Finite Group Databasebeta

← #34079593

Subgroups — #34079593

Order 19328.

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

normal subgroups only

This group has 596 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×#18012765C211yesmaximal, characteristic, complemented
2C2×#18012764C211yesmaximal, characteristic, complemented
3C2×#18012759C211yesmaximal, characteristic, complemented
4C22×#14558989C211yesmaximal, characteristic, complemented
5#23752781C211yesmaximal, characteristic, complemented
6#23752602C212yesmaximal, complemented
7#23752599C212yesmaximal, complemented
8#23752594C212yesmaximal, complemented
9#23752588C212yesmaximal, complemented
10#23752168C211yesmaximal, characteristic, complemented
11#535×C151C211yesmaximal, characteristic, complemented
12C2×#14559004C2211yescharacteristic
13C22×D604C2211yescharacteristic
14#18012765—24no—
15#18012764—24no—
16#18012759—24no—
17C2×#14558994C2211yescharacteristic, complemented
18C2×#14558992C2211yescharacteristic, complemented
19C2×#14558992C2212yescomplemented
20C2×#14558991C2211yescharacteristic, complemented
21C2×#14558991C2212yescomplemented
22C2×#14558989—24no—
23C2×#14558989C2212yes—
24C2×#14558989C2212yes—
25C2×#14558989C2211yescharacteristic, complemented
26C2×#14558989C2212yescomplemented
27C2×#14558989C2212yescomplemented
28C2×#14558988C2211yescharacteristic
29C22×C151⋊C8C2211yescharacteristic
30#18012736C2212yescomplemented
31#18012727C2212yescomplemented
32#18012714—22no—
33#18012709—22no—
34#18012650C2212yescomplemented
35C4×C151⋊C8C2212yescomplemented
36C2×#41×C151C2211yescharacteristic
37C22×D4×C151C2211yescharacteristic
38#127×C151C2212yescomplemented
39#124×C151C2212yescomplemented
40#121×C151—22no—
41#120×C151—22no—
42#117×C151C2211yescharacteristic
43C23×D151—21no—
44#14559004—22no—
45#14559004—22no—
46C2×Dic302C2311yescharacteristic
47C2×D604—22no—
48C2×D604—22no—
49C2×D604—21no—
50C2×D604—24no—
51C2×D604C2312yes—
52C2×D604C2311yescharacteristic
53C2×C22⋊D151—21no—
54C2×C4×D151—21no—
55#14558994—22no—
56#14558992—22no—
57#14558992—24no—
58#14558991—22no—
59#14558991—24no—
60#14558989—24no—
61#14558989—24no—
62#14558989—22no—
63#14558989—24no—
64#14558989—24no—
65#14558988D414yescomplemented
66C2×C151⋊C8D414yescomplemented
67C2×C151⋊C8C2311yescharacteristic
68C2×C151⋊C8C2311yescharacteristic
69C2×C151⋊C8C2312yes—
70(C2×D151)⋊C4—24no—
71C24×C151—21no—
72#41×C151—22no—
73#41×C151—22no—
74C2×Q8×C151C2311yescharacteristic
75C2×D4×C151—21no—
76C2×D4×C151—22no—
77C2×D4×C151—22no—
78C2×D4×C151—21no—
79C2×D4×C151—24no—
80C2×D4×C151C2312yes—
81C2×D4×C151C2311yescharacteristic
82C22×C4×C151—21no—
83C22×C4×C151C2311yescharacteristic
84C4⋊C4×C151D412yes—
85C22⋊C4×C151—24no—
86C22⋊C4×C151D412yes—
87C42×C151C2312yes—
88C22×D151—22no—
89C22×D151—21no—
90C22×D151—42no—
91C22×D151—82no—
92Dic302—21no—
93Dic302—21no—
94D604—22no—
95D604—21no—
96D604—22no—
97D604—21no—
98D604—42no—
99D604—84no—
100C22⋊D151—42no—
101C2×Dic151—21no—
102C4×D151—42no—
103C151⋊C8C2×D412yes—
104C151⋊C8C2×D412yes—
105C151⋊C8C2×D414yes—
106C23×C151—22no—
107C23×C151—21no—
108C23×C151—42no—
109C23×C151—82no—
110C23×C151C2×D411yescharacteristic
111Q8×C151—21no—
112Q8×C151—21no—
113D4×C151—21no—
114D4×C151—21no—
115D4×C151—22no—
116D4×C151—22no—
117D4×C151—42no—
118D4×C151—42no—
119D4×C151—84no—
120C2×C4×C151—21no—
121C2×C4×C151—42no—
122C2×C4×C151C2×D412yes—
123C2×C4×C151C2×D412yes—
124C2×C4×C151C2×D414yes—
125C2×C4×C151C2×D411yescharacteristic
126C2×C4×C151C2411yescharacteristic
127C22×C151—22no—
128C22×C151—41no—
129C22×C151—42no—
130C22×C151—42no—
131C22×C151—44no—
132C22×C151—84no—
133C22×C151#12712yes—
134C22×C151C22×D411yescharacteristic
135C2×D151—41no—
136C2×D151—42no—
137C2×D151—42no—
138C2×D151—44no—
139C2×D151—84no—
140C4×C151—24no—
141C4×C151—41no—
142C4×C151#12712yes—
143C4×C151C22×D411yescharacteristic
144C4×C151C22×D411yescharacteristic
145Dic151—41no—
146C2×C151—22no—
147C2×C151—81no—
148C2×C151—82no—
149C2×C151C2×#12711yescharacteristic
150C2×C151#57612yes—
151D151—81no—
152D151—82no—
153C151#315511yescharacteristic, complemented, Sylow
154#3155—1511nomaximal, Sylow
155C2×AGL(1,ℤ/8)—1511no—
156C2×AGL(1,ℤ/8)—1511no—
157C2×#135—1511no—
158C22×D8—1511no—
159#535—1511no—
160#535D15111yescharacteristic, complemented
161#496—1512no—
162#496—1512no—
163#495—1512no—
164#493—1512no—
165#405—1511no—
166C2×#41—1511no—
167C2×#41C2×D15111yescharacteristic
168C22×D4—1511no—
169C22×D4C2×D15111yescharacteristic
170AGL(1,ℤ/8)—3024no—
171AGL(1,ℤ/8)—3024no—
172#135—3024no—
173C2×Q16—1511no—
174C2×SD16—1511no—
175C2×SD16—1512no—
176C2×SD16—1511no—
177C2×SD16—1512no—
178C2×D8—3024no—
179C2×D8—1512no—
180C2×D8—1512no—
181C2×D8—1511no—
182C2×D8—1512no—
183C2×D8—1512no—
184C2×M16—1511no—
185C22×C8—1511no—
186#127—1512no—
187#127C2×D15112yescomplemented
188#124—1512no—
189#124C2×D15112yescomplemented
190#121—22no—
191#121—3022no—
192#120—22no—
193#120—3022no—
194#117C2×D15111yescharacteristic
195#97—1512no—
196C4×C8—1512no—
197C24—21no—
198C24—3021no—
199#41—22no—
200#41—22no—
201#41—3022no—
202#41—3022no—
203C2×Q8—1511no—
204C2×Q8C22×D15111yescharacteristic
205C2×D4—21no—
206C2×D4—22no—
207C2×D4—22no—
208C2×D4—21no—
209C2×D4—24no—
210C2×D4—3021no—
211C2×D4—3022no—
212C2×D4—3022no—
213C2×D4—3021no—
214C2×D4—3024no—
215C2×D4—1512no—
216C2×D4—1511no—
217C2×D4C22×D15112yes—
218C2×D4C22×D15111yescharacteristic
219C22×C4—21no—
220C22×C4—3021no—
221C22×C4C22×D15111yescharacteristic
222Q16—3022no—
223SD16—3022no—
224SD16—3024no—
225SD16—3022no—
226SD16—3024no—
227D8—3024no—
228D8—3024no—
229D8—3022no—
230D8—3024no—
231D8—3024no—
232M16—1514no—
233C2×C8—1514no—
234C2×C8—1511no—
235C2×C8—1512no—
236C2×C8—1511no—
237C4⋊C4C22⋊D15112yes—
238C22⋊C4—24no—
239C22⋊C4—3024no—
240C22⋊C4C22⋊D15112yes—
241C42C22×D15112yes—
242C23—22no—
243C23—21no—
244C23—42no—
245C23—82no—
246C23—3022no—
247C23—3021no—
248C23—6042no—
249C23—12082no—
250C23C2×C22⋊D15111yescharacteristic
251Q8—21no—
252Q8—21no—
253Q8—3021no—
254Q8—3021no—
255D4—22no—
256D4—21no—
257D4—22no—
258D4—21no—
259D4—42no—
260D4—42no—
261D4—84no—
262D4—3022no—
263D4—3021no—
264D4—3022no—
265D4—3021no—
266D4—6042no—
267D4—6042no—
268D4—12084no—
269C2×C4—21no—
270C2×C4—42no—
271C2×C4—3021no—
272C2×C4—6042no—
273C2×C4D4×D15112yes—
274C2×C4D4×D15112yes—
275C2×C4C2×C22⋊D15114yes—
276C2×C4C2×C22⋊D15111yescharacteristic
277C2×C4C23×D15111yescharacteristic
278C8—1512no—
279C8—1512no—
280C8—1514no—
281C22—22no—
282C22—41no—
283C22—42no—
284C22—42no—
285C22—44no—
286C22—84no—
287C22—6041no—
288C22—6042no—
289C22—6042no—
290C22—6044no—
291C22—12084no—
292C22#1801273512yes—
293C22C22×C22⋊D15111yescharacteristic
294C4—24no—
295C4—41no—
296C4—6041no—
297C4#1801273512yes—
298C4C2×D4×D15111yescharacteristic
299C4C2×D4×D15111yescharacteristic
300C2—22no—
301C2—82no—
302C2—81no—
303C2—12082no—
304C2—12081no—
305C2C2×#1801273511yescharacteristic
306C2#2375301512yes—
subgroupG/H
centerC22C22×C22⋊D151
commutator, cosocleC2×C4×C151C24
FrattiniC2×C4C23×D151
Fitting#535×C151C2
socleC22×C151C22×D4
hypercenter#535D151
hypocenterC151#3155
LCSG ▷ C2×C4×C151 ▷ C2×C151 ▷ C151
UCSC1 ◁ C22 ◁ #117 ◁ #535

Complements

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

NH ≅ G/Ntype
1. C2×#18012765C2semidirect
2. C2×#18012764C2semidirect
3. C2×#18012759C2semidirect
4. C22×#14558989C2semidirect
5. #23752781C2semidirect
6. #23752602C2semidirect
7. #23752599C2semidirect
8. #23752594C2semidirect
9. #23752588C2semidirect
10. #23752168C2semidirect
11. #535×C151C2semidirect
17. C2×#14558994C22semidirect
18. C2×#14558992C22semidirect
19. C2×#14558992C22semidirect
20. C2×#14558991C22semidirect
21. C2×#14558991C22semidirect
25. C2×#14558989C22semidirect
26. C2×#14558989C22semidirect
27. C2×#14558989C22semidirect
30. #18012736C22semidirect
31. #18012727C22semidirect
34. #18012650C22semidirect
35. C4×C151⋊C8C22semidirect
38. #127×C151C22semidirect
39. #124×C151C22semidirect
65. #14558988D4semidirect
66. C2×C151⋊C8D4semidirect
153. C151#3155semidirect
160. #535D151semidirect
187. #127C2×D151semidirect
189. #124C2×D151semidirect

Maximal subgroups

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

subgroupindex
C2×#180127652
C2×#180127642
C2×#180127592
C22×#145589892
#237527812
#237526022
#237525992
#237525942
#237525882
#237521682
#535×C1512
#3155151