Subgroups — #34059835

Order 19072.

78 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#23750536	C₂	1	2	yes	maximal
2	#23749994	C₂	1	1	yes	maximal, characteristic
3	#18011972	—	2	2	no	—
4	#18011911	C₂²	1	1	yes	characteristic
5	#18011903	C₄	1	1	yes	characteristic
6	#18011836	—	2	2	no	—
7	#97×C₁₄₉	C₄	1	1	yes	characteristic
8	#14558745	—	4	2	no	—
9	C₂×Dic₂₉₈	D₄	1	2	yes	—
10	C₄⋊Dic₁₄₉	—	2	1	no	—
11	C₄⋊Dic₁₄₉	—	4	1	no	—
12	#14558715	—	4	1	no	—
13	C₂×C₈×C₁₄₉	—	2	1	no	—
14	C₄²×C₁₄₉	C₂×C₄	1	1	yes	characteristic
15	#11924753	—	8	2	no	—
16	Dic₂₉₈	—	4	2	no	—
17	C₂×Dic₁₄₉	—	2	2	no	—
18	C₂×Dic₁₄₉	—	4	1	no	—
19	C₂×C₄×C₁₄₉	—	2	1	no	—
20	C₂×C₄×C₁₄₉	C₂²⋊C₄	1	1	yes	characteristic
21	C₈×C₁₄₉	—	4	1	no	—
22	C₂²×C₁₄₉	#99	1	1	yes	characteristic
23	C₄×C₁₄₉	—	2	1	no	—
24	C₄×C₁₄₉	—	4	1	no	—
25	Dic₁₄₉	—	4	2	no	—
26	Dic₁₄₉	—	8	1	no	—
27	C₂×C₁₄₉	—	2	1	no	—
28	C₂×C₁₄₉	#354	1	1	yes	characteristic
29	C₁₄₉	#1413	1	1	yes	characteristic, complemented, Sylow
30	#1413	—	149	1	no	maximal, Sylow
31	#491	—	149	1	no	—
32	#356	—	149	2	no	—
33	C₄⋊Q₈	—	149	1	no	—
34	#125	—	149	1	no	—
35	#103	—	298	2	no	—
36	#101	—	298	2	no	—
37	#97	#10597010	1	1	yes	characteristic
38	C₂×Q₈	—	149	2	no	—
39	M₁₆	—	596	2	no	—
40	C₂×C₈	—	2	1	no	—
41	C₄⋊C₄	—	298	1	no	—
42	C₄⋊C₄	—	596	1	no	—
43	C₄⋊C₄	—	596	1	no	—
44	C₄²	C₂×#10597010	1	1	yes	characteristic
45	Q₈	—	596	2	no	—
46	C₂×C₄	—	2	1	no	—
47	C₂×C₄	—	298	2	no	—
48	C₂×C₄	—	596	1	no	—
49	C₂×C₄	C₂²⋊#10597010	1	1	yes	characteristic
50	C₈	—	4	1	no	—
51	C₈	—	1192	2	no	—
52	C₂²	#18011970	1	1	yes	characteristic
53	C₄	—	2	1	no	—
54	C₄	—	4	1	no	—
55	C₄	—	596	2	no	—
56	C₄	—	1192	1	no	—
57	C₂	—	2	1	no	—
58	C₂	#23750532	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#23750532
commutator	C₄²×C₁₄₉	C₂×C₄
Frattini	C₄²	C₂×#10597010
Fitting	#97×C₁₄₉	C₄
socle	C₂×C₁₄₉	#354
prime radical	C₂²×C₁₄₉	#99
cosocle	#18011911	C₂²
hypercenter	#97	#10597010
hypocenter	C₁₄₉	#1413
LCS	G ▷ C₄²×C₁₄₉ ▷ C₂×C₄×C₁₄₉ ▷ C₂²×C₁₄₉ ▷ C₂×C₁₄₉ ▷ C₁₄₉
UCS	C₁ ◁ C₂ ◁ C₂² ◁ C₂×C₄ ◁ C₄² ◁ #97

Complements

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

N	H ≅ G/N	type
29. C₁₄₉	#1413	semidirect

Maximal subgroups

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

subgroup	index
#23750536	2
#23749994	2
#1413	149