Subgroups — C₂²×#11719047 #16807998

Order 3328.

4126 conjugacy classes of subgroups.

The subgroup lattice has 204 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×D₁₃⋊C₈	C₂	1	2	yes	maximal
2	C₂×#11719047	C₂	1	24	yes	maximal, direct product factor
3	C₂²×#88110	C₂	1	4	yes	maximal, complemented
4	C₂²×C₄²×D₁₃	C₂	1	1	yes	maximal, characteristic
5	C₂³×C₄×D₁₃	C₄	1	2	yes	—
6	C₂³×C₄×D₁₃	C₂²	1	1	yes	characteristic
7	C₂³×#1057	C₂²	1	4	yes	—
8	C₂²×D₁₃⋊C₈	C₄	1	32	yes	complemented
9	C₂²×D₁₃⋊C₈	C₂²	1	24	yes	—
10	C₂²×C₄²×C₁₃	C₄	1	1	yes	characteristic
11	C₂²×C₄×Dic₁₃	C₄	1	1	yes	characteristic
12	C₂²×C₄×Dic₁₃	C₂²	1	2	yes	—
13	C₂×C₄²×D₁₃	C₄	1	12	yes	—
14	C₂×C₄²×D₁₃	C₂²	1	12	yes	—
15	C₂×#88110	C₂²	1	48	yes	complemented
16	#11719047	C₂²	1	64	yes	direct product factor
17	C₂⁴×D₁₃	C₂×C₄	1	1	yes	characteristic
18	C₂³×C₄×C₁₃	C₂×C₄	1	2	yes	—
19	C₂³×C₄×C₁₃	C₂×C₄	1	1	yes	characteristic
20	C₂³×Dic₁₃	C₂×C₄	1	2	yes	—
21	C₂³×Dic₁₃	C₂³	1	1	yes	characteristic
22	C₂²×C₄×D₁₃	—	2	16	no	—
23	C₂²×C₄×D₁₃	C₂×C₄	1	24	yes	—
24	C₂²×C₄×D₁₃	C₂×C₄	1	6	yes	—
25	C₂²×C₄×D₁₃	C₂×C₄	1	16	yes	—
26	C₂²×C₄×D₁₃	C₂³	1	6	yes	—
27	C₂²×#1057	C₂×C₄	1	32	yes	complemented
28	C₂²×#1057	C₂³	1	24	yes	—
29	C₂×D₁₃⋊C₈	C₂×C₄	1	192	yes	complemented
30	C₂×D₁₃⋊C₈	C₂³	1	32	yes	—
31	C₂×C₄²×C₁₃	C₂×C₄	1	12	yes	—
32	C₂×C₄×Dic₁₃	C₂×C₄	1	12	yes	—
33	C₂×C₄×Dic₁₃	C₂×C₄	1	12	yes	—
34	C₂×C₄×Dic₁₃	C₂³	1	12	yes	—
35	C₄²×D₁₃	C₂×C₄	1	48	yes	—
36	C₄²×D₁₃	C₂³	1	16	yes	—
37	#88110	C₂³	1	64	yes	complemented
38	C₂³×#97	—	13	1	no	maximal, Sylow
39	C₂⁴×C₁₃	C₂²×C₄	1	1	yes	characteristic
40	C₂³×D₁₃	C₄²	1	8	yes	—
41	C₂³×D₁₃	M₁₆	1	16	yes	—
42	C₂³×D₁₃	C₂²×C₄	1	6	yes	—
43	C₂²×C₄×C₁₃	—	2	8	no	—
44	C₂²×C₄×C₁₃	C₄²	1	8	yes	—
45	C₂²×C₄×C₁₃	C₂²×C₄	1	12	yes	—
46	C₂²×C₄×C₁₃	C₂²×C₄	1	6	yes	—
47	C₂²×Dic₁₃	—	2	8	no	—
48	C₂²×Dic₁₃	C₂²×C₄	1	12	yes	—
49	C₂²×Dic₁₃	C₂²×C₄	1	3	yes	—
50	C₂²×Dic₁₃	C₂²×C₄	1	8	yes	—
51	C₂²×Dic₁₃	C₂⁴	1	3	yes	—
52	C₂×C₄×D₁₃	—	2	96	no	—
53	C₂×C₄×D₁₃	C₄²	1	48	yes	—
54	C₂×C₄×D₁₃	C₂²×C₄	1	32	yes	—
55	C₂×C₄×D₁₃	C₂²×C₄	1	12	yes	—
56	C₂×C₄×D₁₃	C₂²×C₄	1	48	yes	—
57	C₂×C₄×D₁₃	C₂⁴	1	4	yes	—
58	C₂×#1057	C₂²×C₄	1	96	yes	complemented
59	C₂×#1057	C₂⁴	1	16	yes	—
60	D₁₃⋊C₈	C₂²×C₄	1	128	yes	complemented
61	C₄²×C₁₃	C₂²×C₄	1	16	yes	—
62	C₄×Dic₁₃	C₂²×C₄	1	24	yes	—
63	C₄×Dic₁₃	C₂²×C₄	1	16	yes	—
64	C₄×Dic₁₃	C₂⁴	1	8	yes	—
65	C₂⁴×C₈	—	13	2	no	—
66	C₂³×C₄²	—	13	1	no	—
67	C₂²×#97	—	13	4	no	—
68	C₂²×#97	—	13	24	no	—
69	C₂³×C₁₃	C₂×C₄²	1	4	yes	—
70	C₂³×C₁₃	C₂×M₁₆	1	8	yes	—
71	C₂³×C₁₃	C₂³×C₄	1	3	yes	—
72	C₂²×D₁₃	#97	1	64	yes	complemented
73	C₂²×D₁₃	C₂×C₄²	1	24	yes	—
74	C₂²×D₁₃	C₂×M₁₆	1	48	yes	—
75	C₂²×D₁₃	C₂³×C₄	1	4	yes	—
76	C₂×C₄×C₁₃	—	2	24	no	—
77	C₂×C₄×C₁₃	C₂×C₄²	1	24	yes	—
78	C₂×C₄×C₁₃	C₂³×C₄	1	8	yes	—
79	C₂×C₄×C₁₃	C₂³×C₄	1	4	yes	—
80	C₂×Dic₁₃	—	2	24	no	—
81	C₂×Dic₁₃	C₂×C₄²	1	12	yes	—
82	C₂×Dic₁₃	C₂³×C₄	1	8	yes	—
83	C₂×Dic₁₃	C₂³×C₄	1	12	yes	—
84	C₂×Dic₁₃	C₂³×C₄	1	3	yes	—
85	C₂×Dic₁₃	C₂⁵	1	1	yes	characteristic
86	C₄×D₁₃	—	2	64	no	—
87	C₄×D₁₃	C₂×C₄²	1	48	yes	—
88	C₄×D₁₃	C₂³×C₄	1	16	yes	—
89	#1057	C₂³×C₄	1	32	yes	complemented
90	C₂⁴×C₄	—	13	1	no	—
91	C₂⁴×C₄	—	13	2	no	—
92	C₂³×C₈	—	13	24	no	—
93	C₂³×C₈	—	13	4	no	—
94	C₂³×C₈	—	13	32	no	—
95	C₂²×C₄²	—	13	2	no	—
96	C₂²×C₄²	—	13	1	no	—
97	C₂²×C₄²	—	13	12	no	—
98	C₂²×C₄²	—	13	12	no	—
99	C₂²×C₄²	#261	1	1	yes	characteristic
100	C₂×#97	—	13	64	no	—
101	C₂×#97	—	13	48	no	—
102	C₂²×C₁₃	C₂×#97	1	16	yes	complemented
103	C₂²×C₁₃	C₂²×C₄²	1	6	yes	—
104	C₂²×C₁₃	C₂²×M₁₆	1	12	yes	—
105	C₂²×C₁₃	C₂⁴×C₄	1	1	yes	characteristic
106	C₂×D₁₃	C₂×#97	1	96	yes	complemented
107	C₂×D₁₃	C₂²×C₄²	1	8	yes	—
108	C₂×D₁₃	C₂²×M₁₆	1	16	yes	—
109	C₄×C₁₃	—	2	8	no	—
110	C₄×C₁₃	C₂²×C₄²	1	8	yes	—
111	Dic₁₃	—	2	8	no	—
112	Dic₁₃	C₂²×C₄²	1	6	yes	—
113	Dic₁₃	C₂⁴×C₄	1	2	yes	—
114	C₂⁵	—	13	1	no	—
115	C₂³×C₄	—	13	1	no	—
116	C₂³×C₄	—	13	16	no	—
117	C₂³×C₄	—	13	6	no	—
118	C₂³×C₄	—	13	6	no	—
119	C₂³×C₄	—	13	2	no	—
120	C₂³×C₄	—	13	24	no	—
121	C₂³×C₄	—	26	16	no	—
122	C₂³×C₄	C₂×#261	1	2	yes	—
123	C₂³×C₄	C₂×#261	1	1	yes	characteristic
124	C₂²×C₈	—	13	32	no	—
125	C₂²×C₈	—	13	24	no	—
126	C₂²×C₈	—	13	192	no	—
127	C₂²×C₈	—	13	32	no	—
128	C₂×C₄²	—	13	12	no	—
129	C₂×C₄²	—	13	12	no	—
130	C₂×C₄²	—	13	12	no	—
131	C₂×C₄²	—	13	48	no	—
132	C₂×C₄²	—	13	16	no	—
133	C₂×C₄²	C₂×#261	1	12	yes	—
134	#97	—	13	64	no	—
135	C₂×C₁₃	C₂²×#97	1	12	yes	complemented
136	C₂×C₁₃	C₂³×C₄²	1	1	yes	characteristic
137	C₂×C₁₃	C₂³×M₁₆	1	2	yes	—
138	D₁₃	C₂²×#97	1	16	yes	complemented
139	C₂⁴	—	13	16	no	—
140	C₂⁴	—	13	8	no	—
141	C₂⁴	—	13	6	no	—
142	C₂⁴	C₂²×#261	1	1	yes	characteristic
143	C₂²×C₄	—	2	8	no	—
144	C₂²×C₄	—	13	8	no	—
145	C₂²×C₄	—	13	3	no	—
146	C₂²×C₄	—	13	3	no	—
147	C₂²×C₄	—	13	48	no	—
148	C₂²×C₄	—	13	48	no	—
149	C₂²×C₄	—	13	4	no	—
150	C₂²×C₄	—	13	12	no	—
151	C₂²×C₄	—	13	12	no	—
152	C₂²×C₄	—	13	32	no	—
153	C₂²×C₄	—	26	96	no	—
154	C₂²×C₄	—	26	8	no	—
155	C₂²×C₄	C₄×#261	1	8	yes	—
156	C₂²×C₄	C₂²×#261	1	12	yes	—
157	C₂²×C₄	C₂²×#261	1	6	yes	—
158	C₂×C₈	—	13	16	no	—
159	C₂×C₈	—	13	128	no	—
160	C₂×C₈	—	13	96	no	—
161	C₄²	—	13	8	no	—
162	C₄²	—	13	24	no	—
163	C₄²	—	13	16	no	—
164	C₄²	C₂²×#261	1	16	yes	—
165	C₁₃	C₂³×#97	1	1	yes	characteristic, complemented, Sylow
166	C₂³	—	13	64	no	—
167	C₂³	—	13	48	no	—
168	C₂³	—	13	24	no	—
169	C₂³	—	13	4	no	—
170	C₂³	D₁₃⋊M₁₆	1	8	yes	—
171	C₂³	C₂×C₄×#261	1	4	yes	—
172	C₂³	C₂³×#261	1	3	yes	—
173	C₂×C₄	—	2	24	no	—
174	C₂×C₄	—	13	12	no	—
175	C₂×C₄	—	13	12	no	—
176	C₂×C₄	—	13	1	no	—
177	C₂×C₄	—	13	3	no	—
178	C₂×C₄	—	13	16	no	—
179	C₂×C₄	—	13	48	no	—
180	C₂×C₄	—	13	8	no	—
181	C₂×C₄	—	26	64	no	—
182	C₂×C₄	—	26	24	no	—
183	C₂×C₄	C₂×C₄×#261	1	24	yes	—
184	C₂×C₄	C₂³×#261	1	8	yes	—
185	C₂×C₄	C₂³×#261	1	4	yes	—
186	C₈	—	13	32	no	—
187	C₂²	—	13	8	no	—
188	C₂²	—	13	16	no	—
189	C₂²	—	13	96	no	—
190	C₂²	#11719047	1	16	yes	direct product factor
191	C₂²	C₂×D₁₃⋊M₁₆	1	12	yes	—
192	C₂²	C₂²×C₄×#261	1	6	yes	—
193	C₂²	C₂⁴×#261	1	1	yes	characteristic
194	C₄	—	2	8	no	—
195	C₄	—	13	2	no	—
196	C₄	—	13	6	no	—
197	C₄	—	26	8	no	—
198	C₄	C₂²×C₄×#261	1	8	yes	—
199	C₂	—	13	16	no	—
200	C₂	C₂×#11719047	1	12	yes	direct product factor
201	C₂	C₂³×C₄×#261	1	1	yes	characteristic
202	C₂	C₂²×D₁₃⋊M₁₆	1	2	yes	—

	subgroup	G/H
center	C₂³×C₄	C₂×#261
commutator	C₂×C₁₃	C₂³×C₄²
Frattini	C₂²	C₂⁴×#261
Fitting	C₂²×C₄²×C₁₃	C₄
socle	C₂⁴×C₁₃	C₂²×C₄
prime radical	C₂⁴×D₁₃	C₂×C₄
cosocle	C₂×Dic₁₃	C₂⁵
hypercenter	C₂²×C₄²	#261
hypocenter	C₁₃	C₂³×#97
LCS	G ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂³×C₄ ◁ C₂²×C₄²

Complements

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

N	H ≅ G/N	type
2. C₂×#11719047	C₂	direct (N × H)
3. C₂²×#88110	C₂	semidirect
8. C₂²×D₁₃⋊C₈	C₄	semidirect
15. C₂×#88110	C₂²	semidirect
16. #11719047	C₂²	direct (N × H)
27. C₂²×#1057	C₂×C₄	semidirect
29. C₂×D₁₃⋊C₈	C₂×C₄	semidirect
37. #88110	C₂³	semidirect
58. C₂×#1057	C₂²×C₄	semidirect
60. D₁₃⋊C₈	C₂²×C₄	semidirect
72. C₂²×D₁₃	#97	semidirect
89. #1057	C₂³×C₄	semidirect
102. C₂²×C₁₃	C₂×#97	semidirect
106. C₂×D₁₃	C₂×#97	semidirect
135. C₂×C₁₃	C₂²×#97	semidirect
138. D₁₃	C₂²×#97	semidirect
165. C₁₃	C₂³×#97	semidirect
190. C₂²	#11719047	direct (N × H)
200. C₂	C₂×#11719047	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×D₁₃⋊C₈	2
C₂×#11719047	2
C₂²×#88110	2
C₂²×C₄²×D₁₃	2
C₂³×#97	13

Subgroups — C22×#11719047 #16807998

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²×#11719047 #16807998