Finite Group Databasebeta

← #11781224

Subgroups — #11781224

Order 1152.

244 conjugacy classes of subgroups; only the 47 normal subgroups are shown.

normal subgroups only

This group has 244 conjugacy classes of subgroups — too many to draw. Only its 47 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#10593393C212yesmaximal
2#10590902C211yesmaximal, characteristic
3C8×#627C211yesmaximal, characteristic
4#10590171C211yesmaximal, characteristic
5#10590040C212yesmaximal
6#63919C2212yes—
7C4×#627C2211yescharacteristic
8C4⋊#622C2212yes—
9#63743—22no—
10#63740—22no—
11C8×C3⋊Dic3C2211yescharacteristic
12C3×#818—21no—
13C3×C8×Dic3—21no—
14#63576—21no—
15#63572C2211yescharacteristic
16Dic3⋊(C3⋊C8)—21no—
17#4874—61no—
18C8×Dic6—61no—
19C2×#627—22no—
20C2×#627D411yescharacteristic
21C2×#622—22no—
22C2×C32×C8D411yescharacteristic
23C4×C3⋊Dic3C2311yescharacteristic
24C2×C3⋊(C3⋊C8)D411yescharacteristic
25C3×C4⋊Dic3—22no—
26C3×C4×Dic3—21no—
27C2×C3×C3⋊C8—21no—
28#3724—22no—
29#3724D411yescharacteristic
30Dic3⋊Dic3—21no—
31#1676—91nomaximal, Sylow
32#888—62no—
33C4×Dic6—61no—
34C3×#107—61no—
35C3×C4×C8—61no—
36#818—21no—
37Dic3⋊C8—61no—
38Dic3⋊C8—61no—
39C8×Dic3—21no—
40C8×Dic3—61no—
41C8×Dic3—61no—
42#807—62no—
43C4⋊(C3⋊C8)—61no—
44C2×C32×C4C2×D411yescharacteristic
45C2×C3⋊Dic3C2×D411yescharacteristic
46C2×C3⋊Dic3#4111yescharacteristic
47C2×C3×Dic3—21no—
48C2×C3×Dic3—21no—
49C2×C3×Dic3—42no—
50#627—21no—
51#627—82no—
52#627Q1612yes—
53#622—42no—
54C32×C8Q1612yes—
55C3⋊(C3⋊C8)—21no—
56C3×C3⋊C8—41no—
57#500—91no—
58#477—92no—
59C8×Q8—91no—
60#335—91no—
61#333—92no—
62C2×Dic6—61no—
63C2×Dic6—122no—
64C2×C3×C8—21no—
65C2×C3×C8—21no—
66C2×C3×C8—61no—
67C3×C4⋊C4—62no—
68C3×C42—61no—
69C4⋊Dic3—22no—
70C4⋊Dic3—61no—
71Dic3⋊C4—61no—
72Dic3⋊C4—61no—
73Dic3⋊C4—122no—
74C4×Dic3—21no—
75C4×Dic3—61no—
76C4×Dic3—61no—
77C2×C3⋊C8—21no—
78C2×C3⋊C8—61no—
79C2×C3⋊C8—61no—
80C22×C32#12111yescharacteristic
81C32×C4C2×Q1611yescharacteristic
82C32×C4#13711yescharacteristic
83C3⋊Dic3—21no—
84C3⋊Dic3C2×Q1611yescharacteristic
85C3⋊Dic3#13511yescharacteristic
86C3×Dic3—22no—
87C3×Dic3—41no—
88C3×Dic3—82no—
89C4⋊Q8—92no—
90C4×Q8—91no—
91#107—61no—
92#107—181no—
93#107—182no—
94C4⋊C8—91no—
95C4⋊C8—92no—
96C4⋊C8—181no—
97#103—182no—
98C4×C8—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—62no—
113Dic6—62no—
114Dic6—244no—
115C3×C8—22no—
116C3×C8—22no—
117C3×C8—121no—
118C3⋊C8—41no—
119C3⋊C8—62no—
120C3⋊C8—121no—
121C2×C32#46211yescharacteristic
122C2×C32#46711yescharacteristic
123C2×C32#47211yescharacteristic
124C2×Q8—91no—
125C2×Q8—182no—
126C2×C8—61no—
127C2×C8—91no—
128C2×C8—182no—
129C2×C8GO+(4,𝔽2)11yescharacteristic
130C4⋊C4—62no—
131C4⋊C4—91no—
132C4⋊C4—181no—
133C4⋊C4—182no—
134C42—61no—
135C42—91no—
136C22×C3—21no—
137C22×C3—21no—
138C3×C4—21no—
139C3×C4—21no—
140C3×C4—21no—
141C3×C4—21no—
142C3×C4—62no—
143C3×C4—121no—
144C3×C4—242no—
145Dic3—22no—
146Dic3—41no—
147Dic3—61no—
148Dic3—61no—
149Dic3—61no—
150Dic3—61no—
151Dic3—62no—
152Dic3—82no—
153Dic3—121no—
154C32#167611yescharacteristic, complemented, Sylow
155Q8—92no—
156Q8—181no—
157Q8—722no—
158C2×C4—61no—
159C2×C4—61no—
160C2×C4—91no—
161C2×C4—91no—
162C2×C4—122no—
163C2×C4C2×GO+(4,𝔽2)11yescharacteristic
164C8—121no—
165C8—181no—
166C8—362no—
167C8#377612yes—
168C2×C3—21no—
169C2×C3—21no—
170C2×C3—21no—
171C2×C3—21no—
172C2×C3—21no—
173C2×C3—21no—
174C22#6423011yescharacteristic
175C4—62no—
176C4—91no—
177C4—91no—
178C4—121no—
179C4—181no—
180C4—242no—
181C4#6422611yescharacteristic
182C4C2×#377611yescharacteristic
183C3—21no—
184C3—21no—
185C2#1059328811yescharacteristic
186C2#1059330111yescharacteristic
187C2#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#1676
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
154. C32#1676semidirect

Maximal subgroups

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

subgroupindex
#105933932
#105909022
C8×#6272
#105901712
#105900402
#16769