Finite Group Databasebeta

← #34056709

Subgroups — #34056709

Order 19072.

450 conjugacy classes of subgroups.

The subgroup lattice has 392 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#23750313C211yesmaximal, characteristic, complemented
2D4×D596C211yesmaximal, characteristic
3#23749991C211yesmaximal, characteristic, complemented
4#23749951C211yesmaximal, characteristic, complemented
5#23749940C211yesmaximal, characteristic, complemented
6#23749872C211yesmaximal, characteristic, complemented
7#23749855C211yesmaximal, characteristic, complemented
8#23749826C211yesmaximal, characteristic, complemented
9#23749777C211yesmaximal, characteristic, complemented
10#23749777C211yesmaximal, characteristic, complemented
11#23749725C211yesmaximal, characteristic, complemented
12#23749695C211yesmaximal, characteristic, complemented
13#23749628C211yesmaximal, characteristic, complemented
14#102×D149C211yesmaximal, characteristic, complemented
15#478×C149C211yesmaximal, characteristic, complemented
16C22×D596—21no—
17C2×D4×D149C2211yescharacteristic
18C2×D4×D149C2211yescharacteristic
19C2×#14558725C2211yescharacteristic, complemented
20C2×#14558725C2211yescharacteristic, complemented
21C2×#14558724C2211yescharacteristic
22C2×#14558719C2211yescharacteristic, complemented
23C2×C8×D149C2211yescharacteristic, complemented
24#18011908C2211yescharacteristic
25#18011906—21no—
26#18011902—21no—
27#18011896—21no—
28#18011891C2211yescharacteristic, complemented
29#18011891C2211yescharacteristic, complemented
30#18011886C2211yescharacteristic
31#18011886C2211yescharacteristic
32#18011885—21no—
33#18011881—21no—
34#18011881—21no—
35C4×Dic298C2211yescharacteristic, complemented
36C4×D596C2211yescharacteristic
37#18011869—21no—
38#18011869C2211yescharacteristic, complemented
39C4⋊C4×D149C2211yescharacteristic, complemented
40#18011844C2211yescharacteristic, complemented
41#18011834C2211yescharacteristic, complemented
42#18011833C2211yescharacteristic, complemented
43#18011833C2211yescharacteristic, complemented
44#18011832C2211yescharacteristic
45#18011831C2211yescharacteristic, complemented
46#18011831C2211yescharacteristic, complemented
47#18011831C2211yescharacteristic, complemented
48#18011831C2211yescharacteristic, complemented
49#18011823C2211yescharacteristic, complemented
50#18011823C2211yescharacteristic, complemented
51#18011822C2211yescharacteristic, complemented
52#125×C149C2211yescharacteristic, complemented
53C4×D4×C149C2211yescharacteristic
54#107×C149C2211yescharacteristic, complemented
55#106×C149C2211yescharacteristic, complemented
56C4⋊C8×C149C2211yescharacteristic, complemented
57#102×C149C2211yescharacteristic
58#102×C149C2211yescharacteristic
59C23×D149—21no—
60C23×D149—21no—
61C2×Dic298C2311yescharacteristic
62C2×D596—21no—
63C2×D596—21no—
64C2×D596—21no—
65C2×D596—21no—
66C2×D596—44no—
67C2×D596D411yescharacteristic
68C2×D596C2311yescharacteristic
69C2×D596C2311yescharacteristic
70C2×C22⋊D149—21no—
71C2×C22⋊D149—21no—
72D4×D149—22no—
73D4×D149—22no—
74D4×D149—41no—
75D4×D149—41no—
76C2×C4×D149—21no—
77C2×C4×D149C2311yescharacteristic
78C2×C4×D149C2311yescharacteristic
79#14558725—41no—
80#14558725—41no—
81#14558724—22no—
82#14558719—41no—
83C2×#11924746C2311yescharacteristic
84C2×#11924746C2311yescharacteristic
85C8×D149—41no—
86C4⋊Dic149—21no—
87C4⋊Dic149—21no—
88C4⋊Dic149D411yescharacteristic
89C4⋊Dic149C2311yescharacteristic
90#14558715—21no—
91#14558715—21no—
92#14558713—21no—
93#14558713—21no—
94#14558713—21no—
95#14558713—21no—
96#14558713—21no—
97#14558713D411yescharacteristic
98#14558713D411yescharacteristic
99C4×Dic149—21no—
100C4×Dic149—21no—
101C2×D4×C149C2311yescharacteristic
102C22×C4×C149—21no—
103C2×C8×C149C2311yescharacteristic
104C2×C8×C149C2311yescharacteristic
105C4⋊C4×C149—21no—
106C4⋊C4×C149—21no—
107C4⋊C4×C149C2311yescharacteristic
108C4⋊C4×C149C2311yescharacteristic
109C4⋊C4×C149C2311yescharacteristic
110C22⋊C4×C149—21no—
111C42×C149C2311yescharacteristic
112C22×D149—21no—
113C22×D149—21no—
114C22×D149—42no—
115C22×D149—42no—
116C22×D149—42no—
117C22×D149—42no—
118C22×D149—81no—
119C22×D149—81no—
120C22×D149C2×D411yescharacteristic
121C22×D149C2×D411yescharacteristic
122Dic298—21no—
123Dic298—21no—
124D596—22no—
125D596—21no—
126D596—21no—
127D596—21no—
128D596—21no—
129D596—42no—
130D596—42no—
131D596—42no—
132D596—81no—
133C22⋊D149—42no—
134C22⋊D149—42no—
135C2×Dic149—21no—
136C2×Dic149—21no—
137C2×Dic149C2×D411yescharacteristic
138C2×Dic149C2×D411yescharacteristic
139C4×D149—21no—
140C4×D149—21no—
141C4×D149—21no—
142C4×D149—21no—
143C4×D149—42no—
144#11924746—21no—
145#11924746—21no—
146C23×C149—21no—
147D4×C149—21no—
148D4×C149#4112yes—
149C2×C4×C149—21no—
150C2×C4×C149—21no—
151C2×C4×C149—21no—
152C2×C4×C149—42no—
153C2×C4×C149C2×D411yescharacteristic
154C2×C4×C149C2×D411yescharacteristic
155C2×C4×C149C2411yescharacteristic
156C8×C149—21no—
157C8×C149—21no—
158C22×C149—22no—
159C22×C149—41no—
160C22×C149—41no—
161C22×C149C22×D411yescharacteristic
162C2×D149—21no—
163C2×D149—21no—
164C2×D149—21no—
165C2×D149—21no—
166C2×D149—21no—
167C2×D149—41no—
168C2×D149—41no—
169C2×D149—41no—
170C2×D149—41no—
171C2×D149—41no—
172C2×D149—41no—
173C2×D149—84no—
174C2×D149—84no—
175C2×D149AGL(1,ℤ/8)12yes—
176C4×C149—21no—
177C4×C149—21no—
178C4×C149—41no—
179C4×C149—41no—
180C4×C149—41no—
181C4×C149C2×#4111yescharacteristic
182C4×C149H(5,𝔽2)11yescharacteristic
183Dic149—21no—
184Dic149—21no—
185Dic149—41no—
186Dic149—41no—
187C2×C149—42no—
188C2×C149#54611yescharacteristic
189C2×C149C2×AGL(1,ℤ/8)11yescharacteristic
190C2×C149#57711yescharacteristic
191D149—22no—
192D149—41no—
193D149—81no—
194D149—81no—
195C149#331011yescharacteristic, complemented, Sylow
196#3310—1491nomaximal, Sylow
197#552—1491no—
198D42—1491no—
199#490—1491no—
200#482—1491no—
201#480—1491no—
202#478D14911yescharacteristic, complemented
203#468—1491no—
204#465—1491no—
205#460—1491no—
206#450—1491no—
207#450—1491no—
208#440—1491no—
209#435—1491no—
210#418—1491no—
211C2×#102—1491no—
212C22×D4—2981no—
213C22×D4—1491no—
214C22×D4—1491no—
215C2×SD16—1491no—
216C2×SD16—1491no—
217C2×SD16—1491no—
218C2×M16—1491no—
219C22×C8—1491no—
220#127—1491no—
221#126—2981no—
222#125—2981no—
223#125C2×D14911yescharacteristic, complemented
224#123—2981no—
225C22⋊Q8—1491no—
226C22⋊Q8—1491no—
227#121—2981no—
228#121—1491no—
229#121—1491no—
230#120—2981no—
231#120—2981no—
232C4×Q8—1491no—
233C4×D4—1491no—
234C4×D4C2×D14911yescharacteristic
235#117—2981no—
236#117—1491no—
237C2×C4⋊C4—1491no—
238#107—1491no—
239#107C2×D14911yescharacteristic, complemented
240#106C2×D14911yescharacteristic, complemented
241C4⋊C8C2×D14911yescharacteristic, complemented
242#103—1491no—
243#102—1491no—
244#102—1491no—
245#102—1491no—
246#102—1491no—
247#102—1491no—
248#102—1491no—
249#102—1491no—
250#102C2×D14911yescharacteristic
251#102C2×D14911yescharacteristic
252C22⋊C8—1491no—
253C22⋊C8—1491no—
254#97—1491no—
255C24—2981no—
256C24—2981no—
257C2×Q8—1491no—
258C2×D4—2981no—
259C2×D4—2981no—
260C2×D4—2982no—
261C2×D4—2982no—
262C2×D4—2981no—
263C2×D4—2981no—
264C2×D4—2981no—
265C2×D4—2981no—
266C2×D4—5964no—
267C2×D4—5961no—
268C2×D4—5961no—
269C2×D4—1491no—
270C2×D4—1491no—
271C2×D4—1491no—
272C2×D4C22×D14911yescharacteristic
273C22×C4—21no—
274C22×C4—2981no—
275C22×C4—1491no—
276C22×C4—1491no—
277SD16—2982no—
278SD16—5961no—
279SD16—5961no—
280M16—5961no—
281C2×C8—5961no—
282C2×C8—1491no—
283C2×C8—1491no—
284C2×C8C22×D14911yescharacteristic
285C2×C8C22×D14911yescharacteristic
286C4⋊C4—21no—
287C4⋊C4—21no—
288C4⋊C4—2981no—
289C4⋊C4—2981no—
290C4⋊C4—2981no—
291C4⋊C4—2981no—
292C4⋊C4—1491no—
293C4⋊C4—1491no—
294C4⋊C4C22×D14911yescharacteristic
295C4⋊C4C22×D14911yescharacteristic
296C4⋊C4C22×D14911yescharacteristic
297C22⋊C4—21no—
298C22⋊C4—2981no—
299C22⋊C4—2981no—
300C22⋊C4—2981no—
301C22⋊C4—2981no—
302C22⋊C4—2981no—
303C22⋊C4—1491no—
304C22⋊C4—1491no—
305C42—2981no—
306C42—2981no—
307C42C22×D14911yescharacteristic
308C23—21no—
309C23—2981no—
310C23—2981no—
311C23—5962no—
312C23—5962no—
313C23—5962no—
314C23—5962no—
315C23—1491no—
316C23—1491no—
317C23—11921no—
318C23—11921no—
319Q8—2981no—
320Q8—2981no—
321D4—21no—
322D4—2982no—
323D4—2981no—
324D4—2981no—
325D4—2981no—
326D4—2981no—
327D4—5962no—
328D4—5962no—
329D4—5962no—
330D4—5962no—
331D4—5962no—
332D4—11921no—
333D4#1455873712yes—
334C2×C4—21no—
335C2×C4—21no—
336C2×C4—21no—
337C2×C4—42no—
338C2×C4—2981no—
339C2×C4—2981no—
340C2×C4—2981no—
341C2×C4—2981no—
342C2×C4—2981no—
343C2×C4—2981no—
344C2×C4—5962no—
345C2×C4—1491no—
346C2×C4—1491no—
347C2×C4D4×D14911yescharacteristic
348C2×C4D4×D14911yescharacteristic
349C2×C4C23×D14911yescharacteristic
350C8—21no—
351C8—21no—
352C8—2981no—
353C8—2981no—
354C22—22no—
355C22—41no—
356C22—41no—
357C22—2981no—
358C22—2981no—
359C22—2981no—
360C22—2981no—
361C22—2981no—
362C22—5961no—
363C22—5961no—
364C22—5961no—
365C22—5961no—
366C22—5961no—
367C22—5961no—
368C22—1492no—
369C22—11924no—
370C22—11924no—
371C22C2×D4×D14911yescharacteristic
372C4—21no—
373C4—21no—
374C4—41no—
375C4—41no—
376C4—41no—
377C4—2981no—
378C4—2981no—
379C4—5961no—
380C4—5961no—
381C4C2×#1455873711yescharacteristic
382C4#1801195711yescharacteristic
383C2—42no—
384C2—2982no—
385C2—5961no—
386C2—11921no—
387C2—11921no—
388C2#2375026611yescharacteristic
389C2AGL(1,ℤ/8)×D14911yescharacteristic
390C2#2375043211yescharacteristic
subgroupG/H
centerC22C2×D4×D149
commutator, cosocleC2×C4×C149C24
FrattiniC2×C4C23×D149
Fitting#478×C149C2
socleC22×C149C22×D4
prime radicalD4×D596C2
hypercenter#478D149
hypocenterC149#3310
LCSG ▷ C2×C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C22 ◁ C42 ◁ #478

Complements

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

NH ≅ G/Ntype
1. #23750313C2semidirect
3. #23749991C2semidirect
4. #23749951C2semidirect
5. #23749940C2semidirect
6. #23749872C2semidirect
7. #23749855C2semidirect
8. #23749826C2semidirect
9. #23749777C2semidirect
10. #23749777C2semidirect
11. #23749725C2semidirect
12. #23749695C2semidirect
13. #23749628C2semidirect
14. #102×D149C2semidirect
15. #478×C149C2semidirect
19. C2×#14558725C22semidirect
20. C2×#14558725C22semidirect
22. C2×#14558719C22semidirect
23. C2×C8×D149C22semidirect
28. #18011891C22semidirect
29. #18011891C22semidirect
35. C4×Dic298C22semidirect
38. #18011869C22semidirect
39. C4⋊C4×D149C22semidirect
40. #18011844C22semidirect
41. #18011834C22semidirect
42. #18011833C22semidirect
43. #18011833C22semidirect
45. #18011831C22semidirect
46. #18011831C22semidirect
47. #18011831C22semidirect
48. #18011831C22semidirect
49. #18011823C22semidirect
50. #18011823C22semidirect
51. #18011822C22semidirect
52. #125×C149C22semidirect
54. #107×C149C22semidirect
55. #106×C149C22semidirect
56. C4⋊C8×C149C22semidirect
195. C149#3310semidirect
202. #478D149semidirect
223. #125C2×D149semidirect
239. #107C2×D149semidirect
240. #106C2×D149semidirect
241. C4⋊C8C2×D149semidirect

Maximal subgroups

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

subgroupindex
#237503132
D4×D5962
#237499912
#237499512
#237499402
#237498722
#237498552
#237498262
#237497772
#237497252
#237496952
#237496282
#102×D1492
#478×C1492
#3310149