Finite Group Databasebeta

← #10591508

Subgroups — #10591508

Order 576.

254 conjugacy classes of subgroups; only the 54 normal subgroups are shown.

normal subgroups only

This group has 254 conjugacy classes of subgroups — too many to draw. Only its 54 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
1C2×#3753C211yesmaximal, characteristic, complemented
2C3×#932C211yesmaximal, characteristic, complemented
3#63825C211yesmaximal, characteristic, complemented
4#63815C211yesmaximal, characteristic, complemented
5C3×#833C211yesmaximal, characteristic, complemented
6#63578C211yesmaximal, characteristic, complemented
7#63559C211yesmaximal, characteristic, complemented
8#5199—31nomaximal
9#4749—31nomaximal
10C2×C32×D4C2211yescharacteristic
11C2×C4⋊(C3⋊D3)C2211yescharacteristic
12C3×#235C2211yescharacteristic
13#3753—21no—
14#3753—21no—
15C2×C3⋊(C3⋊C8)C2211yescharacteristic
16C3×#214—21no—
17C3×#213—21no—
18C3×#208C2211yescharacteristic
19C3×#208C2211yescharacteristic
20C3×#208C2211yescharacteristic
21#3717—21no—
22#3714—21no—
23#3711—21no—
24D3×C3⋊C8—21no—
25C3×AGL(1,ℤ/8)—31no—
26#949—31no—
27#948—31no—
28#932D311yescharacteristic, complemented
29C2×#213—31no—
30C2×#213—31no—
31C2×#213—61no—
32#908—31no—
33#907—31no—
34C3×#100—31no—
35#833D311yescharacteristic, complemented
36#823—31no—
37#823—31no—
38#822—31no—
39#822—31no—
40C23×C32—21no—
41C22×C3⋊D3—21no—
42C32×D4—21no—
43C32×D4—21no—
44C2×C32×C4C2311yescharacteristic
45C4⋊(C3⋊D3)—21no—
46C4⋊(C3⋊D3)—21no—
47C3×#67—21no—
48C3×D12D411yescharacteristic
49C3×C4×D3—21no—
50C3×Dic6D411yescharacteristic
51C3⋊(C3⋊C8)D411yescharacteristic
52C3⋊(C3⋊C8)D411yescharacteristic
53C3×C3⋊C8—21no—
54C3×C3⋊C8—21no—
55C3×C3⋊C8—21no—
56#472—91noSylow
57C3×#41—31no—
58C2×C3×D4—21no—
59C2×C3×D4C2×D311yescharacteristic
60C2×C3×D4C2×D311yescharacteristic
61#235C2×D311yescharacteristic
62C2×D12—31no—
63C2×D12—31no—
64C2×D12—61no—
65C3×SD16—61no—
66C3×D8—61no—
67C3×M16—31no—
68C3×M16—31no—
69C3×M16—31no—
70#215—61no—
71#214—21no—
72#213—21no—
73#213—61no—
74#213—61no—
75#213—61no—
76#213—61no—
77#213—61no—
78#213—62no—
79#213—62no—
80#208—61no—
81#208C2×D311yescharacteristic
82#208C2×D311yescharacteristic
83#208C2×D311yescharacteristic
84C2×C3⋊C8—31no—
85C2×C3⋊C8—31no—
86C2×C3⋊C8—61no—
87C2×C3⋊C8—61no—
88D24—61no—
89#204—61no—
90ΓL(1,𝔽25)—61no—
91D3×C8—61no—
92C22×C32—41no—
93C22×C32—81no—
94C22×C32#4111yescharacteristic
95C2×C3⋊D3—41no—
96C2×C3⋊D3—81no—
97C2×C3×D3—21no—
98C32×C4C2×D411yescharacteristic
99C32×C4C2×D411yescharacteristic
100C3×Dic3—21no—
101AGL(1,ℤ/8)—31no—
102AGL(1,ℤ/8)—91no—
103C2×D8—91no—
104#131—91no—
105#108—91no—
106#100—31no—
107#100—91no—
108C23×C3—21no—
109C23×C3—21no—
110C23×C3—41no—
111C22×D3—61no—
112C22×D3—61no—
113C22×D3—121no—
114C3×Q8—31no—
115C3×D4—22no—
116C3×D4—21no—
117C3×D4—21no—
118C3×D4—21no—
119C3×D4—21no—
120C3×D4—31no—
121C3×D4—41no—
122C3×D4—61no—
123C2×C3×C4—21no—
124C2×C3×C4—61no—
125C2×C3×C4C22×D311yescharacteristic
126C2×C3×C4C22×D311yescharacteristic
127#67—21no—
128D12—62no—
129D12—61no—
130D12—61no—
131D12—61no—
132D12—61no—
133D12—121no—
134D12#6711yescharacteristic
135C4×D3—21no—
136Dic6#6711yescharacteristic
137C3×C8—61no—
138C3×C8—61no—
139C3×C8—61no—
140C3⋊C8—21no—
141C3⋊C8—21no—
142C3⋊C8—21no—
143C3⋊C8—31no—
144C3⋊C8—31no—
145C3⋊C8—31no—
146C3⋊C8—31no—
147C3⋊C8—61no—
148C3⋊C8—61no—
149C2×C32—21no—
150C2×C32—81no—
151C2×C32#12111yescharacteristic
152C3⋊D3—81no—
153C3×D3—41no—
154#41—31no—
155C2×D4—91no—
156C2×D4D3211yescharacteristic
157SD16—61no—
158SD16—181no—
159D8—61no—
160D8—181no—
161D8—181no—
162D8—181no—
163M16—31no—
164M16—31no—
165M16—31no—
166M16—181no—
167C2×C8—91no—
168C2×C8—181no—
169C22×C3—21no—
170C22×C3—42no—
171C22×C3—41no—
172C22×C3—41no—
173C22×C3—61no—
174C22×C3—81no—
175C22×C3—81no—
176C22×C3—82no—
177C22×C3#23511yescharacteristic
178C22×C3#23711yescharacteristic
179C2×D3—21no—
180C2×D3—122no—
181C2×D3—121no—
182C2×D3—121no—
183C2×D3—242no—
184C2×D3—241no—
185C2×D3—241no—
186C3×C4—21no—
187C3×C4—21no—
188C3×C4—61no—
189C3×C4D3×D411yescharacteristic
190C3×C4D3×D411yescharacteristic
191C3×C4D3×D411yescharacteristic
192C3×C4C2×#6711yescharacteristic
193Dic3—21no—
194C32#47211yescharacteristic, complemented, Sylow
195C23—21no—
196C23—181no—
197Q8—31no—
198D4—21no—
199D4—21no—
200D4—31no—
201D4—61no—
202D4—181no—
203D4—181no—
204C2×C4—61no—
205C2×C4C2×D3211yescharacteristic
206C8—61no—
207C8—61no—
208C8—61no—
209C8—91no—
210C8—91no—
211C2×C3—22no—
212C2×C3—21no—
213C2×C3—21no—
214C2×C3—21no—
215C2×C3—82no—
216C2×C3—81no—
217C2×C3—81no—
218C2×C3—121no—
219C2×C3#88411yescharacteristic
220C2×C3#93911yescharacteristic
221D3—41no—
222D3—242no—
223D3—241no—
224D3—241no—
225C22—41no—
226C22—61no—
227C22—81no—
228C22—361no—
229C22—721no—
230C22#380411yescharacteristic
231C4—61no—
232C4D3×#6711yescharacteristic
233C4#381111yescharacteristic
234C3—21no—
235C3#474911yescharacteristic, complemented
236C3#519911yescharacteristic, complemented
237C2—21no—
238C2—81no—
239C2—121no—
240C2—721no—
241C2#6397111yescharacteristic
subgroupG/H
centerC2#63971
commutator, cosocleC2×C32×C4C23
FrattiniC2×C4C2×D32
FittingC2×C32×D4C22
socleC2×C32#121
hypercenterC2×D4D32
hypocenterC32#472
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×D4

Complements

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

NH ≅ G/Ntype
1. C2×#3753C2semidirect
2. C3×#932C2semidirect
3. #63825C2semidirect
4. #63815C2semidirect
5. C3×#833C2semidirect
6. #63578C2semidirect
7. #63559C2semidirect
28. #932D3semidirect
35. #833D3semidirect
194. C32#472semidirect
235. C3#4749semidirect
236. C3#5199semidirect

Maximal subgroups

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

subgroupindex
C2×#37532
C3×#9322
#638252
#638152
C3×#8332
#635782
#635592
#51993
#47493