Finite Group Databasebeta

← #34079589

Subgroups — #34079589

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×#18012767C211yesmaximal, characteristic, complemented
2C2×#18012759C211yesmaximal, characteristic, complemented
3C22×#14558991C211yesmaximal, characteristic, complemented
4#23752786C211yesmaximal, characteristic, complemented
5#23752776C211yesmaximal, characteristic, complemented
6#23752605C212yesmaximal, complemented
7#23752598C212yesmaximal, complemented
8#23752597C212yesmaximal, complemented
9#23752583C212yesmaximal, complemented
10#23752170C211yesmaximal, characteristic, complemented
11C2×#137×C151C211yesmaximal, characteristic, complemented
12C2×#14559004C2211yescharacteristic
13C22×D604C2211yescharacteristic
14#18012767—24no—
15#18012759—24no—
16C2×#14558994C2211yescharacteristic, complemented
17C2×#14558993C2212yes—
18C2×#14558992C2211yescharacteristic, complemented
19C2×#14558991—24no—
20C2×#14558991C2212yes—
21C2×#14558991C2212yes—
22C2×#14558991C2211yescharacteristic, complemented
23C2×D1208C2212yes—
24C2×#14558989C2211yescharacteristic, complemented
25C22×C151⋊C8C2211yescharacteristic
26#18012737C2212yescomplemented
27#18012735C2212yes—
28#18012728C2212yes—
29#18012728C2212yescomplemented
30#18012722—22no—
31#18012715—22no—
32#18012713—22no—
33#18012707—22no—
34#18012698C2211yescharacteristic
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—24no—
53C2×C22⋊D151—21no—
54C2×C4×D151—21no—
55#14558994—22no—
56#14558993—24no—
57#14558992—22no—
58#14558991—24no—
59#14558991—24no—
60#14558991—22no—
61D1208—24no—
62#14558989—22no—
63C2×C151⋊C8D414yescomplemented
64C2×C151⋊C8C2311yescharacteristic
65C2×C151⋊C8C2311yescharacteristic
66C4⋊Dic151D412yes—
67Dic151⋊C4—24no—
68C22⋊Dic151D412yes—
69(C2×D151)⋊C4—24no—
70(C2×D151)⋊C4—24no—
71C4×Dic151C2312yes—
72#41×C151—22no—
73#41×C151—22no—
74C2×Q8×C151—21no—
75C2×Q8×C151—22no—
76C2×Q8×C151—22no—
77C2×Q8×C151C2311yescharacteristic
78C2×Q8×C151C2312yes—
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—21no—
89C22×D151—22no—
90C22×D151—42no—
91C22×D151—82no—
92Dic302—21no—
93Dic302—21no—
94D604—21no—
95D604—21no—
96D604—22no—
97D604—22no—
98D604—42no—
99C22⋊D151—42no—
100C22⋊D151—84no—
101C2×Dic151—21no—
102C2×Dic151C2×D414yes—
103C4×D151—42no—
104C151⋊C8C2×D412yes—
105C151⋊C8C2×D412yes—
106C23×C151—21no—
107C23×C151C2×D411yescharacteristic
108Q8×C151—22no—
109Q8×C151—22no—
110Q8×C151—21no—
111Q8×C151—21no—
112Q8×C151—42no—
113D4×C151—21no—
114D4×C151—21no—
115D4×C151—42no—
116C2×C4×C151—22no—
117C2×C4×C151—21no—
118C2×C4×C151—42no—
119C2×C4×C151—42no—
120C2×C4×C151C2×D411yescharacteristic
121C2×C4×C151C2×D412yes—
122C2×C4×C151C2×D412yes—
123C2×C4×C151C2411yescharacteristic
124C8×C151C2×D414yes—
125C22×C151—22no—
126C22×C151—41no—
127C22×C151—42no—
128C22×C151#12712yes—
129C22×C151C22×D411yescharacteristic
130C2×D151—41no—
131C2×D151—42no—
132C2×D151—44no—
133C2×D151—42no—
134C2×D151—84no—
135C4×C151—41no—
136C4×C151—42no—
137C4×C151#12712yes—
138C4×C151C22×D411yescharacteristic
139C4×C151C22×D411yescharacteristic
140Dic151—24no—
141Dic151—41no—
142C2×C151—22no—
143C2×C151—81no—
144C2×C151C2×#12711yescharacteristic
145C2×C151#57712yes—
146D151—81no—
147D151—82no—
148C151#315411yescharacteristic, complemented, Sylow
149#3154—1511nomaximal, Sylow
150C2×#137D15111yescharacteristic, complemented
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#405—1511no—
161C2×#41—1511no—
162C2×#41C2×D15111yescharacteristic
163C22×Q8C2×D15111yescharacteristic
164C22×D4—1511no—
165#137—24no—
166AGL(1,ℤ/8)—3024no—
167#135—3024no—
168C2×Q16—1511no—
169C2×Q16C2×D15112yescomplemented
170C2×SD16—3024no—
171C2×SD16—1512no—
172C2×SD16—1512no—
173C2×SD16—1511no—
174C2×SD16—1511no—
175C2×SD16—1512no—
176C2×SD16C2×D15112yescomplemented
177C2×D8—1511no—
178C2×D8—1512no—
179C2×M16C2×D15111yescharacteristic
180C22×C8—1511no—
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#117—1511no—
190#97—1512no—
191C4×C8—1512no—
192C24—3021no—
193#41—22no—
194#41—22no—
195#41—3022no—
196#41—3022no—
197C2×Q8—21no—
198C2×Q8—22no—
199C2×Q8—22no—
200C2×Q8—1511no—
201C2×Q8C22×D15111yescharacteristic
202C2×Q8C22×D15112yes—
203C2×D4—21no—
204C2×D4—3021no—
205C2×D4—3024no—
206C2×D4—3022no—
207C2×D4—3021no—
208C2×D4—3022no—
209C2×D4—1511no—
210C2×D4—1512no—
211C2×D4C22×D15111yescharacteristic
212C22×C4—21no—
213C22×C4—21no—
214C22×C4—3021no—
215C22×C4C22×D15111yescharacteristic
216Q16—24no—
217Q16—3022no—
218SD16—24no—
219SD16—3022no—
220SD16—3024no—
221SD16—3024no—
222SD16—3022no—
223SD16—3024no—
224D8—3022no—
225D8—3024no—
226M16C22⋊D15114yescomplemented
227C2×C8—1514no—
228C2×C8—1511no—
229C2×C8—1511no—
230C2×C8C22×D15112yes—
231C4⋊C4—3024no—
232C4⋊C4—1512no—
233C22⋊C4—3024no—
234C22⋊C4—3024no—
235C22⋊C4—1512no—
236C42—1512no—
237C23—21no—
238C23—3021no—
239C23—3022no—
240C23—6042no—
241C23—12082no—
242C23D4×D15111yescharacteristic
243Q8—22no—
244Q8—21no—
245Q8—22no—
246Q8—21no—
247Q8—42no—
248Q8—3021no—
249Q8—3021no—
250D4—21no—
251D4—21no—
252D4—42no—
253D4—3021no—
254D4—3022no—
255D4—3021no—
256D4—3022no—
257D4—6042no—
258D4—6042no—
259D4—12084no—
260C2×C4—21no—
261C2×C4—22no—
262C2×C4—42no—
263C2×C4—42no—
264C2×C4—3021no—
265C2×C4—6042no—
266C2×C4—1514no—
267C2×C4D4×D15111yescharacteristic
268C2×C4D4×D15112yes—
269C2×C4C2×C22⋊D15112yes—
270C2×C4C23×D15111yescharacteristic
271C8—1512no—
272C8—1512no—
273C8C2×C22⋊D15114yes—
274C22—22no—
275C22—41no—
276C22—42no—
277C22—6041no—
278C22—6042no—
279C22—6044no—
280C22—6042no—
281C22—12084no—
282C22#1801273512yes—
283C22C2×D4×D15111yescharacteristic
284C4—41no—
285C4—42no—
286C4—3024no—
287C4—6041no—
288C4#1801273512yes—
289C4C2×D4×D15111yescharacteristic
290C4C22×C22⋊D15111yescharacteristic
291C2—22no—
292C2—81no—
293C2—12082no—
294C2—12081no—
295C2C2×#1801273511yescharacteristic
296C2#2375302112yes—
subgroupG/H
centerC22C2×D4×D151
commutator, cosocleC2×C4×C151C24
FrattiniC2×C4C23×D151
FittingC2×#137×C151C2
socleC22×C151C22×D4
hypercenterC2×#137D151
hypocenterC151#3154
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×#18012767C2semidirect
2. C2×#18012759C2semidirect
3. C22×#14558991C2semidirect
4. #23752786C2semidirect
5. #23752776C2semidirect
6. #23752605C2semidirect
7. #23752598C2semidirect
8. #23752597C2semidirect
9. #23752583C2semidirect
10. #23752170C2semidirect
11. C2×#137×C151C2semidirect
16. C2×#14558994C22semidirect
18. C2×#14558992C22semidirect
22. C2×#14558991C22semidirect
24. C2×#14558989C22semidirect
26. #18012737C22semidirect
29. #18012728C22semidirect
35. #18012649C22semidirect
36. C8×Dic151C22semidirect
40. C2×Q16×C151C22semidirect
41. C2×SD16×C151C22semidirect
63. C2×C151⋊C8D4semidirect
86. M16×C151D4semidirect
148. C151#3154semidirect
150. C2×#137D151semidirect
169. C2×Q16C2×D151semidirect
176. C2×SD16C2×D151semidirect
226. M16C22⋊D151semidirect

Maximal subgroups

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

subgroupindex
C2×#180127672
C2×#180127592
C22×#145589912
#237527862
#237527762
#237526052
#237525982
#237525972
#237525832
#237521702
C2×#137×C1512
#3154151