Finite Group Databasebeta

← #34056488

Subgroups — #34056488

Order 19072.

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

normal subgroups only

This group has 476 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#23750428C212yesmaximal, complemented
2#23750427C211yesmaximal, characteristic, complemented
3#23750000C211yesmaximal, characteristic, complemented
4#23749895C211yesmaximal, characteristic, complemented
5#23749893C212yesmaximal, complemented
6#23749892C211yesmaximal, characteristic, complemented
7#23749793C212yesmaximal, complemented
8#23749791C212yesmaximal, complemented
9#23749742C211yesmaximal, characteristic, complemented
10#23749740C211yesmaximal, characteristic, complemented
11#576×C149C211yesmaximal, characteristic, complemented
12#18011957C2212yescomplemented
13#18011938—22no—
14#18011937—22no—
15#18011937C2212yescomplemented
16#18011936—22no—
17#18011936C2212yescomplemented
18#18011936C2212yescomplemented
19#18011934—21no—
20#18011931—22no—
21#18011931C2211yescharacteristic
22C2×D1192C2211yescharacteristic, complemented
23C2×#14558721—22no—
24C2×#14558721C2212yescomplemented
25D8×D149—21no—
26#18011918C2212yescomplemented
27#18011917C2211yescharacteristic, complemented
28#18011907C2212yescomplemented
29#18011847C2211yescharacteristic, complemented
30#18011846C2211yescharacteristic, complemented
31#18011838C2211yescharacteristic, complemented
32#18011838C2212yescomplemented
33#18011837C2211yescharacteristic, complemented
34#18011828C2212yescomplemented
35#18011827C2212yescomplemented
36C8×Dic149C2211yescharacteristic, complemented
37H(5,𝔽2)×C149C2212yescomplemented
38AGL(1,ℤ/8)×C149—22no—
39AGL(1,ℤ/8)×C149C2212yescomplemented
40#135×C149—21no—
41#135×C149C2211yescharacteristic
42C2×D8×C149—21no—
43C2×D8×C149C2211yescharacteristic, complemented
44#131×C149C2211yescharacteristic, complemented
45#14558737—22no—
46#14558736—22no—
47#14558736C2311yescharacteristic
48C2×D596—22no—
49C2×D596C2312yes—
50C2×C22⋊D149—42no—
51D4×D149—22no—
52D4×D149—42no—
53#14558726D411yescharacteristic, complemented
54#14558724—22no—
55#14558724D411yescharacteristic, complemented
56#14558723—22no—
57#14558723—22no—
58#14558723D411yescharacteristic, complemented
59D1192—21no—
60D1192—21no—
61#14558721—22no—
62#14558721—22no—
63#14558721—22no—
64#14558721—22no—
65#14558721—22no—
66#14558721D411yescharacteristic, complemented
67#14558720—22no—
68#14558720C2311yescharacteristic
69#14558720C2312yes—
70#14558719—21no—
71C2×#11924746—22no—
72C2×#11924746C2311yescharacteristic
73C8×D149—21no—
74C4×Dic149C2311yescharacteristic
75#41×C149—22no—
76#41×C149—22no—
77#41×C149C2312yes—
78#41×C149C2311yescharacteristic
79C2×D4×C149—22no—
80C2×D4×C149—22no—
81C2×D4×C149—42no—
82C2×D4×C149C2312yes—
83Q16×C149D411yescharacteristic, complemented
84SD16×C149—22no—
85SD16×C149D412yescomplemented
86D8×C149—22no—
87D8×C149—21no—
88D8×C149—21no—
89D8×C149D411yescharacteristic, complemented
90M16×C149—21no—
91M16×C149C2311yescharacteristic
92C2×C8×C149—21no—
93C2×C8×C149C2311yescharacteristic
94C22×D149—22no—
95C22×D149—42no—
96Dic298C2×D411yescharacteristic
97D596—22no—
98D596—22no—
99D596—42no—
100D596C2×D411yescharacteristic
101C22⋊D149—21no—
102C22⋊D149—42no—
103C22⋊D149—84no—
104C2×Dic149—21no—
105C4×D149—21no—
106C4×D149—42no—
107#11924746—22no—
108#11924746—21no—
109#11924746C2×D411yescharacteristic
110#11924746C2×D411yescharacteristic
111C23×C149—22no—
112C23×C149—42no—
113Q8×C149C2×D411yescharacteristic
114Q8×C149C2×D412yes—
115D4×C149—22no—
116D4×C149—21no—
117D4×C149—22no—
118D4×C149—22no—
119D4×C149—42no—
120D4×C149—42no—
121D4×C149C2×D411yescharacteristic
122D4×C149C2×D412yes—
123C2×C4×C149—22no—
124C2×C4×C149—21no—
125C2×C4×C149—42no—
126C2×C4×C149C2411yescharacteristic
127C8×C149—21no—
128C8×C149C2×D411yescharacteristic
129C8×C149C2×D411yescharacteristic
130C22×C149—21no—
131C22×C149—22no—
132C22×C149—42no—
133C22×C149—82no—
134C22×C149—162no—
135C22×C149H(5,𝔽2)11yescharacteristic
136C2×D149—21no—
137C2×D149—42no—
138C2×D149—82no—
139C2×D149—162no—
140C4×C149—21no—
141C4×C149—22no—
142C4×C149C22×D411yescharacteristic
143C4×C149C22×D411yescharacteristic
144Dic149—22no—
145Dic149—21no—
146C2×C149—21no—
147C2×C149—42no—
148C2×C149—41no—
149C2×C149—82no—
150C2×C149D4211yescharacteristic
151D149—41no—
152D149—82no—
153C149#329211yescharacteristic, complemented, Sylow
154#3292—1491nomaximal, Sylow
155#576—1492no—
156#576—1491no—
157#576D14911yescharacteristic, complemented
158#493—1491no—
159#472—1492no—
160#472—1491no—
161#472—1491no—
162#453—1492no—
163#453—1492no—
164#443—1491no—
165#443—1491no—
166H(5,𝔽2)—1492no—
167H(5,𝔽2)C2×D14912yescomplemented
168AGL(1,ℤ/8)—22no—
169AGL(1,ℤ/8)—2982no—
170AGL(1,ℤ/8)—2982no—
171AGL(1,ℤ/8)—2982no—
172AGL(1,ℤ/8)—1492no—
173AGL(1,ℤ/8)—1492no—
174AGL(1,ℤ/8)—1492no—
175AGL(1,ℤ/8)C2×D14912yescomplemented
176#135—21no—
177#135—2982no—
178#135—2981no—
179#135—1491no—
180#135C2×D14911yescharacteristic
181C2×D8—21no—
182C2×D8—2982no—
183C2×D8—2981no—
184C2×D8—1492no—
185C2×D8—1491no—
186C2×D8C2×D14911yescharacteristic, complemented
187#131—1492no—
188#131—1491no—
189#131C2×D14911yescharacteristic, complemented
190#127—1492no—
191#108—1491no—
192#108—1491no—
193#104—1491no—
194#104—1492no—
195#104—1491no—
196#100—1492no—
197#100—1492no—
198C4×C8—1491no—
199#41—22no—
200#41—22no—
201#41—2982no—
202#41—2982no—
203#41—1491no—
204#41C22×D14911yescharacteristic
205#41C22×D14912yes—
206C2×D4—22no—
207C2×D4—22no—
208C2×D4—42no—
209C2×D4—2982no—
210C2×D4—2982no—
211C2×D4—5962no—
212C2×D4—5962no—
213C2×D4—1492no—
214C2×D4C22×D14912yes—
215Q16—1491no—
216Q16C22⋊D14911yescharacteristic, complemented
217SD16—22no—
218SD16—2982no—
219SD16—2982no—
220SD16—2982no—
221SD16—1491no—
222SD16—1491no—
223SD16C22⋊D14912yescomplemented
224D8—22no—
225D8—21no—
226D8—21no—
227D8—2982no—
228D8—2982no—
229D8—2982no—
230D8—2982no—
231D8—2982no—
232D8—2981no—
233D8—2981no—
234D8—1491no—
235D8C22⋊D14911yescharacteristic, complemented
236M16—21no—
237M16—2982no—
238M16—2981no—
239M16—1492no—
240M16—1491no—
241M16C22×D14911yescharacteristic
242C2×C8—21no—
243C2×C8—2982no—
244C2×C8—2981no—
245C2×C8—1491no—
246C2×C8C22×D14911yescharacteristic
247C42—1491no—
248C23—22no—
249C23—42no—
250C23—2982no—
251C23—5962no—
252Q8—1491no—
253Q8D4×D14911yescharacteristic
254Q8C2×C22⋊D14912yes—
255D4—21no—
256D4—22no—
257D4—22no—
258D4—22no—
259D4—42no—
260D4—42no—
261D4—2981no—
262D4—2982no—
263D4—2982no—
264D4—5962no—
265D4—5962no—
266D4—1491no—
267D4—11924no—
268D4D4×D14911yescharacteristic
269D4C2×C22⋊D14912yes—
270C2×C4—22no—
271C2×C4—21no—
272C2×C4—42no—
273C2×C4—2981no—
274C2×C4—2981no—
275C2×C4—5962no—
276C2×C4C23×D14911yescharacteristic
277C8—21no—
278C8—2982no—
279C8—2981no—
280C8—1491no—
281C8—1491no—
282C8C2×C22⋊D14911yescharacteristic
283C8C2×C22⋊D14911yescharacteristic
284C22—21no—
285C22—22no—
286C22—42no—
287C22—82no—
288C22—162no—
289C22—2981no—
290C22—23842no—
291C22—5962no—
292C22—11922no—
293C22#1801195611yescharacteristic
294C4—21no—
295C4—22no—
296C4—2982no—
297C4—2981no—
298C4C2×D4×D14911yescharacteristic
299C4C22×C22⋊D14911yescharacteristic
300C2—21no—
301C2—41no—
302C2—42no—
303C2—82no—
304C2—5961no—
305C2—11922no—
306C2D4×C22⋊D14911yescharacteristic
subgroupG/H
centerC2D4×C22⋊D149
commutator, cosocleC2×C4×C149C24
FrattiniC2×C4C23×D149
Fitting#576×C149C2
socleC2×C149D42
hypercenter#576D149
hypocenterC149#3292
LCSG ▷ C2×C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C2 ◁ C2×C4 ◁ #576

Complements

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

NH ≅ G/Ntype
1. #23750428C2semidirect
2. #23750427C2semidirect
3. #23750000C2semidirect
4. #23749895C2semidirect
5. #23749893C2semidirect
6. #23749892C2semidirect
7. #23749793C2semidirect
8. #23749791C2semidirect
9. #23749742C2semidirect
10. #23749740C2semidirect
11. #576×C149C2semidirect
12. #18011957C22semidirect
15. #18011937C22semidirect
17. #18011936C22semidirect
18. #18011936C22semidirect
22. C2×D1192C22semidirect
24. C2×#14558721C22semidirect
26. #18011918C22semidirect
27. #18011917C22semidirect
28. #18011907C22semidirect
29. #18011847C22semidirect
30. #18011846C22semidirect
31. #18011838C22semidirect
32. #18011838C22semidirect
33. #18011837C22semidirect
34. #18011828C22semidirect
35. #18011827C22semidirect
36. C8×Dic149C22semidirect
37. H(5,𝔽2)×C149C22semidirect
39. AGL(1,ℤ/8)×C149C22semidirect
43. C2×D8×C149C22semidirect
44. #131×C149C22semidirect
53. #14558726D4semidirect
55. #14558724D4semidirect
58. #14558723D4semidirect
66. #14558721D4semidirect
83. Q16×C149D4semidirect
85. SD16×C149D4semidirect
89. D8×C149D4semidirect
153. C149#3292semidirect
157. #576D149semidirect
167. H(5,𝔽2)C2×D149semidirect
175. AGL(1,ℤ/8)C2×D149semidirect
186. C2×D8C2×D149semidirect
189. #131C2×D149semidirect
216. Q16C22⋊D149semidirect
223. SD16C22⋊D149semidirect
235. D8C22⋊D149semidirect

Maximal subgroups

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

subgroupindex
#237504282
#237504272
#237500002
#237498952
#237498932
#237498922
#237497932
#237497912
#237497422
#237497402
#576×C1492
#3292149