Subgroups — C₂²×#11718093 #16015893

Order 3328.

862 conjugacy classes of subgroups.

The subgroup lattice has 168 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×#6090	C₂	1	1	yes	maximal, characteristic
2	C₂²×C₈×Dic₁₃	C₂	1	1	yes	maximal, characteristic
3	C₂×#11718093	C₂	1	12	yes	maximal, direct product factor
4	C₂³×C₁₃×C₁₆	C₂	1	1	yes	maximal, characteristic
5	C₂³×C₈×C₁₃	C₂²	1	1	yes	characteristic
6	C₂²×C₄×Dic₁₃	C₄	1	1	yes	characteristic
7	C₂³×#1055	C₄	1	1	yes	characteristic
8	C₂²×C₁₃×C₁₆	—	2	4	no	—
9	C₂²×C₁₃×C₁₆	C₂²	1	6	yes	—
10	C₂×C₈×Dic₁₃	C₄	1	6	yes	—
11	C₂×C₈×Dic₁₃	C₂²	1	6	yes	—
12	C₂²×#6090	—	2	4	no	—
13	C₂²×#6090	C₂²	1	6	yes	—
14	#11718093	C₂²	1	16	yes	direct product factor
15	C₂³×C₄×C₁₃	C₂×C₄	1	1	yes	characteristic
16	C₂³×Dic₁₃	C₈	1	1	yes	characteristic
17	C₂³×Dic₁₃	C₈	1	1	yes	characteristic
18	C₂²×C₈×C₁₃	C₂×C₄	1	3	yes	—
19	C₂²×C₈×C₁₃	D₄	1	4	yes	—
20	C₂²×C₈×C₁₃	Q₈	1	4	yes	—
21	C₂²×C₈×C₁₃	C₂³	1	3	yes	—
22	C₂×C₄×Dic₁₃	C₈	1	6	yes	—
23	C₂×C₄×Dic₁₃	C₂×C₄	1	6	yes	—
24	C₂²×#1055	—	2	4	no	—
25	C₂²×#1055	C₂×C₄	1	6	yes	—
26	C₂×C₁₃×C₁₆	—	2	12	no	—
27	C₂×C₁₃×C₁₆	C₂³	1	4	yes	—
28	C₈×Dic₁₃	C₂×C₄	1	12	yes	—
29	C₈×Dic₁₃	C₂³	1	4	yes	—
30	C₂×#6090	—	2	12	no	—
31	C₂×#6090	C₂³	1	4	yes	—
32	C₂²×C₄⋊C₁₆	—	13	1	no	maximal, Sylow
33	C₂⁴×C₁₃	C₂×C₈	1	1	yes	characteristic
34	C₂²×C₄×C₁₃	C₄⋊C₄	1	4	yes	—
35	C₂²×C₄×C₁₃	C₂×C₈	1	3	yes	—
36	C₂²×C₄×C₁₃	M₁₆	1	4	yes	—
37	C₂²×C₄×C₁₃	C₂²×C₄	1	3	yes	—
38	C₂²×Dic₁₃	—	2	4	no	—
39	C₂²×Dic₁₃	C₁₆	1	8	yes	complemented
40	C₂²×Dic₁₃	C₂×C₈	1	6	yes	—
41	C₂²×Dic₁₃	C₂×C₈	1	6	yes	—
42	C₂×C₈×C₁₃	C₄⋊C₄	1	12	yes	—
43	C₂×C₈×C₁₃	C₂²×C₄	1	3	yes	—
44	C₂×C₈×C₁₃	C₂×D₄	1	6	yes	—
45	C₂×C₈×C₁₃	C₂×Q₈	1	6	yes	—
46	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
47	C₄×Dic₁₃	C₂×C₈	1	12	yes	—
48	C₄×Dic₁₃	C₂²×C₄	1	4	yes	—
49	C₂×#1055	—	2	12	no	—
50	C₂×#1055	C₂²×C₄	1	4	yes	—
51	C₁₃×C₁₆	—	2	4	no	—
52	#6090	—	2	4	no	—
53	C₂³×C₁₆	—	13	1	no	—
54	C₂³×C₁₆	D₁₃	1	1	yes	characteristic
55	C₂²×C₄×C₈	—	13	1	no	—
56	C₂×C₄⋊C₁₆	—	13	12	no	—
57	C₂³×C₁₃	C₄⋊C₈	1	4	yes	—
58	C₂³×C₁₃	C₂×C₁₆	1	4	yes	—
59	C₂³×C₁₃	M₃₂	1	4	yes	—
60	C₂³×C₁₃	C₂²×C₈	1	3	yes	—
61	C₂×C₄×C₁₃	C₄⋊C₈	1	12	yes	—
62	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	6	yes	—
63	C₂×C₄×C₁₃	C₂²×C₈	1	3	yes	—
64	C₂×C₄×C₁₃	C₂×M₁₆	1	6	yes	—
65	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
66	C₂×Dic₁₃	—	2	12	no	—
67	C₂×Dic₁₃	C₂×C₁₆	1	24	yes	complemented
68	C₂×Dic₁₃	C₂²×C₈	1	4	yes	—
69	C₂×Dic₁₃	C₂²×C₈	1	4	yes	—
70	C₈×C₁₃	C₂×C₄⋊C₄	1	6	yes	—
71	C₈×C₁₃	C₂²×D₄	1	1	yes	characteristic
72	C₈×C₁₃	C₂²×Q₈	1	1	yes	characteristic
73	#1055	—	2	4	no	—
74	C₂³×C₈	—	13	1	no	—
75	C₂³×C₈	C₂×D₁₃	1	1	yes	characteristic
76	C₂²×C₄²	—	13	1	no	—
77	C₂²×C₁₆	—	2	4	no	—
78	C₂²×C₁₆	—	13	6	no	—
79	C₂²×C₁₆	—	26	4	no	—
80	C₂²×C₁₆	C₂×D₁₃	1	6	yes	—
81	C₂×C₄×C₈	—	13	6	no	—
82	C₂×C₄×C₈	—	13	6	no	—
83	C₄⋊C₁₆	—	13	16	no	—
84	C₂²×C₁₃	C₄⋊C₁₆	1	16	yes	complemented
85	C₂²×C₁₃	C₂×C₄⋊C₈	1	6	yes	—
86	C₂²×C₁₃	C₂²×C₁₆	1	6	yes	—
87	C₂²×C₁₃	C₂×M₃₂	1	6	yes	—
88	C₂²×C₁₃	C₂³×C₈	1	1	yes	characteristic
89	C₄×C₁₃	C₂×C₄⋊C₈	1	6	yes	—
90	C₄×C₁₃	C₂²×C₄⋊C₄	1	1	yes	characteristic
91	C₄×C₁₃	C₂²×M₁₆	1	1	yes	characteristic
92	Dic₁₃	—	2	4	no	—
93	Dic₁₃	C₂²×C₁₆	1	8	yes	complemented
94	C₂³×C₄	—	13	1	no	—
95	C₂³×C₄	—	13	1	no	—
96	C₂³×C₄	C₄×D₁₃	1	1	yes	characteristic
97	C₂²×C₈	—	13	6	no	—
98	C₂²×C₈	—	26	4	no	—
99	C₂²×C₈	Dic₂₆	1	4	yes	—
100	C₂²×C₈	C₄×D₁₃	1	3	yes	—
101	C₂²×C₈	C₂²⋊D₁₃	1	4	yes	—
102	C₂²×C₈	C₂²×D₁₃	1	3	yes	—
103	C₂×C₄²	—	13	6	no	—
104	C₂×C₄²	—	13	6	no	—
105	C₂×C₁₆	—	2	12	no	—
106	C₂×C₁₆	—	13	4	no	—
107	C₂×C₁₆	—	26	12	no	—
108	C₂×C₁₆	C₂²×D₁₃	1	4	yes	—
109	C₄×C₈	—	13	12	no	—
110	C₄×C₈	—	13	4	no	—
111	C₂×C₁₃	C₂×C₄⋊C₁₆	1	12	yes	complemented
112	C₂×C₁₃	C₂²×C₄⋊C₈	1	1	yes	characteristic
113	C₂×C₁₃	C₂³×C₁₆	1	1	yes	characteristic
114	C₂×C₁₃	C₂²×M₃₂	1	1	yes	characteristic
115	C₂⁴	C₈×D₁₃	1	1	yes	characteristic
116	C₂²×C₄	—	13	6	no	—
117	C₂²×C₄	—	13	8	no	—
118	C₂²×C₄	—	13	6	no	—
119	C₂²×C₄	—	26	4	no	—
120	C₂²×C₄	C₈×D₁₃	1	3	yes	—
121	C₂²×C₄	#6094	1	4	yes	—
122	C₂²×C₄	#6101	1	4	yes	—
123	C₂²×C₄	C₂×C₄×D₁₃	1	3	yes	—
124	C₂×C₈	—	13	4	no	—
125	C₂×C₈	—	26	12	no	—
126	C₂×C₈	#6101	1	12	yes	—
127	C₂×C₈	C₂×Dic₂₆	1	6	yes	—
128	C₂×C₈	C₂×C₄×D₁₃	1	3	yes	—
129	C₂×C₈	C₂×C₂²⋊D₁₃	1	6	yes	—
130	C₂×C₈	C₂³×D₁₃	1	1	yes	characteristic
131	C₄²	—	13	12	no	—
132	C₄²	—	13	4	no	—
133	C₁₆	—	2	4	no	—
134	C₁₆	—	26	4	no	—
135	C₁₃	C₂²×C₄⋊C₁₆	1	1	yes	characteristic, complemented, Sylow
136	C₂³	C₁₆×D₁₃	1	4	yes	—
137	C₂³	#88038	1	4	yes	—
138	C₂³	#88054	1	4	yes	—
139	C₂³	C₂×C₈×D₁₃	1	3	yes	—
140	C₂×C₄	—	13	4	no	—
141	C₂×C₄	—	13	24	no	—
142	C₂×C₄	—	13	4	no	—
143	C₂×C₄	—	26	12	no	—
144	C₂×C₄	#88054	1	12	yes	—
145	C₂×C₄	C₂×C₈×D₁₃	1	3	yes	—
146	C₂×C₄	C₂×#6094	1	6	yes	—
147	C₂×C₄	C₂×#6101	1	6	yes	—
148	C₂×C₄	C₂²×C₄×D₁₃	1	1	yes	characteristic
149	C₈	—	26	4	no	—
150	C₈	C₂×#6101	1	6	yes	—
151	C₈	C₂²×Dic₂₆	1	1	yes	characteristic
152	C₈	C₂²×C₂²⋊D₁₃	1	1	yes	characteristic
153	C₂²	#11718093	1	16	yes	direct product factor
154	C₂²	C₂×C₁₆×D₁₃	1	6	yes	—
155	C₂²	C₂×#88038	1	6	yes	—
156	C₂²	C₂×#88054	1	6	yes	—
157	C₂²	C₂²×C₈×D₁₃	1	1	yes	characteristic
158	C₄	—	13	8	no	—
159	C₄	—	26	4	no	—
160	C₄	C₂×#88054	1	6	yes	—
161	C₄	C₂²×#6094	1	1	yes	characteristic
162	C₄	C₂²×#6101	1	1	yes	characteristic
163	C₂	C₂×#11718093	1	12	yes	direct product factor
164	C₂	C₂²×#88054	1	1	yes	characteristic
165	C₂	C₂²×C₁₆×D₁₃	1	1	yes	characteristic
166	C₂	C₂²×#88038	1	1	yes	characteristic

	subgroup	G/H
center	C₂³×C₈	C₂×D₁₃
commutator	C₂×C₁₃	C₂³×C₁₆
Frattini	C₂×C₈	C₂³×D₁₃
Fitting	C₂³×C₁₃×C₁₆	C₂
socle, prime radical	C₂⁴×C₁₃	C₂×C₈
cosocle	C₂×C₈×C₁₃	C₂⁴
hypercenter	C₂³×C₁₆	D₁₃
hypocenter	C₁₃	C₂²×C₄⋊C₁₆
LCS	G ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂³×C₈ ◁ C₂³×C₁₆

Complements

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

N	H ≅ G/N	type
3. C₂×#11718093	C₂	direct (N × H)
14. #11718093	C₂²	direct (N × H)
39. C₂²×Dic₁₃	C₁₆	semidirect
67. C₂×Dic₁₃	C₂×C₁₆	semidirect
84. C₂²×C₁₃	C₄⋊C₁₆	semidirect
93. Dic₁₃	C₂²×C₁₆	semidirect
111. C₂×C₁₃	C₂×C₄⋊C₁₆	semidirect
135. C₁₃	C₂²×C₄⋊C₁₆	semidirect
153. C₂²	#11718093	direct (N × H)
163. C₂	C₂×#11718093	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂³×#6090	2
C₂²×C₈×Dic₁₃	2
C₂×#11718093	2
C₂³×C₁₃×C₁₆	2
C₂²×C₄⋊C₁₆	13

Subgroups — C22×#11718093 #16015893

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²×#11718093 #16015893