Finite Group Databasebeta

← #34080899

Subgroups — #34080899

Order 19328.

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#23753025C211yesmaximal, characteristic, complemented
2#23753021C212yesmaximal, complemented
3#23753017C211yesmaximal, characteristic, complemented
4#23752597C211yesmaximal, characteristic, complemented
5#23752483C211yesmaximal, characteristic, complemented
6#23752478C212yesmaximal, complemented
7#23752388C212yesmaximal, complemented
8#23752387C212yesmaximal, complemented
9#23752328C211yesmaximal, characteristic, complemented
10#23752327C211yesmaximal, characteristic, complemented
11#473×C151C211yesmaximal, characteristic, complemented
12#18012787C2212yescomplemented
13#18012785C2212yes—
14#18012771—22no—
15#18012771—22no—
16#18012770C2212yescomplemented
17#18012767—22no—
18#18012767C2212yes—
19#18012767C2212yescomplemented
20#18012766—22no—
21#18012762—22no—
22#18012762—21no—
23#18012761—21no—
24#18012761C2211yescharacteristic
25#18012759C2211yescharacteristic
26Q16×D151—21no—
27C2×#14558991C2212yescomplemented
28SD16×D151—22no—
29C2×D1208—21no—
30C2×D1208C2211yescharacteristic
31#18012747C2212yescomplemented
32#18012745C2211yescharacteristic, complemented
33#18012728C2212yescomplemented
34#18012674C2211yescharacteristic, complemented
35#18012666C2211yescharacteristic
36#18012665C2211yescharacteristic, complemented
37#18012665C2212yescomplemented
38#18012655C2212yescomplemented
39C8×Dic151C2211yescharacteristic, complemented
40#137×C151C2212yes—
41C2×Q16×C151C2211yescharacteristic, complemented
42#131×C151C2211yescharacteristic
43#108×C151C2211yescharacteristic, complemented
44#101×C151C2212yescomplemented
45#14559005—22no—
46#14559005—22no—
47#14559005—22no—
48#14559004—22no—
49#14559004—42no—
50#14559004C2311yescharacteristic
51#14559004C2312yes—
52Q8×D151—22no—
53Q8×D151—22no—
54C2×D604—22no—
55C2×D604C2312yes—
56D4×D151—22no—
57D4×D151—42no—
58Dic604D411yescharacteristic
59#14558994—22no—
60#14558994D411yescharacteristic
61#14558993—22no—
62#14558993—22no—
63#14558993D412yes—
64#14558992D411yescharacteristic
65#14558991—22no—
66#14558991—22no—
67#14558991—22no—
68#14558991D411yescharacteristic
69D1208—22no—
70D1208—22no—
71D1208—21no—
72D1208—21no—
73D1208D411yescharacteristic
74#14558989D411yescharacteristic
75#14558988C2311yescharacteristic
76#14558987—22no—
77#14558987—21no—
78C2×C151⋊C8C2311yescharacteristic
79C8×D151—22no—
80C8×D151—21no—
81(C2×D151)⋊C4—42no—
82C4×Dic151C2311yescharacteristic
83#41×C151C2311yescharacteristic
84C2×Q8×C151C2312yes—
85Q16×C151—22no—
86Q16×C151—21no—
87Q16×C151—21no—
88SD16×C151—22no—
89M16×C151—21no—
90M16×C151C2311yescharacteristic
91M16×C151C2312yes—
92C2×C8×C151—21no—
93C2×C8×C151C2311yescharacteristic
94C22×D151—22no—
95C22×D151—42no—
96Dic302—42no—
97Dic302C2×D411yescharacteristic
98Dic302C2×D412yes—
99D604—22no—
100D604—22no—
101D604—42no—
102D604—42no—
103D604C2×D411yescharacteristic
104D604C2×D412yes—
105C22⋊D151—22no—
106C22⋊D151—21no—
107C22⋊D151—42no—
108C2×Dic151—21no—
109C4×D151—22no—
110C4×D151—21no—
111C4×D151—42no—
112C4×D151—42no—
113C4×D151—42no—
114C151⋊C8—21no—
115C151⋊C8C2×D411yescharacteristic
116C151⋊C8C2×D411yescharacteristic
117Q8×C151—22no—
118Q8×C151—22no—
119Q8×C151C2×D411yescharacteristic
120D4×C151—21no—
121D4×C151C2×D411yescharacteristic
122C2×C4×C151—21no—
123C2×C4×C151—22no—
124C2×C4×C151C2411yescharacteristic
125C8×C151—22no—
126C8×C151—21no—
127C8×C151C2×D411yescharacteristic
128C8×C151C2×D411yescharacteristic
129C22×C151—21no—
130C22×C151H(5,𝔽2)11yescharacteristic
131C2×D151—21no—
132C2×D151—22no—
133C2×D151—42no—
134C2×D151—82no—
135C2×D151—162no—
136C4×C151—21no—
137C4×C151—42no—
138C4×C151C22×D411yescharacteristic
139C4×C151C22×D411yescharacteristic
140Dic151—22no—
141Dic151—21no—
142Dic151—41no—
143C2×C151—21no—
144C2×C151—41no—
145C2×C151D4211yescharacteristic
146D151—41no—
147D151—42no—
148D151—82no—
149C151#329011yescharacteristic, complemented, Sylow
150#3290—1511nomaximal, Sylow
151#578—1511no—
152#577—1512no—
153#576—1511no—
154#495—1511no—
155#473D15111yescharacteristic, complemented
156#472—1511no—
157#471—1512no—
158#455—1512no—
159#454—1512no—
160#443—1511no—
161#443—1511no—
1622−1+4—1512no—
163H(5,𝔽2)—1512no—
164#137—3022no—
165#137—3022no—
166#137—1512no—
167#137C2×D15112yes—
168AGL(1,ℤ/8)—3022no—
169AGL(1,ℤ/8)—3022no—
170AGL(1,ℤ/8)—1512no—
171AGL(1,ℤ/8)—1512no—
172#135—3021no—
173#135—3022no—
174#135—3021no—
175#135—1511no—
176#135—1511no—
177C2×Q16—3021no—
178C2×Q16C2×D15111yescharacteristic, complemented
179C2×SD16—3022no—
180C2×SD16—1512no—
181C2×D8—3021no—
182C2×D8—1511no—
183#131—1512no—
184#131—1511no—
185#131C2×D15111yescharacteristic
186#124—1512no—
187#108—1511no—
188#108C2×D15111yescharacteristic, complemented
189#104—1511no—
190#104—1511no—
191#104—1512no—
192#101C2×D15112yescomplemented
193#100—1512no—
194C4×C8—1511no—
195#41—3022no—
196#41—3022no—
197#41—3022no—
198#41—3022no—
199#41—6042no—
200#41—1511no—
201#41—1512no—
202#41C22×D15111yescharacteristic
203C2×Q8—3022no—
204C2×Q8—3022no—
205C2×Q8C22×D15112yes—
206C2×D4—3022no—
207C2×D4—3022no—
208C2×D4—6042no—
209C2×D4—1512no—
210Q16—22no—
211Q16—21no—
212Q16—21no—
213Q16—3022no—
214Q16—1511no—
215Q16—1511no—
216SD16—22no—
217SD16—3022no—
218SD16—3022no—
219SD16—3022no—
220SD16—3022no—
221SD16—3022no—
222SD16—1511no—
223SD16—1511no—
224SD16—1512no—
225D8—3022no—
226D8—3022no—
227D8—3021no—
228D8—3021no—
229D8—1511no—
230D8—1511no—
231M16—21no—
232M16—3022no—
233M16—3021no—
234M16—1511no—
235M16C22×D15112yes—
236M16C22×D15111yescharacteristic
237C2×C8—21no—
238C2×C8—3022no—
239C2×C8—3021no—
240C2×C8—1511no—
241C2×C8C22×D15111yescharacteristic
242C22⋊C4—6042no—
243C42—1511no—
244C23—3022no—
245C23—6042no—
246Q8—22no—
247Q8—22no—
248Q8—6042no—
249Q8—1511no—
250Q8—1512no—
251Q8D4×D15111yescharacteristic
252D4—21no—
253D4—3022no—
254D4—3021no—
255D4—3022no—
256D4—3022no—
257D4—6042no—
258D4—6042no—
259D4—6042no—
260D4—1511no—
261D4—1512no—
262D4D4×D15111yescharacteristic
263C2×C4—21no—
264C2×C4—22no—
265C2×C4—3022no—
266C2×C4—3021no—
267C2×C4—3021no—
268C2×C4—6042no—
269C2×C4—6042no—
270C2×C4—6042no—
271C2×C4C23×D15111yescharacteristic
272C8—21no—
273C8—22no—
274C8—3021no—
275C8—1511no—
276C8—1511no—
277C8D4×D15111yescharacteristic
278C8D4×D15111yescharacteristic
279C22—21no—
280C22—3021no—
281C22—3022no—
282C22—6042no—
283C22—24162no—
284C22—12082no—
285C22#1801278511yescharacteristic
286C4—21no—
287C4—42no—
288C4—3022no—
289C4—3021no—
290C4—6041no—
291C4C2×D4×D15111yescharacteristic
292C4C2×D4×D15111yescharacteristic
293C2—21no—
294C2—41no—
295C2—6042no—
296C2—6041no—
297C2—12082no—
298C2#2375284611yescharacteristic
subgroupG/H
centerC2#23752846
commutator, cosocleC2×C4×C151C24
FrattiniC2×C4C23×D151
Fitting#473×C151C2
socleC2×C151D42
hypercenter#473D151
hypocenterC151#3290
LCSG ▷ C2×C4×C151 ▷ C2×C151 ▷ C151
UCSC1 ◁ C2 ◁ C2×C4 ◁ #473

Complements

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

NH ≅ G/Ntype
1. #23753025C2semidirect
2. #23753021C2semidirect
3. #23753017C2semidirect
4. #23752597C2semidirect
5. #23752483C2semidirect
6. #23752478C2semidirect
7. #23752388C2semidirect
8. #23752387C2semidirect
9. #23752328C2semidirect
10. #23752327C2semidirect
11. #473×C151C2semidirect
12. #18012787C22semidirect
16. #18012770C22semidirect
19. #18012767C22semidirect
27. C2×#14558991C22semidirect
31. #18012747C22semidirect
32. #18012745C22semidirect
33. #18012728C22semidirect
34. #18012674C22semidirect
36. #18012665C22semidirect
37. #18012665C22semidirect
38. #18012655C22semidirect
39. C8×Dic151C22semidirect
41. C2×Q16×C151C22semidirect
43. #108×C151C22semidirect
44. #101×C151C22semidirect
149. C151#3290semidirect
155. #473D151semidirect
178. C2×Q16C2×D151semidirect
188. #108C2×D151semidirect
192. #101C2×D151semidirect

Maximal subgroups

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

subgroupindex
#237530252
#237530212
#237530172
#237525972
#237524832
#237524782
#237523882
#237523872
#237523282
#237523272
#473×C1512
#3290151