Subgroups — #26198545

Order 12032.

694 conjugacy classes of subgroups.

The subgroup lattice has 456 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20253898	C₂	1	1	yes	maximal, characteristic, complemented
2	#20253396	C₂	1	1	yes	maximal, characteristic
3	C₂×D₄×C₄₇⋊C₈	C₂	1	1	yes	maximal, characteristic
4	#20242785	C₂	1	2	yes	maximal, complemented
5	#20242775	C₂	1	2	yes	maximal, complemented
6	#20242765	C₂	1	2	yes	maximal, complemented
7	#20242761	C₂	1	2	yes	maximal, complemented
8	#20242134	C₂	1	1	yes	maximal, characteristic, complemented
9	#20242045	C₂	1	1	yes	maximal, characteristic, complemented
10	#20242043	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄₇×#3101	C₂	1	1	yes	maximal, characteristic
12	C₂³×C₄₇⋊C₈	—	2	1	no	—
13	#15689680	C₂²	1	1	yes	characteristic
14	#15689526	C₂²	1	1	yes	characteristic, complemented
15	#15689526	C₂²	1	1	yes	characteristic, complemented
16	#15689522	—	2	1	no	—
17	#15689522	—	2	1	no	—
18	#15689519	C₂²	1	1	yes	characteristic, complemented
19	#15689519	C₂²	1	1	yes	characteristic, complemented
20	#15689453	—	2	1	no	—
21	#15689413	C₂²	1	2	yes	—
22	#15689328	C₂²	1	2	yes	—
23	#15689274	—	2	1	no	—
24	C₄×#10625335	—	2	2	no	—
25	D₄×C₄₇⋊C₈	—	2	1	no	—
26	D₄×C₄₇⋊C₈	—	2	1	no	—
27	D₄×C₄₇⋊C₈	C₂²	1	2	yes	—
28	D₄×C₄₇⋊C₈	C₂²	1	2	yes	—
29	#15689176	C₂²	1	1	yes	characteristic
30	#15689159	—	2	1	no	—
31	#15689159	—	2	1	no	—
32	C₂×C₄⋊(C₄₇⋊C₈)	C₂²	1	1	yes	characteristic
33	C₂×C₂²⋊(C₄₇⋊C₈)	—	2	1	no	—
34	C₂×C₄×C₄₇⋊C₈	C₂²	1	1	yes	characteristic
35	#15688875	C₂²	1	2	yes	complemented
36	#15688873	C₂²	1	2	yes	complemented
37	#15688872	C₂²	1	2	yes	complemented
38	#15688871	C₂²	1	2	yes	complemented
39	#15688870	C₂²	1	2	yes	complemented
40	#15688869	C₂²	1	2	yes	complemented
41	C₄₇×#533	C₂²	1	1	yes	characteristic
42	C₂×C₄×D₄×C₄₇	C₂²	1	1	yes	characteristic
43	C₄₇×#483	—	2	1	no	—
44	C₄₇×#476	C₂²	1	2	yes	—
45	C₄₇×#461	C₂²	1	2	yes	—
46	C₄₇×#450	—	2	1	no	—
47	C₄×SD₁₆×C₄₇	—	2	2	no	—
48	C₄₇×#431	C₂²	1	1	yes	characteristic
49	C₂×#10625335	—	2	2	no	—
50	C₂²×C₄₇⋊C₈	—	2	1	no	—
51	C₂²×C₄₇⋊C₈	—	2	2	no	—
52	C₂²×C₄₇⋊C₈	—	2	2	no	—
53	C₂²×C₄₇⋊C₈	—	4	4	no	—
54	C₂²×C₄₇⋊C₈	D₄	1	1	yes	characteristic
55	C₂²×C₄₇⋊C₈	D₄	1	1	yes	characteristic
56	#13094024	C₂³	1	1	yes	characteristic
57	#13094024	C₂³	1	1	yes	characteristic
58	#13094016	—	2	1	no	—
59	#13094003	—	2	1	no	—
60	#13094003	—	2	1	no	—
61	C₄×Dic₉₄	—	2	1	no	—
62	C₄×Dic₉₄	—	2	1	no	—
63	#13093983	—	2	1	no	—
64	#13093957	—	2	1	no	—
65	#13093957	—	2	1	no	—
66	#13093957	—	2	1	no	—
67	#13093957	—	2	1	no	—
68	#13093955	—	2	2	no	—
69	#13093955	—	2	1	no	—
70	#13093955	—	2	1	no	—
71	#13093955	—	2	1	no	—
72	#13093955	—	2	1	no	—
73	C₄⋊(C₄₇⋊C₈)	—	2	1	no	—
74	C₄⋊(C₄₇⋊C₈)	C₂³	1	2	yes	—
75	C₄⋊(C₄₇⋊C₈)	C₂³	1	2	yes	—
76	#13093947	—	2	2	no	—
77	#13093945	—	2	2	no	—
78	C₂²⋊(C₄₇⋊C₈)	—	2	1	no	—
79	C₂²⋊(C₄₇⋊C₈)	—	2	2	no	—
80	C₂²⋊(C₄₇⋊C₈)	—	2	2	no	—
81	C₄×C₄₇⋊C₈	—	2	1	no	—
82	C₄×C₄₇⋊C₈	D₄	1	1	yes	characteristic
83	C₄×C₄₇⋊C₈	D₄	1	1	yes	characteristic
84	C₄×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
85	C₄×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
86	C₂²×D₄×C₄₇	D₄	1	1	yes	characteristic
87	C₂³×C₄×C₄₇	—	2	1	no	—
88	C₂×SD₁₆×C₄₇	—	2	2	no	—
89	C₄⋊Q₈×C₄₇	C₂³	1	1	yes	characteristic
90	C₄⋊Q₈×C₄₇	C₂³	1	1	yes	characteristic
91	#125×C₄₇	—	2	1	no	—
92	C₂²⋊Q₈×C₄₇	—	2	1	no	—
93	C₂²⋊Q₈×C₄₇	—	2	1	no	—
94	C₄×Q₈×C₄₇	—	2	1	no	—
95	C₄×Q₈×C₄₇	—	2	1	no	—
96	C₄×D₄×C₄₇	—	2	1	no	—
97	C₄×D₄×C₄₇	—	2	1	no	—
98	C₄×D₄×C₄₇	D₄	1	2	yes	—
99	C₄×D₄×C₄₇	C₂³	1	2	yes	—
100	#117×C₄₇	—	2	1	no	—
101	C₂×C₄⋊C₄×C₄₇	D₄	1	1	yes	characteristic
102	C₂×C₂²⋊C₄×C₄₇	—	2	1	no	—
103	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
104	#106×C₄₇	—	2	2	no	—
105	C₄⋊C₈×C₄₇	C₂³	1	2	yes	—
106	#103×C₄₇	—	2	2	no	—
107	#102×C₄₇	—	2	2	no	—
108	C₂²⋊C₈×C₄₇	—	2	1	no	—
109	C₄×C₈×C₄₇	—	2	1	no	—
110	C₂⁴×C₄₇	—	2	1	no	—
111	C₂×Q₈×C₄₇	—	2	1	no	—
112	C₂×Q₈×C₄₇	—	2	1	no	—
113	C₂×D₄×C₄₇	—	2	4	no	—
114	C₂×D₄×C₄₇	—	2	1	no	—
115	C₂×D₄×C₄₇	C₂×D₄	1	2	yes	—
116	C₂²×C₄×C₄₇	—	2	1	no	—
117	C₂²×C₄×C₄₇	—	2	2	no	—
118	C₂²×C₄×C₄₇	—	2	2	no	—
119	C₂²×C₄×C₄₇	—	4	2	no	—
120	C₂²×C₄×C₄₇	—	4	2	no	—
121	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
122	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
123	C₂²×C₄×C₄₇	#41	1	1	yes	characteristic
124	C₂×Dic₉₄	—	2	1	no	—
125	C₂×Dic₉₄	—	2	1	no	—
126	SD₁₆×C₄₇	—	4	4	no	—
127	C₂×C₈×C₄₇	—	2	2	no	—
128	C₄⋊C₄×C₄₇	—	2	1	no	—
129	C₄⋊C₄×C₄₇	—	2	1	no	—
130	C₄⋊C₄×C₄₇	—	2	1	no	—
131	C₄⋊C₄×C₄₇	—	2	1	no	—
132	C₄⋊C₄×C₄₇	—	2	1	no	—
133	C₄⋊C₄×C₄₇	—	4	1	no	—
134	C₄⋊C₄×C₄₇	—	4	1	no	—
135	C₄⋊C₄×C₄₇	C₂×D₄	1	2	yes	—
136	C₂²⋊C₄×C₄₇	—	2	2	no	—
137	C₂²⋊C₄×C₄₇	—	2	2	no	—
138	C₂²⋊C₄×C₄₇	—	4	1	no	—
139	C₄²×C₄₇	—	4	1	no	—
140	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
141	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
142	C₄²×C₄₇	#41	1	1	yes	characteristic
143	C₄²×C₄₇	C₂⁴	1	1	yes	characteristic
144	C₂²⋊Dic₄₇	—	4	1	no	—
145	#10625335	—	4	4	no	—
146	C₄⋊Dic₄₇	—	2	1	no	—
147	C₄⋊Dic₄₇	—	2	1	no	—
148	C₄⋊Dic₄₇	—	2	1	no	—
149	C₄⋊Dic₄₇	—	2	1	no	—
150	Dic₄₇⋊C₄	—	4	1	no	—
151	Dic₄₇⋊C₄	—	4	1	no	—
152	C₄×Dic₄₇	—	4	1	no	—
153	C₂×C₄₇⋊C₈	—	2	2	no	—
154	C₂×C₄₇⋊C₈	—	2	2	no	—
155	C₂×C₄₇⋊C₈	—	2	2	no	—
156	C₂×C₄₇⋊C₈	—	4	2	no	—
157	C₂×C₄₇⋊C₈	—	4	4	no	—
158	C₂×C₄₇⋊C₈	—	4	4	no	—
159	C₂×C₄₇⋊C₈	SD₁₆	1	4	yes	complemented
160	C₂×C₄₇⋊C₈	C₂×D₄	1	1	yes	characteristic
161	C₂×C₄₇⋊C₈	C₂×D₄	1	1	yes	characteristic
162	C₂×C₄₇⋊C₈	C₂×D₄	1	1	yes	characteristic
163	C₂×C₄₇⋊C₈	C₂×D₄	1	1	yes	characteristic
164	C₂³×C₄₇	—	2	4	no	—
165	C₂³×C₄₇	—	2	2	no	—
166	C₂³×C₄₇	—	4	2	no	—
167	C₂³×C₄₇	—	4	2	no	—
168	C₂³×C₄₇	#121	1	1	yes	characteristic
169	Q₈×C₄₇	—	4	2	no	—
170	Q₈×C₄₇	—	8	1	no	—
171	D₄×C₄₇	—	2	4	no	—
172	D₄×C₄₇	—	2	2	no	—
173	D₄×C₄₇	#135	1	4	yes	—
174	C₂×C₄×C₄₇	—	2	2	no	—
175	C₂×C₄×C₄₇	—	2	2	no	—
176	C₂×C₄×C₄₇	—	4	1	no	—
177	C₂×C₄×C₄₇	—	4	2	no	—
178	C₂×C₄×C₄₇	—	4	2	no	—
179	C₂×C₄×C₄₇	—	4	2	no	—
180	C₂×C₄×C₄₇	—	4	4	no	—
181	C₂×C₄×C₄₇	—	4	1	no	—
182	C₂×C₄×C₄₇	—	4	1	no	—
183	C₂×C₄×C₄₇	#121	1	1	yes	characteristic
184	C₂×C₄×C₄₇	#121	1	1	yes	characteristic
185	C₂×C₄×C₄₇	#121	1	1	yes	characteristic
186	C₂×C₄×C₄₇	C₂×SD₁₆	1	2	yes	—
187	C₂×C₄×C₄₇	#137	1	2	yes	—
188	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
189	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
190	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
191	C₂×Dic₄₇	—	4	1	no	—
192	C₂×Dic₄₇	—	4	1	no	—
193	Dic₉₄	—	4	2	no	—
194	Dic₉₄	—	8	1	no	—
195	C₈×C₄₇	—	4	2	no	—
196	C₄₇⋊C₈	—	2	1	no	—
197	C₄₇⋊C₈	—	2	1	no	—
198	C₄₇⋊C₈	—	4	2	no	—
199	C₄₇⋊C₈	—	4	2	no	—
200	C₄₇⋊C₈	C₂×SD₁₆	1	2	yes	—
201	C₄₇⋊C₈	C₂×SD₁₆	1	2	yes	—
202	#19105	—	47	1	no	maximal, Sylow
203	C₂²×C₄₇	—	2	1	no	—
204	C₂²×C₄₇	—	2	1	no	—
205	C₂²×C₄₇	—	2	4	no	—
206	C₂²×C₄₇	—	4	8	no	—
207	C₂²×C₄₇	—	4	2	no	—
208	C₂²×C₄₇	—	4	2	no	—
209	C₂²×C₄₇	#461	1	2	yes	—
210	C₂²×C₄₇	C₂×#121	1	1	yes	characteristic
211	C₄×C₄₇	—	2	1	no	—
212	C₄×C₄₇	—	2	1	no	—
213	C₄×C₄₇	—	2	1	no	—
214	C₄×C₄₇	—	4	2	no	—
215	C₄×C₄₇	—	8	1	no	—
216	C₄×C₄₇	—	8	1	no	—
217	C₄×C₄₇	#461	1	2	yes	—
218	C₄×C₄₇	C₂²×SD₁₆	1	1	yes	characteristic
219	C₄×C₄₇	C₂×#135	1	2	yes	—
220	C₄×C₄₇	C₂×#137	1	1	yes	characteristic
221	Dic₄₇	—	8	1	no	—
222	Dic₄₇	—	8	1	no	—
223	#3160	—	47	1	no	—
224	#3101	—	47	1	no	—
225	#3101	D₄₇	1	1	yes	characteristic
226	C₂×C₈×D₄	—	47	1	no	—
227	#1675	—	47	2	no	—
228	#1673	—	47	2	no	—
229	#1671	—	47	2	no	—
230	#1671	—	47	2	no	—
231	#1564	—	47	1	no	—
232	#1542	—	47	1	no	—
233	#1542	—	47	1	no	—
234	C₂×C₄₇	—	2	2	no	—
235	C₂×C₄₇	—	4	4	no	—
236	C₂×C₄₇	C₂×#461	1	1	yes	characteristic
237	C₂×C₄₇	#3050	1	1	yes	characteristic
238	C₂×C₄₇	#3067	1	1	yes	characteristic
239	C₂³×C₈	—	94	1	no	—
240	#533	—	47	1	no	—
241	#533	C₂×D₄₇	1	1	yes	characteristic
242	C₂×C₄×D₄	C₂×D₄₇	1	1	yes	characteristic
243	#500	—	47	1	no	—
244	#500	—	47	1	no	—
245	#499	—	94	1	no	—
246	#499	—	94	1	no	—
247	#498	—	47	1	no	—
248	#498	—	47	1	no	—
249	#483	—	2	1	no	—
250	#483	—	94	1	no	—
251	#476	—	47	2	no	—
252	#476	C₂×D₄₇	1	2	yes	—
253	#461	—	47	2	no	—
254	#461	C₂×D₄₇	1	2	yes	—
255	#450	—	2	1	no	—
256	#450	—	94	1	no	—
257	C₄×SD₁₆	—	2	2	no	—
258	C₄×SD₁₆	—	94	2	no	—
259	C₈×D₄	—	47	2	no	—
260	C₈×D₄	—	47	2	no	—
261	C₈×D₄	—	94	1	no	—
262	C₈×D₄	—	94	1	no	—
263	#431	—	47	1	no	—
264	#431	C₂×D₄₇	1	1	yes	characteristic
265	#427	—	94	1	no	—
266	#427	—	94	1	no	—
267	C₂×C₄⋊C₈	—	47	1	no	—
268	C₂×C₂²⋊C₈	—	94	1	no	—
269	C₂×C₄×C₈	—	47	1	no	—
270	#335	—	47	2	no	—
271	#334	—	47	2	no	—
272	#333	—	47	2	no	—
273	#333	—	47	2	no	—
274	#332	—	47	2	no	—
275	#332	—	47	2	no	—
276	C₄₇	#19105	1	1	yes	characteristic, complemented, Sylow
277	C₂²×D₄	C₂²⋊D₄₇	1	1	yes	characteristic
278	C₂³×C₄	—	2	1	no	—
279	C₂×SD₁₆	—	2	2	no	—
280	C₂×SD₁₆	—	94	2	no	—
281	C₂²×C₈	—	47	1	no	—
282	C₂²×C₈	—	47	1	no	—
283	C₂²×C₈	—	94	2	no	—
284	C₂²×C₈	—	94	2	no	—
285	C₂²×C₈	—	94	1	no	—
286	C₂²×C₈	—	188	4	no	—
287	C₄⋊Q₈	—	47	1	no	—
288	C₄⋊Q₈	—	47	1	no	—
289	C₄⋊Q₈	C₂²×D₄₇	1	1	yes	characteristic
290	C₄⋊Q₈	C₂²×D₄₇	1	1	yes	characteristic
291	#125	—	2	1	no	—
292	#125	—	94	1	no	—
293	C₂²⋊Q₈	—	2	1	no	—
294	C₂²⋊Q₈	—	2	1	no	—
295	C₂²⋊Q₈	—	94	1	no	—
296	C₂²⋊Q₈	—	94	1	no	—
297	C₄×Q₈	—	2	1	no	—
298	C₄×Q₈	—	2	1	no	—
299	C₄×Q₈	—	94	1	no	—
300	C₄×Q₈	—	94	1	no	—
301	C₄×D₄	—	2	1	no	—
302	C₄×D₄	—	2	1	no	—
303	C₄×D₄	C₂²⋊D₄₇	1	2	yes	—
304	C₄×D₄	C₂²×D₄₇	1	2	yes	—
305	#117	—	2	1	no	—
306	#117	—	94	1	no	—
307	C₂×C₄⋊C₄	C₂²⋊D₄₇	1	1	yes	characteristic
308	C₂×C₂²⋊C₄	—	2	1	no	—
309	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
310	#107	—	94	1	no	—
311	#107	—	94	1	no	—
312	#107	—	94	1	no	—
313	#107	—	94	1	no	—
314	#106	—	2	2	no	—
315	#106	—	94	1	no	—
316	#106	—	94	1	no	—
317	#106	—	94	1	no	—
318	#106	—	94	1	no	—
319	#106	—	94	2	no	—
320	C₄⋊C₈	—	47	2	no	—
321	C₄⋊C₈	—	47	2	no	—
322	C₄⋊C₈	—	94	1	no	—
323	C₄⋊C₈	C₂²×D₄₇	1	2	yes	—
324	#103	—	2	2	no	—
325	#103	—	94	2	no	—
326	#102	—	2	2	no	—
327	#102	—	94	2	no	—
328	C₂²⋊C₈	—	2	1	no	—
329	C₂²⋊C₈	—	94	2	no	—
330	C₂²⋊C₈	—	94	2	no	—
331	C₂²⋊C₈	—	94	1	no	—
332	C₄×C₈	—	2	1	no	—
333	C₄×C₈	—	47	1	no	—
334	C₄×C₈	—	47	1	no	—
335	C₄×C₈	—	47	1	no	—
336	C₄×C₈	—	47	1	no	—
337	C₄×C₈	—	94	1	no	—
338	C₂⁴	—	2	1	no	—
339	C₂×Q₈	—	2	1	no	—
340	C₂×Q₈	—	2	1	no	—
341	C₂×Q₈	—	94	1	no	—
342	C₂×Q₈	—	94	1	no	—
343	C₂×D₄	—	2	4	no	—
344	C₂×D₄	—	2	1	no	—
345	C₂×D₄	C₂×C₂²⋊D₄₇	1	2	yes	—
346	C₂²×C₄	—	2	1	no	—
347	C₂²×C₄	—	2	2	no	—
348	C₂²×C₄	—	2	2	no	—
349	C₂²×C₄	—	4	2	no	—
350	C₂²×C₄	—	4	2	no	—
351	C₂²×C₄	D₄×D₄₇	1	1	yes	characteristic
352	C₂²×C₄	#10625352	1	1	yes	characteristic
353	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
354	SD₁₆	—	4	4	no	—
355	SD₁₆	—	188	4	no	—
356	C₂×C₈	—	2	2	no	—
357	C₂×C₈	—	47	4	no	—
358	C₂×C₈	—	47	1	no	—
359	C₂×C₈	—	47	1	no	—
360	C₂×C₈	—	47	1	no	—
361	C₂×C₈	—	47	1	no	—
362	C₂×C₈	—	94	2	no	—
363	C₂×C₈	—	94	2	no	—
364	C₂×C₈	—	94	2	no	—
365	C₂×C₈	—	188	4	no	—
366	C₂×C₈	—	188	4	no	—
367	C₂×C₈	—	188	2	no	—
368	C₄⋊C₄	—	2	1	no	—
369	C₄⋊C₄	—	2	1	no	—
370	C₄⋊C₄	—	2	1	no	—
371	C₄⋊C₄	—	2	1	no	—
372	C₄⋊C₄	—	2	1	no	—
373	C₄⋊C₄	—	4	1	no	—
374	C₄⋊C₄	—	4	1	no	—
375	C₄⋊C₄	—	94	1	no	—
376	C₄⋊C₄	—	94	1	no	—
377	C₄⋊C₄	—	94	1	no	—
378	C₄⋊C₄	—	94	1	no	—
379	C₄⋊C₄	—	188	1	no	—
380	C₄⋊C₄	—	188	1	no	—
381	C₄⋊C₄	C₂×C₂²⋊D₄₇	1	2	yes	—
382	C₂²⋊C₄	—	2	2	no	—
383	C₂²⋊C₄	—	2	2	no	—
384	C₂²⋊C₄	—	4	1	no	—
385	C₂²⋊C₄	—	188	1	no	—
386	C₄²	—	4	1	no	—
387	C₄²	—	188	1	no	—
388	C₄²	D₄×D₄₇	1	1	yes	characteristic
389	C₄²	#10625352	1	1	yes	characteristic
390	C₄²	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
391	C₄²	C₂³×D₄₇	1	1	yes	characteristic
392	C₂³	—	2	4	no	—
393	C₂³	—	2	2	no	—
394	C₂³	—	4	2	no	—
395	C₂³	—	4	2	no	—
396	C₂³	#13093996	1	1	yes	characteristic
397	Q₈	—	4	2	no	—
398	Q₈	—	8	1	no	—
399	Q₈	—	376	1	no	—
400	Q₈	—	188	2	no	—
401	D₄	—	2	4	no	—
402	D₄	—	2	2	no	—
403	D₄	#13094044	1	4	yes	—
404	C₂×C₄	—	2	2	no	—
405	C₂×C₄	—	2	2	no	—
406	C₂×C₄	—	4	1	no	—
407	C₂×C₄	—	4	2	no	—
408	C₂×C₄	—	4	4	no	—
409	C₂×C₄	—	4	2	no	—
410	C₂×C₄	—	4	2	no	—
411	C₂×C₄	—	4	1	no	—
412	C₂×C₄	—	4	1	no	—
413	C₂×C₄	—	188	1	no	—
414	C₂×C₄	—	188	1	no	—
415	C₂×C₄	#13093996	1	1	yes	characteristic
416	C₂×C₄	#13093996	1	1	yes	characteristic
417	C₂×C₄	#13093996	1	1	yes	characteristic
418	C₂×C₄	SD₁₆×D₄₇	1	2	yes	—
419	C₂×C₄	#13094053	1	2	yes	—
420	C₂×C₄	C₂×D₄×D₄₇	1	1	yes	characteristic
421	C₂×C₄	C₂²×C₂²⋊D₄₇	1	1	yes	characteristic
422	C₂×C₄	C₂×#10625352	1	1	yes	characteristic
423	C₈	—	4	2	no	—
424	C₈	—	47	2	no	—
425	C₈	—	47	2	no	—
426	C₈	—	94	1	no	—
427	C₈	—	94	1	no	—
428	C₈	—	188	2	no	—
429	C₈	—	188	2	no	—
430	C₂²	—	2	1	no	—
431	C₂²	—	2	1	no	—
432	C₂²	—	2	4	no	—
433	C₂²	—	4	8	no	—
434	C₂²	—	4	2	no	—
435	C₂²	—	4	2	no	—
436	C₂²	#15689326	1	2	yes	—
437	C₂²	C₂×#13093996	1	1	yes	characteristic
438	C₄	—	2	1	no	—
439	C₄	—	2	1	no	—
440	C₄	—	2	1	no	—
441	C₄	—	4	2	no	—
442	C₄	—	8	1	no	—
443	C₄	—	8	1	no	—
444	C₄	—	376	1	no	—
445	C₄	—	376	1	no	—
446	C₄	#15689326	1	2	yes	—
447	C₄	C₂×SD₁₆×D₄₇	1	1	yes	characteristic
448	C₄	C₂×#13094044	1	2	yes	—
449	C₄	C₂×#13094053	1	1	yes	characteristic
450	C₂	—	2	2	no	—
451	C₂	—	4	4	no	—
452	C₂	C₂×#15689326	1	1	yes	characteristic
453	C₂	#20252966	1	1	yes	characteristic
454	C₂	#20253105	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	#13093996
commutator, cosocle	C₄²×C₄₇	C₂⁴
Frattini	C₄²	C₂³×D₄₇
Fitting	C₄₇×#3101	C₂
socle	C₂²×C₄₇	C₂×#121
prime radical	C₂²×D₄×C₄₇	D₄
hypercenter	#3101	D₄₇
hypocenter	C₄₇	#19105
LCS	G ▷ C₄²×C₄₇ ▷ C₂²×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #3101

Complements

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

N	H ≅ G/N	type
1. #20253898	C₂	semidirect
4. #20242785	C₂	semidirect
5. #20242775	C₂	semidirect
6. #20242765	C₂	semidirect
7. #20242761	C₂	semidirect
8. #20242134	C₂	semidirect
9. #20242045	C₂	semidirect
10. #20242043	C₂	semidirect
14. #15689526	C₂²	semidirect
15. #15689526	C₂²	semidirect
18. #15689519	C₂²	semidirect
19. #15689519	C₂²	semidirect
35. #15688875	C₂²	semidirect
36. #15688873	C₂²	semidirect
37. #15688872	C₂²	semidirect
38. #15688871	C₂²	semidirect
39. #15688870	C₂²	semidirect
40. #15688869	C₂²	semidirect
159. C₂×C₄₇⋊C₈	SD₁₆	semidirect
276. C₄₇	#19105	semidirect

Maximal subgroups

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

subgroup	index
#20253898	2
#20253396	2
C₂×D₄×C₄₇⋊C₈	2
#20242785	2
#20242775	2
#20242765	2
#20242761	2
#20242134	2
#20242045	2
#20242043	2
C₄₇×#3101	2
#19105	47