Finite Group Databasebeta

← C22×#10619530 #72268911

Subgroups — C22×#10619530 #72268911

Order 2592.

1531 conjugacy classes of subgroups; only the 250 normal subgroups are shown.

normal subgroups only

This group has 1531 conjugacy classes of subgroups — too many to draw. Only its 250 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
1C23×C9⋊D9C211yesmaximal, characteristic, complemented
2C23×C9×D9C211yesmaximal, characteristic, complemented
3C22×C9×Dic9C211yesmaximal, characteristic, complemented
4C2×#10619530C2112yesmaximal, direct product factor
5C22×#6195—31nomaximal
6C22×#6192—31nomaximal
7C23×C92C2211yescharacteristic
8C22×C9⋊D9—24no—
9C22×C9⋊D9C2216yescomplemented
10C22×C9×D9—24no—
11C22×C9×D9C2216yescomplemented
12C2×C9×Dic9C2216yescomplemented
13#10619530C22116yesdirect product factor
14C23×C3⋊D9—31no—
15C23×C3⋊D9—31no—
16C23×C3⋊D9—61no—
17C23×D3×C9—31no—
18C23×C3×D9D311yescharacteristic
19C22×C9×Dic3—31no—
20C22×C3×Dic9D311yescharacteristic
21C2×#6195—312no—
22C2×#6192—312no—
23C22×C92D414yescomplemented
24C22×C92C2313yes—
25C2×C9⋊D9—212no—
26C2×C9⋊D9C2314yescomplemented
27C2×C9×D9—212no—
28C2×C9×D9C2314yescomplemented
29C9×Dic9C2314yescomplemented
30C22×#626—91no—
31C22×#611—91no—
32C22×D36—91no—
33C23×C3×C9—21no—
34C23×C3×C9C2×D311yescharacteristic
35C23×C3×C9C2×D311yescharacteristic
36C22×C3⋊D9—36no—
37C22×C3⋊D9—36no—
38C22×C3⋊D9—66no—
39C22×C3⋊D9—68no—
40C22×C3⋊D9—64no—
41C22×C3⋊D9—64no—
42C22×D3×C9—36no—
43C22×D3×C9—64no—
44C22×C3×D9—24no—
45C22×C3×D9C2×D316yes—
46C2×C9×Dic3—36no—
47C2×C3×Dic9C2×D316yes—
48#6195—316no—
49#6192—316no—
50C2×C92C2×D416yescomplemented
51C2×C92C2411yescharacteristic
52C9⋊D9—24no—
53C9×D9—24no—
54C23×C3⋊D3—91no—
55C23×C3×D3—31no—
56C22×C3×Dic3—31no—
57C2×#626—912no—
58C24×C9—91no—
59C23×D9—91no—
60C23×D9—91no—
61C23×D9—181no—
62C23×D9—181no—
63C23×D9—183no—
64C23×D9D911yescharacteristic, complemented
65C22×C4×C9—91no—
66C2×#611—912no—
67C22×Dic9D911yescharacteristic, complemented
68C2×D36—912no—
69C22×C3×C9—24no—
70C22×C3×C9—23no—
71C22×C3×C9D1214yes—
72C22×C3×C9#6714yes—
73C22×C3×C9C22×D313yes—
74C22×C3×C9C22×D313yes—
75C2×C3⋊D9—34no—
76C2×C3⋊D9—34no—
77C2×C3⋊D9—64no—
78C2×C3⋊D9—624no—
79C2×C3⋊D9—612no—
80C2×C3⋊D9—612no—
81C2×D3×C9—34no—
82C2×D3×C9—612no—
83C2×C3×D9—212no—
84C2×C3×D9C22×D314yes—
85C9×Dic3—34no—
86C3×Dic9C22×D314yes—
87C22×#67—271no—
88C22×D12—271no—
89C92C22×D411yescharacteristic, complemented, Sylow
90C23×C32D3211yescharacteristic
91C22×C3⋊D3—96no—
92C22×C3⋊D3—184no—
93C22×C3×D3—36no—
94C22×C3×D3—64no—
95C2×C3×Dic3—36no—
96#626—916no—
97C23×C9—23no—
98C23×C9—21no—
99C23×C9—21no—
100C23×C9—96no—
101C23×C9—184no—
102C23×C9C2×D911yescharacteristic
103C23×C9C2×D911yescharacteristic
104C22×D9—24no—
105C22×D9—96no—
106C22×D9—96no—
107C22×D9—186no—
108C22×D9—186no—
109C22×D9—1818no—
110C22×D9—1824no—
111C22×D9—188no—
112C22×D9—188no—
113C22×D9—184no—
114C22×D9—184no—
115C22×D9C2×D916yescomplemented
116C2×C4×C9—96no—
117#611—916no—
118C2×Dic9C2×D916yescomplemented
119D36—916no—
120C2×C3×C9—21no—
121C2×C3×C9—26no—
122C2×C3×C9C2×D1216yes—
123C2×C3×C9C2×#6716yes—
124C2×C3×C9C23×D311yescharacteristic
125C2×C3×C9C23×D311yescharacteristic
126C3⋊D9—68no—
127C3⋊D9—64no—
128C3⋊D9—64no—
129D3×C9—64no—
130C3×D9—24no—
131C24×C3—91no—
132C23×D3—31no—
133C23×D3—271no—
134C23×D3—271no—
135C23×D3—541no—
136C22×C3×C4—91no—
137C2×#67—2712no—
138C22×Dic3—31no—
139C2×D12—2712no—
140C22×C32#62614yes—
141C22×C32C2×D3213yes—
142C2×C3⋊D3—94no—
143C2×C3⋊D3—1812no—
144C2×C3×D3—34no—
145C2×C3×D3—612no—
146C3×Dic3—34no—
147C22×C9—29no—
148C22×C9—212no—
149C22×C9—24no—
150C22×C9—24no—
151C22×C9—23no—
152C22×C9—23no—
153C22×C9—94no—
154C22×C9—1812no—
155C22×C9D3614yescomplemented
156C22×C9#61114yescomplemented
157C22×C9C22×D913yes—
158C22×C9C22×D913yes—
159C2×D9—212no—
160C2×D9—94no—
161C2×D9—94no—
162C2×D9—184no—
163C2×D9—184no—
164C2×D9—1812no—
165C2×D9—1872no—
166C2×D9—1824no—
167C2×D9—1824no—
168C2×D9—1812no—
169C2×D9—1812no—
170C2×D9C22×D914yescomplemented
171C4×C9—94no—
172Dic9C22×D914yescomplemented
173C22×D4—811noSylow
174C3×C9—21no—
175C3×C9C22×D1211yescharacteristic
176C3×C9C22×#6711yescharacteristic
177C23×C3—21no—
178C23×C3—96no—
179C23×C3—184no—
180C23×C3D3×D911yescharacteristic
181C23×C3D3×D911yescharacteristic
182C22×D3—36no—
183C22×D3—64no—
184C22×D3—276no—
185C22×D3—276no—
186C22×D3—546no—
187C22×D3—548no—
188C22×D3—544no—
189C22×D3—544no—
190C2×C3×C4—96no—
191#67—2716no—
192C2×Dic3—36no—
193D12—2716no—
194C2×C32C2×#62616yes—
195C2×C32C22×D3211yescharacteristic
196C3⋊D3—184no—
197C3×D3—64no—
198C2×C9—23no—
199C2×C9—218no—
200C2×C9—21no—
201C2×C9—21no—
202C2×C9—26no—
203C2×C9—26no—
204C2×C9—184no—
205C2×C9C2×D3616yescomplemented
206C2×C9C2×#61116yescomplemented
207C2×C9C23×D911yescharacteristic
208C2×C9C23×D911yescharacteristic
209D9—24no—
210D9—1824no—
211D9—188no—
212D9—188no—
213D9—184no—
214D9—184no—
215C24—91no—
216C24—811no—
217C2×D4—8112no—
218C22×C4—91no—
219C22×C3—23no—
220C22×C3—24no—
221C22×C3—94no—
222C22×C3—1812no—
223C22×C3#619214yes—
224C22×C3#619514yes—
225C22×C3C2×D3×D913yes—
226C22×C3C2×D3×D913yes—
227C2×D3—34no—
228C2×D3—612no—
229C2×D3—274no—
230C2×D3—274no—
231C2×D3—544no—
232C2×D3—5424no—
233C2×D3—5412no—
234C2×D3—5412no—
235C3×C4—94no—
236Dic3—34no—
237C32C22×#62611yescharacteristic
238C9—23no—
239C9—21no—
240C9—21no—
241C9C22×D3611yescharacteristic, complemented
242C9C22×#61111yescharacteristic, complemented
243C23—96no—
244C23—184no—
245C23—816no—
246C23—1624no—
247C23D9211yescharacteristic
248D4—8116no—
249C2×C4—96no—
250C2×C3—21no—
251C2×C3—26no—
252C2×C3—184no—
253C2×C3C2×#619216yes—
254C2×C3C2×#619516yes—
255C2×C3C22×D3×D911yescharacteristic
256C2×C3C22×D3×D911yescharacteristic
257D3—64no—
258D3—548no—
259D3—544no—
260D3—544no—
261C22—94no—
262C22—1812no—
263C22—814no—
264C22—16212no—
265C22#1061953014yesdirect product factor
266C22C2×D9213yes—
267C4—94no—
268C3—21no—
269C3C22×#619211yescharacteristic
270C3C22×#619511yescharacteristic
271C2—184no—
272C2—1624no—
273C2C2×#1061953016yesdirect product factor
274C2C22×D9211yescharacteristic
subgroupG/H
center, hypercenterC23D92
commutator, cosocleC2×C92C24
FrattiniC2×C32C22×D32
FittingC23×C92C22
socleC23×C32D32
hypocenterC92C22×D4
LCSG ▷ C2×C92 ▷ C92
UCSC1 ◁ C23

Complements

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

NH ≅ G/Ntype
1. C23×C9⋊D9C2semidirect
2. C23×C9×D9C2semidirect
3. C22×C9×Dic9C2semidirect
4. C2×#10619530C2direct (N × H)
9. C22×C9⋊D9C22semidirect
11. C22×C9×D9C22semidirect
12. C2×C9×Dic9C22semidirect
13. #10619530C22direct (N × H)
23. C22×C92D4semidirect
26. C2×C9⋊D9C23semidirect
28. C2×C9×D9C23semidirect
29. C9×Dic9C23semidirect
50. C2×C92C2×D4semidirect
64. C23×D9D9semidirect
67. C22×Dic9D9semidirect
89. C92C22×D4semidirect
115. C22×D9C2×D9semidirect
118. C2×Dic9C2×D9semidirect
155. C22×C9D36semidirect
156. C22×C9#611semidirect
170. C2×D9C22×D9semidirect
172. Dic9C22×D9semidirect
205. C2×C9C2×D36semidirect
206. C2×C9C2×#611semidirect
241. C9C22×D36semidirect
242. C9C22×#611semidirect
265. C22#10619530direct (N × H)
273. C2C2×#10619530direct (N × H)

Maximal subgroups

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

subgroupindex
C23×C9⋊D92
C23×C9×D92
C22×C9×Dic92
C2×#106195302
C22×#61953
C22×#61923