Finite Group Databasebeta

← #1618

Subgroups — #1618

Order 128.

120 conjugacy classes of subgroups; only the 32 normal subgroups are shown.

normal subgroups only

This group has 120 conjugacy classes of subgroups — too many to draw. Only its 32 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#538C211yesmaximal, characteristic
2#484C211yesmaximal, characteristic, complemented
3#481C211yesmaximal, characteristic, complemented
4#399C211yesmaximal, characteristic, complemented
5#328C211yesmaximal, characteristic, complemented
6#327C211yesmaximal, characteristic, complemented
7#323C211yesmaximal, characteristic, complemented
8#126—21no—
9#124—21no—
10#123—21no—
11C22⋊Q8C2211yescharacteristic
12#121—21no—
13#121C2211yescharacteristic
14#120—21no—
15C4×D4—21no—
16C2×C4⋊C4—21no—
17C2×C4⋊C4C2211yescharacteristic
18C2×C22⋊C4—21no—
19C2×C22⋊C4C2211yescharacteristic
20#107—21no—
21#106—21no—
22#103—21no—
23#102—21no—
24C22⋊C8C2211yescharacteristic
25C22⋊C8C2211yescharacteristic
26#95C2211yescharacteristic
27C24D411yescharacteristic
28C2×Q8D411yescharacteristic
29C2×D4—21no—
30C2×D4—21no—
31C2×D4—21no—
32C2×D4D411yescharacteristic
33C22×C4—21no—
34C22×C4—21no—
35C22×C4—21no—
36C22×C4D411yescharacteristic
37C22×C4C2311yescharacteristic
38C2×C8—21no—
39C2×C8—21no—
40C4⋊C4—21no—
41C4⋊C4—21no—
42C4⋊C4—21no—
43C4⋊C4—21no—
44C4⋊C4—42no—
45C4⋊C4D411yescharacteristic
46C4⋊C4D411yescharacteristic
47C22⋊C4—21no—
48C22⋊C4—21no—
49C22⋊C4—21no—
50C22⋊C4—21no—
51C22⋊C4—21no—
52C22⋊C4—21no—
53C22⋊C4—21no—
54C22⋊C4—42no—
55C42—21no—
56C23—21no—
57C23—21no—
58C23—21no—
59C23—21no—
60C23—41no—
61C23—41no—
62C23C2×D411yescharacteristic
63Q8—41no—
64D4—41no—
65D4—41no—
66D4—41no—
67D4—81no—
68D4—81no—
69C2×C4—22no—
70C2×C4—21no—
71C2×C4—21no—
72C2×C4—21no—
73C2×C4—21no—
74C2×C4—41no—
75C2×C4—41no—
76C2×C4—41no—
77C2×C4—41no—
78C2×C4—41no—
79C2×C4—41no—
80C2×C4—41no—
81C2×C4—81no—
82C2×C4C2×D411yescharacteristic
83C2×C4C2×D411yescharacteristic
84C8—41no—
85C8—41no—
86C22—21no—
87C22—21no—
88C22—42no—
89C22—41no—
90C22—41no—
91C22—41no—
92C22—41no—
93C22—41no—
94C22—41no—
95C22—81no—
96C22#12011yescharacteristic
97C22#13511yescharacteristic
98C22#13711yescharacteristic
99C4—21no—
100C4—21no—
101C4—42no—
102C4—41no—
103C4—41no—
104C4—41no—
105C4—41no—
106C4—81no—
107C2—21no—
108C2—21no—
109C2—81no—
110C2—81no—
111C2#45211yescharacteristic
112C2#45311yescharacteristic
113C2#45811yescharacteristic
subgroupG/H
center, socleC22#120
commutator, Frattini, cosocleC22×C4C23
prime radical#538C2
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22 ◁ C22×C4 ◁ G
LECSG ▷ C22×C4 ▷ C22 ▷ C1

Complements

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

NH ≅ G/Ntype
2. #484C2semidirect
3. #481C2semidirect
4. #399C2semidirect
5. #328C2semidirect
6. #327C2semidirect
7. #323C2semidirect

Maximal subgroups

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

subgroupindex
#5382
#4842
#4812
#3992
#3282
#3272
#3232