Subgroups — C₂×#13112900 #15774461

Order 3328.

286 conjugacy classes of subgroups.

The subgroup lattice has 168 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄⋊#6090	C₂	1	2	yes	maximal
2	#13112900	C₂	1	4	yes	maximal, direct product factor
3	C₂×C₈²×C₁₃	C₂	1	1	yes	maximal, characteristic
4	C₂×C₄×C₈×C₁₃	C₄	1	1	yes	characteristic
5	C₂×C₄×C₈×C₁₃	C₄	1	1	yes	characteristic
6	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
7	C₂²×#6090	—	2	2	no	—
8	C₈²×C₁₃	C₄	1	2	yes	—
9	C₈²×C₁₃	C₂²	1	2	yes	—
10	C₄⋊#6090	—	2	2	no	—
11	C₄⋊#6090	C₂²	1	4	yes	—
12	C₂²×C₈×C₁₃	—	2	1	no	—
13	C₂²×C₈×C₁₃	C₈	1	1	yes	characteristic
14	C₂²×C₈×C₁₃	C₈	1	1	yes	characteristic
15	C₂²×C₈×C₁₃	D₄	1	1	yes	characteristic
16	C₂²×C₈×C₁₃	Q₈	1	1	yes	characteristic
17	C₂×C₄²×C₁₃	C₂×C₄	1	1	yes	characteristic
18	C₄×C₈×C₁₃	—	2	1	no	—
19	C₄×C₈×C₁₃	C₈	1	2	yes	—
20	C₄×C₈×C₁₃	C₂×C₄	1	2	yes	—
21	C₄×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
22	C₄×C₈×C₁₃	C₂×C₄	1	2	yes	—
23	C₄×C₈×C₁₃	D₄	1	1	yes	characteristic
24	C₄×C₈×C₁₃	Q₈	1	1	yes	characteristic
25	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
26	C₂×#6090	—	2	4	no	—
27	C₂×#6090	—	4	4	no	—
28	C₂×#1367	—	13	1	no	maximal, Sylow
29	C₂²×C₄×C₁₃	C₄⋊C₄	1	1	yes	characteristic
30	C₂²×C₄×C₁₃	C₂×C₈	1	1	yes	characteristic
31	C₂²×C₄×C₁₃	M₁₆	1	1	yes	characteristic
32	C₂×C₈×C₁₃	—	2	4	no	—
33	C₂×C₈×C₁₃	—	2	2	no	—
34	C₂×C₈×C₁₃	—	2	2	no	—
35	C₂×C₈×C₁₃	—	2	2	no	—
36	C₂×C₈×C₁₃	C₁₆	1	4	yes	complemented
37	C₂×C₈×C₁₃	C₄⋊C₄	1	1	yes	characteristic
38	C₂×C₈×C₁₃	C₄⋊C₄	1	1	yes	characteristic
39	C₂×C₈×C₁₃	C₂×C₈	1	2	yes	—
40	C₂×C₈×C₁₃	C₂×C₈	1	2	yes	—
41	C₂×C₈×C₁₃	SD₁₆	1	4	yes	—
42	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
43	C₂×C₈×C₁₃	C₂×Q₈	1	1	yes	characteristic
44	C₄²×C₁₃	C₄⋊C₄	1	1	yes	characteristic
45	C₄²×C₁₃	C₂×C₈	1	1	yes	characteristic
46	C₄²×C₁₃	M₁₆	1	1	yes	characteristic
47	C₄²×C₁₃	C₂²×C₄	1	1	yes	characteristic
48	#6090	—	4	4	no	—
49	C₂×C₄⋊C₁₆	—	13	2	no	—
50	C₂×C₈²	D₁₃	1	1	yes	characteristic
51	#1367	—	13	4	no	—
52	C₂³×C₁₃	C₄⋊C₈	1	1	yes	characteristic
53	C₂×C₄×C₁₃	—	2	2	no	—
54	C₂×C₄×C₁₃	C₄⋊C₈	1	1	yes	characteristic
55	C₂×C₄×C₁₃	C₄⋊C₈	1	1	yes	characteristic
56	C₂×C₄×C₁₃	C₄⋊C₈	1	1	yes	characteristic
57	C₂×C₄×C₁₃	#106	1	2	yes	—
58	C₂×C₄×C₁₃	#108	1	2	yes	—
59	C₂×C₄×C₁₃	C₂×C₁₆	1	2	yes	—
60	C₂×C₄×C₁₃	M₃₂	1	2	yes	—
61	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
62	C₂×C₄×C₁₃	C₂²×C₈	1	1	yes	characteristic
63	C₂×C₄×C₁₃	C₂×M₁₆	1	1	yes	characteristic
64	C₈×C₁₃	—	2	4	no	—
65	C₈×C₁₃	—	2	1	no	—
66	C₈×C₁₃	—	2	1	no	—
67	C₈×C₁₃	—	2	2	no	—
68	C₈×C₁₃	#106	1	2	yes	—
69	C₈×C₁₃	C₂×C₁₆	1	4	yes	complemented
70	C₈×C₁₃	C₂×SD₁₆	1	2	yes	—
71	C₂²×C₁₆	—	26	2	no	—
72	C₂×C₄×C₈	Dic₁₃	1	1	yes	characteristic
73	C₂×C₄×C₈	Dic₁₃	1	1	yes	characteristic
74	C₂×C₄×C₈	C₂×D₁₃	1	1	yes	characteristic
75	C₄⋊C₁₆	—	13	4	no	—
76	C₄⋊C₁₆	—	26	2	no	—
77	C₈²	Dic₁₃	1	2	yes	—
78	C₈²	C₂×D₁₃	1	2	yes	—
79	C₂²×C₁₃	#334	1	2	yes	—
80	C₂²×C₁₃	C₄⋊C₁₆	1	2	yes	—
81	C₂²×C₁₃	#364	1	2	yes	—
82	C₂²×C₁₃	C₂×C₄⋊C₈	1	1	yes	characteristic
83	C₄×C₁₃	—	2	1	no	—
84	C₄×C₁₃	—	2	1	no	—
85	C₄×C₁₃	#334	1	2	yes	—
86	C₄×C₁₃	C₄⋊C₁₆	1	2	yes	—
87	C₄×C₁₃	C₂×#106	1	1	yes	characteristic
88	C₄×C₁₃	C₂×#108	1	1	yes	characteristic
89	C₄×C₁₃	C₂²×C₁₆	1	1	yes	characteristic
90	C₄×C₁₃	C₂×M₃₂	1	1	yes	characteristic
91	C₂²×C₈	—	2	1	no	—
92	C₂²×C₈	#1055	1	1	yes	characteristic
93	C₂²×C₈	#1055	1	1	yes	characteristic
94	C₂²×C₈	Dic₂₆	1	1	yes	characteristic
95	C₂²×C₈	D₅₂	1	1	yes	characteristic
96	C₂×C₄²	C₂×Dic₁₃	1	1	yes	characteristic
97	C₂×C₁₆	—	26	4	no	—
98	C₂×C₁₆	—	52	4	no	—
99	C₄×C₈	—	2	1	no	—
100	C₄×C₈	#1055	1	2	yes	—
101	C₄×C₈	Dic₂₆	1	1	yes	characteristic
102	C₄×C₈	D₅₂	1	1	yes	characteristic
103	C₄×C₈	C₂×Dic₁₃	1	2	yes	—
104	C₄×C₈	C₂×Dic₁₃	1	2	yes	—
105	C₄×C₈	C₂×Dic₁₃	1	1	yes	characteristic
106	C₄×C₈	C₂²×D₁₃	1	1	yes	characteristic
107	C₂×C₁₃	#1367	1	4	yes	complemented
108	C₂×C₁₃	C₂×#334	1	1	yes	characteristic
109	C₂×C₁₃	C₂×C₄⋊C₁₆	1	1	yes	characteristic
110	C₂×C₁₃	C₂×#364	1	1	yes	characteristic
111	C₂²×C₄	C₂×#1055	1	1	yes	characteristic
112	C₂²×C₄	#6099	1	1	yes	characteristic
113	C₂²×C₄	C₄⋊Dic₁₃	1	1	yes	characteristic
114	C₂×C₈	—	2	4	no	—
115	C₂×C₈	—	2	2	no	—
116	C₂×C₈	—	2	2	no	—
117	C₂×C₈	—	2	2	no	—
118	C₂×C₈	#6090	1	4	yes	complemented
119	C₂×C₈	#6095	1	4	yes	—
120	C₂×C₈	C₂×#1055	1	2	yes	—
121	C₂×C₈	C₂×#1055	1	2	yes	—
122	C₂×C₈	C₄⋊Dic₁₃	1	1	yes	characteristic
123	C₂×C₈	C₄⋊Dic₁₃	1	1	yes	characteristic
124	C₂×C₈	C₂×Dic₂₆	1	1	yes	characteristic
125	C₂×C₈	C₂×D₅₂	1	1	yes	characteristic
126	C₄²	C₂×#1055	1	1	yes	characteristic
127	C₄²	#6099	1	1	yes	characteristic
128	C₄²	C₄⋊Dic₁₃	1	1	yes	characteristic
129	C₄²	C₂²×Dic₁₃	1	1	yes	characteristic
130	C₁₆	—	52	4	no	—
131	C₁₃	C₂×#1367	1	1	yes	characteristic, complemented, Sylow
132	C₂³	C₄⋊#1055	1	1	yes	characteristic
133	C₂×C₄	—	2	2	no	—
134	C₂×C₄	C₄⋊#1055	1	1	yes	characteristic
135	C₂×C₄	C₄⋊#1055	1	1	yes	characteristic
136	C₂×C₄	C₄⋊#1055	1	1	yes	characteristic
137	C₂×C₄	C₂×#6090	1	2	yes	—
138	C₂×C₄	#88052	1	2	yes	—
139	C₂×C₄	#88057	1	2	yes	—
140	C₂×C₄	#88059	1	2	yes	—
141	C₂×C₄	C₂²×#1055	1	1	yes	characteristic
142	C₂×C₄	C₂×#6099	1	1	yes	characteristic
143	C₂×C₄	C₂×C₄⋊Dic₁₃	1	1	yes	characteristic
144	C₈	—	2	4	no	—
145	C₈	—	2	2	no	—
146	C₈	—	2	1	no	—
147	C₈	—	2	1	no	—
148	C₈	C₂×#6090	1	4	yes	complemented
149	C₈	#88057	1	2	yes	—
150	C₈	C₂×#6095	1	2	yes	—
151	C₂²	#11718049	1	2	yes	—
152	C₂²	C₄⋊#6090	1	2	yes	—
153	C₂²	#11718055	1	2	yes	—
154	C₂²	C₂×C₄⋊#1055	1	1	yes	characteristic
155	C₄	—	2	1	no	—
156	C₄	—	2	1	no	—
157	C₄	#11718049	1	2	yes	—
158	C₄	C₄⋊#6090	1	2	yes	—
159	C₄	C₂²×#6090	1	1	yes	characteristic
160	C₄	C₂×#88052	1	1	yes	characteristic
161	C₄	C₂×#88057	1	1	yes	characteristic
162	C₄	C₂×#88059	1	1	yes	characteristic
163	C₂	#13112900	1	4	yes	direct product factor
164	C₂	C₂×#11718049	1	1	yes	characteristic
165	C₂	C₂×C₄⋊#6090	1	1	yes	characteristic
166	C₂	C₂×#11718055	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₈	D₅₂
commutator	C₄×C₁₃	C₂²×C₁₆
Frattini	C₄×C₈	C₂²×D₁₃
Fitting	C₂×C₈²×C₁₃	C₂
socle, prime radical	C₂³×C₁₃	C₄⋊C₈
cosocle	C₄×C₈×C₁₃	C₂³
hypercenter	C₂×C₈²	D₁₃
hypocenter	C₁₃	C₂×#1367
LCS	G ▷ C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂²×C₈ ◁ C₂×C₄×C₈ ◁ C₂×C₈²

Complements

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

N	H ≅ G/N	type
2. #13112900	C₂	direct (N × H)
36. C₂×C₈×C₁₃	C₁₆	semidirect
69. C₈×C₁₃	C₂×C₁₆	semidirect
107. C₂×C₁₃	#1367	semidirect
118. C₂×C₈	#6090	semidirect
131. C₁₃	C₂×#1367	semidirect
148. C₈	C₂×#6090	semidirect
163. C₂	#13112900	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×C₄⋊#6090	2
#13112900	2
C₂×C₈²×C₁₃	2
C₂×#1367	13

Subgroups — C2×#13112900 #15774461

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#13112900 #15774461