Subgroups — #14566903

Order 2432.

528 conjugacy classes of subgroups.

The subgroup lattice has 258 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄×Dic₃₈	C₂	1	1	yes	maximal, characteristic, complemented
2	#11926483	C₂	1	1	yes	maximal, characteristic, complemented
3	#11926480	C₂	1	1	yes	maximal, characteristic
4	#11926477	C₂	1	2	yes	maximal, complemented
5	#11926467	C₂	1	2	yes	maximal
6	#11926464	C₂	1	1	yes	maximal, characteristic, complemented
7	#11926456	C₂	1	1	yes	maximal, characteristic
8	C₄×Dic₁₉⋊C₄	C₂	1	2	yes	maximal, complemented
9	C₄×C₄⋊Dic₁₉	C₂	1	1	yes	maximal, characteristic, complemented
10	C₄×C₂²⋊Dic₁₉	C₂	1	2	yes	maximal
11	C₂×C₁₉×#117	C₂	1	1	yes	maximal, characteristic
12	C₂³×C₄×C₁₉	C₂²	1	1	yes	characteristic
13	C₂²×Dic₃₈	C₂²	1	1	yes	characteristic
14	C₁₉×#117	—	2	4	no	—
15	C₂×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
16	C₂×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
17	C₂×C₂²⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
18	C₂×C₂²⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
19	C₂×C₄²×C₁₉	C₂²	1	1	yes	characteristic
20	C₂×C₄²×C₁₉	C₂²	1	1	yes	characteristic
21	C₂×C₂²⋊Dic₁₉	C₂²	1	2	yes	—
22	C₂×C₂²⋊Dic₁₉	C₂²	1	2	yes	—
23	C₂×C₄⋊Dic₁₉	C₂²	1	2	yes	—
24	C₂×C₄⋊Dic₁₉	C₂²	1	1	yes	characteristic
25	C₂×Dic₁₉⋊C₄	C₂²	1	2	yes	—
26	C₂×Dic₁₉⋊C₄	C₂²	1	2	yes	—
27	C₂×Dic₁₉⋊C₄	C₂²	1	2	yes	—
28	C₂×C₄×Dic₁₉	C₂²	1	2	yes	—
29	C₂×C₄×Dic₁₉	C₂²	1	2	yes	—
30	C₄×Dic₃₈	—	2	4	no	—
31	C₁₉⋊#95	C₂²	1	2	yes	—
32	C₁₉⋊#95	C₂²	1	2	yes	—
33	C₁₉⋊#95	C₂²	1	1	yes	characteristic
34	C₁₉⋊#95	C₂²	1	1	yes	characteristic
35	C₁₉⋊#95	C₂²	1	2	yes	—
36	C₁₉⋊#95	C₂²	1	2	yes	—
37	C₂⁴×C₁₉	C₂³	1	1	yes	characteristic
38	C₂²×C₄×C₁₉	—	2	2	no	—
39	C₂²×C₄×C₁₉	—	2	2	no	—
40	C₂²×C₄×C₁₉	Q₈	1	4	yes	complemented
41	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
42	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
43	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
44	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
45	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
46	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
47	C₂²×Dic₁₉	C₂³	1	2	yes	—
48	C₂²×Dic₁₉	C₂³	1	2	yes	—
49	C₂²×Dic₁₉	C₂³	1	2	yes	—
50	C₂²×Dic₁₉	C₂³	1	2	yes	—
51	C₂×Dic₃₈	—	2	2	no	—
52	C₂×Dic₃₈	—	2	4	no	—
53	C₄⋊C₄×C₁₉	—	2	2	no	—
54	C₄⋊C₄×C₁₉	—	2	2	no	—
55	C₂²⋊C₄×C₁₉	—	2	2	no	—
56	C₂²⋊C₄×C₁₉	—	2	2	no	—
57	C₄²×C₁₉	—	2	2	no	—
58	C₄²×C₁₉	D₄	1	4	yes	—
59	C₂²⋊Dic₁₉	—	2	4	no	—
60	C₂²⋊Dic₁₉	—	2	4	no	—
61	C₄⋊Dic₁₉	—	2	2	no	—
62	C₄⋊Dic₁₉	—	2	4	no	—
63	Dic₁₉⋊C₄	—	2	4	no	—
64	Dic₁₉⋊C₄	—	2	4	no	—
65	Dic₁₉⋊C₄	—	2	4	no	—
66	C₄×Dic₁₉	—	2	4	no	—
67	C₄×Dic₁₉	—	2	4	no	—
68	C₂³×C₁₉	—	2	1	no	—
69	C₂³×C₁₉	—	2	2	no	—
70	C₂³×C₁₉	—	2	2	no	—
71	C₂³×C₁₉	—	2	1	no	—
72	C₂³×C₁₉	C₂×Q₈	1	2	yes	—
73	C₂³×C₁₉	C₂⁴	1	1	yes	characteristic
74	C₂×C₄×C₁₉	—	2	1	no	—
75	C₂×C₄×C₁₉	—	2	2	no	—
76	C₂×C₄×C₁₉	—	2	2	no	—
77	C₂×C₄×C₁₉	—	2	1	no	—
78	C₂×C₄×C₁₉	—	2	8	no	—
79	C₂×C₄×C₁₉	—	2	1	no	—
80	C₂×C₄×C₁₉	—	2	1	no	—
81	C₂×C₄×C₁₉	—	2	2	no	—
82	C₂×C₄×C₁₉	—	2	2	no	—
83	C₂×C₄×C₁₉	C₂×D₄	1	2	yes	—
84	C₂×C₄×C₁₉	C₂×D₄	1	2	yes	—
85	C₂×C₄×C₁₉	C₂×D₄	1	2	yes	—
86	C₂×C₄×C₁₉	C₂×Q₈	1	2	yes	—
87	C₂×C₄×C₁₉	C₂×Q₈	1	2	yes	—
88	C₂×C₄×C₁₉	#41	1	2	yes	—
89	C₂×Dic₁₉	—	2	2	no	—
90	C₂×Dic₁₉	—	2	2	no	—
91	C₂×Dic₁₉	—	2	2	no	—
92	C₂×Dic₁₉	—	2	2	no	—
93	C₂×Dic₁₉	—	2	2	no	—
94	C₂×Dic₁₉	—	2	2	no	—
95	C₂×Dic₁₉	—	2	2	no	—
96	C₂×Dic₁₉	—	2	2	no	—
97	C₂×Dic₁₉	—	2	2	no	—
98	C₂×Dic₁₉	—	2	2	no	—
99	C₂×Dic₁₉	#41	1	4	yes	—
100	C₂×Dic₁₉	#41	1	4	yes	—
101	Dic₃₈	—	2	8	no	—
102	#2396	—	19	1	no	maximal, Sylow
103	C₂²×C₁₉	—	2	2	no	—
104	C₂²×C₁₉	—	2	4	no	—
105	C₂²×C₁₉	—	4	1	no	—
106	C₂²×C₁₉	—	4	2	no	—
107	C₂²×C₁₉	—	4	1	no	—
108	C₂²×C₁₉	C₂²×D₄	1	1	yes	characteristic
109	C₂²×C₁₉	C₂²×Q₈	1	1	yes	characteristic
110	C₂²×C₁₉	C₂×#41	1	1	yes	characteristic
111	C₂²×C₁₉	C₂×#41	1	2	yes	—
112	C₂²×C₁₉	C₂×#41	1	2	yes	—
113	C₄×C₁₉	—	2	2	no	—
114	C₄×C₁₉	—	2	2	no	—
115	C₄×C₁₉	—	2	2	no	—
116	C₄×C₁₉	—	4	1	no	—
117	C₄×C₁₉	—	4	1	no	—
118	C₄×C₁₉	C₂²⋊Q₈	1	4	yes	—
119	Dic₁₉	—	2	4	no	—
120	Dic₁₉	—	2	4	no	—
121	Dic₁₉	—	4	2	no	—
122	Dic₁₉	—	4	2	no	—
123	C₂×C₄×Q₈	—	19	1	no	—
124	C₂×#117	D₁₉	1	1	yes	characteristic
125	#400	—	19	1	no	—
126	#399	—	19	1	no	—
127	#398	—	19	2	no	—
128	#396	—	19	2	no	—
129	#395	—	19	1	no	—
130	#393	—	19	1	no	—
131	C₄×C₄⋊C₄	—	19	1	no	—
132	C₄×C₄⋊C₄	—	19	2	no	—
133	C₄×C₂²⋊C₄	—	19	2	no	—
134	C₂×C₁₉	—	4	2	no	—
135	C₂×C₁₉	C₂×C₂²⋊Q₈	1	1	yes	characteristic
136	C₂×C₁₉	#525	1	1	yes	characteristic
137	C₂×C₁₉	#529	1	2	yes	—
138	C₂×C₁₉	#532	1	1	yes	characteristic
139	C₂×C₁₉	#533	1	2	yes	—
140	C₂²×Q₈	—	19	1	no	—
141	C₂³×C₄	C₂×D₁₉	1	1	yes	characteristic
142	C₄×Q₈	—	38	4	no	—
143	#117	—	2	4	no	—
144	C₂×C₄⋊C₄	—	19	2	no	—
145	C₂×C₄⋊C₄	—	19	1	no	—
146	C₂×C₄⋊C₄	—	19	2	no	—
147	C₂×C₄⋊C₄	—	19	2	no	—
148	C₂×C₄⋊C₄	—	19	2	no	—
149	C₂×C₄⋊C₄	C₂×D₁₉	1	1	yes	characteristic
150	C₂×C₄⋊C₄	C₂×D₁₉	1	1	yes	characteristic
151	C₂×C₂²⋊C₄	—	19	2	no	—
152	C₂×C₂²⋊C₄	—	19	2	no	—
153	C₂×C₂²⋊C₄	C₂×D₁₉	1	1	yes	characteristic
154	C₂×C₂²⋊C₄	C₂×D₁₉	1	1	yes	characteristic
155	C₂×C₄²	—	19	2	no	—
156	C₂×C₄²	—	19	2	no	—
157	C₂×C₄²	C₂×D₁₉	1	1	yes	characteristic
158	C₂×C₄²	C₂×D₁₉	1	1	yes	characteristic
159	#95	—	19	2	no	—
160	#95	—	19	2	no	—
161	#95	—	19	2	no	—
162	#95	—	19	1	no	—
163	#95	—	19	1	no	—
164	#95	—	19	2	no	—
165	C₁₉	#2396	1	1	yes	characteristic, complemented, Sylow
166	C₂⁴	C₂²×D₁₉	1	1	yes	characteristic
167	C₂×Q₈	—	38	4	no	—
168	C₂×Q₈	—	38	2	no	—
169	C₂²×C₄	—	2	2	no	—
170	C₂²×C₄	—	2	2	no	—
171	C₂²×C₄	—	19	2	no	—
172	C₂²×C₄	—	19	2	no	—
173	C₂²×C₄	—	19	2	no	—
174	C₂²×C₄	—	19	2	no	—
175	C₂²×C₄	Dic₃₈	1	4	yes	complemented
176	C₂²×C₄	C₂²×D₁₉	1	1	yes	characteristic
177	C₂²×C₄	C₂²×D₁₉	1	1	yes	characteristic
178	C₂²×C₄	C₂²×D₁₉	1	1	yes	characteristic
179	C₂²×C₄	C₂²×D₁₉	1	1	yes	characteristic
180	C₂²×C₄	C₂²×D₁₉	1	1	yes	characteristic
181	C₂²×C₄	C₂²×D₁₉	1	1	yes	characteristic
182	C₄⋊C₄	—	2	2	no	—
183	C₄⋊C₄	—	2	2	no	—
184	C₄⋊C₄	—	38	4	no	—
185	C₄⋊C₄	—	38	4	no	—
186	C₄⋊C₄	—	38	4	no	—
187	C₄⋊C₄	—	38	4	no	—
188	C₄⋊C₄	—	38	2	no	—
189	C₂²⋊C₄	—	2	2	no	—
190	C₂²⋊C₄	—	2	2	no	—
191	C₂²⋊C₄	—	38	4	no	—
192	C₂²⋊C₄	—	38	4	no	—
193	C₄²	—	2	2	no	—
194	C₄²	—	38	4	no	—
195	C₄²	—	38	4	no	—
196	C₄²	C₂²⋊D₁₉	1	4	yes	—
197	C₂³	—	2	1	no	—
198	C₂³	—	2	2	no	—
199	C₂³	—	2	2	no	—
200	C₂³	—	2	1	no	—
201	C₂³	C₂×Dic₃₈	1	2	yes	—
202	C₂³	C₂³×D₁₉	1	1	yes	characteristic
203	Q₈	—	38	8	no	—
204	C₂×C₄	—	2	1	no	—
205	C₂×C₄	—	2	2	no	—
206	C₂×C₄	—	2	2	no	—
207	C₂×C₄	—	2	1	no	—
208	C₂×C₄	—	2	8	no	—
209	C₂×C₄	—	2	2	no	—
210	C₂×C₄	—	2	2	no	—
211	C₂×C₄	—	2	1	no	—
212	C₂×C₄	—	2	1	no	—
213	C₂×C₄	—	19	4	no	—
214	C₂×C₄	—	19	4	no	—
215	C₂×C₄	—	38	2	no	—
216	C₂×C₄	—	38	2	no	—
217	C₂×C₄	—	38	2	no	—
218	C₂×C₄	—	38	2	no	—
219	C₂×C₄	—	38	2	no	—
220	C₂×C₄	—	38	2	no	—
221	C₂×C₄	—	38	2	no	—
222	C₂×C₄	—	38	2	no	—
223	C₂×C₄	—	38	2	no	—
224	C₂×C₄	—	38	2	no	—
225	C₂×C₄	C₂×Dic₃₈	1	2	yes	—
226	C₂×C₄	C₂×Dic₃₈	1	2	yes	—
227	C₂×C₄	#64541	1	2	yes	—
228	C₂×C₄	C₂×C₂²⋊D₁₉	1	2	yes	—
229	C₂×C₄	C₂×C₂²⋊D₁₉	1	2	yes	—
230	C₂×C₄	C₂×C₂²⋊D₁₉	1	2	yes	—
231	C₂²	—	2	2	no	—
232	C₂²	—	2	4	no	—
233	C₂²	—	4	1	no	—
234	C₂²	—	4	2	no	—
235	C₂²	—	4	1	no	—
236	C₂²	C₂²×Dic₃₈	1	1	yes	characteristic
237	C₂²	C₂×#64541	1	1	yes	characteristic
238	C₂²	#41×D₁₉	1	2	yes	—
239	C₂²	#41×D₁₉	1	2	yes	—
240	C₂²	C₂²×C₂²⋊D₁₉	1	1	yes	characteristic
241	C₄	—	2	2	no	—
242	C₄	—	2	2	no	—
243	C₄	—	2	2	no	—
244	C₄	—	4	1	no	—
245	C₄	—	4	1	no	—
246	C₄	—	38	4	no	—
247	C₄	—	38	4	no	—
248	C₄	—	76	2	no	—
249	C₄	—	76	2	no	—
250	C₄	#10597370	1	4	yes	—
251	C₂	—	4	2	no	—
252	C₂	C₂×#10597370	1	1	yes	characteristic
253	C₂	#11927051	1	1	yes	characteristic
254	C₂	#11927072	1	2	yes	—
255	C₂	#11927090	1	1	yes	characteristic
256	C₂	#11927097	1	2	yes	—

	subgroup	G/H
center	C₂²×C₄	C₂²×D₁₉
commutator, socle, cosocle	C₂³×C₁₉	C₂⁴
Frattini	C₂³	C₂³×D₁₉
Fitting	C₂×C₁₉×#117	C₂
prime radical	C₂⁴×C₁₉	C₂³
hypercenter	C₂×#117	D₁₉
hypocenter	C₁₉	#2396
LCS	G ▷ C₂³×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂²×C₄ ◁ C₂×#117

Complements

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

N	H ≅ G/N	type
1. C₂×C₄×Dic₃₈	C₂	semidirect
2. #11926483	C₂	semidirect
4. #11926477	C₂	semidirect
6. #11926464	C₂	semidirect
8. C₄×Dic₁₉⋊C₄	C₂	semidirect
9. C₄×C₄⋊Dic₁₉	C₂	semidirect
40. C₂²×C₄×C₁₉	Q₈	semidirect
165. C₁₉	#2396	semidirect
175. C₂²×C₄	Dic₃₈	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₄×Dic₃₈	2
#11926483	2
#11926480	2
#11926477	2
#11926467	2
#11926464	2
#11926456	2
C₄×Dic₁₉⋊C₄	2
C₄×C₄⋊Dic₁₉	2
C₄×C₂²⋊Dic₁₉	2
C₂×C₁₉×#117	2
#2396	19