Subgroups — C₁₀₃×#7099 #39912374

Order 26368.

98 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₀₃×#1367	C₂	1	2	yes	maximal
2	C₁₀₃×#1311	C₂	1	1	yes	maximal, characteristic
3	C₄⋊C₁₆×C₁₀₃	—	2	2	no	—
4	C₄×C₁₆×C₁₀₃	C₄	1	1	yes	characteristic
5	C₄×C₁₆×C₁₀₃	C₄	1	1	yes	characteristic
6	C₈²×C₁₀₃	C₂²	1	1	yes	characteristic
7	C₂×C₁₆×C₁₀₃	—	2	1	no	—
8	C₂×C₁₆×C₁₀₃	—	4	2	no	—
9	C₂×C₁₆×C₁₀₃	C₈	1	1	yes	characteristic
10	C₂×C₁₆×C₁₀₃	C₈	1	1	yes	characteristic
11	C₄×C₈×C₁₀₃	C₂×C₄	1	1	yes	characteristic
12	C₄×C₈×C₁₀₃	D₄	1	1	yes	characteristic
13	C₄×C₈×C₁₀₃	Q₈	1	1	yes	characteristic
14	C₂×C₈×C₁₀₃	—	2	1	no	—
15	C₂×C₈×C₁₀₃	C₂×C₈	1	1	yes	characteristic
16	C₂×C₈×C₁₀₃	M₁₆	1	1	yes	characteristic
17	C₂×C₈×C₁₀₃	SD₁₆	1	2	yes	—
18	C₄²×C₁₀₃	C₄⋊C₄	1	1	yes	characteristic
19	C₁₆×C₁₀₃	—	2	2	no	—
20	C₁₆×C₁₀₃	—	2	1	no	—
21	C₁₆×C₁₀₃	—	8	2	no	—
22	C₁₆×C₁₀₃	C₁₆	1	2	yes	complemented
23	C₂×C₄×C₁₀₃	C₄⋊C₈	1	1	yes	characteristic
24	C₂×C₄×C₁₀₃	#106	1	1	yes	characteristic
25	C₂×C₄×C₁₀₃	#108	1	1	yes	characteristic
26	C₈×C₁₀₃	—	2	1	no	—
27	C₈×C₁₀₃	—	2	2	no	—
28	C₈×C₁₀₃	—	4	1	no	—
29	C₈×C₁₀₃	C₂×C₁₆	1	1	yes	characteristic
30	C₈×C₁₀₃	M₃₂	1	1	yes	characteristic
31	C₂²×C₁₀₃	#334	1	1	yes	characteristic
32	C₄×C₁₀₃	—	2	1	no	—
33	C₄×C₁₀₃	C₄⋊C₁₆	1	1	yes	characteristic
34	C₄×C₁₀₃	#364	1	1	yes	characteristic
35	C₄×C₁₀₃	#365	1	2	yes	—
36	#7099	C₁₀₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
37	C₂×C₁₀₃	#1367	1	1	yes	characteristic
38	C₂×C₁₀₃	#1368	1	1	yes	characteristic
39	C₂×C₁₀₃	#1369	1	1	yes	characteristic
40	#1367	C₂×C₁₀₃	1	2	yes	—
41	#1311	C₂×C₁₀₃	1	1	yes	characteristic
42	C₁₀₃	#7099	1	1	yes	characteristic, direct product factor, Sylow
43	C₄⋊C₁₆	—	2	2	no	—
44	C₄×C₁₆	C₄×C₁₀₃	1	1	yes	characteristic
45	C₄×C₁₆	C₄×C₁₀₃	1	1	yes	characteristic
46	C₈²	C₂²×C₁₀₃	1	1	yes	characteristic
47	C₂×C₁₆	—	2	1	no	—
48	C₂×C₁₆	—	4	2	no	—
49	C₂×C₁₆	C₈×C₁₀₃	1	1	yes	characteristic
50	C₂×C₁₆	C₈×C₁₀₃	1	1	yes	characteristic
51	C₄×C₈	C₂×C₄×C₁₀₃	1	1	yes	characteristic
52	C₄×C₈	D₄×C₁₀₃	1	1	yes	characteristic
53	C₄×C₈	Q₈×C₁₀₃	1	1	yes	characteristic
54	C₂×C₈	—	2	1	no	—
55	C₂×C₈	C₂×C₈×C₁₀₃	1	1	yes	characteristic
56	C₂×C₈	M₁₆×C₁₀₃	1	1	yes	characteristic
57	C₂×C₈	SD₁₆×C₁₀₃	1	2	yes	—
58	C₄²	C₄⋊C₄×C₁₀₃	1	1	yes	characteristic
59	C₁₆	—	2	2	no	—
60	C₁₆	—	2	1	no	—
61	C₁₆	—	8	2	no	—
62	C₁₆	C₁₆×C₁₀₃	1	2	yes	complemented
63	C₂×C₄	C₄⋊C₈×C₁₀₃	1	1	yes	characteristic
64	C₂×C₄	#106×C₁₀₃	1	1	yes	characteristic
65	C₂×C₄	#108×C₁₀₃	1	1	yes	characteristic
66	C₈	—	2	1	no	—
67	C₈	—	2	2	no	—
68	C₈	—	4	1	no	—
69	C₈	C₂×C₁₆×C₁₀₃	1	1	yes	characteristic
70	C₈	M₃₂×C₁₀₃	1	1	yes	characteristic
71	C₂²	#334×C₁₀₃	1	1	yes	characteristic
72	C₄	—	2	1	no	—
73	C₄	C₄⋊C₁₆×C₁₀₃	1	1	yes	characteristic
74	C₄	#364×C₁₀₃	1	1	yes	characteristic
75	C₄	#365×C₁₀₃	1	2	yes	—
76	C₂	C₁₀₃×#1367	1	1	yes	characteristic
77	C₂	C₁₀₃×#1368	1	1	yes	characteristic
78	C₂	C₁₀₃×#1369	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₁₀₃	#106
commutator	C₈	C₂×C₁₆×C₁₀₃
Frattini, cosocle	C₈²	C₂²×C₁₀₃
socle, prime radical	C₂²×C₁₀₃	#334
LCS	G ▷ C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₁₀₃ ◁ C₄×C₈×C₁₀₃ ◁ C₈²×C₁₀₃ ◁ G

Complements

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

N	H ≅ G/N	type
22. C₁₆×C₁₀₃	C₁₆	semidirect
36. #7099	C₁₀₃	direct (N × H)
42. C₁₀₃	#7099	direct (N × H)
62. C₁₆	C₁₆×C₁₀₃	semidirect

Maximal subgroups

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

subgroup	index
C₁₀₃×#1367	2
C₁₀₃×#1311	2
#7099	103

Subgroups — C103×#7099 #39912374

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₀₃×#7099 #39912374