Subgroups — #26122752

Order 12032.

926 conjugacy classes of subgroups.

The subgroup lattice has 618 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#15689105	C₂	1	1	yes	maximal, characteristic
2	C₂×#15689096	C₂	1	1	yes	maximal, characteristic
3	C₂×#15689091	C₂	1	1	yes	maximal, characteristic
4	C₂×#15689081	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×#15688894	C₂	1	1	yes	maximal, characteristic, complemented
6	#20243085	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₄₇×#344	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂²×#10625350	C₂²	1	1	yes	characteristic
9	C₂²×#10625329	C₂²	1	1	yes	characteristic
10	C₂³×C₄₇⋊C₈	C₂²	1	1	yes	characteristic
11	C₂×#13093983	C₂²	1	1	yes	characteristic
12	#15689105	—	2	2	no	—
13	#15689105	—	2	2	no	—
14	C₂×#13093942	C₄	1	2	yes	complemented
15	C₂×#13093940	C₄	1	2	yes	complemented
16	#15689096	—	2	2	no	—
17	#15689096	—	2	2	no	—
18	C₂×#13093938	C₄	1	4	yes	—
19	#15689091	—	2	1	no	—
20	#15689091	—	2	1	no	—
21	#15689091	—	2	2	no	—
22	C₂×(C₂×D₄₇)⋊C₈	C₄	1	4	yes	complemented
23	#15689081	—	2	2	no	—
24	#15689081	—	2	2	no	—
25	C₂×#13093934	—	2	1	no	—
26	C₂×C₈×Dic₄₇	—	2	1	no	—
27	#15688894	—	2	2	no	—
28	#15688878	—	2	2	no	—
29	C₂²×M₁₆×C₄₇	C₂²	1	1	yes	characteristic
30	C₂²×M₁₆×C₄₇	C₂²	1	1	yes	characteristic
31	C₂×#117×C₄₇	C₂²	1	1	yes	characteristic
32	C₄₇×#344	—	2	2	no	—
33	C₂×#10625350	—	2	1	no	—
34	C₂×#10625350	—	2	1	no	—
35	C₂×#10625350	—	2	1	no	—
36	C₂×#10625350	—	2	1	no	—
37	C₂×#10625350	—	2	1	no	—
38	C₂×#10625350	—	2	1	no	—
39	C₂×#10625350	—	2	1	no	—
40	C₂×#10625350	—	2	1	no	—
41	C₂×#10625350	—	2	1	no	—
42	C₂×#10625350	—	2	1	no	—
43	C₂×#10625350	—	2	1	no	—
44	C₂×#10625350	—	2	1	no	—
45	C₂²×Dic₉₄	C₂×C₄	1	1	yes	characteristic
46	C₂²×D₁₈₈	C₂×C₄	1	1	yes	characteristic
47	C₂²×C₂²⋊D₄₇	C₂×C₄	1	2	yes	—
48	C₂²×C₄×D₄₇	C₂×C₄	1	2	yes	—
49	C₂×#10625329	—	2	1	no	—
50	C₂×#10625329	—	2	1	no	—
51	C₂×#10625329	—	2	1	no	—
52	C₂×#10625329	—	2	1	no	—
53	C₂×#10625329	—	2	1	no	—
54	C₂×#10625329	C₂×C₄	1	2	yes	—
55	C₂²×C₄₇⋊C₈	—	2	1	no	—
56	C₂²×C₄₇⋊C₈	—	2	1	no	—
57	C₂²×C₄₇⋊C₈	—	2	1	no	—
58	C₂²×C₄₇⋊C₈	—	2	1	no	—
59	C₂²×C₄₇⋊C₈	—	2	1	no	—
60	C₂²×C₄₇⋊C₈	C₂×C₄	1	2	yes	—
61	C₂²×C₄₇⋊C₈	D₄	1	1	yes	characteristic
62	C₂²×C₄₇⋊C₈	D₄	1	1	yes	characteristic
63	C₂²×C₄₇⋊C₈	D₄	1	2	yes	—
64	#13093983	—	2	1	no	—
65	#13093983	—	2	1	no	—
66	#13093983	D₄	1	2	yes	—
67	#13093983	D₄	1	2	yes	—
68	C₂×C₄⋊Dic₄₇	—	2	1	no	—
69	C₂×C₂²⋊Dic₄₇	C₂×C₄	1	2	yes	—
70	C₂×C₄×Dic₄₇	—	2	1	no	—
71	#13093942	—	2	4	no	—
72	#13093940	—	2	4	no	—
73	#13093938	—	2	8	no	—
74	(C₂×D₄₇)⋊C₈	—	2	4	no	—
75	(C₂×D₄₇)⋊C₈	—	2	4	no	—
76	#13093934	—	2	4	no	—
77	C₈×Dic₄₇	—	2	4	no	—
78	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
79	C₂×M₁₆×C₄₇	—	2	1	no	—
80	C₂×M₁₆×C₄₇	—	2	1	no	—
81	C₂×M₁₆×C₄₇	—	2	1	no	—
82	C₂×M₁₆×C₄₇	—	2	1	no	—
83	C₂×M₁₆×C₄₇	—	2	1	no	—
84	C₂×M₁₆×C₄₇	—	2	1	no	—
85	C₂×M₁₆×C₄₇	—	2	1	no	—
86	C₂×M₁₆×C₄₇	—	2	1	no	—
87	C₂×M₁₆×C₄₇	—	2	1	no	—
88	C₂×M₁₆×C₄₇	C₂×C₄	1	2	yes	—
89	C₂×M₁₆×C₄₇	D₄	1	2	yes	—
90	C₂×M₁₆×C₄₇	D₄	1	2	yes	—
91	C₂²×C₈×C₄₇	—	2	1	no	—
92	C₂²×C₈×C₄₇	C₂×C₄	1	2	yes	—
93	#117×C₄₇	—	2	1	no	—
94	#117×C₄₇	—	2	1	no	—
95	#117×C₄₇	—	2	1	no	—
96	#117×C₄₇	—	2	1	no	—
97	C₂×C₄⋊C₄×C₄₇	—	2	1	no	—
98	C₂×C₂²⋊C₄×C₄₇	C₂×C₄	1	2	yes	—
99	C₂×C₄²×C₄₇	—	2	1	no	—
100	C₂⁴×C₄₇	C₂²×C₄	1	1	yes	characteristic
101	C₂³×D₄₇	C₄²	1	2	yes	—
102	C₂²×C₄×C₄₇	—	2	2	no	—
103	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
104	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
105	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
106	C₂²×C₄×C₄₇	C₂×D₄	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	#41	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	C₂×C₂²⋊D₄₇	—	2	2	no	—
118	C₂×C₂²⋊D₄₇	—	2	2	no	—
119	C₂×C₂²⋊D₄₇	—	2	2	no	—
120	C₂×C₂²⋊D₄₇	—	2	2	no	—
121	C₂×C₂²⋊D₄₇	—	2	2	no	—
122	C₂×C₂²⋊D₄₇	—	2	2	no	—
123	C₂²×Dic₄₇	—	2	2	no	—
124	C₂²×Dic₄₇	C₄²	1	2	yes	—
125	#10625350	—	4	1	no	—
126	#10625350	—	4	1	no	—
127	#10625350	—	4	1	no	—
128	#10625350	—	4	1	no	—
129	#10625350	—	4	1	no	—
130	#10625350	—	4	1	no	—
131	#10625350	—	4	1	no	—
132	#10625350	—	4	1	no	—
133	#10625350	—	4	1	no	—
134	#10625350	—	4	1	no	—
135	#10625350	—	4	1	no	—
136	#10625350	—	4	1	no	—
137	#10625350	—	4	1	no	—
138	#10625350	—	4	1	no	—
139	#10625350	—	4	1	no	—
140	#10625350	—	4	1	no	—
141	C₂×D₁₈₈	—	2	1	no	—
142	C₂×D₁₈₈	—	2	1	no	—
143	C₂×D₁₈₈	—	2	1	no	—
144	C₂×D₁₈₈	—	2	1	no	—
145	C₂×D₁₈₈	—	2	1	no	—
146	C₂×D₁₈₈	—	2	1	no	—
147	C₂×C₄×D₄₇	—	2	2	no	—
148	C₂×C₄×D₄₇	—	2	2	no	—
149	C₂×C₄×D₄₇	—	2	2	no	—
150	C₂×C₄×D₄₇	—	2	2	no	—
151	C₂×C₄×D₄₇	—	2	2	no	—
152	C₂×C₄×D₄₇	—	2	2	no	—
153	C₂×Dic₉₄	—	2	1	no	—
154	C₂×Dic₉₄	—	2	1	no	—
155	C₂×Dic₉₄	—	2	1	no	—
156	C₂×Dic₉₄	—	2	1	no	—
157	C₂×Dic₉₄	—	2	1	no	—
158	C₂×Dic₉₄	—	2	1	no	—
159	M₁₆×C₄₇	—	2	2	no	—
160	M₁₆×C₄₇	—	2	2	no	—
161	M₁₆×C₄₇	—	2	2	no	—
162	M₁₆×C₄₇	—	4	1	no	—
163	M₁₆×C₄₇	—	4	1	no	—
164	M₁₆×C₄₇	—	4	1	no	—
165	M₁₆×C₄₇	—	4	1	no	—
166	M₁₆×C₄₇	C₂²⋊C₄	1	4	yes	—
167	C₂×C₈×C₄₇	—	2	2	no	—
168	C₂×C₈×C₄₇	—	2	2	no	—
169	C₂×C₈×C₄₇	—	2	2	no	—
170	C₂×C₈×C₄₇	—	2	2	no	—
171	C₂×C₈×C₄₇	—	2	2	no	—
172	C₂×C₈×C₄₇	—	2	2	no	—
173	C₄⋊C₄×C₄₇	—	4	1	no	—
174	C₄⋊C₄×C₄₇	—	4	1	no	—
175	C₂²⋊C₄×C₄₇	—	2	2	no	—
176	C₂²⋊C₄×C₄₇	—	2	2	no	—
177	C₄²×C₄₇	—	4	1	no	—
178	C₄²×C₄₇	—	4	1	no	—
179	C₂²⋊Dic₄₇	—	2	2	no	—
180	C₂²⋊Dic₄₇	C₂²⋊C₄	1	4	yes	—
181	C₄⋊Dic₄₇	—	2	2	no	—
182	C₄⋊Dic₄₇	—	2	2	no	—
183	C₄×Dic₄₇	—	2	2	no	—
184	C₄×Dic₄₇	—	2	2	no	—
185	#10625329	—	2	2	no	—
186	#10625329	—	2	2	no	—
187	#10625329	—	4	1	no	—
188	#10625329	—	4	1	no	—
189	C₂×C₄₇⋊C₈	—	2	2	no	—
190	C₂×C₄₇⋊C₈	—	2	2	no	—
191	C₂×C₄₇⋊C₈	—	2	1	no	—
192	C₂×C₄₇⋊C₈	—	2	1	no	—
193	C₂×C₄₇⋊C₈	—	2	2	no	—
194	C₂×C₄₇⋊C₈	—	2	2	no	—
195	C₂×C₄₇⋊C₈	—	2	1	no	—
196	C₂×C₄₇⋊C₈	—	2	1	no	—
197	C₂×C₄₇⋊C₈	—	2	2	no	—
198	C₂×C₄₇⋊C₈	—	4	1	no	—
199	C₂×C₄₇⋊C₈	—	4	1	no	—
200	C₂×C₄₇⋊C₈	C₂²⋊C₄	1	2	yes	—
201	C₂×C₄₇⋊C₈	C₂²⋊C₄	1	2	yes	—
202	C₂³×C₄₇	—	4	2	no	—
203	C₂³×C₄₇	C₂×C₄²	1	1	yes	characteristic
204	C₂³×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
205	C₂³×C₄₇	#117	1	1	yes	characteristic
206	C₂³×C₄₇	C₄×D₄	1	1	yes	characteristic
207	C₂³×C₄₇	C₄×D₄	1	1	yes	characteristic
208	C₂³×C₄₇	C₄×D₄	1	1	yes	characteristic
209	C₂³×C₄₇	C₄×D₄	1	1	yes	characteristic
210	C₂²×D₄₇	—	2	2	no	—
211	C₂²×D₄₇	—	2	2	no	—
212	C₂²×D₄₇	—	2	2	no	—
213	C₂²×D₄₇	—	4	4	no	—
214	C₂×C₄×C₄₇	—	4	4	no	—
215	C₂×C₄×C₄₇	—	4	2	no	—
216	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
217	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
218	C₂×C₄×C₄₇	#117	1	1	yes	characteristic
219	C₂×C₄×C₄₇	#117	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	#120	1	1	yes	characteristic
229	C₂×C₄×C₄₇	#121	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	#121	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	#123	1	1	yes	characteristic
238	C₂×C₄×C₄₇	#124	1	1	yes	characteristic
239	C₂×C₄×C₄₇	#124	1	1	yes	characteristic
240	C₂×C₄×C₄₇	#124	1	1	yes	characteristic
241	C₂×C₄×C₄₇	#126	1	1	yes	characteristic
242	C₂×C₄×C₄₇	#126	1	1	yes	characteristic
243	C₂×C₄×C₄₇	#127	1	1	yes	characteristic
244	C₂²⋊D₄₇	—	4	2	no	—
245	C₂²⋊D₄₇	—	4	2	no	—
246	C₂²⋊D₄₇	—	4	2	no	—
247	C₂²⋊D₄₇	—	4	2	no	—
248	C₂×Dic₄₇	—	2	2	no	—
249	C₂×Dic₄₇	—	2	2	no	—
250	C₂×Dic₄₇	—	2	2	no	—
251	C₂×Dic₄₇	—	2	4	no	—
252	C₂×Dic₄₇	—	4	4	no	—
253	D₁₈₈	—	4	1	no	—
254	D₁₈₈	—	4	1	no	—
255	D₁₈₈	—	4	1	no	—
256	D₁₈₈	—	4	1	no	—
257	C₄×D₄₇	—	4	2	no	—
258	C₄×D₄₇	—	4	2	no	—
259	C₄×D₄₇	—	4	2	no	—
260	C₄×D₄₇	—	4	2	no	—
261	Dic₉₄	—	4	1	no	—
262	Dic₉₄	—	4	1	no	—
263	Dic₉₄	—	4	1	no	—
264	Dic₉₄	—	4	1	no	—
265	C₈×C₄₇	—	2	4	no	—
266	C₈×C₄₇	—	4	2	no	—
267	C₄₇⋊C₈	—	2	2	no	—
268	C₄₇⋊C₈	—	2	2	no	—
269	C₄₇⋊C₈	—	4	2	no	—
270	#10961	—	47	1	no	maximal, Sylow
271	C₂²×C₄₇	—	2	2	no	—
272	C₂²×C₄₇	—	2	2	no	—
273	C₂²×C₄₇	—	2	2	no	—
274	C₂²×C₄₇	—	4	1	no	—
275	C₂²×C₄₇	—	4	1	no	—
276	C₂²×C₄₇	—	4	1	no	—
277	C₂²×C₄₇	—	4	1	no	—
278	C₂²×C₄₇	C₄×C₂²⋊C₄	1	1	yes	characteristic
279	C₂²×C₄₇	C₄×C₂²⋊C₄	1	1	yes	characteristic
280	C₂²×C₄₇	C₄×C₂²⋊C₄	1	1	yes	characteristic
281	C₂²×C₄₇	#386	1	1	yes	characteristic
282	C₂²×C₄₇	#388	1	1	yes	characteristic
283	C₂²×C₄₇	#388	1	1	yes	characteristic
284	C₂²×C₄₇	#390	1	1	yes	characteristic
285	C₂×D₄₇	—	4	2	no	—
286	C₂×D₄₇	—	4	4	no	—
287	C₂×D₄₇	—	8	2	no	—
288	C₂×D₄₇	—	8	2	no	—
289	C₄×C₄₇	—	8	2	no	—
290	C₄×C₄₇	#386	1	1	yes	characteristic
291	C₄×C₄₇	#386	1	1	yes	characteristic
292	C₄×C₄₇	#388	1	1	yes	characteristic
293	C₄×C₄₇	#388	1	1	yes	characteristic
294	C₄×C₄₇	#388	1	1	yes	characteristic
295	C₄×C₄₇	#388	1	1	yes	characteristic
296	C₄×C₄₇	#390	1	1	yes	characteristic
297	C₄×C₄₇	#390	1	1	yes	characteristic
298	Dic₄₇	—	4	4	no	—
299	Dic₄₇	—	4	2	no	—
300	C₂×#413	—	47	1	no	—
301	C₂×#410	—	47	1	no	—
302	C₂×#408	—	47	1	no	—
303	C₂×#405	—	47	1	no	—
304	C₂×#344	—	47	1	no	—
305	C₂×#344	D₄₇	1	1	yes	characteristic, complemented
306	#1729	—	47	1	no	—
307	C₂×C₄₇	—	2	1	no	—
308	C₂×C₄₇	—	2	1	no	—
309	C₂×C₄₇	—	2	1	no	—
310	C₂×C₄₇	—	2	1	no	—
311	C₂×C₄₇	—	2	1	no	—
312	C₂×C₄₇	—	2	1	no	—
313	C₂×C₄₇	#1437	1	1	yes	characteristic
314	C₂×C₄₇	#1757	1	2	yes	—
315	D₄₇	—	8	2	no	—
316	C₂²×#41	—	47	1	no	—
317	C₂²×M₁₆	—	47	1	no	—
318	C₂²×M₁₆	C₂×D₄₇	1	1	yes	characteristic
319	C₂²×M₁₆	C₂×D₄₇	1	1	yes	characteristic
320	C₂³×C₈	—	47	1	no	—
321	C₂×#117	—	47	1	no	—
322	C₂×#117	C₂×D₄₇	1	1	yes	characteristic
323	#413	—	94	2	no	—
324	#413	—	94	2	no	—
325	C₂×#101	—	47	2	no	—
326	C₂×#100	—	47	2	no	—
327	#410	—	94	2	no	—
328	#410	—	94	2	no	—
329	C₂×#99	—	47	4	no	—
330	#408	—	94	2	no	—
331	#408	—	94	1	no	—
332	#408	—	94	1	no	—
333	C₂×C₂²⋊C₈	—	47	4	no	—
334	#405	—	94	2	no	—
335	#405	—	94	2	no	—
336	C₂×#97	—	94	1	no	—
337	C₂×C₄×C₈	—	94	1	no	—
338	#344	—	2	2	no	—
339	#344	—	94	2	no	—
340	#336	—	94	2	no	—
341	C₄₇	#10961	1	1	yes	characteristic, complemented, Sylow
342	C₂×#41	—	94	1	no	—
343	C₂×#41	—	94	1	no	—
344	C₂×#41	—	94	1	no	—
345	C₂×#41	—	94	1	no	—
346	C₂×#41	—	94	1	no	—
347	C₂×#41	—	94	1	no	—
348	C₂×#41	—	94	1	no	—
349	C₂×#41	—	94	1	no	—
350	C₂×#41	—	94	1	no	—
351	C₂×#41	—	94	1	no	—
352	C₂×#41	—	94	1	no	—
353	C₂×#41	—	94	1	no	—
354	C₂²×Q₈	—	47	1	no	—
355	C₂²×D₄	—	47	2	no	—
356	C₂²×D₄	—	47	1	no	—
357	C₂³×C₄	—	47	2	no	—
358	C₂³×C₄	C₂²×D₄₇	1	1	yes	characteristic
359	C₂×M₁₆	—	2	1	no	—
360	C₂×M₁₆	—	2	1	no	—
361	C₂×M₁₆	—	2	1	no	—
362	C₂×M₁₆	—	2	1	no	—
363	C₂×M₁₆	—	2	1	no	—
364	C₂×M₁₆	—	2	1	no	—
365	C₂×M₁₆	—	2	1	no	—
366	C₂×M₁₆	—	2	1	no	—
367	C₂×M₁₆	—	2	1	no	—
368	C₂×M₁₆	—	47	2	no	—
369	C₂×M₁₆	—	94	1	no	—
370	C₂×M₁₆	—	94	1	no	—
371	C₂×M₁₆	—	94	1	no	—
372	C₂×M₁₆	—	94	1	no	—
373	C₂×M₁₆	—	94	1	no	—
374	C₂×M₁₆	C₄×D₄₇	1	2	yes	—
375	C₂×M₁₆	D₁₈₈	1	2	yes	—
376	C₂×M₁₆	C₂²⋊D₄₇	1	2	yes	—
377	C₂²×C₈	—	2	1	no	—
378	C₂²×C₈	—	47	2	no	—
379	C₂²×C₈	—	47	2	no	—
380	C₂²×C₈	—	47	1	no	—
381	C₂²×C₈	—	47	1	no	—
382	C₂²×C₈	—	94	1	no	—
383	C₂²×C₈	—	94	1	no	—
384	C₂²×C₈	—	94	1	no	—
385	C₂²×C₈	—	94	1	no	—
386	C₂²×C₈	—	94	1	no	—
387	C₂²×C₈	C₄×D₄₇	1	2	yes	—
388	#117	—	2	1	no	—
389	#117	—	2	1	no	—
390	#117	—	2	1	no	—
391	#117	—	2	1	no	—
392	#117	—	47	2	no	—
393	#117	—	47	2	no	—
394	#117	—	94	1	no	—
395	#117	—	94	1	no	—
396	C₂×C₄⋊C₄	—	2	1	no	—
397	C₂×C₄⋊C₄	—	94	1	no	—
398	C₂×C₂²⋊C₄	—	47	2	no	—
399	C₂×C₂²⋊C₄	C₄×D₄₇	1	2	yes	—
400	C₂×C₄²	—	2	1	no	—
401	C₂×C₄²	—	94	1	no	—
402	#101	—	94	4	no	—
403	#100	—	94	4	no	—
404	#99	—	94	8	no	—
405	C₂²⋊C₈	—	94	4	no	—
406	C₂²⋊C₈	—	94	4	no	—
407	#97	—	94	4	no	—
408	C₄×C₈	—	94	4	no	—
409	C₂⁴	—	47	2	no	—
410	C₂⁴	C₂×C₄×D₄₇	1	1	yes	characteristic
411	#41	—	188	1	no	—
412	#41	—	188	1	no	—
413	#41	—	188	1	no	—
414	#41	—	188	1	no	—
415	#41	—	188	1	no	—
416	#41	—	188	1	no	—
417	#41	—	188	1	no	—
418	#41	—	188	1	no	—
419	#41	—	188	1	no	—
420	#41	—	188	1	no	—
421	#41	—	188	1	no	—
422	#41	—	188	1	no	—
423	#41	—	188	1	no	—
424	#41	—	188	1	no	—
425	#41	—	188	1	no	—
426	#41	—	188	1	no	—
427	C₂×Q₈	—	94	1	no	—
428	C₂×Q₈	—	94	1	no	—
429	C₂×Q₈	—	94	1	no	—
430	C₂×Q₈	—	94	1	no	—
431	C₂×Q₈	—	94	1	no	—
432	C₂×Q₈	—	94	1	no	—
433	C₂×D₄	—	94	2	no	—
434	C₂×D₄	—	94	2	no	—
435	C₂×D₄	—	94	2	no	—
436	C₂×D₄	—	94	2	no	—
437	C₂×D₄	—	94	2	no	—
438	C₂×D₄	—	94	2	no	—
439	C₂×D₄	—	94	1	no	—
440	C₂×D₄	—	94	1	no	—
441	C₂×D₄	—	94	1	no	—
442	C₂×D₄	—	94	1	no	—
443	C₂×D₄	—	94	1	no	—
444	C₂×D₄	—	94	1	no	—
445	C₂²×C₄	—	2	2	no	—
446	C₂²×C₄	—	47	2	no	—
447	C₂²×C₄	—	94	2	no	—
448	C₂²×C₄	—	94	2	no	—
449	C₂²×C₄	—	94	2	no	—
450	C₂²×C₄	—	94	2	no	—
451	C₂²×C₄	—	94	2	no	—
452	C₂²×C₄	—	94	2	no	—
453	C₂²×C₄	—	94	2	no	—
454	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
455	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
456	C₂²×C₄	C₂×D₁₈₈	1	1	yes	characteristic
457	C₂²×C₄	#10625350	1	1	yes	characteristic
458	C₂²×C₄	#10625350	1	1	yes	characteristic
459	C₂²×C₄	D₄×D₄₇	1	1	yes	characteristic
460	C₂²×C₄	D₄×D₄₇	1	1	yes	characteristic
461	C₂²×C₄	D₄×D₄₇	1	1	yes	characteristic
462	C₂²×C₄	D₄×D₄₇	1	1	yes	characteristic
463	C₂²×C₄	#10625352	1	1	yes	characteristic
464	C₂²×C₄	#10625352	1	1	yes	characteristic
465	C₂²×C₄	#10625354	1	1	yes	characteristic
466	C₂²×C₄	#10625354	1	1	yes	characteristic
467	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
468	M₁₆	—	2	2	no	—
469	M₁₆	—	2	2	no	—
470	M₁₆	—	2	2	no	—
471	M₁₆	—	4	1	no	—
472	M₁₆	—	4	1	no	—
473	M₁₆	—	4	1	no	—
474	M₁₆	—	4	1	no	—
475	M₁₆	—	94	2	no	—
476	M₁₆	—	94	2	no	—
477	M₁₆	—	188	1	no	—
478	M₁₆	—	188	1	no	—
479	M₁₆	(C₂×D₄₇)⋊C₄	1	4	yes	—
480	C₂×C₈	—	2	2	no	—
481	C₂×C₈	—	2	2	no	—
482	C₂×C₈	—	2	2	no	—
483	C₂×C₈	—	2	2	no	—
484	C₂×C₈	—	2	2	no	—
485	C₂×C₈	—	2	2	no	—
486	C₂×C₈	—	47	2	no	—
487	C₂×C₈	—	47	2	no	—
488	C₂×C₈	—	94	2	no	—
489	C₂×C₈	—	94	2	no	—
490	C₂×C₈	—	94	1	no	—
491	C₂×C₈	—	94	1	no	—
492	C₂×C₈	—	94	2	no	—
493	C₂×C₈	—	94	2	no	—
494	C₂×C₈	—	94	1	no	—
495	C₂×C₈	—	94	1	no	—
496	C₂×C₈	—	94	2	no	—
497	C₂×C₈	—	188	1	no	—
498	C₂×C₈	—	188	1	no	—
499	C₄⋊C₄	—	4	1	no	—
500	C₄⋊C₄	—	4	1	no	—
501	C₄⋊C₄	—	94	2	no	—
502	C₄⋊C₄	—	94	2	no	—
503	C₂²⋊C₄	—	2	2	no	—
504	C₂²⋊C₄	—	2	2	no	—
505	C₂²⋊C₄	—	47	4	no	—
506	C₂²⋊C₄	—	94	2	no	—
507	C₄²	—	4	1	no	—
508	C₄²	—	4	1	no	—
509	C₄²	—	94	2	no	—
510	C₄²	—	94	2	no	—
511	C₂³	—	4	2	no	—
512	C₂³	—	94	2	no	—
513	C₂³	—	94	2	no	—
514	C₂³	—	94	2	no	—
515	C₂³	—	188	4	no	—
516	C₂³	C₄²×D₄₇	1	1	yes	characteristic
517	C₂³	C₂²⋊C₄×D₄₇	1	1	yes	characteristic
518	C₂³	#13093982	1	1	yes	characteristic
519	C₂³	(C₂²⋊D₄₇)⋊C₄	1	1	yes	characteristic
520	C₂³	C₄×C₂²⋊D₄₇	1	1	yes	characteristic
521	C₂³	#13093986	1	1	yes	characteristic
522	C₂³	C₄×D₁₈₈	1	1	yes	characteristic
523	Q₈	—	188	1	no	—
524	Q₈	—	188	1	no	—
525	Q₈	—	188	1	no	—
526	Q₈	—	188	1	no	—
527	D₄	—	188	2	no	—
528	D₄	—	188	2	no	—
529	D₄	—	188	2	no	—
530	D₄	—	188	2	no	—
531	D₄	—	188	1	no	—
532	D₄	—	188	1	no	—
533	D₄	—	188	1	no	—
534	D₄	—	188	1	no	—
535	C₂×C₄	—	4	4	no	—
536	C₂×C₄	—	4	2	no	—
537	C₂×C₄	—	94	2	no	—
538	C₂×C₄	—	94	2	no	—
539	C₂×C₄	—	94	2	no	—
540	C₂×C₄	—	94	4	no	—
541	C₂×C₄	—	188	4	no	—
542	C₂×C₄	—	188	2	no	—
543	C₂×C₄	—	188	2	no	—
544	C₂×C₄	—	188	2	no	—
545	C₂×C₄	—	188	2	no	—
546	C₂×C₄	C₂²⋊C₄×D₄₇	1	1	yes	characteristic
547	C₂×C₄	C₂×(C₂×D₄₇)⋊C₄	1	1	yes	characteristic
548	C₂×C₄	#13093981	1	1	yes	characteristic
549	C₂×C₄	#13093982	1	1	yes	characteristic
550	C₂×C₄	(C₂²⋊D₄₇)⋊C₄	1	1	yes	characteristic
551	C₂×C₄	(C₂²⋊D₄₇)⋊C₄	1	1	yes	characteristic
552	C₂×C₄	(C₂²⋊D₄₇)⋊C₄	1	1	yes	characteristic
553	C₂×C₄	C₄×C₂²⋊D₄₇	1	1	yes	characteristic
554	C₂×C₄	#13093986	1	1	yes	characteristic
555	C₂×C₄	#13093986	1	1	yes	characteristic
556	C₂×C₄	#13093986	1	1	yes	characteristic
557	C₂×C₄	C₄×D₁₈₈	1	1	yes	characteristic
558	C₂×C₄	#13093994	1	1	yes	characteristic
559	C₂×C₄	#13093996	1	1	yes	characteristic
560	C₂×C₄	#13093996	1	1	yes	characteristic
561	C₂×C₄	#13093997	1	1	yes	characteristic
562	C₂×C₄	#13093997	1	1	yes	characteristic
563	C₂×C₄	#13093999	1	1	yes	characteristic
564	C₂×C₄	#13093999	1	1	yes	characteristic
565	C₂×C₄	#13094008	1	1	yes	characteristic
566	C₂×C₄	#13094009	1	1	yes	characteristic
567	C₂×C₄	#13094009	1	1	yes	characteristic
568	C₂×C₄	#13094010	1	1	yes	characteristic
569	C₂×C₄	#13094010	1	1	yes	characteristic
570	C₂×C₄	#13094013	1	1	yes	characteristic
571	C₂×C₄	#13094019	1	1	yes	characteristic
572	C₂×C₄	#13094019	1	1	yes	characteristic
573	C₂×C₄	#13094020	1	1	yes	characteristic
574	C₈	—	2	4	no	—
575	C₈	—	4	2	no	—
576	C₈	—	94	2	no	—
577	C₈	—	94	2	no	—
578	C₈	—	188	2	no	—
579	C₂²	—	2	2	no	—
580	C₂²	—	2	2	no	—
581	C₂²	—	2	2	no	—
582	C₂²	—	4	1	no	—
583	C₂²	—	4	1	no	—
584	C₂²	—	4	1	no	—
585	C₂²	—	4	1	no	—
586	C₂²	—	376	2	no	—
587	C₂²	—	376	2	no	—
588	C₂²	—	188	2	no	—
589	C₂²	—	188	4	no	—
590	C₂²	#15688970	1	1	yes	characteristic
591	C₂²	#15688970	1	1	yes	characteristic
592	C₂²	C₄×(C₂×D₄₇)⋊C₄	1	1	yes	characteristic
593	C₂²	#15689001	1	1	yes	characteristic
594	C₂²	#15689013	1	1	yes	characteristic
595	C₂²	#15689015	1	1	yes	characteristic
596	C₂²	#15689023	1	1	yes	characteristic
597	C₄	—	8	2	no	—
598	C₄	—	188	4	no	—
599	C₄	—	188	2	no	—
600	C₄	#15689000	1	1	yes	characteristic
601	C₄	#15689001	1	1	yes	characteristic
602	C₄	#15689012	1	1	yes	characteristic
603	C₄	#15689012	1	1	yes	characteristic
604	C₄	#15689013	1	1	yes	characteristic
605	C₄	#15689015	1	1	yes	characteristic
606	C₄	#15689023	1	1	yes	characteristic
607	C₄	#15689024	1	1	yes	characteristic
608	C₂	—	2	1	no	—
609	C₂	—	2	1	no	—
610	C₂	—	2	1	no	—
611	C₂	—	2	1	no	—
612	C₂	—	2	1	no	—
613	C₂	—	2	1	no	—
614	C₂	—	376	2	no	—
615	C₂	#20241624	1	1	yes	characteristic
616	C₂	#20243187	1	2	yes	—

	subgroup	G/H
center	C₂×C₄	C₂²⋊C₄×D₄₇
commutator	C₂³×C₄₇	C₂×C₄²
Frattini	C₂³×C₄	C₂²×D₄₇
Fitting	C₂×C₄₇×#344	C₂
socle	C₂²×C₄₇	C₄×C₂²⋊C₄
prime radical	C₂²×#10625350	C₂²
cosocle	C₂³×C₄×C₄₇	C₂³
hypercenter	C₂×#344	D₄₇
hypocenter	C₄₇	#10961
LCS	G ▷ C₂³×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂×C₄ ◁ C₂³×C₄ ◁ C₂×#344

Complements

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

N	H ≅ G/N	type
4. C₂×#15689081	C₂	semidirect
5. C₂×#15688894	C₂	semidirect
6. #20243085	C₂	semidirect
7. C₂×C₄₇×#344	C₂	semidirect
14. C₂×#13093942	C₄	semidirect
15. C₂×#13093940	C₄	semidirect
22. C₂×(C₂×D₄₇)⋊C₈	C₄	semidirect
305. C₂×#344	D₄₇	semidirect
341. C₄₇	#10961	semidirect

Maximal subgroups

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

subgroup	index
C₂×#15689105	2
C₂×#15689096	2
C₂×#15689091	2
C₂×#15689081	2
C₂×#15688894	2
#20243085	2
C₂×C₄₇×#344	2
#10961	47