Subgroups — #26123444

Order 12032.

878 conjugacy classes of subgroups.

The subgroup lattice has 596 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#15689150	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#15689141	C₂	1	1	yes	maximal, characteristic
3	C₂×#15689141	C₂	1	1	yes	maximal, characteristic
4	C₂×#15689091	C₂	1	1	yes	maximal, characteristic
5	#20243115	C₂	1	1	yes	maximal, characteristic, complemented
6	#20243085	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₄₇×H(3,ℤ/4)	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂²×#10625350	C₂²	1	1	yes	characteristic
9	C₂²×#10625329	C₂²	1	1	yes	characteristic
10	C₂²×#10625329	C₂²	1	1	yes	characteristic
11	C₂³×C₄₇⋊C₈	C₂²	1	1	yes	characteristic
12	#15689150	—	2	2	no	—
13	#15689150	—	2	2	no	—
14	C₂×C₄⋊(C₄₇⋊C₈)	—	2	2	no	—
15	#15689141	—	2	2	no	—
16	#15689141	—	2	2	no	—
17	#15689141	—	2	2	no	—
18	#15689141	C₄	1	4	yes	complemented
19	C₂×#13093952	—	2	2	no	—
20	C₂×#13093952	—	2	2	no	—
21	#15689091	—	2	2	no	—
22	#15689091	—	2	2	no	—
23	C₂×(C₂×D₄₇)⋊C₈	—	2	2	no	—
24	#15688888	—	2	2	no	—
25	#15688878	—	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	C₂×#10625350	—	2	1	no	—
31	C₂×#10625350	—	2	1	no	—
32	C₂×#10625350	—	2	1	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	C₂×C₄	1	2	yes	—
41	C₂×#10625350	D₄	1	2	yes	—
42	C₂²×Dic₉₄	Q₈	1	1	yes	characteristic
43	C₂²×D₁₈₈	Q₈	1	1	yes	characteristic
44	C₂²×C₂²⋊D₄₇	—	2	1	no	—
45	C₂²×C₄×D₄₇	—	2	1	no	—
46	C₂×#10625329	—	2	1	no	—
47	C₂×#10625329	—	2	1	no	—
48	C₂×#10625329	—	2	1	no	—
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	—	2	1	no	—
55	C₂×#10625329	—	2	1	no	—
56	C₂×#10625329	C₂×C₄	1	2	yes	—
57	C₂×#10625329	D₄	1	2	yes	—
58	C₂²×C₄₇⋊C₈	—	2	1	no	—
59	C₂²×C₄₇⋊C₈	—	2	1	no	—
60	C₂²×C₄₇⋊C₈	—	2	1	no	—
61	C₂²×C₄₇⋊C₈	—	2	1	no	—
62	C₂²×C₄₇⋊C₈	—	2	1	no	—
63	C₂²×C₄₇⋊C₈	—	2	1	no	—
64	C₂²×C₄₇⋊C₈	—	2	1	no	—
65	C₂²×C₄₇⋊C₈	—	2	1	no	—
66	C₂²×C₄₇⋊C₈	D₄	1	2	yes	—
67	C₄⋊(C₄₇⋊C₈)	—	2	8	no	—
68	#13093952	—	2	8	no	—
69	#13093952	—	2	8	no	—
70	(C₂×D₄₇)⋊C₈	—	2	8	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	—	2	1	no	—
77	C₂×M₁₆×C₄₇	—	2	1	no	—
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	C₂×C₄	1	2	yes	—
86	#117×C₄₇	D₄	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	D₄	1	2	yes	—
92	C₂×C₄²×C₄₇	D₄	1	2	yes	—
93	C₂⁴×C₄₇	#41	1	1	yes	characteristic
94	C₂³×D₄₇	—	2	1	no	—
95	C₂²×C₄×C₄₇	—	2	2	no	—
96	C₂²×C₄×C₄₇	—	2	2	no	—
97	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
98	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
99	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
100	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
101	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
102	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
103	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
104	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
105	C₂²×C₄×C₄₇	C₂×Q₈	1	1	yes	characteristic
106	C₂²×C₄×C₄₇	#41	1	1	yes	characteristic
107	C₂²×C₄×C₄₇	#41	1	1	yes	characteristic
108	C₂²×C₄×C₄₇	#41	1	1	yes	characteristic
109	C₂²×C₄×C₄₇	#41	1	1	yes	characteristic
110	C₂²×C₄×C₄₇	#41	1	1	yes	characteristic
111	C₂×C₂²⋊D₄₇	—	2	2	no	—
112	C₂×C₂²⋊D₄₇	—	2	2	no	—
113	C₂×C₂²⋊D₄₇	—	4	1	no	—
114	C₂×C₂²⋊D₄₇	—	4	1	no	—
115	C₂×C₂²⋊D₄₇	—	4	1	no	—
116	C₂×C₂²⋊D₄₇	—	4	1	no	—
117	C₂²×Dic₄₇	—	2	1	no	—
118	#10625350	—	2	2	no	—
119	#10625350	—	2	2	no	—
120	#10625350	—	2	2	no	—
121	#10625350	—	2	2	no	—
122	#10625350	—	2	2	no	—
123	#10625350	—	2	2	no	—
124	#10625350	—	2	2	no	—
125	#10625350	—	2	2	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	C₂×D₁₈₈	—	2	1	no	—
135	C₂×D₁₈₈	—	2	1	no	—
136	C₂×D₁₈₈	—	2	1	no	—
137	C₂×D₁₈₈	—	2	1	no	—
138	C₂×D₁₈₈	—	2	1	no	—
139	C₂×D₁₈₈	C₄⋊C₄	1	2	yes	—
140	C₂×C₄×D₄₇	—	2	2	no	—
141	C₂×C₄×D₄₇	—	2	2	no	—
142	C₂×C₄×D₄₇	—	4	1	no	—
143	C₂×C₄×D₄₇	—	4	1	no	—
144	C₂×C₄×D₄₇	—	4	1	no	—
145	C₂×C₄×D₄₇	—	4	1	no	—
146	C₂×Dic₉₄	—	2	1	no	—
147	C₂×Dic₉₄	—	2	1	no	—
148	C₂×Dic₉₄	—	2	1	no	—
149	C₂×Dic₉₄	—	2	1	no	—
150	C₂×Dic₉₄	—	2	1	no	—
151	C₂×Dic₉₄	C₄⋊C₄	1	2	yes	—
152	M₁₆×C₄₇	—	4	1	no	—
153	M₁₆×C₄₇	—	4	1	no	—
154	M₁₆×C₄₇	—	4	1	no	—
155	M₁₆×C₄₇	—	4	1	no	—
156	C₂×C₈×C₄₇	—	2	2	no	—
157	C₂×C₈×C₄₇	—	2	2	no	—
158	C₂×C₈×C₄₇	—	2	2	no	—
159	C₄⋊C₄×C₄₇	—	2	2	no	—
160	C₄⋊C₄×C₄₇	—	2	2	no	—
161	C₄⋊C₄×C₄₇	—	4	1	no	—
162	C₄⋊C₄×C₄₇	—	4	1	no	—
163	C₂²⋊C₄×C₄₇	—	2	2	no	—
164	C₂²⋊C₄×C₄₇	—	2	2	no	—
165	C₂²⋊C₄×C₄₇	—	4	1	no	—
166	C₂²⋊C₄×C₄₇	—	4	1	no	—
167	C₄²×C₄₇	—	2	2	no	—
168	C₄²×C₄₇	—	2	2	no	—
169	C₄²×C₄₇	—	2	2	no	—
170	C₄²×C₄₇	C₂²⋊C₄	1	4	yes	—
171	#10625329	—	2	2	no	—
172	#10625329	—	2	2	no	—
173	#10625329	—	2	2	no	—
174	#10625329	—	2	2	no	—
175	#10625329	—	4	1	no	—
176	#10625329	—	4	1	no	—
177	#10625329	—	4	1	no	—
178	#10625329	—	4	1	no	—
179	C₂×C₄₇⋊C₈	—	2	2	no	—
180	C₂×C₄₇⋊C₈	—	2	2	no	—
181	C₂×C₄₇⋊C₈	—	2	2	no	—
182	C₂×C₄₇⋊C₈	—	2	2	no	—
183	C₂×C₄₇⋊C₈	—	2	2	no	—
184	C₂×C₄₇⋊C₈	—	4	1	no	—
185	C₂×C₄₇⋊C₈	—	4	1	no	—
186	C₂×C₄₇⋊C₈	—	4	1	no	—
187	C₂×C₄₇⋊C₈	—	4	1	no	—
188	C₂×C₄₇⋊C₈	—	4	1	no	—
189	C₂×C₄₇⋊C₈	—	4	1	no	—
190	C₂×C₄₇⋊C₈	—	4	1	no	—
191	C₂×C₄₇⋊C₈	—	4	1	no	—
192	C₂³×C₄₇	—	4	2	no	—
193	C₂³×C₄₇	C₄×D₄	1	1	yes	characteristic
194	C₂³×C₄₇	#121	1	1	yes	characteristic
195	C₂³×C₄₇	C₂²⋊Q₈	1	1	yes	characteristic
196	C₂³×C₄₇	#123	1	1	yes	characteristic
197	C₂³×C₄₇	#123	1	1	yes	characteristic
198	C₂³×C₄₇	#123	1	1	yes	characteristic
199	C₂³×C₄₇	#126	1	1	yes	characteristic
200	C₂²×D₄₇	—	2	2	no	—
201	C₂²×D₄₇	—	4	4	no	—
202	C₂²×D₄₇	—	4	1	no	—
203	C₂²×D₄₇	—	4	1	no	—
204	C₂×C₄×C₄₇	—	2	4	no	—
205	C₂×C₄×C₄₇	—	4	4	no	—
206	C₂×C₄×C₄₇	—	4	4	no	—
207	C₂×C₄×C₄₇	—	4	2	no	—
208	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
209	C₂×C₄×C₄₇	C₂×C₄⋊C₄	1	1	yes	characteristic
210	C₂×C₄×C₄₇	#117	1	1	yes	characteristic
211	C₂×C₄×C₄₇	C₄×D₄	1	1	yes	characteristic
212	C₂×C₄×C₄₇	C₄×D₄	1	1	yes	characteristic
213	C₂×C₄×C₄₇	C₄×D₄	1	1	yes	characteristic
214	C₂×C₄×C₄₇	#120	1	1	yes	characteristic
215	C₂×C₄×C₄₇	#120	1	1	yes	characteristic
216	C₂×C₄×C₄₇	#120	1	1	yes	characteristic
217	C₂×C₄×C₄₇	#121	1	1	yes	characteristic
218	C₂×C₄×C₄₇	#121	1	1	yes	characteristic
219	C₂×C₄×C₄₇	#121	1	1	yes	characteristic
220	C₂×C₄×C₄₇	#121	1	1	yes	characteristic
221	C₂×C₄×C₄₇	#121	1	1	yes	characteristic
222	C₂×C₄×C₄₇	#121	1	1	yes	characteristic
223	C₂×C₄×C₄₇	#121	1	1	yes	characteristic
224	C₂×C₄×C₄₇	C₂²⋊Q₈	1	1	yes	characteristic
225	C₂×C₄×C₄₇	C₂²⋊Q₈	1	1	yes	characteristic
226	C₂×C₄×C₄₇	C₂²⋊Q₈	1	1	yes	characteristic
227	C₂×C₄×C₄₇	C₂²⋊Q₈	1	1	yes	characteristic
228	C₂×C₄×C₄₇	C₂²⋊Q₈	1	1	yes	characteristic
229	C₂×C₄×C₄₇	#123	1	1	yes	characteristic
230	C₂×C₄×C₄₇	#123	1	1	yes	characteristic
231	C₂×C₄×C₄₇	#124	1	1	yes	characteristic
232	C₂×C₄×C₄₇	#124	1	1	yes	characteristic
233	C₂×C₄×C₄₇	#124	1	1	yes	characteristic
234	C₂×C₄×C₄₇	#126	1	1	yes	characteristic
235	C₂×C₄×C₄₇	#127	1	1	yes	characteristic
236	C₂²⋊D₄₇	—	4	2	no	—
237	C₂²⋊D₄₇	—	4	2	no	—
238	C₂²⋊D₄₇	—	4	2	no	—
239	C₂²⋊D₄₇	—	4	2	no	—
240	C₂×Dic₄₇	—	2	2	no	—
241	C₂×Dic₄₇	—	4	1	no	—
242	C₂×Dic₄₇	—	4	1	no	—
243	D₁₈₈	—	2	2	no	—
244	D₁₈₈	—	2	2	no	—
245	D₁₈₈	—	4	1	no	—
246	D₁₈₈	—	4	1	no	—
247	C₄×D₄₇	—	4	2	no	—
248	C₄×D₄₇	—	4	2	no	—
249	C₄×D₄₇	—	4	2	no	—
250	C₄×D₄₇	—	4	2	no	—
251	Dic₉₄	—	2	2	no	—
252	Dic₉₄	—	2	2	no	—
253	Dic₉₄	—	4	1	no	—
254	Dic₉₄	—	4	1	no	—
255	C₈×C₄₇	—	4	2	no	—
256	C₄₇⋊C₈	—	4	2	no	—
257	C₄₇⋊C₈	—	4	2	no	—
258	C₄₇⋊C₈	—	4	2	no	—
259	#11084	—	47	1	no	maximal, Sylow
260	C₂²×C₄₇	—	2	2	no	—
261	C₂²×C₄₇	—	2	2	no	—
262	C₂²×C₄₇	—	2	2	no	—
263	C₂²×C₄₇	—	4	1	no	—
264	C₂²×C₄₇	—	4	1	no	—
265	C₂²×C₄₇	—	4	1	no	—
266	C₂²×C₄₇	—	4	1	no	—
267	C₂²×C₄₇	#385	1	1	yes	characteristic
268	C₂²×C₄₇	#386	1	1	yes	characteristic
269	C₂²×C₄₇	#388	1	1	yes	characteristic
270	C₂²×C₄₇	#394	1	1	yes	characteristic
271	C₂²×C₄₇	#396	1	1	yes	characteristic
272	C₂²×C₄₇	#397	1	1	yes	characteristic
273	C₂²×C₄₇	#399	1	1	yes	characteristic
274	C₂×D₄₇	—	4	4	no	—
275	C₂×D₄₇	—	4	2	no	—
276	C₂×D₄₇	—	8	2	no	—
277	C₂×D₄₇	—	8	2	no	—
278	C₄×C₄₇	—	4	4	no	—
279	C₄×C₄₇	—	8	2	no	—
280	C₄×C₄₇	#380	1	1	yes	characteristic
281	C₄×C₄₇	#385	1	1	yes	characteristic
282	C₄×C₄₇	#388	1	1	yes	characteristic
283	C₄×C₄₇	#390	1	1	yes	characteristic
284	C₄×C₄₇	#392	1	1	yes	characteristic
285	C₄×C₄₇	#393	1	1	yes	characteristic
286	C₄×C₄₇	#394	1	1	yes	characteristic
287	C₄×C₄₇	#396	1	1	yes	characteristic
288	Dic₄₇	—	4	2	no	—
289	C₂×#424	—	47	1	no	—
290	C₂×#421	—	47	1	no	—
291	C₂×#421	—	47	1	no	—
292	C₂×#408	—	47	1	no	—
293	#1738	—	47	1	no	—
294	C₂×H(3,ℤ/4)	D₄₇	1	1	yes	characteristic, complemented
295	#1729	—	47	1	no	—
296	C₂×C₄₇	—	2	1	no	—
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	#1439	1	1	yes	characteristic
303	C₂×C₄₇	#2098	1	2	yes	—
304	D₄₇	—	8	2	no	—
305	C₂²×#41	—	47	1	no	—
306	C₂²×M₁₆	—	47	1	no	—
307	C₂²×M₁₆	—	47	1	no	—
308	C₂²×M₁₆	C₂×D₄₇	1	1	yes	characteristic
309	C₂³×C₈	—	47	1	no	—
310	C₂×#117	C₂×D₄₇	1	1	yes	characteristic
311	C₂×#117	C₂×D₄₇	1	1	yes	characteristic
312	#424	—	94	2	no	—
313	#424	—	94	2	no	—
314	C₂×C₄⋊C₈	—	94	2	no	—
315	#421	—	47	4	no	—
316	#421	—	94	2	no	—
317	#421	—	94	2	no	—
318	#421	—	94	2	no	—
319	C₂×#104	—	94	2	no	—
320	C₂×#104	—	94	2	no	—
321	#408	—	94	2	no	—
322	#408	—	94	2	no	—
323	C₂×C₂²⋊C₈	—	94	2	no	—
324	#341	—	94	2	no	—
325	H(3,ℤ/4)	—	2	2	no	—
326	#336	—	94	2	no	—
327	C₄₇	#11084	1	1	yes	characteristic, complemented, Sylow
328	C₂×#41	—	47	2	no	—
329	C₂×#41	—	47	2	no	—
330	C₂×#41	—	94	1	no	—
331	C₂×#41	—	94	1	no	—
332	C₂×#41	—	94	1	no	—
333	C₂×#41	—	94	1	no	—
334	C₂×#41	—	94	1	no	—
335	C₂×#41	—	94	1	no	—
336	C₂×#41	—	94	1	no	—
337	C₂×#41	—	94	1	no	—
338	C₂×#41	—	94	1	no	—
339	C₂×#41	—	94	1	no	—
340	C₂²×Q₈	—	47	1	no	—
341	C₂²×D₄	—	47	1	no	—
342	C₂²×D₄	—	94	1	no	—
343	C₂³×C₄	—	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	—	2	1	no	—
350	C₂×M₁₆	—	2	1	no	—
351	C₂×M₁₆	—	47	2	no	—
352	C₂×M₁₆	—	47	2	no	—
353	C₂×M₁₆	—	94	1	no	—
354	C₂×M₁₆	—	94	1	no	—
355	C₂×M₁₆	—	94	1	no	—
356	C₂×M₁₆	—	94	1	no	—
357	C₂×M₁₆	—	94	1	no	—
358	C₂×M₁₆	—	94	1	no	—
359	C₂×M₁₆	—	94	1	no	—
360	C₂×M₁₆	—	94	1	no	—
361	C₂×M₁₆	—	94	1	no	—
362	C₂×M₁₆	—	94	1	no	—
363	C₂²×C₈	—	47	2	no	—
364	C₂²×C₈	—	94	1	no	—
365	C₂²×C₈	—	94	1	no	—
366	C₂²×C₈	—	94	1	no	—
367	C₂²×C₈	—	94	1	no	—
368	C₂²×C₈	—	94	1	no	—
369	C₂²×C₈	—	94	1	no	—
370	C₂²×C₈	—	94	1	no	—
371	C₂²×C₈	—	94	1	no	—
372	C₂²×C₈	D₁₈₈	1	2	yes	—
373	#117	—	2	1	no	—
374	#117	—	2	1	no	—
375	#117	—	2	1	no	—
376	#117	—	2	1	no	—
377	#117	—	2	1	no	—
378	#117	—	2	1	no	—
379	#117	C₄×D₄₇	1	2	yes	—
380	#117	C₂²⋊D₄₇	1	2	yes	—
381	C₂×C₄⋊C₄	—	2	1	no	—
382	C₂×C₄⋊C₄	—	2	1	no	—
383	C₂×C₂²⋊C₄	—	2	1	no	—
384	C₂×C₂²⋊C₄	—	2	1	no	—
385	C₂×C₄²	D₁₈₈	1	2	yes	—
386	C₂×C₄²	D₁₈₈	1	2	yes	—
387	C₄⋊C₈	—	94	8	no	—
388	#104	—	94	8	no	—
389	#104	—	94	8	no	—
390	C₂²⋊C₈	—	94	8	no	—
391	C₂⁴	—	94	1	no	—
392	C₂⁴	#10625352	1	1	yes	characteristic
393	#41	—	94	2	no	—
394	#41	—	94	2	no	—
395	#41	—	94	2	no	—
396	#41	—	94	2	no	—
397	#41	—	94	2	no	—
398	#41	—	94	2	no	—
399	#41	—	94	2	no	—
400	#41	—	94	2	no	—
401	#41	—	188	1	no	—
402	#41	—	188	1	no	—
403	#41	—	188	1	no	—
404	#41	—	188	1	no	—
405	#41	—	188	1	no	—
406	#41	—	188	1	no	—
407	#41	—	188	1	no	—
408	#41	—	188	1	no	—
409	C₂×Q₈	—	47	2	no	—
410	C₂×Q₈	—	94	1	no	—
411	C₂×Q₈	—	94	1	no	—
412	C₂×Q₈	—	94	1	no	—
413	C₂×Q₈	—	94	1	no	—
414	C₂×Q₈	—	94	1	no	—
415	C₂×D₄	—	47	2	no	—
416	C₂×D₄	—	94	2	no	—
417	C₂×D₄	—	94	2	no	—
418	C₂×D₄	—	94	1	no	—
419	C₂×D₄	—	94	1	no	—
420	C₂×D₄	—	94	1	no	—
421	C₂×D₄	—	94	1	no	—
422	C₂×D₄	—	94	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	C₂²×C₄	—	2	2	no	—
428	C₂²×C₄	—	2	2	no	—
429	C₂²×C₄	—	94	1	no	—
430	C₂²×C₄	—	94	2	no	—
431	C₂²×C₄	—	94	2	no	—
432	C₂²×C₄	—	188	1	no	—
433	C₂²×C₄	—	188	1	no	—
434	C₂²×C₄	—	188	1	no	—
435	C₂²×C₄	—	188	1	no	—
436	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
437	C₂²×C₄	C₂×D₁₈₈	1	1	yes	characteristic
438	C₂²×C₄	C₂×D₁₈₈	1	1	yes	characteristic
439	C₂²×C₄	C₂×D₁₈₈	1	1	yes	characteristic
440	C₂²×C₄	#10625350	1	1	yes	characteristic
441	C₂²×C₄	#10625350	1	1	yes	characteristic
442	C₂²×C₄	D₄×D₄₇	1	1	yes	characteristic
443	C₂²×C₄	D₄×D₄₇	1	1	yes	characteristic
444	C₂²×C₄	D₄×D₄₇	1	1	yes	characteristic
445	C₂²×C₄	#10625352	1	1	yes	characteristic
446	C₂²×C₄	#10625352	1	1	yes	characteristic
447	C₂²×C₄	Q₈×D₄₇	1	1	yes	characteristic
448	C₂²×C₄	#10625354	1	1	yes	characteristic
449	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
450	M₁₆	—	4	1	no	—
451	M₁₆	—	4	1	no	—
452	M₁₆	—	4	1	no	—
453	M₁₆	—	4	1	no	—
454	M₁₆	—	94	2	no	—
455	M₁₆	—	94	2	no	—
456	M₁₆	—	94	2	no	—
457	M₁₆	—	94	2	no	—
458	M₁₆	—	188	1	no	—
459	M₁₆	—	188	1	no	—
460	M₁₆	—	188	1	no	—
461	M₁₆	—	188	1	no	—
462	C₂×C₈	—	2	2	no	—
463	C₂×C₈	—	2	2	no	—
464	C₂×C₈	—	2	2	no	—
465	C₂×C₈	—	94	2	no	—
466	C₂×C₈	—	94	2	no	—
467	C₂×C₈	—	94	2	no	—
468	C₂×C₈	—	94	2	no	—
469	C₂×C₈	—	94	2	no	—
470	C₂×C₈	—	188	1	no	—
471	C₂×C₈	—	188	1	no	—
472	C₂×C₈	—	188	1	no	—
473	C₂×C₈	—	188	1	no	—
474	C₂×C₈	—	188	1	no	—
475	C₂×C₈	—	188	1	no	—
476	C₂×C₈	—	188	1	no	—
477	C₂×C₈	—	188	1	no	—
478	C₄⋊C₄	—	2	2	no	—
479	C₄⋊C₄	—	2	2	no	—
480	C₄⋊C₄	—	4	1	no	—
481	C₄⋊C₄	—	4	1	no	—
482	C₂²⋊C₄	—	2	2	no	—
483	C₂²⋊C₄	—	2	2	no	—
484	C₂²⋊C₄	—	4	1	no	—
485	C₂²⋊C₄	—	4	1	no	—
486	C₄²	—	2	2	no	—
487	C₄²	—	2	2	no	—
488	C₄²	—	2	2	no	—
489	C₄²	(C₂×D₄₇)⋊C₄	1	4	yes	—
490	C₂³	—	4	2	no	—
491	C₂³	—	94	2	no	—
492	C₂³	—	188	4	no	—
493	C₂³	—	188	1	no	—
494	C₂³	—	188	1	no	—
495	C₂³	(C₂²⋊D₄₇)⋊C₄	1	1	yes	characteristic
496	C₂³	#13093996	1	1	yes	characteristic
497	C₂³	#13094004	1	1	yes	characteristic
498	C₂³	#13094006	1	1	yes	characteristic
499	C₂³	#13094008	1	1	yes	characteristic
500	C₂³	#13094008	1	1	yes	characteristic
501	C₂³	#13094019	1	1	yes	characteristic
502	Q₈	—	94	2	no	—
503	Q₈	—	94	2	no	—
504	Q₈	—	188	1	no	—
505	Q₈	—	188	1	no	—
506	D₄	—	94	2	no	—
507	D₄	—	94	2	no	—
508	D₄	—	188	2	no	—
509	D₄	—	188	2	no	—
510	D₄	—	188	2	no	—
511	D₄	—	188	2	no	—
512	D₄	—	188	1	no	—
513	D₄	—	188	1	no	—
514	C₂×C₄	—	2	4	no	—
515	C₂×C₄	—	4	4	no	—
516	C₂×C₄	—	4	4	no	—
517	C₂×C₄	—	4	2	no	—
518	C₂×C₄	—	94	2	no	—
519	C₂×C₄	—	188	1	no	—
520	C₂×C₄	—	188	1	no	—
521	C₂×C₄	—	188	2	no	—
522	C₂×C₄	—	188	2	no	—
523	C₂×C₄	—	188	2	no	—
524	C₂×C₄	—	188	2	no	—
525	C₂×C₄	C₂×(C₂×D₄₇)⋊C₄	1	1	yes	characteristic
526	C₂×C₄	C₄⋊C₄×D₄₇	1	1	yes	characteristic
527	C₂×C₄	#13093982	1	1	yes	characteristic
528	C₂×C₄	(C₂²⋊D₄₇)⋊C₄	1	1	yes	characteristic
529	C₂×C₄	C₄×D₁₈₈	1	1	yes	characteristic
530	C₂×C₄	C₄×D₁₈₈	1	1	yes	characteristic
531	C₂×C₄	#13093994	1	1	yes	characteristic
532	C₂×C₄	#13093994	1	1	yes	characteristic
533	C₂×C₄	#13093994	1	1	yes	characteristic
534	C₂×C₄	#13093995	1	1	yes	characteristic
535	C₂×C₄	#13093996	1	1	yes	characteristic
536	C₂×C₄	#13093998	1	1	yes	characteristic
537	C₂×C₄	#13093998	1	1	yes	characteristic
538	C₂×C₄	#13093999	1	1	yes	characteristic
539	C₂×C₄	#13093999	1	1	yes	characteristic
540	C₂×C₄	#13093999	1	1	yes	characteristic
541	C₂×C₄	#13094000	1	1	yes	characteristic
542	C₂×C₄	#13094002	1	1	yes	characteristic
543	C₂×C₄	#13094002	1	1	yes	characteristic
544	C₂×C₄	#13094004	1	1	yes	characteristic
545	C₂×C₄	#13094004	1	1	yes	characteristic
546	C₂×C₄	#13094006	1	1	yes	characteristic
547	C₂×C₄	#13094008	1	1	yes	characteristic
548	C₂×C₄	#13094010	1	1	yes	characteristic
549	C₂×C₄	#13094010	1	1	yes	characteristic
550	C₂×C₄	#13094012	1	1	yes	characteristic
551	C₂×C₄	#13094019	1	1	yes	characteristic
552	C₂×C₄	#13094021	1	1	yes	characteristic
553	C₈	—	4	2	no	—
554	C₈	—	188	2	no	—
555	C₈	—	188	2	no	—
556	C₈	—	188	2	no	—
557	C₂²	—	2	2	no	—
558	C₂²	—	2	2	no	—
559	C₂²	—	2	2	no	—
560	C₂²	—	4	1	no	—
561	C₂²	—	4	1	no	—
562	C₂²	—	4	1	no	—
563	C₂²	—	4	1	no	—
564	C₂²	—	376	2	no	—
565	C₂²	—	376	2	no	—
566	C₂²	—	188	4	no	—
567	C₂²	—	188	2	no	—
568	C₂²	#15688997	1	1	yes	characteristic
569	C₂²	#15689000	1	1	yes	characteristic
570	C₂²	#15689015	1	1	yes	characteristic
571	C₂²	#15689039	1	1	yes	characteristic
572	C₂²	#15689045	1	1	yes	characteristic
573	C₂²	#15689050	1	1	yes	characteristic
574	C₂²	#15689060	1	1	yes	characteristic
575	C₄	—	4	4	no	—
576	C₄	—	8	2	no	—
577	C₄	—	188	2	no	—
578	C₄	#15688980	1	1	yes	characteristic
579	C₄	#15688997	1	1	yes	characteristic
580	C₄	#15689015	1	1	yes	characteristic
581	C₄	#15689025	1	1	yes	characteristic
582	C₄	#15689033	1	1	yes	characteristic
583	C₄	#15689036	1	1	yes	characteristic
584	C₄	#15689039	1	1	yes	characteristic
585	C₄	#15689045	1	1	yes	characteristic
586	C₂	—	2	1	no	—
587	C₂	—	2	1	no	—
588	C₂	—	2	1	no	—
589	C₂	—	2	1	no	—
590	C₂	—	2	1	no	—
591	C₂	—	2	1	no	—
592	C₂	—	376	2	no	—
593	C₂	#20241634	1	1	yes	characteristic
594	C₂	#20244942	1	2	yes	—

	subgroup	G/H
center	C₂×C₄	#13094021
commutator	C₂²×C₄×C₄₇	C₂²×C₄
Frattini	C₂³×C₄	C₂²×D₄₇
Fitting	C₂×C₄₇×H(3,ℤ/4)	C₂
socle	C₂²×C₄₇	#399
prime radical	C₂²×#10625350	C₂²
cosocle	C₂³×C₄×C₄₇	C₂³
hypercenter	C₂×H(3,ℤ/4)	D₄₇
hypocenter	C₄₇	#11084
LCS	G ▷ C₂²×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂×C₄ ◁ C₂³×C₄ ◁ C₂×H(3,ℤ/4)

Complements

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

N	H ≅ G/N	type
1. C₂×#15689150	C₂	semidirect
5. #20243115	C₂	semidirect
6. #20243085	C₂	semidirect
7. C₂×C₄₇×H(3,ℤ/4)	C₂	semidirect
18. #15689141	C₄	semidirect
294. C₂×H(3,ℤ/4)	D₄₇	semidirect
327. C₄₇	#11084	semidirect

Maximal subgroups

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

subgroup	index
C₂×#15689150	2
C₂×#15689141	2
C₂×#15689091	2
#20243115	2
#20243085	2
C₂×C₄₇×H(3,ℤ/4)	2
#11084	47