Finite Group Databasebeta

← #34056379

Subgroups — #34056379

Order 19072.

526 conjugacy classes of subgroups; only the 123 normal subgroups are shown.

normal subgroups only

This group has 526 conjugacy classes of subgroups — too many to draw. Only its 123 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
1C2×#18011933C211yesmaximal, characteristic, complemented
2C2×D8×D149C211yesmaximal, characteristic, complemented
3#23750272C212yesmaximal, complemented
4#23750008C211yesmaximal, characteristic, complemented
5#23749867C211yesmaximal, characteristic, complemented
6#23749839C212yesmaximal, complemented
7#23749777C212yesmaximal, complemented
8#23749768C212yesmaximal, complemented
9#23749707C211yesmaximal, characteristic, complemented
10C8×C22⋊D149C211yesmaximal, characteristic, complemented
11#466×C149C211yesmaximal, characteristic, complemented
12C2×#14558736C2212yescomplemented
13C2×D4×D149C2212yes—
14#18011933—24no—
15C2×Dic596C2211yescharacteristic, complemented
16C2×#14558725C2212yescomplemented
17C2×#14558724C2212yescomplemented
18C2×D1192C2211yescharacteristic
19C2×#14558721C2212yes—
20D8×D149—24no—
21C2×C8×D149C2211yescharacteristic
22#18011898C2212yescomplemented
23#18011893—22no—
24#18011891C2212yes—
25#18011882—22no—
26#18011879—22no—
27#18011873C2212yescomplemented
28C4×C22⋊D149C2211yescharacteristic
29C22⋊C4×D149—22no—
30#18011840C2211yescharacteristic, complemented
31#18011834C2212yescomplemented
32#18011831C2212yescomplemented
33C22⋊#11924746C2211yescharacteristic, complemented
34#18011823C2211yescharacteristic
35C8×Dic149C2211yescharacteristic, complemented
36C2×D8×C149C2211yescharacteristic
37C22×C8×C149C2211yescharacteristic, complemented
38#121×C149C2212yescomplemented
39#107×C149C2211yescharacteristic, complemented
40#102×C149C2212yescomplemented
41C23×D149—22no—
42#14558736—24no—
43#14558736—42no—
44C2×Dic298C2312yes—
45C2×D596C2312yes—
46C2×C22⋊D149—22no—
47C2×C22⋊D149—22no—
48C2×C22⋊D149D411yescharacteristic
49D4×D149—24no—
50D4×D149—42no—
51C2×C4×D149—22no—
52C2×C4×D149—22no—
53C2×C4×D149C2311yescharacteristic
54Dic596—22no—
55#14558725—24no—
56#14558724—42no—
57D1192D414yescomplemented
58#14558721—24no—
59C2×#11924746C2311yescharacteristic
60C2×#11924746C2311yescharacteristic
61C8×D149—22no—
62C4⋊Dic149—22no—
63#14558715D411yescharacteristic
64C22⋊Dic149—22no—
65C22⋊Dic149—22no—
66C22⋊Dic149D411yescharacteristic
67#14558713—22no—
68#14558713—22no—
69#14558713D411yescharacteristic
70C4×Dic149C2311yescharacteristic
71C2×D4×C149—22no—
72C2×D4×C149C2312yes—
73C22×C4×C149C2311yescharacteristic
74D8×C149—22no—
75C2×C8×C149—22no—
76C2×C8×C149C2311yescharacteristic
77C2×C8×C149C2311yescharacteristic
78C4⋊C4×C149C2312yes—
79C22⋊C4×C149—22no—
80C22×D149—22no—
81C22×D149—44no—
82C22×D149—44no—
83C22×D149—82no—
84C22×D149C2×D411yescharacteristic
85Dic298—22no—
86Dic298—22no—
87D596—22no—
88D596C2×D414yes—
89C22⋊D149—22no—
90C22⋊D149—44no—
91C22⋊D149—44no—
92C2×Dic149—22no—
93C2×Dic149C2×D411yescharacteristic
94C2×Dic149C2×D411yescharacteristic
95C2×Dic149C2×D411yescharacteristic
96C4×D149—21no—
97C4×D149—21no—
98C4×D149—44no—
99C4×D149—82no—
100#11924746—21no—
101#11924746—21no—
102C23×C149—22no—
103C23×C149C2×D411yescharacteristic
104D4×C149—22no—
105D4×C149—22no—
106D4×C149—82no—
107C2×C4×C149—21no—
108C2×C4×C149—21no—
109C2×C4×C149—22no—
110C2×C4×C149C2×D411yescharacteristic
111C2×C4×C149C2411yescharacteristic
112C8×C149—21no—
113C8×C149C2×D412yes—
114C22×C149—21no—
115C22×C149—21no—
116C22×C149—21no—
117C22×C149—42no—
118C22×C149—42no—
119C22×C149—42no—
120C22×C149C22×D411yescharacteristic
121C2×D149—21no—
122C2×D149—21no—
123C2×D149—24no—
124C2×D149—42no—
125C2×D149—42no—
126C2×D149—88no—
127C2×D149#13512yescomplemented
128C4×C149—21no—
129C4×C149—42no—
130C4×C149C22×D411yescharacteristic
131C4×C149H(5,𝔽2)11yescharacteristic
132Dic149—21no—
133Dic149—21no—
134Dic149—21no—
135Dic149—42no—
136C2×C149—41no—
137C2×C149—82no—
138C2×C149D4211yescharacteristic
139C2×C149C2×#13511yescharacteristic
140C2×C149#57611yescharacteristic
141D149—22no—
142D149—44no—
143C149#328011yescharacteristic, complemented, Sylow
144#3280—1491nomaximal, Sylow
145C2×#135—1491no—
146C22×D8—1491no—
147#546—1492no—
148#495—1491no—
149#467—1491no—
150#466D14911yescharacteristic, complemented
151#463—1492no—
152#450—1492no—
153#449—1492no—
154C4×D8—1491no—
155C8×D4—1491no—
156C2×#41—1492no—
157C22×D4—1492no—
158#135—2984no—
159C2×Q16—1491no—
160C2×SD16—1492no—
161C2×SD16—1492no—
162C2×D8—2984no—
163C2×D8—1492no—
164C2×D8—1491no—
165C2×D8C2×D14911yescharacteristic
166C22×C8—1491no—
167C22×C8C2×D14911yescharacteristic, complemented
168#124—1492no—
169#123—2982no—
170C22⋊Q8—1492no—
171#121—2982no—
172#121C2×D14912yescomplemented
173#120—2982no—
174C4×D4—1492no—
175C4×D4—1491no—
176C2×C22⋊C4—2982no—
177#107C2×D14911yescharacteristic, complemented
178C4⋊C8—1491no—
179#103—1492no—
180#102—1492no—
181#102C2×D14912yescomplemented
182C22⋊C8—1491no—
183C22⋊C8—1491no—
184C4×C8—1491no—
185C24—2982no—
186#41—2984no—
187#41—5962no—
188C2×Q8—1492no—
189C2×D4—22no—
190C2×D4—2984no—
191C2×D4—2982no—
192C2×D4—2982no—
193C2×D4—5962no—
194C2×D4—1491no—
195C2×D4—1492no—
196C2×D4C22×D14912yes—
197C22×C4—2982no—
198C22×C4—2982no—
199C22×C4—1491no—
200C22×C4C22×D14911yescharacteristic
201Q16—2982no—
202SD16—2984no—
203SD16—5962no—
204D8—22no—
205D8—2984no—
206D8—1494no—
207C2×C8—22no—
208C2×C8—2982no—
209C2×C8—1491no—
210C2×C8—1491no—
211C2×C8C22×D14911yescharacteristic
212C2×C8C22×D14911yescharacteristic
213C4⋊C4—2982no—
214C4⋊C4—1491no—
215C4⋊C4C22×D14912yes—
216C22⋊C4—22no—
217C22⋊C4—2982no—
218C22⋊C4—2982no—
219C22⋊C4—2982no—
220C22⋊C4—2982no—
221C22⋊C4—1491no—
222C22⋊C4—1491no—
223C42—1491no—
224C23—22no—
225C23—2982no—
226C23—5964no—
227C23—5964no—
228C23—1491no—
229C23—11922no—
230C23D4×D14911yescharacteristic
231Q8—2982no—
232Q8—2982no—
233D4—22no—
234D4—22no—
235D4—82no—
236D4—2982no—
237D4—2982no—
238D4—5964no—
239D4—5964no—
240D4—1494no—
241C2×C4—21no—
242C2×C4—21no—
243C2×C4—22no—
244C2×C4—2981no—
245C2×C4—2981no—
246C2×C4—2982no—
247C2×C4—5964no—
248C2×C4—1491no—
249C2×C4—1491no—
250C2×C4—1491no—
251C2×C4—11922no—
252C2×C4D4×D14911yescharacteristic
253C2×C4C23×D14911yescharacteristic
254C8—21no—
255C8—2981no—
256C8—2981no—
257C8D4×D14912yes—
258C22—21no—
259C22—21no—
260C22—21no—
261C22—42no—
262C22—42no—
263C22—42no—
264C22—2981no—
265C22—2981no—
266C22—2984no—
267C22—5962no—
268C22—5962no—
269C22—1492no—
270C22—11928no—
271C22C2×D4×D14911yescharacteristic
272C4—21no—
273C4—42no—
274C4—2981no—
275C4—2981no—
276C4—2981no—
277C4—5962no—
278C4C2×D4×D14911yescharacteristic
279C4#1801195711yescharacteristic
280C2—41no—
281C2—82no—
282C2—2982no—
283C2—5964no—
284C2#2375025911yescharacteristic
285C2#135×D14911yescharacteristic
286C2#2375042611yescharacteristic
subgroupG/H
centerC22C2×D4×D149
commutator, cosocleC2×C4×C149C24
FrattiniC2×C4C23×D149
Fitting#466×C149C2
socleC22×C149C22×D4
hypercenter#466D149
hypocenterC149#3280
LCSG ▷ C2×C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C22 ◁ C22×C4 ◁ #466

Complements

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

NH ≅ G/Ntype
1. C2×#18011933C2semidirect
2. C2×D8×D149C2semidirect
3. #23750272C2semidirect
4. #23750008C2semidirect
5. #23749867C2semidirect
6. #23749839C2semidirect
7. #23749777C2semidirect
8. #23749768C2semidirect
9. #23749707C2semidirect
10. C8×C22⋊D149C2semidirect
11. #466×C149C2semidirect
12. C2×#14558736C22semidirect
15. C2×Dic596C22semidirect
16. C2×#14558725C22semidirect
17. C2×#14558724C22semidirect
22. #18011898C22semidirect
27. #18011873C22semidirect
30. #18011840C22semidirect
31. #18011834C22semidirect
32. #18011831C22semidirect
33. C22⋊#11924746C22semidirect
35. C8×Dic149C22semidirect
37. C22×C8×C149C22semidirect
38. #121×C149C22semidirect
39. #107×C149C22semidirect
40. #102×C149C22semidirect
57. D1192D4semidirect
127. C2×D149#135semidirect
143. C149#3280semidirect
150. #466D149semidirect
167. C22×C8C2×D149semidirect
172. #121C2×D149semidirect
177. #107C2×D149semidirect
181. #102C2×D149semidirect

Maximal subgroups

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

subgroupindex
C2×#180119332
C2×D8×D1492
#237502722
#237500082
#237498672
#237498392
#237497772
#237497682
#237497072
C8×C22⋊D1492
#466×C1492
#3280149