Subgroups — C₂×#20243947 #26218322

Order 12032.

1134 conjugacy classes of subgroups.

The subgroup lattice has 432 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₄⋊(C₄₇⋊C₈)	C₂	1	1	yes	maximal, characteristic
2	C₂²×C₄×C₄₇⋊C₈	C₂	1	1	yes	maximal, characteristic
3	#20243947	C₂	1	8	yes	maximal, direct product factor
4	C₂×#15688878	C₂	1	1	yes	maximal, characteristic
5	C₂×#15688878	C₂	1	1	yes	maximal, characteristic
6	C₂×#15688878	C₂	1	1	yes	maximal, characteristic
7	C₂×#15688878	C₂	1	1	yes	maximal, characteristic
8	C₂×C₄×C₄⋊C₄×C₄₇	C₂	1	1	yes	maximal, characteristic
9	C₂³×C₄₇⋊C₈	C₂²	1	1	yes	characteristic
10	C₂³×C₄₇⋊C₈	C₂²	1	1	yes	characteristic
11	C₂³×C₄₇⋊C₈	C₂²	1	1	yes	characteristic
12	C₂³×C₄₇⋊C₈	C₂²	1	1	yes	characteristic
13	C₂×C₄⋊(C₄₇⋊C₈)	—	2	4	no	—
14	C₂×C₄⋊(C₄₇⋊C₈)	C₂²	1	4	yes	—
15	C₂×C₄×C₄₇⋊C₈	—	2	4	no	—
16	C₂×C₄×C₄₇⋊C₈	C₂²	1	4	yes	—
17	#15688878	C₂²	1	4	yes	—
18	#15688878	C₂²	1	4	yes	—
19	#15688878	C₂²	1	4	yes	—
20	#15688878	C₂²	1	4	yes	—
21	C₂²×C₄⋊C₄×C₄₇	C₄	1	1	yes	characteristic
22	C₂²×C₄⋊C₄×C₄₇	C₄	1	1	yes	characteristic
23	C₂²×C₄²×C₄₇	C₂²	1	1	yes	characteristic
24	C₂²×C₄²×C₄₇	C₂²	1	1	yes	characteristic
25	C₂²×C₄²×C₄₇	C₂²	1	1	yes	characteristic
26	C₄×C₄⋊C₄×C₄₇	C₄	1	4	yes	—
27	C₄×C₄⋊C₄×C₄₇	C₂²	1	4	yes	—
28	C₂×#95×C₄₇	C₄	1	1	yes	characteristic
29	C₂×#95×C₄₇	C₄	1	1	yes	characteristic
30	C₂²×C₄₇⋊C₈	—	2	2	no	—
31	C₂²×C₄₇⋊C₈	—	2	2	no	—
32	C₂²×C₄₇⋊C₈	—	2	2	no	—
33	C₂²×C₄₇⋊C₈	—	2	2	no	—
34	C₂²×C₄₇⋊C₈	—	2	2	no	—
35	C₂²×C₄₇⋊C₈	—	2	2	no	—
36	C₂²×C₄₇⋊C₈	—	2	2	no	—
37	C₂²×C₄₇⋊C₈	—	2	2	no	—
38	C₂²×C₄₇⋊C₈	—	2	2	no	—
39	C₂²×C₄₇⋊C₈	—	2	2	no	—
40	C₂²×C₄₇⋊C₈	D₄	1	4	yes	—
41	C₂²×C₄₇⋊C₈	Q₈	1	4	yes	—
42	C₂²×C₄₇⋊C₈	C₂³	1	2	yes	—
43	C₂²×C₄₇⋊C₈	C₂³	1	2	yes	—
44	C₂²×C₄₇⋊C₈	C₂³	1	2	yes	—
45	C₂²×C₄₇⋊C₈	C₂³	1	2	yes	—
46	C₄⋊(C₄₇⋊C₈)	—	2	8	no	—
47	C₄×C₄₇⋊C₈	—	2	8	no	—
48	C₂³×C₄×C₄₇	C₂×C₄	1	1	yes	characteristic
49	C₂³×C₄×C₄₇	C₂×C₄	1	1	yes	characteristic
50	C₂³×C₄×C₄₇	C₂×C₄	1	1	yes	characteristic
51	C₂³×C₄×C₄₇	C₂×C₄	1	1	yes	characteristic
52	C₂³×C₄×C₄₇	C₂×C₄	1	1	yes	characteristic
53	C₂³×C₄×C₄₇	C₂×C₄	1	1	yes	characteristic
54	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
55	C₂×C₄⋊C₄×C₄₇	—	2	4	no	—
56	C₂×C₄⋊C₄×C₄₇	C₈	1	8	yes	complemented
57	C₂×C₄⋊C₄×C₄₇	C₂×C₄	1	4	yes	—
58	C₂×C₄⋊C₄×C₄₇	C₂×C₄	1	4	yes	—
59	C₂×C₄²×C₄₇	—	2	2	no	—
60	C₂×C₄²×C₄₇	—	2	2	no	—
61	C₂×C₄²×C₄₇	—	2	2	no	—
62	C₂×C₄²×C₄₇	—	2	2	no	—
63	C₂×C₄²×C₄₇	—	2	2	no	—
64	C₂×C₄²×C₄₇	—	2	2	no	—
65	C₂×C₄²×C₄₇	C₂×C₄	1	2	yes	—
66	C₂×C₄²×C₄₇	C₂×C₄	1	2	yes	—
67	C₂×C₄²×C₄₇	C₂×C₄	1	2	yes	—
68	C₂×C₄²×C₄₇	C₂³	1	2	yes	—
69	C₂×C₄²×C₄₇	C₂³	1	2	yes	—
70	C₂×C₄²×C₄₇	C₂³	1	2	yes	—
71	#95×C₄₇	C₂×C₄	1	4	yes	—
72	#95×C₄₇	C₂×C₄	1	4	yes	—
73	C₂⁴×C₄₇	C₂²×C₄	1	1	yes	characteristic
74	C₂²×C₄×C₄₇	—	2	2	no	—
75	C₂²×C₄×C₄₇	—	2	2	no	—
76	C₂²×C₄×C₄₇	—	2	2	no	—
77	C₂²×C₄×C₄₇	—	2	2	no	—
78	C₂²×C₄×C₄₇	—	2	2	no	—
79	C₂²×C₄×C₄₇	—	2	2	no	—
80	C₂²×C₄×C₄₇	—	2	2	no	—
81	C₂²×C₄×C₄₇	—	2	2	no	—
82	C₂²×C₄×C₄₇	—	2	2	no	—
83	C₂²×C₄×C₄₇	—	2	2	no	—
84	C₂²×C₄×C₄₇	—	2	2	no	—
85	C₂²×C₄×C₄₇	—	2	2	no	—
86	C₂²×C₄×C₄₇	—	2	2	no	—
87	C₂²×C₄×C₄₇	—	2	2	no	—
88	C₂²×C₄×C₄₇	C₂×C₈	1	4	yes	—
89	C₂²×C₄×C₄₇	C₂×C₈	1	4	yes	—
90	C₂²×C₄×C₄₇	C₂×C₈	1	4	yes	—
91	C₂²×C₄×C₄₇	M₁₆	1	4	yes	—
92	C₂²×C₄×C₄₇	C₂²×C₄	1	2	yes	—
93	C₂²×C₄×C₄₇	C₂²×C₄	1	2	yes	—
94	C₂²×C₄×C₄₇	C₂²×C₄	1	2	yes	—
95	C₂²×C₄×C₄₇	C₂²×C₄	1	2	yes	—
96	C₂²×C₄×C₄₇	C₂²×C₄	1	2	yes	—
97	C₂²×C₄×C₄₇	C₂²×C₄	1	2	yes	—
98	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
99	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
100	C₂²×C₄×C₄₇	C₂×Q₈	1	2	yes	—
101	C₂²×C₄×C₄₇	#41	1	2	yes	—
102	C₂²×C₄×C₄₇	#41	1	2	yes	—
103	C₂²×C₄×C₄₇	#41	1	2	yes	—
104	C₂²×C₄×C₄₇	#41	1	2	yes	—
105	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
106	C₄⋊C₄×C₄₇	—	2	8	no	—
107	C₄⋊C₄×C₄₇	C₂×C₈	1	16	yes	complemented
108	C₄²×C₄₇	—	2	4	no	—
109	C₄²×C₄₇	—	2	4	no	—
110	C₄²×C₄₇	—	2	4	no	—
111	C₄²×C₄₇	—	2	2	no	—
112	C₄²×C₄₇	—	2	2	no	—
113	C₄²×C₄₇	—	2	2	no	—
114	C₄²×C₄₇	—	2	2	no	—
115	C₄²×C₄₇	—	2	2	no	—
116	C₄²×C₄₇	—	2	2	no	—
117	C₂×C₄₇⋊C₈	—	2	8	no	—
118	C₂×C₄₇⋊C₈	—	2	8	no	—
119	C₂×C₄₇⋊C₈	—	2	2	no	—
120	C₂×C₄₇⋊C₈	—	2	2	no	—
121	C₂×C₄₇⋊C₈	—	2	2	no	—
122	C₂×C₄₇⋊C₈	—	2	2	no	—
123	C₂×C₄₇⋊C₈	—	2	2	no	—
124	C₂×C₄₇⋊C₈	—	2	2	no	—
125	C₂×C₄₇⋊C₈	—	2	2	no	—
126	C₂×C₄₇⋊C₈	—	2	2	no	—
127	C₂×C₄₇⋊C₈	—	2	2	no	—
128	C₂×C₄₇⋊C₈	—	2	2	no	—
129	C₂×C₄₇⋊C₈	—	4	4	no	—
130	C₂×C₄₇⋊C₈	—	4	4	no	—
131	C₂×C₄₇⋊C₈	C₂×D₄	1	4	yes	—
132	C₂×C₄₇⋊C₈	C₂×Q₈	1	4	yes	—
133	C₂³×C₄₇	#117	1	2	yes	—
134	C₂³×C₄₇	C₄×D₄	1	2	yes	—
135	C₂³×C₄₇	C₄×Q₈	1	2	yes	—
136	C₂³×C₄₇	C₂²×C₈	1	2	yes	—
137	C₂³×C₄₇	C₂×M₁₆	1	2	yes	—
138	C₂³×C₄₇	#131	1	2	yes	—
139	C₂³×C₄₇	#131	1	2	yes	—
140	C₂³×C₄₇	C₂³×C₄	1	1	yes	characteristic
141	C₂×C₄×C₄₇	—	2	2	no	—
142	C₂×C₄×C₄₇	—	2	2	no	—
143	C₂×C₄×C₄₇	—	2	2	no	—
144	C₂×C₄×C₄₇	—	2	2	no	—
145	C₂×C₄×C₄₇	—	2	2	no	—
146	C₂×C₄×C₄₇	—	2	2	no	—
147	C₂×C₄×C₄₇	—	2	2	no	—
148	C₂×C₄×C₄₇	—	2	2	no	—
149	C₂×C₄×C₄₇	—	2	8	no	—
150	C₂×C₄×C₄₇	—	2	8	no	—
151	C₂×C₄×C₄₇	—	2	8	no	—
152	C₂×C₄×C₄₇	—	2	8	no	—
153	C₂×C₄×C₄₇	—	2	2	no	—
154	C₂×C₄×C₄₇	—	2	2	no	—
155	C₂×C₄×C₄₇	—	2	2	no	—
156	C₂×C₄×C₄₇	—	2	2	no	—
157	C₂×C₄×C₄₇	—	2	2	no	—
158	C₂×C₄×C₄₇	—	2	2	no	—
159	C₂×C₄×C₄₇	—	4	4	no	—
160	C₂×C₄×C₄₇	—	4	4	no	—
161	C₂×C₄×C₄₇	#117	1	2	yes	—
162	C₂×C₄×C₄₇	C₄×D₄	1	2	yes	—
163	C₂×C₄×C₄₇	C₄×Q₈	1	2	yes	—
164	C₂×C₄×C₄₇	C₂²⋊Q₈	1	4	yes	—
165	C₂×C₄×C₄₇	#123	1	4	yes	—
166	C₂×C₄×C₄₇	#125	1	4	yes	—
167	C₂×C₄×C₄₇	#126	1	4	yes	—
168	C₂×C₄×C₄₇	C₂²×C₈	1	4	yes	—
169	C₂×C₄×C₄₇	C₂²×C₈	1	4	yes	—
170	C₂×C₄×C₄₇	C₂²×C₈	1	4	yes	—
171	C₂×C₄×C₄₇	C₂×M₁₆	1	4	yes	—
172	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
173	C₂×C₄×C₄₇	C₂²×Q₈	1	1	yes	characteristic
174	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
175	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
176	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
177	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
178	C₄₇⋊C₈	—	2	4	no	—
179	C₄₇⋊C₈	—	2	4	no	—
180	C₄₇⋊C₈	—	4	2	no	—
181	C₄₇⋊C₈	—	4	2	no	—
182	C₂×#1916	—	47	1	no	maximal, Sylow
183	C₂²×C₄₇	#387	1	4	yes	—
184	C₂²×C₄₇	#431	1	4	yes	—
185	C₂²×C₄₇	#433	1	4	yes	—
186	C₂²×C₄₇	C₈×D₄	1	4	yes	—
187	C₂²×C₄₇	#435	1	4	yes	—
188	C₂²×C₄₇	C₈×Q₈	1	4	yes	—
189	C₂²×C₄₇	#446	1	4	yes	—
190	C₂²×C₄₇	C₂×#117	1	1	yes	characteristic
191	C₂²×C₄₇	C₂×C₄×D₄	1	1	yes	characteristic
192	C₂²×C₄₇	C₂×C₄×Q₈	1	1	yes	characteristic
193	C₂²×C₄₇	C₂³×C₈	1	1	yes	characteristic
194	C₂²×C₄₇	C₂²×M₁₆	1	1	yes	characteristic
195	C₂²×C₄₇	C₂×#131	1	1	yes	characteristic
196	C₂²×C₄₇	C₂×#131	1	1	yes	characteristic
197	C₄×C₄₇	—	2	4	no	—
198	C₄×C₄₇	—	2	4	no	—
199	C₄×C₄₇	—	2	4	no	—
200	C₄×C₄₇	—	2	4	no	—
201	C₄×C₄₇	—	4	2	no	—
202	C₄×C₄₇	—	4	2	no	—
203	C₄×C₄₇	#387	1	4	yes	—
204	C₄×C₄₇	C₂×C₂²⋊Q₈	1	1	yes	characteristic
205	C₄×C₄₇	C₂×#123	1	1	yes	characteristic
206	C₄×C₄₇	C₂×#125	1	1	yes	characteristic
207	C₄×C₄₇	C₂×#126	1	1	yes	characteristic
208	C₂²×C₄⋊C₈	—	47	1	no	—
209	C₂²×C₄×C₈	—	47	1	no	—
210	C₂×C₄×C₄⋊C₄	D₄₇	1	1	yes	characteristic
211	#1916	—	47	8	no	—
212	C₂×#336	—	47	1	no	—
213	C₂×#336	—	47	1	no	—
214	C₂×#336	—	47	1	no	—
215	C₂×#336	—	47	1	no	—
216	C₂×C₄₇	#1916	1	8	yes	complemented
217	C₂×C₄₇	C₂×#387	1	1	yes	characteristic
218	C₂×C₄₇	C₂×#431	1	1	yes	characteristic
219	C₂×C₄₇	C₂×#433	1	1	yes	characteristic
220	C₂×C₄₇	C₂×C₈×D₄	1	1	yes	characteristic
221	C₂×C₄₇	C₂×#435	1	1	yes	characteristic
222	C₂×C₄₇	C₂×C₈×Q₈	1	1	yes	characteristic
223	C₂×C₄₇	C₂×#446	1	1	yes	characteristic
224	C₂³×C₈	—	47	1	no	—
225	C₂³×C₈	—	47	1	no	—
226	C₂³×C₈	—	47	1	no	—
227	C₂³×C₈	—	47	1	no	—
228	C₂²×C₄⋊C₄	Dic₄₇	1	1	yes	characteristic
229	C₂²×C₄⋊C₄	Dic₄₇	1	1	yes	characteristic
230	C₂²×C₄²	C₂×D₄₇	1	1	yes	characteristic
231	C₂²×C₄²	C₂×D₄₇	1	1	yes	characteristic
232	C₂²×C₄²	C₂×D₄₇	1	1	yes	characteristic
233	C₂×C₄⋊C₈	—	47	4	no	—
234	C₂×C₄⋊C₈	—	94	4	no	—
235	C₂×C₄×C₈	—	47	4	no	—
236	C₂×C₄×C₈	—	94	4	no	—
237	C₄×C₄⋊C₄	Dic₄₇	1	4	yes	—
238	C₄×C₄⋊C₄	C₂×D₄₇	1	4	yes	—
239	C₂×#95	Dic₄₇	1	1	yes	characteristic
240	C₂×#95	Dic₄₇	1	1	yes	characteristic
241	#336	—	47	4	no	—
242	#336	—	47	4	no	—
243	#336	—	47	4	no	—
244	#336	—	47	4	no	—
245	C₄₇	C₂×#1916	1	1	yes	characteristic, complemented, Sylow
246	C₂³×C₄	C₂×Dic₄₇	1	1	yes	characteristic
247	C₂³×C₄	C₂×Dic₄₇	1	1	yes	characteristic
248	C₂³×C₄	C₂×Dic₄₇	1	1	yes	characteristic
249	C₂³×C₄	C₂×Dic₄₇	1	1	yes	characteristic
250	C₂³×C₄	C₂×Dic₄₇	1	1	yes	characteristic
251	C₂³×C₄	C₂×Dic₄₇	1	1	yes	characteristic
252	C₂³×C₄	C₂²×D₄₇	1	1	yes	characteristic
253	C₂²×C₈	—	47	4	no	—
254	C₂²×C₈	—	47	4	no	—
255	C₂²×C₈	—	47	2	no	—
256	C₂²×C₈	—	47	2	no	—
257	C₂²×C₈	—	47	2	no	—
258	C₂²×C₈	—	47	2	no	—
259	C₂²×C₈	—	94	2	no	—
260	C₂²×C₈	—	94	2	no	—
261	C₂²×C₈	—	94	2	no	—
262	C₂²×C₈	—	94	2	no	—
263	C₂²×C₈	—	94	2	no	—
264	C₂²×C₈	—	94	2	no	—
265	C₂²×C₈	—	94	2	no	—
266	C₂²×C₈	—	94	2	no	—
267	C₂²×C₈	—	94	2	no	—
268	C₂²×C₈	—	94	2	no	—
269	C₂×C₄⋊C₄	—	2	4	no	—
270	C₂×C₄⋊C₄	C₄₇⋊C₈	1	8	yes	complemented
271	C₂×C₄⋊C₄	C₂×Dic₄₇	1	4	yes	—
272	C₂×C₄⋊C₄	C₂×Dic₄₇	1	4	yes	—
273	C₂×C₄²	—	2	2	no	—
274	C₂×C₄²	—	2	2	no	—
275	C₂×C₄²	—	2	2	no	—
276	C₂×C₄²	—	2	2	no	—
277	C₂×C₄²	—	2	2	no	—
278	C₂×C₄²	—	2	2	no	—
279	C₂×C₄²	C₂×Dic₄₇	1	2	yes	—
280	C₂×C₄²	C₂×Dic₄₇	1	2	yes	—
281	C₂×C₄²	C₂×Dic₄₇	1	2	yes	—
282	C₂×C₄²	C₂²×D₄₇	1	2	yes	—
283	C₂×C₄²	C₂²×D₄₇	1	2	yes	—
284	C₂×C₄²	C₂²×D₄₇	1	2	yes	—
285	C₄⋊C₈	—	94	8	no	—
286	C₄×C₈	—	94	8	no	—
287	#95	C₂×Dic₄₇	1	4	yes	—
288	#95	C₂×Dic₄₇	1	4	yes	—
289	C₂⁴	C₂²×Dic₄₇	1	1	yes	characteristic
290	C₂²×C₄	—	2	2	no	—
291	C₂²×C₄	—	2	2	no	—
292	C₂²×C₄	—	2	2	no	—
293	C₂²×C₄	—	2	2	no	—
294	C₂²×C₄	—	2	2	no	—
295	C₂²×C₄	—	2	2	no	—
296	C₂²×C₄	—	2	2	no	—
297	C₂²×C₄	—	2	2	no	—
298	C₂²×C₄	—	2	2	no	—
299	C₂²×C₄	—	2	2	no	—
300	C₂²×C₄	—	2	2	no	—
301	C₂²×C₄	—	2	2	no	—
302	C₂²×C₄	—	2	2	no	—
303	C₂²×C₄	—	2	2	no	—
304	C₂²×C₄	C₂×C₄₇⋊C₈	1	4	yes	—
305	C₂²×C₄	C₂×C₄₇⋊C₈	1	4	yes	—
306	C₂²×C₄	C₂×C₄₇⋊C₈	1	4	yes	—
307	C₂²×C₄	#10625329	1	4	yes	—
308	C₂²×C₄	#10625350	1	2	yes	—
309	C₂²×C₄	#10625350	1	2	yes	—
310	C₂²×C₄	D₄×D₄₇	1	2	yes	—
311	C₂²×C₄	#10625352	1	2	yes	—
312	C₂²×C₄	Q₈×D₄₇	1	2	yes	—
313	C₂²×C₄	#10625354	1	2	yes	—
314	C₂²×C₄	C₂²×Dic₄₇	1	2	yes	—
315	C₂²×C₄	C₂²×Dic₄₇	1	2	yes	—
316	C₂²×C₄	C₂²×Dic₄₇	1	2	yes	—
317	C₂²×C₄	C₂²×Dic₄₇	1	2	yes	—
318	C₂²×C₄	C₂²×Dic₄₇	1	2	yes	—
319	C₂²×C₄	C₂²×Dic₄₇	1	2	yes	—
320	C₂²×C₄	C₂²×Dic₄₇	1	1	yes	characteristic
321	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
322	C₂×C₈	—	47	4	no	—
323	C₂×C₈	—	47	4	no	—
324	C₂×C₈	—	94	8	no	—
325	C₂×C₈	—	94	8	no	—
326	C₂×C₈	—	94	2	no	—
327	C₂×C₈	—	94	2	no	—
328	C₂×C₈	—	94	2	no	—
329	C₂×C₈	—	94	2	no	—
330	C₂×C₈	—	94	2	no	—
331	C₂×C₈	—	94	2	no	—
332	C₂×C₈	—	94	2	no	—
333	C₂×C₈	—	94	2	no	—
334	C₂×C₈	—	94	2	no	—
335	C₂×C₈	—	94	2	no	—
336	C₂×C₈	—	188	4	no	—
337	C₂×C₈	—	188	4	no	—
338	C₄⋊C₄	—	2	8	no	—
339	C₄⋊C₄	C₂×C₄₇⋊C₈	1	16	yes	complemented
340	C₄²	—	2	4	no	—
341	C₄²	—	2	4	no	—
342	C₄²	—	2	4	no	—
343	C₄²	—	2	2	no	—
344	C₄²	—	2	2	no	—
345	C₄²	—	2	2	no	—
346	C₄²	—	2	2	no	—
347	C₄²	—	2	2	no	—
348	C₄²	—	2	2	no	—
349	C₂³	#13093983	1	2	yes	—
350	C₂³	D₄×Dic₄₇	1	2	yes	—
351	C₂³	Q₈×Dic₄₇	1	2	yes	—
352	C₂³	C₂²×C₄₇⋊C₈	1	2	yes	—
353	C₂³	C₂×#10625329	1	2	yes	—
354	C₂³	#13094031	1	2	yes	—
355	C₂³	#13094031	1	2	yes	—
356	C₂³	C₂³×Dic₄₇	1	1	yes	characteristic
357	C₂×C₄	—	2	2	no	—
358	C₂×C₄	—	2	2	no	—
359	C₂×C₄	—	2	2	no	—
360	C₂×C₄	—	2	2	no	—
361	C₂×C₄	—	2	2	no	—
362	C₂×C₄	—	2	2	no	—
363	C₂×C₄	—	2	2	no	—
364	C₂×C₄	—	2	2	no	—
365	C₂×C₄	—	2	8	no	—
366	C₂×C₄	—	2	8	no	—
367	C₂×C₄	—	2	8	no	—
368	C₂×C₄	—	2	8	no	—
369	C₂×C₄	—	2	2	no	—
370	C₂×C₄	—	2	2	no	—
371	C₂×C₄	—	2	2	no	—
372	C₂×C₄	—	2	2	no	—
373	C₂×C₄	—	2	2	no	—
374	C₂×C₄	—	2	2	no	—
375	C₂×C₄	—	4	4	no	—
376	C₂×C₄	—	4	4	no	—
377	C₂×C₄	#13093983	1	2	yes	—
378	C₂×C₄	D₄×Dic₄₇	1	2	yes	—
379	C₂×C₄	Q₈×Dic₄₇	1	2	yes	—
380	C₂×C₄	#13094002	1	4	yes	—
381	C₂×C₄	#13094009	1	4	yes	—
382	C₂×C₄	#13094014	1	4	yes	—
383	C₂×C₄	#13094019	1	4	yes	—
384	C₂×C₄	C₂²×C₄₇⋊C₈	1	4	yes	—
385	C₂×C₄	C₂²×C₄₇⋊C₈	1	4	yes	—
386	C₂×C₄	C₂²×C₄₇⋊C₈	1	4	yes	—
387	C₂×C₄	C₂×#10625329	1	4	yes	—
388	C₂×C₄	C₂×D₄×D₄₇	1	1	yes	characteristic
389	C₂×C₄	C₂×Q₈×D₄₇	1	1	yes	characteristic
390	C₂×C₄	C₂×#10625352	1	1	yes	characteristic
391	C₂×C₄	C₂×#10625350	1	1	yes	characteristic
392	C₂×C₄	C₂×#10625350	1	1	yes	characteristic
393	C₂×C₄	C₂×#10625354	1	1	yes	characteristic
394	C₈	—	94	4	no	—
395	C₈	—	94	4	no	—
396	C₈	—	188	2	no	—
397	C₈	—	188	2	no	—
398	C₂²	#15689009	1	4	yes	—
399	C₂²	#15689176	1	4	yes	—
400	C₂²	#15689184	1	4	yes	—
401	C₂²	D₄×C₄₇⋊C₈	1	4	yes	—
402	C₂²	#15689195	1	4	yes	—
403	C₂²	Q₈×C₄₇⋊C₈	1	4	yes	—
404	C₂²	#15689254	1	4	yes	—
405	C₂²	C₂×#13093983	1	1	yes	characteristic
406	C₂²	C₂×D₄×Dic₄₇	1	1	yes	characteristic
407	C₂²	C₂×Q₈×Dic₄₇	1	1	yes	characteristic
408	C₂²	C₂³×C₄₇⋊C₈	1	1	yes	characteristic
409	C₂²	C₂²×#10625329	1	1	yes	characteristic
410	C₂²	C₂×#13094031	1	1	yes	characteristic
411	C₂²	C₂×#13094031	1	1	yes	characteristic
412	C₄	—	2	4	no	—
413	C₄	—	2	4	no	—
414	C₄	—	2	4	no	—
415	C₄	—	2	4	no	—
416	C₄	—	4	2	no	—
417	C₄	—	4	2	no	—
418	C₄	#15689009	1	4	yes	—
419	C₄	C₂×#13094002	1	1	yes	characteristic
420	C₄	C₂×#13094009	1	1	yes	characteristic
421	C₄	C₂×#13094014	1	1	yes	characteristic
422	C₄	C₂×#13094019	1	1	yes	characteristic
423	C₂	#20243947	1	8	yes	direct product factor
424	C₂	C₂×#15689009	1	1	yes	characteristic
425	C₂	C₂×#15689176	1	1	yes	characteristic
426	C₂	C₂×#15689184	1	1	yes	characteristic
427	C₂	C₂×D₄×C₄₇⋊C₈	1	1	yes	characteristic
428	C₂	C₂×#15689195	1	1	yes	characteristic
429	C₂	C₂×Q₈×C₄₇⋊C₈	1	1	yes	characteristic
430	C₂	C₂×#15689254	1	1	yes	characteristic

	subgroup	G/H
center	C₂³×C₄	C₂²×D₄₇
commutator	C₂²×C₄₇	C₂³×C₈
Frattini	C₂²×C₄	C₂³×D₄₇
Fitting	C₂×C₄×C₄⋊C₄×C₄₇	C₂
socle, prime radical	C₂⁴×C₄₇	C₂²×C₄
cosocle	C₂²×C₄×C₄₇	C₂⁴
hypercenter	C₂×C₄×C₄⋊C₄	D₄₇
hypocenter	C₄₇	C₂×#1916
LCS	G ▷ C₂²×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂³×C₄ ◁ C₂×C₄×C₄⋊C₄

Complements

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

N	H ≅ G/N	type
3. #20243947	C₂	direct (N × H)
56. C₂×C₄⋊C₄×C₄₇	C₈	semidirect
107. C₄⋊C₄×C₄₇	C₂×C₈	semidirect
216. C₂×C₄₇	#1916	semidirect
245. C₄₇	C₂×#1916	semidirect
270. C₂×C₄⋊C₄	C₄₇⋊C₈	semidirect
339. C₄⋊C₄	C₂×C₄₇⋊C₈	semidirect
423. C₂	#20243947	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×C₄⋊(C₄₇⋊C₈)	2
C₂²×C₄×C₄₇⋊C₈	2
#20243947	2
C₂×#15688878	2
C₂×C₄×C₄⋊C₄×C₄₇	2
C₂×#1916	47

Subgroups — C2×#20243947 #26218322

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#20243947 #26218322