Finite Group Databasebeta

← #34078504

Subgroups — #34078504

Order 19328.

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

normal subgroups only

This group has 766 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#23752724C212yesmaximal, complemented
3#23752719C211yesmaximal, characteristic, complemented
4#23752403C214yesmaximal, complemented
5#23752400C214yesmaximal, complemented
6#23752185C212yesmaximal, complemented
7#410×C151C211yesmaximal, characteristic, complemented
8#18012787—21no—
9#18012786—22no—
10#18012785—22no—
11#18012784—21no—
12#18012784C2214yes—
13C2×#14559004—22no—
14C2×#14559004C2212yes—
15#41×D151—24no—
16C22×C4×D151C2211yescharacteristic, complemented
17#18012723C2214yescomplemented
18#18012720C2212yescomplemented
19#18012719—22no—
20#18012715—21no—
21#18012714—22no—
22#18012710—21no—
23#18012709C2214yescomplemented
24#18012707C2212yescomplemented
25C4×D604—24no—
26C4×C22⋊D151—22no—
27#18012698C2211yescharacteristic, complemented
28#18012653C2218yescomplemented
29C2×#41×C151C2211yescharacteristic
30#117×C151C2212yescomplemented
31#99×C151C2214yescomplemented
32C23×D151C2311yescharacteristic
33#14559005—24no—
34#14559004—24no—
35#14559004—24no—
36#14559004—22no—
37#14559004—22no—
38#14559004—24no—
39#14559004—22no—
40#14559004—22no—
41#14559003—24no—
42#14559003—28no—
43C2×Dic302—22no—
44C2×Dic302D412yescomplemented
45Q8×D151—24no—
46C2×D604—22no—
47C2×D604—24no—
48C2×D604D412yescomplemented
49C2×C22⋊D151—24no—
50C2×C22⋊D151—22no—
51C2×C22⋊D151C2314yes—
52D4×D151—24no—
53D4×D151—28no—
54C22×Dic151C2311yescharacteristic
55C2×C4×D151—24no—
56C2×C4×D151—21no—
57C2×C4×D151—22no—
58C2×C4×D151—21no—
59C2×C4×D151—22no—
60C2×C4×D151D414yescomplemented
61C4⋊Dic151—24no—
62C4⋊Dic151—21no—
63Dic151⋊C4—22no—
64C22⋊Dic151—22no—
65C22⋊Dic151C2312yes—
66(C2×D151)⋊C4—24no—
67(C2×D151)⋊C4—24no—
68(C2×D151)⋊C4—22no—
69C4×Dic151—21no—
70#41×C151—22no—
71#41×C151—22no—
72C2×Q8×C151D411yescharacteristic, complemented
73C2×D4×C151D411yescharacteristic, complemented
74C2×D4×C151C2312yes—
75C22×C4×C151D412yescomplemented
76C22×C4×C151C2311yescharacteristic
77C4⋊C4×C151—22no—
78C22⋊C4×C151C2314yes—
79C42×C151—22no—
80C22×D151—21no—
81C22×D151—22no—
82C22×D151—24no—
83C22×D151—42no—
84C22×D151C2×D414yes—
85Dic302—24no—
86Dic302—22no—
87Dic302—22no—
88D604—24no—
89D604—22no—
90D604—22no—
91D604—48no—
92C22⋊D151—28no—
93C22⋊D151—24no—
94C22⋊D151—24no—
95C22⋊D151—44no—
96C2×Dic151—24no—
97C2×Dic151—22no—
98C2×Dic151—22no—
99C2×Dic151—21no—
100C2×Dic151C2×D414yes—
101C4×D151—28no—
102C4×D151—24no—
103C4×D151—24no—
104C4×D151—41no—
105C4×D151—42no—
106C4×D151—41no—
107C23×C151C2×D412yes—
108C23×C151C2411yescharacteristic
109Q8×C151—22no—
110D4×C151—24no—
111D4×C151—22no—
112C2×C4×C151—22no—
113C2×C4×C151—22no—
114C2×C4×C151—24no—
115C2×C4×C151C2×D412yes—
116C2×C4×C151C2×D412yes—
117C2×C4×C151C2×D412yes—
118C2×C4×C151C2×D411yescharacteristic
119C2×C4×C151C2×D411yescharacteristic
120C22×C151—22no—
121C22×C151—41no—
122C22×C151—42no—
123C22×C151C22×D412yes—
124C22×C151C22×D411yescharacteristic
125C2×D151—22no—
126C2×D151—24no—
127C2×D151—24no—
128C2×D151—41no—
129C2×D151—42no—
130C2×D151—41no—
131C2×D151—44no—
132C2×D151—84no—
133C4×C151—22no—
134C4×C151—44no—
135C4×C151#12011yescharacteristic
136C4×C151#12012yes—
137C4×C151#12011yescharacteristic
138Dic151—24no—
139Dic151—42no—
140Dic151—41no—
141C2×C151—21no—
142C2×C151—22no—
143C2×C151—42no—
144C2×C151C2×#12011yescharacteristic
145D151—42no—
146D151—44no—
147C151#302511yescharacteristic, complemented, Sylow
148#3025—1511nomaximal, Sylow
149#585—1511no—
150#525—1511no—
151#525—1512no—
152#458—1514no—
153B(4,𝔽2)—1514no—
154#410—1512no—
155#410D15111yescharacteristic, complemented
1562−1+4—3022no—
1572−1+4—3021no—
158H(5,𝔽2)—3022no—
159H(5,𝔽2)—3021no—
160H(5,𝔽2)—1514no—
161C2×#41—3024no—
162C2×#41—3022no—
163C2×#41—1512no—
164C2×#41C2×D15111yescharacteristic
165C23×C4—1511no—
166#123—1512no—
167#123—1514no—
168C22⋊Q8—3022no—
169C22⋊Q8—3021no—
170#121—3022no—
171#121—3021no—
172#120—1512no—
173#120—1514no—
174C4×D4—3024no—
175C4×D4—3022no—
176#117—1511no—
177#117C2×D15112yescomplemented
178#99—1518no—
179#99C2×D15114yescomplemented
180C24—1511no—
181#41—22no—
182#41—22no—
183#41—3024no—
184#41—3024no—
185#41—3024no—
186#41—3024no—
187#41—3028no—
188#41—3022no—
189#41—3022no—
190#41—3022no—
191#41—3024no—
192#41—3022no—
193C2×Q8—3022no—
194C2×Q8—3024no—
195C2×Q8—1512no—
196C2×Q8D60411yescharacteristic, complemented
197C2×D4—3022no—
198C2×D4—3024no—
199C2×D4—3024no—
200C2×D4—3028no—
201C2×D4—3024no—
202C2×D4—3022no—
203C2×D4—1514no—
204C2×D4—1512no—
205C2×D4D60411yescharacteristic, complemented
206C2×D4C22×D15112yes—
207C22×C4—3024no—
208C22×C4—3022no—
209C22×C4—3022no—
210C22×C4—3021no—
211C22×C4—3021no—
212C22×C4—1511no—
213C22×C4—1514no—
214C22×C4D60412yescomplemented
215C22×C4C22×D15111yescharacteristic
216C4⋊C4—22no—
217C4⋊C4—3024no—
218C4⋊C4—3022no—
219C4⋊C4—3021no—
220C22⋊C4—3024no—
221C22⋊C4—3024no—
222C22⋊C4—3022no—
223C22⋊C4—3022no—
224C22⋊C4—1512no—
225C22⋊C4C22×D15114yes—
226C42—22no—
227C42—3021no—
228C23—3024no—
229C23—3022no—
230C23—3021no—
231C23—6042no—
232C23—1514no—
233C23C2×D60412yes—
234C23C23×D15111yescharacteristic
235Q8—22no—
236Q8—3024no—
237Q8—3022no—
238Q8—3022no—
239D4—24no—
240D4—22no—
241D4—3024no—
242D4—3028no—
243D4—3024no—
244D4—3024no—
245D4—3022no—
246D4—3022no—
247D4—6048no—
248D4—6044no—
249C2×C4—22no—
250C2×C4—22no—
251C2×C4—24no—
252C2×C4—3028no—
253C2×C4—3024no—
254C2×C4—3024no—
255C2×C4—3024no—
256C2×C4—3022no—
257C2×C4—3022no—
258C2×C4—3021no—
259C2×C4—6041no—
260C2×C4—6042no—
261C2×C4—6041no—
262C2×C4—1514no—
263C2×C4D4×D15112yes—
264C2×C4D4×D15112yes—
265C2×C4C2×D60412yes—
266C2×C4C2×D60411yescharacteristic
267C2×C4C2×D60411yescharacteristic
268C22—22no—
269C22—41no—
270C22—42no—
271C22—3024no—
272C22—3022no—
273C22—3024no—
274C22—6044no—
275C22—6042no—
276C22—6041no—
277C22—6041no—
278C22—12084no—
279C22C2×D4×D15112yes—
280C22C22×D60411yescharacteristic
281C4—22no—
282C4—44no—
283C4—3024no—
284C4—6042no—
285C4—6041no—
286C4#1801270911yescharacteristic
287C4#1801270912yes—
288C4#1801270911yescharacteristic
289C2—22no—
290C2—21no—
291C2—42no—
292C2—6042no—
293C2—6044no—
294C2C2×#1801270911yescharacteristic
subgroupG/H
centerC4#18012709
commutator, cosocleC23×C151C24
FrattiniC23C23×D151
Fitting#410×C151C2
socleC2×C151C2×#120
hypercenter#410D151
hypocenterC151#3025
LCSG ▷ C23×C151 ▷ C2×C151 ▷ C151
UCSC1 ◁ C4 ◁ C22×C4 ◁ #410

Complements

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

NH ≅ G/Ntype
1. #23753048C2semidirect
2. #23752724C2semidirect
3. #23752719C2semidirect
4. #23752403C2semidirect
5. #23752400C2semidirect
6. #23752185C2semidirect
7. #410×C151C2semidirect
16. C22×C4×D151C22semidirect
17. #18012723C22semidirect
18. #18012720C22semidirect
23. #18012709C22semidirect
24. #18012707C22semidirect
27. #18012698C22semidirect
28. #18012653C22semidirect
30. #117×C151C22semidirect
31. #99×C151C22semidirect
44. C2×Dic302D4semidirect
48. C2×D604D4semidirect
60. C2×C4×D151D4semidirect
72. C2×Q8×C151D4semidirect
73. C2×D4×C151D4semidirect
75. C22×C4×C151D4semidirect
147. C151#3025semidirect
155. #410D151semidirect
177. #117C2×D151semidirect
179. #99C2×D151semidirect
196. C2×Q8D604semidirect
205. C2×D4D604semidirect
214. C22×C4D604semidirect

Maximal subgroups

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

subgroupindex
#237530482
#237527242
#237527192
#237524032
#237524002
#237521852
#410×C1512
#3025151