Subgroups — C₄×#11719517 #16021170

Order 3328.

3402 conjugacy classes of subgroups.

The subgroup lattice has 214 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#11719517	C₂	1	2	yes	maximal
2	#13117201	C₂	1	8	yes	maximal, complemented
3	#13117193	C₂	1	6	yes	maximal
4	C₄×Q₈×Dic₁₃	C₂	1	8	yes	maximal, complemented
5	C₄×#88180	C₂	1	6	yes	maximal
6	C₂²×C₄×Q₈×C₁₃	C₂	1	1	yes	maximal, characteristic
7	C₂³×Q₈×C₁₃	C₂²	1	1	yes	characteristic
8	C₂×C₄×Q₈×C₁₃	C₄	1	16	yes	complemented
9	C₂×C₄×Q₈×C₁₃	C₂²	1	4	yes	—
10	C₂×C₄×Q₈×C₁₃	C₂²	1	4	yes	—
11	C₂²×C₁₃×C₄⋊C₄	C₂²	1	3	yes	—
12	C₂²×C₄²×C₁₃	C₂²	1	3	yes	—
13	#11719517	C₄	1	32	yes	direct product factor
14	C₂×Q₈×Dic₁₃	C₂²	1	16	yes	—
15	C₂×#88180	C₂²	1	12	yes	—
16	C₄×C₂²⋊Dic₁₃	C₂²	1	12	yes	—
17	C₄×C₂²⋊Dic₁₃	C₂²	1	4	yes	—
18	C₄⋊C₄×Dic₁₃	C₂²	1	48	yes	—
19	C₄×C₄⋊Dic₁₃	C₂²	1	12	yes	—
20	C₄×C₄⋊Dic₁₃	C₂²	1	12	yes	—
21	#11718593	C₂²	1	12	yes	—
22	C₄²×Dic₁₃	C₂²	1	12	yes	—
23	C₂²×Q₈×C₁₃	C₂×C₄	1	16	yes	—
24	C₂²×Q₈×C₁₃	C₂×C₄	1	8	yes	—
25	C₂²×Q₈×C₁₃	C₂³	1	4	yes	—
26	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
27	C₂³×C₄×C₁₃	C₂³	1	3	yes	—
28	C₂³×C₄×C₁₃	C₂³	1	3	yes	—
29	C₄×Q₈×C₁₃	C₂×C₄	1	32	yes	—
30	C₄×Q₈×C₁₃	C₂×C₄	1	32	yes	—
31	C₂×C₁₃×C₄⋊C₄	C₂×C₄	1	24	yes	—
32	C₂×C₁₃×C₄⋊C₄	C₂³	1	12	yes	—
33	C₂×C₄²×C₁₃	C₂×C₄	1	24	yes	—
34	C₂×C₄²×C₁₃	C₂³	1	6	yes	—
35	C₂×C₄²×C₁₃	C₂³	1	6	yes	—
36	C₂×C₂²⋊Dic₁₃	C₂³	1	8	yes	—
37	Q₈×Dic₁₃	C₂×C₄	1	128	yes	complemented
38	#88180	C₂×C₄	1	96	yes	—
39	C₂×C₄⋊Dic₁₃	C₂³	1	24	yes	—
40	C₂×C₄×Dic₁₃	C₂³	1	8	yes	—
41	C₂×C₄×Dic₁₃	C₂³	1	24	yes	—
42	C₂×C₄×Dic₁₃	C₂³	1	24	yes	—
43	#88071	C₂³	1	8	yes	—
44	#88071	C₂³	1	24	yes	—
45	C₄×#519	—	13	1	no	maximal, Sylow
46	C₂⁴×C₁₃	C₂⁴	1	1	yes	characteristic
47	C₂×Q₈×C₁₃	C₄²	1	64	yes	complemented
48	C₂×Q₈×C₁₃	C₂²×C₄	1	32	yes	—
49	C₂×Q₈×C₁₃	C₂²×C₄	1	16	yes	—
50	C₂²×C₄×C₁₃	—	2	4	no	—
51	C₂²×C₄×C₁₃	—	4	6	no	—
52	C₂²×C₄×C₁₃	C₂²×C₄	1	24	yes	—
53	C₂²×C₄×C₁₃	C₂²×C₄	1	4	yes	—
54	C₂²×C₄×C₁₃	C₂²×C₄	1	12	yes	—
55	C₂²×C₄×C₁₃	C₂²×C₄	1	12	yes	—
56	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
57	C₂²×C₄×C₁₃	C₂⁴	1	6	yes	—
58	C₂²×C₄×C₁₃	C₂⁴	1	6	yes	—
59	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
60	C₂²×Dic₁₃	C₂⁴	1	16	yes	—
61	C₁₃×C₄⋊C₄	C₂²×C₄	1	48	yes	—
62	C₄²×C₁₃	C₂²×C₄	1	24	yes	—
63	C₄²×C₁₃	C₂²×C₄	1	24	yes	—
64	C₂²⋊Dic₁₃	C₂²×C₄	1	32	yes	—
65	C₄⋊Dic₁₃	C₂²×C₄	1	96	yes	—
66	C₄×Dic₁₃	—	2	16	no	—
67	C₄×Dic₁₃	—	4	24	no	—
68	C₄×Dic₁₃	C₂²×C₄	1	96	yes	—
69	C₂×#519	—	13	2	no	—
70	C₂²×C₄×Q₈	D₁₃	1	1	yes	characteristic
71	#2276	—	13	8	no	—
72	#2274	—	13	6	no	—
73	C₄²×Q₈	—	13	8	no	—
74	C₄×#117	—	13	6	no	—
75	C₂³×C₁₃	—	2	2	no	—
76	C₂³×C₁₃	—	2	2	no	—
77	C₂³×C₁₃	C₂³×C₄	1	4	yes	—
78	C₂³×C₁₃	C₂³×C₄	1	2	yes	—
79	C₂³×C₁₃	C₂⁵	1	1	yes	characteristic
80	Q₈×C₁₃	C₂×C₄²	1	64	yes	—
81	C₂×C₄×C₁₃	—	2	2	no	—
82	C₂×C₄×C₁₃	—	2	12	no	—
83	C₂×C₄×C₁₃	—	2	8	no	—
84	C₂×C₄×C₁₃	—	4	12	no	—
85	C₂×C₄×C₁₃	C₂×C₄²	1	48	yes	—
86	C₂×C₄×C₁₃	C₂³×C₄	1	2	yes	—
87	C₂×C₄×C₁₃	C₂³×C₄	1	12	yes	—
88	C₂×C₄×C₁₃	C₂³×C₄	1	2	yes	—
89	C₂×C₄×C₁₃	C₂³×C₄	1	24	yes	—
90	C₂×C₄×C₁₃	C₂³×C₄	1	12	yes	—
91	C₂×C₄×C₁₃	2₋¹⁺⁴	1	4	yes	—
92	C₂×Dic₁₃	—	2	16	no	—
93	C₂×Dic₁₃	—	2	16	no	—
94	C₂×Dic₁₃	C₂³×C₄	1	32	yes	—
95	C₂³×Q₈	C₂×D₁₃	1	1	yes	characteristic
96	#519	—	13	32	no	—
97	C₂×C₄×Q₈	—	13	16	no	—
98	C₂×C₄×Q₈	Dic₁₃	1	16	yes	complemented
99	C₂×C₄×Q₈	C₂×D₁₃	1	4	yes	—
100	C₂×C₄×Q₈	C₂×D₁₃	1	4	yes	—
101	C₂×#117	—	13	12	no	—
102	C₂²×C₄⋊C₄	C₂×D₁₃	1	3	yes	—
103	C₂²×C₄²	C₂×D₁₃	1	3	yes	—
104	C₄×C₄⋊C₄	—	13	48	no	—
105	C₄×C₄⋊C₄	—	13	12	no	—
106	C₄×C₄⋊C₄	—	13	12	no	—
107	C₄×C₂²⋊C₄	—	13	4	no	—
108	C₄×C₂²⋊C₄	—	13	12	no	—
109	#376	—	13	12	no	—
110	C₄³	—	13	12	no	—
111	C₂²×C₁₃	—	2	2	no	—
112	C₂²×C₁₃	—	2	2	no	—
113	C₂²×C₁₃	—	2	8	no	—
114	C₂²×C₁₃	C₂²×C₄²	1	4	yes	—
115	C₂²×C₁₃	C₂⁴×C₄	1	2	yes	—
116	C₂²×C₁₃	C₂⁴×C₄	1	1	yes	characteristic
117	C₂²×C₁₃	C₂×2₋¹⁺⁴	1	2	yes	—
118	C₂²×C₁₃	#585	1	2	yes	—
119	C₄×C₁₃	—	2	2	no	—
120	C₄×C₁₃	—	2	12	no	—
121	C₄×C₁₃	C₂²×C₄²	1	24	yes	—
122	C₄×C₁₃	#519	1	4	yes	complemented
123	Dic₁₃	—	2	32	no	—
124	C₂²×Q₈	C₄×D₁₃	1	16	yes	—
125	C₂²×Q₈	C₂×Dic₁₃	1	8	yes	—
126	C₂²×Q₈	C₂²×D₁₃	1	4	yes	—
127	C₂³×C₄	C₂²×D₁₃	1	1	yes	characteristic
128	C₂³×C₄	C₂²×D₁₃	1	3	yes	—
129	C₂³×C₄	C₂²×D₁₃	1	3	yes	—
130	C₄×Q₈	—	13	128	no	—
131	C₄×Q₈	C₂×Dic₁₃	1	32	yes	—
132	C₄×Q₈	C₂×Dic₁₃	1	32	yes	—
133	#117	—	13	96	no	—
134	C₂×C₄⋊C₄	—	13	24	no	—
135	C₂×C₄⋊C₄	C₂×Dic₁₃	1	24	yes	—
136	C₂×C₄⋊C₄	C₂²×D₁₃	1	12	yes	—
137	C₂×C₂²⋊C₄	—	13	8	no	—
138	C₂×C₄²	—	13	24	no	—
139	C₂×C₄²	—	13	8	no	—
140	C₂×C₄²	—	13	24	no	—
141	C₂×C₄²	C₂×Dic₁₃	1	24	yes	—
142	C₂×C₄²	C₂²×D₁₃	1	6	yes	—
143	C₂×C₄²	C₂²×D₁₃	1	6	yes	—
144	#95	—	13	8	no	—
145	#95	—	13	24	no	—
146	C₂×C₁₃	—	2	4	no	—
147	C₂×C₁₃	C₂³×C₄²	1	1	yes	characteristic
148	C₂×C₁₃	C₂×#519	1	1	yes	characteristic
149	C₂×C₁₃	#3428	1	1	yes	characteristic
150	C₂×C₁₃	C₄×2₋¹⁺⁴	1	4	yes	—
151	C₂⁴	C₂³×D₁₃	1	1	yes	characteristic
152	C₂×Q₈	C₄×Dic₁₃	1	64	yes	complemented
153	C₂×Q₈	C₂×C₄×D₁₃	1	32	yes	—
154	C₂×Q₈	C₂²×Dic₁₃	1	16	yes	—
155	C₂²×C₄	—	2	4	no	—
156	C₂²×C₄	—	4	6	no	—
157	C₂²×C₄	—	13	16	no	—
158	C₂²×C₄	C₂×C₄×D₁₃	1	24	yes	—
159	C₂²×C₄	C₂²×Dic₁₃	1	4	yes	—
160	C₂²×C₄	C₂²×Dic₁₃	1	12	yes	—
161	C₂²×C₄	C₂²×Dic₁₃	1	12	yes	—
162	C₂²×C₄	C₂³×D₁₃	1	1	yes	characteristic
163	C₂²×C₄	C₂³×D₁₃	1	6	yes	—
164	C₂²×C₄	C₂³×D₁₃	1	6	yes	—
165	C₂²×C₄	C₂³×D₁₃	1	1	yes	characteristic
166	C₄⋊C₄	—	13	96	no	—
167	C₄⋊C₄	C₂²×Dic₁₃	1	48	yes	—
168	C₂²⋊C₄	—	13	32	no	—
169	C₄²	—	13	96	no	—
170	C₄²	—	26	16	no	—
171	C₄²	—	52	24	no	—
172	C₄²	C₂²×Dic₁₃	1	24	yes	—
173	C₄²	C₂²×Dic₁₃	1	24	yes	—
174	C₁₃	C₄×#519	1	1	yes	characteristic, complemented, Sylow
175	C₂³	—	2	2	no	—
176	C₂³	—	2	2	no	—
177	C₂³	C₂²×C₄×D₁₃	1	4	yes	—
178	C₂³	C₂³×Dic₁₃	1	2	yes	—
179	C₂³	C₂⁴×D₁₃	1	1	yes	characteristic
180	Q₈	C₂×C₄×Dic₁₃	1	64	yes	—
181	C₂×C₄	—	2	2	no	—
182	C₂×C₄	—	2	12	no	—
183	C₂×C₄	—	2	8	no	—
184	C₂×C₄	—	4	12	no	—
185	C₂×C₄	—	13	32	no	—
186	C₂×C₄	—	26	16	no	—
187	C₂×C₄	—	26	16	no	—
188	C₂×C₄	C₂×C₄×Dic₁₃	1	48	yes	—
189	C₂×C₄	C₂²×C₄×D₁₃	1	24	yes	—
190	C₂×C₄	#88254	1	4	yes	—
191	C₂×C₄	C₂³×Dic₁₃	1	2	yes	—
192	C₂×C₄	C₂³×Dic₁₃	1	12	yes	—
193	C₂×C₄	C₂³×Dic₁₃	1	12	yes	—
194	C₂×C₄	C₂³×Dic₁₃	1	2	yes	—
195	C₂²	—	2	2	no	—
196	C₂²	—	2	2	no	—
197	C₂²	—	2	8	no	—
198	C₂²	C₂²×C₄×Dic₁₃	1	4	yes	—
199	C₂²	C₂³×C₄×D₁₃	1	2	yes	—
200	C₂²	C₂×#88254	1	2	yes	—
201	C₂²	#11719648	1	2	yes	—
202	C₂²	C₂⁴×Dic₁₃	1	1	yes	characteristic
203	C₄	—	2	2	no	—
204	C₄	—	2	12	no	—
205	C₄	—	26	32	no	—
206	C₄	C₂²×C₄×Dic₁₃	1	24	yes	—
207	C₄	#11719517	1	4	yes	direct product factor
208	C₂	—	2	4	no	—
209	C₂	C₂³×C₄×Dic₁₃	1	1	yes	characteristic
210	C₂	C₂×#11719517	1	1	yes	characteristic
211	C₂	#13128039	1	1	yes	characteristic
212	C₂	C₄×#88254	1	4	yes	—

	subgroup	G/H
center	C₂²×C₄	C₂³×D₁₃
commutator	C₂×C₁₃	C₂³×C₄²
Frattini	C₂³	C₂⁴×D₁₃
Fitting	C₂²×C₄×Q₈×C₁₃	C₂
socle, cosocle	C₂³×C₁₃	C₂⁵
prime radical	C₂⁴×C₁₃	C₂⁴
hypercenter	C₂²×C₄×Q₈	D₁₃
hypocenter	C₁₃	C₄×#519
LCS	G ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂²×C₄ ◁ C₂²×C₄×Q₈

Complements

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

N	H ≅ G/N	type
2. #13117201	C₂	semidirect
4. C₄×Q₈×Dic₁₃	C₂	semidirect
8. C₂×C₄×Q₈×C₁₃	C₄	semidirect
13. #11719517	C₄	direct (N × H)
37. Q₈×Dic₁₃	C₂×C₄	semidirect
47. C₂×Q₈×C₁₃	C₄²	semidirect
98. C₂×C₄×Q₈	Dic₁₃	semidirect
122. C₄×C₁₃	#519	semidirect
152. C₂×Q₈	C₄×Dic₁₃	semidirect
174. C₁₃	C₄×#519	semidirect
207. C₄	#11719517	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×#11719517	2
#13117201	2
#13117193	2
C₄×Q₈×Dic₁₃	2
C₄×#88180	2
C₂²×C₄×Q₈×C₁₃	2
C₄×#519	13

Subgroups — C4×#11719517 #16021170

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄×#11719517 #16021170