Subgroups — #26369601

Order 12032.

738 conjugacy classes of subgroups.

The subgroup lattice has 436 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#15689558	C₂	1	1	yes	maximal, characteristic
2	#135×Dic₄₇	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#15689205	C₂	1	1	yes	maximal, characteristic, complemented
4	#20245261	C₂	1	2	yes	maximal, complemented
5	#20245255	C₂	1	2	yes	maximal, complemented
6	#20245237	C₂	1	2	yes	maximal, complemented
7	#20245232	C₂	1	2	yes	maximal, complemented
8	#20245174	C₂	1	1	yes	maximal, characteristic, complemented
9	#20245105	C₂	1	1	yes	maximal, characteristic, complemented
10	M₃₂×Dic₄₇	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄₇×#2139	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×D₃₇₆	C₂²	1	1	yes	characteristic
13	#41×Dic₄₇	—	2	1	no	—
14	C₂×#13093986	—	2	1	no	—
15	#15689558	C₄	1	8	yes	complemented
16	C₂×#13093967	C₂²	1	2	yes	—
17	C₂×#13093965	C₂²	1	2	yes	—
18	C₂×#13093964	C₂²	1	1	yes	characteristic
19	Q₁₆×Dic₄₇	C₂²	1	1	yes	characteristic, complemented
20	Q₁₆×Dic₄₇	C₂²	1	1	yes	characteristic, complemented
21	SD₁₆×Dic₄₇	—	2	1	no	—
22	SD₁₆×Dic₄₇	—	2	1	no	—
23	D₈×Dic₄₇	C₂²	1	1	yes	characteristic, complemented
24	D₈×Dic₄₇	C₂²	1	1	yes	characteristic, complemented
25	#15689205	—	2	1	no	—
26	#15689205	—	2	1	no	—
27	#15689205	C₂²	1	2	yes	—
28	#15689205	C₂²	1	2	yes	—
29	#15689161	C₂²	1	1	yes	characteristic
30	#15689119	—	2	1	no	—
31	C₂×#13093944	—	2	1	no	—
32	C₂×C₈×Dic₄₇	C₂²	1	1	yes	characteristic
33	#15688950	C₂²	1	2	yes	complemented
34	#15688948	C₂²	1	2	yes	complemented
35	#15688925	C₂²	1	2	yes	—
36	#15688925	C₂²	1	2	yes	—
37	#15688898	C₂²	1	2	yes	complemented
38	C₁₆×Dic₄₇	C₂²	1	2	yes	complemented
39	C₂×#135×C₄₇	C₂²	1	1	yes	characteristic
40	C₂×M₃₂×C₄₇	C₂²	1	1	yes	characteristic
41	C₂×#107×C₄₇	C₂²	1	1	yes	characteristic
42	C₄₇×#358	C₂²	1	2	yes	complemented
43	C₄₇×#357	C₂²	1	2	yes	complemented
44	C₂²×D₁₈₈	—	2	1	no	—
45	C₂²×C₄×D₄₇	—	4	1	no	—
46	C₂×D₃₇₆	—	2	1	no	—
47	C₂×D₃₇₆	—	2	2	no	—
48	C₂×D₃₇₆	C₂×C₄	1	4	yes	complemented
49	C₂×D₃₇₆	C₂³	1	2	yes	—
50	C₂²×C₄₇⋊C₈	D₄	1	1	yes	characteristic
51	Q₈×Dic₄₇	—	2	1	no	—
52	Q₈×Dic₄₇	—	2	1	no	—
53	D₄×Dic₄₇	—	2	1	no	—
54	D₄×Dic₄₇	—	2	1	no	—
55	D₄×Dic₄₇	—	4	1	no	—
56	D₄×Dic₄₇	—	4	1	no	—
57	#13093986	—	2	2	no	—
58	#13093986	—	2	2	no	—
59	#13093986	—	4	1	no	—
60	#13093986	—	4	1	no	—
61	#13093983	—	2	1	no	—
62	#13093983	—	4	1	no	—
63	C₂×(C₂×D₄₇)⋊C₄	—	4	1	no	—
64	C₂×C₄×Dic₄₇	—	4	1	no	—
65	C₂×C₄×Dic₄₇	D₄	1	1	yes	characteristic
66	#13093967	C₂×C₄	1	8	yes	complemented
67	#13093965	C₂×C₄	1	8	yes	complemented
68	#13093964	C₂×C₄	1	4	yes	complemented
69	C₂×C₄₇⋊C₁₆	C₂³	1	2	yes	—
70	#13093958	C₂³	1	1	yes	characteristic
71	#13093958	C₂³	1	1	yes	characteristic
72	#13093956	—	2	1	no	—
73	#13093948	—	2	1	no	—
74	#13093948	—	2	1	no	—
75	#13093945	—	2	1	no	—
76	#13093945	—	2	1	no	—
77	#13093944	—	2	2	no	—
78	#13093944	—	2	2	no	—
79	C₈×Dic₄₇	D₄	1	1	yes	characteristic
80	C₈×Dic₄₇	D₄	1	1	yes	characteristic
81	C₈×Dic₄₇	C₂³	1	1	yes	characteristic
82	C₈×Dic₄₇	C₂³	1	1	yes	characteristic
83	C₂×#41×C₄₇	—	2	1	no	—
84	#135×C₄₇	—	2	2	no	—
85	#135×C₄₇	C₂×C₄	1	4	yes	complemented
86	C₂×Q₁₆×C₄₇	C₂³	1	1	yes	characteristic
87	C₂×SD₁₆×C₄₇	—	2	1	no	—
88	C₂×D₈×C₄₇	C₂³	1	1	yes	characteristic
89	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
90	C₂×C₄⋊C₄×C₄₇	—	2	1	no	—
91	M₃₂×C₄₇	—	2	2	no	—
92	C₂×C₁₆×C₄₇	C₂³	1	2	yes	—
93	#107×C₄₇	—	2	1	no	—
94	#107×C₄₇	C₂³	1	2	yes	—
95	C₂³×D₄₇	—	4	1	no	—
96	#41×C₄₇	—	2	4	no	—
97	#41×C₄₇	—	4	2	no	—
98	C₂×Q₈×C₄₇	—	2	1	no	—
99	C₂×D₄×C₄₇	—	2	1	no	—
100	C₂×D₄×C₄₇	—	4	1	no	—
101	C₂²×C₄×C₄₇	—	4	1	no	—
102	C₂²×C₄×C₄₇	—	4	1	no	—
103	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
104	C₂²×Dic₄₇	—	4	1	no	—
105	C₂²×Dic₄₇	—	4	1	no	—
106	C₂²×Dic₄₇	D₈	1	1	yes	characteristic
107	C₂²×Dic₄₇	D₈	1	1	yes	characteristic
108	C₂×D₁₈₈	—	2	4	no	—
109	C₂×D₁₈₈	—	2	2	no	—
110	C₂×D₁₈₈	—	4	1	no	—
111	C₂×D₁₈₈	—	4	2	no	—
112	C₂×C₄×D₄₇	—	4	2	no	—
113	C₂×C₄×D₄₇	—	4	2	no	—
114	C₂×C₄×D₄₇	—	8	4	no	—
115	Q₁₆×C₄₇	—	2	1	no	—
116	Q₁₆×C₄₇	C₂²×C₄	1	2	yes	complemented
117	SD₁₆×C₄₇	—	2	4	no	—
118	D₈×C₄₇	—	2	1	no	—
119	D₈×C₄₇	C₂²×C₄	1	2	yes	complemented
120	C₂×C₈×C₄₇	C₂²×C₄	1	2	yes	—
121	C₂×C₈×C₄₇	C₂×D₄	1	1	yes	characteristic
122	C₂×C₈×C₄₇	#41	1	2	yes	—
123	C₂×C₈×C₄₇	C₂⁴	1	1	yes	characteristic
124	C₄⋊C₄×C₄₇	—	2	2	no	—
125	C₄⋊C₄×C₄₇	—	4	1	no	—
126	C₂²⋊Dic₄₇	—	4	1	no	—
127	C₂²⋊Dic₄₇	—	4	1	no	—
128	C₂²⋊Dic₄₇	—	4	1	no	—
129	(C₂×D₄₇)⋊C₄	—	4	2	no	—
130	(C₂×D₄₇)⋊C₄	—	4	2	no	—
131	C₄⋊Dic₄₇	—	2	1	no	—
132	C₄⋊Dic₄₇	—	2	1	no	—
133	C₄⋊Dic₄₇	—	4	1	no	—
134	C₄⋊Dic₄₇	—	4	1	no	—
135	C₄×Dic₄₇	—	4	1	no	—
136	C₄×Dic₄₇	—	4	1	no	—
137	C₄×Dic₄₇	—	4	1	no	—
138	C₄×Dic₄₇	D₈	1	1	yes	characteristic
139	C₄×Dic₄₇	D₈	1	1	yes	characteristic
140	C₄×Dic₄₇	C₂×D₄	1	1	yes	characteristic
141	C₄×Dic₄₇	C₂×D₄	1	1	yes	characteristic
142	C₂×C₄₇⋊C₈	—	2	2	no	—
143	C₂×C₄₇⋊C₈	C₂×D₄	1	1	yes	characteristic
144	C₂×C₄₇⋊C₈	C₂×D₄	1	1	yes	characteristic
145	D₃₇₆	—	2	4	no	—
146	D₃₇₆	—	2	2	no	—
147	D₃₇₆	C₂²×C₄	1	4	yes	—
148	C₁₆×C₄₇	—	2	2	no	—
149	C₄₇⋊C₁₆	C₂²×C₄	1	4	yes	complemented
150	C₂³×C₄₇	—	4	1	no	—
151	C₂³×C₄₇	C₂×D₈	1	1	yes	characteristic
152	C₂²×D₄₇	—	4	2	no	—
153	C₂²×D₄₇	—	4	4	no	—
154	C₂²×D₄₇	—	8	2	no	—
155	C₂²×D₄₇	—	8	2	no	—
156	Q₈×C₄₇	—	2	2	no	—
157	Q₈×C₄₇	—	4	1	no	—
158	D₄×C₄₇	—	2	2	no	—
159	D₄×C₄₇	—	4	4	no	—
160	D₄×C₄₇	—	4	1	no	—
161	C₂×C₄×C₄₇	—	4	1	no	—
162	C₂×C₄×C₄₇	—	4	4	no	—
163	C₂×C₄×C₄₇	—	4	2	no	—
164	C₂×C₄×C₄₇	—	8	2	no	—
165	C₂×C₄×C₄₇	C₄×D₄	1	2	yes	—
166	C₂×C₄×C₄₇	C₂×D₈	1	1	yes	characteristic
167	C₂×C₄×C₄₇	#135	1	2	yes	—
168	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
169	C₂×Dic₄₇	—	2	2	no	—
170	C₂×Dic₄₇	—	4	1	no	—
171	C₂×Dic₄₇	—	4	1	no	—
172	C₂×Dic₄₇	—	4	1	no	—
173	C₂×Dic₄₇	—	8	2	no	—
174	C₂×Dic₄₇	—	8	2	no	—
175	C₂×Dic₄₇	C₂×D₈	1	1	yes	characteristic
176	C₂×Dic₄₇	C₂×D₈	1	1	yes	characteristic
177	C₂×Dic₄₇	C₂×D₈	1	1	yes	characteristic
178	C₂×Dic₄₇	C₂×D₈	1	1	yes	characteristic
179	D₁₈₈	—	2	4	no	—
180	D₁₈₈	—	4	2	no	—
181	D₁₈₈	—	4	4	no	—
182	C₄×D₄₇	—	8	4	no	—
183	C₄×D₄₇	—	8	4	no	—
184	C₈×C₄₇	C₄×D₄	1	2	yes	—
185	C₈×C₄₇	C₂³×C₄	1	1	yes	characteristic
186	C₈×C₄₇	C₂×#41	1	1	yes	characteristic
187	C₄₇⋊C₈	—	2	1	no	—
188	C₄₇⋊C₈	—	2	1	no	—
189	C₄×#509	—	47	1	no	maximal, Sylow
190	C₂²×C₄₇	—	2	1	no	—
191	C₂²×C₄₇	—	2	1	no	—
192	C₂²×C₄₇	—	4	2	no	—
193	C₂²×C₄₇	—	8	1	no	—
194	C₂²×C₄₇	—	8	1	no	—
195	C₂²×C₄₇	C₄×D₈	1	2	yes	—
196	C₂²×C₄₇	C₂²×D₈	1	1	yes	characteristic
197	C₂×D₄₇	—	4	4	no	—
198	C₂×D₄₇	—	8	8	no	—
199	C₂×D₄₇	—	8	2	no	—
200	C₂×D₄₇	—	8	2	no	—
201	C₄×C₄₇	—	4	2	no	—
202	C₄×C₄₇	—	8	2	no	—
203	C₄×C₄₇	C₄×D₈	1	2	yes	—
204	C₄×C₄₇	C₂×C₄×D₄	1	1	yes	characteristic
205	C₄×C₄₇	C₂×#135	1	1	yes	characteristic
206	Dic₄₇	—	2	1	no	—
207	Dic₄₇	—	2	1	no	—
208	Dic₄₇	—	2	1	no	—
209	Dic₄₇	—	8	1	no	—
210	Dic₄₇	—	8	1	no	—
211	Dic₄₇	#509	1	2	yes	complemented
212	C₂×#509	—	47	1	no	—
213	C₄×#135	—	47	1	no	—
214	C₂×C₄×D₈	—	47	1	no	—
215	#2177	—	47	2	no	—
216	#2175	—	47	2	no	—
217	C₄×SD₃₂	—	47	2	no	—
218	C₄×D₁₆	—	47	2	no	—
219	#2159	—	47	1	no	—
220	#2140	—	47	1	no	—
221	#2139	D₄₇	1	1	yes	characteristic, complemented
222	C₄×M₃₂	—	47	1	no	—
223	C₂×C₄₇	—	2	2	no	—
224	C₂×C₄₇	—	8	2	no	—
225	C₂×C₄₇	C₂×C₄×D₈	1	1	yes	characteristic
226	C₂×C₄₇	C₂×#509	1	1	yes	characteristic
227	C₂×C₄₇	#3414	1	1	yes	characteristic
228	D₄₇	—	8	4	no	—
229	C₂×#135	C₂×D₄₇	1	1	yes	characteristic
230	C₂²×D₈	—	47	1	no	—
231	C₄×#41	—	94	1	no	—
232	C₂×C₄×D₄	—	94	1	no	—
233	#509	—	47	8	no	—
234	C₂×SD₃₂	—	47	2	no	—
235	C₂×D₁₆	—	47	2	no	—
236	C₂×M₃₂	—	47	1	no	—
237	C₂×M₃₂	C₂×D₄₇	1	1	yes	characteristic
238	C₄×Q₁₆	—	47	1	no	—
239	C₄×Q₁₆	—	47	1	no	—
240	C₄×SD₁₆	—	94	1	no	—
241	C₄×SD₁₆	—	94	1	no	—
242	C₄×D₈	—	47	1	no	—
243	C₄×D₈	—	47	1	no	—
244	C₄×D₈	—	47	2	no	—
245	C₄×D₈	—	47	2	no	—
246	C₄×D₈	—	94	1	no	—
247	C₄×D₈	—	94	1	no	—
248	#427	—	47	1	no	—
249	C₂×#107	C₂×D₄₇	1	1	yes	characteristic
250	#416	—	94	1	no	—
251	C₂×#102	—	94	1	no	—
252	C₂×C₄×C₈	—	47	1	no	—
253	#367	—	47	2	no	—
254	#366	—	47	2	no	—
255	#358	C₂×D₄₇	1	2	yes	complemented
256	#357	—	47	2	no	—
257	#357	—	47	2	no	—
258	#357	C₂×D₄₇	1	2	yes	complemented
259	#346	—	47	2	no	—
260	C₄×C₁₆	—	47	2	no	—
261	C₄₇	C₄×#509	1	1	yes	characteristic, complemented, Sylow
262	C₂×#41	—	2	1	no	—
263	C₂²×D₄	—	94	1	no	—
264	C₂³×C₄	—	188	1	no	—
265	#135	—	2	2	no	—
266	#135	C₄×D₄₇	1	4	yes	complemented
267	C₂×Q₁₆	C₂²×D₄₇	1	1	yes	characteristic
268	C₂×SD₁₆	—	2	1	no	—
269	C₂×D₈	—	47	4	no	—
270	C₂×D₈	—	47	2	no	—
271	C₂×D₈	—	94	1	no	—
272	C₂×D₈	—	94	2	no	—
273	C₂×D₈	C₂²×D₄₇	1	1	yes	characteristic
274	C₂²×C₈	—	47	1	no	—
275	C₂²×C₈	C₂²×D₄₇	1	1	yes	characteristic
276	C₄×Q₈	—	94	1	no	—
277	C₄×Q₈	—	94	1	no	—
278	C₄×D₄	—	94	2	no	—
279	C₄×D₄	—	94	2	no	—
280	C₄×D₄	—	94	1	no	—
281	C₄×D₄	—	94	1	no	—
282	C₄×D₄	—	188	1	no	—
283	C₄×D₄	—	188	1	no	—
284	C₄×D₄	—	188	1	no	—
285	C₄×D₄	—	188	1	no	—
286	#117	—	94	1	no	—
287	#117	—	188	1	no	—
288	C₂×C₄⋊C₄	—	2	1	no	—
289	C₂×C₂²⋊C₄	—	188	1	no	—
290	C₂×C₄²	—	47	1	no	—
291	C₂×C₄²	—	188	1	no	—
292	SD₃₂	—	47	8	no	—
293	D₁₆	—	47	8	no	—
294	M₃₂	—	2	2	no	—
295	M₃₂	—	47	4	no	—
296	C₂×C₁₆	—	47	2	no	—
297	C₂×C₁₆	C₂²×D₄₇	1	2	yes	—
298	#107	—	2	1	no	—
299	#107	—	47	1	no	—
300	#107	—	47	1	no	—
301	#107	C₂²×D₄₇	1	2	yes	—
302	#106	—	94	1	no	—
303	#103	—	94	1	no	—
304	#103	—	94	1	no	—
305	#102	—	94	2	no	—
306	#102	—	94	2	no	—
307	#102	—	94	1	no	—
308	#102	—	94	1	no	—
309	C₄×C₈	—	47	1	no	—
310	C₄×C₈	—	47	1	no	—
311	C₄×C₈	—	47	1	no	—
312	C₄×C₈	—	47	1	no	—
313	C₂⁴	—	188	1	no	—
314	#41	—	2	4	no	—
315	#41	—	4	2	no	—
316	C₂×Q₈	—	2	1	no	—
317	C₂×D₄	—	2	1	no	—
318	C₂×D₄	—	4	1	no	—
319	C₂×D₄	—	94	4	no	—
320	C₂×D₄	—	94	2	no	—
321	C₂×D₄	—	188	1	no	—
322	C₂×D₄	—	188	2	no	—
323	C₂²×C₄	—	4	1	no	—
324	C₂²×C₄	—	4	1	no	—
325	C₂²×C₄	—	47	1	no	—
326	C₂²×C₄	—	47	1	no	—
327	C₂²×C₄	—	376	4	no	—
328	C₂²×C₄	—	188	2	no	—
329	C₂²×C₄	—	188	2	no	—
330	C₂²×C₄	—	188	1	no	—
331	C₂²×C₄	—	188	1	no	—
332	C₂²×C₄	D₄×D₄₇	1	1	yes	characteristic
333	Q₁₆	—	2	1	no	—
334	Q₁₆	C₂×C₄×D₄₇	1	2	yes	complemented
335	SD₁₆	—	2	4	no	—
336	D₈	—	2	1	no	—
337	D₈	—	47	4	no	—
338	D₈	—	94	4	no	—
339	D₈	—	94	2	no	—
340	D₈	C₂×C₄×D₄₇	1	2	yes	complemented
341	C₂×C₈	—	47	1	no	—
342	C₂×C₈	—	47	1	no	—
343	C₂×C₈	—	94	2	no	—
344	C₂×C₈	C₂×C₄×D₄₇	1	2	yes	—
345	C₂×C₈	D₄×D₄₇	1	1	yes	characteristic
346	C₂×C₈	#10625352	1	2	yes	—
347	C₂×C₈	C₂³×D₄₇	1	1	yes	characteristic
348	C₄⋊C₄	—	2	2	no	—
349	C₄⋊C₄	—	4	1	no	—
350	C₄⋊C₄	—	94	1	no	—
351	C₄⋊C₄	—	94	1	no	—
352	C₄⋊C₄	—	188	1	no	—
353	C₄⋊C₄	—	188	1	no	—
354	C₂²⋊C₄	—	188	2	no	—
355	C₂²⋊C₄	—	188	2	no	—
356	C₂²⋊C₄	—	188	1	no	—
357	C₂²⋊C₄	—	188	1	no	—
358	C₂²⋊C₄	—	188	1	no	—
359	C₄²	—	47	1	no	—
360	C₄²	—	47	1	no	—
361	C₄²	—	47	1	no	—
362	C₄²	—	47	1	no	—
363	C₄²	—	188	1	no	—
364	C₄²	—	188	1	no	—
365	C₄²	—	188	1	no	—
366	C₁₆	—	2	2	no	—
367	C₁₆	—	47	4	no	—
368	C₂³	—	4	1	no	—
369	C₂³	—	376	2	no	—
370	C₂³	—	376	2	no	—
371	C₂³	—	188	2	no	—
372	C₂³	—	188	4	no	—
373	C₂³	D₈×D₄₇	1	1	yes	characteristic
374	Q₈	—	2	2	no	—
375	Q₈	—	4	1	no	—
376	D₄	—	2	2	no	—
377	D₄	—	4	4	no	—
378	D₄	—	4	1	no	—
379	D₄	—	94	4	no	—
380	D₄	—	188	2	no	—
381	D₄	—	188	4	no	—
382	C₂×C₄	—	4	1	no	—
383	C₂×C₄	—	4	4	no	—
384	C₂×C₄	—	4	2	no	—
385	C₂×C₄	—	8	2	no	—
386	C₂×C₄	—	47	1	no	—
387	C₂×C₄	—	47	1	no	—
388	C₂×C₄	—	47	1	no	—
389	C₂×C₄	—	47	1	no	—
390	C₂×C₄	—	94	2	no	—
391	C₂×C₄	—	376	4	no	—
392	C₂×C₄	—	376	4	no	—
393	C₂×C₄	—	376	2	no	—
394	C₂×C₄	—	376	2	no	—
395	C₂×C₄	—	188	1	no	—
396	C₂×C₄	—	188	1	no	—
397	C₂×C₄	—	188	1	no	—
398	C₂×C₄	(C₂²⋊D₄₇)⋊C₄	1	2	yes	—
399	C₂×C₄	D₈×D₄₇	1	1	yes	characteristic
400	C₂×C₄	#13094045	1	2	yes	—
401	C₂×C₄	C₂×D₄×D₄₇	1	1	yes	characteristic
402	C₈	—	94	1	no	—
403	C₈	—	94	1	no	—
404	C₈	(C₂²⋊D₄₇)⋊C₄	1	2	yes	—
405	C₈	C₂²×C₄×D₄₇	1	1	yes	characteristic
406	C₈	C₂×#10625352	1	1	yes	characteristic
407	C₂²	—	2	1	no	—
408	C₂²	—	2	1	no	—
409	C₂²	—	4	2	no	—
410	C₂²	—	8	1	no	—
411	C₂²	—	8	1	no	—
412	C₂²	—	376	8	no	—
413	C₂²	—	376	2	no	—
414	C₂²	—	376	2	no	—
415	C₂²	—	188	4	no	—
416	C₂²	#15689203	1	2	yes	—
417	C₂²	C₂×D₈×D₄₇	1	1	yes	characteristic
418	C₄	—	4	2	no	—
419	C₄	—	8	2	no	—
420	C₄	—	47	2	no	—
421	C₄	—	94	1	no	—
422	C₄	—	94	1	no	—
423	C₄	—	94	1	no	—
424	C₄	—	376	1	no	—
425	C₄	—	376	1	no	—
426	C₄	#15689203	1	2	yes	—
427	C₄	C₂×(C₂²⋊D₄₇)⋊C₄	1	1	yes	characteristic
428	C₄	C₂×#13094045	1	1	yes	characteristic
429	C₂	—	2	2	no	—
430	C₂	—	8	2	no	—
431	C₂	—	376	4	no	—
432	C₂	C₂×#15689203	1	1	yes	characteristic
433	C₂	#509×D₄₇	1	1	yes	characteristic
434	C₂	#20256523	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂×D₈×D₄₇
commutator	C₈×C₄₇	C₂³×C₄
Frattini	C₂×C₈	C₂³×D₄₇
Fitting	C₄₇×#2139	C₂
socle	C₂²×C₄₇	C₂²×D₈
prime radical	C₂×#15689558	C₂
cosocle	C₂×C₈×C₄₇	C₂⁴
hypercenter	#2139	D₄₇
hypocenter	C₄₇	C₄×#509
LCS	G ▷ C₈×C₄₇ ▷ C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂² ◁ C₂²×C₄ ◁ C₂²×C₈ ◁ #2139

Complements

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

N	H ≅ G/N	type
2. #135×Dic₄₇	C₂	semidirect
3. C₂×#15689205	C₂	semidirect
4. #20245261	C₂	semidirect
5. #20245255	C₂	semidirect
6. #20245237	C₂	semidirect
7. #20245232	C₂	semidirect
8. #20245174	C₂	semidirect
9. #20245105	C₂	semidirect
10. M₃₂×Dic₄₇	C₂	semidirect
11. C₄₇×#2139	C₂	semidirect
15. #15689558	C₄	semidirect
19. Q₁₆×Dic₄₇	C₂²	semidirect
20. Q₁₆×Dic₄₇	C₂²	semidirect
23. D₈×Dic₄₇	C₂²	semidirect
24. D₈×Dic₄₇	C₂²	semidirect
33. #15688950	C₂²	semidirect
34. #15688948	C₂²	semidirect
37. #15688898	C₂²	semidirect
38. C₁₆×Dic₄₇	C₂²	semidirect
42. C₄₇×#358	C₂²	semidirect
43. C₄₇×#357	C₂²	semidirect
48. C₂×D₃₇₆	C₂×C₄	semidirect
66. #13093967	C₂×C₄	semidirect
67. #13093965	C₂×C₄	semidirect
68. #13093964	C₂×C₄	semidirect
85. #135×C₄₇	C₂×C₄	semidirect
116. Q₁₆×C₄₇	C₂²×C₄	semidirect
119. D₈×C₄₇	C₂²×C₄	semidirect
149. C₄₇⋊C₁₆	C₂²×C₄	semidirect
211. Dic₄₇	#509	semidirect
221. #2139	D₄₇	semidirect
255. #358	C₂×D₄₇	semidirect
258. #357	C₂×D₄₇	semidirect
261. C₄₇	C₄×#509	semidirect
266. #135	C₄×D₄₇	semidirect
334. Q₁₆	C₂×C₄×D₄₇	semidirect
340. D₈	C₂×C₄×D₄₇	semidirect

Maximal subgroups

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

subgroup	index
C₂×#15689558	2
#135×Dic₄₇	2
C₂×#15689205	2
#20245261	2
#20245255	2
#20245237	2
#20245232	2
#20245174	2
#20245105	2
M₃₂×Dic₄₇	2
C₄₇×#2139	2
C₄×#509	47