Subgroups — #34059604

Order 19072.

92 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×#14558739	C₂	1	2	yes	maximal
2	C₈×#11924746	C₂	1	1	yes	maximal, characteristic
3	C₂×#14558739	C₄	1	4	yes	—
4	C₄×#11924746	C₄	1	1	yes	characteristic
5	C₄×#11924746	C₂²	1	1	yes	characteristic
6	C₄×C₈×C₁₄₉	C₄	1	1	yes	characteristic
7	#14558739	—	2	4	no	—
8	C₂×#11924746	C₈	1	2	yes	—
9	C₂×#11924746	C₂×C₄	1	2	yes	—
10	C₂×C₈×C₁₄₉	C₈	1	2	yes	—
11	C₄²×C₁₄₉	C₂×C₄	1	1	yes	characteristic
12	#11924746	—	2	2	no	—
13	#11924746	M₁₆	1	4	yes	—
14	C₂×C₄×C₁₄₉	C₄²	1	1	yes	characteristic
15	C₂×C₄×C₁₄₉	C₂×C₈	1	1	yes	characteristic
16	C₂×C₄×C₁₄₉	C₂×C₈	1	1	yes	characteristic
17	C₈×C₁₄₉	C₁₆	1	4	yes	complemented
18	C₂²×C₁₄₉	C₄×C₈	1	1	yes	characteristic
19	C₄×C₁₄₉	#97	1	2	yes	—
20	C₄×C₁₄₉	C₂×C₁₆	1	2	yes	—
21	C₄×C₁₄₉	M₃₂	1	2	yes	—
22	C₂×C₁₄₉	#322	1	1	yes	characteristic
23	C₂×C₁₄₉	C₄×C₁₆	1	1	yes	characteristic
24	C₂×C₁₄₉	#346	1	1	yes	characteristic
25	C₁₄₉	#1312	1	1	yes	characteristic, complemented, Sylow
26	#1312	—	149	1	no	maximal, Sylow
27	C₄×C₁₆	—	149	2	no	—
28	C₈²	—	149	1	no	—
29	C₂×C₁₆	—	149	4	no	—
30	C₄×C₈	—	149	1	no	—
31	C₄×C₈	—	149	1	no	—
32	C₄×C₈	#10597010	1	1	yes	characteristic
33	C₂×C₈	—	149	2	no	—
34	C₂×C₈	—	149	2	no	—
35	C₂×C₈	#11924753	1	2	yes	—
36	C₄²	C₂×#10597010	1	1	yes	characteristic
37	C₁₆	—	298	4	no	—
38	C₂×C₄	C₄×#10597010	1	1	yes	characteristic
39	C₂×C₄	C₂×#11924753	1	1	yes	characteristic
40	C₂×C₄	D₁₄₉⋊C₈	1	1	yes	characteristic
41	C₈	—	298	2	no	—
42	C₈	—	149	4	no	—
43	C₈	#14558739	1	4	yes	complemented
44	C₂²	C₄×#11924753	1	1	yes	characteristic
45	C₄	#18011965	1	2	yes	—
46	C₄	C₂×#14558739	1	2	yes	—
47	C₄	#18011986	1	2	yes	—
48	C₂	#23750466	1	1	yes	characteristic
49	C₂	C₄×#14558739	1	1	yes	characteristic
50	C₂	#23750514	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₄²	C₂×#10597010
commutator	C₂×C₁₄₉	C₄×C₁₆
Fitting	C₄×C₈×C₁₄₉	C₄
socle, prime radical	C₂²×C₁₄₉	C₄×C₈
cosocle	C₄×#11924746	C₂²
hypercenter	C₄×C₈	#10597010
hypocenter	C₁₄₉	#1312
LCS	G ▷ C₂×C₁₄₉ ▷ C₁₄₉
UCS	C₁ ◁ C₄² ◁ C₄×C₈

Complements

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

N	H ≅ G/N	type
17. C₈×C₁₄₉	C₁₆	semidirect
25. C₁₄₉	#1312	semidirect
43. C₈	#14558739	semidirect

Maximal subgroups

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

subgroup	index
C₄×#14558739	2
C₈×#11924746	2
#1312	149