Subgroups — #34059828

Order 19072.

94 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#23750536	C₂	1	2	yes	maximal
2	#23750004	C₂	1	1	yes	maximal, characteristic
3	#18011972	—	2	2	no	—
4	C₂×#14558726	—	2	2	no	—
5	#18011911	C₂²	1	1	yes	characteristic
6	C₄×#11924746	C₄	1	1	yes	characteristic
7	C₄⋊Q₈×C₁₄₉	C₄	1	1	yes	characteristic
8	#14558745	—	4	2	no	—
9	C₂×Dic₂₉₈	D₄	1	2	yes	—
10	#14558726	—	4	4	no	—
11	C₂×#11924746	—	2	1	no	—
12	C₄⋊Dic₁₄₉	—	4	1	no	—
13	C₂×Q₈×C₁₄₉	—	2	1	no	—
14	C₄⋊C₄×C₁₄₉	—	4	1	no	—
15	C₄²×C₁₄₉	C₂×C₄	1	1	yes	characteristic
16	#11924753	—	8	2	no	—
17	Dic₂₉₈	—	4	2	no	—
18	C₂×Dic₁₄₉	—	2	2	no	—
19	#11924746	—	2	2	no	—
20	Q₈×C₁₄₉	—	4	2	no	—
21	C₂×C₄×C₁₄₉	—	2	1	no	—
22	C₂×C₄×C₁₄₉	—	4	1	no	—
23	C₂×C₄×C₁₄₉	C₂²⋊C₄	1	1	yes	characteristic
24	C₂²×C₁₄₉	#99	1	1	yes	characteristic
25	C₄×C₁₄₉	—	2	2	no	—
26	C₄×C₁₄₉	—	2	1	no	—
27	C₄×C₁₄₉	—	8	1	no	—
28	Dic₁₄₉	—	4	2	no	—
29	C₂×C₁₄₉	—	2	1	no	—
30	C₂×C₁₄₉	#353	1	1	yes	characteristic
31	C₁₄₉	#1411	1	1	yes	characteristic, complemented, Sylow
32	#1411	—	149	1	no	maximal, Sylow
33	#494	—	149	1	no	—
34	#356	—	149	2	no	—
35	C₂×Q₁₆	—	298	2	no	—
36	C₄⋊Q₈	—	149	1	no	—
37	C₄⋊Q₈	#10597010	1	1	yes	characteristic
38	#101	—	298	2	no	—
39	C₄×C₈	—	149	1	no	—
40	C₂×Q₈	—	2	1	no	—
41	C₂×Q₈	—	149	2	no	—
42	Q₁₆	—	596	4	no	—
43	M₁₆	—	596	2	no	—
44	C₂×C₈	—	298	1	no	—
45	C₄⋊C₄	—	4	1	no	—
46	C₄⋊C₄	—	596	1	no	—
47	C₄²	C₂×#10597010	1	1	yes	characteristic
48	Q₈	—	4	2	no	—
49	Q₈	—	596	2	no	—
50	C₂×C₄	—	2	1	no	—
51	C₂×C₄	—	4	1	no	—
52	C₂×C₄	—	298	2	no	—
53	C₂×C₄	C₂²⋊#10597010	1	1	yes	characteristic
54	C₈	—	298	2	no	—
55	C₈	—	1192	2	no	—
56	C₂²	#18011969	1	1	yes	characteristic
57	C₄	—	2	2	no	—
58	C₄	—	2	1	no	—
59	C₄	—	8	1	no	—
60	C₄	—	596	2	no	—
61	C₂	—	2	1	no	—
62	C₂	#23750529	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#23750529
commutator	C₄²×C₁₄₉	C₂×C₄
Frattini	C₄²	C₂×#10597010
Fitting	C₄⋊Q₈×C₁₄₉	C₄
socle	C₂×C₁₄₉	#353
prime radical	C₂²×C₁₄₉	#99
cosocle	#18011911	C₂²
hypercenter	C₄⋊Q₈	#10597010
hypocenter	C₁₄₉	#1411
LCS	G ▷ C₄²×C₁₄₉ ▷ C₂×C₄×C₁₄₉ ▷ C₂²×C₁₄₉ ▷ C₂×C₁₄₉ ▷ C₁₄₉
UCS	C₁ ◁ C₂ ◁ C₂² ◁ C₂×C₄ ◁ C₄² ◁ C₄⋊Q₈

Complements

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

N	H ≅ G/N	type
31. C₁₄₉	#1411	semidirect

Maximal subgroups

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

subgroup	index
#23750536	2
#23750004	2
#1411	149