Finite Group Databasebeta

← #127×C22⋊C9 #11919711

Subgroups — #127×C22⋊C9 #11919711

Order 1152.

1252 conjugacy classes of subgroups; only the 130 normal subgroups are shown.

normal subgroups only

This group has 1252 conjugacy classes of subgroups — too many to draw. Only its 130 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×D4×C22⋊C9C216yesmaximal, complemented
2C42×C22⋊C9C211yesmaximal, characteristic, complemented
3C22×C3×#127C311yesmaximal, characteristic
4C23×C22⋊C9C2214yes—
5D4×C22⋊C9—212no—
6C2×C4×C22⋊C9C2213yes—
7C9×#127—41nomaximal
8C23×C3×D4C2×C316yes—
9C2×C3×#127—31no—
10C2×C3×#127—31no—
11C2×C3×#127—36no—
12C22×C3×C42C2×C311yescharacteristic
13C22×C22⋊C9—212no—
14C22×C22⋊C9C2311yescharacteristic
15C2×D4×C9—46no—
16C4×C22⋊C9D416yescomplemented
17C42×C9—41no—
18C22×#127C911yescharacteristic, complemented, Sylow
19C25×C3C22×C314yes—
20C22×C3×D4—212no—
21C22×C3×D4—36no—
22C22×C3×D4—36no—
23C22×C3×D4—312no—
24C22×C3×D4—612no—
25C23×C3×C4C22×C313yes—
26C3×#127—38no—
27C3×#127—36no—
28C3×#127—36no—
29C3×#127—31no—
30C3×#127A411yescharacteristic
31C2×C3×C42—31no—
32C2×C3×C42—33no—
33C23×C9—44no—
34C2×C22⋊C9—44no—
35C2×C22⋊C9C2×D413yes—
36D4×C9—812no—
37C2×C4×C9—43no—
38C23×D4C2×C916yescomplemented
39C2×#127—31no—
40C2×#127—31no—
41C2×#127—36no—
42C22×C42C2×C911yescharacteristic, complemented
43C24×C3—212no—
44C24×C3—34no—
45C24×C3—34no—
46C24×C3—612no—
47C24×C3C23×C311yescharacteristic
48C2×C3×D4—312no—
49C2×C3×D4—312no—
50C2×C3×D4—36no—
51C2×C3×D4—612no—
52C2×C3×D4—612no—
53C2×C3×D4—624no—
54C2×C3×D4—612no—
55C2×C3×D4—624no—
56C2×C3×D4—612no—
57C2×C3×D4C2×A416yes—
58C22×C3×C4—33no—
59C22×C3×C4—33no—
60C22×C3×C4—36no—
61C22×C3×C4C3×D416yes—
62C3×C42—32no—
63C3×C42—33no—
64C3×C42C2×A411yescharacteristic
65C22×C9—41no—
66C22×C9—812no—
67C22⋊C9#12711yescharacteristic, direct product factor
68C4×C9—46no—
69C25C22×C914yes—
70C22×D4—212no—
71C22×D4—36no—
72C22×D4—36no—
73C22×D4—312no—
74C22×D4—612no—
75C23×C4C22×C913yes—
76#127—38no—
77#127—36no—
78#127—36no—
79#127—31no—
80#127C22⋊C911yescharacteristic, direct product factor
81C2×C42—31no—
82C2×C42—33no—
83C23×C3—33no—
84C23×C3—31no—
85C23×C3—34no—
86C23×C3—44no—
87C23×C3—612no—
88C23×C3—612no—
89C23×C3—612no—
90C23×C3—612no—
91C23×C3—1212no—
92C23×C3—128no—
93C23×C3C2×C3×D413yes—
94C23×C3C22×A414yes—
95C3×D4—212no—
96C3×D4—624no—
97C3×D4—624no—
98C3×D4—612no—
99C2×C3×C4—36no—
100C2×C3×C4—33no—
101C2×C3×C4—36no—
102C2×C3×C4—36no—
103C2×C3×C4—36no—
104C2×C3×C4C22×A413yes—
105C2×C9—43no—
106C2×C9—164no—
107C24—212no—
108C24—34no—
109C24—34no—
110C24—612no—
111C24C23×C911yescharacteristic
112C2×D4—312no—
113C2×D4—312no—
114C2×D4—36no—
115C2×D4—612no—
116C2×D4—612no—
117C2×D4—624no—
118C2×D4—612no—
119C2×D4—624no—
120C2×D4—612no—
121C2×D4C2×C22⋊C916yescomplemented
122C22×C4—33no—
123C22×C4—33no—
124C22×C4—36no—
125C22×C4D4×C916yescomplemented
126C42—32no—
127C42—33no—
128C42C2×C22⋊C911yescharacteristic, complemented
129C22×C3—212no—
130C22×C3—33no—
131C22×C3—32no—
132C22×C3—33no—
133C22×C3—33no—
134C22×C3—612no—
135C22×C3—124no—
136C22×C3—1212no—
137C22×C3—124no—
138C22×C3—1212no—
139C22×C3C3×#12711yescharacteristic
140C22×C3C23×A411yescharacteristic
141C3×C4—36no—
142C3×C4D4×A416yes—
143C9—41noSylow
144C23—33no—
145C23—31no—
146C23—34no—
147C23—44no—
148C23—612no—
149C23—612no—
150C23—612no—
151C23—612no—
152C23—1212no—
153C23—128no—
154C23C2×D4×C913yes—
155C23C22×C22⋊C914yes—
156D4—212no—
157D4—624no—
158D4—624no—
159D4—612no—
160C2×C4—36no—
161C2×C4—33no—
162C2×C4—36no—
163C2×C4—36no—
164C2×C4—36no—
165C2×C4C22×C22⋊C913yes—
166C2×C3—33no—
167C2×C3—31no—
168C2×C3—44no—
169C2×C3—124no—
170C2×C3C2×D4×A413yes—
171C22—212no—
172C22—33no—
173C22—32no—
174C22—33no—
175C22—33no—
176C22—612no—
177C22—124no—
178C22—1212no—
179C22—124no—
180C22—1212no—
181C22C9×#12711yescharacteristic, complemented
182C22C23×C22⋊C911yescharacteristic
183C4—36no—
184C4D4×C22⋊C916yescomplemented
185C3A4×#12711yescharacteristic
186C2—31no—
187C2—33no—
188C2—44no—
189C2—124no—
190C2C2×D4×C22⋊C913yes—
subgroupG/H
center, FrattiniC22×C3C23×A4
commutatorC24C23×C9
Fitting, prime radicalC22×C3×#127C3
socle, cosocleC24×C3C23×C3
hypercenterC3×#127A4
hypocenterC22C9×#127
LCSG ▷ C24 ▷ C22
UCSC1 ◁ C22×C3 ◁ C3×#127

Complements

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

NH ≅ G/Ntype
1. C2×D4×C22⋊C9C2semidirect
2. C42×C22⋊C9C2semidirect
16. C4×C22⋊C9D4semidirect
18. C22×#127C9semidirect
38. C23×D4C2×C9semidirect
42. C22×C42C2×C9semidirect
67. C22⋊C9#127direct (N × H)
80. #127C22⋊C9direct (N × H)
121. C2×D4C2×C22⋊C9semidirect
125. C22×C4D4×C9semidirect
128. C42C2×C22⋊C9semidirect
181. C22C9×#127semidirect
184. C4D4×C22⋊C9semidirect

Maximal subgroups

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

subgroupindex
C2×D4×C22⋊C92
C42×C22⋊C92
C22×C3×#1273
C9×#1274