Finite Group Databasebeta

← C2×#1353 #11719

Subgroups — C2×#1353 #11719

Order 256.

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

normal subgroups only

This group has 250 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×#400C211yesmaximal, characteristic
2C2×#343C211yesmaximal, characteristic
3C2×#324C211yesmaximal, characteristic
4#1353C214yesmaximal, direct product factor
5C22×M16—21no—
6C22×C4⋊C4C411yescharacteristic
7C22×C4⋊C4C2211yescharacteristic
8C2×C22⋊C8—21no—
9#400—21no—
10#400—21no—
11#400C412yes—
12#400C2212yes—
13C2×#95—21no—
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—21no—
32C2×C4⋊C4—41no—
33C2×C4⋊C4—41no—
34C2×C4⋊C4—41no—
35C2×C4⋊C4—41no—
36C2×C4⋊C4C2×C412yes—
37C2×C4⋊C4C2×C411yescharacteristic
38C2×C4⋊C4D411yescharacteristic
39C2×C4⋊C4D411yescharacteristic
40C2×C4⋊C4C2311yescharacteristic
41C22⋊C8—22no—
42C22⋊C8—41no—
43#95—22no—
44#95—22no—
45#95—21no—
46#95—22no—
47#95—22no—
48#95C2×C412yes—
49C24C22⋊C411yescharacteristic
50C22×C4—21no—
51C22×C4—21no—
52C22×C4—22no—
53C22×C4—21no—
54C22×C4—21no—
55C22×C4—21no—
56C22×C4—21no—
57C22×C4—22no—
58C22×C4—22no—
59C22×C4—42no—
60C22×C4—42no—
61C22×C4—42no—
62C22×C4—42no—
63C22×C4—44no—
64C22×C4—41no—
65C22×C4—41no—
66C22×C4—42no—
67C22×C4C22⋊C411yescharacteristic
68C22×C4C22⋊C411yescharacteristic
69C22×C4C22⋊C411yescharacteristic
70C22×C4SD1612yes—
71C22×C4Q1612yes—
72C22×C4C22×C411yescharacteristic
73C22×C4C2×D411yescharacteristic
74C22×C4C2×D411yescharacteristic
75M16—24no—
76M16—44no—
77M16—42no—
78C2×C8—44no—
79C2×C8—42no—
80C2×C8—42no—
81C2×C8—82no—
82C4⋊C4—41no—
83C4⋊C4—41no—
84C4⋊C4—41no—
85C4⋊C4—41no—
86C4⋊C4—42no—
87C4⋊C4—42no—
88C23—22no—
89C23—22no—
90C23#9911yescharacteristic
91C23#9911yescharacteristic
92C23#10312yes—
93C23#10412yes—
94C23C2×C22⋊C411yescharacteristic
95C2×C4—22no—
96C2×C4—22no—
97C2×C4—22no—
98C2×C4—22no—
99C2×C4—21no—
100C2×C4—21no—
101C2×C4—21no—
102C2×C4—21no—
103C2×C4—21no—
104C2×C4—21no—
105C2×C4—21no—
106C2×C4—21no—
107C2×C4—42no—
108C2×C4—42no—
109C2×C4—42no—
110C2×C4—41no—
111C2×C4—41no—
112C2×C4—41no—
113C2×C4—41no—
114C2×C4—42no—
115C2×C4—42no—
116C2×C4—44no—
117C2×C4—42no—
118C2×C4—42no—
119C2×C4—81no—
120C2×C4—84no—
121C2×C4—82no—
122C2×C4—82no—
123C2×C4#10312yes—
124C2×C4C2×SD1611yescharacteristic
125C2×C4C2×Q1611yescharacteristic
126C8—44no—
127C8—82no—
128C22—21no—
129C22—21no—
130C22—24no—
131C22—24no—
132C22—21no—
133C22—21no—
134C22#32812yes—
135C22#32812yes—
136C22#35212yes—
137C22#35512yes—
138C22C2×#9911yescharacteristic
139C22C2×#10311yescharacteristic
140C22C2×#10411yescharacteristic
141C4—21no—
142C4—22no—
143C4—21no—
144C4—41no—
145C4—41no—
146C4—41no—
147C4—41no—
148C4—82no—
149C4—82no—
150C2—21no—
151C2—22no—
152C2—21no—
153C2#135314yesdirect product factor
154C2C2×#32811yescharacteristic
155C2C2×#35211yescharacteristic
156C2C2×#35511yescharacteristic
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. #1353C2direct (N × H)
153. C2#1353direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#4002
C2×#3432
C2×#3242
#13532