Finite Group Databasebeta

← C2×#20260594 #27144108

Subgroups — C2×#20260594 #27144108

Order 12416.

1232 conjugacy classes of subgroups; only the 349 normal subgroups are shown.

normal subgroups only

This group has 1232 conjugacy classes of subgroups — too many to draw. Only its 349 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
1C23×C4×D97C211yesmaximal, characteristic
2C22×#13095490C212yesmaximal, complemented
3C22×#13095488C212yesmaximal
4#20260594C218yesmaximal, direct product factor
5C2×#15690717C211yesmaximal, characteristic, complemented
6C2×#95×C97C211yesmaximal, characteristic, complemented
7C24×D97C2211yescharacteristic
8C23×Dic97C2212yes—
9C23×Dic97C2211yescharacteristic
10C22×C4×D97—28no—
11C22×C4×D97C418yescomplemented
12C22×C4×D97C2214yes—
13C2×#13095490—28no—
14C2×#13095490C2218yescomplemented
15C2×#13095488—28no—
16C2×#13095488C2218yes—
17#15690717C2214yescomplemented
18C23×C4×C97C2212yes—
19C23×C4×C97C2211yescharacteristic
20#95×C97C2214yescomplemented
21C23×D97—24no—
22C23×D97—24no—
23C23×D97C2×C414yes—
24C23×D97D414yes—
25C23×D97Q814yes—
26C23×D97C2312yes—
27C22×Dic97—24no—
28C22×Dic97—24no—
29C22×Dic97—24no—
30C22×Dic97C2×C414yes—
31C22×Dic97D418yes—
32C22×Dic97C2314yes—
33C22×Dic97C2312yes—
34C2×C4×D97—232no—
35C2×C4×D97—216no—
36C2×C4×D97C2×C4116yescomplemented
37#13095490—216no—
38#13095488—216no—
39C24×C97C2311yescharacteristic
40C22×C4×C97—24no—
41C22×C4×C97—24no—
42C22×C4×C97—24no—
43C22×C4×C97—24no—
44C22×C4×C97C2×C414yes—
45C22×C4×C97C2314yes—
46C22×C4×C97C2312yes—
47C23×C97C22×C412yes—
48C23×C97C2×D414yes—
49C23×C97C2×D412yes—
50C23×C97C2×Q812yes—
51C23×C97#4114yes—
52C23×C97C2411yescharacteristic
53C22×D97—28no—
54C22×D97—28no—
55C22×D97—216no—
56C22×D97—216no—
57C22×D97—24no—
58C22×D97—24no—
59C22×D97C4⋊C4116yescomplemented
60C22×D97C22×C414yes—
61C22×D97C2×D414yes—
62C22×D97C2×Q814yes—
63C2×C4×C97—28no—
64C2×C4×C97—24no—
65C2×C4×C97—24no—
66C2×C4×C97—24no—
67C2×C4×C97—24no—
68C2×C4×C97—48no—
69C2×C4×C97C22×C414yes—
70C2×Dic97—24no—
71C2×Dic97—24no—
72C2×Dic97—24no—
73C2×Dic97—48no—
74C2×Dic97C22⋊C4116yescomplemented
75C2×Dic97C22×C414yes—
76C2×Dic97C2×D418yes—
77C4×D97—232no—
78C22×C97C2×C22⋊C414yes—
79C22×C97C2×C4⋊C414yes—
80C22×C97#11714yes—
81C22×C97#12118yes—
82C22×C97C22⋊Q818yes—
83C22×C97C23×C411yescharacteristic
84C22×C97C22×D412yes—
85C22×C97C22×D411yescharacteristic
86C22×C97C22×Q811yescharacteristic
87C22×C97C2×#4112yes—
88C2×D97—24no—
89C2×D97—24no—
90C2×D97—28no—
91C2×D97—28no—
92C2×D97—232no—
93C2×D97C2×C4⋊C418yescomplemented
94C4×C97—24no—
95C4×C97—44no—
96Dic97—44no—
97Dic97C2×C22⋊C418yescomplemented
98C2×C97#38018yescomplemented
99C2×C97C22×C22⋊C411yescharacteristic
100C2×C97C22×C4⋊C411yescharacteristic
101C2×C97C2×#11711yescharacteristic
102C2×C97C2×#12112yes—
103C2×C97C2×C22⋊Q812yes—
104D97—28no—
105C2×#380—971nomaximal, Sylow
106C97C2×#38011yescharacteristic, complemented, Sylow
107C24×C4—971no—
108C22×C4⋊C4—972no—
109C22×C22⋊C4—972no—
110#380—978no—
111C2×#95—971no—
112C2×#95D9711yescharacteristic, complemented
113C25—971no—
114C23×C4—971no—
115C23×C4—978no—
116C23×C4—974no—
117C23×C4—972no—
118C23×C4—1948no—
119C23×C4C2×D9712yes—
120C23×C4C2×D9711yescharacteristic
121C2×C4⋊C4—978no—
122C2×C4⋊C4—1948no—
123C2×C22⋊C4—978no—
124C2×C22⋊C4—1948no—
125#95—974no—
126#95C2×D9714yescomplemented
127C24—974no—
128C24—974no—
129C24—974no—
130C24—972no—
131C24—1944no—
132C24—1944no—
133C24C22×D9711yescharacteristic
134C22×C4—24no—
135C22×C4—24no—
136C22×C4—24no—
137C22×C4—24no—
138C22×C4—974no—
139C22×C4—978no—
140C22×C4—972no—
141C22×C4—9716no—
142C22×C4—974no—
143C22×C4—19432no—
144C22×C4—19416no—
145C22×C4—1944no—
146C22×C4—1944no—
147C22×C4—1944no—
148C22×C4C4×D9714yes—
149C22×C4C22×D9714yes—
150C22×C4C22×D9712yes—
151C4⋊C4—19416no—
152C22⋊C4—19416no—
153C23—9716no—
154C23—974no—
155C23—974no—
156C23—974no—
157C23—1948no—
158C23—1948no—
159C23—19416no—
160C23—19416no—
161C23—1944no—
162C23—1944no—
163C23C2×C4×D9712yes—
164C23D4×D9714yes—
165C23D4×D9712yes—
166C23Q8×D9712yes—
167C23#1309551114yes—
168C23C23×D9711yescharacteristic
169C2×C4—28no—
170C2×C4—24no—
171C2×C4—24no—
172C2×C4—24no—
173C2×C4—24no—
174C2×C4—48no—
175C2×C4—9716no—
176C2×C4—974no—
177C2×C4—978no—
178C2×C4—3888no—
179C2×C4—19432no—
180C2×C4—1944no—
181C2×C4—1944no—
182C2×C4—1944no—
183C2×C4C2×C4×D9714yes—
184C22—978no—
185C22—1944no—
186C22—1944no—
187C22—1948no—
188C22—1948no—
189C22—19432no—
190C22C22⋊C4×D9714yes—
191C22C4⋊C4×D9714yes—
192C22#1569076714yes—
193C22#1569078318yes—
194C22#1569078818yes—
195C22C22×C4×D9711yescharacteristic
196C22C2×D4×D9712yes—
197C22C2×D4×D9711yescharacteristic
198C22C2×Q8×D9711yescharacteristic
199C22C2×#1309551112yes—
200C4—24no—
201C4—44no—
202C4—978no—
203C4—3884no—
204C2—1948no—
205C2#2026059418yesdirect product factor
206C2C2×C22⋊C4×D9711yescharacteristic
207C2C2×C4⋊C4×D9711yescharacteristic
208C2C2×#1569076711yescharacteristic
209C2C2×#1569078312yes—
210C2C2×#1569078812yes—
subgroupG/H
centerC24C22×D97
commutatorC22×C97C23×C4
FrattiniC23C23×D97
FittingC2×#95×C97C2
socleC24×C97C23
prime radicalC24×D97C22
cosocleC23×C97C24
hypercenterC2×#95D97
hypocenterC97C2×#380
LCSG ▷ C22×C97 ▷ C97
UCSC1 ◁ C24 ◁ C2×#95

Complements

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

NH ≅ G/Ntype
2. C22×#13095490C2semidirect
4. #20260594C2direct (N × H)
5. C2×#15690717C2semidirect
6. C2×#95×C97C2semidirect
11. C22×C4×D97C4semidirect
14. C2×#13095490C22semidirect
17. #15690717C22semidirect
20. #95×C97C22semidirect
36. C2×C4×D97C2×C4semidirect
59. C22×D97C4⋊C4semidirect
74. C2×Dic97C22⋊C4semidirect
93. C2×D97C2×C4⋊C4semidirect
97. Dic97C2×C22⋊C4semidirect
98. C2×C97#380semidirect
106. C97C2×#380semidirect
112. C2×#95D97semidirect
126. #95C2×D97semidirect
205. C2#20260594direct (N × H)

Maximal subgroups

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

subgroupindex
C23×C4×D972
C22×#130954902
C22×#130954882
#202605942
C2×#156907172
C2×#95×C972
C2×#38097