Subgroups — C₂²×#11718099 #16015583

Order 3328.

1470 conjugacy classes of subgroups.

The subgroup lattice has 218 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×C₈×D₁₃	C₂	1	1	yes	maximal, characteristic
2	C₂³×#6090	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#11718099	C₂	1	12	yes	maximal, direct product factor
4	C₂³×C₁₃×C₁₆	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂³×C₄×D₁₃	C₄	1	1	yes	characteristic
6	C₂³×C₈×C₁₃	C₂²	1	1	yes	characteristic
7	C₂³×#1055	C₄	1	1	yes	characteristic
8	C₂²×C₈×D₁₃	—	2	4	no	—
9	C₂²×C₈×D₁₃	—	2	4	no	—
10	C₂²×C₈×D₁₃	C₄	1	6	yes	—
11	C₂²×C₈×D₁₃	C₂²	1	6	yes	—
12	C₂²×C₁₃×C₁₆	—	2	4	no	—
13	C₂²×C₁₃×C₁₆	C₂²	1	6	yes	complemented
14	C₂²×#6090	—	2	4	no	—
15	C₂²×#6090	C₂²	1	6	yes	complemented
16	#11718099	C₂²	1	16	yes	direct product factor
17	C₂⁴×D₁₃	C₈	1	1	yes	characteristic
18	C₂³×C₄×C₁₃	C₂×C₄	1	1	yes	characteristic
19	C₂³×Dic₁₃	C₈	1	1	yes	characteristic
20	C₂²×C₄×D₁₃	—	2	4	no	—
21	C₂²×C₄×D₁₃	—	2	4	no	—
22	C₂²×C₄×D₁₃	C₈	1	6	yes	—
23	C₂²×C₄×D₁₃	C₂×C₄	1	6	yes	—
24	C₂²×C₈×C₁₃	C₂×C₄	1	3	yes	—
25	C₂²×C₈×C₁₃	D₄	1	4	yes	—
26	C₂²×C₈×C₁₃	D₄	1	4	yes	—
27	C₂²×C₈×C₁₃	C₂³	1	3	yes	—
28	C₂²×#1055	—	2	4	no	—
29	C₂²×#1055	C₂×C₄	1	6	yes	—
30	C₂×C₈×D₁₃	—	2	24	no	—
31	C₂×C₈×D₁₃	—	2	12	no	—
32	C₂×C₈×D₁₃	—	2	12	no	—
33	C₂×C₈×D₁₃	C₂×C₄	1	12	yes	—
34	C₂×C₈×D₁₃	C₂³	1	4	yes	—
35	C₂×C₁₃×C₁₆	—	2	12	no	—
36	C₂×C₁₃×C₁₆	C₂³	1	4	yes	complemented
37	C₂×#6090	—	2	12	no	—
38	C₂×#6090	C₂³	1	4	yes	complemented
39	C₂²×C₂²⋊C₁₆	—	13	1	no	maximal, Sylow
40	C₂⁴×C₁₃	C₂×C₈	1	1	yes	characteristic
41	C₂³×D₁₃	—	2	4	no	—
42	C₂³×D₁₃	—	2	4	no	—
43	C₂³×D₁₃	C₁₆	1	8	yes	complemented
44	C₂³×D₁₃	C₂×C₈	1	6	yes	—
45	C₂²×C₄×C₁₃	C₂²⋊C₄	1	4	yes	—
46	C₂²×C₄×C₁₃	C₂×C₈	1	3	yes	—
47	C₂²×C₄×C₁₃	M₁₆	1	4	yes	—
48	C₂²×C₄×C₁₃	C₂²×C₄	1	3	yes	—
49	C₂²×Dic₁₃	—	2	4	no	—
50	C₂²×Dic₁₃	C₂×C₈	1	6	yes	—
51	C₂×C₄×D₁₃	—	2	24	no	—
52	C₂×C₄×D₁₃	—	2	12	no	—
53	C₂×C₄×D₁₃	—	2	12	no	—
54	C₂×C₄×D₁₃	C₂×C₈	1	12	yes	—
55	C₂×C₄×D₁₃	C₂²×C₄	1	4	yes	—
56	C₂×C₈×C₁₃	C₂²⋊C₄	1	12	yes	—
57	C₂×C₈×C₁₃	C₂²×C₄	1	3	yes	—
58	C₂×C₈×C₁₃	C₂×D₄	1	6	yes	—
59	C₂×C₈×C₁₃	C₂×D₄	1	6	yes	—
60	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
61	C₂×#1055	—	2	12	no	—
62	C₂×#1055	C₂²×C₄	1	4	yes	—
63	C₈×D₁₃	—	2	24	no	—
64	C₈×D₁₃	—	2	4	no	—
65	C₈×D₁₃	—	2	4	no	—
66	C₁₃×C₁₆	—	2	4	no	—
67	#6090	—	2	4	no	—
68	C₂⁴×C₈	—	13	1	no	—
69	C₂³×C₁₆	—	13	1	no	—
70	C₂³×C₁₆	D₁₃	1	1	yes	characteristic, complemented
71	C₂×C₂²⋊C₁₆	—	13	12	no	—
72	C₂³×C₁₃	C₂²⋊C₈	1	4	yes	—
73	C₂³×C₁₃	C₂×C₁₆	1	4	yes	—
74	C₂³×C₁₃	M₃₂	1	4	yes	—
75	C₂³×C₁₃	C₂²×C₈	1	3	yes	—
76	C₂²×D₁₃	—	2	32	no	—
77	C₂²×D₁₃	—	2	12	no	—
78	C₂²×D₁₃	—	2	12	no	—
79	C₂²×D₁₃	C₂×C₁₆	1	24	yes	complemented
80	C₂²×D₁₃	C₂²×C₈	1	4	yes	—
81	C₂×C₄×C₁₃	C₂²⋊C₈	1	12	yes	—
82	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	6	yes	—
83	C₂×C₄×C₁₃	C₂²×C₈	1	3	yes	—
84	C₂×C₄×C₁₃	C₂×M₁₆	1	6	yes	—
85	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
86	C₂×Dic₁₃	—	2	12	no	—
87	C₂×Dic₁₃	C₂²×C₈	1	4	yes	—
88	C₄×D₁₃	—	2	4	no	—
89	C₄×D₁₃	—	2	4	no	—
90	C₄×D₁₃	—	2	24	no	—
91	C₈×C₁₃	C₂×C₂²⋊C₄	1	6	yes	—
92	C₈×C₁₃	C₂²×D₄	1	1	yes	characteristic
93	C₈×C₁₃	C₂²×D₄	1	1	yes	characteristic
94	#1055	—	2	4	no	—
95	C₂⁴×C₄	—	13	1	no	—
96	C₂³×C₈	—	13	1	no	—
97	C₂³×C₈	—	13	6	no	—
98	C₂³×C₈	—	13	6	no	—
99	C₂³×C₈	—	26	4	no	—
100	C₂³×C₈	—	26	4	no	—
101	C₂³×C₈	C₂×D₁₃	1	1	yes	characteristic
102	C₂²×C₁₆	—	2	4	no	—
103	C₂²×C₁₆	—	13	6	no	—
104	C₂²×C₁₆	—	26	4	no	—
105	C₂²×C₁₆	C₂×D₁₃	1	6	yes	complemented
106	C₂²⋊C₁₆	—	13	16	no	—
107	C₂²×C₁₃	C₂²⋊C₁₆	1	16	yes	complemented
108	C₂²×C₁₃	C₂×C₂²⋊C₈	1	6	yes	—
109	C₂²×C₁₃	C₂²×C₁₆	1	6	yes	—
110	C₂²×C₁₃	C₂×M₃₂	1	6	yes	—
111	C₂²×C₁₃	C₂³×C₈	1	1	yes	characteristic
112	C₂×D₁₃	—	2	4	no	—
113	C₂×D₁₃	—	2	48	no	—
114	C₂×D₁₃	—	2	4	no	—
115	C₂×D₁₃	C₂²×C₁₆	1	8	yes	complemented
116	C₄×C₁₃	C₂×C₂²⋊C₈	1	6	yes	—
117	C₄×C₁₃	C₂²×C₂²⋊C₄	1	1	yes	characteristic
118	C₄×C₁₃	C₂²×M₁₆	1	1	yes	characteristic
119	Dic₁₃	—	2	4	no	—
120	C₂⁵	—	13	1	no	—
121	C₂³×C₄	—	13	1	no	—
122	C₂³×C₄	—	13	6	no	—
123	C₂³×C₄	—	13	6	no	—
124	C₂³×C₄	—	26	4	no	—
125	C₂³×C₄	—	26	4	no	—
126	C₂³×C₄	C₄×D₁₃	1	1	yes	characteristic
127	C₂²×C₈	—	13	6	no	—
128	C₂²×C₈	—	13	12	no	—
129	C₂²×C₈	—	13	4	no	—
130	C₂²×C₈	—	26	4	no	—
131	C₂²×C₈	—	26	24	no	—
132	C₂²×C₈	—	26	12	no	—
133	C₂²×C₈	—	26	12	no	—
134	C₂²×C₈	C₄×D₁₃	1	3	yes	—
135	C₂²×C₈	D₅₂	1	4	yes	—
136	C₂²×C₈	C₂²⋊D₁₃	1	4	yes	—
137	C₂²×C₈	C₂²×D₁₃	1	3	yes	—
138	C₂×C₁₆	—	2	12	no	—
139	C₂×C₁₆	—	13	4	no	—
140	C₂×C₁₆	—	26	12	no	—
141	C₂×C₁₆	C₂²×D₁₃	1	4	yes	complemented
142	C₂×C₁₃	C₂×C₂²⋊C₁₆	1	12	yes	complemented
143	C₂×C₁₃	C₂²×C₂²⋊C₈	1	1	yes	characteristic
144	C₂×C₁₃	C₂³×C₁₆	1	1	yes	characteristic
145	C₂×C₁₃	C₂²×M₃₂	1	1	yes	characteristic
146	D₁₃	—	2	8	no	—
147	C₂⁴	—	13	6	no	—
148	C₂⁴	—	13	8	no	—
149	C₂⁴	—	26	4	no	—
150	C₂⁴	—	26	4	no	—
151	C₂⁴	C₈×D₁₃	1	1	yes	characteristic
152	C₂²×C₄	—	13	6	no	—
153	C₂²×C₄	—	13	12	no	—
154	C₂²×C₄	—	13	4	no	—
155	C₂²×C₄	—	26	4	no	—
156	C₂²×C₄	—	26	12	no	—
157	C₂²×C₄	—	26	12	no	—
158	C₂²×C₄	—	26	24	no	—
159	C₂²×C₄	C₈×D₁₃	1	3	yes	—
160	C₂²×C₄	#6094	1	4	yes	—
161	C₂²×C₄	#6103	1	4	yes	—
162	C₂²×C₄	C₂×C₄×D₁₃	1	3	yes	—
163	C₂×C₈	—	13	4	no	—
164	C₂×C₈	—	26	12	no	—
165	C₂×C₈	—	26	24	no	—
166	C₂×C₈	—	26	4	no	—
167	C₂×C₈	—	26	4	no	—
168	C₂×C₈	#6103	1	12	yes	—
169	C₂×C₈	C₂×C₄×D₁₃	1	3	yes	—
170	C₂×C₈	C₂×D₅₂	1	6	yes	—
171	C₂×C₈	C₂×C₂²⋊D₁₃	1	6	yes	—
172	C₂×C₈	C₂³×D₁₃	1	1	yes	characteristic
173	C₁₆	—	2	4	no	—
174	C₁₆	—	26	4	no	—
175	C₁₃	C₂²×C₂²⋊C₁₆	1	1	yes	characteristic, complemented, Sylow
176	C₂³	—	13	4	no	—
177	C₂³	—	13	24	no	—
178	C₂³	—	26	12	no	—
179	C₂³	—	26	12	no	—
180	C₂³	—	26	32	no	—
181	C₂³	C₁₆×D₁₃	1	4	yes	—
182	C₂³	#88038	1	4	yes	—
183	C₂³	#88060	1	4	yes	—
184	C₂³	C₂×C₈×D₁₃	1	3	yes	—
185	C₂×C₄	—	13	4	no	—
186	C₂×C₄	—	26	12	no	—
187	C₂×C₄	—	26	4	no	—
188	C₂×C₄	—	26	4	no	—
189	C₂×C₄	—	26	24	no	—
190	C₂×C₄	#88060	1	12	yes	—
191	C₂×C₄	C₂×C₈×D₁₃	1	3	yes	—
192	C₂×C₄	C₂×#6094	1	6	yes	—
193	C₂×C₄	C₂×#6103	1	6	yes	—
194	C₂×C₄	C₂²×C₄×D₁₃	1	1	yes	characteristic
195	C₈	—	26	4	no	—
196	C₈	C₂×#6103	1	6	yes	—
197	C₈	C₂²×D₅₂	1	1	yes	characteristic
198	C₈	C₂²×C₂²⋊D₁₃	1	1	yes	characteristic
199	C₂²	—	13	8	no	—
200	C₂²	—	26	48	no	—
201	C₂²	—	26	4	no	—
202	C₂²	—	26	4	no	—
203	C₂²	#11718099	1	16	yes	direct product factor
204	C₂²	C₂×C₁₆×D₁₃	1	6	yes	—
205	C₂²	C₂×#88038	1	6	yes	—
206	C₂²	C₂×#88060	1	6	yes	—
207	C₂²	C₂²×C₈×D₁₃	1	1	yes	characteristic
208	C₄	—	26	4	no	—
209	C₄	C₂×#88060	1	6	yes	—
210	C₄	C₂²×#6094	1	1	yes	characteristic
211	C₄	C₂²×#6103	1	1	yes	characteristic
212	C₂	—	26	8	no	—
213	C₂	C₂×#11718099	1	12	yes	direct product factor
214	C₂	C₂²×#88060	1	1	yes	characteristic
215	C₂	C₂²×C₁₆×D₁₃	1	1	yes	characteristic
216	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	C₂⁴×C₁₃	C₂×C₈
prime radical	C₂⁴×D₁₃	C₈
cosocle	C₂×C₈×C₁₃	C₂⁴
hypercenter	C₂³×C₁₆	D₁₃
hypocenter	C₁₃	C₂²×C₂²⋊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
2. C₂³×#6090	C₂	semidirect
3. C₂×#11718099	C₂	direct (N × H)
4. C₂³×C₁₃×C₁₆	C₂	semidirect
13. C₂²×C₁₃×C₁₆	C₂²	semidirect
15. C₂²×#6090	C₂²	semidirect
16. #11718099	C₂²	direct (N × H)
36. C₂×C₁₃×C₁₆	C₂³	semidirect
38. C₂×#6090	C₂³	semidirect
43. C₂³×D₁₃	C₁₆	semidirect
70. C₂³×C₁₆	D₁₃	semidirect
79. C₂²×D₁₃	C₂×C₁₆	semidirect
105. C₂²×C₁₆	C₂×D₁₃	semidirect
107. C₂²×C₁₃	C₂²⋊C₁₆	semidirect
115. C₂×D₁₃	C₂²×C₁₆	semidirect
141. C₂×C₁₆	C₂²×D₁₃	semidirect
142. C₂×C₁₃	C₂×C₂²⋊C₁₆	semidirect
175. C₁₃	C₂²×C₂²⋊C₁₆	semidirect
203. C₂²	#11718099	direct (N × H)
213. C₂	C₂×#11718099	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×C₈×D₁₃	2
C₂³×#6090	2
C₂×#11718099	2
C₂³×C₁₃×C₁₆	2
C₂²×C₂²⋊C₁₆	13

Subgroups — C22×#11718099 #16015583

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²×#11718099 #16015583