Subgroups — #16030262

Order 3328.

1598 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	#13120811	C₂	1	8	yes	maximal, complemented
2	#13120806	C₂	1	8	yes	maximal
3	#13118141	C₂	1	8	yes	maximal, complemented
4	#13117319	C₂	1	4	yes	maximal
5	#13117243	C₂	1	2	yes	maximal
6	C₂×C₁₃×#376	C₂	1	1	yes	maximal, characteristic
7	C₂²×C₄²×C₁₃	C₂²	1	2	yes	—
8	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic
9	C₂×#88180	C₂²	1	4	yes	—
10	C₁₃×#376	C₂²	1	4	yes	—
11	C₁₃×#376	C₂²	1	4	yes	—
12	C₂×C₁₃×#95	C₂²	1	4	yes	—
13	#11718873	C₂²	1	8	yes	—
14	#11718871	C₂²	1	16	yes	—
15	#11718597	C₂²	1	4	yes	—
16	#11718596	C₂²	1	4	yes	—
17	C₄×C₄⋊Dic₁₃	C₂²	1	8	yes	—
18	C₄×#6101	C₂²	1	16	yes	—
19	#11718589	C₂²	1	16	yes	—
20	#11718321	C₂²	1	32	yes	—
21	#11718318	C₂²	1	32	yes	—
22	C₂³×C₄×C₁₃	C₂³	1	4	yes	—
23	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
24	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
25	C₂×C₄²×C₁₃	—	2	8	no	—
26	C₂×C₄²×C₁₃	Q₈	1	8	yes	—
27	C₂×C₄²×C₁₃	C₂³	1	4	yes	—
28	C₂×C₄²×C₁₃	C₂³	1	4	yes	—
29	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
30	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
31	C₂×C₂²⋊Dic₁₃	C₂³	1	8	yes	—
32	#88180	—	2	16	no	—
33	C₂×C₄⋊Dic₁₃	C₂³	1	8	yes	—
34	C₂×C₄⋊Dic₁₃	C₂³	1	16	yes	—
35	C₂×#6101	C₂³	1	32	yes	—
36	C₂×C₄×Dic₁₃	C₂³	1	8	yes	—
37	C₁₃×#95	C₂³	1	16	yes	—
38	#88071	C₂³	1	16	yes	—
39	#88071	C₂³	1	32	yes	—
40	#34638	—	13	1	no	maximal, Sylow
41	C₂⁴×C₁₃	C₂⁴	1	1	yes	characteristic
42	C₂²×C₄×C₁₃	—	2	8	no	—
43	C₂²×C₄×C₁₃	—	4	4	no	—
44	C₂²×C₄×C₁₃	—	4	8	no	—
45	C₂²×C₄×C₁₃	C₂×Q₈	1	8	yes	—
46	C₂²×C₄×C₁₃	C₂×Q₈	1	4	yes	—
47	C₂²×C₄×C₁₃	#41	1	8	yes	—
48	C₂²×C₄×C₁₃	C₂⁴	1	8	yes	—
49	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
50	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
51	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
52	C₂²×Dic₁₃	C₂⁴	1	16	yes	—
53	C₄²×C₁₃	—	2	8	no	—
54	C₄²×C₁₃	—	2	8	no	—
55	C₄²×C₁₃	C₂×Q₈	1	8	yes	—
56	C₄²×C₁₃	C₂×Q₈	1	8	yes	—
57	C₂²⋊Dic₁₃	—	2	16	no	—
58	C₄⋊Dic₁₃	—	2	16	no	—
59	C₄⋊Dic₁₃	—	4	16	no	—
60	#6101	—	4	32	no	—
61	C₄×Dic₁₃	—	2	16	no	—
62	#2647	—	13	8	no	—
63	#2646	—	13	8	no	—
64	#2402	—	13	8	no	—
65	#2296	—	13	4	no	—
66	#2285	—	13	2	no	—
67	C₂×#376	D₁₃	1	1	yes	characteristic
68	C₂³×C₁₃	—	2	4	no	—
69	C₂³×C₁₃	C₂²×Q₈	1	2	yes	—
70	C₂³×C₁₃	C₂×#41	1	4	yes	—
71	C₂³×C₁₃	C₂⁵	1	1	yes	characteristic
72	C₂×C₄×C₁₃	—	2	8	no	—
73	C₂×C₄×C₁₃	—	2	8	no	—
74	C₂×C₄×C₁₃	—	2	16	no	—
75	C₂×C₄×C₁₃	—	4	8	no	—
76	C₂×C₄×C₁₃	—	4	16	no	—
77	C₂×C₄×C₁₃	#125	1	16	yes	—
78	C₂×C₄×C₁₃	C₂²×Q₈	1	8	yes	—
79	C₂×C₄×C₁₃	C₂²×Q₈	1	2	yes	—
80	C₂×C₄×C₁₃	C₂²×Q₈	1	2	yes	—
81	C₂×C₄×C₁₃	C₂×#41	1	4	yes	—
82	C₂×C₄×C₁₃	C₂×#41	1	4	yes	—
83	C₂×Dic₁₃	—	2	16	no	—
84	C₂×Dic₁₃	—	2	32	no	—
85	C₂×#117	—	13	4	no	—
86	C₂²×C₄²	C₂×D₁₃	1	2	yes	—
87	C₂²×C₄²	C₂×D₁₃	1	1	yes	characteristic
88	#400	—	13	32	no	—
89	#398	—	13	32	no	—
90	#389	—	13	16	no	—
91	#385	—	13	16	no	—
92	#384	—	13	4	no	—
93	#382	—	13	4	no	—
94	#380	—	13	8	no	—
95	C₄×C₄⋊C₄	—	13	16	no	—
96	C₄×C₄⋊C₄	—	13	8	no	—
97	#376	C₂×D₁₃	1	4	yes	—
98	#376	C₂×D₁₃	1	4	yes	—
99	C₂×#95	C₂×D₁₃	1	4	yes	—
100	C₂²×C₁₃	—	2	8	no	—
101	C₂²×C₁₃	—	2	4	no	—
102	C₂²×C₁₃	C₂×#125	1	4	yes	—
103	C₂²×C₁₃	C₂³×Q₈	1	1	yes	characteristic
104	C₂²×C₁₃	C₂²×#41	1	2	yes	—
105	C₂²×C₁₃	#585	1	4	yes	—
106	C₄×C₁₃	—	2	8	no	—
107	C₄×C₁₃	—	4	8	no	—
108	C₄×C₁₃	C₂×#125	1	4	yes	—
109	C₄×C₁₃	C₂×#125	1	4	yes	—
110	Dic₁₃	—	4	16	no	—
111	C₂³×C₄	C₂²×D₁₃	1	4	yes	—
112	C₂³×C₄	C₂²×D₁₃	1	2	yes	—
113	C₂³×C₄	C₂²×D₁₃	1	1	yes	characteristic
114	#117	—	26	16	no	—
115	C₂×C₄⋊C₄	—	13	8	no	—
116	C₂×C₄⋊C₄	—	13	32	no	—
117	C₂×C₄⋊C₄	—	13	16	no	—
118	C₂×C₂²⋊C₄	—	13	8	no	—
119	C₂×C₄²	—	2	8	no	—
120	C₂×C₄²	—	13	8	no	—
121	C₂×C₄²	Dic₂₆	1	8	yes	—
122	C₂×C₄²	C₂²×D₁₃	1	4	yes	—
123	C₂×C₄²	C₂²×D₁₃	1	4	yes	—
124	C₂×C₄²	C₂²×D₁₃	1	2	yes	—
125	C₂×C₄²	C₂²×D₁₃	1	2	yes	—
126	#95	—	13	16	no	—
127	#95	—	13	32	no	—
128	#95	C₂²×D₁₃	1	16	yes	—
129	C₂×C₁₃	—	2	4	no	—
130	C₂×C₁₃	C₂²×#125	1	1	yes	characteristic
131	C₂×C₁₃	#3455	1	4	yes	—
132	C₂×C₁₃	#3458	1	2	yes	—
133	C₂⁴	C₂³×D₁₃	1	1	yes	characteristic
134	C₂²×C₄	—	2	8	no	—
135	C₂²×C₄	—	4	4	no	—
136	C₂²×C₄	—	4	8	no	—
137	C₂²×C₄	—	13	16	no	—
138	C₂²×C₄	C₂×Dic₂₆	1	8	yes	—
139	C₂²×C₄	C₂×Dic₂₆	1	4	yes	—
140	C₂²×C₄	#6127	1	8	yes	—
141	C₂²×C₄	C₂³×D₁₃	1	8	yes	—
142	C₂²×C₄	C₂³×D₁₃	1	4	yes	—
143	C₂²×C₄	C₂³×D₁₃	1	1	yes	characteristic
144	C₂²×C₄	C₂³×D₁₃	1	1	yes	characteristic
145	C₄⋊C₄	—	26	16	no	—
146	C₄⋊C₄	—	52	32	no	—
147	C₄⋊C₄	—	52	16	no	—
148	C₂²⋊C₄	—	26	16	no	—
149	C₄²	—	2	8	no	—
150	C₄²	—	2	8	no	—
151	C₄²	—	26	16	no	—
152	C₄²	C₂×Dic₂₆	1	8	yes	—
153	C₄²	C₂×Dic₂₆	1	8	yes	—
154	C₁₃	#34638	1	1	yes	characteristic, complemented, Sylow
155	C₂³	—	2	4	no	—
156	C₂³	C₂²×Dic₂₆	1	2	yes	—
157	C₂³	C₂×#6127	1	4	yes	—
158	C₂³	C₂⁴×D₁₃	1	1	yes	characteristic
159	C₂×C₄	—	2	8	no	—
160	C₂×C₄	—	2	8	no	—
161	C₂×C₄	—	2	16	no	—
162	C₂×C₄	—	4	8	no	—
163	C₂×C₄	—	4	16	no	—
164	C₂×C₄	—	26	16	no	—
165	C₂×C₄	—	26	32	no	—
166	C₂×C₄	#88124	1	16	yes	—
167	C₂×C₄	C₂²×Dic₂₆	1	8	yes	—
168	C₂×C₄	C₂²×Dic₂₆	1	2	yes	—
169	C₂×C₄	C₂²×Dic₂₆	1	2	yes	—
170	C₂×C₄	C₂×#6127	1	4	yes	—
171	C₂×C₄	C₂×#6127	1	4	yes	—
172	C₂²	—	2	8	no	—
173	C₂²	—	2	4	no	—
174	C₂²	C₂×#88124	1	4	yes	—
175	C₂²	C₂³×Dic₂₆	1	1	yes	characteristic
176	C₂²	C₂²×#6127	1	2	yes	—
177	C₂²	#11719648	1	4	yes	—
178	C₄	—	2	8	no	—
179	C₄	—	4	8	no	—
180	C₄	—	52	16	no	—
181	C₄	C₂×#88124	1	4	yes	—
182	C₄	C₂×#88124	1	4	yes	—
183	C₂	—	2	4	no	—
184	C₂	C₂²×#88124	1	1	yes	characteristic
185	C₂	#13128226	1	4	yes	—
186	C₂	#13128241	1	2	yes	—

	subgroup	G/H
center	C₂²×C₄	C₂³×D₁₃
commutator, socle, cosocle	C₂³×C₁₃	C₂⁵
Frattini	C₂³	C₂⁴×D₁₃
Fitting	C₂×C₁₃×#376	C₂
prime radical	C₂⁴×C₁₃	C₂⁴
hypercenter	C₂×#376	D₁₃
hypocenter	C₁₃	#34638
LCS	G ▷ C₂³×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂²×C₄ ◁ C₂×#376

Complements

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

N	H ≅ G/N	type
1. #13120811	C₂	semidirect
3. #13118141	C₂	semidirect
154. C₁₃	#34638	semidirect

Maximal subgroups

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

subgroup	index
#13120811	2
#13120806	2
#13118141	2
#13117319	2
#13117243	2
C₂×C₁₃×#376	2
#34638	13