Finite Group Databasebeta

← #34079587

Subgroups — #34079587

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×#18012764C211yesmaximal, characteristic, complemented
3C22×#14558993C211yesmaximal, characteristic, complemented
4#23752783C211yesmaximal, characteristic, complemented
5#23752776C211yesmaximal, characteristic, complemented
6#23752605C212yesmaximal, complemented
7#23752600C212yesmaximal, complemented
8#23752593C212yesmaximal, complemented
9#23752583C212yesmaximal, complemented
10#23752167C211yesmaximal, characteristic, complemented
11C2×#135×C151C211yesmaximal, characteristic, complemented
12C22×Dic302C2211yescharacteristic
13C22×D604C2211yescharacteristic
14#18012769—24no—
15#18012764—24no—
16C2×#14558994C2212yescomplemented
17C2×#14558993—24no—
18C2×#14558993C2212yes—
19C2×#14558993C2212yes—
20C2×#14558992C2212yescomplemented
21C2×#14558991C2212yes—
22C2×#14558989C2212yes—
23C2×#14558988C2211yescharacteristic
24#18012737C2212yescomplemented
25#18012735C2212yes—
26#18012728C2212yes—
27#18012726C2212yescomplemented
28#18012720—22no—
29#18012718—22no—
30#18012713—22no—
31#18012707—22no—
32#18012698C2211yescharacteristic
33#18012649C2212yescomplemented
34C8×Dic151C2212yescomplemented
35C2×#41×C151C2211yescharacteristic
36C2×#41×C151C2211yescharacteristic
37#135×C151—24no—
38C2×Q16×C151C2211yescharacteristic, complemented
39C2×SD16×C151C2211yescharacteristic, complemented
40C2×SD16×C151C2211yescharacteristic, complemented
41C2×D8×C151C2211yescharacteristic, complemented
42C22×C8×C151C2211yescharacteristic
43C23×D151—21no—
44C2×Dic302—21no—
45C2×Dic302—22no—
46C2×Dic302—22no—
47C2×Dic302C2312yes—
48C2×D604—22no—
49C2×D604—22no—
50C2×D604—21no—
51C2×D604C2312yes—
52C2×C22⋊D151—24no—
53C22×Dic151—21no—
54#14558994—24no—
55#14558993—24no—
56#14558993—24no—
57#14558992—24no—
58#14558991—24no—
59#14558989—24no—
60#14558988D414yescomplemented
61C2×C151⋊C8C2312yes—
62C4⋊Dic151D412yes—
63Dic151⋊C4—24no—
64C22⋊Dic151—24no—
65C22⋊Dic151D412yes—
66(C2×D151)⋊C4—24no—
67C4×Dic151C2312yes—
68#41×C151—22no—
69#41×C151—22no—
70#41×C151—22no—
71#41×C151—22no—
72C2×Q8×C151C2311yescharacteristic
73C2×Q8×C151C2311yescharacteristic
74C2×D4×C151—21no—
75C2×D4×C151—21no—
76C2×D4×C151C2311yescharacteristic
77C2×D4×C151C2311yescharacteristic
78C22×C4×C151—21no—
79C22×C4×C151—21no—
80C22×C4×C151C2311yescharacteristic
81Q16×C151—22no—
82SD16×C151—22no—
83SD16×C151—22no—
84D8×C151—22no—
85C2×C8×C151D414yescomplemented
86C2×C8×C151C2311yescharacteristic
87C2×C8×C151C2311yescharacteristic
88C22×D151—22no—
89C22×D151—42no—
90C22×D151—82no—
91Dic302—22no—
92Dic302—22no—
93Dic302—42no—
94D604—22no—
95D604—22no—
96D604—42no—
97C22⋊D151—84no—
98C2×Dic151—22no—
99C2×Dic151—42no—
100C2×Dic151C2×D414yes—
101C151⋊C8C2×D414yes—
102C23×C151—21no—
103C23×C151—21no—
104C23×C151C2×D411yescharacteristic
105Q8×C151—21no—
106Q8×C151—21no—
107Q8×C151—21no—
108Q8×C151—21no—
109D4×C151—21no—
110D4×C151—21no—
111D4×C151—21no—
112D4×C151—21no—
113D4×C151—42no—
114D4×C151—42no—
115C2×C4×C151—21no—
116C2×C4×C151—21no—
117C2×C4×C151—42no—
118C2×C4×C151—42no—
119C2×C4×C151C2×D411yescharacteristic
120C2×C4×C151C2×D412yes—
121C2×C4×C151C2×D412yes—
122C2×C4×C151C2411yescharacteristic
123C8×C151C2×D412yes—
124C8×C151C2×D412yes—
125C22×C151—22no—
126C22×C151—41no—
127C22×C151—41no—
128C22×C151—42no—
129C22×C151—42no—
130C22×C151#12712yes—
131C22×C151C22×D411yescharacteristic
132C2×D151—42no—
133C2×D151—44no—
134C2×D151—84no—
135C4×C151—41no—
136C4×C151—41no—
137C4×C151#12712yes—
138C4×C151C22×D411yescharacteristic
139C4×C151C22×D411yescharacteristic
140Dic151—24no—
141Dic151—42no—
142C2×C151—22no—
143C2×C151—81no—
144C2×C151—81no—
145C2×C151C2×#12711yescharacteristic
146C2×C151#57712yes—
147D151—82no—
148C151#315411yescharacteristic, complemented, Sylow
149#3154—1511nomaximal, Sylow
150C2×#137—1511no—
151C2×AGL(1,ℤ/8)—1511no—
152C2×#135D15111yescharacteristic, complemented
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×#41C2×D15111yescharacteristic
162C2×#41C2×D15111yescharacteristic
163C22×Q8—1511no—
164C22×D4—1511no—
165#137—3024no—
166AGL(1,ℤ/8)—3024no—
167#135—24no—
168C2×Q16—1512no—
169C2×Q16C2×D15111yescharacteristic, complemented
170C2×SD16—3024no—
171C2×SD16—1512no—
172C2×SD16—1512no—
173C2×SD16—1512no—
174C2×SD16—1512no—
175C2×SD16C2×D15111yescharacteristic, complemented
176C2×SD16C2×D15111yescharacteristic, complemented
177C2×D8—1512no—
178C2×D8C2×D15111yescharacteristic, complemented
179C2×M16—1511no—
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#117—1511no—
190#97—1512no—
191C4×C8—1512no—
192C24—3021no—
193#41—22no—
194#41—22no—
195#41—22no—
196#41—22no—
197C2×Q8—3021no—
198C2×Q8—3022no—
199C2×Q8—3022no—
200C2×Q8—1512no—
201C2×Q8C22×D15111yescharacteristic
202C2×Q8C22×D15111yescharacteristic
203C2×D4—21no—
204C2×D4—21no—
205C2×D4—3024no—
206C2×D4—3022no—
207C2×D4—3021no—
208C2×D4—3022no—
209C2×D4—1512no—
210C2×D4C22×D15111yescharacteristic
211C2×D4C22×D15111yescharacteristic
212C22×C4—21no—
213C22×C4—21no—
214C22×C4—3021no—
215C22×C4C22×D15111yescharacteristic
216Q16—22no—
217Q16—3024no—
218SD16—22no—
219SD16—22no—
220SD16—3024no—
221SD16—3024no—
222SD16—3024no—
223SD16—3024no—
224D8—22no—
225D8—3024no—
226M16—1514no—
227C2×C8—1512no—
228C2×C8C22⋊D15114yescomplemented
229C2×C8C22×D15111yescharacteristic
230C2×C8C22×D15111yescharacteristic
231C4⋊C4—3024no—
232C4⋊C4—1512no—
233C22⋊C4—3024no—
234C22⋊C4—3024no—
235C22⋊C4—1512no—
236C42—1512no—
237C23—21no—
238C23—21no—
239C23—3022no—
240C23—6042no—
241C23—12082no—
242C23D4×D15111yescharacteristic
243Q8—21no—
244Q8—21no—
245Q8—21no—
246Q8—21no—
247Q8—3022no—
248Q8—3022no—
249Q8—6042no—
250D4—21no—
251D4—21no—
252D4—21no—
253D4—21no—
254D4—42no—
255D4—42no—
256D4—3022no—
257D4—3022no—
258D4—6042no—
259D4—12084no—
260C2×C4—21no—
261C2×C4—21no—
262C2×C4—42no—
263C2×C4—42no—
264C2×C4—3022no—
265C2×C4—6042no—
266C2×C4—1514no—
267C2×C4D4×D15111yescharacteristic
268C2×C4D4×D15112yes—
269C2×C4C2×C22⋊D15112yes—
270C2×C4C23×D15111yescharacteristic
271C8—1514no—
272C8C2×C22⋊D15112yes—
273C8C2×C22⋊D15112yes—
274C22—22no—
275C22—41no—
276C22—41no—
277C22—42no—
278C22—42no—
279C22—6042no—
280C22—6044no—
281C22—12084no—
282C22#1801273512yes—
283C22C2×D4×D15111yescharacteristic
284C4—41no—
285C4—41no—
286C4—3024no—
287C4—6042no—
288C4#1801273512yes—
289C4C2×D4×D15111yescharacteristic
290C4C22×C22⋊D15111yescharacteristic
291C2—22no—
292C2—81no—
293C2—81no—
294C2—12082no—
295C2C2×#1801273511yescharacteristic
296C2#2375301912yes—
subgroupG/H
centerC22C2×D4×D151
commutator, cosocleC2×C4×C151C24
FrattiniC2×C4C23×D151
FittingC2×#135×C151C2
socleC22×C151C22×D4
hypercenterC2×#135D151
hypocenterC151#3154
LCSG ▷ C2×C4×C151 ▷ C2×C151 ▷ C151
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#135

Complements

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

NH ≅ G/Ntype
1. C2×#18012769C2semidirect
2. C2×#18012764C2semidirect
3. C22×#14558993C2semidirect
4. #23752783C2semidirect
5. #23752776C2semidirect
6. #23752605C2semidirect
7. #23752600C2semidirect
8. #23752593C2semidirect
9. #23752583C2semidirect
10. #23752167C2semidirect
11. C2×#135×C151C2semidirect
16. C2×#14558994C22semidirect
20. C2×#14558992C22semidirect
24. #18012737C22semidirect
27. #18012726C22semidirect
33. #18012649C22semidirect
34. C8×Dic151C22semidirect
38. C2×Q16×C151C22semidirect
39. C2×SD16×C151C22semidirect
40. C2×SD16×C151C22semidirect
41. C2×D8×C151C22semidirect
60. #14558988D4semidirect
85. C2×C8×C151D4semidirect
148. C151#3154semidirect
152. C2×#135D151semidirect
169. C2×Q16C2×D151semidirect
175. C2×SD16C2×D151semidirect
176. C2×SD16C2×D151semidirect
178. C2×D8C2×D151semidirect
228. C2×C8C22⋊D151semidirect

Maximal subgroups

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

subgroupindex
C2×#180127692
C2×#180127642
C22×#145589932
#237527832
#237527762
#237526052
#237526002
#237525932
#237525832
#237521672
C2×#135×C1512
#3154151