Finite Group Databasebeta

← #3529⋊C9 #11919841

Subgroups — #3529⋊C9 #11919841

Order 1152.

439 conjugacy classes of subgroups; only the 42 normal subgroups are shown.

normal subgroups only

This group has 439 conjugacy classes of subgroups — too many to draw. Only its 42 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#10589567C211yesmaximal, characteristic, complemented
2C3×#3529C311yesmaximal, characteristic
3C2×#41⋊C9—41nomaximal
4C2×C4×C22⋊C9—42nomaximal
5C4×Q8⋊C9—42nomaximal
6C3×#563—31no—
7C3×#562—32no—
8C3×H(3,𝔽4)C2×C311yescharacteristic
9C3×#560—32no—
10C3×#532—31no—
11C3×#529—32no—
12C3×#525—32no—
13C22×C22⋊C9—42no—
14#41⋊C9—42no—
15C2×Q8⋊C9—42no—
16C2×Q8⋊C9—41no—
17C4×C22⋊C9—44no—
18#3529C911yescharacteristic, complemented, Sylow
19C2×C3×#41—31no—
20C2×C3×#41A411yescharacteristic
21C23×C3×C4A412yes—
22C3×C4⋊Q8—31no—
23C3×#127—31no—
24C3×#126—34no—
25C3×#125—32no—
26C3×#124—31no—
27C3×#124—32no—
28C3×#124—31no—
29C3×#123—34no—
30C3×#123—32no—
31C3×#123—32no—
32C3×C22⋊Q8—34no—
33C3×C22⋊Q8—32no—
34C3×#121—32no—
35C3×#121—34no—
36C3×#121—34no—
37C3×#120—32no—
38C3×#120—32no—
39C3×C4×Q8A412yes—
40C3×C4×D4—32no—
41C3×C4×D4—34no—
42C3×#117—32no—
43C2×C3×C42—31no—
44C2×C22⋊C9—42no—
45C2×C22⋊C9—44no—
46C2×C4×C9—161no—
47Q8⋊C9—42no—
48Q8⋊C9—41no—
49#563—31no—
50#562—32no—
51H(3,𝔽4)C2×C911yescharacteristic
52#560—32no—
53#532—31no—
54#529—32no—
55#525—32no—
56C24×C3C2×A412yes—
57C3×#41—42no—
58C3×#41—122no—
59C2×C3×Q8—31no—
60C2×C3×Q8C2×A412yes—
61C2×C3×Q8C2×A411yescharacteristic
62C2×C3×D4—31no—
63C2×C3×D4—32no—
64C2×C3×D4—34no—
65C2×C3×D4—31no—
66C2×C3×D4—32no—
67C22×C3×C4—32no—
68C22×C3×C4—31no—
69C22×C3×C4—32no—
70C22×C3×C4—32no—
71C22×C3×C4—44no—
72C3×C4⋊C4—32no—
73C3×C4⋊C4—34no—
74C3×C4⋊C4—34no—
75C3×C4⋊C4—32no—
76C3×C22⋊C4—32no—
77C3×C22⋊C4—32no—
78C3×C22⋊C4—34no—
79C3×C22⋊C4—34no—
80C3×C22⋊C4—34no—
81C3×C42—31no—
82C3×C42—31no—
83C3×C42—32no—
84C22×C9—161no—
85C22⋊C9—42no—
86C4×C9—162no—
87C2×#41—31no—
88C2×#41C22⋊C911yescharacteristic, complemented
89C23×C4C22⋊C912yescomplemented
90C4⋊Q8—31no—
91#127—31no—
92#126—34no—
93#125—32no—
94#124—31no—
95#124—32no—
96#124—31no—
97#123—32no—
98#123—32no—
99#123—34no—
100C22⋊Q8—34no—
101C22⋊Q8—32no—
102#121—34no—
103#121—32no—
104#121—34no—
105#120—32no—
106#120—32no—
107C4×Q8C22⋊C912yescomplemented
108C4×D4—32no—
109C4×D4—34no—
110#117—32no—
111C2×C42—31no—
112C23×C3—32no—
113C23×C3—31no—
114C23×C3—42no—
115C23×C3—44no—
116C3×Q8—42no—
117C3×Q8—41no—
118C3×Q8—121no—
119C3×D4—121no—
120C3×D4—124no—
121C3×D4—122no—
122C3×D4—122no—
123C3×D4—121no—
124C2×C3×C4—32no—
125C2×C3×C4—32no—
126C2×C3×C4—31no—
127C2×C3×C4—32no—
128C2×C3×C4—64no—
129C2×C3×C4—62no—
130C2×C3×C4—122no—
131C2×C3×C4—122no—
132C2×C3×C4C22⋊A411yescharacteristic
133C2×C9—161no—
134C2×C9—162no—
135C24C2×C22⋊C912yes—
136#41—42no—
137#41—122no—
138C2×Q8—31no—
139C2×Q8C2×C22⋊C912yes—
140C2×Q8C2×C22⋊C911yescharacteristic
141C2×D4—31no—
142C2×D4—32no—
143C2×D4—34no—
144C2×D4—31no—
145C2×D4—32no—
146C22×C4—32no—
147C22×C4—31no—
148C22×C4—32no—
149C22×C4—32no—
150C22×C4—44no—
151C4⋊C4—32no—
152C4⋊C4—34no—
153C4⋊C4—34no—
154C4⋊C4—32no—
155C22⋊C4—32no—
156C22⋊C4—32no—
157C22⋊C4—34no—
158C22⋊C4—34no—
159C22⋊C4—34no—
160C42—31no—
161C42—31no—
162C42—32no—
163C22×C3—42no—
164C22×C3—62no—
165C22×C3—61no—
166C22×C3—62no—
167C22×C3—64no—
168C22×C3—122no—
169C22×C3C2×C22⋊A411yescharacteristic
170C3×C4—62no—
171C3×C4—61no—
172C3×C4—62no—
173C3×C4—62no—
174C3×C4#99712yes—
175C9—161noSylow
176C23—32no—
177C23—31no—
178C23—42no—
179C23—44no—
180Q8—41no—
181Q8—42no—
182Q8—121no—
183D4—121no—
184D4—122no—
185D4—121no—
186D4—124no—
187D4—122no—
188C2×C4—32no—
189C2×C4—32no—
190C2×C4—31no—
191C2×C4—32no—
192C2×C4—64no—
193C2×C4—62no—
194C2×C4—122no—
195C2×C4—122no—
196C2×C4C22⋊(C22⋊C9)11yescharacteristic
197C2×C3—122no—
198C2×C3—121no—
199C2×C3C2×#99711yescharacteristic
200C2×C3#595012yes—
201C22—42no—
202C22—62no—
203C22—61no—
204C22—62no—
205C22—64no—
206C22—122no—
207C22C2×C22⋊(C22⋊C9)11yescharacteristic
208C4—62no—
209C4—61no—
210C4—62no—
211C4—62no—
212C4#6370312yes—
213C3#3529⋊C311yescharacteristic
214C2—122no—
215C2—121no—
216C2C2×#6370311yescharacteristic
217C2#1059312512yes—
subgroupG/H
center, hypercenterC2×C3×C4C22⋊A4
commutator, hypocenterH(3,𝔽4)C2×C9
Frattini, socleC22×C3C2×C22⋊A4
Fitting, prime radicalC3×#3529C3
cosocleC3×H(3,𝔽4)C2×C3
LCSG ▷ H(3,𝔽4)
UCSC1 ◁ C2×C3×C4

Complements

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

NH ≅ G/Ntype
1. #10589567C2semidirect
18. #3529C9semidirect
88. C2×#41C22⋊C9semidirect
89. C23×C4C22⋊C9semidirect
107. C4×Q8C22⋊C9semidirect

Maximal subgroups

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

subgroupindex
#105895672
C3×#35293
C2×#41⋊C94
C2×C4×C22⋊C94
C4×Q8⋊C94