Subgroups — #26219803

Order 12032.

906 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×#15689172	C₂	1	1	yes	maximal, characteristic
2	C₂×#15689171	C₂	1	1	yes	maximal, characteristic
3	C₂×#15689146	C₂	1	1	yes	maximal, characteristic
4	C₂×#15689146	C₂	1	1	yes	maximal, characteristic
5	C₂×M₁₆×Dic₄₇	C₂	1	1	yes	maximal, characteristic
6	#20244162	C₂	1	8	yes	maximal, complemented
7	#20243114	C₂	1	1	yes	maximal, characteristic
8	C₄₇×#1738	C₂	1	1	yes	maximal, characteristic
9	C₂²×#10625329	C₂²	1	1	yes	characteristic
10	C₂²×#10625329	C₂²	1	1	yes	characteristic
11	C₂²×#10625329	C₂²	1	1	yes	characteristic
12	C₂²×C₄×Dic₄₇	C₂²	1	1	yes	characteristic
13	#15689172	—	2	4	no	—
14	#15689171	—	2	4	no	—
15	C₂×#13093960	C₂²	1	4	yes	—
16	C₂×#13093959	C₂²	1	4	yes	—
17	#15689146	—	2	1	no	—
18	#15689146	—	2	1	no	—
19	#15689146	C₄	1	2	yes	—
20	#15689146	C₄	1	4	yes	—
21	#15689146	C₄	1	2	yes	—
22	#15689146	C₂²	1	4	yes	—
23	C₂×Dic₄₇⋊C₈	—	2	2	no	—
24	C₂×Dic₄₇⋊C₈	C₂²	1	4	yes	—
25	M₁₆×Dic₄₇	—	2	2	no	—
26	M₁₆×Dic₄₇	C₂²	1	4	yes	—
27	C₂×#13093934	—	2	1	no	—
28	C₂×C₈×Dic₄₇	—	2	1	no	—
29	#15688887	C₂²	1	4	yes	—
30	C₂²×M₁₆×C₄₇	C₂²	1	1	yes	characteristic
31	C₂²×M₁₆×C₄₇	C₂²	1	1	yes	characteristic
32	C₂²×M₁₆×C₄₇	C₂²	1	1	yes	characteristic
33	C₄₇×#341	C₂²	1	4	yes	—
34	C₂³×Dic₄₇	Q₈	1	2	yes	—
35	C₂×#10625329	—	2	1	no	—
36	C₂×#10625329	—	2	2	no	—
37	C₂×#10625329	—	2	2	no	—
38	C₂×#10625329	—	2	2	no	—
39	C₂×#10625329	—	2	1	no	—
40	C₂×#10625329	—	2	2	no	—
41	C₂×#10625329	—	2	2	no	—
42	C₂×#10625329	C₂×C₄	1	2	yes	—
43	C₂×#10625329	C₂×C₄	1	2	yes	—
44	C₂×#10625329	D₄	1	4	yes	—
45	C₂×#10625329	C₂³	1	2	yes	—
46	C₂×#10625329	C₂³	1	2	yes	—
47	C₂²×C₄₇⋊C₈	—	2	1	no	—
48	C₂²×C₄₇⋊C₈	—	2	1	no	—
49	C₂²×C₄₇⋊C₈	C₂³	1	2	yes	—
50	C₂×C₄×Dic₄₇	C₂×C₄	1	1	yes	characteristic
51	C₂×C₄×Dic₄₇	C₂×C₄	1	2	yes	—
52	C₂×C₄×Dic₄₇	C₂×C₄	1	1	yes	characteristic
53	C₂×C₄×Dic₄₇	D₄	1	1	yes	characteristic
54	C₂×C₄×Dic₄₇	D₄	1	1	yes	characteristic
55	C₂×C₄×Dic₄₇	D₄	1	2	yes	—
56	C₂×C₄×Dic₄₇	Q₈	1	1	yes	characteristic
57	C₂×C₄×Dic₄₇	Q₈	1	1	yes	characteristic
58	C₂×C₄×Dic₄₇	C₂³	1	2	yes	—
59	#13093960	—	2	8	no	—
60	#13093959	—	2	8	no	—
61	Dic₄₇⋊C₈	—	2	4	no	—
62	Dic₄₇⋊C₈	—	2	4	no	—
63	Dic₄₇⋊C₈	C₂×C₄	1	8	yes	—
64	Dic₄₇⋊C₈	C₂×C₄	1	8	yes	—
65	#13093934	—	2	4	no	—
66	C₈×Dic₄₇	—	2	4	no	—
67	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
68	C₂×M₁₆×C₄₇	—	2	1	no	—
69	C₂×M₁₆×C₄₇	—	2	2	no	—
70	C₂×M₁₆×C₄₇	—	2	2	no	—
71	C₂×M₁₆×C₄₇	—	2	2	no	—
72	C₂×M₁₆×C₄₇	—	2	1	no	—
73	C₂×M₁₆×C₄₇	—	2	2	no	—
74	C₂×M₁₆×C₄₇	—	2	2	no	—
75	C₂×M₁₆×C₄₇	C₂×C₄	1	2	yes	—
76	C₂×M₁₆×C₄₇	C₂×C₄	1	2	yes	—
77	C₂×M₁₆×C₄₇	Q₈	1	4	yes	—
78	C₂×M₁₆×C₄₇	C₂³	1	2	yes	—
79	C₂×M₁₆×C₄₇	C₂³	1	2	yes	—
80	C₂²×C₈×C₄₇	—	2	1	no	—
81	C₂²×C₈×C₄₇	—	2	1	no	—
82	C₂²×C₈×C₄₇	C₂³	1	2	yes	—
83	C₂⁴×C₄₇	C₂×Q₈	1	1	yes	characteristic
84	C₂²×C₄×C₄₇	C₂²×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×D₄	1	1	yes	characteristic
88	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
89	C₂²×C₄×C₄₇	C₂×Q₈	1	1	yes	characteristic
90	C₂²×C₄×C₄₇	C₂×Q₈	1	2	yes	—
91	C₂²×C₄×C₄₇	#41	1	2	yes	—
92	C₂²×C₄×C₄₇	#41	1	2	yes	—
93	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
94	C₂²×Dic₄₇	—	4	4	no	—
95	C₂²×Dic₄₇	C₄⋊C₄	1	2	yes	—
96	C₂²×Dic₄₇	C₄⋊C₄	1	2	yes	—
97	C₂²×Dic₄₇	C₄⋊C₄	1	2	yes	—
98	C₂²×Dic₄₇	C₄⋊C₄	1	2	yes	—
99	C₂²×Dic₄₇	C₂×Q₈	1	2	yes	—
100	C₂²×Dic₄₇	C₂×Q₈	1	2	yes	—
101	M₁₆×C₄₇	—	2	4	no	—
102	M₁₆×C₄₇	—	2	4	no	—
103	M₁₆×C₄₇	—	2	4	no	—
104	M₁₆×C₄₇	—	2	2	no	—
105	M₁₆×C₄₇	—	2	2	no	—
106	M₁₆×C₄₇	—	2	2	no	—
107	M₁₆×C₄₇	—	4	2	no	—
108	M₁₆×C₄₇	C₂×Q₈	1	4	yes	—
109	C₂×C₈×C₄₇	—	2	4	no	—
110	C₂×C₈×C₄₇	—	2	2	no	—
111	C₂×C₈×C₄₇	—	2	2	no	—
112	C₂×C₈×C₄₇	—	2	2	no	—
113	C₂×C₈×C₄₇	—	2	2	no	—
114	C₂×C₈×C₄₇	—	4	2	no	—
115	C₂×C₈×C₄₇	C₂²×C₄	1	4	yes	—
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	2	yes	—
120	C₄×Dic₄₇	C₄⋊C₄	1	2	yes	—
121	C₄×Dic₄₇	C₄⋊C₄	1	1	yes	characteristic
122	C₄×Dic₄₇	C₂²×C₄	1	2	yes	—
123	C₄×Dic₄₇	C₂²×C₄	1	2	yes	—
124	C₄×Dic₄₇	C₂×D₄	1	2	yes	—
125	C₄×Dic₄₇	C₂×D₄	1	2	yes	—
126	#10625329	—	2	4	no	—
127	#10625329	—	2	4	no	—
128	#10625329	—	2	4	no	—
129	#10625329	—	2	2	no	—
130	#10625329	—	2	2	no	—
131	#10625329	—	2	2	no	—
132	#10625329	—	4	2	no	—
133	#10625329	C₂×D₄	1	4	yes	—
134	C₂×C₄₇⋊C₈	—	2	4	no	—
135	C₂×C₄₇⋊C₈	—	2	2	no	—
136	C₂×C₄₇⋊C₈	—	2	2	no	—
137	C₂×C₄₇⋊C₈	—	2	2	no	—
138	C₂×C₄₇⋊C₈	—	2	2	no	—
139	C₂×C₄₇⋊C₈	—	4	2	no	—
140	C₂×C₄₇⋊C₈	C₂²×C₄	1	4	yes	—
141	C₂³×C₄₇	—	4	2	no	—
142	C₂³×C₄₇	C₂×C₄⋊C₄	1	1	yes	characteristic
143	C₂³×C₄₇	C₂×C₄⋊C₄	1	1	yes	characteristic
144	C₂³×C₄₇	#125	1	2	yes	—
145	C₂³×C₄₇	C₄⋊Q₈	1	2	yes	—
146	C₂³×C₄₇	C₂²×Q₈	1	1	yes	characteristic
147	C₂×C₄×C₄₇	C₂×C₄⋊C₄	1	1	yes	characteristic
148	C₂×C₄×C₄₇	C₂×C₄⋊C₄	1	1	yes	characteristic
149	C₂×C₄×C₄₇	C₄×D₄	1	2	yes	—
150	C₂×C₄×C₄₇	C₄×D₄	1	2	yes	—
151	C₂×C₄×C₄₇	C₄×Q₈	1	2	yes	—
152	C₂×C₄×C₄₇	C₄×Q₈	1	2	yes	—
153	C₂×C₄×C₄₇	#121	1	2	yes	—
154	C₂×C₄×C₄₇	#121	1	2	yes	—
155	C₂×C₄×C₄₇	C₂²⋊Q₈	1	2	yes	—
156	C₂×C₄×C₄₇	C₂²⋊Q₈	1	2	yes	—
157	C₂×C₄×C₄₇	#125	1	2	yes	—
158	C₂×C₄×C₄₇	C₄⋊Q₈	1	2	yes	—
159	C₂×C₄×C₄₇	C₂³×C₄	1	1	yes	characteristic
160	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
161	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
162	C₂×C₄×C₄₇	C₂²×Q₈	1	1	yes	characteristic
163	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
164	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
165	C₂×Dic₄₇	—	2	4	no	—
166	C₂×Dic₄₇	—	2	4	no	—
167	C₂×Dic₄₇	—	2	4	no	—
168	C₂×Dic₄₇	—	4	2	no	—
169	C₂×Dic₄₇	—	4	2	no	—
170	C₂×Dic₄₇	—	4	2	no	—
171	C₂×Dic₄₇	C₂×C₄⋊C₄	1	2	yes	—
172	C₂×Dic₄₇	C₂×C₄⋊C₄	1	2	yes	—
173	C₂×Dic₄₇	C₂×C₄⋊C₄	1	2	yes	—
174	C₂×Dic₄₇	C₂×C₄⋊C₄	1	2	yes	—
175	C₈×C₄₇	—	2	4	no	—
176	C₈×C₄₇	—	2	4	no	—
177	C₈×C₄₇	—	4	2	no	—
178	C₄₇⋊C₈	—	2	4	no	—
179	C₄₇⋊C₈	—	2	4	no	—
180	C₄₇⋊C₈	—	4	2	no	—
181	#21177	—	47	1	no	maximal, Sylow
182	C₂²×C₄₇	—	2	2	no	—
183	C₂²×C₄₇	—	2	2	no	—
184	C₂²×C₄₇	—	2	2	no	—
185	C₂²×C₄₇	—	4	2	no	—
186	C₂²×C₄₇	—	4	2	no	—
187	C₂²×C₄₇	#389	1	2	yes	—
188	C₂²×C₄₇	#389	1	2	yes	—
189	C₂²×C₄₇	C₂²×C₄⋊C₄	1	1	yes	characteristic
190	C₂²×C₄₇	C₂×#125	1	1	yes	characteristic
191	C₂²×C₄₇	C₂×C₄⋊Q₈	1	1	yes	characteristic
192	C₄×C₄₇	#389	1	2	yes	—
193	C₄×C₄₇	#389	1	2	yes	—
194	C₄×C₄₇	C₂×C₄×D₄	1	1	yes	characteristic
195	C₄×C₄₇	C₂×C₄×Q₈	1	1	yes	characteristic
196	C₄×C₄₇	C₂×#121	1	1	yes	characteristic
197	C₄×C₄₇	C₂×C₂²⋊Q₈	1	1	yes	characteristic
198	Dic₄₇	—	2	2	no	—
199	Dic₄₇	—	2	2	no	—
200	Dic₄₇	—	2	2	no	—
201	Dic₄₇	#430	1	4	yes	complemented
202	C₂×#430	—	47	1	no	—
203	C₂×#430	—	47	1	no	—
204	C₂×#423	—	47	1	no	—
205	C₂×#423	—	47	1	no	—
206	C₂×C₄×M₁₆	—	47	1	no	—
207	#1950	—	47	8	no	—
208	#1738	—	47	1	no	—
209	#1738	D₄₇	1	1	yes	characteristic
210	C₂×C₄₇	—	2	1	no	—
211	C₂×C₄₇	—	2	1	no	—
212	C₂×C₄₇	—	2	2	no	—
213	C₂×C₄₇	—	2	2	no	—
214	C₂×C₄₇	C₂×#389	1	1	yes	characteristic
215	C₂×C₄₇	C₂×#430	1	2	yes	—
216	C₂²×M₁₆	—	47	1	no	—
217	C₂²×M₁₆	—	47	1	no	—
218	C₂²×M₁₆	—	47	1	no	—
219	C₂²×M₁₆	C₂×D₄₇	1	1	yes	characteristic
220	C₂²×M₁₆	C₂×D₄₇	1	1	yes	characteristic
221	C₂²×M₁₆	C₂×D₄₇	1	1	yes	characteristic
222	C₂²×C₄²	—	47	1	no	—
223	#430	—	94	4	no	—
224	#430	—	94	4	no	—
225	C₂×#108	—	47	4	no	—
226	C₂×#108	—	47	4	no	—
227	#423	—	47	2	no	—
228	#423	—	47	4	no	—
229	#423	—	47	2	no	—
230	#423	—	47	4	no	—
231	#423	—	94	1	no	—
232	#423	—	94	1	no	—
233	C₂×C₄⋊C₈	—	47	4	no	—
234	C₂×C₄⋊C₈	—	94	2	no	—
235	C₄×M₁₆	—	47	4	no	—
236	C₄×M₁₆	—	94	2	no	—
237	C₂×#97	—	94	1	no	—
238	C₂×C₄×C₈	—	94	1	no	—
239	#341	—	47	4	no	—
240	#341	C₂×D₄₇	1	4	yes	—
241	C₄₇	#21177	1	1	yes	characteristic, complemented, Sylow
242	C₂³×C₄	—	47	2	no	—
243	C₂³×C₄	C₂²×D₄₇	1	1	yes	characteristic
244	C₂×M₁₆	—	2	1	no	—
245	C₂×M₁₆	—	2	2	no	—
246	C₂×M₁₆	—	2	2	no	—
247	C₂×M₁₆	—	2	2	no	—
248	C₂×M₁₆	—	2	1	no	—
249	C₂×M₁₆	—	2	2	no	—
250	C₂×M₁₆	—	2	2	no	—
251	C₂×M₁₆	—	47	2	no	—
252	C₂×M₁₆	—	47	2	no	—
253	C₂×M₁₆	—	47	4	no	—
254	C₂×M₁₆	—	47	2	no	—
255	C₂×M₁₆	—	47	2	no	—
256	C₂×M₁₆	—	94	2	no	—
257	C₂×M₁₆	—	94	1	no	—
258	C₂×M₁₆	—	94	2	no	—
259	C₂×M₁₆	—	94	2	no	—
260	C₂×M₁₆	—	94	1	no	—
261	C₂×M₁₆	—	94	2	no	—
262	C₂×M₁₆	—	94	2	no	—
263	C₂×M₁₆	Dic₉₄	1	4	yes	—
264	C₂×M₁₆	C₄×D₄₇	1	2	yes	—
265	C₂×M₁₆	C₄×D₄₇	1	2	yes	—
266	C₂×M₁₆	C₂²×D₄₇	1	2	yes	—
267	C₂×M₁₆	C₂²×D₄₇	1	2	yes	—
268	C₂²×C₈	—	2	1	no	—
269	C₂²×C₈	—	2	1	no	—
270	C₂²×C₈	—	47	2	no	—
271	C₂²×C₈	—	94	1	no	—
272	C₂²×C₈	—	94	1	no	—
273	C₂²×C₈	C₂²×D₄₇	1	2	yes	—
274	C₂×C₄²	—	47	1	no	—
275	C₂×C₄²	—	47	2	no	—
276	C₂×C₄²	—	47	1	no	—
277	C₂×C₄²	—	47	1	no	—
278	C₂×C₄²	—	47	1	no	—
279	C₂×C₄²	—	47	2	no	—
280	C₂×C₄²	—	47	1	no	—
281	C₂×C₄²	—	47	1	no	—
282	C₂×C₄²	—	47	2	no	—
283	#108	—	94	8	no	—
284	#108	—	94	8	no	—
285	C₄⋊C₈	—	47	8	no	—
286	C₄⋊C₈	—	47	8	no	—
287	C₄⋊C₈	—	94	4	no	—
288	C₄⋊C₈	—	94	4	no	—
289	#97	—	94	4	no	—
290	C₄×C₈	—	94	4	no	—
291	C₂⁴	Q₈×D₄₇	1	1	yes	characteristic
292	C₂²×C₄	—	47	2	no	—
293	C₂²×C₄	—	47	2	no	—
294	C₂²×C₄	—	47	2	no	—
295	C₂²×C₄	—	47	2	no	—
296	C₂²×C₄	—	47	2	no	—
297	C₂²×C₄	—	47	2	no	—
298	C₂²×C₄	—	188	4	no	—
299	C₂²×C₄	C₂×Dic₉₄	1	2	yes	—
300	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
301	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
302	C₂²×C₄	#10625350	1	2	yes	—
303	C₂²×C₄	D₄×D₄₇	1	1	yes	characteristic
304	C₂²×C₄	D₄×D₄₇	1	1	yes	characteristic
305	C₂²×C₄	D₄×D₄₇	1	2	yes	—
306	C₂²×C₄	#10625352	1	2	yes	—
307	C₂²×C₄	Q₈×D₄₇	1	1	yes	characteristic
308	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
309	M₁₆	—	2	4	no	—
310	M₁₆	—	2	4	no	—
311	M₁₆	—	2	4	no	—
312	M₁₆	—	2	2	no	—
313	M₁₆	—	2	2	no	—
314	M₁₆	—	2	2	no	—
315	M₁₆	—	4	2	no	—
316	M₁₆	—	47	4	no	—
317	M₁₆	—	94	4	no	—
318	M₁₆	—	94	4	no	—
319	M₁₆	—	94	4	no	—
320	M₁₆	—	94	2	no	—
321	M₁₆	—	94	2	no	—
322	M₁₆	—	94	2	no	—
323	M₁₆	—	188	2	no	—
324	M₁₆	C₂×Dic₉₄	1	4	yes	—
325	C₂×C₈	—	2	4	no	—
326	C₂×C₈	—	2	2	no	—
327	C₂×C₈	—	2	2	no	—
328	C₂×C₈	—	2	2	no	—
329	C₂×C₈	—	2	2	no	—
330	C₂×C₈	—	4	2	no	—
331	C₂×C₈	—	47	4	no	—
332	C₂×C₈	—	94	4	no	—
333	C₂×C₈	—	94	2	no	—
334	C₂×C₈	—	94	2	no	—
335	C₂×C₈	—	94	2	no	—
336	C₂×C₈	—	94	2	no	—
337	C₂×C₈	—	188	2	no	—
338	C₂×C₈	C₂×C₄×D₄₇	1	4	yes	—
339	C₄²	—	47	1	no	—
340	C₄²	—	47	2	no	—
341	C₄²	—	47	1	no	—
342	C₄²	—	47	1	no	—
343	C₄²	—	47	1	no	—
344	C₄²	—	47	2	no	—
345	C₄²	—	47	2	no	—
346	C₄²	—	47	2	no	—
347	C₄²	—	47	2	no	—
348	C₄²	—	47	2	no	—
349	C₂³	—	4	2	no	—
350	C₂³	C₄⋊C₄×D₄₇	1	1	yes	characteristic
351	C₂³	C₄⋊C₄×D₄₇	1	1	yes	characteristic
352	C₂³	#13094014	1	2	yes	—
353	C₂³	#13094023	1	2	yes	—
354	C₂³	C₂×Q₈×D₄₇	1	1	yes	characteristic
355	C₂×C₄	—	47	2	no	—
356	C₂×C₄	—	47	2	no	—
357	C₂×C₄	—	47	2	no	—
358	C₂×C₄	—	47	2	no	—
359	C₂×C₄	—	94	4	no	—
360	C₂×C₄	—	94	4	no	—
361	C₂×C₄	—	94	4	no	—
362	C₂×C₄	—	188	2	no	—
363	C₂×C₄	—	188	2	no	—
364	C₂×C₄	—	188	2	no	—
365	C₂×C₄	C₄⋊C₄×D₄₇	1	1	yes	characteristic
366	C₂×C₄	C₄⋊C₄×D₄₇	1	1	yes	characteristic
367	C₂×C₄	(C₂²⋊D₄₇)⋊C₄	1	2	yes	—
368	C₂×C₄	(C₂²⋊D₄₇)⋊C₄	1	2	yes	—
369	C₂×C₄	C₄×Dic₉₄	1	2	yes	—
370	C₂×C₄	C₄×Dic₉₄	1	2	yes	—
371	C₂×C₄	#13093997	1	2	yes	—
372	C₂×C₄	#13093997	1	2	yes	—
373	C₂×C₄	#13094001	1	2	yes	—
374	C₂×C₄	#13094001	1	2	yes	—
375	C₂×C₄	#13094014	1	2	yes	—
376	C₂×C₄	#13094023	1	2	yes	—
377	C₂×C₄	C₂²×C₄×D₄₇	1	1	yes	characteristic
378	C₂×C₄	C₂×D₄×D₄₇	1	1	yes	characteristic
379	C₂×C₄	C₂×D₄×D₄₇	1	1	yes	characteristic
380	C₂×C₄	C₂²×Dic₉₄	1	1	yes	characteristic
381	C₂×C₄	C₂×#10625352	1	1	yes	characteristic
382	C₂×C₄	C₂×#10625350	1	1	yes	characteristic
383	C₈	—	2	4	no	—
384	C₈	—	2	4	no	—
385	C₈	—	4	2	no	—
386	C₈	—	94	4	no	—
387	C₈	—	94	4	no	—
388	C₈	—	188	2	no	—
389	C₂²	—	2	2	no	—
390	C₂²	—	2	2	no	—
391	C₂²	—	2	2	no	—
392	C₂²	—	4	2	no	—
393	C₂²	—	4	2	no	—
394	C₂²	#15689020	1	2	yes	—
395	C₂²	#15689020	1	2	yes	—
396	C₂²	C₂×C₄⋊C₄×D₄₇	1	1	yes	characteristic
397	C₂²	C₂×#13094014	1	1	yes	characteristic
398	C₂²	C₂×#13094023	1	1	yes	characteristic
399	C₄	—	47	4	no	—
400	C₄	—	94	2	no	—
401	C₄	—	94	2	no	—
402	C₄	—	94	2	no	—
403	C₄	#15689020	1	2	yes	—
404	C₄	#15689020	1	2	yes	—
405	C₄	C₂×(C₂²⋊D₄₇)⋊C₄	1	1	yes	characteristic
406	C₄	C₂×C₄×Dic₉₄	1	1	yes	characteristic
407	C₄	C₂×#13093997	1	1	yes	characteristic
408	C₄	C₂×#13094001	1	1	yes	characteristic
409	C₂	—	2	2	no	—
410	C₂	—	2	2	no	—
411	C₂	—	2	1	no	—
412	C₂	—	2	1	no	—
413	C₂	C₂×#15689020	1	1	yes	characteristic
414	C₂	#430×D₄₇	1	2	yes	—

	subgroup	G/H
center	C₂×C₄	C₂×D₄×D₄₇
commutator	C₂×C₄×C₄₇	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₄₇
Fitting	C₄₇×#1738	C₂
socle	C₂²×C₄₇	C₂²×C₄⋊C₄
prime radical	C₂⁴×C₄₇	C₂×Q₈
cosocle	C₂²×C₄×C₄₇	C₂⁴
hypercenter	#1738	D₄₇
hypocenter	C₄₇	#21177
LCS	G ▷ C₂×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂×C₄ ◁ C₂³×C₄ ◁ #1738

Complements

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

N	H ≅ G/N	type
6. #20244162	C₂	semidirect
201. Dic₄₇	#430	semidirect
241. C₄₇	#21177	semidirect

Maximal subgroups

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

subgroup	index
C₂×#15689172	2
C₂×#15689171	2
C₂×#15689146	2
C₂×M₁₆×Dic₄₇	2
#20244162	2
#20243114	2
C₄₇×#1738	2
#21177	47