Finite Group Databasebeta

← #34078587

Subgroups — #34078587

Order 19328.

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

normal subgroups only

This group has 584 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×#18012766C212yesmaximal, complemented
2#127×D151C211yesmaximal, characteristic, complemented
3C4×#14559005C211yesmaximal, characteristic, complemented
4#23752412C211yesmaximal, characteristic, complemented
5#23752410C212yesmaximal, complemented
6#23752408C211yesmaximal, characteristic, complemented
7#23752406C212yesmaximal, complemented
8#23752404C211yesmaximal, characteristic, complemented
9#23752234C211yesmaximal, characteristic, complemented
10#23752215C212yesmaximal, complemented
11#460×C151C211yesmaximal, characteristic, complemented
12C2×#14559005C2211yescharacteristic
13C2×D4×D151—21no—
14C2×D4×D151—21no—
15C2×D4×D151C2212yes—
16#18012766—28no—
17C2×#14558991C2212yescomplemented
18C2×D1208C2212yescomplemented
19C2×#14558989C2212yescomplemented
20C2×#14558987C2212yes—
21#18012736C2211yescharacteristic
22#18012735—21no—
23#18012735—21no—
24#18012735C2212yes—
25Q8×Dic151C2211yescharacteristic, complemented
26C4×D604—21no—
27C4×D604C2211yescharacteristic, complemented
28#18012701—21no—
29#18012701C2211yescharacteristic, complemented
30#18012697—21no—
31#18012697C2211yescharacteristic
32C42×D151—21no—
33C42×D151C2211yescharacteristic
34C4⋊(C151⋊C8)C2211yescharacteristic, complemented
35Dic151⋊C8C2212yescomplemented
36#18012661C2212yescomplemented
37#18012660C2212yescomplemented
38#18012659C2212yescomplemented
39C2×SD16×C151C2212yescomplemented
40#127×C151C2211yescharacteristic
41C4×Q8×C151C2211yescharacteristic, complemented
42C4⋊C8×C151C2211yescharacteristic, complemented
43#102×C151C2212yescomplemented
44C23×D151—22no—
45#14559005—22no—
46#14559005D414yescomplemented
47C2×D604—21no—
48C2×D604—21no—
49C2×D604—21no—
50C2×D604C2312yes—
51C2×D604C2311yescharacteristic
52C2×C22⋊D151—22no—
53C2×C22⋊D151—22no—
54C2×C22⋊D151—22no—
55D4×D151—24no—
56D4×D151—24no—
57D4×D151—44no—
58D4×D151—44no—
59C2×C4×D151—21no—
60C2×C4×D151—21no—
61C2×C4×D151—21no—
62C2×C4×D151D411yescharacteristic
63C2×C4×D151D411yescharacteristic
64C2×C4×D151C2311yescharacteristic
65#14558991—24no—
66D1208—24no—
67#14558989—24no—
68#14558987—24no—
69C2×C151⋊C8C2312yes—
70C4⋊Dic151—21no—
71C4⋊Dic151C2311yescharacteristic
72(C2×D151)⋊C4—21no—
73(C2×D151)⋊C4—21no—
74(C2×D151)⋊C4—21no—
75C4×Dic151—21no—
76C4×Dic151—21no—
77C4×Dic151D411yescharacteristic
78C4×Dic151D411yescharacteristic
79C4×Dic151C2311yescharacteristic
80C2×Q8×C151C2311yescharacteristic
81C2×D4×C151—21no—
82C2×D4×C151—21no—
83C2×D4×C151C2312yes—
84SD16×C151—24no—
85C2×C8×C151C2312yes—
86C4⋊C4×C151—21no—
87C4⋊C4×C151C2311yescharacteristic
88C42×C151—21no—
89C42×C151C2311yescharacteristic
90C22×D151—21no—
91C22×D151—22no—
92C22×D151—44no—
93C22×D151—44no—
94C22×D151—44no—
95C22×D151C2×D411yescharacteristic
96D604—24no—
97D604—22no—
98D604—21no—
99D604—22no—
100D604—42no—
101D604—42no—
102D604C2×D412yescomplemented
103C22⋊D151—44no—
104C22⋊D151—44no—
105C22⋊D151—44no—
106C2×Dic151—21no—
107C2×Dic151C2×D411yescharacteristic
108C2×Dic151C2×D411yescharacteristic
109C2×Dic151C2×D411yescharacteristic
110C4×D151—22no—
111C4×D151—24no—
112C4×D151—22no—
113C4×D151—42no—
114C4×D151—42no—
115C4×D151C2×D412yes—
116C4×D151#4112yes—
117C151⋊C8—22no—
118C23×C151—22no—
119Q8×C151—21no—
120Q8×C151C2×D412yescomplemented
121D4×C151—22no—
122D4×C151—22no—
123D4×C151—42no—
124D4×C151—42no—
125C2×C4×C151—21no—
126C2×C4×C151—21no—
127C2×C4×C151C2×D411yescharacteristic
128C2×C4×C151C2×D411yescharacteristic
129C2×C4×C151C2411yescharacteristic
130C8×C151—22no—
131C22×C151—42no—
132C22×C151—42no—
133C22×C151—42no—
134C22×C151C22×D411yescharacteristic
135C2×D151—21no—
136C2×D151—21no—
137C2×D151—22no—
138C2×D151—41no—
139C2×D151—41no—
140C2×D151—42no—
141C2×D151—42no—
142C2×D151—42no—
143C2×D151—88no—
144C2×D151#12112yes—
145C4×C151—22no—
146C4×C151—21no—
147C4×C151—41no—
148C4×C151AGL(1,ℤ/8)12yescomplemented
149C4×C151C22×D411yescharacteristic
150C4×C151C2×#4111yescharacteristic
151Dic151—21no—
152Dic151—41no—
153Dic151#12112yes—
154Dic151AGL(1,ℤ/8)12yescomplemented
155C2×C151—82no—
156C2×C151C2×#12111yescharacteristic
157C2×C151C2×AGL(1,ℤ/8)11yescharacteristic
158C2×C151C2×AGL(1,ℤ/8)11yescharacteristic
159D151—22no—
160D151—42no—
161D151—82no—
162C151#303811yescharacteristic, complemented, Sylow
163#3038—1511nomaximal, Sylow
164C2×AGL(1,ℤ/8)—1512no—
165C2×#127—1511no—
166C4×#41—1511no—
167#460—1512no—
168#460—1511no—
169#460D15111yescharacteristic, complemented
170#459—1511no—
171#459—1511no—
172#459—1512no—
173#423—1511no—
174#418—1512no—
175C2×#41—1511no—
176C22×D4—3021no—
177C22×D4—3021no—
178C22×D4—1512no—
179AGL(1,ℤ/8)—3028no—
180C2×SD16—1512no—
181C2×SD16C2×D15112yescomplemented
182C2×D8—1512no—
183C2×D8—1512no—
184C2×M16—1512no—
185#127—3021no—
186#127—3021no—
187#127—1512no—
188#127—1511no—
189#127C2×D15111yescharacteristic
190C4×Q8—1511no—
191C4×Q8C2×D15111yescharacteristic, complemented
192C4×D4—3021no—
193C4×D4—3021no—
194C4×D4—1511no—
195C4×D4—1511no—
196#117—3021no—
197#117—1511no—
198C2×C42—3021no—
199C2×C42—1511no—
200C4⋊C8—1512no—
201C4⋊C8—1511no—
202C4⋊C8C2×D15111yescharacteristic, complemented
203#102—1512no—
204#102—1512no—
205#102—1512no—
206#102C2×D15112yescomplemented
207C24—3022no—
208#41—3022no—
209#41—1514no—
210C2×Q8C22×D15111yescharacteristic
211C2×D4—21no—
212C2×D4—21no—
213C2×D4—3021no—
214C2×D4—3024no—
215C2×D4—3024no—
216C2×D4—3022no—
217C2×D4—3022no—
218C2×D4—3022no—
219C2×D4—3021no—
220C2×D4—3021no—
221C2×D4—6044no—
222C2×D4—6044no—
223C2×D4—1512no—
224C2×D4—1511no—
225C2×D4C22×D15112yes—
226C22×C4—3021no—
227C22×C4—3021no—
228C22×C4—3021no—
229C22×C4—1511no—
230C22×C4—1511no—
231C22×C4—1511no—
232SD16—24no—
233SD16—3024no—
234D8—3024no—
235D8—3024no—
236M16—3024no—
237C2×C8—1512no—
238C2×C8C22×D15112yes—
239C4⋊C4—21no—
240C4⋊C4—3021no—
241C4⋊C4—1511no—
242C4⋊C4C22×D15111yescharacteristic
243C22⋊C4—3021no—
244C22⋊C4—3021no—
245C22⋊C4—3021no—
246C42—21no—
247C42—3021no—
248C42—3021no—
249C42—1511no—
250C42—1511no—
251C42—1511no—
252C42C22×D15111yescharacteristic
253C23—22no—
254C23—3021no—
255C23—3022no—
256C23—6044no—
257C23—6044no—
258C23—6044no—
259C23—1511no—
260Q8—21no—
261Q8D4×D15112yescomplemented
262D4—22no—
263D4—22no—
264D4—42no—
265D4—42no—
266D4—3024no—
267D4—3022no—
268D4—3021no—
269D4—3022no—
270D4—6042no—
271D4—6044no—
272D4—6044no—
273D4—6044no—
274D4—6042no—
275D4—1512no—
276C2×C4—21no—
277C2×C4—21no—
278C2×C4—3024no—
279C2×C4—3022no—
280C2×C4—3022no—
281C2×C4—3021no—
282C2×C4—6042no—
283C2×C4—6042no—
284C2×C4—1511no—
285C2×C4—1511no—
286C2×C4—1511no—
287C2×C4—1512no—
288C2×C4—1512no—
289C2×C4D4×D15111yescharacteristic
290C2×C4D4×D15111yescharacteristic
291C2×C4C23×D15111yescharacteristic
292C8—22no—
293C8—3022no—
294C22—42no—
295C22—42no—
296C22—42no—
297C22—3021no—
298C22—3021no—
299C22—3022no—
300C22—6041no—
301C22—6041no—
302C22—6042no—
303C22—6042no—
304C22—6042no—
305C22—1512no—
306C22—12088no—
307C22C2×D4×D15111yescharacteristic
308C4—21no—
309C4—22no—
310C4—41no—
311C4—3021no—
312C4—6041no—
313C4—1512no—
314C4—1512no—
315C4#1801276612yescomplemented
316C4C2×D4×D15111yescharacteristic
317C4#41×D15111yescharacteristic
318C2—82no—
319C2—3022no—
320C2—6042no—
321C2—12082no—
322C2#121×D15111yescharacteristic
323C2AGL(1,ℤ/8)×D15111yescharacteristic
324C2C2×#1801276611yescharacteristic
subgroupG/H
centerC22C2×D4×D151
commutator, cosocleC2×C4×C151C24
FrattiniC2×C4C23×D151
Fitting#460×C151C2
socleC22×C151C22×D4
hypercenter#460D151
hypocenterC151#3038
LCSG ▷ C2×C4×C151 ▷ C2×C151 ▷ C151
UCSC1 ◁ C22 ◁ C42 ◁ #460

Complements

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

NH ≅ G/Ntype
1. C2×#18012766C2semidirect
2. #127×D151C2semidirect
3. C4×#14559005C2semidirect
4. #23752412C2semidirect
5. #23752410C2semidirect
6. #23752408C2semidirect
7. #23752406C2semidirect
8. #23752404C2semidirect
9. #23752234C2semidirect
10. #23752215C2semidirect
11. #460×C151C2semidirect
17. C2×#14558991C22semidirect
18. C2×D1208C22semidirect
19. C2×#14558989C22semidirect
25. Q8×Dic151C22semidirect
27. C4×D604C22semidirect
29. #18012701C22semidirect
34. C4⋊(C151⋊C8)C22semidirect
35. Dic151⋊C8C22semidirect
36. #18012661C22semidirect
37. #18012660C22semidirect
38. #18012659C22semidirect
39. C2×SD16×C151C22semidirect
41. C4×Q8×C151C22semidirect
42. C4⋊C8×C151C22semidirect
43. #102×C151C22semidirect
46. #14559005D4semidirect
102. D604C2×D4semidirect
120. Q8×C151C2×D4semidirect
148. C4×C151AGL(1,ℤ/8)semidirect
154. Dic151AGL(1,ℤ/8)semidirect
162. C151#3038semidirect
169. #460D151semidirect
181. C2×SD16C2×D151semidirect
191. C4×Q8C2×D151semidirect
202. C4⋊C8C2×D151semidirect
206. #102C2×D151semidirect
261. Q8D4×D151semidirect
315. C4#18012766semidirect

Maximal subgroups

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

subgroupindex
C2×#180127662
#127×D1512
C4×#145590052
#237524122
#237524102
#237524082
#237524062
#237524042
#237522342
#237522152
#460×C1512
#3038151