Finite Group Databasebeta

← #34080782

Subgroups — #34080782

Order 19328.

620 conjugacy classes of subgroups; only the 133 normal subgroups are shown.

normal subgroups only

This group has 620 conjugacy classes of subgroups — too many to draw. Only its 133 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×D8×D151C212yesmaximal, complemented
2D4×D604C211yesmaximal, characteristic, complemented
3#23752847C211yesmaximal, characteristic, complemented
4#23752588C211yesmaximal, characteristic, complemented
5#23752447C212yesmaximal, complemented
6#23752408C211yesmaximal, characteristic, complemented
7#23752347C212yesmaximal, complemented
8#23752344C212yesmaximal, complemented
9C4×#14558989C211yesmaximal, characteristic, complemented
10#23752277C211yesmaximal, characteristic, complemented
11#459×C151C211yesmaximal, characteristic, complemented
12C22×D604—21no—
13C2×D4×D151—21no—
14C2×D4×D151C2212yescomplemented
15C2×D4×D151C2212yescomplemented
16C2×D1208C2212yescomplemented
17C2×#14558989C2211yescharacteristic
18C2×#14558989C2212yescomplemented
19C2×#14558989C2212yescomplemented
20D8×D151—28no—
21C2×C8×D151C2212yescomplemented
22#18012736C2211yescharacteristic, complemented
23#18012714C2212yescomplemented
24#18012713—21no—
25#18012710—21no—
26#18012710C2212yescomplemented
27#18012709—22no—
28#18012707—22no—
29C4×D604C2211yescharacteristic
30C4×D604C2211yescharacteristic, complemented
31#18012672C2211yescharacteristic, complemented
32#18012661C2212yescomplemented
33#18012660C2211yescharacteristic, complemented
34#18012659C2211yescharacteristic, complemented
35(C2×D151)⋊C8C2212yescomplemented
36C4×C151⋊C8C2211yescharacteristic, complemented
37C2×D8×C151C2212yescomplemented
38#127×C151C2211yescharacteristic, complemented
39C4×D4×C151C2211yescharacteristic, complemented
40C4⋊C8×C151C2211yescharacteristic, complemented
41#102×C151C2212yescomplemented
42C23×D151—22no—
43C23×D151—22no—
44C2×D604—22no—
45C2×D604—21no—
46C2×D604—21no—
47C2×D604—44no—
48C2×D604D411yescharacteristic
49C2×D604C2312yes—
50C2×D604C2311yescharacteristic
51C2×C22⋊D151—22no—
52C2×C22⋊D151—22no—
53C2×C22⋊D151—22no—
54D4×D151—24no—
55D4×D151—24no—
56D4×D151—42no—
57D4×D151—42no—
58D4×D151—44no—
59C2×C4×D151—21no—
60C2×C4×D151C2312yes—
61D1208—24no—
62#14558989—24no—
63#14558989—42no—
64#14558989D414yescomplemented
65C2×C151⋊C8C2311yescharacteristic
66C2×C151⋊C8C2311yescharacteristic
67C8×D151—24no—
68C4⋊Dic151D411yescharacteristic
69C4⋊Dic151C2311yescharacteristic
70C22⋊Dic151—22no—
71(C2×D151)⋊C4—22no—
72(C2×D151)⋊C4—21no—
73(C2×D151)⋊C4D412yes—
74C2×D4×C151—21no—
75C2×D4×C151—21no—
76C2×D4×C151C2312yes—
77C2×D4×C151C2311yescharacteristic
78C22×C4×C151—21no—
79D8×C151—24no—
80C2×C8×C151C2312yes—
81C4⋊C4×C151C2311yescharacteristic
82C22⋊C4×C151—21no—
83C42×C151C2311yescharacteristic
84C22×D151—21no—
85C22×D151—22no—
86C22×D151—44no—
87C22×D151—44no—
88C22×D151—44no—
89C22×D151—44no—
90C22×D151—82no—
91C22×D151—82no—
92C22×D151C2×D412yes—
93D604—22no—
94D604—21no—
95D604—22no—
96D604—44no—
97D604—42no—
98D604—81no—
99D604D814yescomplemented
100D604C2×D412yescomplemented
101C22⋊D151—44no—
102C22⋊D151—44no—
103C22⋊D151—44no—
104C2×Dic151—21no—
105C2×Dic151C2×D412yes—
106C4×D151—22no—
107C4×D151—22no—
108C4×D151—42no—
109C151⋊C8—21no—
110C151⋊C8C2×D412yescomplemented
111C23×C151—21no—
112C23×C151—22no—
113D4×C151—22no—
114D4×C151—21no—
115D4×C151—22no—
116D4×C151—42no—
117D4×C151—81no—
118D4×C151C2×D412yescomplemented
119C2×C4×C151—21no—
120C2×C4×C151—42no—
121C2×C4×C151C2×D411yescharacteristic
122C2×C4×C151C2×D411yescharacteristic
123C2×C4×C151C2411yescharacteristic
124C8×C151—22no—
125C22×C151—22no—
126C22×C151—41no—
127C22×C151—41no—
128C22×C151—42no—
129C22×C151—42no—
130C22×C151—42no—
131C22×C151C22×D411yescharacteristic
132C2×D151—22no—
133C2×D151—22no—
134C2×D151—22no—
135C2×D151—41no—
136C2×D151—41no—
137C2×D151—42no—
138C2×D151—42no—
139C2×D151—42no—
140C2×D151—88no—
141C2×D151—88no—
142C2×D151C2×D814yescomplemented
143C4×C151—21no—
144C4×C151—41no—
145C4×C151C2×D812yescomplemented
146C4×C151C22×D411yescharacteristic
147C4×C151H(5,𝔽2)11yescharacteristic
148Dic151—22no—
149Dic151—41no—
150C2×C151—42no—
151C2×C151—82no—
152C2×C151D4211yescharacteristic
153C2×C151C22×D811yescharacteristic
154C2×C151#57611yescharacteristic
155D151—24no—
156D151—42no—
157D151—82no—
158C151D4×D811yescharacteristic, complemented, Sylow
159D4×D8—1511nomaximal, Sylow
160C22×D8—1512no—
161D42—1511no—
162D42—1511no—
163#493—1511no—
164#466—1512no—
165#459—1511no—
166#459D15111yescharacteristic, complemented
167#447—1512no—
168#447—1512no—
169C4×D8—1511no—
170C8×D4—1511no—
171C22×D4—3021no—
172C22×D4—3021no—
173C22×D4—1512no—
174C22×D4—1512no—
175C2×D8—3028no—
176C2×D8—1512no—
177C2×D8—1512no—
178C2×D8—1511no—
179C2×D8—1512no—
180C2×D8C2×D15112yescomplemented
181C22×C8—1512no—
182#127—1511no—
183#127C2×D15111yescharacteristic, complemented
184#121—3021no—
185#121—3021no—
186#121—1512no—
187#121—1512no—
188#120—3022no—
189#120—3022no—
190C4×D4—1511no—
191C4×D4—1511no—
192C4×D4C2×D15111yescharacteristic, complemented
193#107—1511no—
194C4⋊C8C2×D15111yescharacteristic, complemented
195#102—1511no—
196#102—1512no—
197#102—1511no—
198#102C2×D15112yescomplemented
199C22⋊C8—1512no—
200C4×C8—1511no—
201C24—3022no—
202C24—3022no—
203C2×D4—21no—
204C2×D4—21no—
205C2×D4—3022no—
206C2×D4—3024no—
207C2×D4—3024no—
208C2×D4—3022no—
209C2×D4—3022no—
210C2×D4—3022no—
211C2×D4—3021no—
212C2×D4—3021no—
213C2×D4—6044no—
214C2×D4—6042no—
215C2×D4—6042no—
216C2×D4—6044no—
217C2×D4—1511no—
218C2×D4—1512no—
219C2×D4—1511no—
220C2×D4C22×D15112yes—
221C2×D4C22×D15111yescharacteristic
222C22×C4—21no—
223C22×C4—3021no—
224C22×C4—1512no—
225D8—24no—
226D8—3024no—
227D8—3024no—
228D8—6042no—
229D8—1514no—
230C2×C8—3024no—
231C2×C8—1511no—
232C2×C8—1511no—
233C2×C8C22×D15112yes—
234C4⋊C4—1511no—
235C4⋊C4—1511no—
236C4⋊C4C22×D15111yescharacteristic
237C22⋊C4—21no—
238C22⋊C4—3022no—
239C22⋊C4—3022no—
240C22⋊C4—3021no—
241C22⋊C4—1512no—
242C42C22×D15111yescharacteristic
243C23—21no—
244C23—22no—
245C23—3021no—
246C23—3022no—
247C23—6044no—
248C23—6044no—
249C23—6044no—
250C23—6044no—
251C23—1512no—
252C23—12082no—
253C23—12082no—
254D4—22no—
255D4—21no—
256D4—22no—
257D4—42no—
258D4—81no—
259D4—3022no—
260D4—3021no—
261D4—3022no—
262D4—6044no—
263D4—6044no—
264D4—6044no—
265D4—6044no—
266D4—6042no—
267D4—1514no—
268D4—1512no—
269D4—12081no—
270D4D4×D15112yescomplemented
271C2×C4—21no—
272C2×C4—42no—
273C2×C4—3022no—
274C2×C4—3022no—
275C2×C4—3021no—
276C2×C4—6042no—
277C2×C4—1512no—
278C2×C4D4×D15111yescharacteristic
279C2×C4D4×D15111yescharacteristic
280C2×C4C23×D15111yescharacteristic
281C8—22no—
282C8—3021no—
283C8—1512no—
284C22—22no—
285C22—41no—
286C22—41no—
287C22—42no—
288C22—42no—
289C22—42no—
290C22—3022no—
291C22—3022no—
292C22—3022no—
293C22—6041no—
294C22—6041no—
295C22—6042no—
296C22—6042no—
297C22—6042no—
298C22—1514no—
299C22—12088no—
300C22—12088no—
301C22C2×D4×D15111yescharacteristic
302C4—21no—
303C4—41no—
304C4—3022no—
305C4—6041no—
306C4D8×D15112yescomplemented
307C4C2×D4×D15111yescharacteristic
308C4#1801278511yescharacteristic
309C2—42no—
310C2—82no—
311C2—3024no—
312C2—6042no—
313C2—12082no—
314C2#2375284611yescharacteristic
315C2C2×D8×D15111yescharacteristic
316C2#2375301611yescharacteristic
subgroupG/H
centerC22C2×D4×D151
commutator, cosocleC2×C4×C151C24
FrattiniC2×C4C23×D151
Fitting#459×C151C2
socleC22×C151C22×D4
hypercenter#459D151
hypocenterC151D4×D8
LCSG ▷ C2×C4×C151 ▷ C2×C151 ▷ C151
UCSC1 ◁ C22 ◁ C42 ◁ #459

Complements

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

NH ≅ G/Ntype
1. C2×D8×D151C2semidirect
2. D4×D604C2semidirect
3. #23752847C2semidirect
4. #23752588C2semidirect
5. #23752447C2semidirect
6. #23752408C2semidirect
7. #23752347C2semidirect
8. #23752344C2semidirect
9. C4×#14558989C2semidirect
10. #23752277C2semidirect
11. #459×C151C2semidirect
14. C2×D4×D151C22semidirect
15. C2×D4×D151C22semidirect
16. C2×D1208C22semidirect
18. C2×#14558989C22semidirect
19. C2×#14558989C22semidirect
21. C2×C8×D151C22semidirect
22. #18012736C22semidirect
23. #18012714C22semidirect
26. #18012710C22semidirect
30. C4×D604C22semidirect
31. #18012672C22semidirect
32. #18012661C22semidirect
33. #18012660C22semidirect
34. #18012659C22semidirect
35. (C2×D151)⋊C8C22semidirect
36. C4×C151⋊C8C22semidirect
37. C2×D8×C151C22semidirect
38. #127×C151C22semidirect
39. C4×D4×C151C22semidirect
40. C4⋊C8×C151C22semidirect
41. #102×C151C22semidirect
64. #14558989D4semidirect
99. D604D8semidirect
100. D604C2×D4semidirect
110. C151⋊C8C2×D4semidirect
118. D4×C151C2×D4semidirect
142. C2×D151C2×D8semidirect
145. C4×C151C2×D8semidirect
158. C151D4×D8semidirect
166. #459D151semidirect
180. C2×D8C2×D151semidirect
183. #127C2×D151semidirect
192. C4×D4C2×D151semidirect
194. C4⋊C8C2×D151semidirect
198. #102C2×D151semidirect
270. D4D4×D151semidirect
306. C4D8×D151semidirect

Maximal subgroups

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

subgroupindex
C2×D8×D1512
D4×D6042
#237528472
#237525882
#237524472
#237524082
#237523472
#237523442
C4×#145589892
#237522772
#459×C1512
D4×D8151