Subgroups — #107×D₂₂₃ #28383612

Order 14272.

130 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₈×D₂₂₃	C₂	1	1	yes	maximal, characteristic
2	C₄⋊C₄×D₂₂₃	C₂	1	2	yes	maximal
3	#20297238	C₂	1	1	yes	maximal, characteristic, complemented
4	#20297237	C₂	1	2	yes	maximal, complemented
5	#107×C₂₂₃	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×C₄×D₂₂₃	—	2	2	no	—
7	C₂×C₄×D₂₂₃	C₂²	1	1	yes	characteristic
8	C₂×C₂₂₃⋊C₈	C₂²	1	1	yes	characteristic
9	C₈×D₂₂₃	C₄	1	4	yes	complemented
10	C₄⋊Dic₂₂₃	C₂²	1	2	yes	—
11	Dic₂₂₃⋊C₄	—	2	2	no	—
12	C₂×C₈×C₂₂₃	C₂²	1	1	yes	characteristic
13	C₄⋊C₄×C₂₂₃	C₂²	1	2	yes	—
14	C₂²×D₂₂₃	D₄	1	1	yes	characteristic
15	C₂×Dic₂₂₃	—	2	2	no	—
16	C₂×Dic₂₂₃	D₄	1	1	yes	characteristic
17	C₄×D₂₂₃	—	4	4	no	—
18	C₄×D₂₂₃	C₂×C₄	1	2	yes	—
19	C₄×D₂₂₃	Q₈	1	2	yes	—
20	C₂₂₃⋊C₈	C₂×C₄	1	2	yes	complemented
21	C₂×C₄×C₂₂₃	—	2	2	no	—
22	C₂×C₄×C₂₂₃	C₂³	1	1	yes	characteristic
23	C₈×C₂₂₃	C₂×C₄	1	2	yes	complemented
24	C₂²×C₂₂₃	C₂×D₄	1	1	yes	characteristic
25	C₂×D₂₂₃	C₄⋊C₄	1	2	yes	—
26	C₂×D₂₂₃	D₈	1	2	yes	—
27	C₂×D₂₂₃	Q₁₆	1	2	yes	—
28	C₄×C₂₂₃	—	4	2	no	—
29	C₄×C₂₂₃	C₂²×C₄	1	1	yes	characteristic
30	C₄×C₂₂₃	C₂×Q₈	1	1	yes	characteristic
31	Dic₂₂₃	—	4	2	no	—
32	Dic₂₂₃	C₄⋊C₄	1	2	yes	—
33	C₂×C₂₂₃	C₂×C₄⋊C₄	1	1	yes	characteristic
34	C₂×C₂₂₃	C₂×D₈	1	1	yes	characteristic
35	C₂×C₂₂₃	C₂×Q₁₆	1	1	yes	characteristic
36	D₂₂₃	#107	1	4	yes	direct product factor
37	C₂₂₃	C₂×#107	1	1	yes	characteristic, complemented, Sylow
38	C₂×#107	—	223	1	no	maximal, Sylow
39	C₂²×C₈	—	223	1	no	—
40	C₂×C₄⋊C₄	—	223	2	no	—
41	#107	—	223	1	no	—
42	#107	—	223	2	no	—
43	#107	D₂₂₃	1	1	yes	characteristic, direct product factor
44	C₂²×C₄	—	446	2	no	—
45	C₂²×C₄	—	223	1	no	—
46	C₂×C₈	—	223	1	no	—
47	C₂×C₈	—	223	4	no	—
48	C₂×C₈	C₂×D₂₂₃	1	1	yes	characteristic
49	C₄⋊C₄	—	446	2	no	—
50	C₄⋊C₄	—	223	2	no	—
51	C₄⋊C₄	C₂×D₂₂₃	1	2	yes	—
52	C₂³	—	223	1	no	—
53	C₂×C₄	—	2	2	no	—
54	C₂×C₄	—	892	4	no	—
55	C₂×C₄	—	446	2	no	—
56	C₂×C₄	—	223	1	no	—
57	C₂×C₄	—	223	2	no	—
58	C₂×C₄	—	223	2	no	—
59	C₂×C₄	C₂²×D₂₂₃	1	1	yes	characteristic
60	C₈	—	223	2	no	—
61	C₈	C₄×D₂₂₃	1	2	yes	complemented
62	C₂²	—	223	2	no	—
63	C₂²	—	223	2	no	—
64	C₂²	—	223	2	no	—
65	C₂²	D₄×D₂₂₃	1	1	yes	characteristic
66	C₄	—	4	2	no	—
67	C₄	—	892	2	no	—
68	C₄	—	223	2	no	—
69	C₄	C₂×C₄×D₂₂₃	1	1	yes	characteristic
70	C₄	Q₈×D₂₂₃	1	1	yes	characteristic
71	C₂	—	223	4	no	—
72	C₂	C₄⋊C₄×D₂₂₃	1	1	yes	characteristic
73	C₂	D₈×D₂₂₃	1	1	yes	characteristic
74	C₂	Q₁₆×D₂₂₃	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	D₄×D₂₂₃
commutator	C₄×C₂₂₃	C₂²×C₄
Frattini	C₂×C₄	C₂²×D₂₂₃
Fitting	#107×C₂₂₃	C₂
socle	C₂²×C₂₂₃	C₂×D₄
prime radical	C₂²×D₂₂₃	D₄
cosocle	C₂×C₄×C₂₂₃	C₂³
hypercenter	#107	D₂₂₃
hypocenter	C₂₂₃	C₂×#107
LCS	G ▷ C₄×C₂₂₃ ▷ C₂×C₂₂₃ ▷ C₂₂₃
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ #107

Complements

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

N	H ≅ G/N	type
3. #20297238	C₂	semidirect
4. #20297237	C₂	semidirect
5. #107×C₂₂₃	C₂	semidirect
9. C₈×D₂₂₃	C₄	semidirect
20. C₂₂₃⋊C₈	C₂×C₄	semidirect
23. C₈×C₂₂₃	C₂×C₄	semidirect
36. D₂₂₃	#107	direct (N × H)
37. C₂₂₃	C₂×#107	semidirect
43. #107	D₂₂₃	direct (N × H)
61. C₈	C₄×D₂₂₃	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₈×D₂₂₃	2
C₄⋊C₄×D₂₂₃	2
#20297238	2
#20297237	2
#107×C₂₂₃	2
C₂×#107	223

Subgroups — #107×D223 #28383612

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — #107×D₂₂₃ #28383612