Subgroups — C₂×#13129330 #16770755

Order 3328.

6338 conjugacy classes of subgroups.

The subgroup lattice has 224 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13129330	C₂	1	32	yes	maximal, direct product factor
2	C₂×C₁₃⋊#564	C₂	1	3	yes	maximal, complemented
3	C₂×#11719390	C₂	1	12	yes	maximal, complemented
4	C₂×#11719401	C₂	1	12	yes	maximal
5	C₂×#11719393	C₂	1	3	yes	maximal
6	C₂×C₁₃×#564	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₃×#564	C₂²	1	16	yes	complemented
8	C₂×C₁₃×#125	C₂²	1	12	yes	—
9	C₂×C₁₃×#125	C₂²	1	3	yes	—
10	#11719401	C₂²	1	192	yes	—
11	#11719393	C₂²	1	48	yes	—
12	C₁₃⋊#564	C₂²	1	48	yes	complemented
13	#11719390	C₂²	1	192	yes	complemented
14	C₂×#88152	C₂²	1	12	yes	—
15	C₂×#88150	C₂²	1	12	yes	—
16	C₂×#88146	C₂²	1	6	yes	—
17	C₂×#88144	C₂²	1	12	yes	—
18	C₂×#88143	C₂²	1	12	yes	—
19	C₂×#88143	C₂²	1	12	yes	—
20	C₂×#88143	C₂²	1	12	yes	—
21	C₂×#88142	C₂²	1	12	yes	—
22	C₂×#88142	C₂²	1	6	yes	—
23	C₂×#88141	C₂²	1	12	yes	—
24	C₂×#88141	C₂²	1	12	yes	—
25	C₂×#88130	C₂²	1	4	yes	—
26	C₂×C₄²×D₁₃	C₂²	1	1	yes	characteristic
27	C₂×#88124	C₂²	1	3	yes	—
28	C₂×C₄×Dic₂₆	C₂²	1	12	yes	—
29	C₂²×C₄×D₁₃	C₂³	1	3	yes	—
30	C₂²×Dic₂₆	C₂³	1	12	yes	—
31	C₁₃×#125	C₂³	1	96	yes	—
32	C₁₃×#125	C₂³	1	24	yes	—
33	C₂×C₁₃×C₄⋊C₄	C₂³	1	12	yes	—
34	C₂×C₁₃×C₄⋊C₄	C₂³	1	12	yes	—
35	C₂×C₁₃×C₄⋊C₄	C₂³	1	6	yes	—
36	C₂×C₄²×C₁₃	C₂³	1	4	yes	—
37	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
38	C₂×#6103	C₂³	1	12	yes	—
39	C₂×C₄⋊Dic₁₃	C₂³	1	12	yes	—
40	C₂×C₄⋊Dic₁₃	C₂³	1	6	yes	—
41	C₂×#6101	C₂³	1	12	yes	—
42	C₂×#6101	C₂³	1	12	yes	—
43	C₂×#6101	C₂³	1	12	yes	—
44	C₂×#6101	C₂³	1	12	yes	—
45	C₂×C₄×Dic₁₃	C₂³	1	12	yes	—
46	C₂×C₄×Dic₁₃	C₂³	1	12	yes	—
47	C₂×C₄×Dic₁₃	C₂³	1	3	yes	—
48	#88152	C₂³	1	96	yes	—
49	#88150	C₂³	1	96	yes	—
50	#88146	C₂³	1	48	yes	—
51	#88144	C₂³	1	96	yes	—
52	#88143	C₂³	1	96	yes	—
53	#88143	C₂³	1	96	yes	—
54	#88143	C₂³	1	96	yes	—
55	#88142	C₂³	1	48	yes	—
56	#88142	C₂³	1	96	yes	—
57	#88141	C₂³	1	96	yes	—
58	#88141	C₂³	1	96	yes	—
59	#88130	C₂³	1	32	yes	—
60	C₄²×D₁₃	C₂³	1	8	yes	—
61	#88124	C₂³	1	24	yes	—
62	C₄×Dic₂₆	C₂³	1	96	yes	—
63	C₂×#3556	—	13	1	no	maximal, Sylow
64	C₂³×D₁₃	C₂⁴	1	1	yes	characteristic
65	C₂²×C₄×C₁₃	C₂⁴	1	12	yes	—
66	C₂²×C₄×C₁₃	C₂⁴	1	3	yes	—
67	C₂²×Dic₁₃	C₂⁴	1	12	yes	—
68	C₂²×Dic₁₃	C₂⁴	1	3	yes	—
69	C₂×C₄×D₁₃	—	2	12	no	—
70	C₂×C₄×D₁₃	C₂⁴	1	12	yes	—
71	C₂×Dic₂₆	—	2	48	no	—
72	C₂×Dic₂₆	C₂⁴	1	48	yes	—
73	C₁₃×C₄⋊C₄	C₂⁴	1	48	yes	—
74	C₁₃×C₄⋊C₄	C₂⁴	1	48	yes	—
75	C₁₃×C₄⋊C₄	C₂⁴	1	24	yes	—
76	C₄²×C₁₃	C₂⁴	1	16	yes	—
77	C₄²×C₁₃	C₂⁴	1	4	yes	—
78	#6103	C₂⁴	1	48	yes	—
79	C₄⋊Dic₁₃	C₂⁴	1	48	yes	—
80	C₄⋊Dic₁₃	C₂⁴	1	24	yes	—
81	#6101	C₂⁴	1	48	yes	—
82	#6101	C₂⁴	1	48	yes	—
83	#6101	C₂⁴	1	48	yes	—
84	#6101	C₂⁴	1	48	yes	—
85	C₄×Dic₁₃	C₂⁴	1	48	yes	—
86	C₄×Dic₁₃	C₂⁴	1	48	yes	—
87	C₄×Dic₁₃	C₂⁴	1	12	yes	—
88	#3556	—	13	32	no	—
89	C₂×#564	—	13	3	no	—
90	C₂×#564	D₁₃	1	1	yes	characteristic, complemented
91	C₂×#557	—	13	12	no	—
92	C₂×#541	—	13	12	no	—
93	C₂×#533	—	13	3	no	—
94	C₂³×C₁₃	C₂⁵	1	1	yes	characteristic
95	C₂²×D₁₃	—	2	6	no	—
96	C₂²×D₁₃	C₂⁵	1	2	yes	—
97	C₂×C₄×C₁₃	—	2	24	no	—
98	C₂×C₄×C₁₃	—	2	6	no	—
99	C₂×C₄×C₁₃	C₂⁵	1	24	yes	—
100	C₂×C₄×C₁₃	C₂⁵	1	6	yes	—
101	C₂×Dic₁₃	—	2	24	no	—
102	C₂×Dic₁₃	2₋¹⁺⁴	1	12	yes	—
103	C₂×Dic₁₃	C₂⁵	1	24	yes	—
104	C₂×Dic₁₃	C₂⁵	1	6	yes	—
105	C₄×D₁₃	—	2	24	no	—
106	Dic₂₆	—	2	96	no	—
107	#564	—	13	48	no	—
108	#564	C₂×D₁₃	1	16	yes	complemented
109	#557	—	13	192	no	—
110	#541	—	13	192	no	—
111	#533	—	13	48	no	—
112	C₂×C₄⋊Q₈	—	13	6	no	—
113	C₂×C₄⋊Q₈	—	13	12	no	—
114	C₂×#126	—	13	12	no	—
115	C₂×#126	—	13	4	no	—
116	C₂×#125	—	13	12	no	—
117	C₂×#125	—	13	12	no	—
118	C₂×#125	—	13	12	no	—
119	C₂×#125	—	13	12	no	—
120	C₂×#125	—	13	3	no	—
121	C₂×#125	C₂×D₁₃	1	3	yes	—
122	C₂×#125	C₂×D₁₃	1	12	yes	—
123	C₂×C₂²⋊Q₈	—	13	12	no	—
124	C₂×C₄×Q₈	—	13	12	no	—
125	C₂×C₄×Q₈	—	13	12	no	—
126	C₂×C₄×Q₈	—	13	12	no	—
127	C₂×#117	—	13	6	no	—
128	C₂²×C₄²	—	13	1	no	—
129	C₂²×C₁₃	C₂×2₋¹⁺⁴	1	6	yes	—
130	C₂²×C₁₃	C₂⁶	1	1	yes	characteristic
131	C₂×D₁₃	—	2	6	no	—
132	C₂×D₁₃	—	4	4	no	—
133	C₄×C₁₃	—	2	24	no	—
134	C₄×C₁₃	—	2	6	no	—
135	Dic₁₃	—	2	24	no	—
136	Dic₁₃	C₂×2₋¹⁺⁴	1	12	yes	—
137	C₂²×Q₈	—	13	12	no	—
138	C₂³×C₄	—	13	3	no	—
139	C₄⋊Q₈	—	13	48	no	—
140	C₄⋊Q₈	—	13	96	no	—
141	#126	—	13	96	no	—
142	#126	—	13	32	no	—
143	#125	—	13	96	no	—
144	#125	—	13	96	no	—
145	#125	—	13	96	no	—
146	#125	—	13	96	no	—
147	#125	—	13	24	no	—
148	#125	C₂²×D₁₃	1	24	yes	—
149	#125	C₂²×D₁₃	1	96	yes	—
150	C₂²⋊Q₈	—	13	96	no	—
151	C₄×Q₈	—	13	96	no	—
152	C₄×Q₈	—	13	96	no	—
153	C₄×Q₈	—	13	96	no	—
154	#117	—	13	48	no	—
155	C₂×C₄⋊C₄	—	13	6	no	—
156	C₂×C₄⋊C₄	—	13	12	no	—
157	C₂×C₄⋊C₄	—	13	12	no	—
158	C₂×C₄⋊C₄	—	13	12	no	—
159	C₂×C₄⋊C₄	—	13	12	no	—
160	C₂×C₄⋊C₄	—	13	12	no	—
161	C₂×C₄⋊C₄	C₂²×D₁₃	1	6	yes	—
162	C₂×C₄⋊C₄	C₂²×D₁₃	1	12	yes	—
163	C₂×C₄⋊C₄	C₂²×D₁₃	1	12	yes	—
164	C₂×C₂²⋊C₄	—	13	12	no	—
165	C₂×C₄²	—	13	12	no	—
166	C₂×C₄²	—	13	3	no	—
167	C₂×C₄²	—	13	12	no	—
168	C₂×C₄²	—	13	8	no	—
169	C₂×C₄²	C₂²×D₁₃	1	4	yes	—
170	C₂×C₄²	C₂²×D₁₃	1	1	yes	characteristic
171	C₂×C₁₃	#3556	1	4	yes	complemented
172	C₂×C₁₃	C₂²×2₋¹⁺⁴	1	3	yes	—
173	D₁₃	—	4	2	no	—
174	C₂⁴	—	13	1	no	—
175	C₂×Q₈	—	13	48	no	—
176	C₂×Q₈	—	26	48	no	—
177	C₂²×C₄	—	13	3	no	—
178	C₂²×C₄	—	13	12	no	—
179	C₂²×C₄	—	13	12	no	—
180	C₂²×C₄	—	26	12	no	—
181	C₂²×C₄	C₂³×D₁₃	1	12	yes	—
182	C₂²×C₄	C₂³×D₁₃	1	3	yes	—
183	C₄⋊C₄	—	13	24	no	—
184	C₄⋊C₄	—	13	48	no	—
185	C₄⋊C₄	—	13	48	no	—
186	C₄⋊C₄	—	13	48	no	—
187	C₄⋊C₄	—	13	48	no	—
188	C₄⋊C₄	—	13	48	no	—
189	C₄⋊C₄	C₂³×D₁₃	1	24	yes	—
190	C₄⋊C₄	C₂³×D₁₃	1	48	yes	—
191	C₄⋊C₄	C₂³×D₁₃	1	48	yes	—
192	C₂²⋊C₄	—	13	48	no	—
193	C₄²	—	13	12	no	—
194	C₄²	—	13	48	no	—
195	C₄²	—	13	48	no	—
196	C₄²	C₂³×D₁₃	1	4	yes	—
197	C₄²	C₂³×D₁₃	1	16	yes	—
198	C₁₃	C₂×#3556	1	1	yes	characteristic, complemented, Sylow
199	C₂³	—	13	2	no	—
200	C₂³	—	26	6	no	—
201	C₂³	C₂⁴×D₁₃	1	1	yes	characteristic
202	Q₈	—	26	96	no	—
203	C₂×C₄	—	2	6	no	—
204	C₂×C₄	—	2	24	no	—
205	C₂×C₄	—	13	12	no	—
206	C₂×C₄	—	13	6	no	—
207	C₂×C₄	—	13	24	no	—
208	C₂×C₄	—	26	24	no	—
209	C₂×C₄	—	26	24	no	—
210	C₂×C₄	C₂⁴×D₁₃	1	24	yes	—
211	C₂×C₄	C₂⁴×D₁₃	1	6	yes	—
212	C₂²	—	26	6	no	—
213	C₂²	—	52	4	no	—
214	C₂²	D₁₃×2₋¹⁺⁴	1	6	yes	—
215	C₂²	C₂⁵×D₁₃	1	1	yes	characteristic
216	C₄	—	2	6	no	—
217	C₄	—	2	24	no	—
218	C₄	—	13	12	no	—
219	C₄	—	26	24	no	—
220	C₂	—	52	2	no	—
221	C₂	#13129330	1	4	yes	direct product factor
222	C₂	C₂×D₁₃×2₋¹⁺⁴	1	3	yes	—

	subgroup	G/H
center	C₂³	C₂⁴×D₁₃
commutator, cosocle	C₂²×C₁₃	C₂⁶
Frattini	C₂²	C₂⁵×D₁₃
Fitting	C₂×C₁₃×#564	C₂
socle	C₂³×C₁₃	C₂⁵
prime radical	C₂³×D₁₃	C₂⁴
hypercenter	C₂×#564	D₁₃
hypocenter	C₁₃	C₂×#3556
LCS	G ▷ C₂²×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂³ ◁ C₂×#564

Complements

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

N	H ≅ G/N	type
1. #13129330	C₂	direct (N × H)
2. C₂×C₁₃⋊#564	C₂	semidirect
3. C₂×#11719390	C₂	semidirect
6. C₂×C₁₃×#564	C₂	semidirect
7. C₁₃×#564	C₂²	semidirect
12. C₁₃⋊#564	C₂²	semidirect
13. #11719390	C₂²	semidirect
90. C₂×#564	D₁₃	semidirect
108. #564	C₂×D₁₃	semidirect
171. C₂×C₁₃	#3556	semidirect
198. C₁₃	C₂×#3556	semidirect
221. C₂	#13129330	direct (N × H)

Maximal subgroups

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

subgroup	index
#13129330	2
C₂×C₁₃⋊#564	2
C₂×#11719390	2
C₂×#11719401	2
C₂×#11719393	2
C₂×C₁₃×#564	2
C₂×#3556	13

Subgroups — C2×#13129330 #16770755

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#13129330 #16770755