Finite Group Databasebeta

← #11785980

Subgroups — #11785980

Order 1152.

394 conjugacy classes of subgroups; only the 82 normal subgroups are shown.

normal subgroups only

This group has 394 conjugacy classes of subgroups — too many to draw. Only its 82 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×#63779C211yesmaximal, characteristic
2C2×C4⋊#622C211yesmaximal, characteristic
3#10592347C211yesmaximal, characteristic
4#10590207C214yesmaximal
5C22×#622C2212yes—
6C22×#622C2212yes—
7C2×C4×C3⋊Dic3C2212yes—
8C2×C4×C3⋊Dic3C2211yescharacteristic
9#63779—22no—
10C4⋊#622—22no—
11C32×#95C411yescharacteristic
12#63658C411yescharacteristic
13#63658C412yes—
14#4648—62no—
15C22×C32×C4C2×C412yes—
16C22×C32×C4C2×C411yescharacteristic
17C22×C3⋊Dic3C2×C412yes—
18C22×C3⋊Dic3C2×C411yescharacteristic
19C22×C3⋊Dic3C2311yescharacteristic
20C2×#622—22no—
21C2×#622—22no—
22C2×#622—24no—
23C2×#622—24no—
24C4×C3⋊Dic3—22no—
25C4×C3⋊Dic3—22no—
26C4×C3⋊Dic3D412yes—
27C4×C3⋊Dic3Q812yes—
28#1832—91nomaximal, Sylow
29C2×C4×Dic3—62no—
30C2×C4×Dic3—64no—
31C3×#95—22no—
32C3⋊#95—64no—
33C3⋊#95—62no—
34C23×C32C22×C411yescharacteristic
35C2×C32×C4—22no—
36C2×C32×C4—22no—
37C2×C32×C4—22no—
38C2×C32×C4—22no—
39C2×C32×C4C4⋊C412yes—
40C2×C3⋊Dic3—22no—
41C2×C3⋊Dic3—21no—
42C2×C3⋊Dic3—21no—
43C2×C3⋊Dic3—22no—
44C2×C3⋊Dic3—22no—
45C2×C3⋊Dic3C4⋊C412yes—
46C2×C3⋊Dic3C2×D411yescharacteristic
47C2×C3⋊Dic3C2×Q811yescharacteristic
48C2×C3⋊Dic3#4112yes—
49C2×C3⋊Dic3#4112yes—
50#622—42no—
51#622—42no—
52C2×C4⋊C8—91no—
53C2×C4⋊C8—91no—
54#376—91no—
55#336—94no—
56C22×C3×C4—24no—
57C22×C3×C4—22no—
58C22×Dic3—62no—
59C22×Dic3—62no—
60C22×Dic3—64no—
61C4×Dic3—64no—
62C4×Dic3—64no—
63C4×Dic3—68no—
64C4×Dic3—68no—
65C22×C32C2×C4⋊C411yescharacteristic
66C22×C32#11712yes—
67C22×C32#13111yescharacteristic
68C22×C32#13111yescharacteristic
69C22×C32#13112yes—
70C32×C4—22no—
71C32×C4—42no—
72C3⋊Dic3—22no—
73C3⋊Dic3—42no—
74C3⋊Dic3#12411yescharacteristic
75C3⋊Dic3#12411yescharacteristic
76C3⋊Dic3#12512yes—
77C22×C8—92no—
78C22×C8—92no—
79C2×C42—91no—
80C2×C42—92no—
81C4⋊C8—182no—
82C4⋊C8—182no—
83#95—92no—
84#95—91no—
85#95#15711yescharacteristic
86C23×C3—22no—
87C2×C3×C4—28no—
88C2×C3×C4—24no—
89C2×C3×C4—44no—
90C2×C3×C4—44no—
91C2×C3×C4—44no—
92C2×Dic3—62no—
93C2×Dic3—62no—
94C2×Dic3—64no—
95C2×Dic3—64no—
96C2×Dic3—64no—
97C2×Dic3—68no—
98C2×Dic3—122no—
99C2×Dic3—122no—
100C2×Dic3—124no—
101C2×Dic3—124no—
102C2×C32#38211yescharacteristic
103C2×C32#42411yescharacteristic
104C2×C32#42411yescharacteristic
105C2×C32#43312yes—
106C2×C32#43312yes—
107C22×C4—91no—
108C22×C4—91no—
109C22×C4—92no—
110C22×C4C2×#15712yes—
111C22×C4C2×#15711yescharacteristic
112C2×C8—182no—
113C2×C8—182no—
114C2×C8—184no—
115C2×C8—184no—
116C42—92no—
117C42—92no—
118C42—182no—
119C42—182no—
120C22×C3—22no—
121C22×C3—24no—
122C22×C3—24no—
123C22×C3—22no—
124C22×C3—22no—
125C3×C4—44no—
126C3×C4—48no—
127Dic3—62no—
128Dic3—62no—
129Dic3—64no—
130Dic3—124no—
131Dic3—128no—
132C32#183211yescharacteristic, complemented, Sylow
133C23C22×#15711yescharacteristic
134C2×C4—22no—
135C2×C4—22no—
136C2×C4—22no—
137C2×C4—22no—
138C2×C4—91no—
139C2×C4—91no—
140C2×C4—92no—
141C2×C4—92no—
142C2×C4—92no—
143C2×C4—181no—
144C2×C4—181no—
145C2×C4—182no—
146C2×C4—182no—
147C2×C4—182no—
148C2×C4C4⋊#15712yes—
149C8—362no—
150C8—362no—
151C2×C3—22no—
152C2×C3—22no—
153C2×C3—24no—
154C2×C3—24no—
155C2×C3—22no—
156C22C2×C4⋊#15711yescharacteristic
157C22#6428612yes—
158C22#6428712yes—
159C22#6428711yescharacteristic
160C22#6428911yescharacteristic
161C4—22no—
162C4—42no—
163C4—91no—
164C4—91no—
165C4—92no—
166C4—182no—
167C4—362no—
168C3—22no—
169C2#1059373611yescharacteristic
170C2#1059374311yescharacteristic
171C2#1059374412yes—
172C2#1059375312yes—
173C2#1059375511yescharacteristic
subgroupG/H
center, FrattiniC23C22×#157
commutator, socle, prime radicalC23×C32C22×C4
FittingC32×#95C4
cosocleC22×C3⋊Dic3C23
hypercenter#95#157
hypocenterC32#1832
LCSG ▷ C23×C32 ▷ C32
UCSC1 ◁ C23 ◁ #95

Complements

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

NH ≅ G/Ntype
132. C32#1832semidirect

Maximal subgroups

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

subgroupindex
C2×#637792
C2×C4⋊#6222
#105923472
#105902072
#18329