Subgroups — #26238548

Order 12032.

926 conjugacy classes of subgroups.

The subgroup lattice has 458 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#15689334	C₂	1	1	yes	maximal, characteristic
2	C₂×#15689217	C₂	1	2	yes	maximal
3	#20246446	C₂	1	1	yes	maximal, characteristic
4	#20246300	C₂	1	1	yes	maximal, characteristic
5	#20244189	C₂	1	1	yes	maximal, characteristic
6	#20244062	C₂	1	2	yes	maximal
7	#20243730	C₂	1	2	yes	maximal
8	#20243639	C₂	1	2	yes	maximal
9	#20243253	C₂	1	1	yes	maximal, characteristic
10	C₄×#13093947	C₂	1	1	yes	maximal, characteristic
11	C₄₇×#1947	C₂	1	1	yes	maximal, characteristic
12	C₂²×Dic₁₈₈	C₂²	1	2	yes	—
13	C₂×#13094024	C₂²	1	1	yes	characteristic
14	C₂×C₄×Dic₉₄	C₂²	1	1	yes	characteristic
15	C₂×#13093989	C₂²	1	2	yes	—
16	C₂×#13093989	C₂²	1	2	yes	—
17	#15689334	C₄	1	8	yes	complemented
18	#15689217	—	2	8	no	—
19	C₂×#13093949	C₂²	1	2	yes	—
20	C₂×#13093947	C₂²	1	1	yes	characteristic
21	C₂×#13093947	C₂²	1	2	yes	—
22	C₂×#13093947	C₂²	1	2	yes	—
23	C₂×#13093947	C₂²	1	1	yes	characteristic
24	C₂×C₄×C₄₇⋊C₈	C₂²	1	1	yes	characteristic
25	C₂×C₈×Dic₄₇	C₂²	1	2	yes	—
26	#15689028	C₂²	1	2	yes	—
27	#15689021	—	2	1	no	—
28	#15689019	C₂²	1	2	yes	—
29	#15689018	—	2	2	no	—
30	#15689008	—	2	2	no	—
31	#15688992	—	2	1	no	—
32	C₄⋊C₄×Dic₄₇	—	2	1	no	—
33	C₄×C₄⋊Dic₄₇	—	2	1	no	—
34	C₄×C₄⋊Dic₄₇	C₂²	1	1	yes	characteristic
35	#15688885	C₂²	1	1	yes	characteristic
36	#15688885	C₂²	1	1	yes	characteristic
37	#15688877	C₂²	1	2	yes	—
38	C₂×#107×C₄₇	C₂²	1	2	yes	—
39	C₂×C₄⋊C₈×C₄₇	C₂²	1	1	yes	characteristic
40	C₄₇×#384	C₂²	1	1	yes	characteristic
41	C₄×C₄⋊C₄×C₄₇	C₂²	1	1	yes	characteristic
42	C₄₇×#340	C₂²	1	2	yes	—
43	C₂²×Dic₉₄	C₂³	1	2	yes	—
44	C₂²×Dic₉₄	C₂³	1	1	yes	characteristic
45	C₂×Dic₁₈₈	—	2	4	no	—
46	C₂×Dic₁₈₈	—	2	4	no	—
47	C₂×Dic₁₈₈	C₂×C₄	1	8	yes	—
48	C₂²×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
49	C₂²×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
50	#13094024	—	2	2	no	—
51	#13094024	C₂×C₄	1	4	yes	—
52	C₄×Dic₉₄	—	2	2	no	—
53	C₄×Dic₉₄	C₂×C₄	1	4	yes	—
54	#13093989	—	2	4	no	—
55	#13093989	—	2	4	no	—
56	#13093989	—	4	2	no	—
57	#13093989	—	4	2	no	—
58	C₂×C₄⋊Dic₄₇	—	2	1	no	—
59	C₂×C₄⋊Dic₄₇	—	2	1	no	—
60	C₂×C₄⋊Dic₄₇	D₄	1	1	yes	characteristic
61	C₂×C₄⋊Dic₄₇	D₄	1	1	yes	characteristic
62	C₂×C₄⋊Dic₄₇	C₂³	1	1	yes	characteristic
63	C₂×Dic₄₇⋊C₄	—	2	1	no	—
64	C₂×Dic₄₇⋊C₄	—	2	2	no	—
65	C₂×Dic₄₇⋊C₄	—	2	2	no	—
66	C₂×Dic₄₇⋊C₄	—	2	2	no	—
67	C₂×C₄×Dic₄₇	—	2	1	no	—
68	C₂×C₄×Dic₄₇	—	2	2	no	—
69	C₂×C₄×Dic₄₇	—	2	2	no	—
70	C₂×C₄×Dic₄₇	C₂³	1	2	yes	—
71	#13093949	C₂×C₄	1	8	yes	—
72	#13093947	—	2	2	no	—
73	#13093947	—	2	4	no	—
74	#13093947	—	4	2	no	—
75	#13093947	D₄	1	4	yes	—
76	C₄×C₄₇⋊C₈	—	2	2	no	—
77	C₈×Dic₄₇	—	2	4	no	—
78	C₄₇⋊#95	—	2	2	no	—
79	C₄₇⋊#95	—	2	2	no	—
80	C₄₇⋊#95	—	2	2	no	—
81	C₄₇⋊#95	D₄	1	2	yes	—
82	C₂²×C₈×C₄₇	C₂³	1	2	yes	—
83	C₂×C₄⋊C₄×C₄₇	—	2	1	no	—
84	C₂×C₄⋊C₄×C₄₇	—	2	1	no	—
85	C₂×C₄⋊C₄×C₄₇	C₂³	1	2	yes	—
86	C₂×C₄⋊C₄×C₄₇	C₂³	1	1	yes	characteristic
87	C₂×C₄⋊C₄×C₄₇	C₂³	1	1	yes	characteristic
88	C₂×C₄²×C₄₇	—	2	1	no	—
89	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
90	#107×C₄₇	—	2	4	no	—
91	C₄⋊C₈×C₄₇	C₂×C₄	1	4	yes	—
92	#95×C₄₇	—	2	1	no	—
93	C₂²×C₄×C₄₇	—	2	1	no	—
94	C₂²×C₄×C₄₇	—	2	1	no	—
95	C₂²×C₄×C₄₇	—	2	2	no	—
96	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
97	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
98	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
99	C₂²×Dic₄₇	—	2	1	no	—
100	C₂²×Dic₄₇	—	2	1	no	—
101	C₂²×Dic₄₇	—	2	2	no	—
102	C₂²×Dic₄₇	C₂×D₄	1	2	yes	—
103	C₂²×Dic₄₇	C₂×D₄	1	2	yes	—
104	C₂×Dic₉₄	—	2	1	no	—
105	C₂×Dic₉₄	—	2	1	no	—
106	C₂×Dic₉₄	—	2	1	no	—
107	C₂×Dic₉₄	—	2	2	no	—
108	C₂×Dic₉₄	—	2	2	no	—
109	C₂×Dic₉₄	—	2	2	no	—
110	C₂×Dic₉₄	—	2	2	no	—
111	C₂×Dic₉₄	—	2	2	no	—
112	C₂×Dic₉₄	C₂²×C₄	1	4	yes	—
113	C₂×Dic₉₄	C₂²×C₄	1	2	yes	—
114	C₂×Dic₉₄	C₂×D₄	1	2	yes	—
115	C₂×Dic₉₄	#41	1	2	yes	—
116	C₂×C₈×C₄₇	—	2	2	no	—
117	C₂×C₈×C₄₇	—	2	2	no	—
118	C₂×C₈×C₄₇	C₂²×C₄	1	4	yes	—
119	C₄⋊C₄×C₄₇	—	2	1	no	—
120	C₄⋊C₄×C₄₇	—	2	2	no	—
121	C₄⋊C₄×C₄₇	—	2	1	no	—
122	C₄⋊C₄×C₄₇	—	2	2	no	—
123	C₄⋊C₄×C₄₇	—	2	1	no	—
124	C₄⋊C₄×C₄₇	—	4	2	no	—
125	C₄⋊C₄×C₄₇	—	8	1	no	—
126	C₄⋊C₄×C₄₇	C₂×D₄	1	2	yes	—
127	C₄²×C₄₇	—	4	2	no	—
128	C₄²×C₄₇	C₂²×C₄	1	2	yes	—
129	C₄²×C₄₇	#41	1	2	yes	—
130	C₄⋊Dic₄₇	—	2	4	no	—
131	C₄⋊Dic₄₇	—	2	4	no	—
132	C₄⋊Dic₄₇	—	2	2	no	—
133	C₄⋊Dic₄₇	—	2	1	no	—
134	C₄⋊Dic₄₇	Q₁₆	1	4	yes	complemented
135	C₄⋊Dic₄₇	C₂²×C₄	1	2	yes	—
136	Dic₄₇⋊C₄	—	2	4	no	—
137	Dic₄₇⋊C₄	—	4	4	no	—
138	Dic₄₇⋊C₄	—	4	4	no	—
139	Dic₄₇⋊C₄	—	8	2	no	—
140	C₄×Dic₄₇	—	2	4	no	—
141	C₄×Dic₄₇	—	2	2	no	—
142	C₄×Dic₄₇	—	2	2	no	—
143	C₄×Dic₄₇	—	4	4	no	—
144	C₄×Dic₄₇	—	4	4	no	—
145	C₂×C₄₇⋊C₈	—	2	1	no	—
146	C₂×C₄₇⋊C₈	—	2	1	no	—
147	C₂×C₄₇⋊C₈	—	2	1	no	—
148	C₂×C₄₇⋊C₈	—	2	1	no	—
149	C₂×C₄₇⋊C₈	—	2	1	no	—
150	C₂×C₄₇⋊C₈	C₂×D₄	1	2	yes	—
151	Dic₁₈₈	—	2	16	no	—
152	C₂³×C₄₇	C₂²×D₄	1	1	yes	characteristic
153	C₂×C₄×C₄₇	—	2	1	no	—
154	C₂×C₄×C₄₇	—	2	1	no	—
155	C₂×C₄×C₄₇	—	2	2	no	—
156	C₂×C₄×C₄₇	—	4	1	no	—
157	C₂×C₄×C₄₇	—	4	1	no	—
158	C₂×C₄×C₄₇	—	4	2	no	—
159	C₂×C₄×C₄₇	—	4	1	no	—
160	C₂×C₄×C₄₇	—	4	1	no	—
161	C₂×C₄×C₄₇	—	4	2	no	—
162	C₂×C₄×C₄₇	—	4	2	no	—
163	C₂×C₄×C₄₇	—	4	1	no	—
164	C₂×C₄×C₄₇	C₄×D₄	1	2	yes	—
165	C₂×C₄×C₄₇	C₄×D₄	1	2	yes	—
166	C₂×C₄×C₄₇	C₂×Q₁₆	1	2	yes	—
167	C₂×C₄×C₄₇	#135	1	2	yes	—
168	C₂×C₄×C₄₇	C₂³×C₄	1	1	yes	characteristic
169	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
170	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
171	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
172	C₂×C₄×C₄₇	H(5,𝔽₂)	1	1	yes	characteristic
173	C₂×C₄×C₄₇	2₋¹⁺⁴	1	1	yes	characteristic
174	C₂×Dic₄₇	—	2	2	no	—
175	C₂×Dic₄₇	—	2	2	no	—
176	C₂×Dic₄₇	—	2	2	no	—
177	C₂×Dic₄₇	—	2	2	no	—
178	C₂×Dic₄₇	—	2	2	no	—
179	C₂×Dic₄₇	—	2	2	no	—
180	C₂×Dic₄₇	—	2	4	no	—
181	C₂×Dic₄₇	—	2	2	no	—
182	C₂×Dic₄₇	—	2	2	no	—
183	C₂×Dic₄₇	—	2	2	no	—
184	C₂×Dic₄₇	—	4	2	no	—
185	C₂×Dic₄₇	—	4	2	no	—
186	C₂×Dic₄₇	—	4	1	no	—
187	C₂×Dic₄₇	—	4	1	no	—
188	C₂×Dic₄₇	C₂×Q₁₆	1	4	yes	—
189	Dic₉₄	—	2	2	no	—
190	Dic₉₄	—	2	2	no	—
191	Dic₉₄	—	2	2	no	—
192	Dic₉₄	—	2	4	no	—
193	Dic₉₄	—	2	4	no	—
194	Dic₉₄	—	4	2	no	—
195	Dic₉₄	—	4	2	no	—
196	Dic₉₄	C₄×D₄	1	4	yes	—
197	C₈×C₄₇	—	2	4	no	—
198	C₄₇⋊C₈	—	2	2	no	—
199	C₄₇⋊C₈	—	4	1	no	—
200	#22998	—	47	1	no	maximal, Sylow
201	C₂²×C₄₇	C₂×C₄×D₄	1	1	yes	characteristic
202	C₂²×C₄₇	D₄²	1	1	yes	characteristic
203	C₂²×C₄₇	#548	1	1	yes	characteristic
204	C₂²×C₄₇	C₂²×Q₁₆	1	1	yes	characteristic
205	C₂²×C₄₇	C₂×#135	1	1	yes	characteristic
206	C₂²×C₄₇	#577	1	1	yes	characteristic
207	C₂²×C₄₇	#578	1	1	yes	characteristic
208	C₄×C₄₇	—	2	2	no	—
209	C₄×C₄₇	—	4	2	no	—
210	C₄×C₄₇	—	8	1	no	—
211	C₄×C₄₇	—	8	2	no	—
212	C₄×C₄₇	C₄×Q₁₆	1	4	yes	complemented
213	C₄×C₄₇	C₂×C₄×D₄	1	1	yes	characteristic
214	C₄×C₄₇	#520	1	1	yes	characteristic
215	C₄×C₄₇	#547	1	1	yes	characteristic
216	C₄×C₄₇	#553	1	1	yes	characteristic
217	Dic₄₇	—	2	4	no	—
218	Dic₄₇	—	2	4	no	—
219	Dic₄₇	—	4	4	no	—
220	Dic₄₇	—	4	2	no	—
221	Dic₄₇	—	4	2	no	—
222	C₂×#462	—	47	1	no	—
223	C₂×C₄×Q₁₆	—	47	2	no	—
224	#2365	—	47	1	no	—
225	Q₈×C₄⋊C₄	—	47	1	no	—
226	#1956	—	47	1	no	—
227	#1947	D₄₇	1	1	yes	characteristic
228	#1933	—	47	2	no	—
229	#1878	—	47	2	no	—
230	#1863	—	47	2	no	—
231	C₈×C₄⋊C₄	—	47	1	no	—
232	C₄×#103	—	47	1	no	—
233	C₂×C₄₇	#2361	1	1	yes	characteristic
234	C₂×C₄₇	C₂×C₄×Q₁₆	1	1	yes	characteristic
235	C₂×C₄₇	#2947	1	1	yes	characteristic
236	C₂×C₄₇	#3284	1	1	yes	characteristic
237	C₂×C₄₇	D₄×Q₁₆	1	1	yes	characteristic
238	C₂×C₄₇	#3363	1	1	yes	characteristic
239	C₂×C₄₇	#3364	1	1	yes	characteristic
240	C₂²×Q₁₆	—	47	2	no	—
241	C₂×C₄⋊Q₈	—	47	1	no	—
242	C₂×C₄×Q₈	—	47	2	no	—
243	C₂×C₄×Q₈	—	47	2	no	—
244	C₂×C₄×Q₈	—	47	1	no	—
245	#462	—	47	8	no	—
246	C₄×Q₁₆	—	94	8	no	—
247	C₂×#107	C₂×D₄₇	1	2	yes	—
248	C₂×C₄⋊C₈	C₂×D₄₇	1	1	yes	characteristic
249	C₂×#103	—	47	2	no	—
250	C₂×#103	—	47	1	no	—
251	C₂×#103	—	47	1	no	—
252	C₂×#103	—	47	2	no	—
253	C₂×#103	—	47	2	no	—
254	C₂×C₄×C₈	—	47	2	no	—
255	C₂×C₄×C₈	—	47	1	no	—
256	#391	—	47	2	no	—
257	#389	—	47	2	no	—
258	#389	—	94	2	no	—
259	#389	—	94	1	no	—
260	#387	—	94	2	no	—
261	#384	—	94	1	no	—
262	#384	C₂×D₄₇	1	1	yes	characteristic
263	C₄×C₄⋊C₄	—	47	1	no	—
264	C₄×C₄⋊C₄	—	94	1	no	—
265	C₄×C₄⋊C₄	—	94	1	no	—
266	C₄×C₄⋊C₄	C₂×D₄₇	1	1	yes	characteristic
267	#340	—	47	1	no	—
268	#340	—	47	1	no	—
269	#340	C₂×D₄₇	1	2	yes	—
270	#336	—	47	2	no	—
271	C₄₇	#22998	1	1	yes	characteristic, complemented, Sylow
272	C₂²×Q₈	—	47	1	no	—
273	C₂²×Q₈	—	47	2	no	—
274	C₂×Q₁₆	—	47	8	no	—
275	C₂×Q₁₆	—	94	4	no	—
276	C₂×Q₁₆	—	94	4	no	—
277	C₂²×C₈	—	47	1	no	—
278	C₂²×C₈	—	47	1	no	—
279	C₂²×C₈	C₂²×D₄₇	1	2	yes	—
280	C₄⋊Q₈	—	47	4	no	—
281	C₄⋊Q₈	—	94	2	no	—
282	C₄×Q₈	—	47	4	no	—
283	C₄×Q₈	—	94	2	no	—
284	C₄×Q₈	—	94	4	no	—
285	C₄×Q₈	—	94	4	no	—
286	C₄×Q₈	—	188	2	no	—
287	C₄×Q₈	—	188	2	no	—
288	C₂×C₄⋊C₄	—	2	1	no	—
289	C₂×C₄⋊C₄	—	2	1	no	—
290	C₂×C₄⋊C₄	—	47	1	no	—
291	C₂×C₄⋊C₄	—	47	1	no	—
292	C₂×C₄⋊C₄	—	47	1	no	—
293	C₂×C₄⋊C₄	—	94	1	no	—
294	C₂×C₄⋊C₄	—	94	1	no	—
295	C₂×C₄⋊C₄	—	94	1	no	—
296	C₂×C₄⋊C₄	—	94	2	no	—
297	C₂×C₄⋊C₄	—	94	2	no	—
298	C₂×C₄⋊C₄	—	94	2	no	—
299	C₂×C₄⋊C₄	C₂²×D₄₇	1	2	yes	—
300	C₂×C₄⋊C₄	C₂²×D₄₇	1	1	yes	characteristic
301	C₂×C₄⋊C₄	C₂²×D₄₇	1	1	yes	characteristic
302	C₂×C₄²	—	2	1	no	—
303	C₂×C₄²	—	47	2	no	—
304	C₂×C₄²	—	94	1	no	—
305	C₂×C₄²	—	94	2	no	—
306	C₂×C₄²	—	94	2	no	—
307	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
308	#107	—	2	4	no	—
309	C₄⋊C₈	C₄×D₄₇	1	4	yes	—
310	#103	—	47	8	no	—
311	#103	—	47	4	no	—
312	#103	—	94	4	no	—
313	#103	—	94	2	no	—
314	#103	—	188	2	no	—
315	C₄×C₈	—	94	4	no	—
316	C₄×C₈	—	94	2	no	—
317	#95	—	2	1	no	—
318	#95	—	47	2	no	—
319	#95	—	94	2	no	—
320	#95	—	94	2	no	—
321	#95	—	94	2	no	—
322	C₂×Q₈	—	47	2	no	—
323	C₂×Q₈	—	47	4	no	—
324	C₂×Q₈	—	47	2	no	—
325	C₂×Q₈	—	47	2	no	—
326	C₂×Q₈	—	94	1	no	—
327	C₂×Q₈	—	94	2	no	—
328	C₂×Q₈	—	94	1	no	—
329	C₂×Q₈	—	94	1	no	—
330	C₂×Q₈	—	94	2	no	—
331	C₂×Q₈	—	94	2	no	—
332	C₂×Q₈	—	94	2	no	—
333	C₂×Q₈	—	94	2	no	—
334	C₂²×C₄	—	2	1	no	—
335	C₂²×C₄	—	2	1	no	—
336	C₂²×C₄	—	2	2	no	—
337	C₂²×C₄	—	47	2	no	—
338	C₂²×C₄	—	47	2	no	—
339	C₂²×C₄	—	94	1	no	—
340	C₂²×C₄	—	94	1	no	—
341	C₂²×C₄	—	94	2	no	—
342	C₂²×C₄	D₄×D₄₇	1	1	yes	characteristic
343	C₂²×C₄	D₄×D₄₇	1	1	yes	characteristic
344	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
345	Q₁₆	—	94	16	no	—
346	C₂×C₈	—	2	2	no	—
347	C₂×C₈	—	2	2	no	—
348	C₂×C₈	—	47	2	no	—
349	C₂×C₈	—	94	1	no	—
350	C₂×C₈	—	94	1	no	—
351	C₂×C₈	—	94	1	no	—
352	C₂×C₈	—	94	1	no	—
353	C₂×C₈	—	94	1	no	—
354	C₂×C₈	C₂×C₄×D₄₇	1	4	yes	—
355	C₄⋊C₄	—	2	1	no	—
356	C₄⋊C₄	—	2	2	no	—
357	C₄⋊C₄	—	2	1	no	—
358	C₄⋊C₄	—	2	2	no	—
359	C₄⋊C₄	—	2	1	no	—
360	C₄⋊C₄	—	4	2	no	—
361	C₄⋊C₄	—	8	1	no	—
362	C₄⋊C₄	—	47	4	no	—
363	C₄⋊C₄	—	47	2	no	—
364	C₄⋊C₄	—	94	4	no	—
365	C₄⋊C₄	—	94	4	no	—
366	C₄⋊C₄	—	94	4	no	—
367	C₄⋊C₄	—	94	2	no	—
368	C₄⋊C₄	—	94	1	no	—
369	C₄⋊C₄	—	376	2	no	—
370	C₄⋊C₄	—	188	4	no	—
371	C₄⋊C₄	—	188	4	no	—
372	C₄⋊C₄	D₄×D₄₇	1	2	yes	—
373	C₄²	—	4	2	no	—
374	C₄²	—	94	4	no	—
375	C₄²	—	94	2	no	—
376	C₄²	—	94	2	no	—
377	C₄²	—	188	4	no	—
378	C₄²	—	188	4	no	—
379	C₄²	C₂×C₄×D₄₇	1	2	yes	—
380	C₄²	#10625354	1	2	yes	—
381	C₂³	C₂×D₄×D₄₇	1	1	yes	characteristic
382	Q₈	—	47	4	no	—
383	Q₈	—	94	2	no	—
384	Q₈	—	94	2	no	—
385	Q₈	—	94	2	no	—
386	Q₈	—	94	4	no	—
387	Q₈	—	94	4	no	—
388	Q₈	—	188	2	no	—
389	Q₈	—	188	2	no	—
390	C₂×C₄	—	2	1	no	—
391	C₂×C₄	—	2	1	no	—
392	C₂×C₄	—	2	2	no	—
393	C₂×C₄	—	4	1	no	—
394	C₂×C₄	—	4	1	no	—
395	C₂×C₄	—	4	2	no	—
396	C₂×C₄	—	4	1	no	—
397	C₂×C₄	—	4	1	no	—
398	C₂×C₄	—	4	2	no	—
399	C₂×C₄	—	4	2	no	—
400	C₂×C₄	—	4	1	no	—
401	C₂×C₄	—	47	4	no	—
402	C₂×C₄	—	94	2	no	—
403	C₂×C₄	—	94	2	no	—
404	C₂×C₄	—	94	2	no	—
405	C₂×C₄	—	94	2	no	—
406	C₂×C₄	—	94	2	no	—
407	C₂×C₄	—	94	2	no	—
408	C₂×C₄	—	94	2	no	—
409	C₂×C₄	—	94	4	no	—
410	C₂×C₄	—	94	2	no	—
411	C₂×C₄	—	94	2	no	—
412	C₂×C₄	—	188	2	no	—
413	C₂×C₄	—	188	2	no	—
414	C₂×C₄	—	188	1	no	—
415	C₂×C₄	—	188	1	no	—
416	C₂×C₄	#13093986	1	2	yes	—
417	C₂×C₄	#13093986	1	2	yes	—
418	C₂×C₄	Q₁₆×D₄₇	1	2	yes	—
419	C₂×C₄	#13094043	1	2	yes	—
420	C₂×C₄	C₂²×C₄×D₄₇	1	1	yes	characteristic
421	C₂×C₄	C₂×D₄×D₄₇	1	1	yes	characteristic
422	C₂×C₄	#41×D₄₇	1	1	yes	characteristic
423	C₂×C₄	C₂×#10625354	1	1	yes	characteristic
424	C₂×C₄	#13094070	1	1	yes	characteristic
425	C₂×C₄	#13094072	1	1	yes	characteristic
426	C₈	—	2	4	no	—
427	C₈	—	94	2	no	—
428	C₈	—	188	1	no	—
429	C₂²	C₂×#13093986	1	1	yes	characteristic
430	C₂²	#15689757	1	1	yes	characteristic
431	C₂²	#15689783	1	1	yes	characteristic
432	C₂²	C₂×Q₁₆×D₄₇	1	1	yes	characteristic
433	C₂²	C₂×#13094043	1	1	yes	characteristic
434	C₂²	#15689933	1	1	yes	characteristic
435	C₂²	#15689939	1	1	yes	characteristic
436	C₄	—	2	2	no	—
437	C₄	—	4	2	no	—
438	C₄	—	8	1	no	—
439	C₄	—	8	2	no	—
440	C₄	—	94	4	no	—
441	C₄	—	94	4	no	—
442	C₄	—	188	2	no	—
443	C₄	—	188	4	no	—
444	C₄	—	188	2	no	—
445	C₄	#15689217	1	4	yes	complemented
446	C₄	C₄×D₄×D₄₇	1	1	yes	characteristic
447	C₄	#15689605	1	1	yes	characteristic
448	C₄	#15689776	1	1	yes	characteristic
449	C₄	#15689826	1	1	yes	characteristic
450	C₂	#20246403	1	1	yes	characteristic
451	C₂	C₂×#15689217	1	1	yes	characteristic
452	C₂	#20252229	1	1	yes	characteristic
453	C₂	#20255121	1	1	yes	characteristic
454	C₂	#20255135	1	1	yes	characteristic
455	C₂	#20256065	1	1	yes	characteristic
456	C₂	#20256072	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×#1947	C₂
socle, prime radical	C₂³×C₄₇	C₂²×D₄
cosocle	C₂²×C₄×C₄₇	C₂⁴
hypercenter	#1947	D₄₇
hypocenter	C₄₇	#22998
LCS	G ▷ C₂×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ #1947

Complements

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

N	H ≅ G/N	type
17. #15689334	C₄	semidirect
134. C₄⋊Dic₄₇	Q₁₆	semidirect
212. C₄×C₄₇	C₄×Q₁₆	semidirect
271. C₄₇	#22998	semidirect
445. C₄	#15689217	semidirect

Maximal subgroups

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

subgroup	index
C₂×#15689334	2
C₂×#15689217	2
#20246446	2
#20246300	2
#20244189	2
#20244062	2
#20243730	2
#20243639	2
#20243253	2
C₄×#13093947	2
C₄₇×#1947	2
#22998	47