Subgroups — #18069476

Order 4864.

274 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×#11926320	C₂	1	1	yes	maximal, characteristic
2	C₂×#11926295	C₂	1	1	yes	maximal, characteristic
3	C₄×C₁₉×#107	C₂	1	1	yes	maximal, characteristic
4	C₂²×C₁₉⋊C₁₆	—	2	1	no	—
5	C₂×C₄⋊(C₁₉⋊C₈)	—	2	1	no	—
6	#11926320	—	2	1	no	—
7	#11926320	C₄	1	2	yes	complemented
8	#11926295	—	2	1	no	—
9	#11926295	C₄	1	2	yes	complemented
10	C₂×C₁₉×#107	C₄	1	2	yes	—
11	C₂×C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic
12	C₄×C₄⋊C₄×C₁₉	—	2	1	no	—
13	C₁₉×#340	—	2	1	no	—
14	C₂²×C₈×C₁₉	C₂×C₄	1	1	yes	characteristic
15	C₂²×C₈×C₁₉	D₄	1	1	yes	characteristic
16	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
17	C₂×C₄²×C₁₉	—	4	1	no	—
18	C₂×C₄²×C₁₉	D₄	1	1	yes	characteristic
19	C₂²×C₁₉⋊C₈	—	4	1	no	—
20	C₁₉×#107	—	2	2	no	—
21	C₁₉×#107	C₈	1	4	yes	complemented
22	C₄×C₈×C₁₉	C₂×C₄	1	1	yes	characteristic
23	C₄×C₈×C₁₉	C₂×C₄	1	1	yes	characteristic
24	C₄×C₈×C₁₉	D₄	1	1	yes	characteristic
25	C₄×C₈×C₁₉	Q₈	1	1	yes	characteristic
26	C₁₉×#95	—	4	1	no	—
27	C₂×C₁₉⋊C₁₆	—	2	4	no	—
28	C₂×C₁₉⋊C₁₆	—	2	2	no	—
29	C₄⋊(C₁₉⋊C₈)	—	2	2	no	—
30	C₄⋊(C₁₉⋊C₈)	—	4	1	no	—
31	C₂²×C₄×C₁₉	—	4	2	no	—
32	C₂²×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
33	C₂²×C₄×C₁₉	D₈	1	1	yes	characteristic
34	C₂²×C₄×C₁₉	SD₁₆	1	1	yes	characteristic
35	C₂×C₈×C₁₉	—	2	2	no	—
36	C₂×C₈×C₁₉	C₄²	1	1	yes	characteristic
37	C₂×C₈×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
38	C₂×C₈×C₁₉	C₄⋊C₄	1	1	yes	characteristic
39	C₂×C₈×C₁₉	C₄⋊C₄	1	1	yes	characteristic
40	C₂×C₈×C₁₉	C₂×C₈	1	2	yes	—
41	C₂×C₈×C₁₉	M₁₆	1	2	yes	—
42	C₄⋊C₄×C₁₉	—	2	4	no	—
43	C₄⋊C₄×C₁₉	—	4	2	no	—
44	C₄²×C₁₉	—	8	2	no	—
45	C₄²×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
46	C₄²×C₁₉	C₄⋊C₄	1	1	yes	characteristic
47	C₄²×C₁₉	SD₁₆	1	1	yes	characteristic
48	C₄²×C₁₉	Q₁₆	1	1	yes	characteristic
49	C₂×C₁₉⋊C₈	—	4	2	no	—
50	C₂×C₁₉⋊C₈	—	8	2	no	—
51	C₁₉⋊C₁₆	—	2	4	no	—
52	#7178	—	19	1	no	maximal, Sylow
53	C₂³×C₁₉	#102	1	1	yes	characteristic
54	C₂×C₄×C₁₉	—	2	2	no	—
55	C₂×C₄×C₁₉	—	2	1	no	—
56	C₂×C₄×C₁₉	—	2	1	no	—
57	C₂×C₄×C₁₉	—	4	4	no	—
58	C₂×C₄×C₁₉	—	8	2	no	—
59	C₂×C₄×C₁₉	—	8	2	no	—
60	C₂×C₄×C₁₉	#95	1	1	yes	characteristic
61	C₂×C₄×C₁₉	C₂²⋊C₈	1	2	yes	—
62	C₂×C₄×C₁₉	#102	1	1	yes	characteristic
63	C₂×C₄×C₁₉	#103	1	1	yes	characteristic
64	C₂×C₄×C₁₉	#103	1	1	yes	characteristic
65	C₂×C₄×C₁₉	#104	1	2	yes	—
66	C₂×C₄×C₁₉	#106	1	1	yes	characteristic
67	C₂×C₄×C₁₉	#107	1	1	yes	characteristic
68	C₈×C₁₉	—	2	1	no	—
69	C₈×C₁₉	—	2	1	no	—
70	C₈×C₁₉	C₄×C₈	1	1	yes	characteristic
71	C₈×C₁₉	#97	1	1	yes	characteristic
72	C₈×C₁₉	C₄⋊C₈	1	2	yes	—
73	C₁₉⋊C₈	—	8	2	no	—
74	C₂×#346	—	19	1	no	—
75	C₄×#107	D₁₉	1	1	yes	characteristic
76	C₂×#334	—	19	1	no	—
77	C₂²×C₁₉	D₄⋊C₈	1	2	yes	—
78	C₂²×C₁₉	#340	1	1	yes	characteristic
79	C₂²×C₁₉	#360	1	2	yes	—
80	C₂²×C₁₉	#361	1	1	yes	characteristic
81	C₂²×C₁₉	#362	1	1	yes	characteristic
82	C₄×C₁₉	—	2	1	no	—
83	C₄×C₁₉	—	2	1	no	—
84	C₄×C₁₉	—	2	1	no	—
85	C₄×C₁₉	—	2	1	no	—
86	C₄×C₁₉	—	8	4	no	—
87	C₄×C₁₉	Q₈⋊C₈	1	2	yes	—
88	C₄×C₁₉	#336	1	1	yes	characteristic
89	C₄×C₁₉	#339	1	1	yes	characteristic
90	C₂²×C₁₆	—	38	1	no	—
91	C₂×#107	Dic₁₉	1	2	yes	—
92	C₂×C₄⋊C₈	—	38	1	no	—
93	C₂×C₄×C₈	C₂×D₁₉	1	1	yes	characteristic
94	C₄×C₄⋊C₄	—	2	1	no	—
95	#346	—	19	2	no	—
96	#346	—	38	1	no	—
97	#340	—	2	1	no	—
98	#334	—	19	2	no	—
99	#334	—	38	1	no	—
100	C₂×C₁₉	#1279	1	1	yes	characteristic
101	C₂×C₁₉	#1333	1	2	yes	—
102	C₂×C₁₉	#1334	1	2	yes	—
103	C₂×C₁₉	#1386	1	1	yes	characteristic
104	C₂×C₁₉	#1387	1	1	yes	characteristic
105	C₂²×C₈	—	76	1	no	—
106	C₂²×C₈	C₂×Dic₁₉	1	1	yes	characteristic
107	C₂²×C₈	C₂²⋊D₁₉	1	1	yes	characteristic
108	C₂×C₄⋊C₄	—	2	2	no	—
109	C₂×C₄²	—	4	1	no	—
110	C₂×C₄²	C₂²⋊D₁₉	1	1	yes	characteristic
111	C₂×C₁₆	—	38	4	no	—
112	C₂×C₁₆	—	38	2	no	—
113	#107	—	2	2	no	—
114	#107	C₁₉⋊C₈	1	4	yes	complemented
115	C₄⋊C₈	—	38	2	no	—
116	C₄⋊C₈	—	76	1	no	—
117	C₄×C₈	Dic₃₈	1	1	yes	characteristic
118	C₄×C₈	C₄×D₁₉	1	1	yes	characteristic
119	C₄×C₈	C₄×D₁₉	1	1	yes	characteristic
120	C₄×C₈	D₇₆	1	1	yes	characteristic
121	#95	—	4	1	no	—
122	C₁₉	#7178	1	1	yes	characteristic, complemented, Sylow
123	C₂²×C₄	—	4	2	no	—
124	C₂²×C₄	#64525	1	1	yes	characteristic
125	C₂²×C₄	#64526	1	1	yes	characteristic
126	C₂²×C₄	C₂²⋊Dic₁₉	1	1	yes	characteristic
127	C₂×C₈	—	2	2	no	—
128	C₂×C₈	—	76	2	no	—
129	C₂×C₈	—	152	2	no	—
130	C₂×C₈	C₂×C₁₉⋊C₈	1	2	yes	—
131	C₂×C₈	#64520	1	2	yes	—
132	C₂×C₈	C₄×Dic₁₉	1	1	yes	characteristic
133	C₂×C₈	Dic₁₉⋊C₄	1	1	yes	characteristic
134	C₂×C₈	C₄⋊Dic₁₉	1	1	yes	characteristic
135	C₂×C₈	(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
136	C₄⋊C₄	—	2	4	no	—
137	C₄⋊C₄	—	4	2	no	—
138	C₄²	—	8	2	no	—
139	C₄²	Dic₁₉⋊C₄	1	1	yes	characteristic
140	C₄²	(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
141	C₄²	#64527	1	1	yes	characteristic
142	C₄²	#64528	1	1	yes	characteristic
143	C₁₆	—	38	4	no	—
144	C₂³	#10597289	1	1	yes	characteristic
145	C₂×C₄	—	2	2	no	—
146	C₂×C₄	—	2	1	no	—
147	C₂×C₄	—	2	1	no	—
148	C₂×C₄	—	4	4	no	—
149	C₂×C₄	—	8	2	no	—
150	C₂×C₄	—	8	2	no	—
151	C₂×C₄	#10597264	1	1	yes	characteristic
152	C₂×C₄	#10597265	1	1	yes	characteristic
153	C₂×C₄	#10597266	1	1	yes	characteristic
154	C₂×C₄	#10597267	1	1	yes	characteristic
155	C₂×C₄	C₂²⋊(C₁₉⋊C₈)	1	2	yes	—
156	C₂×C₄	C₁₉⋊#95	1	1	yes	characteristic
157	C₂×C₄	#10597292	1	1	yes	characteristic
158	C₂×C₄	#10597294	1	2	yes	—
159	C₈	—	2	1	no	—
160	C₈	—	2	1	no	—
161	C₈	—	152	2	no	—
162	C₈	C₄×C₁₉⋊C₈	1	1	yes	characteristic
163	C₈	#10597260	1	1	yes	characteristic
164	C₈	C₄⋊(C₁₉⋊C₈)	1	2	yes	—
165	C₂²	D₄⋊(C₁₉⋊C₈)	1	2	yes	—
166	C₂²	#11926306	1	1	yes	characteristic
167	C₂²	#11926354	1	2	yes	—
168	C₂²	#11926357	1	1	yes	characteristic
169	C₂²	#11926360	1	1	yes	characteristic
170	C₄	—	2	1	no	—
171	C₄	—	2	1	no	—
172	C₄	—	2	1	no	—
173	C₄	—	2	1	no	—
174	C₄	—	8	4	no	—
175	C₄	Q₈⋊(C₁₉⋊C₈)	1	2	yes	—
176	C₄	#11926299	1	1	yes	characteristic
177	C₄	#11926303	1	1	yes	characteristic
178	C₂	#14561476	1	1	yes	characteristic
179	C₂	#14561602	1	2	yes	—
180	C₂	#14561605	1	2	yes	—
181	C₂	#14561740	1	1	yes	characteristic
182	C₂	#14561743	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	#10597289
commutator	C₈×C₁₉	C₄×C₈
Frattini	C₂×C₄×C₈	C₂×D₁₉
Fitting	C₄×C₁₉×#107	C₂
socle, prime radical	C₂³×C₁₉	#102
cosocle	C₂×C₄×C₈×C₁₉	C₂²
hypercenter	C₄×#107	D₁₉
hypocenter	C₁₉	#7178
LCS	G ▷ C₈×C₁₉ ▷ C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ C₂×C₄×C₈ ◁ C₄×#107

Complements

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

N	H ≅ G/N	type
7. #11926320	C₄	semidirect
9. #11926295	C₄	semidirect
21. C₁₉×#107	C₈	semidirect
114. #107	C₁₉⋊C₈	semidirect
122. C₁₉	#7178	semidirect

Maximal subgroups

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

subgroup	index
C₂×#11926320	2
C₂×#11926295	2
C₄×C₁₉×#107	2
#7178	19