Finite Group Databasebeta

← #11772578

Subgroups — #11772578

Order 1152.

324 conjugacy classes of subgroups; only the 37 normal subgroups are shown.

normal subgroups only

This group has 324 conjugacy classes of subgroups — too many to draw. Only its 37 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#10593823C211yesmaximal, characteristic
2#10591529C212yesmaximal
3C2×#3830C2211yescharacteristic
4C2×#3788C411yescharacteristic, complemented
5C2×#3787C411yescharacteristic, complemented
6#63957—22no—
7C22⋊#622—22no—
8C3×#834—22no—
9#63581C414yescomplemented
10#4740—62no—
11C2×C32×D4D411yescharacteristic
12C2×#638C2×C412yes—
13C22×C3⋊Dic3D412yes—
14#3830—41no—
15#3830—41no—
16C2×C4×C3⋊D3C2×C411yescharacteristic
17C2×#634Q811yescharacteristic
18C2×#622—21no—
19C2×#622—21no—
20#3788—41no—
21#3787—41no—
22C3×#217—24no—
23#3724—42no—
24Dic32—42no—
25#1391—91nomaximal, Sylow
26C2×#237—62no—
27#877—64no—
28C3×#99—62no—
29#834—22no—
30#806—64no—
31C23×C32C22⋊C412yes—
32C22×C3⋊D3C4211yescharacteristic
33C32×D4—41no—
34C2×C32×C4C4⋊C411yescharacteristic
35#638—42no—
36C2×C3⋊Dic3—22no—
37C2×C3⋊Dic3—22no—
38C2×C3⋊Dic3C22⋊C411yescharacteristic
39C2×C3⋊Dic3C4⋊C412yes—
40C4×C3⋊D3—21no—
41C4×C3⋊D3—21no—
42#634—41no—
43C2×C3×Dic3—44no—
44#622—41no—
45#622—41no—
46#410—92no—
47#408—91no—
48C2×C3×D4—22no—
49C2×#67—62no—
50C2×#67—62no—
51C22×Dic3—62no—
52C22×Dic3—62no—
53#237—124no—
54#237—124no—
55C2×C4×D3—62no—
56C2×Dic6—62no—
57C3×C22⋊C4—64no—
58#217—24no—
59Dic3⋊C4—124no—
60C4×Dic3—124no—
61C22×C32—22no—
62C22×C32—42no—
63C22×C32#9511yescharacteristic
64C2×C3⋊D3—21no—
65C2×C3⋊D3—41no—
66C32×C4—21no—
67C3⋊Dic3—22no—
68C3⋊Dic3#9911yescharacteristic
69C3⋊Dic3#9911yescharacteristic
70C3×Dic3—84no—
71C2×#41—91no—
72C2×M16—91no—
73C22×C8—91no—
74#117—182no—
75#99—62no—
76#99—94no—
77C22⋊C8—182no—
78C23×C3—22no—
79C23×C3—22no—
80C22×D3—62no—
81C3×D4—44no—
82C2×C3×C4—22no—
83C2×C3×C4—124no—
84#67—124no—
85#67—124no—
86C2×Dic3—44no—
87C2×Dic3—62no—
88C2×Dic3—62no—
89C2×Dic3—62no—
90C2×Dic3—64no—
91C2×Dic3—64no—
92C2×Dic3—122no—
93C2×Dic3—122no—
94C4×D3—122no—
95C4×D3—122no—
96Dic6—124no—
97C2×C32—21no—
98C2×C32—42no—
99C2×C32#34211yescharacteristic
100C3⋊D3—41no—
101#41—361no—
102#41—361no—
103C2×Q8—91no—
104C2×D4—92no—
105C2×D4GO+(4,𝔽2)11yescharacteristic
106C22×C4—92no—
107C22×C4—91no—
108M16—361no—
109C2×C8—181no—
110C2×C8—181no—
111C2×C8—361no—
112C4⋊C4—362no—
113C22⋊C4—64no—
114C42—362no—
115C22×C3—24no—
116C22×C3—22no—
117C22×C3—42no—
118C22×C3—82no—
119C22×C3—82no—
120C2×D3—122no—
121C2×D3—242no—
122C3×C4—42no—
123C3×C4—244no—
124Dic3—62no—
125Dic3—62no—
126Dic3—64no—
127Dic3—84no—
128Dic3—122no—
129C32#139111yescharacteristic, complemented, Sylow
130C23—91no—
131C23D32⋊C412yes—
132Q8—361no—
133D4—41no—
134D4—362no—
135C2×C4—91no—
136C2×C4—92no—
137C2×C4—124no—
138C2×C4—181no—
139C2×C4—181no—
140C2×C4—182no—
141C2×C4—182no—
142C2×C4#377311yescharacteristic
143C8—361no—
144C8—361no—
145C2×C3—22no—
146C2×C3—42no—
147C2×C3—44no—
148C2×C3—82no—
149D3—242no—
150C22—22no—
151C22—42no—
152C22—181no—
153C22—361no—
154C22#6373711yescharacteristic
155C4—21no—
156C4—91no—
157C4—91no—
158C4—182no—
159C4—244no—
160C3—22no—
161C2—21no—
162C2—42no—
163C2—361no—
164C2#1059007711yescharacteristic
subgroupG/H
centerC2#10590077
commutatorC22×C3⋊D3C42
Frattini, hypercenterC2×D4GO+(4,𝔽2)
FittingC2×C32×D4D4
socleC2×C32#342
prime radical, cosocleC2×#3830C22
hypocenterC32#1391
LCSG ▷ C22×C3⋊D3 ▷ C22×C32 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2 ◁ C22 ◁ C2×D4

Complements

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

NH ≅ G/Ntype
4. C2×#3788C4semidirect
5. C2×#3787C4semidirect
9. #63581C4semidirect
129. C32#1391semidirect

Maximal subgroups

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

subgroupindex
#105938232
#105915292
#13919