Finite Group Databasebeta

← #11781788

Subgroups — #11781788

Order 1152.

274 conjugacy classes of subgroups; only the 43 normal subgroups are shown.

normal subgroups only

This group has 274 conjugacy classes of subgroups — too many to draw. Only its 43 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#10593821C211yesmaximal, characteristic
2#10593450C211yesmaximal, characteristic, complemented
3#10591494C212yesmaximal
4#10590041C211yesmaximal, characteristic, complemented
5#10590039C212yesmaximal, complemented
6C2×#3792—21no—
7C2×#3776—21no—
8C2×#3776—21no—
9D4×C3⋊Dic3C2211yescharacteristic
10#63919C2212yes—
11C22⋊#622—21no—
12C4⋊#622C2211yescharacteristic
13C4×#622C2211yescharacteristic
14C3×#832—22no—
15#63575—22no—
16#63572C2212yes—
17#4759—62no—
18C2×C32×D4D411yescharacteristic
19C22×C3⋊Dic3—21no—
20C2×#627—22no—
21#3792—42no—
22C2×#622—21no—
23C2×#622D411yescharacteristic
24C2×#622D411yescharacteristic
25#3776—42no—
26#3776—42no—
27#3757—21no—
28C4⋊(C3⋊Dic3)D411yescharacteristic
29C4×C3⋊Dic3C2311yescharacteristic
30C3×C4⋊Dic3—22no—
31C2×C3×C3⋊C8—22no—
32#3724—22no—
33#1689—91nomaximal, Sylow
34D4×Dic3—62no—
35#888—62no—
36C3×#102—62no—
37#832—22no—
38#818—62no—
39Dic3⋊C8—62no—
40#807—62no—
41C23×C32—21no—
42C32×D4—22no—
43C2×C32×C4C2×D411yescharacteristic
44C2×C3⋊Dic3—21no—
45C2×C3⋊Dic3—41no—
46C2×C3⋊Dic3—41no—
47C2×C3⋊Dic3C2×D411yescharacteristic
48C2×C3⋊Dic3#4111yescharacteristic
49C2×C3×Dic3—42no—
50#627—42no—
51#627—42no—
52#622—21no—
53#622—41no—
54#622D812yes—
55C3×C3⋊C8—42no—
56#494—91no—
57#474—92no—
58#436—91no—
59#334—91no—
60#332—92no—
61C2×C3×D4—22no—
62C22×Dic3—122no—
63C2×Dic6—122no—
64C2×C3×C8—62no—
65C3×C4⋊C4—62no—
66#217—122no—
67C4⋊Dic3—22no—
68C4⋊Dic3—62no—
69Dic3⋊C4—122no—
70C4×Dic3—62no—
71C2×C3⋊C8—22no—
72C22×C32—41no—
73C22×C32—41no—
74C22×C32—41no—
75C22×C32#12111yescharacteristic
76C32×C4#13712yes—
77C3⋊Dic3—21no—
78C3⋊Dic3—41no—
79C3⋊Dic3C2×D811yescharacteristic
80C3⋊Dic3AGL(1,ℤ/8)11yescharacteristic
81C3×Dic3—82no—
82C2×Q16—181no—
83C2×Q16—181no—
84C2×M16—181no—
85C4⋊Q8—92no—
86C4×D4—91no—
87#107—182no—
88C4⋊C8—92no—
89C4⋊C8—91no—
90#102—62no—
91C22⋊C8—181no—
92C4×C8—91no—
93C23×C3—42no—
94C3×D4—24no—
95C3×D4—42no—
96C2×C3×C4—22no—
97C2×C3×C4—122no—
98C2×Dic3—42no—
99C2×Dic3—62no—
100C2×Dic3—62no—
101C2×Dic3—122no—
102C2×Dic3—242no—
103C2×Dic3—242no—
104Dic6—242no—
105Dic6—242no—
106C3×C8—122no—
107C3⋊C8—42no—
108C2×C32—81no—
109C2×C32#45911yescharacteristic
110C2×C32#47011yescharacteristic
111C2×C32#47311yescharacteristic
112C2×Q8—182no—
113C2×D4GO+(4,𝔽2)11yescharacteristic
114C22×C4—181no—
115Q16—362no—
116Q16—362no—
117M16—362no—
118C2×C8—62no—
119C2×C8—91no—
120C2×C8—91no—
121C2×C8—181no—
122C4⋊C4—62no—
123C4⋊C4—91no—
124C4⋊C4—182no—
125C22⋊C4—181no—
126C42—91no—
127C22×C3—22no—
128C22×C3—44no—
129C22×C3—82no—
130C22×C3—82no—
131C3×C4—22no—
132C3×C4—22no—
133C3×C4—242no—
134Dic3—62no—
135Dic3—62no—
136Dic3—82no—
137Dic3—122no—
138Dic3—242no—
139C32#168911yescharacteristic, complemented, Sylow
140C23—21no—
141Q8—362no—
142Q8—362no—
143D4—22no—
144C2×C4—91no—
145C2×C4—91no—
146C2×C4—122no—
147C2×C4—181no—
148C2×C4—361no—
149C2×C4—361no—
150C2×C4C2×GO+(4,𝔽2)11yescharacteristic
151C8—92no—
152C8—122no—
153C8—181no—
154C8—361no—
155C2×C3—22no—
156C2×C3—22no—
157C2×C3—22no—
158C2×C3—84no—
159C22—41no—
160C22—41no—
161C22—41no—
162C22#6424211yescharacteristic
163C4—91no—
164C4—91no—
165C4—181no—
166C4—242no—
167C4—361no—
168C4#6423912yes—
169C3—22no—
170C2—81no—
171C2#1059346411yescharacteristic
172C2#1059346811yescharacteristic
173C2#1059350811yescharacteristic
subgroupG/H
centerC22#64242
commutator, cosocleC4×C3⋊Dic3C23
FrattiniC2×C4C2×GO+(4,𝔽2)
Fitting, prime radicalC2×C32×D4D4
socleC22×C32#121
hypercenterC2×D4GO+(4,𝔽2)
hypocenterC32#1689
LCSG ▷ C4×C3⋊Dic3 ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×D4

Complements

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

NH ≅ G/Ntype
2. #10593450C2semidirect
4. #10590041C2semidirect
5. #10590039C2semidirect
139. C32#1689semidirect

Maximal subgroups

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

subgroupindex
#105938212
#105934502
#105914942
#105900412
#105900392
#16899