Subgroups — #26122670

Order 12032.

1074 conjugacy classes of subgroups.

The subgroup lattice has 598 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#15689129	C₂	1	1	yes	maximal, characteristic
2	C₂×#15689127	C₂	1	1	yes	maximal, characteristic
3	#20251806	C₂	1	1	yes	maximal, characteristic, complemented
4	#20245968	C₂	1	1	yes	maximal, characteristic
5	#20243120	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×#15688879	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₄₇×H(3,ℤ/4)	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂³×D₁₈₈	C₂²	1	1	yes	characteristic
9	C₂²×#10625329	C₂²	1	1	yes	characteristic
10	C₂×#13093983	C₂²	1	1	yes	characteristic
11	C₂×#13093983	C₂²	1	1	yes	characteristic
12	#15689129	—	2	2	no	—
13	#15689129	C₄	1	4	yes	complemented
14	#15689127	—	2	2	no	—
15	#15689127	C₄	1	4	yes	complemented
16	C₂×#13093946	—	2	2	no	—
17	C₂×#13093944	—	2	2	no	—
18	#15689081	—	2	2	no	—
19	#15689078	—	2	2	no	—
20	M₁₆×Dic₄₇	—	2	2	no	—
21	#15689025	C₄	1	4	yes	complemented
22	#15689024	—	2	2	no	—
23	#15688978	—	2	2	no	—
24	#15688889	—	2	2	no	—
25	#15688879	—	2	2	no	—
26	C₂²×M₁₆×C₄₇	C₂²	1	1	yes	characteristic
27	C₂×#117×C₄₇	C₂²	1	1	yes	characteristic
28	C₂×#117×C₄₇	C₂²	1	1	yes	characteristic
29	C₄₇×H(3,ℤ/4)	—	2	2	no	—
30	C₂⁴×D₄₇	—	2	1	no	—
31	C₂²×D₁₈₈	—	2	1	no	—
32	C₂²×D₁₈₈	—	2	1	no	—
33	C₂²×D₁₈₈	—	2	1	no	—
34	C₂²×D₁₈₈	—	2	1	no	—
35	C₂²×D₁₈₈	—	2	1	no	—
36	C₂²×D₁₈₈	—	2	1	no	—
37	C₂²×D₁₈₈	—	2	1	no	—
38	C₂²×D₁₈₈	—	2	1	no	—
39	C₂²×D₁₈₈	—	2	1	no	—
40	C₂²×D₁₈₈	—	2	1	no	—
41	C₂²×D₁₈₈	—	2	1	no	—
42	C₂²×D₁₈₈	C₂×C₄	1	2	yes	—
43	C₂²×D₁₈₈	C₂×C₄	1	2	yes	—
44	C₂²×D₁₈₈	C₂×C₄	1	2	yes	—
45	C₂×#10625329	—	2	1	no	—
46	C₂×#10625329	—	2	1	no	—
47	C₂×#10625329	—	2	1	no	—
48	C₂×#10625329	—	2	1	no	—
49	C₂×#10625329	C₂×C₄	1	2	yes	—
50	C₂×#10625329	D₄	1	2	yes	—
51	C₂²×C₄₇⋊C₈	D₄	1	2	yes	—
52	#13093983	—	2	1	no	—
53	#13093983	—	2	1	no	—
54	#13093983	—	2	1	no	—
55	#13093983	—	2	1	no	—
56	#13093983	—	2	1	no	—
57	#13093983	—	2	1	no	—
58	#13093983	—	2	1	no	—
59	#13093983	C₂×C₄	1	2	yes	—
60	C₂×C₄⋊Dic₄₇	—	2	1	no	—
61	C₂×C₄⋊Dic₄₇	C₂×C₄	1	2	yes	—
62	C₂×C₂²⋊Dic₄₇	—	2	1	no	—
63	C₂×C₂²⋊Dic₄₇	D₄	1	2	yes	—
64	C₂×(C₂×D₄₇)⋊C₄	—	2	8	no	—
65	C₂×C₄×Dic₄₇	—	2	1	no	—
66	C₂×C₄×Dic₄₇	D₄	1	2	yes	—
67	#13093946	—	2	8	no	—
68	#13093944	—	2	8	no	—
69	#13093934	—	2	4	no	—
70	C₈×Dic₄₇	—	2	4	no	—
71	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
72	C₂×M₁₆×C₄₇	—	2	1	no	—
73	C₂×M₁₆×C₄₇	—	2	1	no	—
74	C₂×M₁₆×C₄₇	—	2	1	no	—
75	C₂×M₁₆×C₄₇	—	2	1	no	—
76	C₂×M₁₆×C₄₇	C₂×C₄	1	2	yes	—
77	C₂×M₁₆×C₄₇	D₄	1	2	yes	—
78	C₂²×C₈×C₄₇	D₄	1	2	yes	—
79	#117×C₄₇	—	2	1	no	—
80	#117×C₄₇	—	2	1	no	—
81	#117×C₄₇	—	2	1	no	—
82	#117×C₄₇	—	2	1	no	—
83	#117×C₄₇	—	2	1	no	—
84	#117×C₄₇	—	2	1	no	—
85	#117×C₄₇	—	2	1	no	—
86	#117×C₄₇	C₂×C₄	1	2	yes	—
87	C₂×C₄⋊C₄×C₄₇	—	2	1	no	—
88	C₂×C₄⋊C₄×C₄₇	—	2	1	no	—
89	C₂×C₂²⋊C₄×C₄₇	—	2	1	no	—
90	C₂×C₂²⋊C₄×C₄₇	—	2	1	no	—
91	C₂×C₄²×C₄₇	—	2	1	no	—
92	C₂×C₄²×C₄₇	C₂×C₄	1	2	yes	—
93	C₂⁴×C₄₇	C₂×D₄	1	1	yes	characteristic
94	C₂³×D₄₇	—	2	2	no	—
95	C₂³×D₄₇	—	2	2	no	—
96	C₂³×D₄₇	—	2	2	no	—
97	C₂³×D₄₇	—	4	1	no	—
98	C₂³×D₄₇	—	4	1	no	—
99	C₂³×D₄₇	—	4	1	no	—
100	C₂³×D₄₇	—	4	1	no	—
101	C₂³×D₄₇	—	8	4	no	—
102	C₂²×C₄×C₄₇	—	2	2	no	—
103	C₂²×C₄×C₄₇	—	4	1	no	—
104	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
105	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
106	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
107	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
108	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
109	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
110	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
111	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
112	C₂²×C₄×C₄₇	#41	1	1	yes	characteristic
113	C₂²×C₄×C₄₇	#41	1	1	yes	characteristic
114	C₂²×C₄×C₄₇	#41	1	1	yes	characteristic
115	C₂²×C₄×C₄₇	#41	1	1	yes	characteristic
116	C₂²×C₄×C₄₇	#41	1	1	yes	characteristic
117	C₂²×C₄×C₄₇	#41	1	1	yes	characteristic
118	C₂²×Dic₄₇	—	4	1	no	—
119	C₂²×Dic₄₇	C₂²⋊C₄	1	4	yes	—
120	C₂×D₁₈₈	—	2	2	no	—
121	C₂×D₁₈₈	—	2	2	no	—
122	C₂×D₁₈₈	—	2	2	no	—
123	C₂×D₁₈₈	—	2	2	no	—
124	C₂×D₁₈₈	—	2	2	no	—
125	C₂×D₁₈₈	—	2	2	no	—
126	C₂×D₁₈₈	—	2	2	no	—
127	C₂×D₁₈₈	—	2	2	no	—
128	C₂×D₁₈₈	—	2	2	no	—
129	C₂×D₁₈₈	—	2	2	no	—
130	C₂×D₁₈₈	—	2	2	no	—
131	C₂×D₁₈₈	—	2	2	no	—
132	C₂×D₁₈₈	—	2	2	no	—
133	C₂×D₁₈₈	—	2	2	no	—
134	C₂×D₁₈₈	—	2	2	no	—
135	C₂×D₁₈₈	—	4	1	no	—
136	C₂×D₁₈₈	—	4	1	no	—
137	C₂×D₁₈₈	—	4	1	no	—
138	C₂×D₁₈₈	—	4	1	no	—
139	C₂×D₁₈₈	—	4	1	no	—
140	C₂×D₁₈₈	—	4	1	no	—
141	C₂×D₁₈₈	—	4	1	no	—
142	C₂×D₁₈₈	—	4	1	no	—
143	C₂×D₁₈₈	—	4	1	no	—
144	C₂×D₁₈₈	—	4	1	no	—
145	C₂×D₁₈₈	—	4	1	no	—
146	C₂×D₁₈₈	—	4	1	no	—
147	C₂×D₁₈₈	C₄²	1	4	yes	—
148	M₁₆×C₄₇	—	2	2	no	—
149	M₁₆×C₄₇	—	2	2	no	—
150	M₁₆×C₄₇	—	2	2	no	—
151	M₁₆×C₄₇	—	2	2	no	—
152	C₂×C₈×C₄₇	—	2	2	no	—
153	C₂×C₈×C₄₇	—	2	2	no	—
154	C₂×C₈×C₄₇	C₂²⋊C₄	1	4	yes	complemented
155	C₄⋊C₄×C₄₇	—	2	2	no	—
156	C₄⋊C₄×C₄₇	—	4	1	no	—
157	C₄⋊C₄×C₄₇	—	4	1	no	—
158	C₄⋊C₄×C₄₇	—	4	1	no	—
159	C₂²⋊C₄×C₄₇	—	2	2	no	—
160	C₂²⋊C₄×C₄₇	—	4	1	no	—
161	C₂²⋊C₄×C₄₇	—	4	1	no	—
162	C₂²⋊C₄×C₄₇	—	4	1	no	—
163	C₄²×C₄₇	—	2	2	no	—
164	C₄²×C₄₇	—	2	2	no	—
165	C₄²×C₄₇	—	2	2	no	—
166	C₄²×C₄₇	—	4	1	no	—
167	C₂²⋊Dic₄₇	—	2	2	no	—
168	C₂²⋊Dic₄₇	—	2	2	no	—
169	C₂²⋊Dic₄₇	—	2	2	no	—
170	C₂²⋊Dic₄₇	—	4	1	no	—
171	(C₂×D₄₇)⋊C₄	—	8	8	no	—
172	C₄⋊Dic₄₇	—	2	2	no	—
173	C₄⋊Dic₄₇	—	2	2	no	—
174	C₄⋊Dic₄₇	—	2	2	no	—
175	C₄⋊Dic₄₇	—	4	1	no	—
176	C₄×Dic₄₇	—	2	2	no	—
177	C₄×Dic₄₇	—	2	2	no	—
178	C₄×Dic₄₇	—	2	2	no	—
179	C₄×Dic₄₇	—	4	1	no	—
180	#10625329	—	2	2	no	—
181	#10625329	—	2	2	no	—
182	#10625329	—	2	2	no	—
183	#10625329	—	2	2	no	—
184	C₂×C₄₇⋊C₈	—	2	2	no	—
185	C₂×C₄₇⋊C₈	—	2	2	no	—
186	C₂×C₄₇⋊C₈	C₂²⋊C₄	1	4	yes	complemented
187	C₂³×C₄₇	—	4	2	no	—
188	C₂³×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
189	C₂³×C₄₇	C₄×D₄	1	1	yes	characteristic
190	C₂³×C₄₇	C₄×D₄	1	1	yes	characteristic
191	C₂³×C₄₇	#121	1	1	yes	characteristic
192	C₂³×C₄₇	#121	1	1	yes	characteristic
193	C₂³×C₄₇	#124	1	1	yes	characteristic
194	C₂³×C₄₇	#127	1	1	yes	characteristic
195	C₂²×D₄₇	—	2	4	no	—
196	C₂²×D₄₇	—	4	8	no	—
197	C₂²×D₄₇	—	4	2	no	—
198	C₂²×D₄₇	—	4	2	no	—
199	C₂²×D₄₇	—	4	2	no	—
200	C₂²×D₄₇	—	4	2	no	—
201	C₂²×D₄₇	—	4	2	no	—
202	C₂²×D₄₇	—	4	2	no	—
203	C₂²×D₄₇	—	8	4	no	—
204	C₂²×D₄₇	—	8	4	no	—
205	C₂²×D₄₇	—	8	4	no	—
206	C₂²×D₄₇	—	8	4	no	—
207	C₂²×D₄₇	—	8	4	no	—
208	C₂²×D₄₇	—	8	4	no	—
209	C₂×C₄×C₄₇	—	4	4	no	—
210	C₂×C₄×C₄₇	—	4	2	no	—
211	C₂×C₄×C₄₇	—	4	2	no	—
212	C₂×C₄×C₄₇	—	8	2	no	—
213	C₂×C₄×C₄₇	C₂×C₄²	1	1	yes	characteristic
214	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
215	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
216	C₂×C₄×C₄₇	#117	1	1	yes	characteristic
217	C₂×C₄×C₄₇	#117	1	1	yes	characteristic
218	C₂×C₄×C₄₇	#117	1	1	yes	characteristic
219	C₂×C₄×C₄₇	C₄×D₄	1	1	yes	characteristic
220	C₂×C₄×C₄₇	C₄×D₄	1	1	yes	characteristic
221	C₂×C₄×C₄₇	C₄×D₄	1	1	yes	characteristic
222	C₂×C₄×C₄₇	C₄×D₄	1	1	yes	characteristic
223	C₂×C₄×C₄₇	C₄×D₄	1	1	yes	characteristic
224	C₂×C₄×C₄₇	C₄×D₄	1	1	yes	characteristic
225	C₂×C₄×C₄₇	C₄×D₄	1	1	yes	characteristic
226	C₂×C₄×C₄₇	C₄×D₄	1	1	yes	characteristic
227	C₂×C₄×C₄₇	C₄×D₄	1	1	yes	characteristic
228	C₂×C₄×C₄₇	C₄×D₄	1	1	yes	characteristic
229	C₂×C₄×C₄₇	#120	1	1	yes	characteristic
230	C₂×C₄×C₄₇	#121	1	1	yes	characteristic
231	C₂×C₄×C₄₇	#121	1	1	yes	characteristic
232	C₂×C₄×C₄₇	#121	1	1	yes	characteristic
233	C₂×C₄×C₄₇	#121	1	1	yes	characteristic
234	C₂×C₄×C₄₇	#123	1	1	yes	characteristic
235	C₂×C₄×C₄₇	#123	1	1	yes	characteristic
236	C₂×C₄×C₄₇	#123	1	1	yes	characteristic
237	C₂×C₄×C₄₇	#124	1	1	yes	characteristic
238	C₂×C₄×C₄₇	#124	1	1	yes	characteristic
239	C₂×C₄×C₄₇	#126	1	1	yes	characteristic
240	C₂×C₄×C₄₇	#126	1	1	yes	characteristic
241	C₂×Dic₄₇	—	2	4	no	—
242	C₂×Dic₄₇	—	4	4	no	—
243	C₂×Dic₄₇	—	4	2	no	—
244	C₂×Dic₄₇	—	8	2	no	—
245	D₁₈₈	—	2	4	no	—
246	D₁₈₈	—	2	4	no	—
247	D₁₈₈	—	4	2	no	—
248	D₁₈₈	—	4	2	no	—
249	D₁₈₈	—	4	2	no	—
250	D₁₈₈	—	4	2	no	—
251	D₁₈₈	—	4	2	no	—
252	D₁₈₈	—	4	2	no	—
253	C₈×C₄₇	—	2	4	no	—
254	C₄₇⋊C₈	—	2	4	no	—
255	#10948	—	47	1	no	maximal, Sylow
256	C₂²×C₄₇	—	2	2	no	—
257	C₂²×C₄₇	—	2	2	no	—
258	C₂²×C₄₇	—	2	2	no	—
259	C₂²×C₄₇	—	4	1	no	—
260	C₂²×C₄₇	—	4	1	no	—
261	C₂²×C₄₇	—	4	1	no	—
262	C₂²×C₄₇	—	4	1	no	—
263	C₂²×C₄₇	C₄×C₂²⋊C₄	1	1	yes	characteristic
264	C₂²×C₄₇	#386	1	1	yes	characteristic
265	C₂²×C₄₇	#388	1	1	yes	characteristic
266	C₂²×C₄₇	#388	1	1	yes	characteristic
267	C₂²×C₄₇	#390	1	1	yes	characteristic
268	C₂²×C₄₇	#390	1	1	yes	characteristic
269	C₂²×C₄₇	#390	1	1	yes	characteristic
270	C₂×D₄₇	—	4	8	no	—
271	C₂×D₄₇	—	4	4	no	—
272	C₂×D₄₇	—	8	4	no	—
273	C₂×D₄₇	—	8	4	no	—
274	C₂×D₄₇	—	8	4	no	—
275	C₂×D₄₇	—	8	4	no	—
276	C₂×D₄₇	—	8	4	no	—
277	C₂×D₄₇	—	8	4	no	—
278	C₄×C₄₇	—	8	2	no	—
279	C₄×C₄₇	—	8	2	no	—
280	C₄×C₄₇	C₄×C₂²⋊C₄	1	1	yes	characteristic
281	C₄×C₄₇	C₄×C₂²⋊C₄	1	1	yes	characteristic
282	C₄×C₄₇	#386	1	1	yes	characteristic
283	C₄×C₄₇	#386	1	1	yes	characteristic
284	C₄×C₄₇	#388	1	1	yes	characteristic
285	C₄×C₄₇	#388	1	1	yes	characteristic
286	C₄×C₄₇	#388	1	1	yes	characteristic
287	C₄×C₄₇	#388	1	1	yes	characteristic
288	Dic₄₇	—	4	4	no	—
289	Dic₄₇	—	8	2	no	—
290	C₂×#418	—	47	1	no	—
291	C₂×#418	—	47	1	no	—
292	#2873	—	47	1	no	—
293	#2309	—	47	1	no	—
294	#1740	—	47	1	no	—
295	C₂×H(3,ℤ/4)	—	47	1	no	—
296	C₂×H(3,ℤ/4)	D₄₇	1	1	yes	characteristic, complemented
297	C₂×C₄₇	—	2	1	no	—
298	C₂×C₄₇	—	2	1	no	—
299	C₂×C₄₇	—	2	1	no	—
300	C₂×C₄₇	—	2	1	no	—
301	C₂×C₄₇	—	2	1	no	—
302	C₂×C₄₇	—	2	1	no	—
303	C₂×C₄₇	#1437	1	1	yes	characteristic
304	C₂×C₄₇	#1910	1	2	yes	—
305	D₄₇	—	8	4	no	—
306	C₂³×D₄	—	47	1	no	—
307	C₂²×M₁₆	—	47	1	no	—
308	C₂²×M₁₆	C₂×D₄₇	1	1	yes	characteristic
309	C₂×#117	—	47	1	no	—
310	C₂×#117	—	47	1	no	—
311	C₂×#117	C₂×D₄₇	1	1	yes	characteristic
312	C₂×#117	C₂×D₄₇	1	1	yes	characteristic
313	#418	—	47	4	no	—
314	#418	—	47	4	no	—
315	#418	—	94	2	no	—
316	#418	—	94	2	no	—
317	C₂×#102	—	94	2	no	—
318	C₂×#102	—	94	2	no	—
319	#405	—	94	2	no	—
320	#405	—	94	2	no	—
321	C₄×M₁₆	—	94	2	no	—
322	#390	—	47	4	no	—
323	#390	—	94	2	no	—
324	#379	—	94	2	no	—
325	#342	—	94	2	no	—
326	H(3,ℤ/4)	—	2	2	no	—
327	H(3,ℤ/4)	—	94	2	no	—
328	C₄₇	#10948	1	1	yes	characteristic, complemented, Sylow
329	C₂⁵	—	94	1	no	—
330	C₂²×D₄	—	47	2	no	—
331	C₂²×D₄	—	47	2	no	—
332	C₂²×D₄	—	47	2	no	—
333	C₂²×D₄	—	94	1	no	—
334	C₂²×D₄	—	94	1	no	—
335	C₂²×D₄	—	94	1	no	—
336	C₂²×D₄	—	94	1	no	—
337	C₂²×D₄	—	94	1	no	—
338	C₂²×D₄	—	94	1	no	—
339	C₂²×D₄	—	94	1	no	—
340	C₂²×D₄	—	94	1	no	—
341	C₂²×D₄	—	94	1	no	—
342	C₂²×D₄	—	94	1	no	—
343	C₂²×D₄	—	94	1	no	—
344	C₂³×C₄	C₂²×D₄₇	1	1	yes	characteristic
345	C₂×M₁₆	—	2	1	no	—
346	C₂×M₁₆	—	2	1	no	—
347	C₂×M₁₆	—	2	1	no	—
348	C₂×M₁₆	—	2	1	no	—
349	C₂×M₁₆	—	47	2	no	—
350	C₂×M₁₆	—	47	2	no	—
351	C₂×M₁₆	—	94	1	no	—
352	C₂×M₁₆	—	94	1	no	—
353	C₂×M₁₆	—	94	1	no	—
354	C₂×M₁₆	—	94	1	no	—
355	C₂×M₁₆	C₄×D₄₇	1	2	yes	—
356	C₂×M₁₆	C₂²⋊D₄₇	1	2	yes	—
357	C₂²×C₈	—	47	2	no	—
358	C₂²×C₈	D₁₈₈	1	2	yes	—
359	#117	—	2	1	no	—
360	#117	—	2	1	no	—
361	#117	—	2	1	no	—
362	#117	—	2	1	no	—
363	#117	—	2	1	no	—
364	#117	—	2	1	no	—
365	#117	—	2	1	no	—
366	#117	—	47	2	no	—
367	#117	—	94	1	no	—
368	#117	—	94	1	no	—
369	#117	—	94	1	no	—
370	#117	—	94	1	no	—
371	#117	—	94	1	no	—
372	#117	—	94	1	no	—
373	#117	—	94	1	no	—
374	#117	C₄×D₄₇	1	2	yes	—
375	C₂×C₄⋊C₄	—	2	1	no	—
376	C₂×C₄⋊C₄	—	2	1	no	—
377	C₂×C₄⋊C₄	—	47	2	no	—
378	C₂×C₄⋊C₄	—	94	1	no	—
379	C₂×C₂²⋊C₄	—	2	1	no	—
380	C₂×C₂²⋊C₄	—	2	1	no	—
381	C₂×C₂²⋊C₄	—	47	2	no	—
382	C₂×C₂²⋊C₄	—	94	1	no	—
383	C₂×C₂²⋊C₄	—	94	8	no	—
384	C₂×C₄²	—	2	1	no	—
385	C₂×C₄²	—	47	2	no	—
386	C₂×C₄²	—	94	1	no	—
387	C₂×C₄²	C₄×D₄₇	1	2	yes	—
388	#102	—	94	8	no	—
389	#102	—	94	8	no	—
390	#97	—	94	4	no	—
391	C₄×C₈	—	94	4	no	—
392	C₂⁴	—	94	2	no	—
393	C₂⁴	—	94	2	no	—
394	C₂⁴	—	94	2	no	—
395	C₂⁴	—	376	4	no	—
396	C₂⁴	—	188	1	no	—
397	C₂⁴	—	188	1	no	—
398	C₂⁴	—	188	1	no	—
399	C₂⁴	—	188	1	no	—
400	C₂⁴	D₄×D₄₇	1	1	yes	characteristic
401	C₂×D₄	—	47	4	no	—
402	C₂×D₄	—	94	2	no	—
403	C₂×D₄	—	94	2	no	—
404	C₂×D₄	—	94	2	no	—
405	C₂×D₄	—	94	2	no	—
406	C₂×D₄	—	94	2	no	—
407	C₂×D₄	—	94	2	no	—
408	C₂×D₄	—	94	2	no	—
409	C₂×D₄	—	94	2	no	—
410	C₂×D₄	—	94	2	no	—
411	C₂×D₄	—	94	2	no	—
412	C₂×D₄	—	94	2	no	—
413	C₂×D₄	—	94	2	no	—
414	C₂×D₄	—	94	2	no	—
415	C₂×D₄	—	94	2	no	—
416	C₂×D₄	—	94	2	no	—
417	C₂×D₄	—	188	1	no	—
418	C₂×D₄	—	188	1	no	—
419	C₂×D₄	—	188	1	no	—
420	C₂×D₄	—	188	1	no	—
421	C₂×D₄	—	188	1	no	—
422	C₂×D₄	—	188	1	no	—
423	C₂×D₄	—	188	1	no	—
424	C₂×D₄	—	188	1	no	—
425	C₂×D₄	—	188	1	no	—
426	C₂×D₄	—	188	1	no	—
427	C₂×D₄	—	188	1	no	—
428	C₂×D₄	—	188	1	no	—
429	C₂²×C₄	—	2	2	no	—
430	C₂²×C₄	—	4	1	no	—
431	C₂²×C₄	—	47	4	no	—
432	C₂²×C₄	—	188	1	no	—
433	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
434	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
435	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
436	C₂²×C₄	C₂×D₁₈₈	1	1	yes	characteristic
437	C₂²×C₄	#10625350	1	1	yes	characteristic
438	C₂²×C₄	#10625350	1	1	yes	characteristic
439	C₂²×C₄	D₄×D₄₇	1	1	yes	characteristic
440	C₂²×C₄	D₄×D₄₇	1	1	yes	characteristic
441	C₂²×C₄	D₄×D₄₇	1	1	yes	characteristic
442	C₂²×C₄	#10625352	1	1	yes	characteristic
443	C₂²×C₄	#10625352	1	1	yes	characteristic
444	C₂²×C₄	#10625354	1	1	yes	characteristic
445	C₂²×C₄	#10625354	1	1	yes	characteristic
446	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
447	M₁₆	—	2	2	no	—
448	M₁₆	—	2	2	no	—
449	M₁₆	—	2	2	no	—
450	M₁₆	—	2	2	no	—
451	M₁₆	—	94	2	no	—
452	M₁₆	—	94	2	no	—
453	M₁₆	—	94	2	no	—
454	M₁₆	—	94	2	no	—
455	C₂×C₈	—	2	2	no	—
456	C₂×C₈	—	2	2	no	—
457	C₂×C₈	—	47	4	no	—
458	C₂×C₈	—	94	2	no	—
459	C₂×C₈	—	94	2	no	—
460	C₂×C₈	(C₂×D₄₇)⋊C₄	1	4	yes	complemented
461	C₄⋊C₄	—	2	2	no	—
462	C₄⋊C₄	—	4	1	no	—
463	C₄⋊C₄	—	4	1	no	—
464	C₄⋊C₄	—	4	1	no	—
465	C₄⋊C₄	—	94	2	no	—
466	C₄⋊C₄	—	94	2	no	—
467	C₄⋊C₄	—	94	2	no	—
468	C₄⋊C₄	—	188	1	no	—
469	C₂²⋊C₄	—	2	2	no	—
470	C₂²⋊C₄	—	4	1	no	—
471	C₂²⋊C₄	—	4	1	no	—
472	C₂²⋊C₄	—	4	1	no	—
473	C₂²⋊C₄	—	94	2	no	—
474	C₂²⋊C₄	—	94	2	no	—
475	C₂²⋊C₄	—	94	2	no	—
476	C₂²⋊C₄	—	376	8	no	—
477	C₂²⋊C₄	—	188	1	no	—
478	C₄²	—	2	2	no	—
479	C₄²	—	2	2	no	—
480	C₄²	—	2	2	no	—
481	C₄²	—	4	1	no	—
482	C₄²	—	94	2	no	—
483	C₄²	—	94	2	no	—
484	C₄²	—	94	2	no	—
485	C₄²	—	188	1	no	—
486	C₂³	—	4	2	no	—
487	C₂³	—	94	4	no	—
488	C₂³	—	376	4	no	—
489	C₂³	—	376	4	no	—
490	C₂³	—	376	4	no	—
491	C₂³	—	376	4	no	—
492	C₂³	—	376	4	no	—
493	C₂³	—	376	4	no	—
494	C₂³	—	188	8	no	—
495	C₂³	—	188	2	no	—
496	C₂³	—	188	2	no	—
497	C₂³	—	188	2	no	—
498	C₂³	—	188	2	no	—
499	C₂³	—	188	2	no	—
500	C₂³	—	188	2	no	—
501	C₂³	C₂²⋊C₄×D₄₇	1	1	yes	characteristic
502	C₂³	(C₂²⋊D₄₇)⋊C₄	1	1	yes	characteristic
503	C₂³	#13093986	1	1	yes	characteristic
504	C₂³	#13093997	1	1	yes	characteristic
505	C₂³	#13093999	1	1	yes	characteristic
506	C₂³	#13094010	1	1	yes	characteristic
507	C₂³	#13094020	1	1	yes	characteristic
508	D₄	—	94	4	no	—
509	D₄	—	94	4	no	—
510	D₄	—	188	2	no	—
511	D₄	—	188	2	no	—
512	D₄	—	188	2	no	—
513	D₄	—	188	2	no	—
514	D₄	—	188	2	no	—
515	D₄	—	188	2	no	—
516	C₂×C₄	—	4	4	no	—
517	C₂×C₄	—	4	2	no	—
518	C₂×C₄	—	4	2	no	—
519	C₂×C₄	—	8	2	no	—
520	C₂×C₄	—	94	4	no	—
521	C₂×C₄	—	376	2	no	—
522	C₂×C₄	—	188	2	no	—
523	C₂×C₄	—	188	4	no	—
524	C₂×C₄	C₄²×D₄₇	1	1	yes	characteristic
525	C₂×C₄	C₂²⋊C₄×D₄₇	1	1	yes	characteristic
526	C₂×C₄	C₂×(C₂×D₄₇)⋊C₄	1	1	yes	characteristic
527	C₂×C₄	#13093981	1	1	yes	characteristic
528	C₂×C₄	#13093982	1	1	yes	characteristic
529	C₂×C₄	#13093982	1	1	yes	characteristic
530	C₂×C₄	(C₂²⋊D₄₇)⋊C₄	1	1	yes	characteristic
531	C₂×C₄	(C₂²⋊D₄₇)⋊C₄	1	1	yes	characteristic
532	C₂×C₄	(C₂²⋊D₄₇)⋊C₄	1	1	yes	characteristic
533	C₂×C₄	C₄×C₂²⋊D₄₇	1	1	yes	characteristic
534	C₂×C₄	C₄×C₂²⋊D₄₇	1	1	yes	characteristic
535	C₂×C₄	#13093986	1	1	yes	characteristic
536	C₂×C₄	#13093986	1	1	yes	characteristic
537	C₂×C₄	#13093986	1	1	yes	characteristic
538	C₂×C₄	C₄×D₁₈₈	1	1	yes	characteristic
539	C₂×C₄	C₄×D₁₈₈	1	1	yes	characteristic
540	C₂×C₄	#13093994	1	1	yes	characteristic
541	C₂×C₄	#13093996	1	1	yes	characteristic
542	C₂×C₄	#13093996	1	1	yes	characteristic
543	C₂×C₄	#13093997	1	1	yes	characteristic
544	C₂×C₄	#13093999	1	1	yes	characteristic
545	C₂×C₄	#13094008	1	1	yes	characteristic
546	C₂×C₄	#13094009	1	1	yes	characteristic
547	C₂×C₄	#13094009	1	1	yes	characteristic
548	C₂×C₄	#13094010	1	1	yes	characteristic
549	C₂×C₄	#13094013	1	1	yes	characteristic
550	C₂×C₄	#13094019	1	1	yes	characteristic
551	C₂×C₄	#13094019	1	1	yes	characteristic
552	C₈	—	2	4	no	—
553	C₈	—	94	4	no	—
554	C₂²	—	2	2	no	—
555	C₂²	—	2	2	no	—
556	C₂²	—	2	2	no	—
557	C₂²	—	4	1	no	—
558	C₂²	—	4	1	no	—
559	C₂²	—	4	1	no	—
560	C₂²	—	4	1	no	—
561	C₂²	—	376	4	no	—
562	C₂²	—	376	4	no	—
563	C₂²	—	376	4	no	—
564	C₂²	—	376	4	no	—
565	C₂²	—	376	4	no	—
566	C₂²	—	376	4	no	—
567	C₂²	—	188	8	no	—
568	C₂²	—	188	4	no	—
569	C₂²	#15688970	1	1	yes	characteristic
570	C₂²	#15689001	1	1	yes	characteristic
571	C₂²	#15689012	1	1	yes	characteristic
572	C₂²	#15689015	1	1	yes	characteristic
573	C₂²	#15689023	1	1	yes	characteristic
574	C₂²	#15689023	1	1	yes	characteristic
575	C₂²	#15689024	1	1	yes	characteristic
576	C₄	—	8	2	no	—
577	C₄	—	8	2	no	—
578	C₄	—	376	2	no	—
579	C₄	—	188	4	no	—
580	C₄	#15688970	1	1	yes	characteristic
581	C₄	C₄×(C₂×D₄₇)⋊C₄	1	1	yes	characteristic
582	C₄	#15689000	1	1	yes	characteristic
583	C₄	#15689001	1	1	yes	characteristic
584	C₄	#15689012	1	1	yes	characteristic
585	C₄	#15689013	1	1	yes	characteristic
586	C₄	#15689013	1	1	yes	characteristic
587	C₄	#15689015	1	1	yes	characteristic
588	C₂	—	2	1	no	—
589	C₂	—	2	1	no	—
590	C₂	—	2	1	no	—
591	C₂	—	2	1	no	—
592	C₂	—	2	1	no	—
593	C₂	—	2	1	no	—
594	C₂	—	376	4	no	—
595	C₂	#20241624	1	1	yes	characteristic
596	C₂	#20243914	1	2	yes	—

	subgroup	G/H
center	C₂²	#15689001
commutator	C₂×C₄×C₄₇	C₂×C₄²
Frattini	C₂³×C₄	C₂²×D₄₇
Fitting	C₂×C₄₇×H(3,ℤ/4)	C₂
socle	C₂²×C₄₇	#386
prime radical	C₂³×D₁₈₈	C₂²
cosocle	C₂³×C₄×C₄₇	C₂³
hypercenter	C₂×H(3,ℤ/4)	D₄₇
hypocenter	C₄₇	#10948
LCS	G ▷ C₂×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂² ◁ C₂³×C₄ ◁ C₂×H(3,ℤ/4)

Complements

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

N	H ≅ G/N	type
3. #20251806	C₂	semidirect
5. #20243120	C₂	semidirect
6. C₂×#15688879	C₂	semidirect
7. C₂×C₄₇×H(3,ℤ/4)	C₂	semidirect
13. #15689129	C₄	semidirect
15. #15689127	C₄	semidirect
21. #15689025	C₄	semidirect
154. C₂×C₈×C₄₇	C₂²⋊C₄	semidirect
186. C₂×C₄₇⋊C₈	C₂²⋊C₄	semidirect
296. C₂×H(3,ℤ/4)	D₄₇	semidirect
328. C₄₇	#10948	semidirect
460. C₂×C₈	(C₂×D₄₇)⋊C₄	semidirect

Maximal subgroups

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

subgroup	index
C₂×#15689129	2
C₂×#15689127	2
#20251806	2
#20245968	2
#20243120	2
C₂×#15688879	2
C₂×C₄₇×H(3,ℤ/4)	2
#10948	47