Subgroups — #26232738

Order 12032.

1246 conjugacy classes of subgroups.

The subgroup lattice has 550 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#15689201	C₂	1	1	yes	maximal, characteristic, complemented
2	D₄×C₄⋊Dic₄₇	C₂	1	1	yes	maximal, characteristic, complemented
3	#20244350	C₂	1	1	yes	maximal, characteristic, complemented
4	#20244337	C₂	1	1	yes	maximal, characteristic, complemented
5	#20243827	C₂	1	2	yes	maximal, complemented
6	#20243706	C₂	1	2	yes	maximal, complemented
7	#20243483	C₂	1	2	yes	maximal, complemented
8	#20243388	C₂	1	1	yes	maximal, characteristic, complemented
9	C₄×#13093945	C₂	1	1	yes	maximal, characteristic, complemented
10	#20243109	C₂	1	2	yes	maximal, complemented
11	C₂×C₄₇×#555	C₂	1	1	yes	maximal, characteristic
12	C₂²×#10625329	C₂²	1	2	yes	—
13	C₂×D₄×Dic₄₇	—	2	1	no	—
14	C₂²×C₄⋊Dic₄₇	C₂²	1	2	yes	—
15	#15689201	—	2	4	no	—
16	C₂×C₄⋊(C₄₇⋊C₈)	C₂²	1	1	yes	characteristic
17	C₂×#13093945	C₂²	1	1	yes	characteristic
18	C₂×#13093945	C₂²	1	1	yes	characteristic
19	C₂×#13093945	C₂²	1	2	yes	—
20	C₂×C₂²⋊(C₄₇⋊C₈)	C₂²	1	2	yes	—
21	C₂×C₄×C₄₇⋊C₈	C₂²	1	1	yes	characteristic
22	#15689022	—	2	1	no	—
23	#15688998	—	2	2	no	—
24	#15688993	C₂²	1	1	yes	characteristic
25	#15688983	C₂²	1	2	yes	—
26	C₄×C₄⋊Dic₄₇	C₂²	1	1	yes	characteristic
27	#15688885	C₂²	1	1	yes	characteristic
28	#15688885	C₂²	1	1	yes	characteristic
29	#15688885	C₂²	1	2	yes	—
30	#15688885	C₂²	1	2	yes	—
31	#15688885	C₂²	1	2	yes	—
32	#15688885	C₂²	1	2	yes	—
33	#15688885	C₂²	1	2	yes	—
34	C₄₇×#555	—	2	4	no	—
35	C₄₇×#555	C₄	1	8	yes	complemented
36	C₂×C₄⋊Q₈×C₄₇	C₂²	1	1	yes	characteristic
37	C₂×#124×C₄₇	—	2	2	no	—
38	C₂×#121×C₄₇	—	2	1	no	—
39	C₂×#121×C₄₇	C₂²	1	2	yes	—
40	C₂×C₄×D₄×C₄₇	C₂²	1	1	yes	characteristic
41	C₂×C₄×D₄×C₄₇	C₂²	1	1	yes	characteristic
42	C₂×#117×C₄₇	—	2	1	no	—
43	C₂×#117×C₄₇	C₂²	1	2	yes	—
44	C₂³×Dic₄₇	—	2	2	no	—
45	C₂×#10625329	—	2	4	no	—
46	C₂×#10625329	—	2	4	no	—
47	C₂×#10625329	—	4	2	no	—
48	C₂²×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
49	C₂²×C₄₇⋊C₈	C₂³	1	2	yes	—
50	C₂²×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
51	D₄×Dic₄₇	—	4	4	no	—
52	C₂×C₄⋊Dic₄₇	—	2	4	no	—
53	C₂×C₄⋊Dic₄₇	—	2	1	no	—
54	C₂×C₄⋊Dic₄₇	—	2	2	no	—
55	C₂×C₄⋊Dic₄₇	—	2	1	no	—
56	C₂×C₄⋊Dic₄₇	—	4	2	no	—
57	C₂×C₄⋊Dic₄₇	C₂³	1	1	yes	characteristic
58	C₂×C₄⋊Dic₄₇	C₂³	1	2	yes	—
59	C₂×C₄⋊Dic₄₇	C₂³	1	1	yes	characteristic
60	C₂×C₂²⋊Dic₄₇	—	2	2	no	—
61	C₂×C₄×Dic₄₇	—	2	1	no	—
62	C₄⋊(C₄₇⋊C₈)	—	2	2	no	—
63	#13093945	—	2	2	no	—
64	#13093945	—	2	2	no	—
65	#13093945	—	4	2	no	—
66	C₂²⋊(C₄₇⋊C₈)	—	2	4	no	—
67	C₄×C₄₇⋊C₈	—	2	2	no	—
68	C₄₇⋊#95	—	2	1	no	—
69	C₄₇⋊#95	—	2	2	no	—
70	C₂²×Q₈×C₄₇	—	2	1	no	—
71	C₂²×D₄×C₄₇	—	2	2	no	—
72	C₂²×D₄×C₄₇	D₄	1	1	yes	characteristic
73	C₂²×D₄×C₄₇	C₂³	1	1	yes	characteristic
74	C₂³×C₄×C₄₇	—	2	1	no	—
75	C₂³×C₄×C₄₇	C₂³	1	2	yes	—
76	C₄⋊Q₈×C₄₇	—	2	2	no	—
77	C₄⋊Q₈×C₄₇	C₂×C₄	1	4	yes	complemented
78	#124×C₄₇	—	2	16	no	—
79	#121×C₄₇	—	2	8	no	—
80	#121×C₄₇	—	2	4	no	—
81	#121×C₄₇	C₂×C₄	1	8	yes	complemented
82	C₄×D₄×C₄₇	—	2	2	no	—
83	C₄×D₄×C₄₇	C₂×C₄	1	4	yes	—
84	C₄×D₄×C₄₇	C₂×C₄	1	4	yes	complemented
85	C₄×D₄×C₄₇	D₄	1	4	yes	—
86	#117×C₄₇	—	2	4	no	—
87	#117×C₄₇	—	2	8	no	—
88	#117×C₄₇	C₂×C₄	1	8	yes	complemented
89	C₂×C₄⋊C₄×C₄₇	—	2	1	no	—
90	C₂×C₄⋊C₄×C₄₇	D₄	1	1	yes	characteristic
91	C₂×C₄⋊C₄×C₄₇	C₂³	1	1	yes	characteristic
92	C₂×C₄⋊C₄×C₄₇	C₂³	1	2	yes	—
93	C₂×C₂²⋊C₄×C₄₇	—	2	2	no	—
94	C₂×C₂²⋊C₄×C₄₇	—	2	2	no	—
95	C₂×C₂²⋊C₄×C₄₇	—	2	1	no	—
96	C₂×C₂²⋊C₄×C₄₇	D₄	1	2	yes	—
97	C₂×C₄²×C₄₇	—	2	2	no	—
98	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
99	C₂⁴×C₄₇	—	2	1	no	—
100	C₂⁴×C₄₇	C₂×D₄	1	2	yes	—
101	C₂×Q₈×C₄₇	—	2	4	no	—
102	C₂×Q₈×C₄₇	—	8	1	no	—
103	C₂×Q₈×C₄₇	—	8	1	no	—
104	C₂×D₄×C₄₇	—	2	8	no	—
105	C₂×D₄×C₄₇	—	2	2	no	—
106	C₂×D₄×C₄₇	—	2	2	no	—
107	C₂×D₄×C₄₇	—	2	1	no	—
108	C₂×D₄×C₄₇	—	2	1	no	—
109	C₂×D₄×C₄₇	—	2	1	no	—
110	C₂×D₄×C₄₇	—	2	1	no	—
111	C₂×D₄×C₄₇	—	2	1	no	—
112	C₂×D₄×C₄₇	—	8	2	no	—
113	C₂×D₄×C₄₇	—	8	2	no	—
114	C₂×D₄×C₄₇	C₂²⋊C₄	1	4	yes	—
115	C₂×D₄×C₄₇	C₂²×C₄	1	2	yes	—
116	C₂²×C₄×C₄₇	—	2	2	no	—
117	C₂²×C₄×C₄₇	—	2	2	no	—
118	C₂²×C₄×C₄₇	—	2	2	no	—
119	C₂²×C₄×C₄₇	—	2	2	no	—
120	C₂²×C₄×C₄₇	—	2	1	no	—
121	C₂²×C₄×C₄₇	—	2	2	no	—
122	C₂²×C₄×C₄₇	—	2	4	no	—
123	C₂²×C₄×C₄₇	—	4	2	no	—
124	C₂²×C₄×C₄₇	—	4	2	no	—
125	C₂²×C₄×C₄₇	C₂²×C₄	1	4	yes	—
126	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
127	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
128	C₂²×C₄×C₄₇	C₂×D₄	1	4	yes	—
129	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
130	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
131	C₂²×Dic₄₇	—	2	1	no	—
132	C₂²×Dic₄₇	—	2	1	no	—
133	C₂²×Dic₄₇	—	2	2	no	—
134	C₂²×Dic₄₇	—	4	4	no	—
135	C₂²×Dic₄₇	—	4	4	no	—
136	C₂²×Dic₄₇	—	8	2	no	—
137	C₄⋊C₄×C₄₇	—	2	4	no	—
138	C₄⋊C₄×C₄₇	—	2	1	no	—
139	C₄⋊C₄×C₄₇	—	2	2	no	—
140	C₄⋊C₄×C₄₇	C₂²⋊C₄	1	4	yes	—
141	C₄⋊C₄×C₄₇	C₂²×C₄	1	2	yes	—
142	C₄⋊C₄×C₄₇	C₂²×C₄	1	4	yes	—
143	C₂²⋊C₄×C₄₇	—	2	8	no	—
144	C₂²⋊C₄×C₄₇	—	2	8	no	—
145	C₂²⋊C₄×C₄₇	—	2	4	no	—
146	C₂²⋊C₄×C₄₇	C₂²⋊C₄	1	8	yes	—
147	C₄²×C₄₇	—	2	8	no	—
148	C₄²×C₄₇	C₂²×C₄	1	2	yes	—
149	C₄²×C₄₇	C₂×D₄	1	2	yes	—
150	C₂²⋊Dic₄₇	—	4	4	no	—
151	C₄⋊Dic₄₇	—	2	1	no	—
152	C₄⋊Dic₄₇	—	2	1	no	—
153	C₄⋊Dic₄₇	—	2	2	no	—
154	C₄⋊Dic₄₇	—	2	2	no	—
155	C₄⋊Dic₄₇	—	2	1	no	—
156	C₄⋊Dic₄₇	—	4	4	no	—
157	C₄⋊Dic₄₇	—	4	2	no	—
158	C₄⋊Dic₄₇	—	8	1	no	—
159	C₄⋊Dic₄₇	#41	1	2	yes	—
160	C₄×Dic₄₇	—	4	2	no	—
161	#10625329	—	4	8	no	—
162	C₂×C₄₇⋊C₈	—	2	1	no	—
163	C₂×C₄₇⋊C₈	—	2	1	no	—
164	C₂×C₄₇⋊C₈	—	2	1	no	—
165	C₂×C₄₇⋊C₈	—	2	2	no	—
166	C₂×C₄₇⋊C₈	—	2	1	no	—
167	C₂×C₄₇⋊C₈	—	2	2	no	—
168	C₂×C₄₇⋊C₈	—	2	2	no	—
169	C₂×C₄₇⋊C₈	—	2	1	no	—
170	C₂×C₄₇⋊C₈	#41	1	2	yes	—
171	C₂³×C₄₇	—	2	2	no	—
172	C₂³×C₄₇	—	2	2	no	—
173	C₂³×C₄₇	—	2	2	no	—
174	C₂³×C₄₇	—	2	2	no	—
175	C₂³×C₄₇	—	2	2	no	—
176	C₂³×C₄₇	—	2	2	no	—
177	C₂³×C₄₇	—	2	2	no	—
178	C₂³×C₄₇	—	4	1	no	—
179	C₂³×C₄₇	—	4	1	no	—
180	C₂³×C₄₇	—	4	1	no	—
181	C₂³×C₄₇	—	4	1	no	—
182	C₂³×C₄₇	—	4	1	no	—
183	C₂³×C₄₇	—	4	1	no	—
184	C₂³×C₄₇	C₂×C₂²⋊C₄	1	4	yes	—
185	C₂³×C₄₇	C₂²×D₄	1	1	yes	characteristic
186	Q₈×C₄₇	—	8	4	no	—
187	D₄×C₄₇	—	2	2	no	—
188	D₄×C₄₇	—	2	2	no	—
189	D₄×C₄₇	—	2	8	no	—
190	D₄×C₄₇	—	4	1	no	—
191	D₄×C₄₇	—	4	1	no	—
192	D₄×C₄₇	—	8	8	no	—
193	C₂×C₄×C₄₇	—	2	2	no	—
194	C₂×C₄×C₄₇	—	2	2	no	—
195	C₂×C₄×C₄₇	—	2	1	no	—
196	C₂×C₄×C₄₇	—	2	1	no	—
197	C₂×C₄×C₄₇	—	2	4	no	—
198	C₂×C₄×C₄₇	—	2	4	no	—
199	C₂×C₄×C₄₇	—	2	4	no	—
200	C₂×C₄×C₄₇	—	2	4	no	—
201	C₂×C₄×C₄₇	—	2	2	no	—
202	C₂×C₄×C₄₇	—	2	4	no	—
203	C₂×C₄×C₄₇	—	4	1	no	—
204	C₂×C₄×C₄₇	—	4	1	no	—
205	C₂×C₄×C₄₇	—	4	2	no	—
206	C₂×C₄×C₄₇	—	4	2	no	—
207	C₂×C₄×C₄₇	—	4	8	no	—
208	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	4	yes	—
209	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	2	yes	—
210	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	2	yes	—
211	C₂×C₄×C₄₇	AGL(1,ℤ/8)	1	2	yes	—
212	C₂×C₄×C₄₇	#137	1	2	yes	—
213	C₂×C₄×C₄₇	C₂³×C₄	1	1	yes	characteristic
214	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
215	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
216	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
217	C₂×C₄×C₄₇	H(5,𝔽₂)	1	1	yes	characteristic
218	C₂×C₄×C₄₇	2₋¹⁺⁴	1	1	yes	characteristic
219	C₂×Dic₄₇	—	2	2	no	—
220	C₂×Dic₄₇	—	4	1	no	—
221	C₂×Dic₄₇	—	4	1	no	—
222	C₂×Dic₄₇	—	4	2	no	—
223	C₂×Dic₄₇	—	4	1	no	—
224	C₂×Dic₄₇	—	4	1	no	—
225	C₂×Dic₄₇	—	4	2	no	—
226	C₂×Dic₄₇	—	4	2	no	—
227	C₂×Dic₄₇	—	4	1	no	—
228	C₂×Dic₄₇	—	8	8	no	—
229	C₄₇⋊C₈	—	2	2	no	—
230	C₄₇⋊C₈	—	4	2	no	—
231	C₄₇⋊C₈	—	4	1	no	—
232	#22503	—	47	1	no	maximal, Sylow
233	C₂²×C₄₇	—	2	4	no	—
234	C₂²×C₄₇	—	2	4	no	—
235	C₂²×C₄₇	—	2	4	no	—
236	C₂²×C₄₇	—	4	2	no	—
237	C₂²×C₄₇	—	4	2	no	—
238	C₂²×C₄₇	—	4	2	no	—
239	C₂²×C₄₇	—	4	2	no	—
240	C₂²×C₄₇	—	4	2	no	—
241	C₂²×C₄₇	—	4	2	no	—
242	C₂²×C₄₇	—	4	2	no	—
243	C₂²×C₄₇	—	8	1	no	—
244	C₂²×C₄₇	—	8	1	no	—
245	C₂²×C₄₇	—	8	1	no	—
246	C₂²×C₄₇	—	8	1	no	—
247	C₂²×C₄₇	C₂²×C₂²⋊C₄	1	1	yes	characteristic
248	C₂²×C₄₇	#546	1	1	yes	characteristic
249	C₂²×C₄₇	#547	1	1	yes	characteristic
250	C₂²×C₄₇	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
251	C₂²×C₄₇	C₂×#137	1	1	yes	characteristic
252	C₂²×C₄₇	#576	1	1	yes	characteristic
253	C₂²×C₄₇	#577	1	1	yes	characteristic
254	C₄×C₄₇	—	2	4	no	—
255	C₄×C₄₇	—	2	2	no	—
256	C₄×C₄₇	—	4	2	no	—
257	C₄×C₄₇	—	4	4	no	—
258	C₄×C₄₇	#417	1	4	yes	—
259	C₄×C₄₇	C₄×#41	1	1	yes	characteristic
260	C₄×C₄₇	#520	1	1	yes	characteristic
261	C₄×C₄₇	#546	1	1	yes	characteristic
262	C₄×C₄₇	#547	1	1	yes	characteristic
263	Dic₄₇	—	4	2	no	—
264	Dic₄₇	—	8	1	no	—
265	Dic₄₇	—	8	2	no	—
266	C₂×#555	D₄₇	1	1	yes	characteristic
267	C₂×#436	—	47	1	no	—
268	D₄×C₄⋊C₄	—	47	1	no	—
269	#1990	—	47	1	no	—
270	#1987	—	47	1	no	—
271	#1895	—	47	2	no	—
272	#1874	—	47	2	no	—
273	#1825	—	47	2	no	—
274	#1802	—	47	1	no	—
275	C₄×#102	—	47	1	no	—
276	#1736	—	47	2	no	—
277	C₂×C₄₇	—	4	4	no	—
278	C₂×C₄₇	—	8	2	no	—
279	C₂×C₄₇	#2339	1	1	yes	characteristic
280	C₂×C₄₇	C₂×#417	1	1	yes	characteristic
281	C₂×C₄₇	#2897	1	1	yes	characteristic
282	C₂×C₄₇	#3325	1	1	yes	characteristic
283	C₂×C₄₇	#3329	1	1	yes	characteristic
284	C₂×C₄₇	#3354	1	1	yes	characteristic
285	C₂×C₄₇	#3357	1	1	yes	characteristic
286	C₂²×M₁₆	—	47	2	no	—
287	#555	—	2	4	no	—
288	#555	Dic₄₇	1	8	yes	complemented
289	C₂×C₄⋊Q₈	C₂×D₄₇	1	1	yes	characteristic
290	C₂×#124	—	2	2	no	—
291	C₂×#121	—	2	1	no	—
292	C₂×#121	C₂×D₄₇	1	2	yes	—
293	C₂×C₄×D₄	—	94	1	no	—
294	C₂×C₄×D₄	C₂×D₄₇	1	1	yes	characteristic
295	C₂×C₄×D₄	C₂×D₄₇	1	1	yes	characteristic
296	C₂×#117	—	2	1	no	—
297	C₂×#117	C₂×D₄₇	1	2	yes	—
298	C₂²×C₄⋊C₄	—	47	2	no	—
299	#436	—	94	4	no	—
300	C₂×C₄⋊C₈	—	47	1	no	—
301	C₂×#102	—	47	1	no	—
302	C₂×#102	—	47	1	no	—
303	C₂×#102	—	47	2	no	—
304	C₂×C₂²⋊C₈	—	47	2	no	—
305	C₂×C₄×C₈	—	47	1	no	—
306	#389	—	94	1	no	—
307	#385	—	94	2	no	—
308	#384	—	47	1	no	—
309	#380	—	47	2	no	—
310	C₄×C₄⋊C₄	—	47	1	no	—
311	#340	—	47	2	no	—
312	#340	—	47	1	no	—
313	#340	—	47	2	no	—
314	#340	—	47	2	no	—
315	#340	—	47	2	no	—
316	#340	—	47	2	no	—
317	#340	—	47	1	no	—
318	C₄₇	#22503	1	1	yes	characteristic, complemented, Sylow
319	C₂²×Q₈	—	2	1	no	—
320	C₂²×D₄	—	2	2	no	—
321	C₂²×D₄	C₂²⋊D₄₇	1	1	yes	characteristic
322	C₂²×D₄	C₂²×D₄₇	1	1	yes	characteristic
323	C₂³×C₄	—	2	1	no	—
324	C₂³×C₄	—	94	2	no	—
325	C₂³×C₄	C₂²×D₄₇	1	2	yes	—
326	C₂×M₁₆	—	94	4	no	—
327	C₂×M₁₆	—	94	4	no	—
328	C₂×M₁₆	—	188	2	no	—
329	C₂²×C₈	—	47	1	no	—
330	C₂²×C₈	—	47	2	no	—
331	C₂²×C₈	—	47	1	no	—
332	C₄⋊Q₈	—	2	2	no	—
333	C₄⋊Q₈	C₂×Dic₄₇	1	4	yes	complemented
334	#124	—	2	16	no	—
335	#121	—	2	8	no	—
336	#121	—	2	4	no	—
337	#121	C₂×Dic₄₇	1	8	yes	complemented
338	C₄×D₄	—	2	2	no	—
339	C₄×D₄	—	188	4	no	—
340	C₄×D₄	C₂×Dic₄₇	1	4	yes	—
341	C₄×D₄	C₂×Dic₄₇	1	4	yes	complemented
342	C₄×D₄	C₂²⋊D₄₇	1	4	yes	—
343	#117	—	2	4	no	—
344	#117	—	2	8	no	—
345	#117	C₂×Dic₄₇	1	8	yes	complemented
346	C₂×C₄⋊C₄	—	2	1	no	—
347	C₂×C₄⋊C₄	—	47	1	no	—
348	C₂×C₄⋊C₄	—	47	2	no	—
349	C₂×C₄⋊C₄	—	47	1	no	—
350	C₂×C₄⋊C₄	—	94	4	no	—
351	C₂×C₄⋊C₄	—	94	1	no	—
352	C₂×C₄⋊C₄	—	94	2	no	—
353	C₂×C₄⋊C₄	—	94	1	no	—
354	C₂×C₄⋊C₄	—	188	2	no	—
355	C₂×C₄⋊C₄	C₂²⋊D₄₇	1	1	yes	characteristic
356	C₂×C₄⋊C₄	C₂²×D₄₇	1	1	yes	characteristic
357	C₂×C₄⋊C₄	C₂²×D₄₇	1	2	yes	—
358	C₂×C₂²⋊C₄	—	2	2	no	—
359	C₂×C₂²⋊C₄	—	2	2	no	—
360	C₂×C₂²⋊C₄	—	2	1	no	—
361	C₂×C₂²⋊C₄	—	94	2	no	—
362	C₂×C₂²⋊C₄	C₂²⋊D₄₇	1	2	yes	—
363	C₂×C₄²	—	2	2	no	—
364	C₂×C₄²	—	94	1	no	—
365	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
366	C₄⋊C₈	—	94	2	no	—
367	#102	—	94	2	no	—
368	#102	—	94	2	no	—
369	#102	—	188	2	no	—
370	C₂²⋊C₈	—	94	4	no	—
371	C₄×C₈	—	94	2	no	—
372	#95	—	94	1	no	—
373	#95	—	94	2	no	—
374	C₂⁴	—	2	1	no	—
375	C₂⁴	C₂×C₂²⋊D₄₇	1	2	yes	—
376	C₂×Q₈	—	2	4	no	—
377	C₂×Q₈	—	8	1	no	—
378	C₂×Q₈	—	8	1	no	—
379	C₂×D₄	—	2	8	no	—
380	C₂×D₄	—	2	2	no	—
381	C₂×D₄	—	2	2	no	—
382	C₂×D₄	—	2	1	no	—
383	C₂×D₄	—	2	1	no	—
384	C₂×D₄	—	2	1	no	—
385	C₂×D₄	—	2	1	no	—
386	C₂×D₄	—	2	1	no	—
387	C₂×D₄	—	8	2	no	—
388	C₂×D₄	—	8	2	no	—
389	C₂×D₄	C₂²⋊Dic₄₇	1	4	yes	—
390	C₂×D₄	C₂²×Dic₄₇	1	2	yes	—
391	C₂²×C₄	—	2	2	no	—
392	C₂²×C₄	—	2	2	no	—
393	C₂²×C₄	—	2	2	no	—
394	C₂²×C₄	—	2	2	no	—
395	C₂²×C₄	—	2	1	no	—
396	C₂²×C₄	—	2	2	no	—
397	C₂²×C₄	—	2	4	no	—
398	C₂²×C₄	—	4	2	no	—
399	C₂²×C₄	—	4	2	no	—
400	C₂²×C₄	—	94	1	no	—
401	C₂²×C₄	—	94	1	no	—
402	C₂²×C₄	—	94	2	no	—
403	C₂²×C₄	—	376	2	no	—
404	C₂²×C₄	—	188	4	no	—
405	C₂²×C₄	—	188	4	no	—
406	C₂²×C₄	C₂²×Dic₄₇	1	4	yes	—
407	C₂²×C₄	C₂×C₂²⋊D₄₇	1	2	yes	—
408	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
409	C₂²×C₄	C₂×C₂²⋊D₄₇	1	4	yes	—
410	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
411	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
412	M₁₆	—	188	8	no	—
413	C₂×C₈	—	47	2	no	—
414	C₂×C₈	—	94	1	no	—
415	C₂×C₈	—	94	1	no	—
416	C₂×C₈	—	94	1	no	—
417	C₂×C₈	—	94	2	no	—
418	C₂×C₈	—	94	1	no	—
419	C₂×C₈	—	94	2	no	—
420	C₂×C₈	—	94	2	no	—
421	C₂×C₈	—	94	1	no	—
422	C₄⋊C₄	—	2	4	no	—
423	C₄⋊C₄	—	2	1	no	—
424	C₄⋊C₄	—	2	2	no	—
425	C₄⋊C₄	—	47	2	no	—
426	C₄⋊C₄	—	94	1	no	—
427	C₄⋊C₄	—	94	1	no	—
428	C₄⋊C₄	—	94	2	no	—
429	C₄⋊C₄	—	94	2	no	—
430	C₄⋊C₄	—	94	1	no	—
431	C₄⋊C₄	—	376	1	no	—
432	C₄⋊C₄	—	188	4	no	—
433	C₄⋊C₄	—	188	2	no	—
434	C₄⋊C₄	C₂²⋊Dic₄₇	1	4	yes	—
435	C₄⋊C₄	C₂²×Dic₄₇	1	2	yes	—
436	C₄⋊C₄	C₂²×Dic₄₇	1	4	yes	—
437	C₂²⋊C₄	—	2	8	no	—
438	C₂²⋊C₄	—	2	8	no	—
439	C₂²⋊C₄	—	2	4	no	—
440	C₂²⋊C₄	—	188	4	no	—
441	C₂²⋊C₄	C₂²⋊Dic₄₇	1	8	yes	—
442	C₄²	—	2	8	no	—
443	C₄²	—	188	2	no	—
444	C₄²	C₂²×Dic₄₇	1	2	yes	—
445	C₄²	C₂×C₂²⋊D₄₇	1	2	yes	—
446	C₂³	—	2	2	no	—
447	C₂³	—	2	2	no	—
448	C₂³	—	2	2	no	—
449	C₂³	—	2	2	no	—
450	C₂³	—	2	2	no	—
451	C₂³	—	2	2	no	—
452	C₂³	—	2	2	no	—
453	C₂³	—	4	1	no	—
454	C₂³	—	4	1	no	—
455	C₂³	—	4	1	no	—
456	C₂³	—	4	1	no	—
457	C₂³	—	4	1	no	—
458	C₂³	—	4	1	no	—
459	C₂³	C₂×C₂²⋊Dic₄₇	1	4	yes	—
460	C₂³	C₂²×C₂²⋊D₄₇	1	1	yes	characteristic
461	Q₈	—	8	4	no	—
462	D₄	—	2	2	no	—
463	D₄	—	2	2	no	—
464	D₄	—	2	8	no	—
465	D₄	—	4	1	no	—
466	D₄	—	4	1	no	—
467	D₄	—	8	8	no	—
468	C₂×C₄	—	2	2	no	—
469	C₂×C₄	—	2	2	no	—
470	C₂×C₄	—	2	1	no	—
471	C₂×C₄	—	2	1	no	—
472	C₂×C₄	—	2	4	no	—
473	C₂×C₄	—	2	4	no	—
474	C₂×C₄	—	2	4	no	—
475	C₂×C₄	—	2	4	no	—
476	C₂×C₄	—	2	2	no	—
477	C₂×C₄	—	2	4	no	—
478	C₂×C₄	—	4	1	no	—
479	C₂×C₄	—	4	1	no	—
480	C₂×C₄	—	4	2	no	—
481	C₂×C₄	—	4	2	no	—
482	C₂×C₄	—	4	8	no	—
483	C₂×C₄	—	94	2	no	—
484	C₂×C₄	—	376	8	no	—
485	C₂×C₄	—	188	2	no	—
486	C₂×C₄	—	188	1	no	—
487	C₂×C₄	—	188	1	no	—
488	C₂×C₄	—	188	2	no	—
489	C₂×C₄	—	188	2	no	—
490	C₂×C₄	—	188	1	no	—
491	C₂×C₄	—	188	1	no	—
492	C₂×C₄	—	188	1	no	—
493	C₂×C₄	C₂×C₂²⋊Dic₄₇	1	4	yes	—
494	C₂×C₄	C₂×C₂²⋊Dic₄₇	1	2	yes	—
495	C₂×C₄	C₂×C₂²⋊Dic₄₇	1	2	yes	—
496	C₂×C₄	#13094049	1	2	yes	—
497	C₂×C₄	#13094054	1	2	yes	—
498	C₂×C₄	C₂³×Dic₄₇	1	1	yes	characteristic
499	C₂×C₄	C₂²×C₂²⋊D₄₇	1	1	yes	characteristic
500	C₂×C₄	#41×D₄₇	1	1	yes	characteristic
501	C₂×C₄	#41×D₄₇	1	1	yes	characteristic
502	C₂×C₄	#13094070	1	1	yes	characteristic
503	C₂×C₄	#13094071	1	1	yes	characteristic
504	C₈	—	94	2	no	—
505	C₈	—	188	2	no	—
506	C₈	—	188	1	no	—
507	C₂²	—	2	4	no	—
508	C₂²	—	2	4	no	—
509	C₂²	—	2	4	no	—
510	C₂²	—	4	2	no	—
511	C₂²	—	4	2	no	—
512	C₂²	—	4	2	no	—
513	C₂²	—	4	2	no	—
514	C₂²	—	4	2	no	—
515	C₂²	—	4	2	no	—
516	C₂²	—	4	2	no	—
517	C₂²	—	8	1	no	—
518	C₂²	—	8	1	no	—
519	C₂²	—	8	1	no	—
520	C₂²	—	8	1	no	—
521	C₂²	C₂²×C₂²⋊Dic₄₇	1	1	yes	characteristic
522	C₂²	#15689761	1	1	yes	characteristic
523	C₂²	#15689772	1	1	yes	characteristic
524	C₂²	C₂×#13094049	1	1	yes	characteristic
525	C₂²	C₂×#13094054	1	1	yes	characteristic
526	C₂²	#15689926	1	1	yes	characteristic
527	C₂²	#15689934	1	1	yes	characteristic
528	C₄	—	2	2	no	—
529	C₄	—	2	4	no	—
530	C₄	—	4	4	no	—
531	C₄	—	4	2	no	—
532	C₄	—	376	2	no	—
533	C₄	—	376	1	no	—
534	C₄	—	188	2	no	—
535	C₄	#15689124	1	4	yes	—
536	C₄	#41×Dic₄₇	1	1	yes	characteristic
537	C₄	#15689606	1	1	yes	characteristic
538	C₄	#15689761	1	1	yes	characteristic
539	C₄	#15689772	1	1	yes	characteristic
540	C₂	—	4	4	no	—
541	C₂	—	8	2	no	—
542	C₂	#20246218	1	1	yes	characteristic
543	C₂	C₂×#15689124	1	1	yes	characteristic
544	C₂	#20251914	1	1	yes	characteristic
545	C₂	#20255624	1	1	yes	characteristic
546	C₂	#20255676	1	1	yes	characteristic
547	C₂	#20255977	1	1	yes	characteristic
548	C₂	#20256008	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	C₂²×C₂²⋊D₄₇
commutator	C₂×C₄×C₄₇	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₄₇
Fitting, prime radical	C₂×C₄₇×#555	C₂
socle	C₂³×C₄₇	C₂²×D₄
cosocle	C₂²×C₄×C₄₇	C₂⁴
hypercenter	C₂×#555	D₄₇
hypocenter	C₄₇	#22503
LCS	G ▷ C₂×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂³ ◁ C₂×C₄×D₄ ◁ C₂×#555

Complements

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

N	H ≅ G/N	type
1. C₂×#15689201	C₂	semidirect
2. D₄×C₄⋊Dic₄₇	C₂	semidirect
3. #20244350	C₂	semidirect
4. #20244337	C₂	semidirect
5. #20243827	C₂	semidirect
6. #20243706	C₂	semidirect
7. #20243483	C₂	semidirect
8. #20243388	C₂	semidirect
9. C₄×#13093945	C₂	semidirect
10. #20243109	C₂	semidirect
35. C₄₇×#555	C₄	semidirect
77. C₄⋊Q₈×C₄₇	C₂×C₄	semidirect
81. #121×C₄₇	C₂×C₄	semidirect
84. C₄×D₄×C₄₇	C₂×C₄	semidirect
88. #117×C₄₇	C₂×C₄	semidirect
288. #555	Dic₄₇	semidirect
318. C₄₇	#22503	semidirect
333. C₄⋊Q₈	C₂×Dic₄₇	semidirect
337. #121	C₂×Dic₄₇	semidirect
341. C₄×D₄	C₂×Dic₄₇	semidirect
345. #117	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×#15689201	2
D₄×C₄⋊Dic₄₇	2
#20244350	2
#20244337	2
#20243827	2
#20243706	2
#20243483	2
#20243388	2
C₄×#13093945	2
#20243109	2
C₂×C₄₇×#555	2
#22503	47