Finite Group Databasebeta

← #34080949

Subgroups — #34080949

Order 19328.

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#23752904C211yesmaximal, characteristic, complemented
2#23752856C211yesmaximal, characteristic
3#23752565C211yesmaximal, characteristic, complemented
4#23752543C211yesmaximal, characteristic, complemented
5#23752535C211yesmaximal, characteristic, complemented
6#23752514C211yesmaximal, characteristic, complemented
7#23752451C211yesmaximal, characteristic, complemented
8#23752438C211yesmaximal, characteristic, complemented
9#23752432C211yesmaximal, characteristic, complemented
10#23752371C211yesmaximal, characteristic, complemented
11SD16×Dic151C211yesmaximal, characteristic, complemented
12(C22⋊D151)⋊C8C211yesmaximal, characteristic, complemented
13#23752205C211yesmaximal, characteristic, complemented
14C2×#18012660C211yesmaximal, characteristic, complemented
15#450×C151C211yesmaximal, characteristic, complemented
16C2×#14559003C2211yescharacteristic
17C2×#14558994C2211yescharacteristic, complemented
18C22×C151⋊C8C2211yescharacteristic
19C2×C8×D151C2211yescharacteristic, complemented
20#18012734—21no—
21#18012730—21no—
22#18012730C2211yescharacteristic, complemented
23#18012726C2211yescharacteristic
24#18012723—21no—
25#18012720—21no—
26#18012718C2211yescharacteristic
27#18012715C2211yescharacteristic, complemented
28#18012711—21no—
29#18012710C2211yescharacteristic
30#18012708—21no—
31Q8×Dic151C2211yescharacteristic, complemented
32D4×Dic151C2211yescharacteristic
33C4×C22⋊D151C2211yescharacteristic
34#18012697C2211yescharacteristic, complemented
35#18012695—21no—
36C2×C4⋊Dic151C2211yescharacteristic
37C2×C22⋊Dic151—21no—
38#18012672C2211yescharacteristic, complemented
39#18012671C2211yescharacteristic, complemented
40#18012671C2211yescharacteristic, complemented
41Dic151⋊C8C2211yescharacteristic, complemented
42#18012664C2211yescharacteristic, complemented
43#18012664C2211yescharacteristic, complemented
44#18012663C2211yescharacteristic, complemented
45#18012662C2211yescharacteristic, complemented
46#18012660C2211yescharacteristic
47#18012660C2211yescharacteristic
48#18012660C2211yescharacteristic
49#18012660C2211yescharacteristic
50(C2×D151)⋊C8C2211yescharacteristic, complemented
51C8×Dic151C2211yescharacteristic, complemented
52C22×D4×C151C2211yescharacteristic
53C2×SD16×C151C2211yescharacteristic
54C2×SD16×C151C2211yescharacteristic
55C22⋊Q8×C151C2211yescharacteristic
56#102×C151C2211yescharacteristic
57#102×C151C2211yescharacteristic
58C22⋊C8×C151C2211yescharacteristic
59#14559003—22no—
60#14559003—41no—
61C2×Dic302C2311yescharacteristic
62C2×C22⋊D151—21no—
63C2×C22⋊D151—21no—
64C2×C22⋊D151D411yescharacteristic
65C22×Dic151—21no—
66C22×Dic151—21no—
67C22×Dic151—21no—
68C2×C4×D151C2311yescharacteristic
69#14558994—41no—
70C2×C151⋊C8—41no—
71C2×C151⋊C8C2311yescharacteristic
72C2×C151⋊C8C2311yescharacteristic
73C8×D151—41no—
74C4⋊Dic151—21no—
75C4⋊Dic151—21no—
76C4⋊Dic151—21no—
77C4⋊Dic151C2311yescharacteristic
78C4⋊Dic151C2311yescharacteristic
79C4⋊Dic151C2311yescharacteristic
80Dic151⋊C4—21no—
81Dic151⋊C4—21no—
82Dic151⋊C4—21no—
83Dic151⋊C4D411yescharacteristic
84C22⋊Dic151—21no—
85C22⋊Dic151—21no—
86C22⋊Dic151—21no—
87C22⋊Dic151—21no—
88C22⋊Dic151—21no—
89C22⋊Dic151D411yescharacteristic
90(C2×D151)⋊C4—21no—
91(C2×D151)⋊C4—21no—
92(C2×D151)⋊C4D411yescharacteristic
93C4×Dic151—21no—
94C4×Dic151—21no—
95C4×Dic151C2311yescharacteristic
96C24×C151—21no—
97C2×Q8×C151C2311yescharacteristic
98C2×D4×C151—22no—
99C2×D4×C151—21no—
100C2×D4×C151—41no—
101C2×D4×C151C2311yescharacteristic
102C2×D4×C151C2311yescharacteristic
103C22×C4×C151C2311yescharacteristic
104SD16×C151—22no—
105SD16×C151—41no—
106C2×C8×C151C2311yescharacteristic
107C2×C8×C151C2311yescharacteristic
108C4⋊C4×C151—21no—
109C4⋊C4×C151C2311yescharacteristic
110C22⋊C4×C151—21no—
111C22×D151C2×D411yescharacteristic
112Dic302—21no—
113Dic302—21no—
114C22⋊D151—22no—
115C22⋊D151—42no—
116C22⋊D151—81no—
117C2×Dic151—21no—
118C2×Dic151—21no—
119C2×Dic151—21no—
120C2×Dic151—21no—
121C2×Dic151—42no—
122C2×Dic151—42no—
123C2×Dic151—81no—
124C2×Dic151C2×D411yescharacteristic
125C2×Dic151C2×D411yescharacteristic
126C2×Dic151C2×D411yescharacteristic
127C4×D151—21no—
128C4×D151—21no—
129C151⋊C8—21no—
130C151⋊C8—21no—
131C23×C151—21no—
132C23×C151—21no—
133C23×C151—42no—
134C23×C151—42no—
135C23×C151—81no—
136C23×C151C2×D411yescharacteristic
137Q8×C151—21no—
138Q8×C151—21no—
139D4×C151—21no—
140D4×C151—21no—
141D4×C151—21no—
142D4×C151—42no—
143D4×C151#4112yes—
144C2×C4×C151—21no—
145C2×C4×C151—21no—
146C2×C4×C151—21no—
147C2×C4×C151—21no—
148C2×C4×C151C2×D411yescharacteristic
149C2×C4×C151C2411yescharacteristic
150C8×C151—21no—
151C8×C151—21no—
152C22×C151—21no—
153C22×C151—21no—
154C22×C151—22no—
155C22×C151—41no—
156C22×C151—41no—
157C22×C151—41no—
158C22×C151—41no—
159C22×C151—41no—
160C22×C151—84no—
161C22×C151#13512yes—
162C22×C151C22×D411yescharacteristic
163C2×D151—21no—
164C2×D151—21no—
165C2×D151—21no—
166C4×C151—21no—
167C4×C151—41no—
168C4×C151—41no—
169C4×C151C2×#4111yescharacteristic
170C4×C151H(5,𝔽2)11yescharacteristic
171Dic151—21no—
172Dic151—21no—
173Dic151—21no—
174Dic151—41no—
175Dic151—41no—
176Dic151—41no—
177Dic151—41no—
178C2×C151—22no—
179C2×C151—42no—
180C2×C151—81no—
181C2×C151#54611yescharacteristic
182C2×C151C2×#13511yescharacteristic
183C2×C151#57711yescharacteristic
184D151—41no—
185C151#329611yescharacteristic, complemented, Sylow
186#3296—1511nomaximal, Sylow
187#552—1511no—
188#546—1511no—
189#488—1511no—
190#483—1511no—
191#482—1511no—
192#478—1511no—
193#467—1511no—
194#465—1511no—
195#464—1511no—
196#452—1511no—
197#450D15111yescharacteristic, complemented
198C4×SD16—1511no—
199C8×D4—1511no—
200#416—1511no—
201C2×#102—1511no—
202C2×#41—1511no—
203C22×D4C2×D15111yescharacteristic
204C2×Q16—1511no—
205C2×SD16C2×D15111yescharacteristic
206C2×SD16C2×D15111yescharacteristic
207C22×C8—1511no—
208C22×C8—1511no—
209#126—3021no—
210#125—3021no—
211#125—1511no—
212#124—1511no—
213#123—3021no—
214#123—3021no—
215C22⋊Q8—1511no—
216C22⋊Q8—1511no—
217C22⋊Q8C2×D15111yescharacteristic
218#121—3021no—
219#121—1511no—
220#120—3021no—
221C4×Q8—1511no—
222C4×D4—1511no—
223C4×D4—1511no—
224#117—3021no—
225#117—1511no—
226C2×C4⋊C4—1511no—
227C2×C22⋊C4—3021no—
228#107—1511no—
229#106—1511no—
230#106—1511no—
231C4⋊C8—1511no—
232#103—1511no—
233#103—1511no—
234#103—1511no—
235#103—1511no—
236#102—1511no—
237#102—1511no—
238#102—1511no—
239#102—1511no—
240#102C2×D15111yescharacteristic
241#102C2×D15111yescharacteristic
242C22⋊C8—1511no—
243C22⋊C8C2×D15111yescharacteristic
244C4×C8—1511no—
245C24—21no—
246#41—3022no—
247#41—6041no—
248C2×Q8—1511no—
249C2×Q8C22×D15111yescharacteristic
250C2×D4—22no—
251C2×D4—21no—
252C2×D4—41no—
253C2×D4—3021no—
254C2×D4—3021no—
255C2×D4—1511no—
256C2×D4C22×D15111yescharacteristic
257C2×D4C22×D15111yescharacteristic
258C22×C4—3021no—
259C22×C4—3021no—
260C22×C4—3021no—
261C22×C4—1511no—
262C22×C4C22×D15111yescharacteristic
263Q16—6041no—
264SD16—22no—
265SD16—41no—
266C2×C8—6041no—
267C2×C8—6041no—
268C2×C8—1511no—
269C2×C8—1511no—
270C2×C8C22×D15111yescharacteristic
271C2×C8C22×D15111yescharacteristic
272C4⋊C4—21no—
273C4⋊C4—3021no—
274C4⋊C4—3021no—
275C4⋊C4—3021no—
276C4⋊C4—3021no—
277C4⋊C4—3021no—
278C4⋊C4—3021no—
279C4⋊C4—1511no—
280C4⋊C4—1511no—
281C4⋊C4—1511no—
282C4⋊C4—1511no—
283C4⋊C4C22×D15111yescharacteristic
284C22⋊C4—21no—
285C22⋊C4—3021no—
286C22⋊C4—3021no—
287C22⋊C4—3021no—
288C22⋊C4—3021no—
289C22⋊C4—3021no—
290C22⋊C4—3021no—
291C22⋊C4—3021no—
292C22⋊C4—1511no—
293C22⋊C4—1511no—
294C42—3021no—
295C42—3021no—
296C42—1511no—
297C23—21no—
298C23—21no—
299C23—42no—
300C23—42no—
301C23—81no—
302C23—1511no—
303C23D4×D15111yescharacteristic
304Q8—21no—
305Q8—21no—
306Q8—3021no—
307Q8—3021no—
308D4—21no—
309D4—21no—
310D4—21no—
311D4—42no—
312D4—3022no—
313D4—6042no—
314D4—12081no—
315D4#1455900312yes—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—3021no—
321C2×C4—3021no—
322C2×C4—3021no—
323C2×C4—3021no—
324C2×C4—3021no—
325C2×C4—3021no—
326C2×C4—6042no—
327C2×C4—6042no—
328C2×C4—1511no—
329C2×C4—1511no—
330C2×C4—1511no—
331C2×C4—12081no—
332C2×C4D4×D15111yescharacteristic
333C2×C4C23×D15111yescharacteristic
334C8—21no—
335C8—21no—
336C8—3021no—
337C8—3021no—
338C22—21no—
339C22—21no—
340C22—22no—
341C22—41no—
342C22—41no—
343C22—41no—
344C22—41no—
345C22—41no—
346C22—84no—
347C22—3021no—
348C22—3021no—
349C22—3021no—
350C22#1801276012yes—
351C22C2×D4×D15111yescharacteristic
352C4—21no—
353C4—41no—
354C4—41no—
355C4—3021no—
356C4—3021no—
357C4—3021no—
358C4—6041no—
359C4—6041no—
360C4—6041no—
361C4—6041no—
362C4C2×#1455900311yescharacteristic
363C4#1801278411yescharacteristic
364C2—22no—
365C2—42no—
366C2—81no—
367C2—6041no—
368C2#2375284911yescharacteristic
369C2C2×#1801276011yescharacteristic
370C2#2375302211yescharacteristic
subgroupG/H
centerC22C2×D4×D151
commutator, cosocleC2×C4×C151C24
FrattiniC2×C4C23×D151
Fitting#450×C151C2
socleC22×C151C22×D4
prime radical#23752856C2
hypercenter#450D151
hypocenterC151#3296
LCSG ▷ C2×C4×C151 ▷ C2×C151 ▷ C151
UCSC1 ◁ C22 ◁ C22×C4 ◁ #450

Complements

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

NH ≅ G/Ntype
1. #23752904C2semidirect
3. #23752565C2semidirect
4. #23752543C2semidirect
5. #23752535C2semidirect
6. #23752514C2semidirect
7. #23752451C2semidirect
8. #23752438C2semidirect
9. #23752432C2semidirect
10. #23752371C2semidirect
11. SD16×Dic151C2semidirect
12. (C22⋊D151)⋊C8C2semidirect
13. #23752205C2semidirect
14. C2×#18012660C2semidirect
15. #450×C151C2semidirect
17. C2×#14558994C22semidirect
19. C2×C8×D151C22semidirect
22. #18012730C22semidirect
27. #18012715C22semidirect
31. Q8×Dic151C22semidirect
34. #18012697C22semidirect
38. #18012672C22semidirect
39. #18012671C22semidirect
40. #18012671C22semidirect
41. Dic151⋊C8C22semidirect
42. #18012664C22semidirect
43. #18012664C22semidirect
44. #18012663C22semidirect
45. #18012662C22semidirect
50. (C2×D151)⋊C8C22semidirect
51. C8×Dic151C22semidirect
185. C151#3296semidirect
197. #450D151semidirect

Maximal subgroups

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

subgroupindex
#237529042
#237528562
#237525652
#237525432
#237525352
#237525142
#237524512
#237524382
#237524322
#237523712
SD16×Dic1512
(C22⋊D151)⋊C82
#237522052
C2×#180126602
#450×C1512
#3296151