Finite Group Databasebeta

← C11×#23971 #14601164

Subgroups — C11×#23971 #14601164

Order 2816.

1274 conjugacy classes of subgroups.

The subgroup lattice has 818 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#552C211yesmaximal, characteristic, complemented
2C2×C11×#452C211yesmaximal, characteristic, complemented
3C2×C11×#416C211yesmaximal, characteristic, complemented
4C11×#2407C211yesmaximal, characteristic
5C11×#2026C211yesmaximal, characteristic, complemented
6C11×#2025C211yesmaximal, characteristic, complemented
7C11×#2001C211yesmaximal, characteristic, complemented
8C11×#2000C211yesmaximal, characteristic, complemented
9C11×#1892C211yesmaximal, characteristic, complemented
10C11×#1880C211yesmaximal, characteristic, complemented
11C11×#1878C211yesmaximal, characteristic, complemented
12C11×#1874C211yesmaximal, characteristic, complemented
13C11×#1872C211yesmaximal, characteristic, complemented
14C11×#1869C211yesmaximal, characteristic, complemented
15C11×#1825C211yesmaximal, characteristic, complemented
16C22×C11×#41C2211yescharacteristic
17C22×C11×Q16C2211yescharacteristic
18C22×C11×SD16C2211yescharacteristic
19C23×C8×C11C2211yescharacteristic
20C11×#552—24no—
21C11×#552—24no—
22C2×C11×#126—21no—
23C2×C11×#125—21no—
24C2×C11×#125C2211yescharacteristic
25C2×C11×#123—21no—
26C2×C11×C22⋊Q8C2211yescharacteristic
27C2×C11×C22⋊Q8C2211yescharacteristic
28C2×C11×C22⋊Q8C2211yescharacteristic
29C2×C11×#121C2211yescharacteristic
30C2×C4×Q8×C11C2211yescharacteristic
31C2×C4×D4×C11C2211yescharacteristic
32C2×C11×#117—21no—
33C2×C11×#117C2211yescharacteristic
34C22×C11×C4⋊C4C2211yescharacteristic
35C11×#452—24no—
36C11×#416—24no—
37C2×C11×#103C2211yescharacteristic
38C2×C11×#103C2211yescharacteristic
39C2×C11×#103C2211yescharacteristic
40C2×C11×#103C2211yescharacteristic
41C2×C11×#103C2211yescharacteristic
42C2×C11×#102C2211yescharacteristic
43C2×C11×#102C2211yescharacteristic
44C2×C11×#102C2211yescharacteristic
45C2×C11×C22⋊C8C2211yescharacteristic
46C2×C11×C22⋊C8C2211yescharacteristic
47C2×C11×C22⋊C8C2211yescharacteristic
48C11×#394—21no—
49C11×#392—21no—
50C11×#391C2211yescharacteristic
51C11×#390C2211yescharacteristic
52C11×#386—21no—
53C11×#385—21no—
54C11×#380C2211yescharacteristic
55C11×#340C2211yescharacteristic
56C11×#340C2211yescharacteristic
57C11×#340C2211yescharacteristic
58C11×#340C2211yescharacteristic
59C11×#340C2211yescharacteristic
60C11×#340C2211yescharacteristic
61C11×#336C2211yescharacteristic
62C11×#336C2211yescharacteristic
63C2×C11×#41—22no—
64C2×C11×#41—22no—
65C2×C11×#41—22no—
66C2×C11×#41—22no—
67C2×C11×#41—41no—
68C2×C11×#41—41no—
69C22×Q8×C11C2311yescharacteristic
70C22×Q8×C11C2311yescharacteristic
71C22×D4×C11—21no—
72C22×D4×C11—21no—
73C22×D4×C11D411yescharacteristic
74C22×D4×C11C2311yescharacteristic
75C23×C4×C11—21no—
76C23×C4×C11—21no—
77C23×C4×C11C2311yescharacteristic
78C23×C4×C11C2311yescharacteristic
79C2×C11×Q16—22no—
80C2×C11×Q16—22no—
81C2×C11×Q16—41no—
82C2×C11×SD16—22no—
83C2×C11×SD16—22no—
84C2×C11×SD16—41no—
85C22×C8×C11—22no—
86C22×C8×C11—41no—
87C22×C8×C11—41no—
88C22×C8×C11C2311yescharacteristic
89C22×C8×C11C2311yescharacteristic
90C22×C8×C11C2311yescharacteristic
91C22×C8×C11C2311yescharacteristic
92C11×#126—28no—
93C11×#125—28no—
94C11×#125—22no—
95C11×#125—22no—
96C11×#123—28no—
97C11×C22⋊Q8—22no—
98C11×C22⋊Q8—22no—
99C11×C22⋊Q8—22no—
100C11×C22⋊Q8—22no—
101C11×C22⋊Q8—41no—
102C11×C22⋊Q8D414yescomplemented
103C11×#121—22no—
104C11×#121—41no—
105C4×Q8×C11—22no—
106C4×Q8×C11—22no—
107C4×D4×C11—22no—
108C4×D4×C11—22no—
109C11×#117—28no—
110C11×#117—22no—
111C11×#117D414yescomplemented
112C2×C11×C4⋊C4—21no—
113C2×C11×C4⋊C4—21no—
114C2×C11×C4⋊C4—21no—
115C2×C11×C4⋊C4—21no—
116C2×C11×C4⋊C4—21no—
117C2×C11×C4⋊C4—21no—
118C2×C11×C4⋊C4—22no—
119C2×C11×C4⋊C4—22no—
120C2×C11×C4⋊C4—21no—
121C2×C11×C4⋊C4D411yescharacteristic
122C2×C11×C4⋊C4C2311yescharacteristic
123C2×C11×C4⋊C4C2311yescharacteristic
124C2×C11×C4⋊C4C2311yescharacteristic
125C2×C11×C4⋊C4C2311yescharacteristic
126C2×C11×C4⋊C4C2311yescharacteristic
127C2×C11×C22⋊C4—21no—
128C2×C11×C22⋊C4—21no—
129C2×C11×C22⋊C4—21no—
130C2×C11×C22⋊C4—21no—
131C2×C11×C22⋊C4—21no—
132C2×C11×C22⋊C4—21no—
133C2×C11×C22⋊C4—21no—
134C2×C11×C22⋊C4—21no—
135C2×C11×C22⋊C4D411yescharacteristic
136C2×C11×C22⋊C4D411yescharacteristic
137C2×C42×C11—21no—
138C2×C42×C11—21no—
139C2×C42×C11C2311yescharacteristic
140C11×#103—22no—
141C11×#103—22no—
142C11×#103—22no—
143C11×#103—41no—
144C11×#103—41no—
145C11×#102—22no—
146C11×#102—22no—
147C11×#102—22no—
148C11×C22⋊C8—22no—
149C11×C22⋊C8—41no—
150C11×C22⋊C8—41no—
151C11×#95—21no—
152C11×#95—21no—
153C11×#95—21no—
154#23971C1111yesmaximal, characteristic, direct product factor, Sylow
155C24×C11—21no—
156C24×C11C2×D411yescharacteristic
157C24×C11C2×D411yescharacteristic
158C11×#41—28no—
159C11×#41—44no—
160C11×#41—44no—
161C11×#41—44no—
162C2×Q8×C11—21no—
163C2×Q8×C11—21no—
164C2×Q8×C11—21no—
165C2×Q8×C11—21no—
166C2×Q8×C11—21no—
167C2×Q8×C11—21no—
168C2×Q8×C11—21no—
169C2×Q8×C11—21no—
170C2×Q8×C11—21no—
171C2×Q8×C11—21no—
172C2×Q8×C11C2×D412yes—
173C2×Q8×C11#4112yes—
174C2×D4×C11—22no—
175C2×D4×C11—22no—
176C2×D4×C11—21no—
177C2×D4×C11—21no—
178C2×D4×C11—21no—
179C2×D4×C11—21no—
180C2×D4×C11—21no—
181C2×D4×C11—41no—
182C2×D4×C11—42no—
183C2×D4×C11—42no—
184C2×D4×C11—42no—
185C2×D4×C11—42no—
186C2×D4×C11—42no—
187C2×D4×C11—81no—
188C2×D4×C11#4112yes—
189C22×C4×C11—21no—
190C22×C4×C11—21no—
191C22×C4×C11—21no—
192C22×C4×C11—21no—
193C22×C4×C11—24no—
194C22×C4×C11—21no—
195C22×C4×C11—21no—
196C22×C4×C11—21no—
197C22×C4×C11—21no—
198C22×C4×C11—21no—
199C22×C4×C11—21no—
200C22×C4×C11—21no—
201C22×C4×C11—21no—
202C22×C4×C11—21no—
203C22×C4×C11—21no—
204C22×C4×C11—21no—
205C22×C4×C11—21no—
206C22×C4×C11—21no—
207C22×C4×C11—42no—
208C22×C4×C11—42no—
209C22×C4×C11—42no—
210C22×C4×C11—42no—
211C22×C4×C11—42no—
212C22×C4×C11C2×D411yescharacteristic
213C22×C4×C11C2×D411yescharacteristic
214C22×C4×C11C2×D411yescharacteristic
215C22×C4×C11C2×D411yescharacteristic
216C22×C4×C11C2×D412yes—
217C22×C4×C11C2×D412yes—
218C22×C4×C11C2411yescharacteristic
219C11×Q16—44no—
220C11×SD16—44no—
221C2×C8×C11—21no—
222C2×C8×C11—21no—
223C2×C8×C11—21no—
224C2×C8×C11—21no—
225C2×C8×C11—21no—
226C2×C8×C11—21no—
227C2×C8×C11—21no—
228C2×C8×C11—21no—
229C2×C8×C11—21no—
230C2×C8×C11—21no—
231C2×C8×C11—21no—
232C2×C8×C11—21no—
233C2×C8×C11—44no—
234C11×C4⋊C4—24no—
235C11×C4⋊C4—24no—
236C11×C4⋊C4—24no—
237C11×C4⋊C4—24no—
238C11×C4⋊C4—24no—
239C11×C4⋊C4—24no—
240C11×C4⋊C4—22no—
241C11×C4⋊C4—21no—
242C11×C4⋊C4—21no—
243C11×C4⋊C4—21no—
244C11×C4⋊C4—21no—
245C11×C4⋊C4—21no—
246C11×C4⋊C4—21no—
247C11×C4⋊C4—21no—
248C11×C4⋊C4—42no—
249C11×C4⋊C4C2×D412yes—
250C11×C4⋊C4C2×D412yes—
251C11×C4⋊C4C2×D412yes—
252C11×C22⋊C4—24no—
253C11×C22⋊C4—24no—
254C11×C22⋊C4—24no—
255C11×C22⋊C4—22no—
256C11×C22⋊C4—22no—
257C11×C22⋊C4—42no—
258C11×C22⋊C4—42no—
259C11×C22⋊C4—42no—
260C11×C22⋊C4—81no—
261C11×C22⋊C4—81no—
262C42×C11—24no—
263C42×C11—24no—
264C42×C11—21no—
265C42×C11—21no—
266C2×#552C2×C1111yescharacteristic, complemented
267C2×#452C2×C1111yescharacteristic, complemented
268C2×#416C2×C1111yescharacteristic, complemented
269#2407C2×C1111yescharacteristic
270#2026C2×C1111yescharacteristic, complemented
271#2025C2×C1111yescharacteristic, complemented
272#2001C2×C1111yescharacteristic, complemented
273#2000C2×C1111yescharacteristic, complemented
274#1892C2×C1111yescharacteristic, complemented
275#1880C2×C1111yescharacteristic, complemented
276#1878C2×C1111yescharacteristic, complemented
277#1874C2×C1111yescharacteristic, complemented
278#1872C2×C1111yescharacteristic, complemented
279#1869C2×C1111yescharacteristic, complemented
280#1825C2×C1111yescharacteristic, complemented
281C23×C11—21no—
282C23×C11—21no—
283C23×C11—21no—
284C23×C11—21no—
285C23×C11—21no—
286C23×C11—21no—
287C23×C11—21no—
288C23×C11—21no—
289C23×C11—21no—
290C23×C11—21no—
291C23×C11—21no—
292C23×C11—21no—
293C23×C11—22no—
294C23×C11—41no—
295C23×C11—41no—
296C23×C11—41no—
297C23×C11—41no—
298C23×C11—41no—
299C23×C11—41no—
300C23×C11#12012yes—
301C23×C11#13512yes—
302C23×C11C22×D411yescharacteristic
303Q8×C11—22no—
304Q8×C11—22no—
305Q8×C11—22no—
306Q8×C11—22no—
307Q8×C11—41no—
308Q8×C11—41no—
309Q8×C11—41no—
310Q8×C11—41no—
311D4×C11—22no—
312D4×C11—22no—
313D4×C11—44no—
314D4×C11—48no—
315D4×C11—41no—
316D4×C11—41no—
317D4×C11—84no—
318C2×C4×C11—21no—
319C2×C4×C11—21no—
320C2×C4×C11—22no—
321C2×C4×C11—22no—
322C2×C4×C11—22no—
323C2×C4×C11—22no—
324C2×C4×C11—21no—
325C2×C4×C11—22no—
326C2×C4×C11—22no—
327C2×C4×C11—22no—
328C2×C4×C11—21no—
329C2×C4×C11—21no—
330C2×C4×C11—22no—
331C2×C4×C11—21no—
332C2×C4×C11—22no—
333C2×C4×C11—21no—
334C2×C4×C11—21no—
335C2×C4×C11—21no—
336C2×C4×C11—21no—
337C2×C4×C11—21no—
338C2×C4×C11—48no—
339C2×C4×C11—48no—
340C2×C4×C11—41no—
341C2×C4×C11—41no—
342C2×C4×C11—41no—
343C2×C4×C11—41no—
344C2×C4×C11—41no—
345C2×C4×C11—41no—
346C2×C4×C11—41no—
347C2×C4×C11—41no—
348C2×C4×C11—41no—
349C2×C4×C11—41no—
350C2×C4×C11—41no—
351C2×C4×C11—41no—
352C2×C4×C11—41no—
353C2×C4×C11—41no—
354C2×C4×C11—41no—
355C2×C4×C11—41no—
356C2×C4×C11—41no—
357C2×C4×C11—41no—
358C2×C4×C11—41no—
359C2×C4×C11—41no—
360C2×C4×C11#12012yes—
361C2×C4×C11C22×D411yescharacteristic
362C2×C4×C11C22×D411yescharacteristic
363C2×C4×C11C2×#4111yescharacteristic
364C2×C4×C11C2×#4111yescharacteristic
365C2×C4×C11H(5,𝔽2)11yescharacteristic
366C2×C4×C11H(5,𝔽2)11yescharacteristic
367C8×C11—41no—
368C8×C11—41no—
369C8×C11—41no—
370C8×C11—41no—
371C22×#41C22×C1111yescharacteristic
372C22×Q16C22×C1111yescharacteristic
373C22×SD16C22×C1111yescharacteristic
374C23×C8C22×C1111yescharacteristic
375#552—24no—
376#552—24no—
377C2×#126—21no—
378C2×#125—21no—
379C2×#125C22×C1111yescharacteristic
380C2×#123—21no—
381C2×C22⋊Q8C22×C1111yescharacteristic
382C2×C22⋊Q8C22×C1111yescharacteristic
383C2×C22⋊Q8C22×C1111yescharacteristic
384C2×#121C22×C1111yescharacteristic
385C2×C4×Q8C22×C1111yescharacteristic
386C2×C4×D4C22×C1111yescharacteristic
387C2×#117—21no—
388C2×#117C22×C1111yescharacteristic
389C22×C4⋊C4C22×C1111yescharacteristic
390#452—24no—
391#416—24no—
392C2×#103C22×C1111yescharacteristic
393C2×#103C22×C1111yescharacteristic
394C2×#103C22×C1111yescharacteristic
395C2×#103C22×C1111yescharacteristic
396C2×#103C22×C1111yescharacteristic
397C2×#102C22×C1111yescharacteristic
398C2×#102C22×C1111yescharacteristic
399C2×#102C22×C1111yescharacteristic
400C2×C22⋊C8C22×C1111yescharacteristic
401C2×C22⋊C8C22×C1111yescharacteristic
402C2×C22⋊C8C22×C1111yescharacteristic
403#394—21no—
404#392—21no—
405#391C22×C1111yescharacteristic
406#390C22×C1111yescharacteristic
407#386—21no—
408#385—21no—
409#380C22×C1111yescharacteristic
410#340C22×C1111yescharacteristic
411#340C22×C1111yescharacteristic
412#340C22×C1111yescharacteristic
413#340C22×C1111yescharacteristic
414#340C22×C1111yescharacteristic
415#340C22×C1111yescharacteristic
416#336C22×C1111yescharacteristic
417#336C22×C1111yescharacteristic
418C22×C11—22no—
419C22×C11—22no—
420C22×C11—22no—
421C22×C11—22no—
422C22×C11—22no—
423C22×C11—22no—
424C22×C11—41no—
425C22×C11—41no—
426C22×C11—41no—
427C22×C11—41no—
428C22×C11—41no—
429C22×C11—41no—
430C22×C11—41no—
431C22×C11—41no—
432C22×C11—42no—
433C22×C11—42no—
434C22×C11—42no—
435C22×C11—81no—
436C22×C11—81no—
437C22×C11—81no—
438C22×C11—81no—
439C22×C11C2×#12011yescharacteristic
440C22×C11#54611yescharacteristic
441C22×C11#54611yescharacteristic
442C22×C11C2×#13511yescharacteristic
443C22×C11#57511yescharacteristic
444C22×C11#57711yescharacteristic
445C22×C11#57811yescharacteristic
446C4×C11—22no—
447C4×C11—41no—
448C4×C11—42no—
449C4×C11—42no—
450C4×C11—41no—
451C4×C11—42no—
452C4×C11—42no—
453C4×C11—41no—
454C4×C11—42no—
455C4×C11—81no—
456C4×C11—81no—
457C4×C11#52511yescharacteristic
458C4×C11#53511yescharacteristic
459C4×C11#54611yescharacteristic
460C4×C11#54611yescharacteristic
461C2×#41—22no—
462C2×#41—22no—
463C2×#41—22no—
464C2×#41—22no—
465C2×#41—41no—
466C2×#41—41no—
467C22×Q8C23×C1111yescharacteristic
468C22×Q8C23×C1111yescharacteristic
469C22×D4—21no—
470C22×D4—21no—
471C22×D4D4×C1111yescharacteristic
472C22×D4C23×C1111yescharacteristic
473C23×C4—21no—
474C23×C4—21no—
475C23×C4C23×C1111yescharacteristic
476C23×C4C23×C1111yescharacteristic
477C2×Q16—22no—
478C2×Q16—22no—
479C2×Q16—41no—
480C2×SD16—22no—
481C2×SD16—22no—
482C2×SD16—41no—
483C22×C8—22no—
484C22×C8—41no—
485C22×C8—41no—
486C22×C8C23×C1111yescharacteristic
487C22×C8C23×C1111yescharacteristic
488C22×C8C23×C1111yescharacteristic
489C22×C8C23×C1111yescharacteristic
490#126—28no—
491#125—28no—
492#125—22no—
493#125—22no—
494#123—28no—
495C22⋊Q8—22no—
496C22⋊Q8—22no—
497C22⋊Q8—22no—
498C22⋊Q8—22no—
499C22⋊Q8—41no—
500C22⋊Q8D4×C1114yescomplemented
501#121—22no—
502#121—41no—
503C4×Q8—22no—
504C4×Q8—22no—
505C4×D4—22no—
506C4×D4—22no—
507#117—28no—
508#117—22no—
509#117D4×C1114yescomplemented
510C2×C4⋊C4—21no—
511C2×C4⋊C4—21no—
512C2×C4⋊C4—21no—
513C2×C4⋊C4—21no—
514C2×C4⋊C4—21no—
515C2×C4⋊C4—21no—
516C2×C4⋊C4—22no—
517C2×C4⋊C4—22no—
518C2×C4⋊C4—21no—
519C2×C4⋊C4D4×C1111yescharacteristic
520C2×C4⋊C4C23×C1111yescharacteristic
521C2×C4⋊C4C23×C1111yescharacteristic
522C2×C4⋊C4C23×C1111yescharacteristic
523C2×C4⋊C4C23×C1111yescharacteristic
524C2×C4⋊C4C23×C1111yescharacteristic
525C2×C22⋊C4—21no—
526C2×C22⋊C4—21no—
527C2×C22⋊C4—21no—
528C2×C22⋊C4—21no—
529C2×C22⋊C4—21no—
530C2×C22⋊C4—21no—
531C2×C22⋊C4—21no—
532C2×C22⋊C4—21no—
533C2×C22⋊C4D4×C1111yescharacteristic
534C2×C22⋊C4D4×C1111yescharacteristic
535C2×C42—21no—
536C2×C42—21no—
537C2×C42C23×C1111yescharacteristic
538#103—22no—
539#103—22no—
540#103—22no—
541#103—41no—
542#103—41no—
543#102—22no—
544#102—22no—
545#102—22no—
546C22⋊C8—22no—
547C22⋊C8—41no—
548C22⋊C8—41no—
549#95—21no—
550#95—21no—
551#95—21no—
552C2×C11—42no—
553C2×C11—42no—
554C2×C11—82no—
555C2×C11#240411yescharacteristic
556C2×C11#300211yescharacteristic
557C2×C11#301311yescharacteristic
558C2×C11#329611yescharacteristic
559C2×C11#330011yescharacteristic
560C2×C11#331511yescharacteristic
561C2×C11#331711yescharacteristic
562C24—21no—
563C24C2×D4×C1111yescharacteristic
564C24C2×D4×C1111yescharacteristic
565#41—28no—
566#41—44no—
567#41—44no—
568#41—44no—
569C2×Q8—21no—
570C2×Q8—21no—
571C2×Q8—21no—
572C2×Q8—21no—
573C2×Q8—21no—
574C2×Q8—21no—
575C2×Q8—21no—
576C2×Q8—21no—
577C2×Q8—21no—
578C2×Q8—21no—
579C2×Q8C2×D4×C1112yes—
580C2×Q8C11×#4112yes—
581C2×D4—22no—
582C2×D4—22no—
583C2×D4—21no—
584C2×D4—21no—
585C2×D4—21no—
586C2×D4—21no—
587C2×D4—21no—
588C2×D4—41no—
589C2×D4—42no—
590C2×D4—42no—
591C2×D4—42no—
592C2×D4—42no—
593C2×D4—42no—
594C2×D4—81no—
595C2×D4C11×#4112yes—
596C22×C4—21no—
597C22×C4—21no—
598C22×C4—21no—
599C22×C4—21no—
600C22×C4—24no—
601C22×C4—21no—
602C22×C4—21no—
603C22×C4—21no—
604C22×C4—21no—
605C22×C4—21no—
606C22×C4—21no—
607C22×C4—21no—
608C22×C4—21no—
609C22×C4—21no—
610C22×C4—21no—
611C22×C4—21no—
612C22×C4—21no—
613C22×C4—21no—
614C22×C4—42no—
615C22×C4—42no—
616C22×C4—42no—
617C22×C4—42no—
618C22×C4—42no—
619C22×C4C2×D4×C1111yescharacteristic
620C22×C4C2×D4×C1111yescharacteristic
621C22×C4C2×D4×C1111yescharacteristic
622C22×C4C2×D4×C1111yescharacteristic
623C22×C4C2×D4×C1112yes—
624C22×C4C2×D4×C1112yes—
625C22×C4C24×C1111yescharacteristic
626Q16—44no—
627SD16—44no—
628C2×C8—21no—
629C2×C8—21no—
630C2×C8—21no—
631C2×C8—21no—
632C2×C8—21no—
633C2×C8—21no—
634C2×C8—21no—
635C2×C8—21no—
636C2×C8—21no—
637C2×C8—21no—
638C2×C8—21no—
639C2×C8—21no—
640C2×C8—44no—
641C4⋊C4—24no—
642C4⋊C4—24no—
643C4⋊C4—24no—
644C4⋊C4—24no—
645C4⋊C4—24no—
646C4⋊C4—24no—
647C4⋊C4—22no—
648C4⋊C4—21no—
649C4⋊C4—21no—
650C4⋊C4—21no—
651C4⋊C4—21no—
652C4⋊C4—21no—
653C4⋊C4—21no—
654C4⋊C4—21no—
655C4⋊C4—42no—
656C4⋊C4C2×D4×C1112yes—
657C4⋊C4C2×D4×C1112yes—
658C4⋊C4C2×D4×C1112yes—
659C22⋊C4—24no—
660C22⋊C4—24no—
661C22⋊C4—24no—
662C22⋊C4—22no—
663C22⋊C4—22no—
664C22⋊C4—42no—
665C22⋊C4—42no—
666C22⋊C4—42no—
667C22⋊C4—81no—
668C22⋊C4—81no—
669C42—24no—
670C42—24no—
671C42—21no—
672C42—21no—
673C11#2397111yescharacteristic, direct product factor, Sylow
674C23—21no—
675C23—21no—
676C23—21no—
677C23—21no—
678C23—21no—
679C23—21no—
680C23—21no—
681C23—21no—
682C23—21no—
683C23—21no—
684C23—21no—
685C23—21no—
686C23—22no—
687C23—41no—
688C23—41no—
689C23—41no—
690C23—41no—
691C23—41no—
692C23—41no—
693C23C11×#12012yes—
694C23C11×#13512yes—
695C23C22×D4×C1111yescharacteristic
696Q8—22no—
697Q8—22no—
698Q8—22no—
699Q8—22no—
700Q8—41no—
701Q8—41no—
702Q8—41no—
703Q8—41no—
704D4—22no—
705D4—22no—
706D4—44no—
707D4—48no—
708D4—41no—
709D4—41no—
710D4—84no—
711C2×C4—21no—
712C2×C4—21no—
713C2×C4—22no—
714C2×C4—22no—
715C2×C4—22no—
716C2×C4—22no—
717C2×C4—21no—
718C2×C4—22no—
719C2×C4—22no—
720C2×C4—22no—
721C2×C4—21no—
722C2×C4—21no—
723C2×C4—22no—
724C2×C4—21no—
725C2×C4—22no—
726C2×C4—21no—
727C2×C4—21no—
728C2×C4—21no—
729C2×C4—21no—
730C2×C4—21no—
731C2×C4—48no—
732C2×C4—48no—
733C2×C4—41no—
734C2×C4—41no—
735C2×C4—41no—
736C2×C4—41no—
737C2×C4—41no—
738C2×C4—41no—
739C2×C4—41no—
740C2×C4—41no—
741C2×C4—41no—
742C2×C4—41no—
743C2×C4—41no—
744C2×C4—41no—
745C2×C4—41no—
746C2×C4—41no—
747C2×C4—41no—
748C2×C4—41no—
749C2×C4—41no—
750C2×C4—41no—
751C2×C4—41no—
752C2×C4—41no—
753C2×C4C11×#12012yes—
754C2×C4C22×D4×C1111yescharacteristic
755C2×C4C22×D4×C1111yescharacteristic
756C2×C4C2×C11×#4111yescharacteristic
757C2×C4C2×C11×#4111yescharacteristic
758C2×C4C11×H(5,𝔽2)11yescharacteristic
759C2×C4C11×H(5,𝔽2)11yescharacteristic
760C8—41no—
761C8—41no—
762C8—41no—
763C8—41no—
764C22—22no—
765C22—22no—
766C22—22no—
767C22—22no—
768C22—22no—
769C22—22no—
770C22—41no—
771C22—41no—
772C22—41no—
773C22—41no—
774C22—41no—
775C22—41no—
776C22—41no—
777C22—41no—
778C22—42no—
779C22—42no—
780C22—42no—
781C22—81no—
782C22—81no—
783C22—81no—
784C22—81no—
785C22C2×C11×#12011yescharacteristic
786C22C11×#54611yescharacteristic
787C22C11×#54611yescharacteristic
788C22C2×C11×#13511yescharacteristic
789C22C11×#57511yescharacteristic
790C22C11×#57711yescharacteristic
791C22C11×#57811yescharacteristic
792C4—22no—
793C4—41no—
794C4—42no—
795C4—42no—
796C4—41no—
797C4—42no—
798C4—42no—
799C4—41no—
800C4—42no—
801C4—81no—
802C4—81no—
803C4C11×#52511yescharacteristic
804C4C11×#53511yescharacteristic
805C4C11×#54611yescharacteristic
806C4C11×#54611yescharacteristic
807C2—42no—
808C2—42no—
809C2—82no—
810C2C11×#240411yescharacteristic
811C2C11×#300211yescharacteristic
812C2C11×#301311yescharacteristic
813C2C11×#329611yescharacteristic
814C2C11×#330011yescharacteristic
815C2C11×#331511yescharacteristic
816C2C11×#331711yescharacteristic
subgroupG/H
center, socleC23×C11C22×D4
commutator, Frattini, cosocleC22×C4C24×C11
prime radicalC11×#2407C2
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×#552C2semidirect
2. C2×C11×#452C2semidirect
3. C2×C11×#416C2semidirect
5. C11×#2026C2semidirect
6. C11×#2025C2semidirect
7. C11×#2001C2semidirect
8. C11×#2000C2semidirect
9. C11×#1892C2semidirect
10. C11×#1880C2semidirect
11. C11×#1878C2semidirect
12. C11×#1874C2semidirect
13. C11×#1872C2semidirect
14. C11×#1869C2semidirect
15. C11×#1825C2semidirect
102. C11×C22⋊Q8D4semidirect
111. C11×#117D4semidirect
154. #23971C11direct (N × H)
266. C2×#552C2×C11semidirect
267. C2×#452C2×C11semidirect
268. C2×#416C2×C11semidirect
270. #2026C2×C11semidirect
271. #2025C2×C11semidirect
272. #2001C2×C11semidirect
273. #2000C2×C11semidirect
274. #1892C2×C11semidirect
275. #1880C2×C11semidirect
276. #1878C2×C11semidirect
277. #1874C2×C11semidirect
278. #1872C2×C11semidirect
279. #1869C2×C11semidirect
280. #1825C2×C11semidirect
500. C22⋊Q8D4×C11semidirect
509. #117D4×C11semidirect
673. C11#23971direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#5522
C2×C11×#4522
C2×C11×#4162
C11×#24072
C11×#20262
C11×#20252
C11×#20012
C11×#20002
C11×#18922
C11×#18802
C11×#18782
C11×#18742
C11×#18722
C11×#18692
C11×#18252
#2397111