Subgroups — C₂×#26045715 #37559412

Order 23872.

162 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×Dic₇₄₆	C₂	1	1	yes	maximal, characteristic
2	C₂²×#15688412	C₂	1	1	yes	maximal, characteristic
3	#26045715	C₂	1	4	yes	maximal, direct product factor
4	C₂×C₄⋊C₄×C₃₇₃	C₂	1	1	yes	maximal, characteristic
5	C₂×Dic₇₄₆	—	2	1	no	—
6	C₂×Dic₇₄₆	—	2	2	no	—
7	C₂×Dic₇₄₆	C₄	1	4	yes	complemented
8	C₂×Dic₇₄₆	C₂²	1	2	yes	—
9	C₂²×Dic₃₇₃	—	2	1	no	—
10	C₂×#15688412	—	2	2	no	—
11	C₂×#15688412	C₂²	1	2	yes	—
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	—
16	Dic₇₄₆	—	2	4	no	—
17	Dic₇₄₆	—	2	2	no	—
18	Dic₇₄₆	C₂×C₄	1	4	yes	complemented
19	C₂×Dic₃₇₃	—	2	4	no	—
20	C₂×Dic₃₇₃	—	2	2	no	—
21	#15688412	—	2	2	no	—
22	C₂³×C₃₇₃	D₄	1	1	yes	characteristic
23	C₂×C₄×C₃₇₃	—	2	2	no	—
24	C₂×C₄×C₃₇₃	—	4	2	no	—
25	C₂×C₄×C₃₇₃	C₂×C₄	1	2	yes	—
26	C₂×C₄×C₃₇₃	D₄	1	1	yes	characteristic
27	C₂×C₄×C₃₇₃	D₄	1	2	yes	—
28	C₂×C₄×C₃₇₃	C₂³	1	1	yes	characteristic
29	C₂²×C₃₇₃	C₂²⋊C₄	1	2	yes	—
30	C₂²×C₃₇₃	SD₁₆	1	2	yes	—
31	C₂²×C₃₇₃	Q₁₆	1	2	yes	—
32	C₂²×C₃₇₃	C₂×D₄	1	1	yes	characteristic
33	C₄×C₃₇₃	—	4	2	no	—
34	C₄×C₃₇₃	C₂²⋊C₄	1	2	yes	—
35	C₄×C₃₇₃	C₂²×C₄	1	1	yes	characteristic
36	C₄×C₃₇₃	C₂×D₄	1	1	yes	characteristic
37	Dic₃₇₃	—	2	4	no	—
38	C₂×C₃₇₃	#103	1	4	yes	complemented
39	C₂×C₃₇₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
40	C₂×C₃₇₃	C₂×SD₁₆	1	1	yes	characteristic
41	C₂×C₃₇₃	C₂×Q₁₆	1	1	yes	characteristic
42	C₃₇₃	C₂×#103	1	1	yes	characteristic, complemented, Sylow
43	C₂×#103	—	373	1	no	maximal, Sylow
44	C₂²×Q₈	—	373	1	no	—
45	C₂²×C₈	—	373	1	no	—
46	C₂×C₄⋊C₄	D₃₇₃	1	1	yes	characteristic
47	#103	—	373	4	no	—
48	C₂×Q₈	—	373	4	no	—
49	C₂×Q₈	—	373	2	no	—
50	C₂×Q₈	—	746	1	no	—
51	C₂×Q₈	—	746	2	no	—
52	C₂²×C₄	—	2	1	no	—
53	C₂²×C₄	—	746	1	no	—
54	C₂²×C₄	C₂×D₃₇₃	1	1	yes	characteristic
55	C₂×C₈	—	373	2	no	—
56	C₂×C₈	—	746	2	no	—
57	C₄⋊C₄	—	2	1	no	—
58	C₄⋊C₄	C₂×D₃₇₃	1	2	yes	—
59	C₂³	C₂²⋊D₃₇₃	1	1	yes	characteristic
60	Q₈	—	373	4	no	—
61	Q₈	—	746	2	no	—
62	Q₈	—	746	4	no	—
63	C₂×C₄	—	2	2	no	—
64	C₂×C₄	—	4	2	no	—
65	C₂×C₄	—	746	2	no	—
66	C₂×C₄	—	746	4	no	—
67	C₂×C₄	C₄×D₃₇₃	1	2	yes	—
68	C₂×C₄	C₂²⋊D₃₇₃	1	1	yes	characteristic
69	C₂×C₄	D₁₄₉₂	1	2	yes	—
70	C₂×C₄	C₂²×D₃₇₃	1	1	yes	characteristic
71	C₈	—	746	2	no	—
72	C₂²	#20238587	1	2	yes	—
73	C₂²	#20238598	1	2	yes	—
74	C₂²	#20238600	1	2	yes	—
75	C₂²	C₂×C₂²⋊D₃₇₃	1	1	yes	characteristic
76	C₄	—	4	2	no	—
77	C₄	—	746	4	no	—
78	C₄	#20238587	1	2	yes	—
79	C₄	C₂×C₄×D₃₇₃	1	1	yes	characteristic
80	C₄	C₂×D₁₄₉₂	1	1	yes	characteristic
81	C₂	#26045715	1	4	yes	direct product factor
82	C₂	C₂×#20238587	1	1	yes	characteristic
83	C₂	C₂×#20238598	1	1	yes	characteristic
84	C₂	C₂×#20238600	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, prime radical	C₂³×C₃₇₃	D₄
cosocle	C₂×C₄×C₃₇₃	C₂³
hypercenter	C₂×C₄⋊C₄	D₃₇₃
hypocenter	C₃₇₃	C₂×#103
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
3. #26045715	C₂	direct (N × H)
7. C₂×Dic₇₄₆	C₄	semidirect
18. Dic₇₄₆	C₂×C₄	semidirect
38. C₂×C₃₇₃	#103	semidirect
42. C₃₇₃	C₂×#103	semidirect
81. C₂	#26045715	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×Dic₇₄₆	2
C₂²×#15688412	2
#26045715	2
C₂×C₄⋊C₄×C₃₇₃	2
C₂×#103	373

Subgroups — C2×#26045715 #37559412

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#26045715 #37559412