Finite Group Databasebeta

← #11785941

Subgroups — #11785941

Order 1152.

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

normal subgroups only

This group has 502 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#10595987C211yesmaximal, characteristic
2C2×#63780C212yesmaximal
3#10590156C214yesmaximal
4C22×#634C2211yescharacteristic
5C2×#3792C2214yes—
6C32×#117C411yescharacteristic
7#64135C411yescharacteristic
8#64096—22no—
9#64086C412yes—
10#64086C2212yes—
11C4×#634—22no—
12#63780—22no—
13#63780—22no—
14#5516—62no—
15C22×C32×C4C2×C411yescharacteristic
16C22×C3⋊Dic3C2×C411yescharacteristic
17C22×C3⋊Dic3C2311yescharacteristic
18C2×#634—24no—
19C2×#634D412yes—
20C2×#634D412yes—
21#3792—24no—
22#3792—24no—
23C2×#622—24no—
24C32×C4⋊C4—21no—
25C32×C22⋊C4C2×C412yes—
26C32×C42—21no—
27#3757C2×C412yes—
28C4⋊(C3⋊Dic3)—21no—
29#3750—22no—
30#3750—22no—
31C4×C3⋊Dic3—21no—
32C4×C3⋊Dic3—22no—
33C4×C3⋊Dic3—22no—
34#1830—91nomaximal, Sylow
35C22×Dic6—62no—
36C3×#117—22no—
37#926—62no—
38#887—68no—
39#877—64no—
40#877—64no—
41C4×Dic6—68no—
42C23×C32C22×C411yescharacteristic
43C2×C32×C4—22no—
44C2×C32×C4—22no—
45C2×C32×C4C22⋊C411yescharacteristic
46C2×C32×C4C22⋊C411yescharacteristic
47C2×C3⋊Dic3—22no—
48C2×C3⋊Dic3—22no—
49C2×C3⋊Dic3C22⋊C412yes—
50C2×C3⋊Dic3C2×D412yes—
51C2×C3⋊Dic3#4114yes—
52#634—24no—
53#634—24no—
54#622—44no—
55#519—91no—
56C2×#101—92no—
57#344—94no—
58C22×C3×C4—22no—
59C22×Dic3—62no—
60C22×Dic3—62no—
61C2×Dic6—64no—
62C2×Dic6—64no—
63C2×Dic6—616no—
64C3×C4⋊C4—24no—
65C3×C22⋊C4—24no—
66C3×C42—24no—
67#217—64no—
68C4⋊Dic3—64no—
69Dic3⋊C4—68no—
70Dic3⋊C4—68no—
71C4×Dic3—68no—
72C4×Dic3—68no—
73C4×Dic3—64no—
74C22×C32—41no—
75C22×C32C2×C22⋊C411yescharacteristic
76C22×C32#11712yes—
77C32×C4—21no—
78C32×C4—21no—
79C32×C4—42no—
80C3⋊Dic3—22no—
81C3⋊Dic3—42no—
82C3⋊Dic3#12314yes—
83C22×Q8—91no—
84C2×M16—94no—
85C4×Q8—182no—
86C4×Q8—182no—
87#117—91no—
88#117—92no—
89#117—92no—
90#117#15711yescharacteristic
91#101—182no—
92#101—182no—
93C23×C3—22no—
94C2×C3×C4—28no—
95C2×C3×C4—28no—
96C2×C3×C4—22no—
97C2×C3×C4—22no—
98C2×Dic3—64no—
99C2×Dic3—64no—
100C2×Dic3—68no—
101C2×Dic3—68no—
102C2×Dic3—68no—
103Dic6—616no—
104Dic6—616no—
105C2×C32—21no—
106C2×C32—22no—
107C2×C32#38111yescharacteristic
108C2×Q8—92no—
109C2×Q8—92no—
110C2×Q8—184no—
111C22×C4—91no—
112C22×C4—91no—
113C22×C4C2×#15711yescharacteristic
114M16—184no—
115M16—184no—
116C2×C8—184no—
117C4⋊C4—21no—
118C4⋊C4—182no—
119C4⋊C4—182no—
120C4⋊C4—181no—
121C22⋊C4—92no—
122C22⋊C4C2×#15712yes—
123C42—21no—
124C42—182no—
125C42—182no—
126C42—181no—
127C22×C3—24no—
128C22×C3—22no—
129C22×C3—44no—
130C3×C4—24no—
131C3×C4—24no—
132C3×C4—48no—
133Dic3—68no—
134Dic3—68no—
135Dic3—128no—
136C32#183011yescharacteristic, complemented, Sylow
137C23C22×#15711yescharacteristic
138Q8—184no—
139Q8—184no—
140C2×C4—22no—
141C2×C4—22no—
142C2×C4—94no—
143C2×C4—92no—
144C2×C4—92no—
145C2×C4—182no—
146C2×C4—182no—
147C2×C4C22⋊#15711yescharacteristic
148C2×C4C22⋊#15711yescharacteristic
149C8—364no—
150C2×C3—24no—
151C2×C3—22no—
152C2×C3—44no—
153C22—41no—
154C22#6428612yes—
155C22C2×C22⋊#15711yescharacteristic
156C4—21no—
157C4—21no—
158C4—42no—
159C4—94no—
160C4—182no—
161C4—362no—
162C3—22no—
163C2—21no—
164C2—22no—
165C2#1059381111yescharacteristic
subgroupG/H
centerC2#10593811
commutator, prime radicalC23×C32C22×C4
FrattiniC23C22×#157
FittingC32×#117C4
socleC2×C32#381
cosocleC22×C3⋊Dic3C23
hypercenter#117#157
hypocenterC32#1830
LCSG ▷ C23×C32 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2 ◁ C23 ◁ #117

Complements

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

NH ≅ G/Ntype
136. C32#1830semidirect

Maximal subgroups

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

subgroupindex
#105959872
C2×#637802
#105901562
#18309