Finite Group Databasebeta

← #27205942

Subgroups — #27205942

Order 13184.

514 conjugacy classes of subgroups; only the 115 normal subgroups are shown.

normal subgroups only

This group has 514 conjugacy classes of subgroups — too many to draw. Only its 115 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×#15692992C211yesmaximal, characteristic, complemented
2#121×D103C211yesmaximal, characteristic, complemented
3#20268110C211yesmaximal, characteristic, complemented
4#20268108C212yesmaximal, complemented
5#20268107C211yesmaximal, characteristic, complemented
6#20268043C212yesmaximal, complemented
7#20268041C212yesmaximal, complemented
8#20267925C211yesmaximal, characteristic, complemented
9#20267923C212yesmaximal, complemented
10#20267753C211yesmaximal, characteristic, complemented
11#447×C103C211yesmaximal, characteristic, complemented
12C22×C22⋊D103—21no—
13C2×D4×D103—21no—
14C2×D4×D103C2211yescharacteristic, complemented
15C22×C4×D103C2211yescharacteristic
16C2×#13110090C2212yescomplemented
17C2×#13110088C2212yescomplemented
18#15692996C2211yescharacteristic, complemented
19#15692995C2211yescharacteristic
20#15692994—21no—
21#15692993—21no—
22#15692992—21no—
23#15692992—21no—
24#15692992C2212yes—
25#15692992C2211yescharacteristic, complemented
26#15692992C2212yescomplemented
27C2×C4⋊Dic103C2211yescharacteristic, complemented
28C4⋊C4×D103C2211yescharacteristic, complemented
29C2×C22⋊Dic103—21no—
30C22⋊C4×D103—21no—
31#15692953C2212yescomplemented
32#15692952C2212yescomplemented
33#15692943C2212yescomplemented
34#15692942C2212yescomplemented
35#15692942C2212yescomplemented
36C22⋊(C103⋊C8)C2211yescharacteristic, complemented
37(C2×D103)⋊C8C2212yescomplemented
38C22×D4×C103C2211yescharacteristic, complemented
39C2×D8×C103C2212yescomplemented
40#121×C103C2211yescharacteristic
41#102×C103C2212yescomplemented
42C22⋊C8×C103C2211yescharacteristic, complemented
43C23×D103—21no—
44C23×D103D411yescharacteristic
45C2×D412—21no—
46C2×D412C2311yescharacteristic
47C2×C22⋊D103—21no—
48C2×C22⋊D103—21no—
49C2×C22⋊D103—22no—
50C2×C22⋊D103—22no—
51C2×C22⋊D103—21no—
52C2×C22⋊D103—44no—
53D4×D103—42no—
54D4×D103—44no—
55C22×Dic103—21no—
56C22×Dic103D411yescharacteristic
57C2×C4×D103—21no—
58C2×C4×D103—42no—
59C2×C4×D103D411yescharacteristic
60C2×C4×D103D411yescharacteristic
61C2×C4×D103C2311yescharacteristic
62C2×C4×D103C2311yescharacteristic
63#13110090—42no—
64#13110088—42no—
65C2×C103⋊C8C2312yes—
66C4⋊Dic103—21no—
67C4⋊Dic103C2311yescharacteristic
68C4⋊Dic103C2312yes—
69Dic103⋊C4—21no—
70C22⋊Dic103—21no—
71C22⋊Dic103—22no—
72C22⋊Dic103—22no—
73(C2×D103)⋊C4—21no—
74(C2×D103)⋊C4—21no—
75C24×C103—21no—
76C2×D4×C103—21no—
77C2×D4×C103—21no—
78C2×D4×C103—42no—
79C2×D4×C103C2311yescharacteristic
80C2×D4×C103C2312yes—
81C22×C4×C103C2311yescharacteristic
82D8×C103—42no—
83C2×C8×C103C2312yes—
84C4⋊C4×C103C2311yescharacteristic
85C22⋊C4×C103—21no—
86C23×C103—21no—
87C23×C103—22no—
88C23×C103—42no—
89C23×C103—42no—
90C23×C103—42no—
91C23×C103C2×D411yescharacteristic
92C22×D103—22no—
93C22×D103—22no—
94C22×D103—21no—
95C22×D103—41no—
96C22×D103—42no—
97C22×D103—42no—
98C22×D103—42no—
99C22×D103C2×D411yescharacteristic
100C22×D103C2×D411yescharacteristic
101D4×C103—22no—
102D4×C103—22no—
103D4×C103—22no—
104D4×C103—42no—
105D4×C103—42no—
106C2×C4×C103—22no—
107C2×C4×C103—21no—
108C2×C4×C103C2×D411yescharacteristic
109C2×C4×C103C2411yescharacteristic
110C22⋊D103—42no—
111C22⋊D103—42no—
112C22⋊D103—44no—
113C22⋊D103—42no—
114C22⋊D103—44no—
115C2×Dic103—21no—
116C2×Dic103—22no—
117C2×Dic103—41no—
118C2×Dic103—42no—
119C2×Dic103C2×D411yescharacteristic
120C2×Dic103C2×D411yescharacteristic
121D412—22no—
122D412—42no—
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—42no—
134C22×C103—42no—
135C22×C103—41no—
136C22×C103—41no—
137C22×C103—42no—
138C22×C103—84no—
139C22×C103AGL(1,ℤ/8)12yes—
140C22×C103C22×D411yescharacteristic
141C2×D103—21no—
142C2×D103—21no—
143C2×D103—21no—
144C2×D103—21no—
145C2×D103—21no—
146C2×D103—44no—
147C2×D103—41no—
148C2×D103—41no—
149C2×D103—41no—
150C2×D103—84no—
151C2×D103AGL(1,ℤ/8)12yes—
152C4×C103—21no—
153C4×C103—41no—
154C4×C103H(5,𝔽2)12yes—
155Dic103—21no—
156Dic103—21no—
157Dic103—41no—
158Dic103—42no—
159C2×C103—22no—
160C2×C103—81no—
161C2×C103—82no—
162C2×C103#53411yescharacteristic
163C2×C103C2×AGL(1,ℤ/8)11yescharacteristic
164C2×C103C2×AGL(1,ℤ/8)11yescharacteristic
165D103—22no—
166D103—41no—
167D103—81no—
168#3192—1031nomaximal, Sylow
169C103#319211yescharacteristic, complemented, Sylow
170C2×#121—1031no—
171C2×#121—1031no—
172#481—1031no—
173#481—1032no—
174#481—1031no—
175#469—1032no—
176#469—1032no—
177#447—1031no—
178#447—1032no—
179#447D10311yescharacteristic, complemented
180#407—1031no—
181C22×D4—1031no—
182C22×D4—2061no—
183C22×D4—2061no—
184C22×D4C2×D10311yescharacteristic, complemented
185C23×C4—1031no—
186C2×D8—1032no—
187C2×D8C2×D10312yescomplemented
188C2×M16—1032no—
189#121—1032no—
190#121—1031no—
191#121—1032no—
192#121—1031no—
193#121—1031no—
194#121—2061no—
195#121—2061no—
196#121—2061no—
197#121—2061no—
198#121C2×D10311yescharacteristic
199C2×C4⋊C4—1031no—
200C2×C4⋊C4—1031no—
201C2×C22⋊C4—2061no—
202C2×C22⋊C4—2061no—
203#106—1032no—
204#106—1032no—
205#102—1032no—
206#102—1032no—
207#102—1032no—
208#102C2×D10312yescomplemented
209C22⋊C8—1031no—
210C22⋊C8—1032no—
211C22⋊C8C2×D10311yescharacteristic, complemented
212C24—21no—
213C24—1031no—
214C24—2061no—
215C2×D4—21no—
216C2×D4—21no—
217C2×D4—42no—
218C2×D4—1031no—
219C2×D4—4124no—
220C2×D4—4124no—
221C2×D4—4122no—
222C2×D4—2061no—
223C2×D4—2061no—
224C2×D4—2062no—
225C2×D4—2061no—
226C2×D4—2062no—
227C2×D4—2061no—
228C2×D4C22×D10311yescharacteristic
229C2×D4C22×D10312yes—
230C22×C4—1031no—
231C22×C4—1031no—
232C22×C4—1031no—
233C22×C4—1031no—
234C22×C4—1031no—
235C22×C4—4122no—
236C22×C4—2061no—
237C22×C4—2061no—
238C22×C4C22×D10311yescharacteristic
239D8—42no—
240D8—4122no—
241M16—4122no—
242C2×C8—1032no—
243C2×C8C22×D10312yes—
244C4⋊C4—1031no—
245C4⋊C4—1032no—
246C4⋊C4—2061no—
247C4⋊C4—2061no—
248C4⋊C4C22×D10311yescharacteristic
249C22⋊C4—21no—
250C22⋊C4—2061no—
251C22⋊C4—2061no—
252C22⋊C4—2062no—
253C22⋊C4—2062no—
254C22⋊C4—2061no—
255C23—21no—
256C23—22no—
257C23—42no—
258C23—42no—
259C23—42no—
260C23—1031no—
261C23—1031no—
262C23—4121no—
263C23—4122no—
264C23—4122no—
265C23—4122no—
266C23—2062no—
267C23—2061no—
268C23—2062no—
269C23D4×D10311yescharacteristic
270D4—22no—
271D4—22no—
272D4—22no—
273D4—42no—
274D4—42no—
275D4—4122no—
276D4—4124no—
277D4—4124no—
278D4—4122no—
279D4—4122no—
280D4—4122no—
281D4—2062no—
282C2×C4—22no—
283C2×C4—21no—
284C2×C4—1031no—
285C2×C4—1031no—
286C2×C4—4121no—
287C2×C4—4121no—
288C2×C4—4122no—
289C2×C4—4122no—
290C2×C4—4121no—
291C2×C4—2062no—
292C2×C4—2061no—
293C2×C4—2062no—
294C2×C4—2062no—
295C2×C4D4×D10311yescharacteristic
296C2×C4C23×D10311yescharacteristic
297C8—22no—
298C8—2062no—
299C22—21no—
300C22—21no—
301C22—42no—
302C22—41no—
303C22—41no—
304C22—42no—
305C22—42no—
306C22—41no—
307C22—84no—
308C22—8244no—
309C22—1032no—
310C22—4124no—
311C22—4121no—
312C22—4121no—
313C22—4121no—
314C22—2061no—
315C22—2061no—
316C22—2061no—
317C22—2061no—
318C22—2061no—
319C22#1569304512yes—
320C22C2×D4×D10311yescharacteristic
321C4—21no—
322C4—41no—
323C4—4122no—
324C4—4121no—
325C4—2061no—
326C4—2061no—
327C4#1569306612yes—
328C2—22no—
329C2—82no—
330C2—81no—
331C2—8241no—
332C2—4121no—
333C2—2062no—
334C2#2026835111yescharacteristic
335C2AGL(1,ℤ/8)×D10311yescharacteristic
336C2C2×#1569304511yescharacteristic
subgroupG/H
centerC22C2×D4×D103
commutator, cosocleC2×C4×C103C24
FrattiniC2×C4C23×D103
Fitting#447×C103C2
socleC22×C103C22×D4
hypercenter#447D103
hypocenterC103#3192
LCSG ▷ C2×C4×C103 ▷ C2×C103 ▷ C103
UCSC1 ◁ C22 ◁ C22×C4 ◁ #447

Complements

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

NH ≅ G/Ntype
1. C2×#15692992C2semidirect
2. #121×D103C2semidirect
3. #20268110C2semidirect
4. #20268108C2semidirect
5. #20268107C2semidirect
6. #20268043C2semidirect
7. #20268041C2semidirect
8. #20267925C2semidirect
9. #20267923C2semidirect
10. #20267753C2semidirect
11. #447×C103C2semidirect
14. C2×D4×D103C22semidirect
16. C2×#13110090C22semidirect
17. C2×#13110088C22semidirect
18. #15692996C22semidirect
25. #15692992C22semidirect
26. #15692992C22semidirect
27. C2×C4⋊Dic103C22semidirect
28. C4⋊C4×D103C22semidirect
31. #15692953C22semidirect
32. #15692952C22semidirect
33. #15692943C22semidirect
34. #15692942C22semidirect
35. #15692942C22semidirect
36. C22⋊(C103⋊C8)C22semidirect
37. (C2×D103)⋊C8C22semidirect
38. C22×D4×C103C22semidirect
39. C2×D8×C103C22semidirect
41. #102×C103C22semidirect
42. C22⋊C8×C103C22semidirect
169. C103#3192semidirect
179. #447D103semidirect
184. C22×D4C2×D103semidirect
187. C2×D8C2×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×#156929922
#121×D1032
#202681102
#202681082
#202681072
#202680432
#202680412
#202679252
#202679232
#202677532
#447×C1032
#3192103