Finite Group Databasebeta

← C2×#393⋊C9 #11919435

Subgroups — C2×#393⋊C9 #11919435

Order 1152.

441 conjugacy classes of subgroups; only the 57 normal subgroups are shown.

normal subgroups only

This group has 441 conjugacy classes of subgroups — too many to draw. Only its 57 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×C22⋊(Q8⋊C9)C211yesmaximal, characteristic, complemented
2#393⋊C9C212yesmaximal, direct product factor
3C2×C3×#393C311yesmaximal, characteristic
4C23×C22⋊C9—41nomaximal
5C22⋊(Q8⋊C9)C2211yescharacteristic, complemented
6C23×C3×Q8C2×C311yescharacteristic
7C22×C3×C22⋊C4—31no—
8C3×#393—32no—
9C3×#393C2×C312yes—
10C2×C3×#95—31no—
11C22×C22⋊C9—44no—
12C22×C22⋊C9—41no—
13C22×C22⋊C9—42no—
14C2×Q8⋊C9—82no—
15C2×#393C911yescharacteristic, complemented, Sylow
16C25×C3A411yescharacteristic
17C22×C3×Q8—31no—
18C22×C3×Q8—62no—
19C22×C3×Q8—62no—
20C22×C3×Q8C22×C311yescharacteristic
21C23×C3×C4—31no—
22C23×C3×C4—31no—
23C2×C3×C22⋊C4—32no—
24C2×C3×C22⋊C4—32no—
25C2×C3×C22⋊C4—62no—
26C2×C3×C22⋊C4—62no—
27C3×#95—32no—
28C3×#95—32no—
29C23×C9—161no—
30C2×C22⋊C9—44no—
31C2×C22⋊C9—42no—
32C2×C22⋊C9—41no—
33Q8⋊C9—82no—
34C23×Q8C2×C911yescharacteristic, complemented
35C22×C22⋊C4—31no—
36#393—32no—
37#393C2×C912yescomplemented
38C2×#95—31no—
39C24×C3—61no—
40C24×C3—62no—
41C24×C3—61no—
42C24×C3SL(2,𝔽3)14yes—
43C24×C3C2×A411yescharacteristic
44C24×C3C2×A412yes—
45C2×C3×Q8—22no—
46C2×C3×Q8—62no—
47C2×C3×Q8—62no—
48C2×C3×Q8—64no—
49C2×C3×Q8—62no—
50C2×C3×Q8—62no—
51C2×C3×Q8—64no—
52C2×C3×Q8—62no—
53C22×C3×C4—32no—
54C22×C3×C4—32no—
55C22×C3×C4—31no—
56C22×C3×C4—31no—
57C22×C3×C4—32no—
58C22×C3×C4—62no—
59C22×C3×C4—62no—
60C22×C3×C4—61no—
61C22×C3×C4—61no—
62C22×C3×C4—64no—
63C3×C22⋊C4—64no—
64C3×C22⋊C4—64no—
65C22×C9—164no—
66C22×C9—162no—
67C22×C9—161no—
68C22⋊C9—41no—
69C25C22⋊C911yescharacteristic
70C22×Q8—31no—
71C22×Q8—62no—
72C22×Q8—62no—
73C22×Q8C22×C911yescharacteristic, complemented
74C23×C4—31no—
75C23×C4—31no—
76C2×C22⋊C4—32no—
77C2×C22⋊C4—32no—
78C2×C22⋊C4—62no—
79C2×C22⋊C4—62no—
80#95—32no—
81#95—32no—
82C23×C3—31no—
83C23×C3—32no—
84C23×C3—31no—
85C23×C3—41no—
86C23×C3—62no—
87C23×C3—64no—
88C23×C3—64no—
89C23×C3—62no—
90C23×C3—122no—
91C23×C3—121no—
92C23×C3—122no—
93C23×C3C2×SL(2,𝔽3)12yes—
94C23×C3C2×SL(2,𝔽3)14yes—
95C23×C3C22×A411yescharacteristic
96C3×Q8—22no—
97C3×Q8—62no—
98C3×Q8—62no—
99C3×Q8—62no—
100C3×Q8—64no—
101C2×C3×C4—32no—
102C2×C3×C4—32no—
103C2×C3×C4—62no—
104C2×C3×C4—64no—
105C2×C3×C4—62no—
106C2×C3×C4—62no—
107C2×C3×C4—62no—
108C2×C3×C4—62no—
109C2×C3×C4—64no—
110C2×C3×C4—122no—
111C2×C3×C4—122no—
112C2×C9—164no—
113C2×C9—162no—
114C2×C9—161no—
115C24—61no—
116C24—61no—
117C24—62no—
118C24Q8⋊C914yescomplemented
119C24C2×C22⋊C911yescharacteristic
120C24C2×C22⋊C912yes—
121C2×Q8—22no—
122C2×Q8—62no—
123C2×Q8—62no—
124C2×Q8—64no—
125C2×Q8—62no—
126C2×Q8—62no—
127C2×Q8—64no—
128C2×Q8—62no—
129C22×C4—32no—
130C22×C4—32no—
131C22×C4—31no—
132C22×C4—31no—
133C22×C4—32no—
134C22×C4—62no—
135C22×C4—62no—
136C22×C4—61no—
137C22×C4—61no—
138C22×C4—64no—
139C22⋊C4—64no—
140C22⋊C4—64no—
141C22×C3—31no—
142C22×C3—32no—
143C22×C3—32no—
144C22×C3—32no—
145C22×C3—32no—
146C22×C3—31no—
147C22×C3—31no—
148C22×C3—44no—
149C22×C3—42no—
150C22×C3—64no—
151C22×C3—122no—
152C22×C3—124no—
153C22×C3#120⋊C311yescharacteristic
154C22×C3C22×SL(2,𝔽3)11yescharacteristic
155C3×C4—62no—
156C3×C4—62no—
157C3×C4—122no—
158C9—161noSylow
159C23—31no—
160C23—32no—
161C23—31no—
162C23—41no—
163C23—62no—
164C23—64no—
165C23—64no—
166C23—62no—
167C23—121no—
168C23—122no—
169C23—122no—
170C23C2×Q8⋊C912yes—
171C23C2×Q8⋊C914yescomplemented
172C23C22×C22⋊C911yescharacteristic
173Q8—22no—
174Q8—62no—
175Q8—62no—
176Q8—62no—
177Q8—64no—
178C2×C4—32no—
179C2×C4—32no—
180C2×C4—62no—
181C2×C4—64no—
182C2×C4—62no—
183C2×C4—62no—
184C2×C4—62no—
185C2×C4—62no—
186C2×C4—64no—
187C2×C4—122no—
188C2×C4—122no—
189C2×C3—31no—
190C2×C3—31no—
191C2×C3—32no—
192C2×C3—44no—
193C2×C3#393⋊C312yes—
194C2×C3C2×#120⋊C311yescharacteristic
195C22—31no—
196C22—32no—
197C22—32no—
198C22—31no—
199C22—31no—
200C22—32no—
201C22—32no—
202C22—42no—
203C22—44no—
204C22—64no—
205C22—122no—
206C22—124no—
207C22#120⋊C911yescharacteristic
208C22C22×Q8⋊C911yescharacteristic
209C4—62no—
210C4—62no—
211C4—122no—
212C3C2×#393⋊C311yescharacteristic
213C2—31no—
214C2—31no—
215C2—32no—
216C2—44no—
217C2#393⋊C912yesdirect product factor
218C2C2×#120⋊C911yescharacteristic
subgroupG/H
center, hypercenterC22×C3#120⋊C3
commutator, hypocenterC22×Q8C22×C9
FrattiniC23×C3C22×A4
FittingC2×C3×#393C3
socleC24×C3C2×A4
prime radicalC25×C3A4
cosocleC22×C3×Q8C22×C3
LCSG ▷ C22×Q8
UCSC1 ◁ C22×C3

Complements

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

NH ≅ G/Ntype
1. C2×C22⋊(Q8⋊C9)C2semidirect
2. #393⋊C9C2direct (N × H)
5. C22⋊(Q8⋊C9)C22semidirect
15. C2×#393C9semidirect
34. C23×Q8C2×C9semidirect
37. #393C2×C9semidirect
73. C22×Q8C22×C9semidirect
118. C24Q8⋊C9semidirect
171. C23C2×Q8⋊C9semidirect
217. C2#393⋊C9direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C22⋊(Q8⋊C9)2
#393⋊C92
C2×C3×#3933
C23×C22⋊C94