Finite Group Databasebeta

← #2852⋊C9 #11919505

Subgroups — #2852⋊C9 #11919505

Order 1152.

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

normal subgroups only

This group has 250 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
1C2×#126⋊C9C211yesmaximal, characteristic, complemented
2C22×C42⋊C9C211yesmaximal, characteristic, complemented
3#383⋊C9C211yesmaximal, characteristic, complemented
4C3×#2852C311yesmaximal, characteristic
5D4×C22⋊C9—41nomaximal
6#126⋊C9—21no—
7C2×C42⋊C9—21no—
8C2×C42⋊C9C2211yescharacteristic
9C2×C3×#126C2×C311yescharacteristic
10C22×C3×C42C2×C311yescharacteristic
11C3×#388—31no—
12C3×#387—31no—
13C3×#386—31no—
14C3×#385—31no—
15C3×#383C2×C311yescharacteristic
16C22×C22⋊C9—41no—
17C22×C22⋊C9—41no—
18C4×C22⋊C9—41no—
19C42⋊C9D411yescharacteristic, complemented
20#2852C911yescharacteristic, complemented, Sylow
21C22×C3×D4A411yescharacteristic
22C23×C3×C4—31no—
23C3×#126—21no—
24C3×#126—61no—
25C2×C3×C4⋊C4—31no—
26C2×C3×C4⋊C4—31no—
27C2×C3×C22⋊C4—31no—
28C2×C3×C22⋊C4—31no—
29C2×C3×C22⋊C4—31no—
30C2×C3×C42—21no—
31C2×C3×C42—31no—
32C2×C3×C42—61no—
33C2×C3×C42C22×C311yescharacteristic
34C3×#95—31no—
35C3×#95—31no—
36C3×#95—31no—
37C3×#95—31no—
38C2×C22⋊C9—41no—
39C2×C22⋊C9—81no—
40C2×C22⋊C9—81no—
41D4×C9—161no—
42C2×#126C2×C911yescharacteristic, complemented
43C22×C42C2×C911yescharacteristic, complemented
44#388—31no—
45#387—31no—
46#386—31no—
47#385—31no—
48#383C2×C911yescharacteristic, complemented
49C24×C3C2×A411yescharacteristic
50C24×C3C2×A411yescharacteristic
51C2×C3×D4—61no—
52C2×C3×D4—61no—
53C22×C3×C4—31no—
54C22×C3×C4—31no—
55C22×C3×C4—31no—
56C22×C3×C4—31no—
57C22×C3×C4—61no—
58C22×C3×C4—61no—
59C22×C3×C4—62no—
60C22×C3×C4—61no—
61C22×C3×C4—61no—
62C22×C3×C4C2×A411yescharacteristic
63C3×C4⋊C4—61no—
64C3×C4⋊C4—61no—
65C3×C4⋊C4—62no—
66C3×C22⋊C4—61no—
67C3×C22⋊C4—61no—
68C3×C22⋊C4—62no—
69C3×C22⋊C4—61no—
70C3×C22⋊C4—61no—
71C3×C42—31no—
72C3×C42—61no—
73C3×C42—61no—
74C3×C42C3×D411yescharacteristic
75C22×C9—161no—
76C22×C9—161no—
77C22⋊C9—41no—
78C4×C9—161no—
79C22×D4C22⋊C911yescharacteristic
80C23×C4—31no—
81#126—21no—
82#126—61no—
83C2×C4⋊C4—31no—
84C2×C4⋊C4—31no—
85C2×C22⋊C4—31no—
86C2×C22⋊C4—31no—
87C2×C22⋊C4—31no—
88C2×C42—21no—
89C2×C42—31no—
90C2×C42—61no—
91C2×C42C22×C911yescharacteristic
92#95—31no—
93#95—31no—
94#95—31no—
95#95—31no—
96C23×C3—21no—
97C23×C3—21no—
98C23×C3—31no—
99C23×C3—31no—
100C23×C3—61no—
101C23×C3—61no—
102C23×C3—61no—
103C23×C3C22×A411yescharacteristic
104C3×D4—41no—
105C3×D4—121no—
106C2×C3×C4—32no—
107C2×C3×C4—31no—
108C2×C3×C4—31no—
109C2×C3×C4—61no—
110C2×C3×C4—61no—
111C2×C3×C4—61no—
112C2×C3×C4—61no—
113C2×C3×C4—62no—
114C2×C3×C4—62no—
115C2×C3×C4—62no—
116C2×C3×C4—62no—
117C2×C3×C4—61no—
118C2×C3×C4—61no—
119C2×C3×C4—61no—
120C2×C3×C4—61no—
121C2×C3×C4—61no—
122C2×C3×C4—61no—
123C2×C3×C4—61no—
124C2×C9—161no—
125C2×C9—321no—
126C2×C9—321no—
127C24C2×C22⋊C911yescharacteristic
128C24C2×C22⋊C911yescharacteristic
129C2×D4—61no—
130C2×D4—61no—
131C22×C4—31no—
132C22×C4—31no—
133C22×C4—31no—
134C22×C4—31no—
135C22×C4—61no—
136C22×C4—61no—
137C22×C4—62no—
138C22×C4—61no—
139C22×C4—61no—
140C22×C4C2×C22⋊C911yescharacteristic
141C4⋊C4—61no—
142C4⋊C4—61no—
143C4⋊C4—62no—
144C22⋊C4—61no—
145C22⋊C4—61no—
146C22⋊C4—62no—
147C22⋊C4—61no—
148C22⋊C4—61no—
149C42—31no—
150C42—61no—
151C42—61no—
152C42D4×C911yescharacteristic, complemented
153C22×C3—31no—
154C22×C3—31no—
155C22×C3—31no—
156C22×C3—41no—
157C22×C3—61no—
158C22×C3—61no—
159C22×C3—61no—
160C22×C3—61no—
161C22×C3—121no—
162C22×C3—121no—
163C22×C3#126⋊C311yescharacteristic
164C22×C3D4×A411yescharacteristic
165C3×C4—41no—
166C3×C4—62no—
167C3×C4—61no—
168C3×C4—61no—
169C3×C4—121no—
170C3×C4—121no—
171C9—161noSylow
172C23—21no—
173C23—21no—
174C23—31no—
175C23—31no—
176C23—61no—
177C23—61no—
178C23—61no—
179C23C22×C22⋊C911yescharacteristic
180D4—41no—
181D4—121no—
182C2×C4—32no—
183C2×C4—31no—
184C2×C4—31no—
185C2×C4—61no—
186C2×C4—61no—
187C2×C4—61no—
188C2×C4—61no—
189C2×C4—62no—
190C2×C4—62no—
191C2×C4—62no—
192C2×C4—62no—
193C2×C4—61no—
194C2×C4—61no—
195C2×C4—61no—
196C2×C4—61no—
197C2×C4—61no—
198C2×C4—61no—
199C2×C4—61no—
200C2×C3—21no—
201C2×C3—31no—
202C2×C3—31no—
203C2×C3—61no—
204C2×C3—81no—
205C2×C3C2×#126⋊C311yescharacteristic
206C22—31no—
207C22—31no—
208C22—31no—
209C22—41no—
210C22—61no—
211C22—61no—
212C22—61no—
213C22—61no—
214C22—121no—
215C22—121no—
216C22#126⋊C911yescharacteristic, complemented
217C22D4×C22⋊C911yescharacteristic
218C4—41no—
219C4—62no—
220C4—61no—
221C4—61no—
222C4—121no—
223C4—121no—
224C3#2852⋊C311yescharacteristic
225C2—21no—
226C2—31no—
227C2—31no—
228C2—61no—
229C2—81no—
230C2C2×#126⋊C911yescharacteristic
subgroupG/H
centerC2×C3C2×#126⋊C3
commutatorC2×C42C22×C9
Frattini, socleC23×C3C22×A4
FittingC3×#2852C3
prime radicalC22×C3×D4A4
cosocleC2×C3×C42C22×C3
hypercenterC22×C3#126⋊C3
hypocenterC42D4×C9
LCSG ▷ C2×C42 ▷ C42
UCSC1 ◁ C2×C3 ◁ C22×C3

Complements

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

NH ≅ G/Ntype
1. C2×#126⋊C9C2semidirect
2. C22×C42⋊C9C2semidirect
3. #383⋊C9C2semidirect
19. C42⋊C9D4semidirect
20. #2852C9semidirect
42. C2×#126C2×C9semidirect
43. C22×C42C2×C9semidirect
48. #383C2×C9semidirect
152. C42D4×C9semidirect
216. C22#126⋊C9semidirect

Maximal subgroups

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

subgroupindex
C2×#126⋊C92
C22×C42⋊C92
#383⋊C92
C3×#28523
D4×C22⋊C94