Finite Group Databasebeta

← #14780039

Subgroups — #14780039

Order 2816.

802 conjugacy classes of subgroups.

The subgroup lattice has 730 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13071854C211yesmaximal, characteristic
2#13069412C211yesmaximal, characteristic, complemented
3#13069408C211yesmaximal, characteristic, complemented
4#13069226C211yesmaximal, characteristic, complemented
5#13069225C211yesmaximal, characteristic, complemented
6#13069179C211yesmaximal, characteristic, complemented
7#13069174C211yesmaximal, characteristic, complemented
8#13068909C211yesmaximal, characteristic, complemented
9#13068908C211yesmaximal, characteristic, complemented
10#13068906C211yesmaximal, characteristic, complemented
11#13068794C211yesmaximal, characteristic, complemented
12#13068793C211yesmaximal, characteristic, complemented
13#13068686C211yesmaximal, characteristic, complemented
14#13068599C211yesmaximal, characteristic, complemented
15C11×#1869C211yesmaximal, characteristic, complemented
16C23×C8×C11C2211yescharacteristic
17C2×C4×D4×C11C2211yescharacteristic
18C2×C4×C22⋊D11C2211yescharacteristic
19C2×C4×C22⋊D11C2211yescharacteristic
20C23×C11⋊C8C2211yescharacteristic
21C2×#66925C2211yescharacteristic
22C2×C11×C22⋊C8C2211yescharacteristic
23C2×C11×C22⋊C8C2211yescharacteristic
24C2×C11×C22⋊C8C2211yescharacteristic
25#10622836C411yescharacteristic
26#10622835C411yescharacteristic
27C4×C22⋊Dic11C2211yescharacteristic
28C4×C22⋊Dic11C2211yescharacteristic
29C2×C22⋊(C11⋊C8)C2211yescharacteristic
30C2×C22⋊(C11⋊C8)C2211yescharacteristic
31C2×C22⋊(C11⋊C8)C2211yescharacteristic
32C2×(C2×D11)⋊C8C2211yescharacteristic
33C2×(C2×D11)⋊C8C2211yescharacteristic
34C2×(C2×D11)⋊C8C2211yescharacteristic
35C2×(C2×D11)⋊C8C2211yescharacteristic
36C2×#66879C2211yescharacteristic
37C2×Dic11⋊C8C2211yescharacteristic
38C2×Dic11⋊C8C2211yescharacteristic
39C2×Dic11⋊C8C2211yescharacteristic
40C2×Dic11⋊C8C2211yescharacteristic
41C2×C8×Dic11C2211yescharacteristic
42#10622606C411yescharacteristic
43#10622593C411yescharacteristic
44#10622574C411yescharacteristic
45#10622574C411yescharacteristic
46#10622561C411yescharacteristic
47#10622561C411yescharacteristic
48C4×C4⋊Dic11C2211yescharacteristic
49C11×#336C2211yescharacteristic
50C11×#336C2211yescharacteristic
51#10622188C2211yescharacteristic
52#10622188C2211yescharacteristic
53#10622188C2211yescharacteristic
54#10622188C2211yescharacteristic
55#10622188C2211yescharacteristic
56#10622188C2211yescharacteristic
57#10622162C2211yescharacteristic
58#10622162C2211yescharacteristic
59C22×D4×C11C2×C411yescharacteristic
60C23×C4×C11C2311yescharacteristic
61C23×C4×C11C2311yescharacteristic
62C22×C22⋊D11C2×C411yescharacteristic
63C22×C22⋊D11C2×C411yescharacteristic
64C22×C4×D11C2311yescharacteristic
65C22×C8×C11—41no—
66C22×C8×C11—41no—
67C22×C8×C11—41no—
68C22×C8×C11C2311yescharacteristic
69C22×C8×C11C2311yescharacteristic
70C22×C8×C11C2311yescharacteristic
71C22×C8×C11C2311yescharacteristic
72C4×D4×C11—41no—
73C4×D4×C11—41no—
74C2×C11×C4⋊C4C2×C411yescharacteristic
75C2×C11×C22⋊C4C2×C411yescharacteristic
76C2×C11×C22⋊C4C2×C411yescharacteristic
77C2×C42×C11C2311yescharacteristic
78C2×C22⋊Dic11C2×C411yescharacteristic
79C2×C22⋊Dic11C2×C411yescharacteristic
80C2×C22⋊Dic11C2×C411yescharacteristic
81C2×C22⋊Dic11C2×C411yescharacteristic
82C2×C22⋊Dic11C2×C411yescharacteristic
83C2×C22⋊Dic11C2×C411yescharacteristic
84C4×C22⋊D11—41no—
85C4×C22⋊D11—41no—
86C4×C22⋊D11—41no—
87C4×C22⋊D11—41no—
88C2×(C2×D11)⋊C4C2×C411yescharacteristic
89C2×(C2×D11)⋊C4C2×C411yescharacteristic
90C2×(C2×D11)⋊C4C2×C411yescharacteristic
91C2×(C2×D11)⋊C4C2×C411yescharacteristic
92C2×C4⋊Dic11C2×C411yescharacteristic
93C2×C4⋊Dic11C2×C411yescharacteristic
94C2×Dic11⋊C4C2×C411yescharacteristic
95C2×Dic11⋊C4C2×C411yescharacteristic
96C2×Dic11⋊C4C2×C411yescharacteristic
97C2×Dic11⋊C4C2×C411yescharacteristic
98C2×C4×Dic11C2311yescharacteristic
99C2×C4×Dic11C2311yescharacteristic
100C2×C4×Dic11C2311yescharacteristic
101C22×C11⋊C8—41no—
102C22×C11⋊C8—41no—
103C22×C11⋊C8—41no—
104C22×C11⋊C8C2311yescharacteristic
105C22×C11⋊C8C2311yescharacteristic
106C22×C11⋊C8C2311yescharacteristic
107C22×C11⋊C8C2311yescharacteristic
108#66925—41no—
109#66925—41no—
110C11×C22⋊C8—41no—
111C11×C22⋊C8—41no—
112C11×C22⋊C8—41no—
113C11⋊#95C2×C411yescharacteristic
114C11⋊#95C2×C411yescharacteristic
115C11⋊#95C2×C411yescharacteristic
116C11⋊#95C2×C411yescharacteristic
117C11⋊#95C2×C411yescharacteristic
118C11⋊#95C2×C411yescharacteristic
119C22⋊(C11⋊C8)—41no—
120C22⋊(C11⋊C8)—41no—
121C22⋊(C11⋊C8)—41no—
122(C2×D11)⋊C8—41no—
123(C2×D11)⋊C8—41no—
124(C2×D11)⋊C8—41no—
125(C2×D11)⋊C8—41no—
126#66879—41no—
127Dic11⋊C8—41no—
128Dic11⋊C8—41no—
129Dic11⋊C8—41no—
130Dic11⋊C8—41no—
131C8×Dic11—41no—
132#23330—111nomaximal, Sylow
133C24×C11C22×C411yescharacteristic
134C24×C11C22×C411yescharacteristic
135C23×D11C22×C411yescharacteristic
136C2×D4×C11—22no—
137C2×D4×C11—22no—
138C2×D4×C11—41no—
139C22×C4×C11—21no—
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—21no—
149C22×C4×C11—21no—
150C22×C4×C11—21no—
151C22×C4×C11C22×C411yescharacteristic
152C22×C4×C11C22×C411yescharacteristic
153C22×C4×C11C22×C411yescharacteristic
154C22×C4×C11C22×C411yescharacteristic
155C22×C4×C11C2411yescharacteristic
156C2×C22⋊D11—22no—
157C2×C22⋊D11—22no—
158C2×C22⋊D11—22no—
159C2×C22⋊D11—41no—
160C2×C22⋊D11—41no—
161C2×C22⋊D11—41no—
162C22×Dic11C22×C411yescharacteristic
163C22×Dic11C22×C411yescharacteristic
164C22×Dic11C22×C411yescharacteristic
165C22×Dic11C22×C411yescharacteristic
166C22×Dic11C22×C411yescharacteristic
167C22×Dic11C22×C411yescharacteristic
168C22×Dic11C22×C411yescharacteristic
169C2×C4×D11—21no—
170C2×C4×D11—21no—
171C2×C4×D11—21no—
172C2×C4×D11—21no—
173C2×C4×D11—21no—
174C2×C4×D11—21no—
175C2×C8×C11—21no—
176C2×C8×C11—21no—
177C2×C8×C11—21no—
178C2×C8×C11—21no—
179C2×C8×C11—21no—
180C2×C8×C11—21no—
181C2×C8×C11—21no—
182C2×C8×C11—21no—
183C2×C8×C11—21no—
184C2×C8×C11—21no—
185C2×C8×C11—21no—
186C2×C8×C11—21no—
187C2×C8×C11—44no—
188C11×C4⋊C4—41no—
189C11×C22⋊C4—41no—
190C11×C22⋊C4—41no—
191C42×C11—21no—
192C42×C11—21no—
193C22⋊Dic11—22no—
194C22⋊Dic11—22no—
195C22⋊Dic11—22no—
196C22⋊Dic11—41no—
197C22⋊Dic11—41no—
198C22⋊Dic11—41no—
199(C2×D11)⋊C4—41no—
200(C2×D11)⋊C4—41no—
201(C2×D11)⋊C4—41no—
202(C2×D11)⋊C4—41no—
203C4⋊Dic11—22no—
204C4⋊Dic11—41no—
205Dic11⋊C4—41no—
206Dic11⋊C4—41no—
207Dic11⋊C4—41no—
208Dic11⋊C4—41no—
209C4×Dic11—21no—
210C4×Dic11—21no—
211C4×Dic11—21no—
212C4×Dic11—21no—
213C4×Dic11—21no—
214C4×Dic11—21no—
215C2×C11⋊C8—21no—
216C2×C11⋊C8—21no—
217C2×C11⋊C8—21no—
218C2×C11⋊C8—21no—
219C2×C11⋊C8—21no—
220C2×C11⋊C8—21no—
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—44no—
228#2392—111no—
229#1955—111no—
230#1954—111no—
231#1924—111no—
232#1923—111no—
233#1917—111no—
234#1916—111no—
235#1869—111no—
236#1869—111no—
237#1869—111no—
238#1869D1111yescharacteristic, complemented
239#1850—111no—
240#1850—111no—
241#1818—111no—
242#1798—111no—
243C23×C11—21no—
244C23×C11—21no—
245C23×C11—21no—
246C23×C11—21no—
247C23×C11—21no—
248C23×C11—21no—
249C23×C11—21no—
250C23×C11—21no—
251C23×C11—21no—
252C23×C11—21no—
253C23×C11—21no—
254C23×C11—21no—
255C23×C11#13112yes—
256C23×C11#13112yes—
257C23×C11C23×C411yescharacteristic
258C22×D11—21no—
259C22×D11—21no—
260C22×D11—21no—
261C22×D11—21no—
262C22×D11—21no—
263C22×D11—21no—
264C22×D11—21no—
265D4×C11—44no—
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—21no—
274C2×C4×C11—21no—
275C2×C4×C11—21no—
276C2×C4×C11—21no—
277C2×C4×C11—21no—
278C2×C4×C11—41no—
279C2×C4×C11—41no—
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×C11H(5,𝔽2)11yescharacteristic
287C2×C4×C11H(5,𝔽2)11yescharacteristic
288C2×C4×C11H(5,𝔽2)11yescharacteristic
289C2×C4×C11H(5,𝔽2)11yescharacteristic
290C2×C4×C11H(5,𝔽2)11yescharacteristic
291C2×C4×C112−1+411yescharacteristic
292C22⋊D11—44no—
293C22⋊D11—44no—
294C2×Dic11—21no—
295C2×Dic11—21no—
296C2×Dic11—21no—
297C2×Dic11—21no—
298C2×Dic11—21no—
299C2×Dic11—21no—
300C2×Dic11—21no—
301C2×Dic11—21no—
302C2×Dic11—21no—
303C2×Dic11—21no—
304C2×Dic11—21no—
305C2×Dic11—21no—
306C2×Dic11—21no—
307C2×Dic11—21no—
308C2×Dic11—21no—
309C2×Dic11—21no—
310C2×Dic11—21no—
311C2×Dic11—21no—
312C2×Dic11—21no—
313C2×Dic11—21no—
314C2×Dic11#13112yes—
315C4×D11—41no—
316C4×D11—41no—
317C4×D11—41no—
318C4×D11—41no—
319C8×C11—41no—
320C8×C11—41no—
321C8×C11—41no—
322C8×C11—41no—
323C11⋊C8—41no—
324C11⋊C8—41no—
325C11⋊C8—41no—
326C11⋊C8—41no—
327C23×C8—111no—
328C23×C8C2×D1111yescharacteristic
329C2×C4×D4—111no—
330C2×C4×D4—111no—
331C2×C4×D4C2×D1111yescharacteristic
332C2×#117—111no—
333C2×C4⋊C8—111no—
334C2×C4⋊C8—111no—
335C2×C4⋊C8—111no—
336C2×C4⋊C8—111no—
337C2×C22⋊C8—111no—
338C2×C22⋊C8—111no—
339C2×C22⋊C8—111no—
340C2×C22⋊C8—111no—
341C2×C22⋊C8—111no—
342C2×C22⋊C8—111no—
343C2×C22⋊C8—111no—
344C2×C22⋊C8C2×D1111yescharacteristic
345C2×C22⋊C8C2×D1111yescharacteristic
346C2×C22⋊C8C2×D1111yescharacteristic
347C2×#97—111no—
348C2×C4×C8—111no—
349#398—111no—
350#397—111no—
351#396—111no—
352#396—111no—
353#394—111no—
354#394—111no—
355#394—111no—
356#392—111no—
357C4×C4⋊C4—111no—
358C4×C22⋊C4—111no—
359C4×C22⋊C4—111no—
360#336—111no—
361#336—111no—
362#336—111no—
363#336—111no—
364#336—111no—
365#336—111no—
366#336—111no—
367#336—111no—
368#336C2×D1111yescharacteristic
369#336C2×D1111yescharacteristic
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×C11#51811yescharacteristic
385C22×C11#51811yescharacteristic
386C22×C11#52011yescharacteristic
387C22×C11C2×#13111yescharacteristic
388C22×C11C2×#13111yescharacteristic
389C22×C11C2×#13111yescharacteristic
390C22×C11#56811yescharacteristic
391C2×D11—41no—
392C2×D11—41no—
393C2×D11—41no—
394C2×D11—41no—
395C2×D11—41no—
396C2×D11—41no—
397C2×D11—41no—
398C4×C11—41no—
399C4×C11—41no—
400C4×C11—41no—
401C4×C11—41no—
402C4×C11#56011yescharacteristic
403C4×C11#56011yescharacteristic
404C4×C11#56211yescharacteristic
405C4×C11#56211yescharacteristic
406Dic11—22no—
407Dic11—41no—
408Dic11—41no—
409Dic11—41no—
410Dic11—41no—
411Dic11—41no—
412Dic11—41no—
413C22×D4—111no—
414C22×D4—111no—
415C22×D4C4×D1111yescharacteristic
416C23×C4—111no—
417C23×C4C22×D1111yescharacteristic
418C23×C4C22×D1111yescharacteristic
419C22×C8—41no—
420C22×C8—41no—
421C22×C8—41no—
422C22×C8—111no—
423C22×C8—111no—
424C22×C8—111no—
425C22×C8—111no—
426C22×C8—441no—
427C22×C8—441no—
428C22×C8—441no—
429C22×C8C22×D1111yescharacteristic
430C22×C8C22×D1111yescharacteristic
431C22×C8C22×D1111yescharacteristic
432C22×C8C22×D1111yescharacteristic
433C4×D4—41no—
434C4×D4—41no—
435C4×D4—441no—
436C4×D4—441no—
437C4×D4—441no—
438C4×D4—441no—
439#117—441no—
440#117—441no—
441C2×C4⋊C4—111no—
442C2×C4⋊C4—111no—
443C2×C4⋊C4—111no—
444C2×C4⋊C4—111no—
445C2×C4⋊C4—111no—
446C2×C4⋊C4—111no—
447C2×C4⋊C4C4×D1111yescharacteristic
448C2×C22⋊C4—111no—
449C2×C22⋊C4—111no—
450C2×C22⋊C4—111no—
451C2×C22⋊C4—111no—
452C2×C22⋊C4—111no—
453C2×C22⋊C4—111no—
454C2×C22⋊C4—111no—
455C2×C22⋊C4—111no—
456C2×C22⋊C4—111no—
457C2×C22⋊C4—111no—
458C2×C22⋊C4C4×D1111yescharacteristic
459C2×C22⋊C4C4×D1111yescharacteristic
460C2×C42—111no—
461C2×C42—111no—
462C2×C42—111no—
463C2×C42C22×D1111yescharacteristic
464C4⋊C8—441no—
465C4⋊C8—441no—
466C4⋊C8—441no—
467C4⋊C8—441no—
468C22⋊C8—41no—
469C22⋊C8—41no—
470C22⋊C8—41no—
471C22⋊C8—441no—
472C22⋊C8—441no—
473C22⋊C8—441no—
474C22⋊C8—441no—
475C22⋊C8—441no—
476C22⋊C8—441no—
477C22⋊C8—441no—
478#97—441no—
479C4×C8—441no—
480#95—111no—
481#95—111no—
482#95—111no—
483#95—111no—
484#95—111no—
485#95—111no—
486C2×C11—42no—
487C2×C11—42no—
488C2×C11#237711yescharacteristic
489C2×C11#297611yescharacteristic
490C2×C11#297711yescharacteristic
491C2×C11#297711yescharacteristic
492C2×C11#298111yescharacteristic
493C2×C11#299211yescharacteristic
494C2×C11#299411yescharacteristic
495D11—81no—
496C24—111no—
497C24C2×C4×D1111yescharacteristic
498C24C2×C4×D1111yescharacteristic
499C2×D4—22no—
500C2×D4—22no—
501C2×D4—41no—
502C2×D4—222no—
503C2×D4—222no—
504C2×D4—222no—
505C2×D4—441no—
506C2×D4—441no—
507C2×D4—441no—
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—21no—
519C22×C4—21no—
520C22×C4—111no—
521C22×C4—111no—
522C22×C4—111no—
523C22×C4—111no—
524C22×C4—111no—
525C22×C4—111no—
526C22×C4—111no—
527C22×C4—221no—
528C22×C4—221no—
529C22×C4—221no—
530C22×C4—221no—
531C22×C4—221no—
532C22×C4—221no—
533C22×C4C2×C4×D1111yescharacteristic
534C22×C4C2×C4×D1111yescharacteristic
535C22×C4C2×C4×D1111yescharacteristic
536C22×C4C2×C4×D1111yescharacteristic
537C22×C4C23×D1111yescharacteristic
538C2×C8—21no—
539C2×C8—21no—
540C2×C8—21no—
541C2×C8—21no—
542C2×C8—21no—
543C2×C8—21no—
544C2×C8—21no—
545C2×C8—21no—
546C2×C8—21no—
547C2×C8—21no—
548C2×C8—21no—
549C2×C8—21no—
550C2×C8—44no—
551C2×C8—221no—
552C2×C8—221no—
553C2×C8—221no—
554C2×C8—221no—
555C2×C8—221no—
556C2×C8—221no—
557C2×C8—221no—
558C2×C8—221no—
559C2×C8—221no—
560C2×C8—221no—
561C2×C8—221no—
562C2×C8—221no—
563C2×C8—444no—
564C4⋊C4—41no—
565C4⋊C4—222no—
566C4⋊C4—441no—
567C4⋊C4—441no—
568C4⋊C4—441no—
569C4⋊C4—441no—
570C4⋊C4—441no—
571C22⋊C4—41no—
572C22⋊C4—41no—
573C22⋊C4—222no—
574C22⋊C4—222no—
575C22⋊C4—222no—
576C22⋊C4—441no—
577C22⋊C4—441no—
578C22⋊C4—441no—
579C22⋊C4—441no—
580C22⋊C4—441no—
581C22⋊C4—441no—
582C22⋊C4—441no—
583C42—21no—
584C42—21no—
585C42—221no—
586C42—221no—
587C42—221no—
588C42—221no—
589C42—221no—
590C42—221no—
591C11#2333011yescharacteristic, complemented, Sylow
592C23—21no—
593C23—21no—
594C23—21no—
595C23—21no—
596C23—21no—
597C23—21no—
598C23—21no—
599C23—21no—
600C23—21no—
601C23—21no—
602C23—21no—
603C23—21no—
604C23—221no—
605C23—221no—
606C23—221no—
607C23—221no—
608C23—221no—
609C23—221no—
610C23—221no—
611C23#6695412yes—
612C23#6696012yes—
613C23C22×C4×D1111yescharacteristic
614D4—44no—
615D4—444no—
616D4—444no—
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—21no—
628C2×C4—21no—
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—221no—
639C2×C4—221no—
640C2×C4—221no—
641C2×C4—221no—
642C2×C4—221no—
643C2×C4—221no—
644C2×C4—221no—
645C2×C4—221no—
646C2×C4—221no—
647C2×C4—221no—
648C2×C4—221no—
649C2×C4—221no—
650C2×C4—221no—
651C2×C4—221no—
652C2×C4—221no—
653C2×C4—221no—
654C2×C4—221no—
655C2×C4—221no—
656C2×C4—221no—
657C2×C4—221no—
658C2×C4—441no—
659C2×C4—441no—
660C2×C4—441no—
661C2×C4—441no—
662C2×C4#6703711yescharacteristic
663C2×C4#6703711yescharacteristic
664C2×C4#6703711yescharacteristic
665C2×C4#6703711yescharacteristic
666C2×C4#6704211yescharacteristic
667C2×C4#6704311yescharacteristic
668C8—41no—
669C8—41no—
670C8—41no—
671C8—41no—
672C8—441no—
673C8—441no—
674C8—441no—
675C8—441no—
676C22—22no—
677C22—22no—
678C22—22no—
679C22—22no—
680C22—22no—
681C22—22no—
682C22—41no—
683C22—41no—
684C22—41no—
685C22—41no—
686C22—41no—
687C22—41no—
688C22—41no—
689C22—41no—
690C22—441no—
691C22—441no—
692C22—441no—
693C22—441no—
694C22—441no—
695C22—441no—
696C22—441no—
697C22#1062301711yescharacteristic
698C22#1062307611yescharacteristic
699C22#1062307711yescharacteristic
700C22C2×#6695411yescharacteristic
701C22C2×#6696011yescharacteristic
702C22D11×#13111yescharacteristic
703C22#1062328111yescharacteristic
704C4—41no—
705C4—41no—
706C4—41no—
707C4—41no—
708C4—222no—
709C4—441no—
710C4—441no—
711C4—441no—
712C4—441no—
713C4—441no—
714C4—441no—
715C4#1062312611yescharacteristic
716C4#1062315111yescharacteristic
717C4#1062315211yescharacteristic
718C4#1062319811yescharacteristic
719C2—42no—
720C2—42no—
721C2—881no—
722C2#1307176811yescharacteristic
723C2#1307766511yescharacteristic
724C2#1307766911yescharacteristic
725C2#1307767011yescharacteristic
726C2#1307768911yescharacteristic
727C2#1307774911yescharacteristic
728C2#1307776911yescharacteristic
subgroupG/H
center, FrattiniC22×C4C23×D11
commutator, socleC23×C11C23×C4
FittingC11×#1869C2
prime radical#10622836C4
cosocleC22×C4×C11C24
hypercenter#1869D11
hypocenterC11#23330
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C22×C4 ◁ #1869

Complements

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

NH ≅ G/Ntype
2. #13069412C2semidirect
3. #13069408C2semidirect
4. #13069226C2semidirect
5. #13069225C2semidirect
6. #13069179C2semidirect
7. #13069174C2semidirect
8. #13068909C2semidirect
9. #13068908C2semidirect
10. #13068906C2semidirect
11. #13068794C2semidirect
12. #13068793C2semidirect
13. #13068686C2semidirect
14. #13068599C2semidirect
15. C11×#1869C2semidirect
238. #1869D11semidirect
591. C11#23330semidirect

Maximal subgroups

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

subgroupindex
#130718542
#130694122
#130694082
#130692262
#130692252
#130691792
#130691742
#130689092
#130689082
#130689062
#130687942
#130687932
#130686862
#130685992
C11×#18692
#2333011