Subgroups — C₄×#11719047 #16796721

Order 3328.

1790 conjugacy classes of subgroups.

The subgroup lattice has 198 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#11719047	C₂	1	4	yes	maximal
2	C₂×C₄×D₁₃⋊C₈	C₂	1	2	yes	maximal
3	C₄×#88110	C₂	1	8	yes	maximal, complemented
4	C₄³×D₁₃	C₂	1	1	yes	maximal, characteristic
5	C₂²×D₁₃⋊C₈	C₂²	1	4	yes	—
6	C₂×C₄²×D₁₃	C₄	1	4	yes	—
7	C₂×C₄²×D₁₃	C₂²	1	1	yes	characteristic
8	C₂×C₄²×D₁₃	C₂²	1	2	yes	—
9	C₂×#88110	C₂²	1	16	yes	—
10	C₂×C₄×#1057	C₂²	1	8	yes	—
11	#11719047	C₄	1	32	yes	direct product factor
12	C₄×D₁₃⋊C₈	C₄	1	16	yes	complemented
13	C₄³×C₁₃	C₄	1	1	yes	characteristic
14	C₄²×Dic₁₃	C₄	1	2	yes	—
15	C₄²×Dic₁₃	C₄	1	1	yes	characteristic
16	C₄²×Dic₁₃	C₂²	1	4	yes	—
17	C₂²×C₄×D₁₃	C₂×C₄	1	4	yes	—
18	C₂²×C₄×D₁₃	C₂×C₄	1	2	yes	—
19	C₂²×C₄×D₁₃	C₂³	1	1	yes	characteristic
20	C₂²×#1057	C₂³	1	8	yes	—
21	C₂×D₁₃⋊C₈	C₂×C₄	1	16	yes	—
22	C₂×D₁₃⋊C₈	C₂×C₄	1	32	yes	—
23	C₂×C₄²×C₁₃	C₂×C₄	1	4	yes	—
24	C₂×C₄²×C₁₃	C₂×C₄	1	2	yes	—
25	C₂×C₄²×C₁₃	C₂×C₄	1	1	yes	characteristic
26	C₂×C₄×Dic₁₃	C₂×C₄	1	4	yes	—
27	C₂×C₄×Dic₁₃	C₂×C₄	1	8	yes	—
28	C₂×C₄×Dic₁₃	C₂×C₄	1	2	yes	—
29	C₂×C₄×Dic₁₃	C₂×C₄	1	1	yes	characteristic
30	C₂×C₄×Dic₁₃	C₂³	1	2	yes	—
31	C₂×C₄×Dic₁₃	C₂³	1	4	yes	—
32	C₄²×D₁₃	—	2	16	no	—
33	C₄²×D₁₃	C₂×C₄	1	8	yes	—
34	C₄²×D₁₃	C₂×C₄	1	16	yes	—
35	#88110	C₂×C₄	1	64	yes	complemented
36	C₄×#1057	C₂×C₄	1	32	yes	complemented
37	C₂×C₄×#97	—	13	1	no	maximal, Sylow
38	C₂³×D₁₃	C₂²×C₄	1	1	yes	characteristic
39	C₂²×C₄×C₁₃	C₂²×C₄	1	4	yes	—
40	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
41	C₂²×C₄×C₁₃	C₂²×C₄	1	2	yes	—
42	C₂²×Dic₁₃	C₂²×C₄	1	4	yes	—
43	C₂²×Dic₁₃	C₂²×C₄	1	2	yes	—
44	C₂²×Dic₁₃	C₂⁴	1	1	yes	characteristic
45	C₂×C₄×D₁₃	—	2	16	no	—
46	C₂×C₄×D₁₃	C₄²	1	16	yes	—
47	C₂×C₄×D₁₃	C₄²	1	8	yes	—
48	C₂×C₄×D₁₃	M₁₆	1	16	yes	—
49	C₂×C₄×D₁₃	C₂²×C₄	1	4	yes	—
50	C₂×C₄×D₁₃	C₂²×C₄	1	8	yes	—
51	C₂×#1057	C₂²×C₄	1	16	yes	—
52	C₂×#1057	C₂²×C₄	1	32	yes	—
53	D₁₃⋊C₈	C₄²	1	64	yes	complemented
54	C₄²×C₁₃	—	2	8	no	—
55	C₄²×C₁₃	C₄²	1	8	yes	—
56	C₄²×C₁₃	C₄²	1	4	yes	—
57	C₄×Dic₁₃	—	2	8	no	—
58	C₄×Dic₁₃	—	2	16	no	—
59	C₄×Dic₁₃	C₄²	1	8	yes	—
60	C₄×Dic₁₃	C₄²	1	4	yes	—
61	C₄×Dic₁₃	C₂²×C₄	1	8	yes	—
62	C₄×Dic₁₃	C₂²×C₄	1	16	yes	—
63	C₂²×#97	—	13	4	no	—
64	C₂²×C₄×C₈	—	13	2	no	—
65	C₂×C₄³	—	13	1	no	—
66	C₄×#97	—	13	8	no	—
67	C₂³×C₁₃	C₂³×C₄	1	1	yes	characteristic
68	C₂²×D₁₃	C₂×C₄²	1	2	yes	—
69	C₂²×D₁₃	C₂×C₄²	1	4	yes	—
70	C₂²×D₁₃	C₂×M₁₆	1	8	yes	—
71	C₂×C₄×C₁₃	—	2	8	no	—
72	C₂×C₄×C₁₃	C₂×C₄²	1	8	yes	—
73	C₂×C₄×C₁₃	C₂×C₄²	1	2	yes	—
74	C₂×C₄×C₁₃	C₂×C₄²	1	4	yes	—
75	C₂×C₄×C₁₃	C₂×C₄²	1	4	yes	—
76	C₂×C₄×C₁₃	C₂×M₁₆	1	8	yes	—
77	C₂×Dic₁₃	—	2	8	no	—
78	C₂×Dic₁₃	C₂×C₄²	1	8	yes	—
79	C₂×Dic₁₃	C₂×C₄²	1	4	yes	—
80	C₂×Dic₁₃	C₂×M₁₆	1	8	yes	—
81	C₂×Dic₁₃	C₂³×C₄	1	2	yes	—
82	C₂×Dic₁₃	C₂³×C₄	1	4	yes	—
83	C₄×D₁₃	—	2	32	no	—
84	C₄×D₁₃	#97	1	32	yes	complemented
85	C₄×D₁₃	C₂×C₄²	1	16	yes	—
86	#1057	C₂×C₄²	1	32	yes	complemented
87	C₂³×C₈	—	13	4	no	—
88	C₂²×C₄²	—	13	2	no	—
89	C₂²×C₄²	—	13	1	no	—
90	C₂²×C₄²	—	13	4	no	—
91	C₂×#97	—	13	32	no	—
92	C₂×#97	—	13	16	no	—
93	C₂×C₄×C₈	—	13	16	no	—
94	C₂×C₄×C₈	—	13	8	no	—
95	C₄³	—	13	4	no	—
96	C₄³	—	13	2	no	—
97	C₄³	—	13	1	no	—
98	C₄³	#261	1	1	yes	characteristic
99	C₂²×C₁₃	C₂²×C₄²	1	1	yes	characteristic
100	C₂²×C₁₃	C₂²×C₄²	1	2	yes	—
101	C₂²×C₁₃	C₂²×M₁₆	1	4	yes	—
102	C₂×D₁₃	C₄³	1	4	yes	—
103	C₂×D₁₃	C₂×#97	1	8	yes	—
104	C₂×D₁₃	C₄×M₁₆	1	16	yes	—
105	C₄×C₁₃	—	2	8	no	—
106	C₄×C₁₃	C₄³	1	4	yes	—
107	C₄×C₁₃	C₂×#97	1	8	yes	complemented
108	Dic₁₃	—	2	8	no	—
109	Dic₁₃	C₂×#97	1	8	yes	complemented
110	Dic₁₃	C₂²×C₄²	1	4	yes	—
111	C₂³×C₄	—	13	1	no	—
112	C₂³×C₄	—	13	2	no	—
113	C₂³×C₄	—	13	4	no	—
114	C₂²×C₈	—	13	8	no	—
115	C₂²×C₈	—	13	16	no	—
116	C₂²×C₈	—	13	32	no	—
117	C₂×C₄²	—	13	1	no	—
118	C₂×C₄²	—	13	2	no	—
119	C₂×C₄²	—	13	2	no	—
120	C₂×C₄²	—	13	4	no	—
121	C₂×C₄²	—	13	8	no	—
122	C₂×C₄²	—	13	16	no	—
123	C₂×C₄²	—	13	8	no	—
124	C₂×C₄²	—	13	4	no	—
125	C₂×C₄²	—	26	16	no	—
126	C₂×C₄²	C₂×#261	1	4	yes	—
127	C₂×C₄²	C₂×#261	1	2	yes	—
128	C₂×C₄²	C₂×#261	1	1	yes	characteristic
129	#97	—	13	64	no	—
130	C₄×C₈	—	13	32	no	—
131	C₂×C₁₃	C₂×C₄³	1	1	yes	characteristic
132	C₂×C₁₃	C₂²×#97	1	2	yes	—
133	C₂×C₁₃	C₂×C₄×M₁₆	1	4	yes	—
134	D₁₃	C₄×#97	1	8	yes	complemented
135	C₂⁴	—	13	1	no	—
136	C₂²×C₄	—	13	1	no	—
137	C₂²×C₄	—	13	2	no	—
138	C₂²×C₄	—	13	16	no	—
139	C₂²×C₄	—	13	4	no	—
140	C₂²×C₄	—	13	8	no	—
141	C₂²×C₄	—	13	8	no	—
142	C₂²×C₄	—	13	4	no	—
143	C₂²×C₄	—	13	16	no	—
144	C₂²×C₄	—	26	16	no	—
145	C₂²×C₄	C₂²×#261	1	4	yes	—
146	C₂²×C₄	C₂²×#261	1	2	yes	—
147	C₂²×C₄	C₂²×#261	1	1	yes	characteristic
148	C₂×C₈	—	13	16	no	—
149	C₂×C₈	—	13	32	no	—
150	C₂×C₈	—	13	64	no	—
151	C₄²	—	2	8	no	—
152	C₄²	—	13	8	no	—
153	C₄²	—	13	16	no	—
154	C₄²	—	13	4	no	—
155	C₄²	—	13	8	no	—
156	C₄²	—	26	16	no	—
157	C₄²	—	26	8	no	—
158	C₄²	C₄×#261	1	8	yes	—
159	C₄²	C₄×#261	1	4	yes	—
160	C₁₃	C₂×C₄×#97	1	1	yes	characteristic, complemented, Sylow
161	C₂³	—	13	8	no	—
162	C₂³	—	13	2	no	—
163	C₂³	—	13	4	no	—
164	C₂³	C₂³×#261	1	1	yes	characteristic
165	C₂×C₄	—	2	8	no	—
166	C₂×C₄	—	13	8	no	—
167	C₂×C₄	—	13	2	no	—
168	C₂×C₄	—	13	4	no	—
169	C₂×C₄	—	13	4	no	—
170	C₂×C₄	—	13	32	no	—
171	C₂×C₄	—	13	16	no	—
172	C₂×C₄	—	13	8	no	—
173	C₂×C₄	—	26	32	no	—
174	C₂×C₄	—	26	8	no	—
175	C₂×C₄	D₁₃⋊M₁₆	1	8	yes	—
176	C₂×C₄	C₂×C₄×#261	1	8	yes	—
177	C₂×C₄	C₂×C₄×#261	1	4	yes	—
178	C₂×C₄	C₂×C₄×#261	1	2	yes	—
179	C₂×C₄	C₂×C₄×#261	1	4	yes	—
180	C₈	—	13	32	no	—
181	C₂²	—	13	8	no	—
182	C₂²	—	13	16	no	—
183	C₂²	—	13	4	no	—
184	C₂²	C₂×D₁₃⋊M₁₆	1	4	yes	—
185	C₂²	C₂²×C₄×#261	1	1	yes	characteristic
186	C₂²	C₂²×C₄×#261	1	2	yes	—
187	C₄	—	2	8	no	—
188	C₄	—	13	8	no	—
189	C₄	—	13	4	no	—
190	C₄	—	26	8	no	—
191	C₄	#11719047	1	8	yes	direct product factor
192	C₄	C₄²×#261	1	4	yes	—
193	C₂	—	13	8	no	—
194	C₂	C₂×C₄²×#261	1	1	yes	characteristic
195	C₂	C₂×#11719047	1	2	yes	—
196	C₂	C₄×D₁₃⋊M₁₆	1	4	yes	—

	subgroup	G/H
center	C₂×C₄²	C₂×#261
commutator	C₂×C₁₃	C₂×C₄³
Frattini	C₂³	C₂³×#261
Fitting	C₄³×C₁₃	C₄
socle	C₂³×C₁₃	C₂³×C₄
prime radical	C₂³×D₁₃	C₂²×C₄
cosocle	C₂²×Dic₁₃	C₂⁴
hypercenter	C₄³	#261
hypocenter	C₁₃	C₂×C₄×#97
LCS	G ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂×C₄² ◁ C₄³

Complements

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

N	H ≅ G/N	type
3. C₄×#88110	C₂	semidirect
11. #11719047	C₄	direct (N × H)
12. C₄×D₁₃⋊C₈	C₄	semidirect
35. #88110	C₂×C₄	semidirect
36. C₄×#1057	C₂×C₄	semidirect
53. D₁₃⋊C₈	C₄²	semidirect
84. C₄×D₁₃	#97	semidirect
86. #1057	C₂×C₄²	semidirect
107. C₄×C₁₃	C₂×#97	semidirect
109. Dic₁₃	C₂×#97	semidirect
134. D₁₃	C₄×#97	semidirect
160. C₁₃	C₂×C₄×#97	semidirect
191. C₄	#11719047	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×#11719047	2
C₂×C₄×D₁₃⋊C₈	2
C₄×#88110	2
C₄³×D₁₃	2
C₂×C₄×#97	13

Subgroups — C4×#11719047 #16796721

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄×#11719047 #16796721