Finite Group Databasebeta

← C11×#22497 #14599690

Subgroups — C11×#22497 #14599690

Order 2816.

1174 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×#554C211yesmaximal, characteristic
2C2×C11×#435C211yesmaximal, characteristic
3C11×#2352C211yesmaximal, characteristic
4C11×#1993C211yesmaximal, characteristic, complemented
5C11×#1988C211yesmaximal, characteristic, complemented
6C11×#1894C211yesmaximal, characteristic, complemented
7C11×#1892C211yesmaximal, characteristic, complemented
8C11×#1873C211yesmaximal, characteristic, complemented
9C11×#1872C211yesmaximal, characteristic, complemented
10C11×#1824C211yesmaximal, characteristic, complemented
11C11×#1823C211yesmaximal, characteristic, complemented
12C11×#1805C211yesmaximal, characteristic, complemented
13C11×#1763C211yesmaximal, characteristic, complemented
14C11×#1736C211yesmaximal, characteristic, complemented
15C2×C11×#340C211yesmaximal, characteristic, complemented
16C22×C11×M16C2211yescharacteristic
17C23×C8×C11C2211yescharacteristic
18C11×#554—24no—
19C11×#554C418yescomplemented
20C2×C11×C4⋊Q8C2211yescharacteristic
21C2×C11×#125—21no—
22C2×C11×C22⋊Q8—21no—
23C2×C11×C22⋊Q8—21no—
24C2×C11×C22⋊Q8C2211yescharacteristic
25C2×C11×C22⋊Q8C2211yescharacteristic
26C2×C4×Q8×C11C2211yescharacteristic
27C2×C4×D4×C11—21no—
28C2×C4×D4×C11C2211yescharacteristic
29C2×C11×#117C2211yescharacteristic
30C22×C11×C4⋊C4C2211yescharacteristic
31C22×C11×C4⋊C4C2211yescharacteristic
32C22×C11×C4⋊C4C2211yescharacteristic
33C11×#435—24no—
34C2×C11×C4⋊C8C2211yescharacteristic
35C2×C11×#103C2211yescharacteristic
36C2×C11×#103C2211yescharacteristic
37C2×C11×#103C2211yescharacteristic
38C2×C11×#103C2211yescharacteristic
39C2×C11×C22⋊C8C2211yescharacteristic
40C2×C11×C22⋊C8C2211yescharacteristic
41C2×C11×#97C2211yescharacteristic
42C11×#388—21no—
43C11×#387—21no—
44C11×#386—21no—
45C11×#382C2211yescharacteristic
46C11×#380C2211yescharacteristic
47C11×#380C2211yescharacteristic
48C4×C11×C4⋊C4C2211yescharacteristic
49C4×C11×C22⋊C4—21no—
50C11×#340C2211yescharacteristic
51C11×#340C2211yescharacteristic
52C11×#340C2211yescharacteristic
53C11×#340C2211yescharacteristic
54C11×#340C2211yescharacteristic
55C11×#340C2211yescharacteristic
56C11×#340C2211yescharacteristic
57C11×#340C2211yescharacteristic
58C11×#340C2211yescharacteristic
59C11×#340C2211yescharacteristic
60C11×#340C2211yescharacteristic
61C11×#340C2211yescharacteristic
62C22×Q8×C11—21no—
63C22×Q8×C11C2311yescharacteristic
64C22×D4×C11D411yescharacteristic
65C23×C4×C11—21no—
66C23×C4×C11—21no—
67C23×C4×C11—21no—
68C23×C4×C11C2311yescharacteristic
69C23×C4×C11C2311yescharacteristic
70C2×C11×M16—22no—
71C2×C11×M16—22no—
72C2×C11×M16—41no—
73C22×C8×C11—22no—
74C22×C8×C11—22no—
75C22×C8×C11—41no—
76C22×C8×C11C2311yescharacteristic
77C22×C8×C11C2311yescharacteristic
78C22×C8×C11C2311yescharacteristic
79C22×C8×C11C2311yescharacteristic
80C11×C4⋊Q8—22no—
81C11×C4⋊Q8C2×C414yescomplemented
82C11×#125—28no—
83C11×C22⋊Q8—22no—
84C11×C22⋊Q8—22no—
85C11×C22⋊Q8—28no—
86C11×C22⋊Q8—28no—
87C11×C22⋊Q8C2×C414yes—
88C11×C22⋊Q8C2×C414yescomplemented
89C4×Q8×C11—22no—
90C4×Q8×C11C2×C414yescomplemented
91C4×D4×C11—28no—
92C4×D4×C11C2×C414yes—
93C4×D4×C11D414yes—
94C11×#117—22no—
95C11×#117—41no—
96C2×C11×C4⋊C4—21no—
97C2×C11×C4⋊C4—21no—
98C2×C11×C4⋊C4—22no—
99C2×C11×C4⋊C4—22no—
100C2×C11×C4⋊C4—21no—
101C2×C11×C4⋊C4—21no—
102C2×C11×C4⋊C4—21no—
103C2×C11×C4⋊C4—21no—
104C2×C11×C4⋊C4—22no—
105C2×C11×C4⋊C4—21no—
106C2×C11×C4⋊C4—41no—
107C2×C11×C4⋊C4C2×C414yes—
108C2×C11×C4⋊C4C2×C414yescomplemented
109C2×C11×C4⋊C4D411yescharacteristic
110C2×C11×C4⋊C4C2311yescharacteristic
111C2×C11×C4⋊C4C2311yescharacteristic
112C2×C11×C4⋊C4C2311yescharacteristic
113C2×C11×C4⋊C4C2311yescharacteristic
114C2×C11×C4⋊C4C2311yescharacteristic
115C2×C11×C4⋊C4C2311yescharacteristic
116C2×C11×C4⋊C4C2311yescharacteristic
117C2×C11×C22⋊C4—21no—
118C2×C11×C22⋊C4—21no—
119C2×C11×C22⋊C4—21no—
120C2×C11×C22⋊C4—21no—
121C2×C11×C22⋊C4—21no—
122C2×C11×C22⋊C4D411yescharacteristic
123C2×C11×C22⋊C4D411yescharacteristic
124C2×C42×C11—21no—
125C2×C42×C11—21no—
126C2×C42×C11—21no—
127C2×C42×C11C2311yescharacteristic
128C11×C4⋊C8—22no—
129C11×#103—22no—
130C11×#103—22no—
131C11×#103—41no—
132C11×#103—41no—
133C11×C22⋊C8—22no—
134C11×C22⋊C8—22no—
135C11×#97—22no—
136C11×#95—21no—
137C11×#95—21no—
138C11×#95—21no—
139C11×#95—21no—
140C11×#95—21no—
141#22497C1111yesmaximal, characteristic, direct product factor, Sylow
142C24×C11C2×D411yescharacteristic
143C24×C11C2×D411yescharacteristic
144C2×Q8×C11—24no—
145C2×Q8×C11—21no—
146C2×Q8×C11—21no—
147C2×Q8×C11—21no—
148C2×Q8×C11—21no—
149C2×Q8×C11—21no—
150C2×Q8×C11—81no—
151C2×Q8×C11—81no—
152C2×Q8×C11C22×C412yes—
153C2×D4×C11—22no—
154C2×D4×C11—22no—
155C2×D4×C11C22⋊C414yes—
156C22×C4×C11—21no—
157C22×C4×C11—21no—
158C22×C4×C11—21no—
159C22×C4×C11—21no—
160C22×C4×C11—21no—
161C22×C4×C11—21no—
162C22×C4×C11—21no—
163C22×C4×C11—21no—
164C22×C4×C11—21no—
165C22×C4×C11—21no—
166C22×C4×C11—21no—
167C22×C4×C11—21no—
168C22×C4×C11—21no—
169C22×C4×C11—24no—
170C22×C4×C11—24no—
171C22×C4×C11—21no—
172C22×C4×C11—21no—
173C22×C4×C11—21no—
174C22×C4×C11—42no—
175C22×C4×C11—42no—
176C22×C4×C11—81no—
177C22×C4×C11—81no—
178C22×C4×C11—81no—
179C22×C4×C11—81no—
180C22×C4×C11—81no—
181C22×C4×C11C22×C412yes—
182C22×C4×C11C22×C412yes—
183C22×C4×C11C2×D411yescharacteristic
184C22×C4×C11C2×D411yescharacteristic
185C22×C4×C11C2×D411yescharacteristic
186C22×C4×C11C2×D411yescharacteristic
187C22×C4×C11C2×D412yes—
188C22×C4×C11C2×D412yes—
189C22×C4×C11C2411yescharacteristic
190C11×M16—44no—
191C2×C8×C11—21no—
192C2×C8×C11—21no—
193C2×C8×C11—21no—
194C2×C8×C11—21no—
195C2×C8×C11—21no—
196C2×C8×C11—21no—
197C2×C8×C11—21no—
198C2×C8×C11—21no—
199C2×C8×C11—21no—
200C2×C8×C11—21no—
201C2×C8×C11—21no—
202C2×C8×C11—44no—
203C2×C8×C11#4112yes—
204C11×C4⋊C4—24no—
205C11×C4⋊C4—24no—
206C11×C4⋊C4—24no—
207C11×C4⋊C4—24no—
208C11×C4⋊C4—24no—
209C11×C4⋊C4—24no—
210C11×C4⋊C4—21no—
211C11×C4⋊C4—21no—
212C11×C4⋊C4—21no—
213C11×C4⋊C4—21no—
214C11×C4⋊C4—21no—
215C11×C4⋊C4—21no—
216C11×C4⋊C4—21no—
217C11×C4⋊C4—21no—
218C11×C4⋊C4—21no—
219C11×C4⋊C4—21no—
220C11×C4⋊C4—42no—
221C11×C4⋊C4C22⋊C414yes—
222C11×C4⋊C4C22×C412yes—
223C11×C4⋊C4C22×C412yes—
224C11×C4⋊C4C22×C412yes—
225C11×C4⋊C4#4112yes—
226C11×C22⋊C4—24no—
227C11×C22⋊C4—24no—
228C11×C22⋊C4—42no—
229C11×C22⋊C4—42no—
230C11×C22⋊C4—81no—
231C11×C22⋊C4C22⋊C414yes—
232C11×C22⋊C4C22⋊C414yes—
233C42×C11—24no—
234C42×C11—42no—
235C42×C11—81no—
236C42×C11C22×C412yes—
237C42×C11C2×D412yes—
238C2×#554C2×C1111yescharacteristic
239C2×#435C2×C1111yescharacteristic
240#2352C2×C1111yescharacteristic
241#1993C2×C1111yescharacteristic, complemented
242#1988C2×C1111yescharacteristic, complemented
243#1894C2×C1111yescharacteristic, complemented
244#1892C2×C1111yescharacteristic, complemented
245#1873C2×C1111yescharacteristic, complemented
246#1872C2×C1111yescharacteristic, complemented
247#1824C2×C1111yescharacteristic, complemented
248#1823C2×C1111yescharacteristic, complemented
249#1805C2×C1111yescharacteristic, complemented
250#1763C2×C1111yescharacteristic, complemented
251#1736C2×C1111yescharacteristic, complemented
252C2×#340C2×C1111yescharacteristic, complemented
253C23×C11—21no—
254C23×C11—21no—
255C23×C11—21no—
256C23×C11—21no—
257C23×C11—21no—
258C23×C11—21no—
259C23×C11—21no—
260C23×C11—21no—
261C23×C11—21no—
262C23×C11—21no—
263C23×C11C2×C22⋊C412yes—
264C23×C11C2×C22⋊C412yes—
265C23×C11#13712yes—
266C23×C11#13712yes—
267C23×C11C22×D411yescharacteristic
268Q8×C11—22no—
269Q8×C11—22no—
270Q8×C11—41no—
271Q8×C11—41no—
272Q8×C11—84no—
273D4×C11—28no—
274C2×C4×C11—21no—
275C2×C4×C11—21no—
276C2×C4×C11—21no—
277C2×C4×C11—21no—
278C2×C4×C11—21no—
279C2×C4×C11—21no—
280C2×C4×C11—21no—
281C2×C4×C11—21no—
282C2×C4×C11—22no—
283C2×C4×C11—22no—
284C2×C4×C11—22no—
285C2×C4×C11—22no—
286C2×C4×C11—22no—
287C2×C4×C11—22no—
288C2×C4×C11—22no—
289C2×C4×C11—22no—
290C2×C4×C11—22no—
291C2×C4×C11—22no—
292C2×C4×C11—22no—
293C2×C4×C11—22no—
294C2×C4×C11—22no—
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—41no—
309C2×C4×C11—41no—
310C2×C4×C11—41no—
311C2×C4×C11—41no—
312C2×C4×C11—41no—
313C2×C4×C11—41no—
314C2×C4×C11—84no—
315C2×C4×C11—84no—
316C2×C4×C11—84no—
317C2×C4×C11C2×C22⋊C412yes—
318C2×C4×C11C2×C22⋊C412yes—
319C2×C4×C11C2×C22⋊C412yes—
320C2×C4×C11C2×C22⋊C412yes—
321C2×C4×C11C23×C411yescharacteristic
322C2×C4×C11C22×D411yescharacteristic
323C2×C4×C11C2×#4111yescharacteristic
324C2×C4×C11C2×#4111yescharacteristic
325C2×C4×C11H(5,𝔽2)11yescharacteristic
326C2×C4×C112−1+411yescharacteristic
327C8×C11—22no—
328C8×C11—41no—
329C8×C11—41no—
330C8×C11—41no—
331C22×M16C22×C1111yescharacteristic
332C23×C8C22×C1111yescharacteristic
333#554—24no—
334#554C4×C1118yescomplemented
335C2×C4⋊Q8C22×C1111yescharacteristic
336C2×#125—21no—
337C2×C22⋊Q8—21no—
338C2×C22⋊Q8—21no—
339C2×C22⋊Q8C22×C1111yescharacteristic
340C2×C22⋊Q8C22×C1111yescharacteristic
341C2×C4×Q8C22×C1111yescharacteristic
342C2×C4×D4—21no—
343C2×C4×D4C22×C1111yescharacteristic
344C2×#117C22×C1111yescharacteristic
345C22×C4⋊C4C22×C1111yescharacteristic
346C22×C4⋊C4C22×C1111yescharacteristic
347C22×C4⋊C4C22×C1111yescharacteristic
348#435—24no—
349C2×C4⋊C8C22×C1111yescharacteristic
350C2×#103C22×C1111yescharacteristic
351C2×#103C22×C1111yescharacteristic
352C2×#103C22×C1111yescharacteristic
353C2×#103C22×C1111yescharacteristic
354C2×C22⋊C8C22×C1111yescharacteristic
355C2×C22⋊C8C22×C1111yescharacteristic
356C2×#97C22×C1111yescharacteristic
357#388—21no—
358#387—21no—
359#386—21no—
360#382C22×C1111yescharacteristic
361#380C22×C1111yescharacteristic
362#380C22×C1111yescharacteristic
363C4×C4⋊C4C22×C1111yescharacteristic
364C4×C22⋊C4—21no—
365#340C22×C1111yescharacteristic
366#340C22×C1111yescharacteristic
367#340C22×C1111yescharacteristic
368#340C22×C1111yescharacteristic
369#340C22×C1111yescharacteristic
370#340C22×C1111yescharacteristic
371#340C22×C1111yescharacteristic
372#340C22×C1111yescharacteristic
373#340C22×C1111yescharacteristic
374#340C22×C1111yescharacteristic
375#340C22×C1111yescharacteristic
376#340C22×C1111yescharacteristic
377C22×C11—22no—
378C22×C11—22no—
379C22×C11—22no—
380C22×C11—22no—
381C22×C11—22no—
382C22×C11—22no—
383C22×C11—22no—
384C22×C11—22no—
385C22×C11—22no—
386C22×C11—41no—
387C22×C11—41no—
388C22×C11—41no—
389C22×C11—41no—
390C22×C11#41914yes—
391C22×C11C22×C22⋊C411yescharacteristic
392C22×C11#54611yescharacteristic
393C22×C11#54711yescharacteristic
394C22×C11C2×#13711yescharacteristic
395C22×C11C2×#13711yescharacteristic
396C22×C11#57611yescharacteristic
397C22×C11#57711yescharacteristic
398C4×C11—22no—
399C4×C11—22no—
400C4×C11—22no—
401C4×C11—22no—
402C4×C11—42no—
403C4×C11—42no—
404C4×C11—42no—
405C4×C11—42no—
406C4×C11—42no—
407C4×C11—81no—
408C4×C11—81no—
409C4×C11—81no—
410C4×C11C4×#4111yescharacteristic
411C4×C11#52011yescharacteristic
412C4×C11#54611yescharacteristic
413C4×C11#54711yescharacteristic
414C22×Q8—21no—
415C22×Q8C23×C1111yescharacteristic
416C22×D4D4×C1111yescharacteristic
417C23×C4—21no—
418C23×C4—21no—
419C23×C4—21no—
420C23×C4C23×C1111yescharacteristic
421C23×C4C23×C1111yescharacteristic
422C2×M16—22no—
423C2×M16—22no—
424C2×M16—41no—
425C22×C8—22no—
426C22×C8—22no—
427C22×C8—41no—
428C22×C8C23×C1111yescharacteristic
429C22×C8C23×C1111yescharacteristic
430C22×C8C23×C1111yescharacteristic
431C22×C8C23×C1111yescharacteristic
432C4⋊Q8—22no—
433C4⋊Q8C2×C4×C1114yescomplemented
434#125—28no—
435C22⋊Q8—22no—
436C22⋊Q8—22no—
437C22⋊Q8—28no—
438C22⋊Q8—28no—
439C22⋊Q8C2×C4×C1114yes—
440C22⋊Q8C2×C4×C1114yescomplemented
441C4×Q8—22no—
442C4×Q8C2×C4×C1114yescomplemented
443C4×D4—28no—
444C4×D4C2×C4×C1114yes—
445C4×D4D4×C1114yes—
446#117—22no—
447#117—41no—
448C2×C4⋊C4—21no—
449C2×C4⋊C4—21no—
450C2×C4⋊C4—22no—
451C2×C4⋊C4—22no—
452C2×C4⋊C4—21no—
453C2×C4⋊C4—21no—
454C2×C4⋊C4—21no—
455C2×C4⋊C4—21no—
456C2×C4⋊C4—22no—
457C2×C4⋊C4—21no—
458C2×C4⋊C4—41no—
459C2×C4⋊C4C2×C4×C1114yes—
460C2×C4⋊C4C2×C4×C1114yescomplemented
461C2×C4⋊C4D4×C1111yescharacteristic
462C2×C4⋊C4C23×C1111yescharacteristic
463C2×C4⋊C4C23×C1111yescharacteristic
464C2×C4⋊C4C23×C1111yescharacteristic
465C2×C4⋊C4C23×C1111yescharacteristic
466C2×C4⋊C4C23×C1111yescharacteristic
467C2×C4⋊C4C23×C1111yescharacteristic
468C2×C4⋊C4C23×C1111yescharacteristic
469C2×C22⋊C4—21no—
470C2×C22⋊C4—21no—
471C2×C22⋊C4—21no—
472C2×C22⋊C4—21no—
473C2×C22⋊C4—21no—
474C2×C22⋊C4D4×C1111yescharacteristic
475C2×C22⋊C4D4×C1111yescharacteristic
476C2×C42—21no—
477C2×C42—21no—
478C2×C42—21no—
479C2×C42C23×C1111yescharacteristic
480C4⋊C8—22no—
481#103—22no—
482#103—22no—
483#103—41no—
484#103—41no—
485C22⋊C8—22no—
486C22⋊C8—22no—
487#97—22no—
488#95—21no—
489#95—21no—
490#95—21no—
491#95—21no—
492#95—21no—
493C2×C11—24no—
494C2×C11—42no—
495C2×C11#233911yescharacteristic
496C2×C11C2×#41911yescharacteristic
497C2×C11#289711yescharacteristic
498C2×C11#331411yescharacteristic
499C2×C11#331611yescharacteristic
500C2×C11#334411yescharacteristic
501C2×C11#334611yescharacteristic
502C24C2×D4×C1111yescharacteristic
503C24C2×D4×C1111yescharacteristic
504C2×Q8—24no—
505C2×Q8—21no—
506C2×Q8—21no—
507C2×Q8—21no—
508C2×Q8—21no—
509C2×Q8—21no—
510C2×Q8—81no—
511C2×Q8—81no—
512C2×Q8C22×C4×C1112yes—
513C2×D4—22no—
514C2×D4—22no—
515C2×D4C11×C22⋊C414yes—
516C22×C4—21no—
517C22×C4—21no—
518C22×C4—21no—
519C22×C4—21no—
520C22×C4—21no—
521C22×C4—21no—
522C22×C4—21no—
523C22×C4—21no—
524C22×C4—21no—
525C22×C4—21no—
526C22×C4—21no—
527C22×C4—21no—
528C22×C4—21no—
529C22×C4—24no—
530C22×C4—24no—
531C22×C4—21no—
532C22×C4—21no—
533C22×C4—21no—
534C22×C4—42no—
535C22×C4—42no—
536C22×C4—81no—
537C22×C4—81no—
538C22×C4—81no—
539C22×C4—81no—
540C22×C4—81no—
541C22×C4C22×C4×C1112yes—
542C22×C4C22×C4×C1112yes—
543C22×C4C2×D4×C1111yescharacteristic
544C22×C4C2×D4×C1111yescharacteristic
545C22×C4C2×D4×C1111yescharacteristic
546C22×C4C2×D4×C1111yescharacteristic
547C22×C4C2×D4×C1112yes—
548C22×C4C2×D4×C1112yes—
549C22×C4C24×C1111yescharacteristic
550M16—44no—
551C2×C8—21no—
552C2×C8—21no—
553C2×C8—21no—
554C2×C8—21no—
555C2×C8—21no—
556C2×C8—21no—
557C2×C8—21no—
558C2×C8—21no—
559C2×C8—21no—
560C2×C8—21no—
561C2×C8—21no—
562C2×C8—44no—
563C2×C8C11×#4112yes—
564C4⋊C4—24no—
565C4⋊C4—24no—
566C4⋊C4—24no—
567C4⋊C4—24no—
568C4⋊C4—24no—
569C4⋊C4—24no—
570C4⋊C4—21no—
571C4⋊C4—21no—
572C4⋊C4—21no—
573C4⋊C4—21no—
574C4⋊C4—21no—
575C4⋊C4—21no—
576C4⋊C4—21no—
577C4⋊C4—21no—
578C4⋊C4—21no—
579C4⋊C4—21no—
580C4⋊C4—42no—
581C4⋊C4C11×C22⋊C414yes—
582C4⋊C4C22×C4×C1112yes—
583C4⋊C4C22×C4×C1112yes—
584C4⋊C4C22×C4×C1112yes—
585C4⋊C4C11×#4112yes—
586C22⋊C4—24no—
587C22⋊C4—24no—
588C22⋊C4—42no—
589C22⋊C4—42no—
590C22⋊C4—81no—
591C22⋊C4C11×C22⋊C414yes—
592C22⋊C4C11×C22⋊C414yes—
593C42—24no—
594C42—42no—
595C42—81no—
596C42C22×C4×C1112yes—
597C42C2×D4×C1112yes—
598C11#2249711yescharacteristic, direct product factor, Sylow
599C23—21no—
600C23—21no—
601C23—21no—
602C23—21no—
603C23—21no—
604C23—21no—
605C23—21no—
606C23—21no—
607C23—21no—
608C23—21no—
609C23C2×C11×C22⋊C412yes—
610C23C2×C11×C22⋊C412yes—
611C23C11×#13712yes—
612C23C11×#13712yes—
613C23C22×D4×C1111yescharacteristic
614Q8—22no—
615Q8—22no—
616Q8—41no—
617Q8—41no—
618Q8—84no—
619D4—28no—
620C2×C4—21no—
621C2×C4—21no—
622C2×C4—21no—
623C2×C4—21no—
624C2×C4—21no—
625C2×C4—21no—
626C2×C4—21no—
627C2×C4—21no—
628C2×C4—22no—
629C2×C4—22no—
630C2×C4—22no—
631C2×C4—22no—
632C2×C4—22no—
633C2×C4—22no—
634C2×C4—22no—
635C2×C4—22no—
636C2×C4—22no—
637C2×C4—22no—
638C2×C4—22no—
639C2×C4—22no—
640C2×C4—22no—
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—41no—
655C2×C4—41no—
656C2×C4—41no—
657C2×C4—41no—
658C2×C4—41no—
659C2×C4—41no—
660C2×C4—84no—
661C2×C4—84no—
662C2×C4—84no—
663C2×C4C2×C11×C22⋊C412yes—
664C2×C4C2×C11×C22⋊C412yes—
665C2×C4C2×C11×C22⋊C412yes—
666C2×C4C2×C11×C22⋊C412yes—
667C2×C4C23×C4×C1111yescharacteristic
668C2×C4C22×D4×C1111yescharacteristic
669C2×C4C2×C11×#4111yescharacteristic
670C2×C4C2×C11×#4111yescharacteristic
671C2×C4C11×H(5,𝔽2)11yescharacteristic
672C2×C4C11×2−1+411yescharacteristic
673C8—22no—
674C8—41no—
675C8—41no—
676C8—41no—
677C22—22no—
678C22—22no—
679C22—22no—
680C22—22no—
681C22—22no—
682C22—22no—
683C22—22no—
684C22—22no—
685C22—22no—
686C22—41no—
687C22—41no—
688C22—41no—
689C22—41no—
690C22C11×#41914yes—
691C22C22×C11×C22⋊C411yescharacteristic
692C22C11×#54611yescharacteristic
693C22C11×#54711yescharacteristic
694C22C2×C11×#13711yescharacteristic
695C22C2×C11×#13711yescharacteristic
696C22C11×#57611yescharacteristic
697C22C11×#57711yescharacteristic
698C4—22no—
699C4—22no—
700C4—22no—
701C4—22no—
702C4—42no—
703C4—42no—
704C4—42no—
705C4—42no—
706C4—42no—
707C4—81no—
708C4—81no—
709C4—81no—
710C4C4×C11×#4111yescharacteristic
711C4C11×#52011yescharacteristic
712C4C11×#54611yescharacteristic
713C4C11×#54711yescharacteristic
714C2—24no—
715C2—42no—
716C2C11×#233911yescharacteristic
717C2C2×C11×#41911yescharacteristic
718C2C11×#289711yescharacteristic
719C2C11×#331411yescharacteristic
720C2C11×#331611yescharacteristic
721C2C11×#334411yescharacteristic
722C2C11×#334611yescharacteristic
subgroupG/H
center, socleC23×C11C22×D4
commutatorC2×C4C23×C4×C11
Frattini, cosocleC22×C4C24×C11
prime radicalC22×D4×C11D4
LCSG ▷ C2×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
4. C11×#1993C2semidirect
5. C11×#1988C2semidirect
6. C11×#1894C2semidirect
7. C11×#1892C2semidirect
8. C11×#1873C2semidirect
9. C11×#1872C2semidirect
10. C11×#1824C2semidirect
11. C11×#1823C2semidirect
12. C11×#1805C2semidirect
13. C11×#1763C2semidirect
14. C11×#1736C2semidirect
15. C2×C11×#340C2semidirect
19. C11×#554C4semidirect
81. C11×C4⋊Q8C2×C4semidirect
88. C11×C22⋊Q8C2×C4semidirect
90. C4×Q8×C11C2×C4semidirect
108. C2×C11×C4⋊C4C2×C4semidirect
141. #22497C11direct (N × H)
241. #1993C2×C11semidirect
242. #1988C2×C11semidirect
243. #1894C2×C11semidirect
244. #1892C2×C11semidirect
245. #1873C2×C11semidirect
246. #1872C2×C11semidirect
247. #1824C2×C11semidirect
248. #1823C2×C11semidirect
249. #1805C2×C11semidirect
250. #1763C2×C11semidirect
251. #1736C2×C11semidirect
252. C2×#340C2×C11semidirect
334. #554C4×C11semidirect
433. C4⋊Q8C2×C4×C11semidirect
440. C22⋊Q8C2×C4×C11semidirect
442. C4×Q8C2×C4×C11semidirect
460. C2×C4⋊C4C2×C4×C11semidirect
598. C11#22497direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#5542
C2×C11×#4352
C11×#23522
C11×#19932
C11×#19882
C11×#18942
C11×#18922
C11×#18732
C11×#18722
C11×#18242
C11×#18232
C11×#18052
C11×#17632
C11×#17362
C2×C11×#3402
#2249711