Finite Group Databasebeta

← #14658546

Subgroups — #14658546

Order 2816.

292 conjugacy classes of subgroups; only the 95 normal subgroups are shown.

normal subgroups only

This group has 292 conjugacy classes of subgroups — too many to draw. Only its 95 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
1#13068770C211yesmaximal, characteristic
2#13067273C212yesmaximal
3#13066511C212yesmaximal
4#13066445C211yesmaximal, characteristic
5C11×#1995C211yesmaximal, characteristic
6C11×#533C2211yescharacteristic
7C11×#423C2211yescharacteristic
8C11×#376C2211yescharacteristic
9#10622538C2212yes—
10C2×C4⋊(C11⋊C8)—21no—
11C2×C4⋊(C11⋊C8)—21no—
12C2×C4⋊(C11⋊C8)C2212yes—
13C11×#339—21no—
14C11×#339—21no—
15#10622185—22no—
16#10622184—22no—
17C2×C11×M16—21no—
18C11×C4⋊Q8D412yes—
19C11×#125—21no—
20C11×C22⋊Q8—22no—
21C4×Q8×C11—22no—
22C11×#117—21no—
23C2×C42×C11D411yescharacteristic
24C2×C42×C11D411yescharacteristic
25C2×C42×C11C2311yescharacteristic
26C22×C11⋊C8—22no—
27C11×C4⋊C8—22no—
28C11×#95—22no—
29C22⋊(C11⋊C8)—22no—
30C4⋊(C11⋊C8)—22no—
31C4⋊(C11⋊C8)—22no—
32C4⋊(C11⋊C8)—22no—
33C4⋊(C11⋊C8)—42no—
34C4⋊(C11⋊C8)—42no—
35C4×C11⋊C8—22no—
36#10628—111nomaximal, Sylow
37C2×Q8×C11—22no—
38C22×C4×C11—21no—
39C22×C4×C11—21no—
40C22×C4×C11C2×D411yescharacteristic
41C22×C4×C11#4112yes—
42C11×M16—41no—
43C11×M16—41no—
44C2×C8×C11—41no—
45C11×C4⋊C4—22no—
46C11×C4⋊C4—22no—
47C11×C4⋊C4—42no—
48C11×C22⋊C4—41no—
49C42×C11—21no—
50C42×C11—21no—
51C42×C11—41no—
52C42×C11SD1612yes—
53C42×C11Q1612yes—
54C42×C11C2×D411yescharacteristic
55C42×C11#4111yescharacteristic
56C42×C11#4112yes—
57C2×C11⋊C8—42no—
58C2×C11⋊C8—42no—
59C2×C11⋊C8—42no—
60C2×C11⋊C8—42no—
61#1995D1111yescharacteristic
62#1843—111no—
63#1542—112no—
64#1301—112no—
65#1274—111no—
66C23×C11#12311yescharacteristic
67Q8×C11—82no—
68C2×C4×C11—22no—
69C2×C4×C11—22no—
70C2×C4×C11—42no—
71C2×C4×C11—42no—
72C2×C4×C11—42no—
73C2×C4×C11—42no—
74C2×C4×C11#12111yescharacteristic
75C2×C4×C11#12312yes—
76C2×C4×C11#12411yescharacteristic
77C2×C4×C11#12612yes—
78C2×C4×C11C2×SD1611yescharacteristic
79C2×C4×C11C2×Q1611yescharacteristic
80C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
81C2×C4×C11#13711yescharacteristic
82C8×C11—81no—
83C11⋊C8—82no—
84C11⋊C8—82no—
85#533C2×D1111yescharacteristic
86#431—112no—
87#423C2×D1111yescharacteristic
88C2×C4⋊C8—112no—
89C2×C4⋊C8—221no—
90C2×C4⋊C8—221no—
91#376C2×D1111yescharacteristic
92#339—21no—
93#339—21no—
94#333—222no—
95#332—222no—
96C22×C11—22no—
97C22×C11#39711yescharacteristic
98C22×C11#48311yescharacteristic
99C22×C11#48411yescharacteristic
100C4×C11—22no—
101C4×C11—22no—
102C4×C11—42no—
103C4×C11—42no—
104C4×C11—82no—
105C4×C11#46011yescharacteristic
106C4×C11#46211yescharacteristic
107C4×C11#48711yescharacteristic
108C4×C11#48911yescharacteristic
109C2×M16—21no—
110C22×C8—222no—
111C4⋊Q8D4412yes—
112#125—21no—
113C22⋊Q8—22no—
114C4×Q8—22no—
115#117—21no—
116C2×C42C22⋊D1111yescharacteristic
117C2×C42C22⋊D1111yescharacteristic
118C2×C42C22×D1111yescharacteristic
119C4⋊C8—22no—
120C4⋊C8—222no—
121C4⋊C8—222no—
122C4⋊C8—222no—
123C4⋊C8—442no—
124C4⋊C8—442no—
125C22⋊C8—222no—
126C4×C8—222no—
127#95—22no—
128C2×C11—21no—
129C2×C11—21no—
130C2×C11#207211yescharacteristic
131C2×C11#208012yes—
132C2×Q8—22no—
133C22×C4—21no—
134C22×C4—21no—
135C22×C4#434112yes—
136C22×C4C2×C22⋊D1111yescharacteristic
137M16—41no—
138M16—41no—
139C2×C8—41no—
140C2×C8—442no—
141C2×C8—442no—
142C2×C8—442no—
143C2×C8—442no—
144C4⋊C4—22no—
145C4⋊C4—22no—
146C4⋊C4—42no—
147C22⋊C4—41no—
148C42—21no—
149C42—21no—
150C42—41no—
151C42#432512yes—
152C42#432612yes—
153C42C2×D4411yescharacteristic
154C42#433911yescharacteristic
155C42#434112yes—
156C11#1062811yescharacteristic, complemented, Sylow
157C23#6698811yescharacteristic
158Q8—82no—
159C2×C4—22no—
160C2×C4—22no—
161C2×C4—42no—
162C2×C4—42no—
163C2×C4—42no—
164C2×C4—42no—
165C2×C4#6693212yes—
166C2×C4#6693912yes—
167C2×C4#6698311yescharacteristic
168C2×C4#6698911yescharacteristic
169C2×C4C2×#432511yescharacteristic
170C2×C4C2×#432611yescharacteristic
171C2×C4#6700211yescharacteristic
172C2×C4#6700411yescharacteristic
173C8—81no—
174C8—882no—
175C8—882no—
176C22—22no—
177C22#1062256611yescharacteristic
178C22#1062265611yescharacteristic
179C22#1062265711yescharacteristic
180C4—22no—
181C4—22no—
182C4—42no—
183C4—42no—
184C4—82no—
185C4#1062264011yescharacteristic
186C4#1062264411yescharacteristic
187C4#1062266811yescharacteristic
188C4#1062269411yescharacteristic
189C2—21no—
190C2—21no—
191C2#1307002411yescharacteristic
192C2#1307006612yes—
subgroupG/H
centerC2×C4#66989
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC11×#1995C2
socleC22×C11#397
prime radicalC23×C11#123
hypercenter#1995D11
hypocenterC11#10628
LCSG ▷ C2×C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1995

Complements

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

NH ≅ G/Ntype
156. C11#10628semidirect

Maximal subgroups

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

subgroupindex
#130687702
#130672732
#130665112
#130664452
C11×#19952
#1062811