Finite Group Databasebeta

← C11×#24438 #14601631

Subgroups — C11×#24438 #14601631

Order 2816.

1498 conjugacy classes of subgroups.

The subgroup lattice has 910 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#547C211yesmaximal, characteristic, complemented
2C2×C11×#465C211yesmaximal, characteristic, complemented
3C2×C11×#449C211yesmaximal, characteristic, complemented
4C2×C11×#449C211yesmaximal, characteristic, complemented
5C2×C11×#416C211yesmaximal, characteristic, complemented
6C11×#2414C211yesmaximal, characteristic, complemented
7C11×#2043C211yesmaximal, characteristic, complemented
8C11×#2035C211yesmaximal, characteristic, complemented
9C11×#2013C211yesmaximal, characteristic, complemented
10C11×#2000C211yesmaximal, characteristic, complemented
11C11×#1879C211yesmaximal, characteristic, complemented
12C11×#1873C211yesmaximal, characteristic, complemented
13C11×#1869C211yesmaximal, characteristic, complemented
14C11×#1864C211yesmaximal, characteristic, complemented
15C11×#1788C211yesmaximal, characteristic, complemented
16C22×C11×#41C2211yescharacteristic
17C22×C11×#41C2211yescharacteristic
18C22×C11×SD16C2211yescharacteristic
19C22×C11×SD16C2211yescharacteristic
20C22×C11×D8C2211yescharacteristic
21C23×C8×C11C2211yescharacteristic
22C11×#547—24no—
23C11×#547—24no—
24C2×C11×C4⋊Q8C2211yescharacteristic
25C2×C11×#123—21no—
26C2×C11×#123—21no—
27C2×C11×C22⋊Q8C2211yescharacteristic
28C2×C11×C22⋊Q8C2211yescharacteristic
29C2×C11×#121—21no—
30C2×C11×#121C2211yescharacteristic
31C2×C11×#121C2211yescharacteristic
32C2×C4×D4×C11C2211yescharacteristic
33C2×C4×D4×C11C2211yescharacteristic
34C2×C11×#117C2211yescharacteristic
35C22×C11×C4⋊C4—21no—
36C11×#465—24no—
37C11×#449—24no—
38C11×#449—24no—
39C2×C11×#106C2211yescharacteristic
40C11×#416—24no—
41C2×C11×#103C2211yescharacteristic
42C2×C11×#103C2211yescharacteristic
43C2×C11×#103C2211yescharacteristic
44C2×C11×#103C2211yescharacteristic
45C2×C11×#103C2211yescharacteristic
46C2×C11×#103C2211yescharacteristic
47C2×C11×#102C2211yescharacteristic
48C2×C11×#102C2211yescharacteristic
49C2×C11×#102C2211yescharacteristic
50C2×C11×#102C2211yescharacteristic
51C2×C11×C22⋊C8C2211yescharacteristic
52C2×C11×C22⋊C8C2211yescharacteristic
53C2×C11×C22⋊C8C2211yescharacteristic
54C11×#394—21no—
55C11×#392—21no—
56C11×#390—21no—
57C11×#390C2211yescharacteristic
58C11×#389C2211yescharacteristic
59C11×#388—21no—
60C11×#380C2211yescharacteristic
61C11×#340C2211yescharacteristic
62C11×#340C2211yescharacteristic
63C11×#336C2211yescharacteristic
64C11×#336C2211yescharacteristic
65C2×C11×#41—22no—
66C2×C11×#41—22no—
67C2×C11×#41—22no—
68C2×C11×#41—22no—
69C2×C11×#41—22no—
70C2×C11×#41—22no—
71C2×C11×#41—22no—
72C2×C11×#41—41no—
73C2×C11×#41—41no—
74C2×C11×#41—41no—
75C2×C11×#41—41no—
76C2×C11×#41D414yescomplemented
77C22×Q8×C11C2311yescharacteristic
78C22×Q8×C11C2311yescharacteristic
79C22×D4×C11—21no—
80C22×D4×C11—21no—
81C22×D4×C11—21no—
82C22×D4×C11—21no—
83C22×D4×C11D411yescharacteristic
84C22×D4×C11C2311yescharacteristic
85C22×D4×C11C2311yescharacteristic
86C23×C4×C11—21no—
87C23×C4×C11—21no—
88C23×C4×C11—21no—
89C23×C4×C11C2311yescharacteristic
90C23×C4×C11C2311yescharacteristic
91C2×C11×SD16—22no—
92C2×C11×SD16—22no—
93C2×C11×SD16—22no—
94C2×C11×SD16—41no—
95C2×C11×SD16—41no—
96C2×C11×SD16—41no—
97C2×C11×D8—22no—
98C2×C11×D8—22no—
99C2×C11×D8—22no—
100C22×C8×C11—22no—
101C22×C8×C11—22no—
102C22×C8×C11—41no—
103C22×C8×C11C2311yescharacteristic
104C22×C8×C11C2311yescharacteristic
105C22×C8×C11C2311yescharacteristic
106C22×C8×C11C2311yescharacteristic
107C11×C4⋊Q8—22no—
108C11×C4⋊Q8—22no—
109C11×#123—28no—
110C11×#123—28no—
111C11×C22⋊Q8—22no—
112C11×C22⋊Q8—22no—
113C11×C22⋊Q8—22no—
114C11×C22⋊Q8D414yescomplemented
115C11×#121—28no—
116C11×#121—22no—
117C11×#121—22no—
118C11×#121—22no—
119C11×#121—41no—
120C4×D4×C11—22no—
121C4×D4×C11—22no—
122C4×D4×C11—22no—
123C4×D4×C11—22no—
124C11×#117—22no—
125C11×#117—41no—
126C2×C11×C4⋊C4—28no—
127C2×C11×C4⋊C4—21no—
128C2×C11×C4⋊C4—21no—
129C2×C11×C4⋊C4—21no—
130C2×C11×C4⋊C4—21no—
131C2×C11×C4⋊C4—21no—
132C2×C11×C4⋊C4D411yescharacteristic
133C2×C11×C4⋊C4C2311yescharacteristic
134C2×C11×C4⋊C4C2311yescharacteristic
135C2×C11×C4⋊C4C2311yescharacteristic
136C2×C11×C4⋊C4C2311yescharacteristic
137C2×C11×C22⋊C4—21no—
138C2×C11×C22⋊C4—21no—
139C2×C11×C22⋊C4—21no—
140C2×C11×C22⋊C4—21no—
141C2×C11×C22⋊C4—21no—
142C2×C11×C22⋊C4—21no—
143C2×C11×C22⋊C4—21no—
144C2×C11×C22⋊C4—21no—
145C2×C11×C22⋊C4—21no—
146C2×C11×C22⋊C4D411yescharacteristic
147C2×C11×C22⋊C4D411yescharacteristic
148C2×C42×C11—21no—
149C2×C42×C11C2311yescharacteristic
150C11×#106—22no—
151C11×#103—22no—
152C11×#103—22no—
153C11×#103—22no—
154C11×#103—22no—
155C11×#103—22no—
156C11×#103—41no—
157C11×#102—22no—
158C11×#102—22no—
159C11×#102—22no—
160C11×#102D414yescomplemented
161C11×C22⋊C8—22no—
162C11×C22⋊C8—22no—
163C11×C22⋊C8—41no—
164C11×#95—21no—
165C11×#95—21no—
166#24438C1111yesmaximal, characteristic, direct product factor, Sylow
167C24×C11—21no—
168C24×C11—21no—
169C24×C11C2×D411yescharacteristic
170C24×C11C2×D411yescharacteristic
171C11×#41—28no—
172C11×#41—44no—
173C11×#41—44no—
174C11×#41—44no—
175C11×#41—44no—
176C11×#41—44no—
177C11×#41—44no—
178C11×#41—44no—
179C2×Q8×C11—21no—
180C2×Q8×C11—21no—
181C2×Q8×C11—21no—
182C2×Q8×C11—21no—
183C2×Q8×C11—21no—
184C2×Q8×C11—21no—
185C2×Q8×C11—21no—
186C2×Q8×C11—21no—
187C2×Q8×C11—21no—
188C2×Q8×C11—21no—
189C2×Q8×C11C2×D412yes—
190C2×Q8×C11C2×D412yes—
191C2×D4×C11—24no—
192C2×D4×C11—22no—
193C2×D4×C11—24no—
194C2×D4×C11—22no—
195C2×D4×C11—21no—
196C2×D4×C11—21no—
197C2×D4×C11—21no—
198C2×D4×C11—21no—
199C2×D4×C11—21no—
200C2×D4×C11—21no—
201C2×D4×C11—21no—
202C2×D4×C11—21no—
203C2×D4×C11—21no—
204C2×D4×C11—41no—
205C2×D4×C11—42no—
206C2×D4×C11—42no—
207C2×D4×C11—42no—
208C2×D4×C11—42no—
209C2×D4×C11—42no—
210C2×D4×C11—42no—
211C2×D4×C11—42no—
212C2×D4×C11—81no—
213C2×D4×C11—81no—
214C2×D4×C11—81no—
215C2×D4×C11C2×D412yes—
216C2×D4×C11C2×D412yes—
217C2×D4×C11#4112yes—
218C22×C4×C11—21no—
219C22×C4×C11—21no—
220C22×C4×C11—21no—
221C22×C4×C11—21no—
222C22×C4×C11—24no—
223C22×C4×C11—24no—
224C22×C4×C11—21no—
225C22×C4×C11—21no—
226C22×C4×C11—21no—
227C22×C4×C11—21no—
228C22×C4×C11—24no—
229C22×C4×C11—21no—
230C22×C4×C11—21no—
231C22×C4×C11—21no—
232C22×C4×C11—21no—
233C22×C4×C11—21no—
234C22×C4×C11—21no—
235C22×C4×C11—21no—
236C22×C4×C11—21no—
237C22×C4×C11—42no—
238C22×C4×C11—42no—
239C22×C4×C11—42no—
240C22×C4×C11—42no—
241C22×C4×C11—42no—
242C22×C4×C11—42no—
243C22×C4×C11C2×D411yescharacteristic
244C22×C4×C11C2×D411yescharacteristic
245C22×C4×C11C2×D411yescharacteristic
246C22×C4×C11C2×D412yes—
247C22×C4×C11C2×D412yes—
248C22×C4×C11C2×D411yescharacteristic
249C22×C4×C11C2411yescharacteristic
250C11×SD16—44no—
251C11×SD16—44no—
252C11×D8—44no—
253C2×C8×C11—21no—
254C2×C8×C11—21no—
255C2×C8×C11—21no—
256C2×C8×C11—21no—
257C2×C8×C11—21no—
258C2×C8×C11—21no—
259C2×C8×C11—21no—
260C2×C8×C11—21no—
261C2×C8×C11—21no—
262C2×C8×C11—21no—
263C2×C8×C11—21no—
264C2×C8×C11—44no—
265C2×C8×C11C2×D412yes—
266C11×C4⋊C4—24no—
267C11×C4⋊C4—24no—
268C11×C4⋊C4—24no—
269C11×C4⋊C4—22no—
270C11×C4⋊C4—24no—
271C11×C4⋊C4—21no—
272C11×C4⋊C4—21no—
273C11×C4⋊C4—21no—
274C11×C4⋊C4—21no—
275C11×C4⋊C4—21no—
276C11×C4⋊C4—21no—
277C11×C4⋊C4—81no—
278C11×C4⋊C4C2×D412yes—
279C11×C4⋊C4C2×D412yes—
280C11×C22⋊C4—24no—
281C11×C22⋊C4—24no—
282C11×C22⋊C4—24no—
283C11×C22⋊C4—22no—
284C11×C22⋊C4—22no—
285C11×C22⋊C4—42no—
286C11×C22⋊C4—42no—
287C11×C22⋊C4—42no—
288C11×C22⋊C4—42no—
289C11×C22⋊C4—81no—
290C11×C22⋊C4—81no—
291C42×C11—21no—
292C42×C11—21no—
293C42×C11—42no—
294C2×#547C2×C1111yescharacteristic, complemented
295C2×#465C2×C1111yescharacteristic, complemented
296C2×#449C2×C1111yescharacteristic, complemented
297C2×#449C2×C1111yescharacteristic, complemented
298C2×#416C2×C1111yescharacteristic, complemented
299#2414C2×C1111yescharacteristic, complemented
300#2043C2×C1111yescharacteristic, complemented
301#2035C2×C1111yescharacteristic, complemented
302#2013C2×C1111yescharacteristic, complemented
303#2000C2×C1111yescharacteristic, complemented
304#1879C2×C1111yescharacteristic, complemented
305#1873C2×C1111yescharacteristic, complemented
306#1869C2×C1111yescharacteristic, complemented
307#1864C2×C1111yescharacteristic, complemented
308#1788C2×C1111yescharacteristic, complemented
309C23×C11—22no—
310C23×C11—21no—
311C23×C11—22no—
312C23×C11—21no—
313C23×C11—22no—
314C23×C11—21no—
315C23×C11—21no—
316C23×C11—21no—
317C23×C11—21no—
318C23×C11—21no—
319C23×C11—21no—
320C23×C11—21no—
321C23×C11—21no—
322C23×C11—21no—
323C23×C11—21no—
324C23×C11—21no—
325C23×C11—41no—
326C23×C11—41no—
327C23×C11—41no—
328C23×C11—41no—
329C23×C11—41no—
330C23×C11—41no—
331C23×C11—41no—
332C23×C11—41no—
333C23×C11—41no—
334C23×C11—41no—
335C23×C11—41no—
336C23×C11#12012yes—
337C23×C11C22×D411yescharacteristic
338Q8×C11—22no—
339Q8×C11—22no—
340Q8×C11—22no—
341Q8×C11—22no—
342Q8×C11—41no—
343Q8×C11—41no—
344Q8×C11—41no—
345Q8×C11—41no—
346D4×C11—22no—
347D4×C11—22no—
348D4×C11—22no—
349D4×C11—44no—
350D4×C11—48no—
351D4×C11—48no—
352D4×C11—41no—
353D4×C11—41no—
354D4×C11—41no—
355D4×C11—41no—
356D4×C11—84no—
357D4×C11—84no—
358D4×C11#12114yes—
359C2×C4×C11—21no—
360C2×C4×C11—21no—
361C2×C4×C11—21no—
362C2×C4×C11—21no—
363C2×C4×C11—22no—
364C2×C4×C11—22no—
365C2×C4×C11—22no—
366C2×C4×C11—22no—
367C2×C4×C11—21no—
368C2×C4×C11—22no—
369C2×C4×C11—21no—
370C2×C4×C11—22no—
371C2×C4×C11—22no—
372C2×C4×C11—22no—
373C2×C4×C11—21no—
374C2×C4×C11—21no—
375C2×C4×C11—21no—
376C2×C4×C11—21no—
377C2×C4×C11—48no—
378C2×C4×C11—48no—
379C2×C4×C11—48no—
380C2×C4×C11—41no—
381C2×C4×C11—41no—
382C2×C4×C11—41no—
383C2×C4×C11—41no—
384C2×C4×C11—41no—
385C2×C4×C11—41no—
386C2×C4×C11—41no—
387C2×C4×C11—41no—
388C2×C4×C11—41no—
389C2×C4×C11—41no—
390C2×C4×C11—41no—
391C2×C4×C11—41no—
392C2×C4×C11—41no—
393C2×C4×C11—41no—
394C2×C4×C11—41no—
395C2×C4×C11—41no—
396C2×C4×C11—41no—
397C2×C4×C11—41no—
398C2×C4×C11#12012yes—
399C2×C4×C11#13512yes—
400C2×C4×C11C22×D411yescharacteristic
401C2×C4×C11C22×D411yescharacteristic
402C2×C4×C11C22×D411yescharacteristic
403C2×C4×C11C2×#4111yescharacteristic
404C2×C4×C11H(5,𝔽2)11yescharacteristic
405C2×C4×C11H(5,𝔽2)11yescharacteristic
406C8×C11—22no—
407C8×C11—41no—
408C8×C11—41no—
409C8×C11—41no—
410C22×#41C22×C1111yescharacteristic
411C22×#41C22×C1111yescharacteristic
412C22×SD16C22×C1111yescharacteristic
413C22×SD16C22×C1111yescharacteristic
414C22×D8C22×C1111yescharacteristic
415C23×C8C22×C1111yescharacteristic
416#547—24no—
417#547—24no—
418C2×C4⋊Q8C22×C1111yescharacteristic
419C2×#123—21no—
420C2×#123—21no—
421C2×C22⋊Q8C22×C1111yescharacteristic
422C2×C22⋊Q8C22×C1111yescharacteristic
423C2×#121—21no—
424C2×#121C22×C1111yescharacteristic
425C2×#121C22×C1111yescharacteristic
426C2×C4×D4C22×C1111yescharacteristic
427C2×C4×D4C22×C1111yescharacteristic
428C2×#117C22×C1111yescharacteristic
429C22×C4⋊C4—21no—
430#465—24no—
431#449—24no—
432#449—24no—
433C2×#106C22×C1111yescharacteristic
434#416—24no—
435C2×#103C22×C1111yescharacteristic
436C2×#103C22×C1111yescharacteristic
437C2×#103C22×C1111yescharacteristic
438C2×#103C22×C1111yescharacteristic
439C2×#103C22×C1111yescharacteristic
440C2×#103C22×C1111yescharacteristic
441C2×#102C22×C1111yescharacteristic
442C2×#102C22×C1111yescharacteristic
443C2×#102C22×C1111yescharacteristic
444C2×#102C22×C1111yescharacteristic
445C2×C22⋊C8C22×C1111yescharacteristic
446C2×C22⋊C8C22×C1111yescharacteristic
447C2×C22⋊C8C22×C1111yescharacteristic
448#394—21no—
449#392—21no—
450#390—21no—
451#390C22×C1111yescharacteristic
452#389C22×C1111yescharacteristic
453#388—21no—
454#380C22×C1111yescharacteristic
455#340C22×C1111yescharacteristic
456#340C22×C1111yescharacteristic
457#336C22×C1111yescharacteristic
458#336C22×C1111yescharacteristic
459C22×C11—22no—
460C22×C11—24no—
461C22×C11—22no—
462C22×C11—22no—
463C22×C11—42no—
464C22×C11—42no—
465C22×C11—41no—
466C22×C11—42no—
467C22×C11—41no—
468C22×C11—42no—
469C22×C11—41no—
470C22×C11—42no—
471C22×C11—41no—
472C22×C11—42no—
473C22×C11—41no—
474C22×C11—41no—
475C22×C11—41no—
476C22×C11—41no—
477C22×C11—41no—
478C22×C11—41no—
479C22×C11—41no—
480C22×C11—81no—
481C22×C11—81no—
482C22×C11—81no—
483C22×C11—81no—
484C22×C11—81no—
485C22×C11—81no—
486C22×C11—81no—
487C22×C11C2×#12011yescharacteristic
488C22×C11D4211yescharacteristic
489C22×C11#54611yescharacteristic
490C22×C11C2×#13511yescharacteristic
491C22×C11#57511yescharacteristic
492C22×C11#57711yescharacteristic
493C22×C11#57711yescharacteristic
494C4×C11—22no—
495C4×C11—22no—
496C4×C11—41no—
497C4×C11—42no—
498C4×C11—42no—
499C4×C11—42no—
500C4×C11—41no—
501C4×C11—42no—
502C4×C11—81no—
503C4×C11—81no—
504C4×C11C2×#12111yescharacteristic
505C4×C11#53411yescharacteristic
506C4×C11D4211yescharacteristic
507C4×C11#54611yescharacteristic
508C2×#41—22no—
509C2×#41—22no—
510C2×#41—22no—
511C2×#41—22no—
512C2×#41—22no—
513C2×#41—22no—
514C2×#41—22no—
515C2×#41—41no—
516C2×#41—41no—
517C2×#41—41no—
518C2×#41—41no—
519C2×#41D4×C1114yescomplemented
520C22×Q8C23×C1111yescharacteristic
521C22×Q8C23×C1111yescharacteristic
522C22×D4—21no—
523C22×D4—21no—
524C22×D4—21no—
525C22×D4—21no—
526C22×D4D4×C1111yescharacteristic
527C22×D4C23×C1111yescharacteristic
528C22×D4C23×C1111yescharacteristic
529C23×C4—21no—
530C23×C4—21no—
531C23×C4—21no—
532C23×C4C23×C1111yescharacteristic
533C23×C4C23×C1111yescharacteristic
534C2×SD16—22no—
535C2×SD16—22no—
536C2×SD16—22no—
537C2×SD16—41no—
538C2×SD16—41no—
539C2×SD16—41no—
540C2×D8—22no—
541C2×D8—22no—
542C2×D8—22no—
543C22×C8—22no—
544C22×C8—22no—
545C22×C8—41no—
546C22×C8C23×C1111yescharacteristic
547C22×C8C23×C1111yescharacteristic
548C22×C8C23×C1111yescharacteristic
549C22×C8C23×C1111yescharacteristic
550C4⋊Q8—22no—
551C4⋊Q8—22no—
552#123—28no—
553#123—28no—
554C22⋊Q8—22no—
555C22⋊Q8—22no—
556C22⋊Q8—22no—
557C22⋊Q8D4×C1114yescomplemented
558#121—28no—
559#121—22no—
560#121—22no—
561#121—22no—
562#121—41no—
563C4×D4—22no—
564C4×D4—22no—
565C4×D4—22no—
566C4×D4—22no—
567#117—22no—
568#117—41no—
569C2×C4⋊C4—28no—
570C2×C4⋊C4—21no—
571C2×C4⋊C4—21no—
572C2×C4⋊C4—21no—
573C2×C4⋊C4—21no—
574C2×C4⋊C4—21no—
575C2×C4⋊C4D4×C1111yescharacteristic
576C2×C4⋊C4C23×C1111yescharacteristic
577C2×C4⋊C4C23×C1111yescharacteristic
578C2×C4⋊C4C23×C1111yescharacteristic
579C2×C4⋊C4C23×C1111yescharacteristic
580C2×C22⋊C4—21no—
581C2×C22⋊C4—21no—
582C2×C22⋊C4—21no—
583C2×C22⋊C4—21no—
584C2×C22⋊C4—21no—
585C2×C22⋊C4—21no—
586C2×C22⋊C4—21no—
587C2×C22⋊C4—21no—
588C2×C22⋊C4—21no—
589C2×C22⋊C4D4×C1111yescharacteristic
590C2×C22⋊C4D4×C1111yescharacteristic
591C2×C42—21no—
592C2×C42C23×C1111yescharacteristic
593#106—22no—
594#103—22no—
595#103—22no—
596#103—22no—
597#103—22no—
598#103—22no—
599#103—41no—
600#102—22no—
601#102—22no—
602#102—22no—
603#102D4×C1114yescomplemented
604C22⋊C8—22no—
605C22⋊C8—22no—
606C22⋊C8—41no—
607#95—21no—
608#95—21no—
609C2×C11—42no—
610C2×C11—44no—
611C2×C11—81no—
612C2×C11—161no—
613C2×C11#241011yescharacteristic
614C2×C11#300211yescharacteristic
615C2×C11#301011yescharacteristic
616C2×C11#326711yescharacteristic
617C2×C11#328411yescharacteristic
618C2×C11#330311yescharacteristic
619C2×C11#330711yescharacteristic
620C24—21no—
621C24—21no—
622C24C2×D4×C1111yescharacteristic
623C24C2×D4×C1111yescharacteristic
624#41—28no—
625#41—44no—
626#41—44no—
627#41—44no—
628#41—44no—
629#41—44no—
630#41—44no—
631#41—44no—
632C2×Q8—21no—
633C2×Q8—21no—
634C2×Q8—21no—
635C2×Q8—21no—
636C2×Q8—21no—
637C2×Q8—21no—
638C2×Q8—21no—
639C2×Q8—21no—
640C2×Q8—21no—
641C2×Q8—21no—
642C2×Q8C2×D4×C1112yes—
643C2×Q8C2×D4×C1112yes—
644C2×D4—24no—
645C2×D4—22no—
646C2×D4—24no—
647C2×D4—22no—
648C2×D4—21no—
649C2×D4—21no—
650C2×D4—21no—
651C2×D4—21no—
652C2×D4—21no—
653C2×D4—21no—
654C2×D4—21no—
655C2×D4—21no—
656C2×D4—21no—
657C2×D4—41no—
658C2×D4—42no—
659C2×D4—42no—
660C2×D4—42no—
661C2×D4—42no—
662C2×D4—42no—
663C2×D4—42no—
664C2×D4—42no—
665C2×D4—81no—
666C2×D4—81no—
667C2×D4—81no—
668C2×D4C2×D4×C1112yes—
669C2×D4C2×D4×C1112yes—
670C2×D4C11×#4112yes—
671C22×C4—21no—
672C22×C4—21no—
673C22×C4—21no—
674C22×C4—21no—
675C22×C4—24no—
676C22×C4—24no—
677C22×C4—21no—
678C22×C4—21no—
679C22×C4—21no—
680C22×C4—21no—
681C22×C4—24no—
682C22×C4—21no—
683C22×C4—21no—
684C22×C4—21no—
685C22×C4—21no—
686C22×C4—21no—
687C22×C4—21no—
688C22×C4—21no—
689C22×C4—21no—
690C22×C4—42no—
691C22×C4—42no—
692C22×C4—42no—
693C22×C4—42no—
694C22×C4—42no—
695C22×C4—42no—
696C22×C4C2×D4×C1111yescharacteristic
697C22×C4C2×D4×C1111yescharacteristic
698C22×C4C2×D4×C1111yescharacteristic
699C22×C4C2×D4×C1112yes—
700C22×C4C2×D4×C1112yes—
701C22×C4C2×D4×C1111yescharacteristic
702C22×C4C24×C1111yescharacteristic
703SD16—44no—
704SD16—44no—
705D8—44no—
706C2×C8—21no—
707C2×C8—21no—
708C2×C8—21no—
709C2×C8—21no—
710C2×C8—21no—
711C2×C8—21no—
712C2×C8—21no—
713C2×C8—21no—
714C2×C8—21no—
715C2×C8—21no—
716C2×C8—21no—
717C2×C8—44no—
718C2×C8C2×D4×C1112yes—
719C4⋊C4—24no—
720C4⋊C4—24no—
721C4⋊C4—24no—
722C4⋊C4—22no—
723C4⋊C4—24no—
724C4⋊C4—21no—
725C4⋊C4—21no—
726C4⋊C4—21no—
727C4⋊C4—21no—
728C4⋊C4—21no—
729C4⋊C4—21no—
730C4⋊C4—81no—
731C4⋊C4C2×D4×C1112yes—
732C4⋊C4C2×D4×C1112yes—
733C22⋊C4—24no—
734C22⋊C4—24no—
735C22⋊C4—24no—
736C22⋊C4—22no—
737C22⋊C4—22no—
738C22⋊C4—42no—
739C22⋊C4—42no—
740C22⋊C4—42no—
741C22⋊C4—42no—
742C22⋊C4—81no—
743C22⋊C4—81no—
744C42—21no—
745C42—21no—
746C42—42no—
747C11#2443811yescharacteristic, direct product factor, Sylow
748C23—22no—
749C23—21no—
750C23—22no—
751C23—21no—
752C23—22no—
753C23—21no—
754C23—21no—
755C23—21no—
756C23—21no—
757C23—21no—
758C23—21no—
759C23—21no—
760C23—21no—
761C23—21no—
762C23—21no—
763C23—21no—
764C23—41no—
765C23—41no—
766C23—41no—
767C23—41no—
768C23—41no—
769C23—41no—
770C23—41no—
771C23—41no—
772C23—41no—
773C23—41no—
774C23—41no—
775C23C11×#12012yes—
776C23C22×D4×C1111yescharacteristic
777Q8—22no—
778Q8—22no—
779Q8—22no—
780Q8—22no—
781Q8—41no—
782Q8—41no—
783Q8—41no—
784Q8—41no—
785D4—22no—
786D4—22no—
787D4—22no—
788D4—44no—
789D4—48no—
790D4—48no—
791D4—41no—
792D4—41no—
793D4—41no—
794D4—41no—
795D4—84no—
796D4—84no—
797D4C11×#12114yes—
798C2×C4—21no—
799C2×C4—21no—
800C2×C4—21no—
801C2×C4—21no—
802C2×C4—22no—
803C2×C4—22no—
804C2×C4—22no—
805C2×C4—22no—
806C2×C4—21no—
807C2×C4—22no—
808C2×C4—21no—
809C2×C4—22no—
810C2×C4—22no—
811C2×C4—22no—
812C2×C4—21no—
813C2×C4—21no—
814C2×C4—21no—
815C2×C4—21no—
816C2×C4—48no—
817C2×C4—48no—
818C2×C4—48no—
819C2×C4—41no—
820C2×C4—41no—
821C2×C4—41no—
822C2×C4—41no—
823C2×C4—41no—
824C2×C4—41no—
825C2×C4—41no—
826C2×C4—41no—
827C2×C4—41no—
828C2×C4—41no—
829C2×C4—41no—
830C2×C4—41no—
831C2×C4—41no—
832C2×C4—41no—
833C2×C4—41no—
834C2×C4—41no—
835C2×C4—41no—
836C2×C4—41no—
837C2×C4C11×#12012yes—
838C2×C4C11×#13512yes—
839C2×C4C22×D4×C1111yescharacteristic
840C2×C4C22×D4×C1111yescharacteristic
841C2×C4C22×D4×C1111yescharacteristic
842C2×C4C2×C11×#4111yescharacteristic
843C2×C4C11×H(5,𝔽2)11yescharacteristic
844C2×C4C11×H(5,𝔽2)11yescharacteristic
845C8—22no—
846C8—41no—
847C8—41no—
848C8—41no—
849C22—22no—
850C22—24no—
851C22—22no—
852C22—22no—
853C22—42no—
854C22—42no—
855C22—41no—
856C22—42no—
857C22—41no—
858C22—42no—
859C22—41no—
860C22—42no—
861C22—41no—
862C22—42no—
863C22—41no—
864C22—41no—
865C22—41no—
866C22—41no—
867C22—41no—
868C22—41no—
869C22—41no—
870C22—81no—
871C22—81no—
872C22—81no—
873C22—81no—
874C22—81no—
875C22—81no—
876C22—81no—
877C22C2×C11×#12011yescharacteristic
878C22D42×C1111yescharacteristic
879C22C11×#54611yescharacteristic
880C22C2×C11×#13511yescharacteristic
881C22C11×#57511yescharacteristic
882C22C11×#57711yescharacteristic
883C22C11×#57711yescharacteristic
884C4—22no—
885C4—22no—
886C4—41no—
887C4—42no—
888C4—42no—
889C4—42no—
890C4—41no—
891C4—42no—
892C4—81no—
893C4—81no—
894C4C2×C11×#12111yescharacteristic
895C4C11×#53411yescharacteristic
896C4D42×C1111yescharacteristic
897C4C11×#54611yescharacteristic
898C2—42no—
899C2—44no—
900C2—81no—
901C2—161no—
902C2C11×#241011yescharacteristic
903C2C11×#300211yescharacteristic
904C2C11×#301011yescharacteristic
905C2C11×#326711yescharacteristic
906C2C11×#328411yescharacteristic
907C2C11×#330311yescharacteristic
908C2C11×#330711yescharacteristic
subgroupG/H
center, socleC23×C11C22×D4
commutator, Frattini, cosocleC22×C4C24×C11
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C11 ◁ C2×C4×D4×C11 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C11×#547C2semidirect
2. C2×C11×#465C2semidirect
3. C2×C11×#449C2semidirect
4. C2×C11×#449C2semidirect
5. C2×C11×#416C2semidirect
6. C11×#2414C2semidirect
7. C11×#2043C2semidirect
8. C11×#2035C2semidirect
9. C11×#2013C2semidirect
10. C11×#2000C2semidirect
11. C11×#1879C2semidirect
12. C11×#1873C2semidirect
13. C11×#1869C2semidirect
14. C11×#1864C2semidirect
15. C11×#1788C2semidirect
76. C2×C11×#41D4semidirect
114. C11×C22⋊Q8D4semidirect
160. C11×#102D4semidirect
166. #24438C11direct (N × H)
294. C2×#547C2×C11semidirect
295. C2×#465C2×C11semidirect
296. C2×#449C2×C11semidirect
297. C2×#449C2×C11semidirect
298. C2×#416C2×C11semidirect
299. #2414C2×C11semidirect
300. #2043C2×C11semidirect
301. #2035C2×C11semidirect
302. #2013C2×C11semidirect
303. #2000C2×C11semidirect
304. #1879C2×C11semidirect
305. #1873C2×C11semidirect
306. #1869C2×C11semidirect
307. #1864C2×C11semidirect
308. #1788C2×C11semidirect
519. C2×#41D4×C11semidirect
557. C22⋊Q8D4×C11semidirect
603. #102D4×C11semidirect
747. C11#24438direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#5472
C2×C11×#4652
C2×C11×#4492
C2×C11×#4162
C11×#24142
C11×#20432
C11×#20352
C11×#20132
C11×#20002
C11×#18792
C11×#18732
C11×#18692
C11×#18642
C11×#17882
#2443811