Finite Group Databasebeta

← #34077966

Subgroups — #34077966

Order 19328.

492 conjugacy classes of subgroups.

The subgroup lattice has 366 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×SD16×D151C211yesmaximal, characteristic
2#23752688C211yesmaximal, characteristic, complemented
3#23752684C211yesmaximal, characteristic
4#23752314C211yesmaximal, characteristic, complemented
5#23752313C211yesmaximal, characteristic, complemented
6#23752311C211yesmaximal, characteristic, complemented
7#23752303C211yesmaximal, characteristic, complemented
8C4×#14558991C211yesmaximal, characteristic, complemented
9C4×#14558992C211yesmaximal, characteristic, complemented
10#23752297C211yesmaximal, characteristic, complemented
11#23752249C211yesmaximal, characteristic, complemented
12#23752219C211yesmaximal, characteristic, complemented
13#23752215C211yesmaximal, characteristic
14#23752169C211yesmaximal, characteristic, complemented
15#440×C151C211yesmaximal, characteristic, complemented
16C2×Q8×D151C2211yescharacteristic
17C2×D4×D151C2211yescharacteristic
18C2×#14558993C2211yescharacteristic
19C2×#14558992C2211yescharacteristic
20C2×#14558991C2211yescharacteristic
21SD16×D151C418yescomplemented
22C2×#14558987C2211yescharacteristic
23C2×C8×D151C2211yescharacteristic
24Q8×Dic151C2211yescharacteristic, complemented
25C4×Dic302—21no—
26C4×Dic302C2211yescharacteristic, complemented
27#18012704—21no—
28#18012704C2211yescharacteristic, complemented
29C4×D604C2211yescharacteristic
30D4×Dic151C2211yescharacteristic
31#18012701C2211yescharacteristic
32C4×C22⋊D151—21no—
33(C22⋊D151)⋊C4—21no—
34#18012697—21no—
35#18012697C2211yescharacteristic
36#18012697C2211yescharacteristic
37#18012696—21no—
38#18012696C2211yescharacteristic
39C2×(C2×D151)⋊C4—21no—
40C22⋊C4×D151—21no—
41#18012673C2211yescharacteristic, complemented
42#18012670C2211yescharacteristic, complemented
43#18012670C2211yescharacteristic, complemented
44#18012664C2211yescharacteristic, complemented
45#18012663C2211yescharacteristic, complemented
46#18012662C2211yescharacteristic, complemented
47#18012661C2211yescharacteristic
48#18012660C2211yescharacteristic
49#18012659C2211yescharacteristic
50#18012649C2211yescharacteristic, complemented
51C4×C151⋊C8C2211yescharacteristic, complemented
52C8×Dic151C2211yescharacteristic, complemented
53C2×SD16×C151C2211yescharacteristic
54C4×Q8×C151C2211yescharacteristic, complemented
55C4×D4×C151C2211yescharacteristic
56#107×C151C2211yescharacteristic, complemented
57#103×C151C2211yescharacteristic, complemented
58#102×C151C2211yescharacteristic
59#97×C151C2211yescharacteristic, complemented
60C23×D151—21no—
61C2×Dic302—21no—
62C2×Dic302C2311yescharacteristic
63Q8×D151—22no—
64Q8×D151C2×C414yescomplemented
65C2×D604C2311yescharacteristic
66C2×C22⋊D151—21no—
67D4×D151—22no—
68D4×D151C2×C414yes—
69C22×Dic151—21no—
70C2×C4×D151—21no—
71C2×C4×D151—21no—
72C2×C4×D151—21no—
73C2×C4×D151C2311yescharacteristic
74#14558993C2×C414yescomplemented
75#14558992C2×C414yescomplemented
76#14558991C2×C414yescomplemented
77#14558987—22no—
78C2×C151⋊C8C2311yescharacteristic
79C2×C151⋊C8C2311yescharacteristic
80C8×D151C2×C414yescomplemented
81C4⋊Dic151—21no—
82C4⋊Dic151C2311yescharacteristic
83C4⋊Dic151C2311yescharacteristic
84Dic151⋊C4—21no—
85Dic151⋊C4—21no—
86Dic151⋊C4D411yescharacteristic
87Dic151⋊C4D411yescharacteristic
88C22⋊Dic151—21no—
89(C2×D151)⋊C4—21no—
90(C2×D151)⋊C4—21no—
91(C2×D151)⋊C4—21no—
92(C2×D151)⋊C4—21no—
93(C2×D151)⋊C4D411yescharacteristic
94(C2×D151)⋊C4D411yescharacteristic
95C4×Dic151—21no—
96C4×Dic151—21no—
97C4×Dic151—21no—
98C4×Dic151—21no—
99C4×Dic151—21no—
100C4×Dic151C2311yescharacteristic
101C2×Q8×C151C2311yescharacteristic
102C2×D4×C151C2311yescharacteristic
103C22×C4×C151—21no—
104SD16×C151C2×C414yescomplemented
105C2×C8×C151C2311yescharacteristic
106C2×C8×C151C2311yescharacteristic
107C4⋊C4×C151—21no—
108C4⋊C4×C151C2311yescharacteristic
109C4⋊C4×C151C2311yescharacteristic
110C22⋊C4×C151—21no—
111C42×C151—21no—
112C42×C151C2311yescharacteristic
113C22×D151—21no—
114C22×D151—24no—
115C22×D151—81no—
116C22×D151—81no—
117C22×D151C2×D411yescharacteristic
118Dic302—21no—
119Dic302—24no—
120Dic302C22×C412yes—
121D604—21no—
122D604C22×C412yes—
123C22⋊D151—24no—
124C2×Dic151—21no—
125C2×Dic151—21no—
126C2×Dic151—21no—
127C2×Dic151—81no—
128C2×Dic151C2×D411yescharacteristic
129C2×Dic151C2×D411yescharacteristic
130C2×Dic151C2×D411yescharacteristic
131C4×D151—24no—
132C4×D151—81no—
133C4×D151—81no—
134C4×D151C22×C412yes—
135C4×D151#4112yes—
136C151⋊C8—21no—
137C151⋊C8C22×C412yes—
138C23×C151—21no—
139Q8×C151—21no—
140Q8×C151C22×C412yes—
141D4×C151—21no—
142D4×C151C22×C412yes—
143C2×C4×C151—21no—
144C2×C4×C151—21no—
145C2×C4×C151—21no—
146C2×C4×C151—81no—
147C2×C4×C151C2×D411yescharacteristic
148C2×C4×C151C2×D411yescharacteristic
149C2×C4×C151C2411yescharacteristic
150C8×C151—21no—
151C8×C151C22×C412yes—
152C22×C151—22no—
153C22×C151—41no—
154C22×C151—41no—
155C22×C151C22×D411yescharacteristic
156C2×D151—21no—
157C2×D151—21no—
158C2×D151—22no—
159C2×D151—41no—
160C2×D151—41no—
161C2×D151—84no—
162C2×D151C4×D412yes—
163C4×C151—22no—
164C4×C151—21no—
165C4×C151—21no—
166C4×C151—41no—
167C4×C151—41no—
168C4×C151C23×C411yescharacteristic
169C4×C151C2×#4111yescharacteristic
170Dic151—22no—
171Dic151—21no—
172Dic151—21no—
173Dic151—41no—
174Dic151—41no—
175Dic151C4×D412yes—
176C2×C151—42no—
177C2×C151C2×C4×D411yescharacteristic
178C2×C151#57711yescharacteristic
179C2×C151#57711yescharacteristic
180D151—22no—
181D151—42no—
182C151#294911yescharacteristic, complemented, Sylow
183#2949—1511nomaximal, Sylow
184C22×SD16—1511no—
185#519—1511no—
186#518—1511no—
187#440—1511no—
188#440—1511no—
189#440—1511no—
190#440D15111yescharacteristic, complemented
191C4×SD16—1511no—
192C4×SD16—1511no—
193C4×SD16—1511no—
194C4×SD16—1511no—
195#427—1511no—
196#419—1511no—
197#418—1511no—
198#405—1511no—
199C22×Q8—1511no—
200C22×D4—1511no—
201C2×SD16—1511no—
202C2×SD16—1511no—
203C2×SD16—1518no—
204C2×SD16—1511no—
205C2×SD16C2×D15111yescharacteristic
206C2×M16—1511no—
207C22×C8—1511no—
208C4×Q8—3021no—
209C4×Q8—3021no—
210C4×Q8—1511no—
211C4×Q8—1511no—
212C4×Q8—1511no—
213C4×Q8C2×D15111yescharacteristic, complemented
214C4×D4—3021no—
215C4×D4—3021no—
216C4×D4—1511no—
217C4×D4—1511no—
218C4×D4—1511no—
219C4×D4C2×D15111yescharacteristic
220#117—3021no—
221#117—3021no—
222#117—1511no—
223#117—1511no—
224#117—1511no—
225C2×C22⋊C4—3021no—
226C2×C22⋊C4—3021no—
227#107—1511no—
228#107C2×D15111yescharacteristic, complemented
229#106—1511no—
230#106—1511no—
231#103—1511no—
232#103—1511no—
233#103—1511no—
234#103C2×D15111yescharacteristic, complemented
235#102—1511no—
236#102—1511no—
237#102—1511no—
238#102C2×D15111yescharacteristic
239#97—1511no—
240#97C2×D15111yescharacteristic, complemented
241C4×C8—1511no—
242C4×C8—1511no—
243C24—3021no—
244C2×Q8—3021no—
245C2×Q8—3022no—
246C2×Q8—1514no—
247C2×Q8—1511no—
248C2×Q8C22×D15111yescharacteristic
249C2×D4—3022no—
250C2×D4—3021no—
251C2×D4—1514no—
252C2×D4—1511no—
253C2×D4C22×D15111yescharacteristic
254C22×C4—21no—
255C22×C4—3021no—
256C22×C4—3021no—
257C22×C4—3021no—
258C22×C4—3021no—
259C22×C4—1511no—
260SD16—1514no—
261SD16—1514no—
262SD16—1514no—
263SD16C4×D15114yescomplemented
264M16—3022no—
265C2×C8—1511no—
266C2×C8—1511no—
267C2×C8—1514no—
268C2×C8C22×D15111yescharacteristic
269C2×C8C22×D15111yescharacteristic
270C4⋊C4—21no—
271C4⋊C4—3021no—
272C4⋊C4—3021no—
273C4⋊C4—3021no—
274C4⋊C4—1511no—
275C4⋊C4—1511no—
276C4⋊C4—1511no—
277C4⋊C4—1511no—
278C4⋊C4C22×D15111yescharacteristic
279C4⋊C4C22×D15111yescharacteristic
280C22⋊C4—21no—
281C22⋊C4—3021no—
282C22⋊C4—3021no—
283C22⋊C4—3021no—
284C22⋊C4—3021no—
285C22⋊C4—3021no—
286C22⋊C4—1511no—
287C22⋊C4—1511no—
288C42—21no—
289C42—3021no—
290C42—3021no—
291C42—3021no—
292C42—3021no—
293C42—3021no—
294C42—1511no—
295C42C22×D15111yescharacteristic
296C23—21no—
297C23—3024no—
298C23—3021no—
299C23—1511no—
300C23—12081no—
301C23—12081no—
302Q8—21no—
303Q8—3024no—
304Q8—3021no—
305Q8—1512no—
306Q8C2×C4×D15112yes—
307D4—21no—
308D4—3024no—
309D4—3021no—
310D4—1512no—
311D4C2×C4×D15112yes—
312C2×C4—21no—
313C2×C4—21no—
314C2×C4—21no—
315C2×C4—81no—
316C2×C4—3024no—
317C2×C4—3021no—
318C2×C4—3021no—
319C2×C4—3021no—
320C2×C4—1511no—
321C2×C4—1511no—
322C2×C4—1511no—
323C2×C4—1512no—
324C2×C4—1512no—
325C2×C4—12081no—
326C2×C4—12081no—
327C2×C4—12081no—
328C2×C4D4×D15111yescharacteristic
329C2×C4D4×D15111yescharacteristic
330C2×C4C23×D15111yescharacteristic
331C8—21no—
332C8—3021no—
333C8—1512no—
334C8C2×C4×D15112yes—
335C22—22no—
336C22—41no—
337C22—41no—
338C22—3021no—
339C22—3021no—
340C22—3022no—
341C22—6041no—
342C22—6041no—
343C22—1512no—
344C22—12084no—
345C22C2×D4×D15111yescharacteristic
346C4—21no—
347C4—21no—
348C4—22no—
349C4—41no—
350C4—41no—
351C4—3021no—
352C4—3021no—
353C4—3022no—
354C4—6041no—
355C4—6041no—
356C4—1512no—
357C4C22×C4×D15111yescharacteristic
358C4#41×D15111yescharacteristic
359C2—42no—
360C2—3022no—
361C2—6042no—
362C2C4×D4×D15111yescharacteristic
363C2#2375302111yescharacteristic
364C2#2375302211yescharacteristic
subgroupG/H
centerC22C2×D4×D151
commutatorC4×C151C23×C4
FrattiniC2×C4C23×D151
Fitting#440×C151C2
socleC22×C151C22×D4
prime radicalC2×D4×D151C22
cosocleC2×C4×C151C24
hypercenter#440D151
hypocenterC151#2949
LCSG ▷ C4×C151 ▷ C2×C151 ▷ C151
UCSC1 ◁ C22 ◁ C42 ◁ #440

Complements

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

NH ≅ G/Ntype
2. #23752688C2semidirect
4. #23752314C2semidirect
5. #23752313C2semidirect
6. #23752311C2semidirect
7. #23752303C2semidirect
8. C4×#14558991C2semidirect
9. C4×#14558992C2semidirect
10. #23752297C2semidirect
11. #23752249C2semidirect
12. #23752219C2semidirect
14. #23752169C2semidirect
15. #440×C151C2semidirect
21. SD16×D151C4semidirect
24. Q8×Dic151C22semidirect
26. C4×Dic302C22semidirect
28. #18012704C22semidirect
41. #18012673C22semidirect
42. #18012670C22semidirect
43. #18012670C22semidirect
44. #18012664C22semidirect
45. #18012663C22semidirect
46. #18012662C22semidirect
50. #18012649C22semidirect
51. C4×C151⋊C8C22semidirect
52. C8×Dic151C22semidirect
54. C4×Q8×C151C22semidirect
56. #107×C151C22semidirect
57. #103×C151C22semidirect
59. #97×C151C22semidirect
64. Q8×D151C2×C4semidirect
74. #14558993C2×C4semidirect
75. #14558992C2×C4semidirect
76. #14558991C2×C4semidirect
80. C8×D151C2×C4semidirect
104. SD16×C151C2×C4semidirect
182. C151#2949semidirect
190. #440D151semidirect
213. C4×Q8C2×D151semidirect
228. #107C2×D151semidirect
234. #103C2×D151semidirect
240. #97C2×D151semidirect
263. SD16C4×D151semidirect

Maximal subgroups

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

subgroupindex
C2×SD16×D1512
#237526882
#237526842
#237523142
#237523132
#237523112
#237523032
C4×#145589912
C4×#145589922
#237522972
#237522492
#237522192
#237522152
#237521692
#440×C1512
#2949151