Finite Group Databasebeta

← #34056932

Subgroups — #34056932

Order 19072.

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

normal subgroups only

This group has 460 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
1#23750341C211yesmaximal, characteristic, complemented
2#23750260C211yesmaximal, characteristic, complemented
3#23749947C212yesmaximal, complemented
4#23749912C211yesmaximal, characteristic, complemented
5#23749877C212yesmaximal, complemented
6#23749817C211yesmaximal, characteristic, complemented
7#23749760C212yesmaximal, complemented
8C4×D1192C211yesmaximal, characteristic, complemented
9#23749704C211yesmaximal, characteristic, complemented
10#23749628C212yesmaximal, complemented
11#486×C149C211yesmaximal, characteristic, complemented
12C2×D4×D149—21no—
13C2×D4×D149C2212yes—
14C2×D1192C2211yescharacteristic
15C2×#14558721C2212yescomplemented
16C2×#14558719C2212yescomplemented
17#18011900—22no—
18#18011886—21no—
19#18011886C2212yescomplemented
20#18011882—21no—
21#18011882C2212yes—
22#18011879—22no—
23C4×D596C2211yescharacteristic
24C4×D596C2211yescharacteristic
25C4×D596C2211yescharacteristic, complemented
26#18011869—21no—
27#18011869C2212yescomplemented
28#18011845C2211yescharacteristic, complemented
29#18011842C2212yescomplemented
30C4⋊#11924746C2211yescharacteristic, complemented
31#18011833C2211yescharacteristic
32#18011833C2211yescharacteristic, complemented
33#18011832C2212yescomplemented
34#18011831C2212yes—
35#18011823C2212yescomplemented
36C4⋊Q8×C149C2211yescharacteristic, complemented
37#127×C149C2211yescharacteristic
38#102×C149C2212yescomplemented
39#102×C149C2212yescomplemented
40C4×C8×C149C2211yescharacteristic, complemented
41C23×D149—22no—
42C2×D596—22no—
43C2×D596D411yescharacteristic
44C2×D596C2311yescharacteristic
45C2×D596C2311yescharacteristic
46C2×C22⋊D149—22no—
47C2×C22⋊D149—22no—
48D4×D149—24no—
49D4×D149—42no—
50D4×D149—44no—
51C2×C4×D149—21no—
52C2×C4×D149—21no—
53C2×C4×D149C2312yes—
54D1192—22no—
55#14558721—42no—
56#14558719—42no—
57C2×#11924746C2312yes—
58C4⋊Dic149D411yescharacteristic
59C4⋊Dic149C2311yescharacteristic
60C4⋊Dic149C2311yescharacteristic
61C22⋊Dic149—22no—
62#14558713—22no—
63#14558713—22no—
64#14558713—21no—
65#14558713—21no—
66#14558713D412yes—
67C4×Dic149—22no—
68C2×Q8×C149—21no—
69C2×D4×C149—21no—
70C2×D4×C149—21no—
71C2×D4×C149C2312yes—
72C2×C8×C149C2311yescharacteristic
73C2×C8×C149C2311yescharacteristic
74C4⋊C4×C149—21no—
75C4⋊C4×C149C2312yes—
76C42×C149C2311yescharacteristic
77C22×D149—21no—
78C22×D149—21no—
79C22×D149—44no—
80C22×D149—44no—
81C22×D149—82no—
82C22×D149C2×D412yes—
83D596—22no—
84D596—21no—
85D596—21no—
86D596—21no—
87D596—82no—
88D596#4112yes—
89C22⋊D149—44no—
90C22⋊D149—44no—
91C2×Dic149—21no—
92C2×Dic149—21no—
93C2×Dic149C2×D412yes—
94C4×D149—22no—
95C4×D149—22no—
96C4×D149—42no—
97C4×D149—42no—
98#11924746—22no—
99C23×C149—22no—
100Q8×C149—81no—
101D4×C149—22no—
102D4×C149—22no—
103D4×C149—42no—
104D4×C149—81no—
105C2×C4×C149—22no—
106C2×C4×C149C2×D411yescharacteristic
107C2×C4×C149C2×D411yescharacteristic
108C2×C4×C149C2411yescharacteristic
109C8×C149—21no—
110C8×C149—21no—
111C22×C149—42no—
112C22×C149—42no—
113C22×C149—42no—
114C22×C149C22×D411yescharacteristic
115C2×D149—22no—
116C2×D149—22no—
117C2×D149—22no—
118C2×D149—22no—
119C2×D149—41no—
120C2×D149—41no—
121C2×D149—41no—
122C2×D149—41no—
123C2×D149—41no—
124C2×D149—88no—
125C4×C149—21no—
126C4×C149—42no—
127C4×C149AGL(1,ℤ/8)12yes—
128C4×C149C2×#4111yescharacteristic
129C4×C149H(5,𝔽2)11yescharacteristic
130Dic149—22no—
131Dic149—41no—
132Dic149—41no—
133C2×C149—82no—
134C2×C149#54611yescharacteristic
135C2×C149C2×AGL(1,ℤ/8)11yescharacteristic
136C2×C149#57611yescharacteristic
137D149—42no—
138D149—42no—
139D149—81no—
140C149#332511yescharacteristic, complemented, Sylow
141#3325—1491nomaximal, Sylow
142#555—1491no—
143D42—1491no—
144#486D14911yescharacteristic, complemented
145#482—1492no—
146#476—1491no—
147#469—1492no—
148#459—1491no—
149#447—1492no—
150C4×D8—1491no—
151#436—1491no—
152#418—1492no—
153C22×D4—2981no—
154C22×D4—1492no—
155C2×D8—1492no—
156C2×D8—1491no—
157C2×M16—1492no—
158C4⋊Q8C2×D14911yescharacteristic, complemented
159#127C2×D14911yescharacteristic
160#124—2982no—
161#121—2981no—
162#121—2981no—
163#121—1492no—
164#121—1492no—
165#120—2982no—
166C4×D4—1491no—
167C4×D4—1491no—
168C4×D4—1491no—
169#117—2981no—
170#117—1492no—
171#107—1491no—
172#106—1492no—
173C4⋊C8—1491no—
174#102—1492no—
175#102—1491no—
176#102—1491no—
177#102—1492no—
178#102C2×D14912yescomplemented
179#102C2×D14912yescomplemented
180C22⋊C8—1492no—
181C4×C8C2×D14911yescharacteristic, complemented
182C24—2982no—
183C2×Q8—21no—
184C2×D4—21no—
185C2×D4—21no—
186C2×D4—2982no—
187C2×D4—2984no—
188C2×D4—2982no—
189C2×D4—2982no—
190C2×D4—5962no—
191C2×D4—5964no—
192C2×D4—1491no—
193C2×D4—1491no—
194C2×D4—1491no—
195C2×D4C22×D14912yes—
196C22×C4—2981no—
197C22×C4—2981no—
198C22×C4—1492no—
199D8—2982no—
200D8—5962no—
201M16—5962no—
202C2×C8—1492no—
203C2×C8C22×D14911yescharacteristic
204C2×C8C22×D14911yescharacteristic
205C4⋊C4—21no—
206C4⋊C4—1491no—
207C4⋊C4—1491no—
208C4⋊C4—1491no—
209C4⋊C4C22×D14912yes—
210C22⋊C4—2982no—
211C22⋊C4—2982no—
212C22⋊C4—2982no—
213C22⋊C4—2981no—
214C22⋊C4—2981no—
215C22⋊C4—1492no—
216C42—2982no—
217C42C22×D14911yescharacteristic
218C23—22no—
219C23—2981no—
220C23—2981no—
221C23—5964no—
222C23—5964no—
223C23—1492no—
224C23—11922no—
225Q8—81no—
226D4—22no—
227D4—22no—
228D4—42no—
229D4—81no—
230D4—2982no—
231D4—2981no—
232D4—2981no—
233D4—2981no—
234D4—5964no—
235D4—5964no—
236D4—1492no—
237D4—11922no—
238C2×C4—22no—
239C2×C4—2982no—
240C2×C4—2982no—
241C2×C4—2981no—
242C2×C4—2981no—
243C2×C4—5962no—
244C2×C4—5962no—
245C2×C4—1492no—
246C2×C4D4×D14911yescharacteristic
247C2×C4D4×D14911yescharacteristic
248C2×C4C23×D14911yescharacteristic
249C8—21no—
250C8—21no—
251C8—2982no—
252C22—42no—
253C22—42no—
254C22—42no—
255C22—2982no—
256C22—2982no—
257C22—2982no—
258C22—2982no—
259C22—5961no—
260C22—5961no—
261C22—5961no—
262C22—5961no—
263C22—5961no—
264C22—11928no—
265C22C2×D4×D14911yescharacteristic
266C4—21no—
267C4—42no—
268C4—2982no—
269C4—5961no—
270C4—5961no—
271C4#1801193812yes—
272C4#41×D14911yescharacteristic
273C4#1801195711yescharacteristic
274C2—82no—
275C2—5962no—
276C2—5962no—
277C2—11921no—
278C2#2375026811yescharacteristic
279C2C2×#1801193811yescharacteristic
280C2#2375042611yescharacteristic
subgroupG/H
centerC22C2×D4×D149
commutator, cosocleC2×C4×C149C24
FrattiniC2×C4C23×D149
Fitting#486×C149C2
socleC22×C149C22×D4
hypercenter#486D149
hypocenterC149#3325
LCSG ▷ C2×C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C22 ◁ C42 ◁ #486

Complements

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

NH ≅ G/Ntype
1. #23750341C2semidirect
2. #23750260C2semidirect
3. #23749947C2semidirect
4. #23749912C2semidirect
5. #23749877C2semidirect
6. #23749817C2semidirect
7. #23749760C2semidirect
8. C4×D1192C2semidirect
9. #23749704C2semidirect
10. #23749628C2semidirect
11. #486×C149C2semidirect
15. C2×#14558721C22semidirect
16. C2×#14558719C22semidirect
19. #18011886C22semidirect
25. C4×D596C22semidirect
27. #18011869C22semidirect
28. #18011845C22semidirect
29. #18011842C22semidirect
30. C4⋊#11924746C22semidirect
32. #18011833C22semidirect
33. #18011832C22semidirect
35. #18011823C22semidirect
36. C4⋊Q8×C149C22semidirect
38. #102×C149C22semidirect
39. #102×C149C22semidirect
40. C4×C8×C149C22semidirect
140. C149#3325semidirect
144. #486D149semidirect
158. C4⋊Q8C2×D149semidirect
178. #102C2×D149semidirect
179. #102C2×D149semidirect
181. C4×C8C2×D149semidirect

Maximal subgroups

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

subgroupindex
#237503412
#237502602
#237499472
#237499122
#237498772
#237498172
#237497602
C4×D11922
#237497042
#237496282
#486×C1492
#3325149