Subgroups — C₂×#13117129 #16021027

Order 3328.

470 conjugacy classes of subgroups.

The subgroup lattice has 180 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#11718562	C₂	1	1	yes	maximal, characteristic
2	#13117129	C₂	1	8	yes	maximal, direct product factor
3	C₂×#11718091	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×#11718039	C₂	1	2	yes	maximal, complemented
5	C₂×D₁₃×C₃₂	C₂	1	2	yes	maximal, complemented
6	C₂²×C₁₃×C₃₂	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×#88155	C₄	1	1	yes	characteristic
8	C₂²×C₁₃×C₁₆	C₂²	1	1	yes	characteristic
9	C₂×#88052	C₄	1	1	yes	characteristic
10	#11718562	C₄	1	4	yes	—
11	#11718562	C₂²	1	4	yes	—
12	C₂×#88038	C₄	1	2	yes	—
13	C₂×C₁₆×D₁₃	C₂²	1	2	yes	—
14	C₂×C₁₃×C₃₂	C₂²	1	1	yes	characteristic
15	C₂×C₁₃×C₃₂	C₂²	1	1	yes	characteristic
16	C₂×C₁₃×C₃₂	C₂²	1	4	yes	complemented
17	#11718091	C₂²	1	4	yes	complemented
18	C₂×#88034	C₂²	1	2	yes	—
19	#11718039	C₂²	1	8	yes	complemented
20	D₁₃×C₃₂	C₂²	1	8	yes	complemented
21	C₂×#6127	C₈	1	1	yes	characteristic
22	C₂²×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
23	C₂×#6099	C₈	1	1	yes	characteristic
24	#88155	C₈	1	4	yes	—
25	#88155	C₂×C₄	1	4	yes	—
26	C₂×#6094	C₈	1	2	yes	—
27	C₂×C₈×D₁₃	C₂×C₄	1	2	yes	—
28	C₂×C₁₃×C₁₆	C₂×C₄	1	1	yes	characteristic
29	C₂×C₁₃×C₁₆	C₂×C₄	1	2	yes	—
30	C₂×C₁₃×C₁₆	C₂³	1	1	yes	characteristic
31	C₂×C₁₃×C₁₆	C₂³	1	2	yes	—
32	#88052	C₂×C₄	1	4	yes	—
33	C₂×#6090	C₂×C₄	1	2	yes	—
34	#88038	C₂×C₄	1	8	yes	—
35	C₁₆×D₁₃	C₂×C₄	1	4	yes	—
36	C₁₆×D₁₃	C₂³	1	4	yes	—
37	C₁₃×C₃₂	C₂³	1	2	yes	—
38	C₁₃×C₃₂	C₂³	1	2	yes	—
39	#88034	C₂³	1	4	yes	—
40	C₂×#2258	—	13	1	no	maximal, Sylow
41	C₂²×C₄×C₁₃	C₂×C₈	1	1	yes	characteristic
42	C₂×C₂²⋊D₁₃	C₁₆	1	2	yes	—
43	#6127	C₁₆	1	4	yes	—
44	#6127	C₂×C₈	1	4	yes	—
45	C₂×D₅₂	C₁₆	1	1	yes	characteristic
46	C₂×C₄×D₁₃	C₂×C₈	1	2	yes	—
47	C₂×Dic₂₆	C₁₆	1	1	yes	characteristic
48	C₂×C₈×C₁₃	C₂×C₈	1	1	yes	characteristic
49	C₂×C₈×C₁₃	C₂×C₈	1	2	yes	—
50	C₂×C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
51	C₂×C₈×C₁₃	C₂²×C₄	1	2	yes	—
52	#6099	C₂×C₈	1	4	yes	—
53	C₂×#1055	C₂×C₈	1	2	yes	—
54	#6094	C₂×C₈	1	8	yes	—
55	C₈×D₁₃	C₂×C₈	1	4	yes	—
56	C₈×D₁₃	C₂²×C₄	1	4	yes	—
57	C₁₃×C₁₆	C₂²×C₄	1	1	yes	characteristic
58	C₁₃×C₁₆	C₂²×C₄	1	2	yes	—
59	C₁₃×C₁₆	C₂⁴	1	1	yes	characteristic
60	#6090	C₂²×C₄	1	4	yes	—
61	C₂×#504	—	13	1	no	—
62	#2258	—	13	8	no	—
63	C₂×M₆₄	—	13	1	no	—
64	C₂×M₆₄	—	13	2	no	—
65	C₂²×C₃₂	—	13	2	no	—
66	C₂²×C₃₂	D₁₃	1	1	yes	characteristic, complemented
67	C₂³×C₁₃	C₂×C₁₆	1	1	yes	characteristic
68	C₂²×D₁₃	C₂×C₁₆	1	2	yes	—
69	C₂×C₄×C₁₃	C₂×C₁₆	1	1	yes	characteristic
70	C₂×C₄×C₁₃	C₂×C₁₆	1	2	yes	—
71	C₂×C₄×C₁₃	C₂²×C₈	1	1	yes	characteristic
72	C₂×C₄×C₁₃	C₂²×C₈	1	2	yes	—
73	C₂²⋊D₁₃	C₂×C₁₆	1	8	yes	—
74	C₂×Dic₁₃	C₂×C₁₆	1	2	yes	—
75	D₅₂	C₂×C₁₆	1	4	yes	—
76	C₄×D₁₃	C₂×C₁₆	1	4	yes	—
77	C₄×D₁₃	C₂²×C₈	1	4	yes	—
78	Dic₂₆	C₂×C₁₆	1	4	yes	—
79	C₈×C₁₃	C₂²×C₈	1	1	yes	characteristic
80	C₈×C₁₃	C₂²×C₈	1	2	yes	—
81	C₈×C₁₃	C₂³×C₄	1	1	yes	characteristic
82	#1055	C₂²×C₈	1	4	yes	—
83	C₂×#131	—	13	1	no	—
84	#504	—	13	4	no	—
85	#504	—	13	4	no	—
86	C₂×M₃₂	—	13	1	no	—
87	C₂×M₃₂	—	13	2	no	—
88	C₂²×C₁₆	—	13	2	no	—
89	C₂²×C₁₆	C₂×D₁₃	1	1	yes	characteristic
90	M₆₄	—	13	4	no	—
91	M₆₄	—	13	8	no	—
92	C₂×C₃₂	—	13	2	no	—
93	C₂×C₃₂	—	13	8	no	—
94	C₂×C₃₂	C₂×D₁₃	1	1	yes	characteristic
95	C₂×C₃₂	C₂×D₁₃	1	1	yes	characteristic
96	C₂×C₃₂	C₂×D₁₃	1	4	yes	complemented
97	C₂²×C₁₃	—	2	2	no	—
98	C₂²×C₁₃	C₂²×C₁₆	1	2	yes	—
99	C₂²×C₁₃	C₂²×C₁₆	1	1	yes	characteristic
100	C₂×D₁₃	—	2	4	no	—
101	C₂×D₁₃	C₂²×C₁₆	1	4	yes	—
102	C₄×C₁₃	C₂²×C₁₆	1	2	yes	—
103	C₄×C₁₃	C₂²×C₁₆	1	1	yes	characteristic
104	C₄×C₁₃	C₂³×C₈	1	1	yes	characteristic
105	Dic₁₃	C₂²×C₁₆	1	4	yes	—
106	C₂×#41	—	13	1	no	—
107	#131	—	13	4	no	—
108	#131	—	13	4	no	—
109	C₂×M₁₆	—	13	1	no	—
110	C₂×M₁₆	—	13	2	no	—
111	C₂²×C₈	—	13	2	no	—
112	C₂²×C₈	C₄×D₁₃	1	1	yes	characteristic
113	M₃₂	—	13	4	no	—
114	M₃₂	—	13	8	no	—
115	C₂×C₁₆	—	13	2	no	—
116	C₂×C₁₆	—	13	4	no	—
117	C₂×C₁₆	—	13	4	no	—
118	C₂×C₁₆	C₄×D₁₃	1	1	yes	characteristic
119	C₂×C₁₆	C₄×D₁₃	1	2	yes	—
120	C₂×C₁₆	C₂²×D₁₃	1	1	yes	characteristic
121	C₂×C₁₆	C₂²×D₁₃	1	2	yes	—
122	C₃₂	—	13	4	no	—
123	C₃₂	C₂²×D₁₃	1	2	yes	—
124	C₃₂	C₂²×D₁₃	1	2	yes	—
125	C₂×C₁₃	—	2	2	no	—
126	C₂×C₁₃	#2258	1	2	yes	complemented
127	C₂×C₁₃	C₂³×C₁₆	1	1	yes	characteristic
128	D₁₃	—	2	4	no	—
129	#41	—	13	4	no	—
130	#41	—	13	4	no	—
131	C₂×Q₈	—	13	1	no	—
132	C₂×D₄	—	13	2	no	—
133	C₂×D₄	—	13	1	no	—
134	C₂²×C₄	—	13	2	no	—
135	C₂²×C₄	C₈×D₁₃	1	1	yes	characteristic
136	M₁₆	—	13	4	no	—
137	M₁₆	—	13	8	no	—
138	C₂×C₈	—	13	2	no	—
139	C₂×C₈	—	13	4	no	—
140	C₂×C₈	—	13	4	no	—
141	C₂×C₈	C₈×D₁₃	1	1	yes	characteristic
142	C₂×C₈	C₈×D₁₃	1	2	yes	—
143	C₂×C₈	C₂×C₄×D₁₃	1	1	yes	characteristic
144	C₂×C₈	C₂×C₄×D₁₃	1	2	yes	—
145	C₁₆	—	13	4	no	—
146	C₁₆	C₂×C₄×D₁₃	1	1	yes	characteristic
147	C₁₆	C₂×C₄×D₁₃	1	2	yes	—
148	C₁₆	C₂³×D₁₃	1	1	yes	characteristic
149	C₁₃	C₂×#2258	1	1	yes	characteristic, complemented, Sylow
150	C₂³	—	13	2	no	—
151	C₂³	C₁₆×D₁₃	1	1	yes	characteristic
152	Q₈	—	13	4	no	—
153	D₄	—	13	8	no	—
154	D₄	—	13	4	no	—
155	C₂×C₄	—	13	2	no	—
156	C₂×C₄	—	13	4	no	—
157	C₂×C₄	—	13	4	no	—
158	C₂×C₄	C₁₆×D₁₃	1	1	yes	characteristic
159	C₂×C₄	C₁₆×D₁₃	1	2	yes	—
160	C₂×C₄	C₂×C₈×D₁₃	1	1	yes	characteristic
161	C₂×C₄	C₂×C₈×D₁₃	1	2	yes	—
162	C₈	—	13	4	no	—
163	C₈	C₂×C₈×D₁₃	1	1	yes	characteristic
164	C₈	C₂×C₈×D₁₃	1	2	yes	—
165	C₈	C₂²×C₄×D₁₃	1	1	yes	characteristic
166	C₂²	—	2	2	no	—
167	C₂²	—	13	4	no	—
168	C₂²	—	26	4	no	—
169	C₂²	C₂×C₁₆×D₁₃	1	2	yes	—
170	C₂²	C₂×C₁₆×D₁₃	1	1	yes	characteristic
171	C₄	—	13	4	no	—
172	C₄	C₂×C₁₆×D₁₃	1	1	yes	characteristic
173	C₄	C₂×C₁₆×D₁₃	1	2	yes	—
174	C₄	C₂²×C₈×D₁₃	1	1	yes	characteristic
175	C₂	—	2	2	no	—
176	C₂	—	26	4	no	—
177	C₂	#13117129	1	2	yes	direct product factor
178	C₂	C₂²×C₁₆×D₁₃	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₃₂	C₂×D₁₃
commutator	C₂×C₁₃	C₂³×C₁₆
Frattini	C₁₆	C₂³×D₁₃
Fitting	C₂²×C₁₃×C₃₂	C₂
socle	C₂²×C₁₃	C₂²×C₁₆
prime radical	C₂×#6127	C₈
cosocle	C₁₃×C₁₆	C₂⁴
hypercenter	C₂²×C₃₂	D₁₃
hypocenter	C₁₃	C₂×#2258
LCS	G ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂×C₃₂ ◁ C₂²×C₃₂

Complements

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

N	H ≅ G/N	type
2. #13117129	C₂	direct (N × H)
3. C₂×#11718091	C₂	semidirect
4. C₂×#11718039	C₂	semidirect
5. C₂×D₁₃×C₃₂	C₂	semidirect
6. C₂²×C₁₃×C₃₂	C₂	semidirect
16. C₂×C₁₃×C₃₂	C₂²	semidirect
17. #11718091	C₂²	semidirect
19. #11718039	C₂²	semidirect
20. D₁₃×C₃₂	C₂²	semidirect
66. C₂²×C₃₂	D₁₃	semidirect
96. C₂×C₃₂	C₂×D₁₃	semidirect
126. C₂×C₁₃	#2258	semidirect
149. C₁₃	C₂×#2258	semidirect
177. C₂	#13117129	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×#11718562	2
#13117129	2
C₂×#11718091	2
C₂×#11718039	2
C₂×D₁₃×C₃₂	2
C₂²×C₁₃×C₃₂	2
C₂×#2258	13

Subgroups — C2×#13117129 #16021027

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#13117129 #16021027