Finite Group Databasebeta

← C11×#7398 #14584591

Subgroups — C11×#7398 #14584591

Order 2816.

258 conjugacy classes of subgroups; only the 42 normal subgroups are shown.

normal subgroups only

This group has 258 conjugacy classes of subgroups — too many to draw. Only its 42 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×#2018C211yesmaximal, characteristic
2C11×#1391C211yesmaximal, characteristic, complemented
3C11×#1321C211yesmaximal, characteristic, complemented
4C2×C11×AGL(1,ℤ/8)—21no—
5C22×C11×D8C411yescharacteristic, complemented
6C2×C11×#100—21no—
7C11×#410—21no—
8C11×#408C2211yescharacteristic
9C11×#349—21no—
10C11×#341C411yescharacteristic, complemented
11C2×C11×#41D411yescharacteristic
12C22×D4×C11—21no—
13C11×AGL(1,ℤ/8)—42no—
14C11×AGL(1,ℤ/8)—42no—
15C2×C11×SD16—41no—
16C2×C11×D8—41no—
17C2×C11×D8—41no—
18C2×C11×D8—42no—
19C2×C11×M16—21no—
20C2×C11×M16D411yescharacteristic
21C22×C8×C11C2×C411yescharacteristic
22C11×#117—41no—
23C11×M32—41no—
24C11×#100—42no—
25C11×#99—22no—
26C11×#99—41no—
27C11×C22⋊C8—41no—
28#7398C1111yesmaximal, characteristic, direct product factor, Sylow
29C24×C11—41no—
30C11×#41—41no—
31C11×#41—41no—
32C2×Q8×C11SD1611yescharacteristic
33C2×D4×C11—22no—
34C2×D4×C11—21no—
35C2×D4×C11—41no—
36C2×D4×C11—41no—
37C2×D4×C11—41no—
38C2×D4×C11—41no—
39C2×D4×C11—41no—
40C2×D4×C11D811yescharacteristic
41C22×C4×C11—21no—
42C22×C4×C11C22⋊C411yescharacteristic
43C11×SD16—44no—
44C11×D8—42no—
45C11×D8—44no—
46C11×D8—42no—
47C11×M16—22no—
48C11×M16—41no—
49C11×M16—41no—
50C2×C8×C11—21no—
51C2×C8×C11—21no—
52C2×C8×C11—41no—
53C2×C8×C11—41no—
54C11×C4⋊C4—81no—
55C11×C22⋊C4—42no—
56C42×C11—81no—
57C11×C16—81no—
58#2018C2×C1111yescharacteristic
59#1391C2×C1111yescharacteristic, complemented
60#1321C2×C1111yescharacteristic, complemented
61C23×C11—21no—
62C23×C11—42no—
63C23×C11—81no—
64C23×C11—81no—
65C23×C11—162no—
66C23×C11#10411yescharacteristic
67Q8×C11—41no—
68D4×C11—41no—
69D4×C11—42no—
70D4×C11—42no—
71D4×C11—81no—
72D4×C11—81no—
73D4×C11—81no—
74C2×C4×C11—21no—
75C2×C4×C11—21no—
76C2×C4×C11—21no—
77C2×C4×C11—41no—
78C2×C4×C11—41no—
79C2×C4×C11—82no—
80C2×C4×C11#9911yescharacteristic
81C2×C4×C11#10211yescharacteristic
82C8×C11—42no—
83C8×C11—41no—
84C8×C11—41no—
85C2×AGL(1,ℤ/8)—21no—
86C22×D8C4×C1111yescharacteristic, complemented
87C2×#100—21no—
88#410—21no—
89#408C22×C1111yescharacteristic
90#349—21no—
91#341C4×C1111yescharacteristic, complemented
92C22×C11—21no—
93C22×C11—41no—
94C22×C11—41no—
95C22×C11—81no—
96C22×C11—82no—
97C22×C11—162no—
98C22×C11—162no—
99C22×C11—162no—
100C22×C11#32711yescharacteristic
101C4×C11—21no—
102C4×C11—41no—
103C4×C11—162no—
104C4×C11AΣL(1,𝔽16)11yescharacteristic
105C4×C11#35311yescharacteristic
106C2×#41D4×C1111yescharacteristic
107C22×D4—21no—
108AGL(1,ℤ/8)—42no—
109AGL(1,ℤ/8)—42no—
110C2×SD16—41no—
111C2×D8—41no—
112C2×D8—41no—
113C2×D8—42no—
114C2×M16—21no—
115C2×M16D4×C1111yescharacteristic
116C22×C8C2×C4×C1111yescharacteristic
117#117—41no—
118M32—41no—
119#100—42no—
120#99—22no—
121#99—41no—
122C22⋊C8—41no—
123C2×C11—21no—
124C2×C11—41no—
125C2×C11—81no—
126C2×C11—162no—
127C2×C11#134311yescharacteristic
128C24—41no—
129#41—41no—
130#41—41no—
131C2×Q8C11×SD1611yescharacteristic
132C2×D4—22no—
133C2×D4—21no—
134C2×D4—41no—
135C2×D4—41no—
136C2×D4—41no—
137C2×D4—41no—
138C2×D4—41no—
139C2×D4C11×D811yescharacteristic
140C22×C4—21no—
141C22×C4C11×C22⋊C411yescharacteristic
142SD16—44no—
143D8—42no—
144D8—42no—
145D8—44no—
146M16—22no—
147M16—41no—
148M16—41no—
149C2×C8—21no—
150C2×C8—21no—
151C2×C8—41no—
152C2×C8—41no—
153C4⋊C4—81no—
154C22⋊C4—42no—
155C42—81no—
156C16—81no—
157C11#739811yescharacteristic, direct product factor, Sylow
158C23—21no—
159C23—42no—
160C23—81no—
161C23—81no—
162C23—162no—
163C23C11×#10411yescharacteristic
164Q8—41no—
165D4—41no—
166D4—42no—
167D4—42no—
168D4—81no—
169D4—81no—
170D4—81no—
171C2×C4—21no—
172C2×C4—21no—
173C2×C4—21no—
174C2×C4—41no—
175C2×C4—41no—
176C2×C4—82no—
177C2×C4C11×#9911yescharacteristic
178C2×C4C11×#10211yescharacteristic
179C8—42no—
180C8—41no—
181C8—41no—
182C22—21no—
183C22—41no—
184C22—41no—
185C22—81no—
186C22—82no—
187C22—162no—
188C22—162no—
189C22—162no—
190C22C11×#32711yescharacteristic
191C4—21no—
192C4—41no—
193C4—162no—
194C4C11×AΣL(1,𝔽16)11yescharacteristic
195C4C11×#35311yescharacteristic
196C2—21no—
197C2—41no—
198C2—81no—
199C2—162no—
200C2C11×#134311yescharacteristic
subgroupG/H
center, socleC2×C11#1343
commutatorC22×C8C2×C4×C11
Frattini, cosocle#408C22×C11
prime radicalC11×#2018C2
LCSG ▷ C22×C8 ▷ C22×C4 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C2×C11 ◁ C2×C4×C11 ◁ C22×C4×C11 ◁ C11×#408 ◁ G

Complements

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

NH ≅ G/Ntype
2. C11×#1391C2semidirect
3. C11×#1321C2semidirect
5. C22×C11×D8C4semidirect
10. C11×#341C4semidirect
28. #7398C11direct (N × H)
59. #1391C2×C11semidirect
60. #1321C2×C11semidirect
86. C22×D8C4×C11semidirect
91. #341C4×C11semidirect
157. C11#7398direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#20182
C11×#13912
C11×#13212
#739811