Subgroups — #26234502

Order 12032.

978 conjugacy classes of subgroups.

The subgroup lattice has 414 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#15689165	C₂	1	2	yes	maximal, complemented
2	#20246317	C₂	1	2	yes	maximal
3	#20244158	C₂	1	2	yes	maximal, complemented
4	#20243589	C₂	1	2	yes	maximal, complemented
5	#20243578	C₂	1	2	yes	maximal, complemented
6	#20243552	C₂	1	1	yes	maximal, characteristic, complemented
7	#20243421	C₂	1	2	yes	maximal, complemented
8	C₄×#13093958	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×C₄₇×#436	C₂	1	1	yes	maximal, characteristic
10	C₂×#13093983	C₂²	1	2	yes	—
11	C₂²×C₄⋊Dic₄₇	C₂²	1	2	yes	—
12	#15689165	—	2	8	no	—
13	C₂×#13093958	C₂²	1	2	yes	—
14	C₂×#13093958	C₂²	1	1	yes	characteristic
15	C₂×#13093958	C₂²	1	1	yes	characteristic
16	C₂×#13093958	C₂²	1	1	yes	characteristic
17	C₂×#13093958	C₂²	1	1	yes	characteristic
18	C₂×#13093956	C₂²	1	2	yes	—
19	C₂×#13093956	C₂²	1	2	yes	—
20	#15689016	—	2	2	no	—
21	#15689009	—	2	2	no	—
22	#15689003	—	2	2	no	—
23	#15688989	C₂²	1	2	yes	—
24	#15688983	C₂²	1	2	yes	—
25	#15688983	C₂²	1	2	yes	—
26	C₄×C₄⋊Dic₄₇	C₂²	1	2	yes	—
27	C₂²⋊C₄×Dic₄₇	—	2	2	no	—
28	#15688886	C₂²	1	2	yes	—
29	#15688886	C₂²	1	2	yes	—
30	#15688886	C₂²	1	2	yes	—
31	C₂²×M₁₆×C₄₇	C₂²	1	2	yes	—
32	C₂×C₄×D₄×C₄₇	C₂²	1	1	yes	characteristic
33	C₄₇×#436	C₄	1	8	yes	complemented
34	C₂×C₄⋊C₈×C₄₇	C₂²	1	1	yes	characteristic
35	C₂×C₂²⋊C₈×C₄₇	C₂²	1	2	yes	—
36	C₂×C₄×C₈×C₄₇	C₂²	1	1	yes	characteristic
37	C₂³×Dic₄₇	—	2	2	no	—
38	#13093983	—	2	4	no	—
39	#13093983	—	4	2	no	—
40	C₂×C₄⋊Dic₄₇	—	2	4	no	—
41	C₂×C₄⋊Dic₄₇	—	2	2	no	—
42	C₂×C₄⋊Dic₄₇	—	4	2	no	—
43	C₂×C₄⋊Dic₄₇	C₂³	1	2	yes	—
44	C₂×C₄⋊Dic₄₇	C₂³	1	2	yes	—
45	C₂×C₄⋊Dic₄₇	C₂³	1	2	yes	—
46	C₂×C₄⋊Dic₄₇	C₂³	1	2	yes	—
47	C₂×C₂²⋊Dic₄₇	—	2	2	no	—
48	C₂×C₂²⋊Dic₄₇	—	2	2	no	—
49	C₂×C₂²⋊Dic₄₇	—	2	2	no	—
50	C₂×C₄×Dic₄₇	—	2	2	no	—
51	C₂×C₄×Dic₄₇	—	2	2	no	—
52	#13093958	—	2	2	no	—
53	#13093958	—	2	4	no	—
54	#13093958	—	4	1	no	—
55	#13093958	—	4	1	no	—
56	#13093958	D₄	1	4	yes	complemented
57	#13093956	—	2	4	no	—
58	#13093956	—	2	4	no	—
59	C₄₇⋊#95	—	2	2	no	—
60	C₄₇⋊#95	—	2	2	no	—
61	C₄₇⋊#95	—	2	2	no	—
62	C₄₇⋊#95	—	2	2	no	—
63	C₄₇⋊#95	—	2	2	no	—
64	C₂²×D₄×C₄₇	D₄	1	1	yes	characteristic
65	C₂³×C₄×C₄₇	C₂³	1	2	yes	—
66	C₂×M₁₆×C₄₇	—	2	4	no	—
67	C₂×M₁₆×C₄₇	—	2	4	no	—
68	C₂×M₁₆×C₄₇	C₂×C₄	1	8	yes	complemented
69	C₂²×C₈×C₄₇	C₂³	1	2	yes	—
70	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
71	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
72	C₄×D₄×C₄₇	C₂×C₄	1	4	yes	—
73	C₄×D₄×C₄₇	Q₈	1	4	yes	—
74	C₂×C₄⋊C₄×C₄₇	D₄	1	1	yes	characteristic
75	C₂×C₂²⋊C₄×C₄₇	D₄	1	2	yes	—
76	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
77	C₄⋊C₈×C₄₇	C₂×C₄	1	4	yes	complemented
78	C₂²⋊C₈×C₄₇	C₂×C₄	1	8	yes	complemented
79	C₄×C₈×C₄₇	C₂×C₄	1	4	yes	complemented
80	C₂⁴×C₄₇	C₂×D₄	1	2	yes	—
81	C₂×D₄×C₄₇	—	4	1	no	—
82	C₂×D₄×C₄₇	—	4	1	no	—
83	C₂×D₄×C₄₇	C₄⋊C₄	1	4	yes	—
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	C₂²×C₄	1	4	yes	—
89	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
90	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
91	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
92	C₂²×C₄×C₄₇	C₂×Q₈	1	4	yes	—
93	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
94	C₂²×Dic₄₇	—	2	2	no	—
95	C₂²×Dic₄₇	—	2	2	no	—
96	C₂²×Dic₄₇	—	2	2	no	—
97	C₂²×Dic₄₇	—	2	2	no	—
98	C₂²×Dic₄₇	—	4	4	no	—
99	C₂²×Dic₄₇	—	4	4	no	—
100	C₂²×Dic₄₇	—	8	2	no	—
101	M₁₆×C₄₇	—	2	16	no	—
102	C₂×C₈×C₄₇	—	2	2	no	—
103	C₂×C₈×C₄₇	—	2	2	no	—
104	C₂×C₈×C₄₇	—	2	1	no	—
105	C₂×C₈×C₄₇	—	2	1	no	—
106	C₂×C₈×C₄₇	C₂²×C₄	1	4	yes	—
107	C₂×C₈×C₄₇	C₂²×C₄	1	2	yes	—
108	C₂×C₈×C₄₇	C₂²×C₄	1	2	yes	—
109	C₂×C₈×C₄₇	C₂×D₄	1	2	yes	—
110	C₂×C₈×C₄₇	#41	1	2	yes	—
111	C₄⋊C₄×C₄₇	C₄⋊C₄	1	4	yes	—
112	C₂²⋊C₄×C₄₇	C₄⋊C₄	1	8	yes	—
113	C₄²×C₄₇	C₂²×C₄	1	2	yes	—
114	C₄²×C₄₇	C₂×Q₈	1	2	yes	—
115	C₂²⋊Dic₄₇	—	4	4	no	—
116	C₂²⋊Dic₄₇	—	4	4	no	—
117	C₂²⋊Dic₄₇	—	8	2	no	—
118	C₄⋊Dic₄₇	—	2	2	no	—
119	C₄⋊Dic₄₇	—	2	2	no	—
120	C₄⋊Dic₄₇	—	2	2	no	—
121	C₄⋊Dic₄₇	—	2	2	no	—
122	C₄⋊Dic₄₇	—	2	2	no	—
123	C₄⋊Dic₄₇	—	2	2	no	—
124	C₄⋊Dic₄₇	—	2	2	no	—
125	C₄⋊Dic₄₇	—	4	4	no	—
126	C₄⋊Dic₄₇	C₂×D₄	1	4	yes	—
127	C₄×Dic₄₇	—	4	4	no	—
128	C₄×Dic₄₇	—	8	2	no	—
129	C₂³×C₄₇	—	2	2	no	—
130	C₂³×C₄₇	—	2	2	no	—
131	C₂³×C₄₇	—	2	2	no	—
132	C₂³×C₄₇	—	2	2	no	—
133	C₂³×C₄₇	—	2	2	no	—
134	C₂³×C₄₇	—	2	2	no	—
135	C₂³×C₄₇	C₂×C₄⋊C₄	1	4	yes	—
136	C₂³×C₄₇	C₂²×D₄	1	1	yes	characteristic
137	D₄×C₄₇	—	4	4	no	—
138	C₂×C₄×C₄₇	—	2	2	no	—
139	C₂×C₄×C₄₇	—	2	2	no	—
140	C₂×C₄×C₄₇	—	2	1	no	—
141	C₂×C₄×C₄₇	—	2	1	no	—
142	C₂×C₄×C₄₇	—	2	1	no	—
143	C₂×C₄×C₄₇	—	2	1	no	—
144	C₂×C₄×C₄₇	—	2	4	no	—
145	C₂×C₄×C₄₇	—	2	4	no	—
146	C₂×C₄×C₄₇	—	2	4	no	—
147	C₂×C₄×C₄₇	—	2	4	no	—
148	C₂×C₄×C₄₇	C₂×C₄⋊C₄	1	2	yes	—
149	C₂×C₄×C₄₇	C₂×C₄⋊C₄	1	2	yes	—
150	C₂×C₄×C₄₇	C₂×C₄⋊C₄	1	4	yes	—
151	C₂×C₄×C₄₇	C₂³×C₄	1	1	yes	characteristic
152	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
153	C₂×C₄×C₄₇	C₂²×Q₈	1	1	yes	characteristic
154	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
155	C₂×C₄×C₄₇	H(5,𝔽₂)	1	1	yes	characteristic
156	C₂×C₄×C₄₇	2₋¹⁺⁴	1	1	yes	characteristic
157	C₂×Dic₄₇	—	2	4	no	—
158	C₂×Dic₄₇	—	4	2	no	—
159	C₂×Dic₄₇	—	4	2	no	—
160	C₂×Dic₄₇	—	4	2	no	—
161	C₂×Dic₄₇	—	4	2	no	—
162	C₂×Dic₄₇	—	4	2	no	—
163	C₂×Dic₄₇	—	4	2	no	—
164	C₂×Dic₄₇	—	4	2	no	—
165	C₂×Dic₄₇	—	4	2	no	—
166	C₂×Dic₄₇	—	4	2	no	—
167	C₂×Dic₄₇	—	4	2	no	—
168	C₂×Dic₄₇	—	4	2	no	—
169	C₂×Dic₄₇	—	8	8	no	—
170	C₈×C₄₇	—	2	4	no	—
171	C₈×C₄₇	—	2	2	no	—
172	C₈×C₄₇	C₄×D₄	1	4	yes	—
173	#22664	—	47	1	no	maximal, Sylow
174	C₂²×C₄₇	—	2	4	no	—
175	C₂²×C₄₇	—	2	4	no	—
176	C₂²×C₄₇	—	2	4	no	—
177	C₂²×C₄₇	—	4	2	no	—
178	C₂²×C₄₇	—	4	2	no	—
179	C₂²×C₄₇	—	4	2	no	—
180	C₂²×C₄₇	—	4	2	no	—
181	C₂²×C₄₇	C₂²×C₄⋊C₄	1	1	yes	characteristic
182	C₂²×C₄₇	D₄²	1	1	yes	characteristic
183	C₂²×C₄₇	#547	1	1	yes	characteristic
184	C₂²×C₄₇	#575	1	1	yes	characteristic
185	C₂²×C₄₇	#575	1	1	yes	characteristic
186	C₂²×C₄₇	#576	1	1	yes	characteristic
187	C₂²×C₄₇	#578	1	1	yes	characteristic
188	C₄×C₄₇	—	2	4	no	—
189	C₄×C₄₇	—	2	2	no	—
190	C₄×C₄₇	—	2	2	no	—
191	C₄×C₄₇	C₂×C₄×D₄	1	1	yes	characteristic
192	C₄×C₄₇	#520	1	1	yes	characteristic
193	C₄×C₄₇	D₄×Q₈	1	1	yes	characteristic
194	C₄×C₄₇	#554	1	1	yes	characteristic
195	Dic₄₇	—	4	4	no	—
196	Dic₄₇	—	8	2	no	—
197	Dic₄₇	—	8	2	no	—
198	Dic₄₇	—	8	2	no	—
199	C₂×#436	D₄₇	1	1	yes	characteristic
200	C₂×#428	—	47	2	no	—
201	#2352	—	47	2	no	—
202	#1949	—	47	2	no	—
203	#1854	—	47	2	no	—
204	#1852	—	47	2	no	—
205	#1846	—	47	1	no	—
206	#1809	—	47	2	no	—
207	C₄×#107	—	47	1	no	—
208	C₂×C₄₇	—	4	4	no	—
209	C₂×C₄₇	D₄×C₄⋊C₄	1	1	yes	characteristic
210	C₂×C₄₇	#2911	1	1	yes	characteristic
211	C₂×C₄₇	#2913	1	1	yes	characteristic
212	C₂×C₄₇	#3273	1	1	yes	characteristic
213	C₂×C₄₇	#3277	1	1	yes	characteristic
214	C₂×C₄₇	#3352	1	1	yes	characteristic
215	C₂×C₄₇	#3355	1	1	yes	characteristic
216	C₂²×M₁₆	C₂×D₄₇	1	2	yes	—
217	C₂×C₄×D₄	C₂×D₄₇	1	1	yes	characteristic
218	C₂×#117	—	47	2	no	—
219	C₂²×C₄⋊C₄	—	47	2	no	—
220	#436	Dic₄₇	1	8	yes	complemented
221	#428	—	94	8	no	—
222	C₂×#107	—	47	1	no	—
223	C₂×#107	—	47	1	no	—
224	C₂×#107	—	47	2	no	—
225	C₂×#107	—	47	1	no	—
226	C₂×#107	—	47	1	no	—
227	C₂×#106	—	47	2	no	—
228	C₂×#106	—	47	2	no	—
229	C₂×C₄⋊C₈	C₂×D₄₇	1	1	yes	characteristic
230	C₂×C₂²⋊C₈	C₂×D₄₇	1	2	yes	—
231	C₂×C₄×C₈	C₂×D₄₇	1	1	yes	characteristic
232	#388	—	94	2	no	—
233	#387	—	94	2	no	—
234	#386	—	94	2	no	—
235	#382	—	47	2	no	—
236	#380	—	47	2	no	—
237	#380	—	47	2	no	—
238	C₄×C₄⋊C₄	—	47	2	no	—
239	C₄×C₂²⋊C₄	—	94	2	no	—
240	#340	—	47	2	no	—
241	#340	—	47	2	no	—
242	#340	—	47	2	no	—
243	C₄₇	#22664	1	1	yes	characteristic, complemented, Sylow
244	C₂²×D₄	D₁₈₈	1	1	yes	characteristic
245	C₂³×C₄	—	94	2	no	—
246	C₂³×C₄	C₂²×D₄₇	1	2	yes	—
247	C₂×M₁₆	—	2	4	no	—
248	C₂×M₁₆	—	2	4	no	—
249	C₂×M₁₆	C₂×Dic₄₇	1	8	yes	complemented
250	C₂²×C₈	C₂²×D₄₇	1	2	yes	—
251	C₂²×C₈	C₂²×D₄₇	1	1	yes	characteristic
252	C₂²×C₈	C₂²×D₄₇	1	1	yes	characteristic
253	C₄×D₄	Dic₉₄	1	4	yes	—
254	C₄×D₄	C₂×Dic₄₇	1	4	yes	—
255	#117	—	94	4	no	—
256	#117	—	188	2	no	—
257	C₂×C₄⋊C₄	—	47	2	no	—
258	C₂×C₄⋊C₄	—	47	2	no	—
259	C₂×C₄⋊C₄	—	47	2	no	—
260	C₂×C₄⋊C₄	—	47	2	no	—
261	C₂×C₄⋊C₄	—	94	4	no	—
262	C₂×C₄⋊C₄	—	94	2	no	—
263	C₂×C₄⋊C₄	—	188	2	no	—
264	C₂×C₄⋊C₄	D₁₈₈	1	1	yes	characteristic
265	C₂×C₂²⋊C₄	—	94	2	no	—
266	C₂×C₂²⋊C₄	—	94	2	no	—
267	C₂×C₂²⋊C₄	—	94	2	no	—
268	C₂×C₂²⋊C₄	D₁₈₈	1	2	yes	—
269	C₂×C₄²	—	94	2	no	—
270	C₂×C₄²	—	94	2	no	—
271	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
272	#107	—	47	4	no	—
273	#107	—	94	4	no	—
274	#107	—	94	2	no	—
275	#107	—	188	1	no	—
276	#107	—	188	1	no	—
277	#106	—	94	4	no	—
278	#106	—	94	4	no	—
279	C₄⋊C₈	C₂×Dic₄₇	1	4	yes	complemented
280	C₂²⋊C₈	C₂×Dic₄₇	1	8	yes	complemented
281	C₄×C₈	C₂×Dic₄₇	1	4	yes	complemented
282	#95	—	94	2	no	—
283	#95	—	94	2	no	—
284	#95	—	94	2	no	—
285	#95	—	94	2	no	—
286	#95	—	94	2	no	—
287	C₂⁴	C₂×D₁₈₈	1	2	yes	—
288	C₂×D₄	—	4	1	no	—
289	C₂×D₄	—	4	1	no	—
290	C₂×D₄	C₄⋊Dic₄₇	1	4	yes	—
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	—	94	2	no	—
296	C₂²×C₄	—	94	2	no	—
297	C₂²×C₄	—	94	2	no	—
298	C₂²×C₄	—	94	2	no	—
299	C₂²×C₄	—	376	2	no	—
300	C₂²×C₄	—	188	4	no	—
301	C₂²×C₄	—	188	4	no	—
302	C₂²×C₄	C₂×Dic₉₄	1	4	yes	—
303	C₂²×C₄	C₂×D₁₈₈	1	1	yes	characteristic
304	C₂²×C₄	C₂×D₁₈₈	1	1	yes	characteristic
305	C₂²×C₄	C₂×D₁₈₈	1	2	yes	—
306	C₂²×C₄	C₂²×Dic₄₇	1	4	yes	—
307	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
308	M₁₆	—	2	16	no	—
309	C₂×C₈	—	2	2	no	—
310	C₂×C₈	—	2	2	no	—
311	C₂×C₈	—	2	1	no	—
312	C₂×C₈	—	2	1	no	—
313	C₂×C₈	D₄×D₄₇	1	2	yes	—
314	C₂×C₈	#10625352	1	2	yes	—
315	C₂×C₈	C₂²×Dic₄₇	1	2	yes	—
316	C₂×C₈	C₂²×Dic₄₇	1	4	yes	—
317	C₂×C₈	C₂²×Dic₄₇	1	2	yes	—
318	C₄⋊C₄	—	47	4	no	—
319	C₄⋊C₄	—	94	2	no	—
320	C₄⋊C₄	—	94	2	no	—
321	C₄⋊C₄	—	94	2	no	—
322	C₄⋊C₄	—	94	2	no	—
323	C₄⋊C₄	—	94	2	no	—
324	C₄⋊C₄	—	94	2	no	—
325	C₄⋊C₄	—	94	2	no	—
326	C₄⋊C₄	—	188	4	no	—
327	C₄⋊C₄	C₄⋊Dic₄₇	1	4	yes	—
328	C₂²⋊C₄	—	376	2	no	—
329	C₂²⋊C₄	—	188	4	no	—
330	C₂²⋊C₄	—	188	4	no	—
331	C₂²⋊C₄	C₄⋊Dic₄₇	1	8	yes	—
332	C₄²	—	376	2	no	—
333	C₄²	—	188	4	no	—
334	C₄²	C₂×Dic₉₄	1	2	yes	—
335	C₄²	C₂²×Dic₄₇	1	2	yes	—
336	C₂³	—	2	2	no	—
337	C₂³	—	2	2	no	—
338	C₂³	—	2	2	no	—
339	C₂³	—	2	2	no	—
340	C₂³	—	2	2	no	—
341	C₂³	—	2	2	no	—
342	C₂³	C₂×C₄⋊Dic₄₇	1	4	yes	—
343	C₂³	C₂²×D₁₈₈	1	1	yes	characteristic
344	D₄	—	4	4	no	—
345	C₂×C₄	—	2	2	no	—
346	C₂×C₄	—	2	2	no	—
347	C₂×C₄	—	2	1	no	—
348	C₂×C₄	—	2	1	no	—
349	C₂×C₄	—	2	1	no	—
350	C₂×C₄	—	2	1	no	—
351	C₂×C₄	—	2	4	no	—
352	C₂×C₄	—	2	4	no	—
353	C₂×C₄	—	2	4	no	—
354	C₂×C₄	—	2	4	no	—
355	C₂×C₄	—	94	4	no	—
356	C₂×C₄	—	376	8	no	—
357	C₂×C₄	—	188	2	no	—
358	C₂×C₄	—	188	2	no	—
359	C₂×C₄	—	188	2	no	—
360	C₂×C₄	—	188	2	no	—
361	C₂×C₄	—	188	2	no	—
362	C₂×C₄	—	188	2	no	—
363	C₂×C₄	—	188	2	no	—
364	C₂×C₄	—	188	2	no	—
365	C₂×C₄	—	188	2	no	—
366	C₂×C₄	—	188	2	no	—
367	C₂×C₄	—	188	2	no	—
368	C₂×C₄	C₂×C₄⋊Dic₄₇	1	2	yes	—
369	C₂×C₄	C₂×C₄⋊Dic₄₇	1	2	yes	—
370	C₂×C₄	C₂×C₄⋊Dic₄₇	1	4	yes	—
371	C₂×C₄	C₂³×Dic₄₇	1	1	yes	characteristic
372	C₂×C₄	C₂×D₄×D₄₇	1	1	yes	characteristic
373	C₂×C₄	C₂²×Dic₉₄	1	1	yes	characteristic
374	C₂×C₄	C₂×#10625352	1	1	yes	characteristic
375	C₂×C₄	#13094070	1	1	yes	characteristic
376	C₂×C₄	#13094071	1	1	yes	characteristic
377	C₈	—	2	4	no	—
378	C₈	—	2	2	no	—
379	C₈	D₄×Dic₄₇	1	4	yes	—
380	C₂²	—	2	4	no	—
381	C₂²	—	2	4	no	—
382	C₂²	—	2	4	no	—
383	C₂²	—	4	2	no	—
384	C₂²	—	4	2	no	—
385	C₂²	—	4	2	no	—
386	C₂²	—	4	2	no	—
387	C₂²	C₂²×C₄⋊Dic₄₇	1	1	yes	characteristic
388	C₂²	D₄×D₁₈₈	1	1	yes	characteristic
389	C₂²	#15689777	1	1	yes	characteristic
390	C₂²	#15689923	1	1	yes	characteristic
391	C₂²	#15689923	1	1	yes	characteristic
392	C₂²	#15689928	1	1	yes	characteristic
393	C₂²	#15689940	1	1	yes	characteristic
394	C₄	—	2	4	no	—
395	C₄	—	2	2	no	—
396	C₄	—	2	2	no	—
397	C₄	—	376	2	no	—
398	C₄	—	376	2	no	—
399	C₄	—	376	2	no	—
400	C₄	—	188	4	no	—
401	C₄	C₂×D₄×Dic₄₇	1	1	yes	characteristic
402	C₄	#15689606	1	1	yes	characteristic
403	C₄	D₄×Dic₉₄	1	1	yes	characteristic
404	C₄	#15689830	1	1	yes	characteristic
405	C₂	—	4	4	no	—
406	C₂	D₄×C₄⋊Dic₄₇	1	1	yes	characteristic
407	C₂	#20251978	1	1	yes	characteristic
408	C₂	#20251988	1	1	yes	characteristic
409	C₂	#20255000	1	1	yes	characteristic
410	C₂	#20255046	1	1	yes	characteristic
411	C₂	#20255962	1	1	yes	characteristic
412	C₂	#20255993	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	C₂²×D₁₈₈
commutator	C₂×C₄×C₄₇	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₄₇
Fitting	C₂×C₄₇×#436	C₂
socle	C₂³×C₄₇	C₂²×D₄
prime radical	C₂²×D₄×C₄₇	D₄
cosocle	C₂²×C₄×C₄₇	C₂⁴
hypercenter	C₂×#436	D₄₇
hypocenter	C₄₇	#22664
LCS	G ▷ C₂×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂³ ◁ C₂×C₄×D₄ ◁ C₂×#436

Complements

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

N	H ≅ G/N	type
1. C₂×#15689165	C₂	semidirect
3. #20244158	C₂	semidirect
4. #20243589	C₂	semidirect
5. #20243578	C₂	semidirect
6. #20243552	C₂	semidirect
7. #20243421	C₂	semidirect
8. C₄×#13093958	C₂	semidirect
33. C₄₇×#436	C₄	semidirect
56. #13093958	D₄	semidirect
68. C₂×M₁₆×C₄₇	C₂×C₄	semidirect
77. C₄⋊C₈×C₄₇	C₂×C₄	semidirect
78. C₂²⋊C₈×C₄₇	C₂×C₄	semidirect
79. C₄×C₈×C₄₇	C₂×C₄	semidirect
220. #436	Dic₄₇	semidirect
243. C₄₇	#22664	semidirect
249. C₂×M₁₆	C₂×Dic₄₇	semidirect
279. C₄⋊C₈	C₂×Dic₄₇	semidirect
280. C₂²⋊C₈	C₂×Dic₄₇	semidirect
281. C₄×C₈	C₂×Dic₄₇	semidirect

Maximal subgroups

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

subgroup	index
C₂×#15689165	2
#20246317	2
#20244158	2
#20243589	2
#20243578	2
#20243552	2
#20243421	2
C₄×#13093958	2
C₂×C₄₇×#436	2
#22664	47