Subgroups — #26221562

Order 12032.

1070 conjugacy classes of subgroups.

The subgroup lattice has 444 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#15689735	C₂	1	1	yes	maximal, characteristic
2	#20245997	C₂	1	1	yes	maximal, characteristic
3	#20244357	C₂	1	1	yes	maximal, characteristic, complemented
4	#20244353	C₂	1	1	yes	maximal, characteristic, complemented
5	#20244208	C₂	1	1	yes	maximal, characteristic, complemented
6	#20244190	C₂	1	1	yes	maximal, characteristic, complemented
7	#20243821	C₂	1	2	yes	maximal
8	#20243811	C₂	1	2	yes	maximal
9	#20243219	C₂	1	2	yes	maximal, complemented
10	C₄×#13093949	C₂	1	2	yes	maximal, complemented
11	C₂×C₄₇×#405	C₂	1	1	yes	maximal, characteristic
12	#15689735	—	2	4	no	—
13	#15689735	C₄	1	8	yes	complemented
14	C₂×#13094024	C₂²	1	1	yes	characteristic
15	C₂×#13094017	—	2	2	no	—
16	C₂×#13094016	C₂²	1	1	yes	characteristic
17	C₂×#13094014	—	2	2	no	—
18	C₂×#13094003	C₂²	1	2	yes	—
19	C₂×C₄×Dic₉₄	C₂²	1	2	yes	—
20	C₂×#13093949	C₂²	1	2	yes	—
21	C₂×#13093949	C₂²	1	2	yes	—
22	C₂×#13093949	C₂²	1	2	yes	—
23	C₂×#13093949	C₂²	1	2	yes	—
24	#15689016	—	2	2	no	—
25	#15689009	—	2	2	no	—
26	#15688993	C₂²	1	1	yes	characteristic
27	#15688989	C₂²	1	1	yes	characteristic
28	#15688983	C₂²	1	2	yes	—
29	C₄×C₄⋊Dic₄₇	C₂²	1	2	yes	—
30	#15688886	C₂²	1	2	yes	—
31	#15688886	C₂²	1	2	yes	—
32	#15688886	C₂²	1	2	yes	—
33	#15688886	C₂²	1	2	yes	—
34	C₂²×M₁₆×C₄₇	C₂²	1	1	yes	characteristic
35	C₂³×C₈×C₄₇	C₂²	1	1	yes	characteristic
36	C₂×#117×C₄₇	C₂²	1	1	yes	characteristic
37	C₄₇×#405	—	2	4	no	—
38	C₂×#97×C₄₇	C₂²	1	1	yes	characteristic
39	C₂×#97×C₄₇	C₂²	1	1	yes	characteristic
40	C₂×C₄×C₈×C₄₇	C₂²	1	1	yes	characteristic
41	C₂×C₄×C₈×C₄₇	C₂²	1	1	yes	characteristic
42	C₂²×Dic₉₄	C₂³	1	2	yes	—
43	#13094024	—	2	2	no	—
44	#13094024	C₂×C₄	1	4	yes	—
45	#13094017	—	2	16	no	—
46	#13094016	—	2	2	no	—
47	#13094016	C₂×C₄	1	4	yes	—
48	#13094014	—	2	16	no	—
49	#13094003	—	2	4	no	—
50	#13094003	C₂×C₄	1	8	yes	—
51	C₄×Dic₉₄	—	2	4	no	—
52	C₄×Dic₉₄	C₂×C₄	1	8	yes	—
53	C₂×C₄⋊Dic₄₇	—	2	2	no	—
54	C₂×C₄⋊Dic₄₇	—	2	2	no	—
55	C₂×C₄⋊Dic₄₇	C₂³	1	2	yes	—
56	C₂×C₄⋊Dic₄₇	C₂³	1	2	yes	—
57	C₂×C₄⋊Dic₄₇	C₂³	1	2	yes	—
58	C₂×Dic₄₇⋊C₄	—	2	2	no	—
59	C₂×Dic₄₇⋊C₄	—	2	2	no	—
60	C₂×Dic₄₇⋊C₄	—	2	2	no	—
61	C₂×C₂²⋊Dic₄₇	—	2	2	no	—
62	C₂×C₂²⋊Dic₄₇	—	2	2	no	—
63	C₂×C₄×Dic₄₇	—	2	2	no	—
64	C₂×C₄×Dic₄₇	—	2	2	no	—
65	#13093949	—	2	4	no	—
66	#13093949	—	2	4	no	—
67	#13093949	—	2	4	no	—
68	#13093949	—	2	4	no	—
69	C₄₇⋊#95	—	2	2	no	—
70	C₄₇⋊#95	—	2	2	no	—
71	C₄₇⋊#95	—	2	2	no	—
72	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
73	C₂×M₁₆×C₄₇	—	2	2	no	—
74	C₂×M₁₆×C₄₇	—	2	2	no	—
75	C₂×M₁₆×C₄₇	—	2	2	no	—
76	C₂²×C₈×C₄₇	—	2	2	no	—
77	C₂²×C₈×C₄₇	—	2	2	no	—
78	C₂²×C₈×C₄₇	—	2	2	no	—
79	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
80	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
81	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
82	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
83	#117×C₄₇	C₂×C₄	1	4	yes	—
84	#117×C₄₇	D₄	1	4	yes	—
85	C₂×C₄⋊C₄×C₄₇	D₄	1	2	yes	—
86	C₂×C₂²⋊C₄×C₄₇	D₄	1	2	yes	—
87	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
88	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
89	#97×C₄₇	—	2	2	no	—
90	#97×C₄₇	—	2	2	no	—
91	C₄×C₈×C₄₇	—	2	2	no	—
92	C₄×C₈×C₄₇	—	2	2	no	—
93	C₂⁴×C₄₇	C₂×D₄	1	1	yes	characteristic
94	C₂²×C₄×C₄₇	—	2	1	no	—
95	C₂²×C₄×C₄₇	—	2	1	no	—
96	C₂²×C₄×C₄₇	—	2	1	no	—
97	C₂²×C₄×C₄₇	—	2	1	no	—
98	C₂²×C₄×C₄₇	C₂²×C₄	1	2	yes	—
99	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
100	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
101	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
102	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
103	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
104	C₂²×Dic₄₇	—	2	2	no	—
105	C₂²×Dic₄₇	—	2	2	no	—
106	C₂²×Dic₄₇	—	2	2	no	—
107	C₂²×Dic₄₇	—	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	—	2	2	no	—
113	C₂×Dic₉₄	C₂²×C₄	1	4	yes	—
114	M₁₆×C₄₇	—	2	8	no	—
115	C₂×C₈×C₄₇	—	2	8	no	—
116	C₂×C₈×C₄₇	—	2	1	no	—
117	C₂×C₈×C₄₇	—	2	1	no	—
118	C₂×C₈×C₄₇	—	2	1	no	—
119	C₂×C₈×C₄₇	—	2	1	no	—
120	C₂×C₈×C₄₇	—	2	1	no	—
121	C₂×C₈×C₄₇	—	2	1	no	—
122	C₂×C₈×C₄₇	—	2	1	no	—
123	C₂×C₈×C₄₇	—	2	1	no	—
124	C₂×C₈×C₄₇	#41	1	2	yes	—
125	C₂×C₈×C₄₇	#41	1	2	yes	—
126	C₂×C₈×C₄₇	#41	1	2	yes	—
127	C₂×C₈×C₄₇	#41	1	2	yes	—
128	C₄⋊C₄×C₄₇	C₂²⋊C₄	1	8	yes	—
129	C₂²⋊C₄×C₄₇	C₂²⋊C₄	1	8	yes	—
130	C₄²×C₄₇	C₂²×C₄	1	2	yes	—
131	C₄²×C₄₇	C₂²×C₄	1	2	yes	—
132	C₄²×C₄₇	C₂×D₄	1	2	yes	—
133	C₄²×C₄₇	C₂×D₄	1	2	yes	—
134	C₂²⋊Dic₄₇	—	2	8	no	—
135	C₂²⋊Dic₄₇	—	8	2	no	—
136	C₄⋊Dic₄₇	—	2	8	no	—
137	C₄⋊Dic₄₇	—	2	2	no	—
138	C₄⋊Dic₄₇	—	2	2	no	—
139	C₄⋊Dic₄₇	—	2	2	no	—
140	C₄⋊Dic₄₇	—	2	2	no	—
141	C₄⋊Dic₄₇	—	2	2	no	—
142	C₄⋊Dic₄₇	—	8	2	no	—
143	C₄⋊Dic₄₇	C₂²×C₄	1	4	yes	—
144	Dic₄₇⋊C₄	—	2	8	no	—
145	Dic₄₇⋊C₄	—	2	8	no	—
146	Dic₄₇⋊C₄	—	2	8	no	—
147	C₄×Dic₄₇	—	2	8	no	—
148	C₄×Dic₄₇	—	8	2	no	—
149	C₂³×C₄₇	—	2	1	no	—
150	C₂³×C₄₇	—	2	1	no	—
151	C₂³×C₄₇	—	2	2	no	—
152	C₂³×C₄₇	—	2	2	no	—
153	C₂³×C₄₇	C₂×C₂²⋊C₄	1	2	yes	—
154	C₂³×C₄₇	C₂²×D₄	1	1	yes	characteristic
155	C₂×C₄×C₄₇	—	2	1	no	—
156	C₂×C₄×C₄₇	—	2	1	no	—
157	C₂×C₄×C₄₇	—	2	2	no	—
158	C₂×C₄×C₄₇	—	2	2	no	—
159	C₂×C₄×C₄₇	—	2	2	no	—
160	C₂×C₄×C₄₇	—	2	2	no	—
161	C₂×C₄×C₄₇	—	2	2	no	—
162	C₂×C₄×C₄₇	—	2	2	no	—
163	C₂×C₄×C₄₇	—	2	2	no	—
164	C₂×C₄×C₄₇	—	2	2	no	—
165	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	4	yes	—
166	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	2	yes	—
167	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	4	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	C₂×#41	1	1	yes	characteristic
173	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
174	C₂×Dic₄₇	—	2	4	no	—
175	C₂×Dic₄₇	—	2	4	no	—
176	C₂×Dic₄₇	—	4	2	no	—
177	C₂×Dic₄₇	—	4	2	no	—
178	C₂×Dic₄₇	—	4	2	no	—
179	C₂×Dic₄₇	—	4	2	no	—
180	C₂×Dic₄₇	—	4	2	no	—
181	C₂×Dic₄₇	—	4	2	no	—
182	C₂×Dic₄₇	—	4	2	no	—
183	C₂×Dic₄₇	—	4	2	no	—
184	C₂×Dic₄₇	—	4	2	no	—
185	C₂×Dic₄₇	—	4	2	no	—
186	Dic₉₄	—	2	4	no	—
187	Dic₉₄	—	2	4	no	—
188	Dic₉₄	—	4	2	no	—
189	Dic₉₄	—	4	2	no	—
190	C₈×C₄₇	—	2	2	no	—
191	C₈×C₄₇	—	2	2	no	—
192	C₈×C₄₇	—	2	2	no	—
193	C₈×C₄₇	—	2	2	no	—
194	#21413	—	47	1	no	maximal, Sylow
195	C₂²×C₄₇	—	2	4	no	—
196	C₂²×C₄₇	—	2	2	no	—
197	C₂²×C₄₇	—	4	1	no	—
198	C₂²×C₄₇	—	4	1	no	—
199	C₂²×C₄₇	—	4	2	no	—
200	C₂²×C₄₇	C₂²×C₂²⋊C₄	1	1	yes	characteristic
201	C₂²×C₄₇	#532	1	1	yes	characteristic
202	C₂²×C₄₇	#532	1	1	yes	characteristic
203	C₂²×C₄₇	#577	1	2	yes	—
204	C₂²×C₄₇	#578	1	2	yes	—
205	C₄×C₄₇	—	2	4	no	—
206	C₄×C₄₇	—	2	4	no	—
207	C₄×C₄₇	—	2	2	no	—
208	C₄×C₄₇	C₄×#41	1	1	yes	characteristic
209	C₄×C₄₇	C₄×#41	1	1	yes	characteristic
210	C₄×C₄₇	#525	1	1	yes	characteristic
211	C₄×C₄₇	#525	1	1	yes	characteristic
212	Dic₄₇	—	4	4	no	—
213	Dic₄₇	—	4	4	no	—
214	Dic₄₇	—	8	2	no	—
215	Dic₄₇	—	8	2	no	—
216	C₂×#541	—	47	1	no	—
217	C₂×#405	D₄₇	1	1	yes	characteristic
218	#2314	—	47	1	no	—
219	#1992	—	47	1	no	—
220	#1991	—	47	1	no	—
221	#1960	—	47	1	no	—
222	#1956	—	47	1	no	—
223	#1894	—	47	2	no	—
224	#1892	—	47	2	no	—
225	#1763	—	47	2	no	—
226	C₄×#103	—	47	2	no	—
227	C₂×C₄₇	—	4	2	no	—
228	C₂×C₄₇	#2297	1	1	yes	characteristic
229	C₂×C₄₇	#2898	1	2	yes	—
230	C₂×C₄₇	#3174	1	1	yes	characteristic
231	C₂×C₄₇	#3177	1	1	yes	characteristic
232	C₂×C₄₇	#3178	1	2	yes	—
233	C₂²×M₁₆	C₂×D₄₇	1	1	yes	characteristic
234	C₂³×C₈	C₂×D₄₇	1	1	yes	characteristic
235	#541	—	47	8	no	—
236	#541	—	94	4	no	—
237	C₂×C₄⋊Q₈	—	47	1	no	—
238	C₂×#126	—	94	2	no	—
239	C₂×#125	—	47	1	no	—
240	C₂×#125	—	94	2	no	—
241	C₂×C₂²⋊Q₈	—	47	2	no	—
242	C₂×C₄×Q₈	—	47	2	no	—
243	C₂×#117	C₂×D₄₇	1	1	yes	characteristic
244	C₂×#103	—	47	2	no	—
245	C₂×#103	—	47	2	no	—
246	C₂×#103	—	47	2	no	—
247	C₂×#103	—	47	2	no	—
248	#405	—	2	4	no	—
249	C₂×#97	C₂×D₄₇	1	1	yes	characteristic
250	C₂×#97	C₂×D₄₇	1	1	yes	characteristic
251	C₂×C₄×C₈	C₂×D₄₇	1	1	yes	characteristic
252	C₂×C₄×C₈	C₂×D₄₇	1	1	yes	characteristic
253	#388	—	94	2	no	—
254	#387	—	94	2	no	—
255	#384	—	47	1	no	—
256	#382	—	47	1	no	—
257	#380	—	47	2	no	—
258	C₄×C₄⋊C₄	—	47	2	no	—
259	#340	—	47	2	no	—
260	#340	—	47	2	no	—
261	#340	—	47	2	no	—
262	#340	—	47	2	no	—
263	C₄₇	#21413	1	1	yes	characteristic, complemented, Sylow
264	C₂²×Q₈	—	47	2	no	—
265	C₂³×C₄	C₂²×D₄₇	1	1	yes	characteristic
266	C₂×M₁₆	—	2	2	no	—
267	C₂×M₁₆	—	2	2	no	—
268	C₂×M₁₆	—	2	2	no	—
269	C₂²×C₈	—	2	2	no	—
270	C₂²×C₈	—	2	2	no	—
271	C₂²×C₈	—	2	2	no	—
272	C₂²×C₈	C₂²×D₄₇	1	1	yes	characteristic
273	C₂²×C₈	C₂²×D₄₇	1	1	yes	characteristic
274	C₂²×C₈	C₂²×D₄₇	1	1	yes	characteristic
275	C₂²×C₈	C₂²×D₄₇	1	1	yes	characteristic
276	C₄⋊Q₈	—	47	4	no	—
277	C₄⋊Q₈	—	94	2	no	—
278	#126	—	94	16	no	—
279	#125	—	47	4	no	—
280	#125	—	94	16	no	—
281	#125	—	94	2	no	—
282	C₂²⋊Q₈	—	47	8	no	—
283	C₂²⋊Q₈	—	94	4	no	—
284	C₄×Q₈	—	47	8	no	—
285	C₄×Q₈	—	94	4	no	—
286	#117	C₄×D₄₇	1	4	yes	—
287	#117	C₂²⋊D₄₇	1	4	yes	—
288	C₂×C₄⋊C₄	—	47	2	no	—
289	C₂×C₄⋊C₄	—	47	2	no	—
290	C₂×C₄⋊C₄	—	47	2	no	—
291	C₂×C₄⋊C₄	—	94	2	no	—
292	C₂×C₄⋊C₄	—	94	2	no	—
293	C₂×C₄⋊C₄	—	94	2	no	—
294	C₂×C₄⋊C₄	—	94	2	no	—
295	C₂×C₄⋊C₄	—	94	2	no	—
296	C₂×C₄⋊C₄	D₁₈₈	1	2	yes	—
297	C₂×C₂²⋊C₄	—	94	2	no	—
298	C₂×C₂²⋊C₄	—	94	2	no	—
299	C₂×C₂²⋊C₄	D₁₈₈	1	2	yes	—
300	C₂×C₄²	—	94	2	no	—
301	C₂×C₄²	—	94	2	no	—
302	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
303	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
304	#103	—	94	4	no	—
305	#103	—	94	4	no	—
306	#103	—	94	4	no	—
307	#103	—	94	4	no	—
308	#97	—	2	2	no	—
309	#97	—	2	2	no	—
310	C₄×C₈	—	2	2	no	—
311	C₄×C₈	—	2	2	no	—
312	#95	—	94	2	no	—
313	#95	—	94	2	no	—
314	#95	—	94	2	no	—
315	C₂⁴	C₂×D₁₈₈	1	1	yes	characteristic
316	C₂×Q₈	—	47	4	no	—
317	C₂×Q₈	—	94	2	no	—
318	C₂×Q₈	—	94	2	no	—
319	C₂×Q₈	—	94	2	no	—
320	C₂×Q₈	—	94	2	no	—
321	C₂×Q₈	—	94	2	no	—
322	C₂²×C₄	—	2	1	no	—
323	C₂²×C₄	—	2	1	no	—
324	C₂²×C₄	—	2	1	no	—
325	C₂²×C₄	—	2	1	no	—
326	C₂²×C₄	—	94	2	no	—
327	C₂²×C₄	—	94	2	no	—
328	C₂²×C₄	—	94	2	no	—
329	C₂²×C₄	—	94	2	no	—
330	C₂²×C₄	C₂×C₄×D₄₇	1	2	yes	—
331	C₂²×C₄	C₂×D₁₈₈	1	1	yes	characteristic
332	C₂²×C₄	C₂×D₁₈₈	1	2	yes	—
333	C₂²×C₄	C₂×D₁₈₈	1	2	yes	—
334	C₂²×C₄	C₂×C₂²⋊D₄₇	1	2	yes	—
335	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
336	M₁₆	—	2	8	no	—
337	C₂×C₈	—	2	8	no	—
338	C₂×C₈	—	2	1	no	—
339	C₂×C₈	—	2	1	no	—
340	C₂×C₈	—	2	1	no	—
341	C₂×C₈	—	2	1	no	—
342	C₂×C₈	—	2	1	no	—
343	C₂×C₈	—	2	1	no	—
344	C₂×C₈	—	2	1	no	—
345	C₂×C₈	—	2	1	no	—
346	C₂×C₈	#10625350	1	2	yes	—
347	C₂×C₈	#10625350	1	2	yes	—
348	C₂×C₈	#10625350	1	2	yes	—
349	C₂×C₈	#10625350	1	2	yes	—
350	C₄⋊C₄	—	47	4	no	—
351	C₄⋊C₄	—	94	8	no	—
352	C₄⋊C₄	—	94	8	no	—
353	C₄⋊C₄	—	94	8	no	—
354	C₄⋊C₄	—	94	8	no	—
355	C₄⋊C₄	—	94	2	no	—
356	C₄⋊C₄	—	94	2	no	—
357	C₄⋊C₄	—	94	2	no	—
358	C₄⋊C₄	—	94	2	no	—
359	C₄⋊C₄	—	94	2	no	—
360	C₄⋊C₄	—	376	2	no	—
361	C₄⋊C₄	(C₂×D₄₇)⋊C₄	1	8	yes	—
362	C₂²⋊C₄	—	94	8	no	—
363	C₂²⋊C₄	—	376	2	no	—
364	C₂²⋊C₄	(C₂×D₄₇)⋊C₄	1	8	yes	—
365	C₄²	—	94	8	no	—
366	C₄²	—	376	2	no	—
367	C₄²	C₂×C₄×D₄₇	1	2	yes	—
368	C₄²	C₂×C₄×D₄₇	1	2	yes	—
369	C₄²	C₂×C₂²⋊D₄₇	1	2	yes	—
370	C₄²	C₂×C₂²⋊D₄₇	1	2	yes	—
371	C₂³	—	2	1	no	—
372	C₂³	—	2	1	no	—
373	C₂³	—	2	2	no	—
374	C₂³	—	2	2	no	—
375	C₂³	C₂×(C₂×D₄₇)⋊C₄	1	2	yes	—
376	C₂³	C₂²×D₁₈₈	1	1	yes	characteristic
377	Q₈	—	94	4	no	—
378	Q₈	—	94	4	no	—
379	Q₈	—	188	2	no	—
380	Q₈	—	188	2	no	—
381	C₂×C₄	—	2	1	no	—
382	C₂×C₄	—	2	1	no	—
383	C₂×C₄	—	2	2	no	—
384	C₂×C₄	—	2	2	no	—
385	C₂×C₄	—	2	2	no	—
386	C₂×C₄	—	2	2	no	—
387	C₂×C₄	—	2	2	no	—
388	C₂×C₄	—	2	2	no	—
389	C₂×C₄	—	2	2	no	—
390	C₂×C₄	—	2	2	no	—
391	C₂×C₄	—	94	4	no	—
392	C₂×C₄	—	94	4	no	—
393	C₂×C₄	—	188	2	no	—
394	C₂×C₄	—	188	2	no	—
395	C₂×C₄	—	188	2	no	—
396	C₂×C₄	—	188	2	no	—
397	C₂×C₄	—	188	2	no	—
398	C₂×C₄	—	188	2	no	—
399	C₂×C₄	—	188	2	no	—
400	C₂×C₄	—	188	2	no	—
401	C₂×C₄	—	188	2	no	—
402	C₂×C₄	—	188	2	no	—
403	C₂×C₄	C₂×(C₂×D₄₇)⋊C₄	1	4	yes	—
404	C₂×C₄	C₂×(C₂×D₄₇)⋊C₄	1	4	yes	—
405	C₂×C₄	C₂×(C₂×D₄₇)⋊C₄	1	2	yes	—
406	C₂×C₄	C₂²×C₄×D₄₇	1	1	yes	characteristic
407	C₂×C₄	C₂²×C₂²⋊D₄₇	1	1	yes	characteristic
408	C₂×C₄	C₂×#10625350	1	1	yes	characteristic
409	C₂×C₄	C₂×#10625350	1	1	yes	characteristic
410	C₂×C₄	C₂×#10625350	1	1	yes	characteristic
411	C₂×C₄	C₂×#10625350	1	1	yes	characteristic
412	C₈	—	2	2	no	—
413	C₈	—	2	2	no	—
414	C₈	—	2	2	no	—
415	C₈	—	2	2	no	—
416	C₂²	—	2	4	no	—
417	C₂²	—	2	2	no	—
418	C₂²	—	4	1	no	—
419	C₂²	—	4	1	no	—
420	C₂²	—	4	2	no	—
421	C₂²	C₂²×(C₂×D₄₇)⋊C₄	1	1	yes	characteristic
422	C₂²	#15689673	1	1	yes	characteristic
423	C₂²	#15689673	1	1	yes	characteristic
424	C₂²	#15689935	1	2	yes	—
425	C₂²	#15689940	1	2	yes	—
426	C₄	—	2	4	no	—
427	C₄	—	2	4	no	—
428	C₄	—	2	2	no	—
429	C₄	—	376	2	no	—
430	C₄	—	376	2	no	—
431	C₄	—	188	4	no	—
432	C₄	—	188	4	no	—
433	C₄	C₄×#10625350	1	1	yes	characteristic
434	C₄	C₄×#10625350	1	1	yes	characteristic
435	C₄	#15689634	1	1	yes	characteristic
436	C₄	#15689634	1	1	yes	characteristic
437	C₂	—	4	2	no	—
438	C₂	#20245878	1	1	yes	characteristic
439	C₂	#20251922	1	2	yes	—
440	C₂	#20254016	1	1	yes	characteristic
441	C₂	#20254047	1	1	yes	characteristic
442	C₂	#20254056	1	2	yes	—

	subgroup	G/H
center	C₂³	C₂²×D₁₈₈
commutator	C₂×C₄×C₄₇	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₄₇
Fitting	C₂×C₄₇×#405	C₂
socle	C₂³×C₄₇	C₂²×D₄
prime radical	C₂⁴×C₄₇	C₂×D₄
cosocle	C₂²×C₄×C₄₇	C₂⁴
hypercenter	C₂×#405	D₄₇
hypocenter	C₄₇	#21413
LCS	G ▷ C₂×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂³ ◁ C₂×#117 ◁ C₂×#405

Complements

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

N	H ≅ G/N	type
3. #20244357	C₂	semidirect
4. #20244353	C₂	semidirect
5. #20244208	C₂	semidirect
6. #20244190	C₂	semidirect
9. #20243219	C₂	semidirect
10. C₄×#13093949	C₂	semidirect
13. #15689735	C₄	semidirect
263. C₄₇	#21413	semidirect

Maximal subgroups

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

subgroup	index
C₂×#15689735	2
#20245997	2
#20244357	2
#20244353	2
#20244208	2
#20244190	2
#20243821	2
#20243811	2
#20243219	2
C₄×#13093949	2
C₂×C₄₇×#405	2
#21413	47