Finite Group Databasebeta

← #34056363

Subgroups — #34056363

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
1C2×D8×D149C212yesmaximal, complemented
2D4×D596C211yesmaximal, characteristic, complemented
3#23750260C211yesmaximal, characteristic, complemented
4#23750001C211yesmaximal, characteristic, complemented
5#23749860C212yesmaximal, complemented
6#23749821C211yesmaximal, characteristic, complemented
7#23749760C212yesmaximal, complemented
8#23749757C212yesmaximal, complemented
9C4×#14558721C211yesmaximal, characteristic, complemented
10#23749690C211yesmaximal, characteristic, complemented
11#459×C149C211yesmaximal, characteristic, complemented
12C22×D596—21no—
13C2×D4×D149—21no—
14C2×D4×D149C2212yescomplemented
15C2×D4×D149C2212yescomplemented
16C2×D1192C2212yescomplemented
17C2×#14558721C2211yescharacteristic
18C2×#14558721C2212yescomplemented
19C2×#14558721C2212yescomplemented
20D8×D149—28no—
21C2×C8×D149C2212yescomplemented
22#18011908C2211yescharacteristic, complemented
23#18011886C2212yescomplemented
24#18011885—21no—
25#18011882—21no—
26#18011882C2212yescomplemented
27#18011881—22no—
28#18011879—22no—
29C4×D596C2211yescharacteristic
30C4×D596C2211yescharacteristic, complemented
31#18011844C2211yescharacteristic, complemented
32#18011833C2212yescomplemented
33#18011832C2211yescharacteristic, complemented
34#18011831C2211yescharacteristic, complemented
35#18011823C2212yescomplemented
36C4×#11924746C2211yescharacteristic, complemented
37C2×D8×C149C2212yescomplemented
38#127×C149C2211yescharacteristic, complemented
39C4×D4×C149C2211yescharacteristic, complemented
40C4⋊C8×C149C2211yescharacteristic, complemented
41#102×C149C2212yescomplemented
42C23×D149—22no—
43C23×D149—22no—
44C2×D596—22no—
45C2×D596—21no—
46C2×D596—21no—
47C2×D596—44no—
48C2×D596D411yescharacteristic
49C2×D596C2312yes—
50C2×D596C2311yescharacteristic
51C2×C22⋊D149—22no—
52C2×C22⋊D149—22no—
53C2×C22⋊D149—22no—
54D4×D149—24no—
55D4×D149—24no—
56D4×D149—42no—
57D4×D149—42no—
58D4×D149—44no—
59C2×C4×D149—21no—
60C2×C4×D149C2312yes—
61D1192—24no—
62#14558721—24no—
63#14558721—42no—
64#14558721D414yescomplemented
65C2×#11924746C2311yescharacteristic
66C2×#11924746C2311yescharacteristic
67C8×D149—24no—
68C4⋊Dic149D411yescharacteristic
69C4⋊Dic149C2311yescharacteristic
70C22⋊Dic149—22no—
71#14558713—22no—
72#14558713—21no—
73#14558713D412yes—
74C2×D4×C149—21no—
75C2×D4×C149—21no—
76C2×D4×C149C2312yes—
77C2×D4×C149C2311yescharacteristic
78C22×C4×C149—21no—
79D8×C149—24no—
80C2×C8×C149C2312yes—
81C4⋊C4×C149C2311yescharacteristic
82C22⋊C4×C149—21no—
83C42×C149C2311yescharacteristic
84C22×D149—21no—
85C22×D149—22no—
86C22×D149—44no—
87C22×D149—44no—
88C22×D149—44no—
89C22×D149—44no—
90C22×D149—82no—
91C22×D149—82no—
92C22×D149C2×D412yes—
93D596—22no—
94D596—21no—
95D596—22no—
96D596—44no—
97D596—42no—
98D596—81no—
99D596D814yescomplemented
100D596C2×D412yescomplemented
101C22⋊D149—44no—
102C22⋊D149—44no—
103C22⋊D149—44no—
104C2×Dic149—21no—
105C2×Dic149C2×D412yes—
106C4×D149—22no—
107C4×D149—22no—
108C4×D149—42no—
109#11924746—21no—
110#11924746C2×D412yescomplemented
111C23×C149—21no—
112C23×C149—22no—
113D4×C149—22no—
114D4×C149—21no—
115D4×C149—22no—
116D4×C149—42no—
117D4×C149—81no—
118D4×C149C2×D412yescomplemented
119C2×C4×C149—21no—
120C2×C4×C149—42no—
121C2×C4×C149C2×D411yescharacteristic
122C2×C4×C149C2×D411yescharacteristic
123C2×C4×C149C2411yescharacteristic
124C8×C149—22no—
125C22×C149—22no—
126C22×C149—41no—
127C22×C149—41no—
128C22×C149—42no—
129C22×C149—42no—
130C22×C149—42no—
131C22×C149C22×D411yescharacteristic
132C2×D149—22no—
133C2×D149—22no—
134C2×D149—22no—
135C2×D149—41no—
136C2×D149—41no—
137C2×D149—42no—
138C2×D149—42no—
139C2×D149—42no—
140C2×D149—88no—
141C2×D149—88no—
142C2×D149C2×D814yescomplemented
143C4×C149—21no—
144C4×C149—41no—
145C4×C149C2×D812yescomplemented
146C4×C149C22×D411yescharacteristic
147C4×C149H(5,𝔽2)11yescharacteristic
148Dic149—22no—
149Dic149—41no—
150C2×C149—42no—
151C2×C149—82no—
152C2×C149D4211yescharacteristic
153C2×C149C22×D811yescharacteristic
154C2×C149#57611yescharacteristic
155D149—24no—
156D149—42no—
157D149—82no—
158C149D4×D811yescharacteristic, complemented, Sylow
159D4×D8—1491nomaximal, Sylow
160C22×D8—1492no—
161D42—1491no—
162D42—1491no—
163#493—1491no—
164#466—1492no—
165#459—1491no—
166#459D14911yescharacteristic, complemented
167#447—1492no—
168#447—1492no—
169C4×D8—1491no—
170C8×D4—1491no—
171C22×D4—2981no—
172C22×D4—2981no—
173C22×D4—1492no—
174C22×D4—1492no—
175C2×D8—2988no—
176C2×D8—1492no—
177C2×D8—1492no—
178C2×D8—1491no—
179C2×D8—1492no—
180C2×D8C2×D14912yescomplemented
181C22×C8—1492no—
182#127—1491no—
183#127C2×D14911yescharacteristic, complemented
184#121—2981no—
185#121—2981no—
186#121—1492no—
187#121—1492no—
188#120—2982no—
189#120—2982no—
190C4×D4—1491no—
191C4×D4—1491no—
192C4×D4C2×D14911yescharacteristic, complemented
193#107—1491no—
194C4⋊C8C2×D14911yescharacteristic, complemented
195#102—1491no—
196#102—1492no—
197#102—1491no—
198#102C2×D14912yescomplemented
199C22⋊C8—1492no—
200C4×C8—1491no—
201C24—2982no—
202C24—2982no—
203C2×D4—21no—
204C2×D4—21no—
205C2×D4—2982no—
206C2×D4—2984no—
207C2×D4—2984no—
208C2×D4—2982no—
209C2×D4—2982no—
210C2×D4—2982no—
211C2×D4—2981no—
212C2×D4—2981no—
213C2×D4—5964no—
214C2×D4—5962no—
215C2×D4—5962no—
216C2×D4—5964no—
217C2×D4—1491no—
218C2×D4—1492no—
219C2×D4—1491no—
220C2×D4C22×D14912yes—
221C2×D4C22×D14911yescharacteristic
222C22×C4—21no—
223C22×C4—2981no—
224C22×C4—1492no—
225D8—24no—
226D8—2984no—
227D8—2984no—
228D8—5962no—
229D8—1494no—
230C2×C8—2984no—
231C2×C8—1491no—
232C2×C8—1491no—
233C2×C8C22×D14912yes—
234C4⋊C4—1491no—
235C4⋊C4—1491no—
236C4⋊C4C22×D14911yescharacteristic
237C22⋊C4—21no—
238C22⋊C4—2982no—
239C22⋊C4—2982no—
240C22⋊C4—2981no—
241C22⋊C4—1492no—
242C42C22×D14911yescharacteristic
243C23—21no—
244C23—22no—
245C23—2981no—
246C23—2982no—
247C23—5964no—
248C23—5964no—
249C23—5964no—
250C23—5964no—
251C23—1492no—
252C23—11922no—
253C23—11922no—
254D4—22no—
255D4—21no—
256D4—22no—
257D4—42no—
258D4—81no—
259D4—2982no—
260D4—2981no—
261D4—2982no—
262D4—5964no—
263D4—5964no—
264D4—5964no—
265D4—5964no—
266D4—5962no—
267D4—1494no—
268D4—1492no—
269D4—11921no—
270D4D4×D14912yescomplemented
271C2×C4—21no—
272C2×C4—42no—
273C2×C4—2982no—
274C2×C4—2982no—
275C2×C4—2981no—
276C2×C4—5962no—
277C2×C4—1492no—
278C2×C4D4×D14911yescharacteristic
279C2×C4D4×D14911yescharacteristic
280C2×C4C23×D14911yescharacteristic
281C8—22no—
282C8—2981no—
283C8—1492no—
284C22—22no—
285C22—41no—
286C22—41no—
287C22—42no—
288C22—42no—
289C22—42no—
290C22—2982no—
291C22—2982no—
292C22—2982no—
293C22—5961no—
294C22—5961no—
295C22—5962no—
296C22—5962no—
297C22—5962no—
298C22—1494no—
299C22—11928no—
300C22—11928no—
301C22C2×D4×D14911yescharacteristic
302C4—21no—
303C4—41no—
304C4—2982no—
305C4—5961no—
306C4D8×D14912yescomplemented
307C4C2×D4×D14911yescharacteristic
308C4#1801195711yescharacteristic
309C2—42no—
310C2—82no—
311C2—2984no—
312C2—5962no—
313C2—11922no—
314C2#2375025911yescharacteristic
315C2C2×D8×D14911yescharacteristic
316C2#2375042911yescharacteristic
subgroupG/H
centerC22C2×D4×D149
commutator, cosocleC2×C4×C149C24
FrattiniC2×C4C23×D149
Fitting#459×C149C2
socleC22×C149C22×D4
hypercenter#459D149
hypocenterC149D4×D8
LCSG ▷ C2×C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C22 ◁ C42 ◁ #459

Complements

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

NH ≅ G/Ntype
1. C2×D8×D149C2semidirect
2. D4×D596C2semidirect
3. #23750260C2semidirect
4. #23750001C2semidirect
5. #23749860C2semidirect
6. #23749821C2semidirect
7. #23749760C2semidirect
8. #23749757C2semidirect
9. C4×#14558721C2semidirect
10. #23749690C2semidirect
11. #459×C149C2semidirect
14. C2×D4×D149C22semidirect
15. C2×D4×D149C22semidirect
16. C2×D1192C22semidirect
18. C2×#14558721C22semidirect
19. C2×#14558721C22semidirect
21. C2×C8×D149C22semidirect
22. #18011908C22semidirect
23. #18011886C22semidirect
26. #18011882C22semidirect
30. C4×D596C22semidirect
31. #18011844C22semidirect
32. #18011833C22semidirect
33. #18011832C22semidirect
34. #18011831C22semidirect
35. #18011823C22semidirect
36. C4×#11924746C22semidirect
37. C2×D8×C149C22semidirect
38. #127×C149C22semidirect
39. C4×D4×C149C22semidirect
40. C4⋊C8×C149C22semidirect
41. #102×C149C22semidirect
64. #14558721D4semidirect
99. D596D8semidirect
100. D596C2×D4semidirect
110. #11924746C2×D4semidirect
118. D4×C149C2×D4semidirect
142. C2×D149C2×D8semidirect
145. C4×C149C2×D8semidirect
158. C149D4×D8semidirect
166. #459D149semidirect
180. C2×D8C2×D149semidirect
183. #127C2×D149semidirect
192. C4×D4C2×D149semidirect
194. C4⋊C8C2×D149semidirect
198. #102C2×D149semidirect
270. D4D4×D149semidirect
306. C4D8×D149semidirect

Maximal subgroups

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

subgroupindex
C2×D8×D1492
D4×D5962
#237502602
#237500012
#237498602
#237498212
#237497602
#237497572
C4×#145587212
#237496902
#459×C1492
D4×D8149