Finite Group Databasebeta

← #34056933

Subgroups — #34056933

Order 19072.

460 conjugacy classes of subgroups; only the 125 normal subgroups are shown.

normal subgroups only

This group has 460 conjugacy classes of subgroups — too many to draw. Only its 125 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#23750340C211yesmaximal, characteristic, complemented
2#23749971C211yesmaximal, characteristic, complemented
3#23749946C212yesmaximal, complemented
4#23749915C211yesmaximal, characteristic, complemented
5#23749876C212yesmaximal, complemented
6#23749817C211yesmaximal, characteristic, complemented
7#23749759C212yesmaximal, complemented
8C4×#14558721C211yesmaximal, characteristic, complemented
9#23749703C211yesmaximal, characteristic, complemented
10#23749630C212yesmaximal, complemented
11D42×C149C211yesmaximal, characteristic, complemented
12C2×#14558721C2211yescharacteristic
13C2×#14558721C2212yescomplemented
14C2×#14558720C2212yescomplemented
15#18011911C2211yescharacteristic, complemented
16#18011897—22no—
17#18011885C2212yescomplemented
18#18011882—21no—
19C4×D596C2211yescharacteristic, complemented
20#18011870C2212yescomplemented
21#18011869—21no—
22#18011844C2211yescharacteristic, complemented
23#18011842C2212yescomplemented
24C4⋊#11924746C2211yescharacteristic, complemented
25#18011832C2212yes—
26#18011832C2211yescharacteristic
27#18011832C2212yescomplemented
28#18011832C2212yescomplemented
29#18011832C2212yescomplemented
30#18011831C2211yescharacteristic, complemented
31C22⋊#11924746C2212yescomplemented
32C4×#11924746C2211yescharacteristic, complemented
33C22×D4×C149—21no—
34C22×D4×C149C2212yes—
35#127×C149C2211yescharacteristic
36#121×C149—21no—
37#121×C149C2212yes—
38#120×C149—22no—
39C4×D4×C149C2211yescharacteristic
40C4×D4×C149C2211yescharacteristic
41C2×Dic298—21no—
42C2×D596C2311yescharacteristic
43C2×C22⋊D149—22no—
44C2×C4×D149—21no—
45#14558721—22no—
46#14558721—42no—
47#14558720—42no—
48C2×#11924746C2311yescharacteristic
49C2×#11924746C2312yes—
50C2×#11924746C2311yescharacteristic
51C4⋊Dic149—21no—
52C4⋊Dic149C2312yes—
53C4⋊Dic149C2311yescharacteristic
54C22⋊Dic149—22no—
55#14558713—22no—
56#14558713—21no—
57C4×Dic149—22no—
58C24×C149—22no—
59C2×D4×C149—24no—
60C2×D4×C149—22no—
61C2×D4×C149—22no—
62C2×D4×C149—21no—
63C2×D4×C149—21no—
64C2×D4×C149—42no—
65C2×D4×C149—44no—
66C2×D4×C149D411yescharacteristic
67C2×D4×C149C2312yes—
68C2×D4×C149C2311yescharacteristic
69C22×C4×C149—21no—
70C22×C4×C149C2312yes—
71C4⋊C4×C149D411yescharacteristic
72C4⋊C4×C149C2311yescharacteristic
73C22⋊C4×C149—21no—
74C22⋊C4×C149—22no—
75C22⋊C4×C149D412yes—
76C42×C149C2311yescharacteristic
77C22×D149—21no—
78Dic298—81no—
79D596—21no—
80D596—21no—
81C22⋊D149—82no—
82C2×Dic149—21no—
83C2×Dic149—22no—
84C4×D149—42no—
85#11924746—21no—
86#11924746—21no—
87#11924746—22no—
88C23×C149—21no—
89C23×C149—22no—
90C23×C149—44no—
91C23×C149—44no—
92C23×C149—82no—
93C23×C149C2×D412yes—
94D4×C149—22no—
95D4×C149—22no—
96D4×C149—21no—
97D4×C149—22no—
98D4×C149—44no—
99D4×C149—44no—
100D4×C149—42no—
101D4×C149—81no—
102D4×C149#4112yes—
103C2×C4×C149—22no—
104C2×C4×C149—22no—
105C2×C4×C149—21no—
106C2×C4×C149—42no—
107C2×C4×C149C2×D411yescharacteristic
108C2×C4×C149C2×D412yes—
109C2×C4×C149C2×D411yescharacteristic
110C2×C4×C149C2411yescharacteristic
111C22×C149—22no—
112C22×C149—22no—
113C22×C149—22no—
114C22×C149—22no—
115C22×C149—41no—
116C22×C149—41no—
117C22×C149—42no—
118C22×C149—42no—
119C22×C149—42no—
120C22×C149—88no—
121C22×C149C22×D411yescharacteristic
122C2×D149—41no—
123C2×D149—41no—
124C2×D149—41no—
125C4×C149—22no—
126C4×C149—21no—
127C4×C149—41no—
128C4×C149AGL(1,ℤ/8)12yes—
129C4×C149C2×#4111yescharacteristic
130C4×C149H(5,𝔽2)11yescharacteristic
131Dic149—41no—
132Dic149—42no—
133C2×C149—42no—
134C2×C149—42no—
135C2×C149—82no—
136C2×C149#54611yescharacteristic
137C2×C149C2×AGL(1,ℤ/8)11yescharacteristic
138C2×C149#57611yescharacteristic
139D149—81no—
140C149#332511yescharacteristic, complemented, Sylow
141#3325—1491nomaximal, Sylow
142#555—1491no—
143D42D14911yescharacteristic, complemented
144#486—1491no—
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—21no—
154C22×D4C2×D14912yes—
155C2×D8—1491no—
156C2×D8—1492no—
157C2×M16—1492no—
158C4⋊Q8—1491no—
159#127C2×D14911yescharacteristic
160#124—2982no—
161#121—21no—
162#121—2981no—
163#121—1492no—
164#121C2×D14912yes—
165#120—22no—
166C4×D4—1491no—
167C4×D4C2×D14911yescharacteristic
168C4×D4C2×D14911yescharacteristic
169#117—2981no—
170#117—1492no—
171#107—1491no—
172#106—1492no—
173C4⋊C8—1491no—
174#102—1491no—
175#102—1492no—
176#102—1492no—
177#102—1492no—
178#102—1492no—
179#102—1491no—
180C22⋊C8—1492no—
181C4×C8—1491no—
182C24—22no—
183C2×Q8—2981no—
184C2×D4—24no—
185C2×D4—22no—
186C2×D4—22no—
187C2×D4—21no—
188C2×D4—21no—
189C2×D4—42no—
190C2×D4—44no—
191C2×D4—2982no—
192C2×D4—1491no—
193C2×D4C22⋊D14911yescharacteristic
194C2×D4C22×D14912yes—
195C2×D4C22×D14911yescharacteristic
196C22×C4—21no—
197C22×C4—2981no—
198C22×C4C22×D14912yes—
199D8—2982no—
200D8—5962no—
201M16—5962no—
202C2×C8—1491no—
203C2×C8—1491no—
204C2×C8—1492no—
205C4⋊C4—2981no—
206C4⋊C4—1492no—
207C4⋊C4—1491no—
208C4⋊C4C22⋊D14911yescharacteristic
209C4⋊C4C22×D14911yescharacteristic
210C22⋊C4—21no—
211C22⋊C4—22no—
212C22⋊C4—2982no—
213C22⋊C4—2982no—
214C22⋊C4—2981no—
215C22⋊C4C22⋊D14912yes—
216C42—2982no—
217C42C22×D14911yescharacteristic
218C23—21no—
219C23—22no—
220C23—44no—
221C23—44no—
222C23—82no—
223C23—2981no—
224C23C2×C22⋊D14912yes—
225Q8—11921no—
226D4—22no—
227D4—22no—
228D4—21no—
229D4—22no—
230D4—44no—
231D4—44no—
232D4—42no—
233D4—81no—
234D4—2981no—
235D4—2981no—
236D4—11922no—
237D4#1455873512yes—
238C2×C4—22no—
239C2×C4—22no—
240C2×C4—21no—
241C2×C4—42no—
242C2×C4—2981no—
243C2×C4—2982no—
244C2×C4—5962no—
245C2×C4C2×C22⋊D14912yes—
246C2×C4C2×C22⋊D14911yescharacteristic
247C2×C4C2×C22⋊D14911yescharacteristic
248C2×C4C23×D14911yescharacteristic
249C8—2981no—
250C8—2981no—
251C8—2982no—
252C22—22no—
253C22—22no—
254C22—22no—
255C22—22no—
256C22—41no—
257C22—41no—
258C22—42no—
259C22—42no—
260C22—42no—
261C22—88no—
262C22—5961no—
263C22—5961no—
264C22—5961no—
265C22C22×C22⋊D14911yescharacteristic
266C4—21no—
267C4—22no—
268C4—41no—
269C4—5961no—
270C4—5962no—
271C4#1801193712yes—
272C4C2×#1455873511yescharacteristic
273C4#1801195611yescharacteristic
274C2—42no—
275C2—42no—
276C2—82no—
277C2—11921no—
278C2#2375026911yescharacteristic
279C2C2×#1801193711yescharacteristic
280C2#2375042811yescharacteristic
subgroupG/H
centerC22C22×C22⋊D149
commutator, cosocleC2×C4×C149C24
FrattiniC2×C4C23×D149
FittingD42×C149C2
socleC22×C149C22×D4
hypercenterD42D149
hypocenterC149#3325
LCSG ▷ C2×C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C22 ◁ C4×D4 ◁ D42

Complements

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

NH ≅ G/Ntype
1. #23750340C2semidirect
2. #23749971C2semidirect
3. #23749946C2semidirect
4. #23749915C2semidirect
5. #23749876C2semidirect
6. #23749817C2semidirect
7. #23749759C2semidirect
8. C4×#14558721C2semidirect
9. #23749703C2semidirect
10. #23749630C2semidirect
11. D42×C149C2semidirect
13. C2×#14558721C22semidirect
14. C2×#14558720C22semidirect
15. #18011911C22semidirect
17. #18011885C22semidirect
19. C4×D596C22semidirect
20. #18011870C22semidirect
22. #18011844C22semidirect
23. #18011842C22semidirect
24. C4⋊#11924746C22semidirect
27. #18011832C22semidirect
28. #18011832C22semidirect
29. #18011832C22semidirect
30. #18011831C22semidirect
31. C22⋊#11924746C22semidirect
32. C4×#11924746C22semidirect
140. C149#3325semidirect
143. D42D149semidirect

Maximal subgroups

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

subgroupindex
#237503402
#237499712
#237499462
#237499152
#237498762
#237498172
#237497592
C4×#145587212
#237497032
#237496302
D42×C1492
#3325149