Finite Group Databasebeta

← C11×#23108 #14600301

Subgroups — C11×#23108 #14600301

Order 2816.

994 conjugacy classes of subgroups.

The subgroup lattice has 724 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#459C211yesmaximal, characteristic
2C11×#2366C211yesmaximal, characteristic, complemented
3C11×#2357C211yesmaximal, characteristic, complemented
4C11×#1972C211yesmaximal, characteristic, complemented
5C11×#1970C211yesmaximal, characteristic, complemented
6C11×#1961C211yesmaximal, characteristic, complemented
7C11×#1949C211yesmaximal, characteristic, complemented
8C11×#1926C211yesmaximal, characteristic, complemented
9C11×#1925C211yesmaximal, characteristic, complemented
10C11×#1879C211yesmaximal, characteristic, complemented
11C11×#1879C211yesmaximal, characteristic, complemented
12C11×#1771C211yesmaximal, characteristic, complemented
13C11×#1762C211yesmaximal, characteristic, complemented
14C11×#1762C211yesmaximal, 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×C4×D4×C11C2211yescharacteristic
23C11×#459C418yescomplemented
24C2×C11×#107C2211yescharacteristic
25C2×C11×#106C2211yescharacteristic
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×C11×#97C2211yescharacteristic
37C2×C4×C8×C11C2211yescharacteristic
38C11×#390—21no—
39C11×#390C2211yescharacteristic
40C11×#390C2211yescharacteristic
41C11×#390C2211yescharacteristic
42C11×#390C2211yescharacteristic
43C11×#388—21no—
44C11×#388—21no—
45C11×#386—21no—
46C11×#386—21no—
47C11×#382C2211yescharacteristic
48C11×#381—21no—
49C4×C11×C4⋊C4C2211yescharacteristic
50C4×C11×C4⋊C4C2211yescharacteristic
51C4×C11×C4⋊C4C2211yescharacteristic
52C4×C11×C4⋊C4C2211yescharacteristic
53C4×C11×C22⋊C4—21no—
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—22no—
82C4×D4×C11—22no—
83C4×D4×C11—41no—
84C4×D4×C11—41no—
85C4×D4×C11—44no—
86C4×D4×C11C2×C414yescomplemented
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×C42×C11—21no—
106C2×C42×C11—21no—
107C2×C42×C11—21no—
108C2×C42×C11C2311yescharacteristic
109C2×C42×C11C2311yescharacteristic
110C2×C42×C11C2311yescharacteristic
111C11×#107—41no—
112C11×#106—41no—
113C11×C4⋊C8C2×C414yescomplemented
114C11×#102—22no—
115C11×#102—22no—
116C11×#102—22no—
117C11×#102—22no—
118C11×#102—41no—
119C11×#102—41no—
120C11×#102C2×C414yescomplemented
121C11×#102C2×C414yescomplemented
122C11×#97—22no—
123C11×#97—41no—
124C4×C8×C11—41no—
125C11×#95—21no—
126C11×#95—21no—
127C11×#95—21no—
128C11×#95—21no—
129C11×#95—21no—
130C11×#95D411yescharacteristic
131C11×#95D411yescharacteristic
132#23108C1111yesmaximal, characteristic, direct product factor, Sylow
133C24×C11—21no—
134C24×C11—21no—
135C24×C11—21no—
136C2×D4×C11—24no—
137C2×D4×C11—24no—
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—21no—
153C2×D4×C11—42no—
154C2×D4×C11—42no—
155C2×D4×C11—81no—
156C2×D4×C11—81no—
157C2×D4×C11C22×C412yes—
158C2×D4×C11C22×C412yes—
159C2×D4×C11C22×C412yes—
160C22×C4×C11—21no—
161C22×C4×C11—21no—
162C22×C4×C11—24no—
163C22×C4×C11—21no—
164C22×C4×C11—21no—
165C22×C4×C11—21no—
166C22×C4×C11—42no—
167C22×C4×C11—42no—
168C22×C4×C11—42no—
169C22×C4×C11—42no—
170C22×C4×C11—81no—
171C22×C4×C11—81no—
172C22×C4×C11—81no—
173C22×C4×C11—81no—
174C22×C4×C11C2×D411yescharacteristic
175C22×C4×C11C2×D411yescharacteristic
176C22×C4×C11C2×D411yescharacteristic
177C22×C4×C11C2×D411yescharacteristic
178C22×C4×C11C2×D411yescharacteristic
179C22×C4×C11C2×D411yescharacteristic
180C22×C4×C11C2411yescharacteristic
181C11×D8—44no—
182C11×D8—44no—
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—
194C2×C8×C11#4112yes—
195C11×C4⋊C4—22no—
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—21no—
204C11×C4⋊C4—41no—
205C11×C4⋊C4C22×C412yes—
206C11×C4⋊C4#4112yes—
207C11×C22⋊C4—24no—
208C11×C22⋊C4—42no—
209C11×C22⋊C4—42no—
210C11×C22⋊C4—42no—
211C11×C22⋊C4—42no—
212C11×C22⋊C4—42no—
213C11×C22⋊C4—42no—
214C11×C22⋊C4—81no—
215C11×C22⋊C4—81no—
216C11×C22⋊C4—81no—
217C11×C22⋊C4—81no—
218C42×C11—21no—
219C42×C11—21no—
220C42×C11—21no—
221C42×C11—21no—
222C42×C11—42no—
223C42×C11—81no—
224C42×C11—81no—
225C42×C11C22×C412yes—
226C42×C11#4112yes—
227C2×#459C2×C1111yescharacteristic
228#2366C2×C1111yescharacteristic, complemented
229#2357C2×C1111yescharacteristic, complemented
230#1972C2×C1111yescharacteristic, complemented
231#1970C2×C1111yescharacteristic, complemented
232#1961C2×C1111yescharacteristic, complemented
233#1949C2×C1111yescharacteristic, complemented
234#1926C2×C1111yescharacteristic, complemented
235#1925C2×C1111yescharacteristic, complemented
236#1879C2×C1111yescharacteristic, complemented
237#1879C2×C1111yescharacteristic, complemented
238#1771C2×C1111yescharacteristic, complemented
239#1762C2×C1111yescharacteristic, complemented
240#1762C2×C1111yescharacteristic, complemented
241C4×#102C2×C1111yescharacteristic, complemented
242C23×C11—22no—
243C23×C11—22no—
244C23×C11—22no—
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×C11—41no—
261C23×C11—41no—
262C23×C11—41no—
263C23×C11C22×D411yescharacteristic
264D4×C11—22no—
265D4×C11—22no—
266D4×C11—22no—
267D4×C11—22no—
268D4×C11—22no—
269D4×C11—22no—
270D4×C11—48no—
271D4×C11—41no—
272D4×C11—41no—
273D4×C11—41no—
274D4×C11—41no—
275D4×C11—41no—
276D4×C11—41no—
277D4×C11—84no—
278C2×C4×C11—21no—
279C2×C4×C11—21no—
280C2×C4×C11—21no—
281C2×C4×C11—21no—
282C2×C4×C11—21no—
283C2×C4×C11—21no—
284C2×C4×C11—22no—
285C2×C4×C11—21no—
286C2×C4×C11—21no—
287C2×C4×C11—21no—
288C2×C4×C11—22no—
289C2×C4×C11—21no—
290C2×C4×C11—21no—
291C2×C4×C11—21no—
292C2×C4×C11—21no—
293C2×C4×C11—21no—
294C2×C4×C11—21no—
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—41no—
307C2×C4×C11—41no—
308C2×C4×C11—84no—
309C2×C4×C11—84no—
310C2×C4×C11—84no—
311C2×C4×C11C4×D412yes—
312C2×C4×C11C4×D412yes—
313C2×C4×C11AGL(1,ℤ/8)12yes—
314C2×C4×C11C23×C411yescharacteristic
315C2×C4×C11C2×#4111yescharacteristic
316C2×C4×C11C2×#4111yescharacteristic
317C2×C4×C11C2×#4111yescharacteristic
318C2×C4×C11H(5,𝔽2)11yescharacteristic
319C2×C4×C11H(5,𝔽2)11yescharacteristic
320C8×C11—22no—
321C8×C11—22no—
322C8×C11—22no—
323C8×C11—41no—
324C22×D8C22×C1111yescharacteristic
325C22×D8C22×C1111yescharacteristic
326C2×#127C22×C1111yescharacteristic
327C2×C4×D4—21no—
328C2×C4×D4C22×C1111yescharacteristic
329C2×C4×D4C22×C1111yescharacteristic
330C2×C4×D4C22×C1111yescharacteristic
331#459C4×C1118yescomplemented
332C2×#107C22×C1111yescharacteristic
333C2×#106C22×C1111yescharacteristic
334C2×C4⋊C8C22×C1111yescharacteristic
335C2×#102C22×C1111yescharacteristic
336C2×#102C22×C1111yescharacteristic
337C2×#102C22×C1111yescharacteristic
338C2×#102C22×C1111yescharacteristic
339C2×#102C22×C1111yescharacteristic
340C2×#102C22×C1111yescharacteristic
341C2×#102C22×C1111yescharacteristic
342C2×#102C22×C1111yescharacteristic
343C2×#97C22×C1111yescharacteristic
344C2×#97C22×C1111yescharacteristic
345C2×C4×C8C22×C1111yescharacteristic
346#390—21no—
347#390C22×C1111yescharacteristic
348#390C22×C1111yescharacteristic
349#390C22×C1111yescharacteristic
350#390C22×C1111yescharacteristic
351#388—21no—
352#388—21no—
353#386—21no—
354#386—21no—
355#382C22×C1111yescharacteristic
356#381—21no—
357C4×C4⋊C4C22×C1111yescharacteristic
358C4×C4⋊C4C22×C1111yescharacteristic
359C4×C4⋊C4C22×C1111yescharacteristic
360C4×C4⋊C4C22×C1111yescharacteristic
361C4×C22⋊C4—21no—
362#340C22×C1111yescharacteristic
363#340C22×C1111yescharacteristic
364#340C22×C1111yescharacteristic
365#340C22×C1111yescharacteristic
366#336C22×C1111yescharacteristic
367#336C22×C1111yescharacteristic
368C22×C11—42no—
369C22×C11—42no—
370C22×C11—42no—
371C22×C11—42no—
372C22×C11—42no—
373C22×C11—42no—
374C22×C11—42no—
375C22×C11—42no—
376C22×C11—42no—
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×C11—81no—
387C22×C11—81no—
388C22×C11—81no—
389C22×C11C2×C4×D411yescharacteristic
390C22×C11#54611yescharacteristic
391C22×C11#55011yescharacteristic
392C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
393C22×C11#57511yescharacteristic
394C22×C11#57611yescharacteristic
395C22×C11#57611yescharacteristic
396C4×C11—22no—
397C4×C11—22no—
398C4×C11—22no—
399C4×C11—42no—
400C4×C11—41no—
401C4×C11—41no—
402C4×C11—41no—
403C4×C11—42no—
404C4×C11—81no—
405C4×C11—81no—
406C4×C11—81no—
407C4×C11C4×#4111yescharacteristic
408C4×C11#51811yescharacteristic
409C4×C11#55311yescharacteristic
410C4×C11#55511yescharacteristic
411C22×D4—21no—
412C22×D4—21no—
413C22×D4C23×C1111yescharacteristic
414C22×D4C23×C1111yescharacteristic
415C22×D4C23×C1111yescharacteristic
416C23×C4—21no—
417C23×C4—21no—
418C23×C4—21no—
419C2×D8—41no—
420C2×D8—41no—
421C2×D8—41no—
422C2×D8—41no—
423C2×D8C2×C4×C1114yescomplemented
424C2×D8C2×C4×C1114yescomplemented
425C22×C8C23×C1111yescharacteristic
426C22×C8C23×C1111yescharacteristic
427C22×C8C23×C1111yescharacteristic
428C22×C8C23×C1111yescharacteristic
429#127—22no—
430#127C2×C4×C1114yes—
431C4×D4—22no—
432C4×D4—22no—
433C4×D4—22no—
434C4×D4—41no—
435C4×D4—41no—
436C4×D4—44no—
437C4×D4C2×C4×C1114yescomplemented
438C2×C4⋊C4D4×C1111yescharacteristic
439C2×C4⋊C4D4×C1111yescharacteristic
440C2×C4⋊C4C23×C1111yescharacteristic
441C2×C4⋊C4C23×C1111yescharacteristic
442C2×C4⋊C4C23×C1111yescharacteristic
443C2×C4⋊C4C23×C1111yescharacteristic
444C2×C4⋊C4C23×C1111yescharacteristic
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×C22⋊C4—21no—
453C2×C22⋊C4—21no—
454C2×C22⋊C4—21no—
455C2×C22⋊C4—21no—
456C2×C42—21no—
457C2×C42—21no—
458C2×C42—21no—
459C2×C42C23×C1111yescharacteristic
460C2×C42C23×C1111yescharacteristic
461C2×C42C23×C1111yescharacteristic
462#107—41no—
463#106—41no—
464C4⋊C8C2×C4×C1114yescomplemented
465#102—22no—
466#102—22no—
467#102—22no—
468#102—22no—
469#102—41no—
470#102—41no—
471#102C2×C4×C1114yescomplemented
472#102C2×C4×C1114yescomplemented
473#97—22no—
474#97—41no—
475C4×C8—41no—
476#95—21no—
477#95—21no—
478#95—21no—
479#95—21no—
480#95—21no—
481#95D4×C1111yescharacteristic
482#95D4×C1111yescharacteristic
483C2×C11—82no—
484C2×C11—82no—
485C2×C11—82no—
486C2×C11#236311yescharacteristic
487C2×C11C4×AGL(1,ℤ/8)11yescharacteristic
488C2×C11#294811yescharacteristic
489C2×C11#330911yescharacteristic
490C2×C11#331811yescharacteristic
491C2×C11#339911yescharacteristic
492C2×C11#340311yescharacteristic
493C24—21no—
494C24—21no—
495C24—21no—
496C2×D4—24no—
497C2×D4—24no—
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—21no—
510C2×D4—21no—
511C2×D4—21no—
512C2×D4—21no—
513C2×D4—42no—
514C2×D4—42no—
515C2×D4—81no—
516C2×D4—81no—
517C2×D4C22×C4×C1112yes—
518C2×D4C22×C4×C1112yes—
519C2×D4C22×C4×C1112yes—
520C22×C4—21no—
521C22×C4—21no—
522C22×C4—24no—
523C22×C4—21no—
524C22×C4—21no—
525C22×C4—21no—
526C22×C4—42no—
527C22×C4—42no—
528C22×C4—42no—
529C22×C4—42no—
530C22×C4—81no—
531C22×C4—81no—
532C22×C4—81no—
533C22×C4—81no—
534C22×C4C2×D4×C1111yescharacteristic
535C22×C4C2×D4×C1111yescharacteristic
536C22×C4C2×D4×C1111yescharacteristic
537C22×C4C2×D4×C1111yescharacteristic
538C22×C4C2×D4×C1111yescharacteristic
539C22×C4C2×D4×C1111yescharacteristic
540C22×C4C24×C1111yescharacteristic
541D8—44no—
542D8—44no—
543C2×C8—21no—
544C2×C8—21no—
545C2×C8—21no—
546C2×C8—21no—
547C2×C8—21no—
548C2×C8—21no—
549C2×C8—21no—
550C2×C8—21no—
551C2×C8—21no—
552C2×C8C22×C4×C1112yes—
553C2×C8C22×C4×C1112yes—
554C2×C8C11×#4112yes—
555C4⋊C4—22no—
556C4⋊C4—21no—
557C4⋊C4—21no—
558C4⋊C4—21no—
559C4⋊C4—21no—
560C4⋊C4—21no—
561C4⋊C4—21no—
562C4⋊C4—21no—
563C4⋊C4—21no—
564C4⋊C4—41no—
565C4⋊C4C22×C4×C1112yes—
566C4⋊C4C11×#4112yes—
567C22⋊C4—24no—
568C22⋊C4—42no—
569C22⋊C4—42no—
570C22⋊C4—42no—
571C22⋊C4—42no—
572C22⋊C4—42no—
573C22⋊C4—42no—
574C22⋊C4—81no—
575C22⋊C4—81no—
576C22⋊C4—81no—
577C22⋊C4—81no—
578C42—21no—
579C42—21no—
580C42—21no—
581C42—21no—
582C42—42no—
583C42—81no—
584C42—81no—
585C42C22×C4×C1112yes—
586C42C11×#4112yes—
587C11#2310811yescharacteristic, direct product factor, Sylow
588C23—22no—
589C23—22no—
590C23—22no—
591C23—41no—
592C23—41no—
593C23—41no—
594C23—41no—
595C23—41no—
596C23—41no—
597C23—41no—
598C23—41no—
599C23—41no—
600C23—41no—
601C23—41no—
602C23—41no—
603C23—41no—
604C23—41no—
605C23—41no—
606C23—41no—
607C23—41no—
608C23—41no—
609C23C22×D4×C1111yescharacteristic
610D4—22no—
611D4—22no—
612D4—22no—
613D4—22no—
614D4—22no—
615D4—22no—
616D4—48no—
617D4—41no—
618D4—41no—
619D4—41no—
620D4—41no—
621D4—41no—
622D4—41no—
623D4—84no—
624C2×C4—21no—
625C2×C4—21no—
626C2×C4—21no—
627C2×C4—21no—
628C2×C4—21no—
629C2×C4—21no—
630C2×C4—22no—
631C2×C4—21no—
632C2×C4—21no—
633C2×C4—21no—
634C2×C4—22no—
635C2×C4—21no—
636C2×C4—21no—
637C2×C4—21no—
638C2×C4—21no—
639C2×C4—21no—
640C2×C4—21no—
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—41no—
650C2×C4—41no—
651C2×C4—41no—
652C2×C4—41no—
653C2×C4—41no—
654C2×C4—84no—
655C2×C4—84no—
656C2×C4—84no—
657C2×C4C4×D4×C1112yes—
658C2×C4C4×D4×C1112yes—
659C2×C4C11×AGL(1,ℤ/8)12yes—
660C2×C4C23×C4×C1111yescharacteristic
661C2×C4C2×C11×#4111yescharacteristic
662C2×C4C2×C11×#4111yescharacteristic
663C2×C4C2×C11×#4111yescharacteristic
664C2×C4C11×H(5,𝔽2)11yescharacteristic
665C2×C4C11×H(5,𝔽2)11yescharacteristic
666C8—22no—
667C8—22no—
668C8—22no—
669C8—41no—
670C22—42no—
671C22—42no—
672C22—42no—
673C22—42no—
674C22—42no—
675C22—42no—
676C22—42no—
677C22—42no—
678C22—42no—
679C22—81no—
680C22—81no—
681C22—81no—
682C22—81no—
683C22—81no—
684C22—81no—
685C22—81no—
686C22—81no—
687C22—81no—
688C22—81no—
689C22—81no—
690C22—81no—
691C22C2×C4×D4×C1111yescharacteristic
692C22C11×#54611yescharacteristic
693C22C11×#55011yescharacteristic
694C22C2×C11×AGL(1,ℤ/8)11yescharacteristic
695C22C11×#57511yescharacteristic
696C22C11×#57611yescharacteristic
697C22C11×#57611yescharacteristic
698C4—22no—
699C4—22no—
700C4—22no—
701C4—42no—
702C4—41no—
703C4—41no—
704C4—41no—
705C4—42no—
706C4—81no—
707C4—81no—
708C4—81no—
709C4C4×C11×#4111yescharacteristic
710C4C11×#51811yescharacteristic
711C4C11×#55311yescharacteristic
712C4C11×#55511yescharacteristic
713C2—82no—
714C2—82no—
715C2—82no—
716C2C11×#236311yescharacteristic
717C2C4×C11×AGL(1,ℤ/8)11yescharacteristic
718C2C11×#294811yescharacteristic
719C2C11×#330911yescharacteristic
720C2C11×#331811yescharacteristic
721C2C11×#339911yescharacteristic
722C2C11×#340311yescharacteristic
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 ◁ C4×C11×C4⋊C4 ◁ G

Complements

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

NH ≅ G/Ntype
2. C11×#2366C2semidirect
3. C11×#2357C2semidirect
4. C11×#1972C2semidirect
5. C11×#1970C2semidirect
6. C11×#1961C2semidirect
7. C11×#1949C2semidirect
8. C11×#1926C2semidirect
9. C11×#1925C2semidirect
10. C11×#1879C2semidirect
11. C11×#1879C2semidirect
12. C11×#1771C2semidirect
13. C11×#1762C2semidirect
14. C11×#1762C2semidirect
15. C4×C11×#102C2semidirect
23. C11×#459C4semidirect
72. C2×C11×D8C2×C4semidirect
73. C2×C11×D8C2×C4semidirect
86. C4×D4×C11C2×C4semidirect
113. C11×C4⋊C8C2×C4semidirect
120. C11×#102C2×C4semidirect
121. C11×#102C2×C4semidirect
132. #23108C11direct (N × H)
228. #2366C2×C11semidirect
229. #2357C2×C11semidirect
230. #1972C2×C11semidirect
231. #1970C2×C11semidirect
232. #1961C2×C11semidirect
233. #1949C2×C11semidirect
234. #1926C2×C11semidirect
235. #1925C2×C11semidirect
236. #1879C2×C11semidirect
237. #1879C2×C11semidirect
238. #1771C2×C11semidirect
239. #1762C2×C11semidirect
240. #1762C2×C11semidirect
241. C4×#102C2×C11semidirect
331. #459C4×C11semidirect
423. C2×D8C2×C4×C11semidirect
424. C2×D8C2×C4×C11semidirect
437. C4×D4C2×C4×C11semidirect
464. C4⋊C8C2×C4×C11semidirect
471. #102C2×C4×C11semidirect
472. #102C2×C4×C11semidirect
587. C11#23108direct (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×#23662
C11×#23572
C11×#19722
C11×#19702
C11×#19612
C11×#19492
C11×#19262
C11×#19252
C11×#18792
C11×#17712
C11×#17622
C4×C11×#1022
#2310811