Finite Group Databasebeta

← C11×#22158 #14599351

Subgroups — C11×#22158 #14599351

Order 2816.

928 conjugacy classes of subgroups.

The subgroup lattice has 718 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#459C211yesmaximal, characteristic
2C11×#2328C211yesmaximal, characteristic, complemented
3C11×#2319C211yesmaximal, characteristic, complemented
4C11×#1982C211yesmaximal, characteristic, complemented
5C11×#1972C211yesmaximal, characteristic, complemented
6C11×#1970C211yesmaximal, characteristic, complemented
7C11×#1949C211yesmaximal, characteristic, complemented
8C11×#1936C211yesmaximal, characteristic, complemented
9C11×#1934C211yesmaximal, characteristic, complemented
10C11×#1879C211yesmaximal, characteristic, complemented
11C11×#1879C211yesmaximal, characteristic, complemented
12C11×#1864C211yesmaximal, characteristic, complemented
13C11×#1862C211yesmaximal, characteristic, complemented
14C11×#1804C211yesmaximal, characteristic, complemented
15C11×#1768C211yesmaximal, characteristic, complemented
16C22×C11×D8C2211yescharacteristic
17C22×C11×D8C2211yescharacteristic
18C2×C11×#127C2211yescharacteristic
19C2×C4×D4×C11C2211yescharacteristic
20C2×C4×D4×C11C2211yescharacteristic
21C2×C4×D4×C11C2211yescharacteristic
22C11×#459C418yescomplemented
23C2×C11×#107C2211yescharacteristic
24C2×C11×#106C2211yescharacteristic
25C2×C11×C4⋊C8C2211yescharacteristic
26C2×C11×C4⋊C8C2211yescharacteristic
27C2×C11×#102C2211yescharacteristic
28C2×C11×#102C2211yescharacteristic
29C2×C11×#102C2211yescharacteristic
30C2×C11×#102C2211yescharacteristic
31C2×C11×#102C2211yescharacteristic
32C2×C11×#102C2211yescharacteristic
33C2×C11×#102C2211yescharacteristic
34C2×C11×#102C2211yescharacteristic
35C2×C11×#97C2211yescharacteristic
36C2×C4×C8×C11C2211yescharacteristic
37C11×#390C2211yescharacteristic
38C11×#390C2211yescharacteristic
39C11×#390C2211yescharacteristic
40C11×#390C2211yescharacteristic
41C11×#389C2211yescharacteristic
42C11×#389C2211yescharacteristic
43C11×#388—21no—
44C11×#388—21no—
45C11×#386—21no—
46C11×#386—21no—
47C11×#386—21no—
48C11×#386—21no—
49C11×#382C2211yescharacteristic
50C11×#381—21no—
51C11×#380—21no—
52C4×C11×C4⋊C4C2211yescharacteristic
53C11×#376C2211yescharacteristic
54C11×#340C2211yescharacteristic
55C11×#340C2211yescharacteristic
56C11×#340C2211yescharacteristic
57C11×#340C2211yescharacteristic
58C11×#336C2211yescharacteristic
59C11×#336C2211yescharacteristic
60C22×D4×C11—21no—
61C22×D4×C11—21no—
62C22×D4×C11C2311yescharacteristic
63C22×D4×C11C2311yescharacteristic
64C22×D4×C11C2311yescharacteristic
65C23×C4×C11—21no—
66C23×C4×C11—21no—
67C23×C4×C11—21no—
68C2×C11×D8—41no—
69C2×C11×D8—41no—
70C2×C11×D8—41no—
71C2×C11×D8—41no—
72C2×C11×D8C2×C414yescomplemented
73C2×C11×D8C2×C414yescomplemented
74C22×C8×C11C2311yescharacteristic
75C22×C8×C11C2311yescharacteristic
76C22×C8×C11C2311yescharacteristic
77C22×C8×C11C2311yescharacteristic
78C11×#127—22no—
79C11×#127C2×C414yes—
80C4×D4×C11—22no—
81C4×D4×C11—41no—
82C4×D4×C11—41no—
83C4×D4×C11—41no—
84C4×D4×C11—41no—
85C4×D4×C11C2×C414yescomplemented
86C2×C11×C4⋊C4—21no—
87C2×C11×C4⋊C4—21no—
88C2×C11×C4⋊C4C2311yescharacteristic
89C2×C11×C4⋊C4C2311yescharacteristic
90C2×C11×C4⋊C4C2311yescharacteristic
91C2×C11×C4⋊C4C2311yescharacteristic
92C2×C11×C4⋊C4C2311yescharacteristic
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×C11×C22⋊C4—21no—
104C2×C42×C11—21no—
105C2×C42×C11C2311yescharacteristic
106C2×C42×C11C2311yescharacteristic
107C2×C42×C11C2311yescharacteristic
108C11×#107—41no—
109C11×#106—41no—
110C11×C4⋊C8—22no—
111C11×C4⋊C8C2×C414yescomplemented
112C11×#102—41no—
113C11×#102—41no—
114C11×#102—41no—
115C11×#102—41no—
116C11×#102—41no—
117C11×#102—41no—
118C11×#102C2×C414yescomplemented
119C11×#102C2×C414yescomplemented
120C11×#97—41no—
121C4×C8×C11—41no—
122C11×#95—21no—
123C11×#95—21no—
124C11×#95—21no—
125C11×#95—21no—
126C11×#95—21no—
127C11×#95D411yescharacteristic
128C11×#95D411yescharacteristic
129C11×#95D411yescharacteristic
130C11×#95D411yescharacteristic
131#22158C1111yesmaximal, characteristic, direct product factor, Sylow
132C24×C11—21no—
133C24×C11—21no—
134C24×C11—21no—
135C2×D4×C11—24no—
136C2×D4×C11—24no—
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—21no—
151C2×D4×C11—21no—
152C2×D4×C11—81no—
153C2×D4×C11—81no—
154C2×D4×C11—81no—
155C2×D4×C11—81no—
156C2×D4×C11C22×C412yes—
157C2×D4×C11C22×C412yes—
158C2×D4×C11C22×C412yes—
159C22×C4×C11—21no—
160C22×C4×C11—24no—
161C22×C4×C11—21no—
162C22×C4×C11—21no—
163C22×C4×C11—21no—
164C22×C4×C11—21no—
165C22×C4×C11—42no—
166C22×C4×C11—42no—
167C22×C4×C11—81no—
168C22×C4×C11—81no—
169C22×C4×C11—81no—
170C22×C4×C11—81no—
171C22×C4×C11—81no—
172C22×C4×C11—81no—
173C22×C4×C11C2×D411yescharacteristic
174C22×C4×C11C2×D411yescharacteristic
175C22×C4×C11C2×D411yescharacteristic
176C22×C4×C11C2×D411yescharacteristic
177C22×C4×C11C2×D411yescharacteristic
178C22×C4×C11C2×D411yescharacteristic
179C22×C4×C11C2411yescharacteristic
180C11×D8—44no—
181C11×D8—44no—
182C2×C8×C11—21no—
183C2×C8×C11—21no—
184C2×C8×C11—21no—
185C2×C8×C11—21no—
186C2×C8×C11—21no—
187C2×C8×C11—21no—
188C2×C8×C11—21no—
189C2×C8×C11—21no—
190C2×C8×C11—21no—
191C2×C8×C11—21no—
192C2×C8×C11C22×C412yes—
193C2×C8×C11C22×C412yes—
194C11×C4⋊C4—21no—
195C11×C4⋊C4—21no—
196C11×C4⋊C4—21no—
197C11×C4⋊C4—21no—
198C11×C4⋊C4—21no—
199C11×C4⋊C4—21no—
200C11×C4⋊C4—21no—
201C11×C4⋊C4—21no—
202C11×C4⋊C4—21no—
203C11×C4⋊C4—81no—
204C11×C4⋊C4—81no—
205C11×C4⋊C4C22×C412yes—
206C11×C22⋊C4—24no—
207C11×C22⋊C4—42no—
208C11×C22⋊C4—42no—
209C11×C22⋊C4—81no—
210C11×C22⋊C4—81no—
211C11×C22⋊C4—81no—
212C11×C22⋊C4—81no—
213C11×C22⋊C4—81no—
214C11×C22⋊C4—81no—
215C11×C22⋊C4—81no—
216C11×C22⋊C4—81no—
217C42×C11—21no—
218C42×C11—21no—
219C42×C11—21no—
220C42×C11—21no—
221C42×C11—81no—
222C42×C11C22×C412yes—
223C42×C11#4112yes—
224C2×#459C2×C1111yescharacteristic
225#2328C2×C1111yescharacteristic, complemented
226#2319C2×C1111yescharacteristic, complemented
227#1982C2×C1111yescharacteristic, complemented
228#1972C2×C1111yescharacteristic, complemented
229#1970C2×C1111yescharacteristic, complemented
230#1949C2×C1111yescharacteristic, complemented
231#1936C2×C1111yescharacteristic, complemented
232#1934C2×C1111yescharacteristic, complemented
233#1879C2×C1111yescharacteristic, complemented
234#1879C2×C1111yescharacteristic, complemented
235#1864C2×C1111yescharacteristic, complemented
236#1862C2×C1111yescharacteristic, complemented
237#1804C2×C1111yescharacteristic, complemented
238#1768C2×C1111yescharacteristic, complemented
239C23×C11—22no—
240C23×C11—22no—
241C23×C11—22no—
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×C11—41no—
260C23×C11C22×D411yescharacteristic
261D4×C11—22no—
262D4×C11—22no—
263D4×C11—22no—
264D4×C11—22no—
265D4×C11—22no—
266D4×C11—22no—
267D4×C11—41no—
268D4×C11—41no—
269D4×C11—41no—
270D4×C11—41no—
271D4×C11—41no—
272D4×C11—41no—
273D4×C11—84no—
274D4×C11—84no—
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—21no—
289C2×C4×C11—21no—
290C2×C4×C11—21no—
291C2×C4×C11—21no—
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—41no—
305C2×C4×C11—41no—
306C2×C4×C11—84no—
307C2×C4×C11—84no—
308C2×C4×C11—84no—
309C2×C4×C11C4×D412yes—
310C2×C4×C11C4×D412yes—
311C2×C4×C11C23×C411yescharacteristic
312C2×C4×C11C2×#4111yescharacteristic
313C2×C4×C11H(5,𝔽2)11yescharacteristic
314C2×C4×C11H(5,𝔽2)11yescharacteristic
315C2×C4×C11H(5,𝔽2)11yescharacteristic
316C2×C4×C112−1+411yescharacteristic
317C8×C11—22no—
318C8×C11—22no—
319C8×C11—41no—
320C8×C11—41no—
321C22×D8C22×C1111yescharacteristic
322C22×D8C22×C1111yescharacteristic
323C2×#127C22×C1111yescharacteristic
324C2×C4×D4C22×C1111yescharacteristic
325C2×C4×D4C22×C1111yescharacteristic
326C2×C4×D4C22×C1111yescharacteristic
327#459C4×C1118yescomplemented
328C2×#107C22×C1111yescharacteristic
329C2×#106C22×C1111yescharacteristic
330C2×C4⋊C8C22×C1111yescharacteristic
331C2×C4⋊C8C22×C1111yescharacteristic
332C2×#102C22×C1111yescharacteristic
333C2×#102C22×C1111yescharacteristic
334C2×#102C22×C1111yescharacteristic
335C2×#102C22×C1111yescharacteristic
336C2×#102C22×C1111yescharacteristic
337C2×#102C22×C1111yescharacteristic
338C2×#102C22×C1111yescharacteristic
339C2×#102C22×C1111yescharacteristic
340C2×#97C22×C1111yescharacteristic
341C2×C4×C8C22×C1111yescharacteristic
342#390C22×C1111yescharacteristic
343#390C22×C1111yescharacteristic
344#390C22×C1111yescharacteristic
345#390C22×C1111yescharacteristic
346#389C22×C1111yescharacteristic
347#389C22×C1111yescharacteristic
348#388—21no—
349#388—21no—
350#386—21no—
351#386—21no—
352#386—21no—
353#386—21no—
354#382C22×C1111yescharacteristic
355#381—21no—
356#380—21no—
357C4×C4⋊C4C22×C1111yescharacteristic
358#376C22×C1111yescharacteristic
359#340C22×C1111yescharacteristic
360#340C22×C1111yescharacteristic
361#340C22×C1111yescharacteristic
362#340C22×C1111yescharacteristic
363#336C22×C1111yescharacteristic
364#336C22×C1111yescharacteristic
365C22×C11—42no—
366C22×C11—42no—
367C22×C11—42no—
368C22×C11—42no—
369C22×C11—42no—
370C22×C11—42no—
371C22×C11—42no—
372C22×C11—42no—
373C22×C11—42no—
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—81no—
384C22×C11—81no—
385C22×C11—81no—
386C22×C11C2×C4×D411yescharacteristic
387C22×C11#53511yescharacteristic
388C22×C11#53711yescharacteristic
389C22×C11#57611yescharacteristic
390C22×C11#57611yescharacteristic
391C22×C11#57611yescharacteristic
392C22×C11#57711yescharacteristic
393C4×C11—22no—
394C4×C11—22no—
395C4×C11—42no—
396C4×C11—41no—
397C4×C11—41no—
398C4×C11—41no—
399C4×C11—41no—
400C4×C11—81no—
401C4×C11—81no—
402C4×C11—81no—
403C4×C11—81no—
404C4×C11#51811yescharacteristic
405C4×C11#52011yescharacteristic
406C4×C11#54011yescharacteristic
407C4×C11#54211yescharacteristic
408C22×D4—21no—
409C22×D4—21no—
410C22×D4C23×C1111yescharacteristic
411C22×D4C23×C1111yescharacteristic
412C22×D4C23×C1111yescharacteristic
413C23×C4—21no—
414C23×C4—21no—
415C23×C4—21no—
416C2×D8—41no—
417C2×D8—41no—
418C2×D8—41no—
419C2×D8—41no—
420C2×D8C2×C4×C1114yescomplemented
421C2×D8C2×C4×C1114yescomplemented
422C22×C8C23×C1111yescharacteristic
423C22×C8C23×C1111yescharacteristic
424C22×C8C23×C1111yescharacteristic
425C22×C8C23×C1111yescharacteristic
426#127—22no—
427#127C2×C4×C1114yes—
428C4×D4—22no—
429C4×D4—41no—
430C4×D4—41no—
431C4×D4—41no—
432C4×D4—41no—
433C4×D4C2×C4×C1114yescomplemented
434C2×C4⋊C4—21no—
435C2×C4⋊C4—21no—
436C2×C4⋊C4C23×C1111yescharacteristic
437C2×C4⋊C4C23×C1111yescharacteristic
438C2×C4⋊C4C23×C1111yescharacteristic
439C2×C4⋊C4C23×C1111yescharacteristic
440C2×C4⋊C4C23×C1111yescharacteristic
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×C42C23×C1111yescharacteristic
454C2×C42C23×C1111yescharacteristic
455C2×C42C23×C1111yescharacteristic
456#107—41no—
457#106—41no—
458C4⋊C8—22no—
459C4⋊C8C2×C4×C1114yescomplemented
460#102—41no—
461#102—41no—
462#102—41no—
463#102—41no—
464#102—41no—
465#102—41no—
466#102C2×C4×C1114yescomplemented
467#102C2×C4×C1114yescomplemented
468#97—41no—
469C4×C8—41no—
470#95—21no—
471#95—21no—
472#95—21no—
473#95—21no—
474#95—21no—
475#95D4×C1111yescharacteristic
476#95D4×C1111yescharacteristic
477#95D4×C1111yescharacteristic
478#95D4×C1111yescharacteristic
479C2×C11—82no—
480C2×C11—82no—
481C2×C11—82no—
482C2×C11#232411yescharacteristic
483C2×C11#294611yescharacteristic
484C2×C11#294811yescharacteristic
485C2×C11#322011yescharacteristic
486C2×C11#322411yescharacteristic
487C2×C11#325711yescharacteristic
488C2×C11#325911yescharacteristic
489C24—21no—
490C24—21no—
491C24—21no—
492C2×D4—24no—
493C2×D4—24no—
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—21no—
506C2×D4—21no—
507C2×D4—21no—
508C2×D4—21no—
509C2×D4—81no—
510C2×D4—81no—
511C2×D4—81no—
512C2×D4—81no—
513C2×D4C22×C4×C1112yes—
514C2×D4C22×C4×C1112yes—
515C2×D4C22×C4×C1112yes—
516C22×C4—21no—
517C22×C4—24no—
518C22×C4—21no—
519C22×C4—21no—
520C22×C4—21no—
521C22×C4—21no—
522C22×C4—42no—
523C22×C4—42no—
524C22×C4—81no—
525C22×C4—81no—
526C22×C4—81no—
527C22×C4—81no—
528C22×C4—81no—
529C22×C4—81no—
530C22×C4C2×D4×C1111yescharacteristic
531C22×C4C2×D4×C1111yescharacteristic
532C22×C4C2×D4×C1111yescharacteristic
533C22×C4C2×D4×C1111yescharacteristic
534C22×C4C2×D4×C1111yescharacteristic
535C22×C4C2×D4×C1111yescharacteristic
536C22×C4C24×C1111yescharacteristic
537D8—44no—
538D8—44no—
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×C8C22×C4×C1112yes—
550C2×C8C22×C4×C1112yes—
551C4⋊C4—21no—
552C4⋊C4—21no—
553C4⋊C4—21no—
554C4⋊C4—21no—
555C4⋊C4—21no—
556C4⋊C4—21no—
557C4⋊C4—21no—
558C4⋊C4—21no—
559C4⋊C4—21no—
560C4⋊C4—81no—
561C4⋊C4—81no—
562C4⋊C4C22×C4×C1112yes—
563C22⋊C4—24no—
564C22⋊C4—42no—
565C22⋊C4—42no—
566C22⋊C4—81no—
567C22⋊C4—81no—
568C22⋊C4—81no—
569C22⋊C4—81no—
570C22⋊C4—81no—
571C22⋊C4—81no—
572C22⋊C4—81no—
573C22⋊C4—81no—
574C42—21no—
575C42—21no—
576C42—21no—
577C42—21no—
578C42—81no—
579C42C22×C4×C1112yes—
580C42C11×#4112yes—
581C11#2215811yescharacteristic, direct product factor, Sylow
582C23—22no—
583C23—22no—
584C23—22no—
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—
600C23—41no—
601C23—41no—
602C23—41no—
603C23C22×D4×C1111yescharacteristic
604D4—22no—
605D4—22no—
606D4—22no—
607D4—22no—
608D4—22no—
609D4—22no—
610D4—41no—
611D4—41no—
612D4—41no—
613D4—41no—
614D4—41no—
615D4—41no—
616D4—84no—
617D4—84no—
618C2×C4—21no—
619C2×C4—21no—
620C2×C4—21no—
621C2×C4—21no—
622C2×C4—22no—
623C2×C4—21no—
624C2×C4—21no—
625C2×C4—21no—
626C2×C4—21no—
627C2×C4—21no—
628C2×C4—21no—
629C2×C4—21no—
630C2×C4—21no—
631C2×C4—21no—
632C2×C4—21no—
633C2×C4—21no—
634C2×C4—21no—
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—41no—
646C2×C4—41no—
647C2×C4—41no—
648C2×C4—41no—
649C2×C4—84no—
650C2×C4—84no—
651C2×C4—84no—
652C2×C4C4×D4×C1112yes—
653C2×C4C4×D4×C1112yes—
654C2×C4C23×C4×C1111yescharacteristic
655C2×C4C2×C11×#4111yescharacteristic
656C2×C4C11×H(5,𝔽2)11yescharacteristic
657C2×C4C11×H(5,𝔽2)11yescharacteristic
658C2×C4C11×H(5,𝔽2)11yescharacteristic
659C2×C4C11×2−1+411yescharacteristic
660C8—22no—
661C8—22no—
662C8—41no—
663C8—41no—
664C22—42no—
665C22—42no—
666C22—42no—
667C22—42no—
668C22—42no—
669C22—42no—
670C22—42no—
671C22—42no—
672C22—42no—
673C22—81no—
674C22—81no—
675C22—81no—
676C22—81no—
677C22—81no—
678C22—81no—
679C22—81no—
680C22—81no—
681C22—81no—
682C22—81no—
683C22—81no—
684C22—81no—
685C22C2×C4×D4×C1111yescharacteristic
686C22C11×#53511yescharacteristic
687C22C11×#53711yescharacteristic
688C22C11×#57611yescharacteristic
689C22C11×#57611yescharacteristic
690C22C11×#57611yescharacteristic
691C22C11×#57711yescharacteristic
692C4—22no—
693C4—22no—
694C4—42no—
695C4—41no—
696C4—41no—
697C4—41no—
698C4—41no—
699C4—81no—
700C4—81no—
701C4—81no—
702C4—81no—
703C4C11×#51811yescharacteristic
704C4C11×#52011yescharacteristic
705C4C11×#54011yescharacteristic
706C4C11×#54211yescharacteristic
707C2—82no—
708C2—82no—
709C2—82no—
710C2C11×#232411yescharacteristic
711C2C11×#294611yescharacteristic
712C2C11×#294811yescharacteristic
713C2C11×#322011yescharacteristic
714C2C11×#322411yescharacteristic
715C2C11×#325711yescharacteristic
716C2C11×#325911yescharacteristic
subgroupG/H
center, socleC23×C11C22×D4
commutatorC2×C4C23×C4×C11
Frattini, cosocleC22×C4C24×C11
prime radicalC2×C11×#459C2
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C11 ◁ C11×#376 ◁ G

Complements

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

NH ≅ G/Ntype
2. C11×#2328C2semidirect
3. C11×#2319C2semidirect
4. C11×#1982C2semidirect
5. C11×#1972C2semidirect
6. C11×#1970C2semidirect
7. C11×#1949C2semidirect
8. C11×#1936C2semidirect
9. C11×#1934C2semidirect
10. C11×#1879C2semidirect
11. C11×#1879C2semidirect
12. C11×#1864C2semidirect
13. C11×#1862C2semidirect
14. C11×#1804C2semidirect
15. C11×#1768C2semidirect
22. C11×#459C4semidirect
72. C2×C11×D8C2×C4semidirect
73. C2×C11×D8C2×C4semidirect
85. C4×D4×C11C2×C4semidirect
111. C11×C4⋊C8C2×C4semidirect
118. C11×#102C2×C4semidirect
119. C11×#102C2×C4semidirect
131. #22158C11direct (N × H)
225. #2328C2×C11semidirect
226. #2319C2×C11semidirect
227. #1982C2×C11semidirect
228. #1972C2×C11semidirect
229. #1970C2×C11semidirect
230. #1949C2×C11semidirect
231. #1936C2×C11semidirect
232. #1934C2×C11semidirect
233. #1879C2×C11semidirect
234. #1879C2×C11semidirect
235. #1864C2×C11semidirect
236. #1862C2×C11semidirect
237. #1804C2×C11semidirect
238. #1768C2×C11semidirect
327. #459C4×C11semidirect
420. C2×D8C2×C4×C11semidirect
421. C2×D8C2×C4×C11semidirect
433. C4×D4C2×C4×C11semidirect
459. C4⋊C8C2×C4×C11semidirect
466. #102C2×C4×C11semidirect
467. #102C2×C4×C11semidirect
581. C11#22158direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#4592
C11×#23282
C11×#23192
C11×#19822
C11×#19722
C11×#19702
C11×#19492
C11×#19362
C11×#19342
C11×#18792
C11×#18642
C11×#18622
C11×#18042
C11×#17682
#2215811