Subgroups — Q₈×#11924753 #23750673

Order 9536.

102 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄⋊#11924753	C₂	1	3	yes	maximal
2	C₄×#11924753	C₂	1	3	yes	maximal
3	Q₈×Dic₁₄₉	C₂	1	1	yes	maximal, characteristic
4	C₂×#11924753	C₂²	1	3	yes	—
5	C₂×#11924753	C₂²	1	1	yes	characteristic
6	C₄⋊Dic₁₄₉	C₄	1	3	yes	—
7	C₄×Dic₁₄₉	C₂²	1	3	yes	—
8	C₂×Q₈×C₁₄₉	C₄	1	1	yes	characteristic
9	#11924753	—	2	3	no	—
10	#11924753	Q₈	1	2	yes	direct product factor
11	C₂×Dic₁₄₉	C₂×C₄	1	3	yes	—
12	C₂×Dic₁₄₉	C₂³	1	1	yes	characteristic
13	Q₈×C₁₄₉	C₈	1	4	yes	complemented
14	C₂×C₄×C₁₄₉	C₂×C₄	1	3	yes	—
15	C₂²×C₁₄₉	C₂²×C₄	1	1	yes	characteristic
16	C₄×C₁₄₉	C₂×C₈	1	6	yes	—
17	Dic₁₄₉	—	2	3	no	—
18	Dic₁₄₉	C₂×Q₈	1	1	yes	characteristic
19	Dic₁₄₉	#41	1	1	yes	characteristic
20	C₂×C₁₄₉	C₄×Q₈	1	1	yes	characteristic
21	C₂×C₁₄₉	C₂²×C₈	1	1	yes	characteristic
22	C₂×C₁₄₉	#131	1	1	yes	characteristic
23	C₁₄₉	C₈×Q₈	1	1	yes	characteristic, complemented, Sylow
24	C₈×Q₈	—	149	1	no	maximal, Sylow
25	C₄×Q₈	—	149	1	no	—
26	C₄⋊C₈	—	149	3	no	—
27	C₄×C₈	—	149	3	no	—
28	C₂×Q₈	#10597010	1	1	yes	characteristic
29	C₂×C₈	—	149	3	no	—
30	C₂×C₈	—	149	1	no	—
31	C₄⋊C₄	—	149	3	no	—
32	C₄²	—	149	3	no	—
33	Q₈	#11924753	1	4	yes	direct product factor
34	C₂×C₄	—	149	3	no	—
35	C₂×C₄	—	149	1	no	—
36	C₂×C₄	C₂×#10597010	1	3	yes	—
37	C₈	—	298	3	no	—
38	C₈	—	149	2	no	—
39	C₂²	C₂²×#10597010	1	1	yes	characteristic
40	C₄	—	298	3	no	—
41	C₄	—	149	1	no	—
42	C₄	—	149	1	no	—
43	C₄	C₂×#11924753	1	6	yes	—
44	C₂	Q₈×#10597010	1	1	yes	characteristic
45	C₂	C₂²×#11924753	1	1	yes	characteristic
46	C₂	#18011999	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂²×#10597010
commutator	C₂×C₁₄₉	C₂²×C₈
Fitting	C₂×Q₈×C₁₄₉	C₄
socle, prime radical	C₂²×C₁₄₉	C₂²×C₄
cosocle	C₂×Dic₁₄₉	C₂³
hypercenter	C₂×Q₈	#10597010
hypocenter	C₁₄₉	C₈×Q₈
LCS	G ▷ C₂×C₁₄₉ ▷ C₁₄₉
UCS	C₁ ◁ C₂² ◁ C₂×Q₈

Complements

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

N	H ≅ G/N	type
10. #11924753	Q₈	direct (N × H)
13. Q₈×C₁₄₉	C₈	semidirect
23. C₁₄₉	C₈×Q₈	semidirect
33. Q₈	#11924753	direct (N × H)

Subgroups — Q8×#11924753 #23750673

Conjugacy classes of subgroups

Complements

Subgroups — Q₈×#11924753 #23750673