Subgroups — #15781045

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×#11718086	C₂	1	2	yes	maximal
2	#13116592	C₂	1	1	yes	maximal, characteristic
3	#13114993	C₂	1	1	yes	maximal, characteristic
4	#13112936	C₂	1	2	yes	maximal
5	C₄×C₁₃×#108	C₂	1	1	yes	maximal, characteristic
6	C₂×C₁₃×#108	C₂²	1	1	yes	characteristic
7	C₂×C₁₃×#108	C₂²	1	1	yes	characteristic
8	C₄×C₁₃×M₁₆	—	2	1	no	—
9	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
10	C₂×#88057	—	2	1	no	—
11	C₂×#88057	C₂²	1	2	yes	—
12	C₂×#88052	C₂²	1	2	yes	—
13	#11718596	—	2	1	no	—
14	C₁₃×#341	—	2	1	no	—
15	#11718086	—	2	4	no	—
16	C₄⋊#6090	C₄	1	4	yes	complemented
17	C₂×C₁₃×M₁₆	—	2	1	no	—
18	C₂×C₁₃×M₁₆	—	2	1	no	—
19	C₂²×C₈×C₁₃	D₄	1	1	yes	characteristic
20	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
21	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
22	C₂×C₄⋊Dic₁₃	—	2	2	no	—
23	C₂×C₄⋊Dic₁₃	—	4	2	no	—
24	C₁₃×#108	—	2	1	no	—
25	C₁₃×#108	—	2	1	no	—
26	C₁₃×#108	D₄	1	2	yes	—
27	C₁₃×#108	Q₈	1	2	yes	—
28	C₁₃×#97	—	4	1	no	—
29	C₄×C₈×C₁₃	—	4	1	no	—
30	C₄×C₈×C₁₃	C₂×C₄	1	2	yes	—
31	C₄×C₈×C₁₃	Q₈	1	2	yes	—
32	#88057	—	2	2	no	—
33	#88057	—	2	2	no	—
34	#88057	—	4	2	no	—
35	#88052	—	2	2	no	—
36	#88052	—	2	2	no	—
37	C₂×#6090	C₂×C₄	1	4	yes	—
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	C₁₃×M₁₆	—	2	2	no	—
43	C₁₃×M₁₆	—	2	2	no	—
44	C₁₃×M₁₆	—	4	1	no	—
45	C₁₃×M₁₆	—	4	1	no	—
46	C₂×C₈×C₁₃	—	2	1	no	—
47	C₂×C₈×C₁₃	—	2	1	no	—
48	C₂×C₈×C₁₃	—	4	1	no	—
49	C₂×C₈×C₁₃	—	4	1	no	—
50	C₂×C₈×C₁₃	C₄⋊C₄	1	2	yes	—
51	C₂×C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
52	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
53	C₂×C₈×C₁₃	C₂×Q₈	1	1	yes	characteristic
54	C₂×C₈×C₁₃	C₂×Q₈	1	1	yes	characteristic
55	C₂×C₈×C₁₃	#41	1	1	yes	characteristic
56	C₂×C₈×C₁₃	#41	1	1	yes	characteristic
57	C₄²×C₁₃	C₄⋊C₄	1	2	yes	—
58	C₄²×C₁₃	SD₁₆	1	1	yes	characteristic
59	C₄²×C₁₃	SD₁₆	1	1	yes	characteristic
60	C₄⋊Dic₁₃	—	4	2	no	—
61	C₄⋊Dic₁₃	—	4	2	no	—
62	C₄⋊Dic₁₃	—	8	4	no	—
63	#6090	—	2	4	no	—
64	C₂×#365	—	13	2	no	—
65	#2150	—	13	1	no	—
66	#1844	—	13	1	no	—
67	C₄×#108	D₁₃	1	1	yes	characteristic
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	—	4	2	no	—
83	C₈×C₁₃	—	4	2	no	—
84	C₈×C₁₃	C₄×D₄	1	1	yes	characteristic
85	C₈×C₁₃	C₄×Q₈	1	1	yes	characteristic
86	C₈×C₁₃	#125	1	1	yes	characteristic
87	C₈×C₁₃	C₄⋊Q₈	1	1	yes	characteristic
88	C₂×M₃₂	—	13	2	no	—
89	C₂×#108	C₂×D₁₃	1	1	yes	characteristic
90	C₂×#108	C₂×D₁₃	1	1	yes	characteristic
91	C₂×#106	—	13	2	no	—
92	C₂×#106	—	26	1	no	—
93	C₄×M₁₆	—	2	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	—	13	4	no	—
98	#341	—	2	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	—	2	1	no	—
111	C₂×M₁₆	—	2	1	no	—
112	C₂²×C₈	C₂²⋊D₁₃	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	C₂²⋊D₁₃	1	1	yes	characteristic
117	M₃₂	—	26	2	no	—
118	M₃₂	—	26	2	no	—
119	C₂×C₁₆	—	13	4	no	—
120	#108	—	2	1	no	—
121	#108	—	2	1	no	—
122	#108	Dic₂₆	1	2	yes	—
123	#108	D₅₂	1	2	yes	—
124	#106	—	26	2	no	—
125	#106	—	26	2	no	—
126	#106	—	52	2	no	—
127	#97	—	4	1	no	—
128	C₄×C₈	—	4	1	no	—
129	C₄×C₈	Dic₂₆	1	2	yes	—
130	C₄×C₈	C₄×D₁₃	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	#6106	1	2	yes	—
137	C₂²×C₄	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
138	M₁₆	—	2	2	no	—
139	M₁₆	—	2	2	no	—
140	M₁₆	—	4	1	no	—
141	M₁₆	—	4	1	no	—
142	C₂×C₈	—	2	1	no	—
143	C₂×C₈	—	2	1	no	—
144	C₂×C₈	—	4	1	no	—
145	C₂×C₈	—	4	1	no	—
146	C₂×C₈	#6101	1	2	yes	—
147	C₂×C₈	C₂×Dic₂₆	1	1	yes	characteristic
148	C₂×C₈	C₂×Dic₂₆	1	1	yes	characteristic
149	C₂×C₈	C₂×C₄×D₁₃	1	1	yes	characteristic
150	C₂×C₈	C₂×D₅₂	1	1	yes	characteristic
151	C₂×C₈	#6127	1	1	yes	characteristic
152	C₂×C₈	#6127	1	1	yes	characteristic
153	C₄⋊C₄	—	52	2	no	—
154	C₄⋊C₄	—	52	2	no	—
155	C₄⋊C₄	—	104	4	no	—
156	C₄²	#6101	1	2	yes	—
157	C₄²	#6105	1	1	yes	characteristic
158	C₄²	#6105	1	1	yes	characteristic
159	C₁₆	—	26	4	no	—
160	C₁₃	#13183	1	1	yes	characteristic, complemented, Sylow
161	C₂³	C₂×#6106	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	#88048	1	2	yes	—
166	C₂×C₄	#88048	1	2	yes	—
167	C₂×C₄	C₂×#6101	1	1	yes	characteristic
168	C₂×C₄	#88178	1	1	yes	characteristic
169	C₂×C₄	#88184	1	1	yes	characteristic
170	C₂×C₄	C₂×#6105	1	1	yes	characteristic
171	C₂×C₄	#88203	1	1	yes	characteristic
172	C₂×C₄	#88205	1	1	yes	characteristic
173	C₈	—	2	2	no	—
174	C₈	—	4	2	no	—
175	C₈	—	4	2	no	—
176	C₈	C₄×Dic₂₆	1	1	yes	characteristic
177	C₈	#88123	1	1	yes	characteristic
178	C₈	#88124	1	1	yes	characteristic
179	C₈	C₄×D₅₂	1	1	yes	characteristic
180	C₂²	—	2	2	no	—
181	C₂²	C₂×#88048	1	1	yes	characteristic
182	C₂²	#11718681	1	1	yes	characteristic
183	C₂²	#11718688	1	1	yes	characteristic
184	C₄	—	2	2	no	—
185	C₄	—	208	2	no	—
186	C₄	#11718086	1	4	yes	complemented
187	C₄	#11718589	1	1	yes	characteristic
188	C₄	#11718656	1	1	yes	characteristic
189	C₄	#11718669	1	1	yes	characteristic
190	C₄	#11718680	1	1	yes	characteristic
191	C₂	—	2	1	no	—
192	C₂	—	2	1	no	—
193	C₂	#13115599	1	1	yes	characteristic
194	C₂	C₂×#11718086	1	2	yes	—

	subgroup	G/H
center	C₂²	C₂×#88048
commutator	C₂×C₈×C₁₃	C₂²×C₄
Frattini	C₂²×C₈	C₂²×D₁₃
Fitting	C₄×C₁₃×#108	C₂
socle	C₂²×C₁₃	C₂×#106
prime radical	C₂³×C₁₃	C₂×SD₁₆
cosocle	C₂²×C₈×C₁₃	C₂³
hypercenter	C₄×#108	D₁₃
hypocenter	C₁₃	#13183
LCS	G ▷ C₂×C₈×C₁₃ ▷ C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ C₂×C₄×C₈ ◁ C₄×#108

Complements

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

N	H ≅ G/N	type
16. C₄⋊#6090	C₄	semidirect
104. C₄×C₁₃	#365	semidirect
160. C₁₃	#13183	semidirect
186. C₄	#11718086	semidirect

Maximal subgroups

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

subgroup	index
C₂×#11718086	2
#13116592	2
#13114993	2
#13112936	2
C₄×C₁₃×#108	2
#13183	13