Finite Group Databasebeta

← #34079018

Subgroups — #34079018

Order 19328.

420 conjugacy classes of subgroups; only the 121 normal subgroups are shown.

normal subgroups only

This group has 420 conjugacy classes of subgroups — too many to draw. Only its 121 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#23752722C211yesmaximal, characteristic
2C2×#18012697C211yesmaximal, characteristic, complemented
3#23752555C212yesmaximal, complemented
4#23752548C211yesmaximal, characteristic, complemented
5#23752542C211yesmaximal, characteristic, complemented
6#23752534C212yesmaximal, complemented
7#23752528C211yesmaximal, characteristic, complemented
8#23752249C212yesmaximal, complemented
9#23752205C212yesmaximal, complemented
10C22⋊C8×D151C211yesmaximal, characteristic, complemented
11#480×C151C211yesmaximal, characteristic, complemented
12C2×#14559003C2211yescharacteristic
13C22×C4×D151C2211yescharacteristic
14C2×C8×D151C2212yes—
15#18012721—21no—
16#18012719C2211yescharacteristic
17#18012718C2211yescharacteristic
18#18012710C2211yescharacteristic
19#18012707—21no—
20D4×Dic151—21no—
21(C22⋊D151)⋊C4—21no—
22#18012697—21no—
23#18012697—21no—
24#18012697C2212yes—
25#18012697C2211yescharacteristic
26#18012697C2212yes—
27C2×C4⋊Dic151C2211yescharacteristic
28C2×(C2×D151)⋊C4—21no—
29C2×C4×Dic151—21no—
30#18012673C2212yescomplemented
31#18012670C2212yescomplemented
32#18012670C2212yescomplemented
33#18012664C2212yescomplemented
34#18012662C2212yescomplemented
35#18012660C2212yescomplemented
36C22⋊(C151⋊C8)C2211yescharacteristic
37(C2×D151)⋊C8C2212yes—
38#121×C151C2211yescharacteristic
39C2×C4⋊C4×C151C2211yescharacteristic
40#107×C151C2212yescomplemented
41#102×C151C2212yescomplemented
42C22⋊C8×C151C2211yescharacteristic
43C23×D151D411yescharacteristic
44#14559003—24no—
45C2×Dic302C2311yescharacteristic
46C2×C22⋊D151—21no—
47C2×C22⋊D151—21no—
48C22×Dic151—21no—
49C22×Dic151—21no—
50C22×Dic151D411yescharacteristic
51C2×C4×D151—24no—
52C2×C4×D151D411yescharacteristic
53C2×C4×D151D411yescharacteristic
54C2×C4×D151C2311yescharacteristic
55C2×C4×D151C2311yescharacteristic
56C2×C151⋊C8C2312yes—
57C8×D151—24no—
58C4⋊Dic151—21no—
59C4⋊Dic151—21no—
60C4⋊Dic151C2311yescharacteristic
61C4⋊Dic151C2312yes—
62Dic151⋊C4—21no—
63C22⋊Dic151—21no—
64C22⋊Dic151—21no—
65(C2×D151)⋊C4—22no—
66(C2×D151)⋊C4—22no—
67(C2×D151)⋊C4—21no—
68(C2×D151)⋊C4—21no—
69C4×Dic151—22no—
70C4×Dic151—22no—
71C4×Dic151—21no—
72C2×D4×C151—21no—
73C2×D4×C151C2311yescharacteristic
74C22×C4×C151—21no—
75C22×C4×C151C2311yescharacteristic
76C2×C8×C151C2312yes—
77C4⋊C4×C151—21no—
78C4⋊C4×C151C2312yes—
79C4⋊C4×C151C2311yescharacteristic
80C22⋊C4×C151—21no—
81C22×D151—22no—
82C22×D151—22no—
83C22×D151—41no—
84C22×D151C2×D411yescharacteristic
85C22×D151C2×D411yescharacteristic
86Dic302—22no—
87C22⋊D151—42no—
88C22⋊D151—42no—
89C2×Dic151—22no—
90C2×Dic151—22no—
91C2×Dic151—21no—
92C2×Dic151—21no—
93C2×Dic151—42no—
94C2×Dic151—42no—
95C2×Dic151C2×D411yescharacteristic
96C2×Dic151C2×D411yescharacteristic
97C4×D151—22no—
98C4×D151—22no—
99C4×D151—22no—
100C4×D151#4114yes—
101C151⋊C8—22no—
102C23×C151—21no—
103C23×C151C2×D411yescharacteristic
104D4×C151—22no—
105D4×C151—42no—
106C2×C4×C151—22no—
107C2×C4×C151—22no—
108C2×C4×C151—21no—
109C2×C4×C151—42no—
110C2×C4×C151C2×D411yescharacteristic
111C2×C4×C151C2411yescharacteristic
112C8×C151—22no—
113C22×C151—21no—
114C22×C151—21no—
115C22×C151—41no—
116C22×C151—41no—
117C22×C151—41no—
118C22×C151#13512yes—
119C22×C151C22×D411yescharacteristic
120C2×D151—21no—
121C2×D151—21no—
122C2×D151—21no—
123C2×D151—21no—
124C2×D151—21no—
125C2×D151—44no—
126C2×D151#12312yes—
127C4×C151—21no—
128C4×C151—42no—
129C4×C151—41no—
130C4×C151C2×#4112yes—
131Dic151—21no—
132Dic151—41no—
133Dic151—42no—
134Dic151—41no—
135Dic151#12312yes—
136C2×C151—22no—
137C2×C151—81no—
138C2×C151C2×#12311yescharacteristic
139C2×C151C2×#13511yescharacteristic
140C2×C151#57511yescharacteristic
141D151—22no—
142D151—41no—
143C151#309111yescharacteristic, complemented, Sylow
144#3091—1511nomaximal, Sylow
145#525—1511no—
146C2×#117—1511no—
147#485—1512no—
148#484—1511no—
149#483—1511no—
150#482—1512no—
151#481—1511no—
152#480D15111yescharacteristic, complemented
153#427—1512no—
154#416—1512no—
155C2×C22⋊C8—1511no—
156C2×#41—1511no—
157C23×C4—1511no—
158C22×C8—1512no—
159#123—3021no—
160C22⋊Q8—1511no—
161C22⋊Q8—1511no—
162#121—1511no—
163#121C2×D15111yescharacteristic
164#120—3021no—
165C4×D4—3021no—
166C4×D4—3021no—
167#117—3021no—
168#117—3021no—
169#117—1512no—
170#117—1512no—
171#117—1511no—
172C2×C4⋊C4—1511no—
173C2×C4⋊C4C2×D15111yescharacteristic
174C2×C22⋊C4—3021no—
175C2×C42—3021no—
176#107—1512no—
177#107C2×D15112yescomplemented
178#106—1512no—
179#106—1512no—
180#103—1512no—
181#103—1512no—
182#102—1512no—
183#102C2×D15112yescomplemented
184C22⋊C8—1511no—
185C22⋊C8—1512no—
186C22⋊C8C2×D15111yescharacteristic
187C24—1511no—
188#41—3024no—
189C2×Q8—1511no—
190C2×D4—21no—
191C2×D4—3021no—
192C2×D4—3021no—
193C2×D4C22×D15111yescharacteristic
194C22×C4—21no—
195C22×C4—3024no—
196C22×C4—3021no—
197C22×C4—3021no—
198C22×C4—1511no—
199C22×C4—1511no—
200C22×C4—1511no—
201C22×C4—1511no—
202C22×C4—1511no—
203C22×C4C22×D15111yescharacteristic
204C2×C8—3024no—
205C2×C8—1512no—
206C2×C8C22×D15112yes—
207C4⋊C4—21no—
208C4⋊C4—3021no—
209C4⋊C4—3021no—
210C4⋊C4—3021no—
211C4⋊C4—1512no—
212C4⋊C4—1511no—
213C4⋊C4C22×D15112yes—
214C4⋊C4C22×D15111yescharacteristic
215C22⋊C4—21no—
216C22⋊C4—3022no—
217C22⋊C4—3022no—
218C22⋊C4—3021no—
219C22⋊C4—3021no—
220C22⋊C4—3021no—
221C22⋊C4—3021no—
222C42—3022no—
223C42—3022no—
224C42—3021no—
225C23—21no—
226C23—3022no—
227C23—3022no—
228C23—6041no—
229C23—1511no—
230C23—1511no—
231C23D4×D15111yescharacteristic
232Q8—3022no—
233D4—22no—
234D4—42no—
235D4—6042no—
236D4—6042no—
237C2×C4—22no—
238C2×C4—22no—
239C2×C4—21no—
240C2×C4—42no—
241C2×C4—3022no—
242C2×C4—3022no—
243C2×C4—3022no—
244C2×C4—3022no—
245C2×C4—3022no—
246C2×C4—3021no—
247C2×C4—3021no—
248C2×C4—6042no—
249C2×C4—6042no—
250C2×C4—1511no—
251C2×C4—1511no—
252C2×C4—1514no—
253C2×C4D4×D15111yescharacteristic
254C2×C4C23×D15111yescharacteristic
255C8—22no—
256C8—3022no—
257C22—21no—
258C22—21no—
259C22—41no—
260C22—41no—
261C22—41no—
262C22—3021no—
263C22—3021no—
264C22—3021no—
265C22—3021no—
266C22—3021no—
267C22—6044no—
268C22—1512no—
269C22#1801275812yes—
270C22C2×D4×D15111yescharacteristic
271C4—21no—
272C4—42no—
273C4—41no—
274C4—3021no—
275C4—6041no—
276C4—6042no—
277C4—6041no—
278C4—1512no—
279C4#41×D15112yes—
280C2—22no—
281C2—81no—
282C2—3022no—
283C2—6041no—
284C2#123×D15111yescharacteristic
285C2C2×#1801275811yescharacteristic
286C2#2375301111yescharacteristic
subgroupG/H
centerC22C2×D4×D151
commutator, cosocleC2×C4×C151C24
FrattiniC2×C4C23×D151
Fitting#480×C151C2
socleC22×C151C22×D4
prime radical#23752722C2
hypercenter#480D151
hypocenterC151#3091
LCSG ▷ C2×C4×C151 ▷ C2×C151 ▷ C151
UCSC1 ◁ C22 ◁ C22×C4 ◁ #480

Complements

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

NH ≅ G/Ntype
2. C2×#18012697C2semidirect
3. #23752555C2semidirect
4. #23752548C2semidirect
5. #23752542C2semidirect
6. #23752534C2semidirect
7. #23752528C2semidirect
8. #23752249C2semidirect
9. #23752205C2semidirect
10. C22⋊C8×D151C2semidirect
11. #480×C151C2semidirect
30. #18012673C22semidirect
31. #18012670C22semidirect
32. #18012670C22semidirect
33. #18012664C22semidirect
34. #18012662C22semidirect
35. #18012660C22semidirect
40. #107×C151C22semidirect
41. #102×C151C22semidirect
143. C151#3091semidirect
152. #480D151semidirect
177. #107C2×D151semidirect
183. #102C2×D151semidirect

Maximal subgroups

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

subgroupindex
#237527222
C2×#180126972
#237525552
#237525482
#237525422
#237525342
#237525282
#237522492
#237522052
C22⋊C8×D1512
#480×C1512
#3091151