Finite Group Databasebeta

← #34079857

Subgroups — #34079857

Order 19328.

520 conjugacy classes of subgroups; only the 121 normal subgroups are shown.

normal subgroups only

This group has 520 conjugacy classes of subgroups — too many to draw. Only its 121 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#121×D151C212yesmaximal, complemented
2#23752527C212yesmaximal, complemented
3#23752524C212yesmaximal, complemented
4#23752448C211yesmaximal, characteristic, complemented
5#23752446C212yesmaximal, complemented
6#23752347C212yesmaximal, complemented
7#23752344C212yesmaximal, complemented
8C2×(C2×D151)⋊C8C211yesmaximal, characteristic, complemented
9#466×C151C211yesmaximal, characteristic, complemented
10C2×D4×D151—22no—
11C2×D4×D151C2212yescomplemented
12C22×C4×D151C2211yescharacteristic
13C2×D1208C2211yescharacteristic, complemented
14C2×#14558989C2212yescomplemented
15C22×C151⋊C8C2211yescharacteristic, complemented
16#18012714C2212yes—
17#18012713C2212yescomplemented
18#18012712—22no—
19#18012711—22no—
20#18012710C2212yes—
21C4⋊C4×D151C2212yescomplemented
22C22⋊C4×D151—22no—
23#18012673C2211yescharacteristic, complemented
24#18012672C2212yescomplemented
25#18012661C2212yescomplemented
26#18012660C2212yescomplemented
27#18012659C2212yescomplemented
28(C2×D151)⋊C8C2212yescomplemented
29(C2×D151)⋊C8C2212yescomplemented
30C2×D8×C151C2211yescharacteristic, complemented
31C22×C8×C151C2211yescharacteristic, complemented
32#121×C151C2212yescomplemented
33#107×C151C2211yescharacteristic, complemented
34#102×C151C2212yescomplemented
35C23×D151—22no—
36C23×D151D411yescharacteristic
37C2×D604—22no—
38C2×D604C2312yes—
39C2×C22⋊D151—22no—
40C2×C22⋊D151—22no—
41C2×C22⋊D151—22no—
42D4×D151—42no—
43D4×D151—42no—
44D4×D151—48no—
45C22×Dic151D411yescharacteristic
46C2×C4×D151—22no—
47C2×C4×D151—41no—
48C2×C4×D151—41no—
49C2×C4×D151D412yes—
50C2×C4×D151C2312yes—
51D1208—41no—
52#14558989—42no—
53C2×C151⋊C8—41no—
54C2×C151⋊C8C2312yes—
55C4⋊Dic151C2312yes—
56Dic151⋊C4—22no—
57C22⋊Dic151—22no—
58(C2×D151)⋊C4—22no—
59(C2×D151)⋊C4—22no—
60C2×D4×C151—22no—
61C2×D4×C151C2312yes—
62C22×C4×C151C2311yescharacteristic
63D8×C151—41no—
64C2×C8×C151—41no—
65C2×C8×C151C2311yescharacteristic
66C2×C8×C151C2311yescharacteristic
67C4⋊C4×C151C2312yes—
68C22⋊C4×C151—22no—
69C22×D151—22no—
70C22×D151—41no—
71C22×D151—41no—
72C22×D151—44no—
73C22×D151—44no—
74C22×D151—44no—
75C22×D151D814yescomplemented
76C22×D151C2×D412yes—
77D604—22no—
78D604—22no—
79D604—44no—
80C22⋊D151—44no—
81C22⋊D151—44no—
82C22⋊D151—44no—
83C2×Dic151—22no—
84C2×Dic151—41no—
85C2×Dic151C2×D412yes—
86C4×D151—22no—
87C4×D151—22no—
88C4×D151—42no—
89C4×D151—44no—
90C151⋊C8—22no—
91C23×C151—22no—
92C23×C151C2×D411yescharacteristic
93D4×C151—22no—
94D4×C151—22no—
95D4×C151—44no—
96C2×C4×C151—21no—
97C2×C4×C151—21no—
98C2×C4×C151—22no—
99C2×C4×C151C2×D411yescharacteristic
100C2×C4×C151C2411yescharacteristic
101C8×C151—21no—
102C8×C151—21no—
103C22×C151—21no—
104C22×C151—21no—
105C22×C151—42no—
106C22×C151—42no—
107C22×C151—42no—
108C22×C151C2×D812yes—
109C22×C151C22×D411yescharacteristic
110C2×D151—22no—
111C2×D151—22no—
112C2×D151—44no—
113C2×D151—42no—
114C2×D151—42no—
115C2×D151—42no—
116C2×D151—88no—
117C2×D151C2×D814yes—
118C4×C151—21no—
119C4×C151—42no—
120C4×C151H(5,𝔽2)11yescharacteristic
121C4×C151H(5,𝔽2)11yescharacteristic
122Dic151—22no—
123Dic151—42no—
124C2×C151—22no—
125C2×C151—82no—
126C2×C151#53411yescharacteristic
127C2×C151C22×D811yescharacteristic
128C2×C151#57511yescharacteristic
129D151—24no—
130D151—82no—
131C151#318611yescharacteristic, complemented, Sylow
132#3186—1511nomaximal, Sylow
133C2×#121—1512no—
134#480—1512no—
135#480—1512no—
136#466—1511no—
137#466—1512no—
138#466D15111yescharacteristic, complemented
139#447—1512no—
140#447—1512no—
141C2×C22⋊C8—1511no—
142C22×D4—3022no—
143C22×D4—1512no—
144C23×C4—1511no—
145C2×D8—1512no—
146C2×D8—1511no—
147C2×D8C2×D15111yescharacteristic, complemented
148C22×C8—1511no—
149C22×C8C2×D15111yescharacteristic, complemented
150#121—3022no—
151#121—3022no—
152#121—1512no—
153#121—1512no—
154#121—1512no—
155#121C2×D15112yescomplemented
156C2×C4⋊C4—1512no—
157C2×C22⋊C4—3022no—
158#107—1511no—
159#107—1512no—
160#107C2×D15111yescharacteristic, complemented
161#102—1512no—
162#102—1512no—
163#102—1512no—
164#102C2×D15112yescomplemented
165C22⋊C8—1512no—
166C22⋊C8—1512no—
167C24—3022no—
168C24—1511no—
169C2×D4—22no—
170C2×D4—3022no—
171C2×D4—3022no—
172C2×D4—3022no—
173C2×D4—3022no—
174C2×D4—6042no—
175C2×D4—6042no—
176C2×D4—6048no—
177C2×D4—1512no—
178C2×D4C22×D15112yes—
179C22×C4—3022no—
180C22×C4—6041no—
181C22×C4—6041no—
182C22×C4—1512no—
183C22×C4—1511no—
184C22×C4—1512no—
185C22×C4C22×D15111yescharacteristic
186D8—41no—
187D8—6041no—
188D8—6042no—
189C2×C8—41no—
190C2×C8—6041no—
191C2×C8—1512no—
192C2×C8C22×D15111yescharacteristic
193C2×C8C22×D15111yescharacteristic
194C4⋊C4—3022no—
195C4⋊C4—1512no—
196C4⋊C4C22×D15112yes—
197C22⋊C4—22no—
198C22⋊C4—3022no—
199C22⋊C4—3022no—
200C22⋊C4—3022no—
201C23—22no—
202C23—3022no—
203C23—6041no—
204C23—6041no—
205C23—6044no—
206C23—6044no—
207C23—6044no—
208C23—1512no—
209C23—1514no—
210C23D4×D15111yescharacteristic
211D4—22no—
212D4—22no—
213D4—44no—
214D4—3022no—
215D4—3022no—
216D4—6044no—
217D4—6044no—
218D4—6044no—
219D4—6044no—
220C2×C4—21no—
221C2×C4—21no—
222C2×C4—22no—
223C2×C4—3022no—
224C2×C4—3022no—
225C2×C4—3022no—
226C2×C4—6042no—
227C2×C4—6044no—
228C2×C4—6041no—
229C2×C4—1512no—
230C2×C4D4×D15111yescharacteristic
231C2×C4C23×D15111yescharacteristic
232C8—21no—
233C8—21no—
234C8—3022no—
235C22—21no—
236C22—21no—
237C22—42no—
238C22—42no—
239C22—42no—
240C22—3022no—
241C22—3022no—
242C22—6044no—
243C22—6042no—
244C22—6042no—
245C22—6042no—
246C22—1514no—
247C22—12088no—
248C22D8×D15112yes—
249C22C2×D4×D15111yescharacteristic
250C4—21no—
251C4—42no—
252C4—3022no—
253C4—6042no—
254C4#1801278411yescharacteristic
255C4#1801278511yescharacteristic
256C2—22no—
257C2—82no—
258C2—3024no—
259C2—12082no—
260C2#2375277011yescharacteristic
261C2C2×D8×D15111yescharacteristic
262C2#2375300911yescharacteristic
subgroupG/H
centerC22C2×D4×D151
commutator, cosocleC2×C4×C151C24
FrattiniC2×C4C23×D151
Fitting#466×C151C2
socleC22×C151C22×D4
hypercenter#466D151
hypocenterC151#3186
LCSG ▷ C2×C4×C151 ▷ C2×C151 ▷ C151
UCSC1 ◁ C22 ◁ C22×C4 ◁ #466

Complements

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

NH ≅ G/Ntype
1. #121×D151C2semidirect
2. #23752527C2semidirect
3. #23752524C2semidirect
4. #23752448C2semidirect
5. #23752446C2semidirect
6. #23752347C2semidirect
7. #23752344C2semidirect
8. C2×(C2×D151)⋊C8C2semidirect
9. #466×C151C2semidirect
11. C2×D4×D151C22semidirect
13. C2×D1208C22semidirect
14. C2×#14558989C22semidirect
15. C22×C151⋊C8C22semidirect
17. #18012713C22semidirect
21. C4⋊C4×D151C22semidirect
23. #18012673C22semidirect
24. #18012672C22semidirect
25. #18012661C22semidirect
26. #18012660C22semidirect
27. #18012659C22semidirect
28. (C2×D151)⋊C8C22semidirect
29. (C2×D151)⋊C8C22semidirect
30. C2×D8×C151C22semidirect
31. C22×C8×C151C22semidirect
32. #121×C151C22semidirect
33. #107×C151C22semidirect
34. #102×C151C22semidirect
75. C22×D151D8semidirect
131. C151#3186semidirect
138. #466D151semidirect
147. C2×D8C2×D151semidirect
149. C22×C8C2×D151semidirect
155. #121C2×D151semidirect
160. #107C2×D151semidirect
164. #102C2×D151semidirect

Maximal subgroups

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

subgroupindex
#121×D1512
#237525272
#237525242
#237524482
#237524462
#237523472
#237523442
C2×(C2×D151)⋊C82
#466×C1512
#3186151