Finite Group Databasebeta

← C11×#1517 #13064355

Subgroups — C11×#1517 #13064355

Order 1408.

264 conjugacy classes of subgroups; only the 104 normal subgroups are shown.

normal subgroups only

This group has 264 conjugacy classes of subgroups — too many to draw. Only its 104 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×#532C211yesmaximal, characteristic
2C11×#431C211yesmaximal, characteristic, complemented
3C11×#382C211yesmaximal, characteristic, complemented
4C11×#327C214yesmaximal, complemented
5C2×C11×#41—21no—
6C11×C4⋊Q8C411yescharacteristic, complemented
7C11×#127C411yescharacteristic, complemented
8C11×#124—21no—
9C11×#121—21no—
10C11×#121C2212yes—
11C4×D4×C11—21no—
12C4×D4×C11C412yescomplemented
13C2×C11×C4⋊C4—21no—
14C2×C42×C11C2211yescharacteristic
15C11×C4⋊C8—21no—
16C11×C22⋊C8C2212yes—
17C4×C8×C11—21no—
18C11×#95—21no—
19C11×#95C2212yes—
20C11×#41—42no—
21C11×#41—42no—
22C2×Q8×C11—21no—
23C2×D4×C11—22no—
24C2×D4×C11—21no—
25C2×D4×C11—21no—
26C2×D4×C11C2×C412yes—
27C22×C4×C11—22no—
28C22×C4×C11—22no—
29C22×C4×C11D411yescharacteristic
30C22×C4×C11D411yescharacteristic
31C22×C4×C11C2311yescharacteristic
32C2×C8×C11—22no—
33C11×C4⋊C4—21no—
34C11×C4⋊C4—42no—
35C11×C4⋊C4C2×C412yes—
36C11×C22⋊C4—22no—
37C11×C22⋊C4—22no—
38C42×C11C2×C411yescharacteristic
39C42×C11C2×C411yescharacteristic
40C42×C11D411yescharacteristic
41C42×C11D411yescharacteristic
42#1517C1111yesmaximal, characteristic, direct product factor, Sylow
43C23×C11—22no—
44C23×C11C2×D411yescharacteristic
45Q8×C11—42no—
46D4×C11—42no—
47D4×C11—42no—
48D4×C11—42no—
49D4×C11—42no—
50D4×C11—42no—
51C2×C4×C11—22no—
52C2×C4×C11—41no—
53C2×C4×C11—41no—
54C2×C4×C11—44no—
55C2×C4×C11—42no—
56C2×C4×C11—42no—
57C2×C4×C11—42no—
58C2×C4×C11C22⋊C411yescharacteristic
59C2×C4×C11C22⋊C411yescharacteristic
60C2×C4×C11C22⋊C411yescharacteristic
61C2×C4×C11C22⋊C411yescharacteristic
62C2×C4×C11D812yes—
63C2×C4×C11SD1612yes—
64C2×C4×C11C22×C411yescharacteristic
65C2×C4×C11C2×D411yescharacteristic
66C8×C11—42no—
67#532C2×C1111yescharacteristic
68#431C2×C1111yescharacteristic, complemented
69#382C2×C1111yescharacteristic, complemented
70#327C2×C1114yescomplemented
71C22×C11—21no—
72C22×C11—21no—
73C22×C11—42no—
74C22×C11—42no—
75C22×C11—42no—
76C22×C11C2×C22⋊C411yescharacteristic
77C22×C11C2×D811yescharacteristic
78C22×C11C2×SD1611yescharacteristic
79C4×C11—21no—
80C4×C11—21no—
81C4×C11—21no—
82C4×C11—21no—
83C4×C11—42no—
84C4×C11—82no—
85C4×C11#10212yes—
86C4×C11#10212yes—
87C2×#41—21no—
88C4⋊Q8C4×C1111yescharacteristic, complemented
89#127C4×C1111yescharacteristic, complemented
90#124—21no—
91#121—21no—
92#121C22×C1112yes—
93C4×D4—21no—
94C4×D4C4×C1112yescomplemented
95C2×C4⋊C4—21no—
96C2×C42C22×C1111yescharacteristic
97C4⋊C8—21no—
98C22⋊C8C22×C1112yes—
99C4×C8—21no—
100#95—21no—
101#95C22×C1112yes—
102C2×C11—21no—
103C2×C11—21no—
104C2×C11—82no—
105C2×C11#41011yescharacteristic
106C2×C11C2×#10211yescharacteristic
107C2×C11#42111yescharacteristic
108#41—42no—
109#41—42no—
110C2×Q8—21no—
111C2×D4—22no—
112C2×D4—21no—
113C2×D4—21no—
114C2×D4C2×C4×C1112yes—
115C22×C4—22no—
116C22×C4—22no—
117C22×C4D4×C1111yescharacteristic
118C22×C4D4×C1111yescharacteristic
119C22×C4C23×C1111yescharacteristic
120C2×C8—22no—
121C4⋊C4—21no—
122C4⋊C4—42no—
123C4⋊C4C2×C4×C1112yes—
124C22⋊C4—22no—
125C22⋊C4—22no—
126C42C2×C4×C1111yescharacteristic
127C42C2×C4×C1111yescharacteristic
128C42D4×C1111yescharacteristic
129C42D4×C1111yescharacteristic
130C11#151711yescharacteristic, direct product factor, Sylow
131C23—22no—
132C23C2×D4×C1111yescharacteristic
133Q8—42no—
134D4—42no—
135D4—42no—
136D4—42no—
137D4—42no—
138D4—42no—
139C2×C4—22no—
140C2×C4—41no—
141C2×C4—41no—
142C2×C4—44no—
143C2×C4—42no—
144C2×C4—42no—
145C2×C4—42no—
146C2×C4C11×C22⋊C411yescharacteristic
147C2×C4C11×C22⋊C411yescharacteristic
148C2×C4C11×C22⋊C411yescharacteristic
149C2×C4C11×C22⋊C411yescharacteristic
150C2×C4C11×D812yes—
151C2×C4C11×SD1612yes—
152C2×C4C22×C4×C1111yescharacteristic
153C2×C4C2×D4×C1111yescharacteristic
154C8—42no—
155C22—21no—
156C22—21no—
157C22—42no—
158C22—42no—
159C22—42no—
160C22C2×C11×C22⋊C411yescharacteristic
161C22C2×C11×D811yescharacteristic
162C22C2×C11×SD1611yescharacteristic
163C4—21no—
164C4—21no—
165C4—21no—
166C4—21no—
167C4—42no—
168C4—82no—
169C4C11×#10212yes—
170C4C11×#10212yes—
171C2—21no—
172C2—21no—
173C2—82no—
174C2C11×#41011yescharacteristic
175C2C2×C11×#10211yescharacteristic
176C2C11×#42111yescharacteristic
subgroupG/H
center, socleC22×C11C2×C22⋊C4
commutatorC2×C4C22×C4×C11
Frattini, cosocleC22×C4C23×C11
prime radicalC11×#532C2
LCSG ▷ C2×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C11 ◁ C2×C42×C11 ◁ G

Complements

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

NH ≅ G/Ntype
2. C11×#431C2semidirect
3. C11×#382C2semidirect
4. C11×#327C2semidirect
6. C11×C4⋊Q8C4semidirect
7. C11×#127C4semidirect
12. C4×D4×C11C4semidirect
42. #1517C11direct (N × H)
68. #431C2×C11semidirect
69. #382C2×C11semidirect
70. #327C2×C11semidirect
88. C4⋊Q8C4×C11semidirect
89. #127C4×C11semidirect
94. C4×D4C4×C11semidirect
130. C11#1517direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#5322
C11×#4312
C11×#3822
C11×#3272
#151711