Finite Group Databasebeta

← #49133077

Subgroups — #49133077

Order 36224.

494 conjugacy classes of subgroups; only the 123 normal subgroups are shown.

normal subgroups only

This group has 494 conjugacy classes of subgroups — too many to draw. Only its 123 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
1#31827120C211yesmaximal, characteristic, complemented
2#31827100C211yesmaximal, characteristic, complemented
3#31826811C211yesmaximal, characteristic, complemented
4#31826777C212yesmaximal, complemented
5#31826746C211yesmaximal, characteristic, complemented
6#31826698C212yesmaximal, complemented
7#31826597C212yesmaximal, complemented
8C4×#17985377C211yesmaximal, characteristic, complemented
9#31826530C211yesmaximal, characteristic, complemented
10#102×D283C212yesmaximal, complemented
11#459×C283C211yesmaximal, characteristic, complemented
12C2×#17985392—21no—
13C2×D4×D283—21no—
14C2×D4×D283C2212yes—
15C2×#17985377C2211yescharacteristic
16C2×C8×D283C2212yescomplemented
17#22583610C2211yescharacteristic, complemented
18#22583592—22no—
19#22583589—21no—
20#22583581—21no—
21#22583581C2212yes—
22#22583581C2212yescomplemented
23#22583578—22no—
24C4×D1132C2211yescharacteristic
25C4×D1132C2211yescharacteristic
26C4⋊C4×D283C2212yescomplemented
27#22583544C2212yescomplemented
28#22583543C2211yescharacteristic, complemented
29#22583532C2212yes—
30#22583531C2211yescharacteristic, complemented
31#22583531C2212yescomplemented
32#22583531C2212yescomplemented
33#22583530C2211yescharacteristic
34(C2×D283)⋊C8C2212yescomplemented
35C4×C283⋊C8C2211yescharacteristic, complemented
36C2×D8×C283C2212yescomplemented
37#127×C283C2211yescharacteristic
38C4×D4×C283C2211yescharacteristic, complemented
39C4⋊C8×C283C2211yescharacteristic, complemented
40#102×C283C2212yescomplemented
41C23×D283—22no—
42#17985392—44no—
43C2×Dic566—21no—
44C2×D1132D411yescharacteristic
45C2×D1132C2311yescharacteristic
46C2×C22⋊D283—22no—
47C2×C22⋊D283—22no—
48C2×C22⋊D283—22no—
49D4×D283—24no—
50D4×D283—42no—
51D4×D283—44no—
52C2×C4×D283—22no—
53C2×C4×D283—21no—
54C2×C4×D283C2312yes—
55#17985377—22no—
56C2×C283⋊C8C2311yescharacteristic
57C2×C283⋊C8C2311yescharacteristic
58C8×D283—42no—
59C4⋊Dic283—21no—
60C4⋊Dic283D411yescharacteristic
61C4⋊Dic283C2312yes—
62C4⋊Dic283C2311yescharacteristic
63Dic283⋊C4—22no—
64C22⋊Dic283—22no—
65C22⋊Dic283—22no—
66(C2×D283)⋊C4—21no—
67(C2×D283)⋊C4D412yes—
68C2×D4×C283—21no—
69C2×D4×C283—21no—
70C2×D4×C283C2312yes—
71C2×D4×C283C2311yescharacteristic
72C22×C4×C283—21no—
73D8×C283—42no—
74C2×C8×C283C2312yes—
75C4⋊C4×C283C2311yescharacteristic
76C22⋊C4×C283—21no—
77C42×C283C2311yescharacteristic
78C22×D283—21no—
79C22×D283—44no—
80C22×D283—44no—
81C22×D283—82no—
82C22×D283C2×D412yes—
83Dic566—42no—
84D1132—21no—
85D1132D814yescomplemented
86D1132#4112yescomplemented
87C22⋊D283—44no—
88C22⋊D283—44no—
89C22⋊D283—44no—
90C2×Dic283—21no—
91C2×Dic283—22no—
92C2×Dic283C2×D412yes—
93C4×D283—22no—
94C4×D283—22no—
95C4×D283—44no—
96C4×D283—42no—
97C283⋊C8—21no—
98C283⋊C8—21no—
99C23×C283—21no—
100C23×C283—22no—
101D4×C283—21no—
102D4×C283—22no—
103D4×C283—21no—
104D4×C283—22no—
105D4×C283—42no—
106D4×C283—81no—
107C2×C4×C283—21no—
108C2×C4×C283—42no—
109C2×C4×C283C2×D411yescharacteristic
110C2×C4×C283C2×D411yescharacteristic
111C2×C4×C283C2411yescharacteristic
112C8×C283—22no—
113C22×C283—41no—
114C22×C283—42no—
115C22×C283—41no—
116C22×C283—42no—
117C22×C283—42no—
118C22×C283—41no—
119C22×C283C22×D411yescharacteristic
120C2×D283—22no—
121C2×D283—22no—
122C2×D283—22no—
123C2×D283—41no—
124C2×D283—41no—
125C2×D283—88no—
126C2×D283C2×D814yes—
127C4×C283—21no—
128C4×C283—41no—
129C4×C283C2×D812yes—
130C4×C283C2×#4111yescharacteristic
131C4×C283H(5,𝔽2)11yescharacteristic
132Dic283—22no—
133Dic283—41no—
134Dic283—42no—
135C2×C283—82no—
136C2×C283—81no—
137C2×C283#54611yescharacteristic
138C2×C283C22×D811yescharacteristic
139C2×C283#57711yescharacteristic
140D283—24no—
141D283—42no—
142C283#329411yescharacteristic, complemented, Sylow
143#3294—2831nomaximal, Sylow
144#547—2831no—
145D42—2831no—
146#486—2831no—
147#480—2832no—
148#474—2831no—
149#466—2832no—
150#459D28311yescharacteristic, complemented
151#447—2832no—
152C4×D8—2831no—
153C8×D4—2831no—
154C2×#102—2832no—
155C2×#41—5661no—
156C22×D4—2832no—
157C22×D4—5661no—
158C2×D8—2831no—
159C2×D8C2×D28312yescomplemented
160C22×C8—2832no—
161C4⋊Q8—2831no—
162#127C2×D28311yescharacteristic
163#123—5662no—
164C22⋊Q8—5661no—
165#121—2832no—
166#121—2832no—
167#121—5661no—
168#120—5662no—
169C4×D4—2831no—
170C4×D4—2831no—
171C4×D4C2×D28311yescharacteristic, complemented
172C2×C4⋊C4—2832no—
173#107—2832no—
174#107—2831no—
175C4⋊C8C2×D28311yescharacteristic, complemented
176#102—2832no—
177#102—2831no—
178#102—2832no—
179#102—2832no—
180#102—2831no—
181#102C2×D28312yescomplemented
182C22⋊C8—2832no—
183C4×C8—2831no—
184C24—5662no—
185#41—11324no—
186C2×Q8—5661no—
187C2×D4—21no—
188C2×D4—21no—
189C2×D4—2831no—
190C2×D4—2831no—
191C2×D4—5662no—
192C2×D4—5664no—
193C2×D4—5662no—
194C2×D4—5662no—
195C2×D4—11322no—
196C2×D4—11324no—
197C2×D4C22×D28312yes—
198C2×D4C22×D28311yescharacteristic
199C22×C4—21no—
200C22×C4—2832no—
201C22×C4—5662no—
202C22×C4—5661no—
203D8—42no—
204D8—5662no—
205C2×C8—2831no—
206C2×C8—2831no—
207C2×C8—11322no—
208C2×C8C22×D28312yes—
209C4⋊C4—2831no—
210C4⋊C4—2832no—
211C4⋊C4—2831no—
212C4⋊C4—5662no—
213C4⋊C4—5661no—
214C4⋊C4C22×D28311yescharacteristic
215C22⋊C4—21no—
216C22⋊C4—2832no—
217C22⋊C4—5662no—
218C22⋊C4—5662no—
219C22⋊C4—5661no—
220C42C22×D28311yescharacteristic
221C23—21no—
222C23—22no—
223C23—2832no—
224C23—5661no—
225C23—11324no—
226C23—11324no—
227C23—22642no—
228Q8—11322no—
229D4—21no—
230D4—22no—
231D4—21no—
232D4—22no—
233D4—42no—
234D4—81no—
235D4—2834no—
236D4—2832no—
237D4—5661no—
238D4—11324no—
239D4—11324no—
240D4—11324no—
241C2×C4—21no—
242C2×C4—42no—
243C2×C4—2832no—
244C2×C4—5662no—
245C2×C4—5662no—
246C2×C4—5661no—
247C2×C4—5662no—
248C2×C4—11324no—
249C2×C4—11322no—
250C2×C4D4×D28311yescharacteristic
251C2×C4D4×D28311yescharacteristic
252C2×C4C23×D28311yescharacteristic
253C8—22no—
254C8—5661no—
255C8—5661no—
256C22—41no—
257C22—42no—
258C22—42no—
259C22—41no—
260C22—42no—
261C22—41no—
262C22—2834no—
263C22—5662no—
264C22—5662no—
265C22—5662no—
266C22—11321no—
267C22—11321no—
268C22—22648no—
269C22C2×D4×D28311yescharacteristic
270C4—21no—
271C4—41no—
272C4—5662no—
273C4—11321no—
274C4—11322no—
275C4D8×D28312yes—
276C4#41×D28311yescharacteristic
277C4#2258365511yescharacteristic
278C2—82no—
279C2—81no—
280C2—5664no—
281C2—11322no—
282C2#3182711211yescharacteristic
283C2C2×D8×D28311yescharacteristic
284C2#3182727511yescharacteristic
subgroupG/H
centerC22C2×D4×D283
commutator, cosocleC2×C4×C283C24
FrattiniC2×C4C23×D283
Fitting#459×C283C2
socleC22×C283C22×D4
hypercenter#459D283
hypocenterC283#3294
LCSG ▷ C2×C4×C283 ▷ C2×C283 ▷ C283
UCSC1 ◁ C22 ◁ C42 ◁ #459

Complements

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

NH ≅ G/Ntype
1. #31827120C2semidirect
2. #31827100C2semidirect
3. #31826811C2semidirect
4. #31826777C2semidirect
5. #31826746C2semidirect
6. #31826698C2semidirect
7. #31826597C2semidirect
8. C4×#17985377C2semidirect
9. #31826530C2semidirect
10. #102×D283C2semidirect
11. #459×C283C2semidirect
16. C2×C8×D283C22semidirect
17. #22583610C22semidirect
22. #22583581C22semidirect
26. C4⋊C4×D283C22semidirect
27. #22583544C22semidirect
28. #22583543C22semidirect
30. #22583531C22semidirect
31. #22583531C22semidirect
32. #22583531C22semidirect
34. (C2×D283)⋊C8C22semidirect
35. C4×C283⋊C8C22semidirect
36. C2×D8×C283C22semidirect
38. C4×D4×C283C22semidirect
39. C4⋊C8×C283C22semidirect
40. #102×C283C22semidirect
85. D1132D8semidirect
86. D1132#41semidirect
142. C283#3294semidirect
150. #459D283semidirect
159. C2×D8C2×D283semidirect
171. C4×D4C2×D283semidirect
175. C4⋊C8C2×D283semidirect
181. #102C2×D283semidirect

Maximal subgroups

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

subgroupindex
#318271202
#318271002
#318268112
#318267772
#318267462
#318266982
#318265972
C4×#179853772
#318265302
#102×D2832
#459×C2832
#3294283