Finite Group Databasebeta

← #11781160

Subgroups — #11781160

Order 1152.

256 conjugacy classes of subgroups; only the 45 normal subgroups are shown.

normal subgroups only

This group has 256 conjugacy classes of subgroups — too many to draw. Only its 45 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#10593447C212yesmaximal
2#10590902C211yesmaximal, characteristic
3#10590645C211yesmaximal, characteristic
4#10590173C211yesmaximal, characteristic
5#10590039C212yesmaximal
6C2×#3776—22no—
7#63919C2212yes—
8C4×#627C2211yescharacteristic
9C4⋊#622C2212yes—
10#63740—22no—
11C8×C3⋊Dic3C2211yescharacteristic
12C3×#818—21no—
13C3×Dic3⋊C8—21no—
14#63576—21no—
15#63572C2211yescharacteristic
16Dic3×C3⋊C8—21no—
17#4874—61no—
18#4830—61no—
19C2×#627—22no—
20C2×#627D411yescharacteristic
21C2×#622—22no—
22#3776—44no—
23C2×C32×C8D411yescharacteristic
24C4×C3⋊Dic3C2311yescharacteristic
25C2×C3⋊(C3⋊C8)D411yescharacteristic
26C3×C4⋊Dic3—22no—
27C3×C4×Dic3—21no—
28C2×C3×C3⋊C8—21no—
29#3724—22no—
30#3724D411yescharacteristic
31Dic3⋊Dic3—21no—
32#1674—91nomaximal, Sylow
33#888—62no—
34C4×Dic6—61no—
35C3×#107—61no—
36C3×C4⋊C8—61no—
37#818—21no—
38Dic3⋊C8—21no—
39Dic3⋊C8—61no—
40C8×Dic3—61no—
41C8×Dic3—61no—
42C8×Dic3—61no—
43#807—62no—
44C4×C3⋊C8—61no—
45C2×C32×C4C2×D411yescharacteristic
46C2×C3⋊Dic3C2×D411yescharacteristic
47C2×C3⋊Dic3#4111yescharacteristic
48C2×C3×Dic3—21no—
49C2×C3×Dic3—21no—
50C2×C3×Dic3—42no—
51#627—21no—
52#627—42no—
53#627—42no—
54#627D812yes—
55#622—42no—
56C32×C8—21no—
57C3⋊(C3⋊C8)Q1612yescomplemented
58C3×C3⋊C8—41no—
59#500—91no—
60#462—92no—
61C8×Q8—91no—
62#335—91no—
63#332—92no—
64C2×Dic6—61no—
65C2×Dic6—122no—
66C2×C3×C8—21no—
67C2×C3×C8—21no—
68C2×C3×C8—61no—
69C3×C4⋊C4—62no—
70C3×C42—61no—
71C4⋊Dic3—22no—
72C4⋊Dic3—61no—
73Dic3⋊C4—61no—
74Dic3⋊C4—61no—
75Dic3⋊C4—122no—
76C4×Dic3—21no—
77C4×Dic3—61no—
78C4×Dic3—61no—
79C2×C3⋊C8—21no—
80C2×C3⋊C8—61no—
81C2×C3⋊C8—61no—
82C22×C32#12111yescharacteristic
83C32×C4C2×Q1611yescharacteristic
84C32×C4#13711yescharacteristic
85C3⋊Dic3—21no—
86C3⋊Dic3C2×D811yescharacteristic
87C3⋊Dic3#13511yescharacteristic
88C3×Dic3—22no—
89C3×Dic3—41no—
90C3×Dic3—82no—
91C2×Q16—182no—
92C4⋊Q8—92no—
93C4×Q8—91no—
94#107—61no—
95#107—181no—
96C4⋊C8—61no—
97C4⋊C8—91no—
98C4⋊C8—92no—
99#103—182no—
100C4×C8—91no—
101C4×C8—181no—
102C2×C3×C4—21no—
103C2×C3×C4—21no—
104C2×C3×C4—61no—
105C2×C3×C4—61no—
106C2×C3×C4—122no—
107C2×Dic3—21no—
108C2×Dic3—21no—
109C2×Dic3—42no—
110C2×Dic3—61no—
111C2×Dic3—61no—
112C2×Dic3—61no—
113C2×Dic3—61no—
114Dic6—62no—
115Dic6—62no—
116Dic6—242no—
117Dic6—242no—
118C3×C8—22no—
119C3×C8—41no—
120C3×C8—121no—
121C3⋊C8—41no—
122C3⋊C8—62no—
123C3⋊C8—62no—
124C2×C32#46211yescharacteristic
125C2×C32#46611yescharacteristic
126C2×C32#47311yescharacteristic
127C2×Q8—91no—
128C2×Q8—182no—
129Q16—364no—
130C2×C8—61no—
131C2×C8—91no—
132C2×C8—182no—
133C2×C8GO+(4,𝔽2)11yescharacteristic
134C4⋊C4—62no—
135C4⋊C4—91no—
136C4⋊C4—181no—
137C4⋊C4—182no—
138C42—61no—
139C42—91no—
140C22×C3—21no—
141C22×C3—21no—
142C3×C4—21no—
143C3×C4—21no—
144C3×C4—21no—
145C3×C4—21no—
146C3×C4—62no—
147C3×C4—121no—
148C3×C4—242no—
149Dic3—22no—
150Dic3—41no—
151Dic3—61no—
152Dic3—61no—
153Dic3—61no—
154Dic3—61no—
155Dic3—62no—
156Dic3—82no—
157Dic3—121no—
158C32#167411yescharacteristic, complemented, Sylow
159Q8—92no—
160Q8—181no—
161Q8—362no—
162Q8—362no—
163C2×C4—61no—
164C2×C4—61no—
165C2×C4—91no—
166C2×C4—91no—
167C2×C4—122no—
168C2×C4C2×GO+(4,𝔽2)11yescharacteristic
169C8—21no—
170C8—92no—
171C8—121no—
172C8—362no—
173C2×C3—21no—
174C2×C3—21no—
175C2×C3—21no—
176C2×C3—21no—
177C2×C3—21no—
178C2×C3—21no—
179C22#6423011yescharacteristic
180C4—62no—
181C4—91no—
182C4—91no—
183C4—121no—
184C4—181no—
185C4—242no—
186C4#6422811yescharacteristic
187C4#6423911yescharacteristic
188C3—21no—
189C3—21no—
190C2#1059328511yescharacteristic
191C2#1059330511yescharacteristic
192C2#1059344811yescharacteristic
subgroupG/H
centerC22#64230
commutator, cosocleC4×C3⋊Dic3C23
FrattiniC2×C4C2×GO+(4,𝔽2)
FittingC2×C32×C8D4
socle, prime radicalC22×C32#121
hypercenterC2×C8GO+(4,𝔽2)
hypocenterC32#1674
LCSG ▷ C4×C3⋊Dic3 ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×C8

Complements

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

NH ≅ G/Ntype
57. C3⋊(C3⋊C8)Q16semidirect
158. C32#1674semidirect

Maximal subgroups

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

subgroupindex
#105934472
#105909022
#105906452
#105901732
#105900392
#16749