Subgroups — C₄×#11718786 #15861026

Order 3328.

1034 conjugacy classes of subgroups.

The subgroup lattice has 240 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#11718786	C₂	1	2	yes	maximal
2	C₂×C₄×#6099	C₂	1	2	yes	maximal
3	#13114742	C₂	1	4	yes	maximal, complemented
4	C₄×#88059	C₂	1	4	yes	maximal, complemented
5	#13114563	C₂	1	2	yes	maximal
6	C₂×C₄×C₁₃×M₁₆	C₂	1	1	yes	maximal, characteristic
7	C₂²×C₁₃×M₁₆	C₂²	1	1	yes	characteristic
8	C₂²×C₁₃×M₁₆	C₂²	1	1	yes	characteristic
9	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic
10	C₂²×#6099	C₂²	1	4	yes	—
11	C₄×C₁₃×M₁₆	C₄	1	8	yes	—
12	C₂×C₁₃×#97	C₂²	1	2	yes	—
13	C₂×C₄×C₈×C₁₃	C₂²	1	2	yes	—
14	#11718786	C₄	1	16	yes	direct product factor
15	C₂×#88059	C₂²	1	8	yes	—
16	C₄×#6099	—	2	2	no	—
17	C₄×#6099	—	2	2	no	—
18	C₄×#6099	C₂²	1	4	yes	—
19	C₄×#6099	C₂²	1	4	yes	—
20	C₂×#88043	—	2	2	no	—
21	C₂×C₄×#1055	—	2	2	no	—
22	#11718144	C₂²	1	8	yes	—
23	C₂³×C₄×C₁₃	Q₈	1	2	yes	—
24	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
25	C₂×C₁₃×M₁₆	—	2	4	no	—
26	C₂×C₁₃×M₁₆	C₂×C₄	1	8	yes	—
27	C₂×C₁₃×M₁₆	C₂×C₄	1	4	yes	—
28	C₂×C₁₃×M₁₆	C₂×C₄	1	4	yes	—
29	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
30	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
31	C₂×C₄²×C₁₃	C₂×C₄	1	4	yes	—
32	C₂×C₄²×C₁₃	D₄	1	2	yes	—
33	C₂×C₄²×C₁₃	D₄	1	2	yes	—
34	C₂×C₄²×C₁₃	Q₈	1	2	yes	—
35	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
36	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
37	C₂×#6099	—	2	4	no	—
38	C₂×#6099	—	2	8	no	—
39	C₂×#6099	C₂×C₄	1	16	yes	—
40	C₂×#6099	C₂³	1	8	yes	—
41	C₂²×#1055	—	2	4	no	—
42	C₁₃×#97	C₂×C₄	1	8	yes	—
43	C₄×C₈×C₁₃	C₂×C₄	1	8	yes	—
44	#88059	C₂×C₄	1	32	yes	complemented
45	#88043	—	2	4	no	—
46	#88043	—	2	4	no	—
47	C₄×#1055	—	2	4	no	—
48	C₄×#1055	—	2	4	no	—
49	C₄×#430	—	13	1	no	maximal, Sylow
50	C₂⁴×C₁₃	C₂×Q₈	1	1	yes	characteristic
51	C₂²×C₄×C₁₃	—	4	4	no	—
52	C₂²×C₄×C₁₃	C₄⋊C₄	1	4	yes	—
53	C₂²×C₄×C₁₃	C₄⋊C₄	1	4	yes	—
54	C₂²×C₄×C₁₃	C₂²×C₄	1	4	yes	—
55	C₂²×C₄×C₁₃	C₂²×C₄	1	2	yes	—
56	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
57	C₂²×C₄×C₁₃	C₂×Q₈	1	2	yes	—
58	C₂²×C₄×C₁₃	C₂×Q₈	1	2	yes	—
59	C₂²×C₄×C₁₃	C₂×Q₈	1	1	yes	characteristic
60	C₂²×C₄×C₁₃	#41	1	4	yes	—
61	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
62	C₁₃×M₁₆	—	2	8	no	—
63	C₁₃×M₁₆	C₄²	1	16	yes	—
64	C₂×C₈×C₁₃	—	2	4	no	—
65	C₂×C₈×C₁₃	C₂²×C₄	1	4	yes	—
66	C₂×C₈×C₁₃	C₂²×C₄	1	8	yes	—
67	C₂×C₈×C₁₃	C₂²×C₄	1	4	yes	—
68	C₄²×C₁₃	C₄⋊C₄	1	4	yes	—
69	C₄²×C₁₃	C₄⋊C₄	1	4	yes	—
70	C₄²×C₁₃	C₂²×C₄	1	2	yes	—
71	C₄²×C₁₃	C₂²×C₄	1	2	yes	—
72	C₄²×C₁₃	C₂×D₄	1	2	yes	—
73	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
74	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
75	#6099	—	2	16	no	—
76	#6099	—	2	8	no	—
77	#6099	C₂²×C₄	1	16	yes	—
78	C₂×#1055	—	2	16	no	—
79	C₂×#1055	—	2	8	no	—
80	C₂×#430	—	13	2	no	—
81	C₂×C₄×M₁₆	—	13	2	no	—
82	C₂×C₄×M₁₆	D₁₃	1	1	yes	characteristic
83	#1778	—	13	4	no	—
84	C₄×#108	—	13	4	no	—
85	#1738	—	13	2	no	—
86	C₂³×C₁₃	—	4	2	no	—
87	C₂³×C₁₃	C₂×C₄⋊C₄	1	2	yes	—
88	C₂³×C₁₃	C₄×Q₈	1	4	yes	—
89	C₂³×C₁₃	C₂²×Q₈	1	1	yes	characteristic
90	C₂×C₄×C₁₃	—	2	8	no	—
91	C₂×C₄×C₁₃	—	2	4	no	—
92	C₂×C₄×C₁₃	—	4	4	no	—
93	C₂×C₄×C₁₃	—	4	2	no	—
94	C₂×C₄×C₁₃	C₂×C₄²	1	4	yes	—
95	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	2	yes	—
96	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	4	yes	—
97	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	2	yes	—
98	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	2	yes	—
99	C₂×C₄×C₁₃	#117	1	4	yes	—
100	C₂×C₄×C₁₃	C₄×D₄	1	8	yes	—
101	C₂×C₄×C₁₃	C₄×Q₈	1	4	yes	—
102	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
103	C₂×C₄×C₁₃	C₂³×C₄	1	2	yes	—
104	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
105	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
106	C₈×C₁₃	—	2	4	no	—
107	C₈×C₁₃	C₂×C₄²	1	8	yes	—
108	#1055	—	2	16	no	—
109	C₂²×M₁₆	—	13	4	no	—
110	C₂²×M₁₆	C₂×D₁₃	1	1	yes	characteristic
111	C₂²×M₁₆	C₂×D₁₃	1	1	yes	characteristic
112	C₂²×C₄²	C₂×D₁₃	1	1	yes	characteristic
113	#430	—	13	16	no	—
114	C₂×#108	—	13	8	no	—
115	C₄×M₁₆	—	13	4	no	—
116	C₄×M₁₆	—	13	4	no	—
117	C₄×M₁₆	—	26	2	no	—
118	C₄×M₁₆	—	26	2	no	—
119	C₄×M₁₆	Dic₁₃	1	8	yes	—
120	C₂×#97	—	26	2	no	—
121	C₂×#97	C₂×D₁₃	1	2	yes	—
122	C₂×C₄×C₈	—	26	2	no	—
123	C₂×C₄×C₈	C₂×D₁₃	1	2	yes	—
124	#341	—	13	8	no	—
125	C₂²×C₁₃	—	2	4	no	—
126	C₂²×C₁₃	—	2	2	no	—
127	C₂²×C₁₃	—	4	4	no	—
128	C₂²×C₁₃	C₄×C₄⋊C₄	1	4	yes	—
129	C₂²×C₁₃	C₂²×C₄⋊C₄	1	1	yes	characteristic
130	C₂²×C₁₃	C₂×C₄×Q₈	1	2	yes	—
131	C₄×C₁₃	—	2	4	no	—
132	C₄×C₁₃	—	2	2	no	—
133	C₄×C₁₃	C₄×C₄⋊C₄	1	4	yes	—
134	C₄×C₁₃	#430	1	4	yes	complemented
135	C₄×C₁₃	C₂²×C₄²	1	1	yes	characteristic
136	C₄×C₁₃	C₂×#117	1	1	yes	characteristic
137	C₄×C₁₃	C₂×C₄×D₄	1	2	yes	—
138	C₂³×C₄	Dic₂₆	1	2	yes	—
139	C₂³×C₄	C₂²×D₁₃	1	1	yes	characteristic
140	C₂×M₁₆	—	2	4	no	—
141	C₂×M₁₆	—	13	16	no	—
142	C₂×M₁₆	—	13	8	no	—
143	C₂×M₁₆	—	26	4	no	—
144	C₂×M₁₆	—	26	8	no	—
145	C₂×M₁₆	C₄×D₁₃	1	8	yes	—
146	C₂×M₁₆	C₂×Dic₁₃	1	4	yes	—
147	C₂×M₁₆	C₂×Dic₁₃	1	4	yes	—
148	C₂²×C₈	—	26	4	no	—
149	C₂²×C₈	C₂²×D₁₃	1	2	yes	—
150	C₂²×C₈	C₂²×D₁₃	1	2	yes	—
151	C₂×C₄²	Dic₂₆	1	2	yes	—
152	C₂×C₄²	D₅₂	1	2	yes	—
153	C₂×C₄²	D₅₂	1	2	yes	—
154	C₂×C₄²	C₂×Dic₁₃	1	4	yes	—
155	C₂×C₄²	C₂²×D₁₃	1	1	yes	characteristic
156	C₂×C₄²	C₂²×D₁₃	1	1	yes	characteristic
157	#108	—	13	32	no	—
158	#97	—	26	4	no	—
159	#97	—	26	4	no	—
160	#97	C₂×Dic₁₃	1	8	yes	—
161	C₄×C₈	—	26	4	no	—
162	C₄×C₈	—	26	4	no	—
163	C₄×C₈	C₂×Dic₁₃	1	8	yes	—
164	C₂×C₁₃	—	2	2	no	—
165	C₂×C₁₃	—	2	4	no	—
166	C₂×C₁₃	C₂×C₄×C₄⋊C₄	1	1	yes	characteristic
167	C₂×C₁₃	C₂×#430	1	2	yes	—
168	C₂⁴	C₂×Dic₂₆	1	1	yes	characteristic
169	C₂²×C₄	—	4	4	no	—
170	C₂²×C₄	C₄⋊Dic₁₃	1	4	yes	—
171	C₂²×C₄	C₄⋊Dic₁₃	1	4	yes	—
172	C₂²×C₄	C₂×Dic₂₆	1	2	yes	—
173	C₂²×C₄	C₂×Dic₂₆	1	2	yes	—
174	C₂²×C₄	C₂×Dic₂₆	1	1	yes	characteristic
175	C₂²×C₄	C₂×C₄×D₁₃	1	4	yes	—
176	C₂²×C₄	C₂×D₅₂	1	2	yes	—
177	C₂²×C₄	#6127	1	4	yes	—
178	C₂²×C₄	C₂²×Dic₁₃	1	2	yes	—
179	C₂²×C₄	C₂³×D₁₃	1	1	yes	characteristic
180	M₁₆	—	2	8	no	—
181	M₁₆	—	13	16	no	—
182	M₁₆	—	26	16	no	—
183	M₁₆	—	26	8	no	—
184	M₁₆	C₄×Dic₁₃	1	16	yes	—
185	C₂×C₈	—	2	4	no	—
186	C₂×C₈	—	26	16	no	—
187	C₂×C₈	—	26	8	no	—
188	C₂×C₈	C₂×C₄×D₁₃	1	8	yes	—
189	C₂×C₈	C₂²×Dic₁₃	1	4	yes	—
190	C₂×C₈	C₂²×Dic₁₃	1	4	yes	—
191	C₄²	C₄⋊Dic₁₃	1	4	yes	—
192	C₄²	C₄⋊Dic₁₃	1	4	yes	—
193	C₄²	C₂×D₅₂	1	2	yes	—
194	C₄²	C₂×D₅₂	1	1	yes	characteristic
195	C₄²	C₂×D₅₂	1	1	yes	characteristic
196	C₄²	C₂²×Dic₁₃	1	2	yes	—
197	C₄²	C₂²×Dic₁₃	1	2	yes	—
198	C₁₃	C₄×#430	1	1	yes	characteristic, complemented, Sylow
199	C₂³	—	4	2	no	—
200	C₂³	C₄×Dic₂₆	1	4	yes	—
201	C₂³	C₂×C₄⋊Dic₁₃	1	2	yes	—
202	C₂³	C₂²×Dic₂₆	1	1	yes	characteristic
203	C₂×C₄	—	2	8	no	—
204	C₂×C₄	—	2	4	no	—
205	C₂×C₄	—	4	4	no	—
206	C₂×C₄	—	4	2	no	—
207	C₂×C₄	C₄×Dic₂₆	1	4	yes	—
208	C₂×C₄	C₄×D₅₂	1	8	yes	—
209	C₂×C₄	C₂×C₄×Dic₁₃	1	4	yes	—
210	C₂×C₄	C₂×C₄⋊Dic₁₃	1	4	yes	—
211	C₂×C₄	C₂×C₄⋊Dic₁₃	1	2	yes	—
212	C₂×C₄	C₂×C₄⋊Dic₁₃	1	2	yes	—
213	C₂×C₄	C₂×C₄⋊Dic₁₃	1	2	yes	—
214	C₂×C₄	#88180	1	4	yes	—
215	C₂×C₄	C₂²×C₄×D₁₃	1	2	yes	—
216	C₂×C₄	C₂²×D₅₂	1	1	yes	characteristic
217	C₂×C₄	C₂×#6127	1	2	yes	—
218	C₂×C₄	C₂³×Dic₁₃	1	1	yes	characteristic
219	C₈	—	2	4	no	—
220	C₈	—	26	16	no	—
221	C₈	C₂×C₄×Dic₁₃	1	8	yes	—
222	C₂²	—	2	4	no	—
223	C₂²	—	2	2	no	—
224	C₂²	—	4	4	no	—
225	C₂²	C₄×C₄⋊Dic₁₃	1	4	yes	—
226	C₂²	C₂×C₄×Dic₂₆	1	2	yes	—
227	C₂²	C₂²×C₄⋊Dic₁₃	1	1	yes	characteristic
228	C₄	—	2	4	no	—
229	C₄	—	2	2	no	—
230	C₄	C₄×C₄⋊Dic₁₃	1	4	yes	—
231	C₄	#11718786	1	4	yes	direct product factor
232	C₄	C₂×C₄×D₅₂	1	2	yes	—
233	C₄	C₂²×C₄×Dic₁₃	1	1	yes	characteristic
234	C₄	C₂×#88180	1	1	yes	characteristic
235	C₂	—	2	2	no	—
236	C₂	—	2	4	no	—
237	C₂	C₂×C₄×C₄⋊Dic₁₃	1	1	yes	characteristic
238	C₂	C₂×#11718786	1	2	yes	—

	subgroup	G/H
center	C₄²	C₂×D₅₂
commutator	C₄×C₁₃	C₂²×C₄²
Frattini	C₂²×C₄	C₂³×D₁₃
Fitting	C₂×C₄×C₁₃×M₁₆	C₂
socle	C₂²×C₁₃	C₂²×C₄⋊C₄
prime radical	C₂⁴×C₁₃	C₂×Q₈
cosocle	C₂²×C₄×C₁₃	C₂⁴
hypercenter	C₂×C₄×M₁₆	D₁₃
hypocenter	C₁₃	C₄×#430
LCS	G ▷ C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₄² ◁ C₂²×C₄² ◁ C₂×C₄×M₁₆

Complements

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

N	H ≅ G/N	type
3. #13114742	C₂	semidirect
4. C₄×#88059	C₂	semidirect
14. #11718786	C₄	direct (N × H)
44. #88059	C₂×C₄	semidirect
134. C₄×C₁₃	#430	semidirect
198. C₁₃	C₄×#430	semidirect
231. C₄	#11718786	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×#11718786	2
C₂×C₄×#6099	2
#13114742	2
C₄×#88059	2
#13114563	2
C₂×C₄×C₁₃×M₁₆	2
C₄×#430	13

Subgroups — C4×#11718786 #15861026

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄×#11718786 #15861026