Finite Group Databasebeta

← C2×#560⋊C9 #11919771

Subgroups — C2×#560⋊C9 #11919771

Order 1152.

560 conjugacy classes of subgroups; only the 84 normal subgroups are shown.

normal subgroups only

This group has 560 conjugacy classes of subgroups — too many to draw. Only its 84 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#560⋊C9C214yesmaximal, direct product factor
2C2×#127⋊C9C211yesmaximal, characteristic, complemented
3C2×#126⋊C9C212yesmaximal, complemented
4C2×C3×#560C311yesmaximal, characteristic
5C23×C22⋊C9—41nomaximal
6#127⋊C9C2212yescomplemented
7#126⋊C9C2214yescomplemented
8C2×C42⋊C9C2211yescharacteristic, complemented
9C3×#560—34no—
10C3×#560C2×C314yes—
11C2×C3×#127C2×C311yescharacteristic
12C2×C3×#126C2×C312yes—
13C2×C3×#123—31no—
14C2×C3×#121—32no—
15C2×C3×#120—31no—
16C22×C22⋊C9—42no—
17C22×C22⋊C9—41no—
18C22×C22⋊C9—44no—
19C42⋊C9C2311yescharacteristic, complemented
20C2×#560C911yescharacteristic, complemented, Sylow
21C25×C3A411yescharacteristic
22C22×C3×D4—31no—
23C22×C3×D4—32no—
24C22×C3×D4—31no—
25C23×C3×C4—31no—
26C3×#127—32no—
27C3×#127C22×C312yes—
28C3×#126—34no—
29C3×#126C22×C314yes—
30C3×#123—34no—
31C3×#123—34no—
32C3×#121—38no—
33C3×#121—38no—
34C3×#120—34no—
35C3×#120—34no—
36C2×C3×C4⋊C4—32no—
37C2×C3×C22⋊C4—31no—
38C2×C3×C22⋊C4—32no—
39C2×C3×C22⋊C4—31no—
40C2×C3×C42C22×C311yescharacteristic
41C23×C9—161no—
42C2×C22⋊C9—41no—
43C2×C22⋊C9—44no—
44C2×C22⋊C9—42no—
45#560—34no—
46#560C2×C914yescomplemented
47C2×#127C2×C911yescharacteristic, complemented
48C2×#126C2×C912yescomplemented
49C2×#123—31no—
50C2×#121—32no—
51C2×#120—31no—
52C24×C3—31no—
53C24×C3—121no—
54C24×C3—121no—
55C24×C3C2×A412yes—
56C24×C3C2×A411yescharacteristic
57C24×C3C2×A414yes—
58C2×C3×D4—32no—
59C2×C3×D4—32no—
60C2×C3×D4—38no—
61C2×C3×D4—32no—
62C2×C3×D4—32no—
63C2×C3×D4—122no—
64C2×C3×D4—122no—
65C2×C3×D4—121no—
66C2×C3×D4—121no—
67C2×C3×D4—121no—
68C2×C3×D4—121no—
69C22×C3×C4—31no—
70C22×C3×C4—32no—
71C22×C3×C4—34no—
72C22×C3×C4—121no—
73C22×C3×C4—121no—
74C3×C4⋊C4—34no—
75C3×C4⋊C4—34no—
76C3×C22⋊C4—34no—
77C3×C22⋊C4—34no—
78C3×C22⋊C4—34no—
79C3×C22⋊C4—34no—
80C3×C42—31no—
81C3×C42C23×C311yescharacteristic
82C22×C9—164no—
83C22×C9—162no—
84C22×C9—161no—
85C22⋊C9—41no—
86C25C22⋊C911yescharacteristic
87C22×D4—31no—
88C22×D4—32no—
89C22×D4—31no—
90C23×C4—31no—
91#127—32no—
92#127C22×C912yescomplemented
93#126—34no—
94#126C22×C914yescomplemented
95#123—34no—
96#123—34no—
97#121—38no—
98#121—38no—
99#120—34no—
100#120—34no—
101C2×C4⋊C4—32no—
102C2×C22⋊C4—31no—
103C2×C22⋊C4—32no—
104C2×C22⋊C4—31no—
105C2×C42C22×C911yescharacteristic, complemented
106C23×C3—32no—
107C23×C3—41no—
108C23×C3—62no—
109C23×C3—61no—
110C23×C3—62no—
111C23×C3—61no—
112C23×C3—61no—
113C23×C3—61no—
114C23×C3—62no—
115C23×C3—62no—
116C23×C3—121no—
117C23×C3—124no—
118C23×C3—124no—
119C23×C3C22×A411yescharacteristic
120C23×C3C22×A414yes—
121C23×C3C22×A412yes—
122C3×D4—128no—
123C3×D4—122no—
124C3×D4—122no—
125C3×D4—122no—
126C3×D4—122no—
127C2×C3×C4—31no—
128C2×C3×C4—31no—
129C2×C3×C4—34no—
130C2×C3×C4—62no—
131C2×C3×C4—62no—
132C2×C3×C4—61no—
133C2×C3×C4—61no—
134C2×C3×C4—124no—
135C2×C9—164no—
136C2×C9—162no—
137C2×C9—161no—
138C24—31no—
139C24—121no—
140C24—121no—
141C24C2×C22⋊C912yes—
142C24C2×C22⋊C911yescharacteristic
143C24C2×C22⋊C914yes—
144C2×D4—32no—
145C2×D4—32no—
146C2×D4—38no—
147C2×D4—32no—
148C2×D4—32no—
149C2×D4—122no—
150C2×D4—122no—
151C2×D4—121no—
152C2×D4—121no—
153C2×D4—121no—
154C2×D4—121no—
155C22×C4—31no—
156C22×C4—32no—
157C22×C4—34no—
158C22×C4—121no—
159C22×C4—121no—
160C4⋊C4—34no—
161C4⋊C4—34no—
162C22⋊C4—34no—
163C22⋊C4—34no—
164C22⋊C4—34no—
165C22⋊C4—34no—
166C42—31no—
167C42C23×C911yescharacteristic, complemented
168C22×C3—31no—
169C22×C3—31no—
170C22×C3—44no—
171C22×C3—42no—
172C22×C3—41no—
173C22×C3—64no—
174C22×C3—62no—
175C22×C3—62no—
176C22×C3—64no—
177C22×C3—122no—
178C22×C3—121no—
179C22×C3—122no—
180C22×C3—121no—
181C22×C3—124no—
182C22×C3—121no—
183C22×C3C23×A411yescharacteristic
184C3×C4—64no—
185C3×C4—61no—
186C3×C4—61no—
187C9—161noSylow
188C23—32no—
189C23—41no—
190C23—62no—
191C23—61no—
192C23—62no—
193C23—61no—
194C23—61no—
195C23—61no—
196C23—62no—
197C23—62no—
198C23—121no—
199C23—124no—
200C23—124no—
201C23C22×C22⋊C911yescharacteristic
202C23C22×C22⋊C914yes—
203C23C22×C22⋊C912yes—
204D4—128no—
205D4—122no—
206D4—122no—
207D4—122no—
208D4—122no—
209C2×C4—31no—
210C2×C4—31no—
211C2×C4—34no—
212C2×C4—62no—
213C2×C4—62no—
214C2×C4—61no—
215C2×C4—61no—
216C2×C4—124no—
217C2×C3—31no—
218C2×C3—31no—
219C2×C3—44no—
220C2×C3—42no—
221C2×C3—122no—
222C2×C3#560⋊C311yescharacteristic
223C22—31no—
224C22—31no—
225C22—44no—
226C22—42no—
227C22—41no—
228C22—64no—
229C22—62no—
230C22—62no—
231C22—64no—
232C22—122no—
233C22—121no—
234C22—122no—
235C22—121no—
236C22—124no—
237C22—121no—
238C22C23×C22⋊C911yescharacteristic
239C4—64no—
240C4—61no—
241C4—61no—
242C3C2×#560⋊C311yescharacteristic
243C2—31no—
244C2—31no—
245C2—44no—
246C2—42no—
247C2—122no—
248C2#560⋊C911yescharacteristic, direct product factor
subgroupG/H
center, hypercenterC2×C3#560⋊C3
commutator, hypocenterC42C23×C9
FrattiniC22×C3C23×A4
Fitting, prime radicalC2×C3×#560C3
socleC23×C3C22×A4
cosocleC3×C42C23×C3
LCSG ▷ C42
UCSC1 ◁ C2×C3

Complements

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

NH ≅ G/Ntype
1. #560⋊C9C2direct (N × H)
2. C2×#127⋊C9C2semidirect
3. C2×#126⋊C9C2semidirect
6. #127⋊C9C22semidirect
7. #126⋊C9C22semidirect
8. C2×C42⋊C9C22semidirect
19. C42⋊C9C23semidirect
20. C2×#560C9semidirect
46. #560C2×C9semidirect
47. C2×#127C2×C9semidirect
48. C2×#126C2×C9semidirect
92. #127C22×C9semidirect
94. #126C22×C9semidirect
105. C2×C42C22×C9semidirect
167. C42C23×C9semidirect
248. C2#560⋊C9direct (N × H)

Maximal subgroups

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

subgroupindex
#560⋊C92
C2×#127⋊C92
C2×#126⋊C92
C2×C3×#5603
C23×C22⋊C94