Finite Group Databasebeta

← #11771127

Subgroups — #11771127

Order 1152.

268 conjugacy classes of subgroups; only the 50 normal subgroups are shown.

normal subgroups only

This group has 268 conjugacy classes of subgroups — too many to draw. Only its 50 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#10593728C211yesmaximal, characteristic
2C4×#3788C211yesmaximal, characteristic
3#10592532C211yesmaximal, characteristic
4C2×#3788—21no—
5C2×#3788C412yes—
6C42×C3⋊D3C2211yescharacteristic
7#63777C412yes—
8C4⋊#622—21no—
9C4⋊#622—21no—
10C4×#622—21no—
11C32×C4⋊C8C411yescharacteristic
12#63647—21no—
13C8×C3⋊Dic3—21no—
14C4⋊(C3⋊(C3⋊C8))C411yescharacteristic
15#4833—62no—
16C2×C4×C3⋊D3C2×C411yescharacteristic
17C2×C4×C3⋊D3D411yescharacteristic
18C2×C4×C3⋊D3Q811yescharacteristic
19C2×#622—22no—
20C2×#622—22no—
21#3788—22no—
22#3788—22no—
23#3788—42no—
24C2×C32×C8—21no—
25C32×C42C2×C411yescharacteristic
26C4×C3⋊Dic3C2×C411yescharacteristic
27C4×C3⋊Dic3D411yescharacteristic
28C4×C3⋊Dic3D411yescharacteristic
29C2×C3⋊(C3⋊C8)—21no—
30#1299—91nomaximal, Sylow
31C42×D3—62no—
32C3×C4⋊C8—22no—
33(C2×D3)⋊C8—64no—
34C8×Dic3—64no—
35C4⋊(C3⋊C8)—62no—
36C22×C3⋊D3C4⋊C411yescharacteristic
37C2×C32×C4C4211yescharacteristic
38C2×C32×C4C22⋊C411yescharacteristic
39C2×C32×C4C4⋊C411yescharacteristic
40C2×C3⋊Dic3C22⋊C411yescharacteristic
41C2×C3⋊Dic3C22⋊C411yescharacteristic
42C2×C3⋊Dic3C4⋊C411yescharacteristic
43C4×C3⋊D3—21no—
44C4×C3⋊D3—21no—
45C4×C3⋊D3—21no—
46C4×C3⋊D3—21no—
47C4×C3⋊D3—21no—
48C4×C3⋊D3—21no—
49#622—24no—
50#622—42no—
51C32×C8—41no—
52C3⋊(C3⋊C8)—41no—
53#431—91no—
54#423—91no—
55C4×M16—91no—
56C2×C4×D3—62no—
57C2×C4×D3—62no—
58C2×C4×D3—62no—
59C2×C3×C8—24no—
60C3×C42—22no—
61C4×Dic3—62no—
62C4×Dic3—62no—
63C4×Dic3—62no—
64C2×C3⋊C8—64no—
65C22×C32#9511yescharacteristic
66C2×C3⋊D3—21no—
67C2×C3⋊D3—21no—
68C2×C3⋊D3—21no—
69C32×C4—21no—
70C32×C4#10411yescharacteristic
71C32×C4#10411yescharacteristic
72C32×C4#10811yescharacteristic
73C32×C4#10811yescharacteristic
74C3⋊Dic3—21no—
75C3⋊Dic3—21no—
76C3⋊Dic3#10011yescharacteristic
77C3⋊Dic3#10111yescharacteristic
78C2×M16—92no—
79C2×M16—181no—
80C2×C42—91no—
81C4⋊C8—91no—
82C4⋊C8—181no—
83C4⋊C8—181no—
84C4⋊C8#15711yescharacteristic
85C22⋊C8—181no—
86#97—92no—
87C4×C8—181no—
88C4×C8—181no—
89C22×D3—62no—
90C2×C3×C4—22no—
91C2×C3×C4—22no—
92C2×C3×C4—22no—
93C2×Dic3—62no—
94C2×Dic3—62no—
95C2×Dic3—62no—
96C4×D3—64no—
97C4×D3—64no—
98C4×D3—122no—
99C4×D3—122no—
100C4×D3—122no—
101C4×D3—122no—
102C3×C8—44no—
103C3⋊C8—124no—
104C2×C32#33911yescharacteristic
105C2×C32#34111yescharacteristic
106C2×C32#34311yescharacteristic
107C3⋊D3—41no—
108C22×C4—91no—
109C22×C4—91no—
110C22×C4—91no—
111M16—182no—
112M16—182no—
113M16—362no—
114C2×C8—21no—
115C2×C8—182no—
116C2×C8—182no—
117C2×C8—181no—
118C42—91no—
119C42—91no—
120C42—91no—
121C42C2×#15711yescharacteristic
122C22×C3—22no—
123C2×D3—64no—
124C2×D3—122no—
125C2×D3—122no—
126C3×C4—22no—
127C3×C4—22no—
128C3×C4—22no—
129C3×C4—22no—
130C3×C4—42no—
131Dic3—62no—
132Dic3—62no—
133Dic3—64no—
134Dic3—122no—
135C32#129911yescharacteristic, complemented, Sylow
136C23—91no—
137C2×C4—91no—
138C2×C4—91no—
139C2×C4—91no—
140C2×C4—181no—
141C2×C4—181no—
142C2×C4—181no—
143C2×C4—181no—
144C2×C4—181no—
145C2×C4—181no—
146C2×C4C4×#15711yescharacteristic
147C2×C4C4⋊#15711yescharacteristic
148C2×C4C22⋊#15711yescharacteristic
149C8—41no—
150C8—184no—
151C8—362no—
152C8—361no—
153C2×C3—22no—
154C2×C3—22no—
155C2×C3—22no—
156D3—124no—
157C22—181no—
158C22—181no—
159C22—181no—
160C22#6378111yescharacteristic
161C4—21no—
162C4—91no—
163C4—91no—
164C4—181no—
165C4—181no—
166C4#6377011yescharacteristic
167C4#6377111yescharacteristic
168C4#6378311yescharacteristic
169C4#6378511yescharacteristic
170C3—22no—
171C2—361no—
172C2#1059016411yescharacteristic
173C2#1059018511yescharacteristic
174C2#1059018811yescharacteristic
subgroupG/H
centerC22#63781
commutatorC2×C32×C4C42
FrattiniC42C2×#157
FittingC32×C4⋊C8C4
socleC22×C32#95
prime radicalC22×C3⋊D3C4⋊C4
cosocleC42×C3⋊D3C22
hypercenterC4⋊C8#157
hypocenterC32#1299
LCSG ▷ C2×C32×C4 ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ C4⋊C8

Complements

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

NH ≅ G/Ntype
135. C32#1299semidirect

Maximal subgroups

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

subgroupindex
#105937282
C4×#37882
#105925322
#12999