Subgroups — #34059732

Order 19072.

140 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#18011985	C₂	1	2	yes	maximal
2	C₂×#18011822	C₂	1	1	yes	maximal, characteristic
3	#18011985	—	2	2	no	—
4	#18011985	—	2	2	no	—
5	C₂×#14558739	C₄	1	4	yes	complemented
6	C₂²×#11924746	C₄	1	1	yes	characteristic
7	C₂²×#11924746	C₂²	1	1	yes	characteristic
8	#18011822	—	2	2	no	—
9	C₂×C₄²×C₁₄₉	C₄	1	1	yes	characteristic
10	#14558739	—	2	4	no	—
11	C₂×#11924746	—	2	1	no	—
12	C₂×#11924746	—	2	1	no	—
13	C₂×#11924746	C₈	1	2	yes	—
14	C₂×#11924746	C₂×C₄	1	2	yes	—
15	C₂×#11924746	D₄	1	2	yes	—
16	C₂×#11924746	D₄	1	1	yes	characteristic
17	C₂×#11924746	Q₈	1	1	yes	characteristic
18	C₂²×C₄×C₁₄₉	—	2	1	no	—
19	C₂²×C₄×C₁₄₉	C₂×C₄	1	1	yes	characteristic
20	C₄²×C₁₄₉	—	2	1	no	—
21	C₄²×C₁₄₉	C₈	1	2	yes	—
22	#11924746	—	2	2	no	—
23	#11924746	C₂²⋊C₄	1	2	yes	—
24	#11924746	C₄⋊C₄	1	2	yes	—
25	C₂³×C₁₄₉	M₁₆	1	1	yes	characteristic
26	C₂×C₄×C₁₄₉	—	2	2	no	—
27	C₂×C₄×C₁₄₉	—	4	2	no	—
28	C₂×C₄×C₁₄₉	C₄²	1	1	yes	characteristic
29	C₂×C₄×C₁₄₉	C₂²⋊C₄	1	1	yes	characteristic
30	C₂×C₄×C₁₄₉	C₄⋊C₄	1	1	yes	characteristic
31	C₂×C₄×C₁₄₉	C₂×C₈	1	1	yes	characteristic
32	C₂×C₄×C₁₄₉	C₂×C₈	1	1	yes	characteristic
33	C₂×C₄×C₁₄₉	M₁₆	1	1	yes	characteristic
34	C₂²×C₁₄₉	—	2	2	no	—
35	C₂²×C₁₄₉	#97	1	1	yes	characteristic
36	C₂²×C₁₄₉	C₂²⋊C₈	1	1	yes	characteristic
37	C₂²×C₁₄₉	C₄⋊C₈	1	1	yes	characteristic
38	C₄×C₁₄₉	—	4	2	no	—
39	C₄×C₁₄₉	#95	1	1	yes	characteristic
40	C₄×C₁₄₉	C₄×C₈	1	1	yes	characteristic
41	C₄×C₁₄₉	C₂²⋊C₈	1	1	yes	characteristic
42	C₄×C₁₄₉	C₄⋊C₈	1	1	yes	characteristic
43	C₂×C₁₄₉	—	2	1	no	—
44	C₂×C₁₄₉	—	2	1	no	—
45	C₂×C₁₄₉	#336	1	1	yes	characteristic
46	C₂×C₁₄₉	#347	1	2	yes	—
47	C₁₄₉	#1375	1	1	yes	characteristic, complemented, Sylow
48	#1375	—	149	1	no	maximal, Sylow
49	C₂×M₃₂	—	149	2	no	—
50	C₂×#97	—	149	1	no	—
51	C₂²×C₈	—	149	1	no	—
52	C₂²×C₈	—	149	1	no	—
53	C₂×C₄²	#10597010	1	1	yes	characteristic
54	M₃₂	—	298	2	no	—
55	M₃₂	—	298	2	no	—
56	C₂×C₁₆	—	149	4	no	—
57	#97	—	298	2	no	—
58	C₂²×C₄	—	2	1	no	—
59	C₂²×C₄	C₂×#10597010	1	1	yes	characteristic
60	C₂×C₈	—	298	1	no	—
61	C₂×C₈	—	298	1	no	—
62	C₂×C₈	—	149	2	no	—
63	C₂×C₈	—	149	2	no	—
64	C₂×C₈	—	149	2	no	—
65	C₂×C₈	—	149	1	no	—
66	C₂×C₈	—	149	1	no	—
67	C₄²	—	2	1	no	—
68	C₄²	#11924753	1	2	yes	—
69	C₁₆	—	298	4	no	—
70	C₂³	#14558745	1	1	yes	characteristic
71	C₂×C₄	—	2	2	no	—
72	C₂×C₄	—	4	2	no	—
73	C₂×C₄	C₄×#10597010	1	1	yes	characteristic
74	C₂×C₄	C₂²⋊#10597010	1	1	yes	characteristic
75	C₂×C₄	C₄⋊#10597010	1	1	yes	characteristic
76	C₂×C₄	C₂×#11924753	1	1	yes	characteristic
77	C₂×C₄	D₁₄₉⋊C₈	1	1	yes	characteristic
78	C₂×C₄	#14558746	1	1	yes	characteristic
79	C₈	—	298	2	no	—
80	C₈	—	149	2	no	—
81	C₈	—	149	2	no	—
82	C₂²	—	2	2	no	—
83	C₂²	#18011966	1	1	yes	characteristic
84	C₂²	C₂²⋊#11924753	1	1	yes	characteristic
85	C₂²	#18011978	1	1	yes	characteristic
86	C₄	—	4	2	no	—
87	C₄	(C₂×#10597010)⋊C₄	1	1	yes	characteristic
88	C₄	C₄×#11924753	1	1	yes	characteristic
89	C₄	#18011968	1	1	yes	characteristic
90	C₄	C₄⋊#11924753	1	1	yes	characteristic
91	C₂	—	2	1	no	—
92	C₂	—	2	1	no	—
93	C₂	#23750491	1	1	yes	characteristic
94	C₂	#23750517	1	2	yes	—

	subgroup	G/H
center	C₂×C₄	C₄×#10597010
commutator	C₄×C₁₄₉	C₄×C₈
Frattini	C₂²×C₄	C₂×#10597010
Fitting	C₂×C₄²×C₁₄₉	C₄
socle	C₂²×C₁₄₉	#97
prime radical	C₂³×C₁₄₉	M₁₆
cosocle	C₂²×#11924746	C₂²
hypercenter	C₂×C₄²	#10597010
hypocenter	C₁₄₉	#1375
LCS	G ▷ C₄×C₁₄₉ ▷ C₁₄₉
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄²

Complements

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

N	H ≅ G/N	type
5. C₂×#14558739	C₄	semidirect
47. C₁₄₉	#1375	semidirect

Maximal subgroups

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

subgroup	index
C₂×#18011985	2
C₂×#18011822	2
#1375	149