Finite Group Databasebeta

← #27156826

Subgroups — #27156826

Order 12416.

158 conjugacy classes of subgroups; only the 38 normal subgroups are shown.

normal subgroups only

This group has 158 conjugacy classes of subgroups — too many to draw. Only its 38 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#20261722C211yesmaximal, characteristic
2#20261708C211yesmaximal, characteristic
3#20260716C211yesmaximal, characteristic
4C2×#13095520—21no—
5C2×#13095520C411yescharacteristic
6C22×#11715897C411yescharacteristic
7#15690871—21no—
8#15690870C412yes—
9#15690867—21no—
10C22⋊#11715897—21no—
11C2×#13095510C2211yescharacteristic
12M16×D97—21no—
13#15690728—21no—
14#15690727C411yescharacteristic
15#100×C97C411yescharacteristic
16#13095520—22no—
17#13095520—41no—
18#13095520—41no—
19C2×#11715897—21no—
20C2×#11715897—21no—
21C2×#11715897—41no—
22C2×#11715897—41no—
23#13095510—41no—
24#13095510—41no—
25C2×Dic194D411yescharacteristic
26C2×C22⋊D97C2×C411yescharacteristic
27C2×C22⋊D97Q811yescharacteristic
28C22×Dic97C2×C411yescharacteristic
29C22×Dic97D411yescharacteristic
30C2×C4×D97D411yescharacteristic
31#13095495—21no—
32#13095494—41no—
33C8×D97—41no—
34C2×D4×C97C2×C411yescharacteristic
35M16×C97—21no—
36C23×C97C4211yescharacteristic
37C23×C97C4⋊C411yescharacteristic
38C22×D97C4⋊C411yescharacteristic
39D4×C97—41no—
40C2×C4×C97C22⋊C411yescharacteristic
41C22⋊D97—41no—
42C22⋊D97—41no—
43C2×Dic97—21no—
44C2×Dic97—21no—
45C2×Dic97—21no—
46C2×Dic97—21no—
47C2×Dic97C22⋊C411yescharacteristic
48C2×Dic97C22⋊C411yescharacteristic
49C2×Dic97C4⋊C411yescharacteristic
50C4×D97—21no—
51C4×D97—21no—
52Dic194—41no—
53#11715897—42no—
54#11715897—41no—
55#11715897—41no—
56C8×C97—41no—
57#11715895—41no—
58C22×C97—21no—
59C22×C97—21no—
60C22×C97—41no—
61C22×C97—41no—
62C22×C97#9511yescharacteristic
63C2×D97—21no—
64C2×D97—41no—
65C4×C97—21no—
66Dic97—21no—
67Dic97—21no—
68Dic97#9911yescharacteristic
69Dic97#9911yescharacteristic
70C2×C97—21no—
71C2×C97—41no—
72C2×C97—41no—
73C2×C97#34211yescharacteristic
74D97—41no—
75#1392—971nomaximal, Sylow
76C97#139211yescharacteristic, complemented, Sylow
77#413—971no—
78#413—971no—
79#408—971no—
80C2×#41—971no—
81C2×M16—971no—
82C2×M16—1941no—
83C2×M16—1941no—
84C22×C8—971no—
85#101—1941no—
86#101—1941no—
87#100—972no—
88#100—971no—
89#100#8760411yescharacteristic
90C22⋊C8—1941no—
91C22⋊C8—1941no—
92#41—3881no—
93#41—3881no—
94C2×Q8—971no—
95C2×D4—971no—
96C2×D4—971no—
97C2×D4C2×#8760411yescharacteristic
98C22×C4—971no—
99C22×C4—971no—
100C22×C4—971no—
101M16—21no—
102M16—3881no—
103M16—3881no—
104M16—3881no—
105M16—1942no—
106M16—1941no—
107C2×C8—3881no—
108C2×C8—3881no—
109C2×C8—3881no—
110C2×C8—1941no—
111C2×C8—1941no—
112C23—971no—
113C23C4×#8760411yescharacteristic
114C23C4⋊#8760411yescharacteristic
115Q8—3881no—
116D4—41no—
117D4—3881no—
118D4—3881no—
119C2×C4—971no—
120C2×C4—971no—
121C2×C4—971no—
122C2×C4—1941no—
123C2×C4—1941no—
124C2×C4—1941no—
125C2×C4—1941no—
126C2×C4—1941no—
127C2×C4—1941no—
128C2×C4C22⋊#8760411yescharacteristic
129C8—41no—
130C8—3881no—
131C8—3881no—
132C8—3881no—
133C8—3882no—
134C22—21no—
135C22—21no—
136C22—41no—
137C22—41no—
138C22—3881no—
139C22—1941no—
140C22(C2×#87604)⋊C411yescharacteristic
141C4—21no—
142C4—971no—
143C4—971no—
144C4—1941no—
145C4—1941no—
146C2—21no—
147C2—41no—
148C2—41no—
149C2—3881no—
150C2#2026161211yescharacteristic
subgroupG/H
centerC2#20261612
commutatorC23×C97C42
FrattiniC2×D4C2×#87604
Fitting#100×C97C4
socleC2×C97#342
prime radical, cosocleC2×#13095510C22
hypercenter#100#87604
hypocenterC97#1392
LCSG ▷ C23×C97 ▷ C22×C97 ▷ C2×C97 ▷ C97
UCSC1 ◁ C2 ◁ C22 ◁ C2×D4 ◁ #100

Complements

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

NH ≅ G/Ntype
76. C97#1392semidirect

Maximal subgroups

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

subgroupindex
#202617222
#202617082
#202607162
#139297