Subgroups — #16018433

Order 3328.

474 conjugacy classes of subgroups.

The subgroup lattice has 210 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13125372	C₂	1	2	yes	maximal
2	#13117121	C₂	1	4	yes	maximal, complemented
3	#13117117	C₂	1	2	yes	maximal, complemented
4	#13117114	C₂	1	2	yes	maximal, complemented
5	#13116622	C₂	1	2	yes	maximal
6	#13116620	C₂	1	1	yes	maximal, characteristic
7	#13116432	C₂	1	1	yes	maximal, characteristic
8	C₂×C₁₃×#367	C₂	1	1	yes	maximal, characteristic
9	#11719205	—	2	2	no	—
10	C₂²×C₁₃×C₁₆	C₂²	1	1	yes	characteristic
11	C₂×C₁₃×#107	C₂²	1	2	yes	—
12	#11718767	C₂²	1	2	yes	—
13	#11718762	C₂²	1	1	yes	characteristic
14	C₂×#88052	C₂²	1	1	yes	characteristic
15	#11718625	—	2	2	no	—
16	#11718539	C₂²	1	4	yes	—
17	#11718537	—	2	4	no	—
18	#11718535	C₂²	1	4	yes	—
19	C₁₃×#367	C₂²	1	2	yes	—
20	C₁₃×#367	C₂²	1	2	yes	—
21	#11718097	C₂²	1	1	yes	characteristic
22	#11718097	C₂²	1	1	yes	characteristic
23	#11718096	C₂²	1	2	yes	—
24	#11718094	C₂²	1	2	yes	—
25	C₁₆×Dic₁₃	C₂²	1	2	yes	—
26	#11718082	C₂²	1	4	yes	—
27	#11718081	C₂²	1	4	yes	—
28	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
29	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
30	#88180	—	2	2	no	—
31	#88180	D₄	1	1	yes	characteristic
32	#88178	—	4	4	no	—
33	C₂×#6099	D₄	1	1	yes	characteristic
34	#88144	—	2	4	no	—
35	#88144	—	4	2	no	—
36	#88142	—	2	4	no	—
37	#88142	—	4	2	no	—
38	C₂×C₁₃×C₁₆	Q₈	1	4	yes	complemented
39	C₂×C₁₃×C₁₆	C₂³	1	1	yes	characteristic
40	C₂×C₁₃×C₁₆	C₂³	1	1	yes	characteristic
41	C₁₃×#107	—	2	2	no	—
42	C₁₃×#107	C₂³	1	4	yes	—
43	#88058	C₂³	1	2	yes	—
44	#88058	C₂³	1	2	yes	—
45	#88057	—	2	2	no	—
46	#88055	D₄	1	2	yes	—
47	C₈×Dic₁₃	C₂³	1	2	yes	—
48	#88052	Q₈	1	4	yes	complemented
49	C₂×#6090	C₂³	1	2	yes	—
50	#88048	—	2	4	no	—
51	#88047	—	2	4	no	—
52	#33730	—	13	1	no	maximal, Sylow
53	C₂²×C₄×C₁₃	—	4	2	no	—
54	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
55	C₂×Dic₂₆	—	4	4	no	—
56	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
57	C₂×C₈×C₁₃	C₂×Q₈	1	2	yes	—
58	C₂×C₈×C₁₃	C₂×Q₈	1	2	yes	—
59	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
60	C₁₃×C₄⋊C₄	—	2	4	no	—
61	C₁₃×C₄⋊C₄	—	4	2	no	—
62	C₂²⋊Dic₁₃	—	4	2	no	—
63	C₂²⋊Dic₁₃	D₈	1	2	yes	—
64	C₄⋊Dic₁₃	—	2	2	no	—
65	C₄⋊Dic₁₃	—	2	2	no	—
66	C₄⋊Dic₁₃	—	4	4	no	—
67	C₄⋊Dic₁₃	D₈	1	2	yes	—
68	#6101	—	4	4	no	—
69	#6101	—	4	4	no	—
70	C₄×Dic₁₃	—	4	2	no	—
71	C₄×Dic₁₃	C₂×D₄	1	2	yes	—
72	#6099	Q₁₆	1	4	yes	—
73	C₂×#1055	C₂×D₄	1	2	yes	—
74	C₁₃×C₁₆	C₂×Q₈	1	2	yes	—
75	C₁₃×C₁₆	C₂×Q₈	1	2	yes	—
76	#6090	C₂×Q₈	1	4	yes	—
77	#3164	—	13	2	no	—
78	#2255	—	13	4	no	—
79	#2254	—	13	2	no	—
80	#2253	—	13	2	no	—
81	#2159	—	13	2	no	—
82	#2158	—	13	1	no	—
83	C₂×#367	D₁₃	1	1	yes	characteristic
84	#2108	—	13	1	no	—
85	C₂³×C₁₃	C₂×D₈	1	1	yes	characteristic
86	C₂×C₄×C₁₃	—	4	4	no	—
87	C₂×C₄×C₁₃	—	16	2	no	—
88	C₂×C₄×C₁₃	C₄⋊Q₈	1	2	yes	—
89	C₂×C₄×C₁₃	C₂×D₈	1	1	yes	characteristic
90	C₂×C₄×C₁₃	C₂×Q₁₆	1	2	yes	—
91	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
92	C₂×Dic₁₃	—	4	2	no	—
93	C₂×Dic₁₃	—	4	2	no	—
94	C₂×Dic₁₃	C₂×D₈	1	4	yes	—
95	Dic₂₆	—	16	4	no	—
96	C₈×C₁₃	C₄⋊Q₈	1	2	yes	—
97	C₈×C₁₃	C₂²×Q₈	1	1	yes	characteristic
98	C₈×C₁₃	C₂²×Q₈	1	1	yes	characteristic
99	#1055	C₂×Q₁₆	1	4	yes	—
100	#544	—	26	2	no	—
101	C₂×M₃₂	—	13	1	no	—
102	C₂²×C₁₆	C₂×D₁₃	1	1	yes	characteristic
103	#501	—	26	4	no	—
104	#500	—	13	4	no	—
105	#499	—	13	4	no	—
106	#428	—	26	2	no	—
107	#427	—	13	2	no	—
108	C₂×#107	C₂×D₁₃	1	2	yes	—
109	#405	—	13	1	no	—
110	#367	—	13	1	no	—
111	#367	—	13	1	no	—
112	#367	—	13	4	no	—
113	#367	C₂×D₁₃	1	2	yes	—
114	#367	C₂×D₁₃	1	2	yes	—
115	#366	—	13	2	no	—
116	#366	—	13	4	no	—
117	#346	—	13	2	no	—
118	C₄×C₁₆	—	13	2	no	—
119	C₂²×C₁₃	—	2	2	no	—
120	C₂²×C₁₃	#500	1	2	yes	—
121	C₂²×C₁₃	C₂²×D₈	1	1	yes	characteristic
122	C₄×C₁₃	—	8	4	no	—
123	C₄×C₁₃	#500	1	2	yes	—
124	C₄×C₁₃	C₂×C₄⋊Q₈	1	1	yes	characteristic
125	C₄×C₁₃	C₂²×Q₁₆	1	1	yes	characteristic
126	Dic₁₃	—	2	4	no	—
127	Dic₁₃	—	8	2	no	—
128	Dic₁₃	—	8	2	no	—
129	C₂×M₁₆	—	13	1	no	—
130	C₂²×C₈	C₂²×D₁₃	1	1	yes	characteristic
131	C₄⋊Q₈	—	26	4	no	—
132	C₄⋊Q₈	—	52	2	no	—
133	#125	—	26	4	no	—
134	#125	—	52	2	no	—
135	C₂²⋊Q₈	—	52	4	no	—
136	#117	—	13	1	no	—
137	#117	—	26	2	no	—
138	C₂×C₄⋊C₄	—	2	2	no	—
139	M₃₂	—	13	4	no	—
140	C₂×C₁₆	—	13	2	no	—
141	C₂×C₁₆	Dic₂₆	1	4	yes	complemented
142	C₂×C₁₆	C₂²×D₁₃	1	1	yes	characteristic
143	C₂×C₁₆	C₂²×D₁₃	1	1	yes	characteristic
144	#107	—	2	2	no	—
145	#107	—	13	2	no	—
146	#107	—	13	2	no	—
147	#107	—	26	4	no	—
148	#107	C₂²×D₁₃	1	4	yes	—
149	#106	—	26	4	no	—
150	#106	—	26	2	no	—
151	#97	—	13	2	no	—
152	C₄×C₈	—	13	2	no	—
153	C₂×C₁₃	—	2	2	no	—
154	C₂×C₁₃	C₂×#500	1	1	yes	characteristic
155	C₂×C₁₃	#3416	1	2	yes	—
156	C₂×Q₈	—	52	4	no	—
157	C₂²×C₄	—	4	2	no	—
158	C₂²×C₄	D₄×D₁₃	1	1	yes	characteristic
159	M₁₆	—	13	4	no	—
160	C₂×C₈	—	13	2	no	—
161	C₂×C₈	C₂×Dic₂₆	1	2	yes	—
162	C₂×C₈	D₄×D₁₃	1	1	yes	characteristic
163	C₂×C₈	Q₈×D₁₃	1	2	yes	—
164	C₂×C₈	C₂³×D₁₃	1	1	yes	characteristic
165	C₄⋊C₄	—	2	4	no	—
166	C₄⋊C₄	—	4	2	no	—
167	C₄⋊C₄	—	13	2	no	—
168	C₄⋊C₄	—	26	2	no	—
169	C₄⋊C₄	—	26	2	no	—
170	C₄⋊C₄	—	52	4	no	—
171	C₄⋊C₄	—	52	4	no	—
172	C₄⋊C₄	—	52	4	no	—
173	C₂²⋊C₄	—	13	2	no	—
174	C₂²⋊C₄	—	52	2	no	—
175	C₄²	—	13	2	no	—
176	C₄²	—	52	2	no	—
177	C₁₆	—	13	4	no	—
178	C₁₆	C₂×Dic₂₆	1	2	yes	—
179	C₁₆	C₂×Dic₂₆	1	2	yes	—
180	C₁₃	#33730	1	1	yes	characteristic, complemented, Sylow
181	C₂³	D₈×D₁₃	1	1	yes	characteristic
182	Q₈	—	208	4	no	—
183	C₂×C₄	—	4	4	no	—
184	C₂×C₄	—	13	4	no	—
185	C₂×C₄	—	16	2	no	—
186	C₂×C₄	—	52	2	no	—
187	C₂×C₄	—	52	2	no	—
188	C₂×C₄	#88142	1	2	yes	—
189	C₂×C₄	D₈×D₁₃	1	1	yes	characteristic
190	C₂×C₄	Q₁₆×D₁₃	1	2	yes	—
191	C₂×C₄	C₂×D₄×D₁₃	1	1	yes	characteristic
192	C₈	—	13	4	no	—
193	C₈	#88142	1	2	yes	—
194	C₈	C₂²×Dic₂₆	1	1	yes	characteristic
195	C₈	C₂×Q₈×D₁₃	1	1	yes	characteristic
196	C₂²	—	2	2	no	—
197	C₂²	#11718535	1	2	yes	—
198	C₂²	C₂×D₈×D₁₃	1	1	yes	characteristic
199	C₄	—	8	4	no	—
200	C₄	—	26	4	no	—
201	C₄	—	104	2	no	—
202	C₄	—	104	2	no	—
203	C₄	#11718535	1	2	yes	—
204	C₄	C₂×#88142	1	1	yes	characteristic
205	C₄	C₂×Q₁₆×D₁₃	1	1	yes	characteristic
206	C₂	—	2	2	no	—
207	C₂	C₂×#11718535	1	1	yes	characteristic
208	C₂	#13127978	1	2	yes	—

	subgroup	G/H
center	C₂²	C₂×D₈×D₁₃
commutator, cosocle	C₂×C₈×C₁₃	C₂⁴
Frattini	C₂×C₈	C₂³×D₁₃
Fitting	C₂×C₁₃×#367	C₂
socle	C₂²×C₁₃	C₂²×D₈
prime radical	C₂³×C₁₃	C₂×D₈
hypercenter	C₂×#367	D₁₃
hypocenter	C₁₃	#33730
LCS	G ▷ C₂×C₈×C₁₃ ▷ C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂² ◁ C₂²×C₄ ◁ C₂²×C₈ ◁ C₂×#367

Complements

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

N	H ≅ G/N	type
2. #13117121	C₂	semidirect
3. #13117117	C₂	semidirect
4. #13117114	C₂	semidirect
38. C₂×C₁₃×C₁₆	Q₈	semidirect
48. #88052	Q₈	semidirect
141. C₂×C₁₆	Dic₂₆	semidirect
180. C₁₃	#33730	semidirect

Maximal subgroups

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

subgroup	index
#13125372	2
#13117121	2
#13117117	2
#13117114	2
#13116622	2
#13116620	2
#13116432	2
C₂×C₁₃×#367	2
#33730	13