Finite Group Databasebeta

← #49133056

Subgroups — #49133056

Order 36224.

460 conjugacy classes of subgroups; only the 117 normal subgroups are shown.

normal subgroups only

This group has 460 conjugacy classes of subgroups — too many to draw. Only its 117 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#31827276C212yesmaximal, complemented
2#31827275C212yesmaximal, complemented
3#31826837C211yesmaximal, characteristic, complemented
4#31826727C212yesmaximal, complemented
5#31826726C212yesmaximal, complemented
6#31826649C212yesmaximal, complemented
7#31826632C211yesmaximal, characteristic, complemented
8#31826579C212yesmaximal, complemented
9#453×C283C211yesmaximal, characteristic, complemented
10#22583657C2212yes—
11#22583655C2211yescharacteristic, complemented
12#22583643C2212yescomplemented
13#22583640—22no—
14#22583640C2212yescomplemented
15#22583639—22no—
16#22583636—22no—
17#22583636C2212yes—
18#22583634—22no—
19#22583630—22no—
20#22583630C2212yes—
21#22583629—22no—
22C2×#17985380—22no—
23C2×#17985380C2212yescomplemented
24C2×#17985380C2212yescomplemented
25SD16×D283—22no—
26#22583618C2212yescomplemented
27#22583617C2212yescomplemented
28#22583610C2211yescharacteristic, complemented
29#22583545C2212yescomplemented
30#22583538C2212yescomplemented
31#22583528C2212yescomplemented
32#22583527C2211yescharacteristic, complemented
33C4×C283⋊C8C2211yescharacteristic, complemented
34H(5,𝔽2)×C283C2211yescharacteristic, complemented
35AGL(1,ℤ/8)×C283C2212yes—
36#127×C283C2211yescharacteristic
37#104×C283C2212yescomplemented
38#100×C283C2211yescharacteristic, complemented
39#17985392—22no—
40#17985392C2312yes—
41#17985391—22no—
42#17985391—22no—
43#17985391—42no—
44C2×Dic566—22no—
45C2×Dic566C2312yes—
46Q8×D283—22no—
47C2×C22⋊D283—41no—
48D4×D283—22no—
49Dic1132—22no—
50#17985382—22no—
51#17985382D412yescomplemented
52#17985381—22no—
53#17985380—22no—
54#17985380—22no—
55#17985380—22no—
56#17985380—22no—
57#17985380—22no—
58#17985380—22no—
59#17985380D412yescomplemented
60#17985379D412yescomplemented
61#17985377—22no—
62#17985377D412yescomplemented
63#17985376—22no—
64#17985376C2312yes—
65#17985375—22no—
66C2×C283⋊C8—22no—
67C2×C283⋊C8C2312yes—
68C8×D283—22no—
69C4⋊Dic283—41no—
70#41×C283—22no—
71#41×C283C2312yes—
72C2×D4×C283—22no—
73C2×D4×C283—41no—
74C2×D4×C283—41no—
75C2×D4×C283C2311yescharacteristic
76C2×D4×C283C2311yescharacteristic
77SD16×C283—22no—
78D8×C283—22no—
79M16×C283C2312yes—
80C42×C283C2311yescharacteristic
81C22×D283—41no—
82Dic566—22no—
83Dic566—22no—
84Dic566—42no—
85Dic566C2×D412yes—
86D1132C2×D412yes—
87C22⋊D283—22no—
88C22⋊D283—42no—
89C22⋊D283—42no—
90C2×Dic283—22no—
91C2×Dic283—41no—
92C2×Dic283—42no—
93C4×D283—22no—
94C4×D283—42no—
95C283⋊C8—22no—
96C283⋊C8C2×D412yes—
97C283⋊C8C2×D412yes—
98C23×C283—21no—
99C23×C283—21no—
100C23×C283—41no—
101Q8×C283C2×D412yes—
102D4×C283—22no—
103D4×C283—22no—
104D4×C283—22no—
105D4×C283—42no—
106D4×C283—82no—
107D4×C283C2×D412yes—
108C2×C4×C283—21no—
109C2×C4×C283—22no—
110C2×C4×C283—41no—
111C2×C4×C283C2411yescharacteristic
112C8×C283—22no—
113C22×C283—22no—
114C22×C283—41no—
115C22×C283—41no—
116C22×C283—81no—
117C22×C283—81no—
118C22×C283—161no—
119C22×C283H(5,𝔽2)11yescharacteristic
120C2×D283—22no—
121C2×D283—161no—
122C4×C283—22no—
123C4×C283—22no—
124C4×C283C22×D412yes—
125Dic283—22no—
126Dic283—42no—
127C2×C283—21no—
128C2×C283—42no—
129C2×C283—81no—
130C2×C283—81no—
131C2×C283D4211yescharacteristic
132D283—42no—
133C283#329111yescharacteristic, complemented, Sylow
134#3291—2831nomaximal, Sylow
135#577—2832no—
136#577—2832no—
137#492—2831no—
138#471—2832no—
139#471—2832no—
140#456—2832no—
141#453—2831no—
142#453D28311yescharacteristic, complemented
143#443—2832no—
1442−1+4—2832no—
145H(5,𝔽2)—2831no—
146H(5,𝔽2)C2×D28311yescharacteristic, complemented
147#137—2832no—
148#137—2832no—
149#137—5662no—
150#137—5662no—
151AGL(1,ℤ/8)—2832no—
152AGL(1,ℤ/8)—5662no—
153AGL(1,ℤ/8)—5662no—
154AGL(1,ℤ/8)C2×D28312yes—
155#135—2832no—
156#135—5662no—
157#135—5662no—
158C2×SD16—2832no—
159C2×SD16—2832no—
160C2×SD16—5662no—
161C2×SD16—5662no—
162#131—2832no—
163#131—2832no—
164C4⋊Q8—2831no—
165#127C2×D28311yescharacteristic
166#108—2832no—
167#104—2832no—
168#104C2×D28312yescomplemented
169#101—2832no—
170#100—2831no—
171#100C2×D28311yescharacteristic, complemented
172C4×C8—2831no—
173#41—22no—
174#41—2832no—
175#41—5662no—
176#41—5662no—
177#41—5662no—
178#41—11322no—
179#41C22×D28312yes—
180C2×Q8—2832no—
181C2×Q8—5662no—
182C2×Q8—5662no—
183C2×D4—22no—
184C2×D4—41no—
185C2×D4—41no—
186C2×D4—5662no—
187C2×D4—11321no—
188C2×D4C22×D28311yescharacteristic
189C2×D4C22×D28311yescharacteristic
190Q16—2832no—
191Q16—5662no—
192Q16—5662no—
193SD16—22no—
194SD16—2832no—
195SD16—2832no—
196SD16—5662no—
197SD16—5662no—
198SD16—5662no—
199SD16—5662no—
200SD16—5662no—
201SD16—5662no—
202SD16—5662no—
203D8—22no—
204D8—2832no—
205D8—5662no—
206M16—2832no—
207M16—5662no—
208M16—5662no—
209M16C22×D28312yes—
210C2×C8—2832no—
211C2×C8—5662no—
212C2×C8—5662no—
213C4⋊C4—11321no—
214C42C22×D28311yescharacteristic
215C23—21no—
216C23—21no—
217C23—41no—
218C23—11321no—
219Q8—2832no—
220Q8—5662no—
221Q8—5662no—
222Q8—11322no—
223Q8D4×D28312yes—
224D4—22no—
225D4—22no—
226D4—22no—
227D4—42no—
228D4—82no—
229D4—2832no—
230D4—5662no—
231D4—11322no—
232D4—11322no—
233D4D4×D28312yes—
234C2×C4—21no—
235C2×C4—22no—
236C2×C4—41no—
237C2×C4—5662no—
238C2×C4—5662no—
239C2×C4—11322no—
240C2×C4—11321no—
241C2×C4—11322no—
242C2×C4C23×D28311yescharacteristic
243C8—22no—
244C8—2832no—
245C8—2832no—
246C8—5662no—
247C22—22no—
248C22—41no—
249C22—41no—
250C22—81no—
251C22—81no—
252C22—161no—
253C22—5662no—
254C22—45281no—
255C22#2258365511yescharacteristic
256C4—22no—
257C4—22no—
258C4—5662no—
259C4—11322no—
260C4C2×D4×D28312yes—
261C2—21no—
262C2—42no—
263C2—81no—
264C2—81no—
265C2—11322no—
266C2#3182709711yescharacteristic
subgroupG/H
centerC2#31827097
commutator, cosocleC2×C4×C283C24
FrattiniC2×C4C23×D283
Fitting#453×C283C2
socleC2×C283D42
hypercenter#453D283
hypocenterC283#3291
LCSG ▷ C2×C4×C283 ▷ C2×C283 ▷ C283
UCSC1 ◁ C2 ◁ C2×C4 ◁ #453

Complements

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

NH ≅ G/Ntype
1. #31827276C2semidirect
2. #31827275C2semidirect
3. #31826837C2semidirect
4. #31826727C2semidirect
5. #31826726C2semidirect
6. #31826649C2semidirect
7. #31826632C2semidirect
8. #31826579C2semidirect
9. #453×C283C2semidirect
11. #22583655C22semidirect
12. #22583643C22semidirect
14. #22583640C22semidirect
23. C2×#17985380C22semidirect
24. C2×#17985380C22semidirect
26. #22583618C22semidirect
27. #22583617C22semidirect
28. #22583610C22semidirect
29. #22583545C22semidirect
30. #22583538C22semidirect
31. #22583528C22semidirect
32. #22583527C22semidirect
33. C4×C283⋊C8C22semidirect
34. H(5,𝔽2)×C283C22semidirect
37. #104×C283C22semidirect
38. #100×C283C22semidirect
51. #17985382D4semidirect
59. #17985380D4semidirect
60. #17985379D4semidirect
62. #17985377D4semidirect
133. C283#3291semidirect
142. #453D283semidirect
146. H(5,𝔽2)C2×D283semidirect
168. #104C2×D283semidirect
171. #100C2×D283semidirect

Maximal subgroups

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

subgroupindex
#318272762
#318272752
#318268372
#318267272
#318267262
#318266492
#318266322
#318265792
#453×C2832
#3291283