Finite Group Databasebeta

← #34079586

Subgroups — #34079586

Order 19328.

564 conjugacy classes of subgroups; only the 165 normal subgroups are shown.

normal subgroups only

This group has 564 conjugacy classes of subgroups — too many to draw. Only its 165 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×#18012772C211yesmaximal, characteristic, complemented
2C2×#18012767C211yesmaximal, characteristic, complemented
3C2×#18012761C211yesmaximal, characteristic, complemented
4C22×#14558993C211yesmaximal, characteristic, complemented
5#23752788C211yesmaximal, characteristic, complemented
6#23752781C211yesmaximal, characteristic, complemented
7#23752606C212yesmaximal, complemented
8#23752601C212yesmaximal, complemented
9#23752596C212yesmaximal, complemented
10#23752585C212yesmaximal, complemented
11#405×C151C211yesmaximal, characteristic, complemented
12C2×#14559004C2211yescharacteristic
13C2×#14559004C2211yescharacteristic
14C22×Dic302C2211yescharacteristic
15C22×D604C2211yescharacteristic
16#18012772—24no—
17#18012767—24no—
18#18012761—24no—
19C2×Dic604C2211yescharacteristic, complemented
20C2×Dic604C2212yescomplemented
21C2×#14558993—24no—
22C2×#14558993C2212yes—
23C2×#14558993C2212yes—
24C2×#14558993C2212yes—
25C2×#14558993C2211yescharacteristic, complemented
26C2×#14558993C2211yescharacteristic, complemented
27C2×#14558993C2212yescomplemented
28C2×D1208C2212yes—
29C2×D1208C2211yescharacteristic, complemented
30#18012739C2212yescomplemented
31#18012736C2212yes—
32#18012727C2212yes—
33#18012727C2212yescomplemented
34#18012723—22no—
35#18012719—22no—
36#18012714—22no—
37#18012709—22no—
38C2×M16×C151C2211yescharacteristic
39C22×C8×C151C2211yescharacteristic
40#117×C151C2211yescharacteristic
41#97×C151C2212yescomplemented
42C4×C8×C151C2212yescomplemented
43C23×D151—21no—
44#14559004—22no—
45#14559004—22no—
46#14559004—22no—
47#14559004—22no—
48C2×Dic302—21no—
49C2×Dic302—22no—
50C2×Dic302—22no—
51C2×Dic302C2311yescharacteristic
52C2×Dic302C2312yes—
53C2×Dic302C2311yescharacteristic
54C2×D604—22no—
55C2×D604—22no—
56C2×D604—21no—
57C2×D604—24no—
58C2×D604C2312yes—
59C2×D604C2311yescharacteristic
60C2×D604C2311yescharacteristic
61C2×C22⋊D151—21no—
62C2×C22⋊D151—21no—
63C22×Dic151—21no—
64C2×C4×D151—21no—
65C2×C4×D151—21no—
66Dic604—22no—
67Dic604—24no—
68#14558993—24no—
69#14558993—24no—
70#14558993—24no—
71#14558993—22no—
72#14558993—22no—
73#14558993—24no—
74D1208—24no—
75D1208—22no—
76C4⋊Dic151—24no—
77(C2×D151)⋊C4—24no—
78(C2×D151)⋊C4—24no—
79C22×C4×C151C2311yescharacteristic
80M16×C151D414yescomplemented
81C2×C8×C151D414yescomplemented
82C2×C8×C151C2312yes—
83C2×C8×C151C2311yescharacteristic
84C2×C8×C151C2311yescharacteristic
85C4⋊C4×C151D412yes—
86C22⋊C4×C151D412yes—
87C42×C151C2312yes—
88C22×D151—21no—
89C22×D151—22no—
90C22×D151—21no—
91C22×D151—42no—
92C22×D151—82no—
93Dic302—22no—
94Dic302—21no—
95Dic302—22no—
96Dic302—21no—
97Dic302—21no—
98Dic302—21no—
99Dic302—42no—
100D604—21no—
101D604—22no—
102D604—21no—
103D604—21no—
104D604—22no—
105D604—21no—
106D604—42no—
107D604—84no—
108C22⋊D151—42no—
109C22⋊D151—42no—
110C2×Dic151—21no—
111C2×Dic151—22no—
112C2×Dic151—21no—
113C2×Dic151—42no—
114C4×D151—42no—
115C4×D151—42no—
116C23×C151C2×D411yescharacteristic
117C2×C4×C151C2×D414yes—
118C2×C4×C151C2×D411yescharacteristic
119C2×C4×C151C2×D412yes—
120C2×C4×C151C2×D412yes—
121C2×C4×C151C2411yescharacteristic
122C8×C151C2×D412yes—
123C8×C151C2×D414yes—
124C8×C151C2×D412yes—
125C22×C151—22no—
126C22×C151#12712yes—
127C22×C151C22×D411yescharacteristic
128C2×D151—41no—
129C2×D151—41no—
130C2×D151—42no—
131C2×D151—42no—
132C2×D151—44no—
133C2×D151—42no—
134C2×D151—84no—
135C4×C151—24no—
136C4×C151#12712yes—
137C4×C151C22×D411yescharacteristic
138C4×C151C22×D411yescharacteristic
139Dic151—41no—
140Dic151—41no—
141Dic151—42no—
142C2×C151—22no—
143C2×C151C2×#12711yescharacteristic
144C2×C151#57712yes—
145D151—81no—
146D151—81no—
147D151—82no—
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#535—1511no—
156#497—1512no—
157#496—1512no—
158#495—1512no—
159#492—1512no—
160#405D15111yescharacteristic, complemented
161C2×#41—1511no—
162C2×#41—1511no—
163C22×Q8—1511no—
164C22×D4—1511no—
165#137—3024no—
166AGL(1,ℤ/8)—3024no—
167#135—3024no—
168C2×Q16—1511no—
169C2×Q16—1512no—
170C2×SD16—3024no—
171C2×SD16—1512no—
172C2×SD16—1512no—
173C2×SD16—1511no—
174C2×SD16—1511no—
175C2×SD16—1512no—
176C2×SD16—1512no—
177C2×D8—1511no—
178C2×D8—1512no—
179C2×M16C2×D15111yescharacteristic
180C22×C8C2×D15111yescharacteristic
181C4⋊Q8—1512no—
182#127—1512no—
183#124—1512no—
184#124—1512no—
185#123—3022no—
186C22⋊Q8—3022no—
187#121—3022no—
188#120—3022no—
189#117C2×D15111yescharacteristic
190#97C2×D15112yescomplemented
191C4×C8C2×D15112yescomplemented
192C24—3021no—
193#41—3022no—
194#41—3022no—
195#41—3022no—
196#41—3022no—
197C2×Q8—3021no—
198C2×Q8—3022no—
199C2×Q8—3022no—
200C2×Q8—1511no—
201C2×Q8—1512no—
202C2×Q8—1511no—
203C2×D4—3021no—
204C2×D4—3021no—
205C2×D4—3022no—
206C2×D4—3022no—
207C2×D4—3021no—
208C2×D4—3024no—
209C2×D4—1511no—
210C2×D4—1512no—
211C2×D4—1511no—
212C22×C4—3021no—
213C22×C4—3021no—
214C22×C4—3021no—
215C22×C4C22×D15111yescharacteristic
216Q16—3022no—
217Q16—3024no—
218SD16—3024no—
219SD16—3024no—
220SD16—3022no—
221SD16—3022no—
222SD16—3024no—
223SD16—3024no—
224D8—3022no—
225D8—3024no—
226M16D60414yescomplemented
227C2×C8D60414yescomplemented
228C2×C8C22×D15111yescharacteristic
229C2×C8C22×D15112yes—
230C2×C8C22×D15111yescharacteristic
231C4⋊C4—3024no—
232C4⋊C4D60412yes—
233C22⋊C4—3024no—
234C22⋊C4—3024no—
235C22⋊C4D60412yes—
236C42C22×D15112yes—
237C23—3021no—
238C23—3022no—
239C23—3021no—
240C23—6042no—
241C23—12082no—
242C23C2×D60411yescharacteristic
243Q8—3022no—
244Q8—3021no—
245Q8—3022no—
246Q8—3021no—
247Q8—3021no—
248Q8—3021no—
249Q8—6042no—
250D4—3021no—
251D4—3022no—
252D4—3021no—
253D4—3021no—
254D4—3022no—
255D4—3021no—
256D4—6042no—
257D4—6042no—
258D4—6042no—
259D4—12084no—
260C2×C4—3021no—
261C2×C4—3022no—
262C2×C4—3021no—
263C2×C4—6042no—
264C2×C4—6042no—
265C2×C4—6042no—
266C2×C4C2×D60414yes—
267C2×C4C2×D60411yescharacteristic
268C2×C4C2×D60412yes—
269C2×C4C2×D60412yes—
270C2×C4C23×D15111yescharacteristic
271C8C2×D60412yes—
272C8C2×D60412yes—
273C8C2×D60414yes—
274C22—22no—
275C22—6041no—
276C22—6041no—
277C22—6042no—
278C22—6042no—
279C22—6044no—
280C22—6042no—
281C22—12084no—
282C22#1801273612yes—
283C22C22×D60411yescharacteristic
284C4—24no—
285C4—6041no—
286C4—6041no—
287C4—6042no—
288C4#1801273612yes—
289C4C22×D60411yescharacteristic
290C4C22×D60411yescharacteristic
291C2—22no—
292C2—12082no—
293C2—12081no—
294C2—12081no—
295C2C2×#1801273611yescharacteristic
296C2#2375302412yes—
subgroupG/H
centerC22C22×D604
commutator, cosocleC2×C4×C151C24
FrattiniC2×C4C23×D151
Fitting#405×C151C2
socleC22×C151C22×D4
hypercenter#405D151
hypocenterC151#3154
LCSG ▷ C2×C4×C151 ▷ C2×C151 ▷ C151
UCSC1 ◁ C22 ◁ #117 ◁ #405

Complements

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

NH ≅ G/Ntype
1. C2×#18012772C2semidirect
2. C2×#18012767C2semidirect
3. C2×#18012761C2semidirect
4. C22×#14558993C2semidirect
5. #23752788C2semidirect
6. #23752781C2semidirect
7. #23752606C2semidirect
8. #23752601C2semidirect
9. #23752596C2semidirect
10. #23752585C2semidirect
11. #405×C151C2semidirect
19. C2×Dic604C22semidirect
20. C2×Dic604C22semidirect
25. C2×#14558993C22semidirect
26. C2×#14558993C22semidirect
27. C2×#14558993C22semidirect
29. C2×D1208C22semidirect
30. #18012739C22semidirect
33. #18012727C22semidirect
41. #97×C151C22semidirect
42. C4×C8×C151C22semidirect
80. M16×C151D4semidirect
81. C2×C8×C151D4semidirect
148. C151#3154semidirect
160. #405D151semidirect
190. #97C2×D151semidirect
191. C4×C8C2×D151semidirect
226. M16D604semidirect
227. C2×C8D604semidirect

Maximal subgroups

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

subgroupindex
C2×#180127722
C2×#180127672
C2×#180127612
C22×#145589932
#237527882
#237527812
#237526062
#237526012
#237525962
#237525852
#405×C1512
#3154151