Finite Group Databasebeta

← #125×C22⋊C9 #11919703

Subgroups — #125×C22⋊C9 #11919703

Order 1152.

528 conjugacy classes of subgroups; only the 110 normal subgroups are shown.

normal subgroups only

This group has 528 conjugacy classes of subgroups — too many to draw. Only its 110 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
1C4⋊C4×C22⋊C9C214yesmaximal
2C4⋊C4×C22⋊C9C212yesmaximal
3C42×C22⋊C9C211yesmaximal, characteristic
4C22×C3×#125C311yesmaximal, characteristic
5C2×C4×C22⋊C9C2212yes—
6C2×C4×C22⋊C9C2214yes—
7C2×C4×C22⋊C9C2211yescharacteristic
8C9×#125—41nomaximal
9C2×C3×#125—31no—
10C2×C3×#125—32no—
11C2×C3×#125—34no—
12C2×C3×#125—31no—
13C22×C3×C4⋊C4C2×C314yes—
14C22×C3×C4⋊C4C2×C312yes—
15C22×C3×C42C2×C311yescharacteristic
16C22×C22⋊C9C2311yescharacteristic
17C4×C22⋊C9—22no—
18C4×C22⋊C9—24no—
19C4×C22⋊C9Q812yes—
20C9×C4⋊C4—42no—
21C9×C4⋊C4—44no—
22C42×C9—41no—
23C22×#125C911yescharacteristic, complemented, Sylow
24C23×C3×C4C22×C312yes—
25C23×C3×C4C22×C314yes—
26C23×C3×C4C22×C311yescharacteristic
27C3×#125—38no—
28C3×#125—34no—
29C3×#125—32no—
30C3×#125—34no—
31C3×#125—32no—
32C3×#125—31no—
33C3×#125A411yescharacteristic
34C2×C3×C4⋊C4—32no—
35C2×C3×C4⋊C4—34no—
36C2×C3×C4⋊C4—32no—
37C2×C3×C4⋊C4—34no—
38C2×C3×C4⋊C4—34no—
39C2×C3×C4⋊C4—38no—
40C2×C3×C42—31no—
41C2×C3×C42—31no—
42C2×C3×C42—32no—
43C2×C22⋊C9C2×Q811yescharacteristic
44C2×C22⋊C9#4112yes—
45C2×C4×C9—41no—
46C2×C4×C9—42no—
47C2×C4×C9—44no—
48C2×#125—31no—
49C2×#125—32no—
50C2×#125—34no—
51C2×#125—31no—
52C22×C4⋊C4C2×C914yes—
53C22×C4⋊C4C2×C912yes—
54C22×C42C2×C911yescharacteristic
55C24×C3C23×C311yescharacteristic
56C22×C3×C4—22no—
57C22×C3×C4—24no—
58C22×C3×C4—31no—
59C22×C3×C4—31no—
60C22×C3×C4—32no—
61C22×C3×C4—32no—
62C22×C3×C4—34no—
63C22×C3×C4—32no—
64C22×C3×C4—34no—
65C22×C3×C4—62no—
66C22×C3×C4—64no—
67C22×C3×C4C3×Q812yes—
68C3×C4⋊C4—34no—
69C3×C4⋊C4—38no—
70C3×C4⋊C4—34no—
71C3×C4⋊C4—38no—
72C3×C4⋊C4—34no—
73C3×C4⋊C4—32no—
74C3×C4⋊C4C2×A414yes—
75C3×C4⋊C4C2×A412yes—
76C3×C42—32no—
77C3×C42—32no—
78C3×C42—31no—
79C3×C42C2×A411yescharacteristic
80C22×C9—41no—
81C22⋊C9#12511yescharacteristic, direct product factor
82C4×C9—42no—
83C4×C9—82no—
84C4×C9—84no—
85C23×C4C22×C914yes—
86C23×C4C22×C912yes—
87C23×C4C22×C911yescharacteristic
88#125—38no—
89#125—34no—
90#125—32no—
91#125—34no—
92#125—32no—
93#125—31no—
94#125C22⋊C911yescharacteristic, direct product factor
95C2×C4⋊C4—32no—
96C2×C4⋊C4—34no—
97C2×C4⋊C4—32no—
98C2×C4⋊C4—34no—
99C2×C4⋊C4—34no—
100C2×C4⋊C4—38no—
101C2×C42—31no—
102C2×C42—31no—
103C2×C42—32no—
104C23×C3—31no—
105C23×C3—32no—
106C23×C3—31no—
107C23×C3C2×C3×Q811yescharacteristic
108C23×C3C3×#4112yes—
109C2×C3×C4—32no—
110C2×C3×C4—31no—
111C2×C3×C4—32no—
112C2×C3×C4—32no—
113C2×C3×C4—32no—
114C2×C3×C4—32no—
115C2×C3×C4—34no—
116C2×C3×C4—62no—
117C2×C3×C4—64no—
118C2×C3×C4—62no—
119C2×C3×C4—64no—
120C2×C3×C4—62no—
121C2×C3×C4—64no—
122C2×C3×C4—62no—
123C2×C3×C4—64no—
124C2×C3×C4C22×A412yes—
125C2×C3×C4C22×A414yes—
126C2×C3×C4C22×A411yescharacteristic
127C2×C9—41no—
128C2×C9—42no—
129C24C23×C911yescharacteristic
130C22×C4—24no—
131C22×C4—22no—
132C22×C4—31no—
133C22×C4—31no—
134C22×C4—32no—
135C22×C4—32no—
136C22×C4—34no—
137C22×C4—32no—
138C22×C4—34no—
139C22×C4—64no—
140C22×C4—62no—
141C22×C4Q8×C912yes—
142C4⋊C4—34no—
143C4⋊C4—38no—
144C4⋊C4—34no—
145C4⋊C4—38no—
146C4⋊C4—34no—
147C4⋊C4—32no—
148C4⋊C4C2×C22⋊C914yes—
149C4⋊C4C2×C22⋊C912yes—
150C42—32no—
151C42—32no—
152C42—31no—
153C42C2×C22⋊C911yescharacteristic
154C22×C3—31no—
155C22×C3—32no—
156C22×C3—32no—
157C22×C3—31no—
158C22×C3—31no—
159C22×C3—32no—
160C22×C3—32no—
161C22×C3C3×#12511yescharacteristic
162C22×C3C23×A411yescharacteristic
163C3×C4—22no—
164C3×C4—24no—
165C3×C4—32no—
166C3×C4—62no—
167C3×C4—64no—
168C3×C4Q8×A412yes—
169C9—41noSylow
170C23—31no—
171C23—32no—
172C23—31no—
173C23C2×Q8×C911yescharacteristic
174C23C9×#4112yes—
175C2×C4—32no—
176C2×C4—31no—
177C2×C4—32no—
178C2×C4—32no—
179C2×C4—32no—
180C2×C4—32no—
181C2×C4—34no—
182C2×C4—62no—
183C2×C4—64no—
184C2×C4—62no—
185C2×C4—64no—
186C2×C4—62no—
187C2×C4—64no—
188C2×C4—62no—
189C2×C4—64no—
190C2×C4C22×C22⋊C912yes—
191C2×C4C22×C22⋊C914yes—
192C2×C4C22×C22⋊C911yescharacteristic
193C2×C3—31no—
194C2×C3—32no—
195C2×C3—31no—
196C2×C3C2×Q8×A411yescharacteristic
197C2×C3A4×#4112yes—
198C22—31no—
199C22—32no—
200C22—32no—
201C22—31no—
202C22—31no—
203C22—32no—
204C22—32no—
205C22C9×#12511yescharacteristic, complemented
206C22C23×C22⋊C911yescharacteristic
207C4—22no—
208C4—24no—
209C4—32no—
210C4—62no—
211C4—64no—
212C4Q8×C22⋊C912yes—
213C3A4×#12511yescharacteristic
214C2—31no—
215C2—31no—
216C2—32no—
217C2C2×Q8×C22⋊C911yescharacteristic
218C2#41×C22⋊C912yes—
subgroupG/H
center, FrattiniC22×C3C23×A4
commutatorC24C23×C9
FittingC22×C3×#125C3
socle, prime radical, cosocleC24×C3C23×C3
hypercenterC3×#125A4
hypocenterC22C9×#125
LCSG ▷ C24 ▷ C22
UCSC1 ◁ C22×C3 ◁ C3×#125

Complements

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

NH ≅ G/Ntype
23. C22×#125C9semidirect
81. C22⋊C9#125direct (N × H)
94. #125C22⋊C9direct (N × H)
205. C22C9×#125semidirect

Maximal subgroups

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

subgroupindex
C4⋊C4×C22⋊C92
C42×C22⋊C92
C22×C3×#1253
C9×#1254