Finite Group Databasebeta

← #484×D149 #34054593

Subgroups — #484×D149 #34054593

Order 19072.

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×D149C211yesmaximal, characteristic
2C2×C4⋊C4×D149C211yesmaximal, characteristic
3#23749962C212yesmaximal, complemented
4#23749961C211yesmaximal, characteristic, complemented
5#23749960C211yesmaximal, characteristic, complemented
6#23749959C212yesmaximal, complemented
7#23749958C211yesmaximal, characteristic, complemented
8#107×D149C212yesmaximal, complemented
9#103×D149C212yesmaximal, complemented
10C22⋊C8×D149C211yesmaximal, characteristic
11#484×C149C211yesmaximal, characteristic, complemented
12C2×Q8×D149C2211yescharacteristic
13C22×C4×D149—21no—
14C22×C4×D149C2211yescharacteristic
15C2×C8×D149C2212yes—
16#18011891C2211yescharacteristic
17#18011890C2211yescharacteristic
18#18011889—21no—
19#18011888—21no—
20#18011887C2211yescharacteristic
21C2×C4⋊Dic149C2211yescharacteristic
22C2×#14558715—21no—
23C4⋊C4×D149—21no—
24C4⋊C4×D149—21no—
25C4⋊C4×D149—21no—
26C4⋊C4×D149C2211yescharacteristic
27C4⋊C4×D149C2212yes—
28C4⋊C4×D149C2212yes—
29C22⋊C4×D149—21no—
30#18011845C2212yescomplemented
31#18011844C2212yescomplemented
32#18011844C2212yescomplemented
33#18011836C2212yescomplemented
34#18011835C2212yescomplemented
35#18011834C2212yescomplemented
36C22⋊#11924746C2211yescharacteristic
37#18011823C2212yes—
38C22⋊Q8×C149C2211yescharacteristic
39C2×C4⋊C4×C149C2211yescharacteristic
40#107×C149C2212yescomplemented
41#103×C149C2212yescomplemented
42C22⋊C8×C149C2211yescharacteristic
43C23×D149D411yescharacteristic
44C2×Dic298—21no—
45C2×Dic298C2311yescharacteristic
46Q8×D149—24no—
47C22×Dic149—21no—
48C22×Dic149D411yescharacteristic
49C2×C4×D149—24no—
50C2×C4×D149—22no—
51C2×C4×D149—22no—
52C2×C4×D149—21no—
53C2×C4×D149—21no—
54C2×C4×D149—44no—
55C2×C4×D149D411yescharacteristic
56C2×C4×D149D411yescharacteristic
57C2×C4×D149C2311yescharacteristic
58C2×C4×D149C2311yescharacteristic
59C2×#11924746C2312yes—
60C8×D149—24no—
61C4⋊Dic149—21no—
62C4⋊Dic149—21no—
63C4⋊Dic149C2312yes—
64C4⋊Dic149C2311yescharacteristic
65#14558715—22no—
66#14558715—22no—
67#14558715—21no—
68#14558715—21no—
69#14558715—21no—
70C22⋊Dic149—21no—
71#14558713—21no—
72#14558713—21no—
73C2×Q8×C149C2311yescharacteristic
74C22×C4×C149—21no—
75C22×C4×C149C2311yescharacteristic
76C2×C8×C149C2312yes—
77C4⋊C4×C149—21no—
78C4⋊C4×C149—21no—
79C4⋊C4×C149C2312yes—
80C4⋊C4×C149C2311yescharacteristic
81C22⋊C4×C149—21no—
82C22×D149—22no—
83C22×D149—22no—
84C22×D149Q1614yes—
85C22×D149C2×D411yescharacteristic
86C22×D149C2×D411yescharacteristic
87Dic298—22no—
88Dic298—42no—
89C2×Dic149—22no—
90C2×Dic149—22no—
91C2×Dic149—21no—
92C2×Dic149—21no—
93C2×Dic149—42no—
94C2×Dic149C2×D411yescharacteristic
95C2×Dic149C2×D411yescharacteristic
96C4×D149—22no—
97C4×D149—22no—
98C4×D149—22no—
99C4×D149—44no—
100C4×D149—42no—
101C4×D149—42no—
102C4×D149—44no—
103C4×D149#4114yes—
104#11924746—22no—
105C23×C149C2×D411yescharacteristic
106Q8×C149—22no—
107C2×C4×C149—22no—
108C2×C4×C149—22no—
109C2×C4×C149—21no—
110C2×C4×C149—21no—
111C2×C4×C149—42no—
112C2×C4×C149C2×D411yescharacteristic
113C2×C4×C149C2411yescharacteristic
114C8×C149—22no—
115C22×C149—21no—
116C22×C149—21no—
117C22×C149C2×Q1612yes—
118C22×C149C22×D411yescharacteristic
119C2×D149—21no—
120C2×D149—21no—
121C2×D149—28no—
122C2×D149#12312yes—
123C2×D149C2×Q1612yes—
124C2×D149C2×Q1612yes—
125C2×D149AGL(1,ℤ/8)12yes—
126C4×C149—21no—
127C4×C149—41no—
128C4×C149—42no—
129C4×C149—41no—
130C4×C149C2×#4112yes—
131Dic149—21no—
132Dic149—41no—
133Dic149—42no—
134Dic149—41no—
135Dic149#12312yes—
136C2×C149—22no—
137C2×C149C2×#12311yescharacteristic
138C2×C149C22×Q1611yescharacteristic
139C2×C149C2×AGL(1,ℤ/8)11yescharacteristic
140D149—22no—
141D149#48414yesdirect product factor
142C149C2×#48411yescharacteristic, complemented, Sylow
143C2×#484—1491nomaximal, Sylow
144C2×C22⋊Q8—1491no—
145C22×C4⋊C4—1491no—
146#484—1491no—
147#484—1491no—
148#484—1492no—
149#484—1492no—
150#484—1491no—
151#484D14911yescharacteristic, direct product factor
152C2×#107—1492no—
153C2×#103—1492no—
154C2×C22⋊C8—1491no—
155C22×Q8—1491no—
156C23×C4—2981no—
157C23×C4—1491no—
158C22×C8—1492no—
159C22⋊Q8—2981no—
160C22⋊Q8—2981no—
161C22⋊Q8—1491no—
162C22⋊Q8—1491no—
163C22⋊Q8—1491no—
164C22⋊Q8C2×D14911yescharacteristic
165C2×C4⋊C4—2981no—
166C2×C4⋊C4—2981no—
167C2×C4⋊C4—2981no—
168C2×C4⋊C4—2981no—
169C2×C4⋊C4—1491no—
170C2×C4⋊C4—1492no—
171C2×C4⋊C4—1492no—
172C2×C4⋊C4—1491no—
173C2×C4⋊C4C2×D14911yescharacteristic
174C2×C22⋊C4—2981no—
175#107—1492no—
176#107—1492no—
177#107—1492no—
178#107C2×D14912yescomplemented
179#103—1492no—
180#103—1492no—
181#103—1492no—
182#103C2×D14912yescomplemented
183C22⋊C8—1491no—
184C22⋊C8—1492no—
185C22⋊C8C2×D14911yescharacteristic
186C24—1491no—
187C2×Q8—2981no—
188C2×Q8—2984no—
189C2×Q8—1491no—
190C2×Q8C22×D14911yescharacteristic
191C22×C4—21no—
192C22×C4—2984no—
193C22×C4—2981no—
194C22×C4—2981no—
195C22×C4—2982no—
196C22×C4—2982no—
197C22×C4—2981no—
198C22×C4—5964no—
199C22×C4—1491no—
200C22×C4—1491no—
201C22×C4—1491no—
202C22×C4—1491no—
203C22×C4—1491no—
204C22×C4C22×D14911yescharacteristic
205C2×C8—2984no—
206C2×C8—1492no—
207C2×C8C22×D14912yes—
208C4⋊C4—21no—
209C4⋊C4—21no—
210C4⋊C4—2982no—
211C4⋊C4—2982no—
212C4⋊C4—2981no—
213C4⋊C4—2981no—
214C4⋊C4—2981no—
215C4⋊C4—2981no—
216C4⋊C4—2981no—
217C4⋊C4—1492no—
218C4⋊C4—1491no—
219C4⋊C4C22×D14912yes—
220C4⋊C4C22×D14911yescharacteristic
221C22⋊C4—21no—
222C22⋊C4—2981no—
223C22⋊C4—2981no—
224C22⋊C4—2981no—
225C23—2982no—
226C23—2982no—
227C23—1494no—
228C23—1491no—
229C23—1491no—
230C23D4×D14911yescharacteristic
231Q8—22no—
232Q8—2982no—
233Q8—5962no—
234C2×C4—22no—
235C2×C4—21no—
236C2×C4—21no—
237C2×C4—22no—
238C2×C4—42no—
239C2×C4—2982no—
240C2×C4—2982no—
241C2×C4—2982no—
242C2×C4—2982no—
243C2×C4—2981no—
244C2×C4—2981no—
245C2×C4—2982no—
246C2×C4—5964no—
247C2×C4—5962no—
248C2×C4—5964no—
249C2×C4—5962no—
250C2×C4—5962no—
251C2×C4—1491no—
252C2×C4—1491no—
253C2×C4—1494no—
254C2×C4D4×D14911yescharacteristic
255C2×C4C23×D14911yescharacteristic
256C8—22no—
257C8—2982no—
258C22—21no—
259C22—21no—
260C22—2988no—
261C22—2981no—
262C22—2981no—
263C22—1492no—
264C22—1492no—
265C22—1492no—
266C22—1492no—
267C22Q16×D14912yes—
268C22C2×D4×D14911yescharacteristic
269C4—21no—
270C4—42no—
271C4—41no—
272C4—41no—
273C4—2981no—
274C4—5962no—
275C4—5961no—
276C4—5961no—
277C4—1492no—
278C4#41×D14912yes—
279C2—22no—
280C2—2982no—
281C2—1494no—
282C2#123×D14911yescharacteristic
283C2C2×Q16×D14911yescharacteristic
284C2AGL(1,ℤ/8)×D14911yescharacteristic
subgroupG/H
centerC22C2×D4×D149
commutator, cosocleC2×C4×C149C24
FrattiniC2×C4C23×D149
Fitting#484×C149C2
socleC22×C149C22×D4
prime radicalC23×D149D4
hypercenter#484D149
hypocenterC149C2×#484
LCSG ▷ C2×C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C22 ◁ C22×C4 ◁ #484

Complements

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

NH ≅ G/Ntype
3. #23749962C2semidirect
4. #23749961C2semidirect
5. #23749960C2semidirect
6. #23749959C2semidirect
7. #23749958C2semidirect
8. #107×D149C2semidirect
9. #103×D149C2semidirect
11. #484×C149C2semidirect
30. #18011845C22semidirect
31. #18011844C22semidirect
32. #18011844C22semidirect
33. #18011836C22semidirect
34. #18011835C22semidirect
35. #18011834C22semidirect
40. #107×C149C22semidirect
41. #103×C149C22semidirect
141. D149#484direct (N × H)
142. C149C2×#484semidirect
151. #484D149direct (N × H)
178. #107C2×D149semidirect
182. #103C2×D149semidirect

Maximal subgroups

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

subgroupindex
C22⋊Q8×D1492
C2×C4⋊C4×D1492
#237499622
#237499612
#237499602
#237499592
#237499582
#107×D1492
#103×D1492
C22⋊C8×D1492
#484×C1492
C2×#484149