Finite Group Databasebeta

← #34079582

Subgroups — #34079582

Order 19328.

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

normal subgroups only

This group has 564 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×#18012769C211yesmaximal, characteristic, complemented
2C2×#18012765C211yesmaximal, characteristic, complemented
3C2×#18012759C211yesmaximal, characteristic, complemented
4C22×#14558992C211yesmaximal, characteristic, complemented
5#23752788C211yesmaximal, characteristic, complemented
6#23752607C212yesmaximal, complemented
7#23752599C212yesmaximal, complemented
8#23752594C212yesmaximal, complemented
9#23752584C212yesmaximal, complemented
10#23752168C211yesmaximal, characteristic, complemented
11#535×C151C211yesmaximal, characteristic, complemented
12C2×#14559004C2211yescharacteristic
13C22×Dic302C2211yescharacteristic
14#18012769—24no—
15#18012765—24no—
16#18012759—24no—
17C2×#14558994C2211yescharacteristic, complemented
18C2×#14558994C2212yescomplemented
19C2×#14558992—24no—
20C2×#14558992C2212yes—
21C2×#14558992C2212yes—
22C2×#14558992C2212yes—
23C2×#14558992C2211yescharacteristic, complemented
24C2×#14558992C2212yescomplemented
25C2×#14558991C2211yescharacteristic, complemented
26C2×#14558989C2212yes—
27C2×#14558989C2211yescharacteristic, complemented
28C2×#14558988C2211yescharacteristic
29C22×C151⋊C8C2211yescharacteristic
30#18012739C2212yescomplemented
31#18012727C2212yescomplemented
32#18012723—22no—
33#18012719—22no—
34#18012650C2212yescomplemented
35C4×C151⋊C8C2212yescomplemented
36C2×#41×C151C2211yescharacteristic
37C22×D4×C151C2211yescharacteristic
38#127×C151C2212yes—
39#124×C151C2212yes—
40#121×C151—22no—
41#120×C151—22no—
42#117×C151C2211yescharacteristic
43#14559004—22no—
44#14559004—22no—
45C2×Dic302—21no—
46C2×Dic302—22no—
47C2×Dic302—22no—
48C2×Dic302C2312yes—
49C2×Dic302C2311yescharacteristic
50C2×D604C2311yescharacteristic
51C2×C22⋊D151—21no—
52C22×Dic151—21no—
53C2×C4×D151—21no—
54#14558994—22no—
55#14558994—24no—
56#14558992—24no—
57#14558992—24no—
58#14558992—24no—
59#14558992—22no—
60#14558992—24no—
61#14558991—22no—
62#14558989—24no—
63#14558989—22no—
64#14558988D414yescomplemented
65C2×C151⋊C8D414yescomplemented
66C2×C151⋊C8C2311yescharacteristic
67C2×C151⋊C8C2311yescharacteristic
68C2×C151⋊C8C2312yes—
69C4⋊Dic151—24no—
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—21no—
89Dic302—22no—
90Dic302—21no—
91Dic302—22no—
92Dic302—21no—
93Dic302—42no—
94D604—21no—
95D604—21no—
96C22⋊D151—42no—
97C2×Dic151—22no—
98C2×Dic151—21no—
99C2×Dic151—42no—
100C4×D151—42no—
101C151⋊C8C2×D412yes—
102C151⋊C8C2×D412yes—
103C151⋊C8C2×D414yes—
104C23×C151—22no—
105C23×C151—21no—
106C23×C151—42no—
107C23×C151—82no—
108C23×C151C2×D411yescharacteristic
109Q8×C151—21no—
110Q8×C151—21no—
111D4×C151—21no—
112D4×C151—21no—
113D4×C151—22no—
114D4×C151—22no—
115D4×C151—42no—
116D4×C151—42no—
117D4×C151—84no—
118C2×C4×C151—21no—
119C2×C4×C151—42no—
120C2×C4×C151C2×D412yes—
121C2×C4×C151C2×D412yes—
122C2×C4×C151C2×D414yes—
123C2×C4×C151C2×D411yescharacteristic
124C2×C4×C151C2411yescharacteristic
125C22×C151—22no—
126C22×C151—41no—
127C22×C151—42no—
128C22×C151—42no—
129C22×C151—44no—
130C22×C151—84no—
131C22×C151#12712yes—
132C22×C151C22×D411yescharacteristic
133C2×D151—41no—
134C2×D151—42no—
135C4×C151—24no—
136C4×C151—41no—
137C4×C151#12712yes—
138C4×C151C22×D411yescharacteristic
139C4×C151C22×D411yescharacteristic
140Dic151—41no—
141Dic151—42no—
142C2×C151—22no—
143C2×C151—81no—
144C2×C151—82no—
145C2×C151C2×#12711yescharacteristic
146C2×C151#57712yes—
147D151—81no—
148C151#315411yescharacteristic, complemented, Sylow
149#3154—1511nomaximal, Sylow
150C2×#137—1511no—
151C2×AGL(1,ℤ/8)—1511no—
152C2×#135—1511no—
153C22×SD16—1511no—
154#536—1511no—
155#535D15111yescharacteristic, complemented
156#497—1512no—
157#496—1512no—
158#495—1512no—
159#492—1512no—
160#405—1511no—
161C2×#41—1511no—
162C2×#41C2×D15111yescharacteristic
163C22×Q8—1511no—
164C22×D4C2×D15111yescharacteristic
165#137—3024no—
166AGL(1,ℤ/8)—3024no—
167#135—3024no—
168C2×Q16—1511no—
169C2×Q16—1512no—
170C2×SD16—3024no—
171C2×SD16—1511no—
172C2×SD16—1512no—
173C2×SD16—1512no—
174C2×SD16—1511no—
175C2×SD16—1512no—
176C2×SD16—1512no—
177C2×D8—1511no—
178C2×D8—1512no—
179C2×M16—1511no—
180C22×C8—1511no—
181C4⋊Q8—1512no—
182#127C2×D15112yes—
183#124—1512no—
184#124C2×D15112yes—
185#123—3022no—
186C22⋊Q8—3022no—
187#121—22no—
188#120—22no—
189#117C2×D15111yescharacteristic
190#97—1512no—
191C4×C8—1512no—
192C24—21no—
193#41—22no—
194#41—22no—
195#41—3022no—
196#41—3022no—
197C2×Q8—3021no—
198C2×Q8—3022no—
199C2×Q8—3022no—
200C2×Q8—1512no—
201C2×Q8—1511no—
202C2×Q8C22×D15111yescharacteristic
203C2×D4—21no—
204C2×D4—22no—
205C2×D4—22no—
206C2×D4—21no—
207C2×D4—24no—
208C2×D4—3021no—
209C2×D4—1511no—
210C2×D4C22×D15112yes—
211C2×D4C22×D15111yescharacteristic
212C22×C4—21no—
213C22×C4—3021no—
214C22×C4—3021no—
215C22×C4C22×D15111yescharacteristic
216Q16—3022no—
217Q16—3024no—
218SD16—3024no—
219SD16—3024no—
220SD16—3022no—
221SD16—3024no—
222SD16—3024no—
223SD16—3022no—
224D8—3022no—
225D8—3024no—
226M16—1514no—
227C2×C8—1514no—
228C2×C8—1511no—
229C2×C8—1512no—
230C2×C8—1511no—
231C4⋊C4—3024no—
232C4⋊C4C22⋊D15112yes—
233C22⋊C4—24no—
234C22⋊C4—3024no—
235C22⋊C4C22⋊D15112yes—
236C42C22×D15112yes—
237C23—22no—
238C23—21no—
239C23—42no—
240C23—82no—
241C23—3021no—
242C23C2×C22⋊D15111yescharacteristic
243Q8—21no—
244Q8—21no—
245Q8—3022no—
246Q8—3021no—
247Q8—3022no—
248Q8—3021no—
249Q8—6042no—
250D4—22no—
251D4—21no—
252D4—22no—
253D4—21no—
254D4—42no—
255D4—42no—
256D4—84no—
257D4—3021no—
258D4—3021no—
259D4—6042no—
260C2×C4—21no—
261C2×C4—42no—
262C2×C4—3022no—
263C2×C4—3021no—
264C2×C4—6042no—
265C2×C4—6042no—
266C2×C4D4×D15112yes—
267C2×C4D4×D15112yes—
268C2×C4C2×C22⋊D15114yes—
269C2×C4C2×C22⋊D15111yescharacteristic
270C2×C4C23×D15111yescharacteristic
271C8—1512no—
272C8—1512no—
273C8—1514no—
274C22—22no—
275C22—41no—
276C22—42no—
277C22—42no—
278C22—44no—
279C22—84no—
280C22—6041no—
281C22—6042no—
282C22#1801273512yes—
283C22C22×C22⋊D15111yescharacteristic
284C4—24no—
285C4—41no—
286C4—6041no—
287C4—6042no—
288C4#1801273512yes—
289C4C2×D4×D15111yescharacteristic
290C4C2×D4×D15111yescharacteristic
291C2—22no—
292C2—82no—
293C2—81no—
294C2—12081no—
295C2C2×#1801273511yescharacteristic
296C2#2375302312yes—
subgroupG/H
centerC22C22×C22⋊D151
commutator, cosocleC2×C4×C151C24
FrattiniC2×C4C23×D151
Fitting#535×C151C2
socleC22×C151C22×D4
hypercenter#535D151
hypocenterC151#3154
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×#18012769C2semidirect
2. C2×#18012765C2semidirect
3. C2×#18012759C2semidirect
4. C22×#14558992C2semidirect
5. #23752788C2semidirect
6. #23752607C2semidirect
7. #23752599C2semidirect
8. #23752594C2semidirect
9. #23752584C2semidirect
10. #23752168C2semidirect
11. #535×C151C2semidirect
17. C2×#14558994C22semidirect
18. C2×#14558994C22semidirect
23. C2×#14558992C22semidirect
24. C2×#14558992C22semidirect
25. C2×#14558991C22semidirect
27. C2×#14558989C22semidirect
30. #18012739C22semidirect
31. #18012727C22semidirect
34. #18012650C22semidirect
35. C4×C151⋊C8C22semidirect
64. #14558988D4semidirect
65. C2×C151⋊C8D4semidirect
148. C151#3154semidirect
155. #535D151semidirect

Maximal subgroups

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

subgroupindex
C2×#180127692
C2×#180127652
C2×#180127592
C22×#145589922
#237527882
#237526072
#237525992
#237525942
#237525842
#237521682
#535×C1512
#3154151