Finite Group Databasebeta

← #11772106

Subgroups — #11772106

Order 1152.

150 conjugacy classes of subgroups; only the 33 normal subgroups are shown.

normal subgroups only

This group has 150 conjugacy classes of subgroups — too many to draw. Only its 33 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#10590314C211yesmaximal, characteristic
2C4⋊#3708C211yesmaximal, characteristic
3#10589098C211yesmaximal, characteristic
4C3×#870—21no—
5C2×#3708—21no—
6C4×C3⋊(C3⋊C8)C2211yescharacteristic
7C3×C4⋊(C3⋊C8)—21no—
8#63576C411yescharacteristic
9#63576C411yescharacteristic
10#63574—21no—
11#5065—61no—
12#4480—61no—
13C32×C42D411yescharacteristic
14C2×C3⋊(C3⋊C8)C2×C411yescharacteristic
15C2×C3⋊(C3⋊C8)D411yescharacteristic
16C3×C4⋊Dic3—21no—
17C3×C4⋊Dic3—21no—
18C3×Dic3⋊C4—41no—
19C3×Dic3⋊C4—41no—
20C2×C3×C3⋊C8—41no—
21#3708—41no—
22#1363—91nomaximal, Sylow
23C3×#125—61no—
24#870—21no—
25C3×C4⋊C8—61no—
26#808—61no—
27#808—61no—
28#807—61no—
29#807—61no—
30C4⋊(C3⋊C8)—21no—
31C4×C3⋊C8—61no—
32C4×C3⋊C8—61no—
33C2×C32×C4C22⋊C411yescharacteristic
34C2×C32×C4D811yescharacteristic
35C2×C32×C4SD1611yescharacteristic
36C2×C3×Dic3—41no—
37C2×C3×Dic3—41no—
38C3⋊(C3⋊C8)—21no—
39C3⋊(C3⋊C8)SD1611yescharacteristic
40C3⋊(C3⋊C8)Q1611yescharacteristic
41C3×C3⋊C8—81no—
42#499—91no—
43C4⋊C16—91no—
44#334—91no—
45C2×C3×C8—121no—
46C3×C4⋊C4—61no—
47C3×C4⋊C4—61no—
48C3×C4⋊C4—121no—
49C3×C4⋊C4—121no—
50C3×C42—21no—
51C3×C42—21no—
52C4⋊Dic3—21no—
53C4⋊Dic3—21no—
54Dic3⋊C4—41no—
55Dic3⋊C4—41no—
56C2×C3⋊C8—41no—
57C2×C3⋊C8—61no—
58C2×C3⋊C8—61no—
59C2×C3⋊C8—61no—
60C2×C3⋊C8—61no—
61C22×C32#10211yescharacteristic
62C32×C4—21no—
63C32×C4—21no—
64C32×C4#10111yescharacteristic
65C32×C4#10311yescharacteristic
66C3×Dic3—81no—
67C3×Dic3—81no—
68#125—61no—
69C2×C16—181no—
70#107—91no—
71#107—91no—
72#106—181no—
73C4⋊C8—61no—
74C4×C8—91no—
75C2×C3×C4—21no—
76C2×C3×C4—21no—
77C2×C3×C4—21no—
78C2×C3×C4—21no—
79C2×C3×C4—21no—
80C2×C3×C4—21no—
81C2×C3×C4—121no—
82C2×C3×C4—121no—
83C2×Dic3—41no—
84C2×Dic3—41no—
85C3×C8—241no—
86C3⋊C8—61no—
87C3⋊C8—61no—
88C3⋊C8—61no—
89C3⋊C8—61no—
90C3⋊C8—62no—
91C3⋊C8—81no—
92C3⋊C8—121no—
93C2×C32#33211yescharacteristic
94C2×C32#35911yescharacteristic
95C2×C32#36011yescharacteristic
96C2×C8—91no—
97C2×C8—91no—
98C2×C8—121no—
99C4⋊C4—61no—
100C4⋊C4—61no—
101C4⋊C4—121no—
102C4⋊C4—121no—
103C42GO+(4,𝔽2)11yescharacteristic
104C16—361no—
105C22×C3—21no—
106C22×C3—21no—
107C3×C4—21no—
108C3×C4—21no—
109C3×C4—21no—
110C3×C4—21no—
111C3×C4—21no—
112C3×C4—21no—
113C3×C4—41no—
114C3×C4—41no—
115C3×C4—41no—
116C3×C4—241no—
117C3×C4—241no—
118Dic3—81no—
119Dic3—81no—
120C32#136311yescharacteristic, complemented, Sylow
121C2×C4—121no—
122C2×C4—121no—
123C2×C4D32⋊C411yescharacteristic
124C2×C4#377411yescharacteristic
125C2×C4#377511yescharacteristic
126C8—91no—
127C8—91no—
128C8—181no—
129C8—241no—
130C2×C3—21no—
131C2×C3—21no—
132C2×C3—21no—
133C2×C3—21no—
134C2×C3—21no—
135C2×C3—21no—
136C22#6373911yescharacteristic
137C4—21no—
138C4—21no—
139C4—241no—
140C4—241no—
141C4#6372811yescharacteristic
142C4#6373011yescharacteristic
143C3—21no—
144C3—21no—
145C2#1059003811yescharacteristic
146C2#1059006311yescharacteristic
147C2#1059006411yescharacteristic
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#1363
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
120. C32#1363semidirect

Maximal subgroups

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

subgroupindex
#105903142
C4⋊#37082
#105890982
#13639