Subgroups — #26185185

Order 12032.

988 conjugacy classes of subgroups.

The subgroup lattice has 542 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20252520	C₂	1	1	yes	maximal, characteristic, complemented
2	#20252513	C₂	1	1	yes	maximal, characteristic, complemented
3	#20242126	C₂	1	1	yes	maximal, characteristic, complemented
4	#20242110	C₂	1	2	yes	maximal, complemented
5	#20242093	C₂	1	2	yes	maximal, complemented
6	#20242065	C₂	1	2	yes	maximal, complemented
7	#20242056	C₂	1	1	yes	maximal, characteristic, complemented
8	#20242056	C₂	1	1	yes	maximal, characteristic, complemented
9	#20242053	C₂	1	1	yes	maximal, characteristic, complemented
10	#20242037	C₂	1	2	yes	maximal, complemented
11	C₄₇×#3508	C₂	1	1	yes	maximal, characteristic
12	#15689254	—	2	1	no	—
13	Q₈×C₄₇⋊C₈	—	2	1	no	—
14	#15689201	—	2	2	no	—
15	#15689201	—	2	1	no	—
16	#15689195	—	2	2	no	—
17	D₄×C₄₇⋊C₈	—	2	1	no	—
18	#15689180	C₂²	1	2	yes	complemented
19	#15689176	C₂²	1	1	yes	characteristic
20	#15689176	C₂²	1	1	yes	characteristic
21	#15689176	C₂²	1	2	yes	complemented
22	#15689147	C₂²	1	1	yes	characteristic
23	#15689147	C₂²	1	1	yes	characteristic
24	#15689147	C₂²	1	2	yes	complemented
25	C₂×C₄⋊(C₄₇⋊C₈)	C₂²	1	2	yes	complemented
26	#15688869	C₂²	1	1	yes	characteristic, complemented
27	#15688869	C₂²	1	2	yes	complemented
28	#15688869	C₂²	1	1	yes	characteristic, complemented
29	#15688869	C₂²	1	1	yes	characteristic, complemented
30	#15688869	C₂²	1	1	yes	characteristic, complemented
31	#15688869	C₂²	1	2	yes	complemented
32	#15688867	C₂²	1	2	yes	—
33	#15688867	C₂²	1	2	yes	—
34	#15688867	C₂²	1	2	yes	—
35	#15688867	C₂²	1	2	yes	—
36	C₄₇×#559	—	2	1	no	—
37	C₄₇×#559	—	2	1	no	—
38	C₄₇×#550	—	2	1	no	—
39	C₄₇×#550	—	2	1	no	—
40	C₄₇×#546	—	2	2	no	—
41	C₄₇×#546	—	2	2	no	—
42	C₄₇×#540	C₄	1	4	yes	—
43	C₄₇×#535	C₄	1	2	yes	—
44	C₄₇×#533	C₂²	1	1	yes	characteristic
45	C₄₇×#532	C₂²	1	2	yes	—
46	C₄₇×#532	C₂²	1	2	yes	—
47	C₂×#127×C₄₇	C₂²	1	1	yes	characteristic
48	C₄₇×#518	C₄	1	2	yes	—
49	C₄×#41×C₄₇	C₂²	1	1	yes	characteristic
50	C₂×#10625329	—	2	1	no	—
51	C₂×#10625329	—	2	1	no	—
52	C₂×#10625329	—	2	2	no	—
53	C₂²×C₄₇⋊C₈	—	2	2	no	—
54	C₄⋊(C₄₇⋊C₈)	—	2	1	no	—
55	C₄⋊(C₄₇⋊C₈)	—	2	2	no	—
56	C₄⋊(C₄₇⋊C₈)	—	2	2	no	—
57	C₄⋊(C₄₇⋊C₈)	—	2	1	no	—
58	C₄⋊(C₄₇⋊C₈)	C₂³	1	1	yes	characteristic
59	C₄⋊(C₄₇⋊C₈)	C₂³	1	2	yes	—
60	C₄⋊(C₄₇⋊C₈)	C₂³	1	2	yes	—
61	C₄⋊(C₄₇⋊C₈)	C₂³	1	1	yes	characteristic
62	C₄⋊(C₄₇⋊C₈)	C₂³	1	1	yes	characteristic
63	C₄⋊(C₄₇⋊C₈)	C₂³	1	1	yes	characteristic
64	C₂²⋊(C₄₇⋊C₈)	—	2	1	no	—
65	C₂²⋊(C₄₇⋊C₈)	—	2	1	no	—
66	C₂²⋊(C₄₇⋊C₈)	—	2	2	no	—
67	C₂²⋊(C₄₇⋊C₈)	—	2	2	no	—
68	#13093935	—	2	2	no	—
69	C₄×C₄₇⋊C₈	—	2	1	no	—
70	C₄×C₄₇⋊C₈	—	2	2	no	—
71	C₄×C₄₇⋊C₈	—	2	1	no	—
72	C₂×#41×C₄₇	—	2	2	no	—
73	C₂×#41×C₄₇	—	2	2	no	—
74	C₂×#41×C₄₇	C₂×C₄	1	1	yes	characteristic
75	C₂²×D₄×C₄₇	—	2	1	no	—
76	C₂²×D₄×C₄₇	—	2	1	no	—
77	C₂²×D₄×C₄₇	C₂×C₄	1	2	yes	—
78	C₄⋊Q₈×C₄₇	C₂³	1	1	yes	characteristic
79	C₄⋊Q₈×C₄₇	C₂³	1	1	yes	characteristic
80	#127×C₄₇	—	2	2	no	—
81	#127×C₄₇	—	2	1	no	—
82	#127×C₄₇	—	2	1	no	—
83	#127×C₄₇	C₂×C₄	1	2	yes	—
84	#127×C₄₇	C₂³	1	2	yes	—
85	#125×C₄₇	C₂×C₄	1	2	yes	—
86	#124×C₄₇	—	2	2	no	—
87	#124×C₄₇	—	2	2	no	—
88	#124×C₄₇	—	2	2	no	—
89	#123×C₄₇	—	2	4	no	—
90	#123×C₄₇	—	2	4	no	—
91	C₂²⋊Q₈×C₄₇	—	2	1	no	—
92	C₂²⋊Q₈×C₄₇	—	2	1	no	—
93	#121×C₄₇	—	2	2	no	—
94	#121×C₄₇	—	2	2	no	—
95	#121×C₄₇	—	2	4	no	—
96	#121×C₄₇	—	2	4	no	—
97	#121×C₄₇	C₂×C₄	1	4	yes	—
98	#121×C₄₇	C₂×C₄	1	4	yes	—
99	#120×C₄₇	—	2	4	no	—
100	C₄×Q₈×C₄₇	—	2	1	no	—
101	C₄×Q₈×C₄₇	—	2	1	no	—
102	C₄×Q₈×C₄₇	D₄	1	1	yes	characteristic
103	C₄×Q₈×C₄₇	D₄	1	1	yes	characteristic
104	C₄×D₄×C₄₇	—	2	2	no	—
105	C₄×D₄×C₄₇	—	2	2	no	—
106	C₄×D₄×C₄₇	—	2	2	no	—
107	C₄×D₄×C₄₇	—	2	2	no	—
108	C₄×D₄×C₄₇	C₂×C₄	1	4	yes	—
109	C₄×D₄×C₄₇	C₂×C₄	1	4	yes	—
110	C₄×D₄×C₄₇	D₄	1	2	yes	—
111	C₄×D₄×C₄₇	D₄	1	2	yes	—
112	C₄×D₄×C₄₇	D₄	1	1	yes	characteristic
113	C₄×D₄×C₄₇	D₄	1	1	yes	characteristic
114	#117×C₄₇	C₂×C₄	1	2	yes	—
115	#117×C₄₇	C₂×C₄	1	1	yes	characteristic
116	#117×C₄₇	C₂×C₄	1	2	yes	—
117	C₂×C₂²⋊C₄×C₄₇	—	2	4	no	—
118	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
119	C₂×C₄²×C₄₇	C₂³	1	2	yes	—
120	C₂⁴×C₄₇	—	2	2	no	—
121	#41×C₄₇	—	4	2	no	—
122	#41×C₄₇	—	8	2	no	—
123	#41×C₄₇	—	8	2	no	—
124	#41×C₄₇	—	8	2	no	—
125	#41×C₄₇	—	8	2	no	—
126	C₂×Q₈×C₄₇	—	2	1	no	—
127	C₂×Q₈×C₄₇	—	2	1	no	—
128	C₂×Q₈×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
129	C₂×D₄×C₄₇	—	2	4	no	—
130	C₂×D₄×C₄₇	—	2	4	no	—
131	C₂×D₄×C₄₇	—	2	2	no	—
132	C₂×D₄×C₄₇	—	2	2	no	—
133	C₂×D₄×C₄₇	—	2	2	no	—
134	C₂×D₄×C₄₇	—	2	2	no	—
135	C₂×D₄×C₄₇	—	2	2	no	—
136	C₂×D₄×C₄₇	—	4	4	no	—
137	C₂×D₄×C₄₇	—	8	1	no	—
138	C₂×D₄×C₄₇	—	8	1	no	—
139	C₂×D₄×C₄₇	—	8	1	no	—
140	C₂×D₄×C₄₇	—	8	1	no	—
141	C₂×D₄×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
142	C₂×D₄×C₄₇	C₂²⋊C₄	1	2	yes	—
143	C₂×D₄×C₄₇	C₂²×C₄	1	4	yes	—
144	C₂²×C₄×C₄₇	—	2	4	no	—
145	C₂²×C₄×C₄₇	—	2	4	no	—
146	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
147	C₂²×C₄×C₄₇	C₂²×C₄	1	2	yes	—
148	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
149	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
150	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
151	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
152	C₄⋊C₄×C₄₇	—	2	2	no	—
153	C₄⋊C₄×C₄₇	—	2	2	no	—
154	C₄⋊C₄×C₄₇	—	2	1	no	—
155	C₄⋊C₄×C₄₇	—	2	1	no	—
156	C₄⋊C₄×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
157	C₄⋊C₄×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
158	C₄⋊C₄×C₄₇	C₂²⋊C₄	1	2	yes	—
159	C₄⋊C₄×C₄₇	C₂²⋊C₄	1	2	yes	—
160	C₄⋊C₄×C₄₇	C₂²×C₄	1	2	yes	—
161	C₄⋊C₄×C₄₇	C₂²×C₄	1	2	yes	—
162	C₂²⋊C₄×C₄₇	—	2	2	no	—
163	C₂²⋊C₄×C₄₇	—	2	4	no	—
164	C₂²⋊C₄×C₄₇	—	2	4	no	—
165	C₂²⋊C₄×C₄₇	—	2	4	no	—
166	C₂²⋊C₄×C₄₇	—	2	4	no	—
167	C₂²⋊C₄×C₄₇	C₂²⋊C₄	1	2	yes	—
168	C₂²⋊C₄×C₄₇	C₂²⋊C₄	1	2	yes	—
169	C₂²⋊C₄×C₄₇	C₂²⋊C₄	1	2	yes	—
170	C₄²×C₄₇	—	2	2	no	—
171	C₄²×C₄₇	C₂²×C₄	1	2	yes	—
172	C₄²×C₄₇	C₂²×C₄	1	1	yes	characteristic
173	C₄²×C₄₇	C₂×D₄	1	2	yes	—
174	C₄²×C₄₇	C₂×D₄	1	2	yes	—
175	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
176	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
177	C₄²×C₄₇	C₂⁴	1	1	yes	characteristic
178	#10625329	—	8	1	no	—
179	#10625329	—	8	1	no	—
180	#10625329	—	8	2	no	—
181	C₂×C₄₇⋊C₈	—	2	1	no	—
182	C₂×C₄₇⋊C₈	—	2	1	no	—
183	C₂×C₄₇⋊C₈	—	2	1	no	—
184	C₂×C₄₇⋊C₈	—	2	1	no	—
185	C₂×C₄₇⋊C₈	—	2	2	no	—
186	C₂×C₄₇⋊C₈	—	2	2	no	—
187	C₂×C₄₇⋊C₈	—	8	2	no	—
188	C₂³×C₄₇	—	2	4	no	—
189	C₂³×C₄₇	—	4	4	no	—
190	C₂³×C₄₇	—	8	2	no	—
191	C₂³×C₄₇	—	8	2	no	—
192	C₂³×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
193	C₂³×C₄₇	C₂×C₂²⋊C₄	1	2	yes	—
194	Q₈×C₄₇	—	2	2	no	—
195	Q₈×C₄₇	—	4	1	no	—
196	Q₈×C₄₇	—	4	1	no	—
197	Q₈×C₄₇	—	4	1	no	—
198	Q₈×C₄₇	—	4	1	no	—
199	D₄×C₄₇	—	2	2	no	—
200	D₄×C₄₇	—	4	2	no	—
201	D₄×C₄₇	—	4	4	no	—
202	D₄×C₄₇	—	4	2	no	—
203	D₄×C₄₇	—	4	2	no	—
204	D₄×C₄₇	—	4	2	no	—
205	D₄×C₄₇	—	4	2	no	—
206	D₄×C₄₇	—	4	4	no	—
207	D₄×C₄₇	—	8	2	no	—
208	D₄×C₄₇	—	8	2	no	—
209	D₄×C₄₇	—	8	4	no	—
210	D₄×C₄₇	—	8	4	no	—
211	C₂×C₄×C₄₇	—	2	2	no	—
212	C₂×C₄×C₄₇	—	2	1	no	—
213	C₂×C₄×C₄₇	—	2	1	no	—
214	C₂×C₄×C₄₇	—	2	2	no	—
215	C₂×C₄×C₄₇	—	2	1	no	—
216	C₂×C₄×C₄₇	—	2	1	no	—
217	C₂×C₄×C₄₇	—	2	2	no	—
218	C₂×C₄×C₄₇	—	2	2	no	—
219	C₂×C₄×C₄₇	—	2	2	no	—
220	C₂×C₄×C₄₇	—	2	2	no	—
221	C₂×C₄×C₄₇	—	2	2	no	—
222	C₂×C₄×C₄₇	—	4	2	no	—
223	C₂×C₄×C₄₇	—	8	4	no	—
224	C₂×C₄×C₄₇	—	8	4	no	—
225	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	2	yes	—
226	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	2	yes	—
227	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
228	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
229	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	2	yes	—
230	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
231	C₂×C₄×C₄₇	C₂³×C₄	1	1	yes	characteristic
232	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
233	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
234	C₄₇⋊C₈	—	4	1	no	—
235	C₄₇⋊C₈	—	4	2	no	—
236	C₄₇⋊C₈	—	4	1	no	—
237	C₄₇⋊C₈	—	4	2	no	—
238	C₄₇⋊C₈	—	4	1	no	—
239	C₄₇⋊C₈	—	4	1	no	—
240	#17776	—	47	1	no	maximal, Sylow
241	C₂²×C₄₇	—	2	1	no	—
242	C₂²×C₄₇	—	2	2	no	—
243	C₂²×C₄₇	—	2	2	no	—
244	C₂²×C₄₇	—	2	2	no	—
245	C₂²×C₄₇	—	2	1	no	—
246	C₂²×C₄₇	—	2	1	no	—
247	C₂²×C₄₇	—	4	4	no	—
248	C₂²×C₄₇	—	4	4	no	—
249	C₂²×C₄₇	—	4	4	no	—
250	C₂²×C₄₇	—	16	4	no	—
251	C₂²×C₄₇	C₂²×C₂²⋊C₄	1	1	yes	characteristic
252	C₄×C₄₇	—	2	1	no	—
253	C₄×C₄₇	—	2	2	no	—
254	C₄×C₄₇	—	2	2	no	—
255	C₄×C₄₇	—	2	2	no	—
256	C₄×C₄₇	—	2	1	no	—
257	C₄×C₄₇	—	2	1	no	—
258	C₄×C₄₇	—	4	2	no	—
259	C₄×C₄₇	—	4	2	no	—
260	C₄×C₄₇	#413	1	2	yes	—
261	C₄×C₄₇	#576	1	1	yes	characteristic
262	C₄×C₄₇	#576	1	1	yes	characteristic
263	C₄×C₄₇	#577	1	1	yes	characteristic
264	C₄×C₄₇	#577	1	1	yes	characteristic
265	#3508	D₄₇	1	1	yes	characteristic
266	#2991	—	47	1	no	—
267	#2990	—	47	1	no	—
268	#1561	—	47	1	no	—
269	#1557	—	47	2	no	—
270	#1553	—	47	2	no	—
271	#1547	—	47	2	no	—
272	#1545	—	47	1	no	—
273	#1545	—	47	1	no	—
274	#1544	—	47	1	no	—
275	#1540	—	47	2	no	—
276	C₂×C₄₇	—	4	2	no	—
277	C₂×C₄₇	—	4	1	no	—
278	C₂×C₄₇	—	8	4	no	—
279	C₂×C₄₇	C₂×#413	1	1	yes	characteristic
280	C₂×C₄₇	#2897	1	1	yes	characteristic
281	C₂×C₄₇	#2897	1	1	yes	characteristic
282	#559	—	2	1	no	—
283	#559	—	2	1	no	—
284	#550	—	2	1	no	—
285	#550	—	2	1	no	—
286	#546	—	2	2	no	—
287	#546	—	2	2	no	—
288	#540	Dic₄₇	1	4	yes	—
289	#535	Dic₄₇	1	2	yes	—
290	#533	C₂×D₄₇	1	1	yes	characteristic
291	#532	C₂×D₄₇	1	2	yes	—
292	#532	C₂×D₄₇	1	2	yes	—
293	C₂×#127	C₂×D₄₇	1	1	yes	characteristic
294	#518	Dic₄₇	1	2	yes	—
295	C₄×#41	C₂×D₄₇	1	1	yes	characteristic
296	#446	—	94	1	no	—
297	C₈×Q₈	—	94	1	no	—
298	#436	—	94	2	no	—
299	#436	—	94	1	no	—
300	#435	—	94	2	no	—
301	C₈×D₄	—	94	1	no	—
302	#432	—	47	2	no	—
303	#431	—	47	2	no	—
304	#431	—	47	1	no	—
305	#431	—	47	1	no	—
306	#423	—	47	1	no	—
307	#423	—	47	1	no	—
308	#423	—	47	2	no	—
309	C₂×C₄⋊C₈	—	47	2	no	—
310	#332	—	47	1	no	—
311	#332	—	47	2	no	—
312	#332	—	47	1	no	—
313	#332	—	47	1	no	—
314	#332	—	47	1	no	—
315	#332	—	47	2	no	—
316	#331	—	47	2	no	—
317	#331	—	47	2	no	—
318	#331	—	47	2	no	—
319	#331	—	47	2	no	—
320	C₄₇	#17776	1	1	yes	characteristic, complemented, Sylow
321	C₂×#41	—	2	2	no	—
322	C₂×#41	—	2	2	no	—
323	C₂×#41	C₂×Dic₄₇	1	1	yes	characteristic
324	C₂²×D₄	—	2	1	no	—
325	C₂²×D₄	—	2	1	no	—
326	C₂²×D₄	C₂×Dic₄₇	1	2	yes	—
327	C₂×M₁₆	—	94	1	no	—
328	C₂×M₁₆	—	94	2	no	—
329	C₂×M₁₆	—	94	1	no	—
330	C₂²×C₈	—	94	2	no	—
331	C₄⋊Q₈	C₂²×D₄₇	1	1	yes	characteristic
332	C₄⋊Q₈	C₂²×D₄₇	1	1	yes	characteristic
333	#127	—	2	2	no	—
334	#127	—	2	1	no	—
335	#127	—	2	1	no	—
336	#127	C₂×Dic₄₇	1	2	yes	—
337	#127	C₂²×D₄₇	1	2	yes	—
338	#125	C₂×Dic₄₇	1	2	yes	—
339	#124	—	2	2	no	—
340	#124	—	2	2	no	—
341	#124	—	2	2	no	—
342	#123	—	2	4	no	—
343	#123	—	2	4	no	—
344	C₂²⋊Q₈	—	2	1	no	—
345	C₂²⋊Q₈	—	2	1	no	—
346	#121	—	2	2	no	—
347	#121	—	2	2	no	—
348	#121	—	2	4	no	—
349	#121	—	2	4	no	—
350	#121	C₂×Dic₄₇	1	4	yes	—
351	#121	C₂×Dic₄₇	1	4	yes	—
352	#120	—	2	4	no	—
353	C₄×Q₈	—	2	1	no	—
354	C₄×Q₈	—	2	1	no	—
355	C₄×Q₈	C₂²⋊D₄₇	1	1	yes	characteristic
356	C₄×Q₈	C₂²⋊D₄₇	1	1	yes	characteristic
357	C₄×D₄	—	2	2	no	—
358	C₄×D₄	—	2	2	no	—
359	C₄×D₄	—	2	2	no	—
360	C₄×D₄	—	2	2	no	—
361	C₄×D₄	C₂×Dic₄₇	1	4	yes	—
362	C₄×D₄	C₂×Dic₄₇	1	4	yes	—
363	C₄×D₄	C₂²⋊D₄₇	1	2	yes	—
364	C₄×D₄	C₂²⋊D₄₇	1	2	yes	—
365	C₄×D₄	C₂²⋊D₄₇	1	1	yes	characteristic
366	C₄×D₄	C₂²⋊D₄₇	1	1	yes	characteristic
367	#117	C₂×Dic₄₇	1	2	yes	—
368	#117	C₂×Dic₄₇	1	1	yes	characteristic
369	#117	C₂×Dic₄₇	1	2	yes	—
370	C₂×C₂²⋊C₄	—	2	4	no	—
371	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
372	C₂×C₄²	C₂²×D₄₇	1	2	yes	—
373	C₄⋊C₈	—	47	1	no	—
374	C₄⋊C₈	—	47	2	no	—
375	C₄⋊C₈	—	47	2	no	—
376	C₄⋊C₈	—	47	1	no	—
377	C₄⋊C₈	—	47	1	no	—
378	C₄⋊C₈	—	47	1	no	—
379	C₄⋊C₈	—	94	2	no	—
380	C₄⋊C₈	—	94	1	no	—
381	C₄⋊C₈	—	94	2	no	—
382	C₄⋊C₈	—	94	1	no	—
383	C₂²⋊C₈	—	94	1	no	—
384	C₂²⋊C₈	—	94	2	no	—
385	C₂²⋊C₈	—	94	1	no	—
386	C₂²⋊C₈	—	94	2	no	—
387	#97	—	94	2	no	—
388	C₄×C₈	—	94	1	no	—
389	C₄×C₈	—	94	2	no	—
390	C₄×C₈	—	94	1	no	—
391	C₂⁴	—	2	2	no	—
392	#41	—	4	2	no	—
393	#41	—	8	2	no	—
394	#41	—	8	2	no	—
395	#41	—	8	2	no	—
396	#41	—	8	2	no	—
397	C₂×Q₈	—	2	1	no	—
398	C₂×Q₈	—	2	1	no	—
399	C₂×Q₈	C₂²⋊Dic₄₇	1	1	yes	characteristic
400	C₂×D₄	—	2	4	no	—
401	C₂×D₄	—	2	4	no	—
402	C₂×D₄	—	2	2	no	—
403	C₂×D₄	—	2	2	no	—
404	C₂×D₄	—	2	2	no	—
405	C₂×D₄	—	2	2	no	—
406	C₂×D₄	—	2	2	no	—
407	C₂×D₄	—	4	4	no	—
408	C₂×D₄	—	8	1	no	—
409	C₂×D₄	—	8	1	no	—
410	C₂×D₄	—	8	1	no	—
411	C₂×D₄	—	8	1	no	—
412	C₂×D₄	C₂²⋊Dic₄₇	1	1	yes	characteristic
413	C₂×D₄	C₂²⋊Dic₄₇	1	2	yes	—
414	C₂×D₄	C₂²×Dic₄₇	1	4	yes	—
415	C₂²×C₄	—	2	4	no	—
416	C₂²×C₄	—	2	4	no	—
417	C₂²×C₄	C₂²×Dic₄₇	1	1	yes	characteristic
418	C₂²×C₄	C₂²×Dic₄₇	1	2	yes	—
419	C₂²×C₄	C₂×C₂²⋊D₄₇	1	2	yes	—
420	C₂²×C₄	C₂×C₂²⋊D₄₇	1	2	yes	—
421	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
422	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
423	M₁₆	—	376	1	no	—
424	M₁₆	—	376	1	no	—
425	M₁₆	—	376	2	no	—
426	C₂×C₈	—	94	1	no	—
427	C₂×C₈	—	94	1	no	—
428	C₂×C₈	—	94	1	no	—
429	C₂×C₈	—	94	1	no	—
430	C₂×C₈	—	94	2	no	—
431	C₂×C₈	—	94	2	no	—
432	C₂×C₈	—	376	2	no	—
433	C₄⋊C₄	—	2	2	no	—
434	C₄⋊C₄	—	2	2	no	—
435	C₄⋊C₄	—	2	1	no	—
436	C₄⋊C₄	—	2	1	no	—
437	C₄⋊C₄	C₂²⋊Dic₄₇	1	1	yes	characteristic
438	C₄⋊C₄	C₂²⋊Dic₄₇	1	1	yes	characteristic
439	C₄⋊C₄	C₂²⋊Dic₄₇	1	2	yes	—
440	C₄⋊C₄	C₂²⋊Dic₄₇	1	2	yes	—
441	C₄⋊C₄	C₂²×Dic₄₇	1	2	yes	—
442	C₄⋊C₄	C₂²×Dic₄₇	1	2	yes	—
443	C₂²⋊C₄	—	2	2	no	—
444	C₂²⋊C₄	—	2	4	no	—
445	C₂²⋊C₄	—	2	4	no	—
446	C₂²⋊C₄	—	2	4	no	—
447	C₂²⋊C₄	—	2	4	no	—
448	C₂²⋊C₄	C₂²⋊Dic₄₇	1	2	yes	—
449	C₂²⋊C₄	C₂²⋊Dic₄₇	1	2	yes	—
450	C₂²⋊C₄	C₂²⋊Dic₄₇	1	2	yes	—
451	C₄²	—	2	2	no	—
452	C₄²	C₂²×Dic₄₇	1	2	yes	—
453	C₄²	C₂²×Dic₄₇	1	1	yes	characteristic
454	C₄²	C₂×C₂²⋊D₄₇	1	2	yes	—
455	C₄²	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
456	C₄²	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
457	C₄²	C₂×C₂²⋊D₄₇	1	2	yes	—
458	C₄²	C₂³×D₄₇	1	1	yes	characteristic
459	C₂³	—	2	4	no	—
460	C₂³	—	4	4	no	—
461	C₂³	—	8	2	no	—
462	C₂³	—	8	2	no	—
463	C₂³	C₂×C₂²⋊Dic₄₇	1	1	yes	characteristic
464	C₂³	C₂×C₂²⋊Dic₄₇	1	2	yes	—
465	Q₈	—	2	2	no	—
466	Q₈	—	4	1	no	—
467	Q₈	—	4	1	no	—
468	Q₈	—	4	1	no	—
469	Q₈	—	4	1	no	—
470	D₄	—	2	2	no	—
471	D₄	—	4	2	no	—
472	D₄	—	4	4	no	—
473	D₄	—	4	4	no	—
474	D₄	—	4	2	no	—
475	D₄	—	4	2	no	—
476	D₄	—	4	2	no	—
477	D₄	—	4	2	no	—
478	D₄	—	8	2	no	—
479	D₄	—	8	2	no	—
480	D₄	—	8	4	no	—
481	D₄	—	8	4	no	—
482	C₂×C₄	—	2	2	no	—
483	C₂×C₄	—	2	2	no	—
484	C₂×C₄	—	2	1	no	—
485	C₂×C₄	—	2	1	no	—
486	C₂×C₄	—	2	2	no	—
487	C₂×C₄	—	2	1	no	—
488	C₂×C₄	—	2	1	no	—
489	C₂×C₄	—	2	2	no	—
490	C₂×C₄	—	2	2	no	—
491	C₂×C₄	—	2	2	no	—
492	C₂×C₄	—	2	2	no	—
493	C₂×C₄	—	4	2	no	—
494	C₂×C₄	—	8	4	no	—
495	C₂×C₄	—	8	4	no	—
496	C₂×C₄	C₂×C₂²⋊Dic₄₇	1	2	yes	—
497	C₂×C₄	C₂×C₂²⋊Dic₄₇	1	2	yes	—
498	C₂×C₄	C₂×C₂²⋊Dic₄₇	1	1	yes	characteristic
499	C₂×C₄	C₂×C₂²⋊Dic₄₇	1	1	yes	characteristic
500	C₂×C₄	C₂×C₂²⋊Dic₄₇	1	2	yes	—
501	C₂×C₄	C₂×C₂²⋊Dic₄₇	1	1	yes	characteristic
502	C₂×C₄	C₂³×Dic₄₇	1	1	yes	characteristic
503	C₂×C₄	C₂²×C₂²⋊D₄₇	1	1	yes	characteristic
504	C₂×C₄	C₂²×C₂²⋊D₄₇	1	1	yes	characteristic
505	C₈	—	188	1	no	—
506	C₈	—	188	2	no	—
507	C₈	—	188	2	no	—
508	C₈	—	188	1	no	—
509	C₈	—	188	1	no	—
510	C₈	—	188	1	no	—
511	C₂²	—	2	2	no	—
512	C₂²	—	2	2	no	—
513	C₂²	—	2	1	no	—
514	C₂²	—	2	1	no	—
515	C₂²	—	2	1	no	—
516	C₂²	—	2	2	no	—
517	C₂²	—	4	4	no	—
518	C₂²	—	4	4	no	—
519	C₂²	—	4	4	no	—
520	C₂²	—	16	4	no	—
521	C₂²	C₂²×C₂²⋊Dic₄₇	1	1	yes	characteristic
522	C₄	—	2	2	no	—
523	C₄	—	2	2	no	—
524	C₄	—	2	1	no	—
525	C₄	—	2	1	no	—
526	C₄	—	2	1	no	—
527	C₄	—	2	2	no	—
528	C₄	—	4	2	no	—
529	C₄	—	4	2	no	—
530	C₄	#15689107	1	2	yes	—
531	C₄	#15689926	1	1	yes	characteristic
532	C₄	#15689926	1	1	yes	characteristic
533	C₄	#15689934	1	1	yes	characteristic
534	C₄	#15689934	1	1	yes	characteristic
535	C₂	—	4	1	no	—
536	C₂	—	4	2	no	—
537	C₂	—	8	4	no	—
538	C₂	C₂×#15689107	1	1	yes	characteristic
539	C₂	#20251914	1	1	yes	characteristic
540	C₂	#20251914	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂²×C₂²⋊Dic₄₇
commutator	C₂×C₄×C₄₇	C₂³×C₄
Frattini	C₄²	C₂³×D₄₇
Fitting, prime radical	C₄₇×#3508	C₂
socle	C₂²×C₄₇	C₂²×C₂²⋊C₄
cosocle	C₄²×C₄₇	C₂⁴
hypercenter	#3508	D₄₇
hypocenter	C₄₇	#17776
LCS	G ▷ C₂×C₄×C₄₇ ▷ C₂²×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂² ◁ C₄×#41 ◁ #3508

Complements

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

N	H ≅ G/N	type
1. #20252520	C₂	semidirect
2. #20252513	C₂	semidirect
3. #20242126	C₂	semidirect
4. #20242110	C₂	semidirect
5. #20242093	C₂	semidirect
6. #20242065	C₂	semidirect
7. #20242056	C₂	semidirect
8. #20242056	C₂	semidirect
9. #20242053	C₂	semidirect
10. #20242037	C₂	semidirect
18. #15689180	C₂²	semidirect
21. #15689176	C₂²	semidirect
24. #15689147	C₂²	semidirect
25. C₂×C₄⋊(C₄₇⋊C₈)	C₂²	semidirect
26. #15688869	C₂²	semidirect
27. #15688869	C₂²	semidirect
28. #15688869	C₂²	semidirect
29. #15688869	C₂²	semidirect
30. #15688869	C₂²	semidirect
31. #15688869	C₂²	semidirect
320. C₄₇	#17776	semidirect

Maximal subgroups

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

subgroup	index
#20252520	2
#20252513	2
#20242126	2
#20242110	2
#20242093	2
#20242065	2
#20242056	2
#20242053	2
#20242037	2
C₄₇×#3508	2
#17776	47