Finite Group Databasebeta

← #34056904

Subgroups — #34056904

Order 19072.

402 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#23750313C211yesmaximal, characteristic, complemented
2#23750270C211yesmaximal, characteristic
3#23749982C211yesmaximal, characteristic, complemented
4#23749968C211yesmaximal, characteristic, complemented
5#23749945C211yesmaximal, characteristic, complemented
6#23749884C211yesmaximal, characteristic, complemented
7#23749872C211yesmaximal, characteristic, complemented
8#23749848C211yesmaximal, characteristic, complemented
9#23749788C211yesmaximal, characteristic, complemented
10#23749777C211yesmaximal, characteristic, complemented
11C4×#14558724C211yesmaximal, characteristic, complemented
12#23749702C211yesmaximal, characteristic, complemented
13#23749628C211yesmaximal, characteristic, complemented
14#23749623C211yesmaximal, characteristic, complemented
15#478×C149C211yesmaximal, characteristic, complemented
16C2×#14558735C2211yescharacteristic
17C2×D4×D149C2211yescharacteristic
18C2×Dic596C2211yescharacteristic, complemented
19C2×#14558725C2211yescharacteristic
20C2×#14558724C2211yescharacteristic
21C2×#14558719C2211yescharacteristic
22C2×#14558719C2211yescharacteristic, complemented
23#18011906—21no—
24#18011902—21no—
25#18011899C2211yescharacteristic
26#18011896—21no—
27#18011895—21no—
28#18011891C2211yescharacteristic
29#18011891C2211yescharacteristic
30#18011891C2211yescharacteristic, complemented
31#18011886C2211yescharacteristic
32#18011885—21no—
33#18011881—21no—
34C4×Dic298C2211yescharacteristic, complemented
35C4×D596C2211yescharacteristic
36#18011869—21no—
37#18011869C2211yescharacteristic
38C4⋊C4×D149C2211yescharacteristic, complemented
39C2×#14558713—21no—
40#18011842C2211yescharacteristic, complemented
41#18011836C2211yescharacteristic, complemented
42#18011834C2211yescharacteristic, complemented
43#18011834C2211yescharacteristic, complemented
44#18011834C2211yescharacteristic, complemented
45#18011833C2211yescharacteristic
46#18011832C2211yescharacteristic
47#18011831C2211yescharacteristic
48#18011831C2211yescharacteristic
49#18011823C2211yescharacteristic
50#18011823C2211yescharacteristic, complemented
51C4×#11924746C2211yescharacteristic, 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—
60#14558735—22no—
61#14558735—41no—
62C2×Dic298C2311yescharacteristic
63C2×Dic298C2311yescharacteristic
64C2×D596—21no—
65C2×D596D411yescharacteristic
66C2×D596C2311yescharacteristic
67C2×C22⋊D149—21no—
68C2×C22⋊D149—21no—
69D4×D149—22no—
70D4×D149—41no—
71C22×Dic149—21no—
72C2×C4×D149—21no—
73C2×C4×D149C2311yescharacteristic
74C2×C4×D149C2311yescharacteristic
75Dic596—41no—
76#14558725—41no—
77#14558724—22no—
78#14558719—41no—
79#14558719—41no—
80C2×#11924746C2311yescharacteristic
81C2×#11924746C2311yescharacteristic
82C4⋊Dic149—21no—
83C4⋊Dic149—21no—
84C4⋊Dic149—21no—
85C4⋊Dic149D411yescharacteristic
86C4⋊Dic149C2311yescharacteristic
87#14558715—21no—
88#14558715—21no—
89#14558713—21no—
90#14558713—21no—
91#14558713—21no—
92#14558713—21no—
93#14558713—21no—
94#14558713—21no—
95#14558713—21no—
96#14558713D411yescharacteristic
97#14558713D411yescharacteristic
98C4×Dic149—21no—
99C4×Dic149—21no—
100C2×D4×C149C2311yescharacteristic
101C22×C4×C149—21no—
102C2×C8×C149C2311yescharacteristic
103C2×C8×C149C2311yescharacteristic
104C4⋊C4×C149—21no—
105C4⋊C4×C149—21no—
106C4⋊C4×C149C2311yescharacteristic
107C4⋊C4×C149C2311yescharacteristic
108C4⋊C4×C149C2311yescharacteristic
109C22⋊C4×C149—21no—
110C42×C149C2311yescharacteristic
111C22×D149—21no—
112C22×D149—42no—
113C22×D149—42no—
114C22×D149—81no—
115C22×D149C2×D411yescharacteristic
116C22×D149C2×D411yescharacteristic
117Dic298—21no—
118Dic298—21no—
119Dic298—21no—
120Dic298—21no—
121D596—21no—
122D596—21no—
123D596—41no—
124D596—81no—
125C22⋊D149—42no—
126C22⋊D149—42no—
127C2×Dic149—21no—
128C2×Dic149—21no—
129C2×Dic149—21no—
130C2×Dic149—42no—
131C2×Dic149C2×D411yescharacteristic
132C2×Dic149C2×D411yescharacteristic
133C4×D149—21no—
134C4×D149—21no—
135C4×D149—21no—
136C4×D149—21no—
137C4×D149—42no—
138#11924746—21no—
139#11924746—21no—
140C23×C149—21no—
141D4×C149—21no—
142D4×C149#4112yes—
143C2×C4×C149—21no—
144C2×C4×C149—21no—
145C2×C4×C149—21no—
146C2×C4×C149—81no—
147C2×C4×C149C2×D411yescharacteristic
148C2×C4×C149C2×D411yescharacteristic
149C2×C4×C149C2411yescharacteristic
150C8×C149—21no—
151C8×C149—21no—
152C22×C149—22no—
153C22×C149—41no—
154C22×C149—41no—
155C22×C149C22×D411yescharacteristic
156C2×D149—21no—
157C2×D149—21no—
158C2×D149—21no—
159C2×D149—21no—
160C2×D149—21no—
161C2×D149—21no—
162C2×D149—41no—
163C2×D149—41no—
164C2×D149—41no—
165C2×D149—84no—
166C4×C149—21no—
167C4×C149—21no—
168C4×C149—41no—
169C4×C149—41no—
170C4×C149—41no—
171C4×C149C2×#4111yescharacteristic
172C4×C149H(5,𝔽2)11yescharacteristic
173Dic149—21no—
174Dic149—21no—
175Dic149—41no—
176Dic149—41no—
177Dic149—41no—
178C2×C149—42no—
179C2×C149#54611yescharacteristic
180C2×C149#57511yescharacteristic
181C2×C149#57711yescharacteristic
182D149—41no—
183D149—41no—
184D149—81no—
185C149#332311yescharacteristic, complemented, Sylow
186#3323—1491nomaximal, Sylow
187#552—1491no—
188#546—1491no—
189#488—1491no—
190#485—1491no—
191#481—1491no—
192#478D14911yescharacteristic, complemented
193#470—1491no—
194#468—1491no—
195#464—1491no—
196#452—1491no—
197#450—1491no—
198C4×SD16—1491no—
199#436—1491no—
200#418—1491no—
201#417—1491no—
202C2×#41—1491no—
203C22×D4—1491no—
204C2×Q16—1491no—
205C2×SD16—1491no—
206C2×SD16—1491no—
207C2×M16—1491no—
208C2×M16—1491no—
209#126—2981no—
210#125—2981no—
211#125C2×D14911yescharacteristic, complemented
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×D4C2×D14911yescharacteristic
224#117—2981no—
225#117—1491no—
226C2×C4⋊C4—1491no—
227C2×C22⋊C4—2981no—
228#107C2×D14911yescharacteristic, complemented
229#106—1491no—
230#106C2×D14911yescharacteristic, complemented
231C4⋊C8C2×D14911yescharacteristic, complemented
232#103—1491no—
233#103—1491no—
234#103—1491no—
235#103—1491no—
236#102—1491no—
237#102—1491no—
238#102—1491no—
239#102—1491no—
240#102C2×D14911yescharacteristic
241#102C2×D14911yescharacteristic
242C22⋊C8—1491no—
243C22⋊C8—1491no—
244C4×C8—1491no—
245C24—2981no—
246#41—2982no—
247#41—5961no—
248C2×Q8—1491no—
249C2×Q8—1491no—
250C2×D4—2981no—
251C2×D4—2982no—
252C2×D4—2981no—
253C2×D4—2981no—
254C2×D4—5961no—
255C2×D4—1491no—
256C2×D4—1491no—
257C2×D4C22×D14911yescharacteristic
258C22×C4—21no—
259C22×C4—2981no—
260C22×C4—2981no—
261C22×C4—1491no—
262C22×C4—1491no—
263Q16—5961no—
264SD16—2982no—
265SD16—5961no—
266M16—5961no—
267M16—5961no—
268C2×C8—1491no—
269C2×C8—1491no—
270C2×C8C22×D14911yescharacteristic
271C2×C8C22×D14911yescharacteristic
272C4⋊C4—21no—
273C4⋊C4—21no—
274C4⋊C4—2981no—
275C4⋊C4—2981no—
276C4⋊C4—2981no—
277C4⋊C4—2981no—
278C4⋊C4—2981no—
279C4⋊C4—1491no—
280C4⋊C4—1491no—
281C4⋊C4C22×D14911yescharacteristic
282C4⋊C4C22×D14911yescharacteristic
283C4⋊C4C22×D14911yescharacteristic
284C22⋊C4—21no—
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—
296C42C22×D14911yescharacteristic
297C23—21no—
298C23—2981no—
299C23—5962no—
300C23—5962no—
301C23—1491no—
302C23—1491no—
303C23—11921no—
304Q8—2981no—
305Q8—2981no—
306Q8—2981no—
307Q8—2981no—
308D4—21no—
309D4—2981no—
310D4—2981no—
311D4—5961no—
312D4—5962no—
313D4—5962no—
314D4—11921no—
315D4#1455873712yes—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—81no—
320C2×C4—2981no—
321C2×C4—2981no—
322C2×C4—2981no—
323C2×C4—2981no—
324C2×C4—2981no—
325C2×C4—2981no—
326C2×C4—2981no—
327C2×C4—5962no—
328C2×C4—5962no—
329C2×C4—1491no—
330C2×C4—1491no—
331C2×C4D4×D14911yescharacteristic
332C2×C4D4×D14911yescharacteristic
333C2×C4C23×D14911yescharacteristic
334C8—21no—
335C8—21no—
336C8—2981no—
337C8—2981no—
338C22—22no—
339C22—41no—
340C22—41no—
341C22—2981no—
342C22—2981no—
343C22—2981no—
344C22—2981no—
345C22—2981no—
346C22—2981no—
347C22—5961no—
348C22—5961no—
349C22—5961no—
350C22—11924no—
351C22C2×D4×D14911yescharacteristic
352C4—21no—
353C4—21no—
354C4—41no—
355C4—41no—
356C4—41no—
357C4—2981no—
358C4—2981no—
359C4—5961no—
360C4—5961no—
361C4—5961no—
362C4C2×#1455873711yescharacteristic
363C4#1801195711yescharacteristic
364C2—42no—
365C2—5961no—
366C2—5961no—
367C2—11921no—
368C2#2375026611yescharacteristic
369C2#2375042211yescharacteristic
370C2#2375043511yescharacteristic
subgroupG/H
centerC22C2×D4×D149
commutator, cosocleC2×C4×C149C24
FrattiniC2×C4C23×D149
Fitting#478×C149C2
socleC22×C149C22×D4
prime radical#23750270C2
hypercenter#478D149
hypocenterC149#3323
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. #23749982C2semidirect
4. #23749968C2semidirect
5. #23749945C2semidirect
6. #23749884C2semidirect
7. #23749872C2semidirect
8. #23749848C2semidirect
9. #23749788C2semidirect
10. #23749777C2semidirect
11. C4×#14558724C2semidirect
12. #23749702C2semidirect
13. #23749628C2semidirect
14. #23749623C2semidirect
15. #478×C149C2semidirect
18. C2×Dic596C22semidirect
22. C2×#14558719C22semidirect
30. #18011891C22semidirect
34. C4×Dic298C22semidirect
38. C4⋊C4×D149C22semidirect
40. #18011842C22semidirect
41. #18011836C22semidirect
42. #18011834C22semidirect
43. #18011834C22semidirect
44. #18011834C22semidirect
50. #18011823C22semidirect
51. C4×#11924746C22semidirect
52. #125×C149C22semidirect
54. #107×C149C22semidirect
55. #106×C149C22semidirect
56. C4⋊C8×C149C22semidirect
185. C149#3323semidirect
192. #478D149semidirect
211. #125C2×D149semidirect
228. #107C2×D149semidirect
230. #106C2×D149semidirect
231. C4⋊C8C2×D149semidirect

Maximal subgroups

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

subgroupindex
#237503132
#237502702
#237499822
#237499682
#237499452
#237498842
#237498722
#237498482
#237497882
#237497772
C4×#145587242
#237497022
#237496282
#237496232
#478×C1492
#3323149