Finite Group Databasebeta

← #11772879

Subgroups — #11772879

Order 1152.

192 conjugacy classes of subgroups; only the 19 normal subgroups are shown.

normal subgroups only

This group has 192 conjugacy classes of subgroups — too many to draw. Only its 19 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#10591480C211yesmaximal, characteristic
2#10590211C211yesmaximal, characteristic
3#10589179C211yesmaximal, characteristic
4#64149C2211yescharacteristic
5#63872C411yescharacteristic, complemented
6#63774—21no—
7C3×#834—21no—
8C3×#832—21no—
9#63564—21no—
10#63555C411yescharacteristic, complemented
11#4764—61no—
12#4474—61no—
13C2×C32×D4D411yescharacteristic
14C2×#638—41no—
15C2×C4⋊(C3⋊D3)D411yescharacteristic
16C22⋊#157—41no—
17C4×C3⋊Dic3C2×C411yescharacteristic
18C3×#217—41no—
19C3×C4⋊Dic3—21no—
20C2×C3×C3⋊C8—21no—
21Dic3⋊Dic3—41no—
22#1412—91nomaximal, Sylow
23#940—61no—
24#940—61no—
25#890—61no—
26C3×#102—61no—
27C3×#99—61no—
28#834—21no—
29#832—21no—
30#821—61no—
31#815—61no—
32#809—61no—
33C23×C32—21no—
34C22×C3⋊D3—21no—
35C2×#157—81no—
36C32×D4—41no—
37C2×C32×C4C22⋊C411yescharacteristic
38#638—82no—
39C2×C3⋊Dic3—21no—
40C4⋊(C3⋊D3)—41no—
41C2×C3×Dic3—41no—
42C2×C3×Dic3—81no—
43C3×C3⋊C8—41no—
44#490—91no—
45#353—91no—
46#353—91no—
47C2×C3×D4—21no—
48C2×C3×D4—21no—
49C2×#67—121no—
50C2×#67—121no—
51C2×#67—121no—
52C2×#67—121no—
53C2×D12—61no—
54C2×D12—61no—
55C2×C3×C8—61no—
56C3×C4⋊C4—61no—
57C3×C22⋊C4—121no—
58#217—41no—
59C4⋊Dic3—21no—
60C4⋊Dic3—121no—
61Dic3⋊C4—121no—
62C4×Dic3—61no—
63C4×Dic3—61no—
64C2×C3⋊C8—21no—
65C22×C32—41no—
66C22×C32—81no—
67C22×C32#9911yescharacteristic
68C2×C3⋊D3—41no—
69C2×C3⋊D3—81no—
70#157—161no—
71C32×C4—21no—
72C3⋊Dic3—41no—
73C3×Dic3—81no—
74C3×Dic3—161no—
75#127—91no—
76#125—91no—
77#102—61no—
78#102—181no—
79#99—61no—
80#99—181no—
81#97—91no—
82C23×C3—21no—
83C23×C3—21no—
84C23×C3—41no—
85C22×D3—121no—
86C22×D3—121no—
87C3×D4—41no—
88C3×D4—41no—
89C3×D4—81no—
90C2×C3×C4—21no—
91C2×C3×C4—21no—
92C2×C3×C4—121no—
93C2×C3×C4—241no—
94#67—242no—
95#67—242no—
96#67—242no—
97#67—242no—
98C2×Dic3—41no—
99C2×Dic3—61no—
100C2×Dic3—61no—
101C2×Dic3—81no—
102C2×Dic3—121no—
103D12—121no—
104D12—121no—
105D12—241no—
106C3×C8—121no—
107C3⋊C8—41no—
108C2×C32—21no—
109C2×C32—81no—
110C2×C32#35411yescharacteristic
111C3⋊D3—81no—
112C2×D4—91no—
113C2×D4—361no—
114C2×D4GO+(4,𝔽2)11yescharacteristic
115C2×C8—61no—
116C4⋊C4—61no—
117C4⋊C4—361no—
118C22⋊C4—121no—
119C22⋊C4—361no—
120C42—91no—
121C22×C3—21no—
122C22×C3—21no—
123C22×C3—41no—
124C22×C3—41no—
125C22×C3—81no—
126C22×C3—81no—
127C22×C3—81no—
128C22×C3—81no—
129C22×C3—81no—
130C2×D3—241no—
131C2×D3—241no—
132C2×D3—241no—
133C2×D3—241no—
134C2×D3—241no—
135C2×D3—241no—
136C3×C4—21no—
137C3×C4—21no—
138C3×C4—41no—
139C3×C4—241no—
140C3×C4—481no—
141Dic3—81no—
142Dic3—121no—
143Dic3—121no—
144Dic3—122no—
145Dic3—161no—
146C32#141211yescharacteristic, complemented, Sylow
147C23—21no—
148C23—181no—
149D4—41no—
150D4—361no—
151D4—722no—
152C2×C4—121no—
153C2×C4—181no—
154C2×C4—241no—
155C2×C4—721no—
156C2×C4D32⋊C411yescharacteristic
157C8—121no—
158C2×C3—21no—
159C2×C3—21no—
160C2×C3—21no—
161C2×C3—21no—
162C2×C3—41no—
163C2×C3—81no—
164C2×C3—81no—
165C2×C3—161no—
166D3—481no—
167D3—481no—
168C22—41no—
169C22—81no—
170C22—361no—
171C22—721no—
172C22#6373811yescharacteristic
173C4—21no—
174C4—241no—
175C4—361no—
176C4—481no—
177C4—1441no—
178C3—21no—
179C3—21no—
180C2—21no—
181C2—81no—
182C2—721no—
183C2#1059008111yescharacteristic
subgroupG/H
centerC2#10590081
commutatorC4×C3⋊Dic3C2×C4
Frattini, hypercenterC2×D4GO+(4,𝔽2)
FittingC2×C32×D4D4
socleC2×C32#354
prime radical, cosocle#64149C22
hypocenterC32#1412
LCSG ▷ C4×C3⋊Dic3 ▷ C2×C32×C4 ▷ C22×C32 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2 ◁ C22 ◁ C2×C4 ◁ C2×D4

Complements

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

NH ≅ G/Ntype
5. #63872C4semidirect
10. #63555C4semidirect
146. C32#1412semidirect

Maximal subgroups

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

subgroupindex
#105914802
#105902112
#105891792
#14129