Finite Group Databasebeta

← #34079246

Subgroups — #34079246

Order 19328.

450 conjugacy classes of subgroups.

The subgroup lattice has 370 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#23752744C211yesmaximal, characteristic, complemented
2C4×D4×D151C211yesmaximal, characteristic, complemented
3#23752544C211yesmaximal, characteristic, complemented
4#23752524C211yesmaximal, characteristic, complemented
5#23752511C211yesmaximal, characteristic, complemented
6#23752510C211yesmaximal, characteristic, complemented
7#23752426C211yesmaximal, characteristic, complemented
8#23752425C211yesmaximal, characteristic, complemented
9#23752364C211yesmaximal, characteristic, complemented
10#23752344C211yesmaximal, characteristic
11#23752322C211yesmaximal, characteristic, complemented
12#23752314C211yesmaximal, characteristic, complemented
13#23752312C211yesmaximal, characteristic, complemented
14#23752267C211yesmaximal, characteristic, complemented
15#442×C151C211yesmaximal, characteristic, complemented
16C2×D4×D151C2211yescharacteristic
17C22×C4×D151—21no—
18C2×#14558993C2211yescharacteristic
19C2×#14558992C2211yescharacteristic
20C2×#14558989C2211yescharacteristic
21#18012732—21no—
22#18012730C2211yescharacteristic, complemented
23#18012726C2211yescharacteristic, complemented
24#18012721—21no—
25#18012719C2211yescharacteristic
26#18012710C2211yescharacteristic
27C4×Dic302C2211yescharacteristic, complemented
28C4×D604C2211yescharacteristic
29D4×Dic151C2211yescharacteristic
30#18012701C2211yescharacteristic
31C4×C22⋊D151—21no—
32C4×C22⋊D151—21no—
33(C22⋊D151)⋊C4—21no—
34#18012698—21no—
35C4⋊C4×D151C2211yescharacteristic
36C22⋊C4×D151—21no—
37C42×D151C2211yescharacteristic
38#18012673C2211yescharacteristic, complemented
39#18012672C2211yescharacteristic, complemented
40#18012670C2211yescharacteristic, complemented
41Dic151⋊C8C2211yescharacteristic, complemented
42Dic151⋊C8C2211yescharacteristic, complemented
43#18012664C2211yescharacteristic, complemented
44#18012662C2211yescharacteristic, complemented
45#18012661C2211yescharacteristic
46#18012660C2211yescharacteristic
47#18012660C2211yescharacteristic, complemented
48#18012659C2211yescharacteristic
49(C2×D151)⋊C8C2211yescharacteristic
50(C2×D151)⋊C8C2211yescharacteristic
51#18012650C2211yescharacteristic, complemented
52C2×D8×C151C2211yescharacteristic
53C4×D4×C151C2211yescharacteristic
54C4×D4×C151C2211yescharacteristic, complemented
55#106×C151C2211yescharacteristic, complemented
56#102×C151C2211yescharacteristic
57#102×C151C2211yescharacteristic, complemented
58#97×C151C2211yescharacteristic, complemented
59C23×D151—21no—
60C2×Dic302C2311yescharacteristic
61C2×D604C2311yescharacteristic
62C2×C22⋊D151—21no—
63C2×C22⋊D151—21no—
64D4×D151—22no—
65D4×D151—22no—
66C22×Dic151—21no—
67C2×C4×D151—21no—
68C2×C4×D151—21no—
69C2×C4×D151—21no—
70C2×C4×D151—44no—
71C2×C4×D151D411yescharacteristic
72C2×C4×D151D411yescharacteristic
73C2×C4×D151C2311yescharacteristic
74#14558993—22no—
75#14558992—22no—
76#14558989—22no—
77C2×C151⋊C8C2311yescharacteristic
78C2×C151⋊C8C2311yescharacteristic
79C4⋊Dic151—21no—
80C4⋊Dic151—21no—
81C4⋊Dic151C2311yescharacteristic
82C4⋊Dic151C2311yescharacteristic
83Dic151⋊C4—21no—
84Dic151⋊C4—21no—
85Dic151⋊C4—21no—
86C22⋊Dic151—21no—
87C22⋊Dic151—21no—
88C22⋊Dic151—21no—
89C22⋊Dic151—21no—
90(C2×D151)⋊C4—21no—
91(C2×D151)⋊C4—21no—
92(C2×D151)⋊C4—21no—
93C4×Dic151—21no—
94C4×Dic151D411yescharacteristic
95C4×Dic151D411yescharacteristic
96C4×Dic151C2311yescharacteristic
97C2×D4×C151C2311yescharacteristic
98C2×D4×C151C2311yescharacteristic
99C22×C4×C151—21no—
100C22×C4×C151—21no—
101D8×C151—22no—
102C2×C8×C151C2311yescharacteristic
103C2×C8×C151C2311yescharacteristic
104C4⋊C4×C151C2311yescharacteristic
105C4⋊C4×C151C2311yescharacteristic
106C22⋊C4×C151—21no—
107C22⋊C4×C151—21no—
108C42×C151C2311yescharacteristic
109C22×D151—24no—
110C22×D151—21no—
111C22×D151—42no—
112C22×D151—42no—
113C22×D151C2×D411yescharacteristic
114Dic302—21no—
115Dic302—21no—
116D604—21no—
117D604#4112yes—
118C22⋊D151—24no—
119C22⋊D151—42no—
120C2×Dic151—21no—
121C2×Dic151—21no—
122C2×Dic151—21no—
123C2×Dic151—42no—
124C2×Dic151C2×D411yescharacteristic
125C2×Dic151C2×D411yescharacteristic
126C2×Dic151C2×D411yescharacteristic
127C4×D151—22no—
128C4×D151—21no—
129C4×D151—21no—
130C4×D151—41no—
131C4×D151—42no—
132C4×D151—42no—
133C4×D151—42no—
134C151⋊C8—21no—
135C151⋊C8—21no—
136C23×C151—21no—
137C23×C151—21no—
138D4×C151—21no—
139D4×C151—21no—
140D4×C151—21no—
141D4×C151#4112yes—
142C2×C4×C151—21no—
143C2×C4×C151—21no—
144C2×C4×C151—42no—
145C2×C4×C151—42no—
146C2×C4×C151C2×D411yescharacteristic
147C2×C4×C151C2×D411yescharacteristic
148C2×C4×C151C2411yescharacteristic
149C8×C151—21no—
150C8×C151—21no—
151C22×C151—22no—
152C22×C151—41no—
153C22×C151—41no—
154C22×C151—41no—
155C22×C151—41no—
156C22×C151—41no—
157C22×C151C22×D411yescharacteristic
158C2×D151—21no—
159C2×D151—21no—
160C2×D151—22no—
161C2×D151—48no—
162C2×D151—41no—
163C2×D151—41no—
164C2×D151AGL(1,ℤ/8)12yes—
165C4×C151—21no—
166C4×C151—21no—
167C4×C151—41no—
168C4×C151—41no—
169C4×C151C2×#4111yescharacteristic
170C4×C151C2×#4111yescharacteristic
171Dic151—21no—
172Dic151—21no—
173Dic151—21no—
174Dic151—41no—
175Dic151—41no—
176Dic151—41no—
177C2×C151—42no—
178C2×C151—81no—
179C2×C151#52511yescharacteristic
180C2×C151C2×AGL(1,ℤ/8)11yescharacteristic
181C2×C151#57511yescharacteristic
182D151—22no—
183D151—42no—
184C151#311411yescharacteristic, complemented, Sylow
185#3114—1511nomaximal, Sylow
186#529—1511no—
187C2×C4×D4—1511no—
188#483—1511no—
189#480—1511no—
190#478—1511no—
191#478—1511no—
192#463—1511no—
193#463—1511no—
194#450—1511no—
195#447—1511no—
196#442—1511no—
197#442D15111yescharacteristic, complemented
198#440—1511no—
199#440—1511no—
200#432—1511no—
201C22×D4—1511no—
202C23×C4—3021no—
203C2×SD16—1511no—
204C2×SD16—1511no—
205C2×D8—1511no—
206C2×D8C2×D15111yescharacteristic
207#126—3021no—
208#125—1511no—
209#124—1511no—
210#123—3021no—
211C22⋊Q8—1511no—
212#121—1511no—
213C4×Q8—1511no—
214C4×D4—3021no—
215C4×D4—3021no—
216C4×D4—3021no—
217C4×D4—1511no—
218C4×D4—1511no—
219C4×D4—1511no—
220C4×D4C2×D15111yescharacteristic
221C4×D4C2×D15111yescharacteristic, complemented
222#117—3021no—
223C2×C4⋊C4—1511no—
224C2×C22⋊C4—3021no—
225C2×C42—1511no—
226#107—1511no—
227#107—1511no—
228#106—1511no—
229#106C2×D15111yescharacteristic, complemented
230C4⋊C8—1511no—
231C4⋊C8—1511no—
232#103—1511no—
233#103—1511no—
234#102—1511no—
235#102—1511no—
236#102—1511no—
237#102—1511no—
238#102C2×D15111yescharacteristic
239#102C2×D15111yescharacteristic, complemented
240C22⋊C8—1511no—
241C22⋊C8—1511no—
242#97—1511no—
243#97C2×D15111yescharacteristic, complemented
244C24—3021no—
245C2×Q8—1511no—
246C2×D4—3022no—
247C2×D4—3022no—
248C2×D4—3021no—
249C2×D4—3021no—
250C2×D4—1511no—
251C2×D4C22×D15111yescharacteristic
252C2×D4C22×D15111yescharacteristic
253C22×C4—21no—
254C22×C4—21no—
255C22×C4—3021no—
256C22×C4—3021no—
257C22×C4—3021no—
258C22×C4—3021no—
259C22×C4—6044no—
260C22×C4—1511no—
261C22×C4—1511no—
262C22×C4—1511no—
263SD16—3022no—
264SD16—3022no—
265D8—22no—
266D8—3022no—
267C2×C8—1511no—
268C2×C8—1511no—
269C2×C8C22×D15111yescharacteristic
270C2×C8C22×D15111yescharacteristic
271C4⋊C4—3021no—
272C4⋊C4—3021no—
273C4⋊C4—3021no—
274C4⋊C4—3021no—
275C4⋊C4—3021no—
276C4⋊C4—1511no—
277C4⋊C4—1511no—
278C4⋊C4C22×D15111yescharacteristic
279C4⋊C4C22×D15111yescharacteristic
280C22⋊C4—21no—
281C22⋊C4—21no—
282C22⋊C4—3021no—
283C22⋊C4—3021no—
284C22⋊C4—3021no—
285C22⋊C4—3021no—
286C22⋊C4—3021no—
287C22⋊C4—3021no—
288C22⋊C4—3021no—
289C42—3021no—
290C42—1511no—
291C42—1511no—
292C42—1511no—
293C42C22×D15111yescharacteristic
294C23—21no—
295C23—21no—
296C23—3024no—
297C23—3021no—
298C23—6042no—
299C23—6042no—
300C23—1511no—
301Q8—3021no—
302Q8—3021no—
303D4—21no—
304D4—21no—
305D4—21no—
306D4—3024no—
307D4—3021no—
308D4—6042no—
309D4—1512no—
310D4#1455900412yes—
311C2×C4—21no—
312C2×C4—21no—
313C2×C4—42no—
314C2×C4—42no—
315C2×C4—3022no—
316C2×C4—3021no—
317C2×C4—3021no—
318C2×C4—3021no—
319C2×C4—3021no—
320C2×C4—3021no—
321C2×C4—6041no—
322C2×C4—6042no—
323C2×C4—6042no—
324C2×C4—6042no—
325C2×C4—6042no—
326C2×C4—1511no—
327C2×C4—1511no—
328C2×C4—1511no—
329C2×C4D4×D15111yescharacteristic
330C2×C4D4×D15111yescharacteristic
331C2×C4C23×D15111yescharacteristic
332C8—21no—
333C8—21no—
334C8—3021no—
335C8—3021no—
336C22—22no—
337C22—41no—
338C22—41no—
339C22—41no—
340C22—41no—
341C22—41no—
342C22—3021no—
343C22—3021no—
344C22—3022no—
345C22—6048no—
346C22—6041no—
347C22—6041no—
348C22—1512no—
349C22C2×D4×D15111yescharacteristic
350C4—21no—
351C4—21no—
352C4—41no—
353C4—41no—
354C4—3021no—
355C4—3021no—
356C4—3021no—
357C4—6041no—
358C4—6041no—
359C4—6041no—
360C4#41×D15111yescharacteristic
361C4C2×#1455900411yescharacteristic
362C2—42no—
363C2—81no—
364C2—3022no—
365C2—6042no—
366C2#2375272111yescharacteristic
367C2AGL(1,ℤ/8)×D15111yescharacteristic
368C2#2375300811yescharacteristic
subgroupG/H
centerC22C2×D4×D151
commutator, cosocleC2×C4×C151C24
FrattiniC2×C4C23×D151
Fitting#442×C151C2
socleC22×C151C22×D4
prime radical#23752344C2
hypercenter#442D151
hypocenterC151#3114
LCSG ▷ C2×C4×C151 ▷ C2×C151 ▷ C151
UCSC1 ◁ C22 ◁ C42 ◁ #442

Complements

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

NH ≅ G/Ntype
1. #23752744C2semidirect
2. C4×D4×D151C2semidirect
3. #23752544C2semidirect
4. #23752524C2semidirect
5. #23752511C2semidirect
6. #23752510C2semidirect
7. #23752426C2semidirect
8. #23752425C2semidirect
9. #23752364C2semidirect
11. #23752322C2semidirect
12. #23752314C2semidirect
13. #23752312C2semidirect
14. #23752267C2semidirect
15. #442×C151C2semidirect
22. #18012730C22semidirect
23. #18012726C22semidirect
27. C4×Dic302C22semidirect
38. #18012673C22semidirect
39. #18012672C22semidirect
40. #18012670C22semidirect
41. Dic151⋊C8C22semidirect
42. Dic151⋊C8C22semidirect
43. #18012664C22semidirect
44. #18012662C22semidirect
47. #18012660C22semidirect
51. #18012650C22semidirect
54. C4×D4×C151C22semidirect
55. #106×C151C22semidirect
57. #102×C151C22semidirect
58. #97×C151C22semidirect
184. C151#3114semidirect
197. #442D151semidirect
221. C4×D4C2×D151semidirect
229. #106C2×D151semidirect
239. #102C2×D151semidirect
243. #97C2×D151semidirect

Maximal subgroups

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

subgroupindex
#237527442
C4×D4×D1512
#237525442
#237525242
#237525112
#237525102
#237524262
#237524252
#237523642
#237523442
#237523222
#237523142
#237523122
#237522672
#442×C1512
#3114151