Finite Group Databasebeta

← #34056286

Subgroups — #34056286

Order 19072.

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

normal subgroups only

This group has 546 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
1C2×#18011935C212yesmaximal, complemented
2#23750279C211yesmaximal, characteristic, complemented
3#23750260C211yesmaximal, characteristic, complemented
4#23749997C211yesmaximal, characteristic, complemented
5#23749870C212yesmaximal, complemented
6#23749831C211yesmaximal, characteristic, complemented
7#23749777C212yesmaximal, complemented
8#23749767C212yesmaximal, complemented
9C4×#14558721C211yesmaximal, characteristic, complemented
10#23749702C211yesmaximal, characteristic, complemented
11#459×C149C211yesmaximal, characteristic, complemented
12C2×#14558735C2212yescomplemented
13C2×D4×D149—21no—
14C2×D4×D149C2212yes—
15#18011935—28no—
16C2×#14558725C2212yes—
17C2×#14558724C2212yescomplemented
18C2×#14558724C2212yescomplemented
19C2×#14558721C2211yescharacteristic
20C2×#14558719C2212yescomplemented
21#18011911C2211yescharacteristic, complemented
22#18011895—22no—
23#18011891C2212yescomplemented
24#18011885—21no—
25#18011882—21no—
26#18011882C2212yes—
27#18011879—22no—
28C4×D596C2211yescharacteristic
29C4×D596C2211yescharacteristic
30C2×C4⋊Dic149—21no—
31#18011844C2211yescharacteristic, complemented
32#18011836C2212yescomplemented
33#18011832C2211yescharacteristic, complemented
34#18011831C2211yescharacteristic
35#18011823C2212yescomplemented
36C4×#11924746C2211yescharacteristic, complemented
37C2×D8×C149C2212yescomplemented
38#127×C149C2211yescharacteristic
39C4×D4×C149C2211yescharacteristic, complemented
40C4⋊C8×C149C2211yescharacteristic, complemented
41#102×C149C2212yescomplemented
42C23×D149—22no—
43#14558735—24no—
44#14558735—42no—
45C2×Dic298C2312yes—
46C2×D596D411yescharacteristic
47C2×D596C2311yescharacteristic
48C2×C22⋊D149—22no—
49C2×C22⋊D149—22no—
50C2×C22⋊D149—22no—
51D4×D149—24no—
52D4×D149—42no—
53D4×D149—44no—
54C22×Dic149—22no—
55C2×C4×D149—21no—
56C2×C4×D149C2312yes—
57#14558725—24no—
58#14558724—24no—
59#14558724—42no—
60#14558721D414yescomplemented
61#14558719—24no—
62C2×#11924746C2311yescharacteristic
63C2×#11924746C2311yescharacteristic
64C4⋊Dic149—22no—
65C4⋊Dic149—21no—
66C4⋊Dic149—21no—
67C4⋊Dic149D411yescharacteristic
68C4⋊Dic149C2311yescharacteristic
69C22⋊Dic149—22no—
70#14558713—22no—
71#14558713—21no—
72#14558713D412yes—
73C2×D4×C149—21no—
74C2×D4×C149—21no—
75C2×D4×C149C2312yes—
76C2×D4×C149C2311yescharacteristic
77C22×C4×C149—21no—
78D8×C149—24no—
79C2×C8×C149C2312yes—
80C4⋊C4×C149C2311yescharacteristic
81C22⋊C4×C149—21no—
82C42×C149C2311yescharacteristic
83C22×D149—21no—
84C22×D149—44no—
85C22×D149—44no—
86C22×D149—82no—
87C22×D149C2×D412yes—
88Dic298—22no—
89Dic298—22no—
90D596—22no—
91D596—21no—
92D596C2×D412yes—
93C22⋊D149—44no—
94C22⋊D149—44no—
95C22⋊D149—44no—
96C2×Dic149—21no—
97C2×Dic149—22no—
98C2×Dic149—44no—
99C2×Dic149C2×D412yes—
100C4×D149—22no—
101C4×D149—22no—
102C4×D149—42no—
103#11924746—21no—
104#11924746C2×D412yescomplemented
105C23×C149—21no—
106C23×C149—22no—
107D4×C149—22no—
108D4×C149—21no—
109D4×C149—22no—
110D4×C149—42no—
111D4×C149—81no—
112D4×C149C2×D412yescomplemented
113C2×C4×C149—21no—
114C2×C4×C149—42no—
115C2×C4×C149C2×D411yescharacteristic
116C2×C4×C149C2×D411yescharacteristic
117C2×C4×C149C2411yescharacteristic
118C8×C149—22no—
119C22×C149—22no—
120C22×C149—41no—
121C22×C149—41no—
122C22×C149—42no—
123C22×C149—42no—
124C22×C149—42no—
125C22×C149C22×D411yescharacteristic
126C2×D149—22no—
127C2×D149—22no—
128C2×D149—22no—
129C2×D149—22no—
130C2×D149—41no—
131C2×D149—41no—
132C2×D149—88no—
133C4×C149—21no—
134C4×C149—41no—
135C4×C149AGL(1,ℤ/8)12yescomplemented
136C4×C149C22×D411yescharacteristic
137C4×C149H(5,𝔽2)11yescharacteristic
138Dic149—22no—
139Dic149—42no—
140Dic149—41no—
141C2×C149—42no—
142C2×C149—82no—
143C2×C149D4211yescharacteristic
144C2×C149C2×AGL(1,ℤ/8)11yescharacteristic
145C2×C149#57711yescharacteristic
146D149—42no—
147D149—42no—
148C149#327211yescharacteristic, complemented, Sylow
149#3272—1491nomaximal, Sylow
150C2×AGL(1,ℤ/8)—1492no—
151#547—1491no—
152D42—1491no—
153#492—1491no—
154#468—1492no—
155#461—1491no—
156#459D14911yescharacteristic, complemented
157#450—1492no—
158#449—1492no—
159C4×D8—1491no—
160#436—1491no—
161C2×#41—1492no—
162C22×D4—2981no—
163C22×D4—1492no—
164AGL(1,ℤ/8)—2988no—
165C2×SD16—1492no—
166C2×SD16—1492no—
167C2×SD16—1492no—
168C2×D8—1491no—
169C2×D8C2×D14912yescomplemented
170C2×M16—1492no—
171C4⋊Q8—1491no—
172#127C2×D14911yescharacteristic
173#123—2982no—
174C22⋊Q8—1492no—
175#121—2981no—
176#121—2981no—
177#121—1492no—
178#120—2982no—
179C4×D4—1491no—
180C4×D4—1491no—
181C4×D4C2×D14911yescharacteristic, complemented
182C2×C4⋊C4—2981no—
183#107—1491no—
184C4⋊C8C2×D14911yescharacteristic, complemented
185#103—1492no—
186#102—1491no—
187#102—1491no—
188#102C2×D14912yescomplemented
189C22⋊C8—1492no—
190C4×C8—1491no—
191C24—2982no—
192#41—2984no—
193#41—5962no—
194C2×Q8—1492no—
195C2×D4—21no—
196C2×D4—21no—
197C2×D4—2984no—
198C2×D4—2982no—
199C2×D4—2982no—
200C2×D4—2982no—
201C2×D4—5962no—
202C2×D4—5964no—
203C2×D4—1491no—
204C2×D4—1491no—
205C2×D4C22×D14912yes—
206C2×D4C22×D14911yescharacteristic
207C22×C4—21no—
208C22×C4—2982no—
209C22×C4—2981no—
210C22×C4—1492no—
211SD16—2984no—
212SD16—2984no—
213SD16—5962no—
214D8—24no—
215D8—1494no—
216M16—2984no—
217C2×C8—1491no—
218C2×C8—1491no—
219C2×C8C22×D14912yes—
220C4⋊C4—2982no—
221C4⋊C4—2981no—
222C4⋊C4—2981no—
223C4⋊C4—1491no—
224C4⋊C4—1491no—
225C4⋊C4C22×D14911yescharacteristic
226C22⋊C4—21no—
227C22⋊C4—2982no—
228C22⋊C4—2982no—
229C22⋊C4—2981no—
230C22⋊C4—1492no—
231C42C22×D14911yescharacteristic
232C23—21no—
233C23—22no—
234C23—2981no—
235C23—5964no—
236C23—5964no—
237C23—1492no—
238C23—11922no—
239Q8—2982no—
240Q8—2982no—
241D4—22no—
242D4—21no—
243D4—22no—
244D4—42no—
245D4—81no—
246D4—2982no—
247D4—2981no—
248D4—5964no—
249D4—5964no—
250D4—5964no—
251D4—1492no—
252D4D4×D14912yescomplemented
253C2×C4—21no—
254C2×C4—42no—
255C2×C4—2982no—
256C2×C4—2982no—
257C2×C4—2981no—
258C2×C4—2982no—
259C2×C4—5964no—
260C2×C4—5962no—
261C2×C4—1492no—
262C2×C4D4×D14911yescharacteristic
263C2×C4D4×D14911yescharacteristic
264C2×C4C23×D14911yescharacteristic
265C8—22no—
266C8—2981no—
267C8—1492no—
268C22—22no—
269C22—41no—
270C22—41no—
271C22—42no—
272C22—42no—
273C22—42no—
274C22—2982no—
275C22—2982no—
276C22—2982no—
277C22—2982no—
278C22—5961no—
279C22—5961no—
280C22—11928no—
281C22C2×D4×D14911yescharacteristic
282C4—21no—
283C4—41no—
284C4—2982no—
285C4—5961no—
286C4—5962no—
287C4#1801193512yescomplemented
288C4C2×D4×D14911yescharacteristic
289C4#1801195711yescharacteristic
290C2—42no—
291C2—82no—
292C2—5962no—
293C2—5962no—
294C2#2375025911yescharacteristic
295C2C2×#1801193511yescharacteristic
296C2#2375043511yescharacteristic
subgroupG/H
centerC22C2×D4×D149
commutator, cosocleC2×C4×C149C24
FrattiniC2×C4C23×D149
Fitting#459×C149C2
socleC22×C149C22×D4
hypercenter#459D149
hypocenterC149#3272
LCSG ▷ C2×C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C22 ◁ C42 ◁ #459

Complements

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

NH ≅ G/Ntype
1. C2×#18011935C2semidirect
2. #23750279C2semidirect
3. #23750260C2semidirect
4. #23749997C2semidirect
5. #23749870C2semidirect
6. #23749831C2semidirect
7. #23749777C2semidirect
8. #23749767C2semidirect
9. C4×#14558721C2semidirect
10. #23749702C2semidirect
11. #459×C149C2semidirect
12. C2×#14558735C22semidirect
17. C2×#14558724C22semidirect
18. C2×#14558724C22semidirect
20. C2×#14558719C22semidirect
21. #18011911C22semidirect
23. #18011891C22semidirect
31. #18011844C22semidirect
32. #18011836C22semidirect
33. #18011832C22semidirect
35. #18011823C22semidirect
36. C4×#11924746C22semidirect
37. C2×D8×C149C22semidirect
39. C4×D4×C149C22semidirect
40. C4⋊C8×C149C22semidirect
41. #102×C149C22semidirect
60. #14558721D4semidirect
104. #11924746C2×D4semidirect
112. D4×C149C2×D4semidirect
135. C4×C149AGL(1,ℤ/8)semidirect
148. C149#3272semidirect
156. #459D149semidirect
169. C2×D8C2×D149semidirect
181. C4×D4C2×D149semidirect
184. C4⋊C8C2×D149semidirect
188. #102C2×D149semidirect
252. D4D4×D149semidirect
287. C4#18011935semidirect

Maximal subgroups

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

subgroupindex
C2×#180119352
#237502792
#237502602
#237499972
#237498702
#237498312
#237497772
#237497672
C4×#145587212
#237497022
#459×C1492
#3272149