Finite Group Databasebeta

← #27140090

Subgroups — #27140090

Order 12416.

204 conjugacy classes of subgroups; only the 63 normal subgroups are shown.

normal subgroups only

This group has 204 conjugacy classes of subgroups — too many to draw. Only its 63 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
1C2×#15690800C211yesmaximal, characteristic
2#20260789C211yesmaximal, characteristic
3#20260785C211yesmaximal, characteristic
4#20260461C211yesmaximal, characteristic
5#20260460C211yesmaximal, characteristic
6#20260460C211yesmaximal, characteristic
7#324×C97C211yesmaximal, characteristic
8#15690800—21no—
9#15690800—21no—
10#15690800—21no—
11#15690800—21no—
12C2×C4⋊Dic97C411yescharacteristic
13C2×#13095490C411yescharacteristic
14C2×#13095490C411yescharacteristic
15C2×#13095490C411yescharacteristic
16C2×#13095490C2211yescharacteristic
17C2×C4×Dic97C2211yescharacteristic
18#15690739—21no—
19#15690739—21no—
20C22⋊#11715895C2211yescharacteristic
21C22⋊#11715895C2211yescharacteristic
22#15690720—21no—
23C8×Dic97—21no—
24C2×C4⋊C4×C97C2211yescharacteristic
25C22⋊C8×C97C2211yescharacteristic
26C22⋊C8×C97C2211yescharacteristic
27C22×Dic97C2×C411yescharacteristic
28C22×Dic97C2×C411yescharacteristic
29C22×Dic97C2×C411yescharacteristic
30C22×Dic97C2×C411yescharacteristic
31C2×#11715895—21no—
32C2×#11715895—21no—
33C4⋊Dic97—21no—
34C4⋊Dic97—21no—
35#13095490—21no—
36#13095490—21no—
37#13095490—21no—
38#13095490—21no—
39#13095490—21no—
40#13095490—21no—
41#13095490—21no—
42#13095490—21no—
43C4×Dic97D411yescharacteristic
44C4×Dic97D411yescharacteristic
45C4×Dic97D411yescharacteristic
46C4×Dic97D411yescharacteristic
47C22×C4×C97C2×C411yescharacteristic
48C22×C4×C97C2×C411yescharacteristic
49C22×C4×C97C2311yescharacteristic
50C2×C8×C97—21no—
51C2×C8×C97—21no—
52C4⋊C4×C97—21no—
53C4⋊C4×C97—21no—
54C23×C97C22×C411yescharacteristic
55C2×C4×C97—21no—
56C2×C4×C97—21no—
57C2×C4×C97—21no—
58C2×C4×C97—21no—
59C2×C4×C97—41no—
60C2×C4×C97—41no—
61C2×C4×C97C2×D411yescharacteristic
62C2×C4×C97C2×D411yescharacteristic
63C2×Dic97—21no—
64C2×Dic97—21no—
65C2×Dic97—22no—
66C2×Dic97—21no—
67C2×Dic97—21no—
68C2×Dic97—21no—
69C2×Dic97—21no—
70C2×Dic97—41no—
71C2×Dic97C22⋊C411yescharacteristic
72C2×Dic97C22⋊C411yescharacteristic
73C2×Dic97C22⋊C411yescharacteristic
74C2×Dic97C22⋊C411yescharacteristic
75C8×C97—41no—
76C8×C97—41no—
77#11715895—41no—
78#11715895—41no—
79C22×C97—21no—
80C22×C97—21no—
81C22×C97C2×C22⋊C411yescharacteristic
82C22×C97#13111yescharacteristic
83C22×C97#13111yescharacteristic
84C4×C97—21no—
85C4×C97—21no—
86C4×C97—41no—
87C4×C97—41no—
88Dic97—21no—
89Dic97—21no—
90Dic97—21no—
91Dic97—41no—
92Dic97—41no—
93Dic97#10112yes—
94C2×C97—21no—
95C2×C97—21no—
96C2×C97#40811yescharacteristic
97C2×C97#41011yescharacteristic
98C2×C97C2×#10111yescharacteristic
99#1470—971nomaximal, Sylow
100C97#147011yescharacteristic, complemented, Sylow
101C2×#125—971no—
102#432—971no—
103#431—971no—
104#324—971no—
105#324—971no—
106#324—971no—
107#324D9711yescharacteristic
108#125—1941no—
109#125—1941no—
110#125—1941no—
111#125—1941no—
112C2×C4⋊C4—971no—
113C2×C4⋊C4—971no—
114C2×C4⋊C4—971no—
115C2×C4⋊C4—971no—
116C2×C4⋊C4—971no—
117C2×C4⋊C4C2×D9711yescharacteristic
118C2×C42—971no—
119C4⋊C8—1941no—
120C4⋊C8—1941no—
121C22⋊C8—971no—
122C22⋊C8—971no—
123C22⋊C8C2×D9711yescharacteristic
124C22⋊C8C2×D9711yescharacteristic
125#97—1941no—
126C4×C8—1941no—
127C22×C4—971no—
128C22×C4—971no—
129C22×C4—971no—
130C22×C4—971no—
131C22×C4C4×D9711yescharacteristic
132C22×C4C4×D9711yescharacteristic
133C22×C4C22×D9711yescharacteristic
134C2×C8—21no—
135C2×C8—21no—
136C2×C8—1941no—
137C2×C8—1941no—
138C4⋊C4—21no—
139C4⋊C4—21no—
140C4⋊C4—1941no—
141C4⋊C4—1941no—
142C4⋊C4—1941no—
143C4⋊C4—1941no—
144C4⋊C4—1941no—
145C4⋊C4—1941no—
146C4⋊C4—1941no—
147C4⋊C4—1941no—
148C4⋊C4—1941no—
149C4⋊C4—1941no—
150C42—971no—
151C42—971no—
152C42—971no—
153C42—971no—
154C23C2×C4×D9711yescharacteristic
155C2×C4—21no—
156C2×C4—21no—
157C2×C4—21no—
158C2×C4—21no—
159C2×C4—41no—
160C2×C4—41no—
161C2×C4—971no—
162C2×C4—971no—
163C2×C4—971no—
164C2×C4—971no—
165C2×C4—3881no—
166C2×C4—1942no—
167C2×C4—1941no—
168C2×C4—1941no—
169C2×C4—1941no—
170C2×C4—1941no—
171C2×C4—1941no—
172C2×C4—1941no—
173C2×C4D4×D9711yescharacteristic
174C2×C4D4×D9711yescharacteristic
175C8—41no—
176C8—41no—
177C8—3881no—
178C8—3881no—
179C22—21no—
180C22—21no—
181C22C22⋊C4×D9711yescharacteristic
182C22#1569081611yescharacteristic
183C22#1569081811yescharacteristic
184C4—21no—
185C4—21no—
186C4—41no—
187C4—41no—
188C4—972no—
189C4—3881no—
190C4—3881no—
191C4—1941no—
192C4—1941no—
193C4—1941no—
194C2—21no—
195C2—21no—
196C2#2026070011yescharacteristic
197C2#2026070711yescharacteristic
198C2#101×D9711yescharacteristic
subgroupG/H
centerC22C22⋊C4×D97
commutator, prime radicalC23×C97C22×C4
FrattiniC22×C4C22×D97
Fitting#324×C97C2
socleC22×C97C2×C22⋊C4
cosocleC22×C4×C97C23
hypercenter#324D97
hypocenterC97#1470
LCSG ▷ C23×C97 ▷ C2×C97 ▷ C97
UCSC1 ◁ C22 ◁ C22×C4 ◁ #324

Complements

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

NH ≅ G/Ntype
100. C97#1470semidirect

Maximal subgroups

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

subgroupindex
C2×#156908002
#202607892
#202607852
#202604612
#202604602
#324×C972
#147097