Subgroups — #20252108

Order 6016.

502 conjugacy classes of subgroups.

The subgroup lattice has 408 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#13094030	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×#10625324	C₂	1	1	yes	maximal, characteristic, complemented
3	#15689632	C₂	1	1	yes	maximal, characteristic
4	#15689202	C₂	1	1	yes	maximal, characteristic, complemented
5	#15689198	C₂	1	1	yes	maximal, characteristic, complemented
6	#15689195	C₂	1	1	yes	maximal, characteristic, complemented
7	#15689194	C₂	1	1	yes	maximal, characteristic, complemented
8	#15689194	C₂	1	1	yes	maximal, characteristic, complemented
9	#15689193	C₂	1	1	yes	maximal, characteristic, complemented
10	(C₂²⋊D₄₇)⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
11	#15689148	C₂	1	1	yes	maximal, characteristic, complemented
12	#15689088	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂²⋊C₈×D₄₇	C₂	1	1	yes	maximal, characteristic, complemented
14	#15689077	C₂	1	1	yes	maximal, characteristic, complemented
15	C₈×D₄×C₄₇	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×#10625350	C₂²	1	1	yes	characteristic
17	C₂²×C₄×D₄₇	C₂²	1	1	yes	characteristic
18	#13094030	—	2	4	no	—
19	C₂×#10625329	C₂²	1	1	yes	characteristic, complemented
20	C₂×#10625324	—	2	4	no	—
21	C₂×#10625324	C₂²	1	1	yes	characteristic
22	C₂×#10625324	C₂²	1	1	yes	characteristic
23	C₂×#10625324	C₂²	1	1	yes	characteristic
24	C₂×#10625324	C₂²	1	1	yes	characteristic
25	C₂×#10625324	C₂²	1	1	yes	characteristic, complemented
26	C₂²×C₄₇⋊C₈	C₂²	1	1	yes	characteristic
27	C₂×C₈×D₄₇	C₂²	1	1	yes	characteristic
28	C₂×C₈×D₄₇	C₂²	1	1	yes	characteristic
29	C₂×C₈×D₄₇	C₂²	1	1	yes	characteristic, complemented
30	#13094009	C₄	1	1	yes	characteristic
31	#13094006	C₄	1	1	yes	characteristic
32	#13094002	C₄	1	1	yes	characteristic
33	#13094001	C₄	1	1	yes	characteristic
34	#13093997	C₄	1	1	yes	characteristic
35	#13093996	C₄	1	1	yes	characteristic
36	#13093994	C₄	1	1	yes	characteristic
37	#13093992	C₄	1	1	yes	characteristic
38	C₄×D₁₈₈	C₂²	1	1	yes	characteristic
39	C₄×C₂²⋊D₄₇	C₂²	1	1	yes	characteristic
40	C₄×C₂²⋊D₄₇	C₂²	1	1	yes	characteristic
41	#13093981	C₂²	1	1	yes	characteristic
42	C₄⋊(C₄₇⋊C₈)	C₂²	1	1	yes	characteristic, complemented
43	Dic₄₇⋊C₈	C₂²	1	1	yes	characteristic, complemented
44	Dic₄₇⋊C₈	C₂²	1	1	yes	characteristic, complemented
45	C₂²⋊(C₄₇⋊C₈)	C₂²	1	1	yes	characteristic
46	C₂²⋊(C₄₇⋊C₈)	C₂²	1	1	yes	characteristic, complemented
47	(C₂×D₄₇)⋊C₈	C₂²	1	1	yes	characteristic
48	(C₂×D₄₇)⋊C₈	C₂²	1	1	yes	characteristic
49	(C₂×D₄₇)⋊C₈	C₂²	1	1	yes	characteristic, complemented
50	(C₂×D₄₇)⋊C₈	C₂²	1	1	yes	characteristic, complemented
51	#13093935	C₂²	1	1	yes	characteristic, complemented
52	#13093934	C₂²	1	1	yes	characteristic, complemented
53	C₈×Dic₄₇	C₂²	1	1	yes	characteristic, complemented
54	C₂²×C₈×C₄₇	C₂²	1	1	yes	characteristic
55	C₂²×C₈×C₄₇	C₂²	1	1	yes	characteristic, complemented
56	C₄×D₄×C₄₇	C₂²	1	1	yes	characteristic
57	C₄⋊C₈×C₄₇	C₂²	1	1	yes	characteristic, complemented
58	C₂²⋊C₈×C₄₇	C₂²	1	1	yes	characteristic
59	C₂²⋊C₈×C₄₇	C₂²	1	1	yes	characteristic, complemented
60	C₄×C₈×C₄₇	C₂²	1	1	yes	characteristic, complemented
61	C₂³×D₄₇	C₂×C₄	1	1	yes	characteristic
62	C₂×D₄×C₄₇	C₂×C₄	1	1	yes	characteristic
63	C₂²×C₄×C₄₇	C₂³	1	1	yes	characteristic
64	C₂²×C₄×C₄₇	C₂³	1	1	yes	characteristic
65	C₂×C₂²⋊D₄₇	C₂×C₄	1	1	yes	characteristic
66	C₂×C₂²⋊D₄₇	C₂×C₄	1	1	yes	characteristic
67	C₂×C₂²⋊D₄₇	C₂×C₄	1	1	yes	characteristic
68	C₂×C₂²⋊D₄₇	C₂×C₄	1	1	yes	characteristic
69	C₂²×Dic₄₇	C₂×C₄	1	1	yes	characteristic
70	#10625350	—	2	2	no	—
71	#10625350	—	2	2	no	—
72	C₂×D₁₈₈	C₂×C₄	1	1	yes	characteristic
73	C₂×D₁₈₈	C₂×C₄	1	1	yes	characteristic
74	C₂×C₄×D₄₇	—	2	2	no	—
75	C₂×C₄×D₄₇	—	2	2	no	—
76	C₂×C₄×D₄₇	C₂×C₄	1	1	yes	characteristic
77	C₂×C₄×D₄₇	C₂×C₄	1	1	yes	characteristic
78	C₂×C₄×D₄₇	C₂³	1	1	yes	characteristic
79	C₂×C₄×D₄₇	C₂³	1	1	yes	characteristic
80	C₂×C₄×D₄₇	C₂³	1	1	yes	characteristic
81	C₂×Dic₉₄	C₂×C₄	1	1	yes	characteristic
82	C₂×C₈×C₄₇	—	2	2	no	—
83	C₂×C₈×C₄₇	—	2	2	no	—
84	C₂×C₈×C₄₇	C₂³	1	1	yes	characteristic
85	C₂×C₈×C₄₇	C₂³	1	1	yes	characteristic
86	C₂×C₈×C₄₇	C₂³	1	1	yes	characteristic
87	C₂×C₈×C₄₇	C₂³	1	1	yes	characteristic
88	C₄⋊C₄×C₄₇	C₂×C₄	1	1	yes	characteristic
89	C₂²⋊C₄×C₄₇	C₂×C₄	1	1	yes	characteristic
90	C₂²⋊C₄×C₄₇	C₂×C₄	1	1	yes	characteristic
91	C₄²×C₄₇	C₂³	1	1	yes	characteristic
92	C₂²⋊Dic₄₇	C₂×C₄	1	1	yes	characteristic
93	C₂²⋊Dic₄₇	C₂×C₄	1	1	yes	characteristic
94	(C₂×D₄₇)⋊C₄	C₂×C₄	1	1	yes	characteristic
95	(C₂×D₄₇)⋊C₄	C₂×C₄	1	1	yes	characteristic
96	(C₂×D₄₇)⋊C₄	C₂×C₄	1	1	yes	characteristic
97	(C₂×D₄₇)⋊C₄	C₂×C₄	1	1	yes	characteristic
98	(C₂×D₄₇)⋊C₄	C₂×C₄	1	1	yes	characteristic
99	(C₂×D₄₇)⋊C₄	C₂×C₄	1	1	yes	characteristic
100	C₄⋊Dic₄₇	C₂×C₄	1	1	yes	characteristic
101	Dic₄₇⋊C₄	C₂×C₄	1	1	yes	characteristic
102	Dic₄₇⋊C₄	C₂×C₄	1	1	yes	characteristic
103	Dic₄₇⋊C₄	C₂×C₄	1	1	yes	characteristic
104	Dic₄₇⋊C₄	C₂×C₄	1	1	yes	characteristic
105	C₄×Dic₄₇	C₂³	1	1	yes	characteristic
106	#10625329	—	2	2	no	—
107	C₂×C₄₇⋊C₈	—	2	2	no	—
108	C₂×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
109	C₂×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
110	C₂×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
111	C₂×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
112	#10625324	—	2	2	no	—
113	#10625324	—	2	2	no	—
114	#10625324	—	2	2	no	—
115	#10625324	—	2	2	no	—
116	#10625324	D₄	1	4	yes	complemented
117	C₈×D₄₇	—	2	2	no	—
118	C₈×D₄₇	—	2	2	no	—
119	C₈×D₄₇	—	2	2	no	—
120	C₂³×C₄₇	C₂²×C₄	1	1	yes	characteristic
121	C₂³×C₄₇	C₂²×C₄	1	1	yes	characteristic
122	C₂²×D₄₇	—	2	2	no	—
123	C₂²×D₄₇	—	2	2	no	—
124	C₂²×D₄₇	—	4	1	no	—
125	C₂²×D₄₇	C₂²×C₄	1	1	yes	characteristic
126	C₂²×D₄₇	C₂²×C₄	1	1	yes	characteristic
127	C₂²×D₄₇	C₂²×C₄	1	1	yes	characteristic
128	D₄×C₄₇	—	2	2	no	—
129	C₂×C₄×C₄₇	—	2	1	no	—
130	C₂×C₄×C₄₇	—	2	1	no	—
131	C₂×C₄×C₄₇	—	2	1	no	—
132	C₂×C₄×C₄₇	—	2	1	no	—
133	C₂×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
134	C₂×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
135	C₂×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
136	C₂×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
137	C₂×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
138	C₂²⋊D₄₇	—	2	2	no	—
139	C₂²⋊D₄₇	—	2	2	no	—
140	C₂²⋊D₄₇	—	2	2	no	—
141	C₂²⋊D₄₇	—	4	1	no	—
142	C₂×Dic₄₇	—	2	2	no	—
143	C₂×Dic₄₇	C₂²×C₄	1	1	yes	characteristic
144	C₂×Dic₄₇	C₂²×C₄	1	1	yes	characteristic
145	C₂×Dic₄₇	C₂²×C₄	1	1	yes	characteristic
146	C₂×Dic₄₇	C₂²×C₄	1	1	yes	characteristic
147	C₂×Dic₄₇	C₂²×C₄	1	1	yes	characteristic
148	D₁₈₈	—	2	2	no	—
149	D₁₈₈	—	4	1	no	—
150	C₄×D₄₇	—	2	2	no	—
151	C₄×D₄₇	—	2	1	no	—
152	C₄×D₄₇	—	2	1	no	—
153	C₄×D₄₇	—	2	1	no	—
154	C₄×D₄₇	—	2	1	no	—
155	C₄×D₄₇	—	2	2	no	—
156	C₄×D₄₇	C₂×D₄	1	2	yes	—
157	C₄×D₄₇	#41	1	2	yes	—
158	Dic₉₄	—	2	2	no	—
159	C₈×C₄₇	—	2	1	no	—
160	C₈×C₄₇	—	2	1	no	—
161	C₈×C₄₇	—	2	1	no	—
162	C₈×C₄₇	C₂×D₄	1	2	yes	—
163	C₄₇⋊C₈	—	2	1	no	—
164	C₄₇⋊C₈	—	2	1	no	—
165	C₄₇⋊C₈	—	2	1	no	—
166	C₄₇⋊C₈	C₂×D₄	1	2	yes	—
167	C₂²×C₄₇	—	2	1	no	—
168	C₂²×C₄₇	—	2	1	no	—
169	C₂²×C₄₇	—	2	1	no	—
170	C₂²×C₄₇	—	2	1	no	—
171	C₂²×C₄₇	—	2	1	no	—
172	C₂²×C₄₇	#131	1	2	yes	complemented
173	C₂²×C₄₇	C₂³×C₄	1	1	yes	characteristic
174	C₂×D₄₇	—	2	1	no	—
175	C₂×D₄₇	—	2	1	no	—
176	C₂×D₄₇	—	2	1	no	—
177	C₂×D₄₇	—	2	1	no	—
178	C₂×D₄₇	—	2	1	no	—
179	C₂×D₄₇	—	2	1	no	—
180	C₂×D₄₇	—	2	1	no	—
181	C₂×D₄₇	—	2	1	no	—
182	C₂×D₄₇	—	4	4	no	—
183	C₂×D₄₇	C₄×D₄	1	2	yes	—
184	C₄×C₄₇	—	2	1	no	—
185	C₄×C₄₇	—	2	1	no	—
186	C₄×C₄₇	—	2	1	no	—
187	C₄×C₄₇	—	2	1	no	—
188	C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
189	C₄×C₄₇	C₂×#41	1	1	yes	characteristic
190	Dic₄₇	—	2	1	no	—
191	Dic₄₇	—	2	1	no	—
192	Dic₄₇	—	2	1	no	—
193	Dic₄₇	—	2	1	no	—
194	Dic₄₇	C₄×D₄	1	2	yes	—
195	#2933	—	47	1	no	maximal, Sylow
196	C₂×C₄₇	—	2	2	no	—
197	C₂×C₄₇	—	4	1	no	—
198	C₂×C₄₇	C₂×C₄×D₄	1	1	yes	characteristic
199	C₂×C₄₇	C₂×#131	1	1	yes	characteristic
200	C₂×C₄₇	#568	1	1	yes	characteristic
201	D₄₇	—	2	2	no	—
202	D₄₇	—	4	1	no	—
203	D₄₇	—	4	1	no	—
204	C₂×#131	—	47	1	no	—
205	C₂²×M₁₆	—	47	1	no	—
206	#525	—	47	1	no	—
207	#436	—	47	1	no	—
208	#436	—	47	1	no	—
209	#435	—	47	1	no	—
210	#435	—	47	1	no	—
211	#435	—	47	1	no	—
212	#435	—	47	1	no	—
213	C₈×D₄	—	47	1	no	—
214	C₈×D₄	D₄₇	1	1	yes	characteristic, complemented
215	#424	—	47	1	no	—
216	#408	—	47	1	no	—
217	C₂×C₂²⋊C₈	—	47	1	no	—
218	#405	—	47	1	no	—
219	C₄₇	#2933	1	1	yes	characteristic, complemented, Sylow
220	C₂×#41	—	47	1	no	—
221	C₂³×C₄	—	47	1	no	—
222	#131	—	94	4	no	—
223	C₂×M₁₆	—	47	1	no	—
224	C₂×M₁₆	—	47	1	no	—
225	C₂×M₁₆	—	47	1	no	—
226	C₂×M₁₆	—	47	1	no	—
227	C₂×M₁₆	—	47	1	no	—
228	C₂×M₁₆	—	47	1	no	—
229	C₂×M₁₆	—	94	4	no	—
230	C₂²×C₈	—	47	1	no	—
231	C₂²×C₈	—	47	1	no	—
232	C₂²×C₈	—	47	1	no	—
233	C₂²×C₈	—	47	1	no	—
234	C₂²×C₈	C₂×D₄₇	1	1	yes	characteristic
235	C₂²×C₈	C₂×D₄₇	1	1	yes	characteristic, complemented
236	#123	—	47	1	no	—
237	#123	—	47	1	no	—
238	C₂²⋊Q₈	—	47	1	no	—
239	C₂²⋊Q₈	—	47	1	no	—
240	#121	—	47	1	no	—
241	#121	—	47	1	no	—
242	#120	—	47	1	no	—
243	#120	—	47	1	no	—
244	C₄×D₄	—	47	1	no	—
245	C₄×D₄	—	47	1	no	—
246	C₄×D₄	—	47	1	no	—
247	C₄×D₄	C₂×D₄₇	1	1	yes	characteristic
248	#117	—	47	1	no	—
249	C₄⋊C₈	—	47	1	no	—
250	C₄⋊C₈	—	47	1	no	—
251	C₄⋊C₈	—	47	1	no	—
252	C₄⋊C₈	C₂×D₄₇	1	1	yes	characteristic, complemented
253	C₂²⋊C₈	—	47	1	no	—
254	C₂²⋊C₈	—	47	1	no	—
255	C₂²⋊C₈	—	47	1	no	—
256	C₂²⋊C₈	—	47	1	no	—
257	C₂²⋊C₈	—	47	1	no	—
258	C₂²⋊C₈	—	47	1	no	—
259	C₂²⋊C₈	C₂×D₄₇	1	1	yes	characteristic
260	C₂²⋊C₈	C₂×D₄₇	1	1	yes	characteristic, complemented
261	#97	—	47	1	no	—
262	#97	—	47	1	no	—
263	C₄×C₈	—	47	1	no	—
264	C₄×C₈	C₂×D₄₇	1	1	yes	characteristic, complemented
265	C₂⁴	—	47	1	no	—
266	#41	—	94	2	no	—
267	#41	—	94	2	no	—
268	C₂×Q₈	—	47	1	no	—
269	C₂×D₄	—	47	1	no	—
270	C₂×D₄	—	47	1	no	—
271	C₂×D₄	—	47	1	no	—
272	C₂×D₄	—	47	1	no	—
273	C₂×D₄	—	47	1	no	—
274	C₂×D₄	—	47	1	no	—
275	C₂×D₄	C₄×D₄₇	1	1	yes	characteristic
276	C₂²×C₄	—	47	1	no	—
277	C₂²×C₄	—	47	1	no	—
278	C₂²×C₄	—	47	1	no	—
279	C₂²×C₄	—	47	1	no	—
280	C₂²×C₄	—	47	1	no	—
281	C₂²×C₄	—	47	1	no	—
282	C₂²×C₄	—	94	2	no	—
283	C₂²×C₄	—	94	2	no	—
284	C₂²×C₄	C₂²×D₄₇	1	1	yes	characteristic
285	C₂²×C₄	C₂²×D₄₇	1	1	yes	characteristic
286	M₁₆	—	47	4	no	—
287	M₁₆	—	94	2	no	—
288	M₁₆	—	94	2	no	—
289	M₁₆	—	94	2	no	—
290	M₁₆	—	94	2	no	—
291	M₁₆	—	94	2	no	—
292	C₂×C₈	—	2	2	no	—
293	C₂×C₈	—	2	2	no	—
294	C₂×C₈	—	47	1	no	—
295	C₂×C₈	—	47	1	no	—
296	C₂×C₈	—	47	1	no	—
297	C₂×C₈	—	47	1	no	—
298	C₂×C₈	—	94	2	no	—
299	C₂×C₈	—	94	2	no	—
300	C₂×C₈	—	94	2	no	—
301	C₂×C₈	—	94	2	no	—
302	C₂×C₈	C₂²×D₄₇	1	1	yes	characteristic
303	C₂×C₈	C₂²×D₄₇	1	1	yes	characteristic
304	C₂×C₈	C₂²×D₄₇	1	1	yes	characteristic
305	C₂×C₈	C₂²×D₄₇	1	1	yes	characteristic
306	C₄⋊C₄	—	47	1	no	—
307	C₄⋊C₄	—	47	1	no	—
308	C₄⋊C₄	—	47	1	no	—
309	C₄⋊C₄	—	47	1	no	—
310	C₄⋊C₄	—	47	1	no	—
311	C₄⋊C₄	C₄×D₄₇	1	1	yes	characteristic
312	C₂²⋊C₄	—	47	1	no	—
313	C₂²⋊C₄	—	47	1	no	—
314	C₂²⋊C₄	—	47	1	no	—
315	C₂²⋊C₄	—	47	1	no	—
316	C₂²⋊C₄	—	47	1	no	—
317	C₂²⋊C₄	—	47	1	no	—
318	C₂²⋊C₄	—	47	1	no	—
319	C₂²⋊C₄	—	47	1	no	—
320	C₂²⋊C₄	C₄×D₄₇	1	1	yes	characteristic
321	C₂²⋊C₄	C₄×D₄₇	1	1	yes	characteristic
322	C₄²	—	47	1	no	—
323	C₄²	C₂²×D₄₇	1	1	yes	characteristic
324	C₂³	—	47	1	no	—
325	C₂³	—	47	1	no	—
326	C₂³	—	47	1	no	—
327	C₂³	—	94	2	no	—
328	C₂³	—	94	2	no	—
329	C₂³	—	188	1	no	—
330	C₂³	C₂×C₄×D₄₇	1	1	yes	characteristic
331	C₂³	C₂×C₄×D₄₇	1	1	yes	characteristic
332	Q₈	—	94	2	no	—
333	D₄	—	2	2	no	—
334	D₄	—	94	2	no	—
335	D₄	—	94	2	no	—
336	D₄	—	94	2	no	—
337	D₄	—	94	2	no	—
338	D₄	—	188	1	no	—
339	D₄	—	188	1	no	—
340	C₂×C₄	—	2	1	no	—
341	C₂×C₄	—	2	1	no	—
342	C₂×C₄	—	2	1	no	—
343	C₂×C₄	—	2	1	no	—
344	C₂×C₄	—	47	1	no	—
345	C₂×C₄	—	47	2	no	—
346	C₂×C₄	—	47	2	no	—
347	C₂×C₄	—	47	1	no	—
348	C₂×C₄	—	47	1	no	—
349	C₂×C₄	—	47	1	no	—
350	C₂×C₄	—	47	1	no	—
351	C₂×C₄	—	94	2	no	—
352	C₂×C₄	—	94	2	no	—
353	C₂×C₄	—	94	2	no	—
354	C₂×C₄	—	94	1	no	—
355	C₂×C₄	—	94	1	no	—
356	C₂×C₄	—	94	1	no	—
357	C₂×C₄	—	94	1	no	—
358	C₂×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
359	C₂×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
360	C₂×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
361	C₂×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
362	C₂×C₄	C₂³×D₄₇	1	1	yes	characteristic
363	C₈	—	2	1	no	—
364	C₈	—	2	1	no	—
365	C₈	—	2	1	no	—
366	C₈	—	47	2	no	—
367	C₈	—	94	1	no	—
368	C₈	—	94	1	no	—
369	C₈	—	94	1	no	—
370	C₈	D₄×D₄₇	1	2	yes	—
371	C₂²	—	2	1	no	—
372	C₂²	—	2	1	no	—
373	C₂²	—	2	1	no	—
374	C₂²	—	2	1	no	—
375	C₂²	—	2	1	no	—
376	C₂²	—	47	2	no	—
377	C₂²	—	94	1	no	—
378	C₂²	—	94	1	no	—
379	C₂²	—	94	1	no	—
380	C₂²	—	94	1	no	—
381	C₂²	—	94	1	no	—
382	C₂²	—	94	1	no	—
383	C₂²	—	94	1	no	—
384	C₂²	—	94	1	no	—
385	C₂²	—	188	4	no	—
386	C₂²	#13094030	1	2	yes	complemented
387	C₂²	C₂²×C₄×D₄₇	1	1	yes	characteristic
388	C₄	—	2	1	no	—
389	C₄	—	2	1	no	—
390	C₄	—	2	1	no	—
391	C₄	—	2	1	no	—
392	C₄	—	47	2	no	—
393	C₄	—	94	1	no	—
394	C₄	—	94	1	no	—
395	C₄	—	94	1	no	—
396	C₄	—	94	1	no	—
397	C₄	C₂×D₄×D₄₇	1	1	yes	characteristic
398	C₄	#41×D₄₇	1	1	yes	characteristic
399	C₂	—	2	2	no	—
400	C₂	—	4	1	no	—
401	C₂	—	94	2	no	—
402	C₂	—	188	1	no	—
403	C₂	—	188	1	no	—
404	C₂	C₄×D₄×D₄₇	1	1	yes	characteristic
405	C₂	C₂×#13094030	1	1	yes	characteristic
406	C₂	#15689888	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂×C₄	C₂³×D₄₇
commutator, socle	C₂²×C₄₇	C₂³×C₄
Fitting	C₈×D₄×C₄₇	C₂
hypercenter	C₈×D₄	D₄₇
hypocenter	C₄₇	#2933
LCS	G ▷ C₂²×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂×C₄ ◁ C₈×D₄

Complements

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

N	H ≅ G/N	type
1. C₂×#13094030	C₂	semidirect
2. C₂²×#10625324	C₂	semidirect
4. #15689202	C₂	semidirect
5. #15689198	C₂	semidirect
6. #15689195	C₂	semidirect
7. #15689194	C₂	semidirect
8. #15689194	C₂	semidirect
9. #15689193	C₂	semidirect
10. (C₂²⋊D₄₇)⋊C₈	C₂	semidirect
11. #15689148	C₂	semidirect
12. #15689088	C₂	semidirect
13. C₂²⋊C₈×D₄₇	C₂	semidirect
14. #15689077	C₂	semidirect
15. C₈×D₄×C₄₇	C₂	semidirect
19. C₂×#10625329	C₂²	semidirect
25. C₂×#10625324	C₂²	semidirect
29. C₂×C₈×D₄₇	C₂²	semidirect
42. C₄⋊(C₄₇⋊C₈)	C₂²	semidirect
43. Dic₄₇⋊C₈	C₂²	semidirect
44. Dic₄₇⋊C₈	C₂²	semidirect
46. C₂²⋊(C₄₇⋊C₈)	C₂²	semidirect
49. (C₂×D₄₇)⋊C₈	C₂²	semidirect
50. (C₂×D₄₇)⋊C₈	C₂²	semidirect
51. #13093935	C₂²	semidirect
52. #13093934	C₂²	semidirect
53. C₈×Dic₄₇	C₂²	semidirect
55. C₂²×C₈×C₄₇	C₂²	semidirect
57. C₄⋊C₈×C₄₇	C₂²	semidirect
59. C₂²⋊C₈×C₄₇	C₂²	semidirect
60. C₄×C₈×C₄₇	C₂²	semidirect
116. #10625324	D₄	semidirect
172. C₂²×C₄₇	#131	semidirect
214. C₈×D₄	D₄₇	semidirect
219. C₄₇	#2933	semidirect
235. C₂²×C₈	C₂×D₄₇	semidirect
252. C₄⋊C₈	C₂×D₄₇	semidirect
260. C₂²⋊C₈	C₂×D₄₇	semidirect
264. C₄×C₈	C₂×D₄₇	semidirect
386. C₂²	#13094030	semidirect