Finite Group Databasebeta

← #11777012

Subgroups — #11777012

Order 1152.

286 conjugacy classes of subgroups; only the 70 normal subgroups are shown.

normal subgroups only

This group has 286 conjugacy classes of subgroups — too many to draw. Only its 70 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
2#10593726C211yesmaximal, characteristic
3#10592532C211yesmaximal, characteristic
4#10590173C212yesmaximal, complemented
5#10590171C212yesmaximal, complemented
6C2×#3788—21no—
7C2×#3787—21no—
8C42×C3⋊D3C2211yescharacteristic
9#63779—21no—
10C4⋊#622—21no—
11C4⋊#622C2211yescharacteristic
12C4⋊#622C2211yescharacteristic
13C4⋊#622C2212yes—
14C32×C4⋊C8C411yescharacteristic
15#63647C412yes—
16C8×C3⋊Dic3C2212yes—
17C4⋊(C3⋊(C3⋊C8))C411yescharacteristic
18#4833—62no—
19C2×C4×C3⋊D3C2×C411yescharacteristic
20C2×C4×C3⋊D3D411yescharacteristic
21C2×C4×C3⋊D3Q811yescharacteristic
22C2×#622—21no—
23C2×#622—21no—
24C2×#622—22no—
25#3788—42no—
26#3787—42no—
27C2×C32×C8C2×C412yes—
28C32×C42C2×C411yescharacteristic
29C4×C3⋊Dic3D411yescharacteristic
30C4×C3⋊Dic3Q811yescharacteristic
31C4×C3⋊Dic3C2311yescharacteristic
32C2×C3⋊(C3⋊C8)C2×C412yes—
33#1571—91nomaximal, Sylow
34C42×D3—62no—
35C3×C4⋊C8—22no—
36(C2×D3)⋊C8—64no—
37C8×Dic3—64no—
38C4⋊(C3⋊C8)—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—21no—
47C4×C3⋊D3—21no—
48C4×C3⋊D3—41no—
49C4×C3⋊D3D812yes—
50C4×C3⋊D3Q1612yes—
51#622—41no—
52#622—41no—
53#622—42no—
54C32×C8—22no—
55C3⋊(C3⋊C8)—22no—
56#431—91no—
57#423—91no—
58C2×C4⋊C8—91no—
59#335—92no—
60#335—92no—
61C2×C4×D3—62no—
62C2×C4×D3—62no—
63C2×C4×D3—62no—
64C2×C3×C8—24no—
65C3×C42—22no—
66C4×Dic3—62no—
67C4×Dic3—62no—
68C4×Dic3—62no—
69C2×C3⋊C8—64no—
70C22×C32C2×C4⋊C411yescharacteristic
71C2×C3⋊D3—21no—
72C2×C3⋊D3—21no—
73C2×C3⋊D3#10712yes—
74C32×C4—21no—
75C32×C4#10712yes—
76C32×C4#13111yescharacteristic
77C32×C4#13111yescharacteristic
78C3⋊Dic3—21no—
79C3⋊Dic3—21no—
80C3⋊Dic3C2×D811yescharacteristic
81C3⋊Dic3C2×Q1611yescharacteristic
82C2×M16—181no—
83C22×C8—181no—
84C2×C42—91no—
85C4⋊C8—91no—
86C4⋊C8—91no—
87C4⋊C8—92no—
88C4⋊C8—91no—
89C4⋊C8—181no—
90C4⋊C8—181no—
91C4⋊C8#15711yescharacteristic
92C22⋊C8—92no—
93C4×C8—92no—
94C22×D3—62no—
95C2×C3×C4—22no—
96C2×C3×C4—22no—
97C2×C3×C4—22no—
98C2×Dic3—62no—
99C2×Dic3—62no—
100C2×Dic3—62no—
101C4×D3—64no—
102C4×D3—64no—
103C4×D3—122no—
104C4×D3—122no—
105C4×D3—124no—
106C3×C8—44no—
107C3⋊C8—124no—
108C2×C32#42411yescharacteristic
109C2×C32C2×#10711yescharacteristic
110C2×C32#43011yescharacteristic
111C3⋊D3—22no—
112C22×C4—91no—
113C22×C4—91no—
114C22×C4—91no—
115M16—362no—
116C2×C8—92no—
117C2×C8—181no—
118C2×C8—181no—
119C2×C8—182no—
120C2×C8—362no—
121C2×C8C2×#15712yes—
122C42—91no—
123C42—91no—
124C42—91no—
125C42C2×#15711yescharacteristic
126C22×C3—22no—
127C2×D3—64no—
128C2×D3—122no—
129C2×D3—122no—
130C3×C4—24no—
131C3×C4—22no—
132C3×C4—22no—
133C3×C4—42no—
134Dic3—62no—
135Dic3—62no—
136Dic3—64no—
137Dic3—122no—
138C32#157111yescharacteristic, complemented, Sylow
139C23—91no—
140C2×C4—91no—
141C2×C4—92no—
142C2×C4—92no—
143C2×C4—91no—
144C2×C4—91no—
145C2×C4—181no—
146C2×C4—181no—
147C2×C4—361no—
148C2×C4C4⋊#15711yescharacteristic
149C2×C4C4⋊#15711yescharacteristic
150C2×C4C22×#15711yescharacteristic
151C8—22no—
152C8—182no—
153C8—361no—
154C8—361no—
155C8—362no—
156C2×C3—22no—
157C2×C3—22no—
158C2×C3—22no—
159D3—124no—
160C22—92no—
161C22—181no—
162C22—181no—
163C22C2×C4⋊#15711yescharacteristic
164C4—21no—
165C4—91no—
166C4—91no—
167C4—181no—
168C4—181no—
169C4#6376912yes—
170C4#6428711yescharacteristic
171C4#6428911yescharacteristic
172C3—22no—
173C2—182no—
174C2#1059375511yescharacteristic
175C2C2×#6376911yescharacteristic
176C2#1059377611yescharacteristic
subgroupG/H
centerC22C2×C4⋊#157
commutatorC2×C32×C4C22×C4
FrattiniC2×C4C22×#157
FittingC32×C4⋊C8C4
socleC22×C32C2×C4⋊C4
prime radicalC22×C3⋊D3C4⋊C4
cosocleC4×C3⋊Dic3C23
hypercenterC4⋊C8#157
hypocenterC32#1571
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ C4⋊C8

Complements

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

NH ≅ G/Ntype
4. #10590173C2semidirect
5. #10590171C2semidirect
138. C32#1571semidirect

Maximal subgroups

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

subgroupindex
#105937282
#105937262
#105925322
#105901732
#105901712
#15719