Finite Group Databasebeta

← #34056370

Subgroups — #34056370

Order 19072.

526 conjugacy classes of subgroups; only the 131 normal subgroups are shown.

normal subgroups only

This group has 526 conjugacy classes of subgroups — too many to draw. Only its 131 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
1C2×D8×D149C211yesmaximal, characteristic, complemented
2#23750263C212yesmaximal, complemented
3#23750010C211yesmaximal, characteristic, complemented
4#23749863C211yesmaximal, characteristic, complemented
5#23749861C211yesmaximal, characteristic, complemented
6#23749842C212yesmaximal, complemented
7#23749774C212yesmaximal, complemented
8#23749770C212yesmaximal, complemented
9D8×Dic149C211yesmaximal, characteristic, complemented
10C8×C22⋊D149C211yesmaximal, characteristic, complemented
11C2×#135×C149C211yesmaximal, characteristic, complemented
12C2×D4×D149C2212yes—
13C2×#14558723C2212yescomplemented
14C2×D1192C2211yescharacteristic
15C2×#14558721C2212yes—
16D8×D149—24no—
17C2×C8×D149C2211yescharacteristic
18#18011900C2212yescomplemented
19#18011894—22no—
20#18011887C2212yes—
21#18011885C2212yescomplemented
22#18011883—22no—
23#18011879—22no—
24D4×Dic149C2212yescomplemented
25C4×C22⋊D149C2211yescharacteristic
26C2×#14558713—22no—
27#18011845C2211yescharacteristic, complemented
28#18011840C2211yescharacteristic, complemented
29#18011835C2212yescomplemented
30#18011833C2212yescomplemented
31#18011832C2212yescomplemented
32C22⋊#11924746C2211yescharacteristic, complemented
33#18011823C2211yescharacteristic
34C8×Dic149C2211yescharacteristic, complemented
35C2×#41×C149C2212yescomplemented
36#135×C149—24no—
37C2×Q16×C149C2211yescharacteristic, complemented
38C2×SD16×C149C2212yescomplemented
39C2×D8×C149C2211yescharacteristic
40C22×C8×C149C2211yescharacteristic, complemented
41C23×D149—22no—
42C2×D596C2312yes—
43C2×C22⋊D149—22no—
44C2×C22⋊D149—22no—
45C2×C22⋊D149D411yescharacteristic
46D4×D149—24no—
47D4×D149—42no—
48C22×Dic149—22no—
49C2×C4×D149C2311yescharacteristic
50#14558723—42no—
51D1192—22no—
52#14558721—24no—
53C2×#11924746C2311yescharacteristic
54C2×#11924746C2311yescharacteristic
55C8×D149—22no—
56C4⋊Dic149C2312yes—
57#14558715—22no—
58#14558715D411yescharacteristic
59C22⋊Dic149—22no—
60C22⋊Dic149D411yescharacteristic
61#14558713—22no—
62#14558713—22no—
63#14558713—22no—
64#14558713—22no—
65#14558713D411yescharacteristic
66C4×Dic149C2311yescharacteristic
67#41×C149—24no—
68#41×C149—42no—
69C2×Q8×C149C2312yes—
70C2×D4×C149—22no—
71C2×D4×C149C2312yes—
72C22×C4×C149—22no—
73C22×C4×C149C2311yescharacteristic
74Q16×C149—22no—
75SD16×C149—24no—
76D8×C149D414yescomplemented
77C2×C8×C149—22no—
78C2×C8×C149C2311yescharacteristic
79C2×C8×C149C2311yescharacteristic
80C22×D149—22no—
81C22×D149—44no—
82C22×D149—44no—
83C22×D149—82no—
84C22×D149C2×D411yescharacteristic
85D596—22no—
86D596—22no—
87C22⋊D149—22no—
88C22⋊D149—44no—
89C22⋊D149—82no—
90C2×Dic149—22no—
91C2×Dic149—82no—
92C2×Dic149C2×D411yescharacteristic
93C2×Dic149C2×D411yescharacteristic
94C2×Dic149C2×D411yescharacteristic
95C4×D149—21no—
96C4×D149—21no—
97#11924746—21no—
98#11924746—21no—
99C23×C149—22no—
100C23×C149C2×D411yescharacteristic
101Q8×C149—22no—
102Q8×C149—22no—
103D4×C149—22no—
104D4×C149—44no—
105D4×C149C2×D414yes—
106C2×C4×C149—21no—
107C2×C4×C149—21no—
108C2×C4×C149—22no—
109C2×C4×C149—44no—
110C2×C4×C149C2×D411yescharacteristic
111C2×C4×C149C2411yescharacteristic
112C8×C149—21no—
113C8×C149C2×D412yes—
114C22×C149—21no—
115C22×C149—24no—
116C22×C149—21no—
117C22×C149—21no—
118C22×C149—42no—
119C22×C149—42no—
120C22×C149C22×D411yescharacteristic
121C2×D149—21no—
122C2×D149—21no—
123C2×D149—42no—
124C2×D149—42no—
125C2×D149—42no—
126C2×D149—88no—
127C2×D149#13512yescomplemented
128C4×C149—21no—
129C4×C149—42no—
130C4×C149C22×D411yescharacteristic
131C4×C149H(5,𝔽2)11yescharacteristic
132Dic149—21no—
133Dic149—21no—
134Dic149—21no—
135Dic149—42no—
136C2×C149—44no—
137C2×C149—41no—
138C2×C149D4211yescharacteristic
139C2×C149C2×#13511yescharacteristic
140C2×C149#57611yescharacteristic
141D149—22no—
142D149—82no—
143C149#328011yescharacteristic, complemented, Sylow
144#3280—1491nomaximal, Sylow
145C2×#135D14911yescharacteristic, complemented
146C22×D8—1491no—
147#546—1492no—
148#495—1491no—
149#467—1491no—
150#466—1491no—
151#463—1492no—
152#450—1492no—
153#449—1492no—
154C4×D8—1491no—
155C8×D4—1491no—
156C2×#41C2×D14912yescomplemented
157C22×D4—1492no—
158#135—24no—
159C2×Q16C2×D14911yescharacteristic, complemented
160C2×SD16—1492no—
161C2×SD16C2×D14912yescomplemented
162C2×D8—2984no—
163C2×D8—1492no—
164C2×D8—1491no—
165C2×D8C2×D14911yescharacteristic
166C22×C8—1491no—
167C22×C8C2×D14911yescharacteristic, complemented
168#124—1492no—
169#123—2982no—
170C22⋊Q8—1492no—
171#121—2982no—
172#121—1492no—
173#120—2982no—
174C4×D4—1492no—
175C4×D4—1491no—
176C2×C22⋊C4—2982no—
177#107—1491no—
178C4⋊C8—1491no—
179#103—1492no—
180#102—1492no—
181#102—1492no—
182C22⋊C8—1491no—
183C22⋊C8—1491no—
184C4×C8—1491no—
185C24—2982no—
186#41—24no—
187#41—42no—
188C2×Q8C22×D14912yes—
189C2×D4—22no—
190C2×D4—2984no—
191C2×D4—2982no—
192C2×D4—2982no—
193C2×D4—5962no—
194C2×D4—1491no—
195C2×D4—1492no—
196C2×D4C22×D14912yes—
197C22×C4—22no—
198C22×C4—2982no—
199C22×C4—1491no—
200C22×C4C22×D14911yescharacteristic
201Q16—22no—
202SD16—24no—
203SD16—5962no—
204D8—2984no—
205D8—2982no—
206D8C22⋊D14914yescomplemented
207C2×C8—22no—
208C2×C8—2982no—
209C2×C8—1491no—
210C2×C8—1491no—
211C2×C8C22×D14911yescharacteristic
212C2×C8C22×D14911yescharacteristic
213C4⋊C4—2982no—
214C4⋊C4—1492no—
215C4⋊C4—1491no—
216C22⋊C4—2982no—
217C22⋊C4—2982no—
218C22⋊C4—2982no—
219C22⋊C4—2982no—
220C22⋊C4—2982no—
221C22⋊C4—1491no—
222C22⋊C4—1491no—
223C42—1491no—
224C23—22no—
225C23—2982no—
226C23—5964no—
227C23—5964no—
228C23—1491no—
229C23—11922no—
230C23D4×D14911yescharacteristic
231Q8—22no—
232Q8—22no—
233D4—22no—
234D4—44no—
235D4—2982no—
236D4—2982no—
237D4—2982no—
238D4—5964no—
239D4—11922no—
240D4C2×C22⋊D14914yes—
241C2×C4—21no—
242C2×C4—21no—
243C2×C4—22no—
244C2×C4—44no—
245C2×C4—2981no—
246C2×C4—2981no—
247C2×C4—2982no—
248C2×C4—1491no—
249C2×C4—1491no—
250C2×C4—1491no—
251C2×C4—11922no—
252C2×C4D4×D14911yescharacteristic
253C2×C4C23×D14911yescharacteristic
254C8—21no—
255C8—2981no—
256C8—2981no—
257C8C2×C22⋊D14912yes—
258C22—21no—
259C22—21no—
260C22—21no—
261C22—24no—
262C22—42no—
263C22—42no—
264C22—2981no—
265C22—2981no—
266C22—5962no—
267C22—5962no—
268C22—5962no—
269C22—1492no—
270C22—11928no—
271C22C2×D4×D14911yescharacteristic
272C4—21no—
273C4—42no—
274C4—2981no—
275C4—2981no—
276C4—2981no—
277C4—5962no—
278C4C22×C22⋊D14911yescharacteristic
279C4#1801195611yescharacteristic
280C2—41no—
281C2—44no—
282C2—2982no—
283C2—11922no—
284C2D4×C22⋊D14911yescharacteristic
285C2#135×D14911yescharacteristic
286C2#2375042711yescharacteristic
subgroupG/H
centerC22C2×D4×D149
commutator, cosocleC2×C4×C149C24
FrattiniC2×C4C23×D149
FittingC2×#135×C149C2
socleC22×C149C22×D4
hypercenterC2×#135D149
hypocenterC149#3280
LCSG ▷ C2×C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#135

Complements

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

NH ≅ G/Ntype
1. C2×D8×D149C2semidirect
2. #23750263C2semidirect
3. #23750010C2semidirect
4. #23749863C2semidirect
5. #23749861C2semidirect
6. #23749842C2semidirect
7. #23749774C2semidirect
8. #23749770C2semidirect
9. D8×Dic149C2semidirect
10. C8×C22⋊D149C2semidirect
11. C2×#135×C149C2semidirect
13. C2×#14558723C22semidirect
18. #18011900C22semidirect
21. #18011885C22semidirect
24. D4×Dic149C22semidirect
27. #18011845C22semidirect
28. #18011840C22semidirect
29. #18011835C22semidirect
30. #18011833C22semidirect
31. #18011832C22semidirect
32. C22⋊#11924746C22semidirect
34. C8×Dic149C22semidirect
35. C2×#41×C149C22semidirect
37. C2×Q16×C149C22semidirect
38. C2×SD16×C149C22semidirect
40. C22×C8×C149C22semidirect
76. D8×C149D4semidirect
127. C2×D149#135semidirect
143. C149#3280semidirect
145. C2×#135D149semidirect
156. C2×#41C2×D149semidirect
159. C2×Q16C2×D149semidirect
161. C2×SD16C2×D149semidirect
167. C22×C8C2×D149semidirect
206. D8C22⋊D149semidirect

Maximal subgroups

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

subgroupindex
C2×D8×D1492
#237502632
#237500102
#237498632
#237498612
#237498422
#237497742
#237497702
D8×Dic1492
C8×C22⋊D1492
C2×#135×C1492
#3280149