Finite Group Databasebeta

← #27205894

Subgroups — #27205894

Order 13184.

520 conjugacy classes of subgroups; only the 121 normal subgroups are shown.

normal subgroups only

This group has 520 conjugacy classes of subgroups — too many to draw. Only its 121 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
1C2×#15692996C211yesmaximal, characteristic, complemented
2#121×D103C211yesmaximal, characteristic, complemented
3#20268106C212yesmaximal, complemented
4#20268104C211yesmaximal, characteristic, complemented
5#20268028C212yesmaximal, complemented
6#20268026C212yesmaximal, complemented
7#20267927C211yesmaximal, characteristic, complemented
8#20267926C212yesmaximal, complemented
9#20267924C211yesmaximal, characteristic, complemented
10C22⋊C8×D103C211yesmaximal, characteristic, complemented
11#480×C103C211yesmaximal, characteristic, complemented
12C22×D412—21no—
13C22×D412C2211yescharacteristic, complemented
14C2×D4×D103—21no—
15C2×D4×D103C2211yescharacteristic, complemented
16C22×C4×D103C2211yescharacteristic
17C2×D824C2212yescomplemented
18C2×#13110090C2212yescomplemented
19C2×C8×D103C2212yescomplemented
20#15692996—21no—
21#15692996—21no—
22#15692996C2212yes—
23#15692996C2211yescharacteristic, complemented
24#15692996C2212yescomplemented
25#15692995C2211yescharacteristic
26#15692994—21no—
27#15692993—21no—
28#15692992C2211yescharacteristic, complemented
29C4⋊C4×D103C2211yescharacteristic, complemented
30C2×(C2×D103)⋊C4—21no—
31C22⋊C4×D103—21no—
32#15692954C2212yescomplemented
33#15692943C2212yescomplemented
34#15692941C2212yescomplemented
35#15692941C2212yescomplemented
36C22⋊(C103⋊C8)C2211yescharacteristic, complemented
37(C2×D103)⋊C8C2212yescomplemented
38#121×C103C2211yescharacteristic
39C2×C4⋊C4×C103C2211yescharacteristic, complemented
40#107×C103C2212yescomplemented
41#102×C103C2212yescomplemented
42C22⋊C8×C103C2211yescharacteristic, complemented
43C23×D103—21no—
44C23×D103—21no—
45C23×D103D411yescharacteristic
46C2×D412—21no—
47C2×D412—22no—
48C2×D412—22no—
49C2×D412—21no—
50C2×D412—42no—
51C2×D412—44no—
52C2×D412C2311yescharacteristic
53C2×D412C2312yes—
54C2×C22⋊D103—21no—
55C2×C22⋊D103—21no—
56C2×C22⋊D103—21no—
57D4×D103—42no—
58D4×D103—44no—
59C22×Dic103D411yescharacteristic
60C2×C4×D103—21no—
61C2×C4×D103—42no—
62C2×C4×D103D411yescharacteristic
63C2×C4×D103D411yescharacteristic
64C2×C4×D103C2311yescharacteristic
65C2×C4×D103C2311yescharacteristic
66D824—42no—
67#13110090—42no—
68C2×C103⋊C8C2312yes—
69C8×D103—42no—
70C4⋊Dic103C2311yescharacteristic
71Dic103⋊C4—21no—
72C22⋊Dic103—21no—
73(C2×D103)⋊C4—21no—
74(C2×D103)⋊C4—21no—
75(C2×D103)⋊C4—22no—
76(C2×D103)⋊C4—22no—
77C2×D4×C103—21no—
78C2×D4×C103C2311yescharacteristic
79C22×C4×C103—21no—
80C22×C4×C103C2311yescharacteristic
81C2×C8×C103C2312yes—
82C4⋊C4×C103—21no—
83C4⋊C4×C103C2312yes—
84C4⋊C4×C103C2311yescharacteristic
85C22⋊C4×C103—21no—
86C23×C103—21no—
87C23×C103C2×D411yescharacteristic
88C22×D103—21no—
89C22×D103—22no—
90C22×D103—41no—
91C22×D103—41no—
92C22×D103—42no—
93C22×D103—42no—
94C22×D103—42no—
95C22×D103—42no—
96C22×D103—42no—
97C22×D103—42no—
98C22×D103D814yescomplemented
99C22×D103C2×D411yescharacteristic
100C22×D103C2×D411yescharacteristic
101D4×C103—22no—
102D4×C103—42no—
103C2×C4×C103—22no—
104C2×C4×C103—21no—
105C2×C4×C103—22no—
106C2×C4×C103—42no—
107C2×C4×C103C2×D411yescharacteristic
108C2×C4×C103C2411yescharacteristic
109C22⋊D103—42no—
110C22⋊D103—42no—
111C22⋊D103—42no—
112C2×Dic103—21no—
113C2×Dic103—41no—
114C2×Dic103C2×D411yescharacteristic
115C2×Dic103C2×D411yescharacteristic
116D412—22no—
117D412—22no—
118D412—22no—
119D412—42no—
120D412—42no—
121D412—44no—
122D412—44no—
123C4×D103—22no—
124C4×D103—22no—
125C4×D103—41no—
126C4×D103—41no—
127C4×D103—42no—
128C8×C103—22no—
129C103⋊C8—22no—
130C22×C103—21no—
131C22×C103—21no—
132C22×C103—41no—
133C22×C103—41no—
134C22×C103—41no—
135C22×C103C2×D812yes—
136C22×C103C22×D411yescharacteristic
137C2×D103—21no—
138C2×D103—21no—
139C2×D103—21no—
140C2×D103—21no—
141C2×D103—44no—
142C2×D103—42no—
143C2×D103—41no—
144C2×D103—42no—
145C2×D103—41no—
146C2×D103—41no—
147C2×D103—42no—
148C2×D103—84no—
149C2×D103—84no—
150C2×D103C2×D812yes—
151C2×D103C2×D812yes—
152C4×C103—21no—
153C4×C103—41no—
154C4×C103—42no—
155C4×C103H(5,𝔽2)12yes—
156Dic103—21no—
157Dic103—21no—
158Dic103—41no—
159C2×C103—22no—
160C2×C103—81no—
161C2×C103#53411yescharacteristic
162C2×C103C22×D811yescharacteristic
163C2×C103#57511yescharacteristic
164D103—22no—
165D103—22no—
166D103—82no—
167D103—81no—
168#3186—1031nomaximal, Sylow
169C103#318611yescharacteristic, complemented, Sylow
170C2×#121—1031no—
171C2×#121—1031no—
172#480—1031no—
173#480—1032no—
174#480D10311yescharacteristic, complemented
175#466—1032no—
176#466—1032no—
177#447—1031no—
178#447—1032no—
179#447—1031no—
180C2×C22⋊C8—1031no—
181C22×D4—1031no—
182C22×D4—1031no—
183C22×D4—2061no—
184C22×D4—2061no—
185C23×C4—1031no—
186C2×D8—1032no—
187C2×D8—1032no—
188C22×C8—1032no—
189#121—1031no—
190#121—1031no—
191#121—1032no—
192#121—1031no—
193#121—1032no—
194#121—2061no—
195#121—2061no—
196#121—2061no—
197#121—2061no—
198#121C2×D10311yescharacteristic
199C2×C4⋊C4—1031no—
200C2×C4⋊C4C2×D10311yescharacteristic, complemented
201C2×C22⋊C4—2061no—
202C2×C22⋊C4—2061no—
203#107—1032no—
204#107C2×D10312yescomplemented
205#102—1032no—
206#102—1032no—
207#102—1032no—
208#102C2×D10312yescomplemented
209C22⋊C8—1031no—
210C22⋊C8—1032no—
211C22⋊C8C2×D10311yescharacteristic, complemented
212C24—1031no—
213C24—2061no—
214C24—2061no—
215C2×D4—21no—
216C2×D4—1031no—
217C2×D4—1032no—
218C2×D4—4122no—
219C2×D4—4124no—
220C2×D4—4124no—
221C2×D4—4122no—
222C2×D4—2061no—
223C2×D4—2062no—
224C2×D4—2062no—
225C2×D4—2061no—
226C2×D4—2061no—
227C2×D4—2061no—
228C2×D4—2061no—
229C2×D4C22×D10311yescharacteristic
230C22×C4—21no—
231C22×C4—1031no—
232C22×C4—1031no—
233C22×C4—1031no—
234C22×C4—1031no—
235C22×C4—1031no—
236C22×C4—4122no—
237C22×C4—2061no—
238C22×C4C22×D10311yescharacteristic
239D8—4122no—
240D8—4122no—
241C2×C8—1032no—
242C2×C8—4122no—
243C2×C8C22×D10312yes—
244C4⋊C4—21no—
245C4⋊C4—1031no—
246C4⋊C4—2061no—
247C4⋊C4C22×D10311yescharacteristic
248C4⋊C4C22×D10312yes—
249C22⋊C4—21no—
250C22⋊C4—2061no—
251C22⋊C4—2062no—
252C22⋊C4—2062no—
253C22⋊C4—2061no—
254C22⋊C4—2061no—
255C23—21no—
256C23—1034no—
257C23—1031no—
258C23—1031no—
259C23—4122no—
260C23—4122no—
261C23—4121no—
262C23—4121no—
263C23—4122no—
264C23—4122no—
265C23—4122no—
266C23—4122no—
267C23—2062no—
268C23—2061no—
269C23D4×D10311yescharacteristic
270D4—22no—
271D4—42no—
272D4—4122no—
273D4—4124no—
274D4—4124no—
275D4—4122no—
276D4—4122no—
277D4—4122no—
278D4—4122no—
279D4—2062no—
280D4—2062no—
281D4—2062no—
282C2×C4—22no—
283C2×C4—21no—
284C2×C4—22no—
285C2×C4—42no—
286C2×C4—1031no—
287C2×C4—1031no—
288C2×C4—4121no—
289C2×C4—4121no—
290C2×C4—4122no—
291C2×C4—4121no—
292C2×C4—2061no—
293C2×C4—2062no—
294C2×C4—2062no—
295C2×C4D4×D10311yescharacteristic
296C2×C4C23×D10311yescharacteristic
297C8—22no—
298C8—2062no—
299C22—21no—
300C22—21no—
301C22—41no—
302C22—41no—
303C22—41no—
304C22—8244no—
305C22—8244no—
306C22—1032no—
307C22—1032no—
308C22—4124no—
309C22—4122no—
310C22—4121no—
311C22—4122no—
312C22—4121no—
313C22—4122no—
314C22—4121no—
315C22—2061no—
316C22—2061no—
317C22—2061no—
318C22—2061no—
319C22D8×D10312yes—
320C22C2×D4×D10311yescharacteristic
321C4—21no—
322C4—42no—
323C4—41no—
324C4—4121no—
325C4—2061no—
326C4—2061no—
327C4#1569306712yes—
328C2—22no—
329C2—81no—
330C2—8242no—
331C2—8241no—
332C2—2062no—
333C2—2062no—
334C2#2026835211yescharacteristic
335C2C2×D8×D10311yescharacteristic
336C2#2026859011yescharacteristic
subgroupG/H
centerC22C2×D4×D103
commutator, cosocleC2×C4×C103C24
FrattiniC2×C4C23×D103
Fitting#480×C103C2
socleC22×C103C22×D4
hypercenter#480D103
hypocenterC103#3186
LCSG ▷ C2×C4×C103 ▷ C2×C103 ▷ C103
UCSC1 ◁ C22 ◁ C22×C4 ◁ #480

Complements

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

NH ≅ G/Ntype
1. C2×#15692996C2semidirect
2. #121×D103C2semidirect
3. #20268106C2semidirect
4. #20268104C2semidirect
5. #20268028C2semidirect
6. #20268026C2semidirect
7. #20267927C2semidirect
8. #20267926C2semidirect
9. #20267924C2semidirect
10. C22⋊C8×D103C2semidirect
11. #480×C103C2semidirect
13. C22×D412C22semidirect
15. C2×D4×D103C22semidirect
17. C2×D824C22semidirect
18. C2×#13110090C22semidirect
19. C2×C8×D103C22semidirect
23. #15692996C22semidirect
24. #15692996C22semidirect
28. #15692992C22semidirect
29. C4⋊C4×D103C22semidirect
32. #15692954C22semidirect
33. #15692943C22semidirect
34. #15692941C22semidirect
35. #15692941C22semidirect
36. C22⋊(C103⋊C8)C22semidirect
37. (C2×D103)⋊C8C22semidirect
39. C2×C4⋊C4×C103C22semidirect
40. #107×C103C22semidirect
41. #102×C103C22semidirect
42. C22⋊C8×C103C22semidirect
98. C22×D103D8semidirect
169. C103#3186semidirect
174. #480D103semidirect
200. C2×C4⋊C4C2×D103semidirect
204. #107C2×D103semidirect
208. #102C2×D103semidirect
211. C22⋊C8C2×D103semidirect

Maximal subgroups

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

subgroupindex
C2×#156929962
#121×D1032
#202681062
#202681042
#202680282
#202680262
#202679272
#202679262
#202679242
C22⋊C8×D1032
#480×C1032
#3186103