Finite Group Databasebeta

← #27208284

Subgroups — #27208284

Order 13184.

370 conjugacy classes of subgroups; only the 113 normal subgroups are shown.

normal subgroups only

This group has 370 conjugacy classes of subgroups — too many to draw. Only its 113 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#20268593C211yesmaximal, characteristic, complemented
2#20268592C211yesmaximal, characteristic, complemented
3#20268229C211yesmaximal, characteristic, complemented
4#20268228C212yesmaximal, complemented
5#20268225C212yesmaximal, complemented
6#20268222C212yesmaximal, complemented
7#20268221C211yesmaximal, characteristic, complemented
8C2×#15692962C211yesmaximal, characteristic, complemented
9D16×D103C212yesmaximal, complemented
10#20268209C211yesmaximal, characteristic, complemented
11#509×C103C211yesmaximal, characteristic, complemented
12#15693067—21no—
13#15693066—21no—
14#15693048—22no—
15#15693047—21no—
16#15693046—21no—
17#15693045—22no—
18#15693044C2212yescomplemented
19#15693043C2211yescharacteristic, complemented
20#15693040C2212yescomplemented
21C2×D824C2211yescharacteristic, complemented
22D8×D103C2212yescomplemented
23D8×D103C2212yescomplemented
24#15693027C2211yescharacteristic
25#15692967C2211yescharacteristic, complemented
26#15692966C2212yescomplemented
27#15692965C2211yescharacteristic, complemented
28#15692964C2211yescharacteristic, complemented
29D1648C2212yescomplemented
30#15692962C2211yescharacteristic, complemented
31#15692962C2212yescomplemented
32#15692962C2212yescomplemented
33#15692960C2212yescomplemented
34C2×C103⋊C16C2211yescharacteristic, complemented
35C16×D103C2212yescomplemented
36#135×C103C2211yescharacteristic, complemented
37C2×D8×C103C2211yescharacteristic, complemented
38SD32×C103C2212yescomplemented
39D16×C103C2212yescomplemented
40M32×C103C2211yescharacteristic, complemented
41#13110106—22no—
42#13110105—21no—
43#13110105—41no—
44#13110105D411yescharacteristic
45#13110104—22no—
46#13110104—41no—
47C2×D412—21no—
48C2×D412—41no—
49C2×C22⋊D103—42no—
50D4×D103—22no—
51D4×D103—22no—
52D4×D103—42no—
53D4×D103—41no—
54Dic412C2311yescharacteristic
55#13110094—21no—
56#13110093—22no—
57#13110092—22no—
58D824—21no—
59D824C2312yes—
60D824C2311yescharacteristic
61#13110090—22no—
62#13110090—22no—
63#13110089D411yescharacteristic
64#13110088D412yes—
65C8×D103C2312yes—
66C103⋊C16C2311yescharacteristic
67C103⋊C16C2311yescharacteristic
68#41×C103—21no—
69C2×D4×C103—21no—
70Q16×C103C2311yescharacteristic
71SD16×C103—21no—
72D8×C103—21no—
73D8×C103C2311yescharacteristic
74D8×C103C2312yes—
75C2×C8×C103C2311yescharacteristic
76C16×C103C2312yes—
77C23×C103—41no—
78C22×D103—41no—
79C22×D103—42no—
80C22×D103—42no—
81Q8×C103—21no—
82D4×C103—22no—
83D4×C103—21no—
84D4×C103—41no—
85D4×C103—41no—
86C2×C4×C103—41no—
87C2×C4×C103C2×D411yescharacteristic
88C22⋊D103—41no—
89C22⋊D103—42no—
90C22⋊D103—42no—
91C22⋊D103—42no—
92C22⋊D103D812yes—
93C2×Dic103—42no—
94D412—21no—
95D412—22no—
96D412—42no—
97D412—41no—
98D412D811yescharacteristic
99C4×D103—41no—
100C4×D103—42no—
101C4×D103C2×D412yes—
102Dic206—21no—
103Dic206D811yescharacteristic
104C8×C103C2×D411yescharacteristic
105C8×C103C2411yescharacteristic
106C103⋊C8C2×D412yes—
107C22×C103—42no—
108C22×C103—41no—
109C22×C103—161no—
110C22×C103C2×D811yescharacteristic
111C2×D103—42no—
112C2×D103—41no—
113C2×D103—162no—
114C2×D103—162no—
115C2×D103—161no—
116C2×D103C2×D812yes—
117C4×C103—41no—
118C4×C103C2×D811yescharacteristic
119C4×C103C22×D411yescharacteristic
120Dic103—41no—
121Dic103C2×D812yes—
122C2×C103—21no—
123C2×C103—81no—
124C2×C103—82no—
125C2×C103C22×D811yescharacteristic
126D103—22no—
127D103—82no—
128D103—81no—
129#3415—1031nomaximal, Sylow
130C103#341511yescharacteristic, complemented, Sylow
131#576—1031no—
132#576—1031no—
133#509—1032no—
134#509—1032no—
135#509—1031no—
136#509D10311yescharacteristic, complemented
137#508—1031no—
138#508—1032no—
139C2×D16—1031no—
140C2×D16—1032no—
141#504—1031no—
142H(5,𝔽2)—2061no—
143H(5,𝔽2)—2061no—
144AGL(1,ℤ/8)—2062no—
145AGL(1,ℤ/8)—2062no—
146AGL(1,ℤ/8)—2061no—
147AGL(1,ℤ/8)—2061no—
148#135—1032no—
149#135—1032no—
150#135—1031no—
151#135C2×D10311yescharacteristic, complemented
152C2×D8—1032no—
153C2×D8—1032no—
154C2×D8—1031no—
155C2×D8C2×D10311yescharacteristic, complemented
156#131—1031no—
157Q32—1031no—
158SD32—1031no—
159SD32—1031no—
160SD32—1032no—
161SD32C2×D10312yescomplemented
162D16—1032no—
163D16—1031no—
164D16—1032no—
165D16—1032no—
166D16C2×D10312yescomplemented
167M32—1032no—
168M32C2×D10311yescharacteristic, complemented
169C2×C16—1031no—
170C2×C16—1032no—
171#41—21no—
172#41—1031no—
173#41—4121no—
174#41—4121no—
175#41—2062no—
176#41—2062no—
177#41—2061no—
178C2×D4—21no—
179C2×D4—4121no—
180C2×D4—4122no—
181C2×D4—4121no—
182C2×D4—4122no—
183C2×D4—2062no—
184C2×D4—2062no—
185C2×D4—2061no—
186Q16—1031no—
187Q16C22×D10311yescharacteristic
188SD16—21no—
189SD16—2062no—
190SD16—2062no—
191SD16—2061no—
192D8—21no—
193D8—1032no—
194D8—1031no—
195D8—2062no—
196D8—2062no—
197D8—2061no—
198D8C22×D10312yes—
199D8C22×D10311yescharacteristic
200M16—1031no—
201M16—1032no—
202C2×C8—1032no—
203C2×C8C22×D10311yescharacteristic
204C16—1031no—
205C16—1031no—
206C16C22×D10312yes—
207C23—41no—
208C23—4122no—
209C23—4122no—
210C23—4121no—
211Q8—21no—
212Q8—1031no—
213Q8—2061no—
214D4—22no—
215D4—21no—
216D4—41no—
217D4—41no—
218D4—1032no—
219D4—1031no—
220D4—4122no—
221D4—4122no—
222D4—4122no—
223D4—4122no—
224D4—4121no—
225D4—4121no—
226D4—2061no—
227D4—2062no—
228C2×C4—41no—
229C2×C4—1032no—
230C2×C4—4122no—
231C2×C4—4122no—
232C2×C4—4121no—
233C2×C4D4×D10311yescharacteristic
234C8—1032no—
235C8D4×D10311yescharacteristic
236C8C23×D10311yescharacteristic
237C22—41no—
238C22—42no—
239C22—161no—
240C22—1032no—
241C22—16481no—
242C22—16482no—
243C22—16482no—
244C22—4122no—
245C22—4121no—
246C22D8×D10311yescharacteristic
247C4—41no—
248C4—1032no—
249C4—4121no—
250C4D8×D10311yescharacteristic
251C4C2×D4×D10311yescharacteristic
252C2—21no—
253C2—82no—
254C2—81no—
255C2—8242no—
256C2—8241no—
257C2—2062no—
258C2C2×D8×D10311yescharacteristic
subgroupG/H
centerC2C2×D8×D103
commutator, cosocleC8×C103C24
FrattiniC8C23×D103
Fitting#509×C103C2
socleC2×C103C22×D8
hypercenter#509D103
hypocenterC103#3415
LCSG ▷ C8×C103 ▷ C4×C103 ▷ C2×C103 ▷ C103
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×C8 ◁ #509

Complements

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

NH ≅ G/Ntype
1. #20268593C2semidirect
2. #20268592C2semidirect
3. #20268229C2semidirect
4. #20268228C2semidirect
5. #20268225C2semidirect
6. #20268222C2semidirect
7. #20268221C2semidirect
8. C2×#15692962C2semidirect
9. D16×D103C2semidirect
10. #20268209C2semidirect
11. #509×C103C2semidirect
18. #15693044C22semidirect
19. #15693043C22semidirect
20. #15693040C22semidirect
21. C2×D824C22semidirect
22. D8×D103C22semidirect
23. D8×D103C22semidirect
25. #15692967C22semidirect
26. #15692966C22semidirect
27. #15692965C22semidirect
28. #15692964C22semidirect
29. D1648C22semidirect
30. #15692962C22semidirect
31. #15692962C22semidirect
32. #15692962C22semidirect
33. #15692960C22semidirect
34. C2×C103⋊C16C22semidirect
35. C16×D103C22semidirect
36. #135×C103C22semidirect
37. C2×D8×C103C22semidirect
38. SD32×C103C22semidirect
39. D16×C103C22semidirect
40. M32×C103C22semidirect
130. C103#3415semidirect
136. #509D103semidirect
151. #135C2×D103semidirect
155. C2×D8C2×D103semidirect
161. SD32C2×D103semidirect
166. D16C2×D103semidirect
168. M32C2×D103semidirect

Maximal subgroups

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

subgroupindex
#202685932
#202685922
#202682292
#202682282
#202682252
#202682222
#202682212
C2×#156929622
D16×D1032
#202682092
#509×C1032
#3415103