Subgroups — #26232935

Order 12032.

1022 conjugacy classes of subgroups.

The subgroup lattice has 462 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#15689853	C₂	1	1	yes	maximal, characteristic
2	C₂×#15689250	C₂	1	1	yes	maximal, characteristic
3	#20246343	C₂	1	1	yes	maximal, characteristic
4	#20244359	C₂	1	2	yes	maximal
5	#20244350	C₂	1	1	yes	maximal, characteristic
6	#20244338	C₂	1	2	yes	maximal
7	#20243402	C₂	1	2	yes	maximal
8	#20243394	C₂	1	1	yes	maximal, characteristic
9	#20243217	C₂	1	2	yes	maximal
10	C₄×#13093947	C₂	1	1	yes	maximal, characteristic
11	C₄₇×#1987	C₂	1	1	yes	maximal, characteristic
12	#15689853	—	2	4	no	—
13	#15689853	C₄	1	8	yes	complemented
14	C₂×#13094023	—	2	1	no	—
15	C₂×#13094023	C₂²	1	2	yes	—
16	C₂×#13094022	—	2	2	no	—
17	C₂×C₄×Dic₉₄	C₂²	1	1	yes	characteristic
18	C₂×C₄×Dic₉₄	C₂²	1	1	yes	characteristic
19	C₂×#13093989	—	2	1	no	—
20	C₂×#13093989	C₂²	1	2	yes	—
21	#15689250	—	2	4	no	—
22	C₂×Dic₄₇⋊C₈	C₂²	1	2	yes	—
23	C₂×#13093949	C₂²	1	2	yes	—
24	C₂×#13093947	C₂²	1	1	yes	characteristic
25	C₂×#13093947	C₂²	1	1	yes	characteristic
26	C₂×#13093934	C₂²	1	2	yes	—
27	C₂×C₄×C₄₇⋊C₈	C₂²	1	1	yes	characteristic
28	#15689029	—	2	1	no	—
29	#15689010	—	2	2	no	—
30	#15688993	C₂²	1	1	yes	characteristic
31	#15688988	C₂²	1	2	yes	—
32	C₄⋊C₄×Dic₄₇	C₂²	1	2	yes	—
33	C₄×C₄⋊Dic₄₇	—	2	1	no	—
34	#15688886	C₂²	1	2	yes	—
35	#15688885	C₂²	1	1	yes	characteristic
36	#15688885	C₂²	1	1	yes	characteristic
37	#15688885	C₂²	1	2	yes	—
38	#15688885	C₂²	1	2	yes	—
39	C₂×C₄⋊Q₈×C₄₇	C₂²	1	1	yes	characteristic
40	C₂×C₄⋊C₈×C₄₇	C₂²	1	1	yes	characteristic
41	C₄×C₄⋊C₄×C₄₇	C₂²	1	1	yes	characteristic
42	C₄₇×#340	C₂²	1	2	yes	—
43	C₄₇×#340	C₂²	1	2	yes	—
44	C₂²×Dic₉₄	—	2	2	no	—
45	C₂²×Dic₉₄	D₄	1	1	yes	characteristic
46	C₂²×Dic₉₄	C₂³	1	1	yes	characteristic
47	C₂²×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
48	C₂²×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
49	#13094023	—	2	8	no	—
50	#13094023	—	2	4	no	—
51	#13094023	C₂×C₄	1	8	yes	—
52	#13094022	—	2	16	no	—
53	C₄×Dic₉₄	—	2	2	no	—
54	C₄×Dic₉₄	C₂×C₄	1	4	yes	—
55	C₄×Dic₉₄	C₂×C₄	1	4	yes	—
56	C₄×Dic₉₄	D₄	1	4	yes	—
57	#13093989	—	2	8	no	—
58	#13093989	—	2	4	no	—
59	#13093989	C₂×C₄	1	8	yes	—
60	C₂×C₄⋊Dic₄₇	—	2	1	no	—
61	C₂×C₄⋊Dic₄₇	—	2	1	no	—
62	C₂×C₄⋊Dic₄₇	D₄	1	1	yes	characteristic
63	C₂×C₄⋊Dic₄₇	C₂³	1	2	yes	—
64	C₂×C₄⋊Dic₄₇	C₂³	1	1	yes	characteristic
65	C₂×Dic₄₇⋊C₄	—	2	1	no	—
66	C₂×Dic₄₇⋊C₄	—	2	2	no	—
67	C₂×Dic₄₇⋊C₄	—	2	2	no	—
68	C₂×Dic₄₇⋊C₄	D₄	1	2	yes	—
69	C₂×C₄×Dic₄₇	—	2	1	no	—
70	C₂×C₄×Dic₄₇	—	2	2	no	—
71	C₂×C₄×Dic₄₇	—	2	2	no	—
72	C₂×C₄×Dic₄₇	C₂³	1	2	yes	—
73	Dic₄₇⋊C₈	—	2	4	no	—
74	#13093949	—	2	4	no	—
75	#13093947	—	2	2	no	—
76	#13093947	Q₈	1	4	yes	complemented
77	#13093934	—	2	4	no	—
78	C₄×C₄₇⋊C₈	—	2	2	no	—
79	C₄₇⋊#95	—	2	2	no	—
80	C₄₇⋊#95	—	2	2	no	—
81	C₄₇⋊#95	—	2	2	no	—
82	C₂²×Q₈×C₄₇	—	2	1	no	—
83	C₂²×C₈×C₄₇	C₂³	1	2	yes	—
84	C₄⋊Q₈×C₄₇	—	2	2	no	—
85	C₄⋊Q₈×C₄₇	C₂×C₄	1	4	yes	—
86	C₂×C₄⋊C₄×C₄₇	—	2	1	no	—
87	C₂×C₄⋊C₄×C₄₇	C₂³	1	1	yes	characteristic
88	C₂×C₄⋊C₄×C₄₇	C₂³	1	2	yes	—
89	C₂×C₄⋊C₄×C₄₇	C₂³	1	1	yes	characteristic
90	C₂×C₄²×C₄₇	—	2	1	no	—
91	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
92	C₄⋊C₈×C₄₇	—	2	2	no	—
93	#95×C₄₇	—	2	1	no	—
94	C₂×Q₈×C₄₇	—	2	4	no	—
95	C₂×Q₈×C₄₇	—	8	1	no	—
96	C₂×Q₈×C₄₇	—	8	1	no	—
97	C₂²×C₄×C₄₇	—	2	1	no	—
98	C₂²×C₄×C₄₇	—	2	2	no	—
99	C₂²×C₄×C₄₇	—	2	1	no	—
100	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
101	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
102	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
103	C₂²×Dic₄₇	—	2	1	no	—
104	C₂²×Dic₄₇	—	2	1	no	—
105	C₂²×Dic₄₇	—	2	2	no	—
106	C₂²×Dic₄₇	C₂×D₄	1	2	yes	—
107	C₂²×Dic₄₇	C₂×D₄	1	2	yes	—
108	C₂×Dic₉₄	—	2	2	no	—
109	C₂×Dic₉₄	—	2	2	no	—
110	C₂×Dic₉₄	—	2	1	no	—
111	C₂×Dic₉₄	—	2	1	no	—
112	C₂×Dic₉₄	—	2	1	no	—
113	C₂×Dic₉₄	—	2	8	no	—
114	C₂×Dic₉₄	—	8	2	no	—
115	C₂×Dic₉₄	—	8	2	no	—
116	C₂×Dic₉₄	C₂²⋊C₄	1	4	yes	—
117	C₂×Dic₉₄	C₂²×C₄	1	2	yes	—
118	C₂×Dic₉₄	C₂×Q₈	1	2	yes	—
119	C₂×Dic₉₄	#41	1	2	yes	—
120	C₂×C₈×C₄₇	—	2	2	no	—
121	C₂×C₈×C₄₇	—	2	2	no	—
122	C₂×C₈×C₄₇	—	2	2	no	—
123	C₄⋊C₄×C₄₇	—	2	4	no	—
124	C₄⋊C₄×C₄₇	—	2	2	no	—
125	C₄⋊C₄×C₄₇	—	2	1	no	—
126	C₄⋊C₄×C₄₇	—	2	1	no	—
127	C₄⋊C₄×C₄₇	—	2	1	no	—
128	C₄⋊C₄×C₄₇	C₂²×C₄	1	4	yes	—
129	C₄⋊C₄×C₄₇	C₂×Q₈	1	2	yes	—
130	C₄²×C₄₇	—	4	2	no	—
131	C₄²×C₄₇	C₂²×C₄	1	2	yes	—
132	C₄²×C₄₇	C₂×D₄	1	2	yes	—
133	C₄⋊Dic₄₇	—	2	1	no	—
134	C₄⋊Dic₄₇	—	2	2	no	—
135	C₄⋊Dic₄₇	—	2	2	no	—
136	C₄⋊Dic₄₇	—	4	2	no	—
137	C₄⋊Dic₄₇	—	8	1	no	—
138	C₄⋊Dic₄₇	C₂²⋊C₄	1	4	yes	—
139	C₄⋊Dic₄₇	C₂²×C₄	1	2	yes	—
140	Dic₄₇⋊C₄	—	2	4	no	—
141	Dic₄₇⋊C₄	—	2	8	no	—
142	Dic₄₇⋊C₄	—	2	8	no	—
143	Dic₄₇⋊C₄	C₂²⋊C₄	1	8	yes	—
144	C₄×Dic₄₇	—	2	4	no	—
145	C₄×Dic₄₇	—	2	8	no	—
146	C₄×Dic₄₇	—	8	2	no	—
147	C₄×Dic₄₇	C₂²×C₄	1	4	yes	—
148	C₄×Dic₄₇	C₂×D₄	1	4	yes	—
149	C₂×C₄₇⋊C₈	—	2	1	no	—
150	C₂×C₄₇⋊C₈	—	2	1	no	—
151	C₂×C₄₇⋊C₈	—	2	1	no	—
152	C₂×C₄₇⋊C₈	—	2	1	no	—
153	C₂×C₄₇⋊C₈	—	2	1	no	—
154	C₂×C₄₇⋊C₈	C₂×Q₈	1	2	yes	—
155	C₂³×C₄₇	C₂²×D₄	1	1	yes	characteristic
156	Q₈×C₄₇	—	8	4	no	—
157	C₂×C₄×C₄₇	—	2	1	no	—
158	C₂×C₄×C₄₇	—	2	1	no	—
159	C₂×C₄×C₄₇	—	2	4	no	—
160	C₂×C₄×C₄₇	—	2	2	no	—
161	C₂×C₄×C₄₇	—	4	1	no	—
162	C₂×C₄×C₄₇	—	4	1	no	—
163	C₂×C₄×C₄₇	—	4	2	no	—
164	C₂×C₄×C₄₇	—	4	2	no	—
165	C₂×C₄×C₄₇	—	4	1	no	—
166	C₂×C₄×C₄₇	—	4	1	no	—
167	C₂×C₄×C₄₇	—	4	1	no	—
168	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	2	yes	—
169	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	2	yes	—
170	C₂×C₄×C₄₇	#137	1	2	yes	—
171	C₂×C₄×C₄₇	#137	1	2	yes	—
172	C₂×C₄×C₄₇	C₂³×C₄	1	1	yes	characteristic
173	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
174	C₂×C₄×C₄₇	C₂²×Q₈	1	1	yes	characteristic
175	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
176	C₂×C₄×C₄₇	2₋¹⁺⁴	1	1	yes	characteristic
177	C₂×C₄×C₄₇	2₋¹⁺⁴	1	1	yes	characteristic
178	C₂×Dic₄₇	—	2	2	no	—
179	C₂×Dic₄₇	—	2	2	no	—
180	C₂×Dic₄₇	—	2	2	no	—
181	C₂×Dic₄₇	—	2	2	no	—
182	C₂×Dic₄₇	—	2	2	no	—
183	C₂×Dic₄₇	—	2	2	no	—
184	C₂×Dic₄₇	—	2	2	no	—
185	C₂×Dic₄₇	—	2	2	no	—
186	C₂×Dic₄₇	—	4	1	no	—
187	C₂×Dic₄₇	—	4	1	no	—
188	C₂×Dic₄₇	—	4	2	no	—
189	C₂×Dic₄₇	—	4	2	no	—
190	C₂×Dic₄₇	—	4	2	no	—
191	C₂×Dic₄₇	C₂×C₂²⋊C₄	1	4	yes	—
192	C₂×Dic₄₇	C₂×C₂²⋊C₄	1	4	yes	—
193	Dic₉₄	—	2	2	no	—
194	Dic₉₄	—	2	2	no	—
195	Dic₉₄	—	2	2	no	—
196	Dic₉₄	—	2	8	no	—
197	Dic₉₄	—	8	8	no	—
198	Dic₉₄	C₄×Q₈	1	4	yes	—
199	C₈×C₄₇	—	4	2	no	—
200	C₄₇⋊C₈	—	2	2	no	—
201	C₄₇⋊C₈	—	4	1	no	—
202	#22525	—	47	1	no	maximal, Sylow
203	C₂²×C₄₇	C₂²×C₂²⋊C₄	1	1	yes	characteristic
204	C₂²×C₄₇	#548	1	1	yes	characteristic
205	C₂²×C₄₇	D₄×Q₈	1	1	yes	characteristic
206	C₂²×C₄₇	C₂×#137	1	1	yes	characteristic
207	C₂²×C₄₇	C₂×#137	1	1	yes	characteristic
208	C₂²×C₄₇	#576	1	1	yes	characteristic
209	C₂²×C₄₇	#577	1	1	yes	characteristic
210	C₄×C₄₇	—	2	2	no	—
211	C₄×C₄₇	—	4	2	no	—
212	C₄×C₄₇	—	4	4	no	—
213	C₄×C₄₇	—	8	1	no	—
214	C₄×C₄₇	#419	1	4	yes	—
215	C₄×C₄₇	C₂×C₄×Q₈	1	1	yes	characteristic
216	C₄×C₄₇	#519	1	1	yes	characteristic
217	C₄×C₄₇	#548	1	1	yes	characteristic
218	C₄×C₄₇	D₄×Q₈	1	1	yes	characteristic
219	Dic₄₇	—	2	4	no	—
220	Dic₄₇	—	2	4	no	—
221	Dic₄₇	—	2	4	no	—
222	Dic₄₇	—	4	2	no	—
223	Dic₄₇	—	8	2	no	—
224	C₂×Q₈²	—	47	1	no	—
225	C₂×#446	—	47	1	no	—
226	#2355	—	47	1	no	—
227	#1993	—	47	2	no	—
228	#1990	—	47	1	no	—
229	#1988	—	47	2	no	—
230	#1987	D₄₇	1	1	yes	characteristic
231	#1805	—	47	2	no	—
232	#1803	—	47	1	no	—
233	#1763	—	47	2	no	—
234	C₄×#103	—	47	1	no	—
235	C₂×C₄₇	Q₈×C₂²⋊C₄	1	1	yes	characteristic
236	C₂×C₄₇	C₂×#419	1	1	yes	characteristic
237	C₂×C₄₇	#2897	1	1	yes	characteristic
238	C₂×C₄₇	#3369	1	1	yes	characteristic
239	C₂×C₄₇	#3375	1	1	yes	characteristic
240	C₂×C₄₇	#3385	1	1	yes	characteristic
241	C₂×C₄₇	#3387	1	1	yes	characteristic
242	Q₈²	—	47	8	no	—
243	Q₈²	—	94	4	no	—
244	C₂×C₄⋊Q₈	—	47	2	no	—
245	C₂×C₄⋊Q₈	—	94	1	no	—
246	C₂×C₄⋊Q₈	—	94	2	no	—
247	C₂×C₄⋊Q₈	C₂×D₄₇	1	1	yes	characteristic
248	C₂×C₄×Q₈	—	47	1	no	—
249	C₂×C₄×Q₈	—	47	2	no	—
250	C₂×C₄×Q₈	—	47	1	no	—
251	C₂×C₄×Q₈	—	94	1	no	—
252	#446	—	94	4	no	—
253	C₂×C₄⋊C₈	—	47	2	no	—
254	C₂×C₄⋊C₈	C₂×D₄₇	1	1	yes	characteristic
255	C₂×#103	—	47	1	no	—
256	C₂×#103	—	47	2	no	—
257	C₂×#103	—	47	1	no	—
258	C₂×#97	—	47	2	no	—
259	C₂×C₄×C₈	—	47	1	no	—
260	#391	—	94	1	no	—
261	#387	—	94	2	no	—
262	#384	—	47	1	no	—
263	#382	—	47	2	no	—
264	C₄×C₄⋊C₄	—	47	2	no	—
265	C₄×C₄⋊C₄	—	94	1	no	—
266	C₄×C₄⋊C₄	C₂×D₄₇	1	1	yes	characteristic
267	#340	—	47	2	no	—
268	#340	—	47	2	no	—
269	#340	—	47	1	no	—
270	#340	—	47	2	no	—
271	#340	—	47	1	no	—
272	#340	C₂×D₄₇	1	2	yes	—
273	#340	C₂×D₄₇	1	2	yes	—
274	C₄₇	#22525	1	1	yes	characteristic, complemented, Sylow
275	C₂²×Q₈	—	2	1	no	—
276	C₂²×Q₈	—	47	1	no	—
277	C₂²×Q₈	—	47	1	no	—
278	C₂²×Q₈	—	94	2	no	—
279	C₂²×C₈	—	47	1	no	—
280	C₂²×C₈	—	47	1	no	—
281	C₂²×C₈	C₂²×D₄₇	1	2	yes	—
282	C₄⋊Q₈	—	2	2	no	—
283	C₄⋊Q₈	—	47	8	no	—
284	C₄⋊Q₈	—	94	4	no	—
285	C₄⋊Q₈	—	94	8	no	—
286	C₄⋊Q₈	—	94	16	no	—
287	C₄⋊Q₈	C₄×D₄₇	1	4	yes	—
288	C₄×Q₈	—	47	4	no	—
289	C₄×Q₈	—	47	4	no	—
290	C₄×Q₈	—	47	8	no	—
291	C₄×Q₈	—	47	4	no	—
292	C₄×Q₈	—	94	4	no	—
293	C₄×Q₈	—	94	8	no	—
294	C₄×Q₈	—	94	2	no	—
295	C₂×C₄⋊C₄	—	2	1	no	—
296	C₂×C₄⋊C₄	—	47	2	no	—
297	C₂×C₄⋊C₄	—	47	1	no	—
298	C₂×C₄⋊C₄	—	47	1	no	—
299	C₂×C₄⋊C₄	—	47	2	no	—
300	C₂×C₄⋊C₄	—	94	2	no	—
301	C₂×C₄⋊C₄	—	94	2	no	—
302	C₂×C₄⋊C₄	—	94	1	no	—
303	C₂×C₄⋊C₄	—	94	1	no	—
304	C₂×C₄⋊C₄	—	94	1	no	—
305	C₂×C₄⋊C₄	C₂²×D₄₇	1	1	yes	characteristic
306	C₂×C₄⋊C₄	C₂²×D₄₇	1	2	yes	—
307	C₂×C₄⋊C₄	C₂²×D₄₇	1	1	yes	characteristic
308	C₂×C₄²	—	2	1	no	—
309	C₂×C₄²	—	47	2	no	—
310	C₂×C₄²	—	94	2	no	—
311	C₂×C₄²	—	94	1	no	—
312	C₂×C₄²	—	94	2	no	—
313	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
314	C₄⋊C₈	—	2	2	no	—
315	C₄⋊C₈	—	94	4	no	—
316	#103	—	47	4	no	—
317	#103	—	94	2	no	—
318	#103	—	94	4	no	—
319	#97	—	94	4	no	—
320	C₄×C₈	—	94	2	no	—
321	#95	—	2	1	no	—
322	#95	—	94	2	no	—
323	#95	—	94	2	no	—
324	#95	—	94	2	no	—
325	C₂×Q₈	—	2	4	no	—
326	C₂×Q₈	—	8	1	no	—
327	C₂×Q₈	—	8	1	no	—
328	C₂×Q₈	—	47	4	no	—
329	C₂×Q₈	—	47	2	no	—
330	C₂×Q₈	—	47	2	no	—
331	C₂×Q₈	—	47	2	no	—
332	C₂×Q₈	—	94	8	no	—
333	C₂×Q₈	—	94	2	no	—
334	C₂×Q₈	—	94	2	no	—
335	C₂×Q₈	—	94	1	no	—
336	C₂×Q₈	—	94	1	no	—
337	C₂×Q₈	—	94	1	no	—
338	C₂×Q₈	—	376	2	no	—
339	C₂×Q₈	—	376	2	no	—
340	C₂²×C₄	—	2	1	no	—
341	C₂²×C₄	—	2	2	no	—
342	C₂²×C₄	—	2	1	no	—
343	C₂²×C₄	—	47	2	no	—
344	C₂²×C₄	—	47	2	no	—
345	C₂²×C₄	—	94	1	no	—
346	C₂²×C₄	—	94	1	no	—
347	C₂²×C₄	—	94	2	no	—
348	C₂²×C₄	D₄×D₄₇	1	1	yes	characteristic
349	C₂²×C₄	D₄×D₄₇	1	1	yes	characteristic
350	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
351	C₂×C₈	—	2	2	no	—
352	C₂×C₈	—	2	2	no	—
353	C₂×C₈	—	2	2	no	—
354	C₂×C₈	—	47	2	no	—
355	C₂×C₈	—	94	1	no	—
356	C₂×C₈	—	94	1	no	—
357	C₂×C₈	—	94	1	no	—
358	C₂×C₈	—	94	1	no	—
359	C₂×C₈	—	94	1	no	—
360	C₄⋊C₄	—	2	4	no	—
361	C₄⋊C₄	—	2	2	no	—
362	C₄⋊C₄	—	2	1	no	—
363	C₄⋊C₄	—	2	1	no	—
364	C₄⋊C₄	—	2	1	no	—
365	C₄⋊C₄	—	47	8	no	—
366	C₄⋊C₄	—	47	4	no	—
367	C₄⋊C₄	—	47	2	no	—
368	C₄⋊C₄	—	94	8	no	—
369	C₄⋊C₄	—	94	8	no	—
370	C₄⋊C₄	—	94	4	no	—
371	C₄⋊C₄	—	94	1	no	—
372	C₄⋊C₄	—	94	2	no	—
373	C₄⋊C₄	—	94	2	no	—
374	C₄⋊C₄	—	376	1	no	—
375	C₄⋊C₄	—	188	2	no	—
376	C₄⋊C₄	C₂×C₄×D₄₇	1	4	yes	—
377	C₄⋊C₄	Q₈×D₄₇	1	2	yes	—
378	C₄²	—	4	2	no	—
379	C₄²	—	47	4	no	—
380	C₄²	—	47	4	no	—
381	C₄²	—	94	8	no	—
382	C₄²	—	94	4	no	—
383	C₄²	—	376	2	no	—
384	C₄²	C₂×C₄×D₄₇	1	2	yes	—
385	C₄²	D₄×D₄₇	1	2	yes	—
386	C₂³	C₂×D₄×D₄₇	1	1	yes	characteristic
387	Q₈	—	8	4	no	—
388	Q₈	—	47	4	no	—
389	Q₈	—	94	2	no	—
390	Q₈	—	94	2	no	—
391	Q₈	—	94	2	no	—
392	Q₈	—	94	8	no	—
393	Q₈	—	376	8	no	—
394	C₂×C₄	—	2	1	no	—
395	C₂×C₄	—	2	1	no	—
396	C₂×C₄	—	2	2	no	—
397	C₂×C₄	—	2	4	no	—
398	C₂×C₄	—	4	1	no	—
399	C₂×C₄	—	4	1	no	—
400	C₂×C₄	—	4	2	no	—
401	C₂×C₄	—	4	2	no	—
402	C₂×C₄	—	4	1	no	—
403	C₂×C₄	—	4	1	no	—
404	C₂×C₄	—	4	1	no	—
405	C₂×C₄	—	47	4	no	—
406	C₂×C₄	—	47	4	no	—
407	C₂×C₄	—	94	2	no	—
408	C₂×C₄	—	94	2	no	—
409	C₂×C₄	—	94	2	no	—
410	C₂×C₄	—	94	2	no	—
411	C₂×C₄	—	94	2	no	—
412	C₂×C₄	—	94	2	no	—
413	C₂×C₄	—	94	2	no	—
414	C₂×C₄	—	94	2	no	—
415	C₂×C₄	—	188	2	no	—
416	C₂×C₄	—	188	2	no	—
417	C₂×C₄	—	188	2	no	—
418	C₂×C₄	—	188	1	no	—
419	C₂×C₄	—	188	1	no	—
420	C₂×C₄	C₂²⋊C₄×D₄₇	1	2	yes	—
421	C₂×C₄	C₂²⋊C₄×D₄₇	1	2	yes	—
422	C₂×C₄	#13094053	1	2	yes	—
423	C₂×C₄	#13094056	1	2	yes	—
424	C₂×C₄	C₂²×C₄×D₄₇	1	1	yes	characteristic
425	C₂×C₄	C₂×D₄×D₄₇	1	1	yes	characteristic
426	C₂×C₄	C₂×Q₈×D₄₇	1	1	yes	characteristic
427	C₂×C₄	#41×D₄₇	1	1	yes	characteristic
428	C₂×C₄	#13094071	1	1	yes	characteristic
429	C₂×C₄	#13094072	1	1	yes	characteristic
430	C₈	—	4	2	no	—
431	C₈	—	94	2	no	—
432	C₈	—	188	1	no	—
433	C₂²	C₂×C₂²⋊C₄×D₄₇	1	1	yes	characteristic
434	C₂²	#15689783	1	1	yes	characteristic
435	C₂²	#15689786	1	1	yes	characteristic
436	C₂²	C₂×#13094053	1	1	yes	characteristic
437	C₂²	C₂×#13094056	1	1	yes	characteristic
438	C₂²	#15689927	1	1	yes	characteristic
439	C₂²	#15689933	1	1	yes	characteristic
440	C₄	—	2	2	no	—
441	C₄	—	4	4	no	—
442	C₄	—	4	2	no	—
443	C₄	—	8	1	no	—
444	C₄	—	94	4	no	—
445	C₄	—	94	4	no	—
446	C₄	—	94	4	no	—
447	C₄	—	376	2	no	—
448	C₄	—	188	2	no	—
449	C₄	#15689130	1	4	yes	—
450	C₄	C₄×Q₈×D₄₇	1	1	yes	characteristic
451	C₄	#15689599	1	1	yes	characteristic
452	C₄	#15689781	1	1	yes	characteristic
453	C₄	#15689788	1	1	yes	characteristic
454	C₂	#20246222	1	1	yes	characteristic
455	C₂	C₂×#15689130	1	1	yes	characteristic
456	C₂	#20251913	1	1	yes	characteristic
457	C₂	#20256127	1	1	yes	characteristic
458	C₂	#20256201	1	1	yes	characteristic
459	C₂	#20256302	1	1	yes	characteristic
460	C₂	#20256324	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×#1987	C₂
socle, prime radical	C₂³×C₄₇	C₂²×D₄
cosocle	C₂²×C₄×C₄₇	C₂⁴
hypercenter	#1987	D₄₇
hypocenter	C₄₇	#22525
LCS	G ▷ C₂×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ #1987

Complements

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

N	H ≅ G/N	type
13. #15689853	C₄	semidirect
76. #13093947	Q₈	semidirect
274. C₄₇	#22525	semidirect

Maximal subgroups

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

subgroup	index
C₂×#15689853	2
C₂×#15689250	2
#20246343	2
#20244359	2
#20244350	2
#20244338	2
#20243402	2
#20243394	2
#20243217	2
C₄×#13093947	2
C₄₇×#1987	2
#22525	47