Subgroups — #26186869

Order 12032.

594 conjugacy classes of subgroups.

The subgroup lattice has 438 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20253988	C₂	1	1	yes	maximal, characteristic
2	#20252357	C₂	1	1	yes	maximal, characteristic
3	#20252323	C₂	1	1	yes	maximal, characteristic, complemented
4	#20242294	C₂	1	2	yes	maximal, complemented
5	#20242293	C₂	1	2	yes	maximal, complemented
6	#20242192	C₂	1	2	yes	maximal, complemented
7	#20242185	C₂	1	2	yes	maximal, complemented
8	#20242156	C₂	1	1	yes	maximal, characteristic, complemented
9	#20241854	C₂	1	1	yes	maximal, characteristic
10	#20241669	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄₇×#1497	C₂	1	1	yes	maximal, characteristic, complemented
12	#15689657	C₂²	1	1	yes	characteristic
13	#15689529	C₄	1	1	yes	characteristic
14	#15689515	C₄	1	1	yes	characteristic
15	#15689491	C₄	1	1	yes	characteristic
16	#15689485	C₄	1	1	yes	characteristic
17	#15689379	C₄	1	2	yes	—
18	#15689371	C₄	1	2	yes	—
19	#15689254	—	2	1	no	—
20	#15689254	C₂²	1	2	yes	—
21	#15689250	C₂²	1	1	yes	characteristic
22	Q₈×C₄₇⋊C₈	—	2	1	no	—
23	Q₈×C₄₇⋊C₈	C₂²	1	2	yes	—
24	#15689247	C₂²	1	1	yes	characteristic
25	C₄×#10625337	C₂²	1	2	yes	—
26	C₄×#10625336	C₂²	1	2	yes	—
27	#15689200	C₂²	1	1	yes	characteristic
28	#15689191	—	2	1	no	—
29	#15689188	C₂²	1	1	yes	characteristic
30	(C₂²⋊D₄₇)⋊C₈	—	2	1	no	—
31	#15689185	—	2	1	no	—
32	#15689150	—	2	1	no	—
33	#15689147	C₂²	1	1	yes	characteristic
34	#15689080	—	2	1	no	—
35	#15689079	—	2	1	no	—
36	C₄×#10625329	C₂²	1	1	yes	characteristic
37	C₂×C₄×C₄₇⋊C₈	C₂²	1	1	yes	characteristic
38	#15688875	C₂²	1	2	yes	—
39	#15688873	C₂²	1	2	yes	—
40	#15688855	C₂²	1	2	yes	—
41	#15688852	C₂²	1	2	yes	—
42	#15688845	C₂²	1	2	yes	—
43	C₈×C₄₇⋊C₈	C₂²	1	2	yes	—
44	C₄₇×#533	C₂²	1	1	yes	characteristic
45	C₄₇×#432	C₂²	1	1	yes	characteristic
46	C₄₇×#431	C₂²	1	1	yes	characteristic
47	C₄₇×Q₈⋊C₈	C₂²	1	2	yes	—
48	C₄₇×Q₈⋊C₈	C₂²	1	2	yes	—
49	C₂×#10625337	C₂×C₄	1	2	yes	—
50	C₂×#10625336	C₂×C₄	1	2	yes	—
51	C₂×#10625329	—	2	1	no	—
52	C₂×#10625329	C₂×C₄	1	2	yes	—
53	C₂×#10625324	—	2	1	no	—
54	C₂²×C₄₇⋊C₈	D₄	1	1	yes	characteristic
55	C₂²×C₄₇⋊C₈	D₄	1	1	yes	characteristic
56	C₂×C₈×D₄₇	—	2	1	no	—
57	#13094018	—	2	1	no	—
58	#13094016	C₂×C₄	1	1	yes	characteristic
59	#13094012	C₂×C₄	1	1	yes	characteristic
60	#13094007	—	2	1	no	—
61	#13094003	C₂×C₄	1	1	yes	characteristic
62	#13093998	C₂×C₄	1	1	yes	characteristic
63	C₄×Dic₉₄	C₂³	1	1	yes	characteristic
64	C₄×D₁₈₈	C₂³	1	1	yes	characteristic
65	C₄×C₂²⋊D₄₇	—	2	1	no	—
66	#13093981	—	2	1	no	—
67	#13093957	C₂×C₄	1	2	yes	—
68	#13093955	C₂×C₄	1	2	yes	—
69	C₄⋊(C₄₇⋊C₈)	—	2	1	no	—
70	C₄⋊(C₄₇⋊C₈)	—	2	2	no	—
71	C₄⋊(C₄₇⋊C₈)	—	2	2	no	—
72	C₄⋊(C₄₇⋊C₈)	C₂³	1	2	yes	—
73	Dic₄₇⋊C₈	—	2	1	no	—
74	Dic₄₇⋊C₈	—	2	1	no	—
75	#13093948	C₂×C₄	1	2	yes	—
76	#13093948	C₂×C₄	1	2	yes	—
77	#13093947	C₂×C₄	1	2	yes	—
78	#13093944	C₂×C₄	1	2	yes	—
79	(C₂×D₄₇)⋊C₈	—	2	1	no	—
80	(C₂×D₄₇)⋊C₈	—	2	1	no	—
81	#13093935	—	2	2	no	—
82	#13093935	C₂×C₄	1	1	yes	characteristic
83	#13093935	C₂×C₄	1	1	yes	characteristic
84	#13093934	—	2	1	no	—
85	C₄×C₄₇⋊C₈	—	2	2	no	—
86	C₄×C₄₇⋊C₈	D₄	1	1	yes	characteristic
87	C₄×C₄₇⋊C₈	D₄	1	1	yes	characteristic
88	C₄×C₄₇⋊C₈	C₂³	1	2	yes	—
89	C₄×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
90	C₄×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
91	C₈×Dic₄₇	—	2	1	no	—
92	C₄⋊Q₈×C₄₇	C₂×C₄	1	1	yes	characteristic
93	C₄⋊Q₈×C₄₇	C₂×C₄	1	1	yes	characteristic
94	#125×C₄₇	—	2	1	no	—
95	C₂²⋊Q₈×C₄₇	—	2	1	no	—
96	C₂²⋊Q₈×C₄₇	C₂×C₄	1	2	yes	—
97	C₄×Q₈×C₄₇	—	2	1	no	—
98	C₄×Q₈×C₄₇	C₂³	1	2	yes	—
99	#117×C₄₇	—	2	1	no	—
100	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
101	C₄⋊C₈×C₄₇	—	2	1	no	—
102	C₄⋊C₈×C₄₇	C₂³	1	1	yes	characteristic
103	C₄⋊C₈×C₄₇	C₂³	1	1	yes	characteristic
104	C₂²⋊C₈×C₄₇	—	2	1	no	—
105	C₂²⋊C₈×C₄₇	—	2	1	no	—
106	#97×C₄₇	—	2	1	no	—
107	C₄×C₈×C₄₇	C₂³	1	2	yes	—
108	C₂×Q₈×C₄₇	—	2	1	no	—
109	C₂×Q₈×C₄₇	C₂²×C₄	1	2	yes	—
110	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
111	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
112	C₂²×C₄×C₄₇	#41	1	1	yes	characteristic
113	C₂×C₂²⋊D₄₇	—	2	1	no	—
114	C₂×D₁₈₈	C₂²×C₄	1	1	yes	characteristic
115	C₂×C₄×D₄₇	—	2	1	no	—
116	C₂×Dic₉₄	C₂²×C₄	1	1	yes	characteristic
117	C₂×C₈×C₄₇	—	2	1	no	—
118	C₂×C₈×C₄₇	—	2	1	no	—
119	C₂×C₈×C₄₇	—	2	2	no	—
120	C₄⋊C₄×C₄₇	—	2	1	no	—
121	C₄⋊C₄×C₄₇	—	2	1	no	—
122	C₄⋊C₄×C₄₇	—	2	1	no	—
123	C₄⋊C₄×C₄₇	—	2	2	no	—
124	C₄⋊C₄×C₄₇	—	2	2	no	—
125	C₄⋊C₄×C₄₇	C₂²×C₄	1	2	yes	—
126	C₂²⋊C₄×C₄₇	—	2	2	no	—
127	C₄²×C₄₇	—	2	2	no	—
128	C₄²×C₄₇	C₂²×C₄	1	1	yes	characteristic
129	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
130	C₄²×C₄₇	#41	1	1	yes	characteristic
131	C₄²×C₄₇	C₂⁴	1	1	yes	characteristic
132	C₂²⋊Dic₄₇	—	2	1	no	—
133	#10625337	—	2	4	no	—
134	#10625336	—	2	4	no	—
135	(C₂×D₄₇)⋊C₄	—	2	1	no	—
136	(C₂×D₄₇)⋊C₄	—	2	1	no	—
137	(C₂×D₄₇)⋊C₄	—	2	1	no	—
138	(C₂×D₄₇)⋊C₄	—	2	1	no	—
139	C₄⋊Dic₄₇	C₂²×C₄	1	1	yes	characteristic
140	C₄⋊Dic₄₇	C₂²×C₄	1	1	yes	characteristic
141	Dic₄₇⋊C₄	—	2	1	no	—
142	Dic₄₇⋊C₄	—	2	1	no	—
143	Dic₄₇⋊C₄	—	2	1	no	—
144	Dic₄₇⋊C₄	—	2	1	no	—
145	C₄×Dic₄₇	—	2	1	no	—
146	#10625329	—	2	4	no	—
147	#10625329	—	4	2	no	—
148	C₂×C₄₇⋊C₈	—	2	2	no	—
149	C₂×C₄₇⋊C₈	—	2	2	no	—
150	C₂×C₄₇⋊C₈	—	4	1	no	—
151	C₂×C₄₇⋊C₈	C₂²×C₄	1	2	yes	—
152	C₂×C₄₇⋊C₈	C₂²×C₄	1	2	yes	—
153	C₂×C₄₇⋊C₈	C₂×D₄	1	1	yes	characteristic
154	C₂×C₄₇⋊C₈	C₂×D₄	1	1	yes	characteristic
155	C₂×C₄₇⋊C₈	C₂×D₄	1	1	yes	characteristic
156	C₂×C₄₇⋊C₈	C₂×D₄	1	1	yes	characteristic
157	#10625324	—	4	2	no	—
158	C₈×D₄₇	—	4	2	no	—
159	C₂³×C₄₇	C₄×D₄	1	1	yes	characteristic
160	C₂²×D₄₇	—	2	1	no	—
161	Q₈×C₄₇	—	2	2	no	—
162	Q₈×C₄₇	—	2	2	no	—
163	Q₈×C₄₇	—	4	2	no	—
164	C₂×C₄×C₄₇	—	2	2	no	—
165	C₂×C₄×C₄₇	—	2	1	no	—
166	C₂×C₄×C₄₇	—	2	1	no	—
167	C₂×C₄×C₄₇	—	2	2	no	—
168	C₂×C₄×C₄₇	—	2	2	no	—
169	C₂×C₄×C₄₇	—	4	1	no	—
170	C₂×C₄×C₄₇	C₄×D₄	1	1	yes	characteristic
171	C₂×C₄×C₄₇	C₄×D₄	1	1	yes	characteristic
172	C₂×C₄×C₄₇	C₄×D₄	1	1	yes	characteristic
173	C₂×C₄×C₄₇	C₂³×C₄	1	1	yes	characteristic
174	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
175	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
176	C₂²⋊D₄₇	—	4	2	no	—
177	C₂×Dic₄₇	—	2	1	no	—
178	C₂×Dic₄₇	—	2	1	no	—
179	C₂×Dic₄₇	—	2	1	no	—
180	D₁₈₈	—	2	2	no	—
181	C₄×D₄₇	—	4	1	no	—
182	C₄×D₄₇	—	4	1	no	—
183	Dic₉₄	—	2	2	no	—
184	C₈×C₄₇	—	4	2	no	—
185	C₈×C₄₇	—	4	1	no	—
186	C₈×C₄₇	—	4	1	no	—
187	C₄₇⋊C₈	—	2	2	no	—
188	C₄₇⋊C₈	—	2	1	no	—
189	C₄₇⋊C₈	—	2	1	no	—
190	C₄₇⋊C₈	—	2	1	no	—
191	C₄₇⋊C₈	—	4	2	no	—
192	C₄₇⋊C₈	#131	1	4	yes	—
193	C₄₇⋊C₈	#137	1	2	yes	—
194	#17965	—	47	1	no	maximal, Sylow
195	C₂²×C₄₇	—	2	1	no	—
196	C₂²×C₄₇	—	2	1	no	—
197	C₂²×C₄₇	—	2	1	no	—
198	C₂²×C₄₇	C₂×C₄×D₄	1	1	yes	characteristic
199	C₂×D₄₇	—	4	1	no	—
200	C₂×D₄₇	—	4	1	no	—
201	C₂×D₄₇	—	4	1	no	—
202	C₄×C₄₇	—	2	1	no	—
203	C₄×C₄₇	—	2	1	no	—
204	C₄×C₄₇	—	2	1	no	—
205	C₄×C₄₇	—	2	1	no	—
206	C₄×C₄₇	—	4	2	no	—
207	C₄×C₄₇	—	4	2	no	—
208	C₄×C₄₇	C₂×#131	1	2	yes	—
209	C₄×C₄₇	C₂×#137	1	1	yes	characteristic
210	C₄×C₄₇	#575	1	1	yes	characteristic
211	Dic₄₇	—	4	1	no	—
212	Dic₄₇	—	4	1	no	—
213	Dic₄₇	—	4	1	no	—
214	#3172	—	47	1	no	—
215	#2966	—	47	1	no	—
216	#2960	—	47	1	no	—
217	#1593	—	47	2	no	—
218	#1592	—	47	2	no	—
219	C₈×Q₁₆	—	47	2	no	—
220	C₈×SD₁₆	—	47	2	no	—
221	#1569	—	47	1	no	—
222	#1497	D₄₇	1	1	yes	characteristic, complemented
223	#1495	—	47	1	no	—
224	C₈×M₁₆	—	47	1	no	—
225	C₂×C₄₇	—	4	1	no	—
226	C₂×C₄₇	#2931	1	1	yes	characteristic
227	C₂×C₄₇	C₄×#137	1	1	yes	characteristic
228	C₂×C₄₇	#2955	1	1	yes	characteristic
229	D₄₇	—	8	1	no	—
230	#533	C₂×D₄₇	1	1	yes	characteristic
231	#529	—	47	1	no	—
232	#501	—	47	1	no	—
233	#497	—	47	1	no	—
234	#491	—	47	1	no	—
235	#489	—	47	1	no	—
236	#470	—	47	2	no	—
237	#468	—	47	2	no	—
238	#446	—	47	2	no	—
239	#446	—	47	1	no	—
240	#446	—	94	1	no	—
241	C₈×Q₈	—	47	2	no	—
242	C₈×Q₈	—	47	1	no	—
243	C₈×Q₈	—	94	1	no	—
244	C₄×Q₁₆	—	47	2	no	—
245	C₄×SD₁₆	—	47	2	no	—
246	#436	—	47	1	no	—
247	#435	—	94	1	no	—
248	C₈×D₄	—	47	1	no	—
249	C₈×D₄	—	94	1	no	—
250	#433	—	94	1	no	—
251	#432	C₂×D₄₇	1	1	yes	characteristic
252	#431	C₂×D₄₇	1	1	yes	characteristic
253	#424	—	94	1	no	—
254	#423	—	47	1	no	—
255	#405	—	94	1	no	—
256	#405	—	94	1	no	—
257	C₄×M₁₆	—	47	1	no	—
258	C₂×C₄×C₈	—	47	1	no	—
259	#335	—	47	2	no	—
260	#334	—	47	2	no	—
261	Q₈⋊C₈	—	47	2	no	—
262	Q₈⋊C₈	C₂×D₄₇	1	2	yes	—
263	Q₈⋊C₈	C₂×D₄₇	1	2	yes	—
264	D₄⋊C₈	—	47	2	no	—
265	#322	—	47	2	no	—
266	C₈²	—	47	2	no	—
267	C₄₇	#17965	1	1	yes	characteristic, complemented, Sylow
268	C₂×Q₁₆	—	47	2	no	—
269	C₂×SD₁₆	—	47	2	no	—
270	C₂×M₁₆	—	47	2	no	—
271	C₂×M₁₆	—	94	1	no	—
272	C₂×M₁₆	—	94	1	no	—
273	C₂²×C₈	—	47	1	no	—
274	C₂²×C₈	—	47	1	no	—
275	C₂²×C₈	—	94	1	no	—
276	C₄⋊Q₈	C₄×D₄₇	1	1	yes	characteristic
277	C₄⋊Q₈	C₄×D₄₇	1	1	yes	characteristic
278	#126	—	94	1	no	—
279	#125	—	2	1	no	—
280	#125	—	47	1	no	—
281	#124	—	47	1	no	—
282	#123	—	94	1	no	—
283	C₂²⋊Q₈	—	2	1	no	—
284	C₂²⋊Q₈	—	47	1	no	—
285	C₂²⋊Q₈	C₄×D₄₇	1	2	yes	—
286	#121	—	47	1	no	—
287	C₄×Q₈	—	2	1	no	—
288	C₄×Q₈	—	47	1	no	—
289	C₄×Q₈	C₂²×D₄₇	1	2	yes	—
290	C₄×D₄	—	47	1	no	—
291	C₄×D₄	—	94	1	no	—
292	#117	—	2	1	no	—
293	#117	—	94	1	no	—
294	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
295	#107	—	47	2	no	—
296	#106	—	47	2	no	—
297	C₄⋊C₈	—	2	1	no	—
298	C₄⋊C₈	—	47	2	no	—
299	C₄⋊C₈	—	94	2	no	—
300	C₄⋊C₈	—	94	2	no	—
301	C₄⋊C₈	—	94	1	no	—
302	C₄⋊C₈	—	94	1	no	—
303	C₄⋊C₈	—	94	1	no	—
304	C₄⋊C₈	C₂²×D₄₇	1	1	yes	characteristic
305	C₄⋊C₈	C₂²×D₄₇	1	1	yes	characteristic
306	#103	—	47	2	no	—
307	#103	—	47	2	no	—
308	#103	—	47	2	no	—
309	#102	—	47	2	no	—
310	C₂²⋊C₈	—	2	1	no	—
311	C₂²⋊C₈	—	2	1	no	—
312	C₂²⋊C₈	—	94	1	no	—
313	C₂²⋊C₈	—	94	1	no	—
314	#97	—	2	1	no	—
315	#97	—	47	1	no	—
316	#97	—	47	1	no	—
317	#97	—	94	2	no	—
318	#97	—	94	1	no	—
319	C₄×C₈	—	47	1	no	—
320	C₄×C₈	—	47	1	no	—
321	C₄×C₈	—	47	1	no	—
322	C₄×C₈	—	47	2	no	—
323	C₄×C₈	—	47	1	no	—
324	C₄×C₈	—	94	2	no	—
325	C₄×C₈	—	94	1	no	—
326	C₄×C₈	C₂²×D₄₇	1	2	yes	—
327	C₂×Q₈	—	2	1	no	—
328	C₂×Q₈	—	47	1	no	—
329	C₂×Q₈	C₂×C₄×D₄₇	1	2	yes	—
330	C₂×D₄	—	47	1	no	—
331	C₂×D₄	—	94	1	no	—
332	C₂²×C₄	—	94	1	no	—
333	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
334	C₂²×C₄	D₄×D₄₇	1	1	yes	characteristic
335	C₂²×C₄	#10625352	1	1	yes	characteristic
336	Q₁₆	—	94	4	no	—
337	SD₁₆	—	94	4	no	—
338	M₁₆	—	94	4	no	—
339	M₁₆	—	188	2	no	—
340	M₁₆	—	188	2	no	—
341	C₂×C₈	—	2	1	no	—
342	C₂×C₈	—	2	1	no	—
343	C₂×C₈	—	2	2	no	—
344	C₂×C₈	—	47	2	no	—
345	C₂×C₈	—	47	1	no	—
346	C₂×C₈	—	47	2	no	—
347	C₂×C₈	—	47	1	no	—
348	C₂×C₈	—	47	1	no	—
349	C₂×C₈	—	47	1	no	—
350	C₂×C₈	—	94	2	no	—
351	C₂×C₈	—	94	2	no	—
352	C₂×C₈	—	188	2	no	—
353	C₂×C₈	—	188	1	no	—
354	C₄⋊C₄	—	2	1	no	—
355	C₄⋊C₄	—	2	1	no	—
356	C₄⋊C₄	—	2	1	no	—
357	C₄⋊C₄	—	2	2	no	—
358	C₄⋊C₄	—	2	2	no	—
359	C₄⋊C₄	—	47	1	no	—
360	C₄⋊C₄	—	47	1	no	—
361	C₄⋊C₄	—	94	1	no	—
362	C₄⋊C₄	—	94	1	no	—
363	C₄⋊C₄	—	94	1	no	—
364	C₄⋊C₄	—	94	1	no	—
365	C₄⋊C₄	C₂×C₄×D₄₇	1	2	yes	—
366	C₂²⋊C₄	—	2	2	no	—
367	C₂²⋊C₄	—	94	1	no	—
368	C₂²⋊C₄	—	94	1	no	—
369	C₂²⋊C₄	—	94	1	no	—
370	C₂²⋊C₄	—	94	1	no	—
371	C₂²⋊C₄	—	94	1	no	—
372	C₄²	—	2	2	no	—
373	C₄²	—	94	1	no	—
374	C₄²	C₂×C₄×D₄₇	1	1	yes	characteristic
375	C₄²	D₄×D₄₇	1	1	yes	characteristic
376	C₄²	#10625352	1	1	yes	characteristic
377	C₄²	C₂³×D₄₇	1	1	yes	characteristic
378	C₂³	—	94	1	no	—
379	C₂³	(C₂²⋊D₄₇)⋊C₄	1	1	yes	characteristic
380	Q₈	—	2	2	no	—
381	Q₈	—	2	2	no	—
382	Q₈	—	4	2	no	—
383	Q₈	—	94	2	no	—
384	D₄	—	94	2	no	—
385	D₄	—	188	2	no	—
386	C₂×C₄	—	2	2	no	—
387	C₂×C₄	—	2	1	no	—
388	C₂×C₄	—	2	1	no	—
389	C₂×C₄	—	2	2	no	—
390	C₂×C₄	—	2	2	no	—
391	C₂×C₄	—	4	1	no	—
392	C₂×C₄	—	94	1	no	—
393	C₂×C₄	—	94	1	no	—
394	C₂×C₄	—	94	1	no	—
395	C₂×C₄	—	188	1	no	—
396	C₂×C₄	—	188	1	no	—
397	C₂×C₄	(C₂²⋊D₄₇)⋊C₄	1	1	yes	characteristic
398	C₂×C₄	(C₂²⋊D₄₇)⋊C₄	1	1	yes	characteristic
399	C₂×C₄	(C₂²⋊D₄₇)⋊C₄	1	1	yes	characteristic
400	C₂×C₄	C₂²×C₄×D₄₇	1	1	yes	characteristic
401	C₂×C₄	C₂×D₄×D₄₇	1	1	yes	characteristic
402	C₂×C₄	C₂×#10625352	1	1	yes	characteristic
403	C₈	—	4	2	no	—
404	C₈	—	4	1	no	—
405	C₈	—	4	1	no	—
406	C₈	—	47	4	no	—
407	C₈	—	47	2	no	—
408	C₈	—	94	2	no	—
409	C₈	—	94	1	no	—
410	C₈	—	94	1	no	—
411	C₈	—	94	1	no	—
412	C₈	—	188	2	no	—
413	C₂²	—	2	1	no	—
414	C₂²	—	2	1	no	—
415	C₂²	—	2	1	no	—
416	C₂²	—	188	1	no	—
417	C₂²	—	188	1	no	—
418	C₂²	—	188	1	no	—
419	C₂²	C₂×(C₂²⋊D₄₇)⋊C₄	1	1	yes	characteristic
420	C₄	—	2	1	no	—
421	C₄	—	2	1	no	—
422	C₄	—	2	1	no	—
423	C₄	—	2	1	no	—
424	C₄	—	4	2	no	—
425	C₄	—	4	2	no	—
426	C₄	—	188	1	no	—
427	C₄	—	188	1	no	—
428	C₄	—	188	1	no	—
429	C₄	#131×D₄₇	1	2	yes	—
430	C₄	#137×D₄₇	1	1	yes	characteristic
431	C₄	#15689922	1	1	yes	characteristic
432	C₂	—	4	1	no	—
433	C₂	—	376	1	no	—
434	C₂	#20252096	1	1	yes	characteristic
435	C₂	#20252203	1	1	yes	characteristic
436	C₂	#20252287	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂×D₄×D₄₇
commutator	C₂×C₄×C₄₇	C₂³×C₄
Frattini	C₄²	C₂³×D₄₇
Fitting	C₄₇×#1497	C₂
socle	C₂²×C₄₇	C₂×C₄×D₄
prime radical	#13093998	C₂×C₄
cosocle	C₄²×C₄₇	C₂⁴
hypercenter	#1497	D₄₇
hypocenter	C₄₇	#17965
LCS	G ▷ C₂×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #1497

Complements

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

N	H ≅ G/N	type
3. #20252323	C₂	semidirect
4. #20242294	C₂	semidirect
5. #20242293	C₂	semidirect
6. #20242192	C₂	semidirect
7. #20242185	C₂	semidirect
8. #20242156	C₂	semidirect
10. #20241669	C₂	semidirect
11. C₄₇×#1497	C₂	semidirect
222. #1497	D₄₇	semidirect
267. C₄₇	#17965	semidirect

Maximal subgroups

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

subgroup	index
#20253988	2
#20252357	2
#20252323	2
#20242294	2
#20242293	2
#20242192	2
#20242185	2
#20242156	2
#20241854	2
#20241669	2
C₄₇×#1497	2
#17965	47