Finite Group Databasebeta

← #11771777

Subgroups — #11771777

Order 1152.

184 conjugacy classes of subgroups; only the 25 normal subgroups are shown.

normal subgroups only

This group has 184 conjugacy classes of subgroups — too many to draw. Only its 25 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#10590856C211yesmaximal, characteristic
2#10590186C211yesmaximal, characteristic
3#10589110C211yesmaximal, characteristic
4#64283—21no—
5C2×#3743C2211yescharacteristic
6#63871—21no—
7C2×#3718C411yescharacteristic
8C3×#816—21no—
9C3×#812—21no—
10#63574C411yescharacteristic
11#4816—61no—
12#4514—61no—
13C2×C4×C3⋊D3D411yescharacteristic
14C2×C3×Dic6—21no—
15#3792—41no—
16#3788—41no—
17#3787—22no—
18C2×C32×C8D411yescharacteristic
19C2×C3⋊(C3⋊C8)C2×C411yescharacteristic
20#3743—41no—
21C3×C4⋊Dic3—21no—
22Dic3⋊Dic3—41no—
23#3722—41no—
24#3718—41no—
25C3×C3⋊C16—41no—
26#1342—91nomaximal, Sylow
27#946—61no—
28C2×#216—61no—
29C2×ΓL(1,𝔽25)—61no—
30C2×ΓL(1,𝔽25)—61no—
31#897—61no—
32C3×M32—61no—
33C3×#103—61no—
34#816—21no—
35#812—21no—
36#808—61no—
37C22×C3⋊D3SD1611yescharacteristic
38C2×C32×C4C22⋊C411yescharacteristic
39C2×C3⋊Dic3D811yescharacteristic
40C4×C3⋊D3—21no—
41C4×C3⋊D3—21no—
42C2×C3×Dic3—41no—
43C2×C3×Dic3—41no—
44C3×Dic6—41no—
45C3×Dic6—41no—
46#622—42no—
47C32×C8—21no—
48C3⋊(C3⋊C8)—21no—
49#470—91no—
50#349—91no—
51#338—91no—
52C2×C3×Q8—61no—
53C2×C4×D3—61no—
54C2×C4×D3—61no—
55C2×Dic6—21no—
56C2×C3×C8—21no—
57C2×C3×C8—21no—
58C3×C4⋊C4—61no—
59#216—122no—
60(C2×D3)⋊C4—121no—
61(C2×D3)⋊C4—121no—
62C4⋊Dic3—21no—
63C4⋊Dic3—121no—
64Dic3⋊C4—121no—
65C2×C3⋊C8—61no—
66C2×C3⋊C8—61no—
67ΓL(1,𝔽25)—122no—
68ΓL(1,𝔽25)—121no—
69ΓL(1,𝔽25)—121no—
70C3×C16—121no—
71C3⋊C16—41no—
72C22×C32#10211yescharacteristic
73C2×C3⋊D3—21no—
74C2×C3⋊D3—41no—
75C32×C4#9911yescharacteristic
76C32×C4#10411yescharacteristic
77C3⋊Dic3—21no—
78C3×Dic3—81no—
79C3×Dic3—81no—
80C2×Q16—91no—
81C2×M16—91no—
82C2×M16—181no—
83C22⋊Q8—181no—
84M32—61no—
85#106—91no—
86#103—61no—
87C22×D3—61no—
88C22×D3—61no—
89C3×Q8—121no—
90C3×Q8—121no—
91C2×C3×C4—21no—
92C2×C3×C4—21no—
93C2×C3×C4—121no—
94C2×C3×C4—121no—
95C2×Dic3—41no—
96C2×Dic3—41no—
97C2×Dic3—61no—
98C2×Dic3—61no—
99C4×D3—121no—
100C4×D3—121no—
101C4×D3—121no—
102C4×D3—121no—
103Dic6—41no—
104Dic6—41no—
105C3×C8—21no—
106C3×C8—21no—
107C3×C8—41no—
108C3⋊C8—62no—
109C3⋊C8—121no—
110C2×C32—21no—
111C2×C32#32711yescharacteristic
112C3⋊D3—41no—
113C2×Q8—61no—
114C22×C4—91no—
115Q16—361no—
116M16—361no—
117M16—361no—
118M16—361no—
119C2×C8—91no—
120C2×C8—182no—
121C2×C8GO+(4,𝔽2)11yescharacteristic
122C4⋊C4—61no—
123C4⋊C4—361no—
124C22⋊C4—361no—
125C16—121no—
126C22×C3—21no—
127C22×C3—21no—
128C2×D3—121no—
129C2×D3—121no—
130C2×D3—121no—
131C2×D3—121no—
132C2×D3—241no—
133C3×C4—21no—
134C3×C4—21no—
135C3×C4—21no—
136C3×C4—21no—
137C3×C4—241no—
138C3×C4—241no—
139Dic3—81no—
140Dic3—81no—
141Dic3—121no—
142Dic3—121no—
143C32#134211yescharacteristic, complemented, Sylow
144C23—91no—
145Q8—121no—
146Q8—121no—
147C2×C4—91no—
148C2×C4—121no—
149C2×C4—121no—
150C2×C4—181no—
151C2×C4—181no—
152C2×C4D32⋊C411yescharacteristic
153C8—21no—
154C8—181no—
155C8—362no—
156C2×C3—21no—
157C2×C3—21no—
158C2×C3—21no—
159C2×C3—21no—
160C2×C3—41no—
161D3—241no—
162D3—241no—
163C22—181no—
164C22—361no—
165C22#6372911yescharacteristic
166C4—181no—
167C4—241no—
168C4—241no—
169C4#6373111yescharacteristic
170C4#6373811yescharacteristic
171C3—21no—
172C3—21no—
173C2—21no—
174C2—361no—
175C2#1059003311yescharacteristic
subgroupG/H
centerC2#10590033
commutatorC2×C3⋊(C3⋊C8)C2×C4
Frattini, hypercenterC2×C8GO+(4,𝔽2)
FittingC2×C32×C8D4
socleC2×C32#327
prime radicalC22×C3⋊D3SD16
cosocleC2×#3743C22
hypocenterC32#1342
LCSG ▷ C2×C3⋊(C3⋊C8) ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×C8

Complements

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

NH ≅ G/Ntype
143. C32#1342semidirect

Maximal subgroups

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

subgroupindex
#105908562
#105901862
#105891102
#13429