Subgroups — #26121913

Order 12032.

802 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×C₄⋊C₄×Dic₄₇	C₂	1	1	yes	maximal, characteristic
2	C₂×#15688892	C₂	1	1	yes	maximal, characteristic
3	C₂×#15688891	C₂	1	2	yes	maximal
4	#20243081	C₂	1	2	yes	maximal
5	C₂×C₄₇×#343	C₂	1	1	yes	maximal, characteristic
6	C₂²×#10625329	C₂²	1	2	yes	—
7	C₂²×C₄⋊Dic₄₇	C₂²	1	1	yes	characteristic
8	C₂²×C₄×Dic₄₇	C₄	1	2	yes	—
9	C₂²×C₄×Dic₄₇	C₂²	1	1	yes	characteristic
10	C₄⋊C₄×Dic₄₇	—	2	2	no	—
11	C₄⋊C₄×Dic₄₇	—	2	2	no	—
12	C₂×C₄₇⋊#95	C₄	1	2	yes	—
13	#15688892	C₄	1	4	yes	complemented
14	#15688891	—	2	4	no	—
15	#15688877	—	2	2	no	—
16	#15688877	—	2	2	no	—
17	C₂²×M₁₆×C₄₇	C₂²	1	2	yes	—
18	C₂²×C₄⋊C₄×C₄₇	C₂²	1	1	yes	characteristic
19	C₄₇×#343	C₄	1	4	yes	complemented
20	C₂³×Dic₄₇	C₂×C₄	1	1	yes	characteristic
21	C₂³×Dic₄₇	C₂×C₄	1	1	yes	characteristic
22	C₂³×Dic₄₇	C₂×C₄	1	2	yes	—
23	C₂×#10625329	—	2	2	no	—
24	C₂×#10625329	—	2	2	no	—
25	C₂×#10625329	—	2	2	no	—
26	C₂×#10625329	—	2	2	no	—
27	C₂×#10625329	—	2	2	no	—
28	C₂×#10625329	C₂×C₄	1	4	yes	—
29	C₂²×C₄₇⋊C₈	—	2	2	no	—
30	C₂×C₄⋊Dic₄₇	—	2	2	no	—
31	C₂×C₄⋊Dic₄₇	—	2	2	no	—
32	C₂×C₄⋊Dic₄₇	D₄	1	2	yes	—
33	C₂×C₄⋊Dic₄₇	Q₈	1	2	yes	—
34	C₂×C₄×Dic₄₇	—	2	2	no	—
35	C₂×C₄×Dic₄₇	—	2	1	no	—
36	C₂×C₄×Dic₄₇	—	2	1	no	—
37	C₂×C₄×Dic₄₇	—	2	2	no	—
38	C₂×C₄×Dic₄₇	—	2	2	no	—
39	C₂×C₄×Dic₄₇	—	4	4	no	—
40	C₂×C₄×Dic₄₇	D₄	1	2	yes	—
41	C₂×C₄×Dic₄₇	D₄	1	2	yes	—
42	C₄₇⋊#95	—	2	4	no	—
43	C₂³×C₄×C₄₇	C₂×C₄	1	2	yes	—
44	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
45	C₂×M₁₆×C₄₇	—	2	2	no	—
46	C₂×M₁₆×C₄₇	—	2	2	no	—
47	C₂×M₁₆×C₄₇	—	2	2	no	—
48	C₂×M₁₆×C₄₇	—	2	2	no	—
49	C₂×M₁₆×C₄₇	—	2	2	no	—
50	C₂×M₁₆×C₄₇	C₂×C₄	1	4	yes	—
51	C₂²×C₈×C₄₇	—	2	2	no	—
52	C₂×C₄⋊C₄×C₄₇	—	2	2	no	—
53	C₂×C₄⋊C₄×C₄₇	—	2	2	no	—
54	C₂×C₄⋊C₄×C₄₇	C₂×C₄	1	2	yes	—
55	C₂×C₄⋊C₄×C₄₇	C₂×C₄	1	2	yes	—
56	C₂⁴×C₄₇	C₂²×C₄	1	1	yes	characteristic
57	C₂²×C₄×C₄₇	—	2	2	no	—
58	C₂²×C₄×C₄₇	—	2	2	no	—
59	C₂²×C₄×C₄₇	—	4	2	no	—
60	C₂²×C₄×C₄₇	—	4	2	no	—
61	C₂²×C₄×C₄₇	C₄²	1	4	yes	—
62	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
63	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
64	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
65	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
66	C₂²×C₄×C₄₇	C₂×Q₈	1	1	yes	characteristic
67	C₂²×C₄×C₄₇	#41	1	2	yes	—
68	C₂²×C₄×C₄₇	#41	1	2	yes	—
69	C₂²×C₄×C₄₇	#41	1	2	yes	—
70	C₂²×C₄×C₄₇	#41	1	1	yes	characteristic
71	C₂²×C₄×C₄₇	#41	1	1	yes	characteristic
72	C₂²×Dic₄₇	—	2	1	no	—
73	C₂²×Dic₄₇	—	2	1	no	—
74	C₂²×Dic₄₇	—	2	2	no	—
75	C₂²×Dic₄₇	—	2	2	no	—
76	C₂²×Dic₄₇	—	2	2	no	—
77	C₂²×Dic₄₇	—	2	1	no	—
78	C₂²×Dic₄₇	—	2	1	no	—
79	C₂²×Dic₄₇	—	2	2	no	—
80	C₂²×Dic₄₇	—	4	1	no	—
81	C₂²×Dic₄₇	—	4	1	no	—
82	C₂²×Dic₄₇	—	4	2	no	—
83	C₂²×Dic₄₇	—	4	2	no	—
84	C₂²×Dic₄₇	C₂²⋊C₄	1	2	yes	—
85	C₂²×Dic₄₇	C₂²⋊C₄	1	1	yes	characteristic
86	C₂²×Dic₄₇	C₂²⋊C₄	1	1	yes	characteristic
87	C₂²×Dic₄₇	C₄⋊C₄	1	4	yes	—
88	M₁₆×C₄₇	—	2	4	no	—
89	M₁₆×C₄₇	—	2	4	no	—
90	M₁₆×C₄₇	—	4	2	no	—
91	M₁₆×C₄₇	—	4	2	no	—
92	C₂×C₈×C₄₇	—	2	4	no	—
93	C₂×C₈×C₄₇	—	4	2	no	—
94	C₂×C₈×C₄₇	—	4	2	no	—
95	C₄⋊C₄×C₄₇	—	2	4	no	—
96	C₄⋊C₄×C₄₇	—	2	4	no	—
97	C₄⋊Dic₄₇	—	2	4	no	—
98	C₄⋊Dic₄₇	—	2	4	no	—
99	C₄×Dic₄₇	—	2	2	no	—
100	C₄×Dic₄₇	—	2	2	no	—
101	C₄×Dic₄₇	—	2	2	no	—
102	C₄×Dic₄₇	—	2	2	no	—
103	C₄×Dic₄₇	—	4	4	no	—
104	C₄×Dic₄₇	—	4	4	no	—
105	#10625329	—	2	4	no	—
106	#10625329	—	2	4	no	—
107	#10625329	—	4	2	no	—
108	#10625329	—	4	2	no	—
109	C₂×C₄₇⋊C₈	—	2	4	no	—
110	C₂×C₄₇⋊C₈	—	4	2	no	—
111	C₂×C₄₇⋊C₈	—	4	2	no	—
112	C₂³×C₄₇	—	2	1	no	—
113	C₂³×C₄₇	—	2	1	no	—
114	C₂³×C₄₇	—	2	1	no	—
115	C₂³×C₄₇	—	2	1	no	—
116	C₂³×C₄₇	C₂×C₄²	1	1	yes	characteristic
117	C₂³×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
118	C₂³×C₄₇	C₂×C₄⋊C₄	1	1	yes	characteristic
119	C₂³×C₄₇	#117	1	1	yes	characteristic
120	C₂³×C₄₇	#117	1	1	yes	characteristic
121	C₂³×C₄₇	#117	1	1	yes	characteristic
122	C₂³×C₄₇	#117	1	1	yes	characteristic
123	C₂×C₄×C₄₇	—	2	4	no	—
124	C₂×C₄×C₄₇	—	4	4	no	—
125	C₂×C₄×C₄₇	—	4	2	no	—
126	C₂×C₄×C₄₇	—	4	2	no	—
127	C₂×C₄×C₄₇	—	4	4	no	—
128	C₂×C₄×C₄₇	#117	1	2	yes	—
129	C₂×C₄×C₄₇	#117	1	2	yes	—
130	C₂×C₄×C₄₇	C₄×D₄	1	2	yes	—
131	C₂×C₄×C₄₇	C₄×D₄	1	1	yes	characteristic
132	C₂×C₄×C₄₇	C₄×D₄	1	2	yes	—
133	C₂×C₄×C₄₇	C₄×D₄	1	1	yes	characteristic
134	C₂×C₄×C₄₇	C₄×Q₈	1	1	yes	characteristic
135	C₂×C₄×C₄₇	C₄×Q₈	1	1	yes	characteristic
136	C₂×C₄×C₄₇	#121	1	2	yes	—
137	C₂×C₄×C₄₇	C₂²⋊Q₈	1	2	yes	—
138	C₂×C₄×C₄₇	#123	1	2	yes	—
139	C₂×C₄×C₄₇	#123	1	2	yes	—
140	C₂×C₄×C₄₇	#124	1	2	yes	—
141	C₂×C₄×C₄₇	#125	1	2	yes	—
142	C₂×C₄×C₄₇	#126	1	2	yes	—
143	C₂×C₄×C₄₇	#126	1	2	yes	—
144	C₂×Dic₄₇	—	2	4	no	—
145	C₂×Dic₄₇	—	2	4	no	—
146	C₂×Dic₄₇	—	2	1	no	—
147	C₂×Dic₄₇	—	2	1	no	—
148	C₂×Dic₄₇	—	2	1	no	—
149	C₂×Dic₄₇	—	2	1	no	—
150	C₂×Dic₄₇	—	2	4	no	—
151	C₂×Dic₄₇	—	2	2	no	—
152	C₂×Dic₄₇	—	2	2	no	—
153	C₂×Dic₄₇	—	2	2	no	—
154	C₂×Dic₄₇	—	4	4	no	—
155	C₂×Dic₄₇	—	4	2	no	—
156	C₂×Dic₄₇	—	4	2	no	—
157	C₂×Dic₄₇	—	4	2	no	—
158	C₂×Dic₄₇	—	4	2	no	—
159	C₂×Dic₄₇	—	4	4	no	—
160	C₂×Dic₄₇	#100	1	2	yes	—
161	C₂×Dic₄₇	#101	1	2	yes	—
162	C₈×C₄₇	—	4	4	no	—
163	C₄₇⋊C₈	—	4	4	no	—
164	#10802	—	47	1	no	maximal, Sylow
165	C₂²×C₄₇	—	2	1	no	—
166	C₂²×C₄₇	—	2	1	no	—
167	C₂²×C₄₇	—	2	1	no	—
168	C₂²×C₄₇	—	2	1	no	—
169	C₂²×C₄₇	—	2	1	no	—
170	C₂²×C₄₇	—	2	1	no	—
171	C₂²×C₄₇	—	2	1	no	—
172	C₂²×C₄₇	—	2	1	no	—
173	C₂²×C₄₇	—	2	1	no	—
174	C₂²×C₄₇	—	2	1	no	—
175	C₂²×C₄₇	—	2	1	no	—
176	C₂²×C₄₇	—	2	1	no	—
177	C₂²×C₄₇	#376	1	1	yes	characteristic
178	C₂²×C₄₇	C₄×C₂²⋊C₄	1	1	yes	characteristic
179	C₂²×C₄₇	C₄×C₄⋊C₄	1	1	yes	characteristic
180	C₂²×C₄₇	#380	1	1	yes	characteristic
181	C₂²×C₄₇	#381	1	1	yes	characteristic
182	C₂²×C₄₇	#382	1	1	yes	characteristic
183	C₂²×C₄₇	#383	1	1	yes	characteristic
184	C₂²×C₄₇	C₂×#100	1	1	yes	characteristic
185	C₂²×C₄₇	C₂×#101	1	1	yes	characteristic
186	C₂²×C₄₇	#413	1	1	yes	characteristic
187	C₂²×C₄₇	#413	1	1	yes	characteristic
188	C₄×C₄₇	—	4	4	no	—
189	C₄×C₄₇	#387	1	2	yes	—
190	C₄×C₄₇	#387	1	2	yes	—
191	C₄×C₄₇	#388	1	2	yes	—
192	C₄×C₄₇	#388	1	2	yes	—
193	Dic₄₇	—	2	2	no	—
194	Dic₄₇	—	2	2	no	—
195	Dic₄₇	—	4	4	no	—
196	Dic₄₇	—	4	2	no	—
197	C₂×C₄×C₄⋊C₄	—	47	1	no	—
198	C₂×#343	—	47	2	no	—
199	C₂×#343	—	47	1	no	—
200	C₂×#343	D₄₇	1	1	yes	characteristic
201	#1728	—	47	2	no	—
202	C₂×C₄₇	—	2	1	no	—
203	C₂×C₄₇	—	2	1	no	—
204	C₂×C₄₇	—	2	1	no	—
205	C₂×C₄₇	—	2	1	no	—
206	C₂×C₄₇	#1434	1	1	yes	characteristic
207	C₂×C₄₇	C₄×#100	1	1	yes	characteristic
208	C₂×C₄₇	C₄×#101	1	1	yes	characteristic
209	C₂×C₄₇	#1800	1	1	yes	characteristic
210	C₂×C₄₇	#1801	1	1	yes	characteristic
211	C₂×C₄₇	#1821	1	1	yes	characteristic
212	C₂×C₄₇	#1822	1	1	yes	characteristic
213	C₂²×M₁₆	—	47	2	no	—
214	C₂²×M₁₆	C₂×D₄₇	1	2	yes	—
215	C₂²×C₄⋊C₄	—	47	1	no	—
216	C₂²×C₄⋊C₄	C₂×D₄₇	1	1	yes	characteristic
217	C₂²×C₄²	—	47	1	no	—
218	C₂²×C₄²	—	47	2	no	—
219	C₄×C₄⋊C₄	—	94	2	no	—
220	C₄×C₄⋊C₄	—	94	2	no	—
221	C₂×#95	—	47	2	no	—
222	#343	—	47	4	no	—
223	#343	—	94	4	no	—
224	#343	Dic₄₇	1	4	yes	complemented
225	#336	—	94	2	no	—
226	#336	—	94	2	no	—
227	C₄₇	#10802	1	1	yes	characteristic, complemented, Sylow
228	C₂³×C₄	—	47	1	no	—
229	C₂³×C₄	—	47	2	no	—
230	C₂³×C₄	—	47	1	no	—
231	C₂³×C₄	C₄×D₄₇	1	2	yes	—
232	C₂³×C₄	C₂²×D₄₇	1	1	yes	characteristic
233	C₂×M₁₆	—	2	2	no	—
234	C₂×M₁₆	—	2	2	no	—
235	C₂×M₁₆	—	2	2	no	—
236	C₂×M₁₆	—	2	2	no	—
237	C₂×M₁₆	—	2	2	no	—
238	C₂×M₁₆	—	47	4	no	—
239	C₂×M₁₆	—	94	2	no	—
240	C₂×M₁₆	—	94	2	no	—
241	C₂×M₁₆	—	94	2	no	—
242	C₂×M₁₆	—	94	2	no	—
243	C₂×M₁₆	—	94	2	no	—
244	C₂×M₁₆	C₂×Dic₄₇	1	4	yes	—
245	C₂²×C₈	—	2	2	no	—
246	C₂²×C₈	—	94	2	no	—
247	C₂×C₄⋊C₄	—	2	2	no	—
248	C₂×C₄⋊C₄	—	2	2	no	—
249	C₂×C₄⋊C₄	—	47	2	no	—
250	C₂×C₄⋊C₄	—	47	2	no	—
251	C₂×C₄⋊C₄	—	94	2	no	—
252	C₂×C₄⋊C₄	—	94	2	no	—
253	C₂×C₄⋊C₄	C₄×D₄₇	1	2	yes	—
254	C₂×C₄⋊C₄	C₂×Dic₄₇	1	2	yes	—
255	C₂×C₄²	—	47	2	no	—
256	C₂×C₄²	—	47	2	no	—
257	C₂×C₄²	—	94	2	no	—
258	C₂×C₄²	—	94	1	no	—
259	C₂×C₄²	—	94	1	no	—
260	C₂×C₄²	—	94	2	no	—
261	C₂×C₄²	—	94	2	no	—
262	C₂×C₄²	—	188	4	no	—
263	#95	—	94	4	no	—
264	C₂⁴	C₂×C₄×D₄₇	1	1	yes	characteristic
265	C₂²×C₄	—	2	2	no	—
266	C₂²×C₄	—	2	2	no	—
267	C₂²×C₄	—	4	2	no	—
268	C₂²×C₄	—	4	2	no	—
269	C₂²×C₄	—	47	1	no	—
270	C₂²×C₄	—	47	1	no	—
271	C₂²×C₄	—	47	2	no	—
272	C₂²×C₄	—	47	4	no	—
273	C₂²×C₄	—	94	2	no	—
274	C₂²×C₄	—	94	2	no	—
275	C₂²×C₄	—	94	1	no	—
276	C₂²×C₄	—	94	1	no	—
277	C₂²×C₄	—	94	2	no	—
278	C₂²×C₄	—	94	1	no	—
279	C₂²×C₄	—	94	2	no	—
280	C₂²×C₄	—	94	1	no	—
281	C₂²×C₄	—	188	1	no	—
282	C₂²×C₄	—	188	1	no	—
283	C₂²×C₄	—	188	2	no	—
284	C₂²×C₄	—	188	2	no	—
285	C₂²×C₄	C₄×Dic₄₇	1	4	yes	—
286	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
287	C₂²×C₄	#10625350	1	2	yes	—
288	C₂²×C₄	#10625350	1	2	yes	—
289	C₂²×C₄	D₄×D₄₇	1	2	yes	—
290	C₂²×C₄	D₄×D₄₇	1	1	yes	characteristic
291	C₂²×C₄	#10625352	1	2	yes	—
292	C₂²×C₄	#10625352	1	1	yes	characteristic
293	C₂²×C₄	Q₈×D₄₇	1	1	yes	characteristic
294	C₂²×C₄	#10625354	1	1	yes	characteristic
295	C₂²×C₄	C₂²×Dic₄₇	1	1	yes	characteristic
296	M₁₆	—	2	4	no	—
297	M₁₆	—	2	4	no	—
298	M₁₆	—	4	2	no	—
299	M₁₆	—	4	2	no	—
300	M₁₆	—	94	4	no	—
301	M₁₆	—	94	4	no	—
302	M₁₆	—	188	2	no	—
303	M₁₆	—	188	2	no	—
304	C₂×C₈	—	2	4	no	—
305	C₂×C₈	—	4	2	no	—
306	C₂×C₈	—	4	2	no	—
307	C₂×C₈	—	94	4	no	—
308	C₂×C₈	—	188	2	no	—
309	C₂×C₈	—	188	2	no	—
310	C₄⋊C₄	—	2	4	no	—
311	C₄⋊C₄	—	2	4	no	—
312	C₄⋊C₄	—	94	4	no	—
313	C₄⋊C₄	—	94	4	no	—
314	C₄²	—	94	2	no	—
315	C₄²	—	94	2	no	—
316	C₄²	—	94	2	no	—
317	C₄²	—	94	2	no	—
318	C₄²	—	188	4	no	—
319	C₄²	—	188	4	no	—
320	C₂³	—	2	1	no	—
321	C₂³	—	2	1	no	—
322	C₂³	—	2	1	no	—
323	C₂³	—	2	1	no	—
324	C₂³	C₂×C₄×Dic₄₇	1	1	yes	characteristic
325	C₂³	C₂²⋊C₄×D₄₇	1	1	yes	characteristic
326	C₂³	C₄⋊C₄×D₄₇	1	1	yes	characteristic
327	C₂³	#13093980	1	1	yes	characteristic
328	C₂³	#13093981	1	1	yes	characteristic
329	C₂³	#13093981	1	1	yes	characteristic
330	C₂³	#13093982	1	1	yes	characteristic
331	C₂×C₄	—	2	4	no	—
332	C₂×C₄	—	4	4	no	—
333	C₂×C₄	—	4	2	no	—
334	C₂×C₄	—	4	2	no	—
335	C₂×C₄	—	4	4	no	—
336	C₂×C₄	—	47	2	no	—
337	C₂×C₄	—	47	2	no	—
338	C₂×C₄	—	94	4	no	—
339	C₂×C₄	—	94	4	no	—
340	C₂×C₄	—	94	1	no	—
341	C₂×C₄	—	94	1	no	—
342	C₂×C₄	—	94	1	no	—
343	C₂×C₄	—	94	1	no	—
344	C₂×C₄	—	94	4	no	—
345	C₂×C₄	—	94	2	no	—
346	C₂×C₄	—	94	2	no	—
347	C₂×C₄	—	94	2	no	—
348	C₂×C₄	—	188	2	no	—
349	C₂×C₄	—	188	2	no	—
350	C₂×C₄	—	188	4	no	—
351	C₂×C₄	—	188	2	no	—
352	C₂×C₄	—	188	2	no	—
353	C₂×C₄	—	188	4	no	—
354	C₂×C₄	#13093981	1	2	yes	—
355	C₂×C₄	#13093983	1	2	yes	—
356	C₂×C₄	(C₂²⋊D₄₇)⋊C₄	1	2	yes	—
357	C₂×C₄	#13093986	1	1	yes	characteristic
358	C₂×C₄	D₄×Dic₄₇	1	2	yes	—
359	C₂×C₄	D₄×Dic₄₇	1	1	yes	characteristic
360	C₂×C₄	#13093989	1	1	yes	characteristic
361	C₂×C₄	Q₈×Dic₄₇	1	1	yes	characteristic
362	C₂×C₄	#13093997	1	2	yes	—
363	C₂×C₄	#13094002	1	2	yes	—
364	C₂×C₄	#13094006	1	2	yes	—
365	C₂×C₄	#13094009	1	2	yes	—
366	C₂×C₄	#13094010	1	2	yes	—
367	C₂×C₄	#13094014	1	2	yes	—
368	C₂×C₄	#13094017	1	2	yes	—
369	C₂×C₄	#13094019	1	2	yes	—
370	C₈	—	4	4	no	—
371	C₈	—	188	4	no	—
372	C₂²	—	2	1	no	—
373	C₂²	—	2	1	no	—
374	C₂²	—	2	1	no	—
375	C₂²	—	2	1	no	—
376	C₂²	—	2	1	no	—
377	C₂²	—	2	1	no	—
378	C₂²	—	2	1	no	—
379	C₂²	—	2	1	no	—
380	C₂²	—	2	1	no	—
381	C₂²	—	2	1	no	—
382	C₂²	—	2	1	no	—
383	C₂²	—	2	1	no	—
384	C₂²	#15688969	1	1	yes	characteristic
385	C₂²	C₂²⋊C₄×Dic₄₇	1	1	yes	characteristic
386	C₂²	C₄⋊C₄×Dic₄₇	1	1	yes	characteristic
387	C₂²	#15688982	1	1	yes	characteristic
388	C₂²	#15688985	1	1	yes	characteristic
389	C₂²	#15688987	1	1	yes	characteristic
390	C₂²	#15688990	1	1	yes	characteristic
391	C₂²	#100×D₄₇	1	1	yes	characteristic
392	C₂²	#101×D₄₇	1	1	yes	characteristic
393	C₂²	#15689104	1	1	yes	characteristic
394	C₂²	#15689106	1	1	yes	characteristic
395	C₄	—	4	4	no	—
396	C₄	—	94	2	no	—
397	C₄	—	94	2	no	—
398	C₄	—	188	2	no	—
399	C₄	—	188	4	no	—
400	C₄	#15689005	1	2	yes	—
401	C₄	#15689009	1	2	yes	—
402	C₄	#15689012	1	2	yes	—
403	C₄	#15689016	1	2	yes	—
404	C₂	—	2	1	no	—
405	C₂	—	2	1	no	—
406	C₂	—	2	1	no	—
407	C₂	—	2	1	no	—
408	C₂	#20241613	1	1	yes	characteristic
409	C₂	#100×Dic₄₇	1	1	yes	characteristic
410	C₂	#101×Dic₄₇	1	1	yes	characteristic
411	C₂	#20243379	1	1	yes	characteristic
412	C₂	#20243383	1	1	yes	characteristic
413	C₂	#20243467	1	1	yes	characteristic
414	C₂	#20243470	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	C₂²⋊C₄×D₄₇
commutator	C₂³×C₄₇	C₂×C₄²
Frattini	C₂³×C₄	C₂²×D₄₇
Fitting	C₂×C₄₇×#343	C₂
socle	C₂³×C₄₇	C₂×C₂²⋊C₄
prime radical	C₂⁴×C₄₇	C₂²×C₄
cosocle	C₂³×C₄×C₄₇	C₂³
hypercenter	C₂×#343	D₄₇
hypocenter	C₄₇	#10802
LCS	G ▷ C₂³×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂³ ◁ C₂³×C₄ ◁ C₂×#343

Complements

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

N	H ≅ G/N	type
13. #15688892	C₄	semidirect
19. C₄₇×#343	C₄	semidirect
224. #343	Dic₄₇	semidirect
227. C₄₇	#10802	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₄⋊C₄×Dic₄₇	2
C₂×#15688892	2
C₂×#15688891	2
#20243081	2
C₂×C₄₇×#343	2
#10802	47