Finite Group Databasebeta

← C2×#1346 #11696

Subgroups — C2×#1346 #11696

Order 256.

272 conjugacy classes of subgroups; only the 71 normal subgroups are shown.

normal subgroups only

This group has 272 conjugacy classes of subgroups — too many to draw. Only its 71 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×#398C211yesmaximal, characteristic
2C2×#343C211yesmaximal, characteristic
3C2×#324C211yesmaximal, characteristic
4#1346C214yesmaximal, direct product factor
5C22×M16—21no—
6C22×C4⋊C4—21no—
7C22×C4⋊C4C411yescharacteristic
8C22×C4⋊C4C2211yescharacteristic
9C2×C22⋊C8—21no—
10#398—21no—
11#398—21no—
12#398C412yes—
13#398C2212yes—
14C2×#95—21no—
15C2×#95C411yescharacteristic
16#343—21no—
17#343C2212yes—
18#324—21no—
19#324C2212yes—
20C23×C4—21no—
21C23×C4—21no—
22C23×C4C2×C411yescharacteristic
23C23×C4D411yescharacteristic
24C23×C4D411yescharacteristic
25C2×M16—24no—
26C2×M16—22no—
27C2×M16—41no—
28C2×M16—42no—
29C22×C8—41no—
30C22×C8—41no—
31C2×C4⋊C4—22no—
32C2×C4⋊C4—21no—
33C2×C4⋊C4—22no—
34C2×C4⋊C4—41no—
35C2×C4⋊C4—41no—
36C2×C4⋊C4—41no—
37C2×C4⋊C4—41no—
38C2×C4⋊C4—42no—
39C2×C4⋊C4—42no—
40C2×C4⋊C4C2×C412yes—
41C2×C4⋊C4C2×C411yescharacteristic
42C2×C4⋊C4D411yescharacteristic
43C2×C4⋊C4D411yescharacteristic
44C2×C4⋊C4C2311yescharacteristic
45C22⋊C8—22no—
46C22⋊C8—41no—
47#95—22no—
48#95—21no—
49#95—22no—
50#95C2×C412yes—
51C24C22⋊C411yescharacteristic
52C22×C4—21no—
53C22×C4—21no—
54C22×C4—22no—
55C22×C4—24no—
56C22×C4—21no—
57C22×C4—21no—
58C22×C4—21no—
59C22×C4—22no—
60C22×C4—21no—
61C22×C4—22no—
62C22×C4—42no—
63C22×C4—42no—
64C22×C4—42no—
65C22×C4—42no—
66C22×C4—41no—
67C22×C4—41no—
68C22×C4—42no—
69C22×C4—42no—
70C22×C4C22⋊C411yescharacteristic
71C22×C4C22⋊C411yescharacteristic
72C22×C4C22⋊C411yescharacteristic
73C22×C4D812yes—
74C22×C4SD1612yes—
75C22×C4C22×C411yescharacteristic
76C22×C4C2×D411yescharacteristic
77C22×C4C2×D411yescharacteristic
78M16—24no—
79M16—44no—
80M16—42no—
81C2×C8—44no—
82C2×C8—42no—
83C2×C8—42no—
84C2×C8—82no—
85C4⋊C4—41no—
86C4⋊C4—41no—
87C4⋊C4—41no—
88C4⋊C4—41no—
89C4⋊C4—42no—
90C4⋊C4—42no—
91C4⋊C4—44no—
92C4⋊C4—42no—
93C4⋊C4—42no—
94C23—22no—
95C23—22no—
96C23#9911yescharacteristic
97C23#9911yescharacteristic
98C23#10212yes—
99C23#10412yes—
100C23C2×C22⋊C411yescharacteristic
101C2×C4—22no—
102C2×C4—22no—
103C2×C4—22no—
104C2×C4—22no—
105C2×C4—21no—
106C2×C4—21no—
107C2×C4—21no—
108C2×C4—21no—
109C2×C4—24no—
110C2×C4—21no—
111C2×C4—21no—
112C2×C4—21no—
113C2×C4—21no—
114C2×C4—48no—
115C2×C4—42no—
116C2×C4—42no—
117C2×C4—42no—
118C2×C4—42no—
119C2×C4—42no—
120C2×C4—41no—
121C2×C4—41no—
122C2×C4—41no—
123C2×C4—41no—
124C2×C4—42no—
125C2×C4—42no—
126C2×C4—42no—
127C2×C4—81no—
128C2×C4—82no—
129C2×C4—82no—
130C2×C4#10212yes—
131C2×C4C2×D811yescharacteristic
132C2×C4C2×SD1611yescharacteristic
133C8—44no—
134C8—82no—
135C22—24no—
136C22—24no—
137C22—21no—
138C22—21no—
139C22—21no—
140C22—21no—
141C22#32712yes—
142C22#32712yes—
143C22#35212yes—
144C22#35612yes—
145C22C2×#9911yescharacteristic
146C22C2×#10211yescharacteristic
147C22C2×#10411yescharacteristic
148C4—21no—
149C4—22no—
150C4—21no—
151C4—44no—
152C4—41no—
153C4—41no—
154C4—41no—
155C4—41no—
156C4—82no—
157C2—21no—
158C2—22no—
159C2—21no—
160C2#134614yesdirect product factor
161C2C2×#32711yescharacteristic
162C2C2×#35211yescharacteristic
163C2C2×#35611yescharacteristic
subgroupG/H
center, socleC23#99
commutatorC22×C4C22×C4
Frattini, cosocleC2×C4⋊C4C23
prime radicalC24C22⋊C4
LCSG ▷ C22×C4 ▷ C23 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C24 ◁ C22×C4⋊C4 ◁ G
LECSG ▷ C2×C4⋊C4 ▷ C23 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
4. #1346C2direct (N × H)
160. C2#1346direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#3982
C2×#3432
C2×#3242
#13462