Finite Group Databasebeta

← #11800639

Subgroups — #11800639

Order 1152.

187 conjugacy classes of subgroups; only the 31 normal subgroups are shown.

normal subgroups only

This group has 187 conjugacy classes of subgroups — too many to draw. Only its 31 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#10590245C211yesmaximal, characteristic
2#10590240C211yesmaximal, characteristic, complemented
3#10590133C211yesmaximal, characteristic, complemented
4#10590026C212yesmaximal, complemented
5#10590025C212yesmaximal, complemented
6#63810—21no—
7#63802—21no—
8C16×C3⋊D3C2211yescharacteristic
9C3×Dic24—21no—
10C3×#800—21no—
11#63550C2212yes—
12#63550C2211yescharacteristic
13#63545C2211yescharacteristic
14#63540C2212yes—
15D3×Q32—61no—
16#4916—61no—
17#3797—41no—
18#3796—41no—
19C8×C3⋊D3D411yescharacteristic
20C3×Dic12—22no—
21C3×Dic12—21no—
22C3×D24—21no—
23#3718—41no—
24#3715—41no—
25C32×C16D411yescharacteristic
26C3⋊(C3⋊C16)C2311yescharacteristic
27#2264—91nomaximal, Sylow
28#919—61no—
29D3×Q16—62no—
30#912—61no—
31C3×Q32—61no—
32C3×SD32—61no—
33#829—61no—
34#829—62no—
35#826—61no—
36Dic24—21no—
37#800—21no—
38D3×C16—61no—
39D3×C16—61no—
40C4×C3⋊D3D811yescharacteristic
41C3×D12—41no—
42C3×Dic6—41no—
43C3×Dic6—42no—
44#627—81no—
45#626—81no—
46#624—81no—
47D3×Dic3—81no—
48C32×C8C2×D411yescharacteristic
49C3⋊(C3⋊C8)D811yescharacteristic
50#508—91no—
51C2×Q32—91no—
52Q64—92no—
53SD64—92no—
54M64—91no—
55#239—121no—
56D3×Q8—122no—
57#237—121no—
58C3×Q16—61no—
59C3×Q16—62no—
60C3×D8—61no—
61#216—122no—
62#215—121no—
63#214—121no—
64Dic12—21no—
65Dic12—22no—
66D24—21no—
67D3×C8—61no—
68D3×C8—61no—
69C3×C16—21no—
70C3×C16—21no—
71C3⋊C16—61no—
72C3⋊C16—61no—
73C2×C3⋊D3D1611yescharacteristic
74C2×C3×D3—81no—
75C32×C4C2×D811yescharacteristic
76C3⋊Dic3D1611yescharacteristic
77C3×Dic3—81no—
78C3×Dic3—82no—
79#135—181no—
80C2×Q16—181no—
81Q32—61no—
82Q32—92no—
83Q32—91no—
84SD32—61no—
85D16—91no—
86C2×C16—91no—
87C32—92no—
88C3×Q8—121no—
89C3×Q8—122no—
90C3×D4—121no—
91#67—241no—
92C2×Dic3—241no—
93D12—41no—
94D12—241no—
95C4×D3—61no—
96C4×D3—61no—
97C4×D3—241no—
98C4×D3—242no—
99Dic6—41no—
100Dic6—42no—
101Dic6—242no—
102C3×C8—21no—
103C3×C8—21no—
104C3⋊C8—61no—
105C3⋊C8—61no—
106C2×C32C2×D1611yescharacteristic
107C3⋊D3—21no—
108C3×D3—161no—
109#41—361no—
110C2×Q8—361no—
111Q16—61no—
112Q16—62no—
113Q16—361no—
114SD16—361no—
115D8—61no—
116C2×C8—91no—
117C16—91no—
118C16GO+(4,𝔽2)11yescharacteristic
119C22×C3—241no—
120C2×D3—61no—
121C2×D3—61no—
122C2×D3—81no—
123C3×C4—21no—
124C3×C4—21no—
125C3×C4—242no—
126C3×C4—241no—
127Dic3—61no—
128Dic3—61no—
129Dic3—82no—
130Dic3—81no—
131C32#226411yescharacteristic, complemented, Sylow
132Q8—121no—
133Q8—122no—
134Q8—721no—
135D4—121no—
136D4—721no—
137C2×C4—91no—
138C2×C4—721no—
139C2×C4—721no—
140C8—91no—
141C8C2×GO+(4,𝔽2)11yescharacteristic
142C2×C3—21no—
143C2×C3—21no—
144C2×C3—481no—
145D3—62no—
146D3—121no—
147D3—161no—
148C22—91no—
149C22—241no—
150C4—91no—
151C4—241no—
152C4—242no—
153C4#6422511yescharacteristic
154C3—21no—
155C3—21no—
156C2—181no—
157C2—481no—
158C2#1059327611yescharacteristic
subgroupG/H
centerC2#10593276
commutator, cosocleC3⋊(C3⋊C16)C23
FrattiniC8C2×GO+(4,𝔽2)
FittingC32×C16D4
socleC2×C32C2×D16
prime radical#10590245C2
hypercenterC16GO+(4,𝔽2)
hypocenterC32#2264
LCSG ▷ C3⋊(C3⋊C16) ▷ C32×C8 ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2 ◁ C4 ◁ C8 ◁ C16

Complements

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

NH ≅ G/Ntype
2. #10590240C2semidirect
3. #10590133C2semidirect
4. #10590026C2semidirect
5. #10590025C2semidirect
131. C32#2264semidirect

Maximal subgroups

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

subgroupindex
#105902452
#105902402
#105901332
#105900262
#105900252
#22649