Finite Group Databasebeta

← #10594963

Subgroups — #10594963

Order 576.

522 conjugacy classes of subgroups; only the 132 normal subgroups are shown.

normal subgroups only

This group has 522 conjugacy classes of subgroups — too many to draw. Only its 132 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×C4×C3⋊Dic3C211yesmaximal, characteristic, complemented
2C3×#929C212yesmaximal, complemented
3#63982C211yesmaximal, characteristic, complemented
4#63980C211yesmaximal, characteristic
5#67⋊Dic3C212yesmaximal, complemented
6#63915C211yesmaximal, characteristic, complemented
7#63902C211yesmaximal, characteristic, complemented
8#63878C212yesmaximal, complemented
9#63870C211yesmaximal, characteristic, complemented
10#63862C212yesmaximal, complemented
11#63838C211yesmaximal, characteristic, complemented
12#5649—32nomaximal
13C22×C32×C4C2211yescharacteristic
14C22×C3⋊Dic3C2211yescharacteristic
15C22×C3⋊Dic3C2211yescharacteristic
16C2×C3×#67C2212yes—
17C2×#627C2211yescharacteristic
18C2×#625C2211yescharacteristic
19C2×D3×Dic3C2212yes—
20C4×C3⋊Dic3C2211yescharacteristic
21C4×C3⋊Dic3C2211yescharacteristic
22C4×C3⋊Dic3C2211yescharacteristic
23C4×C3⋊Dic3C2211yescharacteristic
24C3×#217C2212yes—
25C3×(C2×D3)⋊C4C2212yes—
26C3×(C2×D3)⋊C4C2212yes—
27C3×Dic3⋊C4C2212yes—
28C3×Dic3⋊C4C2212yes—
29#3724C2211yescharacteristic
30#3724C2211yescharacteristic
31Dic3⋊Dic3C2212yes—
32Dic3⋊Dic3C2212yes—
33(C2×D3)⋊Dic3C2212yes—
34(C2×D3)⋊Dic3C2212yes—
35Dic32C2212yes—
36C3×#123—32no—
37#939—32no—
38D4×Dic3—32no—
39#929D312yescomplemented
40C2×C4×Dic3—32no—
41C2×C4×Dic3—61no—
42#898—32no—
43#892—32no—
44#889—32no—
45#887—32no—
46#885—32no—
47#67⋊C4—32no—
48#67⋊C4—32no—
49#879—32no—
50#878—32no—
51#877—32no—
52C23×C32C2311yescharacteristic
53C22×C3×D3C2312yes—
54C2×C32×C4—22no—
55C2×C32×C4C2311yescharacteristic
56C2×C32×C4C2311yescharacteristic
57C2×C3⋊Dic3—22no—
58C2×C3⋊Dic3—22no—
59C2×C3⋊Dic3C2311yescharacteristic
60C2×C3⋊Dic3C2311yescharacteristic
61C2×C3⋊Dic3C2311yescharacteristic
62C2×C3⋊Dic3C2311yescharacteristic
63C3×#67—24no—
64C2×C3×Dic3C2312yes—
65C2×C3×Dic3C2312yes—
66C2×C3×Dic3C2312yes—
67#627—22no—
68#625—22no—
69D3×Dic3—24no—
70#529—91noSylow
71C2×C3×D4—32no—
72C22×C3×C4—21no—
73C22×C3×C4C2×D312yes—
74C2×#67—32no—
75C2×#67C2×D312yes—
76C22×Dic3—32no—
77C22×Dic3—32no—
78C22×Dic3—32no—
79C22×Dic3—61no—
80C22×Dic3—61no—
81C2×C4×D3—32no—
82C2×Dic6—32no—
83C3×C4⋊C4—32no—
84C3×C4⋊C4—32no—
85C3×C22⋊C4—32no—
86C3×C22⋊C4—32no—
87C3×C22⋊C4—32no—
88#217—32no—
89#217—32no—
90#217C2×D312yes—
91(C2×D3)⋊C4—32no—
92(C2×D3)⋊C4—32no—
93(C2×D3)⋊C4C2×D312yes—
94(C2×D3)⋊C4C2×D312yes—
95C4⋊Dic3—32no—
96C4⋊Dic3—32no—
97Dic3⋊C4—32no—
98Dic3⋊C4—32no—
99Dic3⋊C4—32no—
100Dic3⋊C4—32no—
101Dic3⋊C4C2×D312yes—
102Dic3⋊C4C2×D312yes—
103C4×Dic3—32no—
104C4×Dic3—32no—
105C4×Dic3—32no—
106C4×Dic3—32no—
107C4×Dic3—32no—
108C4×Dic3—32no—
109C4×Dic3—61no—
110C4×Dic3—61no—
111C4×Dic3—61no—
112C4×Dic3—61no—
113C22×C32—21no—
114C22×C32—21no—
115C22×C32#4112yes—
116C22×C32C2411yescharacteristic
117C2×C3×D3—22no—
118C2×C3×D3—22no—
119C2×C3×D3—22no—
120C32×C4—21no—
121C32×C4—21no—
122C3⋊Dic3—21no—
123C3⋊Dic3—21no—
124C3⋊Dic3#4112yes—
125C3⋊Dic3#4112yes—
126C3×Dic3—22no—
127C3×Dic3—22no—
128C3×Dic3—22no—
129#126—92no—
130#125—91no—
131#124—91no—
132#123—32no—
133C22⋊Q8—91no—
134#121—91no—
135C4×Q8—91no—
136C4×D4—91no—
137C4×D4—92no—
138#117—92no—
139C2×C42—91no—
140C23×C3—21no—
141C23×C3—32no—
142C23×C3C22×D312yes—
143C22×D3C22×D312yes—
144C3×D4—64no—
145C2×C3×C4—24no—
146C2×C3×C4—24no—
147C2×C3×C4—21no—
148C2×C3×C4—21no—
149C2×C3×C4—32no—
150C2×C3×C4—32no—
151C2×C3×C4—32no—
152C2×C3×C4C22×D312yes—
153C2×C3×C4C22×D312yes—
154#67—24no—
155#67—64no—
156C2×Dic3—32no—
157C2×Dic3—32no—
158C2×Dic3—32no—
159C2×Dic3—32no—
160C2×Dic3—61no—
161C2×Dic3—61no—
162C2×Dic3—61no—
163C2×Dic3—61no—
164C2×Dic3—64no—
165C2×Dic3—64no—
166C2×Dic3—64no—
167C2×Dic3—64no—
168C2×Dic3—64no—
169C2×Dic3C22×D312yes—
170C2×Dic3C22×D312yes—
171C2×Dic3C22×D312yes—
172C4×D3—64no—
173Dic6—64no—
174C2×C32—22no—
175C2×C32C2×#4111yescharacteristic
176C2×C32C2×#4111yescharacteristic
177C2×C32C2×#4111yescharacteristic
178C3×D3—42no—
179C2×Q8—91no—
180C2×D4—32no—
181C2×D4—91no—
182C22×C4—92no—
183C22×C4—91no—
184C22×C4—91no—
185C22×C4D3211yescharacteristic
186C4⋊C4—32no—
187C4⋊C4—32no—
188C4⋊C4—92no—
189C4⋊C4—91no—
190C4⋊C4—92no—
191C4⋊C4—91no—
192C22⋊C4—32no—
193C22⋊C4—32no—
194C22⋊C4—32no—
195C22⋊C4—92no—
196C22⋊C4—92no—
197C42—92no—
198C42—91no—
199C42—91no—
200C42—91no—
201C42—91no—
202C22×C3—22no—
203C22×C3—22no—
204C22×C3—22no—
205C22×C3—22no—
206C22×C3—21no—
207C22×C3—22no—
208C22×C3—62no—
209C22×C3—62no—
210C22×C3—62no—
211C22×C3#23714yes—
212C22×C3C23×D312yes—
213C2×D3—22no—
214C2×D3—22no—
215C2×D3—22no—
216C3×C4—22no—
217C3×C4—22no—
218C3×C4—22no—
219C3×C4—22no—
220C3×C4—62no—
221C3×C4—62no—
222C3×C4—62no—
223Dic3—22no—
224Dic3—22no—
225Dic3—22no—
226Dic3—34no—
227Dic3—34no—
228Dic3—62no—
229Dic3—62no—
230Dic3—62no—
231Dic3—62no—
232Dic3—62no—
233Dic3—62no—
234C32#52911yescharacteristic, complemented, Sylow
235C23—32no—
236C23C2×D3211yescharacteristic
237Q8—182no—
238D4—64no—
239D4—182no—
240C2×C4—22no—
241C2×C4—32no—
242C2×C4—32no—
243C2×C4—32no—
244C2×C4—91no—
245C2×C4—91no—
246C2×C4—91no—
247C2×C4—91no—
248C2×C4—184no—
249C2×C4—182no—
250C2×C4—182no—
251C2×C4C2×D3211yescharacteristic
252C2×C4C2×D3211yescharacteristic
253C2×C3—24no—
254C2×C3—24no—
255C2×C3—21no—
256C2×C3—21no—
257C2×C3—21no—
258C2×C3—122no—
259C2×C3C2×#23712yes—
260C2×C3D3×#4112yes—
261C2×C3D3×#4112yes—
262D3—42no—
263C22—21no—
264C22—21no—
265C22—62no—
266C22—62no—
267C22—62no—
268C22#380512yes—
269C22C22×D3211yescharacteristic
270C4—21no—
271C4—21no—
272C4—62no—
273C4—62no—
274C4—62no—
275C4—92no—
276C4—92no—
277C4—181no—
278C4—181no—
279C3—21no—
280C3#564912yescomplemented
281C2—22no—
282C2—122no—
283C2#6430611yescharacteristic
284C2#6430611yescharacteristic
285C2C2×#380511yescharacteristic
subgroupG/H
center, FrattiniC22C22×D32
commutator, socle, cosocleC22×C32C24
FittingC22×C32×C4C22
prime radical#63980C2
hypercenterC22×C4D32
hypocenterC32#529
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4

Complements

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

NH ≅ G/Ntype
1. C2×C4×C3⋊Dic3C2semidirect
2. C3×#929C2semidirect
3. #63982C2semidirect
5. #67⋊Dic3C2semidirect
6. #63915C2semidirect
7. #63902C2semidirect
8. #63878C2semidirect
9. #63870C2semidirect
10. #63862C2semidirect
11. #63838C2semidirect
39. #929D3semidirect
234. C32#529semidirect
280. C3#5649semidirect

Maximal subgroups

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

subgroupindex
C2×C4×C3⋊Dic32
C3×#9292
#639822
#639802
#67⋊Dic32
#639152
#639022
#638782
#638702
#638622
#638382
#56493