Subgroups — #15761486

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	#13115554	C₂	1	2	yes	maximal
2	C₄×#88058	C₂	1	1	yes	maximal, characteristic
3	C₂×#11718049	C₂	1	1	yes	maximal, characteristic
4	#13112676	C₂	1	2	yes	maximal
5	C₂×C₁₃×#322	C₂	1	1	yes	maximal, characteristic
6	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
7	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
8	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
9	C₂×#88058	C₄	1	2	yes	—
10	C₂×#88054	—	2	2	no	—
11	C₄×C₄⋊Dic₁₃	C₂²	1	2	yes	—
12	C₂×C₄⋊#1055	C₂²	1	2	yes	—
13	C₁₃×#322	—	2	2	no	—
14	#11718143	C₄	1	1	yes	characteristic
15	#11718143	C₄	1	1	yes	characteristic
16	#11718142	—	2	2	no	—
17	#11718049	—	2	2	no	—
18	C₂²×C₈×C₁₃	—	2	1	no	—
19	C₂²×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
20	C₂²×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
21	C₂²×C₈×C₁₃	D₄	1	2	yes	—
22	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
23	C₂×C₄⋊Dic₁₃	C₂×C₄	1	2	yes	—
24	C₂×C₄⋊Dic₁₃	C₂×C₄	1	2	yes	—
25	C₂×C₄×Dic₁₃	—	2	2	no	—
26	C₂²×#1055	—	2	2	no	—
27	C₄×C₈×C₁₃	—	2	1	no	—
28	C₄×C₈×C₁₃	—	2	1	no	—
29	C₄×C₈×C₁₃	—	2	1	no	—
30	C₄×C₈×C₁₃	D₄	1	2	yes	—
31	C₄×C₈×C₁₃	Q₈	1	2	yes	—
32	C₄×C₈×C₁₃	Q₈	1	2	yes	—
33	#88071	—	2	2	no	—
34	#88058	—	2	4	no	—
35	#88054	—	4	4	no	—
36	C₄⋊#1055	—	2	2	no	—
37	C₄⋊#1055	—	2	2	no	—
38	#9599	—	13	1	no	maximal, Sylow
39	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
40	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
41	C₂²×C₄×C₁₃	#41	1	1	yes	characteristic
42	C₂²×Dic₁₃	—	2	2	no	—
43	C₂²×Dic₁₃	—	2	2	no	—
44	C₂×C₈×C₁₃	—	2	4	no	—
45	C₂×C₈×C₁₃	—	2	2	no	—
46	C₂×C₈×C₁₃	—	2	2	no	—
47	C₂×C₈×C₁₃	—	2	2	no	—
48	C₂×C₈×C₁₃	—	2	2	no	—
49	C₂×C₈×C₁₃	—	2	2	no	—
50	C₂×C₈×C₁₃	—	2	2	no	—
51	C₂×C₈×C₁₃	C₄⋊C₄	1	2	yes	—
52	C₂×C₈×C₁₃	C₄⋊C₄	1	2	yes	—
53	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
54	C₄²×C₁₃	C₂×Q₈	1	1	yes	characteristic
55	C₄²×C₁₃	C₂×Q₈	1	1	yes	characteristic
56	C₄²×C₁₃	#41	1	1	yes	characteristic
57	C₄⋊Dic₁₃	—	2	2	no	—
58	C₄⋊Dic₁₃	—	2	2	no	—
59	C₄⋊Dic₁₃	—	2	2	no	—
60	C₄⋊Dic₁₃	M₁₆	1	4	yes	—
61	C₄×Dic₁₃	—	4	2	no	—
62	C₄×Dic₁₃	—	4	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	—	13	1	no	—
68	C₂×#334	—	13	1	no	—
69	C₂×#322	D₁₃	1	1	yes	characteristic
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	C₂×C₄⋊C₄	1	1	yes	characteristic
74	C₂×C₄×C₁₃	C₄×Q₈	1	1	yes	characteristic
75	C₂×C₄×C₁₃	#121	1	1	yes	characteristic
76	C₂×C₄×C₁₃	C₂²⋊Q₈	1	1	yes	characteristic
77	C₂×C₄×C₁₃	#125	1	1	yes	characteristic
78	C₂×C₄×C₁₃	C₄⋊Q₈	1	1	yes	characteristic
79	C₂×C₄×C₁₃	C₂×M₁₆	1	2	yes	—
80	C₂×C₄×C₁₃	#131	1	2	yes	—
81	C₂×C₄×C₁₃	AGL(1,ℤ/8)	1	2	yes	—
82	C₂×C₄×C₁₃	#137	1	2	yes	—
83	C₂×Dic₁₃	—	2	4	no	—
84	C₂×Dic₁₃	—	4	2	no	—
85	C₂×Dic₁₃	—	4	2	no	—
86	C₂×Dic₁₃	—	4	2	no	—
87	C₂×Dic₁₃	—	4	2	no	—
88	C₂×Dic₁₃	—	4	2	no	—
89	C₈×C₁₃	—	2	4	no	—
90	C₈×C₁₃	—	2	2	no	—
91	C₈×C₁₃	—	2	2	no	—
92	C₈×C₁₃	—	4	2	no	—
93	#1055	—	8	2	no	—
94	C₂×#107	—	13	2	no	—
95	C₂×C₄⋊C₈	—	13	2	no	—
96	C₂×C₄⋊C₈	—	26	2	no	—
97	C₂×C₄×C₈	C₂×D₁₃	1	1	yes	characteristic
98	C₂×C₄×C₈	C₂×D₁₃	1	1	yes	characteristic
99	C₂×C₄×C₈	C₂×D₁₃	1	1	yes	characteristic
100	C₄×C₄⋊C₄	—	13	2	no	—
101	#340	—	13	1	no	—
102	#340	—	13	1	no	—
103	#336	—	26	2	no	—
104	#334	—	26	2	no	—
105	#322	—	2	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	#423	1	1	yes	characteristic
114	C₄×C₁₃	#424	1	1	yes	characteristic
115	C₄×C₁₃	#446	1	2	yes	—
116	C₄×C₁₃	#468	1	2	yes	—
117	C₄×C₁₃	#501	1	2	yes	—
118	Dic₁₃	—	4	4	no	—
119	Dic₁₃	—	8	2	no	—
120	C₂²×C₈	—	2	1	no	—
121	C₂²×C₈	—	26	2	no	—
122	C₂²×C₈	C₄×D₁₃	1	1	yes	characteristic
123	C₂²×C₈	C₄×D₁₃	1	1	yes	characteristic
124	C₂²×C₈	D₅₂	1	2	yes	—
125	C₂×C₄⋊C₄	—	13	2	no	—
126	C₂×C₄⋊C₄	—	13	2	no	—
127	C₂×C₄²	—	26	2	no	—
128	C₂×C₄²	C₂²×D₁₃	1	1	yes	characteristic
129	#107	—	26	4	no	—
130	C₄⋊C₈	—	26	2	no	—
131	C₄⋊C₈	—	26	2	no	—
132	C₄⋊C₈	—	52	4	no	—
133	C₄×C₈	—	2	1	no	—
134	C₄×C₈	—	2	1	no	—
135	C₄×C₈	—	2	1	no	—
136	C₄×C₈	Dic₂₆	1	2	yes	—
137	C₄×C₈	Dic₂₆	1	2	yes	—
138	C₄×C₈	C₂²⋊D₁₃	1	2	yes	—
139	#95	—	26	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	—	26	2	no	—
146	C₂²×C₄	—	26	2	no	—
147	C₂²×C₄	C₂×C₄×D₁₃	1	1	yes	characteristic
148	C₂²×C₄	C₂×D₅₂	1	1	yes	characteristic
149	C₂²×C₄	#6127	1	1	yes	characteristic
150	C₂×C₈	—	2	4	no	—
151	C₂×C₈	—	2	2	no	—
152	C₂×C₈	—	2	2	no	—
153	C₂×C₈	—	2	2	no	—
154	C₂×C₈	—	2	2	no	—
155	C₂×C₈	—	2	2	no	—
156	C₂×C₈	—	2	2	no	—
157	C₂×C₈	—	52	2	no	—
158	C₂×C₈	—	52	2	no	—
159	C₂×C₈	—	52	2	no	—
160	C₂×C₈	#6101	1	2	yes	—
161	C₂×C₈	#6101	1	2	yes	—
162	C₄⋊C₄	—	13	4	no	—
163	C₄⋊C₄	—	26	2	no	—
164	C₄⋊C₄	—	26	2	no	—
165	C₄⋊C₄	—	26	2	no	—
166	C₄²	—	52	2	no	—
167	C₄²	—	52	2	no	—
168	C₄²	C₂×Dic₂₆	1	1	yes	characteristic
169	C₄²	C₂×Dic₂₆	1	1	yes	characteristic
170	C₄²	#6127	1	1	yes	characteristic
171	C₄²	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
172	C₁₃	#9599	1	1	yes	characteristic, complemented, Sylow
173	C₂³	C₄×D₅₂	1	1	yes	characteristic
174	C₂×C₄	—	2	2	no	—
175	C₂×C₄	—	26	4	no	—
176	C₂×C₄	—	52	2	no	—
177	C₂×C₄	—	52	2	no	—
178	C₂×C₄	—	52	2	no	—
179	C₂×C₄	—	52	2	no	—
180	C₂×C₄	—	52	2	no	—
181	C₂×C₄	C₄×Dic₂₆	1	1	yes	characteristic
182	C₂×C₄	#88123	1	1	yes	characteristic
183	C₂×C₄	#88124	1	1	yes	characteristic
184	C₂×C₄	M₁₆×D₁₃	1	2	yes	—
185	C₂×C₄	#88161	1	2	yes	—
186	C₂×C₄	#88162	1	2	yes	—
187	C₂×C₄	#88163	1	2	yes	—
188	C₂×C₄	C₂×#6101	1	1	yes	characteristic
189	C₂×C₄	#88178	1	1	yes	characteristic
190	C₂×C₄	#88184	1	1	yes	characteristic
191	C₈	—	2	4	no	—
192	C₈	—	2	2	no	—
193	C₈	—	2	2	no	—
194	C₈	—	4	2	no	—
195	C₈	—	104	2	no	—
196	C₂²	#11718361	1	2	yes	—
197	C₂²	#11718367	1	2	yes	—
198	C₂²	#11718372	1	1	yes	characteristic
199	C₂²	#11718377	1	1	yes	characteristic
200	C₂²	#11718589	1	1	yes	characteristic
201	C₄	—	2	1	no	—
202	C₄	—	2	1	no	—
203	C₄	—	52	4	no	—
204	C₄	—	104	2	no	—
205	C₄	#11718362	1	2	yes	—
206	C₄	#11718363	1	2	yes	—
207	C₄	#11718779	1	1	yes	characteristic
208	C₄	#11718780	1	1	yes	characteristic
209	C₄	#11718795	1	2	yes	—
210	C₂	#13113702	1	2	yes	—
211	C₂	#13113709	1	2	yes	—
212	C₂	#13115559	1	1	yes	characteristic
213	C₂	#13115574	1	1	yes	characteristic
214	C₂	#13115584	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄	C₂×D₅₂
commutator	C₂²×C₄×C₁₃	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₁₃
Fitting	C₂×C₁₃×#322	C₂
socle, prime radical	C₂³×C₁₃	C₄×D₄
cosocle	C₂×C₄²×C₁₃	C₂³
hypercenter	C₂×#322	D₁₃
hypocenter	C₁₃	#9599
LCS	G ▷ C₂²×C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂²×C₄ ◁ C₂×C₄×C₈ ◁ C₂×#322

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
#13115554	2
C₄×#88058	2
C₂×#11718049	2
#13112676	2
C₂×C₁₃×#322	2
#9599	13