Finite Group Databasebeta

← #49131266

Subgroups — #49131266

Order 36224.

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

normal subgroups only

This group has 448 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#31827017C211yesmaximal, characteristic, complemented
2C2×#22583572C211yesmaximal, characteristic
3#31826795C211yesmaximal, characteristic, complemented
4#31826754C212yesmaximal, complemented
5#31826669C212yesmaximal, complemented
6#31826618C211yesmaximal, characteristic
7#31826615C211yesmaximal, characteristic
8#31826552C212yesmaximal, complemented
9#31826550C212yesmaximal, complemented
10#31826515C211yesmaximal, characteristic, complemented
11#483×C283C211yesmaximal, characteristic, complemented
12C22×D1132C2211yescharacteristic
13C22×C4×D283—21no—
14C2×#17985381C2212yes—
15C2×#17985379C2212yes—
16#22583609C2211yescharacteristic, complemented
17#22583608C2211yescharacteristic, complemented
18#22583600—21no—
19#22583589C2211yescharacteristic
20#22583587—21no—
21Q8×Dic283C2211yescharacteristic, complemented
22#22583575—21no—
23#22583575C2211yescharacteristic, complemented
24#22583572—21no—
25#22583572—21no—
26#22583572C2212yes—
27#22583572C2212yes—
28#22583566—21no—
29C2×(C2×D283)⋊C4—21no—
30C2×C4×Dic283C2211yescharacteristic
31#22583541C2212yescomplemented
32Dic283⋊C8C2212yescomplemented
33#22583533C2212yescomplemented
34#22583532C2212yes—
35#22583530C2212yes—
36C22⋊(C283⋊C8)C2211yescharacteristic
37C8×Dic283C2212yescomplemented
38C22⋊Q8×C283C2211yescharacteristic
39C2×C4⋊C4×C283C2211yescharacteristic
40#106×C283C2212yescomplemented
41#103×C283C2212yescomplemented
42C22⋊C8×C283C2211yescharacteristic
43C23×D283—21no—
44C2×Dic566—21no—
45C2×Dic566C2311yescharacteristic
46C2×D1132—24no—
47C2×D1132—21no—
48C2×D1132C2312yes—
49C22×Dic283D411yescharacteristic
50C22×Dic283D411yescharacteristic
51C2×C4×D283—22no—
52C2×C4×D283—22no—
53C2×C4×D283—44no—
54#17985381—24no—
55#17985379—24no—
56C2×C283⋊C8C2312yes—
57C4⋊Dic283—21no—
58C4⋊Dic283C2311yescharacteristic
59Dic283⋊C4—21no—
60Dic283⋊C4—21no—
61Dic283⋊C4—21no—
62Dic283⋊C4—21no—
63Dic283⋊C4—21no—
64C22⋊Dic283—21no—
65(C2×D283)⋊C4—22no—
66(C2×D283)⋊C4—22no—
67C4×Dic283—21no—
68C4×Dic283—21no—
69C4×Dic283D411yescharacteristic
70C4×Dic283D411yescharacteristic
71C4×Dic283C2311yescharacteristic
72C4×Dic283C2311yescharacteristic
73C2×Q8×C283C2311yescharacteristic
74C22×C4×C283—21no—
75C22×C4×C283C2311yescharacteristic
76C2×C8×C283C2312yes—
77C4⋊C4×C283—21no—
78C4⋊C4×C283—21no—
79C4⋊C4×C283C2312yes—
80C4⋊C4×C283C2311yescharacteristic
81C22⋊C4×C283—21no—
82C22×D283—24no—
83C22×D283—22no—
84C22×D283—42no—
85C22×D283—42no—
86Dic566—22no—
87Dic566—42no—
88D1132—24no—
89D1132—22no—
90D1132#4114yes—
91C2×Dic283—21no—
92C2×Dic283—21no—
93C2×Dic283—41no—
94C2×Dic283SD1614yescomplemented
95C2×Dic283C2×D411yescharacteristic
96C2×Dic283C2×D411yescharacteristic
97C2×Dic283C2×D411yescharacteristic
98C2×Dic283C2×D411yescharacteristic
99C4×D283—44no—
100C4×D283—44no—
101C283⋊C8—22no—
102C23×C283C2×D411yescharacteristic
103Q8×C283—22no—
104C2×C4×C283—22no—
105C2×C4×C283—21no—
106C2×C4×C283—21no—
107C2×C4×C283—22no—
108C2×C4×C283—42no—
109C2×C4×C283C2×D411yescharacteristic
110C2×C4×C283C2411yescharacteristic
111C8×C283—22no—
112C22×C283—21no—
113C22×C283—21no—
114C22×C283C2×SD1612yes—
115C22×C283C22×D411yescharacteristic
116C2×D283—24no—
117C2×D283—48no—
118C2×D283—42no—
119C2×D283—42no—
120C4×C283—21no—
121C4×C283—41no—
122C4×C283—42no—
123C4×C283—41no—
124C4×C283C2×#4112yes—
125Dic283—21no—
126Dic283—21no—
127Dic283—41no—
128Dic283—41no—
129Dic283C2×SD1612yes—
130Dic283C2×SD1612yes—
131C2×C283—22no—
132C2×C283#52511yescharacteristic
133C2×C283C22×SD1611yescharacteristic
134C2×C283#57511yescharacteristic
135D283—44no—
136C283#310111yescharacteristic, complemented, Sylow
137#3101—2831nomaximal, Sylow
138#533—2831no—
139C2×C4×D4—2831no—
140#483—2831no—
141#483D28311yescharacteristic, complemented
142#476—2832no—
143#461—2832no—
144#450—2831no—
145#450—2831no—
146C4×SD16—2832no—
147C4×SD16—2832no—
148#431—2831no—
149C22×D4—2831no—
150C23×C4—5661no—
151C2×SD16—2832no—
152C2×SD16—2832no—
153C4⋊Q8—2831no—
154C4⋊Q8—2831no—
155#125—5661no—
156C22⋊Q8—2831no—
157C22⋊Q8—5661no—
158C22⋊Q8C2×D28311yescharacteristic
159C4×Q8—2831no—
160C4×Q8—2831no—
161C4×Q8—5661no—
162C4×D4—2832no—
163C4×D4—2832no—
164C4×D4—5661no—
165C4×D4—5661no—
166#117—5661no—
167C2×C4⋊C4C2×D28311yescharacteristic
168C2×C22⋊C4—5661no—
169C2×C42—2831no—
170#106—2832no—
171#106C2×D28312yescomplemented
172C4⋊C8—2832no—
173#103—2832no—
174#103C2×D28312yescomplemented
175#102—2832no—
176#102—2832no—
177C22⋊C8—2831no—
178C22⋊C8C2×D28311yescharacteristic
179C4×C8—2832no—
180C24—5661no—
181C2×Q8—2831no—
182C2×Q8—5661no—
183C2×Q8C22×D28311yescharacteristic
184C2×D4—2832no—
185C2×D4—5664no—
186C2×D4—5661no—
187C22×C4—21no—
188C22×C4—2831no—
189C22×C4—2831no—
190C22×C4—5662no—
191C22×C4—5662no—
192C22×C4—11324no—
193C22×C4C22×D28311yescharacteristic
194SD16—5664no—
195SD16—5664no—
196C2×C8—2832no—
197C2×C8C22×D28312yes—
198C4⋊C4—21no—
199C4⋊C4—21no—
200C4⋊C4—2831no—
201C4⋊C4—5661no—
202C4⋊C4—5661no—
203C4⋊C4—5661no—
204C4⋊C4—5661no—
205C4⋊C4—5661no—
206C4⋊C4—5661no—
207C4⋊C4C22×D28311yescharacteristic
208C4⋊C4C22×D28312yes—
209C22⋊C4—21no—
210C22⋊C4—5662no—
211C22⋊C4—5662no—
212C22⋊C4—5661no—
213C42—2831no—
214C42—2831no—
215C42—2831no—
216C42—2831no—
217C42—5661no—
218C42—5661no—
219C23—5664no—
220C23—5662no—
221C23—11322no—
222C23—11322no—
223C23D4×D28311yescharacteristic
224Q8—22no—
225Q8—5662no—
226Q8—11322no—
227D4—2834no—
228D4—5664no—
229D4—5662no—
230C2×C4—22no—
231C2×C4—21no—
232C2×C4—21no—
233C2×C4—22no—
234C2×C4—42no—
235C2×C4—2834no—
236C2×C4—2831no—
237C2×C4—2831no—
238C2×C4—2831no—
239C2×C4—2831no—
240C2×C4—5661no—
241C2×C4—5661no—
242C2×C4—11324no—
243C2×C4—11324no—
244C2×C4—11321no—
245C2×C4D4×D28311yescharacteristic
246C2×C4C23×D28311yescharacteristic
247C8—22no—
248C8—5662no—
249C22—21no—
250C22—21no—
251C22—5664no—
252C22—11328no—
253C22—11322no—
254C22—11322no—
255C22SD16×D28312yes—
256C22C2×D4×D28311yescharacteristic
257C4—21no—
258C4—41no—
259C4—42no—
260C4—41no—
261C4—2832no—
262C4—2832no—
263C4—5661no—
264C4—5661no—
265C4—11321no—
266C4—11321no—
267C4#41×D28312yes—
268C2—22no—
269C2—11324no—
270C2#3182697311yescharacteristic
271C2C2×SD16×D28311yescharacteristic
272C2#3182726411yescharacteristic
subgroupG/H
centerC22C2×D4×D283
commutator, cosocleC2×C4×C283C24
FrattiniC2×C4C23×D283
Fitting#483×C283C2
socleC22×C283C22×D4
prime radicalC22×D1132C22
hypercenter#483D283
hypocenterC283#3101
LCSG ▷ C2×C4×C283 ▷ C2×C283 ▷ C283
UCSC1 ◁ C22 ◁ C22×C4 ◁ #483

Complements

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

NH ≅ G/Ntype
1. #31827017C2semidirect
3. #31826795C2semidirect
4. #31826754C2semidirect
5. #31826669C2semidirect
8. #31826552C2semidirect
9. #31826550C2semidirect
10. #31826515C2semidirect
11. #483×C283C2semidirect
16. #22583609C22semidirect
17. #22583608C22semidirect
21. Q8×Dic283C22semidirect
23. #22583575C22semidirect
31. #22583541C22semidirect
32. Dic283⋊C8C22semidirect
33. #22583533C22semidirect
37. C8×Dic283C22semidirect
40. #106×C283C22semidirect
41. #103×C283C22semidirect
94. C2×Dic283SD16semidirect
136. C283#3101semidirect
141. #483D283semidirect
171. #106C2×D283semidirect
174. #103C2×D283semidirect

Maximal subgroups

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

subgroupindex
#318270172
C2×#225835722
#318267952
#318267542
#318266692
#318266182
#318266152
#318265522
#318265502
#318265152
#483×C2832
#3101283