Subgroups — C₄×#10597334 #14566205

Order 2432.

588 conjugacy classes of subgroups.

The subgroup lattice has 260 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#10597334	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄×Dic₃₈	C₂	1	2	yes	maximal
3	#11926448	C₂	1	2	yes	maximal
4	#11926443	C₂	1	1	yes	maximal, characteristic
5	#11926441	C₂	1	2	yes	maximal
6	#11926440	C₂	1	1	yes	maximal, characteristic
7	#11926413	C₂	1	1	yes	maximal, characteristic
8	C₄×Dic₁₉⋊C₄	C₂	1	2	yes	maximal
9	C₄×C₄⋊Dic₁₉	C₂	1	1	yes	maximal, characteristic
10	C₄²×Dic₁₉	C₂	1	1	yes	maximal, characteristic
11	C₄×C₄⋊C₄×C₁₉	C₂	1	1	yes	maximal, characteristic
12	C₂²×Dic₃₈	C₂²	1	2	yes	—
13	C₂×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
14	C₂×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
15	C₂×C₄²×C₁₉	C₂²	1	2	yes	—
16	C₂×C₄²×C₁₉	C₂²	1	1	yes	characteristic
17	C₂×C₄⋊Dic₁₉	C₂²	1	1	yes	characteristic
18	C₂×C₄⋊Dic₁₉	C₂²	1	2	yes	—
19	C₂×C₄⋊Dic₁₉	C₂²	1	1	yes	characteristic
20	C₂×Dic₁₉⋊C₄	C₂²	1	2	yes	—
21	C₂×Dic₁₉⋊C₄	C₂²	1	2	yes	—
22	C₂×Dic₁₉⋊C₄	C₂²	1	2	yes	—
23	C₂×Dic₁₉⋊C₄	C₂²	1	2	yes	—
24	C₂×C₄×Dic₁₉	C₂²	1	1	yes	characteristic
25	C₂×C₄×Dic₁₉	C₂²	1	1	yes	characteristic
26	C₂×C₄×Dic₁₉	C₂²	1	1	yes	characteristic
27	C₂×C₄×Dic₁₉	C₂²	1	2	yes	—
28	C₂×C₄×Dic₁₉	C₂²	1	1	yes	characteristic
29	C₂×C₄×Dic₁₉	C₂²	1	1	yes	characteristic
30	C₂×C₄×Dic₁₉	C₂²	1	1	yes	characteristic
31	#10597334	C₄	1	8	yes	direct product factor
32	C₄×Dic₃₈	—	2	8	no	—
33	C₁₉×#95	C₂²	1	2	yes	—
34	C₁₉⋊#95	C₂²	1	2	yes	—
35	C₁₉⋊#95	C₂²	1	2	yes	—
36	C₁₉⋊#95	C₂²	1	2	yes	—
37	C₂²×C₄×C₁₉	C₂³	1	2	yes	—
38	C₂²×C₄×C₁₉	C₂³	1	2	yes	—
39	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
40	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
41	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
42	C₂²×Dic₁₉	C₂³	1	2	yes	—
43	C₂²×Dic₁₉	C₂³	1	2	yes	—
44	C₂²×Dic₁₉	C₂³	1	1	yes	characteristic
45	C₂²×Dic₁₉	C₂³	1	1	yes	characteristic
46	C₂²×Dic₁₉	C₂³	1	1	yes	characteristic
47	C₂²×Dic₁₉	C₂³	1	1	yes	characteristic
48	C₂×Dic₃₈	—	2	4	no	—
49	C₂×Dic₃₈	—	2	4	no	—
50	C₂×Dic₃₈	C₂×C₄	1	8	yes	—
51	C₄⋊C₄×C₁₉	—	2	2	no	—
52	C₄⋊C₄×C₁₉	C₂×C₄	1	4	yes	—
53	C₄²×C₁₉	—	2	4	no	—
54	C₄²×C₁₉	Q₈	1	4	yes	complemented
55	C₄⋊Dic₁₉	—	2	2	no	—
56	C₄⋊Dic₁₉	—	2	4	no	—
57	C₄⋊Dic₁₉	C₂×C₄	1	4	yes	—
58	Dic₁₉⋊C₄	—	2	4	no	—
59	Dic₁₉⋊C₄	—	2	4	no	—
60	Dic₁₉⋊C₄	—	2	4	no	—
61	Dic₁₉⋊C₄	C₂×C₄	1	8	yes	—
62	C₄×Dic₁₉	—	2	4	no	—
63	C₄×Dic₁₉	—	2	2	no	—
64	C₄×Dic₁₉	—	2	2	no	—
65	C₄×Dic₁₉	—	2	2	no	—
66	C₄×Dic₁₉	C₂×C₄	1	4	yes	—
67	C₄×Dic₁₉	D₄	1	4	yes	—
68	C₄×Dic₁₉	Q₈	1	4	yes	complemented
69	C₂³×C₁₉	C₂⁴	1	1	yes	characteristic
70	C₂×C₄×C₁₉	—	2	2	no	—
71	C₂×C₄×C₁₉	—	2	1	no	—
72	C₂×C₄×C₁₉	—	2	1	no	—
73	C₂×C₄×C₁₉	—	2	2	no	—
74	C₂×C₄×C₁₉	—	2	2	no	—
75	C₂×C₄×C₁₉	—	2	2	no	—
76	C₂×C₄×C₁₉	—	2	2	no	—
77	C₂×C₄×C₁₉	C₂²×C₄	1	4	yes	—
78	C₂×C₄×C₁₉	C₂²×C₄	1	2	yes	—
79	C₂×C₄×C₁₉	C₂×D₄	1	2	yes	—
80	C₂×C₄×C₁₉	C₂×Q₈	1	2	yes	—
81	C₂×C₄×C₁₉	C₂×Q₈	1	2	yes	—
82	C₂×C₄×C₁₉	C₂×Q₈	1	2	yes	—
83	C₂×C₄×C₁₉	C₂×Q₈	1	2	yes	—
84	C₂×C₄×C₁₉	#41	1	2	yes	—
85	C₂×Dic₁₉	—	2	2	no	—
86	C₂×Dic₁₉	—	2	1	no	—
87	C₂×Dic₁₉	—	2	1	no	—
88	C₂×Dic₁₉	—	2	1	no	—
89	C₂×Dic₁₉	—	2	1	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	C₂²×C₄	1	4	yes	—
95	C₂×Dic₁₉	C₂²×C₄	1	2	yes	—
96	C₂×Dic₁₉	C₂²×C₄	1	2	yes	—
97	C₂×Dic₁₉	C₂×D₄	1	2	yes	—
98	C₂×Dic₁₉	C₂×D₄	1	2	yes	—
99	C₂×Dic₁₉	C₂×Q₈	1	2	yes	—
100	C₂×Dic₁₉	C₂×Q₈	1	2	yes	—
101	C₂×Dic₁₉	#41	1	2	yes	—
102	C₂×Dic₁₉	#41	1	2	yes	—
103	Dic₃₈	—	2	16	no	—
104	C₄×C₄⋊Q₈	—	19	1	no	maximal, Sylow
105	C₂²×C₁₉	C₂³×C₄	1	1	yes	characteristic
106	C₂²×C₁₉	C₂²×D₄	1	1	yes	characteristic
107	C₂²×C₁₉	C₂²×Q₈	1	1	yes	characteristic
108	C₂²×C₁₉	C₂²×Q₈	1	1	yes	characteristic
109	C₂²×C₁₉	C₂×#41	1	1	yes	characteristic
110	C₂²×C₁₉	C₂×#41	1	1	yes	characteristic
111	C₂²×C₁₉	C₂×#41	1	1	yes	characteristic
112	C₄×C₁₉	—	2	4	no	—
113	C₄×C₁₉	—	2	2	no	—
114	C₄×C₁₉	—	4	2	no	—
115	C₄×C₁₉	C₄×Q₈	1	4	yes	complemented
116	C₄×C₁₉	C₄⋊Q₈	1	4	yes	complemented
117	Dic₁₉	—	2	4	no	—
118	Dic₁₉	—	2	2	no	—
119	Dic₁₉	—	2	2	no	—
120	Dic₁₉	—	4	2	no	—
121	Dic₁₉	C₄×D₄	1	4	yes	—
122	Dic₁₉	C₄×Q₈	1	4	yes	complemented
123	C₂×C₄⋊Q₈	—	19	1	no	—
124	C₂×C₄×Q₈	—	19	2	no	—
125	#391	—	19	2	no	—
126	#389	—	19	1	no	—
127	#389	—	19	1	no	—
128	#389	—	19	2	no	—
129	#384	—	19	1	no	—
130	C₄×C₄⋊C₄	—	19	1	no	—
131	C₄×C₄⋊C₄	—	19	2	no	—
132	C₄×C₄⋊C₄	D₁₉	1	1	yes	characteristic
133	C₄³	—	19	1	no	—
134	C₂×C₁₉	C₂×C₄×D₄	1	1	yes	characteristic
135	C₂×C₁₉	C₂×C₄×Q₈	1	1	yes	characteristic
136	C₂×C₁₉	C₂×C₄×Q₈	1	1	yes	characteristic
137	C₂×C₁₉	C₂×C₄⋊Q₈	1	1	yes	characteristic
138	C₂×C₁₉	#532	1	1	yes	characteristic
139	C₂×C₁₉	#533	1	1	yes	characteristic
140	C₂×C₁₉	#533	1	1	yes	characteristic
141	C₂²×Q₈	—	19	2	no	—
142	C₄⋊Q₈	—	19	8	no	—
143	C₄×Q₈	—	38	8	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	—	19	2	no	—
150	C₂×C₄⋊C₄	—	19	1	no	—
151	C₂×C₄⋊C₄	C₂×D₁₉	1	1	yes	characteristic
152	C₂×C₄⋊C₄	C₂×D₁₉	1	1	yes	characteristic
153	C₂×C₄²	—	19	1	no	—
154	C₂×C₄²	—	19	1	no	—
155	C₂×C₄²	—	19	1	no	—
156	C₂×C₄²	—	19	1	no	—
157	C₂×C₄²	—	19	1	no	—
158	C₂×C₄²	—	19	1	no	—
159	C₂×C₄²	—	19	2	no	—
160	C₂×C₄²	C₂×D₁₉	1	2	yes	—
161	C₂×C₄²	C₂×D₁₉	1	1	yes	characteristic
162	#95	—	19	2	no	—
163	#95	—	19	2	no	—
164	#95	—	19	2	no	—
165	#95	C₂×D₁₉	1	2	yes	—
166	C₁₉	C₄×C₄⋊Q₈	1	1	yes	characteristic, complemented, Sylow
167	C₂×Q₈	—	19	8	no	—
168	C₂×Q₈	—	38	4	no	—
169	C₂×Q₈	—	38	4	no	—
170	C₂²×C₄	—	19	1	no	—
171	C₂²×C₄	—	19	1	no	—
172	C₂²×C₄	—	19	1	no	—
173	C₂²×C₄	—	19	2	no	—
174	C₂²×C₄	—	19	1	no	—
175	C₂²×C₄	—	19	2	no	—
176	C₂²×C₄	C₂²×D₁₉	1	2	yes	—
177	C₂²×C₄	C₂²×D₁₉	1	1	yes	characteristic
178	C₂²×C₄	C₂²×D₁₉	1	2	yes	—
179	C₂²×C₄	C₂²×D₁₉	1	1	yes	characteristic
180	C₂²×C₄	C₂²×D₁₉	1	1	yes	characteristic
181	C₄⋊C₄	—	2	2	no	—
182	C₄⋊C₄	—	19	8	no	—
183	C₄⋊C₄	—	19	4	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	C₄⋊C₄	C₄×D₁₉	1	4	yes	—
190	C₄²	—	2	4	no	—
191	C₄²	—	19	4	no	—
192	C₄²	—	19	4	no	—
193	C₄²	—	19	4	no	—
194	C₄²	—	38	2	no	—
195	C₄²	—	38	2	no	—
196	C₄²	—	38	2	no	—
197	C₄²	—	38	4	no	—
198	C₄²	Dic₃₈	1	4	yes	complemented
199	C₂³	C₂³×D₁₉	1	1	yes	characteristic
200	Q₈	—	38	16	no	—
201	C₂×C₄	—	2	2	no	—
202	C₂×C₄	—	2	1	no	—
203	C₂×C₄	—	2	1	no	—
204	C₂×C₄	—	2	2	no	—
205	C₂×C₄	—	2	2	no	—
206	C₂×C₄	—	2	2	no	—
207	C₂×C₄	—	2	2	no	—
208	C₂×C₄	—	19	2	no	—
209	C₂×C₄	—	19	2	no	—
210	C₂×C₄	—	19	2	no	—
211	C₂×C₄	—	19	2	no	—
212	C₂×C₄	—	19	2	no	—
213	C₂×C₄	—	19	2	no	—
214	C₂×C₄	—	19	4	no	—
215	C₂×C₄	—	19	2	no	—
216	C₂×C₄	—	19	2	no	—
217	C₂×C₄	—	38	1	no	—
218	C₂×C₄	—	38	1	no	—
219	C₂×C₄	—	38	2	no	—
220	C₂×C₄	—	38	1	no	—
221	C₂×C₄	—	38	1	no	—
222	C₂×C₄	—	38	2	no	—
223	C₂×C₄	—	38	2	no	—
224	C₂×C₄	—	38	2	no	—
225	C₂×C₄	—	38	2	no	—
226	C₂×C₄	C₂×Dic₃₈	1	2	yes	—
227	C₂×C₄	C₂×Dic₃₈	1	2	yes	—
228	C₂×C₄	C₂×Dic₃₈	1	2	yes	—
229	C₂×C₄	C₂×C₄×D₁₉	1	4	yes	—
230	C₂×C₄	C₂×C₄×D₁₉	1	2	yes	—
231	C₂×C₄	#64541	1	2	yes	—
232	C₂×C₄	D₄×D₁₉	1	2	yes	—
233	C₂×C₄	Q₈×D₁₉	1	2	yes	—
234	C₂²	C₂²×Dic₃₈	1	1	yes	characteristic
235	C₂²	C₂²×C₄×D₁₉	1	1	yes	characteristic
236	C₂²	C₂×#64541	1	1	yes	characteristic
237	C₂²	C₂×D₄×D₁₉	1	1	yes	characteristic
238	C₂²	C₂×Q₈×D₁₉	1	1	yes	characteristic
239	C₂²	#41×D₁₉	1	1	yes	characteristic
240	C₂²	#41×D₁₉	1	1	yes	characteristic
241	C₄	—	2	2	no	—
242	C₄	—	2	4	no	—
243	C₄	—	4	2	no	—
244	C₄	—	19	4	no	—
245	C₄	—	19	4	no	—
246	C₄	—	38	2	no	—
247	C₄	—	38	2	no	—
248	C₄	—	38	4	no	—
249	C₄	—	76	2	no	—
250	C₄	C₄×Dic₃₈	1	4	yes	complemented
251	C₄	#10597334	1	4	yes	direct product factor
252	C₂	C₄×D₄×D₁₉	1	1	yes	characteristic
253	C₂	C₄×Q₈×D₁₉	1	1	yes	characteristic
254	C₂	C₂×C₄×Dic₃₈	1	1	yes	characteristic
255	C₂	C₂×#10597334	1	1	yes	characteristic
256	C₂	#11927091	1	1	yes	characteristic
257	C₂	#11927097	1	1	yes	characteristic
258	C₂	#11927098	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄	C₂²×D₁₉
commutator	C₂²×C₁₉	C₂³×C₄
Frattini	C₂³	C₂³×D₁₉
Fitting	C₄×C₄⋊C₄×C₁₉	C₂
socle, prime radical, cosocle	C₂³×C₁₉	C₂⁴
hypercenter	C₄×C₄⋊C₄	D₁₉
hypocenter	C₁₉	C₄×C₄⋊Q₈
LCS	G ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂²×C₄ ◁ C₄×C₄⋊C₄

Complements

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

N	H ≅ G/N	type
31. #10597334	C₄	direct (N × H)
54. C₄²×C₁₉	Q₈	semidirect
68. C₄×Dic₁₉	Q₈	semidirect
115. C₄×C₁₉	C₄×Q₈	semidirect
116. C₄×C₁₉	C₄⋊Q₈	semidirect
122. Dic₁₉	C₄×Q₈	semidirect
166. C₁₉	C₄×C₄⋊Q₈	semidirect
198. C₄²	Dic₃₈	semidirect
250. C₄	C₄×Dic₃₈	semidirect
251. C₄	#10597334	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×#10597334	2
C₂×C₄×Dic₃₈	2
#11926448	2
#11926443	2
#11926441	2
#11926440	2
#11926413	2
C₄×Dic₁₉⋊C₄	2
C₄×C₄⋊Dic₁₉	2
C₄²×Dic₁₉	2
C₄×C₄⋊C₄×C₁₉	2
C₄×C₄⋊Q₈	19

Subgroups — C4×#10597334 #14566205

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄×#10597334 #14566205