Finite Group Databasebeta

← #11781947

Subgroups — #11781947

Order 1152.

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

normal subgroups only

This group has 286 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#10593752C211yesmaximal, characteristic
2#10593388C211yesmaximal, characteristic, complemented
3#10590565C212yesmaximal
4#10590041C211yesmaximal, characteristic, complemented
5#10590038C212yesmaximal, complemented
6C2×#3788—21no—
7#64102C2211yescharacteristic
8#63873C2212yes—
9C2×#3717—22no—
10#63778—21no—
11C4⋊#622C2211yescharacteristic
12C4×#622C2211yescharacteristic
13#63743—21no—
14#63743—21no—
15C3×#810—22no—
16#63572C2212yes—
17#4818—62no—
18C2×C4⋊(C3⋊D3)D411yescharacteristic
19C2×C4×C3⋊D3—21no—
20C2×C3×Dic6—22no—
21C2×#622—21no—
22C2×#622D411yescharacteristic
23C2×#622D411yescharacteristic
24#3788—42no—
25C32×C4⋊C4D411yescharacteristic
26#3752—21no—
27C4×C3⋊Dic3C2311yescharacteristic
28C2×C3×C3⋊C8—22no—
29#3724—22no—
30#3724—22no—
31#3717—44no—
32#1693—91nomaximal, Sylow
33#944—62no—
34C2×#215—62no—
35C2×#204—62no—
36#893—62no—
37C3×#103—62no—
38Dic3⋊C8—62no—
39#810—22no—
40C22×C3⋊D3—21no—
41C2×C32×C4—21no—
42C2×C32×C4C2×D411yescharacteristic
43C2×C3⋊Dic3C2×D411yescharacteristic
44C2×C3⋊Dic3#4111yescharacteristic
45C4⋊(C3⋊D3)—22no—
46C4×C3⋊D3—41no—
47C4×C3⋊D3—41no—
48C2×C3×Dic3—42no—
49C3×Dic6—42no—
50C3×Dic6—42no—
51#622—21no—
52#622—41no—
53#622SD1612yescomplemented
54C3×C3⋊C8—42no—
55#500—91no—
56#461—92no—
57#436—91no—
58#334—91no—
59#332—92no—
60C2×C3×Q8—62no—
61C2×D12—62no—
62C2×C4×D3—122no—
63C2×Dic6—22no—
64C2×C3×C8—62no—
65C3×C4⋊C4—22no—
66#215—124no—
67(C2×D3)⋊C4—122no—
68Dic3⋊C4—122no—
69Dic3⋊C4—122no—
70C4×Dic3—62no—
71C2×C3⋊C8—22no—
72#204—124no—
73C22×C32#12111yescharacteristic
74C2×C3⋊D3—41no—
75C2×C3⋊D3—41no—
76C2×C3⋊D3—41no—
77C32×C4—41no—
78C32×C4AGL(1,ℤ/8)12yes—
79C3⋊Dic3—21no—
80C3⋊Dic3C2×SD1611yescharacteristic
81C3⋊Dic3#13711yescharacteristic
82C3×Dic3—82no—
83C2×SD16—182no—
84C2×M16—181no—
85C4⋊Q8—92no—
86C4×D4—91no—
87#107—181no—
88#107—181no—
89C4⋊C8—92no—
90C4⋊C8—91no—
91#103—62no—
92C22⋊C8—181no—
93C4×C8—91no—
94C22×D3—122no—
95C3×Q8—122no—
96C3×Q8—122no—
97C2×C3×C4—22no—
98C2×C3×C4—42no—
99C2×C3×C4—122no—
100C2×Dic3—42no—
101C2×Dic3—62no—
102C2×Dic3—62no—
103D12—64no—
104D12—122no—
105C4×D3—242no—
106C4×D3—242no—
107Dic6—42no—
108Dic6—42no—
109C3×C8—122no—
110C3⋊C8—42no—
111C2×C32#46111yescharacteristic
112C2×C32#46911yescharacteristic
113C2×C32#47311yescharacteristic
114C3⋊D3—81no—
115C2×Q8—62no—
116C2×D4—91no—
117C22×C4—181no—
118SD16—364no—
119M16—362no—
120C2×C8—62no—
121C2×C8—91no—
122C2×C8—91no—
123C2×C8—181no—
124C4⋊C4—182no—
125C4⋊C4—182no—
126C4⋊C4GO+(4,𝔽2)11yescharacteristic
127C22⋊C4—181no—
128C42—91no—
129C22×C3—22no—
130C2×D3—124no—
131C2×D3—242no—
132C2×D3—242no—
133C3×C4—22no—
134C3×C4—22no—
135C3×C4—82no—
136C3×C4—242no—
137Dic3—62no—
138Dic3—62no—
139Dic3—82no—
140Dic3—122no—
141C32#169311yescharacteristic, complemented, Sylow
142C23—181no—
143Q8—122no—
144Q8—122no—
145D4—182no—
146C2×C4—21no—
147C2×C4—91no—
148C2×C4—91no—
149C2×C4—122no—
150C2×C4—361no—
151C2×C4—361no—
152C2×C4C2×GO+(4,𝔽2)11yescharacteristic
153C8—92no—
154C8—122no—
155C8—181no—
156C8—361no—
157C2×C3—22no—
158C2×C3—22no—
159C2×C3—22no—
160D3—244no—
161C22—361no—
162C22—361no—
163C22—361no—
164C22#6424211yescharacteristic
165C4—41no—
166C4—91no—
167C4—91no—
168C4—181no—
169C4—242no—
170C4#6422412yes—
171C3—22no—
172C2—721no—
173C2#1059342911yescharacteristic
174C2#1059346511yescharacteristic
175C2#1059348211yescharacteristic
subgroupG/H
centerC22#64242
commutator, cosocleC4×C3⋊Dic3C23
FrattiniC2×C4C2×GO+(4,𝔽2)
FittingC32×C4⋊C4D4
socleC22×C32#121
prime radicalC2×C4⋊(C3⋊D3)D4
hypercenterC4⋊C4GO+(4,𝔽2)
hypocenterC32#1693
LCSG ▷ C4×C3⋊Dic3 ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ C4⋊C4

Complements

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

NH ≅ G/Ntype
2. #10593388C2semidirect
4. #10590041C2semidirect
5. #10590038C2semidirect
53. #622SD16semidirect
141. C32#1693semidirect

Maximal subgroups

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

subgroupindex
#105937522
#105933882
#105905652
#105900412
#105900382
#16939