Subgroups — #26121671

Order 12032.

1210 conjugacy classes of subgroups.

The subgroup lattice has 452 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#15689107	C₂	1	1	yes	maximal, characteristic
2	#20245980	C₂	1	1	yes	maximal, characteristic
3	C₂×#15688895	C₂	1	2	yes	maximal, complemented
4	C₂×#15688891	C₂	1	2	yes	maximal, complemented
5	C₂×C₄₇×#568	C₂	1	1	yes	maximal, characteristic
6	C₂²×#10625329	C₂²	1	2	yes	—
7	C₂×#13093983	C₂²	1	1	yes	characteristic
8	C₂²×C₄⋊Dic₄₇	C₂²	1	1	yes	characteristic
9	#15689107	—	2	2	no	—
10	#15689107	C₄	1	4	yes	complemented
11	C₂×#13093943	—	2	1	no	—
12	C₂×#13093941	—	2	1	no	—
13	#15689030	—	2	1	no	—
14	#15689026	—	2	1	no	—
15	#15689003	C₄	1	4	yes	—
16	#15688983	—	2	2	no	—
17	#15688895	—	2	4	no	—
18	#15688891	—	2	4	no	—
19	C₂²×#41×C₄₇	C₂²	1	1	yes	characteristic
20	C₄₇×#568	—	2	2	no	—
21	C₄₇×#568	—	2	4	no	—
22	C₄₇×#568	C₄	1	4	yes	complemented
23	C₂×#131×C₄₇	—	2	4	no	—
24	C₂²×M₁₆×C₄₇	—	2	2	no	—
25	C₂²×M₁₆×C₄₇	C₂²	1	2	yes	—
26	C₂³×Dic₄₇	C₂×C₄	1	2	yes	—
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	—	2	2	no	—
32	C₂×#10625329	C₂×C₄	1	4	yes	—
33	C₂²×C₄₇⋊C₈	—	2	2	no	—
34	#13093983	—	2	2	no	—
35	#13093983	—	2	2	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×C₂²⋊Dic₄₇	—	2	4	no	—
42	C₂×C₂²⋊Dic₄₇	C₂×C₄	1	2	yes	—
43	C₂×C₄×Dic₄₇	—	2	1	no	—
44	#13093943	—	2	4	no	—
45	#13093941	—	2	4	no	—
46	C₄₇⋊#95	—	2	4	no	—
47	C₂×#41×C₄₇	—	2	2	no	—
48	C₂×#41×C₄₇	—	2	2	no	—
49	C₂×#41×C₄₇	—	2	2	no	—
50	C₂×#41×C₄₇	—	2	2	no	—
51	C₂×#41×C₄₇	C₂×C₄	1	2	yes	—
52	C₂×#41×C₄₇	C₂×C₄	1	2	yes	—
53	C₂×#41×C₄₇	D₄	1	2	yes	—
54	C₂×#41×C₄₇	Q₈	1	2	yes	—
55	C₂²×Q₈×C₄₇	D₄	1	1	yes	characteristic
56	C₂²×D₄×C₄₇	C₂×C₄	1	2	yes	—
57	C₂²×D₄×C₄₇	D₄	1	1	yes	characteristic
58	C₂³×C₄×C₄₇	D₄	1	2	yes	—
59	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
60	#131×C₄₇	—	2	16	no	—
61	#131×C₄₇	—	2	16	no	—
62	C₂×M₁₆×C₄₇	—	2	4	no	—
63	C₂×M₁₆×C₄₇	—	2	8	no	—
64	C₂×M₁₆×C₄₇	—	2	8	no	—
65	C₂×M₁₆×C₄₇	—	2	2	no	—
66	C₂×M₁₆×C₄₇	—	2	2	no	—
67	C₂×M₁₆×C₄₇	—	2	2	no	—
68	C₂×M₁₆×C₄₇	C₂×C₄	1	4	yes	—
69	C₂×M₁₆×C₄₇	D₄	1	4	yes	—
70	C₂×M₁₆×C₄₇	D₄	1	4	yes	—
71	C₂²×C₈×C₄₇	—	2	4	no	—
72	C₂²×C₈×C₄₇	—	2	2	no	—
73	C₂⁴×C₄₇	C₂²⋊C₄	1	2	yes	—
74	C₂⁴×C₄₇	C₂²×C₄	1	1	yes	characteristic
75	#41×C₄₇	—	2	4	no	—
76	#41×C₄₇	—	2	4	no	—
77	#41×C₄₇	—	2	4	no	—
78	#41×C₄₇	—	2	4	no	—
79	#41×C₄₇	—	2	4	no	—
80	#41×C₄₇	—	2	4	no	—
81	#41×C₄₇	—	2	4	no	—
82	#41×C₄₇	—	2	4	no	—
83	C₂×Q₈×C₄₇	—	2	2	no	—
84	C₂×Q₈×C₄₇	—	2	2	no	—
85	C₂×Q₈×C₄₇	C₂²⋊C₄	1	2	yes	—
86	C₂×Q₈×C₄₇	C₄⋊C₄	1	2	yes	—
87	C₂×D₄×C₄₇	—	2	4	no	—
88	C₂×D₄×C₄₇	—	2	4	no	—
89	C₂×D₄×C₄₇	—	2	2	no	—
90	C₂×D₄×C₄₇	—	2	2	no	—
91	C₂×D₄×C₄₇	C₄²	1	4	yes	—
92	C₂×D₄×C₄₇	C₂²⋊C₄	1	2	yes	—
93	C₂×D₄×C₄₇	C₄⋊C₄	1	4	yes	—
94	C₂×D₄×C₄₇	C₄⋊C₄	1	2	yes	—
95	C₂²×C₄×C₄₇	—	2	2	no	—
96	C₂²×C₄×C₄₇	—	2	2	no	—
97	C₂²×C₄×C₄₇	—	2	2	no	—
98	C₂²×C₄×C₄₇	—	2	2	no	—
99	C₂²×C₄×C₄₇	C₂²⋊C₄	1	2	yes	—
100	C₂²×C₄×C₄₇	C₂²⋊C₄	1	4	yes	—
101	C₂²×C₄×C₄₇	C₄⋊C₄	1	4	yes	—
102	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
103	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
104	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
105	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
106	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
107	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
108	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
109	C₂²×C₄×C₄₇	C₂×Q₈	1	1	yes	characteristic
110	C₂²×C₄×C₄₇	#41	1	2	yes	—
111	C₂²×C₄×C₄₇	#41	1	2	yes	—
112	C₂²×Dic₄₇	—	2	2	no	—
113	C₂²×Dic₄₇	—	2	2	no	—
114	C₂²×Dic₄₇	—	2	4	no	—
115	C₂²×Dic₄₇	—	8	2	no	—
116	M₁₆×C₄₇	—	2	16	no	—
117	M₁₆×C₄₇	—	2	4	no	—
118	M₁₆×C₄₇	—	2	4	no	—
119	M₁₆×C₄₇	—	2	4	no	—
120	M₁₆×C₄₇	C₂²⋊C₄	1	8	yes	complemented
121	C₂×C₈×C₄₇	—	2	16	no	—
122	C₂×C₈×C₄₇	—	2	4	no	—
123	C₂×C₈×C₄₇	—	2	4	no	—
124	C₂×C₈×C₄₇	—	2	4	no	—
125	C₂²⋊Dic₄₇	—	2	4	no	—
126	C₂²⋊Dic₄₇	—	8	4	no	—
127	C₄⋊Dic₄₇	—	4	1	no	—
128	C₄⋊Dic₄₇	—	4	1	no	—
129	C₄⋊Dic₄₇	—	4	2	no	—
130	C₄⋊Dic₄₇	—	4	1	no	—
131	C₄⋊Dic₄₇	—	4	1	no	—
132	C₄×Dic₄₇	—	4	2	no	—
133	#10625329	—	2	4	no	—
134	#10625329	—	2	4	no	—
135	#10625329	—	4	2	no	—
136	#10625329	—	4	2	no	—
137	C₂×C₄₇⋊C₈	—	2	4	no	—
138	C₂×C₄₇⋊C₈	—	4	2	no	—
139	C₂×C₄₇⋊C₈	—	4	2	no	—
140	C₂³×C₄₇	—	2	2	no	—
141	C₂³×C₄₇	—	2	2	no	—
142	C₂³×C₄₇	—	4	1	no	—
143	C₂³×C₄₇	—	4	1	no	—
144	C₂³×C₄₇	—	4	2	no	—
145	C₂³×C₄₇	—	4	2	no	—
146	C₂³×C₄₇	#95	1	4	yes	—
147	C₂³×C₄₇	C₂×C₄²	1	1	yes	characteristic
148	C₂³×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
149	C₂³×C₄₇	C₂×C₄⋊C₄	1	1	yes	characteristic
150	C₂³×C₄₇	C₄×D₄	1	2	yes	—
151	C₂³×C₄₇	C₄×D₄	1	2	yes	—
152	Q₈×C₄₇	—	2	4	no	—
153	Q₈×C₄₇	—	2	4	no	—
154	D₄×C₄₇	—	2	8	no	—
155	D₄×C₄₇	—	2	8	no	—
156	D₄×C₄₇	—	2	4	no	—
157	D₄×C₄₇	—	2	4	no	—
158	C₂×C₄×C₄₇	—	2	2	no	—
159	C₂×C₄×C₄₇	—	2	2	no	—
160	C₂×C₄×C₄₇	—	2	4	no	—
161	C₂×C₄×C₄₇	—	2	4	no	—
162	C₂×C₄×C₄₇	—	2	4	no	—
163	C₂×C₄×C₄₇	—	2	4	no	—
164	C₂×C₄×C₄₇	#95	1	4	yes	—
165	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
166	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	2	yes	—
167	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
168	C₂×C₄×C₄₇	C₂×C₄⋊C₄	1	1	yes	characteristic
169	C₂×C₄×C₄₇	C₂×C₄⋊C₄	1	1	yes	characteristic
170	C₂×C₄×C₄₇	#117	1	2	yes	—
171	C₂×C₄×C₄₇	C₄×D₄	1	2	yes	—
172	C₂×C₄×C₄₇	C₄×D₄	1	2	yes	—
173	C₂×C₄×C₄₇	#120	1	1	yes	characteristic
174	C₂×C₄×C₄₇	#120	1	1	yes	characteristic
175	C₂×C₄×C₄₇	#120	1	2	yes	—
176	C₂×C₄×C₄₇	#121	1	2	yes	—
177	C₂×C₄×C₄₇	#121	1	2	yes	—
178	C₂×C₄×C₄₇	C₂²⋊Q₈	1	2	yes	—
179	C₂×C₄×C₄₇	C₂²⋊Q₈	1	2	yes	—
180	C₂×C₄×C₄₇	#123	1	1	yes	characteristic
181	C₂×C₄×C₄₇	#123	1	1	yes	characteristic
182	C₂×C₄×C₄₇	#123	1	2	yes	—
183	C₂×Dic₄₇	—	4	2	no	—
184	C₂×Dic₄₇	—	4	4	no	—
185	C₂×Dic₄₇	—	4	2	no	—
186	C₂×Dic₄₇	—	4	2	no	—
187	C₂×Dic₄₇	—	4	2	no	—
188	C₂×Dic₄₇	—	8	4	no	—
189	C₈×C₄₇	—	2	8	no	—
190	C₄₇⋊C₈	—	4	4	no	—
191	#10755	—	47	1	no	maximal, Sylow
192	C₂²×C₄₇	—	2	1	no	—
193	C₂²×C₄₇	—	2	2	no	—
194	C₂²×C₄₇	—	2	1	no	—
195	C₂²×C₄₇	—	2	2	no	—
196	C₂²×C₄₇	—	2	4	no	—
197	C₂²×C₄₇	—	4	1	no	—
198	C₂²×C₄₇	—	4	1	no	—
199	C₂²×C₄₇	—	4	2	no	—
200	C₂²×C₄₇	—	4	4	no	—
201	C₂²×C₄₇	—	4	2	no	—
202	C₂²×C₄₇	—	4	2	no	—
203	C₂²×C₄₇	—	8	2	no	—
204	C₂²×C₄₇	C₂×#95	1	1	yes	characteristic
205	C₂²×C₄₇	C₄×C₂²⋊C₄	1	2	yes	—
206	C₂²×C₄₇	#385	1	2	yes	—
207	C₂²×C₄₇	#386	1	1	yes	characteristic
208	C₂²×C₄₇	#386	1	1	yes	characteristic
209	C₄×C₄₇	—	2	4	no	—
210	C₄×C₄₇	#379	1	1	yes	characteristic
211	C₄×C₄₇	#380	1	2	yes	—
212	C₄×C₄₇	#381	1	1	yes	characteristic
213	C₄×C₄₇	#385	1	1	yes	characteristic
214	C₄×C₄₇	#385	1	1	yes	characteristic
215	C₄×C₄₇	#386	1	2	yes	—
216	Dic₄₇	—	8	2	no	—
217	Dic₄₇	—	8	2	no	—
218	C₂×#568	D₄₇	1	1	yes	characteristic
219	C₂×#413	—	47	1	no	—
220	#2311	—	47	1	no	—
221	C₂×#344	—	47	2	no	—
222	C₂×#343	—	47	2	no	—
223	C₂×C₄₇	—	2	1	no	—
224	C₂×C₄₇	—	2	1	no	—
225	C₂×C₄₇	—	2	2	no	—
226	C₂×C₄₇	—	2	2	no	—
227	C₂×C₄₇	—	4	4	no	—
228	C₂×C₄₇	C₂²⋊#95	1	1	yes	characteristic
229	C₂×C₄₇	#1914	1	1	yes	characteristic
230	C₂×C₄₇	#1915	1	1	yes	characteristic
231	C₂²×#41	C₂×D₄₇	1	1	yes	characteristic
232	#568	—	2	2	no	—
233	#568	—	2	4	no	—
234	#568	Dic₄₇	1	4	yes	complemented
235	C₂×#131	—	2	4	no	—
236	C₂²×M₁₆	—	2	2	no	—
237	C₂²×M₁₆	—	47	2	no	—
238	C₂²×M₁₆	C₂×D₄₇	1	2	yes	—
239	C₂×#117	—	47	1	no	—
240	C₂²×C₄⋊C₄	—	47	1	no	—
241	#413	—	47	4	no	—
242	#413	—	94	2	no	—
243	C₂×#101	—	94	1	no	—
244	C₂×#100	—	94	1	no	—
245	#391	—	94	1	no	—
246	#390	—	94	1	no	—
247	#386	—	47	4	no	—
248	#380	—	94	2	no	—
249	#344	—	94	4	no	—
250	#343	—	94	4	no	—
251	C₄₇	#10755	1	1	yes	characteristic, complemented, Sylow
252	C₂×#41	—	2	2	no	—
253	C₂×#41	—	2	2	no	—
254	C₂×#41	—	2	2	no	—
255	C₂×#41	—	2	2	no	—
256	C₂×#41	Dic₉₄	1	2	yes	—
257	C₂×#41	C₄×D₄₇	1	2	yes	—
258	C₂×#41	C₂×Dic₄₇	1	2	yes	—
259	C₂×#41	C₂²⋊D₄₇	1	2	yes	—
260	C₂²×Q₈	D₁₈₈	1	1	yes	characteristic
261	C₂²×D₄	C₄×D₄₇	1	2	yes	—
262	C₂²×D₄	D₁₈₈	1	1	yes	characteristic
263	C₂³×C₄	—	47	2	no	—
264	C₂³×C₄	C₂²⋊D₄₇	1	2	yes	—
265	C₂³×C₄	C₂²×D₄₇	1	1	yes	characteristic
266	#131	—	2	16	no	—
267	#131	—	2	16	no	—
268	C₂×M₁₆	—	2	4	no	—
269	C₂×M₁₆	—	2	8	no	—
270	C₂×M₁₆	—	2	8	no	—
271	C₂×M₁₆	—	2	2	no	—
272	C₂×M₁₆	—	2	2	no	—
273	C₂×M₁₆	—	2	2	no	—
274	C₂×M₁₆	—	47	4	no	—
275	C₂×M₁₆	—	94	2	no	—
276	C₂×M₁₆	—	94	2	no	—
277	C₂×M₁₆	—	94	2	no	—
278	C₂×M₁₆	—	94	2	no	—
279	C₂×M₁₆	—	94	2	no	—
280	C₂×M₁₆	C₂×Dic₄₇	1	4	yes	—
281	C₂×M₁₆	C₂²⋊D₄₇	1	4	yes	—
282	C₂×M₁₆	C₂²⋊D₄₇	1	4	yes	—
283	C₂²×C₈	—	2	4	no	—
284	C₂²×C₈	—	2	2	no	—
285	C₂²×C₈	—	94	2	no	—
286	#117	—	94	2	no	—
287	#117	—	94	2	no	—
288	C₂×C₄⋊C₄	—	94	1	no	—
289	C₂×C₄⋊C₄	—	94	2	no	—
290	C₂×C₄⋊C₄	—	94	2	no	—
291	C₂×C₄⋊C₄	—	94	1	no	—
292	C₂×C₄⋊C₄	—	94	1	no	—
293	C₂×C₂²⋊C₄	—	47	2	no	—
294	C₂×C₂²⋊C₄	—	94	4	no	—
295	C₂×C₄²	—	94	1	no	—
296	#101	—	94	4	no	—
297	#100	—	94	4	no	—
298	#95	—	94	4	no	—
299	C₂⁴	(C₂×D₄₇)⋊C₄	1	2	yes	—
300	C₂⁴	C₂×C₄×D₄₇	1	1	yes	characteristic
301	#41	—	2	4	no	—
302	#41	—	2	4	no	—
303	#41	—	2	4	no	—
304	#41	—	2	4	no	—
305	#41	—	2	4	no	—
306	#41	—	2	4	no	—
307	#41	—	2	4	no	—
308	#41	—	2	4	no	—
309	C₂×Q₈	—	2	2	no	—
310	C₂×Q₈	—	2	2	no	—
311	C₂×Q₈	C₄⋊Dic₄₇	1	2	yes	—
312	C₂×Q₈	(C₂×D₄₇)⋊C₄	1	2	yes	—
313	C₂×D₄	—	2	4	no	—
314	C₂×D₄	—	2	4	no	—
315	C₂×D₄	—	2	2	no	—
316	C₂×D₄	—	2	2	no	—
317	C₂×D₄	C₄×Dic₄₇	1	4	yes	—
318	C₂×D₄	Dic₄₇⋊C₄	1	4	yes	—
319	C₂×D₄	C₄⋊Dic₄₇	1	2	yes	—
320	C₂×D₄	(C₂×D₄₇)⋊C₄	1	2	yes	—
321	C₂²×C₄	—	2	2	no	—
322	C₂²×C₄	—	2	2	no	—
323	C₂²×C₄	—	2	2	no	—
324	C₂²×C₄	—	2	2	no	—
325	C₂²×C₄	—	94	4	no	—
326	C₂²×C₄	—	94	2	no	—
327	C₂²×C₄	—	94	2	no	—
328	C₂²×C₄	—	376	2	no	—
329	C₂²×C₄	Dic₄₇⋊C₄	1	4	yes	—
330	C₂²×C₄	(C₂×D₄₇)⋊C₄	1	2	yes	—
331	C₂²×C₄	C₂²⋊Dic₄₇	1	4	yes	—
332	C₂²×C₄	C₂×Dic₉₄	1	1	yes	characteristic
333	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
334	C₂²×C₄	C₂×D₁₈₈	1	1	yes	characteristic
335	C₂²×C₄	#10625350	1	2	yes	—
336	C₂²×C₄	#10625350	1	2	yes	—
337	C₂²×C₄	C₂²×Dic₄₇	1	1	yes	characteristic
338	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
339	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
340	C₂²×C₄	C₂×C₂²⋊D₄₇	1	2	yes	—
341	C₂²×C₄	C₂×C₂²⋊D₄₇	1	2	yes	—
342	M₁₆	—	2	16	no	—
343	M₁₆	—	2	4	no	—
344	M₁₆	—	2	4	no	—
345	M₁₆	—	2	4	no	—
346	M₁₆	—	94	4	no	—
347	M₁₆	—	94	4	no	—
348	M₁₆	—	188	2	no	—
349	M₁₆	—	188	2	no	—
350	M₁₆	C₂²⋊Dic₄₇	1	8	yes	complemented
351	C₂×C₈	—	2	16	no	—
352	C₂×C₈	—	2	4	no	—
353	C₂×C₈	—	2	4	no	—
354	C₂×C₈	—	2	4	no	—
355	C₂×C₈	—	94	4	no	—
356	C₂×C₈	—	188	2	no	—
357	C₂×C₈	—	188	2	no	—
358	C₄⋊C₄	—	188	1	no	—
359	C₄⋊C₄	—	188	1	no	—
360	C₄⋊C₄	—	188	2	no	—
361	C₄⋊C₄	—	188	1	no	—
362	C₄⋊C₄	—	188	1	no	—
363	C₂²⋊C₄	—	94	4	no	—
364	C₂²⋊C₄	—	376	4	no	—
365	C₄²	—	188	2	no	—
366	C₂³	—	2	2	no	—
367	C₂³	—	2	2	no	—
368	C₂³	—	4	1	no	—
369	C₂³	—	4	1	no	—
370	C₂³	—	4	2	no	—
371	C₂³	—	4	2	no	—
372	C₂³	C₄₇⋊#95	1	4	yes	—
373	C₂³	C₂×C₄×Dic₄₇	1	1	yes	characteristic
374	C₂³	C₂×(C₂×D₄₇)⋊C₄	1	1	yes	characteristic
375	C₂³	C₂×Dic₄₇⋊C₄	1	1	yes	characteristic
376	C₂³	C₄×C₂²⋊D₄₇	1	2	yes	—
377	C₂³	C₄×C₂²⋊D₄₇	1	2	yes	—
378	Q₈	—	2	4	no	—
379	Q₈	—	2	4	no	—
380	D₄	—	2	8	no	—
381	D₄	—	2	8	no	—
382	D₄	—	2	4	no	—
383	D₄	—	2	4	no	—
384	C₂×C₄	—	2	2	no	—
385	C₂×C₄	—	2	2	no	—
386	C₂×C₄	—	2	4	no	—
387	C₂×C₄	—	2	4	no	—
388	C₂×C₄	—	2	4	no	—
389	C₂×C₄	—	2	4	no	—
390	C₂×C₄	—	376	4	no	—
391	C₂×C₄	—	188	2	no	—
392	C₂×C₄	—	188	4	no	—
393	C₂×C₄	—	188	2	no	—
394	C₂×C₄	—	188	2	no	—
395	C₂×C₄	—	188	2	no	—
396	C₂×C₄	C₄₇⋊#95	1	4	yes	—
397	C₂×C₄	C₂×(C₂×D₄₇)⋊C₄	1	1	yes	characteristic
398	C₂×C₄	C₂×C₂²⋊Dic₄₇	1	2	yes	—
399	C₂×C₄	C₂×C₂²⋊Dic₄₇	1	1	yes	characteristic
400	C₂×C₄	C₂×Dic₄₇⋊C₄	1	1	yes	characteristic
401	C₂×C₄	C₂×C₄⋊Dic₄₇	1	1	yes	characteristic
402	C₂×C₄	#13093983	1	2	yes	—
403	C₂×C₄	C₄×C₂²⋊D₄₇	1	2	yes	—
404	C₂×C₄	C₄×C₂²⋊D₄₇	1	2	yes	—
405	C₂×C₄	#13093993	1	1	yes	characteristic
406	C₂×C₄	#13093993	1	1	yes	characteristic
407	C₂×C₄	#13093993	1	2	yes	—
408	C₂×C₄	#13093998	1	2	yes	—
409	C₂×C₄	#13093998	1	2	yes	—
410	C₂×C₄	#13094003	1	2	yes	—
411	C₂×C₄	#13094003	1	2	yes	—
412	C₂×C₄	#13094007	1	1	yes	characteristic
413	C₂×C₄	#13094007	1	1	yes	characteristic
414	C₂×C₄	#13094007	1	2	yes	—
415	C₈	—	2	8	no	—
416	C₈	—	188	4	no	—
417	C₂²	—	2	2	no	—
418	C₂²	—	2	1	no	—
419	C₂²	—	2	1	no	—
420	C₂²	—	2	2	no	—
421	C₂²	—	2	4	no	—
422	C₂²	—	4	1	no	—
423	C₂²	—	4	1	no	—
424	C₂²	—	4	2	no	—
425	C₂²	—	4	4	no	—
426	C₂²	—	4	2	no	—
427	C₂²	—	4	2	no	—
428	C₂²	—	8	2	no	—
429	C₂²	C₂×C₄₇⋊#95	1	1	yes	characteristic
430	C₂²	C₄×C₂²⋊Dic₄₇	1	2	yes	—
431	C₂²	#15688996	1	2	yes	—
432	C₂²	#15689002	1	1	yes	characteristic
433	C₂²	#15689002	1	1	yes	characteristic
434	C₄	—	2	4	no	—
435	C₄	—	376	2	no	—
436	C₄	—	376	2	no	—
437	C₄	#15688979	1	1	yes	characteristic
438	C₄	#15688983	1	2	yes	—
439	C₄	#15688986	1	1	yes	characteristic
440	C₄	#15688996	1	1	yes	characteristic
441	C₄	#15688996	1	1	yes	characteristic
442	C₄	#15689002	1	2	yes	—
443	C₂	—	2	1	no	—
444	C₂	—	2	1	no	—
445	C₂	—	2	2	no	—
446	C₂	—	2	2	no	—
447	C₂	—	4	4	no	—
448	C₂	#20241611	1	1	yes	characteristic
449	C₂	#20243935	1	1	yes	characteristic
450	C₂	#20243940	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	#15689002
commutator	C₂³×C₄₇	C₂×C₄²
Frattini	C₂³×C₄	C₂²×D₄₇
Fitting	C₂×C₄₇×#568	C₂
socle	C₂²×C₄₇	#386
prime radical	C₂²×#41×C₄₇	C₂²
cosocle	C₂³×C₄×C₄₇	C₂³
hypercenter	C₂×#568	D₄₇
hypocenter	C₄₇	#10755
LCS	G ▷ C₂³×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂² ◁ C₂³×C₄ ◁ C₂×#568

Complements

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

N	H ≅ G/N	type
3. C₂×#15688895	C₂	semidirect
4. C₂×#15688891	C₂	semidirect
10. #15689107	C₄	semidirect
22. C₄₇×#568	C₄	semidirect
120. M₁₆×C₄₇	C₂²⋊C₄	semidirect
234. #568	Dic₄₇	semidirect
251. C₄₇	#10755	semidirect
350. M₁₆	C₂²⋊Dic₄₇	semidirect

Maximal subgroups

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

subgroup	index
C₂×#15689107	2
#20245980	2
C₂×#15688895	2
C₂×#15688891	2
C₂×C₄₇×#568	2
#10755	47