Subgroups — #26186147

Order 12032.

774 conjugacy classes of subgroups.

The subgroup lattice has 408 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20252100	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×D₄×C₄₇⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
3	#20242218	C₂	1	4	yes	maximal, complemented
4	D₈×C₄₇⋊C₈	C₂	1	4	yes	maximal, complemented
5	#20242163	C₂	1	1	yes	maximal, characteristic, complemented
6	#20241813	C₂	1	1	yes	maximal, characteristic, complemented
7	#20241787	C₂	1	1	yes	maximal, characteristic, complemented
8	#20241672	C₂	1	1	yes	maximal, characteristic, complemented
9	C₄₇×#3100	C₂	1	1	yes	maximal, characteristic
10	C₂×#13094031	—	2	1	no	—
11	C₂³×C₄₇⋊C₈	—	2	1	no	—
12	#15689201	—	2	1	no	—
13	#15689201	C₂²	1	2	yes	complemented
14	D₄×C₄₇⋊C₈	—	2	1	no	—
15	D₄×C₄₇⋊C₈	—	2	1	no	—
16	D₄×C₄₇⋊C₈	—	2	1	no	—
17	D₄×C₄₇⋊C₈	C₂²	1	2	yes	—
18	D₄×C₄₇⋊C₈	C₂²	1	2	yes	—
19	D₄×C₄₇⋊C₈	C₂²	1	2	yes	complemented
20	#15689176	C₂²	1	1	yes	characteristic
21	#15689147	C₂²	1	1	yes	characteristic
22	C₂×C₄⋊(C₄₇⋊C₈)	C₂²	1	1	yes	characteristic
23	#15689090	—	2	1	no	—
24	C₂×C₂²⋊(C₄₇⋊C₈)	—	2	1	no	—
25	C₂×C₄×C₄₇⋊C₈	C₂²	1	1	yes	characteristic
26	#15688876	C₂²	1	4	yes	complemented
27	D₄⋊(C₄₇⋊C₈)	C₂²	1	4	yes	—
28	D₄⋊(C₄₇⋊C₈)	C₂²	1	4	yes	complemented
29	#15688845	C₂²	1	2	yes	complemented
30	C₈×C₄₇⋊C₈	C₂²	1	2	yes	complemented
31	C₄₇×#532	C₂²	1	1	yes	characteristic
32	C₂×C₄×D₄×C₄₇	C₂²	1	1	yes	characteristic
33	C₄₇×#480	C₄	1	2	yes	—
34	C₄₇×#474	C₄	1	2	yes	—
35	C₄₇×#459	C₄	1	2	yes	—
36	C₄₇×#447	C₄	1	2	yes	—
37	C₄×D₈×C₄₇	C₂²	1	4	yes	—
38	C₄₇×#431	C₂²	1	1	yes	characteristic
39	#13094031	—	4	4	no	—
40	C₂×#10625329	—	2	1	no	—
41	C₂×#10625329	—	2	2	no	—
42	C₂²×C₄₇⋊C₈	—	2	1	no	—
43	C₂²×C₄₇⋊C₈	—	2	2	no	—
44	C₂²×C₄₇⋊C₈	—	2	2	no	—
45	C₂²×C₄₇⋊C₈	—	2	2	no	—
46	C₂²×C₄₇⋊C₈	—	4	4	no	—
47	C₂²×C₄₇⋊C₈	D₄	1	1	yes	characteristic
48	C₂²×C₄₇⋊C₈	D₄	1	1	yes	characteristic
49	C₄⋊(C₄₇⋊C₈)	—	2	1	no	—
50	C₄⋊(C₄₇⋊C₈)	—	2	1	no	—
51	C₄⋊(C₄₇⋊C₈)	—	2	1	no	—
52	C₄⋊(C₄₇⋊C₈)	C₂³	1	2	yes	—
53	C₄⋊(C₄₇⋊C₈)	C₂³	1	2	yes	—
54	C₂²⋊(C₄₇⋊C₈)	—	2	1	no	—
55	C₂²⋊(C₄₇⋊C₈)	—	2	2	no	—
56	C₂²⋊(C₄₇⋊C₈)	—	2	2	no	—
57	C₂²⋊(C₄₇⋊C₈)	—	2	2	no	—
58	C₂²⋊(C₄₇⋊C₈)	—	2	2	no	—
59	C₄×C₄₇⋊C₈	D₄	1	1	yes	characteristic
60	C₄×C₄₇⋊C₈	D₄	1	1	yes	characteristic
61	C₄×C₄₇⋊C₈	C₂³	1	2	yes	—
62	C₄×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
63	C₄×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
64	C₂×#41×C₄₇	—	2	1	no	—
65	C₂²×D₄×C₄₇	C₂×C₄	1	1	yes	characteristic
66	C₂³×C₄×C₄₇	—	2	1	no	—
67	C₂×D₈×C₄₇	C₂×C₄	1	4	yes	—
68	C₄⋊Q₈×C₄₇	C₂×C₄	1	1	yes	characteristic
69	#127×C₄₇	C₂×C₄	1	1	yes	characteristic
70	#124×C₄₇	—	2	1	no	—
71	#121×C₄₇	—	2	1	no	—
72	#121×C₄₇	C₂×C₄	1	2	yes	—
73	C₄×D₄×C₄₇	—	2	1	no	—
74	C₄×D₄×C₄₇	—	2	1	no	—
75	C₄×D₄×C₄₇	—	2	1	no	—
76	C₄×D₄×C₄₇	C₂×C₄	1	2	yes	—
77	C₄×D₄×C₄₇	C₂³	1	2	yes	—
78	C₄×D₄×C₄₇	C₂³	1	2	yes	—
79	C₂×C₄⋊C₄×C₄₇	C₂×C₄	1	1	yes	characteristic
80	C₂×C₂²⋊C₄×C₄₇	—	2	1	no	—
81	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
82	#107×C₄₇	C₂×C₄	1	4	yes	—
83	C₄⋊C₈×C₄₇	C₂×C₄	1	2	yes	—
84	#102×C₄₇	C₂×C₄	1	4	yes	—
85	#102×C₄₇	C₂×C₄	1	4	yes	—
86	C₂²⋊C₈×C₄₇	C₂×C₄	1	2	yes	—
87	C₄×C₈×C₄₇	C₂³	1	2	yes	—
88	C₂⁴×C₄₇	—	2	1	no	—
89	#41×C₄₇	—	4	2	no	—
90	#41×C₄₇	—	4	2	no	—
91	C₂×Q₈×C₄₇	—	2	1	no	—
92	C₂×D₄×C₄₇	—	2	4	no	—
93	C₂×D₄×C₄₇	—	2	2	no	—
94	C₂×D₄×C₄₇	—	2	1	no	—
95	C₂×D₄×C₄₇	—	2	1	no	—
96	C₂×D₄×C₄₇	—	2	1	no	—
97	C₂×D₄×C₄₇	C₂²×C₄	1	2	yes	—
98	C₂×D₄×C₄₇	C₂²×C₄	1	2	yes	—
99	C₂²×C₄×C₄₇	—	2	1	no	—
100	C₂²×C₄×C₄₇	—	2	2	no	—
101	C₂²×C₄×C₄₇	—	2	2	no	—
102	C₂²×C₄×C₄₇	—	2	2	no	—
103	C₂²×C₄×C₄₇	—	4	2	no	—
104	C₂²×C₄×C₄₇	—	4	2	no	—
105	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
106	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
107	C₂²×C₄×C₄₇	#41	1	1	yes	characteristic
108	D₈×C₄₇	—	2	8	no	—
109	C₂×C₈×C₄₇	C₂²×C₄	1	4	yes	—
110	C₄⋊C₄×C₄₇	—	2	1	no	—
111	C₄⋊C₄×C₄₇	—	2	1	no	—
112	C₄⋊C₄×C₄₇	C₂²×C₄	1	2	yes	—
113	C₄⋊C₄×C₄₇	C₂²×C₄	1	2	yes	—
114	C₂²⋊C₄×C₄₇	—	2	2	no	—
115	C₂²⋊C₄×C₄₇	—	2	2	no	—
116	C₂²⋊C₄×C₄₇	—	2	2	no	—
117	C₂²⋊C₄×C₄₇	—	2	2	no	—
118	C₄²×C₄₇	C₂²×C₄	1	1	yes	characteristic
119	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
120	C₄²×C₄₇	#41	1	1	yes	characteristic
121	C₄²×C₄₇	C₂⁴	1	1	yes	characteristic
122	#10625329	—	4	2	no	—
123	#10625329	—	4	4	no	—
124	C₂×C₄₇⋊C₈	—	2	2	no	—
125	C₂×C₄₇⋊C₈	—	2	2	no	—
126	C₂×C₄₇⋊C₈	—	2	2	no	—
127	C₂×C₄₇⋊C₈	—	2	2	no	—
128	C₂×C₄₇⋊C₈	—	4	2	no	—
129	C₂×C₄₇⋊C₈	—	4	4	no	—
130	C₂×C₄₇⋊C₈	—	4	4	no	—
131	C₂×C₄₇⋊C₈	—	4	4	no	—
132	C₂×C₄₇⋊C₈	D₈	1	4	yes	complemented
133	C₂×C₄₇⋊C₈	C₂×D₄	1	1	yes	characteristic
134	C₂×C₄₇⋊C₈	C₂×D₄	1	1	yes	characteristic
135	C₂×C₄₇⋊C₈	C₂×D₄	1	1	yes	characteristic
136	C₂×C₄₇⋊C₈	C₂×D₄	1	1	yes	characteristic
137	C₂³×C₄₇	—	2	4	no	—
138	C₂³×C₄₇	—	2	2	no	—
139	C₂³×C₄₇	—	2	2	no	—
140	C₂³×C₄₇	—	4	2	no	—
141	C₂³×C₄₇	—	4	2	no	—
142	C₂³×C₄₇	C₄×D₄	1	1	yes	characteristic
143	Q₈×C₄₇	—	4	2	no	—
144	D₄×C₄₇	—	2	4	no	—
145	D₄×C₄₇	—	2	2	no	—
146	D₄×C₄₇	—	2	4	no	—
147	D₄×C₄₇	—	4	2	no	—
148	D₄×C₄₇	—	4	4	no	—
149	D₄×C₄₇	—	4	2	no	—
150	D₄×C₄₇	#131	1	4	yes	complemented
151	C₂×C₄×C₄₇	—	2	2	no	—
152	C₂×C₄×C₄₇	—	2	2	no	—
153	C₂×C₄×C₄₇	—	2	2	no	—
154	C₂×C₄×C₄₇	—	4	1	no	—
155	C₂×C₄×C₄₇	—	4	2	no	—
156	C₂×C₄×C₄₇	—	4	2	no	—
157	C₂×C₄×C₄₇	—	4	2	no	—
158	C₂×C₄×C₄₇	—	4	2	no	—
159	C₂×C₄×C₄₇	—	4	2	no	—
160	C₂×C₄×C₄₇	—	4	4	no	—
161	C₂×C₄×C₄₇	C₄×D₄	1	1	yes	characteristic
162	C₂×C₄×C₄₇	C₄×D₄	1	1	yes	characteristic
163	C₂×C₄×C₄₇	C₄×D₄	1	1	yes	characteristic
164	C₂×C₄×C₄₇	C₂×D₈	1	2	yes	—
165	C₂×C₄×C₄₇	#135	1	2	yes	—
166	C₂×C₄×C₄₇	C₂³×C₄	1	1	yes	characteristic
167	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
168	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
169	C₈×C₄₇	—	2	4	no	—
170	C₄₇⋊C₈	—	2	1	no	—
171	C₄₇⋊C₈	—	2	1	no	—
172	C₄₇⋊C₈	—	4	2	no	—
173	C₄₇⋊C₈	—	4	2	no	—
174	C₄₇⋊C₈	—	4	2	no	—
175	C₄₇⋊C₈	C₂×D₈	1	2	yes	—
176	C₄₇⋊C₈	C₂×D₈	1	2	yes	—
177	#17900	—	47	1	no	maximal, Sylow
178	C₂²×C₄₇	—	2	1	no	—
179	C₂²×C₄₇	—	2	1	no	—
180	C₂²×C₄₇	—	2	4	no	—
181	C₂²×C₄₇	—	4	8	no	—
182	C₂²×C₄₇	—	4	2	no	—
183	C₂²×C₄₇	—	4	2	no	—
184	C₂²×C₄₇	—	4	2	no	—
185	C₂²×C₄₇	—	4	2	no	—
186	C₂²×C₄₇	—	4	2	no	—
187	C₂²×C₄₇	C₄×D₈	1	2	yes	—
188	C₂²×C₄₇	C₂×C₄×D₄	1	1	yes	characteristic
189	C₄×C₄₇	—	2	1	no	—
190	C₄×C₄₇	—	2	1	no	—
191	C₄×C₄₇	—	2	1	no	—
192	C₄×C₄₇	—	4	2	no	—
193	C₄×C₄₇	—	4	2	no	—
194	C₄×C₄₇	C₄×D₈	1	2	yes	—
195	C₄×C₄₇	C₂×#131	1	2	yes	—
196	C₄×C₄₇	C₂²×D₈	1	1	yes	characteristic
197	C₄×C₄₇	C₂×#135	1	1	yes	characteristic
198	#3100	D₄₇	1	1	yes	characteristic
199	#2931	—	47	1	no	—
200	C₂×C₈×D₄	—	47	1	no	—
201	#1581	—	47	4	no	—
202	C₈×D₈	—	47	4	no	—
203	#1571	—	47	1	no	—
204	#1486	—	47	1	no	—
205	#1480	—	47	1	no	—
206	#1450	—	47	1	no	—
207	C₂×C₄₇	—	2	2	no	—
208	C₂×C₄₇	—	4	4	no	—
209	C₂×C₄₇	—	8	2	no	—
210	C₂×C₄₇	#2929	1	1	yes	characteristic
211	C₂×C₄₇	C₂×C₄×D₈	1	1	yes	characteristic
212	C₂×C₄₇	#2955	1	1	yes	characteristic
213	C₂×#131	—	94	1	no	—
214	C₂³×C₈	—	94	1	no	—
215	#532	C₂×D₄₇	1	1	yes	characteristic
216	C₂×C₄×D₄	C₂×D₄₇	1	1	yes	characteristic
217	#480	Dic₄₇	1	2	yes	—
218	#474	Dic₄₇	1	2	yes	—
219	#459	Dic₄₇	1	2	yes	—
220	#447	Dic₄₇	1	2	yes	—
221	C₄×D₈	C₂×D₄₇	1	4	yes	—
222	#436	—	47	2	no	—
223	#436	—	94	1	no	—
224	C₈×D₄	—	47	2	no	—
225	C₈×D₄	—	47	2	no	—
226	C₈×D₄	—	47	2	no	—
227	C₈×D₄	—	94	1	no	—
228	C₈×D₄	—	94	1	no	—
229	C₈×D₄	—	94	1	no	—
230	#431	—	47	1	no	—
231	#431	C₂×D₄₇	1	1	yes	characteristic
232	#423	—	47	1	no	—
233	C₂×C₄⋊C₈	—	47	1	no	—
234	#408	—	94	1	no	—
235	C₂×C₂²⋊C₈	—	94	1	no	—
236	C₂×C₄×C₈	—	47	1	no	—
237	#335	—	47	4	no	—
238	D₄⋊C₈	—	47	4	no	—
239	D₄⋊C₈	—	47	4	no	—
240	#322	—	47	2	no	—
241	C₈²	—	47	2	no	—
242	C₄₇	#17900	1	1	yes	characteristic, complemented, Sylow
243	C₂×#41	—	2	1	no	—
244	C₂²×D₄	C₂×Dic₄₇	1	1	yes	characteristic
245	C₂³×C₄	—	2	1	no	—
246	C₂×D₈	C₂×Dic₄₇	1	4	yes	—
247	#131	—	188	4	no	—
248	C₂×M₁₆	—	94	2	no	—
249	C₂×M₁₆	—	94	1	no	—
250	C₂²×C₈	—	47	1	no	—
251	C₂²×C₈	—	47	1	no	—
252	C₂²×C₈	—	94	2	no	—
253	C₂²×C₈	—	94	2	no	—
254	C₂²×C₈	—	94	2	no	—
255	C₂²×C₈	—	94	1	no	—
256	C₂²×C₈	—	188	4	no	—
257	C₄⋊Q₈	C₂×Dic₄₇	1	1	yes	characteristic
258	#127	C₂×Dic₄₇	1	1	yes	characteristic
259	#124	—	2	1	no	—
260	#121	—	2	1	no	—
261	#121	C₂×Dic₄₇	1	2	yes	—
262	C₄×D₄	—	2	1	no	—
263	C₄×D₄	—	2	1	no	—
264	C₄×D₄	—	2	1	no	—
265	C₄×D₄	C₂×Dic₄₇	1	2	yes	—
266	C₄×D₄	C₂²×D₄₇	1	2	yes	—
267	C₄×D₄	C₂²×D₄₇	1	2	yes	—
268	C₂×C₄⋊C₄	C₂×Dic₄₇	1	1	yes	characteristic
269	C₂×C₂²⋊C₄	—	2	1	no	—
270	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
271	#107	C₂×Dic₄₇	1	4	yes	—
272	C₄⋊C₈	—	47	2	no	—
273	C₄⋊C₈	—	47	2	no	—
274	C₄⋊C₈	—	94	1	no	—
275	C₄⋊C₈	—	94	1	no	—
276	C₄⋊C₈	—	94	1	no	—
277	C₄⋊C₈	C₂×Dic₄₇	1	2	yes	—
278	#102	C₂×Dic₄₇	1	4	yes	—
279	#102	C₂×Dic₄₇	1	4	yes	—
280	C₂²⋊C₈	—	94	2	no	—
281	C₂²⋊C₈	—	94	2	no	—
282	C₂²⋊C₈	—	94	2	no	—
283	C₂²⋊C₈	—	94	2	no	—
284	C₂²⋊C₈	—	94	1	no	—
285	C₂²⋊C₈	C₂×Dic₄₇	1	2	yes	—
286	C₄×C₈	—	47	1	no	—
287	C₄×C₈	—	47	1	no	—
288	C₄×C₈	—	47	1	no	—
289	C₄×C₈	—	47	1	no	—
290	C₄×C₈	—	47	2	no	—
291	C₄×C₈	C₂²×D₄₇	1	2	yes	—
292	C₂⁴	—	2	1	no	—
293	#41	—	4	2	no	—
294	#41	—	4	2	no	—
295	C₂×Q₈	—	2	1	no	—
296	C₂×D₄	—	2	4	no	—
297	C₂×D₄	—	2	2	no	—
298	C₂×D₄	—	2	1	no	—
299	C₂×D₄	—	2	1	no	—
300	C₂×D₄	—	2	1	no	—
301	C₂×D₄	C₂²×Dic₄₇	1	2	yes	—
302	C₂×D₄	C₂²×Dic₄₇	1	2	yes	—
303	C₂²×C₄	—	2	1	no	—
304	C₂²×C₄	—	2	2	no	—
305	C₂²×C₄	—	2	2	no	—
306	C₂²×C₄	—	2	2	no	—
307	C₂²×C₄	—	4	2	no	—
308	C₂²×C₄	—	4	2	no	—
309	C₂²×C₄	D₄×D₄₇	1	1	yes	characteristic
310	C₂²×C₄	#10625352	1	1	yes	characteristic
311	C₂²×C₄	C₂²×Dic₄₇	1	1	yes	characteristic
312	D₈	—	2	8	no	—
313	M₁₆	—	188	4	no	—
314	M₁₆	—	188	2	no	—
315	C₂×C₈	—	47	4	no	—
316	C₂×C₈	—	47	1	no	—
317	C₂×C₈	—	47	1	no	—
318	C₂×C₈	—	47	1	no	—
319	C₂×C₈	—	47	1	no	—
320	C₂×C₈	—	94	2	no	—
321	C₂×C₈	—	94	2	no	—
322	C₂×C₈	—	94	2	no	—
323	C₂×C₈	—	94	2	no	—
324	C₂×C₈	—	188	4	no	—
325	C₂×C₈	—	188	4	no	—
326	C₂×C₈	—	188	4	no	—
327	C₂×C₈	—	188	2	no	—
328	C₂×C₈	C₂²×Dic₄₇	1	4	yes	—
329	C₄⋊C₄	—	2	1	no	—
330	C₄⋊C₄	—	2	1	no	—
331	C₄⋊C₄	C₂²×Dic₄₇	1	2	yes	—
332	C₄⋊C₄	C₂²×Dic₄₇	1	2	yes	—
333	C₂²⋊C₄	—	2	2	no	—
334	C₂²⋊C₄	—	2	2	no	—
335	C₂²⋊C₄	—	2	2	no	—
336	C₂²⋊C₄	—	2	2	no	—
337	C₄²	D₄×D₄₇	1	1	yes	characteristic
338	C₄²	#10625352	1	1	yes	characteristic
339	C₄²	C₂²×Dic₄₇	1	1	yes	characteristic
340	C₄²	C₂³×D₄₇	1	1	yes	characteristic
341	C₂³	—	2	4	no	—
342	C₂³	—	2	2	no	—
343	C₂³	—	2	2	no	—
344	C₂³	—	4	2	no	—
345	C₂³	—	4	2	no	—
346	C₂³	D₄×Dic₄₇	1	1	yes	characteristic
347	Q₈	—	4	2	no	—
348	D₄	—	2	4	no	—
349	D₄	—	2	2	no	—
350	D₄	—	2	4	no	—
351	D₄	—	4	2	no	—
352	D₄	—	4	4	no	—
353	D₄	—	4	2	no	—
354	D₄	#13094031	1	4	yes	complemented
355	C₂×C₄	—	2	2	no	—
356	C₂×C₄	—	2	2	no	—
357	C₂×C₄	—	2	2	no	—
358	C₂×C₄	—	4	1	no	—
359	C₂×C₄	—	4	2	no	—
360	C₂×C₄	—	4	2	no	—
361	C₂×C₄	—	4	2	no	—
362	C₂×C₄	—	4	2	no	—
363	C₂×C₄	—	4	2	no	—
364	C₂×C₄	—	4	4	no	—
365	C₂×C₄	D₄×Dic₄₇	1	1	yes	characteristic
366	C₂×C₄	D₄×Dic₄₇	1	1	yes	characteristic
367	C₂×C₄	D₄×Dic₄₇	1	1	yes	characteristic
368	C₂×C₄	D₈×D₄₇	1	2	yes	—
369	C₂×C₄	#13094043	1	2	yes	—
370	C₂×C₄	C₂³×Dic₄₇	1	1	yes	characteristic
371	C₂×C₄	C₂×D₄×D₄₇	1	1	yes	characteristic
372	C₂×C₄	C₂×#10625352	1	1	yes	characteristic
373	C₈	—	2	4	no	—
374	C₈	—	47	2	no	—
375	C₈	—	47	2	no	—
376	C₈	—	94	1	no	—
377	C₈	—	94	1	no	—
378	C₈	—	188	2	no	—
379	C₈	—	188	2	no	—
380	C₈	—	188	2	no	—
381	C₂²	—	2	1	no	—
382	C₂²	—	2	1	no	—
383	C₂²	—	2	4	no	—
384	C₂²	—	4	8	no	—
385	C₂²	—	4	2	no	—
386	C₂²	—	4	2	no	—
387	C₂²	—	4	2	no	—
388	C₂²	—	4	2	no	—
389	C₂²	—	4	2	no	—
390	C₂²	D₈×Dic₄₇	1	2	yes	—
391	C₂²	C₂×D₄×Dic₄₇	1	1	yes	characteristic
392	C₄	—	2	1	no	—
393	C₄	—	2	1	no	—
394	C₄	—	2	1	no	—
395	C₄	—	4	2	no	—
396	C₄	—	4	2	no	—
397	C₄	D₈×Dic₄₇	1	2	yes	—
398	C₄	C₂×#13094031	1	2	yes	—
399	C₄	C₂×D₈×D₄₇	1	1	yes	characteristic
400	C₄	C₂×#13094043	1	1	yes	characteristic
401	C₂	—	2	2	no	—
402	C₂	—	4	4	no	—
403	C₂	—	8	2	no	—
404	C₂	#20252083	1	1	yes	characteristic
405	C₂	C₂×D₈×Dic₄₇	1	1	yes	characteristic
406	C₂	#20252291	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂×D₄×D₄₇
commutator	C₂×C₄×C₄₇	C₂³×C₄
Frattini	C₄²	C₂³×D₄₇
Fitting, prime radical	C₄₇×#3100	C₂
socle	C₂²×C₄₇	C₂×C₄×D₄
cosocle	C₄²×C₄₇	C₂⁴
hypercenter	#3100	D₄₇
hypocenter	C₄₇	#17900
LCS	G ▷ C₂×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #3100

Complements

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

N	H ≅ G/N	type
1. #20252100	C₂	semidirect
2. C₂×D₄×C₄₇⋊C₈	C₂	semidirect
3. #20242218	C₂	semidirect
4. D₈×C₄₇⋊C₈	C₂	semidirect
5. #20242163	C₂	semidirect
6. #20241813	C₂	semidirect
7. #20241787	C₂	semidirect
8. #20241672	C₂	semidirect
13. #15689201	C₂²	semidirect
19. D₄×C₄₇⋊C₈	C₂²	semidirect
26. #15688876	C₂²	semidirect
28. D₄⋊(C₄₇⋊C₈)	C₂²	semidirect
29. #15688845	C₂²	semidirect
30. C₈×C₄₇⋊C₈	C₂²	semidirect
132. C₂×C₄₇⋊C₈	D₈	semidirect
150. D₄×C₄₇	#131	semidirect
242. C₄₇	#17900	semidirect
354. D₄	#13094031	semidirect

Maximal subgroups

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

subgroup	index
#20252100	2
C₂×D₄×C₄₇⋊C₈	2
#20242218	2
D₈×C₄₇⋊C₈	2
#20242163	2
#20241813	2
#20241787	2
#20241672	2
C₄₇×#3100	2
#17900	47