Finite Group Databasebeta

← #11772808

Subgroups — #11772808

Order 1152.

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

normal subgroups only

This group has 212 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#10591621C211yesmaximal, characteristic
2#10590217C211yesmaximal, characteristic, complemented
3#10589183C211yesmaximal, characteristic, complemented
4#64156C2211yescharacteristic
5C2×C3×#215—21no—
6#63914C411yescharacteristic, complemented
7C2×#3714—21no—
8#63774—21no—
9C3×#836—21no—
10#63555C411yescharacteristic, complemented
11#5176—61no—
12#4477—61no—
13C2×C32×Q8D411yescharacteristic
14C2×C4⋊(C3⋊D3)D411yescharacteristic
15C2×C3×D12—21no—
16C2×#625—41no—
17C22⋊#157—41no—
18#3752—41no—
19C4×C3⋊Dic3C2×C411yescharacteristic
20C3×#215—42no—
21C3×#208—41no—
22C2×C3×C3⋊C8—21no—
23#3714—42no—
24#1406—91nomaximal, Sylow
25C2×C3×SD16—61no—
26#947—61no—
27#947—61no—
28C2×#215—21no—
29#940—61no—
30C2×#213—61no—
31C2×D24—61no—
32C3×#101—61no—
33#836—21no—
34#815—61no—
35C22×C3⋊D3—21no—
36C22×C3×D3—41no—
37C2×#157—81no—
38C32×Q8—41no—
39C2×C32×C4—21no—
40C2×C32×C4C22⋊C411yescharacteristic
41C2×C3⋊Dic3—21no—
42C4⋊(C3⋊D3)—41no—
43C3×D12—41no—
44C3×D12—41no—
45#625—82no—
46C3×C3⋊C8—22no—
47C3×C3⋊C8—81no—
48#496—91no—
49#355—91no—
50#354—91no—
51C2×C3×Q8—21no—
52C2×C3×Q8—21no—
53C2×C3×D4—61no—
54C2×#67—122no—
55C2×D12—21no—
56C2×D12—61no—
57C2×D12—61no—
58C3×SD16—122no—
59C3×M16—121no—
60C2×C3×C8—61no—
61#215—42no—
62#213—122no—
63(C2×D3)⋊C4—122no—
64(C2×D3)⋊C4—121no—
65(C2×D3)⋊C4—121no—
66C4×Dic3—61no—
67C4×Dic3—61no—
68#208—41no—
69C2×C3⋊C8—21no—
70D24—122no—
71C22×C32#9911yescharacteristic
72C2×C3⋊D3—41no—
73C2×C3⋊D3—81no—
74C2×C3×D3—82no—
75C2×C3×D3—81no—
76#157—161no—
77C32×C4—21no—
78C32×C4—41no—
79C3⋊Dic3—41no—
80C2×SD16—61no—
81C2×D8—181no—
82#127—91no—
83#124—91no—
84#101—61no—
85#99—181no—
86#97—91no—
87C23×C3—121no—
88C22×D3—41no—
89C22×D3—121no—
90C22×D3—121no—
91C3×Q8—41no—
92C3×Q8—41no—
93C3×Q8—81no—
94C3×D4—121no—
95C3×D4—121no—
96C2×C3×C4—21no—
97C2×C3×C4—21no—
98C2×C3×C4—21no—
99C2×C3×C4—21no—
100C2×C3×C4—41no—
101#67—244no—
102C2×Dic3—62no—
103C2×Dic3—121no—
104D12—41no—
105D12—41no—
106D12—121no—
107D12—121no—
108D12—241no—
109C3×C8—62no—
110C3×C8—241no—
111C3⋊C8—22no—
112C3⋊C8—81no—
113C2×C32—21no—
114C2×C32#35311yescharacteristic
115C3⋊D3—81no—
116C3×D3—161no—
117C2×Q8GO+(4,𝔽2)11yescharacteristic
118C2×D4—61no—
119C2×D4—91no—
120C2×D4—361no—
121SD16—122no—
122D8—362no—
123M16—121no—
124C2×C8—61no—
125C22⋊C4—361no—
126C22⋊C4—361no—
127C42—91no—
128C22×C3—21no—
129C22×C3—21no—
130C22×C3—242no—
131C22×C3—241no—
132C2×D3—81no—
133C2×D3—82no—
134C2×D3—241no—
135C2×D3—241no—
136C2×D3—242no—
137C2×D3—242no—
138C3×C4—21no—
139C3×C4—21no—
140C3×C4—41no—
141C3×C4—41no—
142C3×C4—41no—
143C3×C4—81no—
144Dic3—122no—
145Dic3—241no—
146C32#140611yescharacteristic, complemented, Sylow
147C23—121no—
148C23—181no—
149Q8—41no—
150D4—121no—
151D4—121no—
152D4—361no—
153D4—722no—
154C2×C4—21no—
155C2×C4—181no—
156C2×C4—721no—
157C2×C4D32⋊C411yescharacteristic
158C8—62no—
159C8—241no—
160C2×C3—22no—
161C2×C3—21no—
162C2×C3—21no—
163C2×C3—41no—
164C2×C3—481no—
165D3—161no—
166D3—481no—
167D3—481no—
168C22—242no—
169C22—241no—
170C22—361no—
171C22—721no—
172C22#6373811yescharacteristic
173C4—21no—
174C4—41no—
175C4—361no—
176C4—1441no—
177C3—21no—
178C3—21no—
179C2—21no—
180C2—481no—
181C2—721no—
182C2#1059008011yescharacteristic
subgroupG/H
centerC2#10590080
commutatorC4×C3⋊Dic3C2×C4
Frattini, hypercenterC2×Q8GO+(4,𝔽2)
FittingC2×C32×Q8D4
socleC2×C32#353
prime radical#10591621C2
cosocle#64156C22
hypocenterC32#1406
LCSG ▷ C4×C3⋊Dic3 ▷ C2×C32×C4 ▷ C22×C32 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2 ◁ C22 ◁ C2×C4 ◁ C2×Q8

Complements

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

NH ≅ G/Ntype
2. #10590217C2semidirect
3. #10589183C2semidirect
6. #63914C4semidirect
10. #63555C4semidirect
146. C32#1406semidirect

Maximal subgroups

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

subgroupindex
#105916212
#105902172
#105891832
#14069