Subgroups — #18081238

Order 4864.

298 conjugacy classes of subgroups.

The subgroup lattice has 200 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14564410	C₂	1	2	yes	maximal
2	#14562391	C₂	1	1	yes	maximal, characteristic
3	C₂×#11926295	C₂	1	1	yes	maximal, characteristic
4	#14561531	C₂	1	2	yes	maximal
5	C₈×M₁₆×C₁₉	C₂	1	1	yes	maximal, characteristic
6	C₂×#10597279	—	2	2	no	—
7	#11926568	C₂²	1	2	yes	—
8	C₂×C₄⋊(C₁₉⋊C₈)	C₂²	1	2	yes	—
9	#11926308	—	2	2	no	—
10	#11926295	—	2	1	no	—
11	#11926295	—	2	1	no	—
12	#11926295	C₄	1	2	yes	—
13	#11926295	C₄	1	2	yes	—
14	C₁₉×#431	C₂²	1	1	yes	characteristic
15	C₄×M₁₆×C₁₉	C₂²	1	1	yes	characteristic
16	C₂×C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic
17	C₁₉×#322	—	2	1	no	—
18	C₈²×C₁₉	—	2	1	no	—
19	C₂×M₁₆×C₁₉	D₄	1	2	yes	—
20	C₂²×C₈×C₁₉	Q₈	1	1	yes	characteristic
21	C₂²×C₈×C₁₉	Q₈	1	1	yes	characteristic
22	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
23	C₂×#64520	—	2	2	no	—
24	C₂²×C₁₉⋊C₈	—	2	2	no	—
25	C₁₉×C₄⋊C₈	—	2	1	no	—
26	C₁₉×C₂²⋊C₈	Q₈	1	2	yes	—
27	C₁₉×#97	—	2	1	no	—
28	C₄×C₈×C₁₉	—	2	1	no	—
29	C₄×C₈×C₁₉	—	2	1	no	—
30	C₄×C₈×C₁₉	C₂×C₄	1	1	yes	characteristic
31	C₄×C₈×C₁₉	C₂×C₄	1	1	yes	characteristic
32	C₄×C₈×C₁₉	D₄	1	1	yes	characteristic
33	C₄×C₈×C₁₉	D₄	1	1	yes	characteristic
34	#10597279	—	4	4	no	—
35	C₄⋊(C₁₉⋊C₈)	—	2	2	no	—
36	C₄⋊(C₁₉⋊C₈)	—	2	2	no	—
37	C₄⋊(C₁₉⋊C₈)	—	2	2	no	—
38	C₄⋊(C₁₉⋊C₈)	C₂×C₄	1	4	yes	—
39	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
40	C₂²×C₄×C₁₉	C₂×Q₈	1	1	yes	characteristic
41	C₂²×C₄×C₁₉	C₂×Q₈	1	1	yes	characteristic
42	M₁₆×C₁₉	—	2	2	no	—
43	M₁₆×C₁₉	SD₁₆	1	4	yes	—
44	C₂×C₈×C₁₉	—	2	2	no	—
45	C₂×C₈×C₁₉	—	2	2	no	—
46	C₂×C₈×C₁₉	—	2	2	no	—
47	C₂×C₈×C₁₉	—	4	1	no	—
48	C₂×C₈×C₁₉	C₄⋊C₄	1	1	yes	characteristic
49	C₂×C₈×C₁₉	C₄⋊C₄	1	1	yes	characteristic
50	C₂×C₈×C₁₉	C₄⋊C₄	1	1	yes	characteristic
51	C₂×C₈×C₁₉	C₄⋊C₄	1	1	yes	characteristic
52	C₄²×C₁₉	C₂²×C₄	1	1	yes	characteristic
53	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
54	C₄²×C₁₉	#41	1	1	yes	characteristic
55	C₄²×C₁₉	#41	1	1	yes	characteristic
56	#64520	—	4	2	no	—
57	#64520	—	4	2	no	—
58	C₂×C₁₉⋊C₈	—	2	4	no	—
59	C₂×C₁₉⋊C₈	—	4	2	no	—
60	C₂×C₁₉⋊C₈	—	4	2	no	—
61	C₂×C₁₉⋊C₈	—	4	2	no	—
62	#9623	—	19	1	no	maximal, Sylow
63	C₂³×C₁₉	C₄⋊Q₈	1	1	yes	characteristic
64	C₂×C₄×C₁₉	—	2	1	no	—
65	C₂×C₄×C₁₉	—	2	1	no	—
66	C₂×C₄×C₁₉	—	4	1	no	—
67	C₂×C₄×C₁₉	C₂×C₄⋊C₄	1	1	yes	characteristic
68	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
69	C₂×C₄×C₁₉	C₄×Q₈	1	1	yes	characteristic
70	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
71	C₂×C₄×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
72	C₂×C₄×C₁₉	#125	1	1	yes	characteristic
73	C₂×C₄×C₁₉	C₂×SD₁₆	1	2	yes	—
74	C₂×C₄×C₁₉	#135	1	2	yes	—
75	C₈×C₁₉	—	2	1	no	—
76	C₈×C₁₉	—	2	1	no	—
77	C₈×C₁₉	—	2	1	no	—
78	C₈×C₁₉	—	2	4	no	—
79	C₈×C₁₉	—	4	2	no	—
80	C₈×C₁₉	#108	1	2	yes	complemented
81	C₁₉⋊C₈	—	4	4	no	—
82	C₁₉⋊C₈	—	8	2	no	—
83	#1950	—	19	2	no	—
84	#1566	—	19	1	no	—
85	C₂×#334	—	19	1	no	—
86	C₈×M₁₆	D₁₉	1	1	yes	characteristic
87	#1301	—	19	2	no	—
88	C₂²×C₁₉	—	2	1	no	—
89	C₂²×C₁₉	—	2	1	no	—
90	C₂²×C₁₉	#389	1	1	yes	characteristic
91	C₂²×C₁₉	#498	1	1	yes	characteristic
92	C₂²×C₁₉	#499	1	1	yes	characteristic
93	C₄×C₁₉	—	2	1	no	—
94	C₄×C₁₉	—	2	1	no	—
95	C₄×C₁₉	—	2	1	no	—
96	C₄×C₁₉	C₂×#108	1	1	yes	characteristic
97	C₄×C₁₉	#430	1	1	yes	characteristic
98	C₄×C₁₉	C₄×SD₁₆	1	2	yes	—
99	C₄×C₁₉	#465	1	2	yes	—
100	#431	C₂×D₁₉	1	1	yes	characteristic
101	C₂×#108	—	38	2	no	—
102	#423	—	19	2	no	—
103	C₂×C₄⋊C₈	—	19	2	no	—
104	C₄×M₁₆	C₂×D₁₉	1	1	yes	characteristic
105	C₂×C₄×C₈	C₂×D₁₉	1	1	yes	characteristic
106	#341	—	38	2	no	—
107	#334	—	19	2	no	—
108	#334	—	19	2	no	—
109	#334	—	38	1	no	—
110	#334	—	38	1	no	—
111	#322	—	2	1	no	—
112	C₈²	—	2	1	no	—
113	C₂×C₁₉	—	2	1	no	—
114	C₂×C₁₉	—	2	1	no	—
115	C₂×C₁₉	#1941	1	1	yes	characteristic
116	C₂×C₁₉	#1950	1	1	yes	characteristic
117	C₂×C₁₉	#1953	1	1	yes	characteristic
118	C₂×M₁₆	—	38	2	no	—
119	C₂×M₁₆	D₇₆	1	2	yes	—
120	C₂²×C₈	—	38	2	no	—
121	C₂²×C₈	Dic₃₈	1	1	yes	characteristic
122	C₂²×C₈	Dic₃₈	1	1	yes	characteristic
123	C₂×C₄²	C₂²×D₁₉	1	1	yes	characteristic
124	#108	—	76	4	no	—
125	C₄⋊C₈	—	2	1	no	—
126	C₄⋊C₈	—	19	4	no	—
127	C₄⋊C₈	—	38	2	no	—
128	C₄⋊C₈	—	38	2	no	—
129	C₄⋊C₈	—	38	2	no	—
130	C₂²⋊C₈	Dic₃₈	1	2	yes	—
131	#97	—	2	1	no	—
132	C₄×C₈	—	2	1	no	—
133	C₄×C₈	—	2	1	no	—
134	C₄×C₈	C₄×D₁₉	1	1	yes	characteristic
135	C₄×C₈	C₄×D₁₉	1	1	yes	characteristic
136	C₄×C₈	C₂²⋊D₁₉	1	1	yes	characteristic
137	C₄×C₈	C₂²⋊D₁₉	1	1	yes	characteristic
138	C₁₉	#9623	1	1	yes	characteristic, complemented, Sylow
139	C₂²×C₄	C₂×Dic₃₈	1	1	yes	characteristic
140	C₂²×C₄	C₂×Dic₃₈	1	1	yes	characteristic
141	C₂²×C₄	C₂×D₇₆	1	1	yes	characteristic
142	M₁₆	—	2	2	no	—
143	M₁₆	—	76	2	no	—
144	M₁₆	—	76	2	no	—
145	M₁₆	#64516	1	4	yes	—
146	C₂×C₈	—	2	2	no	—
147	C₂×C₈	—	2	2	no	—
148	C₂×C₈	—	2	2	no	—
149	C₂×C₈	—	4	1	no	—
150	C₂×C₈	—	38	4	no	—
151	C₂×C₈	—	76	2	no	—
152	C₂×C₈	—	76	2	no	—
153	C₂×C₈	—	76	2	no	—
154	C₂×C₈	Dic₁₉⋊C₄	1	1	yes	characteristic
155	C₂×C₈	Dic₁₉⋊C₄	1	1	yes	characteristic
156	C₂×C₈	Dic₁₉⋊C₄	1	1	yes	characteristic
157	C₂×C₈	Dic₁₉⋊C₄	1	1	yes	characteristic
158	C₄²	C₂×C₄×D₁₉	1	1	yes	characteristic
159	C₄²	#64541	1	1	yes	characteristic
160	C₄²	#64541	1	1	yes	characteristic
161	C₄²	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
162	C₂³	#10597315	1	1	yes	characteristic
163	C₂×C₄	—	2	1	no	—
164	C₂×C₄	—	2	1	no	—
165	C₂×C₄	—	4	1	no	—
166	C₂×C₄	C₄×Dic₃₈	1	1	yes	characteristic
167	C₂×C₄	#10597316	1	1	yes	characteristic
168	C₂×C₄	C₄×D₇₆	1	1	yes	characteristic
169	C₂×C₄	C₂×#64516	1	2	yes	—
170	C₂×C₄	#10597350	1	2	yes	—
171	C₂×C₄	C₂×Dic₁₉⋊C₄	1	1	yes	characteristic
172	C₂×C₄	#10597370	1	1	yes	characteristic
173	C₂×C₄	#10597376	1	1	yes	characteristic
174	C₈	—	2	1	no	—
175	C₈	—	2	1	no	—
176	C₈	—	2	1	no	—
177	C₈	—	2	4	no	—
178	C₈	—	4	2	no	—
179	C₈	—	76	4	no	—
180	C₈	—	152	2	no	—
181	C₈	#10597279	1	2	yes	complemented
182	C₂²	—	2	1	no	—
183	C₂²	—	2	1	no	—
184	C₂²	#11926442	1	1	yes	characteristic
185	C₂²	#11926942	1	1	yes	characteristic
186	C₂²	#11926946	1	1	yes	characteristic
187	C₄	—	2	1	no	—
188	C₄	—	2	1	no	—
189	C₄	—	2	1	no	—
190	C₄	C₂×#10597279	1	1	yes	characteristic
191	C₄	#11926592	1	1	yes	characteristic
192	C₄	C₄×#64516	1	2	yes	—
193	C₄	#11926773	1	2	yes	—
194	C₂	—	2	1	no	—
195	C₂	—	2	1	no	—
196	C₂	#14564363	1	1	yes	characteristic
197	C₂	#14564410	1	1	yes	characteristic
198	C₂	#14564425	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	#10597376
commutator	C₄²×C₁₉	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₁₉
Fitting	C₈×M₁₆×C₁₉	C₂
socle	C₂²×C₁₉	#389
prime radical	C₂³×C₁₉	C₄⋊Q₈
cosocle	C₂×C₄²×C₁₉	C₂³
hypercenter	C₈×M₁₆	D₁₉
hypocenter	C₁₉	#9623
LCS	G ▷ C₄²×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ C₈×M₁₆

Complements

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

N	H ≅ G/N	type
80. C₈×C₁₉	#108	semidirect
138. C₁₉	#9623	semidirect
181. C₈	#10597279	semidirect

Maximal subgroups

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

subgroup	index
#14564410	2
#14562391	2
C₂×#11926295	2
#14561531	2
C₈×M₁₆×C₁₉	2
#9623	19