Finite Group Databasebeta

← C4×#352 #12620

Subgroups — C4×#352 #12620

Order 256.

288 conjugacy classes of subgroups; only the 83 normal subgroups are shown.

normal subgroups only

This group has 288 conjugacy classes of subgroups — too many to draw. Only its 83 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
1C4×#123C211yesmaximal, characteristic
2C2×#352C212yesmaximal
3C4×#100C211yesmaximal, characteristic
4C4×#99C211yesmaximal, characteristic
5#1390C212yesmaximal
6C2×#123C2211yescharacteristic
7C2×C4×D4C2211yescharacteristic
8C22×C42C411yescharacteristic, complemented
9C2×#100C2212yes—
10C2×#99C2212yes—
11C4×M16—21no—
12#388—21no—
13#387—21no—
14#386C2211yescharacteristic
15#385C411yescharacteristic, complemented
16#381C411yescharacteristic, complemented
17C4×C4⋊C4—21no—
18C4×C22⋊C4—21no—
19C4×C22⋊C4—21no—
20C4×C22⋊C4C411yescharacteristic, complemented
21#352C418yesdirect product factor
22#343—21no—
23#342—21no—
24C22×D4C2311yescharacteristic
25C23×C4C2×C411yescharacteristic
26C23×C4C2×C411yescharacteristic
27C23×C4C2×C411yescharacteristic
28C23×C4D411yescharacteristic
29C2×M16—22no—
30#123—22no—
31#123C2×C414yes—
32C4×D4—41no—
33C4×D4—41no—
34C2×C4⋊C4—21no—
35C2×C4⋊C4—21no—
36C2×C4⋊C4D411yescharacteristic
37C2×C22⋊C4—21no—
38C2×C22⋊C4—22no—
39C2×C22⋊C4—21no—
40C2×C22⋊C4C2×C411yescharacteristic
41C2×C22⋊C4C2×C411yescharacteristic
42C2×C22⋊C4C2×C411yescharacteristic
43C2×C22⋊C4D411yescharacteristic
44C2×C42—21no—
45C2×C42—21no—
46C2×C42—21no—
47C2×C42—41no—
48C2×C42—41no—
49C2×C42—41no—
50C2×C42D411yescharacteristic
51#100—22no—
52#100C2×C414yes—
53#99—22no—
54#99C2×C414yes—
55#97—41no—
56C4×C8—41no—
57#95—21no—
58#95—21no—
59#95—21no—
60#95—21no—
61#95—21no—
62#95—41no—
63C24C22×C411yescharacteristic
64C24C2×D411yescharacteristic
65C2×D4—41no—
66C2×D4—41no—
67C2×D4C22×C412yes—
68C2×D4#4112yes—
69C22×C4—21no—
70C22×C4—21no—
71C22×C4—21no—
72C22×C4—21no—
73C22×C4—21no—
74C22×C4—21no—
75C22×C4—21no—
76C22×C4—21no—
77C22×C4—21no—
78C22×C4—42no—
79C22×C4—42no—
80C22×C4—42no—
81C22×C4—41no—
82C22×C4—41no—
83C22×C4—41no—
84C22×C4—42no—
85C22×C4C4212yescomplemented
86C22×C4C22⋊C411yescharacteristic
87C22×C4C22⋊C411yescharacteristic
88C22×C4C22⋊C411yescharacteristic
89C22×C4C22⋊C411yescharacteristic
90C22×C4C2×D411yescharacteristic
91M16—24no—
92M16—42no—
93C2×C8—42no—
94C4⋊C4—24no—
95C4⋊C4—41no—
96C4⋊C4—42no—
97C22⋊C4—21no—
98C22⋊C4—24no—
99C22⋊C4—24no—
100C22⋊C4—41no—
101C22⋊C4—41no—
102C22⋊C4—42no—
103C22⋊C4—42no—
104C22⋊C4—41no—
105C22⋊C4C4212yescomplemented
106C42—21no—
107C42—21no—
108C42—42no—
109C42—42no—
110C42—41no—
111C42—41no—
112C42—82no—
113C23—21no—
114C23—21no—
115C23—21no—
116C23—21no—
117C23—41no—
118C23—41no—
119C23—41no—
120C23—41no—
121C23C2×C4211yescharacteristic
122C23C2×C22⋊C411yescharacteristic
123C23#11711yescharacteristic
124C23C4×D412yes—
125D4—42no—
126D4—42no—
127C2×C4—21no—
128C2×C4—21no—
129C2×C4—22no—
130C2×C4—22no—
131C2×C4—22no—
132C2×C4—22no—
133C2×C4—21no—
134C2×C4—21no—
135C2×C4—21no—
136C2×C4—42no—
137C2×C4—41no—
138C2×C4—41no—
139C2×C4—41no—
140C2×C4—42no—
141C2×C4—42no—
142C2×C4—41no—
143C2×C4—41no—
144C2×C4—41no—
145C2×C4—42no—
146C2×C4—42no—
147C2×C4—41no—
148C2×C4—42no—
149C2×C4—41no—
150C2×C4—41no—
151C2×C4—42no—
152C2×C4—41no—
153C2×C4—44no—
154C2×C4—41no—
155C2×C4—41no—
156C2×C4—81no—
157C2×C4—82no—
158C2×C4—82no—
159C2×C4#9911yescharacteristic
160C2×C4#9911yescharacteristic
161C2×C4C4×D412yes—
162C8—44no—
163C22—21no—
164C22—21no—
165C22—21no—
166C22—21no—
167C22—22no—
168C22—41no—
169C22—41no—
170C22—42no—
171C22—42no—
172C22—41no—
173C22—41no—
174C22—41no—
175C22—41no—
176C22—81no—
177C22C4×C22⋊C411yescharacteristic
178C22C2×#9911yescharacteristic
179C22#41011yescharacteristic
180C4—21no—
181C4—22no—
182C4—42no—
183C4—41no—
184C4—41no—
185C4—41no—
186C4—42no—
187C4—42no—
188C4—81no—
189C4—84no—
190C4#35212yesdirect product factor
191C2—21no—
192C2—21no—
193C2—42no—
194C2—41no—
195C2—41no—
196C2C4×#9911yescharacteristic
197C2C2×#35211yescharacteristic
198C2#212011yescharacteristic
subgroupG/H
centerC2×C4#99
commutatorC23C2×C42
Frattini, prime radical, cosocleC22×D4C23
socleC22C2×#99
LCSG ▷ C23 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C2×C4×D4 ◁ G
LECSG ▷ C22×D4 ▷ C22 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
8. C22×C42C4semidirect
15. #385C4semidirect
16. #381C4semidirect
20. C4×C22⋊C4C4semidirect
21. #352C4direct (N × H)
85. C22×C4C42semidirect
105. C22⋊C4C42semidirect
190. C4#352direct (N × H)

Maximal subgroups

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

subgroupindex
C4×#1232
C2×#3522
C4×#1002
C4×#992
#13902