Subgroups — #41×C₂²⋊D₄₇ #20256873

Order 6016.

1648 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	C₂×#41×D₄₇	C₂	1	1	yes	maximal, characteristic, complemented
2	#15689792	C₂	1	1	yes	maximal, characteristic, complemented
3	Q₈×C₂²⋊D₄₇	C₂	1	1	yes	maximal, characteristic, complemented
4	#15689784	C₂	1	1	yes	maximal, characteristic, complemented
5	#15689780	C₂	1	1	yes	maximal, characteristic, complemented
6	#15689772	C₂	1	3	yes	maximal, complemented
7	#15689767	C₂	1	3	yes	maximal, complemented
8	#15689761	C₂	1	3	yes	maximal, complemented
9	D₄×C₂²⋊D₄₇	C₂	1	3	yes	maximal, complemented
10	#15689669	C₂	1	3	yes	maximal, complemented
11	#15689634	C₂	1	3	yes	maximal, complemented
12	#15689630	C₂	1	3	yes	maximal, complemented
13	#41×Dic₄₇	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂×C₄×C₂²⋊D₄₇	C₂	1	3	yes	maximal, complemented
15	C₂²×#41×C₄₇	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×#10625354	C₂²	1	1	yes	characteristic, complemented
17	C₂×#10625350	C₂²	1	3	yes	complemented
18	C₂×#10625352	C₂²	1	3	yes	complemented
19	#41×D₄₇	—	2	8	no	—
20	C₂×Q₈×D₄₇	C₂²	1	1	yes	characteristic, complemented
21	C₂²×C₂²⋊D₄₇	C₂²	1	3	yes	—
22	C₂×D₄×D₄₇	C₂²	1	3	yes	complemented
23	C₂²×C₄×D₄₇	C₂²	1	3	yes	complemented
24	#13094022	C₂²	1	3	yes	complemented
25	#13094020	C₂²	1	3	yes	complemented
26	#13094013	C₂²	1	3	yes	complemented
27	#13094011	C₂²	1	3	yes	complemented
28	#13094007	C₂²	1	6	yes	complemented
29	#13094005	C₂²	1	6	yes	complemented
30	#13094003	C₂²	1	3	yes	complemented
31	#13094003	C₂²	1	3	yes	complemented
32	#13094000	C₂²	1	3	yes	complemented
33	#13094000	C₂²	1	3	yes	complemented
34	#13093998	C₂²	1	3	yes	complemented
35	#13093998	C₂²	1	3	yes	complemented
36	#13093996	C₂²	1	6	yes	complemented
37	#13093996	C₂²	1	6	yes	complemented
38	#13093995	C₂²	1	3	yes	complemented
39	#13093995	C₂²	1	3	yes	complemented
40	#13093993	C₂²	1	6	yes	complemented
41	#13093992	C₂²	1	6	yes	complemented
42	Q₈×Dic₄₇	C₂²	1	1	yes	characteristic, complemented
43	Q₈×Dic₄₇	C₂²	1	1	yes	characteristic, complemented
44	D₄×Dic₄₇	C₂²	1	3	yes	complemented
45	D₄×Dic₄₇	C₂²	1	3	yes	complemented
46	C₄×C₂²⋊D₄₇	C₂²	1	3	yes	—
47	C₄×C₂²⋊D₄₇	C₂²	1	1	yes	characteristic
48	C₄×C₂²⋊D₄₇	C₂²	1	3	yes	complemented
49	C₄×C₂²⋊D₄₇	C₂²	1	3	yes	complemented
50	C₄×C₂²⋊D₄₇	C₂²	1	3	yes	complemented
51	C₄×C₂²⋊D₄₇	C₂²	1	3	yes	complemented
52	C₄×C₂²⋊D₄₇	C₂²	1	3	yes	complemented
53	C₄×C₂²⋊D₄₇	C₂²	1	3	yes	complemented
54	C₄×C₂²⋊D₄₇	C₂²	1	6	yes	complemented
55	#13093983	C₂²	1	3	yes	complemented
56	C₂×Dic₄₇⋊C₄	C₂²	1	3	yes	complemented
57	C₂×C₂²⋊Dic₄₇	C₂²	1	3	yes	complemented
58	C₂×(C₂×D₄₇)⋊C₄	C₂²	1	3	yes	complemented
59	C₂×C₄×Dic₄₇	C₂²	1	3	yes	complemented
60	C₂×#41×C₄₇	—	2	8	no	—
61	C₂×#41×C₄₇	C₂²	1	1	yes	characteristic
62	C₂×#41×C₄₇	C₂²	1	3	yes	complemented
63	C₂×#41×C₄₇	C₂²	1	1	yes	characteristic, complemented
64	C₂×#41×C₄₇	C₂²	1	3	yes	complemented
65	C₂²×Q₈×C₄₇	C₂²	1	1	yes	characteristic, complemented
66	C₂²×D₄×C₄₇	C₂²	1	3	yes	complemented
67	C₂³×C₄×C₄₇	C₂²	1	3	yes	complemented
68	C₂⁴×C₄₇	C₂³	1	3	yes	—
69	C₂³×D₄₇	C₂³	1	3	yes	—
70	#41×C₄₇	—	2	4	no	—
71	#41×C₄₇	—	2	12	no	—
72	#41×C₄₇	—	2	12	no	—
73	#41×C₄₇	D₄	1	8	yes	complemented
74	C₂×Q₈×C₄₇	—	2	4	no	—
75	C₂×Q₈×C₄₇	C₂³	1	3	yes	—
76	C₂×Q₈×C₄₇	C₂³	1	1	yes	characteristic
77	C₂×D₄×C₄₇	—	2	12	no	—
78	C₂×D₄×C₄₇	C₂³	1	6	yes	—
79	C₂×D₄×C₄₇	C₂³	1	3	yes	—
80	C₂×D₄×C₄₇	C₂³	1	3	yes	—
81	C₂²×C₄×C₄₇	—	2	12	no	—
82	C₂²×C₄×C₄₇	C₂³	1	1	yes	characteristic
83	C₂²×C₄×C₄₇	C₂³	1	3	yes	—
84	C₂²×C₄×C₄₇	C₂³	1	3	yes	—
85	C₂²×C₄×C₄₇	C₂³	1	3	yes	—
86	C₂²×C₄×C₄₇	C₂³	1	3	yes	—
87	C₂²×C₄×C₄₇	C₂³	1	3	yes	—
88	C₂×C₂²⋊D₄₇	—	2	12	no	—
89	C₂×C₂²⋊D₄₇	C₂³	1	3	yes	—
90	C₂×C₂²⋊D₄₇	C₂³	1	3	yes	—
91	C₂×C₂²⋊D₄₇	C₂³	1	3	yes	—
92	C₂×C₂²⋊D₄₇	C₂³	1	6	yes	—
93	C₂×C₂²⋊D₄₇	C₂³	1	6	yes	—
94	C₂×C₂²⋊D₄₇	C₂³	1	1	yes	characteristic
95	C₂²×Dic₄₇	C₂³	1	3	yes	—
96	C₂²×Dic₄₇	C₂³	1	3	yes	—
97	C₂²×Dic₄₇	C₂³	1	3	yes	—
98	#10625354	—	2	4	no	—
99	Q₈×D₄₇	—	2	4	no	—
100	#10625352	—	2	12	no	—
101	D₄×D₄₇	—	2	12	no	—
102	#10625350	—	2	12	no	—
103	C₂×D₁₈₈	C₂³	1	3	yes	—
104	C₂×C₄×D₄₇	—	2	12	no	—
105	C₂×C₄×D₄₇	C₂³	1	1	yes	characteristic
106	C₂×C₄×D₄₇	C₂³	1	3	yes	—
107	C₂×C₄×D₄₇	C₂³	1	3	yes	—
108	C₂×C₄×D₄₇	C₂³	1	3	yes	—
109	C₂×Dic₉₄	C₂³	1	3	yes	—
110	C₂²⋊Dic₄₇	C₂³	1	1	yes	characteristic
111	C₂²⋊Dic₄₇	C₂³	1	3	yes	—
112	C₂²⋊Dic₄₇	C₂³	1	3	yes	—
113	C₂²⋊Dic₄₇	C₂³	1	3	yes	—
114	C₂²⋊Dic₄₇	C₂³	1	6	yes	—
115	C₂²⋊Dic₄₇	C₂³	1	6	yes	—
116	(C₂×D₄₇)⋊C₄	C₂³	1	1	yes	characteristic
117	(C₂×D₄₇)⋊C₄	C₂³	1	3	yes	—
118	(C₂×D₄₇)⋊C₄	C₂³	1	3	yes	—
119	(C₂×D₄₇)⋊C₄	C₂³	1	3	yes	—
120	(C₂×D₄₇)⋊C₄	C₂³	1	6	yes	—
121	C₄⋊Dic₄₇	C₂³	1	3	yes	—
122	C₄⋊Dic₄₇	C₂³	1	3	yes	—
123	Dic₄₇⋊C₄	C₂³	1	1	yes	characteristic
124	Dic₄₇⋊C₄	C₂³	1	3	yes	—
125	Dic₄₇⋊C₄	C₂³	1	3	yes	—
126	Dic₄₇⋊C₄	C₂³	1	3	yes	—
127	Dic₄₇⋊C₄	C₂³	1	6	yes	—
128	C₄×Dic₄₇	C₂³	1	1	yes	characteristic
129	C₄×Dic₄₇	C₂³	1	3	yes	—
130	C₄×Dic₄₇	C₂³	1	3	yes	—
131	C₄×Dic₄₇	C₂³	1	3	yes	—
132	C₂³×C₄₇	—	2	6	no	—
133	C₂³×C₄₇	—	2	6	no	—
134	C₂³×C₄₇	—	4	3	no	—
135	C₂³×C₄₇	C₂⁴	1	3	yes	—
136	C₂³×C₄₇	C₂⁴	1	3	yes	—
137	C₂³×C₄₇	C₂⁴	1	1	yes	characteristic
138	C₂²×D₄₇	—	2	6	no	—
139	C₂²×D₄₇	—	2	6	no	—
140	C₂²×D₄₇	—	4	3	no	—
141	C₂²×D₄₇	C₂⁴	1	3	yes	—
142	C₂²×D₄₇	C₂⁴	1	1	yes	characteristic
143	Q₈×C₄₇	—	2	6	no	—
144	Q₈×C₄₇	C₂×D₄	1	4	yes	complemented
145	D₄×C₄₇	—	2	12	no	—
146	D₄×C₄₇	—	2	6	no	—
147	D₄×C₄₇	C₂×D₄	1	12	yes	complemented
148	C₂×C₄×C₄₇	—	2	6	no	—
149	C₂×C₄×C₄₇	—	2	2	no	—
150	C₂×C₄×C₄₇	—	2	6	no	—
151	C₂×C₄×C₄₇	—	2	6	no	—
152	C₂×C₄×C₄₇	—	2	6	no	—
153	C₂×C₄×C₄₇	C₂×D₄	1	12	yes	complemented
154	C₂×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
155	C₂×C₄×C₄₇	C₂⁴	1	3	yes	—
156	C₂×C₄×C₄₇	C₂⁴	1	3	yes	—
157	C₂×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
158	C₂²⋊D₄₇	—	2	12	no	—
159	C₂²⋊D₄₇	—	2	6	no	—
160	C₂²⋊D₄₇	—	2	6	no	—
161	C₂²⋊D₄₇	—	2	6	no	—
162	C₂²⋊D₄₇	—	4	6	no	—
163	C₂²⋊D₄₇	#41	1	4	yes	direct product factor
164	C₂×Dic₄₇	—	2	6	no	—
165	C₂×Dic₄₇	—	2	6	no	—
166	C₂×Dic₄₇	—	4	3	no	—
167	C₂×Dic₄₇	C₂⁴	1	1	yes	characteristic
168	C₂×Dic₄₇	C₂⁴	1	3	yes	—
169	C₂×Dic₄₇	C₂⁴	1	3	yes	—
170	C₂×Dic₄₇	C₂⁴	1	3	yes	—
171	C₂×Dic₄₇	C₂⁴	1	1	yes	characteristic
172	C₂×Dic₄₇	C₂⁴	1	1	yes	characteristic
173	D₁₈₈	—	2	6	no	—
174	C₄×D₄₇	—	2	2	no	—
175	C₄×D₄₇	—	2	6	no	—
176	C₄×D₄₇	—	2	6	no	—
177	C₄×D₄₇	—	2	6	no	—
178	Dic₉₄	—	2	6	no	—
179	C₂²×C₄₇	—	2	1	no	—
180	C₂²×C₄₇	—	2	3	no	—
181	C₂²×C₄₇	—	2	3	no	—
182	C₂²×C₄₇	—	2	1	no	—
183	C₂²×C₄₇	—	2	3	no	—
184	C₂²×C₄₇	—	2	3	no	—
185	C₂²×C₄₇	—	2	3	no	—
186	C₂²×C₄₇	—	4	12	no	—
187	C₂²×C₄₇	C₂²×D₄	1	6	yes	—
188	C₂²×C₄₇	C₂×#41	1	2	yes	complemented
189	C₂²×C₄₇	C₂⁵	1	1	yes	characteristic
190	C₂×D₄₇	—	2	1	no	—
191	C₂×D₄₇	—	2	1	no	—
192	C₂×D₄₇	—	2	3	no	—
193	C₂×D₄₇	—	2	3	no	—
194	C₂×D₄₇	—	2	3	no	—
195	C₂×D₄₇	—	4	12	no	—
196	C₂×D₄₇	C₂×#41	1	2	yes	complemented
197	C₄×C₄₇	—	2	1	no	—
198	C₄×C₄₇	—	2	3	no	—
199	C₄×C₄₇	C₂²×D₄	1	6	yes	—
200	C₄×C₄₇	C₂²×D₄	1	2	yes	—
201	Dic₄₇	—	2	3	no	—
202	Dic₄₇	—	2	1	no	—
203	Dic₄₇	—	2	3	no	—
204	Dic₄₇	—	2	1	no	—
205	Dic₄₇	—	2	3	no	—
206	Dic₄₇	C₂×#41	1	2	yes	complemented
207	D₄×#41	—	47	1	no	maximal, Sylow
208	C₂×C₄₇	—	2	6	no	—
209	C₂×C₄₇	—	2	2	no	—
210	C₂×C₄₇	—	4	3	no	—
211	C₂×C₄₇	C₂³×D₄	1	1	yes	characteristic
212	C₂×C₄₇	C₂²×#41	1	1	yes	characteristic
213	C₂×C₄₇	#585	1	1	yes	characteristic
214	D₄₇	—	2	2	no	—
215	D₄₇	—	4	3	no	—
216	C₂²×#41	—	47	1	no	—
217	C₂²×#41	D₄₇	1	1	yes	characteristic, complemented
218	#550	—	47	1	no	—
219	D₄×Q₈	—	47	1	no	—
220	#548	—	47	1	no	—
221	#548	—	47	1	no	—
222	#547	—	47	3	no	—
223	#546	—	47	3	no	—
224	#546	—	47	3	no	—
225	D₄²	—	47	3	no	—
226	#532	—	47	3	no	—
227	#525	—	47	3	no	—
228	#525	—	47	3	no	—
229	C₄×#41	—	47	1	no	—
230	C₂×C₄×D₄	—	47	3	no	—
231	C₄₇	D₄×#41	1	1	yes	characteristic, complemented, Sylow
232	C₂×#41	—	2	8	no	—
233	C₂×#41	—	47	1	no	—
234	C₂×#41	—	47	3	no	—
235	C₂×#41	—	47	3	no	—
236	C₂×#41	—	94	8	no	—
237	C₂×#41	C₂×D₄₇	1	1	yes	characteristic
238	C₂×#41	C₂×D₄₇	1	3	yes	complemented
239	C₂×#41	C₂×D₄₇	1	3	yes	complemented
240	C₂×#41	C₂×D₄₇	1	1	yes	characteristic, complemented
241	C₂²×Q₈	—	47	1	no	—
242	C₂²×Q₈	C₂×D₄₇	1	1	yes	characteristic, complemented
243	C₂²×D₄	—	47	3	no	—
244	C₂²×D₄	—	47	3	no	—
245	C₂²×D₄	C₂×D₄₇	1	3	yes	complemented
246	C₂³×C₄	—	47	3	no	—
247	C₂³×C₄	C₂×D₄₇	1	3	yes	complemented
248	C₄⋊Q₈	—	47	3	no	—
249	#127	—	47	3	no	—
250	#124	—	47	3	no	—
251	#124	—	47	3	no	—
252	#123	—	47	6	no	—
253	#123	—	47	6	no	—
254	C₂²⋊Q₈	—	47	3	no	—
255	C₂²⋊Q₈	—	47	3	no	—
256	C₂²⋊Q₈	—	47	3	no	—
257	C₂²⋊Q₈	—	47	3	no	—
258	#121	—	47	3	no	—
259	#121	—	47	3	no	—
260	#121	—	47	6	no	—
261	#121	—	47	6	no	—
262	#121	—	47	3	no	—
263	#121	—	47	3	no	—
264	#120	—	47	6	no	—
265	#120	—	47	6	no	—
266	C₄×Q₈	—	47	1	no	—
267	C₄×Q₈	—	47	1	no	—
268	C₄×D₄	—	47	3	no	—
269	C₄×D₄	—	47	3	no	—
270	C₄×D₄	—	47	1	no	—
271	C₄×D₄	—	47	3	no	—
272	C₄×D₄	—	47	3	no	—
273	C₄×D₄	—	47	3	no	—
274	C₄×D₄	—	47	3	no	—
275	C₄×D₄	—	47	3	no	—
276	C₄×D₄	—	47	3	no	—
277	C₄×D₄	—	47	3	no	—
278	C₄×D₄	—	47	6	no	—
279	#117	—	47	3	no	—
280	C₂×C₄⋊C₄	—	47	3	no	—
281	C₂×C₂²⋊C₄	—	47	3	no	—
282	C₂×C₂²⋊C₄	—	47	3	no	—
283	C₂×C₄²	—	47	3	no	—
284	C₂⁴	—	47	3	no	—
285	C₂⁴	C₂²×D₄₇	1	3	yes	—
286	#41	—	2	4	no	—
287	#41	—	2	12	no	—
288	#41	—	2	12	no	—
289	#41	—	94	4	no	—
290	#41	—	94	12	no	—
291	#41	—	94	12	no	—
292	#41	C₂²⋊D₄₇	1	8	yes	direct product factor
293	C₂×Q₈	—	2	4	no	—
294	C₂×Q₈	—	47	3	no	—
295	C₂×Q₈	—	94	4	no	—
296	C₂×Q₈	C₂²×D₄₇	1	3	yes	—
297	C₂×Q₈	C₂²×D₄₇	1	1	yes	characteristic
298	C₂×D₄	—	2	12	no	—
299	C₂×D₄	—	47	1	no	—
300	C₂×D₄	—	47	3	no	—
301	C₂×D₄	—	47	3	no	—
302	C₂×D₄	—	47	3	no	—
303	C₂×D₄	—	47	6	no	—
304	C₂×D₄	—	47	6	no	—
305	C₂×D₄	—	47	3	no	—
306	C₂×D₄	—	94	12	no	—
307	C₂×D₄	—	94	12	no	—
308	C₂×D₄	C₂²×D₄₇	1	6	yes	—
309	C₂×D₄	C₂²×D₄₇	1	3	yes	—
310	C₂×D₄	C₂²×D₄₇	1	3	yes	—
311	C₂²×C₄	—	2	12	no	—
312	C₂²×C₄	—	47	3	no	—
313	C₂²×C₄	—	47	3	no	—
314	C₂²×C₄	—	47	3	no	—
315	C₂²×C₄	—	47	3	no	—
316	C₂²×C₄	—	47	3	no	—
317	C₂²×C₄	—	47	1	no	—
318	C₂²×C₄	—	47	3	no	—
319	C₂²×C₄	—	94	12	no	—
320	C₂²×C₄	C₂²×D₄₇	1	3	yes	—
321	C₂²×C₄	C₂²×D₄₇	1	3	yes	—
322	C₂²×C₄	C₂²×D₄₇	1	3	yes	—
323	C₂²×C₄	C₂²×D₄₇	1	1	yes	characteristic
324	C₂²×C₄	C₂²×D₄₇	1	3	yes	—
325	C₂²×C₄	C₂²×D₄₇	1	3	yes	—
326	C₄⋊C₄	—	47	1	no	—
327	C₄⋊C₄	—	47	3	no	—
328	C₄⋊C₄	—	47	3	no	—
329	C₄⋊C₄	—	47	3	no	—
330	C₄⋊C₄	—	47	6	no	—
331	C₄⋊C₄	—	47	3	no	—
332	C₄⋊C₄	—	47	3	no	—
333	C₂²⋊C₄	—	47	1	no	—
334	C₂²⋊C₄	—	47	3	no	—
335	C₂²⋊C₄	—	47	3	no	—
336	C₂²⋊C₄	—	47	3	no	—
337	C₂²⋊C₄	—	47	6	no	—
338	C₂²⋊C₄	—	47	6	no	—
339	C₂²⋊C₄	—	47	1	no	—
340	C₂²⋊C₄	—	47	3	no	—
341	C₂²⋊C₄	—	47	3	no	—
342	C₂²⋊C₄	—	47	3	no	—
343	C₂²⋊C₄	—	47	6	no	—
344	C₄²	—	47	3	no	—
345	C₄²	—	47	3	no	—
346	C₄²	—	47	1	no	—
347	C₄²	—	47	3	no	—
348	C₂³	—	2	6	no	—
349	C₂³	—	2	6	no	—
350	C₂³	—	4	3	no	—
351	C₂³	—	47	1	no	—
352	C₂³	—	47	3	no	—
353	C₂³	—	94	6	no	—
354	C₂³	—	94	6	no	—
355	C₂³	—	188	3	no	—
356	C₂³	C₂³×D₄₇	1	3	yes	—
357	C₂³	C₂³×D₄₇	1	3	yes	—
358	C₂³	C₂³×D₄₇	1	1	yes	characteristic
359	Q₈	—	2	6	no	—
360	Q₈	—	94	6	no	—
361	Q₈	C₂×C₂²⋊D₄₇	1	4	yes	complemented
362	D₄	—	2	12	no	—
363	D₄	—	2	6	no	—
364	D₄	—	47	4	no	—
365	D₄	—	94	6	no	—
366	D₄	—	94	6	no	—
367	D₄	—	94	12	no	—
368	D₄	—	94	6	no	—
369	D₄	—	94	6	no	—
370	D₄	—	188	6	no	—
371	D₄	C₂×C₂²⋊D₄₇	1	12	yes	complemented
372	C₂×C₄	—	2	6	no	—
373	C₂×C₄	—	2	2	no	—
374	C₂×C₄	—	2	6	no	—
375	C₂×C₄	—	2	6	no	—
376	C₂×C₄	—	2	6	no	—
377	C₂×C₄	—	47	1	no	—
378	C₂×C₄	—	47	1	no	—
379	C₂×C₄	—	47	3	no	—
380	C₂×C₄	—	47	3	no	—
381	C₂×C₄	—	47	1	no	—
382	C₂×C₄	—	47	3	no	—
383	C₂×C₄	—	94	6	no	—
384	C₂×C₄	—	94	6	no	—
385	C₂×C₄	—	94	2	no	—
386	C₂×C₄	—	94	6	no	—
387	C₂×C₄	—	94	6	no	—
388	C₂×C₄	—	94	6	no	—
389	C₂×C₄	—	188	3	no	—
390	C₂×C₄	C₂×C₂²⋊D₄₇	1	12	yes	complemented
391	C₂×C₄	C₂³×D₄₇	1	1	yes	characteristic
392	C₂×C₄	C₂³×D₄₇	1	3	yes	—
393	C₂×C₄	C₂³×D₄₇	1	3	yes	—
394	C₂×C₄	C₂³×D₄₇	1	1	yes	characteristic
395	C₂²	—	2	1	no	—
396	C₂²	—	2	3	no	—
397	C₂²	—	2	3	no	—
398	C₂²	—	2	1	no	—
399	C₂²	—	2	3	no	—
400	C₂²	—	2	3	no	—
401	C₂²	—	2	3	no	—
402	C₂²	—	4	12	no	—
403	C₂²	—	47	2	no	—
404	C₂²	—	94	1	no	—
405	C₂²	—	94	1	no	—
406	C₂²	—	94	3	no	—
407	C₂²	—	94	3	no	—
408	C₂²	—	94	3	no	—
409	C₂²	—	188	12	no	—
410	C₂²	C₂²×C₂²⋊D₄₇	1	6	yes	—
411	C₂²	#41×D₄₇	1	2	yes	complemented
412	C₂²	C₂⁴×D₄₇	1	1	yes	characteristic
413	C₄	—	2	1	no	—
414	C₄	—	2	3	no	—
415	C₄	—	47	2	no	—
416	C₄	—	94	1	no	—
417	C₄	—	94	3	no	—
418	C₄	—	94	3	no	—
419	C₄	—	94	1	no	—
420	C₄	—	94	3	no	—
421	C₄	C₂²×C₂²⋊D₄₇	1	2	yes	—
422	C₄	C₂²×C₂²⋊D₄₇	1	6	yes	—
423	C₂	—	2	2	no	—
424	C₂	—	2	6	no	—
425	C₂	—	4	3	no	—
426	C₂	—	94	2	no	—
427	C₂	—	188	3	no	—
428	C₂	C₂³×C₂²⋊D₄₇	1	1	yes	characteristic
429	C₂	C₂×#41×D₄₇	1	1	yes	characteristic
430	C₂	#15689959	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂³×D₄₇
commutator, socle	C₂²×C₄₇	C₂⁵
Frattini	C₂²	C₂⁴×D₄₇
Fitting	C₂²×#41×C₄₇	C₂
hypercenter	C₂²×#41	D₄₇
hypocenter	C₄₇	D₄×#41
LCS	G ▷ C₂²×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂×C₄ ◁ C₂²×#41

Complements

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

N	H ≅ G/N	type
1. C₂×#41×D₄₇	C₂	semidirect
2. #15689792	C₂	semidirect
3. Q₈×C₂²⋊D₄₇	C₂	semidirect
4. #15689784	C₂	semidirect
5. #15689780	C₂	semidirect
6. #15689772	C₂	semidirect
7. #15689767	C₂	semidirect
8. #15689761	C₂	semidirect
9. D₄×C₂²⋊D₄₇	C₂	semidirect
10. #15689669	C₂	semidirect
11. #15689634	C₂	semidirect
12. #15689630	C₂	semidirect
13. #41×Dic₄₇	C₂	semidirect
14. C₂×C₄×C₂²⋊D₄₇	C₂	semidirect
15. C₂²×#41×C₄₇	C₂	semidirect
16. C₂×#10625354	C₂²	semidirect
17. C₂×#10625350	C₂²	semidirect
18. C₂×#10625352	C₂²	semidirect
20. C₂×Q₈×D₄₇	C₂²	semidirect
22. C₂×D₄×D₄₇	C₂²	semidirect
23. C₂²×C₄×D₄₇	C₂²	semidirect
24. #13094022	C₂²	semidirect
25. #13094020	C₂²	semidirect
26. #13094013	C₂²	semidirect
27. #13094011	C₂²	semidirect
28. #13094007	C₂²	semidirect
29. #13094005	C₂²	semidirect
30. #13094003	C₂²	semidirect
31. #13094003	C₂²	semidirect
32. #13094000	C₂²	semidirect
33. #13094000	C₂²	semidirect
34. #13093998	C₂²	semidirect
35. #13093998	C₂²	semidirect
36. #13093996	C₂²	semidirect
37. #13093996	C₂²	semidirect
38. #13093995	C₂²	semidirect
39. #13093995	C₂²	semidirect
40. #13093993	C₂²	semidirect
41. #13093992	C₂²	semidirect
42. Q₈×Dic₄₇	C₂²	semidirect
43. Q₈×Dic₄₇	C₂²	semidirect
44. D₄×Dic₄₇	C₂²	semidirect
45. D₄×Dic₄₇	C₂²	semidirect
48. C₄×C₂²⋊D₄₇	C₂²	semidirect
49. C₄×C₂²⋊D₄₇	C₂²	semidirect
50. C₄×C₂²⋊D₄₇	C₂²	semidirect
51. C₄×C₂²⋊D₄₇	C₂²	semidirect
52. C₄×C₂²⋊D₄₇	C₂²	semidirect
53. C₄×C₂²⋊D₄₇	C₂²	semidirect
54. C₄×C₂²⋊D₄₇	C₂²	semidirect
55. #13093983	C₂²	semidirect
56. C₂×Dic₄₇⋊C₄	C₂²	semidirect
57. C₂×C₂²⋊Dic₄₇	C₂²	semidirect
58. C₂×(C₂×D₄₇)⋊C₄	C₂²	semidirect
59. C₂×C₄×Dic₄₇	C₂²	semidirect
62. C₂×#41×C₄₇	C₂²	semidirect
63. C₂×#41×C₄₇	C₂²	semidirect
64. C₂×#41×C₄₇	C₂²	semidirect
65. C₂²×Q₈×C₄₇	C₂²	semidirect
66. C₂²×D₄×C₄₇	C₂²	semidirect
67. C₂³×C₄×C₄₇	C₂²	semidirect
73. #41×C₄₇	D₄	semidirect
144. Q₈×C₄₇	C₂×D₄	semidirect
147. D₄×C₄₇	C₂×D₄	semidirect
153. C₂×C₄×C₄₇	C₂×D₄	semidirect
163. C₂²⋊D₄₇	#41	direct (N × H)
188. C₂²×C₄₇	C₂×#41	semidirect
196. C₂×D₄₇	C₂×#41	semidirect
206. Dic₄₇	C₂×#41	semidirect
217. C₂²×#41	D₄₇	semidirect
231. C₄₇	D₄×#41	semidirect
238. C₂×#41	C₂×D₄₇	semidirect
239. C₂×#41	C₂×D₄₇	semidirect
240. C₂×#41	C₂×D₄₇	semidirect
242. C₂²×Q₈	C₂×D₄₇	semidirect
245. C₂²×D₄	C₂×D₄₇	semidirect
247. C₂³×C₄	C₂×D₄₇	semidirect
292. #41	C₂²⋊D₄₇	direct (N × H)
361. Q₈	C₂×C₂²⋊D₄₇	semidirect
371. D₄	C₂×C₂²⋊D₄₇	semidirect
390. C₂×C₄	C₂×C₂²⋊D₄₇	semidirect
411. C₂²	#41×D₄₇	semidirect

Subgroups — #41×C22⋊D47 #20256873

Conjugacy classes of subgroups

Complements

Subgroups — #41×C₂²⋊D₄₇ #20256873