Subgroups — Q₈×C₁₉×#117 #18040083

Order 4864.

2434 conjugacy classes of subgroups.

The subgroup lattice has 336 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₄×Q₈×C₁₉	C₂	1	1	yes	maximal, characteristic
2	C₁₉×#2355	C₂	1	6	yes	maximal, complemented
3	Q₈×C₄⋊C₄×C₁₉	C₂	1	2	yes	maximal, complemented
4	C₁₉×#2345	C₂	1	6	yes	maximal
5	Q₈×C₂²⋊C₄×C₁₉	C₂	1	2	yes	maximal
6	C₁₉×#2295	C₂	1	6	yes	maximal, complemented
7	C₁₉×#2285	C₂	1	3	yes	maximal
8	C₄²×Q₈×C₁₉	C₂	1	2	yes	maximal, complemented
9	C₄×C₁₉×#117	C₂	1	3	yes	maximal
10	C₂³×Q₈×C₁₉	C₂²	1	1	yes	characteristic
11	C₂×C₄×Q₈×C₁₉	C₄	1	16	yes	complemented
12	C₂×C₄×Q₈×C₁₉	C₂²	1	4	yes	—
13	C₂×C₄×Q₈×C₁₉	C₂²	1	1	yes	characteristic
14	C₂×C₄×Q₈×C₁₉	C₂²	1	3	yes	—
15	C₂×C₄×Q₈×C₁₉	C₂²	1	1	yes	characteristic
16	C₂×C₄×Q₈×C₁₉	C₂²	1	3	yes	—
17	C₂×C₁₉×#117	C₂²	1	3	yes	—
18	C₂×C₁₉×#117	C₂²	1	1	yes	characteristic
19	C₂²×C₄⋊C₄×C₁₉	C₂²	1	3	yes	—
20	C₂²×C₄²×C₁₉	C₂²	1	3	yes	—
21	C₁₉×#391	C₂²	1	12	yes	—
22	C₁₉×#389	C₂²	1	12	yes	—
23	C₁₉×#387	C₂²	1	24	yes	—
24	C₁₉×#384	C₂²	1	6	yes	—
25	C₁₉×#382	C₂²	1	6	yes	—
26	C₁₉×#380	C₂²	1	6	yes	—
27	C₁₉×#380	C₂²	1	6	yes	—
28	C₄×C₄⋊C₄×C₁₉	C₂²	1	6	yes	—
29	C₄×C₄⋊C₄×C₁₉	C₂²	1	6	yes	—
30	C₄×C₄⋊C₄×C₁₉	C₂²	1	6	yes	—
31	C₄×C₄⋊C₄×C₁₉	C₂²	1	12	yes	—
32	C₄×C₄⋊C₄×C₁₉	C₂²	1	6	yes	—
33	C₄×C₂²⋊C₄×C₁₉	C₂²	1	6	yes	—
34	C₄×C₂²⋊C₄×C₁₉	C₂²	1	6	yes	—
35	C₁₉×#376	C₂²	1	6	yes	—
36	C₄³×C₁₉	C₂²	1	6	yes	—
37	C₂²×Q₈×C₁₉	—	2	8	no	—
38	C₂²×Q₈×C₁₉	C₂×C₄	1	8	yes	—
39	C₂²×Q₈×C₁₉	C₂³	1	3	yes	—
40	C₂²×Q₈×C₁₉	C₂³	1	1	yes	characteristic
41	C₂³×C₄×C₁₉	C₂³	1	3	yes	—
42	C₂³×C₄×C₁₉	C₂³	1	3	yes	—
43	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
44	C₄×Q₈×C₁₉	—	2	16	no	—
45	C₄×Q₈×C₁₉	C₂×C₄	1	24	yes	—
46	C₄×Q₈×C₁₉	C₂×C₄	1	24	yes	—
47	C₄×Q₈×C₁₉	C₂×C₄	1	8	yes	—
48	C₄×Q₈×C₁₉	C₂×C₄	1	8	yes	—
49	C₁₉×#117	—	2	12	no	—
50	C₁₉×#117	Q₈	1	8	yes	direct product factor
51	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	24	yes	—
52	C₂×C₄⋊C₄×C₁₉	C₂³	1	12	yes	—
53	C₂×C₄⋊C₄×C₁₉	C₂³	1	6	yes	—
54	C₂×C₄⋊C₄×C₁₉	C₂³	1	12	yes	—
55	C₂×C₄⋊C₄×C₁₉	C₂³	1	3	yes	—
56	C₂×C₄⋊C₄×C₁₉	C₂³	1	6	yes	—
57	C₂×C₄⋊C₄×C₁₉	C₂³	1	3	yes	—
58	C₂×C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
59	C₂×C₂²⋊C₄×C₁₉	C₂³	1	6	yes	—
60	C₂×C₂²⋊C₄×C₁₉	C₂³	1	2	yes	—
61	C₂×C₄²×C₁₉	C₂×C₄	1	24	yes	—
62	C₂×C₄²×C₁₉	C₂³	1	12	yes	—
63	C₂×C₄²×C₁₉	C₂³	1	6	yes	—
64	C₂×C₄²×C₁₉	C₂³	1	12	yes	—
65	C₂×C₄²×C₁₉	C₂³	1	3	yes	—
66	C₂×C₄²×C₁₉	C₂³	1	3	yes	—
67	C₂×C₄²×C₁₉	C₂³	1	3	yes	—
68	C₂×C₄²×C₁₉	C₂³	1	3	yes	—
69	C₂×C₄²×C₁₉	C₂³	1	2	yes	—
70	C₁₉×#95	C₂³	1	12	yes	—
71	C₁₉×#95	C₂³	1	12	yes	—
72	C₁₉×#95	C₂³	1	12	yes	—
73	C₁₉×#95	C₂³	1	12	yes	—
74	C₂⁴×C₁₉	C₂⁴	1	1	yes	characteristic
75	C₂×Q₈×C₁₉	—	2	32	no	—
76	C₂×Q₈×C₁₉	—	2	12	no	—
77	C₂×Q₈×C₁₉	C₂²×C₄	1	12	yes	—
78	C₂×Q₈×C₁₉	C₂²×C₄	1	4	yes	—
79	C₂×Q₈×C₁₉	#41	1	8	yes	—
80	C₂²×C₄×C₁₉	—	2	12	no	—
81	C₂²×C₄×C₁₉	—	4	6	no	—
82	C₂²×C₄×C₁₉	C₂²×C₄	1	12	yes	—
83	C₂²×C₄×C₁₉	C₂²×C₄	1	12	yes	—
84	C₂²×C₄×C₁₉	C₂²×C₄	1	4	yes	—
85	C₂²×C₄×C₁₉	C₂×Q₈	1	4	yes	—
86	C₂²×C₄×C₁₉	#41	1	4	yes	—
87	C₂²×C₄×C₁₉	C₂⁴	1	12	yes	—
88	C₂²×C₄×C₁₉	C₂⁴	1	3	yes	—
89	C₂²×C₄×C₁₉	C₂⁴	1	3	yes	—
90	C₂²×C₄×C₁₉	C₂⁴	1	3	yes	—
91	C₂²×C₄×C₁₉	C₂⁴	1	4	yes	—
92	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
93	C₂²×C₄×C₁₉	C₂⁴	1	3	yes	—
94	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
95	C₄⋊C₄×C₁₉	—	2	12	no	—
96	C₄⋊C₄×C₁₉	—	2	24	no	—
97	C₄⋊C₄×C₁₉	—	4	12	no	—
98	C₄⋊C₄×C₁₉	C₂²×C₄	1	24	yes	—
99	C₄⋊C₄×C₁₉	C₂²×C₄	1	12	yes	—
100	C₄⋊C₄×C₁₉	C₂²×C₄	1	12	yes	—
101	C₄⋊C₄×C₁₉	C₂×Q₈	1	8	yes	complemented
102	C₂²⋊C₄×C₁₉	—	2	12	no	—
103	C₂²⋊C₄×C₁₉	C₂×Q₈	1	8	yes	—
104	C₄²×C₁₉	—	2	12	no	—
105	C₄²×C₁₉	—	2	24	no	—
106	C₄²×C₁₉	—	4	12	no	—
107	C₄²×C₁₉	C₂²×C₄	1	12	yes	—
108	C₄²×C₁₉	C₂²×C₄	1	12	yes	—
109	C₄²×C₁₉	C₂²×C₄	1	12	yes	—
110	C₄²×C₁₉	C₂²×C₄	1	12	yes	—
111	C₄²×C₁₉	C₂×Q₈	1	8	yes	complemented
112	Q₈×#117	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
113	C₂³×C₁₉	—	2	2	no	—
114	C₂³×C₁₉	—	2	2	no	—
115	C₂³×C₁₉	C₂³×C₄	1	2	yes	—
116	C₂³×C₁₉	C₂²×Q₈	1	2	yes	—
117	C₂³×C₁₉	C₂×#41	1	2	yes	—
118	C₂³×C₁₉	C₂⁵	1	1	yes	characteristic
119	Q₈×C₁₉	—	2	24	no	—
120	Q₈×C₁₉	#117	1	16	yes	direct product factor
121	C₂×C₄×C₁₉	—	2	4	no	—
122	C₂×C₄×C₁₉	—	2	6	no	—
123	C₂×C₄×C₁₉	—	2	4	no	—
124	C₂×C₄×C₁₉	—	2	6	no	—
125	C₂×C₄×C₁₉	—	2	6	no	—
126	C₂×C₄×C₁₉	—	2	24	no	—
127	C₂×C₄×C₁₉	—	2	12	no	—
128	C₂×C₄×C₁₉	—	2	12	no	—
129	C₂×C₄×C₁₉	—	2	12	no	—
130	C₂×C₄×C₁₉	—	4	12	no	—
131	C₂×C₄×C₁₉	C₄×Q₈	1	16	yes	complemented
132	C₂×C₄×C₁₉	C₂³×C₄	1	6	yes	—
133	C₂×C₄×C₁₉	C₂³×C₄	1	6	yes	—
134	C₂×C₄×C₁₉	C₂³×C₄	1	6	yes	—
135	C₂×C₄×C₁₉	C₂³×C₄	1	6	yes	—
136	C₂×C₄×C₁₉	C₂³×C₄	1	2	yes	—
137	C₂×C₄×C₁₉	C₂³×C₄	1	2	yes	—
138	C₂×C₄×C₁₉	C₂²×Q₈	1	8	yes	—
139	C₂×C₄×C₁₉	C₂²×Q₈	1	2	yes	—
140	C₂×C₄×C₁₉	C₂²×Q₈	1	2	yes	—
141	C₂×C₄×C₁₉	C₂×#41	1	12	yes	—
142	C₂×C₄×C₁₉	C₂×#41	1	2	yes	—
143	C₂×C₄×C₁₉	C₂×#41	1	2	yes	—
144	C₂²×C₄×Q₈	C₂×C₁₉	1	1	yes	characteristic
145	#2355	C₂×C₁₉	1	6	yes	complemented
146	Q₈×C₄⋊C₄	C₂×C₁₉	1	2	yes	complemented
147	#2345	C₂×C₁₉	1	6	yes	—
148	Q₈×C₂²⋊C₄	C₂×C₁₉	1	2	yes	—
149	#2295	C₂×C₁₉	1	6	yes	complemented
150	#2285	C₂×C₁₉	1	3	yes	—
151	C₄²×Q₈	C₂×C₁₉	1	2	yes	complemented
152	C₄×#117	C₂×C₁₉	1	3	yes	—
153	C₂²×C₁₉	—	2	2	no	—
154	C₂²×C₁₉	—	2	2	no	—
155	C₂²×C₁₉	—	2	4	no	—
156	C₂²×C₁₉	—	2	4	no	—
157	C₂²×C₁₉	C₂×C₄×Q₈	1	4	yes	—
158	C₂²×C₁₉	C₂⁴×C₄	1	1	yes	characteristic
159	C₂²×C₁₉	C₂³×Q₈	1	1	yes	characteristic
160	C₂²×C₁₉	C₂²×#41	1	2	yes	—
161	C₂²×C₁₉	C₂²×#41	1	1	yes	characteristic
162	C₂²×C₁₉	#585	1	2	yes	—
163	C₄×C₁₉	—	2	6	no	—
164	C₄×C₁₉	—	2	6	no	—
165	C₄×C₁₉	—	2	6	no	—
166	C₄×C₁₉	—	2	8	no	—
167	C₄×C₁₉	—	4	12	no	—
168	C₄×C₁₉	C₂×#117	1	12	yes	—
169	C₄×C₁₉	C₂×C₄×Q₈	1	4	yes	—
170	C₄×C₁₉	C₂×C₄×Q₈	1	4	yes	—
171	C₂³×Q₈	C₂²×C₁₉	1	1	yes	characteristic
172	C₂×C₄×Q₈	C₄×C₁₉	1	16	yes	complemented
173	C₂×C₄×Q₈	C₂²×C₁₉	1	4	yes	—
174	C₂×C₄×Q₈	C₂²×C₁₉	1	1	yes	characteristic
175	C₂×C₄×Q₈	C₂²×C₁₉	1	3	yes	—
176	C₂×C₄×Q₈	C₂²×C₁₉	1	1	yes	characteristic
177	C₂×C₄×Q₈	C₂²×C₁₉	1	3	yes	—
178	C₂×#117	C₂²×C₁₉	1	3	yes	—
179	C₂×#117	C₂²×C₁₉	1	1	yes	characteristic
180	C₂²×C₄⋊C₄	C₂²×C₁₉	1	3	yes	—
181	C₂²×C₄²	C₂²×C₁₉	1	3	yes	—
182	#391	C₂²×C₁₉	1	12	yes	—
183	#389	C₂²×C₁₉	1	12	yes	—
184	#387	C₂²×C₁₉	1	24	yes	—
185	#384	C₂²×C₁₉	1	6	yes	—
186	#382	C₂²×C₁₉	1	6	yes	—
187	#380	C₂²×C₁₉	1	6	yes	—
188	#380	C₂²×C₁₉	1	6	yes	—
189	C₄×C₄⋊C₄	C₂²×C₁₉	1	12	yes	—
190	C₄×C₄⋊C₄	C₂²×C₁₉	1	6	yes	—
191	C₄×C₄⋊C₄	C₂²×C₁₉	1	6	yes	—
192	C₄×C₄⋊C₄	C₂²×C₁₉	1	6	yes	—
193	C₄×C₄⋊C₄	C₂²×C₁₉	1	6	yes	—
194	C₄×C₂²⋊C₄	C₂²×C₁₉	1	6	yes	—
195	C₄×C₂²⋊C₄	C₂²×C₁₉	1	6	yes	—
196	#376	C₂²×C₁₉	1	6	yes	—
197	C₄³	C₂²×C₁₉	1	6	yes	—
198	C₂×C₁₉	—	2	4	no	—
199	C₂×C₁₉	C₂²×#117	1	1	yes	characteristic
200	C₂×C₁₉	C₂²×C₄×Q₈	1	1	yes	characteristic
201	C₂×C₁₉	#3428	1	1	yes	characteristic
202	C₂×C₁₉	Q₈×#41	1	2	yes	—
203	C₂×C₁₉	#3480	1	2	yes	—
204	C₂²×Q₈	—	2	8	no	—
205	C₂²×Q₈	C₂×C₄×C₁₉	1	8	yes	—
206	C₂²×Q₈	C₂³×C₁₉	1	3	yes	—
207	C₂²×Q₈	C₂³×C₁₉	1	1	yes	characteristic
208	C₂³×C₄	C₂³×C₁₉	1	3	yes	—
209	C₂³×C₄	C₂³×C₁₉	1	3	yes	—
210	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
211	C₄×Q₈	—	2	16	no	—
212	C₄×Q₈	C₂×C₄×C₁₉	1	24	yes	—
213	C₄×Q₈	C₂×C₄×C₁₉	1	24	yes	—
214	C₄×Q₈	C₂×C₄×C₁₉	1	8	yes	—
215	C₄×Q₈	C₂×C₄×C₁₉	1	8	yes	—
216	#117	—	2	12	no	—
217	#117	Q₈×C₁₉	1	8	yes	direct product factor
218	C₂×C₄⋊C₄	C₂×C₄×C₁₉	1	24	yes	—
219	C₂×C₄⋊C₄	C₂³×C₁₉	1	6	yes	—
220	C₂×C₄⋊C₄	C₂³×C₁₉	1	12	yes	—
221	C₂×C₄⋊C₄	C₂³×C₁₉	1	12	yes	—
222	C₂×C₄⋊C₄	C₂³×C₁₉	1	3	yes	—
223	C₂×C₄⋊C₄	C₂³×C₁₉	1	6	yes	—
224	C₂×C₄⋊C₄	C₂³×C₁₉	1	3	yes	—
225	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
226	C₂×C₂²⋊C₄	C₂³×C₁₉	1	6	yes	—
227	C₂×C₂²⋊C₄	C₂³×C₁₉	1	2	yes	—
228	C₂×C₄²	C₂×C₄×C₁₉	1	24	yes	—
229	C₂×C₄²	C₂³×C₁₉	1	6	yes	—
230	C₂×C₄²	C₂³×C₁₉	1	12	yes	—
231	C₂×C₄²	C₂³×C₁₉	1	12	yes	—
232	C₂×C₄²	C₂³×C₁₉	1	3	yes	—
233	C₂×C₄²	C₂³×C₁₉	1	3	yes	—
234	C₂×C₄²	C₂³×C₁₉	1	3	yes	—
235	C₂×C₄²	C₂³×C₁₉	1	3	yes	—
236	C₂×C₄²	C₂³×C₁₉	1	2	yes	—
237	#95	C₂³×C₁₉	1	12	yes	—
238	#95	C₂³×C₁₉	1	12	yes	—
239	#95	C₂³×C₁₉	1	12	yes	—
240	#95	C₂³×C₁₉	1	12	yes	—
241	C₁₉	Q₈×#117	1	1	yes	characteristic, direct product factor, Sylow
242	C₂⁴	C₂⁴×C₁₉	1	1	yes	characteristic
243	C₂×Q₈	—	2	32	no	—
244	C₂×Q₈	—	2	12	no	—
245	C₂×Q₈	C₂²×C₄×C₁₉	1	12	yes	—
246	C₂×Q₈	C₂²×C₄×C₁₉	1	4	yes	—
247	C₂×Q₈	#41×C₁₉	1	8	yes	—
248	C₂²×C₄	—	2	12	no	—
249	C₂²×C₄	—	4	6	no	—
250	C₂²×C₄	C₂²×C₄×C₁₉	1	12	yes	—
251	C₂²×C₄	C₂²×C₄×C₁₉	1	12	yes	—
252	C₂²×C₄	C₂²×C₄×C₁₉	1	4	yes	—
253	C₂²×C₄	C₂×Q₈×C₁₉	1	4	yes	—
254	C₂²×C₄	#41×C₁₉	1	4	yes	—
255	C₂²×C₄	C₂⁴×C₁₉	1	12	yes	—
256	C₂²×C₄	C₂⁴×C₁₉	1	3	yes	—
257	C₂²×C₄	C₂⁴×C₁₉	1	3	yes	—
258	C₂²×C₄	C₂⁴×C₁₉	1	3	yes	—
259	C₂²×C₄	C₂⁴×C₁₉	1	4	yes	—
260	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
261	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
262	C₂²×C₄	C₂⁴×C₁₉	1	3	yes	—
263	C₄⋊C₄	—	2	12	no	—
264	C₄⋊C₄	—	2	24	no	—
265	C₄⋊C₄	—	4	12	no	—
266	C₄⋊C₄	C₂²×C₄×C₁₉	1	24	yes	—
267	C₄⋊C₄	C₂²×C₄×C₁₉	1	12	yes	—
268	C₄⋊C₄	C₂²×C₄×C₁₉	1	12	yes	—
269	C₄⋊C₄	C₂×Q₈×C₁₉	1	8	yes	complemented
270	C₂²⋊C₄	—	2	12	no	—
271	C₂²⋊C₄	C₂×Q₈×C₁₉	1	8	yes	—
272	C₄²	—	2	12	no	—
273	C₄²	—	2	24	no	—
274	C₄²	—	4	12	no	—
275	C₄²	C₂²×C₄×C₁₉	1	12	yes	—
276	C₄²	C₂²×C₄×C₁₉	1	12	yes	—
277	C₄²	C₂²×C₄×C₁₉	1	12	yes	—
278	C₄²	C₂²×C₄×C₁₉	1	12	yes	—
279	C₄²	C₂×Q₈×C₁₉	1	8	yes	complemented
280	C₂³	—	2	2	no	—
281	C₂³	—	2	2	no	—
282	C₂³	C₂³×C₄×C₁₉	1	2	yes	—
283	C₂³	C₂²×Q₈×C₁₉	1	2	yes	—
284	C₂³	C₂×#41×C₁₉	1	2	yes	—
285	C₂³	C₂⁵×C₁₉	1	1	yes	characteristic
286	Q₈	—	2	24	no	—
287	Q₈	C₁₉×#117	1	16	yes	direct product factor
288	C₂×C₄	—	2	4	no	—
289	C₂×C₄	—	2	6	no	—
290	C₂×C₄	—	2	4	no	—
291	C₂×C₄	—	2	6	no	—
292	C₂×C₄	—	2	6	no	—
293	C₂×C₄	—	2	24	no	—
294	C₂×C₄	—	2	12	no	—
295	C₂×C₄	—	2	12	no	—
296	C₂×C₄	—	2	12	no	—
297	C₂×C₄	—	4	12	no	—
298	C₂×C₄	C₄×Q₈×C₁₉	1	16	yes	complemented
299	C₂×C₄	C₂³×C₄×C₁₉	1	6	yes	—
300	C₂×C₄	C₂³×C₄×C₁₉	1	6	yes	—
301	C₂×C₄	C₂³×C₄×C₁₉	1	6	yes	—
302	C₂×C₄	C₂³×C₄×C₁₉	1	6	yes	—
303	C₂×C₄	C₂³×C₄×C₁₉	1	2	yes	—
304	C₂×C₄	C₂³×C₄×C₁₉	1	2	yes	—
305	C₂×C₄	C₂²×Q₈×C₁₉	1	8	yes	—
306	C₂×C₄	C₂²×Q₈×C₁₉	1	2	yes	—
307	C₂×C₄	C₂²×Q₈×C₁₉	1	2	yes	—
308	C₂×C₄	C₂×#41×C₁₉	1	12	yes	—
309	C₂×C₄	C₂×#41×C₁₉	1	2	yes	—
310	C₂×C₄	C₂×#41×C₁₉	1	2	yes	—
311	C₂²	—	2	2	no	—
312	C₂²	—	2	4	no	—
313	C₂²	—	2	4	no	—
314	C₂²	—	2	2	no	—
315	C₂²	C₂×C₄×Q₈×C₁₉	1	4	yes	—
316	C₂²	C₂⁴×C₄×C₁₉	1	1	yes	characteristic
317	C₂²	C₂³×Q₈×C₁₉	1	1	yes	characteristic
318	C₂²	C₂²×#41×C₁₉	1	1	yes	characteristic
319	C₂²	C₂²×#41×C₁₉	1	2	yes	—
320	C₂²	C₁₉×#585	1	2	yes	—
321	C₄	—	2	6	no	—
322	C₄	—	2	6	no	—
323	C₄	—	2	8	no	—
324	C₄	—	2	6	no	—
325	C₄	—	4	12	no	—
326	C₄	C₂×C₁₉×#117	1	12	yes	—
327	C₄	C₂×C₄×Q₈×C₁₉	1	4	yes	—
328	C₄	C₂×C₄×Q₈×C₁₉	1	4	yes	—
329	C₂	—	2	4	no	—
330	C₂	C₂²×C₁₉×#117	1	1	yes	characteristic
331	C₂	C₂²×C₄×Q₈×C₁₉	1	1	yes	characteristic
332	C₂	C₁₉×#3428	1	1	yes	characteristic
333	C₂	Q₈×#41×C₁₉	1	2	yes	—
334	C₂	C₁₉×#3480	1	2	yes	—

	subgroup	G/H
center	C₂²×C₄×C₁₉	C₂⁴
commutator	C₂²	C₂⁴×C₄×C₁₉
Frattini, cosocle	C₂³	C₂⁵×C₁₉
socle	C₂³×C₁₉	C₂⁵
prime radical	C₂⁴×C₁₉	C₂⁴
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₄×C₁₉ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₁₉×#2355	C₂	semidirect
3. Q₈×C₄⋊C₄×C₁₉	C₂	semidirect
6. C₁₉×#2295	C₂	semidirect
8. C₄²×Q₈×C₁₉	C₂	semidirect
11. C₂×C₄×Q₈×C₁₉	C₄	semidirect
50. C₁₉×#117	Q₈	direct (N × H)
101. C₄⋊C₄×C₁₉	C₂×Q₈	semidirect
111. C₄²×C₁₉	C₂×Q₈	semidirect
112. Q₈×#117	C₁₉	direct (N × H)
120. Q₈×C₁₉	#117	direct (N × H)
131. C₂×C₄×C₁₉	C₄×Q₈	semidirect
145. #2355	C₂×C₁₉	semidirect
146. Q₈×C₄⋊C₄	C₂×C₁₉	semidirect
149. #2295	C₂×C₁₉	semidirect
151. C₄²×Q₈	C₂×C₁₉	semidirect
172. C₂×C₄×Q₈	C₄×C₁₉	semidirect
217. #117	Q₈×C₁₉	direct (N × H)
241. C₁₉	Q₈×#117	direct (N × H)
269. C₄⋊C₄	C₂×Q₈×C₁₉	semidirect
279. C₄²	C₂×Q₈×C₁₉	semidirect
287. Q₈	C₁₉×#117	direct (N × H)
298. C₂×C₄	C₄×Q₈×C₁₉	semidirect

Maximal subgroups

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

subgroup	index
C₂²×C₄×Q₈×C₁₉	2
C₁₉×#2355	2
Q₈×C₄⋊C₄×C₁₉	2
C₁₉×#2345	2
Q₈×C₂²⋊C₄×C₁₉	2
C₁₉×#2295	2
C₁₉×#2285	2
C₄²×Q₈×C₁₉	2
C₄×C₁₉×#117	2
Q₈×#117	19

Subgroups — Q8×C19×#117 #18040083

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — Q₈×C₁₉×#117 #18040083