Subgroups — C₄×#10597355 #14572458

Order 2432.

484 conjugacy classes of subgroups.

The subgroup lattice has 288 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#10597355	C₂	1	1	yes	maximal, characteristic
2	C₄×#64541	C₂	1	1	yes	maximal, characteristic
3	C₂×C₄×Dic₃₈	C₂	1	1	yes	maximal, characteristic, complemented
4	#11926652	C₂	1	2	yes	maximal, complemented
5	#11926646	C₂	1	2	yes	maximal, complemented
6	C₄×Dic₇₆	C₂	1	2	yes	maximal, complemented
7	C₄×#64516	C₂	1	2	yes	maximal, complemented
8	#11926586	C₂	1	1	yes	maximal, characteristic, complemented
9	#11926554	C₂	1	1	yes	maximal, characteristic, complemented
10	#11926546	C₂	1	1	yes	maximal, characteristic
11	C₄×M₁₆×C₁₉	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#64541	C₂²	1	1	yes	characteristic
13	C₂²×Dic₃₈	C₂²	1	1	yes	characteristic
14	C₂×M₁₆×C₁₉	C₂²	1	1	yes	characteristic
15	C₂×M₁₆×C₁₉	C₂²	1	1	yes	characteristic
16	C₂×C₄²×C₁₉	C₂²	1	1	yes	characteristic
17	C₄×C₂²⋊D₁₉	—	2	1	no	—
18	C₄×C₂²⋊D₁₉	—	2	1	no	—
19	#10597372	C₂²	1	1	yes	characteristic
20	C₂×C₄⋊Dic₁₉	C₂²	1	1	yes	characteristic
21	C₂×Dic₁₉⋊C₄	—	2	1	no	—
22	C₂×C₄×Dic₁₉	—	2	1	no	—
23	#10597355	C₄	1	8	yes	direct product factor
24	C₂×Dic₇₆	C₂²	1	2	yes	—
25	C₂×#64516	C₂²	1	2	yes	—
26	C₄×D₇₆	C₂²	1	1	yes	characteristic
27	C₄×D₇₆	C₂²	1	1	yes	characteristic
28	#10597318	—	2	1	no	—
29	C₄²×D₁₉	—	2	1	no	—
30	C₄×Dic₃₈	—	2	1	no	—
31	C₄×Dic₃₈	—	2	1	no	—
32	C₄×Dic₃₈	C₂²	1	2	yes	—
33	C₄×Dic₃₈	C₂²	1	1	yes	characteristic
34	C₄×Dic₃₈	C₂²	1	2	yes	—
35	C₄×Dic₃₈	C₂²	1	1	yes	characteristic
36	C₁₉×#97	C₂²	1	2	yes	—
37	C₄×C₈×C₁₉	C₂²	1	2	yes	—
38	#10597278	C₂²	1	2	yes	—
39	#10597275	C₂²	1	2	yes	—
40	#10597274	C₂²	1	2	yes	—
41	#10597273	C₂²	1	2	yes	—
42	#10597273	C₂²	1	2	yes	—
43	#10597273	C₂²	1	2	yes	—
44	C₂²×C₄×C₁₉	D₄	1	1	yes	characteristic
45	C₂²×C₄×C₁₉	D₄	1	1	yes	characteristic
46	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
47	C₂×C₂²⋊D₁₉	—	2	1	no	—
48	C₂²×Dic₁₉	—	2	1	no	—
49	C₂²×Dic₁₉	—	2	1	no	—
50	#64541	—	2	2	no	—
51	#64541	C₂×C₄	1	4	yes	—
52	C₂×D₇₆	C₂³	1	1	yes	characteristic
53	C₂×C₄×D₁₉	—	2	1	no	—
54	C₂×C₄×D₁₉	—	2	1	no	—
55	C₂×C₄×D₁₉	—	2	1	no	—
56	C₂×Dic₃₈	—	2	1	no	—
57	C₂×Dic₃₈	—	2	2	no	—
58	C₂×Dic₃₈	C₂×C₄	1	4	yes	complemented
59	C₂×Dic₃₈	C₂³	1	2	yes	—
60	C₂×Dic₃₈	C₂³	1	1	yes	characteristic
61	M₁₆×C₁₉	—	2	2	no	—
62	M₁₆×C₁₉	C₂×C₄	1	4	yes	complemented
63	C₂×C₈×C₁₉	C₂³	1	2	yes	—
64	C₂×C₈×C₁₉	C₂³	1	2	yes	—
65	C₄²×C₁₉	D₄	1	1	yes	characteristic
66	C₄²×C₁₉	D₄	1	1	yes	characteristic
67	C₄²×C₁₉	C₂³	1	1	yes	characteristic
68	C₄²×C₁₉	C₂³	1	1	yes	characteristic
69	C₂²⋊Dic₁₉	—	2	1	no	—
70	(C₂×D₁₉)⋊C₄	—	2	1	no	—
71	(C₂×D₁₉)⋊C₄	—	2	1	no	—
72	C₄⋊Dic₁₉	—	2	1	no	—
73	C₄⋊Dic₁₉	C₂³	1	1	yes	characteristic
74	C₄⋊Dic₁₉	C₂³	1	1	yes	characteristic
75	C₄⋊Dic₁₉	C₂³	1	2	yes	—
76	Dic₁₉⋊C₄	—	2	2	no	—
77	Dic₁₉⋊C₄	—	2	2	no	—
78	Dic₁₉⋊C₄	—	2	1	no	—
79	Dic₁₉⋊C₄	—	2	1	no	—
80	C₄×Dic₁₉	—	2	2	no	—
81	C₄×Dic₁₉	—	2	2	no	—
82	C₄×Dic₁₉	—	2	1	no	—
83	C₄×Dic₁₉	—	2	1	no	—
84	C₄×Dic₁₉	—	2	1	no	—
85	Dic₇₆	C₂×C₄	1	8	yes	complemented
86	#64516	C₂×C₄	1	8	yes	complemented
87	C₂³×C₁₉	C₂×D₄	1	1	yes	characteristic
88	C₂²×D₁₉	—	2	1	no	—
89	C₂×C₄×C₁₉	—	2	2	no	—
90	C₂×C₄×C₁₉	—	4	1	no	—
91	C₂×C₄×C₁₉	C₂²×C₄	1	2	yes	—
92	C₂×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
93	C₂×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
94	C₂×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
95	C₂×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
96	C₂×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
97	C₂×C₄×C₁₉	#41	1	2	yes	—
98	C₂×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
99	C₂²⋊D₁₉	—	2	4	no	—
100	C₂×Dic₁₉	—	2	4	no	—
101	C₂×Dic₁₉	—	2	2	no	—
102	C₂×Dic₁₉	—	2	1	no	—
103	C₂×Dic₁₉	—	2	2	no	—
104	C₂×Dic₁₉	—	2	1	no	—
105	C₂×Dic₁₉	—	2	1	no	—
106	C₂×Dic₁₉	—	4	2	no	—
107	D₇₆	—	2	1	no	—
108	D₇₆	C₂²×C₄	1	2	yes	—
109	C₄×D₁₉	—	2	4	no	—
110	C₄×D₁₉	—	4	2	no	—
111	C₄×D₁₉	—	4	2	no	—
112	Dic₃₈	—	2	4	no	—
113	Dic₃₈	—	2	2	no	—
114	Dic₃₈	—	2	1	no	—
115	Dic₃₈	C₂²×C₄	1	4	yes	—
116	Dic₃₈	C₂²×C₄	1	2	yes	—
117	C₈×C₁₉	—	2	2	no	—
118	C₈×C₁₉	C₂²×C₄	1	4	yes	—
119	C₄×#137	—	19	1	no	maximal, Sylow
120	C₂²×C₁₉	—	2	1	no	—
121	C₂²×C₁₉	—	2	1	no	—
122	C₂²×C₁₉	C₄×D₄	1	2	yes	—
123	C₂²×C₁₉	C₂²×D₄	1	1	yes	characteristic
124	C₂×D₁₉	—	2	2	no	—
125	C₂×D₁₉	—	4	1	no	—
126	C₂×D₁₉	—	4	1	no	—
127	C₄×C₁₉	—	2	1	no	—
128	C₄×C₁₉	—	2	1	no	—
129	C₄×C₁₉	—	2	1	no	—
130	C₄×C₁₉	C₄×D₄	1	2	yes	—
131	C₄×C₁₉	#137	1	2	yes	complemented
132	C₄×C₁₉	C₂³×C₄	1	1	yes	characteristic
133	C₄×C₁₉	C₂×#41	1	1	yes	characteristic
134	Dic₁₉	—	2	4	no	—
135	Dic₁₉	—	2	2	no	—
136	Dic₁₉	—	4	1	no	—
137	Dic₁₉	—	4	1	no	—
138	Dic₁₉	—	4	2	no	—
139	C₂×#137	—	19	1	no	—
140	C₄×#41	—	19	1	no	—
141	C₂×C₄×Q₈	—	19	1	no	—
142	#441	—	19	2	no	—
143	#440	—	19	2	no	—
144	C₄×Q₁₆	—	19	2	no	—
145	C₄×SD₁₆	—	19	2	no	—
146	#428	—	19	1	no	—
147	#419	—	19	1	no	—
148	#417	—	19	1	no	—
149	C₄×M₁₆	D₁₉	1	1	yes	characteristic, complemented
150	C₂×C₁₉	—	2	2	no	—
151	C₂×C₁₉	C₂×C₄×D₄	1	1	yes	characteristic
152	C₂×C₁₉	C₂×#137	1	1	yes	characteristic
153	C₂×C₁₉	#575	1	1	yes	characteristic
154	D₁₉	—	4	2	no	—
155	C₂×#41	—	19	1	no	—
156	C₂²×Q₈	—	19	1	no	—
157	#137	—	19	8	no	—
158	C₂×Q₁₆	—	19	2	no	—
159	C₂×SD₁₆	—	19	2	no	—
160	C₂×M₁₆	C₂×D₁₉	1	1	yes	characteristic
161	C₂×M₁₆	C₂×D₁₉	1	1	yes	characteristic
162	C₄×Q₈	—	19	2	no	—
163	C₄×Q₈	—	19	2	no	—
164	C₄×Q₈	—	19	1	no	—
165	C₄×Q₈	—	19	1	no	—
166	C₄×Q₈	—	38	1	no	—
167	C₄×Q₈	—	38	1	no	—
168	C₄×D₄	—	19	1	no	—
169	C₄×D₄	—	19	1	no	—
170	C₄×D₄	—	38	1	no	—
171	C₄×D₄	—	38	1	no	—
172	#117	—	19	1	no	—
173	#117	—	38	1	no	—
174	C₂×C₄⋊C₄	—	19	1	no	—
175	C₂×C₄⋊C₄	—	38	1	no	—
176	C₂×C₄²	—	38	1	no	—
177	C₂×C₄²	—	38	1	no	—
178	C₂×C₄²	C₂×D₁₉	1	1	yes	characteristic
179	#107	—	19	2	no	—
180	#106	—	19	2	no	—
181	#103	—	19	2	no	—
182	#103	—	19	2	no	—
183	#103	—	19	2	no	—
184	#102	—	19	2	no	—
185	#97	C₂×D₁₉	1	2	yes	—
186	C₄×C₈	C₂×D₁₉	1	2	yes	—
187	C₁₉	C₄×#137	1	1	yes	characteristic, complemented, Sylow
188	#41	—	19	4	no	—
189	#41	—	38	2	no	—
190	C₂×Q₈	—	19	4	no	—
191	C₂×Q₈	—	19	2	no	—
192	C₂×Q₈	—	19	1	no	—
193	C₂×Q₈	—	38	1	no	—
194	C₂×Q₈	—	38	2	no	—
195	C₂×D₄	—	19	1	no	—
196	C₂×D₄	—	38	1	no	—
197	C₂²×C₄	—	38	1	no	—
198	C₂²×C₄	—	38	1	no	—
199	C₂²×C₄	—	38	1	no	—
200	C₂²×C₄	—	38	1	no	—
201	C₂²×C₄	—	38	1	no	—
202	C₂²×C₄	D₇₆	1	1	yes	characteristic
203	C₂²×C₄	D₇₆	1	1	yes	characteristic
204	C₂²×C₄	C₂²×D₁₉	1	1	yes	characteristic
205	Q₁₆	—	19	8	no	—
206	SD₁₆	—	19	8	no	—
207	M₁₆	—	2	2	no	—
208	M₁₆	C₄×D₁₉	1	4	yes	complemented
209	C₂×C₈	C₂²×D₁₉	1	2	yes	—
210	C₂×C₈	C₂²×D₁₉	1	2	yes	—
211	C₄⋊C₄	—	19	2	no	—
212	C₄⋊C₄	—	19	1	no	—
213	C₄⋊C₄	—	19	1	no	—
214	C₄⋊C₄	—	38	2	no	—
215	C₄⋊C₄	—	38	2	no	—
216	C₄⋊C₄	—	38	1	no	—
217	C₄⋊C₄	—	38	1	no	—
218	C₄⋊C₄	—	38	1	no	—
219	C₂²⋊C₄	—	38	1	no	—
220	C₂²⋊C₄	—	38	1	no	—
221	C₂²⋊C₄	—	38	1	no	—
222	C₄²	—	38	1	no	—
223	C₄²	—	38	1	no	—
224	C₄²	—	38	2	no	—
225	C₄²	—	38	1	no	—
226	C₄²	—	38	2	no	—
227	C₄²	D₇₆	1	1	yes	characteristic
228	C₄²	D₇₆	1	1	yes	characteristic
229	C₄²	C₂²×D₁₉	1	1	yes	characteristic
230	C₄²	C₂²×D₁₉	1	1	yes	characteristic
231	C₂³	—	38	1	no	—
232	C₂³	C₂×D₇₆	1	1	yes	characteristic
233	Q₈	—	19	4	no	—
234	Q₈	—	19	2	no	—
235	Q₈	—	38	2	no	—
236	Q₈	—	38	1	no	—
237	Q₈	—	38	4	no	—
238	D₄	—	19	2	no	—
239	D₄	—	38	4	no	—
240	D₄	—	38	1	no	—
241	C₂×C₄	—	2	2	no	—
242	C₂×C₄	—	4	1	no	—
243	C₂×C₄	—	38	1	no	—
244	C₂×C₄	—	38	2	no	—
245	C₂×C₄	—	38	4	no	—
246	C₂×C₄	—	38	4	no	—
247	C₂×C₄	—	38	1	no	—
248	C₂×C₄	—	38	1	no	—
249	C₂×C₄	—	38	2	no	—
250	C₂×C₄	—	76	2	no	—
251	C₂×C₄	—	76	2	no	—
252	C₂×C₄	—	76	2	no	—
253	C₂×C₄	C₂×C₄×D₁₉	1	2	yes	—
254	C₂×C₄	C₂×D₇₆	1	1	yes	characteristic
255	C₂×C₄	C₂×D₇₆	1	1	yes	characteristic
256	C₂×C₄	C₂×D₇₆	1	1	yes	characteristic
257	C₂×C₄	C₂×D₇₆	1	1	yes	characteristic
258	C₂×C₄	C₂×D₇₆	1	1	yes	characteristic
259	C₂×C₄	#64541	1	2	yes	—
260	C₂×C₄	C₂³×D₁₉	1	1	yes	characteristic
261	C₈	—	2	2	no	—
262	C₈	C₂×C₄×D₁₉	1	4	yes	—
263	C₂²	—	2	1	no	—
264	C₂²	—	2	1	no	—
265	C₂²	—	38	2	no	—
266	C₂²	—	76	1	no	—
267	C₂²	—	76	1	no	—
268	C₂²	C₄×D₇₆	1	2	yes	—
269	C₂²	C₂²×D₇₆	1	1	yes	characteristic
270	C₄	—	2	1	no	—
271	C₄	—	2	1	no	—
272	C₄	—	2	1	no	—
273	C₄	—	38	2	no	—
274	C₄	—	38	4	no	—
275	C₄	—	76	1	no	—
276	C₄	—	76	1	no	—
277	C₄	—	76	2	no	—
278	C₄	C₄×D₇₆	1	2	yes	—
279	C₄	#10597355	1	2	yes	direct product factor
280	C₄	C₂²×C₄×D₁₉	1	1	yes	characteristic
281	C₄	C₂×#64541	1	1	yes	characteristic
282	C₂	—	2	2	no	—
283	C₂	—	76	2	no	—
284	C₂	C₂×C₄×D₇₆	1	1	yes	characteristic
285	C₂	C₂×#10597355	1	1	yes	characteristic
286	C₂	#11927344	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂×D₇₆
commutator	C₄×C₁₉	C₂³×C₄
Frattini	C₂×C₄	C₂³×D₁₉
Fitting	C₄×M₁₆×C₁₉	C₂
socle	C₂²×C₁₉	C₂²×D₄
prime radical	C₂×#64541	C₂²
cosocle	C₂×C₄×C₁₉	C₂⁴
hypercenter	C₄×M₁₆	D₁₉
hypocenter	C₁₉	C₄×#137
LCS	G ▷ C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ C₄×M₁₆

Complements

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

N	H ≅ G/N	type
3. C₂×C₄×Dic₃₈	C₂	semidirect
4. #11926652	C₂	semidirect
5. #11926646	C₂	semidirect
6. C₄×Dic₇₆	C₂	semidirect
7. C₄×#64516	C₂	semidirect
8. #11926586	C₂	semidirect
9. #11926554	C₂	semidirect
11. C₄×M₁₆×C₁₉	C₂	semidirect
23. #10597355	C₄	direct (N × H)
58. C₂×Dic₃₈	C₂×C₄	semidirect
62. M₁₆×C₁₉	C₂×C₄	semidirect
85. Dic₇₆	C₂×C₄	semidirect
86. #64516	C₂×C₄	semidirect
131. C₄×C₁₉	#137	semidirect
149. C₄×M₁₆	D₁₉	semidirect
187. C₁₉	C₄×#137	semidirect
208. M₁₆	C₄×D₁₉	semidirect
279. C₄	#10597355	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×#10597355	2
C₄×#64541	2
C₂×C₄×Dic₃₈	2
#11926652	2
#11926646	2
C₄×Dic₇₆	2
C₄×#64516	2
#11926586	2
#11926554	2
#11926546	2
C₄×M₁₆×C₁₉	2
C₄×#137	19

Subgroups — C4×#10597355 #14572458

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄×#10597355 #14572458