Finite Group Databasebeta

← #11771913

Subgroups — #11771913

Order 1152.

194 conjugacy classes of subgroups; only the 29 normal subgroups are shown.

normal subgroups only

This group has 194 conjugacy classes of subgroups — too many to draw. Only its 29 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#10590855C211yesmaximal, characteristic
2#10590185C211yesmaximal, characteristic
3#10589108C211yesmaximal, characteristic
4C2×#3788—21no—
5C2×C8×C3⋊D3C2211yescharacteristic
6#63871—21no—
7C2×#3718C411yescharacteristic
8C3×#816—21no—
9C2×C3×C3⋊C16—21no—
10#63576C411yescharacteristic
11#4813—61no—
12(C2×D3)⋊C16—61no—
13C2×C4×C3⋊D3D411yescharacteristic
14C2×C3×Dic6—21no—
15C2×#622—41no—
16#3788—22no—
17#3788—41no—
18C2×C32×C8D411yescharacteristic
19C2×C3⋊(C3⋊C8)C2×C411yescharacteristic
20C8×C3⋊D3—41no—
21C3×C4⋊Dic3—21no—
22Dic3⋊Dic3—41no—
23#3722—41no—
24#3718—41no—
25C3×C3⋊C16—41no—
26#1350—91nomaximal, Sylow
27#946—61no—
28C2×#216—61no—
29C2×D3×C8—61no—
30C2×D3×C8—61no—
31#897—61no—
32C2×C3×C16—61no—
33C3×#103—61no—
34#816—21no—
35C2×C3⋊C16—21no—
36#807—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#467—91no—
50C22⋊C16—91no—
51#341—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—
67D3×C8—122no—
68D3×C8—121no—
69D3×C8—121no—
70C3×C16—121no—
71C3⋊C16—41no—
72C22×C32#10211yescharacteristic
73C2×C3⋊D3—21no—
74C2×C3⋊D3—21no—
75C2×C3⋊D3—21no—
76C32×C4#9911yescharacteristic
77C32×C4#10411yescharacteristic
78C3⋊Dic3—21no—
79C3×Dic3—81no—
80C3×Dic3—81no—
81C2×Q16—91no—
82C2×M16—181no—
83C22×C8—91no—
84C22⋊Q8—181no—
85C2×C16—61no—
86#107—91no—
87#103—61no—
88C22×D3—61no—
89C22×D3—61no—
90C3×Q8—121no—
91C3×Q8—121no—
92C2×C3×C4—21no—
93C2×C3×C4—21no—
94C2×C3×C4—121no—
95C2×C3×C4—121no—
96C2×Dic3—41no—
97C2×Dic3—41no—
98C2×Dic3—61no—
99C2×Dic3—61no—
100C4×D3—121no—
101C4×D3—121no—
102C4×D3—121no—
103C4×D3—121no—
104Dic6—41no—
105Dic6—41no—
106C3×C8—21no—
107C3×C8—21no—
108C3×C8—41no—
109C3⋊C8—62no—
110C3⋊C8—121no—
111C2×C32#32711yescharacteristic
112C2×C32#35911yescharacteristic
113C2×C32#36211yescharacteristic
114C3⋊D3—41no—
115C2×Q8—61no—
116C22×C4—91no—
117Q16—361no—
118M16—182no—
119M16—361no—
120C2×C8—91no—
121C2×C8—361no—
122C2×C8—361no—
123C2×C8GO+(4,𝔽2)11yescharacteristic
124C4⋊C4—61no—
125C4⋊C4—361no—
126C22⋊C4—361no—
127C16—121no—
128C22×C3—21no—
129C22×C3—21no—
130C2×D3—62no—
131C2×D3—62no—
132C2×D3—121no—
133C2×D3—121no—
134C2×D3—121no—
135C2×D3—121no—
136C3×C4—21no—
137C3×C4—21no—
138C3×C4—21no—
139C3×C4—21no—
140C3×C4—241no—
141C3×C4—241no—
142Dic3—81no—
143Dic3—81no—
144Dic3—121no—
145Dic3—121no—
146C32#135011yescharacteristic, complemented, Sylow
147C23—91no—
148Q8—121no—
149Q8—121no—
150C2×C4—91no—
151C2×C4—121no—
152C2×C4—121no—
153C2×C4—181no—
154C2×C4—181no—
155C2×C4D32⋊C411yescharacteristic
156C8—21no—
157C8—181no—
158C8—362no—
159C2×C3—21no—
160C2×C3—21no—
161C2×C3—21no—
162C2×C3—21no—
163C2×C3—21no—
164C2×C3—21no—
165D3—122no—
166D3—122no—
167C22—181no—
168C22—181no—
169C22—181no—
170C22#6372911yescharacteristic
171C4—181no—
172C4—241no—
173C4—241no—
174C4#6373111yescharacteristic
175C4#6373811yescharacteristic
176C3—21no—
177C3—21no—
178C2—361no—
179C2#1059001811yescharacteristic
180C2#1059002111yescharacteristic
181C2#1059003311yescharacteristic
subgroupG/H
centerC22#63729
commutatorC2×C3⋊(C3⋊C8)C2×C4
Frattini, hypercenterC2×C8GO+(4,𝔽2)
FittingC2×C32×C8D4
socleC22×C32#102
prime radicalC22×C3⋊D3SD16
cosocleC2×C8×C3⋊D3C22
hypocenterC32#1350
LCSG ▷ C2×C3⋊(C3⋊C8) ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×C8

Complements

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

NH ≅ G/Ntype
146. C32#1350semidirect

Maximal subgroups

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

subgroupindex
#105908552
#105901852
#105891082
#13509