Finite Group Databasebeta

← C11×#2031 #13064869

Subgroups — C11×#2031 #13064869

Order 1408.

244 conjugacy classes of subgroups; only the 80 normal subgroups are shown.

normal subgroups only

This group has 244 conjugacy classes of subgroups — too many to draw. Only its 80 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×#533C211yesmaximal, characteristic, complemented
2C11×#421C211yesmaximal, characteristic
3C2×C11×#104C211yesmaximal, characteristic
4C11×#410C211yesmaximal, characteristic
5C11×#344C211yesmaximal, characteristic, complemented
6C11×#339C211yesmaximal, characteristic, complemented
7C11×H(3,ℤ/4)C211yesmaximal, characteristic, complemented
8C2×C11×#41C2211yescharacteristic
9C2×C11×M16C2211yescharacteristic
10C2×C11×M16C2211yescharacteristic
11C11×C4⋊Q8—21no—
12C11×#125—21no—
13C11×C22⋊Q8—22no—
14C4×Q8×C11—22no—
15C11×#117C2211yescharacteristic
16C11×#117C2211yescharacteristic
17C11×#117C2211yescharacteristic
18C2×C42×C11C2211yescharacteristic
19C11×#104—21no—
20C11×#104—21no—
21C11×#104—22no—
22C11×#99—22no—
23C11×#41—21no—
24C11×#41—21no—
25C11×#41—21no—
26C11×#41—21no—
27C2×Q8×C11—22no—
28C2×Q8×C11Q811yescharacteristic, complemented
29C2×D4×C11—21no—
30C2×D4×C11Q811yescharacteristic, complemented
31C22×C4×C11—21no—
32C22×C4×C11—21no—
33C22×C4×C11C2311yescharacteristic
34C11×M16—21no—
35C11×M16—21no—
36C11×M16—21no—
37C11×M16—21no—
38C2×C8×C11—21no—
39C2×C8×C11—21no—
40C11×C4⋊C4—24no—
41C11×C4⋊C4—22no—
42C11×C4⋊C4—21no—
43C11×C4⋊C4—21no—
44C11×C4⋊C4—21no—
45C11×C22⋊C4—21no—
46C11×C22⋊C4—21no—
47C11×C22⋊C4D412yes—
48C42×C11—21no—
49C42×C11—21no—
50C42×C11—21no—
51C42×C11D411yescharacteristic
52C42×C11D411yescharacteristic
53C42×C11D412yes—
54#2031C1111yesmaximal, characteristic, direct product factor, Sylow
55C23×C11—21no—
56C23×C11C2×D411yescharacteristic
57Q8×C11—21no—
58Q8×C11—21no—
59Q8×C11—44no—
60D4×C11—21no—
61D4×C11—21no—
62D4×C11—41no—
63D4×C11—41no—
64C2×C4×C11—21no—
65C2×C4×C11—21no—
66C2×C4×C11—22no—
67C2×C4×C11—22no—
68C2×C4×C11—21no—
69C2×C4×C11—42no—
70C2×C4×C11—41no—
71C2×C4×C11—41no—
72C2×C4×C11—41no—
73C2×C4×C11C2×D411yescharacteristic
74C2×C4×C11C2×D411yescharacteristic
75C2×C4×C11C2×Q811yescharacteristic
76C2×C4×C11#4111yescharacteristic
77C2×C4×C11#4111yescharacteristic
78C2×C4×C11#4111yescharacteristic
79C8×C11—41no—
80C8×C11—41no—
81#533C2×C1111yescharacteristic, complemented
82#421C2×C1111yescharacteristic
83C2×#104C2×C1111yescharacteristic
84#410C2×C1111yescharacteristic
85#344C2×C1111yescharacteristic, complemented
86#339C2×C1111yescharacteristic, complemented
87H(3,ℤ/4)C2×C1111yescharacteristic, complemented
88C22×C11—41no—
89C22×C11—41no—
90C22×C11—81no—
91C22×C11#12011yescharacteristic
92C22×C11C22⋊Q811yescharacteristic
93C22×C11#12411yescharacteristic
94C4×C11—22no—
95C4×C11—41no—
96C4×C11—42no—
97C4×C11—42no—
98C4×C11—41no—
99C4×C11—81no—
100C4×C11C22⋊Q811yescharacteristic
101C4×C11C22⋊Q811yescharacteristic
102C4×C11#12411yescharacteristic
103C4×C11#12411yescharacteristic
104C2×#41C22×C1111yescharacteristic
105C2×M16C22×C1111yescharacteristic
106C2×M16C22×C1111yescharacteristic
107C4⋊Q8—21no—
108#125—21no—
109C22⋊Q8—22no—
110C4×Q8—22no—
111#117C22×C1111yescharacteristic
112#117C22×C1111yescharacteristic
113#117C22×C1111yescharacteristic
114C2×C42C22×C1111yescharacteristic
115#104—21no—
116#104—21no—
117#104—22no—
118#99—22no—
119C2×C11—21no—
120C2×C11—21no—
121C2×C11—21no—
122C2×C11—81no—
123C2×C11#39311yescharacteristic
124#41—21no—
125#41—21no—
126#41—21no—
127#41—21no—
128C2×Q8—22no—
129C2×Q8Q8×C1111yescharacteristic, complemented
130C2×D4—21no—
131C2×D4Q8×C1111yescharacteristic, complemented
132C22×C4—21no—
133C22×C4—21no—
134C22×C4C23×C1111yescharacteristic
135M16—21no—
136M16—21no—
137M16—21no—
138M16—21no—
139C2×C8—21no—
140C2×C8—21no—
141C4⋊C4—24no—
142C4⋊C4—22no—
143C4⋊C4—21no—
144C4⋊C4—21no—
145C4⋊C4—21no—
146C22⋊C4—21no—
147C22⋊C4—21no—
148C22⋊C4D4×C1112yes—
149C42—21no—
150C42—21no—
151C42—21no—
152C42D4×C1111yescharacteristic
153C42D4×C1111yescharacteristic
154C42D4×C1112yes—
155C11#203111yescharacteristic, direct product factor, Sylow
156C23—21no—
157C23C2×D4×C1111yescharacteristic
158Q8—21no—
159Q8—21no—
160Q8—44no—
161D4—21no—
162D4—21no—
163D4—41no—
164D4—41no—
165C2×C4—21no—
166C2×C4—21no—
167C2×C4—22no—
168C2×C4—22no—
169C2×C4—21no—
170C2×C4—42no—
171C2×C4—41no—
172C2×C4—41no—
173C2×C4—41no—
174C2×C4C2×D4×C1111yescharacteristic
175C2×C4C2×D4×C1111yescharacteristic
176C2×C4C2×Q8×C1111yescharacteristic
177C2×C4C11×#4111yescharacteristic
178C2×C4C11×#4111yescharacteristic
179C2×C4C11×#4111yescharacteristic
180C8—41no—
181C8—41no—
182C22—41no—
183C22—41no—
184C22—81no—
185C22C11×#12011yescharacteristic
186C22C11×C22⋊Q811yescharacteristic
187C22C11×#12411yescharacteristic
188C4—22no—
189C4—41no—
190C4—42no—
191C4—42no—
192C4—41no—
193C4—81no—
194C4C11×C22⋊Q811yescharacteristic
195C4C11×C22⋊Q811yescharacteristic
196C4C11×#12411yescharacteristic
197C4C11×#12411yescharacteristic
198C2—21no—
199C2—21no—
200C2—21no—
201C2—81no—
202C2C11×#39311yescharacteristic
subgroupG/H
centerC4×C11#124
commutator, Frattini, cosocleC22×C4C23×C11
socleC2×C11#393
prime radicalC2×C11×#41C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C4×C11 ◁ C22×C4×C11 ◁ G

Complements

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

NH ≅ G/Ntype
1. C11×#533C2semidirect
5. C11×#344C2semidirect
6. C11×#339C2semidirect
7. C11×H(3,ℤ/4)C2semidirect
28. C2×Q8×C11Q8semidirect
30. C2×D4×C11Q8semidirect
54. #2031C11direct (N × H)
81. #533C2×C11semidirect
85. #344C2×C11semidirect
86. #339C2×C11semidirect
87. H(3,ℤ/4)C2×C11semidirect
129. C2×Q8Q8×C11semidirect
131. C2×D4Q8×C11semidirect
155. C11#2031direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#5332
C11×#4212
C2×C11×#1042
C11×#4102
C11×#3442
C11×#3392
C11×H(3,ℤ/4)2
#203111