Finite Group Databasebeta

← #10591134

Subgroups — #10591134

Order 576.

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

normal subgroups only

This group has 229 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#64133C211yesmaximal, characteristic
2C3×#926C211yesmaximal, characteristic
3C3×#830C211yesmaximal, characteristic
4#63575C211yesmaximal, characteristic, complemented
5#63573C211yesmaximal, characteristic, complemented
6#63567C211yesmaximal, characteristic, complemented
7#63567C211yesmaximal, characteristic, complemented
8#4996—31nomaximal
9#4723—31nomaximal
10C22×C32×C4C2211yescharacteristic
11C2×#634C2211yescharacteristic
12#3757—21no—
13C4⋊(C3⋊Dic3)C2211yescharacteristic
14#3750—21no—
15C3×#217—21no—
16C3×C4⋊Dic3C2211yescharacteristic
17C3×C4⋊Dic3C2211yescharacteristic
18C3×C4×Dic3—21no—
19C2×C3×C3⋊C8C2211yescharacteristic
20C2×C3×C3⋊C8C2211yescharacteristic
21C3×#117—31no—
22#926D311yescharacteristic
23#924—31no—
24#924—31no—
25#924—61no—
26C3×C22⋊C8—31no—
27#830D311yescharacteristic
28#818—31no—
29#817—31no—
30#816—31no—
31#816—31no—
32#810—31no—
33#810—31no—
34#808—31no—
35#807—31no—
36C23×C32D411yescharacteristic
37C2×C32×C4—21no—
38C2×C32×C4—21no—
39C2×C32×C4D411yescharacteristic
40C2×C32×C4C2311yescharacteristic
41C2×C3⋊Dic3—21no—
42C2×C3⋊Dic3—21no—
43#634—21no—
44#634—21no—
45C2×C3×Dic3—21no—
46C2×C3×Dic3—21no—
47C3×C3⋊C8—21no—
48C3×C3⋊C8—21no—
49#485—91noSylow
50C22×C3×C4—21no—
51C22×C3×C4C2×D311yescharacteristic
52C22×C3×C4C2×D311yescharacteristic
53C2×Dic6—31no—
54C2×Dic6—31no—
55C2×Dic6—61no—
56C2×C3×C8—31no—
57C2×C3×C8—31no—
58C3×C4⋊C4—31no—
59C3×C4⋊C4—31no—
60C3×C22⋊C4—61no—
61C3×C42—61no—
62#217—21no—
63#217—62no—
64#217—61no—
65#217—61no—
66C4⋊Dic3—31no—
67C4⋊Dic3—31no—
68C4⋊Dic3—61no—
69C4⋊Dic3C2×D311yescharacteristic
70C4⋊Dic3C2×D311yescharacteristic
71Dic3⋊C4—62no—
72Dic3⋊C4—61no—
73Dic3⋊C4—61no—
74C4×Dic3—21no—
75C2×C3⋊C8C2×D311yescharacteristic
76C2×C3⋊C8C2×D311yescharacteristic
77C22×C32—21no—
78C22×C32—21no—
79C22×C32—21no—
80C22×C32C2×D411yescharacteristic
81C32×C4—21no—
82C32×C4#4111yescharacteristic
83C32×C4#4111yescharacteristic
84C3⋊Dic3—41no—
85C3⋊Dic3—41no—
86C3×Dic3—41no—
87C3×Dic3—41no—
88C22⋊Q8—91no—
89#117—31no—
90#107—91no—
91#106—91no—
92#103—91no—
93#103—91no—
94C22⋊C8—31no—
95C23×C3—21no—
96C23×C3D1211yescharacteristic
97C23×C3#6711yescharacteristic
98C2×C3×C4—21no—
99C2×C3×C4—21no—
100C2×C3×C4—21no—
101C2×C3×C4—21no—
102C2×C3×C4—21no—
103C2×C3×C4—21no—
104C2×C3×C4—41no—
105C2×C3×C4—41no—
106C2×C3×C4—61no—
107C2×C3×C4—61no—
108C2×C3×C4D1211yescharacteristic
109C2×C3×C4#6711yescharacteristic
110C2×C3×C4C22×D311yescharacteristic
111C2×C3×C4C22×D311yescharacteristic
112C2×Dic3—21no—
113C2×Dic3—21no—
114C2×Dic3—62no—
115C2×Dic3—62no—
116C2×Dic3—61no—
117C2×Dic3—61no—
118C2×Dic3—61no—
119C2×Dic3—61no—
120Dic6—61no—
121Dic6—61no—
122Dic6—61no—
123Dic6—61no—
124Dic6—121no—
125Dic6—121no—
126C3×C8—61no—
127C3×C8—61no—
128C3⋊C8—21no—
129C3⋊C8—21no—
130C2×C32—41no—
131C2×C32#12311yescharacteristic
132C2×C32#13511yescharacteristic
133C2×C32#13711yescharacteristic
134C2×Q8—91no—
135C22×C4D3211yescharacteristic
136C2×C8—31no—
137C2×C8—31no—
138C4⋊C4—31no—
139C4⋊C4—31no—
140C4⋊C4—91no—
141C4⋊C4—181no—
142C22⋊C4—61no—
143C22⋊C4—181no—
144C42—61no—
145C22×C3—22no—
146C22×C3—21no—
147C22×C3—21no—
148C22×C3—21no—
149C22×C3—21no—
150C22×C3—21no—
151C22×C3—21no—
152C22×C3—21no—
153C22×C3—41no—
154C22×C3—41no—
155C22×C3C2×D1211yescharacteristic
156C22×C3C2×#6711yescharacteristic
157C3×C4—21no—
158C3×C4—21no—
159C3×C4—21no—
160C3×C4—21no—
161C3×C4—41no—
162C3×C4—121no—
163C3×C4—121no—
164C3×C4#23511yescharacteristic
165C3×C4#23511yescharacteristic
166C3×C4#23711yescharacteristic
167C3×C4#23711yescharacteristic
168Dic3—41no—
169Dic3—41no—
170Dic3—122no—
171Dic3—122no—
172Dic3—121no—
173Dic3—121no—
174Dic3—121no—
175Dic3—121no—
176C32#48511yescharacteristic, complemented, Sylow
177C23#62611yescharacteristic
178Q8—181no—
179Q8—181no—
180C2×C4—21no—
181C2×C4—21no—
182C2×C4—61no—
183C2×C4—61no—
184C2×C4—181no—
185C2×C4—181no—
186C2×C4#62611yescharacteristic
187C2×C4C2×D3211yescharacteristic
188C8—61no—
189C8—61no—
190C2×C3—21no—
191C2×C3—21no—
192C2×C3—21no—
193C2×C3—42no—
194C2×C3—41no—
195C2×C3—41no—
196C2×C3#88611yescharacteristic
197C2×C3#90411yescharacteristic
198C2×C3#90911yescharacteristic
199C2×C3#92911yescharacteristic
200C2×C3#95011yescharacteristic
201C2×C3#95111yescharacteristic
202C22—21no—
203C22—21no—
204C22—21no—
205C22C2×#62611yescharacteristic
206C4—21no—
207C4—121no—
208C4—121no—
209C4—361no—
210C4—361no—
211C4#380411yescharacteristic
212C4#380411yescharacteristic
213C3—21no—
214C3#472311yescharacteristic, complemented
215C3#499611yescharacteristic, complemented
216C2—41no—
217C2#6382911yescharacteristic
218C2#6383111yescharacteristic
219C2#6396611yescharacteristic
subgroupG/H
centerC22C2×#626
commutator, cosocleC2×C32×C4C23
FrattiniC2×C4C2×D32
FittingC22×C32×C4C22
socleC22×C32C2×D4
prime radicalC23×C32D4
hypercenterC22×C4D32
hypocenterC32#485
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4

Complements

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

NH ≅ G/Ntype
4. #63575C2semidirect
5. #63573C2semidirect
6. #63567C2semidirect
7. #63567C2semidirect
176. C32#485semidirect
214. C3#4723semidirect
215. C3#4996semidirect

Maximal subgroups

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

subgroupindex
#641332
C3×#9262
C3×#8302
#635752
#635732
#635672
#49963
#47233