Finite Group Databasebeta

← #2897⋊C9 #11919545

Subgroups — #2897⋊C9 #11919545

Order 1152.

348 conjugacy classes of subgroups; only the 61 normal subgroups are shown.

normal subgroups only

This group has 348 conjugacy classes of subgroups — too many to draw. Only its 61 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×#63700C211yesmaximal, characteristic
2C2×#131⋊C9C211yesmaximal, characteristic, complemented
3#520⋊C9C211yesmaximal, characteristic, complemented
4C3×#2897C311yesmaximal, characteristic
5#63700—21no—
6#63700C412yescomplemented
7C2×#41⋊C9—21no—
8C2×#41⋊C9C2211yescharacteristic
9#131⋊C9—21no—
10C4×Q8⋊C9—21no—
11C9×#103—41nomaximal
12C2×C3×H(5,𝔽2)C2×C311yescharacteristic
13C2×C3×#131C2×C311yescharacteristic
14C3×#520C2×C311yescharacteristic
15C3×#418—31no—
16C3×#417—31no—
17C3×#416—31no—
18C2×C3×#102—31no—
19C2×Q8×C9—41no—
20#41⋊C9—22no—
21#41⋊C9C2×C411yescharacteristic
22#41⋊C9D411yescharacteristic
23C2×Q8⋊C9D411yescharacteristic
24C2×C8×C9—41no—
25C9×C4⋊C4—41no—
26#2897C911yescharacteristic, complemented, Sylow
27C3×H(5,𝔽2)—21no—
28C3×H(5,𝔽2)—32no—
29C3×H(5,𝔽2)—61no—
30C3×H(5,𝔽2)C3×C412yes—
31C2×C3×#41—21no—
32C2×C3×#41—31no—
33C2×C3×#41C22×C311yescharacteristic
34C22×C3×D4—31no—
35C22×C3×D4—61no—
36C3×#131—21no—
37C3×#131—61no—
38C2×C3×M16—31no—
39C22×C3×C8—31no—
40C3×C4×Q8—21no—
41C3×C4×D4—61no—
42C3×#117—31no—
43C2×C3×C4⋊C4—31no—
44C3×#103—31no—
45C3×#103A411yescharacteristic
46C3×#102—32no—
47C3×#102—31no—
48C3×#102—31no—
49Q8×C9—42no—
50Q8×C9—81no—
51C2×C4×C9—41no—
52C2×C4×C9—81no—
53C2×C4×C9—81no—
54Q8⋊C9C22⋊C411yescharacteristic
55C8×C9—81no—
56C2×H(5,𝔽2)C2×C911yescharacteristic
57C2×#131C2×C911yescharacteristic
58#520C2×C911yescharacteristic
59#418—31no—
60#417—31no—
61#416—31no—
62C2×#102—31no—
63C24×C3—61no—
64C3×#41—22no—
65C3×#41—31no—
66C3×#41—31no—
67C3×#41—32no—
68C3×#41—32no—
69C3×#41—61no—
70C3×#41—61no—
71C3×#41—62no—
72C3×#41C2×C3×C411yescharacteristic
73C3×#41C3×D411yescharacteristic
74C2×C3×Q8C3×D411yescharacteristic
75C2×C3×Q8C2×A411yescharacteristic
76C2×C3×D4—31no—
77C2×C3×D4—32no—
78C2×C3×D4—32no—
79C2×C3×D4—31no—
80C2×C3×D4—61no—
81C2×C3×D4—61no—
82C2×C3×D4—61no—
83C2×C3×D4—61no—
84C2×C3×D4—64no—
85C2×C3×D4—62no—
86C2×C3×D4—62no—
87C22×C3×C4—31no—
88C22×C3×C4—61no—
89C22×C3×C4—61no—
90C3×M16—61no—
91C3×M16—61no—
92C2×C3×C8—31no—
93C2×C3×C8—61no—
94C2×C3×C8—61no—
95C2×C3×C8C2×A411yescharacteristic
96C3×C4⋊C4—31no—
97C3×C4⋊C4—61no—
98C3×C4⋊C4C2×A411yescharacteristic
99C3×C22⋊C4—61no—
100C3×C42—61no—
101C22×C9—41no—
102C4×C9—41no—
103C4×C9—41no—
104C4×C9—82no—
105C4×C9—161no—
106H(5,𝔽2)—21no—
107H(5,𝔽2)—32no—
108H(5,𝔽2)—61no—
109H(5,𝔽2)C4×C912yescomplemented
110C2×#41—21no—
111C2×#41—31no—
112C2×#41C22×C911yescharacteristic
113C22×D4—31no—
114C22×D4—61no—
115#131—21no—
116#131—61no—
117C2×M16—31no—
118C22×C8—31no—
119C4×Q8—21no—
120C4×D4—61no—
121#117—31no—
122C2×C4⋊C4—31no—
123#103—31no—
124#103C22⋊C911yescharacteristic
125#102—32no—
126#102—31no—
127#102—31no—
128C23×C3—31no—
129C23×C3—62no—
130C23×C3—62no—
131C23×C3—61no—
132C23×C3—241no—
133C23×C3—241no—
134C3×Q8—21no—
135C3×Q8—31no—
136C3×Q8C3×C22⋊C411yescharacteristic
137C3×Q8C4×A412yes—
138C3×D4—31no—
139C3×D4—31no—
140C3×D4—32no—
141C3×D4—32no—
142C3×D4—62no—
143C3×D4—62no—
144C3×D4—62no—
145C3×D4—62no—
146C3×D4—61no—
147C2×C3×C4—21no—
148C2×C3×C4—21no—
149C2×C3×C4—31no—
150C2×C3×C4—31no—
151C2×C3×C4—31no—
152C2×C3×C4—31no—
153C2×C3×C4—31no—
154C2×C3×C4—62no—
155C2×C3×C4—62no—
156C2×C3×C4—61no—
157C2×C3×C4—241no—
158C2×C3×C4C22×A411yescharacteristic
159C3×C8—21no—
160C3×C8—61no—
161C2×C9—41no—
162C2×C9—41no—
163C2×C9—41no—
164C24—61no—
165#41—22no—
166#41—31no—
167#41—31no—
168#41—32no—
169#41—32no—
170#41—61no—
171#41—61no—
172#41—62no—
173#41C2×C4×C911yescharacteristic
174#41D4×C911yescharacteristic
175C2×Q8D4×C911yescharacteristic
176C2×Q8C2×C22⋊C911yescharacteristic
177C2×D4—31no—
178C2×D4—32no—
179C2×D4—32no—
180C2×D4—31no—
181C2×D4—61no—
182C2×D4—61no—
183C2×D4—61no—
184C2×D4—61no—
185C2×D4—64no—
186C2×D4—62no—
187C2×D4—62no—
188C22×C4—31no—
189C22×C4—61no—
190C22×C4—61no—
191M16—61no—
192M16—61no—
193C2×C8—31no—
194C2×C8—61no—
195C2×C8—61no—
196C2×C8C2×C22⋊C911yescharacteristic
197C4⋊C4—31no—
198C4⋊C4—61no—
199C4⋊C4C2×C22⋊C911yescharacteristic
200C22⋊C4—61no—
201C42—61no—
202C22×C3—31no—
203C22×C3—31no—
204C22×C3—61no—
205C22×C3—61no—
206C22×C3—62no—
207C22×C3—121no—
208C22×C3—121no—
209C22×C3—242no—
210C22×C3—242no—
211C22×C3D4×A411yescharacteristic
212C3×C4—22no—
213C3×C4—31no—
214C3×C4—31no—
215C3×C4—41no—
216C3×C4—121no—
217C3×C4C2×C4×A411yescharacteristic
218C3×C4D4×A411yescharacteristic
219C9—41noSylow
220C23—31no—
221C23—62no—
222C23—62no—
223C23—61no—
224C23—241no—
225C23—241no—
226Q8—21no—
227Q8—31no—
228Q8C9×C22⋊C411yescharacteristic
229Q8C4×C22⋊C912yes—
230D4—31no—
231D4—31no—
232D4—32no—
233D4—32no—
234D4—62no—
235D4—62no—
236D4—62no—
237D4—62no—
238D4—61no—
239C2×C4—21no—
240C2×C4—21no—
241C2×C4—31no—
242C2×C4—31no—
243C2×C4—31no—
244C2×C4—31no—
245C2×C4—31no—
246C2×C4—62no—
247C2×C4—62no—
248C2×C4—61no—
249C2×C4—241no—
250C2×C4C22×C22⋊C911yescharacteristic
251C8—21no—
252C8—61no—
253C2×C3—61no—
254C2×C3—61no—
255C2×C3—122no—
256C2×C3A4×C22⋊C411yescharacteristic
257C2×C3#576⋊C311yescharacteristic
258C2×C3#577⋊C311yescharacteristic
259C22—31no—
260C22—31no—
261C22—61no—
262C22—61no—
263C22—62no—
264C22—121no—
265C22—121no—
266C22—242no—
267C22—242no—
268C22D4×C22⋊C911yescharacteristic
269C4—22no—
270C4—31no—
271C4—31no—
272C4—41no—
273C4—121no—
274C4C2×C4×C22⋊C911yescharacteristic
275C4D4×C22⋊C911yescharacteristic
276C3#2897⋊C311yescharacteristic
277C2—61no—
278C2—61no—
279C2—122no—
280C2C22⋊C4×C22⋊C911yescharacteristic
281C2#576⋊C911yescharacteristic
282C2#577⋊C911yescharacteristic
subgroupG/H
center, socleC22×C3D4×A4
commutator#41C2×C4×C9
FrattiniC2×C3×C4C22×A4
FittingC3×#2897C3
prime radicalC2×C3×H(5,𝔽2)C2×C3
cosocleC2×C3×#41C22×C3
hypercenterC3×#103A4
hypocenterQ8C9×C22⋊C4
LCSG ▷ #41 ▷ Q8
UCSC1 ◁ C22×C3 ◁ C2×C3×C4 ◁ C3×#103

Complements

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

NH ≅ G/Ntype
2. C2×#131⋊C9C2semidirect
3. #520⋊C9C2semidirect
6. #63700C4semidirect
26. #2897C9semidirect
109. H(5,𝔽2)C4×C9semidirect

Maximal subgroups

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

subgroupindex
C2×#637002
C2×#131⋊C92
#520⋊C92
C3×#28973
C9×#1034