Subgroups — #26214137

Order 12032.

1490 conjugacy classes of subgroups.

The subgroup lattice has 516 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#15689890	C₂	1	1	yes	maximal, characteristic
2	C₂²×#13093951	C₂	1	1	yes	maximal, characteristic
3	#20251807	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×M₁₆×Dic₄₇	C₂	1	1	yes	maximal, characteristic, complemented
5	#20243235	C₂	1	4	yes	maximal, complemented
6	#20243228	C₂	1	4	yes	maximal, complemented
7	#20243115	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×#15688882	C₂	1	1	yes	maximal, characteristic, complemented
9	C₄₇×#2896	C₂	1	1	yes	maximal, characteristic
10	#15689890	—	2	4	no	—
11	#15689890	C₄	1	8	yes	complemented
12	C₂×#13094031	—	2	2	no	—
13	C₂×#13094031	C₂²	1	4	yes	—
14	C₂²×#10625329	—	2	2	no	—
15	C₂²×#10625329	C₂²	1	1	yes	characteristic
16	C₂²×#10625329	C₂²	1	1	yes	characteristic
17	C₂²×#10625329	C₂²	1	1	yes	characteristic
18	C₂²×C₄×Dic₄₇	C₂²	1	1	yes	characteristic
19	C₂×#13093951	C₄	1	8	yes	complemented
20	C₂×#13093951	C₂²	1	2	yes	—
21	C₂×#13093951	C₂²	1	2	yes	—
22	#15689079	—	2	2	no	—
23	#15689079	C₂²	1	4	yes	complemented
24	C₄×#10625329	—	2	2	no	—
25	M₁₆×Dic₄₇	—	2	4	no	—
26	C₂×#13093934	C₂²	1	2	yes	complemented
27	C₂×C₈×Dic₄₇	C₂²	1	2	yes	complemented
28	#15688888	C₂²	1	4	yes	complemented
29	#15688882	C₂²	1	2	yes	complemented
30	#15688882	C₂²	1	2	yes	complemented
31	C₂²×#41×C₄₇	C₂²	1	1	yes	characteristic
32	C₂²×M₁₆×C₄₇	C₂²	1	1	yes	characteristic
33	C₂×#117×C₄₇	C₂²	1	1	yes	characteristic
34	C₄₇×#419	C₄	1	2	yes	complemented
35	C₄₇×#418	C₄	1	2	yes	complemented
36	C₄₇×#417	C₄	1	4	yes	complemented
37	C₄₇×#416	C₂²	1	4	yes	—
38	C₂³×Dic₄₇	—	2	1	no	—
39	#13094031	—	2	16	no	—
40	#13094031	—	2	8	no	—
41	#13094031	C₂×C₄	1	16	yes	complemented
42	C₂×#10625329	—	2	1	no	—
43	C₂×#10625329	—	2	1	no	—
44	C₂×#10625329	—	2	2	no	—
45	C₂×#10625329	—	2	2	no	—
46	C₂×#10625329	—	2	16	no	—
47	C₂×#10625329	—	2	4	no	—
48	C₂×#10625329	C₂×C₄	1	4	yes	—
49	C₂×#10625329	C₂×C₄	1	4	yes	—
50	C₂×#10625329	C₂×C₄	1	4	yes	—
51	C₂×#10625329	D₄	1	4	yes	—
52	C₂×#10625329	D₄	1	2	yes	—
53	C₂×#10625329	D₄	1	2	yes	—
54	C₂×#10625329	C₂³	1	2	yes	—
55	C₂×#10625329	C₂³	1	2	yes	—
56	C₂²×C₄₇⋊C₈	—	2	1	no	—
57	C₂²×C₄₇⋊C₈	—	2	1	no	—
58	C₂²×C₄₇⋊C₈	—	2	4	no	—
59	C₂²×C₄₇⋊C₈	C₂³	1	2	yes	—
60	C₂×C₄×Dic₄₇	—	2	2	no	—
61	C₂×C₄×Dic₄₇	—	2	1	no	—
62	C₂×C₄×Dic₄₇	C₂×C₄	1	4	yes	—
63	C₂×C₄×Dic₄₇	C₂³	1	1	yes	characteristic
64	C₂×C₄×Dic₄₇	C₂³	1	1	yes	characteristic
65	#13093951	C₂×C₄	1	8	yes	complemented
66	#13093951	C₂×C₄	1	8	yes	complemented
67	#13093935	—	2	4	no	—
68	#13093934	—	2	4	no	—
69	C₄×C₄₇⋊C₈	—	2	4	no	—
70	C₈×Dic₄₇	—	2	4	no	—
71	C₂×#41×C₄₇	—	2	1	no	—
72	C₂×#41×C₄₇	—	2	2	no	—
73	C₂×#41×C₄₇	—	2	1	no	—
74	C₂×#41×C₄₇	—	2	2	no	—
75	C₂×#41×C₄₇	C₂×C₄	1	4	yes	—
76	C₂×#41×C₄₇	C₂×C₄	1	4	yes	—
77	C₂×#41×C₄₇	C₂×C₄	1	2	yes	—
78	C₂×#41×C₄₇	C₂³	1	2	yes	—
79	C₂²×Q₈×C₄₇	C₂×C₄	1	1	yes	characteristic
80	C₂²×D₄×C₄₇	—	2	1	no	—
81	C₂²×D₄×C₄₇	C₂×C₄	1	1	yes	characteristic
82	C₂³×C₄×C₄₇	—	2	1	no	—
83	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
84	C₂×M₁₆×C₄₇	—	2	2	no	—
85	C₂×M₁₆×C₄₇	—	2	2	no	—
86	C₂×M₁₆×C₄₇	C₂×C₄	1	2	yes	—
87	C₂×M₁₆×C₄₇	C₂×C₄	1	2	yes	—
88	C₂²×C₈×C₄₇	C₂³	1	2	yes	—
89	#117×C₄₇	—	2	1	no	—
90	#117×C₄₇	—	2	1	no	—
91	#117×C₄₇	C₂×C₄	1	2	yes	—
92	#117×C₄₇	C₂³	1	2	yes	—
93	C₂×C₄⋊C₄×C₄₇	C₂×C₄	1	2	yes	—
94	C₂×C₂²⋊C₄×C₄₇	—	2	1	no	—
95	C₂×C₄²×C₄₇	—	2	1	no	—
96	#103×C₄₇	C₂×C₄	1	8	yes	complemented
97	#102×C₄₇	C₂×C₄	1	8	yes	complemented
98	C₂⁴×C₄₇	—	2	1	no	—
99	C₂⁴×C₄₇	#41	1	1	yes	characteristic
100	#41×C₄₇	—	2	4	no	—
101	#41×C₄₇	—	2	4	no	—
102	#41×C₄₇	—	2	4	no	—
103	#41×C₄₇	—	2	4	no	—
104	#41×C₄₇	—	2	4	no	—
105	#41×C₄₇	—	2	2	no	—
106	#41×C₄₇	—	2	2	no	—
107	#41×C₄₇	C₄²	1	8	yes	—
108	#41×C₄₇	C₂²×C₄	1	4	yes	—
109	#41×C₄₇	C₂²×C₄	1	4	yes	—
110	C₂×Q₈×C₄₇	—	2	1	no	—
111	C₂×Q₈×C₄₇	—	2	2	no	—
112	C₂×Q₈×C₄₇	C₄²	1	4	yes	—
113	C₂×Q₈×C₄₇	C₂²×C₄	1	2	yes	—
114	C₂×D₄×C₄₇	—	2	4	no	—
115	C₂×D₄×C₄₇	—	2	2	no	—
116	C₂×D₄×C₄₇	—	2	4	no	—
117	C₂×D₄×C₄₇	—	2	2	no	—
118	C₂×D₄×C₄₇	—	2	2	no	—
119	C₂×D₄×C₄₇	—	2	1	no	—
120	C₂×D₄×C₄₇	C₄²	1	4	yes	—
121	C₂×D₄×C₄₇	C₂²×C₄	1	2	yes	—
122	C₂²×C₄×C₄₇	—	2	1	no	—
123	C₂²×C₄×C₄₇	—	2	4	no	—
124	C₂²×C₄×C₄₇	—	2	2	no	—
125	C₂²×C₄×C₄₇	—	2	4	no	—
126	C₂²×C₄×C₄₇	—	2	2	no	—
127	C₂²×C₄×C₄₇	—	2	2	no	—
128	C₂²×C₄×C₄₇	C₂²×C₄	1	2	yes	—
129	C₂²×C₄×C₄₇	C₂²×C₄	1	2	yes	—
130	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
131	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
132	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
133	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
134	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
135	C₂²×C₄×C₄₇	#41	1	1	yes	characteristic
136	C₂²×C₄×C₄₇	#41	1	2	yes	—
137	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
138	C₂²×Dic₄₇	—	2	1	no	—
139	C₂²×Dic₄₇	—	2	4	no	—
140	C₂²×Dic₄₇	—	2	1	no	—
141	C₂²×Dic₄₇	—	4	4	no	—
142	M₁₆×C₄₇	—	2	4	no	—
143	M₁₆×C₄₇	—	2	4	no	—
144	C₂×C₈×C₄₇	—	2	2	no	—
145	C₂×C₈×C₄₇	—	2	2	no	—
146	C₂×C₈×C₄₇	C₂²×C₄	1	4	yes	—
147	C₄⋊C₄×C₄₇	—	2	2	no	—
148	C₄⋊C₄×C₄₇	C₂²×C₄	1	4	yes	—
149	C₂²⋊C₄×C₄₇	—	2	2	no	—
150	C₂²⋊C₄×C₄₇	—	2	2	no	—
151	C₄²×C₄₇	—	2	2	no	—
152	C₄²×C₄₇	—	2	2	no	—
153	C₄×Dic₄₇	—	2	4	no	—
154	C₄×Dic₄₇	—	2	1	no	—
155	C₄×Dic₄₇	—	2	1	no	—
156	C₄×Dic₄₇	C₂²×C₄	1	2	yes	—
157	C₄×Dic₄₇	C₂²×C₄	1	2	yes	—
158	#10625329	—	2	4	no	—
159	#10625329	—	2	4	no	—
160	#10625329	—	2	2	no	—
161	#10625329	—	2	2	no	—
162	#10625329	—	2	16	no	—
163	#10625329	C₂²⋊C₄	1	8	yes	—
164	#10625329	C₂²⋊C₄	1	8	yes	—
165	#10625329	C₂²×C₄	1	4	yes	—
166	#10625329	C₂²×C₄	1	4	yes	—
167	C₂×C₄₇⋊C₈	—	2	4	no	—
168	C₂×C₄₇⋊C₈	—	2	4	no	—
169	C₂×C₄₇⋊C₈	—	2	2	no	—
170	C₂×C₄₇⋊C₈	—	2	2	no	—
171	C₂×C₄₇⋊C₈	—	2	16	no	—
172	C₂×C₄₇⋊C₈	C₂²×C₄	1	4	yes	—
173	C₂×C₄₇⋊C₈	C₂×D₄	1	4	yes	—
174	C₂×C₄₇⋊C₈	C₂×D₄	1	4	yes	—
175	C₂³×C₄₇	—	2	2	no	—
176	C₂³×C₄₇	—	2	4	no	—
177	C₂³×C₄₇	—	4	2	no	—
178	C₂³×C₄₇	—	8	2	no	—
179	C₂³×C₄₇	#117	1	2	yes	—
180	C₂³×C₄₇	C₄×D₄	1	2	yes	—
181	C₂³×C₄₇	C₄×D₄	1	1	yes	characteristic
182	C₂³×C₄₇	C₄×D₄	1	1	yes	characteristic
183	C₂³×C₄₇	C₂×#41	1	1	yes	characteristic
184	Q₈×C₄₇	—	2	2	no	—
185	Q₈×C₄₇	—	2	4	no	—
186	Q₈×C₄₇	C₂×C₄²	1	4	yes	—
187	D₄×C₄₇	—	2	4	no	—
188	D₄×C₄₇	—	2	4	no	—
189	D₄×C₄₇	—	2	8	no	—
190	D₄×C₄₇	—	2	2	no	—
191	D₄×C₄₇	—	2	4	no	—
192	D₄×C₄₇	C₂×C₄²	1	4	yes	—
193	C₂×C₄×C₄₇	—	2	2	no	—
194	C₂×C₄×C₄₇	—	2	4	no	—
195	C₂×C₄×C₄₇	—	2	4	no	—
196	C₂×C₄×C₄₇	—	2	4	no	—
197	C₂×C₄×C₄₇	—	2	8	no	—
198	C₂×C₄×C₄₇	—	2	4	no	—
199	C₂×C₄×C₄₇	—	8	2	no	—
200	C₂×C₄×C₄₇	C₂×C₄²	1	2	yes	—
201	C₂×C₄×C₄₇	C₂×C₄²	1	2	yes	—
202	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	2	yes	—
203	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	2	yes	—
204	C₂×C₄×C₄₇	#117	1	2	yes	—
205	C₂×C₄×C₄₇	C₄×D₄	1	2	yes	—
206	C₂×C₄×C₄₇	C₄×D₄	1	2	yes	—
207	C₂×C₄×C₄₇	C₄×D₄	1	2	yes	—
208	C₂×C₄×C₄₇	C₄×D₄	1	2	yes	—
209	C₂×C₄×C₄₇	C₄×D₄	1	2	yes	—
210	C₂×C₄×C₄₇	C₄×D₄	1	1	yes	characteristic
211	C₂×C₄×C₄₇	C₄×D₄	1	1	yes	characteristic
212	C₂×C₄×C₄₇	C₂³×C₄	1	1	yes	characteristic
213	C₂×C₄×C₄₇	C₂³×C₄	1	1	yes	characteristic
214	C₂×C₄×C₄₇	C₂³×C₄	1	1	yes	characteristic
215	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
216	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
217	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
218	C₂×Dic₄₇	—	2	4	no	—
219	C₂×Dic₄₇	—	2	2	no	—
220	C₂×Dic₄₇	—	2	2	no	—
221	C₂×Dic₄₇	—	4	8	no	—
222	C₂×Dic₄₇	—	4	2	no	—
223	C₈×C₄₇	—	2	4	no	—
224	C₄₇⋊C₈	—	2	4	no	—
225	C₄₇⋊C₈	—	2	4	no	—
226	C₄₇⋊C₈	C₂×C₂²⋊C₄	1	8	yes	—
227	#20421	—	47	1	no	maximal, Sylow
228	C₂²×C₄₇	—	2	2	no	—
229	C₂²×C₄₇	—	2	2	no	—
230	C₂²×C₄₇	—	2	2	no	—
231	C₂²×C₄₇	—	2	4	no	—
232	C₂²×C₄₇	—	4	2	no	—
233	C₂²×C₄₇	—	4	2	no	—
234	C₂²×C₄₇	—	4	4	no	—
235	C₂²×C₄₇	—	8	4	no	—
236	C₂²×C₄₇	C₄×C₂²⋊C₄	1	2	yes	—
237	C₂²×C₄₇	C₄×C₂²⋊C₄	1	2	yes	—
238	C₂²×C₄₇	C₂×#117	1	1	yes	characteristic
239	C₂²×C₄₇	C₂×C₄×D₄	1	1	yes	characteristic
240	C₂²×C₄₇	C₂×C₄×D₄	1	1	yes	characteristic
241	C₄×C₄₇	—	2	4	no	—
242	C₄×C₄₇	—	4	4	no	—
243	C₄×C₄₇	C₄×C₂²⋊C₄	1	2	yes	—
244	C₄×C₄₇	C₄×C₂²⋊C₄	1	2	yes	—
245	C₄×C₄₇	C₂²×C₄²	1	1	yes	characteristic
246	C₄×C₄₇	C₂²×C₂²⋊C₄	1	1	yes	characteristic
247	C₄×C₄₇	C₂×C₄×D₄	1	1	yes	characteristic
248	C₄×C₄₇	C₂×C₄×D₄	1	1	yes	characteristic
249	Dic₄₇	—	2	4	no	—
250	Dic₄₇	—	4	2	no	—
251	C₂×#568	—	47	1	no	—
252	C₂²×#104	—	47	1	no	—
253	#2896	D₄₇	1	1	yes	characteristic
254	#2873	—	47	1	no	—
255	C₂×C₄×M₁₆	—	47	1	no	—
256	#1765	—	47	4	no	—
257	#1764	—	47	4	no	—
258	#1738	—	47	1	no	—
259	C₂×#339	—	47	1	no	—
260	C₂×C₄₇	—	2	1	no	—
261	C₂×C₄₇	—	2	2	no	—
262	C₂×C₄₇	—	2	1	no	—
263	C₂×C₄₇	—	2	2	no	—
264	C₂×C₄₇	—	4	4	no	—
265	C₂×C₄₇	C₂×C₄×C₂²⋊C₄	1	1	yes	characteristic
266	C₂×C₄₇	#2956	1	2	yes	—
267	C₂²×#41	C₂×D₄₇	1	1	yes	characteristic
268	#568	—	47	8	no	—
269	#568	—	94	4	no	—
270	C₂×#131	—	47	4	no	—
271	C₂×#131	—	94	2	no	—
272	C₂²×M₁₆	—	47	1	no	—
273	C₂²×M₁₆	—	47	1	no	—
274	C₂²×M₁₆	—	47	1	no	—
275	C₂²×M₁₆	—	94	2	no	—
276	C₂²×M₁₆	C₂×D₄₇	1	1	yes	characteristic
277	C₂×#117	C₂×D₄₇	1	1	yes	characteristic
278	C₂²×C₄²	—	47	1	no	—
279	C₂×#104	—	47	8	no	—
280	C₂×#104	—	47	2	no	—
281	C₂×#104	—	47	2	no	—
282	#419	Dic₄₇	1	2	yes	complemented
283	#418	Dic₄₇	1	2	yes	complemented
284	#417	Dic₄₇	1	4	yes	complemented
285	#416	C₂×D₄₇	1	4	yes	—
286	#405	—	47	4	no	—
287	#405	—	94	2	no	—
288	C₄×M₁₆	—	94	2	no	—
289	C₄×M₁₆	—	94	4	no	—
290	C₂×#97	—	47	2	no	—
291	C₂×C₄×C₈	—	47	2	no	—
292	#341	—	47	4	no	—
293	#339	—	47	2	no	—
294	#339	—	47	2	no	—
295	C₄₇	#20421	1	1	yes	characteristic, complemented, Sylow
296	C₂×#41	—	2	1	no	—
297	C₂×#41	—	2	2	no	—
298	C₂×#41	—	2	2	no	—
299	C₂×#41	—	2	1	no	—
300	C₂×#41	C₄×D₄₇	1	4	yes	—
301	C₂×#41	C₄×D₄₇	1	4	yes	—
302	C₂×#41	C₂×Dic₄₇	1	2	yes	—
303	C₂×#41	C₂²×D₄₇	1	2	yes	—
304	C₂²×Q₈	C₂×Dic₄₇	1	1	yes	characteristic
305	C₂²×D₄	—	2	1	no	—
306	C₂²×D₄	C₂×Dic₄₇	1	1	yes	characteristic
307	C₂³×C₄	—	2	1	no	—
308	C₂³×C₄	—	94	1	no	—
309	C₂³×C₄	C₂²×D₄₇	1	1	yes	characteristic
310	#131	—	47	16	no	—
311	#131	—	94	8	no	—
312	#131	—	94	16	no	—
313	C₂×M₁₆	—	2	2	no	—
314	C₂×M₁₆	—	2	2	no	—
315	C₂×M₁₆	—	47	4	no	—
316	C₂×M₁₆	—	47	2	no	—
317	C₂×M₁₆	—	47	2	no	—
318	C₂×M₁₆	—	47	4	no	—
319	C₂×M₁₆	—	47	4	no	—
320	C₂×M₁₆	—	47	4	no	—
321	C₂×M₁₆	—	47	2	no	—
322	C₂×M₁₆	—	47	2	no	—
323	C₂×M₁₆	—	94	4	no	—
324	C₂×M₁₆	—	94	16	no	—
325	C₂×M₁₆	—	94	1	no	—
326	C₂×M₁₆	—	94	2	no	—
327	C₂×M₁₆	—	94	1	no	—
328	C₂×M₁₆	—	94	2	no	—
329	C₂×M₁₆	C₂×Dic₄₇	1	2	yes	—
330	C₂×M₁₆	C₂×Dic₄₇	1	2	yes	—
331	C₂²×C₈	—	47	2	no	—
332	C₂²×C₈	—	94	4	no	—
333	C₂²×C₈	—	94	1	no	—
334	C₂²×C₈	—	94	1	no	—
335	C₂²×C₈	C₂²×D₄₇	1	2	yes	—
336	#117	—	2	1	no	—
337	#117	—	2	1	no	—
338	#117	C₂×Dic₄₇	1	2	yes	—
339	#117	C₂²×D₄₇	1	2	yes	—
340	C₂×C₄⋊C₄	C₂×Dic₄₇	1	2	yes	—
341	C₂×C₂²⋊C₄	—	2	1	no	—
342	C₂×C₄²	—	2	1	no	—
343	C₂×C₄²	—	47	4	no	—
344	C₂×C₄²	—	47	1	no	—
345	C₂×C₄²	—	47	1	no	—
346	C₂×C₄²	—	94	2	no	—
347	C₂×C₄²	—	94	1	no	—
348	#104	—	47	8	no	—
349	#104	—	47	8	no	—
350	#103	C₂×Dic₄₇	1	8	yes	complemented
351	#102	C₂×Dic₄₇	1	8	yes	complemented
352	#97	—	94	4	no	—
353	#97	—	94	4	no	—
354	C₄×C₈	—	94	4	no	—
355	C₄×C₈	—	94	4	no	—
356	C₂⁴	—	2	1	no	—
357	C₂⁴	#10625352	1	1	yes	characteristic
358	#41	—	2	4	no	—
359	#41	—	2	4	no	—
360	#41	—	2	4	no	—
361	#41	—	2	4	no	—
362	#41	—	2	4	no	—
363	#41	—	2	2	no	—
364	#41	—	2	2	no	—
365	#41	C₄×Dic₄₇	1	8	yes	—
366	#41	C₂×C₄×D₄₇	1	4	yes	—
367	#41	C₂×C₄×D₄₇	1	4	yes	—
368	C₂×Q₈	—	2	2	no	—
369	C₂×Q₈	—	2	1	no	—
370	C₂×Q₈	C₄×Dic₄₇	1	4	yes	—
371	C₂×Q₈	C₂²×Dic₄₇	1	2	yes	—
372	C₂×D₄	—	2	4	no	—
373	C₂×D₄	—	2	4	no	—
374	C₂×D₄	—	2	2	no	—
375	C₂×D₄	—	2	2	no	—
376	C₂×D₄	—	2	1	no	—
377	C₂×D₄	—	2	2	no	—
378	C₂×D₄	C₄×Dic₄₇	1	4	yes	—
379	C₂×D₄	C₂²×Dic₄₇	1	2	yes	—
380	C₂²×C₄	—	2	1	no	—
381	C₂²×C₄	—	2	4	no	—
382	C₂²×C₄	—	2	4	no	—
383	C₂²×C₄	—	2	2	no	—
384	C₂²×C₄	—	2	2	no	—
385	C₂²×C₄	—	2	2	no	—
386	C₂²×C₄	—	94	1	no	—
387	C₂²×C₄	—	94	4	no	—
388	C₂²×C₄	—	94	1	no	—
389	C₂²×C₄	—	188	4	no	—
390	C₂²×C₄	C₂×C₄×D₄₇	1	2	yes	—
391	C₂²×C₄	C₂×C₄×D₄₇	1	2	yes	—
392	C₂²×C₄	D₄×D₄₇	1	1	yes	characteristic
393	C₂²×C₄	D₄×D₄₇	1	1	yes	characteristic
394	C₂²×C₄	D₄×D₄₇	1	2	yes	—
395	C₂²×C₄	#10625352	1	1	yes	characteristic
396	C₂²×C₄	#10625352	1	2	yes	—
397	C₂²×C₄	C₂²×Dic₄₇	1	1	yes	characteristic
398	C₂²×C₄	C₂²×Dic₄₇	1	1	yes	characteristic
399	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
400	M₁₆	—	2	4	no	—
401	M₁₆	—	2	4	no	—
402	M₁₆	—	47	8	no	—
403	M₁₆	—	47	8	no	—
404	M₁₆	—	47	4	no	—
405	M₁₆	—	47	4	no	—
406	M₁₆	—	94	16	no	—
407	M₁₆	—	94	4	no	—
408	M₁₆	—	94	4	no	—
409	M₁₆	—	94	2	no	—
410	M₁₆	—	94	2	no	—
411	C₂×C₈	—	2	2	no	—
412	C₂×C₈	—	2	2	no	—
413	C₂×C₈	—	47	4	no	—
414	C₂×C₈	—	47	4	no	—
415	C₂×C₈	—	47	4	no	—
416	C₂×C₈	—	94	16	no	—
417	C₂×C₈	—	94	4	no	—
418	C₂×C₈	—	94	4	no	—
419	C₂×C₈	—	94	2	no	—
420	C₂×C₈	—	94	2	no	—
421	C₂×C₈	C₂²×Dic₄₇	1	4	yes	—
422	C₄⋊C₄	—	2	2	no	—
423	C₄⋊C₄	C₂²×Dic₄₇	1	4	yes	—
424	C₂²⋊C₄	—	2	2	no	—
425	C₂²⋊C₄	—	2	2	no	—
426	C₄²	—	2	2	no	—
427	C₄²	—	2	2	no	—
428	C₄²	—	47	2	no	—
429	C₄²	—	47	2	no	—
430	C₄²	—	94	4	no	—
431	C₄²	—	94	1	no	—
432	C₄²	—	94	1	no	—
433	C₂³	—	2	2	no	—
434	C₂³	—	2	4	no	—
435	C₂³	—	4	2	no	—
436	C₂³	—	8	2	no	—
437	C₂³	#13093980	1	2	yes	—
438	C₂³	(C₂²⋊D₄₇)⋊C₄	1	2	yes	—
439	C₂³	D₄×Dic₄₇	1	1	yes	characteristic
440	C₂³	D₄×Dic₄₇	1	1	yes	characteristic
441	C₂³	C₂×#10625352	1	1	yes	characteristic
442	Q₈	—	2	4	no	—
443	Q₈	—	2	2	no	—
444	Q₈	C₂×C₄×Dic₄₇	1	4	yes	—
445	D₄	—	2	8	no	—
446	D₄	—	2	4	no	—
447	D₄	—	2	4	no	—
448	D₄	—	2	4	no	—
449	D₄	—	2	2	no	—
450	D₄	C₂×C₄×Dic₄₇	1	4	yes	—
451	C₂×C₄	—	2	4	no	—
452	C₂×C₄	—	2	2	no	—
453	C₂×C₄	—	2	8	no	—
454	C₂×C₄	—	2	4	no	—
455	C₂×C₄	—	2	4	no	—
456	C₂×C₄	—	2	4	no	—
457	C₂×C₄	—	8	2	no	—
458	C₂×C₄	—	94	4	no	—
459	C₂×C₄	—	94	2	no	—
460	C₂×C₄	—	94	2	no	—
461	C₂×C₄	—	188	8	no	—
462	C₂×C₄	—	188	2	no	—
463	C₂×C₄	C₂×C₄×Dic₄₇	1	2	yes	—
464	C₂×C₄	C₂×C₄×Dic₄₇	1	2	yes	—
465	C₂×C₄	C₂²⋊C₄×D₄₇	1	2	yes	—
466	C₂×C₄	C₂²⋊C₄×D₄₇	1	2	yes	—
467	C₂×C₄	#13093980	1	2	yes	—
468	C₂×C₄	(C₂²⋊D₄₇)⋊C₄	1	2	yes	—
469	C₂×C₄	(C₂²⋊D₄₇)⋊C₄	1	2	yes	—
470	C₂×C₄	(C₂²⋊D₄₇)⋊C₄	1	2	yes	—
471	C₂×C₄	D₄×Dic₄₇	1	1	yes	characteristic
472	C₂×C₄	D₄×Dic₄₇	1	1	yes	characteristic
473	C₂×C₄	D₄×Dic₄₇	1	2	yes	—
474	C₂×C₄	D₄×Dic₄₇	1	2	yes	—
475	C₂×C₄	C₂²×C₄×D₄₇	1	1	yes	characteristic
476	C₂×C₄	C₂²×C₄×D₄₇	1	1	yes	characteristic
477	C₂×C₄	C₂³×Dic₄₇	1	1	yes	characteristic
478	C₂×C₄	C₂×D₄×D₄₇	1	1	yes	characteristic
479	C₂×C₄	C₂×D₄×D₄₇	1	1	yes	characteristic
480	C₂×C₄	C₂×#10625352	1	1	yes	characteristic
481	C₈	—	2	4	no	—
482	C₈	—	47	8	no	—
483	C₈	—	94	4	no	—
484	C₈	—	94	4	no	—
485	C₂²	—	2	2	no	—
486	C₂²	—	2	2	no	—
487	C₂²	—	2	2	no	—
488	C₂²	—	2	4	no	—
489	C₂²	—	4	2	no	—
490	C₂²	—	4	2	no	—
491	C₂²	—	4	4	no	—
492	C₂²	—	8	4	no	—
493	C₂²	C₂²⋊C₄×Dic₄₇	1	2	yes	—
494	C₂²	C₂²⋊C₄×Dic₄₇	1	2	yes	—
495	C₂²	C₂×#13093980	1	1	yes	characteristic
496	C₂²	C₂×(C₂²⋊D₄₇)⋊C₄	1	1	yes	characteristic
497	C₂²	C₂×D₄×Dic₄₇	1	1	yes	characteristic
498	C₄	—	2	4	no	—
499	C₄	—	4	4	no	—
500	C₄	—	94	4	no	—
501	C₄	—	188	2	no	—
502	C₄	C₂²⋊C₄×Dic₄₇	1	2	yes	—
503	C₄	C₂²⋊C₄×Dic₄₇	1	2	yes	—
504	C₄	C₂²×C₄×Dic₄₇	1	1	yes	characteristic
505	C₄	C₂×C₂²⋊C₄×D₄₇	1	1	yes	characteristic
506	C₄	C₂×(C₂²⋊D₄₇)⋊C₄	1	1	yes	characteristic
507	C₄	C₂×D₄×Dic₄₇	1	1	yes	characteristic
508	C₂	—	2	1	no	—
509	C₂	—	2	2	no	—
510	C₂	—	2	2	no	—
511	C₂	—	2	1	no	—
512	C₂	—	4	4	no	—
513	C₂	C₂×C₂²⋊C₄×Dic₄₇	1	1	yes	characteristic
514	C₂	#20252298	1	2	yes	—

	subgroup	G/H
center	C₂×C₄	C₂×D₄×D₄₇
commutator	C₄×C₄₇	C₂²×C₄²
Frattini	C₂²×C₄	C₂³×D₄₇
Fitting	C₄₇×#2896	C₂
socle	C₂²×C₄₇	C₂×C₄×D₄
prime radical	C₂²×#41×C₄₇	C₂²
cosocle	C₂²×C₄×C₄₇	C₂⁴
hypercenter	#2896	D₄₇
hypocenter	C₄₇	#20421
LCS	G ▷ C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂×C₄ ◁ C₂³×C₄ ◁ #2896

Complements

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

N	H ≅ G/N	type
3. #20251807	C₂	semidirect
4. C₂×M₁₆×Dic₄₇	C₂	semidirect
5. #20243235	C₂	semidirect
6. #20243228	C₂	semidirect
7. #20243115	C₂	semidirect
8. C₂×#15688882	C₂	semidirect
11. #15689890	C₄	semidirect
19. C₂×#13093951	C₄	semidirect
23. #15689079	C₂²	semidirect
26. C₂×#13093934	C₂²	semidirect
27. C₂×C₈×Dic₄₇	C₂²	semidirect
28. #15688888	C₂²	semidirect
29. #15688882	C₂²	semidirect
30. #15688882	C₂²	semidirect
34. C₄₇×#419	C₄	semidirect
35. C₄₇×#418	C₄	semidirect
36. C₄₇×#417	C₄	semidirect
41. #13094031	C₂×C₄	semidirect
65. #13093951	C₂×C₄	semidirect
66. #13093951	C₂×C₄	semidirect
96. #103×C₄₇	C₂×C₄	semidirect
97. #102×C₄₇	C₂×C₄	semidirect
282. #419	Dic₄₇	semidirect
283. #418	Dic₄₇	semidirect
284. #417	Dic₄₇	semidirect
295. C₄₇	#20421	semidirect
350. #103	C₂×Dic₄₇	semidirect
351. #102	C₂×Dic₄₇	semidirect

Maximal subgroups

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

subgroup	index
C₂×#15689890	2
C₂²×#13093951	2
#20251807	2
C₂×M₁₆×Dic₄₇	2
#20243235	2
#20243228	2
#20243115	2
C₂×#15688882	2
C₄₇×#2896	2
#20421	47