Finite Group Databasebeta

← #34056377

Subgroups — #34056377

Order 19072.

526 conjugacy classes of subgroups; only the 131 normal subgroups are shown.

normal subgroups only

This group has 526 conjugacy classes of subgroups — too many to draw. Only its 131 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×#18011930C211yesmaximal, characteristic, complemented
2C2×D8×D149C211yesmaximal, characteristic, complemented
3#23750270C212yesmaximal, complemented
4#23750009C211yesmaximal, characteristic, complemented
5#23749867C211yesmaximal, characteristic, complemented
6#23749862C211yesmaximal, characteristic, complemented
7#23749840C212yesmaximal, complemented
8#23749777C212yesmaximal, complemented
9#23749771C212yesmaximal, complemented
10C8×D596C211yesmaximal, characteristic, complemented
11C4×D8×C149C211yesmaximal, characteristic, complemented
12C2×#14558735C2212yescomplemented
13C2×D4×D149C2212yes—
14#18011930—24no—
15C2×Dic596C2211yescharacteristic, complemented
16C2×#14558725C2212yescomplemented
17C2×#14558724C2212yescomplemented
18C2×D1192C2211yescharacteristic
19C2×#14558721C2212yes—
20D8×D149—24no—
21C2×C8×D149C2211yescharacteristic
22C2×C8×D149C2211yescharacteristic, complemented
23#18011899C2212yescomplemented
24#18011895—22no—
25#18011891C2212yes—
26#18011886C2212yescomplemented
27#18011885—22no—
28#18011881—22no—
29C4×D596C2211yescharacteristic
30C2×#14558713—22no—
31C4⋊#11924746C2211yescharacteristic, complemented
32#18011834C2212yescomplemented
33#18011831C2212yescomplemented
34#18011823C2211yescharacteristic
35#18011823C2211yescharacteristic, complemented
36C2×D8×C149C2211yescharacteristic
37C4×D4×C149C2212yescomplemented
38#107×C149C2211yescharacteristic, complemented
39#102×C149C2212yescomplemented
40C4×C8×C149C2211yescharacteristic, complemented
41C23×D149—22no—
42#14558735—24no—
43#14558735—42no—
44C2×Dic298C2312yes—
45C2×D596—22no—
46C2×D596D411yescharacteristic
47C2×D596C2312yes—
48C2×C22⋊D149—22no—
49C2×C22⋊D149—22no—
50D4×D149—24no—
51D4×D149—42no—
52C22×Dic149—22no—
53C2×C4×D149C2311yescharacteristic
54C2×C4×D149C2311yescharacteristic
55Dic596—22no—
56#14558725—42no—
57#14558724—24no—
58D1192—22no—
59#14558721—24no—
60C2×#11924746C2311yescharacteristic
61C2×#11924746C2311yescharacteristic
62C8×D149—22no—
63C8×D149—22no—
64C4⋊Dic149—22no—
65C4⋊Dic149D411yescharacteristic
66#14558713—22no—
67#14558713—22no—
68#14558713—22no—
69#14558713—22no—
70#14558713D411yescharacteristic
71#14558713D411yescharacteristic
72C2×D4×C149C2312yes—
73C22×C4×C149—22no—
74D8×C149D414yescomplemented
75C2×C8×C149C2311yescharacteristic
76C2×C8×C149C2311yescharacteristic
77C4⋊C4×C149C2312yes—
78C22⋊C4×C149—22no—
79C42×C149C2311yescharacteristic
80C22×D149—22no—
81C22×D149—44no—
82C22×D149—44no—
83C22×D149—82no—
84C22×D149C2×D411yescharacteristic
85C22×D149C2×D411yescharacteristic
86Dic298—22no—
87Dic298—22no—
88D596—22no—
89D596—22no—
90D596—22no—
91D596—82no—
92C22⋊D149—44no—
93C22⋊D149—44no—
94C2×Dic149—22no—
95C2×Dic149—44no—
96C2×Dic149C2×D411yescharacteristic
97C2×Dic149C2×D411yescharacteristic
98C4×D149—21no—
99C4×D149—21no—
100C4×D149—21no—
101C4×D149—21no—
102#11924746—21no—
103#11924746—21no—
104C23×C149—22no—
105D4×C149—22no—
106D4×C149C2×D414yes—
107C2×C4×C149—22no—
108C2×C4×C149—82no—
109C2×C4×C149C2×D411yescharacteristic
110C2×C4×C149C2×D411yescharacteristic
111C2×C4×C149C2411yescharacteristic
112C8×C149—21no—
113C8×C149C2×D412yes—
114C22×C149—24no—
115C22×C149—42no—
116C22×C149—42no—
117C22×C149C22×D411yescharacteristic
118C2×D149—21no—
119C2×D149—21no—
120C2×D149—21no—
121C2×D149—21no—
122C2×D149—21no—
123C2×D149—42no—
124C2×D149—42no—
125C2×D149—42no—
126C2×D149—88no—
127C2×D149#13512yescomplemented
128C4×C149—21no—
129C4×C149—21no—
130C4×C149—42no—
131C4×C149C22×D411yescharacteristic
132C4×C149H(5,𝔽2)11yescharacteristic
133Dic149—21no—
134Dic149—21no—
135Dic149—42no—
136C2×C149—44no—
137C2×C149D4211yescharacteristic
138C2×C149C2×#13511yescharacteristic
139C2×C149#57611yescharacteristic
140D149—22no—
141D149—41no—
142D149—82no—
143C149#328011yescharacteristic, complemented, Sylow
144#3280—1491nomaximal, Sylow
145C2×#135—1491no—
146C22×D8—1491no—
147#546—1492no—
148#495—1491no—
149#467—1491no—
150#466—1491no—
151#463—1492no—
152#450—1492no—
153#449—1492no—
154C4×D8D14911yescharacteristic, complemented
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×C8—1491no—
168#124—1492no—
169#123—2982no—
170C22⋊Q8—1492no—
171#121—2982no—
172#121—1492no—
173#120—2982no—
174C4×D4—1491no—
175C4×D4C2×D14912yescomplemented
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×C8C2×D14911yescharacteristic, complemented
185C24—2982no—
186#41—2984no—
187#41—5962no—
188C2×Q8—1492no—
189C2×D4—2982no—
190C2×D4—2984no—
191C2×D4—2982no—
192C2×D4—2982no—
193C2×D4—5962no—
194C2×D4—1491no—
195C2×D4—1492no—
196C2×D4C22×D14912yes—
197C22×C4—22no—
198C22×C4—2982no—
199C22×C4—1491no—
200C22×C4—1491no—
201Q16—2982no—
202SD16—2984no—
203SD16—5962no—
204D8—2984no—
205D8—2982no—
206D8D59614yescomplemented
207C2×C8—2982no—
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—
223C42C22×D14911yescharacteristic
224C23—22no—
225C23—2982no—
226C23—5964no—
227C23—5964no—
228C23—1491no—
229C23—1491no—
230C23—11922no—
231Q8—2982no—
232Q8—2982no—
233D4—22no—
234D4—2982no—
235D4—2982no—
236D4—2982no—
237D4—5964no—
238D4—5964no—
239D4—11922no—
240D4C2×D59614yes—
241C2×C4—22no—
242C2×C4—82no—
243C2×C4—2981no—
244C2×C4—2981no—
245C2×C4—2981no—
246C2×C4—2981no—
247C2×C4—2982no—
248C2×C4—5964no—
249C2×C4—1491no—
250C2×C4—1491no—
251C2×C4D4×D14911yescharacteristic
252C2×C4D4×D14911yescharacteristic
253C2×C4C23×D14911yescharacteristic
254C8—21no—
255C8—2981no—
256C8—2981no—
257C8C2×D59612yes—
258C22—24no—
259C22—42no—
260C22—42no—
261C22—2981no—
262C22—2981no—
263C22—2981no—
264C22—2981no—
265C22—2981no—
266C22—5962no—
267C22—5962no—
268C22—5962no—
269C22—1492no—
270C22—11928no—
271C22C2×D4×D14911yescharacteristic
272C4—21no—
273C4—21no—
274C4—42no—
275C4—2981no—
276C4—2981no—
277C4—5962no—
278C4C22×D59611yescharacteristic
279C4#1801195711yescharacteristic
280C2—44no—
281C2—2982no—
282C2—5961no—
283C2—11922no—
284C2D4×D59611yescharacteristic
285C2#135×D14911yescharacteristic
286C2#2375042611yescharacteristic
subgroupG/H
centerC22C2×D4×D149
commutator, cosocleC2×C4×C149C24
FrattiniC2×C4C23×D149
FittingC4×D8×C149C2
socleC22×C149C22×D4
hypercenterC4×D8D149
hypocenterC149#3280
LCSG ▷ C2×C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C22 ◁ C42 ◁ C4×D8

Complements

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

NH ≅ G/Ntype
1. C2×#18011930C2semidirect
2. C2×D8×D149C2semidirect
3. #23750270C2semidirect
4. #23750009C2semidirect
5. #23749867C2semidirect
6. #23749862C2semidirect
7. #23749840C2semidirect
8. #23749777C2semidirect
9. #23749771C2semidirect
10. C8×D596C2semidirect
11. C4×D8×C149C2semidirect
12. C2×#14558735C22semidirect
15. C2×Dic596C22semidirect
16. C2×#14558725C22semidirect
17. C2×#14558724C22semidirect
22. C2×C8×D149C22semidirect
23. #18011899C22semidirect
26. #18011886C22semidirect
31. C4⋊#11924746C22semidirect
32. #18011834C22semidirect
33. #18011831C22semidirect
35. #18011823C22semidirect
37. C4×D4×C149C22semidirect
38. #107×C149C22semidirect
39. #102×C149C22semidirect
40. C4×C8×C149C22semidirect
74. D8×C149D4semidirect
127. C2×D149#135semidirect
143. C149#3280semidirect
154. C4×D8D149semidirect
175. C4×D4C2×D149semidirect
177. #107C2×D149semidirect
181. #102C2×D149semidirect
184. C4×C8C2×D149semidirect
206. D8D596semidirect

Maximal subgroups

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

subgroupindex
C2×#180119302
C2×D8×D1492
#237502702
#237500092
#237498672
#237498622
#237498402
#237497772
#237497712
C8×D5962
C4×D8×C1492
#3280149