Finite Group Databasebeta

← #11782011

Subgroups — #11782011

Order 1152.

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

normal subgroups only

This group has 262 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#10593395C211yesmaximal, characteristic, complemented
3#10591495C212yesmaximal
4#10590041C211yesmaximal, characteristic, complemented
5#10590040C212yesmaximal, complemented
6C2×#3792—21no—
7D4×C3⋊Dic3C2211yescharacteristic
8#63919C2212yes—
9C22⋊#622—21no—
10C4⋊#622C2211yescharacteristic
11C4×#622C2211yescharacteristic
12#63743—21no—
13#63743—21no—
14C3×#832—22no—
15#63573—22no—
16#63572C2212yes—
17#4761—62no—
18C2×C32×D4D411yescharacteristic
19C22×C3⋊Dic3—21no—
20C2×#627—22no—
21#3792—42no—
22C2×#622—21no—
23C2×#622D411yescharacteristic
24C2×#622D411yescharacteristic
25#3757—21no—
26C4⋊(C3⋊Dic3)D411yescharacteristic
27C4×C3⋊Dic3C2311yescharacteristic
28C3×C4⋊Dic3—22no—
29C2×C3×C3⋊C8—22no—
30#3724—22no—
31#1695—91nomaximal, Sylow
32D4×Dic3—62no—
33#888—62no—
34C3×#102—62no—
35#832—22no—
36#817—62no—
37Dic3⋊C8—62no—
38#808—62no—
39C23×C32—21no—
40C32×D4—22no—
41C2×C32×C4C2×D411yescharacteristic
42C2×C3⋊Dic3—21no—
43C2×C3⋊Dic3—41no—
44C2×C3⋊Dic3—41no—
45C2×C3⋊Dic3C2×D411yescharacteristic
46C2×C3⋊Dic3#4111yescharacteristic
47C2×C3×Dic3—42no—
48#627—82no—
49#622—21no—
50#622—41no—
51#622SD1612yes—
52C3×C3⋊C8—42no—
53#500—91no—
54#476—92no—
55#436—91no—
56#334—91no—
57#333—92no—
58C2×C3×D4—22no—
59C22×Dic3—122no—
60C2×Dic6—122no—
61C2×C3×C8—62no—
62C3×C4⋊C4—62no—
63#217—122no—
64C4⋊Dic3—22no—
65C4⋊Dic3—62no—
66Dic3⋊C4—122no—
67C4×Dic3—62no—
68C2×C3⋊C8—22no—
69C22×C32—41no—
70C22×C32—41no—
71C22×C32—41no—
72C22×C32#12111yescharacteristic
73C32×C4#13712yes—
74C3⋊Dic3—21no—
75C3⋊Dic3—41no—
76C3⋊Dic3C2×SD1611yescharacteristic
77C3⋊Dic3#13711yescharacteristic
78C3×Dic3—82no—
79C2×M16—181no—
80C4⋊Q8—92no—
81C4×D4—91no—
82#107—181no—
83#107—181no—
84#106—182no—
85C4⋊C8—92no—
86C4⋊C8—91no—
87#102—62no—
88C22⋊C8—181no—
89C4×C8—91no—
90C23×C3—42no—
91C3×D4—24no—
92C3×D4—42no—
93C2×C3×C4—22no—
94C2×C3×C4—122no—
95C2×Dic3—42no—
96C2×Dic3—62no—
97C2×Dic3—62no—
98C2×Dic3—122no—
99C2×Dic3—242no—
100C2×Dic3—242no—
101Dic6—244no—
102C3×C8—122no—
103C3⋊C8—42no—
104C2×C32—81no—
105C2×C32#46111yescharacteristic
106C2×C32#47011yescharacteristic
107C2×C32#47211yescharacteristic
108C2×Q8—182no—
109C2×D4GO+(4,𝔽2)11yescharacteristic
110C22×C4—181no—
111M16—362no—
112C2×C8—62no—
113C2×C8—91no—
114C2×C8—91no—
115C2×C8—181no—
116C4⋊C4—62no—
117C4⋊C4—91no—
118C4⋊C4—182no—
119C22⋊C4—181no—
120C42—91no—
121C22×C3—22no—
122C22×C3—44no—
123C22×C3—82no—
124C22×C3—82no—
125C3×C4—22no—
126C3×C4—22no—
127C3×C4—242no—
128Dic3—62no—
129Dic3—62no—
130Dic3—82no—
131Dic3—122no—
132Dic3—242no—
133C32#169511yescharacteristic, complemented, Sylow
134C23—21no—
135Q8—722no—
136D4—22no—
137C2×C4—91no—
138C2×C4—91no—
139C2×C4—122no—
140C2×C4—181no—
141C2×C4—361no—
142C2×C4—361no—
143C2×C4C2×GO+(4,𝔽2)11yescharacteristic
144C8—92no—
145C8—122no—
146C8—181no—
147C8—361no—
148C2×C3—22no—
149C2×C3—22no—
150C2×C3—22no—
151C2×C3—84no—
152C22—41no—
153C22—41no—
154C22—41no—
155C22#6424211yescharacteristic
156C4—91no—
157C4—91no—
158C4—181no—
159C4—242no—
160C4—361no—
161C4#6423912yes—
162C3—22no—
163C2—81no—
164C2#1059346511yescharacteristic
165C2#1059346611yescharacteristic
166C2#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#1695
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. #10593395C2semidirect
4. #10590041C2semidirect
5. #10590040C2semidirect
133. C32#1695semidirect

Maximal subgroups

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

subgroupindex
#105938212
#105933952
#105914952
#105900412
#105900402
#16959