Finite Group Databasebeta

← #49130493

Subgroups — #49130493

Order 36224.

738 conjugacy classes of subgroups; only the 153 normal subgroups are shown.

normal subgroups only

This group has 738 conjugacy classes of subgroups — too many to draw. Only its 153 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×Q8×D283C211yesmaximal, characteristic, complemented
2C2×#22583640C211yesmaximal, characteristic, complemented
3#31826972C211yesmaximal, characteristic
4#31826619C214yesmaximal, complemented
5#31826602C214yesmaximal, complemented
6#31826475C211yesmaximal, characteristic, complemented
7#31826474C211yesmaximal, characteristic, complemented
8#31826428C211yesmaximal, characteristic, complemented
9C2×#137×C283C211yesmaximal, characteristic, complemented
10C22×Dic566—21no—
11C22×Dic566C2211yescharacteristic
12C2×Q8×D283—24no—
13C2×Q8×D283—22no—
14C2×Q8×D283—24no—
15C2×Q8×D283C2214yes—
16C22×C4×D283—21no—
17C22×C4×D283C2211yescharacteristic
18#22583640—24no—
19C2×#17985382C2212yescomplemented
20C2×#17985380C2212yescomplemented
21C2×#17985376C2211yescharacteristic
22#22583591—21no—
23#22583586C2212yes—
24#22583581C2212yes—
25#22583578—21no—
26C4×C22⋊D283—22no—
27#22583569C2211yescharacteristic
28#22583535C2214yescomplemented
29#22583534C2214yescomplemented
30(C2×D283)⋊C8C2214yes—
31C2×#41×C283C2211yescharacteristic
32C22×Q8×C283C2211yescharacteristic
33#137×C283—24no—
34C2×Q16×C283C2212yescomplemented
35C2×SD16×C283C2212yescomplemented
36C2×M16×C283C2211yescharacteristic
37C23×D283D411yescharacteristic
38C2×Dic566—28no—
39C2×Dic566—24no—
40C2×Dic566—21no—
41C2×Dic566—22no—
42C2×Dic566D414yescomplemented
43C2×Dic566C2312yes—
44Q8×D283—216no—
45Q8×D283—28no—
46Q8×D283—28no—
47C2×C22⋊D283—22no—
48C22×Dic283—21no—
49C22×Dic283D411yescharacteristic
50C2×C4×D283—28no—
51C2×C4×D283—24no—
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—
66#41×C283—22no—
67#41×C283—22no—
68C2×Q8×C283—22no—
69C2×Q8×C283—21no—
70C2×Q8×C283D414yescomplemented
71C2×Q8×C283C2311yescharacteristic
72C2×Q8×C283C2312yes—
73C2×D4×C283—21no—
74C2×D4×C283C2311yescharacteristic
75C22×C4×C283—21no—
76C22×C4×C283—21no—
77C22×C4×C283C2311yescharacteristic
78Q16×C283—24no—
79SD16×C283—24no—
80M16×C283—22no—
81C2×C8×C283C2312yes—
82C22×D283—22no—
83C22×D283—24no—
84C22×D283C2×D412yes—
85Dic566—216no—
86Dic566—24no—
87Dic566—22no—
88Dic566C2×D414yes—
89C22⋊D283—44no—
90C2×Dic283—24no—
91C2×Dic283—22no—
92C2×Dic283—22no—
93C2×Dic283—22no—
94C2×Dic283C2×D412yes—
95C4×D283—216no—
96C4×D283—24no—
97C4×D283—22no—
98C4×D283—22no—
99C283⋊C8—22no—
100C23×C283—21no—
101C23×C283C2×D411yescharacteristic
102Q8×C283—24no—
103Q8×C283—22no—
104Q8×C283—21no—
105Q8×C283—21no—
106Q8×C283C2×D414yes—
107D4×C283—21no—
108D4×C283—21no—
109D4×C283—42no—
110C2×C4×C283—24no—
111C2×C4×C283—22no—
112C2×C4×C283—21no—
113C2×C4×C283—42no—
114C2×C4×C283C2×D411yescharacteristic
115C2×C4×C283C2×D412yes—
116C2×C4×C283C2×D412yes—
117C2×C4×C283C2411yescharacteristic
118C8×C283—22no—
119C22×C283—22no—
120C22×C283—41no—
121C22×C283—42no—
122C22×C283#12012yes—
123C22×C283C22×D411yescharacteristic
124C2×D283—28no—
125C2×D283—22no—
126C2×D283—22no—
127C2×D283#13714yescomplemented
128C4×C283—24no—
129C4×C283—41no—
130C4×C283#12012yes—
131C4×C283C22×D411yescharacteristic
132C4×C283C22×D411yescharacteristic
133Dic283—24no—
134Dic283—22no—
135Dic283—42no—
136C2×C283—22no—
137C2×C283—81no—
138C2×C283C2×#12011yescharacteristic
139C2×C283C2×#13712yes—
140D283—24no—
141C283#300411yescharacteristic, complemented, Sylow
142#3004—2831nomaximal, Sylow
143C23×Q8—2831no—
144C2×#137—2831no—
145C2×#137D28311yescharacteristic, complemented
146#525—2831no—
147#451—2834no—
148#448—2834no—
149#419—2831no—
150#419—2831no—
151#407—2831no—
152C2×#41C2×D28311yescharacteristic
153C22×Q8—2834no—
154C22×Q8—2831no—
155C22×Q8—5661no—
156C22×Q8—5662no—
157C22×Q8—5664no—
158C22×Q8—5664no—
159C22×Q8C2×D28311yescharacteristic
160C23×C4—2831no—
161C23×C4—5661no—
162#137—24no—
163#137—5664no—
164C2×Q16—2832no—
165C2×Q16C2×D28312yescomplemented
166C2×SD16—2832no—
167C2×SD16C2×D28312yescomplemented
168C2×M16—2831no—
169C2×M16C2×D28311yescharacteristic
170#123—5661no—
171C22⋊Q8—2832no—
172#121—2832no—
173#120—5661no—
174C4×D4—5662no—
175#117—2831no—
176#103—2834no—
177#103—2834no—
178C22⋊C8—2834no—
179C24—2831no—
180#41—22no—
181#41—22no—
182C2×Q8—22no—
183C2×Q8—21no—
184C2×Q8—2834no—
185C2×Q8—2832no—
186C2×Q8—5664no—
187C2×Q8—5668no—
188C2×Q8—5668no—
189C2×Q8—56616no—
190C2×Q8—5668no—
191C2×Q8—5661no—
192C2×Q8—5662no—
193C2×Q8C22⋊D28314yescomplemented
194C2×Q8C22×D28311yescharacteristic
195C2×Q8C22×D28312yes—
196C2×D4—21no—
197C2×D4—5662no—
198C2×D4C22×D28311yescharacteristic
199C22×C4—21no—
200C22×C4—21no—
201C22×C4—2831no—
202C22×C4—2832no—
203C22×C4—2832no—
204C22×C4—5664no—
205C22×C4—5668no—
206C22×C4—5661no—
207C22×C4—5662no—
208C22×C4—5662no—
209C22×C4C22×D28311yescharacteristic
210Q16—24no—
211Q16—5664no—
212SD16—24no—
213SD16—5664no—
214M16—22no—
215M16—5662no—
216C2×C8—2832no—
217C2×C8C22×D28312yes—
218C4⋊C4—2832no—
219C4⋊C4—5662no—
220C22⋊C4—5662no—
221C22⋊C4—5662no—
222C22⋊C4—5661no—
223C42—5661no—
224C23—21no—
225C23—2832no—
226C23—5664no—
227C23—5662no—
228C23D4×D28311yescharacteristic
229Q8—24no—
230Q8—22no—
231Q8—21no—
232Q8—21no—
233Q8—2834no—
234Q8—56616no—
235Q8—5664no—
236Q8—5662no—
237Q8C2×C22⋊D28314yes—
238D4—21no—
239D4—21no—
240D4—42no—
241D4—11324no—
242C2×C4—24no—
243C2×C4—22no—
244C2×C4—21no—
245C2×C4—42no—
246C2×C4—2832no—
247C2×C4—56616no—
248C2×C4—5662no—
249C2×C4—5664no—
250C2×C4—5662no—
251C2×C4—5664no—
252C2×C4—5662no—
253C2×C4—5662no—
254C2×C4—5662no—
255C2×C4D4×D28311yescharacteristic
256C2×C4D4×D28312yes—
257C2×C4C2×C22⋊D28312yes—
258C2×C4C23×D28311yescharacteristic
259C8—22no—
260C8—5662no—
261C22—22no—
262C22—41no—
263C22—42no—
264C22—2834no—
265C22—5668no—
266C22—5662no—
267C22—5662no—
268C22#2258357812yes—
269C22C2×D4×D28311yescharacteristic
270C4—24no—
271C4—41no—
272C4—5662no—
273C4—5664no—
274C4—11322no—
275C4#2258357812yes—
276C4C2×D4×D28311yescharacteristic
277C4C22×C22⋊D28311yescharacteristic
278C2—22no—
279C2—81no—
280C2—5664no—
281C2C2×#2258357811yescharacteristic
282C2#137×D28312yes—
subgroupG/H
centerC22C2×D4×D283
commutator, cosocleC2×C4×C283C24
FrattiniC2×C4C23×D283
FittingC2×#137×C283C2
socleC22×C283C22×D4
prime radical#31826972C2
hypercenterC2×#137D283
hypocenterC283#3004
LCSG ▷ C2×C4×C283 ▷ C2×C283 ▷ C283
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#137

Complements

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

NH ≅ G/Ntype
1. C22×Q8×D283C2semidirect
2. C2×#22583640C2semidirect
4. #31826619C2semidirect
5. #31826602C2semidirect
6. #31826475C2semidirect
7. #31826474C2semidirect
8. #31826428C2semidirect
9. C2×#137×C283C2semidirect
19. C2×#17985382C22semidirect
20. C2×#17985380C22semidirect
28. #22583535C22semidirect
29. #22583534C22semidirect
34. C2×Q16×C283C22semidirect
35. C2×SD16×C283C22semidirect
42. C2×Dic566D4semidirect
70. C2×Q8×C283D4semidirect
127. C2×D283#137semidirect
141. C283#3004semidirect
145. C2×#137D283semidirect
165. C2×Q16C2×D283semidirect
167. C2×SD16C2×D283semidirect
193. C2×Q8C22⋊D283semidirect

Maximal subgroups

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

subgroupindex
C22×Q8×D2832
C2×#225836402
#318269722
#318266192
#318266022
#318264752
#318264742
#318264282
C2×#137×C2832
#3004283