Finite Group Databasebeta

← #27206942

Subgroups — #27206942

Order 13184.

476 conjugacy classes of subgroups; only the 117 normal subgroups are shown.

normal subgroups only

This group has 476 conjugacy classes of subgroups — too many to draw. Only its 117 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#20268596C211yesmaximal, characteristic, complemented
2#20268595C212yesmaximal, complemented
3#20268592C211yesmaximal, characteristic, complemented
4#20268166C211yesmaximal, characteristic, complemented
5#20268062C211yesmaximal, characteristic, complemented
6#20268060C212yesmaximal, complemented
7#20267961C212yesmaximal, complemented
8#20267957C212yesmaximal, complemented
9#20267907C211yesmaximal, characteristic, complemented
10#20267906C211yesmaximal, characteristic, complemented
11#472×C103C211yesmaximal, characteristic, complemented
12#15693067C2212yescomplemented
13#15693066C2212yescomplemented
14#15693049—22no—
15#15693049C2212yescomplemented
16#15693049C2212yescomplemented
17#15693048—22no—
18#15693047C2212yescomplemented
19#15693045—22no—
20#15693045—22no—
21#15693043—21no—
22#15693043C2211yescharacteristic
23#15693042—22no—
24#15693041C2211yescharacteristic
25#15693040—21no—
26C2×D824—21no—
27C2×D824C2211yescharacteristic, complemented
28C2×#13110090C2212yescomplemented
29D8×D103—21no—
30D8×D103—22no—
31#15693029C2212yescomplemented
32#15693027C2211yescharacteristic, complemented
33#15693017C2212yescomplemented
34#15692956C2211yescharacteristic, complemented
35#15692948C2211yescharacteristic, complemented
36#15692947C2211yescharacteristic, complemented
37#15692947C2212yescomplemented
38#15692937C2212yescomplemented
39C8×Dic103C2211yescharacteristic, complemented
40AGL(1,ℤ/8)×C103C2212yescomplemented
41C2×D8×C103C2211yescharacteristic, complemented
42#131×C103C2211yescharacteristic, complemented
43#108×C103C2211yescharacteristic, complemented
44#100×C103C2212yescomplemented
45#13110106—22no—
46#13110105—22no—
47#13110105C2311yescharacteristic
48#13110105C2312yes—
49#13110104—22no—
50#13110104—22no—
51C2×D412—22no—
52C2×D412C2312yes—
53C2×C22⋊D103—42no—
54C2×C22⋊D103—42no—
55D4×D103—22no—
56D4×D103—22no—
57D4×D103—22no—
58D4×D103—42no—
59Dic412D411yescharacteristic, complemented
60#13110095D411yescharacteristic, complemented
61#13110094—22no—
62#13110094—22no—
63#13110094D412yescomplemented
64#13110093—22no—
65#13110093D411yescharacteristic, complemented
66#13110092D411yescharacteristic, complemented
67D824—22no—
68D824—22no—
69D824—21no—
70D824—21no—
71D824D411yescharacteristic, complemented
72#13110090—22no—
73#13110090—22no—
74#13110090—22no—
75#13110090D411yescharacteristic, complemented
76#13110089C2311yescharacteristic
77#13110088—21no—
78#13110088—22no—
79C2×C103⋊C8C2311yescharacteristic
80C8×D103—21no—
81C8×D103—22no—
82C4×Dic103C2311yescharacteristic
83#41×C103C2311yescharacteristic
84C2×D4×C103C2312yes—
85SD16×C103—22no—
86D8×C103—22no—
87D8×C103—21no—
88D8×C103—21no—
89M16×C103—21no—
90M16×C103C2311yescharacteristic
91M16×C103C2312yes—
92C2×C8×C103—21no—
93C2×C8×C103C2311yescharacteristic
94C23×C103—22no—
95C22×D103—22no—
96C22×D103—42no—
97C22×D103—42no—
98Q8×C103C2×D411yescharacteristic
99D4×C103—21no—
100D4×C103—22no—
101D4×C103—22no—
102D4×C103C2×D411yescharacteristic
103C2×C4×C103—21no—
104C2×C4×C103C2411yescharacteristic
105C22⋊D103—22no—
106C22⋊D103—21no—
107C22⋊D103—42no—
108C22⋊D103—42no—
109C22⋊D103—42no—
110C22⋊D103—84no—
111C2×Dic103—21no—
112C2×Dic103—42no—
113D412—22no—
114D412—22no—
115D412—42no—
116D412C2×D412yes—
117D412C2×D411yescharacteristic
118C4×D103—21no—
119C4×D103—22no—
120C4×D103—42no—
121Dic206C2×D412yes—
122Dic206C2×D411yescharacteristic
123C8×C103—21no—
124C8×C103—22no—
125C8×C103C2×D411yescharacteristic
126C8×C103C2×D411yescharacteristic
127C103⋊C8—21no—
128C103⋊C8C2×D411yescharacteristic
129C103⋊C8C2×D411yescharacteristic
130C22×C103—21no—
131C22×C103—42no—
132C22×C103—82no—
133C22×C103H(5,𝔽2)11yescharacteristic
134C2×D103—22no—
135C2×D103—21no—
136C2×D103—42no—
137C2×D103—82no—
138C2×D103—162no—
139C2×D103—162no—
140C4×C103—21no—
141C4×C103C22×D411yescharacteristic
142C4×C103C22×D411yescharacteristic
143Dic103—22no—
144Dic103—22no—
145Dic103—21no—
146C2×C103—21no—
147C2×C103—41no—
148C2×C103—82no—
149C2×C103D4211yescharacteristic
150D103—42no—
151D103—41no—
152D103—82no—
153#3292—1031nomaximal, Sylow
154C103#329211yescharacteristic, complemented, Sylow
155#576—1032no—
156#576—1031no—
157#576—1031no—
158#493—1031no—
159#472—1031no—
160#472—1032no—
161#472D10311yescharacteristic, complemented
162#453—1032no—
163#453—1032no—
164#443—1031no—
165#443—1031no—
166H(5,𝔽2)—1032no—
167H(5,𝔽2)—1032no—
168AGL(1,ℤ/8)—1032no—
169AGL(1,ℤ/8)—1032no—
170AGL(1,ℤ/8)—1032no—
171AGL(1,ℤ/8)—2062no—
172AGL(1,ℤ/8)—2062no—
173AGL(1,ℤ/8)—2062no—
174AGL(1,ℤ/8)—2062no—
175AGL(1,ℤ/8)C2×D10312yescomplemented
176#135—1031no—
177#135—1031no—
178#135—2061no—
179#135—2061no—
180#135—2062no—
181C2×D8—1032no—
182C2×D8—1031no—
183C2×D8—2061no—
184C2×D8—2062no—
185C2×D8—2061no—
186C2×D8C2×D10311yescharacteristic, complemented
187#131—1032no—
188#131—1031no—
189#131C2×D10311yescharacteristic, complemented
190#127—1032no—
191#108—1031no—
192#108C2×D10311yescharacteristic, complemented
193#104—1031no—
194#104—1032no—
195#104—1031no—
196#100—1032no—
197#100C2×D10312yescomplemented
198C4×C8—1031no—
199#41—1031no—
200#41—1032no—
201#41—2062no—
202#41—2062no—
203#41—2062no—
204#41—2062no—
205#41C22×D10311yescharacteristic
206C2×D4—1032no—
207C2×D4—4122no—
208C2×D4—4122no—
209C2×D4—4122no—
210C2×D4—2062no—
211C2×D4—2062no—
212C2×D4—2062no—
213C2×D4—2062no—
214C2×D4C22×D10312yes—
215Q16—1031no—
216Q16—1031no—
217SD16—22no—
218SD16—1031no—
219SD16—1031no—
220SD16—1032no—
221SD16—2062no—
222SD16—2062no—
223SD16—2062no—
224D8—22no—
225D8—21no—
226D8—21no—
227D8—1031no—
228D8—1031no—
229D8—2062no—
230D8—2062no—
231D8—2062no—
232D8—2062no—
233D8—2062no—
234D8—2061no—
235D8—2061no—
236M16—21no—
237M16—1031no—
238M16—2062no—
239M16—2061no—
240M16C22×D10312yes—
241M16C22×D10311yescharacteristic
242C2×C8—21no—
243C2×C8—1031no—
244C2×C8—2062no—
245C2×C8—2061no—
246C2×C8C22×D10311yescharacteristic
247C42—1031no—
248C23—22no—
249C23—4122no—
250C23—4122no—
251C23—2062no—
252Q8—1031no—
253Q8—1032no—
254Q8D4×D10311yescharacteristic
255D4—21no—
256D4—22no—
257D4—22no—
258D4—8244no—
259D4—1031no—
260D4—1032no—
261D4—4122no—
262D4—4122no—
263D4—4122no—
264D4—4122no—
265D4—2062no—
266D4—2061no—
267D4—2062no—
268D4—2062no—
269D4D4×D10311yescharacteristic
270C2×C4—21no—
271C2×C4—4122no—
272C2×C4—4122no—
273C2×C4—2061no—
274C2×C4—2062no—
275C2×C4—2061no—
276C2×C4C23×D10311yescharacteristic
277C8—21no—
278C8—22no—
279C8—1031no—
280C8—1031no—
281C8—2061no—
282C8D4×D10311yescharacteristic
283C8D4×D10311yescharacteristic
284C22—21no—
285C22—42no—
286C22—82no—
287C22—8242no—
288C22—16482no—
289C22—16482no—
290C22—4122no—
291C22—2062no—
292C22—2061no—
293C22#1569306711yescharacteristic
294C4—21no—
295C4—2062no—
296C4—2062no—
297C4—2061no—
298C4C2×D4×D10311yescharacteristic
299C4C2×D4×D10311yescharacteristic
300C2—21no—
301C2—41no—
302C2—82no—
303C2—8242no—
304C2—4122no—
305C2—4121no—
306C2#2026842511yescharacteristic
subgroupG/H
centerC2#20268425
commutator, cosocleC2×C4×C103C24
FrattiniC2×C4C23×D103
Fitting#472×C103C2
socleC2×C103D42
hypercenter#472D103
hypocenterC103#3292
LCSG ▷ C2×C4×C103 ▷ C2×C103 ▷ C103
UCSC1 ◁ C2 ◁ C2×C4 ◁ #472

Complements

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

NH ≅ G/Ntype
1. #20268596C2semidirect
2. #20268595C2semidirect
3. #20268592C2semidirect
4. #20268166C2semidirect
5. #20268062C2semidirect
6. #20268060C2semidirect
7. #20267961C2semidirect
8. #20267957C2semidirect
9. #20267907C2semidirect
10. #20267906C2semidirect
11. #472×C103C2semidirect
12. #15693067C22semidirect
13. #15693066C22semidirect
15. #15693049C22semidirect
16. #15693049C22semidirect
18. #15693047C22semidirect
27. C2×D824C22semidirect
28. C2×#13110090C22semidirect
31. #15693029C22semidirect
32. #15693027C22semidirect
33. #15693017C22semidirect
34. #15692956C22semidirect
35. #15692948C22semidirect
36. #15692947C22semidirect
37. #15692947C22semidirect
38. #15692937C22semidirect
39. C8×Dic103C22semidirect
40. AGL(1,ℤ/8)×C103C22semidirect
41. C2×D8×C103C22semidirect
42. #131×C103C22semidirect
43. #108×C103C22semidirect
44. #100×C103C22semidirect
59. Dic412D4semidirect
60. #13110095D4semidirect
63. #13110094D4semidirect
65. #13110093D4semidirect
66. #13110092D4semidirect
71. D824D4semidirect
75. #13110090D4semidirect
154. C103#3292semidirect
161. #472D103semidirect
175. AGL(1,ℤ/8)C2×D103semidirect
186. C2×D8C2×D103semidirect
189. #131C2×D103semidirect
192. #108C2×D103semidirect
197. #100C2×D103semidirect

Maximal subgroups

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

subgroupindex
#202685962
#202685952
#202685922
#202681662
#202680622
#202680602
#202679612
#202679572
#202679072
#202679062
#472×C1032
#3292103