Finite Group Databasebeta

← #34079294

Subgroups — #34079294

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#23752833C211yesmaximal, characteristic, complemented
2#23752553C211yesmaximal, characteristic, complemented
3#23752536C211yesmaximal, characteristic, complemented
4#23752502C211yesmaximal, characteristic, complemented
5#23752492C211yesmaximal, characteristic, complemented
6#23752427C211yesmaximal, characteristic, complemented
7#23752427C211yesmaximal, characteristic, complemented
8#23752363C211yesmaximal, characteristic, complemented
9#23752346C211yesmaximal, characteristic
10#23752322C211yesmaximal, characteristic, complemented
11#23752312C211yesmaximal, characteristic, complemented
12C4×#14558992C211yesmaximal, characteristic, complemented
13C4×#14558989C211yesmaximal, characteristic, complemented
14#23752273C211yesmaximal, characteristic, complemented
15#518×C151C211yesmaximal, characteristic, complemented
16C2×#14558992C2211yescharacteristic
17C2×#14558992C2211yescharacteristic
18C2×#14558989C2211yescharacteristic
19C2×#14558989C2211yescharacteristic
20#18012739C2211yescharacteristic, complemented
21#18012734—21no—
22#18012727C2211yescharacteristic, complemented
23#18012725—21no—
24#18012721—21no—
25#18012718C2211yescharacteristic
26#18012717—21no—
27#18012713C2211yescharacteristic
28C4×Dic302C2211yescharacteristic, complemented
29C4×D604C2211yescharacteristic, complemented
30#18012672C2211yescharacteristic, complemented
31#18012672C2211yescharacteristic, complemented
32#18012670C2211yescharacteristic, complemented
33#18012670C2211yescharacteristic, complemented
34C4⋊(C151⋊C8)C2211yescharacteristic, complemented
35C4⋊(C151⋊C8)C2211yescharacteristic, complemented
36#18012662C2211yescharacteristic, complemented
37#18012662C2211yescharacteristic, complemented
38#18012660C2211yescharacteristic
39#18012660C2211yescharacteristic
40#18012660C2211yescharacteristic
41#18012660C2211yescharacteristic
42#18012659C2211yescharacteristic, complemented
43#18012659C2211yescharacteristic, complemented
44C22⋊(C151⋊C8)C2211yescharacteristic
45C22⋊(C151⋊C8)C2211yescharacteristic
46#18012650C2211yescharacteristic, complemented
47C4×C151⋊C8C2211yescharacteristic, complemented
48C22×D4×C151C2211yescharacteristic
49C4×D4×C151—21no—
50C4×D4×C151—21no—
51C4×D4×C151C2211yescharacteristic
52C4×D4×C151C2211yescharacteristic
53C4×D4×C151C2211yescharacteristic
54C4×D4×C151C2211yescharacteristic
55#117×C151C2211yescharacteristic
56#117×C151C2211yescharacteristic
57C2×C22⋊C4×C151—21no—
58C2×C22⋊C4×C151—21no—
59C2×Dic302—21no—
60C2×Dic302C2311yescharacteristic
61C2×D604C2311yescharacteristic
62C2×C22⋊D151—21no—
63C2×C4×D151—21no—
64#14558992—22no—
65#14558992—22no—
66#14558989—22no—
67#14558989—22no—
68C2×C151⋊C8C2311yescharacteristic
69C2×C151⋊C8C2311yescharacteristic
70C2×C151⋊C8C2311yescharacteristic
71C2×C151⋊C8C2311yescharacteristic
72C4⋊Dic151—21no—
73C4⋊Dic151C2311yescharacteristic
74C4⋊Dic151C2311yescharacteristic
75Dic151⋊C4—21no—
76Dic151⋊C4—21no—
77C22⋊Dic151—21no—
78(C2×D151)⋊C4—21no—
79(C2×D151)⋊C4—21no—
80(C2×D151)⋊C4—21no—
81(C2×D151)⋊C4—21no—
82C4×Dic151—21no—
83C24×C151—21no—
84C2×D4×C151—22no—
85C2×D4×C151—22no—
86C2×D4×C151—21no—
87C2×D4×C151C2311yescharacteristic
88C2×D4×C151C2311yescharacteristic
89C22×C4×C151—21no—
90C22×C4×C151—21no—
91C22×C4×C151—21no—
92C22×C4×C151—21no—
93C22×C4×C151C2311yescharacteristic
94C4⋊C4×C151D411yescharacteristic
95C4⋊C4×C151D411yescharacteristic
96C4⋊C4×C151C2311yescharacteristic
97C4⋊C4×C151C2311yescharacteristic
98C22⋊C4×C151—21no—
99C22⋊C4×C151—21no—
100C22⋊C4×C151—21no—
101C22⋊C4×C151—21no—
102C22⋊C4×C151—21no—
103C22⋊C4×C151D411yescharacteristic
104C22⋊C4×C151D411yescharacteristic
105C42×C151—21no—
106C42×C151C2311yescharacteristic
107C42×C151C2311yescharacteristic
108C22×D151—21no—
109Dic302—21no—
110Dic302—21no—
111Dic302—81no—
112D604—21no—
113D604—21no—
114C22⋊D151—81no—
115C2×Dic151—21no—
116C2×Dic151—21no—
117C2×Dic151—21no—
118C4×D151—81no—
119C151⋊C8—21no—
120C151⋊C8—21no—
121C151⋊C8—21no—
122C151⋊C8—21no—
123C23×C151—24no—
124C23×C151—21no—
125C23×C151—21no—
126C23×C151—81no—
127C23×C151—81no—
128C23×C151C2×D411yescharacteristic
129D4×C151—24no—
130D4×C151—21no—
131D4×C151—21no—
132D4×C151#4112yes—
133D4×C151#4112yes—
134C2×C4×C151—21no—
135C2×C4×C151—21no—
136C2×C4×C151—21no—
137C2×C4×C151—21no—
138C2×C4×C151—81no—
139C2×C4×C151—81no—
140C2×C4×C151—81no—
141C2×C4×C151—81no—
142C2×C4×C151C2×D411yescharacteristic
143C2×C4×C151C2×D411yescharacteristic
144C2×C4×C151C2×D411yescharacteristic
145C2×C4×C151C2×D411yescharacteristic
146C2×C4×C151C2×D411yescharacteristic
147C2×C4×C151C2411yescharacteristic
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—21no—
164C4×C151—21no—
165C4×C151—21no—
166C4×C151—21no—
167C4×C151—41no—
168C4×C151—41no—
169C4×C151C2×#4111yescharacteristic
170C4×C151C2×#4111yescharacteristic
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#518D15111yescharacteristic, complemented
185#485—1511no—
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×D4C2×D15111yescharacteristic
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⋊Q8—1511no—
210#121—1511no—
211C4×Q8—1511no—
212C4×D4—21no—
213C4×D4—21no—
214C4×D4—1511no—
215C4×D4C2×D15111yescharacteristic
216C4×D4C2×D15111yescharacteristic
217C4×D4C2×D15111yescharacteristic
218C4×D4C2×D15111yescharacteristic
219#117C2×D15111yescharacteristic
220#117C2×D15111yescharacteristic
221C2×C22⋊C4—21no—
222C2×C22⋊C4—21no—
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#102—1511no—
236#102—1511no—
237C22⋊C8—1511no—
238C22⋊C8—1511no—
239#97—1511no—
240C4×C8—1511no—
241C24—21no—
242C2×Q8—3021no—
243C2×Q8—1511no—
244C2×D4—22no—
245C2×D4—22no—
246C2×D4—21no—
247C2×D4—3021no—
248C2×D4—1511no—
249C2×D4C22×D15111yescharacteristic
250C2×D4C22×D15111yescharacteristic
251C22×C4—21no—
252C22×C4—21no—
253C22×C4—21no—
254C22×C4—21no—
255C22×C4—3021no—
256C22×C4C22×D15111yescharacteristic
257SD16—3022no—
258SD16—3022no—
259D8—3022no—
260D8—3022no—
261C2×C8—1511no—
262C2×C8—1511no—
263C2×C8—1511no—
264C2×C8—1511no—
265C4⋊C4—3021no—
266C4⋊C4—3021no—
267C4⋊C4—3021no—
268C4⋊C4—1511no—
269C4⋊C4—1511no—
270C4⋊C4C22⋊D15111yescharacteristic
271C4⋊C4C22⋊D15111yescharacteristic
272C4⋊C4C22×D15111yescharacteristic
273C4⋊C4C22×D15111yescharacteristic
274C22⋊C4—21no—
275C22⋊C4—21no—
276C22⋊C4—21no—
277C22⋊C4—21no—
278C22⋊C4—21no—
279C22⋊C4—3021no—
280C22⋊C4—3021no—
281C22⋊C4—3021no—
282C22⋊C4—3021no—
283C22⋊C4—3021no—
284C22⋊C4C22⋊D15111yescharacteristic
285C22⋊C4C22⋊D15111yescharacteristic
286C42—21no—
287C42—3021no—
288C42C22×D15111yescharacteristic
289C42C22×D15111yescharacteristic
290C23—24no—
291C23—21no—
292C23—21no—
293C23—81no—
294C23—81no—
295C23—3021no—
296C23C2×C22⋊D15111yescharacteristic
297Q8—3021no—
298Q8—3021no—
299Q8—12081no—
300D4—24no—
301D4—21no—
302D4—21no—
303D4—3021no—
304D4—3021no—
305D4—12081no—
306D4#1455900412yes—
307D4#1455900412yes—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—21no—
312C2×C4—81no—
313C2×C4—81no—
314C2×C4—81no—
315C2×C4—81no—
316C2×C4—3021no—
317C2×C4—3021no—
318C2×C4—3021no—
319C2×C4—12081no—
320C2×C4C2×C22⋊D15111yescharacteristic
321C2×C4C2×C22⋊D15111yescharacteristic
322C2×C4C2×C22⋊D15111yescharacteristic
323C2×C4C2×C22⋊D15111yescharacteristic
324C2×C4C2×C22⋊D15111yescharacteristic
325C2×C4C23×D15111yescharacteristic
326C8—3021no—
327C8—3021no—
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—
343C22C22×C22⋊D15111yescharacteristic
344C4—21no—
345C4—21no—
346C4—21no—
347C4—21no—
348C4—21no—
349C4—41no—
350C4—41no—
351C4—6041no—
352C4—6041no—
353C4—6041no—
354C4C2×#1455900411yescharacteristic
355C4C2×#1455900411yescharacteristic
356C2—41no—
357C2—42no—
358C2—42no—
359C2—12081no—
360C2#2375272311yescharacteristic
361C2#2375301511yescharacteristic
362C2#2375302311yescharacteristic
subgroupG/H
centerC22C22×C22⋊D151
commutator, cosocleC2×C4×C151C24
FrattiniC2×C4C23×D151
Fitting#518×C151C2
socleC22×C151C22×D4
prime radical#23752346C2
hypercenter#518D151
hypocenterC151#3118
LCSG ▷ C2×C4×C151 ▷ C2×C151 ▷ C151
UCSC1 ◁ C22 ◁ #117 ◁ #518

Complements

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

NH ≅ G/Ntype
1. #23752833C2semidirect
2. #23752553C2semidirect
3. #23752536C2semidirect
4. #23752502C2semidirect
5. #23752492C2semidirect
6. #23752427C2semidirect
7. #23752427C2semidirect
8. #23752363C2semidirect
10. #23752322C2semidirect
11. #23752312C2semidirect
12. C4×#14558992C2semidirect
13. C4×#14558989C2semidirect
14. #23752273C2semidirect
15. #518×C151C2semidirect
20. #18012739C22semidirect
22. #18012727C22semidirect
28. C4×Dic302C22semidirect
29. C4×D604C22semidirect
30. #18012672C22semidirect
31. #18012672C22semidirect
32. #18012670C22semidirect
33. #18012670C22semidirect
34. C4⋊(C151⋊C8)C22semidirect
35. C4⋊(C151⋊C8)C22semidirect
36. #18012662C22semidirect
37. #18012662C22semidirect
42. #18012659C22semidirect
43. #18012659C22semidirect
46. #18012650C22semidirect
47. C4×C151⋊C8C22semidirect
181. C151#3118semidirect
184. #518D151semidirect

Maximal subgroups

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

subgroupindex
#237528332
#237525532
#237525362
#237525022
#237524922
#237524272
#237523632
#237523462
#237523222
#237523122
C4×#145589922
C4×#145589892
#237522732
#518×C1512
#3118151