Finite Group Databasebeta

← #34080780

Subgroups — #34080780

Order 19328.

620 conjugacy classes of subgroups.

The subgroup lattice has 472 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14558989C211yesmaximal, characteristic, complemented
2C2×D8×D151C211yesmaximal, characteristic, complemented
3#23752846C211yesmaximal, characteristic, complemented
4D4×C22⋊D151C211yesmaximal, characteristic, complemented
5#23752587C211yesmaximal, characteristic, complemented
6#23752447C211yesmaximal, characteristic, complemented
7#23752446C211yesmaximal, characteristic, complemented
8#23752406C211yesmaximal, characteristic, complemented
9#23752405C211yesmaximal, characteristic, complemented
10#23752348C211yesmaximal, characteristic, complemented
11#23752347C211yesmaximal, characteristic, complemented
12#23752344C211yesmaximal, characteristic, complemented
13#23752292C211yesmaximal, characteristic, complemented
14(C22⋊D151)⋊C8C211yesmaximal, characteristic, complemented
15#447×C151C211yesmaximal, characteristic, complemented
16C22×D604C2211yescharacteristic, complemented
17C22×C22⋊D151—21no—
18C2×D4×D151—21no—
19C2×D4×D151C2211yescharacteristic, complemented
20C2×D4×D151C2211yescharacteristic, complemented
21C2×D1208C2211yescharacteristic, complemented
22C2×D1208C2211yescharacteristic, complemented
23C2×#14558989—24no—
24C2×#14558989C2211yescharacteristic
25C2×#14558989C2211yescharacteristic, complemented
26C2×#14558989C2211yescharacteristic, complemented
27C2×#14558989C2211yescharacteristic, complemented
28C2×#14558989C2211yescharacteristic, complemented
29D8×D151—24no—
30C22×C151⋊C8C2211yescharacteristic, complemented
31C2×C8×D151C2211yescharacteristic, complemented
32#18012735C2211yescharacteristic, complemented
33#18012735C2211yescharacteristic, complemented
34#18012714C2211yescharacteristic, complemented
35#18012713C2211yescharacteristic, complemented
36#18012712—21no—
37#18012711—21no—
38#18012710C2211yescharacteristic, complemented
39#18012709—21no—
40#18012708—21no—
41#18012707—21no—
42#18012707—21no—
43D4×Dic151C2211yescharacteristic, complemented
44#18012701C2211yescharacteristic, complemented
45C4×C22⋊D151C2211yescharacteristic
46#18012672C2211yescharacteristic, complemented
47Dic151⋊C8C2211yescharacteristic, complemented
48#18012661C2211yescharacteristic, complemented
49#18012661C2211yescharacteristic, complemented
50#18012660C2211yescharacteristic, complemented
51#18012659C2211yescharacteristic, complemented
52(C2×D151)⋊C8C2211yescharacteristic, complemented
53C8×Dic151C2211yescharacteristic, complemented
54C22×D4×C151C2211yescharacteristic, complemented
55C2×D8×C151C2211yescharacteristic, complemented
56C2×D8×C151C2211yescharacteristic, complemented
57#121×C151C2211yescharacteristic, complemented
58#102×C151C2211yescharacteristic, complemented
59#102×C151C2211yescharacteristic, complemented
60C22⋊C8×C151C2211yescharacteristic, complemented
61C23×D151—21no—
62C23×D151—21no—
63C23×D151—21no—
64C2×D604—22no—
65C2×D604—21no—
66C2×D604—21no—
67C2×D604—41no—
68C2×D604C2311yescharacteristic
69C2×D604C2311yescharacteristic
70C2×D604C2311yescharacteristic
71C2×C22⋊D151—21no—
72C2×C22⋊D151—21no—
73C2×C22⋊D151—21no—
74C2×C22⋊D151—21no—
75C2×C22⋊D151—21no—
76C2×C22⋊D151—21no—
77C2×C22⋊D151—21no—
78C2×C22⋊D151—21no—
79C2×C22⋊D151—44no—
80C2×C22⋊D151D411yescharacteristic
81D4×D151—22no—
82D4×D151—22no—
83D4×D151—41no—
84D4×D151—41no—
85D4×D151—44no—
86C22×Dic151—21no—
87C2×C4×D151—21no—
88C2×C4×D151C2311yescharacteristic
89D1208—22no—
90D1208—41no—
91#14558989—22no—
92#14558989—22no—
93#14558989—22no—
94#14558989—22no—
95#14558989D414yescomplemented
96C2×C151⋊C8—22no—
97C2×C151⋊C8C2311yescharacteristic
98C2×C151⋊C8C2311yescharacteristic
99C8×D151—22no—
100C4⋊Dic151C2311yescharacteristic
101Dic151⋊C4D411yescharacteristic
102C22⋊Dic151—21no—
103C22⋊Dic151—21no—
104C22⋊Dic151D411yescharacteristic
105(C2×D151)⋊C4—21no—
106(C2×D151)⋊C4—21no—
107(C2×D151)⋊C4—21no—
108(C2×D151)⋊C4D411yescharacteristic
109C4×Dic151C2311yescharacteristic
110C24×C151—21no—
111C2×D4×C151—22no—
112C2×D4×C151—21no—
113C2×D4×C151—21no—
114C2×D4×C151—41no—
115C2×D4×C151C2311yescharacteristic
116C2×D4×C151C2311yescharacteristic
117C2×D4×C151C2311yescharacteristic
118C22×C4×C151C2311yescharacteristic
119D8×C151—22no—
120D8×C151—41no—
121C2×C8×C151C2311yescharacteristic
122C2×C8×C151C2311yescharacteristic
123C4⋊C4×C151C2311yescharacteristic
124C22⋊C4×C151—21no—
125C22×D151—21no—
126C22×D151—21no—
127C22×D151—21no—
128C22×D151—42no—
129C22×D151—42no—
130C22×D151—42no—
131C22×D151—42no—
132C22×D151—42no—
133C22×D151—42no—
134C22×D151—81no—
135C22×D151—81no—
136C22×D151—81no—
137C22×D151C2×D411yescharacteristic
138D604—21no—
139D604—21no—
140D604—21no—
141D604—21no—
142D604—21no—
143D604—42no—
144D604—42no—
145D604C2×D412yescomplemented
146C22⋊D151—42no—
147C22⋊D151—42no—
148C22⋊D151—42no—
149C22⋊D151—42no—
150C22⋊D151—42no—
151C22⋊D151—42no—
152C22⋊D151—81no—
153C22⋊D151—81no—
154C22⋊D151D814yescomplemented
155C2×Dic151—21no—
156C2×Dic151—42no—
157C2×Dic151C2×D411yescharacteristic
158C2×Dic151C2×D411yescharacteristic
159C2×Dic151C2×D411yescharacteristic
160C4×D151—21no—
161C4×D151—21no—
162C4×D151—42no—
163C151⋊C8—21no—
164C151⋊C8C2×D412yescomplemented
165C23×C151—21no—
166C23×C151—21no—
167C23×C151—21no—
168C23×C151—42no—
169C23×C151—42no—
170C23×C151—81no—
171C23×C151C2×D411yescharacteristic
172D4×C151—21no—
173D4×C151—21no—
174D4×C151—21no—
175D4×C151—21no—
176D4×C151—21no—
177D4×C151—42no—
178D4×C151—42no—
179D4×C151C2×D412yescomplemented
180C2×C4×C151—21no—
181C2×C4×C151—21no—
182C2×C4×C151—21no—
183C2×C4×C151C2×D411yescharacteristic
184C2×C4×C151C2411yescharacteristic
185C8×C151—21no—
186C8×C151—21no—
187C22×C151—21no—
188C22×C151—21no—
189C22×C151—22no—
190C22×C151—41no—
191C22×C151—41no—
192C22×C151—41no—
193C22×C151—41no—
194C22×C151—41no—
195C22×C151—41no—
196C22×C151—41no—
197C22×C151—41no—
198C22×C151—84no—
199C22×C151C2×D812yescomplemented
200C22×C151C22×D411yescharacteristic
201C2×D151—21no—
202C2×D151—21no—
203C2×D151—22no—
204C2×D151—41no—
205C2×D151—41no—
206C2×D151—41no—
207C2×D151—41no—
208C2×D151—41no—
209C2×D151—41no—
210C2×D151—41no—
211C2×D151—41no—
212C2×D151—84no—
213C2×D151—84no—
214C2×D151—84no—
215C2×D151C2×D812yescomplemented
216C4×C151—21no—
217C4×C151—41no—
218C4×C151C22×D411yescharacteristic
219C4×C151H(5,𝔽2)11yescharacteristic
220Dic151—21no—
221Dic151—21no—
222Dic151—41no—
223Dic151C2×D812yescomplemented
224C2×C151—22no—
225C2×C151—42no—
226C2×C151—81no—
227C2×C151—81no—
228C2×C151D4211yescharacteristic
229C2×C151C22×D811yescharacteristic
230C2×C151#57611yescharacteristic
231D151—22no—
232D151—42no—
233D151—81no—
234D151—81no—
235C151D4×D811yescharacteristic, complemented, Sylow
236D4×D8—1511nomaximal, Sylow
237C22×D8—1511no—
238C22×D8—1511no—
239D42—1511no—
240D42—1511no—
241#493—1511no—
242#466—1511no—
243#466—1511no—
244#459—1511no—
245#459—1511no—
246#447—1511no—
247#447—1511no—
248#447—1511no—
249#447D15111yescharacteristic, complemented
250C4×D8—1511no—
251C8×D4—1511no—
252C22×D4—3021no—
253C22×D4—3021no—
254C22×D4—1511no—
255C22×D4—1511no—
256C22×D4—1511no—
257C22×D4C2×D15111yescharacteristic, complemented
258C2×D8—3024no—
259C2×D8—3024no—
260C2×D8—1511no—
261C2×D8—1511no—
262C2×D8—1511no—
263C2×D8—1511no—
264C2×D8—1511no—
265C2×D8—1511no—
266C2×D8—1511no—
267C2×D8C2×D15111yescharacteristic, complemented
268C2×D8C2×D15111yescharacteristic, complemented
269C22×C8—1511no—
270C22×C8—1511no—
271#127—1511no—
272#127—1511no—
273#121—3021no—
274#121—3021no—
275#121—1511no—
276#121—1511no—
277#121—1511no—
278#121C2×D15111yescharacteristic, complemented
279#120—3021no—
280#120—3021no—
281#120—3021no—
282#120—3021no—
283C4×D4—1511no—
284C4×D4—1511no—
285C4×D4—1511no—
286#107—1511no—
287C4⋊C8—1511no—
288#102—1511no—
289#102—1511no—
290#102—1511no—
291#102—1511no—
292#102C2×D15111yescharacteristic, complemented
293#102C2×D15111yescharacteristic, complemented
294C22⋊C8—1511no—
295C22⋊C8C2×D15111yescharacteristic, complemented
296C4×C8—1511no—
297C24—21no—
298C24—3021no—
299C24—3021no—
300C24—3021no—
301C2×D4—22no—
302C2×D4—21no—
303C2×D4—21no—
304C2×D4—41no—
305C2×D4—3022no—
306C2×D4—3021no—
307C2×D4—3022no—
308C2×D4—3022no—
309C2×D4—3021no—
310C2×D4—3021no—
311C2×D4—3021no—
312C2×D4—3021no—
313C2×D4—3021no—
314C2×D4—3021no—
315C2×D4—3021no—
316C2×D4—3021no—
317C2×D4—3021no—
318C2×D4—6041no—
319C2×D4—6041no—
320C2×D4—6041no—
321C2×D4—6044no—
322C2×D4—6044no—
323C2×D4—1511no—
324C2×D4—1511no—
325C2×D4—1511no—
326C2×D4—1511no—
327C2×D4C22×D15111yescharacteristic
328C2×D4C22×D15111yescharacteristic
329C2×D4C22×D15111yescharacteristic
330C22×C4—3021no—
331C22×C4—3021no—
332C22×C4—1511no—
333C22×C4C22×D15111yescharacteristic
334D8—22no—
335D8—41no—
336D8—3022no—
337D8—3022no—
338D8—3022no—
339D8—3022no—
340D8—3022no—
341D8—6041no—
342D8—1514no—
343C2×C8—3022no—
344C2×C8—3022no—
345C2×C8—1511no—
346C2×C8—1511no—
347C2×C8C22×D15111yescharacteristic
348C2×C8C22×D15111yescharacteristic
349C4⋊C4—1511no—
350C4⋊C4—1511no—
351C4⋊C4C22×D15111yescharacteristic
352C22⋊C4—21no—
353C22⋊C4—3021no—
354C22⋊C4—3021no—
355C22⋊C4—3021no—
356C22⋊C4—3021no—
357C22⋊C4—3021no—
358C22⋊C4—1511no—
359C22⋊C4—1511no—
360C42—1511no—
361C23—21no—
362C23—21no—
363C23—21no—
364C23—42no—
365C23—42no—
366C23—81no—
367C23—3021no—
368C23—3021no—
369C23—3021no—
370C23—6042no—
371C23—6042no—
372C23—6042no—
373C23—6042no—
374C23—6042no—
375C23—6042no—
376C23—1511no—
377C23—12081no—
378C23—12081no—
379C23—12081no—
380C23D4×D15111yescharacteristic
381D4—21no—
382D4—21no—
383D4—21no—
384D4—21no—
385D4—21no—
386D4—42no—
387D4—42no—
388D4—3021no—
389D4—3021no—
390D4—3021no—
391D4—3021no—
392D4—3021no—
393D4—6042no—
394D4—6042no—
395D4—6042no—
396D4—6042no—
397D4—6042no—
398D4—6042no—
399D4—6042no—
400D4—6042no—
401D4—1514no—
402D4—1512no—
403D4—12081no—
404D4—12081no—
405D4D4×D15112yescomplemented
406C2×C4—21no—
407C2×C4—21no—
408C2×C4—21no—
409C2×C4—3021no—
410C2×C4—3021no—
411C2×C4—3021no—
412C2×C4—6042no—
413C2×C4—6042no—
414C2×C4—1511no—
415C2×C4—1511no—
416C2×C4—1511no—
417C2×C4D4×D15111yescharacteristic
418C2×C4C23×D15111yescharacteristic
419C8—21no—
420C8—21no—
421C8—3021no—
422C8—1512no—
423C22—21no—
424C22—21no—
425C22—22no—
426C22—41no—
427C22—41no—
428C22—41no—
429C22—41no—
430C22—41no—
431C22—41no—
432C22—41no—
433C22—41no—
434C22—84no—
435C22—3021no—
436C22—3021no—
437C22—3022no—
438C22—6041no—
439C22—6041no—
440C22—6041no—
441C22—6041no—
442C22—6041no—
443C22—6041no—
444C22—6041no—
445C22—6041no—
446C22—1512no—
447C22—12084no—
448C22—12084no—
449C22—12084no—
450C22D8×D15112yescomplemented
451C22C2×D4×D15111yescharacteristic
452C4—21no—
453C4—41no—
454C4—3021no—
455C4—3021no—
456C4—6041no—
457C4—1512no—
458C4C2×D4×D15111yescharacteristic
459C4#1801278411yescharacteristic
460C2—22no—
461C2—42no—
462C2—81no—
463C2—81no—
464C2—3022no—
465C2—6042no—
466C2—12081no—
467C2—12081no—
468C2#2375284411yescharacteristic
469C2C2×D8×D15111yescharacteristic
470C2#2375301611yescharacteristic
subgroupG/H
centerC22C2×D4×D151
commutator, cosocleC2×C4×C151C24
FrattiniC2×C4C23×D151
Fitting#447×C151C2
socleC22×C151C22×D4
hypercenter#447D151
hypocenterC151D4×D8
LCSG ▷ C2×C4×C151 ▷ C2×C151 ▷ C151
UCSC1 ◁ C22 ◁ C22×C4 ◁ #447

Complements

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

NH ≅ G/Ntype
1. C22×#14558989C2semidirect
2. C2×D8×D151C2semidirect
3. #23752846C2semidirect
4. D4×C22⋊D151C2semidirect
5. #23752587C2semidirect
6. #23752447C2semidirect
7. #23752446C2semidirect
8. #23752406C2semidirect
9. #23752405C2semidirect
10. #23752348C2semidirect
11. #23752347C2semidirect
12. #23752344C2semidirect
13. #23752292C2semidirect
14. (C22⋊D151)⋊C8C2semidirect
15. #447×C151C2semidirect
16. C22×D604C22semidirect
19. C2×D4×D151C22semidirect
20. C2×D4×D151C22semidirect
21. C2×D1208C22semidirect
22. C2×D1208C22semidirect
25. C2×#14558989C22semidirect
26. C2×#14558989C22semidirect
27. C2×#14558989C22semidirect
28. C2×#14558989C22semidirect
30. C22×C151⋊C8C22semidirect
31. C2×C8×D151C22semidirect
32. #18012735C22semidirect
33. #18012735C22semidirect
34. #18012714C22semidirect
35. #18012713C22semidirect
38. #18012710C22semidirect
43. D4×Dic151C22semidirect
44. #18012701C22semidirect
46. #18012672C22semidirect
47. Dic151⋊C8C22semidirect
48. #18012661C22semidirect
49. #18012661C22semidirect
50. #18012660C22semidirect
51. #18012659C22semidirect
52. (C2×D151)⋊C8C22semidirect
53. C8×Dic151C22semidirect
54. C22×D4×C151C22semidirect
55. C2×D8×C151C22semidirect
56. C2×D8×C151C22semidirect
57. #121×C151C22semidirect
58. #102×C151C22semidirect
59. #102×C151C22semidirect
60. C22⋊C8×C151C22semidirect
95. #14558989D4semidirect
145. D604C2×D4semidirect
154. C22⋊D151D8semidirect
164. C151⋊C8C2×D4semidirect
179. D4×C151C2×D4semidirect
199. C22×C151C2×D8semidirect
215. C2×D151C2×D8semidirect
223. Dic151C2×D8semidirect
235. C151D4×D8semidirect
249. #447D151semidirect
257. C22×D4C2×D151semidirect
267. C2×D8C2×D151semidirect
268. C2×D8C2×D151semidirect
278. #121C2×D151semidirect
292. #102C2×D151semidirect
293. #102C2×D151semidirect
295. C22⋊C8C2×D151semidirect
405. D4D4×D151semidirect
450. C22D8×D151semidirect

Maximal subgroups

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

subgroupindex
C22×#145589892
C2×D8×D1512
#237528462
D4×C22⋊D1512
#237525872
#237524472
#237524462
#237524062
#237524052
#237523482
#237523472
#237523442
#237522922
(C22⋊D151)⋊C82
#447×C1512
D4×D8151