Finite Group Databasebeta

← C11×#27062 #14604255

Subgroups — C11×#27062 #14604255

Order 2816.

902 conjugacy classes of subgroups.

The subgroup lattice has 714 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#2512C211yesmaximal, characteristic, complemented
2C11×#2366C211yesmaximal, characteristic, complemented
3C11×#2093C211yesmaximal, characteristic, complemented
4C11×#2054C211yesmaximal, characteristic, complemented
5C11×#2041C211yesmaximal, characteristic, complemented
6C11×#2011C211yesmaximal, characteristic
7C11×#1970C211yesmaximal, characteristic, complemented
8C11×#1925C211yesmaximal, characteristic, complemented
9C11×#1925C211yesmaximal, characteristic, complemented
10C11×#1918C211yesmaximal, characteristic, complemented
11C11×#1916C211yesmaximal, characteristic, complemented
12C11×#1879C211yesmaximal, characteristic, complemented
13C11×#1879C211yesmaximal, characteristic, complemented
14C11×#1802C211yesmaximal, characteristic, complemented
15C4×C11×#102C211yesmaximal, characteristic, complemented
16C22×C11×D8C2211yescharacteristic
17C22×C11×D8C2211yescharacteristic
18C2×C11×#127C2211yescharacteristic
19C2×C11×#126—21no—
20C2×C4×D4×C11—21no—
21C2×C4×D4×C11C2211yescharacteristic
22C2×C4×D4×C11C2211yescharacteristic
23C2×C11×#107C2211yescharacteristic
24C2×C11×#107C2211yescharacteristic
25C2×C11×C4⋊C8C2211yescharacteristic
26C2×C11×#102C2211yescharacteristic
27C2×C11×#102C2211yescharacteristic
28C2×C11×#102C2211yescharacteristic
29C2×C11×#102C2211yescharacteristic
30C2×C11×#102C2211yescharacteristic
31C2×C11×#102C2211yescharacteristic
32C2×C11×#102C2211yescharacteristic
33C2×C11×#102C2211yescharacteristic
34C2×C4×C8×C11C2211yescharacteristic
35C11×#397—21no—
36C11×#396—21no—
37C11×#390—21no—
38C11×#390C2211yescharacteristic
39C11×#390C2211yescharacteristic
40C11×#390C2211yescharacteristic
41C11×#390C2211yescharacteristic
42C11×#390C2211yescharacteristic
43C11×#389C2211yescharacteristic
44C11×#388—21no—
45C11×#386—21no—
46C11×#386—21no—
47C11×#384C2211yescharacteristic
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—
78C11×#126—44no—
79C4×D4×C11—22no—
80C4×D4×C11—22no—
81C4×D4×C11—41no—
82C4×D4×C11—41no—
83C4×D4×C11—44no—
84C2×C11×C4⋊C4—21no—
85C2×C11×C4⋊C4—21no—
86C2×C11×C4⋊C4—21no—
87C2×C11×C4⋊C4D411yescharacteristic
88C2×C11×C4⋊C4D411yescharacteristic
89C2×C11×C4⋊C4C2311yescharacteristic
90C2×C11×C4⋊C4C2311yescharacteristic
91C2×C11×C4⋊C4C2311yescharacteristic
92C2×C11×C4⋊C4C2311yescharacteristic
93C2×C11×C4⋊C4C2311yescharacteristic
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×C11×C22⋊C4—21no—
104C2×C11×C22⋊C4—21no—
105C2×C11×C22⋊C4—21no—
106C2×C42×C11—21no—
107C2×C42×C11—21no—
108C2×C42×C11C2311yescharacteristic
109C2×C42×C11C2311yescharacteristic
110C2×C42×C11C2311yescharacteristic
111C11×#107—22no—
112C11×#107—41no—
113C11×C4⋊C8—41no—
114C11×#102—22no—
115C11×#102—22no—
116C11×#102—22no—
117C11×#102—22no—
118C11×#102—41no—
119C11×#102—41no—
120C11×#102—41no—
121C11×#102—41no—
122C4×C8×C11—41no—
123C11×#95—21no—
124C11×#95—21no—
125C11×#95—21no—
126C11×#95D411yescharacteristic
127C11×#95D411yescharacteristic
128#27062C1111yesmaximal, characteristic, direct product factor, Sylow
129C24×C11—21no—
130C24×C11—21no—
131C24×C11—21no—
132C2×D4×C11—24no—
133C2×D4×C11—24no—
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—21no—
150C2×D4×C11—42no—
151C2×D4×C11—42no—
152C2×D4×C11—81no—
153C2×D4×C11—81no—
154C2×D4×C11#4112yes—
155C2×D4×C11#4112yes—
156C22×C4×C11—21no—
157C22×C4×C11—21no—
158C22×C4×C11—21no—
159C22×C4×C11—21no—
160C22×C4×C11—21no—
161C22×C4×C11—42no—
162C22×C4×C11—42no—
163C22×C4×C11—42no—
164C22×C4×C11—42no—
165C22×C4×C11—81no—
166C22×C4×C11—81no—
167C22×C4×C11C2×D411yescharacteristic
168C22×C4×C11C2×D411yescharacteristic
169C22×C4×C11C2×D411yescharacteristic
170C22×C4×C11C2×D411yescharacteristic
171C22×C4×C11C2×D411yescharacteristic
172C22×C4×C11C2×D411yescharacteristic
173C22×C4×C11C2411yescharacteristic
174C11×D8—44no—
175C11×D8—44no—
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#4112yes—
188C11×C4⋊C4—21no—
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—41no—
198C11×C4⋊C4—42no—
199C11×C4⋊C4—42no—
200C11×C4⋊C4—81no—
201C11×C4⋊C4D814yescomplemented
202C11×C4⋊C4#4112yes—
203C11×C22⋊C4—42no—
204C11×C22⋊C4—42no—
205C11×C22⋊C4—42no—
206C11×C22⋊C4—42no—
207C11×C22⋊C4—42no—
208C11×C22⋊C4—42no—
209C11×C22⋊C4—42no—
210C11×C22⋊C4—42no—
211C11×C22⋊C4—81no—
212C11×C22⋊C4—81no—
213C11×C22⋊C4—81no—
214C11×C22⋊C4—81no—
215C42×C11—21no—
216C42×C11—21no—
217C42×C11—21no—
218C42×C11—21no—
219C42×C11—21no—
220C42×C11—21no—
221C42×C11—42no—
222C42×C11—42no—
223#2512C2×C1111yescharacteristic, complemented
224#2366C2×C1111yescharacteristic, complemented
225#2093C2×C1111yescharacteristic, complemented
226#2054C2×C1111yescharacteristic, complemented
227#2041C2×C1111yescharacteristic, complemented
228#2011C2×C1111yescharacteristic
229#1970C2×C1111yescharacteristic, complemented
230#1925C2×C1111yescharacteristic, complemented
231#1925C2×C1111yescharacteristic, complemented
232#1918C2×C1111yescharacteristic, complemented
233#1916C2×C1111yescharacteristic, complemented
234#1879C2×C1111yescharacteristic, complemented
235#1879C2×C1111yescharacteristic, complemented
236#1802C2×C1111yescharacteristic, complemented
237C4×#102C2×C1111yescharacteristic, complemented
238C23×C11—22no—
239C23×C11—22no—
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×C11—41no—
257C23×C11—41no—
258C23×C11—41no—
259C23×C11C22×D411yescharacteristic
260D4×C11—22no—
261D4×C11—22no—
262D4×C11—22no—
263D4×C11—22no—
264D4×C11—48no—
265D4×C11—41no—
266D4×C11—41no—
267D4×C11—41no—
268D4×C11—41no—
269D4×C11—41no—
270D4×C11—41no—
271D4×C11—41no—
272D4×C11—41no—
273D4×C11—84no—
274C2×C4×C11—21no—
275C2×C4×C11—21no—
276C2×C4×C11—21no—
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—22no—
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—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—41no—
303C2×C4×C11—41no—
304C2×C4×C11—84no—
305C2×C4×C11—84no—
306C2×C4×C11C2×D812yes—
307C2×C4×C11C2×D812yes—
308C2×C4×C11C2×D812yes—
309C2×C4×C11C2×#4111yescharacteristic
310C2×C4×C11C2×#4111yescharacteristic
311C2×C4×C11C2×#4111yescharacteristic
312C2×C4×C11C2×#4111yescharacteristic
313C2×C4×C11H(5,𝔽2)11yescharacteristic
314C2×C4×C11H(5,𝔽2)11yescharacteristic
315C8×C11—22no—
316C8×C11—41no—
317C8×C11—41no—
318C8×C11—41no—
319C22×D8C22×C1111yescharacteristic
320C22×D8C22×C1111yescharacteristic
321C2×#127C22×C1111yescharacteristic
322C2×#126—21no—
323C2×C4×D4—21no—
324C2×C4×D4C22×C1111yescharacteristic
325C2×C4×D4C22×C1111yescharacteristic
326C2×#107C22×C1111yescharacteristic
327C2×#107C22×C1111yescharacteristic
328C2×C4⋊C8C22×C1111yescharacteristic
329C2×#102C22×C1111yescharacteristic
330C2×#102C22×C1111yescharacteristic
331C2×#102C22×C1111yescharacteristic
332C2×#102C22×C1111yescharacteristic
333C2×#102C22×C1111yescharacteristic
334C2×#102C22×C1111yescharacteristic
335C2×#102C22×C1111yescharacteristic
336C2×#102C22×C1111yescharacteristic
337C2×C4×C8C22×C1111yescharacteristic
338#397—21no—
339#396—21no—
340#390—21no—
341#390C22×C1111yescharacteristic
342#390C22×C1111yescharacteristic
343#390C22×C1111yescharacteristic
344#390C22×C1111yescharacteristic
345#390C22×C1111yescharacteristic
346#389C22×C1111yescharacteristic
347#388—21no—
348#386—21no—
349#386—21no—
350#384C22×C1111yescharacteristic
351C4×C4⋊C4C22×C1111yescharacteristic
352C4×C4⋊C4C22×C1111yescharacteristic
353C4×C4⋊C4C22×C1111yescharacteristic
354#340C22×C1111yescharacteristic
355#340C22×C1111yescharacteristic
356#340C22×C1111yescharacteristic
357#340C22×C1111yescharacteristic
358#336C22×C1111yescharacteristic
359#336C22×C1111yescharacteristic
360#336C22×C1111yescharacteristic
361#336C22×C1111yescharacteristic
362C22×C11—42no—
363C22×C11—42no—
364C22×C11—42no—
365C22×C11—42no—
366C22×C11—42no—
367C22×C11—42no—
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—81no—
381C22×C11—81no—
382C22×C11—81no—
383C22×C11#52511yescharacteristic
384C22×C11#54611yescharacteristic
385C22×C11#55011yescharacteristic
386C22×C11C22×D811yescharacteristic
387C22×C11#57511yescharacteristic
388C22×C11#57611yescharacteristic
389C22×C11#57711yescharacteristic
390C4×C11—22no—
391C4×C11—22no—
392C4×C11—22no—
393C4×C11—41no—
394C4×C11—42no—
395C4×C11—41no—
396C4×C11—41no—
397C4×C11—81no—
398C4×C11—81no—
399C4×C11—81no—
400C4×C11—81no—
401C4×C11#52911yescharacteristic
402C4×C11#53811yescharacteristic
403C4×C11#55111yescharacteristic
404C4×C11#55311yescharacteristic
405C22×D4—21no—
406C22×D4—21no—
407C22×D4C23×C1111yescharacteristic
408C22×D4C23×C1111yescharacteristic
409C22×D4C23×C1111yescharacteristic
410C23×C4—21no—
411C23×C4—21no—
412C2×D8—22no—
413C2×D8—22no—
414C2×D8—22no—
415C2×D8—41no—
416C2×D8—41no—
417C2×D8—41no—
418C22×C8C23×C1111yescharacteristic
419C22×C8C23×C1111yescharacteristic
420C22×C8C23×C1111yescharacteristic
421C22×C8C23×C1111yescharacteristic
422#127—22no—
423#127—22no—
424#126—44no—
425C4×D4—22no—
426C4×D4—22no—
427C4×D4—41no—
428C4×D4—41no—
429C4×D4—44no—
430C2×C4⋊C4—21no—
431C2×C4⋊C4—21no—
432C2×C4⋊C4—21no—
433C2×C4⋊C4D4×C1111yescharacteristic
434C2×C4⋊C4D4×C1111yescharacteristic
435C2×C4⋊C4C23×C1111yescharacteristic
436C2×C4⋊C4C23×C1111yescharacteristic
437C2×C4⋊C4C23×C1111yescharacteristic
438C2×C4⋊C4C23×C1111yescharacteristic
439C2×C4⋊C4C23×C1111yescharacteristic
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×C22⋊C4—21no—
447C2×C22⋊C4—21no—
448C2×C22⋊C4—21no—
449C2×C22⋊C4—21no—
450C2×C22⋊C4—21no—
451C2×C22⋊C4—21no—
452C2×C42—21no—
453C2×C42—21no—
454C2×C42C23×C1111yescharacteristic
455C2×C42C23×C1111yescharacteristic
456C2×C42C23×C1111yescharacteristic
457#107—22no—
458#107—41no—
459C4⋊C8—41no—
460#102—22no—
461#102—22no—
462#102—22no—
463#102—22no—
464#102—41no—
465#102—41no—
466#102—41no—
467#102—41no—
468C4×C8—41no—
469#95—21no—
470#95—21no—
471#95—21no—
472#95D4×C1111yescharacteristic
473#95D4×C1111yescharacteristic
474C2×C11—82no—
475C2×C11—82no—
476C2×C11—161no—
477C2×C11#246711yescharacteristic
478C2×C11#310011yescharacteristic
479C2×C11#311811yescharacteristic
480C2×C11#329411yescharacteristic
481C2×C11#330911yescharacteristic
482C2×C11#339111yescharacteristic
483C2×C11#340111yescharacteristic
484C24—21no—
485C24—21no—
486C24—21no—
487C2×D4—24no—
488C2×D4—24no—
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—21no—
502C2×D4—21no—
503C2×D4—21no—
504C2×D4—21no—
505C2×D4—42no—
506C2×D4—42no—
507C2×D4—81no—
508C2×D4—81no—
509C2×D4C11×#4112yes—
510C2×D4C11×#4112yes—
511C22×C4—21no—
512C22×C4—21no—
513C22×C4—21no—
514C22×C4—21no—
515C22×C4—21no—
516C22×C4—42no—
517C22×C4—42no—
518C22×C4—42no—
519C22×C4—42no—
520C22×C4—81no—
521C22×C4—81no—
522C22×C4C2×D4×C1111yescharacteristic
523C22×C4C2×D4×C1111yescharacteristic
524C22×C4C2×D4×C1111yescharacteristic
525C22×C4C2×D4×C1111yescharacteristic
526C22×C4C2×D4×C1111yescharacteristic
527C22×C4C2×D4×C1111yescharacteristic
528C22×C4C24×C1111yescharacteristic
529D8—44no—
530D8—44no—
531C2×C8—21no—
532C2×C8—21no—
533C2×C8—21no—
534C2×C8—21no—
535C2×C8—21no—
536C2×C8—21no—
537C2×C8—21no—
538C2×C8—21no—
539C2×C8—21no—
540C2×C8—21no—
541C2×C8—21no—
542C2×C8C11×#4112yes—
543C4⋊C4—21no—
544C4⋊C4—21no—
545C4⋊C4—21no—
546C4⋊C4—21no—
547C4⋊C4—21no—
548C4⋊C4—21no—
549C4⋊C4—21no—
550C4⋊C4—21no—
551C4⋊C4—21no—
552C4⋊C4—41no—
553C4⋊C4—42no—
554C4⋊C4—42no—
555C4⋊C4—81no—
556C4⋊C4C11×D814yescomplemented
557C4⋊C4C11×#4112yes—
558C22⋊C4—42no—
559C22⋊C4—42no—
560C22⋊C4—42no—
561C22⋊C4—42no—
562C22⋊C4—42no—
563C22⋊C4—42no—
564C22⋊C4—42no—
565C22⋊C4—42no—
566C22⋊C4—81no—
567C22⋊C4—81no—
568C22⋊C4—81no—
569C22⋊C4—81no—
570C42—21no—
571C42—21no—
572C42—21no—
573C42—21no—
574C42—21no—
575C42—21no—
576C42—42no—
577C42—42no—
578C11#2706211yescharacteristic, direct product factor, Sylow
579C23—22no—
580C23—22no—
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—
594C23—41no—
595C23—41no—
596C23—41no—
597C23—41no—
598C23—41no—
599C23—41no—
600C23C22×D4×C1111yescharacteristic
601D4—22no—
602D4—22no—
603D4—22no—
604D4—22no—
605D4—48no—
606D4—41no—
607D4—41no—
608D4—41no—
609D4—41no—
610D4—41no—
611D4—41no—
612D4—41no—
613D4—41no—
614D4—84no—
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—22no—
625C2×C4—21no—
626C2×C4—21no—
627C2×C4—21no—
628C2×C4—21no—
629C2×C4—21no—
630C2×C4—21no—
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—41no—
641C2×C4—41no—
642C2×C4—41no—
643C2×C4—41no—
644C2×C4—41no—
645C2×C4—84no—
646C2×C4—84no—
647C2×C4C2×C11×D812yes—
648C2×C4C2×C11×D812yes—
649C2×C4C2×C11×D812yes—
650C2×C4C2×C11×#4111yescharacteristic
651C2×C4C2×C11×#4111yescharacteristic
652C2×C4C2×C11×#4111yescharacteristic
653C2×C4C2×C11×#4111yescharacteristic
654C2×C4C11×H(5,𝔽2)11yescharacteristic
655C2×C4C11×H(5,𝔽2)11yescharacteristic
656C8—22no—
657C8—41no—
658C8—41no—
659C8—41no—
660C22—42no—
661C22—42no—
662C22—42no—
663C22—42no—
664C22—42no—
665C22—42no—
666C22—81no—
667C22—81no—
668C22—81no—
669C22—81no—
670C22—81no—
671C22—81no—
672C22—81no—
673C22—81no—
674C22—81no—
675C22—81no—
676C22—81no—
677C22—81no—
678C22—81no—
679C22—81no—
680C22—81no—
681C22C11×#52511yescharacteristic
682C22C11×#54611yescharacteristic
683C22C11×#55011yescharacteristic
684C22C22×C11×D811yescharacteristic
685C22C11×#57511yescharacteristic
686C22C11×#57611yescharacteristic
687C22C11×#57711yescharacteristic
688C4—22no—
689C4—22no—
690C4—22no—
691C4—42no—
692C4—41no—
693C4—41no—
694C4—41no—
695C4—81no—
696C4—81no—
697C4—81no—
698C4—81no—
699C4C11×#52911yescharacteristic
700C4C11×#53811yescharacteristic
701C4C11×#55111yescharacteristic
702C4C11×#55311yescharacteristic
703C2—82no—
704C2—82no—
705C2—161no—
706C2C11×#246711yescharacteristic
707C2C11×#310011yescharacteristic
708C2C11×#311811yescharacteristic
709C2C11×#329411yescharacteristic
710C2C11×#330911yescharacteristic
711C2C11×#339111yescharacteristic
712C2C11×#340111yescharacteristic
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×#2512C2semidirect
2. C11×#2366C2semidirect
3. C11×#2093C2semidirect
4. C11×#2054C2semidirect
5. C11×#2041C2semidirect
7. C11×#1970C2semidirect
8. C11×#1925C2semidirect
9. C11×#1925C2semidirect
10. C11×#1918C2semidirect
11. C11×#1916C2semidirect
12. C11×#1879C2semidirect
13. C11×#1879C2semidirect
14. C11×#1802C2semidirect
15. C4×C11×#102C2semidirect
128. #27062C11direct (N × H)
201. C11×C4⋊C4D8semidirect
223. #2512C2×C11semidirect
224. #2366C2×C11semidirect
225. #2093C2×C11semidirect
226. #2054C2×C11semidirect
227. #2041C2×C11semidirect
229. #1970C2×C11semidirect
230. #1925C2×C11semidirect
231. #1925C2×C11semidirect
232. #1918C2×C11semidirect
233. #1916C2×C11semidirect
234. #1879C2×C11semidirect
235. #1879C2×C11semidirect
236. #1802C2×C11semidirect
237. C4×#102C2×C11semidirect
556. C4⋊C4C11×D8semidirect
578. C11#27062direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#25122
C11×#23662
C11×#20932
C11×#20542
C11×#20412
C11×#20112
C11×#19702
C11×#19252
C11×#19182
C11×#19162
C11×#18792
C11×#18022
C4×C11×#1022
#2706211