Subgroups — #18082363

Order 4864.

494 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	C₂×#11926949	C₂	1	1	yes	maximal, characteristic
2	#14564596	C₂	1	2	yes	maximal
3	#14564437	C₂	1	2	yes	maximal
4	#14563763	C₂	1	1	yes	maximal, characteristic
5	C₂×C₁₉×#322	C₂	1	1	yes	maximal, characteristic
6	C₂×#10597315	C₂²	1	2	yes	—
7	#11926949	—	2	2	no	—
8	#11926949	C₄	1	4	yes	complemented
9	C₂×#10597275	—	2	2	no	—
10	C₂×#10597273	—	2	4	no	—
11	#11926414	C₂²	1	2	yes	—
12	#11926307	—	2	2	no	—
13	#11926307	—	2	4	no	—
14	C₂×C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic
15	C₂×C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic
16	C₂×C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic
17	C₁₉×#322	—	2	2	no	—
18	C₂²×Dic₃₈	—	2	2	no	—
19	C₂²×C₈×C₁₉	D₄	1	2	yes	—
20	C₂²×C₈×C₁₉	D₄	1	2	yes	—
21	C₂²×C₈×C₁₉	D₄	1	2	yes	—
22	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
23	C₂×C₄⋊Dic₁₉	—	2	2	no	—
24	C₂×C₄⋊Dic₁₉	—	2	2	no	—
25	C₂×C₄⋊Dic₁₉	—	2	2	no	—
26	C₂×C₄⋊Dic₁₉	—	2	2	no	—
27	C₂×C₄⋊Dic₁₉	—	2	2	no	—
28	#10597315	—	2	2	no	—
29	#10597315	—	2	2	no	—
30	#10597315	—	2	2	no	—
31	#10597315	C₂×C₄	1	4	yes	—
32	C₄×C₈×C₁₉	—	2	1	no	—
33	C₄×C₈×C₁₉	—	2	1	no	—
34	C₄×C₈×C₁₉	—	2	1	no	—
35	C₄×C₈×C₁₉	—	2	1	no	—
36	C₄×C₈×C₁₉	C₂×C₄	1	2	yes	—
37	C₄×C₈×C₁₉	D₄	1	2	yes	—
38	#10597275	—	2	8	no	—
39	#10597273	—	4	8	no	—
40	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
41	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
42	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
43	C₂²×Dic₁₉	—	4	2	no	—
44	C₂²×Dic₁₉	—	4	2	no	—
45	C₂×Dic₃₈	—	2	4	no	—
46	C₂×Dic₃₈	—	4	4	no	—
47	C₂×Dic₃₈	—	4	4	no	—
48	C₂×Dic₃₈	—	4	2	no	—
49	C₂×C₈×C₁₉	—	2	2	no	—
50	C₂×C₈×C₁₉	—	2	2	no	—
51	C₂×C₈×C₁₉	—	2	4	no	—
52	C₂×C₈×C₁₉	—	2	2	no	—
53	C₂×C₈×C₁₉	—	2	4	no	—
54	C₂×C₈×C₁₉	C₂²⋊C₄	1	4	yes	—
55	C₂×C₈×C₁₉	Q₁₆	1	4	yes	—
56	C₄²×C₁₉	C₂²×C₄	1	1	yes	characteristic
57	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
58	C₄²×C₁₉	#41	1	1	yes	characteristic
59	C₄²×C₁₉	#41	1	1	yes	characteristic
60	C₄⋊Dic₁₉	—	2	4	no	—
61	C₄⋊Dic₁₉	—	2	4	no	—
62	C₄⋊Dic₁₉	—	4	2	no	—
63	C₄⋊Dic₁₉	—	4	2	no	—
64	C₄⋊Dic₁₉	—	4	4	no	—
65	C₄⋊Dic₁₉	—	4	4	no	—
66	C₄⋊Dic₁₉	—	4	4	no	—
67	#9834	—	19	1	no	maximal, Sylow
68	C₂³×C₁₉	#127	1	1	yes	characteristic
69	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
70	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
71	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
72	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
73	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
74	C₂×C₄×C₁₉	#124	1	1	yes	characteristic
75	C₂×C₄×C₁₉	C₂×Q₁₆	1	2	yes	—
76	C₂×C₄×C₁₉	#135	1	2	yes	—
77	C₂×C₄×C₁₉	AGL(1,ℤ/8)	1	4	yes	—
78	C₂×C₄×C₁₉	#137	1	4	yes	—
79	C₂×Dic₁₉	—	4	4	no	—
80	C₂×Dic₁₉	—	8	2	no	—
81	C₂×Dic₁₉	—	8	2	no	—
82	C₂×Dic₁₉	—	8	2	no	—
83	C₂×Dic₁₉	—	8	2	no	—
84	C₂×Dic₁₉	—	8	2	no	—
85	Dic₃₈	—	4	8	no	—
86	Dic₃₈	—	8	4	no	—
87	C₈×C₁₉	—	2	4	no	—
88	C₈×C₁₉	—	2	4	no	—
89	C₈×C₁₉	—	4	2	no	—
90	C₂×#500	—	19	1	no	—
91	#1990	—	19	2	no	—
92	#1956	—	19	2	no	—
93	#1834	—	19	1	no	—
94	C₂×#322	D₁₉	1	1	yes	characteristic
95	C₂²×C₁₉	#390	1	1	yes	characteristic
96	C₂²×C₁₉	#494	1	1	yes	characteristic
97	C₂²×C₁₉	#495	1	1	yes	characteristic
98	C₂²×C₁₉	#496	1	2	yes	—
99	C₂²×C₁₉	#497	1	2	yes	—
100	C₄×C₁₉	#419	1	2	yes	—
101	C₄×C₁₉	C₄×Q₁₆	1	2	yes	—
102	C₄×C₁₉	#442	1	2	yes	—
103	C₄×C₁₉	#467	1	2	yes	—
104	C₄×C₁₉	#469	1	2	yes	—
105	C₄×C₁₉	#491	1	2	yes	—
106	Dic₁₉	—	8	4	no	—
107	Dic₁₉	—	16	2	no	—
108	C₂×C₄⋊Q₈	—	19	2	no	—
109	#500	—	19	4	no	—
110	#500	—	38	2	no	—
111	C₂×#107	—	38	2	no	—
112	C₂×#103	—	38	4	no	—
113	C₂×C₄×C₈	C₂×D₁₉	1	1	yes	characteristic
114	C₂×C₄×C₈	C₂×D₁₉	1	1	yes	characteristic
115	C₂×C₄×C₈	C₂×D₁₉	1	1	yes	characteristic
116	#384	—	19	2	no	—
117	#340	—	38	2	no	—
118	#340	—	38	4	no	—
119	#322	—	2	2	no	—
120	C₂×C₁₉	#1719	1	2	yes	—
121	C₂×C₁₉	#1723	1	2	yes	—
122	C₂×C₁₉	#1960	1	1	yes	characteristic
123	C₂×C₁₉	#1969	1	1	yes	characteristic
124	C₂×C₁₉	#1972	1	1	yes	characteristic
125	C₂²×Q₈	—	38	2	no	—
126	C₂²×C₈	D₇₆	1	2	yes	—
127	C₂²×C₈	D₇₆	1	2	yes	—
128	C₂²×C₈	D₇₆	1	2	yes	—
129	C₄⋊Q₈	—	19	4	no	—
130	C₄⋊Q₈	—	38	2	no	—
131	C₄⋊Q₈	—	38	2	no	—
132	C₄⋊Q₈	—	38	2	no	—
133	C₂×C₄⋊C₄	—	38	2	no	—
134	C₂×C₄⋊C₄	—	38	2	no	—
135	C₂×C₄⋊C₄	—	38	2	no	—
136	C₂×C₄⋊C₄	—	38	2	no	—
137	C₂×C₄⋊C₄	—	38	2	no	—
138	C₂×C₄²	C₂²×D₁₉	1	1	yes	characteristic
139	#107	—	38	8	no	—
140	#103	—	76	8	no	—
141	C₄×C₈	—	2	1	no	—
142	C₄×C₈	—	2	1	no	—
143	C₄×C₈	—	2	1	no	—
144	C₄×C₈	—	2	1	no	—
145	C₄×C₈	C₄×D₁₉	1	2	yes	—
146	C₄×C₈	C₂²⋊D₁₉	1	2	yes	—
147	C₁₉	#9834	1	1	yes	characteristic, complemented, Sylow
148	C₂×Q₈	—	38	4	no	—
149	C₂×Q₈	—	76	2	no	—
150	C₂×Q₈	—	76	4	no	—
151	C₂×Q₈	—	76	4	no	—
152	C₂²×C₄	—	76	2	no	—
153	C₂²×C₄	—	76	2	no	—
154	C₂²×C₄	C₂×D₇₆	1	1	yes	characteristic
155	C₂²×C₄	C₂×D₇₆	1	1	yes	characteristic
156	C₂²×C₄	C₂×D₇₆	1	1	yes	characteristic
157	C₂×C₈	—	2	2	no	—
158	C₂×C₈	—	2	2	no	—
159	C₂×C₈	—	2	4	no	—
160	C₂×C₈	—	2	2	no	—
161	C₂×C₈	—	2	4	no	—
162	C₂×C₈	Dic₇₆	1	4	yes	—
163	C₂×C₈	(C₂×D₁₉)⋊C₄	1	4	yes	—
164	C₄⋊C₄	—	38	4	no	—
165	C₄⋊C₄	—	38	4	no	—
166	C₄⋊C₄	—	76	2	no	—
167	C₄⋊C₄	—	76	2	no	—
168	C₄⋊C₄	—	76	4	no	—
169	C₄⋊C₄	—	76	4	no	—
170	C₄⋊C₄	—	76	4	no	—
171	C₄²	C₂×C₄×D₁₉	1	1	yes	characteristic
172	C₄²	#64541	1	1	yes	characteristic
173	C₄²	#64541	1	1	yes	characteristic
174	C₄²	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
175	C₂³	#10597320	1	1	yes	characteristic
176	Q₈	—	76	8	no	—
177	Q₈	—	152	4	no	—
178	C₂×C₄	—	76	4	no	—
179	C₂×C₄	—	152	2	no	—
180	C₂×C₄	—	152	2	no	—
181	C₂×C₄	—	152	2	no	—
182	C₂×C₄	—	152	2	no	—
183	C₂×C₄	—	152	2	no	—
184	C₂×C₄	C₄×D₇₆	1	1	yes	characteristic
185	C₂×C₄	C₄×D₇₆	1	1	yes	characteristic
186	C₂×C₄	#10597321	1	1	yes	characteristic
187	C₂×C₄	#10597350	1	2	yes	—
188	C₂×C₄	C₂×Dic₇₆	1	2	yes	—
189	C₂×C₄	#10597354	1	4	yes	—
190	C₂×C₄	#10597355	1	4	yes	—
191	C₂×C₄	C₂×(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
192	C₂×C₄	#10597376	1	1	yes	characteristic
193	C₂×C₄	#10597376	1	1	yes	characteristic
194	C₈	—	2	4	no	—
195	C₈	—	2	4	no	—
196	C₈	—	4	2	no	—
197	C₂²	#11926446	1	1	yes	characteristic
198	C₂²	#11926924	1	1	yes	characteristic
199	C₂²	#11926928	1	1	yes	characteristic
200	C₂²	#11926933	1	2	yes	—
201	C₂²	#11926938	1	2	yes	—
202	C₄	—	304	2	no	—
203	C₄	—	152	4	no	—
204	C₄	#11926554	1	2	yes	—
205	C₄	C₄×Dic₇₆	1	2	yes	—
206	C₄	#11926657	1	2	yes	—
207	C₄	#11926785	1	2	yes	—
208	C₄	#11926797	1	2	yes	—
209	C₄	#11926913	1	2	yes	—
210	C₂	#14563288	1	2	yes	—
211	C₂	#14563312	1	2	yes	—
212	C₂	#14564455	1	1	yes	characteristic
213	C₂	#14564496	1	1	yes	characteristic
214	C₂	#14564511	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	#10597320
commutator	C₄²×C₁₉	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₁₉
Fitting	C₂×C₁₉×#322	C₂
socle, prime radical	C₂³×C₁₉	#127
cosocle	C₂×C₄²×C₁₉	C₂³
hypercenter	C₂×#322	D₁₉
hypocenter	C₁₉	#9834
LCS	G ▷ C₄²×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ C₂×#322

Complements

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

N	H ≅ G/N	type
8. #11926949	C₄	semidirect
147. C₁₉	#9834	semidirect

Maximal subgroups

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

subgroup	index
C₂×#11926949	2
#14564596	2
#14564437	2
#14563763	2
C₂×C₁₉×#322	2
#9834	19