Subgroups — #18082298

Order 4864.

526 conjugacy classes of subgroups.

The subgroup lattice has 234 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	#14563795	C₂	1	1	yes	maximal, characteristic
5	C₂×C₈²×C₁₉	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×#10597275	—	2	2	no	—
11	C₂×#10597273	—	2	4	no	—
12	#11926414	C₂²	1	2	yes	—
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	C₈²×C₁₉	—	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	#10597275	—	4	4	no	—
40	#10597273	—	4	8	no	—
41	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
42	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
43	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
44	C₂²×Dic₁₉	—	4	2	no	—
45	C₂²×Dic₁₉	—	4	2	no	—
46	C₂×Dic₃₈	—	2	4	no	—
47	C₂×Dic₃₈	—	4	4	no	—
48	C₂×Dic₃₈	—	4	4	no	—
49	C₂×Dic₃₈	—	4	2	no	—
50	C₂×C₈×C₁₉	—	2	2	no	—
51	C₂×C₈×C₁₉	—	2	2	no	—
52	C₂×C₈×C₁₉	—	2	2	no	—
53	C₂×C₈×C₁₉	—	2	2	no	—
54	C₂×C₈×C₁₉	C₂²⋊C₄	1	4	yes	—
55	C₂×C₈×C₁₉	D₈	1	4	yes	—
56	C₂×C₈×C₁₉	SD₁₆	1	4	yes	—
57	C₂×C₈×C₁₉	Q₁₆	1	4	yes	—
58	C₂×C₈×C₁₉	Q₁₆	1	4	yes	—
59	C₄²×C₁₉	C₂²×C₄	1	1	yes	characteristic
60	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
61	C₄²×C₁₉	#41	1	1	yes	characteristic
62	C₄²×C₁₉	#41	1	1	yes	characteristic
63	C₄⋊Dic₁₉	—	2	4	no	—
64	C₄⋊Dic₁₉	—	2	4	no	—
65	C₄⋊Dic₁₉	—	4	2	no	—
66	C₄⋊Dic₁₉	—	4	2	no	—
67	C₄⋊Dic₁₉	—	4	4	no	—
68	C₄⋊Dic₁₉	—	4	4	no	—
69	C₄⋊Dic₁₉	—	4	4	no	—
70	#9823	—	19	1	no	maximal, Sylow
71	C₂³×C₁₉	#127	1	1	yes	characteristic
72	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
73	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
74	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
75	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
76	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
77	C₂×C₄×C₁₉	#124	1	1	yes	characteristic
78	C₂×C₄×C₁₉	C₂×D₈	1	2	yes	—
79	C₂×C₄×C₁₉	C₂×SD₁₆	1	2	yes	—
80	C₂×C₄×C₁₉	C₂×Q₁₆	1	2	yes	—
81	C₂×C₄×C₁₉	C₂×Q₁₆	1	2	yes	—
82	C₂×C₄×C₁₉	#135	1	2	yes	—
83	C₂×C₄×C₁₉	#135	1	2	yes	—
84	C₂×Dic₁₉	—	4	4	no	—
85	C₂×Dic₁₉	—	8	2	no	—
86	C₂×Dic₁₉	—	8	2	no	—
87	C₂×Dic₁₉	—	8	2	no	—
88	C₂×Dic₁₉	—	8	2	no	—
89	C₂×Dic₁₉	—	8	2	no	—
90	Dic₃₈	—	4	8	no	—
91	Dic₃₈	—	8	4	no	—
92	C₈×C₁₉	—	2	4	no	—
93	C₈×C₁₉	—	2	4	no	—
94	C₈×C₁₉	#103	1	8	yes	complemented
95	C₂×#500	—	19	1	no	—
96	#1990	—	19	2	no	—
97	#1956	—	19	2	no	—
98	#1845	—	19	1	no	—
99	C₂×C₈²	D₁₉	1	1	yes	characteristic
100	C₂²×C₁₉	#390	1	1	yes	characteristic
101	C₂²×C₁₉	#492	1	1	yes	characteristic
102	C₂²×C₁₉	#493	1	1	yes	characteristic
103	C₂²×C₁₉	#494	1	1	yes	characteristic
104	C₂²×C₁₉	#494	1	1	yes	characteristic
105	C₂²×C₁₉	#495	1	1	yes	characteristic
106	C₂²×C₁₉	#495	1	1	yes	characteristic
107	C₄×C₁₉	C₂×#103	1	2	yes	—
108	C₄×C₁₉	C₄×D₈	1	2	yes	—
109	C₄×C₁₉	C₄×Q₁₆	1	2	yes	—
110	C₄×C₁₉	#466	1	2	yes	—
111	C₄×C₁₉	#467	1	2	yes	—
112	C₄×C₁₉	#487	1	2	yes	—
113	Dic₁₉	—	8	4	no	—
114	Dic₁₉	—	16	2	no	—
115	C₂×C₄⋊Q₈	—	19	2	no	—
116	#500	—	19	4	no	—
117	#500	—	38	2	no	—
118	C₂×#107	—	38	2	no	—
119	C₂×#107	—	38	2	no	—
120	C₂×#103	—	38	4	no	—
121	C₂×C₄×C₈	C₂×D₁₉	1	1	yes	characteristic
122	C₂×C₄×C₈	C₂×D₁₉	1	1	yes	characteristic
123	C₂×C₄×C₈	C₂×D₁₉	1	1	yes	characteristic
124	#384	—	19	2	no	—
125	#340	—	38	4	no	—
126	C₈²	—	2	2	no	—
127	C₂×C₁₉	#1706	1	1	yes	characteristic
128	C₂×C₁₉	#1707	1	1	yes	characteristic
129	C₂×C₁₉	#1710	1	1	yes	characteristic
130	C₂×C₁₉	#1713	1	1	yes	characteristic
131	C₂×C₁₉	#1956	1	1	yes	characteristic
132	C₂×C₁₉	#1969	1	1	yes	characteristic
133	C₂×C₁₉	#1970	1	1	yes	characteristic
134	C₂²×Q₈	—	38	2	no	—
135	C₂²×C₈	D₇₆	1	2	yes	—
136	C₂²×C₈	D₇₆	1	2	yes	—
137	C₂²×C₈	D₇₆	1	2	yes	—
138	C₄⋊Q₈	—	19	4	no	—
139	C₄⋊Q₈	—	38	2	no	—
140	C₄⋊Q₈	—	38	2	no	—
141	C₄⋊Q₈	—	38	2	no	—
142	C₂×C₄⋊C₄	—	38	2	no	—
143	C₂×C₄⋊C₄	—	38	2	no	—
144	C₂×C₄⋊C₄	—	38	2	no	—
145	C₂×C₄⋊C₄	—	38	2	no	—
146	C₂×C₄⋊C₄	—	38	2	no	—
147	C₂×C₄²	C₂²×D₁₉	1	1	yes	characteristic
148	#107	—	38	8	no	—
149	#107	—	76	4	no	—
150	#103	—	76	8	no	—
151	C₄×C₈	—	2	1	no	—
152	C₄×C₈	—	2	1	no	—
153	C₄×C₈	—	2	1	no	—
154	C₄×C₈	—	2	1	no	—
155	C₄×C₈	C₄×D₁₉	1	2	yes	—
156	C₄×C₈	C₂²⋊D₁₉	1	2	yes	—
157	C₁₉	#9823	1	1	yes	characteristic, complemented, Sylow
158	C₂×Q₈	—	38	4	no	—
159	C₂×Q₈	—	76	2	no	—
160	C₂×Q₈	—	76	4	no	—
161	C₂×Q₈	—	76	4	no	—
162	C₂²×C₄	—	76	2	no	—
163	C₂²×C₄	—	76	2	no	—
164	C₂²×C₄	C₂×D₇₆	1	1	yes	characteristic
165	C₂²×C₄	C₂×D₇₆	1	1	yes	characteristic
166	C₂²×C₄	C₂×D₇₆	1	1	yes	characteristic
167	C₂×C₈	—	2	2	no	—
168	C₂×C₈	—	2	2	no	—
169	C₂×C₈	—	2	2	no	—
170	C₂×C₈	—	2	2	no	—
171	C₂×C₈	#64516	1	4	yes	—
172	C₂×C₈	D₁₅₂	1	4	yes	—
173	C₂×C₈	Dic₇₆	1	4	yes	—
174	C₂×C₈	Dic₇₆	1	4	yes	—
175	C₂×C₈	(C₂×D₁₉)⋊C₄	1	4	yes	—
176	C₄⋊C₄	—	38	4	no	—
177	C₄⋊C₄	—	38	4	no	—
178	C₄⋊C₄	—	76	2	no	—
179	C₄⋊C₄	—	76	2	no	—
180	C₄⋊C₄	—	76	4	no	—
181	C₄⋊C₄	—	76	4	no	—
182	C₄⋊C₄	—	76	4	no	—
183	C₄²	C₂×C₄×D₁₉	1	1	yes	characteristic
184	C₄²	#64541	1	1	yes	characteristic
185	C₄²	#64541	1	1	yes	characteristic
186	C₄²	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
187	C₂³	#10597320	1	1	yes	characteristic
188	Q₈	—	76	8	no	—
189	Q₈	—	152	4	no	—
190	C₂×C₄	—	76	4	no	—
191	C₂×C₄	—	152	2	no	—
192	C₂×C₄	—	152	2	no	—
193	C₂×C₄	—	152	2	no	—
194	C₂×C₄	—	152	2	no	—
195	C₂×C₄	—	152	2	no	—
196	C₂×C₄	C₄×D₇₆	1	1	yes	characteristic
197	C₂×C₄	C₄×D₇₆	1	1	yes	characteristic
198	C₂×C₄	#10597321	1	1	yes	characteristic
199	C₂×C₄	C₂×#64516	1	2	yes	—
200	C₂×C₄	C₂×D₁₅₂	1	2	yes	—
201	C₂×C₄	#10597350	1	2	yes	—
202	C₂×C₄	#10597350	1	2	yes	—
203	C₂×C₄	C₂×Dic₇₆	1	2	yes	—
204	C₂×C₄	C₂×Dic₇₆	1	2	yes	—
205	C₂×C₄	C₂×(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
206	C₂×C₄	#10597376	1	1	yes	characteristic
207	C₂×C₄	#10597376	1	1	yes	characteristic
208	C₈	—	2	4	no	—
209	C₈	—	2	4	no	—
210	C₈	#10597273	1	8	yes	complemented
211	C₂²	#11926446	1	1	yes	characteristic
212	C₂²	#11926917	1	1	yes	characteristic
213	C₂²	#11926921	1	1	yes	characteristic
214	C₂²	#11926924	1	1	yes	characteristic
215	C₂²	#11926924	1	1	yes	characteristic
216	C₂²	#11926928	1	1	yes	characteristic
217	C₂²	#11926928	1	1	yes	characteristic
218	C₄	—	304	2	no	—
219	C₄	—	152	4	no	—
220	C₄	C₂×#10597273	1	2	yes	—
221	C₄	C₄×D₁₅₂	1	2	yes	—
222	C₄	C₄×Dic₇₆	1	2	yes	—
223	C₄	#11926780	1	2	yes	—
224	C₄	#11926785	1	2	yes	—
225	C₄	#11926895	1	2	yes	—
226	C₂	#14563227	1	1	yes	characteristic
227	C₂	#14563232	1	1	yes	characteristic
228	C₂	#14563245	1	1	yes	characteristic
229	C₂	#14563253	1	1	yes	characteristic
230	C₂	#14564437	1	1	yes	characteristic
231	C₂	#14564496	1	1	yes	characteristic
232	C₂	#14564501	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	#10597320
commutator	C₄²×C₁₉	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₁₉
Fitting	C₂×C₈²×C₁₉	C₂
socle, prime radical	C₂³×C₁₉	#127
cosocle	C₂×C₄²×C₁₉	C₂³
hypercenter	C₂×C₈²	D₁₉
hypocenter	C₁₉	#9823
LCS	G ▷ C₄²×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ C₂×C₈²

Complements

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

N	H ≅ G/N	type
8. #11926949	C₄	semidirect
94. C₈×C₁₉	#103	semidirect
157. C₁₉	#9823	semidirect
210. C₈	#10597273	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
#14563795	2
C₂×C₈²×C₁₉	2
#9823	19