Subgroups — #15778241

Order 3328.

358 conjugacy classes of subgroups.

The subgroup lattice has 184 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#11718055	C₂	1	2	yes	maximal
2	C₄×#88052	C₂	1	2	yes	maximal
3	#13112918	C₂	1	2	yes	maximal
4	C₁₃×#1726	C₂	1	1	yes	maximal, characteristic
5	C₂×C₁₃×#97	C₄	1	1	yes	characteristic
6	C₂×C₁₃×#97	C₄	1	1	yes	characteristic
7	C₂×C₁₃×#97	C₄	1	1	yes	characteristic
8	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
9	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
10	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
11	C₁₃×#376	C₄	1	1	yes	characteristic
12	C₂×#88052	C₂²	1	4	yes	—
13	#11718055	C₄	1	8	yes	complemented
14	#11718053	—	2	2	no	—
15	C₄×#6090	—	2	2	no	—
16	C₂²×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
17	C₂²×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
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	C₂×C₄²×C₁₃	C₂×C₄	1	1	yes	characteristic
22	C₂×C₄²×C₁₃	C₂×C₄	1	1	yes	characteristic
23	C₁₃×#97	—	2	2	no	—
24	C₁₃×#97	C₈	1	4	yes	—
25	C₁₃×#97	C₈	1	4	yes	—
26	C₄×C₈×C₁₃	—	2	2	no	—
27	C₄×C₈×C₁₃	C₂×C₄	1	4	yes	—
28	C₄×C₈×C₁₃	D₄	1	2	yes	—
29	C₄×C₈×C₁₃	Q₈	1	2	yes	—
30	C₁₃×#95	—	2	2	no	—
31	#88052	—	2	4	no	—
32	#88052	C₂×C₄	1	8	yes	—
33	C₂×#6090	—	2	4	no	—
34	#12656	—	13	1	no	maximal, Sylow
35	C₂²×C₄×C₁₃	—	2	1	no	—
36	C₂²×C₄×C₁₃	—	2	1	no	—
37	C₂²×C₄×C₁₃	M₁₆	1	2	yes	—
38	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
39	C₂×C₈×C₁₃	—	2	1	no	—
40	C₂×C₈×C₁₃	—	2	1	no	—
41	C₂×C₈×C₁₃	C₄²	1	2	yes	—
42	C₂×C₈×C₁₃	C₄⋊C₄	1	2	yes	—
43	C₂×C₈×C₁₃	C₂×C₈	1	2	yes	—
44	C₂×C₈×C₁₃	C₂×C₈	1	2	yes	—
45	C₂×C₈×C₁₃	C₂×C₈	1	2	yes	—
46	C₂×C₈×C₁₃	C₂×C₈	1	2	yes	—
47	C₂×C₈×C₁₃	M₁₆	1	2	yes	—
48	C₂×C₈×C₁₃	C₂²×C₄	1	2	yes	—
49	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
50	C₂×C₈×C₁₃	C₂×Q₈	1	1	yes	characteristic
51	C₂×C₈×C₁₃	#41	1	2	yes	—
52	C₄²×C₁₃	—	2	1	no	—
53	C₄²×C₁₃	—	2	1	no	—
54	C₄²×C₁₃	C₄²	1	2	yes	—
55	C₄²×C₁₃	C₄⋊C₄	1	2	yes	—
56	C₄²×C₁₃	C₂×C₈	1	2	yes	—
57	C₄²×C₁₃	C₂×C₈	1	2	yes	—
58	#6090	—	2	8	no	—
59	C₂×#364	—	13	2	no	—
60	C₄×M₃₂	—	13	2	no	—
61	#1726	D₁₃	1	1	yes	characteristic
62	#1376	—	13	2	no	—
63	C₂³×C₁₃	C₂×M₁₆	1	1	yes	characteristic
64	C₂×C₄×C₁₃	—	2	2	no	—
65	C₂×C₄×C₁₃	—	2	2	no	—
66	C₂×C₄×C₁₃	—	4	2	no	—
67	C₂×C₄×C₁₃	—	4	2	no	—
68	C₂×C₄×C₁₃	—	4	2	no	—
69	C₂×C₄×C₁₃	C₄⋊C₈	1	4	yes	—
70	C₂×C₄×C₁₃	C₂×C₄²	1	1	yes	characteristic
71	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
72	C₂×C₄×C₁₃	#117	1	1	yes	characteristic
73	C₂×C₄×C₁₃	C₂²×C₈	1	1	yes	characteristic
74	C₂×C₄×C₁₃	C₂²×C₈	1	1	yes	characteristic
75	C₂×C₄×C₁₃	C₂×M₁₆	1	1	yes	characteristic
76	C₈×C₁₃	—	2	2	no	—
77	C₈×C₁₃	C₄×C₈	1	4	yes	—
78	C₈×C₁₃	C₄⋊C₈	1	4	yes	—
79	C₈×C₁₃	C₄×D₄	1	2	yes	—
80	C₈×C₁₃	C₄×Q₈	1	2	yes	—
81	C₂×M₃₂	—	13	4	no	—
82	C₂×#97	Dic₁₃	1	1	yes	characteristic
83	C₂×#97	Dic₁₃	1	1	yes	characteristic
84	C₂×#97	Dic₁₃	1	1	yes	characteristic
85	C₂×C₄×C₈	C₂×D₁₃	1	1	yes	characteristic
86	C₂×C₄×C₈	C₂×D₁₃	1	1	yes	characteristic
87	C₂×C₄×C₈	C₂×D₁₃	1	1	yes	characteristic
88	#376	Dic₁₃	1	1	yes	characteristic
89	#364	—	13	8	no	—
90	#346	—	26	2	no	—
91	C₄×C₁₆	—	26	2	no	—
92	C₂²×C₁₃	—	2	2	no	—
93	C₂²×C₁₃	C₄×M₁₆	1	1	yes	characteristic
94	C₂²×C₁₃	C₂×C₄⋊C₈	1	1	yes	characteristic
95	C₂²×C₁₃	#431	1	1	yes	characteristic
96	C₄×C₁₃	—	2	4	no	—
97	C₄×C₁₃	—	4	2	no	—
98	C₄×C₁₃	—	4	2	no	—
99	C₄×C₁₃	C₄×C₄⋊C₄	1	1	yes	characteristic
100	C₄×C₁₃	C₂×C₄×C₈	1	1	yes	characteristic
101	C₄×C₁₃	C₂×C₄⋊C₈	1	1	yes	characteristic
102	C₄×C₁₃	#431	1	1	yes	characteristic
103	C₂²×C₈	C₂×Dic₁₃	1	1	yes	characteristic
104	C₂²×C₈	C₂×Dic₁₃	1	1	yes	characteristic
105	C₂²×C₈	C₂×Dic₁₃	1	1	yes	characteristic
106	C₂²×C₈	C₂²×D₁₃	1	1	yes	characteristic
107	C₂×C₄²	C₂×Dic₁₃	1	1	yes	characteristic
108	C₂×C₄²	C₂×Dic₁₃	1	1	yes	characteristic
109	C₂×C₄²	C₂×Dic₁₃	1	1	yes	characteristic
110	M₃₂	—	13	8	no	—
111	M₃₂	—	26	4	no	—
112	C₂×C₁₆	—	26	4	no	—
113	#97	—	2	2	no	—
114	#97	#1055	1	4	yes	—
115	#97	#1055	1	4	yes	—
116	C₄×C₈	—	2	2	no	—
117	C₄×C₈	Dic₂₆	1	2	yes	—
118	C₄×C₈	C₄×D₁₃	1	4	yes	—
119	C₄×C₈	D₅₂	1	2	yes	—
120	#95	—	2	2	no	—
121	C₂×C₁₃	—	2	1	no	—
122	C₂×C₁₃	—	2	1	no	—
123	C₂×C₁₃	C₄×C₄⋊C₈	1	1	yes	characteristic
124	C₂×C₁₃	#2153	1	2	yes	—
125	C₂²×C₄	—	2	1	no	—
126	C₂²×C₄	—	2	1	no	—
127	C₂²×C₄	#6099	1	2	yes	—
128	C₂²×C₄	C₂²×Dic₁₃	1	1	yes	characteristic
129	C₂×C₈	—	2	1	no	—
130	C₂×C₈	—	2	1	no	—
131	C₂×C₈	C₂×#1055	1	2	yes	—
132	C₂×C₈	C₂×#1055	1	2	yes	—
133	C₂×C₈	C₂×#1055	1	2	yes	—
134	C₂×C₈	C₂×#1055	1	2	yes	—
135	C₂×C₈	#6099	1	2	yes	—
136	C₂×C₈	C₄×Dic₁₃	1	2	yes	—
137	C₂×C₈	C₄⋊Dic₁₃	1	2	yes	—
138	C₂×C₈	C₂×Dic₂₆	1	1	yes	characteristic
139	C₂×C₈	C₂×C₄×D₁₃	1	2	yes	—
140	C₂×C₈	C₂×D₅₂	1	1	yes	characteristic
141	C₂×C₈	#6127	1	2	yes	—
142	C₄²	—	2	1	no	—
143	C₄²	—	2	1	no	—
144	C₄²	C₂×#1055	1	2	yes	—
145	C₄²	C₂×#1055	1	2	yes	—
146	C₄²	C₄×Dic₁₃	1	2	yes	—
147	C₄²	C₄⋊Dic₁₃	1	2	yes	—
148	C₁₆	—	26	8	no	—
149	C₁₃	#12656	1	1	yes	characteristic, complemented, Sylow
150	C₂³	C₂×#6099	1	1	yes	characteristic
151	C₂×C₄	—	2	2	no	—
152	C₂×C₄	—	2	2	no	—
153	C₂×C₄	—	4	2	no	—
154	C₂×C₄	—	4	2	no	—
155	C₂×C₄	—	4	2	no	—
156	C₂×C₄	C₄⋊#1055	1	4	yes	—
157	C₂×C₄	C₂²×#1055	1	1	yes	characteristic
158	C₂×C₄	C₂²×#1055	1	1	yes	characteristic
159	C₂×C₄	C₂×#6099	1	1	yes	characteristic
160	C₂×C₄	C₂×C₄×Dic₁₃	1	1	yes	characteristic
161	C₂×C₄	C₂×C₄⋊Dic₁₃	1	1	yes	characteristic
162	C₂×C₄	#88180	1	1	yes	characteristic
163	C₈	—	2	2	no	—
164	C₈	C₄×#1055	1	4	yes	—
165	C₈	C₄⋊#1055	1	4	yes	—
166	C₈	C₄×Dic₂₆	1	2	yes	—
167	C₈	C₄×D₅₂	1	2	yes	—
168	C₂²	—	2	2	no	—
169	C₂²	C₄×#6099	1	1	yes	characteristic
170	C₂²	C₂×C₄⋊#1055	1	1	yes	characteristic
171	C₂²	#11718586	1	1	yes	characteristic
172	C₄	—	2	4	no	—
173	C₄	—	4	2	no	—
174	C₄	—	4	2	no	—
175	C₄	C₂×C₄×#1055	1	1	yes	characteristic
176	C₄	C₂×C₄⋊#1055	1	1	yes	characteristic
177	C₄	#11718586	1	1	yes	characteristic
178	C₄	C₄×C₄⋊Dic₁₃	1	1	yes	characteristic
179	C₂	—	2	1	no	—
180	C₂	—	2	1	no	—
181	C₂	C₄×C₄⋊#1055	1	1	yes	characteristic
182	C₂	#13116602	1	2	yes	—

	subgroup	G/H
center	C₂×C₈	C₂×D₅₂
commutator	C₄×C₁₃	C₂×C₄×C₈
Frattini	C₂²×C₈	C₂²×D₁₃
Fitting	C₁₃×#1726	C₂
socle	C₂²×C₁₃	C₂×C₄⋊C₈
prime radical	C₂³×C₁₃	C₂×M₁₆
cosocle	C₂²×C₈×C₁₃	C₂³
hypercenter	#1726	D₁₃
hypocenter	C₁₃	#12656
LCS	G ▷ C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂×C₈ ◁ C₂×C₄×C₈ ◁ #1726

Complements

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

N	H ≅ G/N	type
13. #11718055	C₄	semidirect
149. C₁₃	#12656	semidirect

Maximal subgroups

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

subgroup	index
C₂×#11718055	2
C₄×#88052	2
#13112918	2
C₁₃×#1726	2
#12656	13