Subgroups — C₂×#13112898 #15774284

Order 3328.

294 conjugacy classes of subgroups.

The subgroup lattice has 202 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#11718344	C₂	1	1	yes	maximal, characteristic
2	C₂×#11718055	C₂	1	1	yes	maximal, characteristic
3	#13112898	C₂	1	4	yes	maximal, direct product factor
4	C₂×C₁₃×#364	C₂	1	1	yes	maximal, characteristic
5	C₂×#88124	C₄	1	2	yes	—
6	C₂×C₁₃×M₃₂	—	2	1	no	—
7	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
8	C₂×#88058	—	2	1	no	—
9	C₂×#88057	—	2	1	no	—
10	C₂×#88052	—	2	1	no	—
11	#11718344	—	2	1	no	—
12	#11718344	—	2	1	no	—
13	#11718344	C₄	1	2	yes	—
14	#11718344	C₂²	1	2	yes	—
15	C₁₃×#364	—	2	1	no	—
16	C₁₃×#364	C₂²	1	2	yes	—
17	#11718055	—	2	1	no	—
18	#11718055	C₂²	1	2	yes	—
19	C₂²×C₈×C₁₃	D₄	1	1	yes	characteristic
20	C₂²×C₈×C₁₃	D₄	1	1	yes	characteristic
21	C₂×C₄²×C₁₃	C₂×C₄	1	1	yes	characteristic
22	C₂×C₄⋊Dic₁₃	—	2	2	no	—
23	C₂×#6101	—	4	2	no	—
24	#88124	—	2	2	no	—
25	#88124	—	4	2	no	—
26	#88124	C₂×C₄	1	4	yes	—
27	C₁₃×M₃₂	—	2	2	no	—
28	C₁₃×M₃₂	—	4	1	no	—
29	C₂×C₁₃×C₁₆	—	4	1	no	—
30	C₄×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
31	C₄×C₈×C₁₃	D₄	1	1	yes	characteristic
32	C₄×C₈×C₁₃	D₄	1	1	yes	characteristic
33	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
34	#88058	—	2	2	no	—
35	#88058	—	2	2	no	—
36	#88057	—	2	2	no	—
37	#88057	—	2	2	no	—
38	#88052	—	2	2	no	—
39	#88052	—	4	1	no	—
40	C₂×#6090	—	4	1	no	—
41	C₂×#1366	—	13	1	no	maximal, Sylow
42	C₂²×C₄×C₁₃	—	2	1	no	—
43	C₂²×C₄×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
44	C₂²×Dic₁₃	—	4	2	no	—
45	C₂×C₈×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
46	C₂×C₈×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
47	C₂×C₈×C₁₃	SD₁₆	1	1	yes	characteristic
48	C₂×C₈×C₁₃	SD₁₆	1	1	yes	characteristic
49	C₂×C₈×C₁₃	SD₁₆	1	1	yes	characteristic
50	C₂×C₈×C₁₃	SD₁₆	1	1	yes	characteristic
51	C₂×C₈×C₁₃	Q₁₆	1	1	yes	characteristic
52	C₂×C₈×C₁₃	Q₁₆	1	1	yes	characteristic
53	C₂×C₈×C₁₃	Q₁₆	1	1	yes	characteristic
54	C₂×C₈×C₁₃	Q₁₆	1	1	yes	characteristic
55	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
56	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
57	C₄²×C₁₃	—	2	1	no	—
58	C₄²×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
59	C₄²×C₁₃	C₂²×C₄	1	1	yes	characteristic
60	C₄⋊Dic₁₃	—	2	4	no	—
61	C₄⋊Dic₁₃	—	4	2	no	—
62	#6101	—	4	4	no	—
63	#6101	—	4	4	no	—
64	C₁₃×C₁₆	—	4	2	no	—
65	#6090	—	4	2	no	—
66	C₂×#499	—	13	1	no	—
67	C₂×#364	—	13	1	no	—
68	C₂×#364	D₁₃	1	1	yes	characteristic
69	#1366	—	13	4	no	—
70	C₂³×C₁₃	#100	1	1	yes	characteristic
71	C₂×C₄×C₁₃	—	2	1	no	—
72	C₂×C₄×C₁₃	—	2	1	no	—
73	C₂×C₄×C₁₃	—	4	2	no	—
74	C₂×C₄×C₁₃	#100	1	1	yes	characteristic
75	C₂×C₄×C₁₃	#103	1	1	yes	characteristic
76	C₂×C₄×C₁₃	#103	1	1	yes	characteristic
77	C₂×C₄×C₁₃	#103	1	1	yes	characteristic
78	C₂×C₄×C₁₃	#103	1	1	yes	characteristic
79	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
80	C₂×Dic₁₃	—	4	4	no	—
81	C₂×Dic₁₃	—	8	4	no	—
82	C₈×C₁₃	#103	1	1	yes	characteristic
83	C₈×C₁₃	#103	1	1	yes	characteristic
84	C₈×C₁₃	#103	1	1	yes	characteristic
85	C₈×C₁₃	#103	1	1	yes	characteristic
86	C₈×C₁₃	C₂×SD₁₆	1	1	yes	characteristic
87	C₈×C₁₃	C₂×SD₁₆	1	1	yes	characteristic
88	C₈×C₁₃	C₂×Q₁₆	1	1	yes	characteristic
89	C₈×C₁₃	C₂×Q₁₆	1	1	yes	characteristic
90	C₂×#125	—	13	2	no	—
91	C₂×M₃₂	—	2	1	no	—
92	C₂×M₃₂	—	26	1	no	—
93	#499	—	13	2	no	—
94	#499	—	13	2	no	—
95	#499	—	26	1	no	—
96	#499	—	26	1	no	—
97	C₂×#107	—	26	1	no	—
98	C₂×#106	—	26	1	no	—
99	C₂×C₄×C₈	C₂×D₁₃	1	1	yes	characteristic
100	#364	—	2	1	no	—
101	#364	—	13	2	no	—
102	#364	—	26	1	no	—
103	#364	C₂×D₁₃	1	2	yes	—
104	C₂²×C₁₃	—	2	2	no	—
105	C₂²×C₁₃	#333	1	1	yes	characteristic
106	C₂²×C₁₃	#333	1	1	yes	characteristic
107	C₂²×C₁₃	C₂×#100	1	1	yes	characteristic
108	C₄×C₁₃	—	4	1	no	—
109	C₄×C₁₃	—	4	1	no	—
110	C₄×C₁₃	#333	1	1	yes	characteristic
111	C₄×C₁₃	#333	1	1	yes	characteristic
112	C₄×C₁₃	C₂×#103	1	1	yes	characteristic
113	C₄×C₁₃	C₂×#103	1	1	yes	characteristic
114	Dic₁₃	—	8	4	no	—
115	C₂²×C₈	D₅₂	1	1	yes	characteristic
116	C₂²×C₈	C₂²⋊D₁₃	1	1	yes	characteristic
117	#125	—	13	4	no	—
118	#125	—	26	2	no	—
119	#125	—	52	2	no	—
120	C₂×C₄⋊C₄	—	26	2	no	—
121	C₂×C₄⋊C₄	—	52	2	no	—
122	C₂×C₄²	C₄×D₁₃	1	1	yes	characteristic
123	M₃₂	—	2	2	no	—
124	M₃₂	—	4	1	no	—
125	M₃₂	—	26	2	no	—
126	M₃₂	—	52	1	no	—
127	C₂×C₁₆	—	4	1	no	—
128	C₂×C₁₆	—	52	1	no	—
129	#107	—	26	2	no	—
130	#107	—	26	2	no	—
131	#106	—	26	2	no	—
132	#106	—	26	2	no	—
133	C₄×C₈	C₄×D₁₃	1	1	yes	characteristic
134	C₄×C₈	D₅₂	1	1	yes	characteristic
135	C₄×C₈	C₂²⋊D₁₃	1	1	yes	characteristic
136	C₄×C₈	C₂²×D₁₃	1	1	yes	characteristic
137	C₂×C₁₃	—	2	1	no	—
138	C₂×C₁₃	—	2	1	no	—
139	C₂×C₁₃	#1366	1	2	yes	complemented
140	C₂×C₁₃	C₂×#333	1	1	yes	characteristic
141	C₂²×C₄	—	2	1	no	—
142	C₂²×C₄	—	52	2	no	—
143	C₂²×C₄	#6103	1	1	yes	characteristic
144	C₂×C₈	#6095	1	1	yes	characteristic
145	C₂×C₈	#6095	1	1	yes	characteristic
146	C₂×C₈	Dic₅₂	1	1	yes	characteristic
147	C₂×C₈	Dic₅₂	1	1	yes	characteristic
148	C₂×C₈	#6103	1	1	yes	characteristic
149	C₂×C₈	#6103	1	1	yes	characteristic
150	C₂×C₈	#6105	1	1	yes	characteristic
151	C₂×C₈	#6105	1	1	yes	characteristic
152	C₂×C₈	#6107	1	1	yes	characteristic
153	C₂×C₈	#6107	1	1	yes	characteristic
154	C₂×C₈	C₂×D₅₂	1	1	yes	characteristic
155	C₂×C₈	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
156	C₄⋊C₄	—	26	4	no	—
157	C₄⋊C₄	—	52	4	no	—
158	C₄⋊C₄	—	52	4	no	—
159	C₄⋊C₄	—	52	2	no	—
160	C₄²	—	2	1	no	—
161	C₄²	#6103	1	1	yes	characteristic
162	C₄²	C₂×C₄×D₁₃	1	1	yes	characteristic
163	C₁₆	—	4	2	no	—
164	C₁₆	—	52	2	no	—
165	C₁₃	C₂×#1366	1	1	yes	characteristic, complemented, Sylow
166	C₂³	#88063	1	1	yes	characteristic
167	C₂×C₄	—	2	1	no	—
168	C₂×C₄	—	2	1	no	—
169	C₂×C₄	—	4	2	no	—
170	C₂×C₄	—	52	4	no	—
171	C₂×C₄	—	104	4	no	—
172	C₂×C₄	#88050	1	1	yes	characteristic
173	C₂×C₄	#88050	1	1	yes	characteristic
174	C₂×C₄	#88056	1	1	yes	characteristic
175	C₂×C₄	#88056	1	1	yes	characteristic
176	C₂×C₄	#88063	1	1	yes	characteristic
177	C₂×C₄	C₂×#6103	1	1	yes	characteristic
178	C₈	#88050	1	1	yes	characteristic
179	C₈	#88050	1	1	yes	characteristic
180	C₈	#88056	1	1	yes	characteristic
181	C₈	#88056	1	1	yes	characteristic
182	C₈	C₂×#6095	1	1	yes	characteristic
183	C₈	C₂×Dic₅₂	1	1	yes	characteristic
184	C₈	C₂×#6105	1	1	yes	characteristic
185	C₈	C₂×#6107	1	1	yes	characteristic
186	C₂²	—	2	2	no	—
187	C₂²	#11718073	1	1	yes	characteristic
188	C₂²	#11718073	1	1	yes	characteristic
189	C₂²	C₂×#88063	1	1	yes	characteristic
190	C₄	—	4	1	no	—
191	C₄	—	4	1	no	—
192	C₄	—	104	4	no	—
193	C₄	#11718073	1	1	yes	characteristic
194	C₄	#11718073	1	1	yes	characteristic
195	C₄	C₂×#88050	1	1	yes	characteristic
196	C₄	C₂×#88056	1	1	yes	characteristic
197	C₂	—	2	1	no	—
198	C₂	—	2	1	no	—
199	C₂	#13112898	1	2	yes	direct product factor
200	C₂	C₂×#11718073	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	#11718073
commutator	C₄²×C₁₃	C₂²×C₄
Frattini	C₄×C₈	C₂²×D₁₃
Fitting	C₂×C₁₃×#364	C₂
socle	C₂²×C₁₃	#333
prime radical	C₂³×C₁₃	#100
cosocle	C₄×C₈×C₁₃	C₂³
hypercenter	C₂×#364	D₁₃
hypocenter	C₁₃	C₂×#1366
LCS	G ▷ C₄²×C₁₃ ▷ C₂×C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂² ◁ C₂²×C₄ ◁ C₂×C₄×C₈ ◁ C₂×#364

Complements

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

N	H ≅ G/N	type
3. #13112898	C₂	direct (N × H)
139. C₂×C₁₃	#1366	semidirect
165. C₁₃	C₂×#1366	semidirect
199. C₂	#13112898	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×#11718344	2
C₂×#11718055	2
#13112898	2
C₂×C₁₃×#364	2
C₂×#1366	13

Subgroups — C2×#13112898 #15774284

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#13112898 #15774284