Finite Group Databasebeta

← #34056177

Subgroups — #34056177

Order 19072.

568 conjugacy classes of subgroups.

The subgroup lattice has 452 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#18011938C211yesmaximal, characteristic, complemented
2C2×D8×D149C211yesmaximal, characteristic, complemented
3#23750268C211yesmaximal, characteristic, complemented
4D4×D596C211yesmaximal, characteristic, complemented
5#23750015C211yesmaximal, characteristic, complemented
6#23749877C211yesmaximal, characteristic, complemented
7#23749857C211yesmaximal, characteristic, complemented
8#23749821C211yesmaximal, characteristic, complemented
9#23749774C211yesmaximal, characteristic, complemented
10#23749773C211yesmaximal, characteristic, complemented
11#23749760C211yesmaximal, characteristic, complemented
12#23749757C211yesmaximal, characteristic, complemented
13#23749735C211yesmaximal, characteristic, complemented
14#23749695C211yesmaximal, characteristic, complemented
15#463×C149C211yesmaximal, characteristic, complemented
16C2×#14558737C2211yescharacteristic, complemented
17C22×D596—21no—
18C2×D4×D149C2211yescharacteristic
19C2×D4×D149C2211yescharacteristic, complemented
20C2×D4×D149C2211yescharacteristic, complemented
21#18011938—24no—
22C2×#14558723C2211yescharacteristic, complemented
23C2×#14558723C2211yescharacteristic, complemented
24C2×D1192C2211yescharacteristic, complemented
25C2×D1192C2211yescharacteristic, complemented
26C2×#14558721C2211yescharacteristic
27C2×#14558721C2211yescharacteristic, complemented
28C2×#14558721C2211yescharacteristic, complemented
29D8×D149—24no—
30C2×#14558719C2211yescharacteristic, complemented
31C2×C8×D149C2211yescharacteristic, complemented
32#18011908C2211yescharacteristic, complemented
33#18011893—21no—
34#18011887C2211yescharacteristic, complemented
35#18011886C2211yescharacteristic
36#18011886C2211yescharacteristic, complemented
37#18011885—21no—
38#18011884—21no—
39#18011882C2211yescharacteristic, complemented
40#18011881—21no—
41#18011881—21no—
42#18011881—21no—
43C4×D596C2211yescharacteristic
44C4×D596C2211yescharacteristic, complemented
45C22⋊C4×D149—21no—
46#18011842C2211yescharacteristic, complemented
47#18011833C2211yescharacteristic, complemented
48#18011833C2211yescharacteristic, complemented
49#18011832C2211yescharacteristic, complemented
50#18011831C2211yescharacteristic, complemented
51#18011823C2211yescharacteristic, complemented
52#18011823C2211yescharacteristic, complemented
53#18011822C2211yescharacteristic, complemented
54C2×SD16×C149C2211yescharacteristic, complemented
55C2×D8×C149C2211yescharacteristic
56#124×C149C2211yescharacteristic, complemented
57C4×D4×C149C2211yescharacteristic, complemented
58C4⋊C8×C149C2211yescharacteristic, complemented
59#103×C149C2211yescharacteristic, complemented
60#102×C149C2211yescharacteristic, complemented
61C23×D149—21no—
62C23×D149—21no—
63C23×D149—21no—
64#14558737—22no—
65#14558737—41no—
66C2×D596—21no—
67C2×D596—21no—
68C2×D596—21no—
69C2×D596—21no—
70C2×D596—21no—
71C2×D596—44no—
72C2×D596D411yescharacteristic
73C2×D596C2311yescharacteristic
74C2×D596C2311yescharacteristic
75C2×D596C2311yescharacteristic
76C2×C22⋊D149—21no—
77C2×C22⋊D149—21no—
78C2×C22⋊D149—21no—
79C2×C22⋊D149—21no—
80D4×D149—22no—
81D4×D149—22no—
82D4×D149—22no—
83D4×D149—41no—
84D4×D149—41no—
85D4×D149—41no—
86C2×C4×D149—21no—
87C2×C4×D149—21no—
88C2×C4×D149C2311yescharacteristic
89C2×C4×D149C2311yescharacteristic
90#14558723—22no—
91#14558723—41no—
92D1192—22no—
93D1192—22no—
94#14558721—22no—
95#14558721—41no—
96#14558721D414yescomplemented
97#14558719—22no—
98C2×#11924746C2311yescharacteristic
99C2×#11924746C2311yescharacteristic
100C8×D149—22no—
101C4⋊Dic149D411yescharacteristic
102C4⋊Dic149C2311yescharacteristic
103#14558715—21no—
104C22⋊Dic149—21no—
105#14558713—21no—
106#14558713—21no—
107#14558713—21no—
108#14558713—21no—
109#14558713D411yescharacteristic
110#14558713D411yescharacteristic
111C2×Q8×C149C2311yescharacteristic
112C2×D4×C149C2311yescharacteristic
113C2×D4×C149C2311yescharacteristic
114C22×C4×C149—21no—
115SD16×C149—22no—
116D8×C149—22no—
117C2×C8×C149C2311yescharacteristic
118C2×C8×C149C2311yescharacteristic
119C4⋊C4×C149C2311yescharacteristic
120C22⋊C4×C149—21no—
121C22⋊C4×C149—21no—
122C22⋊C4×C149—21no—
123C42×C149C2311yescharacteristic
124C22×D149—21no—
125C22×D149—21no—
126C22×D149—21no—
127C22×D149—42no—
128C22×D149—42no—
129C22×D149—42no—
130C22×D149—42no—
131C22×D149—42no—
132C22×D149—42no—
133C22×D149—81no—
134C22×D149—81no—
135C22×D149—81no—
136C22×D149C2×D411yescharacteristic
137C22×D149C2×D411yescharacteristic
138D596—22no—
139D596—21no—
140D596—21no—
141D596—21no—
142D596—21no—
143D596—21no—
144D596—42no—
145D596—42no—
146D596—42no—
147D596—42no—
148D596—81no—
149D596C2×D412yescomplemented
150C22⋊D149—42no—
151C22⋊D149—42no—
152C22⋊D149—42no—
153C22⋊D149—81no—
154C2×Dic149—21no—
155C2×Dic149C2×D411yescharacteristic
156C2×Dic149C2×D411yescharacteristic
157C4×D149—21no—
158C4×D149—21no—
159C4×D149—21no—
160C4×D149—21no—
161C4×D149—42no—
162C4×D149—81no—
163#11924746—21no—
164#11924746C2×D412yescomplemented
165C23×C149—21no—
166C23×C149—21no—
167Q8×C149—21no—
168Q8×C149—21no—
169D4×C149—21no—
170D4×C149—21no—
171D4×C149—21no—
172D4×C149C2×D412yes—
173C2×C4×C149—21no—
174C2×C4×C149—21no—
175C2×C4×C149—42no—
176C2×C4×C149C2×D411yescharacteristic
177C2×C4×C149C2×D411yescharacteristic
178C2×C4×C149C2411yescharacteristic
179C8×C149—21no—
180C8×C149—21no—
181C22×C149—22no—
182C22×C149—41no—
183C22×C149—41no—
184C22×C149—41no—
185C22×C149—41no—
186C22×C149—41no—
187C22×C149C22×D411yescharacteristic
188C2×D149—21no—
189C2×D149—21no—
190C2×D149—21no—
191C2×D149—22no—
192C2×D149—21no—
193C2×D149—21no—
194C2×D149—41no—
195C2×D149—41no—
196C2×D149—41no—
197C2×D149—41no—
198C2×D149—41no—
199C2×D149—41no—
200C2×D149—41no—
201C2×D149—41no—
202C2×D149—84no—
203C2×D149—84no—
204C2×D149—84no—
205C2×D149AGL(1,ℤ/8)12yescomplemented
206C4×C149—21no—
207C4×C149—21no—
208C4×C149—41no—
209C4×C149—41no—
210C4×C149C22×D411yescharacteristic
211C4×C149H(5,𝔽2)11yescharacteristic
212Dic149—21no—
213Dic149—21no—
214Dic149—41no—
215C2×C149—42no—
216C2×C149—81no—
217C2×C149D4211yescharacteristic
218C2×C149C2×AGL(1,ℤ/8)11yescharacteristic
219C2×C149#57611yescharacteristic
220D149—22no—
221D149—41no—
222D149—42no—
223D149—81no—
224D149—81no—
225C149#326411yescharacteristic, complemented, Sylow
226#3264—1491nomaximal, Sylow
227C2×AGL(1,ℤ/8)—1491no—
228C22×D8—1491no—
229#546—1491no—
230D42—1491no—
231#496—1491no—
232#469—1491no—
233#465—1491no—
234#463D14911yescharacteristic, complemented
235#459—1491no—
236#450—1491no—
237#449—1491no—
238#447—1491no—
239#447—1491no—
240#442—1491no—
241#435—1491no—
242C2×#41—1491no—
243C22×D4—2981no—
244C22×D4—1491no—
245C22×D4—1491no—
246C22×D4—1491no—
247AGL(1,ℤ/8)—2984no—
248C2×SD16—1491no—
249C2×SD16—1491no—
250C2×SD16C2×D14911yescharacteristic, complemented
251C2×D8—2984no—
252C2×D8—1491no—
253C2×D8—1491no—
254C2×D8—1491no—
255C2×D8—1491no—
256C2×D8—1491no—
257C2×D8C2×D14911yescharacteristic
258C2×M16—1491no—
259C22×C8—1491no—
260#127—1491no—
261#124C2×D14911yescharacteristic, complemented
262#123—2981no—
263C22⋊Q8—1491no—
264#121—2981no—
265#121—2981no—
266#121—1491no—
267#121—1491no—
268#121—1491no—
269#120—2981no—
270#120—2981no—
271#120—2981no—
272C4×D4—1491no—
273C4×D4—1491no—
274C4×D4C2×D14911yescharacteristic, complemented
275C2×C22⋊C4—2981no—
276#106—1491no—
277C4⋊C8C2×D14911yescharacteristic, complemented
278#103C2×D14911yescharacteristic, complemented
279#102—1491no—
280#102—1491no—
281#102—1491no—
282#102—1491no—
283#102C2×D14911yescharacteristic, complemented
284C22⋊C8—1491no—
285C22⋊C8—1491no—
286#97—1491no—
287C24—2981no—
288C24—2981no—
289C24—2981no—
290#41—2982no—
291#41—5961no—
292C2×Q8C22×D14911yescharacteristic
293C2×D4—2981no—
294C2×D4—2981no—
295C2×D4—2981no—
296C2×D4—2982no—
297C2×D4—2982no—
298C2×D4—2982no—
299C2×D4—2981no—
300C2×D4—2981no—
301C2×D4—2981no—
302C2×D4—2981no—
303C2×D4—2981no—
304C2×D4—2981no—
305C2×D4—5964no—
306C2×D4—5961no—
307C2×D4—5961no—
308C2×D4—5961no—
309C2×D4—1491no—
310C2×D4—1491no—
311C2×D4—1491no—
312C2×D4—1491no—
313C2×D4C22×D14911yescharacteristic
314C2×D4C22×D14911yescharacteristic
315C22×C4—21no—
316C22×C4—2981no—
317C22×C4—2981no—
318C22×C4—1491no—
319C22×C4—1491no—
320SD16—22no—
321SD16—2982no—
322SD16—5961no—
323D8—22no—
324D8—2982no—
325D8—2982no—
326D8—2982no—
327D8—5961no—
328D8—1494no—
329M16—2982no—
330C2×C8—2982no—
331C2×C8—1491no—
332C2×C8—1491no—
333C2×C8C22×D14911yescharacteristic
334C2×C8C22×D14911yescharacteristic
335C4⋊C4—2981no—
336C4⋊C4—1491no—
337C4⋊C4—1491no—
338C4⋊C4C22×D14911yescharacteristic
339C22⋊C4—21no—
340C22⋊C4—21no—
341C22⋊C4—21no—
342C22⋊C4—2981no—
343C22⋊C4—2981no—
344C22⋊C4—2981no—
345C22⋊C4—2981no—
346C22⋊C4—2981no—
347C22⋊C4—1491no—
348C22⋊C4—1491no—
349C42C22×D14911yescharacteristic
350C23—21no—
351C23—21no—
352C23—2981no—
353C23—2981no—
354C23—2981no—
355C23—5962no—
356C23—5962no—
357C23—5962no—
358C23—5962no—
359C23—5962no—
360C23—5962no—
361C23—1491no—
362C23—1491no—
363C23—11921no—
364C23—11921no—
365C23—11921no—
366Q8—21no—
367Q8—21no—
368D4—21no—
369D4—21no—
370D4—21no—
371D4—2982no—
372D4—2981no—
373D4—2981no—
374D4—2981no—
375D4—2981no—
376D4—2981no—
377D4—5962no—
378D4—5962no—
379D4—5962no—
380D4—5962no—
381D4—5962no—
382D4—5962no—
383D4—5962no—
384D4—1492no—
385D4—11921no—
386D4—11921no—
387D4D4×D14912yes—
388C2×C4—21no—
389C2×C4—21no—
390C2×C4—42no—
391C2×C4—2981no—
392C2×C4—2981no—
393C2×C4—2981no—
394C2×C4—2981no—
395C2×C4—2981no—
396C2×C4—5962no—
397C2×C4—1491no—
398C2×C4—1491no—
399C2×C4—11921no—
400C2×C4D4×D14911yescharacteristic
401C2×C4D4×D14911yescharacteristic
402C2×C4C23×D14911yescharacteristic
403C8—21no—
404C8—21no—
405C8—2981no—
406C8—1492no—
407C22—22no—
408C22—41no—
409C22—41no—
410C22—41no—
411C22—41no—
412C22—41no—
413C22—2981no—
414C22—2981no—
415C22—2981no—
416C22—2981no—
417C22—2981no—
418C22—2982no—
419C22—5961no—
420C22—5961no—
421C22—5961no—
422C22—5961no—
423C22—5961no—
424C22—5961no—
425C22—5961no—
426C22—5961no—
427C22—1492no—
428C22—11924no—
429C22—11924no—
430C22—11924no—
431C22C2×D4×D14911yescharacteristic
432C4—21no—
433C4—21no—
434C4—41no—
435C4—41no—
436C4—2981no—
437C4—2981no—
438C4—5961no—
439C4C2×D4×D14911yescharacteristic
440C4#1801195711yescharacteristic
441C2—42no—
442C2—81no—
443C2—2982no—
444C2—5961no—
445C2—5962no—
446C2—11921no—
447C2—11921no—
448C2#2375025911yescharacteristic
449C2AGL(1,ℤ/8)×D14911yescharacteristic
450C2#2375042711yescharacteristic
subgroupG/H
centerC22C2×D4×D149
commutator, cosocleC2×C4×C149C24
FrattiniC2×C4C23×D149
Fitting#463×C149C2
socleC22×C149C22×D4
hypercenter#463D149
hypocenterC149#3264
LCSG ▷ C2×C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C22 ◁ C42 ◁ #463

Complements

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

NH ≅ G/Ntype
1. C2×#18011938C2semidirect
2. C2×D8×D149C2semidirect
3. #23750268C2semidirect
4. D4×D596C2semidirect
5. #23750015C2semidirect
6. #23749877C2semidirect
7. #23749857C2semidirect
8. #23749821C2semidirect
9. #23749774C2semidirect
10. #23749773C2semidirect
11. #23749760C2semidirect
12. #23749757C2semidirect
13. #23749735C2semidirect
14. #23749695C2semidirect
15. #463×C149C2semidirect
16. C2×#14558737C22semidirect
19. C2×D4×D149C22semidirect
20. C2×D4×D149C22semidirect
22. C2×#14558723C22semidirect
23. C2×#14558723C22semidirect
24. C2×D1192C22semidirect
25. C2×D1192C22semidirect
27. C2×#14558721C22semidirect
28. C2×#14558721C22semidirect
30. C2×#14558719C22semidirect
31. C2×C8×D149C22semidirect
32. #18011908C22semidirect
34. #18011887C22semidirect
36. #18011886C22semidirect
39. #18011882C22semidirect
44. C4×D596C22semidirect
46. #18011842C22semidirect
47. #18011833C22semidirect
48. #18011833C22semidirect
49. #18011832C22semidirect
50. #18011831C22semidirect
51. #18011823C22semidirect
52. #18011823C22semidirect
53. #18011822C22semidirect
54. C2×SD16×C149C22semidirect
56. #124×C149C22semidirect
57. C4×D4×C149C22semidirect
58. C4⋊C8×C149C22semidirect
59. #103×C149C22semidirect
60. #102×C149C22semidirect
96. #14558721D4semidirect
149. D596C2×D4semidirect
164. #11924746C2×D4semidirect
205. C2×D149AGL(1,ℤ/8)semidirect
225. C149#3264semidirect
234. #463D149semidirect
250. C2×SD16C2×D149semidirect
261. #124C2×D149semidirect
274. C4×D4C2×D149semidirect
277. C4⋊C8C2×D149semidirect
278. #103C2×D149semidirect
283. #102C2×D149semidirect

Maximal subgroups

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

subgroupindex
C2×#180119382
C2×D8×D1492
#237502682
D4×D5962
#237500152
#237498772
#237498572
#237498212
#237497742
#237497732
#237497602
#237497572
#237497352
#237496952
#463×C1492
#3264149