Finite Group Databasebeta

← C11×#1646 #13064484

Subgroups — C11×#1646 #13064484

Order 1408.

212 conjugacy classes of subgroups; only the 68 normal subgroups are shown.

normal subgroups only

This group has 212 conjugacy classes of subgroups — too many to draw. Only its 68 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×#555C211yesmaximal, characteristic
2C11×#487C211yesmaximal, characteristic, complemented
3C11×#474C211yesmaximal, characteristic, complemented
4C11×#461C211yesmaximal, characteristic, complemented
5C11×#333C211yesmaximal, characteristic, complemented
6C11×D4⋊C8C211yesmaximal, characteristic, complemented
7C11×D4⋊C8C211yesmaximal, characteristic, complemented
8C2×C11×SD16—21no—
9C11×C4⋊Q8C2211yescharacteristic
10C11×C4⋊Q8C2211yescharacteristic
11C11×#124—22no—
12C11×#121—21no—
13C11×#121—21no—
14C4×D4×C11C2211yescharacteristic
15C4×D4×C11C2211yescharacteristic
16C11×#117—21no—
17C11×#117—21no—
18C11×#107—21no—
19C11×C4⋊C8C2211yescharacteristic
20C11×C4⋊C8C2211yescharacteristic
21C11×#103—22no—
22C11×#103—21no—
23C11×#102—21no—
24C4×C8×C11C2211yescharacteristic
25C2×Q8×C11—21no—
26C2×Q8×C11D412yes—
27C2×D4×C11—22no—
28C2×D4×C11D411yescharacteristic
29C2×D4×C11D411yescharacteristic
30C22×C4×C11—21no—
31C22×C4×C11—21no—
32C11×SD16—42no—
33C2×C8×C11—21no—
34C2×C8×C11—21no—
35C2×C8×C11—21no—
36C11×C4⋊C4—21no—
37C11×C4⋊C4—21no—
38C11×C4⋊C4—21no—
39C11×C4⋊C4—21no—
40C11×C4⋊C4D411yescharacteristic
41C11×C4⋊C4D411yescharacteristic
42C11×C22⋊C4—22no—
43C11×C22⋊C4—22no—
44C11×C22⋊C4—21no—
45C11×C22⋊C4—21no—
46C42×C11—22no—
47C42×C11C2311yescharacteristic
48#1646C1111yesmaximal, characteristic, direct product factor, Sylow
49C23×C11—21no—
50C23×C11—21no—
51Q8×C11—42no—
52Q8×C11—41no—
53Q8×C11—41no—
54D4×C11—21no—
55D4×C11—21no—
56D4×C11—21no—
57D4×C11—21no—
58D4×C11—82no—
59C2×C4×C11—21no—
60C2×C4×C11—21no—
61C2×C4×C11—22no—
62C2×C4×C11—41no—
63C2×C4×C11—41no—
64C2×C4×C11—41no—
65C2×C4×C11—41no—
66C2×C4×C11—41no—
67C2×C4×C11C2×D411yescharacteristic
68C2×C4×C11C2×D411yescharacteristic
69C2×C4×C11C2×D411yescharacteristic
70C8×C11—41no—
71C8×C11—41no—
72C8×C11—41no—
73#555C2×C1111yescharacteristic
74#487C2×C1111yescharacteristic, complemented
75#474C2×C1111yescharacteristic, complemented
76#461C2×C1111yescharacteristic, complemented
77#333C2×C1111yescharacteristic, complemented
78D4⋊C8C2×C1111yescharacteristic, complemented
79D4⋊C8C2×C1111yescharacteristic, complemented
80C22×C11—41no—
81C22×C11—41no—
82C22×C11—41no—
83C22×C11—41no—
84C22×C11—41no—
85C22×C11—41no—
86C22×C11#12011yescharacteristic
87C4×C11—21no—
88C4×C11—41no—
89C4×C11—41no—
90C4×C11—42no—
91C4×C11—81no—
92C4×C11#13511yescharacteristic
93C4×C11#13511yescharacteristic
94C4×C11AGL(1,ℤ/8)11yescharacteristic
95C4×C11#13711yescharacteristic
96C2×SD16—21no—
97C4⋊Q8C22×C1111yescharacteristic
98C4⋊Q8C22×C1111yescharacteristic
99#124—22no—
100#121—21no—
101#121—21no—
102C4×D4C22×C1111yescharacteristic
103C4×D4C22×C1111yescharacteristic
104#117—21no—
105#117—21no—
106#107—21no—
107C4⋊C8C22×C1111yescharacteristic
108C4⋊C8C22×C1111yescharacteristic
109#103—22no—
110#103—21no—
111#102—21no—
112C4×C8C22×C1111yescharacteristic
113C2×C11—81no—
114C2×C11—81no—
115C2×C11#44911yescharacteristic
116C2×C11#45211yescharacteristic
117C2×C11#45511yescharacteristic
118C2×Q8—21no—
119C2×Q8D4×C1112yes—
120C2×D4—22no—
121C2×D4D4×C1111yescharacteristic
122C2×D4D4×C1111yescharacteristic
123C22×C4—21no—
124C22×C4—21no—
125SD16—42no—
126C2×C8—21no—
127C2×C8—21no—
128C2×C8—21no—
129C4⋊C4—21no—
130C4⋊C4—21no—
131C4⋊C4—21no—
132C4⋊C4—21no—
133C4⋊C4D4×C1111yescharacteristic
134C4⋊C4D4×C1111yescharacteristic
135C22⋊C4—22no—
136C22⋊C4—22no—
137C22⋊C4—21no—
138C22⋊C4—21no—
139C42—22no—
140C42C23×C1111yescharacteristic
141C11#164611yescharacteristic, direct product factor, Sylow
142C23—21no—
143C23—21no—
144Q8—42no—
145Q8—41no—
146Q8—41no—
147D4—21no—
148D4—21no—
149D4—21no—
150D4—21no—
151D4—82no—
152C2×C4—21no—
153C2×C4—21no—
154C2×C4—22no—
155C2×C4—41no—
156C2×C4—41no—
157C2×C4—41no—
158C2×C4—41no—
159C2×C4—41no—
160C2×C4C2×D4×C1111yescharacteristic
161C2×C4C2×D4×C1111yescharacteristic
162C2×C4C2×D4×C1111yescharacteristic
163C8—41no—
164C8—41no—
165C8—41no—
166C22—41no—
167C22—41no—
168C22—41no—
169C22—41no—
170C22—41no—
171C22—41no—
172C22C11×#12011yescharacteristic
173C4—21no—
174C4—41no—
175C4—41no—
176C4—42no—
177C4—81no—
178C4C11×#13511yescharacteristic
179C4C11×#13511yescharacteristic
180C4C11×AGL(1,ℤ/8)11yescharacteristic
181C4C11×#13711yescharacteristic
182C2—81no—
183C2—81no—
184C2C11×#44911yescharacteristic
185C2C11×#45211yescharacteristic
186C2C11×#45511yescharacteristic
subgroupG/H
center, socleC22×C11#120
commutator, Frattini, cosocleC42C23×C11
prime radicalC11×#555C2
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C11 ◁ C42×C11 ◁ G

Complements

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

NH ≅ G/Ntype
2. C11×#487C2semidirect
3. C11×#474C2semidirect
4. C11×#461C2semidirect
5. C11×#333C2semidirect
6. C11×D4⋊C8C2semidirect
7. C11×D4⋊C8C2semidirect
48. #1646C11direct (N × H)
74. #487C2×C11semidirect
75. #474C2×C11semidirect
76. #461C2×C11semidirect
77. #333C2×C11semidirect
78. D4⋊C8C2×C11semidirect
79. D4⋊C8C2×C11semidirect
141. C11#1646direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#5552
C11×#4872
C11×#4742
C11×#4612
C11×#3332
C11×D4⋊C82
#164611