Finite Group Databasebeta

← #34056290

Subgroups — #34056290

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×#18011938C212yesmaximal, complemented
2#23750278C211yesmaximal, characteristic, complemented
3#23750260C211yesmaximal, characteristic, complemented
4#23749868C212yesmaximal, complemented
5#23749827C211yesmaximal, characteristic, complemented
6#23749817C211yesmaximal, characteristic, complemented
7#23749774C212yesmaximal, complemented
8#23749769C212yesmaximal, complemented
9C4×D1192C211yesmaximal, characteristic, complemented
10#23749704C211yesmaximal, characteristic, complemented
11#492×C149C211yesmaximal, characteristic, complemented
12C2×#14558737C2212yescomplemented
13C2×D4×D149—21no—
14C2×D4×D149C2212yes—
15#18011938—28no—
16C2×#14558723C2212yes—
17C2×D1192C2211yescharacteristic
18C2×#14558721C2212yescomplemented
19C2×#14558719C2212yescomplemented
20#18011896—22no—
21#18011887C2212yescomplemented
22#18011886—21no—
23#18011882—21no—
24#18011882C2212yes—
25#18011879—22no—
26C4×D596C2211yescharacteristic
27C4×D596C2211yescharacteristic
28C4×D596C2211yescharacteristic, complemented
29C4⋊C4×D149—21no—
30#18011845C2211yescharacteristic, complemented
31C4⋊#11924746C2211yescharacteristic, complemented
32#18011835C2212yescomplemented
33#18011833C2211yescharacteristic
34#18011833C2211yescharacteristic, complemented
35#18011832C2212yescomplemented
36#18011823C2212yescomplemented
37C2×SD16×C149C2212yescomplemented
38C2×SD16×C149C2212yescomplemented
39C4⋊Q8×C149C2211yescharacteristic, complemented
40#127×C149C2211yescharacteristic
41C4×C8×C149C2211yescharacteristic, complemented
42C23×D149—22no—
43#14558737—24no—
44#14558737—42no—
45C2×D596—22no—
46C2×D596D411yescharacteristic
47C2×D596C2311yescharacteristic
48C2×D596C2311yescharacteristic
49C2×C22⋊D149—22no—
50C2×C22⋊D149—22no—
51D4×D149—24no—
52D4×D149—42no—
53D4×D149—44no—
54C2×C4×D149—22no—
55C2×C4×D149—21no—
56C2×C4×D149—21no—
57C2×C4×D149C2312yes—
58#14558723—24no—
59D1192D414yescomplemented
60#14558721—24no—
61#14558719—24no—
62C2×#11924746C2312yes—
63C4⋊Dic149D411yescharacteristic
64C4⋊Dic149C2311yescharacteristic
65C4⋊Dic149C2311yescharacteristic
66#14558715—22no—
67C22⋊Dic149—22no—
68#14558713—22no—
69#14558713—21no—
70#14558713—21no—
71#14558713D412yes—
72C2×Q8×C149C2312yes—
73C2×D4×C149—21no—
74C2×D4×C149—21no—
75C2×D4×C149C2312yes—
76SD16×C149—24no—
77SD16×C149—42no—
78C2×C8×C149C2311yescharacteristic
79C2×C8×C149C2311yescharacteristic
80C4⋊C4×C149—21no—
81C4⋊C4×C149—21no—
82C42×C149C2311yescharacteristic
83C22×D149—21no—
84C22×D149—21no—
85C22×D149—44no—
86C22×D149—44no—
87C22×D149—82no—
88C22×D149C2×D412yes—
89D596—22no—
90D596—21no—
91D596—21no—
92D596—44no—
93D596C2×D412yes—
94D596C2×D412yescomplemented
95C22⋊D149—44no—
96C22⋊D149—44no—
97C2×Dic149—21no—
98C2×Dic149—21no—
99C2×Dic149C2×D412yes—
100C4×D149—22no—
101C4×D149—22no—
102C4×D149—44no—
103C4×D149—42no—
104C4×D149—42no—
105#11924746—22no—
106C23×C149—22no—
107Q8×C149—22no—
108Q8×C149—22no—
109D4×C149—22no—
110D4×C149—22no—
111D4×C149—42no—
112D4×C149—81no—
113C2×C4×C149—22no—
114C2×C4×C149C2×D411yescharacteristic
115C2×C4×C149C2×D411yescharacteristic
116C2×C4×C149C2411yescharacteristic
117C8×C149—21no—
118C8×C149C2×D412yescomplemented
119C22×C149—42no—
120C22×C149—42no—
121C22×C149—42no—
122C22×C149C22×D411yescharacteristic
123C2×D149—22no—
124C2×D149—22no—
125C2×D149—22no—
126C2×D149—22no—
127C2×D149—22no—
128C2×D149—41no—
129C2×D149—41no—
130C2×D149—41no—
131C2×D149—41no—
132C2×D149—88no—
133C4×C149—21no—
134C4×C149—42no—
135C4×C149AGL(1,ℤ/8)12yescomplemented
136C4×C149C22×D411yescharacteristic
137C4×C149H(5,𝔽2)11yescharacteristic
138Dic149—22no—
139Dic149—41no—
140Dic149—41no—
141C2×C149—82no—
142C2×C149D4211yescharacteristic
143C2×C149C2×AGL(1,ℤ/8)11yescharacteristic
144C2×C149#57711yescharacteristic
145D149—42no—
146D149—42no—
147D149—42no—
148C149#327211yescharacteristic, complemented, Sylow
149#3272—1491nomaximal, Sylow
150C2×AGL(1,ℤ/8)—1492no—
151#547—1491no—
152D42—1491no—
153#492D14911yescharacteristic, complemented
154#468—1492no—
155#461—1491no—
156#459—1491no—
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×SD16C2×D14912yescomplemented
167C2×SD16C2×D14912yescomplemented
168C2×D8—1492no—
169C2×D8—1491no—
170C2×M16—1492no—
171C4⋊Q8C2×D14911yescharacteristic, complemented
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×D4—1491no—
182C2×C4⋊C4—2981no—
183#107—1491no—
184C4⋊C8—1491no—
185#103—1492no—
186#102—1492no—
187#102—1491no—
188#102—1491no—
189C22⋊C8—1492no—
190C4×C8C2×D14911yescharacteristic, complemented
191C24—2982no—
192#41—2984no—
193#41—5962no—
194C2×Q8C22×D14912yes—
195C2×D4—21no—
196C2×D4—21no—
197C2×D4—2982no—
198C2×D4—2984no—
199C2×D4—2982no—
200C2×D4—2982no—
201C2×D4—5962no—
202C2×D4—5964no—
203C2×D4—1491no—
204C2×D4—1491no—
205C2×D4—1491no—
206C2×D4C22×D14912yes—
207C22×C4—2982no—
208C22×C4—2981no—
209C22×C4—2981no—
210C22×C4—1492no—
211SD16—24no—
212SD16—42no—
213SD16—2984no—
214D8—2984no—
215D8—1494no—
216M16—2984no—
217C2×C8—1492no—
218C2×C8C22×D14911yescharacteristic
219C2×C8C22×D14911yescharacteristic
220C4⋊C4—21no—
221C4⋊C4—21no—
222C4⋊C4—2982no—
223C4⋊C4—1491no—
224C4⋊C4—1491no—
225C4⋊C4—1491no—
226C22⋊C4—2982no—
227C22⋊C4—2982no—
228C22⋊C4—2981no—
229C22⋊C4—2981no—
230C22⋊C4—1492no—
231C42C22×D14911yescharacteristic
232C23—22no—
233C23—2981no—
234C23—2981no—
235C23—5964no—
236C23—5964no—
237C23—1492no—
238C23—11922no—
239Q8—22no—
240Q8—22no—
241D4—22no—
242D4—22no—
243D4—42no—
244D4—81no—
245D4—2982no—
246D4—2981no—
247D4—2981no—
248D4—5964no—
249D4—5964no—
250D4—5964no—
251D4—1492no—
252D4—1492no—
253C2×C4—22no—
254C2×C4—2982no—
255C2×C4—2982no—
256C2×C4—2981no—
257C2×C4—2981no—
258C2×C4—5964no—
259C2×C4—5962no—
260C2×C4—5962no—
261C2×C4—1492no—
262C2×C4D4×D14911yescharacteristic
263C2×C4D4×D14911yescharacteristic
264C2×C4C23×D14911yescharacteristic
265C8—21no—
266C8—2982no—
267C8D4×D14912yescomplemented
268C22—42no—
269C22—42no—
270C22—42no—
271C22—2982no—
272C22—2982no—
273C22—2982no—
274C22—2982no—
275C22—2982no—
276C22—5961no—
277C22—5961no—
278C22—5961no—
279C22—5961no—
280C22—11928no—
281C22C2×D4×D14911yescharacteristic
282C4—21no—
283C4—42no—
284C4—2982no—
285C4—5961no—
286C4—5961no—
287C4#1801193812yescomplemented
288C4C2×D4×D14911yescharacteristic
289C4#1801195611yescharacteristic
290C2—82no—
291C2—5962no—
292C2—5962no—
293C2—5962no—
294C2#2375026011yescharacteristic
295C2C2×#1801193811yescharacteristic
296C2#2375043111yescharacteristic
subgroupG/H
centerC22C2×D4×D149
commutator, cosocleC2×C4×C149C24
FrattiniC2×C4C23×D149
Fitting#492×C149C2
socleC22×C149C22×D4
hypercenter#492D149
hypocenterC149#3272
LCSG ▷ C2×C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C22 ◁ C42 ◁ #492

Complements

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

NH ≅ G/Ntype
1. C2×#18011938C2semidirect
2. #23750278C2semidirect
3. #23750260C2semidirect
4. #23749868C2semidirect
5. #23749827C2semidirect
6. #23749817C2semidirect
7. #23749774C2semidirect
8. #23749769C2semidirect
9. C4×D1192C2semidirect
10. #23749704C2semidirect
11. #492×C149C2semidirect
12. C2×#14558737C22semidirect
18. C2×#14558721C22semidirect
19. C2×#14558719C22semidirect
21. #18011887C22semidirect
28. C4×D596C22semidirect
30. #18011845C22semidirect
31. C4⋊#11924746C22semidirect
32. #18011835C22semidirect
34. #18011833C22semidirect
35. #18011832C22semidirect
36. #18011823C22semidirect
37. C2×SD16×C149C22semidirect
38. C2×SD16×C149C22semidirect
39. C4⋊Q8×C149C22semidirect
41. C4×C8×C149C22semidirect
59. D1192D4semidirect
94. D596C2×D4semidirect
118. C8×C149C2×D4semidirect
135. C4×C149AGL(1,ℤ/8)semidirect
148. C149#3272semidirect
153. #492D149semidirect
166. C2×SD16C2×D149semidirect
167. C2×SD16C2×D149semidirect
171. C4⋊Q8C2×D149semidirect
190. C4×C8C2×D149semidirect
267. C8D4×D149semidirect
287. C4#18011938semidirect

Maximal subgroups

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

subgroupindex
C2×#180119382
#237502782
#237502602
#237498682
#237498272
#237498172
#237497742
#237497692
C4×D11922
#237497042
#492×C1492
#3272149