Subgroups — C₄×#15689501 #26224711

Order 12032.

1086 conjugacy classes of subgroups.

The subgroup lattice has 412 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#15689501	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄×Dic₁₈₈	C₂	1	1	yes	maximal, characteristic
3	C₂×C₄×#10625337	C₂	1	2	yes	maximal
4	C₄×#13094022	C₂	1	2	yes	maximal
5	#20244250	C₂	1	1	yes	maximal, characteristic
6	#20244247	C₂	1	1	yes	maximal, characteristic
7	#20244246	C₂	1	2	yes	maximal
8	#20244188	C₂	1	2	yes	maximal
9	#20243546	C₂	1	1	yes	maximal, characteristic
10	C₄×C₈×Dic₄₇	C₂	1	1	yes	maximal, characteristic
11	C₂×C₄×Q₁₆×C₄₇	C₂	1	1	yes	maximal, characteristic
12	C₂²×Dic₁₈₈	C₂²	1	1	yes	characteristic
13	C₂²×#10625337	C₂²	1	2	yes	—
14	C₂×#13094022	C₂²	1	2	yes	—
15	C₂×C₄×Dic₉₄	C₂²	1	2	yes	—
16	#15689501	C₄	1	8	yes	direct product factor
17	C₄×Dic₁₈₈	—	2	4	no	—
18	C₄×#10625337	—	2	8	no	—
19	C₂×#13093958	C₂²	1	1	yes	characteristic
20	C₂×#13093957	C₂²	1	2	yes	—
21	C₂×#13093949	C₂²	1	2	yes	—
22	C₂×#13093948	C₂²	1	2	yes	—
23	C₂×#13093947	C₂²	1	2	yes	—
24	C₂×C₄×C₄₇⋊C₈	C₂²	1	1	yes	characteristic
25	C₂×C₈×Dic₄₇	C₂²	1	1	yes	characteristic
26	C₂×C₈×Dic₄₇	C₂²	1	1	yes	characteristic
27	C₂×C₈×Dic₄₇	C₂²	1	1	yes	characteristic
28	C₂×C₈×Dic₄₇	C₂²	1	1	yes	characteristic
29	#15689030	C₂²	1	2	yes	—
30	#15689028	C₂²	1	2	yes	—
31	#15689018	—	2	4	no	—
32	#15688992	C₂²	1	2	yes	—
33	C₄×Dic₄₇⋊C₄	—	2	4	no	—
34	C₄²×Dic₄₇	C₂²	1	1	yes	characteristic
35	C₂²×Q₁₆×C₄₇	C₂²	1	1	yes	characteristic
36	C₂×C₄×Q₈×C₄₇	C₂²	1	2	yes	—
37	C₄×Q₁₆×C₄₇	—	2	4	no	—
38	C₂×#107×C₄₇	C₂²	1	1	yes	characteristic
39	C₂×#103×C₄₇	C₂²	1	2	yes	—
40	C₂×C₄×C₈×C₄₇	C₂²	1	1	yes	characteristic
41	C₂²×Dic₉₄	C₂³	1	2	yes	—
42	C₂×Dic₁₈₈	—	2	2	no	—
43	C₂×Dic₁₈₈	—	2	2	no	—
44	C₂×Dic₁₈₈	C₂×C₄	1	4	yes	—
45	C₂×#10625337	—	2	4	no	—
46	C₂×#10625337	—	2	4	no	—
47	C₂×#10625337	C₂×C₄	1	8	yes	—
48	C₂²×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
49	C₂²×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
50	#13094022	—	2	4	no	—
51	#13094022	C₂×C₄	1	8	yes	—
52	C₄×Dic₉₄	—	2	4	no	—
53	C₄×Dic₉₄	—	2	4	no	—
54	C₂×C₄⋊Dic₄₇	C₂³	1	2	yes	—
55	C₂×Dic₄₇⋊C₄	—	2	4	no	—
56	C₂×Dic₄₇⋊C₄	—	2	2	no	—
57	C₂×Dic₄₇⋊C₄	—	2	4	no	—
58	C₂×C₄×Dic₄₇	—	2	2	no	—
59	C₂×C₄×Dic₄₇	D₄	1	2	yes	—
60	C₂×C₄×Dic₄₇	D₄	1	2	yes	—
61	C₂×C₄×Dic₄₇	C₂³	1	1	yes	characteristic
62	C₂×C₄×Dic₄₇	C₂³	1	1	yes	characteristic
63	#13093958	—	2	2	no	—
64	#13093957	—	2	4	no	—
65	#13093949	—	2	4	no	—
66	#13093948	—	2	4	no	—
67	#13093947	—	2	4	no	—
68	C₄×C₄₇⋊C₈	D₄	1	4	yes	—
69	C₈×Dic₄₇	—	2	2	no	—
70	C₈×Dic₄₇	—	2	2	no	—
71	C₈×Dic₄₇	—	2	2	no	—
72	C₈×Dic₄₇	C₂×C₄	1	4	yes	—
73	C₄₇⋊#95	—	2	4	no	—
74	C₄₇⋊#95	—	2	4	no	—
75	C₂²×Q₈×C₄₇	C₂³	1	2	yes	—
76	C₂×Q₁₆×C₄₇	—	2	2	no	—
77	C₂×Q₁₆×C₄₇	—	2	2	no	—
78	C₂×Q₁₆×C₄₇	C₂×C₄	1	4	yes	—
79	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
80	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
81	C₄×Q₈×C₄₇	—	2	4	no	—
82	C₄×Q₈×C₄₇	—	2	4	no	—
83	C₂×C₄⋊C₄×C₄₇	—	2	2	no	—
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	#107×C₄₇	—	2	2	no	—
88	#103×C₄₇	—	2	4	no	—
89	C₄×C₈×C₄₇	D₄	1	4	yes	—
90	C₂×Q₈×C₄₇	—	2	2	no	—
91	C₂×Q₈×C₄₇	—	2	2	no	—
92	C₂×Q₈×C₄₇	—	2	2	no	—
93	C₂×Q₈×C₄₇	—	2	2	no	—
94	C₂×Q₈×C₄₇	—	2	2	no	—
95	C₂×Q₈×C₄₇	C₂²×C₄	1	4	yes	—
96	C₂²×C₄×C₄₇	—	2	2	no	—
97	C₂²×C₄×C₄₇	—	2	2	no	—
98	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
99	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
100	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
101	C₂²×Dic₄₇	—	2	2	no	—
102	C₂²×Dic₄₇	—	2	2	no	—
103	C₂²×Dic₄₇	C₂×D₄	1	2	yes	—
104	C₂²×Dic₄₇	C₂×D₄	1	2	yes	—
105	C₂×Dic₉₄	—	2	2	no	—
106	C₂×Dic₉₄	—	2	2	no	—
107	C₂×Dic₉₄	—	2	2	no	—
108	C₂×Dic₉₄	—	2	2	no	—
109	C₂×Dic₉₄	—	2	2	no	—
110	C₂×Dic₉₄	C₂²×C₄	1	4	yes	—
111	Q₁₆×C₄₇	—	2	8	no	—
112	C₂×C₈×C₄₇	—	2	1	no	—
113	C₂×C₈×C₄₇	—	2	1	no	—
114	C₂×C₈×C₄₇	C₂²×C₄	1	2	yes	—
115	C₂×C₈×C₄₇	C₂×D₄	1	2	yes	—
116	C₂×C₈×C₄₇	C₂×D₄	1	2	yes	—
117	C₂×C₈×C₄₇	#41	1	2	yes	—
118	C₄⋊C₄×C₄₇	—	2	2	no	—
119	C₄⋊C₄×C₄₇	—	2	2	no	—
120	C₄⋊C₄×C₄₇	—	4	4	no	—
121	C₄²×C₄₇	—	4	4	no	—
122	C₄²×C₄₇	C₂×D₄	1	2	yes	—
123	C₄²×C₄₇	C₂×D₄	1	2	yes	—
124	#10625337	—	2	16	no	—
125	C₄⋊Dic₄₇	—	2	2	no	—
126	C₄⋊Dic₄₇	—	2	2	no	—
127	Dic₄₇⋊C₄	—	2	16	no	—
128	Dic₄₇⋊C₄	—	4	4	no	—
129	Dic₄₇⋊C₄	—	4	8	no	—
130	C₄×Dic₄₇	—	2	1	no	—
131	C₄×Dic₄₇	—	2	1	no	—
132	C₄×Dic₄₇	—	2	4	no	—
133	C₄×Dic₄₇	—	4	4	no	—
134	C₄×Dic₄₇	Q₁₆	1	8	yes	complemented
135	C₄×Dic₄₇	C₂²×C₄	1	2	yes	—
136	C₄×Dic₄₇	#41	1	2	yes	—
137	C₂×C₄₇⋊C₈	—	2	1	no	—
138	C₂×C₄₇⋊C₈	—	2	1	no	—
139	C₂×C₄₇⋊C₈	C₂²×C₄	1	2	yes	—
140	C₂×C₄₇⋊C₈	C₂×D₄	1	2	yes	—
141	C₂×C₄₇⋊C₈	C₂×D₄	1	2	yes	—
142	C₂×C₄₇⋊C₈	#41	1	2	yes	—
143	Dic₁₈₈	—	2	8	no	—
144	C₂³×C₄₇	C₂²×D₄	1	1	yes	characteristic
145	Q₈×C₄₇	—	2	4	no	—
146	Q₈×C₄₇	—	2	4	no	—
147	Q₈×C₄₇	—	4	2	no	—
148	Q₈×C₄₇	—	4	2	no	—
149	C₂×C₄×C₄₇	—	2	2	no	—
150	C₂×C₄×C₄₇	—	2	4	no	—
151	C₂×C₄×C₄₇	—	4	2	no	—
152	C₂×C₄×C₄₇	—	4	2	no	—
153	C₂×C₄×C₄₇	—	4	2	no	—
154	C₂×C₄×C₄₇	—	4	4	no	—
155	C₂×C₄×C₄₇	#127	1	2	yes	—
156	C₂×C₄×C₄₇	#127	1	2	yes	—
157	C₂×C₄×C₄₇	C₂×Q₁₆	1	4	yes	—
158	C₂×C₄×C₄₇	C₂³×C₄	1	1	yes	characteristic
159	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
160	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
161	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
162	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
163	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
164	C₂×Dic₄₇	—	2	2	no	—
165	C₂×Dic₄₇	—	2	2	no	—
166	C₂×Dic₄₇	—	2	4	no	—
167	C₂×Dic₄₇	—	4	2	no	—
168	C₂×Dic₄₇	—	4	2	no	—
169	C₂×Dic₄₇	—	4	2	no	—
170	C₂×Dic₄₇	—	4	4	no	—
171	C₂×Dic₄₇	C₄×D₄	1	4	yes	—
172	C₂×Dic₄₇	C₂×Q₁₆	1	4	yes	—
173	C₂×Dic₄₇	C₂×Q₁₆	1	4	yes	—
174	C₂×Dic₄₇	#135	1	4	yes	—
175	Dic₉₄	—	2	4	no	—
176	Dic₉₄	—	2	4	no	—
177	Dic₉₄	—	4	2	no	—
178	Dic₉₄	—	4	2	no	—
179	C₈×C₄₇	—	2	2	no	—
180	C₈×C₄₇	C₄×D₄	1	4	yes	—
181	C₄₇⋊C₈	—	2	2	no	—
182	C₄₇⋊C₈	C₄×D₄	1	4	yes	—
183	C₄×#494	—	47	1	no	maximal, Sylow
184	C₂²×C₄₇	C₂×C₄×D₄	1	1	yes	characteristic
185	C₂²×C₄₇	C₂×#127	1	1	yes	characteristic
186	C₂²×C₄₇	#532	1	1	yes	characteristic
187	C₂²×C₄₇	C₂²×Q₁₆	1	2	yes	—
188	C₂²×C₄₇	C₂×#135	1	2	yes	—
189	C₄×C₄₇	—	2	2	no	—
190	C₄×C₄₇	—	4	4	no	—
191	C₄×C₄₇	—	8	2	no	—
192	C₄×C₄₇	#494	1	4	yes	complemented
193	C₄×C₄₇	C₂×C₄×D₄	1	1	yes	characteristic
194	C₄×C₄₇	C₂×C₄×D₄	1	1	yes	characteristic
195	C₄×C₄₇	#532	1	1	yes	characteristic
196	C₄×C₄₇	#532	1	1	yes	characteristic
197	Dic₄₇	—	2	4	no	—
198	Dic₄₇	—	4	4	no	—
199	Dic₄₇	—	8	2	no	—
200	Dic₄₇	C₄×Q₁₆	1	8	yes	complemented
201	C₂×#494	—	47	1	no	—
202	C₂×C₄×Q₁₆	—	47	1	no	—
203	C₂×C₄×Q₁₆	—	47	2	no	—
204	C₂×C₄×Q₁₆	D₄₇	1	1	yes	characteristic
205	C₄×C₄⋊Q₈	—	47	2	no	—
206	#1969	—	47	1	no	—
207	#1969	—	47	2	no	—
208	#1969	—	47	1	no	—
209	#1956	—	47	2	no	—
210	#1845	—	47	1	no	—
211	C₄²×C₈	—	47	1	no	—
212	C₂×C₄₇	C₄×#127	1	1	yes	characteristic
213	C₂×C₄₇	C₂×C₄×Q₁₆	1	2	yes	—
214	C₂×C₄₇	C₂×#494	1	1	yes	characteristic
215	C₂×C₄₇	#3147	1	1	yes	characteristic
216	C₂×C₄₇	#3170	1	2	yes	—
217	C₂²×Q₁₆	—	47	2	no	—
218	C₂²×Q₁₆	—	47	1	no	—
219	C₂²×Q₁₆	C₂×D₄₇	1	1	yes	characteristic
220	C₂×C₄⋊Q₈	—	47	2	no	—
221	C₂×C₄×Q₈	—	47	2	no	—
222	C₂×C₄×Q₈	C₂×D₄₇	1	2	yes	—
223	#494	—	47	8	no	—
224	C₄×Q₁₆	—	2	4	no	—
225	C₄×Q₁₆	—	94	8	no	—
226	C₄×Q₁₆	—	94	4	no	—
227	C₂×#107	—	47	1	no	—
228	C₂×#107	—	47	2	no	—
229	C₂×#107	C₂×D₄₇	1	1	yes	characteristic
230	C₂×#103	—	47	2	no	—
231	C₂×#103	—	47	2	no	—
232	C₂×#103	—	47	2	no	—
233	C₂×#103	C₂×D₄₇	1	2	yes	—
234	C₂×C₄×C₈	—	47	1	no	—
235	C₂×C₄×C₈	—	47	1	no	—
236	C₂×C₄×C₈	—	47	1	no	—
237	C₂×C₄×C₈	—	47	1	no	—
238	C₂×C₄×C₈	—	47	1	no	—
239	C₂×C₄×C₈	C₂×D₄₇	1	1	yes	characteristic
240	#391	—	47	2	no	—
241	#391	—	47	2	no	—
242	#389	—	94	4	no	—
243	#384	—	47	2	no	—
244	C₄×C₄⋊C₄	—	94	4	no	—
245	C₄³	—	47	1	no	—
246	C₄₇	C₄×#494	1	1	yes	characteristic, complemented, Sylow
247	C₂²×Q₈	—	47	2	no	—
248	C₂²×Q₈	C₂²×D₄₇	1	2	yes	—
249	C₂×Q₁₆	—	2	2	no	—
250	C₂×Q₁₆	—	2	2	no	—
251	C₂×Q₁₆	—	47	8	no	—
252	C₂×Q₁₆	—	47	4	no	—
253	C₂×Q₁₆	—	94	4	no	—
254	C₂×Q₁₆	—	94	4	no	—
255	C₂×Q₁₆	—	94	2	no	—
256	C₂×Q₁₆	—	94	2	no	—
257	C₂×Q₁₆	C₄×D₄₇	1	4	yes	—
258	C₂²×C₈	—	47	1	no	—
259	C₂²×C₈	—	47	1	no	—
260	C₂²×C₈	C₂²×D₄₇	1	1	yes	characteristic
261	C₂²×C₈	C₂²×D₄₇	1	1	yes	characteristic
262	C₄⋊Q₈	—	47	8	no	—
263	C₄⋊Q₈	—	94	4	no	—
264	C₄×Q₈	—	2	4	no	—
265	C₄×Q₈	—	2	4	no	—
266	C₄×Q₈	—	94	4	no	—
267	C₄×Q₈	—	94	4	no	—
268	C₂×C₄⋊C₄	—	2	2	no	—
269	C₂×C₄⋊C₄	—	47	2	no	—
270	C₂×C₄⋊C₄	—	94	4	no	—
271	C₂×C₄⋊C₄	—	94	4	no	—
272	C₂×C₄⋊C₄	—	94	2	no	—
273	C₂×C₄⋊C₄	C₂²×D₄₇	1	2	yes	—
274	C₂×C₄²	—	2	2	no	—
275	C₂×C₄²	—	47	2	no	—
276	C₂×C₄²	—	47	1	no	—
277	C₂×C₄²	—	47	2	no	—
278	C₂×C₄²	—	47	1	no	—
279	C₂×C₄²	—	94	2	no	—
280	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
281	#107	—	2	2	no	—
282	#107	—	94	4	no	—
283	#107	—	94	2	no	—
284	#103	—	2	4	no	—
285	#103	—	94	4	no	—
286	#103	—	94	4	no	—
287	#103	—	94	4	no	—
288	C₄×C₈	—	47	4	no	—
289	C₄×C₈	—	47	4	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	4	yes	—
294	#95	—	94	4	no	—
295	#95	—	94	4	no	—
296	C₂×Q₈	—	2	2	no	—
297	C₂×Q₈	—	2	2	no	—
298	C₂×Q₈	—	2	2	no	—
299	C₂×Q₈	—	2	2	no	—
300	C₂×Q₈	—	2	2	no	—
301	C₂×Q₈	—	47	4	no	—
302	C₂×Q₈	—	94	2	no	—
303	C₂×Q₈	—	94	2	no	—
304	C₂×Q₈	—	94	2	no	—
305	C₂×Q₈	—	94	2	no	—
306	C₂×Q₈	—	94	2	no	—
307	C₂×Q₈	C₂×C₄×D₄₇	1	4	yes	—
308	C₂²×C₄	—	2	2	no	—
309	C₂²×C₄	—	2	2	no	—
310	C₂²×C₄	—	47	2	no	—
311	C₂²×C₄	—	47	2	no	—
312	C₂²×C₄	—	94	2	no	—
313	C₂²×C₄	—	94	2	no	—
314	C₂²×C₄	D₄×D₄₇	1	1	yes	characteristic
315	C₂²×C₄	D₄×D₄₇	1	1	yes	characteristic
316	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
317	Q₁₆	—	2	8	no	—
318	Q₁₆	—	94	16	no	—
319	Q₁₆	—	94	8	no	—
320	C₂×C₈	—	2	1	no	—
321	C₂×C₈	—	2	1	no	—
322	C₂×C₈	—	47	2	no	—
323	C₂×C₈	—	47	2	no	—
324	C₂×C₈	—	47	2	no	—
325	C₂×C₈	—	47	2	no	—
326	C₂×C₈	—	94	1	no	—
327	C₂×C₈	—	94	1	no	—
328	C₂×C₈	C₂×C₄×D₄₇	1	2	yes	—
329	C₂×C₈	#10625350	1	2	yes	—
330	C₂×C₈	C₂×C₂²⋊D₄₇	1	2	yes	—
331	C₂×C₈	C₂×C₂²⋊D₄₇	1	2	yes	—
332	C₄⋊C₄	—	2	2	no	—
333	C₄⋊C₄	—	2	2	no	—
334	C₄⋊C₄	—	4	4	no	—
335	C₄⋊C₄	—	94	16	no	—
336	C₄⋊C₄	—	94	2	no	—
337	C₄⋊C₄	—	94	2	no	—
338	C₄⋊C₄	—	188	8	no	—
339	C₄⋊C₄	—	188	4	no	—
340	C₄²	—	4	4	no	—
341	C₄²	—	47	8	no	—
342	C₄²	—	47	2	no	—
343	C₄²	—	47	2	no	—
344	C₄²	—	94	4	no	—
345	C₄²	—	94	1	no	—
346	C₄²	—	94	1	no	—
347	C₄²	—	188	4	no	—
348	C₄²	D₄×D₄₇	1	2	yes	—
349	C₄²	C₂×C₂²⋊D₄₇	1	2	yes	—
350	C₂³	C₂×D₄×D₄₇	1	1	yes	characteristic
351	Q₈	—	2	4	no	—
352	Q₈	—	2	4	no	—
353	Q₈	—	4	2	no	—
354	Q₈	—	4	2	no	—
355	Q₈	—	94	4	no	—
356	Q₈	—	94	4	no	—
357	Q₈	—	188	2	no	—
358	Q₈	—	188	2	no	—
359	C₂×C₄	—	2	2	no	—
360	C₂×C₄	—	2	4	no	—
361	C₂×C₄	—	4	2	no	—
362	C₂×C₄	—	4	2	no	—
363	C₂×C₄	—	4	4	no	—
364	C₂×C₄	—	4	2	no	—
365	C₂×C₄	—	47	4	no	—
366	C₂×C₄	—	47	4	no	—
367	C₂×C₄	—	47	4	no	—
368	C₂×C₄	—	47	4	no	—
369	C₂×C₄	—	94	2	no	—
370	C₂×C₄	—	94	2	no	—
371	C₂×C₄	—	94	4	no	—
372	C₂×C₄	—	188	4	no	—
373	C₂×C₄	—	188	2	no	—
374	C₂×C₄	—	188	2	no	—
375	C₂×C₄	—	188	2	no	—
376	C₂×C₄	#13094020	1	2	yes	—
377	C₂×C₄	#13094020	1	2	yes	—
378	C₂×C₄	Q₁₆×D₄₇	1	4	yes	—
379	C₂×C₄	C₂²×C₄×D₄₇	1	1	yes	characteristic
380	C₂×C₄	C₂×D₄×D₄₇	1	1	yes	characteristic
381	C₂×C₄	C₂²×C₂²⋊D₄₇	1	1	yes	characteristic
382	C₂×C₄	#41×D₄₇	1	1	yes	characteristic
383	C₂×C₄	#41×D₄₇	1	1	yes	characteristic
384	C₂×C₄	C₂×#10625350	1	1	yes	characteristic
385	C₈	—	2	2	no	—
386	C₈	—	47	4	no	—
387	C₈	—	94	2	no	—
388	C₈	C₄×C₂²⋊D₄₇	1	4	yes	—
389	C₂²	C₄×D₄×D₄₇	1	1	yes	characteristic
390	C₂²	C₂×#13094020	1	1	yes	characteristic
391	C₂²	#15689670	1	1	yes	characteristic
392	C₂²	C₂×Q₁₆×D₄₇	1	2	yes	—
393	C₂²	#135×D₄₇	1	2	yes	—
394	C₄	—	2	2	no	—
395	C₄	—	4	4	no	—
396	C₄	—	8	2	no	—
397	C₄	—	47	8	no	—
398	C₄	—	94	4	no	—
399	C₄	—	376	2	no	—
400	C₄	—	188	4	no	—
401	C₄	#15689501	1	4	yes	direct product factor
402	C₄	C₄×D₄×D₄₇	1	1	yes	characteristic
403	C₄	C₂×C₄×C₂²⋊D₄₇	1	1	yes	characteristic
404	C₄	#15689669	1	1	yes	characteristic
405	C₄	#15689670	1	1	yes	characteristic
406	C₂	C₄×#13094020	1	1	yes	characteristic
407	C₂	C₄×Q₁₆×D₄₇	1	2	yes	—
408	C₂	C₂×#15689501	1	1	yes	characteristic
409	C₂	#20253812	1	1	yes	characteristic
410	C₂	#20253971	1	2	yes	—

	subgroup	G/H
center	C₂²×C₄	D₄×D₄₇
commutator	C₂×C₄×C₄₇	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₄₇
Fitting	C₂×C₄×Q₁₆×C₄₇	C₂
socle, prime radical	C₂³×C₄₇	C₂²×D₄
cosocle	C₂²×C₄×C₄₇	C₂⁴
hypercenter	C₂×C₄×Q₁₆	D₄₇
hypocenter	C₄₇	C₄×#494
LCS	G ▷ C₂×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂²×C₄ ◁ C₂×C₄² ◁ C₂×C₄×Q₁₆

Complements

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

N	H ≅ G/N	type
16. #15689501	C₄	direct (N × H)
134. C₄×Dic₄₇	Q₁₆	semidirect
192. C₄×C₄₇	#494	semidirect
200. Dic₄₇	C₄×Q₁₆	semidirect
246. C₄₇	C₄×#494	semidirect
401. C₄	#15689501	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×#15689501	2
C₂×C₄×Dic₁₈₈	2
C₂×C₄×#10625337	2
C₄×#13094022	2
#20244250	2
#20244247	2
#20244246	2
#20244188	2
#20243546	2
C₄×C₈×Dic₄₇	2
C₂×C₄×Q₁₆×C₄₇	2
C₄×#494	47

Subgroups — C4×#15689501 #26224711

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄×#15689501 #26224711