Finite Group Databasebeta

← #11800638

Subgroups — #11800638

Order 1152.

187 conjugacy classes of subgroups; only the 35 normal subgroups are shown.

normal subgroups only

This group has 187 conjugacy classes of subgroups — too many to draw. Only its 35 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
1C2×#63550C211yesmaximal, characteristic, complemented
2#10590629C211yesmaximal, characteristic
3#10590166C211yesmaximal, characteristic, complemented
4#10590026C212yesmaximal, complemented
5#10590025C212yesmaximal, complemented
6C2×C3×Dic12—21no—
7C3×#904—21no—
8C2×C3⋊(C3⋊C16)C2211yescharacteristic
9#63550—21no—
10#63550C2212yes—
11#63550C2211yescharacteristic
12#63547—21no—
13#63545C2211yescharacteristic
14#63540C2212yes—
15#5194—61no—
16C2×#829—61no—
17C3×#235—41no—
18C2×C3×Dic6—41no—
19C2×C32×C8D411yescharacteristic
20C3×Dic12—21no—
21C3×Dic12—22no—
22C3×Dic12—41no—
23C3×D24—21no—
24C3×#204—41no—
25C3⋊(C3⋊C16)D411yescharacteristic
26C3⋊(C3⋊C16)C2311yescharacteristic
27#2264—91nomaximal, Sylow
28C3×#135—61no—
29C2×C3×Q16—61no—
30C2×Dic12—21no—
31#904—21no—
32#829—62no—
33#829—61no—
34#829—62no—
35#828—61no—
36#827—61no—
37#826—61no—
38C2×C3⋊C16—61no—
39C2×C3⋊C16—61no—
40C2×C32×C4D811yescharacteristic
41C3×#67—81no—
42C2×C3×Dic3—81no—
43C3×D12—41no—
44C3×C4×D3—81no—
45C3×Dic6—41no—
46C3×Dic6—42no—
47C3×Dic6—81no—
48C32×C8D811yescharacteristic
49C32×C8C2×D411yescharacteristic
50#508—91no—
51C2×Q32—91no—
52Q64—92no—
53SD64—92no—
54M64—91no—
55C3×#41—121no—
56C2×C3×Q8—121no—
57#235—41no—
58C2×Dic6—41no—
59C3×Q16—61no—
60C3×Q16—62no—
61C3×Q16—121no—
62C3×SD16—121no—
63C3×D8—61no—
64C2×C3×C8—21no—
65C2×C3×C8—21no—
66Dic12—21no—
67Dic12—22no—
68Dic12—41no—
69D24—21no—
70#204—41no—
71C3⋊C16—61no—
72C3⋊C16—61no—
73C3⋊C16—61no—
74C3⋊C16—61no—
75C22×C32D1611yescharacteristic
76C2×C3×D3—81no—
77C32×C4D1611yescharacteristic
78C32×C4C2×D811yescharacteristic
79C3×Dic3—82no—
80C3×Dic3—81no—
81#135—61no—
82C2×Q16—61no—
83Q32—92no—
84Q32—91no—
85Q32—181no—
86SD32—181no—
87D16—91no—
88C2×C16—91no—
89C32—92no—
90C3×Q8—121no—
91C3×Q8—122no—
92C3×Q8—241no—
93C3×D4—121no—
94C3×D4—241no—
95C2×C3×C4—21no—
96C2×C3×C4—21no—
97C2×C3×C4—241no—
98C2×C3×C4—241no—
99#67—81no—
100C2×Dic3—81no—
101D12—41no—
102C4×D3—81no—
103Dic6—41no—
104Dic6—42no—
105Dic6—81no—
106C3×C8—21no—
107C3×C8—21no—
108C3×C8—21no—
109C3×C8—21no—
110C2×C32—21no—
111C2×C32C2×D1611yescharacteristic
112C3×D3—161no—
113#41—121no—
114C2×Q8—121no—
115Q16—61no—
116Q16—62no—
117Q16—121no—
118SD16—121no—
119D8—61no—
120C2×C8GO+(4,𝔽2)11yescharacteristic
121C16—91no—
122C16—91no—
123C22×C3—21no—
124C22×C3—21no—
125C22×C3—241no—
126C2×D3—81no—
127C3×C4—21no—
128C3×C4—21no—
129C3×C4—21no—
130C3×C4—21no—
131C3×C4—241no—
132C3×C4—242no—
133Dic3—82no—
134Dic3—81no—
135C32#226411yescharacteristic, complemented, Sylow
136Q8—121no—
137Q8—122no—
138Q8—241no—
139D4—121no—
140D4—241no—
141C2×C4—241no—
142C2×C4—241no—
143C2×C4#377411yescharacteristic
144C8#377411yescharacteristic
145C8C2×GO+(4,𝔽2)11yescharacteristic
146C2×C3—22no—
147C2×C3—21no—
148C2×C3—21no—
149C2×C3—41no—
150C2×C3—481no—
151D3—161no—
152C22—241no—
153C22#6373411yescharacteristic
154C4—241no—
155C4—242no—
156C4#6373411yescharacteristic
157C4C2×#377411yescharacteristic
158C3—21no—
159C3—21no—
160C2—21no—
161C2—481no—
162C2C2×#6373411yescharacteristic
subgroupG/H
centerC2C2×#63734
commutator, cosocleC3⋊(C3⋊C16)C23
FrattiniC8C2×GO+(4,𝔽2)
FittingC2×C32×C8D4
socleC2×C32C2×D16
prime radical#10590629C2
hypercenterC2×C8GO+(4,𝔽2)
hypocenterC32#2264
LCSG ▷ C3⋊(C3⋊C16) ▷ C32×C8 ▷ 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
1. C2×#63550C2semidirect
3. #10590166C2semidirect
4. #10590026C2semidirect
5. #10590025C2semidirect
135. C32#2264semidirect

Maximal subgroups

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

subgroupindex
C2×#635502
#105906292
#105901662
#105900262
#105900252
#22649