Finite Group Databasebeta

← #11771390

Subgroups — #11771390

Order 1152.

428 conjugacy classes of subgroups; only the 36 normal subgroups are shown.

normal subgroups only

This group has 428 conjugacy classes of subgroups — too many to draw. Only its 36 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#10592920C211yesmaximal, characteristic
2#10590202C212yesmaximal, complemented
3C22×C32×D4C411yescharacteristic
4C2×#3757—22no—
5C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
6C2×C4×C3⋊Dic3C411yescharacteristic
7C22⋊#622—22no—
8#5221—62no—
9C24×C32—21no—
10C2×C32×D4—21no—
11C2×C32×D4—41no—
12C2×C32×D4—41no—
13C2×C32×D4C812yescomplemented
14C22×C32×C4C2×C411yescharacteristic
15C22×C3⋊Dic3—21no—
16C22×C3⋊Dic3D412yes—
17C2×#622—42no—
18#3757—44no—
19C4⋊(C3⋊Dic3)—41no—
20C4×C3⋊Dic3—41no—
21#1318—91nomaximal, Sylow
22C22×C3×D4—22no—
23C2×#217—68no—
24C2×C4⋊Dic3—62no—
25C2×C4×Dic3—62no—
26C23×C32—22no—
27C23×C32—42no—
28C23×C32—42no—
29C23×C32—41no—
30C23×C32—41no—
31C23×C32C22⋊C411yescharacteristic
32C32×D4—42no—
33C32×D4—42no—
34C2×C32×C4—21no—
35C2×C32×C4—21no—
36C2×C32×C4C2×C811yescharacteristic
37C2×C32×C4M1611yescharacteristic
38C2×C3⋊Dic3—22no—
39C2×C3⋊Dic3—22no—
40C2×C3⋊Dic3—41no—
41C2×C3⋊Dic3—41no—
42C2×C3⋊Dic3—42no—
43#622—82no—
44#390—91no—
45#324—92no—
46C24×C3—24no—
47C2×C3×D4—24no—
48C2×C3×D4—24no—
49C2×C3×D4—44no—
50C2×C3×D4—44no—
51C22×C3×C4—22no—
52C22×Dic3—64no—
53C22×Dic3—64no—
54#217—1216no—
55C4⋊Dic3—124no—
56C4×Dic3—124no—
57C22×C32—21no—
58C22×C32—21no—
59C22×C32—44no—
60C22×C32—42no—
61C22×C32—82no—
62C22×C32—81no—
63C22×C32—81no—
64C22×C32C22⋊C811yescharacteristic
65C22×C32#9911yescharacteristic
66C22×C32#10011yescharacteristic
67C32×C4—21no—
68C32×C4—21no—
69C3⋊Dic3—42no—
70C3⋊Dic3—42no—
71C22×D4#15711yescharacteristic
72C2×C4⋊C4—91no—
73C2×C22⋊C4—182no—
74C2×C42—91no—
75C22⋊C8—182no—
76C23×C3—28no—
77C23×C3—22no—
78C23×C3—48no—
79C23×C3—44no—
80C23×C3—44no—
81C23×C3—48no—
82C3×D4—48no—
83C3×D4—48no—
84C2×C3×C4—24no—
85C2×C3×C4—24no—
86C2×C3×C4—22no—
87C2×C3×C4—22no—
88C2×Dic3—68no—
89C2×Dic3—124no—
90C2×Dic3—124no—
91C2×Dic3—124no—
92C2×Dic3—128no—
93C2×C32—21no—
94C2×C32—21no—
95C2×C32—82no—
96C2×C32#32311yescharacteristic
97C2×C32#35311yescharacteristic
98C2×C32#35511yescharacteristic
99C24—21no—
100C2×D4—21no—
101C2×D4—41no—
102C2×D4—41no—
103C2×D4#62212yescomplemented
104C22×C4—92no—
105C22×C4—181no—
106C22×C4C2×#15711yescharacteristic
107C2×C8—362no—
108C4⋊C4—361no—
109C22⋊C4—364no—
110C42—361no—
111C22×C3—24no—
112C22×C3—24no—
113C22×C3—22no—
114C22×C3—22no—
115C22×C3—22no—
116C22×C3—48no—
117C22×C3—416no—
118C22×C3—88no—
119C22×C3—84no—
120C22×C3—84no—
121C3×C4—24no—
122C3×C4—24no—
123Dic3—128no—
124Dic3—244no—
125C32#131811yescharacteristic, complemented, Sylow
126C23—22no—
127C23—42no—
128C23—42no—
129C23—41no—
130C23—41no—
131C23C22⋊#15711yescharacteristic
132D4—42no—
133D4—42no—
134C2×C4—21no—
135C2×C4—21no—
136C2×C4—182no—
137C2×C4—182no—
138C2×C4—361no—
139C2×C4—361no—
140C2×C4—362no—
141C2×C4C2×#62211yescharacteristic
142C2×C4#379211yescharacteristic
143C8—722no—
144C2×C3—24no—
145C2×C3—24no—
146C2×C3—22no—
147C2×C3—22no—
148C2×C3—22no—
149C2×C3—88no—
150C22—21no—
151C22—21no—
152C22—44no—
153C22—42no—
154C22—82no—
155C22—81no—
156C22—81no—
157C22#6378611yescharacteristic
158C22C22⋊#62211yescharacteristic
159C22#6378811yescharacteristic
160C4—21no—
161C4—21no—
162C4—362no—
163C4—362no—
164C3—22no—
165C2—21no—
166C2—21no—
167C2—82no—
168C2#1059021111yescharacteristic
169C2#1059021211yescharacteristic
170C2#1059022211yescharacteristic
subgroupG/H
centerC22#63786
commutatorC2×C32×C4C2×C8
FrattiniC22×C4C2×#157
Fitting, prime radicalC22×C32×D4C4
socleC22×C32#99
cosocleC2×C4⋊(C3⋊Dic3)C22
hypercenterC22×D4#157
hypocenterC32#1318
LCSG ▷ C2×C32×C4 ▷ C22×C32 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C23 ◁ C22×C4 ◁ C22×D4

Complements

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

NH ≅ G/Ntype
2. #10590202C2semidirect
13. C2×C32×D4C8semidirect
103. C2×D4#622semidirect
125. C32#1318semidirect

Maximal subgroups

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

subgroupindex
#105929202
#105902022
#13189