Subgroups — #26214759

Order 12032.

1326 conjugacy classes of subgroups.

The subgroup lattice has 440 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#15689236	C₂	1	1	yes	maximal, characteristic
2	C₂×#15689234	C₂	1	1	yes	maximal, characteristic
3	C₂×#15689205	C₂	1	1	yes	maximal, characteristic
4	C₄×#13093986	C₂	1	2	yes	maximal, complemented
5	#20243287	C₂	1	1	yes	maximal, characteristic, complemented
6	#106×Dic₄₇	C₂	1	1	yes	maximal, characteristic, complemented
7	#20243216	C₂	1	2	yes	maximal, complemented
8	#20243212	C₂	1	2	yes	maximal, complemented
9	#20243202	C₂	1	2	yes	maximal, complemented
10	#97×Dic₄₇	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄₇×#1776	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×D₃₇₆	C₂²	1	1	yes	characteristic
13	C₂×C₄×D₁₈₈	C₂²	1	2	yes	—
14	C₂×#13093986	C₂²	1	2	yes	—
15	C₂×#13093986	C₂²	1	2	yes	—
16	C₂×C₄²×D₄₇	—	2	2	no	—
17	#15689236	C₄	1	8	yes	complemented
18	#15689234	C₄	1	8	yes	complemented
19	#15689205	C₄	1	8	yes	complemented
20	C₂×#13093956	C₂²	1	1	yes	characteristic
21	C₂×#13093946	C₂²	1	2	yes	—
22	C₂×#13093944	C₂²	1	2	yes	—
23	C₂×#13093944	C₂²	1	2	yes	—
24	C₂×#13093935	C₂²	1	1	yes	characteristic
25	C₂×#13093934	C₂²	1	1	yes	characteristic
26	C₂×#13093934	C₂²	1	1	yes	characteristic
27	C₂×C₈×Dic₄₇	C₂²	1	1	yes	characteristic
28	C₂×C₈×Dic₄₇	C₂²	1	1	yes	characteristic
29	C₄⋊C₄×Dic₄₇	C₂²	1	2	yes	—
30	C₄⋊C₄×Dic₄₇	C₂²	1	2	yes	—
31	C₄×(C₂×D₄₇)⋊C₄	—	2	2	no	—
32	#15688970	—	2	2	no	—
33	#15688970	—	2	2	no	—
34	C₄²×Dic₄₇	C₂²	1	1	yes	characteristic
35	#15688885	C₂²	1	2	yes	—
36	#15688885	C₂²	1	2	yes	—
37	C₂×#107×C₄₇	C₂²	1	1	yes	characteristic
38	C₂×#106×C₄₇	C₂²	1	1	yes	characteristic
39	C₂×#97×C₄₇	C₂²	1	1	yes	characteristic
40	C₄×C₄⋊C₄×C₄₇	C₂²	1	2	yes	—
41	C₄₇×#340	C₂²	1	2	yes	—
42	C₂²×D₁₈₈	C₂³	1	2	yes	—
43	C₂²×C₄×D₄₇	—	2	2	no	—
44	C₂²×C₄×D₄₇	—	2	2	no	—
45	C₂²×C₄×D₄₇	—	2	2	no	—
46	C₂×D₃₇₆	C₂×C₄	1	4	yes	—
47	C₂×D₃₇₆	C₂×C₄	1	4	yes	—
48	C₂×D₃₇₆	C₂×C₄	1	4	yes	—
49	C₂²×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
50	C₂²×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
51	C₄×D₁₈₈	—	2	4	no	—
52	C₄×D₁₈₈	C₂×C₄	1	8	yes	complemented
53	#13093986	—	2	4	no	—
54	#13093986	—	2	4	no	—
55	#13093986	C₂×C₄	1	8	yes	complemented
56	#13093986	C₂×C₄	1	8	yes	complemented
57	C₂×C₄⋊Dic₄₇	C₂³	1	2	yes	—
58	C₂×(C₂×D₄₇)⋊C₄	—	2	2	no	—
59	C₂×(C₂×D₄₇)⋊C₄	—	2	2	no	—
60	C₂×(C₂×D₄₇)⋊C₄	—	2	2	no	—
61	C₂×C₄×Dic₄₇	—	2	2	no	—
62	C₂×C₄×Dic₄₇	—	2	2	no	—
63	C₂×C₄×Dic₄₇	D₄	1	2	yes	—
64	C₂×C₄×Dic₄₇	D₄	1	2	yes	—
65	C₂×C₄×Dic₄₇	C₂³	1	1	yes	characteristic
66	C₂×C₄×Dic₄₇	C₂³	1	1	yes	characteristic
67	C₄²×D₄₇	—	4	8	no	—
68	#13093956	C₂×C₄	1	4	yes	complemented
69	#13093946	C₂×C₄	1	8	yes	complemented
70	#13093944	C₂×C₄	1	8	yes	complemented
71	#13093944	C₂×C₄	1	8	yes	complemented
72	#13093935	—	2	2	no	—
73	#13093934	—	2	2	no	—
74	#13093934	C₂×C₄	1	4	yes	complemented
75	C₈×Dic₄₇	—	2	2	no	—
76	C₈×Dic₄₇	C₂×C₄	1	4	yes	complemented
77	C₄₇⋊#95	—	2	2	no	—
78	C₄₇⋊#95	—	2	2	no	—
79	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
80	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
81	C₂×C₄⋊C₄×C₄₇	C₂³	1	2	yes	—
82	C₂×C₄⋊C₄×C₄₇	C₂³	1	2	yes	—
83	C₂×C₄²×C₄₇	—	2	2	no	—
84	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
85	#107×C₄₇	C₂×C₄	1	4	yes	complemented
86	#106×C₄₇	C₂×C₄	1	4	yes	complemented
87	#97×C₄₇	C₂×C₄	1	4	yes	complemented
88	#95×C₄₇	—	2	2	no	—
89	C₂³×D₄₇	—	2	2	no	—
90	C₂²×C₄×C₄₇	—	2	2	no	—
91	C₂²×C₄×C₄₇	—	2	2	no	—
92	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
93	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
94	C₂²×Dic₄₇	—	2	2	no	—
95	C₂²×Dic₄₇	C₂×D₄	1	1	yes	characteristic
96	C₂²×Dic₄₇	C₂×D₄	1	2	yes	—
97	C₂²×Dic₄₇	C₂×D₄	1	1	yes	characteristic
98	C₂×D₁₈₈	—	2	2	no	—
99	C₂×D₁₈₈	—	2	2	no	—
100	C₂×D₁₈₈	—	2	2	no	—
101	C₂×D₁₈₈	C₂²×C₄	1	4	yes	—
102	C₂×D₁₈₈	C₂²×C₄	1	4	yes	—
103	C₂×D₁₈₈	C₂²×C₄	1	4	yes	—
104	C₂×C₄×D₄₇	—	2	8	no	—
105	C₂×C₄×D₄₇	—	2	8	no	—
106	C₂×C₄×D₄₇	—	2	8	no	—
107	C₂×C₄×D₄₇	—	4	4	no	—
108	C₂×C₄×D₄₇	—	4	4	no	—
109	C₂×C₄×D₄₇	—	4	4	no	—
110	C₂×C₄×D₄₇	—	4	4	no	—
111	C₂×C₄×D₄₇	—	4	4	no	—
112	C₂×C₄×D₄₇	—	4	4	no	—
113	C₂×C₈×C₄₇	—	2	1	no	—
114	C₂×C₈×C₄₇	—	2	1	no	—
115	C₂×C₈×C₄₇	C₂²×C₄	1	2	yes	—
116	C₂×C₈×C₄₇	C₂²×C₄	1	2	yes	—
117	C₂×C₈×C₄₇	C₂²×C₄	1	2	yes	—
118	C₂×C₈×C₄₇	C₂²×C₄	1	2	yes	—
119	C₄⋊C₄×C₄₇	—	2	2	no	—
120	C₄⋊C₄×C₄₇	—	2	2	no	—
121	C₄⋊C₄×C₄₇	C₂²×C₄	1	4	yes	—
122	C₄⋊C₄×C₄₇	C₂²×C₄	1	4	yes	—
123	C₄²×C₄₇	—	4	4	no	—
124	C₄²×C₄₇	C₂²×C₄	1	2	yes	—
125	C₄²×C₄₇	#41	1	2	yes	—
126	(C₂×D₄₇)⋊C₄	—	2	8	no	—
127	(C₂×D₄₇)⋊C₄	—	2	8	no	—
128	(C₂×D₄₇)⋊C₄	—	2	8	no	—
129	C₄⋊Dic₄₇	—	2	2	no	—
130	C₄⋊Dic₄₇	C₂²×C₄	1	4	yes	—
131	C₄×Dic₄₇	—	2	4	no	—
132	C₄×Dic₄₇	—	4	2	no	—
133	C₄×Dic₄₇	—	4	4	no	—
134	C₄×Dic₄₇	—	4	4	no	—
135	C₄×Dic₄₇	C₂²×C₄	1	2	yes	—
136	C₄×Dic₄₇	C₂²×C₄	1	2	yes	—
137	C₄×Dic₄₇	#41	1	2	yes	—
138	C₄×Dic₄₇	#41	1	2	yes	—
139	C₂×C₄₇⋊C₈	—	2	1	no	—
140	C₂×C₄₇⋊C₈	—	2	1	no	—
141	C₂×C₄₇⋊C₈	—	2	1	no	—
142	C₂×C₄₇⋊C₈	—	2	1	no	—
143	C₂×C₄₇⋊C₈	C₂²×C₄	1	2	yes	—
144	C₂×C₄₇⋊C₈	C₂²×C₄	1	2	yes	—
145	D₃₇₆	C₄²	1	16	yes	complemented
146	C₂³×C₄₇	C₂²×D₄	1	1	yes	characteristic
147	C₂²×D₄₇	—	2	4	no	—
148	C₂²×D₄₇	—	2	4	no	—
149	C₂²×D₄₇	—	2	4	no	—
150	C₂²×D₄₇	—	4	2	no	—
151	C₂²×D₄₇	—	4	2	no	—
152	C₂²×D₄₇	—	4	2	no	—
153	C₂²×D₄₇	—	4	2	no	—
154	C₂×C₄×C₄₇	—	2	2	no	—
155	C₂×C₄×C₄₇	—	2	2	no	—
156	C₂×C₄×C₄₇	—	2	4	no	—
157	C₂×C₄×C₄₇	—	2	4	no	—
158	C₂×C₄×C₄₇	—	4	2	no	—
159	C₂×C₄×C₄₇	—	4	2	no	—
160	C₂×C₄×C₄₇	—	4	2	no	—
161	C₂×C₄×C₄₇	—	4	2	no	—
162	C₂×C₄×C₄₇	C₄×D₄	1	4	yes	—
163	C₂×C₄×C₄₇	C₂³×C₄	1	1	yes	characteristic
164	C₂×C₄×C₄₇	C₂³×C₄	1	1	yes	characteristic
165	C₂×C₄×C₄₇	C₂³×C₄	1	1	yes	characteristic
166	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
167	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
168	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
169	C₂×Dic₄₇	—	2	2	no	—
170	C₂×Dic₄₇	—	2	2	no	—
171	C₂×Dic₄₇	—	2	2	no	—
172	C₂×Dic₄₇	—	2	4	no	—
173	C₂×Dic₄₇	—	4	2	no	—
174	C₂×Dic₄₇	—	4	2	no	—
175	C₂×Dic₄₇	C₄×D₄	1	2	yes	—
176	C₂×Dic₄₇	C₄×D₄	1	4	yes	—
177	C₂×Dic₄₇	C₄×D₄	1	2	yes	—
178	C₂×Dic₄₇	AGL(1,ℤ/8)	1	4	yes	—
179	D₁₈₈	—	2	4	no	—
180	D₁₈₈	—	2	4	no	—
181	D₁₈₈	—	2	4	no	—
182	D₁₈₈	C₂×C₄²	1	8	yes	complemented
183	C₄×D₄₇	—	4	16	no	—
184	C₄×D₄₇	—	4	16	no	—
185	C₄×D₄₇	—	4	16	no	—
186	C₈×C₄₇	—	2	2	no	—
187	C₈×C₄₇	C₂×C₄²	1	4	yes	complemented
188	C₄₇⋊C₈	—	2	2	no	—
189	C₄₇⋊C₈	—	2	2	no	—
190	C₄×#442	—	47	1	no	maximal, Sylow
191	C₂²×C₄₇	C₂×C₄×D₄	1	1	yes	characteristic
192	C₂²×C₄₇	C₂×C₄×D₄	1	1	yes	characteristic
193	C₂²×C₄₇	C₂×C₄×D₄	1	1	yes	characteristic
194	C₂²×C₄₇	C₂×AGL(1,ℤ/8)	1	2	yes	—
195	C₂²×C₄₇	#575	1	2	yes	—
196	C₂×D₄₇	—	2	8	no	—
197	C₂×D₄₇	—	4	4	no	—
198	C₂×D₄₇	—	4	4	no	—
199	C₂×D₄₇	—	4	4	no	—
200	C₂×D₄₇	—	4	4	no	—
201	C₂×D₄₇	—	4	4	no	—
202	C₂×D₄₇	—	4	4	no	—
203	C₄×C₄₇	—	2	4	no	—
204	C₄×C₄₇	—	4	4	no	—
205	C₄×C₄₇	—	4	4	no	—
206	C₄×C₄₇	C₂²×C₄²	1	1	yes	characteristic
207	C₄×C₄₇	C₄×#41	1	1	yes	characteristic
208	C₄×C₄₇	C₄×#41	1	1	yes	characteristic
209	C₄×C₄₇	C₄×#41	1	1	yes	characteristic
210	Dic₄₇	—	2	2	no	—
211	Dic₄₇	—	2	4	no	—
212	Dic₄₇	—	4	4	no	—
213	Dic₄₇	#442	1	4	yes	complemented
214	C₂×#442	—	47	1	no	—
215	C₂×#442	—	47	1	no	—
216	C₂×C₄×D₈	—	47	1	no	—
217	C₄²×D₄	—	47	2	no	—
218	#1776	—	47	1	no	—
219	#1776	D₄₇	1	1	yes	characteristic, complemented
220	C₄×#106	—	47	1	no	—
221	#1762	—	47	2	no	—
222	#1762	—	47	2	no	—
223	C₄×#102	—	47	2	no	—
224	C₄×#97	—	47	1	no	—
225	C₂×C₄₇	C₄²×D₄	1	1	yes	characteristic
226	C₂×C₄₇	C₂×#442	1	1	yes	characteristic
227	C₂×C₄₇	#2943	1	1	yes	characteristic
228	C₂×C₄₇	C₄×AGL(1,ℤ/8)	1	2	yes	—
229	C₂×C₄₇	C₄×AGL(1,ℤ/8)	1	2	yes	—
230	D₄₇	—	4	8	no	—
231	C₂²×D₈	—	47	1	no	—
232	C₂×C₄×D₄	—	47	2	no	—
233	C₂×C₄×D₄	—	47	2	no	—
234	C₂×C₄×D₄	—	47	2	no	—
235	C₂²×C₄²	—	94	2	no	—
236	#442	—	47	8	no	—
237	#442	—	47	8	no	—
238	C₄×D₈	—	47	8	no	—
239	C₂×#107	C₂×D₄₇	1	1	yes	characteristic
240	C₂×#106	—	47	1	no	—
241	C₂×#106	C₂×D₄₇	1	1	yes	characteristic
242	C₂×#102	—	47	2	no	—
243	C₂×#102	—	47	2	no	—
244	C₂×#102	—	47	2	no	—
245	C₂×#97	—	47	1	no	—
246	C₂×#97	—	47	1	no	—
247	C₂×#97	—	47	1	no	—
248	C₂×#97	C₂×D₄₇	1	1	yes	characteristic
249	C₂×C₄×C₈	—	47	1	no	—
250	C₂×C₄×C₈	—	47	1	no	—
251	C₄×C₄⋊C₄	—	47	2	no	—
252	C₄×C₄⋊C₄	—	47	2	no	—
253	C₄×C₄⋊C₄	C₂×D₄₇	1	2	yes	—
254	C₄×C₂²⋊C₄	—	94	2	no	—
255	C₄×C₂²⋊C₄	—	94	2	no	—
256	C₄×C₂²⋊C₄	—	94	2	no	—
257	C₄³	—	47	1	no	—
258	#340	—	47	2	no	—
259	#340	—	47	2	no	—
260	#340	C₂×D₄₇	1	2	yes	—
261	C₄₇	C₄×#442	1	1	yes	characteristic, complemented, Sylow
262	C₂²×D₄	—	47	2	no	—
263	C₂³×C₄	—	94	2	no	—
264	C₂³×C₄	—	94	2	no	—
265	C₂³×C₄	—	94	2	no	—
266	C₂×D₈	—	47	4	no	—
267	C₂×D₈	—	47	4	no	—
268	C₂×D₈	—	47	4	no	—
269	C₂²×C₈	—	47	1	no	—
270	C₂²×C₈	—	47	1	no	—
271	C₂²×C₈	C₂²×D₄₇	1	1	yes	characteristic
272	C₂²×C₈	C₂²×D₄₇	1	1	yes	characteristic
273	C₄×D₄	—	47	8	no	—
274	C₄×D₄	—	47	8	no	—
275	C₄×D₄	—	47	8	no	—
276	C₄×D₄	—	94	4	no	—
277	C₄×D₄	—	94	4	no	—
278	C₄×D₄	—	94	4	no	—
279	C₂×C₄⋊C₄	—	47	2	no	—
280	C₂×C₄⋊C₄	C₂²×D₄₇	1	2	yes	—
281	C₂×C₄⋊C₄	C₂²×D₄₇	1	2	yes	—
282	C₂×C₂²⋊C₄	—	94	2	no	—
283	C₂×C₂²⋊C₄	—	94	2	no	—
284	C₂×C₂²⋊C₄	—	94	2	no	—
285	C₂×C₄²	—	2	2	no	—
286	C₂×C₄²	—	47	1	no	—
287	C₂×C₄²	—	47	1	no	—
288	C₂×C₄²	—	47	2	no	—
289	C₂×C₄²	—	47	2	no	—
290	C₂×C₄²	—	94	2	no	—
291	C₂×C₄²	—	94	2	no	—
292	C₂×C₄²	—	188	8	no	—
293	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
294	#107	C₄×D₄₇	1	4	yes	complemented
295	#106	—	47	4	no	—
296	#106	C₄×D₄₇	1	4	yes	complemented
297	#102	—	47	8	no	—
298	#102	—	47	8	no	—
299	#102	—	47	8	no	—
300	#97	—	47	4	no	—
301	#97	—	94	2	no	—
302	#97	—	94	2	no	—
303	#97	C₄×D₄₇	1	4	yes	complemented
304	C₄×C₈	—	47	4	no	—
305	C₄×C₈	—	94	2	no	—
306	#95	—	2	2	no	—
307	#95	—	94	2	no	—
308	#95	—	94	2	no	—
309	C₂⁴	—	94	2	no	—
310	C₂×D₄	—	47	4	no	—
311	C₂×D₄	—	47	4	no	—
312	C₂×D₄	—	47	4	no	—
313	C₂×D₄	—	94	2	no	—
314	C₂×D₄	—	94	2	no	—
315	C₂×D₄	—	94	2	no	—
316	C₂²×C₄	—	2	2	no	—
317	C₂²×C₄	—	2	2	no	—
318	C₂²×C₄	—	47	1	no	—
319	C₂²×C₄	—	47	1	no	—
320	C₂²×C₄	—	47	2	no	—
321	C₂²×C₄	—	94	8	no	—
322	C₂²×C₄	—	94	8	no	—
323	C₂²×C₄	—	94	2	no	—
324	C₂²×C₄	—	94	8	no	—
325	C₂²×C₄	—	188	4	no	—
326	C₂²×C₄	—	188	4	no	—
327	C₂²×C₄	—	188	4	no	—
328	C₂²×C₄	—	188	4	no	—
329	C₂²×C₄	—	188	4	no	—
330	C₂²×C₄	—	188	4	no	—
331	C₂²×C₄	D₄×D₄₇	1	2	yes	—
332	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
333	D₈	—	47	16	no	—
334	C₂×C₈	—	2	1	no	—
335	C₂×C₈	—	2	1	no	—
336	C₂×C₈	—	47	2	no	—
337	C₂×C₈	—	47	2	no	—
338	C₂×C₈	—	94	1	no	—
339	C₂×C₈	—	94	1	no	—
340	C₂×C₈	—	94	1	no	—
341	C₂×C₈	—	94	1	no	—
342	C₂×C₈	C₂×C₄×D₄₇	1	2	yes	—
343	C₂×C₈	C₂×C₄×D₄₇	1	2	yes	—
344	C₂×C₈	C₂×C₄×D₄₇	1	2	yes	—
345	C₂×C₈	C₂×C₄×D₄₇	1	2	yes	—
346	C₄⋊C₄	—	2	2	no	—
347	C₄⋊C₄	—	2	2	no	—
348	C₄⋊C₄	—	47	4	no	—
349	C₄⋊C₄	—	94	2	no	—
350	C₄⋊C₄	C₂×C₄×D₄₇	1	4	yes	—
351	C₄⋊C₄	C₂×C₄×D₄₇	1	4	yes	—
352	C₂²⋊C₄	—	94	8	no	—
353	C₂²⋊C₄	—	94	8	no	—
354	C₂²⋊C₄	—	94	8	no	—
355	C₄²	—	4	4	no	—
356	C₄²	—	47	2	no	—
357	C₄²	—	47	2	no	—
358	C₄²	—	47	2	no	—
359	C₄²	—	47	2	no	—
360	C₄²	—	94	4	no	—
361	C₄²	—	188	2	no	—
362	C₄²	—	188	4	no	—
363	C₄²	—	188	4	no	—
364	C₄²	C₂×C₄×D₄₇	1	2	yes	—
365	C₄²	#10625354	1	2	yes	—
366	C₂³	—	94	4	no	—
367	C₂³	—	94	4	no	—
368	C₂³	—	94	4	no	—
369	C₂³	—	188	2	no	—
370	C₂³	—	188	2	no	—
371	C₂³	—	188	2	no	—
372	C₂³	—	188	2	no	—
373	C₂³	C₂×D₄×D₄₇	1	1	yes	characteristic
374	D₄	—	47	8	no	—
375	D₄	—	94	4	no	—
376	D₄	—	94	4	no	—
377	D₄	—	94	4	no	—
378	C₂×C₄	—	2	2	no	—
379	C₂×C₄	—	2	2	no	—
380	C₂×C₄	—	2	4	no	—
381	C₂×C₄	—	2	4	no	—
382	C₂×C₄	—	4	2	no	—
383	C₂×C₄	—	4	2	no	—
384	C₂×C₄	—	4	2	no	—
385	C₂×C₄	—	4	2	no	—
386	C₂×C₄	—	47	2	no	—
387	C₂×C₄	—	47	4	no	—
388	C₂×C₄	—	47	2	no	—
389	C₂×C₄	—	47	4	no	—
390	C₂×C₄	—	94	2	no	—
391	C₂×C₄	—	94	2	no	—
392	C₂×C₄	—	94	2	no	—
393	C₂×C₄	—	94	4	no	—
394	C₂×C₄	—	188	16	no	—
395	C₂×C₄	—	188	16	no	—
396	C₂×C₄	—	188	16	no	—
397	C₂×C₄	—	188	2	no	—
398	C₂×C₄	—	188	2	no	—
399	C₂×C₄	#13093986	1	4	yes	—
400	C₂×C₄	C₂²×C₄×D₄₇	1	1	yes	characteristic
401	C₂×C₄	C₂²×C₄×D₄₇	1	1	yes	characteristic
402	C₂×C₄	C₂²×C₄×D₄₇	1	1	yes	characteristic
403	C₂×C₄	#41×D₄₇	1	1	yes	characteristic
404	C₂×C₄	#41×D₄₇	1	1	yes	characteristic
405	C₂×C₄	C₂×#10625354	1	1	yes	characteristic
406	C₈	—	2	2	no	—
407	C₈	—	94	2	no	—
408	C₈	—	94	2	no	—
409	C₈	C₄²×D₄₇	1	4	yes	complemented
410	C₂²	—	94	8	no	—
411	C₂²	—	188	4	no	—
412	C₂²	—	188	4	no	—
413	C₂²	—	188	4	no	—
414	C₂²	—	188	4	no	—
415	C₂²	—	188	4	no	—
416	C₂²	—	188	4	no	—
417	C₂²	C₄×D₄×D₄₇	1	1	yes	characteristic
418	C₂²	C₄×D₄×D₄₇	1	1	yes	characteristic
419	C₂²	C₂×#13093986	1	1	yes	characteristic
420	C₂²	AGL(1,ℤ/8)×D₄₇	1	2	yes	—
421	C₂²	#15689922	1	2	yes	—
422	C₄	—	2	4	no	—
423	C₄	—	4	4	no	—
424	C₄	—	4	4	no	—
425	C₄	—	47	4	no	—
426	C₄	—	94	2	no	—
427	C₄	—	94	4	no	—
428	C₄	—	188	4	no	—
429	C₄	C₂×C₄²×D₄₇	1	1	yes	characteristic
430	C₄	#15689591	1	1	yes	characteristic
431	C₄	C₄×#10625354	1	1	yes	characteristic
432	C₄	C₄×#10625354	1	1	yes	characteristic
433	C₂	—	188	8	no	—
434	C₂	C₄×#13093986	1	1	yes	characteristic
435	C₂	#442×D₄₇	1	1	yes	characteristic
436	C₂	#20252187	1	1	yes	characteristic
437	C₂	#20252193	1	2	yes	—
438	C₂	#20252195	1	2	yes	—

	subgroup	G/H
center	C₂³	C₂×D₄×D₄₇
commutator	C₄×C₄₇	C₂²×C₄²
Frattini	C₂²×C₄	C₂³×D₄₇
Fitting	C₄₇×#1776	C₂
socle	C₂³×C₄₇	C₂²×D₄
prime radical	C₂²×D₃₇₆	C₂²
cosocle	C₂²×C₄×C₄₇	C₂⁴
hypercenter	#1776	D₄₇
hypocenter	C₄₇	C₄×#442
LCS	G ▷ C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ #1776

Complements

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

N	H ≅ G/N	type
4. C₄×#13093986	C₂	semidirect
5. #20243287	C₂	semidirect
6. #106×Dic₄₇	C₂	semidirect
7. #20243216	C₂	semidirect
8. #20243212	C₂	semidirect
9. #20243202	C₂	semidirect
10. #97×Dic₄₇	C₂	semidirect
11. C₄₇×#1776	C₂	semidirect
17. #15689236	C₄	semidirect
18. #15689234	C₄	semidirect
19. #15689205	C₄	semidirect
52. C₄×D₁₈₈	C₂×C₄	semidirect
55. #13093986	C₂×C₄	semidirect
56. #13093986	C₂×C₄	semidirect
68. #13093956	C₂×C₄	semidirect
69. #13093946	C₂×C₄	semidirect
70. #13093944	C₂×C₄	semidirect
71. #13093944	C₂×C₄	semidirect
74. #13093934	C₂×C₄	semidirect
76. C₈×Dic₄₇	C₂×C₄	semidirect
85. #107×C₄₇	C₂×C₄	semidirect
86. #106×C₄₇	C₂×C₄	semidirect
87. #97×C₄₇	C₂×C₄	semidirect
145. D₃₇₆	C₄²	semidirect
182. D₁₈₈	C₂×C₄²	semidirect
187. C₈×C₄₇	C₂×C₄²	semidirect
213. Dic₄₇	#442	semidirect
219. #1776	D₄₇	semidirect
261. C₄₇	C₄×#442	semidirect
294. #107	C₄×D₄₇	semidirect
296. #106	C₄×D₄₇	semidirect
303. #97	C₄×D₄₇	semidirect
409. C₈	C₄²×D₄₇	semidirect

Maximal subgroups

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

subgroup	index
C₂×#15689236	2
C₂×#15689234	2
C₂×#15689205	2
C₄×#13093986	2
#20243287	2
#106×Dic₄₇	2
#20243216	2
#20243212	2
#20243202	2
#97×Dic₄₇	2
C₄₇×#1776	2
C₄×#442	47