Finite Group Databasebeta

← #34056905

Subgroups — #34056905

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#23750314C211yesmaximal, characteristic, complemented
2#23750266C211yesmaximal, characteristic
3#23749981C211yesmaximal, characteristic, complemented
4#23749945C211yesmaximal, characteristic, complemented
5#23749928C211yesmaximal, characteristic, complemented
6#23749881C211yesmaximal, characteristic, complemented
7#23749872C211yesmaximal, characteristic, complemented
8#23749850C211yesmaximal, characteristic, complemented
9#23749790C211yesmaximal, characteristic, complemented
10#23749778C211yesmaximal, characteristic, complemented
11#23749712C211yesmaximal, characteristic, complemented
12#23749700C211yesmaximal, characteristic, complemented
13#23749629C211yesmaximal, characteristic, complemented
14#23749625C211yesmaximal, characteristic, complemented
15#485×C149C211yesmaximal, characteristic, complemented
16C2×#14558737C2211yescharacteristic
17C22×D596C2211yescharacteristic
18C2×#14558726C2211yescharacteristic, complemented
19C2×#14558725C2211yescharacteristic
20C2×#14558725C2211yescharacteristic
21C2×#14558720C2211yescharacteristic
22C2×#14558719C2211yescharacteristic, complemented
23#18011904—21no—
24#18011903—21no—
25#18011902C2211yescharacteristic, complemented
26#18011900C2211yescharacteristic
27#18011896—21no—
28#18011893—21no—
29#18011891C2211yescharacteristic, complemented
30#18011890C2211yescharacteristic
31#18011886—21no—
32#18011886C2211yescharacteristic
33#18011881—21no—
34#18011876C2211yescharacteristic, complemented
35#18011873C2211yescharacteristic
36C4×C22⋊D149C2211yescharacteristic
37#18011868—21no—
38C4⋊C4×D149C2211yescharacteristic, complemented
39C22⋊C4×D149—21no—
40#18011842C2211yescharacteristic, complemented
41#18011840C2211yescharacteristic, complemented
42#18011835C2211yescharacteristic, complemented
43#18011834C2211yescharacteristic, complemented
44#18011833C2211yescharacteristic
45#18011833C2211yescharacteristic
46#18011831C2211yescharacteristic
47#18011831C2211yescharacteristic
48#18011831C2211yescharacteristic
49#18011831C2211yescharacteristic
50#18011823C2211yescharacteristic, complemented
51C8×Dic149C2211yescharacteristic, complemented
52C22⋊Q8×C149C2211yescharacteristic
53#117×C149C2211yescharacteristic
54#107×C149C2211yescharacteristic, complemented
55#106×C149C2211yescharacteristic, complemented
56#103×C149C2211yescharacteristic, complemented
57#103×C149C2211yescharacteristic, complemented
58C22⋊C8×C149C2211yescharacteristic
59C23×D149—21no—
60#14558737—22no—
61#14558737—41no—
62C2×Dic298C2311yescharacteristic
63C2×D596—22no—
64C2×D596—21no—
65C2×D596—21no—
66C2×D596—21no—
67C2×D596—41no—
68C2×D596C2311yescharacteristic
69C2×D596C2311yescharacteristic
70C2×C22⋊D149D411yescharacteristic
71C2×C4×D149—21no—
72C2×C4×D149—21no—
73C2×C4×D149—21no—
74C2×C4×D149C2311yescharacteristic
75#14558726—41no—
76#14558725—22no—
77#14558725—41no—
78#14558720—41no—
79#14558719—41no—
80C2×#11924746C2311yescharacteristic
81C2×#11924746C2311yescharacteristic
82C4⋊Dic149—21no—
83C4⋊Dic149—21no—
84C4⋊Dic149C2311yescharacteristic
85#14558715—21no—
86#14558715—21no—
87#14558715—21no—
88#14558715—21no—
89#14558715D411yescharacteristic
90C22⋊Dic149—21no—
91C22⋊Dic149D411yescharacteristic
92#14558713—21no—
93#14558713—21no—
94#14558713—21no—
95#14558713—21no—
96#14558713—21no—
97#14558713D411yescharacteristic
98C4×Dic149—21no—
99C4×Dic149C2311yescharacteristic
100C2×Q8×C149C2311yescharacteristic
101C22×C4×C149C2311yescharacteristic
102C2×C8×C149C2311yescharacteristic
103C2×C8×C149C2311yescharacteristic
104C4⋊C4×C149—21no—
105C4⋊C4×C149C2311yescharacteristic
106C4⋊C4×C149C2311yescharacteristic
107C4⋊C4×C149C2311yescharacteristic
108C22⋊C4×C149—21no—
109C22⋊C4×C149—21no—
110C42×C149—21no—
111C22×D149—21no—
112C22×D149—21no—
113C22×D149—42no—
114C22×D149—42no—
115C22×D149—81no—
116C22×D149C2×D411yescharacteristic
117Dic298—21no—
118Dic298—21no—
119D596—21no—
120D596—21no—
121D596—21no—
122D596—42no—
123D596—42no—
124D596—81no—
125D596#4112yes—
126C22⋊D149—41no—
127C2×Dic149—21no—
128C2×Dic149—21no—
129C2×Dic149C2×D411yescharacteristic
130C2×Dic149C2×D411yescharacteristic
131C2×Dic149C2×D411yescharacteristic
132C4×D149—21no—
133C4×D149—21no—
134C4×D149—42no—
135C4×D149—42no—
136C4×D149—81no—
137#11924746—21no—
138#11924746—21no—
139C23×C149C2×D411yescharacteristic
140Q8×C149—21no—
141Q8×C149—21no—
142C2×C4×C149—21no—
143C2×C4×C149—21no—
144C2×C4×C149—21no—
145C2×C4×C149—21no—
146C2×C4×C149—21no—
147C2×C4×C149—21no—
148C2×C4×C149C2×D411yescharacteristic
149C2×C4×C149C2411yescharacteristic
150C8×C149—21no—
151C8×C149—21no—
152C22×C149—21no—
153C22×C149—21no—
154C22×C149—21no—
155C22×C149C22×D411yescharacteristic
156C2×D149—21no—
157C2×D149—22no—
158C2×D149—21no—
159C2×D149—21no—
160C2×D149—41no—
161C2×D149—41no—
162C2×D149—41no—
163C2×D149—41no—
164C2×D149—41no—
165C2×D149—84no—
166C4×C149—21no—
167C4×C149—41no—
168C4×C149—41no—
169C4×C149—41no—
170C4×C149—41no—
171C4×C149C2×#4111yescharacteristic
172C4×C149H(5,𝔽2)11yescharacteristic
173Dic149—21no—
174Dic149—21no—
175Dic149—21no—
176Dic149—41no—
177Dic149—41no—
178C2×C149—41no—
179C2×C149#54611yescharacteristic
180C2×C149#57511yescharacteristic
181C2×C149#57711yescharacteristic
182D149—41no—
183D149—42no—
184D149—81no—
185C149#332311yescharacteristic, complemented, Sylow
186#3323—1491nomaximal, Sylow
187#552—1491no—
188#546—1491no—
189#488—1491no—
190#485D14911yescharacteristic, complemented
191#481—1491no—
192#478—1491no—
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#125—1491no—
212#124—1491no—
213#123—2981no—
214#123—2981no—
215C22⋊Q8—1491no—
216C22⋊Q8—1491no—
217C22⋊Q8C2×D14911yescharacteristic
218#121—2981no—
219#121—1491no—
220#120—2981no—
221C4×Q8—1491no—
222C4×D4—1491no—
223C4×D4—1491no—
224#117—2981no—
225#117C2×D14911yescharacteristic
226C2×C4⋊C4—1491no—
227C2×C22⋊C4—2981no—
228#107C2×D14911yescharacteristic, complemented
229#106—1491no—
230#106C2×D14911yescharacteristic, complemented
231C4⋊C8—1491no—
232#103—1491no—
233#103—1491no—
234#103C2×D14911yescharacteristic, complemented
235#103C2×D14911yescharacteristic, complemented
236#102—1491no—
237#102—1491no—
238#102—1491no—
239#102—1491no—
240#102—1491no—
241#102—1491no—
242C22⋊C8—1491no—
243C22⋊C8C2×D14911yescharacteristic
244C4×C8—1491no—
245C24—2981no—
246#41—2982no—
247#41—5961no—
248C2×Q8—1491no—
249C2×Q8C22×D14911yescharacteristic
250C2×D4—2982no—
251C2×D4—2981no—
252C2×D4—2981no—
253C2×D4—2981no—
254C2×D4—5961no—
255C2×D4—1491no—
256C2×D4—1491no—
257C2×D4—1491no—
258C22×C4—2981no—
259C22×C4—2981no—
260C22×C4—2981no—
261C22×C4—1491no—
262C22×C4C22×D14911yescharacteristic
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—2981no—
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—21no—
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—21no—
295C42—2981no—
296C42—1491no—
297C23—2981no—
298C23—2981no—
299C23—5962no—
300C23—5962no—
301C23—1491no—
302C23—11921no—
303C23D4×D14911yescharacteristic
304Q8—21no—
305Q8—21no—
306Q8—2981no—
307Q8—2981no—
308D4—2981no—
309D4—2981no—
310D4—2981no—
311D4—5962no—
312D4—5962no—
313D4—5961no—
314D4—1492no—
315D4—11921no—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—21no—
322C2×C4—2981no—
323C2×C4—2981no—
324C2×C4—2981no—
325C2×C4—2981no—
326C2×C4—5962no—
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—21no—
341C22—2981no—
342C22—2981no—
343C22—2981no—
344C22—2982no—
345C22—5961no—
346C22—5961no—
347C22—5961no—
348C22—5961no—
349C22—5961no—
350C22—11924no—
351C22C2×D4×D14911yescharacteristic
352C4—21no—
353C4—41no—
354C4—41no—
355C4—41no—
356C4—41no—
357C4—2981no—
358C4—2981no—
359C4—2981no—
360C4—5961no—
361C4—5961no—
362C4#41×D14911yescharacteristic
363C4#1801195711yescharacteristic
364C2—41no—
365C2—5961no—
366C2—5962no—
367C2—11921no—
368C2#2375026711yescharacteristic
369C2#2375042411yescharacteristic
370C2#2375043211yescharacteristic
subgroupG/H
centerC22C2×D4×D149
commutator, cosocleC2×C4×C149C24
FrattiniC2×C4C23×D149
Fitting#485×C149C2
socleC22×C149C22×D4
prime radical#23750266C2
hypercenter#485D149
hypocenterC149#3323
LCSG ▷ C2×C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C22 ◁ C22×C4 ◁ #485

Complements

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

NH ≅ G/Ntype
1. #23750314C2semidirect
3. #23749981C2semidirect
4. #23749945C2semidirect
5. #23749928C2semidirect
6. #23749881C2semidirect
7. #23749872C2semidirect
8. #23749850C2semidirect
9. #23749790C2semidirect
10. #23749778C2semidirect
11. #23749712C2semidirect
12. #23749700C2semidirect
13. #23749629C2semidirect
14. #23749625C2semidirect
15. #485×C149C2semidirect
18. C2×#14558726C22semidirect
22. C2×#14558719C22semidirect
25. #18011902C22semidirect
29. #18011891C22semidirect
34. #18011876C22semidirect
38. C4⋊C4×D149C22semidirect
40. #18011842C22semidirect
41. #18011840C22semidirect
42. #18011835C22semidirect
43. #18011834C22semidirect
50. #18011823C22semidirect
51. C8×Dic149C22semidirect
54. #107×C149C22semidirect
55. #106×C149C22semidirect
56. #103×C149C22semidirect
57. #103×C149C22semidirect
185. C149#3323semidirect
190. #485D149semidirect
228. #107C2×D149semidirect
230. #106C2×D149semidirect
234. #103C2×D149semidirect
235. #103C2×D149semidirect

Maximal subgroups

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

subgroupindex
#237503142
#237502662
#237499812
#237499452
#237499282
#237498812
#237498722
#237498502
#237497902
#237497782
#237497122
#237497002
#237496292
#237496252
#485×C1492
#3323149