Finite Group Databasebeta

← #34056480

Subgroups — #34056480

Order 19072.

454 conjugacy classes of subgroups; only the 117 normal subgroups are shown.

normal subgroups only

This group has 454 conjugacy classes of subgroups — too many to draw. Only its 117 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#23750438C211yesmaximal, characteristic, complemented
2#23750434C212yesmaximal, complemented
3#23750430C211yesmaximal, characteristic, complemented
4#23750010C211yesmaximal, characteristic, complemented
5#23749896C211yesmaximal, characteristic, complemented
6#23749891C212yesmaximal, complemented
7#23749801C212yesmaximal, complemented
8#23749800C212yesmaximal, complemented
9#23749741C211yesmaximal, characteristic, complemented
10#23749740C211yesmaximal, characteristic, complemented
11#473×C149C211yesmaximal, characteristic, complemented
12#18011959C2212yescomplemented
13#18011957C2212yes—
14#18011943—22no—
15#18011943—22no—
16#18011942C2212yescomplemented
17#18011939—22no—
18#18011939C2212yes—
19#18011939C2212yescomplemented
20#18011938—22no—
21#18011934—22no—
22#18011934—21no—
23#18011933—21no—
24#18011933C2211yescharacteristic
25#18011931C2211yescharacteristic
26Q16×D149—21no—
27C2×#14558723C2212yescomplemented
28SD16×D149—22no—
29C2×D1192—21no—
30C2×D1192C2211yescharacteristic
31#18011919C2212yescomplemented
32#18011917C2211yescharacteristic, complemented
33#18011900C2212yescomplemented
34#18011846C2211yescharacteristic, complemented
35#18011838C2211yescharacteristic
36#18011837C2211yescharacteristic, complemented
37#18011837C2212yescomplemented
38#18011827C2212yescomplemented
39C8×Dic149C2211yescharacteristic, complemented
40#137×C149C2212yes—
41C2×Q16×C149C2211yescharacteristic, complemented
42#131×C149C2211yescharacteristic
43#108×C149C2211yescharacteristic, complemented
44#101×C149C2212yescomplemented
45#14558737—22no—
46#14558737—22no—
47#14558737—22no—
48#14558736—22no—
49#14558736—42no—
50#14558736C2311yescharacteristic
51#14558736C2312yes—
52Q8×D149—22no—
53Q8×D149—22no—
54C2×D596—22no—
55C2×D596C2312yes—
56D4×D149—22no—
57D4×D149—42no—
58Dic596D411yescharacteristic
59#14558726—22no—
60#14558726D411yescharacteristic
61#14558725—22no—
62#14558725—22no—
63#14558725D412yes—
64#14558724D411yescharacteristic
65#14558723—22no—
66#14558723—22no—
67#14558723—22no—
68#14558723D411yescharacteristic
69D1192—22no—
70D1192—22no—
71D1192—21no—
72D1192—21no—
73D1192D411yescharacteristic
74#14558721D411yescharacteristic
75#14558720C2311yescharacteristic
76#14558719—22no—
77#14558719—21no—
78C2×#11924746C2311yescharacteristic
79C8×D149—22no—
80C8×D149—21no—
81#14558713—42no—
82C4×Dic149C2311yescharacteristic
83#41×C149C2311yescharacteristic
84C2×Q8×C149C2312yes—
85Q16×C149—22no—
86Q16×C149—21no—
87Q16×C149—21no—
88SD16×C149—22no—
89M16×C149—21no—
90M16×C149C2312yes—
91M16×C149C2311yescharacteristic
92C2×C8×C149—21no—
93C2×C8×C149C2311yescharacteristic
94C22×D149—22no—
95C22×D149—42no—
96Dic298—42no—
97Dic298C2×D411yescharacteristic
98Dic298C2×D412yes—
99D596—22no—
100D596—22no—
101D596—42no—
102D596—42no—
103D596C2×D411yescharacteristic
104D596C2×D412yes—
105C22⋊D149—22no—
106C22⋊D149—21no—
107C22⋊D149—42no—
108C2×Dic149—21no—
109C4×D149—22no—
110C4×D149—21no—
111C4×D149—42no—
112C4×D149—42no—
113C4×D149—42no—
114#11924746—21no—
115#11924746C2×D411yescharacteristic
116#11924746C2×D411yescharacteristic
117Q8×C149—22no—
118Q8×C149—22no—
119Q8×C149C2×D411yescharacteristic
120D4×C149—21no—
121D4×C149C2×D411yescharacteristic
122C2×C4×C149—21no—
123C2×C4×C149—22no—
124C2×C4×C149C2411yescharacteristic
125C8×C149—21no—
126C8×C149—22no—
127C8×C149C2×D411yescharacteristic
128C8×C149C2×D411yescharacteristic
129C22×C149—21no—
130C22×C149H(5,𝔽2)11yescharacteristic
131C2×D149—21no—
132C2×D149—22no—
133C2×D149—42no—
134C2×D149—82no—
135C2×D149—162no—
136C4×C149—21no—
137C4×C149—42no—
138C4×C149C22×D411yescharacteristic
139C4×C149C22×D411yescharacteristic
140Dic149—22no—
141Dic149—21no—
142Dic149—41no—
143C2×C149—21no—
144C2×C149—41no—
145C2×C149D4211yescharacteristic
146D149—41no—
147D149—42no—
148D149—82no—
149C149#329011yescharacteristic, complemented, Sylow
150#3290—1491nomaximal, Sylow
151#578—1491no—
152#577—1492no—
153#576—1491no—
154#495—1491no—
155#473D14911yescharacteristic, complemented
156#472—1491no—
157#471—1492no—
158#455—1492no—
159#454—1492no—
160#443—1491no—
161#443—1491no—
1622−1+4—1492no—
163H(5,𝔽2)—1492no—
164#137—2982no—
165#137—2982no—
166#137—1492no—
167#137C2×D14912yes—
168AGL(1,ℤ/8)—2982no—
169AGL(1,ℤ/8)—2982no—
170AGL(1,ℤ/8)—1492no—
171AGL(1,ℤ/8)—1492no—
172#135—2981no—
173#135—2982no—
174#135—2981no—
175#135—1491no—
176#135—1491no—
177C2×Q16—2981no—
178C2×Q16C2×D14911yescharacteristic, complemented
179C2×SD16—2982no—
180C2×SD16—1492no—
181C2×D8—2981no—
182C2×D8—1491no—
183#131—1492no—
184#131—1491no—
185#131C2×D14911yescharacteristic
186#124—1492no—
187#108—1491no—
188#108C2×D14911yescharacteristic, complemented
189#104—1491no—
190#104—1491no—
191#104—1492no—
192#101C2×D14912yescomplemented
193#100—1492no—
194C4×C8—1491no—
195#41—2982no—
196#41—2982no—
197#41—2982no—
198#41—2982no—
199#41—5962no—
200#41—1491no—
201#41—1492no—
202#41C22×D14911yescharacteristic
203C2×Q8—2982no—
204C2×Q8—2982no—
205C2×Q8C22×D14912yes—
206C2×D4—2982no—
207C2×D4—2982no—
208C2×D4—5962no—
209C2×D4—1492no—
210Q16—22no—
211Q16—21no—
212Q16—21no—
213Q16—2982no—
214Q16—1491no—
215Q16—1491no—
216SD16—22no—
217SD16—2982no—
218SD16—2982no—
219SD16—2982no—
220SD16—2982no—
221SD16—2982no—
222SD16—1491no—
223SD16—1491no—
224SD16—1492no—
225D8—2982no—
226D8—2982no—
227D8—2981no—
228D8—2981no—
229D8—1491no—
230D8—1491no—
231M16—21no—
232M16—2982no—
233M16—2981no—
234M16—1491no—
235M16C22×D14912yes—
236M16C22×D14911yescharacteristic
237C2×C8—21no—
238C2×C8—2982no—
239C2×C8—2981no—
240C2×C8—1491no—
241C2×C8C22×D14911yescharacteristic
242C22⋊C4—5962no—
243C42—1491no—
244C23—2982no—
245C23—5962no—
246Q8—22no—
247Q8—22no—
248Q8—5962no—
249Q8—1491no—
250Q8—1492no—
251Q8D4×D14911yescharacteristic
252D4—21no—
253D4—2982no—
254D4—2981no—
255D4—2982no—
256D4—2982no—
257D4—5962no—
258D4—5962no—
259D4—5962no—
260D4—1491no—
261D4—1492no—
262D4D4×D14911yescharacteristic
263C2×C4—21no—
264C2×C4—22no—
265C2×C4—2982no—
266C2×C4—2981no—
267C2×C4—2981no—
268C2×C4—5962no—
269C2×C4—5962no—
270C2×C4—5962no—
271C2×C4C23×D14911yescharacteristic
272C8—21no—
273C8—22no—
274C8—2981no—
275C8—1491no—
276C8—1491no—
277C8D4×D14911yescharacteristic
278C8D4×D14911yescharacteristic
279C22—21no—
280C22—2981no—
281C22—2982no—
282C22—23842no—
283C22—5962no—
284C22—11922no—
285C22#1801195711yescharacteristic
286C4—21no—
287C4—42no—
288C4—2982no—
289C4—2981no—
290C4—5961no—
291C4C2×D4×D14911yescharacteristic
292C4C2×D4×D14911yescharacteristic
293C2—21no—
294C2—41no—
295C2—5962no—
296C2—5961no—
297C2—11922no—
298C2#2375025911yescharacteristic
subgroupG/H
centerC2#23750259
commutator, cosocleC2×C4×C149C24
FrattiniC2×C4C23×D149
Fitting#473×C149C2
socleC2×C149D42
hypercenter#473D149
hypocenterC149#3290
LCSG ▷ C2×C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C2 ◁ C2×C4 ◁ #473

Complements

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

NH ≅ G/Ntype
1. #23750438C2semidirect
2. #23750434C2semidirect
3. #23750430C2semidirect
4. #23750010C2semidirect
5. #23749896C2semidirect
6. #23749891C2semidirect
7. #23749801C2semidirect
8. #23749800C2semidirect
9. #23749741C2semidirect
10. #23749740C2semidirect
11. #473×C149C2semidirect
12. #18011959C22semidirect
16. #18011942C22semidirect
19. #18011939C22semidirect
27. C2×#14558723C22semidirect
31. #18011919C22semidirect
32. #18011917C22semidirect
33. #18011900C22semidirect
34. #18011846C22semidirect
36. #18011837C22semidirect
37. #18011837C22semidirect
38. #18011827C22semidirect
39. C8×Dic149C22semidirect
41. C2×Q16×C149C22semidirect
43. #108×C149C22semidirect
44. #101×C149C22semidirect
149. C149#3290semidirect
155. #473D149semidirect
178. C2×Q16C2×D149semidirect
188. #108C2×D149semidirect
192. #101C2×D149semidirect

Maximal subgroups

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

subgroupindex
#237504382
#237504342
#237504302
#237500102
#237498962
#237498912
#237498012
#237498002
#237497412
#237497402
#473×C1492
#3290149