Finite Group Databasebeta

← #34079920

Subgroups — #34079920

Order 19328.

466 conjugacy classes of subgroups; only the 121 normal subgroups are shown.

normal subgroups only

This group has 466 conjugacy classes of subgroups — too many to draw. Only its 121 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×#18012713C211yesmaximal, characteristic, complemented
2#23752540C211yesmaximal, characteristic, complemented
3#23752536C212yesmaximal, complemented
4#23752523C211yesmaximal, characteristic, complemented
5#23752463C212yesmaximal, complemented
6#23752460C212yesmaximal, complemented
7#23752362C211yesmaximal, characteristic, complemented
8#23752357C212yesmaximal, complemented
9#23752345C211yesmaximal, characteristic, complemented
10#23752176C211yesmaximal, characteristic, complemented
11#525×C151C211yesmaximal, characteristic, complemented
12C22×D604C2211yescharacteristic
13C22×C22⋊D151—21no—
14C2×#14558991C2212yescomplemented
15C2×#14558989C2212yescomplemented
16C2×#14558988C2212yescomplemented
17#18012713—21no—
18#18012713—21no—
19#18012713C2212yes—
20#18012713C2212yes—
21C2×C4⋊Dic151C2211yescharacteristic
22C2×(C2×D151)⋊C4—21no—
23#18012672C2212yescomplemented
24#18012670C2212yescomplemented
25#18012663C2212yescomplemented
26#18012660C2212yescomplemented
27#18012659C2212yescomplemented
28#18012659C2212yescomplemented
29C22⋊(C151⋊C8)C2211yescharacteristic
30C22⋊(C151⋊C8)C2211yescharacteristic
31C22⋊(C151⋊C8)C2212yescomplemented
32C2×#41×C151C2211yescharacteristic, complemented
33C23×C4×C151C2211yescharacteristic
34#123×C151—21no—
35C22⋊Q8×C151C2211yescharacteristic
36C22⋊Q8×C151C2211yescharacteristic, complemented
37#121×C151C2211yescharacteristic
38#121×C151C2211yescharacteristic, complemented
39#120×C151—21no—
40C4×D4×C151—21no—
41C4×D4×C151—21no—
42#117×C151C2211yescharacteristic, complemented
43C23×D151—21no—
44C2×D604—21no—
45C2×D604—42no—
46C2×D604C2312yes—
47C2×C22⋊D151—22no—
48C2×C22⋊D151—22no—
49C2×C22⋊D151—44no—
50C22×Dic151—21no—
51#14558991—42no—
52#14558989—42no—
53#14558988—42no—
54C2×C151⋊C8C2312yes—
55C2×C151⋊C8C2312yes—
56C4⋊Dic151—21no—
57C4⋊Dic151C2312yes—
58(C2×D151)⋊C4—22no—
59(C2×D151)⋊C4—22no—
60C24×C151D411yescharacteristic
61#41×C151—42no—
62C2×Q8×C151C2311yescharacteristic
63C2×D4×C151—21no—
64C2×D4×C151—21no—
65C2×D4×C151—21no—
66C2×D4×C151C2311yescharacteristic
67C22×C4×C151—21no—
68C22×C4×C151—42no—
69C22×C4×C151D411yescharacteristic
70C22×C4×C151D411yescharacteristic
71C22×C4×C151D411yescharacteristic
72C22×C4×C151C2311yescharacteristic
73C22×C4×C151C2311yescharacteristic
74C22×C4×C151C2311yescharacteristic
75C4⋊C4×C151—21no—
76C4⋊C4×C151—21no—
77C4⋊C4×C151C2311yescharacteristic
78C4⋊C4×C151C2311yescharacteristic
79C22⋊C4×C151—21no—
80C22⋊C4×C151—21no—
81C22⋊C4×C151—21no—
82C22⋊C4×C151—21no—
83C22⋊C4×C151—21no—
84C42×C151—21no—
85C22×D151—22no—
86C22×D151—42no—
87C22×D151—42no—
88C22×D151—42no—
89D604—22no—
90D604—22no—
91D604—42no—
92C22⋊D151—44no—
93C22⋊D151—44no—
94C2×Dic151—22no—
95C2×Dic151—42no—
96C151⋊C8—22no—
97C151⋊C8—22no—
98C23×C151—22no—
99C23×C151—21no—
100C23×C151—41no—
101C23×C151—41no—
102C23×C151C2×D411yescharacteristic
103C23×C151C2×D411yescharacteristic
104C23×C151C2×D411yescharacteristic
105Q8×C151—22no—
106D4×C151—22no—
107D4×C151—42no—
108D4×C151—42no—
109D4×C151—42no—
110C2×C4×C151—22no—
111C2×C4×C151—22no—
112C2×C4×C151—22no—
113C2×C4×C151—21no—
114C2×C4×C151—21no—
115C2×C4×C151—21no—
116C2×C4×C151—41no—
117C2×C4×C151—41no—
118C2×C4×C151—41no—
119C2×C4×C151—42no—
120C2×C4×C151C2×D411yescharacteristic
121C2×C4×C151C2×D411yescharacteristic
122C2×C4×C151C2×D411yescharacteristic
123C2×C4×C151C2411yescharacteristic
124C22×C151—21no—
125C22×C151—21no—
126C22×C151—21no—
127C22×C151—21no—
128C22×C151—21no—
129C22×C151—21no—
130C22×C151—21no—
131C22×C151—21no—
132C22×C151—44no—
133C22×C151—41no—
134C22×C151—41no—
135C22×C151—41no—
136C22×C151AGL(1,ℤ/8)12yes—
137C22×C151C22×D411yescharacteristic
138C2×D151—42no—
139C2×D151—42no—
140C2×D151—42no—
141C2×D151—84no—
142C4×C151—21no—
143C4×C151—21no—
144C4×C151—21no—
145C4×C151—41no—
146C4×C151—41no—
147C4×C151—41no—
148C4×C151H(5,𝔽2)12yes—
149Dic151—42no—
150C2×C151—22no—
151C2×C151—41no—
152C2×C151—41no—
153C2×C151—81no—
154C2×C151#53411yescharacteristic
155C2×C151C2×AGL(1,ℤ/8)11yescharacteristic
156C2×C151#57511yescharacteristic
157D151—82no—
158C151#319411yescharacteristic, complemented, Sylow
159#3194—1511nomaximal, Sylow
160#525D15111yescharacteristic, complemented
161C2×#121—1511no—
162#483—1511no—
163#482—1512no—
164#480—1511no—
165#469—1512no—
166#468—1512no—
167#450—1511no—
168#449—1512no—
169#447—1511no—
170#407—1511no—
171C2×#41C2×D15111yescharacteristic, complemented
172C22×D4—3021no—
173C22×D4—1511no—
174C23×C4C2×D15111yescharacteristic
175C2×SD16—1512no—
176C2×D8—1512no—
177C2×M16—1512no—
178#123—21no—
179C22⋊Q8C2×D15111yescharacteristic
180C22⋊Q8C2×D15111yescharacteristic, complemented
181#121—3021no—
182#121—3021no—
183#121—1512no—
184#121—1512no—
185#121C2×D15111yescharacteristic
186#121C2×D15111yescharacteristic, complemented
187#120—21no—
188C4×D4—21no—
189C4×D4—21no—
190#117C2×D15111yescharacteristic, complemented
191C2×C4⋊C4—1511no—
192C2×C22⋊C4—3021no—
193#107—1512no—
194#106—1512no—
195#103—1512no—
196#102—1512no—
197#102—1512no—
198#102—1512no—
199C22⋊C8—1511no—
200C22⋊C8—1512no—
201C22⋊C8—1511no—
202C24—3021no—
203C24C22⋊D15111yescharacteristic
204#41—42no—
205C2×Q8C22×D15111yescharacteristic
206C2×D4—21no—
207C2×D4—21no—
208C2×D4—21no—
209C2×D4—3022no—
210C2×D4—3022no—
211C2×D4—3021no—
212C2×D4—6042no—
213C2×D4—6044no—
214C2×D4—1512no—
215C2×D4C22×D15111yescharacteristic
216C22×C4—21no—
217C22×C4—42no—
218C22×C4—3021no—
219C22×C4C22⋊D15111yescharacteristic
220C22×C4C22⋊D15111yescharacteristic
221C22×C4C22⋊D15111yescharacteristic
222C22×C4C22×D15111yescharacteristic
223C22×C4C22×D15111yescharacteristic
224C22×C4C22×D15111yescharacteristic
225SD16—6042no—
226D8—6042no—
227M16—6042no—
228C2×C8—1512no—
229C2×C8—1512no—
230C4⋊C4—21no—
231C4⋊C4—21no—
232C4⋊C4—3021no—
233C4⋊C4—1512no—
234C4⋊C4C22×D15111yescharacteristic
235C4⋊C4C22×D15111yescharacteristic
236C22⋊C4—21no—
237C22⋊C4—21no—
238C22⋊C4—21no—
239C22⋊C4—21no—
240C22⋊C4—21no—
241C22⋊C4—3022no—
242C22⋊C4—3022no—
243C42—21no—
244C23—22no—
245C23—21no—
246C23—41no—
247C23—41no—
248C23—3022no—
249C23—6042no—
250C23—6042no—
251C23—6042no—
252C23C2×C22⋊D15111yescharacteristic
253C23C2×C22⋊D15111yescharacteristic
254C23C2×C22⋊D15111yescharacteristic
255Q8—22no—
256D4—22no—
257D4—42no—
258D4—42no—
259D4—42no—
260D4—3022no—
261D4—3022no—
262D4—6042no—
263D4—6044no—
264D4—6044no—
265C2×C4—22no—
266C2×C4—22no—
267C2×C4—22no—
268C2×C4—21no—
269C2×C4—21no—
270C2×C4—21no—
271C2×C4—41no—
272C2×C4—41no—
273C2×C4—41no—
274C2×C4—42no—
275C2×C4—3022no—
276C2×C4—6042no—
277C2×C4C2×C22⋊D15111yescharacteristic
278C2×C4C2×C22⋊D15111yescharacteristic
279C2×C4C2×C22⋊D15111yescharacteristic
280C2×C4C23×D15111yescharacteristic
281C8—3022no—
282C8—3022no—
283C22—21no—
284C22—21no—
285C22—21no—
286C22—21no—
287C22—21no—
288C22—21no—
289C22—21no—
290C22—21no—
291C22—44no—
292C22—41no—
293C22—41no—
294C22—41no—
295C22—6042no—
296C22—6042no—
297C22—6042no—
298C22—12084no—
299C22#1801276412yes—
300C22C22×C22⋊D15111yescharacteristic
301C4—21no—
302C4—21no—
303C4—21no—
304C4—41no—
305C4—41no—
306C4—41no—
307C4—6042no—
308C4#1801278412yes—
309C2—22no—
310C2—41no—
311C2—41no—
312C2—81no—
313C2—12082no—
314C2#2375277111yescharacteristic
315C2C2×#1801276411yescharacteristic
316C2#2375301011yescharacteristic
subgroupG/H
centerC22C22×C22⋊D151
commutator, cosocleC2×C4×C151C24
FrattiniC2×C4C23×D151
Fitting#525×C151C2
socleC22×C151C22×D4
hypercenter#525D151
hypocenterC151#3194
LCSG ▷ C2×C4×C151 ▷ C2×C151 ▷ C151
UCSC1 ◁ C22 ◁ C23×C4 ◁ #525

Complements

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

NH ≅ G/Ntype
1. C2×#18012713C2semidirect
2. #23752540C2semidirect
3. #23752536C2semidirect
4. #23752523C2semidirect
5. #23752463C2semidirect
6. #23752460C2semidirect
7. #23752362C2semidirect
8. #23752357C2semidirect
9. #23752345C2semidirect
10. #23752176C2semidirect
11. #525×C151C2semidirect
14. C2×#14558991C22semidirect
15. C2×#14558989C22semidirect
16. C2×#14558988C22semidirect
23. #18012672C22semidirect
24. #18012670C22semidirect
25. #18012663C22semidirect
26. #18012660C22semidirect
27. #18012659C22semidirect
28. #18012659C22semidirect
31. C22⋊(C151⋊C8)C22semidirect
32. C2×#41×C151C22semidirect
36. C22⋊Q8×C151C22semidirect
38. #121×C151C22semidirect
42. #117×C151C22semidirect
158. C151#3194semidirect
160. #525D151semidirect
171. C2×#41C2×D151semidirect
180. C22⋊Q8C2×D151semidirect
186. #121C2×D151semidirect
190. #117C2×D151semidirect

Maximal subgroups

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

subgroupindex
C2×#180127132
#237525402
#237525362
#237525232
#237524632
#237524602
#237523622
#237523572
#237523452
#237521762
#525×C1512
#3194151