Finite Group Databasebeta

← #11771081

Subgroups — #11771081

Order 1152.

374 conjugacy classes of subgroups; only the 76 normal subgroups are shown.

normal subgroups only

This group has 374 conjugacy classes of subgroups — too many to draw. Only its 76 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
1C2×#63779C212yesmaximal
2#10592674C211yesmaximal, characteristic
3C22×#622—22no—
4C2×C32×C4⋊C4C411yescharacteristic
5C2×C4⋊(C3⋊Dic3)C411yescharacteristic
6C2×#3750—22no—
7C2×C4×C3⋊Dic3C2211yescharacteristic
8#63779—22no—
9#63779C414yescomplemented
10#4975—62no—
11C22×C32×C4—21no—
12C22×C32×C4C2×C411yescharacteristic
13C22×C3⋊Dic3—21no—
14C22×C3⋊Dic3D412yes—
15C2×#622—24no—
16C2×#622—42no—
17C2×#622—42no—
18C32×C4⋊C4—41no—
19C4⋊(C3⋊Dic3)—41no—
20#3750—42no—
21#3750—42no—
22C4×C3⋊Dic3C2×C412yes—
23C4×C3⋊Dic3D411yescharacteristic
24C4×C3⋊Dic3Q811yescharacteristic
25#1296—91nomaximal, Sylow
26C2×C3×C4⋊C4—22no—
27C2×C4⋊Dic3—62no—
28C2×Dic3⋊C4—68no—
29C2×C4×Dic3—62no—
30C23×C32C22⋊C411yescharacteristic
31C2×C32×C4—21no—
32C2×C32×C4—21no—
33C2×C32×C4—41no—
34C2×C32×C4—42no—
35C2×C32×C4C4211yescharacteristic
36C2×C32×C4C4⋊C411yescharacteristic
37C2×C3⋊Dic3—41no—
38C2×C3⋊Dic3—42no—
39C2×C3⋊Dic3C22⋊C412yes—
40C2×C3⋊Dic3C4⋊C412yes—
41C2×C3⋊Dic3D812yes—
42C2×C3⋊Dic3SD1612yes—
43C2×C3⋊Dic3SD1612yes—
44C2×C3⋊Dic3Q1612yes—
45#622—44no—
46C2×C4⋊C8—92no—
47#384—91no—
48C22×C3×C4—24no—
49C22×C3×C4—22no—
50C22×Dic3—64no—
51C22×Dic3—64no—
52C3×C4⋊C4—44no—
53C4⋊Dic3—124no—
54Dic3⋊C4—128no—
55Dic3⋊C4—128no—
56C4×Dic3—64no—
57C4×Dic3—62no—
58C4×Dic3—62no—
59C22×C32#9511yescharacteristic
60C22×C32#10011yescharacteristic
61C22×C32#10111yescharacteristic
62C22×C32#10212yes—
63C22×C32#10312yes—
64C32×C4—21no—
65C32×C4—21no—
66C32×C4—81no—
67C3⋊Dic3—81no—
68C3⋊Dic3#10212yes—
69C3⋊Dic3#10312yes—
70C3⋊Dic3#10612yes—
71C3⋊Dic3#10712yes—
72C22×C8—182no—
73C2×C4⋊C4—91no—
74C2×C4⋊C4—182no—
75C2×C4⋊C4#15711yescharacteristic
76C2×C42—91no—
77C4⋊C8—94no—
78C4⋊C8—182no—
79C23×C3—22no—
80C2×C3×C4—24no—
81C2×C3×C4—24no—
82C2×C3×C4—22no—
83C2×C3×C4—22no—
84C2×C3×C4—48no—
85C2×C3×C4—44no—
86C2×Dic3—64no—
87C2×Dic3—64no—
88C2×Dic3—64no—
89C2×Dic3—64no—
90C2×Dic3—64no—
91C2×Dic3—64no—
92C2×Dic3—128no—
93C2×Dic3—124no—
94C2×C32#33111yescharacteristic
95C2×C32#33212yes—
96C2×C32#33311yescharacteristic
97C2×C32#34012yes—
98C2×C32#34311yescharacteristic
99C22×C4—21no—
100C22×C4—92no—
101C22×C4—181no—
102C22×C4C2×#15711yescharacteristic
103C2×C8—184no—
104C2×C8—362no—
105C2×C8—362no—
106C4⋊C4—41no—
107C4⋊C4—361no—
108C4⋊C4—362no—
109C4⋊C4—362no—
110C42—92no—
111C42—91no—
112C42—91no—
113C22×C3—22no—
114C22×C3—22no—
115C22×C3—24no—
116C22×C3—24no—
117C22×C3—22no—
118C3×C4—24no—
119C3×C4—24no—
120C3×C4—84no—
121Dic3—64no—
122Dic3—64no—
123Dic3—64no—
124Dic3—64no—
125Dic3—244no—
126C32#129611yescharacteristic, complemented, Sylow
127C23C22⋊#15711yescharacteristic
128C2×C4—21no—
129C2×C4—21no—
130C2×C4—42no—
131C2×C4—41no—
132C2×C4—92no—
133C2×C4—92no—
134C2×C4—92no—
135C2×C4—92no—
136C2×C4—92no—
137C2×C4—92no—
138C2×C4—362no—
139C2×C4—361no—
140C2×C4C4×#15711yescharacteristic
141C2×C4C4⋊#15711yescharacteristic
142C8—364no—
143C2×C3—22no—
144C2×C3—22no—
145C2×C3—22no—
146C2×C3—24no—
147C2×C3—24no—
148C22#6378011yescharacteristic
149C22#6378111yescharacteristic
150C22#6378212yes—
151C22#6378412yes—
152C22#6378811yescharacteristic
153C4—21no—
154C4—21no—
155C4—81no—
156C4—92no—
157C4—92no—
158C4—92no—
159C4—92no—
160C4—721no—
161C3—22no—
162C2#1059016212yes—
163C2#1059016312yes—
164C2#1059020811yescharacteristic
165C2#1059021411yescharacteristic
166C2#1059022011yescharacteristic
subgroupG/H
centerC23C22⋊#157
commutatorC2×C32×C4C42
FrattiniC22×C4C2×#157
FittingC2×C32×C4⋊C4C4
socle, prime radicalC23×C32C22⋊C4
cosocleC2×C4×C3⋊Dic3C22
hypercenterC2×C4⋊C4#157
hypocenterC32#1296
LCSG ▷ C2×C32×C4 ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C22×C4 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
9. #63779C4semidirect
126. C32#1296semidirect

Maximal subgroups

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

subgroupindex
C2×#637792
#105926742
#12969