Finite Group Databasebeta

← #14764649

Subgroups — #14764649

Order 2816.

744 conjugacy classes of subgroups.

The subgroup lattice has 668 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13069415C211yesmaximal, characteristic
2#13069411C211yesmaximal, characteristic
3#13069340C211yesmaximal, characteristic, complemented
4#13069335C211yesmaximal, characteristic, complemented
5#13069231C211yesmaximal, characteristic, complemented
6#13069231C211yesmaximal, characteristic, complemented
7#13069224C211yesmaximal, characteristic, complemented
8#13069224C211yesmaximal, characteristic, complemented
9#13068687C211yesmaximal, characteristic, complemented
10#13068684C211yesmaximal, characteristic, complemented
11#13068600C211yesmaximal, characteristic, complemented
12#13068596C211yesmaximal, characteristic, complemented
13#13068473C211yesmaximal, characteristic, complemented
14#13068368C211yesmaximal, characteristic, complemented
15C11×#2290C211yesmaximal, characteristic
16C2×C4×D4×C11C2211yescharacteristic
17C2×C11×#117C2211yescharacteristic
18C22×C42×C11C2211yescharacteristic
19C11×#388C411yescharacteristic
20C11×#388C411yescharacteristic
21C11×#387C411yescharacteristic
22C11×#387C411yescharacteristic
23C11×#386C411yescharacteristic
24C11×#386C411yescharacteristic
25C11×#385C411yescharacteristic
26C11×#385C411yescharacteristic
27C4×C11×C4⋊C4C2211yescharacteristic
28C4×C11×C22⋊C4C2211yescharacteristic
29C4×C11×C22⋊C4C2211yescharacteristic
30C11×#376C2211yescharacteristic
31C2×C22⋊(C11⋊C8)C2211yescharacteristic
32C2×C22⋊(C11⋊C8)C2211yescharacteristic
33C2×C22⋊(C11⋊C8)C2211yescharacteristic
34C2×C22⋊(C11⋊C8)C2211yescharacteristic
35C2×C22⋊(C11⋊C8)C2211yescharacteristic
36C2×C22⋊(C11⋊C8)C2211yescharacteristic
37C2×C22⋊(C11⋊C8)C2211yescharacteristic
38C2×C22⋊(C11⋊C8)C2211yescharacteristic
39C2×C4⋊(C11⋊C8)C2211yescharacteristic
40C2×C4⋊(C11⋊C8)C2211yescharacteristic
41C2×C4⋊(C11⋊C8)C2211yescharacteristic
42C2×C4⋊(C11⋊C8)C2211yescharacteristic
43C2×C4⋊(C11⋊C8)C2211yescharacteristic
44C2×C4⋊(C11⋊C8)C2211yescharacteristic
45C2×#66867C2211yescharacteristic
46C2×#66867C2211yescharacteristic
47C2×C4×C11⋊C8C2211yescharacteristic
48C2×C4×C11⋊C8C2211yescharacteristic
49#10622162C2211yescharacteristic
50#10622162C2211yescharacteristic
51#10622162C2211yescharacteristic
52#10622162C2211yescharacteristic
53#10622162C2211yescharacteristic
54#10622162C2211yescharacteristic
55#10622162C2211yescharacteristic
56#10622162C2211yescharacteristic
57#10622162C2211yescharacteristic
58#10622162C2211yescharacteristic
59C22×D4×C11C2×C411yescharacteristic
60C23×C4×C11C2×C411yescharacteristic
61C23×C4×C11C2×C411yescharacteristic
62C23×C4×C11C2311yescharacteristic
63C23×C4×C11C2311yescharacteristic
64C4×D4×C11—22no—
65C4×D4×C11—22no—
66C11×#117—41no—
67C11×#117—41no—
68C2×C11×C4⋊C4C2×C411yescharacteristic
69C2×C11×C4⋊C4C2×C411yescharacteristic
70C2×C11×C4⋊C4C2×C411yescharacteristic
71C2×C11×C4⋊C4C2×C411yescharacteristic
72C2×C11×C4⋊C4C2×C411yescharacteristic
73C2×C11×C22⋊C4C2×C411yescharacteristic
74C2×C11×C22⋊C4C2×C411yescharacteristic
75C2×C11×C22⋊C4C2×C411yescharacteristic
76C2×C11×C22⋊C4C2×C411yescharacteristic
77C2×C11×C22⋊C4C2×C411yescharacteristic
78C2×C11×C22⋊C4C2×C411yescharacteristic
79C2×C11×C22⋊C4C2×C411yescharacteristic
80C2×C11×C22⋊C4C2×C411yescharacteristic
81C2×C42×C11—41no—
82C2×C42×C11—41no—
83C2×C42×C11C2×C411yescharacteristic
84C2×C42×C11C2×C411yescharacteristic
85C2×C42×C11C2311yescharacteristic
86C2×C42×C11C2311yescharacteristic
87C2×C42×C11C2311yescharacteristic
88C2×C42×C11C2311yescharacteristic
89C2×C42×C11C2311yescharacteristic
90C22×C11⋊C8C2311yescharacteristic
91C22×C11⋊C8C2311yescharacteristic
92C22×C11⋊C8C2311yescharacteristic
93C22×C11⋊C8C2311yescharacteristic
94C22×C11⋊C8C2311yescharacteristic
95C22×C11⋊C8C2311yescharacteristic
96C22×C11⋊C8C2311yescharacteristic
97C22×C11⋊C8C2311yescharacteristic
98C11×#95C2×C411yescharacteristic
99C11×#95C2×C411yescharacteristic
100C11×#95C2×C411yescharacteristic
101C11×#95C2×C411yescharacteristic
102C11×#95C2×C411yescharacteristic
103C11×#95C2×C411yescharacteristic
104C11×#95C2×C411yescharacteristic
105C11×#95C2×C411yescharacteristic
106C11×#95C2×C411yescharacteristic
107C11×#95C2×C411yescharacteristic
108C22⋊(C11⋊C8)—41no—
109C22⋊(C11⋊C8)—41no—
110C22⋊(C11⋊C8)—41no—
111C22⋊(C11⋊C8)—41no—
112C22⋊(C11⋊C8)—41no—
113C22⋊(C11⋊C8)—41no—
114C22⋊(C11⋊C8)—41no—
115C22⋊(C11⋊C8)—41no—
116C4⋊(C11⋊C8)—22no—
117C4⋊(C11⋊C8)—22no—
118C4⋊(C11⋊C8)—41no—
119C4⋊(C11⋊C8)—41no—
120C4⋊(C11⋊C8)—41no—
121C4⋊(C11⋊C8)—41no—
122#66867—22no—
123#66867—41no—
124C4×C11⋊C8—22no—
125C4×C11⋊C8—41no—
126#22017—111nomaximal, Sylow
127C24×C11C22×C411yescharacteristic
128C24×C11C22×C411yescharacteristic
129C2×D4×C11—22no—
130C2×D4×C11—22no—
131C2×D4×C11—41no—
132C22×C4×C11—22no—
133C22×C4×C11—22no—
134C22×C4×C11—21no—
135C22×C4×C11—21no—
136C22×C4×C11—21no—
137C22×C4×C11—21no—
138C22×C4×C11—21no—
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—41no—
147C22×C4×C11—41no—
148C22×C4×C11—41no—
149C22×C4×C11—41no—
150C22×C4×C11C22×C411yescharacteristic
151C22×C4×C11C22×C411yescharacteristic
152C22×C4×C11C22×C411yescharacteristic
153C22×C4×C11C22×C411yescharacteristic
154C22×C4×C11C22×C411yescharacteristic
155C22×C4×C11C22×C411yescharacteristic
156C22×C4×C11C22×C411yescharacteristic
157C22×C4×C11C22×C411yescharacteristic
158C22×C4×C11C22×C411yescharacteristic
159C22×C4×C11C22×C411yescharacteristic
160C22×C4×C11C22×C411yescharacteristic
161C22×C4×C11C22×C411yescharacteristic
162C22×C4×C11C2411yescharacteristic
163C11×C4⋊C4—22no—
164C11×C4⋊C4—22no—
165C11×C4⋊C4—41no—
166C11×C4⋊C4—41no—
167C11×C4⋊C4—41no—
168C11×C22⋊C4—22no—
169C11×C22⋊C4—22no—
170C11×C22⋊C4—22no—
171C11×C22⋊C4—22no—
172C11×C22⋊C4—41no—
173C11×C22⋊C4—41no—
174C11×C22⋊C4—41no—
175C11×C22⋊C4—41no—
176C42×C11—21no—
177C42×C11—21no—
178C42×C11—21no—
179C42×C11—21no—
180C42×C11—21no—
181C42×C11—21no—
182C42×C11—21no—
183C42×C11—21no—
184C42×C11—41no—
185C42×C11—41no—
186C42×C11#4112yes—
187C42×C11#4112yes—
188C2×C11⋊C8—21no—
189C2×C11⋊C8—21no—
190C2×C11⋊C8—21no—
191C2×C11⋊C8—21no—
192C2×C11⋊C8—21no—
193C2×C11⋊C8—21no—
194C2×C11⋊C8—21no—
195C2×C11⋊C8—21no—
196C2×C11⋊C8—21no—
197C2×C11⋊C8—21no—
198C2×C11⋊C8—21no—
199C2×C11⋊C8—21no—
200C2×C11⋊C8—21no—
201C2×C11⋊C8—21no—
202C2×C11⋊C8—21no—
203C2×C11⋊C8—21no—
204C2×C11⋊C8—21no—
205C2×C11⋊C8—21no—
206C2×C11⋊C8—21no—
207C2×C11⋊C8—21no—
208C2×C11⋊C8—21no—
209C2×C11⋊C8—21no—
210C2×C11⋊C8—21no—
211C2×C11⋊C8—21no—
212#2290D1111yescharacteristic
213#1955—111no—
214#1954—111no—
215#1940—111no—
216#1939—111no—
217#1924—111no—
218#1924—111no—
219#1923—111no—
220#1923—111no—
221#1818—111no—
222#1817—111no—
223#1798—111no—
224#1797—111no—
225#1768—111no—
226#1746—111no—
227C23×C11—21no—
228C23×C11—21no—
229C23×C11—21no—
230C23×C11—21no—
231C23×C11—21no—
232C23×C11—21no—
233C23×C11—21no—
234C23×C11—21no—
235C23×C11—21no—
236C23×C11—21no—
237C23×C11—21no—
238C23×C11—21no—
239C23×C11—21no—
240C23×C11#13112yes—
241C23×C11C23×C411yescharacteristic
242D4×C11—44no—
243C2×C4×C11—21no—
244C2×C4×C11—21no—
245C2×C4×C11—21no—
246C2×C4×C11—21no—
247C2×C4×C11—21no—
248C2×C4×C11—21no—
249C2×C4×C11—21no—
250C2×C4×C11—21no—
251C2×C4×C11—21no—
252C2×C4×C11—21no—
253C2×C4×C11—21no—
254C2×C4×C11—21no—
255C2×C4×C11—21no—
256C2×C4×C11—21no—
257C2×C4×C11—21no—
258C2×C4×C11—21no—
259C2×C4×C11—21no—
260C2×C4×C11—21no—
261C2×C4×C11—21no—
262C2×C4×C11—21no—
263C2×C4×C11—21no—
264C2×C4×C11—21no—
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—21no—
274C2×C4×C11—21no—
275C2×C4×C11—21no—
276C2×C4×C11—44no—
277C2×C4×C11—44no—
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×C11#11712yes—
287C2×C4×C11#11712yes—
288C2×C4×C11#13112yes—
289C2×C4×C11C2×#4111yescharacteristic
290C2×C4×C11C2×#4111yescharacteristic
291C2×C4×C11H(5,𝔽2)11yescharacteristic
292C2×C4×C11H(5,𝔽2)11yescharacteristic
293C2×C4×C11H(5,𝔽2)11yescharacteristic
294C2×C4×C112−1+411yescharacteristic
295C11⋊C8—41no—
296C11⋊C8—41no—
297C11⋊C8—41no—
298C11⋊C8—41no—
299C11⋊C8—41no—
300C11⋊C8—41no—
301C11⋊C8—41no—
302C11⋊C8—41no—
303C2×C4×D4C2×D1111yescharacteristic
304C2×#117C2×D1111yescharacteristic
305C22×C42C2×D1111yescharacteristic
306C2×C4⋊C8—111no—
307C2×C4⋊C8—111no—
308C2×C4⋊C8—111no—
309C2×C4⋊C8—111no—
310C2×C4⋊C8—111no—
311C2×C4⋊C8—111no—
312C2×C22⋊C8—111no—
313C2×C22⋊C8—111no—
314C2×C22⋊C8—111no—
315C2×C22⋊C8—111no—
316C2×C22⋊C8—111no—
317C2×C22⋊C8—111no—
318C2×C22⋊C8—111no—
319C2×C22⋊C8—111no—
320C2×#97—111no—
321C2×#97—111no—
322C2×C4×C8—111no—
323C2×C4×C8—111no—
324#388Dic1111yescharacteristic
325#388Dic1111yescharacteristic
326#387Dic1111yescharacteristic
327#387Dic1111yescharacteristic
328#386Dic1111yescharacteristic
329#386Dic1111yescharacteristic
330#385Dic1111yescharacteristic
331#385Dic1111yescharacteristic
332C4×C4⋊C4C2×D1111yescharacteristic
333C4×C22⋊C4C2×D1111yescharacteristic
334C4×C22⋊C4C2×D1111yescharacteristic
335#376C2×D1111yescharacteristic
336#336—111no—
337#336—111no—
338#336—111no—
339#336—111no—
340#336—111no—
341#336—111no—
342#336—111no—
343#336—111no—
344#336—111no—
345#336—111no—
346C22×C11—22no—
347C22×C11—22no—
348C22×C11—22no—
349C22×C11—41no—
350C22×C11—41no—
351C22×C11—41no—
352C22×C11—41no—
353C22×C11—41no—
354C22×C11—41no—
355C22×C11—41no—
356C22×C11—41no—
357C22×C11—41no—
358C22×C11—41no—
359C22×C11—41no—
360C22×C11C2×#11711yescharacteristic
361C22×C11#51811yescharacteristic
362C22×C11#52011yescharacteristic
363C22×C11C2×#13111yescharacteristic
364C22×C11C2×#13111yescharacteristic
365C22×C11#56811yescharacteristic
366C22×C11#56811yescharacteristic
367C4×C11—22no—
368C4×C11—22no—
369C4×C11—22no—
370C4×C11—41no—
371C4×C11—41no—
372C4×C11—41no—
373C4×C11—41no—
374C4×C11—41no—
375C4×C11—41no—
376C4×C11—41no—
377C4×C11—41no—
378C4×C11—41no—
379C4×C11#54011yescharacteristic
380C4×C11#54011yescharacteristic
381C4×C11#54211yescharacteristic
382C4×C11#54211yescharacteristic
383C22×D4C2×Dic1111yescharacteristic
384C23×C4C2×Dic1111yescharacteristic
385C23×C4C2×Dic1111yescharacteristic
386C23×C4C22×D1111yescharacteristic
387C23×C4C22×D1111yescharacteristic
388C22×C8—111no—
389C22×C8—111no—
390C22×C8—111no—
391C22×C8—111no—
392C22×C8—111no—
393C22×C8—111no—
394C22×C8—111no—
395C22×C8—111no—
396C4×D4—22no—
397C4×D4—22no—
398#117—41no—
399#117—41no—
400C2×C4⋊C4C2×Dic1111yescharacteristic
401C2×C4⋊C4C2×Dic1111yescharacteristic
402C2×C4⋊C4C2×Dic1111yescharacteristic
403C2×C4⋊C4C2×Dic1111yescharacteristic
404C2×C4⋊C4C2×Dic1111yescharacteristic
405C2×C22⋊C4C2×Dic1111yescharacteristic
406C2×C22⋊C4C2×Dic1111yescharacteristic
407C2×C22⋊C4C2×Dic1111yescharacteristic
408C2×C22⋊C4C2×Dic1111yescharacteristic
409C2×C22⋊C4C2×Dic1111yescharacteristic
410C2×C22⋊C4C2×Dic1111yescharacteristic
411C2×C22⋊C4C2×Dic1111yescharacteristic
412C2×C22⋊C4C2×Dic1111yescharacteristic
413C2×C42—41no—
414C2×C42—41no—
415C2×C42C2×Dic1111yescharacteristic
416C2×C42C2×Dic1111yescharacteristic
417C2×C42C22×D1111yescharacteristic
418C2×C42C22×D1111yescharacteristic
419C2×C42C22×D1111yescharacteristic
420C2×C42C22×D1111yescharacteristic
421C2×C42C22×D1111yescharacteristic
422C4⋊C8—222no—
423C4⋊C8—222no—
424C4⋊C8—441no—
425C4⋊C8—441no—
426C4⋊C8—441no—
427C4⋊C8—441no—
428C22⋊C8—441no—
429C22⋊C8—441no—
430C22⋊C8—441no—
431C22⋊C8—441no—
432C22⋊C8—441no—
433C22⋊C8—441no—
434C22⋊C8—441no—
435C22⋊C8—441no—
436#97—222no—
437#97—441no—
438C4×C8—222no—
439C4×C8—441no—
440#95C2×Dic1111yescharacteristic
441#95C2×Dic1111yescharacteristic
442#95C2×Dic1111yescharacteristic
443#95C2×Dic1111yescharacteristic
444#95C2×Dic1111yescharacteristic
445#95C2×Dic1111yescharacteristic
446#95C2×Dic1111yescharacteristic
447#95C2×Dic1111yescharacteristic
448#95C2×Dic1111yescharacteristic
449#95C2×Dic1111yescharacteristic
450C2×C11—42no—
451C2×C11—81no—
452C2×C11#231911yescharacteristic
453C2×C11#292411yescharacteristic
454C2×C11#292511yescharacteristic
455C2×C11#297711yescharacteristic
456C2×C11#297811yescharacteristic
457C2×C11#299211yescharacteristic
458C2×C11#299311yescharacteristic
459C24C22×Dic1111yescharacteristic
460C24C22×Dic1111yescharacteristic
461C2×D4—22no—
462C2×D4—22no—
463C2×D4—41no—
464C22×C4—22no—
465C22×C4—22no—
466C22×C4—21no—
467C22×C4—21no—
468C22×C4—21no—
469C22×C4—21no—
470C22×C4—21no—
471C22×C4—21no—
472C22×C4—21no—
473C22×C4—21no—
474C22×C4—21no—
475C22×C4—21no—
476C22×C4—21no—
477C22×C4—21no—
478C22×C4—41no—
479C22×C4—41no—
480C22×C4—41no—
481C22×C4—41no—
482C22×C4C22×Dic1111yescharacteristic
483C22×C4C22×Dic1111yescharacteristic
484C22×C4C22×Dic1111yescharacteristic
485C22×C4C22×Dic1111yescharacteristic
486C22×C4C22×Dic1111yescharacteristic
487C22×C4C22×Dic1111yescharacteristic
488C22×C4C22×Dic1111yescharacteristic
489C22×C4C22×Dic1111yescharacteristic
490C22×C4C22×Dic1111yescharacteristic
491C22×C4C22×Dic1111yescharacteristic
492C22×C4C22×Dic1111yescharacteristic
493C22×C4C22×Dic1111yescharacteristic
494C22×C4C23×D1111yescharacteristic
495C2×C8—221no—
496C2×C8—221no—
497C2×C8—221no—
498C2×C8—221no—
499C2×C8—221no—
500C2×C8—221no—
501C2×C8—221no—
502C2×C8—221no—
503C2×C8—221no—
504C2×C8—221no—
505C2×C8—221no—
506C2×C8—221no—
507C2×C8—221no—
508C2×C8—221no—
509C2×C8—221no—
510C2×C8—221no—
511C2×C8—221no—
512C2×C8—221no—
513C2×C8—221no—
514C2×C8—221no—
515C2×C8—221no—
516C2×C8—221no—
517C2×C8—221no—
518C2×C8—221no—
519C4⋊C4—22no—
520C4⋊C4—22no—
521C4⋊C4—41no—
522C4⋊C4—41no—
523C4⋊C4—41no—
524C22⋊C4—22no—
525C22⋊C4—22no—
526C22⋊C4—22no—
527C22⋊C4—22no—
528C22⋊C4—41no—
529C22⋊C4—41no—
530C22⋊C4—41no—
531C22⋊C4—41no—
532C42—21no—
533C42—21no—
534C42—21no—
535C42—21no—
536C42—21no—
537C42—21no—
538C42—21no—
539C42—21no—
540C42—41no—
541C42—41no—
542C42#433912yes—
543C42#433912yes—
544C11#2201711yescharacteristic, complemented, Sylow
545C23—21no—
546C23—21no—
547C23—21no—
548C23—21no—
549C23—21no—
550C23—21no—
551C23—21no—
552C23—21no—
553C23—21no—
554C23—21no—
555C23—21no—
556C23—21no—
557C23—21no—
558C23#6700112yes—
559C23C23×Dic1111yescharacteristic
560D4—44no—
561C2×C4—21no—
562C2×C4—21no—
563C2×C4—21no—
564C2×C4—21no—
565C2×C4—21no—
566C2×C4—21no—
567C2×C4—21no—
568C2×C4—21no—
569C2×C4—21no—
570C2×C4—21no—
571C2×C4—21no—
572C2×C4—21no—
573C2×C4—21no—
574C2×C4—21no—
575C2×C4—21no—
576C2×C4—21no—
577C2×C4—21no—
578C2×C4—21no—
579C2×C4—21no—
580C2×C4—21no—
581C2×C4—21no—
582C2×C4—21no—
583C2×C4—21no—
584C2×C4—21no—
585C2×C4—21no—
586C2×C4—21no—
587C2×C4—21no—
588C2×C4—21no—
589C2×C4—21no—
590C2×C4—21no—
591C2×C4—21no—
592C2×C4—21no—
593C2×C4—21no—
594C2×C4—44no—
595C2×C4—44no—
596C2×C4—41no—
597C2×C4—41no—
598C2×C4—41no—
599C2×C4—41no—
600C2×C4—41no—
601C2×C4—41no—
602C2×C4—41no—
603C2×C4—41no—
604C2×C4#6697912yes—
605C2×C4#6697912yes—
606C2×C4#6700112yes—
607C2×C4C2×#433911yescharacteristic
608C2×C4C2×#433911yescharacteristic
609C2×C4#6703711yescharacteristic
610C2×C4#6703711yescharacteristic
611C2×C4#6704211yescharacteristic
612C2×C4#6704311yescharacteristic
613C8—441no—
614C8—441no—
615C8—441no—
616C8—441no—
617C8—441no—
618C8—441no—
619C8—441no—
620C8—441no—
621C22—22no—
622C22—22no—
623C22—22no—
624C22—41no—
625C22—41no—
626C22—41no—
627C22—41no—
628C22—41no—
629C22—41no—
630C22—41no—
631C22—41no—
632C22—41no—
633C22—41no—
634C22—41no—
635C22C2×#6697911yescharacteristic
636C22#1062332911yescharacteristic
637C22C2×#6700111yescharacteristic
638C22C2×#6700111yescharacteristic
639C22#1062335011yescharacteristic
640C22#1062335011yescharacteristic
641C22#1062335811yescharacteristic
642C4—22no—
643C4—22no—
644C4—22no—
645C4—41no—
646C4—41no—
647C4—41no—
648C4—41no—
649C4—41no—
650C4—41no—
651C4—41no—
652C4—41no—
653C4—41no—
654C4#1062309211yescharacteristic
655C4#1062309211yescharacteristic
656C4#1062309311yescharacteristic
657C4#1062309311yescharacteristic
658C2—42no—
659C2—81no—
660C2#1307125911yescharacteristic
661C2#1307727411yescharacteristic
662C2#1307728211yescharacteristic
663C2#1307767211yescharacteristic
664C2#1307767811yescharacteristic
665C2#1307775511yescharacteristic
666C2#1307776511yescharacteristic
subgroupG/H
center, FrattiniC22×C4C23×D11
commutator, socleC23×C11C23×C4
FittingC11×#2290C2
prime radicalC22×D4×C11C2×C4
cosocleC22×C4×C11C24
hypercenter#2290D11
hypocenterC11#22017
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C22×C4 ◁ #2290

Complements

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

NH ≅ G/Ntype
3. #13069340C2semidirect
4. #13069335C2semidirect
5. #13069231C2semidirect
6. #13069231C2semidirect
7. #13069224C2semidirect
8. #13069224C2semidirect
9. #13068687C2semidirect
10. #13068684C2semidirect
11. #13068600C2semidirect
12. #13068596C2semidirect
13. #13068473C2semidirect
14. #13068368C2semidirect
544. C11#22017semidirect

Maximal subgroups

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

subgroupindex
#130694152
#130694112
#130693402
#130693352
#130692312
#130692242
#130686872
#130686842
#130686002
#130685962
#130684732
#130683682
C11×#22902
#2201711