Finite Group Databasebeta

← C11×#27065 #14604258

Subgroups — C11×#27065 #14604258

Order 2816.

874 conjugacy classes of subgroups.

The subgroup lattice has 708 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#2513C211yesmaximal, characteristic, complemented
2C11×#2366C211yesmaximal, characteristic, complemented
3C11×#2092C211yesmaximal, characteristic, complemented
4C11×#2054C211yesmaximal, characteristic, complemented
5C11×#2041C211yesmaximal, characteristic, complemented
6C11×#2011C211yesmaximal, characteristic
7C11×#1970C211yesmaximal, characteristic, complemented
8C11×#1926C211yesmaximal, characteristic, complemented
9C11×#1926C211yesmaximal, characteristic, complemented
10C11×#1921C211yesmaximal, characteristic, complemented
11C11×#1916C211yesmaximal, characteristic, complemented
12C11×#1879C211yesmaximal, characteristic, complemented
13C11×#1879C211yesmaximal, characteristic, complemented
14C11×#1804C211yesmaximal, characteristic, complemented
15C4×C11×#102C211yesmaximal, characteristic, complemented
16C22×C11×D8C2211yescharacteristic
17C22×C11×D8C2211yescharacteristic
18C2×C11×#127C2211yescharacteristic
19C2×C4×D4×C11—21no—
20C2×C4×D4×C11C2211yescharacteristic
21C2×C4×D4×C11C2211yescharacteristic
22C2×C11×#107C2211yescharacteristic
23C2×C11×#106C2211yescharacteristic
24C2×C11×C4⋊C8C2211yescharacteristic
25C2×C11×#102C2211yescharacteristic
26C2×C11×#102C2211yescharacteristic
27C2×C11×#102C2211yescharacteristic
28C2×C11×#102C2211yescharacteristic
29C2×C11×#102C2211yescharacteristic
30C2×C11×#102C2211yescharacteristic
31C2×C11×#102C2211yescharacteristic
32C2×C11×#102C2211yescharacteristic
33C2×C4×C8×C11C2211yescharacteristic
34C11×#397—21no—
35C11×#397—21no—
36C11×#390—21no—
37C11×#390C2211yescharacteristic
38C11×#390C2211yescharacteristic
39C11×#390C2211yescharacteristic
40C11×#390C2211yescharacteristic
41C11×#390C2211yescharacteristic
42C11×#389C2211yescharacteristic
43C11×#388—21no—
44C11×#388—21no—
45C11×#386—21no—
46C11×#386—21no—
47C11×#382C2211yescharacteristic
48C4×C11×C4⋊C4C2211yescharacteristic
49C4×C11×C4⋊C4C2211yescharacteristic
50C4×C11×C4⋊C4C2211yescharacteristic
51C11×#340C2211yescharacteristic
52C11×#340C2211yescharacteristic
53C11×#340C2211yescharacteristic
54C11×#340C2211yescharacteristic
55C11×#336C2211yescharacteristic
56C11×#336C2211yescharacteristic
57C11×#336C2211yescharacteristic
58C11×#336C2211yescharacteristic
59C22×D4×C11—21no—
60C22×D4×C11—21no—
61C22×D4×C11C2311yescharacteristic
62C22×D4×C11C2311yescharacteristic
63C22×D4×C11C2311yescharacteristic
64C23×C4×C11—21no—
65C23×C4×C11—21no—
66C2×C11×D8—22no—
67C2×C11×D8—22no—
68C2×C11×D8—22no—
69C2×C11×D8—41no—
70C2×C11×D8—41no—
71C2×C11×D8—41no—
72C22×C8×C11C2311yescharacteristic
73C22×C8×C11C2311yescharacteristic
74C22×C8×C11C2311yescharacteristic
75C22×C8×C11C2311yescharacteristic
76C11×#127—22no—
77C11×#127—22no—
78C4×D4×C11—22no—
79C4×D4×C11—22no—
80C4×D4×C11—41no—
81C4×D4×C11—41no—
82C4×D4×C11—44no—
83C2×C11×C4⋊C4—21no—
84C2×C11×C4⋊C4D411yescharacteristic
85C2×C11×C4⋊C4D411yescharacteristic
86C2×C11×C4⋊C4C2311yescharacteristic
87C2×C11×C4⋊C4C2311yescharacteristic
88C2×C11×C4⋊C4C2311yescharacteristic
89C2×C11×C4⋊C4C2311yescharacteristic
90C2×C11×C4⋊C4C2311yescharacteristic
91C2×C11×C22⋊C4—21no—
92C2×C11×C22⋊C4—21no—
93C2×C11×C22⋊C4—21no—
94C2×C11×C22⋊C4—21no—
95C2×C11×C22⋊C4—21no—
96C2×C11×C22⋊C4—21no—
97C2×C11×C22⋊C4—21no—
98C2×C11×C22⋊C4—21no—
99C2×C11×C22⋊C4—21no—
100C2×C11×C22⋊C4—21no—
101C2×C11×C22⋊C4—21no—
102C2×C11×C22⋊C4—21no—
103C2×C42×C11—21no—
104C2×C42×C11—21no—
105C2×C42×C11C2311yescharacteristic
106C2×C42×C11C2311yescharacteristic
107C2×C42×C11C2311yescharacteristic
108C11×#107—22no—
109C11×#106—41no—
110C11×C4⋊C8—41no—
111C11×#102—22no—
112C11×#102—22no—
113C11×#102—22no—
114C11×#102—22no—
115C11×#102—41no—
116C11×#102—41no—
117C11×#102—41no—
118C11×#102—41no—
119C4×C8×C11—41no—
120C11×#95—21no—
121C11×#95—21no—
122C11×#95—21no—
123C11×#95—21no—
124C11×#95—21no—
125C11×#95D411yescharacteristic
126C11×#95D411yescharacteristic
127#27065C1111yesmaximal, characteristic, direct product factor, Sylow
128C24×C11—21no—
129C24×C11—21no—
130C24×C11—21no—
131C2×D4×C11—24no—
132C2×D4×C11—24no—
133C2×D4×C11—21no—
134C2×D4×C11—21no—
135C2×D4×C11—21no—
136C2×D4×C11—21no—
137C2×D4×C11—21no—
138C2×D4×C11—21no—
139C2×D4×C11—21no—
140C2×D4×C11—21no—
141C2×D4×C11—21no—
142C2×D4×C11—21no—
143C2×D4×C11—21no—
144C2×D4×C11—21no—
145C2×D4×C11—21no—
146C2×D4×C11—21no—
147C2×D4×C11—21no—
148C2×D4×C11—21no—
149C2×D4×C11—42no—
150C2×D4×C11—42no—
151C2×D4×C11—81no—
152C2×D4×C11—81no—
153C2×D4×C11#4112yes—
154C2×D4×C11#4112yes—
155C22×C4×C11—21no—
156C22×C4×C11—21no—
157C22×C4×C11—21no—
158C22×C4×C11—21no—
159C22×C4×C11—21no—
160C22×C4×C11—42no—
161C22×C4×C11—42no—
162C22×C4×C11—42no—
163C22×C4×C11—42no—
164C22×C4×C11—81no—
165C22×C4×C11—81no—
166C22×C4×C11C2×D411yescharacteristic
167C22×C4×C11C2×D411yescharacteristic
168C22×C4×C11C2×D411yescharacteristic
169C22×C4×C11C2×D411yescharacteristic
170C22×C4×C11C2×D411yescharacteristic
171C22×C4×C11C2×D411yescharacteristic
172C22×C4×C11C2411yescharacteristic
173C11×D8—44no—
174C11×D8—44no—
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#4112yes—
187C11×C4⋊C4—22no—
188C11×C4⋊C4—22no—
189C11×C4⋊C4—21no—
190C11×C4⋊C4—21no—
191C11×C4⋊C4—21no—
192C11×C4⋊C4—21no—
193C11×C4⋊C4—21no—
194C11×C4⋊C4—21no—
195C11×C4⋊C4—21no—
196C11×C4⋊C4—21no—
197C11×C4⋊C4—21no—
198C11×C4⋊C4—81no—
199C11×C4⋊C4#4112yes—
200C11×C22⋊C4—42no—
201C11×C22⋊C4—42no—
202C11×C22⋊C4—42no—
203C11×C22⋊C4—42no—
204C11×C22⋊C4—42no—
205C11×C22⋊C4—42no—
206C11×C22⋊C4—81no—
207C11×C22⋊C4—81no—
208C11×C22⋊C4—81no—
209C11×C22⋊C4—81no—
210C11×C22⋊C4—81no—
211C11×C22⋊C4—81no—
212C42×C11—21no—
213C42×C11—21no—
214C42×C11—21no—
215C42×C11—21no—
216C42×C11—21no—
217C42×C11—21no—
218C42×C11—42no—
219C42×C11—81no—
220#2513C2×C1111yescharacteristic, complemented
221#2366C2×C1111yescharacteristic, complemented
222#2092C2×C1111yescharacteristic, complemented
223#2054C2×C1111yescharacteristic, complemented
224#2041C2×C1111yescharacteristic, complemented
225#2011C2×C1111yescharacteristic
226#1970C2×C1111yescharacteristic, complemented
227#1926C2×C1111yescharacteristic, complemented
228#1926C2×C1111yescharacteristic, complemented
229#1921C2×C1111yescharacteristic, complemented
230#1916C2×C1111yescharacteristic, complemented
231#1879C2×C1111yescharacteristic, complemented
232#1879C2×C1111yescharacteristic, complemented
233#1804C2×C1111yescharacteristic, complemented
234C4×#102C2×C1111yescharacteristic, complemented
235C23×C11—22no—
236C23×C11—22no—
237C23×C11—41no—
238C23×C11—41no—
239C23×C11—41no—
240C23×C11—41no—
241C23×C11—41no—
242C23×C11—41no—
243C23×C11—41no—
244C23×C11—41no—
245C23×C11—41no—
246C23×C11—41no—
247C23×C11—41no—
248C23×C11—41no—
249C23×C11—41no—
250C23×C11—41no—
251C23×C11—41no—
252C23×C11—41no—
253C23×C11—41no—
254C23×C11—41no—
255C23×C11—41no—
256C23×C11C22×D411yescharacteristic
257D4×C11—22no—
258D4×C11—22no—
259D4×C11—22no—
260D4×C11—22no—
261D4×C11—48no—
262D4×C11—41no—
263D4×C11—41no—
264D4×C11—41no—
265D4×C11—41no—
266D4×C11—41no—
267D4×C11—41no—
268D4×C11—41no—
269D4×C11—41no—
270D4×C11—84no—
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—21no—
279C2×C4×C11—22no—
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—41no—
289C2×C4×C11—41no—
290C2×C4×C11—41no—
291C2×C4×C11—41no—
292C2×C4×C11—41no—
293C2×C4×C11—41no—
294C2×C4×C11—41no—
295C2×C4×C11—41no—
296C2×C4×C11—41no—
297C2×C4×C11—41no—
298C2×C4×C11—41no—
299C2×C4×C11—41no—
300C2×C4×C11—41no—
301C2×C4×C11—41no—
302C2×C4×C11—84no—
303C2×C4×C11—84no—
304C2×C4×C11#13512yes—
305C2×C4×C11AGL(1,ℤ/8)12yes—
306C2×C4×C11C2×#4111yescharacteristic
307C2×C4×C11C2×#4111yescharacteristic
308C2×C4×C11C2×#4111yescharacteristic
309C2×C4×C11C2×#4111yescharacteristic
310C2×C4×C11H(5,𝔽2)11yescharacteristic
311C2×C4×C11H(5,𝔽2)11yescharacteristic
312C8×C11—22no—
313C8×C11—41no—
314C8×C11—41no—
315C8×C11—41no—
316C22×D8C22×C1111yescharacteristic
317C22×D8C22×C1111yescharacteristic
318C2×#127C22×C1111yescharacteristic
319C2×C4×D4—21no—
320C2×C4×D4C22×C1111yescharacteristic
321C2×C4×D4C22×C1111yescharacteristic
322C2×#107C22×C1111yescharacteristic
323C2×#106C22×C1111yescharacteristic
324C2×C4⋊C8C22×C1111yescharacteristic
325C2×#102C22×C1111yescharacteristic
326C2×#102C22×C1111yescharacteristic
327C2×#102C22×C1111yescharacteristic
328C2×#102C22×C1111yescharacteristic
329C2×#102C22×C1111yescharacteristic
330C2×#102C22×C1111yescharacteristic
331C2×#102C22×C1111yescharacteristic
332C2×#102C22×C1111yescharacteristic
333C2×C4×C8C22×C1111yescharacteristic
334#397—21no—
335#397—21no—
336#390—21no—
337#390C22×C1111yescharacteristic
338#390C22×C1111yescharacteristic
339#390C22×C1111yescharacteristic
340#390C22×C1111yescharacteristic
341#390C22×C1111yescharacteristic
342#389C22×C1111yescharacteristic
343#388—21no—
344#388—21no—
345#386—21no—
346#386—21no—
347#382C22×C1111yescharacteristic
348C4×C4⋊C4C22×C1111yescharacteristic
349C4×C4⋊C4C22×C1111yescharacteristic
350C4×C4⋊C4C22×C1111yescharacteristic
351#340C22×C1111yescharacteristic
352#340C22×C1111yescharacteristic
353#340C22×C1111yescharacteristic
354#340C22×C1111yescharacteristic
355#336C22×C1111yescharacteristic
356#336C22×C1111yescharacteristic
357#336C22×C1111yescharacteristic
358#336C22×C1111yescharacteristic
359C22×C11—42no—
360C22×C11—42no—
361C22×C11—42no—
362C22×C11—42no—
363C22×C11—42no—
364C22×C11—42no—
365C22×C11—81no—
366C22×C11—81no—
367C22×C11—81no—
368C22×C11—81no—
369C22×C11—81no—
370C22×C11—81no—
371C22×C11—81no—
372C22×C11—81no—
373C22×C11—81no—
374C22×C11—81no—
375C22×C11—81no—
376C22×C11—81no—
377C22×C11—81no—
378C22×C11—81no—
379C22×C11—81no—
380C22×C11#52511yescharacteristic
381C22×C11#54611yescharacteristic
382C22×C11#55011yescharacteristic
383C22×C11C2×#13511yescharacteristic
384C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
385C22×C11#57611yescharacteristic
386C22×C11#57611yescharacteristic
387C4×C11—22no—
388C4×C11—22no—
389C4×C11—41no—
390C4×C11—41no—
391C4×C11—41no—
392C4×C11—41no—
393C4×C11—42no—
394C4×C11—81no—
395C4×C11—81no—
396C4×C11—81no—
397C4×C11—81no—
398C4×C11#52911yescharacteristic
399C4×C11#53811yescharacteristic
400C4×C11#55111yescharacteristic
401C4×C11#55311yescharacteristic
402C22×D4—21no—
403C22×D4—21no—
404C22×D4C23×C1111yescharacteristic
405C22×D4C23×C1111yescharacteristic
406C22×D4C23×C1111yescharacteristic
407C23×C4—21no—
408C23×C4—21no—
409C2×D8—22no—
410C2×D8—22no—
411C2×D8—22no—
412C2×D8—41no—
413C2×D8—41no—
414C2×D8—41no—
415C22×C8C23×C1111yescharacteristic
416C22×C8C23×C1111yescharacteristic
417C22×C8C23×C1111yescharacteristic
418C22×C8C23×C1111yescharacteristic
419#127—22no—
420#127—22no—
421C4×D4—22no—
422C4×D4—22no—
423C4×D4—41no—
424C4×D4—41no—
425C4×D4—44no—
426C2×C4⋊C4—21no—
427C2×C4⋊C4D4×C1111yescharacteristic
428C2×C4⋊C4D4×C1111yescharacteristic
429C2×C4⋊C4C23×C1111yescharacteristic
430C2×C4⋊C4C23×C1111yescharacteristic
431C2×C4⋊C4C23×C1111yescharacteristic
432C2×C4⋊C4C23×C1111yescharacteristic
433C2×C4⋊C4C23×C1111yescharacteristic
434C2×C22⋊C4—21no—
435C2×C22⋊C4—21no—
436C2×C22⋊C4—21no—
437C2×C22⋊C4—21no—
438C2×C22⋊C4—21no—
439C2×C22⋊C4—21no—
440C2×C22⋊C4—21no—
441C2×C22⋊C4—21no—
442C2×C22⋊C4—21no—
443C2×C22⋊C4—21no—
444C2×C22⋊C4—21no—
445C2×C22⋊C4—21no—
446C2×C42—21no—
447C2×C42—21no—
448C2×C42C23×C1111yescharacteristic
449C2×C42C23×C1111yescharacteristic
450C2×C42C23×C1111yescharacteristic
451#107—22no—
452#106—41no—
453C4⋊C8—41no—
454#102—22no—
455#102—22no—
456#102—22no—
457#102—22no—
458#102—41no—
459#102—41no—
460#102—41no—
461#102—41no—
462C4×C8—41no—
463#95—21no—
464#95—21no—
465#95—21no—
466#95—21no—
467#95—21no—
468#95D4×C1111yescharacteristic
469#95D4×C1111yescharacteristic
470C2×C11—82no—
471C2×C11—82no—
472C2×C11—161no—
473C2×C11#246711yescharacteristic
474C2×C11#310511yescharacteristic
475C2×C11#312211yescharacteristic
476C2×C11#330511yescharacteristic
477C2×C11#331811yescharacteristic
478C2×C11#339611yescharacteristic
479C2×C11#339911yescharacteristic
480C24—21no—
481C24—21no—
482C24—21no—
483C2×D4—24no—
484C2×D4—24no—
485C2×D4—21no—
486C2×D4—21no—
487C2×D4—21no—
488C2×D4—21no—
489C2×D4—21no—
490C2×D4—21no—
491C2×D4—21no—
492C2×D4—21no—
493C2×D4—21no—
494C2×D4—21no—
495C2×D4—21no—
496C2×D4—21no—
497C2×D4—21no—
498C2×D4—21no—
499C2×D4—21no—
500C2×D4—21no—
501C2×D4—42no—
502C2×D4—42no—
503C2×D4—81no—
504C2×D4—81no—
505C2×D4C11×#4112yes—
506C2×D4C11×#4112yes—
507C22×C4—21no—
508C22×C4—21no—
509C22×C4—21no—
510C22×C4—21no—
511C22×C4—21no—
512C22×C4—42no—
513C22×C4—42no—
514C22×C4—42no—
515C22×C4—42no—
516C22×C4—81no—
517C22×C4—81no—
518C22×C4C2×D4×C1111yescharacteristic
519C22×C4C2×D4×C1111yescharacteristic
520C22×C4C2×D4×C1111yescharacteristic
521C22×C4C2×D4×C1111yescharacteristic
522C22×C4C2×D4×C1111yescharacteristic
523C22×C4C2×D4×C1111yescharacteristic
524C22×C4C24×C1111yescharacteristic
525D8—44no—
526D8—44no—
527C2×C8—21no—
528C2×C8—21no—
529C2×C8—21no—
530C2×C8—21no—
531C2×C8—21no—
532C2×C8—21no—
533C2×C8—21no—
534C2×C8—21no—
535C2×C8—21no—
536C2×C8—21no—
537C2×C8—21no—
538C2×C8C11×#4112yes—
539C4⋊C4—22no—
540C4⋊C4—22no—
541C4⋊C4—21no—
542C4⋊C4—21no—
543C4⋊C4—21no—
544C4⋊C4—21no—
545C4⋊C4—21no—
546C4⋊C4—21no—
547C4⋊C4—21no—
548C4⋊C4—21no—
549C4⋊C4—21no—
550C4⋊C4—81no—
551C4⋊C4C11×#4112yes—
552C22⋊C4—42no—
553C22⋊C4—42no—
554C22⋊C4—42no—
555C22⋊C4—42no—
556C22⋊C4—42no—
557C22⋊C4—42no—
558C22⋊C4—81no—
559C22⋊C4—81no—
560C22⋊C4—81no—
561C22⋊C4—81no—
562C22⋊C4—81no—
563C22⋊C4—81no—
564C42—21no—
565C42—21no—
566C42—21no—
567C42—21no—
568C42—21no—
569C42—21no—
570C42—42no—
571C42—81no—
572C11#2706511yescharacteristic, direct product factor, Sylow
573C23—22no—
574C23—22no—
575C23—41no—
576C23—41no—
577C23—41no—
578C23—41no—
579C23—41no—
580C23—41no—
581C23—41no—
582C23—41no—
583C23—41no—
584C23—41no—
585C23—41no—
586C23—41no—
587C23—41no—
588C23—41no—
589C23—41no—
590C23—41no—
591C23—41no—
592C23—41no—
593C23—41no—
594C23C22×D4×C1111yescharacteristic
595D4—22no—
596D4—22no—
597D4—22no—
598D4—22no—
599D4—48no—
600D4—41no—
601D4—41no—
602D4—41no—
603D4—41no—
604D4—41no—
605D4—41no—
606D4—41no—
607D4—41no—
608D4—84no—
609C2×C4—21no—
610C2×C4—21no—
611C2×C4—21no—
612C2×C4—21no—
613C2×C4—21no—
614C2×C4—21no—
615C2×C4—21no—
616C2×C4—21no—
617C2×C4—22no—
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—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—41no—
637C2×C4—41no—
638C2×C4—41no—
639C2×C4—41no—
640C2×C4—84no—
641C2×C4—84no—
642C2×C4C11×#13512yes—
643C2×C4C11×AGL(1,ℤ/8)12yes—
644C2×C4C2×C11×#4111yescharacteristic
645C2×C4C2×C11×#4111yescharacteristic
646C2×C4C2×C11×#4111yescharacteristic
647C2×C4C2×C11×#4111yescharacteristic
648C2×C4C11×H(5,𝔽2)11yescharacteristic
649C2×C4C11×H(5,𝔽2)11yescharacteristic
650C8—22no—
651C8—41no—
652C8—41no—
653C8—41no—
654C22—42no—
655C22—42no—
656C22—42no—
657C22—42no—
658C22—42no—
659C22—42no—
660C22—81no—
661C22—81no—
662C22—81no—
663C22—81no—
664C22—81no—
665C22—81no—
666C22—81no—
667C22—81no—
668C22—81no—
669C22—81no—
670C22—81no—
671C22—81no—
672C22—81no—
673C22—81no—
674C22—81no—
675C22C11×#52511yescharacteristic
676C22C11×#54611yescharacteristic
677C22C11×#55011yescharacteristic
678C22C2×C11×#13511yescharacteristic
679C22C2×C11×AGL(1,ℤ/8)11yescharacteristic
680C22C11×#57611yescharacteristic
681C22C11×#57611yescharacteristic
682C4—22no—
683C4—22no—
684C4—41no—
685C4—41no—
686C4—41no—
687C4—42no—
688C4—41no—
689C4—81no—
690C4—81no—
691C4—81no—
692C4—81no—
693C4C11×#52911yescharacteristic
694C4C11×#53811yescharacteristic
695C4C11×#55111yescharacteristic
696C4C11×#55311yescharacteristic
697C2—82no—
698C2—82no—
699C2—161no—
700C2C11×#246711yescharacteristic
701C2C11×#310511yescharacteristic
702C2C11×#312211yescharacteristic
703C2C11×#330511yescharacteristic
704C2C11×#331811yescharacteristic
705C2C11×#339611yescharacteristic
706C2C11×#339911yescharacteristic
subgroupG/H
center, socleC23×C11C22×D4
commutator, Frattini, cosocleC22×C4C24×C11
prime radicalC11×#2011C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C11 ◁ C4×C11×C4⋊C4 ◁ G

Complements

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

NH ≅ G/Ntype
1. C11×#2513C2semidirect
2. C11×#2366C2semidirect
3. C11×#2092C2semidirect
4. C11×#2054C2semidirect
5. C11×#2041C2semidirect
7. C11×#1970C2semidirect
8. C11×#1926C2semidirect
9. C11×#1926C2semidirect
10. C11×#1921C2semidirect
11. C11×#1916C2semidirect
12. C11×#1879C2semidirect
13. C11×#1879C2semidirect
14. C11×#1804C2semidirect
15. C4×C11×#102C2semidirect
127. #27065C11direct (N × H)
220. #2513C2×C11semidirect
221. #2366C2×C11semidirect
222. #2092C2×C11semidirect
223. #2054C2×C11semidirect
224. #2041C2×C11semidirect
226. #1970C2×C11semidirect
227. #1926C2×C11semidirect
228. #1926C2×C11semidirect
229. #1921C2×C11semidirect
230. #1916C2×C11semidirect
231. #1879C2×C11semidirect
232. #1879C2×C11semidirect
233. #1804C2×C11semidirect
234. C4×#102C2×C11semidirect
572. C11#27065direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#25132
C11×#23662
C11×#20922
C11×#20542
C11×#20412
C11×#20112
C11×#19702
C11×#19262
C11×#19212
C11×#19162
C11×#18792
C11×#18042
C4×C11×#1022
#2706511