Subgroups — #26245449

Order 12032.

848 conjugacy classes of subgroups.

The subgroup lattice has 454 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄×#10625337	C₂	1	2	yes	maximal
2	#20245865	C₂	1	1	yes	maximal, characteristic
3	#20244860	C₂	1	1	yes	maximal, characteristic
4	#20244797	C₂	1	1	yes	maximal, characteristic
5	#20244783	C₂	1	2	yes	maximal
6	#20244710	C₂	1	2	yes	maximal
7	#20244631	C₂	1	1	yes	maximal, characteristic
8	#20244488	C₂	1	1	yes	maximal, characteristic
9	C₄×C₄⋊(C₄₇⋊C₈)	C₂	1	1	yes	maximal, characteristic
10	C₄×#13093948	C₂	1	2	yes	maximal
11	C₄×C₄⋊Q₈×C₄₇	C₂	1	1	yes	maximal, characteristic
12	C₂²×#10625337	C₂²	1	2	yes	—
13	C₂×C₄×Dic₉₄	C₂²	1	1	yes	characteristic
14	C₄×#10625337	—	2	8	no	—
15	C₂×#13093957	C₂²	1	2	yes	—
16	C₂×C₄⋊(C₄₇⋊C₈)	C₂²	1	2	yes	—
17	C₂×#13093948	C₂²	1	2	yes	—
18	C₂×#13093948	C₂²	1	2	yes	—
19	C₂×#13093948	C₂²	1	2	yes	—
20	C₂×#13093947	C₂²	1	2	yes	—
21	C₂×C₄×C₄₇⋊C₈	C₂²	1	2	yes	—
22	#15689029	C₂²	1	1	yes	characteristic
23	#15689029	C₂²	1	1	yes	characteristic
24	#15689021	C₂²	1	1	yes	characteristic
25	#15689021	C₂²	1	1	yes	characteristic
26	#15689007	—	2	1	no	—
27	#15689007	—	2	1	no	—
28	C₄×Dic₄₇⋊C₄	—	2	1	no	—
29	C₄×C₄⋊Dic₄₇	C₂²	1	1	yes	characteristic
30	#15688969	—	2	1	no	—
31	#15688885	C₂²	1	2	yes	—
32	#15688885	C₂²	1	2	yes	—
33	#15688878	C₂²	1	1	yes	characteristic
34	#15688878	C₂²	1	1	yes	characteristic
35	C₂×C₄⋊Q₈×C₄₇	C₂²	1	1	yes	characteristic
36	C₂×C₄×Q₈×C₄₇	C₂²	1	2	yes	—
37	C₄₇×#391	C₂²	1	2	yes	—
38	C₄₇×#389	—	2	1	no	—
39	C₄₇×#389	—	2	1	no	—
40	C₄₇×#384	C₂²	1	1	yes	characteristic
41	C₄×C₄⋊C₄×C₄₇	—	2	1	no	—
42	C₄×C₄⋊C₄×C₄₇	—	2	1	no	—
43	C₄³×C₄₇	C₂²	1	1	yes	characteristic
44	C₂²×Dic₉₄	C₂³	1	1	yes	characteristic
45	C₂×#10625337	—	2	4	no	—
46	C₂×#10625337	—	2	4	no	—
47	C₂×#10625337	—	2	4	no	—
48	C₂²×C₄₇⋊C₈	C₂³	1	2	yes	—
49	C₂²×C₄₇⋊C₈	C₂³	1	2	yes	—
50	C₄×Dic₉₄	—	2	2	no	—
51	C₄×Dic₉₄	D₄	1	4	yes	—
52	C₂×C₄⋊Dic₄₇	C₂³	1	1	yes	characteristic
53	C₂×C₄⋊Dic₄₇	C₂³	1	1	yes	characteristic
54	C₂×C₄⋊Dic₄₇	C₂³	1	1	yes	characteristic
55	C₂×Dic₄₇⋊C₄	—	2	1	no	—
56	C₂×Dic₄₇⋊C₄	—	2	1	no	—
57	C₂×Dic₄₇⋊C₄	—	2	1	no	—
58	C₂×C₄×Dic₄₇	—	2	1	no	—
59	C₂×C₄×Dic₄₇	—	2	1	no	—
60	#13093957	—	2	4	no	—
61	C₄⋊(C₄₇⋊C₈)	—	2	4	no	—
62	#13093948	—	2	4	no	—
63	#13093948	—	2	4	no	—
64	#13093948	—	2	4	no	—
65	#13093947	—	2	4	no	—
66	C₄×C₄₇⋊C₈	—	2	4	no	—
67	C₄₇⋊#95	—	2	1	no	—
68	C₄₇⋊#95	—	2	1	no	—
69	C₄₇⋊#95	—	2	1	no	—
70	C₄₇⋊#95	—	2	1	no	—
71	C₄₇⋊#95	—	2	1	no	—
72	C₄₇⋊#95	—	2	1	no	—
73	C₄₇⋊#95	—	2	1	no	—
74	C₂²×Q₈×C₄₇	C₂³	1	2	yes	—
75	C₄⋊Q₈×C₄₇	—	2	4	no	—
76	C₄×Q₈×C₄₇	—	2	4	no	—
77	C₄×Q₈×C₄₇	—	2	4	no	—
78	C₂×C₄⋊C₄×C₄₇	—	2	1	no	—
79	C₂×C₄⋊C₄×C₄₇	—	2	1	no	—
80	C₂×C₄⋊C₄×C₄₇	—	2	2	no	—
81	C₂×C₄⋊C₄×C₄₇	—	2	1	no	—
82	C₂×C₄⋊C₄×C₄₇	—	2	1	no	—
83	C₂×C₄⋊C₄×C₄₇	C₂³	1	2	yes	—
84	C₂×C₄²×C₄₇	—	2	2	no	—
85	C₂×C₄²×C₄₇	D₄	1	1	yes	characteristic
86	C₂×C₄²×C₄₇	D₄	1	1	yes	characteristic
87	C₂×C₄²×C₄₇	D₄	1	1	yes	characteristic
88	C₂×C₄²×C₄₇	D₄	1	1	yes	characteristic
89	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
90	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
91	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
92	#95×C₄₇	—	2	2	no	—
93	#95×C₄₇	—	2	2	no	—
94	C₂×Q₈×C₄₇	—	2	2	no	—
95	C₂×Q₈×C₄₇	—	2	2	no	—
96	C₂×Q₈×C₄₇	—	2	2	no	—
97	C₂×Q₈×C₄₇	—	2	2	no	—
98	C₂×Q₈×C₄₇	—	2	2	no	—
99	C₂×Q₈×C₄₇	#41	1	4	yes	—
100	C₂²×C₄×C₄₇	—	2	2	no	—
101	C₂²×C₄×C₄₇	—	2	2	no	—
102	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
103	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
104	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
105	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
106	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
107	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
108	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
109	C₂²×Dic₄₇	—	2	1	no	—
110	C₂²×Dic₄₇	—	2	1	no	—
111	C₂²×Dic₄₇	—	2	1	no	—
112	C₂²×Dic₄₇	—	2	1	no	—
113	C₂×Dic₉₄	—	2	2	no	—
114	C₂×Dic₉₄	—	2	2	no	—
115	C₂×Dic₉₄	—	2	1	no	—
116	C₂×Dic₉₄	C₂×D₄	1	2	yes	—
117	C₄⋊C₄×C₄₇	—	2	4	no	—
118	C₄⋊C₄×C₄₇	—	2	4	no	—
119	C₄⋊C₄×C₄₇	—	2	2	no	—
120	C₄⋊C₄×C₄₇	—	2	2	no	—
121	C₄⋊C₄×C₄₇	—	4	2	no	—
122	C₄⋊C₄×C₄₇	—	4	4	no	—
123	C₄⋊C₄×C₄₇	—	4	2	no	—
124	C₄²×C₄₇	—	2	2	no	—
125	C₄²×C₄₇	—	2	2	no	—
126	C₄²×C₄₇	—	2	2	no	—
127	C₄²×C₄₇	—	2	2	no	—
128	C₄²×C₄₇	—	4	1	no	—
129	C₄²×C₄₇	—	4	4	no	—
130	C₄²×C₄₇	Q₁₆	1	4	yes	complemented
131	C₄²×C₄₇	C₂×D₄	1	2	yes	—
132	C₄²×C₄₇	#41	1	2	yes	—
133	#10625337	—	2	16	no	—
134	C₄⋊Dic₄₇	—	2	1	no	—
135	C₄⋊Dic₄₇	—	2	2	no	—
136	C₄⋊Dic₄₇	—	2	2	no	—
137	C₄⋊Dic₄₇	C₂×D₄	1	2	yes	—
138	Dic₄₇⋊C₄	—	2	4	no	—
139	Dic₄₇⋊C₄	—	4	2	no	—
140	Dic₄₇⋊C₄	—	4	2	no	—
141	C₄×Dic₄₇	—	2	4	no	—
142	C₄×Dic₄₇	—	4	2	no	—
143	C₂×C₄₇⋊C₈	—	2	2	no	—
144	C₂×C₄₇⋊C₈	—	2	2	no	—
145	C₂×C₄₇⋊C₈	—	2	2	no	—
146	C₂×C₄₇⋊C₈	—	2	2	no	—
147	C₂×C₄₇⋊C₈	—	2	2	no	—
148	C₂×C₄₇⋊C₈	#41	1	4	yes	—
149	C₂³×C₄₇	C₂²×D₄	1	1	yes	characteristic
150	Q₈×C₄₇	—	2	4	no	—
151	Q₈×C₄₇	—	2	4	no	—
152	Q₈×C₄₇	—	4	2	no	—
153	Q₈×C₄₇	—	4	2	no	—
154	C₂×C₄×C₄₇	—	2	1	no	—
155	C₂×C₄×C₄₇	—	2	1	no	—
156	C₂×C₄×C₄₇	—	2	1	no	—
157	C₂×C₄×C₄₇	—	2	1	no	—
158	C₂×C₄×C₄₇	—	2	1	no	—
159	C₂×C₄×C₄₇	—	2	1	no	—
160	C₂×C₄×C₄₇	—	2	1	no	—
161	C₂×C₄×C₄₇	—	2	1	no	—
162	C₂×C₄×C₄₇	—	2	4	no	—
163	C₂×C₄×C₄₇	—	2	1	no	—
164	C₂×C₄×C₄₇	—	2	1	no	—
165	C₂×C₄×C₄₇	—	2	1	no	—
166	C₂×C₄×C₄₇	—	4	2	no	—
167	C₂×C₄×C₄₇	—	4	2	no	—
168	C₂×C₄×C₄₇	—	4	2	no	—
169	C₂×C₄×C₄₇	—	4	2	no	—
170	C₂×C₄×C₄₇	—	4	2	no	—
171	C₂×C₄×C₄₇	#121	1	2	yes	—
172	C₂×C₄×C₄₇	#121	1	2	yes	—
173	C₂×C₄×C₄₇	C₂×Q₁₆	1	2	yes	—
174	C₂×C₄×C₄₇	C₂×Q₁₆	1	2	yes	—
175	C₂×C₄×C₄₇	C₂×Q₁₆	1	2	yes	—
176	C₂×C₄×C₄₇	#135	1	2	yes	—
177	C₂×C₄×C₄₇	#137	1	2	yes	—
178	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
179	C₂×C₄×C₄₇	C₂×#41	1	2	yes	—
180	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
181	C₂×C₄×C₄₇	C₂×#41	1	2	yes	—
182	C₂×Dic₄₇	—	2	2	no	—
183	C₂×Dic₄₇	—	2	2	no	—
184	C₂×Dic₄₇	—	4	1	no	—
185	C₂×Dic₄₇	—	4	1	no	—
186	C₂×Dic₄₇	—	4	1	no	—
187	C₂×Dic₄₇	—	4	1	no	—
188	C₂×Dic₄₇	—	4	1	no	—
189	C₂×Dic₄₇	—	4	1	no	—
190	C₂×Dic₄₇	—	4	1	no	—
191	C₂×Dic₄₇	—	4	1	no	—
192	C₂×Dic₄₇	—	4	1	no	—
193	C₂×Dic₄₇	—	4	1	no	—
194	Dic₉₄	—	2	4	no	—
195	Dic₉₄	—	4	2	no	—
196	C₄₇⋊C₈	—	2	4	no	—
197	C₄₇⋊C₈	—	4	2	no	—
198	#23679	—	47	1	no	maximal, Sylow
199	C₂²×C₄₇	C₂×#121	1	1	yes	characteristic
200	C₂²×C₄₇	#525	1	1	yes	characteristic
201	C₂²×C₄₇	#532	1	1	yes	characteristic
202	C₂²×C₄₇	C₂²×Q₁₆	1	1	yes	characteristic
203	C₂²×C₄₇	C₂×#135	1	1	yes	characteristic
204	C₂²×C₄₇	C₂×#137	1	1	yes	characteristic
205	C₂²×C₄₇	#575	1	1	yes	characteristic
206	C₄×C₄₇	—	2	2	no	—
207	C₄×C₄₇	—	2	2	no	—
208	C₄×C₄₇	—	2	2	no	—
209	C₄×C₄₇	—	2	2	no	—
210	C₄×C₄₇	—	4	4	no	—
211	C₄×C₄₇	—	4	1	no	—
212	C₄×C₄₇	—	8	2	no	—
213	C₄×C₄₇	#462	1	4	yes	—
214	C₄×C₄₇	#525	1	2	yes	—
215	C₄×C₄₇	#529	1	2	yes	—
216	Dic₄₇	—	4	2	no	—
217	Dic₄₇	—	4	2	no	—
218	Dic₄₇	—	8	1	no	—
219	Dic₄₇	—	8	1	no	—
220	C₂×C₄×Q₁₆	—	47	2	no	—
221	C₄×C₄⋊Q₈	D₄₇	1	1	yes	characteristic
222	#2295	—	47	1	no	—
223	#2083	—	47	1	no	—
224	#2072	—	47	1	no	—
225	#2068	—	47	2	no	—
226	#2056	—	47	2	no	—
227	#2043	—	47	1	no	—
228	#2016	—	47	1	no	—
229	C₄×C₄⋊C₈	—	47	1	no	—
230	C₄×#103	—	47	2	no	—
231	C₂×C₄₇	#2392	1	1	yes	characteristic
232	C₂×C₄₇	C₂×#462	1	1	yes	characteristic
233	C₂×C₄₇	#3035	1	1	yes	characteristic
234	C₂×C₄₇	#3104	1	1	yes	characteristic
235	C₂×C₄₇	#3108	1	1	yes	characteristic
236	C₂×C₄₇	#3170	1	1	yes	characteristic
237	C₂×C₄₇	#3172	1	1	yes	characteristic
238	C₂²×Q₁₆	—	47	2	no	—
239	C₂×C₄⋊Q₈	C₂×D₄₇	1	1	yes	characteristic
240	C₂×C₄×Q₈	—	47	1	no	—
241	C₂×C₄×Q₈	C₂×D₄₇	1	2	yes	—
242	C₄×Q₁₆	—	94	8	no	—
243	C₂×#107	—	47	2	no	—
244	C₂×C₄⋊C₈	—	47	2	no	—
245	C₂×#103	—	47	2	no	—
246	C₂×#103	—	47	2	no	—
247	C₂×#103	—	47	2	no	—
248	C₂×#103	—	47	2	no	—
249	C₂×C₄×C₈	—	47	2	no	—
250	#391	—	47	1	no	—
251	#391	—	47	1	no	—
252	#391	C₂×D₄₇	1	2	yes	—
253	#389	—	2	1	no	—
254	#389	—	2	1	no	—
255	#389	—	47	1	no	—
256	#389	—	47	1	no	—
257	#387	—	94	1	no	—
258	#387	—	94	1	no	—
259	#384	C₂×D₄₇	1	1	yes	characteristic
260	C₄×C₄⋊C₄	—	2	1	no	—
261	C₄×C₄⋊C₄	—	2	1	no	—
262	C₄×C₄⋊C₄	—	47	1	no	—
263	C₄×C₄⋊C₄	—	94	1	no	—
264	#376	—	94	1	no	—
265	C₄³	C₂×D₄₇	1	1	yes	characteristic
266	#340	—	47	2	no	—
267	#340	—	47	2	no	—
268	#336	—	47	1	no	—
269	#336	—	47	1	no	—
270	C₄₇	#23679	1	1	yes	characteristic, complemented, Sylow
271	C₂²×Q₈	—	47	1	no	—
272	C₂²×Q₈	C₂²×D₄₇	1	2	yes	—
273	C₂×Q₁₆	—	94	4	no	—
274	C₂×Q₁₆	—	94	4	no	—
275	C₂×Q₁₆	—	94	4	no	—
276	C₂²×C₈	—	47	2	no	—
277	C₂²×C₈	—	47	2	no	—
278	C₄⋊Q₈	—	2	4	no	—
279	C₄×Q₈	—	2	4	no	—
280	C₄×Q₈	—	2	4	no	—
281	C₄×Q₈	—	47	4	no	—
282	C₄×Q₈	—	94	2	no	—
283	C₂×C₄⋊C₄	—	2	1	no	—
284	C₂×C₄⋊C₄	—	2	1	no	—
285	C₂×C₄⋊C₄	—	2	2	no	—
286	C₂×C₄⋊C₄	—	2	1	no	—
287	C₂×C₄⋊C₄	—	2	1	no	—
288	C₂×C₄⋊C₄	—	47	1	no	—
289	C₂×C₄⋊C₄	—	47	1	no	—
290	C₂×C₄⋊C₄	—	47	1	no	—
291	C₂×C₄⋊C₄	—	94	1	no	—
292	C₂×C₄⋊C₄	—	94	1	no	—
293	C₂×C₄⋊C₄	—	94	1	no	—
294	C₂×C₄⋊C₄	C₂²×D₄₇	1	2	yes	—
295	C₂×C₄²	—	2	2	no	—
296	C₂×C₄²	—	94	1	no	—
297	C₂×C₄²	—	94	1	no	—
298	C₂×C₄²	C₂²⋊D₄₇	1	1	yes	characteristic
299	C₂×C₄²	C₂²⋊D₄₇	1	1	yes	characteristic
300	C₂×C₄²	C₂²⋊D₄₇	1	1	yes	characteristic
301	C₂×C₄²	C₂²⋊D₄₇	1	1	yes	characteristic
302	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
303	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
304	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
305	#107	—	94	4	no	—
306	C₄⋊C₈	—	94	4	no	—
307	#103	—	94	4	no	—
308	#103	—	94	4	no	—
309	#103	—	94	4	no	—
310	#103	—	94	4	no	—
311	C₄×C₈	—	94	4	no	—
312	#95	—	2	2	no	—
313	#95	—	2	2	no	—
314	#95	—	94	1	no	—
315	#95	—	94	1	no	—
316	#95	—	94	1	no	—
317	#95	—	94	1	no	—
318	#95	—	94	1	no	—
319	#95	—	94	1	no	—
320	#95	—	94	1	no	—
321	C₂×Q₈	—	2	2	no	—
322	C₂×Q₈	—	2	2	no	—
323	C₂×Q₈	—	2	2	no	—
324	C₂×Q₈	—	2	2	no	—
325	C₂×Q₈	—	2	2	no	—
326	C₂×Q₈	—	47	2	no	—
327	C₂×Q₈	—	94	1	no	—
328	C₂×Q₈	—	94	2	no	—
329	C₂×Q₈	—	94	2	no	—
330	C₂×Q₈	#10625350	1	4	yes	—
331	C₂²×C₄	—	2	2	no	—
332	C₂²×C₄	—	2	2	no	—
333	C₂²×C₄	—	94	1	no	—
334	C₂²×C₄	—	94	1	no	—
335	C₂²×C₄	—	94	1	no	—
336	C₂²×C₄	—	94	1	no	—
337	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
338	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
339	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
340	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
341	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
342	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
343	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
344	Q₁₆	—	94	16	no	—
345	C₂×C₈	—	47	4	no	—
346	C₂×C₈	—	94	2	no	—
347	C₂×C₈	—	94	2	no	—
348	C₂×C₈	—	94	2	no	—
349	C₂×C₈	—	94	2	no	—
350	C₂×C₈	—	94	2	no	—
351	C₄⋊C₄	—	2	4	no	—
352	C₄⋊C₄	—	2	4	no	—
353	C₄⋊C₄	—	2	2	no	—
354	C₄⋊C₄	—	2	2	no	—
355	C₄⋊C₄	—	4	2	no	—
356	C₄⋊C₄	—	4	4	no	—
357	C₄⋊C₄	—	4	2	no	—
358	C₄⋊C₄	—	47	2	no	—
359	C₄⋊C₄	—	94	4	no	—
360	C₄⋊C₄	—	94	1	no	—
361	C₄⋊C₄	—	94	2	no	—
362	C₄⋊C₄	—	94	2	no	—
363	C₄⋊C₄	—	188	2	no	—
364	C₄⋊C₄	—	188	2	no	—
365	C₄²	—	2	2	no	—
366	C₄²	—	2	2	no	—
367	C₄²	—	2	2	no	—
368	C₄²	—	2	2	no	—
369	C₄²	—	4	1	no	—
370	C₄²	—	4	4	no	—
371	C₄²	—	94	4	no	—
372	C₄²	—	188	2	no	—
373	C₄²	#10625337	1	4	yes	complemented
374	C₄²	D₄×D₄₇	1	2	yes	—
375	C₄²	#10625352	1	2	yes	—
376	C₂³	C₂²×C₂²⋊D₄₇	1	1	yes	characteristic
377	Q₈	—	2	4	no	—
378	Q₈	—	2	4	no	—
379	Q₈	—	4	2	no	—
380	Q₈	—	4	2	no	—
381	Q₈	—	94	4	no	—
382	Q₈	—	188	2	no	—
383	C₂×C₄	—	2	1	no	—
384	C₂×C₄	—	2	1	no	—
385	C₂×C₄	—	2	1	no	—
386	C₂×C₄	—	2	1	no	—
387	C₂×C₄	—	2	1	no	—
388	C₂×C₄	—	2	1	no	—
389	C₂×C₄	—	2	1	no	—
390	C₂×C₄	—	2	1	no	—
391	C₂×C₄	—	2	4	no	—
392	C₂×C₄	—	2	1	no	—
393	C₂×C₄	—	2	1	no	—
394	C₂×C₄	—	2	1	no	—
395	C₂×C₄	—	4	2	no	—
396	C₂×C₄	—	4	2	no	—
397	C₂×C₄	—	4	2	no	—
398	C₂×C₄	—	4	2	no	—
399	C₂×C₄	—	4	2	no	—
400	C₂×C₄	—	94	2	no	—
401	C₂×C₄	—	94	2	no	—
402	C₂×C₄	—	188	1	no	—
403	C₂×C₄	—	188	1	no	—
404	C₂×C₄	—	188	1	no	—
405	C₂×C₄	—	188	1	no	—
406	C₂×C₄	—	188	1	no	—
407	C₂×C₄	—	188	1	no	—
408	C₂×C₄	—	188	1	no	—
409	C₂×C₄	—	188	1	no	—
410	C₂×C₄	—	188	1	no	—
411	C₂×C₄	—	188	1	no	—
412	C₂×C₄	#13093995	1	2	yes	—
413	C₂×C₄	#13093995	1	2	yes	—
414	C₂×C₄	C₂×#10625337	1	2	yes	—
415	C₂×C₄	C₂×#10625337	1	2	yes	—
416	C₂×C₄	C₂×#10625337	1	2	yes	—
417	C₂×C₄	#13094044	1	2	yes	—
418	C₂×C₄	#13094055	1	2	yes	—
419	C₂×C₄	C₂×D₄×D₄₇	1	1	yes	characteristic
420	C₂×C₄	#41×D₄₇	1	2	yes	—
421	C₂×C₄	C₂×#10625352	1	1	yes	characteristic
422	C₂×C₄	C₂×#10625350	1	2	yes	—
423	C₈	—	94	4	no	—
424	C₈	—	188	2	no	—
425	C₂²	C₂×#13093995	1	1	yes	characteristic
426	C₂²	#15689634	1	1	yes	characteristic
427	C₂²	#15689669	1	1	yes	characteristic
428	C₂²	C₂²×#10625337	1	1	yes	characteristic
429	C₂²	C₂×#13094044	1	1	yes	characteristic
430	C₂²	C₂×#13094055	1	1	yes	characteristic
431	C₂²	#15689921	1	1	yes	characteristic
432	C₄	—	2	2	no	—
433	C₄	—	2	2	no	—
434	C₄	—	2	2	no	—
435	C₄	—	2	2	no	—
436	C₄	—	4	1	no	—
437	C₄	—	4	4	no	—
438	C₄	—	8	2	no	—
439	C₄	—	376	1	no	—
440	C₄	—	376	1	no	—
441	C₄	—	188	2	no	—
442	C₄	—	188	2	no	—
443	C₄	#15689330	1	4	yes	—
444	C₄	#15689632	1	2	yes	—
445	C₄	#15689653	1	2	yes	—
446	C₂	#20246626	1	1	yes	characteristic
447	C₂	C₂×#15689330	1	1	yes	characteristic
448	C₂	#20252837	1	1	yes	characteristic
449	C₂	#20253427	1	1	yes	characteristic
450	C₂	#20253468	1	1	yes	characteristic
451	C₂	#20253970	1	1	yes	characteristic
452	C₂	#20253988	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄	C₂×C₂²⋊D₄₇
commutator, cosocle	C₂²×C₄×C₄₇	C₂⁴
Frattini	C₂²×C₄	C₂³×D₄₇
Fitting	C₄×C₄⋊Q₈×C₄₇	C₂
socle, prime radical	C₂³×C₄₇	C₂²×D₄
hypercenter	C₄×C₄⋊Q₈	D₄₇
hypocenter	C₄₇	#23679
LCS	G ▷ C₂²×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂²×C₄ ◁ C₄³ ◁ C₄×C₄⋊Q₈

Complements

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

N	H ≅ G/N	type
130. C₄²×C₄₇	Q₁₆	semidirect
270. C₄₇	#23679	semidirect
373. C₄²	#10625337	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₄×#10625337	2
#20245865	2
#20244860	2
#20244797	2
#20244783	2
#20244710	2
#20244631	2
#20244488	2
C₄×C₄⋊(C₄₇⋊C₈)	2
C₄×#13093948	2
C₄×C₄⋊Q₈×C₄₇	2
#23679	47