Finite Group Databasebeta

← C2×C9×#557 #11768197

Subgroups — C2×C9×#557 #11768197

Order 1152.

1572 conjugacy classes of subgroups.

The subgroup lattice has 192 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C9×#557C2116yesmaximal, direct product factor
2C2×C9×C4⋊Q8C213yesmaximal
3C2×C9×#125C216yesmaximal
4C2×C4×Q8×C9C212yesmaximal
5C2×C4×Q8×C9C213yesmaximal
6C2×C4×Q8×C9C211yesmaximal, characteristic
7C2×C3×#557C311yesmaximal, characteristic
8C22×Q8×C9C2213yes—
9C22×Q8×C9C2211yescharacteristic
10C9×C4⋊Q8C22124yes—
11C9×#125C22148yes—
12C4×Q8×C9C22116yes—
13C4×Q8×C9C22124yes—
14C4×Q8×C9C2218yes—
15C2×C9×C4⋊C4C2216yes—
16C2×C9×C4⋊C4C2216yes—
17C2×C9×C4⋊C4C2213yes—
18C2×C9×C4⋊C4C2216yes—
19C2×C9×C4⋊C4C2211yescharacteristic
20C2×C42×C9C2216yes—
21C2×C42×C9C2213yes—
22C3×#557C2×C3116yes—
23C2×C3×C4⋊Q8C2×C313yes—
24C2×C3×#125C2×C316yes—
25C2×C3×C4×Q8C2×C312yes—
26C2×C3×C4×Q8C2×C313yes—
27C2×C3×C4×Q8C2×C311yescharacteristic
28C2×Q8×C9—212no—
29C2×Q8×C9Q818yescomplemented
30C2×Q8×C9C23112yes—
31C2×Q8×C9C2314yes—
32C22×C4×C9C2312yes—
33C22×C4×C9C2313yes—
34C22×C4×C9C2316yes—
35C22×C4×C9C2313yes—
36C22×C4×C9C2311yescharacteristic
37C9×C4⋊C4C2314yes—
38C9×C4⋊C4C23124yes—
39C9×C4⋊C4C23112yes—
40C9×C4⋊C4C23124yes—
41C9×C4⋊C4C23124yes—
42C42×C9C23124yes—
43C42×C9C23112yes—
44C2×#557C911yescharacteristic, direct product factor, Sylow
45C22×C3×Q8C22×C313yes—
46C22×C3×Q8C22×C311yescharacteristic
47C3×C4⋊Q8C22×C3124yes—
48C3×#125C22×C3148yes—
49C3×C4×Q8C22×C3116yes—
50C3×C4×Q8C22×C3124yes—
51C3×C4×Q8C22×C318yes—
52C2×C3×C4⋊C4C22×C311yescharacteristic
53C2×C3×C4⋊C4C22×C316yes—
54C2×C3×C4⋊C4C22×C313yes—
55C2×C3×C4⋊C4C22×C316yes—
56C2×C3×C4⋊C4C22×C316yes—
57C2×C3×C42C22×C316yes—
58C2×C3×C42C22×C313yes—
59C23×C9C2411yescharacteristic
60Q8×C9—224no—
61Q8×C9C2×Q8116yescomplemented
62C2×C4×C9—212no—
63C2×C4×C9—24no—
64C2×C4×C9—26no—
65C2×C4×C9C2×Q8112yes—
66C2×C4×C9#4114yes—
67C2×C4×C9C2414yes—
68C2×C4×C9C2416yes—
69C2×C4×C9C24112yes—
70C2×C4×C9C2416yes—
71C2×C4×C9C2412yes—
72#557C2×C9116yesdirect product factor
73C2×C4⋊Q8C2×C913yes—
74C2×#125C2×C916yes—
75C2×C4×Q8C2×C912yes—
76C2×C4×Q8C2×C913yes—
77C2×C4×Q8C2×C911yescharacteristic
78C2×C3×Q8—212no—
79C2×C3×Q8C3×Q818yes—
80C2×C3×Q8C23×C3112yes—
81C2×C3×Q8C23×C314yes—
82C22×C3×C4C23×C312yes—
83C22×C3×C4C23×C313yes—
84C22×C3×C4C23×C316yes—
85C22×C3×C4C23×C313yes—
86C22×C3×C4C23×C311yescharacteristic
87C3×C4⋊C4C23×C314yes—
88C3×C4⋊C4C23×C3124yes—
89C3×C4⋊C4C23×C3112yes—
90C3×C4⋊C4C23×C3124yes—
91C3×C4⋊C4C23×C3124yes—
92C3×C42C23×C3124yes—
93C3×C42C23×C3112yes—
94C22×C9C22×Q812yes—
95C22×C9C2×#4112yes—
96C22×C92−1+412yes—
97C22×C9C2511yescharacteristic
98C4×C9—212no—
99C4×C9—24no—
100C4×C9—26no—
101C4×C9C22×Q8112yes—
102C4×C9C2×#4114yes—
103C22×Q8C22×C913yes—
104C22×Q8C22×C911yescharacteristic
105C4⋊Q8C22×C9124yes—
106#125C22×C9148yes—
107C4×Q8C22×C9116yes—
108C4×Q8C22×C9124yes—
109C4×Q8C22×C918yes—
110C2×C4⋊C4C22×C911yescharacteristic
111C2×C4⋊C4C22×C916yes—
112C2×C4⋊C4C22×C913yes—
113C2×C4⋊C4C22×C916yes—
114C2×C4⋊C4C22×C916yes—
115C2×C42C22×C916yes—
116C2×C42C22×C913yes—
117C23×C3C24×C311yescharacteristic
118C3×Q8—224no—
119C3×Q8C2×C3×Q8116yes—
120C2×C3×C4—212no—
121C2×C3×C4—24no—
122C2×C3×C4—26no—
123C2×C3×C4C2×C3×Q8112yes—
124C2×C3×C4C3×#4114yes—
125C2×C3×C4C24×C314yes—
126C2×C3×C4C24×C316yes—
127C2×C3×C4C24×C3112yes—
128C2×C3×C4C24×C316yes—
129C2×C3×C4C24×C312yes—
130C2×C9#55714yesdirect product factor
131C2×C9C23×Q811yescharacteristic
132C2×C9C22×#4111yescharacteristic
133C2×C9C2×2−1+411yescharacteristic
134C2×Q8—212no—
135C2×Q8Q8×C918yescomplemented
136C2×Q8C23×C9112yes—
137C2×Q8C23×C914yes—
138C22×C4C23×C912yes—
139C22×C4C23×C913yes—
140C22×C4C23×C916yes—
141C22×C4C23×C913yes—
142C22×C4C23×C911yescharacteristic
143C4⋊C4C23×C914yes—
144C4⋊C4C23×C9124yes—
145C4⋊C4C23×C9112yes—
146C4⋊C4C23×C9124yes—
147C4⋊C4C23×C9124yes—
148C42C23×C9124yes—
149C42C23×C9112yes—
150C22×C3C22×C3×Q812yes—
151C22×C3C2×C3×#4112yes—
152C22×C3C3×2−1+412yes—
153C22×C3C25×C311yescharacteristic
154C3×C4—212no—
155C3×C4—24no—
156C3×C4—26no—
157C3×C4C22×C3×Q8112yes—
158C3×C4C2×C3×#4114yes—
159C9C2×#55711yescharacteristic, direct product factor, Sylow
160C23C24×C911yescharacteristic
161Q8—224no—
162Q8C2×Q8×C9116yescomplemented
163C2×C4—212no—
164C2×C4—24no—
165C2×C4—26no—
166C2×C4C2×Q8×C9112yes—
167C2×C4C9×#4114yes—
168C2×C4C24×C914yes—
169C2×C4C24×C916yes—
170C2×C4C24×C9112yes—
171C2×C4C24×C916yes—
172C2×C4C24×C912yes—
173C2×C3C3×#55714yes—
174C2×C3C23×C3×Q811yescharacteristic
175C2×C3C22×C3×#4111yescharacteristic
176C2×C3C2×C3×2−1+411yescharacteristic
177C22C22×Q8×C912yes—
178C22C2×C9×#4112yes—
179C22C9×2−1+412yes—
180C22C25×C911yescharacteristic
181C4—212no—
182C4—24no—
183C4—26no—
184C4C22×Q8×C9112yes—
185C4C2×C9×#4114yes—
186C3C2×C3×#55711yescharacteristic
187C2C9×#55714yesdirect product factor
188C2C23×Q8×C911yescharacteristic
189C2C22×C9×#4111yescharacteristic
190C2C2×C9×2−1+411yescharacteristic
subgroupG/H
centerC23×C9C24
commutatorC22C25×C9
Frattini, cosocleC22×C3C25×C3
socle, prime radicalC23×C3C24×C3
LCSG ▷ C22 ▷ C1
UCSC1 ◁ C23×C9 ◁ G

Complements

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

NH ≅ G/Ntype
1. C9×#557C2direct (N × H)
29. C2×Q8×C9Q8semidirect
44. C2×#557C9direct (N × H)
61. Q8×C9C2×Q8semidirect
72. #557C2×C9direct (N × H)
130. C2×C9#557direct (N × H)
135. C2×Q8Q8×C9semidirect
159. C9C2×#557direct (N × H)
162. Q8C2×Q8×C9semidirect
187. C2C9×#557direct (N × H)

Maximal subgroups

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

subgroupindex
C9×#5572
C2×C9×C4⋊Q82
C2×C9×#1252
C2×C4×Q8×C92
C2×C3×#5573