Finite Group Databasebeta

← #27156617

Subgroups — #27156617

Order 12416.

246 conjugacy classes of subgroups; only the 48 normal subgroups are shown.

normal subgroups only

This group has 246 conjugacy classes of subgroups — too many to draw. Only its 48 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#20261706C211yesmaximal, characteristic
2C4×C22⋊#87604C211yesmaximal, characteristic
3#20260582C211yesmaximal, characteristic
4C2×#13095521C412yescomplemented
5C2×C22⋊#87604—21no—
6C2×C4×#87604—21no—
7#15690867—21no—
8C22⋊#11715897—21no—
9(C2×#87604)⋊C4C412yescomplemented
10C22×C4×D97C2211yescharacteristic
11C2×#13095488—21no—
12C2×C4×Dic97—21no—
13#15690717C411yescharacteristic, complemented
14#95×C97C411yescharacteristic, complemented
15C22×#87604—22no—
16#13095521—42no—
17C2×#11715897—22no—
18C22⋊#87604—22no—
19C22⋊#87604—22no—
20C4×#87604—42no—
21C23×D97D411yescharacteristic
22C22×Dic97—21no—
23C22×Dic97D411yescharacteristic
24C2×C4×D97—42no—
25C2×C4×D97C2×C411yescharacteristic
26C2×C4×D97C2×C411yescharacteristic
27C2×C4×D97D411yescharacteristic
28C2×C4×D97Q811yescharacteristic
29#13095488—24no—
30C4×Dic97—42no—
31C22×C4×C97—21no—
32C22×C4×C97C2×C411yescharacteristic
33C23×C97C22⋊C411yescharacteristic
34C22×D97—21no—
35C22×D97—21no—
36C22×D97—22no—
37C22×D97—41no—
38C22×D97C22⋊C411yescharacteristic
39C22×D97C4⋊C411yescharacteristic
40C2×#87604—24no—
41C2×#87604—42no—
42C2×#87604—42no—
43C2×C4×C97—22no—
44C2×C4×C97—41no—
45C2×C4×C97—41no—
46C2×C4×C97—41no—
47C2×C4×C97C4211yescharacteristic
48C2×C4×C97C4⋊C411yescharacteristic
49C2×Dic97—22no—
50C2×Dic97—22no—
51C2×Dic97—41no—
52C2×Dic97—41no—
53C2×Dic97C22⋊C411yescharacteristic
54C2×Dic97C4⋊C411yescharacteristic
55C4×D97—22no—
56C4×D97—22no—
57C4×D97—41no—
58C4×D97—41no—
59#11715897—42no—
60C22×C97—21no—
61C22×C97—21no—
62C22×C97#9511yescharacteristic
63C22×C97#10411yescharacteristic
64C22×C97#10411yescharacteristic
65C2×D97—21no—
66C2×D97—21no—
67C2×D97—21no—
68C2×D97—21no—
69C2×D97—21no—
70C2×D97—42no—
71C2×D97—42no—
72C2×D97#10412yes—
73#87604—44no—
74C4×C97—21no—
75C4×C97—21no—
76C4×C97—42no—
77Dic97—21no—
78Dic97—42no—
79Dic97#9912yes—
80C2×C97—21no—
81C2×C97—21no—
82C2×C97#33911yescharacteristic
83C2×C97#33911yescharacteristic
84C2×C97#34211yescharacteristic
85D97—22no—
86D97—41no—
87#1297—971nomaximal, Sylow
88C97#129711yescharacteristic, complemented, Sylow
89#407—971no—
90C4×C22⋊C4—971no—
91C4×C22⋊C4—971no—
92C23×C4—971no—
93C2×M16—972no—
94C2×C22⋊C4—1941no—
95C2×C22⋊C4—1941no—
96C2×C42—1941no—
97C2×C42—1941no—
98C22⋊C8—1941no—
99C22⋊C8—1941no—
100#95—972no—
101#95—971no—
102#95#8760411yescharacteristic, complemented
103C24—971no—
104C22×C4—21no—
105C22×C4—971no—
106C22×C4—971no—
107C22×C4—971no—
108C22×C4—971no—
109C22×C4—971no—
110C22×C4—3882no—
111C22×C4—1942no—
112C22×C4—1941no—
113C22×C4C2×#8760411yescharacteristic
114M16—3882no—
115C2×C8—1942no—
116C22⋊C4—1944no—
117C22⋊C4—1942no—
118C22⋊C4—1942no—
119C42—3882no—
120C42—3882no—
121C23—971no—
122C23—971no—
123C23—3881no—
124C23—1942no—
125C23—1941no—
126C23—1941no—
127C23C22⋊#8760411yescharacteristic
128C2×C4—22no—
129C2×C4—41no—
130C2×C4—41no—
131C2×C4—41no—
132C2×C4—971no—
133C2×C4—971no—
134C2×C4—3881no—
135C2×C4—3881no—
136C2×C4—3881no—
137C2×C4—3882no—
138C2×C4—3882no—
139C2×C4—3881no—
140C2×C4—1942no—
141C2×C4—1942no—
142C2×C4—1942no—
143C2×C4—1942no—
144C2×C4—1944no—
145C2×C4C4×#8760411yescharacteristic
146C2×C4C4⋊#8760411yescharacteristic
147C8—3882no—
148C22—21no—
149C22—21no—
150C22—972no—
151C22—3882no—
152C22—3882no—
153C22—1941no—
154C22—1941no—
155C22—1941no—
156C22—1941no—
157C22—1941no—
158C22(C2×#87604)⋊C411yescharacteristic
159C22#1569087411yescharacteristic
160C22#1569087511yescharacteristic
161C4—21no—
162C4—21no—
163C4—42no—
164C4—972no—
165C4—3882no—
166C4—3884no—
167C4—1941no—
168C2—21no—
169C2—21no—
170C2—3881no—
171C2—1942no—
172C2#2026160511yescharacteristic
173C2#2026160611yescharacteristic
174C2#2026161211yescharacteristic
subgroupG/H
centerC22(C2×#87604)⋊C4
commutatorC2×C4×C97C42
FrattiniC22×C4C2×#87604
Fitting#95×C97C4
socleC22×C97#95
prime radicalC23×D97D4
cosocleC22×C4×D97C22
hypercenter#95#87604
hypocenterC97#1297
LCSG ▷ C2×C4×C97 ▷ C22×C97 ▷ C97
UCSC1 ◁ C22 ◁ C22×C4 ◁ #95

Complements

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

NH ≅ G/Ntype
4. C2×#13095521C4semidirect
9. (C2×#87604)⋊C4C4semidirect
13. #15690717C4semidirect
14. #95×C97C4semidirect
88. C97#1297semidirect
102. #95#87604semidirect

Maximal subgroups

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

subgroupindex
#202617062
C4×C22⋊#876042
#202605822
#129797