Finite Group Databasebeta

← C11×#22071 #14599264

Subgroups — C11×#22071 #14599264

Order 2816.

874 conjugacy classes of subgroups.

The subgroup lattice has 688 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#435C211yesmaximal, characteristic
2C2×C11×#423C211yesmaximal, characteristic, complemented
3C4×C11×#123C211yesmaximal, characteristic
4C11×#1940C211yesmaximal, characteristic, complemented
5C11×#1939C211yesmaximal, characteristic, complemented
6C11×#1924C211yesmaximal, characteristic, complemented
7C11×#1923C211yesmaximal, characteristic, complemented
8C11×#1917C211yesmaximal, characteristic, complemented
9C11×#1917C211yesmaximal, characteristic, complemented
10C11×#1870C211yesmaximal, characteristic
11C11×#1851C211yesmaximal, characteristic, complemented
12C11×#1850C211yesmaximal, characteristic, complemented
13C11×#1850C211yesmaximal, characteristic, complemented
14C11×#1817C211yesmaximal, characteristic, complemented
15C11×#1753C211yesmaximal, characteristic, complemented
16C22×C11×M16C2211yescharacteristic
17C22×C11×M16C2211yescharacteristic
18C23×C8×C11C2211yescharacteristic
19C2×C11×#123C411yescharacteristic
20C2×C4×D4×C11C2211yescharacteristic
21C22×C42×C11C2211yescharacteristic
22C11×#435—24no—
23C11×#423—24no—
24C2×C11×C4⋊C8C2211yescharacteristic
25C2×C11×C4⋊C8C2211yescharacteristic
26C2×C11×C4⋊C8C2211yescharacteristic
27C2×C11×C4⋊C8C2211yescharacteristic
28C2×C11×C4⋊C8C2211yescharacteristic
29C2×C11×C4⋊C8C2211yescharacteristic
30C2×C11×C4⋊C8C2211yescharacteristic
31C2×C11×C22⋊C8C2211yescharacteristic
32C2×C11×C22⋊C8C2211yescharacteristic
33C2×C11×C22⋊C8C2211yescharacteristic
34C2×C11×C22⋊C8C2211yescharacteristic
35C2×C11×C22⋊C8C2211yescharacteristic
36C2×C11×#97C2211yescharacteristic
37C2×C11×#97C2211yescharacteristic
38C2×C4×C8×C11C2211yescharacteristic
39C11×#388C411yescharacteristic
40C11×#388C411yescharacteristic
41C11×#387C411yescharacteristic
42C11×#387C411yescharacteristic
43C11×#386C411yescharacteristic
44C11×#385C411yescharacteristic
45C11×#381C411yescharacteristic
46C4×C11×C4⋊C4C2211yescharacteristic
47C4×C11×C4⋊C4C2211yescharacteristic
48C4×C11×C22⋊C4C2211yescharacteristic
49C4×C11×C22⋊C4C2211yescharacteristic
50C4×C11×C22⋊C4C2211yescharacteristic
51C11×#336C2211yescharacteristic
52C11×#336C2211yescharacteristic
53C11×#336C2211yescharacteristic
54C11×#336C2211yescharacteristic
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
66C2×C11×M16—22no—
67C2×C11×M16—41no—
68C2×C11×M16—41no—
69C2×C11×M16—41no—
70C2×C11×M16—41no—
71C2×C11×M16D414yes—
72C22×C8×C11—22no—
73C22×C8×C11—41no—
74C22×C8×C11—41no—
75C22×C8×C11C2311yescharacteristic
76C22×C8×C11C2311yescharacteristic
77C22×C8×C11C2311yescharacteristic
78C22×C8×C11C2311yescharacteristic
79C22×C8×C11C2311yescharacteristic
80C22×C8×C11C2311yescharacteristic
81C22×C8×C11C2311yescharacteristic
82C22×C8×C11C2311yescharacteristic
83C11×#123—24no—
84C4×D4×C11—22no—
85C4×D4×C11—22no—
86C2×C11×C4⋊C4C2×C411yescharacteristic
87C2×C11×C4⋊C4C2×C411yescharacteristic
88C2×C11×C4⋊C4C2×C411yescharacteristic
89C2×C11×C4⋊C4C2×C411yescharacteristic
90C2×C11×C4⋊C4C2×C411yescharacteristic
91C2×C11×C22⋊C4C2×C411yescharacteristic
92C2×C11×C22⋊C4C2×C411yescharacteristic
93C2×C11×C22⋊C4C2×C411yescharacteristic
94C2×C11×C22⋊C4C2×C411yescharacteristic
95C2×C11×C22⋊C4C2×C411yescharacteristic
96C2×C11×C22⋊C4C2×C411yescharacteristic
97C2×C11×C22⋊C4C2×C411yescharacteristic
98C2×C11×C22⋊C4C2×C411yescharacteristic
99C2×C42×C11—22no—
100C2×C42×C11—22no—
101C2×C42×C11C2×C411yescharacteristic
102C2×C42×C11C2×C411yescharacteristic
103C2×C42×C11C2311yescharacteristic
104C2×C42×C11C2311yescharacteristic
105C2×C42×C11C2311yescharacteristic
106C2×C42×C11C2311yescharacteristic
107C2×C42×C11C2311yescharacteristic
108C11×C4⋊C8—22no—
109C11×C4⋊C8—22no—
110C11×C4⋊C8—22no—
111C11×C4⋊C8—22no—
112C11×C4⋊C8—22no—
113C11×C4⋊C8—41no—
114C11×C4⋊C8—41no—
115C11×C22⋊C8—22no—
116C11×C22⋊C8—22no—
117C11×C22⋊C8—22no—
118C11×C22⋊C8—41no—
119C11×C22⋊C8—41no—
120C11×#97—22no—
121C11×#97—41no—
122C4×C8×C11—41no—
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
132C11×#95C2×C411yescharacteristic
133#22071C1111yesmaximal, characteristic, direct product factor, Sylow
134C24×C11C22×C411yescharacteristic
135C24×C11C22×C411yescharacteristic
136C2×D4×C11—22no—
137C2×D4×C11—22no—
138C2×D4×C11—41no—
139C22×C4×C11—21no—
140C22×C4×C11—21no—
141C22×C4×C11—21no—
142C22×C4×C11—21no—
143C22×C4×C11—22no—
144C22×C4×C11—22no—
145C22×C4×C11—22no—
146C22×C4×C11—22no—
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×C11C22×C411yescharacteristic
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×C11C2×D412yes—
168C22×C4×C11#4112yes—
169C22×C4×C11C2411yescharacteristic
170C11×M16—44no—
171C11×M16—44no—
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×C11—21no—
192C2×C8×C11—21no—
193C2×C8×C11—21no—
194C2×C8×C11—44no—
195C2×C8×C11C2×D412yes—
196C2×C8×C11C2×D412yes—
197C11×C4⋊C4—22no—
198C11×C4⋊C4—22no—
199C11×C4⋊C4—22no—
200C11×C4⋊C4—22no—
201C11×C4⋊C4—41no—
202C11×C22⋊C4—22no—
203C11×C22⋊C4—22no—
204C11×C22⋊C4—22no—
205C11×C22⋊C4—22no—
206C11×C22⋊C4—22no—
207C11×C22⋊C4—41no—
208C11×C22⋊C4—41no—
209C11×C22⋊C4M1614yescomplemented
210C42×C11—22no—
211C42×C11—22no—
212C42×C11—21no—
213C42×C11—21no—
214C42×C11—21no—
215C42×C11—21no—
216C42×C11—21no—
217C42×C11—21no—
218C42×C11—21no—
219C42×C11—21no—
220C42×C11—21no—
221C42×C11—21no—
222C2×#435C2×C1111yescharacteristic
223C2×#423C2×C1111yescharacteristic, complemented
224C4×#123C2×C1111yescharacteristic
225#1940C2×C1111yescharacteristic, complemented
226#1939C2×C1111yescharacteristic, complemented
227#1924C2×C1111yescharacteristic, complemented
228#1923C2×C1111yescharacteristic, complemented
229#1917C2×C1111yescharacteristic, complemented
230#1917C2×C1111yescharacteristic, complemented
231#1870C2×C1111yescharacteristic
232#1851C2×C1111yescharacteristic, complemented
233#1850C2×C1111yescharacteristic, complemented
234#1850C2×C1111yescharacteristic, complemented
235#1817C2×C1111yescharacteristic, complemented
236#1753C2×C1111yescharacteristic, complemented
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—21no—
247C23×C11—21no—
248C23×C11—21no—
249C23×C11C4×D412yes—
250C23×C11C2×M1612yes—
251C23×C11C23×C411yescharacteristic
252D4×C11—44no—
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—22no—
262C2×C4×C11—22no—
263C2×C4×C11—22no—
264C2×C4×C11—22no—
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—21no—
282C2×C4×C11—21no—
283C2×C4×C11—21no—
284C2×C4×C11—21no—
285C2×C4×C11—21no—
286C2×C4×C11—21no—
287C2×C4×C11—21no—
288C2×C4×C11—21no—
289C2×C4×C11—44no—
290C2×C4×C11—44no—
291C2×C4×C11—41no—
292C2×C4×C11—41no—
293C2×C4×C11—41no—
294C2×C4×C11—41no—
295C2×C4×C11C4×D412yes—
296C2×C4×C11C2×M1612yes—
297C2×C4×C11C2×M1612yes—
298C2×C4×C11#13112yes—
299C2×C4×C11C22×D411yescharacteristic
300C2×C4×C11C2×#4111yescharacteristic
301C2×C4×C11H(5,𝔽2)11yescharacteristic
302C2×C4×C11H(5,𝔽2)11yescharacteristic
303C2×C4×C112−1+411yescharacteristic
304C2×C4×C112−1+411yescharacteristic
305C8×C11—22no—
306C8×C11—22no—
307C8×C11—41no—
308C8×C11—41no—
309C8×C11—41no—
310C8×C11—41no—
311C8×C11—41no—
312C8×C11—41no—
313C22×M16C22×C1111yescharacteristic
314C22×M16C22×C1111yescharacteristic
315C23×C8C22×C1111yescharacteristic
316C2×#123C4×C1111yescharacteristic
317C2×C4×D4C22×C1111yescharacteristic
318C22×C42C22×C1111yescharacteristic
319#435—24no—
320#423—24no—
321C2×C4⋊C8C22×C1111yescharacteristic
322C2×C4⋊C8C22×C1111yescharacteristic
323C2×C4⋊C8C22×C1111yescharacteristic
324C2×C4⋊C8C22×C1111yescharacteristic
325C2×C4⋊C8C22×C1111yescharacteristic
326C2×C4⋊C8C22×C1111yescharacteristic
327C2×C4⋊C8C22×C1111yescharacteristic
328C2×C22⋊C8C22×C1111yescharacteristic
329C2×C22⋊C8C22×C1111yescharacteristic
330C2×C22⋊C8C22×C1111yescharacteristic
331C2×C22⋊C8C22×C1111yescharacteristic
332C2×C22⋊C8C22×C1111yescharacteristic
333C2×#97C22×C1111yescharacteristic
334C2×#97C22×C1111yescharacteristic
335C2×C4×C8C22×C1111yescharacteristic
336#388C4×C1111yescharacteristic
337#388C4×C1111yescharacteristic
338#387C4×C1111yescharacteristic
339#387C4×C1111yescharacteristic
340#386C4×C1111yescharacteristic
341#385C4×C1111yescharacteristic
342#381C4×C1111yescharacteristic
343C4×C4⋊C4C22×C1111yescharacteristic
344C4×C4⋊C4C22×C1111yescharacteristic
345C4×C22⋊C4C22×C1111yescharacteristic
346C4×C22⋊C4C22×C1111yescharacteristic
347C4×C22⋊C4C22×C1111yescharacteristic
348#336C22×C1111yescharacteristic
349#336C22×C1111yescharacteristic
350#336C22×C1111yescharacteristic
351#336C22×C1111yescharacteristic
352#336C22×C1111yescharacteristic
353#336C22×C1111yescharacteristic
354#336C22×C1111yescharacteristic
355#336C22×C1111yescharacteristic
356#336C22×C1111yescharacteristic
357#336C22×C1111yescharacteristic
358C22×C11—22no—
359C22×C11—22no—
360C22×C11—22no—
361C22×C11—22no—
362C22×C11—22no—
363C22×C11—22no—
364C22×C11—41no—
365C22×C11—41no—
366C22×C11—41no—
367C22×C11—41no—
368C22×C11—41no—
369C22×C11—41no—
370C22×C11—41no—
371C22×C11—41no—
372C22×C11C2×C4×D411yescharacteristic
373C22×C11#52011yescharacteristic
374C22×C11#52011yescharacteristic
375C22×C11C22×M1611yescharacteristic
376C22×C11C2×#13111yescharacteristic
377C22×C11#56811yescharacteristic
378C22×C11#56811yescharacteristic
379C4×C11—22no—
380C4×C11—22no—
381C4×C11—22no—
382C4×C11—22no—
383C4×C11—41no—
384C4×C11—41no—
385C4×C11—41no—
386C4×C11—41no—
387C4×C11—41no—
388C4×C11—41no—
389C4×C11—41no—
390C4×C11—41no—
391C4×C11#53411yescharacteristic
392C4×C11#53611yescharacteristic
393C4×C11#53911yescharacteristic
394C4×C11#53911yescharacteristic
395C22×D4C2×C4×C1111yescharacteristic
396C23×C4C2×C4×C1111yescharacteristic
397C23×C4C2×C4×C1111yescharacteristic
398C23×C4C23×C1111yescharacteristic
399C23×C4C23×C1111yescharacteristic
400C2×M16—22no—
401C2×M16—41no—
402C2×M16—41no—
403C2×M16—41no—
404C2×M16—41no—
405C2×M16D4×C1114yes—
406C22×C8—22no—
407C22×C8—41no—
408C22×C8—41no—
409C22×C8C23×C1111yescharacteristic
410C22×C8C23×C1111yescharacteristic
411C22×C8C23×C1111yescharacteristic
412C22×C8C23×C1111yescharacteristic
413C22×C8C23×C1111yescharacteristic
414C22×C8C23×C1111yescharacteristic
415C22×C8C23×C1111yescharacteristic
416C22×C8C23×C1111yescharacteristic
417#123—24no—
418C4×D4—22no—
419C4×D4—22no—
420C2×C4⋊C4C2×C4×C1111yescharacteristic
421C2×C4⋊C4C2×C4×C1111yescharacteristic
422C2×C4⋊C4C2×C4×C1111yescharacteristic
423C2×C4⋊C4C2×C4×C1111yescharacteristic
424C2×C4⋊C4C2×C4×C1111yescharacteristic
425C2×C22⋊C4C2×C4×C1111yescharacteristic
426C2×C22⋊C4C2×C4×C1111yescharacteristic
427C2×C22⋊C4C2×C4×C1111yescharacteristic
428C2×C22⋊C4C2×C4×C1111yescharacteristic
429C2×C22⋊C4C2×C4×C1111yescharacteristic
430C2×C22⋊C4C2×C4×C1111yescharacteristic
431C2×C22⋊C4C2×C4×C1111yescharacteristic
432C2×C22⋊C4C2×C4×C1111yescharacteristic
433C2×C42—22no—
434C2×C42—22no—
435C2×C42C2×C4×C1111yescharacteristic
436C2×C42C2×C4×C1111yescharacteristic
437C2×C42C23×C1111yescharacteristic
438C2×C42C23×C1111yescharacteristic
439C2×C42C23×C1111yescharacteristic
440C2×C42C23×C1111yescharacteristic
441C2×C42C23×C1111yescharacteristic
442C4⋊C8—22no—
443C4⋊C8—22no—
444C4⋊C8—22no—
445C4⋊C8—22no—
446C4⋊C8—22no—
447C4⋊C8—41no—
448C4⋊C8—41no—
449C22⋊C8—22no—
450C22⋊C8—22no—
451C22⋊C8—22no—
452C22⋊C8—41no—
453C22⋊C8—41no—
454#97—22no—
455#97—41no—
456C4×C8—41no—
457#95C2×C4×C1111yescharacteristic
458#95C2×C4×C1111yescharacteristic
459#95C2×C4×C1111yescharacteristic
460#95C2×C4×C1111yescharacteristic
461#95C2×C4×C1111yescharacteristic
462#95C2×C4×C1111yescharacteristic
463#95C2×C4×C1111yescharacteristic
464#95C2×C4×C1111yescharacteristic
465#95C2×C4×C1111yescharacteristic
466#95C2×C4×C1111yescharacteristic
467C2×C11—42no—
468C2×C11—42no—
469C2×C11#232211yescharacteristic
470C2×C11#293311yescharacteristic
471C2×C11D4×M1611yescharacteristic
472C2×C11#298911yescharacteristic
473C2×C11#299011yescharacteristic
474C2×C11#299311yescharacteristic
475C2×C11#299511yescharacteristic
476C24C22×C4×C1111yescharacteristic
477C24C22×C4×C1111yescharacteristic
478C2×D4—22no—
479C2×D4—22no—
480C2×D4—41no—
481C22×C4—21no—
482C22×C4—21no—
483C22×C4—21no—
484C22×C4—21no—
485C22×C4—22no—
486C22×C4—22no—
487C22×C4—22no—
488C22×C4—22no—
489C22×C4—21no—
490C22×C4—21no—
491C22×C4—21no—
492C22×C4—21no—
493C22×C4—21no—
494C22×C4—21no—
495C22×C4—41no—
496C22×C4—41no—
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×C4C22×C4×C1111yescharacteristic
507C22×C4C22×C4×C1111yescharacteristic
508C22×C4C22×C4×C1111yescharacteristic
509C22×C4C2×D4×C1112yes—
510C22×C4C11×#4112yes—
511C22×C4C24×C1111yescharacteristic
512M16—44no—
513M16—44no—
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×C8—21no—
530C2×C8—21no—
531C2×C8—21no—
532C2×C8—21no—
533C2×C8—21no—
534C2×C8—21no—
535C2×C8—21no—
536C2×C8—44no—
537C2×C8C2×D4×C1112yes—
538C2×C8C2×D4×C1112yes—
539C4⋊C4—22no—
540C4⋊C4—22no—
541C4⋊C4—22no—
542C4⋊C4—22no—
543C4⋊C4—41no—
544C22⋊C4—22no—
545C22⋊C4—22no—
546C22⋊C4—22no—
547C22⋊C4—22no—
548C22⋊C4—22no—
549C22⋊C4—41no—
550C22⋊C4—41no—
551C22⋊C4C11×M1614yescomplemented
552C42—22no—
553C42—22no—
554C42—21no—
555C42—21no—
556C42—21no—
557C42—21no—
558C42—21no—
559C42—21no—
560C42—21no—
561C42—21no—
562C42—21no—
563C42—21no—
564C11#2207111yescharacteristic, direct product factor, Sylow
565C23—21no—
566C23—21no—
567C23—21no—
568C23—21no—
569C23—21no—
570C23—21no—
571C23—21no—
572C23—21no—
573C23—21no—
574C23—21no—
575C23—21no—
576C23—21no—
577C23C4×D4×C1112yes—
578C23C2×C11×M1612yes—
579C23C23×C4×C1111yescharacteristic
580D4—44no—
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—22no—
590C2×C4—22no—
591C2×C4—22no—
592C2×C4—22no—
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—21no—
606C2×C4—21no—
607C2×C4—21no—
608C2×C4—21no—
609C2×C4—21no—
610C2×C4—21no—
611C2×C4—21no—
612C2×C4—21no—
613C2×C4—21no—
614C2×C4—21no—
615C2×C4—21no—
616C2×C4—21no—
617C2×C4—44no—
618C2×C4—44no—
619C2×C4—41no—
620C2×C4—41no—
621C2×C4—41no—
622C2×C4—41no—
623C2×C4C4×D4×C1112yes—
624C2×C4C2×C11×M1612yes—
625C2×C4C2×C11×M1612yes—
626C2×C4C11×#13112yes—
627C2×C4C22×D4×C1111yescharacteristic
628C2×C4C2×C11×#4111yescharacteristic
629C2×C4C11×H(5,𝔽2)11yescharacteristic
630C2×C4C11×H(5,𝔽2)11yescharacteristic
631C2×C4C11×2−1+411yescharacteristic
632C2×C4C11×2−1+411yescharacteristic
633C8—22no—
634C8—22no—
635C8—41no—
636C8—41no—
637C8—41no—
638C8—41no—
639C8—41no—
640C8—41no—
641C22—22no—
642C22—22no—
643C22—22no—
644C22—22no—
645C22—22no—
646C22—22no—
647C22—41no—
648C22—41no—
649C22—41no—
650C22—41no—
651C22—41no—
652C22—41no—
653C22—41no—
654C22—41no—
655C22C2×C4×D4×C1111yescharacteristic
656C22C11×#52011yescharacteristic
657C22C11×#52011yescharacteristic
658C22C22×C11×M1611yescharacteristic
659C22C2×C11×#13111yescharacteristic
660C22C11×#56811yescharacteristic
661C22C11×#56811yescharacteristic
662C4—22no—
663C4—22no—
664C4—22no—
665C4—22no—
666C4—41no—
667C4—41no—
668C4—41no—
669C4—41no—
670C4—41no—
671C4—41no—
672C4—41no—
673C4—41no—
674C4C11×#53411yescharacteristic
675C4C11×#53611yescharacteristic
676C4C11×#53911yescharacteristic
677C4C11×#53911yescharacteristic
678C2—42no—
679C2—42no—
680C2C11×#232211yescharacteristic
681C2C11×#293311yescharacteristic
682C2D4×C11×M1611yescharacteristic
683C2C11×#298911yescharacteristic
684C2C11×#299011yescharacteristic
685C2C11×#299311yescharacteristic
686C2C11×#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
2. C2×C11×#423C2semidirect
4. C11×#1940C2semidirect
5. C11×#1939C2semidirect
6. C11×#1924C2semidirect
7. C11×#1923C2semidirect
8. C11×#1917C2semidirect
9. C11×#1917C2semidirect
11. C11×#1851C2semidirect
12. C11×#1850C2semidirect
13. C11×#1850C2semidirect
14. C11×#1817C2semidirect
15. C11×#1753C2semidirect
133. #22071C11direct (N × H)
209. C11×C22⋊C4M16semidirect
223. C2×#423C2×C11semidirect
225. #1940C2×C11semidirect
226. #1939C2×C11semidirect
227. #1924C2×C11semidirect
228. #1923C2×C11semidirect
229. #1917C2×C11semidirect
230. #1917C2×C11semidirect
232. #1851C2×C11semidirect
233. #1850C2×C11semidirect
234. #1850C2×C11semidirect
235. #1817C2×C11semidirect
236. #1753C2×C11semidirect
551. C22⋊C4C11×M16semidirect
564. C11#22071direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#4352
C2×C11×#4232
C4×C11×#1232
C11×#19402
C11×#19392
C11×#19242
C11×#19232
C11×#19172
C11×#18702
C11×#18512
C11×#18502
C11×#18172
C11×#17532
#2207111