Finite Group Databasebeta

← #11776952

Subgroups — #11776952

Order 1152.

308 conjugacy classes of subgroups; only the 64 normal subgroups are shown.

normal subgroups only

This group has 308 conjugacy classes of subgroups — too many to draw. Only its 64 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#10593730C211yesmaximal, characteristic
2#10593728C211yesmaximal, characteristic
3#10592406C211yesmaximal, characteristic
4#10590173C212yesmaximal, complemented
5#10590172C212yesmaximal, complemented
6C2×#3788—21no—
7C2×#3743C412yes—
8C42×C3⋊D3C2211yescharacteristic
9#63778—21no—
10#63777—21no—
11C4⋊#622—21no—
12C4⋊#622C2212yes—
13C4⋊#622C2211yescharacteristic
14C4⋊#622C2211yescharacteristic
15C32×#97C411yescharacteristic
16C8×C3⋊Dic3C2212yes—
17#63630C411yescharacteristic
18#4707—62no—
19C2×C4×C3⋊D3C2×C411yescharacteristic
20C2×C4×C3⋊D3D411yescharacteristic
21C2×C4×C3⋊D3Q811yescharacteristic
22C2×#622—22no—
23C2×#622—21no—
24C2×#622—21no—
25#3788—42no—
26C2×C32×C8C2×C412yes—
27C32×C42C2×C411yescharacteristic
28C4×C3⋊Dic3D411yescharacteristic
29C4×C3⋊Dic3Q811yescharacteristic
30C4×C3⋊Dic3C2311yescharacteristic
31C2×C3⋊(C3⋊C8)C2×C412yes—
32#3743—24no—
33#1569—91nomaximal, Sylow
34C2×ΓL(1,𝔽25)—64no—
35C42×D3—62no—
36C3×#97—22no—
37C8×Dic3—64no—
38#803—62no—
39C22×C3⋊D3C4⋊C411yescharacteristic
40C2×C32×C4C4⋊C411yescharacteristic
41C2×C32×C4C4⋊C411yescharacteristic
42C2×C32×C4C22×C411yescharacteristic
43C2×C3⋊Dic3C4⋊C411yescharacteristic
44C2×C3⋊Dic3C2×D411yescharacteristic
45C2×C3⋊Dic3C2×Q811yescharacteristic
46C4×C3⋊D3—22no—
47C4×C3⋊D3—21no—
48C4×C3⋊D3—21no—
49C4×C3⋊D3—41no—
50#622—42no—
51#622—41no—
52#622—41no—
53C32×C8—22no—
54C3⋊(C3⋊C8)M1614yescomplemented
55#432—91no—
56#423—91no—
57C4×M16—91no—
58#335—92no—
59#334—92no—
60C2×C4×D3—62no—
61C2×C4×D3—62no—
62C2×C4×D3—62no—
63C2×C3×C8—24no—
64C3×C42—22no—
65C4×Dic3—62no—
66C4×Dic3—62no—
67C4×Dic3—62no—
68C2×C3⋊C8—64no—
69ΓL(1,𝔽25)—616no—
70C22×C32C2×C4⋊C411yescharacteristic
71C2×C3⋊D3—21no—
72C2×C3⋊D3—21no—
73C2×C3⋊D3—21no—
74C32×C4—21no—
75C32×C4—21no—
76C32×C4C2×M1612yes—
77C3⋊Dic3—21no—
78C3⋊Dic3—21no—
79C3⋊Dic3AGL(1,ℤ/8)11yescharacteristic
80C3⋊Dic3#13711yescharacteristic
81C2×M16—92no—
82C2×M16—181no—
83C2×C42—91no—
84C4⋊C8—91no—
85C4⋊C8—92no—
86C4⋊C8—91no—
87C4⋊C8—181no—
88C22⋊C8—181no—
89#97—91no—
90#97—181no—
91#97#15711yescharacteristic
92C4×C8—92no—
93C22×D3—62no—
94C2×C3×C4—22no—
95C2×C3×C4—22no—
96C2×C3×C4—22no—
97C2×Dic3—62no—
98C2×Dic3—62no—
99C2×Dic3—62no—
100C4×D3—68no—
101C4×D3—122no—
102C4×D3—122no—
103C4×D3—124no—
104C3×C8—28no—
105C3⋊C8—68no—
106C2×C32#42311yescharacteristic
107C2×C32#42811yescharacteristic
108C2×C32#43011yescharacteristic
109C3⋊D3—41no—
110C22×C4—91no—
111C22×C4—91no—
112C22×C4—91no—
113M16—184no—
114M16—362no—
115C2×C8—92no—
116C2×C8—181no—
117C2×C8—181no—
118C2×C8—182no—
119C2×C8C2×#15712yes—
120C42—91no—
121C42—91no—
122C42—91no—
123C42C2×#15711yescharacteristic
124C22×C3—22no—
125C2×D3—64no—
126C2×D3—122no—
127C2×D3—122no—
128C3×C4—24no—
129C3×C4—42no—
130C3×C4—42no—
131Dic3—62no—
132Dic3—62no—
133Dic3—64no—
134Dic3—64no—
135C32#156911yescharacteristic, complemented, Sylow
136C23—91no—
137C2×C4—91no—
138C2×C4—91no—
139C2×C4—91no—
140C2×C4—181no—
141C2×C4—181no—
142C2×C4—182no—
143C2×C4—361no—
144C2×C4C4⋊#15711yescharacteristic
145C2×C4C4⋊#15711yescharacteristic
146C2×C4C22×#15711yescharacteristic
147C8—22no—
148C8—94no—
149C8—362no—
150C8—361no—
151C8—361no—
152C2×C3—22no—
153C2×C3—22no—
154C2×C3—22no—
155D3—124no—
156C22—181no—
157C22—181no—
158C22—181no—
159C22C2×C4⋊#15711yescharacteristic
160C4—21no—
161C4—21no—
162C4—91no—
163C4—91no—
164C4—181no—
165C4—181no—
166C4#6428312yes—
167C3—22no—
168C2—361no—
169C2#1059372911yescharacteristic
170C2#1059377411yescharacteristic
171C2#1059377611yescharacteristic
subgroupG/H
centerC22C2×C4⋊#157
commutatorC2×C32×C4C22×C4
FrattiniC2×C4C22×#157
FittingC32×#97C4
socleC22×C32C2×C4⋊C4
prime radicalC22×C3⋊D3C4⋊C4
cosocleC4×C3⋊Dic3C23
hypercenter#97#157
hypocenterC32#1569
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ #97

Complements

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

NH ≅ G/Ntype
4. #10590173C2semidirect
5. #10590172C2semidirect
54. C3⋊(C3⋊C8)M16semidirect
135. C32#1569semidirect

Maximal subgroups

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

subgroupindex
#105937302
#105937282
#105924062
#105901732
#105901722
#15699