Finite Group Databasebeta

← #11799433

Subgroups — #11799433

Order 1152.

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

normal subgroups only

This group has 223 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
1#10593304C212yesmaximal
2#10590240C211yesmaximal, characteristic, complemented
3#10590229C211yesmaximal, characteristic
4#10590141C211yesmaximal, characteristic, complemented
5#10590021C212yesmaximal, complemented
6#64226—22no—
7#63803C2211yescharacteristic
8#63802C2212yes—
9#63771C2212yes—
10#63728—22no—
11C16×C3⋊D3C2211yescharacteristic
12C3×Dic24—21no—
13C3×#798—21no—
14#63550—21no—
15#63544C2211yescharacteristic
16D3×C3⋊C16—21no—
17D3×Q32—61no—
18#4907—61no—
19#3798D411yescharacteristic
20#3797—22no—
21#3788—22no—
22#3776—42no—
23#3775—42no—
24C8×C3⋊D3C2311yescharacteristic
25C3×Dic12—22no—
26C3×D3×C8—21no—
27#3718—22no—
28#3712D411yescharacteristic
29#3711—21no—
30C32×C16D411yescharacteristic
31C3⋊(C3⋊C16)D411yescharacteristic
32C3×C3⋊C16—21no—
33#2222—91nomaximal, Sylow
34D3×Q16—62no—
35#901—61no—
36C3×Q32—61no—
37C3×M32—61no—
38#829—62no—
39C2×C3⋊C16—61no—
40Dic24—21no—
41#798—21no—
42#798—61no—
43D3×C16—61no—
44D3×C16—61no—
45D3×C16—61no—
46C4×C3⋊D3C2×D411yescharacteristic
47C3×C4×D3—21no—
48C3×Dic6—42no—
49#627—42no—
50#627D811yescharacteristic
51#626—21no—
52#625D811yescharacteristic
53#624—42no—
54#622—42no—
55C32×C8C2×D411yescharacteristic
56C3⋊(C3⋊C8)#4111yescharacteristic
57C3×C3⋊C8—21no—
58C2×Q32—91no—
59#504—91no—
60#473—92no—
61#368—91no—
62#362—92no—
63D3×Q8—122no—
64#235—61no—
65C3×Q16—62no—
66C2×C3×C8—61no—
67#216—122no—
68#208—61no—
69Dic12—22no—
70ΓL(1,𝔽25)—61no—
71ΓL(1,𝔽25)—61no—
72D3×C8—21no—
73D3×C8—61no—
74D3×C8—61no—
75C3×C16—21no—
76C3×C16—21no—
77C3×C16—61no—
78C3⋊C16—21no—
79C3⋊C16—61no—
80C3⋊C16—61no—
81C2×C3⋊D3#13511yescharacteristic
82C2×C3×D3—21no—
83C32×C4#12111yescharacteristic
84C3⋊Dic3C2×D811yescharacteristic
85C3×Dic3—21no—
86C3×Dic3—82no—
87#137—182no—
88C2×Q16—92no—
89#131—91no—
90Q32—61no—
91Q32—181no—
92M32—61no—
93M32—91no—
94C2×C16—91no—
95C2×C16—181no—
96#108—92no—
97#101—182no—
98C3×Q8—122no—
99C2×C3×C4—61no—
100#67—61no—
101#67—61no—
102D12—61no—
103C4×D3—21no—
104C4×D3—61no—
105C4×D3—61no—
106C4×D3—242no—
107Dic6—42no—
108Dic6—61no—
109Dic6—242no—
110C3×C8—21no—
111C3×C8—21no—
112C3×C8—61no—
113C3⋊C8—21no—
114C3⋊C8—61no—
115C3⋊C8—61no—
116C2×C32#46611yescharacteristic
117C3⋊D3—21no—
118C3×D3—41no—
119#41—91no—
120C2×Q8—182no—
121Q16—62no—
122Q16—182no—
123Q16—362no—
124SD16—362no—
125M16—91no—
126M16—181no—
127M16—182no—
128C2×C8—61no—
129C2×C8—91no—
130C16—61no—
131C16—91no—
132C16GO+(4,𝔽2)11yescharacteristic
133C22×C3—61no—
134C2×D3—21no—
135C2×D3—61no—
136C2×D3—61no—
137C3×C4—21no—
138C3×C4—21no—
139C3×C4—61no—
140C3×C4—242no—
141Dic3—21no—
142Dic3—61no—
143Dic3—61no—
144Dic3—82no—
145C32#222211yescharacteristic, complemented, Sylow
146Q8—91no—
147Q8—122no—
148Q8—362no—
149D4—91no—
150D4—181no—
151C2×C4—61no—
152C2×C4—91no—
153C2×C4—362no—
154C8—61no—
155C8—91no—
156C8—362no—
157C8C2×GO+(4,𝔽2)11yescharacteristic
158C2×C3—21no—
159C2×C3—21no—
160C2×C3—121no—
161D3—41no—
162D3—62no—
163D3—121no—
164C22—61no—
165C22—91no—
166C4—61no—
167C4—91no—
168C4—242no—
169C4#6423011yescharacteristic
170C3—21no—
171C3—21no—
172C2—121no—
173C2—181no—
174C2#1059328511yescharacteristic
subgroupG/H
centerC2#10593285
commutator, cosocleC8×C3⋊D3C23
FrattiniC8C2×GO+(4,𝔽2)
FittingC32×C16D4
socleC2×C32#466
prime radical#3798D4
hypercenterC16GO+(4,𝔽2)
hypocenterC32#2222
LCSG ▷ C8×C3⋊D3 ▷ 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
4. #10590141C2semidirect
5. #10590021C2semidirect
145. C32#2222semidirect

Maximal subgroups

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

subgroupindex
#105933042
#105902402
#105902292
#105901412
#105900212
#22229