Finite Group Databasebeta

← #27186473

Subgroups — #27186473

Order 12928.

316 conjugacy classes of subgroups; only the 68 normal subgroups are shown.

normal subgroups only

This group has 316 conjugacy classes of subgroups — too many to draw. Only its 68 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#20266198C211yesmaximal, characteristic, complemented
2C4×#13108083C211yesmaximal, characteristic, complemented
3#20266025C214yesmaximal, complemented
4C2×#15692217C211yesmaximal, characteristic
5C2×#13108083—21no—
6C4⋊#11717581C2212yescomplemented
7C22⋊#11717581—21no—
8#15692310—21no—
9#15692310—21no—
10C4×#11717581C2212yescomplemented
11C22×D404C411yescharacteristic
12C22×C4×D101—21no—
13#15692217—21no—
14#15692217—21no—
15#15692217C412yes—
16#15692217C2212yes—
17C2×#13108051—21no—
18C2×C4×Dic101C2211yescharacteristic
19C2×C4⋊C4×C101C411yescharacteristic
20#13108083—24no—
21C2×#11717581—22no—
22C2×#11717581—22no—
23C23×D101—21no—
24C2×D404—21no—
25C2×D404—24no—
26C2×D404C2×C412yes—
27C22×Dic101D411yescharacteristic
28C22×Dic101D411yescharacteristic
29C2×C4×D101—22no—
30C2×C4×D101—22no—
31C2×C4×D101—44no—
32#13108051—22no—
33#13108051—22no—
34C4×Dic101C2×C411yescharacteristic
35C4×Dic101D411yescharacteristic
36C4×Dic101D411yescharacteristic
37C4×Dic101C2311yescharacteristic
38C22×C4×C101—21no—
39C22×C4×C101C2×C411yescharacteristic
40C4⋊C4×C101—21no—
41C4⋊C4×C101C2×C412yes—
42C23×C101C22⋊C411yescharacteristic
43C22×D101—24no—
44C22×D101—22no—
45C22×D101—42no—
46C22×D101—42no—
47C2×C4×C101—22no—
48C2×C4×C101—22no—
49C2×C4×C101—42no—
50C2×C4×C101C22⋊C411yescharacteristic
51C2×C4×C101C22×C411yescharacteristic
52C2×Dic101—22no—
53C2×Dic101—22no—
54C2×Dic101C22⋊C411yescharacteristic
55C2×Dic101C22⋊C411yescharacteristic
56C2×Dic101C2×D411yescharacteristic
57C2×Dic101C2×D411yescharacteristic
58D404—24no—
59D404—22no—
60D404M1614yescomplemented
61C4×D101—44no—
62C4×D101—44no—
63#11717581—24no—
64#11717581—42no—
65C22×C101—21no—
66C22×C101—21no—
67C22×C101#10412yes—
68C22×C101C2×C22⋊C411yescharacteristic
69C2×D101—24no—
70C2×D101—48no—
71C2×D101—42no—
72C2×D101—42no—
73C4×C101—21no—
74C4×C101—42no—
75C4×C101C2×M1612yes—
76Dic101—21no—
77Dic101—21no—
78Dic101—21no—
79Dic101AGL(1,ℤ/8)12yes—
80C2×C101—22no—
81C2×C101#40711yescharacteristic
82C2×C101#41811yescharacteristic
83C2×C101C2×#10411yescharacteristic
84D101—44no—
85#1490—1011nomaximal, Sylow
86C101#149011yescharacteristic, complemented, Sylow
87C2×C4×D4—1011no—
88#432—1011no—
89C4×M16—1011no—
90D4⋊C8—1014no—
91C22×D4—1011no—
92C23×C4—2021no—
93C2×M16—2021no—
94C4×D4—1012no—
95C4×D4—1012no—
96C4×D4—2021no—
97C4×D4—2021no—
98C2×C4⋊C4#8793811yescharacteristic
99C2×C22⋊C4—2021no—
100C2×C42—1011no—
101C4⋊C8—1012no—
102C22⋊C8—2021no—
103#97—2021no—
104#97—2021no—
105C4×C8—1012no—
106C24—2021no—
107C2×D4—1012no—
108C2×D4—2024no—
109C2×D4—2021no—
110C22×C4—21no—
111C22×C4—1011no—
112C22×C4—1011no—
113C22×C4—4044no—
114C22×C4—2022no—
115C22×C4—2022no—
116C22×C4C2×#8793811yescharacteristic
117M16—2024no—
118C2×C8—2022no—
119C2×C8—2022no—
120C4⋊C4—21no—
121C4⋊C4C2×#8793812yes—
122C22⋊C4—2022no—
123C22⋊C4—2022no—
124C42—1011no—
125C42—1011no—
126C42—1011no—
127C42—1011no—
128C23—4042no—
129C23—4042no—
130C23—2024no—
131C23—2022no—
132C23C22⋊#8793811yescharacteristic
133D4—1014no—
134D4—2024no—
135D4—2022no—
136C2×C4—22no—
137C2×C4—22no—
138C2×C4—42no—
139C2×C4—1011no—
140C2×C4—1011no—
141C2×C4—1011no—
142C2×C4—1011no—
143C2×C4—4044no—
144C2×C4—4044no—
145C2×C4—2022no—
146C2×C4—2022no—
147C2×C4C22⋊#8793811yescharacteristic
148C2×C4C22×#8793811yescharacteristic
149C8—4042no—
150C8—2024no—
151C22—21no—
152C22—21no—
153C22—4048no—
154C22—4042no—
155C22—4042no—
156C22—2024no—
157C22#1569232012yes—
158C22C2×C22⋊#8793811yescharacteristic
159C4—21no—
160C4—42no—
161C4—1012no—
162C4—2021no—
163C4—2021no—
164C4—2021no—
165C4D101⋊M1612yes—
166C2—22no—
167C2—4044no—
168C2#2026614911yescharacteristic
169C2#2026616911yescharacteristic
170C2C2×#1569232011yescharacteristic
subgroupG/H
centerC22C2×C22⋊#87938
commutatorC2×C4×C101C22×C4
FrattiniC2×C4C22×#87938
FittingC2×C4⋊C4×C101C4
socleC22×C101C2×C22⋊C4
prime radicalC22×D404C4
cosocleC4×Dic101C23
hypercenterC2×C4⋊C4#87938
hypocenterC101#1490
LCSG ▷ C2×C4×C101 ▷ C2×C101 ▷ C101
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
1. #20266198C2semidirect
2. C4×#13108083C2semidirect
3. #20266025C2semidirect
6. C4⋊#11717581C22semidirect
10. C4×#11717581C22semidirect
60. D404M16semidirect
86. C101#1490semidirect

Maximal subgroups

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

subgroupindex
#202661982
C4×#131080832
#202660252
C2×#156922172
#1490101