Subgroups — #36368578

Order 22144.

98 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#26012412	C₂	1	1	yes	maximal, characteristic
2	#26012355	C₂	1	1	yes	maximal, characteristic
3	#26011869	C₂	1	1	yes	maximal, characteristic
4	C₂×#14583829	—	2	1	no	—
5	C₄⋊#13063443	—	2	1	no	—
6	C₂×Dic₆₉₂	C₄	1	1	yes	characteristic
7	C₂×#14583816	—	2	1	no	—
8	#19149677	—	2	1	no	—
9	C₈×Dic₁₇₃	C₂²	1	1	yes	characteristic
10	C₂×Q₁₆×C₁₇₃	C₄	1	1	yes	characteristic
11	C₂×#13063443	—	4	1	no	—
12	#14583829	—	4	1	no	—
13	C₂×Dic₃₄₆	—	2	1	no	—
14	Dic₆₉₂	—	4	1	no	—
15	#14583816	—	4	1	no	—
16	#14583816	—	4	1	no	—
17	C₂×#13063436	D₄	1	1	yes	characteristic
18	#14583805	—	4	1	no	—
19	#14583805	—	4	1	no	—
20	C₄×Dic₁₇₃	D₄	1	1	yes	characteristic
21	C₂×Q₈×C₁₇₃	—	2	1	no	—
22	Q₁₆×C₁₇₃	—	4	1	no	—
23	C₂×C₈×C₁₇₃	C₂×C₄	1	1	yes	characteristic
24	#13063443	—	8	1	no	—
25	Dic₃₄₆	—	4	1	no	—
26	Dic₃₄₆	—	4	1	no	—
27	C₂×Dic₁₇₃	—	4	1	no	—
28	C₂×Dic₁₇₃	D₈	1	1	yes	characteristic
29	C₂×Dic₁₇₃	SD₁₆	1	1	yes	characteristic
30	#13063436	D₈	1	1	yes	characteristic
31	#13063436	SD₁₆	1	1	yes	characteristic
32	Q₈×C₁₇₃	—	4	1	no	—
33	Q₈×C₁₇₃	—	4	1	no	—
34	C₂×C₄×C₁₇₃	—	4	1	no	—
35	C₂×C₄×C₁₇₃	C₂²⋊C₄	1	1	yes	characteristic
36	C₈×C₁₇₃	—	2	1	no	—
37	C₂²×C₁₇₃	#102	1	1	yes	characteristic
38	C₄×C₁₇₃	—	8	1	no	—
39	C₄×C₁₇₃	#100	1	1	yes	characteristic
40	C₄×C₁₇₃	#102	1	1	yes	characteristic
41	Dic₁₇₃	—	2	1	no	—
42	Dic₁₇₃	—	8	1	no	—
43	Dic₁₇₃	SD₃₂	1	1	yes	characteristic
44	Dic₁₇₃	Q₃₂	1	1	yes	characteristic
45	C₂×C₁₇₃	#331	1	1	yes	characteristic
46	C₂×C₁₇₃	#358	1	1	yes	characteristic
47	C₂×C₁₇₃	#362	1	1	yes	characteristic
48	C₁₇₃	#1362	1	1	yes	characteristic, complemented, Sylow
49	#1362	—	173	1	no	maximal, Sylow
50	#494	—	173	1	no	—
51	C₄⋊C₁₆	—	173	1	no	—
52	#335	—	173	1	no	—
53	C₂×Q₁₆	—	346	1	no	—
54	C₂×Q₁₆	—	173	1	no	—
55	C₂×Q₁₆	#10621924	1	1	yes	characteristic
56	C₄⋊Q₈	—	346	1	no	—
57	C₂×C₁₆	—	346	1	no	—
58	C₄⋊C₈	—	346	1	no	—
59	C₄×C₈	—	173	1	no	—
60	C₂×Q₈	—	2	1	no	—
61	C₂×Q₈	—	346	1	no	—
62	Q₁₆	—	4	1	no	—
63	Q₁₆	—	692	1	no	—
64	Q₁₆	—	692	1	no	—
65	Q₁₆	—	692	1	no	—
66	C₂×C₈	—	173	1	no	—
67	C₂×C₈	—	692	1	no	—
68	C₂×C₈	C₂×#10621924	1	1	yes	characteristic
69	C₄⋊C₄	—	692	1	no	—
70	C₄⋊C₄	—	692	1	no	—
71	C₄²	—	173	1	no	—
72	C₁₆	—	692	1	no	—
73	Q₈	—	4	1	no	—
74	Q₈	—	4	1	no	—
75	Q₈	—	692	1	no	—
76	Q₈	—	692	1	no	—
77	C₂×C₄	—	4	1	no	—
78	C₂×C₄	—	173	1	no	—
79	C₂×C₄	—	173	1	no	—
80	C₂×C₄	—	692	1	no	—
81	C₂×C₄	C₂²⋊#10621924	1	1	yes	characteristic
82	C₈	—	2	1	no	—
83	C₈	—	1384	1	no	—
84	C₈	—	173	1	no	—
85	C₈	—	173	1	no	—
86	C₂²	#19149741	1	1	yes	characteristic
87	C₄	—	8	1	no	—
88	C₄	—	346	1	no	—
89	C₄	—	1384	1	no	—
90	C₄	—	173	1	no	—
91	C₄	—	173	1	no	—
92	C₄	#19149739	1	1	yes	characteristic
93	C₄	#19149741	1	1	yes	characteristic
94	C₂	#26012349	1	1	yes	characteristic
95	C₂	#26012404	1	1	yes	characteristic
96	C₂	#26012410	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	#19149741
commutator	C₂×C₈×C₁₇₃	C₂×C₄
Frattini	C₂×C₈	C₂×#10621924
Fitting	C₂×Q₁₆×C₁₇₃	C₄
socle, prime radical	C₂²×C₁₇₃	#102
cosocle	C₈×Dic₁₇₃	C₂²
hypercenter	C₂×Q₁₆	#10621924
hypocenter	C₁₇₃	#1362
LCS	G ▷ C₂×C₈×C₁₇₃ ▷ C₂×C₄×C₁₇₃ ▷ C₂×C₁₇₃ ▷ C₁₇₃
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×C₈ ◁ C₂×Q₁₆

Complements

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

N	H ≅ G/N	type
48. C₁₇₃	#1362	semidirect

Maximal subgroups

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

subgroup	index
#26012412	2
#26012355	2
#26011869	2
#1362	173