Finite Group Databasebeta

← #481×D103 #27205040

Subgroups — #481×D103 #27205040

Order 13184.

512 conjugacy classes of subgroups; only the 135 normal subgroups are shown.

normal subgroups only

This group has 512 conjugacy classes of subgroups — too many to draw. Only its 135 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#121×D103C211yesmaximal, characteristic
2C2×C4⋊C4×D103C211yesmaximal, characteristic, complemented
3#20268111C212yesmaximal, complemented
4#20268110C211yesmaximal, characteristic, complemented
5#20268109C211yesmaximal, characteristic, complemented
6#20268108C212yesmaximal, complemented
7#20268107C211yesmaximal, characteristic, complemented
8#106×D103C212yesmaximal, complemented
9#102×D103C212yesmaximal, complemented
10C22⋊C8×D103C211yesmaximal, characteristic, complemented
11#481×C103C211yesmaximal, characteristic, complemented
12C2×D4×D103—21no—
13C2×D4×D103C2211yescharacteristic
14C22×C4×D103—21no—
15C22×C4×D103C2211yescharacteristic
16C2×C8×D103C2212yes—
17#15692996C2211yescharacteristic
18#15692995C2211yescharacteristic
19#15692994—21no—
20#15692993—21no—
21#15692992C2211yescharacteristic
22C2×C4⋊Dic103C2211yescharacteristic, complemented
23C2×Dic103⋊C4—21no—
24C4⋊C4×D103—21no—
25C4⋊C4×D103—21no—
26C4⋊C4×D103C2212yes—
27C4⋊C4×D103C2211yescharacteristic
28C4⋊C4×D103C2212yescomplemented
29C22⋊C4×D103—21no—
30#15692953C2212yescomplemented
31#15692952C2212yescomplemented
32#15692952C2212yescomplemented
33#15692943C2212yescomplemented
34#15692942C2212yescomplemented
35#15692941C2212yescomplemented
36C22⋊(C103⋊C8)C2211yescharacteristic, complemented
37(C2×D103)⋊C8C2212yescomplemented
38#121×C103C2211yescharacteristic
39C2×C4⋊C4×C103C2211yescharacteristic, complemented
40#106×C103C2212yescomplemented
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—21no—
50D4×D103—24no—
51D4×D103—44no—
52C22×Dic103—21no—
53C22×Dic103D411yescharacteristic
54C2×C4×D103—24no—
55C2×C4×D103—21no—
56C2×C4×D103—22no—
57C2×C4×D103—22no—
58C2×C4×D103—44no—
59C2×C4×D103D411yescharacteristic
60C2×C4×D103D411yescharacteristic
61C2×C4×D103C2311yescharacteristic
62C2×C4×D103C2311yescharacteristic
63C2×C103⋊C8C2312yes—
64C8×D103—24no—
65C4⋊Dic103—21no—
66C4⋊Dic103C2312yes—
67C4⋊Dic103C2311yescharacteristic
68Dic103⋊C4—22no—
69Dic103⋊C4—22no—
70Dic103⋊C4—21no—
71C22⋊Dic103—21no—
72(C2×D103)⋊C4—21no—
73(C2×D103)⋊C4—21no—
74C2×D4×C103—21no—
75C2×D4×C103C2311yescharacteristic
76C22×C4×C103—21no—
77C22×C4×C103C2311yescharacteristic
78C2×C8×C103C2312yes—
79C4⋊C4×C103—21no—
80C4⋊C4×C103C2312yes—
81C4⋊C4×C103C2311yescharacteristic
82C22⋊C4×C103—21no—
83C23×C103—21no—
84C23×C103C2×D411yescharacteristic
85C22×D103—22no—
86C22×D103—22no—
87C22×D103—21no—
88C22×D103—42no—
89C22×D103—42no—
90C22×D103—42no—
91C22×D103SD1614yes—
92C22×D103C2×D411yescharacteristic
93C22×D103C2×D411yescharacteristic
94D4×C103—22no—
95D4×C103—42no—
96C2×C4×C103—22no—
97C2×C4×C103—21no—
98C2×C4×C103—22no—
99C2×C4×C103—42no—
100C2×C4×C103C2×D411yescharacteristic
101C2×C4×C103C2411yescharacteristic
102C22⋊D103—42no—
103C22⋊D103—42no—
104C22⋊D103—42no—
105C2×Dic103—22no—
106C2×Dic103—21no—
107C2×Dic103—22no—
108C2×Dic103—42no—
109C2×Dic103C2×D411yescharacteristic
110C2×Dic103C2×D411yescharacteristic
111D412—22no—
112D412—42no—
113C4×D103—22no—
114C4×D103—22no—
115C4×D103—22no—
116C4×D103—44no—
117C4×D103—42no—
118C4×D103—44no—
119C4×D103#4114yes—
120C8×C103—22no—
121C103⋊C8—22no—
122C22×C103—21no—
123C22×C103—21no—
124C22×C103—41no—
125C22×C103—41no—
126C22×C103—41no—
127C22×C103C2×SD1612yes—
128C22×C103C22×D411yescharacteristic
129C2×D103—21no—
130C2×D103—21no—
131C2×D103—28no—
132C2×D103—41no—
133C2×D103—41no—
134C2×D103—41no—
135C2×D103—84no—
136C2×D103#12312yes—
137C2×D103C2×SD1612yes—
138C2×D103C2×SD1612yes—
139C2×D103AGL(1,ℤ/8)12yes—
140C4×C103—21no—
141C4×C103—41no—
142C4×C103—42no—
143C4×C103C2×#4112yes—
144Dic103—21no—
145Dic103—41no—
146Dic103—42no—
147Dic103#12312yes—
148C2×C103—22no—
149C2×C103—81no—
150C2×C103C2×#12311yescharacteristic
151C2×C103C22×SD1611yescharacteristic
152C2×C103C2×AGL(1,ℤ/8)11yescharacteristic
153D103—22no—
154D103—81no—
155D103#48114yesdirect product factor
156C2×#481—1031nomaximal, Sylow
157C103C2×#48111yescharacteristic, complemented, Sylow
158C2×#121—1031no—
159C22×C4⋊C4—1031no—
160#481—1031no—
161#481—1031no—
162#481—1032no—
163#481—1032no—
164#481—1031no—
165#481D10311yescharacteristic, direct product factor
166C2×#106—1032no—
167C2×#102—1032no—
168C2×C22⋊C8—1031no—
169C22×D4—1031no—
170C22×D4—2061no—
171C23×C4—1031no—
172C23×C4—2061no—
173C22×C8—1032no—
174#121—1031no—
175#121—1031no—
176#121—1031no—
177#121—2061no—
178#121—2061no—
179#121C2×D10311yescharacteristic
180C2×C4⋊C4—1031no—
181C2×C4⋊C4—1032no—
182C2×C4⋊C4—1032no—
183C2×C4⋊C4—1031no—
184C2×C4⋊C4—2061no—
185C2×C4⋊C4—2061no—
186C2×C4⋊C4—2061no—
187C2×C4⋊C4C2×D10311yescharacteristic, complemented
188C2×C22⋊C4—2061no—
189#106—1032no—
190#106—1032no—
191#106—1032no—
192#106C2×D10312yescomplemented
193#102—1032no—
194#102—1032no—
195#102—1032no—
196#102C2×D10312yescomplemented
197C22⋊C8—1031no—
198C22⋊C8—1032no—
199C22⋊C8C2×D10311yescharacteristic, complemented
200C24—1031no—
201C24—2061no—
202C2×D4—21no—
203C2×D4—1031no—
204C2×D4—4124no—
205C2×D4—2061no—
206C2×D4—2064no—
207C2×D4—2061no—
208C2×D4—2061no—
209C2×D4—2061no—
210C2×D4C22×D10311yescharacteristic
211C22×C4—21no—
212C22×C4—1031no—
213C22×C4—1031no—
214C22×C4—1031no—
215C22×C4—1031no—
216C22×C4—1031no—
217C22×C4—4124no—
218C22×C4—2064no—
219C22×C4—2061no—
220C22×C4—2062no—
221C22×C4—2062no—
222C22×C4—2061no—
223C22×C4C22×D10311yescharacteristic
224C2×C8—1032no—
225C2×C8—2064no—
226C2×C8C22×D10312yes—
227C4⋊C4—21no—
228C4⋊C4—1032no—
229C4⋊C4—1031no—
230C4⋊C4—2062no—
231C4⋊C4—2062no—
232C4⋊C4—2061no—
233C4⋊C4—2061no—
234C4⋊C4C22×D10312yes—
235C4⋊C4C22×D10311yescharacteristic
236C22⋊C4—21no—
237C22⋊C4—2061no—
238C22⋊C4—2061no—
239C22⋊C4—2061no—
240C23—21no—
241C23—1031no—
242C23—1031no—
243C23—1034no—
244C23—4122no—
245C23—4122no—
246C23—4122no—
247C23—2062no—
248C23—2062no—
249C23—2061no—
250C23D4×D10311yescharacteristic
251D4—22no—
252D4—42no—
253D4—4122no—
254D4—4122no—
255D4—4122no—
256D4—4122no—
257D4—2062no—
258C2×C4—22no—
259C2×C4—21no—
260C2×C4—22no—
261C2×C4—42no—
262C2×C4—1031no—
263C2×C4—1034no—
264C2×C4—1031no—
265C2×C4—4124no—
266C2×C4—4122no—
267C2×C4—4124no—
268C2×C4—4122no—
269C2×C4—2062no—
270C2×C4—2062no—
271C2×C4—2062no—
272C2×C4—2061no—
273C2×C4—2062no—
274C2×C4—2062no—
275C2×C4D4×D10311yescharacteristic
276C2×C4C23×D10311yescharacteristic
277C8—22no—
278C8—2062no—
279C22—21no—
280C22—21no—
281C22—41no—
282C22—41no—
283C22—41no—
284C22—8244no—
285C22—1032no—
286C22—1032no—
287C22—1032no—
288C22—1032no—
289C22—4121no—
290C22—4121no—
291C22—4121no—
292C22—2068no—
293C22—2061no—
294C22—2061no—
295C22SD16×D10312yes—
296C22C2×D4×D10311yescharacteristic
297C4—21no—
298C4—41no—
299C4—42no—
300C4—1032no—
301C4—4121no—
302C4—4122no—
303C4—2061no—
304C4#41×D10312yes—
305C2—22no—
306C2—81no—
307C2—8241no—
308C2—1034no—
309C2—2062no—
310C2#123×D10311yescharacteristic
311C2C2×SD16×D10311yescharacteristic
312C2AGL(1,ℤ/8)×D10311yescharacteristic
subgroupG/H
centerC22C2×D4×D103
commutator, cosocleC2×C4×C103C24
FrattiniC2×C4C23×D103
Fitting#481×C103C2
socleC22×C103C22×D4
prime radical#121×D103C2
hypercenter#481D103
hypocenterC103C2×#481
LCSG ▷ C2×C4×C103 ▷ C2×C103 ▷ C103
UCSC1 ◁ C22 ◁ C22×C4 ◁ #481

Complements

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

NH ≅ G/Ntype
2. C2×C4⋊C4×D103C2semidirect
3. #20268111C2semidirect
4. #20268110C2semidirect
5. #20268109C2semidirect
6. #20268108C2semidirect
7. #20268107C2semidirect
8. #106×D103C2semidirect
9. #102×D103C2semidirect
10. C22⋊C8×D103C2semidirect
11. #481×C103C2semidirect
22. C2×C4⋊Dic103C22semidirect
28. C4⋊C4×D103C22semidirect
30. #15692953C22semidirect
31. #15692952C22semidirect
32. #15692952C22semidirect
33. #15692943C22semidirect
34. #15692942C22semidirect
35. #15692941C22semidirect
36. C22⋊(C103⋊C8)C22semidirect
37. (C2×D103)⋊C8C22semidirect
39. C2×C4⋊C4×C103C22semidirect
40. #106×C103C22semidirect
41. #102×C103C22semidirect
42. C22⋊C8×C103C22semidirect
155. D103#481direct (N × H)
157. C103C2×#481semidirect
165. #481D103direct (N × H)
187. C2×C4⋊C4C2×D103semidirect
192. #106C2×D103semidirect
196. #102C2×D103semidirect
199. C22⋊C8C2×D103semidirect

Maximal subgroups

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

subgroupindex
#121×D1032
C2×C4⋊C4×D1032
#202681112
#202681102
#202681092
#202681082
#202681072
#106×D1032
#102×D1032
C22⋊C8×D1032
#481×C1032
C2×#481103