Finite Group Databasebeta

← #34078902

Subgroups — #34078902

Order 19328.

440 conjugacy classes of subgroups; only the 131 normal subgroups are shown.

normal subgroups only

This group has 440 conjugacy classes of subgroups — too many to draw. Only its 131 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
1#23752767C211yesmaximal, characteristic, complemented
2C4×D4×D151C211yesmaximal, characteristic
3#23752515C212yesmaximal, complemented
4#23752514C212yesmaximal, complemented
5#23752503C211yesmaximal, characteristic, complemented
6#23752502C211yesmaximal, characteristic, complemented
7#23752489C211yesmaximal, characteristic, complemented
8#23752253C212yesmaximal, complemented
9#23752234C211yesmaximal, characteristic, complemented
10#23752215C212yesmaximal
11#474×C151C211yesmaximal, characteristic, complemented
12C2×D4×D151C2211yescharacteristic
13C22×C4×D151—21no—
14C2×#14558987C2212yes—
15#18012739C2211yescharacteristic, complemented
16#18012730C2212yescomplemented
17#18012719—21no—
18#18012715—21no—
19Q8×Dic151—21no—
20#18012704—21no—
21C4×D604C2211yescharacteristic
22D4×Dic151C2211yescharacteristic
23#18012701C2211yescharacteristic
24C4×C22⋊D151—21no—
25(C22⋊D151)⋊C4—21no—
26#18012697C2212yes—
27C4⋊C4×D151C2211yescharacteristic
28C22⋊C4×D151—21no—
29C42×D151C2211yescharacteristic
30#18012672C2212yescomplemented
31#18012671C2212yescomplemented
32#18012670C2212yescomplemented
33C4⋊(C151⋊C8)C2211yescharacteristic, complemented
34Dic151⋊C8C2212yescomplemented
35#18012661C2212yes—
36#18012660C2212yes—
37#18012659C2212yes—
38C4⋊Q8×C151C2211yescharacteristic, complemented
39C4×D4×C151C2211yescharacteristic
40#107×C151C2212yescomplemented
41C4⋊C8×C151C2211yescharacteristic, complemented
42#102×C151C2212yes—
43C23×D151—21no—
44C2×Dic302—21no—
45C2×D604C2311yescharacteristic
46C2×C22⋊D151—21no—
47D4×D151—22no—
48D4×D151Q814yescomplemented
49C22×Dic151—21no—
50C2×C4×D151—21no—
51C2×C4×D151—21no—
52C2×C4×D151—21no—
53C2×C4×D151—44no—
54C2×C4×D151D411yescharacteristic
55C2×C4×D151D411yescharacteristic
56C2×C4×D151C2311yescharacteristic
57#14558987—24no—
58C2×C151⋊C8C2312yes—
59C4⋊Dic151—22no—
60C4⋊Dic151—21no—
61C4⋊Dic151C2311yescharacteristic
62C4⋊Dic151C2312yes—
63Dic151⋊C4—21no—
64Dic151⋊C4—22no—
65C22⋊Dic151—21no—
66(C2×D151)⋊C4—22no—
67(C2×D151)⋊C4—21no—
68(C2×D151)⋊C4—21no—
69C4×Dic151—22no—
70C4×Dic151D411yescharacteristic
71C4×Dic151D411yescharacteristic
72C4×Dic151C2311yescharacteristic
73C2×Q8×C151—21no—
74C2×D4×C151C2311yescharacteristic
75C22×C4×C151—21no—
76C2×C8×C151C2312yes—
77C4⋊C4×C151—21no—
78C4⋊C4×C151C2312yes—
79C4⋊C4×C151C2311yescharacteristic
80C22⋊C4×C151—21no—
81C42×C151C2311yescharacteristic
82C22×D151—21no—
83C22×D151—24no—
84C22×D151—42no—
85C22×D151—42no—
86C22×D151C2×D411yescharacteristic
87Dic302—42no—
88D604—21no—
89D604C2×Q812yes—
90C22⋊D151—24no—
91C2×Dic151—22no—
92C2×Dic151—21no—
93C2×Dic151—42no—
94C2×Dic151C2×D411yescharacteristic
95C2×Dic151C2×D411yescharacteristic
96C2×Dic151C2×D411yescharacteristic
97C4×D151—22no—
98C4×D151—41no—
99C4×D151—42no—
100C4×D151—42no—
101C4×D151—42no—
102C4×D151C2×Q812yes—
103C4×D151#4112yes—
104C151⋊C8—22no—
105C23×C151—21no—
106Q8×C151—42no—
107D4×C151—21no—
108D4×C151C2×Q812yes—
109C2×C4×C151—22no—
110C2×C4×C151—21no—
111C2×C4×C151—42no—
112C2×C4×C151C2×D411yescharacteristic
113C2×C4×C151C2×D411yescharacteristic
114C2×C4×C151C2411yescharacteristic
115C8×C151—22no—
116C22×C151—22no—
117C22×C151—41no—
118C22×C151—41no—
119C22×C151C22×D411yescharacteristic
120C2×D151—21no—
121C2×D151—21no—
122C2×D151—22no—
123C2×D151—48no—
124C2×D151—41no—
125C2×D151—41no—
126C2×D151C22⋊Q812yes—
127C4×C151—21no—
128C4×C151—41no—
129C4×C151—42no—
130C4×C151AGL(1,ℤ/8)12yes—
131C4×C151C22×Q811yescharacteristic
132C4×C151C2×#4111yescharacteristic
133Dic151—21no—
134Dic151—21no—
135Dic151—41no—
136Dic151—42no—
137Dic151C22⋊Q812yes—
138C2×C151—42no—
139C2×C151C2×C22⋊Q811yescharacteristic
140C2×C151C2×AGL(1,ℤ/8)11yescharacteristic
141C2×C151#57511yescharacteristic
142D151—22no—
143D151—42no—
144C151#307711yescharacteristic, complemented, Sylow
145#3077—1511nomaximal, Sylow
146#533—1511no—
147C2×C4×D4—1511no—
148#478—1512no—
149#478—1512no—
150#476—1511no—
151#476—1511no—
152#474—1511no—
153#474D15111yescharacteristic, complemented
154#428—1512no—
155#423—1511no—
156#418—1512no—
157C22×D4—1511no—
158C23×C4—3021no—
159C2×M16—1512no—
160C4⋊Q8—1511no—
161C4⋊Q8C2×D15111yescharacteristic, complemented
162#125—1512no—
163C22⋊Q8—3021no—
164C22⋊Q8—3021no—
165C4×Q8—3021no—
166C4×Q8—3021no—
167C4×D4—3021no—
168C4×D4—3021no—
169C4×D4—1511no—
170C4×D4—1511no—
171C4×D4—1511no—
172C4×D4C2×D15111yescharacteristic
173#117—1512no—
174C2×C4⋊C4—1511no—
175C2×C22⋊C4—3021no—
176C2×C42—1511no—
177#107—1512no—
178#107C2×D15112yescomplemented
179#106—1512no—
180#106—1512no—
181C4⋊C8—1512no—
182C4⋊C8—1511no—
183C4⋊C8C2×D15111yescharacteristic, complemented
184#102—1512no—
185#102—1512no—
186#102—1512no—
187#102C2×D15112yes—
188C24—3021no—
189C2×Q8—21no—
190C2×Q8—3021no—
191C2×D4—3022no—
192C2×D4—3021no—
193C2×D4—1514no—
194C2×D4—1511no—
195C2×D4C22×D15111yescharacteristic
196C22×C4—21no—
197C22×C4—3021no—
198C22×C4—3021no—
199C22×C4—3021no—
200C22×C4—3021no—
201C22×C4—6044no—
202C22×C4—1511no—
203C22×C4—1511no—
204C22×C4—1511no—
205M16—3024no—
206C2×C8—1512no—
207C2×C8C22×D15112yes—
208C4⋊C4—21no—
209C4⋊C4—3021no—
210C4⋊C4—3022no—
211C4⋊C4—3022no—
212C4⋊C4—3021no—
213C4⋊C4—1512no—
214C4⋊C4—1511no—
215C4⋊C4C22×D15112yes—
216C4⋊C4C22×D15111yescharacteristic
217C22⋊C4—21no—
218C22⋊C4—3022no—
219C22⋊C4—3021no—
220C22⋊C4—3021no—
221C22⋊C4—3021no—
222C42—3022no—
223C42—1511no—
224C42—1511no—
225C42—1511no—
226C42C22×D15111yescharacteristic
227C23—21no—
228C23—3024no—
229C23—3021no—
230C23—6042no—
231C23—6042no—
232C23—1511no—
233Q8—42no—
234Q8—6042no—
235D4—21no—
236D4—3024no—
237D4—3021no—
238D4—1512no—
239D4Q8×D15112yes—
240C2×C4—22no—
241C2×C4—21no—
242C2×C4—42no—
243C2×C4—3022no—
244C2×C4—3022no—
245C2×C4—3021no—
246C2×C4—6041no—
247C2×C4—6042no—
248C2×C4—6042no—
249C2×C4—6042no—
250C2×C4—6042no—
251C2×C4—1511no—
252C2×C4—1511no—
253C2×C4—1511no—
254C2×C4—1512no—
255C2×C4—1512no—
256C2×C4D4×D15111yescharacteristic
257C2×C4D4×D15111yescharacteristic
258C2×C4C23×D15111yescharacteristic
259C8—22no—
260C8—3022no—
261C22—22no—
262C22—41no—
263C22—41no—
264C22—3021no—
265C22—3021no—
266C22—3022no—
267C22—6048no—
268C22—6041no—
269C22—6041no—
270C22—1512no—
271C22C2×D4×D15111yescharacteristic
272C4—21no—
273C4—41no—
274C4—42no—
275C4—3021no—
276C4—3021no—
277C4—6041no—
278C4—6042no—
279C4—1512no—
280C4#1801276312yes—
281C4C2×Q8×D15111yescharacteristic
282C4#41×D15111yescharacteristic
283C2—42no—
284C2—3022no—
285C2—6042no—
286C2C22⋊Q8×D15111yescharacteristic
287C2C2×#1801276311yescharacteristic
288C2#2375301111yescharacteristic
subgroupG/H
centerC22C2×D4×D151
commutator, cosocleC2×C4×C151C24
FrattiniC2×C4C23×D151
Fitting#474×C151C2
socleC22×C151C22×D4
prime radicalC2×D4×D151C22
hypercenter#474D151
hypocenterC151#3077
LCSG ▷ C2×C4×C151 ▷ C2×C151 ▷ C151
UCSC1 ◁ C22 ◁ C42 ◁ #474

Complements

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

NH ≅ G/Ntype
1. #23752767C2semidirect
3. #23752515C2semidirect
4. #23752514C2semidirect
5. #23752503C2semidirect
6. #23752502C2semidirect
7. #23752489C2semidirect
8. #23752253C2semidirect
9. #23752234C2semidirect
11. #474×C151C2semidirect
15. #18012739C22semidirect
16. #18012730C22semidirect
30. #18012672C22semidirect
31. #18012671C22semidirect
32. #18012670C22semidirect
33. C4⋊(C151⋊C8)C22semidirect
34. Dic151⋊C8C22semidirect
38. C4⋊Q8×C151C22semidirect
40. #107×C151C22semidirect
41. C4⋊C8×C151C22semidirect
48. D4×D151Q8semidirect
144. C151#3077semidirect
153. #474D151semidirect
161. C4⋊Q8C2×D151semidirect
178. #107C2×D151semidirect
183. C4⋊C8C2×D151semidirect

Maximal subgroups

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

subgroupindex
#237527672
C4×D4×D1512
#237525152
#237525142
#237525032
#237525022
#237524892
#237522532
#237522342
#237522152
#474×C1512
#3077151