Finite Group Databasebeta

← #49130500

Subgroups — #49130500

Order 36224.

758 conjugacy classes of subgroups; only the 149 normal subgroups are shown.

normal subgroups only

This group has 758 conjugacy classes of subgroups — too many to draw. Only its 149 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×#17985391C211yesmaximal, characteristic, complemented
2C2×#22583640C211yesmaximal, characteristic, complemented
3#31826972C211yesmaximal, characteristic, complemented
4#31826624C214yesmaximal, complemented
5#31826607C214yesmaximal, complemented
6#31826475C211yesmaximal, characteristic, complemented
7#31826470C211yesmaximal, characteristic, complemented
8#31826428C211yesmaximal, characteristic, complemented
9C2×AGL(1,ℤ/8)×C283C211yesmaximal, characteristic, complemented
10C2×#17985391—24no—
11C2×#17985391—22no—
12C2×#17985391—24no—
13C2×#17985391C2214yes—
14C22×Dic566C2211yescharacteristic
15C22×C22⋊D283—21no—
16C23×Dic283—21no—
17C22×C4×D283C2211yescharacteristic
18#22583640—24no—
19C2×#17985382C2212yescomplemented
20C2×#17985380C2212yescomplemented
21C2×#17985376C2211yescharacteristic
22#22583591—21no—
23#22583586C2212yescomplemented
24#22583581C2212yescomplemented
25#22583578—21no—
26C4×C22⋊D283—22no—
27#22583569C2211yescharacteristic
28#22583535C2214yescomplemented
29#22583531C2214yescomplemented
30(C2×D283)⋊C8C2214yescomplemented
31C2×#41×C283C2211yescharacteristic
32C22×D4×C283C2211yescharacteristic
33AGL(1,ℤ/8)×C283—24no—
34C2×SD16×C283C2212yescomplemented
35C2×D8×C283C2212yescomplemented
36C2×M16×C283C2211yescharacteristic
37C23×D283D411yescharacteristic
38#17985391—216no—
39#17985391—28no—
40#17985391—28no—
41C2×Dic566—21no—
42C2×Dic566—22no—
43C2×Dic566D414yescomplemented
44C2×Dic566C2312yes—
45C2×C22⋊D283—28no—
46C2×C22⋊D283—24no—
47C2×C22⋊D283—22no—
48C22×Dic283—28no—
49C22×Dic283—24no—
50C22×Dic283—21no—
51C22×Dic283D411yescharacteristic
52C2×C4×D283—22no—
53C2×C4×D283—22no—
54C2×C4×D283D412yes—
55C2×C4×D283C2312yes—
56#17985382—24no—
57#17985380—24no—
58#17985376—22no—
59C2×C283⋊C8C2312yes—
60C4⋊Dic283C2312yes—
61Dic283⋊C4—22no—
62C22⋊Dic283—22no—
63C22⋊Dic283—21no—
64(C2×D283)⋊C4—22no—
65C4×Dic283—21no—
66C24×C283—21no—
67#41×C283—22no—
68#41×C283—22no—
69C2×Q8×C283C2311yescharacteristic
70C2×D4×C283—21no—
71C2×D4×C283—21no—
72C2×D4×C283—22no—
73C2×D4×C283D414yescomplemented
74C2×D4×C283C2311yescharacteristic
75C2×D4×C283C2312yes—
76C22×C4×C283—21no—
77C22×C4×C283C2311yescharacteristic
78SD16×C283—24no—
79D8×C283—24no—
80M16×C283—22no—
81C2×C8×C283C2312yes—
82C22×D283—22no—
83C22×D283—42no—
84C22×D283C2×D412yes—
85Dic566—24no—
86Dic566—22no—
87Dic566C2×D414yes—
88C22⋊D283—216no—
89C22⋊D283—44no—
90C2×Dic283—216no—
91C2×Dic283—22no—
92C2×Dic283—24no—
93C2×Dic283—22no—
94C2×Dic283—22no—
95C2×Dic283C2×D412yes—
96C4×D283—24no—
97C4×D283—22no—
98C4×D283—22no—
99C283⋊C8—22no—
100C23×C283—24no—
101C23×C283—22no—
102C23×C283—21no—
103C23×C283—44no—
104C23×C283C2×D411yescharacteristic
105Q8×C283—21no—
106Q8×C283—21no—
107D4×C283—24no—
108D4×C283—22no—
109D4×C283—21no—
110D4×C283—21no—
111D4×C283—42no—
112D4×C283C2×D414yes—
113C2×C4×C283—21no—
114C2×C4×C283—42no—
115C2×C4×C283C2×D411yescharacteristic
116C2×C4×C283C2×D412yes—
117C2×C4×C283C2×D412yes—
118C2×C4×C283C2411yescharacteristic
119C8×C283—22no—
120C22×C283—22no—
121C22×C283—24no—
122C22×C283—48no—
123C22×C283—44no—
124C22×C283—41no—
125C22×C283—42no—
126C22×C283#12012yes—
127C22×C283C22×D411yescharacteristic
128C2×D283—22no—
129C2×D283—22no—
130C2×D283—22no—
131C2×D283—44no—
132C4×C283—41no—
133C4×C283#12012yes—
134C4×C283C22×D411yescharacteristic
135C4×C283C22×D411yescharacteristic
136Dic283—22no—
137Dic283—24no—
138Dic283—42no—
139C2×C283—22no—
140C2×C283—44no—
141C2×C283—81no—
142C2×C283C2×#12011yescharacteristic
143C2×C283#57512yes—
144D283—42no—
145C283#300511yescharacteristic, complemented, Sylow
146#3005—2831nomaximal, Sylow
147C22×#41—2831no—
148C2×#137—2831no—
149C2×AGL(1,ℤ/8)D28311yescharacteristic, complemented
150#525—2831no—
151#452—2834no—
152#449—2834no—
153#419—2831no—
154#418—2831no—
155#407—2831no—
156C2×#41—2834no—
157C2×#41—5662no—
158C2×#41—5664no—
159C2×#41—5664no—
160C2×#41C2×D28311yescharacteristic
161C22×Q8—2831no—
162C22×D4—5661no—
163C22×D4C2×D28311yescharacteristic
164C23×C4—2831no—
165C23×C4—5661no—
166#137—5664no—
167AGL(1,ℤ/8)—24no—
168C2×Q16—2832no—
169C2×SD16—2832no—
170C2×SD16C2×D28312yescomplemented
171C2×D8C2×D28312yescomplemented
172C2×M16—2831no—
173C2×M16C2×D28311yescharacteristic
174#123—5661no—
175C22⋊Q8—2832no—
176#121—2832no—
177#120—5661no—
178C4×D4—5662no—
179#117—2831no—
180#103—2834no—
181#102—2834no—
182C22⋊C8—2834no—
183C24—21no—
184C24—2831no—
185#41—22no—
186#41—22no—
187#41—5668no—
188#41—56616no—
189#41—5668no—
190C2×Q8—2834no—
191C2×Q8—2832no—
192C2×Q8—5661no—
193C2×Q8—5662no—
194C2×Q8C22×D28311yescharacteristic
195C2×D4—21no—
196C2×D4—21no—
197C2×D4—22no—
198C2×D4—5664no—
199C2×D4—5668no—
200C2×D4—5662no—
201C2×D4C22⋊D28314yescomplemented
202C2×D4C22×D28311yescharacteristic
203C2×D4C22×D28312yes—
204C22×C4—21no—
205C22×C4—2831no—
206C22×C4—2832no—
207C22×C4—2832no—
208C22×C4—5664no—
209C22×C4—5668no—
210C22×C4—5661no—
211C22×C4—5662no—
212C22×C4—5662no—
213C22×C4C22×D28311yescharacteristic
214Q16—5664no—
215SD16—24no—
216SD16—5664no—
217D8—24no—
218M16—22no—
219M16—5662no—
220C2×C8—2832no—
221C2×C8C22×D28312yes—
222C4⋊C4—2832no—
223C4⋊C4—5662no—
224C22⋊C4—5662no—
225C22⋊C4—5662no—
226C22⋊C4—5661no—
227C42—5661no—
228C23—24no—
229C23—22no—
230C23—21no—
231C23—44no—
232C23—2832no—
233C23—5662no—
234C23—11322no—
235C23D4×D28311yescharacteristic
236Q8—21no—
237Q8—21no—
238Q8—2834no—
239Q8—5664no—
240Q8—5662no—
241D4—24no—
242D4—22no—
243D4—21no—
244D4—21no—
245D4—42no—
246D4—56616no—
247D4—11324no—
248D4C2×C22⋊D28314yes—
249C2×C4—21no—
250C2×C4—42no—
251C2×C4—2832no—
252C2×C4—56616no—
253C2×C4—5662no—
254C2×C4—5664no—
255C2×C4—5662no—
256C2×C4—5664no—
257C2×C4—5662no—
258C2×C4—5662no—
259C2×C4—5662no—
260C2×C4D4×D28311yescharacteristic
261C2×C4D4×D28312yes—
262C2×C4C2×C22⋊D28312yes—
263C2×C4C23×D28311yescharacteristic
264C8—22no—
265C8—5662no—
266C22—22no—
267C22—24no—
268C22—48no—
269C22—44no—
270C22—41no—
271C22—42no—
272C22—5662no—
273C22—5662no—
274C22—5662no—
275C22—11324no—
276C22#2258357812yes—
277C22C2×D4×D28311yescharacteristic
278C4—41no—
279C4—5662no—
280C4—5664no—
281C4—11322no—
282C4#2258357812yes—
283C4C2×D4×D28311yescharacteristic
284C4C22×C22⋊D28311yescharacteristic
285C2—22no—
286C2—44no—
287C2—81no—
288C2—11322no—
289C2C2×#2258357811yescharacteristic
290C2#3182726112yes—
subgroupG/H
centerC22C2×D4×D283
commutator, cosocleC2×C4×C283C24
FrattiniC2×C4C23×D283
FittingC2×AGL(1,ℤ/8)×C283C2
socleC22×C283C22×D4
hypercenterC2×AGL(1,ℤ/8)D283
hypocenterC283#3005
LCSG ▷ C2×C4×C283 ▷ C2×C283 ▷ C283
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×AGL(1,ℤ/8)

Complements

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

NH ≅ G/Ntype
1. C22×#17985391C2semidirect
2. C2×#22583640C2semidirect
3. #31826972C2semidirect
4. #31826624C2semidirect
5. #31826607C2semidirect
6. #31826475C2semidirect
7. #31826470C2semidirect
8. #31826428C2semidirect
9. C2×AGL(1,ℤ/8)×C283C2semidirect
19. C2×#17985382C22semidirect
20. C2×#17985380C22semidirect
23. #22583586C22semidirect
24. #22583581C22semidirect
28. #22583535C22semidirect
29. #22583531C22semidirect
30. (C2×D283)⋊C8C22semidirect
34. C2×SD16×C283C22semidirect
35. C2×D8×C283C22semidirect
43. C2×Dic566D4semidirect
73. C2×D4×C283D4semidirect
145. C283#3005semidirect
149. C2×AGL(1,ℤ/8)D283semidirect
170. C2×SD16C2×D283semidirect
171. C2×D8C2×D283semidirect
201. C2×D4C22⋊D283semidirect

Maximal subgroups

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

subgroupindex
C22×#179853912
C2×#225836402
#318269722
#318266242
#318266072
#318264752
#318264702
#318264282
C2×AGL(1,ℤ/8)×C2832
#3005283