Finite Group Databasebeta

← #34078398

Subgroups — #34078398

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×#18012767C211yesmaximal, characteristic, complemented
3C22×#14558993C211yesmaximal, characteristic, complemented
4#23752776C211yesmaximal, characteristic, complemented
5#23752359C214yesmaximal, complemented
6#23752353C214yesmaximal, complemented
7#23752222C211yesmaximal, characteristic, complemented
8#23752209C211yesmaximal, characteristic, complemented
9#408×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—
19C22×D604C2211yescharacteristic
20#18012767—24no—
21C2×#14558993—24no—
22C2×#14558993C2214yes—
23C2×#14558993C2212yes—
24C2×D1208C2212yes—
25#18012735—21no—
26#18012728—21no—
27#18012713C2214yes—
28#18012707—22no—
29#18012698C2211yescharacteristic
30#18012664C2212yescomplemented
31#18012664C2214yescomplemented
32#18012661C2212yescomplemented
33C2×#41×C151C2211yescharacteristic
34C2×M16×C151C2211yescharacteristic
35C22×C8×C151C2211yescharacteristic
36C22⋊C8×C151C2214yescomplemented
37C23×D151—21no—
38#14559004—24no—
39#14559004—24no—
40#14559004—22no—
41#14559004D414yescomplemented
42#14559003—216no—
43#14559003—28no—
44C2×Dic302—24no—
45C2×Dic302—24no—
46C2×Dic302—21no—
47C2×Dic302—22no—
48C2×Dic302—22no—
49C2×Dic302D414yescomplemented
50C2×Dic302C2312yes—
51C2×Dic302C2311yescharacteristic
52Q8×D151—28no—
53C2×D604—22no—
54C2×D604—22no—
55C2×D604—21no—
56C2×D604C2312yes—
57C2×D604C2311yescharacteristic
58C2×C22⋊D151—21no—
59C2×C22⋊D151—22no—
60C2×C22⋊D151—24no—
61C22×Dic151—21no—
62C22×Dic151—22no—
63C2×C4×D151—21no—
64C2×C4×D151—22no—
65#14558993—28no—
66#14558993—24no—
67D1208—24no—
68C4⋊Dic151C2312yes—
69C22⋊Dic151—21no—
70(C2×D151)⋊C4—24no—
71C4×Dic151—21no—
72#41×C151—22no—
73#41×C151—22no—
74C2×Q8×C151D411yescharacteristic
75C2×D4×C151D412yes—
76C2×D4×C151D411yescharacteristic
77C22×C4×C151C2312yes—
78C22×C4×C151C2311yescharacteristic
79M16×C151—22no—
80C2×C8×C151—22no—
81C2×C8×C151C2312yes—
82C2×C8×C151C2312yes—
83C22×D151—21no—
84C22×D151—22no—
85C22×D151—42no—
86C22×D151—82no—
87Dic302—28no—
88Dic302—24no—
89Dic302—21no—
90Dic302—22no—
91Dic302C2×D412yes—
92Dic302C2×D414yes—
93D604—21no—
94D604—22no—
95D604—22no—
96D604—42no—
97D604C2×D412yes—
98C22⋊D151—28no—
99C22⋊D151—24no—
100C22⋊D151—84no—
101C2×Dic151—28no—
102C2×Dic151—24no—
103C2×Dic151—21no—
104C2×Dic151—22no—
105C2×Dic151—22no—
106C4×D151—28no—
107C4×D151—24no—
108C23×C151C2×D412yes—
109C23×C151C2×D411yescharacteristic
110Q8×C151—22no—
111D4×C151—24no—
112D4×C151—22no—
113C2×C4×C151—22no—
114C2×C4×C151—22no—
115C2×C4×C151C2×D412yes—
116C2×C4×C151C2×D412yes—
117C2×C4×C151C2×D412yes—
118C2×C4×C151C2×D411yescharacteristic
119C2×C4×C151C2411yescharacteristic
120C8×C151—22no—
121C8×C151—22no—
122C22×C151—22no—
123C22×C151—22no—
124C22×C151—24no—
125C22×C151#12012yes—
126C22×C151C22×D411yescharacteristic
127C2×D151—22no—
128C2×D151—42no—
129C2×D151—42no—
130C2×D151—44no—
131C2×D151—84no—
132C4×C151—22no—
133C4×C151#12012yes—
134C4×C151C22×D411yescharacteristic
135C4×C151C22×D411yescharacteristic
136Dic151—24no—
137Dic151—22no—
138Dic151—42no—
139C2×C151—22no—
140C2×C151—42no—
141C2×C151C2×#12011yescharacteristic
142C2×C151#57712yes—
143D151—42no—
144D151—82no—
145C151#301011yescharacteristic, complemented, Sylow
146#3010—1511nomaximal, Sylow
147C2×2−1+4—1511no—
148C2×AGL(1,ℤ/8)—1511no—
149C22×SD16—1511no—
150#535—1511no—
151#449—1514no—
152#448—1514no—
153#419—1511no—
154#416—1511no—
155#408D15111yescharacteristic, complemented
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×D4—1511no—
167AGL(1,ℤ/8)—3024no—
168C2×SD16—3024no—
169C2×SD16—1514no—
170C2×SD16—1512no—
171C2×D8—1512no—
172C2×M16C2×D15111yescharacteristic
173C22×C8C2×D15111yescharacteristic
174#127—3021no—
175#124—3021no—
176#121—1514no—
177#120—3022no—
178#117—1511no—
179#103—1512no—
180#103—1514no—
181#102—1512no—
182C22⋊C8C2×D15114yescomplemented
183C24—3021no—
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×Q8D60411yescharacteristic
202C2×D4—3022no—
203C2×D4—3021no—
204C2×D4—3024no—
205C2×D4—3022no—
206C2×D4—3022no—
207C2×D4—3021no—
208C2×D4—1512no—
209C2×D4—1511no—
210C2×D4D60412yes—
211C2×D4D60411yescharacteristic
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—22no—
222C2×C8—22no—
223C2×C8C22×D15112yes—
224C2×C8C22×D15112yes—
225C4⋊C4—1512no—
226C22⋊C4—3021no—
227C22⋊C4—3024no—
228C42—3021no—
229C23—3021no—
230C23—3022no—
231C23—6042no—
232C23—12082no—
233C23C2×D60412yes—
234C23C2×D60411yescharacteristic
235Q8—22no—
236Q8—3028no—
237Q8—3024no—
238Q8—3021no—
239Q8—3022no—
240Q8—1512no—
241Q8—1514no—
242D4—24no—
243D4—22no—
244D4—3028no—
245D4—3024no—
246D4—3021no—
247D4—3022no—
248D4—3022no—
249D4—6042no—
250D4—1512no—
251D4—12084no—
252C2×C4—22no—
253C2×C4—22no—
254C2×C4—3028no—
255C2×C4—3028no—
256C2×C4—3024no—
257C2×C4—3022no—
258C2×C4—3021no—
259C2×C4—3024no—
260C2×C4—3022no—
261C2×C4D4×D15112yes—
262C2×C4D4×D15112yes—
263C2×C4C2×D60412yes—
264C2×C4C2×D60411yescharacteristic
265C2×C4C23×D15111yescharacteristic
266C8—22no—
267C8—22no—
268C22—22no—
269C22—24no—
270C22—22no—
271C22—3022no—
272C22—6042no—
273C22—6044no—
274C22—6042no—
275C22—12084no—
276C22#1801270912yes—
277C22C22×D60411yescharacteristic
278C4—22no—
279C4—3024no—
280C4—3022no—
281C4—6042no—
282C4#1801270912yes—
283C4C2×D4×D15111yescharacteristic
284C4C2×D4×D15111yescharacteristic
285C2—22no—
286C2—42no—
287C2—6042no—
288C2—12082no—
289C2C2×#1801270911yescharacteristic
290C2#2375302412yes—
subgroupG/H
centerC22C22×D604
commutator, cosocleC2×C4×C151C24
FrattiniC2×C4C23×D151
Fitting#408×C151C2
socleC22×C151C22×D4
hypercenter#408D151
hypocenterC151#3010
LCSG ▷ C2×C4×C151 ▷ C2×C151 ▷ C151
UCSC1 ◁ C22 ◁ C2×#41 ◁ #408

Complements

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

NH ≅ G/Ntype
1. C2×#18012786C2semidirect
2. C2×#18012767C2semidirect
3. C22×#14558993C2semidirect
4. #23752776C2semidirect
5. #23752359C2semidirect
6. #23752353C2semidirect
7. #23752222C2semidirect
8. #23752209C2semidirect
9. #408×C151C2semidirect
13. C2×#14559004C22semidirect
17. C22×Dic302C22semidirect
30. #18012664C22semidirect
31. #18012664C22semidirect
32. #18012661C22semidirect
36. C22⋊C8×C151C22semidirect
41. #14559004D4semidirect
49. C2×Dic302D4semidirect
145. C151#3010semidirect
155. #408D151semidirect
182. C22⋊C8C2×D151semidirect

Maximal subgroups

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

subgroupindex
C2×#180127862
C2×#180127672
C22×#145589932
#237527762
#237523592
#237523532
#237522222
#237522092
#408×C1512
#3010151