Finite Group Databasebeta

← #27206958

Subgroups — #27206958

Order 13184.

494 conjugacy classes of subgroups; only the 139 normal subgroups are shown.

normal subgroups only

This group has 494 conjugacy classes of subgroups — too many to draw. Only its 139 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#20268445C211yesmaximal, characteristic, complemented
2D4×D412C211yesmaximal, characteristic, complemented
3#20268138C211yesmaximal, characteristic, complemented
4#20268105C212yesmaximal, complemented
5#20268072C211yesmaximal, characteristic, complemented
6#20268027C212yesmaximal, complemented
7#20267987C211yesmaximal, characteristic, complemented
8#20267927C212yesmaximal, complemented
9C4×D824C211yesmaximal, characteristic, complemented
10C2×#15692943C212yesmaximal, complemented
11C8×D4×C103C211yesmaximal, characteristic, complemented
12C2×#13110104—21no—
13C22×D412C2212yes—
14C2×D4×D103—21no—
15C2×D824C2211yescharacteristic
16C2×D824C2212yescomplemented
17#15693021C2211yescharacteristic, complemented
18#15693018C2211yescharacteristic
19#15693005—22no—
20#15693001—21no—
21#15692996—21no—
22#15692995C2212yes—
23#15692995C2212yescomplemented
24#15692991—22no—
25C4×D412C2211yescharacteristic
26C4×D412C2211yescharacteristic, complemented
27C2×C4⋊Dic103C2212yescomplemented
28#15692955C2212yescomplemented
29#15692955C2211yescharacteristic, complemented
30#15692943C2211yescharacteristic
31#15692943C2212yes—
32#15692943C2212yescomplemented
33#15692943C2212yescomplemented
34#15692943C2212yescomplemented
35#15692943C2211yescharacteristic, complemented
36C22×C8×C103C2212yescomplemented
37C4×D4×C103C2211yescharacteristic
38C4⋊C8×C103C2211yescharacteristic, complemented
39C22⋊C8×C103C2212yescomplemented
40C4×C8×C103C2211yescharacteristic, complemented
41C23×D103—22no—
42#13110104—44no—
43C2×Dic206—21no—
44C2×D412—24no—
45C2×D412—21no—
46C2×D412—22no—
47C2×D412—21no—
48C2×D412—42no—
49C2×D412C2312yes—
50C2×D412C2311yescharacteristic
51C2×D412C2311yescharacteristic
52C2×C22⋊D103—22no—
53C2×C22⋊D103—22no—
54D4×D103—44no—
55C22×Dic103—22no—
56C2×C4×D103—21no—
57C2×C4×D103—21no—
58D824—22no—
59D824—42no—
60C4⋊Dic103—22no—
61C4⋊Dic103—21no—
62C4⋊Dic103C2311yescharacteristic
63C4⋊Dic103C2312yes—
64C4⋊Dic103C2311yescharacteristic
65(C2×D103)⋊C4—21no—
66(C2×D103)⋊C4—21no—
67(C2×D103)⋊C4—22no—
68(C2×D103)⋊C4—22no—
69C2×D4×C103D411yescharacteristic
70C22×C4×C103C2312yes—
71C2×C8×C103—42no—
72C2×C8×C103C2311yescharacteristic
73C2×C8×C103C2311yescharacteristic
74C2×C8×C103C2312yes—
75C4⋊C4×C103D411yescharacteristic
76C22⋊C4×C103D412yes—
77C42×C103C2311yescharacteristic
78C23×C103C2×D412yes—
79C22×D103—21no—
80C22×D103—21no—
81C22×D103—22no—
82C22×D103—44no—
83C22×D103—44no—
84C22×D103—82no—
85D4×C103D814yescomplemented
86C2×C4×C103—22no—
87C2×C4×C103—22no—
88C2×C4×C103C2×D411yescharacteristic
89C2×C4×C103C2×D412yes—
90C2×C4×C103C2×D411yescharacteristic
91C2×C4×C103C2411yescharacteristic
92C22⋊D103—44no—
93C22⋊D103—44no—
94C2×Dic103—21no—
95C2×Dic103—21no—
96C2×Dic103—22no—
97C2×Dic103—44no—
98D412—21no—
99D412—22no—
100D412—21no—
101D412—21no—
102D412—22no—
103D412—44no—
104D412—42no—
105D412—81no—
106D412#4112yescomplemented
107C4×D103—42no—
108C4×D103—42no—
109Dic206—42no—
110C8×C103—21no—
111C8×C103—21no—
112C8×C103—22no—
113C22×C103—22no—
114C22×C103—22no—
115C22×C103C2×D814yes—
116C22×C103C22×D411yescharacteristic
117C2×D103—22no—
118C2×D103—41no—
119C2×D103—41no—
120C2×D103—42no—
121C2×D103—41no—
122C2×D103—41no—
123C2×D103—42no—
124C2×D103—42no—
125C2×D103—41no—
126C2×D103—88no—
127C4×C103—22no—
128C4×C103—21no—
129C4×C103C2×D812yes—
130C4×C103C2×#4111yescharacteristic
131C4×C103H(5,𝔽2)11yescharacteristic
132Dic103—42no—
133Dic103—41no—
134Dic103—41no—
135C2×C103—24no—
136C2×C103#54611yescharacteristic
137C2×C103C22×D811yescharacteristic
138C2×C103#57711yescharacteristic
139D103—42no—
140D103—81no—
141D103—82no—
142#3294—1031nomaximal, Sylow
143C103#329411yescharacteristic, complemented, Sylow
144#547—1031no—
145D42—1031no—
146#486—1031no—
147#480—1032no—
148#474—1031no—
149#466—1032no—
150#459—1031no—
151#447—1032no—
152C4×D8—1031no—
153C8×D4D10311yescharacteristic, complemented
154C2×#102—1032no—
155C2×#41—2061no—
156C22×D4—1032no—
157C22×D4—2061no—
158C2×D8—1032no—
159C2×D8—1031no—
160C22×C8C2×D10312yescomplemented
161C4⋊Q8—1031no—
162#127—1031no—
163#123—2062no—
164C22⋊Q8—2061no—
165#121—1032no—
166#121—1032no—
167#121—2061no—
168#120—2062no—
169C4×D4—1031no—
170C4×D4—1031no—
171C4×D4C2×D10311yescharacteristic
172C2×C4⋊C4—1032no—
173#107—1031no—
174#107—1032no—
175C4⋊C8C2×D10311yescharacteristic, complemented
176#102—1031no—
177#102—1032no—
178#102—1032no—
179#102—1032no—
180#102—1031no—
181#102—1032no—
182C22⋊C8C2×D10312yescomplemented
183C4×C8C2×D10311yescharacteristic, complemented
184C24—2062no—
185#41—4124no—
186C2×Q8—2061no—
187C2×D4—1031no—
188C2×D4—1032no—
189C2×D4—1031no—
190C2×D4—4122no—
191C2×D4—4124no—
192C2×D4—2064no—
193C2×D4—2062no—
194C2×D4—2062no—
195C2×D4—2061no—
196C2×D4—2062no—
197C2×D4—2061no—
198C2×D4D41211yescharacteristic
199C22×C4—2062no—
200C22×C4—2061no—
201C22×C4—2061no—
202C22×C4C22×D10312yes—
203D8—4122no—
204D8—2062no—
205C2×C8—42no—
206C2×C8C22×D10311yescharacteristic
207C2×C8C22×D10311yescharacteristic
208C2×C8C22×D10312yes—
209C4⋊C4—1031no—
210C4⋊C4—1032no—
211C4⋊C4—1031no—
212C4⋊C4—2062no—
213C4⋊C4—2061no—
214C4⋊C4D41211yescharacteristic
215C22⋊C4—2061no—
216C22⋊C4—2061no—
217C22⋊C4—2062no—
218C22⋊C4—2062no—
219C22⋊C4D41212yes—
220C42C22×D10311yescharacteristic
221C23—8242no—
222C23—4124no—
223C23—4124no—
224C23—2061no—
225C23—2062no—
226C23—2061no—
227C23C2×D41212yes—
228Q8—4122no—
229D4—8241no—
230D4—1032no—
231D4—4124no—
232D4—4124no—
233D4—4124no—
234D4—4122no—
235D4—2061no—
236D4—2062no—
237D4—2061no—
238D4—2062no—
239D4—2061no—
240D4D82414yescomplemented
241C2×C4—22no—
242C2×C4—22no—
243C2×C4—4124no—
244C2×C4—4122no—
245C2×C4—4122no—
246C2×C4—2061no—
247C2×C4—2061no—
248C2×C4—2062no—
249C2×C4C2×D41211yescharacteristic
250C2×C4C2×D41212yes—
251C2×C4C2×D41211yescharacteristic
252C2×C4C23×D10311yescharacteristic
253C8—21no—
254C8—21no—
255C8—22no—
256C22—22no—
257C22—22no—
258C22—8248no—
259C22—4121no—
260C22—4122no—
261C22—4122no—
262C22—4121no—
263C22—4122no—
264C22—4121no—
265C22—4121no—
266C22—4121no—
267C22—2062no—
268C22C2×D82414yes—
269C22C22×D41211yescharacteristic
270C4—21no—
271C4—22no—
272C4—4121no—
273C4—4121no—
274C4—4122no—
275C4C2×D82412yes—
276C4#41×D10311yescharacteristic
277C4#1569306611yescharacteristic
278C2—24no—
279C2—8242no—
280C2—8241no—
281C2—4122no—
282C2#2026843611yescharacteristic
283C2C22×D82411yescharacteristic
284C2#2026860311yescharacteristic
subgroupG/H
centerC22C22×D412
commutator, cosocleC2×C4×C103C24
FrattiniC2×C4C23×D103
FittingC8×D4×C103C2
socleC22×C103C22×D4
hypercenterC8×D4D103
hypocenterC103#3294
LCSG ▷ C2×C4×C103 ▷ C2×C103 ▷ C103
UCSC1 ◁ C22 ◁ C4×D4 ◁ C8×D4

Complements

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

NH ≅ G/Ntype
1. #20268445C2semidirect
2. D4×D412C2semidirect
3. #20268138C2semidirect
4. #20268105C2semidirect
5. #20268072C2semidirect
6. #20268027C2semidirect
7. #20267987C2semidirect
8. #20267927C2semidirect
9. C4×D824C2semidirect
10. C2×#15692943C2semidirect
11. C8×D4×C103C2semidirect
16. C2×D824C22semidirect
17. #15693021C22semidirect
23. #15692995C22semidirect
26. C4×D412C22semidirect
27. C2×C4⋊Dic103C22semidirect
28. #15692955C22semidirect
29. #15692955C22semidirect
32. #15692943C22semidirect
33. #15692943C22semidirect
34. #15692943C22semidirect
35. #15692943C22semidirect
36. C22×C8×C103C22semidirect
38. C4⋊C8×C103C22semidirect
39. C22⋊C8×C103C22semidirect
40. C4×C8×C103C22semidirect
85. D4×C103D8semidirect
106. D412#41semidirect
143. C103#3294semidirect
153. C8×D4D103semidirect
160. C22×C8C2×D103semidirect
175. C4⋊C8C2×D103semidirect
182. C22⋊C8C2×D103semidirect
183. C4×C8C2×D103semidirect
240. D4D824semidirect

Maximal subgroups

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

subgroupindex
#202684452
D4×D4122
#202681382
#202681052
#202680722
#202680272
#202679872
#202679272
C4×D8242
C2×#156929432
C8×D4×C1032
#3294103