Subgroups — C₂×#11927078 #14576901

Order 2432.

1232 conjugacy classes of subgroups.

The subgroup lattice has 300 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#11927078	C₂	1	16	yes	maximal, direct product factor
2	C₂×#10597322	C₂	1	2	yes	maximal, complemented
3	C₂×#10597316	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×#10597321	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×#10597375	C₂	1	2	yes	maximal, complemented
6	C₂×#10597370	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×#10597376	C₂	1	1	yes	maximal, characteristic
8	C₂×C₄×Dic₃₈	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×C₄×D₇₆	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×C₄×C₂²⋊D₁₉	C₂	1	2	yes	maximal, complemented
11	C₂×#10597318	C₂	1	2	yes	maximal, complemented
12	C₂²×C₄²×C₁₉	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂³×C₄×C₁₉	C₂²	1	1	yes	characteristic
14	C₂³×C₄×C₁₉	C₂²	1	1	yes	characteristic
15	C₂³×C₄×C₁₉	C₂²	1	1	yes	characteristic
16	C₂²×C₂²⋊D₁₉	C₂²	1	2	yes	—
17	C₂²×D₇₆	C₂²	1	1	yes	characteristic
18	C₂²×C₄×D₁₉	C₂²	1	2	yes	—
19	C₂²×Dic₃₈	C₂²	1	1	yes	characteristic
20	C₂×C₄²×C₁₉	C₂²	1	1	yes	characteristic
21	C₂×C₄²×C₁₉	C₂²	1	1	yes	characteristic
22	C₂×C₄²×C₁₉	C₂²	1	1	yes	characteristic
23	C₂×C₄²×C₁₉	C₂²	1	1	yes	characteristic
24	C₂×C₄²×C₁₉	C₂²	1	8	yes	complemented
25	C₂×C₂²⋊Dic₁₉	C₂²	1	2	yes	—
26	#10597376	C₂²	1	8	yes	—
27	#10597375	C₂²	1	16	yes	complemented
28	C₄×C₂²⋊D₁₉	C₂²	1	16	yes	complemented
29	C₂×(C₂×D₁₉)⋊C₄	C₂²	1	2	yes	—
30	C₂×(C₂×D₁₉)⋊C₄	C₂²	1	2	yes	—
31	C₂×(C₂×D₁₉)⋊C₄	C₂²	1	2	yes	—
32	C₂×(C₂×D₁₉)⋊C₄	C₂²	1	2	yes	—
33	C₂×C₄⋊Dic₁₉	C₂²	1	1	yes	characteristic
34	C₂×C₄⋊Dic₁₉	C₂²	1	1	yes	characteristic
35	#10597370	C₂²	1	8	yes	complemented
36	C₂×Dic₁₉⋊C₄	C₂²	1	2	yes	—
37	C₂×Dic₁₉⋊C₄	C₂²	1	2	yes	—
38	C₂×Dic₁₉⋊C₄	C₂²	1	2	yes	—
39	C₂×Dic₁₉⋊C₄	C₂²	1	2	yes	—
40	C₂×C₄×Dic₁₉	C₂²	1	2	yes	—
41	#10597322	C₂²	1	16	yes	complemented
42	#10597321	C₂²	1	8	yes	complemented
43	C₄×D₇₆	C₂²	1	8	yes	complemented
44	#10597318	C₂²	1	16	yes	complemented
45	#10597316	C₂²	1	8	yes	complemented
46	C₄×Dic₃₈	C₂²	1	8	yes	complemented
47	C₂⁴×C₁₉	C₂³	1	1	yes	characteristic
48	C₂³×D₁₉	C₂³	1	2	yes	—
49	C₂²×C₄×C₁₉	—	2	4	no	—
50	C₂²×C₄×C₁₉	—	2	4	no	—
51	C₂²×C₄×C₁₉	—	2	4	no	—
52	C₂²×C₄×C₁₉	C₂³	1	4	yes	—
53	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
54	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
55	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
56	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
57	C₂²×C₄×C₁₉	C₂³	1	4	yes	—
58	C₂²×C₄×C₁₉	C₂³	1	4	yes	—
59	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
60	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
61	C₂×C₂²⋊D₁₉	—	2	8	no	—
62	C₂×C₂²⋊D₁₉	C₂³	1	8	yes	—
63	C₂²×Dic₁₉	C₂³	1	2	yes	—
64	C₂²×Dic₁₉	C₂³	1	2	yes	—
65	C₂²×Dic₁₉	C₂³	1	2	yes	—
66	C₂×D₇₆	—	2	4	no	—
67	C₂×D₇₆	C₂³	1	4	yes	—
68	C₂×C₄×D₁₉	—	2	8	no	—
69	C₂×C₄×D₁₉	C₂³	1	8	yes	—
70	C₂×Dic₃₈	—	2	4	no	—
71	C₂×Dic₃₈	C₂³	1	4	yes	—
72	C₄²×C₁₉	C₂³	1	4	yes	—
73	C₄²×C₁₉	C₂³	1	4	yes	—
74	C₄²×C₁₉	C₂³	1	4	yes	—
75	C₄²×C₁₉	C₂³	1	4	yes	—
76	C₂²⋊Dic₁₉	C₂³	1	8	yes	—
77	(C₂×D₁₉)⋊C₄	C₂³	1	8	yes	—
78	(C₂×D₁₉)⋊C₄	C₂³	1	8	yes	—
79	(C₂×D₁₉)⋊C₄	C₂³	1	8	yes	—
80	(C₂×D₁₉)⋊C₄	C₂³	1	8	yes	—
81	C₄⋊Dic₁₉	C₂³	1	4	yes	—
82	C₄⋊Dic₁₉	C₂³	1	4	yes	—
83	Dic₁₉⋊C₄	C₂³	1	8	yes	—
84	Dic₁₉⋊C₄	C₂³	1	8	yes	—
85	Dic₁₉⋊C₄	C₂³	1	8	yes	—
86	Dic₁₉⋊C₄	C₂³	1	8	yes	—
87	C₄×Dic₁₉	C₂³	1	8	yes	—
88	C₂³×C₁₉	—	2	2	no	—
89	C₂³×C₁₉	—	2	2	no	—
90	C₂³×C₁₉	#41	1	4	yes	—
91	C₂³×C₁₉	C₂⁴	1	2	yes	—
92	C₂³×C₁₉	C₂⁴	1	1	yes	characteristic
93	C₂²×D₁₉	—	2	4	no	—
94	C₂²×D₁₉	—	2	4	no	—
95	C₂²×D₁₉	—	2	4	no	—
96	C₂²×D₁₉	C₂⁴	1	4	yes	—
97	C₂×C₄×C₁₉	—	2	8	no	—
98	C₂×C₄×C₁₉	—	2	2	no	—
99	C₂×C₄×C₁₉	—	2	2	no	—
100	C₂×C₄×C₁₉	—	2	2	no	—
101	C₂×C₄×C₁₉	—	2	2	no	—
102	C₂×C₄×C₁₉	—	2	8	no	—
103	C₂×C₄×C₁₉	—	2	8	no	—
104	C₂×C₄×C₁₉	#41	1	4	yes	—
105	C₂×C₄×C₁₉	#41	1	4	yes	—
106	C₂×C₄×C₁₉	C₂⁴	1	2	yes	—
107	C₂×C₄×C₁₉	C₂⁴	1	2	yes	—
108	C₂×C₄×C₁₉	C₂⁴	1	2	yes	—
109	C₂×C₄×C₁₉	C₂⁴	1	2	yes	—
110	C₂×C₄×C₁₉	C₂⁴	1	2	yes	—
111	C₂×C₄×C₁₉	C₂⁴	1	2	yes	—
112	C₂²⋊D₁₉	—	2	16	no	—
113	C₂×Dic₁₉	—	2	4	no	—
114	C₂×Dic₁₉	—	2	4	no	—
115	C₂×Dic₁₉	—	2	4	no	—
116	C₂×Dic₁₉	C₂⁴	1	4	yes	—
117	C₂×Dic₁₉	C₂⁴	1	4	yes	—
118	C₂×Dic₁₉	C₂⁴	1	4	yes	—
119	D₇₆	—	2	8	no	—
120	C₄×D₁₉	—	2	16	no	—
121	Dic₃₈	—	2	8	no	—
122	C₂×#529	—	19	1	no	maximal, Sylow
123	C₂²×C₁₉	—	2	8	no	—
124	C₂²×C₁₉	—	2	2	no	—
125	C₂²×C₁₉	—	2	2	no	—
126	C₂²×C₁₉	C₂×#41	1	4	yes	—
127	C₂²×C₁₉	C₂×#41	1	2	yes	—
128	C₂²×C₁₉	C₂×#41	1	2	yes	—
129	C₂²×C₁₉	C₂×#41	1	2	yes	—
130	C₂²×C₁₉	C₂⁵	1	1	yes	characteristic
131	C₂×D₁₉	—	2	4	no	—
132	C₂×D₁₉	—	2	4	no	—
133	C₂×D₁₉	—	2	4	no	—
134	C₂×D₁₉	—	4	8	no	—
135	C₄×C₁₉	—	2	2	no	—
136	C₄×C₁₉	—	2	2	no	—
137	C₄×C₁₉	—	2	2	no	—
138	C₄×C₁₉	—	2	2	no	—
139	C₄×C₁₉	C₂×#41	1	4	yes	—
140	C₄×C₁₉	C₂×#41	1	4	yes	—
141	Dic₁₉	—	2	4	no	—
142	Dic₁₉	—	2	4	no	—
143	Dic₁₉	—	2	4	no	—
144	#529	—	19	16	no	—
145	C₂×#126	—	19	2	no	—
146	C₂×#125	—	19	1	no	—
147	C₂×#124	—	19	1	no	—
148	C₂×#123	—	19	2	no	—
149	C₂×C₂²⋊Q₈	—	19	1	no	—
150	C₂×#121	—	19	1	no	—
151	C₂×C₄×Q₈	—	19	1	no	—
152	C₂×C₄×D₄	—	19	2	no	—
153	C₂×C₄×D₄	—	19	1	no	—
154	C₂×#117	—	19	2	no	—
155	C₂²×C₄²	D₁₉	1	1	yes	characteristic, complemented
156	C₂×C₁₉	—	2	4	no	—
157	C₂×C₁₉	#529	1	4	yes	complemented
158	C₂×C₁₉	C₂²×#41	1	1	yes	characteristic
159	C₂×C₁₉	C₂²×#41	1	1	yes	characteristic
160	C₂×C₁₉	C₂²×#41	1	1	yes	characteristic
161	D₁₉	—	4	4	no	—
162	C₂²×Q₈	—	19	1	no	—
163	C₂²×D₄	—	19	2	no	—
164	C₂²×D₄	—	19	1	no	—
165	C₂³×C₄	—	19	2	no	—
166	C₂³×C₄	C₂×D₁₉	1	1	yes	characteristic
167	C₂³×C₄	C₂×D₁₉	1	1	yes	characteristic
168	C₂³×C₄	C₂×D₁₉	1	1	yes	characteristic
169	#126	—	19	16	no	—
170	#125	—	19	8	no	—
171	#124	—	19	8	no	—
172	#123	—	19	16	no	—
173	C₂²⋊Q₈	—	19	8	no	—
174	#121	—	19	8	no	—
175	C₄×Q₈	—	19	8	no	—
176	C₄×D₄	—	19	16	no	—
177	C₄×D₄	—	19	8	no	—
178	#117	—	19	16	no	—
179	C₂×C₄⋊C₄	—	19	2	no	—
180	C₂×C₄⋊C₄	—	19	2	no	—
181	C₂×C₄⋊C₄	—	19	1	no	—
182	C₂×C₄⋊C₄	—	19	2	no	—
183	C₂×C₄⋊C₄	—	19	1	no	—
184	C₂×C₄⋊C₄	—	19	2	no	—
185	C₂×C₂²⋊C₄	—	19	2	no	—
186	C₂×C₂²⋊C₄	—	19	2	no	—
187	C₂×C₂²⋊C₄	—	19	2	no	—
188	C₂×C₂²⋊C₄	—	19	2	no	—
189	C₂×C₂²⋊C₄	—	19	2	no	—
190	C₂×C₄²	—	19	2	no	—
191	C₂×C₄²	C₂×D₁₉	1	1	yes	characteristic
192	C₂×C₄²	C₂×D₁₉	1	1	yes	characteristic
193	C₂×C₄²	C₂×D₁₉	1	1	yes	characteristic
194	C₂×C₄²	C₂×D₁₉	1	1	yes	characteristic
195	C₂×C₄²	C₂×D₁₉	1	8	yes	complemented
196	C₁₉	C₂×#529	1	1	yes	characteristic, complemented, Sylow
197	C₂⁴	—	19	2	no	—
198	C₂⁴	C₂²×D₁₉	1	1	yes	characteristic
199	C₂×Q₈	—	19	4	no	—
200	C₂×Q₈	—	38	4	no	—
201	C₂×D₄	—	19	8	no	—
202	C₂×D₄	—	19	4	no	—
203	C₂×D₄	—	38	8	no	—
204	C₂×D₄	—	38	4	no	—
205	C₂²×C₄	—	2	4	no	—
206	C₂²×C₄	—	2	4	no	—
207	C₂²×C₄	—	2	4	no	—
208	C₂²×C₄	—	19	2	no	—
209	C₂²×C₄	—	19	2	no	—
210	C₂²×C₄	—	19	2	no	—
211	C₂²×C₄	—	19	8	no	—
212	C₂²×C₄	—	38	8	no	—
213	C₂²×C₄	C₂²×D₁₉	1	1	yes	characteristic
214	C₂²×C₄	C₂²×D₁₉	1	1	yes	characteristic
215	C₂²×C₄	C₂²×D₁₉	1	1	yes	characteristic
216	C₂²×C₄	C₂²×D₁₉	1	1	yes	characteristic
217	C₂²×C₄	C₂²×D₁₉	1	4	yes	—
218	C₂²×C₄	C₂²×D₁₉	1	4	yes	—
219	C₂²×C₄	C₂²×D₁₉	1	4	yes	—
220	C₂²×C₄	C₂²×D₁₉	1	1	yes	characteristic
221	C₂²×C₄	C₂²×D₁₉	1	1	yes	characteristic
222	C₄⋊C₄	—	19	8	no	—
223	C₄⋊C₄	—	19	8	no	—
224	C₄⋊C₄	—	19	8	no	—
225	C₄⋊C₄	—	19	8	no	—
226	C₄⋊C₄	—	19	4	no	—
227	C₄⋊C₄	—	19	4	no	—
228	C₂²⋊C₄	—	19	8	no	—
229	C₂²⋊C₄	—	19	8	no	—
230	C₂²⋊C₄	—	19	8	no	—
231	C₂²⋊C₄	—	19	8	no	—
232	C₂²⋊C₄	—	19	8	no	—
233	C₄²	—	19	8	no	—
234	C₄²	C₂²×D₁₉	1	4	yes	—
235	C₄²	C₂²×D₁₉	1	4	yes	—
236	C₄²	C₂²×D₁₉	1	4	yes	—
237	C₄²	C₂²×D₁₉	1	4	yes	—
238	C₂³	—	2	2	no	—
239	C₂³	—	2	2	no	—
240	C₂³	—	19	4	no	—
241	C₂³	—	38	4	no	—
242	C₂³	—	38	4	no	—
243	C₂³	—	38	4	no	—
244	C₂³	#64541	1	4	yes	—
245	C₂³	C₂³×D₁₉	1	2	yes	—
246	C₂³	C₂³×D₁₉	1	1	yes	characteristic
247	Q₈	—	38	8	no	—
248	D₄	—	38	16	no	—
249	D₄	—	38	8	no	—
250	C₂×C₄	—	2	8	no	—
251	C₂×C₄	—	2	2	no	—
252	C₂×C₄	—	2	2	no	—
253	C₂×C₄	—	2	2	no	—
254	C₂×C₄	—	2	2	no	—
255	C₂×C₄	—	2	8	no	—
256	C₂×C₄	—	2	8	no	—
257	C₂×C₄	—	19	4	no	—
258	C₂×C₄	—	19	4	no	—
259	C₂×C₄	—	19	4	no	—
260	C₂×C₄	—	38	4	no	—
261	C₂×C₄	—	38	4	no	—
262	C₂×C₄	—	38	4	no	—
263	C₂×C₄	—	38	16	no	—
264	C₂×C₄	#64541	1	4	yes	—
265	C₂×C₄	#64541	1	4	yes	—
266	C₂×C₄	C₂³×D₁₉	1	2	yes	—
267	C₂×C₄	C₂³×D₁₉	1	2	yes	—
268	C₂×C₄	C₂³×D₁₉	1	2	yes	—
269	C₂×C₄	C₂³×D₁₉	1	2	yes	—
270	C₂×C₄	C₂³×D₁₉	1	2	yes	—
271	C₂×C₄	C₂³×D₁₉	1	2	yes	—
272	C₂²	—	2	8	no	—
273	C₂²	—	2	2	no	—
274	C₂²	—	2	2	no	—
275	C₂²	—	38	4	no	—
276	C₂²	—	38	4	no	—
277	C₂²	—	38	4	no	—
278	C₂²	—	76	8	no	—
279	C₂²	C₂×#64541	1	4	yes	—
280	C₂²	C₂×#64541	1	2	yes	—
281	C₂²	C₂×#64541	1	2	yes	—
282	C₂²	C₂×#64541	1	2	yes	—
283	C₂²	C₂⁴×D₁₉	1	1	yes	characteristic
284	C₄	—	2	2	no	—
285	C₄	—	2	2	no	—
286	C₄	—	2	2	no	—
287	C₄	—	2	2	no	—
288	C₄	—	38	4	no	—
289	C₄	—	38	4	no	—
290	C₄	—	38	4	no	—
291	C₄	C₂×#64541	1	4	yes	—
292	C₄	C₂×#64541	1	4	yes	—
293	C₂	—	2	4	no	—
294	C₂	—	76	4	no	—
295	C₂	#11927078	1	4	yes	direct product factor
296	C₂	C₂²×#64541	1	1	yes	characteristic
297	C₂	C₂²×#64541	1	1	yes	characteristic
298	C₂	C₂²×#64541	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄	C₂²×D₁₉
commutator, cosocle	C₂²×C₁₉	C₂⁵
Frattini	C₂²	C₂⁴×D₁₉
Fitting	C₂²×C₄²×C₁₉	C₂
socle	C₂³×C₁₉	C₂⁴
prime radical	C₂×#10597376	C₂
hypercenter	C₂²×C₄²	D₁₉
hypocenter	C₁₉	C₂×#529
LCS	G ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂²×C₄ ◁ C₂²×C₄²

Complements

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

N	H ≅ G/N	type
1. #11927078	C₂	direct (N × H)
2. C₂×#10597322	C₂	semidirect
3. C₂×#10597316	C₂	semidirect
4. C₂×#10597321	C₂	semidirect
5. C₂×#10597375	C₂	semidirect
6. C₂×#10597370	C₂	semidirect
8. C₂×C₄×Dic₃₈	C₂	semidirect
9. C₂×C₄×D₇₆	C₂	semidirect
10. C₂×C₄×C₂²⋊D₁₉	C₂	semidirect
11. C₂×#10597318	C₂	semidirect
12. C₂²×C₄²×C₁₉	C₂	semidirect
24. C₂×C₄²×C₁₉	C₂²	semidirect
27. #10597375	C₂²	semidirect
28. C₄×C₂²⋊D₁₉	C₂²	semidirect
35. #10597370	C₂²	semidirect
41. #10597322	C₂²	semidirect
42. #10597321	C₂²	semidirect
43. C₄×D₇₆	C₂²	semidirect
44. #10597318	C₂²	semidirect
45. #10597316	C₂²	semidirect
46. C₄×Dic₃₈	C₂²	semidirect
155. C₂²×C₄²	D₁₉	semidirect
157. C₂×C₁₉	#529	semidirect
195. C₂×C₄²	C₂×D₁₉	semidirect
196. C₁₉	C₂×#529	semidirect
295. C₂	#11927078	direct (N × H)

Maximal subgroups

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

subgroup	index
#11927078	2
C₂×#10597322	2
C₂×#10597316	2
C₂×#10597321	2
C₂×#10597375	2
C₂×#10597370	2
C₂×#10597376	2
C₂×C₄×Dic₃₈	2
C₂×C₄×D₇₆	2
C₂×C₄×C₂²⋊D₁₉	2
C₂×#10597318	2
C₂²×C₄²×C₁₉	2
C₂×#529	19

Subgroups — C2×#11927078 #14576901

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#11927078 #14576901