Finite Group Databasebeta

← #49130868

Subgroups — #49130868

Order 36224.

500 conjugacy classes of subgroups; only the 127 normal subgroups are shown.

normal subgroups only

This group has 500 conjugacy classes of subgroups — too many to draw. Only its 127 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
1C2×#22583629C211yesmaximal, characteristic, complemented
2C2×M16×D283C211yesmaximal, characteristic, complemented
3#31826975C212yesmaximal, complemented
4#31826724C211yesmaximal, characteristic, complemented
5#31826723C211yesmaximal, characteristic, complemented
6#31826715C211yesmaximal, characteristic, complemented
7#31826710C212yesmaximal, complemented
8#31826709C212yesmaximal, complemented
9#31826500C211yesmaximal, characteristic, complemented
10#31826458C212yesmaximal, complemented
11#469×C283C211yesmaximal, characteristic, complemented
12C2×#17985391C2212yes—
13C22×C4×D283C2211yescharacteristic
14#22583629—24no—
15C2×Dic1132C2211yescharacteristic, complemented
16C2×#17985380C2212yescomplemented
17C2×#17985376C2211yescharacteristic
18C2×#17985375C2211yescharacteristic
19C2×#17985375C2211yescharacteristic
20M16×D283—24no—
21C2×C8×D283C2211yescharacteristic
22C2×C8×D283C2211yescharacteristic
23#22583592—22no—
24#22583590C2212yes—
25#22583589C2212yes—
26#22583581C2212yes—
27#22583578—22no—
28D4×Dic283—22no—
29(C22⋊D283)⋊C4—22no—
30#22583568C2212yes—
31#22583543C2212yescomplemented
32#22583542C2211yescharacteristic, complemented
33#22583535C2212yescomplemented
34#22583533C2212yescomplemented
35#22583531C2212yescomplemented
36C2×D8×C283C2211yescharacteristic, complemented
37C2×M16×C283C2211yescharacteristic
38#121×C283C2212yes—
39#106×C283C2211yescharacteristic, complemented
40#102×C283C2212yescomplemented
41C23×D283D411yescharacteristic
42#17985391—24no—
43#17985391—24no—
44C2×Dic566C2312yes—
45C2×C22⋊D283—22no—
46C2×C22⋊D283—22no—
47C22×Dic283—22no—
48C22×Dic283D411yescharacteristic
49C2×C4×D283—22no—
50C2×C4×D283—22no—
51C2×C4×D283D411yescharacteristic
52C2×C4×D283D411yescharacteristic
53C2×C4×D283C2311yescharacteristic
54C2×C4×D283C2311yescharacteristic
55Dic1132—22no—
56#17985380—24no—
57#17985376—22no—
58#17985375—22no—
59#17985375—22no—
60C2×C283⋊C8C2311yescharacteristic
61C2×C283⋊C8C2311yescharacteristic
62C8×D283—22no—
63C8×D283D414yescomplemented
64C4⋊Dic283—22no—
65C4⋊Dic283C2312yes—
66Dic283⋊C4—22no—
67C22⋊Dic283—22no—
68C22⋊Dic283—22no—
69(C2×D283)⋊C4—22no—
70(C2×D283)⋊C4—22no—
71C4×Dic283—22no—
72C2×D4×C283—22no—
73C2×D4×C283C2312yes—
74C22×C4×C283C2311yescharacteristic
75D8×C283—22no—
76M16×C283—22no—
77C2×C8×C283C2311yescharacteristic
78C2×C8×C283C2311yescharacteristic
79C4⋊C4×C283C2312yes—
80C22⋊C4×C283—22no—
81C22×D283—22no—
82C22×D283—42no—
83C22×D283C2×D411yescharacteristic
84C22×D283C2×D411yescharacteristic
85Dic566—22no—
86Dic566—22no—
87C22⋊D283—44no—
88C22⋊D283—44no—
89C2×Dic283—22no—
90C2×Dic283—22no—
91C2×Dic283—22no—
92C2×Dic283—44no—
93C2×Dic283C2×D411yescharacteristic
94C2×Dic283C2×D411yescharacteristic
95C4×D283—22no—
96C4×D283—21no—
97C4×D283—21no—
98C4×D283—22no—
99C4×D283C2×D412yes—
100C4×D283#4112yes—
101C283⋊C8—21no—
102C283⋊C8C2×D412yes—
103C23×C283—22no—
104C23×C283C2×D411yescharacteristic
105D4×C283—22no—
106D4×C283—22no—
107D4×C283—44no—
108C2×C4×C283—21no—
109C2×C4×C283—21no—
110C2×C4×C283—22no—
111C2×C4×C283C2×D411yescharacteristic
112C2×C4×C283C2411yescharacteristic
113C8×C283—21no—
114C8×C283C2×D412yes—
115C22×C283—21no—
116C22×C283—22no—
117C22×C283—42no—
118C22×C283—42no—
119C22×C283—42no—
120C22×C283C22×D411yescharacteristic
121C2×D283—22no—
122C2×D283—21no—
123C2×D283—22no—
124C2×D283—44no—
125C2×D283#12112yes—
126C4×C283—21no—
127C4×C283—42no—
128C4×C283C22×D411yescharacteristic
129C4×C283C2×#4111yescharacteristic
130Dic283—21no—
131Dic283—42no—
132Dic283—42no—
133Dic283#12112yes—
134C2×C283—41no—
135C2×C283—82no—
136C2×C283C2×#12111yescharacteristic
137C2×C283#57512yes—
138D283—22no—
139D283—41no—
140C283#305411yescharacteristic, complemented, Sylow
141#3054—2831nomaximal, Sylow
142C2×#135—2831no—
143C22×M16—2831no—
144#525—2832no—
145#470—2831no—
146#470—2831no—
147#469—2831no—
148#469D28311yescharacteristic, complemented
149#468—2832no—
150#468—2832no—
151#427—2831no—
152#416—2832no—
153C2×#41—2832no—
154C23×C4—2831no—
155#135—5664no—
156C2×Q16—2831no—
157C2×SD16—2832no—
158C2×D8C2×D28311yescharacteristic, complemented
159C2×M16—2831no—
160C2×M16—2831no—
161C2×M16—2831no—
162C2×M16—5664no—
163C2×M16C2×D28311yescharacteristic
164C22×C8—2831no—
165C22×C8—2831no—
166#123—5662no—
167C22⋊Q8—2832no—
168C22⋊Q8—2832no—
169#121—2832no—
170#121C2×D28312yes—
171#120—5662no—
172C4×D4—5662no—
173C4×D4—5662no—
174#117—2832no—
175#107—2832no—
176#106—2831no—
177#106C2×D28311yescharacteristic, complemented
178#103—2832no—
179#103—2832no—
180#102—2832no—
181#102C2×D28312yescomplemented
182C24—2831no—
183#41—5664no—
184#41—5664no—
185C2×Q8—2832no—
186C2×D4—22no—
187C2×D4—5662no—
188C2×D4—5662no—
189C2×D4C22×D28312yes—
190C22×C4—2831no—
191C22×C4—2831no—
192C22×C4—2831no—
193C22×C4—2831no—
194C22×C4—2831no—
195C22×C4—5662no—
196C22×C4—5662no—
197C22×C4—5662no—
198C22×C4C22×D28311yescharacteristic
199Q16—5662no—
200SD16—5664no—
201D8—22no—
202M16—22no—
203M16—5662no—
204M16—5662no—
205M16—5662no—
206C2×C8—2831no—
207C2×C8—2834no—
208C2×C8—2831no—
209C2×C8—5662no—
210C2×C8C22×D28311yescharacteristic
211C2×C8C22×D28311yescharacteristic
212C4⋊C4—2832no—
213C4⋊C4—5662no—
214C4⋊C4—5662no—
215C4⋊C4C22×D28312yes—
216C22⋊C4—22no—
217C22⋊C4—5662no—
218C22⋊C4—5662no—
219C22⋊C4—5662no—
220C22⋊C4—5662no—
221C42—5662no—
222C23—22no—
223C23—2831no—
224C23—2831no—
225C23—5662no—
226C23—11322no—
227C23D4×D28311yescharacteristic
228Q8—5662no—
229Q8—5662no—
230D4—22no—
231D4—22no—
232D4—44no—
233D4—11324no—
234D4—11324no—
235C2×C4—21no—
236C2×C4—21no—
237C2×C4—22no—
238C2×C4—2831no—
239C2×C4—2832no—
240C2×C4—2832no—
241C2×C4—2831no—
242C2×C4—5662no—
243C2×C4—5662no—
244C2×C4—5662no—
245C2×C4—5661no—
246C2×C4—5661no—
247C2×C4—5662no—
248C2×C4—5662no—
249C2×C4—11324no—
250C2×C4D4×D28311yescharacteristic
251C2×C4C23×D28311yescharacteristic
252C8—21no—
253C8—2832no—
254C8—5661no—
255C8D4×D28312yes—
256C22—21no—
257C22—22no—
258C22—42no—
259C22—42no—
260C22—42no—
261C22—2832no—
262C22—5662no—
263C22—5661no—
264C22—5662no—
265C22—11324no—
266C22C2×D4×D28311yescharacteristic
267C4—21no—
268C4—42no—
269C4—2832no—
270C4—5661no—
271C4—11322no—
272C4—11322no—
273C4C2×D4×D28311yescharacteristic
274C4#41×D28311yescharacteristic
275C2—41no—
276C2—82no—
277C2—5662no—
278C2—11321no—
279C2#121×D28311yescharacteristic
280C2#3182726112yes—
subgroupG/H
centerC22C2×D4×D283
commutator, cosocleC2×C4×C283C24
FrattiniC2×C4C23×D283
Fitting#469×C283C2
socleC22×C283C22×D4
hypercenter#469D283
hypocenterC283#3054
LCSG ▷ C2×C4×C283 ▷ C2×C283 ▷ C283
UCSC1 ◁ C22 ◁ C22×C4 ◁ #469

Complements

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

NH ≅ G/Ntype
1. C2×#22583629C2semidirect
2. C2×M16×D283C2semidirect
3. #31826975C2semidirect
4. #31826724C2semidirect
5. #31826723C2semidirect
6. #31826715C2semidirect
7. #31826710C2semidirect
8. #31826709C2semidirect
9. #31826500C2semidirect
10. #31826458C2semidirect
11. #469×C283C2semidirect
15. C2×Dic1132C22semidirect
16. C2×#17985380C22semidirect
31. #22583543C22semidirect
32. #22583542C22semidirect
33. #22583535C22semidirect
34. #22583533C22semidirect
35. #22583531C22semidirect
36. C2×D8×C283C22semidirect
39. #106×C283C22semidirect
40. #102×C283C22semidirect
63. C8×D283D4semidirect
140. C283#3054semidirect
148. #469D283semidirect
158. C2×D8C2×D283semidirect
177. #106C2×D283semidirect
181. #102C2×D283semidirect

Maximal subgroups

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

subgroupindex
C2×#225836292
C2×M16×D2832
#318269752
#318267242
#318267232
#318267152
#318267102
#318267092
#318265002
#318264582
#469×C2832
#3054283