Finite Group Databasebeta

← #11772123

Subgroups — #11772123

Order 1152.

162 conjugacy classes of subgroups; only the 37 normal subgroups are shown.

normal subgroups only

This group has 162 conjugacy classes of subgroups — too many to draw. Only its 37 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#10590312C211yesmaximal, characteristic
2C4⋊#3708C211yesmaximal, characteristic
3#10589100C211yesmaximal, characteristic
4C3×#869—21no—
5C2×#3708—21no—
6C4×C3⋊(C3⋊C8)C2211yescharacteristic
7C3×C4⋊(C3⋊C8)—21no—
8#63576—21no—
9#63576C412yes—
10#5078—61no—
11#4479—61no—
12C2×C3×Dic6—41no—
13C32×C42D411yescharacteristic
14C2×C3⋊(C3⋊C8)C2×C411yescharacteristic
15C2×C3⋊(C3⋊C8)D411yescharacteristic
16C3×C4⋊Dic3—22no—
17C3×C4⋊Dic3—41no—
18C2×C3×C3⋊C8—41no—
19#3708—41no—
20#1364—91nomaximal, Sylow
21C3×C4⋊Q8—61no—
22#869—21no—
23C3×C4⋊C8—61no—
24#807—62no—
25#807—62no—
26C4⋊(C3⋊C8)—21no—
27C4×C3⋊C8—61no—
28C4×C3⋊C8—61no—
29C2×C32×C4C22⋊C411yescharacteristic
30C2×C32×C4D811yescharacteristic
31C2×C32×C4SD1611yescharacteristic
32C2×C3×Dic3—42no—
33C3×Dic6—81no—
34C3×Dic6—81no—
35C3⋊(C3⋊C8)—21no—
36C3⋊(C3⋊C8)SD1611yescharacteristic
37C3⋊(C3⋊C8)Q1611yescharacteristic
38C3×C3⋊C8—81no—
39#500—91no—
40C4⋊C16—91no—
41#335—91no—
42C2×C3×Q8—121no—
43C2×Dic6—41no—
44C2×C3×C8—121no—
45C3×C4⋊C4—62no—
46C3×C4⋊C4—121no—
47C3×C42—21no—
48C3×C42—21no—
49C4⋊Dic3—22no—
50C4⋊Dic3—41no—
51C2×C3⋊C8—41no—
52C2×C3⋊C8—61no—
53C2×C3⋊C8—61no—
54C2×C3⋊C8—61no—
55C2×C3⋊C8—61no—
56C22×C32#10211yescharacteristic
57C32×C4—21no—
58C32×C4#10111yescharacteristic
59C32×C4#10311yescharacteristic
60C32×C4D1611yescharacteristic
61C32×C4SD3211yescharacteristic
62C3×Dic3—82no—
63C4⋊Q8—61no—
64C2×C16—181no—
65#107—92no—
66#107—181no—
67C4⋊C8—61no—
68C4×C8—91no—
69C3×Q8—241no—
70C3×Q8—241no—
71C2×C3×C4—21no—
72C2×C3×C4—21no—
73C2×C3×C4—21no—
74C2×C3×C4—21no—
75C2×C3×C4—21no—
76C2×C3×C4—21no—
77C2×C3×C4—122no—
78C2×Dic3—42no—
79Dic6—81no—
80Dic6—81no—
81C3×C8—241no—
82C3⋊C8—61no—
83C3⋊C8—61no—
84C3⋊C8—61no—
85C3⋊C8—61no—
86C3⋊C8—62no—
87C3⋊C8—81no—
88C3⋊C8—121no—
89C2×C32#33211yescharacteristic
90C2×C32#35711yescharacteristic
91C2×C32#36211yescharacteristic
92C2×Q8—121no—
93C2×C8—91no—
94C2×C8—91no—
95C2×C8—121no—
96C4⋊C4—62no—
97C4⋊C4—121no—
98C42GO+(4,𝔽2)11yescharacteristic
99C16—361no—
100C22×C3—21no—
101C22×C3—21no—
102C3×C4—22no—
103C3×C4—21no—
104C3×C4—21no—
105C3×C4—21no—
106C3×C4—21no—
107C3×C4—21no—
108C3×C4—21no—
109C3×C4—21no—
110C3×C4—21no—
111C3×C4—41no—
112C3×C4—242no—
113Dic3—82no—
114C32#136411yescharacteristic, complemented, Sylow
115Q8—241no—
116Q8—241no—
117C2×C4—122no—
118C2×C4D32⋊C411yescharacteristic
119C2×C4#377411yescharacteristic
120C2×C4#377511yescharacteristic
121C8—91no—
122C8—91no—
123C8—181no—
124C8—241no—
125C2×C3—21no—
126C2×C3—21no—
127C2×C3—21no—
128C2×C3—21no—
129C2×C3—21no—
130C2×C3—21no—
131C22#6373911yescharacteristic
132C4—21no—
133C4—242no—
134C4#6372811yescharacteristic
135C4#6373011yescharacteristic
136C4#6373411yescharacteristic
137C4#6373511yescharacteristic
138C3—21no—
139C3—21no—
140C2#1059003811yescharacteristic
141C2#1059006111yescharacteristic
142C2#1059006611yescharacteristic
subgroupG/H
centerC22#63739
commutatorC2×C3⋊(C3⋊C8)C2×C4
Frattini, hypercenterC42GO+(4,𝔽2)
FittingC32×C42D4
socle, prime radicalC22×C32#102
cosocleC4×C3⋊(C3⋊C8)C22
hypocenterC32#1364
LCSG ▷ C2×C3⋊(C3⋊C8) ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42

Complements

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

NH ≅ G/Ntype
114. C32#1364semidirect

Maximal subgroups

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

subgroupindex
#105903122
C4⋊#37082
#105891002
#13649