Finite Group Databasebeta

← #34080124

Subgroups — #34080124

Order 19328.

490 conjugacy classes of subgroups; only the 113 normal subgroups are shown.

normal subgroups only

This group has 490 conjugacy classes of subgroups — too many to draw. Only its 113 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#127×D151C211yesmaximal, characteristic, complemented
2#23752741C211yesmaximal, characteristic, complemented
3#23752602C211yesmaximal, characteristic, complemented
4#23752577C211yesmaximal, characteristic, complemented
5#23752576C211yesmaximal, characteristic, complemented
6#23752410C212yesmaximal, complemented
7#23752405C212yesmaximal, complemented
8#23752361C212yesmaximal, complemented
9#23752344C212yesmaximal, complemented
10#23752267C211yesmaximal, characteristic, complemented
11#496×C151C211yesmaximal, characteristic, complemented
12C2×D4×D151—21no—
13C2×D4×D151—21no—
14C2×D4×D151C2212yes—
15C2×#14558991C2212yescomplemented
16C2×#14558989C2212yescomplemented
17#18012736C2211yescharacteristic
18#18012735—21no—
19#18012735—21no—
20#18012735C2212yes—
21#18012732—21no—
22#18012731C2211yescharacteristic, complemented
23#18012721—21no—
24#18012715C2211yescharacteristic
25#18012710C2211yescharacteristic
26Q8×Dic151C2211yescharacteristic, complemented
27D4×Dic151C2211yescharacteristic, complemented
28(C22⋊D151)⋊C4—21no—
29#18012695—21no—
30C42×D151C2211yescharacteristic
31Dic151⋊C8C2212yescomplemented
32#18012661C2212yescomplemented
33#18012661C2212yescomplemented
34#18012660C2212yescomplemented
35#18012660C2212yescomplemented
36(C2×D151)⋊C8C2212yes—
37#18012650C2211yescharacteristic, complemented
38C2×SD16×C151C2212yescomplemented
39C2×D8×C151C2212yescomplemented
40#127×C151C2211yescharacteristic
41#124×C151C2211yescharacteristic, complemented
42#97×C151C2211yescharacteristic, complemented
43C23×D151—22no—
44C2×D604—21no—
45C2×D604—21no—
46C2×D604C2312yes—
47C2×C22⋊D151—21no—
48C2×C22⋊D151—22no—
49C2×C22⋊D151—22no—
50C2×C22⋊D151—22no—
51D4×D151—42no—
52D4×D151—42no—
53D4×D151—44no—
54D4×D151—44no—
55C22×Dic151—21no—
56C2×C4×D151D411yescharacteristic
57C2×C4×D151D411yescharacteristic
58C2×C4×D151C2311yescharacteristic
59#14558991—42no—
60#14558989—42no—
61C2×C151⋊C8C2312yes—
62C4⋊Dic151—21no—
63C4⋊Dic151C2311yescharacteristic
64C4⋊Dic151C2311yescharacteristic
65Dic151⋊C4—21no—
66Dic151⋊C4—21no—
67Dic151⋊C4—21no—
68C22⋊Dic151—21no—
69C22⋊Dic151—21no—
70(C2×D151)⋊C4—21no—
71C4×Dic151—21no—
72C4×Dic151D411yescharacteristic
73C4×Dic151D411yescharacteristic
74C4×Dic151C2311yescharacteristic
75C2×Q8×C151C2311yescharacteristic
76C2×D4×C151—21no—
77C2×D4×C151—21no—
78C2×D4×C151C2311yescharacteristic
79C2×D4×C151C2312yes—
80SD16×C151—42no—
81D8×C151—42no—
82C2×C8×C151C2312yes—
83C22⋊C4×C151—21no—
84C22⋊C4×C151—21no—
85C42×C151C2311yescharacteristic
86C22×D151—22no—
87C22×D151—44no—
88C22×D151—44no—
89C22×D151—44no—
90C22×D151C2×D411yescharacteristic
91D604—22no—
92D604—22no—
93D604—42no—
94D604—42no—
95C22⋊D151—44no—
96C22⋊D151—44no—
97C22⋊D151—42no—
98C22⋊D151—44no—
99C2×Dic151—21no—
100C2×Dic151—21no—
101C2×Dic151—42no—
102C2×Dic151C2×D411yescharacteristic
103C2×Dic151C2×D411yescharacteristic
104C2×Dic151C2×D411yescharacteristic
105C4×D151—22no—
106C4×D151—22no—
107C4×D151—22no—
108C151⋊C8—22no—
109C23×C151—21no—
110C23×C151—22no—
111Q8×C151—22no—
112D4×C151—22no—
113D4×C151—22no—
114D4×C151—22no—
115D4×C151—42no—
116D4×C151—42no—
117C2×C4×C151—21no—
118C2×C4×C151C2×D411yescharacteristic
119C2×C4×C151C2×D411yescharacteristic
120C2×C4×C151C2411yescharacteristic
121C8×C151—22no—
122C22×C151—41no—
123C22×C151—42no—
124C22×C151—42no—
125C22×C151—42no—
126C22×C151—41no—
127C22×C151—41no—
128C22×C151C22×D411yescharacteristic
129C2×D151—21no—
130C2×D151—21no—
131C2×D151—42no—
132C2×D151—42no—
133C2×D151—42no—
134C2×D151—88no—
135C2×D151AGL(1,ℤ/8)12yes—
136C4×C151—21no—
137C4×C151—21no—
138C4×C151—41no—
139C4×C151H(5,𝔽2)12yes—
140Dic151—21no—
141Dic151—21no—
142Dic151—41no—
143Dic151—41no—
144Dic151AGL(1,ℤ/8)12yes—
145C2×C151—82no—
146C2×C151—81no—
147C2×C151#53511yescharacteristic
148C2×C151C2×AGL(1,ℤ/8)11yescharacteristic
149C2×C151C2×AGL(1,ℤ/8)11yescharacteristic
150D151—22no—
151D151—82no—
152C151#321711yescharacteristic, complemented, Sylow
153#3217—1511nomaximal, Sylow
154C2×#127—1511no—
155#529—1511no—
156#496—1511no—
157#496D15111yescharacteristic, complemented
158#490—1511no—
159#490—1511no—
160#460—1512no—
161#459—1512no—
162#450—1512no—
163#447—1512no—
164#432—1511no—
165C22×D4—3021no—
166C22×D4—3021no—
167C22×D4—1512no—
168C2×SD16—1512no—
169C2×SD16C2×D15112yescomplemented
170C2×D8—1512no—
171C2×D8C2×D15112yescomplemented
172#127—3021no—
173#127—3021no—
174#127—1512no—
175#127—1511no—
176#127C2×D15111yescharacteristic
177#126—3021no—
178#125—1511no—
179#124C2×D15111yescharacteristic, complemented
180#123—3021no—
181C22⋊Q8—1511no—
182#121—1511no—
183C4×Q8—1511no—
184C4×D4—3021no—
185C4×D4—1511no—
186#117—3021no—
187C2×C42—1511no—
188C4⋊C8—1512no—
189#102—1512no—
190#102—1512no—
191#102—1512no—
192#102—1512no—
193C22⋊C8—1512no—
194#97—1511no—
195#97C2×D15111yescharacteristic, complemented
196C24—3022no—
197C2×Q8C22×D15111yescharacteristic
198C2×D4—21no—
199C2×D4—21no—
200C2×D4—3021no—
201C2×D4—3022no—
202C2×D4—3022no—
203C2×D4—3022no—
204C2×D4—3021no—
205C2×D4—3021no—
206C2×D4—6042no—
207C2×D4—6042no—
208C2×D4—6044no—
209C2×D4—6044no—
210C2×D4—1512no—
211C2×D4C22×D15112yes—
212C2×D4C22×D15111yescharacteristic
213C22×C4—3021no—
214C22×C4—1511no—
215C22×C4—1511no—
216C22×C4—1511no—
217SD16—42no—
218SD16—6042no—
219D8—42no—
220D8—6042no—
221C2×C8—1512no—
222C2×C8C22×D15112yes—
223C4⋊C4—3021no—
224C4⋊C4—3021no—
225C4⋊C4—3021no—
226C4⋊C4—3021no—
227C4⋊C4—1511no—
228C4⋊C4—1511no—
229C22⋊C4—21no—
230C22⋊C4—21no—
231C22⋊C4—3021no—
232C22⋊C4—3021no—
233C22⋊C4—3021no—
234C42—3021no—
235C42—1511no—
236C42—1511no—
237C42—1511no—
238C42C22×D15111yescharacteristic
239C23—21no—
240C23—22no—
241C23—3022no—
242C23—6044no—
243C23—6044no—
244C23—6044no—
245C23—1511no—
246Q8—22no—
247D4—22no—
248D4—22no—
249D4—22no—
250D4—42no—
251D4—42no—
252D4—3022no—
253D4—3022no—
254D4—6042no—
255D4—6042no—
256D4—6044no—
257D4—6044no—
258D4—6042no—
259D4—6044no—
260C2×C4—21no—
261C2×C4—3022no—
262C2×C4—3022no—
263C2×C4—3022no—
264C2×C4—3021no—
265C2×C4—3021no—
266C2×C4—6042no—
267C2×C4—1511no—
268C2×C4—1511no—
269C2×C4—1511no—
270C2×C4D4×D15111yescharacteristic
271C2×C4D4×D15111yescharacteristic
272C2×C4C23×D15111yescharacteristic
273C8—22no—
274C8—3022no—
275C22—41no—
276C22—42no—
277C22—42no—
278C22—41no—
279C22—42no—
280C22—41no—
281C22—3021no—
282C22—3021no—
283C22—6042no—
284C22—6042no—
285C22—6042no—
286C22—1512no—
287C22—12088no—
288C22C2×D4×D15111yescharacteristic
289C4—21no—
290C4—21no—
291C4—41no—
292C4—3021no—
293C4—3021no—
294C4—6041no—
295C4—6041no—
296C4—1512no—
297C4#1801278412yes—
298C2—82no—
299C2—81no—
300C2—3022no—
301C2—12082no—
302C2#2375277511yescharacteristic
303C2AGL(1,ℤ/8)×D15111yescharacteristic
304C2AGL(1,ℤ/8)×D15111yescharacteristic
subgroupG/H
centerC22C2×D4×D151
commutator, cosocleC2×C4×C151C24
FrattiniC2×C4C23×D151
Fitting#496×C151C2
socleC22×C151C22×D4
hypercenter#496D151
hypocenterC151#3217
LCSG ▷ C2×C4×C151 ▷ C2×C151 ▷ C151
UCSC1 ◁ C22 ◁ C42 ◁ #496

Complements

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

NH ≅ G/Ntype
1. #127×D151C2semidirect
2. #23752741C2semidirect
3. #23752602C2semidirect
4. #23752577C2semidirect
5. #23752576C2semidirect
6. #23752410C2semidirect
7. #23752405C2semidirect
8. #23752361C2semidirect
9. #23752344C2semidirect
10. #23752267C2semidirect
11. #496×C151C2semidirect
15. C2×#14558991C22semidirect
16. C2×#14558989C22semidirect
22. #18012731C22semidirect
26. Q8×Dic151C22semidirect
27. D4×Dic151C22semidirect
31. Dic151⋊C8C22semidirect
32. #18012661C22semidirect
33. #18012661C22semidirect
34. #18012660C22semidirect
35. #18012660C22semidirect
37. #18012650C22semidirect
38. C2×SD16×C151C22semidirect
39. C2×D8×C151C22semidirect
41. #124×C151C22semidirect
42. #97×C151C22semidirect
152. C151#3217semidirect
157. #496D151semidirect
169. C2×SD16C2×D151semidirect
171. C2×D8C2×D151semidirect
179. #124C2×D151semidirect
195. #97C2×D151semidirect

Maximal subgroups

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

subgroupindex
#127×D1512
#237527412
#237526022
#237525772
#237525762
#237524102
#237524052
#237523612
#237523442
#237522672
#496×C1512
#3217151