Subgroups — C₄×#11718143 #15768100

Order 3328.

1182 conjugacy classes of subgroups.

The subgroup lattice has 246 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄×C₄⋊Dic₁₃	C₂	1	2	yes	maximal
2	C₂×#11718143	C₂	1	4	yes	maximal
3	C₂²×C₄×C₈×C₁₃	C₂	1	1	yes	maximal, characteristic
4	C₂³×C₈×C₁₃	C₂²	1	2	yes	—
5	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic
6	C₂²×C₄⋊Dic₁₃	C₂²	1	4	yes	—
7	C₂²×C₄×Dic₁₃	—	2	2	no	—
8	C₂×C₄×C₈×C₁₃	—	2	4	no	—
9	C₂×C₄×C₈×C₁₃	C₄	1	4	yes	complemented
10	C₂×#88071	—	2	2	no	—
11	C₄×C₄⋊Dic₁₃	—	2	4	no	—
12	C₄×C₄⋊Dic₁₃	C₄	1	8	yes	complemented
13	#11718143	C₄	1	16	yes	direct product factor
14	C₂³×C₄×C₁₃	D₄	1	1	yes	characteristic
15	C₂³×C₄×C₁₃	D₄	1	1	yes	characteristic
16	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
17	C₂³×Dic₁₃	—	2	4	no	—
18	C₂²×C₈×C₁₃	—	2	4	no	—
19	C₂²×C₈×C₁₃	—	2	4	no	—
20	C₂²×C₈×C₁₃	C₂×C₄	1	8	yes	—
21	C₂²×C₈×C₁₃	C₂×C₄	1	4	yes	—
22	C₂×C₄²×C₁₃	C₂×C₄	1	4	yes	—
23	C₂×C₄²×C₁₃	C₂×C₄	1	2	yes	—
24	C₂×C₄²×C₁₃	D₄	1	4	yes	—
25	C₂×C₄²×C₁₃	Q₈	1	2	yes	—
26	C₂×C₄⋊Dic₁₃	—	2	4	no	—
27	C₂×C₄⋊Dic₁₃	—	2	8	no	—
28	C₂×C₄⋊Dic₁₃	C₂×C₄	1	8	yes	—
29	C₂×C₄⋊Dic₁₃	C₂×C₄	1	16	yes	—
30	C₂×C₄×Dic₁₃	—	2	8	no	—
31	C₂×C₄×Dic₁₃	—	4	4	no	—
32	C₂×C₄×Dic₁₃	—	4	4	no	—
33	C₄×C₈×C₁₃	—	2	8	no	—
34	#88071	—	2	8	no	—
35	C₄×#340	—	13	1	no	maximal, Sylow
36	C₂⁴×C₁₃	C₂×D₄	1	1	yes	characteristic
37	C₂²×C₄×C₁₃	—	2	4	no	—
38	C₂²×C₄×C₁₃	C₂²⋊C₄	1	4	yes	—
39	C₂²×C₄×C₁₃	C₂²⋊C₄	1	4	yes	—
40	C₂²×C₄×C₁₃	C₄⋊C₄	1	2	yes	—
41	C₂²×C₄×C₁₃	C₄⋊C₄	1	2	yes	—
42	C₂²×C₄×C₁₃	D₈	1	2	yes	—
43	C₂²×C₄×C₁₃	SD₁₆	1	4	yes	—
44	C₂²×C₄×C₁₃	Q₁₆	1	2	yes	—
45	C₂²×C₄×C₁₃	C₂²×C₄	1	2	yes	—
46	C₂²×C₄×C₁₃	C₂²×C₄	1	4	yes	—
47	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
48	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
49	C₂²×C₄×C₁₃	C₂×Q₈	1	1	yes	characteristic
50	C₂²×C₄×C₁₃	#41	1	4	yes	—
51	C₂²×Dic₁₃	—	2	8	no	—
52	C₂²×Dic₁₃	—	2	16	no	—
53	C₂²×Dic₁₃	—	4	4	no	—
54	C₂²×Dic₁₃	—	4	4	no	—
55	C₂²×Dic₁₃	—	4	8	no	—
56	C₂×C₈×C₁₃	—	2	4	no	—
57	C₂×C₈×C₁₃	—	2	4	no	—
58	C₂×C₈×C₁₃	—	2	16	no	—
59	C₂×C₈×C₁₃	C₄²	1	8	yes	complemented
60	C₄²×C₁₃	C₄²	1	4	yes	—
61	C₄²×C₁₃	C₂²⋊C₄	1	4	yes	—
62	C₄²×C₁₃	C₄⋊C₄	1	8	yes	—
63	C₄⋊Dic₁₃	—	2	8	no	—
64	C₄⋊Dic₁₃	—	2	16	no	—
65	C₄⋊Dic₁₃	C₄²	1	16	yes	complemented
66	C₄×Dic₁₃	—	4	16	no	—
67	C₂²×C₄×C₈	D₁₃	1	1	yes	characteristic
68	C₂×C₄×C₄⋊C₄	—	13	2	no	—
69	C₂×#340	—	13	4	no	—
70	C₂³×C₁₃	C₂×C₂²⋊C₄	1	2	yes	—
71	C₂³×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
72	C₂³×C₁₃	C₄×D₄	1	4	yes	—
73	C₂³×C₁₃	C₂×D₈	1	1	yes	characteristic
74	C₂³×C₁₃	C₂×SD₁₆	1	2	yes	—
75	C₂³×C₁₃	C₂×Q₁₆	1	1	yes	characteristic
76	C₂³×C₁₃	#135	1	4	yes	—
77	C₂×C₄×C₁₃	—	2	8	no	—
78	C₂×C₄×C₁₃	—	2	4	no	—
79	C₂×C₄×C₁₃	#95	1	4	yes	—
80	C₂×C₄×C₁₃	#95	1	4	yes	—
81	C₂×C₄×C₁₃	#102	1	8	yes	—
82	C₂×C₄×C₁₃	#103	1	8	yes	—
83	C₂×C₄×C₁₃	#106	1	4	yes	—
84	C₂×C₄×C₁₃	#107	1	4	yes	—
85	C₂×C₄×C₁₃	C₂×C₄²	1	1	yes	characteristic
86	C₂×C₄×C₁₃	C₂×C₄²	1	2	yes	—
87	C₂×C₄×C₁₃	C₂×C₄²	1	4	yes	—
88	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
89	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	2	yes	—
90	C₂×C₄×C₁₃	#117	1	2	yes	—
91	C₂×C₄×C₁₃	#117	1	4	yes	—
92	C₂×C₄×C₁₃	C₄×D₄	1	8	yes	—
93	C₂×C₄×C₁₃	C₄×Q₈	1	4	yes	—
94	C₂×Dic₁₃	—	2	16	no	—
95	C₂×Dic₁₃	—	4	8	no	—
96	C₂×Dic₁₃	—	4	8	no	—
97	C₂×Dic₁₃	—	4	16	no	—
98	C₂×Dic₁₃	—	4	16	no	—
99	C₈×C₁₃	—	2	8	no	—
100	C₂³×C₈	C₂×D₁₃	1	2	yes	—
101	C₂²×C₄⋊C₄	—	13	4	no	—
102	C₂²×C₄²	—	26	2	no	—
103	C₂²×C₄²	C₂×D₁₃	1	1	yes	characteristic
104	C₂×C₄×C₈	—	2	4	no	—
105	C₂×C₄×C₈	Dic₁₃	1	4	yes	complemented
106	C₄×C₄⋊C₄	—	13	8	no	—
107	C₄×C₄⋊C₄	—	26	4	no	—
108	C₂×#95	—	26	2	no	—
109	#340	—	13	16	no	—
110	C₂²×C₁₃	C₂×#95	1	1	yes	characteristic
111	C₂²×C₁₃	C₄×C₂²⋊C₄	1	4	yes	—
112	C₂²×C₁₃	C₄×C₄⋊C₄	1	2	yes	—
113	C₂²×C₁₃	C₂×#102	1	2	yes	—
114	C₂²×C₁₃	C₂×#103	1	2	yes	—
115	C₂²×C₁₃	#416	1	4	yes	—
116	C₂²×C₁₃	C₂×#106	1	1	yes	characteristic
117	C₂²×C₁₃	C₂×#107	1	1	yes	characteristic
118	C₂²×C₁₃	#427	1	2	yes	—
119	C₂²×C₁₃	C₄×D₈	1	4	yes	—
120	C₂²×C₁₃	C₄×SD₁₆	1	8	yes	—
121	C₂²×C₁₃	C₄×Q₁₆	1	4	yes	—
122	C₄×C₁₃	—	2	4	no	—
123	C₄×C₁₃	#340	1	8	yes	complemented
124	C₄×C₁₃	C₄³	1	1	yes	characteristic
125	C₄×C₁₃	#376	1	1	yes	characteristic
126	C₄×C₁₃	C₄×C₂²⋊C₄	1	2	yes	—
127	C₄×C₁₃	C₄×C₄⋊C₄	1	4	yes	—
128	Dic₁₃	—	4	16	no	—
129	C₂³×C₄	—	26	4	no	—
130	C₂³×C₄	D₅₂	1	1	yes	characteristic
131	C₂³×C₄	D₅₂	1	1	yes	characteristic
132	C₂³×C₄	C₂²×D₁₃	1	1	yes	characteristic
133	C₂²×C₈	—	2	4	no	—
134	C₂²×C₈	—	2	4	no	—
135	C₂²×C₈	C₄×D₁₃	1	8	yes	—
136	C₂²×C₈	C₂×Dic₁₃	1	4	yes	—
137	C₂×C₄⋊C₄	—	13	16	no	—
138	C₂×C₄⋊C₄	—	13	8	no	—
139	C₂×C₄⋊C₄	—	26	8	no	—
140	C₂×C₄⋊C₄	—	26	4	no	—
141	C₂×C₄²	—	26	8	no	—
142	C₂×C₄²	—	52	4	no	—
143	C₂×C₄²	—	52	4	no	—
144	C₂×C₄²	Dic₂₆	1	2	yes	—
145	C₂×C₄²	C₄×D₁₃	1	4	yes	—
146	C₂×C₄²	C₂×Dic₁₃	1	2	yes	—
147	C₂×C₄²	C₂²⋊D₁₃	1	4	yes	—
148	C₄×C₈	—	2	8	no	—
149	#95	—	26	8	no	—
150	C₂×C₁₃	C₄×#95	1	1	yes	characteristic
151	C₂×C₁₃	C₂×#340	1	1	yes	characteristic
152	C₂×C₁₃	#1735	1	1	yes	characteristic
153	C₂×C₁₃	C₄×#102	1	4	yes	—
154	C₂×C₁₃	C₄×#103	1	4	yes	—
155	C₂×C₁₃	C₄×#106	1	2	yes	—
156	C₂×C₁₃	C₄×#107	1	2	yes	—
157	C₂⁴	C₂×D₅₂	1	1	yes	characteristic
158	C₂²×C₄	—	2	4	no	—
159	C₂²×C₄	—	26	16	no	—
160	C₂²×C₄	—	26	8	no	—
161	C₂²×C₄	—	52	4	no	—
162	C₂²×C₄	—	52	4	no	—
163	C₂²×C₄	—	52	8	no	—
164	C₂²×C₄	#6095	1	4	yes	—
165	C₂²×C₄	D₁₀₄	1	2	yes	—
166	C₂²×C₄	Dic₅₂	1	2	yes	—
167	C₂²×C₄	C₄⋊Dic₁₃	1	2	yes	—
168	C₂²×C₄	C₄⋊Dic₁₃	1	2	yes	—
169	C₂²×C₄	#6103	1	4	yes	—
170	C₂²×C₄	#6103	1	4	yes	—
171	C₂²×C₄	C₂×Dic₂₆	1	1	yes	characteristic
172	C₂²×C₄	C₂×C₄×D₁₃	1	4	yes	—
173	C₂²×C₄	C₂×C₄×D₁₃	1	2	yes	—
174	C₂²×C₄	#6127	1	4	yes	—
175	C₂²×C₄	C₂²×Dic₁₃	1	1	yes	characteristic
176	C₂²×C₄	C₂×C₂²⋊D₁₃	1	2	yes	—
177	C₂×C₈	—	2	4	no	—
178	C₂×C₈	—	2	16	no	—
179	C₂×C₈	—	2	4	no	—
180	C₂×C₈	C₄×Dic₁₃	1	8	yes	complemented
181	C₄⋊C₄	—	13	16	no	—
182	C₄⋊C₄	—	26	8	no	—
183	C₄⋊C₄	—	26	16	no	—
184	C₄²	—	52	16	no	—
185	C₄²	C₄×Dic₁₃	1	4	yes	—
186	C₄²	#6101	1	8	yes	—
187	C₄²	C₂²⋊Dic₁₃	1	4	yes	—
188	C₁₃	C₄×#340	1	1	yes	characteristic, complemented, Sylow
189	C₂³	C₄×D₅₂	1	4	yes	—
190	C₂³	C₂×#6095	1	2	yes	—
191	C₂³	C₂×D₁₀₄	1	1	yes	characteristic
192	C₂³	#88158	1	4	yes	—
193	C₂³	C₂×Dic₅₂	1	1	yes	characteristic
194	C₂³	C₂×C₄⋊Dic₁₃	1	1	yes	characteristic
195	C₂³	C₂×#6103	1	2	yes	—
196	C₂×C₄	—	2	4	no	—
197	C₂×C₄	—	2	8	no	—
198	C₂×C₄	—	26	16	no	—
199	C₂×C₄	—	52	8	no	—
200	C₂×C₄	—	52	8	no	—
201	C₂×C₄	—	52	16	no	—
202	C₂×C₄	—	52	16	no	—
203	C₂×C₄	#88056	1	8	yes	—
204	C₂×C₄	#88057	1	4	yes	—
205	C₂×C₄	#88058	1	4	yes	—
206	C₂×C₄	#88061	1	8	yes	—
207	C₂×C₄	#88071	1	4	yes	—
208	C₂×C₄	#88071	1	4	yes	—
209	C₂×C₄	C₄×Dic₂₆	1	4	yes	—
210	C₂×C₄	C₄²×D₁₃	1	4	yes	—
211	C₂×C₄	#88126	1	4	yes	—
212	C₂×C₄	C₂×C₄×Dic₁₃	1	1	yes	characteristic
213	C₂×C₄	C₂×C₄×Dic₁₃	1	2	yes	—
214	C₂×C₄	C₂×#6101	1	2	yes	—
215	C₂×C₄	#88180	1	2	yes	—
216	C₂×C₄	C₄×C₂²⋊D₁₃	1	8	yes	—
217	C₂×C₄	C₂×C₂²⋊Dic₁₃	1	1	yes	characteristic
218	C₈	—	2	8	no	—
219	C₂²	C₄×#6095	1	8	yes	—
220	C₂²	C₄×D₁₀₄	1	4	yes	—
221	C₂²	C₄×Dic₅₂	1	4	yes	—
222	C₂²	C₄×C₄⋊Dic₁₃	1	2	yes	—
223	C₂²	C₄×#6103	1	4	yes	—
224	C₂²	C₂×#88056	1	2	yes	—
225	C₂²	C₂×#88057	1	1	yes	characteristic
226	C₂²	C₂×#88058	1	1	yes	characteristic
227	C₂²	#11718767	1	2	yes	—
228	C₂²	C₂×#88061	1	2	yes	—
229	C₂²	#11718774	1	4	yes	—
230	C₂²	C₂×#88071	1	1	yes	characteristic
231	C₄	—	2	4	no	—
232	C₄	—	52	16	no	—
233	C₄	#11718143	1	8	yes	direct product factor
234	C₄	C₄²×Dic₁₃	1	1	yes	characteristic
235	C₄	C₄×#6101	1	4	yes	—
236	C₄	#11718593	1	1	yes	characteristic
237	C₄	C₄×C₂²⋊Dic₁₃	1	2	yes	—
238	C₂	C₄×#88071	1	1	yes	characteristic
239	C₂	C₂×#11718143	1	1	yes	characteristic
240	C₂	#13114553	1	1	yes	characteristic
241	C₂	C₄×#88061	1	4	yes	—
242	C₂	C₄×#88056	1	4	yes	—
243	C₂	C₄×#88057	1	2	yes	—
244	C₂	C₄×#88058	1	2	yes	—

	subgroup	G/H
center	C₂³×C₄	D₅₂
commutator	C₄×C₁₃	C₄³
Frattini	C₂³×C₄	C₂²×D₁₃
Fitting	C₂²×C₄×C₈×C₁₃	C₂
socle, prime radical	C₂⁴×C₁₃	C₂×D₄
cosocle	C₂³×C₄×C₁₃	C₂³
hypercenter	C₂²×C₄×C₈	D₁₃
hypocenter	C₁₃	C₄×#340
LCS	G ▷ C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂³×C₄ ◁ C₂²×C₄² ◁ C₂²×C₄×C₈

Complements

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

N	H ≅ G/N	type
9. C₂×C₄×C₈×C₁₃	C₄	semidirect
12. C₄×C₄⋊Dic₁₃	C₄	semidirect
13. #11718143	C₄	direct (N × H)
59. C₂×C₈×C₁₃	C₄²	semidirect
65. C₄⋊Dic₁₃	C₄²	semidirect
105. C₂×C₄×C₈	Dic₁₃	semidirect
123. C₄×C₁₃	#340	semidirect
180. C₂×C₈	C₄×Dic₁₃	semidirect
188. C₁₃	C₄×#340	semidirect
233. C₄	#11718143	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×C₄⋊Dic₁₃	2
C₂×#11718143	2
C₂²×C₄×C₈×C₁₃	2
C₄×#340	13

Subgroups — C4×#11718143 #15768100

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄×#11718143 #15768100