Subgroups — C₄×#11718145 #15777959

Order 3328.

522 conjugacy classes of subgroups.

The subgroup lattice has 264 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#11718145	C₂	1	2	yes	maximal
2	C₄×#88052	C₂	1	2	yes	maximal, complemented
3	#13112920	C₂	1	2	yes	maximal, complemented
4	C₂×C₄×C₁₃×M₁₆	C₂	1	1	yes	maximal, characteristic
5	C₂²×C₁₃×M₁₆	C₄	1	1	yes	characteristic
6	C₂²×C₁₃×M₁₆	C₂²	1	1	yes	characteristic
7	C₂²×C₄²×C₁₃	C₄	1	1	yes	characteristic
8	C₄×C₁₃×M₁₆	—	2	2	no	—
9	C₄×C₁₃×M₁₆	—	2	2	no	—
10	C₂×C₁₃×#97	C₄	1	1	yes	characteristic
11	C₂×C₁₃×#97	C₂²	1	1	yes	characteristic
12	C₂×C₄×C₈×C₁₃	C₄	1	1	yes	characteristic
13	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
14	C₂×#88052	C₂²	1	4	yes	—
15	#11718145	C₄	1	8	yes	direct product factor
16	#11718053	—	2	2	no	—
17	C₄×#6090	—	2	2	no	—
18	C₂³×C₄×C₁₃	C₈	1	2	yes	—
19	C₂³×C₄×C₁₃	C₂×C₄	1	1	yes	characteristic
20	C₂×C₁₃×M₁₆	—	2	2	no	—
21	C₂×C₁₃×M₁₆	—	2	2	no	—
22	C₂×C₁₃×M₁₆	—	2	2	no	—
23	C₂×C₁₃×M₁₆	—	2	2	no	—
24	C₂×C₁₃×M₁₆	C₈	1	4	yes	—
25	C₂×C₁₃×M₁₆	C₂×C₄	1	4	yes	—
26	C₂²×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
27	C₂²×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
28	C₂²×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
29	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
30	C₂×C₄²×C₁₃	—	2	1	no	—
31	C₂×C₄²×C₁₃	—	2	1	no	—
32	C₂×C₄²×C₁₃	—	2	2	no	—
33	C₂×C₄²×C₁₃	C₈	1	2	yes	—
34	C₂×C₄²×C₁₃	C₂×C₄	1	1	yes	characteristic
35	C₂×C₄²×C₁₃	C₂×C₄	1	1	yes	characteristic
36	C₁₃×#97	—	2	2	no	—
37	C₁₃×#97	—	2	2	no	—
38	C₄×C₈×C₁₃	—	2	1	no	—
39	C₄×C₈×C₁₃	—	2	1	no	—
40	C₄×C₈×C₁₃	D₄	1	2	yes	—
41	C₄×C₈×C₁₃	D₄	1	2	yes	—
42	#88052	—	2	4	no	—
43	#88052	C₂×C₄	1	8	yes	complemented
44	C₂×#6090	—	2	4	no	—
45	C₄×#349	—	13	1	no	maximal, Sylow
46	C₂⁴×C₁₃	C₂×C₈	1	1	yes	characteristic
47	C₂²×C₄×C₁₃	—	2	1	no	—
48	C₂²×C₄×C₁₃	—	2	1	no	—
49	C₂²×C₄×C₁₃	—	2	1	no	—
50	C₂²×C₄×C₁₃	—	2	1	no	—
51	C₂²×C₄×C₁₃	—	2	2	no	—
52	C₂²×C₄×C₁₃	—	2	2	no	—
53	C₂²×C₄×C₁₃	—	4	4	no	—
54	C₂²×C₄×C₁₃	C₄²	1	2	yes	—
55	C₂²×C₄×C₁₃	C₂×C₈	1	1	yes	characteristic
56	C₂²×C₄×C₁₃	C₂×C₈	1	2	yes	—
57	C₂²×C₄×C₁₃	C₂×C₈	1	2	yes	—
58	C₂²×C₄×C₁₃	C₂×C₈	1	2	yes	—
59	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
60	C₁₃×M₁₆	—	2	8	no	—
61	C₁₃×M₁₆	—	2	8	no	—
62	C₂×C₈×C₁₃	—	2	1	no	—
63	C₂×C₈×C₁₃	—	2	1	no	—
64	C₂×C₈×C₁₃	—	2	1	no	—
65	C₂×C₈×C₁₃	—	2	1	no	—
66	C₂×C₈×C₁₃	C₄²	1	2	yes	—
67	C₂×C₈×C₁₃	C₂²⋊C₄	1	2	yes	—
68	C₂×C₈×C₁₃	C₂×C₈	1	2	yes	—
69	C₂×C₈×C₁₃	C₂×C₈	1	2	yes	—
70	C₂×C₈×C₁₃	M₁₆	1	2	yes	—
71	C₂×C₈×C₁₃	C₂²×C₄	1	2	yes	—
72	C₂×C₈×C₁₃	C₂×D₄	1	2	yes	—
73	C₂×C₈×C₁₃	#41	1	2	yes	—
74	C₄²×C₁₃	—	2	2	no	—
75	C₄²×C₁₃	—	2	2	no	—
76	C₄²×C₁₃	—	2	1	no	—
77	C₄²×C₁₃	—	2	1	no	—
78	C₄²×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
79	C₄²×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
80	C₄²×C₁₃	M₁₆	1	2	yes	—
81	#6090	—	2	8	no	—
82	C₂×C₄×M₁₆	D₁₃	1	1	yes	characteristic
83	C₂×#349	—	13	2	no	—
84	C₄×M₃₂	—	13	2	no	—
85	#1377	—	13	2	no	—
86	C₂³×C₁₃	—	2	1	no	—
87	C₂³×C₁₃	—	2	1	no	—
88	C₂³×C₁₃	—	4	2	no	—
89	C₂³×C₁₃	C₄×C₈	1	2	yes	—
90	C₂³×C₁₃	C₂²×C₈	1	1	yes	characteristic
91	C₂×C₄×C₁₃	—	2	1	no	—
92	C₂×C₄×C₁₃	—	2	1	no	—
93	C₂×C₄×C₁₃	—	2	4	no	—
94	C₂×C₄×C₁₃	—	2	2	no	—
95	C₂×C₄×C₁₃	—	2	2	no	—
96	C₂×C₄×C₁₃	—	2	2	no	—
97	C₂×C₄×C₁₃	—	2	2	no	—
98	C₂×C₄×C₁₃	—	2	2	no	—
99	C₂×C₄×C₁₃	—	4	4	no	—
100	C₂×C₄×C₁₃	—	4	4	no	—
101	C₂×C₄×C₁₃	—	4	2	no	—
102	C₂×C₄×C₁₃	C₄×C₈	1	2	yes	—
103	C₂×C₄×C₁₃	C₂²⋊C₈	1	2	yes	—
104	C₂×C₄×C₁₃	C₂²⋊C₈	1	2	yes	—
105	C₂×C₄×C₁₃	C₂×C₄²	1	1	yes	characteristic
106	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
107	C₂×C₄×C₁₃	#117	1	1	yes	characteristic
108	C₂×C₄×C₁₃	C₂²×C₈	1	1	yes	characteristic
109	C₂×C₄×C₁₃	C₂×M₁₆	1	1	yes	characteristic
110	C₂×C₄×C₁₃	C₂×M₁₆	1	1	yes	characteristic
111	C₈×C₁₃	—	2	2	no	—
112	C₈×C₁₃	—	2	2	no	—
113	C₈×C₁₃	C₂²⋊C₈	1	4	yes	—
114	C₈×C₁₃	C₄×D₄	1	4	yes	—
115	C₂²×M₁₆	Dic₁₃	1	1	yes	characteristic
116	C₂²×M₁₆	C₂×D₁₃	1	1	yes	characteristic
117	C₂²×C₄²	Dic₁₃	1	1	yes	characteristic
118	C₂×M₃₂	—	13	4	no	—
119	C₄×M₁₆	—	2	2	no	—
120	C₄×M₁₆	—	2	2	no	—
121	C₂×#97	Dic₁₃	1	1	yes	characteristic
122	C₂×#97	C₂×D₁₃	1	1	yes	characteristic
123	C₂×C₄×C₈	Dic₁₃	1	1	yes	characteristic
124	C₂×C₄×C₈	C₂×D₁₃	1	1	yes	characteristic
125	#349	—	13	8	no	—
126	#346	—	26	2	no	—
127	C₄×C₁₆	—	26	2	no	—
128	C₂²×C₁₃	—	2	2	no	—
129	C₂²×C₁₃	—	2	2	no	—
130	C₂²×C₁₃	—	4	2	no	—
131	C₂²×C₁₃	—	4	2	no	—
132	C₂²×C₁₃	—	4	2	no	—
133	C₂²×C₁₃	C₂×C₄×C₈	1	1	yes	characteristic
134	C₂²×C₁₃	C₂×C₂²⋊C₈	1	1	yes	characteristic
135	C₂²×C₁₃	#431	1	1	yes	characteristic
136	C₄×C₁₃	—	2	2	no	—
137	C₄×C₁₃	—	2	2	no	—
138	C₄×C₁₃	—	4	2	no	—
139	C₄×C₁₃	#349	1	4	yes	complemented
140	C₄×C₁₃	C₄×C₂²⋊C₄	1	1	yes	characteristic
141	C₄×C₁₃	C₄×M₁₆	1	1	yes	characteristic
142	C₄×C₁₃	C₂×C₂²⋊C₈	1	1	yes	characteristic
143	C₄×C₁₃	#431	1	1	yes	characteristic
144	C₂³×C₄	#1055	1	2	yes	—
145	C₂³×C₄	C₂×Dic₁₃	1	1	yes	characteristic
146	C₂×M₁₆	—	2	2	no	—
147	C₂×M₁₆	—	2	2	no	—
148	C₂×M₁₆	—	2	2	no	—
149	C₂×M₁₆	—	2	2	no	—
150	C₂×M₁₆	#1055	1	4	yes	—
151	C₂×M₁₆	C₄×D₁₃	1	4	yes	—
152	C₂²×C₈	C₂×Dic₁₃	1	1	yes	characteristic
153	C₂²×C₈	C₂×Dic₁₃	1	1	yes	characteristic
154	C₂²×C₈	C₂×Dic₁₃	1	1	yes	characteristic
155	C₂²×C₈	C₂²×D₁₃	1	1	yes	characteristic
156	C₂×C₄²	—	2	2	no	—
157	C₂×C₄²	—	2	1	no	—
158	C₂×C₄²	—	2	1	no	—
159	C₂×C₄²	#1055	1	2	yes	—
160	C₂×C₄²	C₂×Dic₁₃	1	1	yes	characteristic
161	C₂×C₄²	C₂×Dic₁₃	1	1	yes	characteristic
162	M₃₂	—	13	8	no	—
163	M₃₂	—	26	4	no	—
164	C₂×C₁₆	—	26	4	no	—
165	#97	—	2	2	no	—
166	#97	—	2	2	no	—
167	C₄×C₈	—	2	1	no	—
168	C₄×C₈	—	2	1	no	—
169	C₄×C₈	C₂²⋊D₁₃	1	2	yes	—
170	C₄×C₈	C₂²⋊D₁₃	1	2	yes	—
171	C₂×C₁₃	—	2	1	no	—
172	C₂×C₁₃	—	2	1	no	—
173	C₂×C₁₃	—	4	2	no	—
174	C₂×C₁₃	C₄×C₂²⋊C₈	1	1	yes	characteristic
175	C₂×C₁₃	C₂×#349	1	2	yes	—
176	C₂⁴	C₂×#1055	1	1	yes	characteristic
177	C₂²×C₄	—	2	1	no	—
178	C₂²×C₄	—	2	1	no	—
179	C₂²×C₄	—	2	1	no	—
180	C₂²×C₄	—	2	1	no	—
181	C₂²×C₄	—	2	2	no	—
182	C₂²×C₄	—	2	2	no	—
183	C₂²×C₄	—	4	4	no	—
184	C₂²×C₄	C₂×#1055	1	2	yes	—
185	C₂²×C₄	C₂×#1055	1	2	yes	—
186	C₂²×C₄	C₂×#1055	1	1	yes	characteristic
187	C₂²×C₄	C₂×#1055	1	2	yes	—
188	C₂²×C₄	C₄×Dic₁₃	1	2	yes	—
189	C₂²×C₄	C₂²×Dic₁₃	1	1	yes	characteristic
190	M₁₆	—	2	8	no	—
191	M₁₆	—	2	8	no	—
192	C₂×C₈	—	2	1	no	—
193	C₂×C₈	—	2	1	no	—
194	C₂×C₈	—	2	1	no	—
195	C₂×C₈	—	2	1	no	—
196	C₂×C₈	C₂×#1055	1	2	yes	—
197	C₂×C₈	C₂×#1055	1	2	yes	—
198	C₂×C₈	#6099	1	2	yes	—
199	C₂×C₈	C₄×Dic₁₃	1	2	yes	—
200	C₂×C₈	C₂²⋊Dic₁₃	1	2	yes	—
201	C₂×C₈	C₂×C₄×D₁₃	1	2	yes	—
202	C₂×C₈	#6127	1	2	yes	—
203	C₂×C₈	C₂×C₂²⋊D₁₃	1	2	yes	—
204	C₄²	—	2	2	no	—
205	C₄²	—	2	2	no	—
206	C₄²	—	2	1	no	—
207	C₄²	—	2	1	no	—
208	C₄²	#6099	1	2	yes	—
209	C₄²	C₂²⋊Dic₁₃	1	1	yes	characteristic
210	C₄²	C₂²⋊Dic₁₃	1	1	yes	characteristic
211	C₁₆	—	26	8	no	—
212	C₁₃	C₄×#349	1	1	yes	characteristic, complemented, Sylow
213	C₂³	—	2	1	no	—
214	C₂³	—	2	1	no	—
215	C₂³	—	4	2	no	—
216	C₂³	C₄×#1055	1	2	yes	—
217	C₂³	C₂²×#1055	1	1	yes	characteristic
218	C₂×C₄	—	2	1	no	—
219	C₂×C₄	—	2	1	no	—
220	C₂×C₄	—	2	4	no	—
221	C₂×C₄	—	2	2	no	—
222	C₂×C₄	—	2	2	no	—
223	C₂×C₄	—	2	2	no	—
224	C₂×C₄	—	2	2	no	—
225	C₂×C₄	—	2	2	no	—
226	C₂×C₄	—	4	4	no	—
227	C₂×C₄	—	4	4	no	—
228	C₂×C₄	—	4	2	no	—
229	C₂×C₄	C₄×#1055	1	2	yes	—
230	C₂×C₄	C₂²⋊#1055	1	2	yes	—
231	C₂×C₄	C₂²⋊#1055	1	2	yes	—
232	C₂×C₄	C₂²×#1055	1	1	yes	characteristic
233	C₂×C₄	C₂×#6099	1	1	yes	characteristic
234	C₂×C₄	C₂×#6099	1	1	yes	characteristic
235	C₂×C₄	C₂×C₄×Dic₁₃	1	1	yes	characteristic
236	C₂×C₄	#88180	1	1	yes	characteristic
237	C₂×C₄	C₂×C₂²⋊Dic₁₃	1	1	yes	characteristic
238	C₈	—	2	2	no	—
239	C₈	—	2	2	no	—
240	C₈	C₂²⋊#1055	1	4	yes	—
241	C₈	C₄×C₂²⋊D₁₃	1	4	yes	—
242	C₂²	—	2	2	no	—
243	C₂²	—	2	2	no	—
244	C₂²	—	4	2	no	—
245	C₂²	—	4	2	no	—
246	C₂²	—	4	2	no	—
247	C₂²	C₂×C₄×#1055	1	1	yes	characteristic
248	C₂²	#11718586	1	1	yes	characteristic
249	C₂²	C₂×C₂²⋊#1055	1	1	yes	characteristic
250	C₄	—	2	2	no	—
251	C₄	—	2	2	no	—
252	C₄	—	4	2	no	—
253	C₄	#11718145	1	4	yes	direct product factor
254	C₄	C₄×#6099	1	1	yes	characteristic
255	C₄	#11718586	1	1	yes	characteristic
256	C₄	C₂×C₂²⋊#1055	1	1	yes	characteristic
257	C₄	C₄×C₂²⋊Dic₁₃	1	1	yes	characteristic
258	C₂	—	2	1	no	—
259	C₂	—	2	1	no	—
260	C₂	—	4	2	no	—
261	C₂	C₄×C₂²⋊#1055	1	1	yes	characteristic
262	C₂	C₂×#11718145	1	2	yes	—

	subgroup	G/H
center	C₄²	C₂²⋊Dic₁₃
commutator	C₂²×C₁₃	C₂×C₄×C₈
Frattini	C₂²×C₈	C₂²×D₁₃
Fitting	C₂×C₄×C₁₃×M₁₆	C₂
socle	C₂²×C₁₃	C₂×C₂²⋊C₈
prime radical	C₂⁴×C₁₃	C₂×C₈
cosocle	C₂²×C₈×C₁₃	C₂³
hypercenter	C₂×C₄×M₁₆	D₁₃
hypocenter	C₁₃	C₄×#349
LCS	G ▷ C₂²×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₄² ◁ C₂×C₄×C₈ ◁ C₂×C₄×M₁₆

Complements

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

N	H ≅ G/N	type
2. C₄×#88052	C₂	semidirect
3. #13112920	C₂	semidirect
15. #11718145	C₄	direct (N × H)
43. #88052	C₂×C₄	semidirect
139. C₄×C₁₃	#349	semidirect
212. C₁₃	C₄×#349	semidirect
253. C₄	#11718145	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×#11718145	2
C₄×#88052	2
#13112920	2
C₂×C₄×C₁₃×M₁₆	2
C₄×#349	13

Subgroups — C4×#11718145 #15777959

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄×#11718145 #15777959