Finite Group Databasebeta

← #34080926

Subgroups — #34080926

Order 19328.

494 conjugacy classes of subgroups; only the 123 normal subgroups are shown.

normal subgroups only

This group has 494 conjugacy classes of subgroups — too many to draw. Only its 123 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#23752867C211yesmaximal, characteristic, complemented
2#23752847C211yesmaximal, characteristic, complemented
3#23752558C211yesmaximal, characteristic, complemented
4#23752524C212yesmaximal, complemented
5#23752493C211yesmaximal, characteristic, complemented
6#23752445C212yesmaximal, complemented
7#23752344C212yesmaximal, complemented
8C4×#14558989C211yesmaximal, characteristic, complemented
9#23752277C211yesmaximal, characteristic, complemented
10#102×D151C212yesmaximal, complemented
11#459×C151C211yesmaximal, characteristic, complemented
12C2×#14559004—21no—
13C2×D4×D151—21no—
14C2×D4×D151C2212yes—
15C2×#14558989C2211yescharacteristic
16C2×C8×D151C2212yescomplemented
17#18012739C2211yescharacteristic, complemented
18#18012721—22no—
19#18012718—21no—
20#18012710—21no—
21#18012710C2212yes—
22#18012710C2212yescomplemented
23#18012707—22no—
24C4×D604C2211yescharacteristic
25C4×D604C2211yescharacteristic
26C4⋊C4×D151C2212yescomplemented
27#18012673C2212yescomplemented
28#18012672C2211yescharacteristic, complemented
29#18012661C2212yes—
30#18012660C2212yescomplemented
31#18012660C2212yescomplemented
32#18012660C2211yescharacteristic, complemented
33#18012659C2211yescharacteristic
34(C2×D151)⋊C8C2212yescomplemented
35C4×C151⋊C8C2211yescharacteristic, complemented
36C2×D8×C151C2212yescomplemented
37#127×C151C2211yescharacteristic
38C4×D4×C151C2211yescharacteristic, complemented
39C4⋊C8×C151C2211yescharacteristic, complemented
40#102×C151C2212yescomplemented
41C23×D151—22no—
42#14559004—44no—
43C2×Dic302—21no—
44C2×D604D411yescharacteristic
45C2×D604C2311yescharacteristic
46C2×C22⋊D151—22no—
47C2×C22⋊D151—22no—
48C2×C22⋊D151—22no—
49D4×D151—24no—
50D4×D151—42no—
51D4×D151—44no—
52C2×C4×D151—22no—
53C2×C4×D151—21no—
54C2×C4×D151C2312yes—
55#14558989—22no—
56C2×C151⋊C8C2311yescharacteristic
57C2×C151⋊C8C2311yescharacteristic
58C8×D151—42no—
59C4⋊Dic151—21no—
60C4⋊Dic151D411yescharacteristic
61C4⋊Dic151C2311yescharacteristic
62C4⋊Dic151C2312yes—
63Dic151⋊C4—22no—
64C22⋊Dic151—22no—
65C22⋊Dic151—22no—
66(C2×D151)⋊C4—21no—
67(C2×D151)⋊C4D412yes—
68C2×D4×C151—21no—
69C2×D4×C151—21no—
70C2×D4×C151C2312yes—
71C2×D4×C151C2311yescharacteristic
72C22×C4×C151—21no—
73D8×C151—42no—
74C2×C8×C151C2312yes—
75C4⋊C4×C151C2311yescharacteristic
76C22⋊C4×C151—21no—
77C42×C151C2311yescharacteristic
78C22×D151—21no—
79C22×D151—44no—
80C22×D151—44no—
81C22×D151—82no—
82C22×D151C2×D412yes—
83Dic302—42no—
84D604—21no—
85D604D814yescomplemented
86D604#4112yescomplemented
87C22⋊D151—44no—
88C22⋊D151—44no—
89C22⋊D151—44no—
90C2×Dic151—21no—
91C2×Dic151—22no—
92C2×Dic151C2×D412yes—
93C4×D151—22no—
94C4×D151—22no—
95C4×D151—44no—
96C4×D151—42no—
97C151⋊C8—21no—
98C151⋊C8—21no—
99C23×C151—21no—
100C23×C151—22no—
101D4×C151—21no—
102D4×C151—22no—
103D4×C151—22no—
104D4×C151—21no—
105D4×C151—42no—
106D4×C151—81no—
107C2×C4×C151—21no—
108C2×C4×C151—42no—
109C2×C4×C151C2×D411yescharacteristic
110C2×C4×C151C2×D411yescharacteristic
111C2×C4×C151C2411yescharacteristic
112C8×C151—22no—
113C22×C151—41no—
114C22×C151—42no—
115C22×C151—41no—
116C22×C151—42no—
117C22×C151—42no—
118C22×C151—41no—
119C22×C151C22×D411yescharacteristic
120C2×D151—22no—
121C2×D151—22no—
122C2×D151—22no—
123C2×D151—41no—
124C2×D151—41no—
125C2×D151—88no—
126C2×D151C2×D814yes—
127C4×C151—21no—
128C4×C151—41no—
129C4×C151C2×D812yes—
130C4×C151C2×#4111yescharacteristic
131C4×C151H(5,𝔽2)11yescharacteristic
132Dic151—22no—
133Dic151—41no—
134Dic151—42no—
135C2×C151—82no—
136C2×C151—81no—
137C2×C151#54611yescharacteristic
138C2×C151C22×D811yescharacteristic
139C2×C151#57711yescharacteristic
140D151—24no—
141D151—42no—
142C151#329411yescharacteristic, complemented, Sylow
143#3294—1511nomaximal, Sylow
144#547—1511no—
145D42—1511no—
146#486—1511no—
147#480—1512no—
148#474—1511no—
149#466—1512no—
150#459D15111yescharacteristic, complemented
151#447—1512no—
152C4×D8—1511no—
153C8×D4—1511no—
154C2×#102—1512no—
155C2×#41—3021no—
156C22×D4—3021no—
157C22×D4—1512no—
158C2×D8—1511no—
159C2×D8C2×D15112yescomplemented
160C22×C8—1512no—
161C4⋊Q8—1511no—
162#127C2×D15111yescharacteristic
163#123—3022no—
164C22⋊Q8—3021no—
165#121—3021no—
166#121—1512no—
167#121—1512no—
168#120—3022no—
169C4×D4—1511no—
170C4×D4—1511no—
171C4×D4C2×D15111yescharacteristic, complemented
172C2×C4⋊C4—1512no—
173#107—1512no—
174#107—1511no—
175C4⋊C8C2×D15111yescharacteristic, complemented
176#102—1512no—
177#102—1511no—
178#102—1512no—
179#102—1512no—
180#102—1511no—
181#102C2×D15112yescomplemented
182C22⋊C8—1512no—
183C4×C8—1511no—
184C24—3022no—
185#41—6044no—
186C2×Q8—3021no—
187C2×D4—21no—
188C2×D4—21no—
189C2×D4—3024no—
190C2×D4—3022no—
191C2×D4—3022no—
192C2×D4—3022no—
193C2×D4—6042no—
194C2×D4—6044no—
195C2×D4—1511no—
196C2×D4—1511no—
197C2×D4C22×D15112yes—
198C2×D4C22×D15111yescharacteristic
199C22×C4—21no—
200C22×C4—3022no—
201C22×C4—3021no—
202C22×C4—1512no—
203D8—42no—
204D8—3022no—
205C2×C8—6042no—
206C2×C8—1511no—
207C2×C8—1511no—
208C2×C8C22×D15112yes—
209C4⋊C4—3022no—
210C4⋊C4—3021no—
211C4⋊C4—1512no—
212C4⋊C4—1511no—
213C4⋊C4—1511no—
214C4⋊C4C22×D15111yescharacteristic
215C22⋊C4—21no—
216C22⋊C4—3022no—
217C22⋊C4—3022no—
218C22⋊C4—3021no—
219C22⋊C4—1512no—
220C42C22×D15111yescharacteristic
221C23—21no—
222C23—22no—
223C23—3021no—
224C23—6044no—
225C23—6044no—
226C23—1512no—
227C23—12082no—
228Q8—6042no—
229D4—21no—
230D4—22no—
231D4—21no—
232D4—22no—
233D4—42no—
234D4—81no—
235D4—3021no—
236D4—6044no—
237D4—6044no—
238D4—6044no—
239D4—1514no—
240D4—1512no—
241C2×C4—21no—
242C2×C4—42no—
243C2×C4—3022no—
244C2×C4—3022no—
245C2×C4—3021no—
246C2×C4—3022no—
247C2×C4—6044no—
248C2×C4—6042no—
249C2×C4—1512no—
250C2×C4D4×D15111yescharacteristic
251C2×C4D4×D15111yescharacteristic
252C2×C4C23×D15111yescharacteristic
253C8—22no—
254C8—3021no—
255C8—3021no—
256C22—41no—
257C22—42no—
258C22—42no—
259C22—41no—
260C22—42no—
261C22—41no—
262C22—3022no—
263C22—3022no—
264C22—3022no—
265C22—6041no—
266C22—6041no—
267C22—1514no—
268C22—12088no—
269C22C2×D4×D15111yescharacteristic
270C4—21no—
271C4—41no—
272C4—3022no—
273C4—6041no—
274C4—6042no—
275C4D8×D15112yes—
276C4#41×D15111yescharacteristic
277C4#1801278411yescharacteristic
278C2—82no—
279C2—81no—
280C2—3024no—
281C2—6042no—
282C2#2375285911yescharacteristic
283C2C2×D8×D15111yescharacteristic
284C2#2375302211yescharacteristic
subgroupG/H
centerC22C2×D4×D151
commutator, cosocleC2×C4×C151C24
FrattiniC2×C4C23×D151
Fitting#459×C151C2
socleC22×C151C22×D4
hypercenter#459D151
hypocenterC151#3294
LCSG ▷ C2×C4×C151 ▷ C2×C151 ▷ C151
UCSC1 ◁ C22 ◁ C42 ◁ #459

Complements

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

NH ≅ G/Ntype
1. #23752867C2semidirect
2. #23752847C2semidirect
3. #23752558C2semidirect
4. #23752524C2semidirect
5. #23752493C2semidirect
6. #23752445C2semidirect
7. #23752344C2semidirect
8. C4×#14558989C2semidirect
9. #23752277C2semidirect
10. #102×D151C2semidirect
11. #459×C151C2semidirect
16. C2×C8×D151C22semidirect
17. #18012739C22semidirect
22. #18012710C22semidirect
26. C4⋊C4×D151C22semidirect
27. #18012673C22semidirect
28. #18012672C22semidirect
30. #18012660C22semidirect
31. #18012660C22semidirect
32. #18012660C22semidirect
34. (C2×D151)⋊C8C22semidirect
35. C4×C151⋊C8C22semidirect
36. C2×D8×C151C22semidirect
38. C4×D4×C151C22semidirect
39. C4⋊C8×C151C22semidirect
40. #102×C151C22semidirect
85. D604D8semidirect
86. D604#41semidirect
142. C151#3294semidirect
150. #459D151semidirect
159. C2×D8C2×D151semidirect
171. C4×D4C2×D151semidirect
175. C4⋊C8C2×D151semidirect
181. #102C2×D151semidirect

Maximal subgroups

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

subgroupindex
#237528672
#237528472
#237525582
#237525242
#237524932
#237524452
#237523442
C4×#145589892
#237522772
#102×D1512
#459×C1512
#3294151