Finite Group Databasebeta

← C2×#20260655 #27144946

Subgroups — C2×#20260655 #27144946

Order 12416.

908 conjugacy classes of subgroups; only the 277 normal subgroups are shown.

normal subgroups only

This group has 908 conjugacy classes of subgroups — too many to draw. Only its 277 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×Dic194C211yesmaximal, characteristic
2C22×#13095490C212yesmaximal
3#20260655C218yesmaximal, direct product factor
4C2×#15690717C212yesmaximal
5C2×#15690717C211yesmaximal, characteristic
6C22×C4⋊C4×C97C211yesmaximal, characteristic
7C22×Dic194—28no—
8C22×Dic194—24no—
9C22×Dic194C2214yes—
10C23×Dic97C2212yes—
11C23×Dic97C2212yes—
12C2×#13095490—28no—
13C2×#13095490C2218yes—
14#15690717C2214yes—
15#15690717C2218yes—
16C23×C4×C97C2211yescharacteristic
17C23×C4×C97C2211yescharacteristic
18C23×C4×C97C2211yescharacteristic
19C2×C4⋊C4×C97—24no—
20C2×C4⋊C4×C97C2214yes—
21C2×Dic194—232no—
22C2×Dic194—28no—
23C2×Dic194—216no—
24C22×Dic97—24no—
25C22×Dic97—24no—
26C22×Dic97—24no—
27C22×Dic97—24no—
28C22×Dic97D418yes—
29C22×Dic97Q818yescomplemented
30C22×Dic97C2314yes—
31C22×Dic97C2314yes—
32#13095490—216no—
33C24×C97C2311yescharacteristic
34C22×C4×C97—24no—
35C22×C4×C97—22no—
36C22×C4×C97—22no—
37C22×C4×C97—24no—
38C22×C4×C97—22no—
39C22×C4×C97D414yes—
40C22×C4×C97Q814yescomplemented
41C22×C4×C97C2312yes—
42C22×C4×C97C2312yes—
43C22×C4×C97C2312yes—
44C4⋊C4×C97—28no—
45C23×C97C2×D414yes—
46C23×C97C2×D412yes—
47C23×C97C2×Q814yes—
48C23×C97C2×Q812yes—
49C23×C97#4112yes—
50C23×C97C2411yescharacteristic
51C2×C4×C97—28no—
52C2×C4×C97—28no—
53C2×C4×C97—22no—
54C2×C4×C97—24no—
55C2×C4×C97—22no—
56C2×C4×C97—22no—
57C2×C4×C97—24no—
58C2×C4×C97—44no—
59C2×C4×C97C2×D414yes—
60C2×C4×C97C2×Q814yescomplemented
61C2×Dic97—216no—
62C2×Dic97—216no—
63C2×Dic97—24no—
64C2×Dic97—24no—
65C2×Dic97—24no—
66C2×Dic97—24no—
67C2×Dic97C2×D418yes—
68C2×Dic97C2×Q818yescomplemented
69Dic194—232no—
70C22×C97#12014yes—
71C22×C97C22⋊Q818yes—
72C22×C97C22⋊Q814yes—
73C22×C97C4⋊Q814yes—
74C22×C97C4⋊Q818yes—
75C22×C97C22×D412yes—
76C22×C97C22×D411yescharacteristic
77C22×C97C22×Q812yes—
78C22×C97C22×Q811yescharacteristic
79C22×C97C2×#4111yescharacteristic
80C4×C97—24no—
81C4×C97—24no—
82C4×C97—42no—
83Dic97—28no—
84Dic97—28no—
85C2×C97#39518yescomplemented
86C2×C97C2×#12011yescharacteristic
87C2×C97C2×C22⋊Q812yes—
88C2×C97C2×C22⋊Q811yescharacteristic
89C2×C97C2×C4⋊Q811yescharacteristic
90C2×C97C2×C4⋊Q812yes—
91C2×#395—971nomaximal, Sylow
92C97C2×#39511yescharacteristic, complemented, Sylow
93C23×Q8—971no—
94C22×C4⋊C4—972no—
95C22×C4⋊C4D9711yescharacteristic
96#395—978no—
97C2×#95—972no—
98C2×#95—971no—
99C22×Q8—974no—
100C22×Q8—1948no—
101C22×Q8—1944no—
102C23×C4—972no—
103C23×C4—972no—
104C23×C4C2×D9711yescharacteristic
105C23×C4C2×D9711yescharacteristic
106C23×C4C2×D9711yescharacteristic
107C2×C4⋊C4—24no—
108C2×C4⋊C4—978no—
109C2×C4⋊C4—1948no—
110C2×C4⋊C4C2×D9714yes—
111#95—974no—
112#95—978no—
113C24C22×D9711yescharacteristic
114C2×Q8—19416no—
115C2×Q8—19432no—
116C2×Q8—1948no—
117C22×C4—24no—
118C22×C4—22no—
119C22×C4—22no—
120C22×C4—24no—
121C22×C4—22no—
122C22×C4—978no—
123C22×C4—978no—
124C22×C4—974no—
125C22×C4—974no—
126C22×C4—1944no—
127C22×C4—1944no—
128C22×C4—1944no—
129C22×C4—1944no—
130C22×C4Dic19414yescomplemented
131C22×C4C22⋊D9714yes—
132C22×C4C22×D9712yes—
133C22×C4C22×D9712yes—
134C22×C4C22×D9712yes—
135C4⋊C4—28no—
136C4⋊C4—19416no—
137C23D4×D9714yes—
138C23C2×C22⋊D9712yes—
139C23Q8×D9714yes—
140C23C2×Dic19412yes—
141C23#1309551112yes—
142C23C23×D9711yescharacteristic
143Q8—19432no—
144C2×C4—28no—
145C2×C4—28no—
146C2×C4—24no—
147C2×C4—22no—
148C2×C4—22no—
149C2×C4—24no—
150C2×C4—22no—
151C2×C4—44no—
152C2×C4—978no—
153C2×C4—978no—
154C2×C4—19416no—
155C2×C4—19416no—
156C2×C4—1944no—
157C2×C4—1944no—
158C2×C4—1944no—
159C2×C4—1944no—
160C2×C4C2×C22⋊D9714yes—
161C2×C4C2×Dic19414yescomplemented
162C22#1569077814yes—
163C22#1569078818yes—
164C22#1569078914yes—
165C22#1569080814yes—
166C22#1569080918yes—
167C22C2×D4×D9712yes—
168C22C22×C22⋊D9711yescharacteristic
169C22C2×Q8×D9712yes—
170C22C22×Dic19411yescharacteristic
171C22C2×#1309551111yescharacteristic
172C4—24no—
173C4—24no—
174C4—42no—
175C4—1948no—
176C4—1948no—
177C2#2026065518yesdirect product factor
178C2C2×#1569077811yescharacteristic
179C2C2×#1569078812yes—
180C2C2×#1569078911yescharacteristic
181C2C2×#1569080811yescharacteristic
182C2C2×#1569080912yes—
subgroupG/H
centerC24C22×D97
commutator, cosocleC23×C97C24
FrattiniC23C23×D97
FittingC22×C4⋊C4×C97C2
socle, prime radicalC24×C97C23
hypercenterC22×C4⋊C4D97
hypocenterC97C2×#395
LCSG ▷ C23×C97 ▷ C97
UCSC1 ◁ C24 ◁ C22×C4⋊C4

Complements

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

NH ≅ G/Ntype
3. #20260655C2direct (N × H)
29. C22×Dic97Q8semidirect
40. C22×C4×C97Q8semidirect
60. C2×C4×C97C2×Q8semidirect
68. C2×Dic97C2×Q8semidirect
85. C2×C97#395semidirect
92. C97C2×#395semidirect
130. C22×C4Dic194semidirect
161. C2×C4C2×Dic194semidirect
177. C2#20260655direct (N × H)

Maximal subgroups

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

subgroupindex
C23×Dic1942
C22×#130954902
#202606552
C2×#156907172
C22×C4⋊C4×C972
C2×#39597