Finite Group Databasebeta

← #11781789

Subgroups — #11781789

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#10593752C211yesmaximal, characteristic
2#10593450C211yesmaximal, characteristic, complemented
3#10590430C212yesmaximal
4#10590041C211yesmaximal, characteristic, complemented
5#10590039C212yesmaximal, complemented
6C2×#3788—21no—
7C2×#3776—21no—
8C2×#3776—21no—
9#64102C2211yescharacteristic
10#63919C2212yes—
11#63778—21no—
12C4⋊#622C2211yescharacteristic
13C4×#622C2211yescharacteristic
14C3×#807—22no—
15#63572C2212yes—
16#63564—22no—
17#4890—62no—
18C2×C4⋊(C3⋊D3)D411yescharacteristic
19C2×C4×C3⋊D3—21no—
20C2×#627—22no—
21C2×#622—21no—
22C2×#622D411yescharacteristic
23C2×#622D411yescharacteristic
24#3788—42no—
25#3776—42no—
26#3776—42no—
27C32×C4⋊C4D411yescharacteristic
28#3752—21no—
29C4×C3⋊Dic3C2311yescharacteristic
30C3×C4⋊Dic3—22no—
31C2×C3×C3⋊C8—22no—
32#3724—22no—
33#1689—91nomaximal, Sylow
34#893—62no—
35#888—62no—
36C3×#107—62no—
37#821—62no—
38Dic3⋊C8—62no—
39#809—62no—
40#807—22no—
41C22×C3⋊D3—21no—
42C2×C32×C4—21no—
43C2×C32×C4C2×D411yescharacteristic
44C2×C3⋊Dic3C2×D411yescharacteristic
45C2×C3⋊Dic3#4111yescharacteristic
46C4⋊(C3⋊D3)—22no—
47C4×C3⋊D3—41no—
48C4×C3⋊D3—41no—
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×D12—62no—
62C2×C4×D3—122no—
63C2×Dic6—122no—
64C2×C3×C8—62no—
65C3×C4⋊C4—22no—
66C3×C4⋊C4—62no—
67(C2×D3)⋊C4—122no—
68C4⋊Dic3—22no—
69Dic3⋊C4—122no—
70C4×Dic3—62no—
71C2×C3⋊C8—22no—
72C22×C32#12111yescharacteristic
73C2×C3⋊D3—41no—
74C2×C3⋊D3—41no—
75C2×C3⋊D3—41no—
76C32×C4—41no—
77C32×C4#13712yes—
78C3⋊Dic3—21no—
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—62no—
88C4⋊C8—92no—
89C4⋊C8—91no—
90#102—182no—
91C22⋊C8—181no—
92C4×C8—91no—
93C22×D3—122no—
94C2×C3×C4—22no—
95C2×C3×C4—42no—
96C2×C3×C4—122no—
97C2×Dic3—42no—
98C2×Dic3—62no—
99C2×Dic3—62no—
100D12—64no—
101D12—122no—
102C4×D3—242no—
103C4×D3—242no—
104Dic6—242no—
105Dic6—242no—
106C3×C8—122no—
107C3⋊C8—42no—
108C2×C32#45911yescharacteristic
109C2×C32#47011yescharacteristic
110C2×C32#47311yescharacteristic
111C3⋊D3—81no—
112C2×Q8—182no—
113C2×D4—91no—
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—182no—
124C4⋊C4GO+(4,𝔽2)11yescharacteristic
125C22⋊C4—181no—
126C42—91no—
127C22×C3—22no—
128C2×D3—124no—
129C2×D3—242no—
130C2×D3—242no—
131C3×C4—22no—
132C3×C4—22no—
133C3×C4—82no—
134C3×C4—242no—
135Dic3—62no—
136Dic3—62no—
137Dic3—82no—
138Dic3—122no—
139C32#168911yescharacteristic, complemented, Sylow
140C23—181no—
141Q8—362no—
142Q8—362no—
143D4—182no—
144C2×C4—21no—
145C2×C4—91no—
146C2×C4—91no—
147C2×C4—122no—
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—
158D3—244no—
159C22—361no—
160C22—361no—
161C22—361no—
162C22#6424211yescharacteristic
163C4—41no—
164C4—91no—
165C4—91no—
166C4—181no—
167C4—242no—
168C4#6422612yes—
169C3—22no—
170C2—721no—
171C2#1059344911yescharacteristic
172C2#1059346411yescharacteristic
173C2#1059348211yescharacteristic
subgroupG/H
centerC22#64242
commutator, cosocleC4×C3⋊Dic3C23
FrattiniC2×C4C2×GO+(4,𝔽2)
FittingC32×C4⋊C4D4
socleC22×C32#121
prime radicalC2×C4⋊(C3⋊D3)D4
hypercenterC4⋊C4GO+(4,𝔽2)
hypocenterC32#1689
LCSG ▷ C4×C3⋊Dic3 ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ C4⋊C4

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
#105937522
#105934502
#105904302
#105900412
#105900392
#16899