Finite Group Databasebeta

← C11×#11892 #14589085

Subgroups — C11×#11892 #14589085

Order 2816.

396 conjugacy classes of subgroups; only the 122 normal subgroups are shown.

normal subgroups only

This group has 396 conjugacy classes of subgroups — too many to draw. Only its 122 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#467C211yesmaximal, characteristic
2C2×C11×C22⋊C16C211yesmaximal, characteristic
3C11×#1810C211yesmaximal, characteristic
4C11×#1350C214yesmaximal, complemented
5C22×C11×Q16C411yescharacteristic
6C23×C8×C11C2211yescharacteristic
7C2×C11×C22⋊Q8—21no—
8C22×C11×C16—21no—
9C11×#467—21no—
10C11×#467—21no—
11C11×#467C412yes—
12C11×#467C2212yes—
13C2×C11×#108—21no—
14C2×C11×#107C411yescharacteristic
15C2×C11×#103—21no—
16C11×#407—21no—
17C11×C22⋊C16—21no—
18C11×C22⋊C16C2212yes—
19C11×#341C2212yes—
20C22×Q8×C11—21no—
21C23×C4×C11D411yescharacteristic
22C2×C11×Q16—21no—
23C2×C11×Q16—42no—
24C2×C11×Q16C2×C412yes—
25C2×C11×M16—22no—
26C22×C8×C11—42no—
27C22×C8×C11C2×C411yescharacteristic
28C22×C8×C11C2×C411yescharacteristic
29C22×C8×C11D411yescharacteristic
30C22×C8×C11D411yescharacteristic
31C22×C8×C11D411yescharacteristic
32C22×C8×C11C2311yescharacteristic
33C11×C22⋊Q8—22no—
34C11×C22⋊Q8—22no—
35C11×C22⋊Q8—41no—
36C11×C22⋊Q8—41no—
37C2×C11×C4⋊C4—21no—
38C2×C11×C4⋊C4—41no—
39C2×C11×C22⋊C4—41no—
40C2×C11×C16—22no—
41C2×C11×C16—42no—
42C11×#108—42no—
43C11×#107—21no—
44C11×#107C2×C412yes—
45C11×#103—22no—
46C11×#103—22no—
47C11×C22⋊C8—41no—
48C11×C22⋊C8—41no—
49#11892C1111yesmaximal, characteristic, direct product factor, Sylow
50C24×C11SD1611yescharacteristic
51C2×Q8×C11—22no—
52C2×Q8×C11—42no—
53C2×Q8×C11—42no—
54C2×Q8×C11—41no—
55C22×C4×C11—41no—
56C22×C4×C11—41no—
57C22×C4×C11—41no—
58C22×C4×C11—41no—
59C22×C4×C11C22⋊C411yescharacteristic
60C22×C4×C11C22⋊C411yescharacteristic
61C22×C4×C11D811yescharacteristic
62C22×C4×C11D811yescharacteristic
63C22×C4×C11SD1611yescharacteristic
64C22×C4×C11C2×D411yescharacteristic
65C11×Q16—42no—
66C11×Q16—42no—
67C11×M16—42no—
68C11×M16—42no—
69C2×C8×C11—22no—
70C2×C8×C11—22no—
71C2×C8×C11—22no—
72C2×C8×C11—41no—
73C2×C8×C11—41no—
74C2×C8×C11—41no—
75C2×C8×C11—42no—
76C2×C8×C11C22⋊C411yescharacteristic
77C2×C8×C11C22⋊C411yescharacteristic
78C2×C8×C11C22×C411yescharacteristic
79C2×C8×C11C2×D411yescharacteristic
80C11×C4⋊C4—22no—
81C11×C4⋊C4—41no—
82C11×C4⋊C4—42no—
83C11×C4⋊C4—42no—
84C11×C22⋊C4—42no—
85C11×C22⋊C4—42no—
86C11×C16—42no—
87C2×#467C2×C1111yescharacteristic
88C2×C22⋊C16C2×C1111yescharacteristic
89#1810C2×C1111yescharacteristic
90#1350C2×C1114yescomplemented
91C23×C11—22no—
92C23×C11—22no—
93C23×C11—41no—
94C23×C11#10211yescharacteristic
95C23×C11#10211yescharacteristic
96C23×C11C2×SD1611yescharacteristic
97Q8×C11—42no—
98Q8×C11—42no—
99Q8×C11—82no—
100C2×C4×C11—21no—
101C2×C4×C11—21no—
102C2×C4×C11—21no—
103C2×C4×C11—21no—
104C2×C4×C11—21no—
105C2×C4×C11—21no—
106C2×C4×C11—41no—
107C2×C4×C11—41no—
108C2×C4×C11—41no—
109C2×C4×C11—42no—
110C2×C4×C11—42no—
111C2×C4×C11—82no—
112C2×C4×C11—82no—
113C2×C4×C11#10211yescharacteristic
114C2×C4×C11#10211yescharacteristic
115C2×C4×C11C2×C22⋊C411yescharacteristic
116C2×C4×C11C2×D811yescharacteristic
117C8×C11—21no—
118C8×C11—21no—
119C8×C11—21no—
120C8×C11—82no—
121C8×C11#9912yes—
122C22×Q16C4×C1111yescharacteristic
123C23×C8C22×C1111yescharacteristic
124C2×C22⋊Q8—21no—
125C22×C16—21no—
126#467—21no—
127#467—21no—
128#467C4×C1112yes—
129#467C22×C1112yes—
130C2×#108—21no—
131C2×#107C4×C1111yescharacteristic
132C2×#103—21no—
133#407—21no—
134C22⋊C16—21no—
135C22⋊C16C22×C1112yes—
136#341C22×C1112yes—
137C22×C11—21no—
138C22×C11—21no—
139C22×C11—21no—
140C22×C11—21no—
141C22×C11—21no—
142C22×C11—21no—
143C22×C11—21no—
144C22×C11—44no—
145C22×C11#35912yes—
146C22×C11#36212yes—
147C22×C11C2×#10211yescharacteristic
148C4×C11—21no—
149C4×C11—21no—
150C4×C11—21no—
151C4×C11—82no—
152C4×C11—82no—
153C4×C11C2×#9911yescharacteristic
154C4×C11#42111yescharacteristic
155C22×Q8—21no—
156C23×C4D4×C1111yescharacteristic
157C2×Q16—21no—
158C2×Q16—42no—
159C2×Q16C2×C4×C1112yes—
160C2×M16—22no—
161C22×C8—42no—
162C22×C8C2×C4×C1111yescharacteristic
163C22×C8C2×C4×C1111yescharacteristic
164C22×C8D4×C1111yescharacteristic
165C22×C8D4×C1111yescharacteristic
166C22×C8D4×C1111yescharacteristic
167C22×C8C23×C1111yescharacteristic
168C22⋊Q8—22no—
169C22⋊Q8—22no—
170C22⋊Q8—41no—
171C22⋊Q8—41no—
172C2×C4⋊C4—21no—
173C2×C4⋊C4—41no—
174C2×C22⋊C4—41no—
175C2×C16—22no—
176C2×C16—42no—
177#108—42no—
178#107—21no—
179#107C2×C4×C1112yes—
180#103—22no—
181#103—22no—
182C22⋊C8—41no—
183C22⋊C8—41no—
184C2×C11—22no—
185C2×C11—22no—
186C2×C11—41no—
187C2×C11#151911yescharacteristic
188C2×C11C2×#35911yescharacteristic
189C2×C11C2×#36211yescharacteristic
190C24C11×SD1611yescharacteristic
191C2×Q8—22no—
192C2×Q8—42no—
193C2×Q8—42no—
194C2×Q8—41no—
195C22×C4—41no—
196C22×C4—41no—
197C22×C4—41no—
198C22×C4—41no—
199C22×C4C11×C22⋊C411yescharacteristic
200C22×C4C11×C22⋊C411yescharacteristic
201C22×C4C11×D811yescharacteristic
202C22×C4C11×D811yescharacteristic
203C22×C4C11×SD1611yescharacteristic
204C22×C4C2×D4×C1111yescharacteristic
205Q16—42no—
206Q16—42no—
207M16—42no—
208M16—42no—
209C2×C8—22no—
210C2×C8—22no—
211C2×C8—22no—
212C2×C8—41no—
213C2×C8—41no—
214C2×C8—41no—
215C2×C8—42no—
216C2×C8C11×C22⋊C411yescharacteristic
217C2×C8C11×C22⋊C411yescharacteristic
218C2×C8C22×C4×C1111yescharacteristic
219C2×C8C2×D4×C1111yescharacteristic
220C4⋊C4—22no—
221C4⋊C4—41no—
222C4⋊C4—42no—
223C4⋊C4—42no—
224C22⋊C4—42no—
225C22⋊C4—42no—
226C16—42no—
227C11#1189211yescharacteristic, direct product factor, Sylow
228C23—22no—
229C23—22no—
230C23—41no—
231C23C11×#10211yescharacteristic
232C23C11×#10211yescharacteristic
233C23C2×C11×SD1611yescharacteristic
234Q8—42no—
235Q8—42no—
236Q8—82no—
237C2×C4—21no—
238C2×C4—21no—
239C2×C4—21no—
240C2×C4—21no—
241C2×C4—21no—
242C2×C4—21no—
243C2×C4—41no—
244C2×C4—41no—
245C2×C4—41no—
246C2×C4—42no—
247C2×C4—42no—
248C2×C4—82no—
249C2×C4—82no—
250C2×C4C11×#10211yescharacteristic
251C2×C4C11×#10211yescharacteristic
252C2×C4C2×C11×C22⋊C411yescharacteristic
253C2×C4C2×C11×D811yescharacteristic
254C8—21no—
255C8—21no—
256C8—21no—
257C8—82no—
258C8C11×#9912yes—
259C22—21no—
260C22—21no—
261C22—21no—
262C22—21no—
263C22—21no—
264C22—21no—
265C22—21no—
266C22—44no—
267C22C11×#35912yes—
268C22C11×#36212yes—
269C22C2×C11×#10211yescharacteristic
270C4—21no—
271C4—21no—
272C4—21no—
273C4—82no—
274C4—82no—
275C4C2×C11×#9911yescharacteristic
276C4C11×#42111yescharacteristic
277C2—22no—
278C2—22no—
279C2—41no—
280C2C11×#151911yescharacteristic
281C2C2×C11×#35911yescharacteristic
282C2C2×C11×#36211yescharacteristic
subgroupG/H
center, socleC22×C11C2×#102
commutatorC2×C8C22×C4×C11
Frattini, cosocleC22×C8C23×C11
prime radicalC24×C11SD16
LCSG ▷ C2×C8 ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C11 ◁ C23×C4×C11 ◁ C23×C8×C11 ◁ G

Complements

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

NH ≅ G/Ntype
4. C11×#1350C2semidirect
49. #11892C11direct (N × H)
90. #1350C2×C11semidirect
227. C11#11892direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#4672
C2×C11×C22⋊C162
C11×#18102
C11×#13502
#1189211