Finite Group Databasebeta

← #10590541

Subgroups — #10590541

Order 576.

234 conjugacy classes of subgroups; only the 58 normal subgroups are shown.

normal subgroups only

This group has 234 conjugacy classes of subgroups — too many to draw. Only its 58 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#64097C211yesmaximal, characteristic, complemented
2#63863C211yesmaximal, characteristic
3C3×#810C211yesmaximal, characteristic, complemented
4C3×#809C211yesmaximal, characteristic
5#63566C211yesmaximal, characteristic, complemented
6#63563C211yesmaximal, characteristic
7#63555C211yesmaximal, characteristic, complemented
8#4794—31nomaximal
9#4765—31nomaximal
10C2×#634—21no—
11C2×C3×D12C2211yescharacteristic
12C2×C3×Dic6C2211yescharacteristic
13C32×C4⋊C4C2211yescharacteristic
14C4⋊(C3⋊Dic3)C2211yescharacteristic
15#3750—21no—
16C4×C3⋊Dic3C2211yescharacteristic
17C2×C3×C3⋊C8C2211yescharacteristic
18C2×C3×C3⋊C8C2211yescharacteristic
19(C2×D3)⋊Dic3—21no—
20(C2×D3)⋊Dic3—21no—
21#947—31no—
22#936—31no—
23#888—31no—
24#888—31no—
25#888—61no—
26C3×#103—31no—
27C3×#102—31no—
28#835—31no—
29#832—31no—
30#821—31no—
31#816—31no—
32#815—31no—
33#815—31no—
34#810D311yescharacteristic, complemented
35#809D311yescharacteristic
36C22×C3×D3—21no—
37C2×C32×C4—21no—
38C2×C32×C4C2311yescharacteristic
39C2×C3⋊Dic3—21no—
40C2×C3⋊Dic3D411yescharacteristic
41C2×C3⋊Dic3D411yescharacteristic
42#634—42no—
43C2×C3×Dic3—21no—
44C3×D12—21no—
45C3×D12—21no—
46C3×Dic6—21no—
47C3×Dic6—21no—
48C3×C3⋊C8—21no—
49C3×C3⋊C8—21no—
50#489—91noSylow
51C2×C3×Q8—31no—
52C2×C3×D4—31no—
53C2×D12C2×D311yescharacteristic
54C2×Dic6—61no—
55C2×Dic6—61no—
56C2×Dic6—62no—
57C2×Dic6C2×D311yescharacteristic
58C2×C3×C8—31no—
59C2×C3×C8—31no—
60C3×C4⋊C4—21no—
61C3×C4⋊C4C2×D311yescharacteristic
62C3×C4⋊C4C2×D311yescharacteristic
63#217—61no—
64#217—61no—
65(C2×D3)⋊C4—61no—
66(C2×D3)⋊C4—61no—
67C4⋊Dic3—31no—
68C4⋊Dic3—31no—
69C4⋊Dic3—61no—
70Dic3⋊C4—61no—
71Dic3⋊C4—61no—
72Dic3⋊C4—62no—
73C4×Dic3—31no—
74C4×Dic3—31no—
75C4×Dic3—61no—
76C2×C3⋊C8C2×D311yescharacteristic
77C2×C3⋊C8C2×D311yescharacteristic
78C22×C32C2×D411yescharacteristic
79C2×C3×D3—41no—
80C2×C3×D3—41no—
81C2×C3×D3—41no—
82C32×C4—41no—
83C32×C4#4111yescharacteristic
84C32×C4#4111yescharacteristic
85C3⋊Dic3—21no—
86C3⋊Dic3—21no—
87C3⋊Dic3—41no—
88C3×Dic3—41no—
89C4⋊Q8—91no—
90#124—91no—
91#103—31no—
92#103—91no—
93#102—31no—
94#102—91no—
95#97—91no—
96C23×C3—61no—
97C22×D3—21no—
98C3×Q8—61no—
99C3×Q8—61no—
100C3×D4—61no—
101C3×D4—61no—
102C2×C3×C4—22no—
103C2×C3×C4—21no—
104C2×C3×C4—21no—
105C2×C3×C4—21no—
106C2×C3×C4—61no—
107C2×C3×C4C22×D311yescharacteristic
108C2×C3×C4C22×D311yescharacteristic
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—
119D12—21no—
120D12—21no—
121Dic6—21no—
122Dic6—21no—
123Dic6—124no—
124Dic6—122no—
125Dic6—122no—
126C3×C8—61no—
127C3×C8—61no—
128C3⋊C8—21no—
129C3⋊C8—21no—
130C2×C32#12411yescharacteristic
131C2×C32AGL(1,ℤ/8)11yescharacteristic
132C2×C32#13711yescharacteristic
133C3×D3—81no—
134C2×Q8—31no—
135C2×Q8—181no—
136C2×D4—31no—
137C2×C8—31no—
138C2×C8—31no—
139C4⋊C4—91no—
140C4⋊C4—181no—
141C4⋊C4D3211yescharacteristic
142C22⋊C4—181no—
143C22⋊C4—181no—
144C42—91no—
145C22×C3—21no—
146C22×C3—121no—
147C22×C3—121no—
148C22×C3—121no—
149C22×C3D3×D411yescharacteristic
150C22×C3D3×D411yescharacteristic
151C2×D3—41no—
152C2×D3—41no—
153C2×D3—41no—
154C3×C4—21no—
155C3×C4—21no—
156C3×C4—42no—
157C3×C4—41no—
158C3×C4—41no—
159C3×C4—121no—
160C3×C4#23511yescharacteristic
161C3×C4#23511yescharacteristic
162C3×C4#23711yescharacteristic
163C3×C4#23711yescharacteristic
164Dic3—41no—
165Dic3—62no—
166Dic3—62no—
167Dic3—61no—
168Dic3—61no—
169Dic3—61no—
170Dic3—61no—
171Dic3—122no—
172Dic3—121no—
173Dic3—121no—
174C32#48911yescharacteristic, complemented, Sylow
175C23—61no—
176Q8—61no—
177Q8—61no—
178Q8—362no—
179D4—61no—
180D4—61no—
181C2×C4—21no—
182C2×C4—61no—
183C2×C4—91no—
184C2×C4—91no—
185C2×C4—181no—
186C2×C4C2×D3211yescharacteristic
187C8—61no—
188C8—61no—
189C2×C3—21no—
190C2×C3—21no—
191C2×C3—21no—
192C2×C3—241no—
193C2×C3#88511yescharacteristic
194C2×C3#88511yescharacteristic
195C2×C3#91111yescharacteristic
196C2×C3#91411yescharacteristic
197C2×C3#91511yescharacteristic
198C2×C3#91811yescharacteristic
199D3—81no—
200C22—121no—
201C22—121no—
202C22—121no—
203C22#381111yescharacteristic
204C4—41no—
205C4—121no—
206C4—181no—
207C4—181no—
208C4—361no—
209C4#379511yescharacteristic
210C4#379511yescharacteristic
211C3—21no—
212C3#476511yescharacteristic, complemented
213C3#479411yescharacteristic, complemented
214C2—241no—
215C2#6391311yescharacteristic
216C2#6393711yescharacteristic
217C2#6395111yescharacteristic
subgroupG/H
centerC22#3811
commutator, cosocleC2×C32×C4C23
FrattiniC2×C4C2×D32
FittingC32×C4⋊C4C22
socleC22×C32C2×D4
prime radicalC2×C3×D12C22
hypercenterC4⋊C4D32
hypocenterC32#489
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ C4⋊C4

Complements

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

NH ≅ G/Ntype
1. #64097C2semidirect
3. C3×#810C2semidirect
5. #63566C2semidirect
7. #63555C2semidirect
34. #810D3semidirect
174. C32#489semidirect
212. C3#4765semidirect
213. C3#4794semidirect

Maximal subgroups

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

subgroupindex
#640972
#638632
C3×#8102
C3×#8092
#635662
#635632
#635552
#47943
#47653