Finite Group Databasebeta

← #10591479

Subgroups — #10591479

Order 576.

251 conjugacy classes of subgroups; only the 66 normal subgroups are shown.

normal subgroups only

This group has 251 conjugacy classes of subgroups — too many to draw. Only its 66 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
1D4×C3⋊Dic3C211yesmaximal, characteristic
2#63872C211yesmaximal, characteristic, complemented
3C3×#832C211yesmaximal, characteristic
4C3×#832C211yesmaximal, characteristic
5#63575C211yesmaximal, characteristic, complemented
6#63573C211yesmaximal, characteristic, complemented
7#63572C211yesmaximal, characteristic, complemented
8#4766—31nomaximal
9#4763—31nomaximal
10C2×C32×D4C2211yescharacteristic
11C22×C3⋊Dic3—21no—
12#3757—21no—
13C4⋊(C3⋊Dic3)C2211yescharacteristic
14C4×C3⋊Dic3C2211yescharacteristic
15C3×C4⋊Dic3C2211yescharacteristic
16C3×C4⋊Dic3C2211yescharacteristic
17C2×C3×C3⋊C8C2211yescharacteristic
18C2×C3×C3⋊C8C2211yescharacteristic
19Dic3⋊Dic3—21no—
20Dic3⋊Dic3—21no—
21D4×Dic3—31no—
22D4×Dic3—31no—
23D4×Dic3—61no—
24#890—31no—
25#890—31no—
26C3×#102—31no—
27C3×#102—31no—
28#832D311yescharacteristic
29#832D311yescharacteristic
30#818—31no—
31#817—31no—
32Dic3⋊C8—31no—
33Dic3⋊C8—31no—
34#808—31no—
35#807—31no—
36C23×C32—21no—
37C32×D4—21no—
38C32×D4Q812yes—
39C2×C32×C4C2311yescharacteristic
40C2×C3⋊Dic3—21no—
41C2×C3⋊Dic3—42no—
42C2×C3⋊Dic3D411yescharacteristic
43C2×C3⋊Dic3D411yescharacteristic
44C2×C3×Dic3—21no—
45C2×C3×Dic3—21no—
46C3×C3⋊C8—21no—
47C3×C3⋊C8—21no—
48#478—91noSylow
49C2×C3×D4—21no—
50C2×C3×D4C2×D311yescharacteristic
51C2×C3×D4C2×D311yescharacteristic
52C22×Dic3—61no—
53C22×Dic3—61no—
54C22×Dic3—62no—
55C2×C3×C8—31no—
56C2×C3×C8—31no—
57C3×C4⋊C4—31no—
58C3×C4⋊C4—31no—
59#217—61no—
60#217—61no—
61#217—62no—
62C4⋊Dic3—31no—
63C4⋊Dic3—31no—
64C4⋊Dic3—61no—
65C4⋊Dic3—61no—
66C4⋊Dic3—61no—
67C4⋊Dic3C2×D311yescharacteristic
68C4⋊Dic3C2×D311yescharacteristic
69Dic3⋊C4—61no—
70Dic3⋊C4—61no—
71C4×Dic3—31no—
72C4×Dic3—31no—
73C4×Dic3—61no—
74C2×C3⋊C8C2×D311yescharacteristic
75C2×C3⋊C8C2×D311yescharacteristic
76C22×C32—22no—
77C22×C32—41no—
78C22×C32—41no—
79C22×C32C2×D411yescharacteristic
80C32×C4C2×Q811yescharacteristic
81C32×C4#4111yescharacteristic
82C3⋊Dic3—21no—
83C3⋊Dic3—21no—
84C3⋊Dic3—41no—
85C3×Dic3—41no—
86C3×Dic3—41no—
87#125—91no—
88C4×D4—91no—
89#107—91no—
90#106—91no—
91C4⋊C8—91no—
92#102—31no—
93#102—31no—
94C23×C3—22no—
95C23×C3—21no—
96C23×C3—21no—
97C3×D4—22no—
98C3×D4—21no—
99C3×D4—21no—
100C3×D4—22no—
101C3×D4Dic612yes—
102C3×D4Dic612yes—
103C2×C3×C4—21no—
104C2×C3×C4—61no—
105C2×C3×C4—61no—
106C2×C3×C4C22×D311yescharacteristic
107C2×C3×C4C22×D311yescharacteristic
108C2×Dic3—21no—
109C2×Dic3—21no—
110C2×Dic3—31no—
111C2×Dic3—31no—
112C2×Dic3—31no—
113C2×Dic3—31no—
114C2×Dic3—61no—
115C2×Dic3—61no—
116C2×Dic3—62no—
117C2×Dic3—61no—
118C2×Dic3—61no—
119C2×Dic3—124no—
120C2×Dic3—122no—
121C2×Dic3—122no—
122C3×C8—61no—
123C3×C8—61no—
124C3⋊C8—21no—
125C3⋊C8—21no—
126C2×C32—42no—
127C2×C32C22⋊Q811yescharacteristic
128C2×C32#13511yescharacteristic
129C2×C32AGL(1,ℤ/8)11yescharacteristic
130C2×D4D3211yescharacteristic
131C22×C4—181no—
132C2×C8—31no—
133C2×C8—31no—
134C4⋊C4—31no—
135C4⋊C4—31no—
136C4⋊C4—91no—
137C4⋊C4—181no—
138C4⋊C4—181no—
139C22⋊C4—181no—
140C42—91no—
141C22×C3—24no—
142C22×C3—22no—
143C22×C3—22no—
144C22×C3—21no—
145C22×C3—42no—
146C22×C3—42no—
147C22×C3—41no—
148C22×C3—41no—
149C22×C3—41no—
150C22×C3—41no—
151C22×C3D3×D411yescharacteristic
152C22×C3D3×D411yescharacteristic
153C3×C4—21no—
154C3×C4—21no—
155C3×C4—121no—
156C3×C4—121no—
157C3×C4C2×Dic611yescharacteristic
158C3×C4C2×Dic611yescharacteristic
159C3×C4#23711yescharacteristic
160C3×C4#23711yescharacteristic
161Dic3—41no—
162Dic3—41no—
163Dic3—62no—
164Dic3—61no—
165Dic3—61no—
166Dic3—61no—
167Dic3—61no—
168Dic3—121no—
169Dic3—122no—
170Dic3—121no—
171Dic3—121no—
172C32#47811yescharacteristic, complemented, Sylow
173C23—21no—
174D4—21no—
175D4#62712yes—
176C2×C4—61no—
177C2×C4—61no—
178C2×C4—91no—
179C2×C4—91no—
180C2×C4—181no—
181C2×C4—362no—
182C2×C4C2×D3211yescharacteristic
183C8—61no—
184C8—61no—
185C2×C3—21no—
186C2×C3—21no—
187C2×C3—21no—
188C2×C3—44no—
189C2×C3—42no—
190C2×C3—42no—
191C2×C3#87811yescharacteristic
192C2×C3#87811yescharacteristic
193C2×C3#91111yescharacteristic
194C2×C3#91211yescharacteristic
195C2×C3#91411yescharacteristic
196C2×C3#91611yescharacteristic
197C22—22no—
198C22—41no—
199C22—41no—
200C22#381111yescharacteristic
201C4—121no—
202C4—121no—
203C4—181no—
204C4—181no—
205C4—361no—
206C4#380511yescharacteristic
207C4C2×#62711yescharacteristic
208C3—21no—
209C3#476311yescharacteristic, complemented
210C3#476611yescharacteristic, complemented
211C2—42no—
212C2#6393611yescharacteristic
213C2#6393711yescharacteristic
214C2#6398211yescharacteristic
subgroupG/H
centerC22#3811
commutator, cosocleC2×C32×C4C23
FrattiniC2×C4C2×D32
Fitting, prime radicalC2×C32×D4C22
socleC22×C32C2×D4
hypercenterC2×D4D32
hypocenterC32#478
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×D4

Complements

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

NH ≅ G/Ntype
2. #63872C2semidirect
5. #63575C2semidirect
6. #63573C2semidirect
7. #63572C2semidirect
172. C32#478semidirect
209. C3#4763semidirect
210. C3#4766semidirect

Maximal subgroups

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

subgroupindex
D4×C3⋊Dic32
#638722
C3×#8322
#635752
#635732
#635722
#47663
#47633