Finite Group Databasebeta

← C11×#22801 #14599994

Subgroups — C11×#22801 #14599994

Order 2816.

830 conjugacy classes of subgroups.

The subgroup lattice has 680 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#433C211yesmaximal, characteristic, complemented
2C2×C11×#432C211yesmaximal, characteristic, complemented
3C11×#2290C211yesmaximal, characteristic
4C11×#1955C211yesmaximal, characteristic
5C11×#1954C211yesmaximal, characteristic
6C11×#1924C211yesmaximal, characteristic, complemented
7C11×#1924C211yesmaximal, characteristic, complemented
8C11×#1924C211yesmaximal, characteristic, complemented
9C11×#1923C211yesmaximal, characteristic, complemented
10C11×#1843C211yesmaximal, characteristic, complemented
11C11×#1798C211yesmaximal, characteristic, complemented
12C11×#1797C211yesmaximal, characteristic, complemented
13C11×#1771C211yesmaximal, characteristic, complemented
14C11×#1770C211yesmaximal, characteristic, complemented
15C11×#1768C211yesmaximal, characteristic, complemented
16C2×C4×D4×C11C2211yescharacteristic
17C2×C11×#117C2211yescharacteristic
18C22×C42×C11C2211yescharacteristic
19C11×#433—24no—
20C11×#432—24no—
21C2×C11×C4⋊C8C2211yescharacteristic
22C2×C11×C4⋊C8C2211yescharacteristic
23C2×C11×C4⋊C8C2211yescharacteristic
24C2×C11×C4⋊C8C2211yescharacteristic
25C2×C11×C4⋊C8C2211yescharacteristic
26C2×C11×C4⋊C8C2211yescharacteristic
27C2×C11×C4⋊C8C2211yescharacteristic
28C2×C11×C4⋊C8C2211yescharacteristic
29C2×C11×C22⋊C8C2211yescharacteristic
30C2×C11×C22⋊C8C2211yescharacteristic
31C2×C11×C22⋊C8C2211yescharacteristic
32C2×C11×C22⋊C8C2211yescharacteristic
33C2×C11×C22⋊C8C2211yescharacteristic
34C2×C11×C22⋊C8C2211yescharacteristic
35C2×C11×C22⋊C8C2211yescharacteristic
36C2×C11×C22⋊C8C2211yescharacteristic
37C2×C11×#97C2211yescharacteristic
38C2×C11×#97C2211yescharacteristic
39C2×C11×#97C2211yescharacteristic
40C2×C11×#97C2211yescharacteristic
41C2×C4×C8×C11C2211yescharacteristic
42C2×C4×C8×C11C2211yescharacteristic
43C11×#388C411yescharacteristic
44C11×#388C411yescharacteristic
45C11×#387C411yescharacteristic
46C11×#387C411yescharacteristic
47C11×#386C411yescharacteristic
48C11×#386C411yescharacteristic
49C11×#385C411yescharacteristic
50C11×#385C411yescharacteristic
51C4×C11×C4⋊C4C2211yescharacteristic
52C4×C11×C22⋊C4C2211yescharacteristic
53C4×C11×C22⋊C4C2211yescharacteristic
54C11×#376C2211yescharacteristic
55C11×#336C2211yescharacteristic
56C11×#336C2211yescharacteristic
57C11×#336C2211yescharacteristic
58C11×#336C2211yescharacteristic
59C11×#336C2211yescharacteristic
60C11×#336C2211yescharacteristic
61C22×D4×C11C2×C411yescharacteristic
62C23×C4×C11C2×C411yescharacteristic
63C23×C4×C11C2×C411yescharacteristic
64C23×C4×C11C2311yescharacteristic
65C23×C4×C11C2311yescharacteristic
66C22×C8×C11C2311yescharacteristic
67C22×C8×C11C2311yescharacteristic
68C22×C8×C11C2311yescharacteristic
69C22×C8×C11C2311yescharacteristic
70C22×C8×C11C2311yescharacteristic
71C22×C8×C11C2311yescharacteristic
72C22×C8×C11C2311yescharacteristic
73C22×C8×C11C2311yescharacteristic
74C4×D4×C11—22no—
75C4×D4×C11—22no—
76C11×#117—22no—
77C11×#117—22no—
78C2×C11×C4⋊C4C2×C411yescharacteristic
79C2×C11×C4⋊C4C2×C411yescharacteristic
80C2×C11×C4⋊C4C2×C411yescharacteristic
81C2×C11×C4⋊C4C2×C411yescharacteristic
82C2×C11×C4⋊C4C2×C411yescharacteristic
83C2×C11×C22⋊C4C2×C411yescharacteristic
84C2×C11×C22⋊C4C2×C411yescharacteristic
85C2×C11×C22⋊C4C2×C411yescharacteristic
86C2×C11×C22⋊C4C2×C411yescharacteristic
87C2×C11×C22⋊C4C2×C411yescharacteristic
88C2×C11×C22⋊C4C2×C411yescharacteristic
89C2×C11×C22⋊C4C2×C411yescharacteristic
90C2×C11×C22⋊C4C2×C411yescharacteristic
91C2×C42×C11—22no—
92C2×C42×C11—22no—
93C2×C42×C11C2×C411yescharacteristic
94C2×C42×C11C2×C411yescharacteristic
95C2×C42×C11C2311yescharacteristic
96C2×C42×C11C2311yescharacteristic
97C2×C42×C11C2311yescharacteristic
98C2×C42×C11C2311yescharacteristic
99C2×C42×C11C2311yescharacteristic
100C11×C4⋊C8—22no—
101C11×C4⋊C8—22no—
102C11×C4⋊C8—22no—
103C11×C4⋊C8—22no—
104C11×C4⋊C8—22no—
105C11×C4⋊C8—41no—
106C11×C4⋊C8—41no—
107C11×C4⋊C8D414yescomplemented
108C11×C22⋊C8—22no—
109C11×C22⋊C8—22no—
110C11×C22⋊C8—22no—
111C11×C22⋊C8—22no—
112C11×C22⋊C8—41no—
113C11×C22⋊C8—41no—
114C11×C22⋊C8—41no—
115C11×C22⋊C8—41no—
116C11×#97—22no—
117C11×#97—22no—
118C11×#97—22no—
119C11×#97—22no—
120C4×C8×C11—22no—
121C4×C8×C11—22no—
122C11×#95C2×C411yescharacteristic
123C11×#95C2×C411yescharacteristic
124C11×#95C2×C411yescharacteristic
125C11×#95C2×C411yescharacteristic
126C11×#95C2×C411yescharacteristic
127C11×#95C2×C411yescharacteristic
128C11×#95C2×C411yescharacteristic
129C11×#95C2×C411yescharacteristic
130C11×#95C2×C411yescharacteristic
131C11×#95C2×C411yescharacteristic
132#22801C1111yesmaximal, characteristic, direct product factor, Sylow
133C24×C11C22×C411yescharacteristic
134C24×C11C22×C411yescharacteristic
135C2×D4×C11—22no—
136C2×D4×C11—22no—
137C2×D4×C11—41no—
138C22×C4×C11—22no—
139C22×C4×C11—22no—
140C22×C4×C11—22no—
141C22×C4×C11—21no—
142C22×C4×C11—21no—
143C22×C4×C11—21no—
144C22×C4×C11—21no—
145C22×C4×C11—21no—
146C22×C4×C11—21no—
147C22×C4×C11—21no—
148C22×C4×C11—21no—
149C22×C4×C11—21no—
150C22×C4×C11—21no—
151C22×C4×C11—21no—
152C22×C4×C11—21no—
153C22×C4×C11—41no—
154C22×C4×C11—41no—
155C22×C4×C11—41no—
156C22×C4×C11C22×C411yescharacteristic
157C22×C4×C11C22×C411yescharacteristic
158C22×C4×C11C22×C411yescharacteristic
159C22×C4×C11C22×C411yescharacteristic
160C22×C4×C11C22×C411yescharacteristic
161C22×C4×C11C22×C411yescharacteristic
162C22×C4×C11C22×C411yescharacteristic
163C22×C4×C11C22×C411yescharacteristic
164C22×C4×C11C22×C411yescharacteristic
165C22×C4×C11C22×C411yescharacteristic
166C22×C4×C11C22×C411yescharacteristic
167C22×C4×C11C22×C411yescharacteristic
168C22×C4×C11C2411yescharacteristic
169C2×C8×C11—21no—
170C2×C8×C11—21no—
171C2×C8×C11—21no—
172C2×C8×C11—21no—
173C2×C8×C11—21no—
174C2×C8×C11—21no—
175C2×C8×C11—21no—
176C2×C8×C11—21no—
177C2×C8×C11—21no—
178C2×C8×C11—21no—
179C2×C8×C11—21no—
180C2×C8×C11—21no—
181C2×C8×C11—21no—
182C2×C8×C11—21no—
183C2×C8×C11—21no—
184C2×C8×C11—21no—
185C2×C8×C11—21no—
186C2×C8×C11—21no—
187C2×C8×C11—21no—
188C2×C8×C11—21no—
189C2×C8×C11—21no—
190C2×C8×C11—21no—
191C2×C8×C11C2×D412yes—
192C2×C8×C11C2×D412yes—
193C11×C4⋊C4—22no—
194C11×C4⋊C4—22no—
195C11×C4⋊C4—22no—
196C11×C4⋊C4—41no—
197C11×C4⋊C4—41no—
198C11×C22⋊C4—22no—
199C11×C22⋊C4—22no—
200C11×C22⋊C4—22no—
201C11×C22⋊C4—22no—
202C11×C22⋊C4—22no—
203C11×C22⋊C4—41no—
204C11×C22⋊C4—41no—
205C11×C22⋊C4—41no—
206C42×C11—22no—
207C42×C11—22no—
208C42×C11—21no—
209C42×C11—21no—
210C42×C11—21no—
211C42×C11—21no—
212C42×C11—21no—
213C42×C11—21no—
214C42×C11C2×D412yes—
215C42×C11#4112yes—
216C42×C11#4112yes—
217C42×C11#4112yes—
218C2×#433C2×C1111yescharacteristic, complemented
219C2×#432C2×C1111yescharacteristic, complemented
220#2290C2×C1111yescharacteristic
221#1955C2×C1111yescharacteristic
222#1954C2×C1111yescharacteristic
223#1924C2×C1111yescharacteristic, complemented
224#1924C2×C1111yescharacteristic, complemented
225#1924C2×C1111yescharacteristic, complemented
226#1923C2×C1111yescharacteristic, complemented
227#1843C2×C1111yescharacteristic, complemented
228#1798C2×C1111yescharacteristic, complemented
229#1797C2×C1111yescharacteristic, complemented
230#1771C2×C1111yescharacteristic, complemented
231#1770C2×C1111yescharacteristic, complemented
232#1768C2×C1111yescharacteristic, complemented
233C23×C11—21no—
234C23×C11—21no—
235C23×C11—21no—
236C23×C11—21no—
237C23×C11—21no—
238C23×C11—21no—
239C23×C11—21no—
240C23×C11—21no—
241C23×C11—21no—
242C23×C11—21no—
243C23×C11—21no—
244C23×C11—21no—
245C23×C11—21no—
246C23×C11#13112yes—
247C23×C11C23×C411yescharacteristic
248D4×C11—44no—
249C2×C4×C11—21no—
250C2×C4×C11—21no—
251C2×C4×C11—21no—
252C2×C4×C11—21no—
253C2×C4×C11—21no—
254C2×C4×C11—21no—
255C2×C4×C11—21no—
256C2×C4×C11—21no—
257C2×C4×C11—21no—
258C2×C4×C11—21no—
259C2×C4×C11—21no—
260C2×C4×C11—21no—
261C2×C4×C11—21no—
262C2×C4×C11—21no—
263C2×C4×C11—21no—
264C2×C4×C11—21no—
265C2×C4×C11—21no—
266C2×C4×C11—21no—
267C2×C4×C11—21no—
268C2×C4×C11—21no—
269C2×C4×C11—21no—
270C2×C4×C11—21no—
271C2×C4×C11—21no—
272C2×C4×C11—21no—
273C2×C4×C11—21no—
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—44no—
282C2×C4×C11—44no—
283C2×C4×C11—41no—
284C2×C4×C11—41no—
285C2×C4×C11—41no—
286C2×C4×C11—41no—
287C2×C4×C11—41no—
288C2×C4×C11—41no—
289C2×C4×C11—41no—
290C2×C4×C11—41no—
291C2×C4×C11#11712yes—
292C2×C4×C11#11712yes—
293C2×C4×C11C4×D412yes—
294C2×C4×C11C4×D412yes—
295C2×C4×C11C22×D411yescharacteristic
296C2×C4×C11C2×#4111yescharacteristic
297C2×C4×C11C2×#4111yescharacteristic
298C2×C4×C11C2×#4111yescharacteristic
299C2×C4×C11H(5,𝔽2)11yescharacteristic
300C2×C4×C112−1+411yescharacteristic
301C8×C11—22no—
302C8×C11—22no—
303C8×C11—41no—
304C8×C11—41no—
305C8×C11—41no—
306C8×C11—41no—
307C8×C11—41no—
308C8×C11—41no—
309C2×C4×D4C22×C1111yescharacteristic
310C2×#117C22×C1111yescharacteristic
311C22×C42C22×C1111yescharacteristic
312#433—24no—
313#432—24no—
314C2×C4⋊C8C22×C1111yescharacteristic
315C2×C4⋊C8C22×C1111yescharacteristic
316C2×C4⋊C8C22×C1111yescharacteristic
317C2×C4⋊C8C22×C1111yescharacteristic
318C2×C4⋊C8C22×C1111yescharacteristic
319C2×C4⋊C8C22×C1111yescharacteristic
320C2×C4⋊C8C22×C1111yescharacteristic
321C2×C4⋊C8C22×C1111yescharacteristic
322C2×C22⋊C8C22×C1111yescharacteristic
323C2×C22⋊C8C22×C1111yescharacteristic
324C2×C22⋊C8C22×C1111yescharacteristic
325C2×C22⋊C8C22×C1111yescharacteristic
326C2×C22⋊C8C22×C1111yescharacteristic
327C2×C22⋊C8C22×C1111yescharacteristic
328C2×C22⋊C8C22×C1111yescharacteristic
329C2×C22⋊C8C22×C1111yescharacteristic
330C2×#97C22×C1111yescharacteristic
331C2×#97C22×C1111yescharacteristic
332C2×#97C22×C1111yescharacteristic
333C2×#97C22×C1111yescharacteristic
334C2×C4×C8C22×C1111yescharacteristic
335C2×C4×C8C22×C1111yescharacteristic
336#388C4×C1111yescharacteristic
337#388C4×C1111yescharacteristic
338#387C4×C1111yescharacteristic
339#387C4×C1111yescharacteristic
340#386C4×C1111yescharacteristic
341#386C4×C1111yescharacteristic
342#385C4×C1111yescharacteristic
343#385C4×C1111yescharacteristic
344C4×C4⋊C4C22×C1111yescharacteristic
345C4×C22⋊C4C22×C1111yescharacteristic
346C4×C22⋊C4C22×C1111yescharacteristic
347#376C22×C1111yescharacteristic
348#336C22×C1111yescharacteristic
349#336C22×C1111yescharacteristic
350#336C22×C1111yescharacteristic
351#336C22×C1111yescharacteristic
352#336C22×C1111yescharacteristic
353#336C22×C1111yescharacteristic
354C22×C11—22no—
355C22×C11—22no—
356C22×C11—22no—
357C22×C11—41no—
358C22×C11—41no—
359C22×C11—41no—
360C22×C11—41no—
361C22×C11—41no—
362C22×C11—41no—
363C22×C11—41no—
364C22×C11—41no—
365C22×C11—41no—
366C22×C11—41no—
367C22×C11—41no—
368C22×C11C2×#11711yescharacteristic
369C22×C11C2×C4×D411yescharacteristic
370C22×C11#52011yescharacteristic
371C22×C11C2×#13111yescharacteristic
372C22×C11#56811yescharacteristic
373C22×C11#56811yescharacteristic
374C22×C11#56811yescharacteristic
375C4×C11—22no—
376C4×C11—22no—
377C4×C11—22no—
378C4×C11—22no—
379C4×C11—41no—
380C4×C11—41no—
381C4×C11—41no—
382C4×C11—41no—
383C4×C11—41no—
384C4×C11—41no—
385C4×C11—41no—
386C4×C11—41no—
387C4×C11#54711yescharacteristic
388C4×C11#55011yescharacteristic
389C4×C11#55511yescharacteristic
390C4×C11#55611yescharacteristic
391C22×D4C2×C4×C1111yescharacteristic
392C23×C4C2×C4×C1111yescharacteristic
393C23×C4C2×C4×C1111yescharacteristic
394C23×C4C23×C1111yescharacteristic
395C23×C4C23×C1111yescharacteristic
396C22×C8C23×C1111yescharacteristic
397C22×C8C23×C1111yescharacteristic
398C22×C8C23×C1111yescharacteristic
399C22×C8C23×C1111yescharacteristic
400C22×C8C23×C1111yescharacteristic
401C22×C8C23×C1111yescharacteristic
402C22×C8C23×C1111yescharacteristic
403C22×C8C23×C1111yescharacteristic
404C4×D4—22no—
405C4×D4—22no—
406#117—22no—
407#117—22no—
408C2×C4⋊C4C2×C4×C1111yescharacteristic
409C2×C4⋊C4C2×C4×C1111yescharacteristic
410C2×C4⋊C4C2×C4×C1111yescharacteristic
411C2×C4⋊C4C2×C4×C1111yescharacteristic
412C2×C4⋊C4C2×C4×C1111yescharacteristic
413C2×C22⋊C4C2×C4×C1111yescharacteristic
414C2×C22⋊C4C2×C4×C1111yescharacteristic
415C2×C22⋊C4C2×C4×C1111yescharacteristic
416C2×C22⋊C4C2×C4×C1111yescharacteristic
417C2×C22⋊C4C2×C4×C1111yescharacteristic
418C2×C22⋊C4C2×C4×C1111yescharacteristic
419C2×C22⋊C4C2×C4×C1111yescharacteristic
420C2×C22⋊C4C2×C4×C1111yescharacteristic
421C2×C42—22no—
422C2×C42—22no—
423C2×C42C2×C4×C1111yescharacteristic
424C2×C42C2×C4×C1111yescharacteristic
425C2×C42C23×C1111yescharacteristic
426C2×C42C23×C1111yescharacteristic
427C2×C42C23×C1111yescharacteristic
428C2×C42C23×C1111yescharacteristic
429C2×C42C23×C1111yescharacteristic
430C4⋊C8—22no—
431C4⋊C8—22no—
432C4⋊C8—22no—
433C4⋊C8—22no—
434C4⋊C8—22no—
435C4⋊C8—41no—
436C4⋊C8—41no—
437C4⋊C8D4×C1114yescomplemented
438C22⋊C8—22no—
439C22⋊C8—22no—
440C22⋊C8—22no—
441C22⋊C8—22no—
442C22⋊C8—41no—
443C22⋊C8—41no—
444C22⋊C8—41no—
445C22⋊C8—41no—
446#97—22no—
447#97—22no—
448#97—22no—
449#97—22no—
450C4×C8—22no—
451C4×C8—22no—
452#95C2×C4×C1111yescharacteristic
453#95C2×C4×C1111yescharacteristic
454#95C2×C4×C1111yescharacteristic
455#95C2×C4×C1111yescharacteristic
456#95C2×C4×C1111yescharacteristic
457#95C2×C4×C1111yescharacteristic
458#95C2×C4×C1111yescharacteristic
459#95C2×C4×C1111yescharacteristic
460#95C2×C4×C1111yescharacteristic
461#95C2×C4×C1111yescharacteristic
462C2×C11—42no—
463C2×C11—81no—
464C2×C11#235411yescharacteristic
465C2×C11#292311yescharacteristic
466C2×C11#292411yescharacteristic
467C2×C11#293011yescharacteristic
468C2×C11#293311yescharacteristic
469C2×C11#299211yescharacteristic
470C2×C11#299511yescharacteristic
471C24C22×C4×C1111yescharacteristic
472C24C22×C4×C1111yescharacteristic
473C2×D4—22no—
474C2×D4—22no—
475C2×D4—41no—
476C22×C4—22no—
477C22×C4—22no—
478C22×C4—22no—
479C22×C4—21no—
480C22×C4—21no—
481C22×C4—21no—
482C22×C4—21no—
483C22×C4—21no—
484C22×C4—21no—
485C22×C4—21no—
486C22×C4—21no—
487C22×C4—21no—
488C22×C4—21no—
489C22×C4—21no—
490C22×C4—21no—
491C22×C4—41no—
492C22×C4—41no—
493C22×C4—41no—
494C22×C4C22×C4×C1111yescharacteristic
495C22×C4C22×C4×C1111yescharacteristic
496C22×C4C22×C4×C1111yescharacteristic
497C22×C4C22×C4×C1111yescharacteristic
498C22×C4C22×C4×C1111yescharacteristic
499C22×C4C22×C4×C1111yescharacteristic
500C22×C4C22×C4×C1111yescharacteristic
501C22×C4C22×C4×C1111yescharacteristic
502C22×C4C22×C4×C1111yescharacteristic
503C22×C4C22×C4×C1111yescharacteristic
504C22×C4C22×C4×C1111yescharacteristic
505C22×C4C22×C4×C1111yescharacteristic
506C22×C4C24×C1111yescharacteristic
507C2×C8—21no—
508C2×C8—21no—
509C2×C8—21no—
510C2×C8—21no—
511C2×C8—21no—
512C2×C8—21no—
513C2×C8—21no—
514C2×C8—21no—
515C2×C8—21no—
516C2×C8—21no—
517C2×C8—21no—
518C2×C8—21no—
519C2×C8—21no—
520C2×C8—21no—
521C2×C8—21no—
522C2×C8—21no—
523C2×C8—21no—
524C2×C8—21no—
525C2×C8—21no—
526C2×C8—21no—
527C2×C8—21no—
528C2×C8—21no—
529C2×C8C2×D4×C1112yes—
530C2×C8C2×D4×C1112yes—
531C4⋊C4—22no—
532C4⋊C4—22no—
533C4⋊C4—22no—
534C4⋊C4—41no—
535C4⋊C4—41no—
536C22⋊C4—22no—
537C22⋊C4—22no—
538C22⋊C4—22no—
539C22⋊C4—22no—
540C22⋊C4—22no—
541C22⋊C4—41no—
542C22⋊C4—41no—
543C22⋊C4—41no—
544C42—22no—
545C42—22no—
546C42—21no—
547C42—21no—
548C42—21no—
549C42—21no—
550C42—21no—
551C42—21no—
552C42C2×D4×C1112yes—
553C42C11×#4112yes—
554C42C11×#4112yes—
555C42C11×#4112yes—
556C11#2280111yescharacteristic, direct product factor, Sylow
557C23—21no—
558C23—21no—
559C23—21no—
560C23—21no—
561C23—21no—
562C23—21no—
563C23—21no—
564C23—21no—
565C23—21no—
566C23—21no—
567C23—21no—
568C23—21no—
569C23—21no—
570C23C11×#13112yes—
571C23C23×C4×C1111yescharacteristic
572D4—44no—
573C2×C4—21no—
574C2×C4—21no—
575C2×C4—21no—
576C2×C4—21no—
577C2×C4—21no—
578C2×C4—21no—
579C2×C4—21no—
580C2×C4—21no—
581C2×C4—21no—
582C2×C4—21no—
583C2×C4—21no—
584C2×C4—21no—
585C2×C4—21no—
586C2×C4—21no—
587C2×C4—21no—
588C2×C4—21no—
589C2×C4—21no—
590C2×C4—21no—
591C2×C4—21no—
592C2×C4—21no—
593C2×C4—21no—
594C2×C4—21no—
595C2×C4—21no—
596C2×C4—21no—
597C2×C4—21no—
598C2×C4—21no—
599C2×C4—21no—
600C2×C4—21no—
601C2×C4—21no—
602C2×C4—21no—
603C2×C4—21no—
604C2×C4—21no—
605C2×C4—44no—
606C2×C4—44no—
607C2×C4—41no—
608C2×C4—41no—
609C2×C4—41no—
610C2×C4—41no—
611C2×C4—41no—
612C2×C4—41no—
613C2×C4—41no—
614C2×C4—41no—
615C2×C4C11×#11712yes—
616C2×C4C11×#11712yes—
617C2×C4C4×D4×C1112yes—
618C2×C4C4×D4×C1112yes—
619C2×C4C22×D4×C1111yescharacteristic
620C2×C4C2×C11×#4111yescharacteristic
621C2×C4C2×C11×#4111yescharacteristic
622C2×C4C2×C11×#4111yescharacteristic
623C2×C4C11×H(5,𝔽2)11yescharacteristic
624C2×C4C11×2−1+411yescharacteristic
625C8—22no—
626C8—22no—
627C8—41no—
628C8—41no—
629C8—41no—
630C8—41no—
631C8—41no—
632C8—41no—
633C22—22no—
634C22—22no—
635C22—22no—
636C22—41no—
637C22—41no—
638C22—41no—
639C22—41no—
640C22—41no—
641C22—41no—
642C22—41no—
643C22—41no—
644C22—41no—
645C22—41no—
646C22—41no—
647C22C2×C11×#11711yescharacteristic
648C22C2×C4×D4×C1111yescharacteristic
649C22C11×#52011yescharacteristic
650C22C2×C11×#13111yescharacteristic
651C22C11×#56811yescharacteristic
652C22C11×#56811yescharacteristic
653C22C11×#56811yescharacteristic
654C4—22no—
655C4—22no—
656C4—22no—
657C4—22no—
658C4—41no—
659C4—41no—
660C4—41no—
661C4—41no—
662C4—41no—
663C4—41no—
664C4—41no—
665C4—41no—
666C4C11×#54711yescharacteristic
667C4C11×#55011yescharacteristic
668C4C11×#55511yescharacteristic
669C4C11×#55611yescharacteristic
670C2—42no—
671C2—81no—
672C2C11×#235411yescharacteristic
673C2C11×#292311yescharacteristic
674C2C11×#292411yescharacteristic
675C2C11×#293011yescharacteristic
676C2C11×#293311yescharacteristic
677C2C11×#299211yescharacteristic
678C2C11×#299511yescharacteristic
subgroupG/H
centerC22×C4×C11C24
commutatorC23C23×C4×C11
Frattini, cosocleC22×C4C24×C11
socleC23×C11C23×C4
prime radicalC22×D4×C11C2×C4
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C22×C4×C11 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C11×#433C2semidirect
2. C2×C11×#432C2semidirect
6. C11×#1924C2semidirect
7. C11×#1924C2semidirect
8. C11×#1924C2semidirect
9. C11×#1923C2semidirect
10. C11×#1843C2semidirect
11. C11×#1798C2semidirect
12. C11×#1797C2semidirect
13. C11×#1771C2semidirect
14. C11×#1770C2semidirect
15. C11×#1768C2semidirect
107. C11×C4⋊C8D4semidirect
132. #22801C11direct (N × H)
218. C2×#433C2×C11semidirect
219. C2×#432C2×C11semidirect
223. #1924C2×C11semidirect
224. #1924C2×C11semidirect
225. #1924C2×C11semidirect
226. #1923C2×C11semidirect
227. #1843C2×C11semidirect
228. #1798C2×C11semidirect
229. #1797C2×C11semidirect
230. #1771C2×C11semidirect
231. #1770C2×C11semidirect
232. #1768C2×C11semidirect
437. C4⋊C8D4×C11semidirect
556. C11#22801direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#4332
C2×C11×#4322
C11×#22902
C11×#19552
C11×#19542
C11×#19242
C11×#19232
C11×#18432
C11×#17982
C11×#17972
C11×#17712
C11×#17702
C11×#17682
#2280111