Finite Group Databasebeta

← #496×D149 #34055121

Subgroups — #496×D149 #34055121

Order 19072.

668 conjugacy classes of subgroups; only the 145 normal subgroups are shown.

normal subgroups only

This group has 668 conjugacy classes of subgroups — too many to draw. Only its 145 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×SD16×D149C212yesmaximal, complemented
2C2×D8×D149C212yesmaximal, complemented
3#127×D149C211yesmaximal, characteristic, complemented
4#124×D149C211yesmaximal, characteristic, complemented
5#23750015C211yesmaximal, characteristic, complemented
6#23750014C211yesmaximal, characteristic, complemented
7#23750013C212yesmaximal, complemented
8#23750012C211yesmaximal, characteristic, complemented
9#23750011C212yesmaximal, complemented
10#97×D149C211yesmaximal, characteristic, complemented
11#496×C149C211yesmaximal, characteristic, complemented
12C2×Q8×D149C2211yescharacteristic
13C2×D4×D149—22no—
14C2×D4×D149C2212yes—
15C2×D4×D149C2211yescharacteristic
16C2×#14558725C2212yescomplemented
17C2×#14558724C2212yescomplemented
18C2×#14558723C2212yescomplemented
19SD16×D149—28no—
20C2×D1192C2212yescomplemented
21C2×#14558721C2212yescomplemented
22C2×#14558721C2212yescomplemented
23D8×D149—28no—
24C2×C8×D149C2212yes—
25#18011908C2211yescharacteristic, complemented
26#18011907—22no—
27#18011907C2212yescomplemented
28#18011900C2211yescharacteristic, complemented
29#18011899C2211yescharacteristic, complemented
30#18011898C2211yescharacteristic, complemented
31#18011897—22no—
32C22⋊C4×D149—22no—
33C42×D149C2211yescharacteristic
34#18011822C2211yescharacteristic, complemented
35#18011821C2212yescomplemented
36C2×SD16×C149C2212yescomplemented
37C2×D8×C149C2212yescomplemented
38#127×C149C2211yescharacteristic, complemented
39#124×C149C2211yescharacteristic, complemented
40#97×C149C2211yescharacteristic, complemented
41C23×D149—22no—
42C23×D149—21no—
43C2×Dic298—21no—
44C2×Dic298C2311yescharacteristic
45Q8×D149—24no—
46C2×D596—22no—
47C2×D596C2312yes—
48C2×D596C2311yescharacteristic
49C2×C22⋊D149—22no—
50C2×C22⋊D149—24no—
51C2×C22⋊D149—21no—
52D4×D149—24no—
53D4×D149—24no—
54D4×D149—24no—
55D4×D149—48no—
56C2×C4×D149—21no—
57C2×C4×D149D412yes—
58C2×C4×D149C2311yescharacteristic
59#14558725—24no—
60#14558724—24no—
61#14558723—24no—
62D1192—24no—
63#14558721—24no—
64#14558721—24no—
65C2×#11924746C2312yes—
66C8×D149D418yescomplemented
67C22⋊Dic149—22no—
68#14558713—22no—
69#14558713—22no—
70C4×Dic149D412yes—
71C4×Dic149C2311yescharacteristic
72C2×Q8×C149C2311yescharacteristic
73C2×D4×C149—22no—
74C2×D4×C149C2312yes—
75C2×D4×C149C2311yescharacteristic
76SD16×C149—24no—
77D8×C149—24no—
78C2×C8×C149C2312yes—
79C22⋊C4×C149—22no—
80C42×C149C2311yescharacteristic
81C22×D149—22no—
82C22×D149—21no—
83C22×D149—42no—
84C22×D149—44no—
85C22×D149—48no—
86C22×D149—44no—
87C22×D149C2×D411yescharacteristic
88Dic298—22no—
89Dic298—42no—
90D596—22no—
91D596—22no—
92D596—22no—
93D596—44no—
94C22⋊D149—48no—
95C22⋊D149—42no—
96C22⋊D149—44no—
97C2×Dic149—21no—
98C2×Dic149C2×D412yes—
99C2×Dic149C2×D411yescharacteristic
100C4×D149—24no—
101C4×D149—42no—
102C4×D149C2×D414yes—
103#11924746C2×D414yescomplemented
104C23×C149—22no—
105C23×C149—21no—
106Q8×C149—22no—
107D4×C149—22no—
108D4×C149—22no—
109D4×C149—22no—
110D4×C149—44no—
111C2×C4×C149—21no—
112C2×C4×C149C2×D412yes—
113C2×C4×C149C2411yescharacteristic
114C8×C149C2×D414yescomplemented
115C22×C149—41no—
116C22×C149—42no—
117C22×C149—44no—
118C22×C149—42no—
119C22×C149C22×D411yescharacteristic
120C2×D149—41no—
121C2×D149—42no—
122C2×D149—44no—
123C2×D149—42no—
124C2×D149—88no—
125C2×D149—84no—
126C2×D149#12712yes—
127C2×D149AGL(1,ℤ/8)14yes—
128C4×C149—22no—
129C4×C149—41no—
130C4×C149C22×D412yes—
131Dic149—22no—
132Dic149—41no—
133Dic149#12712yes—
134C2×C149—82no—
135C2×C149—81no—
136C2×C149C2×#12711yescharacteristic
137C2×C149C2×AGL(1,ℤ/8)12yes—
138D149—82no—
139D149—81no—
140D149#49614yesdirect product factor
141C149C2×#49611yescharacteristic, complemented, Sylow
142C2×#496—1491nomaximal, Sylow
143C22×SD16—1492no—
144C22×D8—1492no—
145C2×#127—1491no—
146C2×#124—1491no—
147#496—1492no—
148#496—1492no—
149#496—1491no—
150#496—1491no—
151#496—1491no—
152#496D14911yescharacteristic, direct product factor
153C2×#97—1491no—
154C22×Q8—1491no—
155C22×D4—2982no—
156C22×D4—1491no—
157C22×D4—1492no—
158C2×SD16—2988no—
159C2×SD16—1492no—
160C2×SD16—1492no—
161C2×SD16—1492no—
162C2×SD16C2×D14912yescomplemented
163C2×D8—2988no—
164C2×D8—1492no—
165C2×D8—1492no—
166C2×D8—1492no—
167C2×D8C2×D14912yescomplemented
168C22×C8—1492no—
169#127—2982no—
170#127—1492no—
171#127—1491no—
172#127C2×D14911yescharacteristic, complemented
173#124—2982no—
174#124—1491no—
175#124—1491no—
176#124—1491no—
177#124C2×D14911yescharacteristic, complemented
178C2×C22⋊C4—2982no—
179C2×C42—1491no—
180#97—1492no—
181#97—1491no—
182#97C2×D14911yescharacteristic, complemented
183C24—2981no—
184C24—2982no—
185C2×Q8—2981no—
186C2×Q8—2984no—
187C2×Q8—1491no—
188C2×Q8C22×D14911yescharacteristic
189C2×D4—22no—
190C2×D4—2984no—
191C2×D4—2984no—
192C2×D4—2984no—
193C2×D4—2981no—
194C2×D4—2982no—
195C2×D4—2984no—
196C2×D4—2982no—
197C2×D4—5968no—
198C2×D4—1491no—
199C2×D4—1492no—
200C2×D4C22×D14911yescharacteristic
201C2×D4C22×D14912yes—
202C22×C4—2981no—
203C22×C4—1492no—
204C22×C4—1491no—
205SD16—24no—
206SD16—2984no—
207SD16—2984no—
208SD16—2984no—
209D8—24no—
210D8—2984no—
211D8—2984no—
212D8—2984no—
213C2×C8—1492no—
214C2×C8—1498no—
215C2×C8C22×D14912yes—
216C22⋊C4—22no—
217C22⋊C4—2982no—
218C22⋊C4—2982no—
219C22⋊C4—2982no—
220C42—1492no—
221C42—1491no—
222C42C22×D14911yescharacteristic
223C23—21no—
224C23—22no—
225C23—2981no—
226C23—2982no—
227C23—5962no—
228C23—5964no—
229C23—5968no—
230C23—5964no—
231C23—1491no—
232Q8—22no—
233Q8—2982no—
234Q8—5962no—
235D4—22no—
236D4—22no—
237D4—22no—
238D4—44no—
239D4—2982no—
240D4—2982no—
241D4—2982no—
242D4—5964no—
243D4—5968no—
244D4—5962no—
245D4—5964no—
246C2×C4—21no—
247C2×C4—2984no—
248C2×C4—2981no—
249C2×C4—5962no—
250C2×C4—1492no—
251C2×C4—1491no—
252C2×C4—1494no—
253C2×C4D4×D14912yes—
254C2×C4C23×D14911yescharacteristic
255C8—1494no—
256C8D4×D14914yescomplemented
257C22—44no—
258C22—42no—
259C22—41no—
260C22—42no—
261C22—5964no—
262C22—5962no—
263C22—5961no—
264C22—5962no—
265C22—1494no—
266C22—1492no—
267C22—11928no—
268C22—11924no—
269C22C2×D4×D14911yescharacteristic
270C4—22no—
271C4—41no—
272C4—2982no—
273C4—5961no—
274C4—1492no—
275C4C2×D4×D14912yes—
276C2—82no—
277C2—81no—
278C2—1494no—
279C2—11922no—
280C2—11921no—
281C2#127×D14911yescharacteristic
282C2AGL(1,ℤ/8)×D14912yes—
subgroupG/H
centerC22C2×D4×D149
commutator, cosocleC2×C4×C149C24
FrattiniC2×C4C23×D149
Fitting#496×C149C2
socleC22×C149C22×D4
hypercenter#496D149
hypocenterC149C2×#496
LCSG ▷ C2×C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C22 ◁ C42 ◁ #496

Complements

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

NH ≅ G/Ntype
1. C2×SD16×D149C2semidirect
2. C2×D8×D149C2semidirect
3. #127×D149C2semidirect
4. #124×D149C2semidirect
5. #23750015C2semidirect
6. #23750014C2semidirect
7. #23750013C2semidirect
8. #23750012C2semidirect
9. #23750011C2semidirect
10. #97×D149C2semidirect
11. #496×C149C2semidirect
16. C2×#14558725C22semidirect
17. C2×#14558724C22semidirect
18. C2×#14558723C22semidirect
20. C2×D1192C22semidirect
21. C2×#14558721C22semidirect
22. C2×#14558721C22semidirect
25. #18011908C22semidirect
27. #18011907C22semidirect
28. #18011900C22semidirect
29. #18011899C22semidirect
30. #18011898C22semidirect
34. #18011822C22semidirect
35. #18011821C22semidirect
36. C2×SD16×C149C22semidirect
37. C2×D8×C149C22semidirect
38. #127×C149C22semidirect
39. #124×C149C22semidirect
40. #97×C149C22semidirect
66. C8×D149D4semidirect
103. #11924746C2×D4semidirect
114. C8×C149C2×D4semidirect
140. D149#496direct (N × H)
141. C149C2×#496semidirect
152. #496D149direct (N × H)
162. C2×SD16C2×D149semidirect
167. C2×D8C2×D149semidirect
172. #127C2×D149semidirect
177. #124C2×D149semidirect
182. #97C2×D149semidirect
256. C8D4×D149semidirect

Maximal subgroups

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

subgroupindex
C2×SD16×D1492
C2×D8×D1492
#127×D1492
#124×D1492
#237500152
#237500142
#237500132
#237500122
#237500112
#97×D1492
#496×C1492
C2×#496149