Finite Group Databasebeta

← #34079971

Subgroups — #34079971

Order 19328.

442 conjugacy classes of subgroups; only the 117 normal subgroups are shown.

normal subgroups only

This group has 442 conjugacy classes of subgroups — too many to draw. Only its 117 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#23752776C211yesmaximal, characteristic, complemented
2#23752536C212yesmaximal, complemented
3#23752533C212yesmaximal, complemented
4#23752463C212yesmaximal, complemented
5#23752446C212yesmaximal, complemented
6#23752346C212yesmaximal, complemented
7#23752345C212yesmaximal, complemented
8#23752179C211yesmaximal, characteristic, complemented
9#535×C151C211yesmaximal, characteristic, complemented
10C22×D604C2211yescharacteristic, complemented
11C2×#14558989C2212yes—
12C2×#14558989C2212yes—
13C2×#14558988C2211yescharacteristic, complemented
14C22×C151⋊C8C2211yescharacteristic, complemented
15#18012735—21no—
16#18012728—21no—
17#18012713C2212yes—
18#18012713C2212yescomplemented
19#18012707—21no—
20#18012707—21no—
21#18012698C2211yescharacteristic, complemented
22#18012672C2212yescomplemented
23#18012670C2212yescomplemented
24#18012660C2212yescomplemented
25#18012660C2212yescomplemented
26#18012659C2212yescomplemented
27#18012659C2212yescomplemented
28C22⋊(C151⋊C8)C2212yescomplemented
29C22⋊(C151⋊C8)C2212yescomplemented
30C2×#41×C151C2211yescharacteristic
31C22×D4×C151C2211yescharacteristic, complemented
32#127×C151—21no—
33#124×C151—21no—
34#121×C151C2212yes—
35#121×C151C2212yescomplemented
36#120×C151—21no—
37#120×C151—21no—
38#117×C151C2211yescharacteristic, complemented
39C23×D151—21no—
40C2×D604—21no—
41C2×D604—41no—
42C2×D604—41no—
43C2×D604C2312yes—
44C2×C22⋊D151—22no—
45C2×C22⋊D151—22no—
46#14558989—42no—
47#14558989—42no—
48#14558988—41no—
49C2×C151⋊C8—41no—
50C2×C151⋊C8C2312yes—
51C2×C151⋊C8C2312yes—
52C4⋊Dic151C2312yes—
53C22⋊Dic151—21no—
54(C2×D151)⋊C4—22no—
55(C2×D151)⋊C4—22no—
56C4×Dic151—21no—
57C24×C151—21no—
58#41×C151—41no—
59#41×C151—41no—
60C2×Q8×C151D411yescharacteristic
61C2×D4×C151—22no—
62C2×D4×C151—22no—
63C2×D4×C151—21no—
64C2×D4×C151—41no—
65C2×D4×C151—41no—
66C2×D4×C151D411yescharacteristic
67C2×D4×C151D411yescharacteristic
68C2×D4×C151D411yescharacteristic
69C2×D4×C151C2312yes—
70C22×C4×C151C2311yescharacteristic
71C22×C4×C151C2311yescharacteristic
72C22×C4×C151C2311yescharacteristic
73C4⋊C4×C151C2312yes—
74C22⋊C4×C151—21no—
75C22⋊C4×C151—22no—
76C22⋊C4×C151—22no—
77C42×C151—21no—
78C22×D151—22no—
79C22×D151—42no—
80C22×D151—82no—
81D604—22no—
82D604—22no—
83D604—42no—
84C22⋊D151—82no—
85C22⋊D151—82no—
86C2×Dic151—22no—
87C151⋊C8—22no—
88C151⋊C8—22no—
89C23×C151—22no—
90C23×C151—42no—
91C23×C151—82no—
92C23×C151C2×D411yescharacteristic
93C23×C151C2×D411yescharacteristic
94C23×C151C2×D411yescharacteristic
95Q8×C151—41no—
96D4×C151—22no—
97D4×C151—22no—
98D4×C151—41no—
99D4×C151—41no—
100D4×C151—41no—
101D4×C151—42no—
102D4×C151—82no—
103D4×C151—82no—
104C2×C4×C151—21no—
105C2×C4×C151—21no—
106C2×C4×C151—21no—
107C2×C4×C151—21no—
108C2×C4×C151—21no—
109C2×C4×C151—21no—
110C2×C4×C151—22no—
111C2×C4×C151C2×D411yescharacteristic
112C2×C4×C151C2×D411yescharacteristic
113C2×C4×C151C2×D411yescharacteristic
114C2×C4×C151C2411yescharacteristic
115C22×C151—21no—
116C22×C151—21no—
117C22×C151—21no—
118C22×C151—22no—
119C22×C151—22no—
120C22×C151—22no—
121C22×C151—42no—
122C22×C151—42no—
123C22×C151—42no—
124C22×C151—84no—
125C22×C151C22×D411yescharacteristic
126C2×D151—42no—
127C2×D151—42no—
128C2×D151—42no—
129C2×D151—84no—
130C4×C151—21no—
131C4×C151—21no—
132C4×C151—21no—
133C4×C151—42no—
134C4×C151H(5,𝔽2)11yescharacteristic
135C4×C151H(5,𝔽2)11yescharacteristic
136Dic151—42no—
137C2×C151—41no—
138C2×C151—41no—
139C2×C151—41no—
140C2×C151—82no—
141C2×C151#53411yescharacteristic
142C2×C151#57612yes—
143D151—82no—
144C151#319911yescharacteristic, complemented, Sylow
145#3199—1511nomaximal, Sylow
146#535—1511no—
147#535D15111yescharacteristic, complemented
148#482—1512no—
149#482—1512no—
150#469—1512no—
151#466—1512no—
152#447—1512no—
153#447—1512no—
154#408—1511no—
155C2×#41C2×D15111yescharacteristic
156C22×D4—1511no—
157C22×D4C2×D15111yescharacteristic, complemented
158C2×D8—1512no—
159C2×D8—1512no—
160C2×M16—1511no—
161C22×C8—1511no—
162#127—21no—
163#127—3021no—
164#124—21no—
165#124—3021no—
166#121—1512no—
167#121—1512no—
168#121C2×D15112yes—
169#121C2×D15112yescomplemented
170#120—21no—
171#120—21no—
172#120—3021no—
173#120—3021no—
174#117—1511no—
175#117C2×D15111yescharacteristic, complemented
176#107—1512no—
177#106—1512no—
178#102—1512no—
179#102—1512no—
180#102—1512no—
181#102—1512no—
182C22⋊C8—1512no—
183C22⋊C8—1512no—
184C24—21no—
185C24—3021no—
186#41—41no—
187#41—41no—
188C2×Q8C22⋊D15111yescharacteristic
189C2×D4—22no—
190C2×D4—22no—
191C2×D4—21no—
192C2×D4—41no—
193C2×D4—41no—
194C2×D4—3022no—
195C2×D4—3022no—
196C2×D4—3021no—
197C2×D4—6041no—
198C2×D4—6041no—
199C2×D4—1512no—
200C2×D4C22⋊D15111yescharacteristic
201C2×D4C22⋊D15111yescharacteristic
202C2×D4C22⋊D15111yescharacteristic
203C2×D4C22×D15112yes—
204C22×C4C22×D15111yescharacteristic
205C22×C4C22×D15111yescharacteristic
206C22×C4C22×D15111yescharacteristic
207D8—6042no—
208D8—6042no—
209M16—6041no—
210C2×C8—6041no—
211C2×C8—1512no—
212C2×C8—1512no—
213C4⋊C4—1512no—
214C4⋊C4C22×D15112yes—
215C22⋊C4—21no—
216C22⋊C4—22no—
217C22⋊C4—22no—
218C22⋊C4—3021no—
219C22⋊C4—3022no—
220C22⋊C4—3022no—
221C42—21no—
222C42—3021no—
223C23—22no—
224C23—42no—
225C23—82no—
226C23—3022no—
227C23—6042no—
228C23—12082no—
229C23C2×C22⋊D15111yescharacteristic
230C23C2×C22⋊D15111yescharacteristic
231C23C2×C22⋊D15111yescharacteristic
232Q8—41no—
233D4—22no—
234D4—22no—
235D4—41no—
236D4—41no—
237D4—41no—
238D4—42no—
239D4—82no—
240D4—82no—
241D4—3022no—
242D4—3022no—
243D4—6042no—
244D4—12082no—
245D4—12082no—
246C2×C4—21no—
247C2×C4—21no—
248C2×C4—21no—
249C2×C4—21no—
250C2×C4—21no—
251C2×C4—21no—
252C2×C4—22no—
253C2×C4—3022no—
254C2×C4C2×C22⋊D15111yescharacteristic
255C2×C4C2×C22⋊D15111yescharacteristic
256C2×C4C2×C22⋊D15111yescharacteristic
257C2×C4C23×D15111yescharacteristic
258C8—3022no—
259C8—3022no—
260C22—22no—
261C22—22no—
262C22—22no—
263C22—21no—
264C22—21no—
265C22—21no—
266C22—42no—
267C22—42no—
268C22—42no—
269C22—84no—
270C22—6042no—
271C22—6042no—
272C22—6042no—
273C22—12084no—
274C22C22×C22⋊D15111yescharacteristic
275C4—21no—
276C4—21no—
277C4—21no—
278C4—42no—
279C4—6042no—
280C4#1801278411yescharacteristic
281C4#1801278411yescharacteristic
282C2—41no—
283C2—41no—
284C2—41no—
285C2—82no—
286C2—12082no—
287C2#2375277111yescharacteristic
288C2#2375301512yes—
subgroupG/H
centerC22C22×C22⋊D151
commutator, cosocleC2×C4×C151C24
FrattiniC2×C4C23×D151
Fitting#535×C151C2
socleC22×C151C22×D4
hypercenter#535D151
hypocenterC151#3199
LCSG ▷ C2×C4×C151 ▷ C2×C151 ▷ C151
UCSC1 ◁ C22 ◁ C2×#41 ◁ #535

Complements

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

NH ≅ G/Ntype
1. #23752776C2semidirect
2. #23752536C2semidirect
3. #23752533C2semidirect
4. #23752463C2semidirect
5. #23752446C2semidirect
6. #23752346C2semidirect
7. #23752345C2semidirect
8. #23752179C2semidirect
9. #535×C151C2semidirect
10. C22×D604C22semidirect
13. C2×#14558988C22semidirect
14. C22×C151⋊C8C22semidirect
18. #18012713C22semidirect
21. #18012698C22semidirect
22. #18012672C22semidirect
23. #18012670C22semidirect
24. #18012660C22semidirect
25. #18012660C22semidirect
26. #18012659C22semidirect
27. #18012659C22semidirect
28. C22⋊(C151⋊C8)C22semidirect
29. C22⋊(C151⋊C8)C22semidirect
31. C22×D4×C151C22semidirect
35. #121×C151C22semidirect
38. #117×C151C22semidirect
144. C151#3199semidirect
147. #535D151semidirect
157. C22×D4C2×D151semidirect
169. #121C2×D151semidirect
175. #117C2×D151semidirect

Maximal subgroups

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

subgroupindex
#237527762
#237525362
#237525332
#237524632
#237524462
#237523462
#237523452
#237521792
#535×C1512
#3199151