Subgroups — #18082351

Order 4864.

694 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×#11926921	C₂	1	1	yes	maximal, characteristic
2	#14564441	C₂	1	2	yes	maximal, complemented
3	#14564441	C₂	1	2	yes	maximal, complemented
4	#14563763	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₁₉×#322	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂²×D₁₅₂	—	2	2	no	—
7	C₂×#10597320	C₂²	1	2	yes	—
8	#11926921	—	2	2	no	—
9	#11926921	C₄	1	4	yes	complemented
10	C₂×#10597278	—	2	4	no	—
11	C₂×#10597278	—	2	4	no	—
12	#11926414	C₂²	1	2	yes	—
13	#11926307	—	2	2	no	—
14	C₂×C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic
15	C₂×C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic
16	C₂×C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic
17	C₁₉×#322	—	2	2	no	—
18	C₂²×D₇₆	—	2	2	no	—
19	C₂²×D₇₆	—	2	2	no	—
20	C₂²×D₇₆	—	2	2	no	—
21	C₂²×C₈×C₁₉	D₄	1	2	yes	—
22	C₂²×C₈×C₁₉	D₄	1	2	yes	—
23	C₂²×C₈×C₁₉	D₄	1	2	yes	—
24	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
25	C₂×C₄⋊Dic₁₉	—	2	2	no	—
26	C₂×C₄⋊Dic₁₉	—	2	2	no	—
27	C₂×C₄⋊Dic₁₉	—	2	2	no	—
28	C₂×D₁₅₂	—	2	8	no	—
29	C₂×D₁₅₂	—	4	8	no	—
30	#10597320	—	2	2	no	—
31	#10597320	—	2	2	no	—
32	#10597320	—	2	2	no	—
33	#10597320	C₂×C₄	1	4	yes	—
34	C₄×C₈×C₁₉	—	2	1	no	—
35	C₄×C₈×C₁₉	—	2	1	no	—
36	C₄×C₈×C₁₉	—	2	1	no	—
37	C₄×C₈×C₁₉	—	2	1	no	—
38	C₄×C₈×C₁₉	C₂×C₄	1	2	yes	—
39	C₄×C₈×C₁₉	D₄	1	2	yes	—
40	#10597278	—	4	8	no	—
41	#10597278	—	4	8	no	—
42	C₂³×D₁₉	—	4	2	no	—
43	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
44	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
45	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
46	C₂²×Dic₁₉	—	4	2	no	—
47	C₂×D₇₆	—	2	4	no	—
48	C₂×D₇₆	—	2	4	no	—
49	C₂×D₇₆	—	2	4	no	—
50	C₂×D₇₆	—	4	4	no	—
51	C₂×D₇₆	—	4	4	no	—
52	C₂×D₇₆	—	4	4	no	—
53	C₂×D₇₆	—	4	4	no	—
54	C₂×D₇₆	—	4	4	no	—
55	C₂×D₇₆	—	4	4	no	—
56	C₂×D₇₆	—	4	2	no	—
57	C₂×D₇₆	—	4	2	no	—
58	C₂×D₇₆	—	4	2	no	—
59	C₂×C₈×C₁₉	—	2	2	no	—
60	C₂×C₈×C₁₉	—	2	2	no	—
61	C₂×C₈×C₁₉	—	2	4	no	—
62	C₂×C₈×C₁₉	—	2	2	no	—
63	C₂×C₈×C₁₉	—	2	4	no	—
64	C₂×C₈×C₁₉	C₂²⋊C₄	1	4	yes	—
65	C₂×C₈×C₁₉	D₈	1	4	yes	complemented
66	C₄²×C₁₉	C₂²×C₄	1	1	yes	characteristic
67	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
68	C₄²×C₁₉	#41	1	1	yes	characteristic
69	C₄²×C₁₉	#41	1	1	yes	characteristic
70	C₄⋊Dic₁₉	—	4	4	no	—
71	C₄⋊Dic₁₉	—	4	4	no	—
72	C₄⋊Dic₁₉	—	4	4	no	—
73	D₁₅₂	—	4	16	no	—
74	#9832	—	19	1	no	maximal, Sylow
75	C₂³×C₁₉	#127	1	1	yes	characteristic
76	C₂²×D₁₉	—	4	4	no	—
77	C₂²×D₁₉	—	8	2	no	—
78	C₂²×D₁₉	—	8	2	no	—
79	C₂²×D₁₉	—	8	2	no	—
80	C₂²×D₁₉	—	8	2	no	—
81	C₂²×D₁₉	—	8	2	no	—
82	C₂²×D₁₉	—	8	2	no	—
83	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
84	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
85	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
86	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
87	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
88	C₂×C₄×C₁₉	#124	1	1	yes	characteristic
89	C₂×C₄×C₁₉	C₂×D₈	1	2	yes	—
90	C₂×C₄×C₁₉	#135	1	2	yes	—
91	C₂×C₄×C₁₉	AGL(1,ℤ/8)	1	4	yes	—
92	C₂×C₄×C₁₉	AGL(1,ℤ/8)	1	4	yes	—
93	C₂×Dic₁₉	—	8	2	no	—
94	C₂×Dic₁₉	—	8	2	no	—
95	C₂×Dic₁₉	—	8	2	no	—
96	D₇₆	—	4	8	no	—
97	D₇₆	—	4	8	no	—
98	D₇₆	—	4	8	no	—
99	D₇₆	—	8	4	no	—
100	D₇₆	—	8	4	no	—
101	D₇₆	—	8	4	no	—
102	C₈×C₁₉	—	2	4	no	—
103	C₈×C₁₉	—	2	4	no	—
104	C₈×C₁₉	—	4	2	no	—
105	C₂×#493	—	19	1	no	—
106	#1957	—	19	2	no	—
107	#1957	—	19	2	no	—
108	#1834	—	19	1	no	—
109	C₂×#322	D₁₉	1	1	yes	characteristic, complemented
110	C₂²×C₁₉	#390	1	1	yes	characteristic
111	C₂²×C₁₉	#493	1	1	yes	characteristic
112	C₂²×C₁₉	#495	1	1	yes	characteristic
113	C₂²×C₁₉	#496	1	2	yes	—
114	C₂²×C₁₉	#496	1	2	yes	—
115	C₂×D₁₉	—	8	4	no	—
116	C₂×D₁₉	—	8	4	no	—
117	C₂×D₁₉	—	8	4	no	—
118	C₂×D₁₉	—	16	2	no	—
119	C₂×D₁₉	—	16	2	no	—
120	C₂×D₁₉	—	16	2	no	—
121	C₂×D₁₉	—	16	2	no	—
122	C₄×C₁₉	#418	1	2	yes	—
123	C₄×C₁₉	C₄×D₈	1	2	yes	—
124	C₄×C₁₉	#442	1	2	yes	—
125	C₄×C₁₉	#466	1	2	yes	—
126	C₄×C₁₉	#469	1	2	yes	—
127	C₄×C₁₉	#490	1	2	yes	—
128	Dic₁₉	—	16	2	no	—
129	C₂²×D₈	—	38	2	no	—
130	C₂×#127	—	19	2	no	—
131	#493	—	19	4	no	—
132	#493	—	38	2	no	—
133	C₂×#102	—	38	4	no	—
134	C₂×#102	—	38	4	no	—
135	C₂×C₄×C₈	C₂×D₁₉	1	1	yes	characteristic
136	C₂×C₄×C₈	C₂×D₁₉	1	1	yes	characteristic
137	C₂×C₄×C₈	C₂×D₁₉	1	1	yes	characteristic
138	#384	—	19	2	no	—
139	#340	—	38	2	no	—
140	#322	—	2	2	no	—
141	C₂×C₁₉	#1717	1	2	yes	—
142	C₂×C₁₉	#1721	1	2	yes	—
143	C₂×C₁₉	#1961	1	1	yes	characteristic
144	C₂×C₁₉	#1970	1	1	yes	characteristic
145	C₂×C₁₉	#1972	1	1	yes	characteristic
146	D₁₉	—	16	4	no	—
147	C₂²×D₄	—	38	2	no	—
148	C₂²×D₄	—	38	2	no	—
149	C₂²×D₄	—	38	2	no	—
150	C₂×D₈	—	38	8	no	—
151	C₂×D₈	—	76	8	no	—
152	C₂²×C₈	D₇₆	1	2	yes	—
153	C₂²×C₈	D₇₆	1	2	yes	—
154	C₂²×C₈	D₇₆	1	2	yes	—
155	#127	—	19	4	no	—
156	#127	—	38	2	no	—
157	#127	—	38	2	no	—
158	#127	—	38	2	no	—
159	C₂×C₄⋊C₄	—	38	2	no	—
160	C₂×C₄⋊C₄	—	38	2	no	—
161	C₂×C₄⋊C₄	—	38	2	no	—
162	C₂×C₄²	C₂²×D₁₉	1	1	yes	characteristic
163	#102	—	76	8	no	—
164	#102	—	76	8	no	—
165	C₄×C₈	—	2	1	no	—
166	C₄×C₈	—	2	1	no	—
167	C₄×C₈	—	2	1	no	—
168	C₄×C₈	—	2	1	no	—
169	C₄×C₈	C₄×D₁₉	1	2	yes	—
170	C₄×C₈	C₂²⋊D₁₉	1	2	yes	—
171	C₁₉	#9832	1	1	yes	characteristic, complemented, Sylow
172	C₂⁴	—	76	2	no	—
173	C₂×D₄	—	38	4	no	—
174	C₂×D₄	—	38	4	no	—
175	C₂×D₄	—	38	4	no	—
176	C₂×D₄	—	76	2	no	—
177	C₂×D₄	—	76	2	no	—
178	C₂×D₄	—	76	2	no	—
179	C₂×D₄	—	76	4	no	—
180	C₂×D₄	—	76	4	no	—
181	C₂×D₄	—	76	4	no	—
182	C₂×D₄	—	76	4	no	—
183	C₂×D₄	—	76	4	no	—
184	C₂×D₄	—	76	4	no	—
185	C₂²×C₄	—	76	2	no	—
186	C₂²×C₄	C₂×D₇₆	1	1	yes	characteristic
187	C₂²×C₄	C₂×D₇₆	1	1	yes	characteristic
188	C₂²×C₄	C₂×D₇₆	1	1	yes	characteristic
189	D₈	—	76	16	no	—
190	C₂×C₈	—	2	2	no	—
191	C₂×C₈	—	2	2	no	—
192	C₂×C₈	—	2	4	no	—
193	C₂×C₈	—	2	2	no	—
194	C₂×C₈	—	2	4	no	—
195	C₂×C₈	D₁₅₂	1	4	yes	complemented
196	C₂×C₈	(C₂×D₁₉)⋊C₄	1	4	yes	—
197	C₄⋊C₄	—	76	4	no	—
198	C₄⋊C₄	—	76	4	no	—
199	C₄⋊C₄	—	76	4	no	—
200	C₄²	C₂×C₄×D₁₉	1	1	yes	characteristic
201	C₄²	#64541	1	1	yes	characteristic
202	C₄²	#64541	1	1	yes	characteristic
203	C₄²	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
204	C₂³	—	76	4	no	—
205	C₂³	—	152	2	no	—
206	C₂³	—	152	2	no	—
207	C₂³	—	152	2	no	—
208	C₂³	—	152	2	no	—
209	C₂³	—	152	2	no	—
210	C₂³	—	152	2	no	—
211	C₂³	#10597320	1	1	yes	characteristic
212	D₄	—	76	8	no	—
213	D₄	—	76	8	no	—
214	D₄	—	76	8	no	—
215	D₄	—	152	4	no	—
216	D₄	—	152	4	no	—
217	D₄	—	152	4	no	—
218	C₂×C₄	—	152	2	no	—
219	C₂×C₄	—	152	2	no	—
220	C₂×C₄	—	152	2	no	—
221	C₂×C₄	C₄×D₇₆	1	1	yes	characteristic
222	C₂×C₄	C₄×D₇₆	1	1	yes	characteristic
223	C₂×C₄	#10597321	1	1	yes	characteristic
224	C₂×C₄	C₂×D₁₅₂	1	2	yes	—
225	C₂×C₄	#10597350	1	2	yes	—
226	C₂×C₄	#10597354	1	4	yes	—
227	C₂×C₄	#10597354	1	4	yes	—
228	C₂×C₄	C₂×(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
229	C₂×C₄	#10597376	1	1	yes	characteristic
230	C₂×C₄	#10597376	1	1	yes	characteristic
231	C₈	—	2	4	no	—
232	C₈	—	2	4	no	—
233	C₈	—	4	2	no	—
234	C₂²	—	304	2	no	—
235	C₂²	—	304	2	no	—
236	C₂²	—	304	2	no	—
237	C₂²	—	304	2	no	—
238	C₂²	—	152	4	no	—
239	C₂²	—	152	4	no	—
240	C₂²	—	152	4	no	—
241	C₂²	#11926446	1	1	yes	characteristic
242	C₂²	#11926921	1	1	yes	characteristic
243	C₂²	#11926928	1	1	yes	characteristic
244	C₂²	#11926933	1	2	yes	—
245	C₂²	#11926933	1	2	yes	—
246	C₄	—	304	2	no	—
247	C₄	#11926550	1	2	yes	—
248	C₄	C₄×D₁₅₂	1	2	yes	—
249	C₄	#11926657	1	2	yes	—
250	C₄	#11926780	1	2	yes	—
251	C₄	#11926797	1	2	yes	—
252	C₄	#11926909	1	2	yes	—
253	C₂	—	304	4	no	—
254	C₂	#14563274	1	2	yes	—
255	C₂	#14563301	1	2	yes	—
256	C₂	#14564459	1	1	yes	characteristic
257	C₂	#14564501	1	1	yes	characteristic
258	C₂	#14564511	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	#10597320
commutator	C₄²×C₁₉	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₁₉
Fitting	C₂×C₁₉×#322	C₂
socle	C₂³×C₁₉	#127
prime radical	C₂×#11926921	C₂
cosocle	C₂×C₄²×C₁₉	C₂³
hypercenter	C₂×#322	D₁₉
hypocenter	C₁₉	#9832
LCS	G ▷ C₄²×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ C₂×#322

Complements

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

N	H ≅ G/N	type
2. #14564441	C₂	semidirect
3. #14564441	C₂	semidirect
4. #14563763	C₂	semidirect
5. C₂×C₁₉×#322	C₂	semidirect
9. #11926921	C₄	semidirect
65. C₂×C₈×C₁₉	D₈	semidirect
109. C₂×#322	D₁₉	semidirect
171. C₁₉	#9832	semidirect
195. C₂×C₈	D₁₅₂	semidirect

Maximal subgroups

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

subgroup	index
C₂×#11926921	2
#14564441	2
#14563763	2
C₂×C₁₉×#322	2
#9832	19