Finite Group Databasebeta

← #11781128

Subgroups — #11781128

Order 1152.

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

normal subgroups only

This group has 292 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
2#10593388C211yesmaximal, characteristic, complemented
3#10591497C212yesmaximal
4#10590042C211yesmaximal, characteristic, complemented
5#10590038C212yesmaximal, complemented
6C22×#622—21no—
7D4×C3⋊Dic3C2211yescharacteristic
8C2×C3×#214—22no—
9#63873C2212yes—
10C22⋊#622—21no—
11C4⋊#622C2211yescharacteristic
12C4×#622C2211yescharacteristic
13#63743—21no—
14#63743—21no—
15#63572C2212yes—
16#63566—22no—
17#5162—62no—
18C2×C32×D4D411yescharacteristic
19C22×C3⋊Dic3—21no—
20C2×C3×Dic6—22no—
21C2×#622—21no—
22C2×#622—42no—
23C2×#622D411yescharacteristic
24C2×#622D411yescharacteristic
25#3757—21no—
26C4⋊(C3⋊Dic3)D411yescharacteristic
27C4×C3⋊Dic3C2311yescharacteristic
28C3×#214—44no—
29C2×C3×C3⋊C8—22no—
30#3724—22no—
31#3724—22no—
32#1673—91nomaximal, Sylow
33C2×C3×SD16—62no—
34#944—62no—
35D4×Dic3—62no—
36C2×#214—22no—
37#835—62no—
38#816—62no—
39Dic3⋊C8—62no—
40C23×C32—21no—
41C32×D4—21no—
42C32×D4D812yes—
43C2×C32×C4C2×D411yescharacteristic
44C2×C3⋊Dic3—21no—
45C2×C3⋊Dic3—41no—
46C2×C3⋊Dic3—41no—
47C2×C3⋊Dic3C2×D411yescharacteristic
48C2×C3⋊Dic3#4111yescharacteristic
49C2×C3×Dic3—42no—
50C3×Dic6—42no—
51C3×Dic6—42no—
52#622—21no—
53#622—41no—
54#622SD1612yescomplemented
55C3×C3⋊C8—42no—
56#500—91no—
57#461—92no—
58C8×D4—91no—
59#335—91no—
60#332—92no—
61C2×C3×Q8—62no—
62C2×C3×D4—22no—
63C22×Dic3—122no—
64C2×Dic6—22no—
65C3×SD16—124no—
66C2×C3×C8—62no—
67#217—122no—
68#214—44no—
69C4⋊Dic3—62no—
70Dic3⋊C4—122no—
71Dic3⋊C4—122no—
72C4×Dic3—62no—
73C2×C3⋊C8—22no—
74C22×C32—22no—
75C22×C32—41no—
76C22×C32—41no—
77C22×C32#12111yescharacteristic
78C32×C4C2×D811yescharacteristic
79C32×C4#13511yescharacteristic
80C3⋊Dic3—21no—
81C3⋊Dic3—41no—
82C3⋊Dic3C2×SD1611yescharacteristic
83C3⋊Dic3#13711yescharacteristic
84C3×Dic3—82no—
85C2×SD16—62no—
86C22×C8—181no—
87C4⋊Q8—92no—
88C4×D4—91no—
89#107—181no—
90#107—181no—
91C4⋊C8—92no—
92C4⋊C8—91no—
93#103—182no—
94C22⋊C8—181no—
95C4×C8—91no—
96C23×C3—42no—
97C3×Q8—122no—
98C3×Q8—122no—
99C3×D4—24no—
100C3×D4—42no—
101C2×C3×C4—22no—
102C2×C3×C4—122no—
103C2×Dic3—42no—
104C2×Dic3—62no—
105C2×Dic3—62no—
106C2×Dic3—122no—
107C2×Dic3—242no—
108C2×Dic3—242no—
109Dic6—42no—
110Dic6—42no—
111C3×C8—122no—
112C3⋊C8—42no—
113C2×C32—42no—
114C2×C32#46111yescharacteristic
115C2×C32#46611yescharacteristic
116C2×C32#47311yescharacteristic
117C2×Q8—62no—
118C2×D4GO+(4,𝔽2)11yescharacteristic
119C22×C4—181no—
120SD16—124no—
121C2×C8—62no—
122C2×C8—91no—
123C2×C8—91no—
124C2×C8—181no—
125C2×C8—362no—
126C4⋊C4—91no—
127C4⋊C4—182no—
128C4⋊C4—182no—
129C22⋊C4—181no—
130C42—91no—
131C22×C3—22no—
132C22×C3—44no—
133C22×C3—82no—
134C22×C3—82no—
135C3×C4—22no—
136C3×C4—22no—
137C3×C4—242no—
138Dic3—62no—
139Dic3—62no—
140Dic3—82no—
141Dic3—122no—
142Dic3—242no—
143C32#167311yescharacteristic, complemented, Sylow
144C23—21no—
145Q8—122no—
146Q8—122no—
147D4—21no—
148D4#377412yes—
149C2×C4—91no—
150C2×C4—91no—
151C2×C4—122no—
152C2×C4—181no—
153C2×C4—361no—
154C2×C4—361no—
155C2×C4C2×GO+(4,𝔽2)11yescharacteristic
156C8—92no—
157C8—122no—
158C8—181no—
159C8—361no—
160C2×C3—22no—
161C2×C3—22no—
162C2×C3—22no—
163C2×C3—84no—
164C22—22no—
165C22—41no—
166C22—41no—
167C22#6424211yescharacteristic
168C4—91no—
169C4—91no—
170C4—181no—
171C4—242no—
172C4—361no—
173C4C2×#377411yescharacteristic
174C4#6423711yescharacteristic
175C3—22no—
176C2—42no—
177C2#1059346511yescharacteristic
178C2#1059346811yescharacteristic
179C2#1059352011yescharacteristic
subgroupG/H
centerC22#64242
commutator, cosocleC4×C3⋊Dic3C23
FrattiniC2×C4C2×GO+(4,𝔽2)
Fitting, prime radicalC2×C32×D4D4
socleC22×C32#121
hypercenterC2×D4GO+(4,𝔽2)
hypocenterC32#1673
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
2. #10593388C2semidirect
4. #10590042C2semidirect
5. #10590038C2semidirect
54. #622SD16semidirect
143. C32#1673semidirect

Maximal subgroups

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

subgroupindex
D4×#6222
#105933882
#105914972
#105900422
#105900382
#16739