Finite Group Databasebeta

← C22×2−1+4⋊C9 #11919879

Subgroups — C22×2−1+4⋊C9 #11919879

Order 1152.

2389 conjugacy classes of subgroups; only the 357 normal subgroups are shown.

normal subgroups only

This group has 2389 conjugacy classes of subgroups — too many to draw. Only its 357 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⋊C9C2112yesmaximal, direct product factor
2C22×#41⋊C9C211yesmaximal, characteristic, complemented
3C23×Q8⋊C9C212yesmaximal, complemented
4C22×C3×2−1+4C311yesmaximal, characteristic
5C22×D4×C9—41nomaximal
62−1+4⋊C9C22116yesdirect product factor
7C2×#41⋊C9C2216yescomplemented
8C22×Q8⋊C9C2211yescharacteristic
9C22×Q8⋊C9C22112yescomplemented
10C2×C3×2−1+4—312no—
11C2×C3×2−1+4C2×C3112yes—
12C22×C3×#41—31no—
13C22×C3×#41—32no—
14C22×C3×#41C2×C311yescharacteristic
15C23×C3×Q8—31no—
16C23×C3×Q8C2×C312yes—
17C24×C9—42no—
18C2×D4×C9—412no—
19C22×C4×C9—41no—
20#41⋊C9C2314yescomplemented
21C2×Q8⋊C9C2313yes—
22C2×Q8⋊C9C2318yescomplemented
23C22×2−1+4C911yescharacteristic, complemented, Sylow
24C3×2−1+4—348no—
25C3×2−1+4—332no—
26C3×2−1+4C22×C3116yes—
27C2×C3×#41—324no—
28C2×C3×#41—312no—
29C2×C3×#41—312no—
30C2×C3×#41—324no—
31C2×C3×#41—36no—
32C2×C3×#41C22×C316yes—
33C22×C3×Q8—312no—
34C22×C3×Q8—312no—
35C22×C3×Q8—31no—
36C22×C3×Q8—32no—
37C22×C3×Q8—312no—
38C22×C3×Q8C22×C311yescharacteristic
39C22×C3×Q8C22×C3112yes—
40C22×C3×D4—31no—
41C22×C3×D4—32no—
42C22×C3×D4A411yescharacteristic
43C23×C3×C4—32no—
44C23×C3×C4—32no—
45C23×C3×C4—31no—
46C23×C9—412no—
47C23×C9—41no—
48C23×C9—88no—
49D4×C9—416no—
50C2×C4×C9—46no—
51Q8⋊C9C2411yescharacteristic
52C2×2−1+4—312no—
53C2×2−1+4C2×C9112yescomplemented
54C22×#41—31no—
55C22×#41—32no—
56C22×#41C2×C911yescharacteristic, complemented
57C23×Q8—31no—
58C23×Q8C2×C912yescomplemented
59C24×C3—31no—
60C24×C3C2×A412yes—
61C3×#41—396no—
62C3×#41—38no—
63C3×#41—348no—
64C3×#41—316no—
65C3×#41—332no—
66C3×#41—312no—
67C3×#41C23×C314yes—
68C2×C3×Q8—316no—
69C2×C3×Q8—312no—
70C2×C3×Q8—348no—
71C2×C3×Q8—316no—
72C2×C3×Q8—312no—
73C2×C3×Q8—33no—
74C2×C3×Q8—312no—
75C2×C3×Q8—324no—
76C2×C3×Q8C23×C313yes—
77C2×C3×Q8C23×C318yes—
78C2×C3×D4—36no—
79C2×C3×D4—36no—
80C2×C3×D4—324no—
81C2×C3×D4C2×A4112yes—
82C22×C3×C4—324no—
83C22×C3×C4—312no—
84C22×C3×C4—312no—
85C22×C3×C4—32no—
86C22×C3×C4—31no—
87C22×C3×C4—36no—
88C22×C3×C4—36no—
89C22×C3×C4C2×A411yescharacteristic
90C22×C9—44no—
91C22×C9—43no—
92C22×C9—48no—
93C22×C9—824no—
94C4×C9—44no—
952−1+4—348no—
962−1+4—332no—
972−1+4C22×C9116yescomplemented
98C2×#41—324no—
99C2×#41—312no—
100C2×#41—312no—
101C2×#41—324no—
102C2×#41—36no—
103C2×#41C22×C916yescomplemented
104C22×Q8—312no—
105C22×Q8—312no—
106C22×Q8—31no—
107C22×Q8—32no—
108C22×Q8—312no—
109C22×Q8C22×C911yescharacteristic
110C22×Q8C22×C9112yescomplemented
111C22×D4—31no—
112C22×D4—32no—
113C22×D4C22⋊C911yescharacteristic
114C23×C4—32no—
115C23×C4—32no—
116C23×C4—31no—
117C23×C3—28no—
118C23×C3—36no—
119C23×C3—64no—
120C23×C3C22×A4112yes—
121C23×C3C22×A411yescharacteristic
122C3×Q8—33no—
123C3×Q8—38no—
124C3×Q8—324no—
125C3×Q8—32no—
126C3×Q8—316no—
127C3×Q8C24×C311yescharacteristic
128C3×D4—34no—
129C3×D4—312no—
130C3×D4—332no—
131C3×D4C22×A4116yes—
132C2×C3×C4—332no—
133C2×C3×C4—312no—
134C2×C3×C4—33no—
135C2×C3×C4—33no—
136C2×C3×C4—38no—
137C2×C3×C4—324no—
138C2×C3×C4—312no—
139C2×C3×C4—34no—
140C2×C3×C4C22×A416yes—
141C2×C9—46no—
142C2×C9—41no—
143C2×C9—88no—
144C24—31no—
145C24C2×C22⋊C912yes—
146#41—396no—
147#41—38no—
148#41—316no—
149#41—348no—
150#41—332no—
151#41—312no—
152#41C23×C914yescomplemented
153C2×Q8—316no—
154C2×Q8—312no—
155C2×Q8—348no—
156C2×Q8—316no—
157C2×Q8—312no—
158C2×Q8—33no—
159C2×Q8—312no—
160C2×Q8—324no—
161C2×Q8C23×C913yes—
162C2×Q8C23×C918yescomplemented
163C2×D4—36no—
164C2×D4—36no—
165C2×D4—324no—
166C2×D4C2×C22⋊C9112yes—
167C22×C4—324no—
168C22×C4—31no—
169C22×C4—32no—
170C22×C4—312no—
171C22×C4—312no—
172C22×C4—36no—
173C22×C4—36no—
174C22×C4C2×C22⋊C911yescharacteristic
175C22×C3—224no—
176C22×C3—34no—
177C22×C3—612no—
178C22×C32−1+4⋊C314yes—
179C22×C3C23×A418yes—
180C22×C3C23×A413yes—
181C3×C4—38no—
182C3×C4—33no—
183C3×C4—31no—
184C3×C4C23×A414yes—
185C9—41noSylow
186C23—28no—
187C23—36no—
188C23—64no—
189C23C22×C22⋊C9112yes—
190C23C22×C22⋊C911yescharacteristic
191Q8—33no—
192Q8—38no—
193Q8—324no—
194Q8—32no—
195Q8—316no—
196Q8C24×C911yescharacteristic
197D4—34no—
198D4—312no—
199D4—332no—
200D4C22×C22⋊C9116yes—
201C2×C4—332no—
202C2×C4—33no—
203C2×C4—312no—
204C2×C4—33no—
205C2×C4—38no—
206C2×C4—324no—
207C2×C4—34no—
208C2×C4—312no—
209C2×C4C22×C22⋊C916yes—
210C2×C3—28no—
211C2×C3—64no—
212C2×C3C2×2−1+4⋊C316yes—
213C2×C3C24×A411yescharacteristic
214C22—224no—
215C22—34no—
216C22—612no—
217C222−1+4⋊C914yesdirect product factor
218C22C23×C22⋊C918yes—
219C22C23×C22⋊C913yes—
220C4—31no—
221C4—38no—
222C4—33no—
223C4C23×C22⋊C914yes—
224C3C22×2−1+4⋊C311yescharacteristic
225C2—28no—
226C2—64no—
227C2C2×2−1+4⋊C916yesdirect product factor
228C2C24×C22⋊C911yescharacteristic
subgroupG/H
center, socleC23×C3C22×A4
commutator, hypocenterQ8C24×C9
FrattiniC2×C3C24×A4
Fitting, prime radicalC22×C3×2−1+4C3
cosocleC3×Q8C24×C3
hypercenterC22×C3×D4A4
LCSG ▷ Q8
UCSC1 ◁ C23×C3 ◁ C22×C3×D4

Complements

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

NH ≅ G/Ntype
1. C2×2−1+4⋊C9C2direct (N × H)
2. C22×#41⋊C9C2semidirect
3. C23×Q8⋊C9C2semidirect
6. 2−1+4⋊C9C22direct (N × H)
7. C2×#41⋊C9C22semidirect
9. C22×Q8⋊C9C22semidirect
20. #41⋊C9C23semidirect
22. C2×Q8⋊C9C23semidirect
23. C22×2−1+4C9semidirect
53. C2×2−1+4C2×C9semidirect
56. C22×#41C2×C9semidirect
58. C23×Q8C2×C9semidirect
97. 2−1+4C22×C9semidirect
103. C2×#41C22×C9semidirect
110. C22×Q8C22×C9semidirect
152. #41C23×C9semidirect
162. C2×Q8C23×C9semidirect
217. C222−1+4⋊C9direct (N × H)
227. C2C2×2−1+4⋊C9direct (N × H)

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
C22×#41⋊C92
C23×Q8⋊C92
C22×C3×2−1+43
C22×D4×C94