Finite Group Databasebeta

← #10590507

Subgroups — #10590507

Order 576.

285 conjugacy classes of subgroups; only the 64 normal subgroups are shown.

normal subgroups only

This group has 285 conjugacy classes of subgroups — too many to draw. Only its 64 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#64106C211yesmaximal, characteristic, complemented
2#63916C211yesmaximal, characteristic
3C2×#3716C211yesmaximal, characteristic, complemented
4C2×#3710C211yesmaximal, characteristic, complemented
5C3×#809C211yesmaximal, characteristic, complemented
6C3×#808C211yesmaximal, characteristic, complemented
7#63567C211yesmaximal, characteristic, complemented
8#4864—31nomaximal
9#4778—31nomaximal
10C2×C4×C3⋊D3C2211yescharacteristic
11C2×#634C2211yescharacteristic
12C2×C3×D12C2211yescharacteristic
13C2×#626—21no—
14C32×C4⋊C4C2211yescharacteristic
15#3752—21no—
16C4⋊(C3⋊Dic3)—21no—
17C3×C4⋊Dic3C2211yescharacteristic
18C2×C3×C3⋊C8C2211yescharacteristic
19C2×C3×C3⋊C8C2211yescharacteristic
20(C2×D3)⋊Dic3—21no—
21#3716—22no—
22#3710—22no—
23#938—31no—
24C2×#214—31no—
25C2×#204—31no—
26C2×D3×C8—31no—
27C2×D3×C8—31no—
28#897—31no—
29#897—31no—
30#897—61no—
31#895—31no—
32C3×#106—31no—
33C3×#102—31no—
34#816—31no—
35#810—31no—
36#809D311yescharacteristic, complemented
37#808D311yescharacteristic, complemented
38C22×C3⋊D3D411yescharacteristic
39C22×C3×D3—21no—
40C2×C32×C4—21no—
41C2×C32×C4C2311yescharacteristic
42C2×C3⋊Dic3—21no—
43C2×C3⋊Dic3D411yescharacteristic
44C4×C3⋊D3—21no—
45C4×C3⋊D3—21no—
46#634—21no—
47#634—21no—
48C2×C3×Dic3—21no—
49C3×D12—21no—
50C3×D12—21no—
51#626—42no—
52C3×C3⋊C8—21no—
53C3×C3⋊C8D412yescomplemented
54#465—91noSylow
55C2×C3×D4—31no—
56C2×#67—61no—
57C2×D12—61no—
58C2×D12C2×D311yescharacteristic
59C2×C4×D3—31no—
60C2×C4×D3—31no—
61C2×C4×D3—61no—
62C2×Dic6—31no—
63C2×Dic6—31no—
64C2×Dic6—61no—
65C2×C3×C8—31no—
66C2×C3×C8—31no—
67C3×C4⋊C4—21no—
68C3×C4⋊C4—31no—
69C3×C4⋊C4C2×D311yescharacteristic
70C3×C4⋊C4C2×D311yescharacteristic
71#217—61no—
72#214—62no—
73(C2×D3)⋊C4—61no—
74(C2×D3)⋊C4—61no—
75(C2×D3)⋊C4—61no—
76(C2×D3)⋊C4—62no—
77C4⋊Dic3—61no—
78C4⋊Dic3—61no—
79C4⋊Dic3—62no—
80C4⋊Dic3C2×D311yescharacteristic
81C2×C3⋊C8C2×D311yescharacteristic
82C2×C3⋊C8C2×D311yescharacteristic
83#204—62no—
84D3×C8—62no—
85D3×C8—62no—
86C22×C32C2×D411yescharacteristic
87C2×C3⋊D3—21no—
88C2×C3⋊D3—21no—
89C2×C3⋊D3SD1612yescomplemented
90C2×C3×D3—41no—
91C2×C3×D3—41no—
92C2×C3×D3—41no—
93C32×C4—41no—
94C32×C4C2×D411yescharacteristic
95C32×C4#4111yescharacteristic
96C3⋊Dic3—21no—
97C3⋊Dic3—41no—
98C3×Dic3—41no—
99C2×SD16—91no—
100C22×C8—91no—
101C22⋊Q8—91no—
102#121—91no—
103#106—31no—
104#103—91no—
105#102—31no—
106C23×C3—61no—
107C22×D3—21no—
108C22×D3—31no—
109C22×D3—31no—
110C22×D3—61no—
111C3×D4—61no—
112C3×D4—61no—
113C2×C3×C4—22no—
114C2×C3×C4—21no—
115C2×C3×C4—21no—
116C2×C3×C4—21no—
117C2×C3×C4—61no—
118C2×C3×C4C22×D311yescharacteristic
119C2×C3×C4C22×D311yescharacteristic
120#67—122no—
121C2×Dic3—21no—
122C2×Dic3—31no—
123C2×Dic3—31no—
124C2×Dic3—61no—
125C2×Dic3—62no—
126C2×Dic3—61no—
127C2×Dic3—61no—
128D12—21no—
129D12—21no—
130D12—122no—
131C4×D3—61no—
132C4×D3—61no—
133C4×D3—61no—
134C4×D3—61no—
135C4×D3—121no—
136C4×D3—121no—
137Dic6—61no—
138Dic6—61no—
139Dic6—61no—
140Dic6—61no—
141Dic6—121no—
142Dic6—121no—
143C3×C8—32no—
144C3×C8—61no—
145C3⋊C8—21no—
146C3⋊C8D1212yescomplemented
147C2×C32#12111yescharacteristic
148C2×C32C2×SD1611yescharacteristic
149C2×C32#13511yescharacteristic
150C3⋊D3—22no—
151C3×D3—81no—
152C2×Q8—91no—
153C2×D4—31no—
154C2×D4—181no—
155C22×C4—91no—
156SD16—182no—
157C2×C8—31no—
158C2×C8—31no—
159C2×C8—182no—
160C4⋊C4—31no—
161C4⋊C4—181no—
162C4⋊C4D3211yescharacteristic
163C22⋊C4—181no—
164C22⋊C4—181no—
165C22×C3—21no—
166C22×C3—121no—
167C22×C3—121no—
168C22×C3—121no—
169C22×C3D3×D411yescharacteristic
170C22×C3D3×D411yescharacteristic
171C2×D3—32no—
172C2×D3—32no—
173C2×D3—41no—
174C2×D3—41no—
175C2×D3—41no—
176C2×D3—62no—
177C2×D3—61no—
178C2×D3—61no—
179C2×D3—61no—
180C2×D3—61no—
181C2×D3—121no—
182C2×D3—121no—
183C3×C4—21no—
184C3×C4—21no—
185C3×C4—42no—
186C3×C4—41no—
187C3×C4—41no—
188C3×C4—121no—
189C3×C4C2×D1211yescharacteristic
190C3×C4#23511yescharacteristic
191C3×C4D3×D411yescharacteristic
192C3×C4#23911yescharacteristic
193Dic3—41no—
194Dic3—61no—
195Dic3—61no—
196Dic3—121no—
197Dic3—122no—
198Dic3—121no—
199Dic3—121no—
200C32#46511yescharacteristic, complemented, Sylow
201C23—61no—
202C23—91no—
203Q8—181no—
204Q8—181no—
205D4—61no—
206D4—61no—
207D4—362no—
208C2×C4—21no—
209C2×C4—61no—
210C2×C4—91no—
211C2×C4—181no—
212C2×C4—181no—
213C2×C4—181no—
214C2×C4C2×D3211yescharacteristic
215C8—32no—
216C8—61no—
217C2×C3—21no—
218C2×C3—21no—
219C2×C3—21no—
220C2×C3—241no—
221C2×C3#88411yescharacteristic
222C2×C3#89511yescharacteristic
223C2×C3#91211yescharacteristic
224C2×C3D3×SD1611yescharacteristic
225C2×C3D3×SD1611yescharacteristic
226C2×C3#91611yescharacteristic
227D3—62no—
228D3—62no—
229D3—81no—
230D3—122no—
231C22—92no—
232C22—121no—
233C22—121no—
234C22—121no—
235C22—181no—
236C22—181no—
237C22#381111yescharacteristic
238C4—41no—
239C4—121no—
240C4—181no—
241C4—361no—
242C4#379911yescharacteristic
243C4D3×D1211yescharacteristic
244C3—21no—
245C3#477811yescharacteristic, complemented
246C3#486411yescharacteristic, complemented
247C2—182no—
248C2—241no—
249C2#6391011yescharacteristic
250C2#6393611yescharacteristic
251C2#6394011yescharacteristic
subgroupG/H
centerC22#3811
commutator, cosocleC2×C32×C4C23
FrattiniC2×C4C2×D32
FittingC32×C4⋊C4C22
socleC22×C32C2×D4
prime radical#63916C2
hypercenterC4⋊C4D32
hypocenterC32#465
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. #64106C2semidirect
3. C2×#3716C2semidirect
4. C2×#3710C2semidirect
5. C3×#809C2semidirect
6. C3×#808C2semidirect
7. #63567C2semidirect
36. #809D3semidirect
37. #808D3semidirect
53. C3×C3⋊C8D4semidirect
89. C2×C3⋊D3SD16semidirect
146. C3⋊C8D12semidirect
200. C32#465semidirect
245. C3#4778semidirect
246. C3#4864semidirect

Maximal subgroups

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

subgroupindex
#641062
#639162
C2×#37162
C2×#37102
C3×#8092
C3×#8082
#635672
#48643
#47783