Finite Group Databasebeta

← C2×#30656527 #45665956

Subgroups — C2×#30656527 #45665956

Order 32896.

278 conjugacy classes of subgroups; only the 77 normal subgroups are shown.

normal subgroups only

This group has 278 conjugacy classes of subgroups — too many to draw. Only its 77 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×#22551509C211yesmaximal, characteristic
2C2×#22551507C211yesmaximal, characteristic
3#30656527C214yesmaximal, direct product factor
4C2×#123×C257C211yesmaximal, characteristic
5C2×#16861602—21no—
6C2×C22⋊Dic257—21no—
7#22551509—21no—
8#22551509C2212yes—
9#22551507—21no—
10#22551507C2212yes—
11C22×D4×C257C2211yescharacteristic
12C23×C4×C257C411yescharacteristic, complemented
13#123×C257—21no—
14#123×C257—21no—
15#123×C257C412yescomplemented
16#123×C257C2212yes—
17C2×C4⋊C4×C257—21no—
18C2×C22⋊C4×C257—21no—
19C2×C22⋊C4×C257C411yescharacteristic, complemented
20C22×Dic257—41no—
21#16861602—22no—
22#16861602—41no—
23C2×#14523339—41no—
24C22⋊Dic257—22no—
25C22⋊Dic257—41no—
26C24×C257C2×C411yescharacteristic
27C24×C257D411yescharacteristic
28C2×D4×C257—41no—
29C2×D4×C257—41no—
30C2×D4×C257C2×C411yescharacteristic
31C2×D4×C257D411yescharacteristic
32C2×D4×C257D411yescharacteristic
33C2×D4×C257C2311yescharacteristic
34C22×C4×C257—21no—
35C22×C4×C257—21no—
36C22×C4×C257—21no—
37C22×C4×C257—41no—
38C22×C4×C257—41no—
39C22×C4×C257C2×C412yescomplemented
40C22×C4×C257D411yescharacteristic
41C4⋊C4×C257—22no—
42C4⋊C4×C257—22no—
43C22⋊C4×C257—22no—
44C22⋊C4×C257—21no—
45C22⋊C4×C257—22no—
46C22⋊C4×C257C2×C412yescomplemented
47C2×Dic257—42no—
48C2×Dic257—82no—
49#14523339—42no—
50C23×C257—21no—
51C23×C257—21no—
52C23×C257—21no—
53C23×C257—21no—
54C23×C257—42no—
55C23×C257—42no—
56C23×C257C22⋊C411yescharacteristic
57C23×C257C22⋊C411yescharacteristic
58C23×C257C22⋊C411yescharacteristic
59C23×C257C22×C411yescharacteristic
60C23×C257C2×D411yescharacteristic
61D4×C257—41no—
62D4×C257—41no—
63D4×C257—41no—
64D4×C257—41no—
65C2×C4×C257—21no—
66C2×C4×C257—21no—
67C2×C4×C257—22no—
68C2×C4×C257—22no—
69C2×C4×C257—42no—
70C2×C4×C257—42no—
71C2×C4×C257—41no—
72C2×C4×C257—41no—
73C2×C4×C257—42no—
74C2×C4×C257C22⋊C411yescharacteristic
75C2×C4×C257C2×D411yescharacteristic
76C22×C257—22no—
77C22×C257—21no—
78C22×C257—21no—
79C22×C257—21no—
80C22×C257—21no—
81C22×C257—41no—
82C22×C257—41no—
83C22×C257—41no—
84C22×C257—41no—
85C22×C257—42no—
86C22×C257—42no—
87C22×C257—42no—
88C22×C257—81no—
89C22×C257#9911yescharacteristic
90C22×C257#9911yescharacteristic
91C22×C257C2×C22⋊C411yescharacteristic
92C4×C257—21no—
93C4×C257—21no—
94C4×C257—42no—
95C4×C257—42no—
96Dic257—82no—
97C2×C257—21no—
98C2×C257—21no—
99C2×C257—41no—
100C2×C257—41no—
101C2×C257—41no—
102C2×C257—41no—
103C2×C257#35212yescomplemented
104C2×C257C2×#9911yescharacteristic
105C257C2×#35211yescharacteristic, complemented, Sylow
106C2×#352—2571nomaximal, Sylow
107C2×#123D25711yescharacteristic
108C2×#100—2571no—
109C2×#99—2571no—
110#352—2574no—
111C22×D4C2×D25711yescharacteristic
112C23×C4Dic25711yescharacteristic, complemented
113C2×M16—5141no—
114#123—21no—
115#123—21no—
116#123Dic25712yescomplemented
117#123C2×D25712yes—
118C2×C4⋊C4—21no—
119C2×C22⋊C4—21no—
120C2×C22⋊C4—5141no—
121C2×C22⋊C4Dic25711yescharacteristic, complemented
122#100—2572no—
123#100—5141no—
124#99—2572no—
125#99—5141no—
126C24C2×Dic25711yescharacteristic
127C24C22⋊D25711yescharacteristic
128C2×D4—41no—
129C2×D4—41no—
130C2×D4C2×Dic25711yescharacteristic
131C2×D4C22⋊D25711yescharacteristic
132C2×D4C22⋊D25711yescharacteristic
133C2×D4C22×D25711yescharacteristic
134C22×C4—21no—
135C22×C4—21no—
136C22×C4—21no—
137C22×C4—41no—
138C22×C4—41no—
139C22×C4—10281no—
140C22×C4C2×Dic25712yescomplemented
141C22×C4C22⋊D25711yescharacteristic
142M16—5142no—
143M16—10281no—
144C2×C8—10281no—
145C4⋊C4—22no—
146C4⋊C4—22no—
147C22⋊C4—22no—
148C22⋊C4—21no—
149C22⋊C4—22no—
150C22⋊C4—5142no—
151C22⋊C4—10281no—
152C22⋊C4C2×Dic25712yescomplemented
153C23—21no—
154C23—21no—
155C23—21no—
156C23—21no—
157C23—42no—
158C23—42no—
159C23C22⋊Dic25711yescharacteristic
160C23C22⋊Dic25711yescharacteristic
161C23C22⋊Dic25711yescharacteristic
162C23C22×Dic25711yescharacteristic
163C23C2×C22⋊D25711yescharacteristic
164D4—41no—
165D4—41no—
166D4—41no—
167D4—41no—
168C2×C4—21no—
169C2×C4—21no—
170C2×C4—22no—
171C2×C4—22no—
172C2×C4—42no—
173C2×C4—42no—
174C2×C4—41no—
175C2×C4—41no—
176C2×C4—42no—
177C2×C4—10282no—
178C2×C4—20562no—
179C2×C4C22⋊Dic25711yescharacteristic
180C2×C4C2×C22⋊D25711yescharacteristic
181C8—10282no—
182C22—22no—
183C22—21no—
184C22—21no—
185C22—21no—
186C22—21no—
187C22—41no—
188C22—41no—
189C22—41no—
190C22—41no—
191C22—42no—
192C22—42no—
193C22—42no—
194C22—81no—
195C22#2255150711yescharacteristic
196C22#2255150711yescharacteristic
197C22C2×C22⋊Dic25711yescharacteristic
198C4—21no—
199C4—21no—
200C4—42no—
201C4—42no—
202C4—20562no—
203C2—21no—
204C2—21no—
205C2—41no—
206C2—41no—
207C2—41no—
208C2—41no—
209C2#3065652712yesdirect product factor
210C2C2×#2255150711yescharacteristic
subgroupG/H
centerC22#22551507
commutatorC23×C257C22×C4
FrattiniC2×D4C22×D257
FittingC2×#123×C257C2
socleC22×C257#99
prime radicalC22×D4×C257C22
cosocleC2×D4×C257C23
hypercenterC2×#123D257
hypocenterC257C2×#352
LCSG ▷ C23×C257 ▷ C22×C257 ▷ C2×C257 ▷ C257
UCSC1 ◁ C22 ◁ C23 ◁ C22×D4 ◁ C2×#123

Complements

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

NH ≅ G/Ntype
3. #30656527C2direct (N × H)
12. C23×C4×C257C4semidirect
15. #123×C257C4semidirect
19. C2×C22⋊C4×C257C4semidirect
39. C22×C4×C257C2×C4semidirect
46. C22⋊C4×C257C2×C4semidirect
103. C2×C257#352semidirect
105. C257C2×#352semidirect
112. C23×C4Dic257semidirect
116. #123Dic257semidirect
121. C2×C22⋊C4Dic257semidirect
140. C22×C4C2×Dic257semidirect
152. C22⋊C4C2×Dic257semidirect
209. C2#30656527direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#225515092
C2×#225515072
#306565272
C2×#123×C2572
C2×#352257