Finite Group Databasebeta

← C11×#24452 #14601645

Subgroups — C11×#24452 #14601645

Order 2816.

1592 conjugacy classes of subgroups.

The subgroup lattice has 928 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#546C211yesmaximal, characteristic
2C2×C11×#468C211yesmaximal, characteristic, complemented
3C2×C11×#452C211yesmaximal, characteristic, complemented
4C2×C11×#450C211yesmaximal, characteristic, complemented
5C2×C11×#417C211yesmaximal, characteristic, complemented
6C11×#2417C211yesmaximal, characteristic, complemented
7C11×#2042C211yesmaximal, characteristic, complemented
8C11×#2036C211yesmaximal, characteristic, complemented
9C11×#2015C211yesmaximal, characteristic, complemented
10C11×#2001C211yesmaximal, characteristic, complemented
11C11×#1877C211yesmaximal, characteristic, complemented
12C11×#1874C211yesmaximal, characteristic, complemented
13C11×#1870C211yesmaximal, characteristic, complemented
14C11×#1862C211yesmaximal, characteristic, complemented
15C11×#1786C211yesmaximal, characteristic, complemented
16C22×C11×#41C2211yescharacteristic
17C23×D4×C11C2211yescharacteristic
18C22×C11×Q16C2211yescharacteristic, complemented
19C22×C11×SD16C2211yescharacteristic
20C22×C11×SD16C2211yescharacteristic
21C22×C11×M16C2211yescharacteristic, complemented
22C11×#546—24no—
23C11×#546—24no—
24C2×C11×#124C2211yescharacteristic
25C2×C11×#123—21no—
26C2×C11×C22⋊Q8C2211yescharacteristic
27C2×C11×C22⋊Q8C2211yescharacteristic
28C2×C11×C22⋊Q8C2211yescharacteristic, complemented
29C2×C11×#121—21no—
30C2×C11×#121C2211yescharacteristic
31C2×C11×#120—21no—
32C2×C4×D4×C11C2211yescharacteristic
33C2×C4×D4×C11C2211yescharacteristic
34C22×C11×C4⋊C4C2211yescharacteristic, complemented
35C22×C11×C22⋊C4—21no—
36C11×#468—24no—
37C11×#452—24no—
38C11×#450—24no—
39C2×C11×#107C2211yescharacteristic, complemented
40C11×#417—24no—
41C2×C11×#103C2211yescharacteristic, complemented
42C2×C11×#103C2211yescharacteristic, complemented
43C2×C11×#103C2211yescharacteristic, complemented
44C2×C11×#103C2211yescharacteristic, complemented
45C2×C11×#102C2211yescharacteristic
46C2×C11×#102C2211yescharacteristic
47C2×C11×#102C2211yescharacteristic
48C2×C11×#102C2211yescharacteristic
49C2×C11×#102C2211yescharacteristic
50C2×C11×#102C2211yescharacteristic
51C2×C11×C22⋊C8C2211yescharacteristic
52C2×C11×C22⋊C8C2211yescharacteristic
53C2×C11×C22⋊C8C2211yescharacteristic, complemented
54C11×#398—21no—
55C11×#396—21no—
56C11×#391C2211yescharacteristic, complemented
57C11×#389C2211yescharacteristic, complemented
58C11×#386—21no—
59C11×#380—21no—
60C11×#380C2211yescharacteristic
61C11×#340C2211yescharacteristic, complemented
62C11×#340C2211yescharacteristic, complemented
63C11×#336C2211yescharacteristic, complemented
64C11×#336C2211yescharacteristic, complemented
65C25×C11—21no—
66C2×C11×#41—22no—
67C2×C11×#41—22no—
68C2×C11×#41—22no—
69C2×C11×#41—41no—
70C2×C11×#41—41no—
71C2×C11×#41D414yes—
72C22×Q8×C11C2311yescharacteristic
73C22×Q8×C11C2311yescharacteristic
74C22×D4×C11—21no—
75C22×D4×C11—21no—
76C22×D4×C11—22no—
77C22×D4×C11—22no—
78C22×D4×C11—22no—
79C22×D4×C11—22no—
80C22×D4×C11—21no—
81C22×D4×C11—41no—
82C22×D4×C11—41no—
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×Q16—22no—
92C2×C11×Q16—41no—
93C2×C11×Q16—41no—
94C2×C11×SD16—22no—
95C2×C11×SD16—22no—
96C2×C11×SD16—22no—
97C2×C11×SD16—22no—
98C2×C11×SD16—22no—
99C2×C11×SD16—41no—
100C2×C11×M16—22no—
101C2×C11×M16—22no—
102C2×C11×M16—41no—
103C22×C8×C11C2311yescharacteristic
104C22×C8×C11C2311yescharacteristic
105C22×C8×C11C2311yescharacteristic
106C22×C8×C11C2311yescharacteristic
107C11×#124—22no—
108C11×#124—22no—
109C11×#123—28no—
110C11×C22⋊Q8—22no—
111C11×C22⋊Q8—22no—
112C11×C22⋊Q8—22no—
113C11×C22⋊Q8—22no—
114C11×C22⋊Q8—22no—
115C11×C22⋊Q8—41no—
116C11×#121—28no—
117C11×#121—22no—
118C11×#121D414yes—
119C11×#120—28no—
120C4×D4×C11—22no—
121C4×D4×C11—22no—
122C4×D4×C11—22no—
123C4×D4×C11—22no—
124C2×C11×C4⋊C4—21no—
125C2×C11×C4⋊C4—22no—
126C2×C11×C4⋊C4—21no—
127C2×C11×C4⋊C4—21no—
128C2×C11×C4⋊C4—21no—
129C2×C11×C4⋊C4—21no—
130C2×C11×C4⋊C4—41no—
131C2×C11×C4⋊C4D411yescharacteristic
132C2×C11×C4⋊C4C2311yescharacteristic
133C2×C11×C4⋊C4C2311yescharacteristic
134C2×C11×C4⋊C4C2311yescharacteristic
135C2×C11×C4⋊C4C2311yescharacteristic
136C2×C11×C22⋊C4—28no—
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⋊C4D411yescharacteristic
146C2×C11×C22⋊C4D411yescharacteristic
147C2×C42×C11C2311yescharacteristic
148C11×#107—22no—
149C11×#103—22no—
150C11×#103—22no—
151C11×#103—22no—
152C11×#103—22no—
153C11×#102—22no—
154C11×#102—22no—
155C11×#102—22no—
156C11×#102—22no—
157C11×#102—41no—
158C11×#102D414yescomplemented
159C11×C22⋊C8—22no—
160C11×C22⋊C8—22no—
161C11×C22⋊C8—41no—
162C11×#95—21no—
163C11×#95—21no—
164C11×#95—21no—
165C11×#95—21no—
166#24452C1111yesmaximal, characteristic, direct product factor, Sylow
167C24×C11—21no—
168C24×C11—24no—
169C24×C11—21no—
170C24×C11—42no—
171C24×C11—42no—
172C24×C11—42no—
173C24×C11—42no—
174C24×C11—81no—
175C24×C11—81no—
176C24×C11C2×D411yescharacteristic
177C24×C11C2×D411yescharacteristic
178C11×#41—28no—
179C11×#41—44no—
180C11×#41—44no—
181C11×#41—44no—
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—21no—
193C2×Q8×C11C2×D412yes—
194C2×D4×C11—24no—
195C2×D4×C11—22no—
196C2×D4×C11—24no—
197C2×D4×C11—22no—
198C2×D4×C11—24no—
199C2×D4×C11—21no—
200C2×D4×C11—21no—
201C2×D4×C11—21no—
202C2×D4×C11—21no—
203C2×D4×C11—21no—
204C2×D4×C11—21no—
205C2×D4×C11—21no—
206C2×D4×C11—21no—
207C2×D4×C11—41no—
208C2×D4×C11—42no—
209C2×D4×C11—42no—
210C2×D4×C11—44no—
211C2×D4×C11—44no—
212C2×D4×C11—44no—
213C2×D4×C11—42no—
214C2×D4×C11—42no—
215C2×D4×C11—44no—
216C2×D4×C11—81no—
217C2×D4×C11—81no—
218C2×D4×C11C2×D412yes—
219C2×D4×C11C2×D412yes—
220C2×D4×C11C2×D412yes—
221C2×D4×C11#4112yes—
222C22×C4×C11—21no—
223C22×C4×C11—21no—
224C22×C4×C11—21no—
225C22×C4×C11—21no—
226C22×C4×C11—21no—
227C22×C4×C11—21no—
228C22×C4×C11—21no—
229C22×C4×C11—24no—
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—42no—
241C22×C4×C11—42no—
242C22×C4×C11—42no—
243C22×C4×C11—42no—
244C22×C4×C11—81no—
245C22×C4×C11—81no—
246C22×C4×C11—81no—
247C22×C4×C11C2×D411yescharacteristic
248C22×C4×C11C2×D411yescharacteristic
249C22×C4×C11C2×D411yescharacteristic
250C22×C4×C11C2×D411yescharacteristic
251C22×C4×C11C2×D412yes—
252C22×C4×C11C2×D412yes—
253C22×C4×C11C2411yescharacteristic
254C11×Q16—44no—
255C11×SD16—44no—
256C11×SD16—44no—
257C11×M16—44no—
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—21no—
267C2×C8×C11—21no—
268C2×C8×C11—21no—
269C2×C8×C11C2×D412yes—
270C11×C4⋊C4—24no—
271C11×C4⋊C4—22no—
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—42no—
279C11×C4⋊C4—42no—
280C11×C4⋊C4—42no—
281C11×C4⋊C4—81no—
282C11×C4⋊C4C2×D412yes—
283C11×C4⋊C4C2×D412yes—
284C11×C22⋊C4—24no—
285C11×C22⋊C4—24no—
286C11×C22⋊C4—24no—
287C11×C22⋊C4—24no—
288C11×C22⋊C4—22no—
289C11×C22⋊C4—22no—
290C11×C22⋊C4—24no—
291C11×C22⋊C4—42no—
292C11×C22⋊C4—42no—
293C11×C22⋊C4—81no—
294C42×C11—21no—
295C42×C11—21no—
296C2×#546C2×C1111yescharacteristic
297C2×#468C2×C1111yescharacteristic, complemented
298C2×#452C2×C1111yescharacteristic, complemented
299C2×#450C2×C1111yescharacteristic, complemented
300C2×#417C2×C1111yescharacteristic, complemented
301#2417C2×C1111yescharacteristic, complemented
302#2042C2×C1111yescharacteristic, complemented
303#2036C2×C1111yescharacteristic, complemented
304#2015C2×C1111yescharacteristic, complemented
305#2001C2×C1111yescharacteristic, complemented
306#1877C2×C1111yescharacteristic, complemented
307#1874C2×C1111yescharacteristic, complemented
308#1870C2×C1111yescharacteristic, complemented
309#1862C2×C1111yescharacteristic, complemented
310#1786C2×C1111yescharacteristic, complemented
311C23×C11—21no—
312C23×C11—22no—
313C23×C11—21no—
314C23×C11—21no—
315C23×C11—22no—
316C23×C11—21no—
317C23×C11—21no—
318C23×C11—22no—
319C23×C11—21no—
320C23×C11—21no—
321C23×C11—21no—
322C23×C11—21no—
323C23×C11—21no—
324C23×C11—21no—
325C23×C11—21no—
326C23×C11—22no—
327C23×C11—48no—
328C23×C11—48no—
329C23×C11—41no—
330C23×C11—41no—
331C23×C11—41no—
332C23×C11—41no—
333C23×C11—41no—
334C23×C11—41no—
335C23×C11—41no—
336C23×C11—41no—
337C23×C11—41no—
338C23×C11—41no—
339C23×C11—84no—
340C23×C11—84no—
341C23×C11—84no—
342C23×C11—84no—
343C23×C11—84no—
344C23×C11#12012yes—
345C23×C11#13712yes—
346C23×C11C22×D411yescharacteristic
347Q8×C11—22no—
348Q8×C11—22no—
349Q8×C11—41no—
350Q8×C11—41no—
351Q8×C11—41no—
352Q8×C11—41no—
353Q8×C11—41no—
354Q8×C11—41no—
355D4×C11—22no—
356D4×C11—22no—
357D4×C11—22no—
358D4×C11—22no—
359D4×C11—22no—
360D4×C11—44no—
361D4×C11—48no—
362D4×C11—48no—
363D4×C11—41no—
364D4×C11—41no—
365D4×C11—84no—
366D4×C11#12114yes—
367C2×C4×C11—21no—
368C2×C4×C11—21no—
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—22no—
376C2×C4×C11—22no—
377C2×C4×C11—21no—
378C2×C4×C11—22no—
379C2×C4×C11—21no—
380C2×C4×C11—21no—
381C2×C4×C11—21no—
382C2×C4×C11—21no—
383C2×C4×C11—21no—
384C2×C4×C11—21no—
385C2×C4×C11—48no—
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—41no—
400C2×C4×C11—41no—
401C2×C4×C11—41no—
402C2×C4×C11—41no—
403C2×C4×C11—41no—
404C2×C4×C11—41no—
405C2×C4×C11—84no—
406C2×C4×C11—84no—
407C2×C4×C11#12012yes—
408C2×C4×C11C22×D411yescharacteristic
409C2×C4×C11C22×D411yescharacteristic
410C2×C4×C11C22×D411yescharacteristic
411C2×C4×C11C2×#4111yescharacteristic
412C2×C4×C11H(5,𝔽2)11yescharacteristic
413C2×C4×C11H(5,𝔽2)11yescharacteristic
414C8×C11—22no—
415C8×C11—41no—
416C8×C11—41no—
417C8×C11—41no—
418C22×#41C22×C1111yescharacteristic
419C23×D4C22×C1111yescharacteristic
420C22×Q16C22×C1111yescharacteristic, complemented
421C22×SD16C22×C1111yescharacteristic
422C22×SD16C22×C1111yescharacteristic
423C22×M16C22×C1111yescharacteristic, complemented
424#546—24no—
425#546—24no—
426C2×#124C22×C1111yescharacteristic
427C2×#123—21no—
428C2×C22⋊Q8C22×C1111yescharacteristic
429C2×C22⋊Q8C22×C1111yescharacteristic
430C2×C22⋊Q8C22×C1111yescharacteristic, complemented
431C2×#121—21no—
432C2×#121C22×C1111yescharacteristic
433C2×#120—21no—
434C2×C4×D4C22×C1111yescharacteristic
435C2×C4×D4C22×C1111yescharacteristic
436C22×C4⋊C4C22×C1111yescharacteristic, complemented
437C22×C22⋊C4—21no—
438#468—24no—
439#452—24no—
440#450—24no—
441C2×#107C22×C1111yescharacteristic, complemented
442#417—24no—
443C2×#103C22×C1111yescharacteristic, complemented
444C2×#103C22×C1111yescharacteristic, complemented
445C2×#103C22×C1111yescharacteristic, complemented
446C2×#103C22×C1111yescharacteristic, complemented
447C2×#102C22×C1111yescharacteristic
448C2×#102C22×C1111yescharacteristic
449C2×#102C22×C1111yescharacteristic
450C2×#102C22×C1111yescharacteristic
451C2×#102C22×C1111yescharacteristic
452C2×#102C22×C1111yescharacteristic
453C2×C22⋊C8C22×C1111yescharacteristic
454C2×C22⋊C8C22×C1111yescharacteristic
455C2×C22⋊C8C22×C1111yescharacteristic, complemented
456#398—21no—
457#396—21no—
458#391C22×C1111yescharacteristic, complemented
459#389C22×C1111yescharacteristic, complemented
460#386—21no—
461#380—21no—
462#380C22×C1111yescharacteristic
463#340C22×C1111yescharacteristic, complemented
464#340C22×C1111yescharacteristic, complemented
465#336C22×C1111yescharacteristic, complemented
466#336C22×C1111yescharacteristic, complemented
467C22×C11—22no—
468C22×C11—24no—
469C22×C11—22no—
470C22×C11—22no—
471C22×C11—22no—
472C22×C11—22no—
473C22×C11—22no—
474C22×C11—41no—
475C22×C11—42no—
476C22×C11—41no—
477C22×C11—42no—
478C22×C11—42no—
479C22×C11—41no—
480C22×C11—41no—
481C22×C11—41no—
482C22×C11—42no—
483C22×C11—41no—
484C22×C11—42no—
485C22×C11—41no—
486C22×C11—41no—
487C22×C11—42no—
488C22×C11—42no—
489C22×C11—42no—
490C22×C11—42no—
491C22×C11—816no—
492C22×C11—81no—
493C22×C11—81no—
494C22×C11—81no—
495C22×C11—81no—
496C22×C11C2×#12011yescharacteristic
497C22×C11D4211yescharacteristic
498C22×C11#54611yescharacteristic
499C22×C11C2×#13711yescharacteristic
500C22×C11#57511yescharacteristic
501C22×C11#57611yescharacteristic
502C22×C11#57711yescharacteristic
503C4×C11—22no—
504C4×C11—41no—
505C4×C11—42no—
506C4×C11—41no—
507C4×C11—41no—
508C4×C11—42no—
509C4×C11—42no—
510C4×C11—81no—
511C4×C11—81no—
512C4×C11—81no—
513C4×C11C2×#12111yescharacteristic
514C4×C11#53411yescharacteristic
515C4×C11D4211yescharacteristic
516C4×C11#54611yescharacteristic
517C25—21no—
518C2×#41—22no—
519C2×#41—22no—
520C2×#41—22no—
521C2×#41—41no—
522C2×#41—41no—
523C2×#41D4×C1114yes—
524C22×Q8C23×C1111yescharacteristic
525C22×Q8C23×C1111yescharacteristic
526C22×D4—21no—
527C22×D4—21no—
528C22×D4—22no—
529C22×D4—22no—
530C22×D4—22no—
531C22×D4—22no—
532C22×D4—21no—
533C22×D4—41no—
534C22×D4—41no—
535C22×D4D4×C1111yescharacteristic
536C22×D4C23×C1111yescharacteristic
537C22×D4C23×C1111yescharacteristic
538C23×C4—21no—
539C23×C4—21no—
540C23×C4—21no—
541C23×C4C23×C1111yescharacteristic
542C23×C4C23×C1111yescharacteristic
543C2×Q16—22no—
544C2×Q16—41no—
545C2×Q16—41no—
546C2×SD16—22no—
547C2×SD16—22no—
548C2×SD16—22no—
549C2×SD16—22no—
550C2×SD16—22no—
551C2×SD16—41no—
552C2×M16—22no—
553C2×M16—22no—
554C2×M16—41no—
555C22×C8C23×C1111yescharacteristic
556C22×C8C23×C1111yescharacteristic
557C22×C8C23×C1111yescharacteristic
558C22×C8C23×C1111yescharacteristic
559#124—22no—
560#124—22no—
561#123—28no—
562C22⋊Q8—22no—
563C22⋊Q8—22no—
564C22⋊Q8—22no—
565C22⋊Q8—22no—
566C22⋊Q8—22no—
567C22⋊Q8—41no—
568#121—28no—
569#121—22no—
570#121D4×C1114yes—
571#120—28no—
572C4×D4—22no—
573C4×D4—22no—
574C4×D4—22no—
575C4×D4—22no—
576C2×C4⋊C4—21no—
577C2×C4⋊C4—22no—
578C2×C4⋊C4—21no—
579C2×C4⋊C4—21no—
580C2×C4⋊C4—21no—
581C2×C4⋊C4—21no—
582C2×C4⋊C4—41no—
583C2×C4⋊C4D4×C1111yescharacteristic
584C2×C4⋊C4C23×C1111yescharacteristic
585C2×C4⋊C4C23×C1111yescharacteristic
586C2×C4⋊C4C23×C1111yescharacteristic
587C2×C4⋊C4C23×C1111yescharacteristic
588C2×C22⋊C4—28no—
589C2×C22⋊C4—21no—
590C2×C22⋊C4—21no—
591C2×C22⋊C4—21no—
592C2×C22⋊C4—21no—
593C2×C22⋊C4—21no—
594C2×C22⋊C4—21no—
595C2×C22⋊C4—21no—
596C2×C22⋊C4—21no—
597C2×C22⋊C4D4×C1111yescharacteristic
598C2×C22⋊C4D4×C1111yescharacteristic
599C2×C42C23×C1111yescharacteristic
600#107—22no—
601#103—22no—
602#103—22no—
603#103—22no—
604#103—22no—
605#102—22no—
606#102—22no—
607#102—22no—
608#102—22no—
609#102—41no—
610#102D4×C1114yescomplemented
611C22⋊C8—22no—
612C22⋊C8—22no—
613C22⋊C8—41no—
614#95—21no—
615#95—21no—
616#95—21no—
617#95—21no—
618C2×C11—42no—
619C2×C11—42no—
620C2×C11—44no—
621C2×C11—82no—
622C2×C11#241011yescharacteristic
623C2×C11#300711yescharacteristic
624C2×C11#301211yescharacteristic
625C2×C11#326611yescharacteristic
626C2×C11#327311yescharacteristic
627C2×C11#331411yescharacteristic
628C2×C11#332311yescharacteristic
629C24—21no—
630C24—24no—
631C24—21no—
632C24—42no—
633C24—42no—
634C24—42no—
635C24—42no—
636C24—81no—
637C24—81no—
638C24C2×D4×C1111yescharacteristic
639C24C2×D4×C1111yescharacteristic
640#41—28no—
641#41—44no—
642#41—44no—
643#41—44no—
644C2×Q8—21no—
645C2×Q8—21no—
646C2×Q8—21no—
647C2×Q8—21no—
648C2×Q8—21no—
649C2×Q8—21no—
650C2×Q8—21no—
651C2×Q8—21no—
652C2×Q8—21no—
653C2×Q8—21no—
654C2×Q8—21no—
655C2×Q8C2×D4×C1112yes—
656C2×D4—24no—
657C2×D4—22no—
658C2×D4—24no—
659C2×D4—22no—
660C2×D4—24no—
661C2×D4—21no—
662C2×D4—21no—
663C2×D4—21no—
664C2×D4—21no—
665C2×D4—21no—
666C2×D4—21no—
667C2×D4—21no—
668C2×D4—21no—
669C2×D4—41no—
670C2×D4—42no—
671C2×D4—42no—
672C2×D4—44no—
673C2×D4—44no—
674C2×D4—44no—
675C2×D4—42no—
676C2×D4—42no—
677C2×D4—44no—
678C2×D4—81no—
679C2×D4—81no—
680C2×D4C2×D4×C1112yes—
681C2×D4C2×D4×C1112yes—
682C2×D4C2×D4×C1112yes—
683C2×D4C11×#4112yes—
684C22×C4—21no—
685C22×C4—21no—
686C22×C4—21no—
687C22×C4—21no—
688C22×C4—21no—
689C22×C4—21no—
690C22×C4—21no—
691C22×C4—24no—
692C22×C4—24no—
693C22×C4—21no—
694C22×C4—21no—
695C22×C4—21no—
696C22×C4—21no—
697C22×C4—21no—
698C22×C4—21no—
699C22×C4—21no—
700C22×C4—21no—
701C22×C4—21no—
702C22×C4—42no—
703C22×C4—42no—
704C22×C4—42no—
705C22×C4—42no—
706C22×C4—81no—
707C22×C4—81no—
708C22×C4—81no—
709C22×C4C2×D4×C1111yescharacteristic
710C22×C4C2×D4×C1111yescharacteristic
711C22×C4C2×D4×C1111yescharacteristic
712C22×C4C2×D4×C1111yescharacteristic
713C22×C4C2×D4×C1112yes—
714C22×C4C2×D4×C1112yes—
715C22×C4C24×C1111yescharacteristic
716Q16—44no—
717SD16—44no—
718SD16—44no—
719M16—44no—
720C2×C8—21no—
721C2×C8—21no—
722C2×C8—21no—
723C2×C8—21no—
724C2×C8—21no—
725C2×C8—21no—
726C2×C8—21no—
727C2×C8—21no—
728C2×C8—21no—
729C2×C8—21no—
730C2×C8—21no—
731C2×C8C2×D4×C1112yes—
732C4⋊C4—24no—
733C4⋊C4—22no—
734C4⋊C4—21no—
735C4⋊C4—21no—
736C4⋊C4—21no—
737C4⋊C4—21no—
738C4⋊C4—21no—
739C4⋊C4—21no—
740C4⋊C4—42no—
741C4⋊C4—42no—
742C4⋊C4—42no—
743C4⋊C4—81no—
744C4⋊C4C2×D4×C1112yes—
745C4⋊C4C2×D4×C1112yes—
746C22⋊C4—24no—
747C22⋊C4—24no—
748C22⋊C4—24no—
749C22⋊C4—24no—
750C22⋊C4—22no—
751C22⋊C4—22no—
752C22⋊C4—24no—
753C22⋊C4—42no—
754C22⋊C4—42no—
755C22⋊C4—81no—
756C42—21no—
757C42—21no—
758C11#2445211yescharacteristic, direct product factor, Sylow
759C23—21no—
760C23—22no—
761C23—21no—
762C23—21no—
763C23—22no—
764C23—21no—
765C23—21no—
766C23—22no—
767C23—21no—
768C23—21no—
769C23—21no—
770C23—21no—
771C23—21no—
772C23—21no—
773C23—21no—
774C23—22no—
775C23—48no—
776C23—48no—
777C23—41no—
778C23—41no—
779C23—41no—
780C23—41no—
781C23—41no—
782C23—41no—
783C23—41no—
784C23—41no—
785C23—41no—
786C23—41no—
787C23—84no—
788C23—84no—
789C23—84no—
790C23—84no—
791C23—84no—
792C23C11×#12012yes—
793C23C11×#13712yes—
794C23C22×D4×C1111yescharacteristic
795Q8—22no—
796Q8—22no—
797Q8—41no—
798Q8—41no—
799Q8—41no—
800Q8—41no—
801Q8—41no—
802Q8—41no—
803D4—22no—
804D4—22no—
805D4—22no—
806D4—22no—
807D4—22no—
808D4—44no—
809D4—48no—
810D4—48no—
811D4—41no—
812D4—41no—
813D4—84no—
814D4C11×#12114yes—
815C2×C4—21no—
816C2×C4—21no—
817C2×C4—22no—
818C2×C4—22no—
819C2×C4—22no—
820C2×C4—22no—
821C2×C4—21no—
822C2×C4—21no—
823C2×C4—22no—
824C2×C4—22no—
825C2×C4—21no—
826C2×C4—22no—
827C2×C4—21no—
828C2×C4—21no—
829C2×C4—21no—
830C2×C4—21no—
831C2×C4—21no—
832C2×C4—21no—
833C2×C4—48no—
834C2×C4—41no—
835C2×C4—41no—
836C2×C4—41no—
837C2×C4—41no—
838C2×C4—41no—
839C2×C4—41no—
840C2×C4—41no—
841C2×C4—41no—
842C2×C4—41no—
843C2×C4—41no—
844C2×C4—41no—
845C2×C4—41no—
846C2×C4—41no—
847C2×C4—41no—
848C2×C4—41no—
849C2×C4—41no—
850C2×C4—41no—
851C2×C4—41no—
852C2×C4—41no—
853C2×C4—84no—
854C2×C4—84no—
855C2×C4C11×#12012yes—
856C2×C4C22×D4×C1111yescharacteristic
857C2×C4C22×D4×C1111yescharacteristic
858C2×C4C22×D4×C1111yescharacteristic
859C2×C4C2×C11×#4111yescharacteristic
860C2×C4C11×H(5,𝔽2)11yescharacteristic
861C2×C4C11×H(5,𝔽2)11yescharacteristic
862C8—22no—
863C8—41no—
864C8—41no—
865C8—41no—
866C22—22no—
867C22—24no—
868C22—22no—
869C22—22no—
870C22—22no—
871C22—22no—
872C22—22no—
873C22—41no—
874C22—42no—
875C22—41no—
876C22—42no—
877C22—42no—
878C22—41no—
879C22—41no—
880C22—41no—
881C22—42no—
882C22—41no—
883C22—42no—
884C22—41no—
885C22—41no—
886C22—42no—
887C22—42no—
888C22—42no—
889C22—42no—
890C22—816no—
891C22—81no—
892C22—81no—
893C22—81no—
894C22—81no—
895C22C2×C11×#12011yescharacteristic
896C22D42×C1111yescharacteristic
897C22C11×#54611yescharacteristic
898C22C2×C11×#13711yescharacteristic
899C22C11×#57511yescharacteristic
900C22C11×#57611yescharacteristic
901C22C11×#57711yescharacteristic
902C4—22no—
903C4—41no—
904C4—42no—
905C4—41no—
906C4—41no—
907C4—42no—
908C4—42no—
909C4—81no—
910C4—81no—
911C4—81no—
912C4C2×C11×#12111yescharacteristic
913C4C11×#53411yescharacteristic
914C4D42×C1111yescharacteristic
915C4C11×#54611yescharacteristic
916C2—42no—
917C2—42no—
918C2—44no—
919C2—82no—
920C2C11×#241011yescharacteristic
921C2C11×#300711yescharacteristic
922C2C11×#301211yescharacteristic
923C2C11×#326611yescharacteristic
924C2C11×#327311yescharacteristic
925C2C11×#331411yescharacteristic
926C2C11×#332311yescharacteristic
subgroupG/H
center, socleC23×C11C22×D4
commutator, Frattini, cosocleC22×C4C24×C11
prime radicalC2×C11×#546C2
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
2. C2×C11×#468C2semidirect
3. C2×C11×#452C2semidirect
4. C2×C11×#450C2semidirect
5. C2×C11×#417C2semidirect
6. C11×#2417C2semidirect
7. C11×#2042C2semidirect
8. C11×#2036C2semidirect
9. C11×#2015C2semidirect
10. C11×#2001C2semidirect
11. C11×#1877C2semidirect
12. C11×#1874C2semidirect
13. C11×#1870C2semidirect
14. C11×#1862C2semidirect
15. C11×#1786C2semidirect
18. C22×C11×Q16C22semidirect
21. C22×C11×M16C22semidirect
28. C2×C11×C22⋊Q8C22semidirect
34. C22×C11×C4⋊C4C22semidirect
39. C2×C11×#107C22semidirect
41. C2×C11×#103C22semidirect
42. C2×C11×#103C22semidirect
43. C2×C11×#103C22semidirect
44. C2×C11×#103C22semidirect
53. C2×C11×C22⋊C8C22semidirect
56. C11×#391C22semidirect
57. C11×#389C22semidirect
61. C11×#340C22semidirect
62. C11×#340C22semidirect
63. C11×#336C22semidirect
64. C11×#336C22semidirect
158. C11×#102D4semidirect
166. #24452C11direct (N × H)
297. C2×#468C2×C11semidirect
298. C2×#452C2×C11semidirect
299. C2×#450C2×C11semidirect
300. C2×#417C2×C11semidirect
301. #2417C2×C11semidirect
302. #2042C2×C11semidirect
303. #2036C2×C11semidirect
304. #2015C2×C11semidirect
305. #2001C2×C11semidirect
306. #1877C2×C11semidirect
307. #1874C2×C11semidirect
308. #1870C2×C11semidirect
309. #1862C2×C11semidirect
310. #1786C2×C11semidirect
420. C22×Q16C22×C11semidirect
423. C22×M16C22×C11semidirect
430. C2×C22⋊Q8C22×C11semidirect
436. C22×C4⋊C4C22×C11semidirect
441. C2×#107C22×C11semidirect
443. C2×#103C22×C11semidirect
444. C2×#103C22×C11semidirect
445. C2×#103C22×C11semidirect
446. C2×#103C22×C11semidirect
455. C2×C22⋊C8C22×C11semidirect
458. #391C22×C11semidirect
459. #389C22×C11semidirect
463. #340C22×C11semidirect
464. #340C22×C11semidirect
465. #336C22×C11semidirect
466. #336C22×C11semidirect
610. #102D4×C11semidirect
758. C11#24452direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#5462
C2×C11×#4682
C2×C11×#4522
C2×C11×#4502
C2×C11×#4172
C11×#24172
C11×#20422
C11×#20362
C11×#20152
C11×#20012
C11×#18772
C11×#18742
C11×#18702
C11×#18622
C11×#17862
#2445211