Finite Group Databasebeta

← #10595120

Subgroups — #10595120

Order 576.

475 conjugacy classes of subgroups; only the 130 normal subgroups are shown.

normal subgroups only

This group has 475 conjugacy classes of subgroups — too many to draw. Only its 130 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
1D4×C3⋊Dic3C211yesmaximal, characteristic
2C3×#935C212yesmaximal
3#63982C211yesmaximal, characteristic, complemented
4#63982C211yesmaximal, characteristic, complemented
5C2×#3724C211yesmaximal, characteristic, complemented
6#63957C211yesmaximal, characteristic, complemented
7#63956C212yesmaximal, complemented
8#63955C212yesmaximal, complemented
9#63870C211yesmaximal, characteristic, complemented
10#63845C212yesmaximal, complemented
11#63838C211yesmaximal, characteristic, complemented
12#5650—32nomaximal
13C2×C32×D4C2211yescharacteristic
14C22×C3⋊Dic3C2211yescharacteristic
15C22×C3⋊Dic3C2211yescharacteristic
16C22×C3×Dic3C2212yes—
17C2×#627C2211yescharacteristic
18#3757C2211yescharacteristic
19#3757C2211yescharacteristic
20C4⋊(C3⋊Dic3)C2211yescharacteristic
21C4×C3⋊Dic3C2211yescharacteristic
22C3×#217C2212yes—
23C3×#217C2212yes—
24C3×#217C2212yes—
25C3×Dic3⋊C4C2212yes—
26C3×Dic3⋊C4C2212yes—
27#3724C2211yescharacteristic
28#3724C2212yes—
29#3724C2211yescharacteristic
30#3724C2211yescharacteristic
31Dic3⋊Dic3C2212yes—
32Dic3⋊Dic3C2212yes—
33Dic3⋊Dic3C2212yes—
34Dic32C2212yes—
35Dic32C2212yes—
36C3×#123—32no—
37#935D312yes—
38D4×Dic3—32no—
39D4×Dic3—61no—
40#926—32no—
41C2×Dic3⋊C4—32no—
42#890—32no—
43#889—32no—
44#889—32no—
45#887—32no—
46#879—32no—
47#879—32no—
48#878—32no—
49#878—32no—
50#877—32no—
51#877—32no—
52C23×C32C2311yescharacteristic
53C23×C32C2311yescharacteristic
54C32×D4—22no—
55C2×C32×C4C2311yescharacteristic
56C2×C3⋊Dic3—22no—
57C2×C3⋊Dic3—22no—
58C2×C3⋊Dic3C2311yescharacteristic
59C2×C3⋊Dic3C2311yescharacteristic
60C2×C3⋊Dic3C2311yescharacteristic
61C2×C3⋊Dic3C2311yescharacteristic
62C2×C3×Dic3—24no—
63C2×C3×Dic3C2312yes—
64C2×C3×Dic3C2312yes—
65C2×C3×Dic3C2312yes—
66C2×C3×Dic3C2312yes—
67#627—22no—
68#552—91noSylow
69C2×C3×D4—21no—
70C2×C3×D4C2×D312yes—
71C22×C3×C4—32no—
72C22×Dic3—32no—
73C22×Dic3—32no—
74C22×Dic3—61no—
75C22×Dic3—61no—
76C22×Dic3C2×D312yes—
77C2×Dic6—32no—
78C3×C4⋊C4—32no—
79C3×C4⋊C4—32no—
80C3×C22⋊C4—32no—
81C3×C22⋊C4—32no—
82C3×C22⋊C4—32no—
83#217—32no—
84#217—32no—
85#217—61no—
86#217—61no—
87#217C2×D312yes—
88#217C2×D312yes—
89#217C2×D312yes—
90C4⋊Dic3—32no—
91C4⋊Dic3—32no—
92C4⋊Dic3—32no—
93C4⋊Dic3—32no—
94C4⋊Dic3—61no—
95Dic3⋊C4—32no—
96Dic3⋊C4—32no—
97Dic3⋊C4—32no—
98Dic3⋊C4—32no—
99Dic3⋊C4—32no—
100Dic3⋊C4—32no—
101Dic3⋊C4—32no—
102Dic3⋊C4—32no—
103Dic3⋊C4C2×D312yes—
104Dic3⋊C4C2×D312yes—
105C4×Dic3—32no—
106C4×Dic3—32no—
107C4×Dic3—32no—
108C4×Dic3—32no—
109C4×Dic3—32no—
110C4×Dic3—61no—
111C22×C32—21no—
112C22×C32—21no—
113C22×C32—21no—
114C22×C32—21no—
115C22×C32—21no—
116C22×C32#4112yes—
117C22×C32C2411yescharacteristic
118C32×C4—21no—
119C3⋊Dic3—21no—
120C3⋊Dic3—21no—
121C3⋊Dic3—21no—
122C3⋊Dic3#4112yes—
123C3×Dic3—22no—
124C3×Dic3—22no—
125C3×Dic3—22no—
126C3×Dic3—22no—
127#126—92no—
128#125—91no—
129#125—92no—
130#123—32no—
131C22⋊Q8—91no—
132C22⋊Q8—91no—
133C4×Q8—91no—
134C4×D4—91no—
135#117—91no—
136#117—92no—
137C2×C4⋊C4—91no—
138C23×C3—21no—
139C23×C3—21no—
140C23×C3C22×D312yes—
141C23×C3C22×D312yes—
142C3×D4—24no—
143C3×D4—24no—
144C2×C3×C4—21no—
145C2×C3×C4—32no—
146C2×C3×C4—32no—
147C2×C3×C4—32no—
148C2×C3×C4—32no—
149C2×C3×C4—64no—
150C2×C3×C4C22×D312yes—
151C2×Dic3—24no—
152C2×Dic3—32no—
153C2×Dic3—32no—
154C2×Dic3—32no—
155C2×Dic3—32no—
156C2×Dic3—61no—
157C2×Dic3—61no—
158C2×Dic3—61no—
159C2×Dic3—61no—
160C2×Dic3—64no—
161C2×Dic3—64no—
162C2×Dic3—122no—
163C2×Dic3—122no—
164C2×Dic3C22×D312yes—
165C2×Dic3C22×D312yes—
166C2×Dic3C22×D312yes—
167C2×Dic3C22×D312yes—
168Dic6—64no—
169C2×C32—22no—
170C2×C32—41no—
171C2×C32C2×#4111yescharacteristic
172C2×C32C2×#4111yescharacteristic
173C2×C322−1+411yescharacteristic
174C2×Q8—91no—
175C2×D4D3211yescharacteristic
176C22×C4—32no—
177C22×C4—91no—
178C22×C4—91no—
179C4⋊C4—32no—
180C4⋊C4—32no—
181C4⋊C4—91no—
182C4⋊C4—91no—
183C4⋊C4—92no—
184C4⋊C4—91no—
185C4⋊C4—92no—
186C4⋊C4—92no—
187C4⋊C4—92no—
188C4⋊C4—91no—
189C22⋊C4—32no—
190C22⋊C4—32no—
191C22⋊C4—32no—
192C22⋊C4—91no—
193C22⋊C4—91no—
194C42—92no—
195C42—92no—
196C42—91no—
197C22×C3—22no—
198C22×C3—22no—
199C22×C3—22no—
200C22×C3—22no—
201C22×C3—22no—
202C22×C3—22no—
203C22×C3—21no—
204C22×C3—22no—
205C22×C3—41no—
206C22×C3—41no—
207C22×C3—41no—
208C22×C3—41no—
209C22×C3#23714yes—
210C22×C3C23×D312yes—
211C3×C4—22no—
212C3×C4—22no—
213C3×C4—62no—
214C3×C4—62no—
215C3×C4—62no—
216C3×C4—62no—
217Dic3—22no—
218Dic3—22no—
219Dic3—22no—
220Dic3—22no—
221Dic3—34no—
222Dic3—62no—
223Dic3—62no—
224Dic3—62no—
225Dic3—62no—
226Dic3—121no—
227Dic3—121no—
228Dic3—121no—
229C32#55211yescharacteristic, complemented, Sylow
230C23C2×D3211yescharacteristic
231C23C2×D3211yescharacteristic
232Q8—182no—
233D4—22no—
234C2×C4—32no—
235C2×C4—32no—
236C2×C4—32no—
237C2×C4—32no—
238C2×C4—64no—
239C2×C4—91no—
240C2×C4—91no—
241C2×C4—91no—
242C2×C4—91no—
243C2×C4—182no—
244C2×C4—182no—
245C2×C4C2×D3211yescharacteristic
246C2×C3—24no—
247C2×C3—21no—
248C2×C3—21no—
249C2×C3—21no—
250C2×C3—42no—
251C2×C3—42no—
252C2×C3—42no—
253C2×C3C2×#23712yes—
254C2×C3D3×#4112yes—
255C2×C3#101012yes—
256C22—21no—
257C22—21no—
258C22—21no—
259C22—21no—
260C22—21no—
261C22#380512yes—
262C22C22×D3211yescharacteristic
263C4—21no—
264C4—62no—
265C4—62no—
266C4—62no—
267C4—62no—
268C4—92no—
269C4—181no—
270C4—181no—
271C4—181no—
272C3—21no—
273C3#565012yescomplemented
274C2—22no—
275C2—41no—
276C2#6430911yescharacteristic
277C2#6431211yescharacteristic
278C2C2×#380511yescharacteristic
subgroupG/H
center, FrattiniC22C22×D32
commutator, socle, cosocleC22×C32C24
Fitting, prime radicalC2×C32×D4C22
hypercenterC2×D4D32
hypocenterC32#552
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×D4

Complements

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

NH ≅ G/Ntype
3. #63982C2semidirect
4. #63982C2semidirect
5. C2×#3724C2semidirect
6. #63957C2semidirect
7. #63956C2semidirect
8. #63955C2semidirect
9. #63870C2semidirect
10. #63845C2semidirect
11. #63838C2semidirect
229. C32#552semidirect
273. C3#5650semidirect

Maximal subgroups

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

subgroupindex
D4×C3⋊Dic32
C3×#9352
#639822
C2×#37242
#639572
#639562
#639552
#638702
#638452
#638382
#56503