Finite Group Databasebeta

← #34078379

Subgroups — #34078379

Order 19328.

784 conjugacy classes of subgroups; only the 149 normal subgroups are shown.

normal subgroups only

This group has 784 conjugacy classes of subgroups — too many to draw. Only its 149 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
1C2×#18012784C211yesmaximal, characteristic, complemented
2C2×#18012767C211yesmaximal, characteristic, complemented
3C22×#14558989C211yesmaximal, characteristic, complemented
4#23752781C211yesmaximal, characteristic, complemented
5#23752358C214yesmaximal, complemented
6#23752347C214yesmaximal, complemented
7#23752206C211yesmaximal, characteristic, complemented
8#23752180C211yesmaximal, characteristic, complemented
9#418×C151C211yesmaximal, characteristic, complemented
10#18012784—24no—
11#18012784—24no—
12C2×#14559004C2211yescharacteristic
13C2×#14559004C2211yescharacteristic
14C2×#14559003—21no—
15C2×#14559003C2212yescomplemented
16C22×D604C2211yescharacteristic, complemented
17C22×C22⋊D151—22no—
18C2×D4×D151—21no—
19C2×D4×D151C2212yescomplemented
20#18012767—24no—
21C2×#14558993C2212yescomplemented
22C2×D1208C2212yescomplemented
23C2×#14558989—24no—
24C2×#14558989C2214yescomplemented
25C22×C151⋊C8C2211yescharacteristic, complemented
26#18012736—21no—
27#18012727—21no—
28#18012714C2214yescomplemented
29#18012709—22no—
30#18012662C2212yescomplemented
31#18012659C2212yescomplemented
32(C2×D151)⋊C8C2214yescomplemented
33C22×D4×C151C2211yescharacteristic
34C2×M16×C151C2211yescharacteristic, complemented
35#117×C151C2211yescharacteristic, complemented
36#102×C151C2214yescomplemented
37C23×D151—22no—
38C23×D151—21no—
39#14559004—22no—
40#14559004—22no—
41#14559004—22no—
42#14559004D414yescomplemented
43#14559003—28no—
44#14559003—24no—
45#14559003—24no—
46C2×Dic302D411yescharacteristic
47C2×Dic302C2311yescharacteristic
48C2×D604—24no—
49C2×D604—22no—
50C2×D604—22no—
51C2×D604—21no—
52C2×D604D411yescharacteristic
53C2×D604C2312yes—
54C2×D604C2311yescharacteristic
55C2×C22⋊D151—216no—
56C2×C22⋊D151—22no—
57C2×C22⋊D151—22no—
58C2×C22⋊D151—21no—
59C2×C22⋊D151D412yes—
60D4×D151—28no—
61D4×D151—24no—
62D4×D151—24no—
63C22×Dic151—22no—
64C2×C4×D151—21no—
65C2×C4×D151C2312yes—
66#14558993—24no—
67D1208—24no—
68#14558989—28no—
69C2×C151⋊C8—22no—
70C2×C151⋊C8C2312yes—
71(C2×D151)⋊C4—24no—
72C24×C151—21no—
73C2×D4×C151—21no—
74C2×D4×C151—22no—
75C2×D4×C151D414yescomplemented
76C2×D4×C151C2312yes—
77C22×C4×C151C2311yescharacteristic
78M16×C151—22no—
79C2×C8×C151C2312yes—
80C4⋊C4×C151C2312yes—
81C22⋊C4×C151—21no—
82C42×C151—21no—
83C22×D151—21no—
84C22×D151—28no—
85C22×D151—22no—
86C22×D151—42no—
87C22×D151—84no—
88C22×D151—82no—
89C22×D151C2×D412yes—
90Dic302—22no—
91Dic302—21no—
92Dic302C2×D412yes—
93D604—22no—
94D604—21no—
95D604—22no—
96D604—22no—
97D604—42no—
98D604—84no—
99D604C2×D412yes—
100C22⋊D151—28no—
101C22⋊D151—28no—
102C22⋊D151—24no—
103C22⋊D151—24no—
104C2×Dic151—28no—
105C2×Dic151—21no—
106C2×Dic151C2×D412yes—
107C4×D151—24no—
108C4×D151—22no—
109C4×D151—22no—
110C151⋊C8—22no—
111C23×C151—22no—
112C23×C151—24no—
113C23×C151—82no—
114C23×C151C2×D411yescharacteristic
115D4×C151—24no—
116D4×C151—22no—
117D4×C151C2×D414yes—
118C2×C4×C151—22no—
119C2×C4×C151C2×D411yescharacteristic
120C2×C4×C151C2×D412yes—
121C2×C4×C151C2×D412yes—
122C2×C4×C151C2411yescharacteristic
123C8×C151—22no—
124C22×C151—22no—
125C22×C151—24no—
126C22×C151—44no—
127C22×C151—84no—
128C22×C151#12012yes—
129C22×C151C22×D411yescharacteristic
130C2×D151—22no—
131C2×D151—22no—
132C2×D151—24no—
133C2×D151—42no—
134C2×D151—42no—
135C2×D151—44no—
136C2×D151—88no—
137C2×D151—84no—
138C4×C151—42no—
139C4×C151#12012yes—
140C4×C151C22×D411yescharacteristic
141C4×C151C22×D411yescharacteristic
142Dic151—22no—
143Dic151—22no—
144C2×C151—22no—
145C2×C151—44no—
146C2×C151C2×#12011yescharacteristic
147C2×C151#57612yes—
148D151—42no—
149D151—42no—
150D151—82no—
151C151#300811yescharacteristic, complemented, Sylow
152#3008—1511nomaximal, Sylow
153C2×H(5,𝔽2)—1511no—
154C2×AGL(1,ℤ/8)—1511no—
155C22×D8—1511no—
156#535—1511no—
157#449—1514no—
158#447—1514no—
159#418D15111yescharacteristic, complemented
160#416—1511no—
161#408—1511no—
162H(5,𝔽2)—3024no—
163H(5,𝔽2)—3024no—
164C2×#41—3021no—
165C2×#41—1512no—
166C2×#41—1511no—
167C2×#41—1511no—
168C22×D4—3021no—
169C22×D4—3022no—
170C22×D4—1512no—
171C22×D4—1511no—
172C22×D4C2×D15111yescharacteristic
173AGL(1,ℤ/8)—3024no—
174C2×SD16—1512no—
175C2×D8—3024no—
176C2×D8—1514no—
177C2×D8—1512no—
178C2×M16C2×D15111yescharacteristic, complemented
179C22×C8—1511no—
180#127—3021no—
181#124—3021no—
182#121—1514no—
183#120—3022no—
184#117C2×D15111yescharacteristic, complemented
185#103—1512no—
186#102—1512no—
187#102C2×D15114yescomplemented
188C22⋊C8—1514no—
189C24—21no—
190C24—3022no—
191C24—3021no—
192#41—3028no—
193#41—3024no—
194#41—3024no—
195#41—3022no—
196#41—3022no—
197#41—3022no—
198#41—1514no—
199C2×Q8—1511no—
200C2×Q8—1511no—
201C2×D4—21no—
202C2×D4—22no—
203C2×D4—3024no—
204C2×D4—3028no—
205C2×D4—3024no—
206C2×D4—30216no—
207C2×D4—3022no—
208C2×D4—3021no—
209C2×D4—3024no—
210C2×D4—3022no—
211C2×D4—3022no—
212C2×D4—3021no—
213C2×D4—3022no—
214C2×D4—1512no—
215C2×D4—1511no—
216C2×D4—1512no—
217C2×D4—1511no—
218C2×D4D60414yescomplemented
219C2×D4C22×D15112yes—
220C22×C4—3022no—
221C22×C4—3021no—
222C22×C4—1512no—
223C22×C4C22×D15111yescharacteristic
224SD16—3024no—
225D8—3024no—
226D8—3028no—
227M16—22no—
228C2×C8—3022no—
229C2×C8—1512no—
230C2×C8C22×D15112yes—
231C4⋊C4C22×D15112yes—
232C22⋊C4—21no—
233C22⋊C4—3024no—
234C42—21no—
235C23—22no—
236C23—24no—
237C23—82no—
238C23—3028no—
239C23—3021no—
240C23—3022no—
241C23—6042no—
242C23—1512no—
243C23—12082no—
244C23—12084no—
245C23D4×D15111yescharacteristic
246Q8—3022no—
247Q8—3021no—
248Q8—1512no—
249D4—24no—
250D4—22no—
251D4—3028no—
252D4—3028no—
253D4—3024no—
254D4—3024no—
255D4—3022no—
256D4—3022no—
257D4—3021no—
258D4—3022no—
259D4—6042no—
260D4—1512no—
261D4—12084no—
262D4C2×D60414yes—
263C2×C4—22no—
264C2×C4—3028no—
265C2×C4—3021no—
266C2×C4—3024no—
267C2×C4—3022no—
268C2×C4—3022no—
269C2×C4—1512no—
270C2×C4D4×D15111yescharacteristic
271C2×C4D4×D15112yes—
272C2×C4C2×D60412yes—
273C2×C4C23×D15111yescharacteristic
274C8—22no—
275C8—3022no—
276C22—22no—
277C22—24no—
278C22—44no—
279C22—84no—
280C22—3024no—
281C22—3022no—
282C22—3022no—
283C22—6042no—
284C22—6044no—
285C22—6042no—
286C22—12084no—
287C22—12088no—
288C22#1801270912yes—
289C22C2×D4×D15111yescharacteristic
290C4—42no—
291C4—3022no—
292C4—3022no—
293C4#1801270912yes—
294C4C2×D4×D15111yescharacteristic
295C4C22×D60411yescharacteristic
296C2—22no—
297C2—44no—
298C2—6042no—
299C2—6042no—
300C2—12082no—
301C2C2×#1801270911yescharacteristic
302C2#2375301612yes—
subgroupG/H
centerC22C2×D4×D151
commutator, cosocleC2×C4×C151C24
FrattiniC2×C4C23×D151
Fitting#418×C151C2
socleC22×C151C22×D4
hypercenter#418D151
hypocenterC151#3008
LCSG ▷ C2×C4×C151 ▷ C2×C151 ▷ C151
UCSC1 ◁ C22 ◁ C22×C4 ◁ #418

Complements

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

NH ≅ G/Ntype
1. C2×#18012784C2semidirect
2. C2×#18012767C2semidirect
3. C22×#14558989C2semidirect
4. #23752781C2semidirect
5. #23752358C2semidirect
6. #23752347C2semidirect
7. #23752206C2semidirect
8. #23752180C2semidirect
9. #418×C151C2semidirect
15. C2×#14559003C22semidirect
16. C22×D604C22semidirect
19. C2×D4×D151C22semidirect
21. C2×#14558993C22semidirect
22. C2×D1208C22semidirect
24. C2×#14558989C22semidirect
25. C22×C151⋊C8C22semidirect
28. #18012714C22semidirect
30. #18012662C22semidirect
31. #18012659C22semidirect
32. (C2×D151)⋊C8C22semidirect
34. C2×M16×C151C22semidirect
35. #117×C151C22semidirect
36. #102×C151C22semidirect
42. #14559004D4semidirect
75. C2×D4×C151D4semidirect
151. C151#3008semidirect
159. #418D151semidirect
178. C2×M16C2×D151semidirect
184. #117C2×D151semidirect
187. #102C2×D151semidirect
218. C2×D4D604semidirect

Maximal subgroups

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

subgroupindex
C2×#180127842
C2×#180127672
C22×#145589892
#237527812
#237523582
#237523472
#237522062
#237521802
#418×C1512
#3008151