Subgroups — #26218284

Order 12032.

1732 conjugacy classes of subgroups.

The subgroup lattice has 610 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20256591	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#15689140	C₂	1	2	yes	maximal, complemented
3	C₂×#15689107	C₂	1	1	yes	maximal, characteristic, complemented
4	#20243926	C₂	1	4	yes	maximal, complemented
5	#20243921	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	C₂²×#10625329	C₂²	1	2	yes	—
9	#15689606	—	2	4	no	—
10	#15689601	C₂²	1	2	yes	complemented
11	#15689598	—	2	2	no	—
12	#15689598	C₂²	1	2	yes	complemented
13	#41×Dic₄₇	—	2	4	no	—
14	C₂×#13093983	—	2	2	no	—
15	C₂×#13093983	C₂²	1	2	yes	—
16	#15689140	—	2	4	no	—
17	#15689140	C₂²	1	8	yes	—
18	C₂×#13093951	—	2	4	no	—
19	#15689107	—	2	2	no	—
20	#15689107	—	2	2	no	—
21	C₂×#13093943	C₂²	1	2	yes	complemented
22	C₂×#13093941	C₂²	1	2	yes	complemented
23	#15688879	C₂²	1	8	yes	complemented
24	C₂²×#41×C₄₇	C₂²	1	1	yes	characteristic
25	C₂²×#41×C₄₇	C₂²	1	1	yes	characteristic
26	C₄₇×#537	—	2	2	no	—
27	C₄₇×#536	C₄	1	2	yes	complemented
28	C₄₇×#536	C₂²	1	2	yes	—
29	C₄₇×#535	C₄	1	2	yes	complemented
30	C₄₇×#535	C₂²	1	2	yes	—
31	C₄₇×#534	—	2	2	no	—
32	C₄₇×#532	C₄	1	4	yes	complemented
33	C₄₇×#525	—	2	2	no	—
34	C₄₇×#525	—	2	2	no	—
35	C₂×#117×C₄₇	C₂²	1	1	yes	characteristic
36	C₂×#10625329	—	2	2	no	—
37	C₂×#10625329	—	2	2	no	—
38	C₂×#10625329	—	2	2	no	—
39	C₂×#10625329	—	2	2	no	—
40	C₂×#10625329	—	2	2	no	—
41	C₂×#10625329	C₂³	1	4	yes	—
42	C₂²×C₄₇⋊C₈	—	2	2	no	—
43	Q₈×Dic₄₇	—	2	8	no	—
44	D₄×Dic₄₇	—	2	16	no	—
45	D₄×Dic₄₇	—	2	8	no	—
46	#13093983	—	2	4	no	—
47	#13093983	—	2	4	no	—
48	#13093983	—	2	2	no	—
49	#13093983	—	2	4	no	—
50	#13093983	—	2	2	no	—
51	#13093983	D₄	1	4	yes	complemented
52	#13093983	C₂³	1	4	yes	—
53	C₂×C₄⋊Dic₄₇	—	2	4	no	—
54	C₂×C₄⋊Dic₄₇	—	2	2	no	—
55	C₂×C₂²⋊Dic₄₇	—	2	4	no	—
56	C₂×C₂²⋊Dic₄₇	—	2	2	no	—
57	C₂×C₄×Dic₄₇	—	2	4	no	—
58	C₂×C₄×Dic₄₇	D₄	1	4	yes	complemented
59	#13093951	—	2	16	no	—
60	#13093943	—	2	4	no	—
61	#13093941	—	2	4	no	—
62	C₂×#41×C₄₇	—	2	2	no	—
63	C₂×#41×C₄₇	—	2	2	no	—
64	C₂×#41×C₄₇	—	2	1	no	—
65	C₂×#41×C₄₇	—	2	1	no	—
66	C₂×#41×C₄₇	—	2	2	no	—
67	C₂×#41×C₄₇	—	2	2	no	—
68	C₂×#41×C₄₇	—	2	2	no	—
69	C₂×#41×C₄₇	—	2	2	no	—
70	C₂×#41×C₄₇	—	2	2	no	—
71	C₂×#41×C₄₇	—	2	2	no	—
72	C₂×#41×C₄₇	C₂×C₄	1	2	yes	—
73	C₂×#41×C₄₇	C₂×C₄	1	2	yes	—
74	C₂×#41×C₄₇	C₂×C₄	1	2	yes	complemented
75	C₂×#41×C₄₇	D₄	1	2	yes	—
76	C₂×#41×C₄₇	D₄	1	2	yes	—
77	C₂×#41×C₄₇	C₂³	1	2	yes	—
78	C₂²×Q₈×C₄₇	C₂×C₄	1	1	yes	characteristic, complemented
79	C₂²×Q₈×C₄₇	C₂³	1	1	yes	characteristic
80	C₂²×D₄×C₄₇	—	2	1	no	—
81	C₂²×D₄×C₄₇	C₂×C₄	1	1	yes	characteristic, complemented
82	C₂²×D₄×C₄₇	D₄	1	2	yes	—
83	C₂²×D₄×C₄₇	C₂³	1	1	yes	characteristic
84	C₂³×C₄×C₄₇	—	2	1	no	—
85	C₂³×C₄×C₄₇	D₄	1	2	yes	—
86	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
87	C₄⋊Q₈×C₄₇	C₂×C₄	1	4	yes	complemented
88	#127×C₄₇	C₂×C₄	1	4	yes	complemented
89	#124×C₄₇	C₂×C₄	1	4	yes	complemented
90	#124×C₄₇	C₂×C₄	1	4	yes	complemented
91	#123×C₄₇	—	2	4	no	—
92	#123×C₄₇	—	2	4	no	—
93	C₂²⋊Q₈×C₄₇	—	2	4	no	—
94	C₂²⋊Q₈×C₄₇	—	2	4	no	—
95	#121×C₄₇	—	2	8	no	—
96	#121×C₄₇	—	2	4	no	—
97	#121×C₄₇	—	2	4	no	—
98	#120×C₄₇	—	2	4	no	—
99	#120×C₄₇	—	2	4	no	—
100	C₄×D₄×C₄₇	—	2	8	no	—
101	#117×C₄₇	—	2	1	no	—
102	#117×C₄₇	—	2	1	no	—
103	#117×C₄₇	C₂×C₄	1	2	yes	complemented
104	#117×C₄₇	C₂³	1	2	yes	—
105	C₂×C₄⋊C₄×C₄₇	—	2	1	no	—
106	C₂×C₂²⋊C₄×C₄₇	—	2	1	no	—
107	C₂×C₄²×C₄₇	C₂×C₄	1	2	yes	complemented
108	C₂⁴×C₄₇	—	2	1	no	—
109	C₂⁴×C₄₇	C₂×D₄	1	2	yes	—
110	C₂⁴×C₄₇	C₂×D₄	1	1	yes	characteristic
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	—	2	4	no	—
120	#41×C₄₇	—	2	4	no	—
121	#41×C₄₇	—	2	4	no	—
122	#41×C₄₇	—	2	4	no	—
123	#41×C₄₇	—	4	1	no	—
124	#41×C₄₇	—	4	1	no	—
125	#41×C₄₇	—	4	2	no	—
126	#41×C₄₇	—	4	2	no	—
127	#41×C₄₇	—	4	1	no	—
128	#41×C₄₇	—	4	1	no	—
129	C₂×Q₈×C₄₇	—	2	1	no	—
130	C₂×Q₈×C₄₇	—	2	2	no	—
131	C₂×Q₈×C₄₇	—	2	2	no	—
132	C₂×Q₈×C₄₇	—	2	2	no	—
133	C₂×Q₈×C₄₇	—	2	2	no	—
134	C₂×Q₈×C₄₇	C₂²×C₄	1	2	yes	—
135	C₂×Q₈×C₄₇	C₂²×C₄	1	2	yes	—
136	C₂×Q₈×C₄₇	C₂×D₄	1	2	yes	—
137	C₂×D₄×C₄₇	—	2	4	no	—
138	C₂×D₄×C₄₇	—	2	4	no	—
139	C₂×D₄×C₄₇	—	2	2	no	—
140	C₂×D₄×C₄₇	—	2	2	no	—
141	C₂×D₄×C₄₇	—	2	8	no	—
142	C₂×D₄×C₄₇	—	2	1	no	—
143	C₂×D₄×C₄₇	—	2	2	no	—
144	C₂×D₄×C₄₇	—	2	2	no	—
145	C₂×D₄×C₄₇	—	2	2	no	—
146	C₂×D₄×C₄₇	—	2	2	no	—
147	C₂×D₄×C₄₇	—	4	2	no	—
148	C₂×D₄×C₄₇	—	4	2	no	—
149	C₂×D₄×C₄₇	C₂²⋊C₄	1	4	yes	—
150	C₂×D₄×C₄₇	C₂²⋊C₄	1	4	yes	—
151	C₂×D₄×C₄₇	C₂²×C₄	1	2	yes	—
152	C₂×D₄×C₄₇	C₂²×C₄	1	2	yes	—
153	C₂×D₄×C₄₇	C₂×D₄	1	2	yes	—
154	C₂²×C₄×C₄₇	—	2	2	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	—	2	1	no	—
159	C₂²×C₄×C₄₇	—	2	2	no	—
160	C₂²×C₄×C₄₇	—	2	2	no	—
161	C₂²×C₄×C₄₇	—	2	2	no	—
162	C₂²×C₄×C₄₇	—	4	2	no	—
163	C₂²×C₄×C₄₇	—	4	2	no	—
164	C₂²×C₄×C₄₇	C₂²⋊C₄	1	4	yes	—
165	C₂²×C₄×C₄₇	C₂²⋊C₄	1	4	yes	—
166	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
167	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
168	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
169	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
170	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
171	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
172	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
173	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
174	C₂²×C₄×C₄₇	#41	1	2	yes	—
175	C₂²×C₄×C₄₇	#41	1	2	yes	—
176	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
177	C₂²×Dic₄₇	—	2	8	no	—
178	C₂²×Dic₄₇	—	2	4	no	—
179	C₄⋊C₄×C₄₇	—	2	2	no	—
180	C₄⋊C₄×C₄₇	—	2	8	no	—
181	C₄⋊C₄×C₄₇	—	2	2	no	—
182	C₂²⋊C₄×C₄₇	—	2	2	no	—
183	C₂²⋊C₄×C₄₇	—	2	8	no	—
184	C₂²⋊C₄×C₄₇	—	2	2	no	—
185	C₂²⋊C₄×C₄₇	—	2	8	no	—
186	C₄²×C₄₇	—	2	2	no	—
187	C₄²×C₄₇	C₂²×C₄	1	4	yes	—
188	C₂²⋊Dic₄₇	—	2	8	no	—
189	C₂²⋊Dic₄₇	—	2	4	no	—
190	C₂²⋊Dic₄₇	—	2	4	no	—
191	C₄⋊Dic₄₇	—	2	8	no	—
192	C₄⋊Dic₄₇	—	2	4	no	—
193	C₄⋊Dic₄₇	—	2	4	no	—
194	C₄×Dic₄₇	—	2	8	no	—
195	C₄×Dic₄₇	—	2	4	no	—
196	C₄×Dic₄₇	C₂×D₄	1	8	yes	—
197	#10625329	—	2	4	no	—
198	#10625329	—	2	4	no	—
199	#10625329	—	4	2	no	—
200	#10625329	—	4	2	no	—
201	C₂×C₄₇⋊C₈	—	2	4	no	—
202	C₂×C₄₇⋊C₈	—	4	2	no	—
203	C₂×C₄₇⋊C₈	—	4	2	no	—
204	C₂³×C₄₇	—	2	2	no	—
205	C₂³×C₄₇	—	2	2	no	—
206	C₂³×C₄₇	—	2	2	no	—
207	C₂³×C₄₇	—	4	2	no	—
208	C₂³×C₄₇	—	8	1	no	—
209	C₂³×C₄₇	—	8	2	no	—
210	C₂³×C₄₇	—	8	2	no	—
211	C₂³×C₄₇	C₂×C₂²⋊C₄	1	4	yes	—
212	C₂³×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
213	C₂³×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
214	C₂³×C₄₇	#120	1	2	yes	—
215	C₂³×C₄₇	#123	1	2	yes	—
216	C₂³×C₄₇	C₂²×D₄	1	1	yes	characteristic
217	Q₈×C₄₇	—	2	4	no	—
218	Q₈×C₄₇	—	2	4	no	—
219	Q₈×C₄₇	—	2	4	no	—
220	Q₈×C₄₇	—	4	1	no	—
221	Q₈×C₄₇	—	4	1	no	—
222	D₄×C₄₇	—	2	8	no	—
223	D₄×C₄₇	—	2	8	no	—
224	D₄×C₄₇	—	2	4	no	—
225	D₄×C₄₇	—	2	4	no	—
226	D₄×C₄₇	—	2	4	no	—
227	D₄×C₄₇	—	4	2	no	—
228	D₄×C₄₇	—	4	2	no	—
229	D₄×C₄₇	—	4	4	no	—
230	D₄×C₄₇	—	4	1	no	—
231	D₄×C₄₇	—	4	1	no	—
232	D₄×C₄₇	—	8	8	no	—
233	C₂×C₄×C₄₇	—	2	2	no	—
234	C₂×C₄×C₄₇	—	2	2	no	—
235	C₂×C₄×C₄₇	—	2	4	no	—
236	C₂×C₄×C₄₇	—	2	4	no	—
237	C₂×C₄×C₄₇	—	2	4	no	—
238	C₂×C₄×C₄₇	—	2	4	no	—
239	C₂×C₄×C₄₇	—	2	4	no	—
240	C₂×C₄×C₄₇	—	2	2	no	—
241	C₂×C₄×C₄₇	—	4	2	no	—
242	C₂×C₄×C₄₇	—	4	4	no	—
243	C₂×C₄×C₄₇	—	4	2	no	—
244	C₂×C₄×C₄₇	—	4	2	no	—
245	C₂×C₄×C₄₇	—	8	2	no	—
246	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	4	yes	—
247	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
248	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
249	C₂×C₄×C₄₇	C₄×D₄	1	2	yes	—
250	C₂×C₄×C₄₇	C₄×D₄	1	2	yes	—
251	C₂×C₄×C₄₇	C₄×D₄	1	2	yes	—
252	C₂×C₄×C₄₇	C₄×D₄	1	2	yes	—
253	C₂×C₄×C₄₇	#120	1	1	yes	characteristic
254	C₂×C₄×C₄₇	#120	1	1	yes	characteristic
255	C₂×C₄×C₄₇	#121	1	2	yes	—
256	C₂×C₄×C₄₇	#121	1	2	yes	—
257	C₂×C₄×C₄₇	#121	1	2	yes	—
258	C₂×C₄×C₄₇	#121	1	2	yes	—
259	C₂×C₄×C₄₇	#123	1	1	yes	characteristic
260	C₂×C₄×C₄₇	#123	1	1	yes	characteristic
261	C₂×C₄×C₄₇	C₂³×C₄	1	1	yes	characteristic
262	C₂×C₄×C₄₇	C₂²×D₄	1	2	yes	—
263	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
264	C₂×C₄×C₄₇	C₂×#41	1	2	yes	—
265	C₂×Dic₄₇	—	2	8	no	—
266	C₂×Dic₄₇	—	8	4	no	—
267	C₂×Dic₄₇	—	8	8	no	—
268	C₄₇⋊C₈	—	4	4	no	—
269	#21012	—	47	1	no	maximal, Sylow
270	C₂²×C₄₇	—	2	4	no	—
271	C₂²×C₄₇	—	4	2	no	—
272	C₂²×C₄₇	—	4	1	no	—
273	C₂²×C₄₇	—	4	1	no	—
274	C₂²×C₄₇	—	4	1	no	—
275	C₂²×C₄₇	—	4	2	no	—
276	C₂²×C₄₇	—	4	4	no	—
277	C₂²×C₄₇	—	4	4	no	—
278	C₂²×C₄₇	—	4	4	no	—
279	C₂²×C₄₇	—	4	2	no	—
280	C₂²×C₄₇	—	8	2	no	—
281	C₂²×C₄₇	—	8	4	no	—
282	C₂²×C₄₇	#386	1	2	yes	—
283	C₂²×C₄₇	#386	1	2	yes	—
284	C₂²×C₄₇	C₂²×C₂²⋊C₄	1	1	yes	characteristic
285	C₂²×C₄₇	C₂×#120	1	1	yes	characteristic
286	C₂²×C₄₇	C₂×#123	1	1	yes	characteristic
287	C₄×C₄₇	—	2	4	no	—
288	C₄×C₄₇	—	4	4	no	—
289	C₄×C₄₇	—	4	2	no	—
290	C₄×C₄₇	#386	1	1	yes	characteristic
291	C₄×C₄₇	#386	1	1	yes	characteristic
292	C₄×C₄₇	#386	1	1	yes	characteristic
293	C₄×C₄₇	#386	1	1	yes	characteristic
294	C₄×C₄₇	C₂×C₄×D₄	1	2	yes	—
295	C₄×C₄₇	C₂×#121	1	2	yes	—
296	Dic₄₇	—	4	8	no	—
297	#3449	D₄₇	1	1	yes	characteristic
298	#3428	—	47	1	no	—
299	C₂×#421	—	47	2	no	—
300	C₂×#413	—	47	1	no	—
301	#1912	—	47	4	no	—
302	#1911	—	47	4	no	—
303	C₂×H(3,ℤ/4)	—	47	2	no	—
304	C₂×C₄₇	—	2	1	no	—
305	C₂×C₄₇	—	2	1	no	—
306	C₂×C₄₇	—	2	1	no	—
307	C₂×C₄₇	—	2	2	no	—
308	C₂×C₄₇	—	2	2	no	—
309	C₂×C₄₇	—	4	4	no	—
310	C₂×C₄₇	—	8	2	no	—
311	C₂×C₄₇	C₂×#386	1	1	yes	characteristic
312	C₂²×#41	C₂×D₄₇	1	1	yes	characteristic
313	C₂²×#41	C₂×D₄₇	1	1	yes	characteristic
314	C₂²×M₁₆	—	47	2	no	—
315	#537	—	2	2	no	—
316	#536	Dic₄₇	1	2	yes	complemented
317	#536	C₂×D₄₇	1	2	yes	—
318	#535	Dic₄₇	1	2	yes	complemented
319	#535	C₂×D₄₇	1	2	yes	—
320	#534	—	2	2	no	—
321	#532	Dic₄₇	1	4	yes	complemented
322	#525	—	2	2	no	—
323	#525	—	2	2	no	—
324	#520	—	94	4	no	—
325	#519	—	47	2	no	—
326	#518	—	47	2	no	—
327	#518	—	94	2	no	—
328	C₄×#41	—	94	4	no	—
329	C₂×#117	—	47	2	no	—
330	C₂×#117	—	94	2	no	—
331	C₂×#117	C₂×D₄₇	1	1	yes	characteristic
332	#421	—	47	8	no	—
333	#421	—	94	4	no	—
334	C₂×#104	—	94	4	no	—
335	#413	—	94	2	no	—
336	#413	—	94	2	no	—
337	C₂×#101	—	47	2	no	—
338	C₂×#100	—	47	2	no	—
339	H(3,ℤ/4)	—	47	8	no	—
340	C₄₇	#21012	1	1	yes	characteristic, complemented, Sylow
341	C₂×#41	—	2	2	no	—
342	C₂×#41	—	2	2	no	—
343	C₂×#41	—	2	2	no	—
344	C₂×#41	—	2	2	no	—
345	C₂×#41	—	2	1	no	—
346	C₂×#41	—	2	1	no	—
347	C₂×#41	—	2	2	no	—
348	C₂×#41	—	2	2	no	—
349	C₂×#41	—	2	2	no	—
350	C₂×#41	—	2	2	no	—
351	C₂×#41	C₂×Dic₄₇	1	2	yes	—
352	C₂×#41	C₂×Dic₄₇	1	2	yes	—
353	C₂×#41	C₂×Dic₄₇	1	2	yes	complemented
354	C₂×#41	C₂²⋊D₄₇	1	2	yes	—
355	C₂×#41	C₂²⋊D₄₇	1	2	yes	—
356	C₂×#41	C₂²×D₄₇	1	2	yes	—
357	C₂²×Q₈	C₂×Dic₄₇	1	1	yes	characteristic, complemented
358	C₂²×Q₈	C₂²×D₄₇	1	1	yes	characteristic
359	C₂²×D₄	—	2	1	no	—
360	C₂²×D₄	C₂×Dic₄₇	1	1	yes	characteristic, complemented
361	C₂²×D₄	C₂²⋊D₄₇	1	2	yes	—
362	C₂²×D₄	C₂²×D₄₇	1	1	yes	characteristic
363	C₂³×C₄	—	2	1	no	—
364	C₂³×C₄	C₂²⋊D₄₇	1	2	yes	—
365	C₂³×C₄	C₂²×D₄₇	1	1	yes	characteristic
366	C₂×M₁₆	—	47	4	no	—
367	C₂×M₁₆	—	94	2	no	—
368	C₂×M₁₆	—	94	2	no	—
369	C₂×M₁₆	—	94	2	no	—
370	C₂×M₁₆	—	94	2	no	—
371	C₂×M₁₆	—	94	2	no	—
372	C₂²×C₈	—	94	2	no	—
373	C₄⋊Q₈	C₂×Dic₄₇	1	4	yes	complemented
374	#127	C₂×Dic₄₇	1	4	yes	complemented
375	#124	C₂×Dic₄₇	1	4	yes	complemented
376	#124	C₂×Dic₄₇	1	4	yes	complemented
377	#123	—	2	4	no	—
378	#123	—	2	4	no	—
379	C₂²⋊Q₈	—	2	4	no	—
380	C₂²⋊Q₈	—	2	4	no	—
381	#121	—	2	8	no	—
382	#121	—	2	4	no	—
383	#121	—	2	4	no	—
384	#120	—	2	4	no	—
385	#120	—	2	4	no	—
386	C₄×Q₈	—	94	8	no	—
387	C₄×D₄	—	2	8	no	—
388	C₄×D₄	—	94	8	no	—
389	C₄×D₄	—	94	16	no	—
390	#117	—	2	1	no	—
391	#117	—	2	1	no	—
392	#117	—	47	4	no	—
393	#117	—	47	4	no	—
394	#117	—	94	4	no	—
395	#117	—	94	4	no	—
396	#117	—	94	2	no	—
397	#117	—	94	2	no	—
398	#117	—	94	4	no	—
399	#117	C₂×Dic₄₇	1	2	yes	complemented
400	#117	C₂²×D₄₇	1	2	yes	—
401	C₂×C₄⋊C₄	—	2	1	no	—
402	C₂×C₄⋊C₄	—	94	4	no	—
403	C₂×C₄⋊C₄	—	94	2	no	—
404	C₂×C₂²⋊C₄	—	2	1	no	—
405	C₂×C₂²⋊C₄	—	94	2	no	—
406	C₂×C₂²⋊C₄	—	94	4	no	—
407	C₂×C₄²	—	47	4	no	—
408	C₂×C₄²	—	94	4	no	—
409	C₂×C₄²	C₂×Dic₄₇	1	2	yes	complemented
410	#104	—	94	16	no	—
411	#101	—	94	4	no	—
412	#100	—	94	4	no	—
413	C₂⁴	—	2	1	no	—
414	C₂⁴	C₂×C₂²⋊D₄₇	1	2	yes	—
415	C₂⁴	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
416	#41	—	2	4	no	—
417	#41	—	2	4	no	—
418	#41	—	2	4	no	—
419	#41	—	2	4	no	—
420	#41	—	2	4	no	—
421	#41	—	2	4	no	—
422	#41	—	2	4	no	—
423	#41	—	2	4	no	—
424	#41	—	2	4	no	—
425	#41	—	2	4	no	—
426	#41	—	2	4	no	—
427	#41	—	2	4	no	—
428	#41	—	4	1	no	—
429	#41	—	4	1	no	—
430	#41	—	4	2	no	—
431	#41	—	4	2	no	—
432	#41	—	4	1	no	—
433	#41	—	4	1	no	—
434	C₂×Q₈	—	2	1	no	—
435	C₂×Q₈	—	2	2	no	—
436	C₂×Q₈	—	2	2	no	—
437	C₂×Q₈	—	2	2	no	—
438	C₂×Q₈	—	2	2	no	—
439	C₂×Q₈	C₂²×Dic₄₇	1	2	yes	—
440	C₂×Q₈	C₂²×Dic₄₇	1	2	yes	—
441	C₂×Q₈	C₂×C₂²⋊D₄₇	1	2	yes	—
442	C₂×D₄	—	2	4	no	—
443	C₂×D₄	—	2	4	no	—
444	C₂×D₄	—	2	2	no	—
445	C₂×D₄	—	2	2	no	—
446	C₂×D₄	—	2	8	no	—
447	C₂×D₄	—	2	1	no	—
448	C₂×D₄	—	2	2	no	—
449	C₂×D₄	—	2	2	no	—
450	C₂×D₄	—	2	2	no	—
451	C₂×D₄	—	2	2	no	—
452	C₂×D₄	—	4	2	no	—
453	C₂×D₄	—	4	2	no	—
454	C₂×D₄	C₂²⋊Dic₄₇	1	4	yes	—
455	C₂×D₄	C₂²⋊Dic₄₇	1	4	yes	—
456	C₂×D₄	C₂²×Dic₄₇	1	2	yes	—
457	C₂×D₄	C₂²×Dic₄₇	1	2	yes	—
458	C₂×D₄	C₂×C₂²⋊D₄₇	1	2	yes	—
459	C₂²×C₄	—	2	2	no	—
460	C₂²×C₄	—	2	2	no	—
461	C₂²×C₄	—	2	2	no	—
462	C₂²×C₄	—	2	2	no	—
463	C₂²×C₄	—	2	1	no	—
464	C₂²×C₄	—	2	2	no	—
465	C₂²×C₄	—	2	2	no	—
466	C₂²×C₄	—	2	2	no	—
467	C₂²×C₄	—	4	2	no	—
468	C₂²×C₄	—	4	2	no	—
469	C₂²×C₄	—	94	8	no	—
470	C₂²×C₄	—	94	4	no	—
471	C₂²×C₄	C₂²⋊Dic₄₇	1	4	yes	—
472	C₂²×C₄	C₂²⋊Dic₄₇	1	4	yes	—
473	C₂²×C₄	D₄×D₄₇	1	2	yes	—
474	C₂²×C₄	D₄×D₄₇	1	2	yes	—
475	C₂²×C₄	#10625352	1	2	yes	—
476	C₂²×C₄	#10625352	1	2	yes	—
477	C₂²×C₄	C₂²×Dic₄₇	1	1	yes	characteristic
478	C₂²×C₄	C₂²×Dic₄₇	1	1	yes	characteristic
479	C₂²×C₄	C₂×C₂²⋊D₄₇	1	2	yes	—
480	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
481	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
482	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
483	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
484	M₁₆	—	94	4	no	—
485	M₁₆	—	94	4	no	—
486	M₁₆	—	188	2	no	—
487	M₁₆	—	188	2	no	—
488	C₂×C₈	—	94	4	no	—
489	C₂×C₈	—	188	2	no	—
490	C₂×C₈	—	188	2	no	—
491	C₄⋊C₄	—	2	2	no	—
492	C₄⋊C₄	—	2	8	no	—
493	C₄⋊C₄	—	2	2	no	—
494	C₄⋊C₄	—	94	8	no	—
495	C₄⋊C₄	—	94	4	no	—
496	C₄⋊C₄	—	94	4	no	—
497	C₂²⋊C₄	—	2	2	no	—
498	C₂²⋊C₄	—	2	8	no	—
499	C₂²⋊C₄	—	2	2	no	—
500	C₂²⋊C₄	—	2	8	no	—
501	C₂²⋊C₄	—	94	8	no	—
502	C₂²⋊C₄	—	94	4	no	—
503	C₂²⋊C₄	—	94	4	no	—
504	C₄²	—	2	2	no	—
505	C₄²	—	47	8	no	—
506	C₄²	—	94	8	no	—
507	C₄²	—	94	4	no	—
508	C₄²	C₂²×Dic₄₇	1	4	yes	—
509	C₂³	—	2	2	no	—
510	C₂³	—	2	2	no	—
511	C₂³	—	2	2	no	—
512	C₂³	—	4	2	no	—
513	C₂³	—	8	1	no	—
514	C₂³	—	8	2	no	—
515	C₂³	—	8	2	no	—
516	C₂³	C₂×C₂²⋊Dic₄₇	1	4	yes	—
517	C₂³	C₂×C₂²⋊Dic₄₇	1	1	yes	characteristic
518	C₂³	C₂×C₂²⋊Dic₄₇	1	1	yes	characteristic
519	C₂³	#13093992	1	2	yes	—
520	C₂³	#13094005	1	2	yes	—
521	C₂³	C₂²×C₂²⋊D₄₇	1	1	yes	characteristic
522	Q₈	—	2	4	no	—
523	Q₈	—	2	4	no	—
524	Q₈	—	2	4	no	—
525	Q₈	—	4	1	no	—
526	Q₈	—	4	1	no	—
527	D₄	—	2	8	no	—
528	D₄	—	2	8	no	—
529	D₄	—	2	4	no	—
530	D₄	—	2	4	no	—
531	D₄	—	2	4	no	—
532	D₄	—	4	4	no	—
533	D₄	—	4	2	no	—
534	D₄	—	4	2	no	—
535	D₄	—	4	1	no	—
536	D₄	—	4	1	no	—
537	D₄	—	8	8	no	—
538	C₂×C₄	—	2	2	no	—
539	C₂×C₄	—	2	2	no	—
540	C₂×C₄	—	2	4	no	—
541	C₂×C₄	—	2	4	no	—
542	C₂×C₄	—	2	4	no	—
543	C₂×C₄	—	2	4	no	—
544	C₂×C₄	—	2	4	no	—
545	C₂×C₄	—	2	2	no	—
546	C₂×C₄	—	4	2	no	—
547	C₂×C₄	—	4	2	no	—
548	C₂×C₄	—	4	2	no	—
549	C₂×C₄	—	4	4	no	—
550	C₂×C₄	—	8	2	no	—
551	C₂×C₄	—	94	8	no	—
552	C₂×C₄	—	376	4	no	—
553	C₂×C₄	—	376	8	no	—
554	C₂×C₄	C₂×C₂²⋊Dic₄₇	1	4	yes	—
555	C₂×C₄	C₂×C₂²⋊Dic₄₇	1	1	yes	characteristic
556	C₂×C₄	C₂×C₂²⋊Dic₄₇	1	1	yes	characteristic
557	C₂×C₄	D₄×Dic₄₇	1	2	yes	—
558	C₂×C₄	D₄×Dic₄₇	1	2	yes	—
559	C₂×C₄	D₄×Dic₄₇	1	2	yes	—
560	C₂×C₄	D₄×Dic₄₇	1	2	yes	—
561	C₂×C₄	#13093992	1	1	yes	characteristic
562	C₂×C₄	#13093992	1	1	yes	characteristic
563	C₂×C₄	#13093996	1	2	yes	—
564	C₂×C₄	#13093996	1	2	yes	—
565	C₂×C₄	#13093996	1	2	yes	—
566	C₂×C₄	#13093996	1	2	yes	—
567	C₂×C₄	#13094005	1	1	yes	characteristic
568	C₂×C₄	#13094005	1	1	yes	characteristic
569	C₂×C₄	C₂³×Dic₄₇	1	1	yes	characteristic
570	C₂×C₄	C₂×D₄×D₄₇	1	2	yes	—
571	C₂×C₄	C₂²×C₂²⋊D₄₇	1	1	yes	characteristic
572	C₂×C₄	C₂×#10625352	1	2	yes	—
573	C₈	—	188	4	no	—
574	C₂²	—	2	4	no	—
575	C₂²	—	4	1	no	—
576	C₂²	—	4	2	no	—
577	C₂²	—	4	1	no	—
578	C₂²	—	4	1	no	—
579	C₂²	—	4	2	no	—
580	C₂²	—	4	4	no	—
581	C₂²	—	4	4	no	—
582	C₂²	—	4	4	no	—
583	C₂²	—	4	2	no	—
584	C₂²	—	8	2	no	—
585	C₂²	—	8	4	no	—
586	C₂²	#15689003	1	2	yes	—
587	C₂²	#15689003	1	2	yes	—
588	C₂²	C₂²×C₂²⋊Dic₄₇	1	1	yes	characteristic
589	C₂²	C₂×#13093992	1	1	yes	characteristic
590	C₂²	C₂×#13094005	1	1	yes	characteristic
591	C₄	—	2	4	no	—
592	C₄	—	4	4	no	—
593	C₄	—	4	2	no	—
594	C₄	—	188	8	no	—
595	C₄	#15689003	1	1	yes	characteristic
596	C₄	#15689003	1	1	yes	characteristic
597	C₄	#15689003	1	1	yes	characteristic
598	C₄	#15689003	1	1	yes	characteristic
599	C₄	C₂×D₄×Dic₄₇	1	2	yes	—
600	C₄	C₂×#13093996	1	2	yes	—
601	C₂	—	2	1	no	—
602	C₂	—	2	1	no	—
603	C₂	—	2	2	no	—
604	C₂	—	2	1	no	—
605	C₂	—	2	2	no	—
606	C₂	—	4	4	no	—
607	C₂	—	8	2	no	—
608	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	#21012
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. #20256591	C₂	semidirect
2. C₂×#15689140	C₂	semidirect
3. C₂×#15689107	C₂	semidirect
4. #20243926	C₂	semidirect
5. #20243921	C₂	semidirect
6. C₂×#15688879	C₂	semidirect
10. #15689601	C₂²	semidirect
12. #15689598	C₂²	semidirect
21. C₂×#13093943	C₂²	semidirect
22. C₂×#13093941	C₂²	semidirect
23. #15688879	C₂²	semidirect
27. C₄₇×#536	C₄	semidirect
29. C₄₇×#535	C₄	semidirect
32. C₄₇×#532	C₄	semidirect
51. #13093983	D₄	semidirect
58. C₂×C₄×Dic₄₇	D₄	semidirect
74. C₂×#41×C₄₇	C₂×C₄	semidirect
78. C₂²×Q₈×C₄₇	C₂×C₄	semidirect
81. C₂²×D₄×C₄₇	C₂×C₄	semidirect
87. C₄⋊Q₈×C₄₇	C₂×C₄	semidirect
88. #127×C₄₇	C₂×C₄	semidirect
89. #124×C₄₇	C₂×C₄	semidirect
90. #124×C₄₇	C₂×C₄	semidirect
103. #117×C₄₇	C₂×C₄	semidirect
107. C₂×C₄²×C₄₇	C₂×C₄	semidirect
316. #536	Dic₄₇	semidirect
318. #535	Dic₄₇	semidirect
321. #532	Dic₄₇	semidirect
340. C₄₇	#21012	semidirect
353. C₂×#41	C₂×Dic₄₇	semidirect
357. C₂²×Q₈	C₂×Dic₄₇	semidirect
360. C₂²×D₄	C₂×Dic₄₇	semidirect
373. C₄⋊Q₈	C₂×Dic₄₇	semidirect
374. #127	C₂×Dic₄₇	semidirect
375. #124	C₂×Dic₄₇	semidirect
376. #124	C₂×Dic₄₇	semidirect
399. #117	C₂×Dic₄₇	semidirect
409. C₂×C₄²	C₂×Dic₄₇	semidirect

Maximal subgroups

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

subgroup	index
#20256591	2
C₂×#15689140	2
C₂×#15689107	2
#20243926	2
#20243921	2
C₂×#15688879	2
C₄₇×#3449	2
#21012	47