Finite Group Databasebeta

← #27206959

Subgroups — #27206959

Order 13184.

494 conjugacy classes of subgroups; only the 125 normal subgroups are shown.

normal subgroups only

This group has 494 conjugacy classes of subgroups — too many to draw. Only its 125 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#20268446C211yesmaximal, characteristic, complemented
2D4×D412C211yesmaximal, characteristic, complemented
3#20268138C211yesmaximal, characteristic, complemented
4#20268106C212yesmaximal, complemented
5#20268071C211yesmaximal, characteristic, complemented
6#20268026C212yesmaximal, complemented
7#20267986C211yesmaximal, characteristic, complemented
8#20267923C212yesmaximal, complemented
9C8×D412C211yesmaximal, characteristic, complemented
10#102×D103C212yesmaximal, complemented
11C4×D8×C103C211yesmaximal, characteristic, complemented
12C2×#13110105—21no—
13C22×D412—21no—
14C2×D4×D103C2212yes—
15C2×#13110090C2212yescomplemented
16C2×C8×D103C2212yescomplemented
17#15693021C2211yescharacteristic, complemented
18#15693018C2211yescharacteristic
19#15693003—22no—
20#15693000—21no—
21#15692996C2212yes—
22#15692995—21no—
23#15692992C2212yescomplemented
24#15692991—22no—
25C4×D412C2211yescharacteristic
26C4⋊C4×D103C2212yescomplemented
27#15692954C2212yescomplemented
28C4⋊(C103⋊C8)C2211yescharacteristic, complemented
29#15692943C2212yescomplemented
30#15692943C2212yescomplemented
31#15692942C2212yes—
32#15692941C2212yescomplemented
33(C2×D103)⋊C8C2212yescomplemented
34C2×D8×C103C2211yescharacteristic
35C4×D4×C103C2211yescharacteristic
36C4×D4×C103C2211yescharacteristic, complemented
37#107×C103C2211yescharacteristic, complemented
38#102×C103C2211yescharacteristic
39#102×C103C2211yescharacteristic, complemented
40C4×C8×C103C2211yescharacteristic, complemented
41C23×D103—22no—
42#13110105—44no—
43C2×Dic206—21no—
44C2×D412—22no—
45C2×D412—21no—
46C2×D412—21no—
47C2×D412—44no—
48C2×D412D411yescharacteristic
49C2×D412C2312yes—
50C2×C22⋊D103—22no—
51C2×C22⋊D103—22no—
52D4×D103—24no—
53D4×D103—42no—
54C2×C4×D103—22no—
55C2×C4×D103C2312yes—
56#13110090—42no—
57C2×C103⋊C8C2312yes—
58C8×D103—42no—
59C4⋊Dic103—21no—
60C4⋊Dic103D411yescharacteristic
61C4⋊Dic103C2312yes—
62Dic103⋊C4—22no—
63C22⋊Dic103—22no—
64(C2×D103)⋊C4—22no—
65(C2×D103)⋊C4D412yes—
66C2×D4×C103C2311yescharacteristic
67C2×D4×C103C2311yescharacteristic
68C22×C4×C103—21no—
69C22×C4×C103—21no—
70D8×C103—22no—
71C2×C8×C103C2311yescharacteristic
72C2×C8×C103C2311yescharacteristic
73C4⋊C4×C103C2311yescharacteristic
74C4⋊C4×C103C2311yescharacteristic
75C22⋊C4×C103—21no—
76C22⋊C4×C103—21no—
77C42×C103C2311yescharacteristic
78C23×C103—21no—
79C23×C103—21no—
80C22×D103—22no—
81C22×D103—44no—
82C22×D103—44no—
83C22×D103—82no—
84C22×D103C2×D412yes—
85D4×C103—21no—
86D4×C103—21no—
87D4×C103—21no—
88D4×C103#4112yescomplemented
89C2×C4×C103—21no—
90C2×C4×C103—21no—
91C2×C4×C103—42no—
92C2×C4×C103—42no—
93C2×C4×C103C2×D411yescharacteristic
94C2×C4×C103C2×D411yescharacteristic
95C2×C4×C103C2411yescharacteristic
96C22⋊D103—44no—
97C22⋊D103—44no—
98C2×Dic103—22no—
99C2×Dic103C2×D412yes—
100D412—22no—
101D412—22no—
102D412—44no—
103D412—42no—
104D412—81no—
105D412D814yescomplemented
106C4×D103—22no—
107C4×D103—22no—
108C4×D103—44no—
109Dic206—42no—
110C8×C103—21no—
111C8×C103—21no—
112C103⋊C8—22no—
113C22×C103—22no—
114C22×C103—41no—
115C22×C103—41no—
116C22×C103—41no—
117C22×C103—41no—
118C22×C103—41no—
119C22×C103C22×D411yescharacteristic
120C2×D103—22no—
121C2×D103—22no—
122C2×D103—42no—
123C2×D103—42no—
124C2×D103—42no—
125C2×D103—88no—
126C2×D103C2×D814yes—
127C4×C103—21no—
128C4×C103—41no—
129C4×C103—41no—
130C4×C103C2×D812yes—
131C4×C103C2×#4111yescharacteristic
132C4×C103H(5,𝔽2)11yescharacteristic
133Dic103—22no—
134Dic103—42no—
135C2×C103—42no—
136C2×C103—81no—
137C2×C103#54611yescharacteristic
138C2×C103C22×D811yescharacteristic
139C2×C103#57711yescharacteristic
140D103—24no—
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×D8D10311yescharacteristic, complemented
153C8×D4—1031no—
154C2×#102—1032no—
155C2×#41—2061no—
156C22×D4—1032no—
157C22×D4—2061no—
158C2×D8—1032no—
159C2×D8C2×D10311yescharacteristic
160C22×C8—1032no—
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×D4C2×D10311yescharacteristic
171C4×D4C2×D10311yescharacteristic, complemented
172C2×C4⋊C4—1032no—
173#107—1032no—
174#107C2×D10311yescharacteristic, complemented
175C4⋊C8—1031no—
176#102—1032no—
177#102—1032no—
178#102—1032no—
179#102—1032no—
180#102C2×D10311yescharacteristic
181#102C2×D10311yescharacteristic, complemented
182C22⋊C8—1032no—
183C4×C8C2×D10311yescharacteristic, complemented
184C24—2062no—
185#41—4124no—
186C2×Q8—2061no—
187C2×D4—1031no—
188C2×D4—1032no—
189C2×D4—4124no—
190C2×D4—4122no—
191C2×D4—2062no—
192C2×D4—2062no—
193C2×D4—2062no—
194C2×D4—2064no—
195C2×D4—2061no—
196C2×D4—2061no—
197C2×D4C22×D10311yescharacteristic
198C2×D4C22×D10311yescharacteristic
199C22×C4—21no—
200C22×C4—21no—
201C22×C4—1032no—
202C22×C4—2062no—
203D8—22no—
204D8—4122no—
205C2×C8—1032no—
206C2×C8—4122no—
207C2×C8C22×D10311yescharacteristic
208C2×C8C22×D10311yescharacteristic
209C4⋊C4—1031no—
210C4⋊C4—1032no—
211C4⋊C4—2062no—
212C4⋊C4—2061no—
213C4⋊C4C22×D10311yescharacteristic
214C4⋊C4C22×D10311yescharacteristic
215C22⋊C4—21no—
216C22⋊C4—21no—
217C22⋊C4—1032no—
218C22⋊C4—2062no—
219C22⋊C4—2062no—
220C42C22×D10311yescharacteristic
221C23—21no—
222C23—21no—
223C23—8242no—
224C23—1032no—
225C23—4124no—
226C23—4124no—
227C23—2062no—
228Q8—4122no—
229D4—21no—
230D4—21no—
231D4—21no—
232D4—8241no—
233D4—1034no—
234D4—4124no—
235D4—4124no—
236D4—4124no—
237D4—4122no—
238D4—2062no—
239D4—2062no—
240D4#1311010512yescomplemented
241C2×C4—21no—
242C2×C4—21no—
243C2×C4—42no—
244C2×C4—42no—
245C2×C4—1032no—
246C2×C4—4124no—
247C2×C4—2062no—
248C2×C4—2062no—
249C2×C4—2062no—
250C2×C4D4×D10311yescharacteristic
251C2×C4D4×D10311yescharacteristic
252C2×C4C23×D10311yescharacteristic
253C8—21no—
254C8—21no—
255C8—2062no—
256C22—22no—
257C22—41no—
258C22—41no—
259C22—41no—
260C22—41no—
261C22—41no—
262C22—8248no—
263C22—1034no—
264C22—4122no—
265C22—4122no—
266C22—4122no—
267C22—2062no—
268C22—2062no—
269C22C2×D4×D10311yescharacteristic
270C4—21no—
271C4—41no—
272C4—41no—
273C4—4122no—
274C4—2062no—
275C4D8×D10312yes—
276C4C2×#1311010511yescharacteristic
277C4#1569306711yescharacteristic
278C2—42no—
279C2—81no—
280C2—8242no—
281C2—2064no—
282C2#2026843711yescharacteristic
283C2C2×D8×D10311yescharacteristic
284C2#2026859811yescharacteristic
subgroupG/H
centerC22C2×D4×D103
commutator, cosocleC2×C4×C103C24
FrattiniC2×C4C23×D103
FittingC4×D8×C103C2
socleC22×C103C22×D4
hypercenterC4×D8D103
hypocenterC103#3294
LCSG ▷ C2×C4×C103 ▷ C2×C103 ▷ C103
UCSC1 ◁ C22 ◁ C42 ◁ C4×D8

Complements

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

NH ≅ G/Ntype
1. #20268446C2semidirect
2. D4×D412C2semidirect
3. #20268138C2semidirect
4. #20268106C2semidirect
5. #20268071C2semidirect
6. #20268026C2semidirect
7. #20267986C2semidirect
8. #20267923C2semidirect
9. C8×D412C2semidirect
10. #102×D103C2semidirect
11. C4×D8×C103C2semidirect
15. C2×#13110090C22semidirect
16. C2×C8×D103C22semidirect
17. #15693021C22semidirect
23. #15692992C22semidirect
26. C4⋊C4×D103C22semidirect
27. #15692954C22semidirect
28. C4⋊(C103⋊C8)C22semidirect
29. #15692943C22semidirect
30. #15692943C22semidirect
32. #15692941C22semidirect
33. (C2×D103)⋊C8C22semidirect
36. C4×D4×C103C22semidirect
37. #107×C103C22semidirect
39. #102×C103C22semidirect
40. C4×C8×C103C22semidirect
88. D4×C103#41semidirect
105. D412D8semidirect
143. C103#3294semidirect
152. C4×D8D103semidirect
171. C4×D4C2×D103semidirect
174. #107C2×D103semidirect
181. #102C2×D103semidirect
183. C4×C8C2×D103semidirect
240. D4#13110105semidirect

Maximal subgroups

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

subgroupindex
#202684462
D4×D4122
#202681382
#202681062
#202680712
#202680262
#202679862
#202679232
C8×D4122
#102×D1032
C4×D8×C1032
#3294103