C4semidirect
23. C11×#484C4semidirect
24. C11×#483C4semidirect
25. C11×#482C4semidirect
26. C11×#482C4semidirect
27. C11×#481C4semidirect
28. C11×#480C4semidirect
110. C11×#107C2×C4semidirect
111. C11×#107C2×C4semidirect
112. C11×#107C2×C4semidirect
113. C11×#107C2×C4semidirect
114. C11×#106C2×C4semidirect
115. C11×#106C2×C4semidirect
116. C11×#106C2×C4semidirect
117. C11×#106C2×C4semidirect
118. C11×#103C2×C4semidirect
119. C11×#103C2×C4semidirect
120. C11×#103C2×C4semidirect
121. C11×#103C2×C4semidirect
122. C11×#102C2×C4semidirect
123. C11×#102C2×C4semidirect
124. C11×#102C2×C4semidirect
125. C11×#102C2×C4semidirect
330. #485Dic11semidirect
331. #485Dic11semidirect
332. #484Dic11semidirect
333. #483Dic11semidirect
334. #482Dic11semidirect
335. #482Dic11semidirect
336. #481Dic11semidirect
337. #480Dic11semidirect
452. #107C2×Dic11semidirect
453. #107C2×Dic11semidirect
454. #107C2×Dic11semidirect
455. #107C2×Dic11semidirect
456. #106C2×Dic11semidirect
457. #106C2×Dic11semidirect
458. #106C2×Dic11semidirect
459. #106C2×Dic11semidirect
468. #103C2×Dic11semidirect
469. #103C2×Dic11semidirect
470. #103C2×Dic11semidirect
471. #103C2×Dic11semidirect
472. #102C2×Dic11semidirect
473. #102C2×Dic11semidirect
474. #102C2×Dic11semidirect
475. #102C2×Dic11semidirect
593. C11#22950semidirect

Maximal subgroups

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

subgroupindex
#130773432
#130772742
#130693702
#130693292
#130692662
#130692172
#130690602
#130688932
#130688232
#130685022
#130684632
#130683802
C2×#106221702
C11×#30912
#2295011