Subgroups — #26214301

Order 12032.

1042 conjugacy classes of subgroups.

The subgroup lattice has 416 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#15689170	C₂	1	1	yes	maximal, characteristic
2	#20251976	C₂	1	1	yes	maximal, characteristic
3	#20251804	C₂	1	2	yes	maximal
4	C₂×C₄×#10625324	C₂	1	1	yes	maximal, characteristic
5	#20243275	C₂	1	1	yes	maximal, characteristic, complemented
6	#20243274	C₂	1	1	yes	maximal, characteristic, complemented
7	#20243273	C₂	1	2	yes	maximal, complemented
8	#20243267	C₂	1	1	yes	maximal, characteristic, complemented
9	#20243266	C₂	1	2	yes	maximal, complemented
10	#339×D₄₇	C₂	1	2	yes	maximal
11	C₄₇×#1772	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×#10625324	C₂²	1	1	yes	characteristic
13	C₂²×#10625324	C₂²	1	1	yes	characteristic
14	C₂×M₁₆×D₄₇	C₂²	1	2	yes	—
15	#117×D₄₇	C₂²	1	2	yes	—
16	C₂×C₄²×D₄₇	C₂²	1	1	yes	characteristic
17	#15689170	C₄	1	8	yes	complemented
18	C₂×#13093960	C₂²	1	1	yes	characteristic
19	C₂×#13093959	C₂²	1	2	yes	—
20	#15689164	C₄	1	4	yes	complemented
21	#15689162	C₄	1	4	yes	complemented
22	#15689161	C₂²	1	1	yes	characteristic
23	#15689159	C₂²	1	2	yes	—
24	#15689081	C₂²	1	2	yes	—
25	#15689080	—	2	2	no	—
26	#15689079	C₂²	1	2	yes	—
27	#15689078	C₂²	1	2	yes	—
28	#15689077	—	2	2	no	—
29	#15689075	—	2	2	no	—
30	C₄×#10625324	—	2	2	no	—
31	C₄×#10625324	C₄	1	8	yes	complemented
32	C₂×#13093934	C₂²	1	1	yes	characteristic
33	C₂×#13093934	C₂²	1	1	yes	characteristic
34	C₂×C₄×C₄₇⋊C₈	C₂²	1	1	yes	characteristic
35	#15688884	C₂²	1	2	yes	—
36	#15688883	C₂²	1	2	yes	—
37	#15688882	C₂²	1	2	yes	—
38	C₂×#108×C₄₇	C₂²	1	1	yes	characteristic
39	C₄₇×#427	C₂²	1	1	yes	characteristic
40	C₄₇×#405	C₂²	1	2	yes	—
41	C₂×C₄×C₈×C₄₇	C₂²	1	1	yes	characteristic
42	C₄₇×#339	C₂²	1	2	yes	—
43	C₂²×C₄×D₄₇	—	2	1	no	—
44	C₂²×C₄×D₄₇	C₂³	1	1	yes	characteristic
45	C₂×#10625329	C₂³	1	2	yes	—
46	C₂×#10625324	—	2	2	no	—
47	C₂×#10625324	C₂×C₄	1	4	yes	—
48	C₂×#10625324	C₂×C₄	1	2	yes	—
49	C₂×#10625324	C₂×C₄	1	2	yes	—
50	C₂×#10625324	C₂×C₄	1	4	yes	—
51	C₂×#10625324	C₂×C₄	1	4	yes	—
52	C₂×#10625324	D₄	1	2	yes	—
53	C₂×#10625324	D₄	1	2	yes	—
54	C₂×#10625324	Q₈	1	4	yes	—
55	M₁₆×D₄₇	—	2	4	no	—
56	M₁₆×D₄₇	C₂×C₄	1	8	yes	—
57	C₂²×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
58	C₂²×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
59	C₂×C₈×D₄₇	—	2	2	no	—
60	#13093983	C₂³	1	2	yes	—
61	#13093982	C₂×C₄	1	4	yes	—
62	#13093981	—	2	2	no	—
63	#13093980	—	2	2	no	—
64	C₄⋊C₄×D₄₇	C₂×C₄	1	4	yes	—
65	C₂²⋊C₄×D₄₇	—	2	2	no	—
66	C₂×C₄×Dic₄₇	—	2	1	no	—
67	C₂×C₄×Dic₄₇	C₂³	1	1	yes	characteristic
68	C₄²×D₄₇	—	2	2	no	—
69	C₄²×D₄₇	—	2	2	no	—
70	C₄²×D₄₇	C₂×C₄	1	4	yes	—
71	#13093960	C₂×C₄	1	4	yes	complemented
72	#13093959	C₂×C₄	1	8	yes	complemented
73	#13093958	C₂×C₄	1	2	yes	complemented
74	#13093957	C₂×C₄	1	4	yes	complemented
75	#13093956	C₂×C₄	1	2	yes	complemented
76	#13093955	C₂×C₄	1	4	yes	complemented
77	#13093935	—	2	2	no	—
78	#13093934	—	2	2	no	—
79	#13093934	—	2	2	no	—
80	#13093934	C₂×C₄	1	4	yes	complemented
81	#13093934	C₂×C₄	1	4	yes	complemented
82	C₄×C₄₇⋊C₈	—	2	2	no	—
83	C₄×C₄₇⋊C₈	C₂×C₄	1	4	yes	complemented
84	C₈×Dic₄₇	—	2	2	no	—
85	C₈×Dic₄₇	—	2	2	no	—
86	C₂×M₁₆×C₄₇	C₂³	1	2	yes	—
87	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
88	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
89	#117×C₄₇	C₂³	1	2	yes	—
90	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
91	#108×C₄₇	C₂×C₄	1	4	yes	complemented
92	#107×C₄₇	C₂×C₄	1	2	yes	complemented
93	#106×C₄₇	C₂×C₄	1	2	yes	complemented
94	#97×C₄₇	—	2	2	no	—
95	C₄×C₈×C₄₇	—	2	2	no	—
96	C₄×C₈×C₄₇	C₂×C₄	1	4	yes	complemented
97	C₂³×D₄₇	#41	1	1	yes	characteristic
98	C₂²×C₄×C₄₇	—	2	1	no	—
99	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
100	C₂²×Dic₄₇	—	2	1	no	—
101	C₂²×Dic₄₇	#41	1	1	yes	characteristic
102	C₂×C₄×D₄₇	—	2	4	no	—
103	C₂×C₄×D₄₇	—	2	4	no	—
104	C₂×C₄×D₄₇	—	4	4	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×D₄	1	2	yes	—
109	C₂×C₄×D₄₇	C₂×Q₈	1	2	yes	—
110	C₂×C₄×D₄₇	#41	1	2	yes	—
111	M₁₆×C₄₇	—	2	2	no	—
112	M₁₆×C₄₇	C₂²×C₄	1	4	yes	—
113	C₂×C₈×C₄₇	—	2	2	no	—
114	C₂×C₈×C₄₇	C₂²×C₄	1	1	yes	characteristic
115	C₂×C₈×C₄₇	C₂²×C₄	1	1	yes	characteristic
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	C₂×C₈×C₄₇	C₂×D₄	1	1	yes	characteristic
120	C₂×C₈×C₄₇	C₂×D₄	1	1	yes	characteristic
121	C₂×C₈×C₄₇	C₂×Q₈	1	2	yes	—
122	C₄⋊C₄×C₄₇	C₂²×C₄	1	4	yes	—
123	C₂²⋊C₄×C₄₇	—	2	2	no	—
124	C₄²×C₄₇	—	2	2	no	—
125	C₄²×C₄₇	—	2	1	no	—
126	C₄²×C₄₇	C₂²×C₄	1	2	yes	—
127	C₂²⋊Dic₄₇	—	2	2	no	—
128	(C₂×D₄₇)⋊C₄	—	2	4	no	—
129	C₄⋊Dic₄₇	C₂²×C₄	1	4	yes	—
130	Dic₄₇⋊C₄	—	2	4	no	—
131	C₄×Dic₄₇	—	2	2	no	—
132	C₄×Dic₄₇	—	2	1	no	—
133	C₄×Dic₄₇	—	2	4	no	—
134	C₄×Dic₄₇	—	2	4	no	—
135	C₄×Dic₄₇	C₂²×C₄	1	2	yes	—
136	#10625329	—	2	2	no	—
137	#10625329	C₂²×C₄	1	4	yes	—
138	C₂×C₄₇⋊C₈	—	2	2	no	—
139	C₂×C₄₇⋊C₈	C₂²×C₄	1	2	yes	—
140	C₂×C₄₇⋊C₈	C₂²×C₄	1	2	yes	—
141	C₂×C₄₇⋊C₈	C₂²×C₄	1	2	yes	—
142	C₂×C₄₇⋊C₈	C₂²×C₄	1	2	yes	—
143	C₂×C₄₇⋊C₈	C₂×D₄	1	2	yes	—
144	C₂×C₄₇⋊C₈	C₂×Q₈	1	2	yes	—
145	#10625324	—	2	8	no	—
146	#10625324	C₄²	1	8	yes	—
147	#10625324	C₄²	1	8	yes	—
148	#10625324	C₄⋊C₄	1	8	yes	—
149	#10625324	C₄⋊C₄	1	8	yes	—
150	C₈×D₄₇	—	2	8	no	—
151	C₂³×C₄₇	C₂×#41	1	1	yes	characteristic
152	C₂²×D₄₇	—	4	2	no	—
153	C₂²×D₄₇	#117	1	2	yes	—
154	C₂²×D₄₇	C₄×D₄	1	2	yes	—
155	C₂²×D₄₇	C₄×Q₈	1	2	yes	—
156	C₂×C₄×C₄₇	—	2	4	no	—
157	C₂×C₄×C₄₇	—	2	2	no	—
158	C₂×C₄×C₄₇	—	2	4	no	—
159	C₂×C₄×C₄₇	C₂³×C₄	1	1	yes	characteristic
160	C₂×C₄×C₄₇	C₂³×C₄	1	1	yes	characteristic
161	C₂×C₄×C₄₇	C₂³×C₄	1	1	yes	characteristic
162	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
163	C₂×C₄×C₄₇	C₂²×Q₈	1	1	yes	characteristic
164	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
165	C₂×Dic₄₇	—	2	2	no	—
166	C₂×Dic₄₇	—	2	4	no	—
167	C₂×Dic₄₇	—	4	2	no	—
168	C₂×Dic₄₇	#117	1	2	yes	—
169	C₂×Dic₄₇	C₄×D₄	1	2	yes	—
170	C₂×Dic₄₇	C₄×Q₈	1	2	yes	—
171	C₄×D₄₇	—	4	8	no	—
172	C₄×D₄₇	—	8	4	no	—
173	C₄×D₄₇	C₂×C₄²	1	4	yes	—
174	C₄×D₄₇	C₂×C₄⋊C₄	1	4	yes	—
175	C₄×D₄₇	C₄×D₄	1	4	yes	—
176	C₄×D₄₇	C₄×Q₈	1	4	yes	—
177	C₈×C₄₇	—	2	4	no	—
178	C₈×C₄₇	C₂×C₄²	1	2	yes	—
179	C₈×C₄₇	C₂×C₄²	1	2	yes	—
180	C₈×C₄₇	C₂×C₄⋊C₄	1	2	yes	—
181	C₈×C₄₇	C₂×C₄⋊C₄	1	2	yes	—
182	C₄₇⋊C₈	—	2	4	no	—
183	C₄₇⋊C₈	C₂×C₄²	1	4	yes	—
184	C₄₇⋊C₈	C₂×C₄⋊C₄	1	4	yes	—
185	#20445	—	47	1	no	maximal, Sylow
186	C₂²×C₄₇	—	2	2	no	—
187	C₂²×C₄₇	C₂×#117	1	1	yes	characteristic
188	C₂²×C₄₇	C₂×C₄×D₄	1	1	yes	characteristic
189	C₂²×C₄₇	C₂×C₄×Q₈	1	1	yes	characteristic
190	C₂×D₄₇	—	2	4	no	—
191	C₂×D₄₇	—	4	2	no	—
192	C₂×D₄₇	—	4	2	no	—
193	C₂×D₄₇	C₄×C₄⋊C₄	1	4	yes	—
194	C₄×C₄₇	—	2	4	no	—
195	C₄×C₄₇	—	4	4	no	—
196	C₄×C₄₇	C₂²×C₄²	1	1	yes	characteristic
197	C₄×C₄₇	C₂²×C₄⋊C₄	1	1	yes	characteristic
198	C₄×C₄₇	C₂×C₄×D₄	1	1	yes	characteristic
199	C₄×C₄₇	C₂×C₄×Q₈	1	1	yes	characteristic
200	Dic₄₇	—	4	2	no	—
201	Dic₄₇	—	4	4	no	—
202	Dic₄₇	C₄×C₄⋊C₄	1	4	yes	—
203	C₂×#430	—	47	1	no	—
204	#2911	—	47	1	no	—
205	#2873	—	47	2	no	—
206	C₂×C₄×M₁₆	—	47	1	no	—
207	#1773	—	47	1	no	—
208	#1773	—	47	1	no	—
209	#1773	—	47	2	no	—
210	#1772	—	47	1	no	—
211	#1772	—	47	2	no	—
212	#1772	D₄₇	1	1	yes	characteristic, complemented
213	C₂×#339	—	47	2	no	—
214	C₂×C₄₇	—	2	1	no	—
215	C₂×C₄₇	—	2	1	no	—
216	C₂×C₄₇	C₂×C₄×C₄⋊C₄	1	1	yes	characteristic
217	C₂×C₄₇	#2956	1	2	yes	—
218	D₄₇	—	2	4	no	—
219	C₂²×M₁₆	—	47	1	no	—
220	C₂²×M₁₆	—	47	1	no	—
221	C₂²×M₁₆	—	47	2	no	—
222	C₂×#117	—	47	2	no	—
223	C₂²×C₄²	—	47	1	no	—
224	#430	—	47	8	no	—
225	C₂×#108	—	47	2	no	—
226	C₂×#108	—	47	1	no	—
227	C₂×#108	C₂×D₄₇	1	1	yes	characteristic
228	#428	—	47	4	no	—
229	#428	—	47	4	no	—
230	#427	—	47	1	no	—
231	#427	—	47	2	no	—
232	#427	C₂×D₄₇	1	1	yes	characteristic
233	#405	—	47	2	no	—
234	#405	—	47	2	no	—
235	#405	—	47	2	no	—
236	#405	—	94	2	no	—
237	#405	—	94	2	no	—
238	#405	C₂×D₄₇	1	2	yes	—
239	C₄×M₁₆	—	47	8	no	—
240	C₄×M₁₆	—	94	2	no	—
241	C₄×M₁₆	—	94	2	no	—
242	C₂×#97	—	47	1	no	—
243	C₂×#97	—	47	1	no	—
244	C₂×C₄×C₈	—	47	1	no	—
245	C₂×C₄×C₈	C₂×D₄₇	1	1	yes	characteristic
246	#339	—	47	2	no	—
247	#339	—	47	2	no	—
248	#339	—	47	2	no	—
249	#339	C₂×D₄₇	1	2	yes	—
250	C₄₇	#20445	1	1	yes	characteristic, complemented, Sylow
251	C₂³×C₄	—	47	1	no	—
252	C₂³×C₄	—	94	1	no	—
253	C₂×M₁₆	—	47	4	no	—
254	C₂×M₁₆	—	47	4	no	—
255	C₂×M₁₆	—	47	2	no	—
256	C₂×M₁₆	—	47	2	no	—
257	C₂×M₁₆	—	47	4	no	—
258	C₂×M₁₆	—	47	2	no	—
259	C₂×M₁₆	—	47	2	no	—
260	C₂×M₁₆	—	47	4	no	—
261	C₂×M₁₆	—	47	2	no	—
262	C₂×M₁₆	—	47	8	no	—
263	C₂×M₁₆	—	94	2	no	—
264	C₂×M₁₆	—	94	4	no	—
265	C₂×M₁₆	C₂²×D₄₇	1	2	yes	—
266	C₂²×C₈	—	47	1	no	—
267	C₂²×C₈	—	47	1	no	—
268	C₂²×C₈	—	94	2	no	—
269	C₂²×C₈	C₂²×D₄₇	1	1	yes	characteristic
270	C₂²×C₈	C₂²×D₄₇	1	1	yes	characteristic
271	#117	—	47	2	no	—
272	#117	—	47	4	no	—
273	#117	—	94	2	no	—
274	#117	—	94	2	no	—
275	#117	C₂²×D₄₇	1	2	yes	—
276	C₂×C₄⋊C₄	—	47	4	no	—
277	C₂×C₂²⋊C₄	—	94	2	no	—
278	C₂×C₄²	—	47	1	no	—
279	C₂×C₄²	—	47	4	no	—
280	C₂×C₄²	—	94	2	no	—
281	C₂×C₄²	—	94	2	no	—
282	C₂×C₄²	—	94	1	no	—
283	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
284	#108	—	47	8	no	—
285	#108	—	47	4	no	—
286	#108	C₄×D₄₇	1	4	yes	complemented
287	#107	—	47	2	no	—
288	#107	—	47	4	no	—
289	#107	C₄×D₄₇	1	2	yes	complemented
290	#106	—	47	2	no	—
291	#106	—	47	4	no	—
292	#106	C₄×D₄₇	1	2	yes	complemented
293	#97	—	2	2	no	—
294	#97	—	47	4	no	—
295	#97	—	47	4	no	—
296	#97	—	94	2	no	—
297	#97	—	94	2	no	—
298	#97	—	94	2	no	—
299	C₄×C₈	—	2	2	no	—
300	C₄×C₈	—	47	4	no	—
301	C₄×C₈	—	94	2	no	—
302	C₄×C₈	—	94	2	no	—
303	C₄×C₈	—	94	2	no	—
304	C₄×C₈	C₄×D₄₇	1	4	yes	complemented
305	C₂⁴	—	47	1	no	—
306	C₂²×C₄	—	2	1	no	—
307	C₂²×C₄	—	47	1	no	—
308	C₂²×C₄	—	47	2	no	—
309	C₂²×C₄	—	47	2	no	—
310	C₂²×C₄	—	47	2	no	—
311	C₂²×C₄	—	47	2	no	—
312	C₂²×C₄	—	47	2	no	—
313	C₂²×C₄	—	47	2	no	—
314	C₂²×C₄	—	94	4	no	—
315	C₂²×C₄	—	94	4	no	—
316	C₂²×C₄	—	94	1	no	—
317	C₂²×C₄	—	188	4	no	—
318	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
319	M₁₆	—	2	2	no	—
320	M₁₆	—	47	8	no	—
321	M₁₆	—	47	8	no	—
322	M₁₆	—	47	8	no	—
323	M₁₆	—	47	8	no	—
324	M₁₆	—	47	4	no	—
325	M₁₆	—	94	8	no	—
326	M₁₆	—	94	2	no	—
327	M₁₆	C₂×C₄×D₄₇	1	4	yes	—
328	C₂×C₈	—	2	2	no	—
329	C₂×C₈	—	47	2	no	—
330	C₂×C₈	—	47	2	no	—
331	C₂×C₈	—	47	2	no	—
332	C₂×C₈	—	47	2	no	—
333	C₂×C₈	—	47	2	no	—
334	C₂×C₈	—	47	2	no	—
335	C₂×C₈	—	94	8	no	—
336	C₂×C₈	—	94	2	no	—
337	C₂×C₈	C₂×C₄×D₄₇	1	2	yes	—
338	C₂×C₈	C₂×C₄×D₄₇	1	1	yes	characteristic
339	C₂×C₈	C₂×C₄×D₄₇	1	1	yes	characteristic
340	C₂×C₈	C₂×C₄×D₄₇	1	2	yes	—
341	C₂×C₈	C₂×C₄×D₄₇	1	2	yes	—
342	C₂×C₈	D₄×D₄₇	1	1	yes	characteristic
343	C₂×C₈	D₄×D₄₇	1	1	yes	characteristic
344	C₂×C₈	Q₈×D₄₇	1	2	yes	—
345	C₄⋊C₄	—	47	4	no	—
346	C₄⋊C₄	—	94	4	no	—
347	C₄⋊C₄	C₂×C₄×D₄₇	1	4	yes	—
348	C₂²⋊C₄	—	2	2	no	—
349	C₂²⋊C₄	—	94	4	no	—
350	C₂²⋊C₄	—	94	2	no	—
351	C₄²	—	2	2	no	—
352	C₄²	—	2	1	no	—
353	C₄²	—	47	2	no	—
354	C₄²	—	94	4	no	—
355	C₄²	—	94	4	no	—
356	C₄²	—	94	2	no	—
357	C₄²	—	94	1	no	—
358	C₄²	C₂×C₄×D₄₇	1	2	yes	—
359	C₂³	—	47	2	no	—
360	C₂³	—	47	2	no	—
361	C₂³	—	47	2	no	—
362	C₂³	—	188	2	no	—
363	C₂³	#41×D₄₇	1	1	yes	characteristic
364	C₂×C₄	—	2	4	no	—
365	C₂×C₄	—	2	2	no	—
366	C₂×C₄	—	2	4	no	—
367	C₂×C₄	—	47	2	no	—
368	C₂×C₄	—	47	2	no	—
369	C₂×C₄	—	47	2	no	—
370	C₂×C₄	—	47	4	no	—
371	C₂×C₄	—	47	4	no	—
372	C₂×C₄	—	47	4	no	—
373	C₂×C₄	—	47	4	no	—
374	C₂×C₄	—	94	2	no	—
375	C₂×C₄	—	94	4	no	—
376	C₂×C₄	—	376	4	no	—
377	C₂×C₄	—	188	8	no	—
378	C₂×C₄	—	188	2	no	—
379	C₂×C₄	C₂²×C₄×D₄₇	1	1	yes	characteristic
380	C₂×C₄	C₂²×C₄×D₄₇	1	1	yes	characteristic
381	C₂×C₄	C₂²×C₄×D₄₇	1	1	yes	characteristic
382	C₂×C₄	C₂×D₄×D₄₇	1	1	yes	characteristic
383	C₂×C₄	C₂×Q₈×D₄₇	1	1	yes	characteristic
384	C₂×C₄	#41×D₄₇	1	1	yes	characteristic
385	C₈	—	2	4	no	—
386	C₈	—	47	4	no	—
387	C₈	—	47	4	no	—
388	C₈	—	94	4	no	—
389	C₈	C₄²×D₄₇	1	2	yes	—
390	C₈	C₄²×D₄₇	1	2	yes	—
391	C₈	C₄⋊C₄×D₄₇	1	2	yes	—
392	C₈	C₄⋊C₄×D₄₇	1	2	yes	—
393	C₂²	—	2	2	no	—
394	C₂²	—	47	4	no	—
395	C₂²	—	94	4	no	—
396	C₂²	—	188	2	no	—
397	C₂²	—	188	2	no	—
398	C₂²	#117×D₄₇	1	1	yes	characteristic
399	C₂²	C₄×D₄×D₄₇	1	1	yes	characteristic
400	C₂²	C₄×Q₈×D₄₇	1	1	yes	characteristic
401	C₄	—	2	4	no	—
402	C₄	—	4	4	no	—
403	C₄	—	47	4	no	—
404	C₄	—	188	2	no	—
405	C₄	—	188	4	no	—
406	C₄	C₂×C₄²×D₄₇	1	1	yes	characteristic
407	C₄	C₂×C₄⋊C₄×D₄₇	1	1	yes	characteristic
408	C₄	C₄×D₄×D₄₇	1	1	yes	characteristic
409	C₄	C₄×Q₈×D₄₇	1	1	yes	characteristic
410	C₂	—	2	1	no	—
411	C₂	—	2	1	no	—
412	C₂	—	94	4	no	—
413	C₂	C₄×C₄⋊C₄×D₄₇	1	1	yes	characteristic
414	C₂	#20252293	1	2	yes	—

	subgroup	G/H
center	C₂×C₄	C₂×D₄×D₄₇
commutator	C₄×C₄₇	C₂²×C₄²
Frattini	C₂²×C₄	C₂³×D₄₇
Fitting	C₄₇×#1772	C₂
socle	C₂²×C₄₇	C₂×C₄×D₄
prime radical	C₂³×D₄₇	#41
cosocle	C₂²×C₄×C₄₇	C₂⁴
hypercenter	#1772	D₄₇
hypocenter	C₄₇	#20445
LCS	G ▷ C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂×C₄ ◁ C₂²×C₈ ◁ #1772

Complements

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

N	H ≅ G/N	type
5. #20243275	C₂	semidirect
6. #20243274	C₂	semidirect
7. #20243273	C₂	semidirect
8. #20243267	C₂	semidirect
9. #20243266	C₂	semidirect
11. C₄₇×#1772	C₂	semidirect
17. #15689170	C₄	semidirect
20. #15689164	C₄	semidirect
21. #15689162	C₄	semidirect
31. C₄×#10625324	C₄	semidirect
71. #13093960	C₂×C₄	semidirect
72. #13093959	C₂×C₄	semidirect
73. #13093958	C₂×C₄	semidirect
74. #13093957	C₂×C₄	semidirect
75. #13093956	C₂×C₄	semidirect
76. #13093955	C₂×C₄	semidirect
80. #13093934	C₂×C₄	semidirect
81. #13093934	C₂×C₄	semidirect
83. C₄×C₄₇⋊C₈	C₂×C₄	semidirect
91. #108×C₄₇	C₂×C₄	semidirect
92. #107×C₄₇	C₂×C₄	semidirect
93. #106×C₄₇	C₂×C₄	semidirect
96. C₄×C₈×C₄₇	C₂×C₄	semidirect
212. #1772	D₄₇	semidirect
250. C₄₇	#20445	semidirect
286. #108	C₄×D₄₇	semidirect
289. #107	C₄×D₄₇	semidirect
292. #106	C₄×D₄₇	semidirect
304. 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×#15689170	2
#20251976	2
#20251804	2
C₂×C₄×#10625324	2
#20243275	2
#20243274	2
#20243273	2
#20243267	2
#20243266	2
#339×D₄₇	2
C₄₇×#1772	2
#20445	47