Finite Group Databasebeta

← #34056903

Subgroups — #34056903

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#23750269C211yesmaximal, characteristic
3#23749978C211yesmaximal, characteristic, complemented
4#23749966C211yesmaximal, characteristic, complemented
5#23749942C211yesmaximal, characteristic, complemented
6#23749927C211yesmaximal, characteristic, complemented
7#23749883C211yesmaximal, characteristic, complemented
8#23749870C211yesmaximal, characteristic, complemented
9#23749846C211yesmaximal, characteristic, complemented
10#23749788C211yesmaximal, characteristic, complemented
11#23749776C211yesmaximal, characteristic, complemented
12#23749716C211yesmaximal, characteristic, complemented
13#23749701C211yesmaximal, characteristic, complemented
14#23749623C211yesmaximal, characteristic, complemented
15#418×C149C211yesmaximal, characteristic, complemented
16C2×#14558735C2211yescharacteristic
17C2×Dic596C2211yescharacteristic, complemented
18C2×#14558724C2211yescharacteristic
19C2×#14558724C2211yescharacteristic
20C2×#14558719C2211yescharacteristic, complemented
21#18011904—21no—
22#18011903—21no—
23#18011902C2211yescharacteristic, complemented
24#18011898C2211yescharacteristic
25#18011893—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#18011868—21no—
37C4⋊C4×D149C2211yescharacteristic, complemented
38C2×C22⋊Dic149—21no—
39#18011844C2211yescharacteristic, complemented
40#18011843C2211yescharacteristic, 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
53C2×M16×C149C2211yescharacteristic
54#117×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×D149—21no—
69C2×C4×D149C2311yescharacteristic
70Dic596—41no—
71#14558724—22no—
72#14558724—41no—
73#14558719—41no—
74C2×#11924746C2311yescharacteristic
75C2×#11924746C2311yescharacteristic
76C4⋊Dic149—21no—
77C4⋊Dic149—21no—
78C4⋊Dic149C2311yescharacteristic
79C4⋊Dic149C2311yescharacteristic
80#14558715—21no—
81#14558715—21no—
82#14558715—21no—
83#14558715—21no—
84#14558715—21no—
85#14558715D411yescharacteristic
86C22⋊Dic149—21no—
87C22⋊Dic149—21no—
88C22⋊Dic149—21no—
89C22⋊Dic149—21no—
90C22⋊Dic149—21no—
91C22⋊Dic149—21no—
92C22⋊Dic149D411yescharacteristic
93#14558713—21no—
94#14558713D411yescharacteristic
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×C149C2311yescharacteristic
104M16×C149—41no—
105C2×C8×C149C2311yescharacteristic
106C2×C8×C149C2311yescharacteristic
107C4⋊C4×C149C2311yescharacteristic
108C4⋊C4×C149C2311yescharacteristic
109C22⋊C4×C149—21no—
110C42×C149—21no—
111C22×D149C2×D411yescharacteristic
112Dic298—21no—
113Dic298—21no—
114Dic298—21no—
115Dic298—21no—
116C22⋊D149—41no—
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—
130C4×D149—42no—
131#11924746—21no—
132#11924746—21no—
133C23×C149—21no—
134C23×C149—21no—
135C23×C149—42no—
136C23×C149—42no—
137C23×C149—81no—
138C23×C149C2×D411yescharacteristic
139D4×C149—21no—
140D4×C149—21no—
141D4×C149—21no—
142D4×C149—42no—
143D4×C149#4112yes—
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—22no—
154C22×C149—21no—
155C22×C149—21no—
156C22×C149—41no—
157C22×C149—41no—
158C22×C149—41no—
159C22×C149—41no—
160C22×C149—41no—
161C22×C149—84no—
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—41no—
179C2×C149—42no—
180C2×C149—81no—
181C2×C149#54611yescharacteristic
182C2×C149#57511yescharacteristic
183C2×C149#57711yescharacteristic
184D149—41no—
185C149#332311yescharacteristic, complemented, Sylow
186#3323—1491nomaximal, Sylow
187#552—1491no—
188#546—1491no—
189#488—1491no—
190#485—1491no—
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#418D14911yescharacteristic, complemented
201#417—1491no—
202C2×#41—1491no—
203C22×D4C2×D14911yescharacteristic
204C2×Q16—1491no—
205C2×SD16—1491no—
206C2×SD16—1491no—
207C2×M16—1491no—
208C2×M16C2×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#117C2×D14911yescharacteristic
226C2×C4⋊C4—1491no—
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—2981no—
259C22×C4—2981no—
260C22×C4—2981no—
261C22×C4—1491no—
262C22×C4C22×D14911yescharacteristic
263Q16—5961no—
264SD16—2982no—
265SD16—5961no—
266M16—41no—
267M16—5961no—
268C2×C8—1491no—
269C2×C8—1491no—
270C2×C8C22×D14911yescharacteristic
271C2×C8C22×D14911yescharacteristic
272C4⋊C4—2981no—
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—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—21no—
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—5961no—
313D4—5962no—
314D4—11921no—
315D4#1455873612yes—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—2981no—
321C2×C4—2981no—
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—22no—
342C22—41no—
343C22—41no—
344C22—41no—
345C22—41no—
346C22—41no—
347C22—84no—
348C22—2981no—
349C22—2981no—
350C22—2981no—
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—41no—
365C2—42no—
366C2—81no—
367C2—5961no—
368C2#2375026511yescharacteristic
369C2#2375042111yescharacteristic
370C2#2375043511yescharacteristic
subgroupG/H
centerC22C2×D4×D149
commutator, cosocleC2×C4×C149C24
FrattiniC2×C4C23×D149
Fitting#418×C149C2
socleC22×C149C22×D4
prime radical#23750269C2
hypercenter#418D149
hypocenterC149#3323
LCSG ▷ C2×C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C22 ◁ C22×C4 ◁ #418

Complements

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

NH ≅ G/Ntype
1. #23750314C2semidirect
3. #23749978C2semidirect
4. #23749966C2semidirect
5. #23749942C2semidirect
6. #23749927C2semidirect
7. #23749883C2semidirect
8. #23749870C2semidirect
9. #23749846C2semidirect
10. #23749788C2semidirect
11. #23749776C2semidirect
12. #23749716C2semidirect
13. #23749701C2semidirect
14. #23749623C2semidirect
15. #418×C149C2semidirect
17. C2×Dic596C22semidirect
20. C2×#14558719C22semidirect
23. #18011902C22semidirect
27. #18011891C22semidirect
33. #18011876C22semidirect
37. C4⋊C4×D149C22semidirect
39. #18011844C22semidirect
40. #18011843C22semidirect
41. #18011842C22semidirect
42. #18011840C22semidirect
43. #18011836C22semidirect
44. #18011836C22semidirect
45. #18011834C22semidirect
46. #18011834C22semidirect
50. #18011823C22semidirect
51. C8×Dic149C22semidirect
185. C149#3323semidirect
200. #418D149semidirect

Maximal subgroups

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

subgroupindex
#237503142
#237502692
#237499782
#237499662
#237499422
#237499272
#237498832
#237498702
#237498462
#237497882
#237497762
#237497162
#237497012
#237496232
#418×C1492
#3323149