Finite Group Databasebeta

← #46822559

Subgroups — #46822559

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
1C22×D2152C211yesmaximal, characteristic, complemented
2C2×D8×D269C211yesmaximal, characteristic, complemented
3#31771239C212yesmaximal, complemented
4#31770980C211yesmaximal, characteristic, complemented
5#31770842C211yesmaximal, characteristic, complemented
6#31770799C212yesmaximal, complemented
7#31770740C212yesmaximal, complemented
8#31770738C212yesmaximal, complemented
9#31770687C211yesmaximal, characteristic, complemented
10C8×C22⋊D269C211yesmaximal, characteristic, complemented
11#466×C269C211yesmaximal, characteristic, complemented
12C22×D1076C2212yescomplemented
13C2×D4×D269—22no—
14C2×D4×D269C2212yescomplemented
15C2×D2152—24no—
16C2×D2152C2211yescharacteristic
17C2×D2152C2211yescharacteristic, complemented
18C2×D2152C2212yescomplemented
19C2×#16864387C2212yescomplemented
20C2×#16864387C2212yescomplemented
21D8×D269—24no—
22C2×C8×D269C2211yescharacteristic, complemented
23#22575449C2212yescomplemented
24#22575428C2212yescomplemented
25#22575426—22no—
26#22575423—22no—
27#22575421—22no—
28#22575415C2212yescomplemented
29C4×C22⋊D269C2211yescharacteristic
30#22575382C2211yescharacteristic, complemented
31#22575373C2212yescomplemented
32#22575373C2212yescomplemented
33C22⋊#14524130C2211yescharacteristic, complemented
34#22575365C2211yescharacteristic, complemented
35C8×Dic269C2211yescharacteristic, complemented
36C2×D8×C269C2211yescharacteristic, complemented
37C22×C8×C269C2211yescharacteristic, complemented
38#121×C269C2212yescomplemented
39#107×C269C2211yescharacteristic, complemented
40#102×C269C2212yescomplemented
41C23×D269—22no—
42C23×D269—22no—
43C2×D1076—24no—
44C2×D1076—22no—
45C2×D1076—22no—
46C2×D1076—42no—
47C2×D1076C2312yes—
48C2×D1076C2312yes—
49C2×C22⋊D269—22no—
50C2×C22⋊D269—22no—
51C2×C22⋊D269—22no—
52C2×C22⋊D269D411yescharacteristic
53D4×D269—24no—
54D4×D269—42no—
55D4×D269—48no—
56C2×C4×D269—22no—
57C2×C4×D269C2311yescharacteristic
58D2152—24no—
59D2152—22no—
60D2152D414yescomplemented
61#16864387—24no—
62#16864387—42no—
63C2×#14524130C2311yescharacteristic
64C2×#14524130C2311yescharacteristic
65C8×D269—22no—
66#16864381D411yescharacteristic
67C22⋊Dic269D411yescharacteristic
68#16864379—22no—
69#16864379—22no—
70#16864379D411yescharacteristic
71C4×Dic269C2311yescharacteristic
72C2×D4×C269—22no—
73C2×D4×C269C2312yes—
74C22×C4×C269C2311yescharacteristic
75D8×C269—22no—
76C2×C8×C269—22no—
77C2×C8×C269C2311yescharacteristic
78C2×C8×C269C2311yescharacteristic
79C4⋊C4×C269C2312yes—
80C22⋊C4×C269—22no—
81C22×D269—22no—
82C22×D269—22no—
83C22×D269—44no—
84C22×D269—44no—
85C22×D269—44no—
86C22×D269—44no—
87C22×D269—82no—
88C22×D269—82no—
89C22×D269C2×D411yescharacteristic
90D1076—22no—
91D1076—22no—
92D1076—22no—
93D1076—44no—
94D1076—44no—
95D1076C2×D414yescomplemented
96C22⋊D269—44no—
97C22⋊D269—44no—
98C22⋊D269—82no—
99C22⋊D269D814yescomplemented
100C2×Dic269C2×D411yescharacteristic
101C2×Dic269C2×D411yescharacteristic
102C2×Dic269C2×D411yescharacteristic
103C4×D269—21no—
104C4×D269—21no—
105C4×D269—44no—
106#14524130—21no—
107#14524130—21no—
108C23×C269—22no—
109C23×C269C2×D411yescharacteristic
110D4×C269—22no—
111D4×C269—22no—
112D4×C269—44no—
113C2×C4×C269—21no—
114C2×C4×C269—21no—
115C2×C4×C269—22no—
116C2×C4×C269C2×D411yescharacteristic
117C2×C4×C269C2411yescharacteristic
118C8×C269—21no—
119C8×C269C2×D412yescomplemented
120C22×C269—21no—
121C22×C269—21no—
122C22×C269—42no—
123C22×C269—42no—
124C22×C269—42no—
125C22×C269C2×D812yescomplemented
126C22×C269C22×D411yescharacteristic
127C2×D269—21no—
128C2×D269—21no—
129C2×D269—24no—
130C2×D269—42no—
131C2×D269—42no—
132C2×D269—42no—
133C2×D269—42no—
134C2×D269—42no—
135C2×D269—88no—
136C2×D269—88no—
137C2×D269C2×D812yescomplemented
138C4×C269—21no—
139C4×C269—42no—
140C4×C269C22×D411yescharacteristic
141C4×C269H(5,𝔽2)11yescharacteristic
142Dic269—21no—
143Dic269—21no—
144Dic269C2×D812yescomplemented
145C2×C269—22no—
146C2×C269—82no—
147C2×C269D4211yescharacteristic
148C2×C269C22×D811yescharacteristic
149C2×C269#57611yescharacteristic
150D269—22no—
151D269—44no—
152D269—82no—
153C269D4×D811yescharacteristic, complemented, Sylow
154D4×D8—2691nomaximal, Sylow
155C22×D8—2691no—
156C22×D8—2691no—
157D42—2692no—
158#493—2691no—
159#466—2691no—
160#466D26911yescharacteristic, complemented
161#459—2692no—
162#447—2692no—
163#447—2692no—
164C4×D8—2691no—
165C8×D4—2691no—
166C22×D4—2692no—
167C22×D4—2692no—
168C22×D4—5382no—
169C2×D8—2692no—
170C2×D8—2692no—
171C2×D8—2691no—
172C2×D8—2692no—
173C2×D8—2691no—
174C2×D8—5384no—
175C2×D8—5384no—
176C2×D8C2×D26911yescharacteristic, complemented
177C22×C8—2691no—
178C22×C8C2×D26911yescharacteristic, complemented
179#127—2692no—
180#121—2692no—
181#121—5382no—
182#121C2×D26912yescomplemented
183#120—5382no—
184#120—5382no—
185C4×D4—2691no—
186C4×D4—2692no—
187#107C2×D26911yescharacteristic, complemented
188C4⋊C8—2691no—
189#102—2692no—
190#102—2692no—
191#102C2×D26912yescomplemented
192C22⋊C8—2691no—
193C22⋊C8—2691no—
194C4×C8—2691no—
195C24—5382no—
196C24—5382no—
197C2×D4—22no—
198C2×D4—2691no—
199C2×D4—2692no—
200C2×D4—2692no—
201C2×D4—5384no—
202C2×D4—5382no—
203C2×D4—5382no—
204C2×D4—5382no—
205C2×D4—5382no—
206C2×D4—5384no—
207C2×D4—5382no—
208C2×D4—10762no—
209C2×D4—10762no—
210C2×D4—10768no—
211C2×D4C22×D26912yes—
212C22×C4—2691no—
213C22×C4—5382no—
214C22×C4C22×D26911yescharacteristic
215D8—22no—
216D8—2694no—
217D8—5384no—
218D8—5384no—
219D8—5382no—
220D8—10762no—
221C2×C8—22no—
222C2×C8—2691no—
223C2×C8—2691no—
224C2×C8—5382no—
225C2×C8C22×D26911yescharacteristic
226C2×C8C22×D26911yescharacteristic
227C4⋊C4—2691no—
228C4⋊C4C22×D26912yes—
229C22⋊C4—22no—
230C22⋊C4—2691no—
231C22⋊C4—2691no—
232C22⋊C4—5382no—
233C22⋊C4—5382no—
234C42—2691no—
235C23—22no—
236C23—2691no—
237C23—5382no—
238C23—5382no—
239C23—10764no—
240C23—10764no—
241C23—10764no—
242C23—10764no—
243C23—21522no—
244C23—21522no—
245C23D4×D26911yescharacteristic
246D4—22no—
247D4—22no—
248D4—44no—
249D4—2694no—
250D4—2694no—
251D4—5382no—
252D4—5382no—
253D4—5382no—
254D4—10764no—
255D4—10764no—
256D4—10764no—
257D4—10764no—
258D4—21522no—
259C2×C4—21no—
260C2×C4—21no—
261C2×C4—22no—
262C2×C4—2691no—
263C2×C4—2691no—
264C2×C4—2691no—
265C2×C4—5381no—
266C2×C4—5381no—
267C2×C4—10764no—
268C2×C4D4×D26911yescharacteristic
269C2×C4C23×D26911yescharacteristic
270C8—21no—
271C8—5381no—
272C8—5381no—
273C8D4×D26912yescomplemented
274C22—21no—
275C22—21no—
276C22—42no—
277C22—42no—
278C22—42no—
279C22—2692no—
280C22—5381no—
281C22—5381no—
282C22—5384no—
283C22—10762no—
284C22—10762no—
285C22—10762no—
286C22—10762no—
287C22—10762no—
288C22—21528no—
289C22—21528no—
290C22D8×D26912yescomplemented
291C22C2×D4×D26911yescharacteristic
292C4—21no—
293C4—42no—
294C4—2692no—
295C4—5381no—
296C4—5381no—
297C4C2×D4×D26911yescharacteristic
298C4#2257549911yescharacteristic
299C2—22no—
300C2—82no—
301C2—5382no—
302C2—10764no—
303C2—21522no—
304C2#3177123911yescharacteristic
305C2C2×D8×D26911yescharacteristic
306C2#3177140711yescharacteristic
subgroupG/H
centerC22C2×D4×D269
commutator, cosocleC2×C4×C269C24
FrattiniC2×C4C23×D269
Fitting#466×C269C2
socleC22×C269C22×D4
hypercenter#466D269
hypocenterC269D4×D8
LCSG ▷ C2×C4×C269 ▷ C2×C269 ▷ C269
UCSC1 ◁ C22 ◁ C22×C4 ◁ #466

Complements

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

NH ≅ G/Ntype
1. C22×D2152C2semidirect
2. C2×D8×D269C2semidirect
3. #31771239C2semidirect
4. #31770980C2semidirect
5. #31770842C2semidirect
6. #31770799C2semidirect
7. #31770740C2semidirect
8. #31770738C2semidirect
9. #31770687C2semidirect
10. C8×C22⋊D269C2semidirect
11. #466×C269C2semidirect
12. C22×D1076C22semidirect
14. C2×D4×D269C22semidirect
17. C2×D2152C22semidirect
18. C2×D2152C22semidirect
19. C2×#16864387C22semidirect
20. C2×#16864387C22semidirect
22. C2×C8×D269C22semidirect
23. #22575449C22semidirect
24. #22575428C22semidirect
28. #22575415C22semidirect
30. #22575382C22semidirect
31. #22575373C22semidirect
32. #22575373C22semidirect
33. C22⋊#14524130C22semidirect
34. #22575365C22semidirect
35. C8×Dic269C22semidirect
36. C2×D8×C269C22semidirect
37. C22×C8×C269C22semidirect
38. #121×C269C22semidirect
39. #107×C269C22semidirect
40. #102×C269C22semidirect
60. D2152D4semidirect
95. D1076C2×D4semidirect
99. C22⋊D269D8semidirect
119. C8×C269C2×D4semidirect
125. C22×C269C2×D8semidirect
137. C2×D269C2×D8semidirect
144. Dic269C2×D8semidirect
153. C269D4×D8semidirect
160. #466D269semidirect
176. C2×D8C2×D269semidirect
178. C22×C8C2×D269semidirect
182. #121C2×D269semidirect
187. #107C2×D269semidirect
191. #102C2×D269semidirect
273. C8D4×D269semidirect
290. C22D8×D269semidirect

Maximal subgroups

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

subgroupindex
C22×D21522
C2×D8×D2692
#317712392
#317709802
#317708422
#317707992
#317707402
#317707382
#317706872
C8×C22⋊D2692
#466×C2692
D4×D8269