Finite Group Databasebeta

← #34054826

Subgroups — #34054826

Order 19072.

450 conjugacy classes of subgroups; only the 117 normal subgroups are shown.

normal subgroups only

This group has 450 conjugacy classes of subgroups — too many to draw. Only its 117 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#23750156C211yesmaximal, characteristic, complemented
2C2×#18011873C211yesmaximal, characteristic, complemented
3#23749955C211yesmaximal, characteristic, complemented
4#23749928C212yesmaximal, complemented
5#23749839C212yesmaximal, complemented
6#23749778C211yesmaximal, characteristic, complemented
7#23749758C211yesmaximal, characteristic
8#23749734C212yesmaximal, complemented
9#23749724C212yesmaximal, complemented
10#23749679C211yesmaximal, characteristic, complemented
11#480×C149C211yesmaximal, characteristic, complemented
12C22×D596C2211yescharacteristic
13C22×C4×D149—21no—
14C2×#14558725C2212yes—
15C2×#14558721C2212yes—
16#18011904—21no—
17#18011902C2211yescharacteristic, complemented
18#18011898C2211yescharacteristic, complemented
19#18011892—21no—
20#18011890C2211yescharacteristic
21#18011876C2211yescharacteristic, complemented
22D4×Dic149—21no—
23D4×Dic149C2211yescharacteristic, complemented
24#18011873—21no—
25#18011873—21no—
26#18011873C2212yes—
27#18011873C2212yes—
28#18011867—21no—
29C2×#14558713—21no—
30C2×C4×Dic149C2211yescharacteristic
31#18011842C2212yescomplemented
32#18011840C2212yescomplemented
33#18011834C2212yescomplemented
34#18011833C2212yes—
35#18011831C2212yes—
36C22⋊#11924746C2211yescharacteristic
37#18011821C2212yescomplemented
38#121×C149C2211yescharacteristic
39C2×C4⋊C4×C149C2211yescharacteristic
40#107×C149C2212yescomplemented
41#102×C149C2212yescomplemented
42C22⋊C8×C149C2211yescharacteristic
43C23×D149—21no—
44C2×Dic298C2311yescharacteristic
45C2×D596—24no—
46C2×D596—21no—
47C2×D596C2312yes—
48C22×Dic149—21no—
49C22×Dic149D411yescharacteristic
50C22×Dic149D411yescharacteristic
51C2×C4×D149—22no—
52C2×C4×D149—22no—
53C2×C4×D149—44no—
54#14558725—24no—
55#14558721—24no—
56C2×#11924746C2312yes—
57C4⋊Dic149—21no—
58C4⋊Dic149C2311yescharacteristic
59#14558715—21no—
60#14558715—21no—
61#14558715—21no—
62C22⋊Dic149—21no—
63C22⋊Dic149—21no—
64C22⋊Dic149—21no—
65C22⋊Dic149—21no—
66#14558713—22no—
67#14558713—22no—
68C4×Dic149—21no—
69C4×Dic149D411yescharacteristic
70C4×Dic149D411yescharacteristic
71C4×Dic149C2311yescharacteristic
72C4×Dic149C2311yescharacteristic
73C2×D4×C149—21no—
74C2×D4×C149C2311yescharacteristic
75C22×C4×C149—21no—
76C22×C4×C149C2311yescharacteristic
77C2×C8×C149C2312yes—
78C4⋊C4×C149—21no—
79C4⋊C4×C149C2312yes—
80C4⋊C4×C149C2311yescharacteristic
81C22⋊C4×C149—21no—
82C22×D149—24no—
83C22×D149—22no—
84C22×D149—42no—
85C22×D149—42no—
86Dic298—22no—
87D596—24no—
88D596—22no—
89D596#4114yes—
90C2×Dic149—22no—
91C2×Dic149—21no—
92C2×Dic149—21no—
93C2×Dic149—41no—
94C2×Dic149—42no—
95C2×Dic149C2×D411yescharacteristic
96C2×Dic149C2×D411yescharacteristic
97C2×Dic149C2×D411yescharacteristic
98C2×Dic149C2×D411yescharacteristic
99C4×D149—44no—
100C4×D149—44no—
101#11924746—22no—
102C23×C149—21no—
103C23×C149C2×D411yescharacteristic
104D4×C149—22no—
105D4×C149—42no—
106C2×C4×C149—22no—
107C2×C4×C149—22no—
108C2×C4×C149—21no—
109C2×C4×C149—42no—
110C2×C4×C149C2×D411yescharacteristic
111C2×C4×C149C2411yescharacteristic
112C8×C149—22no—
113C22×C149—21no—
114C22×C149—21no—
115C22×C149—41no—
116C22×C149—41no—
117C22×C149—41no—
118C22×C149AGL(1,ℤ/8)12yes—
119C22×C149C22×D411yescharacteristic
120C2×D149—24no—
121C2×D149—48no—
122C2×D149—42no—
123C2×D149—42no—
124C4×C149—21no—
125C4×C149—42no—
126C4×C149—41no—
127C4×C149C2×#4112yes—
128Dic149—21no—
129Dic149—21no—
130Dic149—21no—
131Dic149—21no—
132Dic149—41no—
133Dic149—41no—
134C2×C149—22no—
135C2×C149—81no—
136C2×C149#52511yescharacteristic
137C2×C149C2×AGL(1,ℤ/8)11yescharacteristic
138C2×C149#57511yescharacteristic
139D149—44no—
140C149#311411yescharacteristic, complemented, Sylow
141#3114—1491nomaximal, Sylow
142#529—1491no—
143C2×C4×D4—1491no—
144#483—1491no—
145#480D14911yescharacteristic, complemented
146#478—1492no—
147#463—1492no—
148#450—1491no—
149#447—1491no—
150#442—1492no—
151#440—1492no—
152#432—1491no—
153C22×D4—1491no—
154C23×C4—2981no—
155C2×SD16—1492no—
156C2×D8—1492no—
157#126—2981no—
158#125—1491no—
159#124—1491no—
160#123—2981no—
161C22⋊Q8—1491no—
162#121C2×D14911yescharacteristic
163C4×Q8—1491no—
164C4×D4—2981no—
165C4×D4—2981no—
166C4×D4—2981no—
167C4×D4—1491no—
168C4×D4—1492no—
169C4×D4—1492no—
170#117—2981no—
171C2×C4⋊C4C2×D14911yescharacteristic
172C2×C22⋊C4—2981no—
173C2×C42—1491no—
174#107C2×D14912yescomplemented
175#106—1492no—
176C4⋊C8—1492no—
177#103—1492no—
178#102—1492no—
179#102—1492no—
180#102C2×D14912yescomplemented
181C22⋊C8—1491no—
182C22⋊C8C2×D14911yescharacteristic
183#97—1492no—
184C24—2981no—
185C2×Q8—1491no—
186C2×D4—21no—
187C2×D4—2984no—
188C2×D4—2981no—
189C2×D4—1492no—
190C2×D4C22×D14911yescharacteristic
191C22×C4—21no—
192C22×C4—2982no—
193C22×C4—2982no—
194C22×C4—2981no—
195C22×C4—5964no—
196C22×C4—1491no—
197C22×C4—1491no—
198C22×C4C22×D14911yescharacteristic
199SD16—2984no—
200D8—2984no—
201C2×C8—1492no—
202C2×C8C22×D14912yes—
203C4⋊C4—21no—
204C4⋊C4—2981no—
205C4⋊C4—2981no—
206C4⋊C4—2981no—
207C4⋊C4—2981no—
208C4⋊C4—1491no—
209C4⋊C4C22×D14911yescharacteristic
210C4⋊C4C22×D14912yes—
211C22⋊C4—21no—
212C22⋊C4—2982no—
213C22⋊C4—2982no—
214C22⋊C4—2981no—
215C22⋊C4—2981no—
216C22⋊C4—2981no—
217C22⋊C4—2981no—
218C42—2981no—
219C42—1491no—
220C42—1491no—
221C42—1491no—
222C42—1491no—
223C23—21no—
224C23—2984no—
225C23—2982no—
226C23—5962no—
227C23—5962no—
228C23D4×D14911yescharacteristic
229Q8—2982no—
230D4—22no—
231D4—42no—
232D4—2984no—
233D4—2982no—
234D4—1494no—
235C2×C4—22no—
236C2×C4—21no—
237C2×C4—22no—
238C2×C4—42no—
239C2×C4—2982no—
240C2×C4—2981no—
241C2×C4—2981no—
242C2×C4—5964no—
243C2×C4—5964no—
244C2×C4—5961no—
245C2×C4—5962no—
246C2×C4—1491no—
247C2×C4—1491no—
248C2×C4—1491no—
249C2×C4—1491no—
250C2×C4D4×D14911yescharacteristic
251C2×C4C23×D14911yescharacteristic
252C8—22no—
253C8—2982no—
254C22—21no—
255C22—21no—
256C22—41no—
257C22—41no—
258C22—41no—
259C22—2984no—
260C22—5968no—
261C22—5962no—
262C22—5962no—
263C22#1801193512yes—
264C22C2×D4×D14911yescharacteristic
265C4—21no—
266C4—42no—
267C4—41no—
268C4—2981no—
269C4—2981no—
270C4—2981no—
271C4—2981no—
272C4—5961no—
273C4—5961no—
274C4#41×D14912yes—
275C2—22no—
276C2—81no—
277C2—5964no—
278C2#2375013311yescharacteristic
279C2C2×#1801193511yescharacteristic
280C2#2375042411yescharacteristic
subgroupG/H
centerC22C2×D4×D149
commutator, cosocleC2×C4×C149C24
FrattiniC2×C4C23×D149
Fitting#480×C149C2
socleC22×C149C22×D4
prime radical#23749758C2
hypercenter#480D149
hypocenterC149#3114
LCSG ▷ C2×C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C22 ◁ C22×C4 ◁ #480

Complements

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

NH ≅ G/Ntype
1. #23750156C2semidirect
2. C2×#18011873C2semidirect
3. #23749955C2semidirect
4. #23749928C2semidirect
5. #23749839C2semidirect
6. #23749778C2semidirect
8. #23749734C2semidirect
9. #23749724C2semidirect
10. #23749679C2semidirect
11. #480×C149C2semidirect
17. #18011902C22semidirect
18. #18011898C22semidirect
21. #18011876C22semidirect
23. D4×Dic149C22semidirect
31. #18011842C22semidirect
32. #18011840C22semidirect
33. #18011834C22semidirect
37. #18011821C22semidirect
40. #107×C149C22semidirect
41. #102×C149C22semidirect
140. C149#3114semidirect
145. #480D149semidirect
174. #107C2×D149semidirect
180. #102C2×D149semidirect

Maximal subgroups

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

subgroupindex
#237501562
C2×#180118732
#237499552
#237499282
#237498392
#237497782
#237497582
#237497342
#237497242
#237496792
#480×C1492
#3114149