Finite Group Databasebeta

← #2898⋊C9 #11919547

Subgroups — #2898⋊C9 #11919547

Order 1152.

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

normal subgroups only

This group has 340 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
1C2×2−1+4⋊C9C211yesmaximal, characteristic
2C2×#131⋊C9C211yesmaximal, characteristic, complemented
3#520⋊C9C211yesmaximal, characteristic, complemented
4C3×#2898C311yesmaximal, characteristic
52−1+4⋊C9—21no—
62−1+4⋊C9C412yescomplemented
7C2×#41⋊C9C2211yescharacteristic
8C22×Q8⋊C9—21no—
9#131⋊C9—21no—
10C4×Q8⋊C9—21no—
11C9×#102—41nomaximal
12C2×C3×2−1+4C2×C311yescharacteristic
13C2×C3×#131C2×C311yescharacteristic
14C3×#520C2×C311yescharacteristic
15C3×#419—31no—
16C3×#417—31no—
17C3×#416—31no—
18C2×C3×#103—31no—
19C2×D4×C9—41no—
20#41⋊C9C2×C411yescharacteristic
21#41⋊C9D411yescharacteristic
22C2×Q8⋊C9—22no—
23C2×Q8⋊C9D411yescharacteristic
24C2×C8×C9—41no—
25C9×C4⋊C4—41no—
26#2898C911yescharacteristic, complemented, Sylow
27C3×2−1+4—21no—
28C3×2−1+4—32no—
29C3×2−1+4—61no—
30C3×2−1+4C3×C412yes—
31C2×C3×#41—31no—
32C2×C3×#41—61no—
33C2×C3×#41C22×C311yescharacteristic
34C22×C3×Q8—21no—
35C22×C3×Q8—31no—
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—32no—
45C3×#103—31no—
46C3×#103—31no—
47C3×#102—31no—
48C3×#102A411yescharacteristic
49C23×C9—81no—
50D4×C9—42no—
51D4×C9—81no—
52C2×C4×C9—41no—
53C2×C4×C9—81no—
54Q8⋊C9C22⋊C411yescharacteristic
55C8×C9—81no—
56C2×2−1+4C2×C911yescharacteristic
57C2×#131C2×C911yescharacteristic, complemented
58#520C2×C911yescharacteristic, complemented
59#419—31no—
60#417—31no—
61#416—31no—
62C2×#103—31no—
63C3×#41—31no—
64C3×#41—31no—
65C3×#41—32no—
66C3×#41—32no—
67C3×#41—61no—
68C3×#41—61no—
69C3×#41—64no—
70C3×#41—62no—
71C3×#41—62no—
72C3×#41C2×C3×C411yescharacteristic
73C3×#41C3×D411yescharacteristic
74C2×C3×Q8—22no—
75C2×C3×Q8—32no—
76C2×C3×Q8—32no—
77C2×C3×Q8—31no—
78C2×C3×Q8—61no—
79C2×C3×Q8—61no—
80C2×C3×Q8—61no—
81C2×C3×Q8—62no—
82C2×C3×Q8C3×D411yescharacteristic
83C2×C3×D4—31no—
84C2×C3×D4—61no—
85C2×C3×D4C2×A411yescharacteristic
86C22×C3×C4—31no—
87C22×C3×C4—61no—
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—
102C22×C9—82no—
103C22×C9—161no—
104C22×C9—161no—
105C4×C9—41no—
106C4×C9—41no—
107C4×C9—161no—
1082−1+4—21no—
1092−1+4—32no—
1102−1+4—61no—
1112−1+4C4×C912yescomplemented
112C2×#41—31no—
113C2×#41—61no—
114C2×#41C22×C911yescharacteristic
115C22×Q8—21no—
116C22×Q8—31no—
117#131—21no—
118#131—61no—
119C2×M16—31no—
120C22×C8—31no—
121C4×Q8—21no—
122C4×D4—61no—
123#117—31no—
124C2×C4⋊C4—31no—
125#103—32no—
126#103—31no—
127#103—31no—
128#102—31no—
129#102C22⋊C911yescharacteristic
130C23×C3—21no—
131C23×C3—31no—
132C3×Q8—31no—
133C3×Q8—32no—
134C3×Q8—62no—
135C3×Q8—62no—
136C3×Q8—61no—
137C3×Q8C3×C22⋊C411yescharacteristic
138C3×D4—21no—
139C3×D4—31no—
140C3×D4—31no—
141C3×D4—32no—
142C3×D4—62no—
143C3×D4—62no—
144C3×D4C4×A412yes—
145C2×C3×C4—21no—
146C2×C3×C4—31no—
147C2×C3×C4—31no—
148C2×C3×C4—31no—
149C2×C3×C4—31no—
150C2×C3×C4—31no—
151C2×C3×C4—62no—
152C2×C3×C4—62no—
153C2×C3×C4—62no—
154C2×C3×C4—61no—
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—
164C2×C9—162no—
165#41—31no—
166#41—31no—
167#41—32no—
168#41—32no—
169#41—61no—
170#41—61no—
171#41—64no—
172#41—62no—
173#41—62no—
174#41C2×C4×C911yescharacteristic
175#41D4×C911yescharacteristic
176C2×Q8—22no—
177C2×Q8—32no—
178C2×Q8—32no—
179C2×Q8—31no—
180C2×Q8—61no—
181C2×Q8—61no—
182C2×Q8—61no—
183C2×Q8—62no—
184C2×Q8D4×C911yescharacteristic
185C2×D4—31no—
186C2×D4—61no—
187C2×D4C2×C22⋊C911yescharacteristic
188C22×C4—31no—
189C22×C4—61no—
190C22×C4—61no—
191C22×C4—61no—
192M16—61no—
193M16—61no—
194C2×C8—31no—
195C2×C8—61no—
196C2×C8—61no—
197C2×C8C2×C22⋊C911yescharacteristic
198C4⋊C4—31no—
199C4⋊C4—61no—
200C4⋊C4C2×C22⋊C911yescharacteristic
201C22⋊C4—61no—
202C42—61no—
203C22×C3—22no—
204C22×C3—31no—
205C22×C3—31no—
206C22×C3—41no—
207C22×C3—41no—
208C22×C3—61no—
209C22×C3—61no—
210C22×C3D4×A411yescharacteristic
211C3×C4—31no—
212C3×C4—31no—
213C3×C4—41no—
214C3×C4—62no—
215C3×C4—121no—
216C3×C4C2×C4×A411yescharacteristic
217C3×C4D4×A411yescharacteristic
218C9—41noSylow
219C23—21no—
220C23—31no—
221Q8—31no—
222Q8—32no—
223Q8—62no—
224Q8—62no—
225Q8—61no—
226Q8C9×C22⋊C411yescharacteristic
227D4—21no—
228D4—31no—
229D4—31no—
230D4—32no—
231D4—62no—
232D4—62no—
233D4C4×C22⋊C912yes—
234C2×C4—21no—
235C2×C4—31no—
236C2×C4—31no—
237C2×C4—31no—
238C2×C4—31no—
239C2×C4—31no—
240C2×C4—62no—
241C2×C4—62no—
242C2×C4—62no—
243C2×C4—61no—
244C2×C4—62no—
245C2×C4—61no—
246C2×C4—241no—
247C2×C4C22×C22⋊C911yescharacteristic
248C8—21no—
249C8—61no—
250C2×C3—42no—
251C2×C3—61no—
252C2×C3—61no—
253C2×C3A4×C22⋊C411yescharacteristic
254C2×C3#577⋊C311yescharacteristic
255C2×C3#578⋊C311yescharacteristic
256C22—22no—
257C22—31no—
258C22—31no—
259C22—41no—
260C22—41no—
261C22—61no—
262C22—61no—
263C22D4×C22⋊C911yescharacteristic
264C4—31no—
265C4—31no—
266C4—41no—
267C4—62no—
268C4—121no—
269C4C2×C4×C22⋊C911yescharacteristic
270C4D4×C22⋊C911yescharacteristic
271C3#2898⋊C311yescharacteristic
272C2—42no—
273C2—61no—
274C2—61no—
275C2C22⋊C4×C22⋊C911yescharacteristic
276C2#577⋊C911yescharacteristic
277C2#578⋊C911yescharacteristic
subgroupG/H
center, socleC22×C3D4×A4
commutator#41C2×C4×C9
FrattiniC2×C3×C4C22×A4
FittingC3×#2898C3
prime radicalC2×C3×2−1+4C2×C3
cosocleC2×C3×#41C22×C3
hypercenterC3×#102A4
hypocenterQ8C9×C22⋊C4
LCSG ▷ #41 ▷ Q8
UCSC1 ◁ C22×C3 ◁ C2×C3×C4 ◁ C3×#102

Complements

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

NH ≅ G/Ntype
2. C2×#131⋊C9C2semidirect
3. #520⋊C9C2semidirect
6. 2−1+4⋊C9C4semidirect
26. #2898C9semidirect
57. C2×#131C2×C9semidirect
58. #520C2×C9semidirect
111. 2−1+4C4×C9semidirect

Maximal subgroups

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

subgroupindex
C2×2−1+4⋊C92
C2×#131⋊C92
#520⋊C92
C3×#28983
C9×#1024