Finite Group Databasebeta

← #34056479

Subgroups — #34056479

Order 19072.

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

normal subgroups only

This group has 454 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
1#23750439C211yesmaximal, characteristic, complemented
2#23750437C212yesmaximal, complemented
3#23750427C211yesmaximal, characteristic, complemented
4#23750009C211yesmaximal, characteristic, complemented
5#23749901C211yesmaximal, characteristic, complemented
6#23749896C211yesmaximal, characteristic, complemented
7#23749888C212yesmaximal, complemented
8#23749804C212yesmaximal, complemented
9#23749799C212yesmaximal, complemented
10#23749743C211yesmaximal, characteristic, complemented
11#443×C149C211yesmaximal, characteristic, complemented
12#18011958C2212yescomplemented
13#18011957C2212yes—
14#18011944—22no—
15#18011944C2212yes—
16#18011941C2212yescomplemented
17#18011940—22no—
18#18011939—22no—
19#18011939C2212yescomplemented
20#18011938—22no—
21#18011936C2212yes—
22#18011934—21no—
23#18011933—22no—
24#18011933C2211yescharacteristic
25#18011930—21no—
26C2×Dic596C2211yescharacteristic, complemented
27Q16×D149—21no—
28C2×#14558725—22no—
29C2×#14558725C2212yescomplemented
30C2×D1192C2211yescharacteristic
31D8×D149—21no—
32#18011917C2211yescharacteristic
33#18011917C2211yescharacteristic, complemented
34#18011899C2212yescomplemented
35#18011847C2211yescharacteristic, complemented
36#18011839C2211yescharacteristic
37#18011839C2211yescharacteristic, complemented
38#18011829C2212yescomplemented
39#18011827C2212yescomplemented
40#135×C149C2211yescharacteristic
41#131×C149C2212yescomplemented
42#108×C149C2211yescharacteristic, complemented
43#104×C149C2212yescomplemented
44C4×C8×C149C2211yescharacteristic, complemented
45#14558737—22no—
46#14558736—22no—
47#14558736—22no—
48#14558736C2311yescharacteristic
49#14558736C2311yescharacteristic
50#14558735—22no—
51#14558735—42no—
52C2×Dic298—22no—
53C2×Dic298C2312yes—
54Q8×D149—22no—
55C2×D596—22no—
56C2×D596C2312yes—
57D4×D149—22no—
58D4×D149—42no—
59Dic596—22no—
60Dic596—21no—
61Dic596—21no—
62Dic596D411yescharacteristic
63#14558726—22no—
64#14558725—22no—
65#14558725—22no—
66#14558725—22no—
67#14558725—22no—
68#14558725D411yescharacteristic
69#14558725D411yescharacteristic
70#14558724—22no—
71#14558723—22no—
72D1192—22no—
73D1192—21no—
74D1192—21no—
75D1192D411yescharacteristic
76#14558721—22no—
77#14558720C2311yescharacteristic
78#14558720C2311yescharacteristic
79#14558719—21no—
80#14558719—21no—
81C8×D149—21no—
82C8×D149—21no—
83#14558713—42no—
84#41×C149C2312yes—
85Q16×C149D411yescharacteristic
86SD16×C149D412yes—
87D8×C149D411yescharacteristic
88M16×C149—22no—
89M16×C149C2312yes—
90C2×C8×C149—22no—
91C2×C8×C149C2311yescharacteristic
92C2×C8×C149C2311yescharacteristic
93C42×C149C2311yescharacteristic
94C22×D149—22no—
95C22×D149—42no—
96Dic298—22no—
97Dic298—22no—
98Dic298—42no—
99Dic298C2×D411yescharacteristic
100Dic298C2×D411yescharacteristic
101D596—22no—
102D596—22no—
103D596—42no—
104D596C2×D411yescharacteristic
105D596C2×D411yescharacteristic
106C22⋊D149—21no—
107C22⋊D149—21no—
108C22⋊D149—42no—
109C22⋊D149—42no—
110C2×Dic149—22no—
111C2×Dic149—42no—
112C4×D149—21no—
113C4×D149—21no—
114C4×D149—42no—
115C4×D149—42no—
116#11924746—21no—
117#11924746—21no—
118Q8×C149C2×D412yes—
119D4×C149—22no—
120D4×C149C2×D412yes—
121C2×C4×C149—22no—
122C2×C4×C149—21no—
123C2×C4×C149C2411yescharacteristic
124C8×C149—22no—
125C8×C149C2×D411yescharacteristic
126C8×C149C2×D411yescharacteristic
127C8×C149C2×D411yescharacteristic
128C8×C149C2×D411yescharacteristic
129C22×C149—22no—
130C22×C149H(5,𝔽2)11yescharacteristic
131C2×D149—21no—
132C2×D149—21no—
133C2×D149—42no—
134C2×D149—82no—
135C2×D149—162no—
136C4×C149—22no—
137C4×C149—41no—
138C4×C149C22×D411yescharacteristic
139C4×C149C22×D411yescharacteristic
140Dic149—21no—
141Dic149—21no—
142Dic149—42no—
143C2×C149—21no—
144C2×C149—42no—
145C2×C149D4211yescharacteristic
146D149—41no—
147D149—41no—
148D149—82no—
149C149#329011yescharacteristic, complemented, Sylow
150#3290—1491nomaximal, Sylow
151#578—1491no—
152#577—1492no—
153#576—1491no—
154#495—1491no—
155#473—1491no—
156#472—1491no—
157#471—1492no—
158#455—1492no—
159#454—1492no—
160#443—1491no—
161#443D14911yescharacteristic, complemented
1622−1+4—1492no—
163H(5,𝔽2)—1492no—
164#137—2982no—
165#137—2982no—
166#137—1492no—
167#137—1492no—
168AGL(1,ℤ/8)—2982no—
169AGL(1,ℤ/8)—2982no—
170AGL(1,ℤ/8)—1492no—
171AGL(1,ℤ/8)—1492no—
172#135—2982no—
173#135—2981no—
174#135—2981no—
175#135—1491no—
176#135C2×D14911yescharacteristic
177C2×Q16—2981no—
178C2×Q16—1491no—
179C2×SD16—2982no—
180C2×SD16—1492no—
181C2×D8—2981no—
182C2×D8—1491no—
183#131—1491no—
184#131—1491no—
185#131C2×D14912yescomplemented
186#124—1492no—
187#108—1491no—
188#108C2×D14911yescharacteristic, complemented
189#104—1491no—
190#104—1491no—
191#104C2×D14912yescomplemented
192#101—1492no—
193#100—1492no—
194C4×C8C2×D14911yescharacteristic, complemented
195#41—2982no—
196#41—2982no—
197#41—2982no—
198#41—2982no—
199#41—5962no—
200#41—1491no—
201#41—1491no—
202#41C22×D14912yes—
203C2×Q8—2982no—
204C2×Q8—2982no—
205C2×Q8—1492no—
206C2×D4—2982no—
207C2×D4—2982no—
208C2×D4—5962no—
209C2×D4—1492no—
210Q16—2982no—
211Q16—2982no—
212Q16—2981no—
213Q16—2981no—
214Q16—1491no—
215Q16D59611yescharacteristic
216SD16—2982no—
217SD16—2982no—
218SD16—2982no—
219SD16—2982no—
220SD16—2982no—
221SD16—2982no—
222SD16—1491no—
223SD16—1491no—
224SD16D59612yes—
225D8—2982no—
226D8—2982no—
227D8—2981no—
228D8—2981no—
229D8—1491no—
230D8D59611yescharacteristic
231M16—22no—
232M16—2981no—
233M16—2981no—
234M16—1491no—
235M16—1491no—
236M16C22×D14912yes—
237C2×C8—22no—
238C2×C8—2981no—
239C2×C8—2981no—
240C2×C8C22×D14911yescharacteristic
241C2×C8C22×D14911yescharacteristic
242C22⋊C4—5962no—
243C42C22×D14911yescharacteristic
244C23—2982no—
245C23—5962no—
246Q8—2982no—
247Q8—2982no—
248Q8—5962no—
249Q8—1491no—
250Q8—1491no—
251Q8C2×D59612yes—
252D4—22no—
253D4—2981no—
254D4—2981no—
255D4—2982no—
256D4—2982no—
257D4—5962no—
258D4—5962no—
259D4—5962no—
260D4—1491no—
261D4—1491no—
262D4C2×D59612yes—
263C2×C4—22no—
264C2×C4—21no—
265C2×C4—2981no—
266C2×C4—2981no—
267C2×C4—2982no—
268C2×C4—5962no—
269C2×C4—5962no—
270C2×C4—5962no—
271C2×C4C23×D14911yescharacteristic
272C8—22no—
273C8—2981no—
274C8—2981no—
275C8D4×D14911yescharacteristic
276C8D4×D14911yescharacteristic
277C8C2×D59611yescharacteristic
278C8C2×D59611yescharacteristic
279C22—22no—
280C22—2981no—
281C22—2981no—
282C22—23842no—
283C22—5962no—
284C22—11922no—
285C22#1801195711yescharacteristic
286C4—22no—
287C4—41no—
288C4—2981no—
289C4—2981no—
290C4—5962no—
291C4C2×D4×D14911yescharacteristic
292C4C22×D59611yescharacteristic
293C2—21no—
294C2—42no—
295C2—5961no—
296C2—5961no—
297C2—11922no—
298C2D4×D59611yescharacteristic
subgroupG/H
centerC2D4×D596
commutator, cosocleC2×C4×C149C24
FrattiniC2×C4C23×D149
Fitting#443×C149C2
socleC2×C149D42
hypercenter#443D149
hypocenterC149#3290
LCSG ▷ C2×C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C2 ◁ C2×C4 ◁ #443

Complements

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

NH ≅ G/Ntype
1. #23750439C2semidirect
2. #23750437C2semidirect
3. #23750427C2semidirect
4. #23750009C2semidirect
5. #23749901C2semidirect
6. #23749896C2semidirect
7. #23749888C2semidirect
8. #23749804C2semidirect
9. #23749799C2semidirect
10. #23749743C2semidirect
11. #443×C149C2semidirect
12. #18011958C22semidirect
16. #18011941C22semidirect
19. #18011939C22semidirect
26. C2×Dic596C22semidirect
29. C2×#14558725C22semidirect
33. #18011917C22semidirect
34. #18011899C22semidirect
35. #18011847C22semidirect
37. #18011839C22semidirect
38. #18011829C22semidirect
39. #18011827C22semidirect
41. #131×C149C22semidirect
42. #108×C149C22semidirect
43. #104×C149C22semidirect
44. C4×C8×C149C22semidirect
149. C149#3290semidirect
161. #443D149semidirect
185. #131C2×D149semidirect
188. #108C2×D149semidirect
191. #104C2×D149semidirect
194. C4×C8C2×D149semidirect

Maximal subgroups

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

subgroupindex
#237504392
#237504372
#237504272
#237500092
#237499012
#237498962
#237498882
#237498042
#237497992
#237497432
#443×C1492
#3290149