Finite Group Databasebeta

← #10590789

Subgroups — #10590789

Order 576.

207 conjugacy classes of subgroups; only the 76 normal subgroups are shown.

normal subgroups only

This group has 207 conjugacy classes of subgroups — too many to draw. Only its 76 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
1C4×#627C211yesmaximal, characteristic
2#63641C211yesmaximal, characteristic
3C3×#815C211yesmaximal, characteristic
4C3×Dic3⋊C8C211yesmaximal, characteristic
5Dic3⋊(C3⋊C8)C211yesmaximal, characteristic
6#63554C211yesmaximal, characteristic
7#63553C211yesmaximal, characteristic
8#4828—31nomaximal
9#4701—31nomaximal
10C2×#627C411yescharacteristic
11C2×C32×C8C2211yescharacteristic
12C4×C3⋊Dic3C2211yescharacteristic
13C2×C3⋊(C3⋊C8)C2211yescharacteristic
14C3×C4×Dic3C2211yescharacteristic
15C3×C4×Dic3C2211yescharacteristic
16C2×C3×C3⋊C8C2211yescharacteristic
17C2×C3×C3⋊C8C2211yescharacteristic
18#3724C411yescharacteristic
19Dic3⋊Dic3C411yescharacteristic
20Dic3⋊Dic3C411yescharacteristic
21C4×Dic6—31no—
22C4×Dic6—31no—
23C3×C4⋊C8—31no—
24C3×#97—31no—
25#815—31no—
26#815D311yescharacteristic
27Dic3⋊C8—31no—
28Dic3⋊C8—31no—
29Dic3⋊C8—31no—
30Dic3⋊C8—61no—
31Dic3⋊C8D311yescharacteristic
32C8×Dic3—31no—
33C8×Dic3—31no—
34C4⋊(C3⋊C8)—31no—
35#803—31no—
36C2×C32×C4C2311yescharacteristic
37C2×C3⋊Dic3C2×C411yescharacteristic
38C2×C3⋊Dic3C2×C411yescharacteristic
39C2×C3×Dic3C2×C411yescharacteristic
40C2×C3×Dic3C2×C411yescharacteristic
41C2×C3×Dic3C2×C411yescharacteristic
42C2×C3×Dic3C2×C411yescharacteristic
43#627—22no—
44C32×C8—21no—
45C3⋊(C3⋊C8)—21no—
46C3×C3⋊C8—21no—
47C3×C3⋊C8Q812yescomplemented
48#446—91noSylow
49C2×Dic6—31no—
50C2×Dic6—31no—
51C2×C3×C8—21no—
52C2×C3×C8—31no—
53C2×C3×C8—31no—
54C2×C3×C8C2×D311yescharacteristic
55C2×C3×C8C2×D311yescharacteristic
56C3×C42—31no—
57C3×C42—31no—
58C4⋊Dic3—31no—
59C4⋊Dic3—31no—
60Dic3⋊C4—31no—
61Dic3⋊C4—31no—
62Dic3⋊C4—31no—
63Dic3⋊C4—31no—
64C4×Dic3—31no—
65C4×Dic3—31no—
66C4×Dic3—61no—
67C4×Dic3C2×D311yescharacteristic
68C4×Dic3C2×D311yescharacteristic
69C2×C3⋊C8—31no—
70C2×C3⋊C8—31no—
71C2×C3⋊C8—61no—
72C2×C3⋊C8C2×D311yescharacteristic
73C2×C3⋊C8C2×D311yescharacteristic
74C22×C32C22×C411yescharacteristic
75C32×C4C2×Q811yescharacteristic
76C32×C4#4111yescharacteristic
77C3⋊Dic3—21no—
78C3⋊Dic3M1612yes—
79C3×Dic3—21no—
80C3×Dic3—21no—
81C3×Dic3—21no—
82C3×Dic3—21no—
83C4×Q8—91no—
84C4⋊C8—31no—
85C4⋊C8—91no—
86C4⋊C8—91no—
87#97—31no—
88#97—91no—
89C4×C8—91no—
90C2×C3×C4—21no—
91C2×C3×C4—31no—
92C2×C3×C4—31no—
93C2×C3×C4—31no—
94C2×C3×C4—31no—
95C2×C3×C4C22×D311yescharacteristic
96C2×C3×C4C22×D311yescharacteristic
97C2×Dic3—31no—
98C2×Dic3—31no—
99C2×Dic3—31no—
100C2×Dic3—31no—
101C2×Dic3—61no—
102C2×Dic3—61no—
103C2×Dic3C4×D311yescharacteristic
104C2×Dic3C4×D311yescharacteristic
105C2×Dic3C4×D311yescharacteristic
106C2×Dic3C4×D311yescharacteristic
107Dic6—62no—
108Dic6—62no—
109C3×C8—21no—
110C3×C8—21no—
111C3×C8—32no—
112C3×C8—41no—
113C3×C8—61no—
114C3⋊C8—21no—
115C3⋊C8—61no—
116C3⋊C8—61no—
117C3⋊C8—121no—
118C3⋊C8Dic612yescomplemented
119C2×C32C4×Q811yescharacteristic
120C2×C32C2×M1611yescharacteristic
121C2×C32#13111yescharacteristic
122C2×Q8—91no—
123C2×C8—31no—
124C2×C8—31no—
125C2×C8—91no—
126C2×C8D3211yescharacteristic
127C4⋊C4—91no—
128C4⋊C4—91no—
129C4⋊C4—91no—
130C42—31no—
131C42—31no—
132C42—91no—
133C22×C3—21no—
134C22×C3C2×C4×D311yescharacteristic
135C22×C3C2×C4×D311yescharacteristic
136C3×C4—21no—
137C3×C4—21no—
138C3×C4—61no—
139C3×C4—61no—
140C3×C4—61no—
141C3×C4—61no—
142C3×C4C2×Dic611yescharacteristic
143C3×C4#23511yescharacteristic
144C3×C4#23711yescharacteristic
145C3×C4D3×Q811yescharacteristic
146Dic3—21no—
147Dic3—21no—
148Dic3—21no—
149Dic3—21no—
150Dic3—32no—
151Dic3—32no—
152Dic3—62no—
153Dic3—61no—
154Dic3—61no—
155Dic3—121no—
156C32#44611yescharacteristic, complemented, Sylow
157Q8—182no—
158C2×C4—31no—
159C2×C4—31no—
160C2×C4—31no—
161C2×C4—31no—
162C2×C4—91no—
163C2×C4—91no—
164C2×C4C2×D3211yescharacteristic
165C8—21no—
166C8—32no—
167C8—61no—
168C8—181no—
169C2×C3—21no—
170C2×C3—21no—
171C2×C3—21no—
172C2×C3C4×Dic611yescharacteristic
173C2×C3#88711yescharacteristic
174C2×C3#90111yescharacteristic
175C2×C3D3×M1611yescharacteristic
176C2×C3D3×M1611yescharacteristic
177C2×C3#90711yescharacteristic
178C22C4×D3211yescharacteristic
179C4—61no—
180C4—61no—
181C4—61no—
182C4—61no—
183C4—92no—
184C4—181no—
185C4D3×Dic611yescharacteristic
186C4#380411yescharacteristic
187C3—21no—
188C3#470111yescharacteristic, complemented
189C3#482811yescharacteristic, complemented
190C2#6379111yescharacteristic
191C2#6380411yescharacteristic
192C2#6383711yescharacteristic
subgroupG/H
center, FrattiniC2×C4C2×D32
commutator, socle, prime radicalC22×C32C22×C4
FittingC2×C32×C8C22
cosocleC2×C32×C4C23
hypercenterC2×C8D32
hypocenterC32#446
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ C2×C8

Complements

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

NH ≅ G/Ntype
47. C3×C3⋊C8Q8semidirect
118. C3⋊C8Dic6semidirect
156. C32#446semidirect
188. C3#4701semidirect
189. C3#4828semidirect

Maximal subgroups

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

subgroupindex
C4×#6272
#636412
C3×#8152
C3×Dic3⋊C82
Dic3⋊(C3⋊C8)2
#635542
#635532
#48283
#47013