Subgroups — #26124194

Order 12032.

870 conjugacy classes of subgroups.

The subgroup lattice has 432 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#15689021	C₂	1	1	yes	maximal, characteristic
2	C₂×#15688989	C₂	1	1	yes	maximal, characteristic
3	C₂×#15688886	C₂	1	2	yes	maximal
4	C₂×#15688886	C₂	1	2	yes	maximal
5	C₂×C₄₇×#336	C₂	1	1	yes	maximal, characteristic
6	C₂²×C₄⋊Dic₄₇	C₂²	1	1	yes	characteristic
7	C₂²×C₄⋊Dic₄₇	C₂²	1	2	yes	—
8	C₂²×C₄⋊Dic₄₇	C₂²	1	1	yes	characteristic
9	C₂²×Dic₄₇⋊C₄	—	2	1	no	—
10	#15689021	—	2	2	no	—
11	#15689021	C₄	1	4	yes	complemented
12	#15688989	—	2	4	no	—
13	C₂×C₄₇⋊#95	—	2	1	no	—
14	C₂×C₄₇⋊#95	—	2	1	no	—
15	C₂×C₄₇⋊#95	—	2	1	no	—
16	#15688886	—	2	4	no	—
17	#15688886	—	2	4	no	—
18	C₂³×C₈×C₄₇	C₂²	1	2	yes	—
19	C₂²×C₄²×C₄₇	C₂²	1	1	yes	characteristic
20	C₄₇×#336	—	2	2	no	—
21	C₂³×Dic₄₇	—	2	1	no	—
22	C₂³×Dic₄₇	—	2	2	no	—
23	C₂³×Dic₄₇	—	2	1	no	—
24	C₂×C₄⋊Dic₄₇	—	2	1	no	—
25	C₂×C₄⋊Dic₄₇	—	2	1	no	—
26	C₂×C₄⋊Dic₄₇	—	2	1	no	—
27	C₂×C₄⋊Dic₄₇	—	2	2	no	—
28	C₂×C₄⋊Dic₄₇	—	2	2	no	—
29	C₂×C₄⋊Dic₄₇	—	2	2	no	—
30	C₂×C₄⋊Dic₄₇	—	2	2	no	—
31	C₂×C₄⋊Dic₄₇	—	2	2	no	—
32	C₂×C₄⋊Dic₄₇	—	2	2	no	—
33	C₂×C₄⋊Dic₄₇	—	2	2	no	—
34	C₂×C₄⋊Dic₄₇	—	2	1	no	—
35	C₂×C₄⋊Dic₄₇	C₂×C₄	1	2	yes	—
36	C₂×C₄⋊Dic₄₇	C₂×C₄	1	2	yes	—
37	C₂×C₄⋊Dic₄₇	D₄	1	4	yes	—
38	C₂×C₄⋊Dic₄₇	D₄	1	2	yes	—
39	C₂×C₄⋊Dic₄₇	Q₈	1	2	yes	—
40	C₂×Dic₄₇⋊C₄	—	2	4	no	—
41	C₂×Dic₄₇⋊C₄	—	4	4	no	—
42	C₄₇⋊#95	—	2	4	no	—
43	C₄₇⋊#95	—	2	4	no	—
44	C₄₇⋊#95	—	2	4	no	—
45	C₂³×C₄×C₄₇	D₄	1	1	yes	characteristic
46	C₂³×C₄×C₄₇	D₄	1	1	yes	characteristic
47	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
48	C₂²×C₈×C₄₇	—	2	2	no	—
49	C₂²×C₈×C₄₇	—	2	2	no	—
50	C₂²×C₈×C₄₇	—	2	2	no	—
51	C₂²×C₈×C₄₇	—	2	2	no	—
52	C₂²×C₈×C₄₇	—	2	2	no	—
53	C₂²×C₈×C₄₇	—	2	2	no	—
54	C₂²×C₈×C₄₇	Q₈	1	4	yes	—
55	C₂×C₄²×C₄₇	—	2	2	no	—
56	C₂×C₄²×C₄₇	—	2	2	no	—
57	C₂×C₄²×C₄₇	C₂×C₄	1	2	yes	—
58	C₂×C₄²×C₄₇	D₄	1	2	yes	—
59	C₂⁴×C₄₇	C₂×D₄	1	1	yes	characteristic
60	C₂²×C₄×C₄₇	—	2	1	no	—
61	C₂²×C₄×C₄₇	—	2	1	no	—
62	C₂²×C₄×C₄₇	—	2	1	no	—
63	C₂²×C₄×C₄₇	—	2	1	no	—
64	C₂²×C₄×C₄₇	—	2	2	no	—
65	C₂²×C₄×C₄₇	—	2	2	no	—
66	C₂²×C₄×C₄₇	—	2	2	no	—
67	C₂²×C₄×C₄₇	—	2	2	no	—
68	C₂²×C₄×C₄₇	C₂²⋊C₄	1	2	yes	—
69	C₂²×C₄×C₄₇	C₂²⋊C₄	1	2	yes	—
70	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
71	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
72	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
73	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
74	C₂²×C₄×C₄₇	C₂×Q₈	1	1	yes	characteristic
75	C₂²×C₄×C₄₇	C₂×Q₈	1	2	yes	—
76	C₂²×C₄×C₄₇	#41	1	1	yes	characteristic
77	C₂²×C₄×C₄₇	#41	1	1	yes	characteristic
78	C₂²×C₄×C₄₇	#41	1	2	yes	—
79	C₂²×C₄×C₄₇	#41	1	2	yes	—
80	C₂²×Dic₄₇	—	2	2	no	—
81	C₂²×Dic₄₇	—	2	2	no	—
82	C₂²×Dic₄₇	—	2	2	no	—
83	C₂²×Dic₄₇	—	2	2	no	—
84	C₂²×Dic₄₇	—	2	4	no	—
85	C₂²×Dic₄₇	—	4	2	no	—
86	C₂²×Dic₄₇	—	4	2	no	—
87	C₂²×Dic₄₇	—	4	1	no	—
88	C₂²×Dic₄₇	—	4	2	no	—
89	C₂²×Dic₄₇	—	4	1	no	—
90	C₂²×Dic₄₇	—	4	2	no	—
91	C₂²×Dic₄₇	—	4	2	no	—
92	C₂²×Dic₄₇	—	4	2	no	—
93	C₂²×Dic₄₇	—	4	2	no	—
94	C₂²×Dic₄₇	—	4	2	no	—
95	C₂²×Dic₄₇	—	4	2	no	—
96	C₂²×Dic₄₇	—	4	2	no	—
97	C₂×C₈×C₄₇	—	2	4	no	—
98	C₂×C₈×C₄₇	—	2	4	no	—
99	C₂×C₈×C₄₇	—	2	4	no	—
100	C₂×C₈×C₄₇	—	4	2	no	—
101	C₂×C₈×C₄₇	—	4	2	no	—
102	C₂×C₈×C₄₇	—	4	2	no	—
103	C₂×C₈×C₄₇	—	4	2	no	—
104	C₄²×C₄₇	—	2	4	no	—
105	C₄²×C₄₇	—	2	4	no	—
106	C₄⋊Dic₄₇	—	2	2	no	—
107	C₄⋊Dic₄₇	—	2	2	no	—
108	C₄⋊Dic₄₇	—	2	2	no	—
109	C₄⋊Dic₄₇	—	2	4	no	—
110	C₄⋊Dic₄₇	—	2	4	no	—
111	C₄⋊Dic₄₇	—	2	4	no	—
112	C₄⋊Dic₄₇	—	4	2	no	—
113	C₄⋊Dic₄₇	—	4	2	no	—
114	C₄⋊Dic₄₇	—	4	2	no	—
115	C₄⋊Dic₄₇	C₄⋊C₄	1	4	yes	—
116	Dic₄₇⋊C₄	—	4	8	no	—
117	C₂³×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
118	C₂³×C₄₇	#120	1	1	yes	characteristic
119	C₂³×C₄₇	#121	1	1	yes	characteristic
120	C₂³×C₄₇	C₂²⋊Q₈	1	1	yes	characteristic
121	C₂³×C₄₇	#123	1	1	yes	characteristic
122	C₂³×C₄₇	#124	1	1	yes	characteristic
123	C₂³×C₄₇	C₄⋊Q₈	1	1	yes	characteristic
124	C₂³×C₄₇	#135	1	2	yes	—
125	C₂³×C₄₇	#135	1	2	yes	—
126	C₂³×C₄₇	AGL(1,ℤ/8)	1	2	yes	—
127	C₂³×C₄₇	#137	1	2	yes	—
128	C₂×C₄×C₄₇	—	2	2	no	—
129	C₂×C₄×C₄₇	—	2	2	no	—
130	C₂×C₄×C₄₇	—	2	2	no	—
131	C₂×C₄×C₄₇	—	2	2	no	—
132	C₂×C₄×C₄₇	—	2	2	no	—
133	C₂×C₄×C₄₇	—	2	2	no	—
134	C₂×C₄×C₄₇	—	4	2	no	—
135	C₂×C₄×C₄₇	—	4	2	no	—
136	C₂×C₄×C₄₇	—	4	2	no	—
137	C₂×C₄×C₄₇	—	4	2	no	—
138	C₂×C₄×C₄₇	C₂×C₄⋊C₄	1	1	yes	characteristic
139	C₂×C₄×C₄₇	#117	1	1	yes	characteristic
140	C₂×C₄×C₄₇	C₄×D₄	1	2	yes	—
141	C₂×C₄×C₄₇	C₄×Q₈	1	2	yes	—
142	C₂×C₄×C₄₇	#121	1	1	yes	characteristic
143	C₂×C₄×C₄₇	#121	1	2	yes	—
144	C₂×C₄×C₄₇	#121	1	2	yes	—
145	C₂×C₄×C₄₇	C₂²⋊Q₈	1	1	yes	characteristic
146	C₂×C₄×C₄₇	C₂²⋊Q₈	1	2	yes	—
147	C₂×C₄×C₄₇	C₂²⋊Q₈	1	2	yes	—
148	C₂×C₄×C₄₇	C₂²⋊Q₈	1	2	yes	—
149	C₂×C₄×C₄₇	#123	1	2	yes	—
150	C₂×C₄×C₄₇	#125	1	2	yes	—
151	C₂×C₄×C₄₇	#125	1	2	yes	—
152	C₂×C₄×C₄₇	#126	1	2	yes	—
153	C₂×C₄×C₄₇	C₄⋊Q₈	1	2	yes	—
154	C₂×Dic₄₇	—	2	4	no	—
155	C₂×Dic₄₇	—	4	2	no	—
156	C₂×Dic₄₇	—	4	2	no	—
157	C₂×Dic₄₇	—	4	4	no	—
158	C₂×Dic₄₇	—	4	4	no	—
159	C₂×Dic₄₇	—	4	2	no	—
160	C₂×Dic₄₇	—	4	4	no	—
161	C₂×Dic₄₇	—	4	2	no	—
162	C₂×Dic₄₇	—	4	2	no	—
163	C₂×Dic₄₇	—	4	4	no	—
164	C₂×Dic₄₇	—	4	4	no	—
165	C₂×Dic₄₇	—	8	2	no	—
166	C₂×Dic₄₇	—	8	2	no	—
167	C₂×Dic₄₇	—	8	2	no	—
168	C₂×Dic₄₇	—	8	2	no	—
169	C₂×Dic₄₇	—	8	2	no	—
170	C₂×Dic₄₇	—	8	2	no	—
171	C₈×C₄₇	—	4	4	no	—
172	#11208	—	47	1	no	maximal, Sylow
173	C₂²×C₄₇	#380	1	1	yes	characteristic
174	C₂²×C₄₇	#386	1	1	yes	characteristic
175	C₂²×C₄₇	#391	1	1	yes	characteristic
176	C₂²×C₄₇	#394	1	1	yes	characteristic
177	C₂²×C₄₇	#395	1	1	yes	characteristic
178	C₂²×C₄₇	#398	1	1	yes	characteristic
179	C₂²×C₄₇	#400	1	1	yes	characteristic
180	C₂²×C₄₇	#416	1	1	yes	characteristic
181	C₂²×C₄₇	#416	1	1	yes	characteristic
182	C₂²×C₄₇	#418	1	1	yes	characteristic
183	C₂²×C₄₇	#419	1	1	yes	characteristic
184	C₂²×C₄₇	#449	1	2	yes	—
185	C₂²×C₄₇	#452	1	2	yes	—
186	C₂²×C₄₇	#463	1	2	yes	—
187	C₂²×C₄₇	#464	1	2	yes	—
188	C₂²×C₄₇	#478	1	2	yes	—
189	C₂²×C₄₇	#479	1	2	yes	—
190	C₂²×C₄₇	#482	1	2	yes	—
191	C₂²×C₄₇	#485	1	2	yes	—
192	C₂²×C₄₇	#488	1	2	yes	—
193	C₂²×C₄₇	#489	1	2	yes	—
194	C₂²×C₄₇	#499	1	2	yes	—
195	C₂²×C₄₇	#501	1	2	yes	—
196	C₄×C₄₇	—	4	2	no	—
197	C₄×C₄₇	—	4	2	no	—
198	C₄×C₄₇	#387	1	2	yes	—
199	C₄×C₄₇	#389	1	2	yes	—
200	C₄×C₄₇	#396	1	2	yes	—
201	C₄×C₄₇	#398	1	2	yes	—
202	Dic₄₇	—	4	4	no	—
203	Dic₄₇	—	8	2	no	—
204	Dic₄₇	—	8	4	no	—
205	C₂×#389	—	47	1	no	—
206	C₂×#382	—	47	1	no	—
207	C₂×#340	—	47	2	no	—
208	C₂×#340	—	47	2	no	—
209	C₂×#336	D₄₇	1	1	yes	characteristic
210	C₂×C₄₇	#1441	1	1	yes	characteristic
211	C₂×C₄₇	#1804	1	1	yes	characteristic
212	C₂×C₄₇	#1805	1	1	yes	characteristic
213	C₂×C₄₇	#1873	1	1	yes	characteristic
214	C₂×C₄₇	#1875	1	1	yes	characteristic
215	C₂×C₄₇	#1991	1	1	yes	characteristic
216	C₂×C₄₇	#1993	1	1	yes	characteristic
217	C₂×C₄₇	#2042	1	2	yes	—
218	C₂×C₄₇	#2059	1	2	yes	—
219	C₂×C₄₇	#2085	1	2	yes	—
220	C₂×C₄₇	#2101	1	2	yes	—
221	C₂³×C₈	C₂×D₄₇	1	2	yes	—
222	C₂²×C₄⋊C₄	—	47	1	no	—
223	C₂²×C₄⋊C₄	—	47	2	no	—
224	C₂²×C₄⋊C₄	—	47	1	no	—
225	C₂²×C₄⋊C₄	—	94	1	no	—
226	C₂²×C₄²	C₂×D₄₇	1	1	yes	characteristic
227	#389	—	47	4	no	—
228	#389	—	94	2	no	—
229	#382	—	94	4	no	—
230	C₂×#95	—	94	1	no	—
231	C₂×#95	—	94	1	no	—
232	C₂×#95	—	94	1	no	—
233	#340	—	94	4	no	—
234	#340	—	94	4	no	—
235	#336	—	2	2	no	—
236	C₄₇	#11208	1	1	yes	characteristic, complemented, Sylow
237	C₂³×C₄	—	94	1	no	—
238	C₂³×C₄	—	94	1	no	—
239	C₂³×C₄	—	94	2	no	—
240	C₂³×C₄	D₁₈₈	1	1	yes	characteristic
241	C₂³×C₄	D₁₈₈	1	1	yes	characteristic
242	C₂³×C₄	C₂²×D₄₇	1	1	yes	characteristic
243	C₂²×C₈	—	2	2	no	—
244	C₂²×C₈	—	2	2	no	—
245	C₂²×C₈	—	2	2	no	—
246	C₂²×C₈	—	2	2	no	—
247	C₂²×C₈	—	2	2	no	—
248	C₂²×C₈	—	2	2	no	—
249	C₂²×C₈	Dic₉₄	1	4	yes	—
250	C₂×C₄⋊C₄	—	47	2	no	—
251	C₂×C₄⋊C₄	—	47	2	no	—
252	C₂×C₄⋊C₄	—	47	2	no	—
253	C₂×C₄⋊C₄	—	47	2	no	—
254	C₂×C₄⋊C₄	—	47	4	no	—
255	C₂×C₄⋊C₄	—	94	1	no	—
256	C₂×C₄⋊C₄	—	94	1	no	—
257	C₂×C₄⋊C₄	—	94	1	no	—
258	C₂×C₄⋊C₄	—	94	2	no	—
259	C₂×C₄⋊C₄	—	94	2	no	—
260	C₂×C₄⋊C₄	—	94	2	no	—
261	C₂×C₄⋊C₄	—	94	2	no	—
262	C₂×C₄⋊C₄	—	94	2	no	—
263	C₂×C₄⋊C₄	—	94	2	no	—
264	C₂×C₄⋊C₄	—	94	4	no	—
265	C₂×C₄⋊C₄	—	94	2	no	—
266	C₂×C₄⋊C₄	—	94	1	no	—
267	C₂×C₄⋊C₄	—	188	4	no	—
268	C₂×C₄²	—	2	2	no	—
269	C₂×C₄²	—	2	2	no	—
270	C₂×C₄²	C₄×D₄₇	1	2	yes	—
271	C₂×C₄²	C₂²⋊D₄₇	1	2	yes	—
272	#95	—	94	4	no	—
273	#95	—	94	4	no	—
274	#95	—	94	4	no	—
275	C₂⁴	C₂×D₁₈₈	1	1	yes	characteristic
276	C₂²×C₄	—	2	1	no	—
277	C₂²×C₄	—	2	1	no	—
278	C₂²×C₄	—	2	1	no	—
279	C₂²×C₄	—	2	1	no	—
280	C₂²×C₄	—	2	2	no	—
281	C₂²×C₄	—	2	2	no	—
282	C₂²×C₄	—	2	2	no	—
283	C₂²×C₄	—	2	2	no	—
284	C₂²×C₄	—	94	2	no	—
285	C₂²×C₄	—	94	2	no	—
286	C₂²×C₄	—	94	2	no	—
287	C₂²×C₄	—	94	2	no	—
288	C₂²×C₄	—	94	4	no	—
289	C₂²×C₄	—	188	1	no	—
290	C₂²×C₄	—	188	2	no	—
291	C₂²×C₄	—	188	1	no	—
292	C₂²×C₄	—	188	2	no	—
293	C₂²×C₄	—	188	2	no	—
294	C₂²×C₄	—	188	2	no	—
295	C₂²×C₄	—	188	2	no	—
296	C₂²×C₄	—	188	2	no	—
297	C₂²×C₄	—	188	2	no	—
298	C₂²×C₄	—	188	2	no	—
299	C₂²×C₄	—	188	2	no	—
300	C₂²×C₄	—	188	2	no	—
301	C₂²×C₄	(C₂×D₄₇)⋊C₄	1	2	yes	—
302	C₂²×C₄	(C₂×D₄₇)⋊C₄	1	2	yes	—
303	C₂²×C₄	C₂×Dic₉₄	1	2	yes	—
304	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
305	C₂²×C₄	#10625350	1	2	yes	—
306	C₂²×C₄	D₄×D₄₇	1	1	yes	characteristic
307	C₂²×C₄	D₄×D₄₇	1	2	yes	—
308	C₂²×C₄	#10625352	1	1	yes	characteristic
309	C₂²×C₄	#10625352	1	2	yes	—
310	C₂²×C₄	Q₈×D₄₇	1	1	yes	characteristic
311	C₂²×C₄	#10625354	1	1	yes	characteristic
312	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
313	C₂×C₈	—	2	4	no	—
314	C₂×C₈	—	2	4	no	—
315	C₂×C₈	—	2	4	no	—
316	C₂×C₈	—	4	2	no	—
317	C₂×C₈	—	4	2	no	—
318	C₂×C₈	—	4	2	no	—
319	C₂×C₈	—	4	2	no	—
320	C₄⋊C₄	—	47	4	no	—
321	C₄⋊C₄	—	94	2	no	—
322	C₄⋊C₄	—	94	2	no	—
323	C₄⋊C₄	—	94	2	no	—
324	C₄⋊C₄	—	94	4	no	—
325	C₄⋊C₄	—	94	4	no	—
326	C₄⋊C₄	—	94	4	no	—
327	C₄⋊C₄	—	188	8	no	—
328	C₄⋊C₄	—	188	2	no	—
329	C₄⋊C₄	—	188	2	no	—
330	C₄⋊C₄	—	188	2	no	—
331	C₄²	—	2	4	no	—
332	C₄²	—	2	4	no	—
333	C₂³	C₂×(C₂×D₄₇)⋊C₄	1	1	yes	characteristic
334	C₂³	#13093994	1	1	yes	characteristic
335	C₂³	#13093999	1	1	yes	characteristic
336	C₂³	#13094004	1	1	yes	characteristic
337	C₂³	#13094008	1	1	yes	characteristic
338	C₂³	#13094012	1	1	yes	characteristic
339	C₂³	#13094024	1	1	yes	characteristic
340	C₂³	#13094046	1	2	yes	—
341	C₂³	#13094046	1	2	yes	—
342	C₂³	#13094052	1	2	yes	—
343	C₂³	#13094057	1	2	yes	—
344	C₂×C₄	—	2	2	no	—
345	C₂×C₄	—	2	2	no	—
346	C₂×C₄	—	2	2	no	—
347	C₂×C₄	—	2	2	no	—
348	C₂×C₄	—	2	2	no	—
349	C₂×C₄	—	2	2	no	—
350	C₂×C₄	—	4	2	no	—
351	C₂×C₄	—	4	2	no	—
352	C₂×C₄	—	4	2	no	—
353	C₂×C₄	—	4	2	no	—
354	C₂×C₄	—	94	4	no	—
355	C₂×C₄	—	376	2	no	—
356	C₂×C₄	—	376	2	no	—
357	C₂×C₄	—	376	2	no	—
358	C₂×C₄	—	376	2	no	—
359	C₂×C₄	—	376	2	no	—
360	C₂×C₄	—	376	2	no	—
361	C₂×C₄	—	188	2	no	—
362	C₂×C₄	—	188	4	no	—
363	C₂×C₄	—	188	4	no	—
364	C₂×C₄	—	188	4	no	—
365	C₂×C₄	—	188	2	no	—
366	C₂×C₄	—	188	2	no	—
367	C₂×C₄	—	188	4	no	—
368	C₂×C₄	—	188	2	no	—
369	C₂×C₄	—	188	2	no	—
370	C₂×C₄	—	188	4	no	—
371	C₂×C₄	C₄⋊C₄×D₄₇	1	1	yes	characteristic
372	C₂×C₄	#13093982	1	1	yes	characteristic
373	C₂×C₄	(C₂²⋊D₄₇)⋊C₄	1	2	yes	—
374	C₂×C₄	C₄×Dic₉₄	1	2	yes	—
375	C₂×C₄	#13093995	1	1	yes	characteristic
376	C₂×C₄	#13093996	1	2	yes	—
377	C₂×C₄	#13093997	1	2	yes	—
378	C₂×C₄	#13094000	1	1	yes	characteristic
379	C₂×C₄	#13094001	1	2	yes	—
380	C₂×C₄	#13094001	1	2	yes	—
381	C₂×C₄	#13094003	1	2	yes	—
382	C₂×C₄	#13094009	1	2	yes	—
383	C₂×C₄	#13094014	1	2	yes	—
384	C₂×C₄	#13094015	1	2	yes	—
385	C₂×C₄	#13094017	1	2	yes	—
386	C₂×C₄	#13094023	1	2	yes	—
387	C₈	—	4	4	no	—
388	C₂²	#15688980	1	1	yes	characteristic
389	C₂²	#15689000	1	1	yes	characteristic
390	C₂²	#15689029	1	1	yes	characteristic
391	C₂²	#15689041	1	1	yes	characteristic
392	C₂²	#15689044	1	1	yes	characteristic
393	C₂²	#15689055	1	1	yes	characteristic
394	C₂²	#15689063	1	1	yes	characteristic
395	C₂²	#15689120	1	1	yes	characteristic
396	C₂²	#15689120	1	1	yes	characteristic
397	C₂²	#15689129	1	1	yes	characteristic
398	C₂²	#15689133	1	1	yes	characteristic
399	C₂²	#15689270	1	2	yes	—
400	C₂²	#15689287	1	2	yes	—
401	C₂²	#15689339	1	2	yes	—
402	C₂²	#15689346	1	2	yes	—
403	C₂²	#15689424	1	2	yes	—
404	C₂²	#15689431	1	2	yes	—
405	C₂²	#15689448	1	2	yes	—
406	C₂²	#15689465	1	2	yes	—
407	C₂²	#15689478	1	2	yes	—
408	C₂²	#15689483	1	2	yes	—
409	C₂²	#15689525	1	2	yes	—
410	C₂²	#15689532	1	2	yes	—
411	C₄	—	4	2	no	—
412	C₄	—	4	2	no	—
413	C₄	—	376	4	no	—
414	C₄	—	376	2	no	—
415	C₄	—	188	4	no	—
416	C₄	#15689010	1	2	yes	—
417	C₄	#15689020	1	2	yes	—
418	C₄	#15689046	1	2	yes	—
419	C₄	#15689056	1	2	yes	—
420	C₂	#20241642	1	1	yes	characteristic
421	C₂	#20243399	1	1	yes	characteristic
422	C₂	#20243404	1	1	yes	characteristic
423	C₂	#20243698	1	1	yes	characteristic
424	C₂	#20243708	1	1	yes	characteristic
425	C₂	#20244353	1	1	yes	characteristic
426	C₂	#20244361	1	1	yes	characteristic
427	C₂	#20244630	1	2	yes	—
428	C₂	#20244727	1	2	yes	—
429	C₂	#20244871	1	2	yes	—
430	C₂	#20244957	1	2	yes	—

	subgroup	G/H
center	C₂⁴	C₂×D₁₈₈
commutator	C₂²×C₄×C₄₇	C₂²×C₄
Frattini	C₂³×C₄	C₂²×D₄₇
Fitting	C₂×C₄₇×#336	C₂
socle, prime radical	C₂⁴×C₄₇	C₂×D₄
cosocle	C₂³×C₄×C₄₇	C₂³
hypercenter	C₂×#336	D₄₇
hypocenter	C₄₇	#11208
LCS	G ▷ C₂²×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂⁴ ◁ C₂²×C₄² ◁ C₂×#336

Complements

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

N	H ≅ G/N	type
11. #15689021	C₄	semidirect
236. C₄₇	#11208	semidirect

Maximal subgroups

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

subgroup	index
C₂×#15689021	2
C₂×#15688989	2
C₂×#15688886	2
C₂×C₄₇×#336	2
#11208	47