Finite Group Databasebeta

← #468×D151 #34078694

Subgroups — #468×D151 #34078694

Order 19328.

544 conjugacy classes of subgroups.

The subgroup lattice has 420 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×SD16×D151C211yesmaximal, characteristic, complemented
2C2×M16×D151C211yesmaximal, characteristic, complemented
3C22⋊Q8×D151C211yesmaximal, characteristic, complemented
4#121×D151C211yesmaximal, characteristic
5#23752461C211yesmaximal, characteristic, complemented
6#23752460C211yesmaximal, characteristic, complemented
7#23752459C211yesmaximal, characteristic, complemented
8#23752458C211yesmaximal, characteristic, complemented
9#23752457C211yesmaximal, characteristic, complemented
10#23752456C211yesmaximal, characteristic, complemented
11#23752455C211yesmaximal, characteristic, complemented
12#107×D151C211yesmaximal, characteristic, complemented
13#103×D151C211yesmaximal, characteristic, complemented
14#102×D151C211yesmaximal, characteristic, complemented
15#468×C151C211yesmaximal, characteristic, complemented
16C2×Q8×D151C2211yescharacteristic
17C2×D4×D151—21no—
18C2×D4×D151C2211yescharacteristic
19C22×C4×D151C2211yescharacteristic
20C2×#14558993C2211yescharacteristic, complemented
21C2×#14558992C2211yescharacteristic, complemented
22C2×#14558991C2211yescharacteristic, complemented
23SD16×D151—24no—
24C2×#14558988C2211yescharacteristic, complemented
25C2×#14558987C2211yescharacteristic, complemented
26C2×#14558987C2211yescharacteristic, complemented
27M16×D151—24no—
28C2×C8×D151C2211yescharacteristic
29C2×C8×D151C2211yescharacteristic
30#18012719C2211yescharacteristic, complemented
31#18012718C2211yescharacteristic, complemented
32#18012717—21no—
33#18012716—21no—
34#18012715C2211yescharacteristic, complemented
35#18012714C2211yescharacteristic
36#18012713C2211yescharacteristic
37#18012712—21no—
38#18012711—21no—
39#18012710C2211yescharacteristic
40C4⋊C4×D151—21no—
41C4⋊C4×D151C2211yescharacteristic
42C4⋊C4×D151C2211yescharacteristic
43C22⋊C4×D151—21no—
44C22⋊C4×D151—21no—
45#18012673C2211yescharacteristic, complemented
46#18012672C2211yescharacteristic, complemented
47#18012672C2211yescharacteristic, complemented
48#18012664C2211yescharacteristic, complemented
49#18012663C2211yescharacteristic, complemented
50#18012662C2211yescharacteristic, complemented
51#18012661C2211yescharacteristic, complemented
52#18012660C2211yescharacteristic, complemented
53#18012659C2211yescharacteristic, complemented
54C2×SD16×C151C2211yescharacteristic, complemented
55C2×M16×C151C2211yescharacteristic, complemented
56C22⋊Q8×C151C2211yescharacteristic, complemented
57#121×C151C2211yescharacteristic
58#107×C151C2211yescharacteristic, complemented
59#103×C151C2211yescharacteristic, complemented
60#102×C151C2211yescharacteristic, complemented
61C23×D151—21no—
62C23×D151D411yescharacteristic
63C2×Dic302—21no—
64C2×Dic302C2311yescharacteristic
65Q8×D151—22no—
66Q8×D151—22no—
67C2×D604—21no—
68C2×D604C2311yescharacteristic
69C2×C22⋊D151—21no—
70C2×C22⋊D151—21no—
71C2×C22⋊D151—21no—
72D4×D151—22no—
73D4×D151—22no—
74D4×D151—44no—
75C22×Dic151D411yescharacteristic
76C2×C4×D151—22no—
77C2×C4×D151—22no—
78C2×C4×D151—21no—
79C2×C4×D151—21no—
80C2×C4×D151—21no—
81C2×C4×D151D411yescharacteristic
82C2×C4×D151D411yescharacteristic
83C2×C4×D151C2311yescharacteristic
84C2×C4×D151C2311yescharacteristic
85#14558993—22no—
86#14558992—22no—
87#14558991—22no—
88#14558988—22no—
89#14558987—22no—
90#14558987—22no—
91C2×C151⋊C8C2311yescharacteristic
92C2×C151⋊C8C2311yescharacteristic
93C8×D151—22no—
94C8×D151D414yescomplemented
95C4⋊Dic151—21no—
96C4⋊Dic151C2311yescharacteristic
97C4⋊Dic151C2311yescharacteristic
98Dic151⋊C4—21no—
99Dic151⋊C4—21no—
100Dic151⋊C4—21no—
101Dic151⋊C4—21no—
102C22⋊Dic151—21no—
103C22⋊Dic151—21no—
104(C2×D151)⋊C4—21no—
105(C2×D151)⋊C4—21no—
106(C2×D151)⋊C4—21no—
107(C2×D151)⋊C4—21no—
108C2×Q8×C151C2311yescharacteristic
109C2×D4×C151—21no—
110C2×D4×C151C2311yescharacteristic
111C22×C4×C151C2311yescharacteristic
112SD16×C151—22no—
113M16×C151—22no—
114C2×C8×C151C2311yescharacteristic
115C2×C8×C151C2311yescharacteristic
116C4⋊C4×C151—21no—
117C4⋊C4×C151C2311yescharacteristic
118C4⋊C4×C151C2311yescharacteristic
119C22⋊C4×C151—21no—
120C22⋊C4×C151—21no—
121C22×D151—22no—
122C22×D151—22no—
123C22×D151—22no—
124C22×D151—21no—
125C22×D151—42no—
126C22×D151—42no—
127C22×D151—42no—
128C22×D151C2×D411yescharacteristic
129C22×D151C2×D411yescharacteristic
130Dic302—21no—
131Dic302—21no—
132Dic302—42no—
133D604—21no—
134D604—21no—
135D604—42no—
136C22⋊D151—42no—
137C22⋊D151—42no—
138C22⋊D151—42no—
139C2×Dic151—22no—
140C2×Dic151—21no—
141C2×Dic151—21no—
142C2×Dic151—21no—
143C2×Dic151C2×D411yescharacteristic
144C2×Dic151C2×D411yescharacteristic
145C4×D151—22no—
146C4×D151—21no—
147C4×D151—21no—
148C4×D151—22no—
149C4×D151—42no—
150C4×D151—42no—
151C4×D151—42no—
152C4×D151C2×D412yes—
153C4×D151#4112yes—
154C151⋊C8—21no—
155C151⋊C8C2×D412yescomplemented
156C23×C151—21no—
157C23×C151C2×D411yescharacteristic
158Q8×C151—21no—
159Q8×C151—21no—
160D4×C151—21no—
161D4×C151—21no—
162D4×C151—42no—
163C2×C4×C151—21no—
164C2×C4×C151—21no—
165C2×C4×C151—21no—
166C2×C4×C151—21no—
167C2×C4×C151—21no—
168C2×C4×C151C2×D411yescharacteristic
169C2×C4×C151C2411yescharacteristic
170C8×C151—21no—
171C8×C151C2×D412yescomplemented
172C22×C151—21no—
173C22×C151—21no—
174C22×C151—21no—
175C22×C151—41no—
176C22×C151—41no—
177C22×C151—41no—
178C22×C151C22×D411yescharacteristic
179C2×D151—21no—
180C2×D151—21no—
181C2×D151—21no—
182C2×D151—44no—
183C2×D151—41no—
184C2×D151—41no—
185C2×D151—41no—
186C2×D151—84no—
187C2×D151#12112yes—
188C2×D151AGL(1,ℤ/8)12yes—
189C2×D151#13712yes—
190C4×C151—21no—
191C4×C151—41no—
192C4×C151—41no—
193C4×C151—41no—
194C4×C151C22×D411yescharacteristic
195C4×C151C2×#4111yescharacteristic
196Dic151—21no—
197Dic151—41no—
198Dic151—41no—
199Dic151—41no—
200Dic151#12112yes—
201C2×C151—41no—
202C2×C151—81no—
203C2×C151C2×#12111yescharacteristic
204C2×C151C2×AGL(1,ℤ/8)11yescharacteristic
205C2×C151C2×#13711yescharacteristic
206D151—41no—
207D151—81no—
208D151#46814yesdirect product factor
209C151C2×#46811yescharacteristic, complemented, Sylow
210C2×#468—1511nomaximal, Sylow
211C22×SD16—1511no—
212C22×M16—1511no—
213C2×C22⋊Q8—1511no—
214C2×#121—1511no—
215#468—1511no—
216#468—1511no—
217#468—1511no—
218#468—1511no—
219#468—1511no—
220#468—1511no—
221#468—1511no—
222#468D15111yescharacteristic, direct product factor
223C2×#107—1511no—
224C2×#103—1511no—
225C2×#102—1511no—
226C22×Q8—1511no—
227C22×D4—3021no—
228C22×D4—1511no—
229C23×C4—1511no—
230C2×SD16—3024no—
231C2×SD16—1511no—
232C2×SD16—1511no—
233C2×SD16—1511no—
234C2×SD16C2×D15111yescharacteristic, complemented
235C2×M16—3024no—
236C2×M16—1511no—
237C2×M16—1511no—
238C2×M16—1511no—
239C2×M16C2×D15111yescharacteristic, complemented
240C22×C8—1511no—
241C22×C8—1511no—
242C22⋊Q8—3021no—
243C22⋊Q8—3021no—
244C22⋊Q8—1511no—
245C22⋊Q8—1511no—
246C22⋊Q8—1511no—
247C22⋊Q8C2×D15111yescharacteristic, complemented
248#121—3021no—
249#121—3021no—
250#121—1511no—
251#121—1511no—
252#121—1511no—
253#121C2×D15111yescharacteristic
254C2×C4⋊C4—3021no—
255C2×C4⋊C4—1511no—
256C2×C4⋊C4—1511no—
257C2×C22⋊C4—3021no—
258C2×C22⋊C4—3021no—
259#107—1511no—
260#107—1511no—
261#107—1511no—
262#107C2×D15111yescharacteristic, complemented
263#103—1511no—
264#103—1511no—
265#103—1511no—
266#103C2×D15111yescharacteristic, complemented
267#102—1511no—
268#102—1511no—
269#102—1511no—
270#102C2×D15111yescharacteristic, complemented
271C24—3021no—
272C24—1511no—
273C2×Q8—3021no—
274C2×Q8—3022no—
275C2×Q8—3022no—
276C2×Q8—1511no—
277C2×Q8C22×D15111yescharacteristic
278C2×D4—21no—
279C2×D4—3021no—
280C2×D4—3021no—
281C2×D4—3021no—
282C2×D4—3022no—
283C2×D4—3022no—
284C2×D4—3021no—
285C2×D4—6044no—
286C2×D4—1511no—
287C2×D4C22×D15111yescharacteristic
288C22×C4—3022no—
289C22×C4—3022no—
290C22×C4—3021no—
291C22×C4—3021no—
292C22×C4—3021no—
293C22×C4—1511no—
294C22×C4—1511no—
295C22×C4—1511no—
296C22×C4—1511no—
297C22×C4—1511no—
298C22×C4C22×D15111yescharacteristic
299SD16—22no—
300SD16—3022no—
301SD16—3022no—
302SD16—3022no—
303M16—22no—
304M16—3022no—
305M16—3022no—
306M16—3022no—
307C2×C8—3022no—
308C2×C8—1511no—
309C2×C8—1511no—
310C2×C8—1514no—
311C2×C8C22×D15111yescharacteristic
312C2×C8C22×D15111yescharacteristic
313C4⋊C4—21no—
314C4⋊C4—3021no—
315C4⋊C4—3021no—
316C4⋊C4—3021no—
317C4⋊C4—3021no—
318C4⋊C4—3021no—
319C4⋊C4—1511no—
320C4⋊C4—1511no—
321C4⋊C4C22×D15111yescharacteristic
322C4⋊C4C22×D15111yescharacteristic
323C22⋊C4—21no—
324C22⋊C4—21no—
325C22⋊C4—3021no—
326C22⋊C4—3021no—
327C22⋊C4—3021no—
328C22⋊C4—3021no—
329C22⋊C4—3021no—
330C22⋊C4—3021no—
331C23—21no—
332C23—3022no—
333C23—3022no—
334C23—3022no—
335C23—3021no—
336C23—6042no—
337C23—6042no—
338C23—6042no—
339C23—1511no—
340C23—1511no—
341C23D4×D15111yescharacteristic
342Q8—21no—
343Q8—21no—
344Q8—3021no—
345Q8—3021no—
346Q8—6042no—
347D4—21no—
348D4—21no—
349D4—42no—
350D4—3021no—
351D4—3021no—
352D4—6042no—
353D4—6042no—
354D4—6042no—
355D4—6042no—
356C2×C4—21no—
357C2×C4—21no—
358C2×C4—21no—
359C2×C4—21no—
360C2×C4—21no—
361C2×C4—3022no—
362C2×C4—3022no—
363C2×C4—3022no—
364C2×C4—3021no—
365C2×C4—3021no—
366C2×C4—3021no—
367C2×C4—3021no—
368C2×C4—3021no—
369C2×C4—6042no—
370C2×C4—6042no—
371C2×C4—6042no—
372C2×C4—1511no—
373C2×C4—1511no—
374C2×C4—1512no—
375C2×C4—1512no—
376C2×C4D4×D15111yescharacteristic
377C2×C4C23×D15111yescharacteristic
378C8—21no—
379C8—3021no—
380C8—1512no—
381C8D4×D15112yescomplemented
382C22—21no—
383C22—21no—
384C22—21no—
385C22—41no—
386C22—41no—
387C22—41no—
388C22—3021no—
389C22—3021no—
390C22—3021no—
391C22—6044no—
392C22—6041no—
393C22—6041no—
394C22—6041no—
395C22—1512no—
396C22—1512no—
397C22—1512no—
398C22—12084no—
399C22C2×D4×D15111yescharacteristic
400C4—21no—
401C4—41no—
402C4—41no—
403C4—41no—
404C4—3021no—
405C4—6041no—
406C4—6041no—
407C4—6041no—
408C4—1512no—
409C4C2×D4×D15111yescharacteristic
410C4#41×D15111yescharacteristic
411C2—41no—
412C2—81no—
413C2—6041no—
414C2—1514no—
415C2—12081no—
416C2#121×D15111yescharacteristic
417C2AGL(1,ℤ/8)×D15111yescharacteristic
418C2#137×D15111yescharacteristic
subgroupG/H
centerC22C2×D4×D151
commutator, cosocleC2×C4×C151C24
FrattiniC2×C4C23×D151
Fitting#468×C151C2
socleC22×C151C22×D4
prime radical#121×D151C2
hypercenter#468D151
hypocenterC151C2×#468
LCSG ▷ C2×C4×C151 ▷ C2×C151 ▷ C151
UCSC1 ◁ C22 ◁ C22×C4 ◁ #468

Complements

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

NH ≅ G/Ntype
1. C2×SD16×D151C2semidirect
2. C2×M16×D151C2semidirect
3. C22⋊Q8×D151C2semidirect
5. #23752461C2semidirect
6. #23752460C2semidirect
7. #23752459C2semidirect
8. #23752458C2semidirect
9. #23752457C2semidirect
10. #23752456C2semidirect
11. #23752455C2semidirect
12. #107×D151C2semidirect
13. #103×D151C2semidirect
14. #102×D151C2semidirect
15. #468×C151C2semidirect
20. C2×#14558993C22semidirect
21. C2×#14558992C22semidirect
22. C2×#14558991C22semidirect
24. C2×#14558988C22semidirect
25. C2×#14558987C22semidirect
26. C2×#14558987C22semidirect
30. #18012719C22semidirect
31. #18012718C22semidirect
34. #18012715C22semidirect
45. #18012673C22semidirect
46. #18012672C22semidirect
47. #18012672C22semidirect
48. #18012664C22semidirect
49. #18012663C22semidirect
50. #18012662C22semidirect
51. #18012661C22semidirect
52. #18012660C22semidirect
53. #18012659C22semidirect
54. C2×SD16×C151C22semidirect
55. C2×M16×C151C22semidirect
56. C22⋊Q8×C151C22semidirect
58. #107×C151C22semidirect
59. #103×C151C22semidirect
60. #102×C151C22semidirect
94. C8×D151D4semidirect
155. C151⋊C8C2×D4semidirect
171. C8×C151C2×D4semidirect
208. D151#468direct (N × H)
209. C151C2×#468semidirect
222. #468D151direct (N × H)
234. C2×SD16C2×D151semidirect
239. C2×M16C2×D151semidirect
247. C22⋊Q8C2×D151semidirect
262. #107C2×D151semidirect
266. #103C2×D151semidirect
270. #102C2×D151semidirect
381. C8D4×D151semidirect

Maximal subgroups

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

subgroupindex
C2×SD16×D1512
C2×M16×D1512
C22⋊Q8×D1512
#121×D1512
#237524612
#237524602
#237524592
#237524582
#237524572
#237524562
#237524552
#107×D1512
#103×D1512
#102×D1512
#468×C1512
C2×#468151