Finite Group Databasebeta

← C11×#10437 #14587630

Subgroups — C11×#10437 #14587630

Order 2816.

478 conjugacy classes of subgroups; only the 146 normal subgroups are shown.

normal subgroups only

This group has 478 conjugacy classes of subgroups — too many to draw. Only its 146 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
1C11×#2582C211yesmaximal, characteristic
2C11×#1844C211yesmaximal, characteristic
3C11×#1803C212yesmaximal
4C2×C11×Q8⋊C8C212yesmaximal
5C11×#1296C211yesmaximal, characteristic
6C2×C4×Q8×C11C2212yes—
7C2×C11×#106—22no—
8C2×C11×C4⋊C8C2212yes—
9C2×C11×#103—22no—
10C2×C4×C8×C11C2211yescharacteristic
11C11×#398—22no—
12C11×#391—22no—
13C11×#389—22no—
14C11×#384C2211yescharacteristic
15C11×#384C2211yescharacteristic
16C11×#340—22no—
17C11×Q8⋊C8—24no—
18C22×Q8×C11D412yes—
19C22×C8×C11—21no—
20C22×C8×C11—22no—
21C4×Q8×C11—22no—
22C4×Q8×C11—22no—
23C4×Q8×C11—22no—
24C4×Q8×C11—22no—
25C2×C11×C4⋊C4—22no—
26C2×C11×C4⋊C4—22no—
27C2×C11×C4⋊C4—22no—
28C2×C11×C4⋊C4—21no—
29C2×C11×C4⋊C4—22no—
30C2×C11×C4⋊C4D412yes—
31C2×C11×C4⋊C4D412yes—
32C2×C42×C11—22no—
33C2×C42×C11C2311yescharacteristic
34C11×#106—44no—
35C11×C4⋊C8—22no—
36C11×C4⋊C8—22no—
37C11×#103—44no—
38C4×C8×C11—21no—
39C4×C8×C11D412yes—
40C11×#95—24no—
41C11×#95—22no—
42#10437C1111yesmaximal, characteristic, direct product factor, Sylow
43C2×Q8×C11—22no—
44C2×Q8×C11—22no—
45C2×Q8×C11—22no—
46C2×Q8×C11—22no—
47C2×Q8×C11—22no—
48C2×Q8×C11SD1614yes—
49C22×C4×C11—22no—
50C22×C4×C11—22no—
51C22×C4×C11—22no—
52C22×C4×C11—41no—
53C22×C4×C11C2×D411yescharacteristic
54C22×C4×C11C2×D412yes—
55C2×C8×C11—22no—
56C2×C8×C11—22no—
57C2×C8×C11—22no—
58C2×C8×C11—42no—
59C2×C8×C11—42no—
60C2×C8×C11—42no—
61C11×C4⋊C4—22no—
62C11×C4⋊C4—22no—
63C11×C4⋊C4—42no—
64C11×C4⋊C4—42no—
65C11×C4⋊C4—42no—
66C11×C4⋊C4—42no—
67C11×C4⋊C4—42no—
68C11×C4⋊C4—42no—
69C11×C4⋊C4—42no—
70C11×C4⋊C4—42no—
71C11×C4⋊C4—82no—
72C42×C11—42no—
73C42×C11—42no—
74C42×C11C2×D411yescharacteristic
75C42×C11#4111yescharacteristic
76C42×C11#4112yes—
77#2582C2×C1111yescharacteristic
78#1844C2×C1111yescharacteristic
79#1803C2×C1112yes—
80C2×Q8⋊C8C2×C1112yes—
81#1296C2×C1111yescharacteristic
82C23×C11#12011yescharacteristic
83Q8×C11—24no—
84Q8×C11—24no—
85Q8×C11—42no—
86Q8×C11—42no—
87C2×C4×C11—21no—
88C2×C4×C11—21no—
89C2×C4×C11—24no—
90C2×C4×C11—42no—
91C2×C4×C11—42no—
92C2×C4×C11—42no—
93C2×C4×C11—44no—
94C2×C4×C11—42no—
95C2×C4×C11—42no—
96C2×C4×C11—42no—
97C2×C4×C11—82no—
98C2×C4×C11—81no—
99C2×C4×C11#12111yescharacteristic
100C2×C4×C11#12112yes—
101C2×C4×C11#12312yes—
102C2×C4×C11#12411yescharacteristic
103C2×C4×C11C2×SD1612yes—
104C2×C4×C11#13512yes—
105C2×C4×C11#13712yes—
106C2×C4×C11#13712yes—
107C8×C11—24no—
108C8×C11—82no—
109C2×C4×Q8C22×C1112yes—
110C2×#106—22no—
111C2×C4⋊C8C22×C1112yes—
112C2×#103—22no—
113C2×C4×C8C22×C1111yescharacteristic
114#398—22no—
115#391—22no—
116#389—22no—
117#384C22×C1111yescharacteristic
118#384C22×C1111yescharacteristic
119#340—22no—
120Q8⋊C8—24no—
121C22×C11#39411yescharacteristic
122C22×C11#44812yes—
123C22×C11#45212yes—
124C22×C11#45311yescharacteristic
125C22×C11#45611yescharacteristic
126C4×C11—21no—
127C4×C11—21no—
128C4×C11—44no—
129C4×C11—82no—
130C4×C11—82no—
131C4×C11—161no—
132C4×C11#46512yes—
133C4×C11#47012yes—
134C4×C11#48312yes—
135C4×C11#48512yes—
136C22×Q8D4×C1112yes—
137C22×C8—21no—
138C22×C8—22no—
139C4×Q8—22no—
140C4×Q8—22no—
141C4×Q8—22no—
142C4×Q8—22no—
143C2×C4⋊C4—22no—
144C2×C4⋊C4—22no—
145C2×C4⋊C4—22no—
146C2×C4⋊C4—21no—
147C2×C4⋊C4—22no—
148C2×C4⋊C4D4×C1112yes—
149C2×C4⋊C4D4×C1112yes—
150C2×C42—22no—
151C2×C42C23×C1111yescharacteristic
152#106—44no—
153C4⋊C8—22no—
154C4⋊C8—22no—
155#103—44no—
156C4×C8—21no—
157C4×C8D4×C1112yes—
158#95—24no—
159#95—22no—
160C2×C11#162311yescharacteristic
161C2×C11#163011yescharacteristic
162C2×C11#165312yes—
163C2×C11#203512yes—
164C2×C11#203911yescharacteristic
165C2×Q8—22no—
166C2×Q8—22no—
167C2×Q8—22no—
168C2×Q8—22no—
169C2×Q8—22no—
170C2×Q8C11×SD1614yes—
171C22×C4—22no—
172C22×C4—22no—
173C22×C4—22no—
174C22×C4—41no—
175C22×C4C2×D4×C1111yescharacteristic
176C22×C4C2×D4×C1112yes—
177C2×C8—22no—
178C2×C8—22no—
179C2×C8—22no—
180C2×C8—42no—
181C2×C8—42no—
182C2×C8—42no—
183C4⋊C4—22no—
184C4⋊C4—22no—
185C4⋊C4—42no—
186C4⋊C4—42no—
187C4⋊C4—42no—
188C4⋊C4—42no—
189C4⋊C4—42no—
190C4⋊C4—42no—
191C4⋊C4—42no—
192C4⋊C4—42no—
193C4⋊C4—82no—
194C42—42no—
195C42—42no—
196C42C2×D4×C1111yescharacteristic
197C42C11×#4111yescharacteristic
198C42C11×#4112yes—
199C11#1043711yescharacteristic, direct product factor, Sylow
200C23C11×#12011yescharacteristic
201Q8—24no—
202Q8—24no—
203Q8—42no—
204Q8—42no—
205C2×C4—21no—
206C2×C4—21no—
207C2×C4—24no—
208C2×C4—42no—
209C2×C4—42no—
210C2×C4—42no—
211C2×C4—44no—
212C2×C4—42no—
213C2×C4—42no—
214C2×C4—42no—
215C2×C4—82no—
216C2×C4—81no—
217C2×C4C11×#12111yescharacteristic
218C2×C4C11×#12112yes—
219C2×C4C11×#12312yes—
220C2×C4C11×#12411yescharacteristic
221C2×C4C2×C11×SD1612yes—
222C2×C4C11×#13512yes—
223C2×C4C11×#13712yes—
224C2×C4C11×#13712yes—
225C8—24no—
226C8—82no—
227C22C11×#39411yescharacteristic
228C22C11×#44812yes—
229C22C11×#45212yes—
230C22C11×#45311yescharacteristic
231C22C11×#45611yescharacteristic
232C4—21no—
233C4—21no—
234C4—44no—
235C4—82no—
236C4—82no—
237C4—161no—
238C4C11×#46512yes—
239C4C11×#47012yes—
240C4C11×#48312yes—
241C4C11×#48512yes—
242C2C11×#162311yescharacteristic
243C2C11×#163011yescharacteristic
244C2C11×#165312yes—
245C2C11×#203512yes—
246C2C11×#203911yescharacteristic
subgroupG/H
center, socle, prime radicalC23×C11#120
commutator, Frattini, cosocleC2×C42C23×C11
LCSG ▷ C2×C42 ▷ C22 ▷ C1
UCSC1 ◁ C23×C11 ◁ C2×C42×C11 ◁ G

Complements

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

NH ≅ G/Ntype
42. #10437C11direct (N × H)
199. C11#10437direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#25822
C11×#18442
C11×#18032
C2×C11×Q8⋊C82
C11×#12962
#1043711