Finite Group Databasebeta

← #27186386

Subgroups — #27186386

Order 12928.

252 conjugacy classes of subgroups; only the 64 normal subgroups are shown.

normal subgroups only

This group has 252 conjugacy classes of subgroups — too many to draw. Only its 64 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#20266198C212yesmaximal, complemented
2#20266022C212yesmaximal, complemented
3#20266021C212yesmaximal
4C2×#15692213C211yesmaximal, characteristic
5C4⋊#11717581—22no—
6C22⋊#11717581C2214yes—
7#15692310—22no—
8C22×C4×D101C411yescharacteristic
9#15692213—22no—
10#15692213—22no—
11C2×C4⋊Dic101C2211yescharacteristic
12C2×#13108051C411yescharacteristic
13C2×#13108051C2211yescharacteristic
14C2×C4×Dic101C411yescharacteristic
15C2×C4×Dic101C2211yescharacteristic
16C2×C4⋊C4×C101C411yescharacteristic
17C2×#11717581—24no—
18C23×D101C2×C411yescharacteristic
19C22×Dic101C2×C411yescharacteristic
20C22×Dic101C2×C411yescharacteristic
21C22×Dic101C2311yescharacteristic
22C2×C4×D101—22no—
23C2×C4×D101—22no—
24C2×C4×D101—21no—
25C2×C4×D101—21no—
26C4⋊Dic101—22no—
27#13108051—22no—
28#13108051—22no—
29C4×Dic101—21no—
30C4×Dic101—21no—
31C4×Dic101D412yes—
32C4×Dic101D412yes—
33C22×C4×C101C2×C411yescharacteristic
34C22×C4×C101C2×C411yescharacteristic
35C22×C4×C101C2×C411yescharacteristic
36C4⋊C4×C101—22no—
37C23×C101C22×C411yescharacteristic
38C22×D101—21no—
39C22×D101—21no—
40C22×D101—41no—
41C22×D101—41no—
42C22×D101M1612yes—
43C2×C4×C101—21no—
44C2×C4×C101—21no—
45C2×C4×C101—21no—
46C2×C4×C101—41no—
47C2×C4×C101—41no—
48C2×C4×C101C22⋊C412yes—
49C2×C4×C101M1612yes—
50C2×Dic101—21no—
51C2×Dic101—21no—
52C2×Dic101—21no—
53C2×Dic101—41no—
54C2×Dic101—41no—
55C2×Dic101C22⋊C411yescharacteristic
56C2×Dic101C22⋊C411yescharacteristic
57C2×Dic101C2×D412yes—
58C4×D101—24no—
59C4×D101—24no—
60#11717581—44no—
61C22×C101—21no—
62C22×C101—21no—
63C22×C101C2×C22⋊C411yescharacteristic
64C22×C101C2×M1611yescharacteristic
65C22×C101C2×M1611yescharacteristic
66C2×D101—22no—
67C2×D101—42no—
68C2×D101—41no—
69C2×D101—41no—
70C2×D101—42no—
71C4×C101—22no—
72C4×C101—22no—
73C4×C101—41no—
74Dic101—21no—
75Dic101—21no—
76Dic101—22no—
77Dic101—41no—
78C2×C101—21no—
79C2×C101—21no—
80C2×C101#40711yescharacteristic
81C2×C101#41011yescharacteristic
82C2×C101#41311yescharacteristic
83D101—42no—
84#1464—1011nomaximal, Sylow
85C101#146411yescharacteristic, complemented, Sylow
86C2×#117—1011no—
87#432—1012no—
88#324—1012no—
89#323—1012no—
90C23×C4—1011no—
91#117—2022no—
92#117—2022no—
93C2×C4⋊C4—1011no—
94C2×C4⋊C4#8793811yescharacteristic
95C2×C22⋊C4—1011no—
96C2×C22⋊C4—1011no—
97C2×C42—1011no—
98C2×C42—1011no—
99C4⋊C8—2022no—
100C22⋊C8—1014no—
101#97—2022no—
102C24—1011no—
103C22×C4—1011no—
104C22×C4—1011no—
105C22×C4—1011no—
106C22×C4—2021no—
107C22×C4—2021no—
108C22×C4—2022no—
109C22×C4—2022no—
110C22×C4C2×#8793811yescharacteristic
111C22×C4C2×#8793811yescharacteristic
112C22×C4C2×#8793811yescharacteristic
113C2×C8—2024no—
114C4⋊C4—22no—
115C4⋊C4—2022no—
116C22⋊C4—2022no—
117C22⋊C4—2022no—
118C42—1012no—
119C42—1012no—
120C42—2021no—
121C42—2021no—
122C23—1012no—
123C23—4041no—
124C23—4041no—
125C23—2021no—
126C23—2021no—
127C23C22×#8793811yescharacteristic
128C2×C4—21no—
129C2×C4—21no—
130C2×C4—21no—
131C2×C4—41no—
132C2×C4—41no—
133C2×C4—1011no—
134C2×C4—1011no—
135C2×C4—1012no—
136C2×C4—4041no—
137C2×C4—4041no—
138C2×C4—2024no—
139C2×C4—2024no—
140C2×C4—2021no—
141C2×C4—2021no—
142C2×C4—2021no—
143C2×C4C22⋊#8793812yes—
144C2×C4#1310808412yes—
145C8—4044no—
146C22—21no—
147C22—21no—
148C22—4042no—
149C22—4042no—
150C22—4041no—
151C22—4041no—
152C22—2022no—
153C22C2×C22⋊#8793811yescharacteristic
154C22D101⋊M1611yescharacteristic
155C22C2×#1310808411yescharacteristic
156C4—22no—
157C4—22no—
158C4—41no—
159C4—4041no—
160C4—2021no—
161C4—2021no—
162C4—2022no—
163C2—21no—
164C2—21no—
165C2—4042no—
166C2#2026614811yescharacteristic
167C2#2026615811yescharacteristic
168C2#2026616411yescharacteristic
subgroupG/H
centerC22C2×C22⋊#87938
commutatorC23×C101C22×C4
FrattiniC23C22×#87938
FittingC2×C4⋊C4×C101C4
socleC22×C101C2×C22⋊C4
prime radicalC23×D101C2×C4
cosocleC22×Dic101C23
hypercenterC2×C4⋊C4#87938
hypocenterC101#1464
LCSG ▷ C23×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. #20266022C2semidirect
85. C101#1464semidirect

Maximal subgroups

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

subgroupindex
#202661982
#202660222
#202660212
C2×#156922132
#1464101