Finite Group Databasebeta

← #34056522

Subgroups — #34056522

Order 19072.

408 conjugacy classes of subgroups.

The subgroup lattice has 372 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#23750310C211yesmaximal, characteristic, complemented
2#23750269C211yesmaximal, characteristic
3#23749978C211yesmaximal, characteristic, complemented
4#23749955C211yesmaximal, characteristic, complemented
5#23749947C211yesmaximal, characteristic, complemented
6#23749923C211yesmaximal, characteristic, complemented
7#23749866C211yesmaximal, characteristic, complemented
8#23749853C211yesmaximal, characteristic, complemented
9#23749846C211yesmaximal, characteristic, complemented
10#23749788C211yesmaximal, characteristic, complemented
11#23749776C211yesmaximal, characteristic, complemented
12#23749716C211yesmaximal, characteristic, complemented
13C8×C22⋊D149C211yesmaximal, characteristic, complemented
14#23749618C211yesmaximal, characteristic, complemented
15C2×#102×C149C211yesmaximal, characteristic, complemented
16C2×#14558735C2211yescharacteristic
17C2×Dic596C2211yescharacteristic, complemented
18C2×#14558724C2211yescharacteristic
19C2×#14558724C2211yescharacteristic
20C2×C8×D149C2211yescharacteristic, complemented
21#18011906—21no—
22#18011902C2211yescharacteristic, complemented
23#18011901—21no—
24#18011898C2211yescharacteristic
25#18011894—21no—
26#18011892—21no—
27#18011891C2211yescharacteristic, complemented
28#18011890C2211yescharacteristic
29#18011890C2211yescharacteristic
30#18011883—21no—
31#18011882C2211yescharacteristic
32#18011880—21no—
33#18011876C2211yescharacteristic, complemented
34D4×Dic149C2211yescharacteristic
35C4×C22⋊D149C2211yescharacteristic
36#18011870—21no—
37#18011869C2211yescharacteristic, complemented
38C2×C22⋊Dic149—21no—
39#18011845C2211yescharacteristic, complemented
40#18011842C2211yescharacteristic, complemented
41#18011842C2211yescharacteristic, complemented
42#18011840C2211yescharacteristic, complemented
43#18011836C2211yescharacteristic, complemented
44#18011836C2211yescharacteristic, complemented
45#18011834C2211yescharacteristic, complemented
46#18011834C2211yescharacteristic, complemented
47#18011832C2211yescharacteristic
48#18011832C2211yescharacteristic
49C22⋊#11924746C2211yescharacteristic
50#18011823C2211yescharacteristic, complemented
51C8×Dic149C2211yescharacteristic, complemented
52C22×D4×C149C2211yescharacteristic
53C22×C8×C149C2211yescharacteristic
54C2×C4⋊C4×C149C2211yescharacteristic
55#102×C149C2211yescharacteristic
56#102×C149C2211yescharacteristic
57#102×C149C2211yescharacteristic
58#102×C149C2211yescharacteristic
59#14558735—22no—
60#14558735—41no—
61C2×Dic298C2311yescharacteristic
62C2×Dic298C2311yescharacteristic
63C2×C22⋊D149—21no—
64C2×C22⋊D149—21no—
65C2×C22⋊D149D411yescharacteristic
66C22×Dic149—21no—
67C22×Dic149—21no—
68C2×C4×D149C2311yescharacteristic
69Dic596—41no—
70#14558724—22no—
71#14558724—41no—
72C2×#11924746C2311yescharacteristic
73C2×#11924746C2311yescharacteristic
74C8×D149—41no—
75C4⋊Dic149—21no—
76C4⋊Dic149—21no—
77C4⋊Dic149C2311yescharacteristic
78C4⋊Dic149C2311yescharacteristic
79#14558715—21no—
80#14558715—21no—
81#14558715—21no—
82#14558715—21no—
83#14558715D411yescharacteristic
84C22⋊Dic149—21no—
85C22⋊Dic149—21no—
86C22⋊Dic149—21no—
87C22⋊Dic149—21no—
88C22⋊Dic149—21no—
89C22⋊Dic149—21no—
90C22⋊Dic149D411yescharacteristic
91#14558713—21no—
92#14558713—21no—
93#14558713D411yescharacteristic
94C4×Dic149—21no—
95C4×Dic149—21no—
96C4×Dic149C2311yescharacteristic
97C24×C149—21no—
98C2×D4×C149—22no—
99C2×D4×C149—21no—
100C2×D4×C149—41no—
101C2×D4×C149C2311yescharacteristic
102C2×D4×C149C2311yescharacteristic
103C22×C4×C149—21no—
104C22×C4×C149C2311yescharacteristic
105C2×C8×C149—41no—
106C2×C8×C149C2311yescharacteristic
107C2×C8×C149C2311yescharacteristic
108C4⋊C4×C149—21no—
109C4⋊C4×C149C2311yescharacteristic
110C4⋊C4×C149C2311yescharacteristic
111C22×D149C2×D411yescharacteristic
112Dic298—21no—
113Dic298—21no—
114Dic298—21no—
115Dic298—21no—
116C22⋊D149—22no—
117C22⋊D149—42no—
118C22⋊D149—81no—
119C2×Dic149—21no—
120C2×Dic149—21no—
121C2×Dic149—21no—
122C2×Dic149—21no—
123C2×Dic149—42no—
124C2×Dic149—81no—
125C2×Dic149C2×D411yescharacteristic
126C2×Dic149C2×D411yescharacteristic
127C2×Dic149C2×D411yescharacteristic
128C4×D149—21no—
129C4×D149—21no—
130#11924746—21no—
131#11924746—21no—
132C23×C149—21no—
133C23×C149—21no—
134C23×C149—42no—
135C23×C149—42no—
136C23×C149—81no—
137C23×C149C2×D411yescharacteristic
138D4×C149—21no—
139D4×C149—21no—
140D4×C149—21no—
141D4×C149—42no—
142D4×C149#4112yes—
143C2×C4×C149—21no—
144C2×C4×C149—21no—
145C2×C4×C149—21no—
146C2×C4×C149—21no—
147C2×C4×C149—42no—
148C2×C4×C149C2×D411yescharacteristic
149C2×C4×C149C2411yescharacteristic
150C8×C149—21no—
151C8×C149—21no—
152C22×C149—21no—
153C22×C149—21no—
154C22×C149—22no—
155C22×C149—41no—
156C22×C149—41no—
157C22×C149—41no—
158C22×C149—41no—
159C22×C149—41no—
160C22×C149—84no—
161C22×C149#13512yes—
162C22×C149C22×D411yescharacteristic
163C2×D149—21no—
164C2×D149—21no—
165C2×D149—21no—
166C4×C149—21no—
167C4×C149—41no—
168C4×C149—41no—
169C4×C149C2×#4111yescharacteristic
170C4×C149H(5,𝔽2)11yescharacteristic
171Dic149—21no—
172Dic149—21no—
173Dic149—21no—
174Dic149—41no—
175Dic149—41no—
176Dic149—41no—
177Dic149—41no—
178C2×C149—22no—
179C2×C149—42no—
180C2×C149—81no—
181C2×C149#54611yescharacteristic
182C2×C149C2×#13511yescharacteristic
183C2×C149#57711yescharacteristic
184D149—41no—
185C149#329611yescharacteristic, complemented, Sylow
186#3296—1491nomaximal, Sylow
187#552—1491no—
188#546—1491no—
189#488—1491no—
190#483—1491no—
191#482—1491no—
192#478—1491no—
193#467—1491no—
194#465—1491no—
195#464—1491no—
196#452—1491no—
197#450—1491no—
198C4×SD16—1491no—
199C8×D4—1491no—
200#416—1491no—
201C2×#102D14911yescharacteristic, complemented
202C2×#41—1491no—
203C22×D4C2×D14911yescharacteristic
204C2×Q16—1491no—
205C2×SD16—1491no—
206C2×SD16—1491no—
207C22×C8—1491no—
208C22×C8C2×D14911yescharacteristic
209#126—2981no—
210#125—2981no—
211#125—1491no—
212#124—1491no—
213#123—2981no—
214#123—2981no—
215C22⋊Q8—1491no—
216C22⋊Q8—1491no—
217C22⋊Q8—1491no—
218#121—2981no—
219#121—1491no—
220#120—2981no—
221C4×Q8—1491no—
222C4×D4—1491no—
223C4×D4—1491no—
224#117—2981no—
225#117—1491no—
226C2×C4⋊C4C2×D14911yescharacteristic
227C2×C22⋊C4—2981no—
228#107—1491no—
229#106—1491no—
230#106—1491no—
231C4⋊C8—1491no—
232#103—1491no—
233#103—1491no—
234#103—1491no—
235#103—1491no—
236#102—1491no—
237#102—1491no—
238#102C2×D14911yescharacteristic
239#102C2×D14911yescharacteristic
240#102C2×D14911yescharacteristic
241#102C2×D14911yescharacteristic
242C22⋊C8—1491no—
243C22⋊C8—1491no—
244C4×C8—1491no—
245C24—21no—
246#41—2982no—
247#41—5961no—
248C2×Q8—1491no—
249C2×Q8—1491no—
250C2×D4—22no—
251C2×D4—21no—
252C2×D4—41no—
253C2×D4—2981no—
254C2×D4—2981no—
255C2×D4—1491no—
256C2×D4C22×D14911yescharacteristic
257C2×D4C22×D14911yescharacteristic
258C22×C4—21no—
259C22×C4—2981no—
260C22×C4—2981no—
261C22×C4—1491no—
262C22×C4C22×D14911yescharacteristic
263Q16—5961no—
264SD16—2982no—
265SD16—5961no—
266C2×C8—41no—
267C2×C8—5961no—
268C2×C8—1491no—
269C2×C8—1491no—
270C2×C8C22×D14911yescharacteristic
271C2×C8C22×D14911yescharacteristic
272C4⋊C4—21no—
273C4⋊C4—2981no—
274C4⋊C4—2981no—
275C4⋊C4—2981no—
276C4⋊C4—2981no—
277C4⋊C4—2981no—
278C4⋊C4—2981no—
279C4⋊C4—1491no—
280C4⋊C4—1491no—
281C4⋊C4—1491no—
282C4⋊C4C22×D14911yescharacteristic
283C4⋊C4C22×D14911yescharacteristic
284C22⋊C4—2981no—
285C22⋊C4—2981no—
286C22⋊C4—2981no—
287C22⋊C4—2981no—
288C22⋊C4—2981no—
289C22⋊C4—2981no—
290C22⋊C4—2981no—
291C22⋊C4—2981no—
292C22⋊C4—1491no—
293C22⋊C4—1491no—
294C42—2981no—
295C42—2981no—
296C42—1491no—
297C23—21no—
298C23—21no—
299C23—42no—
300C23—42no—
301C23—81no—
302C23—1491no—
303C23D4×D14911yescharacteristic
304Q8—2981no—
305Q8—2981no—
306Q8—2981no—
307Q8—2981no—
308D4—21no—
309D4—21no—
310D4—21no—
311D4—42no—
312D4—2982no—
313D4—5962no—
314D4—11921no—
315D4#1455873612yes—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—42no—
321C2×C4—2981no—
322C2×C4—2981no—
323C2×C4—2981no—
324C2×C4—2981no—
325C2×C4—2981no—
326C2×C4—2981no—
327C2×C4—5962no—
328C2×C4—1491no—
329C2×C4—1491no—
330C2×C4—1491no—
331C2×C4—11921no—
332C2×C4D4×D14911yescharacteristic
333C2×C4C23×D14911yescharacteristic
334C8—21no—
335C8—21no—
336C8—2981no—
337C8—2981no—
338C22—21no—
339C22—21no—
340C22—22no—
341C22—41no—
342C22—41no—
343C22—41no—
344C22—41no—
345C22—41no—
346C22—84no—
347C22—2981no—
348C22—2981no—
349C22—2981no—
350C22#1801193012yes—
351C22C2×D4×D14911yescharacteristic
352C4—21no—
353C4—41no—
354C4—41no—
355C4—2981no—
356C4—2981no—
357C4—2981no—
358C4—5961no—
359C4—5961no—
360C4—5961no—
361C4—5961no—
362C4C2×#1455873611yescharacteristic
363C4#1801195611yescharacteristic
364C2—22no—
365C2—42no—
366C2—81no—
367C2—5961no—
368C2#2375026511yescharacteristic
369C2C2×#1801193011yescharacteristic
370C2#2375043111yescharacteristic
subgroupG/H
centerC22C2×D4×D149
commutator, cosocleC2×C4×C149C24
FrattiniC2×C4C23×D149
FittingC2×#102×C149C2
socleC22×C149C22×D4
prime radical#23750269C2
hypercenterC2×#102D149
hypocenterC149#3296
LCSG ▷ C2×C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#102

Complements

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

NH ≅ G/Ntype
1. #23750310C2semidirect
3. #23749978C2semidirect
4. #23749955C2semidirect
5. #23749947C2semidirect
6. #23749923C2semidirect
7. #23749866C2semidirect
8. #23749853C2semidirect
9. #23749846C2semidirect
10. #23749788C2semidirect
11. #23749776C2semidirect
12. #23749716C2semidirect
13. C8×C22⋊D149C2semidirect
14. #23749618C2semidirect
15. C2×#102×C149C2semidirect
17. C2×Dic596C22semidirect
20. C2×C8×D149C22semidirect
22. #18011902C22semidirect
27. #18011891C22semidirect
33. #18011876C22semidirect
37. #18011869C22semidirect
39. #18011845C22semidirect
40. #18011842C22semidirect
41. #18011842C22semidirect
42. #18011840C22semidirect
43. #18011836C22semidirect
44. #18011836C22semidirect
45. #18011834C22semidirect
46. #18011834C22semidirect
50. #18011823C22semidirect
51. C8×Dic149C22semidirect
185. C149#3296semidirect
201. C2×#102D149semidirect

Maximal subgroups

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

subgroupindex
#237503102
#237502692
#237499782
#237499552
#237499472
#237499232
#237498662
#237498532
#237498462
#237497882
#237497762
#237497162
C8×C22⋊D1492
#237496182
C2×#102×C1492
#3296149