Subgroups — #36368608

Order 22144.

148 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#19149753	C₂	1	2	yes	maximal
2	C₂×C₈×Dic₁₇₃	C₂	1	1	yes	maximal, characteristic
3	#19149753	—	2	2	no	—
4	#19149753	C₄	1	4	yes	complemented
5	C₂×#14583829	—	2	2	no	—
6	C₂²×#13063436	C₂²	1	1	yes	characteristic
7	C₂×C₄×Dic₁₇₃	C₄	1	1	yes	characteristic
8	C₈×Dic₁₇₃	—	2	2	no	—
9	C₂²×C₈×C₁₇₃	C₄	1	1	yes	characteristic
10	#14583829	—	2	4	no	—
11	C₂²×Dic₁₇₃	—	2	1	no	—
12	C₂×#13063436	C₂×C₄	1	2	yes	—
13	C₂×#13063436	D₄	1	2	yes	—
14	C₂×#13063436	D₄	1	1	yes	characteristic
15	C₂×#13063436	Q₈	1	1	yes	characteristic
16	C₄×Dic₁₇₃	—	2	1	no	—
17	C₄×Dic₁₇₃	C₈	1	2	yes	—
18	C₂²×C₄×C₁₇₃	C₂×C₄	1	1	yes	characteristic
19	C₂×C₈×C₁₇₃	—	2	1	no	—
20	C₂×C₈×C₁₇₃	—	2	1	no	—
21	C₂×C₈×C₁₇₃	C₈	1	2	yes	—
22	C₂×Dic₁₇₃	—	2	4	no	—
23	C₂×Dic₁₇₃	—	2	2	no	—
24	#13063436	C₂²⋊C₄	1	2	yes	—
25	#13063436	C₄⋊C₄	1	2	yes	—
26	C₂³×C₁₇₃	M₁₆	1	1	yes	characteristic
27	C₂×C₄×C₁₇₃	C₄²	1	1	yes	characteristic
28	C₂×C₄×C₁₇₃	C₂²⋊C₄	1	1	yes	characteristic
29	C₂×C₄×C₁₇₃	C₄⋊C₄	1	1	yes	characteristic
30	C₂×C₄×C₁₇₃	C₂×C₈	1	1	yes	characteristic
31	C₂×C₄×C₁₇₃	C₂×C₈	1	1	yes	characteristic
32	C₂×C₄×C₁₇₃	M₁₆	1	1	yes	characteristic
33	C₈×C₁₇₃	—	2	2	no	—
34	C₂²×C₁₇₃	—	2	2	no	—
35	C₂²×C₁₇₃	#97	1	1	yes	characteristic
36	C₂²×C₁₇₃	C₂²⋊C₈	1	1	yes	characteristic
37	C₂²×C₁₇₃	C₄⋊C₈	1	1	yes	characteristic
38	C₄×C₁₇₃	#95	1	1	yes	characteristic
39	C₄×C₁₇₃	C₄×C₈	1	1	yes	characteristic
40	C₄×C₁₇₃	C₂²⋊C₈	1	1	yes	characteristic
41	C₄×C₁₇₃	C₄⋊C₈	1	1	yes	characteristic
42	Dic₁₇₃	—	2	4	no	—
43	C₂×C₁₇₃	—	2	1	no	—
44	C₂×C₁₇₃	—	2	1	no	—
45	C₂×C₁₇₃	#336	1	1	yes	characteristic
46	C₂×C₁₇₃	#364	1	2	yes	—
47	C₁₇₃	#1376	1	1	yes	characteristic, complemented, Sylow
48	#1376	—	173	1	no	maximal, Sylow
49	C₂×M₃₂	—	173	2	no	—
50	C₂×C₄×C₈	—	173	1	no	—
51	C₂²×C₈	—	173	1	no	—
52	C₂²×C₈	#10621924	1	1	yes	characteristic
53	C₂×C₄²	—	173	1	no	—
54	M₃₂	—	346	2	no	—
55	M₃₂	—	173	4	no	—
56	C₂×C₁₆	—	346	2	no	—
57	C₄×C₈	—	346	2	no	—
58	C₂²×C₄	—	346	1	no	—
59	C₂²×C₄	C₂×#10621924	1	1	yes	characteristic
60	C₂×C₈	—	2	1	no	—
61	C₂×C₈	—	2	1	no	—
62	C₂×C₈	—	173	2	no	—
63	C₂×C₈	—	173	2	no	—
64	C₂×C₈	—	173	1	no	—
65	C₂×C₈	—	173	1	no	—
66	C₂×C₈	#13063443	1	2	yes	—
67	C₄²	—	346	1	no	—
68	C₄²	—	173	2	no	—
69	C₁₆	—	346	4	no	—
70	C₂³	#14583836	1	1	yes	characteristic
71	C₂×C₄	—	346	4	no	—
72	C₂×C₄	—	346	2	no	—
73	C₂×C₄	C₄×#10621924	1	1	yes	characteristic
74	C₂×C₄	C₂²⋊#10621924	1	1	yes	characteristic
75	C₂×C₄	C₄⋊#10621924	1	1	yes	characteristic
76	C₂×C₄	C₂×#13063443	1	1	yes	characteristic
77	C₂×C₄	D₁₇₃⋊C₈	1	1	yes	characteristic
78	C₂×C₄	#14583835	1	1	yes	characteristic
79	C₈	—	2	2	no	—
80	C₈	—	173	2	no	—
81	C₈	—	173	2	no	—
82	C₂²	—	2	2	no	—
83	C₂²	#19149734	1	1	yes	characteristic
84	C₂²	#19149736	1	1	yes	characteristic
85	C₂²	C₄⋊#13063443	1	1	yes	characteristic
86	C₄	—	346	4	no	—
87	C₄	(C₂×#10621924)⋊C₄	1	1	yes	characteristic
88	C₄	C₄×#13063443	1	1	yes	characteristic
89	C₄	C₂²⋊#13063443	1	1	yes	characteristic
90	C₄	#19149746	1	1	yes	characteristic
91	C₂	—	2	1	no	—
92	C₂	—	2	1	no	—
93	C₂	#26012357	1	1	yes	characteristic
94	C₂	#26012413	1	2	yes	—

	subgroup	G/H
center	C₂×C₄	C₄⋊#10621924
commutator	C₄×C₁₇₃	C₄×C₈
Frattini	C₂²×C₄	C₂×#10621924
Fitting	C₂²×C₈×C₁₇₃	C₄
socle	C₂²×C₁₇₃	C₄⋊C₈
prime radical	C₂³×C₁₇₃	M₁₆
cosocle	C₂²×#13063436	C₂²
hypercenter	C₂²×C₈	#10621924
hypocenter	C₁₇₃	#1376
LCS	G ▷ C₄×C₁₇₃ ▷ C₂×C₁₇₃ ▷ C₁₇₃
UCS	C₁ ◁ C₂×C₄ ◁ C₂²×C₄ ◁ C₂²×C₈

Complements

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

N	H ≅ G/N	type
4. #19149753	C₄	semidirect
47. C₁₇₃	#1376	semidirect

Maximal subgroups

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

subgroup	index
C₂×#19149753	2
C₂×C₈×Dic₁₇₃	2
#1376	173