Finite Group Databasebeta

← #49133082

Subgroups — #49133082

Order 36224.

462 conjugacy classes of subgroups; only the 125 normal subgroups are shown.

normal subgroups only

This group has 462 conjugacy classes of subgroups — too many to draw. Only its 125 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#31827176C211yesmaximal, characteristic, complemented
2D4×D1132C211yesmaximal, characteristic
3#31826813C211yesmaximal, characteristic, complemented
4#31826785C212yesmaximal, complemented
5#31826695C212yesmaximal, complemented
6#31826666C211yesmaximal, characteristic, complemented
7#31826617C212yesmaximal, complemented
8C4×#17985380C211yesmaximal, characteristic, complemented
9#31826530C211yesmaximal, characteristic, complemented
10#102×D283C212yesmaximal, complemented
11#476×C283C211yesmaximal, characteristic, complemented
12C22×D1132—21no—
13C2×D4×D283C2212yes—
14C2×#17985381C2212yescomplemented
15C2×#17985380C2211yescharacteristic
16C2×C8×D283C2212yescomplemented
17#22583607C2211yescharacteristic
18#22583601—21no—
19#22583590C2212yescomplemented
20#22583586—22no—
21#22583585C2212yes—
22#22583584—21no—
23#22583580—22no—
24C4×Dic566C2211yescharacteristic, complemented
25C4×D1132C2211yescharacteristic
26#22583572—21no—
27C4⋊C4×D283C2212yescomplemented
28#22583541C2211yescharacteristic, complemented
29#22583533C2211yescharacteristic, complemented
30#22583532C2212yescomplemented
31#22583531C2211yescharacteristic
32#22583530C2212yescomplemented
33#22583530C2212yescomplemented
34(C2×D283)⋊C8C2212yescomplemented
35C4×C283⋊C8C2211yescharacteristic, complemented
36C4⋊Q8×C283C2211yescharacteristic, complemented
37C4×D4×C283C2211yescharacteristic
38#106×C283C2212yescomplemented
39C4⋊C8×C283C2211yescharacteristic, complemented
40#102×C283C2212yes—
41C23×D283—22no—
42C2×Dic566C2311yescharacteristic
43C2×D1132—22no—
44C2×D1132—21no—
45C2×D1132—21no—
46C2×D1132—44no—
47C2×D1132D411yescharacteristic
48C2×D1132C2312yes—
49C2×C22⋊D283—22no—
50D4×D283—24no—
51D4×D283—42no—
52C2×C4×D283—22no—
53C2×C4×D283C2312yes—
54#17985381—42no—
55#17985380—22no—
56C2×C283⋊C8C2311yescharacteristic
57C2×C283⋊C8C2311yescharacteristic
58C8×D283—42no—
59C4⋊Dic283—22no—
60C4⋊Dic283D411yescharacteristic
61C4⋊Dic283C2311yescharacteristic
62Dic283⋊C4—22no—
63Dic283⋊C4—21no—
64(C2×D283)⋊C4—22no—
65(C2×D283)⋊C4—22no—
66(C2×D283)⋊C4D412yes—
67C4×Dic283—21no—
68C2×Q8×C283—21no—
69C2×D4×C283C2311yescharacteristic
70C22×C4×C283—21no—
71C2×C8×C283C2312yes—
72C4⋊C4×C283—21no—
73C4⋊C4×C283C2312yes—
74C4⋊C4×C283C2311yescharacteristic
75C22⋊C4×C283—21no—
76C42×C283C2311yescharacteristic
77C22×D283—22no—
78C22×D283—44no—
79C22×D283—44no—
80C22×D283—82no—
81C22×D283C2×D412yes—
82Dic566—21no—
83Dic566—21no—
84D1132—22no—
85D1132—22no—
86D1132—44no—
87D1132—42no—
88D1132—81no—
89D1132SD1614yescomplemented
90C22⋊D283—44no—
91C2×Dic283—21no—
92C2×Dic283—21no—
93C2×Dic283C2×D412yes—
94C4×D283—22no—
95C4×D283—22no—
96C4×D283—82no—
97C283⋊C8—21no—
98C283⋊C8—21no—
99C23×C283—21no—
100Q8×C283—81no—
101D4×C283—21no—
102D4×C283#4112yes—
103C2×C4×C283—21no—
104C2×C4×C283—22no—
105C2×C4×C283—42no—
106C2×C4×C283C2×D411yescharacteristic
107C2×C4×C283C2×D411yescharacteristic
108C2×C4×C283C2411yescharacteristic
109C8×C283—22no—
110C22×C283—22no—
111C22×C283—41no—
112C22×C283—41no—
113C22×C283C22×D411yescharacteristic
114C2×D283—22no—
115C2×D283—22no—
116C2×D283—42no—
117C2×D283—42no—
118C2×D283—42no—
119C2×D283—88no—
120C2×D283C2×SD1614yes—
121C4×C283—21no—
122C4×C283—41no—
123C4×C283—42no—
124C4×C283C2×SD1612yes—
125C4×C283C2×#4111yescharacteristic
126C4×C283H(5,𝔽2)11yescharacteristic
127Dic283—22no—
128Dic283—41no—
129Dic283—41no—
130C2×C283—42no—
131C2×C283#54611yescharacteristic
132C2×C283C22×SD1611yescharacteristic
133C2×C283#57611yescharacteristic
134D283—24no—
135D283—82no—
136C283#329511yescharacteristic, complemented, Sylow
137#3295—2831nomaximal, Sylow
138#554—2831no—
139D42—2831no—
140#486—2831no—
141#481—2832no—
142#476D28311yescharacteristic, complemented
143#465—2832no—
144#460—2831no—
145#450—2832no—
146C4×SD16—2831no—
147C8×D4—2831no—
148C2×#102—2832no—
149C22×D4—2832no—
150C22×D4—5661no—
151C2×SD16—2831no—
152C2×SD16—2832no—
153C22×C8—2832no—
154C4⋊Q8C2×D28311yescharacteristic, complemented
155#127—2831no—
156#125—5661no—
157C22⋊Q8—2832no—
158C22⋊Q8—5662no—
159#121—2832no—
160#121—5661no—
161#120—5662no—
162C4×Q8—2831no—
163C4×D4—2831no—
164C4×D4—5661no—
165C4×D4C2×D28311yescharacteristic
166C2×C4⋊C4—2832no—
167#106—2831no—
168#106C2×D28312yescomplemented
169C4⋊C8C2×D28311yescharacteristic, complemented
170#103—2831no—
171#102—2831no—
172#102—2832no—
173#102—2832no—
174#102—2832no—
175#102C2×D28312yes—
176C22⋊C8—2832no—
177C4×C8—2831no—
178C24—5662no—
179C2×Q8—21no—
180C2×Q8—2831no—
181C2×D4—2831no—
182C2×D4—2832no—
183C2×D4—5662no—
184C2×D4—5662no—
185C2×D4—5664no—
186C2×D4—5661no—
187C2×D4—5661no—
188C2×D4—11324no—
189C2×D4—11322no—
190C2×D4C22×D28311yescharacteristic
191C22×C4—21no—
192C22×C4—2832no—
193C22×C4—5662no—
194SD16—5662no—
195SD16—11322no—
196C2×C8—2831no—
197C2×C8—2831no—
198C2×C8—11322no—
199C2×C8C22×D28312yes—
200C4⋊C4—21no—
201C4⋊C4—2831no—
202C4⋊C4—2831no—
203C4⋊C4—5662no—
204C4⋊C4—5662no—
205C4⋊C4—5661no—
206C4⋊C4C22×D28312yes—
207C4⋊C4C22×D28311yescharacteristic
208C22⋊C4—21no—
209C22⋊C4—2832no—
210C22⋊C4—5662no—
211C22⋊C4—5662no—
212C42—5661no—
213C42C22×D28311yescharacteristic
214C23—21no—
215C23—2832no—
216C23—5662no—
217C23—11324no—
218C23—11324no—
219C23—22642no—
220Q8—81no—
221Q8—5661no—
222Q8—5661no—
223D4—21no—
224D4—2834no—
225D4—5662no—
226D4—5662no—
227D4—11324no—
228D4—11324no—
229D4—11322no—
230D4—22641no—
231D4#1798539312yes—
232C2×C4—21no—
233C2×C4—22no—
234C2×C4—42no—
235C2×C4—2832no—
236C2×C4—5662no—
237C2×C4—5662no—
238C2×C4—5661no—
239C2×C4—5661no—
240C2×C4—22642no—
241C2×C4D4×D28311yescharacteristic
242C2×C4D4×D28311yescharacteristic
243C2×C4C23×D28311yescharacteristic
244C8—22no—
245C8—5661no—
246C8—5661no—
247C22—22no—
248C22—41no—
249C22—41no—
250C22—2834no—
251C22—5662no—
252C22—5662no—
253C22—11322no—
254C22—11322no—
255C22—11322no—
256C22—22648no—
257C22C2×D4×D28311yescharacteristic
258C4—21no—
259C4—41no—
260C4—42no—
261C4—5662no—
262C4—11321no—
263C4—11321no—
264C4SD16×D28312yes—
265C4C2×#1798539311yescharacteristic
266C4#2258365611yescharacteristic
267C2—42no—
268C2—5664no—
269C2—22642no—
270C2#3182710611yescharacteristic
271C2C2×SD16×D28311yescharacteristic
272C2#3182726911yescharacteristic
subgroupG/H
centerC22C2×D4×D283
commutator, cosocleC2×C4×C283C24
FrattiniC2×C4C23×D283
Fitting#476×C283C2
socleC22×C283C22×D4
prime radicalD4×D1132C2
hypercenter#476D283
hypocenterC283#3295
LCSG ▷ C2×C4×C283 ▷ C2×C283 ▷ C283
UCSC1 ◁ C22 ◁ C42 ◁ #476

Complements

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

NH ≅ G/Ntype
1. #31827176C2semidirect
3. #31826813C2semidirect
4. #31826785C2semidirect
5. #31826695C2semidirect
6. #31826666C2semidirect
7. #31826617C2semidirect
8. C4×#17985380C2semidirect
9. #31826530C2semidirect
10. #102×D283C2semidirect
11. #476×C283C2semidirect
14. C2×#17985381C22semidirect
16. C2×C8×D283C22semidirect
19. #22583590C22semidirect
24. C4×Dic566C22semidirect
27. C4⋊C4×D283C22semidirect
28. #22583541C22semidirect
29. #22583533C22semidirect
30. #22583532C22semidirect
32. #22583530C22semidirect
33. #22583530C22semidirect
34. (C2×D283)⋊C8C22semidirect
35. C4×C283⋊C8C22semidirect
36. C4⋊Q8×C283C22semidirect
38. #106×C283C22semidirect
39. C4⋊C8×C283C22semidirect
89. D1132SD16semidirect
136. C283#3295semidirect
142. #476D283semidirect
154. C4⋊Q8C2×D283semidirect
168. #106C2×D283semidirect
169. C4⋊C8C2×D283semidirect

Maximal subgroups

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

subgroupindex
#318271762
D4×D11322
#318268132
#318267852
#318266952
#318266662
#318266172
C4×#179853802
#318265302
#102×D2832
#476×C2832
#3295283