Finite Group Databasebeta

← C2×#20261638 #27157986

Subgroups — C2×#20261638 #27157986

Order 12416.

278 conjugacy classes of subgroups; only the 58 normal subgroups are shown.

normal subgroups only

This group has 278 conjugacy classes of subgroups — too many to draw. Only its 58 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×#15690870C211yesmaximal, characteristic
2C2×#15690868C211yesmaximal, characteristic
3#20261638C214yesmaximal, direct product factor
4C2×#15690794C211yesmaximal, characteristic
5C2×#13095520—21no—
6C2×C22⋊#87604—21no—
7#15690870—21no—
8#15690870C2212yes—
9#15690868—21no—
10#15690868C2212yes—
11C22×C22⋊D97C2211yescharacteristic
12C23×Dic97C411yescharacteristic, complemented
13#15690794—21no—
14#15690794—21no—
15#15690794C412yescomplemented
16#15690794C2212yes—
17C2×C4⋊Dic97—21no—
18C2×#13095488—21no—
19C2×C22⋊C4×C97C411yescharacteristic, complemented
20C22×#87604—41no—
21#13095520—22no—
22#13095520—41no—
23C2×#11715897—41no—
24C22⋊#87604—22no—
25C22⋊#87604—41no—
26C23×D97D411yescharacteristic
27C2×C22⋊D97—41no—
28C2×C22⋊D97—41no—
29C2×C22⋊D97C2×C411yescharacteristic
30C2×C22⋊D97D411yescharacteristic
31C2×C22⋊D97D411yescharacteristic
32C2×C22⋊D97C2311yescharacteristic
33C22×Dic97—21no—
34C22×Dic97—21no—
35C22×Dic97—41no—
36C22×Dic97—41no—
37C22×Dic97C2×C412yescomplemented
38C22×Dic97D411yescharacteristic
39C4⋊Dic97—22no—
40C4⋊Dic97—22no—
41#13095488—22no—
42#13095488—22no—
43C24×C97C2×C411yescharacteristic
44C22×C4×C97—21no—
45C22⋊C4×C97—21no—
46C22⋊C4×C97C2×C412yescomplemented
47C23×C97—21no—
48C23×C97—21no—
49C23×C97—42no—
50C23×C97C22⋊C411yescharacteristic
51C23×C97C22⋊C411yescharacteristic
52C23×C97C22×C411yescharacteristic
53C22×D97—21no—
54C22×D97—21no—
55C22×D97—42no—
56C22×D97C22⋊C411yescharacteristic
57C22×D97C2×D411yescharacteristic
58C2×#87604—42no—
59C2×#87604—82no—
60C2×C4×C97—22no—
61C2×C4×C97—42no—
62C22⋊D97—41no—
63C22⋊D97—41no—
64C22⋊D97—41no—
65C22⋊D97—41no—
66C2×Dic97—21no—
67C2×Dic97—21no—
68C2×Dic97—22no—
69C2×Dic97—42no—
70C2×Dic97—41no—
71C2×Dic97—41no—
72C2×Dic97—42no—
73C2×Dic97C22⋊C411yescharacteristic
74C2×Dic97C2×D411yescharacteristic
75#11715897—42no—
76C22×C97—22no—
77C22×C97—21no—
78C22×C97—21no—
79C22×C97—41no—
80C22×C97—41no—
81C22×C97—42no—
82C22×C97—42no—
83C22×C97#9911yescharacteristic
84C22×C97#9911yescharacteristic
85C22×C97C2×C22⋊C411yescharacteristic
86C2×D97—21no—
87C2×D97—21no—
88C2×D97—42no—
89C2×D97—41no—
90C2×D97—41no—
91C2×D97—81no—
92#87604—82no—
93C4×C97—42no—
94Dic97—21no—
95Dic97—21no—
96Dic97—42no—
97C2×C97—21no—
98C2×C97—21no—
99C2×C97—41no—
100C2×C97—41no—
101C2×C97#35212yescomplemented
102C2×C97C2×#9911yescharacteristic
103D97—41no—
104D97—41no—
105C2×#352—971nomaximal, Sylow
106C97C2×#35211yescharacteristic, complemented, Sylow
107C2×#123—971no—
108C2×#100—971no—
109C2×#99—971no—
110#352—974no—
111C22×D4—971no—
112C23×C4—971no—
113C2×M16—1941no—
114#123—972no—
115#123—972no—
116#123—1941no—
117#123—1941no—
118C2×C4⋊C4—1941no—
119C2×C22⋊C4—1941no—
120C2×C22⋊C4—1941no—
121C2×C22⋊C4#8760411yescharacteristic, complemented
122#100—972no—
123#100—1941no—
124#99—972no—
125#99—1941no—
126C24—971no—
127C24C2×#8760411yescharacteristic
128C2×D4—971no—
129C2×D4—971no—
130C2×D4—971no—
131C2×D4—971no—
132C2×D4—3881no—
133C2×D4—3881no—
134C22×C4—21no—
135C22×C4—971no—
136C22×C4—972no—
137C22×C4—3881no—
138C22×C4—3881no—
139C22×C4—3881no—
140C22×C4—1941no—
141C22×C4—1941no—
142M16—3881no—
143M16—1942no—
144C2×C8—3881no—
145C4⋊C4—1942no—
146C4⋊C4—1942no—
147C22⋊C4—21no—
148C22⋊C4—3881no—
149C22⋊C4—1942no—
150C22⋊C4—1942no—
151C22⋊C4—1942no—
152C22⋊C4C2×#8760412yescomplemented
153C23—21no—
154C23—21no—
155C23—42no—
156C23—971no—
157C23—971no—
158C23—3882no—
159C23—1941no—
160C23—1941no—
161C23C22⋊#8760411yescharacteristic
162C23C22⋊#8760411yescharacteristic
163C23C22×#8760411yescharacteristic
164D4—3881no—
165D4—3881no—
166D4—3881no—
167D4—3881no—
168C2×C4—22no—
169C2×C4—42no—
170C2×C4—7762no—
171C2×C4—971no—
172C2×C4—971no—
173C2×C4—3882no—
174C2×C4—3882no—
175C2×C4—3881no—
176C2×C4—3881no—
177C2×C4—3882no—
178C2×C4—1942no—
179C2×C4—1941no—
180C2×C4—1941no—
181C8—3882no—
182C22—22no—
183C22—21no—
184C22—21no—
185C22—41no—
186C22—41no—
187C22—42no—
188C22—42no—
189C22—7761no—
190C22—3881no—
191C22—3881no—
192C22—3882no—
193C22—1941no—
194C22—1941no—
195C22#1569086911yescharacteristic
196C22#1569086911yescharacteristic
197C22C2×C22⋊#8760411yescharacteristic
198C4—42no—
199C4—7762no—
200C4—3882no—
201C4—1941no—
202C4—1941no—
203C2—21no—
204C2—21no—
205C2—41no—
206C2—41no—
207C2—3881no—
208C2—3881no—
209C2#2026163812yesdirect product factor
210C2C2×#1569086911yescharacteristic
subgroupG/H
centerC22#15690869
commutatorC23×C97C22×C4
FrattiniC23C22×#87604
FittingC2×C22⋊C4×C97C4
socleC22×C97#99
prime radicalC22×C22⋊D97C22
cosocleC2×C22⋊D97C23
hypercenterC2×C22⋊C4#87604
hypocenterC97C2×#352
LCSG ▷ C23×C97 ▷ C22×C97 ▷ C2×C97 ▷ C97
UCSC1 ◁ C22 ◁ C23 ◁ C24 ◁ C2×C22⋊C4

Complements

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

NH ≅ G/Ntype
3. #20261638C2direct (N × H)
12. C23×Dic97C4semidirect
15. #15690794C4semidirect
19. C2×C22⋊C4×C97C4semidirect
37. C22×Dic97C2×C4semidirect
46. C22⋊C4×C97C2×C4semidirect
101. C2×C97#352semidirect
106. C97C2×#352semidirect
121. C2×C22⋊C4#87604semidirect
152. C22⋊C4C2×#87604semidirect
209. C2#20261638direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#156908702
C2×#156908682
#202616382
C2×#156907942
C2×#35297