Subgroups — #26121912

Order 12032.

802 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×C₄×C₄⋊Dic₄₇	C₂	1	1	yes	maximal, characteristic
2	C₂×#15688891	C₂	1	2	yes	maximal
3	C₂×#15688891	C₂	1	2	yes	maximal
4	#20243082	C₂	1	1	yes	maximal, characteristic
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×C₄×Dic₄₇	C₄	1	2	yes	—
10	C₄×C₄⋊Dic₄₇	—	2	1	no	—
11	C₄×C₄⋊Dic₄₇	—	2	1	no	—
12	C₄×C₄⋊Dic₄₇	—	2	1	no	—
13	C₄×C₄⋊Dic₄₇	—	2	1	no	—
14	C₂×C₄₇⋊#95	C₄	1	2	yes	—
15	#15688891	—	2	4	no	—
16	#15688891	C₄	1	8	yes	complemented
17	#15688878	—	2	1	no	—
18	#15688878	—	2	1	no	—
19	C₂²×M₁₆×C₄₇	C₂²	1	2	yes	—
20	C₂²×C₄²×C₄₇	C₂²	1	1	yes	characteristic
21	C₄₇×#336	—	2	1	no	—
22	C₄₇×#336	—	2	1	no	—
23	C₂³×Dic₄₇	C₂×C₄	1	2	yes	—
24	C₂³×Dic₄₇	C₂×C₄	1	2	yes	—
25	C₂×#10625329	—	2	2	no	—
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	C₂×C₄	1	4	yes	—
31	C₂²×C₄₇⋊C₈	—	2	2	no	—
32	C₂×C₄⋊Dic₄₇	—	2	1	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	2	no	—
37	C₂×C₄⋊Dic₄₇	—	2	1	no	—
38	C₂×C₄⋊Dic₄₇	—	2	1	no	—
39	C₂×C₄⋊Dic₄₇	C₂×C₄	1	4	yes	—
40	C₂×C₄⋊Dic₄₇	D₄	1	2	yes	—
41	C₂×C₄⋊Dic₄₇	Q₈	1	2	yes	—
42	C₂×C₄×Dic₄₇	—	2	2	no	—
43	C₂×C₄×Dic₄₇	—	2	2	no	—
44	C₂×C₄×Dic₄₇	—	4	4	no	—
45	C₄₇⋊#95	—	2	2	no	—
46	C₄₇⋊#95	—	2	2	no	—
47	C₂³×C₄×C₄₇	C₂×C₄	1	1	yes	characteristic
48	C₂³×C₄×C₄₇	C₂×C₄	1	1	yes	characteristic
49	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
50	C₂×M₁₆×C₄₇	—	2	2	no	—
51	C₂×M₁₆×C₄₇	—	2	2	no	—
52	C₂×M₁₆×C₄₇	—	2	2	no	—
53	C₂×M₁₆×C₄₇	—	2	2	no	—
54	C₂×M₁₆×C₄₇	—	2	2	no	—
55	C₂×M₁₆×C₄₇	C₂×C₄	1	4	yes	—
56	C₂²×C₈×C₄₇	—	2	2	no	—
57	C₂×C₄²×C₄₇	—	2	2	no	—
58	C₂×C₄²×C₄₇	—	2	2	no	—
59	C₂×C₄²×C₄₇	D₄	1	1	yes	characteristic
60	C₂×C₄²×C₄₇	D₄	1	1	yes	characteristic
61	C₂×C₄²×C₄₇	D₄	1	1	yes	characteristic
62	C₂×C₄²×C₄₇	D₄	1	1	yes	characteristic
63	C₂⁴×C₄₇	C₂²×C₄	1	1	yes	characteristic
64	C₂²×C₄×C₄₇	—	2	1	no	—
65	C₂²×C₄×C₄₇	—	2	1	no	—
66	C₂²×C₄×C₄₇	—	2	2	no	—
67	C₂²×C₄×C₄₇	—	2	2	no	—
68	C₂²×C₄×C₄₇	—	2	1	no	—
69	C₂²×C₄×C₄₇	—	2	1	no	—
70	C₂²×C₄×C₄₇	—	4	1	no	—
71	C₂²×C₄×C₄₇	—	4	1	no	—
72	C₂²×C₄×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
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	2	yes	—
77	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
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×Q₈	1	1	yes	characteristic
81	C₂²×C₄×C₄₇	#41	1	1	yes	characteristic
82	C₂²×C₄×C₄₇	#41	1	1	yes	characteristic
83	C₂²×C₄×C₄₇	#41	1	2	yes	—
84	C₂²×C₄×C₄₇	#41	1	2	yes	—
85	C₂²×C₄×C₄₇	#41	1	2	yes	—
86	C₂²×Dic₄₇	—	2	2	no	—
87	C₂²×Dic₄₇	—	2	2	no	—
88	C₂²×Dic₄₇	—	2	2	no	—
89	C₂²×Dic₄₇	—	2	2	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	C₄²	1	4	yes	—
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	2	no	—
104	C₄²×C₄₇	—	2	2	no	—
105	C₄²×C₄₇	—	2	2	no	—
106	C₄²×C₄₇	—	2	2	no	—
107	C₄⋊Dic₄₇	—	2	4	no	—
108	C₄⋊Dic₄₇	—	2	4	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	4	no	—
114	C₄×Dic₄₇	—	4	4	no	—
115	#10625329	—	2	4	no	—
116	#10625329	—	2	4	no	—
117	#10625329	—	4	2	no	—
118	#10625329	—	4	2	no	—
119	C₂×C₄₇⋊C₈	—	2	4	no	—
120	C₂×C₄₇⋊C₈	—	4	2	no	—
121	C₂×C₄₇⋊C₈	—	4	2	no	—
122	C₂³×C₄₇	—	2	1	no	—
123	C₂³×C₄₇	—	2	1	no	—
124	C₂³×C₄₇	—	2	1	no	—
125	C₂³×C₄₇	—	2	1	no	—
126	C₂³×C₄₇	C₂×C₄²	1	1	yes	characteristic
127	C₂³×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
128	C₂³×C₄₇	C₂×C₄⋊C₄	1	1	yes	characteristic
129	C₂³×C₄₇	#117	1	1	yes	characteristic
130	C₂³×C₄₇	#117	1	1	yes	characteristic
131	C₂³×C₄₇	#117	1	1	yes	characteristic
132	C₂³×C₄₇	#117	1	1	yes	characteristic
133	C₂×C₄×C₄₇	—	2	4	no	—
134	C₂×C₄×C₄₇	—	2	4	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	—	2	1	no	—
145	C₂×C₄×C₄₇	—	4	2	no	—
146	C₂×C₄×C₄₇	—	4	2	no	—
147	C₂×C₄×C₄₇	#100	1	2	yes	—
148	C₂×C₄×C₄₇	#101	1	2	yes	—
149	C₂×C₄×C₄₇	#117	1	2	yes	—
150	C₂×C₄×C₄₇	#117	1	2	yes	—
151	C₂×C₄×C₄₇	C₄×D₄	1	2	yes	—
152	C₂×C₄×C₄₇	C₄×D₄	1	2	yes	—
153	C₂×C₄×C₄₇	C₄×D₄	1	2	yes	—
154	C₂×C₄×C₄₇	C₄×Q₈	1	2	yes	—
155	C₂×C₄×C₄₇	#121	1	1	yes	characteristic
156	C₂×C₄×C₄₇	#121	1	1	yes	characteristic
157	C₂×C₄×C₄₇	C₂²⋊Q₈	1	1	yes	characteristic
158	C₂×C₄×C₄₇	C₂²⋊Q₈	1	1	yes	characteristic
159	C₂×C₄×C₄₇	#123	1	2	yes	—
160	C₂×C₄×C₄₇	#123	1	2	yes	—
161	C₂×C₄×C₄₇	#124	1	2	yes	—
162	C₂×C₄×C₄₇	#125	1	2	yes	—
163	C₂×C₄×C₄₇	#126	1	2	yes	—
164	C₂×C₄×C₄₇	#126	1	2	yes	—
165	C₂×Dic₄₇	—	2	4	no	—
166	C₂×Dic₄₇	—	2	4	no	—
167	C₂×Dic₄₇	—	4	4	no	—
168	C₂×Dic₄₇	—	4	4	no	—
169	C₂×Dic₄₇	—	4	2	no	—
170	C₂×Dic₄₇	—	4	2	no	—
171	C₂×Dic₄₇	—	4	2	no	—
172	C₂×Dic₄₇	—	4	2	no	—
173	C₂×Dic₄₇	—	4	4	no	—
174	C₂×Dic₄₇	—	4	4	no	—
175	C₈×C₄₇	—	4	4	no	—
176	C₄₇⋊C₈	—	4	4	no	—
177	#10802	—	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	1	no	—
183	C₂²×C₄₇	—	2	1	no	—
184	C₂²×C₄₇	—	2	1	no	—
185	C₂²×C₄₇	—	2	1	no	—
186	C₂²×C₄₇	—	2	1	no	—
187	C₂²×C₄₇	—	2	1	no	—
188	C₂²×C₄₇	—	2	1	no	—
189	C₂²×C₄₇	—	2	1	no	—
190	C₂²×C₄₇	#376	1	1	yes	characteristic
191	C₂²×C₄₇	C₄×C₂²⋊C₄	1	1	yes	characteristic
192	C₂²×C₄₇	C₄×C₄⋊C₄	1	1	yes	characteristic
193	C₂²×C₄₇	#380	1	1	yes	characteristic
194	C₂²×C₄₇	#381	1	1	yes	characteristic
195	C₂²×C₄₇	#382	1	1	yes	characteristic
196	C₂²×C₄₇	#383	1	1	yes	characteristic
197	C₂²×C₄₇	C₂×#100	1	1	yes	characteristic
198	C₂²×C₄₇	C₂×#101	1	1	yes	characteristic
199	C₂²×C₄₇	#413	1	1	yes	characteristic
200	C₂²×C₄₇	#413	1	1	yes	characteristic
201	C₄×C₄₇	—	2	2	no	—
202	C₄×C₄₇	—	2	2	no	—
203	C₄×C₄₇	—	4	1	no	—
204	C₄×C₄₇	—	4	1	no	—
205	C₄×C₄₇	#387	1	2	yes	—
206	C₄×C₄₇	#387	1	2	yes	—
207	C₄×C₄₇	#388	1	2	yes	—
208	C₄×C₄₇	#388	1	2	yes	—
209	Dic₄₇	—	4	4	no	—
210	Dic₄₇	—	4	4	no	—
211	C₂×C₄×C₄⋊C₄	—	47	1	no	—
212	C₂×#343	—	47	2	no	—
213	C₂×#343	—	47	2	no	—
214	#1728	—	47	1	no	—
215	#1728	D₄₇	1	1	yes	characteristic
216	C₂×C₄₇	—	2	1	no	—
217	C₂×C₄₇	—	2	1	no	—
218	C₂×C₄₇	—	2	1	no	—
219	C₂×C₄₇	—	2	1	no	—
220	C₂×C₄₇	#1434	1	1	yes	characteristic
221	C₂×C₄₇	C₄×#100	1	1	yes	characteristic
222	C₂×C₄₇	C₄×#101	1	1	yes	characteristic
223	C₂×C₄₇	#1800	1	1	yes	characteristic
224	C₂×C₄₇	#1801	1	1	yes	characteristic
225	C₂×C₄₇	#1821	1	1	yes	characteristic
226	C₂×C₄₇	#1822	1	1	yes	characteristic
227	C₂²×M₁₆	—	47	2	no	—
228	C₂²×M₁₆	C₂×D₄₇	1	2	yes	—
229	C₂²×C₄⋊C₄	—	47	1	no	—
230	C₂²×C₄⋊C₄	—	47	1	no	—
231	C₂²×C₄²	—	47	2	no	—
232	C₂²×C₄²	C₂×D₄₇	1	1	yes	characteristic
233	C₄×C₄⋊C₄	—	94	1	no	—
234	C₄×C₄⋊C₄	—	94	1	no	—
235	C₄×C₄⋊C₄	—	94	1	no	—
236	C₄×C₄⋊C₄	—	94	1	no	—
237	C₂×#95	—	47	2	no	—
238	#343	—	47	8	no	—
239	#343	—	94	4	no	—
240	#336	—	2	1	no	—
241	#336	—	2	1	no	—
242	#336	—	94	1	no	—
243	#336	—	94	1	no	—
244	C₄₇	#10802	1	1	yes	characteristic, complemented, Sylow
245	C₂³×C₄	—	47	2	no	—
246	C₂³×C₄	—	47	2	no	—
247	C₂³×C₄	C₄×D₄₇	1	1	yes	characteristic
248	C₂³×C₄	C₄×D₄₇	1	1	yes	characteristic
249	C₂³×C₄	C₂²×D₄₇	1	1	yes	characteristic
250	C₂×M₁₆	—	2	2	no	—
251	C₂×M₁₆	—	2	2	no	—
252	C₂×M₁₆	—	2	2	no	—
253	C₂×M₁₆	—	2	2	no	—
254	C₂×M₁₆	—	2	2	no	—
255	C₂×M₁₆	—	47	4	no	—
256	C₂×M₁₆	—	94	2	no	—
257	C₂×M₁₆	—	94	2	no	—
258	C₂×M₁₆	—	94	2	no	—
259	C₂×M₁₆	—	94	2	no	—
260	C₂×M₁₆	—	94	2	no	—
261	C₂×M₁₆	C₄×D₄₇	1	4	yes	—
262	C₂²×C₈	—	2	2	no	—
263	C₂²×C₈	—	94	2	no	—
264	C₂×C₄⋊C₄	—	47	4	no	—
265	C₂×C₄⋊C₄	—	47	2	no	—
266	C₂×C₄⋊C₄	—	47	2	no	—
267	C₂×C₄⋊C₄	—	94	1	no	—
268	C₂×C₄⋊C₄	—	94	1	no	—
269	C₂×C₄⋊C₄	—	94	2	no	—
270	C₂×C₄⋊C₄	—	94	1	no	—
271	C₂×C₄⋊C₄	—	94	1	no	—
272	C₂×C₄⋊C₄	—	94	1	no	—
273	C₂×C₄⋊C₄	—	94	1	no	—
274	C₂×C₄²	—	2	2	no	—
275	C₂×C₄²	—	2	2	no	—
276	C₂×C₄²	—	94	2	no	—
277	C₂×C₄²	—	94	2	no	—
278	C₂×C₄²	—	188	4	no	—
279	C₂×C₄²	D₁₈₈	1	1	yes	characteristic
280	C₂×C₄²	D₁₈₈	1	1	yes	characteristic
281	C₂×C₄²	C₂²⋊D₄₇	1	1	yes	characteristic
282	C₂×C₄²	C₂²⋊D₄₇	1	1	yes	characteristic
283	#95	—	94	2	no	—
284	#95	—	94	2	no	—
285	C₂⁴	C₂×C₄×D₄₇	1	1	yes	characteristic
286	C₂²×C₄	—	2	1	no	—
287	C₂²×C₄	—	2	1	no	—
288	C₂²×C₄	—	2	2	no	—
289	C₂²×C₄	—	2	2	no	—
290	C₂²×C₄	—	2	1	no	—
291	C₂²×C₄	—	2	1	no	—
292	C₂²×C₄	—	4	1	no	—
293	C₂²×C₄	—	4	1	no	—
294	C₂²×C₄	—	47	4	no	—
295	C₂²×C₄	—	47	4	no	—
296	C₂²×C₄	—	94	2	no	—
297	C₂²×C₄	—	94	2	no	—
298	C₂²×C₄	—	94	2	no	—
299	C₂²×C₄	—	94	2	no	—
300	C₂²×C₄	—	188	2	no	—
301	C₂²×C₄	—	188	2	no	—
302	C₂²×C₄	—	188	2	no	—
303	C₂²×C₄	—	188	2	no	—
304	C₂²×C₄	(C₂×D₄₇)⋊C₄	1	1	yes	characteristic
305	C₂²×C₄	(C₂×D₄₇)⋊C₄	1	1	yes	characteristic
306	C₂²×C₄	(C₂×D₄₇)⋊C₄	1	1	yes	characteristic
307	C₂²×C₄	(C₂×D₄₇)⋊C₄	1	1	yes	characteristic
308	C₂²×C₄	C₂×C₄×D₄₇	1	2	yes	—
309	C₂²×C₄	C₂×D₁₈₈	1	1	yes	characteristic
310	C₂²×C₄	#10625350	1	2	yes	—
311	C₂²×C₄	D₄×D₄₇	1	1	yes	characteristic
312	C₂²×C₄	#10625352	1	1	yes	characteristic
313	C₂²×C₄	#10625352	1	2	yes	—
314	C₂²×C₄	#10625352	1	2	yes	—
315	C₂²×C₄	Q₈×D₄₇	1	1	yes	characteristic
316	C₂²×C₄	#10625354	1	1	yes	characteristic
317	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
318	M₁₆	—	2	4	no	—
319	M₁₆	—	2	4	no	—
320	M₁₆	—	4	2	no	—
321	M₁₆	—	4	2	no	—
322	M₁₆	—	94	4	no	—
323	M₁₆	—	94	4	no	—
324	M₁₆	—	188	2	no	—
325	M₁₆	—	188	2	no	—
326	C₂×C₈	—	2	4	no	—
327	C₂×C₈	—	4	2	no	—
328	C₂×C₈	—	4	2	no	—
329	C₂×C₈	—	94	4	no	—
330	C₂×C₈	—	188	2	no	—
331	C₂×C₈	—	188	2	no	—
332	C₄⋊C₄	—	94	4	no	—
333	C₄⋊C₄	—	94	4	no	—
334	C₄⋊C₄	—	94	2	no	—
335	C₄⋊C₄	—	94	2	no	—
336	C₄⋊C₄	—	94	2	no	—
337	C₄⋊C₄	—	94	2	no	—
338	C₄²	—	2	2	no	—
339	C₄²	—	2	2	no	—
340	C₄²	—	2	2	no	—
341	C₄²	—	2	2	no	—
342	C₄²	—	188	4	no	—
343	C₄²	—	188	4	no	—
344	C₂³	—	2	1	no	—
345	C₂³	—	2	1	no	—
346	C₂³	—	2	1	no	—
347	C₂³	—	2	1	no	—
348	C₂³	C₄²×D₄₇	1	1	yes	characteristic
349	C₂³	C₂×(C₂×D₄₇)⋊C₄	1	1	yes	characteristic
350	C₂³	C₄⋊C₄×D₄₇	1	1	yes	characteristic
351	C₂³	#13093980	1	1	yes	characteristic
352	C₂³	#13093980	1	1	yes	characteristic
353	C₂³	#13093981	1	1	yes	characteristic
354	C₂³	#13093982	1	1	yes	characteristic
355	C₂×C₄	—	2	4	no	—
356	C₂×C₄	—	2	4	no	—
357	C₂×C₄	—	2	1	no	—
358	C₂×C₄	—	2	1	no	—
359	C₂×C₄	—	2	1	no	—
360	C₂×C₄	—	2	1	no	—
361	C₂×C₄	—	2	1	no	—
362	C₂×C₄	—	2	1	no	—
363	C₂×C₄	—	2	1	no	—
364	C₂×C₄	—	2	1	no	—
365	C₂×C₄	—	2	1	no	—
366	C₂×C₄	—	2	1	no	—
367	C₂×C₄	—	4	2	no	—
368	C₂×C₄	—	4	2	no	—
369	C₂×C₄	—	94	4	no	—
370	C₂×C₄	—	94	4	no	—
371	C₂×C₄	—	188	4	no	—
372	C₂×C₄	—	188	4	no	—
373	C₂×C₄	—	188	2	no	—
374	C₂×C₄	—	188	2	no	—
375	C₂×C₄	—	188	2	no	—
376	C₂×C₄	—	188	2	no	—
377	C₂×C₄	—	188	4	no	—
378	C₂×C₄	—	188	4	no	—
379	C₂×C₄	#13093940	1	2	yes	—
380	C₂×C₄	#13093942	1	2	yes	—
381	C₂×C₄	#13093980	1	2	yes	—
382	C₂×C₄	#13093982	1	2	yes	—
383	C₂×C₄	(C₂²⋊D₄₇)⋊C₄	1	2	yes	—
384	C₂×C₄	C₄×C₂²⋊D₄₇	1	2	yes	—
385	C₂×C₄	C₄×D₁₈₈	1	2	yes	—
386	C₂×C₄	#13093989	1	2	yes	—
387	C₂×C₄	#13093995	1	1	yes	characteristic
388	C₂×C₄	#13093999	1	1	yes	characteristic
389	C₂×C₄	#13094000	1	1	yes	characteristic
390	C₂×C₄	#13094004	1	1	yes	characteristic
391	C₂×C₄	#13094005	1	2	yes	—
392	C₂×C₄	#13094008	1	2	yes	—
393	C₂×C₄	#13094010	1	2	yes	—
394	C₂×C₄	#13094014	1	2	yes	—
395	C₂×C₄	#13094017	1	2	yes	—
396	C₂×C₄	#13094019	1	2	yes	—
397	C₈	—	4	4	no	—
398	C₈	—	188	4	no	—
399	C₂²	—	2	1	no	—
400	C₂²	—	2	1	no	—
401	C₂²	—	2	1	no	—
402	C₂²	—	2	1	no	—
403	C₂²	—	2	1	no	—
404	C₂²	—	2	1	no	—
405	C₂²	—	2	1	no	—
406	C₂²	—	2	1	no	—
407	C₂²	—	2	1	no	—
408	C₂²	—	2	1	no	—
409	C₂²	—	2	1	no	—
410	C₂²	—	2	1	no	—
411	C₂²	#15688968	1	1	yes	characteristic
412	C₂²	C₄×(C₂×D₄₇)⋊C₄	1	1	yes	characteristic
413	C₂²	#15688974	1	1	yes	characteristic
414	C₂²	#15688980	1	1	yes	characteristic
415	C₂²	#15688984	1	1	yes	characteristic
416	C₂²	#15688987	1	1	yes	characteristic
417	C₂²	#15688990	1	1	yes	characteristic
418	C₂²	C₂×#13093940	1	1	yes	characteristic
419	C₂²	C₂×#13093942	1	1	yes	characteristic
420	C₂²	#15689105	1	1	yes	characteristic
421	C₂²	#15689105	1	1	yes	characteristic
422	C₄	—	2	2	no	—
423	C₄	—	2	2	no	—
424	C₄	—	4	1	no	—
425	C₄	—	4	1	no	—
426	C₄	—	188	4	no	—
427	C₄	—	188	4	no	—
428	C₄	#15689004	1	2	yes	—
429	C₄	#15689008	1	2	yes	—
430	C₄	#15689011	1	2	yes	—
431	C₄	#15689015	1	2	yes	—
432	C₂	—	2	1	no	—
433	C₂	—	2	1	no	—
434	C₂	—	2	1	no	—
435	C₂	—	2	1	no	—
436	C₂	#20241612	1	1	yes	characteristic
437	C₂	C₄×#13093940	1	1	yes	characteristic
438	C₂	C₄×#13093942	1	1	yes	characteristic
439	C₂	#20243377	1	1	yes	characteristic
440	C₂	#20243381	1	1	yes	characteristic
441	C₂	#20243466	1	1	yes	characteristic
442	C₂	#20243469	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	C₂×(C₂×D₄₇)⋊C₄
commutator	C₂³×C₄₇	C₂×C₄²
Frattini	C₂³×C₄	C₂²×D₄₇
Fitting	C₄₇×#1728	C₂
socle	C₂³×C₄₇	C₂×C₂²⋊C₄
prime radical	C₂⁴×C₄₇	C₂²×C₄
cosocle	C₂³×C₄×C₄₇	C₂³
hypercenter	#1728	D₄₇
hypocenter	C₄₇	#10802
LCS	G ▷ C₂³×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
16. #15688891	C₄	semidirect
244. C₄₇	#10802	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₄×C₄⋊Dic₄₇	2
C₂×#15688891	2
#20243082	2
C₄₇×#1728	2
#10802	47