Finite Group Databasebeta

← C11×#24393 #14601586

Subgroups — C11×#24393 #14601586

Order 2816.

1450 conjugacy classes of subgroups.

The subgroup lattice has 914 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#537C211yesmaximal, characteristic
2C2×C11×#468C211yesmaximal, characteristic, complemented
3C2×C11×#467C211yesmaximal, characteristic, complemented
4C2×C11×#452C211yesmaximal, characteristic, complemented
5C2×C11×#408C211yesmaximal, characteristic, complemented
6C11×#2616C211yesmaximal, characteristic, complemented
7C11×#2036C211yesmaximal, characteristic, complemented
8C11×#2033C211yesmaximal, characteristic, complemented
9C11×#2001C211yesmaximal, characteristic, complemented
10C11×#2000C211yesmaximal, characteristic, complemented
11C11×#1894C211yesmaximal, characteristic, complemented
12C11×#1893C211yesmaximal, characteristic, complemented
13C11×#1872C211yesmaximal, characteristic, complemented
14C11×#1852C211yesmaximal, characteristic, complemented
15C11×#1788C211yesmaximal, characteristic, complemented
16C22×C11×#41C2211yescharacteristic
17C22×C11×#41C2211yescharacteristic
18C22×C11×Q16C2211yescharacteristic
19C22×C11×SD16C2211yescharacteristic
20C22×C11×M16C2211yescharacteristic
21C23×C8×C11C2211yescharacteristic
22C11×#537—24no—
23C11×#537—24no—
24C2×C11×C22⋊Q8—21no—
25C2×C11×C22⋊Q8C2211yescharacteristic
26C2×C11×C22⋊Q8C2211yescharacteristic
27C2×C11×C22⋊Q8C2211yescharacteristic
28C2×C11×C22⋊Q8C2211yescharacteristic
29C2×C11×C22⋊Q8C2211yescharacteristic
30C2×C11×#121—21no—
31C2×C11×#121—21no—
32C2×C11×#121—21no—
33C2×C11×#121C2211yescharacteristic
34C2×C11×#121C2211yescharacteristic
35C22×C11×C4⋊C4C2211yescharacteristic
36C11×#468—24no—
37C11×#467—24no—
38C11×#452—24no—
39C2×C11×#107C2211yescharacteristic
40C2×C11×#107C2211yescharacteristic
41C2×C11×#103C2211yescharacteristic
42C2×C11×#103C2211yescharacteristic
43C2×C11×#103C2211yescharacteristic
44C2×C11×#103C2211yescharacteristic
45C2×C11×#103C2211yescharacteristic
46C2×C11×#102C2211yescharacteristic
47C2×C11×#102C2211yescharacteristic
48C2×C11×#102C2211yescharacteristic
49C11×#408—24no—
50C2×C11×C22⋊C8C2211yescharacteristic
51C2×C11×C22⋊C8C2211yescharacteristic
52C2×C11×C22⋊C8C2211yescharacteristic
53C2×C11×C22⋊C8C2211yescharacteristic
54C11×#395—21no—
55C11×#394—21no—
56C11×#394—21no—
57C11×#394—21no—
58C11×#380C2211yescharacteristic
59C11×#380C2211yescharacteristic
60C11×#380C2211yescharacteristic
61C11×#340C2211yescharacteristic
62C11×#340C2211yescharacteristic
63C11×#340C2211yescharacteristic
64C11×#340C2211yescharacteristic
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—22no—
73C2×C11×#41—41no—
74C2×C11×#41—41no—
75C2×C11×#41—41no—
76C2×C11×#41—41no—
77C22×Q8×C11D411yescharacteristic
78C22×Q8×C11C2311yescharacteristic
79C22×Q8×C11C2311yescharacteristic
80C22×D4×C11—21no—
81C22×D4×C11—21no—
82C22×D4×C11—21no—
83C22×D4×C11D411yescharacteristic
84C22×D4×C11D411yescharacteristic
85C22×D4×C11D411yescharacteristic
86C22×D4×C11C2311yescharacteristic
87C23×C4×C11—21no—
88C23×C4×C11—21no—
89C23×C4×C11C2311yescharacteristic
90C23×C4×C11C2311yescharacteristic
91C23×C4×C11C2311yescharacteristic
92C2×C11×Q16—22no—
93C2×C11×Q16—22no—
94C2×C11×Q16—41no—
95C2×C11×SD16—22no—
96C2×C11×SD16—22no—
97C2×C11×SD16—41no—
98C2×C11×M16—22no—
99C2×C11×M16—22no—
100C2×C11×M16—41no—
101C22×C8×C11—22no—
102C22×C8×C11—22no—
103C22×C8×C11—41no—
104C22×C8×C11C2311yescharacteristic
105C22×C8×C11C2311yescharacteristic
106C22×C8×C11C2311yescharacteristic
107C22×C8×C11C2311yescharacteristic
108C11×C22⋊Q8—28no—
109C11×C22⋊Q8—22no—
110C11×C22⋊Q8—22no—
111C11×C22⋊Q8—22no—
112C11×C22⋊Q8—22no—
113C11×C22⋊Q8—22no—
114C11×C22⋊Q8—22no—
115C11×C22⋊Q8—22no—
116C11×C22⋊Q8—41no—
117C11×C22⋊Q8—41no—
118C11×C22⋊Q8D414yes—
119C11×#121—28no—
120C11×#121—28no—
121C11×#121—28no—
122C11×#121—22no—
123C11×#121—22no—
124C11×#121—22no—
125C11×#121D414yes—
126C2×C11×C4⋊C4—21no—
127C2×C11×C4⋊C4—21no—
128C2×C11×C4⋊C4—21no—
129C2×C11×C4⋊C4—22no—
130C2×C11×C4⋊C4—22no—
131C2×C11×C4⋊C4—21no—
132C2×C11×C4⋊C4—21no—
133C2×C11×C4⋊C4—21no—
134C2×C11×C4⋊C4C2311yescharacteristic
135C2×C11×C4⋊C4C2311yescharacteristic
136C2×C11×C4⋊C4C2311yescharacteristic
137C2×C11×C4⋊C4C2311yescharacteristic
138C2×C11×C4⋊C4C2311yescharacteristic
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⋊C4—21no—
147C2×C11×C22⋊C4—21no—
148C2×C11×C22⋊C4—21no—
149C11×#107—22no—
150C11×#107—22no—
151C11×#103—22no—
152C11×#103—22no—
153C11×#103—22no—
154C11×#103—22no—
155C11×#103—41no—
156C11×#102—22no—
157C11×#102—22no—
158C11×#102—41no—
159C11×C22⋊C8—22no—
160C11×C22⋊C8—22no—
161C11×C22⋊C8—22no—
162C11×C22⋊C8D414yescomplemented
163C11×#95—21no—
164C11×#95—21no—
165C11×#95—21no—
166#24393C1111yesmaximal, characteristic, direct product factor, Sylow
167C24×C11—21no—
168C24×C11C2×D411yescharacteristic
169C24×C11C2×D411yescharacteristic
170C24×C11C2×D411yescharacteristic
171C11×#41—44no—
172C11×#41—44no—
173C11×#41—44no—
174C11×#41—44no—
175C11×#41—44no—
176C11×#41—44no—
177C11×#41—44no—
178C11×#41—44no—
179C2×Q8×C11—22no—
180C2×Q8×C11—22no—
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×C11—21no—
190C2×Q8×C11—21no—
191C2×Q8×C11—21no—
192C2×Q8×C11—41no—
193C2×Q8×C11C2×D412yes—
194C2×D4×C11—24no—
195C2×D4×C11—22no—
196C2×D4×C11—22no—
197C2×D4×C11—22no—
198C2×D4×C11—22no—
199C2×D4×C11—24no—
200C2×D4×C11—24no—
201C2×D4×C11—22no—
202C2×D4×C11—22no—
203C2×D4×C11—21no—
204C2×D4×C11—21no—
205C2×D4×C11—21no—
206C2×D4×C11—21no—
207C2×D4×C11—21no—
208C2×D4×C11—41no—
209C2×D4×C11—41no—
210C2×D4×C11—41no—
211C2×D4×C11—42no—
212C2×D4×C11—42no—
213C2×D4×C11—81no—
214C2×D4×C11—81no—
215C2×D4×C11—81no—
216C2×D4×C11—81no—
217C2×D4×C11C2×D412yes—
218C22×C4×C11—21no—
219C22×C4×C11—21no—
220C22×C4×C11—21no—
221C22×C4×C11—21no—
222C22×C4×C11—21no—
223C22×C4×C11—21no—
224C22×C4×C11—21no—
225C22×C4×C11—21no—
226C22×C4×C11—24no—
227C22×C4×C11—21no—
228C22×C4×C11—21no—
229C22×C4×C11—21no—
230C22×C4×C11—24no—
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—21no—
238C22×C4×C11—21no—
239C22×C4×C11—21no—
240C22×C4×C11—21no—
241C22×C4×C11—42no—
242C22×C4×C11—42no—
243C22×C4×C11—81no—
244C22×C4×C11—81no—
245C22×C4×C11C2×D411yescharacteristic
246C22×C4×C11C2×D411yescharacteristic
247C22×C4×C11C2×D412yes—
248C22×C4×C11C2×D412yes—
249C22×C4×C11C2×D411yescharacteristic
250C22×C4×C11C2×D412yes—
251C22×C4×C11#4112yes—
252C22×C4×C11C2411yescharacteristic
253C11×Q16—44no—
254C11×SD16—44no—
255C11×M16—44no—
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—21no—
265C2×C8×C11—21no—
266C2×C8×C11—44no—
267C2×C8×C11C2×D412yes—
268C2×C8×C11C2×D412yes—
269C11×C4⋊C4—24no—
270C11×C4⋊C4—24no—
271C11×C4⋊C4—24no—
272C11×C4⋊C4—21no—
273C11×C4⋊C4—21no—
274C11×C4⋊C4—21no—
275C11×C4⋊C4—21no—
276C11×C4⋊C4—21no—
277C11×C4⋊C4—21no—
278C11×C4⋊C4—21no—
279C11×C4⋊C4—21no—
280C11×C4⋊C4—42no—
281C11×C4⋊C4—42no—
282C11×C4⋊C4—42no—
283C11×C4⋊C4C2×D412yes—
284C11×C4⋊C4C2×D412yes—
285C11×C22⋊C4—24no—
286C11×C22⋊C4—24no—
287C11×C22⋊C4—24no—
288C11×C22⋊C4—24no—
289C11×C22⋊C4—42no—
290C11×C22⋊C4—42no—
291C11×C22⋊C4—42no—
292C11×C22⋊C4—81no—
293C11×C22⋊C4—81no—
294C11×C22⋊C4—81no—
295C2×#537C2×C1111yescharacteristic
296C2×#468C2×C1111yescharacteristic, complemented
297C2×#467C2×C1111yescharacteristic, complemented
298C2×#452C2×C1111yescharacteristic, complemented
299C2×#408C2×C1111yescharacteristic, complemented
300#2616C2×C1111yescharacteristic, complemented
301#2036C2×C1111yescharacteristic, complemented
302#2033C2×C1111yescharacteristic, complemented
303#2001C2×C1111yescharacteristic, complemented
304#2000C2×C1111yescharacteristic, complemented
305#1894C2×C1111yescharacteristic, complemented
306#1893C2×C1111yescharacteristic, complemented
307#1872C2×C1111yescharacteristic, complemented
308#1852C2×C1111yescharacteristic, complemented
309#1788C2×C1111yescharacteristic, complemented
310C23×C11—21no—
311C23×C11—21no—
312C23×C11—21no—
313C23×C11—21no—
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—22no—
324C23×C11—21no—
325C23×C11—21no—
326C23×C11—21no—
327C23×C11—21no—
328C23×C11—21no—
329C23×C11—21no—
330C23×C11—41no—
331C23×C11—41no—
332C23×C11—41no—
333C23×C11—41no—
334C23×C11—41no—
335C23×C11—41no—
336C23×C11#12012yes—
337C23×C11#12112yes—
338C23×C11C22×D411yescharacteristic
339Q8×C11—22no—
340Q8×C11—22no—
341Q8×C11—44no—
342Q8×C11—41no—
343Q8×C11—41no—
344Q8×C11—41no—
345Q8×C11—41no—
346Q8×C11—41no—
347Q8×C11—41no—
348D4×C11—22no—
349D4×C11—22no—
350D4×C11—44no—
351D4×C11—44no—
352D4×C11—44no—
353D4×C11—48no—
354D4×C11—41no—
355D4×C11—41no—
356D4×C11—84no—
357D4×C11—84no—
358C2×C4×C11—21no—
359C2×C4×C11—21no—
360C2×C4×C11—21no—
361C2×C4×C11—21no—
362C2×C4×C11—22no—
363C2×C4×C11—22no—
364C2×C4×C11—22no—
365C2×C4×C11—22no—
366C2×C4×C11—22no—
367C2×C4×C11—22no—
368C2×C4×C11—22no—
369C2×C4×C11—22no—
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—48no—
377C2×C4×C11—41no—
378C2×C4×C11—41no—
379C2×C4×C11—41no—
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—41no—
399C2×C4×C11—84no—
400C2×C4×C11#12012yes—
401C2×C4×C11#12112yes—
402C2×C4×C11C22×D411yescharacteristic
403C2×C4×C11C22×D411yescharacteristic
404C2×C4×C11C22×D411yescharacteristic
405C2×C4×C11C2×#4111yescharacteristic
406C2×C4×C11H(5,𝔽2)11yescharacteristic
407C2×C4×C11H(5,𝔽2)11yescharacteristic
408C8×C11—22no—
409C8×C11—22no—
410C8×C11—41no—
411C8×C11—41no—
412C22×#41C22×C1111yescharacteristic
413C22×#41C22×C1111yescharacteristic
414C22×Q16C22×C1111yescharacteristic
415C22×SD16C22×C1111yescharacteristic
416C22×M16C22×C1111yescharacteristic
417C23×C8C22×C1111yescharacteristic
418#537—24no—
419#537—24no—
420C2×C22⋊Q8—21no—
421C2×C22⋊Q8C22×C1111yescharacteristic
422C2×C22⋊Q8C22×C1111yescharacteristic
423C2×C22⋊Q8C22×C1111yescharacteristic
424C2×C22⋊Q8C22×C1111yescharacteristic
425C2×C22⋊Q8C22×C1111yescharacteristic
426C2×#121—21no—
427C2×#121—21no—
428C2×#121—21no—
429C2×#121C22×C1111yescharacteristic
430C2×#121C22×C1111yescharacteristic
431C22×C4⋊C4C22×C1111yescharacteristic
432#468—24no—
433#467—24no—
434#452—24no—
435C2×#107C22×C1111yescharacteristic
436C2×#107C22×C1111yescharacteristic
437C2×#103C22×C1111yescharacteristic
438C2×#103C22×C1111yescharacteristic
439C2×#103C22×C1111yescharacteristic
440C2×#103C22×C1111yescharacteristic
441C2×#103C22×C1111yescharacteristic
442C2×#102C22×C1111yescharacteristic
443C2×#102C22×C1111yescharacteristic
444C2×#102C22×C1111yescharacteristic
445#408—24no—
446C2×C22⋊C8C22×C1111yescharacteristic
447C2×C22⋊C8C22×C1111yescharacteristic
448C2×C22⋊C8C22×C1111yescharacteristic
449C2×C22⋊C8C22×C1111yescharacteristic
450#395—21no—
451#394—21no—
452#394—21no—
453#394—21no—
454#380C22×C1111yescharacteristic
455#380C22×C1111yescharacteristic
456#380C22×C1111yescharacteristic
457#340C22×C1111yescharacteristic
458#340C22×C1111yescharacteristic
459#340C22×C1111yescharacteristic
460#340C22×C1111yescharacteristic
461C22×C11—22no—
462C22×C11—22no—
463C22×C11—22no—
464C22×C11—22no—
465C22×C11—22no—
466C22×C11—22no—
467C22×C11—41no—
468C22×C11—41no—
469C22×C11—41no—
470C22×C11—41no—
471C22×C11—41no—
472C22×C11—41no—
473C22×C11—41no—
474C22×C11—41no—
475C22×C11—42no—
476C22×C11—41no—
477C22×C11—41no—
478C22×C11—41no—
479C22×C11—41no—
480C22×C11—42no—
481C22×C11—41no—
482C22×C11—42no—
483C22×C11—41no—
484C22×C11—41no—
485C22×C11—81no—
486C22×C11—81no—
487C22×C11—81no—
488C22×C11—81no—
489C22×C11C2×#12011yescharacteristic
490C22×C11C2×#12111yescharacteristic
491C22×C11#53411yescharacteristic
492C22×C11#57611yescharacteristic
493C22×C11#57711yescharacteristic
494C22×C11#57811yescharacteristic
495C22×C11#57811yescharacteristic
496C4×C11—22no—
497C4×C11—22no—
498C4×C11—41no—
499C4×C11—42no—
500C4×C11—42no—
501C4×C11—42no—
502C4×C11—81no—
503C4×C11—81no—
504C4×C11—81no—
505C4×C11—81no—
506C4×C11D4211yescharacteristic
507C4×C11D4211yescharacteristic
508C4×C11#54611yescharacteristic
509C4×C11#54611yescharacteristic
510C2×#41—22no—
511C2×#41—22no—
512C2×#41—22no—
513C2×#41—22no—
514C2×#41—22no—
515C2×#41—22no—
516C2×#41—22no—
517C2×#41—22no—
518C2×#41—41no—
519C2×#41—41no—
520C2×#41—41no—
521C2×#41—41no—
522C22×Q8D4×C1111yescharacteristic
523C22×Q8C23×C1111yescharacteristic
524C22×Q8C23×C1111yescharacteristic
525C22×D4—21no—
526C22×D4—21no—
527C22×D4—21no—
528C22×D4D4×C1111yescharacteristic
529C22×D4D4×C1111yescharacteristic
530C22×D4D4×C1111yescharacteristic
531C22×D4C23×C1111yescharacteristic
532C23×C4—21no—
533C23×C4—21no—
534C23×C4C23×C1111yescharacteristic
535C23×C4C23×C1111yescharacteristic
536C23×C4C23×C1111yescharacteristic
537C2×Q16—22no—
538C2×Q16—22no—
539C2×Q16—41no—
540C2×SD16—22no—
541C2×SD16—22no—
542C2×SD16—41no—
543C2×M16—22no—
544C2×M16—22no—
545C2×M16—41no—
546C22×C8—22no—
547C22×C8—22no—
548C22×C8—41no—
549C22×C8C23×C1111yescharacteristic
550C22×C8C23×C1111yescharacteristic
551C22×C8C23×C1111yescharacteristic
552C22×C8C23×C1111yescharacteristic
553C22⋊Q8—28no—
554C22⋊Q8—22no—
555C22⋊Q8—22no—
556C22⋊Q8—22no—
557C22⋊Q8—22no—
558C22⋊Q8—22no—
559C22⋊Q8—22no—
560C22⋊Q8—22no—
561C22⋊Q8—41no—
562C22⋊Q8—41no—
563C22⋊Q8D4×C1114yes—
564#121—28no—
565#121—28no—
566#121—28no—
567#121—22no—
568#121—22no—
569#121—22no—
570#121D4×C1114yes—
571C2×C4⋊C4—21no—
572C2×C4⋊C4—21no—
573C2×C4⋊C4—21no—
574C2×C4⋊C4—22no—
575C2×C4⋊C4—22no—
576C2×C4⋊C4—21no—
577C2×C4⋊C4—21no—
578C2×C4⋊C4—21no—
579C2×C4⋊C4C23×C1111yescharacteristic
580C2×C4⋊C4C23×C1111yescharacteristic
581C2×C4⋊C4C23×C1111yescharacteristic
582C2×C4⋊C4C23×C1111yescharacteristic
583C2×C4⋊C4C23×C1111yescharacteristic
584C2×C22⋊C4—21no—
585C2×C22⋊C4—21no—
586C2×C22⋊C4—21no—
587C2×C22⋊C4—21no—
588C2×C22⋊C4—21no—
589C2×C22⋊C4—21no—
590C2×C22⋊C4—21no—
591C2×C22⋊C4—21no—
592C2×C22⋊C4—21no—
593C2×C22⋊C4—21no—
594#107—22no—
595#107—22no—
596#103—22no—
597#103—22no—
598#103—22no—
599#103—22no—
600#103—41no—
601#102—22no—
602#102—22no—
603#102—41no—
604C22⋊C8—22no—
605C22⋊C8—22no—
606C22⋊C8—22no—
607C22⋊C8D4×C1114yescomplemented
608#95—21no—
609#95—21no—
610#95—21no—
611C2×C11—42no—
612C2×C11—42no—
613C2×C11—81no—
614C2×C11—82no—
615C2×C11#241011yescharacteristic
616C2×C11#301111yescharacteristic
617C2×C11#301211yescharacteristic
618C2×C11#306111yescharacteristic
619C2×C11#306311yescharacteristic
620C2×C11#320111yescharacteristic
621C2×C11#320311yescharacteristic
622C24—21no—
623C24C2×D4×C1111yescharacteristic
624C24C2×D4×C1111yescharacteristic
625C24C2×D4×C1111yescharacteristic
626#41—44no—
627#41—44no—
628#41—44no—
629#41—44no—
630#41—44no—
631#41—44no—
632#41—44no—
633#41—44no—
634C2×Q8—22no—
635C2×Q8—22no—
636C2×Q8—21no—
637C2×Q8—21no—
638C2×Q8—21no—
639C2×Q8—21no—
640C2×Q8—21no—
641C2×Q8—21no—
642C2×Q8—21no—
643C2×Q8—21no—
644C2×Q8—21no—
645C2×Q8—21no—
646C2×Q8—21no—
647C2×Q8—41no—
648C2×Q8C2×D4×C1112yes—
649C2×D4—24no—
650C2×D4—22no—
651C2×D4—22no—
652C2×D4—22no—
653C2×D4—22no—
654C2×D4—24no—
655C2×D4—24no—
656C2×D4—22no—
657C2×D4—22no—
658C2×D4—21no—
659C2×D4—21no—
660C2×D4—21no—
661C2×D4—21no—
662C2×D4—21no—
663C2×D4—41no—
664C2×D4—41no—
665C2×D4—41no—
666C2×D4—42no—
667C2×D4—42no—
668C2×D4—81no—
669C2×D4—81no—
670C2×D4—81no—
671C2×D4—81no—
672C2×D4C2×D4×C1112yes—
673C22×C4—21no—
674C22×C4—21no—
675C22×C4—21no—
676C22×C4—21no—
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—24no—
686C22×C4—21no—
687C22×C4—21no—
688C22×C4—21no—
689C22×C4—21no—
690C22×C4—21no—
691C22×C4—21no—
692C22×C4—21no—
693C22×C4—21no—
694C22×C4—21no—
695C22×C4—21no—
696C22×C4—42no—
697C22×C4—42no—
698C22×C4—81no—
699C22×C4—81no—
700C22×C4C2×D4×C1111yescharacteristic
701C22×C4C2×D4×C1111yescharacteristic
702C22×C4C2×D4×C1112yes—
703C22×C4C2×D4×C1112yes—
704C22×C4C2×D4×C1111yescharacteristic
705C22×C4C2×D4×C1112yes—
706C22×C4C11×#4112yes—
707C22×C4C24×C1111yescharacteristic
708Q16—44no—
709SD16—44no—
710M16—44no—
711C2×C8—21no—
712C2×C8—21no—
713C2×C8—21no—
714C2×C8—21no—
715C2×C8—21no—
716C2×C8—21no—
717C2×C8—21no—
718C2×C8—21no—
719C2×C8—21no—
720C2×C8—21no—
721C2×C8—44no—
722C2×C8C2×D4×C1112yes—
723C2×C8C2×D4×C1112yes—
724C4⋊C4—24no—
725C4⋊C4—24no—
726C4⋊C4—24no—
727C4⋊C4—21no—
728C4⋊C4—21no—
729C4⋊C4—21no—
730C4⋊C4—21no—
731C4⋊C4—21no—
732C4⋊C4—21no—
733C4⋊C4—21no—
734C4⋊C4—21no—
735C4⋊C4—42no—
736C4⋊C4—42no—
737C4⋊C4—42no—
738C4⋊C4C2×D4×C1112yes—
739C4⋊C4C2×D4×C1112yes—
740C22⋊C4—24no—
741C22⋊C4—24no—
742C22⋊C4—24no—
743C22⋊C4—24no—
744C22⋊C4—42no—
745C22⋊C4—42no—
746C22⋊C4—42no—
747C22⋊C4—81no—
748C22⋊C4—81no—
749C22⋊C4—81no—
750C11#2439311yescharacteristic, direct product factor, Sylow
751C23—21no—
752C23—21no—
753C23—21no—
754C23—21no—
755C23—21no—
756C23—21no—
757C23—21no—
758C23—21no—
759C23—21no—
760C23—21no—
761C23—21no—
762C23—21no—
763C23—21no—
764C23—22no—
765C23—21no—
766C23—21no—
767C23—21no—
768C23—21no—
769C23—21no—
770C23—21no—
771C23—41no—
772C23—41no—
773C23—41no—
774C23—41no—
775C23—41no—
776C23—41no—
777C23C11×#12012yes—
778C23C11×#12112yes—
779C23C22×D4×C1111yescharacteristic
780Q8—22no—
781Q8—22no—
782Q8—44no—
783Q8—41no—
784Q8—41no—
785Q8—41no—
786Q8—41no—
787Q8—41no—
788Q8—41no—
789D4—22no—
790D4—22no—
791D4—44no—
792D4—44no—
793D4—44no—
794D4—48no—
795D4—41no—
796D4—41no—
797D4—84no—
798D4—84no—
799C2×C4—21no—
800C2×C4—21no—
801C2×C4—21no—
802C2×C4—21no—
803C2×C4—22no—
804C2×C4—22no—
805C2×C4—22no—
806C2×C4—22no—
807C2×C4—22no—
808C2×C4—22no—
809C2×C4—22no—
810C2×C4—22no—
811C2×C4—22no—
812C2×C4—22no—
813C2×C4—22no—
814C2×C4—21no—
815C2×C4—21no—
816C2×C4—21no—
817C2×C4—48no—
818C2×C4—41no—
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×C4—41no—
838C2×C4—41no—
839C2×C4—41no—
840C2×C4—84no—
841C2×C4C11×#12012yes—
842C2×C4C11×#12112yes—
843C2×C4C22×D4×C1111yescharacteristic
844C2×C4C22×D4×C1111yescharacteristic
845C2×C4C22×D4×C1111yescharacteristic
846C2×C4C2×C11×#4111yescharacteristic
847C2×C4C11×H(5,𝔽2)11yescharacteristic
848C2×C4C11×H(5,𝔽2)11yescharacteristic
849C8—22no—
850C8—22no—
851C8—41no—
852C8—41no—
853C22—22no—
854C22—22no—
855C22—22no—
856C22—22no—
857C22—22no—
858C22—22no—
859C22—41no—
860C22—41no—
861C22—41no—
862C22—41no—
863C22—41no—
864C22—41no—
865C22—41no—
866C22—41no—
867C22—42no—
868C22—41no—
869C22—41no—
870C22—41no—
871C22—41no—
872C22—42no—
873C22—41no—
874C22—42no—
875C22—41no—
876C22—41no—
877C22—81no—
878C22—81no—
879C22—81no—
880C22—81no—
881C22C2×C11×#12011yescharacteristic
882C22C2×C11×#12111yescharacteristic
883C22C11×#53411yescharacteristic
884C22C11×#57611yescharacteristic
885C22C11×#57711yescharacteristic
886C22C11×#57811yescharacteristic
887C22C11×#57811yescharacteristic
888C4—22no—
889C4—22no—
890C4—41no—
891C4—42no—
892C4—42no—
893C4—42no—
894C4—81no—
895C4—81no—
896C4—81no—
897C4—81no—
898C4D42×C1111yescharacteristic
899C4D42×C1111yescharacteristic
900C4C11×#54611yescharacteristic
901C4C11×#54611yescharacteristic
902C2—42no—
903C2—42no—
904C2—81no—
905C2—82no—
906C2C11×#241011yescharacteristic
907C2C11×#301111yescharacteristic
908C2C11×#301211yescharacteristic
909C2C11×#306111yescharacteristic
910C2C11×#306311yescharacteristic
911C2C11×#320111yescharacteristic
912C2C11×#320311yescharacteristic
subgroupG/H
center, socleC23×C11C22×D4
commutator, Frattini, cosocleC22×C4C24×C11
prime radicalC2×C11×#537C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C11 ◁ C22×C11×#41 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C11×#468C2semidirect
3. C2×C11×#467C2semidirect
4. C2×C11×#452C2semidirect
5. C2×C11×#408C2semidirect
6. C11×#2616C2semidirect
7. C11×#2036C2semidirect
8. C11×#2033C2semidirect
9. C11×#2001C2semidirect
10. C11×#2000C2semidirect
11. C11×#1894C2semidirect
12. C11×#1893C2semidirect
13. C11×#1872C2semidirect
14. C11×#1852C2semidirect
15. C11×#1788C2semidirect
162. C11×C22⋊C8D4semidirect
166. #24393C11direct (N × H)
296. C2×#468C2×C11semidirect
297. C2×#467C2×C11semidirect
298. C2×#452C2×C11semidirect
299. C2×#408C2×C11semidirect
300. #2616C2×C11semidirect
301. #2036C2×C11semidirect
302. #2033C2×C11semidirect
303. #2001C2×C11semidirect
304. #2000C2×C11semidirect
305. #1894C2×C11semidirect
306. #1893C2×C11semidirect
307. #1872C2×C11semidirect
308. #1852C2×C11semidirect
309. #1788C2×C11semidirect
607. C22⋊C8D4×C11semidirect
750. C11#24393direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#5372
C2×C11×#4682
C2×C11×#4672
C2×C11×#4522
C2×C11×#4082
C11×#26162
C11×#20362
C11×#20332
C11×#20012
C11×#20002
C11×#18942
C11×#18932
C11×#18722
C11×#18522
C11×#17882
#2439311