Finite Group Databasebeta

← #11885729

Subgroups — #11885729

Order 1152.

930 conjugacy classes of subgroups; only the 162 normal subgroups are shown.

normal subgroups only

This group has 930 conjugacy classes of subgroups — too many to draw. Only its 162 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×D8×D9C212yesmaximal, complemented
2#10589819C212yesmaximal, complemented
3C9×#493C211yesmaximal, characteristic, complemented
4#10588837C212yesmaximal, complemented
5#10588836C214yesmaximal, complemented
6#10588754C212yesmaximal, complemented
7C4×D72C211yesmaximal, characteristic, complemented
8C8×D36C211yesmaximal, characteristic, complemented
9#81789—31nomaximal
10C2×D4×D9—22no—
11C2×D4×D9C2214yescomplemented
12C2×C9×D8C2212yescomplemented
13C2×C9×D8C2212yescomplemented
14C9×#127C2212yescomplemented
15#63500—22no—
16#63500C2214yescomplemented
17#63499—24no—
18C2×#3673C2214yescomplemented
19D8×D9—28no—
20C2×D72C2211yescharacteristic
21C2×C8×D9C2212yescomplemented
22C4×D36C2211yescharacteristic
23C4×D36C2212yescomplemented
24C4×C8×C9C2211yescharacteristic, complemented
25#63392C2214yescomplemented
26#63380C2212yescomplemented
27(C2×D9)⋊C8C2212yescomplemented
28#63378C2211yescharacteristic, complemented
29C4⋊(C9⋊C8)C2211yescharacteristic, complemented
30C2×D3×D8—32no—
31#5717—32no—
32C3×#493D311yescharacteristic
33#5157—32no—
34#5156—34no—
35#5072—32no—
36C4×D24—31no—
37C8×D12—31no—
38C23×D9—24no—
39C2×D4×C9—22no—
40C2×D4×C9—22no—
41C2×D4×C9C2314yes—
42C2×#611—24no—
43C2×#611—24no—
44D4×D9—28no—
45D4×D9—44no—
46D4×D9—48no—
47C2×D36D411yescharacteristic
48C2×D36C2312yes—
49C2×C4×D9—22no—
50C2×C4×D9C2312yes—
51C9×D8—24no—
52C9×D8—42no—
53C2×C8×C9C2311yescharacteristic
54C2×C8×C9C2311yescharacteristic
55C42×C9C2311yescharacteristic
56#3676—24no—
57#3673—28no—
58(C2×D9)⋊C4—22no—
59(C2×D9)⋊C4D412yes—
60C4⋊Dic9D411yescharacteristic
61C4⋊Dic9C2312yes—
62C2×C9⋊C8C2312yes—
63D72D414yescomplemented
64C8×D9—24no—
65D4×D8—91noSylow
66C2×D3×D4—34no—
67C2×D3×D4—62no—
68C2×C3×D8C2×D312yes—
69C2×C3×D8C2×D312yes—
70C3×#127C2×D312yes—
71#938—34no—
72#938—62no—
73#937—64no—
74C2×#213—34no—
75D3×D8—68no—
76C2×D24—31no—
77C2×D3×C8—32no—
78C4×D12—31no—
79C4×D12—32no—
80C3×C4×C8C2×D311yescharacteristic
81#832—34no—
82#821—32no—
83(C2×D3)⋊C8—32no—
84#818—31no—
85C4⋊(C3⋊C8)—31no—
86C23×C9—24no—
87C22×D9—22no—
88C22×D9—48no—
89C22×D9—48no—
90C22×D9—84no—
91C22×D9C2×D412yes—
92D4×C9—24no—
93D4×C9—24no—
94D4×C9—44no—
95D4×C9—82no—
96C2×C4×C9C2×D411yescharacteristic
97C2×C4×C9C2×D411yescharacteristic
98C2×C4×C9C2411yescharacteristic
99#611—48no—
100#611—48no—
101C2×Dic9—22no—
102C2×Dic9C2×D412yes—
103D36—22no—
104D36D814yescomplemented
105D36C2×D414yescomplemented
106C4×D9—22no—
107C4×D9—22no—
108C4×D9—44no—
109C8×C9—21no—
110C8×C9C2×D412yescomplemented
111C9⋊C8—22no—
112C22×D8—92no—
113D42—92no—
114#493D911yescharacteristic, complemented
115#466—92no—
116#459—92no—
117#447—94no—
118C4×D8—91no—
119C8×D4—91no—
120C23×D3—64no—
121C2×C3×D4—22no—
122C2×C3×D4—22no—
123C2×C3×D4C22×D314yes—
124C2×#67—64no—
125C2×#67—64no—
126D3×D4—68no—
127D3×D4—124no—
128D3×D4—128no—
129C2×D12—31no—
130C2×D12—32no—
131C2×C4×D3—32no—
132C2×C4×D3—62no—
133C3×D8—24no—
134C3×D8—42no—
135C2×C3×C8C22×D311yescharacteristic
136C2×C3×C8C22×D311yescharacteristic
137C3×C42C22×D311yescharacteristic
138#217—64no—
139#213—68no—
140(C2×D3)⋊C4—32no—
141(C2×D3)⋊C4—62no—
142C4⋊Dic3—31no—
143C4⋊Dic3—32no—
144C2×C3⋊C8—32no—
145D24—34no—
146D3×C8—64no—
147C22×C9—44no—
148C22×C9—44no—
149C22×C9—44no—
150C22×C9C22×D411yescharacteristic
151C2×D9—22no—
152C2×D9—22no—
153C2×D9—24no—
154C2×D9—42no—
155C2×D9—42no—
156C2×D9—816no—
157C2×D9C2×D814yescomplemented
158C4×C9—21no—
159C4×C9C2×D812yescomplemented
160C4×C9C22×D411yescharacteristic
161C4×C9H(5,𝔽2)11yescharacteristic
162Dic9—22no—
163Dic9—42no—
164C22×D4—94no—
165C22×D4—182no—
166C2×D8—94no—
167C2×D8—91no—
168C2×D8—188no—
169C2×D8C2×D912yescomplemented
170C2×D8C2×D912yescomplemented
171C22×C8—92no—
172#127C2×D912yescomplemented
173#121—94no—
174#121—182no—
175#120—184no—
176C4×D4—91no—
177C4×D4—92no—
178#107—91no—
179C4⋊C8—91no—
180#102—94no—
181#102—92no—
182C22⋊C8—92no—
183C4×C8C2×D911yescharacteristic, complemented
184C23×C3—24no—
185C22×D3—32no—
186C22×D3—62no—
187C22×D3—128no—
188C22×D3—128no—
189C22×D3—244no—
190C3×D4—24no—
191C3×D4—24no—
192C3×D4—44no—
193C3×D4—82no—
194C2×C3×C4D3×D411yescharacteristic
195C2×C3×C4D3×D411yescharacteristic
196C2×C3×C4C23×D311yescharacteristic
197#67—128no—
198#67—128no—
199C2×Dic3—32no—
200C2×Dic3—62no—
201D12—34no—
202D12—34no—
203D12—62no—
204C4×D3—62no—
205C4×D3—62no—
206C4×D3—124no—
207C3×C8—21no—
208C3×C8D3×D412yes—
209C3⋊C8—62no—
210C2×C9—84no—
211C2×C9D4211yescharacteristic
212C2×C9C22×D811yescharacteristic
213C2×C9#57611yescharacteristic
214D9—24no—
215D9—44no—
216C24—184no—
217C2×D4—22no—
218C2×D4—22no—
219C2×D4—91no—
220C2×D4—92no—
221C2×D4—184no—
222C2×D4—188no—
223C2×D4—184no—
224C2×D4—364no—
225C2×D4—368no—
226C2×D4C22×D914yes—
227C22×C4—92no—
228C22×C4—182no—
229D8—24no—
230D8—42no—
231D8—94no—
232D8—188no—
233C2×C8—92no—
234C2×C8—184no—
235C2×C8C22×D911yescharacteristic
236C2×C8C22×D911yescharacteristic
237C4⋊C4—91no—
238C4⋊C4—92no—
239C22⋊C4—92no—
240C22⋊C4—184no—
241C22⋊C4—182no—
242C42C22×D911yescharacteristic
243C22×C3—44no—
244C22×C3—44no—
245C22×C3—44no—
246C22×C3C2×D3×D411yescharacteristic
247C2×D3—34no—
248C2×D3—62no—
249C2×D3—62no—
250C2×D3—64no—
251C2×D3—122no—
252C2×D3—122no—
253C2×D3—2416no—
254C3×C4—21no—
255C3×C4D3×D812yes—
256C3×C4C2×D3×D411yescharacteristic
257C3×C4#100411yescharacteristic
258Dic3—62no—
259Dic3—122no—
260C9D4×D811yescharacteristic, complemented, Sylow
261C23—24no—
262C23—92no—
263C23—182no—
264C23—368no—
265C23—368no—
266C23—724no—
267D4—24no—
268D4—24no—
269D4—44no—
270D4—82no—
271D4—94no—
272D4—94no—
273D4—182no—
274D4—368no—
275D4—368no—
276C2×C4—92no—
277C2×C4—182no—
278C2×C4—182no—
279C2×C4—182no—
280C2×C4—364no—
281C2×C4D4×D911yescharacteristic
282C2×C4D4×D911yescharacteristic
283C2×C4C23×D911yescharacteristic
284C8—21no—
285C8—182no—
286C8D4×D912yescomplemented
287C2×C3—84no—
288C2×C3#571711yescharacteristic
289C2×C3C2×D3×D811yescharacteristic
290C2×C3#575711yescharacteristic
291D3—64no—
292D3—124no—
293C22—44no—
294C22—44no—
295C22—44no—
296C22—94no—
297C22—182no—
298C22—182no—
299C22—184no—
300C22—362no—
301C22—362no—
302C22—7216no—
303C22C2×D4×D911yescharacteristic
304C4—21no—
305C4—182no—
306C4—362no—
307C4D8×D912yescomplemented
308C4C2×D4×D911yescharacteristic
309C4#6371011yescharacteristic
310C3#8178911yescharacteristic
311C2—84no—
312C2—184no—
313C2—364no—
314C2#1058981911yescharacteristic
315C2C2×D8×D911yescharacteristic
316C2#1058985911yescharacteristic
subgroupG/H
centerC22C2×D4×D9
commutator, cosocleC2×C4×C9C24
FrattiniC2×C3×C4C23×D3
FittingC9×#493C2
socleC22×C3C2×D3×D4
hypercenter#493D9
hypocenterC9D4×D8
LCSG ▷ C2×C4×C9 ▷ C2×C9 ▷ C9
UCSC1 ◁ C22 ◁ C42 ◁ #493

Complements

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

NH ≅ G/Ntype
1. C2×D8×D9C2semidirect
2. #10589819C2semidirect
3. C9×#493C2semidirect
4. #10588837C2semidirect
5. #10588836C2semidirect
6. #10588754C2semidirect
7. C4×D72C2semidirect
8. C8×D36C2semidirect
11. C2×D4×D9C22semidirect
12. C2×C9×D8C22semidirect
13. C2×C9×D8C22semidirect
14. C9×#127C22semidirect
16. #63500C22semidirect
18. C2×#3673C22semidirect
21. C2×C8×D9C22semidirect
23. C4×D36C22semidirect
24. C4×C8×C9C22semidirect
25. #63392C22semidirect
26. #63380C22semidirect
27. (C2×D9)⋊C8C22semidirect
28. #63378C22semidirect
29. C4⋊(C9⋊C8)C22semidirect
63. D72D4semidirect
104. D36D8semidirect
105. D36C2×D4semidirect
110. C8×C9C2×D4semidirect
114. #493D9semidirect
157. C2×D9C2×D8semidirect
159. C4×C9C2×D8semidirect
169. C2×D8C2×D9semidirect
170. C2×D8C2×D9semidirect
172. #127C2×D9semidirect
183. C4×C8C2×D9semidirect
260. C9D4×D8semidirect
286. C8D4×D9semidirect
307. C4D8×D9semidirect

Maximal subgroups

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

subgroupindex
C2×D8×D92
#105898192
C9×#4932
#105888372
#105888362
#105887542
C4×D722
C8×D362
#817893