Finite Group Databasebeta

← #483×D101 #27181006

Subgroups — #483×D101 #27181006

Order 12928.

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×D101C211yesmaximal, characteristic
2C2×C4⋊C4×D101C211yesmaximal, characteristic
3#20265509C212yesmaximal, complemented
4#20265508C211yesmaximal, characteristic, complemented
5#20265507C211yesmaximal, characteristic, complemented
6#20265506C212yesmaximal, complemented
7#20265505C211yesmaximal, characteristic, complemented
8#106×D101C212yesmaximal, complemented
9#103×D101C212yesmaximal, complemented
10C22⋊C8×D101C211yesmaximal, characteristic
11#483×C101C211yesmaximal, characteristic, complemented
12C2×Q8×D101C2211yescharacteristic
13C22×C4×D101—21no—
14C22×C4×D101C2211yescharacteristic
15C2×C8×D101C2212yes—
16#15692235C2211yescharacteristic
17#15692234C2211yescharacteristic
18#15692233—21no—
19#15692232—21no—
20#15692231C2211yescharacteristic
21C2×C4⋊Dic101C2211yescharacteristic
22C2×#13108053—21no—
23C4⋊C4×D101—21no—
24C4⋊C4×D101—21no—
25C4⋊C4×D101—21no—
26C4⋊C4×D101C2212yes—
27C4⋊C4×D101C2212yes—
28C4⋊C4×D101C2211yescharacteristic
29C22⋊C4×D101—21no—
30#15692187C2212yescomplemented
31#15692186C2212yescomplemented
32#15692186C2212yescomplemented
33#15692180C2212yescomplemented
34#15692179C2212yescomplemented
35#15692178C2212yescomplemented
36C22⋊#11717579C2211yescharacteristic
37#15692167C2212yes—
38C22⋊Q8×C101C2211yescharacteristic
39C2×C4⋊C4×C101C2211yescharacteristic
40#106×C101C2212yescomplemented
41#103×C101C2212yescomplemented
42C22⋊C8×C101C2211yescharacteristic
43C23×D101D411yescharacteristic
44C2×Dic202—21no—
45C2×Dic202C2311yescharacteristic
46Q8×D101—24no—
47C22×Dic101—21no—
48C22×Dic101D411yescharacteristic
49C2×C4×D101—24no—
50C2×C4×D101—22no—
51C2×C4×D101—22no—
52C2×C4×D101—21no—
53C2×C4×D101—21no—
54C2×C4×D101—44no—
55C2×C4×D101D411yescharacteristic
56C2×C4×D101D411yescharacteristic
57C2×C4×D101C2311yescharacteristic
58C2×C4×D101C2311yescharacteristic
59C2×#11717579C2312yes—
60C8×D101—24no—
61C4⋊Dic101—21no—
62C4⋊Dic101—21no—
63C4⋊Dic101C2312yes—
64C4⋊Dic101C2311yescharacteristic
65#13108053—21no—
66#13108053—22no—
67#13108053—22no—
68#13108053—21no—
69#13108053—21no—
70C22⋊Dic101—21no—
71#13108051—21no—
72#13108051—21no—
73C2×Q8×C101C2311yescharacteristic
74C22×C4×C101—21no—
75C22×C4×C101C2311yescharacteristic
76C2×C8×C101C2312yes—
77C4⋊C4×C101—21no—
78C4⋊C4×C101—21no—
79C4⋊C4×C101C2312yes—
80C4⋊C4×C101C2311yescharacteristic
81C22⋊C4×C101—21no—
82C23×C101C2×D411yescharacteristic
83C22×D101—22no—
84C22×D101—22no—
85C22×D101SD1614yes—
86C22×D101C2×D411yescharacteristic
87C22×D101C2×D411yescharacteristic
88Q8×C101—22no—
89C2×C4×C101—22no—
90C2×C4×C101—21no—
91C2×C4×C101—21no—
92C2×C4×C101—22no—
93C2×C4×C101—42no—
94C2×C4×C101C2×D411yescharacteristic
95C2×C4×C101C2411yescharacteristic
96C2×Dic101—22no—
97C2×Dic101—21no—
98C2×Dic101—21no—
99C2×Dic101—22no—
100C2×Dic101—42no—
101C2×Dic101C2×D411yescharacteristic
102C2×Dic101C2×D411yescharacteristic
103C4×D101—22no—
104C4×D101—22no—
105C4×D101—22no—
106C4×D101—42no—
107C4×D101—44no—
108C4×D101—44no—
109C4×D101—42no—
110C4×D101#4114yes—
111Dic202—22no—
112Dic202—42no—
113C8×C101—22no—
114#11717579—22no—
115C22×C101—21no—
116C22×C101—21no—
117C22×C101C2×SD1612yes—
118C22×C101C22×D411yescharacteristic
119C2×D101—21no—
120C2×D101—21no—
121C2×D101—28no—
122C2×D101#12312yes—
123C2×D101C2×SD1612yes—
124C2×D101C2×SD1612yes—
125C2×D101#13712yes—
126C4×C101—21no—
127C4×C101—41no—
128C4×C101—42no—
129C4×C101—41no—
130C4×C101C2×#4112yes—
131Dic101—21no—
132Dic101—41no—
133Dic101—42no—
134Dic101—41no—
135Dic101#12312yes—
136C2×C101—22no—
137C2×C101C2×#12311yescharacteristic
138C2×C101C22×SD1611yescharacteristic
139C2×C101C2×#13711yescharacteristic
140D101—22no—
141D101#48314yesdirect product factor
142C2×#483—1011nomaximal, Sylow
143C101C2×#48311yescharacteristic, complemented, Sylow
144C2×C22⋊Q8—1011no—
145C22×C4⋊C4—1011no—
146#483—1011no—
147#483—1011no—
148#483—1012no—
149#483—1012no—
150#483—1011no—
151#483D10111yescharacteristic, direct product factor
152C2×#106—1012no—
153C2×#103—1012no—
154C2×C22⋊C8—1011no—
155C22×Q8—1011no—
156C23×C4—1011no—
157C23×C4—2021no—
158C22×C8—1012no—
159C22⋊Q8—1011no—
160C22⋊Q8—1011no—
161C22⋊Q8—1011no—
162C22⋊Q8—2021no—
163C22⋊Q8—2021no—
164C22⋊Q8C2×D10111yescharacteristic
165C2×C4⋊C4—1011no—
166C2×C4⋊C4—1012no—
167C2×C4⋊C4—1012no—
168C2×C4⋊C4—1011no—
169C2×C4⋊C4—2021no—
170C2×C4⋊C4—2021no—
171C2×C4⋊C4—2021no—
172C2×C4⋊C4—2021no—
173C2×C4⋊C4C2×D10111yescharacteristic
174C2×C22⋊C4—2021no—
175#106—1012no—
176#106—1012no—
177#106—1012no—
178#106C2×D10112yescomplemented
179#103—1012no—
180#103—1012no—
181#103—1012no—
182#103C2×D10112yescomplemented
183C22⋊C8—1011no—
184C22⋊C8—1012no—
185C22⋊C8C2×D10111yescharacteristic
186C24—1011no—
187C2×Q8—1011no—
188C2×Q8—2021no—
189C2×Q8—2024no—
190C2×Q8C22×D10111yescharacteristic
191C22×C4—21no—
192C22×C4—1011no—
193C22×C4—1011no—
194C22×C4—1011no—
195C22×C4—1011no—
196C22×C4—1011no—
197C22×C4—4044no—
198C22×C4—2024no—
199C22×C4—2021no—
200C22×C4—2021no—
201C22×C4—2022no—
202C22×C4—2022no—
203C22×C4—2021no—
204C22×C4C22×D10111yescharacteristic
205C2×C8—1012no—
206C2×C8—2024no—
207C2×C8C22×D10112yes—
208C4⋊C4—21no—
209C4⋊C4—21no—
210C4⋊C4—1012no—
211C4⋊C4—1011no—
212C4⋊C4—2022no—
213C4⋊C4—2022no—
214C4⋊C4—2021no—
215C4⋊C4—2021no—
216C4⋊C4—2021no—
217C4⋊C4—2021no—
218C4⋊C4—2021no—
219C4⋊C4C22×D10112yes—
220C4⋊C4C22×D10111yescharacteristic
221C22⋊C4—21no—
222C22⋊C4—2021no—
223C22⋊C4—2021no—
224C22⋊C4—2021no—
225C23—1011no—
226C23—1011no—
227C23—1014no—
228C23—2022no—
229C23—2022no—
230C23D4×D10111yescharacteristic
231Q8—22no—
232Q8—4042no—
233Q8—2022no—
234C2×C4—22no—
235C2×C4—21no—
236C2×C4—21no—
237C2×C4—22no—
238C2×C4—42no—
239C2×C4—1011no—
240C2×C4—1014no—
241C2×C4—1011no—
242C2×C4—4044no—
243C2×C4—4044no—
244C2×C4—4042no—
245C2×C4—4042no—
246C2×C4—4042no—
247C2×C4—2022no—
248C2×C4—2022no—
249C2×C4—2022no—
250C2×C4—2021no—
251C2×C4—2021no—
252C2×C4—2022no—
253C2×C4—2022no—
254C2×C4D4×D10111yescharacteristic
255C2×C4C23×D10111yescharacteristic
256C8—22no—
257C8—2022no—
258C22—21no—
259C22—21no—
260C22—1012no—
261C22—1012no—
262C22—1012no—
263C22—1012no—
264C22—2028no—
265C22—2021no—
266C22—2021no—
267C22SD16×D10112yes—
268C22C2×D4×D10111yescharacteristic
269C4—21no—
270C4—41no—
271C4—42no—
272C4—41no—
273C4—1012no—
274C4—4041no—
275C4—4042no—
276C4—4041no—
277C4—2021no—
278C4#41×D10112yes—
279C2—22no—
280C2—1014no—
281C2—2022no—
282C2#123×D10111yescharacteristic
283C2C2×SD16×D10111yescharacteristic
284C2#137×D10111yescharacteristic
subgroupG/H
centerC22C2×D4×D101
commutator, cosocleC2×C4×C101C24
FrattiniC2×C4C23×D101
Fitting#483×C101C2
socleC22×C101C22×D4
prime radicalC23×D101D4
hypercenter#483D101
hypocenterC101C2×#483
LCSG ▷ C2×C4×C101 ▷ C2×C101 ▷ C101
UCSC1 ◁ C22 ◁ C22×C4 ◁ #483

Complements

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

NH ≅ G/Ntype
3. #20265509C2semidirect
4. #20265508C2semidirect
5. #20265507C2semidirect
6. #20265506C2semidirect
7. #20265505C2semidirect
8. #106×D101C2semidirect
9. #103×D101C2semidirect
11. #483×C101C2semidirect
30. #15692187C22semidirect
31. #15692186C22semidirect
32. #15692186C22semidirect
33. #15692180C22semidirect
34. #15692179C22semidirect
35. #15692178C22semidirect
40. #106×C101C22semidirect
41. #103×C101C22semidirect
141. D101#483direct (N × H)
143. C101C2×#483semidirect
151. #483D101direct (N × H)
178. #106C2×D101semidirect
182. #103C2×D101semidirect

Maximal subgroups

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

subgroupindex
C22⋊Q8×D1012
C2×C4⋊C4×D1012
#202655092
#202655082
#202655072
#202655062
#202655052
#106×D1012
#103×D1012
C22⋊C8×D1012
#483×C1012
C2×#483101