Subgroups — C₂×C₄×#100×C₄₇ #26060092

Order 12032.

1970 conjugacy classes of subgroups.

The subgroup lattice has 398 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₄×D₄×C₄₇	C₂	1	1	yes	maximal, characteristic
2	C₂²×#100×C₄₇	C₂	1	2	yes	maximal
3	C₂×C₄×M₁₆×C₄₇	C₂	1	2	yes	maximal, complemented
4	C₄×#100×C₄₇	C₂	1	8	yes	maximal, direct product factor
5	C₂×C₄₇×#343	C₂	1	2	yes	maximal, complemented
6	C₂³×D₄×C₄₇	C₂²	1	1	yes	characteristic
7	C₂⁴×C₄×C₄₇	C₄	1	2	yes	—
8	C₂²×M₁₆×C₄₇	C₂²	1	4	yes	—
9	C₂×C₄×D₄×C₄₇	—	2	2	no	—
10	C₂×C₄×D₄×C₄₇	—	2	4	no	—
11	C₂×C₄×D₄×C₄₇	—	2	2	no	—
12	C₂×C₄×D₄×C₄₇	C₄	1	4	yes	—
13	C₂×C₄×D₄×C₄₇	C₂²	1	4	yes	—
14	C₂²×C₄⋊C₄×C₄₇	C₂²	1	1	yes	characteristic
15	C₂²×C₂²⋊C₄×C₄₇	C₄	1	2	yes	—
16	C₂²×C₄²×C₄₇	C₂²	1	1	yes	characteristic
17	C₂×#100×C₄₇	C₄	1	16	yes	direct product factor
18	C₂×#100×C₄₇	C₂²	1	8	yes	—
19	C₄×M₁₆×C₄₇	—	2	4	no	—
20	C₄×M₁₆×C₄₇	C₂²	1	8	yes	complemented
21	C₂×#97×C₄₇	—	2	2	no	—
22	C₂×C₄×C₈×C₄₇	—	2	2	no	—
23	C₄₇×#343	C₂²	1	8	yes	complemented
24	C₂⁵×C₄₇	C₂×C₄	1	2	yes	—
25	C₂²×D₄×C₄₇	—	2	2	no	—
26	C₂²×D₄×C₄₇	—	2	2	no	—
27	C₂²×D₄×C₄₇	—	2	4	no	—
28	C₂²×D₄×C₄₇	C₂×C₄	1	2	yes	—
29	C₂²×D₄×C₄₇	C₂×C₄	1	8	yes	—
30	C₂²×D₄×C₄₇	C₂³	1	2	yes	—
31	C₂³×C₄×C₄₇	—	2	4	no	—
32	C₂³×C₄×C₄₇	—	2	2	no	—
33	C₂³×C₄×C₄₇	—	2	2	no	—
34	C₂³×C₄×C₄₇	—	4	8	no	—
35	C₂³×C₄×C₄₇	C₂×C₄	1	1	yes	characteristic
36	C₂³×C₄×C₄₇	C₂×C₄	1	2	yes	—
37	C₂³×C₄×C₄₇	C₂×C₄	1	8	yes	—
38	C₂³×C₄×C₄₇	C₂×C₄	1	1	yes	characteristic
39	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
40	C₂×M₁₆×C₄₇	—	2	4	no	—
41	C₂×M₁₆×C₄₇	—	2	8	no	—
42	C₂×M₁₆×C₄₇	C₂×C₄	1	16	yes	complemented
43	C₂×M₁₆×C₄₇	C₂³	1	8	yes	—
44	C₂²×C₈×C₄₇	—	2	4	no	—
45	C₄×D₄×C₄₇	—	2	8	no	—
46	C₄×D₄×C₄₇	—	2	8	no	—
47	C₄×D₄×C₄₇	—	2	8	no	—
48	C₄×D₄×C₄₇	—	2	8	no	—
49	C₂×C₄⋊C₄×C₄₇	—	2	2	no	—
50	C₂×C₄⋊C₄×C₄₇	—	2	2	no	—
51	C₂×C₄⋊C₄×C₄₇	C₂×C₄	1	2	yes	—
52	C₂×C₄⋊C₄×C₄₇	C₂³	1	2	yes	—
53	C₂×C₂²⋊C₄×C₄₇	—	2	4	no	—
54	C₂×C₂²⋊C₄×C₄₇	—	2	4	no	—
55	C₂×C₂²⋊C₄×C₄₇	C₂×C₄	1	8	yes	—
56	C₂×C₄²×C₄₇	C₂×C₄	1	2	yes	—
57	C₂×C₄²×C₄₇	D₄	1	2	yes	—
58	C₂×C₄²×C₄₇	D₄	1	4	yes	—
59	C₂×C₄²×C₄₇	D₄	1	2	yes	—
60	C₂×C₄²×C₄₇	C₂³	1	2	yes	—
61	#100×C₄₇	C₂×C₄	1	32	yes	direct product factor
62	#97×C₄₇	—	2	8	no	—
63	C₄×C₈×C₄₇	—	2	8	no	—
64	C₂⁴×C₄₇	—	2	2	no	—
65	C₂⁴×C₄₇	—	2	2	no	—
66	C₂⁴×C₄₇	—	2	4	no	—
67	C₂⁴×C₄₇	—	4	4	no	—
68	C₂⁴×C₄₇	—	4	4	no	—
69	C₂⁴×C₄₇	C₄²	1	8	yes	—
70	C₂⁴×C₄₇	C₂²×C₄	1	1	yes	characteristic
71	C₂⁴×C₄₇	C₂²×C₄	1	4	yes	—
72	C₂×D₄×C₄₇	—	2	4	no	—
73	C₂×D₄×C₄₇	—	2	4	no	—
74	C₂×D₄×C₄₇	—	2	16	no	—
75	C₂×D₄×C₄₇	—	2	16	no	—
76	C₂×D₄×C₄₇	—	2	4	no	—
77	C₂×D₄×C₄₇	—	2	4	no	—
78	C₂×D₄×C₄₇	C₄²	1	8	yes	—
79	C₂×D₄×C₄₇	C₂²×C₄	1	8	yes	—
80	C₂²×C₄×C₄₇	—	2	4	no	—
81	C₂²×C₄×C₄₇	—	2	2	no	—
82	C₂²×C₄×C₄₇	—	2	2	no	—
83	C₂²×C₄×C₄₇	—	2	8	no	—
84	C₂²×C₄×C₄₇	—	2	8	no	—
85	C₂²×C₄×C₄₇	—	4	2	no	—
86	C₂²×C₄×C₄₇	—	4	8	no	—
87	C₂²×C₄×C₄₇	—	4	16	no	—
88	C₂²×C₄×C₄₇	—	4	16	no	—
89	C₂²×C₄×C₄₇	—	4	8	no	—
90	C₂²×C₄×C₄₇	—	4	4	no	—
91	C₂²×C₄×C₄₇	C₂²⋊C₄	1	2	yes	—
92	C₂²×C₄×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
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	1	yes	characteristic
96	C₂²×C₄×C₄₇	C₂²×C₄	1	2	yes	—
97	C₂²×C₄×C₄₇	C₂²×C₄	1	4	yes	—
98	C₂²×C₄×C₄₇	C₂²×C₄	1	2	yes	—
99	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
100	C₂²×C₄×C₄₇	C₂²×C₄	1	4	yes	—
101	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
102	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
103	C₂²×C₄×C₄₇	#41	1	4	yes	—
104	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
105	M₁₆×C₄₇	—	2	16	no	—
106	M₁₆×C₄₇	—	2	8	no	—
107	M₁₆×C₄₇	C₂²×C₄	1	16	yes	complemented
108	C₂×C₈×C₄₇	—	2	16	no	—
109	C₂×C₈×C₄₇	—	2	8	no	—
110	C₄⋊C₄×C₄₇	—	2	4	no	—
111	C₄⋊C₄×C₄₇	—	2	4	no	—
112	C₂²⋊C₄×C₄₇	—	2	16	no	—
113	C₄²×C₄₇	C₂²⋊C₄	1	4	yes	—
114	C₄²×C₄₇	C₂²⋊C₄	1	4	yes	—
115	C₄²×C₄₇	C₂×D₄	1	4	yes	—
116	C₄²×C₄₇	C₂×D₄	1	4	yes	—
117	C₂³×C₄₇	—	2	2	no	—
118	C₂³×C₄₇	—	2	2	no	—
119	C₂³×C₄₇	—	2	4	no	—
120	C₂³×C₄₇	—	2	4	no	—
121	C₂³×C₄₇	—	2	8	no	—
122	C₂³×C₄₇	—	2	8	no	—
123	C₂³×C₄₇	—	4	4	no	—
124	C₂³×C₄₇	—	4	16	no	—
125	C₂³×C₄₇	—	4	4	no	—
126	C₂³×C₄₇	—	4	4	no	—
127	C₂³×C₄₇	—	4	4	no	—
128	C₂³×C₄₇	—	4	16	no	—
129	C₂³×C₄₇	—	4	4	no	—
130	C₂³×C₄₇	—	4	4	no	—
131	C₂³×C₄₇	C₂×C₄²	1	2	yes	—
132	C₂³×C₄₇	C₂×C₄²	1	8	yes	—
133	C₂³×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
134	C₂³×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
135	C₂³×C₄₇	#117	1	2	yes	—
136	C₂³×C₄₇	C₂³×C₄	1	1	yes	characteristic
137	D₄×C₄₇	—	2	16	no	—
138	D₄×C₄₇	—	2	16	no	—
139	C₂×C₄×C₄₇	—	2	2	no	—
140	C₂×C₄×C₄₇	—	2	4	no	—
141	C₂×C₄×C₄₇	—	2	4	no	—
142	C₂×C₄×C₄₇	—	2	4	no	—
143	C₂×C₄×C₄₇	—	2	4	no	—
144	C₂×C₄×C₄₇	—	4	2	no	—
145	C₂×C₄×C₄₇	—	4	2	no	—
146	C₂×C₄×C₄₇	—	4	16	no	—
147	C₂×C₄×C₄₇	—	4	4	no	—
148	C₂×C₄×C₄₇	—	4	4	no	—
149	C₂×C₄×C₄₇	—	4	16	no	—
150	C₂×C₄×C₄₇	—	4	4	no	—
151	C₂×C₄×C₄₇	#100	1	4	yes	direct product factor
152	C₂×C₄×C₄₇	C₂×C₄²	1	2	yes	—
153	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	4	yes	—
154	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	2	yes	—
155	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	2	yes	—
156	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	2	yes	—
157	C₂×C₄×C₄₇	#117	1	2	yes	—
158	C₂×C₄×C₄₇	C₄×D₄	1	8	yes	—
159	C₂×C₄×C₄₇	C₄×D₄	1	8	yes	—
160	C₂×C₄×C₄₇	C₂³×C₄	1	2	yes	—
161	C₂×C₄×C₄₇	C₂²×D₄	1	2	yes	—
162	C₂×C₄×C₄₇	C₂×#41	1	2	yes	—
163	C₈×C₄₇	—	2	16	no	—
164	C₂×C₄×#100	C₄₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
165	C₂²×C₄₇	—	2	1	no	—
166	C₂²×C₄₇	—	2	1	no	—
167	C₂²×C₄₇	—	2	1	no	—
168	C₂²×C₄₇	—	2	1	no	—
169	C₂²×C₄₇	—	2	4	no	—
170	C₂²×C₄₇	—	2	4	no	—
171	C₂²×C₄₇	—	2	8	no	—
172	C₂²×C₄₇	—	4	8	no	—
173	C₂²×C₄₇	—	4	8	no	—
174	C₂²×C₄₇	—	4	16	no	—
175	C₂²×C₄₇	—	4	4	no	—
176	C₂²×C₄₇	—	4	4	no	—
177	C₂²×C₄₇	—	4	16	no	—
178	C₂²×C₄₇	C₄×C₂²⋊C₄	1	2	yes	—
179	C₂²×C₄₇	C₄×C₂²⋊C₄	1	2	yes	—
180	C₂²×C₄₇	C₂×#100	1	2	yes	—
181	C₂²×C₄₇	#413	1	2	yes	—
182	C₂²×C₄₇	C₂²×C₄²	1	1	yes	characteristic
183	C₂²×C₄₇	C₂²×C₂²⋊C₄	1	1	yes	characteristic
184	C₂²×C₄₇	C₂×#117	1	1	yes	characteristic
185	C₄×C₄₇	—	2	2	no	—
186	C₄×C₄₇	—	2	4	no	—
187	C₄×C₄₇	—	4	4	no	—
188	C₄×C₄₇	C₄×C₂²⋊C₄	1	4	yes	—
189	C₄×C₄₇	C₂×#100	1	4	yes	direct product factor
190	C₄×C₄₇	C₂×C₄×D₄	1	4	yes	—
191	C₂²×C₄×D₄	C₂×C₄₇	1	1	yes	characteristic
192	C₂²×#100	C₂×C₄₇	1	2	yes	—
193	C₂×C₄×M₁₆	C₂×C₄₇	1	2	yes	complemented
194	C₄×#100	C₂×C₄₇	1	8	yes	direct product factor
195	C₂×#343	C₂×C₄₇	1	2	yes	complemented
196	C₂×C₄₇	—	2	1	no	—
197	C₂×C₄₇	—	2	2	no	—
198	C₂×C₄₇	—	2	1	no	—
199	C₂×C₄₇	—	4	8	no	—
200	C₂×C₄₇	C₄×#100	1	4	yes	direct product factor
201	C₂×C₄₇	C₂×C₄×C₂²⋊C₄	1	1	yes	characteristic
202	C₂×C₄₇	C₂²×#100	1	1	yes	characteristic
203	C₂×C₄₇	C₂×#413	1	1	yes	characteristic
204	C₂³×D₄	C₂²×C₄₇	1	1	yes	characteristic
205	C₂⁴×C₄	C₄×C₄₇	1	2	yes	—
206	C₂²×M₁₆	C₂²×C₄₇	1	4	yes	—
207	C₂×C₄×D₄	—	2	2	no	—
208	C₂×C₄×D₄	—	2	2	no	—
209	C₂×C₄×D₄	—	2	4	no	—
210	C₂×C₄×D₄	C₄×C₄₇	1	4	yes	—
211	C₂×C₄×D₄	C₂²×C₄₇	1	4	yes	—
212	C₂²×C₄⋊C₄	C₂²×C₄₇	1	1	yes	characteristic
213	C₂²×C₂²⋊C₄	C₄×C₄₇	1	2	yes	—
214	C₂²×C₄²	C₂²×C₄₇	1	1	yes	characteristic
215	C₂×#100	C₄×C₄₇	1	16	yes	direct product factor
216	C₂×#100	C₂²×C₄₇	1	8	yes	—
217	C₄×M₁₆	—	2	4	no	—
218	C₄×M₁₆	C₂²×C₄₇	1	8	yes	complemented
219	C₂×#97	—	2	2	no	—
220	C₂×C₄×C₈	—	2	2	no	—
221	#343	C₂²×C₄₇	1	8	yes	complemented
222	C₄₇	C₂×C₄×#100	1	1	yes	characteristic, direct product factor, Sylow
223	C₂⁵	C₂×C₄×C₄₇	1	2	yes	—
224	C₂²×D₄	—	2	2	no	—
225	C₂²×D₄	—	2	2	no	—
226	C₂²×D₄	—	2	4	no	—
227	C₂²×D₄	C₂×C₄×C₄₇	1	2	yes	—
228	C₂²×D₄	C₂×C₄×C₄₇	1	8	yes	—
229	C₂²×D₄	C₂³×C₄₇	1	2	yes	—
230	C₂³×C₄	—	2	4	no	—
231	C₂³×C₄	—	2	2	no	—
232	C₂³×C₄	—	2	2	no	—
233	C₂³×C₄	—	4	8	no	—
234	C₂³×C₄	C₂×C₄×C₄₇	1	1	yes	characteristic
235	C₂³×C₄	C₂×C₄×C₄₇	1	2	yes	—
236	C₂³×C₄	C₂×C₄×C₄₇	1	8	yes	—
237	C₂³×C₄	C₂×C₄×C₄₇	1	1	yes	characteristic
238	C₂³×C₄	C₂³×C₄₇	1	1	yes	characteristic
239	C₂×M₁₆	—	2	4	no	—
240	C₂×M₁₆	—	2	8	no	—
241	C₂×M₁₆	C₂×C₄×C₄₇	1	16	yes	complemented
242	C₂×M₁₆	C₂³×C₄₇	1	8	yes	—
243	C₂²×C₈	—	2	4	no	—
244	C₄×D₄	—	2	8	no	—
245	C₄×D₄	—	2	8	no	—
246	C₄×D₄	—	2	8	no	—
247	C₄×D₄	—	2	8	no	—
248	C₂×C₄⋊C₄	—	2	2	no	—
249	C₂×C₄⋊C₄	—	2	2	no	—
250	C₂×C₄⋊C₄	C₂×C₄×C₄₇	1	2	yes	—
251	C₂×C₄⋊C₄	C₂³×C₄₇	1	2	yes	—
252	C₂×C₂²⋊C₄	—	2	4	no	—
253	C₂×C₂²⋊C₄	—	2	4	no	—
254	C₂×C₂²⋊C₄	C₂×C₄×C₄₇	1	8	yes	—
255	C₂×C₄²	C₂×C₄×C₄₇	1	2	yes	—
256	C₂×C₄²	D₄×C₄₇	1	2	yes	—
257	C₂×C₄²	D₄×C₄₇	1	2	yes	—
258	C₂×C₄²	D₄×C₄₇	1	4	yes	—
259	C₂×C₄²	C₂³×C₄₇	1	2	yes	—
260	#100	C₂×C₄×C₄₇	1	32	yes	direct product factor
261	#97	—	2	8	no	—
262	C₄×C₈	—	2	8	no	—
263	C₂⁴	—	2	2	no	—
264	C₂⁴	—	2	2	no	—
265	C₂⁴	—	2	4	no	—
266	C₂⁴	—	4	4	no	—
267	C₂⁴	—	4	4	no	—
268	C₂⁴	C₄²×C₄₇	1	8	yes	—
269	C₂⁴	C₂²×C₄×C₄₇	1	1	yes	characteristic
270	C₂⁴	C₂²×C₄×C₄₇	1	4	yes	—
271	C₂×D₄	—	2	4	no	—
272	C₂×D₄	—	2	4	no	—
273	C₂×D₄	—	2	16	no	—
274	C₂×D₄	—	2	16	no	—
275	C₂×D₄	—	2	4	no	—
276	C₂×D₄	—	2	4	no	—
277	C₂×D₄	C₄²×C₄₇	1	8	yes	—
278	C₂×D₄	C₂²×C₄×C₄₇	1	8	yes	—
279	C₂²×C₄	—	2	4	no	—
280	C₂²×C₄	—	2	2	no	—
281	C₂²×C₄	—	2	2	no	—
282	C₂²×C₄	—	2	8	no	—
283	C₂²×C₄	—	2	8	no	—
284	C₂²×C₄	—	4	2	no	—
285	C₂²×C₄	—	4	8	no	—
286	C₂²×C₄	—	4	16	no	—
287	C₂²×C₄	—	4	16	no	—
288	C₂²×C₄	—	4	8	no	—
289	C₂²×C₄	—	4	4	no	—
290	C₂²×C₄	C₂²⋊C₄×C₄₇	1	2	yes	—
291	C₂²×C₄	C₂²⋊C₄×C₄₇	1	1	yes	characteristic
292	C₂²×C₄	C₂²⋊C₄×C₄₇	1	2	yes	—
293	C₂²×C₄	C₂²⋊C₄×C₄₇	1	2	yes	—
294	C₂²×C₄	C₂²⋊C₄×C₄₇	1	1	yes	characteristic
295	C₂²×C₄	C₂²×C₄×C₄₇	1	2	yes	—
296	C₂²×C₄	C₂²×C₄×C₄₇	1	4	yes	—
297	C₂²×C₄	C₂²×C₄×C₄₇	1	2	yes	—
298	C₂²×C₄	C₂²×C₄×C₄₇	1	1	yes	characteristic
299	C₂²×C₄	C₂²×C₄×C₄₇	1	4	yes	—
300	C₂²×C₄	C₂×D₄×C₄₇	1	2	yes	—
301	C₂²×C₄	C₂×D₄×C₄₇	1	2	yes	—
302	C₂²×C₄	#41×C₄₇	1	4	yes	—
303	C₂²×C₄	C₂⁴×C₄₇	1	1	yes	characteristic
304	M₁₆	—	2	16	no	—
305	M₁₆	—	2	8	no	—
306	M₁₆	C₂²×C₄×C₄₇	1	16	yes	complemented
307	C₂×C₈	—	2	16	no	—
308	C₂×C₈	—	2	8	no	—
309	C₄⋊C₄	—	2	4	no	—
310	C₄⋊C₄	—	2	4	no	—
311	C₂²⋊C₄	—	2	16	no	—
312	C₄²	C₂²⋊C₄×C₄₇	1	4	yes	—
313	C₄²	C₂²⋊C₄×C₄₇	1	4	yes	—
314	C₄²	C₂×D₄×C₄₇	1	4	yes	—
315	C₄²	C₂×D₄×C₄₇	1	4	yes	—
316	C₂³	—	2	2	no	—
317	C₂³	—	2	2	no	—
318	C₂³	—	2	4	no	—
319	C₂³	—	2	4	no	—
320	C₂³	—	2	8	no	—
321	C₂³	—	2	8	no	—
322	C₂³	—	4	4	no	—
323	C₂³	—	4	16	no	—
324	C₂³	—	4	4	no	—
325	C₂³	—	4	4	no	—
326	C₂³	—	4	16	no	—
327	C₂³	—	4	4	no	—
328	C₂³	—	4	4	no	—
329	C₂³	—	4	4	no	—
330	C₂³	C₂×C₄²×C₄₇	1	2	yes	—
331	C₂³	C₂×C₄²×C₄₇	1	8	yes	—
332	C₂³	C₂×C₂²⋊C₄×C₄₇	1	1	yes	characteristic
333	C₂³	C₂×C₂²⋊C₄×C₄₇	1	1	yes	characteristic
334	C₂³	#117×C₄₇	1	2	yes	—
335	C₂³	C₂³×C₄×C₄₇	1	1	yes	characteristic
336	D₄	—	2	16	no	—
337	D₄	—	2	16	no	—
338	C₂×C₄	—	2	2	no	—
339	C₂×C₄	—	2	4	no	—
340	C₂×C₄	—	2	4	no	—
341	C₂×C₄	—	2	4	no	—
342	C₂×C₄	—	2	4	no	—
343	C₂×C₄	—	4	2	no	—
344	C₂×C₄	—	4	2	no	—
345	C₂×C₄	—	4	16	no	—
346	C₂×C₄	—	4	4	no	—
347	C₂×C₄	—	4	4	no	—
348	C₂×C₄	—	4	16	no	—
349	C₂×C₄	—	4	4	no	—
350	C₂×C₄	#100×C₄₇	1	4	yes	direct product factor
351	C₂×C₄	C₂×C₄²×C₄₇	1	2	yes	—
352	C₂×C₄	C₂×C₂²⋊C₄×C₄₇	1	4	yes	—
353	C₂×C₄	C₂×C₂²⋊C₄×C₄₇	1	2	yes	—
354	C₂×C₄	C₂×C₂²⋊C₄×C₄₇	1	2	yes	—
355	C₂×C₄	C₂×C₂²⋊C₄×C₄₇	1	2	yes	—
356	C₂×C₄	#117×C₄₇	1	2	yes	—
357	C₂×C₄	C₄×D₄×C₄₇	1	8	yes	—
358	C₂×C₄	C₄×D₄×C₄₇	1	8	yes	—
359	C₂×C₄	C₂³×C₄×C₄₇	1	2	yes	—
360	C₂×C₄	C₂²×D₄×C₄₇	1	2	yes	—
361	C₂×C₄	C₂×#41×C₄₇	1	2	yes	—
362	C₈	—	2	16	no	—
363	C₂²	—	2	4	no	—
364	C₂²	—	2	4	no	—
365	C₂²	—	2	1	no	—
366	C₂²	—	2	1	no	—
367	C₂²	—	2	1	no	—
368	C₂²	—	2	1	no	—
369	C₂²	—	2	8	no	—
370	C₂²	—	4	8	no	—
371	C₂²	—	4	8	no	—
372	C₂²	—	4	16	no	—
373	C₂²	—	4	16	no	—
374	C₂²	—	4	4	no	—
375	C₂²	—	4	4	no	—
376	C₂²	C₄×C₂²⋊C₄×C₄₇	1	2	yes	—
377	C₂²	C₄×C₂²⋊C₄×C₄₇	1	2	yes	—
378	C₂²	C₂×#100×C₄₇	1	2	yes	—
379	C₂²	C₄₇×#413	1	2	yes	—
380	C₂²	C₂²×C₄²×C₄₇	1	1	yes	characteristic
381	C₂²	C₂²×C₂²⋊C₄×C₄₇	1	1	yes	characteristic
382	C₂²	C₂×#117×C₄₇	1	1	yes	characteristic
383	C₄	—	2	2	no	—
384	C₄	—	2	4	no	—
385	C₄	—	4	4	no	—
386	C₄	C₄×C₂²⋊C₄×C₄₇	1	4	yes	—
387	C₄	C₂×#100×C₄₇	1	4	yes	direct product factor
388	C₄	C₂×C₄×D₄×C₄₇	1	4	yes	—
389	C₂	—	2	1	no	—
390	C₂	—	2	1	no	—
391	C₂	—	2	2	no	—
392	C₂	—	4	8	no	—
393	C₂	C₄×#100×C₄₇	1	4	yes	direct product factor
394	C₂	C₂×C₄×C₂²⋊C₄×C₄₇	1	1	yes	characteristic
395	C₂	C₂²×#100×C₄₇	1	1	yes	characteristic
396	C₂	C₂×C₄₇×#413	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄×C₄₇	C₂²⋊C₄
commutator	C₂²	C₂²×C₄²×C₄₇
Frattini, cosocle	C₂²×C₄	C₂⁴×C₄₇
socle	C₂³×C₄₇	C₂×C₂²⋊C₄
prime radical	C₂³×D₄×C₄₇	C₂²
LCS	G ▷ C₂² ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₄×C₄₇ ◁ C₂²×C₄²×C₄₇ ◁ G

Complements

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

N	H ≅ G/N	type
3. C₂×C₄×M₁₆×C₄₇	C₂	semidirect
4. C₄×#100×C₄₇	C₂	direct (N × H)
5. C₂×C₄₇×#343	C₂	semidirect
17. C₂×#100×C₄₇	C₄	direct (N × H)
20. C₄×M₁₆×C₄₇	C₂²	semidirect
23. C₄₇×#343	C₂²	semidirect
42. C₂×M₁₆×C₄₇	C₂×C₄	semidirect
61. #100×C₄₇	C₂×C₄	direct (N × H)
107. M₁₆×C₄₇	C₂²×C₄	semidirect
151. C₂×C₄×C₄₇	#100	direct (N × H)
164. C₂×C₄×#100	C₄₇	direct (N × H)
189. C₄×C₄₇	C₂×#100	direct (N × H)
193. C₂×C₄×M₁₆	C₂×C₄₇	semidirect
194. C₄×#100	C₂×C₄₇	direct (N × H)
195. C₂×#343	C₂×C₄₇	semidirect
200. C₂×C₄₇	C₄×#100	direct (N × H)
215. C₂×#100	C₄×C₄₇	direct (N × H)
218. C₄×M₁₆	C₂²×C₄₇	semidirect
221. #343	C₂²×C₄₇	semidirect
222. C₄₇	C₂×C₄×#100	direct (N × H)
241. C₂×M₁₆	C₂×C₄×C₄₇	semidirect
260. #100	C₂×C₄×C₄₇	direct (N × H)
306. M₁₆	C₂²×C₄×C₄₇	semidirect
350. C₂×C₄	#100×C₄₇	direct (N × H)
387. C₄	C₂×#100×C₄₇	direct (N × H)
393. C₂	C₄×#100×C₄₇	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×D₄×C₄₇	2
C₂²×#100×C₄₇	2
C₂×C₄×M₁₆×C₄₇	2
C₄×#100×C₄₇	2
C₂×C₄₇×#343	2
C₂×C₄×#100	47

Subgroups — C2×C4×#100×C47 #26060092

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₄×#100×C₄₇ #26060092