Finite Group Databasebeta

← #34080940

Subgroups — #34080940

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#23752896C211yesmaximal, characteristic, complemented
2#23752859C211yesmaximal, characteristic
3#23752565C211yesmaximal, characteristic, complemented
4#23752544C211yesmaximal, characteristic, complemented
5#23752533C211yesmaximal, characteristic, complemented
6#23752511C211yesmaximal, characteristic, complemented
7#23752452C211yesmaximal, characteristic, complemented
8#23752432C211yesmaximal, characteristic, complemented
9#23752372C211yesmaximal, characteristic, complemented
10#23752361C211yesmaximal, characteristic, complemented
11#23752297C211yesmaximal, characteristic, complemented
12C8×C22⋊D151C211yesmaximal, characteristic, complemented
13#23752209C211yesmaximal, characteristic, complemented
14#102×D151C211yesmaximal, characteristic, complemented
15#465×C151C211yesmaximal, characteristic, complemented
16C2×#14559004C2211yescharacteristic
17C2×D4×D151C2211yescharacteristic
18C2×#14558994C2211yescharacteristic, complemented
19C2×#14558991C2211yescharacteristic
20C2×C8×D151C2211yescharacteristic
21#18012732—21no—
22#18012730C2211yescharacteristic, complemented
23#18012729—21no—
24#18012726C2211yescharacteristic
25#18012721—21no—
26#18012721—21no—
27#18012719C2211yescharacteristic
28#18012715C2211yescharacteristic
29#18012710—21no—
30#18012707—21no—
31Q8×Dic151C2211yescharacteristic, complemented
32#18012701C2211yescharacteristic
33C4×C22⋊D151C2211yescharacteristic
34#18012698C2211yescharacteristic, complemented
35#18012697—21no—
36C4⋊C4×D151C2211yescharacteristic
37C22⋊C4×D151—21no—
38#18012672C2211yescharacteristic, complemented
39#18012670C2211yescharacteristic, complemented
40Dic151⋊C8C2211yescharacteristic, complemented
41#18012664C2211yescharacteristic, complemented
42#18012664C2211yescharacteristic, complemented
43#18012662C2211yescharacteristic, complemented
44#18012661C2211yescharacteristic
45#18012661C2211yescharacteristic
46#18012660C2211yescharacteristic
47#18012660C2211yescharacteristic
48#18012659C2211yescharacteristic
49C22⋊(C151⋊C8)C2211yescharacteristic, complemented
50(C2×D151)⋊C8C2211yescharacteristic
51C8×Dic151C2211yescharacteristic, complemented
52C2×SD16×C151C2211yescharacteristic
53C22×C8×C151C2211yescharacteristic, complemented
54C22⋊Q8×C151C2211yescharacteristic, complemented
55#121×C151C2211yescharacteristic
56#106×C151C2211yescharacteristic, complemented
57#103×C151C2211yescharacteristic, complemented
58#102×C151C2211yescharacteristic
59C23×D151—21no—
60#14559004—22no—
61#14559004—41no—
62C2×Dic302C2311yescharacteristic
63C2×D604C2311yescharacteristic
64C2×C22⋊D151—21no—
65C2×C22⋊D151—21no—
66C2×C22⋊D151D411yescharacteristic
67D4×D151—22no—
68D4×D151—41no—
69C2×C4×D151—21no—
70C2×C4×D151—21no—
71C2×C4×D151—21no—
72C2×C4×D151C2311yescharacteristic
73#14558994—41no—
74#14558991—22no—
75C2×C151⋊C8C2311yescharacteristic
76C2×C151⋊C8C2311yescharacteristic
77C8×D151—41no—
78C4⋊Dic151—21no—
79C4⋊Dic151—21no—
80C4⋊Dic151—21no—
81C4⋊Dic151C2311yescharacteristic
82C4⋊Dic151C2311yescharacteristic
83Dic151⋊C4—21no—
84Dic151⋊C4—21no—
85Dic151⋊C4—21no—
86Dic151⋊C4D411yescharacteristic
87C22⋊Dic151—21no—
88C22⋊Dic151—21no—
89C22⋊Dic151—21no—
90C22⋊Dic151D411yescharacteristic
91(C2×D151)⋊C4—21no—
92(C2×D151)⋊C4—21no—
93(C2×D151)⋊C4—21no—
94(C2×D151)⋊C4D411yescharacteristic
95C4×Dic151—21no—
96C4×Dic151—21no—
97C4×Dic151C2311yescharacteristic
98C2×Q8×C151C2311yescharacteristic
99C2×D4×C151—21no—
100C2×D4×C151C2311yescharacteristic
101C22×C4×C151C2311yescharacteristic
102SD16×C151—41no—
103C2×C8×C151—41no—
104C2×C8×C151C2311yescharacteristic
105C2×C8×C151C2311yescharacteristic
106C4⋊C4×C151—21no—
107C4⋊C4×C151C2311yescharacteristic
108C4⋊C4×C151C2311yescharacteristic
109C22⋊C4×C151—21no—
110C22⋊C4×C151—21no—
111C22×D151—21no—
112C22×D151—42no—
113C22×D151—42no—
114C22×D151—81no—
115C22×D151C2×D411yescharacteristic
116Dic302—21no—
117Dic302—21no—
118D604—21no—
119D604#4112yes—
120C22⋊D151—22no—
121C22⋊D151—42no—
122C22⋊D151—42no—
123C2×Dic151—21no—
124C2×Dic151—21no—
125C2×Dic151—21no—
126C2×Dic151C2×D411yescharacteristic
127C2×Dic151C2×D411yescharacteristic
128C2×Dic151C2×D411yescharacteristic
129C4×D151—21no—
130C4×D151—21no—
131C4×D151—42no—
132C4×D151—42no—
133C4×D151—81no—
134C151⋊C8—21no—
135C151⋊C8—21no—
136C23×C151—21no—
137C23×C151C2×D411yescharacteristic
138Q8×C151—21no—
139Q8×C151—21no—
140D4×C151—21no—
141D4×C151—21no—
142D4×C151—81no—
143C2×C4×C151—21no—
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—21no—
155C22×C151—41no—
156C22×C151—41no—
157C22×C151—41no—
158C22×C151C22×D411yescharacteristic
159C2×D151—21no—
160C2×D151—21no—
161C2×D151—22no—
162C2×D151—41no—
163C2×D151—41no—
164C2×D151—84no—
165C2×D151#13512yes—
166C4×C151—21no—
167C4×C151—41no—
168C4×C151—41no—
169C4×C151—41no—
170C4×C151C2×#4111yescharacteristic
171C4×C151H(5,𝔽2)11yescharacteristic
172Dic151—21no—
173Dic151—21no—
174Dic151—21no—
175Dic151—41no—
176Dic151—41no—
177Dic151—41no—
178C2×C151—41no—
179C2×C151—81no—
180C2×C151#54611yescharacteristic
181C2×C151C2×#13511yescharacteristic
182C2×C151#57711yescharacteristic
183D151—22no—
184D151—42no—
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#465D15111yescharacteristic, complemented
195#464—1511no—
196#452—1511no—
197#450—1511no—
198C4×SD16—1511no—
199C8×D4—1511no—
200#416—1511no—
201C2×#102—1511no—
202C2×#41—1511no—
203C22×D4—1511no—
204C2×Q16—1511no—
205C2×SD16—1511no—
206C2×SD16C2×D15111yescharacteristic
207C22×C8—1511no—
208C22×C8C2×D15111yescharacteristic, complemented
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, complemented
218#121—3021no—
219#121C2×D15111yescharacteristic
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#106C2×D15111yescharacteristic, complemented
231C4⋊C8—1511no—
232#103—1511no—
233#103—1511no—
234#103—1511no—
235#103C2×D15111yescharacteristic, complemented
236#102—1511no—
237#102—1511no—
238#102—1511no—
239#102—1511no—
240#102—1511no—
241#102C2×D15111yescharacteristic
242C22⋊C8—1511no—
243C22⋊C8—1511no—
244C4×C8—1511no—
245C24—3021no—
246#41—3022no—
247#41—6041no—
248C2×Q8—1511no—
249C2×Q8C22×D15111yescharacteristic
250C2×D4—21no—
251C2×D4—3022no—
252C2×D4—3021no—
253C2×D4—3021no—
254C2×D4—6041no—
255C2×D4—1511no—
256C2×D4—1511no—
257C2×D4C22×D15111yescharacteristic
258C22×C4—3021no—
259C22×C4—3021no—
260C22×C4—3021no—
261C22×C4—1511no—
262C22×C4C22×D15111yescharacteristic
263Q16—6041no—
264SD16—41no—
265SD16—3022no—
266C2×C8—41no—
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⋊C4C22×D15111yescharacteristic
283C4⋊C4C22×D15111yescharacteristic
284C22⋊C4—21no—
285C22⋊C4—21no—
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—3021no—
299C23—6042no—
300C23—6042no—
301C23—1511no—
302C23—12081no—
303C23D4×D15111yescharacteristic
304Q8—21no—
305Q8—21no—
306Q8—3021no—
307Q8—3021no—
308D4—21no—
309D4—21no—
310D4—81no—
311D4—3022no—
312D4—3021no—
313D4—6042no—
314D4—6042no—
315D4—1512no—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—21no—
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—21no—
341C22—41no—
342C22—41no—
343C22—41no—
344C22—3021no—
345C22—3021no—
346C22—3022no—
347C22—6041no—
348C22—6041no—
349C22—1512no—
350C22—12084no—
351C22C2×D4×D15111yescharacteristic
352C4—21no—
353C4—41no—
354C4—41no—
355C4—41no—
356C4—3021no—
357C4—3021no—
358C4—3021no—
359C4—6041no—
360C4—6041no—
361C4—6041no—
362C4#41×D15111yescharacteristic
363C4#1801278411yescharacteristic
364C2—41no—
365C2—81no—
366C2—3022no—
367C2—6042no—
368C2#2375285111yescharacteristic
369C2#135×D15111yescharacteristic
370C2#2375301811yescharacteristic
subgroupG/H
centerC22C2×D4×D151
commutator, cosocleC2×C4×C151C24
FrattiniC2×C4C23×D151
Fitting#465×C151C2
socleC22×C151C22×D4
prime radical#23752859C2
hypercenter#465D151
hypocenterC151#3296
LCSG ▷ C2×C4×C151 ▷ C2×C151 ▷ C151
UCSC1 ◁ C22 ◁ C22×C4 ◁ #465

Complements

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

NH ≅ G/Ntype
1. #23752896C2semidirect
3. #23752565C2semidirect
4. #23752544C2semidirect
5. #23752533C2semidirect
6. #23752511C2semidirect
7. #23752452C2semidirect
8. #23752432C2semidirect
9. #23752372C2semidirect
10. #23752361C2semidirect
11. #23752297C2semidirect
12. C8×C22⋊D151C2semidirect
13. #23752209C2semidirect
14. #102×D151C2semidirect
15. #465×C151C2semidirect
18. C2×#14558994C22semidirect
22. #18012730C22semidirect
31. Q8×Dic151C22semidirect
34. #18012698C22semidirect
38. #18012672C22semidirect
39. #18012670C22semidirect
40. Dic151⋊C8C22semidirect
41. #18012664C22semidirect
42. #18012664C22semidirect
43. #18012662C22semidirect
49. C22⋊(C151⋊C8)C22semidirect
51. C8×Dic151C22semidirect
53. C22×C8×C151C22semidirect
54. C22⋊Q8×C151C22semidirect
56. #106×C151C22semidirect
57. #103×C151C22semidirect
185. C151#3296semidirect
194. #465D151semidirect
208. C22×C8C2×D151semidirect
217. C22⋊Q8C2×D151semidirect
230. #106C2×D151semidirect
235. #103C2×D151semidirect

Maximal subgroups

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

subgroupindex
#237528962
#237528592
#237525652
#237525442
#237525332
#237525112
#237524522
#237524322
#237523722
#237523612
#237522972
C8×C22⋊D1512
#237522092
#102×D1512
#465×C1512
#3296151