Subgroups — C₂×#13129953 #16791176

Order 3328.

294 conjugacy classes of subgroups.

The subgroup lattice has 220 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#11718249	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×#88036	C₂	1	1	yes	maximal, characteristic, complemented
3	#13129953	C₂	1	4	yes	maximal, direct product factor
4	C₂×#11718801	C₂	1	1	yes	maximal, characteristic
5	C₂×C₁₃×#131	C₄	1	1	yes	characteristic
6	#11718801	—	2	1	no	—
7	#11718801	—	2	1	no	—
8	#11718801	C₄	1	2	yes	—
9	#11718801	C₂²	1	2	yes	—
10	C₂×#88052	—	2	1	no	—
11	C₂×#88052	C₄	1	1	yes	characteristic
12	C₂²×#6090	—	2	1	no	—
13	C₂²×#6090	C₂²	1	1	yes	characteristic
14	#11718249	—	2	1	no	—
15	#11718249	C₂²	1	2	yes	complemented
16	C₂×#88036	—	2	1	no	—
17	C₂×#88036	—	2	1	no	—
18	C₂×#88036	—	2	1	no	—
19	C₂×#88036	C₂²	1	2	yes	complemented
20	C₂×C₁₃×#41	C₈	1	1	yes	characteristic
21	C₁₃×#131	—	2	1	no	—
22	C₁₃×#131	—	2	1	no	—
23	C₁₃×#131	C₈	1	2	yes	—
24	C₁₃×#131	C₂×C₄	1	2	yes	—
25	C₂×C₁₃×M₁₆	—	2	1	no	—
26	C₂×C₁₃×M₁₆	C₈	1	1	yes	characteristic
27	C₂²×C₈×C₁₃	—	2	1	no	—
28	C₂²×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
29	#88052	—	2	1	no	—
30	#88052	—	2	2	no	—
31	#88052	—	2	2	no	—
32	#88052	C₂×C₄	1	2	yes	—
33	C₂×#6090	—	2	1	no	—
34	C₂×#6090	—	2	2	no	—
35	C₂×#6090	—	2	2	no	—
36	C₂×#6090	C₂×C₄	1	1	yes	characteristic
37	C₂×#6090	D₄	1	1	yes	characteristic
38	C₂×#6090	D₄	1	1	yes	characteristic
39	C₂×#6090	D₄	1	1	yes	characteristic
40	C₂×#6090	D₄	1	1	yes	characteristic
41	C₂×#6090	C₂³	1	1	yes	characteristic
42	#88036	—	2	2	no	—
43	#88036	—	2	2	no	—
44	C₂×#1401	—	13	1	no	maximal, Sylow
45	C₁₃×#41	—	2	1	no	—
46	C₁₃×#41	—	2	1	no	—
47	C₁₃×#41	C₁₆	1	2	yes	—
48	C₁₃×#41	C₂×C₈	1	2	yes	—
49	C₂×Q₈×C₁₃	C₁₆	1	1	yes	characteristic
50	C₂×D₄×C₁₃	—	2	1	no	—
51	C₂×D₄×C₁₃	C₁₆	1	1	yes	characteristic
52	C₂²×C₄×C₁₃	—	2	1	no	—
53	C₂²×C₄×C₁₃	C₂×C₈	1	1	yes	characteristic
54	C₁₃×M₁₆	—	2	1	no	—
55	C₁₃×M₁₆	—	2	2	no	—
56	C₁₃×M₁₆	—	2	2	no	—
57	C₁₃×M₁₆	C₂×C₈	1	2	yes	—
58	C₂×C₈×C₁₃	—	2	1	no	—
59	C₂×C₈×C₁₃	—	2	2	no	—
60	C₂×C₈×C₁₃	—	2	2	no	—
61	C₂×C₈×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
62	C₂×C₈×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
63	C₂×C₈×C₁₃	C₂×C₈	1	1	yes	characteristic
64	C₂×C₈×C₁₃	M₁₆	1	1	yes	characteristic
65	C₂×C₈×C₁₃	M₁₆	1	1	yes	characteristic
66	C₂×C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
67	#6090	—	2	2	no	—
68	#6090	C₂²⋊C₄	1	1	yes	characteristic
69	#6090	C₂²⋊C₄	1	1	yes	characteristic
70	#6090	C₂×D₄	1	1	yes	characteristic
71	#6090	C₂×D₄	1	1	yes	characteristic
72	C₂×#504	—	13	1	no	—
73	C₂×M₆₄	—	13	1	no	—
74	C₂²×C₃₂	—	13	1	no	—
75	#1401	—	13	4	no	—
76	C₂³×C₁₃	—	2	1	no	—
77	C₂³×C₁₃	M₃₂	1	1	yes	characteristic
78	Q₈×C₁₃	—	2	1	no	—
79	Q₈×C₁₃	C₂×C₁₆	1	2	yes	—
80	D₄×C₁₃	—	2	2	no	—
81	D₄×C₁₃	—	2	2	no	—
82	D₄×C₁₃	—	2	1	no	—
83	D₄×C₁₃	C₂×C₁₆	1	2	yes	—
84	C₂×C₄×C₁₃	—	2	1	no	—
85	C₂×C₄×C₁₃	—	2	2	no	—
86	C₂×C₄×C₁₃	—	2	2	no	—
87	C₂×C₄×C₁₃	C₂²⋊C₈	1	1	yes	characteristic
88	C₂×C₄×C₁₃	C₂²⋊C₈	1	1	yes	characteristic
89	C₂×C₄×C₁₃	C₂×C₁₆	1	1	yes	characteristic
90	C₂×C₄×C₁₃	C₂×C₁₆	1	1	yes	characteristic
91	C₂×C₄×C₁₃	M₃₂	1	1	yes	characteristic
92	C₂×C₄×C₁₃	C₂²×C₈	1	1	yes	characteristic
93	C₈×C₁₃	—	2	2	no	—
94	C₈×C₁₃	C₂²⋊C₈	1	1	yes	characteristic
95	C₈×C₁₃	C₂²⋊C₈	1	1	yes	characteristic
96	C₈×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
97	C₈×C₁₃	C₂×M₁₆	1	1	yes	characteristic
98	C₂×#131	#261	1	1	yes	characteristic
99	#504	—	13	2	no	—
100	#504	—	13	2	no	—
101	#504	—	26	1	no	—
102	#504	—	26	1	no	—
103	C₂×M₃₂	—	13	1	no	—
104	C₂×M₃₂	—	26	1	no	—
105	C₂²×C₁₆	—	13	1	no	—
106	C₂²×C₁₆	—	26	1	no	—
107	M₆₄	—	13	2	no	—
108	M₆₄	—	26	1	no	—
109	C₂×C₃₂	—	13	2	no	—
110	C₂×C₃₂	—	26	1	no	—
111	C₂×C₃₂	—	26	1	no	—
112	C₂×C₃₂	—	26	1	no	—
113	C₂²×C₁₃	—	2	2	no	—
114	C₂²×C₁₃	—	2	2	no	—
115	C₂²×C₁₃	—	4	2	no	—
116	C₂²×C₁₃	C₂²⋊C₁₆	1	1	yes	characteristic
117	C₂²×C₁₃	C₂²⋊C₁₆	1	1	yes	characteristic
118	C₂²×C₁₃	C₂×M₃₂	1	1	yes	characteristic
119	C₄×C₁₃	—	2	2	no	—
120	C₄×C₁₃	C₂²⋊C₁₆	1	1	yes	characteristic
121	C₄×C₁₃	C₂²⋊C₁₆	1	1	yes	characteristic
122	C₄×C₁₃	C₂×C₂²⋊C₈	1	1	yes	characteristic
123	C₄×C₁₃	C₂²×C₁₆	1	1	yes	characteristic
124	C₂×#41	#1057	1	1	yes	characteristic
125	#131	—	2	1	no	—
126	#131	—	2	1	no	—
127	#131	#1057	1	2	yes	—
128	#131	C₂×#261	1	2	yes	—
129	C₂×M₁₆	—	2	1	no	—
130	C₂×M₁₆	#1057	1	1	yes	characteristic
131	C₂²×C₈	—	2	1	no	—
132	C₂²×C₈	C₂×#261	1	1	yes	characteristic
133	M₃₂	—	13	2	no	—
134	M₃₂	—	26	2	no	—
135	M₃₂	—	26	2	no	—
136	M₃₂	—	26	1	no	—
137	C₂×C₁₆	—	13	1	no	—
138	C₂×C₁₆	—	13	1	no	—
139	C₂×C₁₆	—	13	1	no	—
140	C₂×C₁₆	—	13	1	no	—
141	C₂×C₁₆	—	13	1	no	—
142	C₂×C₁₆	—	13	1	no	—
143	C₂×C₁₆	—	26	2	no	—
144	C₂×C₁₆	—	26	2	no	—
145	C₂×C₁₆	—	26	1	no	—
146	C₃₂	—	26	2	no	—
147	C₃₂	—	26	2	no	—
148	C₂×C₁₃	—	2	1	no	—
149	C₂×C₁₃	—	2	1	no	—
150	C₂×C₁₃	—	4	2	no	—
151	C₂×C₁₃	#1401	1	2	yes	complemented
152	C₂×C₁₃	C₂×C₂²⋊C₁₆	1	1	yes	characteristic
153	#41	—	2	1	no	—
154	#41	—	2	1	no	—
155	#41	#6092	1	2	yes	—
156	#41	C₂×#1057	1	2	yes	—
157	C₂×Q₈	#6092	1	1	yes	characteristic
158	C₂×D₄	—	2	1	no	—
159	C₂×D₄	#6092	1	1	yes	characteristic
160	C₂²×C₄	—	2	1	no	—
161	C₂²×C₄	C₂×#1057	1	1	yes	characteristic
162	M₁₆	—	2	1	no	—
163	M₁₆	—	2	2	no	—
164	M₁₆	—	2	2	no	—
165	M₁₆	C₂×#1057	1	2	yes	—
166	C₂×C₈	—	2	1	no	—
167	C₂×C₈	—	2	2	no	—
168	C₂×C₈	—	2	2	no	—
169	C₂×C₈	C₂×#1057	1	1	yes	characteristic
170	C₂×C₈	#6122	1	1	yes	characteristic
171	C₂×C₈	#6122	1	1	yes	characteristic
172	C₂×C₈	C₂²⋊#261	1	1	yes	characteristic
173	C₂×C₈	C₂²⋊#261	1	1	yes	characteristic
174	C₂×C₈	C₂²×#261	1	1	yes	characteristic
175	C₁₆	—	13	1	no	—
176	C₁₆	—	13	1	no	—
177	C₁₆	—	13	1	no	—
178	C₁₆	—	13	1	no	—
179	C₁₆	—	26	2	no	—
180	C₁₃	C₂×#1401	1	1	yes	characteristic, complemented, Sylow
181	C₂³	—	2	1	no	—
182	C₂³	#88106	1	1	yes	characteristic
183	Q₈	—	2	1	no	—
184	Q₈	C₂×#6092	1	2	yes	—
185	D₄	—	2	2	no	—
186	D₄	—	2	2	no	—
187	D₄	—	2	1	no	—
188	D₄	C₂×#6092	1	2	yes	—
189	C₂×C₄	—	2	1	no	—
190	C₂×C₄	—	2	2	no	—
191	C₂×C₄	—	2	2	no	—
192	C₂×C₄	C₂×#6092	1	1	yes	characteristic
193	C₂×C₄	C₂×#6092	1	1	yes	characteristic
194	C₂×C₄	#88106	1	1	yes	characteristic
195	C₂×C₄	C₂²⋊#1057	1	1	yes	characteristic
196	C₂×C₄	C₂²⋊#1057	1	1	yes	characteristic
197	C₂×C₄	C₂²×#1057	1	1	yes	characteristic
198	C₈	—	2	2	no	—
199	C₈	C₂²⋊#1057	1	1	yes	characteristic
200	C₈	C₂²⋊#1057	1	1	yes	characteristic
201	C₈	C₂×#6122	1	1	yes	characteristic
202	C₈	C₂×C₂²⋊#261	1	1	yes	characteristic
203	C₂²	—	2	2	no	—
204	C₂²	—	2	2	no	—
205	C₂²	—	4	2	no	—
206	C₂²	C₂²⋊#6092	1	1	yes	characteristic
207	C₂²	C₂²⋊#6092	1	1	yes	characteristic
208	C₂²	C₂×#88106	1	1	yes	characteristic
209	C₄	—	2	2	no	—
210	C₄	C₂²⋊#6092	1	1	yes	characteristic
211	C₄	C₂²⋊#6092	1	1	yes	characteristic
212	C₄	C₂²×#6092	1	1	yes	characteristic
213	C₄	C₂×C₂²⋊#1057	1	1	yes	characteristic
214	C₂	—	2	1	no	—
215	C₂	—	2	1	no	—
216	C₂	—	4	2	no	—
217	C₂	#13129953	1	2	yes	direct product factor
218	C₂	C₂×C₂²⋊#6092	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₈	C₂²⋊#261
commutator	C₄×C₁₃	C₂²×C₁₆
Frattini	C₂×C₈	C₂²×#261
Fitting	C₂×C₁₃×#131	C₄
socle	C₂²×C₁₃	C₂²⋊C₁₆
prime radical	C₂×C₁₃×#41	C₈
cosocle	C₂×#6090	C₂³
hypercenter	C₂×#131	#261
hypocenter	C₁₃	C₂×#1401
LCS	G ▷ C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂×C₈ ◁ C₂²×C₈ ◁ C₂×#131

Complements

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

N	H ≅ G/N	type
1. C₂×#11718249	C₂	semidirect
2. C₂²×#88036	C₂	semidirect
3. #13129953	C₂	direct (N × H)
15. #11718249	C₂²	semidirect
19. C₂×#88036	C₂²	semidirect
151. C₂×C₁₃	#1401	semidirect
180. C₁₃	C₂×#1401	semidirect
217. C₂	#13129953	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×#11718249	2
C₂²×#88036	2
#13129953	2
C₂×#11718801	2
C₂×#1401	13

Subgroups — C2×#13129953 #16791176

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#13129953 #16791176