Finite Group Databasebeta

← #34078376

Subgroups — #34078376

Order 19328.

784 conjugacy classes of subgroups; only the 149 normal subgroups are shown.

normal subgroups only

This group has 784 conjugacy classes of subgroups — too many to draw. Only its 149 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×#18012785C211yesmaximal, characteristic, complemented
2C2×#18012765C211yesmaximal, characteristic, complemented
3C22×#14558989C211yesmaximal, characteristic, complemented
4#23752355C214yesmaximal, complemented
5#23752345C214yesmaximal, complemented
6#23752216C211yesmaximal, characteristic, complemented
7#23752206C211yesmaximal, characteristic, complemented
8#23752179C211yesmaximal, characteristic, complemented
9#535×C151C211yesmaximal, characteristic, complemented
10#18012785—24no—
11#18012785—24no—
12C2×#14559005—21no—
13C2×#14559004C2211yescharacteristic
14C2×#14559004C2212yescomplemented
15C22×D604C2211yescharacteristic
16C22×D604C2212yescomplemented
17C2×D4×D151—21no—
18C2×D4×D151—22no—
19#18012765—24no—
20C2×#14558992C2212yescomplemented
21C2×#14558989—24no—
22C2×#14558989C2214yescomplemented
23C2×#14558989C2212yescomplemented
24C2×#14558988C2211yescharacteristic, complemented
25C22×C151⋊C8C2211yescharacteristic, complemented
26#18012662C2212yescomplemented
27#18012659C2212yescomplemented
28#18012659C2214yescomplemented
29C22⋊(C151⋊C8)C2214yescomplemented
30C2×#41×C151C2211yescharacteristic
31C22×D4×C151C2211yescharacteristic, complemented
32#127×C151—21no—
33#124×C151—21no—
34#121×C151C2214yescomplemented
35#120×C151—22no—
36#117×C151C2211yescharacteristic, complemented
37C23×D151—21no—
38C23×D151—22no—
39#14559005—28no—
40#14559004—24no—
41#14559004—24no—
42#14559004—22no—
43#14559004D414yescomplemented
44C2×Dic302C2311yescharacteristic
45C2×D604—24no—
46C2×D604—24no—
47C2×D604—21no—
48C2×D604—22no—
49C2×D604—22no—
50C2×D604D414yescomplemented
51C2×D604C2312yes—
52C2×D604C2311yescharacteristic
53C2×C22⋊D151—21no—
54C2×C22⋊D151—22no—
55D4×D151—216no—
56D4×D151—28no—
57C2×C4×D151—21no—
58C2×C4×D151—22no—
59#14558992—24no—
60#14558989—28no—
61#14558989—24no—
62#14558988—22no—
63C2×C151⋊C8—22no—
64C2×C151⋊C8C2312yes—
65C2×C151⋊C8C2312yes—
66C24×C151—21no—
67#41×C151—22no—
68#41×C151—22no—
69C2×Q8×C151D411yescharacteristic
70C2×D4×C151—24no—
71C2×D4×C151—22no—
72C2×D4×C151—22no—
73C2×D4×C151—21no—
74C2×D4×C151D412yes—
75C2×D4×C151D411yescharacteristic
76C2×D4×C151C2312yes—
77C22×C4×C151C2312yes—
78C22×C4×C151C2311yescharacteristic
79C4⋊C4×C151C2312yes—
80C22⋊C4×C151—21no—
81C22⋊C4×C151—24no—
82C42×C151—21no—
83C22×D151—21no—
84C22×D151—22no—
85C22×D151—28no—
86C22×D151—24no—
87C22×D151—82no—
88C22×D151—84no—
89Dic302—21no—
90Dic302C2×D412yes—
91D604—28no—
92D604—24no—
93D604—22no—
94D604—21no—
95D604C2×D412yes—
96D604C2×D414yes—
97C22⋊D151—28no—
98C22⋊D151—24no—
99C2×Dic151—21no—
100C4×D151—28no—
101C4×D151—24no—
102C151⋊C8—22no—
103C151⋊C8—22no—
104C23×C151—22no—
105C23×C151—42no—
106C23×C151—82no—
107C23×C151C2×D412yes—
108C23×C151C2×D411yescharacteristic
109Q8×C151—22no—
110D4×C151—24no—
111D4×C151—22no—
112D4×C151—22no—
113D4×C151—22no—
114D4×C151—42no—
115D4×C151—84no—
116C2×C4×C151—22no—
117C2×C4×C151—22no—
118C2×C4×C151—22no—
119C2×C4×C151C2×D412yes—
120C2×C4×C151C2×D412yes—
121C2×C4×C151C2×D412yes—
122C2×C4×C151C2×D411yescharacteristic
123C2×C4×C151C2411yescharacteristic
124C22×C151—22no—
125C22×C151—22no—
126C22×C151—24no—
127C22×C151—42no—
128C22×C151—44no—
129C22×C151—84no—
130C22×C151#12012yes—
131C22×C151C22×D411yescharacteristic
132C2×D151—24no—
133C2×D151—22no—
134C2×D151—44no—
135C2×D151—42no—
136C2×D151—84no—
137C2×D151—88no—
138C4×C151—22no—
139C4×C151—42no—
140C4×C151#12012yes—
141C4×C151C22×D411yescharacteristic
142C4×C151C22×D411yescharacteristic
143Dic151—22no—
144C2×C151—22no—
145C2×C151—42no—
146C2×C151—82no—
147C2×C151C2×#12011yescharacteristic
148C2×C151#57612yes—
149D151—44no—
150D151—42no—
151C151#300811yescharacteristic, complemented, Sylow
152#3008—1511nomaximal, Sylow
153C2×H(5,𝔽2)—1511no—
154C2×AGL(1,ℤ/8)—1511no—
155C22×D8—1511no—
156#535D15111yescharacteristic, complemented
157#449—1514no—
158#447—1514no—
159#418—1511no—
160#416—1511no—
161#408—1511no—
162H(5,𝔽2)—3024no—
163H(5,𝔽2)—3024no—
164C2×#41—3021no—
165C2×#41—1512no—
166C2×#41—1511no—
167C2×#41C2×D15111yescharacteristic
168C22×D4—3022no—
169C22×D4—3021no—
170C22×D4—1512no—
171C22×D4—1511no—
172C22×D4C2×D15111yescharacteristic, complemented
173AGL(1,ℤ/8)—3024no—
174C2×SD16—1512no—
175C2×D8—3024no—
176C2×D8—1514no—
177C2×D8—1512no—
178C2×M16—1511no—
179C22×C8—1511no—
180#127—21no—
181#124—21no—
182#121C2×D15114yescomplemented
183#120—22no—
184#117C2×D15111yescharacteristic, complemented
185#103—1512no—
186#102—1512no—
187#102—1514no—
188C22⋊C8—1514no—
189C24—21no—
190C24—3022no—
191C24—3021no—
192#41—22no—
193#41—22no—
194#41—3024no—
195#41—3024no—
196#41—3028no—
197#41—3022no—
198#41—1514no—
199C2×Q8—1511no—
200C2×Q8C22⋊D15111yescharacteristic
201C2×D4—24no—
202C2×D4—22no—
203C2×D4—22no—
204C2×D4—21no—
205C2×D4—3024no—
206C2×D4—3024no—
207C2×D4—30216no—
208C2×D4—3028no—
209C2×D4—3022no—
210C2×D4—3021no—
211C2×D4—3022no—
212C2×D4—3022no—
213C2×D4—3021no—
214C2×D4—1514no—
215C2×D4—1511no—
216C2×D4—1512no—
217C2×D4C22⋊D15112yes—
218C2×D4C22⋊D15111yescharacteristic
219C2×D4C22×D15112yes—
220C22×C4—3022no—
221C22×C4—3021no—
222C22×C4C22×D15112yes—
223C22×C4C22×D15111yescharacteristic
224SD16—3024no—
225D8—3028no—
226D8—3024no—
227M16—3022no—
228C2×C8—3022no—
229C2×C8—1512no—
230C2×C8—1512no—
231C4⋊C4C22×D15112yes—
232C22⋊C4—21no—
233C22⋊C4—24no—
234C42—21no—
235C23—22no—
236C23—42no—
237C23—82no—
238C23—3028no—
239C23—3022no—
240C23—3021no—
241C23—3024no—
242C23—12082no—
243C23—12084no—
244C23C2×C22⋊D15112yes—
245C23C2×C22⋊D15111yescharacteristic
246Q8—22no—
247Q8—3021no—
248Q8—1512no—
249D4—24no—
250D4—22no—
251D4—22no—
252D4—22no—
253D4—42no—
254D4—84no—
255D4—3028no—
256D4—3028no—
257D4—3024no—
258D4—3024no—
259D4—3022no—
260D4—3021no—
261D4—1512no—
262D4—1514no—
263C2×C4—22no—
264C2×C4—22no—
265C2×C4—22no—
266C2×C4—3028no—
267C2×C4—3021no—
268C2×C4—3024no—
269C2×C4D4×D15112yes—
270C2×C4D4×D15112yes—
271C2×C4C2×C22⋊D15112yes—
272C2×C4C2×C22⋊D15111yescharacteristic
273C2×C4C23×D15111yescharacteristic
274C8—3022no—
275C8—3022no—
276C22—22no—
277C22—24no—
278C22—22no—
279C22—44no—
280C22—42no—
281C22—84no—
282C22—3024no—
283C22—3022no—
284C22—6044no—
285C22—6042no—
286C22—12084no—
287C22—12088no—
288C22#1801270712yes—
289C22C22×C22⋊D15111yescharacteristic
290C4—22no—
291C4—42no—
292C4—3022no—
293C4#1801270712yes—
294C4C2×D4×D15111yescharacteristic
295C4C2×D4×D15111yescharacteristic
296C2—22no—
297C2—42no—
298C2—82no—
299C2—6044no—
300C2—6042no—
301C2C2×#1801270711yescharacteristic
302C2#2375301512yes—
subgroupG/H
centerC22C22×C22⋊D151
commutator, cosocleC2×C4×C151C24
FrattiniC2×C4C23×D151
Fitting#535×C151C2
socleC22×C151C22×D4
hypercenter#535D151
hypocenterC151#3008
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. C2×#18012785C2semidirect
2. C2×#18012765C2semidirect
3. C22×#14558989C2semidirect
4. #23752355C2semidirect
5. #23752345C2semidirect
6. #23752216C2semidirect
7. #23752206C2semidirect
8. #23752179C2semidirect
9. #535×C151C2semidirect
14. C2×#14559004C22semidirect
16. C22×D604C22semidirect
20. C2×#14558992C22semidirect
22. C2×#14558989C22semidirect
23. C2×#14558989C22semidirect
24. C2×#14558988C22semidirect
25. C22×C151⋊C8C22semidirect
26. #18012662C22semidirect
27. #18012659C22semidirect
28. #18012659C22semidirect
29. C22⋊(C151⋊C8)C22semidirect
31. C22×D4×C151C22semidirect
34. #121×C151C22semidirect
36. #117×C151C22semidirect
43. #14559004D4semidirect
50. C2×D604D4semidirect
151. C151#3008semidirect
156. #535D151semidirect
172. C22×D4C2×D151semidirect
182. #121C2×D151semidirect
184. #117C2×D151semidirect

Maximal subgroups

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

subgroupindex
C2×#180127852
C2×#180127652
C22×#145589892
#237523552
#237523452
#237522162
#237522062
#237521792
#535×C1512
#3008151