Subgroups — #26124174

Order 12032.

778 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×#15689147	C₂	1	1	yes	maximal, characteristic
2	C₂×#15689021	C₂	1	1	yes	maximal, characteristic
3	C₂×#15688891	C₂	1	2	yes	maximal
4	C₂×#15688891	C₂	1	2	yes	maximal
5	C₄₇×#1728	C₂	1	1	yes	maximal, characteristic
6	C₂²×#10625329	C₂²	1	2	yes	—
7	C₂²×C₄⋊Dic₄₇	C₂²	1	1	yes	characteristic
8	C₂²×C₄⋊Dic₄₇	C₂²	1	1	yes	characteristic
9	C₂²×Dic₄₇⋊C₄	C₄	1	2	yes	—
10	#15689147	—	2	4	no	—
11	C₂×C₄⋊(C₄₇⋊C₈)	—	2	1	no	—
12	C₂×C₄⋊(C₄₇⋊C₈)	—	2	1	no	—
13	#15689021	—	2	1	no	—
14	#15689021	—	2	1	no	—
15	#15689021	—	2	1	no	—
16	#15689021	—	2	1	no	—
17	C₂×C₄₇⋊#95	C₄	1	2	yes	—
18	#15688891	—	2	4	no	—
19	#15688891	—	2	4	no	—
20	C₂²×M₁₆×C₄₇	C₂²	1	2	yes	—
21	C₂²×C₄²×C₄₇	C₂²	1	1	yes	characteristic
22	C₄₇×#336	—	2	1	no	—
23	C₄₇×#336	—	2	1	no	—
24	C₂³×Dic₄₇	C₂×C₄	1	2	yes	—
25	C₂³×Dic₄₇	C₂×C₄	1	2	yes	—
26	C₂×#10625329	—	2	2	no	—
27	C₂×#10625329	—	2	2	no	—
28	C₂×#10625329	—	2	2	no	—
29	C₂×#10625329	—	2	2	no	—
30	C₂×#10625329	—	2	2	no	—
31	C₂×#10625329	D₄	1	4	yes	—
32	C₂²×C₄₇⋊C₈	—	2	2	no	—
33	C₂×C₄⋊Dic₄₇	—	2	1	no	—
34	C₂×C₄⋊Dic₄₇	—	2	1	no	—
35	C₂×C₄⋊Dic₄₇	—	2	1	no	—
36	C₂×C₄⋊Dic₄₇	—	2	1	no	—
37	C₂×C₄⋊Dic₄₇	—	2	1	no	—
38	C₂×C₄⋊Dic₄₇	—	2	1	no	—
39	C₂×C₄⋊Dic₄₇	—	2	2	no	—
40	C₂×C₄⋊Dic₄₇	—	2	2	no	—
41	C₂×C₄⋊Dic₄₇	D₄	1	2	yes	—
42	C₂×C₄⋊Dic₄₇	Q₈	1	2	yes	—
43	C₂×Dic₄₇⋊C₄	—	2	2	no	—
44	C₂×Dic₄₇⋊C₄	—	2	2	no	—
45	C₂×Dic₄₇⋊C₄	—	4	4	no	—
46	C₄⋊(C₄₇⋊C₈)	—	2	4	no	—
47	C₄⋊(C₄₇⋊C₈)	—	2	4	no	—
48	C₄₇⋊#95	—	2	2	no	—
49	C₄₇⋊#95	—	2	2	no	—
50	C₂³×C₄×C₄₇	C₂×C₄	1	1	yes	characteristic
51	C₂³×C₄×C₄₇	C₂×C₄	1	1	yes	characteristic
52	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
53	C₂×M₁₆×C₄₇	—	2	2	no	—
54	C₂×M₁₆×C₄₇	—	2	2	no	—
55	C₂×M₁₆×C₄₇	—	2	2	no	—
56	C₂×M₁₆×C₄₇	—	2	2	no	—
57	C₂×M₁₆×C₄₇	—	2	2	no	—
58	C₂×M₁₆×C₄₇	Q₈	1	4	yes	—
59	C₂²×C₈×C₄₇	—	2	2	no	—
60	C₂×C₄²×C₄₇	—	2	2	no	—
61	C₂×C₄²×C₄₇	—	2	2	no	—
62	C₂×C₄²×C₄₇	D₄	1	1	yes	characteristic
63	C₂×C₄²×C₄₇	D₄	1	1	yes	characteristic
64	C₂×C₄²×C₄₇	D₄	1	1	yes	characteristic
65	C₂×C₄²×C₄₇	D₄	1	1	yes	characteristic
66	C₂⁴×C₄₇	C₂²×C₄	1	1	yes	characteristic
67	C₂²×C₄×C₄₇	—	2	2	no	—
68	C₂²×C₄×C₄₇	—	2	2	no	—
69	C₂²×C₄×C₄₇	—	2	2	no	—
70	C₂²×C₄×C₄₇	—	2	2	no	—
71	C₂²×C₄×C₄₇	—	4	1	no	—
72	C₂²×C₄×C₄₇	—	4	1	no	—
73	C₂²×C₄×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
74	C₂²×C₄×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
75	C₂²×C₄×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
76	C₂²×C₄×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
77	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
78	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
79	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
80	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
81	C₂²×C₄×C₄₇	C₂×Q₈	1	2	yes	—
82	C₂²×C₄×C₄₇	C₂×Q₈	1	1	yes	characteristic
83	C₂²×C₄×C₄₇	#41	1	1	yes	characteristic
84	C₂²×C₄×C₄₇	#41	1	1	yes	characteristic
85	C₂²×C₄×C₄₇	#41	1	2	yes	—
86	C₂²×C₄×C₄₇	#41	1	2	yes	—
87	C₂²×Dic₄₇	—	2	2	no	—
88	C₂²×Dic₄₇	—	2	2	no	—
89	C₂²×Dic₄₇	—	2	2	no	—
90	C₂²×Dic₄₇	—	2	4	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	C₄⋊C₄	1	4	yes	—
96	M₁₆×C₄₇	—	2	4	no	—
97	M₁₆×C₄₇	—	2	4	no	—
98	M₁₆×C₄₇	—	4	2	no	—
99	M₁₆×C₄₇	—	4	2	no	—
100	C₂×C₈×C₄₇	—	2	4	no	—
101	C₂×C₈×C₄₇	—	4	2	no	—
102	C₂×C₈×C₄₇	—	4	2	no	—
103	C₄²×C₄₇	—	2	1	no	—
104	C₄²×C₄₇	—	2	1	no	—
105	C₄²×C₄₇	—	2	2	no	—
106	C₄²×C₄₇	—	2	2	no	—
107	C₄²×C₄₇	—	2	1	no	—
108	C₄²×C₄₇	—	2	1	no	—
109	C₄⋊Dic₄₇	—	2	2	no	—
110	C₄⋊Dic₄₇	—	2	2	no	—
111	C₄⋊Dic₄₇	—	2	2	no	—
112	C₄⋊Dic₄₇	—	2	2	no	—
113	C₄⋊Dic₄₇	—	4	1	no	—
114	C₄⋊Dic₄₇	—	4	2	no	—
115	C₄⋊Dic₄₇	—	4	1	no	—
116	Dic₄₇⋊C₄	—	4	4	no	—
117	Dic₄₇⋊C₄	—	4	4	no	—
118	#10625329	—	2	4	no	—
119	#10625329	—	2	4	no	—
120	#10625329	—	4	2	no	—
121	#10625329	—	4	2	no	—
122	C₂×C₄₇⋊C₈	—	2	4	no	—
123	C₂×C₄₇⋊C₈	—	4	2	no	—
124	C₂×C₄₇⋊C₈	—	4	2	no	—
125	C₂³×C₄₇	—	2	1	no	—
126	C₂³×C₄₇	—	2	1	no	—
127	C₂³×C₄₇	—	2	1	no	—
128	C₂³×C₄₇	—	2	1	no	—
129	C₂³×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
130	C₂³×C₄₇	C₂×C₄⋊C₄	1	1	yes	characteristic
131	C₂³×C₄₇	#117	1	1	yes	characteristic
132	C₂³×C₄₇	C₄×D₄	1	2	yes	—
133	C₂³×C₄₇	C₄×Q₈	1	2	yes	—
134	C₂×C₄×C₄₇	—	2	1	no	—
135	C₂×C₄×C₄₇	—	2	1	no	—
136	C₂×C₄×C₄₇	—	2	1	no	—
137	C₂×C₄×C₄₇	—	2	1	no	—
138	C₂×C₄×C₄₇	—	2	1	no	—
139	C₂×C₄×C₄₇	—	2	1	no	—
140	C₂×C₄×C₄₇	—	2	1	no	—
141	C₂×C₄×C₄₇	—	2	1	no	—
142	C₂×C₄×C₄₇	—	2	1	no	—
143	C₂×C₄×C₄₇	—	2	1	no	—
144	C₂×C₄×C₄₇	—	4	4	no	—
145	C₂×C₄×C₄₇	—	4	4	no	—
146	C₂×C₄×C₄₇	#100	1	2	yes	—
147	C₂×C₄×C₄₇	#101	1	2	yes	—
148	C₂×C₄×C₄₇	#120	1	1	yes	characteristic
149	C₂×C₄×C₄₇	#121	1	1	yes	characteristic
150	C₂×C₄×C₄₇	#121	1	2	yes	—
151	C₂×C₄×C₄₇	#121	1	2	yes	—
152	C₂×C₄×C₄₇	#121	1	1	yes	characteristic
153	C₂×C₄×C₄₇	C₂²⋊Q₈	1	1	yes	characteristic
154	C₂×C₄×C₄₇	C₂²⋊Q₈	1	2	yes	—
155	C₂×C₄×C₄₇	C₂²⋊Q₈	1	2	yes	—
156	C₂×C₄×C₄₇	C₂²⋊Q₈	1	2	yes	—
157	C₂×C₄×C₄₇	C₂²⋊Q₈	1	1	yes	characteristic
158	C₂×C₄×C₄₇	#123	1	1	yes	characteristic
159	C₂×C₄×C₄₇	#123	1	2	yes	—
160	C₂×C₄×C₄₇	#124	1	1	yes	characteristic
161	C₂×C₄×C₄₇	#125	1	2	yes	—
162	C₂×C₄×C₄₇	#125	1	2	yes	—
163	C₂×C₄×C₄₇	#126	1	2	yes	—
164	C₂×C₄×C₄₇	C₄⋊Q₈	1	2	yes	—
165	C₂×C₄×C₄₇	C₄⋊Q₈	1	1	yes	characteristic
166	C₂×Dic₄₇	—	2	4	no	—
167	C₂×Dic₄₇	—	4	4	no	—
168	C₂×Dic₄₇	—	4	2	no	—
169	C₂×Dic₄₇	—	4	2	no	—
170	C₂×Dic₄₇	—	4	4	no	—
171	C₂×Dic₄₇	—	4	2	no	—
172	C₂×Dic₄₇	—	4	2	no	—
173	C₂×Dic₄₇	—	4	2	no	—
174	C₂×Dic₄₇	—	8	4	no	—
175	C₈×C₄₇	—	4	4	no	—
176	C₄₇⋊C₈	—	4	4	no	—
177	#11204	—	47	1	no	maximal, Sylow
178	C₂²×C₄₇	—	2	1	no	—
179	C₂²×C₄₇	—	2	1	no	—
180	C₂²×C₄₇	—	2	1	no	—
181	C₂²×C₄₇	—	2	1	no	—
182	C₂²×C₄₇	—	2	2	no	—
183	C₂²×C₄₇	—	2	2	no	—
184	C₂²×C₄₇	—	2	2	no	—
185	C₂²×C₄₇	—	2	2	no	—
186	C₂²×C₄₇	#380	1	1	yes	characteristic
187	C₂²×C₄₇	#386	1	1	yes	characteristic
188	C₂²×C₄₇	#387	1	2	yes	—
189	C₂²×C₄₇	#389	1	2	yes	—
190	C₂²×C₄₇	#391	1	1	yes	characteristic
191	C₂²×C₄₇	C₂×#100	1	1	yes	characteristic
192	C₂²×C₄₇	C₂×#101	1	1	yes	characteristic
193	C₂²×C₄₇	#413	1	1	yes	characteristic
194	C₂²×C₄₇	#413	1	1	yes	characteristic
195	C₄×C₄₇	—	2	2	no	—
196	C₄×C₄₇	—	2	2	no	—
197	C₄×C₄₇	—	4	1	no	—
198	C₄×C₄₇	—	4	1	no	—
199	C₄×C₄₇	#394	1	1	yes	characteristic
200	C₄×C₄₇	#395	1	1	yes	characteristic
201	C₄×C₄₇	#396	1	2	yes	—
202	C₄×C₄₇	#398	1	1	yes	characteristic
203	C₄×C₄₇	#398	1	2	yes	—
204	C₄×C₄₇	#400	1	1	yes	characteristic
205	Dic₄₇	—	4	4	no	—
206	Dic₄₇	—	8	2	no	—
207	C₂×#423	—	47	1	no	—
208	C₂×#389	—	47	1	no	—
209	C₂×#343	—	47	2	no	—
210	C₂×#343	—	47	2	no	—
211	#1728	D₄₇	1	1	yes	characteristic
212	C₂×C₄₇	—	2	2	no	—
213	C₂×C₄₇	—	2	2	no	—
214	C₂×C₄₇	#1441	1	1	yes	characteristic
215	C₂×C₄₇	#1800	1	1	yes	characteristic
216	C₂×C₄₇	#1801	1	1	yes	characteristic
217	C₂×C₄₇	#1900	1	1	yes	characteristic
218	C₂×C₄₇	#1901	1	1	yes	characteristic
219	C₂×C₄₇	#1997	1	1	yes	characteristic
220	C₂×C₄₇	#1998	1	1	yes	characteristic
221	C₂²×M₁₆	—	47	2	no	—
222	C₂²×M₁₆	C₂×D₄₇	1	2	yes	—
223	C₂²×C₄⋊C₄	—	47	1	no	—
224	C₂²×C₄⋊C₄	—	47	1	no	—
225	C₂²×C₄⋊C₄	—	47	2	no	—
226	C₂²×C₄²	C₂×D₄₇	1	1	yes	characteristic
227	#423	—	94	4	no	—
228	C₂×C₄⋊C₈	—	94	1	no	—
229	C₂×C₄⋊C₈	—	94	1	no	—
230	#389	—	94	1	no	—
231	#389	—	94	1	no	—
232	#389	—	94	1	no	—
233	#389	—	94	1	no	—
234	C₂×#95	—	47	2	no	—
235	#343	—	94	4	no	—
236	#343	—	94	4	no	—
237	#336	—	2	1	no	—
238	#336	—	2	1	no	—
239	C₄₇	#11204	1	1	yes	characteristic, complemented, Sylow
240	C₂³×C₄	—	47	2	no	—
241	C₂³×C₄	—	47	2	no	—
242	C₂³×C₄	C₄×D₄₇	1	1	yes	characteristic
243	C₂³×C₄	C₄×D₄₇	1	1	yes	characteristic
244	C₂³×C₄	C₂²×D₄₇	1	1	yes	characteristic
245	C₂×M₁₆	—	2	2	no	—
246	C₂×M₁₆	—	2	2	no	—
247	C₂×M₁₆	—	2	2	no	—
248	C₂×M₁₆	—	2	2	no	—
249	C₂×M₁₆	—	2	2	no	—
250	C₂×M₁₆	—	47	4	no	—
251	C₂×M₁₆	—	94	2	no	—
252	C₂×M₁₆	—	94	2	no	—
253	C₂×M₁₆	—	94	2	no	—
254	C₂×M₁₆	—	94	2	no	—
255	C₂×M₁₆	—	94	2	no	—
256	C₂×M₁₆	Dic₉₄	1	4	yes	—
257	C₂²×C₈	—	2	2	no	—
258	C₂²×C₈	—	94	2	no	—
259	C₂×C₄⋊C₄	—	47	2	no	—
260	C₂×C₄⋊C₄	—	47	2	no	—
261	C₂×C₄⋊C₄	—	94	1	no	—
262	C₂×C₄⋊C₄	—	94	1	no	—
263	C₂×C₄⋊C₄	—	94	1	no	—
264	C₂×C₄⋊C₄	—	94	1	no	—
265	C₂×C₄⋊C₄	—	94	2	no	—
266	C₂×C₄⋊C₄	—	94	2	no	—
267	C₂×C₄⋊C₄	—	94	1	no	—
268	C₂×C₄⋊C₄	—	94	2	no	—
269	C₂×C₄⋊C₄	—	94	2	no	—
270	C₂×C₄⋊C₄	—	94	1	no	—
271	C₂×C₄⋊C₄	—	188	4	no	—
272	C₂×C₄²	—	2	2	no	—
273	C₂×C₄²	—	2	2	no	—
274	C₂×C₄²	D₁₈₈	1	1	yes	characteristic
275	C₂×C₄²	D₁₈₈	1	1	yes	characteristic
276	C₂×C₄²	C₂²⋊D₄₇	1	1	yes	characteristic
277	C₂×C₄²	C₂²⋊D₄₇	1	1	yes	characteristic
278	C₄⋊C₈	—	94	4	no	—
279	C₄⋊C₈	—	94	4	no	—
280	#95	—	94	2	no	—
281	#95	—	94	2	no	—
282	C₂⁴	C₂×C₄×D₄₇	1	1	yes	characteristic
283	C₂²×C₄	—	2	2	no	—
284	C₂²×C₄	—	2	2	no	—
285	C₂²×C₄	—	2	2	no	—
286	C₂²×C₄	—	2	2	no	—
287	C₂²×C₄	—	4	1	no	—
288	C₂²×C₄	—	4	1	no	—
289	C₂²×C₄	—	47	4	no	—
290	C₂²×C₄	—	94	2	no	—
291	C₂²×C₄	—	94	2	no	—
292	C₂²×C₄	—	94	4	no	—
293	C₂²×C₄	—	94	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	(C₂×D₄₇)⋊C₄	1	1	yes	characteristic
299	C₂²×C₄	(C₂×D₄₇)⋊C₄	1	1	yes	characteristic
300	C₂²×C₄	(C₂×D₄₇)⋊C₄	1	1	yes	characteristic
301	C₂²×C₄	(C₂×D₄₇)⋊C₄	1	1	yes	characteristic
302	C₂²×C₄	C₂×Dic₉₄	1	2	yes	—
303	C₂²×C₄	C₂×D₁₈₈	1	1	yes	characteristic
304	C₂²×C₄	#10625350	1	2	yes	—
305	C₂²×C₄	D₄×D₄₇	1	2	yes	—
306	C₂²×C₄	D₄×D₄₇	1	1	yes	characteristic
307	C₂²×C₄	#10625352	1	1	yes	characteristic
308	C₂²×C₄	#10625352	1	2	yes	—
309	C₂²×C₄	Q₈×D₄₇	1	1	yes	characteristic
310	C₂²×C₄	#10625354	1	1	yes	characteristic
311	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
312	M₁₆	—	2	4	no	—
313	M₁₆	—	2	4	no	—
314	M₁₆	—	4	2	no	—
315	M₁₆	—	4	2	no	—
316	M₁₆	—	94	4	no	—
317	M₁₆	—	94	4	no	—
318	M₁₆	—	188	2	no	—
319	M₁₆	—	188	2	no	—
320	C₂×C₈	—	2	4	no	—
321	C₂×C₈	—	4	2	no	—
322	C₂×C₈	—	4	2	no	—
323	C₂×C₈	—	94	4	no	—
324	C₂×C₈	—	188	2	no	—
325	C₂×C₈	—	188	2	no	—
326	C₄⋊C₄	—	94	2	no	—
327	C₄⋊C₄	—	94	2	no	—
328	C₄⋊C₄	—	94	2	no	—
329	C₄⋊C₄	—	94	2	no	—
330	C₄⋊C₄	—	188	4	no	—
331	C₄⋊C₄	—	188	4	no	—
332	C₄⋊C₄	—	188	1	no	—
333	C₄⋊C₄	—	188	2	no	—
334	C₄⋊C₄	—	188	1	no	—
335	C₄²	—	2	1	no	—
336	C₄²	—	2	1	no	—
337	C₄²	—	2	2	no	—
338	C₄²	—	2	2	no	—
339	C₄²	—	2	1	no	—
340	C₄²	—	2	1	no	—
341	C₂³	—	2	1	no	—
342	C₂³	—	2	1	no	—
343	C₂³	—	2	1	no	—
344	C₂³	—	2	1	no	—
345	C₂³	C₂×(C₂×D₄₇)⋊C₄	1	1	yes	characteristic
346	C₂³	C₄⋊C₄×D₄₇	1	1	yes	characteristic
347	C₂³	#13093982	1	1	yes	characteristic
348	C₂³	(C₂²⋊D₄₇)⋊C₄	1	2	yes	—
349	C₂³	C₄×Dic₉₄	1	2	yes	—
350	C₂×C₄	—	2	1	no	—
351	C₂×C₄	—	2	1	no	—
352	C₂×C₄	—	2	1	no	—
353	C₂×C₄	—	2	1	no	—
354	C₂×C₄	—	2	1	no	—
355	C₂×C₄	—	2	1	no	—
356	C₂×C₄	—	2	1	no	—
357	C₂×C₄	—	2	1	no	—
358	C₂×C₄	—	2	1	no	—
359	C₂×C₄	—	2	1	no	—
360	C₂×C₄	—	4	4	no	—
361	C₂×C₄	—	4	4	no	—
362	C₂×C₄	—	94	4	no	—
363	C₂×C₄	—	376	4	no	—
364	C₂×C₄	—	188	2	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	#13093940	1	2	yes	—
372	C₂×C₄	#13093942	1	2	yes	—
373	C₂×C₄	#13093994	1	1	yes	characteristic
374	C₂×C₄	#13093995	1	1	yes	characteristic
375	C₂×C₄	#13093996	1	2	yes	—
376	C₂×C₄	#13093997	1	2	yes	—
377	C₂×C₄	#13093999	1	1	yes	characteristic
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	#13094004	1	1	yes	characteristic
383	C₂×C₄	#13094008	1	1	yes	characteristic
384	C₂×C₄	#13094009	1	2	yes	—
385	C₂×C₄	#13094012	1	1	yes	characteristic
386	C₂×C₄	#13094014	1	2	yes	—
387	C₂×C₄	#13094015	1	2	yes	—
388	C₂×C₄	#13094017	1	2	yes	—
389	C₂×C₄	#13094023	1	2	yes	—
390	C₂×C₄	#13094024	1	1	yes	characteristic
391	C₈	—	4	4	no	—
392	C₈	—	188	4	no	—
393	C₂²	—	2	2	no	—
394	C₂²	—	2	2	no	—
395	C₂²	—	2	2	no	—
396	C₂²	—	2	2	no	—
397	C₂²	—	2	1	no	—
398	C₂²	—	2	1	no	—
399	C₂²	—	2	1	no	—
400	C₂²	—	2	1	no	—
401	C₂²	#15688980	1	1	yes	characteristic
402	C₂²	#15689000	1	1	yes	characteristic
403	C₂²	#15689010	1	2	yes	—
404	C₂²	#15689020	1	2	yes	—
405	C₂²	#15689029	1	1	yes	characteristic
406	C₂²	C₂×#13093940	1	1	yes	characteristic
407	C₂²	C₂×#13093942	1	1	yes	characteristic
408	C₂²	#15689105	1	1	yes	characteristic
409	C₂²	#15689105	1	1	yes	characteristic
410	C₄	—	2	2	no	—
411	C₄	—	2	2	no	—
412	C₄	—	4	1	no	—
413	C₄	—	4	1	no	—
414	C₄	—	376	2	no	—
415	C₄	—	188	4	no	—
416	C₄	#15689041	1	1	yes	characteristic
417	C₄	#15689044	1	1	yes	characteristic
418	C₄	#15689046	1	2	yes	—
419	C₄	#15689055	1	1	yes	characteristic
420	C₄	#15689056	1	2	yes	—
421	C₄	#15689063	1	1	yes	characteristic
422	C₂	—	2	2	no	—
423	C₂	—	2	2	no	—
424	C₂	#20241642	1	1	yes	characteristic
425	C₂	#20243377	1	1	yes	characteristic
426	C₂	#20243381	1	1	yes	characteristic
427	C₂	#20243849	1	1	yes	characteristic
428	C₂	#20243854	1	1	yes	characteristic
429	C₂	#20244377	1	1	yes	characteristic
430	C₂	#20244381	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	C₂×(C₂×D₄₇)⋊C₄
commutator, prime radical	C₂⁴×C₄₇	C₂²×C₄
Frattini	C₂³×C₄	C₂²×D₄₇
Fitting	C₄₇×#1728	C₂
socle	C₂³×C₄₇	C₂×C₂²⋊C₄
cosocle	C₂³×C₄×C₄₇	C₂³
hypercenter	#1728	D₄₇
hypocenter	C₄₇	#11204
LCS	G ▷ C₂⁴×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂³ ◁ C₂²×C₄² ◁ #1728

Complements

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

N	H ≅ G/N	type
239. C₄₇	#11204	semidirect

Maximal subgroups

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

subgroup	index
C₂×#15689147	2
C₂×#15689021	2
C₂×#15688891	2
C₄₇×#1728	2
#11204	47