Finite Group Databasebeta

← #34078721

Subgroups — #34078721

Order 19328.

500 conjugacy classes of subgroups; only the 127 normal subgroups are shown.

normal subgroups only

This group has 500 conjugacy classes of subgroups — too many to draw. Only its 127 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×#18012762C211yesmaximal, characteristic, complemented
2C2×M16×D151C211yesmaximal, characteristic, complemented
3#23752725C212yesmaximal, complemented
4#23752467C211yesmaximal, characteristic, complemented
5#23752466C211yesmaximal, characteristic, complemented
6#23752465C211yesmaximal, characteristic, complemented
7#23752461C212yesmaximal, complemented
8#23752460C212yesmaximal, complemented
9#23752247C211yesmaximal, characteristic, complemented
10#23752207C212yesmaximal, complemented
11#470×C151C211yesmaximal, characteristic, complemented
12C2×#14559005C2212yes—
13C22×C4×D151C2211yescharacteristic
14#18012762—24no—
15C2×#14558991C2212yescomplemented
16C2×D1208C2211yescharacteristic, complemented
17C2×#14558988C2211yescharacteristic
18C2×#14558987C2211yescharacteristic
19C2×#14558987C2211yescharacteristic
20M16×D151—24no—
21C2×C8×D151C2211yescharacteristic
22C2×C8×D151C2211yescharacteristic
23#18012724—22no—
24#18012715C2212yes—
25#18012714C2212yes—
26#18012713C2212yes—
27#18012709—22no—
28#18012701—22no—
29(C22⋊D151)⋊C4—22no—
30#18012697C2212yes—
31#18012672C2212yescomplemented
32#18012671C2211yescharacteristic, complemented
33#18012663C2212yescomplemented
34#18012661C2212yescomplemented
35#18012659C2212yescomplemented
36C2×Q16×C151C2211yescharacteristic, complemented
37C2×M16×C151C2211yescharacteristic
38C22⋊Q8×C151C2212yes—
39#106×C151C2211yescharacteristic, complemented
40#103×C151C2212yescomplemented
41C23×D151D411yescharacteristic
42#14559005—24no—
43#14559005—24no—
44C2×D604—22no—
45C2×D604—22no—
46C2×D604C2312yes—
47C2×C22⋊D151—22no—
48C22×Dic151D411yescharacteristic
49C2×C4×D151—22no—
50C2×C4×D151—22no—
51C2×C4×D151—22no—
52C2×C4×D151D411yescharacteristic
53C2×C4×D151D411yescharacteristic
54C2×C4×D151C2311yescharacteristic
55C2×C4×D151C2311yescharacteristic
56#14558991—24no—
57D1208—22no—
58#14558988—22no—
59#14558987—22no—
60#14558987—22no—
61C2×C151⋊C8C2311yescharacteristic
62C2×C151⋊C8C2311yescharacteristic
63C8×D151—22no—
64C8×D151D414yescomplemented
65C4⋊Dic151C2312yes—
66Dic151⋊C4—22no—
67(C2×D151)⋊C4—22no—
68(C2×D151)⋊C4—22no—
69(C2×D151)⋊C4—22no—
70(C2×D151)⋊C4—22no—
71C4×Dic151—22no—
72C2×Q8×C151C2312yes—
73C22×C4×C151C2311yescharacteristic
74Q16×C151—22no—
75M16×C151—22no—
76C2×C8×C151C2311yescharacteristic
77C2×C8×C151C2311yescharacteristic
78C4⋊C4×C151—22no—
79C4⋊C4×C151C2312yes—
80C22⋊C4×C151—22no—
81C22×D151—22no—
82C22×D151—22no—
83C22×D151—42no—
84C22×D151C2×D411yescharacteristic
85C22×D151C2×D411yescharacteristic
86D604—22no—
87D604—22no—
88D604—44no—
89D604—44no—
90C22⋊D151—44no—
91C2×Dic151—22no—
92C2×Dic151—22no—
93C2×Dic151C2×D411yescharacteristic
94C2×Dic151C2×D411yescharacteristic
95C4×D151—22no—
96C4×D151—21no—
97C4×D151—21no—
98C4×D151—22no—
99C4×D151—44no—
100C4×D151C2×D412yes—
101C4×D151#4112yes—
102C151⋊C8—21no—
103C151⋊C8C2×D412yes—
104C23×C151C2×D411yescharacteristic
105Q8×C151—22no—
106Q8×C151—22no—
107C2×C4×C151—21no—
108C2×C4×C151—21no—
109C2×C4×C151—22no—
110C2×C4×C151—22no—
111C2×C4×C151C2×D411yescharacteristic
112C2×C4×C151C2411yescharacteristic
113C8×C151—21no—
114C8×C151C2×D412yes—
115C22×C151—21no—
116C22×C151—22no—
117C22×C151C22×D411yescharacteristic
118C2×D151—22no—
119C2×D151—21no—
120C2×D151—22no—
121C2×D151—44no—
122C2×D151—42no—
123C2×D151—42no—
124C2×D151—42no—
125C2×D151#12112yes—
126C4×C151—21no—
127C4×C151—42no—
128C4×C151—42no—
129C4×C151C22×D411yescharacteristic
130C4×C151C2×#4111yescharacteristic
131Dic151—21no—
132Dic151—42no—
133Dic151#12112yes—
134C2×C151—41no—
135C2×C151C2×#12111yescharacteristic
136C2×C151#57512yes—
137D151—22no—
138D151—41no—
139D151—82no—
140C151#305411yescharacteristic, complemented, Sylow
141#3054—1511nomaximal, Sylow
142C2×#135—1511no—
143C22×M16—1511no—
144#525—1512no—
145#470—1511no—
146#470D15111yescharacteristic, complemented
147#469—1511no—
148#469—1511no—
149#468—1512no—
150#468—1512no—
151#427—1511no—
152#416—1512no—
153C2×#41—1512no—
154C23×C4—1511no—
155#135—3024no—
156C2×Q16C2×D15111yescharacteristic, complemented
157C2×SD16—1512no—
158C2×D8—1511no—
159C2×M16—3024no—
160C2×M16—1511no—
161C2×M16—1511no—
162C2×M16—1511no—
163C2×M16C2×D15111yescharacteristic
164C22×C8—1511no—
165C22×C8—1511no—
166#123—3022no—
167C22⋊Q8—1512no—
168C22⋊Q8C2×D15112yes—
169#121—1512no—
170#121—1512no—
171#120—3022no—
172C4×D4—3022no—
173C4×D4—3022no—
174#117—1512no—
175#107—1512no—
176#106—1511no—
177#106C2×D15111yescharacteristic, complemented
178#103—1512no—
179#103C2×D15112yescomplemented
180#102—1512no—
181#102—1512no—
182C24—1511no—
183#41—3024no—
184#41—3024no—
185C2×Q8C22×D15112yes—
186C2×D4—3022no—
187C2×D4—3022no—
188C2×D4—3022no—
189C2×D4—1512no—
190C22×C4—3022no—
191C22×C4—3022no—
192C22×C4—3022no—
193C22×C4—1511no—
194C22×C4—1511no—
195C22×C4—1511no—
196C22×C4—1511no—
197C22×C4—1511no—
198C22×C4C22×D15111yescharacteristic
199Q16—22no—
200SD16—3024no—
201D8—3022no—
202M16—22no—
203M16—3022no—
204M16—3022no—
205M16—3022no—
206C2×C8—3022no—
207C2×C8—1511no—
208C2×C8—1511no—
209C2×C8—1514no—
210C2×C8C22×D15111yescharacteristic
211C2×C8C22×D15111yescharacteristic
212C4⋊C4—22no—
213C4⋊C4—3022no—
214C4⋊C4—1512no—
215C4⋊C4C22×D15112yes—
216C22⋊C4—22no—
217C22⋊C4—3022no—
218C22⋊C4—3022no—
219C22⋊C4—3022no—
220C22⋊C4—3022no—
221C42—3022no—
222C23—3022no—
223C23—3022no—
224C23—6042no—
225C23—1511no—
226C23—1511no—
227C23D4×D15111yescharacteristic
228Q8—22no—
229Q8—22no—
230D4—3022no—
231D4—3022no—
232D4—6044no—
233D4—6044no—
234D4—6044no—
235C2×C4—21no—
236C2×C4—21no—
237C2×C4—22no—
238C2×C4—22no—
239C2×C4—3022no—
240C2×C4—3022no—
241C2×C4—3022no—
242C2×C4—3021no—
243C2×C4—3021no—
244C2×C4—3022no—
245C2×C4—6044no—
246C2×C4—1511no—
247C2×C4—1511no—
248C2×C4—1512no—
249C2×C4—1512no—
250C2×C4D4×D15111yescharacteristic
251C2×C4C23×D15111yescharacteristic
252C8—21no—
253C8—3021no—
254C8—1512no—
255C8D4×D15112yes—
256C22—22no—
257C22—21no—
258C22—3022no—
259C22—3022no—
260C22—3021no—
261C22—6044no—
262C22—6042no—
263C22—6042no—
264C22—6042no—
265C22—1512no—
266C22C2×D4×D15111yescharacteristic
267C4—21no—
268C4—42no—
269C4—42no—
270C4—3021no—
271C4—6042no—
272C4—1512no—
273C4C2×D4×D15111yescharacteristic
274C4#41×D15111yescharacteristic
275C2—41no—
276C2—3022no—
277C2—6041no—
278C2—12082no—
279C2#121×D15111yescharacteristic
280C2#2375301112yes—
subgroupG/H
centerC22C2×D4×D151
commutator, cosocleC2×C4×C151C24
FrattiniC2×C4C23×D151
Fitting#470×C151C2
socleC22×C151C22×D4
hypercenter#470D151
hypocenterC151#3054
LCSG ▷ C2×C4×C151 ▷ C2×C151 ▷ C151
UCSC1 ◁ C22 ◁ C22×C4 ◁ #470

Complements

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

NH ≅ G/Ntype
1. C2×#18012762C2semidirect
2. C2×M16×D151C2semidirect
3. #23752725C2semidirect
4. #23752467C2semidirect
5. #23752466C2semidirect
6. #23752465C2semidirect
7. #23752461C2semidirect
8. #23752460C2semidirect
9. #23752247C2semidirect
10. #23752207C2semidirect
11. #470×C151C2semidirect
15. C2×#14558991C22semidirect
16. C2×D1208C22semidirect
31. #18012672C22semidirect
32. #18012671C22semidirect
33. #18012663C22semidirect
34. #18012661C22semidirect
35. #18012659C22semidirect
36. C2×Q16×C151C22semidirect
39. #106×C151C22semidirect
40. #103×C151C22semidirect
64. C8×D151D4semidirect
140. C151#3054semidirect
146. #470D151semidirect
156. C2×Q16C2×D151semidirect
177. #106C2×D151semidirect
179. #103C2×D151semidirect

Maximal subgroups

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

subgroupindex
C2×#180127622
C2×M16×D1512
#237527252
#237524672
#237524662
#237524652
#237524612
#237524602
#237522472
#237522072
#470×C1512
#3054151