Finite Group Databasebeta

← #11777076

Subgroups — #11777076

Order 1152.

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

normal subgroups only

This group has 278 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#10593806C211yesmaximal, characteristic
2C2×C4⋊#622C211yesmaximal, characteristic
3#10592417C211yesmaximal, characteristic
4#10590172C212yesmaximal, complemented
5#10590171C212yesmaximal, complemented
6C22×#622—21no—
7C2×C4×C3⋊Dic3C2211yescharacteristic
8C22⋊#622—21no—
9#63777—21no—
10C4⋊#622—21no—
11C4⋊#622C2212yes—
12C4⋊#622C2211yescharacteristic
13C4⋊#622C2211yescharacteristic
14C32×C22⋊C8C411yescharacteristic
15#63657C411yescharacteristic
16#63641C412yes—
17C8×C3⋊Dic3C2212yes—
18#4718—62no—
19C22×C32×C4C2×C411yescharacteristic
20C22×C3⋊Dic3D411yescharacteristic
21C22×C3⋊Dic3Q811yescharacteristic
22C2×#622—22no—
23C2×#622—21no—
24C2×#622—21no—
25C2×#622—42no—
26C2×C32×C8C2×C412yes—
27C4×C3⋊Dic3C2×C411yescharacteristic
28C4×C3⋊Dic3D411yescharacteristic
29C4×C3⋊Dic3Q811yescharacteristic
30C4×C3⋊Dic3C2311yescharacteristic
31C2×C3⋊(C3⋊C8)C2×C412yes—
32#1573—91nomaximal, Sylow
33C2×C4×Dic3—62no—
34C3×C22⋊C8—22no—
35#830—62no—
36Dic3⋊C8—64no—
37C8×Dic3—64no—
38C23×C32C4⋊C411yescharacteristic
39C2×C32×C4—22no—
40C2×C32×C4C4⋊C411yescharacteristic
41C2×C32×C4C22×C411yescharacteristic
42C2×C3⋊Dic3—22no—
43C2×C3⋊Dic3—21no—
44C2×C3⋊Dic3—21no—
45C2×C3⋊Dic3C4⋊C411yescharacteristic
46C2×C3⋊Dic3C4⋊C411yescharacteristic
47C2×C3⋊Dic3C2×D411yescharacteristic
48C2×C3⋊Dic3C2×Q811yescharacteristic
49#622—41no—
50#622—42no—
51#622—41no—
52C32×C8—22no—
53C3⋊(C3⋊C8)—22no—
54#432—91no—
55#431—91no—
56C2×C4⋊C8—91no—
57#335—92no—
58#334—92no—
59C22×C3×C4—22no—
60C22×Dic3—62no—
61C22×Dic3—62no—
62C2×C3×C8—24no—
63C4×Dic3—62no—
64C4×Dic3—62no—
65C4×Dic3—62no—
66C4×Dic3—62no—
67C2×C3⋊C8—64no—
68C22×C32—21no—
69C22×C32—21no—
70C22×C32#10812yes—
71C22×C32C2×C4⋊C411yescharacteristic
72C32×C4—21no—
73C32×C4#13112yes—
74C3⋊Dic3—21no—
75C3⋊Dic3—21no—
76C3⋊Dic3—21no—
77C3⋊Dic3AGL(1,ℤ/8)11yescharacteristic
78C3⋊Dic3#13711yescharacteristic
79C22×C8—181no—
80C2×C42—91no—
81C4⋊C8—92no—
82C4⋊C8—91no—
83C4⋊C8—92no—
84C4⋊C8—91no—
85C4⋊C8—181no—
86C22⋊C8—91no—
87C22⋊C8—181no—
88C22⋊C8#15711yescharacteristic
89#97—181no—
90C4×C8—92no—
91C23×C3—22no—
92C2×C3×C4—22no—
93C2×C3×C4—22no—
94C2×C3×C4—44no—
95C2×Dic3—62no—
96C2×Dic3—62no—
97C2×Dic3—62no—
98C2×Dic3—62no—
99C2×Dic3—68no—
100C2×Dic3—122no—
101C2×Dic3—122no—
102C3×C8—44no—
103C3⋊C8—124no—
104C2×C32—22no—
105C2×C32#42411yescharacteristic
106C2×C32#42811yescharacteristic
107C2×C32C2×#10811yescharacteristic
108C22×C4—91no—
109C22×C4—91no—
110C22×C4C2×#15711yescharacteristic
111C2×C8—92no—
112C2×C8—181no—
113C2×C8—181no—
114C2×C8—182no—
115C2×C8—362no—
116C2×C8C2×#15712yes—
117C42—91no—
118C42—91no—
119C42—91no—
120C42—91no—
121C22×C3—24no—
122C22×C3—22no—
123C22×C3—42no—
124C22×C3—42no—
125C3×C4—24no—
126C3×C4—42no—
127Dic3—62no—
128Dic3—62no—
129Dic3—64no—
130Dic3—64no—
131Dic3—122no—
132C32#157311yescharacteristic, complemented, Sylow
133C23C4⋊#15711yescharacteristic
134C2×C4—22no—
135C2×C4—91no—
136C2×C4—91no—
137C2×C4—91no—
138C2×C4—91no—
139C2×C4—181no—
140C2×C4—181no—
141C2×C4—182no—
142C2×C4C4⋊#15711yescharacteristic
143C2×C4C22×#15711yescharacteristic
144C8—22no—
145C8—182no—
146C8—362no—
147C8—361no—
148C8—361no—
149C2×C3—22no—
150C2×C3—22no—
151C2×C3—22no—
152C2×C3—44no—
153C22—21no—
154C22—21no—
155C22#6377112yes—
156C22C2×C4⋊#15711yescharacteristic
157C4—21no—
158C4—91no—
159C4—91no—
160C4—181no—
161C4—181no—
162C4—181no—
163C4#6428712yes—
164C3—22no—
165C2—22no—
166C2#1059374311yescharacteristic
167C2C2×#6377111yescharacteristic
168C2#1059377411yescharacteristic
subgroupG/H
centerC22C2×C4⋊#157
commutatorC2×C32×C4C22×C4
FrattiniC2×C4C22×#157
FittingC32×C22⋊C8C4
socleC22×C32C2×C4⋊C4
prime radicalC23×C32C4⋊C4
cosocleC4×C3⋊Dic3C23
hypercenterC22⋊C8#157
hypocenterC32#1573
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22⋊C8

Complements

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

NH ≅ G/Ntype
4. #10590172C2semidirect
5. #10590171C2semidirect
132. C32#1573semidirect

Maximal subgroups

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

subgroupindex
#105938062
C2×C4⋊#6222
#105924172
#105901722
#105901712
#15739