Finite Group Databasebeta

← #34079052

Subgroups — #34079052

Order 19328.

462 conjugacy classes of subgroups; only the 127 normal subgroups are shown.

normal subgroups only

This group has 462 conjugacy classes of subgroups — too many to draw. Only its 127 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×#18012714C211yesmaximal, characteristic
2#117×D151C211yesmaximal, characteristic, complemented
3#23752539C212yesmaximal, complemented
4#23752538C212yesmaximal, complemented
5#23752532C212yesmaximal, complemented
6#23752527C212yesmaximal, complemented
7#23752252C211yesmaximal, characteristic, complemented
8#23752218C211yesmaximal, characteristic, complemented
9#23752216C211yesmaximal, characteristic, complemented
10#23752175C211yesmaximal, characteristic, complemented
11#428×C151C211yesmaximal, characteristic, complemented
12C22×D604—21no—
13C22×D604C2211yescharacteristic
14C22×C4×D151C2211yescharacteristic
15C2×#14558988C2211yescharacteristic
16#18012714—21no—
17#18012714—21no—
18#18012714C2212yes—
19#18012714C2212yes—
20#18012698C2211yescharacteristic
21#18012697C2211yescharacteristic, complemented
22#18012697C2211yescharacteristic, complemented
23#18012696—21no—
24#18012695—21no—
25C4⋊C4×D151C2211yescharacteristic, complemented
26C4⋊C4×D151C2211yescharacteristic, complemented
27C2×(C2×D151)⋊C4—21no—
28C22⋊C4×D151—21no—
29C42×D151—21no—
30#18012672C2212yescomplemented
31#18012670C2212yescomplemented
32#18012661C2212yescomplemented
33#18012661C2212yescomplemented
34#18012659C2212yescomplemented
35#18012659C2212yescomplemented
36(C2×D151)⋊C8C2212yescomplemented
37(C2×D151)⋊C8C2212yescomplemented
38C2×M16×C151C2211yescharacteristic
39#117×C151C2211yescharacteristic
40C2×C4⋊C4×C151C2211yescharacteristic
41#107×C151C2212yescomplemented
42#106×C151C2212yescomplemented
43C23×D151—21no—
44C23×D151D411yescharacteristic
45C2×D604—22no—
46C2×D604—22no—
47C2×D604—21no—
48C2×D604—22no—
49C2×D604—22no—
50C2×D604—44no—
51C2×D604C2312yes—
52C22×Dic151D411yescharacteristic
53C2×C4×D151—21no—
54C2×C4×D151—21no—
55C2×C4×D151—22no—
56C2×C4×D151—22no—
57C2×C4×D151D411yescharacteristic
58C2×C4×D151D411yescharacteristic
59C2×C4×D151C2311yescharacteristic
60C2×C4×D151C2311yescharacteristic
61#14558988—22no—
62C2×C151⋊C8C2312yes—
63C4⋊Dic151C2311yescharacteristic
64C4⋊Dic151C2311yescharacteristic
65Dic151⋊C4—21no—
66Dic151⋊C4—21no—
67C22⋊Dic151—21no—
68(C2×D151)⋊C4—21no—
69(C2×D151)⋊C4—21no—
70(C2×D151)⋊C4—22no—
71(C2×D151)⋊C4—22no—
72C4×Dic151—21no—
73C4×Dic151—21no—
74C4×Dic151—21no—
75C22×C4×C151—21no—
76C22×C4×C151C2311yescharacteristic
77M16×C151—22no—
78C2×C8×C151C2312yes—
79C4⋊C4×C151—21no—
80C4⋊C4×C151C2312yes—
81C4⋊C4×C151C2311yescharacteristic
82C4⋊C4×C151C2311yescharacteristic
83C22⋊C4×C151—21no—
84C42×C151—21no—
85C22×D151—22no—
86C22×D151—22no—
87C22×D151—22no—
88C22×D151—41no—
89C22×D151—42no—
90C22×D151—42no—
91C22×D151—42no—
92C22×D151C2×D411yescharacteristic
93C22×D151C2×D411yescharacteristic
94D604—22no—
95D604—22no—
96D604—44no—
97D604—44no—
98D604—42no—
99C2×Dic151—22no—
100C2×Dic151—21no—
101C2×Dic151—21no—
102C2×Dic151C2×D411yescharacteristic
103C2×Dic151C2×D411yescharacteristic
104C4×D151—22no—
105C4×D151—22no—
106C4×D151—21no—
107C4×D151—21no—
108C4×D151—21no—
109C4×D151—21no—
110C4×D151—42no—
111C4×D151—42no—
112C151⋊C8—22no—
113C23×C151C2×D411yescharacteristic
114C2×C4×C151—21no—
115C2×C4×C151—21no—
116C2×C4×C151—22no—
117C2×C4×C151—42no—
118C2×C4×C151C2×D411yescharacteristic
119C2×C4×C151#4112yes—
120C2×C4×C151#4112yes—
121C2×C4×C151C2411yescharacteristic
122C8×C151—22no—
123C22×C151—21no—
124C22×C151—21no—
125C22×C151#12312yes—
126C22×C151C22×D411yescharacteristic
127C2×D151—21no—
128C2×D151—21no—
129C2×D151—21no—
130C2×D151—21no—
131C2×D151—21no—
132C2×D151—44no—
133C2×D151—42no—
134C2×D151—42no—
135C2×D151—42no—
136C2×D151—84no—
137C2×D151AGL(1,ℤ/8)12yes—
138C4×C151—42no—
139C4×C151—41no—
140C4×C151—41no—
141C4×C151#12312yes—
142C4×C151C2×#4111yescharacteristic
143C4×C151C2×#4111yescharacteristic
144Dic151—21no—
145Dic151—21no—
146Dic151—41no—
147Dic151—41no—
148C2×C151—22no—
149C2×C151C2×#12311yescharacteristic
150C2×C151C2×AGL(1,ℤ/8)11yescharacteristic
151C2×C151#57511yescharacteristic
152D151—22no—
153D151—41no—
154D151—82no—
155C151#309411yescharacteristic, complemented, Sylow
156#3094—1511nomaximal, Sylow
157C2×#121—1511no—
158C2×#117—1511no—
159#482—1512no—
160#482—1512no—
161#481—1512no—
162#480—1512no—
163#428—1511no—
164#428D15111yescharacteristic, complemented
165#418—1511no—
166#418—1511no—
167#407—1511no—
168C22×D4—3021no—
169C22×D4—1511no—
170C23×C4—1511no—
171C2×M16—1511no—
172C2×M16C2×D15111yescharacteristic
173#121—3021no—
174#121—3021no—
175#121—1512no—
176#121—1512no—
177#117—3021no—
178#117—3021no—
179#117—1511no—
180#117—1511no—
181#117—1511no—
182#117C2×D15111yescharacteristic
183C2×C4⋊C4—1511no—
184C2×C4⋊C4—1511no—
185C2×C4⋊C4C2×D15111yescharacteristic
186C2×C22⋊C4—3021no—
187C2×C22⋊C4—3021no—
188C2×C42—3021no—
189#107—1512no—
190#107C2×D15112yescomplemented
191#106—1512no—
192#106C2×D15112yescomplemented
193#102—1512no—
194#102—1512no—
195#102—1512no—
196#102—1512no—
197C22⋊C8—1512no—
198C22⋊C8—1512no—
199C24—3021no—
200C24—1511no—
201C2×D4—3022no—
202C2×D4—3022no—
203C2×D4—3021no—
204C2×D4—3022no—
205C2×D4—3022no—
206C2×D4—6044no—
207C2×D4—1512no—
208C22×C4—21no—
209C22×C4—3021no—
210C22×C4—3021no—
211C22×C4—3022no—
212C22×C4—3022no—
213C22×C4—1511no—
214C22×C4—1511no—
215C22×C4—1511no—
216C22×C4—1511no—
217C22×C4—1511no—
218C22×C4C22×D15111yescharacteristic
219M16—22no—
220M16—3022no—
221C2×C8—1512no—
222C2×C8C22×D15112yes—
223C4⋊C4—21no—
224C4⋊C4—3021no—
225C4⋊C4—3021no—
226C4⋊C4—1511no—
227C4⋊C4—1511no—
228C4⋊C4C22×D15111yescharacteristic
229C4⋊C4C22×D15111yescharacteristic
230C4⋊C4C22×D15112yes—
231C22⋊C4—21no—
232C22⋊C4—3021no—
233C22⋊C4—3021no—
234C22⋊C4—3022no—
235C22⋊C4—3022no—
236C22⋊C4—3021no—
237C42—21no—
238C42—3021no—
239C42—3021no—
240C42—3021no—
241C23—3022no—
242C23—3022no—
243C23—3022no—
244C23—6041no—
245C23—6042no—
246C23—6042no—
247C23—6042no—
248C23—1511no—
249C23—1511no—
250C23D4×D15111yescharacteristic
251D4—3022no—
252D4—3022no—
253D4—6044no—
254D4—6044no—
255D4—6042no—
256C2×C4—21no—
257C2×C4—21no—
258C2×C4—22no—
259C2×C4—42no—
260C2×C4—3022no—
261C2×C4—3022no—
262C2×C4—3022no—
263C2×C4—3021no—
264C2×C4—3021no—
265C2×C4—3021no—
266C2×C4—3021no—
267C2×C4—3021no—
268C2×C4—3021no—
269C2×C4—6042no—
270C2×C4—6042no—
271C2×C4—1511no—
272C2×C4—1511no—
273C2×C4D4×D15111yescharacteristic
274C2×C4#1455900412yes—
275C2×C4#1455900512yes—
276C2×C4C23×D15111yescharacteristic
277C8—22no—
278C8—3022no—
279C22—21no—
280C22—21no—
281C22—3021no—
282C22—3021no—
283C22—3021no—
284C22—3021no—
285C22—3021no—
286C22—6044no—
287C22—6042no—
288C22—6042no—
289C22—6042no—
290C22—1512no—
291C22—12084no—
292C22#1801272412yes—
293C22C2×D4×D15111yescharacteristic
294C4—42no—
295C4—41no—
296C4—41no—
297C4—3021no—
298C4—3021no—
299C4—6041no—
300C4—6041no—
301C4#1801272412yes—
302C4C2×#1455900411yescharacteristic
303C4C2×#1455900511yescharacteristic
304C2—22no—
305C2—3022no—
306C2—6041no—
307C2—12082no—
308C2C2×#1801272411yescharacteristic
309C2AGL(1,ℤ/8)×D15111yescharacteristic
310C2#2375301111yescharacteristic
subgroupG/H
centerC22C2×D4×D151
commutator, cosocleC2×C4×C151C24
FrattiniC2×C4C23×D151
Fitting#428×C151C2
socleC22×C151C22×D4
prime radicalC2×#18012714C2
hypercenter#428D151
hypocenterC151#3094
LCSG ▷ C2×C4×C151 ▷ C2×C151 ▷ C151
UCSC1 ◁ C22 ◁ C22×C4 ◁ #428

Complements

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

NH ≅ G/Ntype
2. #117×D151C2semidirect
3. #23752539C2semidirect
4. #23752538C2semidirect
5. #23752532C2semidirect
6. #23752527C2semidirect
7. #23752252C2semidirect
8. #23752218C2semidirect
9. #23752216C2semidirect
10. #23752175C2semidirect
11. #428×C151C2semidirect
21. #18012697C22semidirect
22. #18012697C22semidirect
25. C4⋊C4×D151C22semidirect
26. C4⋊C4×D151C22semidirect
30. #18012672C22semidirect
31. #18012670C22semidirect
32. #18012661C22semidirect
33. #18012661C22semidirect
34. #18012659C22semidirect
35. #18012659C22semidirect
36. (C2×D151)⋊C8C22semidirect
37. (C2×D151)⋊C8C22semidirect
41. #107×C151C22semidirect
42. #106×C151C22semidirect
155. C151#3094semidirect
164. #428D151semidirect
190. #107C2×D151semidirect
192. #106C2×D151semidirect

Maximal subgroups

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

subgroupindex
C2×#180127142
#117×D1512
#237525392
#237525382
#237525322
#237525272
#237522522
#237522182
#237522162
#237521752
#428×C1512
#3094151