Finite Group Databasebeta

← C2×D8×C22⋊C9 #11919787

Subgroups — C2×D8×C22⋊C9 #11919787

Order 1152.

836 conjugacy classes of subgroups; only the 110 normal subgroups are shown.

normal subgroups only

This group has 836 conjugacy classes of subgroups — too many to draw. Only its 110 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×D4×C22⋊C9C212yesmaximal, complemented
2D8×C22⋊C9C214yesmaximal, direct product factor
3C2×C8×C22⋊C9C211yesmaximal, characteristic, complemented
4C23×C3×D8C311yesmaximal, characteristic
5C23×C22⋊C9—22no—
6D4×C22⋊C9—22no—
7D4×C22⋊C9C2214yescomplemented
8C2×C4×C22⋊C9C2211yescharacteristic
9C2×C9×D8—41nomaximal
10C8×C22⋊C9C2212yescomplemented
11C23×C3×D4C2×C312yes—
12C22×C3×D8—31no—
13C22×C3×D8—31no—
14C22×C3×D8—32no—
15C22×C3×D8—34no—
16C22×C3×D8C2×C314yes—
17C23×C3×C8C2×C311yescharacteristic
18C22×C22⋊C9—24no—
19C22×C22⋊C9—44no—
20C22×C22⋊C9D411yescharacteristic
21C2×D4×C9—42no—
22C4×C22⋊C9D411yescharacteristic
23C4×C22⋊C9C2311yescharacteristic
24C9×D8—44no—
25C2×C8×C9—41no—
26C23×D8C911yescharacteristic, complemented, Sylow
27C25×C3—22no—
28C22×C3×D4—22no—
29C22×C3×D4—32no—
30C22×C3×D4—32no—
31C22×C3×D4—34no—
32C22×C3×D4—62no—
33C22×C3×D4—62no—
34C22×C3×D4C22×C314yes—
35C23×C3×C4C22×C311yescharacteristic
36C2×C3×D8—38no—
37C2×C3×D8—32no—
38C2×C3×D8—34no—
39C2×C3×D8—32no—
40C2×C3×D8—34no—
41C2×C3×D8—34no—
42C2×C3×D8—34no—
43C2×C3×D8—38no—
44C2×C3×D8—31no—
45C2×C3×D8A411yescharacteristic
46C22×C3×C8—31no—
47C22×C3×C8—31no—
48C22×C3×C8—32no—
49C22×C3×C8C22×C312yes—
50C23×C9—82no—
51C2×C22⋊C9—44no—
52C2×C22⋊C9D812yesdirect product factor
53C2×C22⋊C9C2×D411yescharacteristic
54D4×C9—44no—
55D4×C9—82no—
56C2×C4×C9—41no—
57C8×C9—42no—
58C23×D4C2×C912yescomplemented
59C22×D8—31no—
60C22×D8—31no—
61C22×D8—32no—
62C22×D8—34no—
63C22×D8C2×C914yescomplemented
64C23×C8C2×C911yescharacteristic, complemented
65C24×C3—24no—
66C24×C3—44no—
67C24×C3—62no—
68C24×C3—64no—
69C24×C3—62no—
70C24×C3—124no—
71C24×C3C3×D411yescharacteristic
72C2×C3×D4—34no—
73C2×C3×D4—34no—
74C2×C3×D4—34no—
75C2×C3×D4—34no—
76C2×C3×D4—32no—
77C2×C3×D4—62no—
78C2×C3×D4—62no—
79C2×C3×D4—62no—
80C2×C3×D4—62no—
81C2×C3×D4—68no—
82C2×C3×D4—62no—
83C2×C3×D4—64no—
84C2×C3×D4—62no—
85C2×C3×D4—64no—
86C2×C3×D4C2×A412yes—
87C22×C3×C4—31no—
88C22×C3×C4—31no—
89C22×C3×C4—31no—
90C22×C3×C4—31no—
91C22×C3×C4C3×D411yescharacteristic
92C22×C3×C4C23×C311yescharacteristic
93C3×D8—38no—
94C3×D8—38no—
95C3×D8—34no—
96C3×D8C2×A414yes—
97C2×C3×C8—32no—
98C2×C3×C8—31no—
99C2×C3×C8—32no—
100C2×C3×C8—32no—
101C2×C3×C8—32no—
102C2×C3×C8C2×A411yescharacteristic
103C22×C9—41no—
104C22×C9—84no—
105C22×C9—164no—
106C22⋊C9C2×D811yescharacteristic, direct product factor
107C4×C9—41no—
108C4×C9—41no—
109C25—22no—
110C22×D4—22no—
111C22×D4—32no—
112C22×D4—32no—
113C22×D4—34no—
114C22×D4—62no—
115C22×D4—62no—
116C22×D4C22×C914yescomplemented
117C23×C4C22×C911yescharacteristic
118C2×D8—38no—
119C2×D8—32no—
120C2×D8—34no—
121C2×D8—32no—
122C2×D8—34no—
123C2×D8—34no—
124C2×D8—34no—
125C2×D8—38no—
126C2×D8—31no—
127C2×D8C22⋊C911yescharacteristic, direct product factor
128C22×C8—31no—
129C22×C8—31no—
130C22×C8—32no—
131C22×C8C22×C912yescomplemented
132C23×C3—22no—
133C23×C3—31no—
134C23×C3—32no—
135C23×C3—31no—
136C23×C3—44no—
137C23×C3—64no—
138C23×C3—64no—
139C23×C3—64no—
140C23×C3—64no—
141C23×C3—62no—
142C23×C3—124no—
143C23×C3—124no—
144C23×C3—124no—
145C23×C3—128no—
146C23×C3—124no—
147C23×C3—124no—
148C23×C3—128no—
149C23×C3C3×D812yes—
150C23×C3C2×C3×D411yescharacteristic
151C3×D4—22no—
152C3×D4—34no—
153C3×D4—64no—
154C3×D4—64no—
155C3×D4—64no—
156C3×D4—64no—
157C3×D4—62no—
158C3×D4C22×A414yes—
159C2×C3×C4—32no—
160C2×C3×C4—31no—
161C2×C3×C4—31no—
162C2×C3×C4—31no—
163C2×C3×C4—31no—
164C2×C3×C4—31no—
165C2×C3×C4—31no—
166C2×C3×C4—31no—
167C2×C3×C4C22×A411yescharacteristic
168C3×C8—32no—
169C3×C8C22×A412yes—
170C2×C9—41no—
171C2×C9—42no—
172C2×C9—164no—
173C24—24no—
174C24—44no—
175C24—62no—
176C24—64no—
177C24—62no—
178C24—124no—
179C24D4×C911yescharacteristic
180C2×D4—34no—
181C2×D4—34no—
182C2×D4—34no—
183C2×D4—34no—
184C2×D4—32no—
185C2×D4—62no—
186C2×D4—62no—
187C2×D4—62no—
188C2×D4—62no—
189C2×D4—68no—
190C2×D4—62no—
191C2×D4—64no—
192C2×D4—62no—
193C2×D4—64no—
194C2×D4C2×C22⋊C912yescomplemented
195C22×C4—31no—
196C22×C4—31no—
197C22×C4—31no—
198C22×C4—31no—
199C22×C4D4×C911yescharacteristic
200C22×C4C23×C911yescharacteristic
201D8—38no—
202D8—38no—
203D8—34no—
204D8C2×C22⋊C914yesdirect product factor
205C2×C8—32no—
206C2×C8—31no—
207C2×C8—32no—
208C2×C8—32no—
209C2×C8—32no—
210C2×C8C2×C22⋊C911yescharacteristic, complemented
211C22×C3—24no—
212C22×C3—32no—
213C22×C3—31no—
214C22×C3—32no—
215C22×C3—31no—
216C22×C3—31no—
217C22×C3—32no—
218C22×C3—32no—
219C22×C3—44no—
220C22×C3—64no—
221C22×C3—124no—
222C22×C3—124no—
223C22×C3—128no—
224C22×C3—124no—
225C22×C3—124no—
226C22×C3—128no—
227C22×C3—124no—
228C22×C3C2×C3×D811yescharacteristic
229C22×C3D4×A411yescharacteristic
230C3×C4—31no—
231C3×C4—31no—
232C3×C4D4×A411yescharacteristic
233C3×C4C23×A411yescharacteristic
234C9—41noSylow
235C23—22no—
236C23—31no—
237C23—32no—
238C23—31no—
239C23—44no—
240C23—64no—
241C23—64no—
242C23—64no—
243C23—64no—
244C23—62no—
245C23—124no—
246C23—124no—
247C23—124no—
248C23—128no—
249C23—124no—
250C23—124no—
251C23—128no—
252C23C9×D812yescomplemented
253C23C2×D4×C911yescharacteristic
254D4—22no—
255D4—34no—
256D4—64no—
257D4—64no—
258D4—64no—
259D4—64no—
260D4—62no—
261D4C22×C22⋊C914yescomplemented
262C2×C4—32no—
263C2×C4—31no—
264C2×C4—31no—
265C2×C4—31no—
266C2×C4—31no—
267C2×C4—31no—
268C2×C4—31no—
269C2×C4—31no—
270C2×C4C22×C22⋊C911yescharacteristic
271C8—32no—
272C8C22×C22⋊C912yescomplemented
273C2×C3—32no—
274C2×C3—31no—
275C2×C3—31no—
276C2×C3—44no—
277C2×C3—124no—
278C2×C3A4×D812yes—
279C2×C3C2×D4×A411yescharacteristic
280C22—24no—
281C22—32no—
282C22—31no—
283C22—32no—
284C22—31no—
285C22—31no—
286C22—32no—
287C22—32no—
288C22—44no—
289C22—64no—
290C22—124no—
291C22—124no—
292C22—128no—
293C22—124no—
294C22—124no—
295C22—128no—
296C22—124no—
297C22C2×C9×D811yescharacteristic, complemented
298C22D4×C22⋊C911yescharacteristic
299C4—31no—
300C4—31no—
301C4D4×C22⋊C911yescharacteristic
302C4C23×C22⋊C911yescharacteristic
303C3C2×A4×D811yescharacteristic
304C2—31no—
305C2—32no—
306C2—31no—
307C2—44no—
308C2—124no—
309C2D8×C22⋊C912yesdirect product factor
310C2C2×D4×C22⋊C911yescharacteristic
subgroupG/H
centerC22×C3D4×A4
commutatorC22×C4C23×C9
FrattiniC3×C4C23×A4
Fitting, prime radicalC23×C3×D8C3
socleC24×C3C3×D4
cosocleC22×C3×C4C23×C3
hypercenterC2×C3×D8A4
hypocenterC22C2×C9×D8
LCSG ▷ C22×C4 ▷ C23 ▷ C22
UCSC1 ◁ C22×C3 ◁ C2×C3×C4 ◁ C2×C3×D8

Complements

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

NH ≅ G/Ntype
1. C2×D4×C22⋊C9C2semidirect
2. D8×C22⋊C9C2direct (N × H)
3. C2×C8×C22⋊C9C2semidirect
7. D4×C22⋊C9C22semidirect
10. C8×C22⋊C9C22semidirect
26. C23×D8C9semidirect
52. C2×C22⋊C9D8direct (N × H)
58. C23×D4C2×C9semidirect
63. C22×D8C2×C9semidirect
64. C23×C8C2×C9semidirect
106. C22⋊C9C2×D8direct (N × H)
116. C22×D4C22×C9semidirect
127. C2×D8C22⋊C9direct (N × H)
131. C22×C8C22×C9semidirect
194. C2×D4C2×C22⋊C9semidirect
204. D8C2×C22⋊C9direct (N × H)
210. C2×C8C2×C22⋊C9semidirect
252. C23C9×D8semidirect
261. D4C22×C22⋊C9semidirect
272. C8C22×C22⋊C9semidirect
297. C22C2×C9×D8semidirect
309. C2D8×C22⋊C9direct (N × H)

Maximal subgroups

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

subgroupindex
C2×D4×C22⋊C92
D8×C22⋊C92
C2×C8×C22⋊C92
C23×C3×D83
C2×C9×D84