Subgroups — C₂×#13112909 #15774499

Order 3328.

262 conjugacy classes of subgroups.

The subgroup lattice has 178 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄×#6090	C₂	1	1	yes	maximal, characteristic
2	C₂×#11718050	C₂	1	1	yes	maximal, characteristic
3	#13112909	C₂	1	4	yes	maximal, direct product factor
4	C₂×C₁₃×#335	C₂	1	1	yes	maximal, characteristic
5	C₂×C₁₃×C₄⋊C₈	—	2	1	no	—
6	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
7	C₂²×#6090	C₄	1	1	yes	characteristic
8	C₂²×#6090	C₄	1	1	yes	characteristic
9	C₂×C₄⋊#1055	—	2	1	no	—
10	C₁₃×#335	—	2	1	no	—
11	C₁₃×#335	C₂²	1	2	yes	—
12	C₄×#6090	C₄	1	2	yes	—
13	C₄×#6090	C₂²	1	2	yes	—
14	#11718050	—	2	1	no	—
15	#11718050	C₂²	1	2	yes	—
16	C₂²×C₈×C₁₃	—	4	1	no	—
17	C₂²×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
18	C₂²×C₈×C₁₃	Q₈	1	1	yes	characteristic
19	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
20	C₂²×#1055	—	4	1	no	—
21	C₁₃×C₄⋊C₈	—	2	2	no	—
22	C₁₃×C₄⋊C₈	—	4	1	no	—
23	C₄×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
24	C₄×C₈×C₁₃	D₄	1	1	yes	characteristic
25	C₄×C₈×C₁₃	Q₈	1	1	yes	characteristic
26	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
27	C₂×#6090	—	2	2	no	—
28	C₂×#6090	C₈	1	4	yes	complemented
29	C₂×#6090	C₂×C₄	1	2	yes	—
30	C₂×#6090	C₂×C₄	1	2	yes	—
31	C₄⋊#1055	—	2	2	no	—
32	C₄⋊#1055	—	4	1	no	—
33	C₂×#1372	—	13	1	no	maximal, Sylow
34	C₂²×C₄×C₁₃	C₄⋊C₄	1	1	yes	characteristic
35	C₂²×C₄×C₁₃	D₈	1	1	yes	characteristic
36	C₂²×C₄×C₁₃	Q₁₆	1	1	yes	characteristic
37	C₂×C₈×C₁₃	—	2	2	no	—
38	C₂×C₈×C₁₃	—	4	2	no	—
39	C₂×C₈×C₁₃	—	8	2	no	—
40	C₂×C₈×C₁₃	C₄⋊C₄	1	1	yes	characteristic
41	C₂×C₈×C₁₃	C₄⋊C₄	1	1	yes	characteristic
42	C₂×C₈×C₁₃	C₂×C₈	1	2	yes	—
43	C₂×C₈×C₁₃	M₁₆	1	2	yes	—
44	C₂×C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
45	C₂×C₈×C₁₃	C₂×Q₈	1	1	yes	characteristic
46	C₄²×C₁₃	C₄⋊C₄	1	1	yes	characteristic
47	C₄²×C₁₃	D₈	1	1	yes	characteristic
48	C₄²×C₁₃	Q₁₆	1	1	yes	characteristic
49	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
50	C₂×#1055	—	4	2	no	—
51	C₂×#1055	—	8	2	no	—
52	#6090	—	2	2	no	—
53	#6090	C₂×C₈	1	4	yes	complemented
54	C₂×C₄×C₁₆	—	13	1	no	—
55	C₂×#335	—	13	1	no	—
56	C₂×#335	D₁₃	1	1	yes	characteristic
57	#1372	—	13	4	no	—
58	C₂³×C₁₃	#107	1	1	yes	characteristic
59	C₂×C₄×C₁₃	—	2	2	no	—
60	C₂×C₄×C₁₃	C₄⋊C₈	1	2	yes	—
61	C₂×C₄×C₁₃	#107	1	1	yes	characteristic
62	C₂×C₄×C₁₃	#107	1	1	yes	characteristic
63	C₂×C₄×C₁₃	#107	1	1	yes	characteristic
64	C₂×C₄×C₁₃	#108	1	2	yes	—
65	C₂×C₄×C₁₃	SD₃₂	1	2	yes	—
66	C₂×C₄×C₁₃	SD₃₂	1	2	yes	—
67	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
68	C₂×C₄×C₁₃	C₂×D₈	1	1	yes	characteristic
69	C₂×C₄×C₁₃	C₂×Q₁₆	1	1	yes	characteristic
70	C₈×C₁₃	—	2	1	no	—
71	C₈×C₁₃	—	2	1	no	—
72	C₈×C₁₃	—	8	2	no	—
73	C₈×C₁₃	C₄⋊C₈	1	2	yes	—
74	C₈×C₁₃	C₂²×C₈	1	1	yes	characteristic
75	C₈×C₁₃	C₂×M₁₆	1	1	yes	characteristic
76	#1055	—	8	2	no	—
77	C₂²×C₁₆	—	13	1	no	—
78	C₂²×C₁₆	—	13	1	no	—
79	C₂×C₄⋊C₈	—	2	1	no	—
80	C₂×C₄⋊C₈	—	26	1	no	—
81	C₂×C₄×C₈	C₂×D₁₃	1	1	yes	characteristic
82	C₄×C₁₆	—	13	2	no	—
83	C₄×C₁₆	—	13	2	no	—
84	#335	—	2	1	no	—
85	#335	—	13	2	no	—
86	#335	—	26	1	no	—
87	#335	C₂×D₁₃	1	2	yes	—
88	C₂²×C₁₃	#335	1	2	yes	—
89	C₂²×C₁₃	#367	1	2	yes	—
90	C₂²×C₁₃	#368	1	2	yes	—
91	C₂²×C₁₃	C₂×#107	1	1	yes	characteristic
92	C₄×C₁₃	—	2	1	no	—
93	C₄×C₁₃	—	2	1	no	—
94	C₄×C₁₃	#335	1	2	yes	—
95	C₄×C₁₃	#367	1	2	yes	—
96	C₄×C₁₃	C₂×C₄⋊C₈	1	1	yes	characteristic
97	C₄×C₁₃	C₂×#108	1	1	yes	characteristic
98	C₄×C₁₃	C₂×SD₃₂	1	1	yes	characteristic
99	C₄×C₁₃	C₂×SD₃₂	1	1	yes	characteristic
100	C₂²×C₈	—	4	1	no	—
101	C₂²×C₈	—	52	1	no	—
102	C₂²×C₈	Dic₂₆	1	1	yes	characteristic
103	C₂²×C₈	C₄×D₁₃	1	1	yes	characteristic
104	C₂×C₄²	C₂²⋊D₁₃	1	1	yes	characteristic
105	C₂×C₁₆	—	13	4	no	—
106	C₂×C₁₆	—	13	2	no	—
107	C₂×C₁₆	—	13	2	no	—
108	C₂×C₁₆	—	26	2	no	—
109	C₄⋊C₈	—	2	2	no	—
110	C₄⋊C₈	—	4	1	no	—
111	C₄⋊C₈	—	26	2	no	—
112	C₄⋊C₈	—	52	1	no	—
113	C₄×C₈	Dic₂₆	1	1	yes	characteristic
114	C₄×C₈	C₄×D₁₃	1	1	yes	characteristic
115	C₄×C₈	C₂²⋊D₁₃	1	1	yes	characteristic
116	C₄×C₈	C₂²×D₁₃	1	1	yes	characteristic
117	C₂×C₁₃	#1372	1	4	yes	complemented
118	C₂×C₁₃	C₂×#335	1	1	yes	characteristic
119	C₂×C₁₃	C₂×#367	1	1	yes	characteristic
120	C₂×C₁₃	C₂×#368	1	1	yes	characteristic
121	C₂²×C₄	#6101	1	1	yes	characteristic
122	C₂²×C₄	#6104	1	1	yes	characteristic
123	C₂²×C₄	#6107	1	1	yes	characteristic
124	C₂×C₈	—	2	2	no	—
125	C₂×C₈	—	4	2	no	—
126	C₂×C₈	—	8	2	no	—
127	C₂×C₈	—	52	2	no	—
128	C₂×C₈	—	104	2	no	—
129	C₂×C₈	C₈×D₁₃	1	2	yes	—
130	C₂×C₈	#6094	1	2	yes	—
131	C₂×C₈	#6101	1	1	yes	characteristic
132	C₂×C₈	#6101	1	1	yes	characteristic
133	C₂×C₈	C₂×Dic₂₆	1	1	yes	characteristic
134	C₂×C₈	C₂×C₄×D₁₃	1	1	yes	characteristic
135	C₄²	#6101	1	1	yes	characteristic
136	C₄²	#6104	1	1	yes	characteristic
137	C₄²	#6107	1	1	yes	characteristic
138	C₄²	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
139	C₁₆	—	13	4	no	—
140	C₁₆	—	26	2	no	—
141	C₁₃	C₂×#1372	1	1	yes	characteristic, complemented, Sylow
142	C₂³	#88047	1	1	yes	characteristic
143	C₂×C₄	—	2	2	no	—
144	C₂×C₄	#88047	1	1	yes	characteristic
145	C₂×C₄	#88047	1	1	yes	characteristic
146	C₂×C₄	#88047	1	1	yes	characteristic
147	C₂×C₄	#88054	1	2	yes	—
148	C₂×C₄	#88062	1	2	yes	—
149	C₂×C₄	#88067	1	2	yes	—
150	C₂×C₄	#88068	1	2	yes	—
151	C₂×C₄	C₂×#6101	1	1	yes	characteristic
152	C₂×C₄	C₂×#6104	1	1	yes	characteristic
153	C₂×C₄	C₂×#6107	1	1	yes	characteristic
154	C₈	—	2	1	no	—
155	C₈	—	2	1	no	—
156	C₈	—	8	2	no	—
157	C₈	—	104	2	no	—
158	C₈	#88054	1	2	yes	—
159	C₈	C₂×C₈×D₁₃	1	1	yes	characteristic
160	C₈	C₂×#6094	1	1	yes	characteristic
161	C₂²	#11718071	1	2	yes	—
162	C₂²	#11718082	1	2	yes	—
163	C₂²	#11718085	1	2	yes	—
164	C₂²	C₂×#88047	1	1	yes	characteristic
165	C₄	—	2	1	no	—
166	C₄	—	2	1	no	—
167	C₄	#11718071	1	2	yes	—
168	C₄	#11718082	1	2	yes	—
169	C₄	C₂×#88054	1	1	yes	characteristic
170	C₄	C₂×#88062	1	1	yes	characteristic
171	C₄	C₂×#88067	1	1	yes	characteristic
172	C₄	C₂×#88068	1	1	yes	characteristic
173	C₂	#13112909	1	4	yes	direct product factor
174	C₂	C₂×#11718071	1	1	yes	characteristic
175	C₂	C₂×#11718082	1	1	yes	characteristic
176	C₂	C₂×#11718085	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄	#6104
commutator	C₈×C₁₃	C₂²×C₈
Frattini	C₄×C₈	C₂²×D₁₃
Fitting	C₂×C₁₃×#335	C₂
socle, prime radical	C₂³×C₁₃	#107
cosocle	C₄×C₈×C₁₃	C₂³
hypercenter	C₂×#335	D₁₃
hypocenter	C₁₃	C₂×#1372
LCS	G ▷ C₈×C₁₃ ▷ C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂²×C₄ ◁ C₂×C₄² ◁ C₂×C₄×C₈ ◁ C₂×#335

Complements

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

N	H ≅ G/N	type
3. #13112909	C₂	direct (N × H)
28. C₂×#6090	C₈	semidirect
53. #6090	C₂×C₈	semidirect
117. C₂×C₁₃	#1372	semidirect
141. C₁₃	C₂×#1372	semidirect
173. C₂	#13112909	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×C₄×#6090	2
C₂×#11718050	2
#13112909	2
C₂×C₁₃×#335	2
C₂×#1372	13

Subgroups — C2×#13112909 #15774499

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#13112909 #15774499