Finite Group Databasebeta

← #34078511

Subgroups — #34078511

Order 19328.

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

normal subgroups only

This group has 772 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
1#23753048C211yesmaximal, characteristic, complemented
2#23752779C212yesmaximal, complemented
3#23752398C218yesmaximal, complemented
4#23752186C211yesmaximal, characteristic, complemented
5#23752185C212yesmaximal, complemented
6#535×C151C211yesmaximal, characteristic, complemented
7#18012787—21no—
8#18012786—22no—
9#18012785—22no—
10#18012784—21no—
11#18012784C2214yes—
12C2×#14559004—22no—
13C2×#14559004C2212yes—
14#41×D151—24no—
15#18012735—22no—
16#18012726—22no—
17#18012710—24no—
18#18012708C2218yescomplemented
19#18012698C2212yescomplemented
20#18012654C2214yescomplemented
21#18012653C2218yescomplemented
22C2×#41×C151C2211yescharacteristic
23C22×D4×C151C2211yescharacteristic, complemented
24#127×C151—21no—
25#124×C151—21no—
26#121×C151—22no—
27#120×C151C2214yescomplemented
28#117×C151C2211yescharacteristic, complemented
29#14559005—24no—
30#14559004—24no—
31#14559004—24no—
32#14559004—22no—
33#14559004—22no—
34#14559004—24no—
35#14559004—22no—
36#14559004—22no—
37#14559003—24no—
38#14559003—28no—
39C2×Dic302—22no—
40C2×Dic302D412yescomplemented
41Q8×D151—24no—
42C2×D604—22no—
43C2×D604D412yescomplemented
44C2×C22⋊D151—28no—
45C2×C22⋊D151—24no—
46C2×C22⋊D151C2314yes—
47D4×D151—24no—
48D4×D151—28no—
49C2×C4×D151—24no—
50C2×C4×D151D414yescomplemented
51C4⋊Dic151—22no—
52C22⋊Dic151—28no—
53C22⋊Dic151C2314yes—
54C4×Dic151—22no—
55C24×C151C2312yes—
56#41×C151—22no—
57#41×C151—22no—
58C2×Q8×C151D411yescharacteristic, complemented
59C2×D4×C151—24no—
60C2×D4×C151—22no—
61C2×D4×C151—22no—
62C2×D4×C151—21no—
63C2×D4×C151—21no—
64C2×D4×C151D411yescharacteristic, complemented
65C2×D4×C151C2312yes—
66C22×C4×C151D412yescomplemented
67C22×C4×C151C2311yescharacteristic
68C4⋊C4×C151—21no—
69C22⋊C4×C151—24no—
70C22⋊C4×C151C2312yes—
71C42×C151—21no—
72C22×D151—24no—
73C22×D151C2×D414yes—
74Dic302—24no—
75Dic302—22no—
76Dic302—22no—
77D604—24no—
78D604—22no—
79D604—22no—
80C22⋊D151—28no—
81C22⋊D151—24no—
82C22⋊D151—24no—
83C22⋊D151—88no—
84C2×Dic151—24no—
85C2×Dic151—24no—
86C2×Dic151C2×D414yes—
87C4×D151—28no—
88C4×D151—24no—
89C4×D151—24no—
90C23×C151—24no—
91C23×C151—22no—
92C23×C151—82no—
93C23×C151C2×D412yes—
94C23×C151C2411yescharacteristic
95Q8×C151—22no—
96D4×C151—24no—
97D4×C151—22no—
98D4×C151—41no—
99D4×C151—41no—
100D4×C151—42no—
101D4×C151—84no—
102C2×C4×C151—22no—
103C2×C4×C151—22no—
104C2×C4×C151—22no—
105C2×C4×C151C2×D412yes—
106C2×C4×C151C2×D412yes—
107C2×C4×C151C2×D412yes—
108C2×C4×C151C2×D411yescharacteristic
109C2×C4×C151C2×D411yescharacteristic
110C22×C151—22no—
111C22×C151—41no—
112C22×C151—42no—
113C22×C151—44no—
114C22×C151—48no—
115C22×C151—42no—
116C22×C151C22×D412yes—
117C22×C151C22×D411yescharacteristic
118C2×D151—24no—
119C2×D151—44no—
120C2×D151—84no—
121C4×C151—22no—
122C4×C151—42no—
123C4×C151#12011yescharacteristic
124C4×C151#12011yescharacteristic
125C4×C151#12012yes—
126Dic151—24no—
127Dic151—44no—
128C2×C151—22no—
129C2×C151—21no—
130C2×C151—42no—
131C2×C151—82no—
132C2×C151C2×#12011yescharacteristic
133D151—44no—
134C151#302711yescharacteristic, complemented, Sylow
135#3027—1511nomaximal, Sylow
136#585—1511no—
137#535—1512no—
138#535D15111yescharacteristic, complemented
139B(4,𝔽2)—1518no—
140#410—1511no—
141#410—1512no—
1422−1+4—3022no—
1432−1+4—3021no—
144H(5,𝔽2)—3022no—
145H(5,𝔽2)—3021no—
146H(5,𝔽2)—1514no—
147C2×#41—3024no—
148C2×#41—3022no—
149C2×#41—1512no—
150C2×#41C2×D15111yescharacteristic
151C22×D4C2×D15111yescharacteristic, complemented
152#127—21no—
153#127—3022no—
154#124—21no—
155#124—3022no—
156#121—22no—
157#121—3024no—
158#120—1518no—
159#120C2×D15114yescomplemented
160#117—1512no—
161#117C2×D15111yescharacteristic, complemented
162#99—1514no—
163#99—1518no—
164C24C22×D15112yes—
165#41—22no—
166#41—22no—
167#41—3024no—
168#41—3024no—
169#41—3024no—
170#41—3024no—
171#41—3028no—
172#41—3022no—
173#41—3022no—
174#41—3022no—
175#41—3024no—
176#41—3022no—
177C2×Q8—3022no—
178C2×Q8—3024no—
179C2×Q8—1512no—
180C2×Q8C22⋊D15111yescharacteristic, complemented
181C2×D4—24no—
182C2×D4—22no—
183C2×D4—22no—
184C2×D4—21no—
185C2×D4—21no—
186C2×D4—3022no—
187C2×D4—3024no—
188C2×D4—3028no—
189C2×D4—3024no—
190C2×D4—3028no—
191C2×D4—1514no—
192C2×D4—1512no—
193C2×D4C22⋊D15111yescharacteristic, complemented
194C2×D4C22×D15112yes—
195C22×C4—3024no—
196C22×C4—1514no—
197C22×C4C22⋊D15112yescomplemented
198C22×C4C22×D15111yescharacteristic
199C4⋊C4—21no—
200C4⋊C4—3022no—
201C22⋊C4—24no—
202C22⋊C4—3028no—
203C22⋊C4—1514no—
204C22⋊C4C22×D15112yes—
205C42—21no—
206C42—3022no—
207C23—24no—
208C23—22no—
209C23—82no—
210C23—3024no—
211C23—1514no—
212C23C2×C22⋊D15112yes—
213C23C23×D15111yescharacteristic
214Q8—22no—
215Q8—3024no—
216Q8—3022no—
217Q8—3022no—
218D4—24no—
219D4—22no—
220D4—41no—
221D4—41no—
222D4—42no—
223D4—84no—
224D4—3024no—
225D4—3028no—
226D4—3024no—
227D4—3024no—
228D4—3022no—
229D4—3022no—
230D4—12088no—
231C2×C4—22no—
232C2×C4—22no—
233C2×C4—22no—
234C2×C4—3028no—
235C2×C4—3024no—
236C2×C4—3024no—
237C2×C4—3024no—
238C2×C4—3024no—
239C2×C4—1514no—
240C2×C4D4×D15112yes—
241C2×C4D4×D15112yes—
242C2×C4C2×C22⋊D15112yes—
243C2×C4C2×C22⋊D15111yescharacteristic
244C2×C4C2×C22⋊D15111yescharacteristic
245C22—22no—
246C22—41no—
247C22—42no—
248C22—44no—
249C22—48no—
250C22—42no—
251C22—3024no—
252C22—6044no—
253C22—12084no—
254C22C2×D4×D15112yes—
255C22C22×C22⋊D15111yescharacteristic
256C4—22no—
257C4—42no—
258C4—3024no—
259C4—6044no—
260C4#1801270711yescharacteristic
261C4#1801270711yescharacteristic
262C4#1801270712yes—
263C2—21no—
264C2—22no—
265C2—42no—
266C2—82no—
267C2—6044no—
268C2C2×#1801270711yescharacteristic
subgroupG/H
centerC2C2×#18012707
commutator, cosocleC23×C151C24
FrattiniC23C23×D151
Fitting#535×C151C2
socleC2×C151C2×#120
hypercenter#535D151
hypocenterC151#3027
LCSG ▷ C23×C151 ▷ C2×C151 ▷ C151
UCSC1 ◁ C2 ◁ C22×C4 ◁ #535

Complements

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

NH ≅ G/Ntype
1. #23753048C2semidirect
2. #23752779C2semidirect
3. #23752398C2semidirect
4. #23752186C2semidirect
5. #23752185C2semidirect
6. #535×C151C2semidirect
18. #18012708C22semidirect
19. #18012698C22semidirect
20. #18012654C22semidirect
21. #18012653C22semidirect
23. C22×D4×C151C22semidirect
27. #120×C151C22semidirect
28. #117×C151C22semidirect
40. C2×Dic302D4semidirect
43. C2×D604D4semidirect
50. C2×C4×D151D4semidirect
58. C2×Q8×C151D4semidirect
64. C2×D4×C151D4semidirect
66. C22×C4×C151D4semidirect
134. C151#3027semidirect
138. #535D151semidirect
151. C22×D4C2×D151semidirect
159. #120C2×D151semidirect
161. #117C2×D151semidirect
180. C2×Q8C22⋊D151semidirect
193. C2×D4C22⋊D151semidirect
197. C22×C4C22⋊D151semidirect

Maximal subgroups

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

subgroupindex
#237530482
#237527792
#237523982
#237521862
#237521852
#535×C1512
#3027151