Finite Group Databasebeta

← #10590841

Subgroups — #10590841

Order 576.

286 conjugacy classes of subgroups; only the 62 normal subgroups are shown.

normal subgroups only

This group has 286 conjugacy classes of subgroups — too many to draw. Only its 62 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×C8×C3⋊D3C211yesmaximal, characteristic, complemented
2#63916C211yesmaximal, characteristic
3#63871C211yesmaximal, characteristic, complemented
4C2×#3715C211yesmaximal, characteristic, complemented
5C3×#821C211yesmaximal, characteristic, complemented
6C3×#816C211yesmaximal, characteristic, complemented
7#63574C211yesmaximal, characteristic, complemented
8#4807—31nomaximal
9#4778—31nomaximal
10C2×C4×C3⋊D3C2211yescharacteristic
11C2×C3×D12C2211yescharacteristic
12C2×C3×Dic6C2211yescharacteristic
13C2×#626—21no—
14C2×C32×C8C2211yescharacteristic
15C2×C3⋊(C3⋊C8)C2211yescharacteristic
16C8×C3⋊D3—22no—
17C3×C4⋊Dic3C2211yescharacteristic
18C3×C4⋊Dic3C2211yescharacteristic
19Dic3⋊Dic3—21no—
20#3722—21no—
21(C2×D3)⋊Dic3—21no—
22#3715—22no—
23#946—31no—
24C2×#215—31no—
25#938—31no—
26C2×#214—31no—
27C2×D3×C8—31no—
28C2×D3×C8—31no—
29C2×D3×C8—61no—
30#897—31no—
31#895—31no—
32C3×#103—31no—
33C3×#102—31no—
34#821D311yescharacteristic, complemented
35#816D311yescharacteristic, complemented
36#808—31no—
37#808—31no—
38C22×C3⋊D3D411yescharacteristic
39C22×C3×D3—21no—
40C2×C32×C4C2311yescharacteristic
41C2×C3⋊Dic3D411yescharacteristic
42C4×C3⋊D3—21no—
43C4×C3⋊D3—21no—
44C2×C3×Dic3—21no—
45C2×C3×Dic3—21no—
46C2×C3×Dic3—21no—
47C3×D12—21no—
48C3×D12—21no—
49C3×Dic6—21no—
50C3×Dic6—21no—
51#626—42no—
52C32×C8—21no—
53C3⋊(C3⋊C8)D412yescomplemented
54#465—91noSylow
55C2×C3×Q8—31no—
56C2×C3×D4—31no—
57C2×#67—61no—
58C2×D12—61no—
59C2×D12C2×D311yescharacteristic
60C2×C4×D3—31no—
61C2×C4×D3—31no—
62C2×C4×D3—61no—
63C2×Dic6C2×D311yescharacteristic
64C2×C3×C8—21no—
65C2×C3×C8C2×D311yescharacteristic
66C2×C3×C8C2×D311yescharacteristic
67C3×C4⋊C4—31no—
68C3×C4⋊C4—31no—
69#217—61no—
70#215—62no—
71#214—62no—
72(C2×D3)⋊C4—61no—
73(C2×D3)⋊C4—61no—
74(C2×D3)⋊C4—61no—
75C4⋊Dic3—61no—
76C4⋊Dic3C2×D311yescharacteristic
77C4⋊Dic3C2×D311yescharacteristic
78Dic3⋊C4—61no—
79C2×C3⋊C8—31no—
80C2×C3⋊C8—31no—
81C2×C3⋊C8—61no—
82D3×C8—62no—
83D3×C8—62no—
84D3×C8—64no—
85C22×C32C2×D411yescharacteristic
86C2×C3⋊D3—21no—
87C2×C3⋊D3—21no—
88C2×C3⋊D3SD1612yescomplemented
89C2×C3×D3—41no—
90C2×C3×D3—41no—
91C2×C3×D3—41no—
92C32×C4C2×D411yescharacteristic
93C32×C4#4111yescharacteristic
94C3⋊Dic3—21no—
95C3×Dic3—41no—
96C3×Dic3—41no—
97C3×Dic3—41no—
98C2×SD16—91no—
99C22×C8—91no—
100C22⋊Q8—91no—
101#121—91no—
102#106—91no—
103#103—31no—
104#102—31no—
105C23×C3—61no—
106C22×D3—21no—
107C22×D3—31no—
108C22×D3—31no—
109C22×D3—61no—
110C3×Q8—61no—
111C3×Q8—61no—
112C3×D4—61no—
113C3×D4—61no—
114C2×C3×C4—21no—
115C2×C3×C4—61no—
116C2×C3×C4—61no—
117C2×C3×C4—61no—
118C2×C3×C4C22×D311yescharacteristic
119C2×C3×C4C22×D311yescharacteristic
120#67—122no—
121C2×Dic3—21no—
122C2×Dic3—21no—
123C2×Dic3—21no—
124C2×Dic3—31no—
125C2×Dic3—31no—
126C2×Dic3—61no—
127D12—21no—
128D12—21no—
129D12—122no—
130C4×D3—62no—
131C4×D3—62no—
132C4×D3—61no—
133C4×D3—61no—
134C4×D3—61no—
135C4×D3—61no—
136Dic6—21no—
137Dic6—21no—
138C3×C8—22no—
139C3×C8—21no—
140C3×C8—21no—
141C3⋊C8—32no—
142C3⋊C8—32no—
143C3⋊C8—62no—
144C2×C32#12111yescharacteristic
145C2×C32C2×SD1611yescharacteristic
146C2×C32#13511yescharacteristic
147C3⋊D3—22no—
148C3×D3—81no—
149C2×Q8—31no—
150C2×D4—31no—
151C2×D4—181no—
152C22×C4—91no—
153SD16—182no—
154C2×C8—91no—
155C2×C8—182no—
156C2×C8D3211yescharacteristic
157C4⋊C4—31no—
158C4⋊C4—31no—
159C4⋊C4—181no—
160C22⋊C4—181no—
161C22⋊C4—181no—
162C22×C3—21no—
163C22×C3—121no—
164C22×C3—121no—
165C22×C3—121no—
166C22×C3D3×D411yescharacteristic
167C22×C3D3×D411yescharacteristic
168C2×D3—32no—
169C2×D3—32no—
170C2×D3—41no—
171C2×D3—41no—
172C2×D3—41no—
173C2×D3—62no—
174C2×D3—62no—
175C2×D3—62no—
176C2×D3—61no—
177C2×D3—61no—
178C2×D3—61no—
179C2×D3—61no—
180C3×C4—21no—
181C3×C4—21no—
182C3×C4—121no—
183C3×C4—121no—
184C3×C4—121no—
185C3×C4#23511yescharacteristic
186C3×C4#23511yescharacteristic
187C3×C4D3×D411yescharacteristic
188C3×C4D3×D411yescharacteristic
189Dic3—41no—
190Dic3—41no—
191Dic3—41no—
192Dic3—62no—
193Dic3—61no—
194Dic3—61no—
195C32#46511yescharacteristic, complemented, Sylow
196C23—61no—
197C23—91no—
198Q8—61no—
199Q8—61no—
200D4—61no—
201D4—61no—
202D4—362no—
203C2×C4—61no—
204C2×C4—61no—
205C2×C4—61no—
206C2×C4—91no—
207C2×C4—181no—
208C2×C4—181no—
209C2×C4C2×D3211yescharacteristic
210C8—21no—
211C8—92no—
212C2×C3—21no—
213C2×C3—21no—
214C2×C3—21no—
215C2×C3—241no—
216C2×C3#88411yescharacteristic
217C2×C3#88411yescharacteristic
218C2×C3#91211yescharacteristic
219C2×C3D3×SD1611yescharacteristic
220C2×C3D3×SD1611yescharacteristic
221C2×C3#91911yescharacteristic
222D3—64no—
223D3—62no—
224D3—62no—
225D3—81no—
226C22—92no—
227C22—121no—
228C22—121no—
229C22—121no—
230C22—181no—
231C22—181no—
232C22#380211yescharacteristic
233C4—121no—
234C4—121no—
235C4—121no—
236C4—181no—
237C4#379811yescharacteristic
238C4#381111yescharacteristic
239C3—21no—
240C3#477811yescharacteristic, complemented
241C3#480711yescharacteristic, complemented
242C2—182no—
243C2—241no—
244C2#6379611yescharacteristic
245C2#6381011yescharacteristic
246C2#6391211yescharacteristic
subgroupG/H
centerC22#3802
commutator, cosocleC2×C32×C4C23
FrattiniC2×C4C2×D32
FittingC2×C32×C8C22
socleC22×C32C2×D4
prime radical#63916C2
hypercenterC2×C8D32
hypocenterC32#465
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×C8

Complements

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

NH ≅ G/Ntype
1. C2×C8×C3⋊D3C2semidirect
3. #63871C2semidirect
4. C2×#3715C2semidirect
5. C3×#821C2semidirect
6. C3×#816C2semidirect
7. #63574C2semidirect
34. #821D3semidirect
35. #816D3semidirect
53. C3⋊(C3⋊C8)D4semidirect
88. C2×C3⋊D3SD16semidirect
195. C32#465semidirect
240. C3#4778semidirect
241. C3#4807semidirect

Maximal subgroups

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

subgroupindex
C2×C8×C3⋊D32
#639162
#638712
C2×#37152
C3×#8212
C3×#8162
#635742
#48073
#47783