Subgroups — #26238098

Order 12032.

822 conjugacy classes of subgroups.

The subgroup lattice has 434 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#15689409	C₂	1	1	yes	maximal, characteristic
2	#20246444	C₂	1	1	yes	maximal, characteristic
3	#20246300	C₂	1	1	yes	maximal, characteristic
4	#20244348	C₂	1	1	yes	maximal, characteristic
5	#20244114	C₂	1	2	yes	maximal
6	#20243972	C₂	1	2	yes	maximal
7	#20243653	C₂	1	2	yes	maximal
8	#20243253	C₂	1	1	yes	maximal, characteristic
9	C₄×#13093947	C₂	1	1	yes	maximal, characteristic
10	#20243207	C₂	1	2	yes	maximal
11	C₄₇×#1948	C₂	1	1	yes	maximal, characteristic
12	C₂×#13094024	C₂²	1	1	yes	characteristic
13	C₂×C₄×Dic₉₄	—	2	1	no	—
14	C₂×C₄×Dic₉₄	C₂²	1	1	yes	characteristic
15	C₂×#13093989	C₂²	1	2	yes	—
16	#15689409	C₄	1	8	yes	complemented
17	C₂×#13093956	C₂²	1	2	yes	—
18	C₂×#13093949	C₂²	1	2	yes	—
19	C₂×#13093947	C₂²	1	1	yes	characteristic
20	C₂×#13093947	C₂²	1	1	yes	characteristic
21	C₂×C₄×C₄₇⋊C₈	C₂²	1	1	yes	characteristic
22	C₂×C₈×Dic₄₇	C₂²	1	2	yes	—
23	#15689029	—	2	1	no	—
24	#15689019	C₂²	1	2	yes	—
25	#15689019	C₂²	1	2	yes	—
26	#15689018	—	2	2	no	—
27	#15689006	—	2	2	no	—
28	#15688992	—	2	1	no	—
29	C₄⋊C₄×Dic₄₇	—	2	1	no	—
30	C₄⋊C₄×Dic₄₇	C₂²	1	2	yes	—
31	C₄×C₄⋊Dic₄₇	C₂²	1	1	yes	characteristic
32	#15688885	C₂²	1	1	yes	characteristic
33	#15688885	C₂²	1	2	yes	—
34	#15688885	C₂²	1	2	yes	—
35	#15688885	C₂²	1	1	yes	characteristic
36	#15688877	C₂²	1	2	yes	—
37	C₂×#106×C₄₇	C₂²	1	2	yes	—
38	C₂×C₄⋊C₈×C₄₇	C₂²	1	1	yes	characteristic
39	C₄₇×#384	C₂²	1	1	yes	characteristic
40	C₄×C₄⋊C₄×C₄₇	C₂²	1	1	yes	characteristic
41	C₄₇×#340	C₂²	1	2	yes	—
42	C₂²×Dic₉₄	—	2	1	no	—
43	C₂²×Dic₉₄	C₂³	1	1	yes	characteristic
44	C₂²×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
45	C₂²×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
46	#13094024	—	2	2	no	—
47	#13094024	C₂×C₄	1	4	yes	—
48	C₄×Dic₉₄	—	2	2	no	—
49	C₄×Dic₉₄	—	4	4	no	—
50	C₄×Dic₉₄	C₂×C₄	1	4	yes	—
51	#13093989	—	2	4	no	—
52	#13093989	—	4	2	no	—
53	C₂×C₄⋊Dic₄₇	—	2	1	no	—
54	C₂×C₄⋊Dic₄₇	D₄	1	1	yes	characteristic
55	C₂×C₄⋊Dic₄₇	D₄	1	1	yes	characteristic
56	C₂×C₄⋊Dic₄₇	C₂³	1	2	yes	—
57	C₂×C₄⋊Dic₄₇	C₂³	1	1	yes	characteristic
58	C₂×Dic₄₇⋊C₄	—	2	1	no	—
59	C₂×Dic₄₇⋊C₄	—	2	2	no	—
60	C₂×Dic₄₇⋊C₄	—	2	2	no	—
61	C₂×Dic₄₇⋊C₄	—	2	2	no	—
62	C₂×C₄×Dic₄₇	—	2	1	no	—
63	C₂×C₄×Dic₄₇	—	2	2	no	—
64	C₂×C₄×Dic₄₇	—	2	2	no	—
65	C₂×C₄×Dic₄₇	C₂³	1	2	yes	—
66	#13093956	C₂×C₄	1	8	yes	—
67	#13093949	C₂×C₄	1	8	yes	—
68	#13093947	—	2	2	no	—
69	#13093947	Q₈	1	4	yes	complemented
70	C₄×C₄₇⋊C₈	—	2	2	no	—
71	C₈×Dic₄₇	—	4	2	no	—
72	C₄₇⋊#95	—	2	2	no	—
73	C₄₇⋊#95	—	2	2	no	—
74	C₄₇⋊#95	—	2	2	no	—
75	C₄₇⋊#95	D₄	1	2	yes	—
76	C₂²×C₈×C₄₇	C₂³	1	2	yes	—
77	C₂×C₄⋊C₄×C₄₇	—	2	1	no	—
78	C₂×C₄⋊C₄×C₄₇	—	2	1	no	—
79	C₂×C₄⋊C₄×C₄₇	C₂³	1	1	yes	characteristic
80	C₂×C₄⋊C₄×C₄₇	C₂³	1	2	yes	—
81	C₂×C₄⋊C₄×C₄₇	C₂³	1	1	yes	characteristic
82	C₂×C₄²×C₄₇	—	2	1	no	—
83	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
84	#106×C₄₇	—	4	2	no	—
85	C₄⋊C₈×C₄₇	C₂×C₄	1	4	yes	—
86	#95×C₄₇	—	2	1	no	—
87	C₂²×C₄×C₄₇	—	2	1	no	—
88	C₂²×C₄×C₄₇	—	2	1	no	—
89	C₂²×C₄×C₄₇	—	2	2	no	—
90	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
91	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
92	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
93	C₂²×Dic₄₇	—	2	1	no	—
94	C₂²×Dic₄₇	—	2	1	no	—
95	C₂²×Dic₄₇	—	2	2	no	—
96	C₂²×Dic₄₇	C₂×D₄	1	2	yes	—
97	C₂²×Dic₄₇	C₂×D₄	1	2	yes	—
98	C₂×Dic₉₄	—	2	1	no	—
99	C₂×Dic₉₄	—	2	1	no	—
100	C₂×Dic₉₄	—	2	1	no	—
101	C₂×Dic₉₄	—	2	4	no	—
102	C₂×Dic₉₄	—	4	2	no	—
103	C₂×Dic₉₄	—	4	2	no	—
104	C₂×Dic₉₄	C₂²×C₄	1	2	yes	—
105	C₂×Dic₉₄	C₂×Q₈	1	2	yes	—
106	C₂×Dic₉₄	#41	1	2	yes	—
107	C₂×C₈×C₄₇	—	2	2	no	—
108	C₂×C₈×C₄₇	—	2	2	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	—	2	2	no	—
113	C₄⋊C₄×C₄₇	—	2	1	no	—
114	C₄⋊C₄×C₄₇	—	2	2	no	—
115	C₄⋊C₄×C₄₇	—	4	2	no	—
116	C₄⋊C₄×C₄₇	—	8	1	no	—
117	C₄⋊C₄×C₄₇	C₂×Q₈	1	2	yes	—
118	C₄²×C₄₇	—	4	2	no	—
119	C₄²×C₄₇	C₂²×C₄	1	2	yes	—
120	C₄²×C₄₇	#41	1	2	yes	—
121	C₄⋊Dic₄₇	—	2	4	no	—
122	C₄⋊Dic₄₇	—	2	2	no	—
123	C₄⋊Dic₄₇	—	2	1	no	—
124	C₄⋊Dic₄₇	—	2	2	no	—
125	C₄⋊Dic₄₇	SD₁₆	1	4	yes	—
126	C₄⋊Dic₄₇	C₂²×C₄	1	4	yes	—
127	C₄⋊Dic₄₇	C₂²×C₄	1	2	yes	—
128	Dic₄₇⋊C₄	—	2	4	no	—
129	Dic₄₇⋊C₄	—	4	4	no	—
130	Dic₄₇⋊C₄	—	4	4	no	—
131	Dic₄₇⋊C₄	—	8	2	no	—
132	C₄×Dic₄₇	—	2	4	no	—
133	C₄×Dic₄₇	—	2	2	no	—
134	C₄×Dic₄₇	—	2	2	no	—
135	C₄×Dic₄₇	—	4	4	no	—
136	C₄×Dic₄₇	—	4	4	no	—
137	C₂×C₄₇⋊C₈	—	2	1	no	—
138	C₂×C₄₇⋊C₈	—	2	1	no	—
139	C₂×C₄₇⋊C₈	—	2	1	no	—
140	C₂×C₄₇⋊C₈	—	2	1	no	—
141	C₂×C₄₇⋊C₈	—	2	1	no	—
142	C₂×C₄₇⋊C₈	C₂×Q₈	1	2	yes	—
143	C₂³×C₄₇	C₂²×D₄	1	1	yes	characteristic
144	C₂×C₄×C₄₇	—	2	1	no	—
145	C₂×C₄×C₄₇	—	2	1	no	—
146	C₂×C₄×C₄₇	—	2	2	no	—
147	C₂×C₄×C₄₇	—	4	1	no	—
148	C₂×C₄×C₄₇	—	4	1	no	—
149	C₂×C₄×C₄₇	—	4	2	no	—
150	C₂×C₄×C₄₇	—	4	1	no	—
151	C₂×C₄×C₄₇	—	4	1	no	—
152	C₂×C₄×C₄₇	—	4	2	no	—
153	C₂×C₄×C₄₇	—	4	2	no	—
154	C₂×C₄×C₄₇	—	4	1	no	—
155	C₂×C₄×C₄₇	C₄×D₄	1	2	yes	—
156	C₂×C₄×C₄₇	C₄×D₄	1	2	yes	—
157	C₂×C₄×C₄₇	C₂×SD₁₆	1	2	yes	—
158	C₂×C₄×C₄₇	#135	1	2	yes	—
159	C₂×C₄×C₄₇	C₂³×C₄	1	1	yes	characteristic
160	C₂×C₄×C₄₇	C₂²×Q₈	1	1	yes	characteristic
161	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
162	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
163	C₂×C₄×C₄₇	H(5,𝔽₂)	1	1	yes	characteristic
164	C₂×C₄×C₄₇	2₋¹⁺⁴	1	1	yes	characteristic
165	C₂×Dic₄₇	—	2	2	no	—
166	C₂×Dic₄₇	—	2	2	no	—
167	C₂×Dic₄₇	—	2	2	no	—
168	C₂×Dic₄₇	—	2	2	no	—
169	C₂×Dic₄₇	—	2	2	no	—
170	C₂×Dic₄₇	—	2	2	no	—
171	C₂×Dic₄₇	—	2	4	no	—
172	C₂×Dic₄₇	—	2	2	no	—
173	C₂×Dic₄₇	—	2	2	no	—
174	C₂×Dic₄₇	—	2	2	no	—
175	C₂×Dic₄₇	—	4	2	no	—
176	C₂×Dic₄₇	—	4	2	no	—
177	C₂×Dic₄₇	—	4	1	no	—
178	C₂×Dic₄₇	—	4	1	no	—
179	C₂×Dic₄₇	C₂×SD₁₆	1	4	yes	—
180	Dic₉₄	—	2	2	no	—
181	Dic₉₄	—	2	2	no	—
182	Dic₉₄	—	2	2	no	—
183	Dic₉₄	—	4	8	no	—
184	Dic₉₄	C₄×Q₈	1	4	yes	complemented
185	C₈×C₄₇	—	2	4	no	—
186	C₄₇⋊C₈	—	2	2	no	—
187	C₄₇⋊C₈	—	4	1	no	—
188	#22964	—	47	1	no	maximal, Sylow
189	C₂²×C₄₇	C₂×C₄×D₄	1	1	yes	characteristic
190	C₂²×C₄₇	#546	1	1	yes	characteristic
191	C₂²×C₄₇	D₄×Q₈	1	1	yes	characteristic
192	C₂²×C₄₇	C₂²×SD₁₆	1	1	yes	characteristic
193	C₂²×C₄₇	C₂×#135	1	1	yes	characteristic
194	C₂²×C₄₇	#577	1	1	yes	characteristic
195	C₂²×C₄₇	#578	1	1	yes	characteristic
196	C₄×C₄₇	—	2	2	no	—
197	C₄×C₄₇	—	4	2	no	—
198	C₄×C₄₇	—	8	1	no	—
199	C₄×C₄₇	—	8	2	no	—
200	C₄×C₄₇	C₄×SD₁₆	1	4	yes	—
201	C₄×C₄₇	C₂×C₄×Q₈	1	1	yes	characteristic
202	C₄×C₄₇	#520	1	1	yes	characteristic
203	C₄×C₄₇	#552	1	1	yes	characteristic
204	C₄×C₄₇	#554	1	1	yes	characteristic
205	Dic₄₇	—	2	4	no	—
206	Dic₄₇	—	2	4	no	—
207	Dic₄₇	—	4	4	no	—
208	Dic₄₇	—	4	2	no	—
209	Dic₄₇	—	4	2	no	—
210	C₂×#475	—	47	1	no	—
211	#2365	—	47	1	no	—
212	Q₈×C₄⋊C₄	—	47	1	no	—
213	#1990	—	47	1	no	—
214	#1948	D₄₇	1	1	yes	characteristic
215	#1941	—	47	2	no	—
216	#1920	—	47	2	no	—
217	#1865	—	47	2	no	—
218	C₈×C₄⋊C₄	—	47	1	no	—
219	C₄×#103	—	47	1	no	—
220	C₄×#103	—	47	2	no	—
221	C₂×C₄₇	#2360	1	1	yes	characteristic
222	C₂×C₄₇	C₂×C₄×SD₁₆	1	1	yes	characteristic
223	C₂×C₄₇	#2947	1	1	yes	characteristic
224	C₂×C₄₇	#3298	1	1	yes	characteristic
225	C₂×C₄₇	#3304	1	1	yes	characteristic
226	C₂×C₄₇	Q₈×SD₁₆	1	1	yes	characteristic
227	C₂×C₄₇	#3383	1	1	yes	characteristic
228	C₂×C₄⋊Q₈	—	47	1	no	—
229	C₂×C₄×Q₈	—	47	2	no	—
230	C₂×C₄×Q₈	—	47	1	no	—
231	C₂×C₄×Q₈	—	94	1	no	—
232	#475	—	47	8	no	—
233	C₂×#106	—	47	2	no	—
234	C₂×#106	C₂×D₄₇	1	2	yes	—
235	C₂×C₄⋊C₈	C₂×D₄₇	1	1	yes	characteristic
236	C₂×#103	—	47	2	no	—
237	C₂×#103	—	47	1	no	—
238	C₂×#103	—	47	1	no	—
239	C₂×C₄×C₈	—	47	1	no	—
240	C₂×C₄×C₈	—	47	2	no	—
241	#391	—	94	1	no	—
242	#389	—	47	2	no	—
243	#389	—	47	2	no	—
244	#389	—	94	2	no	—
245	#387	—	94	2	no	—
246	#384	—	94	1	no	—
247	#384	C₂×D₄₇	1	1	yes	characteristic
248	C₄×C₄⋊C₄	—	47	1	no	—
249	C₄×C₄⋊C₄	—	47	2	no	—
250	C₄×C₄⋊C₄	—	94	1	no	—
251	C₄×C₄⋊C₄	C₂×D₄₇	1	1	yes	characteristic
252	#340	—	47	2	no	—
253	#340	—	47	1	no	—
254	#340	—	47	1	no	—
255	#340	—	47	2	no	—
256	#340	C₂×D₄₇	1	2	yes	—
257	#336	—	47	2	no	—
258	C₄₇	#22964	1	1	yes	characteristic, complemented, Sylow
259	C₂²×Q₈	—	47	1	no	—
260	C₂²×Q₈	—	94	1	no	—
261	C₂²×C₈	—	47	1	no	—
262	C₂²×C₈	—	47	1	no	—
263	C₂²×C₈	C₂²×D₄₇	1	2	yes	—
264	C₄⋊Q₈	—	47	4	no	—
265	C₄⋊Q₈	—	94	2	no	—
266	C₄×Q₈	—	47	4	no	—
267	C₄×Q₈	—	94	2	no	—
268	C₄×Q₈	—	94	4	no	—
269	C₄×Q₈	—	188	4	no	—
270	C₄×Q₈	—	188	2	no	—
271	C₂×C₄⋊C₄	—	2	1	no	—
272	C₂×C₄⋊C₄	—	2	1	no	—
273	C₂×C₄⋊C₄	—	47	1	no	—
274	C₂×C₄⋊C₄	—	47	1	no	—
275	C₂×C₄⋊C₄	—	47	2	no	—
276	C₂×C₄⋊C₄	—	47	1	no	—
277	C₂×C₄⋊C₄	—	94	1	no	—
278	C₂×C₄⋊C₄	—	94	1	no	—
279	C₂×C₄⋊C₄	—	94	2	no	—
280	C₂×C₄⋊C₄	—	94	2	no	—
281	C₂×C₄⋊C₄	—	94	2	no	—
282	C₂×C₄⋊C₄	C₂²×D₄₇	1	2	yes	—
283	C₂×C₄⋊C₄	C₂²×D₄₇	1	1	yes	characteristic
284	C₂×C₄⋊C₄	C₂²×D₄₇	1	1	yes	characteristic
285	C₂×C₄²	—	2	1	no	—
286	C₂×C₄²	—	47	2	no	—
287	C₂×C₄²	—	94	1	no	—
288	C₂×C₄²	—	94	2	no	—
289	C₂×C₄²	—	94	2	no	—
290	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
291	#106	—	4	2	no	—
292	#106	—	47	8	no	—
293	C₄⋊C₈	C₄×D₄₇	1	4	yes	—
294	#103	—	47	8	no	—
295	#103	—	47	4	no	—
296	#103	—	94	2	no	—
297	C₄×C₈	—	94	2	no	—
298	C₄×C₈	—	188	2	no	—
299	#95	—	2	1	no	—
300	#95	—	47	2	no	—
301	#95	—	94	2	no	—
302	#95	—	94	2	no	—
303	#95	—	94	2	no	—
304	C₂×Q₈	—	47	2	no	—
305	C₂×Q₈	—	47	2	no	—
306	C₂×Q₈	—	47	2	no	—
307	C₂×Q₈	—	94	4	no	—
308	C₂×Q₈	—	94	1	no	—
309	C₂×Q₈	—	94	1	no	—
310	C₂×Q₈	—	94	1	no	—
311	C₂×Q₈	—	188	2	no	—
312	C₂×Q₈	—	188	2	no	—
313	C₂²×C₄	—	2	1	no	—
314	C₂²×C₄	—	2	1	no	—
315	C₂²×C₄	—	2	2	no	—
316	C₂²×C₄	—	47	2	no	—
317	C₂²×C₄	—	47	2	no	—
318	C₂²×C₄	—	94	1	no	—
319	C₂²×C₄	—	94	1	no	—
320	C₂²×C₄	—	94	2	no	—
321	C₂²×C₄	D₄×D₄₇	1	1	yes	characteristic
322	C₂²×C₄	D₄×D₄₇	1	1	yes	characteristic
323	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
324	C₂×C₈	—	2	2	no	—
325	C₂×C₈	—	2	2	no	—
326	C₂×C₈	—	47	2	no	—
327	C₂×C₈	—	94	1	no	—
328	C₂×C₈	—	94	1	no	—
329	C₂×C₈	—	94	1	no	—
330	C₂×C₈	—	94	1	no	—
331	C₂×C₈	—	94	1	no	—
332	C₂×C₈	C₂×C₄×D₄₇	1	4	yes	—
333	C₄⋊C₄	—	2	1	no	—
334	C₄⋊C₄	—	2	1	no	—
335	C₄⋊C₄	—	2	2	no	—
336	C₄⋊C₄	—	2	1	no	—
337	C₄⋊C₄	—	2	2	no	—
338	C₄⋊C₄	—	4	2	no	—
339	C₄⋊C₄	—	8	1	no	—
340	C₄⋊C₄	—	47	4	no	—
341	C₄⋊C₄	—	47	4	no	—
342	C₄⋊C₄	—	47	2	no	—
343	C₄⋊C₄	—	94	4	no	—
344	C₄⋊C₄	—	94	4	no	—
345	C₄⋊C₄	—	94	2	no	—
346	C₄⋊C₄	—	94	1	no	—
347	C₄⋊C₄	—	94	2	no	—
348	C₄⋊C₄	—	376	2	no	—
349	C₄⋊C₄	—	188	4	no	—
350	C₄⋊C₄	—	188	4	no	—
351	C₄⋊C₄	Q₈×D₄₇	1	2	yes	—
352	C₄²	—	4	2	no	—
353	C₄²	—	94	4	no	—
354	C₄²	—	94	2	no	—
355	C₄²	—	94	2	no	—
356	C₄²	—	188	4	no	—
357	C₄²	—	188	4	no	—
358	C₄²	C₂×C₄×D₄₇	1	2	yes	—
359	C₄²	#10625354	1	2	yes	—
360	C₂³	C₂×D₄×D₄₇	1	1	yes	characteristic
361	Q₈	—	47	4	no	—
362	Q₈	—	94	2	no	—
363	Q₈	—	94	2	no	—
364	Q₈	—	94	2	no	—
365	Q₈	—	188	8	no	—
366	C₂×C₄	—	2	1	no	—
367	C₂×C₄	—	2	1	no	—
368	C₂×C₄	—	2	2	no	—
369	C₂×C₄	—	4	1	no	—
370	C₂×C₄	—	4	1	no	—
371	C₂×C₄	—	4	2	no	—
372	C₂×C₄	—	4	1	no	—
373	C₂×C₄	—	4	1	no	—
374	C₂×C₄	—	4	2	no	—
375	C₂×C₄	—	4	2	no	—
376	C₂×C₄	—	4	1	no	—
377	C₂×C₄	—	47	4	no	—
378	C₂×C₄	—	94	2	no	—
379	C₂×C₄	—	94	2	no	—
380	C₂×C₄	—	94	2	no	—
381	C₂×C₄	—	94	2	no	—
382	C₂×C₄	—	94	2	no	—
383	C₂×C₄	—	94	2	no	—
384	C₂×C₄	—	94	2	no	—
385	C₂×C₄	—	94	4	no	—
386	C₂×C₄	—	94	2	no	—
387	C₂×C₄	—	94	2	no	—
388	C₂×C₄	—	188	2	no	—
389	C₂×C₄	—	188	2	no	—
390	C₂×C₄	—	188	1	no	—
391	C₂×C₄	—	188	1	no	—
392	C₂×C₄	#13093986	1	2	yes	—
393	C₂×C₄	#13093986	1	2	yes	—
394	C₂×C₄	SD₁₆×D₄₇	1	2	yes	—
395	C₂×C₄	#13094045	1	2	yes	—
396	C₂×C₄	C₂²×C₄×D₄₇	1	1	yes	characteristic
397	C₂×C₄	C₂×Q₈×D₄₇	1	1	yes	characteristic
398	C₂×C₄	#41×D₄₇	1	1	yes	characteristic
399	C₂×C₄	C₂×#10625354	1	1	yes	characteristic
400	C₂×C₄	#13094069	1	1	yes	characteristic
401	C₂×C₄	#13094071	1	1	yes	characteristic
402	C₈	—	2	4	no	—
403	C₈	—	94	2	no	—
404	C₈	—	188	1	no	—
405	C₂²	C₂×#13093986	1	1	yes	characteristic
406	C₂²	#15689770	1	1	yes	characteristic
407	C₂²	#15689786	1	1	yes	characteristic
408	C₂²	C₂×SD₁₆×D₄₇	1	1	yes	characteristic
409	C₂²	C₂×#13094045	1	1	yes	characteristic
410	C₂²	#15689933	1	1	yes	characteristic
411	C₂²	#15689939	1	1	yes	characteristic
412	C₄	—	2	2	no	—
413	C₄	—	4	2	no	—
414	C₄	—	8	1	no	—
415	C₄	—	8	2	no	—
416	C₄	—	94	4	no	—
417	C₄	—	94	4	no	—
418	C₄	—	188	2	no	—
419	C₄	—	188	2	no	—
420	C₄	—	188	4	no	—
421	C₄	#15689210	1	4	yes	—
422	C₄	C₄×Q₈×D₄₇	1	1	yes	characteristic
423	C₄	#15689602	1	1	yes	characteristic
424	C₄	#15689811	1	1	yes	characteristic
425	C₄	#15689834	1	1	yes	characteristic
426	C₂	#20246392	1	1	yes	characteristic
427	C₂	C₂×#15689210	1	1	yes	characteristic
428	C₂	#20252229	1	1	yes	characteristic
429	C₂	#20255256	1	1	yes	characteristic
430	C₂	#20255330	1	1	yes	characteristic
431	C₂	#20256243	1	1	yes	characteristic
432	C₂	#20256278	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	C₂×D₄×D₄₇
commutator	C₂×C₄×C₄₇	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₄₇
Fitting	C₄₇×#1948	C₂
socle, prime radical	C₂³×C₄₇	C₂²×D₄
cosocle	C₂²×C₄×C₄₇	C₂⁴
hypercenter	#1948	D₄₇
hypocenter	C₄₇	#22964
LCS	G ▷ C₂×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ #1948

Complements

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

N	H ≅ G/N	type
16. #15689409	C₄	semidirect
69. #13093947	Q₈	semidirect
184. Dic₉₄	C₄×Q₈	semidirect
258. C₄₇	#22964	semidirect

Maximal subgroups

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

subgroup	index
C₂×#15689409	2
#20246444	2
#20246300	2
#20244348	2
#20244114	2
#20243972	2
#20243653	2
#20243253	2
C₄×#13093947	2
#20243207	2
C₄₇×#1948	2
#22964	47