Finite Group Databasebeta

← #34078352

Subgroups — #34078352

Order 19328.

758 conjugacy classes of subgroups; only the 165 normal subgroups are shown.

normal subgroups only

This group has 758 conjugacy classes of subgroups — too many to draw. Only its 165 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
1C2×#18012770C211yesmaximal, characteristic, complemented
2C2×#18012765C211yesmaximal, characteristic, complemented
3#23752723C211yesmaximal, characteristic, complemented
4#23752374C214yesmaximal, complemented
5#23752357C214yesmaximal, complemented
6#23752221C211yesmaximal, characteristic, complemented
7#23752217C211yesmaximal, characteristic, complemented
8#23752176C211yesmaximal, characteristic, complemented
9C22×#41×C151C211yesmaximal, characteristic, complemented
10C2×#14559004C2211yescharacteristic
11#18012770—24no—
12#18012765—24no—
13C2×#14558994C2212yescomplemented
14C2×#14558992C2212yescomplemented
15C2×#14558991C2212yescomplemented
16C2×#14558989C2212yescomplemented
17C2×#14558988C2211yescharacteristic
18C2×#14558988C2211yescharacteristic
19#18012722—21no—
20#18012718C2212yescomplemented
21#18012713C2212yescomplemented
22#18012708—21no—
23C4×C22⋊D151—22no—
24#18012698C2211yescharacteristic
25#18012663C2214yescomplemented
26#18012660C2214yescomplemented
27C22⋊(C151⋊C8)C2214yescomplemented
28C2×#41×C151—24no—
29C2×#41×C151—22no—
30C2×#41×C151—24no—
31C2×#41×C151C2214yes—
32C22×Q8×C151C2211yescharacteristic
33C22×D4×C151—21no—
34C22×D4×C151C2211yescharacteristic
35C23×C4×C151—21no—
36C23×C4×C151C2211yescharacteristic
37#14559004—22no—
38#14559004—22no—
39C2×Dic302C2311yescharacteristic
40C2×D604C2311yescharacteristic
41C2×C22⋊D151—22no—
42C2×C22⋊D151—21no—
43C2×C4×D151—21no—
44#14558994—24no—
45#14558992—24no—
46#14558991—24no—
47#14558989—24no—
48#14558988—22no—
49#14558988—22no—
50C2×C151⋊C8C2312yes—
51C2×C151⋊C8C2312yes—
52C4⋊Dic151C2312yes—
53Dic151⋊C4—22no—
54C22⋊Dic151—21no—
55C22⋊Dic151—22no—
56(C2×D151)⋊C4—22no—
57C4×Dic151—21no—
58C24×C151—21no—
59C24×C151D411yescharacteristic
60#41×C151—216no—
61#41×C151—28no—
62#41×C151—28no—
63C2×Q8×C151—22no—
64C2×Q8×C151—21no—
65C2×Q8×C151D414yescomplemented
66C2×Q8×C151C2312yes—
67C2×D4×C151—28no—
68C2×D4×C151—24no—
69C2×D4×C151—21no—
70C2×D4×C151—22no—
71C2×D4×C151D414yescomplemented
72C2×D4×C151C2312yes—
73C22×C4×C151—28no—
74C22×C4×C151—21no—
75C22×C4×C151—24no—
76C22×C4×C151—22no—
77C22×C4×C151—22no—
78C22×C4×C151D412yes—
79C22×C4×C151D411yescharacteristic
80C22×C4×C151C2312yes—
81C22×C4×C151C2311yescharacteristic
82C22×D151—21no—
83Dic302—21no—
84Dic302—21no—
85D604—21no—
86D604—21no—
87C22⋊D151—44no—
88C22⋊D151—42no—
89C2×Dic151—22no—
90C2×Dic151—21no—
91C4×D151—42no—
92C151⋊C8—22no—
93C151⋊C8—22no—
94C23×C151—24no—
95C23×C151—22no—
96C23×C151—22no—
97C23×C151—42no—
98C23×C151—44no—
99C23×C151C2×D412yes—
100C23×C151C2×D411yescharacteristic
101Q8×C151—24no—
102Q8×C151—22no—
103Q8×C151C2×D414yes—
104D4×C151—216no—
105D4×C151—24no—
106D4×C151—22no—
107D4×C151C2×D414yes—
108C2×C4×C151—216no—
109C2×C4×C151—24no—
110C2×C4×C151—22no—
111C2×C4×C151—22no—
112C2×C4×C151—24no—
113C2×C4×C151—22no—
114C2×C4×C151—22no—
115C2×C4×C151C2×D412yes—
116C2×C4×C151C2×D411yescharacteristic
117C2×C4×C151C2×D412yes—
118C2×C4×C151C2×D412yes—
119C2×C4×C151C2411yescharacteristic
120C22×C151—22no—
121C22×C151—22no—
122C22×C151—24no—
123C22×C151—22no—
124C22×C151—22no—
125C22×C151—44no—
126C22×C151—48no—
127C22×C151—44no—
128C22×C151#12012yes—
129C22×C151C22×D411yescharacteristic
130C2×D151—41no—
131C2×D151—42no—
132C4×C151—22no—
133C4×C151—24no—
134C4×C151#12012yes—
135C4×C151C22×D411yescharacteristic
136C4×C151C22×D411yescharacteristic
137Dic151—41no—
138Dic151—42no—
139C2×C151—22no—
140C2×C151—42no—
141C2×C151—44no—
142C2×C151C2×#12011yescharacteristic
143C2×C151#57512yes—
144D151—81no—
145C151#300511yescharacteristic, complemented, Sylow
146#3005—1511nomaximal, Sylow
147C22×#41D15111yescharacteristic, complemented
148C2×#137—1511no—
149C2×AGL(1,ℤ/8)—1511no—
150#525—1511no—
151#452—1514no—
152#449—1514no—
153#419—1511no—
154#418—1511no—
155#407—1511no—
156C2×#41—24no—
157C2×#41—24no—
158C2×#41—22no—
159C2×#41—1511no—
160C2×#41C2×D15114yes—
161C22×Q8C2×D15111yescharacteristic
162C22×D4—21no—
163C22×D4C2×D15111yescharacteristic
164C23×C4—21no—
165C23×C4C2×D15111yescharacteristic
166#137—3024no—
167AGL(1,ℤ/8)—3024no—
168C2×Q16—1512no—
169C2×SD16—1512no—
170C2×SD16—1512no—
171C2×D8—1512no—
172C2×M16—1511no—
173C2×M16—1511no—
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—
184C24C22⋊D15111yescharacteristic
185#41—216no—
186#41—28no—
187#41—28no—
188#41—3022no—
189#41—3022no—
190C2×Q8—22no—
191C2×Q8—21no—
192C2×Q8—1511no—
193C2×Q8C22⋊D15114yescomplemented
194C2×Q8C22×D15112yes—
195C2×D4—28no—
196C2×D4—24no—
197C2×D4—21no—
198C2×D4—22no—
199C2×D4—3022no—
200C2×D4—3021no—
201C2×D4—1511no—
202C2×D4C22⋊D15114yescomplemented
203C2×D4C22×D15112yes—
204C22×C4—28no—
205C22×C4—21no—
206C22×C4—24no—
207C22×C4—22no—
208C22×C4—22no—
209C22×C4—3021no—
210C22×C4C22⋊D15112yes—
211C22×C4C22⋊D15111yescharacteristic
212C22×C4C22×D15112yes—
213C22×C4C22×D15111yescharacteristic
214Q16—3024no—
215SD16—3024no—
216SD16—3024no—
217D8—3024no—
218M16—3022no—
219M16—3022no—
220C2×C8—1512no—
221C2×C8—1512no—
222C4⋊C4—3022no—
223C4⋊C4—1512no—
224C22⋊C4—3021no—
225C22⋊C4—3022no—
226C22⋊C4—3022no—
227C42—3021no—
228C23—22no—
229C23—24no—
230C23—22no—
231C23—42no—
232C23—44no—
233C23—3021no—
234C23C2×C22⋊D15112yes—
235C23C2×C22⋊D15111yescharacteristic
236Q8—24no—
237Q8—22no—
238Q8—3021no—
239Q8—3021no—
240Q8C2×C22⋊D15114yes—
241D4—216no—
242D4—24no—
243D4—22no—
244D4—3021no—
245D4—3021no—
246D4—6044no—
247D4—6042no—
248D4C2×C22⋊D15114yes—
249C2×C4—216no—
250C2×C4—22no—
251C2×C4—24no—
252C2×C4—22no—
253C2×C4—24no—
254C2×C4—22no—
255C2×C4—22no—
256C2×C4—3022no—
257C2×C4—3021no—
258C2×C4—6042no—
259C2×C4C2×C22⋊D15112yes—
260C2×C4C2×C22⋊D15111yescharacteristic
261C2×C4C2×C22⋊D15112yes—
262C2×C4C2×C22⋊D15112yes—
263C2×C4C23×D15111yescharacteristic
264C8—3022no—
265C8—3022no—
266C22—22no—
267C22—22no—
268C22—22no—
269C22—22no—
270C22—24no—
271C22—44no—
272C22—48no—
273C22—44no—
274C22—6042no—
275C22—6041no—
276C22#1801270812yes—
277C22C22×C22⋊D15111yescharacteristic
278C4—22no—
279C4—24no—
280C4—6042no—
281C4—6041no—
282C4#1801270812yes—
283C4C22×C22⋊D15111yescharacteristic
284C4C22×C22⋊D15111yescharacteristic
285C2—22no—
286C2—42no—
287C2—44no—
288C2—12081no—
289C2C2×#1801270811yescharacteristic
290C2#2375301012yes—
subgroupG/H
centerC22C22×C22⋊D151
commutator, cosocleC2×C4×C151C24
FrattiniC2×C4C23×D151
FittingC22×#41×C151C2
socleC22×C151C22×D4
hypercenterC22×#41D151
hypocenterC151#3005
LCSG ▷ C2×C4×C151 ▷ C2×C151 ▷ C151
UCSC1 ◁ C22 ◁ C23×C4 ◁ C22×#41

Complements

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

NH ≅ G/Ntype
1. C2×#18012770C2semidirect
2. C2×#18012765C2semidirect
3. #23752723C2semidirect
4. #23752374C2semidirect
5. #23752357C2semidirect
6. #23752221C2semidirect
7. #23752217C2semidirect
8. #23752176C2semidirect
9. C22×#41×C151C2semidirect
13. C2×#14558994C22semidirect
14. C2×#14558992C22semidirect
15. C2×#14558991C22semidirect
16. C2×#14558989C22semidirect
20. #18012718C22semidirect
21. #18012713C22semidirect
25. #18012663C22semidirect
26. #18012660C22semidirect
27. C22⋊(C151⋊C8)C22semidirect
65. C2×Q8×C151D4semidirect
71. C2×D4×C151D4semidirect
145. C151#3005semidirect
147. C22×#41D151semidirect
193. C2×Q8C22⋊D151semidirect
202. C2×D4C22⋊D151semidirect

Maximal subgroups

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

subgroupindex
C2×#180127702
C2×#180127652
#237527232
#237523742
#237523572
#237522212
#237522172
#237521762
C22×#41×C1512
#3005151