Finite Group Databasebeta

← #34079295

Subgroups — #34079295

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#23752687C211yesmaximal, characteristic, complemented
3#23752550C211yesmaximal, characteristic, complemented
4#23752537C211yesmaximal, characteristic, complemented
5#23752500C211yesmaximal, characteristic, complemented
6#23752490C211yesmaximal, characteristic, complemented
7#23752429C211yesmaximal, characteristic, complemented
8#23752429C211yesmaximal, characteristic, complemented
9#23752346C211yesmaximal, characteristic
10#23752321C211yesmaximal, characteristic, complemented
11#23752313C211yesmaximal, characteristic, complemented
12SD16×Dic151C211yesmaximal, characteristic, complemented
13#23752292C211yesmaximal, characteristic, complemented
14#23752270C211yesmaximal, characteristic, complemented
15#450×C151C211yesmaximal, characteristic, complemented
16C2×#14558989C2211yescharacteristic
17C2×#14558989C2211yescharacteristic
18#18012738C2211yescharacteristic, complemented
19#18012734—21no—
20#18012728C2211yescharacteristic, complemented
21#18012725—21no—
22#18012721—21no—
23#18012719—21no—
24#18012713C2211yescharacteristic
25Q8×Dic151C2211yescharacteristic, complemented
26D4×Dic151—21no—
27D4×Dic151—21no—
28D4×Dic151C2211yescharacteristic
29D4×Dic151C2211yescharacteristic
30D4×Dic151C2211yescharacteristic
31D4×Dic151C2211yescharacteristic
32#18012701C2211yescharacteristic, complemented
33#18012698C2211yescharacteristic
34#18012698C2211yescharacteristic
35C2×C22⋊Dic151—21no—
36C2×C22⋊Dic151—21no—
37#18012673C2211yescharacteristic, complemented
38#18012672C2211yescharacteristic, complemented
39#18012671C2211yescharacteristic, complemented
40#18012670C2211yescharacteristic, complemented
41Dic151⋊C8C2211yescharacteristic, complemented
42Dic151⋊C8C2211yescharacteristic, complemented
43#18012663C2211yescharacteristic, complemented
44#18012663C2211yescharacteristic, complemented
45#18012661C2211yescharacteristic, complemented
46#18012661C2211yescharacteristic, complemented
47#18012660C2211yescharacteristic
48#18012660C2211yescharacteristic
49C22⋊(C151⋊C8)C2211yescharacteristic
50#18012649C2211yescharacteristic, 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
59C2×Dic302—21no—
60C2×D604C2311yescharacteristic
61C2×C22⋊D151—21no—
62C22×Dic151—21no—
63C22×Dic151—21no—
64C22×Dic151—21no—
65C22×Dic151—21no—
66C2×C4×D151—21no—
67#14558989—22no—
68#14558989—22no—
69C2×C151⋊C8C2311yescharacteristic
70C2×C151⋊C8C2311yescharacteristic
71C4⋊Dic151—21no—
72C4⋊Dic151D411yescharacteristic
73C4⋊Dic151D411yescharacteristic
74C4⋊Dic151C2311yescharacteristic
75C4⋊Dic151C2311yescharacteristic
76C4⋊Dic151C2311yescharacteristic
77Dic151⋊C4—21no—
78C22⋊Dic151—21no—
79C22⋊Dic151—21no—
80C22⋊Dic151—21no—
81C22⋊Dic151—21no—
82C22⋊Dic151—21no—
83C22⋊Dic151D411yescharacteristic
84C22⋊Dic151D411yescharacteristic
85(C2×D151)⋊C4—21no—
86(C2×D151)⋊C4—21no—
87(C2×D151)⋊C4—21no—
88(C2×D151)⋊C4—21no—
89C4×Dic151—21no—
90C4×Dic151—21no—
91C4×Dic151C2311yescharacteristic
92C4×Dic151C2311yescharacteristic
93C24×C151—21no—
94C2×Q8×C151C2311yescharacteristic
95C2×D4×C151—22no—
96C2×D4×C151—22no—
97C2×D4×C151—21no—
98C2×D4×C151C2311yescharacteristic
99C2×D4×C151C2311yescharacteristic
100C22×C4×C151C2311yescharacteristic
101SD16×C151—22no—
102SD16×C151—22no—
103C2×C8×C151C2311yescharacteristic
104C2×C8×C151C2311yescharacteristic
105C4⋊C4×C151—21no—
106C4⋊C4×C151C2311yescharacteristic
107C22⋊C4×C151—21no—
108C22×D151—21no—
109Dic302—81no—
110D604—21no—
111D604—21no—
112C22⋊D151—81no—
113C2×Dic151—21no—
114C2×Dic151—21no—
115C2×Dic151—21no—
116C2×Dic151—81no—
117C2×Dic151—81no—
118C2×Dic151—81no—
119C2×Dic151—81no—
120C2×Dic151C2×D411yescharacteristic
121C2×Dic151C2×D411yescharacteristic
122C2×Dic151C2×D411yescharacteristic
123C2×Dic151C2×D411yescharacteristic
124C4×D151—81no—
125C151⋊C8—21no—
126C151⋊C8—21no—
127C23×C151—24no—
128C23×C151—21no—
129C23×C151—21no—
130C23×C151—81no—
131C23×C151—81no—
132C23×C151C2×D411yescharacteristic
133Q8×C151—21no—
134Q8×C151—21no—
135D4×C151—24no—
136D4×C151—21no—
137D4×C151—21no—
138D4×C151#4112yes—
139D4×C151#4112yes—
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—22no—
150C22×C151—22no—
151C22×C151—21no—
152C22×C151—21no—
153C22×C151—41no—
154C22×C151—41no—
155C22×C151—41no—
156C22×C151—41no—
157C22×C151—84no—
158C22×C151C22×D411yescharacteristic
159C2×D151—41no—
160C2×D151—41no—
161C2×D151—41no—
162C4×C151—21no—
163C4×C151—41no—
164C4×C151—41no—
165C4×C151C2×#4111yescharacteristic
166C4×C151C2×#4111yescharacteristic
167Dic151—21no—
168Dic151—21no—
169Dic151—21no—
170Dic151—21no—
171Dic151—41no—
172Dic151—41no—
173Dic151—41no—
174C2×C151—41no—
175C2×C151—42no—
176C2×C151—42no—
177C2×C151#52511yescharacteristic
178C2×C151#57611yescharacteristic
179C2×C151#57711yescharacteristic
180D151—81no—
181C151#311811yescharacteristic, complemented, Sylow
182#3118—1511nomaximal, Sylow
183#542—1511no—
184#518—1511no—
185#485—1511no—
186#482—1511no—
187#476—1511no—
188#474—1511no—
189#463—1511no—
190#463—1511no—
191#450D15111yescharacteristic, complemented
192#447—1511no—
193#442—1511no—
194#440—1511no—
195C4×SD16—1511no—
196C4×D8—1511no—
197#433—1511no—
198C22×D4C2×D15111yescharacteristic
199C2×SD16C2×D15111yescharacteristic
200C2×SD16C2×D15111yescharacteristic
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#117—1511no—
221C2×C22⋊C4—3021no—
222C2×C22⋊C4—3021no—
223#107—1511no—
224#107—1511no—
225#106—1511no—
226#106—1511no—
227C4⋊C8—1511no—
228C4⋊C8—1511no—
229#103—1511no—
230#103—1511no—
231#102—1511no—
232#102—1511no—
233#102—1511no—
234#102—1511no—
235#102C2×D15111yescharacteristic
236#102C2×D15111yescharacteristic
237C22⋊C8—1511no—
238C22⋊C8C2×D15111yescharacteristic
239#97—1511no—
240C4×C8—1511no—
241C24—21no—
242C2×Q8—3021no—
243C2×Q8C22×D15111yescharacteristic
244C2×D4—22no—
245C2×D4—22no—
246C2×D4—21no—
247C2×D4—3021no—
248C2×D4—1511no—
249C2×D4C22×D15111yescharacteristic
250C2×D4C22×D15111yescharacteristic
251C22×C4—3021no—
252C22×C4—3021no—
253C22×C4—3021no—
254C22×C4—3021no—
255C22×C4—3021no—
256C22×C4C22×D15111yescharacteristic
257SD16—22no—
258SD16—22no—
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⋊C4—1511no—
272C4⋊C4—1511no—
273C4⋊C4C22×D15111yescharacteristic
274C22⋊C4—21no—
275C22⋊C4—3021no—
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—3021no—
287C42—3021no—
288C42—1511no—
289C42—1511no—
290C23—24no—
291C23—21no—
292C23—21no—
293C23—81no—
294C23—81no—
295C23—3021no—
296C23D4×D15111yescharacteristic
297Q8—21no—
298Q8—21no—
299Q8—12081no—
300D4—24no—
301D4—21no—
302D4—21no—
303D4—3021no—
304D4—3021no—
305D4—12081no—
306D4#1455900312yes—
307D4#1455900312yes—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—21no—
312C2×C4—3021no—
313C2×C4—3021no—
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—22no—
332C22—22no—
333C22—21no—
334C22—21no—
335C22—41no—
336C22—41no—
337C22—41no—
338C22—41no—
339C22—84no—
340C22—6041no—
341C22—6041no—
342C22—6041no—
343C22C2×D4×D15111yescharacteristic
344C4—21no—
345C4—41no—
346C4—41no—
347C4—3021no—
348C4—3021no—
349C4—3021no—
350C4—3021no—
351C4—6041no—
352C4—6041no—
353C4—6041no—
354C4C2×#1455900311yescharacteristic
355C4C2×#1455900311yescharacteristic
356C2—41no—
357C2—42no—
358C2—42no—
359C2—12081no—
360C2#2375271811yescharacteristic
361C2#2375301611yescharacteristic
362C2#2375301811yescharacteristic
subgroupG/H
centerC22C2×D4×D151
commutator, cosocleC2×C4×C151C24
FrattiniC2×C4C23×D151
Fitting#450×C151C2
socleC22×C151C22×D4
prime radical#23752346C2
hypercenter#450D151
hypocenterC151#3118
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. #23752835C2semidirect
2. #23752687C2semidirect
3. #23752550C2semidirect
4. #23752537C2semidirect
5. #23752500C2semidirect
6. #23752490C2semidirect
7. #23752429C2semidirect
8. #23752429C2semidirect
10. #23752321C2semidirect
11. #23752313C2semidirect
12. SD16×Dic151C2semidirect
13. #23752292C2semidirect
14. #23752270C2semidirect
15. #450×C151C2semidirect
18. #18012738C22semidirect
20. #18012728C22semidirect
25. Q8×Dic151C22semidirect
32. #18012701C22semidirect
37. #18012673C22semidirect
38. #18012672C22semidirect
39. #18012671C22semidirect
40. #18012670C22semidirect
41. Dic151⋊C8C22semidirect
42. Dic151⋊C8C22semidirect
43. #18012663C22semidirect
44. #18012663C22semidirect
45. #18012661C22semidirect
46. #18012661C22semidirect
50. #18012649C22semidirect
51. C8×Dic151C22semidirect
181. C151#3118semidirect
191. #450D151semidirect

Maximal subgroups

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

subgroupindex
#237528352
#237526872
#237525502
#237525372
#237525002
#237524902
#237524292
#237523462
#237523212
#237523132
SD16×Dic1512
#237522922
#237522702
#450×C1512
#3118151