Finite Group Databasebeta

← #11780903

Subgroups — #11780903

Order 1152.

344 conjugacy classes of subgroups; only the 47 normal subgroups are shown.

normal subgroups only

This group has 344 conjugacy classes of subgroups — too many to draw. Only its 47 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
1D4×#622C211yesmaximal, characteristic, complemented
2#10593418C211yesmaximal, characteristic, complemented
3#10591486C212yesmaximal, complemented
4#10590042C211yesmaximal, characteristic, complemented
5#10590037C212yesmaximal, complemented
6C22×#622—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—
23C2×#622—21no—
24C2×#622—42no—
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#1667—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—21no—
45C32×D4D812yescomplemented
46C2×C32×C4C2×D411yescharacteristic
47C2×C3⋊Dic3—21no—
48C2×C3⋊Dic3—41no—
49C2×C3⋊Dic3—41no—
50C2×C3⋊Dic3C2×D411yescharacteristic
51C2×C3⋊Dic3#4111yescharacteristic
52C3×D12—42no—
53C3×D12—42no—
54#625—42no—
55#625—42no—
56#625—82no—
57#622—21no—
58#622—41no—
59#622D812yescomplemented
60C3×C3⋊C8—42no—
61#493—91no—
62#459—92no—
63C8×D4—91no—
64#335—91no—
65#331—92no—
66C2×C3×D4—22no—
67C2×C3×D4—62no—
68C2×#67—122no—
69C2×#67—122no—
70C22×Dic3—122no—
71C2×D12—22no—
72C3×D8—124no—
73C2×C3×C8—62no—
74#217—122no—
75#213—44no—
76C4⋊Dic3—62no—
77C4×Dic3—62no—
78C2×C3⋊C8—22no—
79C22×C32—22no—
80C22×C32—41no—
81C22×C32—41no—
82C22×C32#12111yescharacteristic
83C2×C3×D3—82no—
84C2×C3×D3—82no—
85C2×C3×D3—82no—
86C32×C4C2×D811yescharacteristic
87C32×C4#13511yescharacteristic
88C3⋊Dic3—21no—
89C3⋊Dic3—41no—
90C3⋊Dic3C2×D811yescharacteristic
91C3⋊Dic3AGL(1,ℤ/8)11yescharacteristic
92C2×D8—62no—
93C2×D8—181no—
94C2×D8—181no—
95C22×C8—181no—
96#127—92no—
97C4×D4—91no—
98C4⋊C8—92no—
99C4⋊C8—91no—
100#102—182no—
101C22⋊C8—181no—
102C4×C8—91no—
103C23×C3—42no—
104C23×C3—122no—
105C22×D3—42no—
106C3×D4—24no—
107C3×D4—42no—
108C3×D4—122no—
109C3×D4—122no—
110C2×C3×C4—22no—
111#67—242no—
112#67—242no—
113#67—244no—
114C2×Dic3—62no—
115C2×Dic3—62no—
116C2×Dic3—122no—
117C2×Dic3—242no—
118C2×Dic3—242no—
119D12—42no—
120D12—42no—
121C3×C8—122no—
122C3⋊C8—42no—
123C2×C32—42no—
124C2×C32#45911yescharacteristic
125C2×C32#46611yescharacteristic
126C2×C32#47211yescharacteristic
127C3×D3—162no—
128C2×D4—62no—
129C2×D4—182no—
130C2×D4—182no—
131C2×D4GO+(4,𝔽2)11yescharacteristic
132C22×C4—181no—
133D8—124no—
134D8—362no—
135D8—362no—
136C2×C8—62no—
137C2×C8—91no—
138C2×C8—91no—
139C2×C8—181no—
140C2×C8—362no—
141C4⋊C4—91no—
142C22⋊C4—181no—
143C42—91no—
144C22×C3—22no—
145C22×C3—44no—
146C22×C3—82no—
147C22×C3—82no—
148C22×C3—242no—
149C22×C3—242no—
150C22×C3—242no—
151C2×D3—82no—
152C2×D3—82no—
153C2×D3—82no—
154C3×C4—22no—
155C3×C4—22no—
156Dic3—62no—
157Dic3—62no—
158Dic3—122no—
159Dic3—242no—
160C32#166711yescharacteristic, complemented, Sylow
161C23—21no—
162C23—122no—
163D4—21no—
164D4—122no—
165D4—122no—
166D4—362no—
167D4—362no—
168D4—722no—
169D4#377412yescomplemented
170C2×C4—91no—
171C2×C4—91no—
172C2×C4—181no—
173C2×C4—361no—
174C2×C4—361no—
175C2×C4C2×GO+(4,𝔽2)11yescharacteristic
176C8—92no—
177C8—122no—
178C8—181no—
179C8—361no—
180C2×C3—22no—
181C2×C3—22no—
182C2×C3—22no—
183C2×C3—84no—
184C2×C3—482no—
185D3—162no—
186C22—22no—
187C22—41no—
188C22—41no—
189C22—242no—
190C22—242no—
191C22—242no—
192C22#6424211yescharacteristic
193C4—91no—
194C4—91no—
195C4—181no—
196C4—361no—
197C4C2×#377411yescharacteristic
198C4#6423711yescharacteristic
199C3—22no—
200C2—42no—
201C2—482no—
202C2#1059346411yescharacteristic
203C2#1059346611yescharacteristic
204C2#1059352011yescharacteristic
subgroupG/H
centerC22#64242
commutator, cosocleC4×C3⋊Dic3C23
FrattiniC2×C4C2×GO+(4,𝔽2)
FittingC2×C32×D4D4
socleC22×C32#121
hypercenterC2×D4GO+(4,𝔽2)
hypocenterC32#1667
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. D4×#622C2semidirect
2. #10593418C2semidirect
3. #10591486C2semidirect
4. #10590042C2semidirect
5. #10590037C2semidirect
45. C32×D4D8semidirect
59. #622D8semidirect
160. C32#1667semidirect
169. D4#3774semidirect

Maximal subgroups

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

subgroupindex
D4×#6222
#105934182
#105914862
#105900422
#105900372
#16679