Subgroups — #26185347

Order 12032.

668 conjugacy classes of subgroups.

The subgroup lattice has 420 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20252020	C₂	1	1	yes	maximal, characteristic
2	C₂×#15689175	C₂	1	1	yes	maximal, characteristic
3	#431×D₄₇	C₂	1	1	yes	maximal, characteristic
4	#20242165	C₂	1	4	yes	maximal, complemented
5	#20242164	C₂	1	1	yes	maximal, characteristic, complemented
6	#20242162	C₂	1	1	yes	maximal, characteristic, complemented
7	#20242159	C₂	1	1	yes	maximal, characteristic, complemented
8	#20242133	C₂	1	4	yes	maximal, complemented
9	C₄₇×#1570	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×C₄²×D₄₇	C₂²	1	1	yes	characteristic
11	#15689179	—	2	1	no	—
12	#15689179	C₂²	1	2	yes	—
13	#15689176	C₂²	1	1	yes	characteristic
14	#15689175	—	2	1	no	—
15	#15689175	—	2	1	no	—
16	#15689175	—	2	1	no	—
17	#15689175	C₄	1	2	yes	—
18	#15689175	C₂²	1	2	yes	—
19	#15689175	C₂²	1	2	yes	—
20	#15689175	C₂²	1	2	yes	—
21	#15689174	C₂²	1	2	yes	—
22	#15689173	C₄	1	2	yes	—
23	#15689147	C₂²	1	1	yes	characteristic
24	C₂×C₄⋊(C₄₇⋊C₈)	C₂²	1	1	yes	characteristic
25	C₄⋊C₈×D₄₇	C₄	1	2	yes	—
26	#15689086	—	2	1	no	—
27	C₂×(C₂×D₄₇)⋊C₈	—	2	1	no	—
28	C₂²⋊C₈×D₄₇	C₄	1	2	yes	—
29	M₁₆×Dic₄₇	—	2	1	no	—
30	C₂×C₈×Dic₄₇	—	2	1	no	—
31	C₄×C₈×D₄₇	C₂²	1	2	yes	—
32	#15688875	C₂²	1	4	yes	complemented
33	#15688875	C₂²	1	4	yes	complemented
34	#15688874	C₂²	1	4	yes	complemented
35	C₄₇×#431	C₂²	1	1	yes	characteristic
36	C₄₇×#423	C₂²	1	1	yes	characteristic
37	C₂×C₄⋊C₈×C₄₇	C₂²	1	1	yes	characteristic
38	C₄₇×#334	C₂²	1	4	yes	complemented
39	C₂²×C₄×D₄₇	C₂×C₄	1	1	yes	characteristic
40	C₂²×C₄×D₄₇	D₄	1	1	yes	characteristic
41	C₂²×C₄×D₄₇	Q₈	1	1	yes	characteristic
42	C₂×#10625329	—	2	1	no	—
43	C₂²×C₄₇⋊C₈	—	2	1	no	—
44	C₂×C₈×D₄₇	C₂×C₄	1	4	yes	—
45	C₂×C₄×Dic₄₇	C₂×C₄	1	1	yes	characteristic
46	C₂×C₄×Dic₄₇	D₄	1	1	yes	characteristic
47	C₂×C₄×Dic₄₇	Q₈	1	1	yes	characteristic
48	C₄²×D₄₇	C₂×C₄	1	1	yes	characteristic
49	C₄²×D₄₇	C₂×C₄	1	1	yes	characteristic
50	C₄²×D₄₇	D₄	1	1	yes	characteristic
51	C₄²×D₄₇	D₄	1	1	yes	characteristic
52	C₄²×D₄₇	Q₈	1	1	yes	characteristic
53	C₄²×D₄₇	Q₈	1	1	yes	characteristic
54	C₄²×D₄₇	C₂³	1	1	yes	characteristic
55	C₄²×D₄₇	C₂³	1	1	yes	characteristic
56	C₄⋊(C₄₇⋊C₈)	—	2	1	no	—
57	C₄⋊(C₄₇⋊C₈)	—	2	1	no	—
58	C₄⋊(C₄₇⋊C₈)	C₂×C₄	1	2	yes	—
59	C₄⋊(C₄₇⋊C₈)	C₂³	1	2	yes	—
60	C₄⋊(C₄₇⋊C₈)	C₂³	1	2	yes	—
61	Dic₄₇⋊C₈	C₂×C₄	1	4	yes	—
62	C₂²⋊(C₄₇⋊C₈)	C₂×C₄	1	2	yes	—
63	(C₂×D₄₇)⋊C₈	—	2	2	no	—
64	(C₂×D₄₇)⋊C₈	—	2	2	no	—
65	(C₂×D₄₇)⋊C₈	—	2	2	no	—
66	(C₂×D₄₇)⋊C₈	—	2	2	no	—
67	(C₂×D₄₇)⋊C₈	C₂×C₄	1	4	yes	—
68	#13093934	—	2	2	no	—
69	C₄×C₄₇⋊C₈	C₂³	1	2	yes	—
70	C₈×Dic₄₇	—	2	2	no	—
71	C₈×Dic₄₇	—	2	2	no	—
72	C₈×Dic₄₇	—	2	2	no	—
73	C₈×Dic₄₇	C₂×C₄	1	4	yes	—
74	C₂×M₁₆×C₄₇	—	2	1	no	—
75	C₂²×C₈×C₄₇	—	2	1	no	—
76	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
77	C₄⋊C₈×C₄₇	—	2	1	no	—
78	C₄⋊C₈×C₄₇	—	2	1	no	—
79	C₄⋊C₈×C₄₇	C₂×C₄	1	2	yes	—
80	C₄⋊C₈×C₄₇	C₂³	1	2	yes	—
81	C₄⋊C₈×C₄₇	C₂³	1	2	yes	—
82	C₂²⋊C₈×C₄₇	C₂×C₄	1	2	yes	—
83	C₄×C₈×C₄₇	C₂³	1	2	yes	—
84	C₂³×D₄₇	C₄⋊C₄	1	1	yes	characteristic
85	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
86	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
87	C₂²×C₄×C₄₇	C₂×Q₈	1	1	yes	characteristic
88	C₂²×Dic₄₇	C₄⋊C₄	1	1	yes	characteristic
89	C₂²×Dic₄₇	C₄⋊C₄	1	1	yes	characteristic
90	C₂²×Dic₄₇	C₄⋊C₄	1	1	yes	characteristic
91	C₂×C₄×D₄₇	—	2	2	no	—
92	C₂×C₄×D₄₇	—	2	2	no	—
93	C₂×C₄×D₄₇	—	2	4	no	—
94	C₂×C₄×D₄₇	—	4	2	no	—
95	C₂×C₄×D₄₇	C₄⋊C₄	1	1	yes	characteristic
96	C₂×C₄×D₄₇	C₄⋊C₄	1	1	yes	characteristic
97	C₂×C₄×D₄₇	C₄⋊C₄	1	1	yes	characteristic
98	C₂×C₄×D₄₇	C₄⋊C₄	1	1	yes	characteristic
99	C₂×C₄×D₄₇	C₄⋊C₄	1	1	yes	characteristic
100	C₂×C₄×D₄₇	C₄⋊C₄	1	1	yes	characteristic
101	C₂×C₄×D₄₇	C₂²×C₄	1	1	yes	characteristic
102	C₂×C₄×D₄₇	C₂²×C₄	1	1	yes	characteristic
103	C₂×C₄×D₄₇	C₂×D₄	1	1	yes	characteristic
104	C₂×C₄×D₄₇	C₂×D₄	1	1	yes	characteristic
105	C₂×C₄×D₄₇	C₂×Q₈	1	1	yes	characteristic
106	C₂×C₄×D₄₇	C₂×Q₈	1	1	yes	characteristic
107	M₁₆×C₄₇	—	4	2	no	—
108	C₂×C₈×C₄₇	—	2	2	no	—
109	C₂×C₈×C₄₇	—	2	2	no	—
110	C₂×C₈×C₄₇	—	4	2	no	—
111	C₂×C₈×C₄₇	C₂²×C₄	1	4	yes	—
112	C₄²×C₄₇	C₂²×C₄	1	1	yes	characteristic
113	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
114	C₄²×C₄₇	C₂×Q₈	1	1	yes	characteristic
115	C₄²×C₄₇	C₂⁴	1	1	yes	characteristic
116	C₄×Dic₄₇	C₄⋊C₄	1	1	yes	characteristic
117	C₄×Dic₄₇	C₄⋊C₄	1	1	yes	characteristic
118	C₄×Dic₄₇	C₄⋊C₄	1	1	yes	characteristic
119	C₄×Dic₄₇	C₄⋊C₄	1	1	yes	characteristic
120	C₄×Dic₄₇	C₄⋊C₄	1	1	yes	characteristic
121	C₄×Dic₄₇	C₄⋊C₄	1	1	yes	characteristic
122	C₄×Dic₄₇	C₂²×C₄	1	1	yes	characteristic
123	C₄×Dic₄₇	C₂²×C₄	1	1	yes	characteristic
124	C₄×Dic₄₇	C₂×D₄	1	1	yes	characteristic
125	C₄×Dic₄₇	C₂×D₄	1	1	yes	characteristic
126	C₄×Dic₄₇	C₂×Q₈	1	1	yes	characteristic
127	C₄×Dic₄₇	C₂×Q₈	1	1	yes	characteristic
128	#10625329	—	4	2	no	—
129	C₂×C₄₇⋊C₈	—	2	2	no	—
130	C₂×C₄₇⋊C₈	—	2	2	no	—
131	C₂×C₄₇⋊C₈	—	4	2	no	—
132	C₂×C₄₇⋊C₈	C₂²×C₄	1	4	yes	—
133	C₈×D₄₇	—	2	8	no	—
134	C₂³×C₄₇	C₂×C₄⋊C₄	1	1	yes	characteristic
135	C₂²×D₄₇	—	2	2	no	—
136	C₂²×D₄₇	—	2	2	no	—
137	C₂²×D₄₇	—	4	1	no	—
138	C₂²×D₄₇	C₂×C₄⋊C₄	1	1	yes	characteristic
139	C₂²×D₄₇	C₂×C₄⋊C₄	1	1	yes	characteristic
140	C₂×C₄×C₄₇	—	2	2	no	—
141	C₂×C₄×C₄₇	—	4	1	no	—
142	C₂×C₄×C₄₇	C₂×C₄⋊C₄	1	1	yes	characteristic
143	C₂×C₄×C₄₇	C₂×C₄⋊C₄	1	1	yes	characteristic
144	C₂×C₄×C₄₇	C₂×C₄⋊C₄	1	1	yes	characteristic
145	C₂×C₄×C₄₇	#135	1	2	yes	—
146	C₂×C₄×C₄₇	#135	1	2	yes	—
147	C₂×C₄×C₄₇	C₂³×C₄	1	1	yes	characteristic
148	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
149	C₂×C₄×C₄₇	C₂²×Q₈	1	1	yes	characteristic
150	C₂×Dic₄₇	—	2	2	no	—
151	C₂×Dic₄₇	—	2	2	no	—
152	C₂×Dic₄₇	—	2	2	no	—
153	C₂×Dic₄₇	C₂×C₄⋊C₄	1	1	yes	characteristic
154	C₂×Dic₄₇	C₂×C₄⋊C₄	1	1	yes	characteristic
155	C₂×Dic₄₇	C₂×C₄⋊C₄	1	1	yes	characteristic
156	C₂×Dic₄₇	C₂×C₄⋊C₄	1	1	yes	characteristic
157	C₂×Dic₄₇	C₂×C₄⋊C₄	1	1	yes	characteristic
158	C₂×Dic₄₇	C₂×C₄⋊C₄	1	1	yes	characteristic
159	C₄×D₄₇	—	2	2	no	—
160	C₄×D₄₇	—	2	2	no	—
161	C₄×D₄₇	—	2	1	no	—
162	C₄×D₄₇	—	2	1	no	—
163	C₄×D₄₇	—	2	1	no	—
164	C₄×D₄₇	—	2	1	no	—
165	C₄×D₄₇	—	2	2	no	—
166	C₄×D₄₇	—	2	2	no	—
167	C₄×D₄₇	—	2	2	no	—
168	C₄×D₄₇	—	2	2	no	—
169	C₄×D₄₇	—	2	2	no	—
170	C₄×D₄₇	—	4	1	no	—
171	C₄×D₄₇	—	4	1	no	—
172	C₄×D₄₇	#131	1	4	yes	—
173	C₈×C₄₇	—	2	4	no	—
174	C₈×C₄₇	—	4	2	no	—
175	C₈×C₄₇	—	4	2	no	—
176	C₄₇⋊C₈	—	2	4	no	—
177	C₄₇⋊C₈	—	4	2	no	—
178	C₄₇⋊C₈	—	4	2	no	—
179	#17803	—	47	1	no	maximal, Sylow
180	C₂²×C₄₇	—	2	1	no	—
181	C₂²×C₄₇	—	2	1	no	—
182	C₂²×C₄₇	#427	1	2	yes	—
183	C₂²×C₄₇	C₂²×C₄⋊C₄	1	1	yes	characteristic
184	C₂×D₄₇	—	2	1	no	—
185	C₂×D₄₇	—	2	1	no	—
186	C₂×D₄₇	—	2	1	no	—
187	C₂×D₄₇	—	2	1	no	—
188	C₂×D₄₇	—	2	1	no	—
189	C₂×D₄₇	—	4	4	no	—
190	C₂×D₄₇	#424	1	2	yes	—
191	C₄×C₄₇	—	2	1	no	—
192	C₄×C₄₇	—	2	1	no	—
193	C₄×C₄₇	—	2	1	no	—
194	C₄×C₄₇	#427	1	2	yes	—
195	C₄×C₄₇	C₂×#131	1	2	yes	—
196	C₄×C₄₇	C₂×#135	1	1	yes	characteristic
197	C₄×C₄₇	C₂×#135	1	1	yes	characteristic
198	Dic₄₇	—	2	1	no	—
199	Dic₄₇	—	2	1	no	—
200	Dic₄₇	—	2	1	no	—
201	Dic₄₇	—	2	1	no	—
202	Dic₄₇	#424	1	2	yes	—
203	Dic₄₇	#430	1	2	yes	—
204	#2920	—	47	1	no	—
205	C₂×#431	—	47	1	no	—
206	C₂×#431	—	47	1	no	—
207	#1572	—	47	4	no	—
208	#1571	—	47	1	no	—
209	#1571	—	47	1	no	—
210	#1570	—	47	1	no	—
211	#1570	D₄₇	1	1	yes	characteristic, complemented
212	#1564	—	47	4	no	—
213	C₂×C₄₇	—	2	2	no	—
214	C₂×C₄₇	C₂×#424	1	1	yes	characteristic
215	C₂×C₄₇	C₂×#427	1	1	yes	characteristic
216	C₂×C₄₇	C₂×#430	1	1	yes	characteristic
217	D₄₇	—	2	2	no	—
218	D₄₇	—	4	1	no	—
219	C₂²×C₄²	—	47	1	no	—
220	#432	—	47	2	no	—
221	#432	—	94	1	no	—
222	#431	—	47	1	no	—
223	#431	—	47	2	no	—
224	#431	—	47	2	no	—
225	#431	—	47	2	no	—
226	#431	—	47	2	no	—
227	#431	—	47	2	no	—
228	#431	—	47	2	no	—
229	#431	—	94	1	no	—
230	#431	—	94	1	no	—
231	#431	—	94	1	no	—
232	#431	C₂×D₄₇	1	1	yes	characteristic
233	#423	—	47	1	no	—
234	#423	C₂×D₄₇	1	1	yes	characteristic
235	C₂×C₄⋊C₈	—	47	2	no	—
236	C₂×C₄⋊C₈	—	47	1	no	—
237	C₂×C₄⋊C₈	C₂×D₄₇	1	1	yes	characteristic
238	#407	—	94	1	no	—
239	C₂×C₂²⋊C₈	—	47	2	no	—
240	C₂×C₂²⋊C₈	—	94	1	no	—
241	C₄×M₁₆	—	94	1	no	—
242	C₂×C₄×C₈	—	47	2	no	—
243	C₂×C₄×C₈	—	94	1	no	—
244	#335	—	47	4	no	—
245	#335	—	47	4	no	—
246	#334	—	47	4	no	—
247	#334	C₂×D₄₇	1	4	yes	complemented
248	C₄₇	#17803	1	1	yes	characteristic, complemented, Sylow
249	C₂³×C₄	—	47	1	no	—
250	C₂³×C₄	—	47	1	no	—
251	C₂³×C₄	—	47	1	no	—
252	C₂×M₁₆	—	2	1	no	—
253	C₂×M₁₆	—	94	1	no	—
254	C₂²×C₈	—	2	1	no	—
255	C₂²×C₈	—	47	4	no	—
256	C₂²×C₈	—	94	1	no	—
257	C₂×C₄²	—	47	1	no	—
258	C₂×C₄²	—	47	1	no	—
259	C₂×C₄²	—	47	1	no	—
260	C₂×C₄²	—	47	1	no	—
261	C₂×C₄²	—	47	1	no	—
262	C₂×C₄²	—	47	1	no	—
263	C₂×C₄²	—	47	1	no	—
264	C₂×C₄²	—	47	1	no	—
265	C₂×C₄²	—	47	1	no	—
266	C₂×C₄²	—	47	1	no	—
267	C₂×C₄²	—	47	1	no	—
268	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
269	C₄⋊C₈	—	2	1	no	—
270	C₄⋊C₈	—	2	1	no	—
271	C₄⋊C₈	—	47	4	no	—
272	C₄⋊C₈	—	47	2	no	—
273	C₄⋊C₈	—	47	2	no	—
274	C₄⋊C₈	—	47	2	no	—
275	C₄⋊C₈	—	94	1	no	—
276	C₄⋊C₈	—	94	1	no	—
277	C₄⋊C₈	C₄×D₄₇	1	2	yes	—
278	C₄⋊C₈	C₂²×D₄₇	1	2	yes	—
279	C₄⋊C₈	C₂²×D₄₇	1	2	yes	—
280	C₂²⋊C₈	—	47	2	no	—
281	C₂²⋊C₈	—	47	4	no	—
282	C₂²⋊C₈	—	94	2	no	—
283	C₂²⋊C₈	—	94	2	no	—
284	C₂²⋊C₈	—	94	2	no	—
285	C₂²⋊C₈	—	94	2	no	—
286	C₂²⋊C₈	C₄×D₄₇	1	2	yes	—
287	#97	—	94	2	no	—
288	C₄×C₈	—	47	4	no	—
289	C₄×C₈	—	47	2	no	—
290	C₄×C₈	—	94	2	no	—
291	C₄×C₈	—	94	2	no	—
292	C₄×C₈	—	94	2	no	—
293	C₄×C₈	C₂²×D₄₇	1	2	yes	—
294	C₂⁴	—	47	1	no	—
295	C₂²×C₄	—	47	1	no	—
296	C₂²×C₄	—	47	1	no	—
297	C₂²×C₄	—	47	1	no	—
298	C₂²×C₄	—	47	1	no	—
299	C₂²×C₄	—	47	1	no	—
300	C₂²×C₄	—	47	1	no	—
301	C₂²×C₄	—	47	1	no	—
302	C₂²×C₄	—	47	1	no	—
303	C₂²×C₄	—	47	1	no	—
304	C₂²×C₄	—	47	1	no	—
305	C₂²×C₄	—	47	1	no	—
306	C₂²×C₄	—	47	1	no	—
307	C₂²×C₄	—	47	1	no	—
308	C₂²×C₄	—	47	1	no	—
309	C₂²×C₄	—	47	1	no	—
310	C₂²×C₄	—	94	4	no	—
311	C₂²×C₄	—	94	2	no	—
312	C₂²×C₄	—	94	2	no	—
313	C₂²×C₄	—	188	2	no	—
314	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
315	C₂²×C₄	D₄×D₄₇	1	1	yes	characteristic
316	C₂²×C₄	Q₈×D₄₇	1	1	yes	characteristic
317	M₁₆	—	4	2	no	—
318	M₁₆	—	188	2	no	—
319	C₂×C₈	—	2	2	no	—
320	C₂×C₈	—	2	2	no	—
321	C₂×C₈	—	4	2	no	—
322	C₂×C₈	—	47	4	no	—
323	C₂×C₈	—	94	8	no	—
324	C₂×C₈	—	94	2	no	—
325	C₂×C₈	—	94	2	no	—
326	C₂×C₈	—	188	2	no	—
327	C₂×C₈	C₂×C₄×D₄₇	1	4	yes	—
328	C₄²	—	47	1	no	—
329	C₄²	—	47	1	no	—
330	C₄²	—	47	1	no	—
331	C₄²	—	47	1	no	—
332	C₄²	—	47	1	no	—
333	C₄²	—	47	1	no	—
334	C₄²	—	47	1	no	—
335	C₄²	—	47	1	no	—
336	C₄²	—	47	1	no	—
337	C₄²	—	47	1	no	—
338	C₄²	—	47	1	no	—
339	C₄²	—	47	1	no	—
340	C₄²	C₂×C₄×D₄₇	1	1	yes	characteristic
341	C₄²	D₄×D₄₇	1	1	yes	characteristic
342	C₄²	Q₈×D₄₇	1	1	yes	characteristic
343	C₄²	C₂³×D₄₇	1	1	yes	characteristic
344	C₂³	—	47	1	no	—
345	C₂³	—	47	1	no	—
346	C₂³	—	94	2	no	—
347	C₂³	—	94	2	no	—
348	C₂³	—	188	1	no	—
349	C₂³	C₄⋊C₄×D₄₇	1	1	yes	characteristic
350	C₂×C₄	—	2	2	no	—
351	C₂×C₄	—	4	1	no	—
352	C₂×C₄	—	47	1	no	—
353	C₂×C₄	—	47	1	no	—
354	C₂×C₄	—	47	4	no	—
355	C₂×C₄	—	47	1	no	—
356	C₂×C₄	—	47	1	no	—
357	C₂×C₄	—	47	1	no	—
358	C₂×C₄	—	47	1	no	—
359	C₂×C₄	—	94	2	no	—
360	C₂×C₄	—	94	2	no	—
361	C₂×C₄	—	94	2	no	—
362	C₂×C₄	—	94	2	no	—
363	C₂×C₄	—	94	2	no	—
364	C₂×C₄	—	94	2	no	—
365	C₂×C₄	—	94	2	no	—
366	C₂×C₄	—	94	2	no	—
367	C₂×C₄	—	94	1	no	—
368	C₂×C₄	—	94	1	no	—
369	C₂×C₄	—	94	1	no	—
370	C₂×C₄	—	94	1	no	—
371	C₂×C₄	—	94	2	no	—
372	C₂×C₄	—	94	2	no	—
373	C₂×C₄	—	188	1	no	—
374	C₂×C₄	—	188	1	no	—
375	C₂×C₄	C₄⋊C₄×D₄₇	1	1	yes	characteristic
376	C₂×C₄	C₄⋊C₄×D₄₇	1	1	yes	characteristic
377	C₂×C₄	C₄⋊C₄×D₄₇	1	1	yes	characteristic
378	C₂×C₄	#13094045	1	2	yes	—
379	C₂×C₄	#13094045	1	2	yes	—
380	C₂×C₄	C₂²×C₄×D₄₇	1	1	yes	characteristic
381	C₂×C₄	C₂×D₄×D₄₇	1	1	yes	characteristic
382	C₂×C₄	C₂×Q₈×D₄₇	1	1	yes	characteristic
383	C₈	—	2	4	no	—
384	C₈	—	4	2	no	—
385	C₈	—	4	2	no	—
386	C₈	—	94	4	no	—
387	C₈	—	188	2	no	—
388	C₈	—	188	2	no	—
389	C₂²	—	2	1	no	—
390	C₂²	—	2	1	no	—
391	C₂²	—	47	2	no	—
392	C₂²	—	94	1	no	—
393	C₂²	—	94	1	no	—
394	C₂²	—	94	1	no	—
395	C₂²	—	94	1	no	—
396	C₂²	—	94	1	no	—
397	C₂²	—	188	4	no	—
398	C₂²	#15689158	1	2	yes	—
399	C₂²	C₂×C₄⋊C₄×D₄₇	1	1	yes	characteristic
400	C₄	—	2	1	no	—
401	C₄	—	2	1	no	—
402	C₄	—	2	1	no	—
403	C₄	—	47	2	no	—
404	C₄	—	47	2	no	—
405	C₄	—	94	1	no	—
406	C₄	—	94	1	no	—
407	C₄	—	94	1	no	—
408	C₄	—	94	1	no	—
409	C₄	#15689158	1	2	yes	—
410	C₄	#131×D₄₇	1	2	yes	—
411	C₄	C₂×#13094045	1	1	yes	characteristic
412	C₄	C₂×#13094045	1	1	yes	characteristic
413	C₂	—	2	2	no	—
414	C₂	—	94	2	no	—
415	C₂	—	188	1	no	—
416	C₂	#424×D₄₇	1	1	yes	characteristic
417	C₂	C₂×#15689158	1	1	yes	characteristic
418	C₂	#430×D₄₇	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂×D₄×D₄₇
commutator	C₂×C₄×C₄₇	C₂³×C₄
Frattini	C₄²	C₂³×D₄₇
Fitting	C₄₇×#1570	C₂
socle	C₂²×C₄₇	C₂²×C₄⋊C₄
prime radical	C₂³×D₄₇	C₄⋊C₄
cosocle	C₄²×C₄₇	C₂⁴
hypercenter	#1570	D₄₇
hypocenter	C₄₇	#17803
LCS	G ▷ C₂×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #1570

Complements

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

N	H ≅ G/N	type
4. #20242165	C₂	semidirect
5. #20242164	C₂	semidirect
6. #20242162	C₂	semidirect
7. #20242159	C₂	semidirect
8. #20242133	C₂	semidirect
9. C₄₇×#1570	C₂	semidirect
32. #15688875	C₂²	semidirect
33. #15688875	C₂²	semidirect
34. #15688874	C₂²	semidirect
38. C₄₇×#334	C₂²	semidirect
211. #1570	D₄₇	semidirect
247. #334	C₂×D₄₇	semidirect
248. C₄₇	#17803	semidirect

Maximal subgroups

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

subgroup	index
#20252020	2
C₂×#15689175	2
#431×D₄₇	2
#20242165	2
#20242164	2
#20242162	2
#20242159	2
#20242133	2
C₄₇×#1570	2
#17803	47