Finite Group Databasebeta

← C11×#12310 #14589503

Subgroups — C11×#12310 #14589503

Order 2816.

406 conjugacy classes of subgroups; only the 78 normal subgroups are shown.

normal subgroups only

This group has 406 conjugacy classes of subgroups — too many to draw. Only its 78 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×#3292C211yesmaximal, characteristic, complemented
2C11×#2213C212yesmaximal, complemented
3C11×#1712C211yesmaximal, characteristic, complemented
4C11×#1357C211yesmaximal, characteristic, complemented
5C11×#1335C212yesmaximal, complemented
6C11×#576—22no—
7C11×#509—22no—
8C11×#493—22no—
9C11×#493C2211yescharacteristic
10C11×#493C2211yescharacteristic, complemented
11C11×#472—22no—
12C11×#453—22no—
13C11×#443C2212yes—
14C11×#364C2212yescomplemented
15C11×#361—22no—
16C82×C11C2211yescharacteristic, complemented
17C11×H(5,𝔽2)—22no—
18C11×AGL(1,ℤ/8)—24no—
19C11×AGL(1,ℤ/8)—44no—
20C11×#135—42no—
21C11×#135D412yes—
22C2×C11×D8—22no—
23C2×C11×D8—22no—
24C2×C11×D8—44no—
25C2×C11×D8—42no—
26C11×#131—22no—
27C11×#127—21no—
28C11×#127D412yes—
29C11×SD32—42no—
30C11×D16—42no—
31C11×M32—22no—
32C11×#108D412yes—
33C11×#104—22no—
34C11×#100—22no—
35C4×C8×C11—21no—
36C4×C8×C11C2311yescharacteristic
37#12310C1111yesmaximal, characteristic, direct product factor, Sylow
38C11×#41—22no—
39C11×#41—44no—
40C2×D4×C11—22no—
41C2×D4×C11—42no—
42C2×D4×C11—42no—
43C2×D4×C11—44no—
44C2×D4×C11—41no—
45C2×D4×C11—82no—
46C11×Q16D812yescomplemented
47C11×SD16—22no—
48C11×SD16—44no—
49C11×D8—44no—
50C11×D8—42no—
51C11×D8—42no—
52C11×D8—42no—
53C11×D8—42no—
54C11×D8—88no—
55C11×D8D812yescomplemented
56C11×M16—22no—
57C11×M16—42no—
58C2×C8×C11—22no—
59C2×C8×C11—42no—
60C2×C8×C11C2×D412yes—
61C42×C11C2×D411yescharacteristic
62C11×C16—42no—
63#3292C2×C1111yescharacteristic, complemented
64#2213C2×C1112yescomplemented
65#1712C2×C1111yescharacteristic, complemented
66#1357C2×C1111yescharacteristic, complemented
67#1335C2×C1112yescomplemented
68C23×C11—42no—
69C23×C11—82no—
70C23×C11—81no—
71Q8×C11—22no—
72D4×C11—22no—
73D4×C11—42no—
74D4×C11—44no—
75D4×C11—84no—
76D4×C11—84no—
77D4×C11—84no—
78D4×C11—82no—
79C2×C4×C11—21no—
80C2×C4×C11—42no—
81C2×C4×C11—82no—
82C2×C4×C11#12011yescharacteristic
83C8×C11—24no—
84C8×C11—42no—
85C8×C11C2×D812yes—
86C8×C11AGL(1,ℤ/8)12yes—
87#576—22no—
88#509—22no—
89#493—22no—
90#493C22×C1111yescharacteristic
91#493C22×C1111yescharacteristic, complemented
92#472—22no—
93#453—22no—
94#443C22×C1112yes—
95#364C22×C1112yescomplemented
96#361—22no—
97C82C22×C1111yescharacteristic, complemented
98C22×C11—42no—
99C22×C11—82no—
100C22×C11—162no—
101C22×C11—162no—
102C22×C11—161no—
103C22×C11—322no—
104C22×C11#45311yescharacteristic
105C4×C11—22no—
106C4×C11—42no—
107C4×C11#44712yes—
108H(5,𝔽2)—22no—
109AGL(1,ℤ/8)—24no—
110AGL(1,ℤ/8)—44no—
111#135—42no—
112#135D4×C1112yes—
113C2×D8—22no—
114C2×D8—22no—
115C2×D8—44no—
116C2×D8—42no—
117#131—22no—
118#127—21no—
119#127D4×C1112yes—
120SD32—42no—
121D16—42no—
122M32—22no—
123#108D4×C1112yes—
124#104—22no—
125#100—22no—
126C4×C8—21no—
127C4×C8C23×C1111yescharacteristic
128C2×C11—21no—
129C2×C11—82no—
130C2×C11—162no—
131C2×C11—321no—
132C2×C11#161911yescharacteristic
133#41—22no—
134#41—44no—
135C2×D4—22no—
136C2×D4—42no—
137C2×D4—42no—
138C2×D4—44no—
139C2×D4—41no—
140C2×D4—82no—
141Q16C11×D812yescomplemented
142SD16—22no—
143SD16—44no—
144D8—44no—
145D8—42no—
146D8—42no—
147D8—42no—
148D8—42no—
149D8—88no—
150D8C11×D812yescomplemented
151M16—22no—
152M16—42no—
153C2×C8—22no—
154C2×C8—42no—
155C2×C8C2×D4×C1112yes—
156C42C2×D4×C1111yescharacteristic
157C16—42no—
158C11#1231011yescharacteristic, direct product factor, Sylow
159C23—42no—
160C23—82no—
161C23—81no—
162Q8—22no—
163D4—22no—
164D4—42no—
165D4—44no—
166D4—84no—
167D4—84no—
168D4—84no—
169D4—82no—
170C2×C4—21no—
171C2×C4—42no—
172C2×C4—82no—
173C2×C4C11×#12011yescharacteristic
174C8—24no—
175C8—42no—
176C8C2×C11×D812yes—
177C8C11×AGL(1,ℤ/8)12yes—
178C22—42no—
179C22—82no—
180C22—162no—
181C22—162no—
182C22—161no—
183C22—322no—
184C22C11×#45311yescharacteristic
185C4—22no—
186C4—42no—
187C4C11×#44712yes—
188C2—21no—
189C2—82no—
190C2—162no—
191C2—321no—
192C2C11×#161911yescharacteristic
subgroupG/H
center, socleC2×C11#1619
commutator, Frattini, cosocleC4×C8C23×C11
LCSG ▷ C4×C8 ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C2×C11 ◁ C2×C4×C11 ◁ C4×C8×C11 ◁ G

Complements

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

NH ≅ G/Ntype
1. C11×#3292C2semidirect
2. C11×#2213C2semidirect
3. C11×#1712C2semidirect
4. C11×#1357C2semidirect
5. C11×#1335C2semidirect
10. C11×#493C22semidirect
14. C11×#364C22semidirect
16. C82×C11C22semidirect
37. #12310C11direct (N × H)
46. C11×Q16D8semidirect
55. C11×D8D8semidirect
63. #3292C2×C11semidirect
64. #2213C2×C11semidirect
65. #1712C2×C11semidirect
66. #1357C2×C11semidirect
67. #1335C2×C11semidirect
91. #493C22×C11semidirect
95. #364C22×C11semidirect
97. C82C22×C11semidirect
141. Q16C11×D8semidirect
150. D8C11×D8semidirect
158. C11#12310direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#32922
C11×#22132
C11×#17122
C11×#13572
C11×#13352
#1231011