Subgroups — #15778286

Order 3328.

326 conjugacy classes of subgroups.

The subgroup lattice has 188 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13116435	C₂	1	2	yes	maximal
2	C₂×#11718053	C₂	1	1	yes	maximal, characteristic
3	#13114715	C₂	1	1	yes	maximal, characteristic
4	#13112926	C₂	1	2	yes	maximal
5	C₂×C₁₃×#364	C₂	1	1	yes	maximal, characteristic
6	C₂×C₁₃×M₃₂	C₂²	1	2	yes	—
7	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
8	C₂×#88059	C₄	1	1	yes	characteristic
9	#11718767	C₄	1	1	yes	characteristic
10	#11718762	C₂²	1	2	yes	—
11	C₂²×#6090	C₂²	1	1	yes	characteristic
12	C₂²×#6090	C₂²	1	1	yes	characteristic
13	C₁₃×#364	C₄	1	4	yes	complemented
14	#11718115	C₄	1	2	yes	—
15	#11718094	—	2	2	no	—
16	C₁₆×Dic₁₃	—	2	2	no	—
17	#11718053	C₄	1	4	yes	complemented
18	C₂²×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
19	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
20	C₂×C₄²×C₁₃	C₂×C₄	1	1	yes	characteristic
21	#88180	C₂×C₄	1	2	yes	—
22	C₂×#6099	C₂×C₄	1	2	yes	—
23	C₁₃×M₃₂	—	2	2	no	—
24	C₁₃×M₃₂	C₂×C₄	1	4	yes	—
25	C₂×C₁₃×C₁₆	—	2	2	no	—
26	C₄×C₈×C₁₃	C₂×C₄	1	2	yes	—
27	C₄×C₈×C₁₃	C₂×C₄	1	2	yes	—
28	#88059	C₈	1	4	yes	—
29	#88058	C₈	1	2	yes	—
30	#88057	C₈	1	2	yes	—
31	#88055	—	2	2	no	—
32	C₈×Dic₁₃	—	2	2	no	—
33	C₂×#6090	—	2	1	no	—
34	C₂×#6090	—	2	1	no	—
35	C₂×#6090	C₂×C₄	1	2	yes	—
36	C₂×#6090	C₂×C₄	1	2	yes	—
37	C₂×#6090	D₄	1	2	yes	—
38	C₂×#6090	Q₈	1	2	yes	—
39	#12665	—	13	1	no	maximal, Sylow
40	C₂²×C₄×C₁₃	—	2	1	no	—
41	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
42	C₂×C₈×C₁₃	C₄²	1	2	yes	—
43	C₂×C₈×C₁₃	C₂×C₈	1	1	yes	characteristic
44	C₂×C₈×C₁₃	C₂×C₈	1	1	yes	characteristic
45	C₂×C₈×C₁₃	C₂×C₈	1	2	yes	—
46	C₂×C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
47	C₂×C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
48	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
49	C₂×C₈×C₁₃	C₂×Q₈	1	1	yes	characteristic
50	C₂×C₈×C₁₃	#41	1	1	yes	characteristic
51	C₂×C₈×C₁₃	#41	1	1	yes	characteristic
52	C₄²×C₁₃	—	2	1	no	—
53	C₄²×C₁₃	C₄²	1	2	yes	—
54	C₂²⋊Dic₁₃	—	2	2	no	—
55	C₄⋊Dic₁₃	C₂×C₈	1	4	yes	—
56	C₄×Dic₁₃	—	2	2	no	—
57	#6099	—	2	2	no	—
58	#6099	C₂×C₈	1	4	yes	—
59	C₂×#1055	—	2	2	no	—
60	C₁₃×C₁₆	—	2	4	no	—
61	#6090	—	2	2	no	—
62	#6090	C₄⋊C₄	1	4	yes	—
63	C₂×#364	D₁₃	1	1	yes	characteristic
64	#2108	—	13	2	no	—
65	C₂×#346	—	13	1	no	—
66	#1772	—	13	1	no	—
67	#1379	—	13	2	no	—
68	C₂³×C₁₃	#131	1	1	yes	characteristic
69	C₂×C₄×C₁₃	—	2	2	no	—
70	C₂×C₄×C₁₃	—	4	2	no	—
71	C₂×C₄×C₁₃	C₂×C₄²	1	1	yes	characteristic
72	C₂×C₄×C₁₃	C₄×D₄	1	1	yes	characteristic
73	C₂×C₄×C₁₃	C₄×Q₈	1	1	yes	characteristic
74	C₂×C₄×C₁₃	C₂²×C₈	1	1	yes	characteristic
75	C₂×C₄×C₁₃	C₂²×C₈	1	1	yes	characteristic
76	C₂×C₄×C₁₃	#131	1	1	yes	characteristic
77	C₂×Dic₁₃	—	2	4	no	—
78	C₈×C₁₃	C₄×C₈	1	2	yes	—
79	C₈×C₁₃	C₄×C₈	1	2	yes	—
80	C₈×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
81	C₈×C₁₃	#117	1	1	yes	characteristic
82	C₈×C₁₃	C₄×D₄	1	1	yes	characteristic
83	C₈×C₁₃	C₄×Q₈	1	1	yes	characteristic
84	#1055	—	2	4	no	—
85	C₂×M₃₂	C₂×D₁₃	1	2	yes	—
86	C₂²×C₁₆	—	13	1	no	—
87	C₂²×C₁₆	—	13	1	no	—
88	C₂×#108	—	13	1	no	—
89	#427	—	13	1	no	—
90	#405	—	13	2	no	—
91	C₂×C₄×C₈	C₂×D₁₃	1	1	yes	characteristic
92	#364	Dic₁₃	1	4	yes	complemented
93	#346	—	13	4	no	—
94	#346	—	26	2	no	—
95	C₄×C₁₆	—	26	2	no	—
96	#339	—	13	2	no	—
97	C₂²×C₁₃	—	2	2	no	—
98	C₂²×C₁₃	#405	1	1	yes	characteristic
99	C₂²×C₁₃	C₈×D₄	1	1	yes	characteristic
100	C₂²×C₁₃	C₈×Q₈	1	1	yes	characteristic
101	C₄×C₁₃	—	4	2	no	—
102	C₄×C₁₃	C₄×C₄⋊C₄	1	1	yes	characteristic
103	C₄×C₁₃	C₂×C₄×C₈	1	1	yes	characteristic
104	C₄×C₁₃	C₈×D₄	1	1	yes	characteristic
105	C₄×C₁₃	C₈×Q₈	1	1	yes	characteristic
106	Dic₁₃	—	4	4	no	—
107	C₂×M₁₆	—	13	2	no	—
108	C₂²×C₈	C₄×D₁₃	1	1	yes	characteristic
109	C₂²×C₈	C₂²×D₁₃	1	1	yes	characteristic
110	#117	—	13	2	no	—
111	C₂×C₄²	C₄×D₁₃	1	1	yes	characteristic
112	M₃₂	—	2	2	no	—
113	M₃₂	C₂×Dic₁₃	1	4	yes	—
114	C₂×C₁₆	—	2	2	no	—
115	C₂×C₁₆	—	13	2	no	—
116	C₂×C₁₆	—	13	2	no	—
117	C₂×C₁₆	—	13	2	no	—
118	C₂×C₁₆	—	13	2	no	—
119	C₂×C₁₆	—	26	1	no	—
120	C₂×C₁₆	—	26	1	no	—
121	#108	—	13	4	no	—
122	#107	—	13	2	no	—
123	#106	—	13	2	no	—
124	#97	—	26	2	no	—
125	C₄×C₈	—	26	2	no	—
126	C₄×C₈	C₄×D₁₃	1	2	yes	—
127	C₄×C₈	C₂×Dic₁₃	1	2	yes	—
128	C₂×C₁₃	—	2	1	no	—
129	C₂×C₁₃	—	2	1	no	—
130	C₂×C₁₃	C₈×C₄⋊C₄	1	1	yes	characteristic
131	C₂×C₁₃	#2171	1	2	yes	—
132	C₂²×C₄	—	2	1	no	—
133	C₂²×C₄	C₂×C₄×D₁₃	1	1	yes	characteristic
134	M₁₆	—	13	4	no	—
135	M₁₆	—	26	2	no	—
136	C₂×C₈	—	26	2	no	—
137	C₂×C₈	C₈×D₁₃	1	1	yes	characteristic
138	C₂×C₈	C₈×D₁₃	1	1	yes	characteristic
139	C₂×C₈	C₈×D₁₃	1	2	yes	—
140	C₂×C₈	C₄×Dic₁₃	1	2	yes	—
141	C₂×C₈	C₂×C₄×D₁₃	1	1	yes	characteristic
142	C₂×C₈	D₄×D₁₃	1	1	yes	characteristic
143	C₂×C₈	#6129	1	1	yes	characteristic
144	C₂×C₈	Q₈×D₁₃	1	1	yes	characteristic
145	C₂×C₈	#6131	1	1	yes	characteristic
146	C₂×C₈	C₂²×Dic₁₃	1	1	yes	characteristic
147	C₄⋊C₄	—	13	4	no	—
148	C₂²⋊C₄	—	26	2	no	—
149	C₄²	—	2	1	no	—
150	C₄²	—	26	2	no	—
151	C₄²	C₄×Dic₁₃	1	2	yes	—
152	C₁₆	—	2	4	no	—
153	C₁₆	—	13	4	no	—
154	C₁₆	—	26	2	no	—
155	C₁₃	#12665	1	1	yes	characteristic, complemented, Sylow
156	C₂³	#88161	1	1	yes	characteristic
157	C₂×C₄	—	2	2	no	—
158	C₂×C₄	—	4	2	no	—
159	C₂×C₄	—	26	4	no	—
160	C₂×C₄	#88141	1	1	yes	characteristic
161	C₂×C₄	#88147	1	1	yes	characteristic
162	C₂×C₄	C₂×C₈×D₁₃	1	1	yes	characteristic
163	C₂×C₄	C₂×C₈×D₁₃	1	1	yes	characteristic
164	C₂×C₄	#88161	1	1	yes	characteristic
165	C₂×C₄	C₂×C₄×Dic₁₃	1	1	yes	characteristic
166	C₈	—	26	4	no	—
167	C₈	C₈×Dic₁₃	1	2	yes	—
168	C₈	C₈×Dic₁₃	1	2	yes	—
169	C₈	C₄⋊C₄×D₁₃	1	1	yes	characteristic
170	C₈	#88146	1	1	yes	characteristic
171	C₈	D₄×Dic₁₃	1	1	yes	characteristic
172	C₈	Q₈×Dic₁₃	1	1	yes	characteristic
173	C₂²	—	2	2	no	—
174	C₂²	#11718491	1	1	yes	characteristic
175	C₂²	#11718495	1	1	yes	characteristic
176	C₂²	#11718783	1	1	yes	characteristic
177	C₄	—	4	2	no	—
178	C₄	—	52	4	no	—
179	C₄	#11718491	1	1	yes	characteristic
180	C₄	#11718495	1	1	yes	characteristic
181	C₄	C₄⋊C₄×Dic₁₃	1	1	yes	characteristic
182	C₄	C₂×C₈×Dic₁₃	1	1	yes	characteristic
183	C₂	—	2	1	no	—
184	C₂	—	2	1	no	—
185	C₂	#13114701	1	1	yes	characteristic
186	C₂	#13116677	1	2	yes	—

	subgroup	G/H
center	C₂×C₈	D₄×D₁₃
commutator	C₄×C₁₃	C₂×C₄×C₈
Frattini	C₂²×C₈	C₂²×D₁₃
Fitting	C₂×C₁₃×#364	C₂
socle	C₂²×C₁₃	C₈×D₄
prime radical	C₂³×C₁₃	#131
cosocle	C₂²×C₈×C₁₃	C₂³
hypercenter	C₂×#364	D₁₃
hypocenter	C₁₃	#12665
LCS	G ▷ C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂×C₈ ◁ C₂²×C₈ ◁ C₂×#364

Complements

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

N	H ≅ G/N	type
13. C₁₃×#364	C₄	semidirect
17. #11718053	C₄	semidirect
92. #364	Dic₁₃	semidirect
155. C₁₃	#12665	semidirect

Maximal subgroups

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

subgroup	index
#13116435	2
C₂×#11718053	2
#13114715	2
#13112926	2
C₂×C₁₃×#364	2
#12665	13