Finite Group Databasebeta

← #34079577

Subgroups — #34079577

Order 19328.

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

normal subgroups only

This group has 572 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×#18012770C211yesmaximal, characteristic, complemented
2C2×#18012767C211yesmaximal, characteristic, complemented
3C2×#18012764C211yesmaximal, characteristic, complemented
4#23752758C211yesmaximal, characteristic, complemented
5C2×#18012728C211yesmaximal, characteristic, complemented
6#23752605C212yesmaximal, complemented
7#23752598C212yesmaximal, complemented
8#23752597C212yesmaximal, complemented
9#23752593C212yesmaximal, complemented
10M16×Dic151C211yesmaximal, characteristic, complemented
11C2×#137×C151C211yesmaximal, characteristic, complemented
12C2×#14559004C2211yescharacteristic
13C22×D604C2211yescharacteristic
14#18012770—24no—
15#18012767—24no—
16#18012764—24no—
17C2×#14558994C2212yescomplemented
18C2×#14558993C2212yes—
19C2×#14558991C2212yes—
20C2×#14558991C2212yescomplemented
21C2×D1208C2212yes—
22C2×#14558989C2212yes—
23C2×#14558988C2211yescharacteristic
24#18012737C2211yescharacteristic, complemented
25#18012735C2211yescharacteristic, complemented
26#18012728—22no—
27#18012728C2212yes—
28#18012728C2212yes—
29#18012728C2211yescharacteristic, complemented
30#18012726C2211yescharacteristic, complemented
31#18012711—22no—
32C4×C22⋊D151—22no—
33C2×(C2×D151)⋊C4—22no—
34C2×C4×Dic151C2211yescharacteristic
35#18012649C2212yescomplemented
36C8×Dic151C2212yescomplemented
37C2×#41×C151C2211yescharacteristic
38C22×Q8×C151C2211yescharacteristic
39#137×C151—24no—
40C2×Q16×C151C2212yescomplemented
41C2×SD16×C151C2212yescomplemented
42C2×M16×C151C2211yescharacteristic
43C23×D151—21no—
44#14559004—22no—
45#14559004—22no—
46C2×Dic302C2311yescharacteristic
47C2×D604—22no—
48C2×D604—22no—
49C2×D604—21no—
50C2×D604C2312yes—
51C2×D604C2311yescharacteristic
52C2×C22⋊D151—22no—
53C2×C22⋊D151—21no—
54C22×Dic151D412yes—
55C2×C4×D151—21no—
56#14558994—24no—
57#14558993—24no—
58#14558991—24no—
59#14558991—24no—
60D1208—24no—
61#14558989—24no—
62#14558988D414yescomplemented
63C2×C151⋊C8C2312yes—
64Dic151⋊C4—22no—
65C22⋊Dic151—22no—
66(C2×D151)⋊C4—24no—
67(C2×D151)⋊C4—24no—
68(C2×D151)⋊C4—22no—
69C4×Dic151D412yes—
70C4×Dic151C2311yescharacteristic
71C4×Dic151C2311yescharacteristic
72#41×C151—22no—
73#41×C151—22no—
74C2×Q8×C151—21no—
75C2×Q8×C151—22no—
76C2×Q8×C151—22no—
77C2×Q8×C151C2312yes—
78C2×Q8×C151C2311yescharacteristic
79C2×D4×C151—21no—
80C2×D4×C151C2311yescharacteristic
81C22×C4×C151—21no—
82C22×C4×C151—21no—
83C22×C4×C151C2311yescharacteristic
84Q16×C151—24no—
85SD16×C151—24no—
86M16×C151D414yescomplemented
87C2×C8×C151C2312yes—
88C22×D151—22no—
89C22×D151—21no—
90C22×D151—44no—
91C22×D151—42no—
92Dic302—21no—
93Dic302—21no—
94D604—22no—
95D604—21no—
96D604—22no—
97D604—21no—
98D604—42no—
99C22⋊D151—44no—
100C22⋊D151—42no—
101C2×Dic151—21no—
102C2×Dic151—42no—
103C2×Dic151C2×D412yes—
104C2×Dic151C2×D412yes—
105C4×D151—42no—
106C151⋊C8C2×D414yes—
107C23×C151—21no—
108C23×C151C2×D411yescharacteristic
109Q8×C151—22no—
110Q8×C151—22no—
111Q8×C151—21no—
112Q8×C151—21no—
113Q8×C151—42no—
114D4×C151—21no—
115D4×C151—21no—
116D4×C151—42no—
117C2×C4×C151—22no—
118C2×C4×C151—21no—
119C2×C4×C151—42no—
120C2×C4×C151—42no—
121C2×C4×C151C2×D411yescharacteristic
122C2×C4×C151C2×D412yes—
123C2×C4×C151C2×D412yes—
124C2×C4×C151C2411yescharacteristic
125C8×C151C2×D414yes—
126C22×C151—22no—
127C22×C151—41no—
128C22×C151—42no—
129C22×C151#12712yes—
130C22×C151C22×D411yescharacteristic
131C2×D151—41no—
132C2×D151—42no—
133C2×D151—42no—
134C2×D151—44no—
135C2×D151—84no—
136C4×C151—41no—
137C4×C151—42no—
138C4×C151#12712yes—
139C4×C151C22×D411yescharacteristic
140C4×C151C22×D411yescharacteristic
141Dic151—22no—
142Dic151—22no—
143Dic151—41no—
144C2×C151—22no—
145C2×C151—81no—
146C2×C151C2×#12711yescharacteristic
147C2×C151#57512yes—
148D151—81no—
149D151—82no—
150C151#315311yescharacteristic, complemented, Sylow
151#3153—1511nomaximal, Sylow
152C2×#137—1511no—
153C2×#137D15111yescharacteristic, complemented
154C2×AGL(1,ℤ/8)—1511no—
155C2×AGL(1,ℤ/8)—1511no—
156#532—1511no—
157C2×#124—1511no—
158#497—1512no—
159#496—1512no—
160#495—1512no—
161#495—1512no—
162C4×M16—1511no—
163C2×#41—1511no—
164C2×#41C2×D15111yescharacteristic
165C22×Q8C2×D15111yescharacteristic
166C22×D4—1511no—
167#137—24no—
168#137—3024no—
169AGL(1,ℤ/8)—3024no—
170AGL(1,ℤ/8)—3024no—
171C2×Q16—1512no—
172C2×Q16C2×D15112yescomplemented
173C2×SD16—1512no—
174C2×SD16—1512no—
175C2×SD16—1512no—
176C2×SD16C2×D15112yescomplemented
177C2×D8—1512no—
178C2×D8—1512no—
179C2×M16—1511no—
180C2×M16C2×D15111yescharacteristic
181C4⋊Q8—1511no—
182#127—1511no—
183#124—3022no—
184#124—1512no—
185#124—1512no—
186#124—1511no—
187#124—1511no—
188#121—3022no—
189C4×D4—3022no—
190C2×C22⋊C4—3022no—
191C2×C42—1511no—
192#97—1512no—
193C4×C8—1512no—
194C24—3021no—
195#41—22no—
196#41—22no—
197#41—3022no—
198#41—3022no—
199C2×Q8—21no—
200C2×Q8—22no—
201C2×Q8—22no—
202C2×Q8—1511no—
203C2×Q8C22×D15112yes—
204C2×Q8C22×D15111yescharacteristic
205C2×D4—21no—
206C2×D4—3021no—
207C2×D4—3022no—
208C2×D4—3022no—
209C2×D4—3021no—
210C2×D4—3022no—
211C2×D4—1512no—
212C2×D4—1511no—
213C2×D4C22×D15111yescharacteristic
214C22×C4—21no—
215C22×C4—21no—
216C22×C4—3021no—
217C22×C4—1512no—
218C22×C4C22×D15111yescharacteristic
219Q16—24no—
220Q16—3024no—
221SD16—24no—
222SD16—3024no—
223SD16—3024no—
224SD16—3024no—
225D8—3024no—
226D8—3024no—
227M16—1514no—
228M16C22⋊D15114yescomplemented
229C2×C8—1512no—
230C2×C8C22×D15112yes—
231C4⋊C4—3022no—
232C22⋊C4—3024no—
233C22⋊C4—3024no—
234C22⋊C4—3022no—
235C22⋊C4—3022no—
236C42—1512no—
237C42—1511no—
238C42—1511no—
239C23—21no—
240C23—3022no—
241C23—3021no—
242C23—6044no—
243C23—6042no—
244C23D4×D15111yescharacteristic
245Q8—21no—
246Q8—22no—
247Q8—22no—
248Q8—21no—
249Q8—42no—
250Q8—3021no—
251Q8—3021no—
252D4—21no—
253D4—21no—
254D4—42no—
255D4—3022no—
256D4—3021no—
257D4—3021no—
258D4—3022no—
259D4—6044no—
260D4—6042no—
261D4—6042no—
262C2×C4—22no—
263C2×C4—21no—
264C2×C4—42no—
265C2×C4—42no—
266C2×C4—3021no—
267C2×C4—6042no—
268C2×C4—6042no—
269C2×C4—1512no—
270C2×C4—1512no—
271C2×C4D4×D15111yescharacteristic
272C2×C4D4×D15112yes—
273C2×C4C2×C22⋊D15112yes—
274C2×C4C23×D15111yescharacteristic
275C8—1514no—
276C8C2×C22⋊D15114yes—
277C22—22no—
278C22—41no—
279C22—42no—
280C22—6041no—
281C22—6042no—
282C22—6042no—
283C22—6044no—
284C22—12084no—
285C22#1801273512yes—
286C22C2×D4×D15111yescharacteristic
287C4—41no—
288C4—42no—
289C4—3022no—
290C4—3022no—
291C4—6041no—
292C4#1801273512yes—
293C4C2×D4×D15111yescharacteristic
294C4C22×C22⋊D15111yescharacteristic
295C2—22no—
296C2—81no—
297C2—12082no—
298C2—12081no—
299C2C2×#1801273511yescharacteristic
300C2#2375301112yes—
subgroupG/H
centerC22C2×D4×D151
commutator, cosocleC2×C4×C151C24
FrattiniC2×C4C23×D151
FittingC2×#137×C151C2
socleC22×C151C22×D4
hypercenterC2×#137D151
hypocenterC151#3153
LCSG ▷ C2×C4×C151 ▷ C2×C151 ▷ C151
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#137

Complements

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

NH ≅ G/Ntype
1. C2×#18012770C2semidirect
2. C2×#18012767C2semidirect
3. C2×#18012764C2semidirect
4. #23752758C2semidirect
5. C2×#18012728C2semidirect
6. #23752605C2semidirect
7. #23752598C2semidirect
8. #23752597C2semidirect
9. #23752593C2semidirect
10. M16×Dic151C2semidirect
11. C2×#137×C151C2semidirect
17. C2×#14558994C22semidirect
20. C2×#14558991C22semidirect
24. #18012737C22semidirect
25. #18012735C22semidirect
29. #18012728C22semidirect
30. #18012726C22semidirect
35. #18012649C22semidirect
36. C8×Dic151C22semidirect
40. C2×Q16×C151C22semidirect
41. C2×SD16×C151C22semidirect
62. #14558988D4semidirect
86. M16×C151D4semidirect
150. C151#3153semidirect
153. C2×#137D151semidirect
172. C2×Q16C2×D151semidirect
176. C2×SD16C2×D151semidirect
228. M16C22⋊D151semidirect

Maximal subgroups

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

subgroupindex
C2×#180127702
C2×#180127672
C2×#180127642
#237527582
C2×#180127282
#237526052
#237525982
#237525972
#237525932
M16×Dic1512
C2×#137×C1512
#3153151