Finite Group Databasebeta

← C11×#9068 #14586261

Subgroups — C11×#9068 #14586261

Order 2816.

404 conjugacy classes of subgroups; only the 126 normal subgroups are shown.

normal subgroups only

This group has 404 conjugacy classes of subgroups — too many to draw. Only its 126 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×#3160C211yesmaximal, characteristic
2C11×#2986C211yesmaximal, characteristic
3C11×#1526C211yesmaximal, characteristic
4C11×#1485C212yesmaximal
5C11×#1278C212yesmaximal
6C11×#533C2211yescharacteristic
7C11×#533C2211yescharacteristic
8C11×#500C412yes—
9C11×#499—22no—
10C11×#498C412yes—
11C11×#446—22no—
12C8×Q8×C11—22no—
13C11×#433—22no—
14C11×#431C2212yes—
15C11×#427—22no—
16C4×C11×M16C2212yes—
17C2×C4×C8×C11C2211yescharacteristic
18C11×#330—22no—
19C11×Q8⋊C8—22no—
20C11×Q8⋊C8—22no—
21C2×C11×M16—22no—
22C22×C8×C11—21no—
23C11×C4⋊Q8C2×C412yes—
24C11×C4⋊Q8C2×C412yes—
25C11×#125—21no—
26C11×#125D412yes—
27C11×C22⋊Q8—22no—
28C11×C22⋊Q8—22no—
29C4×Q8×C11—22no—
30C4×Q8×C11—22no—
31C11×#117—21no—
32C11×#117D412yes—
33C2×C42×C11C2311yescharacteristic
34C11×#107—24no—
35C11×#106—24no—
36C11×C4⋊C8—24no—
37C11×C4⋊C8D412yes—
38C11×C4⋊C8D412yes—
39C11×C22⋊C8—22no—
40C11×#97—22no—
41C11×#97—22no—
42C4×C8×C11—22no—
43C4×C8×C11—21no—
44C4×C8×C11—22no—
45C4×C8×C11—22no—
46C4×C8×C11C2×C411yescharacteristic
47C4×C8×C11C2×C411yescharacteristic
48#9068C1111yesmaximal, characteristic, direct product factor, Sylow
49C2×Q8×C11—22no—
50C2×Q8×C11—22no—
51C22×C4×C11C2×D411yescharacteristic
52C22×C4×C11#4112yes—
53C11×M16—24no—
54C11×M16—42no—
55C2×C8×C11—24no—
56C2×C8×C11—21no—
57C2×C8×C11—21no—
58C2×C8×C11—22no—
59C2×C8×C11—22no—
60C2×C8×C11—42no—
61C11×C4⋊C4—22no—
62C11×C4⋊C4—24no—
63C11×C4⋊C4—22no—
64C11×C4⋊C4—22no—
65C11×C4⋊C4—42no—
66C11×C4⋊C4C22⋊C414yes—
67C11×C22⋊C4—22no—
68C11×C22⋊C4—41no—
69C42×C11—22no—
70C42×C11—41no—
71C42×C11C22×C411yescharacteristic
72C42×C11C2×D411yescharacteristic
73C42×C11C2×D412yes—
74#3160C2×C1111yescharacteristic
75#2986C2×C1111yescharacteristic
76#1526C2×C1111yescharacteristic
77#1485C2×C1112yes—
78#1278C2×C1112yes—
79C23×C11#12311yescharacteristic
80Q8×C11—42no—
81Q8×C11—42no—
82Q8×C11—42no—
83Q8×C11—42no—
84C2×C4×C11—22no—
85C2×C4×C11—22no—
86C2×C4×C11—22no—
87C2×C4×C11—24no—
88C2×C4×C11—42no—
89C2×C4×C11C2×C22⋊C411yescharacteristic
90C2×C4×C11C4×D412yes—
91C2×C4×C11#12011yescharacteristic
92C2×C4×C11#12112yes—
93C8×C11—22no—
94C8×C11—22no—
95C8×C11—44no—
96C8×C11—42no—
97C8×C11—42no—
98#533C22×C1111yescharacteristic
99#533C22×C1111yescharacteristic
100#500C4×C1112yes—
101#499—22no—
102#498C4×C1112yes—
103#446—22no—
104C8×Q8—22no—
105#433—22no—
106#431C22×C1112yes—
107#427—22no—
108C4×M16C22×C1112yes—
109C2×C4×C8C22×C1111yescharacteristic
110#330—22no—
111Q8⋊C8—22no—
112Q8⋊C8—22no—
113C22×C11—22no—
114C22×C11—21no—
115C22×C11#38611yescharacteristic
116C4×C11—22no—
117C4×C11—21no—
118C4×C11—44no—
119C4×C11—82no—
120C4×C11#44312yes—
121C4×C11#44412yes—
122C4×C11#45612yes—
123C2×M16—22no—
124C22×C8—21no—
125C4⋊Q8C2×C4×C1112yes—
126C4⋊Q8C2×C4×C1112yes—
127#125—21no—
128#125D4×C1112yes—
129C22⋊Q8—22no—
130C22⋊Q8—22no—
131C4×Q8—22no—
132C4×Q8—22no—
133#117—21no—
134#117D4×C1112yes—
135C2×C42C23×C1111yescharacteristic
136#107—24no—
137#106—24no—
138C4⋊C8—24no—
139C4⋊C8D4×C1112yes—
140C4⋊C8D4×C1112yes—
141C22⋊C8—22no—
142#97—22no—
143#97—22no—
144C4×C8—22no—
145C4×C8—21no—
146C4×C8—22no—
147C4×C8—22no—
148C4×C8C2×C4×C1111yescharacteristic
149C4×C8C2×C4×C1111yescharacteristic
150C2×C11—41no—
151C2×C11#187612yes—
152C2×C11#188611yescharacteristic
153C2×Q8—22no—
154C2×Q8—22no—
155C22×C4C2×D4×C1111yescharacteristic
156C22×C4C11×#4112yes—
157M16—24no—
158M16—42no—
159C2×C8—24no—
160C2×C8—21no—
161C2×C8—21no—
162C2×C8—22no—
163C2×C8—22no—
164C2×C8—42no—
165C4⋊C4—22no—
166C4⋊C4—24no—
167C4⋊C4—22no—
168C4⋊C4—22no—
169C4⋊C4—42no—
170C4⋊C4C11×C22⋊C414yes—
171C22⋊C4—22no—
172C22⋊C4—41no—
173C42—22no—
174C42—41no—
175C42C22×C4×C1111yescharacteristic
176C42C2×D4×C1111yescharacteristic
177C42C2×D4×C1112yes—
178C11#906811yescharacteristic, direct product factor, Sylow
179C23C11×#12311yescharacteristic
180Q8—42no—
181Q8—42no—
182Q8—42no—
183Q8—42no—
184C2×C4—22no—
185C2×C4—22no—
186C2×C4—22no—
187C2×C4—24no—
188C2×C4—42no—
189C2×C4C2×C11×C22⋊C411yescharacteristic
190C2×C4C4×D4×C1112yes—
191C2×C4C11×#12011yescharacteristic
192C2×C4C11×#12112yes—
193C8—22no—
194C8—22no—
195C8—44no—
196C8—42no—
197C8—42no—
198C22—22no—
199C22—21no—
200C22C11×#38611yescharacteristic
201C4—22no—
202C4—21no—
203C4—44no—
204C4—82no—
205C4C11×#44312yes—
206C4C11×#44412yes—
207C4C11×#45612yes—
208C2—41no—
209C2C11×#187612yes—
210C2C11×#188611yescharacteristic
subgroupG/H
centerC2×C4×C11#120
commutatorC42C22×C4×C11
Frattini, cosocleC2×C42C23×C11
socleC22×C11#386
prime radicalC23×C11#123
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C2×C4×C11 ◁ C2×C42×C11 ◁ G

Complements

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

NH ≅ G/Ntype
48. #9068C11direct (N × H)
178. C11#9068direct (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×#29862
C11×#15262
C11×#14852
C11×#12782
#906811