Subgroups — C₂×C₄₇×#3199 #26100441

Order 12032.

2506 conjugacy classes of subgroups.

The subgroup lattice has 406 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄₇×#535	C₂	1	2	yes	maximal, complemented
2	C₄₇×#3199	C₂	1	16	yes	maximal, direct product factor
3	C₂×C₄₇×#482	C₂	1	4	yes	maximal, complemented
4	C₂×C₄₇×#469	C₂	1	2	yes	maximal, complemented
5	C₂×C₄₇×#466	C₂	1	2	yes	maximal, complemented
6	C₂×C₄₇×#447	C₂	1	4	yes	maximal, complemented
7	C₂×C₄₇×#408	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂²×#41×C₄₇	C₂²	1	1	yes	characteristic
9	C₂³×D₄×C₄₇	C₂²	1	2	yes	complemented
10	C₂²×D₈×C₄₇	C₂²	1	2	yes	—
11	C₂²×D₈×C₄₇	C₂²	1	2	yes	—
12	C₂²×M₁₆×C₄₇	C₂²	1	1	yes	characteristic, complemented
13	C₂³×C₈×C₄₇	C₂²	1	1	yes	characteristic, complemented
14	C₄₇×#535	—	2	8	no	—
15	C₄₇×#535	C₂²	1	16	yes	complemented
16	C₂×#127×C₄₇	—	2	2	no	—
17	C₂×#124×C₄₇	—	2	2	no	—
18	C₂×#121×C₄₇	C₂²	1	4	yes	—
19	C₂×#121×C₄₇	C₂²	1	4	yes	complemented
20	C₂×#120×C₄₇	—	2	2	no	—
21	C₂×#120×C₄₇	—	2	2	no	—
22	C₂×#117×C₄₇	C₂²	1	2	yes	complemented
23	C₄₇×#482	C₂²	1	32	yes	complemented
24	C₄₇×#469	C₂²	1	16	yes	complemented
25	C₄₇×#466	C₂²	1	16	yes	complemented
26	C₄₇×#447	C₂²	1	32	yes	complemented
27	C₂×#107×C₄₇	C₂²	1	2	yes	complemented
28	C₂×#106×C₄₇	C₂²	1	2	yes	complemented
29	C₂×#102×C₄₇	C₂²	1	4	yes	complemented
30	C₂×#102×C₄₇	C₂²	1	4	yes	complemented
31	C₄₇×#408	C₂²	1	8	yes	complemented
32	C₂×C₂²⋊C₈×C₄₇	C₂²	1	4	yes	complemented
33	C₂⁵×C₄₇	—	2	2	no	—
34	C₂×#41×C₄₇	—	4	2	no	—
35	C₂×#41×C₄₇	—	4	2	no	—
36	C₂×#41×C₄₇	D₄	1	4	yes	—
37	C₂×#41×C₄₇	C₂³	1	4	yes	—
38	C₂²×Q₈×C₄₇	D₄	1	1	yes	characteristic
39	C₂²×D₄×C₄₇	—	2	4	no	—
40	C₂²×D₄×C₄₇	—	2	4	no	—
41	C₂²×D₄×C₄₇	—	2	2	no	—
42	C₂²×D₄×C₄₇	—	2	4	no	—
43	C₂²×D₄×C₄₇	—	4	4	no	—
44	C₂²×D₄×C₄₇	—	4	4	no	—
45	C₂²×D₄×C₄₇	D₄	1	1	yes	characteristic
46	C₂²×D₄×C₄₇	D₄	1	2	yes	—
47	C₂²×D₄×C₄₇	C₂³	1	4	yes	—
48	C₂²×D₄×C₄₇	C₂³	1	8	yes	complemented
49	C₂³×C₄×C₄₇	C₂³	1	2	yes	—
50	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
51	C₂×D₈×C₄₇	—	4	4	no	—
52	C₂×D₈×C₄₇	—	4	4	no	—
53	C₂×D₈×C₄₇	C₂³	1	8	yes	—
54	C₂×D₈×C₄₇	C₂³	1	8	yes	—
55	C₂×M₁₆×C₄₇	—	4	2	no	—
56	C₂×M₁₆×C₄₇	C₂³	1	4	yes	complemented
57	C₂²×C₈×C₄₇	—	4	2	no	—
58	C₂²×C₈×C₄₇	C₂³	1	2	yes	—
59	C₂²×C₈×C₄₇	C₂³	1	2	yes	—
60	C₂²×C₈×C₄₇	C₂³	1	4	yes	complemented
61	#127×C₄₇	—	2	16	no	—
62	#124×C₄₇	—	2	16	no	—
63	#121×C₄₇	—	2	8	no	—
64	#121×C₄₇	—	2	8	no	—
65	#121×C₄₇	C₂³	1	16	yes	—
66	#121×C₄₇	C₂³	1	16	yes	complemented
67	#120×C₄₇	—	2	16	no	—
68	#120×C₄₇	—	2	16	no	—
69	#117×C₄₇	—	2	4	no	—
70	#117×C₄₇	C₂³	1	8	yes	complemented
71	C₂×C₄⋊C₄×C₄₇	C₂³	1	4	yes	—
72	C₂×C₂²⋊C₄×C₄₇	—	2	2	no	—
73	C₂×C₂²⋊C₄×C₄₇	—	2	4	no	—
74	C₂×C₂²⋊C₄×C₄₇	—	2	4	no	—
75	C₂×C₄²×C₄₇	—	2	2	no	—
76	#107×C₄₇	C₂³	1	8	yes	complemented
77	#106×C₄₇	C₂³	1	8	yes	complemented
78	#102×C₄₇	C₂³	1	16	yes	complemented
79	#102×C₄₇	C₂³	1	16	yes	complemented
80	C₂²⋊C₈×C₄₇	C₂³	1	16	yes	complemented
81	C₂⁴×C₄₇	—	2	4	no	—
82	C₂⁴×C₄₇	—	2	8	no	—
83	C₂⁴×C₄₇	—	4	8	no	—
84	C₂⁴×C₄₇	—	8	8	no	—
85	C₂⁴×C₄₇	C₂×D₄	1	2	yes	—
86	C₂⁴×C₄₇	C₂×D₄	1	1	yes	characteristic
87	#41×C₄₇	—	4	8	no	—
88	#41×C₄₇	—	4	4	no	—
89	#41×C₄₇	—	4	4	no	—
90	C₂×Q₈×C₄₇	—	4	2	no	—
91	C₂×Q₈×C₄₇	C₂×D₄	1	4	yes	—
92	C₂×D₄×C₄₇	—	2	16	no	—
93	C₂×D₄×C₄₇	—	2	16	no	—
94	C₂×D₄×C₄₇	—	2	4	no	—
95	C₂×D₄×C₄₇	—	2	8	no	—
96	C₂×D₄×C₄₇	—	2	8	no	—
97	C₂×D₄×C₄₇	—	2	8	no	—
98	C₂×D₄×C₄₇	—	4	8	no	—
99	C₂×D₄×C₄₇	—	4	8	no	—
100	C₂×D₄×C₄₇	—	4	4	no	—
101	C₂×D₄×C₄₇	—	4	2	no	—
102	C₂×D₄×C₄₇	—	4	8	no	—
103	C₂×D₄×C₄₇	—	4	16	no	—
104	C₂×D₄×C₄₇	—	8	8	no	—
105	C₂×D₄×C₄₇	—	8	8	no	—
106	C₂×D₄×C₄₇	C₂×D₄	1	4	yes	—
107	C₂×D₄×C₄₇	C₂×D₄	1	8	yes	—
108	C₂×D₄×C₄₇	C₂⁴	1	8	yes	—
109	C₂²×C₄×C₄₇	—	2	2	no	—
110	C₂²×C₄×C₄₇	—	2	2	no	—
111	C₂²×C₄×C₄₇	—	2	4	no	—
112	C₂²×C₄×C₄₇	—	2	4	no	—
113	C₂²×C₄×C₄₇	—	2	4	no	—
114	C₂²×C₄×C₄₇	C₂×D₄	1	4	yes	—
115	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
116	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
117	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
118	C₂²×C₄×C₄₇	C₂⁴	1	4	yes	—
119	C₂²×C₄×C₄₇	C₂⁴	1	2	yes	—
120	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
121	D₈×C₄₇	—	4	8	no	—
122	D₈×C₄₇	—	4	8	no	—
123	M₁₆×C₄₇	—	4	4	no	—
124	C₂×C₈×C₄₇	—	2	4	no	—
125	C₂×C₈×C₄₇	—	2	4	no	—
126	C₂×C₈×C₄₇	—	4	4	no	—
127	C₂×C₈×C₄₇	C₂⁴	1	4	yes	—
128	C₂×C₈×C₄₇	C₂⁴	1	4	yes	—
129	C₄⋊C₄×C₄₇	—	2	4	no	—
130	C₄⋊C₄×C₄₇	C₂⁴	1	8	yes	—
131	C₂²⋊C₄×C₄₇	—	2	8	no	—
132	C₂²⋊C₄×C₄₇	—	2	16	no	—
133	C₂²⋊C₄×C₄₇	—	2	16	no	—
134	C₄²×C₄₇	—	2	8	no	—
135	C₂³×C₄₇	—	2	4	no	—
136	C₂³×C₄₇	—	2	2	no	—
137	C₂³×C₄₇	—	2	4	no	—
138	C₂³×C₄₇	—	2	8	no	—
139	C₂³×C₄₇	—	2	8	no	—
140	C₂³×C₄₇	—	4	16	no	—
141	C₂³×C₄₇	—	4	8	no	—
142	C₂³×C₄₇	—	4	8	no	—
143	C₂³×C₄₇	—	4	8	no	—
144	C₂³×C₄₇	—	8	16	no	—
145	C₂³×C₄₇	—	8	32	no	—
146	C₂³×C₄₇	C₂²×D₄	1	4	yes	—
147	C₂³×C₄₇	C₂²×D₄	1	2	yes	—
148	C₂³×C₄₇	C₂²×D₄	1	1	yes	characteristic
149	Q₈×C₄₇	—	4	4	no	—
150	D₄×C₄₇	—	2	8	no	—
151	D₄×C₄₇	—	2	8	no	—
152	D₄×C₄₇	—	4	8	no	—
153	D₄×C₄₇	—	4	4	no	—
154	D₄×C₄₇	—	4	16	no	—
155	D₄×C₄₇	—	4	8	no	—
156	D₄×C₄₇	—	8	16	no	—
157	D₄×C₄₇	—	8	16	no	—
158	C₂×C₄×C₄₇	—	2	4	no	—
159	C₂×C₄×C₄₇	—	2	2	no	—
160	C₂×C₄×C₄₇	—	2	8	no	—
161	C₂×C₄×C₄₇	—	2	4	no	—
162	C₂×C₄×C₄₇	—	2	2	no	—
163	C₂×C₄×C₄₇	—	2	2	no	—
164	C₂×C₄×C₄₇	—	2	4	no	—
165	C₂×C₄×C₄₇	—	2	4	no	—
166	C₂×C₄×C₄₇	—	2	8	no	—
167	C₂×C₄×C₄₇	—	4	8	no	—
168	C₂×C₄×C₄₇	C₂²×D₄	1	4	yes	—
169	C₂×C₄×C₄₇	C₂²×D₄	1	2	yes	—
170	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
171	C₂×C₄×C₄₇	H(5,𝔽₂)	1	2	yes	—
172	C₂×C₄×C₄₇	H(5,𝔽₂)	1	2	yes	—
173	C₂×C₄×C₄₇	C₂⁵	1	1	yes	characteristic
174	C₈×C₄₇	—	2	4	no	—
175	C₈×C₄₇	—	2	4	no	—
176	C₂×#3199	C₄₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
177	C₂²×C₄₇	—	2	4	no	—
178	C₂²×C₄₇	—	2	2	no	—
179	C₂²×C₄₇	—	2	4	no	—
180	C₂²×C₄₇	—	2	8	no	—
181	C₂²×C₄₇	—	4	4	no	—
182	C₂²×C₄₇	—	4	8	no	—
183	C₂²×C₄₇	—	4	8	no	—
184	C₂²×C₄₇	—	4	8	no	—
185	C₂²×C₄₇	—	4	8	no	—
186	C₂²×C₄₇	—	8	32	no	—
187	C₂²×C₄₇	—	8	16	no	—
188	C₂²×C₄₇	#534	1	2	yes	—
189	C₂²×C₄₇	#576	1	4	yes	—
190	C₂²×C₄₇	C₂³×D₄	1	1	yes	characteristic
191	C₄×C₄₇	—	2	4	no	—
192	C₄×C₄₇	—	2	2	no	—
193	C₄×C₄₇	—	4	8	no	—
194	C₄×C₄₇	#534	1	2	yes	—
195	C₄×C₄₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
196	C₄×C₄₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
197	C₂×#535	C₂×C₄₇	1	2	yes	complemented
198	#3199	C₂×C₄₇	1	16	yes	direct product factor
199	C₂×#482	C₂×C₄₇	1	4	yes	complemented
200	C₂×#469	C₂×C₄₇	1	2	yes	complemented
201	C₂×#466	C₂×C₄₇	1	2	yes	complemented
202	C₂×#447	C₂×C₄₇	1	4	yes	complemented
203	C₂×#408	C₂×C₄₇	1	1	yes	characteristic, complemented
204	C₂×C₄₇	—	4	2	no	—
205	C₂×C₄₇	—	4	4	no	—
206	C₂×C₄₇	—	8	8	no	—
207	C₂×C₄₇	#3199	1	4	yes	direct product factor
208	C₂×C₄₇	C₂×#534	1	1	yes	characteristic
209	C₂×C₄₇	C₂×#576	1	2	yes	—
210	C₂²×#41	C₂²×C₄₇	1	1	yes	characteristic
211	C₂³×D₄	C₂²×C₄₇	1	2	yes	complemented
212	C₂²×D₈	C₂²×C₄₇	1	2	yes	—
213	C₂²×D₈	C₂²×C₄₇	1	2	yes	—
214	C₂²×M₁₆	C₂²×C₄₇	1	1	yes	characteristic, complemented
215	C₂³×C₈	C₂²×C₄₇	1	1	yes	characteristic, complemented
216	#535	—	2	8	no	—
217	#535	C₂²×C₄₇	1	16	yes	complemented
218	C₂×#127	—	2	2	no	—
219	C₂×#124	—	2	2	no	—
220	C₂×#121	C₂²×C₄₇	1	4	yes	—
221	C₂×#121	C₂²×C₄₇	1	4	yes	complemented
222	C₂×#120	—	2	2	no	—
223	C₂×#120	—	2	2	no	—
224	C₂×#117	C₂²×C₄₇	1	2	yes	complemented
225	#482	C₂²×C₄₇	1	32	yes	complemented
226	#469	C₂²×C₄₇	1	16	yes	complemented
227	#466	C₂²×C₄₇	1	16	yes	complemented
228	#447	C₂²×C₄₇	1	32	yes	complemented
229	C₂×#107	C₂²×C₄₇	1	2	yes	complemented
230	C₂×#106	C₂²×C₄₇	1	2	yes	complemented
231	C₂×#102	C₂²×C₄₇	1	4	yes	complemented
232	C₂×#102	C₂²×C₄₇	1	4	yes	complemented
233	#408	C₂²×C₄₇	1	8	yes	complemented
234	C₂×C₂²⋊C₈	C₂²×C₄₇	1	4	yes	complemented
235	C₄₇	C₂×#3199	1	1	yes	characteristic, direct product factor, Sylow
236	C₂⁵	—	2	2	no	—
237	C₂×#41	—	4	2	no	—
238	C₂×#41	—	4	2	no	—
239	C₂×#41	D₄×C₄₇	1	4	yes	—
240	C₂×#41	C₂³×C₄₇	1	4	yes	—
241	C₂²×Q₈	D₄×C₄₇	1	1	yes	characteristic
242	C₂²×D₄	—	2	4	no	—
243	C₂²×D₄	—	2	4	no	—
244	C₂²×D₄	—	2	2	no	—
245	C₂²×D₄	—	2	4	no	—
246	C₂²×D₄	—	4	4	no	—
247	C₂²×D₄	—	4	4	no	—
248	C₂²×D₄	D₄×C₄₇	1	1	yes	characteristic
249	C₂²×D₄	D₄×C₄₇	1	2	yes	—
250	C₂²×D₄	C₂³×C₄₇	1	4	yes	—
251	C₂²×D₄	C₂³×C₄₇	1	8	yes	complemented
252	C₂³×C₄	C₂³×C₄₇	1	2	yes	—
253	C₂³×C₄	C₂³×C₄₇	1	1	yes	characteristic
254	C₂×D₈	—	4	4	no	—
255	C₂×D₈	—	4	4	no	—
256	C₂×D₈	C₂³×C₄₇	1	8	yes	—
257	C₂×D₈	C₂³×C₄₇	1	8	yes	—
258	C₂×M₁₆	—	4	2	no	—
259	C₂×M₁₆	C₂³×C₄₇	1	4	yes	complemented
260	C₂²×C₈	—	4	2	no	—
261	C₂²×C₈	C₂³×C₄₇	1	2	yes	—
262	C₂²×C₈	C₂³×C₄₇	1	2	yes	—
263	C₂²×C₈	C₂³×C₄₇	1	4	yes	complemented
264	#127	—	2	16	no	—
265	#124	—	2	16	no	—
266	#121	—	2	8	no	—
267	#121	—	2	8	no	—
268	#121	C₂³×C₄₇	1	16	yes	—
269	#121	C₂³×C₄₇	1	16	yes	complemented
270	#120	—	2	16	no	—
271	#120	—	2	16	no	—
272	#117	—	2	4	no	—
273	#117	C₂³×C₄₇	1	8	yes	complemented
274	C₂×C₄⋊C₄	C₂³×C₄₇	1	4	yes	—
275	C₂×C₂²⋊C₄	—	2	2	no	—
276	C₂×C₂²⋊C₄	—	2	4	no	—
277	C₂×C₂²⋊C₄	—	2	4	no	—
278	C₂×C₄²	—	2	2	no	—
279	#107	C₂³×C₄₇	1	8	yes	complemented
280	#106	C₂³×C₄₇	1	8	yes	complemented
281	#102	C₂³×C₄₇	1	16	yes	complemented
282	#102	C₂³×C₄₇	1	16	yes	complemented
283	C₂²⋊C₈	C₂³×C₄₇	1	16	yes	complemented
284	C₂⁴	—	2	4	no	—
285	C₂⁴	—	2	8	no	—
286	C₂⁴	—	4	8	no	—
287	C₂⁴	—	8	8	no	—
288	C₂⁴	C₂×D₄×C₄₇	1	2	yes	—
289	C₂⁴	C₂×D₄×C₄₇	1	1	yes	characteristic
290	#41	—	4	8	no	—
291	#41	—	4	4	no	—
292	#41	—	4	4	no	—
293	C₂×Q₈	—	4	2	no	—
294	C₂×Q₈	C₂×D₄×C₄₇	1	4	yes	—
295	C₂×D₄	—	2	16	no	—
296	C₂×D₄	—	2	16	no	—
297	C₂×D₄	—	2	4	no	—
298	C₂×D₄	—	2	8	no	—
299	C₂×D₄	—	2	8	no	—
300	C₂×D₄	—	2	8	no	—
301	C₂×D₄	—	4	8	no	—
302	C₂×D₄	—	4	8	no	—
303	C₂×D₄	—	4	4	no	—
304	C₂×D₄	—	4	2	no	—
305	C₂×D₄	—	4	8	no	—
306	C₂×D₄	—	4	16	no	—
307	C₂×D₄	—	8	8	no	—
308	C₂×D₄	—	8	8	no	—
309	C₂×D₄	C₂×D₄×C₄₇	1	4	yes	—
310	C₂×D₄	C₂×D₄×C₄₇	1	8	yes	—
311	C₂×D₄	C₂⁴×C₄₇	1	8	yes	—
312	C₂²×C₄	—	2	2	no	—
313	C₂²×C₄	—	2	2	no	—
314	C₂²×C₄	—	2	4	no	—
315	C₂²×C₄	—	2	4	no	—
316	C₂²×C₄	—	2	4	no	—
317	C₂²×C₄	C₂×D₄×C₄₇	1	2	yes	—
318	C₂²×C₄	C₂×D₄×C₄₇	1	1	yes	characteristic
319	C₂²×C₄	C₂×D₄×C₄₇	1	4	yes	—
320	C₂²×C₄	C₂×D₄×C₄₇	1	2	yes	—
321	C₂²×C₄	C₂⁴×C₄₇	1	4	yes	—
322	C₂²×C₄	C₂⁴×C₄₇	1	2	yes	—
323	C₂²×C₄	C₂⁴×C₄₇	1	1	yes	characteristic
324	D₈	—	4	8	no	—
325	D₈	—	4	8	no	—
326	M₁₆	—	4	4	no	—
327	C₂×C₈	—	2	4	no	—
328	C₂×C₈	—	2	4	no	—
329	C₂×C₈	—	4	4	no	—
330	C₂×C₈	C₂⁴×C₄₇	1	4	yes	—
331	C₂×C₈	C₂⁴×C₄₇	1	4	yes	—
332	C₄⋊C₄	—	2	4	no	—
333	C₄⋊C₄	C₂⁴×C₄₇	1	8	yes	—
334	C₂²⋊C₄	—	2	8	no	—
335	C₂²⋊C₄	—	2	16	no	—
336	C₂²⋊C₄	—	2	16	no	—
337	C₄²	—	2	8	no	—
338	C₂³	—	2	4	no	—
339	C₂³	—	2	2	no	—
340	C₂³	—	2	4	no	—
341	C₂³	—	2	8	no	—
342	C₂³	—	2	8	no	—
343	C₂³	—	4	16	no	—
344	C₂³	—	4	8	no	—
345	C₂³	—	4	8	no	—
346	C₂³	—	4	8	no	—
347	C₂³	—	8	16	no	—
348	C₂³	—	8	32	no	—
349	C₂³	C₂²×D₄×C₄₇	1	4	yes	—
350	C₂³	C₂²×D₄×C₄₇	1	2	yes	—
351	C₂³	C₂²×D₄×C₄₇	1	1	yes	characteristic
352	Q₈	—	4	4	no	—
353	D₄	—	2	8	no	—
354	D₄	—	2	8	no	—
355	D₄	—	4	8	no	—
356	D₄	—	4	4	no	—
357	D₄	—	4	16	no	—
358	D₄	—	4	8	no	—
359	D₄	—	8	16	no	—
360	D₄	—	8	16	no	—
361	C₂×C₄	—	2	4	no	—
362	C₂×C₄	—	2	2	no	—
363	C₂×C₄	—	2	8	no	—
364	C₂×C₄	—	2	4	no	—
365	C₂×C₄	—	2	2	no	—
366	C₂×C₄	—	2	2	no	—
367	C₂×C₄	—	2	4	no	—
368	C₂×C₄	—	2	4	no	—
369	C₂×C₄	—	2	8	no	—
370	C₂×C₄	—	4	8	no	—
371	C₂×C₄	C₂²×D₄×C₄₇	1	4	yes	—
372	C₂×C₄	C₂²×D₄×C₄₇	1	2	yes	—
373	C₂×C₄	C₂²×D₄×C₄₇	1	1	yes	characteristic
374	C₂×C₄	H(5,𝔽₂)×C₄₇	1	2	yes	—
375	C₂×C₄	H(5,𝔽₂)×C₄₇	1	2	yes	—
376	C₂×C₄	C₂⁵×C₄₇	1	1	yes	characteristic
377	C₈	—	2	4	no	—
378	C₈	—	2	4	no	—
379	C₂²	—	2	4	no	—
380	C₂²	—	2	8	no	—
381	C₂²	—	2	4	no	—
382	C₂²	—	2	2	no	—
383	C₂²	—	4	8	no	—
384	C₂²	—	4	4	no	—
385	C₂²	—	4	8	no	—
386	C₂²	—	4	8	no	—
387	C₂²	—	4	8	no	—
388	C₂²	—	8	32	no	—
389	C₂²	—	8	16	no	—
390	C₂²	C₄₇×#534	1	2	yes	—
391	C₂²	C₄₇×#576	1	4	yes	—
392	C₂²	C₂³×D₄×C₄₇	1	1	yes	characteristic
393	C₄	—	2	4	no	—
394	C₄	—	2	2	no	—
395	C₄	—	4	8	no	—
396	C₄	C₄₇×#534	1	2	yes	—
397	C₄	C₂×H(5,𝔽₂)×C₄₇	1	1	yes	characteristic
398	C₄	C₂×H(5,𝔽₂)×C₄₇	1	1	yes	characteristic
399	C₂	—	4	4	no	—
400	C₂	—	4	2	no	—
401	C₂	—	8	8	no	—
402	C₂	C₄₇×#3199	1	4	yes	direct product factor
403	C₂	C₂×C₄₇×#534	1	1	yes	characteristic
404	C₂	C₂×C₄₇×#576	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₄₇	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₄₇
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₄₇ ◁ C₂²×#41×C₄₇ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₄₇×#535	C₂	semidirect
2. C₄₇×#3199	C₂	direct (N × H)
3. C₂×C₄₇×#482	C₂	semidirect
4. C₂×C₄₇×#469	C₂	semidirect
5. C₂×C₄₇×#466	C₂	semidirect
6. C₂×C₄₇×#447	C₂	semidirect
7. C₂×C₄₇×#408	C₂	semidirect
9. C₂³×D₄×C₄₇	C₂²	semidirect
12. C₂²×M₁₆×C₄₇	C₂²	semidirect
13. C₂³×C₈×C₄₇	C₂²	semidirect
15. C₄₇×#535	C₂²	semidirect
19. C₂×#121×C₄₇	C₂²	semidirect
22. C₂×#117×C₄₇	C₂²	semidirect
23. C₄₇×#482	C₂²	semidirect
24. C₄₇×#469	C₂²	semidirect
25. C₄₇×#466	C₂²	semidirect
26. C₄₇×#447	C₂²	semidirect
27. C₂×#107×C₄₇	C₂²	semidirect
28. C₂×#106×C₄₇	C₂²	semidirect
29. C₂×#102×C₄₇	C₂²	semidirect
30. C₂×#102×C₄₇	C₂²	semidirect
31. C₄₇×#408	C₂²	semidirect
32. C₂×C₂²⋊C₈×C₄₇	C₂²	semidirect
48. C₂²×D₄×C₄₇	C₂³	semidirect
56. C₂×M₁₆×C₄₇	C₂³	semidirect
60. C₂²×C₈×C₄₇	C₂³	semidirect
66. #121×C₄₇	C₂³	semidirect
70. #117×C₄₇	C₂³	semidirect
76. #107×C₄₇	C₂³	semidirect
77. #106×C₄₇	C₂³	semidirect
78. #102×C₄₇	C₂³	semidirect
79. #102×C₄₇	C₂³	semidirect
80. C₂²⋊C₈×C₄₇	C₂³	semidirect
176. C₂×#3199	C₄₇	direct (N × H)
197. C₂×#535	C₂×C₄₇	semidirect
198. #3199	C₂×C₄₇	direct (N × H)
199. C₂×#482	C₂×C₄₇	semidirect
200. C₂×#469	C₂×C₄₇	semidirect
201. C₂×#466	C₂×C₄₇	semidirect
202. C₂×#447	C₂×C₄₇	semidirect
203. C₂×#408	C₂×C₄₇	semidirect
207. C₂×C₄₇	#3199	direct (N × H)
211. C₂³×D₄	C₂²×C₄₇	semidirect
214. C₂²×M₁₆	C₂²×C₄₇	semidirect
215. C₂³×C₈	C₂²×C₄₇	semidirect
217. #535	C₂²×C₄₇	semidirect
221. C₂×#121	C₂²×C₄₇	semidirect
224. C₂×#117	C₂²×C₄₇	semidirect
225. #482	C₂²×C₄₇	semidirect
226. #469	C₂²×C₄₇	semidirect
227. #466	C₂²×C₄₇	semidirect
228. #447	C₂²×C₄₇	semidirect
229. C₂×#107	C₂²×C₄₇	semidirect
230. C₂×#106	C₂²×C₄₇	semidirect
231. C₂×#102	C₂²×C₄₇	semidirect
232. C₂×#102	C₂²×C₄₇	semidirect
233. #408	C₂²×C₄₇	semidirect
234. C₂×C₂²⋊C₈	C₂²×C₄₇	semidirect
235. C₄₇	C₂×#3199	direct (N × H)
251. C₂²×D₄	C₂³×C₄₇	semidirect
259. C₂×M₁₆	C₂³×C₄₇	semidirect
263. C₂²×C₈	C₂³×C₄₇	semidirect
269. #121	C₂³×C₄₇	semidirect
273. #117	C₂³×C₄₇	semidirect
279. #107	C₂³×C₄₇	semidirect
280. #106	C₂³×C₄₇	semidirect
281. #102	C₂³×C₄₇	semidirect
282. #102	C₂³×C₄₇	semidirect
283. C₂²⋊C₈	C₂³×C₄₇	semidirect
402. C₂	C₄₇×#3199	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₄₇×#535	2
C₄₇×#3199	2
C₂×C₄₇×#482	2
C₂×C₄₇×#469	2
C₂×C₄₇×#466	2
C₂×C₄₇×#447	2
C₂×C₄₇×#408	2
C₂×#3199	47

Subgroups — C2×C47×#3199 #26100441

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₄₇×#3199 #26100441