Subgroups — #16806731

Order 3328.

826 conjugacy classes of subgroups.

The subgroup lattice has 234 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×D₁₃⋊M₃₂	C₂	1	2	yes	maximal
2	#13131046	C₂	1	8	yes	maximal, complemented
3	#13131042	C₂	1	2	yes	maximal, complemented
4	C₄×#88106	C₂	1	2	yes	maximal, complemented
5	C₂×#11718369	C₂	1	1	yes	maximal, characteristic
6	C₂²×#6094	C₄	1	1	yes	characteristic
7	C₂²×C₈×D₁₃	C₂²	1	1	yes	characteristic
8	C₂×#88126	C₄	1	1	yes	characteristic
9	C₂×#88106	C₂²	1	4	yes	—
10	D₁₃⋊M₃₂	C₄	1	16	yes	complemented
11	C₂×#88098	C₂²	1	4	yes	—
12	C₂×D₁₃⋊C₁₆	C₂²	1	4	yes	—
13	C₂×C₁₃×#97	C₄	1	1	yes	characteristic
14	C₂×#88055	C₄	1	1	yes	characteristic
15	C₂×C₈×Dic₁₃	C₂²	1	1	yes	characteristic
16	C₂×C₄×#1055	C₂²	1	1	yes	characteristic
17	#11718369	C₄	1	4	yes	—
18	#11718369	C₂²	1	4	yes	—
19	#11718258	C₂²	1	4	yes	complemented
20	#11718257	C₂²	1	4	yes	complemented
21	#11718231	C₂²	1	4	yes	complemented
22	C₄×#6092	C₂²	1	4	yes	complemented
23	C₂²×C₄×D₁₃	C₂×C₄	1	1	yes	characteristic
24	C₂²×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
25	C₂²×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
26	C₂×C₄²×C₁₃	C₂×C₄	1	1	yes	characteristic
27	C₂×#6103	C₈	1	2	yes	—
28	C₂×#6101	C₈	1	2	yes	—
29	C₂×C₄×Dic₁₃	C₂×C₄	1	1	yes	characteristic
30	C₂²×#1055	C₂×C₄	1	1	yes	characteristic
31	C₂²×#1055	C₂³	1	1	yes	characteristic
32	C₂×#6094	C₈	1	8	yes	—
33	C₂×#6094	C₂×C₄	1	4	yes	—
34	C₂×C₈×D₁₃	C₂×C₄	1	2	yes	—
35	C₂×C₈×D₁₃	C₂×C₄	1	8	yes	—
36	C₂×C₈×D₁₃	C₂³	1	2	yes	—
37	#88126	C₈	1	4	yes	—
38	#88126	C₂×C₄	1	4	yes	—
39	#88106	C₂×C₄	1	16	yes	—
40	C₂×#6092	C₂³	1	8	yes	—
41	#88098	C₂×C₄	1	16	yes	complemented
42	D₁₃⋊C₁₆	C₂×C₄	1	16	yes	complemented
43	C₁₃×#97	C₂×C₄	1	4	yes	—
44	#88055	C₂×C₄	1	4	yes	—
45	C₈×Dic₁₃	C₂×C₄	1	2	yes	—
46	C₈×Dic₁₃	C₂³	1	2	yes	—
47	C₄×#1055	C₂×C₄	1	2	yes	—
48	C₄×#1055	C₂³	1	2	yes	—
49	#33324	—	13	1	no	maximal, Sylow
50	C₂³×D₁₃	C₂×C₈	1	1	yes	characteristic
51	C₂²×C₄×C₁₃	C₂×C₈	1	2	yes	—
52	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
53	C₂²×Dic₁₃	C₂×C₈	1	2	yes	—
54	C₂²×Dic₁₃	C₂×C₈	1	1	yes	characteristic
55	C₂×C₄×D₁₃	C₄²	1	4	yes	—
56	C₂×C₄×D₁₃	C₂×C₈	1	2	yes	—
57	C₂×C₄×D₁₃	C₂×C₈	1	4	yes	—
58	C₂×C₄×D₁₃	C₂²×C₄	1	2	yes	—
59	C₂×C₈×C₁₃	C₄²	1	4	yes	—
60	C₂×C₈×C₁₃	C₂×C₈	1	4	yes	—
61	C₂×C₈×C₁₃	C₂²×C₄	1	2	yes	—
62	C₂×C₈×C₁₃	C₂²×C₄	1	2	yes	—
63	C₄²×C₁₃	C₂×C₈	1	2	yes	—
64	C₄²×C₁₃	C₂²×C₄	1	2	yes	—
65	#6103	C₂×C₈	1	8	yes	—
66	#6101	C₂×C₈	1	8	yes	—
67	C₄×Dic₁₃	C₂×C₈	1	2	yes	—
68	C₄×Dic₁₃	C₂²×C₄	1	2	yes	—
69	C₂×#1055	C₂×C₈	1	4	yes	—
70	C₂×#1055	C₂²×C₄	1	1	yes	characteristic
71	C₂×#1055	C₂²×C₄	1	4	yes	—
72	C₂×#1055	C₂²×C₄	1	2	yes	—
73	C₂×#1055	C₂⁴	1	1	yes	characteristic
74	#6094	C₂×C₈	1	16	yes	—
75	C₈×D₁₃	C₄²	1	8	yes	—
76	C₈×D₁₃	C₂²×C₄	1	4	yes	—
77	C₈×D₁₃	C₂²×C₄	1	4	yes	—
78	#6092	C₂²×C₄	1	16	yes	—
79	C₂²×M₃₂	—	13	2	no	—
80	C₂×#405	—	13	1	no	—
81	#2108	—	13	8	no	—
82	C₄×M₃₂	—	13	2	no	—
83	C₄×M₃₂	—	13	2	no	—
84	C₂³×C₁₃	C₂²×C₈	1	1	yes	characteristic
85	C₂²×D₁₃	—	4	2	no	—
86	C₂²×D₁₃	C₄×C₈	1	4	yes	—
87	C₂²×D₁₃	C₂²×C₈	1	2	yes	—
88	C₂×C₄×C₁₃	—	4	2	no	—
89	C₂×C₄×C₁₃	C₂×C₄²	1	2	yes	—
90	C₂×C₄×C₁₃	C₂²×C₈	1	4	yes	—
91	C₂×C₄×C₁₃	C₂²×C₈	1	2	yes	—
92	C₂×C₄×C₁₃	C₂²×C₈	1	1	yes	characteristic
93	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
94	C₂×Dic₁₃	—	4	2	no	—
95	C₂×Dic₁₃	C₄×C₈	1	4	yes	—
96	C₂×Dic₁₃	C₂²×C₈	1	4	yes	—
97	C₂×Dic₁₃	C₂²×C₈	1	2	yes	—
98	C₄×D₁₃	C₄×C₈	1	8	yes	—
99	C₄×D₁₃	C₂×C₄²	1	4	yes	—
100	C₄×D₁₃	C₂²×C₈	1	4	yes	—
101	C₈×C₁₃	C₂×C₄²	1	4	yes	—
102	C₈×C₁₃	C₂²×C₈	1	4	yes	—
103	#1055	C₂×C₄²	1	2	yes	—
104	#1055	C₂²×C₈	1	4	yes	—
105	#1055	C₂³×C₄	1	2	yes	—
106	C₂²×M₁₆	—	13	1	no	—
107	C₂³×C₈	—	13	1	no	—
108	C₂×#117	—	13	1	no	—
109	C₂×M₃₂	—	13	4	no	—
110	C₂×M₃₂	—	13	4	no	—
111	C₂×M₃₂	—	13	16	no	—
112	C₂²×C₁₆	—	13	4	no	—
113	#405	—	13	4	no	—
114	#405	—	13	4	no	—
115	C₂×#97	—	13	1	no	—
116	C₂×#97	#261	1	1	yes	characteristic
117	C₂×C₄×C₈	—	13	1	no	—
118	C₂×C₄×C₈	—	13	1	no	—
119	#346	—	13	4	no	—
120	#346	—	13	4	no	—
121	C₄×C₁₆	—	13	4	no	—
122	C₄×C₁₆	—	13	4	no	—
123	C₂²×C₁₃	—	2	2	no	—
124	C₂²×C₁₃	C₂×C₄×C₈	1	2	yes	—
125	C₂²×C₁₃	C₂³×C₈	1	1	yes	characteristic
126	C₂×D₁₃	—	2	4	no	—
127	C₂×D₁₃	—	4	4	no	—
128	C₂×D₁₃	C₂×C₄×C₈	1	4	yes	—
129	C₄×C₁₃	—	2	4	no	—
130	C₄×C₁₃	C₂×C₄×C₈	1	2	yes	—
131	C₄×C₁₃	C₂²×C₄²	1	1	yes	characteristic
132	C₄×C₁₃	C₂³×C₈	1	1	yes	characteristic
133	Dic₁₃	—	2	4	no	—
134	Dic₁₃	C₂×C₄×C₈	1	4	yes	—
135	C₂³×C₄	—	13	1	no	—
136	C₂×M₁₆	—	13	8	no	—
137	C₂×M₁₆	—	13	4	no	—
138	C₂²×C₈	—	13	1	no	—
139	C₂²×C₈	—	13	1	no	—
140	C₂²×C₈	—	13	8	no	—
141	C₂²×C₈	—	13	2	no	—
142	C₂²×C₈	—	13	2	no	—
143	C₂²×C₈	C₂×#261	1	1	yes	characteristic
144	C₂²×C₈	C₂×#261	1	1	yes	characteristic
145	#117	—	13	4	no	—
146	#117	—	13	4	no	—
147	C₂×C₄⋊C₄	—	13	2	no	—
148	C₂×C₂²⋊C₄	—	13	2	no	—
149	C₂×C₄²	—	13	1	no	—
150	C₂×C₄²	C₂×#261	1	1	yes	characteristic
151	M₃₂	—	13	16	no	—
152	M₃₂	—	13	16	no	—
153	C₂×C₁₆	—	13	16	no	—
154	C₂×C₁₆	—	13	8	no	—
155	#97	—	13	4	no	—
156	#97	C₂×#261	1	4	yes	—
157	C₄×C₈	—	13	2	no	—
158	C₄×C₈	—	13	2	no	—
159	C₄×C₈	—	13	2	no	—
160	C₄×C₈	—	13	2	no	—
161	C₂×C₁₃	—	2	2	no	—
162	C₂×C₁₃	C₂²×C₄×C₈	1	1	yes	characteristic
163	C₂×C₁₃	#3407	1	2	yes	—
164	D₁₃	—	2	4	no	—
165	C₂⁴	—	13	1	no	—
166	C₂²×C₄	—	13	1	no	—
167	C₂²×C₄	—	13	2	no	—
168	C₂²×C₄	—	13	4	no	—
169	C₂²×C₄	—	13	4	no	—
170	C₂²×C₄	—	13	2	no	—
171	C₂²×C₄	—	13	2	no	—
172	C₂²×C₄	D₁₃⋊C₈	1	2	yes	—
173	C₂²×C₄	C₂²×#261	1	1	yes	characteristic
174	M₁₆	—	13	16	no	—
175	C₂×C₈	—	13	4	no	—
176	C₂×C₈	—	13	4	no	—
177	C₂×C₈	—	13	1	no	—
178	C₂×C₈	—	13	1	no	—
179	C₂×C₈	—	13	2	no	—
180	C₂×C₈	—	13	4	no	—
181	C₂×C₈	—	13	4	no	—
182	C₂×C₈	—	13	8	no	—
183	C₂×C₈	D₁₃⋊C₈	1	4	yes	—
184	C₂×C₈	C₄×#261	1	4	yes	—
185	C₂×C₈	C₂²×#261	1	2	yes	—
186	C₂×C₈	C₂²×#261	1	2	yes	—
187	C₄⋊C₄	—	13	8	no	—
188	C₂²⋊C₄	—	13	8	no	—
189	C₄²	—	13	2	no	—
190	C₄²	—	13	2	no	—
191	C₄²	D₁₃⋊C₈	1	2	yes	—
192	C₄²	C₂²×#261	1	2	yes	—
193	C₁₆	—	13	16	no	—
194	C₁₃	#33324	1	1	yes	characteristic, complemented, Sylow
195	C₂³	—	13	2	no	—
196	C₂³	—	13	4	no	—
197	C₂³	—	52	2	no	—
198	C₂³	C₂×D₁₃⋊C₈	1	1	yes	characteristic
199	C₂×C₄	—	4	2	no	—
200	C₂×C₄	—	13	4	no	—
201	C₂×C₄	—	13	2	no	—
202	C₂×C₄	—	13	8	no	—
203	C₂×C₄	—	13	4	no	—
204	C₂×C₄	—	13	4	no	—
205	C₂×C₄	—	13	4	no	—
206	C₂×C₄	—	52	2	no	—
207	C₂×C₄	C₂×D₁₃⋊C₈	1	4	yes	—
208	C₂×C₄	C₂×D₁₃⋊C₈	1	1	yes	characteristic
209	C₂×C₄	C₂×D₁₃⋊C₈	1	2	yes	—
210	C₂×C₄	C₂×C₄×#261	1	2	yes	—
211	C₂×C₄	C₂³×#261	1	1	yes	characteristic
212	C₈	—	13	4	no	—
213	C₈	—	13	2	no	—
214	C₈	—	13	2	no	—
215	C₈	C₂×D₁₃⋊C₈	1	4	yes	—
216	C₈	C₂×C₄×#261	1	4	yes	—
217	C₂²	—	2	2	no	—
218	C₂²	—	13	4	no	—
219	C₂²	—	26	4	no	—
220	C₂²	—	52	4	no	—
221	C₂²	C₄×D₁₃⋊C₈	1	2	yes	—
222	C₂²	C₂²×D₁₃⋊C₈	1	1	yes	characteristic
223	C₄	—	2	4	no	—
224	C₄	—	13	4	no	—
225	C₄	—	26	4	no	—
226	C₄	C₄×D₁₃⋊C₈	1	2	yes	—
227	C₄	C₂²×D₁₃⋊C₈	1	1	yes	characteristic
228	C₄	C₂²×C₄×#261	1	1	yes	characteristic
229	C₂	—	2	2	no	—
230	C₂	—	26	4	no	—
231	C₂	C₂×C₄×D₁₃⋊C₈	1	1	yes	characteristic
232	C₂	#13131805	1	2	yes	—

	subgroup	G/H
center, Frattini	C₂×C₄	C₂³×#261
commutator	C₂×C₁₃	C₂²×C₄×C₈
Fitting	C₂×C₁₃×#97	C₄
socle	C₂²×C₁₃	C₂³×C₈
prime radical	C₂³×D₁₃	C₂×C₈
cosocle	C₂×#1055	C₂⁴
hypercenter	C₂×#97	#261
hypocenter	C₁₃	#33324
LCS	G ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂×C₄ ◁ C₂×#97

Complements

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

N	H ≅ G/N	type
2. #13131046	C₂	semidirect
3. #13131042	C₂	semidirect
4. C₄×#88106	C₂	semidirect
10. D₁₃⋊M₃₂	C₄	semidirect
19. #11718258	C₂²	semidirect
20. #11718257	C₂²	semidirect
21. #11718231	C₂²	semidirect
22. C₄×#6092	C₂²	semidirect
41. #88098	C₂×C₄	semidirect
42. D₁₃⋊C₁₆	C₂×C₄	semidirect
194. C₁₃	#33324	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂×D₁₃⋊M₃₂	2
#13131046	2
#13131042	2
C₄×#88106	2
C₂×#11718369	2
#33324	13