Finite Group Databasebeta

← #34080907

Subgroups — #34080907

Order 19328.

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#23753015C212yesmaximal, complemented
2#23753014C211yesmaximal, characteristic, complemented
3#23752587C211yesmaximal, characteristic, complemented
4#23752482C211yesmaximal, characteristic, complemented
5#23752480C212yesmaximal, complemented
6#23752479C211yesmaximal, characteristic, complemented
7#23752380C212yesmaximal, complemented
8#23752378C212yesmaximal, complemented
9#23752329C211yesmaximal, characteristic, complemented
10#23752327C211yesmaximal, characteristic, complemented
11#576×C151C211yesmaximal, characteristic, complemented
12#18012785C2212yescomplemented
13#18012766—22no—
14#18012765—22no—
15#18012765C2212yescomplemented
16#18012764—22no—
17#18012764C2212yescomplemented
18#18012764C2212yescomplemented
19#18012762—21no—
20#18012759—22no—
21#18012759C2211yescharacteristic
22C2×D1208C2211yescharacteristic, complemented
23C2×#14558989—22no—
24C2×#14558989C2212yescomplemented
25D8×D151—21no—
26#18012746C2212yescomplemented
27#18012745C2211yescharacteristic, complemented
28#18012735C2212yescomplemented
29#18012675C2211yescharacteristic, complemented
30#18012674C2211yescharacteristic, complemented
31#18012666C2211yescharacteristic, complemented
32#18012666C2212yescomplemented
33#18012665C2211yescharacteristic, complemented
34#18012656C2212yescomplemented
35#18012655C2212yescomplemented
36C8×Dic151C2211yescharacteristic, complemented
37H(5,𝔽2)×C151C2212yescomplemented
38AGL(1,ℤ/8)×C151—22no—
39AGL(1,ℤ/8)×C151C2212yescomplemented
40#135×C151—21no—
41#135×C151C2211yescharacteristic
42C2×D8×C151—21no—
43C2×D8×C151C2211yescharacteristic, complemented
44#131×C151C2211yescharacteristic, complemented
45#14559005—22no—
46#14559004—22no—
47#14559004C2311yescharacteristic
48C2×D604—22no—
49C2×D604C2312yes—
50C2×C22⋊D151—42no—
51D4×D151—22no—
52D4×D151—42no—
53#14558994D411yescharacteristic, complemented
54#14558992—22no—
55#14558992D411yescharacteristic, complemented
56#14558991—22no—
57#14558991—22no—
58#14558991D411yescharacteristic, complemented
59D1208—21no—
60D1208—21no—
61#14558989—22no—
62#14558989—22no—
63#14558989—22no—
64#14558989—22no—
65#14558989—22no—
66#14558989D411yescharacteristic, complemented
67#14558988—22no—
68#14558988C2311yescharacteristic
69#14558988C2312yes—
70#14558987—21no—
71C2×C151⋊C8—22no—
72C2×C151⋊C8C2311yescharacteristic
73C8×D151—21no—
74C4×Dic151C2311yescharacteristic
75#41×C151—22no—
76#41×C151—22no—
77#41×C151C2312yes—
78#41×C151C2311yescharacteristic
79C2×D4×C151—22no—
80C2×D4×C151—22no—
81C2×D4×C151—42no—
82C2×D4×C151C2312yes—
83Q16×C151D411yescharacteristic, complemented
84SD16×C151—22no—
85SD16×C151D412yescomplemented
86D8×C151—22no—
87D8×C151—21no—
88D8×C151—21no—
89D8×C151D411yescharacteristic, complemented
90M16×C151—21no—
91M16×C151C2311yescharacteristic
92C2×C8×C151—21no—
93C2×C8×C151C2311yescharacteristic
94C22×D151—22no—
95C22×D151—42no—
96Dic302C2×D411yescharacteristic
97D604—22no—
98D604—22no—
99D604—42no—
100D604C2×D411yescharacteristic
101C22⋊D151—21no—
102C22⋊D151—42no—
103C22⋊D151—84no—
104C2×Dic151—21no—
105C4×D151—21no—
106C4×D151—42no—
107C151⋊C8—21no—
108C151⋊C8—22no—
109C151⋊C8C2×D411yescharacteristic
110C151⋊C8C2×D411yescharacteristic
111C23×C151—22no—
112C23×C151—42no—
113Q8×C151C2×D411yescharacteristic
114Q8×C151C2×D412yes—
115D4×C151—22no—
116D4×C151—21no—
117D4×C151—22no—
118D4×C151—22no—
119D4×C151—42no—
120D4×C151—42no—
121D4×C151C2×D411yescharacteristic
122D4×C151C2×D412yes—
123C2×C4×C151—21no—
124C2×C4×C151—22no—
125C2×C4×C151—42no—
126C2×C4×C151C2411yescharacteristic
127C8×C151—21no—
128C8×C151C2×D411yescharacteristic
129C8×C151C2×D411yescharacteristic
130C22×C151—21no—
131C22×C151—22no—
132C22×C151—42no—
133C22×C151—82no—
134C22×C151—162no—
135C22×C151H(5,𝔽2)11yescharacteristic
136C2×D151—21no—
137C2×D151—42no—
138C2×D151—82no—
139C2×D151—162no—
140C4×C151—21no—
141C4×C151—22no—
142C4×C151C22×D411yescharacteristic
143C4×C151C22×D411yescharacteristic
144Dic151—22no—
145Dic151—21no—
146C2×C151—21no—
147C2×C151—42no—
148C2×C151—41no—
149C2×C151—82no—
150C2×C151D4211yescharacteristic
151D151—41no—
152D151—82no—
153C151#329211yescharacteristic, complemented, Sylow
154#3292—1511nomaximal, Sylow
155#576—1512no—
156#576—1511no—
157#576D15111yescharacteristic, complemented
158#493—1511no—
159#472—1512no—
160#472—1511no—
161#472—1511no—
162#453—1512no—
163#453—1512no—
164#443—1511no—
165#443—1511no—
166H(5,𝔽2)—1512no—
167H(5,𝔽2)C2×D15112yescomplemented
168AGL(1,ℤ/8)—22no—
169AGL(1,ℤ/8)—3022no—
170AGL(1,ℤ/8)—3022no—
171AGL(1,ℤ/8)—3022no—
172AGL(1,ℤ/8)—1512no—
173AGL(1,ℤ/8)—1512no—
174AGL(1,ℤ/8)—1512no—
175AGL(1,ℤ/8)C2×D15112yescomplemented
176#135—21no—
177#135—3022no—
178#135—3021no—
179#135—1511no—
180#135C2×D15111yescharacteristic
181C2×D8—21no—
182C2×D8—3022no—
183C2×D8—3021no—
184C2×D8—1512no—
185C2×D8—1511no—
186C2×D8C2×D15111yescharacteristic, complemented
187#131—1512no—
188#131—1511no—
189#131C2×D15111yescharacteristic, complemented
190#127—1512no—
191#108—1511no—
192#108—1511no—
193#104—1511no—
194#104—1512no—
195#104—1511no—
196#100—1512no—
197#100—1512no—
198C4×C8—1511no—
199#41—22no—
200#41—22no—
201#41—3022no—
202#41—3022no—
203#41—1511no—
204#41C22×D15111yescharacteristic
205#41C22×D15112yes—
206C2×D4—22no—
207C2×D4—22no—
208C2×D4—42no—
209C2×D4—3022no—
210C2×D4—3022no—
211C2×D4—6042no—
212C2×D4—6042no—
213C2×D4—1512no—
214C2×D4C22×D15112yes—
215Q16—1511no—
216Q16C22⋊D15111yescharacteristic, complemented
217SD16—22no—
218SD16—3022no—
219SD16—3022no—
220SD16—3022no—
221SD16—1511no—
222SD16—1511no—
223SD16C22⋊D15112yescomplemented
224D8—22no—
225D8—21no—
226D8—21no—
227D8—3022no—
228D8—3022no—
229D8—3022no—
230D8—3022no—
231D8—3022no—
232D8—3021no—
233D8—3021no—
234D8—1511no—
235D8C22⋊D15111yescharacteristic, complemented
236M16—21no—
237M16—3022no—
238M16—3021no—
239M16—1512no—
240M16—1511no—
241M16C22×D15111yescharacteristic
242C2×C8—21no—
243C2×C8—3022no—
244C2×C8—3021no—
245C2×C8—1511no—
246C2×C8C22×D15111yescharacteristic
247C42—1511no—
248C23—22no—
249C23—42no—
250C23—3022no—
251C23—6042no—
252Q8—1511no—
253Q8D4×D15111yescharacteristic
254Q8C2×C22⋊D15112yes—
255D4—21no—
256D4—22no—
257D4—22no—
258D4—22no—
259D4—42no—
260D4—42no—
261D4—3021no—
262D4—3022no—
263D4—3022no—
264D4—6042no—
265D4—6042no—
266D4—1511no—
267D4—12084no—
268D4D4×D15111yescharacteristic
269D4C2×C22⋊D15112yes—
270C2×C4—22no—
271C2×C4—21no—
272C2×C4—42no—
273C2×C4—3021no—
274C2×C4—3021no—
275C2×C4—6042no—
276C2×C4C23×D15111yescharacteristic
277C8—21no—
278C8—3022no—
279C8—3021no—
280C8—1511no—
281C8—1511no—
282C8C2×C22⋊D15111yescharacteristic
283C8C2×C22⋊D15111yescharacteristic
284C22—21no—
285C22—22no—
286C22—42no—
287C22—82no—
288C22—162no—
289C22—3021no—
290C22—6042no—
291C22—24162no—
292C22—12082no—
293C22#1801278411yescharacteristic
294C4—21no—
295C4—22no—
296C4—3022no—
297C4—3021no—
298C4C2×D4×D15111yescharacteristic
299C4C22×C22⋊D15111yescharacteristic
300C2—21no—
301C2—41no—
302C2—42no—
303C2—82no—
304C2—6041no—
305C2—12082no—
306C2D4×C22⋊D15111yescharacteristic
subgroupG/H
centerC2D4×C22⋊D151
commutator, cosocleC2×C4×C151C24
FrattiniC2×C4C23×D151
Fitting#576×C151C2
socleC2×C151D42
hypercenter#576D151
hypocenterC151#3292
LCSG ▷ C2×C4×C151 ▷ C2×C151 ▷ C151
UCSC1 ◁ C2 ◁ C2×C4 ◁ #576

Complements

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

NH ≅ G/Ntype
1. #23753015C2semidirect
2. #23753014C2semidirect
3. #23752587C2semidirect
4. #23752482C2semidirect
5. #23752480C2semidirect
6. #23752479C2semidirect
7. #23752380C2semidirect
8. #23752378C2semidirect
9. #23752329C2semidirect
10. #23752327C2semidirect
11. #576×C151C2semidirect
12. #18012785C22semidirect
15. #18012765C22semidirect
17. #18012764C22semidirect
18. #18012764C22semidirect
22. C2×D1208C22semidirect
24. C2×#14558989C22semidirect
26. #18012746C22semidirect
27. #18012745C22semidirect
28. #18012735C22semidirect
29. #18012675C22semidirect
30. #18012674C22semidirect
31. #18012666C22semidirect
32. #18012666C22semidirect
33. #18012665C22semidirect
34. #18012656C22semidirect
35. #18012655C22semidirect
36. C8×Dic151C22semidirect
37. H(5,𝔽2)×C151C22semidirect
39. AGL(1,ℤ/8)×C151C22semidirect
43. C2×D8×C151C22semidirect
44. #131×C151C22semidirect
53. #14558994D4semidirect
55. #14558992D4semidirect
58. #14558991D4semidirect
66. #14558989D4semidirect
83. Q16×C151D4semidirect
85. SD16×C151D4semidirect
89. D8×C151D4semidirect
153. C151#3292semidirect
157. #576D151semidirect
167. H(5,𝔽2)C2×D151semidirect
175. AGL(1,ℤ/8)C2×D151semidirect
186. C2×D8C2×D151semidirect
189. #131C2×D151semidirect
216. Q16C22⋊D151semidirect
223. SD16C22⋊D151semidirect
235. D8C22⋊D151semidirect

Maximal subgroups

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

subgroupindex
#237530152
#237530142
#237525872
#237524822
#237524802
#237524792
#237523802
#237523782
#237523292
#237523272
#576×C1512
#3292151