Subgroups — #26218265

Order 12032.

1708 conjugacy classes of subgroups.

The subgroup lattice has 596 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, complemented
2	#20251907	C₂	1	2	yes	maximal, complemented
3	C₂×#15689097	C₂	1	1	yes	maximal, characteristic, complemented
4	#20243916	C₂	1	4	yes	maximal, complemented
5	#20243911	C₂	1	4	yes	maximal, complemented
6	C₂×#15688879	C₂	1	2	yes	maximal, complemented
7	C₄₇×#3449	C₂	1	1	yes	maximal, characteristic
8	#15689890	—	2	4	no	—
9	#15689890	—	2	2	no	—
10	#15689890	C₂²	1	4	yes	—
11	C₂×#13094031	—	2	4	no	—
12	C₂²×#10625329	—	2	2	no	—
13	C₂²×#10625329	C₂²	1	2	yes	—
14	C₂×#13093983	C₂²	1	2	yes	—
15	#15689132	C₂²	1	4	yes	complemented
16	#15689128	C₂²	1	4	yes	complemented
17	#15689124	—	2	4	no	—
18	#15689119	—	2	4	no	—
19	#15689097	—	2	2	no	—
20	#15689097	C₂²	1	4	yes	—
21	C₂×#13093939	—	2	2	no	—
22	#15688879	C₂²	1	8	yes	complemented
23	C₂²×#41×C₄₇	C₂²	1	1	yes	characteristic
24	C₂²×#41×C₄₇	C₂²	1	1	yes	characteristic
25	C₄₇×#537	—	2	2	no	—
26	C₄₇×#536	C₄	1	2	yes	complemented
27	C₄₇×#536	C₂²	1	2	yes	—
28	C₄₇×#535	C₄	1	2	yes	complemented
29	C₄₇×#535	C₂²	1	2	yes	—
30	C₄₇×#534	—	2	2	no	—
31	C₄₇×#532	C₄	1	4	yes	complemented
32	C₄₇×#525	—	2	2	no	—
33	C₄₇×#525	—	2	2	no	—
34	C₂×#117×C₄₇	C₂²	1	1	yes	characteristic
35	#13094031	—	2	16	no	—
36	#13094031	—	2	16	no	—
37	C₂×#10625329	—	2	4	no	—
38	C₂×#10625329	—	2	8	no	—
39	C₂×#10625329	—	2	2	no	—
40	C₂×#10625329	—	2	8	no	—
41	C₂×#10625329	—	2	2	no	—
42	C₂×#10625329	—	2	2	no	—
43	C₂×#10625329	—	2	2	no	—
44	C₂×#10625329	D₄	1	4	yes	complemented
45	C₂×#10625329	C₂³	1	4	yes	—
46	C₂²×C₄₇⋊C₈	—	2	4	no	—
47	C₂²×C₄₇⋊C₈	D₄	1	4	yes	complemented
48	#13093983	—	2	2	no	—
49	#13093983	—	2	2	no	—
50	#13093983	—	2	2	no	—
51	#13093983	C₂³	1	4	yes	—
52	C₂×C₄⋊Dic₄₇	—	2	2	no	—
53	C₂×C₂²⋊Dic₄₇	—	2	2	no	—
54	C₂×C₄×Dic₄₇	—	2	2	no	—
55	#13093948	—	2	8	no	—
56	#13093945	—	2	8	no	—
57	#13093939	—	2	8	no	—
58	C₂×#41×C₄₇	—	2	2	no	—
59	C₂×#41×C₄₇	—	2	2	no	—
60	C₂×#41×C₄₇	—	2	1	no	—
61	C₂×#41×C₄₇	—	2	1	no	—
62	C₂×#41×C₄₇	—	2	2	no	—
63	C₂×#41×C₄₇	—	2	2	no	—
64	C₂×#41×C₄₇	—	2	2	no	—
65	C₂×#41×C₄₇	—	2	2	no	—
66	C₂×#41×C₄₇	—	2	2	no	—
67	C₂×#41×C₄₇	—	2	2	no	—
68	C₂×#41×C₄₇	C₂×C₄	1	2	yes	—
69	C₂×#41×C₄₇	C₂×C₄	1	2	yes	—
70	C₂×#41×C₄₇	C₂×C₄	1	2	yes	—
71	C₂×#41×C₄₇	D₄	1	2	yes	—
72	C₂×#41×C₄₇	D₄	1	2	yes	—
73	C₂×#41×C₄₇	C₂³	1	2	yes	—
74	C₂²×Q₈×C₄₇	C₂×C₄	1	1	yes	characteristic
75	C₂²×Q₈×C₄₇	C₂³	1	1	yes	characteristic
76	C₂²×D₄×C₄₇	—	2	1	no	—
77	C₂²×D₄×C₄₇	C₂×C₄	1	1	yes	characteristic
78	C₂²×D₄×C₄₇	D₄	1	2	yes	—
79	C₂²×D₄×C₄₇	C₂³	1	1	yes	characteristic
80	C₂³×C₄×C₄₇	—	2	1	no	—
81	C₂³×C₄×C₄₇	D₄	1	2	yes	—
82	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
83	C₄⋊Q₈×C₄₇	C₂×C₄	1	4	yes	complemented
84	#127×C₄₇	C₂×C₄	1	4	yes	complemented
85	#124×C₄₇	C₂×C₄	1	4	yes	complemented
86	#124×C₄₇	C₂×C₄	1	4	yes	complemented
87	#123×C₄₇	—	2	4	no	—
88	#123×C₄₇	—	2	4	no	—
89	C₂²⋊Q₈×C₄₇	—	2	4	no	—
90	C₂²⋊Q₈×C₄₇	—	2	4	no	—
91	#121×C₄₇	—	2	4	no	—
92	#121×C₄₇	—	2	8	no	—
93	#121×C₄₇	—	2	4	no	—
94	#120×C₄₇	—	2	4	no	—
95	#120×C₄₇	—	2	4	no	—
96	C₄×D₄×C₄₇	—	2	8	no	—
97	#117×C₄₇	—	2	1	no	—
98	#117×C₄₇	—	2	1	no	—
99	#117×C₄₇	C₂×C₄	1	2	yes	—
100	#117×C₄₇	C₂³	1	2	yes	—
101	C₂×C₄⋊C₄×C₄₇	—	2	1	no	—
102	C₂×C₂²⋊C₄×C₄₇	—	2	1	no	—
103	C₂×C₄²×C₄₇	C₂×C₄	1	2	yes	—
104	C₂⁴×C₄₇	—	2	1	no	—
105	C₂⁴×C₄₇	C₂²⋊C₄	1	2	yes	—
106	C₂⁴×C₄₇	C₂×D₄	1	1	yes	characteristic
107	#41×C₄₇	—	2	4	no	—
108	#41×C₄₇	—	2	4	no	—
109	#41×C₄₇	—	2	4	no	—
110	#41×C₄₇	—	2	4	no	—
111	#41×C₄₇	—	2	4	no	—
112	#41×C₄₇	—	2	4	no	—
113	#41×C₄₇	—	2	4	no	—
114	#41×C₄₇	—	2	4	no	—
115	#41×C₄₇	—	2	4	no	—
116	#41×C₄₇	—	2	4	no	—
117	#41×C₄₇	—	2	4	no	—
118	#41×C₄₇	—	2	4	no	—
119	#41×C₄₇	—	4	1	no	—
120	#41×C₄₇	—	4	2	no	—
121	#41×C₄₇	—	4	1	no	—
122	#41×C₄₇	—	4	1	no	—
123	#41×C₄₇	—	4	1	no	—
124	#41×C₄₇	—	4	2	no	—
125	C₂×Q₈×C₄₇	—	2	2	no	—
126	C₂×Q₈×C₄₇	—	2	2	no	—
127	C₂×Q₈×C₄₇	—	2	1	no	—
128	C₂×Q₈×C₄₇	—	2	2	no	—
129	C₂×Q₈×C₄₇	—	2	2	no	—
130	C₂×Q₈×C₄₇	C₂²⋊C₄	1	2	yes	—
131	C₂×Q₈×C₄₇	C₂²×C₄	1	2	yes	—
132	C₂×Q₈×C₄₇	C₂²×C₄	1	2	yes	—
133	C₂×D₄×C₄₇	—	2	4	no	—
134	C₂×D₄×C₄₇	—	2	4	no	—
135	C₂×D₄×C₄₇	—	2	2	no	—
136	C₂×D₄×C₄₇	—	2	2	no	—
137	C₂×D₄×C₄₇	—	2	8	no	—
138	C₂×D₄×C₄₇	—	2	2	no	—
139	C₂×D₄×C₄₇	—	2	2	no	—
140	C₂×D₄×C₄₇	—	2	2	no	—
141	C₂×D₄×C₄₇	—	2	1	no	—
142	C₂×D₄×C₄₇	—	2	2	no	—
143	C₂×D₄×C₄₇	—	4	2	no	—
144	C₂×D₄×C₄₇	—	4	2	no	—
145	C₂×D₄×C₄₇	C₂²⋊C₄	1	2	yes	—
146	C₂×D₄×C₄₇	C₂²⋊C₄	1	4	yes	—
147	C₂×D₄×C₄₇	C₂²×C₄	1	2	yes	—
148	C₂×D₄×C₄₇	C₂²×C₄	1	2	yes	—
149	C₂×D₄×C₄₇	C₂×D₄	1	4	yes	—
150	C₂²×C₄×C₄₇	—	2	2	no	—
151	C₂²×C₄×C₄₇	—	2	2	no	—
152	C₂²×C₄×C₄₇	—	2	2	no	—
153	C₂²×C₄×C₄₇	—	2	2	no	—
154	C₂²×C₄×C₄₇	—	2	1	no	—
155	C₂²×C₄×C₄₇	—	2	2	no	—
156	C₂²×C₄×C₄₇	—	2	2	no	—
157	C₂²×C₄×C₄₇	—	2	2	no	—
158	C₂²×C₄×C₄₇	—	4	2	no	—
159	C₂²×C₄×C₄₇	—	4	2	no	—
160	C₂²×C₄×C₄₇	C₂²⋊C₄	1	4	yes	—
161	C₂²×C₄×C₄₇	C₂²⋊C₄	1	2	yes	—
162	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
163	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
164	C₂²×C₄×C₄₇	C₂×D₄	1	4	yes	—
165	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
166	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
167	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
168	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
169	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
170	C₂²×C₄×C₄₇	#41	1	2	yes	—
171	C₂²×C₄×C₄₇	#41	1	2	yes	—
172	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
173	C₂²×Dic₄₇	—	4	2	no	—
174	C₄⋊C₄×C₄₇	—	2	2	no	—
175	C₄⋊C₄×C₄₇	—	2	8	no	—
176	C₄⋊C₄×C₄₇	—	2	2	no	—
177	C₂²⋊C₄×C₄₇	—	2	2	no	—
178	C₂²⋊C₄×C₄₇	—	2	8	no	—
179	C₂²⋊C₄×C₄₇	—	2	2	no	—
180	C₂²⋊C₄×C₄₇	—	2	8	no	—
181	C₄²×C₄₇	—	2	2	no	—
182	C₄²×C₄₇	C₂²×C₄	1	4	yes	—
183	C₂²⋊Dic₄₇	—	2	4	no	—
184	C₂²⋊Dic₄₇	—	4	2	no	—
185	C₄⋊Dic₄₇	—	2	4	no	—
186	C₄⋊Dic₄₇	—	4	2	no	—
187	C₄×Dic₄₇	—	2	4	no	—
188	C₄×Dic₄₇	—	4	2	no	—
189	#10625329	—	2	16	no	—
190	#10625329	—	2	4	no	—
191	#10625329	—	2	4	no	—
192	#10625329	—	2	4	no	—
193	#10625329	—	2	4	no	—
194	C₂×C₄₇⋊C₈	—	2	16	no	—
195	C₂×C₄₇⋊C₈	—	2	4	no	—
196	C₂×C₄₇⋊C₈	—	2	4	no	—
197	C₂×C₄₇⋊C₈	C₂×D₄	1	8	yes	—
198	C₂³×C₄₇	—	2	2	no	—
199	C₂³×C₄₇	—	2	2	no	—
200	C₂³×C₄₇	—	2	2	no	—
201	C₂³×C₄₇	—	4	2	no	—
202	C₂³×C₄₇	—	8	1	no	—
203	C₂³×C₄₇	—	8	2	no	—
204	C₂³×C₄₇	—	8	2	no	—
205	C₂³×C₄₇	C₂×C₂²⋊C₄	1	4	yes	—
206	C₂³×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
207	C₂³×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
208	C₂³×C₄₇	#121	1	2	yes	—
209	C₂³×C₄₇	#121	1	2	yes	—
210	C₂³×C₄₇	C₂²×D₄	1	1	yes	characteristic
211	Q₈×C₄₇	—	2	4	no	—
212	Q₈×C₄₇	—	2	4	no	—
213	Q₈×C₄₇	—	2	4	no	—
214	Q₈×C₄₇	—	4	1	no	—
215	Q₈×C₄₇	—	4	1	no	—
216	D₄×C₄₇	—	2	8	no	—
217	D₄×C₄₇	—	2	8	no	—
218	D₄×C₄₇	—	2	4	no	—
219	D₄×C₄₇	—	2	4	no	—
220	D₄×C₄₇	—	2	4	no	—
221	D₄×C₄₇	—	4	2	no	—
222	D₄×C₄₇	—	4	2	no	—
223	D₄×C₄₇	—	4	4	no	—
224	D₄×C₄₇	—	4	1	no	—
225	D₄×C₄₇	—	4	1	no	—
226	D₄×C₄₇	—	8	8	no	—
227	C₂×C₄×C₄₇	—	2	2	no	—
228	C₂×C₄×C₄₇	—	2	2	no	—
229	C₂×C₄×C₄₇	—	2	4	no	—
230	C₂×C₄×C₄₇	—	2	4	no	—
231	C₂×C₄×C₄₇	—	2	4	no	—
232	C₂×C₄×C₄₇	—	2	4	no	—
233	C₂×C₄×C₄₇	—	2	4	no	—
234	C₂×C₄×C₄₇	—	2	2	no	—
235	C₂×C₄×C₄₇	—	4	2	no	—
236	C₂×C₄×C₄₇	—	4	2	no	—
237	C₂×C₄×C₄₇	—	4	4	no	—
238	C₂×C₄×C₄₇	—	4	2	no	—
239	C₂×C₄×C₄₇	—	8	2	no	—
240	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	4	yes	—
241	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
242	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
243	C₂×C₄×C₄₇	C₄×D₄	1	2	yes	—
244	C₂×C₄×C₄₇	C₄×D₄	1	2	yes	—
245	C₂×C₄×C₄₇	C₄×D₄	1	2	yes	—
246	C₂×C₄×C₄₇	C₄×D₄	1	2	yes	—
247	C₂×C₄×C₄₇	#120	1	1	yes	characteristic
248	C₂×C₄×C₄₇	#120	1	2	yes	—
249	C₂×C₄×C₄₇	#120	1	1	yes	characteristic
250	C₂×C₄×C₄₇	#121	1	2	yes	—
251	C₂×C₄×C₄₇	#121	1	2	yes	—
252	C₂×C₄×C₄₇	#123	1	1	yes	characteristic
253	C₂×C₄×C₄₇	#123	1	1	yes	characteristic
254	C₂×C₄×C₄₇	#123	1	2	yes	—
255	C₂×C₄×C₄₇	C₂³×C₄	1	1	yes	characteristic
256	C₂×C₄×C₄₇	C₂²×D₄	1	2	yes	—
257	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
258	C₂×C₄×C₄₇	C₂×#41	1	2	yes	—
259	C₂×Dic₄₇	—	4	4	no	—
260	C₂×Dic₄₇	—	8	4	no	—
261	C₄₇⋊C₈	—	2	8	no	—
262	#21009	—	47	1	no	maximal, Sylow
263	C₂²×C₄₇	—	2	4	no	—
264	C₂²×C₄₇	—	4	2	no	—
265	C₂²×C₄₇	—	4	1	no	—
266	C₂²×C₄₇	—	4	1	no	—
267	C₂²×C₄₇	—	4	1	no	—
268	C₂²×C₄₇	—	4	2	no	—
269	C₂²×C₄₇	—	4	4	no	—
270	C₂²×C₄₇	—	4	4	no	—
271	C₂²×C₄₇	—	4	4	no	—
272	C₂²×C₄₇	—	4	2	no	—
273	C₂²×C₄₇	—	8	2	no	—
274	C₂²×C₄₇	—	8	4	no	—
275	C₂²×C₄₇	#386	1	1	yes	characteristic
276	C₂²×C₄₇	#386	1	1	yes	characteristic
277	C₂²×C₄₇	#386	1	2	yes	—
278	C₂²×C₄₇	C₂²×C₂²⋊C₄	1	1	yes	characteristic
279	C₂²×C₄₇	C₂×#121	1	2	yes	—
280	C₄×C₄₇	—	2	4	no	—
281	C₄×C₄₇	—	4	4	no	—
282	C₄×C₄₇	—	4	2	no	—
283	C₄×C₄₇	#386	1	1	yes	characteristic
284	C₄×C₄₇	#386	1	2	yes	—
285	C₄×C₄₇	#386	1	1	yes	characteristic
286	C₄×C₄₇	C₂×C₄×D₄	1	2	yes	—
287	C₄×C₄₇	C₂×#120	1	1	yes	characteristic
288	C₄×C₄₇	C₂×#123	1	1	yes	characteristic
289	Dic₄₇	—	8	4	no	—
290	C₂×#568	—	47	1	no	—
291	#3449	D₄₇	1	1	yes	characteristic
292	#2896	—	47	2	no	—
293	C₂×#410	—	47	1	no	—
294	#1910	—	47	4	no	—
295	#1909	—	47	4	no	—
296	C₂×H(3,ℤ/4)	—	47	2	no	—
297	C₂×C₄₇	—	2	2	no	—
298	C₂×C₄₇	—	2	1	no	—
299	C₂×C₄₇	—	2	1	no	—
300	C₂×C₄₇	—	2	1	no	—
301	C₂×C₄₇	—	2	2	no	—
302	C₂×C₄₇	—	4	4	no	—
303	C₂×C₄₇	—	8	2	no	—
304	C₂×C₄₇	C₂×#386	1	1	yes	characteristic
305	C₂²×#41	C₂×D₄₇	1	1	yes	characteristic
306	C₂²×#41	C₂×D₄₇	1	1	yes	characteristic
307	#568	—	47	4	no	—
308	#568	—	94	4	no	—
309	#568	—	94	2	no	—
310	C₂×#131	—	94	4	no	—
311	C₂²×M₁₆	—	47	2	no	—
312	C₂²×M₁₆	—	94	2	no	—
313	#537	—	2	2	no	—
314	#536	Dic₄₇	1	2	yes	complemented
315	#536	C₂×D₄₇	1	2	yes	—
316	#535	Dic₄₇	1	2	yes	complemented
317	#535	C₂×D₄₇	1	2	yes	—
318	#534	—	2	2	no	—
319	#532	Dic₄₇	1	4	yes	complemented
320	#525	—	2	2	no	—
321	#525	—	2	2	no	—
322	C₂×#117	—	47	2	no	—
323	C₂×#117	C₂×D₄₇	1	1	yes	characteristic
324	#419	—	47	4	no	—
325	#418	—	47	4	no	—
326	#417	—	94	4	no	—
327	#416	—	94	4	no	—
328	#410	—	47	4	no	—
329	#410	—	94	2	no	—
330	C₂×#99	—	94	2	no	—
331	H(3,ℤ/4)	—	47	8	no	—
332	C₄₇	#21009	1	1	yes	characteristic, complemented, Sylow
333	C₂×#41	—	2	2	no	—
334	C₂×#41	—	2	2	no	—
335	C₂×#41	—	2	2	no	—
336	C₂×#41	—	2	2	no	—
337	C₂×#41	—	2	1	no	—
338	C₂×#41	—	2	1	no	—
339	C₂×#41	—	2	2	no	—
340	C₂×#41	—	2	2	no	—
341	C₂×#41	—	2	2	no	—
342	C₂×#41	—	2	2	no	—
343	C₂×#41	C₂×Dic₄₇	1	2	yes	—
344	C₂×#41	C₂×Dic₄₇	1	2	yes	—
345	C₂×#41	C₂×Dic₄₇	1	2	yes	—
346	C₂×#41	C₂²⋊D₄₇	1	2	yes	—
347	C₂×#41	C₂²⋊D₄₇	1	2	yes	—
348	C₂×#41	C₂²×D₄₇	1	2	yes	—
349	C₂²×Q₈	C₂×Dic₄₇	1	1	yes	characteristic
350	C₂²×Q₈	C₂²×D₄₇	1	1	yes	characteristic
351	C₂²×D₄	—	2	1	no	—
352	C₂²×D₄	C₂×Dic₄₇	1	1	yes	characteristic
353	C₂²×D₄	C₂²⋊D₄₇	1	2	yes	—
354	C₂²×D₄	C₂²×D₄₇	1	1	yes	characteristic
355	C₂³×C₄	—	2	1	no	—
356	C₂³×C₄	C₂²⋊D₄₇	1	2	yes	—
357	C₂³×C₄	C₂²×D₄₇	1	1	yes	characteristic
358	#131	—	94	16	no	—
359	#131	—	94	16	no	—
360	C₂×M₁₆	—	47	4	no	—
361	C₂×M₁₆	—	47	4	no	—
362	C₂×M₁₆	—	94	4	no	—
363	C₂×M₁₆	—	94	8	no	—
364	C₂×M₁₆	—	94	2	no	—
365	C₂×M₁₆	—	94	2	no	—
366	C₂×M₁₆	—	94	2	no	—
367	C₂×M₁₆	—	94	2	no	—
368	C₂×M₁₆	—	94	8	no	—
369	C₂²×C₈	—	47	4	no	—
370	C₂²×C₈	—	94	4	no	—
371	C₄⋊Q₈	C₂×Dic₄₇	1	4	yes	complemented
372	#127	C₂×Dic₄₇	1	4	yes	complemented
373	#124	C₂×Dic₄₇	1	4	yes	complemented
374	#124	C₂×Dic₄₇	1	4	yes	complemented
375	#123	—	2	4	no	—
376	#123	—	2	4	no	—
377	C₂²⋊Q₈	—	2	4	no	—
378	C₂²⋊Q₈	—	2	4	no	—
379	#121	—	2	4	no	—
380	#121	—	2	8	no	—
381	#121	—	2	4	no	—
382	#120	—	2	4	no	—
383	#120	—	2	4	no	—
384	C₄×D₄	—	2	8	no	—
385	#117	—	2	1	no	—
386	#117	—	2	1	no	—
387	#117	—	47	4	no	—
388	#117	—	94	2	no	—
389	#117	—	94	2	no	—
390	#117	—	94	2	no	—
391	#117	C₂×Dic₄₇	1	2	yes	—
392	#117	C₂²×D₄₇	1	2	yes	—
393	C₂×C₄⋊C₄	—	2	1	no	—
394	C₂×C₄⋊C₄	—	94	2	no	—
395	C₂×C₂²⋊C₄	—	2	1	no	—
396	C₂×C₂²⋊C₄	—	94	2	no	—
397	C₂×C₄²	—	94	2	no	—
398	C₂×C₄²	C₂×Dic₄₇	1	2	yes	—
399	#103	—	94	8	no	—
400	#102	—	94	8	no	—
401	#99	—	94	8	no	—
402	C₂⁴	—	2	1	no	—
403	C₂⁴	C₂²⋊Dic₄₇	1	2	yes	—
404	C₂⁴	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
405	#41	—	2	4	no	—
406	#41	—	2	4	no	—
407	#41	—	2	4	no	—
408	#41	—	2	4	no	—
409	#41	—	2	4	no	—
410	#41	—	2	4	no	—
411	#41	—	2	4	no	—
412	#41	—	2	4	no	—
413	#41	—	2	4	no	—
414	#41	—	2	4	no	—
415	#41	—	2	4	no	—
416	#41	—	2	4	no	—
417	#41	—	4	2	no	—
418	#41	—	4	1	no	—
419	#41	—	4	1	no	—
420	#41	—	4	1	no	—
421	#41	—	4	2	no	—
422	#41	—	4	1	no	—
423	C₂×Q₈	—	2	2	no	—
424	C₂×Q₈	—	2	2	no	—
425	C₂×Q₈	—	2	1	no	—
426	C₂×Q₈	—	2	2	no	—
427	C₂×Q₈	—	2	2	no	—
428	C₂×Q₈	C₂²⋊Dic₄₇	1	2	yes	—
429	C₂×Q₈	C₂²×Dic₄₇	1	2	yes	—
430	C₂×Q₈	C₂²×Dic₄₇	1	2	yes	—
431	C₂×D₄	—	2	4	no	—
432	C₂×D₄	—	2	4	no	—
433	C₂×D₄	—	2	2	no	—
434	C₂×D₄	—	2	2	no	—
435	C₂×D₄	—	2	8	no	—
436	C₂×D₄	—	2	2	no	—
437	C₂×D₄	—	2	2	no	—
438	C₂×D₄	—	2	2	no	—
439	C₂×D₄	—	2	1	no	—
440	C₂×D₄	—	2	2	no	—
441	C₂×D₄	—	4	2	no	—
442	C₂×D₄	—	4	2	no	—
443	C₂×D₄	C₂²⋊Dic₄₇	1	2	yes	—
444	C₂×D₄	C₂²⋊Dic₄₇	1	4	yes	—
445	C₂×D₄	C₂²×Dic₄₇	1	2	yes	—
446	C₂×D₄	C₂²×Dic₄₇	1	2	yes	—
447	C₂×D₄	C₂×C₂²⋊D₄₇	1	4	yes	—
448	C₂²×C₄	—	2	2	no	—
449	C₂²×C₄	—	2	2	no	—
450	C₂²×C₄	—	2	2	no	—
451	C₂²×C₄	—	2	2	no	—
452	C₂²×C₄	—	2	1	no	—
453	C₂²×C₄	—	2	2	no	—
454	C₂²×C₄	—	2	2	no	—
455	C₂²×C₄	—	2	2	no	—
456	C₂²×C₄	—	4	2	no	—
457	C₂²×C₄	—	4	2	no	—
458	C₂²×C₄	—	188	2	no	—
459	C₂²×C₄	C₂²⋊Dic₄₇	1	4	yes	—
460	C₂²×C₄	C₂²⋊Dic₄₇	1	2	yes	—
461	C₂²×C₄	D₄×D₄₇	1	2	yes	—
462	C₂²×C₄	D₄×D₄₇	1	2	yes	—
463	C₂²×C₄	#10625352	1	2	yes	—
464	C₂²×C₄	#10625352	1	2	yes	—
465	C₂²×C₄	C₂²×Dic₄₇	1	1	yes	characteristic
466	C₂²×C₄	C₂²×Dic₄₇	1	1	yes	characteristic
467	C₂²×C₄	C₂×C₂²⋊D₄₇	1	4	yes	—
468	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
469	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
470	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
471	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
472	M₁₆	—	94	16	no	—
473	M₁₆	—	94	4	no	—
474	M₁₆	—	94	4	no	—
475	M₁₆	—	94	4	no	—
476	M₁₆	—	94	4	no	—
477	C₂×C₈	—	47	8	no	—
478	C₂×C₈	—	94	16	no	—
479	C₂×C₈	—	94	4	no	—
480	C₂×C₈	—	94	4	no	—
481	C₄⋊C₄	—	2	2	no	—
482	C₄⋊C₄	—	2	8	no	—
483	C₄⋊C₄	—	2	2	no	—
484	C₄⋊C₄	—	94	4	no	—
485	C₄⋊C₄	—	188	2	no	—
486	C₂²⋊C₄	—	2	2	no	—
487	C₂²⋊C₄	—	2	8	no	—
488	C₂²⋊C₄	—	2	2	no	—
489	C₂²⋊C₄	—	2	8	no	—
490	C₂²⋊C₄	—	94	4	no	—
491	C₂²⋊C₄	—	188	2	no	—
492	C₄²	—	2	2	no	—
493	C₄²	—	94	4	no	—
494	C₄²	—	188	2	no	—
495	C₄²	C₂²×Dic₄₇	1	4	yes	—
496	C₂³	—	2	2	no	—
497	C₂³	—	2	2	no	—
498	C₂³	—	2	2	no	—
499	C₂³	—	4	2	no	—
500	C₂³	—	8	1	no	—
501	C₂³	—	8	2	no	—
502	C₂³	—	8	2	no	—
503	C₂³	C₂×C₂²⋊Dic₄₇	1	4	yes	—
504	C₂³	C₂×C₂²⋊Dic₄₇	1	1	yes	characteristic
505	C₂³	C₂×C₂²⋊Dic₄₇	1	1	yes	characteristic
506	C₂³	#13093996	1	2	yes	—
507	C₂³	#13093996	1	2	yes	—
508	C₂³	C₂²×C₂²⋊D₄₇	1	1	yes	characteristic
509	Q₈	—	2	4	no	—
510	Q₈	—	2	4	no	—
511	Q₈	—	2	4	no	—
512	Q₈	—	4	1	no	—
513	Q₈	—	4	1	no	—
514	D₄	—	2	8	no	—
515	D₄	—	2	8	no	—
516	D₄	—	2	4	no	—
517	D₄	—	2	4	no	—
518	D₄	—	2	4	no	—
519	D₄	—	4	2	no	—
520	D₄	—	4	2	no	—
521	D₄	—	4	4	no	—
522	D₄	—	4	1	no	—
523	D₄	—	4	1	no	—
524	D₄	—	8	8	no	—
525	C₂×C₄	—	2	2	no	—
526	C₂×C₄	—	2	2	no	—
527	C₂×C₄	—	2	4	no	—
528	C₂×C₄	—	2	4	no	—
529	C₂×C₄	—	2	4	no	—
530	C₂×C₄	—	2	4	no	—
531	C₂×C₄	—	2	4	no	—
532	C₂×C₄	—	2	2	no	—
533	C₂×C₄	—	4	2	no	—
534	C₂×C₄	—	4	2	no	—
535	C₂×C₄	—	4	4	no	—
536	C₂×C₄	—	4	2	no	—
537	C₂×C₄	—	8	2	no	—
538	C₂×C₄	—	376	4	no	—
539	C₂×C₄	—	188	4	no	—
540	C₂×C₄	C₂×C₂²⋊Dic₄₇	1	4	yes	—
541	C₂×C₄	C₂×C₂²⋊Dic₄₇	1	1	yes	characteristic
542	C₂×C₄	C₂×C₂²⋊Dic₄₇	1	1	yes	characteristic
543	C₂×C₄	D₄×Dic₄₇	1	2	yes	—
544	C₂×C₄	D₄×Dic₄₇	1	2	yes	—
545	C₂×C₄	D₄×Dic₄₇	1	2	yes	—
546	C₂×C₄	D₄×Dic₄₇	1	2	yes	—
547	C₂×C₄	#13093992	1	2	yes	—
548	C₂×C₄	#13093992	1	1	yes	characteristic
549	C₂×C₄	#13093992	1	1	yes	characteristic
550	C₂×C₄	#13093996	1	2	yes	—
551	C₂×C₄	#13093996	1	2	yes	—
552	C₂×C₄	#13094005	1	1	yes	characteristic
553	C₂×C₄	#13094005	1	2	yes	—
554	C₂×C₄	#13094005	1	1	yes	characteristic
555	C₂×C₄	C₂³×Dic₄₇	1	1	yes	characteristic
556	C₂×C₄	C₂×D₄×D₄₇	1	2	yes	—
557	C₂×C₄	C₂²×C₂²⋊D₄₇	1	1	yes	characteristic
558	C₂×C₄	C₂×#10625352	1	2	yes	—
559	C₈	—	94	8	no	—
560	C₂²	—	2	4	no	—
561	C₂²	—	4	1	no	—
562	C₂²	—	4	2	no	—
563	C₂²	—	4	1	no	—
564	C₂²	—	4	1	no	—
565	C₂²	—	4	2	no	—
566	C₂²	—	4	4	no	—
567	C₂²	—	4	4	no	—
568	C₂²	—	4	4	no	—
569	C₂²	—	4	2	no	—
570	C₂²	—	8	2	no	—
571	C₂²	—	8	4	no	—
572	C₂²	#15689003	1	1	yes	characteristic
573	C₂²	#15689003	1	1	yes	characteristic
574	C₂²	#15689003	1	2	yes	—
575	C₂²	C₂²×C₂²⋊Dic₄₇	1	1	yes	characteristic
576	C₂²	C₂×#13093996	1	2	yes	—
577	C₄	—	2	4	no	—
578	C₄	—	4	4	no	—
579	C₄	—	4	2	no	—
580	C₄	—	376	4	no	—
581	C₄	#15689003	1	1	yes	characteristic
582	C₄	#15689003	1	2	yes	—
583	C₄	#15689003	1	1	yes	characteristic
584	C₄	C₂×D₄×Dic₄₇	1	2	yes	—
585	C₄	C₂×#13093992	1	1	yes	characteristic
586	C₄	C₂×#13094005	1	1	yes	characteristic
587	C₂	—	2	1	no	—
588	C₂	—	2	2	no	—
589	C₂	—	2	1	no	—
590	C₂	—	2	1	no	—
591	C₂	—	2	2	no	—
592	C₂	—	4	4	no	—
593	C₂	—	8	2	no	—
594	C₂	C₂×#15689003	1	1	yes	characteristic

	subgroup	G/H
center	C₄	#15689003
commutator	C₂×C₄×C₄₇	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₄₇
Fitting, prime radical	C₄₇×#3449	C₂
socle	C₂×C₄₇	C₂×#386
cosocle	C₂²×C₄×C₄₇	C₂⁴
hypercenter	#3449	D₄₇
hypocenter	C₄₇	#21009
LCS	G ▷ C₂×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₄ ◁ C₂³×C₄ ◁ #3449

Complements

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

N	H ≅ G/N	type
1. C₂×#15689890	C₂	semidirect
2. #20251907	C₂	semidirect
3. C₂×#15689097	C₂	semidirect
4. #20243916	C₂	semidirect
5. #20243911	C₂	semidirect
6. C₂×#15688879	C₂	semidirect
15. #15689132	C₂²	semidirect
16. #15689128	C₂²	semidirect
22. #15688879	C₂²	semidirect
26. C₄₇×#536	C₄	semidirect
28. C₄₇×#535	C₄	semidirect
31. C₄₇×#532	C₄	semidirect
44. C₂×#10625329	D₄	semidirect
47. C₂²×C₄₇⋊C₈	D₄	semidirect
83. C₄⋊Q₈×C₄₇	C₂×C₄	semidirect
84. #127×C₄₇	C₂×C₄	semidirect
85. #124×C₄₇	C₂×C₄	semidirect
86. #124×C₄₇	C₂×C₄	semidirect
314. #536	Dic₄₇	semidirect
316. #535	Dic₄₇	semidirect
319. #532	Dic₄₇	semidirect
332. C₄₇	#21009	semidirect
371. C₄⋊Q₈	C₂×Dic₄₇	semidirect
372. #127	C₂×Dic₄₇	semidirect
373. #124	C₂×Dic₄₇	semidirect
374. #124	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
#20251907	2
C₂×#15689097	2
#20243916	2
#20243911	2
C₂×#15688879	2
C₄₇×#3449	2
#21009	47