Subgroups — Q₈×#14558739 #34061104

Order 19072.

134 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄⋊#14558739	C₂	1	3	yes	maximal
2	C₄×#14558739	C₂	1	3	yes	maximal
3	Q₈×#11924746	C₂	1	1	yes	maximal, characteristic
4	C₂×#14558739	C₂²	1	3	yes	—
5	C₂×#14558739	C₂²	1	1	yes	characteristic
6	C₄⋊#11924746	C₄	1	3	yes	—
7	C₄×#11924746	C₂²	1	3	yes	—
8	C₄×Q₈×C₁₄₉	C₄	1	1	yes	characteristic
9	#14558739	—	2	3	no	—
10	#14558739	Q₈	1	2	yes	direct product factor
11	C₂×#11924746	C₂×C₄	1	3	yes	—
12	C₂×#11924746	C₂³	1	1	yes	characteristic
13	C₂×Q₈×C₁₄₉	C₈	1	1	yes	characteristic
14	C₄⋊C₄×C₁₄₉	C₈	1	3	yes	—
15	C₄²×C₁₄₉	C₂×C₄	1	3	yes	—
16	#11924746	—	2	3	no	—
17	#11924746	C₂×Q₈	1	1	yes	characteristic
18	#11924746	#41	1	1	yes	characteristic
19	Q₈×C₁₄₉	C₁₆	1	4	yes	complemented
20	C₂×C₄×C₁₄₉	C₂×C₈	1	3	yes	—
21	C₂×C₄×C₁₄₉	C₂×C₈	1	3	yes	—
22	C₂×C₄×C₁₄₉	C₂²×C₄	1	1	yes	characteristic
23	C₂²×C₁₄₉	C₂²×C₈	1	1	yes	characteristic
24	C₄×C₁₄₉	—	2	3	no	—
25	C₄×C₁₄₉	C₂×C₁₆	1	6	yes	—
26	C₄×C₁₄₉	C₄×Q₈	1	1	yes	characteristic
27	C₄×C₁₄₉	#131	1	1	yes	characteristic
28	C₂×C₁₄₉	C₈×Q₈	1	1	yes	characteristic
29	C₂×C₁₄₉	C₂²×C₁₆	1	1	yes	characteristic
30	C₂×C₁₄₉	#504	1	1	yes	characteristic
31	C₁₄₉	Q₈×C₁₆	1	1	yes	characteristic, complemented, Sylow
32	Q₈×C₁₆	—	149	1	no	maximal, Sylow
33	C₈×Q₈	—	149	1	no	—
34	C₄⋊C₁₆	—	149	3	no	—
35	C₄×C₁₆	—	149	3	no	—
36	C₄×Q₈	#10597010	1	1	yes	characteristic
37	C₂×C₁₆	—	149	3	no	—
38	C₂×C₁₆	—	149	1	no	—
39	C₄⋊C₈	—	149	3	no	—
40	C₄×C₈	—	149	3	no	—
41	C₂×Q₈	#11924753	1	1	yes	characteristic
42	C₂×C₈	—	149	3	no	—
43	C₂×C₈	—	149	1	no	—
44	C₄⋊C₄	#11924753	1	3	yes	—
45	C₄²	C₂×#10597010	1	3	yes	—
46	C₁₆	—	298	3	no	—
47	C₁₆	—	149	2	no	—
48	Q₈	#14558739	1	4	yes	direct product factor
49	C₂×C₄	C₂×#11924753	1	3	yes	—
50	C₂×C₄	C₂×#11924753	1	3	yes	—
51	C₂×C₄	C₂²×#10597010	1	1	yes	characteristic
52	C₈	—	298	3	no	—
53	C₈	—	149	1	no	—
54	C₈	—	149	1	no	—
55	C₂²	C₂²×#11924753	1	1	yes	characteristic
56	C₄	—	2	3	no	—
57	C₄	C₂×#14558739	1	6	yes	—
58	C₄	Q₈×#10597010	1	1	yes	characteristic
59	C₄	#18011999	1	1	yes	characteristic
60	C₂	Q₈×#11924753	1	1	yes	characteristic
61	C₂	C₂²×#14558739	1	1	yes	characteristic
62	C₂	#23750683	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂×C₄	C₂²×#10597010
commutator	C₂×C₁₄₉	C₂²×C₁₆
Fitting	C₄×Q₈×C₁₄₉	C₄
socle, prime radical	C₂²×C₁₄₉	C₂²×C₈
cosocle	C₂×#11924746	C₂³
hypercenter	C₄×Q₈	#10597010
hypocenter	C₁₄₉	Q₈×C₁₆
LCS	G ▷ C₂×C₁₄₉ ▷ C₁₄₉
UCS	C₁ ◁ C₂×C₄ ◁ C₄×Q₈

Complements

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

N	H ≅ G/N	type
10. #14558739	Q₈	direct (N × H)
19. Q₈×C₁₄₉	C₁₆	semidirect
31. C₁₄₉	Q₈×C₁₆	semidirect
48. Q₈	#14558739	direct (N × H)

Maximal subgroups

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

subgroup	index
C₄⋊#14558739	2
C₄×#14558739	2
Q₈×#11924746	2
Q₈×C₁₆	149

Subgroups — Q8×#14558739 #34061104

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — Q₈×#14558739 #34061104