Finite Group Databasebeta

← #3549⋊C9 #11919847

Subgroups — #3549⋊C9 #11919847

Order 1152.

466 conjugacy classes of subgroups; only the 32 normal subgroups are shown.

normal subgroups only

This group has 466 conjugacy classes of subgroups — too many to draw. Only its 32 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#10589566C211yesmaximal, characteristic, complemented
2C3×#3549C311yesmaximal, characteristic
3#127⋊C9—42nomaximal
4#120⋊C9—42nomaximal
5C2×C42⋊C9—41nomaximal
6C3×H(3,𝔽4)—31no—
7C3×H(3,𝔽4)C2×C311yescharacteristic
8C3×#555—32no—
9C3×D42—32no—
10C3×#535—32no—
11C3×#535—32no—
12C3×#532—31no—
13C22⋊(C22⋊C9)—42no—
14C42⋊C9—41no—
15C42⋊C9—42no—
16#3549C911yescharacteristic, complemented, Sylow
17C2×C3×#41—31no—
18C2×C3×#41—31no—
19C22×C3×D4—32no—
20C22×C3×D4—32no—
21C3×C4⋊Q8—31no—
22C3×#127—31no—
23C3×#127—32no—
24C3×#127A412yes—
25C3×#124—32no—
26C3×#124—34no—
27C3×#124—31no—
28C3×#124—31no—
29C3×#124—32no—
30C3×#121—34no—
31C3×#121—34no—
32C3×#121—34no—
33C3×#120—34no—
34C3×#120—32no—
35C3×#120—32no—
36C3×#120—32no—
37C3×#120A412yes—
38C3×C4×D4—34no—
39C3×#117—32no—
40C3×#117—32no—
41C2×C3×C42A411yescharacteristic
42C2×C22⋊C9—161no—
43H(3,𝔽4)—31no—
44H(3,𝔽4)C2×C911yescharacteristic, complemented
45#555—32no—
46D42—32no—
47#535—32no—
48#535—32no—
49#532—31no—
50C24×C3—32no—
51C24×C3C2×A412yes—
52C3×#41—122no—
53C3×#41—122no—
54C2×C3×Q8—31no—
55C2×C3×Q8—31no—
56C2×C3×D4—34no—
57C2×C3×D4—32no—
58C2×C3×D4—31no—
59C2×C3×D4—31no—
60C2×C3×D4—34no—
61C2×C3×D4—32no—
62C2×C3×D4—32no—
63C2×C3×D4—32no—
64C2×C3×D4—124no—
65C2×C3×D4—124no—
66C22×C3×C4—32no—
67C22×C3×C4—32no—
68C22×C3×C4—31no—
69C3×C4⋊C4—34no—
70C3×C22⋊C4—34no—
71C3×C22⋊C4—32no—
72C3×C22⋊C4—34no—
73C3×C22⋊C4—34no—
74C3×C22⋊C4—32no—
75C3×C42—31no—
76C3×C42—32no—
77C3×C42C2×A411yescharacteristic
78C3×C42C2×A412yes—
79C22⋊C9—161no—
80C22⋊C9—324no—
81C2×#41—31no—
82C2×#41—31no—
83C22×D4—32no—
84C22×D4—32no—
85C4⋊Q8—31no—
86#127—31no—
87#127—32no—
88#127C22⋊C912yescomplemented
89#124—32no—
90#124—34no—
91#124—31no—
92#124—31no—
93#124—32no—
94#121—34no—
95#121—34no—
96#121—34no—
97#120—32no—
98#120—34no—
99#120—32no—
100#120—32no—
101#120C22⋊C912yescomplemented
102C4×D4—34no—
103#117—32no—
104#117—32no—
105C2×C42C22⋊C911yescharacteristic, complemented
106C23×C3—32no—
107C23×C3—32no—
108C23×C3—122no—
109C23×C3—122no—
110C23×C3—124no—
111C23×C3C22⋊A411yescharacteristic
112C3×Q8—121no—
113C3×Q8—121no—
114C3×D4—68no—
115C3×D4—122no—
116C3×D4—124no—
117C3×D4—122no—
118C3×D4—122no—
119C3×D4—122no—
120C3×D4—121no—
121C3×D4—121no—
122C2×C3×C4—31no—
123C2×C3×C4—32no—
124C2×C3×C4—31no—
125C2×C3×C4—32no—
126C2×C3×C4—64no—
127C2×C3×C4—64no—
128C2×C3×C4—62no—
129C2×C9—641no—
130C24—32no—
131C24C2×C22⋊C912yes—
132#41—122no—
133#41—122no—
134C2×Q8—31no—
135C2×Q8—31no—
136C2×D4—34no—
137C2×D4—32no—
138C2×D4—31no—
139C2×D4—31no—
140C2×D4—34no—
141C2×D4—32no—
142C2×D4—32no—
143C2×D4—32no—
144C2×D4—124no—
145C2×D4—124no—
146C22×C4—32no—
147C22×C4—32no—
148C22×C4—31no—
149C4⋊C4—34no—
150C22⋊C4—34no—
151C22⋊C4—32no—
152C22⋊C4—34no—
153C22⋊C4—34no—
154C22⋊C4—32no—
155C42—31no—
156C42—32no—
157C42C2×C22⋊C911yescharacteristic
158C42C2×C22⋊C912yes—
159C22×C3—61no—
160C22×C3—62no—
161C22×C3—62no—
162C22×C3—64no—
163C22×C3—64no—
164C22×C3—84no—
165C22×C3—244no—
166C22×C3C2×C22⋊A411yescharacteristic
167C3×C4—32no—
168C3×C4—62no—
169C3×C4—62no—
170C3×C4—61no—
171C9—641noSylow
172C23—32no—
173C23—32no—
174C23—122no—
175C23—122no—
176C23—124no—
177C23C22⋊(C22⋊C9)11yescharacteristic
178Q8—121no—
179Q8—121no—
180D4—68no—
181D4—122no—
182D4—124no—
183D4—122no—
184D4—122no—
185D4—122no—
186D4—121no—
187D4—121no—
188C2×C4—31no—
189C2×C4—32no—
190C2×C4—31no—
191C2×C4—32no—
192C2×C4—64no—
193C2×C4—64no—
194C2×C4—62no—
195C2×C3—31no—
196C2×C3—41no—
197C2×C3—122no—
198C2×C3—122no—
199C22—61no—
200C22—62no—
201C22—62no—
202C22—64no—
203C22—64no—
204C22—84no—
205C22—244no—
206C22C2×C22⋊(C22⋊C9)11yescharacteristic
207C4—32no—
208C4—62no—
209C4—62no—
210C4—61no—
211C3#3549⋊C311yescharacteristic
212C2—31no—
213C2—41no—
214C2—122no—
215C2—122no—
subgroupG/H
center, hypercenterC3#3549⋊C3
commutator, hypocenterH(3,𝔽4)C2×C9
Frattini, socleC22×C3C2×C22⋊A4
Fitting, prime radicalC3×#3549C3
cosocleC3×H(3,𝔽4)C2×C3
LCSG ▷ H(3,𝔽4)
UCSC1 ◁ C3

Complements

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

NH ≅ G/Ntype
1. #10589566C2semidirect
16. #3549C9semidirect
44. H(3,𝔽4)C2×C9semidirect
88. #127C22⋊C9semidirect
101. #120C22⋊C9semidirect
105. C2×C42C22⋊C9semidirect

Maximal subgroups

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

subgroupindex
#105895662
C3×#35493
#127⋊C94
#120⋊C94
C2×C42⋊C94