Finite Group Databasebeta

← #34056365

Subgroups — #34056365

Order 19072.

620 conjugacy classes of subgroups; only the 133 normal subgroups are shown.

normal subgroups only

This group has 620 conjugacy classes of subgroups — too many to draw. Only its 133 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
1C22×D1192C211yesmaximal, characteristic, complemented
2C2×D8×D149C211yesmaximal, characteristic, complemented
3#23750259C212yesmaximal, complemented
4#23750000C211yesmaximal, characteristic, complemented
5#23749862C211yesmaximal, characteristic, complemented
6#23749819C212yesmaximal, complemented
7#23749760C212yesmaximal, complemented
8#23749758C212yesmaximal, complemented
9#23749707C211yesmaximal, characteristic, complemented
10C8×C22⋊D149C211yesmaximal, characteristic, complemented
11#466×C149C211yesmaximal, characteristic, complemented
12C22×D596C2212yescomplemented
13C2×D4×D149—22no—
14C2×D4×D149C2212yescomplemented
15C2×D1192—24no—
16C2×D1192C2211yescharacteristic
17C2×D1192C2211yescharacteristic, complemented
18C2×D1192C2212yescomplemented
19C2×#14558721C2212yescomplemented
20C2×#14558721C2212yescomplemented
21D8×D149—24no—
22C2×C8×D149C2211yescharacteristic, complemented
23#18011907C2212yescomplemented
24#18011886C2212yescomplemented
25#18011884—22no—
26#18011881—22no—
27#18011879—22no—
28#18011873C2212yescomplemented
29C4×C22⋊D149C2211yescharacteristic
30#18011840C2211yescharacteristic, complemented
31#18011831C2212yescomplemented
32#18011831C2212yescomplemented
33C22⋊#11924746C2211yescharacteristic, complemented
34#18011823C2211yescharacteristic, complemented
35C8×Dic149C2211yescharacteristic, complemented
36C2×D8×C149C2211yescharacteristic, complemented
37C22×C8×C149C2211yescharacteristic, complemented
38#121×C149C2212yescomplemented
39#107×C149C2211yescharacteristic, complemented
40#102×C149C2212yescomplemented
41C23×D149—22no—
42C23×D149—22no—
43C2×D596—24no—
44C2×D596—22no—
45C2×D596—22no—
46C2×D596—42no—
47C2×D596C2312yes—
48C2×D596C2312yes—
49C2×C22⋊D149—22no—
50C2×C22⋊D149—22no—
51C2×C22⋊D149—22no—
52C2×C22⋊D149D411yescharacteristic
53D4×D149—24no—
54D4×D149—42no—
55D4×D149—48no—
56C2×C4×D149—22no—
57C2×C4×D149C2311yescharacteristic
58D1192—24no—
59D1192—22no—
60D1192D414yescomplemented
61#14558721—24no—
62#14558721—42no—
63C2×#11924746C2311yescharacteristic
64C2×#11924746C2311yescharacteristic
65C8×D149—22no—
66#14558715D411yescharacteristic
67C22⋊Dic149D411yescharacteristic
68#14558713—22no—
69#14558713—22no—
70#14558713D411yescharacteristic
71C4×Dic149C2311yescharacteristic
72C2×D4×C149—22no—
73C2×D4×C149C2312yes—
74C22×C4×C149C2311yescharacteristic
75D8×C149—22no—
76C2×C8×C149—22no—
77C2×C8×C149C2311yescharacteristic
78C2×C8×C149C2311yescharacteristic
79C4⋊C4×C149C2312yes—
80C22⋊C4×C149—22no—
81C22×D149—22no—
82C22×D149—22no—
83C22×D149—44no—
84C22×D149—44no—
85C22×D149—44no—
86C22×D149—44no—
87C22×D149—82no—
88C22×D149—82no—
89C22×D149C2×D411yescharacteristic
90D596—22no—
91D596—22no—
92D596—22no—
93D596—44no—
94D596—44no—
95D596C2×D414yescomplemented
96C22⋊D149—44no—
97C22⋊D149—44no—
98C22⋊D149—82no—
99C22⋊D149D814yescomplemented
100C2×Dic149C2×D411yescharacteristic
101C2×Dic149C2×D411yescharacteristic
102C2×Dic149C2×D411yescharacteristic
103C4×D149—21no—
104C4×D149—21no—
105C4×D149—44no—
106#11924746—21no—
107#11924746—21no—
108C23×C149—22no—
109C23×C149C2×D411yescharacteristic
110D4×C149—22no—
111D4×C149—22no—
112D4×C149—44no—
113C2×C4×C149—21no—
114C2×C4×C149—21no—
115C2×C4×C149—22no—
116C2×C4×C149C2×D411yescharacteristic
117C2×C4×C149C2411yescharacteristic
118C8×C149—21no—
119C8×C149C2×D412yescomplemented
120C22×C149—21no—
121C22×C149—21no—
122C22×C149—42no—
123C22×C149—42no—
124C22×C149—42no—
125C22×C149C2×D812yescomplemented
126C22×C149C22×D411yescharacteristic
127C2×D149—21no—
128C2×D149—21no—
129C2×D149—24no—
130C2×D149—42no—
131C2×D149—42no—
132C2×D149—42no—
133C2×D149—42no—
134C2×D149—42no—
135C2×D149—88no—
136C2×D149—88no—
137C2×D149C2×D812yescomplemented
138C4×C149—21no—
139C4×C149—42no—
140C4×C149C22×D411yescharacteristic
141C4×C149H(5,𝔽2)11yescharacteristic
142Dic149—21no—
143Dic149—21no—
144Dic149C2×D812yescomplemented
145C2×C149—22no—
146C2×C149—82no—
147C2×C149D4211yescharacteristic
148C2×C149C22×D811yescharacteristic
149C2×C149#57611yescharacteristic
150D149—22no—
151D149—44no—
152D149—82no—
153C149D4×D811yescharacteristic, complemented, Sylow
154D4×D8—1491nomaximal, Sylow
155C22×D8—1491no—
156C22×D8—1491no—
157D42—1492no—
158#493—1491no—
159#466—1491no—
160#466D14911yescharacteristic, complemented
161#459—1492no—
162#447—1492no—
163#447—1492no—
164C4×D8—1491no—
165C8×D4—1491no—
166C22×D4—2982no—
167C22×D4—1492no—
168C22×D4—1492no—
169C2×D8—2984no—
170C2×D8—2984no—
171C2×D8—1492no—
172C2×D8—1492no—
173C2×D8—1492no—
174C2×D8—1491no—
175C2×D8—1491no—
176C2×D8C2×D14911yescharacteristic, complemented
177C22×C8—1491no—
178C22×C8C2×D14911yescharacteristic, complemented
179#127—1492no—
180#121—2982no—
181#121—1492no—
182#121C2×D14912yescomplemented
183#120—2982no—
184#120—2982no—
185C4×D4—1492no—
186C4×D4—1491no—
187#107C2×D14911yescharacteristic, complemented
188C4⋊C8—1491no—
189#102—1492no—
190#102—1492no—
191#102C2×D14912yescomplemented
192C22⋊C8—1491no—
193C22⋊C8—1491no—
194C4×C8—1491no—
195C24—2982no—
196C24—2982no—
197C2×D4—22no—
198C2×D4—2984no—
199C2×D4—2982no—
200C2×D4—2984no—
201C2×D4—2982no—
202C2×D4—2982no—
203C2×D4—2982no—
204C2×D4—2982no—
205C2×D4—5962no—
206C2×D4—5962no—
207C2×D4—5968no—
208C2×D4—1491no—
209C2×D4—1492no—
210C2×D4—1492no—
211C2×D4C22×D14912yes—
212C22×C4—2982no—
213C22×C4—1491no—
214C22×C4C22×D14911yescharacteristic
215D8—22no—
216D8—2984no—
217D8—2984no—
218D8—2982no—
219D8—5962no—
220D8—1494no—
221C2×C8—22no—
222C2×C8—2982no—
223C2×C8—1491no—
224C2×C8—1491no—
225C2×C8C22×D14911yescharacteristic
226C2×C8C22×D14911yescharacteristic
227C4⋊C4—1491no—
228C4⋊C4C22×D14912yes—
229C22⋊C4—22no—
230C22⋊C4—2982no—
231C22⋊C4—2982no—
232C22⋊C4—1491no—
233C22⋊C4—1491no—
234C42—1491no—
235C23—22no—
236C23—2982no—
237C23—2982no—
238C23—5964no—
239C23—5964no—
240C23—5964no—
241C23—5964no—
242C23—1491no—
243C23—11922no—
244C23—11922no—
245C23D4×D14911yescharacteristic
246D4—22no—
247D4—22no—
248D4—44no—
249D4—2982no—
250D4—2982no—
251D4—2982no—
252D4—5964no—
253D4—5964no—
254D4—5964no—
255D4—5964no—
256D4—1494no—
257D4—1494no—
258D4—11922no—
259C2×C4—21no—
260C2×C4—21no—
261C2×C4—22no—
262C2×C4—2981no—
263C2×C4—2981no—
264C2×C4—5964no—
265C2×C4—1491no—
266C2×C4—1491no—
267C2×C4—1491no—
268C2×C4D4×D14911yescharacteristic
269C2×C4C23×D14911yescharacteristic
270C8—21no—
271C8—2981no—
272C8—2981no—
273C8D4×D14912yescomplemented
274C22—21no—
275C22—21no—
276C22—42no—
277C22—42no—
278C22—42no—
279C22—2981no—
280C22—2981no—
281C22—2984no—
282C22—5962no—
283C22—5962no—
284C22—5962no—
285C22—5962no—
286C22—5962no—
287C22—1492no—
288C22—11928no—
289C22—11928no—
290C22D8×D14912yescomplemented
291C22C2×D4×D14911yescharacteristic
292C4—21no—
293C4—42no—
294C4—2981no—
295C4—2981no—
296C4—1492no—
297C4C2×D4×D14911yescharacteristic
298C4#1801195711yescharacteristic
299C2—22no—
300C2—82no—
301C2—2982no—
302C2—5964no—
303C2—11922no—
304C2#2375025911yescharacteristic
305C2C2×D8×D14911yescharacteristic
306C2#2375042711yescharacteristic
subgroupG/H
centerC22C2×D4×D149
commutator, cosocleC2×C4×C149C24
FrattiniC2×C4C23×D149
Fitting#466×C149C2
socleC22×C149C22×D4
hypercenter#466D149
hypocenterC149D4×D8
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. C22×D1192C2semidirect
2. C2×D8×D149C2semidirect
3. #23750259C2semidirect
4. #23750000C2semidirect
5. #23749862C2semidirect
6. #23749819C2semidirect
7. #23749760C2semidirect
8. #23749758C2semidirect
9. #23749707C2semidirect
10. C8×C22⋊D149C2semidirect
11. #466×C149C2semidirect
12. C22×D596C22semidirect
14. C2×D4×D149C22semidirect
17. C2×D1192C22semidirect
18. C2×D1192C22semidirect
19. C2×#14558721C22semidirect
20. C2×#14558721C22semidirect
22. C2×C8×D149C22semidirect
23. #18011907C22semidirect
24. #18011886C22semidirect
28. #18011873C22semidirect
30. #18011840C22semidirect
31. #18011831C22semidirect
32. #18011831C22semidirect
33. C22⋊#11924746C22semidirect
34. #18011823C22semidirect
35. C8×Dic149C22semidirect
36. C2×D8×C149C22semidirect
37. C22×C8×C149C22semidirect
38. #121×C149C22semidirect
39. #107×C149C22semidirect
40. #102×C149C22semidirect
60. D1192D4semidirect
95. D596C2×D4semidirect
99. C22⋊D149D8semidirect
119. C8×C149C2×D4semidirect
125. C22×C149C2×D8semidirect
137. C2×D149C2×D8semidirect
144. Dic149C2×D8semidirect
153. C149D4×D8semidirect
160. #466D149semidirect
176. C2×D8C2×D149semidirect
178. C22×C8C2×D149semidirect
182. #121C2×D149semidirect
187. #107C2×D149semidirect
191. #102C2×D149semidirect
273. C8D4×D149semidirect
290. C22D8×D149semidirect

Maximal subgroups

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

subgroupindex
C22×D11922
C2×D8×D1492
#237502592
#237500002
#237498622
#237498192
#237497602
#237497582
#237497072
C8×C22⋊D1492
#466×C1492
D4×D8149