Subgroups — C₂×#13131177 #16807010

Order 3328.

698 conjugacy classes of subgroups.

The subgroup lattice has 244 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#88106	C₂	1	2	yes	maximal
2	#13131177	C₂	1	8	yes	maximal, direct product factor
3	C₂×#11718261	C₂	1	4	yes	maximal, complemented
4	C₂×#11718783	C₂	1	1	yes	maximal, characteristic
5	C₂²×C₁₃×M₁₆	C₄	1	1	yes	characteristic
6	C₂×#88180	C₄	1	1	yes	characteristic
7	C₂³×#1055	C₂²	1	1	yes	characteristic
8	C₂×#88106	—	2	2	no	—
9	C₂×#88106	—	2	4	no	—
10	C₂×#88106	C₂²	1	4	yes	—
11	C₂×#88106	C₂²	1	8	yes	—
12	C₂²×#6092	—	2	2	no	—
13	#11718783	C₄	1	4	yes	—
14	#11718783	C₂²	1	4	yes	—
15	C₂×#88055	C₄	1	2	yes	—
16	C₂×C₈×Dic₁₃	C₂²	1	2	yes	—
17	#11718261	C₂²	1	16	yes	complemented
18	C₂³×C₄×C₁₃	C₂×C₄	1	1	yes	characteristic
19	C₂×C₁₃×M₁₆	C₈	1	4	yes	—
20	C₂×C₁₃×M₁₆	C₈	1	4	yes	—
21	C₂×C₁₃×M₁₆	C₂×C₄	1	4	yes	—
22	C₂²×C₈×C₁₃	C₂×C₄	1	2	yes	—
23	C₂×C₂²⋊Dic₁₃	—	2	1	no	—
24	#88180	—	2	2	no	—
25	#88180	C₂×C₄	1	4	yes	—
26	C₂×C₄⋊Dic₁₃	—	2	1	no	—
27	C₂×C₄×Dic₁₃	C₂×C₄	1	2	yes	—
28	C₂²×#1055	C₂×C₄	1	1	yes	characteristic
29	C₂²×#1055	C₂×C₄	1	2	yes	—
30	C₂²×#1055	D₄	1	2	yes	—
31	C₂²×#1055	D₄	1	2	yes	—
32	C₂²×#1055	Q₈	1	2	yes	—
33	C₂²×#1055	Q₈	1	2	yes	—
34	C₂²×#1055	C₂³	1	1	yes	characteristic
35	C₂²×#1055	C₂³	1	2	yes	—
36	#88106	—	2	8	no	—
37	#88106	—	2	4	no	—
38	#88106	C₂³	1	8	yes	—
39	C₂×#6092	—	2	4	no	—
40	C₂×#6092	—	2	8	no	—
41	#88055	C₂×C₄	1	8	yes	—
42	C₈×Dic₁₃	C₂×C₄	1	4	yes	—
43	C₈×Dic₁₃	C₂³	1	4	yes	—
44	C₂×#2153	—	13	1	no	maximal, Sylow
45	C₂⁴×C₁₃	M₁₆	1	1	yes	characteristic
46	C₂²×C₄×C₁₃	C₄⋊C₄	1	2	yes	—
47	C₂²×C₄×C₁₃	C₄⋊C₄	1	2	yes	—
48	C₂²×C₄×C₁₃	C₂×C₈	1	2	yes	—
49	C₂²×C₄×C₁₃	C₂×C₈	1	2	yes	—
50	C₂²×C₄×C₁₃	M₁₆	1	1	yes	characteristic
51	C₂²×C₄×C₁₃	M₁₆	1	2	yes	—
52	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
53	C₂²×C₄×C₁₃	C₂²×C₄	1	2	yes	—
54	C₂²×Dic₁₃	—	2	2	no	—
55	C₁₃×M₁₆	C₂×C₈	1	16	yes	—
56	C₂×C₈×C₁₃	C₂×C₈	1	4	yes	—
57	C₂×C₈×C₁₃	C₂×C₈	1	4	yes	—
58	C₂×C₈×C₁₃	C₂²×C₄	1	4	yes	—
59	C₂²⋊Dic₁₃	—	2	4	no	—
60	C₄⋊Dic₁₃	—	2	4	no	—
61	C₄×Dic₁₃	—	2	2	no	—
62	C₄×Dic₁₃	C₂²×C₄	1	4	yes	—
63	C₂×#1055	C₄⋊C₄	1	2	yes	—
64	C₂×#1055	C₄⋊C₄	1	4	yes	—
65	C₂×#1055	C₄⋊C₄	1	4	yes	—
66	C₂×#1055	C₄⋊C₄	1	2	yes	—
67	C₂×#1055	C₂²×C₄	1	1	yes	characteristic
68	C₂×#1055	C₂²×C₄	1	2	yes	—
69	C₂×#1055	C₂×D₄	1	1	yes	characteristic
70	C₂×#1055	C₂×D₄	1	4	yes	—
71	C₂×#1055	C₂×D₄	1	1	yes	characteristic
72	C₂×#1055	C₂×Q₈	1	1	yes	characteristic
73	C₂×#1055	C₂×Q₈	1	4	yes	—
74	C₂×#1055	C₂×Q₈	1	1	yes	characteristic
75	C₂×#1055	C₂⁴	1	1	yes	characteristic
76	#6092	—	2	8	no	—
77	C₂²×M₃₂	—	13	2	no	—
78	C₂×#405	—	13	1	no	—
79	#2153	—	13	8	no	—
80	C₂×#364	—	13	4	no	—
81	C₂³×C₁₃	—	4	2	no	—
82	C₂³×C₁₃	C₄⋊C₈	1	2	yes	—
83	C₂³×C₁₃	C₄⋊C₈	1	2	yes	—
84	C₂³×C₁₃	C₂×M₁₆	1	1	yes	characteristic
85	C₂³×C₁₃	C₂×M₁₆	1	2	yes	—
86	C₂×C₄×C₁₃	C₄⋊C₈	1	2	yes	—
87	C₂×C₄×C₁₃	C₄⋊C₈	1	4	yes	—
88	C₂×C₄×C₁₃	C₄⋊C₈	1	4	yes	—
89	C₂×C₄×C₁₃	C₄⋊C₈	1	2	yes	—
90	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	4	yes	—
91	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
92	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
93	C₂×C₄×C₁₃	C₂²×C₈	1	1	yes	characteristic
94	C₂×C₄×C₁₃	C₂²×C₈	1	1	yes	characteristic
95	C₂×C₄×C₁₃	C₂²×C₈	1	4	yes	—
96	C₂×C₄×C₁₃	C₂×M₁₆	1	1	yes	characteristic
97	C₂×C₄×C₁₃	C₂×M₁₆	1	2	yes	—
98	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
99	C₂×Dic₁₃	—	2	4	no	—
100	C₂×Dic₁₃	—	4	4	no	—
101	C₈×C₁₃	C₂²×C₈	1	8	yes	—
102	#1055	C₂×C₄⋊C₄	1	1	yes	characteristic
103	#1055	C₂×C₄⋊C₄	1	1	yes	characteristic
104	#1055	C₂×C₄⋊C₄	1	4	yes	—
105	#1055	C₂²×D₄	1	1	yes	characteristic
106	#1055	C₂²×Q₈	1	1	yes	characteristic
107	C₂²×M₁₆	#261	1	1	yes	characteristic
108	C₂³×C₈	—	13	1	no	—
109	C₂×#117	—	13	1	no	—
110	C₂×M₃₂	—	13	4	no	—
111	C₂×M₃₂	—	13	8	no	—
112	C₂×M₃₂	—	26	2	no	—
113	C₂×M₃₂	—	26	4	no	—
114	C₂²×C₁₆	—	26	2	no	—
115	#405	—	13	4	no	—
116	#405	—	13	4	no	—
117	C₂×#97	—	13	2	no	—
118	C₂×C₄×C₈	—	13	2	no	—
119	#364	—	13	16	no	—
120	C₂²×C₁₃	—	2	2	no	—
121	C₂²×C₁₃	—	2	4	no	—
122	C₂²×C₁₃	—	4	2	no	—
123	C₂²×C₁₃	—	4	2	no	—
124	C₂²×C₁₃	C₂×C₄⋊C₈	1	1	yes	characteristic
125	C₂²×C₁₃	C₂×C₄⋊C₈	1	4	yes	—
126	C₂²×C₁₃	C₂×C₄⋊C₈	1	1	yes	characteristic
127	C₂²×C₁₃	C₂²×M₁₆	1	1	yes	characteristic
128	C₄×C₁₃	C₂×C₄⋊C₈	1	1	yes	characteristic
129	C₄×C₁₃	C₂×C₄⋊C₈	1	4	yes	—
130	C₄×C₁₃	C₂×C₄⋊C₈	1	1	yes	characteristic
131	C₄×C₁₃	C₂²×C₄⋊C₄	1	1	yes	characteristic
132	C₄×C₁₃	C₂³×C₈	1	1	yes	characteristic
133	Dic₁₃	—	4	4	no	—
134	C₂³×C₄	C₂×#261	1	1	yes	characteristic
135	C₂×M₁₆	#1057	1	4	yes	—
136	C₂×M₁₆	#1057	1	4	yes	—
137	C₂×M₁₆	C₂×#261	1	4	yes	—
138	C₂²×C₈	—	13	2	no	—
139	C₂²×C₈	—	13	2	no	—
140	C₂²×C₈	—	13	2	no	—
141	C₂²×C₈	—	13	2	no	—
142	C₂²×C₈	—	13	1	no	—
143	C₂²×C₈	—	13	2	no	—
144	C₂²×C₈	—	13	1	no	—
145	C₂²×C₈	—	13	2	no	—
146	C₂²×C₈	C₂×#261	1	2	yes	—
147	#117	—	13	4	no	—
148	#117	—	26	2	no	—
149	C₂×C₄⋊C₄	—	26	1	no	—
150	C₂×C₂²⋊C₄	—	26	1	no	—
151	C₂×C₄²	—	13	2	no	—
152	M₃₂	—	13	8	no	—
153	M₃₂	—	26	8	no	—
154	M₃₂	—	26	4	no	—
155	C₂×C₁₆	—	26	8	no	—
156	C₂×C₁₆	—	26	4	no	—
157	#97	—	13	8	no	—
158	C₄×C₈	—	13	4	no	—
159	C₄×C₈	—	13	4	no	—
160	C₂×C₁₃	—	2	1	no	—
161	C₂×C₁₃	—	2	1	no	—
162	C₂×C₁₃	—	2	4	no	—
163	C₂×C₁₃	#2153	1	2	yes	complemented
164	C₂×C₁₃	C₂²×C₄⋊C₈	1	1	yes	characteristic
165	C₂⁴	#6118	1	1	yes	characteristic
166	C₂²×C₄	—	26	2	no	—
167	C₂²×C₄	#6118	1	1	yes	characteristic
168	C₂²×C₄	#6118	1	2	yes	—
169	C₂²×C₄	C₄⋊#261	1	2	yes	—
170	C₂²×C₄	C₄⋊#261	1	2	yes	—
171	C₂²×C₄	C₂×#1057	1	2	yes	—
172	C₂²×C₄	C₂×#1057	1	2	yes	—
173	C₂²×C₄	C₂²×#261	1	2	yes	—
174	C₂²×C₄	C₂²×#261	1	1	yes	characteristic
175	M₁₆	C₂×#1057	1	16	yes	—
176	C₂×C₈	—	13	4	no	—
177	C₂×C₈	—	13	1	no	—
178	C₂×C₈	—	13	4	no	—
179	C₂×C₈	—	13	2	no	—
180	C₂×C₈	—	13	4	no	—
181	C₂×C₈	—	13	1	no	—
182	C₂×C₈	—	13	4	no	—
183	C₂×C₈	—	13	1	no	—
184	C₂×C₈	—	13	2	no	—
185	C₂×C₈	—	13	1	no	—
186	C₂×C₈	—	13	1	no	—
187	C₂×C₈	—	13	1	no	—
188	C₂×C₈	—	13	2	no	—
189	C₂×C₈	C₂×#1057	1	4	yes	—
190	C₂×C₈	C₂×#1057	1	4	yes	—
191	C₂×C₈	C₂²×#261	1	4	yes	—
192	C₄⋊C₄	—	26	4	no	—
193	C₂²⋊C₄	—	26	4	no	—
194	C₄²	—	13	4	no	—
195	C₄²	—	26	2	no	—
196	C₁₆	—	26	8	no	—
197	C₁₃	C₂×#2153	1	1	yes	characteristic, complemented, Sylow
198	C₂³	—	4	2	no	—
199	C₂³	C₄⋊#1057	1	2	yes	—
200	C₂³	C₄⋊#1057	1	2	yes	—
201	C₂³	C₂×#6118	1	1	yes	characteristic
202	C₂³	C₂×#6118	1	2	yes	—
203	C₂×C₄	—	26	4	no	—
204	C₂×C₄	—	52	4	no	—
205	C₂×C₄	C₄⋊#1057	1	2	yes	—
206	C₂×C₄	C₄⋊#1057	1	4	yes	—
207	C₂×C₄	C₄⋊#1057	1	2	yes	—
208	C₂×C₄	C₄⋊#1057	1	4	yes	—
209	C₂×C₄	C₂×#6118	1	1	yes	characteristic
210	C₂×C₄	C₂×#6118	1	2	yes	—
211	C₂×C₄	C₂×C₄⋊#261	1	4	yes	—
212	C₂×C₄	C₂×C₄⋊#261	1	1	yes	characteristic
213	C₂×C₄	C₂×C₄⋊#261	1	1	yes	characteristic
214	C₂×C₄	C₂²×#1057	1	1	yes	characteristic
215	C₂×C₄	C₂²×#1057	1	1	yes	characteristic
216	C₂×C₄	C₂²×#1057	1	4	yes	—
217	C₂×C₄	C₂³×#261	1	1	yes	characteristic
218	C₈	—	13	1	no	—
219	C₈	—	13	4	no	—
220	C₈	—	13	1	no	—
221	C₈	—	13	1	no	—
222	C₈	—	13	1	no	—
223	C₈	C₂²×#1057	1	8	yes	—
224	C₂²	—	2	2	no	—
225	C₂²	—	2	4	no	—
226	C₂²	—	4	2	no	—
227	C₂²	—	4	2	no	—
228	C₂²	C₂×C₄⋊#1057	1	1	yes	characteristic
229	C₂²	C₂×C₄⋊#1057	1	4	yes	—
230	C₂²	C₂×C₄⋊#1057	1	1	yes	characteristic
231	C₂²	C₂²×#6118	1	1	yes	characteristic
232	C₄	—	52	4	no	—
233	C₄	C₂×C₄⋊#1057	1	1	yes	characteristic
234	C₄	C₂×C₄⋊#1057	1	4	yes	—
235	C₄	C₂×C₄⋊#1057	1	1	yes	characteristic
236	C₄	C₂²×C₄⋊#261	1	1	yes	characteristic
237	C₄	C₂³×#1057	1	1	yes	characteristic
238	C₂	—	2	1	no	—
239	C₂	—	2	1	no	—
240	C₂	—	2	4	no	—
241	C₂	#13131177	1	2	yes	direct product factor
242	C₂	C₂²×C₄⋊#1057	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂×C₄⋊#261
commutator	C₄×C₁₃	C₂³×C₈
Frattini	C₂×C₄	C₂³×#261
Fitting	C₂²×C₁₃×M₁₆	C₄
socle	C₂²×C₁₃	C₂×C₄⋊C₈
prime radical	C₂⁴×C₁₃	M₁₆
cosocle	C₂×#1055	C₂⁴
hypercenter	C₂²×M₁₆	#261
hypocenter	C₁₃	C₂×#2153
LCS	G ▷ C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂×C₄ ◁ C₂³×C₄ ◁ C₂²×M₁₆

Complements

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

N	H ≅ G/N	type
2. #13131177	C₂	direct (N × H)
3. C₂×#11718261	C₂	semidirect
17. #11718261	C₂²	semidirect
163. C₂×C₁₃	#2153	semidirect
197. C₁₃	C₂×#2153	semidirect
241. C₂	#13131177	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×#88106	2
#13131177	2
C₂×#11718261	2
C₂×#11718783	2
C₂×#2153	13

Subgroups — C2×#13131177 #16807010

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#13131177 #16807010