Finite Group Databasebeta

← #10591187

Subgroups — #10591187

Order 576.

265 conjugacy classes of subgroups; only the 76 normal subgroups are shown.

normal subgroups only

This group has 265 conjugacy classes of subgroups — too many to draw. Only its 76 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×#924C211yesmaximal, characteristic
3C22×C3×C3⋊C8C211yesmaximal, characteristic
4C2×#3719C211yesmaximal, characteristic, complemented
5#63575C211yesmaximal, characteristic, complemented
6#63567C211yesmaximal, characteristic, complemented
7#63566C211yesmaximal, characteristic, complemented
8#5116—31nomaximal
9#5051—31nomaximal
10C22×C32×C4C2211yescharacteristic
11C2×#634C2211yescharacteristic
12C2×C3×Dic6C2211yescharacteristic
13#3757—21no—
14C4⋊(C3⋊Dic3)C2211yescharacteristic
15#3750—21no—
16C3×#217—21no—
17C3×C4⋊Dic3C2211yescharacteristic
18C3×Dic3⋊C4—21no—
19C2×C3×C3⋊C8—22no—
20C2×C3×C3⋊C8C2211yescharacteristic
21C2×C3×C3⋊C8C2211yescharacteristic
22#3719—22no—
23C22×C3×C8—31no—
24C3×C22⋊Q8—31no—
25C2×#216—31no—
26#924—31no—
27#924—31no—
28#924—61no—
29#924D311yescharacteristic
30C22×C3⋊C8D311yescharacteristic
31C2×Dic12—31no—
32#835—31no—
33#818—31no—
34#816—31no—
35#816—31no—
36#810—31no—
37#807—31no—
38C23×C32D411yescharacteristic
39C2×C32×C4—21no—
40C2×C32×C4—21no—
41C2×C32×C4D411yescharacteristic
42C2×C32×C4C2311yescharacteristic
43C2×C3⋊Dic3—21no—
44C2×C3⋊Dic3—21no—
45#634—21no—
46#634—21no—
47C2×C3×Dic3—21no—
48C2×C3×Dic3—21no—
49C3×Dic6—21no—
50C3×Dic6—21no—
51C3×C3⋊C8—21no—
52C3×C3⋊C8D412yes—
53#467—91noSylow
54C2×C3×Q8—31no—
55C22×C3×C4—21no—
56C22×C3×C4C2×D311yescharacteristic
57C22×C3×C4C2×D311yescharacteristic
58C2×Dic6—31no—
59C2×Dic6—31no—
60C2×Dic6—61no—
61C2×Dic6C2×D311yescharacteristic
62C2×C3×C8—31no—
63C2×C3×C8—31no—
64C2×C3×C8—62no—
65C3×C4⋊C4—31no—
66C3×C4⋊C4—61no—
67C3×C22⋊C4—61no—
68#217—21no—
69#217—62no—
70#217—61no—
71#217—61no—
72#216—62no—
73C4⋊Dic3—31no—
74C4⋊Dic3—31no—
75C4⋊Dic3—61no—
76C4⋊Dic3C2×D311yescharacteristic
77Dic3⋊C4—21no—
78Dic3⋊C4—62no—
79Dic3⋊C4—61no—
80Dic3⋊C4—61no—
81C2×C3⋊C8—22no—
82C2×C3⋊C8C2×D311yescharacteristic
83C2×C3⋊C8C2×D311yescharacteristic
84Dic12—62no—
85C22×C32—21no—
86C22×C32—21no—
87C22×C32Q1612yescomplemented
88C22×C32C2×D411yescharacteristic
89C32×C4—21no—
90C32×C4C2×D411yescharacteristic
91C32×C4#4111yescharacteristic
92C3⋊Dic3—41no—
93C3⋊Dic3—41no—
94C3×Dic3—41no—
95C3×Dic3—41no—
96C2×Q16—91no—
97C22×C8—31no—
98C22⋊Q8—31no—
99C22⋊Q8—91no—
100#107—91no—
101#103—91no—
102#103—91no—
103C23×C3—21no—
104C23×C3D1211yescharacteristic
105C23×C3#6711yescharacteristic
106C3×Q8—61no—
107C3×Q8—61no—
108C2×C3×C4—21no—
109C2×C3×C4—21no—
110C2×C3×C4—21no—
111C2×C3×C4—21no—
112C2×C3×C4—21no—
113C2×C3×C4—21no—
114C2×C3×C4—41no—
115C2×C3×C4—41no—
116C2×C3×C4—61no—
117C2×C3×C4—61no—
118C2×C3×C4D1211yescharacteristic
119C2×C3×C4#6711yescharacteristic
120C2×C3×C4C22×D311yescharacteristic
121C2×C3×C4C22×D311yescharacteristic
122C2×Dic3—21no—
123C2×Dic3—21no—
124C2×Dic3—62no—
125C2×Dic3—62no—
126C2×Dic3—61no—
127C2×Dic3—61no—
128C2×Dic3—61no—
129C2×Dic3—61no—
130Dic6—21no—
131Dic6—21no—
132Dic6—61no—
133Dic6—61no—
134Dic6—61no—
135Dic6—61no—
136Dic6—121no—
137Dic6—121no—
138C3×C8—32no—
139C3×C8—61no—
140C3⋊C8—21no—
141C3⋊C8#6712yes—
142C2×C32—22no—
143C2×C32#12111yescharacteristic
144C2×C32C2×Q1611yescharacteristic
145C2×C32#13511yescharacteristic
146C2×Q8—31no—
147C2×Q8—91no—
148C22×C4D3211yescharacteristic
149Q16—182no—
150C2×C8—31no—
151C2×C8—31no—
152C2×C8—62no—
153C4⋊C4—31no—
154C4⋊C4—61no—
155C4⋊C4—91no—
156C4⋊C4—181no—
157C22⋊C4—61no—
158C22⋊C4—181no—
159C22×C3—21no—
160C22×C3—21no—
161C22×C3—21no—
162C22×C3—21no—
163C22×C3—22no—
164C22×C3—21no—
165C22×C3—41no—
166C22×C3—41no—
167C22×C3Dic1212yescomplemented
168C22×C3#21612yescomplemented
169C22×C3C2×D1211yescharacteristic
170C22×C3C2×#6711yescharacteristic
171C3×C4—21no—
172C3×C4—21no—
173C3×C4—21no—
174C3×C4—21no—
175C3×C4—41no—
176C3×C4—121no—
177C3×C4—121no—
178C3×C4#23511yescharacteristic
179C3×C4D3×D411yescharacteristic
180C3×C4#23711yescharacteristic
181C3×C4C2×#6711yescharacteristic
182Dic3—41no—
183Dic3—41no—
184Dic3—122no—
185Dic3—122no—
186Dic3—121no—
187Dic3—121no—
188Dic3—121no—
189Dic3—121no—
190C32#46711yescharacteristic, complemented, Sylow
191C23#62611yescharacteristic
192Q8—61no—
193Q8—61no—
194Q8—181no—
195Q8—181no—
196C2×C4—21no—
197C2×C4—21no—
198C2×C4—61no—
199C2×C4—61no—
200C2×C4—181no—
201C2×C4—181no—
202C2×C4#62611yescharacteristic
203C2×C4C2×D3211yescharacteristic
204C8—32no—
205C8—61no—
206C2×C3—22no—
207C2×C3—22no—
208C2×C3—21no—
209C2×C3—21no—
210C2×C3—21no—
211C2×C3—42no—
212C2×C3#90411yescharacteristic
213C2×C3C2×Dic1211yescharacteristic
214C2×C3#93011yescharacteristic
215C2×C3#93911yescharacteristic
216C2×C3C2×#21611yescharacteristic
217C2×C3#95011yescharacteristic
218C22—21no—
219C22—21no—
220C22#371912yescomplemented
221C22C2×#62611yescharacteristic
222C4—21no—
223C4—121no—
224C4—121no—
225C4—361no—
226C4—361no—
227C4#380411yescharacteristic
228C4D3×#6711yescharacteristic
229C3—21no—
230C3#505111yescharacteristic, complemented
231C3#511611yescharacteristic, complemented
232C2—22no—
233C2#6382911yescharacteristic
234C2C2×#371911yescharacteristic
235C2#6397811yescharacteristic
subgroupG/H
centerC22C2×#626
commutator, cosocleC2×C32×C4C23
FrattiniC2×C4C2×D32
FittingC22×C32×C4C22
socleC22×C32C2×D4
prime radicalC23×C32D4
hypercenterC22×C4D32
hypocenterC32#467
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. C2×#3719C2semidirect
5. #63575C2semidirect
6. #63567C2semidirect
7. #63566C2semidirect
87. C22×C32Q16semidirect
167. C22×C3Dic12semidirect
168. C22×C3#216semidirect
190. C32#467semidirect
220. C22#3719semidirect
230. C3#5051semidirect
231. C3#5116semidirect

Maximal subgroups

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

subgroupindex
#641332
C3×#9242
C22×C3×C3⋊C82
C2×#37192
#635752
#635672
#635662
#51163
#50513