Finite Group Databasebeta

← C11×#9070 #14586263

Subgroups — C11×#9070 #14586263

Order 2816.

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

normal subgroups only

This group has 426 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×#3131C211yesmaximal, characteristic
2C11×#2986C211yesmaximal, characteristic, complemented
3C11×#1526C211yesmaximal, characteristic, complemented
4C11×#1484C212yesmaximal
5C11×#1278C212yesmaximal, complemented
6C11×#533C2211yescharacteristic
7C11×#532C2211yescharacteristic
8C11×#488—22no—
9C11×#487C412yes—
10C11×#486C412yes—
11C11×#446—22no—
12C8×Q8×C11—22no—
13C11×#433—22no—
14C11×#431C2212yes—
15C11×#416—22no—
16C4×C11×M16C2212yes—
17C2×C4×C8×C11C2211yescharacteristic
18C11×#330—22no—
19C11×D4⋊C8—22no—
20C11×D4⋊C8—22no—
21C2×C11×#41—21no—
22C2×C11×M16—22no—
23C22×C8×C11—21no—
24C11×C4⋊Q8C2×C411yescharacteristic
25C11×C4⋊Q8C2×C412yes—
26C11×#127C2×C411yescharacteristic
27C11×#125D412yes—
28C11×#124—21no—
29C11×C22⋊Q8—22no—
30C11×#121—22no—
31C4×Q8×C11—22no—
32C4×D4×C11—22no—
33C11×#117D412yes—
34C2×C42×C11C2311yescharacteristic
35C11×C4⋊C8—24no—
36C11×C4⋊C8D412yes—
37C11×C4⋊C8D412yes—
38C11×#103—24no—
39C11×#102—24no—
40C11×C22⋊C8—22no—
41C11×#97—22no—
42C11×#97—22no—
43C4×C8×C11—22no—
44C4×C8×C11—21no—
45C4×C8×C11—22no—
46C4×C8×C11—22no—
47C4×C8×C11C2×C412yes—
48#9070C1111yesmaximal, characteristic, direct product factor, Sylow
49C11×#41—44no—
50C2×Q8×C11—22no—
51C2×Q8×C11—21no—
52C2×D4×C11—21no—
53C2×D4×C11—22no—
54C2×D4×C11—41no—
55C22×C4×C11—41no—
56C22×C4×C11C2×D411yescharacteristic
57C22×C4×C11#4112yes—
58C11×M16—24no—
59C11×M16—42no—
60C2×C8×C11—22no—
61C2×C8×C11—22no—
62C2×C8×C11—22no—
63C2×C8×C11—42no—
64C2×C8×C11—42no—
65C11×C4⋊C4—22no—
66C11×C4⋊C4—24no—
67C11×C4⋊C4—22no—
68C11×C4⋊C4C22⋊C414yes—
69C11×C22⋊C4—22no—
70C11×C22⋊C4—42no—
71C42×C11—22no—
72C42×C11C22×C411yescharacteristic
73C42×C11C2×D411yescharacteristic
74C42×C11C2×D412yes—
75#3131C2×C1111yescharacteristic
76#2986C2×C1111yescharacteristic, complemented
77#1526C2×C1111yescharacteristic, complemented
78#1484C2×C1112yes—
79#1278C2×C1112yescomplemented
80C23×C11—41no—
81C23×C11#12311yescharacteristic
82Q8×C11—42no—
83Q8×C11—42no—
84Q8×C11—42no—
85D4×C11—42no—
86D4×C11—42no—
87D4×C11—42no—
88D4×C11—82no—
89C2×C4×C11—22no—
90C2×C4×C11—22no—
91C2×C4×C11—22no—
92C2×C4×C11—24no—
93C2×C4×C11—41no—
94C2×C4×C11—82no—
95C2×C4×C11C2×C22⋊C411yescharacteristic
96C2×C4×C11C4×D412yes—
97C2×C4×C11#12011yescharacteristic
98C2×C4×C11#12112yes—
99C8×C11—42no—
100C8×C11—44no—
101C8×C11—42no—
102C8×C11—42no—
103#533C22×C1111yescharacteristic
104#532C22×C1111yescharacteristic
105#488—22no—
106#487C4×C1112yes—
107#486C4×C1112yes—
108#446—22no—
109C8×Q8—22no—
110#433—22no—
111#431C22×C1112yes—
112#416—22no—
113C4×M16C22×C1112yes—
114C2×C4×C8C22×C1111yescharacteristic
115#330—22no—
116D4⋊C8—22no—
117D4⋊C8—22no—
118C22×C11—22no—
119C22×C11—21no—
120C22×C11—82no—
121C22×C11—81no—
122C22×C11#38611yescharacteristic
123C4×C11—22no—
124C4×C11—21no—
125C4×C11—44no—
126C4×C11—81no—
127C4×C11#44312yes—
128C4×C11#44412yes—
129C4×C11#45412yes—
130C2×#41—21no—
131C2×M16—22no—
132C22×C8—21no—
133C4⋊Q8C2×C4×C1111yescharacteristic
134C4⋊Q8C2×C4×C1112yes—
135#127C2×C4×C1111yescharacteristic
136#125D4×C1112yes—
137#124—21no—
138C22⋊Q8—22no—
139#121—22no—
140C4×Q8—22no—
141C4×D4—22no—
142#117D4×C1112yes—
143C2×C42C23×C1111yescharacteristic
144C4⋊C8—24no—
145C4⋊C8D4×C1112yes—
146C4⋊C8D4×C1112yes—
147#103—24no—
148#102—24no—
149C22⋊C8—22no—
150#97—22no—
151#97—22no—
152C4×C8—22no—
153C4×C8—21no—
154C4×C8—22no—
155C4×C8—22no—
156C4×C8C2×C4×C1112yes—
157C2×C11—41no—
158C2×C11—161no—
159C2×C11#187612yes—
160C2×C11#188811yescharacteristic
161#41—44no—
162C2×Q8—22no—
163C2×Q8—21no—
164C2×D4—21no—
165C2×D4—22no—
166C2×D4—41no—
167C22×C4—41no—
168C22×C4C2×D4×C1111yescharacteristic
169C22×C4C11×#4112yes—
170M16—24no—
171M16—42no—
172C2×C8—22no—
173C2×C8—22no—
174C2×C8—22no—
175C2×C8—42no—
176C2×C8—42no—
177C4⋊C4—22no—
178C4⋊C4—24no—
179C4⋊C4—22no—
180C4⋊C4C11×C22⋊C414yes—
181C22⋊C4—22no—
182C22⋊C4—42no—
183C42—22no—
184C42C22×C4×C1111yescharacteristic
185C42C2×D4×C1111yescharacteristic
186C42C2×D4×C1112yes—
187C11#907011yescharacteristic, direct product factor, Sylow
188C23—41no—
189C23C11×#12311yescharacteristic
190Q8—42no—
191Q8—42no—
192Q8—42no—
193D4—42no—
194D4—42no—
195D4—42no—
196D4—82no—
197C2×C4—22no—
198C2×C4—22no—
199C2×C4—22no—
200C2×C4—24no—
201C2×C4—41no—
202C2×C4—82no—
203C2×C4C2×C11×C22⋊C411yescharacteristic
204C2×C4C4×D4×C1112yes—
205C2×C4C11×#12011yescharacteristic
206C2×C4C11×#12112yes—
207C8—42no—
208C8—44no—
209C8—42no—
210C8—42no—
211C22—22no—
212C22—21no—
213C22—82no—
214C22—81no—
215C22C11×#38611yescharacteristic
216C4—22no—
217C4—21no—
218C4—44no—
219C4—81no—
220C4C11×#44312yes—
221C4C11×#44412yes—
222C4C11×#45412yes—
223C2—41no—
224C2—161no—
225C2C11×#187612yes—
226C2C11×#188811yescharacteristic
subgroupG/H
centerC2×C4×C11#120
commutatorC42C22×C4×C11
Frattini, cosocleC2×C42C23×C11
socleC22×C11#386
prime radicalC11×#532C22
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
2. C11×#2986C2semidirect
3. C11×#1526C2semidirect
5. C11×#1278C2semidirect
48. #9070C11direct (N × H)
76. #2986C2×C11semidirect
77. #1526C2×C11semidirect
79. #1278C2×C11semidirect
187. C11#9070direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#31312
C11×#29862
C11×#15262
C11×#14842
C11×#12782
#907011