Finite Group Databasebeta

← C11×#21885 #14599078

Subgroups — C11×#21885 #14599078

Order 2816.

1162 conjugacy classes of subgroups.

The subgroup lattice has 386 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#533C211yesmaximal, characteristic
2C22×C11×C4⋊C8C211yesmaximal, characteristic
3C11×#2285C211yesmaximal, characteristic
4C11×#1987C212yesmaximal, complemented
5C11×#1981C212yesmaximal, complemented
6C11×#1892C214yesmaximal
7C11×#1803C214yesmaximal, complemented
8C23×C8×C11C2212yes—
9C11×#533—24no—
10C11×#533C418yescomplemented
11C2×C11×C4⋊Q8C2211yescharacteristic
12C2×C11×C4⋊Q8C2211yescharacteristic
13C2×C11×#125—21no—
14C2×C11×C22⋊Q8—21no—
15C2×C11×C22⋊Q8C2212yes—
16C2×C4×Q8×C11—21no—
17C2×C4×Q8×C11C2212yes—
18C2×C11×#117—21no—
19C2×C11×#117—21no—
20C22×C42×C11C2211yescharacteristic
21C2×C11×C4⋊C8—24no—
22C2×C11×C4⋊C8C2212yes—
23C2×C11×C4⋊C8C2212yes—
24C2×C11×#103C2218yes—
25C11×#384C2212yes—
26C11×#382—21no—
27C11×#380—21no—
28C11×#380C2212yes—
29C4×C11×C4⋊C4—21no—
30C4×C11×C4⋊C4C2212yes—
31C11×#340C2218yes—
32C22×Q8×C11—21no—
33C22×Q8×C11C2312yes—
34C23×C4×C11D411yescharacteristic
35C23×C4×C11D411yescharacteristic
36C23×C4×C11C2311yescharacteristic
37C22×C8×C11—24no—
38C22×C8×C11—44no—
39C22×C8×C11C2314yes—
40C11×C4⋊Q8—22no—
41C11×C4⋊Q8—22no—
42C11×C4⋊Q8C2×C414yes—
43C11×C4⋊Q8C2×C414yes—
44C11×#125—28no—
45C11×C22⋊Q8—28no—
46C11×C22⋊Q8—24no—
47C11×C22⋊Q8C2×C418yes—
48C4×Q8×C11—28no—
49C4×Q8×C11—24no—
50C4×Q8×C11C2×C418yes—
51C11×#117—28no—
52C11×#117—44no—
53C2×C11×C4⋊C4—21no—
54C2×C11×C4⋊C4—21no—
55C2×C11×C4⋊C4—21no—
56C2×C11×C4⋊C4—22no—
57C2×C11×C4⋊C4—22no—
58C2×C11×C4⋊C4—22no—
59C2×C11×C4⋊C4—22no—
60C2×C11×C4⋊C4C2314yes—
61C2×C11×C4⋊C4C2312yes—
62C2×C11×C22⋊C4—22no—
63C2×C11×C22⋊C4—22no—
64C2×C42×C11—22no—
65C2×C42×C11—22no—
66C2×C42×C11C2×C414yes—
67C2×C42×C11D411yescharacteristic
68C2×C42×C11D411yescharacteristic
69C2×C42×C11D414yes—
70C2×C42×C11C2311yescharacteristic
71C2×C42×C11C2311yescharacteristic
72C11×C4⋊C8—24no—
73C11×C4⋊C8—24no—
74C11×#103—48no—
75C11×#95—22no—
76C11×#95—22no—
77#21885C1111yesmaximal, characteristic, direct product factor, Sylow
78C24×C11C2×D411yescharacteristic
79C2×Q8×C11—24no—
80C2×Q8×C11—22no—
81C2×Q8×C11—24no—
82C2×Q8×C11—24no—
83C2×Q8×C11—44no—
84C2×Q8×C11C22×C414yes—
85C22×C4×C11—22no—
86C22×C4×C11—22no—
87C22×C4×C11—22no—
88C22×C4×C11—22no—
89C22×C4×C11—24no—
90C22×C4×C11—42no—
91C22×C4×C11C22⋊C414yes—
92C22×C4×C11C22⋊C414yes—
93C22×C4×C11SD1614yes—
94C22×C4×C11Q1614yes—
95C22×C4×C11C22×C412yes—
96C22×C4×C11C2×D411yescharacteristic
97C22×C4×C11C2×D411yescharacteristic
98C22×C4×C11C2×D411yescharacteristic
99C22×C4×C11C2×D412yes—
100C22×C4×C11C2×D411yescharacteristic
101C22×C4×C11C2×D411yescharacteristic
102C22×C4×C11C2411yescharacteristic
103C2×C8×C11—24no—
104C2×C8×C11—28no—
105C2×C8×C11—48no—
106C11×C4⋊C4—24no—
107C11×C4⋊C4—24no—
108C11×C4⋊C4—24no—
109C11×C4⋊C4—28no—
110C11×C4⋊C4—28no—
111C11×C4⋊C4—22no—
112C11×C4⋊C4—24no—
113C11×C4⋊C4—24no—
114C11×C4⋊C4—44no—
115C11×C4⋊C4—44no—
116C11×C4⋊C4C22×C414yes—
117C11×C22⋊C4—28no—
118C11×C22⋊C4—44no—
119C42×C11—28no—
120C42×C11—44no—
121C42×C11C22⋊C414yes—
122C42×C11C22⋊C414yes—
123C42×C11C22×C412yes—
124C42×C11C22×C412yes—
125C42×C11C2×D412yes—
126C42×C11C2×D412yes—
127C2×#533C2×C1111yescharacteristic
128C22×C4⋊C8C2×C1111yescharacteristic
129#2285C2×C1111yescharacteristic
130#1987C2×C1112yescomplemented
131#1981C2×C1112yescomplemented
132#1892C2×C1114yes—
133#1803C2×C1114yescomplemented
134C23×C11—22no—
135C23×C11—22no—
136C23×C11C2×C22⋊C412yes—
137C23×C11C2×SD1612yes—
138C23×C11C2×Q1612yes—
139C23×C11C22×D411yescharacteristic
140Q8×C11—28no—
141Q8×C11—48no—
142Q8×C11—42no—
143Q8×C11—42no—
144C2×C4×C11—22no—
145C2×C4×C11—22no—
146C2×C4×C11—22no—
147C2×C4×C11—24no—
148C2×C4×C11—22no—
149C2×C4×C11—22no—
150C2×C4×C11—24no—
151C2×C4×C11—24no—
152C2×C4×C11—44no—
153C2×C4×C11—44no—
154C2×C4×C11—44no—
155C2×C4×C11—44no—
156C2×C4×C11—44no—
157C2×C4×C11—44no—
158C2×C4×C11#103116yescomplemented
159C2×C4×C11C2×C22⋊C412yes—
160C2×C4×C11C2×C22⋊C412yes—
161C2×C4×C11C2×C22⋊C412yes—
162C2×C4×C11C2×C22⋊C412yes—
163C2×C4×C11C2×C22⋊C412yes—
164C2×C4×C11C2×SD1612yes—
165C2×C4×C11C2×SD1612yes—
166C2×C4×C11C2×Q1612yes—
167C2×C4×C11C2×Q1612yes—
168C2×C4×C11C23×C411yescharacteristic
169C2×C4×C11C22×D411yescharacteristic
170C2×C4×C11H(5,𝔽2)12yes—
171C2×C4×C112−1+412yes—
172C8×C11—44no—
173C23×C8C22×C1112yes—
174#533—24no—
175#533C4×C1118yescomplemented
176C2×C4⋊Q8C22×C1111yescharacteristic
177C2×C4⋊Q8C22×C1111yescharacteristic
178C2×#125—21no—
179C2×C22⋊Q8—21no—
180C2×C22⋊Q8C22×C1112yes—
181C2×C4×Q8—21no—
182C2×C4×Q8C22×C1112yes—
183C2×#117—21no—
184C2×#117—21no—
185C22×C42C22×C1111yescharacteristic
186C2×C4⋊C8—24no—
187C2×C4⋊C8C22×C1112yes—
188C2×C4⋊C8C22×C1112yes—
189C2×#103C22×C1118yes—
190#384C22×C1112yes—
191#382—21no—
192#380—21no—
193#380C22×C1112yes—
194C4×C4⋊C4—21no—
195C4×C4⋊C4C22×C1112yes—
196#340C22×C1118yes—
197C22×C11—22no—
198C22×C11—22no—
199C22×C11—24no—
200C22×C11—24no—
201C22×C11C2×#10314yes—
202C22×C11C22×C22⋊C411yescharacteristic
203C22×C11#53712yes—
204C22×C11C22×SD1611yescharacteristic
205C22×C11C22×Q1611yescharacteristic
206C22×C11#57512yes—
207C4×C11—22no—
208C4×C11—22no—
209C4×C11—22no—
210C4×C11—44no—
211C4×C11—44no—
212C4×C11—84no—
213C4×C11C2×#10314yes—
214C4×C11C2×#10314yes—
215C4×C11#52012yes—
216C4×C11#53511yescharacteristic
217C4×C11#53611yescharacteristic
218C22×Q8—21no—
219C22×Q8C23×C1112yes—
220C23×C4D4×C1111yescharacteristic
221C23×C4D4×C1111yescharacteristic
222C23×C4C23×C1111yescharacteristic
223C22×C8—24no—
224C22×C8—44no—
225C22×C8C23×C1114yes—
226C4⋊Q8—22no—
227C4⋊Q8—22no—
228C4⋊Q8C2×C4×C1114yes—
229C4⋊Q8C2×C4×C1114yes—
230#125—28no—
231C22⋊Q8—28no—
232C22⋊Q8—24no—
233C22⋊Q8C2×C4×C1118yes—
234C4×Q8—28no—
235C4×Q8—24no—
236C4×Q8C2×C4×C1118yes—
237#117—28no—
238#117—44no—
239C2×C4⋊C4—21no—
240C2×C4⋊C4—21no—
241C2×C4⋊C4—21no—
242C2×C4⋊C4—22no—
243C2×C4⋊C4—22no—
244C2×C4⋊C4—22no—
245C2×C4⋊C4—22no—
246C2×C4⋊C4C23×C1114yes—
247C2×C4⋊C4C23×C1112yes—
248C2×C22⋊C4—22no—
249C2×C22⋊C4—22no—
250C2×C42—22no—
251C2×C42—22no—
252C2×C42C2×C4×C1114yes—
253C2×C42D4×C1111yescharacteristic
254C2×C42D4×C1111yescharacteristic
255C2×C42D4×C1114yes—
256C2×C42C23×C1111yescharacteristic
257C2×C42C23×C1111yescharacteristic
258C4⋊C8—24no—
259C4⋊C8—24no—
260#103—48no—
261#95—22no—
262#95—22no—
263C2×C11—24no—
264C2×C11#231111yescharacteristic
265C2×C11C22×#10311yescharacteristic
266C2×C11#289611yescharacteristic
267C2×C11#324612yes—
268C2×C11#324912yes—
269C24C2×D4×C1111yescharacteristic
270C2×Q8—24no—
271C2×Q8—22no—
272C2×Q8—24no—
273C2×Q8—24no—
274C2×Q8—44no—
275C2×Q8C22×C4×C1114yes—
276C22×C4—22no—
277C22×C4—22no—
278C22×C4—22no—
279C22×C4—22no—
280C22×C4—24no—
281C22×C4—42no—
282C22×C4C11×C22⋊C414yes—
283C22×C4C11×C22⋊C414yes—
284C22×C4C11×SD1614yes—
285C22×C4C11×Q1614yes—
286C22×C4C22×C4×C1112yes—
287C22×C4C2×D4×C1111yescharacteristic
288C22×C4C2×D4×C1111yescharacteristic
289C22×C4C2×D4×C1111yescharacteristic
290C22×C4C2×D4×C1112yes—
291C22×C4C2×D4×C1111yescharacteristic
292C22×C4C2×D4×C1111yescharacteristic
293C22×C4C24×C1111yescharacteristic
294C2×C8—24no—
295C2×C8—28no—
296C2×C8—48no—
297C4⋊C4—24no—
298C4⋊C4—24no—
299C4⋊C4—24no—
300C4⋊C4—28no—
301C4⋊C4—28no—
302C4⋊C4—22no—
303C4⋊C4—24no—
304C4⋊C4—24no—
305C4⋊C4—44no—
306C4⋊C4—44no—
307C4⋊C4C22×C4×C1114yes—
308C22⋊C4—28no—
309C22⋊C4—44no—
310C42—28no—
311C42—44no—
312C42C11×C22⋊C414yes—
313C42C11×C22⋊C414yes—
314C42C22×C4×C1112yes—
315C42C22×C4×C1112yes—
316C42C2×D4×C1112yes—
317C42C2×D4×C1112yes—
318C11#2188511yescharacteristic, direct product factor, Sylow
319C23—22no—
320C23—22no—
321C23C2×C11×C22⋊C412yes—
322C23C2×C11×SD1612yes—
323C23C2×C11×Q1612yes—
324C23C22×D4×C1111yescharacteristic
325Q8—28no—
326Q8—48no—
327Q8—42no—
328Q8—42no—
329C2×C4—22no—
330C2×C4—22no—
331C2×C4—22no—
332C2×C4—24no—
333C2×C4—22no—
334C2×C4—22no—
335C2×C4—24no—
336C2×C4—24no—
337C2×C4—44no—
338C2×C4—44no—
339C2×C4—44no—
340C2×C4—44no—
341C2×C4—44no—
342C2×C4—44no—
343C2×C4C11×#103116yescomplemented
344C2×C4C2×C11×C22⋊C412yes—
345C2×C4C2×C11×C22⋊C412yes—
346C2×C4C2×C11×C22⋊C412yes—
347C2×C4C2×C11×C22⋊C412yes—
348C2×C4C2×C11×C22⋊C412yes—
349C2×C4C2×C11×SD1612yes—
350C2×C4C2×C11×SD1612yes—
351C2×C4C2×C11×Q1612yes—
352C2×C4C2×C11×Q1612yes—
353C2×C4C23×C4×C1111yescharacteristic
354C2×C4C22×D4×C1111yescharacteristic
355C2×C4C11×H(5,𝔽2)12yes—
356C2×C4C11×2−1+412yes—
357C8—44no—
358C22—22no—
359C22—24no—
360C22—24no—
361C22—22no—
362C22C2×C11×#10314yes—
363C22C22×C11×C22⋊C411yescharacteristic
364C22C11×#53712yes—
365C22C22×C11×SD1611yescharacteristic
366C22C22×C11×Q1611yescharacteristic
367C22C11×#57512yes—
368C4—22no—
369C4—22no—
370C4—22no—
371C4—44no—
372C4—44no—
373C4—84no—
374C4C2×C11×#10314yes—
375C4C2×C11×#10314yes—
376C4C11×#52012yes—
377C4C11×#53511yescharacteristic
378C4C11×#53611yescharacteristic
379C2—24no—
380C2C11×#231111yescharacteristic
381C2C22×C11×#10311yescharacteristic
382C2C11×#289611yescharacteristic
383C2C11×#324612yes—
384C2C11×#324912yes—
subgroupG/H
center, socleC23×C11C22×D4
commutatorC2×C4C23×C4×C11
Frattini, cosocleC22×C4C24×C11
prime radicalC24×C11C2×D4
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C11 ◁ C22×C42×C11 ◁ G

Complements

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

NH ≅ G/Ntype
4. C11×#1987C2semidirect
5. C11×#1981C2semidirect
7. C11×#1803C2semidirect
10. C11×#533C4semidirect
77. #21885C11direct (N × H)
130. #1987C2×C11semidirect
131. #1981C2×C11semidirect
133. #1803C2×C11semidirect
158. C2×C4×C11#103semidirect
175. #533C4×C11semidirect
318. C11#21885direct (N × H)
343. C2×C4C11×#103semidirect

Maximal subgroups

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

subgroupindex
C2×C11×#5332
C22×C11×C4⋊C82
C11×#22852
C11×#19872
C11×#19812
C11×#18922
C11×#18032
#2188511