Finite Group Databasebeta

← #11776241

Subgroups — #11776241

Order 1152.

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

normal subgroups only

This group has 424 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
2#10593801C212yesmaximal
3#10590162C214yesmaximal, complemented
4C32×#117C411yescharacteristic
5#64135C411yescharacteristic
6C2×C4×C3⋊Dic3C2211yescharacteristic
7#64099C412yes—
8#64097C2212yes—
9#64087—22no—
10C4×#634—22no—
11C22⋊#622—22no—
12#63779C2214yes—
13C4×#622—22no—
14#5517—62no—
15C22×C32×C4C2×C411yescharacteristic
16C22×C3⋊Dic3D412yes—
17C2×#634—22no—
18C2×#622—24no—
19C32×C4⋊C4C2×C412yes—
20C32×C22⋊C4—21no—
21C32×C42—21no—
22#3757—21no—
23C4⋊(C3⋊Dic3)—22no—
24C4⋊(C3⋊Dic3)C2×C412yes—
25#3750—22no—
26#3750—22no—
27C4×C3⋊Dic3—21no—
28C4×C3⋊Dic3C2×C411yescharacteristic
29C4×C3⋊Dic3D412yes—
30C4×C3⋊Dic3C2311yescharacteristic
31#1544—91nomaximal, Sylow
32C3×#117—22no—
33#926—62no—
34C2×C4×Dic3—62no—
35#890—64no—
36#888—64no—
37#878—68no—
38C4×Dic6—68no—
39C23×C32C22⋊C411yescharacteristic
40C2×C32×C4—22no—
41C2×C32×C4—22no—
42C2×C32×C4C22⋊C411yescharacteristic
43C2×C32×C4C22×C411yescharacteristic
44C2×C3⋊Dic3—22no—
45C2×C3⋊Dic3—24no—
46C2×C3⋊Dic3C22⋊C412yes—
47C2×C3⋊Dic3C2×D412yes—
48#634—44no—
49#622—44no—
50#533—91no—
51#431—92no—
52#332—94no—
53C22×C3×C4—22no—
54C22×Dic3—64no—
55C2×Dic6—68no—
56C3×C4⋊C4—24no—
57C3×C22⋊C4—24no—
58C3×C42—24no—
59#217—64no—
60C4⋊Dic3—64no—
61C4⋊Dic3—68no—
62Dic3⋊C4—68no—
63Dic3⋊C4—68no—
64C4×Dic3—64no—
65C4×Dic3—62no—
66C4×Dic3—62no—
67C4×Dic3—64no—
68C22×C32—21no—
69C22×C32—22no—
70C22×C32C2×C22⋊C411yescharacteristic
71C32×C4—21no—
72C32×C4—42no—
73C32×C4#10112yes—
74C3⋊Dic3—22no—
75C3⋊Dic3—42no—
76C3⋊Dic3#13514yes—
77C4⋊Q8—92no—
78#125—92no—
79C22⋊Q8—182no—
80C4×Q8—182no—
81#117—91no—
82#117#15711yescharacteristic
83C2×C42—91no—
84C4⋊C8—94no—
85C22⋊C8—182no—
86C4×C8—182no—
87C23×C3—22no—
88C2×C3×C4—28no—
89C2×C3×C4—28no—
90C2×C3×C4—22no—
91C2×C3×C4—22no—
92C2×Dic3—64no—
93C2×Dic3—64no—
94C2×Dic3—68no—
95C2×Dic3—128no—
96Dic6—1216no—
97C2×C32—41no—
98C2×C32C2×#10111yescharacteristic
99C2×C32#41612yes—
100C2×Q8—182no—
101C22×C4—92no—
102C22×C4C2×#15711yescharacteristic
103C2×C8—184no—
104C4⋊C4—92no—
105C4⋊C4—182no—
106C4⋊C4—182no—
107C4⋊C4—182no—
108C4⋊C4C2×#15712yes—
109C22⋊C4—21no—
110C22⋊C4—181no—
111C42—21no—
112C42—91no—
113C42—91no—
114C42—92no—
115C42—181no—
116C22×C3—24no—
117C22×C3—22no—
118C22×C3—44no—
119C3×C4—24no—
120C3×C4—24no—
121C3×C4—48no—
122Dic3—68no—
123Dic3—124no—
124Dic3—128no—
125C32#154411yescharacteristic, complemented, Sylow
126C23C22⋊#15711yescharacteristic
127Q8—364no—
128C2×C4—22no—
129C2×C4—22no—
130C2×C4—92no—
131C2×C4—92no—
132C2×C4—184no—
133C2×C4—182no—
134C2×C4C22⋊#15711yescharacteristic
135C2×C4C22×#15711yescharacteristic
136C8—364no—
137C2×C3—22no—
138C2×C3—24no—
139C2×C3—44no—
140C22—21no—
141C22—22no—
142C22C2×C22⋊#15711yescharacteristic
143C4—21no—
144C4—42no—
145C4—94no—
146C4—182no—
147C4—362no—
148C4#6378012yes—
149C3—22no—
150C2—41no—
151C2C2×#6378011yescharacteristic
152C2#1059384112yes—
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#1544
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. #10590162C2semidirect
125. C32#1544semidirect

Maximal subgroups

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

subgroupindex
#105959882
#105938012
#105901622
#15449