Subgroups — C₂×#26045712 #37559408

Order 23872.

202 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×D₁₄₉₂	C₂	1	1	yes	maximal, characteristic
2	C₂²×#15688412	C₂	1	1	yes	maximal, characteristic, complemented
3	#26045712	C₂	1	4	yes	maximal, direct product factor
4	C₂×C₄⋊C₄×C₃₇₃	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂³×D₃₇₃	—	2	1	no	—
6	C₂×D₁₄₉₂	—	2	1	no	—
7	C₂×D₁₄₉₂	—	2	2	no	—
8	C₂×D₁₄₉₂	C₄	1	4	yes	complemented
9	C₂×D₁₄₉₂	C₂²	1	2	yes	—
10	C₂×#15688412	—	2	2	no	—
11	C₂×#15688412	C₂²	1	2	yes	complemented
12	C₂²×C₄×C₃₇₃	—	2	1	no	—
13	C₂²×C₄×C₃₇₃	C₂²	1	1	yes	characteristic
14	C₄⋊C₄×C₃₇₃	—	2	1	no	—
15	C₄⋊C₄×C₃₇₃	C₂²	1	2	yes	complemented
16	C₂²×D₃₇₃	—	2	4	no	—
17	C₂²×D₃₇₃	—	2	2	no	—
18	C₂²×D₃₇₃	—	4	2	no	—
19	C₂²×D₃₇₃	—	4	2	no	—
20	D₁₄₉₂	—	2	4	no	—
21	D₁₄₉₂	—	2	2	no	—
22	D₁₄₉₂	C₂×C₄	1	4	yes	complemented
23	#15688412	—	2	2	no	—
24	C₂³×C₃₇₃	D₄	1	1	yes	characteristic
25	C₂×C₄×C₃₇₃	—	2	2	no	—
26	C₂×C₄×C₃₇₃	—	4	2	no	—
27	C₂×C₄×C₃₇₃	C₂×C₄	1	2	yes	—
28	C₂×C₄×C₃₇₃	D₄	1	1	yes	characteristic
29	C₂×C₄×C₃₇₃	D₄	1	2	yes	—
30	C₂×C₄×C₃₇₃	C₂³	1	1	yes	characteristic
31	C₂²×C₃₇₃	C₂²⋊C₄	1	2	yes	—
32	C₂²×C₃₇₃	D₈	1	2	yes	—
33	C₂²×C₃₇₃	SD₁₆	1	2	yes	—
34	C₂²×C₃₇₃	C₂×D₄	1	1	yes	characteristic
35	C₂×D₃₇₃	—	2	4	no	—
36	C₂×D₃₇₃	—	4	8	no	—
37	C₂×D₃₇₃	—	4	2	no	—
38	C₂×D₃₇₃	—	4	2	no	—
39	C₄×C₃₇₃	—	4	2	no	—
40	C₄×C₃₇₃	C₂²⋊C₄	1	2	yes	—
41	C₄×C₃₇₃	C₂²×C₄	1	1	yes	characteristic
42	C₄×C₃₇₃	C₂×D₄	1	1	yes	characteristic
43	C₂×C₃₇₃	#102	1	4	yes	complemented
44	C₂×C₃₇₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
45	C₂×C₃₇₃	C₂×D₈	1	1	yes	characteristic
46	C₂×C₃₇₃	C₂×SD₁₆	1	1	yes	characteristic
47	D₃₇₃	—	4	4	no	—
48	C₃₇₃	C₂×#102	1	1	yes	characteristic, complemented, Sylow
49	C₂×#102	—	373	1	no	maximal, Sylow
50	C₂²×D₄	—	373	1	no	—
51	C₂²×C₈	—	373	1	no	—
52	C₂×C₄⋊C₄	D₃₇₃	1	1	yes	characteristic, complemented
53	#102	—	373	4	no	—
54	C₂⁴	—	746	1	no	—
55	C₂×D₄	—	373	4	no	—
56	C₂×D₄	—	373	2	no	—
57	C₂×D₄	—	746	1	no	—
58	C₂×D₄	—	746	2	no	—
59	C₂²×C₄	—	2	1	no	—
60	C₂²×C₄	C₂×D₃₇₃	1	1	yes	characteristic
61	C₂×C₈	—	373	2	no	—
62	C₂×C₈	—	746	2	no	—
63	C₄⋊C₄	—	2	1	no	—
64	C₄⋊C₄	C₂×D₃₇₃	1	2	yes	complemented
65	C₂³	—	1492	2	no	—
66	C₂³	—	1492	2	no	—
67	C₂³	—	746	2	no	—
68	C₂³	—	746	4	no	—
69	C₂³	C₂²⋊D₃₇₃	1	1	yes	characteristic
70	D₄	—	373	4	no	—
71	D₄	—	746	2	no	—
72	D₄	—	746	4	no	—
73	C₂×C₄	—	2	2	no	—
74	C₂×C₄	—	4	2	no	—
75	C₂×C₄	C₄×D₃₇₃	1	2	yes	—
76	C₂×C₄	C₂²⋊D₃₇₃	1	1	yes	characteristic
77	C₂×C₄	D₁₄₉₂	1	2	yes	—
78	C₂×C₄	C₂²×D₃₇₃	1	1	yes	characteristic
79	C₈	—	746	2	no	—
80	C₂²	—	1492	8	no	—
81	C₂²	—	1492	2	no	—
82	C₂²	—	1492	2	no	—
83	C₂²	—	746	4	no	—
84	C₂²	#20238587	1	2	yes	—
85	C₂²	#20238595	1	2	yes	—
86	C₂²	#20238597	1	2	yes	—
87	C₂²	C₂×C₂²⋊D₃₇₃	1	1	yes	characteristic
88	C₄	—	4	2	no	—
89	C₄	#20238587	1	2	yes	—
90	C₄	C₂×C₄×D₃₇₃	1	1	yes	characteristic
91	C₄	C₂×D₁₄₉₂	1	1	yes	characteristic
92	C₂	—	1492	4	no	—
93	C₂	#26045712	1	4	yes	direct product factor
94	C₂	C₂×#20238587	1	1	yes	characteristic
95	C₂	C₂×#20238595	1	1	yes	characteristic
96	C₂	C₂×#20238597	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	C₂²⋊D₃₇₃
commutator	C₄×C₃₇₃	C₂²×C₄
Frattini	C₂×C₄	C₂²×D₃₇₃
Fitting	C₂×C₄⋊C₄×C₃₇₃	C₂
socle	C₂³×C₃₇₃	D₄
prime radical	C₂²×D₁₄₉₂	C₂
cosocle	C₂×C₄×C₃₇₃	C₂³
hypercenter	C₂×C₄⋊C₄	D₃₇₃
hypocenter	C₃₇₃	C₂×#102
LCS	G ▷ C₄×C₃₇₃ ▷ C₂×C₃₇₃ ▷ C₃₇₃
UCS	C₁ ◁ C₂³ ◁ C₂²×C₄ ◁ C₂×C₄⋊C₄

Complements

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

N	H ≅ G/N	type
2. C₂²×#15688412	C₂	semidirect
3. #26045712	C₂	direct (N × H)
4. C₂×C₄⋊C₄×C₃₇₃	C₂	semidirect
8. C₂×D₁₄₉₂	C₄	semidirect
11. C₂×#15688412	C₂²	semidirect
15. C₄⋊C₄×C₃₇₃	C₂²	semidirect
22. D₁₄₉₂	C₂×C₄	semidirect
43. C₂×C₃₇₃	#102	semidirect
48. C₃₇₃	C₂×#102	semidirect
52. C₂×C₄⋊C₄	D₃₇₃	semidirect
64. C₄⋊C₄	C₂×D₃₇₃	semidirect
93. C₂	#26045712	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×D₁₄₉₂	2
C₂²×#15688412	2
#26045712	2
C₂×C₄⋊C₄×C₃₇₃	2
C₂×#102	373

Subgroups — C2×#26045712 #37559408

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#26045712 #37559408