Finite Group Databasebeta

← #34078513

Subgroups — #34078513

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#23752781C212yesmaximal, complemented
3#23752776C211yesmaximal, characteristic, complemented
4#23752400C218yesmaximal, complemented
5#23752185C212yesmaximal, complemented
6#410×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—
15C22×D604C2211yescharacteristic, complemented
16#18012736—22no—
17#18012735—21no—
18#18012728—21no—
19#18012727—22no—
20#18012714—24no—
21#18012713—22no—
22#18012709C2218yescomplemented
23#18012707C2214yescomplemented
24#18012698C2211yescharacteristic, complemented
25#18012653C2218yescomplemented
26C2×#41×C151C2211yescharacteristic
27#117×C151C2212yescomplemented
28#99×C151C2214yescomplemented
29C23×D151C2312yes—
30#14559005—24no—
31#14559004—24no—
32#14559004—24no—
33#14559004—22no—
34#14559004—22no—
35#14559004—24no—
36#14559004—22no—
37#14559004—22no—
38#14559003—24no—
39#14559003—28no—
40C2×Dic302—22no—
41C2×Dic302D412yescomplemented
42Q8×D151—24no—
43C2×D604—22no—
44C2×D604—28no—
45C2×D604—21no—
46C2×D604—22no—
47C2×D604—22no—
48C2×D604—21no—
49C2×D604D412yescomplemented
50C2×C22⋊D151—24no—
51C2×C22⋊D151—24no—
52C2×C22⋊D151C2314yes—
53D4×D151—24no—
54D4×D151—28no—
55C2×C4×D151—24no—
56C2×C4×D151D414yescomplemented
57C4⋊Dic151—21no—
58C22⋊Dic151C2312yes—
59(C2×D151)⋊C4—28no—
60(C2×D151)⋊C4—24no—
61C4×Dic151—21no—
62#41×C151—22no—
63#41×C151—22no—
64C2×Q8×C151D411yescharacteristic, complemented
65C2×D4×C151D411yescharacteristic, complemented
66C2×D4×C151C2312yes—
67C22×C4×C151D412yescomplemented
68C22×C4×C151C2311yescharacteristic
69C4⋊C4×C151—22no—
70C22⋊C4×C151C2314yes—
71C42×C151—22no—
72C22×D151—24no—
73C22×D151—22no—
74C22×D151—24no—
75C22×D151—82no—
76C22×D151C2×D414yes—
77Dic302—24no—
78Dic302—22no—
79Dic302—22no—
80D604—24no—
81D604—22no—
82D604—22no—
83D604—41no—
84D604—41no—
85D604—42no—
86D604—88no—
87C22⋊D151—28no—
88C22⋊D151—24no—
89C22⋊D151—24no—
90C22⋊D151—84no—
91C2×Dic151—24no—
92C2×Dic151—22no—
93C2×Dic151C2×D414yes—
94C4×D151—28no—
95C4×D151—24no—
96C4×D151—24no—
97C23×C151C2×D412yes—
98C23×C151C2411yescharacteristic
99Q8×C151—22no—
100D4×C151—24no—
101D4×C151—22no—
102C2×C4×C151—22no—
103C2×C4×C151—22no—
104C2×C4×C151—24no—
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×C151C22×D412yes—
114C22×C151C22×D411yescharacteristic
115C2×D151—24no—
116C2×D151—44no—
117C2×D151—44no—
118C2×D151—48no—
119C2×D151—42no—
120C2×D151—84no—
121C4×C151—22no—
122C4×C151—44no—
123C4×C151#12011yescharacteristic
124C4×C151#12011yescharacteristic
125C4×C151#12012yes—
126Dic151—24no—
127Dic151—42no—
128C2×C151—21no—
129C2×C151—22no—
130C2×C151—42no—
131C2×C151C2×#12011yescharacteristic
132D151—44no—
133D151—82no—
134C151#302711yescharacteristic, complemented, Sylow
135#3027—1511nomaximal, Sylow
136#585—1511no—
137#535—1511no—
138#535—1512no—
139B(4,𝔽2)—1518no—
140#410—1512no—
141#410D15111yescharacteristic, complemented
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×D4—1511no—
152#127—3022no—
153#127—3021no—
154#124—3022no—
155#124—3021no—
156#121—3024no—
157#121—3022no—
158#120—1514no—
159#120—1518no—
160#117—1511no—
161#117C2×D15112yescomplemented
162#99—1518no—
163#99C2×D15114yescomplemented
164C24—1512no—
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×Q8D60411yescharacteristic, complemented
181C2×D4—3022no—
182C2×D4—3028no—
183C2×D4—3024no—
184C2×D4—3028no—
185C2×D4—3024no—
186C2×D4—3024no—
187C2×D4—3022no—
188C2×D4—3022no—
189C2×D4—3021no—
190C2×D4—3021no—
191C2×D4—1514no—
192C2×D4—1512no—
193C2×D4D60411yescharacteristic, complemented
194C2×D4C22×D15112yes—
195C22×C4—3024no—
196C22×C4—1514no—
197C22×C4D60412yescomplemented
198C22×C4C22×D15111yescharacteristic
199C4⋊C4—22no—
200C4⋊C4—3021no—
201C22⋊C4—3028no—
202C22⋊C4—3024no—
203C22⋊C4—1512no—
204C22⋊C4C22×D15114yes—
205C42—22no—
206C42—3021no—
207C23—3024no—
208C23—3024no—
209C23—3022no—
210C23—1514no—
211C23—12082no—
212C23C2×D60412yes—
213C23C23×D15111yescharacteristic
214Q8—22no—
215Q8—3024no—
216Q8—3022no—
217Q8—3022no—
218D4—24no—
219D4—22no—
220D4—3024no—
221D4—3028no—
222D4—3024no—
223D4—3024no—
224D4—3022no—
225D4—3022no—
226D4—6041no—
227D4—6041no—
228D4—6042no—
229D4—12088no—
230D4—12084no—
231C2×C4—22no—
232C2×C4—22no—
233C2×C4—24no—
234C2×C4—3028no—
235C2×C4—3024no—
236C2×C4—3024no—
237C2×C4—3024no—
238C2×C4—3022no—
239C2×C4—1514no—
240C2×C4D4×D15112yes—
241C2×C4D4×D15112yes—
242C2×C4C2×D60412yes—
243C2×C4C2×D60411yescharacteristic
244C2×C4C2×D60411yescharacteristic
245C22—22no—
246C22—41no—
247C22—42no—
248C22—3024no—
249C22—6044no—
250C22—6048no—
251C22—6044no—
252C22—6042no—
253C22—12084no—
254C22C2×D4×D15112yes—
255C22C22×D60411yescharacteristic
256C4—22no—
257C4—44no—
258C4—3024no—
259C4—6042no—
260C4#1801270911yescharacteristic
261C4#1801270911yescharacteristic
262C4#1801270912yes—
263C2—22no—
264C2—21no—
265C2—42no—
266C2—6044no—
267C2—12082no—
268C2C2×#1801270911yescharacteristic
subgroupG/H
centerC2C2×#18012709
commutator, cosocleC23×C151C24
FrattiniC23C23×D151
Fitting#410×C151C2
socleC2×C151C2×#120
hypercenter#410D151
hypocenterC151#3027
LCSG ▷ C23×C151 ▷ C2×C151 ▷ C151
UCSC1 ◁ C2 ◁ C22×C4 ◁ #410

Complements

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

NH ≅ G/Ntype
1. #23753048C2semidirect
2. #23752781C2semidirect
3. #23752776C2semidirect
4. #23752400C2semidirect
5. #23752185C2semidirect
6. #410×C151C2semidirect
15. C22×D604C22semidirect
22. #18012709C22semidirect
23. #18012707C22semidirect
24. #18012698C22semidirect
25. #18012653C22semidirect
27. #117×C151C22semidirect
28. #99×C151C22semidirect
41. C2×Dic302D4semidirect
49. C2×D604D4semidirect
56. C2×C4×D151D4semidirect
64. C2×Q8×C151D4semidirect
65. C2×D4×C151D4semidirect
67. C22×C4×C151D4semidirect
134. C151#3027semidirect
141. #410D151semidirect
161. #117C2×D151semidirect
163. #99C2×D151semidirect
180. C2×Q8D604semidirect
193. C2×D4D604semidirect
197. C22×C4D604semidirect

Maximal subgroups

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

subgroupindex
#237530482
#237527812
#237527762
#237524002
#237521852
#410×C1512
#3027151