Finite Group Databasebeta

← #34078394

Subgroups — #34078394

Order 19328.

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

normal subgroups only

This group has 732 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
1C2×#18012786C211yesmaximal, characteristic, complemented
2C2×#18012765C211yesmaximal, characteristic, complemented
3C22×#14558992C211yesmaximal, characteristic, complemented
4#23752355C214yesmaximal, complemented
5#23752350C214yesmaximal, complemented
6#23752220C211yesmaximal, characteristic, complemented
7#23752206C211yesmaximal, characteristic, complemented
8#23752179C211yesmaximal, characteristic, complemented
9#535×C151C211yesmaximal, characteristic, complemented
10#18012786—24no—
11#18012786—24no—
12C2×#14559004C2211yescharacteristic
13C2×#14559004C2212yescomplemented
14C2×#14559003—21no—
15C2×#14559003—22no—
16C22×Dic302C2211yescharacteristic
17C22×Dic302C2212yescomplemented
18C2×Q8×D151—21no—
19#18012765—24no—
20C2×#14558992—24no—
21C2×#14558992C2214yes—
22C2×#14558992C2212yes—
23C2×#14558989C2212yes—
24C2×#14558988C2211yescharacteristic
25C22×C151⋊C8C2211yescharacteristic
26#18012662C2212yescomplemented
27#18012662C2214yescomplemented
28#18012659C2212yescomplemented
29C22⋊(C151⋊C8)C2214yescomplemented
30C2×#41×C151C2211yescharacteristic
31C22×D4×C151C2211yescharacteristic
32#127×C151—21no—
33#124×C151—21no—
34#121×C151C2214yes—
35#120×C151—22no—
36#117×C151C2211yescharacteristic
37#14559004—24no—
38#14559004—24no—
39#14559004—22no—
40#14559004D414yescomplemented
41#14559003—216no—
42#14559003—28no—
43C2×Dic302—24no—
44C2×Dic302—24no—
45C2×Dic302—21no—
46C2×Dic302—22no—
47C2×Dic302—22no—
48C2×Dic302D414yescomplemented
49C2×Dic302C2312yes—
50C2×Dic302C2311yescharacteristic
51Q8×D151—28no—
52C2×D604C2311yescharacteristic
53C2×C22⋊D151—21no—
54C2×C22⋊D151—22no—
55C22×Dic151—21no—
56C22×Dic151—22no—
57C2×C4×D151—21no—
58C2×C4×D151—22no—
59#14558992—28no—
60#14558992—24no—
61#14558989—24no—
62#14558988—22no—
63C2×C151⋊C8—22no—
64C2×C151⋊C8C2312yes—
65C2×C151⋊C8C2312yes—
66C24×C151—21no—
67#41×C151—22no—
68#41×C151—22no—
69C2×Q8×C151D411yescharacteristic
70C2×D4×C151—24no—
71C2×D4×C151—22no—
72C2×D4×C151—22no—
73C2×D4×C151—21no—
74C2×D4×C151D412yes—
75C2×D4×C151D411yescharacteristic
76C2×D4×C151C2312yes—
77C22×C4×C151C2312yes—
78C22×C4×C151C2311yescharacteristic
79C4⋊C4×C151C2312yes—
80C22⋊C4×C151—21no—
81C22⋊C4×C151—24no—
82C42×C151—21no—
83C22×D151—21no—
84Dic302—28no—
85Dic302—24no—
86Dic302—21no—
87Dic302—22no—
88Dic302C2×D412yes—
89Dic302C2×D414yes—
90D604—21no—
91D604C2×D412yes—
92C22⋊D151—28no—
93C22⋊D151—24no—
94C2×Dic151—28no—
95C2×Dic151—24no—
96C2×Dic151—21no—
97C2×Dic151—22no—
98C4×D151—28no—
99C4×D151—24no—
100C151⋊C8—22no—
101C151⋊C8—22no—
102C23×C151—22no—
103C23×C151—42no—
104C23×C151—82no—
105C23×C151C2×D412yes—
106C23×C151C2×D411yescharacteristic
107Q8×C151—22no—
108D4×C151—24no—
109D4×C151—22no—
110D4×C151—22no—
111D4×C151—22no—
112D4×C151—42no—
113D4×C151—84no—
114C2×C4×C151—22no—
115C2×C4×C151—22no—
116C2×C4×C151—22no—
117C2×C4×C151C2×D412yes—
118C2×C4×C151C2×D412yes—
119C2×C4×C151C2×D412yes—
120C2×C4×C151C2×D411yescharacteristic
121C2×C4×C151C2411yescharacteristic
122C22×C151—22no—
123C22×C151—22no—
124C22×C151—24no—
125C22×C151—42no—
126C22×C151—44no—
127C22×C151—84no—
128C22×C151#12012yes—
129C22×C151C22×D411yescharacteristic
130C2×D151—22no—
131C2×D151—42no—
132C4×C151—22no—
133C4×C151—42no—
134C4×C151#12012yes—
135C4×C151C22×D411yescharacteristic
136C4×C151C22×D411yescharacteristic
137Dic151—24no—
138Dic151—22no—
139C2×C151—22no—
140C2×C151—42no—
141C2×C151—82no—
142C2×C151C2×#12011yescharacteristic
143C2×C151#57712yes—
144D151—42no—
145C151#301011yescharacteristic, complemented, Sylow
146#3010—1511nomaximal, Sylow
147C2×2−1+4—1511no—
148C2×AGL(1,ℤ/8)—1511no—
149C22×SD16—1511no—
150#535D15111yescharacteristic, complemented
151#449—1514no—
152#448—1514no—
153#419—1511no—
154#416—1511no—
155#408—1511no—
1562−1+4—3024no—
1572−1+4—3024no—
158C2×#41—3022no—
159C2×#41—3021no—
160C2×#41—1512no—
161C2×#41—1511no—
162C2×#41C2×D15111yescharacteristic
163C22×Q8—3021no—
164C22×Q8—1512no—
165C22×Q8—1511no—
166C22×D4C2×D15111yescharacteristic
167AGL(1,ℤ/8)—3024no—
168C2×SD16—3024no—
169C2×SD16—1514no—
170C2×SD16—1512no—
171C2×D8—1512no—
172C2×M16—1511no—
173C22×C8—1511no—
174#127—21no—
175#124—21no—
176#121C2×D15114yes—
177#120—22no—
178#117C2×D15111yescharacteristic
179#103—1512no—
180#103—1514no—
181#102—1512no—
182C22⋊C8—1514no—
183C24—21no—
184#41—22no—
185#41—22no—
186#41—3024no—
187#41—3024no—
188#41—30216no—
189#41—3028no—
190#41—3022no—
191#41—1514no—
192C2×Q8—3024no—
193C2×Q8—3024no—
194C2×Q8—3028no—
195C2×Q8—3022no—
196C2×Q8—3022no—
197C2×Q8—3021no—
198C2×Q8—1514no—
199C2×Q8—1511no—
200C2×Q8—1512no—
201C2×Q8C22⋊D15111yescharacteristic
202C2×D4—24no—
203C2×D4—22no—
204C2×D4—22no—
205C2×D4—21no—
206C2×D4—3022no—
207C2×D4—3021no—
208C2×D4—1511no—
209C2×D4C22⋊D15112yes—
210C2×D4C22⋊D15111yescharacteristic
211C2×D4C22×D15112yes—
212C22×C4—3022no—
213C22×C4—3021no—
214C22×C4—3022no—
215C22×C4—3021no—
216C22×C4C22×D15112yes—
217C22×C4C22×D15111yescharacteristic
218SD16—3028no—
219SD16—3024no—
220D8—3024no—
221M16—3022no—
222C2×C8—3022no—
223C2×C8—1512no—
224C2×C8—1512no—
225C4⋊C4C22×D15112yes—
226C22⋊C4—21no—
227C22⋊C4—24no—
228C42—21no—
229C23—22no—
230C23—42no—
231C23—82no—
232C23—3021no—
233C23C2×C22⋊D15112yes—
234C23C2×C22⋊D15111yescharacteristic
235Q8—22no—
236Q8—3028no—
237Q8—3024no—
238Q8—3021no—
239Q8—3022no—
240Q8—1512no—
241Q8—1514no—
242D4—24no—
243D4—22no—
244D4—22no—
245D4—22no—
246D4—42no—
247D4—84no—
248D4—3028no—
249D4—3024no—
250D4—3021no—
251D4—1512no—
252C2×C4—22no—
253C2×C4—22no—
254C2×C4—22no—
255C2×C4—3028no—
256C2×C4—3028no—
257C2×C4—3024no—
258C2×C4—3022no—
259C2×C4—3021no—
260C2×C4—3024no—
261C2×C4D4×D15112yes—
262C2×C4D4×D15112yes—
263C2×C4C2×C22⋊D15112yes—
264C2×C4C2×C22⋊D15111yescharacteristic
265C2×C4C23×D15111yescharacteristic
266C8—3022no—
267C8—3022no—
268C22—22no—
269C22—24no—
270C22—22no—
271C22—44no—
272C22—42no—
273C22—84no—
274C22—3022no—
275C22—6042no—
276C22#1801270712yes—
277C22C22×C22⋊D15111yescharacteristic
278C4—22no—
279C4—42no—
280C4—3024no—
281C4—3022no—
282C4#1801270712yes—
283C4C2×D4×D15111yescharacteristic
284C4C2×D4×D15111yescharacteristic
285C2—22no—
286C2—42no—
287C2—82no—
288C2—6042no—
289C2C2×#1801270711yescharacteristic
290C2#2375302312yes—
subgroupG/H
centerC22C22×C22⋊D151
commutator, cosocleC2×C4×C151C24
FrattiniC2×C4C23×D151
Fitting#535×C151C2
socleC22×C151C22×D4
hypercenter#535D151
hypocenterC151#3010
LCSG ▷ C2×C4×C151 ▷ C2×C151 ▷ C151
UCSC1 ◁ C22 ◁ C2×#41 ◁ #535

Complements

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

NH ≅ G/Ntype
1. C2×#18012786C2semidirect
2. C2×#18012765C2semidirect
3. C22×#14558992C2semidirect
4. #23752355C2semidirect
5. #23752350C2semidirect
6. #23752220C2semidirect
7. #23752206C2semidirect
8. #23752179C2semidirect
9. #535×C151C2semidirect
13. C2×#14559004C22semidirect
17. C22×Dic302C22semidirect
26. #18012662C22semidirect
27. #18012662C22semidirect
28. #18012659C22semidirect
29. C22⋊(C151⋊C8)C22semidirect
40. #14559004D4semidirect
48. C2×Dic302D4semidirect
145. C151#3010semidirect
150. #535D151semidirect

Maximal subgroups

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

subgroupindex
C2×#180127862
C2×#180127652
C22×#145589922
#237523552
#237523502
#237522202
#237522062
#237521792
#535×C1512
#3010151