Finite Group Databasebeta

← #440×D151 #34077885

Subgroups — #440×D151 #34077885

Order 19328.

544 conjugacy classes of subgroups.

The subgroup lattice has 376 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×SD16×D151C211yesmaximal, characteristic
2C4×Q8×D151C211yesmaximal, characteristic, complemented
3C4×D4×D151C211yesmaximal, characteristic
4#23752315C211yesmaximal, characteristic, complemented
5#23752314C211yesmaximal, characteristic, complemented
6#23752313C211yesmaximal, characteristic, complemented
7#23752312C211yesmaximal, characteristic, complemented
8#23752311C211yesmaximal, characteristic, complemented
9#23752310C211yesmaximal, characteristic, complemented
10#23752309C211yesmaximal, characteristic, complemented
11#107×D151C211yesmaximal, characteristic, complemented
12#103×D151C211yesmaximal, characteristic, complemented
13#102×D151C211yesmaximal, characteristic
14#97×D151C211yesmaximal, characteristic, complemented
15#440×C151C211yesmaximal, characteristic, complemented
16C2×Q8×D151C2211yescharacteristic
17C2×D4×D151C2211yescharacteristic
18C22×C4×D151—21no—
19C2×#14558993C2211yescharacteristic
20C2×#14558992C2211yescharacteristic
21C2×#14558991C2211yescharacteristic
22SD16×D151C418yescomplemented
23C2×C8×D151C2211yescharacteristic
24C2×C8×D151C2211yescharacteristic
25Q8×Dic151C2211yescharacteristic, complemented
26C4×Dic302—21no—
27C4×Dic302C2211yescharacteristic, complemented
28#18012704—21no—
29#18012704C2211yescharacteristic, complemented
30C4×D604C2211yescharacteristic
31D4×Dic151C2211yescharacteristic
32#18012701C2211yescharacteristic
33C4×C22⋊D151—21no—
34(C22⋊D151)⋊C4—21no—
35C4⋊C4×D151—21no—
36C4⋊C4×D151C2211yescharacteristic
37C4⋊C4×D151C2211yescharacteristic
38C22⋊C4×D151—21no—
39C42×D151—21no—
40C42×D151C2211yescharacteristic
41#18012673C2211yescharacteristic, complemented
42#18012672C2211yescharacteristic, complemented
43#18012672C2211yescharacteristic, complemented
44#18012664C2211yescharacteristic, complemented
45#18012663C2211yescharacteristic, complemented
46#18012662C2211yescharacteristic, complemented
47#18012661C2211yescharacteristic
48#18012660C2211yescharacteristic
49#18012659C2211yescharacteristic
50#18012650C2211yescharacteristic, complemented
51#18012649C2211yescharacteristic, complemented
52#18012649C2211yescharacteristic, complemented
53C2×SD16×C151C2211yescharacteristic
54C4×Q8×C151C2211yescharacteristic, complemented
55C4×D4×C151C2211yescharacteristic
56#107×C151C2211yescharacteristic, complemented
57#103×C151C2211yescharacteristic, complemented
58#102×C151C2211yescharacteristic
59#97×C151C2211yescharacteristic, complemented
60C23×D151—21no—
61C2×Dic302—21no—
62C2×Dic302C2311yescharacteristic
63Q8×D151—22no—
64Q8×D151C2×C414yescomplemented
65C2×D604C2311yescharacteristic
66C2×C22⋊D151—21no—
67D4×D151—22no—
68D4×D151C2×C414yes—
69C22×Dic151—21no—
70C2×C4×D151—21no—
71C2×C4×D151—21no—
72C2×C4×D151—21no—
73C2×C4×D151—21no—
74C2×C4×D151—21no—
75C2×C4×D151—44no—
76C2×C4×D151D411yescharacteristic
77C2×C4×D151D411yescharacteristic
78C2×C4×D151C2311yescharacteristic
79#14558993C2×C414yescomplemented
80#14558992C2×C414yescomplemented
81#14558991C2×C414yescomplemented
82C2×C151⋊C8C2311yescharacteristic
83C2×C151⋊C8C2311yescharacteristic
84C8×D151—22no—
85C8×D151C2×C414yescomplemented
86C4⋊Dic151—21no—
87C4⋊Dic151C2311yescharacteristic
88C4⋊Dic151C2311yescharacteristic
89Dic151⋊C4—21no—
90Dic151⋊C4—21no—
91Dic151⋊C4—21no—
92Dic151⋊C4—21no—
93C22⋊Dic151—21no—
94(C2×D151)⋊C4—21no—
95(C2×D151)⋊C4—21no—
96C4×Dic151—21no—
97C4×Dic151—21no—
98C4×Dic151—21no—
99C4×Dic151D411yescharacteristic
100C4×Dic151D411yescharacteristic
101C4×Dic151C2311yescharacteristic
102C2×Q8×C151C2311yescharacteristic
103C2×D4×C151C2311yescharacteristic
104C22×C4×C151—21no—
105SD16×C151C2×C414yescomplemented
106C2×C8×C151C2311yescharacteristic
107C2×C8×C151C2311yescharacteristic
108C4⋊C4×C151—21no—
109C4⋊C4×C151C2311yescharacteristic
110C4⋊C4×C151C2311yescharacteristic
111C22⋊C4×C151—21no—
112C42×C151—21no—
113C42×C151C2311yescharacteristic
114C22×D151—21no—
115C22×D151—24no—
116C22×D151—42no—
117C22×D151—42no—
118C22×D151C2×D411yescharacteristic
119Dic302—21no—
120Dic302—24no—
121Dic302C22×C412yescomplemented
122D604—21no—
123D604C22×C412yes—
124C22⋊D151—24no—
125C2×Dic151—21no—
126C2×Dic151—21no—
127C2×Dic151—21no—
128C2×Dic151—42no—
129C2×Dic151C2×D411yescharacteristic
130C2×Dic151C2×D411yescharacteristic
131C2×Dic151C2×D411yescharacteristic
132C4×D151—24no—
133C4×D151—22no—
134C4×D151—22no—
135C4×D151—42no—
136C4×D151—42no—
137C4×D151—42no—
138C4×D151—42no—
139C4×D151C22×C412yes—
140C4×D151#4112yes—
141C151⋊C8—21no—
142C151⋊C8C22×C412yescomplemented
143C23×C151—21no—
144Q8×C151—21no—
145Q8×C151C22×C412yescomplemented
146D4×C151—21no—
147D4×C151C22×C412yes—
148C2×C4×C151—21no—
149C2×C4×C151—21no—
150C2×C4×C151—21no—
151C2×C4×C151—42no—
152C2×C4×C151C2×D411yescharacteristic
153C2×C4×C151C2×D411yescharacteristic
154C2×C4×C151C2411yescharacteristic
155C8×C151—21no—
156C8×C151C22×C412yescomplemented
157C22×C151—22no—
158C22×C151—41no—
159C22×C151—41no—
160C22×C151C22×D411yescharacteristic
161C2×D151—22no—
162C2×D151—41no—
163C2×D151—41no—
164C2×D151—48no—
165C2×D151C4×D412yes—
166C2×D151AGL(1,ℤ/8)12yes—
167C2×D151#13712yes—
168C4×C151—22no—
169C4×C151—21no—
170C4×C151—21no—
171C4×C151—41no—
172C4×C151—41no—
173C4×C151C23×C411yescharacteristic
174C4×C151C2×#4111yescharacteristic
175Dic151—22no—
176Dic151—21no—
177Dic151—21no—
178Dic151—41no—
179Dic151—41no—
180Dic151C4×D412yes—
181C2×C151—42no—
182C2×C151C2×C4×D411yescharacteristic
183C2×C151C2×AGL(1,ℤ/8)11yescharacteristic
184C2×C151C2×#13711yescharacteristic
185D151—42no—
186D151#44014yesdirect product factor
187C151C2×#44011yescharacteristic, complemented, Sylow
188C2×#440—1511nomaximal, Sylow
189C22×SD16—1511no—
190C2×C4×Q8—1511no—
191C2×C4×D4—1511no—
192#440—1511no—
193#440—1511no—
194#440—1511no—
195#440—1511no—
196#440—1511no—
197#440—1511no—
198#440—1511no—
199#440D15111yescharacteristic, direct product factor
200C2×#107—1511no—
201C2×#103—1511no—
202C2×#102—1511no—
203C2×#97—1511no—
204C22×Q8—1511no—
205C22×D4—1511no—
206C23×C4—3021no—
207C2×SD16—1511no—
208C2×SD16—1511no—
209C2×SD16—1518no—
210C2×SD16—1511no—
211C2×SD16C2×D15111yescharacteristic
212C22×C8—1511no—
213C22×C8—1511no—
214C4×Q8—3021no—
215C4×Q8—3021no—
216C4×Q8—1511no—
217C4×Q8—1511no—
218C4×Q8—1511no—
219C4×Q8C2×D15111yescharacteristic, complemented
220C4×D4—3021no—
221C4×D4—3021no—
222C4×D4—1511no—
223C4×D4—1511no—
224C4×D4—1511no—
225C4×D4C2×D15111yescharacteristic
226C2×C4⋊C4—3021no—
227C2×C4⋊C4—1511no—
228C2×C4⋊C4—1511no—
229C2×C22⋊C4—3021no—
230C2×C42—3021no—
231C2×C42—1511no—
232#107—1511no—
233#107—1511no—
234#107—1511no—
235#107C2×D15111yescharacteristic, complemented
236#103—1511no—
237#103—1511no—
238#103—1511no—
239#103C2×D15111yescharacteristic, complemented
240#102—1511no—
241#102—1511no—
242#102—1511no—
243#102C2×D15111yescharacteristic
244#97—1511no—
245#97—1511no—
246#97—1511no—
247#97C2×D15111yescharacteristic, complemented
248C24—3021no—
249C2×Q8—3021no—
250C2×Q8—3022no—
251C2×Q8—1514no—
252C2×Q8—1511no—
253C2×Q8C22×D15111yescharacteristic
254C2×D4—3022no—
255C2×D4—3021no—
256C2×D4—1514no—
257C2×D4—1511no—
258C2×D4C22×D15111yescharacteristic
259C22×C4—21no—
260C22×C4—3021no—
261C22×C4—3021no—
262C22×C4—3021no—
263C22×C4—3021no—
264C22×C4—3021no—
265C22×C4—3021no—
266C22×C4—6044no—
267C22×C4—1511no—
268C22×C4—1511no—
269C22×C4—1511no—
270SD16—1514no—
271SD16—1514no—
272SD16—1514no—
273SD16C4×D15114yescomplemented
274C2×C8—3022no—
275C2×C8—1511no—
276C2×C8—1511no—
277C2×C8—1514no—
278C2×C8C22×D15111yescharacteristic
279C2×C8C22×D15111yescharacteristic
280C4⋊C4—21no—
281C4⋊C4—3021no—
282C4⋊C4—3021no—
283C4⋊C4—3021no—
284C4⋊C4—3021no—
285C4⋊C4—3021no—
286C4⋊C4—1511no—
287C4⋊C4—1511no—
288C4⋊C4C22×D15111yescharacteristic
289C4⋊C4C22×D15111yescharacteristic
290C22⋊C4—21no—
291C22⋊C4—3021no—
292C22⋊C4—3021no—
293C22⋊C4—3021no—
294C42—21no—
295C42—3021no—
296C42—3021no—
297C42—3021no—
298C42—1511no—
299C42—1511no—
300C42—1511no—
301C42C22×D15111yescharacteristic
302C23—21no—
303C23—3024no—
304C23—3021no—
305C23—6042no—
306C23—6042no—
307C23—1511no—
308Q8—21no—
309Q8—3024no—
310Q8—3021no—
311Q8—1512no—
312Q8C2×C4×D15112yescomplemented
313D4—21no—
314D4—3024no—
315D4—3021no—
316D4—1512no—
317D4C2×C4×D15112yes—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—42no—
322C2×C4—3024no—
323C2×C4—3022no—
324C2×C4—3022no—
325C2×C4—3021no—
326C2×C4—3021no—
327C2×C4—3021no—
328C2×C4—6042no—
329C2×C4—6042no—
330C2×C4—6042no—
331C2×C4—6042no—
332C2×C4—6042no—
333C2×C4—1511no—
334C2×C4—1511no—
335C2×C4—1511no—
336C2×C4—1512no—
337C2×C4—1512no—
338C2×C4D4×D15111yescharacteristic
339C2×C4D4×D15111yescharacteristic
340C2×C4C23×D15111yescharacteristic
341C8—21no—
342C8—3021no—
343C8—1512no—
344C8C2×C4×D15112yescomplemented
345C22—22no—
346C22—41no—
347C22—41no—
348C22—3022no—
349C22—6048no—
350C22—6041no—
351C22—6041no—
352C22—1512no—
353C22—1512no—
354C22—1512no—
355C22C2×D4×D15111yescharacteristic
356C4—21no—
357C4—21no—
358C4—22no—
359C4—41no—
360C4—41no—
361C4—3021no—
362C4—3021no—
363C4—3022no—
364C4—6041no—
365C4—6041no—
366C4—1512no—
367C4C22×C4×D15111yescharacteristic
368C4#41×D15111yescharacteristic
369C2—42no—
370C2—6042no—
371C2—1514no—
372C2C4×D4×D15111yescharacteristic
373C2AGL(1,ℤ/8)×D15111yescharacteristic
374C2#137×D15111yescharacteristic
subgroupG/H
centerC22C2×D4×D151
commutatorC4×C151C23×C4
FrattiniC2×C4C23×D151
Fitting#440×C151C2
socleC22×C151C22×D4
prime radicalC2×D4×D151C22
cosocleC2×C4×C151C24
hypercenter#440D151
hypocenterC151C2×#440
LCSG ▷ C4×C151 ▷ C2×C151 ▷ C151
UCSC1 ◁ C22 ◁ C42 ◁ #440

Complements

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

NH ≅ G/Ntype
2. C4×Q8×D151C2semidirect
4. #23752315C2semidirect
5. #23752314C2semidirect
6. #23752313C2semidirect
7. #23752312C2semidirect
8. #23752311C2semidirect
9. #23752310C2semidirect
10. #23752309C2semidirect
11. #107×D151C2semidirect
12. #103×D151C2semidirect
14. #97×D151C2semidirect
15. #440×C151C2semidirect
22. SD16×D151C4semidirect
25. Q8×Dic151C22semidirect
27. C4×Dic302C22semidirect
29. #18012704C22semidirect
41. #18012673C22semidirect
42. #18012672C22semidirect
43. #18012672C22semidirect
44. #18012664C22semidirect
45. #18012663C22semidirect
46. #18012662C22semidirect
50. #18012650C22semidirect
51. #18012649C22semidirect
52. #18012649C22semidirect
54. C4×Q8×C151C22semidirect
56. #107×C151C22semidirect
57. #103×C151C22semidirect
59. #97×C151C22semidirect
64. Q8×D151C2×C4semidirect
79. #14558993C2×C4semidirect
80. #14558992C2×C4semidirect
81. #14558991C2×C4semidirect
85. C8×D151C2×C4semidirect
105. SD16×C151C2×C4semidirect
121. Dic302C22×C4semidirect
142. C151⋊C8C22×C4semidirect
145. Q8×C151C22×C4semidirect
156. C8×C151C22×C4semidirect
186. D151#440direct (N × H)
187. C151C2×#440semidirect
199. #440D151direct (N × H)
219. C4×Q8C2×D151semidirect
235. #107C2×D151semidirect
239. #103C2×D151semidirect
247. #97C2×D151semidirect
273. SD16C4×D151semidirect
312. Q8C2×C4×D151semidirect
344. C8C2×C4×D151semidirect

Maximal subgroups

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

subgroupindex
C2×SD16×D1512
C4×Q8×D1512
C4×D4×D1512
#237523152
#237523142
#237523132
#237523122
#237523112
#237523102
#237523092
#107×D1512
#103×D1512
#102×D1512
#97×D1512
#440×C1512
C2×#440151