Finite Group Databasebeta

← #10590519

Subgroups — #10590519

Order 576.

210 conjugacy classes of subgroups; only the 60 normal subgroups are shown.

normal subgroups only

This group has 210 conjugacy classes of subgroups — too many to draw. Only its 60 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
1C3×#892C211yesmaximal, characteristic
2#63856C211yesmaximal, characteristic
3#63635C211yesmaximal, characteristic, complemented
4C3×#810C211yesmaximal, characteristic, complemented
5#63575C211yesmaximal, characteristic, complemented
6#63565C211yesmaximal, characteristic, complemented
7(C2×D3)⋊(C3⋊C8)C211yesmaximal, characteristic
8#4996—31nomaximal
9#4814—31nomaximal
10C2×C3×C4×D3C2211yescharacteristic
11C2×C3×Dic6C2211yescharacteristic
12C32×C4⋊C4C2211yescharacteristic
13C4⋊(C3⋊Dic3)C2211yescharacteristic
14C2×C3⋊(C3⋊C8)C2211yescharacteristic
15C3×(C2×D3)⋊C4—21no—
16C3×C4⋊Dic3C2211yescharacteristic
17C3×C4×Dic3—21no—
18C2×C3×C3⋊C8C2211yescharacteristic
19#3724—21no—
20(C2×D3)⋊Dic3—21no—
21C3×#117—31no—
22#946—31no—
23#924—31no—
24#892D311yescharacteristic
25C3×#103—31no—
26#835—31no—
27#830—31no—
28(C2×D3)⋊C8—31no—
29#818—31no—
30#810—31no—
31#810D311yescharacteristic, complemented
32#808—31no—
33#808—31no—
34#808—61no—
35#807—31no—
36C22×C3×D3D411yescharacteristic
37C2×C32×C4—21no—
38C2×C32×C4C2311yescharacteristic
39C2×C3⋊Dic3—21no—
40C2×C3×Dic3—21no—
41C2×C3×Dic3—21no—
42C2×C3×Dic3D411yescharacteristic
43C3×C4×D3—21no—
44C3×C4×D3—21no—
45C3×Dic6—21no—
46C3×Dic6—21no—
47C3⋊(C3⋊C8)—21no—
48C3×C3⋊C8—21no—
49#485—91noSylow
50C2×C3×Q8—31no—
51C22×C3×C4—31no—
52C2×C4×D3C2×D311yescharacteristic
53C2×Dic6C2×D311yescharacteristic
54C2×C3×C8—31no—
55C3×C4⋊C4—21no—
56C3×C4⋊C4—31no—
57C3×C4⋊C4C2×D311yescharacteristic
58C3×C4⋊C4C2×D311yescharacteristic
59C3×C22⋊C4—61no—
60C3×C42—61no—
61#217—61no—
62(C2×D3)⋊C4—21no—
63(C2×D3)⋊C4—61no—
64C4⋊Dic3—31no—
65C4⋊Dic3—31no—
66C4⋊Dic3—61no—
67C4⋊Dic3C2×D311yescharacteristic
68Dic3⋊C4—61no—
69Dic3⋊C4—61no—
70C4×Dic3—21no—
71C2×C3⋊C8—31no—
72C2×C3⋊C8—31no—
73C2×C3⋊C8—61no—
74C2×C3⋊C8C2×D311yescharacteristic
75C22×C32C2×D411yescharacteristic
76C2×C3×D3—21no—
77C2×C3×D3—21no—
78C2×C3×D3—21no—
79C32×C4—41no—
80C32×C4#4111yescharacteristic
81C32×C4#4111yescharacteristic
82C3⋊Dic3—41no—
83C3×Dic3—21no—
84C3×Dic3—41no—
85C3×Dic3—41no—
86C22⋊Q8—91no—
87#117—31no—
88#107—91no—
89#106—91no—
90#103—31no—
91#103—91no—
92C22⋊C8—91no—
93C23×C3—31no—
94C22×D3#6711yescharacteristic
95C3×Q8—61no—
96C3×Q8—61no—
97C2×C3×C4—21no—
98C2×C3×C4—21no—
99C2×C3×C4—21no—
100C2×C3×C4—31no—
101C2×C3×C4—41no—
102C2×C3×C4—61no—
103C2×C3×C4—61no—
104C2×C3×C4—61no—
105C2×C3×C4—61no—
106C2×C3×C4C22×D311yescharacteristic
107C2×C3×C4C22×D311yescharacteristic
108C2×Dic3—21no—
109C2×Dic3—21no—
110C2×Dic3—61no—
111C2×Dic3—61no—
112C2×Dic3—121no—
113C2×Dic3#6711yescharacteristic
114C4×D3—21no—
115C4×D3—21no—
116Dic6—21no—
117Dic6—21no—
118C3×C8—61no—
119C3⋊C8—21no—
120C3⋊C8—62no—
121C3⋊C8—61no—
122C3⋊C8—61no—
123C2×C32#12311yescharacteristic
124C2×C32#13511yescharacteristic
125C2×C32#13711yescharacteristic
126C3×D3—41no—
127C2×Q8—31no—
128C22×C4—31no—
129C2×C8—31no—
130C2×C8—91no—
131C4⋊C4—31no—
132C4⋊C4—91no—
133C4⋊C4—181no—
134C4⋊C4D3211yescharacteristic
135C22⋊C4—61no—
136C22⋊C4—181no—
137C42—61no—
138C22×C3—21no—
139C22×C3—61no—
140C22×C3—61no—
141C22×C3—61no—
142C22×C3D3×D411yescharacteristic
143C22×C3C2×#6711yescharacteristic
144C2×D3—21no—
145C2×D3—21no—
146C2×D3—21no—
147C3×C4—21no—
148C3×C4—21no—
149C3×C4—41no—
150C3×C4—41no—
151C3×C4—61no—
152C3×C4—81no—
153C3×C4—121no—
154C3×C4—121no—
155C3×C4#23511yescharacteristic
156C3×C4#23511yescharacteristic
157C3×C4#23511yescharacteristic
158C3×C4#23711yescharacteristic
159Dic3—21no—
160Dic3—41no—
161Dic3—41no—
162Dic3—121no—
163Dic3—121no—
164Dic3—241no—
165C32#48511yescharacteristic, complemented, Sylow
166C23—31no—
167Q8—61no—
168Q8—61no—
169C2×C4—21no—
170C2×C4—31no—
171C2×C4—61no—
172C2×C4—61no—
173C2×C4—61no—
174C2×C4—61no—
175C2×C4—181no—
176C2×C4C2×D3211yescharacteristic
177C8—61no—
178C8—181no—
179C2×C3—21no—
180C2×C3—21no—
181C2×C3—21no—
182C2×C3—121no—
183C2×C3#88311yescharacteristic
184C2×C3#91511yescharacteristic
185C2×C3#91911yescharacteristic
186C2×C3#92911yescharacteristic
187C2×C3#95011yescharacteristic
188C2×C3#95111yescharacteristic
189D3—41no—
190C22—61no—
191C22—61no—
192C22—61no—
193C22D3×#6711yescharacteristic
194C4—41no—
195C4—61no—
196C4—121no—
197C4—121no—
198C4—361no—
199C4#379511yescharacteristic
200C4#379811yescharacteristic
201C3—21no—
202C3#481411yescharacteristic, complemented
203C3#499611yescharacteristic, complemented
204C2—121no—
205C2#6390511yescharacteristic
206C2#6392911yescharacteristic
207C2#6394911yescharacteristic
subgroupG/H
centerC22D3×#67
commutator, cosocleC2×C32×C4C23
FrattiniC2×C4C2×D32
FittingC32×C4⋊C4C22
socleC22×C32C2×D4
prime radicalC22×C3×D3D4
hypercenterC4⋊C4D32
hypocenterC32#485
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
3. #63635C2semidirect
4. C3×#810C2semidirect
5. #63575C2semidirect
6. #63565C2semidirect
31. #810D3semidirect
165. C32#485semidirect
202. C3#4814semidirect
203. C3#4996semidirect

Maximal subgroups

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

subgroupindex
C3×#8922
#638562
#636352
C3×#8102
#635752
#635652
(C2×D3)⋊(C3⋊C8)2
#49963
#48143