Finite Group Databasebeta

← #484×D103 #27205046

Subgroups — #484×D103 #27205046

Order 13184.

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

normal subgroups only

This group has 460 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
1C22⋊Q8×D103C211yesmaximal, characteristic
2C2×C4⋊C4×D103C211yesmaximal, characteristic
3#20268128C212yesmaximal, complemented
4#20268127C211yesmaximal, characteristic, complemented
5#20268126C211yesmaximal, characteristic, complemented
6#20268125C212yesmaximal, complemented
7#20268124C211yesmaximal, characteristic, complemented
8#107×D103C212yesmaximal, complemented
9#103×D103C212yesmaximal, complemented
10C22⋊C8×D103C211yesmaximal, characteristic
11#484×C103C211yesmaximal, characteristic, complemented
12C2×Q8×D103C2211yescharacteristic
13C22×C4×D103—21no—
14C22×C4×D103C2211yescharacteristic
15C2×C8×D103C2212yes—
16#15693001C2211yescharacteristic
17#15693000C2211yescharacteristic
18#15692999—21no—
19#15692998—21no—
20#15692997C2211yescharacteristic
21C2×C4⋊Dic103C2211yescharacteristic
22C2×Dic103⋊C4—21no—
23C4⋊C4×D103—21no—
24C4⋊C4×D103—21no—
25C4⋊C4×D103—21no—
26C4⋊C4×D103C2212yes—
27C4⋊C4×D103C2211yescharacteristic
28C4⋊C4×D103C2212yes—
29C22⋊C4×D103—21no—
30#15692955C2212yescomplemented
31#15692954C2212yescomplemented
32#15692954C2212yescomplemented
33#15692946C2212yescomplemented
34#15692945C2212yescomplemented
35#15692944C2212yescomplemented
36C22⋊(C103⋊C8)C2211yescharacteristic
37(C2×D103)⋊C8C2212yes—
38C22⋊Q8×C103C2211yescharacteristic
39C2×C4⋊C4×C103C2211yescharacteristic
40#107×C103C2212yescomplemented
41#103×C103C2212yescomplemented
42C22⋊C8×C103C2211yescharacteristic
43C23×D103D411yescharacteristic
44C2×Dic206—21no—
45C2×Dic206C2311yescharacteristic
46Q8×D103—24no—
47C22×Dic103—21no—
48C22×Dic103D411yescharacteristic
49C2×C4×D103—24no—
50C2×C4×D103—21no—
51C2×C4×D103—21no—
52C2×C4×D103—22no—
53C2×C4×D103—22no—
54C2×C4×D103—44no—
55C2×C4×D103D411yescharacteristic
56C2×C4×D103D411yescharacteristic
57C2×C4×D103C2311yescharacteristic
58C2×C4×D103C2311yescharacteristic
59C2×C103⋊C8C2312yes—
60C8×D103—24no—
61C4⋊Dic103—21no—
62C4⋊Dic103—21no—
63C4⋊Dic103C2312yes—
64C4⋊Dic103C2311yescharacteristic
65Dic103⋊C4—21no—
66Dic103⋊C4—22no—
67Dic103⋊C4—22no—
68Dic103⋊C4—21no—
69Dic103⋊C4—21no—
70C22⋊Dic103—21no—
71(C2×D103)⋊C4—21no—
72(C2×D103)⋊C4—21no—
73C2×Q8×C103C2311yescharacteristic
74C22×C4×C103—21no—
75C22×C4×C103C2311yescharacteristic
76C2×C8×C103C2312yes—
77C4⋊C4×C103—21no—
78C4⋊C4×C103—21no—
79C4⋊C4×C103C2312yes—
80C4⋊C4×C103C2311yescharacteristic
81C22⋊C4×C103—21no—
82C23×C103C2×D411yescharacteristic
83C22×D103—22no—
84C22×D103—22no—
85C22×D103Q1614yes—
86C22×D103C2×D411yescharacteristic
87C22×D103C2×D411yescharacteristic
88Q8×C103—22no—
89C2×C4×C103—22no—
90C2×C4×C103—21no—
91C2×C4×C103—21no—
92C2×C4×C103—22no—
93C2×C4×C103—42no—
94C2×C4×C103C2×D411yescharacteristic
95C2×C4×C103C2411yescharacteristic
96C2×Dic103—22no—
97C2×Dic103—21no—
98C2×Dic103—21no—
99C2×Dic103—22no—
100C2×Dic103—42no—
101C2×Dic103C2×D411yescharacteristic
102C2×Dic103C2×D411yescharacteristic
103C4×D103—22no—
104C4×D103—22no—
105C4×D103—22no—
106C4×D103—44no—
107C4×D103—42no—
108C4×D103—42no—
109C4×D103—44no—
110C4×D103#4114yes—
111Dic206—22no—
112Dic206—42no—
113C8×C103—22no—
114C103⋊C8—22no—
115C22×C103—21no—
116C22×C103—21no—
117C22×C103C2×Q1612yes—
118C22×C103C22×D411yescharacteristic
119C2×D103—21no—
120C2×D103—21no—
121C2×D103—28no—
122C2×D103#12312yes—
123C2×D103C2×Q1612yes—
124C2×D103C2×Q1612yes—
125C2×D103AGL(1,ℤ/8)12yes—
126C4×C103—21no—
127C4×C103—41no—
128C4×C103—42no—
129C4×C103—41no—
130C4×C103C2×#4112yes—
131Dic103—21no—
132Dic103—41no—
133Dic103—42no—
134Dic103—41no—
135Dic103#12312yes—
136C2×C103—22no—
137C2×C103C2×#12311yescharacteristic
138C2×C103C22×Q1611yescharacteristic
139C2×C103C2×AGL(1,ℤ/8)11yescharacteristic
140D103—22no—
141D103#48414yesdirect product factor
142C2×#484—1031nomaximal, Sylow
143C103C2×#48411yescharacteristic, complemented, Sylow
144C2×C22⋊Q8—1031no—
145C22×C4⋊C4—1031no—
146#484—1031no—
147#484—1031no—
148#484—1032no—
149#484—1032no—
150#484—1031no—
151#484D10311yescharacteristic, direct product factor
152C2×#107—1032no—
153C2×#103—1032no—
154C2×C22⋊C8—1031no—
155C22×Q8—1031no—
156C23×C4—1031no—
157C23×C4—2061no—
158C22×C8—1032no—
159C22⋊Q8—1031no—
160C22⋊Q8—1031no—
161C22⋊Q8—1031no—
162C22⋊Q8—2061no—
163C22⋊Q8—2061no—
164C22⋊Q8C2×D10311yescharacteristic
165C2×C4⋊C4—1031no—
166C2×C4⋊C4—1032no—
167C2×C4⋊C4—1032no—
168C2×C4⋊C4—1031no—
169C2×C4⋊C4—2061no—
170C2×C4⋊C4—2061no—
171C2×C4⋊C4—2061no—
172C2×C4⋊C4—2061no—
173C2×C4⋊C4C2×D10311yescharacteristic
174C2×C22⋊C4—2061no—
175#107—1032no—
176#107—1032no—
177#107—1032no—
178#107C2×D10312yescomplemented
179#103—1032no—
180#103—1032no—
181#103—1032no—
182#103C2×D10312yescomplemented
183C22⋊C8—1031no—
184C22⋊C8—1032no—
185C22⋊C8C2×D10311yescharacteristic
186C24—1031no—
187C2×Q8—1031no—
188C2×Q8—2061no—
189C2×Q8—2064no—
190C2×Q8C22×D10311yescharacteristic
191C22×C4—21no—
192C22×C4—1031no—
193C22×C4—1031no—
194C22×C4—1031no—
195C22×C4—1031no—
196C22×C4—1031no—
197C22×C4—4124no—
198C22×C4—2064no—
199C22×C4—2061no—
200C22×C4—2061no—
201C22×C4—2062no—
202C22×C4—2062no—
203C22×C4—2061no—
204C22×C4C22×D10311yescharacteristic
205C2×C8—1032no—
206C2×C8—2064no—
207C2×C8C22×D10312yes—
208C4⋊C4—21no—
209C4⋊C4—21no—
210C4⋊C4—1032no—
211C4⋊C4—1031no—
212C4⋊C4—2062no—
213C4⋊C4—2062no—
214C4⋊C4—2061no—
215C4⋊C4—2061no—
216C4⋊C4—2061no—
217C4⋊C4—2061no—
218C4⋊C4—2061no—
219C4⋊C4C22×D10312yes—
220C4⋊C4C22×D10311yescharacteristic
221C22⋊C4—21no—
222C22⋊C4—2061no—
223C22⋊C4—2061no—
224C22⋊C4—2061no—
225C23—1031no—
226C23—1031no—
227C23—1034no—
228C23—2062no—
229C23—2062no—
230C23D4×D10311yescharacteristic
231Q8—22no—
232Q8—4122no—
233Q8—2062no—
234C2×C4—22no—
235C2×C4—21no—
236C2×C4—21no—
237C2×C4—22no—
238C2×C4—42no—
239C2×C4—1031no—
240C2×C4—1034no—
241C2×C4—1031no—
242C2×C4—4124no—
243C2×C4—4122no—
244C2×C4—4122no—
245C2×C4—4124no—
246C2×C4—4122no—
247C2×C4—2062no—
248C2×C4—2062no—
249C2×C4—2062no—
250C2×C4—2061no—
251C2×C4—2061no—
252C2×C4—2062no—
253C2×C4—2062no—
254C2×C4D4×D10311yescharacteristic
255C2×C4C23×D10311yescharacteristic
256C8—22no—
257C8—2062no—
258C22—21no—
259C22—21no—
260C22—1032no—
261C22—1032no—
262C22—1032no—
263C22—1032no—
264C22—2068no—
265C22—2061no—
266C22—2061no—
267C22Q16×D10312yes—
268C22C2×D4×D10311yescharacteristic
269C4—21no—
270C4—41no—
271C4—42no—
272C4—41no—
273C4—1032no—
274C4—4121no—
275C4—4122no—
276C4—4121no—
277C4—2061no—
278C4#41×D10312yes—
279C2—22no—
280C2—1034no—
281C2—2062no—
282C2#123×D10311yescharacteristic
283C2C2×Q16×D10311yescharacteristic
284C2AGL(1,ℤ/8)×D10311yescharacteristic
subgroupG/H
centerC22C2×D4×D103
commutator, cosocleC2×C4×C103C24
FrattiniC2×C4C23×D103
Fitting#484×C103C2
socleC22×C103C22×D4
prime radicalC23×D103D4
hypercenter#484D103
hypocenterC103C2×#484
LCSG ▷ C2×C4×C103 ▷ C2×C103 ▷ C103
UCSC1 ◁ C22 ◁ C22×C4 ◁ #484

Complements

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

NH ≅ G/Ntype
3. #20268128C2semidirect
4. #20268127C2semidirect
5. #20268126C2semidirect
6. #20268125C2semidirect
7. #20268124C2semidirect
8. #107×D103C2semidirect
9. #103×D103C2semidirect
11. #484×C103C2semidirect
30. #15692955C22semidirect
31. #15692954C22semidirect
32. #15692954C22semidirect
33. #15692946C22semidirect
34. #15692945C22semidirect
35. #15692944C22semidirect
40. #107×C103C22semidirect
41. #103×C103C22semidirect
141. D103#484direct (N × H)
143. C103C2×#484semidirect
151. #484D103direct (N × H)
178. #107C2×D103semidirect
182. #103C2×D103semidirect

Maximal subgroups

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

subgroupindex
C22⋊Q8×D1032
C2×C4⋊C4×D1032
#202681282
#202681272
#202681262
#202681252
#202681242
#107×D1032
#103×D1032
C22⋊C8×D1032
#484×C1032
C2×#484103