Finite Group Databasebeta

← #14673647

Subgroups — #14673647

Order 2816.

284 conjugacy classes of subgroups; only the 87 normal subgroups are shown.

normal subgroups only

This group has 284 conjugacy classes of subgroups — too many to draw. Only its 87 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#13070229C211yesmaximal, characteristic
2#13068681C212yesmaximal
3#13066724C212yesmaximal, complemented
4#13066710C211yesmaximal, characteristic, complemented
5C2×C11×#366C211yesmaximal, characteristic, complemented
6C2×#66954C2211yescharacteristic
7C22×C11×C16C2211yescharacteristic
8C2×C11×#107C2212yes—
9C2×#66883C2212yes—
10C2×#66876C2211yescharacteristic
11#10622579—22no—
12C11×#366—22no—
13#10622168—22no—
14(C2×D11)⋊C16—22no—
15C2×#4339D411yescharacteristic
16C22×C8×C11C2311yescharacteristic
17C2×C11×C4⋊C4—22no—
18C2×#4318—22no—
19C2×#4318D411yescharacteristic
20#66954—22no—
21#66954—22no—
22C2×#4313—21no—
23C2×C8×D11—21no—
24C2×C11×C16—22no—
25C2×C11×C16D412yes—
26C11×#107—22no—
27C11×#107—22no—
28#66883—22no—
29#66883—22no—
30#66876—22no—
31C2×C11⋊C16—21no—
32#66874—42no—
33#66873—42no—
34#13495—111nomaximal, Sylow
35C22×C4×C11—42no—
36C22×C4×C11C2×D411yescharacteristic
37C2×C22⋊D11—21no—
38#4339—22no—
39#4339—22no—
40C2×D44D811yescharacteristic
41C2×C4×D11—21no—
42C2×Dic22D811yescharacteristic
43C2×C8×C11C2×D411yescharacteristic
44C2×C8×C11#4111yescharacteristic
45C2×C8×C11#4112yes—
46C2×C8×C11#4112yes—
47C11×C4⋊C4—42no—
48C11×C4⋊C4—42no—
49#4318—22no—
50#4318—42no—
51#4318—42no—
52C2×C11⋊C8—21no—
53C2×C11⋊C8—42no—
54#4313—42no—
55C8×D11—41no—
56C8×D11—41no—
57C11×C16—22no—
58C11⋊C16—41no—
59C2×#366D1111yescharacteristic, complemented
60#2113—111no—
61#1816—112no—
62#1387—112no—
63#1381—111no—
64C23×C11#13511yescharacteristic
65C22×D11—21no—
66C2×C4×C11—82no—
67C2×C4×C11—162no—
68C2×C4×C11#12111yescharacteristic
69C2×C4×C11#12312yes—
70C2×C4×C11C2×D811yescharacteristic
71C2×C4×C11#13712yes—
72C22⋊D11—42no—
73C2×Dic11—21no—
74D44—22no—
75C4×D11—41no—
76C4×D11—41no—
77Dic22—22no—
78C8×C11#12311yescharacteristic
79C8×C11#12411yescharacteristic
80C8×C11#12612yes—
81C11⋊C8—41no—
82C11⋊C8—82no—
83C2×#131—111no—
84C2×M32—111no—
85C22×C16C2×D1111yescharacteristic
86C2×#108—112no—
87C2×#107C2×D1112yes—
88#417—222no—
89#366—22no—
90C22⋊C16—222no—
91#343—222no—
92C22×C11—21no—
93C22×C11—21no—
94C22×C11#46611yescharacteristic
95C22×C11#48512yes—
96C2×D11—41no—
97C2×D11—41no—
98C2×D11—41no—
99C4×C11—162no—
100C4×C11#39711yescharacteristic
101C4×C11#47011yescharacteristic
102C4×C11#48012yes—
103Dic11—41no—
104C2×#41—111no—
105#131—222no—
106#131—222no—
107C2×M16—111no—
108C2×M16—221no—
109C2×M16—222no—
110C22×C8—221no—
111C22×C8C22×D1111yescharacteristic
112C2×C4⋊C4—22no—
113M32—222no—
114C2×C16—22no—
115C2×C16—221no—
116C2×C16C22⋊D1112yes—
117#108—222no—
118#108—222no—
119#107—22no—
120#107—22no—
121#103—442no—
122#102—442no—
123C2×C11—22no—
124C2×C11#207511yescharacteristic
125C2×C11#222111yescharacteristic
126C2×C11#222211yescharacteristic
127D11—81no—
128#41—222no—
129#41—222no—
130C2×Q8—111no—
131C2×D4—111no—
132C2×D4—221no—
133C22×C4—42no—
134C22×C4—221no—
135C22×C4D4×D1111yescharacteristic
136M16—222no—
137M16—442no—
138M16—442no—
139M16—442no—
140C2×C8—221no—
141C2×C8—441no—
142C2×C8—441no—
143C2×C8—442no—
144C2×C8#433912yes—
145C2×C8#434111yescharacteristic
146C2×C8#434312yes—
147C2×C8C2×C22⋊D1111yescharacteristic
148C4⋊C4—42no—
149C4⋊C4—42no—
150C16—22no—
151C16—441no—
152C11#1349511yescharacteristic, complemented, Sylow
153C23—221no—
154C23#6696511yescharacteristic
155Q8—222no—
156D4—222no—
157D4—442no—
158C2×C4—82no—
159C2×C4—162no—
160C2×C4—221no—
161C2×C4—441no—
162C2×C4—441no—
163C2×C4#6694712yes—
164C2×C4D8×D1111yescharacteristic
165C2×C4#6697112yes—
166C2×C4#6699111yescharacteristic
167C8—441no—
168C8—882no—
169C8#6695112yes—
170C8#6698211yescharacteristic
171C8#6700011yescharacteristic
172C22—21no—
173C22—21no—
174C22—441no—
175C22—441no—
176C22—441no—
177C22#1062250112yes—
178C22#1062277011yescharacteristic
179C4—162no—
180C4—441no—
181C4#1062249512yes—
182C4#1062260611yescharacteristic
183C4#1062280211yescharacteristic
184C2—22no—
185C2—881no—
186C2#1307004011yescharacteristic
187C2#1307073311yescharacteristic
188C2#1307073811yescharacteristic
subgroupG/H
centerC22#10622770
commutator, cosocleC22×C8×C11C23
FrattiniC22×C8C22×D11
FittingC2×C11×#366C2
socleC22×C11#466
prime radicalC2×#4339D4
hypercenterC2×#366D11
hypocenterC11#13495
LCSG ▷ C22×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ C2×#366

Complements

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

NH ≅ G/Ntype
3. #13066724C2semidirect
4. #13066710C2semidirect
5. C2×C11×#366C2semidirect
59. C2×#366D11semidirect
152. C11#13495semidirect

Maximal subgroups

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

subgroupindex
#130702292
#130686812
#130667242
#130667102
C2×C11×#3662
#1349511