Subgroups — #15761487

Order 3328.

378 conjugacy classes of subgroups.

The subgroup lattice has 216 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13115555	C₂	1	2	yes	maximal
2	C₂×#11718049	C₂	1	1	yes	maximal, characteristic
3	C₂×#11718046	C₂	1	1	yes	maximal, characteristic
4	#13112677	C₂	1	2	yes	maximal
5	C₄×C₁₃×#107	C₂	1	1	yes	maximal, characteristic
6	C₂×C₁₃×#107	C₄	1	2	yes	—
7	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
8	C₄×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
9	C₂×C₄⋊#1055	—	2	2	no	—
10	C₂×C₄⋊#1055	C₂²	1	2	yes	—
11	C₂×C₄×#1055	C₂²	1	1	yes	characteristic
12	C₂×C₄×#1055	C₂²	1	1	yes	characteristic
13	C₁₃×#340	C₄	1	1	yes	characteristic
14	C₁₃×#340	C₄	1	1	yes	characteristic
15	#11718116	—	2	2	no	—
16	#11718049	—	2	2	no	—
17	#11718046	—	2	2	no	—
18	C₂²×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
19	C₂²×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
20	C₂×C₁₃×C₄⋊C₄	C₂×C₄	1	2	yes	—
21	C₂×C₁₃×C₄⋊C₄	C₂×C₄	1	2	yes	—
22	C₂×C₄²×C₁₃	—	2	2	no	—
23	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
24	C₂²×#1055	—	2	1	no	—
25	C₂²×#1055	—	2	2	no	—
26	C₂²×#1055	D₄	1	2	yes	—
27	C₁₃×#107	—	2	4	no	—
28	C₄×C₈×C₁₃	D₄	1	2	yes	—
29	C₄×C₈×C₁₃	Q₈	1	2	yes	—
30	C₁₃×#95	—	2	2	no	—
31	C₄⋊#1055	—	2	2	no	—
32	C₄⋊#1055	—	2	2	no	—
33	C₄⋊#1055	—	4	4	no	—
34	C₄×#1055	—	2	1	no	—
35	C₄×#1055	—	2	1	no	—
36	C₄×#1055	—	2	1	no	—
37	C₄×#1055	Q₈	1	2	yes	—
38	#9599	—	13	1	no	maximal, Sylow
39	C₂²×C₄×C₁₃	—	2	2	no	—
40	C₂²×C₄×C₁₃	—	2	2	no	—
41	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
42	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
43	C₂²×C₄×C₁₃	#41	1	1	yes	characteristic
44	C₂×C₈×C₁₃	—	2	2	no	—
45	C₂×C₈×C₁₃	—	2	2	no	—
46	C₂×C₈×C₁₃	C₄⋊C₄	1	2	yes	—
47	C₂×C₈×C₁₃	C₄⋊C₄	1	2	yes	—
48	C₁₃×C₄⋊C₄	—	2	2	no	—
49	C₁₃×C₄⋊C₄	—	2	2	no	—
50	C₁₃×C₄⋊C₄	—	2	2	no	—
51	C₁₃×C₄⋊C₄	M₁₆	1	4	yes	—
52	C₄²×C₁₃	—	4	2	no	—
53	C₄²×C₁₃	—	4	2	no	—
54	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
55	C₄²×C₁₃	C₂×Q₈	1	1	yes	characteristic
56	C₄²×C₁₃	C₂×Q₈	1	1	yes	characteristic
57	C₄²×C₁₃	#41	1	1	yes	characteristic
58	C₂×#1055	—	2	4	no	—
59	C₂×#1055	—	2	2	no	—
60	C₂×#1055	—	2	2	no	—
61	C₂×#1055	—	2	2	no	—
62	C₂×#1055	—	2	2	no	—
63	C₂×#1055	—	4	2	no	—
64	C₂×#1055	—	4	2	no	—
65	C₂×#1055	—	4	2	no	—
66	#1939	—	13	2	no	—
67	C₄×#107	D₁₃	1	1	yes	characteristic
68	C₂×#334	—	13	1	no	—
69	C₂×#322	—	13	1	no	—
70	#1279	—	13	2	no	—
71	C₂³×C₁₃	C₄×D₄	1	1	yes	characteristic
72	C₂×C₄×C₁₃	—	2	2	no	—
73	C₂×C₄×C₁₃	—	2	4	no	—
74	C₂×C₄×C₁₃	—	4	2	no	—
75	C₂×C₄×C₁₃	—	4	2	no	—
76	C₂×C₄×C₁₃	—	4	2	no	—
77	C₂×C₄×C₁₃	—	4	2	no	—
78	C₂×C₄×C₁₃	—	4	2	no	—
79	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
80	C₂×C₄×C₁₃	C₄×Q₈	1	1	yes	characteristic
81	C₂×C₄×C₁₃	#121	1	1	yes	characteristic
82	C₂×C₄×C₁₃	C₂²⋊Q₈	1	1	yes	characteristic
83	C₂×C₄×C₁₃	#125	1	1	yes	characteristic
84	C₂×C₄×C₁₃	C₄⋊Q₈	1	1	yes	characteristic
85	C₂×C₄×C₁₃	C₂×M₁₆	1	2	yes	—
86	C₂×C₄×C₁₃	#131	1	2	yes	—
87	C₂×C₄×C₁₃	AGL(1,ℤ/8)	1	2	yes	—
88	C₂×C₄×C₁₃	#137	1	2	yes	—
89	C₈×C₁₃	—	2	2	no	—
90	C₈×C₁₃	—	2	2	no	—
91	#1055	—	2	4	no	—
92	#1055	—	4	2	no	—
93	#1055	—	8	2	no	—
94	C₂×#107	Dic₁₃	1	2	yes	—
95	C₂×C₄⋊C₈	—	13	2	no	—
96	C₂×C₄⋊C₈	—	26	2	no	—
97	C₂×C₄×C₈	—	13	1	no	—
98	C₂×C₄×C₈	—	13	1	no	—
99	C₂×C₄×C₈	C₂×D₁₃	1	1	yes	characteristic
100	C₄×C₄⋊C₄	C₂×D₁₃	1	2	yes	—
101	#340	Dic₁₃	1	1	yes	characteristic
102	#340	Dic₁₃	1	1	yes	characteristic
103	#336	—	26	2	no	—
104	#334	—	26	2	no	—
105	#322	—	26	2	no	—
106	C₂²×C₁₃	#389	1	1	yes	characteristic
107	C₂²×C₁₃	#435	1	2	yes	—
108	C₂²×C₁₃	#441	1	1	yes	characteristic
109	C₂²×C₁₃	#442	1	1	yes	characteristic
110	C₂²×C₁₃	#443	1	2	yes	—
111	C₄×C₁₃	—	2	1	no	—
112	C₄×C₁₃	—	2	1	no	—
113	C₄×C₁₃	—	4	4	no	—
114	C₄×C₁₃	—	8	2	no	—
115	C₄×C₁₃	#423	1	1	yes	characteristic
116	C₄×C₁₃	#424	1	1	yes	characteristic
117	C₄×C₁₃	#446	1	2	yes	—
118	C₄×C₁₃	#468	1	2	yes	—
119	C₄×C₁₃	#501	1	2	yes	—
120	C₂²×C₈	—	13	2	no	—
121	C₂²×C₈	—	26	1	no	—
122	C₂²×C₈	—	26	2	no	—
123	C₂²×C₈	C₂×Dic₁₃	1	1	yes	characteristic
124	C₂²×C₈	C₂×Dic₁₃	1	1	yes	characteristic
125	C₂×C₄⋊C₄	C₂×Dic₁₃	1	2	yes	—
126	C₂×C₄⋊C₄	C₂×Dic₁₃	1	2	yes	—
127	C₂×C₄²	—	2	2	no	—
128	C₂×C₄²	C₂²×D₁₃	1	1	yes	characteristic
129	#107	—	2	4	no	—
130	C₄⋊C₈	—	26	2	no	—
131	C₄⋊C₈	—	26	2	no	—
132	C₄⋊C₈	—	52	4	no	—
133	C₄×C₈	—	13	2	no	—
134	C₄×C₈	—	26	1	no	—
135	C₄×C₈	—	26	1	no	—
136	C₄×C₈	—	26	1	no	—
137	C₄×C₈	Dic₂₆	1	2	yes	—
138	C₄×C₈	D₅₂	1	2	yes	—
139	#95	—	2	2	no	—
140	C₂×C₁₃	#1586	1	2	yes	—
141	C₂×C₁₃	#1587	1	2	yes	—
142	C₂×C₁₃	#1940	1	1	yes	characteristic
143	C₂×C₁₃	#1943	1	1	yes	characteristic
144	C₂×C₁₃	#1945	1	1	yes	characteristic
145	C₂²×C₄	—	2	2	no	—
146	C₂²×C₄	—	2	2	no	—
147	C₂²×C₄	D₄×D₁₃	1	1	yes	characteristic
148	C₂²×C₄	#6129	1	1	yes	characteristic
149	C₂²×C₄	C₂²×Dic₁₃	1	1	yes	characteristic
150	C₂×C₈	—	2	2	no	—
151	C₂×C₈	—	2	2	no	—
152	C₂×C₈	—	26	4	no	—
153	C₂×C₈	—	26	2	no	—
154	C₂×C₈	—	26	2	no	—
155	C₂×C₈	—	26	2	no	—
156	C₂×C₈	—	26	2	no	—
157	C₂×C₈	—	52	2	no	—
158	C₂×C₈	—	52	2	no	—
159	C₂×C₈	—	52	2	no	—
160	C₂×C₈	C₄⋊Dic₁₃	1	2	yes	—
161	C₂×C₈	C₄⋊Dic₁₃	1	2	yes	—
162	C₄⋊C₄	—	2	2	no	—
163	C₄⋊C₄	—	2	2	no	—
164	C₄⋊C₄	—	2	2	no	—
165	C₄⋊C₄	#6099	1	4	yes	—
166	C₄²	—	4	2	no	—
167	C₄²	—	4	2	no	—
168	C₄²	C₂×Dic₂₆	1	1	yes	characteristic
169	C₄²	C₂×D₅₂	1	1	yes	characteristic
170	C₄²	Q₈×D₁₃	1	1	yes	characteristic
171	C₄²	#6131	1	1	yes	characteristic
172	C₁₃	#9599	1	1	yes	characteristic, complemented, Sylow
173	C₂³	D₄×Dic₁₃	1	1	yes	characteristic
174	C₂×C₄	—	2	2	no	—
175	C₂×C₄	—	2	4	no	—
176	C₂×C₄	—	4	2	no	—
177	C₂×C₄	—	4	2	no	—
178	C₂×C₄	—	4	2	no	—
179	C₂×C₄	—	4	2	no	—
180	C₂×C₄	—	4	2	no	—
181	C₂×C₄	#88142	1	1	yes	characteristic
182	C₂×C₄	#88144	1	1	yes	characteristic
183	C₂×C₄	#88149	1	1	yes	characteristic
184	C₂×C₄	#88151	1	1	yes	characteristic
185	C₂×C₄	#88165	1	2	yes	—
186	C₂×C₄	#88172	1	2	yes	—
187	C₂×C₄	C₂×#6099	1	2	yes	—
188	C₂×C₄	C₂×C₄⋊Dic₁₃	1	1	yes	characteristic
189	C₂×C₄	Q₈×Dic₁₃	1	1	yes	characteristic
190	C₂×C₄	#88202	1	2	yes	—
191	C₈	—	2	2	no	—
192	C₈	—	2	2	no	—
193	C₈	—	26	4	no	—
194	C₈	—	52	2	no	—
195	C₈	—	104	2	no	—
196	C₂²	#11718646	1	1	yes	characteristic
197	C₂²	#11718672	1	2	yes	—
198	C₂²	#11718813	1	1	yes	characteristic
199	C₂²	#11718845	1	1	yes	characteristic
200	C₂²	#11718857	1	2	yes	—
201	C₄	—	2	1	no	—
202	C₄	—	2	1	no	—
203	C₄	—	4	4	no	—
204	C₄	—	8	2	no	—
205	C₄	#11718537	1	2	yes	—
206	C₄	#11718547	1	2	yes	—
207	C₄	#11718585	1	1	yes	characteristic
208	C₄	#11718660	1	1	yes	characteristic
209	C₄	#11718685	1	2	yes	—
210	C₂	#13113701	1	2	yes	—
211	C₂	#13113708	1	2	yes	—
212	C₂	#13115560	1	1	yes	characteristic
213	C₂	#13115575	1	1	yes	characteristic
214	C₂	#13115585	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄	D₄×D₁₃
commutator	C₂²×C₄×C₁₃	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₁₃
Fitting	C₄×C₁₃×#107	C₂
socle, prime radical	C₂³×C₁₃	C₄×D₄
cosocle	C₂×C₄²×C₁₃	C₂³
hypercenter	C₄×#107	D₁₃
hypocenter	C₁₃	#9599
LCS	G ▷ C₂²×C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂²×C₄ ◁ C₂×C₄² ◁ C₄×#107

Complements

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

N	H ≅ G/N	type
172. C₁₃	#9599	semidirect

Maximal subgroups

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

subgroup	index
#13115555	2
C₂×#11718049	2
C₂×#11718046	2
#13112677	2
C₄×C₁₃×#107	2
#9599	13