Finite Group Databasebeta

← #14673651

Subgroups — #14673651

Order 2816.

284 conjugacy classes of subgroups; only the 91 normal subgroups are shown.

normal subgroups only

This group has 284 conjugacy classes of subgroups — too many to draw. Only its 91 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
1C2×#10622143C211yesmaximal, characteristic, complemented
2#13068680C212yesmaximal
3#13066725C212yesmaximal, complemented
4#13066710C211yesmaximal, characteristic, complemented
5C11×#2113C211yesmaximal, characteristic
6C2×C11×#131C2211yescharacteristic
7C2×C11×M32C2211yescharacteristic
8C22×C11×C16C2211yescharacteristic
9#10622845—22no—
10C2×#66883C2212yes—
11C2×#66882C2212yes—
12C11×C22⋊C16—22no—
13#10622192—22no—
14#10622143—22no—
15C2×C11×#41D411yescharacteristic
16C11×#131—22no—
17C11×#131—22no—
18C2×C11×M16—21no—
19C2×C11×M16D411yescharacteristic
20C22×C8×C11—21no—
21C22×C8×C11C2311yescharacteristic
22C2×C4⋊Dic11—22no—
23C2×#4318—22no—
24C11×M32—22no—
25C2×C11×C16—22no—
26C2×C11×C16—21no—
27C2×C11×C16D412yes—
28#66899—42no—
29#66896—42no—
30#66883—22no—
31#66883—22no—
32#66882—22no—
33#66882—22no—
34#13496—111nomaximal, Sylow
35C11×#41—22no—
36C11×#41—22no—
37C2×Q8×C11D811yescharacteristic
38C2×D4×C11—21no—
39C2×D4×C11D811yescharacteristic
40C22×C4×C11—21no—
41C22×C4×C11C2×D411yescharacteristic
42C22×Dic11—42no—
43C11×M16—22no—
44C11×M16—42no—
45C2×C8×C11—21no—
46C2×C8×C11—41no—
47C2×C8×C11—41no—
48C2×C8×C11C2×D411yescharacteristic
49C2×C8×C11#4111yescharacteristic
50C2×C8×C11#4112yes—
51C2×C8×C11#4112yes—
52C4⋊Dic11—42no—
53C4⋊Dic11—42no—
54#4318—42no—
55#4318—42no—
56C2×C11⋊C8—42no—
57C11×C16—22no—
58C11×C16—41no—
59C2×#367—111no—
60#2113D1111yescharacteristic
61#1816—112no—
62#1387—112no—
63#1381—111no—
64C23×C11—21no—
65C23×C11#13511yescharacteristic
66Q8×C11—22no—
67D4×C11—22no—
68D4×C11—42no—
69C2×C4×C11—21no—
70C2×C4×C11—41no—
71C2×C4×C11—41no—
72C2×C4×C11#12111yescharacteristic
73C2×C4×C11#12312yes—
74C2×C4×C11C2×D811yescharacteristic
75C2×C4×C11#13712yes—
76C2×Dic11—82no—
77C2×Dic11—162no—
78C8×C11—41no—
79C8×C11#12311yescharacteristic
80C8×C11#12411yescharacteristic
81C8×C11#12612yes—
82C11⋊C8—82no—
83C2×#131C2×D1111yescharacteristic
84C2×M32C2×D1111yescharacteristic
85C22×C16C2×D1111yescharacteristic
86C2×#108—112no—
87C2×#107—112no—
88#417—222no—
89#367—222no—
90C22⋊C16—22no—
91#343—222no—
92C22×C11—22no—
93C22×C11—41no—
94C22×C11—42no—
95C22×C11#46611yescharacteristic
96C22×C11#48512yes—
97C4×C11—41no—
98C4×C11#39711yescharacteristic
99C4×C11#47011yescharacteristic
100C4×C11#48012yes—
101Dic11—162no—
102C2×#41D4411yescharacteristic
103#131—22no—
104#131—22no—
105C2×M16—21no—
106C2×M16—222no—
107C2×M16D4411yescharacteristic
108C22×C8—21no—
109C22×C8C22×D1111yescharacteristic
110C2×C4⋊C4—222no—
111M32—22no—
112C2×C16—22no—
113C2×C16—21no—
114C2×C16C22⋊D1112yes—
115#108—222no—
116#108—222no—
117#107—222no—
118#107—222no—
119#103—442no—
120#102—442no—
121C2×C11—22no—
122C2×C11—81no—
123C2×C11#207511yescharacteristic
124C2×C11#222312yes—
125#41—22no—
126#41—22no—
127C2×Q8D8811yescharacteristic
128C2×D4—21no—
129C2×D4D8811yescharacteristic
130C22×C4—21no—
131C22×C4—442no—
132C22×C4C2×D4411yescharacteristic
133M16—22no—
134M16—42no—
135M16—442no—
136M16—442no—
137C2×C8—21no—
138C2×C8—41no—
139C2×C8—41no—
140C2×C8—442no—
141C2×C8#433911yescharacteristic
142C2×C8#434112yes—
143C2×C8#434112yes—
144C2×C8C2×C22⋊D1111yescharacteristic
145C4⋊C4—442no—
146C4⋊C4—442no—
147C16—22no—
148C16—41no—
149C11#1349611yescharacteristic, complemented, Sylow
150C23—21no—
151C23#6695711yescharacteristic
152Q8—22no—
153D4—22no—
154D4—42no—
155C2×C4—21no—
156C2×C4—41no—
157C2×C4—41no—
158C2×C4—882no—
159C2×C4—1762no—
160C2×C4#6693912yes—
161C2×C4C2×D8811yescharacteristic
162C2×C4#6696212yes—
163C2×C4#6698311yescharacteristic
164C8—41no—
165C8—882no—
166C8#6693212yes—
167C8#6698811yescharacteristic
168C8#6698911yescharacteristic
169C22—22no—
170C22—42no—
171C22—41no—
172C22#1062233612yes—
173C22#1062272811yescharacteristic
174C4—41no—
175C4—1762no—
176C4#1062234912yes—
177C4#1062256611yescharacteristic
178C4#1062275011yescharacteristic
179C2—22no—
180C2—81no—
181C2#1307003911yescharacteristic
182C2#1307074612yes—
subgroupG/H
centerC22#10622728
commutator, cosocleC22×C8×C11C23
FrattiniC22×C8C22×D11
FittingC11×#2113C2
socleC22×C11#466
prime radicalC2×C11×#41D4
hypercenter#2113D11
hypocenterC11#13496
LCSG ▷ C22×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#131 ◁ #2113

Complements

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

NH ≅ G/Ntype
1. C2×#10622143C2semidirect
3. #13066725C2semidirect
4. #13066710C2semidirect
149. C11#13496semidirect

Maximal subgroups

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

subgroupindex
C2×#106221432
#130686802
#130667252
#130667102
C11×#21132
#1349611