Subgroups — C₁₀₃×#12911 #39918186

Order 26368.

266 conjugacy classes of subgroups.

The subgroup lattice has 188 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#368×C₁₀₃	C₂	1	1	yes	maximal, characteristic
2	C₁₀₃×#2158	C₂	1	1	yes	maximal, characteristic
3	C₁₀₃×#2155	C₂	1	2	yes	maximal
4	C₁₀₃×#2108	C₂	1	1	yes	maximal, characteristic
5	C₁₀₃×#1833	C₂	1	2	yes	maximal
6	C₂×M₃₂×C₁₀₃	C₂²	1	1	yes	characteristic
7	C₂²×C₁₆×C₁₀₃	C₂²	1	1	yes	characteristic
8	C₂×#108×C₁₀₃	C₂²	1	2	yes	—
9	#427×C₁₀₃	C₂²	1	2	yes	—
10	#405×C₁₀₃	C₂²	1	1	yes	characteristic
11	#368×C₁₀₃	—	2	1	no	—
12	#368×C₁₀₃	—	2	1	no	—
13	#367×C₁₀₃	—	2	1	no	—
14	#366×C₁₀₃	—	2	1	no	—
15	#365×C₁₀₃	—	2	4	no	—
16	#346×C₁₀₃	C₄	1	2	yes	complemented
17	C₄×C₁₆×C₁₀₃	C₄	1	2	yes	complemented
18	#344×C₁₀₃	—	2	2	no	—
19	H(3,ℤ/4)×C₁₀₃	—	2	2	no	—
20	C₂×M₁₆×C₁₀₃	—	2	2	no	—
21	C₂×M₁₆×C₁₀₃	D₄	1	1	yes	characteristic
22	C₂²×C₈×C₁₀₃	C₂³	1	1	yes	characteristic
23	#117×C₁₀₃	—	2	2	no	—
24	#117×C₁₀₃	D₄	1	1	yes	characteristic
25	M₃₂×C₁₀₃	D₄	1	2	yes	—
26	M₃₂×C₁₀₃	Q₈	1	2	yes	—
27	C₂×C₁₆×C₁₀₃	C₂×C₄	1	1	yes	characteristic
28	C₂×C₁₆×C₁₀₃	C₂×C₄	1	2	yes	—
29	C₂×C₁₆×C₁₀₃	C₂×C₄	1	1	yes	characteristic
30	C₂×C₁₆×C₁₀₃	D₄	1	1	yes	characteristic
31	C₂×C₁₆×C₁₀₃	D₄	1	1	yes	characteristic
32	C₂×C₁₆×C₁₀₃	Q₈	1	1	yes	characteristic
33	C₂×C₁₆×C₁₀₃	Q₈	1	1	yes	characteristic
34	#108×C₁₀₃	—	2	2	no	—
35	#108×C₁₀₃	—	2	2	no	—
36	#107×C₁₀₃	—	2	2	no	—
37	#106×C₁₀₃	—	2	2	no	—
38	#97×C₁₀₃	Q₈	1	2	yes	—
39	C₄×C₈×C₁₀₃	C₂×C₄	1	2	yes	—
40	C₂²×C₄×C₁₀₃	C₂×D₄	1	1	yes	characteristic
41	M₁₆×C₁₀₃	—	2	1	no	—
42	M₁₆×C₁₀₃	—	2	1	no	—
43	M₁₆×C₁₀₃	—	4	2	no	—
44	M₁₆×C₁₀₃	—	4	2	no	—
45	C₂×C₈×C₁₀₃	—	4	2	no	—
46	C₂×C₈×C₁₀₃	C₄⋊C₄	1	2	yes	—
47	C₂×C₈×C₁₀₃	C₂²×C₄	1	1	yes	characteristic
48	C₂×C₈×C₁₀₃	C₂×D₄	1	1	yes	characteristic
49	C₂×C₈×C₁₀₃	C₂×D₄	1	1	yes	characteristic
50	C₂×C₈×C₁₀₃	C₂×Q₈	1	1	yes	characteristic
51	C₂×C₈×C₁₀₃	C₂×Q₈	1	1	yes	characteristic
52	C₂×C₈×C₁₀₃	C₂×Q₈	1	1	yes	characteristic
53	C₄⋊C₄×C₁₀₃	—	2	1	no	—
54	C₄⋊C₄×C₁₀₃	—	4	2	no	—
55	C₂²⋊C₄×C₁₀₃	—	2	1	no	—
56	C₂²⋊C₄×C₁₀₃	—	4	2	no	—
57	C₄²×C₁₀₃	—	4	2	no	—
58	C₄²×C₁₀₃	C₄⋊C₄	1	2	yes	—
59	C₁₆×C₁₀₃	C₄⋊C₄	1	1	yes	characteristic
60	C₁₆×C₁₀₃	C₄⋊C₄	1	1	yes	characteristic
61	C₁₆×C₁₀₃	C₄⋊C₄	1	1	yes	characteristic
62	C₁₆×C₁₀₃	C₄⋊C₄	1	1	yes	characteristic
63	C₁₆×C₁₀₃	C₄⋊C₄	1	4	yes	—
64	C₂³×C₁₀₃	#135	1	1	yes	characteristic
65	C₂×C₄×C₁₀₃	—	2	2	no	—
66	C₂×C₄×C₁₀₃	—	8	2	no	—
67	C₂×C₄×C₁₀₃	C₂×C₄⋊C₄	1	1	yes	characteristic
68	C₂×C₄×C₁₀₃	#127	1	1	yes	characteristic
69	C₂×C₄×C₁₀₃	C₄⋊Q₈	1	1	yes	characteristic
70	C₂×C₄×C₁₀₃	#135	1	1	yes	characteristic
71	C₂×C₄×C₁₀₃	#135	1	1	yes	characteristic
72	C₂×C₄×C₁₀₃	#135	1	1	yes	characteristic
73	C₈×C₁₀₃	—	2	2	no	—
74	C₈×C₁₀₃	—	8	2	no	—
75	C₈×C₁₀₃	C₂×C₄⋊C₄	1	1	yes	characteristic
76	C₈×C₁₀₃	C₂×C₄⋊C₄	1	1	yes	characteristic
77	C₈×C₁₀₃	C₄⋊Q₈	1	1	yes	characteristic
78	C₈×C₁₀₃	C₄⋊Q₈	1	1	yes	characteristic
79	C₂²×C₁₀₃	—	4	1	no	—
80	C₂²×C₁₀₃	#427	1	1	yes	characteristic
81	C₂²×C₁₀₃	#495	1	1	yes	characteristic
82	C₂²×C₁₀₃	#499	1	1	yes	characteristic
83	C₄×C₁₀₃	—	4	2	no	—
84	C₄×C₁₀₃	—	16	2	no	—
85	C₄×C₁₀₃	#384	1	1	yes	characteristic
86	C₄×C₁₀₃	#427	1	1	yes	characteristic
87	C₄×C₁₀₃	#495	1	1	yes	characteristic
88	C₄×C₁₀₃	#499	1	1	yes	characteristic
89	#12911	C₁₀₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
90	C₂×C₁₀₃	—	2	1	no	—
91	C₂×C₁₀₃	—	2	1	no	—
92	C₂×C₁₀₃	—	2	1	no	—
93	C₂×C₁₀₃	#1846	1	1	yes	characteristic
94	C₂×#368	C₂×C₁₀₃	1	1	yes	characteristic
95	#2158	C₂×C₁₀₃	1	1	yes	characteristic
96	#2155	C₂×C₁₀₃	1	2	yes	—
97	#2108	C₂×C₁₀₃	1	1	yes	characteristic
98	#1833	C₂×C₁₀₃	1	2	yes	—
99	C₁₀₃	#12911	1	1	yes	characteristic, direct product factor, Sylow
100	C₂×M₃₂	C₂²×C₁₀₃	1	1	yes	characteristic
101	C₂²×C₁₆	C₂²×C₁₀₃	1	1	yes	characteristic
102	C₂×#108	C₂²×C₁₀₃	1	2	yes	—
103	#427	C₂²×C₁₀₃	1	2	yes	—
104	#405	C₂²×C₁₀₃	1	1	yes	characteristic
105	#368	—	2	1	no	—
106	#368	—	2	1	no	—
107	#367	—	2	1	no	—
108	#366	—	2	1	no	—
109	#365	—	2	4	no	—
110	#346	C₄×C₁₀₃	1	2	yes	complemented
111	C₄×C₁₆	C₄×C₁₀₃	1	2	yes	complemented
112	#344	—	2	2	no	—
113	H(3,ℤ/4)	—	2	2	no	—
114	C₂×M₁₆	—	2	2	no	—
115	C₂×M₁₆	D₄×C₁₀₃	1	1	yes	characteristic
116	C₂²×C₈	C₂³×C₁₀₃	1	1	yes	characteristic
117	#117	—	2	2	no	—
118	#117	D₄×C₁₀₃	1	1	yes	characteristic
119	M₃₂	D₄×C₁₀₃	1	2	yes	—
120	M₃₂	Q₈×C₁₀₃	1	2	yes	—
121	C₂×C₁₆	C₂×C₄×C₁₀₃	1	1	yes	characteristic
122	C₂×C₁₆	C₂×C₄×C₁₀₃	1	2	yes	—
123	C₂×C₁₆	C₂×C₄×C₁₀₃	1	1	yes	characteristic
124	C₂×C₁₆	D₄×C₁₀₃	1	1	yes	characteristic
125	C₂×C₁₆	D₄×C₁₀₃	1	1	yes	characteristic
126	C₂×C₁₆	Q₈×C₁₀₃	1	1	yes	characteristic
127	C₂×C₁₆	Q₈×C₁₀₃	1	1	yes	characteristic
128	#108	—	2	2	no	—
129	#108	—	2	2	no	—
130	#107	—	2	2	no	—
131	#106	—	2	2	no	—
132	#97	Q₈×C₁₀₃	1	2	yes	—
133	C₄×C₈	C₂×C₄×C₁₀₃	1	2	yes	—
134	C₂²×C₄	C₂×D₄×C₁₀₃	1	1	yes	characteristic
135	M₁₆	—	2	1	no	—
136	M₁₆	—	2	1	no	—
137	M₁₆	—	4	2	no	—
138	M₁₆	—	4	2	no	—
139	C₂×C₈	—	4	2	no	—
140	C₂×C₈	C₄⋊C₄×C₁₀₃	1	2	yes	—
141	C₂×C₈	C₂²×C₄×C₁₀₃	1	1	yes	characteristic
142	C₂×C₈	C₂×D₄×C₁₀₃	1	1	yes	characteristic
143	C₂×C₈	C₂×D₄×C₁₀₃	1	1	yes	characteristic
144	C₂×C₈	C₂×Q₈×C₁₀₃	1	1	yes	characteristic
145	C₂×C₈	C₂×Q₈×C₁₀₃	1	1	yes	characteristic
146	C₂×C₈	C₂×Q₈×C₁₀₃	1	1	yes	characteristic
147	C₄⋊C₄	—	2	1	no	—
148	C₄⋊C₄	—	4	2	no	—
149	C₂²⋊C₄	—	2	1	no	—
150	C₂²⋊C₄	—	4	2	no	—
151	C₄²	—	4	2	no	—
152	C₄²	C₄⋊C₄×C₁₀₃	1	2	yes	—
153	C₁₆	C₄⋊C₄×C₁₀₃	1	1	yes	characteristic
154	C₁₆	C₄⋊C₄×C₁₀₃	1	1	yes	characteristic
155	C₁₆	C₄⋊C₄×C₁₀₃	1	1	yes	characteristic
156	C₁₆	C₄⋊C₄×C₁₀₃	1	1	yes	characteristic
157	C₁₆	C₄⋊C₄×C₁₀₃	1	4	yes	—
158	C₂³	#135×C₁₀₃	1	1	yes	characteristic
159	C₂×C₄	—	2	2	no	—
160	C₂×C₄	—	8	2	no	—
161	C₂×C₄	C₂×C₄⋊C₄×C₁₀₃	1	1	yes	characteristic
162	C₂×C₄	#127×C₁₀₃	1	1	yes	characteristic
163	C₂×C₄	C₄⋊Q₈×C₁₀₃	1	1	yes	characteristic
164	C₂×C₄	#135×C₁₀₃	1	1	yes	characteristic
165	C₂×C₄	#135×C₁₀₃	1	1	yes	characteristic
166	C₂×C₄	#135×C₁₀₃	1	1	yes	characteristic
167	C₈	—	2	2	no	—
168	C₈	—	8	2	no	—
169	C₈	C₂×C₄⋊C₄×C₁₀₃	1	1	yes	characteristic
170	C₈	C₂×C₄⋊C₄×C₁₀₃	1	1	yes	characteristic
171	C₈	C₄⋊Q₈×C₁₀₃	1	1	yes	characteristic
172	C₈	C₄⋊Q₈×C₁₀₃	1	1	yes	characteristic
173	C₂²	—	4	1	no	—
174	C₂²	#427×C₁₀₃	1	1	yes	characteristic
175	C₂²	#495×C₁₀₃	1	1	yes	characteristic
176	C₂²	#499×C₁₀₃	1	1	yes	characteristic
177	C₄	—	4	2	no	—
178	C₄	—	16	2	no	—
179	C₄	#384×C₁₀₃	1	1	yes	characteristic
180	C₄	#427×C₁₀₃	1	1	yes	characteristic
181	C₄	#495×C₁₀₃	1	1	yes	characteristic
182	C₄	#499×C₁₀₃	1	1	yes	characteristic
183	C₂	—	2	1	no	—
184	C₂	—	2	1	no	—
185	C₂	—	2	1	no	—
186	C₂	C₁₀₃×#1846	1	1	yes	characteristic

	subgroup	G/H
center	C₄×C₁₀₃	#427
commutator	C₂×C₈	C₂²×C₄×C₁₀₃
Frattini, cosocle	C₂²×C₈	C₂³×C₁₀₃
socle	C₂×C₁₀₃	#1846
prime radical	C₂³×C₁₀₃	#135
LCS	G ▷ C₂×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₄×C₁₀₃ ◁ #117×C₁₀₃ ◁ #405×C₁₀₃ ◁ G

Complements

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

N	H ≅ G/N	type
16. #346×C₁₀₃	C₄	semidirect
17. C₄×C₁₆×C₁₀₃	C₄	semidirect
89. #12911	C₁₀₃	direct (N × H)
99. C₁₀₃	#12911	direct (N × H)
110. #346	C₄×C₁₀₃	semidirect
111. C₄×C₁₆	C₄×C₁₀₃	semidirect

Maximal subgroups

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

subgroup	index
C₂×#368×C₁₀₃	2
C₁₀₃×#2158	2
C₁₀₃×#2155	2
C₁₀₃×#2108	2
C₁₀₃×#1833	2
#12911	103

Subgroups — C103×#12911 #39918186

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₀₃×#12911 #39918186