Finite Group Databasebeta

← #2856⋊C9 #11919507

Subgroups — #2856⋊C9 #11919507

Order 1152.

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

normal subgroups only

This group has 364 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×#127⋊C9C211yesmaximal, characteristic, complemented
2C22×C42⋊C9C211yesmaximal, characteristic, complemented
3#384⋊C9C211yesmaximal, characteristic, complemented
4C3×#2856C311yesmaximal, characteristic
5D4×C22⋊C9—41nomaximal
6#127⋊C9—21no—
7C2×C42⋊C9—21no—
8C2×C42⋊C9C2211yescharacteristic
9C2×C3×#127C2×C311yescharacteristic
10C2×C3×#121—31no—
11C2×C3×#121—31no—
12C22×C3×C42C2×C311yescharacteristic
13C3×#390—31no—
14C3×#390—31no—
15C3×#384C2×C311yescharacteristic
16C22×C22⋊C9—41no—
17C22×C22⋊C9—41no—
18C4×C22⋊C9—41no—
19C42⋊C9D411yescharacteristic, complemented
20#2856C911yescharacteristic, complemented, Sylow
21C22×C3×D4—31no—
22C22×C3×D4—31no—
23C22×C3×D4—31no—
24C22×C3×D4A411yescharacteristic
25C23×C3×C4—31no—
26C3×#127—21no—
27C3×#127—61no—
28C3×#121—62no—
29C3×#121—62no—
30C3×#121—62no—
31C3×#121—62no—
32C2×C3×C4⋊C4—31no—
33C2×C3×C4⋊C4—31no—
34C2×C3×C22⋊C4—32no—
35C2×C3×C22⋊C4—31no—
36C2×C3×C22⋊C4—31no—
37C2×C3×C42—21no—
38C2×C3×C42—31no—
39C2×C3×C42—61no—
40C2×C3×C42C22×C311yescharacteristic
41C2×C22⋊C9—41no—
42C2×C22⋊C9—81no—
43C2×C22⋊C9—81no—
44D4×C9—161no—
45C2×#127C2×C911yescharacteristic, complemented
46C2×#121—31no—
47C2×#121—31no—
48C22×C42C2×C911yescharacteristic, complemented
49#390—31no—
50#390—31no—
51#384C2×C911yescharacteristic, complemented
52C24×C3—31no—
53C24×C3C2×A411yescharacteristic
54C24×C3C2×A411yescharacteristic
55C2×C3×D4—61no—
56C2×C3×D4—61no—
57C2×C3×D4—61no—
58C2×C3×D4—61no—
59C2×C3×D4—62no—
60C2×C3×D4—62no—
61C2×C3×D4—62no—
62C2×C3×D4—62no—
63C2×C3×D4—61no—
64C2×C3×D4—62no—
65C2×C3×D4—61no—
66C2×C3×D4—61no—
67C2×C3×D4—62no—
68C2×C3×D4—61no—
69C22×C3×C4—31no—
70C22×C3×C4—32no—
71C22×C3×C4—32no—
72C22×C3×C4—31no—
73C22×C3×C4—31no—
74C22×C3×C4—61no—
75C22×C3×C4—61no—
76C22×C3×C4—62no—
77C22×C3×C4C2×A411yescharacteristic
78C3×C4⋊C4—62no—
79C3×C4⋊C4—62no—
80C3×C22⋊C4—62no—
81C3×C22⋊C4—62no—
82C3×C22⋊C4—64no—
83C3×C42—31no—
84C3×C42—61no—
85C3×C42—61no—
86C3×C42C3×D411yescharacteristic
87C22×C9—161no—
88C22×C9—161no—
89C22⋊C9—41no—
90C4×C9—161no—
91C22×D4—31no—
92C22×D4—31no—
93C22×D4—31no—
94C22×D4C22⋊C911yescharacteristic
95C23×C4—31no—
96#127—21no—
97#127—61no—
98#121—62no—
99#121—62no—
100#121—62no—
101#121—62no—
102C2×C4⋊C4—31no—
103C2×C4⋊C4—31no—
104C2×C22⋊C4—32no—
105C2×C22⋊C4—31no—
106C2×C22⋊C4—31no—
107C2×C42—21no—
108C2×C42—31no—
109C2×C42—61no—
110C2×C42C22×C911yescharacteristic
111C23×C3—21no—
112C23×C3—21no—
113C23×C3—31no—
114C23×C3—31no—
115C23×C3—61no—
116C23×C3—61no—
117C23×C3—61no—
118C23×C3—61no—
119C23×C3—62no—
120C23×C3—61no—
121C23×C3—62no—
122C23×C3—61no—
123C23×C3C22×A411yescharacteristic
124C3×D4—41no—
125C3×D4—122no—
126C3×D4—122no—
127C3×D4—122no—
128C3×D4—122no—
129C3×D4—121no—
130C3×D4—121no—
131C3×D4—122no—
132C3×D4—121no—
133C2×C3×C4—32no—
134C2×C3×C4—32no—
135C2×C3×C4—31no—
136C2×C3×C4—31no—
137C2×C3×C4—32no—
138C2×C3×C4—62no—
139C2×C3×C4—62no—
140C2×C3×C4—62no—
141C2×C3×C4—62no—
142C2×C3×C4—61no—
143C2×C3×C4—61no—
144C2×C3×C4—61no—
145C2×C3×C4—61no—
146C2×C3×C4—62no—
147C2×C9—161no—
148C2×C9—321no—
149C2×C9—321no—
150C24—31no—
151C24C2×C22⋊C911yescharacteristic
152C24C2×C22⋊C911yescharacteristic
153C2×D4—61no—
154C2×D4—61no—
155C2×D4—61no—
156C2×D4—61no—
157C2×D4—62no—
158C2×D4—62no—
159C2×D4—62no—
160C2×D4—62no—
161C2×D4—61no—
162C2×D4—62no—
163C2×D4—61no—
164C2×D4—61no—
165C2×D4—62no—
166C2×D4—61no—
167C22×C4—31no—
168C22×C4—32no—
169C22×C4—32no—
170C22×C4—31no—
171C22×C4—31no—
172C22×C4—61no—
173C22×C4—61no—
174C22×C4—62no—
175C22×C4C2×C22⋊C911yescharacteristic
176C4⋊C4—62no—
177C4⋊C4—62no—
178C22⋊C4—62no—
179C22⋊C4—62no—
180C22⋊C4—64no—
181C42—31no—
182C42—61no—
183C42—61no—
184C42D4×C911yescharacteristic, complemented
185C22×C3—31no—
186C22×C3—31no—
187C22×C3—31no—
188C22×C3—41no—
189C22×C3—61no—
190C22×C3—61no—
191C22×C3—61no—
192C22×C3—61no—
193C22×C3—121no—
194C22×C3—121no—
195C22×C3—121no—
196C22×C3—122no—
197C22×C3—121no—
198C22×C3—122no—
199C22×C3—121no—
200C22×C3#127⋊C311yescharacteristic
201C22×C3D4×A411yescharacteristic
202C3×C4—32no—
203C3×C4—32no—
204C3×C4—41no—
205C3×C4—62no—
206C3×C4—121no—
207C9—161noSylow
208C23—21no—
209C23—21no—
210C23—31no—
211C23—31no—
212C23—61no—
213C23—61no—
214C23—61no—
215C23—61no—
216C23—62no—
217C23—61no—
218C23—62no—
219C23—61no—
220C23C22×C22⋊C911yescharacteristic
221D4—41no—
222D4—122no—
223D4—122no—
224D4—122no—
225D4—122no—
226D4—121no—
227D4—121no—
228D4—122no—
229D4—121no—
230C2×C4—32no—
231C2×C4—32no—
232C2×C4—31no—
233C2×C4—31no—
234C2×C4—32no—
235C2×C4—62no—
236C2×C4—62no—
237C2×C4—62no—
238C2×C4—62no—
239C2×C4—61no—
240C2×C4—61no—
241C2×C4—61no—
242C2×C4—61no—
243C2×C4—62no—
244C2×C3—21no—
245C2×C3—31no—
246C2×C3—31no—
247C2×C3—61no—
248C2×C3—81no—
249C2×C3—241no—
250C2×C3C2×#127⋊C311yescharacteristic
251C22—31no—
252C22—31no—
253C22—31no—
254C22—41no—
255C22—61no—
256C22—61no—
257C22—61no—
258C22—61no—
259C22—121no—
260C22—121no—
261C22—121no—
262C22—122no—
263C22—121no—
264C22—122no—
265C22—121no—
266C22#127⋊C911yescharacteristic, complemented
267C22D4×C22⋊C911yescharacteristic
268C4—32no—
269C4—32no—
270C4—41no—
271C4—62no—
272C4—121no—
273C3#2856⋊C311yescharacteristic
274C2—21no—
275C2—31no—
276C2—31no—
277C2—61no—
278C2—81no—
279C2—241no—
280C2C2×#127⋊C911yescharacteristic
subgroupG/H
centerC2×C3C2×#127⋊C3
commutatorC2×C42C22×C9
Frattini, socleC23×C3C22×A4
Fitting, prime radicalC3×#2856C3
cosocleC2×C3×C42C22×C3
hypercenterC22×C3#127⋊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×#127⋊C9C2semidirect
2. C22×C42⋊C9C2semidirect
3. #384⋊C9C2semidirect
19. C42⋊C9D4semidirect
20. #2856C9semidirect
45. C2×#127C2×C9semidirect
48. C22×C42C2×C9semidirect
51. #384C2×C9semidirect
184. C42D4×C9semidirect
266. C22#127⋊C9semidirect

Maximal subgroups

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

subgroupindex
C2×#127⋊C92
C22×C42⋊C92
#384⋊C92
C3×#28563
D4×C22⋊C94