Subgroups — C₄×#11719524 #16726336

Order 3328.

3250 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×#11719524	C₂	1	2	yes	maximal
2	#13123264	C₂	1	8	yes	maximal, complemented
3	C₄×#88202	C₂	1	8	yes	maximal, complemented
4	#13123255	C₂	1	6	yes	maximal, complemented
5	C₂×C₄×#6099	C₂	1	6	yes	maximal, complemented
6	C₂×C₄×C₁₃×#41	C₂	1	1	yes	maximal, characteristic
7	C₂²×C₁₃×#41	C₂²	1	1	yes	characteristic
8	C₄×C₁₃×#41	C₄	1	8	yes	—
9	C₄×C₁₃×#41	C₂²	1	4	yes	—
10	C₄×C₁₃×#41	C₂²	1	4	yes	—
11	C₂×C₄×Q₈×C₁₃	C₄	1	2	yes	—
12	C₂×C₄×D₄×C₁₃	C₄	1	6	yes	—
13	C₂×C₁₃×#117	C₂²	1	3	yes	—
14	C₂²×C₄²×C₁₃	C₂²	1	3	yes	—
15	#11719524	C₄	1	32	yes	direct product factor
16	C₂×#88202	C₂²	1	16	yes	—
17	C₂²×#6099	C₂²	1	12	yes	—
18	#11718658	C₂²	1	48	yes	complemented
19	C₄×#6099	C₂²	1	4	yes	—
20	C₄×#6099	C₂²	1	12	yes	—
21	C₄×#6099	C₂²	1	12	yes	complemented
22	C₄×#6099	C₂²	1	12	yes	complemented
23	C₂×#88043	C₂²	1	12	yes	complemented
24	C₂×C₄×#1055	C₂²	1	12	yes	complemented
25	C₂×C₁₃×#41	C₂×C₄	1	16	yes	—
26	C₂×C₁₃×#41	C₂×C₄	1	4	yes	—
27	C₂×C₁₃×#41	C₂³	1	4	yes	—
28	C₂²×Q₈×C₁₃	C₂×C₄	1	1	yes	characteristic
29	C₂²×D₄×C₁₃	C₂×C₄	1	3	yes	—
30	C₂³×C₄×C₁₃	C₂×C₄	1	6	yes	—
31	C₂³×C₄×C₁₃	C₂³	1	3	yes	—
32	C₄×Q₈×C₁₃	C₂×C₄	1	8	yes	—
33	C₄×Q₈×C₁₃	C₂×C₄	1	8	yes	—
34	C₄×D₄×C₁₃	C₂×C₄	1	24	yes	—
35	C₄×D₄×C₁₃	C₂×C₄	1	24	yes	—
36	C₁₃×#117	C₂×C₄	1	12	yes	—
37	C₁₃×#117	C₂³	1	12	yes	—
38	C₂×C₁₃×C₄⋊C₄	C₂×C₄	1	6	yes	—
39	C₂×C₁₃×C₂²⋊C₄	C₂×C₄	1	6	yes	—
40	C₂×C₄²×C₁₃	C₂×C₄	1	6	yes	—
41	C₂×C₄²×C₁₃	C₂×C₄	1	12	yes	—
42	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
43	C₂×C₄²×C₁₃	C₂³	1	3	yes	—
44	C₂×C₄²×C₁₃	C₂³	1	6	yes	—
45	C₂×C₄²×C₁₃	C₂³	1	6	yes	—
46	#88202	C₂×C₄	1	128	yes	complemented
47	C₂×#6099	C₂×C₄	1	96	yes	complemented
48	C₂×#6099	C₂³	1	8	yes	—
49	C₂×#6099	C₂³	1	24	yes	—
50	C₂²×#1055	C₂³	1	24	yes	—
51	#88043	C₂³	1	24	yes	—
52	#88043	C₂³	1	8	yes	—
53	C₄×#1055	C₂³	1	24	yes	—
54	C₄×#1055	C₂³	1	8	yes	—
55	C₄×#568	—	13	1	no	maximal, Sylow
56	C₂⁴×C₁₃	C₂²×C₄	1	3	yes	—
57	C₁₃×#41	C₄²	1	32	yes	—
58	C₁₃×#41	C₂²×C₄	1	32	yes	—
59	C₂×Q₈×C₁₃	C₄²	1	8	yes	—
60	C₂×Q₈×C₁₃	C₂²×C₄	1	4	yes	—
61	C₂×D₄×C₁₃	C₄²	1	24	yes	—
62	C₂×D₄×C₁₃	C₂²×C₄	1	12	yes	—
63	C₂²×C₄×C₁₃	—	4	12	no	—
64	C₂²×C₄×C₁₃	C₂²×C₄	1	24	yes	—
65	C₂²×C₄×C₁₃	C₂²×C₄	1	2	yes	—
66	C₂²×C₄×C₁₃	C₂²×C₄	1	12	yes	—
67	C₂²×C₄×C₁₃	C₂²×C₄	1	6	yes	—
68	C₂²×C₄×C₁₃	C₂²×C₄	1	12	yes	—
69	C₂²×C₄×C₁₃	C₂²×C₄	1	3	yes	—
70	C₂²×C₄×C₁₃	C₂²×C₄	1	6	yes	—
71	C₂²×C₄×C₁₃	C₂⁴	1	6	yes	—
72	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
73	C₁₃×C₄⋊C₄	C₂²×C₄	1	24	yes	—
74	C₁₃×C₂²⋊C₄	C₂²×C₄	1	24	yes	—
75	C₄²×C₁₃	C₂²×C₄	1	2	yes	—
76	C₄²×C₁₃	C₂²×C₄	1	6	yes	—
77	C₄²×C₁₃	C₂²×C₄	1	12	yes	—
78	C₄²×C₁₃	C₂²×C₄	1	12	yes	—
79	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
80	C₄²×C₁₃	C₂⁴	1	6	yes	—
81	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
82	#6099	C₂²×C₄	1	32	yes	—
83	#6099	C₂²×C₄	1	96	yes	complemented
84	C₂×#1055	C₂²×C₄	1	96	yes	complemented
85	C₂×#1055	C₂⁴	1	16	yes	—
86	C₂×#568	—	13	2	no	—
87	C₂×C₄×#41	D₁₃	1	1	yes	characteristic
88	#2875	—	13	8	no	—
89	C₄×#131	—	13	8	no	—
90	#2873	—	13	6	no	—
91	C₂×C₄×M₁₆	—	13	6	no	—
92	C₂³×C₁₃	—	4	6	no	—
93	C₂³×C₁₃	C₂×C₄²	1	12	yes	—
94	C₂³×C₁₃	C₂³×C₄	1	6	yes	—
95	C₂³×C₁₃	C₂³×C₄	1	1	yes	characteristic
96	Q₈×C₁₃	C₂×C₄²	1	16	yes	—
97	D₄×C₁₃	C₂×C₄²	1	48	yes	—
98	C₂×C₄×C₁₃	—	2	4	no	—
99	C₂×C₄×C₁₃	—	2	24	no	—
100	C₂×C₄×C₁₃	—	4	12	no	—
101	C₂×C₄×C₁₃	—	4	6	no	—
102	C₂×C₄×C₁₃	C₂×C₄²	1	12	yes	—
103	C₂×C₄×C₁₃	C₂×C₄²	1	24	yes	—
104	C₂×C₄×C₁₃	C₂³×C₄	1	2	yes	—
105	C₂×C₄×C₁₃	C₂³×C₄	1	12	yes	—
106	C₂×C₄×C₁₃	C₂³×C₄	1	2	yes	—
107	C₂×C₄×C₁₃	C₂³×C₄	1	24	yes	—
108	C₂×C₄×C₁₃	C₂³×C₄	1	4	yes	—
109	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
110	C₂×C₄×C₁₃	C₂³×C₄	1	6	yes	—
111	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
112	#1055	C₂³×C₄	1	32	yes	—
113	C₂²×#41	C₂×D₁₃	1	1	yes	characteristic
114	#568	—	13	32	no	—
115	C₂×#131	—	13	16	no	—
116	C₂²×M₁₆	—	13	12	no	—
117	C₄×#41	Dic₁₃	1	8	yes	—
118	C₄×#41	C₂×D₁₃	1	4	yes	—
119	C₄×#41	C₂×D₁₃	1	4	yes	—
120	C₂×C₄×Q₈	Dic₁₃	1	2	yes	—
121	C₂×C₄×D₄	Dic₁₃	1	6	yes	—
122	C₂×#117	C₂×D₁₃	1	3	yes	—
123	C₂²×C₄²	C₂×D₁₃	1	3	yes	—
124	#405	—	13	48	no	—
125	C₄×M₁₆	—	13	4	no	—
126	C₄×M₁₆	—	13	12	no	—
127	C₄×M₁₆	—	13	12	no	—
128	C₄×M₁₆	—	13	12	no	—
129	C₂×#97	—	13	12	no	—
130	C₂×C₄×C₈	—	13	12	no	—
131	C₂²×C₁₃	—	2	2	no	—
132	C₂²×C₁₃	—	2	12	no	—
133	C₂²×C₁₃	—	4	12	no	—
134	C₂²×C₁₃	C₂²×C₄²	1	2	yes	—
135	C₂²×C₁₃	C₂²×C₄²	1	12	yes	—
136	C₂²×C₁₃	C₂⁴×C₄	1	1	yes	characteristic
137	C₄×C₁₃	—	2	2	no	—
138	C₄×C₁₃	—	2	12	no	—
139	C₄×C₁₃	C₂²×C₄²	1	2	yes	—
140	C₄×C₁₃	C₂²×C₄²	1	12	yes	—
141	C₄×C₁₃	#568	1	4	yes	complemented
142	C₄×C₁₃	C₂⁴×C₄	1	2	yes	—
143	C₂×#41	C₄×D₁₃	1	16	yes	—
144	C₂×#41	C₂×Dic₁₃	1	4	yes	—
145	C₂×#41	C₂²×D₁₃	1	4	yes	—
146	C₂²×Q₈	C₂×Dic₁₃	1	1	yes	characteristic
147	C₂²×D₄	C₂×Dic₁₃	1	3	yes	—
148	C₂³×C₄	C₂×Dic₁₃	1	6	yes	—
149	C₂³×C₄	C₂²×D₁₃	1	3	yes	—
150	#131	—	13	128	no	—
151	C₂×M₁₆	—	13	96	no	—
152	C₂×M₁₆	—	13	8	no	—
153	C₂×M₁₆	—	13	24	no	—
154	C₂²×C₈	—	13	24	no	—
155	C₄×Q₈	C₂×Dic₁₃	1	8	yes	—
156	C₄×Q₈	C₂×Dic₁₃	1	8	yes	—
157	C₄×D₄	C₂×Dic₁₃	1	24	yes	—
158	C₄×D₄	C₂×Dic₁₃	1	24	yes	—
159	#117	C₂×Dic₁₃	1	12	yes	—
160	#117	C₂²×D₁₃	1	12	yes	—
161	C₂×C₄⋊C₄	C₂×Dic₁₃	1	6	yes	—
162	C₂×C₂²⋊C₄	C₂×Dic₁₃	1	6	yes	—
163	C₂×C₄²	C₂×Dic₁₃	1	6	yes	—
164	C₂×C₄²	C₂×Dic₁₃	1	12	yes	—
165	C₂×C₄²	C₂²×D₁₃	1	3	yes	—
166	C₂×C₄²	C₂²×D₁₃	1	6	yes	—
167	C₂×C₄²	C₂²×D₁₃	1	6	yes	—
168	C₂×C₄²	C₂²×D₁₃	1	1	yes	characteristic
169	#97	—	13	8	no	—
170	#97	—	13	24	no	—
171	C₄×C₈	—	13	24	no	—
172	C₄×C₈	—	13	8	no	—
173	C₂×C₁₃	—	2	2	no	—
174	C₂×C₁₃	—	2	12	no	—
175	C₂×C₁₃	C₂³×C₄²	1	1	yes	characteristic
176	C₂×C₁₃	C₂×#568	1	2	yes	—
177	C₂⁴	C₂²×Dic₁₃	1	3	yes	—
178	#41	C₄×Dic₁₃	1	32	yes	—
179	#41	C₂×C₄×D₁₃	1	32	yes	—
180	C₂×Q₈	C₄×Dic₁₃	1	8	yes	—
181	C₂×Q₈	C₂²×Dic₁₃	1	4	yes	—
182	C₂×D₄	C₄×Dic₁₃	1	24	yes	—
183	C₂×D₄	C₂²×Dic₁₃	1	12	yes	—
184	C₂²×C₄	—	4	12	no	—
185	C₂²×C₄	C₂×C₄×D₁₃	1	24	yes	—
186	C₂²×C₄	C₂²×Dic₁₃	1	2	yes	—
187	C₂²×C₄	C₂²×Dic₁₃	1	12	yes	—
188	C₂²×C₄	C₂²×Dic₁₃	1	6	yes	—
189	C₂²×C₄	C₂²×Dic₁₃	1	12	yes	—
190	C₂²×C₄	C₂²×Dic₁₃	1	3	yes	—
191	C₂²×C₄	C₂²×Dic₁₃	1	6	yes	—
192	C₂²×C₄	C₂³×D₁₃	1	1	yes	characteristic
193	C₂²×C₄	C₂³×D₁₃	1	6	yes	—
194	M₁₆	—	13	32	no	—
195	M₁₆	—	13	96	no	—
196	C₂×C₈	—	13	96	no	—
197	C₂×C₈	—	13	16	no	—
198	C₄⋊C₄	C₂²×Dic₁₃	1	24	yes	—
199	C₂²⋊C₄	C₂²×Dic₁₃	1	24	yes	—
200	C₄²	C₂²×Dic₁₃	1	2	yes	—
201	C₄²	C₂²×Dic₁₃	1	6	yes	—
202	C₄²	C₂²×Dic₁₃	1	12	yes	—
203	C₄²	C₂²×Dic₁₃	1	12	yes	—
204	C₄²	C₂³×D₁₃	1	6	yes	—
205	C₄²	C₂³×D₁₃	1	1	yes	characteristic
206	C₄²	C₂³×D₁₃	1	1	yes	characteristic
207	C₁₃	C₄×#568	1	1	yes	characteristic, complemented, Sylow
208	C₂³	—	4	6	no	—
209	C₂³	C₂×C₄×Dic₁₃	1	12	yes	—
210	C₂³	C₂³×Dic₁₃	1	6	yes	—
211	C₂³	C₂³×Dic₁₃	1	1	yes	characteristic
212	Q₈	C₂×C₄×Dic₁₃	1	16	yes	—
213	D₄	C₂×C₄×Dic₁₃	1	48	yes	—
214	C₂×C₄	—	2	4	no	—
215	C₂×C₄	—	2	24	no	—
216	C₂×C₄	—	4	12	no	—
217	C₂×C₄	—	4	6	no	—
218	C₂×C₄	C₂×C₄×Dic₁₃	1	12	yes	—
219	C₂×C₄	C₂×C₄×Dic₁₃	1	24	yes	—
220	C₂×C₄	C₂²×C₄×D₁₃	1	24	yes	—
221	C₂×C₄	C₂²×C₄×D₁₃	1	4	yes	—
222	C₂×C₄	C₂³×Dic₁₃	1	2	yes	—
223	C₂×C₄	C₂³×Dic₁₃	1	12	yes	—
224	C₂×C₄	C₂³×Dic₁₃	1	1	yes	characteristic
225	C₂×C₄	C₂³×Dic₁₃	1	6	yes	—
226	C₂×C₄	C₂³×Dic₁₃	1	2	yes	—
227	C₂×C₄	C₂⁴×D₁₃	1	1	yes	characteristic
228	C₈	—	13	32	no	—
229	C₂²	—	2	2	no	—
230	C₂²	—	2	12	no	—
231	C₂²	—	4	12	no	—
232	C₂²	C₂²×C₄×Dic₁₃	1	2	yes	—
233	C₂²	C₂²×C₄×Dic₁₃	1	12	yes	—
234	C₂²	C₂⁴×Dic₁₃	1	1	yes	characteristic
235	C₄	—	2	2	no	—
236	C₄	—	2	12	no	—
237	C₄	C₂²×C₄×Dic₁₃	1	2	yes	—
238	C₄	C₂²×C₄×Dic₁₃	1	12	yes	—
239	C₄	#11719524	1	4	yes	direct product factor
240	C₄	C₂³×C₄×D₁₃	1	2	yes	—
241	C₂	—	2	2	no	—
242	C₂	—	2	12	no	—
243	C₂	C₂³×C₄×Dic₁₃	1	1	yes	characteristic
244	C₂	C₂×#11719524	1	2	yes	—

	subgroup	G/H
center	C₄²	C₂³×D₁₃
commutator	C₂×C₁₃	C₂³×C₄²
Frattini	C₂×C₄	C₂⁴×D₁₃
Fitting	C₂×C₄×C₁₃×#41	C₂
socle	C₂²×C₁₃	C₂⁴×C₄
prime radical	C₂²×C₁₃×#41	C₂²
cosocle	C₂×C₄×C₁₃	C₂⁵
hypercenter	C₂×C₄×#41	D₁₃
hypocenter	C₁₃	C₄×#568
LCS	G ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₄² ◁ C₂×C₄×#41

Complements

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

N	H ≅ G/N	type
2. #13123264	C₂	semidirect
3. C₄×#88202	C₂	semidirect
4. #13123255	C₂	semidirect
5. C₂×C₄×#6099	C₂	semidirect
15. #11719524	C₄	direct (N × H)
18. #11718658	C₂²	semidirect
21. C₄×#6099	C₂²	semidirect
22. C₄×#6099	C₂²	semidirect
23. C₂×#88043	C₂²	semidirect
24. C₂×C₄×#1055	C₂²	semidirect
46. #88202	C₂×C₄	semidirect
47. C₂×#6099	C₂×C₄	semidirect
83. #6099	C₂²×C₄	semidirect
84. C₂×#1055	C₂²×C₄	semidirect
141. C₄×C₁₃	#568	semidirect
207. C₁₃	C₄×#568	semidirect
239. C₄	#11719524	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×#11719524	2
#13123264	2
C₄×#88202	2
#13123255	2
C₂×C₄×#6099	2
C₂×C₄×C₁₃×#41	2
C₄×#568	13

Subgroups — C4×#11719524 #16726336

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄×#11719524 #16726336