Finite Group Databasebeta

← #11781977

Subgroups — #11781977

Order 1152.

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

normal subgroups only

This group has 248 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#10590787C211yesmaximal, characteristic
4#10590170C211yesmaximal, characteristic
5#10590039C212yesmaximal
6C2×#3776—22no—
7#63919C2212yes—
8C4×#627C2211yescharacteristic
9C4⋊#622C2212yes—
10#63740—22no—
11C8×C3⋊Dic3C2211yescharacteristic
12C3×#818—21no—
13C3×#815—21no—
14#63576—21no—
15#63572C2211yescharacteristic
16Dic3⋊(C3⋊C8)—21no—
17#4874—61no—
18#4701—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#1694—91nomaximal, Sylow
33#888—62no—
34C4×Dic6—61no—
35C3×#107—61no—
36C3×#97—61no—
37#818—21no—
38#815—21no—
39Dic3⋊C8—61no—
40Dic3⋊C8—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—22no—
52#627—42no—
53#627—42no—
54#622—42no—
55C32×C8Q1612yescomplemented
56C3⋊(C3⋊C8)—21no—
57C3×C3⋊C8—41no—
58#500—91no—
59#462—92no—
60#446—91no—
61#334—91no—
62#332—92no—
63C2×Dic6—61no—
64C2×Dic6—122no—
65C2×C3×C8—21no—
66C2×C3×C8—21no—
67C2×C3×C8—61no—
68C3×C4⋊C4—62no—
69C3×C42—61no—
70C4⋊Dic3—22no—
71C4⋊Dic3—61no—
72Dic3⋊C4—61no—
73Dic3⋊C4—61no—
74Dic3⋊C4—122no—
75C4×Dic3—21no—
76C4×Dic3—61no—
77C4×Dic3—61no—
78C2×C3⋊C8—21no—
79C2×C3⋊C8—61no—
80C2×C3⋊C8—61no—
81C22×C32#12111yescharacteristic
82C32×C4C2×Q1611yescharacteristic
83C32×C4#13711yescharacteristic
84C3⋊Dic3—21no—
85C3⋊Dic3AGL(1,ℤ/8)12yes—
86C3×Dic3—41no—
87C3×Dic3—41no—
88C3×Dic3—82no—
89C2×Q16—182no—
90C4⋊Q8—92no—
91C4×Q8—91no—
92#107—61no—
93#107—181no—
94C4⋊C8—91no—
95C4⋊C8—92no—
96C4⋊C8—181no—
97#103—182no—
98#97—61no—
99C4×C8—91no—
100C2×C3×C4—21no—
101C2×C3×C4—21no—
102C2×C3×C4—61no—
103C2×C3×C4—61no—
104C2×C3×C4—122no—
105C2×Dic3—21no—
106C2×Dic3—21no—
107C2×Dic3—42no—
108C2×Dic3—61no—
109C2×Dic3—61no—
110C2×Dic3—61no—
111C2×Dic3—61no—
112Dic6—122no—
113Dic6—242no—
114Dic6—242no—
115C3×C8—22no—
116C3×C8—22no—
117C3×C8—121no—
118C3⋊C8—41no—
119C3⋊C8—62no—
120C3⋊C8—121no—
121C2×C32#46211yescharacteristic
122C2×C32#46911yescharacteristic
123C2×C32#47311yescharacteristic
124C2×Q8—91no—
125C2×Q8—182no—
126Q16—364no—
127C2×C8—61no—
128C2×C8—91no—
129C2×C8—182no—
130C2×C8GO+(4,𝔽2)11yescharacteristic
131C4⋊C4—62no—
132C4⋊C4—91no—
133C4⋊C4—181no—
134C4⋊C4—182no—
135C42—61no—
136C42—91no—
137C22×C3—21no—
138C22×C3—21no—
139C3×C4—21no—
140C3×C4—21no—
141C3×C4—21no—
142C3×C4—21no—
143C3×C4—121no—
144C3×C4—121no—
145C3×C4—242no—
146Dic3—41no—
147Dic3—41no—
148Dic3—62no—
149Dic3—62no—
150Dic3—62no—
151Dic3—82no—
152Dic3—121no—
153C32#169411yescharacteristic, complemented, Sylow
154Q8—182no—
155Q8—362no—
156Q8—362no—
157C2×C4—61no—
158C2×C4—61no—
159C2×C4—91no—
160C2×C4—91no—
161C2×C4—122no—
162C2×C4C2×GO+(4,𝔽2)11yescharacteristic
163C8—121no—
164C8—181no—
165C8—362no—
166C8#377612yescomplemented
167C2×C3—21no—
168C2×C3—21no—
169C2×C3—21no—
170C2×C3—21no—
171C2×C3—21no—
172C2×C3—21no—
173C22#6423011yescharacteristic
174C4—92no—
175C4—121no—
176C4—121no—
177C4—181no—
178C4—242no—
179C4#6422611yescharacteristic
180C4C2×#377611yescharacteristic
181C3—21no—
182C3—21no—
183C2#1059328711yescharacteristic
184C2#1059330511yescharacteristic
185C2#1059344711yescharacteristic
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#1694
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
55. C32×C8Q16semidirect
153. C32#1694semidirect
166. C8#3776semidirect

Maximal subgroups

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

subgroupindex
#105934472
#105909022
#105907872
#105901702
#105900392
#16949