Finite Group Databasebeta

← #2848⋊C9 #11919503

Subgroups — #2848⋊C9 #11919503

Order 1152.

412 conjugacy classes of subgroups; only the 36 normal subgroups are shown.

normal subgroups only

This group has 412 conjugacy classes of subgroups — too many to draw. Only its 36 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×C22⋊(C22⋊C9)C211yesmaximal, characteristic
2#379⋊C9C212yesmaximal
3C3×#2848C311yesmaximal, characteristic
4C2×C22⋊(C22⋊C9)C2211yescharacteristic
5Q8×C22⋊C9—41nomaximal
6C24×C3×C4C2×C311yescharacteristic
7C2×C3×C22⋊Q8—31no—
8C3×#385—32no—
9C3×#380—31no—
10C3×#379C2×C312yes—
11C22⋊(C22⋊C9)Q811yescharacteristic, complemented
12C4×C22⋊C9—41no—
13C4×C22⋊C9—42no—
14C4×C22⋊C9—82no—
15#2848C911yescharacteristic, complemented, Sylow
16C25×C3C22×C311yescharacteristic
17C22×C3×Q8A411yescharacteristic
18C23×C3×C4—31no—
19C23×C3×C4—31no—
20C23×C3×C4—62no—
21C23×C3×C4—62no—
22C3×C22⋊Q8—62no—
23C3×C22⋊Q8—62no—
24C2×C3×C4⋊C4—31no—
25C2×C3×C4⋊C4—32no—
26C2×C3×C22⋊C4—32no—
27C2×C3×C22⋊C4—32no—
28C3×#95—32no—
29C2×C22⋊C9—41no—
30C2×C22⋊C9—82no—
31Q8×C9—161no—
32C24×C4C2×C911yescharacteristic
33C2×C22⋊Q8—31no—
34#385—32no—
35#380—31no—
36#379C2×C912yes—
37C24×C3—31no—
38C24×C3—31no—
39C24×C3—62no—
40C24×C3—62no—
41C24×C3C3×Q811yescharacteristic
42C2×C3×Q8—61no—
43C2×C3×Q8—61no—
44C22×C3×C4—22no—
45C22×C3×C4—32no—
46C22×C3×C4—32no—
47C22×C3×C4—31no—
48C22×C3×C4—32no—
49C22×C3×C4—62no—
50C22×C3×C4—62no—
51C22×C3×C4—64no—
52C22×C3×C4—62no—
53C22×C3×C4—62no—
54C22×C3×C4—64no—
55C22×C3×C4—62no—
56C22×C3×C4—62no—
57C22×C3×C4C2×A411yescharacteristic
58C22×C3×C4C2×A412yes—
59C3×C4⋊C4—61no—
60C3×C4⋊C4—61no—
61C3×C4⋊C4—64no—
62C3×C22⋊C4—64no—
63C3×C22⋊C4—64no—
64C22⋊C9—41no—
65C22⋊C9—82no—
66C4×C9—162no—
67C4×C9—161no—
68C25C22×C911yescharacteristic
69C22×Q8C22⋊C911yescharacteristic, complemented
70C23×C4—31no—
71C23×C4—31no—
72C23×C4—62no—
73C23×C4—62no—
74C22⋊Q8—62no—
75C22⋊Q8—62no—
76C2×C4⋊C4—31no—
77C2×C4⋊C4—32no—
78C2×C22⋊C4—32no—
79C2×C22⋊C4—32no—
80#95—32no—
81C23×C3—22no—
82C23×C3—32no—
83C23×C3—32no—
84C23×C3—31no—
85C23×C3—31no—
86C23×C3—62no—
87C23×C3—62no—
88C23×C3—62no—
89C23×C3—62no—
90C23×C3—62no—
91C23×C3—64no—
92C23×C3—62no—
93C23×C3—62no—
94C23×C3—64no—
95C23×C3C22×A411yescharacteristic
96C3×Q8—41no—
97C3×Q8—121no—
98C2×C3×C4—31no—
99C2×C3×C4—31no—
100C2×C3×C4—32no—
101C2×C3×C4—62no—
102C2×C3×C4—64no—
103C2×C3×C4—62no—
104C2×C3×C4—62no—
105C2×C3×C4—64no—
106C2×C3×C4—62no—
107C2×C3×C4—62no—
108C2×C3×C4—62no—
109C2×C3×C4—62no—
110C2×C3×C4—64no—
111C2×C9—161no—
112C24—31no—
113C24—31no—
114C24—62no—
115C24—62no—
116C24Q8×C911yescharacteristic, complemented
117C2×Q8—61no—
118C2×Q8—61no—
119C22×C4—22no—
120C22×C4—32no—
121C22×C4—32no—
122C22×C4—31no—
123C22×C4—32no—
124C22×C4—62no—
125C22×C4—62no—
126C22×C4—64no—
127C22×C4—62no—
128C22×C4—62no—
129C22×C4—64no—
130C22×C4—62no—
131C22×C4—62no—
132C22×C4C2×C22⋊C911yescharacteristic
133C22×C4C2×C22⋊C912yes—
134C4⋊C4—61no—
135C4⋊C4—61no—
136C4⋊C4—64no—
137C22⋊C4—64no—
138C22⋊C4—64no—
139C22×C3—22no—
140C22×C3—31no—
141C22×C3—31no—
142C22×C3—32no—
143C22×C3—32no—
144C22×C3—62no—
145C22×C3—64no—
146C22×C3—62no—
147C22×C3—62no—
148C22×C3—62no—
149C22×C3—62no—
150C22×C3—62no—
151C22×C3—64no—
152C22×C3—62no—
153C22×C3Q8×A411yescharacteristic
154C3×C4—31no—
155C3×C4—42no—
156C3×C4—62no—
157C3×C4—122no—
158C3×C4#120⋊C311yescharacteristic
159C9—161noSylow
160C23—22no—
161C23—32no—
162C23—32no—
163C23—31no—
164C23—31no—
165C23—62no—
166C23—62no—
167C23—62no—
168C23—62no—
169C23—62no—
170C23—64no—
171C23—62no—
172C23—62no—
173C23—64no—
174C23C22×C22⋊C911yescharacteristic
175Q8—41no—
176Q8—121no—
177C2×C4—31no—
178C2×C4—31no—
179C2×C4—32no—
180C2×C4—62no—
181C2×C4—64no—
182C2×C4—62no—
183C2×C4—62no—
184C2×C4—64no—
185C2×C4—62no—
186C2×C4—62no—
187C2×C4—62no—
188C2×C4—62no—
189C2×C4—64no—
190C2×C3—31no—
191C2×C3—31no—
192C2×C3—62no—
193C2×C3—62no—
194C2×C3C2×#120⋊C311yescharacteristic
195C22—22no—
196C22—31no—
197C22—31no—
198C22—32no—
199C22—32no—
200C22—62no—
201C22—64no—
202C22—62no—
203C22—62no—
204C22—62no—
205C22—62no—
206C22—62no—
207C22—64no—
208C22—62no—
209C22Q8×C22⋊C911yescharacteristic
210C4—31no—
211C4—42no—
212C4—62no—
213C4—122no—
214C4#120⋊C911yescharacteristic
215C3#2848⋊C311yescharacteristic
216C2—31no—
217C2—31no—
218C2—62no—
219C2—62no—
220C2C2×#120⋊C911yescharacteristic
subgroupG/H
centerC2×C3C2×#120⋊C3
commutatorC25C22×C9
Frattini, socleC23×C3C22×A4
FittingC3×#2848C3
prime radical, cosocleC25×C3C22×C3
hypercenterC3×C4#120⋊C3
hypocenterC24Q8×C9
LCSG ▷ C25 ▷ C24
UCSC1 ◁ C2×C3 ◁ C3×C4

Complements

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

NH ≅ G/Ntype
11. C22⋊(C22⋊C9)Q8semidirect
15. #2848C9semidirect
69. C22×Q8C22⋊C9semidirect
116. C24Q8×C9semidirect

Maximal subgroups

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

subgroupindex
C4×C22⋊(C22⋊C9)2
#379⋊C92
C3×#28483
Q8×C22⋊C94