Finite Group Databasebeta

← #34079592

Subgroups — #34079592

Order 19328.

596 conjugacy classes of subgroups; only the 137 normal subgroups are shown.

normal subgroups only

This group has 596 conjugacy classes of subgroups — too many to draw. Only its 137 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×#18012766C212yesmaximal, complemented
2C2×#18012762C211yesmaximal, characteristic, complemented
3C2×D8×D151C211yesmaximal, characteristic, complemented
4#23752780C212yesmaximal, complemented
5#23752602C212yesmaximal, complemented
6#23752598C212yesmaximal, complemented
7#23752597C211yesmaximal, characteristic, complemented
8#23752589C211yesmaximal, characteristic, complemented
9#23752587C211yesmaximal, characteristic, complemented
10#23752166C211yesmaximal, characteristic, complemented
11#495×C151C211yesmaximal, characteristic, complemented
12C2×#14559005C2212yes—
13C2×D4×D151C2212yes—
14#18012766—28no—
15#18012762—24no—
16C2×#14558991C2212yescomplemented
17C2×#14558991C2212yescomplemented
18C2×D1208C2211yescharacteristic
19C2×D1208C2211yescharacteristic, complemented
20C2×D1208C2212yescomplemented
21C2×#14558989C2212yes—
22C2×#14558989C2212yescomplemented
23D8×D151—24no—
24C2×#14558987C2211yescharacteristic
25C2×C8×D151C2211yescharacteristic
26#18012736C2212yescomplemented
27#18012735C2212yescomplemented
28#18012728C2212yescomplemented
29#18012712—24no—
30#18012709—24no—
31#18012696C2211yescharacteristic
32#18012650C2211yescharacteristic, complemented
33#18012649C2211yescharacteristic, complemented
34C8×Dic151C2211yescharacteristic, complemented
35C2×Q16×C151C2211yescharacteristic, complemented
36C2×SD16×C151C2212yescomplemented
37C2×D8×C151C2211yescharacteristic
38#124×C151C2212yescomplemented
39C4×C8×C151C2211yescharacteristic, complemented
40C23×D151—22no—
41#14559005—24no—
42#14559005—24no—
43C2×D604—22no—
44C2×D604—24no—
45C2×D604C2312yes—
46C2×D604C2312yes—
47C2×C22⋊D151—22no—
48C2×C22⋊D151—24no—
49D4×D151—24no—
50D4×D151—24no—
51C2×C4×D151—22no—
52C2×C4×D151C2311yescharacteristic
53#14558991—24no—
54#14558991—24no—
55D1208—22no—
56D1208—22no—
57D1208—24no—
58#14558989—24no—
59#14558989—24no—
60#14558987D414yescomplemented
61C2×C151⋊C8C2311yescharacteristic
62C2×C151⋊C8C2311yescharacteristic
63C8×D151D414yescomplemented
64Dic151⋊C4D412yes—
65(C2×D151)⋊C4—24no—
66(C2×D151)⋊C4D412yes—
67C4×Dic151C2311yescharacteristic
68C2×Q8×C151C2312yes—
69C2×D4×C151C2312yes—
70Q16×C151—22no—
71SD16×C151—24no—
72D8×C151—22no—
73C2×C8×C151C2311yescharacteristic
74C2×C8×C151C2311yescharacteristic
75C22⋊C4×C151—24no—
76C42×C151C2311yescharacteristic
77C22×D151—22no—
78C22×D151—22no—
79C22×D151—44no—
80C22×D151—84no—
81C22×D151C2×D411yescharacteristic
82D604—22no—
83D604—22no—
84D604—22no—
85D604—22no—
86D604—44no—
87D604—84no—
88C22⋊D151—44no—
89C22⋊D151—84no—
90C2×Dic151C2×D412yes—
91C2×Dic151C2×D411yescharacteristic
92C4×D151—44no—
93C4×D151C2×D412yes—
94C4×D151C2×D412yes—
95C151⋊C8C2×D412yes—
96C151⋊C8C2×D412yes—
97C23×C151—22no—
98Q8×C151—22no—
99Q8×C151—22no—
100D4×C151—22no—
101D4×C151—22no—
102C2×C4×C151—22no—
103C2×C4×C151C2×D412yes—
104C2×C4×C151C2411yescharacteristic
105C8×C151C2×D412yes—
106C8×C151C2×D412yes—
107C22×C151—42no—
108C22×C151—44no—
109C22×C151C22×D411yescharacteristic
110C2×D151—22no—
111C2×D151—42no—
112C2×D151—42no—
113C2×D151—44no—
114C2×D151—44no—
115C2×D151—88no—
116C2×D151#12712yes—
117C4×C151—22no—
118C4×C151—42no—
119C4×C151C22×D411yescharacteristic
120C4×C151C22×D411yescharacteristic
121Dic151—22no—
122Dic151#12712yes—
123C2×C151—82no—
124C2×C151C2×#12711yescharacteristic
125C2×C151#57612yes—
126D151—22no—
127D151—82no—
128D151—82no—
129C151#315511yescharacteristic, complemented, Sylow
130#3155—1511nomaximal, Sylow
131C2×AGL(1,ℤ/8)—1512no—
132C2×#135—1511no—
133C22×D8—1511no—
134#535—1512no—
135#496—1512no—
136#496—1512no—
137#495—1511no—
138#495D15111yescharacteristic, complemented
139#493—1511no—
140#493—1511no—
141#405—1511no—
142C2×#41—1512no—
143C22×D4—1512no—
144AGL(1,ℤ/8)—3028no—
145#135—3024no—
146C2×Q16C2×D15111yescharacteristic, complemented
147C2×SD16—1512no—
148C2×SD16—1512no—
149C2×SD16C2×D15112yescomplemented
150C2×D8—3024no—
151C2×D8—1512no—
152C2×D8—1512no—
153C2×D8—1511no—
154C2×D8—1511no—
155C2×D8—1512no—
156C2×D8C2×D15111yescharacteristic
157C2×M16—1511no—
158C22×C8—1511no—
159#127—1512no—
160#127—1512no—
161#124—1512no—
162#124C2×D15112yescomplemented
163#121—3024no—
164#120—3024no—
165#117—1511no—
166#97—1511no—
167#97—1511no—
168C4×C8—1511no—
169C4×C8C2×D15111yescharacteristic, complemented
170C24—3022no—
171#41—3024no—
172#41—3024no—
173C2×Q8C22×D15112yes—
174C2×D4—3022no—
175C2×D4—3024no—
176C2×D4—3024no—
177C2×D4—3022no—
178C2×D4—3024no—
179C2×D4—3024no—
180C2×D4—1512no—
181C2×D4—1512no—
182C2×D4C22×D15112yes—
183C22×C4—3022no—
184C22×C4—1511no—
185Q16—22no—
186SD16—24no—
187SD16—3024no—
188SD16—3024no—
189D8—22no—
190D8—3024no—
191D8—3024no—
192D8—3022no—
193D8—3022no—
194D8—3024no—
195M16—1514no—
196C2×C8—1511no—
197C2×C8—1511no—
198C2×C8—1514no—
199C2×C8C22×D15111yescharacteristic
200C2×C8C22×D15111yescharacteristic
201C4⋊C4—1512no—
202C22⋊C4—24no—
203C22⋊C4—3024no—
204C22⋊C4—1512no—
205C42—1511no—
206C42C22×D15111yescharacteristic
207C23—22no—
208C23—3022no—
209C23—3022no—
210C23—6044no—
211C23—1511no—
212C23—12084no—
213Q8—22no—
214Q8—22no—
215D4—22no—
216D4—22no—
217D4—3022no—
218D4—3022no—
219D4—3022no—
220D4—3022no—
221D4—6044no—
222D4—6044no—
223D4—12084no—
224D4—12084no—
225C2×C4—22no—
226C2×C4—6044no—
227C2×C4—1512no—
228C2×C4—1511no—
229C2×C4—1512no—
230C2×C4—1512no—
231C2×C4D4×D15112yes—
232C2×C4C23×D15111yescharacteristic
233C8—1512no—
234C8—1512no—
235C8D4×D15112yes—
236C8D4×D15112yes—
237C22—42no—
238C22—44no—
239C22—3022no—
240C22—6042no—
241C22—6042no—
242C22—6044no—
243C22—6044no—
244C22—1512no—
245C22—12088no—
246C22C2×D4×D15111yescharacteristic
247C4—22no—
248C4—42no—
249C4—3022no—
250C4—1512no—
251C4C2×D4×D15111yescharacteristic
252C4C2×D4×D15111yescharacteristic
253C2—82no—
254C2—3022no—
255C2—12082no—
256C2—12082no—
257C2#127×D15111yescharacteristic
258C2#2375301412yes—
subgroupG/H
centerC22C2×D4×D151
commutator, cosocleC2×C4×C151C24
FrattiniC2×C4C23×D151
Fitting#495×C151C2
socleC22×C151C22×D4
hypercenter#495D151
hypocenterC151#3155
LCSG ▷ C2×C4×C151 ▷ C2×C151 ▷ C151
UCSC1 ◁ C22 ◁ C42 ◁ #495

Complements

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

NH ≅ G/Ntype
1. C2×#18012766C2semidirect
2. C2×#18012762C2semidirect
3. C2×D8×D151C2semidirect
4. #23752780C2semidirect
5. #23752602C2semidirect
6. #23752598C2semidirect
7. #23752597C2semidirect
8. #23752589C2semidirect
9. #23752587C2semidirect
10. #23752166C2semidirect
11. #495×C151C2semidirect
16. C2×#14558991C22semidirect
17. C2×#14558991C22semidirect
19. C2×D1208C22semidirect
20. C2×D1208C22semidirect
22. C2×#14558989C22semidirect
26. #18012736C22semidirect
27. #18012735C22semidirect
28. #18012728C22semidirect
32. #18012650C22semidirect
33. #18012649C22semidirect
34. C8×Dic151C22semidirect
35. C2×Q16×C151C22semidirect
36. C2×SD16×C151C22semidirect
38. #124×C151C22semidirect
39. C4×C8×C151C22semidirect
60. #14558987D4semidirect
63. C8×D151D4semidirect
129. C151#3155semidirect
138. #495D151semidirect
146. C2×Q16C2×D151semidirect
149. C2×SD16C2×D151semidirect
162. #124C2×D151semidirect
169. C4×C8C2×D151semidirect

Maximal subgroups

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

subgroupindex
C2×#180127662
C2×#180127622
C2×D8×D1512
#237527802
#237526022
#237525982
#237525972
#237525892
#237525872
#237521662
#495×C1512
#3155151