Finite Group Databasebeta

← #34079878

Subgroups — #34079878

Order 19328.

472 conjugacy classes of subgroups; only the 115 normal subgroups are shown.

normal subgroups only

This group has 472 conjugacy classes of subgroups — too many to draw. Only its 115 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#23752725C211yesmaximal, characteristic, complemented
2C2×#18012710C211yesmaximal, characteristic, complemented
3#23752545C211yesmaximal, characteristic, complemented
4#23752535C212yesmaximal, complemented
5#23752531C211yesmaximal, characteristic, complemented
6#23752447C212yesmaximal, complemented
7#23752438C212yesmaximal, complemented
8#23752356C212yesmaximal, complemented
9#23752346C211yesmaximal, characteristic, complemented
10C22⋊C8×D151C211yesmaximal, characteristic, complemented
11#450×C151C211yesmaximal, characteristic, complemented
12C2×#14559005C2211yescharacteristic, complemented
13C22×C22⋊D151—21no—
14C22×C4×D151C2211yescharacteristic
15C2×#14558989C2212yescomplemented
16C2×C8×D151C2212yescomplemented
17#18012724—21no—
18#18012715C2211yescharacteristic, complemented
19#18012714C2211yescharacteristic, complemented
20#18012713C2211yescharacteristic
21#18012710—21no—
22#18012710—21no—
23#18012710C2212yes—
24#18012710C2212yes—
25#18012709—21no—
26#18012701—21no—
27(C22⋊D151)⋊C4—21no—
28#18012697C2211yescharacteristic, complemented
29C2×C4⋊Dic151C2211yescharacteristic
30C2×C22⋊Dic151—21no—
31#18012672C2212yescomplemented
32#18012671C2212yescomplemented
33#18012663C2212yescomplemented
34#18012661C2212yescomplemented
35#18012660C2212yescomplemented
36C22⋊(C151⋊C8)C2211yescharacteristic
37(C2×D151)⋊C8C2212yescomplemented
38C22×D4×C151C2211yescharacteristic
39C2×SD16×C151C2212yescomplemented
40C22⋊Q8×C151C2211yescharacteristic
41#102×C151C2212yescomplemented
42C22⋊C8×C151C2211yescharacteristic
43C23×D151D411yescharacteristic
44#14559005—42no—
45C2×D604—21no—
46C2×D604—21no—
47C2×D604C2311yescharacteristic
48C2×C22⋊D151—22no—
49C2×C22⋊D151—22no—
50C2×C22⋊D151—21no—
51C2×C22⋊D151—44no—
52C22×Dic151—21no—
53C22×Dic151D411yescharacteristic
54C2×C4×D151—21no—
55C2×C4×D151—42no—
56C2×C4×D151D411yescharacteristic
57C2×C4×D151D411yescharacteristic
58C2×C4×D151C2311yescharacteristic
59C2×C4×D151C2311yescharacteristic
60#14558989—42no—
61C2×C151⋊C8C2312yes—
62C8×D151—42no—
63C4⋊Dic151—21no—
64C4⋊Dic151C2312yes—
65C4⋊Dic151C2311yescharacteristic
66Dic151⋊C4—21no—
67C22⋊Dic151—22no—
68C22⋊Dic151—22no—
69(C2×D151)⋊C4—21no—
70(C2×D151)⋊C4—21no—
71(C2×D151)⋊C4—21no—
72(C2×D151)⋊C4—21no—
73C4×Dic151—21no—
74C24×C151—21no—
75C2×Q8×C151C2311yescharacteristic
76C2×D4×C151—21no—
77C2×D4×C151—42no—
78C2×D4×C151C2312yes—
79C22×C4×C151C2311yescharacteristic
80SD16×C151—42no—
81C2×C8×C151C2312yes—
82C4⋊C4×C151—21no—
83C4⋊C4×C151C2311yescharacteristic
84C22⋊C4×C151—21no—
85C22×D151—22no—
86C22×D151—22no—
87C22×D151—21no—
88C22×D151—41no—
89C22×D151C2×D411yescharacteristic
90C22×D151C2×D411yescharacteristic
91D604—22no—
92D604—42no—
93D604—42no—
94C22⋊D151—44no—
95C22⋊D151—42no—
96C22⋊D151—44no—
97C2×Dic151—21no—
98C2×Dic151—22no—
99C2×Dic151—41no—
100C2×Dic151—42no—
101C2×Dic151C2×D411yescharacteristic
102C2×Dic151C2×D411yescharacteristic
103C4×D151—22no—
104C4×D151—22no—
105C4×D151—41no—
106C4×D151—41no—
107C4×D151—42no—
108C151⋊C8—22no—
109C23×C151—22no—
110C23×C151—42no—
111C23×C151—42no—
112C23×C151—42no—
113C23×C151C2×D411yescharacteristic
114Q8×C151—22no—
115D4×C151—22no—
116D4×C151—22no—
117D4×C151—42no—
118C2×C4×C151—22no—
119C2×C4×C151—21no—
120C2×C4×C151—21no—
121C2×C4×C151C2×D411yescharacteristic
122C2×C4×C151C2411yescharacteristic
123C8×C151—22no—
124C22×C151—21no—
125C22×C151—21no—
126C22×C151—42no—
127C22×C151—42no—
128C22×C151—42no—
129C22×C151—84no—
130C22×C151#13512yes—
131C22×C151C22×D411yescharacteristic
132C2×D151—21no—
133C2×D151—21no—
134C2×D151—21no—
135C2×D151—21no—
136C2×D151—21no—
137C2×D151—44no—
138C2×D151—41no—
139C2×D151—41no—
140C2×D151—41no—
141C2×D151AGL(1,ℤ/8)12yes—
142C4×C151—21no—
143C4×C151—41no—
144C4×C151—41no—
145C4×C151H(5,𝔽2)12yes—
146Dic151—21no—
147Dic151—21no—
148Dic151—41no—
149Dic151—42no—
150C2×C151—22no—
151C2×C151—82no—
152C2×C151#53411yescharacteristic
153C2×C151C2×#13511yescharacteristic
154C2×C151C2×AGL(1,ℤ/8)11yescharacteristic
155D151—22no—
156D151—41no—
157D151—81no—
158C151#318811yescharacteristic, complemented, Sylow
159#3188—1511nomaximal, Sylow
160#525—1511no—
161C2×#121—1511no—
162#484—1511no—
163#482—1512no—
164#481—1511no—
165#466—1512no—
166#465—1512no—
167#450D15111yescharacteristic, complemented
168#449—1512no—
169#447—1511no—
170C2×C22⋊C8—1511no—
171C2×#41—1511no—
172C22×D4—3021no—
173C22×D4C2×D15111yescharacteristic
174C23×C4—1511no—
175C2×SD16C2×D15112yescomplemented
176C2×D8—1512no—
177C22×C8—1512no—
178#123—3021no—
179C22⋊Q8—1511no—
180C22⋊Q8C2×D15111yescharacteristic
181#121—3021no—
182#121—3021no—
183#121—1512no—
184#121—1512no—
185#121—1511no—
186#121—1511no—
187#120—3021no—
188C4×D4—3021no—
189C4×D4—3021no—
190#117—1511no—
191C2×C4⋊C4—1511no—
192C2×C22⋊C4—3021no—
193#107—1512no—
194#106—1512no—
195#103—1512no—
196#102—1512no—
197#102—1512no—
198#102C2×D15112yescomplemented
199C22⋊C8—1511no—
200C22⋊C8—1512no—
201C22⋊C8C2×D15111yescharacteristic
202C24—21no—
203C24—1511no—
204#41—6042no—
205C2×Q8C22×D15111yescharacteristic
206C2×D4—21no—
207C2×D4—42no—
208C2×D4—3021no—
209C2×D4—3021no—
210C2×D4—3022no—
211C2×D4—3022no—
212C2×D4—3021no—
213C2×D4—6044no—
214C2×D4—1511no—
215C2×D4C22×D15112yes—
216C22×C4—3021no—
217C22×C4—3021no—
218C22×C4—6042no—
219C22×C4—1511no—
220C22×C4—1511no—
221C22×C4—1511no—
222C22×C4—1511no—
223C22×C4—1511no—
224C22×C4C22×D15111yescharacteristic
225SD16—42no—
226D8—6042no—
227C2×C8—6042no—
228C2×C8—1512no—
229C2×C8C22×D15112yes—
230C4⋊C4—21no—
231C4⋊C4—3021no—
232C4⋊C4—3021no—
233C4⋊C4—1511no—
234C4⋊C4—1512no—
235C4⋊C4C22×D15111yescharacteristic
236C22⋊C4—21no—
237C22⋊C4—3021no—
238C22⋊C4—3021no—
239C22⋊C4—3021no—
240C22⋊C4—3022no—
241C22⋊C4—3022no—
242C22⋊C4—3021no—
243C42—3021no—
244C23—22no—
245C23—42no—
246C23—42no—
247C23—42no—
248C23—3022no—
249C23—3022no—
250C23—3021no—
251C23—6041no—
252C23—1511no—
253C23—1511no—
254C23D4×D15111yescharacteristic
255Q8—22no—
256D4—22no—
257D4—22no—
258D4—42no—
259D4—3022no—
260D4—6042no—
261D4—6042no—
262D4—6044no—
263D4—6044no—
264D4—6042no—
265C2×C4—22no—
266C2×C4—21no—
267C2×C4—21no—
268C2×C4—3022no—
269C2×C4—3022no—
270C2×C4—3021no—
271C2×C4—3022no—
272C2×C4—6041no—
273C2×C4—6041no—
274C2×C4—6042no—
275C2×C4—6041no—
276C2×C4—6042no—
277C2×C4—1511no—
278C2×C4—1511no—
279C2×C4D4×D15111yescharacteristic
280C2×C4C23×D15111yescharacteristic
281C8—22no—
282C8—3022no—
283C22—21no—
284C22—21no—
285C22—42no—
286C22—42no—
287C22—42no—
288C22—84no—
289C22—3021no—
290C22—3021no—
291C22—3021no—
292C22—3021no—
293C22—3021no—
294C22—6044no—
295C22—6041no—
296C22—6041no—
297C22—6041no—
298C22—1512no—
299C22#1801276012yes—
300C22C2×D4×D15111yescharacteristic
301C4—21no—
302C4—41no—
303C4—41no—
304C4—3021no—
305C4—3021no—
306C4—6041no—
307C4—6042no—
308C4#1801278412yes—
309C2—22no—
310C2—82no—
311C2—3022no—
312C2—6041no—
313C2—12081no—
314C2#2375277211yescharacteristic
315C2C2×#1801276011yescharacteristic
316C2AGL(1,ℤ/8)×D15111yescharacteristic
subgroupG/H
centerC22C2×D4×D151
commutator, cosocleC2×C4×C151C24
FrattiniC2×C4C23×D151
Fitting#450×C151C2
socleC22×C151C22×D4
hypercenter#450D151
hypocenterC151#3188
LCSG ▷ C2×C4×C151 ▷ C2×C151 ▷ C151
UCSC1 ◁ C22 ◁ C22×C4 ◁ #450

Complements

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

NH ≅ G/Ntype
1. #23752725C2semidirect
2. C2×#18012710C2semidirect
3. #23752545C2semidirect
4. #23752535C2semidirect
5. #23752531C2semidirect
6. #23752447C2semidirect
7. #23752438C2semidirect
8. #23752356C2semidirect
9. #23752346C2semidirect
10. C22⋊C8×D151C2semidirect
11. #450×C151C2semidirect
12. C2×#14559005C22semidirect
15. C2×#14558989C22semidirect
16. C2×C8×D151C22semidirect
18. #18012715C22semidirect
19. #18012714C22semidirect
28. #18012697C22semidirect
31. #18012672C22semidirect
32. #18012671C22semidirect
33. #18012663C22semidirect
34. #18012661C22semidirect
35. #18012660C22semidirect
37. (C2×D151)⋊C8C22semidirect
39. C2×SD16×C151C22semidirect
41. #102×C151C22semidirect
158. C151#3188semidirect
167. #450D151semidirect
175. C2×SD16C2×D151semidirect
198. #102C2×D151semidirect

Maximal subgroups

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

subgroupindex
#237527252
C2×#180127102
#237525452
#237525352
#237525312
#237524472
#237524382
#237523562
#237523462
C22⋊C8×D1512
#450×C1512
#3188151