Subgroups — #26214358

Order 12032.

1126 conjugacy classes of subgroups.

The subgroup lattice has 444 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#15689158	C₂	1	1	yes	maximal, characteristic
2	C₂×#106×D₄₇	C₂	1	1	yes	maximal, characteristic
3	C₂×#15689077	C₂	1	1	yes	maximal, characteristic
4	#20245742	C₂	1	2	yes	maximal
5	#20243286	C₂	1	2	yes	maximal, complemented
6	#20243284	C₂	1	2	yes	maximal, complemented
7	#106×Dic₄₇	C₂	1	1	yes	maximal, characteristic, complemented
8	#106×Dic₄₇	C₂	1	1	yes	maximal, characteristic, complemented
9	C₄×#13093956	C₂	1	1	yes	maximal, characteristic, complemented
10	#20243106	C₂	1	2	yes	maximal
11	C₄×#106×C₄₇	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×#10625324	C₂²	1	1	yes	characteristic
13	C₂²×C₈×D₄₇	C₂²	1	1	yes	characteristic
14	C₂×#13093982	C₂²	1	2	yes	—
15	C₂×#13093981	C₂²	1	1	yes	characteristic
16	C₂×C₄⋊C₄×D₄₇	C₂²	1	2	yes	—
17	#15689158	C₄	1	8	yes	complemented
18	C₂×#13093957	C₂²	1	2	yes	—
19	C₂×#13093956	C₂²	1	1	yes	characteristic
20	C₂×#13093956	C₂²	1	1	yes	characteristic
21	C₂×#13093955	C₂²	1	2	yes	—
22	#106×D₄₇	C₄	1	8	yes	complemented
23	#15689077	C₄	1	8	yes	complemented
24	C₂×#13093935	C₂²	1	1	yes	characteristic
25	C₂×#13093934	C₂²	1	1	yes	characteristic
26	C₂×C₈×Dic₄₇	C₂²	1	1	yes	characteristic
27	C₄⋊C₄×Dic₄₇	C₂²	1	2	yes	—
28	C₄⋊C₄×Dic₄₇	C₂²	1	2	yes	—
29	C₄×Dic₄₇⋊C₄	—	2	2	no	—
30	C₄×C₄⋊Dic₄₇	C₂²	1	2	yes	—
31	#15688974	—	2	2	no	—
32	C₄×(C₂×D₄₇)⋊C₄	—	2	2	no	—
33	#15688970	—	2	2	no	—
34	#15688886	C₂²	1	2	yes	—
35	#15688885	C₂²	1	2	yes	—
36	#15688885	C₂²	1	2	yes	—
37	C₂×#106×C₄₇	C₂²	1	1	yes	characteristic
38	C₂×#106×C₄₇	C₂²	1	1	yes	characteristic
39	C₂×C₄×C₈×C₄₇	C₂²	1	1	yes	characteristic
40	C₄×C₄⋊C₄×C₄₇	C₂²	1	2	yes	—
41	C₄₇×#340	C₂²	1	2	yes	—
42	C₂²×C₄×D₄₇	—	2	2	no	—
43	C₂²×C₄×D₄₇	C₂³	1	1	yes	characteristic
44	C₂×#10625324	—	2	2	no	—
45	C₂×#10625324	—	2	2	no	—
46	C₂×#10625324	C₂×C₄	1	4	yes	—
47	C₂²×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
48	C₂²×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
49	C₂×C₈×D₄₇	C₂×C₄	1	4	yes	—
50	C₂×C₈×D₄₇	C₂×C₄	1	4	yes	—
51	C₂×C₈×D₄₇	C₂×C₄	1	4	yes	—
52	#13093982	—	2	4	no	—
53	#13093982	C₂×C₄	1	8	yes	—
54	#13093981	C₂×C₄	1	4	yes	—
55	#13093981	Q₈	1	4	yes	—
56	C₂×C₄⋊Dic₄₇	C₂³	1	2	yes	—
57	C₂×C₄⋊Dic₄₇	C₂³	1	2	yes	—
58	C₂×Dic₄₇⋊C₄	—	2	2	no	—
59	C₂×Dic₄₇⋊C₄	D₄	1	1	yes	characteristic
60	C₂×Dic₄₇⋊C₄	D₄	1	1	yes	characteristic
61	C₄⋊C₄×D₄₇	—	2	4	no	—
62	C₄⋊C₄×D₄₇	C₂×C₄	1	8	yes	—
63	C₂×(C₂×D₄₇)⋊C₄	—	2	2	no	—
64	C₂×(C₂×D₄₇)⋊C₄	D₄	1	1	yes	characteristic
65	C₂×(C₂×D₄₇)⋊C₄	D₄	1	1	yes	characteristic
66	C₂×C₄×Dic₄₇	—	2	2	no	—
67	C₂×C₄×Dic₄₇	—	2	2	no	—
68	C₂×C₄×Dic₄₇	—	2	2	no	—
69	C₂×C₄×Dic₄₇	—	2	2	no	—
70	C₂×C₄×Dic₄₇	C₂³	1	1	yes	characteristic
71	#13093957	C₂×C₄	1	8	yes	complemented
72	#13093956	C₂×C₄	1	4	yes	—
73	#13093956	C₂×C₄	1	4	yes	complemented
74	#13093955	C₂×C₄	1	8	yes	—
75	#13093935	C₂×C₄	1	4	yes	complemented
76	#13093934	C₂×C₄	1	4	yes	complemented
77	C₈×Dic₄₇	C₂×C₄	1	4	yes	complemented
78	C₄₇⋊#95	—	2	2	no	—
79	C₄₇⋊#95	—	2	2	no	—
80	C₄₇⋊#95	—	2	2	no	—
81	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
82	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
83	C₂×C₄⋊C₄×C₄₇	C₂³	1	2	yes	—
84	C₂×C₄⋊C₄×C₄₇	C₂³	1	2	yes	—
85	C₂×C₄²×C₄₇	—	2	2	no	—
86	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
87	#106×C₄₇	C₂×C₄	1	4	yes	—
88	#106×C₄₇	C₂×C₄	1	4	yes	complemented
89	C₄×C₈×C₄₇	C₂×C₄	1	4	yes	complemented
90	#95×C₄₇	—	2	2	no	—
91	C₂³×D₄₇	C₂×D₄	1	1	yes	characteristic
92	C₂²×C₄×C₄₇	—	2	2	no	—
93	C₂²×C₄×C₄₇	—	2	2	no	—
94	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
95	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
96	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
97	C₂²×Dic₄₇	—	2	2	no	—
98	C₂²×Dic₄₇	—	2	2	no	—
99	C₂²×Dic₄₇	C₂×D₄	1	1	yes	characteristic
100	C₂²×Dic₄₇	C₂×D₄	1	1	yes	characteristic
101	C₂²×Dic₄₇	C₂×D₄	1	1	yes	characteristic
102	C₂×C₄×D₄₇	—	2	8	no	—
103	C₂×C₄×D₄₇	—	8	2	no	—
104	C₂×C₄×D₄₇	—	8	2	no	—
105	C₂×C₄×D₄₇	C₂²×C₄	1	2	yes	—
106	C₂×C₄×D₄₇	C₂²×C₄	1	2	yes	—
107	C₂×C₄×D₄₇	C₂²×C₄	1	2	yes	—
108	C₂×C₄×D₄₇	C₂×Q₈	1	2	yes	—
109	C₂×C₄×D₄₇	#41	1	2	yes	—
110	C₂×C₄×D₄₇	#41	1	2	yes	—
111	C₂×C₈×C₄₇	—	2	1	no	—
112	C₂×C₈×C₄₇	—	2	1	no	—
113	C₂×C₈×C₄₇	C₂²×C₄	1	2	yes	—
114	C₂×C₈×C₄₇	C₂²×C₄	1	2	yes	—
115	C₂×C₈×C₄₇	C₂²×C₄	1	2	yes	—
116	C₂×C₈×C₄₇	C₂²×C₄	1	2	yes	—
117	C₄⋊C₄×C₄₇	—	2	2	no	—
118	C₄⋊C₄×C₄₇	—	2	2	no	—
119	C₄⋊C₄×C₄₇	C₂²×C₄	1	4	yes	—
120	C₄⋊C₄×C₄₇	C₂²×C₄	1	4	yes	—
121	C₄²×C₄₇	—	8	2	no	—
122	C₄²×C₄₇	C₂²×C₄	1	2	yes	—
123	C₄²×C₄₇	C₂×Q₈	1	2	yes	—
124	(C₂×D₄₇)⋊C₄	—	2	8	no	—
125	(C₂×D₄₇)⋊C₄	C₄⋊C₄	1	4	yes	—
126	(C₂×D₄₇)⋊C₄	C₄⋊C₄	1	4	yes	—
127	C₄⋊Dic₄₇	—	2	2	no	—
128	C₄⋊Dic₄₇	—	2	2	no	—
129	C₄⋊Dic₄₇	C₂²×C₄	1	4	yes	—
130	C₄⋊Dic₄₇	C₂²×C₄	1	4	yes	—
131	Dic₄₇⋊C₄	—	2	8	no	—
132	Dic₄₇⋊C₄	C₄⋊C₄	1	4	yes	—
133	Dic₄₇⋊C₄	C₄⋊C₄	1	4	yes	—
134	C₄×Dic₄₇	—	2	8	no	—
135	C₄×Dic₄₇	—	8	2	no	—
136	C₄×Dic₄₇	—	8	2	no	—
137	C₄×Dic₄₇	—	8	2	no	—
138	C₄×Dic₄₇	C₂²×C₄	1	2	yes	—
139	C₄×Dic₄₇	C₂×Q₈	1	2	yes	—
140	C₂×C₄₇⋊C₈	—	2	1	no	—
141	C₂×C₄₇⋊C₈	—	2	1	no	—
142	C₂×C₄₇⋊C₈	C₂²×C₄	1	2	yes	—
143	C₂×C₄₇⋊C₈	C₂²×C₄	1	2	yes	—
144	C₂×C₄₇⋊C₈	C₂²×C₄	1	2	yes	—
145	C₂×C₄₇⋊C₈	C₂²×C₄	1	2	yes	—
146	#10625324	—	2	8	no	—
147	C₈×D₄₇	C₄²	1	16	yes	complemented
148	C₂³×C₄₇	C₂²×D₄	1	1	yes	characteristic
149	C₂²×D₄₇	—	2	2	no	—
150	C₂²×D₄₇	—	2	2	no	—
151	C₂²×D₄₇	C₂×C₄⋊C₄	1	2	yes	—
152	C₂²×D₄₇	C₄×D₄	1	2	yes	—
153	C₂²×D₄₇	C₄×D₄	1	2	yes	—
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	C₂×C₄⋊C₄	1	2	yes	—
163	C₂×C₄×C₄₇	C₂×C₄⋊C₄	1	2	yes	—
164	C₂×C₄×C₄₇	C₂³×C₄	1	1	yes	characteristic
165	C₂×C₄×C₄₇	C₂³×C₄	1	1	yes	characteristic
166	C₂×C₄×C₄₇	C₂³×C₄	1	1	yes	characteristic
167	C₂×C₄×C₄₇	C₂²×Q₈	1	1	yes	characteristic
168	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
169	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
170	C₂×Dic₄₇	—	2	2	no	—
171	C₂×Dic₄₇	—	2	2	no	—
172	C₂×Dic₄₇	—	2	4	no	—
173	C₂×Dic₄₇	—	2	4	no	—
174	C₂×Dic₄₇	—	4	2	no	—
175	C₂×Dic₄₇	—	4	2	no	—
176	C₂×Dic₄₇	—	4	2	no	—
177	C₂×Dic₄₇	—	4	2	no	—
178	C₂×Dic₄₇	C₂×C₄⋊C₄	1	2	yes	—
179	C₂×Dic₄₇	C₂×C₄⋊C₄	1	2	yes	—
180	C₂×Dic₄₇	C₂×C₄⋊C₄	1	2	yes	—
181	C₂×Dic₄₇	C₄×D₄	1	2	yes	—
182	C₂×Dic₄₇	C₄×D₄	1	2	yes	—
183	C₄×D₄₇	—	8	8	no	—
184	C₄×D₄₇	C₂×C₄²	1	4	yes	—
185	C₄×D₄₇	#117	1	4	yes	—
186	C₄×D₄₇	C₄×Q₈	1	4	yes	—
187	C₄×D₄₇	C₄×Q₈	1	4	yes	—
188	C₈×C₄₇	—	2	2	no	—
189	C₈×C₄₇	C₂×C₄²	1	4	yes	—
190	C₄₇⋊C₈	—	2	2	no	—
191	C₄₇⋊C₈	C₂×C₄²	1	4	yes	—
192	#20454	—	47	1	no	maximal, Sylow
193	C₂²×C₄₇	C₂²×C₄⋊C₄	1	1	yes	characteristic
194	C₂²×C₄₇	C₂×C₄×D₄	1	1	yes	characteristic
195	C₂²×C₄₇	C₂×C₄×D₄	1	1	yes	characteristic
196	C₂²×C₄₇	#577	1	2	yes	—
197	C₂²×C₄₇	#577	1	2	yes	—
198	C₂×D₄₇	—	2	2	no	—
199	C₂×D₄₇	—	2	2	no	—
200	C₂×D₄₇	—	2	4	no	—
201	C₂×D₄₇	—	2	4	no	—
202	C₂×D₄₇	C₄×C₄⋊C₄	1	4	yes	—
203	C₄×C₄₇	—	2	2	no	—
204	C₄×C₄₇	—	2	2	no	—
205	C₄×C₄₇	—	4	4	no	—
206	C₄×C₄₇	—	4	4	no	—
207	C₄×C₄₇	C₂²×C₄²	1	1	yes	characteristic
208	C₄×C₄₇	C₂×#117	1	1	yes	characteristic
209	C₄×C₄₇	C₂×C₄×Q₈	1	1	yes	characteristic
210	C₄×C₄₇	C₂×C₄×Q₈	1	1	yes	characteristic
211	Dic₄₇	—	2	2	no	—
212	Dic₄₇	—	2	2	no	—
213	Dic₄₇	—	4	4	no	—
214	Dic₄₇	—	4	4	no	—
215	Dic₄₇	C₄×C₄⋊C₄	1	4	yes	—
216	C₂×#427	—	47	1	no	—
217	C₂²×#106	—	47	1	no	—
218	C₂×#405	—	47	1	no	—
219	#2274	—	47	2	no	—
220	#1776	—	47	2	no	—
221	#1776	—	47	2	no	—
222	C₄×#106	—	47	1	no	—
223	C₄×#106	—	47	1	no	—
224	C₄×#106	—	47	1	no	—
225	C₄×#106	D₄₇	1	1	yes	characteristic, complemented
226	#1736	—	47	2	no	—
227	C₂×C₄₇	C₂×C₄×C₄⋊C₄	1	1	yes	characteristic
228	C₂×C₄₇	#2912	1	1	yes	characteristic
229	C₂×C₄₇	#2912	1	1	yes	characteristic
230	C₂×C₄₇	#2949	1	2	yes	—
231	C₂×C₄₇	#2952	1	2	yes	—
232	D₄₇	—	2	4	no	—
233	C₂²×M₁₆	—	47	1	no	—
234	C₂³×C₈	—	47	1	no	—
235	C₂×#117	—	47	1	no	—
236	C₂×#117	—	47	2	no	—
237	C₂²×C₄⋊C₄	—	47	2	no	—
238	#427	—	47	8	no	—
239	C₂×#107	—	47	2	no	—
240	C₂×#106	—	47	1	no	—
241	C₂×#106	—	47	1	no	—
242	C₂×#106	—	47	2	no	—
243	C₂×#106	—	47	8	no	—
244	C₂×#106	C₂×D₄₇	1	1	yes	characteristic
245	C₂×#106	C₂×D₄₇	1	1	yes	characteristic
246	#405	—	47	8	no	—
247	C₂×#97	—	47	1	no	—
248	C₂×#97	—	47	1	no	—
249	C₂×C₄×C₈	—	47	1	no	—
250	C₂×C₄×C₈	C₂×D₄₇	1	1	yes	characteristic
251	C₄×C₄⋊C₄	—	47	2	no	—
252	C₄×C₄⋊C₄	—	47	2	no	—
253	C₄×C₄⋊C₄	—	47	2	no	—
254	C₄×C₄⋊C₄	—	94	2	no	—
255	C₄×C₄⋊C₄	—	94	2	no	—
256	C₄×C₄⋊C₄	C₂×D₄₇	1	2	yes	—
257	C₄×C₂²⋊C₄	—	94	2	no	—
258	C₄×C₂²⋊C₄	—	94	2	no	—
259	#340	—	47	2	no	—
260	#340	—	47	2	no	—
261	#340	—	47	2	no	—
262	#340	C₂×D₄₇	1	2	yes	—
263	C₄₇	#20454	1	1	yes	characteristic, complemented, Sylow
264	C₂³×C₄	—	47	1	no	—
265	C₂³×C₄	—	94	2	no	—
266	C₂×M₁₆	—	47	4	no	—
267	C₂×M₁₆	—	94	2	no	—
268	C₂×M₁₆	—	94	2	no	—
269	C₂²×C₈	—	47	1	no	—
270	C₂²×C₈	—	47	4	no	—
271	C₂²×C₈	—	47	4	no	—
272	C₂²×C₈	—	47	4	no	—
273	C₂²×C₈	—	47	1	no	—
274	C₂²×C₈	C₂²×D₄₇	1	1	yes	characteristic
275	C₂²×C₈	C₂²×D₄₇	1	1	yes	characteristic
276	#117	—	47	4	no	—
277	#117	—	47	4	no	—
278	#117	—	47	8	no	—
279	#117	—	94	4	no	—
280	C₂×C₄⋊C₄	—	47	1	no	—
281	C₂×C₄⋊C₄	—	47	1	no	—
282	C₂×C₄⋊C₄	—	47	2	no	—
283	C₂×C₄⋊C₄	—	47	2	no	—
284	C₂×C₄⋊C₄	—	47	8	no	—
285	C₂×C₄⋊C₄	—	94	4	no	—
286	C₂×C₄⋊C₄	—	94	2	no	—
287	C₂×C₄⋊C₄	C₂²×D₄₇	1	2	yes	—
288	C₂×C₄⋊C₄	C₂²×D₄₇	1	2	yes	—
289	C₂×C₂²⋊C₄	—	47	1	no	—
290	C₂×C₂²⋊C₄	—	47	1	no	—
291	C₂×C₂²⋊C₄	—	94	2	no	—
292	C₂×C₄²	—	2	2	no	—
293	C₂×C₄²	—	47	1	no	—
294	C₂×C₄²	—	94	2	no	—
295	C₂×C₄²	—	94	2	no	—
296	C₂×C₄²	—	94	2	no	—
297	C₂×C₄²	—	94	2	no	—
298	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
299	#107	—	47	8	no	—
300	#106	—	47	4	no	—
301	#106	—	47	4	no	—
302	#106	—	47	8	no	—
303	#106	C₄×D₄₇	1	4	yes	—
304	#106	C₄×D₄₇	1	4	yes	complemented
305	#97	—	47	4	no	—
306	#97	—	47	4	no	—
307	C₄×C₈	—	47	4	no	—
308	C₄×C₈	C₄×D₄₇	1	4	yes	complemented
309	#95	—	2	2	no	—
310	#95	—	94	2	no	—
311	#95	—	94	2	no	—
312	#95	—	94	2	no	—
313	C₂⁴	—	47	1	no	—
314	C₂²×C₄	—	2	2	no	—
315	C₂²×C₄	—	2	2	no	—
316	C₂²×C₄	—	47	1	no	—
317	C₂²×C₄	—	47	2	no	—
318	C₂²×C₄	—	47	2	no	—
319	C₂²×C₄	—	47	2	no	—
320	C₂²×C₄	—	47	2	no	—
321	C₂²×C₄	—	47	2	no	—
322	C₂²×C₄	—	47	2	no	—
323	C₂²×C₄	—	47	1	no	—
324	C₂²×C₄	—	47	1	no	—
325	C₂²×C₄	—	94	8	no	—
326	C₂²×C₄	—	94	2	no	—
327	C₂²×C₄	—	94	2	no	—
328	C₂²×C₄	—	376	2	no	—
329	C₂²×C₄	—	376	2	no	—
330	C₂²×C₄	D₄×D₄₇	1	1	yes	characteristic
331	C₂²×C₄	D₄×D₄₇	1	1	yes	characteristic
332	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
333	M₁₆	—	94	8	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	—	47	2	no	—
339	C₂×C₈	—	47	16	no	—
340	C₂×C₈	—	47	2	no	—
341	C₂×C₈	—	94	1	no	—
342	C₂×C₈	—	94	1	no	—
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	C₂×C₈	C₂×C₄×D₄₇	1	2	yes	—
347	C₄⋊C₄	—	2	2	no	—
348	C₄⋊C₄	—	2	2	no	—
349	C₄⋊C₄	—	47	4	no	—
350	C₄⋊C₄	—	47	4	no	—
351	C₄⋊C₄	—	47	4	no	—
352	C₄⋊C₄	—	47	4	no	—
353	C₄⋊C₄	—	94	8	no	—
354	C₄⋊C₄	—	94	2	no	—
355	C₄⋊C₄	—	94	2	no	—
356	C₄⋊C₄	C₂×C₄×D₄₇	1	4	yes	—
357	C₄⋊C₄	C₂×C₄×D₄₇	1	4	yes	—
358	C₂²⋊C₄	—	47	4	no	—
359	C₂²⋊C₄	—	47	4	no	—
360	C₂²⋊C₄	—	94	8	no	—
361	C₄²	—	8	2	no	—
362	C₄²	—	47	2	no	—
363	C₄²	—	47	2	no	—
364	C₄²	—	94	8	no	—
365	C₄²	—	376	2	no	—
366	C₄²	—	376	2	no	—
367	C₄²	—	376	2	no	—
368	C₄²	C₂×C₄×D₄₇	1	2	yes	—
369	C₄²	Q₈×D₄₇	1	2	yes	—
370	C₂³	—	47	2	no	—
371	C₂³	—	47	2	no	—
372	C₂³	—	47	2	no	—
373	C₂³	—	94	2	no	—
374	C₂³	—	94	2	no	—
375	C₂³	C₂×D₄×D₄₇	1	1	yes	characteristic
376	C₂×C₄	—	2	2	no	—
377	C₂×C₄	—	2	2	no	—
378	C₂×C₄	—	2	4	no	—
379	C₂×C₄	—	2	4	no	—
380	C₂×C₄	—	4	2	no	—
381	C₂×C₄	—	4	2	no	—
382	C₂×C₄	—	4	2	no	—
383	C₂×C₄	—	4	2	no	—
384	C₂×C₄	—	47	2	no	—
385	C₂×C₄	—	47	2	no	—
386	C₂×C₄	—	47	2	no	—
387	C₂×C₄	—	47	4	no	—
388	C₂×C₄	—	47	4	no	—
389	C₂×C₄	—	47	4	no	—
390	C₂×C₄	—	47	4	no	—
391	C₂×C₄	—	47	2	no	—
392	C₂×C₄	—	47	2	no	—
393	C₂×C₄	—	94	2	no	—
394	C₂×C₄	—	94	2	no	—
395	C₂×C₄	—	94	4	no	—
396	C₂×C₄	—	94	4	no	—
397	C₂×C₄	—	376	8	no	—
398	C₂×C₄	—	188	2	no	—
399	C₂×C₄	—	188	2	no	—
400	C₂×C₄	—	188	2	no	—
401	C₂×C₄	—	188	2	no	—
402	C₂×C₄	C₄⋊C₄×D₄₇	1	2	yes	—
403	C₂×C₄	C₄⋊C₄×D₄₇	1	2	yes	—
404	C₂×C₄	C₂²×C₄×D₄₇	1	1	yes	characteristic
405	C₂×C₄	C₂²×C₄×D₄₇	1	1	yes	characteristic
406	C₂×C₄	C₂²×C₄×D₄₇	1	1	yes	characteristic
407	C₂×C₄	C₂×Q₈×D₄₇	1	1	yes	characteristic
408	C₂×C₄	#41×D₄₇	1	1	yes	characteristic
409	C₂×C₄	#41×D₄₇	1	1	yes	characteristic
410	C₈	—	2	2	no	—
411	C₈	—	47	4	no	—
412	C₈	—	94	2	no	—
413	C₈	C₄²×D₄₇	1	4	yes	—
414	C₂²	—	47	4	no	—
415	C₂²	—	94	2	no	—
416	C₂²	—	94	2	no	—
417	C₂²	—	94	4	no	—
418	C₂²	—	94	4	no	—
419	C₂²	C₂×C₄⋊C₄×D₄₇	1	1	yes	characteristic
420	C₂²	C₄×D₄×D₄₇	1	1	yes	characteristic
421	C₂²	C₄×D₄×D₄₇	1	1	yes	characteristic
422	C₂²	#15689929	1	2	yes	—
423	C₂²	#15689930	1	2	yes	—
424	C₄	—	2	2	no	—
425	C₄	—	2	2	no	—
426	C₄	—	4	4	no	—
427	C₄	—	4	4	no	—
428	C₄	—	47	4	no	—
429	C₄	—	94	2	no	—
430	C₄	—	94	2	no	—
431	C₄	—	188	4	no	—
432	C₄	—	188	4	no	—
433	C₄	C₂×C₄²×D₄₇	1	1	yes	characteristic
434	C₄	#117×D₄₇	1	1	yes	characteristic
435	C₄	C₄×Q₈×D₄₇	1	1	yes	characteristic
436	C₄	C₄×Q₈×D₄₇	1	1	yes	characteristic
437	C₂	—	94	4	no	—
438	C₂	C₄×C₄⋊C₄×D₄₇	1	1	yes	characteristic
439	C₂	#20251979	1	1	yes	characteristic
440	C₂	#20251980	1	1	yes	characteristic
441	C₂	#20252242	1	2	yes	—
442	C₂	#20252266	1	2	yes	—

	subgroup	G/H
center	C₂³	C₂×D₄×D₄₇
commutator	C₄×C₄₇	C₂²×C₄²
Frattini	C₂²×C₄	C₂³×D₄₇
Fitting	C₄×#106×C₄₇	C₂
socle	C₂³×C₄₇	C₂²×D₄
prime radical	C₂³×D₄₇	C₂×D₄
cosocle	C₂²×C₄×C₄₇	C₂⁴
hypercenter	C₄×#106	D₄₇
hypocenter	C₄₇	#20454
LCS	G ▷ C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ C₄×#106

Complements

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

N	H ≅ G/N	type
5. #20243286	C₂	semidirect
6. #20243284	C₂	semidirect
7. #106×Dic₄₇	C₂	semidirect
8. #106×Dic₄₇	C₂	semidirect
9. C₄×#13093956	C₂	semidirect
11. C₄×#106×C₄₇	C₂	semidirect
17. #15689158	C₄	semidirect
22. #106×D₄₇	C₄	semidirect
23. #15689077	C₄	semidirect
71. #13093957	C₂×C₄	semidirect
73. #13093956	C₂×C₄	semidirect
75. #13093935	C₂×C₄	semidirect
76. #13093934	C₂×C₄	semidirect
77. C₈×Dic₄₇	C₂×C₄	semidirect
88. #106×C₄₇	C₂×C₄	semidirect
89. C₄×C₈×C₄₇	C₂×C₄	semidirect
147. C₈×D₄₇	C₄²	semidirect
225. C₄×#106	D₄₇	semidirect
263. C₄₇	#20454	semidirect
304. #106	C₄×D₄₇	semidirect
308. C₄×C₈	C₄×D₄₇	semidirect

Maximal subgroups

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

subgroup	index
C₂×#15689158	2
C₂×#106×D₄₇	2
C₂×#15689077	2
#20245742	2
#20243286	2
#20243284	2
#106×Dic₄₇	2
C₄×#13093956	2
#20243106	2
C₄×#106×C₄₇	2
#20454	47