Finite Group Databasebeta

← #34078388

Subgroups — #34078388

Order 19328.

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

normal subgroups only

This group has 752 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×#18012784C211yesmaximal, characteristic
2C2×#18012772C211yesmaximal, characteristic, complemented
3C22×#14558992C211yesmaximal, characteristic, complemented
4#23752788C211yesmaximal, characteristic, complemented
5#23752375C214yesmaximal, complemented
6#23752364C214yesmaximal, complemented
7#23752206C211yesmaximal, characteristic, complemented
8#23752180C211yesmaximal, characteristic, complemented
9#418×C151C211yesmaximal, characteristic, complemented
10#18012784—24no—
11#18012784—24no—
12C2×#14559004C2211yescharacteristic
13C2×#14559004C2211yescharacteristic
14C2×#14559003—21no—
15C2×#14559003C2212yes—
16C22×Dic302C2211yescharacteristic, complemented
17C22×C22⋊D151—22no—
18C2×D4×D151—21no—
19C2×D4×D151C2212yes—
20#18012772—24no—
21C2×Dic604C2212yescomplemented
22C2×#14558993C2212yescomplemented
23C2×#14558992—24no—
24C2×#14558992C2214yescomplemented
25C22×C151⋊C8C2211yescharacteristic, complemented
26#18012739—21no—
27#18012727—21no—
28#18012723—22no—
29#18012719C2214yescomplemented
30#18012662C2212yescomplemented
31#18012659C2212yescomplemented
32(C2×D151)⋊C8C2214yescomplemented
33C22×D4×C151C2211yescharacteristic
34C2×M16×C151C2211yescharacteristic, complemented
35#117×C151C2211yescharacteristic, complemented
36#102×C151C2214yescomplemented
37C23×D151—22no—
38#14559004—22no—
39#14559004—22no—
40#14559004—22no—
41#14559004D414yes—
42#14559003—28no—
43#14559003—24no—
44#14559003—24no—
45C2×Dic302—21no—
46C2×Dic302—22no—
47C2×Dic302—22no—
48C2×Dic302D411yescharacteristic
49C2×Dic302C2312yes—
50C2×Dic302C2311yescharacteristic
51C2×D604D411yescharacteristic
52C2×D604C2311yescharacteristic
53C2×C22⋊D151—216no—
54C2×C22⋊D151—22no—
55C2×C22⋊D151—22no—
56C2×C22⋊D151—21no—
57C2×C22⋊D151D412yes—
58D4×D151—28no—
59D4×D151—24no—
60D4×D151—24no—
61C22×Dic151—22no—
62C22×Dic151—21no—
63C2×C4×D151—21no—
64C2×C4×D151C2312yes—
65Dic604—24no—
66#14558993—24no—
67#14558992—28no—
68C2×C151⋊C8—22no—
69C2×C151⋊C8C2312yes—
70C4⋊Dic151—24no—
71(C2×D151)⋊C4—24no—
72C24×C151—21no—
73C2×D4×C151—21no—
74C2×D4×C151—22no—
75C2×D4×C151D414yes—
76C2×D4×C151C2312yes—
77C22×C4×C151C2311yescharacteristic
78M16×C151—22no—
79C2×C8×C151C2312yes—
80C4⋊C4×C151C2312yes—
81C22⋊C4×C151—21no—
82C42×C151—21no—
83C22×D151—21no—
84C22×D151—28no—
85C22×D151—84no—
86C22×D151C2×D412yes—
87Dic302—22no—
88Dic302—21no—
89Dic302—22no—
90Dic302—22no—
91Dic302—42no—
92Dic302C2×D412yes—
93D604—22no—
94D604—21no—
95D604C2×D412yes—
96C22⋊D151—28no—
97C22⋊D151—28no—
98C22⋊D151—24no—
99C22⋊D151—24no—
100C2×Dic151—28no—
101C2×Dic151—21no—
102C2×Dic151—22no—
103C2×Dic151—42no—
104C2×Dic151C2×D412yes—
105C4×D151—24no—
106C4×D151—22no—
107C4×D151—22no—
108C151⋊C8—22no—
109C23×C151—22no—
110C23×C151—24no—
111C23×C151—82no—
112C23×C151C2×D411yescharacteristic
113D4×C151—24no—
114D4×C151—22no—
115D4×C151C2×D414yes—
116C2×C4×C151—22no—
117C2×C4×C151C2×D411yescharacteristic
118C2×C4×C151C2×D412yes—
119C2×C4×C151C2×D412yes—
120C2×C4×C151C2411yescharacteristic
121C8×C151—22no—
122C22×C151—22no—
123C22×C151—24no—
124C22×C151—44no—
125C22×C151—84no—
126C22×C151#12012yes—
127C22×C151C22×D411yescharacteristic
128C2×D151—22no—
129C2×D151—22no—
130C2×D151—24no—
131C2×D151—42no—
132C2×D151—88no—
133C4×C151—42no—
134C4×C151#12012yes—
135C4×C151C22×D411yescharacteristic
136C4×C151C22×D411yescharacteristic
137Dic151—22no—
138Dic151—22no—
139Dic151—42no—
140C2×C151—22no—
141C2×C151—44no—
142C2×C151C2×#12011yescharacteristic
143C2×C151#57712yes—
144D151—42no—
145D151—42no—
146C151#300911yescharacteristic, complemented, Sylow
147#3009—1511nomaximal, Sylow
148C2×H(5,𝔽2)—1511no—
149C2×#137—1511no—
150C22×SD16—1511no—
151#536—1511no—
152#452—1514no—
153#450—1514no—
154#418D15111yescharacteristic, complemented
155#416—1511no—
156#408—1511no—
157H(5,𝔽2)—3024no—
158H(5,𝔽2)—3024no—
159C2×#41—3021no—
160C2×#41—1512no—
161C2×#41—1511no—
162C2×#41—1511no—
163C22×Q8—1511no—
164C22×D4—3021no—
165C22×D4—3022no—
166C22×D4—1512no—
167C22×D4C2×D15111yescharacteristic
168#137—3024no—
169C2×Q16—1512no—
170C2×SD16—3024no—
171C2×SD16—1514no—
172C2×SD16—1512no—
173C2×M16C2×D15111yescharacteristic, complemented
174C22×C8—1511no—
175C4⋊Q8—3021no—
176#124—3021no—
177#123—3022no—
178C22⋊Q8—1514no—
179#117C2×D15111yescharacteristic, complemented
180#103—1512no—
181#102—1512no—
182#102C2×D15114yescomplemented
183C22⋊C8—1514no—
184C24—21no—
185C24—3022no—
186#41—3028no—
187#41—3024no—
188#41—3024no—
189#41—3022no—
190#41—3022no—
191#41—3022no—
192#41—1514no—
193C2×Q8—3021no—
194C2×Q8—3022no—
195C2×Q8—3022no—
196C2×Q8—1512no—
197C2×Q8—1511no—
198C2×Q8—1511no—
199C2×D4—21no—
200C2×D4—22no—
201C2×D4—3028no—
202C2×D4—3024no—
203C2×D4—30216no—
204C2×D4—3022no—
205C2×D4—3021no—
206C2×D4—3024no—
207C2×D4—3022no—
208C2×D4—1512no—
209C2×D4—1511no—
210C2×D4—1511no—
211C2×D4D60414yes—
212C2×D4C22×D15112yes—
213C22×C4—3022no—
214C22×C4—3021no—
215C22×C4—3021no—
216C22×C4—1512no—
217C22×C4C22×D15111yescharacteristic
218Q16—3024no—
219SD16—3024no—
220SD16—3028no—
221M16—22no—
222C2×C8—3022no—
223C2×C8—1512no—
224C2×C8C22×D15112yes—
225C4⋊C4—3024no—
226C4⋊C4C22×D15112yes—
227C22⋊C4—21no—
228C22⋊C4—3024no—
229C42—21no—
230C23—22no—
231C23—24no—
232C23—82no—
233C23—3028no—
234C23—3021no—
235C23—1512no—
236C23—12084no—
237C23D4×D15111yescharacteristic
238Q8—3022no—
239Q8—3021no—
240Q8—3022no—
241Q8—3022no—
242Q8—6042no—
243Q8—1512no—
244D4—24no—
245D4—22no—
246D4—3028no—
247D4—3028no—
248D4—3024no—
249D4—3024no—
250D4—3022no—
251D4—3021no—
252D4—1512no—
253D4C2×D60414yes—
254C2×C4—22no—
255C2×C4—3028no—
256C2×C4—3021no—
257C2×C4—3024no—
258C2×C4—3022no—
259C2×C4—3022no—
260C2×C4—3022no—
261C2×C4—6042no—
262C2×C4—1512no—
263C2×C4D4×D15111yescharacteristic
264C2×C4D4×D15112yes—
265C2×C4C2×D60412yes—
266C2×C4C23×D15111yescharacteristic
267C8—22no—
268C8—3022no—
269C22—22no—
270C22—24no—
271C22—44no—
272C22—84no—
273C22—3024no—
274C22—3022no—
275C22—3022no—
276C22—6042no—
277C22—12088no—
278C22#1801270912yes—
279C22C2×D4×D15111yescharacteristic
280C4—42no—
281C4—3022no—
282C4—3022no—
283C4—6042no—
284C4#1801270912yes—
285C4C2×D4×D15111yescharacteristic
286C4C22×D60411yescharacteristic
287C2—22no—
288C2—44no—
289C2—6042no—
290C2—6042no—
291C2C2×#1801270911yescharacteristic
292C2#2375302212yes—
subgroupG/H
centerC22C2×D4×D151
commutator, cosocleC2×C4×C151C24
FrattiniC2×C4C23×D151
Fitting#418×C151C2
socleC22×C151C22×D4
prime radicalC2×#18012784C2
hypercenter#418D151
hypocenterC151#3009
LCSG ▷ C2×C4×C151 ▷ C2×C151 ▷ C151
UCSC1 ◁ C22 ◁ C22×C4 ◁ #418

Complements

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

NH ≅ G/Ntype
2. C2×#18012772C2semidirect
3. C22×#14558992C2semidirect
4. #23752788C2semidirect
5. #23752375C2semidirect
6. #23752364C2semidirect
7. #23752206C2semidirect
8. #23752180C2semidirect
9. #418×C151C2semidirect
16. C22×Dic302C22semidirect
21. C2×Dic604C22semidirect
22. C2×#14558993C22semidirect
24. C2×#14558992C22semidirect
25. C22×C151⋊C8C22semidirect
29. #18012719C22semidirect
30. #18012662C22semidirect
31. #18012659C22semidirect
32. (C2×D151)⋊C8C22semidirect
34. C2×M16×C151C22semidirect
35. #117×C151C22semidirect
36. #102×C151C22semidirect
146. C151#3009semidirect
154. #418D151semidirect
173. C2×M16C2×D151semidirect
179. #117C2×D151semidirect
182. #102C2×D151semidirect

Maximal subgroups

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

subgroupindex
C2×#180127842
C2×#180127722
C22×#145589922
#237527882
#237523752
#237523642
#237522062
#237521802
#418×C1512
#3009151