Finite Group Databasebeta

← #27208287

Subgroups — #27208287

Order 13184.

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

normal subgroups only

This group has 360 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#20268605C211yesmaximal, characteristic, complemented
2#20268593C211yesmaximal, characteristic, complemented
3#20268233C212yesmaximal, complemented
4#20268231C211yesmaximal, characteristic, complemented
5#20268226C211yesmaximal, characteristic, complemented
6#20268225C212yesmaximal, complemented
7#20268222C212yesmaximal, complemented
8C2×#15692966C211yesmaximal, characteristic, complemented
9SD32×D103C212yesmaximal, complemented
10#20268207C211yesmaximal, characteristic, complemented
11#508×C103C211yesmaximal, characteristic, complemented
12#15693068—21no—
13#15693067—21no—
14#15693051—21no—
15#15693050—22no—
16#15693048—22no—
17#15693046—21no—
18#15693044C2212yes—
19#15693040C2212yescomplemented
20C2×Dic412C2211yescharacteristic, complemented
21Q16×D103C2212yescomplemented
22C2×D824C2211yescharacteristic
23D8×D103C2212yes—
24#15693027C2211yescharacteristic
25#15692967C2212yescomplemented
26#15692966C2212yescomplemented
27#15692966C2212yescomplemented
28#15692965C2212yescomplemented
29#15692964C2212yescomplemented
30#15692962C2212yescomplemented
31#15692961C2211yescharacteristic, complemented
32#15692960C2212yescomplemented
33C16×D103C2212yescomplemented
34#135×C103C2211yescharacteristic
35#135×C103C2211yescharacteristic, complemented
36Q32×C103C2211yescharacteristic, complemented
37SD32×C103C2211yescharacteristic, complemented
38SD32×C103C2211yescharacteristic, complemented
39D16×C103C2211yescharacteristic, complemented
40C2×C16×C103C2211yescharacteristic, complemented
41#13110106—22no—
42#13110105—41no—
43#13110105—41no—
44#13110105D411yescharacteristic
45#13110104—22no—
46#13110104—42no—
47C2×Dic206—21no—
48C2×Dic206—41no—
49Q8×D103—22no—
50C2×D412—21no—
51C2×D412—41no—
52D4×D103—22no—
53D4×D103—42no—
54Dic412—21no—
55Dic412C2312yes—
56#13110095—22no—
57#13110093—22no—
58#13110092—22no—
59D824—21no—
60D824C2312yes—
61#13110090—22no—
62#13110089D411yescharacteristic
63#13110088D412yes—
64C8×D103C2312yes—
65C103⋊C16C2312yes—
66#41×C103—21no—
67#41×C103—21no—
68Q16×C103C2311yescharacteristic
69Q16×C103C2311yescharacteristic
70SD16×C103—21no—
71SD16×C103—21no—
72D8×C103C2311yescharacteristic
73D8×C103C2311yescharacteristic
74C2×C8×C103C2311yescharacteristic
75C16×C103C2311yescharacteristic
76C16×C103C2311yescharacteristic
77C22×D103—41no—
78C22×D103—42no—
79Q8×C103—21no—
80Q8×C103—21no—
81D4×C103—21no—
82D4×C103—21no—
83D4×C103—41no—
84D4×C103—41no—
85C2×C4×C103—41no—
86C2×C4×C103—41no—
87C2×C4×C103C2×D411yescharacteristic
88C22⋊D103—42no—
89C22⋊D103—42no—
90C22⋊D103D812yes—
91C2×Dic103—41no—
92C2×Dic103—42no—
93D412—22no—
94D412—42no—
95D412—41no—
96D412D811yescharacteristic
97C4×D103—42no—
98C4×D103—42no—
99C4×D103C2×D412yes—
100Dic206—22no—
101Dic206—41no—
102Dic206—42no—
103Dic206D811yescharacteristic
104C8×C103C2×D411yescharacteristic
105C8×C103C2411yescharacteristic
106C103⋊C8C2×D412yes—
107C22×C103—41no—
108C22×C103—41no—
109C22×C103C2×D811yescharacteristic
110C2×D103—42no—
111C2×D103—162no—
112C2×D103—161no—
113C2×D103C2×D812yes—
114C4×C103—41no—
115C4×C103—41no—
116C4×C103C2×D811yescharacteristic
117C4×C103C22×D411yescharacteristic
118Dic103—42no—
119Dic103C2×D812yes—
120C2×C103—21no—
121C2×C103—81no—
122C2×C103—81no—
123C2×C103C22×D811yescharacteristic
124D103—22no—
125D103—82no—
126#3416—1031nomaximal, Sylow
127C103#341611yescharacteristic, complemented, Sylow
128#578—1031no—
129#576—1031no—
130#510—1031no—
131#510—1032no—
132#509—1031no—
133#509—1032no—
134#508—1032no—
135#508D10311yescharacteristic, complemented
136C2×SD32—1032no—
137C2×SD32—1031no—
138#504—1031no—
1392−1+4—2061no—
140H(5,𝔽2)—2061no—
141#137—2062no—
142#137—2061no—
143AGL(1,ℤ/8)—2062no—
144AGL(1,ℤ/8)—2061no—
145#135—1032no—
146#135—1032no—
147#135C2×D10311yescharacteristic
148#135C2×D10311yescharacteristic, complemented
149C2×Q16—1032no—
150C2×Q16—1031no—
151C2×D8—1032no—
152C2×D8—1031no—
153#131—1031no—
154Q32—1032no—
155Q32C2×D10311yescharacteristic, complemented
156SD32—1032no—
157SD32—1032no—
158SD32—1032no—
159SD32—1032no—
160SD32C2×D10311yescharacteristic, complemented
161SD32C2×D10311yescharacteristic, complemented
162D16—1032no—
163D16C2×D10311yescharacteristic, complemented
164M32—1031no—
165M32—1032no—
166C2×C16—1032no—
167C2×C16C2×D10311yescharacteristic, complemented
168#41—21no—
169#41—21no—
170#41—1031no—
171#41—4121no—
172#41—4121no—
173#41—4122no—
174#41—2062no—
175#41—2062no—
176C2×Q8—4121no—
177C2×Q8—2062no—
178C2×Q8—2061no—
179C2×D4—4121no—
180C2×D4—4122no—
181C2×D4—2062no—
182C2×D4—2061no—
183Q16—1032no—
184Q16—2062no—
185Q16—2061no—
186Q16C22×D10311yescharacteristic
187Q16C22×D10311yescharacteristic
188SD16—21no—
189SD16—21no—
190SD16—2062no—
191SD16—2062no—
192D8—1032no—
193D8—2062no—
194D8—2061no—
195D8C22×D10311yescharacteristic
196D8C22×D10311yescharacteristic
197M16—1031no—
198M16—1032no—
199C2×C8—1032no—
200C2×C8C22×D10311yescharacteristic
201C16—1032no—
202C16C22×D10311yescharacteristic
203C16C22×D10311yescharacteristic
204C23—4122no—
205C23—4121no—
206Q8—21no—
207Q8—21no—
208Q8—1031no—
209Q8—4122no—
210Q8—4121no—
211Q8—2062no—
212D4—21no—
213D4—21no—
214D4—41no—
215D4—41no—
216D4—1032no—
217D4—1031no—
218D4—4122no—
219D4—4122no—
220D4—4122no—
221D4—4121no—
222D4—2062no—
223C2×C4—41no—
224C2×C4—41no—
225C2×C4—1032no—
226C2×C4—4122no—
227C2×C4—4122no—
228C2×C4—4122no—
229C2×C4—4121no—
230C2×C4D4×D10311yescharacteristic
231C8—1032no—
232C8D4×D10311yescharacteristic
233C8C23×D10311yescharacteristic
234C22—41no—
235C22—41no—
236C22—1032no—
237C22—16481no—
238C22—16482no—
239C22—4122no—
240C22D8×D10311yescharacteristic
241C4—41no—
242C4—41no—
243C4—1032no—
244C4—4122no—
245C4D8×D10311yescharacteristic
246C4C2×D4×D10311yescharacteristic
247C2—21no—
248C2—81no—
249C2—81no—
250C2—8242no—
251C2—2062no—
252C2C2×D8×D10311yescharacteristic
subgroupG/H
centerC2C2×D8×D103
commutator, cosocleC8×C103C24
FrattiniC8C23×D103
Fitting#508×C103C2
socleC2×C103C22×D8
hypercenter#508D103
hypocenterC103#3416
LCSG ▷ C8×C103 ▷ C4×C103 ▷ C2×C103 ▷ C103
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×C8 ◁ #508

Complements

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

NH ≅ G/Ntype
1. #20268605C2semidirect
2. #20268593C2semidirect
3. #20268233C2semidirect
4. #20268231C2semidirect
5. #20268226C2semidirect
6. #20268225C2semidirect
7. #20268222C2semidirect
8. C2×#15692966C2semidirect
9. SD32×D103C2semidirect
10. #20268207C2semidirect
11. #508×C103C2semidirect
19. #15693040C22semidirect
20. C2×Dic412C22semidirect
21. Q16×D103C22semidirect
25. #15692967C22semidirect
26. #15692966C22semidirect
27. #15692966C22semidirect
28. #15692965C22semidirect
29. #15692964C22semidirect
30. #15692962C22semidirect
31. #15692961C22semidirect
32. #15692960C22semidirect
33. C16×D103C22semidirect
35. #135×C103C22semidirect
36. Q32×C103C22semidirect
37. SD32×C103C22semidirect
38. SD32×C103C22semidirect
39. D16×C103C22semidirect
40. C2×C16×C103C22semidirect
127. C103#3416semidirect
135. #508D103semidirect
148. #135C2×D103semidirect
155. Q32C2×D103semidirect
160. SD32C2×D103semidirect
161. SD32C2×D103semidirect
163. D16C2×D103semidirect
167. C2×C16C2×D103semidirect

Maximal subgroups

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

subgroupindex
#202686052
#202685932
#202682332
#202682312
#202682262
#202682252
#202682222
C2×#156929662
SD32×D1032
#202682072
#508×C1032
#3416103