Subgroups — #34061114

Order 19072.

106 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#23750557	C₂	1	3	yes	maximal, complemented
2	C₂×#18011961	C₂	1	3	yes	maximal, complemented
3	#23750042	C₂	1	1	yes	maximal, characteristic
4	#18011961	C₂²	1	1	yes	characteristic
5	#18011961	C₂²	1	3	yes	—
6	#18011851	C₄	1	3	yes	—
7	C₂×#14558711	C₂²	1	3	yes	—
8	#131×C₁₄₉	C₄	1	1	yes	characteristic
9	#14558711	C₂×C₄	1	3	yes	—
10	#14558711	C₂³	1	1	yes	characteristic
11	#41×C₁₄₉	C₈	1	1	yes	characteristic
12	M₁₆×C₁₄₉	C₈	1	3	yes	—
13	C₂×C₈×C₁₄₉	C₂×C₄	1	3	yes	—
14	Q₈×C₁₄₉	C₁₆	1	1	yes	characteristic
15	D₄×C₁₄₉	C₁₆	1	3	yes	—
16	C₂×C₄×C₁₄₉	C₂×C₈	1	3	yes	—
17	C₈×C₁₄₉	C₂×C₈	1	3	yes	—
18	C₈×C₁₄₉	C₂²×C₄	1	1	yes	characteristic
19	C₂²×C₁₄₉	C₂×C₁₆	1	3	yes	—
20	C₄×C₁₄₉	C₂×C₁₆	1	3	yes	—
21	C₄×C₁₄₉	C₂²×C₈	1	1	yes	characteristic
22	C₂×C₁₄₉	—	2	3	no	—
23	C₂×C₁₄₉	C₂²×C₁₆	1	1	yes	characteristic
24	C₁₄₉	#2258	1	1	yes	characteristic, complemented, Sylow
25	#2258	—	149	1	no	maximal, Sylow
26	#504	—	149	1	no	—
27	M₆₄	—	149	3	no	—
28	C₂×C₃₂	—	149	3	no	—
29	#131	#10597010	1	1	yes	characteristic
30	M₃₂	—	149	3	no	—
31	C₂×C₁₆	—	149	3	no	—
32	C₃₂	—	149	1	no	—
33	C₃₂	—	149	3	no	—
34	#41	#11924753	1	1	yes	characteristic
35	M₁₆	#11924753	1	3	yes	—
36	C₂×C₈	C₂×#10597010	1	3	yes	—
37	C₁₆	—	149	1	no	—
38	C₁₆	—	149	3	no	—
39	Q₈	#14558739	1	1	yes	characteristic
40	D₄	#14558739	1	3	yes	—
41	C₂×C₄	C₂×#11924753	1	3	yes	—
42	C₈	C₂×#11924753	1	3	yes	—
43	C₈	C₂²×#10597010	1	1	yes	characteristic
44	C₂²	C₂×#14558739	1	3	yes	—
45	C₄	C₂×#14558739	1	3	yes	—
46	C₄	C₂²×#11924753	1	1	yes	characteristic
47	C₂	—	2	3	no	—
48	C₂	C₂²×#14558739	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₈	C₂²×#10597010
commutator, socle	C₂×C₁₄₉	C₂²×C₁₆
Fitting	#131×C₁₄₉	C₄
prime radical	#41×C₁₄₉	C₈
cosocle	#14558711	C₂³
hypercenter	#131	#10597010
hypocenter	C₁₄₉	#2258
LCS	G ▷ C₂×C₁₄₉ ▷ C₁₄₉
UCS	C₁ ◁ C₈ ◁ #131

Complements

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

N	H ≅ G/N	type
1. #23750557	C₂	semidirect
2. C₂×#18011961	C₂	semidirect
24. C₁₄₉	#2258	semidirect

Maximal subgroups

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

subgroup	index
#23750557	2
C₂×#18011961	2
#23750042	2
#2258	149