Finite Group Databasebeta

← #34079297

Subgroups — #34079297

Order 19328.

406 conjugacy classes of subgroups.

The subgroup lattice has 364 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#23752835C211yesmaximal, characteristic, complemented
2#23752686C211yesmaximal, characteristic, complemented
3#23752536C211yesmaximal, characteristic, complemented
4#23752501C211yesmaximal, characteristic, complemented
5#23752491C211yesmaximal, characteristic, complemented
6#23752430C211yesmaximal, characteristic, complemented
7#23752430C211yesmaximal, characteristic, complemented
8#23752362C211yesmaximal, characteristic, complemented
9#23752348C211yesmaximal, characteristic
10#23752323C211yesmaximal, characteristic, complemented
11#23752315C211yesmaximal, characteristic, complemented
12#23752297C211yesmaximal, characteristic, complemented
13#23752294C211yesmaximal, characteristic, complemented
14#23752270C211yesmaximal, characteristic, complemented
15#485×C151C211yesmaximal, characteristic, complemented
16C22×D604C2211yescharacteristic
17C2×#14558991C2211yescharacteristic
18C2×#14558991C2211yescharacteristic
19C2×D1208C2211yescharacteristic
20C2×D1208C2211yescharacteristic
21#18012738C2211yescharacteristic, complemented
22#18012734—21no—
23#18012728C2211yescharacteristic, complemented
24#18012725—21no—
25#18012721—21no—
26#18012719—21no—
27#18012713C2211yescharacteristic
28Q8×Dic151C2211yescharacteristic, complemented
29C4×D604—21no—
30C4×D604—21no—
31#18012701C2211yescharacteristic
32#18012701C2211yescharacteristic
33#18012701C2211yescharacteristic
34#18012701C2211yescharacteristic
35#18012701C2211yescharacteristic, complemented
36#18012698C2211yescharacteristic
37C22⋊C4×D151—21no—
38C22⋊C4×D151—21no—
39#18012672C2211yescharacteristic, complemented
40#18012670C2211yescharacteristic, complemented
41Dic151⋊C8C2211yescharacteristic, complemented
42Dic151⋊C8C2211yescharacteristic, complemented
43#18012661C2211yescharacteristic
44#18012661C2211yescharacteristic
45#18012659C2211yescharacteristic
46#18012659C2211yescharacteristic
47#18012659C2211yescharacteristic, complemented
48#18012659C2211yescharacteristic, complemented
49C22⋊(C151⋊C8)C2211yescharacteristic
50#18012649C2211yescharacteristic, complemented
51C8×Dic151C2211yescharacteristic, complemented
52C22⋊Q8×C151C2211yescharacteristic
53#117×C151C2211yescharacteristic
54#107×C151C2211yescharacteristic, complemented
55#106×C151C2211yescharacteristic, complemented
56#103×C151C2211yescharacteristic, complemented
57#103×C151C2211yescharacteristic, complemented
58C22⋊C8×C151C2211yescharacteristic
59C23×D151—21no—
60C2×Dic302—21no—
61C2×D604—22no—
62C2×D604—22no—
63C2×D604—21no—
64C2×D604C2311yescharacteristic
65C2×D604C2311yescharacteristic
66C2×D604C2311yescharacteristic
67C2×C22⋊D151—21no—
68C2×C4×D151—21no—
69C2×C4×D151—21no—
70C2×C4×D151—21no—
71C2×C4×D151—21no—
72C2×C4×D151—21no—
73#14558991—22no—
74#14558991—22no—
75D1208—22no—
76D1208—22no—
77C2×C151⋊C8C2311yescharacteristic
78C2×C151⋊C8C2311yescharacteristic
79C4⋊Dic151—21no—
80C4⋊Dic151D411yescharacteristic
81C4⋊Dic151D411yescharacteristic
82C4⋊Dic151C2311yescharacteristic
83Dic151⋊C4—21no—
84C22⋊Dic151D411yescharacteristic
85C22⋊Dic151D411yescharacteristic
86(C2×D151)⋊C4—21no—
87(C2×D151)⋊C4—21no—
88(C2×D151)⋊C4—21no—
89(C2×D151)⋊C4—21no—
90(C2×D151)⋊C4—21no—
91(C2×D151)⋊C4—21no—
92(C2×D151)⋊C4—21no—
93(C2×D151)⋊C4—21no—
94C4×Dic151—21no—
95C4×Dic151C2311yescharacteristic
96C4×Dic151C2311yescharacteristic
97C2×Q8×C151C2311yescharacteristic
98C22×C4×C151C2311yescharacteristic
99C2×C8×C151C2311yescharacteristic
100C2×C8×C151C2311yescharacteristic
101C4⋊C4×C151—21no—
102C4⋊C4×C151C2311yescharacteristic
103C4⋊C4×C151C2311yescharacteristic
104C4⋊C4×C151C2311yescharacteristic
105C22⋊C4×C151—21no—
106C22⋊C4×C151—21no—
107C42×C151—21no—
108C22×D151—21no—
109C22×D151—21no—
110C22×D151—24no—
111C22×D151—21no—
112C22×D151—81no—
113C22×D151—81no—
114Dic302—81no—
115D604—24no—
116D604—21no—
117D604—21no—
118D604—21no—
119D604—21no—
120D604#4112yes—
121D604#4112yes—
122C22⋊D151—81no—
123C2×Dic151—21no—
124C2×Dic151C2×D411yescharacteristic
125C2×Dic151C2×D411yescharacteristic
126C2×Dic151C2×D411yescharacteristic
127C2×Dic151C2×D411yescharacteristic
128C4×D151—81no—
129C4×D151—81no—
130C4×D151—81no—
131C4×D151—81no—
132C4×D151—81no—
133C151⋊C8—21no—
134C151⋊C8—21no—
135C23×C151C2×D411yescharacteristic
136Q8×C151—21no—
137Q8×C151—21no—
138C2×C4×C151—21no—
139C2×C4×C151—21no—
140C2×C4×C151—21no—
141C2×C4×C151—21no—
142C2×C4×C151—21no—
143C2×C4×C151—21no—
144C2×C4×C151C2×D411yescharacteristic
145C2×C4×C151C2411yescharacteristic
146C8×C151—21no—
147C8×C151—21no—
148C22×C151—21no—
149C22×C151—21no—
150C22×C151—21no—
151C22×C151C22×D411yescharacteristic
152C2×D151—22no—
153C2×D151—22no—
154C2×D151—41no—
155C2×D151—41no—
156C2×D151—41no—
157C2×D151—41no—
158C2×D151—41no—
159C2×D151—41no—
160C2×D151—41no—
161C2×D151—84no—
162C4×C151—21no—
163C4×C151—41no—
164C4×C151—41no—
165C4×C151—41no—
166C4×C151—41no—
167C4×C151C2×#4111yescharacteristic
168C4×C151C2×#4111yescharacteristic
169Dic151—21no—
170Dic151—21no—
171Dic151—21no—
172Dic151—21no—
173Dic151—41no—
174C2×C151—41no—
175C2×C151#52511yescharacteristic
176C2×C151#57611yescharacteristic
177C2×C151#57711yescharacteristic
178D151—42no—
179D151—42no—
180D151—81no—
181C151#311811yescharacteristic, complemented, Sylow
182#3118—1511nomaximal, Sylow
183#542—1511no—
184#518—1511no—
185#485D15111yescharacteristic, complemented
186#482—1511no—
187#476—1511no—
188#474—1511no—
189#463—1511no—
190#463—1511no—
191#450—1511no—
192#447—1511no—
193#442—1511no—
194#440—1511no—
195C4×SD16—1511no—
196C4×D8—1511no—
197#433—1511no—
198C22×D4—1511no—
199C2×SD16—1511no—
200C2×SD16—1511no—
201C2×D8—1511no—
202C2×D8—1511no—
203C4⋊Q8—1511no—
204#126—3021no—
205#124—3021no—
206#124—1511no—
207#123—3021no—
208C22⋊Q8—3021no—
209C22⋊Q8C2×D15111yescharacteristic
210#121—1511no—
211C4×Q8—1511no—
212C4×D4—3021no—
213C4×D4—3021no—
214C4×D4—1511no—
215C4×D4—1511no—
216C4×D4—1511no—
217C4×D4—1511no—
218C4×D4—1511no—
219#117—1511no—
220#117C2×D15111yescharacteristic
221C2×C22⋊C4—3021no—
222C2×C22⋊C4—3021no—
223#107—1511no—
224#107C2×D15111yescharacteristic, complemented
225#106—1511no—
226#106C2×D15111yescharacteristic, complemented
227C4⋊C8—1511no—
228C4⋊C8—1511no—
229#103C2×D15111yescharacteristic, complemented
230#103C2×D15111yescharacteristic, complemented
231#102—1511no—
232#102—1511no—
233#102—1511no—
234#102—1511no—
235#102—1511no—
236#102—1511no—
237C22⋊C8—1511no—
238C22⋊C8C2×D15111yescharacteristic
239#97—1511no—
240C4×C8—1511no—
241C24—3021no—
242C2×Q8—3021no—
243C2×Q8C22×D15111yescharacteristic
244C2×D4—3022no—
245C2×D4—3022no—
246C2×D4—3021no—
247C2×D4—3021no—
248C2×D4—1511no—
249C2×D4—1511no—
250C2×D4—1511no—
251C22×C4—3021no—
252C22×C4—3021no—
253C22×C4—3021no—
254C22×C4—3021no—
255C22×C4—3021no—
256C22×C4C22×D15111yescharacteristic
257SD16—3022no—
258SD16—3022no—
259D8—3022no—
260D8—3022no—
261C2×C8—1511no—
262C2×C8—1511no—
263C2×C8C22×D15111yescharacteristic
264C2×C8C22×D15111yescharacteristic
265C4⋊C4—21no—
266C4⋊C4—3021no—
267C4⋊C4—3021no—
268C4⋊C4—1511no—
269C4⋊C4—1511no—
270C4⋊C4—1511no—
271C4⋊C4C22×D15111yescharacteristic
272C4⋊C4C22×D15111yescharacteristic
273C4⋊C4C22×D15111yescharacteristic
274C22⋊C4—21no—
275C22⋊C4—21no—
276C22⋊C4—3021no—
277C22⋊C4—3021no—
278C22⋊C4—3021no—
279C22⋊C4—3021no—
280C22⋊C4—3021no—
281C22⋊C4—3021no—
282C22⋊C4—3021no—
283C22⋊C4—3021no—
284C22⋊C4—1511no—
285C22⋊C4—1511no—
286C42—21no—
287C42—3021no—
288C42—1511no—
289C42—1511no—
290C23—3024no—
291C23—3021no—
292C23—3021no—
293C23—3021no—
294C23—12081no—
295C23—12081no—
296C23D4×D15111yescharacteristic
297Q8—21no—
298Q8—21no—
299Q8—12081no—
300D4—3024no—
301D4—3021no—
302D4—3021no—
303D4—3021no—
304D4—3021no—
305D4—1512no—
306D4—1512no—
307D4—12081no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—21no—
312C2×C4—21no—
313C2×C4—21no—
314C2×C4—3021no—
315C2×C4—1511no—
316C2×C4—1511no—
317C2×C4—1511no—
318C2×C4—1511no—
319C2×C4—12081no—
320C2×C4—12081no—
321C2×C4—12081no—
322C2×C4—12081no—
323C2×C4—12081no—
324C2×C4D4×D15111yescharacteristic
325C2×C4C23×D15111yescharacteristic
326C8—21no—
327C8—21no—
328C8—3021no—
329C8—3021no—
330C22—21no—
331C22—21no—
332C22—21no—
333C22—3022no—
334C22—3022no—
335C22—6041no—
336C22—6041no—
337C22—6041no—
338C22—6041no—
339C22—6041no—
340C22—6041no—
341C22—6041no—
342C22—12084no—
343C22C2×D4×D15111yescharacteristic
344C4—21no—
345C4—41no—
346C4—41no—
347C4—41no—
348C4—41no—
349C4—3021no—
350C4—3021no—
351C4—3021no—
352C4—3021no—
353C4—6041no—
354C4#41×D15111yescharacteristic
355C4#41×D15111yescharacteristic
356C2—41no—
357C2—6042no—
358C2—6042no—
359C2—12081no—
360C2#2375272011yescharacteristic
361C2#2375301411yescharacteristic
362C2#2375302111yescharacteristic
subgroupG/H
centerC22C2×D4×D151
commutator, cosocleC2×C4×C151C24
FrattiniC2×C4C23×D151
Fitting#485×C151C2
socleC22×C151C22×D4
prime radical#23752348C2
hypercenter#485D151
hypocenterC151#3118
LCSG ▷ C2×C4×C151 ▷ C2×C151 ▷ C151
UCSC1 ◁ C22 ◁ C22×C4 ◁ #485

Complements

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

NH ≅ G/Ntype
1. #23752835C2semidirect
2. #23752686C2semidirect
3. #23752536C2semidirect
4. #23752501C2semidirect
5. #23752491C2semidirect
6. #23752430C2semidirect
7. #23752430C2semidirect
8. #23752362C2semidirect
10. #23752323C2semidirect
11. #23752315C2semidirect
12. #23752297C2semidirect
13. #23752294C2semidirect
14. #23752270C2semidirect
15. #485×C151C2semidirect
21. #18012738C22semidirect
23. #18012728C22semidirect
28. Q8×Dic151C22semidirect
35. #18012701C22semidirect
39. #18012672C22semidirect
40. #18012670C22semidirect
41. Dic151⋊C8C22semidirect
42. Dic151⋊C8C22semidirect
47. #18012659C22semidirect
48. #18012659C22semidirect
50. #18012649C22semidirect
51. C8×Dic151C22semidirect
54. #107×C151C22semidirect
55. #106×C151C22semidirect
56. #103×C151C22semidirect
57. #103×C151C22semidirect
181. C151#3118semidirect
185. #485D151semidirect
224. #107C2×D151semidirect
226. #106C2×D151semidirect
229. #103C2×D151semidirect
230. #103C2×D151semidirect

Maximal subgroups

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

subgroupindex
#237528352
#237526862
#237525362
#237525012
#237524912
#237524302
#237523622
#237523482
#237523232
#237523152
#237522972
#237522942
#237522702
#485×C1512
#3118151