Finite Group Databasebeta

← #34078349

Subgroups — #34078349

Order 19328.

758 conjugacy classes of subgroups; only the 149 normal subgroups are shown.

normal subgroups only

This group has 758 conjugacy classes of subgroups — too many to draw. Only its 149 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
1C22×#14559003C211yesmaximal, characteristic, complemented
2C2×#18012769C211yesmaximal, characteristic, complemented
3#23752719C211yesmaximal, characteristic, complemented
4#23752371C214yesmaximal, complemented
5#23752354C214yesmaximal, complemented
6#23752222C211yesmaximal, characteristic, complemented
7#23752217C211yesmaximal, characteristic, complemented
8#23752175C211yesmaximal, characteristic, complemented
9C2×AGL(1,ℤ/8)×C151C211yesmaximal, characteristic, complemented
10C2×#14559003—24no—
11C2×#14559003—24no—
12C2×#14559003—22no—
13C2×#14559003C2214yes—
14C22×Dic302C2211yescharacteristic
15C22×C22⋊D151—21no—
16C23×Dic151—21no—
17C22×C4×D151C2211yescharacteristic
18#18012769—24no—
19C2×#14558994C2212yescomplemented
20C2×#14558992C2212yescomplemented
21C2×#14558988C2211yescharacteristic
22#18012720—21no—
23#18012715C2212yescomplemented
24#18012710C2212yescomplemented
25#18012707—21no—
26C4×C22⋊D151—22no—
27#18012698C2211yescharacteristic
28#18012664C2214yescomplemented
29#18012660C2214yescomplemented
30(C2×D151)⋊C8C2214yescomplemented
31C2×#41×C151C2211yescharacteristic
32C22×D4×C151C2211yescharacteristic
33AGL(1,ℤ/8)×C151—24no—
34C2×SD16×C151C2212yescomplemented
35C2×D8×C151C2212yescomplemented
36C2×M16×C151C2211yescharacteristic
37C23×D151D411yescharacteristic
38#14559003—216no—
39#14559003—28no—
40#14559003—28no—
41C2×Dic302—21no—
42C2×Dic302—22no—
43C2×Dic302D414yescomplemented
44C2×Dic302C2312yes—
45C2×C22⋊D151—28no—
46C2×C22⋊D151—24no—
47C2×C22⋊D151—22no—
48C22×Dic151—28no—
49C22×Dic151—24no—
50C22×Dic151—21no—
51C22×Dic151D411yescharacteristic
52C2×C4×D151—22no—
53C2×C4×D151—22no—
54C2×C4×D151D412yes—
55C2×C4×D151C2312yes—
56#14558994—24no—
57#14558992—24no—
58#14558988—22no—
59C2×C151⋊C8C2312yes—
60C4⋊Dic151C2312yes—
61Dic151⋊C4—22no—
62C22⋊Dic151—22no—
63C22⋊Dic151—21no—
64(C2×D151)⋊C4—22no—
65C4×Dic151—21no—
66C24×C151—21no—
67#41×C151—22no—
68#41×C151—22no—
69C2×Q8×C151C2311yescharacteristic
70C2×D4×C151—21no—
71C2×D4×C151—21no—
72C2×D4×C151—22no—
73C2×D4×C151D414yescomplemented
74C2×D4×C151C2311yescharacteristic
75C2×D4×C151C2312yes—
76C22×C4×C151—21no—
77C22×C4×C151C2311yescharacteristic
78SD16×C151—24no—
79D8×C151—24no—
80M16×C151—22no—
81C2×C8×C151C2312yes—
82C22×D151—22no—
83C22×D151—42no—
84C22×D151C2×D412yes—
85Dic302—24no—
86Dic302—22no—
87Dic302C2×D414yes—
88C22⋊D151—216no—
89C22⋊D151—44no—
90C2×Dic151—216no—
91C2×Dic151—22no—
92C2×Dic151—24no—
93C2×Dic151—22no—
94C2×Dic151—22no—
95C2×Dic151C2×D412yes—
96C4×D151—24no—
97C4×D151—22no—
98C4×D151—22no—
99C151⋊C8—22no—
100C23×C151—24no—
101C23×C151—22no—
102C23×C151—21no—
103C23×C151—44no—
104C23×C151C2×D411yescharacteristic
105Q8×C151—21no—
106Q8×C151—21no—
107D4×C151—24no—
108D4×C151—22no—
109D4×C151—21no—
110D4×C151—21no—
111D4×C151—42no—
112D4×C151C2×D414yes—
113C2×C4×C151—21no—
114C2×C4×C151—42no—
115C2×C4×C151C2×D411yescharacteristic
116C2×C4×C151C2×D412yes—
117C2×C4×C151C2×D412yes—
118C2×C4×C151C2411yescharacteristic
119C8×C151—22no—
120C22×C151—22no—
121C22×C151—24no—
122C22×C151—48no—
123C22×C151—44no—
124C22×C151—41no—
125C22×C151—42no—
126C22×C151#12012yes—
127C22×C151C22×D411yescharacteristic
128C2×D151—22no—
129C2×D151—22no—
130C2×D151—22no—
131C2×D151—44no—
132C4×C151—41no—
133C4×C151#12012yes—
134C4×C151C22×D411yescharacteristic
135C4×C151C22×D411yescharacteristic
136Dic151—22no—
137Dic151—24no—
138Dic151—42no—
139C2×C151—22no—
140C2×C151—44no—
141C2×C151—81no—
142C2×C151C2×#12011yescharacteristic
143C2×C151#57512yes—
144D151—42no—
145C151#300511yescharacteristic, complemented, Sylow
146#3005—1511nomaximal, Sylow
147C22×#41—1511no—
148C2×#137—1511no—
149C2×AGL(1,ℤ/8)D15111yescharacteristic, complemented
150#525—1511no—
151#452—1514no—
152#449—1514no—
153#419—1511no—
154#418—1511no—
155#407—1511no—
156C2×#41—3024no—
157C2×#41—3024no—
158C2×#41—3022no—
159C2×#41—1514no—
160C2×#41C2×D15111yescharacteristic
161C22×Q8—1511no—
162C22×D4—3021no—
163C22×D4C2×D15111yescharacteristic
164C23×C4—3021no—
165C23×C4—1511no—
166#137—3024no—
167AGL(1,ℤ/8)—24no—
168C2×Q16—1512no—
169C2×SD16—1512no—
170C2×SD16C2×D15112yescomplemented
171C2×D8C2×D15112yescomplemented
172C2×M16—1511no—
173C2×M16C2×D15111yescharacteristic
174#123—3021no—
175C22⋊Q8—1512no—
176#121—1512no—
177#120—3021no—
178C4×D4—3022no—
179#117—1511no—
180#103—1514no—
181#102—1514no—
182C22⋊C8—1514no—
183C24—21no—
184C24—1511no—
185#41—22no—
186#41—22no—
187#41—30216no—
188#41—3028no—
189#41—3028no—
190C2×Q8—3021no—
191C2×Q8—3022no—
192C2×Q8—1514no—
193C2×Q8—1512no—
194C2×Q8C22×D15111yescharacteristic
195C2×D4—21no—
196C2×D4—21no—
197C2×D4—22no—
198C2×D4—3028no—
199C2×D4—3024no—
200C2×D4—3022no—
201C2×D4C22⋊D15114yescomplemented
202C2×D4C22×D15111yescharacteristic
203C2×D4C22×D15112yes—
204C22×C4—21no—
205C22×C4—3028no—
206C22×C4—3021no—
207C22×C4—3024no—
208C22×C4—3022no—
209C22×C4—3022no—
210C22×C4—1511no—
211C22×C4—1512no—
212C22×C4—1512no—
213C22×C4C22×D15111yescharacteristic
214Q16—3024no—
215SD16—24no—
216SD16—3024no—
217D8—24no—
218M16—22no—
219M16—3022no—
220C2×C8—1512no—
221C2×C8C22×D15112yes—
222C4⋊C4—3022no—
223C4⋊C4—1512no—
224C22⋊C4—3022no—
225C22⋊C4—3021no—
226C22⋊C4—3022no—
227C42—3021no—
228C23—24no—
229C23—22no—
230C23—21no—
231C23—44no—
232C23—3022no—
233C23—6042no—
234C23—1512no—
235C23D4×D15111yescharacteristic
236Q8—21no—
237Q8—21no—
238Q8—3024no—
239Q8—3022no—
240Q8—1514no—
241D4—24no—
242D4—22no—
243D4—21no—
244D4—21no—
245D4—42no—
246D4—30216no—
247D4—6044no—
248D4C2×C22⋊D15114yes—
249C2×C4—21no—
250C2×C4—42no—
251C2×C4—30216no—
252C2×C4—3022no—
253C2×C4—3024no—
254C2×C4—3022no—
255C2×C4—3024no—
256C2×C4—3022no—
257C2×C4—3022no—
258C2×C4—3022no—
259C2×C4—1512no—
260C2×C4D4×D15111yescharacteristic
261C2×C4D4×D15112yes—
262C2×C4C2×C22⋊D15112yes—
263C2×C4C23×D15111yescharacteristic
264C8—22no—
265C8—3022no—
266C22—22no—
267C22—24no—
268C22—48no—
269C22—44no—
270C22—42no—
271C22—41no—
272C22—3022no—
273C22—3022no—
274C22—3022no—
275C22—6044no—
276C22#1801270712yes—
277C22C2×D4×D15111yescharacteristic
278C4—41no—
279C4—3022no—
280C4—3024no—
281C4—6042no—
282C4#1801270712yes—
283C4C2×D4×D15111yescharacteristic
284C4C22×C22⋊D15111yescharacteristic
285C2—22no—
286C2—44no—
287C2—81no—
288C2—6042no—
289C2C2×#1801270711yescharacteristic
290C2#2375300812yes—
subgroupG/H
centerC22C2×D4×D151
commutator, cosocleC2×C4×C151C24
FrattiniC2×C4C23×D151
FittingC2×AGL(1,ℤ/8)×C151C2
socleC22×C151C22×D4
hypercenterC2×AGL(1,ℤ/8)D151
hypocenterC151#3005
LCSG ▷ C2×C4×C151 ▷ C2×C151 ▷ C151
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×AGL(1,ℤ/8)

Complements

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

NH ≅ G/Ntype
1. C22×#14559003C2semidirect
2. C2×#18012769C2semidirect
3. #23752719C2semidirect
4. #23752371C2semidirect
5. #23752354C2semidirect
6. #23752222C2semidirect
7. #23752217C2semidirect
8. #23752175C2semidirect
9. C2×AGL(1,ℤ/8)×C151C2semidirect
19. C2×#14558994C22semidirect
20. C2×#14558992C22semidirect
23. #18012715C22semidirect
24. #18012710C22semidirect
28. #18012664C22semidirect
29. #18012660C22semidirect
30. (C2×D151)⋊C8C22semidirect
34. C2×SD16×C151C22semidirect
35. C2×D8×C151C22semidirect
43. C2×Dic302D4semidirect
73. C2×D4×C151D4semidirect
145. C151#3005semidirect
149. C2×AGL(1,ℤ/8)D151semidirect
170. C2×SD16C2×D151semidirect
171. C2×D8C2×D151semidirect
201. C2×D4C22⋊D151semidirect

Maximal subgroups

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

subgroupindex
C22×#145590032
C2×#180127692
#237527192
#237523712
#237523542
#237522222
#237522172
#237521752
C2×AGL(1,ℤ/8)×C1512
#3005151