Subgroups — #14577057

Order 2432.

1140 conjugacy classes of subgroups.

The subgroup lattice has 298 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#11927175	C₂	1	1	yes	maximal, characteristic, complemented
2	#11927159	C₂	1	4	yes	maximal, complemented
3	#11927145	C₂	1	4	yes	maximal, complemented
4	#11927132	C₂	1	4	yes	maximal, complemented
5	#11927125	C₂	1	1	yes	maximal, characteristic, complemented
6	#11927111	C₂	1	2	yes	maximal, complemented
7	#11927091	C₂	1	4	yes	maximal, complemented
8	#11927076	C₂	1	4	yes	maximal, complemented
9	#11927055	C₂	1	4	yes	maximal, complemented
10	C₄×#64541	C₂	1	2	yes	maximal, complemented
11	C₂×C₄×D₄×C₁₉	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×D₄×C₁₉	C₂²	1	1	yes	characteristic
13	C₂³×C₄×C₁₉	C₂²	1	2	yes	—
14	C₂×#64541	C₂²	1	2	yes	—
15	C₂×#64541	C₂²	1	4	yes	complemented
16	C₄×D₄×C₁₉	C₂²	1	4	yes	—
17	C₄×D₄×C₁₉	C₂²	1	4	yes	—
18	C₂×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
19	C₂×C₂²⋊C₄×C₁₉	C₂²	1	2	yes	—
20	C₂×C₄²×C₁₉	C₂²	1	1	yes	characteristic
21	#10597399	C₂²	1	8	yes	—
22	#10597386	C₂²	1	4	yes	—
23	#10597384	C₂²	1	4	yes	—
24	#10597384	C₂²	1	4	yes	—
25	#10597382	C₂²	1	4	yes	—
26	#10597376	C₂²	1	4	yes	—
27	#10597376	C₂²	1	4	yes	complemented
28	#10597375	C₂²	1	8	yes	complemented
29	C₄×C₂²⋊D₁₉	C₂²	1	4	yes	—
30	C₄×C₂²⋊D₁₉	C₂²	1	4	yes	—
31	C₄×C₂²⋊D₁₉	C₂²	1	8	yes	complemented
32	#10597372	C₂²	1	2	yes	—
33	#10597372	C₂²	1	4	yes	complemented
34	#10597370	C₂²	1	4	yes	—
35	#10597370	C₂²	1	4	yes	complemented
36	#10597343	C₂²	1	4	yes	complemented
37	#10597341	C₂²	1	4	yes	complemented
38	#10597336	C₂²	1	4	yes	complemented
39	#10597334	C₂²	1	4	yes	complemented
40	#10597331	C₂²	1	8	yes	complemented
41	#10597330	C₂²	1	8	yes	complemented
42	#10597329	C₂²	1	8	yes	complemented
43	#10597325	C₂²	1	8	yes	complemented
44	C₄×D₇₆	C₂²	1	2	yes	complemented
45	C₄×D₇₆	C₂²	1	2	yes	complemented
46	#10597318	C₂²	1	4	yes	complemented
47	C₄²×D₁₉	C₂²	1	4	yes	complemented
48	C₄×Dic₃₈	C₂²	1	2	yes	complemented
49	C₄×Dic₃₈	C₂²	1	2	yes	complemented
50	C₂⁴×C₁₉	C₂³	1	2	yes	—
51	C₂×D₄×C₁₉	—	2	4	no	—
52	C₂×D₄×C₁₉	C₂³	1	4	yes	—
53	C₂²×C₄×C₁₉	—	4	4	no	—
54	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
55	C₂²×C₄×C₁₉	C₂³	1	4	yes	—
56	C₂²×C₄×C₁₉	C₂³	1	2	yes	—
57	C₂²×C₄×C₁₉	C₂³	1	4	yes	—
58	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
59	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
60	C₂×C₂²⋊D₁₉	C₂³	1	4	yes	—
61	C₂×C₂²⋊D₁₉	C₂³	1	8	yes	—
62	C₂×C₂²⋊D₁₉	C₂³	1	8	yes	—
63	#64541	—	2	8	no	—
64	#64541	—	4	8	no	—
65	C₂×D₇₆	C₂³	1	2	yes	—
66	C₂×D₇₆	C₂³	1	4	yes	—
67	C₂×C₄×D₁₉	C₂³	1	4	yes	—
68	C₂×C₄×D₁₉	C₂³	1	4	yes	—
69	C₂×C₄×D₁₉	C₂³	1	4	yes	—
70	C₂×Dic₃₈	C₂³	1	2	yes	—
71	C₂×Dic₃₈	C₂³	1	4	yes	—
72	C₄⋊C₄×C₁₉	C₂³	1	4	yes	—
73	C₂²⋊C₄×C₁₉	C₂³	1	8	yes	—
74	C₄²×C₁₉	C₂³	1	2	yes	—
75	C₄²×C₁₉	C₂³	1	2	yes	—
76	C₂²⋊Dic₁₉	C₂³	1	8	yes	—
77	C₂²⋊Dic₁₉	C₂³	1	8	yes	—
78	C₂²⋊Dic₁₉	C₂³	1	4	yes	—
79	(C₂×D₁₉)⋊C₄	C₂³	1	8	yes	—
80	(C₂×D₁₉)⋊C₄	C₂³	1	4	yes	—
81	(C₂×D₁₉)⋊C₄	C₂³	1	4	yes	—
82	C₄⋊Dic₁₉	C₂³	1	4	yes	—
83	C₄⋊Dic₁₉	C₂³	1	4	yes	—
84	C₄⋊Dic₁₉	C₂³	1	2	yes	—
85	C₄⋊Dic₁₉	C₂³	1	2	yes	—
86	Dic₁₉⋊C₄	C₂³	1	4	yes	—
87	Dic₁₉⋊C₄	C₂³	1	4	yes	—
88	Dic₁₉⋊C₄	C₂³	1	8	yes	—
89	C₄×Dic₁₉	C₂³	1	4	yes	—
90	C₄×Dic₁₉	C₂³	1	4	yes	—
91	C₄×Dic₁₉	C₂³	1	4	yes	—
92	C₂³×C₁₉	—	2	4	no	—
93	C₂³×C₁₉	—	4	2	no	—
94	C₂³×C₁₉	—	4	2	no	—
95	C₂³×C₁₉	C₂⁴	1	4	yes	—
96	C₂³×C₁₉	C₂⁴	1	1	yes	characteristic
97	C₂²×D₁₉	C₂⁴	1	4	yes	—
98	D₄×C₁₉	—	2	8	no	—
99	C₂×C₄×C₁₉	—	2	8	no	—
100	C₂×C₄×C₁₉	—	2	2	no	—
101	C₂×C₄×C₁₉	—	4	2	no	—
102	C₂×C₄×C₁₉	—	4	4	no	—
103	C₂×C₄×C₁₉	—	4	1	no	—
104	C₂×C₄×C₁₉	#41	1	4	yes	complemented
105	C₂×C₄×C₁₉	C₂⁴	1	2	yes	—
106	C₂×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
107	C₂×C₄×C₁₉	C₂⁴	1	4	yes	—
108	C₂×C₄×C₁₉	C₂⁴	1	2	yes	—
109	C₂×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
110	C₂²⋊D₁₉	—	2	8	no	—
111	C₂²⋊D₁₉	—	4	8	no	—
112	C₂²⋊D₁₉	—	4	8	no	—
113	C₂×Dic₁₉	C₂⁴	1	4	yes	—
114	C₂×Dic₁₉	C₂⁴	1	4	yes	—
115	C₂×Dic₁₉	C₂⁴	1	4	yes	—
116	D₇₆	—	2	4	no	—
117	D₇₆	—	4	4	no	—
118	C₄×D₁₉	—	2	8	no	—
119	C₄×D₁₉	—	2	8	no	—
120	C₄×D₁₉	—	4	4	no	—
121	Dic₃₈	—	2	4	no	—
122	Dic₃₈	—	4	4	no	—
123	#3460	—	19	1	no	maximal, Sylow
124	C₂²×C₁₉	—	2	1	no	—
125	C₂²×C₁₉	—	2	1	no	—
126	C₂²×C₁₉	—	2	4	no	—
127	C₂²×C₁₉	—	2	4	no	—
128	C₂²×C₁₉	—	2	4	no	—
129	C₂²×C₁₉	—	4	8	no	—
130	C₂²×C₁₉	C₂×#41	1	2	yes	—
131	C₂²×C₁₉	C₂⁵	1	1	yes	characteristic
132	C₂×D₁₉	—	2	4	no	—
133	C₂×D₁₉	—	2	4	no	—
134	C₂×D₁₉	—	2	4	no	—
135	C₄×C₁₉	—	2	4	no	—
136	C₄×C₁₉	—	2	1	no	—
137	C₄×C₁₉	—	2	2	no	—
138	C₄×C₁₉	C₂×#41	1	4	yes	—
139	C₄×C₁₉	H(5,𝔽₂)	1	2	yes	—
140	Dic₁₉	—	2	4	no	—
141	Dic₁₉	—	2	4	no	—
142	Dic₁₉	—	2	4	no	—
143	#544	—	19	1	no	—
144	#542	—	19	4	no	—
145	#540	—	19	4	no	—
146	#538	—	19	4	no	—
147	#537	—	19	1	no	—
148	#535	—	19	2	no	—
149	#532	—	19	4	no	—
150	#529	—	19	4	no	—
151	#525	—	19	4	no	—
152	C₄×#41	—	19	2	no	—
153	C₂×C₄×D₄	D₁₉	1	1	yes	characteristic, complemented
154	C₂×C₁₉	—	2	2	no	—
155	C₂×C₁₉	—	4	4	no	—
156	C₂×C₁₉	C₂²×#41	1	1	yes	characteristic
157	C₂×C₁₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
158	C₂×C₁₉	#585	1	1	yes	characteristic
159	D₁₉	—	4	4	no	—
160	C₂×#41	—	19	2	no	—
161	C₂×#41	—	19	4	no	—
162	C₂²×D₄	C₂×D₁₉	1	1	yes	characteristic
163	C₂³×C₄	C₂×D₁₉	1	2	yes	—
164	C₄⋊Q₈	—	19	4	no	—
165	#127	—	19	4	no	—
166	#126	—	19	8	no	—
167	#125	—	19	4	no	—
168	#124	—	19	4	no	—
169	#124	—	19	8	no	—
170	#123	—	19	8	no	—
171	#123	—	19	8	no	—
172	C₂²⋊Q₈	—	19	4	no	—
173	C₂²⋊Q₈	—	19	4	no	—
174	C₂²⋊Q₈	—	19	4	no	—
175	#121	—	19	4	no	—
176	#121	—	19	4	no	—
177	#121	—	19	4	no	—
178	#121	—	19	4	no	—
179	#121	—	19	4	no	—
180	#121	—	19	8	no	—
181	#120	—	19	8	no	—
182	C₄×Q₈	—	19	2	no	—
183	C₄×Q₈	—	19	2	no	—
184	C₄×D₄	—	19	4	no	—
185	C₄×D₄	—	19	4	no	—
186	C₄×D₄	—	19	8	no	—
187	C₄×D₄	—	19	2	no	—
188	C₄×D₄	—	19	2	no	—
189	C₄×D₄	C₂×D₁₉	1	4	yes	—
190	C₄×D₄	C₂×D₁₉	1	4	yes	—
191	#117	—	19	2	no	—
192	#117	—	19	4	no	—
193	#117	—	19	4	no	—
194	C₂×C₄⋊C₄	C₂×D₁₉	1	1	yes	characteristic
195	C₂×C₂²⋊C₄	C₂×D₁₉	1	2	yes	—
196	C₂×C₄²	—	19	4	no	—
197	C₂×C₄²	C₂×D₁₉	1	1	yes	characteristic
198	C₁₉	#3460	1	1	yes	characteristic, complemented, Sylow
199	C₂⁴	C₂²×D₁₉	1	2	yes	—
200	#41	—	38	8	no	—
201	#41	—	76	8	no	—
202	C₂×Q₈	—	19	2	no	—
203	C₂×Q₈	—	19	4	no	—
204	C₂×D₄	—	2	4	no	—
205	C₂×D₄	—	19	4	no	—
206	C₂×D₄	—	19	8	no	—
207	C₂×D₄	—	19	8	no	—
208	C₂×D₄	—	19	2	no	—
209	C₂×D₄	—	19	4	no	—
210	C₂×D₄	C₂²×D₁₉	1	4	yes	—
211	C₂²×C₄	—	4	4	no	—
212	C₂²×C₄	—	19	4	no	—
213	C₂²×C₄	—	19	4	no	—
214	C₂²×C₄	—	19	4	no	—
215	C₂²×C₄	C₂²×D₁₉	1	1	yes	characteristic
216	C₂²×C₄	C₂²×D₁₉	1	4	yes	—
217	C₂²×C₄	C₂²×D₁₉	1	1	yes	characteristic
218	C₂²×C₄	C₂²×D₁₉	1	2	yes	—
219	C₂²×C₄	C₂²×D₁₉	1	4	yes	—
220	C₂²×C₄	C₂²×D₁₉	1	1	yes	characteristic
221	C₄⋊C₄	—	19	4	no	—
222	C₄⋊C₄	—	19	4	no	—
223	C₄⋊C₄	—	19	8	no	—
224	C₄⋊C₄	—	19	2	no	—
225	C₄⋊C₄	—	19	2	no	—
226	C₄⋊C₄	—	19	4	no	—
227	C₄⋊C₄	—	19	4	no	—
228	C₄⋊C₄	C₂²×D₁₉	1	4	yes	—
229	C₂²⋊C₄	—	19	4	no	—
230	C₂²⋊C₄	—	19	8	no	—
231	C₂²⋊C₄	—	19	8	no	—
232	C₂²⋊C₄	—	19	4	no	—
233	C₂²⋊C₄	—	19	4	no	—
234	C₂²⋊C₄	—	19	8	no	—
235	C₂²⋊C₄	C₂²×D₁₉	1	8	yes	—
236	C₄²	—	19	4	no	—
237	C₄²	—	19	4	no	—
238	C₄²	—	19	4	no	—
239	C₄²	C₂²×D₁₉	1	2	yes	—
240	C₄²	C₂²×D₁₉	1	2	yes	—
241	C₂³	—	2	4	no	—
242	C₂³	—	4	2	no	—
243	C₂³	—	4	2	no	—
244	C₂³	—	19	4	no	—
245	C₂³	C₂³×D₁₉	1	4	yes	—
246	C₂³	C₂³×D₁₉	1	1	yes	characteristic
247	Q₈	—	38	4	no	—
248	Q₈	—	76	4	no	—
249	D₄	—	2	8	no	—
250	D₄	—	38	8	no	—
251	D₄	—	38	4	no	—
252	D₄	—	76	4	no	—
253	D₄	—	76	8	no	—
254	D₄	—	76	8	no	—
255	C₂×C₄	—	2	2	no	—
256	C₂×C₄	—	2	8	no	—
257	C₂×C₄	—	4	4	no	—
258	C₂×C₄	—	4	2	no	—
259	C₂×C₄	—	4	1	no	—
260	C₂×C₄	—	19	4	no	—
261	C₂×C₄	—	19	4	no	—
262	C₂×C₄	—	19	4	no	—
263	C₂×C₄	—	38	8	no	—
264	C₂×C₄	—	38	8	no	—
265	C₂×C₄	—	76	4	no	—
266	C₂×C₄	#64541	1	4	yes	complemented
267	C₂×C₄	C₂³×D₁₉	1	2	yes	—
268	C₂×C₄	C₂³×D₁₉	1	1	yes	characteristic
269	C₂×C₄	C₂³×D₁₉	1	4	yes	—
270	C₂×C₄	C₂³×D₁₉	1	2	yes	—
271	C₂×C₄	C₂³×D₁₉	1	1	yes	characteristic
272	C₂²	—	2	1	no	—
273	C₂²	—	2	1	no	—
274	C₂²	—	2	4	no	—
275	C₂²	—	2	4	no	—
276	C₂²	—	2	4	no	—
277	C₂²	—	4	8	no	—
278	C₂²	—	38	4	no	—
279	C₂²	—	38	4	no	—
280	C₂²	—	38	4	no	—
281	C₂²	C₂×#64541	1	2	yes	—
282	C₂²	C₂⁴×D₁₉	1	1	yes	characteristic
283	C₄	—	2	1	no	—
284	C₄	—	2	4	no	—
285	C₄	—	2	2	no	—
286	C₄	—	38	4	no	—
287	C₄	—	38	4	no	—
288	C₄	—	38	4	no	—
289	C₄	C₂×#64541	1	4	yes	—
290	C₄	#10597430	1	2	yes	—
291	C₂	—	2	2	no	—
292	C₂	—	4	4	no	—
293	C₂	—	76	4	no	—
294	C₂	C₂²×#64541	1	1	yes	characteristic
295	C₂	C₂×#10597430	1	1	yes	characteristic
296	C₂	#11927380	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂³×D₁₉
commutator, socle, cosocle	C₂²×C₁₉	C₂⁵
Frattini	C₂²	C₂⁴×D₁₉
Fitting	C₂×C₄×D₄×C₁₉	C₂
hypercenter	C₂×C₄×D₄	D₁₉
hypocenter	C₁₉	#3460
LCS	G ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄×D₄

Complements

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

N	H ≅ G/N	type
1. #11927175	C₂	semidirect
2. #11927159	C₂	semidirect
3. #11927145	C₂	semidirect
4. #11927132	C₂	semidirect
5. #11927125	C₂	semidirect
6. #11927111	C₂	semidirect
7. #11927091	C₂	semidirect
8. #11927076	C₂	semidirect
9. #11927055	C₂	semidirect
10. C₄×#64541	C₂	semidirect
11. C₂×C₄×D₄×C₁₉	C₂	semidirect
15. C₂×#64541	C₂²	semidirect
27. #10597376	C₂²	semidirect
28. #10597375	C₂²	semidirect
31. C₄×C₂²⋊D₁₉	C₂²	semidirect
33. #10597372	C₂²	semidirect
35. #10597370	C₂²	semidirect
36. #10597343	C₂²	semidirect
37. #10597341	C₂²	semidirect
38. #10597336	C₂²	semidirect
39. #10597334	C₂²	semidirect
40. #10597331	C₂²	semidirect
41. #10597330	C₂²	semidirect
42. #10597329	C₂²	semidirect
43. #10597325	C₂²	semidirect
44. C₄×D₇₆	C₂²	semidirect
45. C₄×D₇₆	C₂²	semidirect
46. #10597318	C₂²	semidirect
47. C₄²×D₁₉	C₂²	semidirect
48. C₄×Dic₃₈	C₂²	semidirect
49. C₄×Dic₃₈	C₂²	semidirect
104. C₂×C₄×C₁₉	#41	semidirect
153. C₂×C₄×D₄	D₁₉	semidirect
198. C₁₉	#3460	semidirect
266. C₂×C₄	#64541	semidirect

Maximal subgroups

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

subgroup	index
#11927175	2
#11927159	2
#11927145	2
#11927132	2
#11927125	2
#11927111	2
#11927091	2
#11927076	2
#11927055	2
C₄×#64541	2
C₂×C₄×D₄×C₁₉	2
#3460	19