Finite Group Databasebeta

← #27156610

Subgroups — #27156610

Order 12416.

276 conjugacy classes of subgroups; only the 60 normal subgroups are shown.

normal subgroups only

This group has 276 conjugacy classes of subgroups — too many to draw. Only its 60 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#20261703C211yesmaximal, characteristic
2#20261677C211yesmaximal, characteristic
3#95×D97C211yesmaximal, characteristic
4C2×#13095519—21no—
5C2×C4⋊#87604C412yescomplemented
6C2×C22⋊#87604—21no—
7#15690867C412yescomplemented
8C22⋊#11715897—21no—
9(C2×#87604)⋊C4—21no—
10C22×C4×D97—21no—
11C22×C4×D97C2211yescharacteristic
12#15690717—21no—
13#15690717C411yescharacteristic, complemented
14#95×C97C411yescharacteristic, complemented
15C22×#87604—22no—
16#13095519—42no—
17C2×#11715897—22no—
18C4⋊#87604—42no—
19C22⋊#87604—41no—
20C22⋊#87604—41no—
21C23×D97D411yescharacteristic
22C22×Dic97—21no—
23C22×Dic97D411yescharacteristic
24C2×C4×D97—24no—
25C2×C4×D97—42no—
26C2×C4×D97—42no—
27C2×C4×D97—41no—
28C2×C4×D97—41no—
29C2×C4×D97C2×C411yescharacteristic
30C2×C4×D97C2×C411yescharacteristic
31C2×C4×D97D411yescharacteristic
32C2×C4×D97Q811yescharacteristic
33C22×C4×C97—21no—
34C22×C4×C97C2×C411yescharacteristic
35C23×C97C22⋊C411yescharacteristic
36C22×D97—22no—
37C22×D97—22no—
38C22×D97C22⋊C411yescharacteristic
39C22×D97C4⋊C411yescharacteristic
40C22×D97D811yescharacteristic
41C22×D97SD1611yescharacteristic
42C22×D97SD1611yescharacteristic
43C22×D97Q1611yescharacteristic
44C2×#87604—42no—
45C2×#87604—42no—
46C2×#87604—42no—
47C2×C4×C97—22no—
48C2×C4×C97—41no—
49C2×C4×C97—41no—
50C2×C4×C97—41no—
51C2×C4×C97C4211yescharacteristic
52C2×C4×C97C4⋊C411yescharacteristic
53C2×Dic97—22no—
54C2×Dic97—41no—
55C2×Dic97—41no—
56C2×Dic97—41no—
57C2×Dic97C22⋊C411yescharacteristic
58C2×Dic97C4⋊C411yescharacteristic
59C4×D97—22no—
60C4×D97—22no—
61C4×D97—41no—
62C4×D97—41no—
63C4×D97—44no—
64C4×D97—44no—
65#11715897—42no—
66C22×C97—21no—
67C22×C97—21no—
68C22×C97#9511yescharacteristic
69C22×C97#10211yescharacteristic
70C22×C97#10311yescharacteristic
71C2×D97—21no—
72C2×D97—21no—
73C2×D97—22no—
74C2×D97—22no—
75C2×D97—22no—
76C2×D97—22no—
77C2×D97#9912yes—
78C2×D97#10211yescharacteristic
79C2×D97#10311yescharacteristic
80C2×D97#10412yes—
81C2×D97#10611yescharacteristic
82C2×D97#10711yescharacteristic
83#87604—82no—
84C4×C97—21no—
85C4×C97—21no—
86C4×C97—42no—
87Dic97—21no—
88Dic97—21no—
89Dic97—42no—
90C2×C97—21no—
91C2×C97—21no—
92C2×C97#33911yescharacteristic
93C2×C97#34011yescharacteristic
94C2×C97#34211yescharacteristic
95D97—21no—
96D97—21no—
97D97#32712yes—
98D97#32812yes—
99#1294—971nomaximal, Sylow
100C97#129411yescharacteristic, complemented, Sylow
101C2×C22⋊C8—971no—
102#380—971no—
103C2×#95—971no—
104C23×C4—971no—
105C23×C4—1941no—
106C22×C8—1941no—
107C2×C4⋊C4—972no—
108C2×C22⋊C4—1941no—
109C22⋊C8—972no—
110C22⋊C8—1941no—
111#95—971no—
112#95—1941no—
113#95—1941no—
114#95#8760411yescharacteristic, complemented
115C24—971no—
116C22×C4—21no—
117C22×C4—971no—
118C22×C4—971no—
119C22×C4—971no—
120C22×C4—971no—
121C22×C4—971no—
122C22×C4—3881no—
123C22×C4—3881no—
124C22×C4—3882no—
125C22×C4—3882no—
126C22×C4—1944no—
127C22×C4—1942no—
128C22×C4—1941no—
129C22×C4C2×#8760411yescharacteristic
130C2×C8—3882no—
131C2×C8—1942no—
132C4⋊C4—3882no—
133C22⋊C4—3881no—
134C22⋊C4—3881no—
135C23—971no—
136C23—971no—
137C23—971no—
138C23—971no—
139C23—971no—
140C23—971no—
141C23—1942no—
142C23—1942no—
143C23C22⋊#8760411yescharacteristic
144C2×C4—22no—
145C2×C4—41no—
146C2×C4—41no—
147C2×C4—41no—
148C2×C4—971no—
149C2×C4—971no—
150C2×C4—3881no—
151C2×C4—3881no—
152C2×C4—3884no—
153C2×C4—3884no—
154C2×C4—3882no—
155C2×C4—3882no—
156C2×C4—3882no—
157C2×C4—3881no—
158C2×C4—3881no—
159C2×C4—3881no—
160C2×C4—1942no—
161C2×C4—1942no—
162C2×C4—1942no—
163C2×C4C4×#8760411yescharacteristic
164C2×C4C4⋊#8760411yescharacteristic
165C8—3882no—
166C22—21no—
167C22—21no—
168C22—972no—
169C22—971no—
170C22—971no—
171C22—972no—
172C22—971no—
173C22—971no—
174C22—1942no—
175C22—1942no—
176C22—1942no—
177C22—1942no—
178C22—1941no—
179C22—1941no—
180C22(C2×#87604)⋊C411yescharacteristic
181C22#1569087211yescharacteristic
182C22#1569087311yescharacteristic
183C4—21no—
184C4—21no—
185C4—42no—
186C4—7762no—
187C4—3882no—
188C4—1941no—
189C4—1941no—
190C2—21no—
191C2—21no—
192C2—972no—
193C2—972no—
194C2—1941no—
195C2—1941no—
196C2#2026160611yescharacteristic
197C2#2026160811yescharacteristic
198C2#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#1294
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
5. C2×C4⋊#87604C4semidirect
7. #15690867C4semidirect
13. #15690717C4semidirect
14. #95×C97C4semidirect
100. C97#1294semidirect
114. #95#87604semidirect

Maximal subgroups

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

subgroupindex
#202617032
#202616772
#95×D972
#129497