Subgroups — C₄×#10597388 #14572454

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×#10597388	C₂	1	1	yes	maximal, characteristic
2	C₄×#64541	C₂	1	1	yes	maximal, characteristic
3	#11926649	C₂	1	2	yes	maximal, complemented
4	#11926642	C₂	1	2	yes	maximal, complemented
5	C₄×#64528	C₂	1	2	yes	maximal, complemented
6	C₄×#64527	C₂	1	2	yes	maximal, complemented
7	#11926584	C₂	1	1	yes	maximal, characteristic, complemented
8	#11926553	C₂	1	1	yes	maximal, characteristic, complemented
9	#11926543	C₂	1	1	yes	maximal, characteristic
10	C₄×#64520	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×C₄×Q₈×C₁₉	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×Q₈×C₁₉	C₂²	1	1	yes	characteristic
13	C₂×#64541	C₂²	1	1	yes	characteristic
14	C₄×Q₈×C₁₉	—	2	1	no	—
15	C₄×Q₈×C₁₉	—	2	1	no	—
16	C₄×Q₈×C₁₉	C₂²	1	2	yes	—
17	C₄×Q₈×C₁₉	C₂²	1	2	yes	—
18	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
19	C₂×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
20	C₂×C₄²×C₁₉	—	2	1	no	—
21	C₂×C₄²×C₁₉	C₂²	1	1	yes	characteristic
22	C₂×#64528	C₂²	1	2	yes	—
23	#10597388	C₄	1	8	yes	direct product factor
24	C₂×#64527	C₂²	1	2	yes	—
25	C₄×C₂²⋊D₁₉	—	2	1	no	—
26	C₄×C₂²⋊D₁₉	—	2	1	no	—
27	#10597372	C₂²	1	1	yes	characteristic
28	C₂×#64520	C₂²	1	1	yes	characteristic
29	C₂×#64520	C₂²	1	1	yes	characteristic
30	C₄×D₇₆	C₂²	1	1	yes	characteristic
31	C₄×D₇₆	C₂²	1	1	yes	characteristic
32	#10597318	—	2	1	no	—
33	C₄²×D₁₉	—	2	1	no	—
34	C₄×Dic₃₈	C₂²	1	1	yes	characteristic
35	C₄×Dic₃₈	C₂²	1	1	yes	characteristic
36	#10597292	C₂²	1	2	yes	—
37	#10597292	C₂²	1	2	yes	—
38	#10597267	C₂²	1	2	yes	—
39	#10597266	C₂²	1	2	yes	—
40	#10597265	C₂²	1	2	yes	—
41	#10597264	C₂²	1	2	yes	—
42	#10597260	C₂²	1	2	yes	—
43	C₄×C₁₉⋊C₈	C₂²	1	2	yes	—
44	C₂×Q₈×C₁₉	—	2	1	no	—
45	C₂×Q₈×C₁₉	—	2	2	no	—
46	C₂×Q₈×C₁₉	C₂×C₄	1	4	yes	complemented
47	C₂×Q₈×C₁₉	C₂³	1	2	yes	—
48	C₂²×C₄×C₁₉	—	2	1	no	—
49	C₂²×C₄×C₁₉	—	2	1	no	—
50	C₂²×C₄×C₁₉	D₄	1	1	yes	characteristic
51	C₂²×C₄×C₁₉	D₄	1	1	yes	characteristic
52	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
53	C₂×C₂²⋊D₁₉	—	2	1	no	—
54	#64541	—	2	2	no	—
55	#64541	C₂×C₄	1	4	yes	—
56	C₂×D₇₆	C₂³	1	1	yes	characteristic
57	C₂×C₄×D₁₉	—	2	1	no	—
58	C₂×C₄×D₁₉	—	2	1	no	—
59	C₂×C₄×D₁₉	—	2	1	no	—
60	C₂×Dic₃₈	C₂³	1	1	yes	characteristic
61	C₄⋊C₄×C₁₉	—	2	2	no	—
62	C₄⋊C₄×C₁₉	—	2	2	no	—
63	C₄⋊C₄×C₁₉	—	2	1	no	—
64	C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
65	C₄²×C₁₉	—	2	2	no	—
66	C₄²×C₁₉	—	2	2	no	—
67	C₄²×C₁₉	D₄	1	1	yes	characteristic
68	C₄²×C₁₉	D₄	1	1	yes	characteristic
69	C₄²×C₁₉	C₂³	1	1	yes	characteristic
70	C₄²×C₁₉	C₂³	1	1	yes	characteristic
71	C₂²⋊Dic₁₉	—	2	1	no	—
72	#64528	C₂×C₄	1	8	yes	complemented
73	#64527	C₂×C₄	1	8	yes	complemented
74	(C₂×D₁₉)⋊C₄	—	2	1	no	—
75	(C₂×D₁₉)⋊C₄	—	2	1	no	—
76	C₄⋊Dic₁₉	C₂³	1	1	yes	characteristic
77	C₄⋊Dic₁₉	C₂³	1	1	yes	characteristic
78	Dic₁₉⋊C₄	—	2	1	no	—
79	Dic₁₉⋊C₄	—	2	1	no	—
80	C₄×Dic₁₉	—	2	1	no	—
81	C₄×Dic₁₉	—	2	1	no	—
82	C₄×Dic₁₉	—	2	1	no	—
83	#64520	—	2	2	no	—
84	#64520	C₂×C₄	1	4	yes	complemented
85	C₂×C₁₉⋊C₈	C₂³	1	2	yes	—
86	C₂×C₁₉⋊C₈	C₂³	1	2	yes	—
87	C₂³×C₁₉	C₂×D₄	1	1	yes	characteristic
88	C₂²×D₁₉	—	2	1	no	—
89	Q₈×C₁₉	—	2	4	no	—
90	Q₈×C₁₉	—	2	2	no	—
91	Q₈×C₁₉	C₂²×C₄	1	4	yes	—
92	C₂×C₄×C₁₉	—	2	4	no	—
93	C₂×C₄×C₁₉	—	2	2	no	—
94	C₂×C₄×C₁₉	—	2	2	no	—
95	C₂×C₄×C₁₉	—	2	2	no	—
96	C₂×C₄×C₁₉	—	4	1	no	—
97	C₂×C₄×C₁₉	—	4	2	no	—
98	C₂×C₄×C₁₉	C₂²×C₄	1	2	yes	—
99	C₂×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
100	C₂×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
101	C₂×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
102	C₂×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
103	C₂×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
104	C₂×C₄×C₁₉	#41	1	2	yes	—
105	C₂×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
106	C₂²⋊D₁₉	—	2	4	no	—
107	C₂×Dic₁₉	—	2	1	no	—
108	C₂×Dic₁₉	—	2	1	no	—
109	C₂×Dic₁₉	—	2	1	no	—
110	D₇₆	—	2	1	no	—
111	D₇₆	C₂²×C₄	1	2	yes	—
112	C₄×D₁₉	—	2	4	no	—
113	C₄×D₁₉	—	4	2	no	—
114	C₄×D₁₉	—	4	2	no	—
115	Dic₃₈	—	2	1	no	—
116	Dic₃₈	C₂²×C₄	1	2	yes	—
117	C₁₉⋊C₈	—	2	2	no	—
118	C₁₉⋊C₈	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	4	no	—
128	C₄×C₁₉	—	2	1	no	—
129	C₄×C₁₉	—	2	1	no	—
130	C₄×C₁₉	—	2	1	no	—
131	C₄×C₁₉	—	4	2	no	—
132	C₄×C₁₉	C₄×D₄	1	2	yes	—
133	C₄×C₁₉	#137	1	2	yes	complemented
134	C₄×C₁₉	C₂³×C₄	1	1	yes	characteristic
135	C₄×C₁₉	C₂×#41	1	1	yes	characteristic
136	Dic₁₉	—	2	2	no	—
137	Dic₁₉	—	4	1	no	—
138	Dic₁₉	—	4	1	no	—
139	C₂×#137	—	19	1	no	—
140	C₄×#41	—	19	1	no	—
141	C₂×C₄×Q₈	D₁₉	1	1	yes	characteristic, complemented
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	—	19	1	no	—
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	C₂×D₁₉	1	1	yes	characteristic
157	#137	—	19	8	no	—
158	C₂×Q₁₆	—	19	2	no	—
159	C₂×SD₁₆	—	19	2	no	—
160	C₂×M₁₆	—	19	1	no	—
161	C₂×M₁₆	—	19	1	no	—
162	C₄×Q₈	—	2	1	no	—
163	C₄×Q₈	—	2	1	no	—
164	C₄×Q₈	—	19	1	no	—
165	C₄×Q₈	—	19	1	no	—
166	C₄×Q₈	C₂×D₁₉	1	2	yes	—
167	C₄×Q₈	C₂×D₁₉	1	2	yes	—
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	—	2	1	no	—
175	C₂×C₄⋊C₄	C₂×D₁₉	1	1	yes	characteristic
176	C₂×C₄²	—	2	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	—	19	2	no	—
186	C₄×C₈	—	19	2	no	—
187	C₁₉	C₄×#137	1	1	yes	characteristic, complemented, Sylow
188	#41	—	19	4	no	—
189	#41	—	38	2	no	—
190	C₂×Q₈	—	2	2	no	—
191	C₂×Q₈	—	2	1	no	—
192	C₂×Q₈	—	19	1	no	—
193	C₂×Q₈	C₄×D₁₉	1	4	yes	complemented
194	C₂×Q₈	C₂²×D₁₉	1	2	yes	—
195	C₂×D₄	—	19	1	no	—
196	C₂×D₄	—	38	1	no	—
197	C₂²×C₄	—	2	1	no	—
198	C₂²×C₄	—	2	1	no	—
199	C₂²×C₄	—	38	1	no	—
200	C₂²×C₄	—	38	1	no	—
201	C₂²×C₄	—	38	1	no	—
202	C₂²×C₄	C₂²⋊D₁₉	1	1	yes	characteristic
203	C₂²×C₄	C₂²⋊D₁₉	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	—	19	4	no	—
208	M₁₆	—	38	2	no	—
209	C₂×C₈	—	19	2	no	—
210	C₂×C₈	—	19	2	no	—
211	C₄⋊C₄	—	2	2	no	—
212	C₄⋊C₄	—	2	2	no	—
213	C₄⋊C₄	—	2	1	no	—
214	C₄⋊C₄	—	19	1	no	—
215	C₄⋊C₄	—	19	1	no	—
216	C₄⋊C₄	—	38	1	no	—
217	C₄⋊C₄	—	38	1	no	—
218	C₄⋊C₄	C₂²×D₁₉	1	2	yes	—
219	C₂²⋊C₄	—	38	1	no	—
220	C₂²⋊C₄	—	38	1	no	—
221	C₂²⋊C₄	—	38	1	no	—
222	C₄²	—	2	2	no	—
223	C₄²	—	2	2	no	—
224	C₄²	—	38	1	no	—
225	C₄²	—	38	1	no	—
226	C₄²	—	38	1	no	—
227	C₄²	C₂²⋊D₁₉	1	1	yes	characteristic
228	C₄²	C₂²⋊D₁₉	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×C₂²⋊D₁₉	1	1	yes	characteristic
233	Q₈	—	2	2	no	—
234	Q₈	—	2	4	no	—
235	Q₈	—	19	2	no	—
236	Q₈	—	38	1	no	—
237	Q₈	C₂×C₄×D₁₉	1	4	yes	—
238	D₄	—	19	2	no	—
239	D₄	—	38	4	no	—
240	D₄	—	38	1	no	—
241	C₂×C₄	—	2	2	no	—
242	C₂×C₄	—	2	4	no	—
243	C₂×C₄	—	2	2	no	—
244	C₂×C₄	—	2	2	no	—
245	C₂×C₄	—	4	1	no	—
246	C₂×C₄	—	4	2	no	—
247	C₂×C₄	—	38	1	no	—
248	C₂×C₄	—	38	4	no	—
249	C₂×C₄	—	38	1	no	—
250	C₂×C₄	—	38	1	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	#64541	1	2	yes	—
255	C₂×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
256	C₂×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
257	C₂×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
258	C₂×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
259	C₂×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
260	C₂×C₄	C₂³×D₁₉	1	1	yes	characteristic
261	C₈	—	19	4	no	—
262	C₈	—	38	2	no	—
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×C₂²⋊D₁₉	1	2	yes	—
269	C₂²	C₂²×C₂²⋊D₁₉	1	1	yes	characteristic
270	C₄	—	2	1	no	—
271	C₄	—	2	1	no	—
272	C₄	—	2	1	no	—
273	C₄	—	2	4	no	—
274	C₄	—	4	2	no	—
275	C₄	—	38	2	no	—
276	C₄	—	76	1	no	—
277	C₄	—	76	1	no	—
278	C₄	C₄×C₂²⋊D₁₉	1	2	yes	—
279	C₄	#10597388	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×C₂²⋊D₁₉	1	1	yes	characteristic
285	C₂	C₂×#10597388	1	1	yes	characteristic
286	C₂	#11927342	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂×C₂²⋊D₁₉
commutator	C₄×C₁₉	C₂³×C₄
Frattini	C₂×C₄	C₂³×D₁₉
Fitting	C₂×C₄×Q₈×C₁₉	C₂
socle	C₂²×C₁₉	C₂²×D₄
prime radical	C₂×#64541	C₂²
cosocle	C₂×C₄×C₁₉	C₂⁴
hypercenter	C₂×C₄×Q₈	D₁₉
hypocenter	C₁₉	C₄×#137
LCS	G ▷ C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ C₂×C₄×Q₈

Complements

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

N	H ≅ G/N	type
3. #11926649	C₂	semidirect
4. #11926642	C₂	semidirect
5. C₄×#64528	C₂	semidirect
6. C₄×#64527	C₂	semidirect
7. #11926584	C₂	semidirect
8. #11926553	C₂	semidirect
10. C₄×#64520	C₂	semidirect
11. C₂×C₄×Q₈×C₁₉	C₂	semidirect
23. #10597388	C₄	direct (N × H)
46. C₂×Q₈×C₁₉	C₂×C₄	semidirect
72. #64528	C₂×C₄	semidirect
73. #64527	C₂×C₄	semidirect
84. #64520	C₂×C₄	semidirect
133. C₄×C₁₉	#137	semidirect
141. C₂×C₄×Q₈	D₁₉	semidirect
187. C₁₉	C₄×#137	semidirect
193. C₂×Q₈	C₄×D₁₉	semidirect
279. C₄	#10597388	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×#10597388	2
C₄×#64541	2
#11926649	2
#11926642	2
C₄×#64528	2
C₄×#64527	2
#11926584	2
#11926553	2
#11926543	2
C₄×#64520	2
C₂×C₄×Q₈×C₁₉	2
C₄×#137	19

Subgroups — C4×#10597388 #14572454

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄×#10597388 #14572454