Finite Group Databasebeta

← #2839

Subgroups — #2839

Order 128.

162 conjugacy classes of subgroups; only the 84 normal subgroups are shown.

normal subgroups only

This group has 162 conjugacy classes of subgroups — too many to draw. Only its 84 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
1#400C211yesmaximal, characteristic
2#400C211yesmaximal, characteristic
3#400C211yesmaximal, characteristic
4#400C211yesmaximal, characteristic
5#400C211yesmaximal, characteristic
6#400C211yesmaximal, characteristic
7#400C211yesmaximal, characteristic
8#398C211yesmaximal, characteristic
9#398C211yesmaximal, characteristic
10#398C211yesmaximal, characteristic
11#398C211yesmaximal, characteristic
12#398C211yesmaximal, characteristic
13#389C211yesmaximal, characteristic
14#387C211yesmaximal, characteristic
15#387C211yesmaximal, characteristic
16C2×C4⋊C4C2211yescharacteristic
17C2×C4⋊C4C2211yescharacteristic
18C2×C4⋊C4C2211yescharacteristic
19C2×C4⋊C4C2211yescharacteristic
20C2×C4⋊C4C2211yescharacteristic
21C2×C4⋊C4C2211yescharacteristic
22C2×C4⋊C4C2211yescharacteristic
23C2×C4⋊C4C2211yescharacteristic
24C2×C4⋊C4C2211yescharacteristic
25C2×C4⋊C4C2211yescharacteristic
26C2×C4⋊C4C2211yescharacteristic
27C2×C4⋊C4C2211yescharacteristic
28C2×C4⋊C4C2211yescharacteristic
29C2×C4⋊C4C2211yescharacteristic
30C2×C42C2211yescharacteristic
31#95C2211yescharacteristic
32#95C2211yescharacteristic
33#95C2211yescharacteristic
34#95C2211yescharacteristic
35#95C2211yescharacteristic
36#95C2211yescharacteristic
37#95C2211yescharacteristic
38#95C2211yescharacteristic
39#95C2211yescharacteristic
40#95C2211yescharacteristic
41#95C2211yescharacteristic
42#95C2211yescharacteristic
43#95C2211yescharacteristic
44#95C2211yescharacteristic
45#95C2211yescharacteristic
46#95C2211yescharacteristic
47#95C2211yescharacteristic
48#95C2211yescharacteristic
49#95C2211yescharacteristic
50#95C2211yescharacteristic
51C22×C4C2311yescharacteristic
52C22×C4C2311yescharacteristic
53C22×C4C2311yescharacteristic
54C22×C4C2311yescharacteristic
55C22×C4C2311yescharacteristic
56C22×C4C2311yescharacteristic
57C22×C4C2311yescharacteristic
58C22×C4C2311yescharacteristic
59C22×C4C2311yescharacteristic
60C22×C4C2311yescharacteristic
61C22×C4C2311yescharacteristic
62C22×C4C2311yescharacteristic
63C22×C4C2311yescharacteristic
64C22×C4C2311yescharacteristic
65C22×C4C2311yescharacteristic
66C4⋊C4—22no—
67C4⋊C4—22no—
68C4⋊C4—22no—
69C4⋊C4—41no—
70C4⋊C4—41no—
71C4⋊C4—41no—
72C4⋊C4—41no—
73C4⋊C4—41no—
74C4⋊C4—41no—
75C4⋊C4—41no—
76C4⋊C4—41no—
77C4⋊C4—41no—
78C4⋊C4—41no—
79C4⋊C4—41no—
80C42—41no—
81C23C2411yescharacteristic
82C2×C4—21no—
83C2×C4—21no—
84C2×C4—21no—
85C2×C4—21no—
86C2×C4—21no—
87C2×C4—21no—
88C2×C4—21no—
89C2×C4—21no—
90C2×C4—21no—
91C2×C4—21no—
92C2×C4—21no—
93C2×C4—21no—
94C2×C4—21no—
95C2×C4—21no—
96C2×C4—21no—
97C2×C4—21no—
98C2×C4—21no—
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—21no—
108C2×C4—21no—
109C2×C4—21no—
110C2×C4—21no—
111C2×C4—21no—
112C2×C4—21no—
113C2×C4—21no—
114C2×C4—21no—
115C2×C4—21no—
116C2×C4—21no—
117C2×C4—21no—
118C2×C4—21no—
119C2×C4—21no—
120C2×C4—21no—
121C2×C4—21no—
122C2×C4—21no—
123C2×C4—21no—
124C2×C4—21no—
125C2×C4—21no—
126C2×C4#4112yes—
127C22C2×#4111yescharacteristic
128C22H(5,𝔽2)11yescharacteristic
129C22H(5,𝔽2)11yescharacteristic
130C222−1+411yescharacteristic
131C222−1+411yescharacteristic
132C222−1+411yescharacteristic
133C222−1+411yescharacteristic
134C4—22no—
135C4—41no—
136C4—41no—
137C4—41no—
138C4—41no—
139C4—41no—
140C4—41no—
141C4—41no—
142C4—41no—
143C4—41no—
144C4—41no—
145C4—41no—
146C4—41no—
147C4—41no—
148C4—41no—
149C2#53911yescharacteristic
150C2#54111yescharacteristic
151C2#54211yescharacteristic
152C2#56211yescharacteristic
153C2#56311yescharacteristic
154C2#56311yescharacteristic
155C2#56411yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, prime radical, cosocleC23C24
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Maximal subgroups

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

subgroupindex
#4002
#3982
#3892
#3872