Finite Group Databasebeta

← C11×#21836 #14599029

Subgroups — C11×#21836 #14599029

Order 2816.

1042 conjugacy classes of subgroups.

The subgroup lattice has 344 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C11×#125C211yesmaximal, characteristic
2C2×C11×#431C211yesmaximal, characteristic
3C11×#2283C211yesmaximal, characteristic
4C11×#1991C214yesmaximal, complemented
5C11×#1989C214yesmaximal, complemented
6C11×#1824C212yesmaximal
7C11×#1823C212yesmaximal
8C2×C11×#125—21no—
9C2×C11×#125—21no—
10C2×C11×#125—24no—
11C2×C11×#125C418yescomplemented
12C2×C11×#125C2212yes—
13C2×C11×#125C2212yes—
14C22×C11×C4⋊C4—21no—
15C22×C11×C4⋊C4—21no—
16C22×C11×C4⋊C4C2211yescharacteristic
17C22×C11×C4⋊C4C2211yescharacteristic
18C22×C42×C11C2211yescharacteristic
19C11×#431—24no—
20C2×C11×C4⋊C8C2212yes—
21C2×C11×C22⋊C8C2212yes—
22C2×C4×C8×C11C2212yes—
23C11×#383—21no—
24C11×#382C2212yes—
25C11×#381—21no—
26C11×#380C2212yes—
27C4×C11×C4⋊C4C2212yes—
28C4×C11×C22⋊C4—21no—
29C11×#376—21no—
30C11×#340C2218yes—
31C11×#340C2218yes—
32C23×C4×C11—21no—
33C23×C4×C11—21no—
34C23×C4×C11D411yescharacteristic
35C23×C4×C11D411yescharacteristic
36C23×C4×C11C2311yescharacteristic
37C22×C8×C11C2314yes—
38C11×#125—28no—
39C11×#125—28no—
40C11×#125—24no—
41C11×#125—24no—
42C11×#125C2×C418yes—
43C11×#125C2×C418yes—
44C2×C11×C4⋊C4—28no—
45C2×C11×C4⋊C4—28no—
46C2×C11×C4⋊C4—22no—
47C2×C11×C4⋊C4—22no—
48C2×C11×C4⋊C4—22no—
49C2×C11×C4⋊C4—22no—
50C2×C11×C4⋊C4—21no—
51C2×C11×C4⋊C4—21no—
52C2×C11×C4⋊C4—22no—
53C2×C11×C4⋊C4—22no—
54C2×C11×C4⋊C4C2×C414yes—
55C2×C11×C4⋊C4C2×C414yes—
56C2×C11×C4⋊C4C2314yes—
57C2×C11×C4⋊C4C2312yes—
58C2×C11×C4⋊C4C2312yes—
59C2×C11×C22⋊C4—22no—
60C2×C42×C11—22no—
61C2×C42×C11C2×C414yes—
62C2×C42×C11D411yescharacteristic
63C2×C42×C11D411yescharacteristic
64C2×C42×C11D414yes—
65C2×C42×C11C2311yescharacteristic
66C2×C42×C11C2311yescharacteristic
67C11×C4⋊C8—24no—
68C11×C22⋊C8—24no—
69C4×C8×C11—24no—
70C11×#95—22no—
71C11×#95—22no—
72C11×#95—22no—
73C11×#95—22no—
74#21836C1111yesmaximal, characteristic, direct product factor, Sylow
75C24×C11C2×D411yescharacteristic
76C22×C4×C11—24no—
77C22×C4×C11—24no—
78C22×C4×C11—24no—
79C22×C4×C11—24no—
80C22×C4×C11—22no—
81C22×C4×C11—22no—
82C22×C4×C11—24no—
83C22×C4×C11—42no—
84C22×C4×C11—44no—
85C22×C4×C11—44no—
86C22×C4×C11C22⋊C414yes—
87C22×C4×C11C22⋊C414yes—
88C22×C4×C11C22×C412yes—
89C22×C4×C11C2×D411yescharacteristic
90C22×C4×C11C2×D411yescharacteristic
91C22×C4×C11C2×D411yescharacteristic
92C22×C4×C11C2×D411yescharacteristic
93C22×C4×C11C2×D411yescharacteristic
94C22×C4×C11C2×D412yes—
95C22×C4×C11C2411yescharacteristic
96C2×C8×C11—24no—
97C2×C8×C11—28no—
98C11×C4⋊C4—28no—
99C11×C4⋊C4—28no—
100C11×C4⋊C4—28no—
101C11×C4⋊C4—28no—
102C11×C4⋊C4—24no—
103C11×C4⋊C4—24no—
104C11×C4⋊C4—22no—
105C11×C4⋊C4—22no—
106C11×C4⋊C4—28no—
107C11×C4⋊C4C22×C414yes—
108C11×C4⋊C4C22×C414yes—
109C11×C22⋊C4—44no—
110C42×C11—44no—
111C42×C11C22⋊C414yes—
112C42×C11C22⋊C414yes—
113C42×C11C22×C412yes—
114C42×C11C22×C412yes—
115C42×C11C2×D412yes—
116C42×C11C2×D412yes—
117C22×#125C2×C1111yescharacteristic
118C2×#431C2×C1111yescharacteristic
119#2283C2×C1111yescharacteristic
120#1991C2×C1114yescomplemented
121#1989C2×C1114yescomplemented
122#1824C2×C1112yes—
123#1823C2×C1112yes—
124C23×C11—22no—
125C23×C11—22no—
126C23×C11C2×C22⋊C412yes—
127C23×C11#13514yes—
128C23×C11C22×D411yescharacteristic
129C2×C4×C11—22no—
130C2×C4×C11—22no—
131C2×C4×C11—22no—
132C2×C4×C11—22no—
133C2×C4×C11—22no—
134C2×C4×C11—28no—
135C2×C4×C11—24no—
136C2×C4×C11—24no—
137C2×C4×C11—24no—
138C2×C4×C11—24no—
139C2×C4×C11—44no—
140C2×C4×C11—48no—
141C2×C4×C11—44no—
142C2×C4×C11—44no—
143C2×C4×C11—48no—
144C2×C4×C11—44no—
145C2×C4×C11—44no—
146C2×C4×C11—44no—
147C2×C4×C11C2×C22⋊C412yes—
148C2×C4×C11C2×C22⋊C412yes—
149C2×C4×C11C2×C22⋊C412yes—
150C2×C4×C11C2×C22⋊C412yes—
151C2×C4×C11C2×C22⋊C412yes—
152C2×C4×C11C23×C411yescharacteristic
153C2×C4×C11C22×D411yescharacteristic
154C2×C4×C112−1+414yes—
155C8×C11—44no—
156C2×#125—21no—
157C2×#125—21no—
158C2×#125—24no—
159C2×#125C4×C1118yescomplemented
160C2×#125C22×C1112yes—
161C2×#125C22×C1112yes—
162C22×C4⋊C4—21no—
163C22×C4⋊C4—21no—
164C22×C4⋊C4C22×C1111yescharacteristic
165C22×C4⋊C4C22×C1111yescharacteristic
166C22×C42C22×C1111yescharacteristic
167#431—24no—
168C2×C4⋊C8C22×C1112yes—
169C2×C22⋊C8C22×C1112yes—
170C2×C4×C8C22×C1112yes—
171#383—21no—
172#382C22×C1112yes—
173#381—21no—
174#380C22×C1112yes—
175C4×C4⋊C4C22×C1112yes—
176C4×C22⋊C4—21no—
177#376—21no—
178#340C22×C1118yes—
179#340C22×C1118yes—
180C22×C11—22no—
181C22×C11—22no—
182C22×C11—28no—
183C22×C11#41614yes—
184C22×C11C22×C22⋊C411yescharacteristic
185C22×C11#53612yes—
186C22×C11C2×#13512yes—
187C22×C11#57512yes—
188C4×C11—22no—
189C4×C11—22no—
190C4×C11—22no—
191C4×C11—22no—
192C4×C11—22no—
193C4×C11—44no—
194C4×C11—44no—
195C4×C11—84no—
196C4×C11#51912yes—
197C4×C11#53612yes—
198C23×C4—21no—
199C23×C4—21no—
200C23×C4D4×C1111yescharacteristic
201C23×C4D4×C1111yescharacteristic
202C23×C4C23×C1111yescharacteristic
203C22×C8C23×C1114yes—
204#125—28no—
205#125—28no—
206#125—24no—
207#125—24no—
208#125C2×C4×C1118yes—
209#125C2×C4×C1118yes—
210C2×C4⋊C4—28no—
211C2×C4⋊C4—28no—
212C2×C4⋊C4—22no—
213C2×C4⋊C4—22no—
214C2×C4⋊C4—22no—
215C2×C4⋊C4—22no—
216C2×C4⋊C4—21no—
217C2×C4⋊C4—21no—
218C2×C4⋊C4—22no—
219C2×C4⋊C4—22no—
220C2×C4⋊C4C2×C4×C1114yes—
221C2×C4⋊C4C2×C4×C1114yes—
222C2×C4⋊C4C23×C1114yes—
223C2×C4⋊C4C23×C1112yes—
224C2×C4⋊C4C23×C1112yes—
225C2×C22⋊C4—22no—
226C2×C42—22no—
227C2×C42C2×C4×C1114yes—
228C2×C42D4×C1111yescharacteristic
229C2×C42D4×C1111yescharacteristic
230C2×C42D4×C1114yes—
231C2×C42C23×C1111yescharacteristic
232C2×C42C23×C1111yescharacteristic
233C4⋊C8—24no—
234C22⋊C8—24no—
235C4×C8—24no—
236#95—22no—
237#95—22no—
238#95—22no—
239#95—22no—
240C2×C11—24no—
241C2×C11#231011yescharacteristic
242C2×C11C2×#41611yescharacteristic
243C2×C11#289611yescharacteristic
244C2×C11#323214yes—
245C24C2×D4×C1111yescharacteristic
246C22×C4—24no—
247C22×C4—24no—
248C22×C4—24no—
249C22×C4—24no—
250C22×C4—22no—
251C22×C4—22no—
252C22×C4—24no—
253C22×C4—42no—
254C22×C4—44no—
255C22×C4—44no—
256C22×C4C11×C22⋊C414yes—
257C22×C4C11×C22⋊C414yes—
258C22×C4C22×C4×C1112yes—
259C22×C4C2×D4×C1111yescharacteristic
260C22×C4C2×D4×C1111yescharacteristic
261C22×C4C2×D4×C1111yescharacteristic
262C22×C4C2×D4×C1111yescharacteristic
263C22×C4C2×D4×C1111yescharacteristic
264C22×C4C2×D4×C1112yes—
265C22×C4C24×C1111yescharacteristic
266C2×C8—24no—
267C2×C8—28no—
268C4⋊C4—28no—
269C4⋊C4—28no—
270C4⋊C4—28no—
271C4⋊C4—28no—
272C4⋊C4—24no—
273C4⋊C4—24no—
274C4⋊C4—22no—
275C4⋊C4—22no—
276C4⋊C4—28no—
277C4⋊C4C22×C4×C1114yes—
278C4⋊C4C22×C4×C1114yes—
279C22⋊C4—44no—
280C42—44no—
281C42C11×C22⋊C414yes—
282C42C11×C22⋊C414yes—
283C42C22×C4×C1112yes—
284C42C22×C4×C1112yes—
285C42C2×D4×C1112yes—
286C42C2×D4×C1112yes—
287C11#2183611yescharacteristic, direct product factor, Sylow
288C23—22no—
289C23—22no—
290C23C2×C11×C22⋊C412yes—
291C23C11×#13514yes—
292C23C22×D4×C1111yescharacteristic
293C2×C4—22no—
294C2×C4—28no—
295C2×C4—22no—
296C2×C4—22no—
297C2×C4—22no—
298C2×C4—22no—
299C2×C4—24no—
300C2×C4—24no—
301C2×C4—24no—
302C2×C4—24no—
303C2×C4—44no—
304C2×C4—48no—
305C2×C4—48no—
306C2×C4—44no—
307C2×C4—44no—
308C2×C4—44no—
309C2×C4—44no—
310C2×C4—44no—
311C2×C4C2×C11×C22⋊C412yes—
312C2×C4C2×C11×C22⋊C412yes—
313C2×C4C2×C11×C22⋊C412yes—
314C2×C4C2×C11×C22⋊C412yes—
315C2×C4C2×C11×C22⋊C412yes—
316C2×C4C23×C4×C1111yescharacteristic
317C2×C4C22×D4×C1111yescharacteristic
318C2×C4C11×2−1+414yes—
319C8—44no—
320C22—22no—
321C22—28no—
322C22—22no—
323C22C11×#41614yes—
324C22C22×C11×C22⋊C411yescharacteristic
325C22C11×#53612yes—
326C22C2×C11×#13512yes—
327C22C11×#57512yes—
328C4—22no—
329C4—22no—
330C4—22no—
331C4—22no—
332C4—22no—
333C4—44no—
334C4—44no—
335C4—84no—
336C4C11×#51912yes—
337C4C11×#53612yes—
338C2—24no—
339C2C11×#231011yescharacteristic
340C2C2×C11×#41611yescharacteristic
341C2C11×#289611yescharacteristic
342C2C11×#323214yes—
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×#1991C2semidirect
5. C11×#1989C2semidirect
11. C2×C11×#125C4semidirect
74. #21836C11direct (N × H)
120. #1991C2×C11semidirect
121. #1989C2×C11semidirect
159. C2×#125C4×C11semidirect
287. C11#21836direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C11×#1252
C2×C11×#4312
C11×#22832
C11×#19912
C11×#19892
C11×#18242
C11×#18232
#2183611