Finite Group Databasebeta

← #14673652

Subgroups — #14673652

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×#367C211yesmaximal, characteristic, complemented
6C2×#66954C2211yescharacteristic
7C22×C11×C16C2211yescharacteristic
8C2×C11×#107C2212yes—
9C2×#66883C2212yes—
10C2×#66876C2211yescharacteristic
11#10622579—22no—
12C11×#367—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#13496—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×#367D1111yescharacteristic, 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#367—22no—
90C22⋊C16—222no—
91#343—222no—
92C22×C11—22no—
93C22×C11#46611yescharacteristic
94C22×C11#48512yes—
95C2×D11—41no—
96C2×D11—42no—
97C4×C11—162no—
98C4×C11#39711yescharacteristic
99C4×C11#47011yescharacteristic
100C4×C11#48012yes—
101Dic11—41no—
102C2×#41—111no—
103#131—222no—
104#131—222no—
105C2×M16—111no—
106C2×M16—221no—
107C2×M16—222no—
108C22×C8—221no—
109C22×C8C22×D1111yescharacteristic
110C2×C4⋊C4—22no—
111M32—222no—
112C2×C16—22no—
113C2×C16—221no—
114C2×C16C22⋊D1112yes—
115#108—222no—
116#108—222no—
117#107—22no—
118#107—22no—
119#103—442no—
120#102—442no—
121C2×C11—22no—
122C2×C11#207511yescharacteristic
123C2×C11#222312yes—
124D11—81no—
125#41—222no—
126#41—222no—
127C2×Q8—111no—
128C2×D4—111no—
129C2×D4—221no—
130C22×C4—42no—
131C22×C4—221no—
132C22×C4D4×D1111yescharacteristic
133M16—222no—
134M16—442no—
135M16—442no—
136M16—442no—
137C2×C8—221no—
138C2×C8—441no—
139C2×C8—441no—
140C2×C8—442no—
141C2×C8#433912yes—
142C2×C8#434111yescharacteristic
143C2×C8#434312yes—
144C2×C8C2×C22⋊D1111yescharacteristic
145C4⋊C4—42no—
146C4⋊C4—42no—
147C16—22no—
148C16—441no—
149C11#1349611yescharacteristic, complemented, Sylow
150C23—221no—
151C23#6696511yescharacteristic
152Q8—222no—
153D4—222no—
154D4—442no—
155C2×C4—82no—
156C2×C4—162no—
157C2×C4—221no—
158C2×C4—441no—
159C2×C4—441no—
160C2×C4#6694712yes—
161C2×C4D8×D1111yescharacteristic
162C2×C4#6697112yes—
163C2×C4#6699111yescharacteristic
164C8—441no—
165C8—882no—
166C8#6695112yes—
167C8#6698211yescharacteristic
168C8#6700011yescharacteristic
169C22—22no—
170C22—442no—
171C22—441no—
172C22#1062250112yes—
173C22#1062277011yescharacteristic
174C4—162no—
175C4—441no—
176C4#1062249512yes—
177C4#1062260611yescharacteristic
178C4#1062280211yescharacteristic
179C2—22no—
180C2—881no—
181C2#1307004011yescharacteristic
182C2#1307074312yes—
subgroupG/H
centerC22#10622770
commutator, cosocleC22×C8×C11C23
FrattiniC22×C8C22×D11
FittingC2×C11×#367C2
socleC22×C11#466
prime radicalC2×#4339D4
hypercenterC2×#367D11
hypocenterC11#13496
LCSG ▷ C22×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ C2×#367

Complements

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

NH ≅ G/Ntype
3. #13066724C2semidirect
4. #13066710C2semidirect
5. C2×C11×#367C2semidirect
59. C2×#367D11semidirect
149. C11#13496semidirect

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×#3672
#1349611