Finite Group Databasebeta

← #34080155

Subgroups — #34080155

Order 19328.

420 conjugacy classes of subgroups; only the 109 normal subgroups are shown.

normal subgroups only

This group has 420 conjugacy classes of subgroups — too many to draw. Only its 109 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#23752816C211yesmaximal, characteristic, complemented
2#23752780C211yesmaximal, characteristic, complemented
3#23752588C211yesmaximal, characteristic, complemented
4#23752577C211yesmaximal, characteristic, complemented
5#23752566C211yesmaximal, characteristic, complemented
6#23752429C212yesmaximal, complemented
7#23752405C212yesmaximal, complemented
8#23752356C212yesmaximal, complemented
9#23752344C212yesmaximal, complemented
10#23752274C211yesmaximal, characteristic, complemented
11#496×C151C211yesmaximal, characteristic, complemented
12C2×#14559005C2211yescharacteristic
13C2×D4×D151C2211yescharacteristic
14C2×#14558989C2212yes—
15C2×#14558989C2212yescomplemented
16#18012736C2211yescharacteristic
17#18012735C2211yescharacteristic
18#18012731C2211yescharacteristic, complemented
19#18012728C2211yescharacteristic
20#18012720—22no—
21#18012712—22no—
22#18012711—22no—
23#18012710C2212yes—
24#18012709—22no—
25D4×Dic151C2212yescomplemented
26#18012696C2211yescharacteristic
27Dic151⋊C8C2212yescomplemented
28#18012663C2212yescomplemented
29#18012661C2212yes—
30#18012661C2212yescomplemented
31#18012660C2212yes—
32(C2×D151)⋊C8C2212yes—
33C4×C151⋊C8C2211yescharacteristic, complemented
34C2×SD16×C151C2212yescomplemented
35C2×D8×C151C2212yes—
36#127×C151C2211yescharacteristic, complemented
37#124×C151C2211yescharacteristic
38#97×C151C2211yescharacteristic, complemented
39C23×D151—21no—
40#14559005—42no—
41C2×D604—21no—
42C2×D604—22no—
43C2×D604C2311yescharacteristic
44C2×D604C2311yescharacteristic
45C2×C22⋊D151—22no—
46C2×C22⋊D151—21no—
47C2×C22⋊D151—22no—
48D4×D151—42no—
49C22×Dic151—22no—
50C2×C4×D151—21no—
51C2×C4×D151C2311yescharacteristic
52#14558989—42no—
53#14558989—42no—
54C2×C151⋊C8C2312yes—
55C4⋊Dic151C2312yes—
56Dic151⋊C4—22no—
57Dic151⋊C4D412yes—
58C22⋊Dic151—22no—
59C22⋊Dic151—22no—
60(C2×D151)⋊C4—22no—
61(C2×D151)⋊C4D412yes—
62C4×Dic151C2311yescharacteristic
63C2×Q8×C151C2311yescharacteristic
64C2×D4×C151—22no—
65C2×D4×C151C2312yes—
66C2×D4×C151C2311yescharacteristic
67SD16×C151—42no—
68D8×C151—42no—
69C2×C8×C151C2312yes—
70C22⋊C4×C151—22no—
71C42×C151C2311yescharacteristic
72C22×D151—21no—
73C22×D151—21no—
74C22×D151—42no—
75C22×D151—82no—
76C22×D151C2×D411yescharacteristic
77D604—22no—
78D604—22no—
79D604—42no—
80D604—82no—
81C22⋊D151—42no—
82C22⋊D151—82no—
83C22⋊D151—82no—
84C2×Dic151—22no—
85C2×Dic151—82no—
86C2×Dic151C2×D412yes—
87C2×Dic151C2×D411yescharacteristic
88C4×D151—22no—
89C4×D151—42no—
90C151⋊C8—22no—
91C23×C151—22no—
92C23×C151—21no—
93Q8×C151—22no—
94D4×C151—22no—
95D4×C151—22no—
96D4×C151—22no—
97D4×C151—82no—
98C2×C4×C151—21no—
99C2×C4×C151C2×D412yes—
100C2×C4×C151C2411yescharacteristic
101C8×C151—22no—
102C22×C151—42no—
103C22×C151—41no—
104C22×C151—42no—
105C22×C151—42no—
106C22×C151—42no—
107C22×C151C22×D411yescharacteristic
108C2×D151—21no—
109C2×D151—22no—
110C2×D151—41no—
111C2×D151—41no—
112C2×D151—42no—
113C2×D151—42no—
114C2×D151—84no—
115C4×C151—22no—
116C4×C151—41no—
117C4×C151H(5,𝔽2)12yes—
118Dic151—21no—
119Dic151—22no—
120Dic151—42no—
121C2×C151—81no—
122C2×C151—82no—
123C2×C151#53511yescharacteristic
124C2×C151#57612yes—
125D151—41no—
126D151—81no—
127D151—81no—
128C151#322011yescharacteristic, complemented, Sylow
129#3220—1511nomaximal, Sylow
130#540—1511no—
131#535—1511no—
132#496D15111yescharacteristic, complemented
133#493—1511no—
134#490—1511no—
135#488—1511no—
136#463—1512no—
137#459—1512no—
138#449—1512no—
139#447—1512no—
140#433—1511no—
141C2×#41—1511no—
142C22×D4—1511no—
143C2×SD16C2×D15112yescomplemented
144C2×D8—1512no—
145C2×D8—1512no—
146C2×D8C2×D15112yes—
147#127—1511no—
148#127—1511no—
149#127C2×D15111yescharacteristic, complemented
150#125—1511no—
151#124—1511no—
152#124C2×D15111yescharacteristic
153#123—3022no—
154#121—3022no—
155#121—3022no—
156#121—1512no—
157#120—3022no—
158C4×D4—1512no—
159#117—1511no—
160C4⋊C8—1512no—
161#103—1512no—
162#102—1512no—
163#102—1512no—
164#102—1512no—
165C22⋊C8—1512no—
166#97C2×D15111yescharacteristic, complemented
167C4×C8—1511no—
168C24—3021no—
169#41—6042no—
170C2×Q8C22×D15111yescharacteristic
171C2×D4—22no—
172C2×D4—3021no—
173C2×D4—3022no—
174C2×D4—3021no—
175C2×D4—3022no—
176C2×D4—3022no—
177C2×D4—6042no—
178C2×D4—1511no—
179C2×D4—1511no—
180C2×D4C22×D15111yescharacteristic
181C2×D4C22×D15112yes—
182C22×C4—3021no—
183C22×C4—3022no—
184C22×C4—1511no—
185SD16—42no—
186D8—42no—
187D8—6042no—
188D8—6042no—
189C2×C8—1512no—
190C2×C8C22×D15112yes—
191C4⋊C4—3022no—
192C4⋊C4—1512no—
193C4⋊C4—1512no—
194C22⋊C4—22no—
195C22⋊C4—3022no—
196C22⋊C4—3022no—
197C22⋊C4—3022no—
198C22⋊C4—1512no—
199C42—1511no—
200C42C22×D15111yescharacteristic
201C23—21no—
202C23—22no—
203C23—3021no—
204C23—3021no—
205C23—6042no—
206C23—1511no—
207C23—12082no—
208Q8—22no—
209D4—22no—
210D4—22no—
211D4—22no—
212D4—82no—
213D4—3022no—
214D4—3022no—
215D4—6042no—
216D4—6042no—
217D4—12082no—
218D4—12082no—
219D4—12082no—
220C2×C4—21no—
221C2×C4—3022no—
222C2×C4—3022no—
223C2×C4—6042no—
224C2×C4—1512no—
225C2×C4—1511no—
226C2×C4—12082no—
227C2×C4D4×D15112yes—
228C2×C4C23×D15111yescharacteristic
229C8—22no—
230C8—3022no—
231C22—42no—
232C22—42no—
233C22—42no—
234C22—41no—
235C22—42no—
236C22—3022no—
237C22—3021no—
238C22—6042no—
239C22—6042no—
240C22—6041no—
241C22—6041no—
242C22—12084no—
243C22C2×D4×D15111yescharacteristic
244C4—22no—
245C4—41no—
246C4—3022no—
247C4—3021no—
248C4—6042no—
249C4#1801278412yes—
250C2—81no—
251C2—82no—
252C2—6041no—
253C2—12081no—
254C2—12081no—
255C2#2375277511yescharacteristic
256C2#2375301612yes—
subgroupG/H
centerC22C2×D4×D151
commutator, cosocleC2×C4×C151C24
FrattiniC2×C4C23×D151
Fitting#496×C151C2
socleC22×C151C22×D4
hypercenter#496D151
hypocenterC151#3220
LCSG ▷ C2×C4×C151 ▷ C2×C151 ▷ C151
UCSC1 ◁ C22 ◁ C42 ◁ #496

Complements

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

NH ≅ G/Ntype
1. #23752816C2semidirect
2. #23752780C2semidirect
3. #23752588C2semidirect
4. #23752577C2semidirect
5. #23752566C2semidirect
6. #23752429C2semidirect
7. #23752405C2semidirect
8. #23752356C2semidirect
9. #23752344C2semidirect
10. #23752274C2semidirect
11. #496×C151C2semidirect
15. C2×#14558989C22semidirect
18. #18012731C22semidirect
25. D4×Dic151C22semidirect
27. Dic151⋊C8C22semidirect
28. #18012663C22semidirect
30. #18012661C22semidirect
33. C4×C151⋊C8C22semidirect
34. C2×SD16×C151C22semidirect
36. #127×C151C22semidirect
38. #97×C151C22semidirect
128. C151#3220semidirect
132. #496D151semidirect
143. C2×SD16C2×D151semidirect
149. #127C2×D151semidirect
166. #97C2×D151semidirect

Maximal subgroups

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

subgroupindex
#237528162
#237527802
#237525882
#237525772
#237525662
#237524292
#237524052
#237523562
#237523442
#237522742
#496×C1512
#3220151