Finite Group Databasebeta

← #46822557

Subgroups — #46822557

Order 34432.

620 conjugacy classes of subgroups; only the 133 normal subgroups are shown.

normal subgroups only

This group has 620 conjugacy classes of subgroups — too many to draw. Only its 133 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×D269C212yesmaximal, complemented
2D4×D1076C211yesmaximal, characteristic, complemented
3#31771240C211yesmaximal, characteristic, complemented
4#31770981C211yesmaximal, characteristic, complemented
5#31770840C212yesmaximal, complemented
6#31770801C211yesmaximal, characteristic, complemented
7#31770740C212yesmaximal, complemented
8#31770737C212yesmaximal, complemented
9C4×#16864387C211yesmaximal, characteristic, complemented
10#31770670C211yesmaximal, characteristic, complemented
11#459×C269C211yesmaximal, characteristic, complemented
12C22×D1076—21no—
13C2×D4×D269—21no—
14C2×D4×D269C2212yescomplemented
15C2×D4×D269C2212yescomplemented
16C2×D2152C2212yescomplemented
17C2×#16864387C2211yescharacteristic
18C2×#16864387C2212yescomplemented
19C2×#16864387C2212yescomplemented
20D8×D269—28no—
21C2×C8×D269C2212yescomplemented
22#22575450C2211yescharacteristic, complemented
23#22575428C2212yescomplemented
24#22575427—21no—
25#22575424—21no—
26#22575424C2212yescomplemented
27#22575423—22no—
28#22575421—22no—
29C4×D1076C2211yescharacteristic
30C4×D1076C2211yescharacteristic, complemented
31#22575386C2211yescharacteristic, complemented
32#22575375C2212yescomplemented
33#22575374C2211yescharacteristic, complemented
34#22575373C2211yescharacteristic, complemented
35#22575365C2212yescomplemented
36C4×#14524130C2211yescharacteristic, complemented
37C2×D8×C269C2212yescomplemented
38#127×C269C2211yescharacteristic, complemented
39C4×D4×C269C2211yescharacteristic, complemented
40C4⋊C8×C269C2211yescharacteristic, complemented
41#102×C269C2212yescomplemented
42C23×D269—22no—
43C23×D269—22no—
44C2×D1076—22no—
45C2×D1076—21no—
46C2×D1076—21no—
47C2×D1076—44no—
48C2×D1076D411yescharacteristic
49C2×D1076C2312yes—
50C2×D1076C2311yescharacteristic
51C2×C22⋊D269—22no—
52C2×C22⋊D269—22no—
53C2×C22⋊D269—22no—
54D4×D269—24no—
55D4×D269—24no—
56D4×D269—42no—
57D4×D269—42no—
58D4×D269—44no—
59C2×C4×D269—21no—
60C2×C4×D269C2312yes—
61D2152—24no—
62#16864387—24no—
63#16864387—42no—
64#16864387D414yescomplemented
65C2×#14524130C2311yescharacteristic
66C2×#14524130C2311yescharacteristic
67C8×D269—24no—
68C4⋊Dic269D411yescharacteristic
69C4⋊Dic269C2311yescharacteristic
70C22⋊Dic269—22no—
71#16864379—22no—
72#16864379—21no—
73#16864379D412yes—
74C2×D4×C269—21no—
75C2×D4×C269—21no—
76C2×D4×C269C2312yes—
77C2×D4×C269C2311yescharacteristic
78C22×C4×C269—21no—
79D8×C269—24no—
80C2×C8×C269C2312yes—
81C4⋊C4×C269C2311yescharacteristic
82C22⋊C4×C269—21no—
83C42×C269C2311yescharacteristic
84C22×D269—21no—
85C22×D269—22no—
86C22×D269—44no—
87C22×D269—44no—
88C22×D269—44no—
89C22×D269—44no—
90C22×D269—82no—
91C22×D269—82no—
92C22×D269C2×D412yes—
93D1076—22no—
94D1076—21no—
95D1076—22no—
96D1076—44no—
97D1076—42no—
98D1076—81no—
99D1076D814yescomplemented
100D1076C2×D412yescomplemented
101C22⋊D269—44no—
102C22⋊D269—44no—
103C22⋊D269—44no—
104C2×Dic269—21no—
105C2×Dic269C2×D412yes—
106C4×D269—22no—
107C4×D269—22no—
108C4×D269—42no—
109#14524130—21no—
110#14524130C2×D412yescomplemented
111C23×C269—21no—
112C23×C269—22no—
113D4×C269—22no—
114D4×C269—21no—
115D4×C269—22no—
116D4×C269—42no—
117D4×C269—81no—
118D4×C269C2×D412yescomplemented
119C2×C4×C269—21no—
120C2×C4×C269—42no—
121C2×C4×C269C2×D411yescharacteristic
122C2×C4×C269C2×D411yescharacteristic
123C2×C4×C269C2411yescharacteristic
124C8×C269—22no—
125C22×C269—22no—
126C22×C269—41no—
127C22×C269—41no—
128C22×C269—42no—
129C22×C269—42no—
130C22×C269—42no—
131C22×C269C22×D411yescharacteristic
132C2×D269—22no—
133C2×D269—22no—
134C2×D269—22no—
135C2×D269—41no—
136C2×D269—41no—
137C2×D269—42no—
138C2×D269—42no—
139C2×D269—42no—
140C2×D269—88no—
141C2×D269—88no—
142C2×D269C2×D814yescomplemented
143C4×C269—21no—
144C4×C269—41no—
145C4×C269C2×D812yescomplemented
146C4×C269C22×D411yescharacteristic
147C4×C269H(5,𝔽2)11yescharacteristic
148Dic269—22no—
149Dic269—41no—
150C2×C269—42no—
151C2×C269—82no—
152C2×C269D4211yescharacteristic
153C2×C269C22×D811yescharacteristic
154C2×C269#57611yescharacteristic
155D269—24no—
156D269—42no—
157D269—82no—
158C269D4×D811yescharacteristic, complemented, Sylow
159D4×D8—2691nomaximal, Sylow
160C22×D8—2692no—
161D42—2691no—
162D42—2691no—
163#493—2691no—
164#466—2692no—
165#459—2691no—
166#459D26911yescharacteristic, complemented
167#447—2692no—
168#447—2692no—
169C4×D8—2691no—
170C8×D4—2691no—
171C22×D4—2692no—
172C22×D4—2692no—
173C22×D4—5381no—
174C22×D4—5381no—
175C2×D8—2691no—
176C2×D8—2692no—
177C2×D8—2692no—
178C2×D8—2692no—
179C2×D8—5388no—
180C2×D8C2×D26912yescomplemented
181C22×C8—2692no—
182#127—2691no—
183#127C2×D26911yescharacteristic, complemented
184#121—2692no—
185#121—2692no—
186#121—5381no—
187#121—5381no—
188#120—5382no—
189#120—5382no—
190C4×D4—2691no—
191C4×D4—2691no—
192C4×D4C2×D26911yescharacteristic, complemented
193#107—2691no—
194C4⋊C8C2×D26911yescharacteristic, complemented
195#102—2691no—
196#102—2692no—
197#102—2691no—
198#102C2×D26912yescomplemented
199C22⋊C8—2692no—
200C4×C8—2691no—
201C24—5382no—
202C24—5382no—
203C2×D4—21no—
204C2×D4—21no—
205C2×D4—2691no—
206C2×D4—2691no—
207C2×D4—2692no—
208C2×D4—5382no—
209C2×D4—5382no—
210C2×D4—5382no—
211C2×D4—5384no—
212C2×D4—5384no—
213C2×D4—5382no—
214C2×D4—5381no—
215C2×D4—5381no—
216C2×D4—10764no—
217C2×D4—10762no—
218C2×D4—10762no—
219C2×D4—10764no—
220C2×D4C22×D26912yes—
221C2×D4C22×D26911yescharacteristic
222C22×C4—21no—
223C22×C4—2692no—
224C22×C4—5381no—
225D8—24no—
226D8—2694no—
227D8—5384no—
228D8—5384no—
229D8—10762no—
230C2×C8—2691no—
231C2×C8—2691no—
232C2×C8—5384no—
233C2×C8C22×D26912yes—
234C4⋊C4—2691no—
235C4⋊C4—2691no—
236C4⋊C4C22×D26911yescharacteristic
237C22⋊C4—21no—
238C22⋊C4—2692no—
239C22⋊C4—5382no—
240C22⋊C4—5382no—
241C22⋊C4—5381no—
242C42C22×D26911yescharacteristic
243C23—21no—
244C23—22no—
245C23—2692no—
246C23—5381no—
247C23—5382no—
248C23—10764no—
249C23—10764no—
250C23—10764no—
251C23—10764no—
252C23—21522no—
253C23—21522no—
254D4—22no—
255D4—21no—
256D4—22no—
257D4—42no—
258D4—81no—
259D4—2694no—
260D4—2692no—
261D4—5382no—
262D4—5381no—
263D4—5382no—
264D4—10764no—
265D4—10764no—
266D4—10764no—
267D4—10764no—
268D4—10762no—
269D4—21521no—
270D4D4×D26912yescomplemented
271C2×C4—21no—
272C2×C4—42no—
273C2×C4—2692no—
274C2×C4—5382no—
275C2×C4—5382no—
276C2×C4—5381no—
277C2×C4—10762no—
278C2×C4D4×D26911yescharacteristic
279C2×C4D4×D26911yescharacteristic
280C2×C4C23×D26911yescharacteristic
281C8—22no—
282C8—2692no—
283C8—5381no—
284C22—22no—
285C22—41no—
286C22—41no—
287C22—42no—
288C22—42no—
289C22—42no—
290C22—2694no—
291C22—5382no—
292C22—5382no—
293C22—5382no—
294C22—10761no—
295C22—10761no—
296C22—10762no—
297C22—10762no—
298C22—10762no—
299C22—21528no—
300C22—21528no—
301C22C2×D4×D26911yescharacteristic
302C4—21no—
303C4—41no—
304C4—5382no—
305C4—10761no—
306C4D8×D26912yescomplemented
307C4C2×D4×D26911yescharacteristic
308C4#2257549911yescharacteristic
309C2—42no—
310C2—82no—
311C2—5384no—
312C2—10762no—
313C2—21522no—
314C2#3177123911yescharacteristic
315C2C2×D8×D26911yescharacteristic
316C2#3177140911yescharacteristic
subgroupG/H
centerC22C2×D4×D269
commutator, cosocleC2×C4×C269C24
FrattiniC2×C4C23×D269
Fitting#459×C269C2
socleC22×C269C22×D4
hypercenter#459D269
hypocenterC269D4×D8
LCSG ▷ C2×C4×C269 ▷ C2×C269 ▷ C269
UCSC1 ◁ C22 ◁ C42 ◁ #459

Complements

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

NH ≅ G/Ntype
1. C2×D8×D269C2semidirect
2. D4×D1076C2semidirect
3. #31771240C2semidirect
4. #31770981C2semidirect
5. #31770840C2semidirect
6. #31770801C2semidirect
7. #31770740C2semidirect
8. #31770737C2semidirect
9. C4×#16864387C2semidirect
10. #31770670C2semidirect
11. #459×C269C2semidirect
14. C2×D4×D269C22semidirect
15. C2×D4×D269C22semidirect
16. C2×D2152C22semidirect
18. C2×#16864387C22semidirect
19. C2×#16864387C22semidirect
21. C2×C8×D269C22semidirect
22. #22575450C22semidirect
23. #22575428C22semidirect
26. #22575424C22semidirect
30. C4×D1076C22semidirect
31. #22575386C22semidirect
32. #22575375C22semidirect
33. #22575374C22semidirect
34. #22575373C22semidirect
35. #22575365C22semidirect
36. C4×#14524130C22semidirect
37. C2×D8×C269C22semidirect
38. #127×C269C22semidirect
39. C4×D4×C269C22semidirect
40. C4⋊C8×C269C22semidirect
41. #102×C269C22semidirect
64. #16864387D4semidirect
99. D1076D8semidirect
100. D1076C2×D4semidirect
110. #14524130C2×D4semidirect
118. D4×C269C2×D4semidirect
142. C2×D269C2×D8semidirect
145. C4×C269C2×D8semidirect
158. C269D4×D8semidirect
166. #459D269semidirect
180. C2×D8C2×D269semidirect
183. #127C2×D269semidirect
192. C4×D4C2×D269semidirect
194. C4⋊C8C2×D269semidirect
198. #102C2×D269semidirect
270. D4D4×D269semidirect
306. C4D8×D269semidirect

Maximal subgroups

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

subgroupindex
C2×D8×D2692
D4×D10762
#317712402
#317709812
#317708402
#317708012
#317707402
#317707372
C4×#168643872
#317706702
#459×C2692
D4×D8269