Subgroups — #26110797

Order 12032.

684 conjugacy classes of subgroups.

The subgroup lattice has 418 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₄⋊(C₄₇⋊C₈)	C₂	1	1	yes	maximal, characteristic
2	C₄×#13094003	C₂	1	1	yes	maximal, characteristic
3	C₂×#15688855	C₂	1	2	yes	maximal, complemented
4	#20241228	C₂	1	2	yes	maximal, complemented
5	C₄×C₂²⋊C₈×C₄₇	C₂	1	1	yes	maximal, characteristic
6	C₂³×C₄₇⋊C₈	—	2	1	no	—
7	C₂×#13094003	C₄	1	1	yes	characteristic
8	C₂×C₄×Dic₉₄	C₂²	1	1	yes	characteristic
9	C₂×C₄⋊(C₄₇⋊C₈)	—	2	4	no	—
10	C₂×C₄⋊(C₄₇⋊C₈)	—	2	1	no	—
11	C₂×C₄⋊(C₄₇⋊C₈)	C₂²	1	2	yes	—
12	#15689029	C₄	1	1	yes	characteristic
13	#15689021	C₄	1	1	yes	characteristic
14	#15689007	—	2	1	no	—
15	#15688996	—	2	1	no	—
16	#15688983	C₄	1	1	yes	characteristic
17	C₄×Dic₄₇⋊C₄	—	2	1	no	—
18	C₄×C₄⋊Dic₄₇	C₂²	1	1	yes	characteristic
19	C₄×C₂²⋊Dic₄₇	—	2	1	no	—
20	#15688855	—	2	4	no	—
21	C₂²×C₄²×C₄₇	C₂²	1	1	yes	characteristic
22	C₂×C₂²⋊C₈×C₄₇	—	2	1	no	—
23	C₂×C₄×C₈×C₄₇	C₂²	1	2	yes	—
24	C₄₇×#336	—	2	1	no	—
25	C₂²×Dic₉₄	C₂×C₄	1	1	yes	characteristic
26	C₂²×C₄₇⋊C₈	—	2	4	no	—
27	C₂²×C₄₇⋊C₈	—	2	2	no	—
28	C₂²×C₄₇⋊C₈	—	4	2	no	—
29	C₂²×C₄₇⋊C₈	—	4	2	no	—
30	#13094003	—	2	2	no	—
31	#13094003	C₈	1	4	yes	complemented
32	C₄×Dic₉₄	—	2	2	no	—
33	C₄×Dic₉₄	—	2	2	no	—
34	C₂×C₄⋊Dic₄₇	C₂×C₄	1	1	yes	characteristic
35	C₂×C₄⋊Dic₄₇	C₂×C₄	1	1	yes	characteristic
36	C₂×C₄⋊Dic₄₇	C₂×C₄	1	1	yes	characteristic
37	C₂×Dic₄₇⋊C₄	—	2	1	no	—
38	C₂×Dic₄₇⋊C₄	—	2	1	no	—
39	C₂×Dic₄₇⋊C₄	—	2	1	no	—
40	C₂×C₂²⋊Dic₄₇	—	2	1	no	—
41	C₂×C₂²⋊Dic₄₇	—	2	1	no	—
42	C₂×C₄×Dic₄₇	—	2	1	no	—
43	C₂×C₄×Dic₄₇	—	2	1	no	—
44	C₄⋊(C₄₇⋊C₈)	—	2	4	no	—
45	C₄⋊(C₄₇⋊C₈)	—	2	2	no	—
46	C₄⋊(C₄₇⋊C₈)	D₄	1	4	yes	—
47	C₄₇⋊#95	—	2	1	no	—
48	C₄₇⋊#95	—	2	1	no	—
49	C₄₇⋊#95	—	2	1	no	—
50	C₄₇⋊#95	—	2	1	no	—
51	C₄₇⋊#95	—	2	1	no	—
52	C₂³×C₄×C₄₇	C₂×C₄	1	1	yes	characteristic
53	C₂³×C₄×C₄₇	D₄	1	1	yes	characteristic
54	C₂³×C₄×C₄₇	D₄	1	1	yes	characteristic
55	C₂²×C₈×C₄₇	—	2	2	no	—
56	C₂×C₄²×C₄₇	—	2	2	no	—
57	C₂×C₄²×C₄₇	—	2	2	no	—
58	C₂×C₄²×C₄₇	C₂×C₄	1	1	yes	characteristic
59	C₂×C₄²×C₄₇	D₄	1	1	yes	characteristic
60	C₂×C₄²×C₄₇	D₄	1	1	yes	characteristic
61	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
62	C₂²⋊C₈×C₄₇	—	2	4	no	—
63	C₄×C₈×C₄₇	—	2	2	no	—
64	C₄×C₈×C₄₇	—	2	2	no	—
65	C₂⁴×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
66	C₂²×C₄×C₄₇	—	2	2	no	—
67	C₂²×C₄×C₄₇	—	2	1	no	—
68	C₂²×C₄×C₄₇	—	2	1	no	—
69	C₂²×C₄×C₄₇	—	2	2	no	—
70	C₂²×C₄×C₄₇	—	2	1	no	—
71	C₂²×C₄×C₄₇	—	2	1	no	—
72	C₂²×C₄×C₄₇	—	2	2	no	—
73	C₂²×C₄×C₄₇	—	2	2	no	—
74	C₂²×C₄×C₄₇	—	4	1	no	—
75	C₂²×C₄×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
76	C₂²×C₄×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
77	C₂²×C₄×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
78	C₂²×C₄×C₄₇	C₂×C₈	1	2	yes	—
79	C₂²×C₄×C₄₇	M₁₆	1	2	yes	—
80	C₂²×C₄×C₄₇	SD₁₆	1	2	yes	—
81	C₂²×C₄×C₄₇	Q₁₆	1	2	yes	—
82	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
83	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
84	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
85	C₂²×Dic₄₇	—	2	1	no	—
86	C₂²×Dic₄₇	—	2	1	no	—
87	C₂²×Dic₄₇	—	2	1	no	—
88	C₂²×Dic₄₇	—	2	1	no	—
89	C₂×Dic₉₄	—	2	2	no	—
90	C₂×Dic₉₄	—	2	2	no	—
91	C₂×Dic₉₄	—	2	1	no	—
92	C₂×Dic₉₄	C₂×C₈	1	2	yes	complemented
93	C₂×C₈×C₄₇	—	2	4	no	—
94	C₂×C₈×C₄₇	—	4	2	no	—
95	C₂×C₈×C₄₇	—	4	2	no	—
96	C₄²×C₄₇	—	2	2	no	—
97	C₄²×C₄₇	—	2	1	no	—
98	C₄²×C₄₇	—	2	2	no	—
99	C₄²×C₄₇	—	2	1	no	—
100	C₄²×C₄₇	C₂×D₄	1	2	yes	—
101	C₄²×C₄₇	#41	1	2	yes	—
102	C₂²⋊Dic₄₇	—	2	4	no	—
103	C₂²⋊Dic₄₇	—	4	2	no	—
104	C₄⋊Dic₄₇	—	2	1	no	—
105	C₄⋊Dic₄₇	—	2	2	no	—
106	C₄⋊Dic₄₇	—	2	2	no	—
107	C₄⋊Dic₄₇	C₂×C₈	1	2	yes	complemented
108	Dic₄₇⋊C₄	—	2	4	no	—
109	Dic₄₇⋊C₄	—	4	2	no	—
110	Dic₄₇⋊C₄	—	4	2	no	—
111	C₄×Dic₄₇	—	4	1	no	—
112	C₄×Dic₄₇	—	4	1	no	—
113	C₄×Dic₄₇	—	4	1	no	—
114	C₄×Dic₄₇	—	4	1	no	—
115	C₂×C₄₇⋊C₈	—	2	4	no	—
116	C₂×C₄₇⋊C₈	—	4	8	no	—
117	C₂×C₄₇⋊C₈	—	4	2	no	—
118	C₂×C₄₇⋊C₈	—	4	2	no	—
119	C₂³×C₄₇	—	2	1	no	—
120	C₂³×C₄₇	—	2	1	no	—
121	C₂³×C₄₇	—	2	1	no	—
122	C₂³×C₄₇	—	2	1	no	—
123	C₂³×C₄₇	C₂²⋊C₈	1	2	yes	—
124	C₂³×C₄₇	#103	1	2	yes	—
125	C₂³×C₄₇	#104	1	2	yes	—
126	C₂³×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
127	C₂×C₄×C₄₇	—	2	1	no	—
128	C₂×C₄×C₄₇	—	2	1	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	—	2	4	no	—
134	C₂×C₄×C₄₇	—	2	4	no	—
135	C₂×C₄×C₄₇	—	2	2	no	—
136	C₂×C₄×C₄₇	—	2	2	no	—
137	C₂×C₄×C₄₇	—	2	2	no	—
138	C₂×C₄×C₄₇	—	2	2	no	—
139	C₂×C₄×C₄₇	—	2	1	no	—
140	C₂×C₄×C₄₇	—	2	1	no	—
141	C₂×C₄×C₄₇	—	2	1	no	—
142	C₂×C₄×C₄₇	—	4	4	no	—
143	C₂×C₄×C₄₇	C₂²⋊C₈	1	2	yes	—
144	C₂×C₄×C₄₇	#103	1	2	yes	—
145	C₂×C₄×C₄₇	C₄×D₄	1	2	yes	—
146	C₂×C₄×C₄₇	#120	1	1	yes	characteristic
147	C₂×C₄×C₄₇	#121	1	2	yes	—
148	C₂×C₄×C₄₇	#123	1	1	yes	characteristic
149	C₂×C₄×C₄₇	C₂²×C₈	1	1	yes	characteristic
150	C₂×C₄×C₄₇	C₂×M₁₆	1	1	yes	characteristic
151	C₂×C₄×C₄₇	#131	1	2	yes	—
152	C₂×C₄×C₄₇	C₂×SD₁₆	1	1	yes	characteristic
153	C₂×C₄×C₄₇	C₂×Q₁₆	1	1	yes	characteristic
154	C₂×C₄×C₄₇	AGL(1,ℤ/8)	1	1	yes	characteristic
155	C₂×C₄×C₄₇	#137	1	1	yes	characteristic
156	C₂×Dic₄₇	—	2	2	no	—
157	C₂×Dic₄₇	—	2	2	no	—
158	C₂×Dic₄₇	—	4	1	no	—
159	C₂×Dic₄₇	—	4	1	no	—
160	C₂×Dic₄₇	—	4	1	no	—
161	C₂×Dic₄₇	—	4	1	no	—
162	C₂×Dic₄₇	—	4	1	no	—
163	C₂×Dic₄₇	—	4	1	no	—
164	C₂×Dic₄₇	—	4	1	no	—
165	C₂×Dic₄₇	—	4	1	no	—
166	C₂×Dic₄₇	—	4	1	no	—
167	C₂×Dic₄₇	—	4	1	no	—
168	Dic₉₄	—	2	4	no	—
169	Dic₉₄	—	4	2	no	—
170	C₈×C₄₇	—	4	4	no	—
171	C₄₇⋊C₈	—	4	4	no	—
172	#8937	—	47	1	no	maximal, Sylow
173	C₂²×C₄₇	—	2	2	no	—
174	C₂²×C₄₇	—	2	2	no	—
175	C₂²×C₄₇	—	2	2	no	—
176	C₂²×C₄₇	—	2	2	no	—
177	C₂²×C₄₇	—	2	2	no	—
178	C₂²×C₄₇	—	2	2	no	—
179	C₂²×C₄₇	Q₈⋊C₈	1	4	yes	complemented
180	C₂²×C₄₇	#386	1	1	yes	characteristic
181	C₂²×C₄₇	C₂×C₂²⋊C₈	1	1	yes	characteristic
182	C₂²×C₄₇	#408	1	1	yes	characteristic
183	C₂²×C₄₇	C₂×#103	1	1	yes	characteristic
184	C₂²×C₄₇	#417	1	1	yes	characteristic
185	C₂²×C₄₇	C₂×#104	1	1	yes	characteristic
186	C₂²×C₄₇	#421	1	1	yes	characteristic
187	C₄×C₄₇	—	2	2	no	—
188	C₄×C₄₇	—	2	2	no	—
189	C₄×C₄₇	—	2	2	no	—
190	C₄×C₄₇	—	4	1	no	—
191	C₄×C₄₇	C₈×D₄	1	2	yes	—
192	C₄×C₄₇	#435	1	2	yes	—
193	C₄×C₄₇	#450	1	1	yes	characteristic
194	C₄×C₄₇	#451	1	1	yes	characteristic
195	C₄×C₄₇	#483	1	1	yes	characteristic
196	C₄×C₄₇	#484	1	1	yes	characteristic
197	Dic₄₇	—	4	2	no	—
198	Dic₄₇	—	4	2	no	—
199	Dic₄₇	—	8	1	no	—
200	Dic₄₇	—	8	1	no	—
201	C₂²×C₄⋊C₈	—	47	1	no	—
202	C₄×C₂²⋊Q₈	—	47	1	no	—
203	C₄×C₂²⋊C₈	D₄₇	1	1	yes	characteristic
204	C₂×Q₈⋊C₈	—	47	2	no	—
205	#1279	—	47	2	no	—
206	C₂×C₄₇	—	2	4	no	—
207	C₂×C₄₇	C₂×Q₈⋊C₈	1	1	yes	characteristic
208	C₂×C₄₇	#1477	1	1	yes	characteristic
209	C₂×C₄₇	#1481	1	1	yes	characteristic
210	C₂×C₄₇	#1483	1	1	yes	characteristic
211	C₂×C₄₇	#1869	1	1	yes	characteristic
212	C₂×C₄₇	#1871	1	1	yes	characteristic
213	C₂×C₄₇	#1872	1	1	yes	characteristic
214	C₂³×C₈	—	94	1	no	—
215	C₂×C₂²⋊Q₈	—	47	1	no	—
216	C₂×C₄×Q₈	—	47	1	no	—
217	C₂²×C₄²	C₂×D₄₇	1	1	yes	characteristic
218	C₂×C₄⋊C₈	—	47	2	no	—
219	C₂×C₄⋊C₈	—	94	4	no	—
220	C₂×C₄⋊C₈	—	94	1	no	—
221	C₂×C₂²⋊C₈	—	2	1	no	—
222	C₂×C₄×C₈	C₂×D₄₇	1	2	yes	—
223	#391	—	47	1	no	—
224	#389	—	47	1	no	—
225	#387	—	94	1	no	—
226	#385	—	94	1	no	—
227	#380	—	47	1	no	—
228	C₄×C₄⋊C₄	—	47	1	no	—
229	C₄×C₄⋊C₄	—	94	1	no	—
230	C₄×C₂²⋊C₄	—	94	1	no	—
231	#336	—	2	1	no	—
232	Q₈⋊C₈	—	94	4	no	—
233	C₄₇	#8937	1	1	yes	characteristic, complemented, Sylow
234	C₂²×Q₈	—	47	1	no	—
235	C₂³×C₄	C₄×D₄₇	1	1	yes	characteristic
236	C₂³×C₄	D₁₈₈	1	1	yes	characteristic
237	C₂³×C₄	C₂²⋊D₄₇	1	1	yes	characteristic
238	C₂²×C₈	—	2	2	no	—
239	C₂²×C₈	—	94	4	no	—
240	C₂²×C₈	—	94	2	no	—
241	C₂²×C₈	—	188	2	no	—
242	C₂²×C₈	—	188	2	no	—
243	C₂²⋊Q₈	—	47	4	no	—
244	C₂²⋊Q₈	—	94	2	no	—
245	C₄×Q₈	—	94	2	no	—
246	C₄×Q₈	—	94	2	no	—
247	C₂×C₄⋊C₄	—	47	1	no	—
248	C₂×C₄⋊C₄	—	47	1	no	—
249	C₂×C₄⋊C₄	—	47	1	no	—
250	C₂×C₄⋊C₄	—	94	1	no	—
251	C₂×C₄⋊C₄	—	94	1	no	—
252	C₂×C₄⋊C₄	—	94	1	no	—
253	C₂×C₂²⋊C₄	—	94	1	no	—
254	C₂×C₂²⋊C₄	—	94	1	no	—
255	C₂×C₄²	—	2	2	no	—
256	C₂×C₄²	—	2	2	no	—
257	C₂×C₄²	—	94	1	no	—
258	C₂×C₄²	—	94	1	no	—
259	C₂×C₄²	C₄×D₄₇	1	1	yes	characteristic
260	C₂×C₄²	D₁₈₈	1	1	yes	characteristic
261	C₂×C₄²	C₂²⋊D₄₇	1	1	yes	characteristic
262	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
263	C₄⋊C₈	—	47	4	no	—
264	C₄⋊C₈	—	94	4	no	—
265	C₄⋊C₈	—	94	2	no	—
266	C₂²⋊C₈	—	2	4	no	—
267	C₄×C₈	—	2	2	no	—
268	C₄×C₈	—	2	2	no	—
269	#95	—	94	1	no	—
270	#95	—	94	1	no	—
271	#95	—	94	1	no	—
272	#95	—	94	1	no	—
273	#95	—	94	1	no	—
274	C₂⁴	(C₂×D₄₇)⋊C₄	1	1	yes	characteristic
275	C₂×Q₈	—	47	2	no	—
276	C₂×Q₈	—	94	1	no	—
277	C₂×Q₈	—	94	2	no	—
278	C₂×Q₈	—	94	2	no	—
279	C₂²×C₄	—	2	2	no	—
280	C₂²×C₄	—	2	1	no	—
281	C₂²×C₄	—	2	1	no	—
282	C₂²×C₄	—	2	2	no	—
283	C₂²×C₄	—	2	1	no	—
284	C₂²×C₄	—	2	1	no	—
285	C₂²×C₄	—	2	2	no	—
286	C₂²×C₄	—	2	2	no	—
287	C₂²×C₄	—	4	1	no	—
288	C₂²×C₄	—	94	1	no	—
289	C₂²×C₄	—	94	1	no	—
290	C₂²×C₄	—	94	1	no	—
291	C₂²×C₄	—	94	1	no	—
292	C₂²×C₄	C₈×D₄₇	1	2	yes	—
293	C₂²×C₄	#10625324	1	2	yes	—
294	C₂²×C₄	#10625325	1	2	yes	—
295	C₂²×C₄	Dic₁₈₈	1	2	yes	—
296	C₂²×C₄	(C₂×D₄₇)⋊C₄	1	1	yes	characteristic
297	C₂²×C₄	(C₂×D₄₇)⋊C₄	1	1	yes	characteristic
298	C₂²×C₄	(C₂×D₄₇)⋊C₄	1	1	yes	characteristic
299	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
300	C₂²×C₄	C₂×D₁₈₈	1	1	yes	characteristic
301	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
302	C₂×C₈	—	2	4	no	—
303	C₂×C₈	—	4	2	no	—
304	C₂×C₈	—	4	2	no	—
305	C₂×C₈	—	94	4	no	—
306	C₂×C₈	—	188	8	no	—
307	C₂×C₈	—	188	2	no	—
308	C₂×C₈	—	188	2	no	—
309	C₄⋊C₄	—	47	2	no	—
310	C₄⋊C₄	—	94	4	no	—
311	C₄⋊C₄	—	94	1	no	—
312	C₄⋊C₄	—	94	2	no	—
313	C₄⋊C₄	—	94	2	no	—
314	C₄⋊C₄	—	188	2	no	—
315	C₄⋊C₄	—	188	2	no	—
316	C₂²⋊C₄	—	94	4	no	—
317	C₂²⋊C₄	—	188	2	no	—
318	C₄²	—	2	2	no	—
319	C₄²	—	2	1	no	—
320	C₄²	—	2	2	no	—
321	C₄²	—	2	1	no	—
322	C₄²	—	188	1	no	—
323	C₄²	—	188	1	no	—
324	C₄²	—	188	1	no	—
325	C₄²	—	188	1	no	—
326	C₄²	D₄×D₄₇	1	2	yes	—
327	C₄²	#10625352	1	2	yes	—
328	C₂³	—	2	1	no	—
329	C₂³	—	2	1	no	—
330	C₂³	—	2	1	no	—
331	C₂³	—	2	1	no	—
332	C₂³	(C₂×D₄₇)⋊C₈	1	2	yes	—
333	C₂³	#13093949	1	2	yes	—
334	C₂³	#13093952	1	2	yes	—
335	C₂³	C₂×(C₂×D₄₇)⋊C₄	1	1	yes	characteristic
336	Q₈	—	94	4	no	—
337	Q₈	—	188	2	no	—
338	C₂×C₄	—	2	1	no	—
339	C₂×C₄	—	2	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	—	2	2	no	—
345	C₂×C₄	—	2	2	no	—
346	C₂×C₄	—	2	4	no	—
347	C₂×C₄	—	2	4	no	—
348	C₂×C₄	—	2	2	no	—
349	C₂×C₄	—	2	2	no	—
350	C₂×C₄	—	2	1	no	—
351	C₂×C₄	—	2	1	no	—
352	C₂×C₄	—	2	1	no	—
353	C₂×C₄	—	4	4	no	—
354	C₂×C₄	—	94	2	no	—
355	C₂×C₄	—	94	2	no	—
356	C₂×C₄	—	188	1	no	—
357	C₂×C₄	—	188	1	no	—
358	C₂×C₄	—	188	1	no	—
359	C₂×C₄	—	188	1	no	—
360	C₂×C₄	—	188	1	no	—
361	C₂×C₄	—	188	1	no	—
362	C₂×C₄	—	188	1	no	—
363	C₂×C₄	—	188	1	no	—
364	C₂×C₄	—	188	1	no	—
365	C₂×C₄	—	188	1	no	—
366	C₂×C₄	(C₂×D₄₇)⋊C₈	1	2	yes	—
367	C₂×C₄	#13093949	1	2	yes	—
368	C₂×C₄	(C₂²⋊D₄₇)⋊C₄	1	2	yes	—
369	C₂×C₄	#13093994	1	1	yes	characteristic
370	C₂×C₄	#13093996	1	2	yes	—
371	C₂×C₄	#13094008	1	1	yes	characteristic
372	C₂×C₄	C₂×C₈×D₄₇	1	1	yes	characteristic
373	C₂×C₄	C₂×#10625324	1	1	yes	characteristic
374	C₂×C₄	#13094032	1	2	yes	—
375	C₂×C₄	C₂×#10625325	1	1	yes	characteristic
376	C₂×C₄	C₂×Dic₁₈₈	1	1	yes	characteristic
377	C₂×C₄	#13094052	1	1	yes	characteristic
378	C₂×C₄	#13094057	1	1	yes	characteristic
379	C₈	—	4	4	no	—
380	C₈	—	188	4	no	—
381	C₂²	—	2	2	no	—
382	C₂²	—	2	2	no	—
383	C₂²	—	2	2	no	—
384	C₂²	—	2	2	no	—
385	C₂²	—	2	2	no	—
386	C₂²	—	2	2	no	—
387	C₂²	#15688855	1	4	yes	complemented
388	C₂²	#15689000	1	1	yes	characteristic
389	C₂²	C₂×(C₂×D₄₇)⋊C₈	1	1	yes	characteristic
390	C₂²	#15689091	1	1	yes	characteristic
391	C₂²	C₂×#13093949	1	1	yes	characteristic
392	C₂²	#15689125	1	1	yes	characteristic
393	C₂²	C₂×#13093952	1	1	yes	characteristic
394	C₂²	#15689141	1	1	yes	characteristic
395	C₄	—	2	2	no	—
396	C₄	—	2	2	no	—
397	C₄	—	2	2	no	—
398	C₄	—	4	1	no	—
399	C₄	—	376	1	no	—
400	C₄	—	376	1	no	—
401	C₄	—	188	2	no	—
402	C₄	—	188	2	no	—
403	C₄	(C₂²⋊D₄₇)⋊C₈	1	2	yes	—
404	C₄	#15689191	1	2	yes	—
405	C₄	#15689276	1	1	yes	characteristic
406	C₄	#15689281	1	1	yes	characteristic
407	C₄	#15689454	1	1	yes	characteristic
408	C₄	#15689459	1	1	yes	characteristic
409	C₂	—	2	4	no	—
410	C₂	C₂×#15688855	1	1	yes	characteristic
411	C₂	#20241776	1	1	yes	characteristic
412	C₂	#20241792	1	1	yes	characteristic
413	C₂	#20241802	1	1	yes	characteristic
414	C₂	#20243678	1	1	yes	characteristic
415	C₂	#20243688	1	1	yes	characteristic
416	C₂	#20243693	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄	C₂×D₁₈₈
commutator	C₂×C₄×C₄₇	C₂²×C₈
Frattini	C₂×C₄²	C₂²×D₄₇
Fitting	C₄×C₂²⋊C₈×C₄₇	C₂
socle	C₂³×C₄₇	C₂×C₂²⋊C₄
prime radical	C₂⁴×C₄₇	C₂²⋊C₄
cosocle	C₂×C₄²×C₄₇	C₂³
hypercenter	C₄×C₂²⋊C₈	D₄₇
hypocenter	C₄₇	#8937
LCS	G ▷ C₂×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂²×C₄ ◁ C₂²×C₄² ◁ C₄×C₂²⋊C₈

Complements

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

N	H ≅ G/N	type
3. C₂×#15688855	C₂	semidirect
4. #20241228	C₂	semidirect
31. #13094003	C₈	semidirect
92. C₂×Dic₉₄	C₂×C₈	semidirect
107. C₄⋊Dic₄₇	C₂×C₈	semidirect
179. C₂²×C₄₇	Q₈⋊C₈	semidirect
233. C₄₇	#8937	semidirect
387. C₂²	#15688855	semidirect

Maximal subgroups

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

subgroup	index
C₂²×C₄⋊(C₄₇⋊C₈)	2
C₄×#13094003	2
C₂×#15688855	2
#20241228	2
C₄×C₂²⋊C₈×C₄₇	2
#8937	47