Finite Group Databasebeta

← C22×Q8×C22⋊C9 #11919867

Subgroups — C22×Q8×C22⋊C9 #11919867

Order 1152.

2452 conjugacy classes of subgroups; only the 390 normal subgroups are shown.

normal subgroups only

This group has 2452 conjugacy classes of subgroups — too many to draw. Only its 390 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×Q8×C22⋊C9C2112yesmaximal, direct product factor
2C22×C4×C22⋊C9C213yesmaximal
3C24×C3×Q8C311yesmaximal, characteristic
4C23×C22⋊C9C2211yescharacteristic
5C22×Q8×C9—41nomaximal
6Q8×C22⋊C9C22116yesdirect product factor
7C2×C4×C22⋊C9C22118yes—
8C23×C3×Q8—33no—
9C23×C3×Q8—312no—
10C23×C3×Q8—31no—
11C23×C3×Q8C2×C3112yes—
12C24×C3×C4C2×C313yes—
13C22×C22⋊C9Q814yesdirect product factor
14C22×C22⋊C9C2313yes—
15C2×Q8×C9—412no—
16C22×C4×C9—43no—
17C4×C22⋊C9C23112yes—
18C24×Q8C911yescharacteristic, complemented, Sylow
19C25×C3C22×C311yescharacteristic
20C22×C3×Q8—336no—
21C22×C3×Q8—348no—
22C22×C3×Q8—332no—
23C22×C3×Q8—336no—
24C22×C3×Q8—32no—
25C22×C3×Q8—312no—
26C22×C3×Q8—312no—
27C22×C3×Q8—33no—
28C22×C3×Q8A411yescharacteristic
29C22×C3×Q8C22×C3116yes—
30C23×C3×C4—33no—
31C23×C3×C4—33no—
32C23×C3×C4—318no—
33C23×C3×C4C22×C3118yes—
34C23×C9—41no—
35C2×C22⋊C9C2×Q816yesdirect product factor
36C2×C22⋊C9C2411yescharacteristic
37Q8×C9—416no—
38C2×C4×C9—418no—
39C23×Q8—33no—
40C23×Q8—312no—
41C23×Q8—31no—
42C23×Q8C2×C9112yescomplemented
43C24×C4C2×C913yes—
44C24×C3—34no—
45C24×C3—33no—
46C24×C3—31no—
47C24×C3C3×Q814yes—
48C24×C3C23×C313yes—
49C2×C3×Q8—348no—
50C2×C3×Q8—3144no—
51C2×C3×Q8—324no—
52C2×C3×Q8—348no—
53C2×C3×Q8—316no—
54C2×C3×Q8—336no—
55C2×C3×Q8C2×A4112yes—
56C22×C3×C4—318no—
57C22×C3×C4—324no—
58C22×C3×C4—33no—
59C22×C3×C4—318no—
60C22×C3×C4—318no—
61C22×C3×C4—318no—
62C22×C3×C4—336no—
63C22×C3×C4C2×A413yes—
64C22×C3×C4C23×C3112yes—
65C22×C9—44no—
66C22×C9—43no—
67C22⋊C9C22×Q811yescharacteristic, direct product factor
68C4×C9—412no—
69C25C22×C911yescharacteristic
70C22×Q8—336no—
71C22×Q8—348no—
72C22×Q8—332no—
73C22×Q8—336no—
74C22×Q8—32no—
75C22×Q8—312no—
76C22×Q8—312no—
77C22×Q8—33no—
78C22×Q8C22⋊C911yescharacteristic, direct product factor
79C22×Q8C22×C9116yescomplemented
80C23×C4—33no—
81C23×C4—33no—
82C23×C4—318no—
83C23×C4C22×C9118yes—
84C23×C3—33no—
85C23×C3—312no—
86C23×C3—36no—
87C23×C3—32no—
88C23×C3—312no—
89C23×C3—34no—
90C23×C3—34no—
91C23×C3—33no—
92C23×C3—33no—
93C23×C3C2×C3×Q816yes—
94C23×C3C22×A411yescharacteristic
95C23×C3C24×C311yescharacteristic
96C3×Q8—332no—
97C3×Q8—348no—
98C3×Q8C22×A4116yes—
99C2×C3×C4—336no—
100C2×C3×C4—318no—
101C2×C3×C4—312no—
102C2×C3×C4—336no—
103C2×C3×C4—312no—
104C2×C3×C4C22×A4118yes—
105C2×C9—46no—
106C2×C9—41no—
107C24—33no—
108C24—34no—
109C24—31no—
110C24Q8×C914yescomplemented
111C24C23×C913yes—
112C2×Q8—348no—
113C2×Q8—3144no—
114C2×Q8—324no—
115C2×Q8—316no—
116C2×Q8—348no—
117C2×Q8—336no—
118C2×Q8C2×C22⋊C9112yesdirect product factor
119C22×C4—318no—
120C22×C4—324no—
121C22×C4—33no—
122C22×C4—318no—
123C22×C4—318no—
124C22×C4—318no—
125C22×C4—336no—
126C22×C4C2×C22⋊C913yes—
127C22×C4C23×C9112yes—
128C22×C3—36no—
129C22×C3—31no—
130C22×C3—36no—
131C22×C3—38no—
132C22×C3—312no—
133C22×C3—36no—
134C22×C3—36no—
135C22×C3—33no—
136C22×C3—31no—
137C22×C3Q8×A414yes—
138C22×C3C22×C3×Q811yescharacteristic
139C22×C3C23×A413yes—
140C3×C4—312no—
141C3×C4C23×A4112yes—
142C9—41noSylow
143C23—33no—
144C23—312no—
145C23—36no—
146C23—32no—
147C23—312no—
148C23—33no—
149C23—33no—
150C23—34no—
151C23—34no—
152C23C2×Q8×C916yescomplemented
153C23C22×C22⋊C911yescharacteristic
154C23C24×C911yescharacteristic
155Q8—332no—
156Q8—348no—
157Q8C22×C22⋊C9116yesdirect product factor
158C2×C4—336no—
159C2×C4—318no—
160C2×C4—312no—
161C2×C4—336no—
162C2×C4—312no—
163C2×C4C22×C22⋊C9118yes—
164C2×C3—36no—
165C2×C3—31no—
166C2×C3—31no—
167C2×C3C2×Q8×A416yes—
168C2×C3C24×A411yescharacteristic
169C22—36no—
170C22—31no—
171C22—36no—
172C22—38no—
173C22—31no—
174C22—33no—
175C22—36no—
176C22—312no—
177C22—36no—
178C22Q8×C22⋊C914yesdirect product factor
179C22C22×Q8×C911yescharacteristic, complemented
180C22C23×C22⋊C913yes—
181C4—312no—
182C4C23×C22⋊C9112yes—
183C3C22×Q8×A411yescharacteristic
184C2—31no—
185C2—36no—
186C2—31no—
187C2C2×Q8×C22⋊C916yesdirect product factor
188C2C24×C22⋊C911yescharacteristic
subgroupG/H
centerC23×C3C22×A4
commutatorC23C24×C9
FrattiniC2×C3C24×A4
FittingC24×C3×Q8C3
socle, prime radicalC25×C3C22×C3
cosocleC23×C3C24×C3
hypercenterC22×C3×Q8A4
hypocenterC22C22×Q8×C9
LCSG ▷ C23 ▷ C22
UCSC1 ◁ C23×C3 ◁ C22×C3×Q8

Complements

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

NH ≅ G/Ntype
1. C2×Q8×C22⋊C9C2direct (N × H)
6. Q8×C22⋊C9C22direct (N × H)
13. C22×C22⋊C9Q8direct (N × H)
18. C24×Q8C9semidirect
35. C2×C22⋊C9C2×Q8direct (N × H)
42. C23×Q8C2×C9semidirect
67. C22⋊C9C22×Q8direct (N × H)
78. C22×Q8C22⋊C9direct (N × H)
79. C22×Q8C22×C9semidirect
110. C24Q8×C9semidirect
118. C2×Q8C2×C22⋊C9direct (N × H)
152. C23C2×Q8×C9semidirect
157. Q8C22×C22⋊C9direct (N × H)
178. C22Q8×C22⋊C9direct (N × H)
179. C22C22×Q8×C9semidirect
187. C2C2×Q8×C22⋊C9direct (N × H)

Maximal subgroups

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

subgroupindex
C2×Q8×C22⋊C92
C22×C4×C22⋊C92
C24×C3×Q83
C22×Q8×C94