Subgroups — #15781046

Order 3328.

310 conjugacy classes of subgroups.

The subgroup lattice has 196 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#11718105	C₂	1	2	yes	maximal
2	#13114993	C₂	1	1	yes	maximal, characteristic
3	C₄×#88059	C₂	1	1	yes	maximal, characteristic
4	#13112935	C₂	1	2	yes	maximal
5	C₁₃×#2150	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	C₂²	1	1	yes	characteristic
9	C₂×#88059	C₂²	1	1	yes	characteristic
10	C₂×#88057	—	2	1	no	—
11	C₂×#88057	C₂²	1	2	yes	—
12	#11718596	—	2	1	no	—
13	C₄×#6099	—	2	1	no	—
14	C₁₃×C₄⋊C₁₆	C₄	1	4	yes	complemented
15	#11718144	—	2	1	no	—
16	#11718105	—	2	4	no	—
17	C₂²×C₈×C₁₃	D₄	1	1	yes	characteristic
18	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
19	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
20	C₂×C₄⋊Dic₁₃	—	2	2	no	—
21	C₂×C₄⋊Dic₁₃	—	4	2	no	—
22	C₂×#6099	—	2	1	no	—
23	C₂×#6099	—	2	1	no	—
24	C₁₃×M₃₂	—	2	2	no	—
25	C₁₃×M₃₂	—	2	2	no	—
26	C₂×C₁₃×C₁₆	C₂×C₄	1	4	yes	—
27	C₄×C₈×C₁₃	C₂×C₄	1	2	yes	—
28	C₄×C₈×C₁₃	Q₈	1	2	yes	—
29	#88059	—	2	1	no	—
30	#88059	—	2	1	no	—
31	#88059	D₄	1	2	yes	—
32	#88059	Q₈	1	2	yes	—
33	#88057	—	2	2	no	—
34	#88057	—	2	2	no	—
35	#88057	—	4	2	no	—
36	#88043	—	4	1	no	—
37	C₄×#1055	—	4	1	no	—
38	#13183	—	13	1	no	maximal, Sylow
39	C₂²×C₄×C₁₃	SD₁₆	1	2	yes	—
40	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
41	C₂²×Dic₁₃	—	4	2	no	—
42	C₂×C₈×C₁₃	—	2	1	no	—
43	C₂×C₈×C₁₃	—	2	1	no	—
44	C₂×C₈×C₁₃	C₄⋊C₄	1	2	yes	—
45	C₂×C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
46	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
47	C₂×C₈×C₁₃	C₂×Q₈	1	1	yes	characteristic
48	C₂×C₈×C₁₃	C₂×Q₈	1	1	yes	characteristic
49	C₂×C₈×C₁₃	#41	1	1	yes	characteristic
50	C₂×C₈×C₁₃	#41	1	1	yes	characteristic
51	C₄²×C₁₃	C₄⋊C₄	1	2	yes	—
52	C₄²×C₁₃	SD₁₆	1	1	yes	characteristic
53	C₄²×C₁₃	SD₁₆	1	1	yes	characteristic
54	C₄⋊Dic₁₃	—	4	2	no	—
55	C₄⋊Dic₁₃	—	4	2	no	—
56	C₄⋊Dic₁₃	—	8	4	no	—
57	#6099	—	2	2	no	—
58	#6099	—	2	2	no	—
59	#6099	—	4	1	no	—
60	#6099	—	4	1	no	—
61	C₂×#1055	—	4	1	no	—
62	C₂×#1055	—	4	1	no	—
63	C₁₃×C₁₆	—	2	4	no	—
64	C₂×#365	—	13	2	no	—
65	#2150	D₁₃	1	1	yes	characteristic
66	#1844	—	13	1	no	—
67	C₄×#108	—	13	1	no	—
68	#1383	—	13	2	no	—
69	C₂³×C₁₃	C₂×SD₁₆	1	1	yes	characteristic
70	C₂×C₄×C₁₃	—	2	4	no	—
71	C₂×C₄×C₁₃	#106	1	2	yes	—
72	C₂×C₄×C₁₃	#106	1	2	yes	—
73	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
74	C₂×C₄×C₁₃	#121	1	1	yes	characteristic
75	C₂×C₄×C₁₃	C₂²⋊Q₈	1	1	yes	characteristic
76	C₂×C₄×C₁₃	C₂×SD₁₆	1	1	yes	characteristic
77	C₂×C₄×C₁₃	AGL(1,ℤ/8)	1	1	yes	characteristic
78	C₂×C₄×C₁₃	#137	1	1	yes	characteristic
79	C₂×Dic₁₃	—	8	4	no	—
80	C₂×Dic₁₃	—	8	2	no	—
81	C₈×C₁₃	—	2	2	no	—
82	C₈×C₁₃	C₄×D₄	1	1	yes	characteristic
83	C₈×C₁₃	C₄×Q₈	1	1	yes	characteristic
84	C₈×C₁₃	#125	1	1	yes	characteristic
85	C₈×C₁₃	C₄⋊Q₈	1	1	yes	characteristic
86	#1055	—	4	2	no	—
87	#1055	—	4	2	no	—
88	C₂×M₃₂	C₂×D₁₃	1	2	yes	—
89	C₂×#108	—	13	1	no	—
90	C₂×#108	—	13	1	no	—
91	C₂×#106	—	13	2	no	—
92	C₂×#106	—	26	1	no	—
93	C₄×M₁₆	—	26	1	no	—
94	C₂×C₄×C₈	C₂×D₁₃	1	1	yes	characteristic
95	#384	—	26	1	no	—
96	#365	—	26	4	no	—
97	C₄⋊C₁₆	Dic₁₃	1	4	yes	complemented
98	#341	—	26	1	no	—
99	C₂²×C₁₃	—	2	2	no	—
100	C₂²×C₁₃	C₂×#106	1	1	yes	characteristic
101	C₂²×C₁₃	#460	1	1	yes	characteristic
102	C₂²×C₁₃	#475	1	1	yes	characteristic
103	C₄×C₁₃	—	2	2	no	—
104	C₄×C₁₃	#365	1	4	yes	complemented
105	C₄×C₁₃	#389	1	1	yes	characteristic
106	C₄×C₁₃	#428	1	1	yes	characteristic
107	C₄×C₁₃	#461	1	1	yes	characteristic
108	C₄×C₁₃	#476	1	1	yes	characteristic
109	Dic₁₃	—	16	2	no	—
110	C₂×M₁₆	—	26	1	no	—
111	C₂×M₁₆	—	26	1	no	—
112	C₂²×C₈	D₅₂	1	1	yes	characteristic
113	C₂²×C₈	C₂²×D₁₃	1	1	yes	characteristic
114	C₂×C₄⋊C₄	—	26	2	no	—
115	C₂×C₄⋊C₄	—	52	2	no	—
116	C₂×C₄²	D₅₂	1	1	yes	characteristic
117	M₃₂	—	2	2	no	—
118	M₃₂	—	2	2	no	—
119	C₂×C₁₆	C₂×Dic₁₃	1	4	yes	—
120	#108	—	13	2	no	—
121	#108	—	13	2	no	—
122	#108	—	26	1	no	—
123	#108	—	26	1	no	—
124	#106	—	26	2	no	—
125	#106	—	26	2	no	—
126	#106	—	52	2	no	—
127	#97	—	52	1	no	—
128	C₄×C₈	—	52	1	no	—
129	C₄×C₈	Dic₂₆	1	2	yes	—
130	C₄×C₈	C₂×Dic₁₃	1	2	yes	—
131	C₂×C₁₃	—	2	1	no	—
132	C₂×C₁₃	—	2	1	no	—
133	C₂×C₁₃	#1948	1	1	yes	characteristic
134	C₂×C₁₃	C₂×#365	1	2	yes	—
135	C₂²×C₄	—	52	2	no	—
136	C₂²×C₄	#6095	1	2	yes	—
137	C₂²×C₄	C₂×D₅₂	1	1	yes	characteristic
138	M₁₆	—	26	2	no	—
139	M₁₆	—	26	2	no	—
140	M₁₆	—	52	1	no	—
141	M₁₆	—	52	1	no	—
142	C₂×C₈	—	2	1	no	—
143	C₂×C₈	—	2	1	no	—
144	C₂×C₈	—	52	1	no	—
145	C₂×C₈	—	52	1	no	—
146	C₂×C₈	C₄⋊Dic₁₃	1	2	yes	—
147	C₂×C₈	C₂×Dic₂₆	1	1	yes	characteristic
148	C₂×C₈	D₄×D₁₃	1	1	yes	characteristic
149	C₂×C₈	#6129	1	1	yes	characteristic
150	C₂×C₈	Q₈×D₁₃	1	1	yes	characteristic
151	C₂×C₈	#6131	1	1	yes	characteristic
152	C₂×C₈	C₂²×Dic₁₃	1	1	yes	characteristic
153	C₄⋊C₄	—	52	2	no	—
154	C₄⋊C₄	—	52	2	no	—
155	C₄⋊C₄	—	104	4	no	—
156	C₄²	#6095	1	1	yes	characteristic
157	C₄²	#6095	1	1	yes	characteristic
158	C₄²	C₄⋊Dic₁₃	1	2	yes	—
159	C₁₆	—	2	4	no	—
160	C₁₃	#13183	1	1	yes	characteristic, complemented, Sylow
161	C₂³	C₂×#6095	1	1	yes	characteristic
162	C₂×C₄	—	2	4	no	—
163	C₂×C₄	—	104	4	no	—
164	C₂×C₄	—	104	2	no	—
165	C₂×C₄	#88057	1	2	yes	—
166	C₂×C₄	#88057	1	2	yes	—
167	C₂×C₄	#88149	1	1	yes	characteristic
168	C₂×C₄	#88151	1	1	yes	characteristic
169	C₂×C₄	C₂×#6095	1	1	yes	characteristic
170	C₂×C₄	#88162	1	1	yes	characteristic
171	C₂×C₄	#88163	1	1	yes	characteristic
172	C₂×C₄	C₂×C₄⋊Dic₁₃	1	1	yes	characteristic
173	C₈	—	2	2	no	—
174	C₈	—	52	2	no	—
175	C₈	—	52	2	no	—
176	C₈	#88142	1	1	yes	characteristic
177	C₈	#88144	1	1	yes	characteristic
178	C₈	D₄×Dic₁₃	1	1	yes	characteristic
179	C₈	Q₈×Dic₁₃	1	1	yes	characteristic
180	C₂²	—	2	2	no	—
181	C₂²	#11718509	1	1	yes	characteristic
182	C₂²	#11718512	1	1	yes	characteristic
183	C₂²	C₂×#88057	1	1	yes	characteristic
184	C₄	—	2	2	no	—
185	C₄	—	208	2	no	—
186	C₄	#11718105	1	4	yes	complemented
187	C₄	#11718502	1	1	yes	characteristic
188	C₄	#11718503	1	1	yes	characteristic
189	C₄	#11718646	1	1	yes	characteristic
190	C₄	#11718782	1	1	yes	characteristic
191	C₂	—	2	1	no	—
192	C₂	—	2	1	no	—
193	C₂	#13115600	1	1	yes	characteristic
194	C₂	C₂×#11718105	1	2	yes	—

	subgroup	G/H
center	C₂²	C₂×#88057
commutator	C₂×C₈×C₁₃	C₂²×C₄
Frattini	C₂²×C₈	C₂²×D₁₃
Fitting	C₁₃×#2150	C₂
socle	C₂²×C₁₃	C₂×#106
prime radical	C₂³×C₁₃	C₂×SD₁₆
cosocle	C₂²×C₈×C₁₃	C₂³
hypercenter	#2150	D₁₃
hypocenter	C₁₃	#13183
LCS	G ▷ C₂×C₈×C₁₃ ▷ C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ C₂×C₄×C₈ ◁ #2150

Complements

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

N	H ≅ G/N	type
14. C₁₃×C₄⋊C₁₆	C₄	semidirect
97. C₄⋊C₁₆	Dic₁₃	semidirect
104. C₄×C₁₃	#365	semidirect
160. C₁₃	#13183	semidirect
186. C₄	#11718105	semidirect

Maximal subgroups

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

subgroup	index
C₂×#11718105	2
#13114993	2
C₄×#88059	2
#13112935	2
C₁₃×#2150	2
#13183	13