Finite Group Databasebeta

← #34078467

Subgroups — #34078467

Order 19328.

762 conjugacy classes of subgroups; only the 161 normal subgroups are shown.

normal subgroups only

This group has 762 conjugacy classes of subgroups — too many to draw. Only its 161 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#23753010C212yesmaximal, complemented
2#23752779C211yesmaximal, characteristic, complemented
3#23752390C214yesmaximal, complemented
4#23752380C214yesmaximal, complemented
5#23752229C212yesmaximal, complemented
6C2×#18012656C211yesmaximal, characteristic, complemented
7C2×H(5,𝔽2)×C151C211yesmaximal, characteristic, complemented
8C2×#14559004C2211yescharacteristic, complemented
9#18012770—22no—
10#18012769C2214yescomplemented
11#18012765—22no—
12#18012764C2214yescomplemented
13#18012759—24no—
14C2×#14558988C2212yescomplemented
15#18012735C2212yescomplemented
16#18012726C2212yescomplemented
17#18012710—22no—
18#18012708—22no—
19#18012698C2211yescharacteristic, complemented
20#18012666C2218yescomplemented
21#18012656C2214yescomplemented
22H(5,𝔽2)×C151—22no—
23H(5,𝔽2)×C151—24no—
24H(5,𝔽2)×C151C2214yes—
25C2×#41×C151—22no—
26C2×#41×C151C2212yes—
27C22×D4×C151—22no—
28C22×D4×C151—22no—
29C22×D4×C151C2211yescharacteristic
30#14559004—22no—
31#14559004—22no—
32C2×Dic302C2311yescharacteristic, complemented
33C2×D604C2311yescharacteristic, complemented
34C2×C22⋊D151—21no—
35C2×C22⋊D151—24no—
36C2×C4×D151—21no—
37#14558994—24no—
38#14558992—24no—
39#14558991—24no—
40#14558989—24no—
41#14558988—22no—
42#14558988C2314yescomplemented
43C2×C151⋊C8—22no—
44C4⋊Dic151—21no—
45C22⋊Dic151—21no—
46C22⋊Dic151—24no—
47C4×Dic151C2312yescomplemented
48C24×C151—22no—
49C24×C151D412yes—
50#41×C151—28no—
51#41×C151—28no—
52#41×C151—22no—
53#41×C151—22no—
54#41×C151D414yescomplemented
55#41×C151C2314yes—
56C2×Q8×C151D412yescomplemented
57C2×D4×C151—24no—
58C2×D4×C151—28no—
59C2×D4×C151—28no—
60C2×D4×C151—22no—
61C2×D4×C151—28no—
62C2×D4×C151—28no—
63C2×D4×C151—22no—
64C2×D4×C151—22no—
65C2×D4×C151D412yes—
66C2×D4×C151D412yescomplemented
67C2×D4×C151C2312yes—
68C22×C4×C151—22no—
69C22×C4×C151—22no—
70C22×C4×C151C2311yescharacteristic
71C22×D151—21no—
72Dic302—22no—
73D604—22no—
74C22⋊D151—41no—
75C22⋊D151—41no—
76C22⋊D151—84no—
77C2×Dic151—22no—
78C2×Dic151—21no—
79C4×D151—42no—
80C151⋊C8—24no—
81C23×C151—28no—
82C23×C151—22no—
83C23×C151—22no—
84C23×C151—22no—
85C23×C151—82no—
86C23×C151—84no—
87C23×C151C2×D414yes—
88C23×C151C2×D411yescharacteristic
89Q8×C151—22no—
90Q8×C151C2×D414yes—
91D4×C151—216no—
92D4×C151—24no—
93D4×C151—24no—
94D4×C151—24no—
95D4×C151—22no—
96D4×C151—24no—
97D4×C151C2×D414yes—
98C2×C4×C151—28no—
99C2×C4×C151—22no—
100C2×C4×C151—24no—
101C2×C4×C151—24no—
102C2×C4×C151C2×D411yescharacteristic
103C2×C4×C151C2×D412yes—
104C2×C4×C151C2×D412yes—
105C2×C4×C151C2411yescharacteristic
106C22×C151—24no—
107C22×C151—24no—
108C22×C151—41no—
109C22×C151—44no—
110C22×C151—44no—
111C22×C151—44no—
112C22×C151—82no—
113C22×C151—88no—
114C22×C151#12011yescharacteristic
115C22×C151#12011yescharacteristic
116C22×C151C22×D411yescharacteristic
117C2×D151—42no—
118C2×D151—41no—
119C4×C151—24no—
120C4×C151#12012yes—
121C4×C151C22×D412yes—
122Dic151—42no—
123Dic151—41no—
124C2×C151—21no—
125C2×C151—21no—
126C2×C151—21no—
127C2×C151—44no—
128C2×C151—44no—
129C2×C151C2×#12011yescharacteristic
130D151—81no—
131C151#301911yescharacteristic, complemented, Sylow
132#3019—1511nomaximal, Sylow
133C2×H(5,𝔽2)D15111yescharacteristic, complemented
134#575—1512no—
135#535—1511no—
136#455—1514no—
137#453—1514no—
138#421—1512no—
139C2×#100—1511no—
140H(5,𝔽2)—24no—
141H(5,𝔽2)—22no—
142H(5,𝔽2)C2×D15114yes—
143C2×#41—22no—
144C2×#41—1511no—
145C2×#41C2×D15112yes—
146C22×D4—22no—
147C22×D4—22no—
148C22×D4C2×D15111yescharacteristic
149#137—3022no—
150#137—1514no—
151AGL(1,ℤ/8)—3022no—
152AGL(1,ℤ/8)—1514no—
153#135—3024no—
154C2×M16—1512no—
155#127—1512no—
156#124—1512no—
157#121—3022no—
158#120—3022no—
159#117—1511no—
160#104—1518no—
161#100—1514no—
162C24—22no—
163C24C22⋊D15112yes—
164#41—28no—
165#41—28no—
166#41—22no—
167#41—22no—
168#41—3022no—
169#41—3022no—
170#41C22⋊D15114yescomplemented
171#41C22×D15114yes—
172C2×Q8—1511no—
173C2×Q8C22⋊D15112yescomplemented
174C2×D4—24no—
175C2×D4—28no—
176C2×D4—28no—
177C2×D4—22no—
178C2×D4—28no—
179C2×D4—28no—
180C2×D4—22no—
181C2×D4—22no—
182C2×D4—3021no—
183C2×D4—3024no—
184C2×D4—1511no—
185C2×D4C22⋊D15112yes—
186C2×D4C22⋊D15112yescomplemented
187C2×D4C22×D15112yes—
188C22×C4—22no—
189C22×C4—22no—
190C22×C4—3021no—
191C22×C4C22×D15111yescharacteristic
192Q16—3024no—
193SD16—3024no—
194SD16—3024no—
195D8—3024no—
196M16—3022no—
197M16—1514no—
198C2×C8—3022no—
199C4⋊C4—3021no—
200C22⋊C4—3021no—
201C22⋊C4—3024no—
202C42—1512no—
203C23—28no—
204C23—22no—
205C23—22no—
206C23—22no—
207C23—82no—
208C23—84no—
209C23—3021no—
210C23C2×C22⋊D15114yes—
211C23C2×C22⋊D15111yescharacteristic
212Q8—22no—
213Q8—3022no—
214Q8C2×C22⋊D15114yes—
215D4—216no—
216D4—24no—
217D4—24no—
218D4—24no—
219D4—22no—
220D4—24no—
221D4—3022no—
222D4—6041no—
223D4—6041no—
224D4—12084no—
225D4C2×C22⋊D15114yes—
226C2×C4—28no—
227C2×C4—22no—
228C2×C4—24no—
229C2×C4—24no—
230C2×C4—3022no—
231C2×C4—3021no—
232C2×C4—6042no—
233C2×C4C2×C22⋊D15111yescharacteristic
234C2×C4C2×C22⋊D15112yes—
235C2×C4C2×C22⋊D15112yes—
236C2×C4C23×D15111yescharacteristic
237C8—3024no—
238C22—24no—
239C22—24no—
240C22—41no—
241C22—44no—
242C22—44no—
243C22—44no—
244C22—82no—
245C22—88no—
246C22—6042no—
247C22—6041no—
248C22#1801270811yescharacteristic
249C22#1801270811yescharacteristic
250C22C22×C22⋊D15111yescharacteristic
251C4—24no—
252C4—6042no—
253C4—6041no—
254C4#1801270812yes—
255C4C22×C22⋊D15112yes—
256C2—21no—
257C2—21no—
258C2—21no—
259C2—44no—
260C2—44no—
261C2—12081no—
262C2C2×#1801270811yescharacteristic
subgroupG/H
centerC2C2×#18012708
commutator, cosocleC2×C4×C151C24
FrattiniC2×C4C23×D151
FittingC2×H(5,𝔽2)×C151C2
socleC2×C151C2×#120
hypercenterC2×H(5,𝔽2)D151
hypocenterC151#3019
LCSG ▷ C2×C4×C151 ▷ C2×C151 ▷ C151
UCSC1 ◁ C2 ◁ C22×C4 ◁ C2×H(5,𝔽2)

Complements

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

NH ≅ G/Ntype
1. #23753010C2semidirect
2. #23752779C2semidirect
3. #23752390C2semidirect
4. #23752380C2semidirect
5. #23752229C2semidirect
6. C2×#18012656C2semidirect
7. C2×H(5,𝔽2)×C151C2semidirect
8. C2×#14559004C22semidirect
10. #18012769C22semidirect
12. #18012764C22semidirect
14. C2×#14558988C22semidirect
15. #18012735C22semidirect
16. #18012726C22semidirect
19. #18012698C22semidirect
20. #18012666C22semidirect
21. #18012656C22semidirect
32. C2×Dic302C23semidirect
33. C2×D604C23semidirect
42. #14558988C23semidirect
47. C4×Dic151C23semidirect
54. #41×C151D4semidirect
56. C2×Q8×C151D4semidirect
66. C2×D4×C151D4semidirect
131. C151#3019semidirect
133. C2×H(5,𝔽2)D151semidirect
170. #41C22⋊D151semidirect
173. C2×Q8C22⋊D151semidirect
186. C2×D4C22⋊D151semidirect

Maximal subgroups

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

subgroupindex
#237530102
#237527792
#237523902
#237523802
#237522292
C2×#180126562
C2×H(5,𝔽2)×C1512
#3019151