Finite Group Databasebeta

← #11799401

Subgroups — #11799401

Order 1152.

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

normal subgroups only

This group has 239 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#10593301C212yesmaximal, complemented
2#10590234C211yesmaximal, characteristic, complemented
3#10590229C211yesmaximal, characteristic, complemented
4#10590141C211yesmaximal, characteristic, complemented
5#10590020C212yesmaximal, complemented
6#64224—22no—
7#63803C2211yescharacteristic
8#63797C2212yes—
9#63771C2212yes—
10#63727—22no—
11C16×C3⋊D3C2211yescharacteristic
12C3×D48—21no—
13C3×#798—21no—
14#63545—21no—
15#63544C2211yescharacteristic
16D3×C3⋊C16—21no—
17D3×D16—61no—
18#4907—61no—
19#3802—22no—
20#3798D411yescharacteristic
21#3788—22no—
22#3775—42no—
23#3774—42no—
24C8×C3⋊D3C2311yescharacteristic
25C3×D24—22no—
26C3×D3×C8—21no—
27#3713—22no—
28#3712D411yescharacteristic
29#3711—21no—
30C32×C16D411yescharacteristic
31C3⋊(C3⋊C16)D411yescharacteristic
32C3×C3⋊C16—21no—
33#2221—91nomaximal, Sylow
34D3×D8—62no—
35#901—61no—
36C3×D16—61no—
37C3×M32—61no—
38#826—62no—
39C2×C3⋊C16—61no—
40D48—21no—
41#798—21no—
42#798—61no—
43D3×C16—61no—
44D3×C16—61no—
45D3×C16—61no—
46C2×D32—42no—
47C4×C3⋊D3C2×D411yescharacteristic
48C3×D12—42no—
49C3×C4×D3—21no—
50#627D811yescharacteristic
51#626—21no—
52#625—42no—
53#625D811yescharacteristic
54#622—42no—
55C32×C8C2×D411yescharacteristic
56C3⋊(C3⋊C8)#4111yescharacteristic
57C3×C3⋊C8—21no—
58C2×D16—91no—
59#504—91no—
60#472—92no—
61#368—91no—
62#361—92no—
63D3×D4—122no—
64#235—61no—
65C3×D8—62no—
66C2×C3×C8—61no—
67#213—122no—
68#208—61no—
69D24—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—
83C2×C3×D3—82no—
84D32—162no—
85C32×C4#12111yescharacteristic
86C3⋊Dic3C2×D811yescharacteristic
87C3×Dic3—21no—
88AGL(1,ℤ/8)—182no—
89C2×D8—92no—
90#131—91no—
91D16—61no—
92D16—181no—
93M32—61no—
94M32—91no—
95C2×C16—91no—
96C2×C16—181no—
97#108—92no—
98#100—182no—
99C22×D3—242no—
100C3×D4—122no—
101C2×C3×C4—61no—
102#67—61no—
103#67—61no—
104#67—242no—
105D12—42no—
106D12—61no—
107C4×D3—21no—
108C4×D3—61no—
109C4×D3—61no—
110Dic6—61no—
111C3×C8—21no—
112C3×C8—21no—
113C3×C8—61no—
114C3⋊C8—21no—
115C3⋊C8—61no—
116C3⋊C8—61no—
117C2×C32#46611yescharacteristic
118C3⋊D3—21no—
119C3×D3—41no—
120C3×D3—162no—
121#41—91no—
122C2×D4—182no—
123SD16—362no—
124D8—62no—
125D8—182no—
126D8—362no—
127M16—91no—
128M16—181no—
129M16—182no—
130C2×C8—61no—
131C2×C8—91no—
132C16—61no—
133C16—91no—
134C16GO+(4,𝔽2)11yescharacteristic
135C22×C3—61no—
136C22×C3—242no—
137C2×D3—21no—
138C2×D3—61no—
139C2×D3—61no—
140C2×D3—82no—
141C2×D3—484no—
142C3×C4—21no—
143C3×C4—21no—
144C3×C4—61no—
145Dic3—21no—
146Dic3—61no—
147Dic3—61no—
148C32#222111yescharacteristic, complemented, Sylow
149C23—362no—
150Q8—91no—
151D4—91no—
152D4—122no—
153D4—181no—
154D4—362no—
155C2×C4—61no—
156C2×C4—91no—
157C8—61no—
158C8—91no—
159C8—362no—
160C8C2×GO+(4,𝔽2)11yescharacteristic
161C2×C3—21no—
162C2×C3—21no—
163C2×C3—121no—
164C2×C3—482no—
165D3—41no—
166D3—62no—
167D3—121no—
168D3—162no—
169C22—61no—
170C22—91no—
171C22—242no—
172C22—1442no—
173C4—61no—
174C4—91no—
175C4#6423011yescharacteristic
176C3—21no—
177C3—21no—
178C2—121no—
179C2—181no—
180C2—482no—
181C2#1059328511yescharacteristic
subgroupG/H
centerC2#10593285
commutator, cosocleC8×C3⋊D3C23
FrattiniC8C2×GO+(4,𝔽2)
FittingC32×C16D4
socleC2×C32#466
hypercenterC16GO+(4,𝔽2)
hypocenterC32#2221
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
1. #10593301C2semidirect
2. #10590234C2semidirect
3. #10590229C2semidirect
4. #10590141C2semidirect
5. #10590020C2semidirect
148. C32#2221semidirect

Maximal subgroups

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

subgroupindex
#105933012
#105902342
#105902292
#105901412
#105900202
#22219