Finite Group Databasebeta

← #34080162

Subgroups — #34080162

Order 19328.

420 conjugacy classes of subgroups; only the 117 normal subgroups are shown.

normal subgroups only

This group has 420 conjugacy classes of subgroups — too many to draw. Only its 117 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#23752817C211yesmaximal, characteristic, complemented
2#23752781C211yesmaximal, characteristic, complemented
3#23752601C211yesmaximal, characteristic, complemented
4#23752589C211yesmaximal, characteristic, complemented
5#23752577C211yesmaximal, characteristic, complemented
6#23752567C211yesmaximal, characteristic, complemented
7#23752428C212yesmaximal, complemented
8#23752408C212yesmaximal, complemented
9#23752359C212yesmaximal, complemented
10#23752348C212yesmaximal, complemented
11#433×C151C211yesmaximal, characteristic, complemented
12C2×#14559004C2211yescharacteristic
13C22×D604C2211yescharacteristic
14C2×#14558993C2212yescomplemented
15C2×D1208C2212yes—
16C2×D1208C2212yes—
17C2×D1208C2212yescomplemented
18#18012736C2211yescharacteristic
19#18012736C2211yescharacteristic
20#18012736C2211yescharacteristic, complemented
21#18012731C2211yescharacteristic, complemented
22#18012727C2211yescharacteristic
23#18012727C2211yescharacteristic
24#18012724—22no—
25#18012714—22no—
26#18012713C2212yes—
27#18012712—22no—
28#18012709—22no—
29C4×D604C2212yescomplemented
30#18012664C2212yescomplemented
31#18012661C2212yes—
32#18012661C2212yes—
33#18012661C2212yescomplemented
34#117×C151C2211yescharacteristic
35C4⋊C8×C151C2212yescomplemented
36C22⋊C8×C151C2212yes—
37#97×C151C2211yescharacteristic, complemented
38C4×C8×C151C2211yescharacteristic, complemented
39C23×D151—21no—
40#14559004—42no—
41C2×Dic302C2311yescharacteristic
42C2×D604—21no—
43C2×D604—22no—
44C2×D604—22no—
45C2×D604—22no—
46C2×D604—42no—
47C2×D604C2312yes—
48C2×D604C2311yescharacteristic
49C2×D604C2311yescharacteristic
50C2×D604C2311yescharacteristic
51C2×C22⋊D151—21no—
52C2×C22⋊D151—22no—
53C2×C4×D151—21no—
54C2×C4×D151—22no—
55#14558993—42no—
56D1208—42no—
57D1208—42no—
58D1208—42no—
59C4⋊Dic151C2312yes—
60Dic151⋊C4—22no—
61(C2×D151)⋊C4—22no—
62(C2×D151)⋊C4—22no—
63(C2×D151)⋊C4—22no—
64(C2×D151)⋊C4—22no—
65C22×C4×C151C2311yescharacteristic
66C2×C8×C151C2312yes—
67C2×C8×C151C2312yes—
68C4⋊C4×C151D412yes—
69C22⋊C4×C151D412yes—
70C42×C151C2311yescharacteristic
71C42×C151C2311yescharacteristic
72C22×D151—22no—
73C22×D151—21no—
74C22×D151—21no—
75C22×D151—21no—
76C22×D151—42no—
77C22×D151—82no—
78Dic302—22no—
79D604—22no—
80D604—22no—
81D604—22no—
82D604—22no—
83D604—22no—
84D604—42no—
85D604—82no—
86D604—82no—
87D604—82no—
88C22⋊D151—42no—
89C22⋊D151—82no—
90C2×Dic151—21no—
91C2×Dic151—22no—
92C4×D151—42no—
93C4×D151—82no—
94C23×C151C2×D411yescharacteristic
95C2×C4×C151—22no—
96C2×C4×C151C2×D412yes—
97C2×C4×C151C2×D411yescharacteristic
98C2×C4×C151C2×D412yes—
99C2×C4×C151C2411yescharacteristic
100C8×C151—22no—
101C8×C151—22no—
102C22×C151—21no—
103C22×C151—22no—
104C22×C151C22×D411yescharacteristic
105C2×D151—41no—
106C2×D151—41no—
107C2×D151—41no—
108C2×D151—42no—
109C2×D151—42no—
110C2×D151—42no—
111C2×D151—42no—
112C2×D151—42no—
113C2×D151—42no—
114C2×D151—84no—
115C4×C151—21no—
116C4×C151—22no—
117C4×C151—22no—
118C4×C151H(5,𝔽2)12yes—
119Dic151—41no—
120Dic151—42no—
121C2×C151—41no—
122C2×C151#53511yescharacteristic
123C2×C151#57612yes—
124D151—81no—
125D151—82no—
126D151—81no—
127D151—81no—
128C151#322011yescharacteristic, complemented, Sylow
129#3220—1511nomaximal, Sylow
130#540—1511no—
131#535—1511no—
132#496—1511no—
133#493—1511no—
134#490—1511no—
135#488—1511no—
136#463—1512no—
137#459—1512no—
138#449—1512no—
139#447—1512no—
140#433D15111yescharacteristic, complemented
141C2×#41—1511no—
142C22×D4—1511no—
143C2×SD16—1512no—
144C2×D8—1512no—
145C2×D8—1512no—
146C2×D8—1512no—
147#127—1511no—
148#127—1511no—
149#127—1511no—
150#125—1511no—
151#124—1511no—
152#124—1511no—
153#123—3022no—
154#121—3022no—
155#121—3022no—
156#121—1512no—
157#120—3022no—
158C4×D4—1512no—
159#117C2×D15111yescharacteristic
160C4⋊C8C2×D15112yescomplemented
161#103—1512no—
162#102—1512no—
163#102—1512no—
164#102—1512no—
165C22⋊C8C2×D15112yes—
166#97C2×D15111yescharacteristic, complemented
167C4×C8C2×D15111yescharacteristic, complemented
168C24—3021no—
169#41—6042no—
170C2×Q8—1511no—
171C2×D4—3021no—
172C2×D4—3022no—
173C2×D4—3021no—
174C2×D4—3022no—
175C2×D4—3022no—
176C2×D4—3022no—
177C2×D4—6042no—
178C2×D4—1511no—
179C2×D4—1511no—
180C2×D4—1511no—
181C2×D4—1512no—
182C22×C4—3021no—
183C22×C4—3022no—
184C22×C4C22×D15111yescharacteristic
185SD16—6042no—
186D8—6042no—
187D8—6042no—
188D8—6042no—
189C2×C8C22×D15112yes—
190C2×C8C22×D15112yes—
191C4⋊C4—3022no—
192C4⋊C4—1512no—
193C4⋊C4D60412yes—
194C22⋊C4—3022no—
195C22⋊C4—3022no—
196C22⋊C4—3022no—
197C22⋊C4—3022no—
198C22⋊C4D60412yes—
199C42C22×D15111yescharacteristic
200C42C22×D15111yescharacteristic
201C23—3022no—
202C23—3021no—
203C23—3021no—
204C23—3021no—
205C23—6042no—
206C23—12082no—
207C23C2×D60411yescharacteristic
208Q8—3022no—
209D4—3022no—
210D4—3022no—
211D4—3022no—
212D4—3022no—
213D4—3022no—
214D4—6042no—
215D4—6042no—
216D4—12082no—
217D4—12082no—
218D4—12082no—
219D4—12082no—
220C2×C4—22no—
221C2×C4—3021no—
222C2×C4—3022no—
223C2×C4—6042no—
224C2×C4—12082no—
225C2×C4C2×D60412yes—
226C2×C4C2×D60412yes—
227C2×C4C2×D60411yescharacteristic
228C2×C4C23×D15111yescharacteristic
229C8—22no—
230C8—22no—
231C22—22no—
232C22—21no—
233C22—6042no—
234C22—6042no—
235C22—6042no—
236C22—6042no—
237C22—6042no—
238C22—6041no—
239C22—6041no—
240C22—6041no—
241C22—6042no—
242C22—12084no—
243C22C22×D60411yescharacteristic
244C4—22no—
245C4—22no—
246C4—21no—
247C4—6042no—
248C4—6041no—
249C4#1801278512yes—
250C2—41no—
251C2—12081no—
252C2—12081no—
253C2—12082no—
254C2—12081no—
255C2#2375278111yescharacteristic
256C2#2375301712yes—
subgroupG/H
centerC22C22×D604
commutator, cosocleC2×C4×C151C24
FrattiniC2×C4C23×D151
Fitting#433×C151C2
socleC22×C151C22×D4
hypercenter#433D151
hypocenterC151#3220
LCSG ▷ C2×C4×C151 ▷ C2×C151 ▷ C151
UCSC1 ◁ C22 ◁ #117 ◁ #433

Complements

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

NH ≅ G/Ntype
1. #23752817C2semidirect
2. #23752781C2semidirect
3. #23752601C2semidirect
4. #23752589C2semidirect
5. #23752577C2semidirect
6. #23752567C2semidirect
7. #23752428C2semidirect
8. #23752408C2semidirect
9. #23752359C2semidirect
10. #23752348C2semidirect
11. #433×C151C2semidirect
14. C2×#14558993C22semidirect
17. C2×D1208C22semidirect
20. #18012736C22semidirect
21. #18012731C22semidirect
29. C4×D604C22semidirect
30. #18012664C22semidirect
33. #18012661C22semidirect
35. C4⋊C8×C151C22semidirect
37. #97×C151C22semidirect
38. C4×C8×C151C22semidirect
128. C151#3220semidirect
140. #433D151semidirect
160. C4⋊C8C2×D151semidirect
166. #97C2×D151semidirect
167. C4×C8C2×D151semidirect

Maximal subgroups

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

subgroupindex
#237528172
#237527812
#237526012
#237525892
#237525772
#237525672
#237524282
#237524082
#237523592
#237523482
#433×C1512
#3220151