Finite Group Databasebeta

← C11×#8928 #14586121

Subgroups — C11×#8928 #14586121

Order 2816.

476 conjugacy classes of subgroups.

The subgroup lattice has 238 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#2369C211yesmaximal, characteristic
2C11×#1956C211yesmaximal, characteristic
3C11×#1948C212yesmaximal
4C2×C11×#333C211yesmaximal, characteristic
5C11×#1279C212yesmaximal
6C2×C11×C4⋊Q8C2211yescharacteristic
7C2×C11×#106—22no—
8C2×C11×C4⋊C8C2212yes—
9C2×C11×#103—22no—
10C2×C4×C8×C11C2211yescharacteristic
11C11×#391—22no—
12C11×#389—22no—
13C11×#384C2211yescharacteristic
14C4×C11×C4⋊C4—22no—
15C4×C11×C4⋊C4C2212yes—
16C11×#340—22no—
17C11×#333C414yescomplemented
18C22×Q8×C11D412yes—
19C22×C8×C11—22no—
20C22×C8×C11—21no—
21C11×C4⋊Q8—22no—
22C11×C4⋊Q8C2×C412yes—
23C11×C4⋊Q8Q812yes—
24C2×C11×C4⋊C4—22no—
25C2×C11×C4⋊C4—22no—
26C2×C11×C4⋊C4—21no—
27C2×C11×C4⋊C4—22no—
28C2×C11×C4⋊C4D412yes—
29C2×C11×C4⋊C4D412yes—
30C2×C42×C11—22no—
31C2×C42×C11—22no—
32C2×C42×C11C2311yescharacteristic
33C11×#106—44no—
34C11×C4⋊C8—22no—
35C11×C4⋊C8C2×C414yes—
36C11×#103—44no—
37C4×C8×C11—22no—
38C11×#95—24no—
39C11×#95—22no—
40#8928C1111yesmaximal, characteristic, direct product factor, Sylow
41C2×Q8×C11—22no—
42C2×Q8×C11—42no—
43C2×Q8×C11—42no—
44C2×Q8×C11C4⋊C414yes—
45C22×C4×C11—22no—
46C22×C4×C11—22no—
47C22×C4×C11—22no—
48C22×C4×C11—41no—
49C22×C4×C11C2×D411yescharacteristic
50C22×C4×C11C2×D412yes—
51C2×C8×C11—22no—
52C2×C8×C11—24no—
53C2×C8×C11—41no—
54C2×C8×C11—41no—
55C2×C8×C11—42no—
56C2×C8×C11—42no—
57C11×C4⋊C4—24no—
58C11×C4⋊C4—24no—
59C11×C4⋊C4—22no—
60C11×C4⋊C4—22no—
61C11×C4⋊C4—22no—
62C11×C4⋊C4—42no—
63C11×C4⋊C4—42no—
64C11×C4⋊C4—42no—
65C11×C4⋊C4—82no—
66C11×C4⋊C4SD1614yes—
67C42×C11—42no—
68C42×C11—42no—
69C42×C11—82no—
70C42×C11C22×C411yescharacteristic
71C42×C11C2×Q811yescharacteristic
72C42×C11#4112yes—
73#2369C2×C1111yescharacteristic
74#1956C2×C1111yescharacteristic
75#1948C2×C1112yes—
76C2×#333C2×C1111yescharacteristic
77#1279C2×C1112yes—
78C23×C11#12011yescharacteristic
79Q8×C11—44no—
80Q8×C11—82no—
81C2×C4×C11—21no—
82C2×C4×C11—21no—
83C2×C4×C11—24no—
84C2×C4×C11—24no—
85C2×C4×C11—42no—
86C2×C4×C11—42no—
87C2×C4×C11—42no—
88C2×C4×C11—42no—
89C2×C4×C11—42no—
90C2×C4×C11—42no—
91C2×C4×C11—42no—
92C2×C4×C11—82no—
93C2×C4×C11—81no—
94C2×C4×C11C2×C4⋊C411yescharacteristic
95C2×C4×C11C4×D412yes—
96C2×C4×C11C22⋊Q812yes—
97C2×C4×C11#12311yescharacteristic
98C2×C4×C11C2×SD1612yes—
99C2×C4×C11#13512yes—
100C2×C4×C11#13712yes—
101C2×C4×C11#13712yes—
102C8×C11—42no—
103C8×C11—44no—
104C2×C4⋊Q8C22×C1111yescharacteristic
105C2×#106—22no—
106C2×C4⋊C8C22×C1112yes—
107C2×#103—22no—
108C2×C4×C8C22×C1111yescharacteristic
109#391—22no—
110#389—22no—
111#384C22×C1111yescharacteristic
112C4×C4⋊C4—22no—
113C4×C4⋊C4C22×C1112yes—
114#340—22no—
115#333C4×C1114yescomplemented
116C22×C11#38511yescharacteristic
117C22×C11#44812yes—
118C22×C11#45212yes—
119C22×C11#45311yescharacteristic
120C22×C11#45511yescharacteristic
121C4×C11—21no—
122C4×C11—21no—
123C4×C11—44no—
124C4×C11—44no—
125C4×C11—82no—
126C4×C11—161no—
127C4×C11C4×SD1612yes—
128C4×C11#44112yes—
129C4×C11#47512yes—
130C4×C11#47912yes—
131C22×Q8D4×C1112yes—
132C22×C8—22no—
133C22×C8—21no—
134C4⋊Q8—22no—
135C4⋊Q8C2×C4×C1112yes—
136C4⋊Q8Q8×C1112yes—
137C2×C4⋊C4—22no—
138C2×C4⋊C4—22no—
139C2×C4⋊C4—21no—
140C2×C4⋊C4—22no—
141C2×C4⋊C4D4×C1112yes—
142C2×C4⋊C4D4×C1112yes—
143C2×C42—22no—
144C2×C42—22no—
145C2×C42C23×C1111yescharacteristic
146#106—44no—
147C4⋊C8—22no—
148C4⋊C8C2×C4×C1114yes—
149#103—44no—
150C4×C8—22no—
151#95—24no—
152#95—22no—
153C2×C11#162311yescharacteristic
154C2×C11#163411yescharacteristic
155C2×C11#164312yes—
156C2×C11#185611yescharacteristic
157C2×C11#186512yes—
158C2×Q8—22no—
159C2×Q8—42no—
160C2×Q8—42no—
161C2×Q8C11×C4⋊C414yes—
162C22×C4—22no—
163C22×C4—22no—
164C22×C4—22no—
165C22×C4—41no—
166C22×C4C2×D4×C1111yescharacteristic
167C22×C4C2×D4×C1112yes—
168C2×C8—22no—
169C2×C8—24no—
170C2×C8—41no—
171C2×C8—41no—
172C2×C8—42no—
173C2×C8—42no—
174C4⋊C4—24no—
175C4⋊C4—24no—
176C4⋊C4—22no—
177C4⋊C4—22no—
178C4⋊C4—22no—
179C4⋊C4—42no—
180C4⋊C4—42no—
181C4⋊C4—42no—
182C4⋊C4—82no—
183C4⋊C4C11×SD1614yes—
184C42—42no—
185C42—42no—
186C42—82no—
187C42C22×C4×C1111yescharacteristic
188C42C2×Q8×C1111yescharacteristic
189C42C11×#4112yes—
190C11#892811yescharacteristic, direct product factor, Sylow
191C23C11×#12011yescharacteristic
192Q8—44no—
193Q8—82no—
194C2×C4—21no—
195C2×C4—21no—
196C2×C4—24no—
197C2×C4—24no—
198C2×C4—42no—
199C2×C4—42no—
200C2×C4—42no—
201C2×C4—42no—
202C2×C4—42no—
203C2×C4—42no—
204C2×C4—42no—
205C2×C4—82no—
206C2×C4—81no—
207C2×C4C2×C11×C4⋊C411yescharacteristic
208C2×C4C4×D4×C1112yes—
209C2×C4C11×C22⋊Q812yes—
210C2×C4C11×#12311yescharacteristic
211C2×C4C2×C11×SD1612yes—
212C2×C4C11×#13512yes—
213C2×C4C11×#13712yes—
214C2×C4C11×#13712yes—
215C8—42no—
216C8—44no—
217C22C11×#38511yescharacteristic
218C22C11×#44812yes—
219C22C11×#45212yes—
220C22C11×#45311yescharacteristic
221C22C11×#45511yescharacteristic
222C4—21no—
223C4—21no—
224C4—44no—
225C4—44no—
226C4—82no—
227C4—161no—
228C4C4×C11×SD1612yes—
229C4C11×#44112yes—
230C4C11×#47512yes—
231C4C11×#47912yes—
232C2C11×#162311yescharacteristic
233C2C11×#163411yescharacteristic
234C2C11×#164312yes—
235C2C11×#185611yescharacteristic
236C2C11×#186512yes—
subgroupG/H
center, socle, prime radicalC23×C11#120
commutatorC42C22×C4×C11
Frattini, cosocleC2×C42C23×C11
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C23×C11 ◁ C2×C42×C11 ◁ G

Complements

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

NH ≅ G/Ntype
17. C11×#333C4semidirect
40. #8928C11direct (N × H)
115. #333C4×C11semidirect
190. C11#8928direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#23692
C11×#19562
C11×#19482
C2×C11×#3332
C11×#12792
#892811