Finite Group Databasebeta

← #34080586

Subgroups — #34080586

Order 19328.

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×#18012765C211yesmaximal, characteristic, complemented
2C22×#14558989C211yesmaximal, characteristic, complemented
3#23752858C211yesmaximal, characteristic, complemented
4#23752599C211yesmaximal, characteristic, complemented
5#23752463C211yesmaximal, characteristic, complemented
6#23752439C211yesmaximal, characteristic, complemented
7#23752427C211yesmaximal, characteristic, complemented
8#23752404C211yesmaximal, characteristic, complemented
9#23752363C211yesmaximal, characteristic, complemented
10#23752355C211yesmaximal, characteristic, complemented
11#23752346C211yesmaximal, characteristic, complemented
12#23752345C211yesmaximal, characteristic, complemented
13#23752322C211yesmaximal, characteristic, complemented
14#23752284C211yesmaximal, characteristic, complemented
15D42×C151C211yesmaximal, characteristic, complemented
16C2×#14559004C2211yescharacteristic, complemented
17C22×D604C2211yescharacteristic, complemented
18#18012765—24no—
19C2×#14558992C2211yescharacteristic, complemented
20C2×#14558992C2211yescharacteristic, complemented
21C2×#14558992C2211yescharacteristic, complemented
22C2×#14558989—24no—
23C2×#14558989C2211yescharacteristic
24C2×#14558989C2211yescharacteristic
25C2×#14558989C2211yescharacteristic, complemented
26C2×#14558989C2211yescharacteristic, complemented
27C2×#14558989C2211yescharacteristic, complemented
28C2×#14558989C2211yescharacteristic, complemented
29C2×#14558988C2211yescharacteristic, complemented
30C22×C151⋊C8C2211yescharacteristic, complemented
31#18012727C2211yescharacteristic, complemented
32#18012724—21no—
33#18012718C2211yescharacteristic, complemented
34#18012713C2211yescharacteristic, complemented
35#18012712—21no—
36#18012707—21no—
37C4×D604C2211yescharacteristic, complemented
38C22⋊C4×D151—21no—
39#18012670C2211yescharacteristic, complemented
40C4⋊(C151⋊C8)C2211yescharacteristic, complemented
41#18012662C2211yescharacteristic, complemented
42#18012660C2211yescharacteristic, complemented
43#18012660C2211yescharacteristic, complemented
44#18012660C2211yescharacteristic, complemented
45#18012659C2211yescharacteristic, complemented
46#18012659C2211yescharacteristic, complemented
47C22⋊(C151⋊C8)C2211yescharacteristic, complemented
48C22⋊(C151⋊C8)C2211yescharacteristic, complemented
49#18012650C2211yescharacteristic, complemented
50C22×D4×C151—21no—
51C22×D4×C151C2211yescharacteristic
52C22×D4×C151C2211yescharacteristic, complemented
53#127×C151C2211yescharacteristic, complemented
54#121×C151—21no—
55#121×C151C2211yescharacteristic
56#121×C151C2211yescharacteristic, complemented
57#120×C151—21no—
58#120×C151—21no—
59C4×D4×C151C2211yescharacteristic
60C4×D4×C151C2211yescharacteristic, complemented
61C23×D151—21no—
62#14559004—22no—
63#14559004—41no—
64C2×Dic302C2311yescharacteristic
65C2×D604—22no—
66C2×D604—21no—
67C2×D604—41no—
68C2×D604C2311yescharacteristic
69C2×D604C2311yescharacteristic
70C2×C22⋊D151—21no—
71C2×C22⋊D151—21no—
72C2×C4×D151—21no—
73C2×C4×D151—21no—
74#14558992—22no—
75#14558992—22no—
76#14558992—41no—
77#14558989—22no—
78#14558989—22no—
79#14558989—22no—
80#14558989—22no—
81#14558989—41no—
82#14558989D414yescomplemented
83#14558988—22no—
84C2×C151⋊C8—22no—
85C2×C151⋊C8C2311yescharacteristic
86C2×C151⋊C8C2311yescharacteristic
87C2×C151⋊C8C2311yescharacteristic
88C2×C151⋊C8C2311yescharacteristic
89C4⋊Dic151C2311yescharacteristic
90Dic151⋊C4—21no—
91C22⋊Dic151—21no—
92(C2×D151)⋊C4—21no—
93(C2×D151)⋊C4—21no—
94(C2×D151)⋊C4—21no—
95(C2×D151)⋊C4—21no—
96C24×C151—21no—
97C24×C151—21no—
98C2×D4×C151—22no—
99C2×D4×C151—22no—
100C2×D4×C151—21no—
101C2×D4×C151—21no—
102C2×D4×C151—21no—
103C2×D4×C151—21no—
104C2×D4×C151—21no—
105C2×D4×C151—21no—
106C2×D4×C151—41no—
107C2×D4×C151—41no—
108C2×D4×C151—44no—
109C2×D4×C151D411yescharacteristic
110C2×D4×C151C2311yescharacteristic
111C2×D4×C151C2311yescharacteristic
112C2×D4×C151C2311yescharacteristic
113C22×C4×C151—21no—
114C22×C4×C151C2311yescharacteristic
115C22×C4×C151C2311yescharacteristic
116C4⋊C4×C151D411yescharacteristic
117C4⋊C4×C151C2311yescharacteristic
118C22⋊C4×C151—21no—
119C22⋊C4×C151—21no—
120C22⋊C4×C151—21no—
121C22⋊C4×C151D411yescharacteristic
122C22⋊C4×C151D411yescharacteristic
123C42×C151C2311yescharacteristic
124C22×D151—21no—
125C22×D151—21no—
126C22×D151—42no—
127C22×D151—42no—
128C22×D151—81no—
129Dic302—21no—
130Dic302—21no—
131D604—21no—
132D604—21no—
133D604—21no—
134D604—42no—
135D604C2×D412yescomplemented
136C22⋊D151—42no—
137C22⋊D151—81no—
138C2×Dic151—21no—
139C2×Dic151—21no—
140C4×D151—42no—
141C4×D151—81no—
142C151⋊C8—21no—
143C151⋊C8—21no—
144C151⋊C8—21no—
145C151⋊C8C2×D412yescomplemented
146C23×C151—21no—
147C23×C151—21no—
148C23×C151—21no—
149C23×C151—42no—
150C23×C151—42no—
151C23×C151—42no—
152C23×C151—42no—
153C23×C151—81no—
154C23×C151—81no—
155C23×C151C2×D411yescharacteristic
156C23×C151C2×D411yescharacteristic
157D4×C151—22no—
158D4×C151—21no—
159D4×C151—21no—
160D4×C151—21no—
161D4×C151—21no—
162D4×C151—21no—
163D4×C151—42no—
164D4×C151—42no—
165D4×C151—42no—
166D4×C151—42no—
167D4×C151—42no—
168D4×C151—81no—
169D4×C151C2×D412yes—
170C2×C4×C151—21no—
171C2×C4×C151—21no—
172C2×C4×C151—21no—
173C2×C4×C151—21no—
174C2×C4×C151—21no—
175C2×C4×C151—42no—
176C2×C4×C151C2×D411yescharacteristic
177C2×C4×C151C2×D411yescharacteristic
178C2×C4×C151C2×D411yescharacteristic
179C2×C4×C151C2×D411yescharacteristic
180C2×C4×C151C2411yescharacteristic
181C22×C151—21no—
182C22×C151—21no—
183C22×C151—21no—
184C22×C151—22no—
185C22×C151—21no—
186C22×C151—21no—
187C22×C151—41no—
188C22×C151—41no—
189C22×C151—41no—
190C22×C151—41no—
191C22×C151—41no—
192C22×C151—41no—
193C22×C151—41no—
194C22×C151—41no—
195C22×C151—84no—
196C22×C151—84no—
197C22×C151AGL(1,ℤ/8)12yescomplemented
198C22×C151C22×D411yescharacteristic
199C2×D151—22no—
200C2×D151—41no—
201C2×D151—41no—
202C2×D151—41no—
203C2×D151—41no—
204C2×D151—41no—
205C2×D151—84no—
206C4×C151—21no—
207C4×C151—21no—
208C4×C151—21no—
209C4×C151—21no—
210C4×C151—41no—
211C4×C151C22×D411yescharacteristic
212C4×C151H(5,𝔽2)11yescharacteristic
213Dic151—41no—
214Dic151—41no—
215C2×C151—22no—
216C2×C151—41no—
217C2×C151—42no—
218C2×C151—81no—
219C2×C151—81no—
220C2×C151D4211yescharacteristic
221C2×C151C2×AGL(1,ℤ/8)11yescharacteristic
222C2×C151#57611yescharacteristic
223D151—42no—
224D151—81no—
225C151#326411yescharacteristic, complemented, Sylow
226#3264—1511nomaximal, Sylow
227C2×AGL(1,ℤ/8)—1511no—
228C22×D8—1511no—
229#546—1511no—
230D42D15111yescharacteristic, complemented
231#496—1511no—
232#469—1511no—
233#465—1511no—
234#463—1511no—
235#459—1511no—
236#450—1511no—
237#449—1511no—
238#447—1511no—
239#447—1511no—
240#442—1511no—
241#435—1511no—
242C2×#41—1511no—
243C22×D4—21no—
244C22×D4—1511no—
245C22×D4C2×D15111yescharacteristic
246C22×D4C2×D15111yescharacteristic, complemented
247AGL(1,ℤ/8)—3024no—
248C2×SD16—1511no—
249C2×SD16—1511no—
250C2×SD16—1511no—
251C2×D8—3024no—
252C2×D8—1511no—
253C2×D8—1511no—
254C2×D8—1511no—
255C2×D8—1511no—
256C2×D8—1511no—
257C2×D8—1511no—
258C2×M16—1511no—
259C22×C8—1511no—
260#127C2×D15111yescharacteristic, complemented
261#124—1511no—
262#123—3021no—
263C22⋊Q8—1511no—
264#121—21no—
265#121—3021no—
266#121—1511no—
267#121C2×D15111yescharacteristic
268#121C2×D15111yescharacteristic, complemented
269#120—21no—
270#120—21no—
271#120—3021no—
272C4×D4—1511no—
273C4×D4C2×D15111yescharacteristic
274C4×D4C2×D15111yescharacteristic, complemented
275C2×C22⋊C4—3021no—
276#106—1511no—
277C4⋊C8—1511no—
278#103—1511no—
279#102—1511no—
280#102—1511no—
281#102—1511no—
282#102—1511no—
283#102—1511no—
284C22⋊C8—1511no—
285C22⋊C8—1511no—
286#97—1511no—
287C24—21no—
288C24—21no—
289C24—3021no—
290#41—3022no—
291#41—6041no—
292C2×Q8—1511no—
293C2×D4—22no—
294C2×D4—22no—
295C2×D4—21no—
296C2×D4—21no—
297C2×D4—21no—
298C2×D4—21no—
299C2×D4—21no—
300C2×D4—21no—
301C2×D4—41no—
302C2×D4—41no—
303C2×D4—44no—
304C2×D4—3022no—
305C2×D4—3021no—
306C2×D4—3021no—
307C2×D4—3021no—
308C2×D4—6041no—
309C2×D4—1511no—
310C2×D4—1511no—
311C2×D4C22⋊D15111yescharacteristic
312C2×D4C22×D15111yescharacteristic
313C2×D4C22×D15111yescharacteristic
314C2×D4C22×D15111yescharacteristic
315C22×C4—21no—
316C22×C4—3021no—
317C22×C4—3021no—
318C22×C4C22×D15111yescharacteristic
319C22×C4C22×D15111yescharacteristic
320SD16—3022no—
321SD16—3022no—
322SD16—6041no—
323D8—3022no—
324D8—3022no—
325D8—3022no—
326D8—3022no—
327D8—6041no—
328D8—1514no—
329M16—3022no—
330C2×C8—3022no—
331C2×C8—1511no—
332C2×C8—1511no—
333C2×C8—1511no—
334C2×C8—1511no—
335C4⋊C4—3021no—
336C4⋊C4—1511no—
337C4⋊C4C22⋊D15111yescharacteristic
338C4⋊C4C22×D15111yescharacteristic
339C22⋊C4—21no—
340C22⋊C4—21no—
341C22⋊C4—21no—
342C22⋊C4—3021no—
343C22⋊C4—3021no—
344C22⋊C4—3021no—
345C22⋊C4—3021no—
346C22⋊C4—3021no—
347C22⋊C4C22⋊D15111yescharacteristic
348C22⋊C4C22⋊D15111yescharacteristic
349C42C22×D15111yescharacteristic
350C23—21no—
351C23—21no—
352C23—21no—
353C23—42no—
354C23—42no—
355C23—42no—
356C23—42no—
357C23—81no—
358C23—81no—
359C23—3021no—
360C23—3021no—
361C23—6042no—
362C23—6042no—
363C23—12081no—
364C23C2×C22⋊D15111yescharacteristic
365C23C2×C22⋊D15111yescharacteristic
366Q8—3021no—
367Q8—3021no—
368D4—22no—
369D4—21no—
370D4—21no—
371D4—21no—
372D4—21no—
373D4—21no—
374D4—42no—
375D4—42no—
376D4—42no—
377D4—42no—
378D4—42no—
379D4—81no—
380D4—3021no—
381D4—3021no—
382D4—3021no—
383D4—6042no—
384D4—6042no—
385D4—1512no—
386D4—12081no—
387D4D4×D15112yes—
388C2×C4—21no—
389C2×C4—21no—
390C2×C4—21no—
391C2×C4—21no—
392C2×C4—21no—
393C2×C4—42no—
394C2×C4—3021no—
395C2×C4—3021no—
396C2×C4—6042no—
397C2×C4—12081no—
398C2×C4C2×C22⋊D15111yescharacteristic
399C2×C4C2×C22⋊D15111yescharacteristic
400C2×C4C2×C22⋊D15111yescharacteristic
401C2×C4C2×C22⋊D15111yescharacteristic
402C2×C4C23×D15111yescharacteristic
403C8—3021no—
404C8—3021no—
405C8—3021no—
406C8—1512no—
407C22—21no—
408C22—21no—
409C22—21no—
410C22—21no—
411C22—21no—
412C22—22no—
413C22—41no—
414C22—41no—
415C22—41no—
416C22—41no—
417C22—41no—
418C22—41no—
419C22—41no—
420C22—41no—
421C22—84no—
422C22—84no—
423C22—3022no—
424C22—6041no—
425C22—6041no—
426C22—6041no—
427C22—6041no—
428C22—6041no—
429C22—12084no—
430C22#1801276512yescomplemented
431C22C22×C22⋊D15111yescharacteristic
432C4—21no—
433C4—21no—
434C4—21no—
435C4—21no—
436C4—41no—
437C4—6041no—
438C4—6041no—
439C4C2×D4×D15111yescharacteristic
440C4#1801278411yescharacteristic
441C2—22no—
442C2—41no—
443C2—42no—
444C2—81no—
445C2—81no—
446C2—6042no—
447C2—12081no—
448C2D4×C22⋊D15111yescharacteristic
449C2C2×#1801276511yescharacteristic
450C2#2375301511yescharacteristic
subgroupG/H
centerC22C22×C22⋊D151
commutator, cosocleC2×C4×C151C24
FrattiniC2×C4C23×D151
FittingD42×C151C2
socleC22×C151C22×D4
hypercenterD42D151
hypocenterC151#3264
LCSG ▷ C2×C4×C151 ▷ C2×C151 ▷ C151
UCSC1 ◁ C22 ◁ C4×D4 ◁ D42

Complements

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

NH ≅ G/Ntype
1. C2×#18012765C2semidirect
2. C22×#14558989C2semidirect
3. #23752858C2semidirect
4. #23752599C2semidirect
5. #23752463C2semidirect
6. #23752439C2semidirect
7. #23752427C2semidirect
8. #23752404C2semidirect
9. #23752363C2semidirect
10. #23752355C2semidirect
11. #23752346C2semidirect
12. #23752345C2semidirect
13. #23752322C2semidirect
14. #23752284C2semidirect
15. D42×C151C2semidirect
16. C2×#14559004C22semidirect
17. C22×D604C22semidirect
19. C2×#14558992C22semidirect
20. C2×#14558992C22semidirect
21. C2×#14558992C22semidirect
25. C2×#14558989C22semidirect
26. C2×#14558989C22semidirect
27. C2×#14558989C22semidirect
28. C2×#14558989C22semidirect
29. C2×#14558988C22semidirect
30. C22×C151⋊C8C22semidirect
31. #18012727C22semidirect
33. #18012718C22semidirect
34. #18012713C22semidirect
37. C4×D604C22semidirect
39. #18012670C22semidirect
40. C4⋊(C151⋊C8)C22semidirect
41. #18012662C22semidirect
42. #18012660C22semidirect
43. #18012660C22semidirect
44. #18012660C22semidirect
45. #18012659C22semidirect
46. #18012659C22semidirect
47. C22⋊(C151⋊C8)C22semidirect
48. C22⋊(C151⋊C8)C22semidirect
49. #18012650C22semidirect
52. C22×D4×C151C22semidirect
53. #127×C151C22semidirect
56. #121×C151C22semidirect
60. C4×D4×C151C22semidirect
82. #14558989D4semidirect
135. D604C2×D4semidirect
145. C151⋊C8C2×D4semidirect
197. C22×C151AGL(1,ℤ/8)semidirect
225. C151#3264semidirect
230. D42D151semidirect
246. C22×D4C2×D151semidirect
260. #127C2×D151semidirect
268. #121C2×D151semidirect
274. C4×D4C2×D151semidirect
430. C22#18012765semidirect

Maximal subgroups

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

subgroupindex
C2×#180127652
C22×#145589892
#237528582
#237525992
#237524632
#237524392
#237524272
#237524042
#237523632
#237523552
#237523462
#237523452
#237523222
#237522842
D42×C1512
#3264151