Finite Group Databasebeta

← #11781723

Subgroups — #11781723

Order 1152.

338 conjugacy classes of subgroups; only the 43 normal subgroups are shown.

normal subgroups only

This group has 338 conjugacy classes of subgroups — too many to draw. Only its 43 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#10593821C211yesmaximal, characteristic, complemented
2#10593418C211yesmaximal, characteristic, complemented
3#10591486C212yesmaximal, complemented
4#10590041C211yesmaximal, characteristic, complemented
5#10590037C212yesmaximal, complemented
6C2×#3792—21no—
7C2×#3774—21no—
8C2×#3774—21no—
9D4×C3⋊Dic3C2211yescharacteristic
10C2×C3×#213—22no—
11#63914C2212yes—
12C22⋊#622—21no—
13C4⋊#622C2211yescharacteristic
14C4×#622C2211yescharacteristic
15#63572C2212yes—
16#63563—22no—
17#5150—62no—
18C2×C32×D4D411yescharacteristic
19C22×C3⋊Dic3—21no—
20C2×C3×D12—22no—
21C2×#625—22no—
22C2×#625—22no—
23#3792—42no—
24C2×#622—21no—
25C2×#622D411yescharacteristic
26C2×#622D411yescharacteristic
27#3774—42no—
28#3774—42no—
29#3757—21no—
30C4⋊(C3⋊Dic3)D411yescharacteristic
31C4×C3⋊Dic3C2311yescharacteristic
32C3×#213—44no—
33C2×C3×C3⋊C8—22no—
34#1687—91nomaximal, Sylow
35C2×C3×D8—62no—
36#940—62no—
37D4×Dic3—62no—
38C2×#213—22no—
39#832—62no—
40#821—62no—
41Dic3⋊C8—62no—
42C23×C32—21no—
43C22×C3×D3—42no—
44C32×D4—22no—
45C2×C32×C4C2×D411yescharacteristic
46C2×C3⋊Dic3—21no—
47C2×C3⋊Dic3—41no—
48C2×C3⋊Dic3—41no—
49C2×C3⋊Dic3C2×D411yescharacteristic
50C2×C3⋊Dic3#4111yescharacteristic
51C3×D12—42no—
52C3×D12—42no—
53#625—42no—
54#625—42no—
55#625—82no—
56#622—21no—
57#622—41no—
58#622D812yescomplemented
59C3×C3⋊C8—42no—
60#493—91no—
61#459—92no—
62#436—91no—
63#334—91no—
64#331—92no—
65C2×C3×D4—22no—
66C2×C3×D4—62no—
67C2×#67—122no—
68C2×#67—122no—
69C22×Dic3—122no—
70C2×D12—22no—
71C3×D8—124no—
72C2×C3×C8—62no—
73#217—122no—
74#213—44no—
75C4⋊Dic3—62no—
76C4×Dic3—62no—
77C2×C3⋊C8—22no—
78C22×C32—41no—
79C22×C32—41no—
80C22×C32—41no—
81C22×C32#12111yescharacteristic
82C2×C3×D3—82no—
83C2×C3×D3—82no—
84C2×C3×D3—82no—
85C32×C4AGL(1,ℤ/8)12yes—
86C3⋊Dic3—21no—
87C3⋊Dic3—41no—
88C3⋊Dic3C2×D811yescharacteristic
89C3⋊Dic3AGL(1,ℤ/8)11yescharacteristic
90C2×D8—62no—
91C2×D8—181no—
92C2×D8—181no—
93C2×M16—181no—
94#127—92no—
95C4×D4—91no—
96C4⋊C8—92no—
97C4⋊C8—91no—
98#102—182no—
99C22⋊C8—181no—
100C4×C8—91no—
101C23×C3—42no—
102C23×C3—122no—
103C22×D3—42no—
104C3×D4—24no—
105C3×D4—42no—
106C3×D4—122no—
107C3×D4—122no—
108C2×C3×C4—22no—
109#67—242no—
110#67—242no—
111#67—244no—
112C2×Dic3—62no—
113C2×Dic3—62no—
114C2×Dic3—122no—
115C2×Dic3—242no—
116C2×Dic3—242no—
117D12—42no—
118D12—42no—
119C3×C8—122no—
120C3⋊C8—42no—
121C2×C32—81no—
122C2×C32#45911yescharacteristic
123C2×C32#46911yescharacteristic
124C2×C32#47211yescharacteristic
125C3×D3—162no—
126C2×D4—62no—
127C2×D4—182no—
128C2×D4—182no—
129C2×D4GO+(4,𝔽2)11yescharacteristic
130C22×C4—181no—
131D8—124no—
132D8—362no—
133D8—362no—
134M16—362no—
135C2×C8—62no—
136C2×C8—91no—
137C2×C8—91no—
138C2×C8—181no—
139C4⋊C4—91no—
140C22⋊C4—181no—
141C42—91no—
142C22×C3—22no—
143C22×C3—44no—
144C22×C3—82no—
145C22×C3—82no—
146C22×C3—242no—
147C22×C3—242no—
148C22×C3—242no—
149C2×D3—82no—
150C2×D3—82no—
151C2×D3—82no—
152C3×C4—22no—
153C3×C4—22no—
154Dic3—62no—
155Dic3—62no—
156Dic3—122no—
157Dic3—242no—
158C32#168711yescharacteristic, complemented, Sylow
159C23—21no—
160C23—122no—
161D4—22no—
162D4—122no—
163D4—122no—
164D4—362no—
165D4—362no—
166D4—722no—
167C2×C4—91no—
168C2×C4—91no—
169C2×C4—181no—
170C2×C4—361no—
171C2×C4—361no—
172C2×C4C2×GO+(4,𝔽2)11yescharacteristic
173C8—92no—
174C8—122no—
175C8—181no—
176C8—361no—
177C2×C3—22no—
178C2×C3—22no—
179C2×C3—22no—
180C2×C3—84no—
181C2×C3—482no—
182D3—162no—
183C22—41no—
184C22—41no—
185C22—41no—
186C22—242no—
187C22—242no—
188C22—242no—
189C22#6424211yescharacteristic
190C4—91no—
191C4—91no—
192C4—181no—
193C4—361no—
194C4#6423612yes—
195C3—22no—
196C2—81no—
197C2—482no—
198C2#1059346411yescharacteristic
199C2#1059346611yescharacteristic
200C2#1059352211yescharacteristic
subgroupG/H
centerC22#64242
commutator, cosocleC4×C3⋊Dic3C23
FrattiniC2×C4C2×GO+(4,𝔽2)
FittingC2×C32×D4D4
socleC22×C32#121
hypercenterC2×D4GO+(4,𝔽2)
hypocenterC32#1687
LCSG ▷ C4×C3⋊Dic3 ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×D4

Complements

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

NH ≅ G/Ntype
1. #10593821C2semidirect
2. #10593418C2semidirect
3. #10591486C2semidirect
4. #10590041C2semidirect
5. #10590037C2semidirect
58. #622D8semidirect
158. C32#1687semidirect

Maximal subgroups

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

subgroupindex
#105938212
#105934182
#105914862
#105900412
#105900372
#16879