Finite Group Databasebeta

← #34078466

Subgroups — #34078466

Order 19328.

762 conjugacy classes of subgroups; only the 145 normal subgroups are shown.

normal subgroups only

This group has 762 conjugacy classes of subgroups — too many to draw. Only its 145 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×#18012784C211yesmaximal, characteristic, complemented
2#23753010C212yesmaximal, complemented
3#23752389C214yesmaximal, complemented
4#23752379C214yesmaximal, complemented
5#23752230C212yesmaximal, complemented
6C2×#18012656C211yesmaximal, characteristic, complemented
7#535×C151C211yesmaximal, characteristic, complemented
8#18012784—22no—
9#18012784—24no—
10#18012784C2214yes—
11C2×#14559004C2212yes—
12C2×#14559003—22no—
13C22×C22⋊D151—22no—
14C2×D4×D151—22no—
15#18012770C2214yescomplemented
16#18012769—22no—
17#18012765C2214yescomplemented
18#18012764—22no—
19#18012759—24no—
20C2×#14558988C2212yescomplemented
21#18012667C2218yescomplemented
22#18012656C2214yescomplemented
23C2×#41×C151C2211yescharacteristic, complemented
24C22×D4×C151C2211yescharacteristic
25#127×C151C2212yescomplemented
26#124×C151C2212yescomplemented
27#121×C151—22no—
28#120×C151—22no—
29#117×C151C2211yescharacteristic, complemented
30C23×D151—22no—
31#14559004—22no—
32#14559004—22no—
33#14559004D414yescomplemented
34#14559004C2314yes—
35#14559003—28no—
36#14559003—28no—
37C2×Dic302D412yescomplemented
38C2×D604D412yescomplemented
39C2×C22⋊D151—24no—
40C2×C22⋊D151—28no—
41C2×C22⋊D151—22no—
42C2×C22⋊D151—28no—
43D4×D151—28no—
44D4×D151—28no—
45C22×Dic151—22no—
46C2×C4×D151—22no—
47#14558994—24no—
48#14558992—24no—
49#14558991—24no—
50#14558989—24no—
51#14558988—22no—
52#14558988C2314yescomplemented
53C2×C151⋊C8—22no—
54C24×C151D412yes—
55#41×C151—22no—
56#41×C151—22no—
57C2×Q8×C151C2311yescharacteristic, complemented
58C2×D4×C151—21no—
59C2×D4×C151—24no—
60C2×D4×C151—22no—
61C2×D4×C151—22no—
62C2×D4×C151D412yes—
63C2×D4×C151C2312yes—
64C2×D4×C151C2311yescharacteristic, complemented
65C22×C4×C151—21no—
66C22×C4×C151C2311yescharacteristic
67C4⋊C4×C151—21no—
68C22⋊C4×C151—21no—
69C22⋊C4×C151—24no—
70C42×C151C2312yescomplemented
71C22×D151—22no—
72C22×D151—28no—
73C22×D151—84no—
74Dic302—22no—
75Dic302C2×D414yes—
76D604—22no—
77D604C2×D414yes—
78C22⋊D151—216no—
79C22⋊D151—24no—
80C22⋊D151—24no—
81C2×Dic151—28no—
82C2×Dic151—22no—
83C4×D151—24no—
84C4×D151—24no—
85C151⋊C8—24no—
86C23×C151—22no—
87C23×C151—22no—
88C23×C151—21no—
89C23×C151—82no—
90C23×C151C2×D414yes—
91C23×C151C2×D411yescharacteristic
92Q8×C151—22no—
93D4×C151—24no—
94D4×C151—24no—
95D4×C151—22no—
96D4×C151—41no—
97D4×C151—41no—
98D4×C151—84no—
99C2×C4×C151—21no—
100C2×C4×C151—22no—
101C2×C4×C151—42no—
102C2×C4×C151C2×D412yes—
103C2×C4×C151C2×D412yes—
104C2×C4×C151C2×D411yescharacteristic
105C2×C4×C151C2411yescharacteristic
106C22×C151—24no—
107C22×C151—41no—
108C22×C151—44no—
109C22×C151—44no—
110C22×C151—42no—
111C22×C151—41no—
112C22×C151—82no—
113C22×C151#12011yescharacteristic
114C22×C151#12011yescharacteristic
115C22×C151C22×D411yescharacteristic
116C2×D151—24no—
117C2×D151—44no—
118C2×D151—88no—
119C4×C151—42no—
120C4×C151—41no—
121C4×C151#12012yes—
122C4×C151C22×D412yes—
123Dic151—24no—
124C2×C151—21no—
125C2×C151—21no—
126C2×C151—21no—
127C2×C151—44no—
128C2×C151—81no—
129C2×C151C2×#12011yescharacteristic
130D151—44no—
131C151#301911yescharacteristic, complemented, Sylow
132#3019—1511nomaximal, Sylow
133C2×H(5,𝔽2)—1511no—
134#575—1512no—
135#535D15111yescharacteristic, complemented
136#455—1514no—
137#453—1514no—
138#421—1512no—
139C2×#100—1511no—
140H(5,𝔽2)—3024no—
141H(5,𝔽2)—3022no—
142H(5,𝔽2)—1514no—
143C2×#41—3022no—
144C2×#41—1512no—
145C2×#41C2×D15111yescharacteristic, complemented
146C22×D4—3022no—
147C22×D4—3022no—
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#127C2×D15112yescomplemented
156#124C2×D15112yescomplemented
157#121—22no—
158#120—22no—
159#117C2×D15111yescharacteristic, complemented
160#104—1518no—
161#100—1514no—
162C24—3022no—
163C24C22⋊D15112yes—
164#41—22no—
165#41—22no—
166#41—3028no—
167#41—3028no—
168#41—3022no—
169#41—3022no—
170#41—1514no—
171#41—1514no—
172C2×Q8—1512no—
173C2×Q8C22×D15111yescharacteristic, complemented
174C2×D4—21no—
175C2×D4—24no—
176C2×D4—22no—
177C2×D4—22no—
178C2×D4—3028no—
179C2×D4—3028no—
180C2×D4—3024no—
181C2×D4—3028no—
182C2×D4—3022no—
183C2×D4—3028no—
184C2×D4—1512no—
185C2×D4C22⋊D15112yes—
186C2×D4C22×D15112yes—
187C2×D4C22×D15111yescharacteristic, complemented
188C22×C4—21no—
189C22×C4—3022no—
190C22×C4—3022no—
191C22×C4C22×D15111yescharacteristic
192Q16—3024no—
193SD16—3024no—
194SD16—3024no—
195D8—3024no—
196M16—3022no—
197M16—1514no—
198C2×C8—3022no—
199C4⋊C4—21no—
200C22⋊C4—21no—
201C22⋊C4—24no—
202C42C22×D15112yescomplemented
203C23—22no—
204C23—22no—
205C23—21no—
206C23—82no—
207C23—3028no—
208C23—3022no—
209C23—12084no—
210C23C2×C22⋊D15114yes—
211C23C2×C22⋊D15111yescharacteristic
212Q8—22no—
213Q8—3022no—
214Q8—1514no—
215D4—24no—
216D4—24no—
217D4—22no—
218D4—41no—
219D4—41no—
220D4—84no—
221D4—30216no—
222D4—3024no—
223D4—3024no—
224D4—3022no—
225D4—1514no—
226C2×C4—22no—
227C2×C4—21no—
228C2×C4—42no—
229C2×C4—3028no—
230C2×C4—3022no—
231C2×C4—3024no—
232C2×C4—3024no—
233C2×C4D4×D15112yes—
234C2×C4D4×D15112yes—
235C2×C4C2×C22⋊D15111yescharacteristic
236C2×C4C23×D15111yescharacteristic
237C8—3024no—
238C22—24no—
239C22—41no—
240C22—44no—
241C22—44no—
242C22—42no—
243C22—41no—
244C22—82no—
245C22—3024no—
246C22—6044no—
247C22—12088no—
248C22#1801270711yescharacteristic
249C22#1801270711yescharacteristic
250C22C22×C22⋊D15111yescharacteristic
251C4—42no—
252C4—41no—
253C4—3024no—
254C4#1801270712yes—
255C4C2×D4×D15112yes—
256C2—21no—
257C2—21no—
258C2—21no—
259C2—44no—
260C2—81no—
261C2—6044no—
262C2C2×#1801270711yescharacteristic
subgroupG/H
centerC2C2×#18012707
commutator, cosocleC2×C4×C151C24
FrattiniC2×C4C23×D151
Fitting#535×C151C2
socleC2×C151C2×#120
hypercenter#535D151
hypocenterC151#3019
LCSG ▷ C2×C4×C151 ▷ C2×C151 ▷ C151
UCSC1 ◁ C2 ◁ C22×C4 ◁ #535

Complements

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

NH ≅ G/Ntype
1. C2×#18012784C2semidirect
2. #23753010C2semidirect
3. #23752389C2semidirect
4. #23752379C2semidirect
5. #23752230C2semidirect
6. C2×#18012656C2semidirect
7. #535×C151C2semidirect
15. #18012770C22semidirect
17. #18012765C22semidirect
20. C2×#14558988C22semidirect
21. #18012667C22semidirect
22. #18012656C22semidirect
23. C2×#41×C151C22semidirect
25. #127×C151C22semidirect
26. #124×C151C22semidirect
29. #117×C151C22semidirect
33. #14559004D4semidirect
37. C2×Dic302D4semidirect
38. C2×D604D4semidirect
52. #14558988C23semidirect
57. C2×Q8×C151C23semidirect
64. C2×D4×C151C23semidirect
70. C42×C151C23semidirect
131. C151#3019semidirect
135. #535D151semidirect
145. C2×#41C2×D151semidirect
155. #127C2×D151semidirect
156. #124C2×D151semidirect
159. #117C2×D151semidirect
173. C2×Q8C22×D151semidirect
187. C2×D4C22×D151semidirect
202. C42C22×D151semidirect

Maximal subgroups

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

subgroupindex
C2×#180127842
#237530102
#237523892
#237523792
#237522302
C2×#180126562
#535×C1512
#3019151