Finite Group Databasebeta

← #11775760

Subgroups — #11775760

Order 1152.

448 conjugacy classes of subgroups; only the 62 normal subgroups are shown.

normal subgroups only

This group has 448 conjugacy classes of subgroups — too many to draw. Only its 62 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#10595988C211yesmaximal, characteristic
2C4×#3792C212yesmaximal
3#10590159C214yesmaximal, complemented
4C2×#3792—22no—
5C32×#117C411yescharacteristic
6#64135C411yescharacteristic
7C2×C4×C3⋊Dic3C2211yescharacteristic
8#64099C2212yes—
9#64097C412yes—
10#64087—22no—
11C4×#634—22no—
12#63777C2214yes—
13C4×#622—22no—
14#5517—62no—
15C22×C32×C4C2×C411yescharacteristic
16C22×C3⋊Dic3D412yes—
17C2×#634—22no—
18#3792—28no—
19C2×#622—24no—
20C32×C4⋊C4C2×C412yes—
21C32×C22⋊C4—21no—
22C32×C42—21no—
23#3757—21no—
24C4⋊(C3⋊Dic3)—22no—
25C4⋊(C3⋊Dic3)C2×C412yes—
26#3750—22no—
27#3750—22no—
28C4×C3⋊Dic3—21no—
29C4×C3⋊Dic3C2×C411yescharacteristic
30C4×C3⋊Dic3D412yes—
31C4×C3⋊Dic3C2311yescharacteristic
32#1526—91nomaximal, Sylow
33C3×#117—22no—
34#926—62no—
35C2×C4×Dic3—62no—
36#890—64no—
37#888—64no—
38#878—68no—
39C4×Dic6—68no—
40C23×C32C22⋊C411yescharacteristic
41C2×C32×C4—22no—
42C2×C32×C4—22no—
43C2×C32×C4C22⋊C411yescharacteristic
44C2×C32×C4C22×C411yescharacteristic
45C2×C3⋊Dic3—22no—
46C2×C3⋊Dic3—24no—
47C2×C3⋊Dic3C22⋊C412yes—
48C2×C3⋊Dic3C2×D412yes—
49#634—44no—
50#622—28no—
51#533—91no—
52C4×M16—92no—
53#330—94no—
54C22×C3×C4—22no—
55C22×Dic3—64no—
56C2×Dic6—68no—
57C3×C4⋊C4—24no—
58C3×C22⋊C4—24no—
59C3×C42—24no—
60#217—64no—
61C4⋊Dic3—64no—
62C4⋊Dic3—68no—
63Dic3⋊C4—68no—
64Dic3⋊C4—68no—
65C4×Dic3—64no—
66C4×Dic3—62no—
67C4×Dic3—62no—
68C4×Dic3—64no—
69C22×C32—21no—
70C22×C32—22no—
71C22×C32C2×C22⋊C411yescharacteristic
72C32×C4—21no—
73C32×C4—42no—
74C32×C4#10112yes—
75C3⋊Dic3—22no—
76C3⋊Dic3—42no—
77C3⋊Dic3#10414yes—
78C2×M16—182no—
79C4⋊Q8—92no—
80#125—92no—
81C22⋊Q8—182no—
82C4×Q8—182no—
83#117—91no—
84#117#15711yescharacteristic
85C2×C42—91no—
86#97—94no—
87C4×C8—182no—
88C23×C3—22no—
89C2×C3×C4—28no—
90C2×C3×C4—28no—
91C2×C3×C4—22no—
92C2×C3×C4—22no—
93C2×Dic3—64no—
94C2×Dic3—64no—
95C2×Dic3—68no—
96C2×Dic3—128no—
97Dic6—1216no—
98C2×C32—41no—
99C2×C32C2×#10111yescharacteristic
100C2×C32C2×#10412yes—
101C2×Q8—182no—
102C22×C4—92no—
103C22×C4C2×#15711yescharacteristic
104M16—188no—
105C2×C8—184no—
106C4⋊C4—92no—
107C4⋊C4—182no—
108C4⋊C4—182no—
109C4⋊C4—182no—
110C4⋊C4C2×#15712yes—
111C22⋊C4—21no—
112C22⋊C4—181no—
113C42—21no—
114C42—91no—
115C42—91no—
116C42—92no—
117C42—181no—
118C22×C3—24no—
119C22×C3—22no—
120C22×C3—44no—
121C3×C4—24no—
122C3×C4—24no—
123C3×C4—48no—
124Dic3—68no—
125Dic3—124no—
126Dic3—128no—
127C32#152611yescharacteristic, complemented, Sylow
128C23C22⋊#15711yescharacteristic
129Q8—364no—
130C2×C4—22no—
131C2×C4—22no—
132C2×C4—92no—
133C2×C4—92no—
134C2×C4—184no—
135C2×C4—182no—
136C2×C4C22⋊#15711yescharacteristic
137C2×C4C22×#15711yescharacteristic
138C8—188no—
139C2×C3—22no—
140C2×C3—24no—
141C2×C3—44no—
142C22—21no—
143C22—22no—
144C22C2×C22⋊#15711yescharacteristic
145C4—21no—
146C4—42no—
147C4—94no—
148C4—182no—
149C4—362no—
150C4#6378012yes—
151C3—22no—
152C2—41no—
153C2C2×#6378011yescharacteristic
154C2#1059383912yes—
subgroupG/H
centerC2×C4C22⋊#157
commutatorC2×C32×C4C22×C4
FrattiniC2×C4C22×#157
FittingC32×#117C4
socleC22×C32C2×C22⋊C4
prime radicalC23×C32C22⋊C4
cosocleC4×C3⋊Dic3C23
hypercenter#117#157
hypocenterC32#1526
LCSG ▷ C2×C32×C4 ▷ C22×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ #117

Complements

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

NH ≅ G/Ntype
3. #10590159C2semidirect
127. C32#1526semidirect

Maximal subgroups

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

subgroupindex
#105959882
C4×#37922
#105901592
#15269