Finite Group Databasebeta

← #3499⋊C9 #11919749

Subgroups — #3499⋊C9 #11919749

Order 1152.

681 conjugacy classes of subgroups; only the 109 normal subgroups are shown.

normal subgroups only

This group has 681 conjugacy classes of subgroups — too many to draw. Only its 109 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
1C2×2−1+4⋊C9C212yesmaximal, complemented
2D4×Q8⋊C9C214yesmaximal, complemented
3C4×#41⋊C9C211yesmaximal, characteristic, complemented
4C3×#3499C311yesmaximal, characteristic
52−1+4⋊C9—24no—
6C2×#41⋊C9C2211yescharacteristic
7C22×Q8⋊C9C2214yes—
8C9×#127—41nomaximal
9C4×Q8⋊C9C2212yes—
10C2×C3×2−1+4C2×C312yes—
11C3×D4×Q8C2×C314yes—
12C3×#547—34no—
13C3×#536—32no—
14C3×#532—31no—
15C2×C3×C4⋊Q8—31no—
16C3×C4×#41C2×C311yescharacteristic
17C2×D4×C9—42no—
18C2×D4×C9—44no—
19#41⋊C9D412yescomplemented
20C2×Q8⋊C9—24no—
21C2×Q8⋊C9C2311yescharacteristic
22C42×C9—41no—
23#3499C911yescharacteristic, complemented, Sylow
24C3×2−1+4—24no—
25C3×2−1+4—64no—
26C2×C3×#41—32no—
27C2×C3×#41—34no—
28C2×C3×#41C22×C311yescharacteristic
29C22×C3×Q8—32no—
30C22×C3×Q8C22×C314yes—
31C3×C4⋊Q8—32no—
32C3×C4⋊Q8—34no—
33C3×C4⋊Q8—31no—
34C3×#127A411yescharacteristic
35C3×#124—32no—
36C3×#123—38no—
37C3×C22⋊Q8—38no—
38C3×#121—34no—
39C3×C4×Q8C22×C312yes—
40C3×C4×D4—34no—
41C3×C4×D4—32no—
42C3×#117—31no—
43C2×C3×C4⋊C4—34no—
44C2×C3×C42—31no—
45C23×C9—44no—
46D4×C9—88no—
47D4×C9—84no—
48C2×C4×C9—42no—
49C2×C4×C9—41no—
50Q8⋊C9C2×D411yescharacteristic
51C2×2−1+4C2×C912yescomplemented
52D4×Q8C2×C914yescomplemented
53#547—34no—
54#536—32no—
55#532—31no—
56C2×C4⋊Q8—31no—
57C4×#41C2×C911yescharacteristic, complemented
58C3×#41—32no—
59C3×#41—64no—
60C3×#41—64no—
61C3×#41—68no—
62C3×#41—68no—
63C3×#41C3×D412yes—
64C2×C3×Q8—24no—
65C2×C3×Q8—32no—
66C2×C3×Q8—34no—
67C2×C3×Q8—64no—
68C2×C3×Q8—64no—
69C2×C3×Q8—64no—
70C2×C3×Q8C23×C311yescharacteristic
71C2×C3×D4—31no—
72C2×C3×D4—34no—
73C2×C3×D4C2×A414yes—
74C2×C3×D4C2×A412yes—
75C22×C3×C4—31no—
76C22×C3×C4—34no—
77C22×C3×C4—34no—
78C22×C3×C4—32no—
79C3×C4⋊C4—32no—
80C3×C4⋊C4—38no—
81C3×C4⋊C4—34no—
82C3×C22⋊C4—32no—
83C3×C22⋊C4—38no—
84C3×C42—31no—
85C3×C42—32no—
86C3×C42C2×A411yescharacteristic
87C22×C9—41no—
88C22×C9—84no—
89C22×C9—88no—
90C4×C9—42no—
91C4×C9—44no—
922−1+4—24no—
932−1+4—64no—
94C2×#41—32no—
95C2×#41—34no—
96C2×#41C22×C911yescharacteristic
97C22×Q8—32no—
98C22×Q8C22×C914yes—
99C4⋊Q8—32no—
100C4⋊Q8—34no—
101C4⋊Q8—31no—
102#127C22⋊C911yescharacteristic
103#124—32no—
104#123—38no—
105C22⋊Q8—38no—
106#121—34no—
107C4×Q8C22×C912yes—
108C4×D4—34no—
109C4×D4—32no—
110#117—31no—
111C2×C4⋊C4—34no—
112C2×C42—31no—
113C23×C3—31no—
114C23×C3C22×A414yes—
115C3×Q8—31no—
116C3×Q8—64no—
117C3×Q8—64no—
118C3×Q8—64no—
119C3×Q8C2×C3×D411yescharacteristic
120C3×D4—24no—
121C3×D4—28no—
122C3×D4—32no—
123C3×D4—32no—
124C3×D4—68no—
125C2×C3×C4—31no—
126C2×C3×C4—32no—
127C2×C3×C4—32no—
128C2×C3×C4—32no—
129C2×C3×C4—34no—
130C2×C3×C4—64no—
131C2×C3×C4—64no—
132C2×C3×C4—68no—
133C2×C3×C4—64no—
134C2×C3×C4C22×A411yescharacteristic
135C2×C3×C4C22×A412yes—
136C2×C9—41no—
137C2×C9—42no—
138C2×C9—164no—
139#41—32no—
140#41—64no—
141#41—64no—
142#41—68no—
143#41—68no—
144#41D4×C912yescomplemented
145C2×Q8—24no—
146C2×Q8—32no—
147C2×Q8—34no—
148C2×Q8—64no—
149C2×Q8—64no—
150C2×Q8—64no—
151C2×Q8C23×C911yescharacteristic
152C2×D4—31no—
153C2×D4—34no—
154C2×D4C2×C22⋊C914yes—
155C2×D4C2×C22⋊C912yes—
156C22×C4—31no—
157C22×C4—34no—
158C22×C4—34no—
159C22×C4—32no—
160C4⋊C4—32no—
161C4⋊C4—38no—
162C4⋊C4—34no—
163C22⋊C4—32no—
164C22⋊C4—38no—
165C42—31no—
166C42—32no—
167C42C2×C22⋊C911yescharacteristic
168C22×C3—24no—
169C22×C3—28no—
170C22×C3—32no—
171C22×C3—62no—
172C22×C3C23×A411yescharacteristic
173C3×C4—31no—
174C3×C4—31no—
175C3×C4—64no—
176C3×C4—62no—
177C3×C4D4×A412yes—
178C3×C42−1+4⋊C314yes—
179C9—41noSylow
180C23—31no—
181C23C22×C22⋊C914yes—
182Q8—31no—
183Q8—64no—
184Q8—64no—
185Q8—64no—
186Q8C2×D4×C911yescharacteristic
187D4—24no—
188D4—28no—
189D4—32no—
190D4—32no—
191D4—68no—
192C2×C4—31no—
193C2×C4—32no—
194C2×C4—32no—
195C2×C4—32no—
196C2×C4—34no—
197C2×C4—64no—
198C2×C4—64no—
199C2×C4—68no—
200C2×C4—64no—
201C2×C4C22×C22⋊C911yescharacteristic
202C2×C4C22×C22⋊C912yes—
203C2×C3—44no—
204C2×C3—62no—
205C2×C3C2×D4×A411yescharacteristic
206C2×C3C2×2−1+4⋊C312yes—
207C22—24no—
208C22—28no—
209C22—32no—
210C22—62no—
211C22C23×C22⋊C911yescharacteristic
212C4—31no—
213C4—31no—
214C4—64no—
215C4—62no—
216C4D4×C22⋊C912yes—
217C42−1+4⋊C914yescomplemented
218C3#3499⋊C311yescharacteristic
219C2—44no—
220C2—62no—
221C2C2×D4×C22⋊C911yescharacteristic
222C2C2×2−1+4⋊C912yes—
subgroupG/H
center, Frattini, socleC22×C3C23×A4
commutatorC2×Q8C23×C9
Fitting, prime radicalC3×#3499C3
cosocleC2×C3×Q8C23×C3
hypercenterC3×#127A4
hypocenterQ8C2×D4×C9
LCSG ▷ C2×Q8 ▷ Q8
UCSC1 ◁ C22×C3 ◁ C3×#127

Complements

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

NH ≅ G/Ntype
1. C2×2−1+4⋊C9C2semidirect
2. D4×Q8⋊C9C2semidirect
3. C4×#41⋊C9C2semidirect
19. #41⋊C9D4semidirect
23. #3499C9semidirect
51. C2×2−1+4C2×C9semidirect
52. D4×Q8C2×C9semidirect
57. C4×#41C2×C9semidirect
144. #41D4×C9semidirect
217. C42−1+4⋊C9semidirect

Maximal subgroups

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

subgroupindex
C2×2−1+4⋊C92
D4×Q8⋊C92
C4×#41⋊C92
C3×#34993
C9×#1274