Finite Group Databasebeta

← C11×#23170 #14600363

Subgroups — C11×#23170 #14600363

Order 2816.

638 conjugacy classes of subgroups.

The subgroup lattice has 322 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#3160C211yesmaximal, characteristic
2C11×#2962C212yesmaximal
3C11×#1986C212yesmaximal
4C11×#1945C212yesmaximal
5C11×#1922C214yesmaximal
6C4×C11×#108C211yesmaximal, characteristic
7C11×#1772C212yesmaximal
8C8×C11×C4⋊C4C211yesmaximal, characteristic
9C11×#533C2212yes—
10C11×#500C411yescharacteristic, complemented
11C11×#500C411yescharacteristic, complemented
12C11×#499C412yescomplemented
13C11×#499C412yescomplemented
14C11×#498C412yescomplemented
15C11×#446—24no—
16C11×#446—22no—
17C8×Q8×C11—22no—
18C2×C11×#108C2211yescharacteristic
19C2×C11×#108C2211yescharacteristic
20C11×#427C2212yes—
21C11×#427C2212yes—
22C11×#424C2214yes—
23C2×C11×C4⋊C8C2211yescharacteristic
24C11×#405C2214yes—
25C4×C11×M16C2212yes—
26C2×C4×C8×C11C2212yes—
27C2×C4×C8×C11C2211yescharacteristic
28C4×C11×C4⋊C4C2211yescharacteristic
29C11×#341C2212yes—
30C11×#339C2214yes—
31C11×#339C2214yes—
32C11×#336C2212yes—
33C2×C11×M16C2312yes—
34C2×C11×M16C2312yes—
35C22×C8×C11C2311yescharacteristic
36C22×C8×C11C2312yes—
37C22×C8×C11C2311yescharacteristic
38C11×C4⋊Q8C2×C412yes—
39C11×C4⋊Q8C2×C412yes—
40C11×#125C2×C414yes—
41C11×C22⋊Q8—22no—
42C11×C22⋊Q8—22no—
43C4×Q8×C11—22no—
44C4×Q8×C11—22no—
45C11×#117C2314yes—
46C2×C11×C4⋊C4—21no—
47C2×C42×C11C2312yes—
48C2×C42×C11C2311yescharacteristic
49C11×#108—22no—
50C11×#108Q814yescomplemented
51C11×#107C2×C412yes—
52C11×#107C2×C412yes—
53C11×#107C2×C412yes—
54C11×#107C2×C412yes—
55C11×#106C2×C414yes—
56C11×#106C2×C414yes—
57C11×C4⋊C8—24no—
58C11×C4⋊C8—24no—
59C11×C4⋊C8D411yescharacteristic
60C11×C4⋊C8D411yescharacteristic
61C11×C4⋊C8D412yes—
62C11×#97—24no—
63C11×#97—22no—
64C4×C8×C11—24no—
65C4×C8×C11—24no—
66C4×C8×C11—22no—
67C4×C8×C11C2×C411yescharacteristic
68C4×C8×C11C2×C411yescharacteristic
69C4×C8×C11C2×C411yescharacteristic
70C4×C8×C11C2×C411yescharacteristic
71C11×#95—21no—
72#23170C1111yesmaximal, characteristic, direct product factor, Sylow
73C2×Q8×C11—22no—
74C2×Q8×C11—22no—
75C22×C4×C11—22no—
76C22×C4×C11#4111yescharacteristic
77C22×C4×C11#4111yescharacteristic
78C22×C4×C11C2411yescharacteristic
79C11×M16—22no—
80C11×M16—22no—
81C11×M16—22no—
82C11×M16C2×Q814yes—
83C2×C8×C11—22no—
84C2×C8×C11—22no—
85C2×C8×C11—22no—
86C2×C8×C11—21no—
87C2×C8×C11—22no—
88C2×C8×C11—21no—
89C2×C8×C11C22×C411yescharacteristic
90C2×C8×C11C22×C411yescharacteristic
91C2×C8×C11C22×C411yescharacteristic
92C2×C8×C11C22×C411yescharacteristic
93C2×C8×C11C2×D412yes—
94C2×C8×C11C2×D412yes—
95C2×C8×C11C2×Q812yes—
96C2×C8×C11#4112yes—
97C11×C4⋊C4—24no—
98C11×C4⋊C4—24no—
99C11×C4⋊C4—24no—
100C11×C4⋊C4—22no—
101C11×C4⋊C4—22no—
102C11×C4⋊C4C22×C414yes—
103C11×C4⋊C4C22×C414yes—
104C11×C22⋊C4—24no—
105C42×C11—24no—
106C42×C11—22no—
107C42×C11—22no—
108C42×C11C22×C411yescharacteristic
109C42×C11C22×C411yescharacteristic
110C42×C11C2×D411yescharacteristic
111C42×C11C2×D411yescharacteristic
112#3160C2×C1111yescharacteristic
113#2962C2×C1112yes—
114#1986C2×C1112yes—
115#1945C2×C1112yes—
116#1922C2×C1114yes—
117C4×#108C2×C1111yescharacteristic
118#1772C2×C1112yes—
119C8×C4⋊C4C2×C1111yescharacteristic
120C23×C11C2×#4111yescharacteristic
121Q8×C11—44no—
122Q8×C11—82no—
123C2×C4×C11—22no—
124C2×C4×C11—24no—
125C2×C4×C11—24no—
126C2×C4×C11—24no—
127C2×C4×C11—41no—
128C2×C4×C11—42no—
129C2×C4×C11—42no—
130C2×C4×C11C4×D411yescharacteristic
131C2×C4×C11C4×D411yescharacteristic
132C2×C4×C11C4×D411yescharacteristic
133C2×C4×C11C4×D411yescharacteristic
134C2×C4×C11C23×C411yescharacteristic
135C2×C4×C11C22×D411yescharacteristic
136C2×C4×C11C22×Q811yescharacteristic
137C2×C4×C11C2×#4111yescharacteristic
138C2×C4×C112−1+411yescharacteristic
139C2×C4×C112−1+411yescharacteristic
140C8×C11—21no—
141C8×C11—21no—
142C8×C11—22no—
143C8×C11—22no—
144C8×C11—24no—
145C8×C11—42no—
146C8×C11C4×Q812yes—
147C8×C11C4×Q812yes—
148#533C22×C1112yes—
149#500C4×C1111yescharacteristic, complemented
150#500C4×C1111yescharacteristic, complemented
151#499C4×C1112yescomplemented
152#499C4×C1112yescomplemented
153#498C4×C1112yescomplemented
154#446—24no—
155#446—22no—
156C8×Q8—22no—
157C2×#108C22×C1111yescharacteristic
158C2×#108C22×C1111yescharacteristic
159#427C22×C1112yes—
160#427C22×C1112yes—
161#424C22×C1114yes—
162C2×C4⋊C8C22×C1111yescharacteristic
163#405C22×C1114yes—
164C4×M16C22×C1112yes—
165C2×C4×C8C22×C1112yes—
166C2×C4×C8C22×C1111yescharacteristic
167C4×C4⋊C4C22×C1111yescharacteristic
168#341C22×C1112yes—
169#339C22×C1114yes—
170#339C22×C1114yes—
171#336C22×C1112yes—
172C22×C11—21no—
173C22×C11—21no—
174C22×C11C2×C4×D411yescharacteristic
175C22×C11#55611yescharacteristic
176C22×C11#55711yescharacteristic
177C4×C11—21no—
178C4×C11—21no—
179C4×C11—21no—
180C4×C11—44no—
181C4×C11—44no—
182C4×C11—44no—
183C4×C11#44312yes—
184C4×C11C2×C4×Q811yescharacteristic
185C4×C11#51911yescharacteristic
186C4×C11#54711yescharacteristic
187C4×C11D4×Q811yescharacteristic
188C2×M16C23×C1112yes—
189C2×M16C23×C1112yes—
190C22×C8C23×C1111yescharacteristic
191C22×C8C23×C1112yes—
192C22×C8C23×C1111yescharacteristic
193C4⋊Q8C2×C4×C1112yes—
194C4⋊Q8C2×C4×C1112yes—
195#125C2×C4×C1114yes—
196C22⋊Q8—22no—
197C22⋊Q8—22no—
198C4×Q8—22no—
199C4×Q8—22no—
200#117C23×C1114yes—
201C2×C4⋊C4—21no—
202C2×C42C23×C1112yes—
203C2×C42C23×C1111yescharacteristic
204#108—22no—
205#108Q8×C1114yescomplemented
206#107C2×C4×C1112yes—
207#107C2×C4×C1112yes—
208#107C2×C4×C1112yes—
209#107C2×C4×C1112yes—
210#106C2×C4×C1114yes—
211#106C2×C4×C1114yes—
212C4⋊C8—24no—
213C4⋊C8—24no—
214C4⋊C8D4×C1111yescharacteristic
215C4⋊C8D4×C1111yescharacteristic
216C4⋊C8D4×C1112yes—
217#97—24no—
218#97—22no—
219C4×C8—24no—
220C4×C8—24no—
221C4×C8—22no—
222C4×C8C2×C4×C1111yescharacteristic
223C4×C8C2×C4×C1111yescharacteristic
224C4×C8C2×C4×C1111yescharacteristic
225C4×C8C2×C4×C1111yescharacteristic
226#95—21no—
227C2×C11—21no—
228C2×C11—21no—
229C2×C11#236511yescharacteristic
230C2×C11C2×#44311yescharacteristic
231C2×C11#295711yescharacteristic
232C2×Q8—22no—
233C2×Q8—22no—
234C22×C4—22no—
235C22×C4C11×#4111yescharacteristic
236C22×C4C11×#4111yescharacteristic
237C22×C4C24×C1111yescharacteristic
238M16—22no—
239M16—22no—
240M16—22no—
241M16C2×Q8×C1114yes—
242C2×C8—22no—
243C2×C8—22no—
244C2×C8—21no—
245C2×C8—21no—
246C2×C8—22no—
247C2×C8—22no—
248C2×C8C22×C4×C1111yescharacteristic
249C2×C8C22×C4×C1111yescharacteristic
250C2×C8C22×C4×C1111yescharacteristic
251C2×C8C22×C4×C1111yescharacteristic
252C2×C8C2×D4×C1112yes—
253C2×C8C2×D4×C1112yes—
254C2×C8C2×Q8×C1112yes—
255C2×C8C11×#4112yes—
256C4⋊C4—24no—
257C4⋊C4—24no—
258C4⋊C4—24no—
259C4⋊C4—22no—
260C4⋊C4—22no—
261C4⋊C4C22×C4×C1114yes—
262C4⋊C4C22×C4×C1114yes—
263C22⋊C4—24no—
264C42—24no—
265C42—22no—
266C42—22no—
267C42C22×C4×C1111yescharacteristic
268C42C22×C4×C1111yescharacteristic
269C42C2×D4×C1111yescharacteristic
270C42C2×D4×C1111yescharacteristic
271C11#2317011yescharacteristic, direct product factor, Sylow
272C23C2×C11×#4111yescharacteristic
273Q8—44no—
274Q8—82no—
275C2×C4—22no—
276C2×C4—24no—
277C2×C4—24no—
278C2×C4—24no—
279C2×C4—41no—
280C2×C4—42no—
281C2×C4—42no—
282C2×C4C4×D4×C1111yescharacteristic
283C2×C4C4×D4×C1111yescharacteristic
284C2×C4C4×D4×C1111yescharacteristic
285C2×C4C4×D4×C1111yescharacteristic
286C2×C4C23×C4×C1111yescharacteristic
287C2×C4C22×D4×C1111yescharacteristic
288C2×C4C22×Q8×C1111yescharacteristic
289C2×C4C2×C11×#4111yescharacteristic
290C2×C4C11×2−1+411yescharacteristic
291C2×C4C11×2−1+411yescharacteristic
292C8—21no—
293C8—21no—
294C8—22no—
295C8—22no—
296C8—24no—
297C8—42no—
298C8C4×Q8×C1112yes—
299C8C4×Q8×C1112yes—
300C22—21no—
301C22—21no—
302C22C2×C4×D4×C1111yescharacteristic
303C22C11×#55611yescharacteristic
304C22C11×#55711yescharacteristic
305C4—21no—
306C4—21no—
307C4—21no—
308C4—44no—
309C4—44no—
310C4—44no—
311C4C11×#44312yes—
312C4C2×C4×Q8×C1111yescharacteristic
313C4C11×#51911yescharacteristic
314C4C11×#54711yescharacteristic
315C4D4×Q8×C1111yescharacteristic
316C2—21no—
317C2—21no—
318C2C11×#236511yescharacteristic
319C2C2×C11×#44311yescharacteristic
320C2C11×#295711yescharacteristic
subgroupG/H
centerC2×C4×C11C22×D4
commutatorC2×C4C23×C4×C11
Frattini, cosocleC22×C4C24×C11
socleC22×C11C2×C4×D4
prime radicalC23×C11C2×#41
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C2×C4×C11 ◁ C2×C11×C4⋊C8 ◁ G

Complements

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

NH ≅ G/Ntype
10. C11×#500C4semidirect
11. C11×#500C4semidirect
12. C11×#499C4semidirect
13. C11×#499C4semidirect
14. C11×#498C4semidirect
50. C11×#108Q8semidirect
72. #23170C11direct (N × H)
149. #500C4×C11semidirect
150. #500C4×C11semidirect
151. #499C4×C11semidirect
152. #499C4×C11semidirect
153. #498C4×C11semidirect
205. #108Q8×C11semidirect
271. C11#23170direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#31602
C11×#29622
C11×#19862
C11×#19452
C11×#19222
C4×C11×#1082
C11×#17722
C8×C11×C4⋊C42
#2317011