Finite Group Databasebeta

← #34080590

Subgroups — #34080590

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×#18012763C211yesmaximal, characteristic, complemented
2#23752856C211yesmaximal, characteristic, complemented
3D4×C22⋊D151C211yesmaximal, characteristic, complemented
4#23752600C211yesmaximal, characteristic, complemented
5#23752462C211yesmaximal, characteristic, complemented
6#23752441C211yesmaximal, characteristic, complemented
7#23752425C211yesmaximal, characteristic, complemented
8#23752405C211yesmaximal, characteristic, complemented
9#23752363C211yesmaximal, characteristic, complemented
10#23752354C211yesmaximal, characteristic, complemented
11#23752346C211yesmaximal, characteristic, complemented
12#23752344C211yesmaximal, characteristic, complemented
13#23752324C211yesmaximal, characteristic, complemented
14#23752283C211yesmaximal, characteristic, complemented
15C22×D8×C151C211yesmaximal, characteristic, complemented
16C2×#14559003C2211yescharacteristic, complemented
17C22×C22⋊D151—21no—
18C2×D4×D151C2211yescharacteristic, complemented
19#18012763—24no—
20C2×#14558993C2211yescharacteristic, complemented
21C2×#14558992C2211yescharacteristic, complemented
22C2×#14558992C2211yescharacteristic, complemented
23C2×#14558989C2211yescharacteristic, complemented
24C2×#14558989C2211yescharacteristic, complemented
25C2×#14558987C2211yescharacteristic, complemented
26#18012735C2211yescharacteristic, complemented
27#18012726C2211yescharacteristic, complemented
28#18012720—21no—
29#18012718C2211yescharacteristic, complemented
30#18012713C2211yescharacteristic
31#18012711—21no—
32#18012711—21no—
33#18012710C2211yescharacteristic, complemented
34#18012710C2211yescharacteristic, complemented
35#18012708—21no—
36#18012708—21no—
37#18012707—21no—
38D4×Dic151C2211yescharacteristic, complemented
39D4×Dic151C2211yescharacteristic, complemented
40C4×C22⋊D151C2211yescharacteristic
41C2×C22⋊Dic151—21no—
42#18012671C2211yescharacteristic, complemented
43Dic151⋊C8C2211yescharacteristic, complemented
44#18012664C2211yescharacteristic, complemented
45#18012661C2211yescharacteristic, complemented
46#18012660C2211yescharacteristic, complemented
47#18012660C2211yescharacteristic, complemented
48#18012660C2211yescharacteristic, complemented
49#18012660C2211yescharacteristic, complemented
50C22⋊(C151⋊C8)C2211yescharacteristic, complemented
51(C2×D151)⋊C8C2211yescharacteristic, complemented
52#18012649C2211yescharacteristic, complemented
53C22×D4×C151C2211yescharacteristic
54C22×D4×C151C2211yescharacteristic, complemented
55C2×D8×C151—24no—
56C2×D8×C151C2211yescharacteristic
57C2×D8×C151C2211yescharacteristic
58C2×D8×C151C2211yescharacteristic, complemented
59C2×D8×C151C2211yescharacteristic, complemented
60C22×C8×C151C2211yescharacteristic, complemented
61C23×D151—21no—
62#14559003—22no—
63#14559003—41no—
64C2×Dic302C2311yescharacteristic
65C2×D604C2311yescharacteristic
66C2×C22⋊D151—21no—
67C2×C22⋊D151—21no—
68C2×C22⋊D151—21no—
69C2×C22⋊D151—21no—
70C2×C22⋊D151—21no—
71C2×C22⋊D151—21no—
72C2×C22⋊D151—21no—
73C2×C22⋊D151—44no—
74C2×C22⋊D151D411yescharacteristic
75D4×D151—22no—
76D4×D151—41no—
77C22×Dic151—21no—
78C22×Dic151—21no—
79C22×Dic151—21no—
80C2×C4×D151C2311yescharacteristic
81#14558993—22no—
82#14558992—22no—
83#14558992—41no—
84#14558989—22no—
85#14558989—41no—
86#14558987—22no—
87C2×C151⋊C8C2311yescharacteristic
88C2×C151⋊C8C2311yescharacteristic
89C4⋊Dic151C2311yescharacteristic
90C4⋊Dic151C2311yescharacteristic
91Dic151⋊C4—21no—
92Dic151⋊C4D411yescharacteristic
93C22⋊Dic151—21no—
94C22⋊Dic151—21no—
95C22⋊Dic151—21no—
96C22⋊Dic151—21no—
97C22⋊Dic151—21no—
98C22⋊Dic151—21no—
99C22⋊Dic151—21no—
100C22⋊Dic151D411yescharacteristic
101(C2×D151)⋊C4—21no—
102(C2×D151)⋊C4D411yescharacteristic
103C4×Dic151C2311yescharacteristic
104C24×C151—21no—
105C24×C151—21no—
106C2×D4×C151—22no—
107C2×D4×C151—22no—
108C2×D4×C151—21no—
109C2×D4×C151—21no—
110C2×D4×C151—41no—
111C2×D4×C151—41no—
112C2×D4×C151C2311yescharacteristic
113C2×D4×C151C2311yescharacteristic
114C2×D4×C151C2311yescharacteristic
115C2×D4×C151C2311yescharacteristic
116C22×C4×C151C2311yescharacteristic
117D8×C151—22no—
118D8×C151—22no—
119D8×C151—22no—
120D8×C151D414yescomplemented
121C2×C8×C151—22no—
122C2×C8×C151C2311yescharacteristic
123C2×C8×C151C2311yescharacteristic
124C22×D151—21no—
125C22×D151—42no—
126C22×D151—42no—
127C22×D151—81no—
128C22×D151C2×D411yescharacteristic
129Dic302—21no—
130Dic302—21no—
131D604—21no—
132D604—21no—
133C22⋊D151—22no—
134C22⋊D151—42no—
135C22⋊D151—42no—
136C22⋊D151—42no—
137C22⋊D151—42no—
138C22⋊D151—42no—
139C22⋊D151—81no—
140C22⋊D151—81no—
141C2×Dic151—21no—
142C2×Dic151—21no—
143C2×Dic151—21no—
144C2×Dic151—42no—
145C2×Dic151—42no—
146C2×Dic151—81no—
147C2×Dic151C2×D411yescharacteristic
148C2×Dic151C2×D411yescharacteristic
149C2×Dic151C2×D411yescharacteristic
150C4×D151—21no—
151C4×D151—21no—
152C151⋊C8—21no—
153C151⋊C8—21no—
154C23×C151—21no—
155C23×C151—21no—
156C23×C151—21no—
157C23×C151—21no—
158C23×C151—42no—
159C23×C151—42no—
160C23×C151—42no—
161C23×C151—42no—
162C23×C151—81no—
163C23×C151—81no—
164C23×C151C2×D411yescharacteristic
165D4×C151—21no—
166D4×C151—21no—
167D4×C151—21no—
168D4×C151—21no—
169D4×C151—21no—
170D4×C151—21no—
171D4×C151—42no—
172D4×C151—42no—
173D4×C151C2×D412yes—
174D4×C151C2×D412yescomplemented
175C2×C4×C151—21no—
176C2×C4×C151—21no—
177C2×C4×C151C2×D411yescharacteristic
178C2×C4×C151C2411yescharacteristic
179C8×C151—21no—
180C8×C151C2×D412yescomplemented
181C22×C151—21no—
182C22×C151—21no—
183C22×C151—22no—
184C22×C151—22no—
185C22×C151—41no—
186C22×C151—41no—
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—21no—
200C2×D151—21no—
201C2×D151—21no—
202C2×D151—41no—
203C2×D151—41no—
204C2×D151—41no—
205C2×D151—84no—
206C4×C151—21no—
207C4×C151C22×D411yescharacteristic
208C4×C151H(5,𝔽2)11yescharacteristic
209Dic151—21no—
210Dic151—21no—
211Dic151—21no—
212Dic151—41no—
213Dic151—41no—
214Dic151—41no—
215C2×C151—22no—
216C2×C151—42no—
217C2×C151—42no—
218C2×C151—81no—
219C2×C151—81no—
220C2×C151D4211yescharacteristic
221C2×C151C2×AGL(1,ℤ/8)11yescharacteristic
222C2×C151#57611yescharacteristic
223D151—41no—
224D151—81no—
225C151#326411yescharacteristic, complemented, Sylow
226#3264—1511nomaximal, Sylow
227C2×AGL(1,ℤ/8)—1511no—
228C22×D8D15111yescharacteristic, complemented
229#546—1511no—
230D42—1511no—
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—3021no—
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—24no—
252C2×D8—1511no—
253C2×D8—1511no—
254C2×D8C2×D15111yescharacteristic
255C2×D8C2×D15111yescharacteristic
256C2×D8C2×D15111yescharacteristic, complemented
257C2×D8C2×D15111yescharacteristic, complemented
258C2×M16—1511no—
259C22×C8C2×D15111yescharacteristic, complemented
260#127—1511no—
261#124—1511no—
262#123—3021no—
263C22⋊Q8—1511no—
264#121—3021no—
265#121—3021no—
266#121—1511no—
267#121—1511no—
268#121—1511no—
269#120—3021no—
270#120—3021no—
271#120—3021no—
272C4×D4—1511no—
273C4×D4—1511no—
274C4×D4—1511no—
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—41no—
298C2×D4—41no—
299C2×D4—3022no—
300C2×D4—3021no—
301C2×D4—3021no—
302C2×D4—3021no—
303C2×D4—3021no—
304C2×D4—3021no—
305C2×D4—3021no—
306C2×D4—3021no—
307C2×D4—6041no—
308C2×D4—6044no—
309C2×D4—1511no—
310C2×D4—1511no—
311C2×D4C22×D15111yescharacteristic
312C2×D4C22×D15111yescharacteristic
313C2×D4C22×D15111yescharacteristic
314C2×D4C22×D15111yescharacteristic
315C22×C4—3021no—
316C22×C4—3021no—
317C22×C4—3021no—
318C22×C4—1511no—
319C22×C4C22×D15111yescharacteristic
320SD16—3022no—
321SD16—3022no—
322SD16—6041no—
323D8—22no—
324D8—22no—
325D8—22no—
326D8—3022no—
327D8—6041no—
328D8C22⋊D15114yescomplemented
329M16—3022no—
330C2×C8—22no—
331C2×C8—1511no—
332C2×C8—1511no—
333C2×C8C22×D15111yescharacteristic
334C2×C8C22×D15111yescharacteristic
335C4⋊C4—3021no—
336C4⋊C4—1511no—
337C4⋊C4—1511no—
338C4⋊C4—1511no—
339C22⋊C4—3021no—
340C22⋊C4—3021no—
341C22⋊C4—3021no—
342C22⋊C4—3021no—
343C22⋊C4—3021no—
344C22⋊C4—3021no—
345C22⋊C4—3021no—
346C22⋊C4—3021no—
347C22⋊C4—1511no—
348C22⋊C4—1511no—
349C42—1511no—
350C23—21no—
351C23—21no—
352C23—21no—
353C23—21no—
354C23—42no—
355C23—42no—
356C23—42no—
357C23—42no—
358C23—81no—
359C23—81no—
360C23—3021no—
361C23—6042no—
362C23—6042no—
363C23—1511no—
364C23—12081no—
365C23D4×D15111yescharacteristic
366Q8—3021no—
367Q8—3021no—
368D4—21no—
369D4—21no—
370D4—21no—
371D4—21no—
372D4—21no—
373D4—21no—
374D4—42no—
375D4—42no—
376D4—3022no—
377D4—3021no—
378D4—3021no—
379D4—6042no—
380D4—6042no—
381D4—6042no—
382D4—6042no—
383D4—6042no—
384D4—12081no—
385D4—12081no—
386D4C2×C22⋊D15112yes—
387D4C2×C22⋊D15112yescomplemented
388C2×C4—21no—
389C2×C4—21no—
390C2×C4—3021no—
391C2×C4—3021no—
392C2×C4—3021no—
393C2×C4—3021no—
394C2×C4—3021no—
395C2×C4—6042no—
396C2×C4—6042no—
397C2×C4—1511no—
398C2×C4—1511no—
399C2×C4—1511no—
400C2×C4—12081no—
401C2×C4D4×D15111yescharacteristic
402C2×C4C23×D15111yescharacteristic
403C8—21no—
404C8—3021no—
405C8—3021no—
406C8C2×C22⋊D15112yescomplemented
407C22—21no—
408C22—21no—
409C22—22no—
410C22—22no—
411C22—41no—
412C22—41no—
413C22—41no—
414C22—41no—
415C22—41no—
416C22—41no—
417C22—41no—
418C22—41no—
419C22—41no—
420C22—41no—
421C22—84no—
422C22—84no—
423C22—3021no—
424C22—3021no—
425C22—3021no—
426C22—6041no—
427C22—6041no—
428C22—6041no—
429C22—12084no—
430C22#1801276312yescomplemented
431C22C2×D4×D15111yescharacteristic
432C4—21no—
433C4—3021no—
434C4—3021no—
435C4—3021no—
436C4—6041no—
437C4—6041no—
438C4—6041no—
439C4C22×C22⋊D15111yescharacteristic
440C4#1801278411yescharacteristic
441C2—22no—
442C2—42no—
443C2—42no—
444C2—81no—
445C2—81no—
446C2—6041no—
447C2—12081no—
448C2D4×C22⋊D15111yescharacteristic
449C2C2×#1801276311yescharacteristic
450C2#2375301311yescharacteristic
subgroupG/H
centerC22C2×D4×D151
commutator, cosocleC2×C4×C151C24
FrattiniC2×C4C23×D151
FittingC22×D8×C151C2
socleC22×C151C22×D4
hypercenterC22×D8D151
hypocenterC151#3264
LCSG ▷ C2×C4×C151 ▷ C2×C151 ▷ C151
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×D8

Complements

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

NH ≅ G/Ntype
1. C2×#18012763C2semidirect
2. #23752856C2semidirect
3. D4×C22⋊D151C2semidirect
4. #23752600C2semidirect
5. #23752462C2semidirect
6. #23752441C2semidirect
7. #23752425C2semidirect
8. #23752405C2semidirect
9. #23752363C2semidirect
10. #23752354C2semidirect
11. #23752346C2semidirect
12. #23752344C2semidirect
13. #23752324C2semidirect
14. #23752283C2semidirect
15. C22×D8×C151C2semidirect
16. C2×#14559003C22semidirect
18. C2×D4×D151C22semidirect
20. C2×#14558993C22semidirect
21. C2×#14558992C22semidirect
22. C2×#14558992C22semidirect
23. C2×#14558989C22semidirect
24. C2×#14558989C22semidirect
25. C2×#14558987C22semidirect
26. #18012735C22semidirect
27. #18012726C22semidirect
29. #18012718C22semidirect
33. #18012710C22semidirect
34. #18012710C22semidirect
38. D4×Dic151C22semidirect
39. D4×Dic151C22semidirect
42. #18012671C22semidirect
43. Dic151⋊C8C22semidirect
44. #18012664C22semidirect
45. #18012661C22semidirect
46. #18012660C22semidirect
47. #18012660C22semidirect
48. #18012660C22semidirect
49. #18012660C22semidirect
50. C22⋊(C151⋊C8)C22semidirect
51. (C2×D151)⋊C8C22semidirect
52. #18012649C22semidirect
54. C22×D4×C151C22semidirect
58. C2×D8×C151C22semidirect
59. C2×D8×C151C22semidirect
60. C22×C8×C151C22semidirect
120. D8×C151D4semidirect
174. D4×C151C2×D4semidirect
180. C8×C151C2×D4semidirect
197. C22×C151AGL(1,ℤ/8)semidirect
225. C151#3264semidirect
228. C22×D8D151semidirect
246. C22×D4C2×D151semidirect
256. C2×D8C2×D151semidirect
257. C2×D8C2×D151semidirect
259. C22×C8C2×D151semidirect
328. D8C22⋊D151semidirect
387. D4C2×C22⋊D151semidirect
406. C8C2×C22⋊D151semidirect
430. C22#18012763semidirect

Maximal subgroups

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

subgroupindex
C2×#180127632
#237528562
D4×C22⋊D1512
#237526002
#237524622
#237524412
#237524252
#237524052
#237523632
#237523542
#237523462
#237523442
#237523242
#237522832
C22×D8×C1512
#3264151