Finite Group Databasebeta

← C11×#1805 #13064643

Subgroups — C11×#1805 #13064643

Order 1408.

292 conjugacy classes of subgroups; only the 136 normal subgroups are shown.

normal subgroups only

This group has 292 conjugacy classes of subgroups — too many to draw. Only its 136 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
1C2×C4×Q8×C11C211yesmaximal, characteristic
2C2×C11×C4⋊C8C211yesmaximal, characteristic
3C2×C11×#103C212yesmaximal
4C11×#382C211yesmaximal, characteristic
5C11×#340C212yesmaximal
6C22×Q8×C11C2211yescharacteristic
7C22×C8×C11C2212yes—
8C4×Q8×C11—22no—
9C4×Q8×C11C414yescomplemented
10C2×C11×C4⋊C4—21no—
11C2×C11×C4⋊C4C2212yes—
12C2×C11×C4⋊C4C2211yescharacteristic
13C2×C42×C11—21no—
14C2×C42×C11C2211yescharacteristic
15C11×C4⋊C8—22no—
16C11×#103—24no—
17C11×#95—21no—
18C11×#95—21no—
19C2×Q8×C11—21no—
20C2×Q8×C11—21no—
21C2×Q8×C11—21no—
22C2×Q8×C11C2×C412yes—
23C2×Q8×C11D412yes—
24C2×Q8×C11Q812yes—
25C22×C4×C11—21no—
26C22×C4×C11—21no—
27C22×C4×C11—22no—
28C22×C4×C11D411yescharacteristic
29C22×C4×C11D411yescharacteristic
30C22×C4×C11C2311yescharacteristic
31C2×C8×C11—22no—
32C2×C8×C11—22no—
33C2×C8×C11—22no—
34C11×C4⋊C4—24no—
35C11×C4⋊C4—21no—
36C11×C4⋊C4—22no—
37C11×C4⋊C4—22no—
38C11×C4⋊C4C2×C412yes—
39C42×C11—24no—
40C42×C11C2×C412yes—
41C42×C11D412yes—
42#1805C1111yesmaximal, characteristic, direct product factor, Sylow
43C23×C11C2×D411yescharacteristic
44Q8×C11—22no—
45Q8×C11—22no—
46Q8×C11—22no—
47Q8×C11C4⋊C414yes—
48C2×C4×C11—22no—
49C2×C4×C11—22no—
50C2×C4×C11—22no—
51C2×C4×C11—22no—
52C2×C4×C11—22no—
53C2×C4×C11—22no—
54C2×C4×C11—42no—
55C2×C4×C11—42no—
56C2×C4×C11—42no—
57C2×C4×C11—42no—
58C2×C4×C11C22⋊C412yes—
59C2×C4×C11C22⋊C412yes—
60C2×C4×C11C22×C411yescharacteristic
61C2×C4×C11C2×D411yescharacteristic
62C2×C4×C11C2×D411yescharacteristic
63C2×C4×C11C2×Q811yescharacteristic
64C2×C4×C11#4111yescharacteristic
65C2×C4×C11#4111yescharacteristic
66C8×C11—42no—
67C2×C4×Q8C2×C1111yescharacteristic
68C2×C4⋊C8C2×C1111yescharacteristic
69C2×#103C2×C1112yes—
70#382C2×C1111yescharacteristic
71#340C2×C1112yes—
72C22×C11C2×C22⋊C411yescharacteristic
73C22×C11#12111yescharacteristic
74C22×C11C22⋊Q811yescharacteristic
75C22×C11#13512yes—
76C22×C11#13712yes—
77C4×C11—24no—
78C4×C11—22no—
79C4×C11—22no—
80C4×C11—42no—
81C4×C11—82no—
82C4×C11C2×C4⋊C411yescharacteristic
83C4×C11#11711yescharacteristic
84C4×C11#12111yescharacteristic
85C4×C11C22⋊Q811yescharacteristic
86C22×Q8C22×C1111yescharacteristic
87C22×C8C22×C1112yes—
88C4×Q8—22no—
89C4×Q8C4×C1114yescomplemented
90C2×C4⋊C4—21no—
91C2×C4⋊C4C22×C1112yes—
92C2×C4⋊C4C22×C1111yescharacteristic
93C2×C42—21no—
94C2×C42C22×C1111yescharacteristic
95C4⋊C8—22no—
96#103—24no—
97#95—21no—
98#95—21no—
99C2×C11#38011yescharacteristic
100C2×C11#41611yescharacteristic
101C2×C11#41911yescharacteristic
102C2×C11#46412yes—
103C2×C11#47912yes—
104C2×Q8—21no—
105C2×Q8—21no—
106C2×Q8—21no—
107C2×Q8C2×C4×C1112yes—
108C2×Q8D4×C1112yes—
109C2×Q8Q8×C1112yes—
110C22×C4—21no—
111C22×C4—21no—
112C22×C4—22no—
113C22×C4D4×C1111yescharacteristic
114C22×C4D4×C1111yescharacteristic
115C22×C4C23×C1111yescharacteristic
116C2×C8—22no—
117C2×C8—22no—
118C2×C8—22no—
119C4⋊C4—24no—
120C4⋊C4—21no—
121C4⋊C4—22no—
122C4⋊C4—22no—
123C4⋊C4C2×C4×C1112yes—
124C42—24no—
125C42C2×C4×C1112yes—
126C42D4×C1112yes—
127C11#180511yescharacteristic, direct product factor, Sylow
128C23C2×D4×C1111yescharacteristic
129Q8—22no—
130Q8—22no—
131Q8—22no—
132Q8C11×C4⋊C414yes—
133C2×C4—22no—
134C2×C4—22no—
135C2×C4—22no—
136C2×C4—22no—
137C2×C4—22no—
138C2×C4—22no—
139C2×C4—42no—
140C2×C4—42no—
141C2×C4—42no—
142C2×C4—42no—
143C2×C4C11×C22⋊C412yes—
144C2×C4C11×C22⋊C412yes—
145C2×C4C22×C4×C1111yescharacteristic
146C2×C4C2×D4×C1111yescharacteristic
147C2×C4C2×D4×C1111yescharacteristic
148C2×C4C2×Q8×C1111yescharacteristic
149C2×C4C11×#4111yescharacteristic
150C2×C4C11×#4111yescharacteristic
151C8—42no—
152C22C2×C11×C22⋊C411yescharacteristic
153C22C11×#12111yescharacteristic
154C22C11×C22⋊Q811yescharacteristic
155C22C11×#13512yes—
156C22C11×#13712yes—
157C4—24no—
158C4—22no—
159C4—22no—
160C4—42no—
161C4—82no—
162C4C2×C11×C4⋊C411yescharacteristic
163C4C11×#11711yescharacteristic
164C4C11×#12111yescharacteristic
165C4C11×C22⋊Q811yescharacteristic
166C2C11×#38011yescharacteristic
167C2C11×#41611yescharacteristic
168C2C11×#41911yescharacteristic
169C2C11×#46412yes—
170C2C11×#47912yes—
subgroupG/H
center, socle, prime radicalC23×C11C2×D4
commutatorC2×C4C22×C4×C11
Frattini, cosocleC22×C4C23×C11
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C11 ◁ C2×C42×C11 ◁ G

Complements

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

NH ≅ G/Ntype
9. C4×Q8×C11C4semidirect
42. #1805C11direct (N × H)
89. C4×Q8C4×C11semidirect
127. C11#1805direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C4×Q8×C112
C2×C11×C4⋊C82
C2×C11×#1032
C11×#3822
C11×#3402
#180511