Subgroups — C₂×#11719272 #13128408

Order 1664.

1048 conjugacy classes of subgroups.

The subgroup lattice has 196 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄×Q₈×C₁₃	C₂	1	1	yes	maximal, characteristic
2	C₂×#88198	C₂	1	2	yes	maximal
3	#11719272	C₂	1	16	yes	maximal, direct product factor
4	C₂×#88143	C₂	1	4	yes	maximal
5	C₂×#88141	C₂	1	2	yes	maximal
6	C₂×#88124	C₂	1	2	yes	maximal
7	C₂×#88123	C₂	1	1	yes	maximal, characteristic
8	C₂×C₄×Dic₂₆	C₂	1	2	yes	maximal
9	C₂×C₄×Dic₂₆	C₂	1	1	yes	maximal, characteristic
10	C₂²×Q₈×C₁₃	C₂²	1	1	yes	characteristic
11	C₂²×Dic₂₆	C₂²	1	2	yes	—
12	C₂²×Dic₂₆	C₂²	1	1	yes	characteristic
13	C₄×Q₈×C₁₃	C₂²	1	8	yes	—
14	C₂×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
15	C₂×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
16	C₂×C₄²×C₁₃	C₂²	1	1	yes	characteristic
17	C₂×C₄²×C₁₃	C₂²	1	2	yes	—
18	#88198	C₂²	1	16	yes	—
19	C₂×C₄⋊Dic₁₃	C₂²	1	2	yes	—
20	C₂×C₄⋊Dic₁₃	C₂²	1	1	yes	characteristic
21	C₂×C₄⋊Dic₁₃	C₂²	1	2	yes	—
22	C₂×#6101	C₂²	1	2	yes	—
23	C₂×#6101	C₂²	1	4	yes	—
24	C₂×#6101	C₂²	1	4	yes	—
25	C₂×#6101	C₂²	1	4	yes	—
26	C₂×C₄×Dic₁₃	C₂²	1	4	yes	—
27	C₂×C₄×Dic₁₃	C₂²	1	2	yes	—
28	#88143	C₂²	1	32	yes	—
29	#88141	C₂²	1	16	yes	—
30	#88124	C₂²	1	16	yes	—
31	#88123	C₂²	1	8	yes	—
32	C₄×Dic₂₆	C₂²	1	16	yes	—
33	C₄×Dic₂₆	C₂²	1	8	yes	—
34	C₂×Q₈×C₁₃	—	2	4	no	—
35	C₂×Q₈×C₁₃	C₂³	1	4	yes	—
36	C₂²×C₄×C₁₃	C₂³	1	2	yes	—
37	C₂²×C₄×C₁₃	C₂³	1	2	yes	—
38	C₂²×C₄×C₁₃	C₂³	1	1	yes	characteristic
39	C₂²×C₄×C₁₃	C₂³	1	1	yes	characteristic
40	C₂²×C₄×C₁₃	C₂³	1	1	yes	characteristic
41	C₂²×Dic₁₃	C₂³	1	2	yes	—
42	C₂²×Dic₁₃	C₂³	1	4	yes	—
43	C₂²×Dic₁₃	C₂³	1	2	yes	—
44	C₂×Dic₂₆	—	2	8	no	—
45	C₂×Dic₂₆	Q₈	1	8	yes	complemented
46	C₂×Dic₂₆	C₂³	1	8	yes	—
47	C₂×Dic₂₆	C₂³	1	4	yes	—
48	C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
49	C₁₃×C₄⋊C₄	C₂³	1	8	yes	—
50	C₄²×C₁₃	C₂³	1	4	yes	—
51	C₄²×C₁₃	C₂³	1	8	yes	—
52	C₄⋊Dic₁₃	C₂³	1	8	yes	—
53	C₄⋊Dic₁₃	C₂³	1	4	yes	—
54	C₄⋊Dic₁₃	C₂³	1	8	yes	—
55	#6101	C₂³	1	8	yes	—
56	#6101	C₂³	1	16	yes	—
57	#6101	C₂³	1	16	yes	—
58	#6101	C₂³	1	16	yes	—
59	C₄×Dic₁₃	C₂³	1	16	yes	—
60	C₄×Dic₁₃	C₂³	1	8	yes	—
61	C₂×#557	—	13	1	no	maximal, Sylow
62	C₂³×C₁₃	C₂⁴	1	1	yes	characteristic
63	Q₈×C₁₃	—	2	8	no	—
64	C₂×C₄×C₁₃	—	2	4	no	—
65	C₂×C₄×C₁₃	—	2	4	no	—
66	C₂×C₄×C₁₃	—	2	2	no	—
67	C₂×C₄×C₁₃	C₂×Q₈	1	4	yes	—
68	C₂×C₄×C₁₃	#41	1	4	yes	—
69	C₂×C₄×C₁₃	C₂⁴	1	4	yes	—
70	C₂×C₄×C₁₃	C₂⁴	1	4	yes	—
71	C₂×C₄×C₁₃	C₂⁴	1	2	yes	—
72	C₂×C₄×C₁₃	C₂⁴	1	2	yes	—
73	C₂×C₄×C₁₃	C₂⁴	1	2	yes	—
74	C₂×Dic₁₃	—	2	8	no	—
75	C₂×Dic₁₃	—	2	4	no	—
76	C₂×Dic₁₃	C₂×Q₈	1	8	yes	—
77	C₂×Dic₁₃	C₂⁴	1	4	yes	—
78	C₂×Dic₁₃	C₂⁴	1	8	yes	—
79	C₂×Dic₁₃	C₂⁴	1	4	yes	—
80	Dic₂₆	—	2	16	no	—
81	Dic₂₆	C₂×Q₈	1	16	yes	complemented
82	#557	—	13	16	no	—
83	C₂×C₄⋊Q₈	—	13	2	no	—
84	C₂×C₄⋊Q₈	—	13	1	no	—
85	C₂×#125	—	13	4	no	—
86	C₂×#125	—	13	2	no	—
87	C₂×C₄×Q₈	—	13	2	no	—
88	C₂×C₄×Q₈	—	13	2	no	—
89	C₂×C₄×Q₈	—	13	1	no	—
90	C₂×C₄×Q₈	D₁₃	1	1	yes	characteristic
91	C₂²×C₁₃	C₂²×Q₈	1	2	yes	—
92	C₂²×C₁₃	C₂×#41	1	2	yes	—
93	C₂²×C₁₃	2₋¹⁺⁴	1	2	yes	—
94	C₂²×C₁₃	C₂⁵	1	1	yes	characteristic
95	C₄×C₁₃	—	2	4	no	—
96	C₄×C₁₃	—	2	4	no	—
97	C₄×C₁₃	—	2	2	no	—
98	C₄×C₁₃	C₂²×Q₈	1	4	yes	—
99	C₄×C₁₃	C₂×#41	1	4	yes	—
100	Dic₁₃	—	2	8	no	—
101	Dic₁₃	—	2	4	no	—
102	Dic₁₃	C₂²×Q₈	1	8	yes	—
103	C₂²×Q₈	—	13	1	no	—
104	C₂²×Q₈	—	13	2	no	—
105	C₂²×Q₈	C₂×D₁₃	1	1	yes	characteristic
106	C₄⋊Q₈	—	13	16	no	—
107	C₄⋊Q₈	—	13	8	no	—
108	#125	—	13	32	no	—
109	#125	—	13	16	no	—
110	C₄×Q₈	—	13	16	no	—
111	C₄×Q₈	—	13	16	no	—
112	C₄×Q₈	—	13	8	no	—
113	C₄×Q₈	C₂×D₁₃	1	8	yes	—
114	C₂×C₄⋊C₄	—	13	2	no	—
115	C₂×C₄⋊C₄	—	13	4	no	—
116	C₂×C₄⋊C₄	—	13	1	no	—
117	C₂×C₄⋊C₄	—	13	4	no	—
118	C₂×C₄⋊C₄	—	13	2	no	—
119	C₂×C₄⋊C₄	—	13	4	no	—
120	C₂×C₄⋊C₄	—	13	2	no	—
121	C₂×C₄⋊C₄	C₂×D₁₃	1	1	yes	characteristic
122	C₂×C₄⋊C₄	C₂×D₁₃	1	2	yes	—
123	C₂×C₄²	—	13	4	no	—
124	C₂×C₄²	—	13	2	no	—
125	C₂×C₄²	C₂×D₁₃	1	2	yes	—
126	C₂×C₄²	C₂×D₁₃	1	1	yes	characteristic
127	C₂×C₁₃	#557	1	4	yes	complemented
128	C₂×C₁₃	C₂³×Q₈	1	1	yes	characteristic
129	C₂×C₁₃	C₂²×#41	1	1	yes	characteristic
130	C₂×C₁₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
131	C₂×Q₈	—	2	4	no	—
132	C₂×Q₈	—	13	8	no	—
133	C₂×Q₈	—	13	4	no	—
134	C₂×Q₈	—	13	8	no	—
135	C₂×Q₈	—	26	8	no	—
136	C₂×Q₈	C₂²×D₁₃	1	4	yes	—
137	C₂²×C₄	—	13	2	no	—
138	C₂²×C₄	—	13	2	no	—
139	C₂²×C₄	—	13	4	no	—
140	C₂²×C₄	C₂²×D₁₃	1	2	yes	—
141	C₂²×C₄	C₂²×D₁₃	1	1	yes	characteristic
142	C₂²×C₄	C₂²×D₁₃	1	2	yes	—
143	C₂²×C₄	C₂²×D₁₃	1	1	yes	characteristic
144	C₂²×C₄	C₂²×D₁₃	1	1	yes	characteristic
145	C₄⋊C₄	—	13	8	no	—
146	C₄⋊C₄	—	13	16	no	—
147	C₄⋊C₄	—	13	4	no	—
148	C₄⋊C₄	—	13	16	no	—
149	C₄⋊C₄	—	13	8	no	—
150	C₄⋊C₄	—	13	16	no	—
151	C₄⋊C₄	—	13	8	no	—
152	C₄⋊C₄	C₂²×D₁₃	1	4	yes	—
153	C₄⋊C₄	C₂²×D₁₃	1	8	yes	—
154	C₄²	—	13	16	no	—
155	C₄²	—	13	8	no	—
156	C₄²	C₂²×D₁₃	1	8	yes	—
157	C₄²	C₂²×D₁₃	1	4	yes	—
158	C₁₃	C₂×#557	1	1	yes	characteristic, complemented, Sylow
159	C₂³	C₂³×D₁₃	1	1	yes	characteristic
160	Q₈	—	2	8	no	—
161	Q₈	—	13	16	no	—
162	Q₈	—	26	16	no	—
163	C₂×C₄	—	2	4	no	—
164	C₂×C₄	—	2	4	no	—
165	C₂×C₄	—	2	2	no	—
166	C₂×C₄	—	13	8	no	—
167	C₂×C₄	—	13	4	no	—
168	C₂×C₄	—	13	4	no	—
169	C₂×C₄	—	13	8	no	—
170	C₂×C₄	—	26	8	no	—
171	C₂×C₄	—	26	4	no	—
172	C₂×C₄	#6127	1	4	yes	—
173	C₂×C₄	Q₈×D₁₃	1	4	yes	—
174	C₂×C₄	C₂³×D₁₃	1	4	yes	—
175	C₂×C₄	C₂³×D₁₃	1	2	yes	—
176	C₂×C₄	C₂³×D₁₃	1	4	yes	—
177	C₂×C₄	C₂³×D₁₃	1	2	yes	—
178	C₂×C₄	C₂³×D₁₃	1	2	yes	—
179	C₂²	C₂×#6127	1	2	yes	—
180	C₂²	C₂×Q₈×D₁₃	1	2	yes	—
181	C₂²	#88257	1	2	yes	—
182	C₂²	C₂⁴×D₁₃	1	1	yes	characteristic
183	C₄	—	2	4	no	—
184	C₄	—	2	4	no	—
185	C₄	—	2	2	no	—
186	C₄	—	13	8	no	—
187	C₄	—	26	8	no	—
188	C₄	—	26	4	no	—
189	C₄	C₂×#6127	1	4	yes	—
190	C₄	C₂×Q₈×D₁₃	1	4	yes	—
191	C₂	#11719272	1	4	yes	direct product factor
192	C₂	C₂²×#6127	1	1	yes	characteristic
193	C₂	C₂²×Q₈×D₁₃	1	1	yes	characteristic
194	C₂	C₂×#88257	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	C₂³×D₁₃
commutator, cosocle	C₂²×C₁₃	C₂⁵
Frattini	C₂²	C₂⁴×D₁₃
Fitting	C₂×C₄×Q₈×C₁₃	C₂
socle, prime radical	C₂³×C₁₃	C₂⁴
hypercenter	C₂×C₄×Q₈	D₁₃
hypocenter	C₁₃	C₂×#557
LCS	G ▷ C₂²×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂³ ◁ C₂×C₄×Q₈

Complements

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

N	H ≅ G/N	type
3. #11719272	C₂	direct (N × H)
45. C₂×Dic₂₆	Q₈	semidirect
81. Dic₂₆	C₂×Q₈	semidirect
127. C₂×C₁₃	#557	semidirect
158. C₁₃	C₂×#557	semidirect
191. C₂	#11719272	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×Q₈×C₁₃	2
C₂×#88198	2
#11719272	2
C₂×#88143	2
C₂×#88141	2
C₂×#88124	2
C₂×#88123	2
C₂×C₄×Dic₂₆	2
C₂×#557	13

Subgroups — C2×#11719272 #13128408

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#11719272 #13128408