Finite Group Databasebeta

← C2×#30631477 #44552001

Subgroups — C2×#30631477 #44552001

Order 32128.

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×#22548632C211yesmaximal, characteristic
2C2×#22548630C211yesmaximal, characteristic
3#30631477C214yesmaximal, direct product factor
4C2×#123×C251C211yesmaximal, characteristic
5C2×#16860794—21no—
6C2×C22⋊Dic251—21no—
7#22548632—21no—
8#22548632C2212yes—
9#22548630—21no—
10#22548630C2212yes—
11C22×D4×C251C2211yescharacteristic
12C23×C4×C251C411yescharacteristic, complemented
13#123×C251—21no—
14#123×C251—21no—
15#123×C251C412yescomplemented
16#123×C251C2212yes—
17C2×C4⋊C4×C251—21no—
18C2×C22⋊C4×C251—21no—
19C2×C22⋊C4×C251C411yescharacteristic, complemented
20C22×Dic251—41no—
21#16860794—22no—
22#16860794—41no—
23C2×C251⋊C8—41no—
24C22⋊Dic251—22no—
25C22⋊Dic251—41no—
26C24×C251C2×C411yescharacteristic
27C24×C251D411yescharacteristic
28C2×D4×C251—41no—
29C2×D4×C251—41no—
30C2×D4×C251C2×C411yescharacteristic
31C2×D4×C251D411yescharacteristic
32C2×D4×C251D411yescharacteristic
33C2×D4×C251C2311yescharacteristic
34C22×C4×C251—21no—
35C22×C4×C251—21no—
36C22×C4×C251—21no—
37C22×C4×C251—41no—
38C22×C4×C251—41no—
39C22×C4×C251C2×C412yescomplemented
40C22×C4×C251D411yescharacteristic
41C4⋊C4×C251—22no—
42C4⋊C4×C251—22no—
43C22⋊C4×C251—22no—
44C22⋊C4×C251—21no—
45C22⋊C4×C251—22no—
46C22⋊C4×C251C2×C412yescomplemented
47C2×Dic251—42no—
48C2×Dic251—82no—
49C251⋊C8—42no—
50C23×C251—21no—
51C23×C251—21no—
52C23×C251—21no—
53C23×C251—21no—
54C23×C251—42no—
55C23×C251—42no—
56C23×C251C22⋊C411yescharacteristic
57C23×C251C22⋊C411yescharacteristic
58C23×C251C22⋊C411yescharacteristic
59C23×C251C22×C411yescharacteristic
60C23×C251C2×D411yescharacteristic
61D4×C251—41no—
62D4×C251—41no—
63D4×C251—41no—
64D4×C251—41no—
65C2×C4×C251—21no—
66C2×C4×C251—21no—
67C2×C4×C251—22no—
68C2×C4×C251—22no—
69C2×C4×C251—42no—
70C2×C4×C251—42no—
71C2×C4×C251—41no—
72C2×C4×C251—41no—
73C2×C4×C251—42no—
74C2×C4×C251C22⋊C411yescharacteristic
75C2×C4×C251C2×D411yescharacteristic
76C22×C251—22no—
77C22×C251—21no—
78C22×C251—21no—
79C22×C251—21no—
80C22×C251—21no—
81C22×C251—41no—
82C22×C251—41no—
83C22×C251—41no—
84C22×C251—41no—
85C22×C251—42no—
86C22×C251—42no—
87C22×C251—42no—
88C22×C251—81no—
89C22×C251#9911yescharacteristic
90C22×C251#9911yescharacteristic
91C22×C251C2×C22⋊C411yescharacteristic
92C4×C251—21no—
93C4×C251—21no—
94C4×C251—42no—
95C4×C251—42no—
96Dic251—82no—
97C2×C251—21no—
98C2×C251—21no—
99C2×C251—41no—
100C2×C251—41no—
101C2×C251—41no—
102C2×C251—41no—
103C2×C251#35212yescomplemented
104C2×C251C2×#9911yescharacteristic
105C251C2×#35211yescharacteristic, complemented, Sylow
106C2×#352—2511nomaximal, Sylow
107C2×#123D25111yescharacteristic
108C2×#100—2511no—
109C2×#99—2511no—
110#352—2514no—
111C22×D4C2×D25111yescharacteristic
112C23×C4Dic25111yescharacteristic, complemented
113C2×M16—5021no—
114#123—21no—
115#123—21no—
116#123Dic25112yescomplemented
117#123C2×D25112yes—
118C2×C4⋊C4—21no—
119C2×C22⋊C4—21no—
120C2×C22⋊C4—5021no—
121C2×C22⋊C4Dic25111yescharacteristic, complemented
122#100—5021no—
123#100—2512no—
124#99—5021no—
125#99—2512no—
126C24C2×Dic25111yescharacteristic
127C24C22⋊D25111yescharacteristic
128C2×D4—41no—
129C2×D4—41no—
130C2×D4C2×Dic25111yescharacteristic
131C2×D4C22⋊D25111yescharacteristic
132C2×D4C22⋊D25111yescharacteristic
133C2×D4C22×D25111yescharacteristic
134C22×C4—21no—
135C22×C4—21no—
136C22×C4—21no—
137C22×C4—41no—
138C22×C4—41no—
139C22×C4—10041no—
140C22×C4C2×Dic25112yescomplemented
141C22×C4C22⋊D25111yescharacteristic
142M16—10041no—
143M16—5022no—
144C2×C8—10041no—
145C4⋊C4—22no—
146C4⋊C4—22no—
147C22⋊C4—22no—
148C22⋊C4—21no—
149C22⋊C4—22no—
150C22⋊C4—10041no—
151C22⋊C4—5022no—
152C22⋊C4C2×Dic25112yescomplemented
153C23—21no—
154C23—21no—
155C23—21no—
156C23—21no—
157C23—42no—
158C23—42no—
159C23C22⋊Dic25111yescharacteristic
160C23C22⋊Dic25111yescharacteristic
161C23C22⋊Dic25111yescharacteristic
162C23C22×Dic25111yescharacteristic
163C23C2×C22⋊D25111yescharacteristic
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—20082no—
178C2×C4—10042no—
179C2×C4C22⋊Dic25111yescharacteristic
180C2×C4C2×C22⋊D25111yescharacteristic
181C8—10042no—
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#2254863011yescharacteristic
196C22#2254863011yescharacteristic
197C22C2×C22⋊Dic25111yescharacteristic
198C4—21no—
199C4—21no—
200C4—42no—
201C4—42no—
202C4—20082no—
203C2—21no—
204C2—21no—
205C2—41no—
206C2—41no—
207C2—41no—
208C2—41no—
209C2#3063147712yesdirect product factor
210C2C2×#2254863011yescharacteristic
subgroupG/H
centerC22#22548630
commutatorC23×C251C22×C4
FrattiniC2×D4C22×D251
FittingC2×#123×C251C2
socleC22×C251#99
prime radicalC22×D4×C251C22
cosocleC2×D4×C251C23
hypercenterC2×#123D251
hypocenterC251C2×#352
LCSG ▷ C23×C251 ▷ C22×C251 ▷ C2×C251 ▷ C251
UCSC1 ◁ C22 ◁ C23 ◁ C22×D4 ◁ C2×#123

Complements

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

NH ≅ G/Ntype
3. #30631477C2direct (N × H)
12. C23×C4×C251C4semidirect
15. #123×C251C4semidirect
19. C2×C22⋊C4×C251C4semidirect
39. C22×C4×C251C2×C4semidirect
46. C22⋊C4×C251C2×C4semidirect
103. C2×C251#352semidirect
105. C251C2×#352semidirect
112. C23×C4Dic251semidirect
116. #123Dic251semidirect
121. C2×C22⋊C4Dic251semidirect
140. C22×C4C2×Dic251semidirect
152. C22⋊C4C2×Dic251semidirect
209. C2#30631477direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#225486322
C2×#225486302
#306314772
C2×#123×C2512
C2×#352251