Subgroups — #26228588

Order 12032.

648 conjugacy classes of subgroups.

The subgroup lattice has 490 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20253170	C₂	1	1	yes	maximal, characteristic
2	#20252323	C₂	1	1	yes	maximal, characteristic, complemented
3	#20252033	C₂	1	1	yes	maximal, characteristic
4	#20244163	C₂	1	1	yes	maximal, characteristic, complemented
5	#20244135	C₂	1	2	yes	maximal, complemented
6	#20244093	C₂	1	2	yes	maximal
7	#20244034	C₂	1	2	yes	maximal
8	#20243985	C₂	1	2	yes	maximal, complemented
9	#20243409	C₂	1	1	yes	maximal, characteristic
10	C₄⋊C₄×C₄₇⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄₇×#1986	C₂	1	1	yes	maximal, characteristic, complemented
12	C₄×#10625350	C₂²	1	1	yes	characteristic
13	#15689427	C₄	1	2	yes	complemented
14	#15689420	C₄	1	2	yes	complemented
15	#15689415	C₄	1	1	yes	characteristic, complemented
16	#15689410	C₄	1	1	yes	characteristic, complemented
17	#15689405	C₄	1	1	yes	characteristic, complemented
18	#15689400	C₄	1	1	yes	characteristic, complemented
19	#15689254	—	2	1	no	—
20	#15689254	—	2	1	no	—
21	Q₈×C₄₇⋊C₈	—	2	1	no	—
22	Q₈×C₄₇⋊C₈	—	2	1	no	—
23	#15689185	—	2	1	no	—
24	#15689185	—	2	1	no	—
25	#15689174	—	2	1	no	—
26	#15689174	—	2	1	no	—
27	C₂×#13093959	C₂²	1	2	yes	—
28	#15689159	C₂²	1	2	yes	—
29	#15689151	C₂²	1	1	yes	characteristic
30	#15689151	C₂²	1	1	yes	characteristic
31	#15689150	C₂²	1	2	yes	—
32	#15689147	C₂²	1	1	yes	characteristic
33	C₂×C₄⋊(C₄₇⋊C₈)	C₂²	1	1	yes	characteristic
34	C₂×#13093952	C₂²	1	2	yes	—
35	#15689117	C₂²	1	2	yes	—
36	#15689091	C₂²	1	1	yes	characteristic
37	#15689091	C₂²	1	1	yes	characteristic
38	#15689079	C₂²	1	2	yes	—
39	C₂×C₄×C₄₇⋊C₈	C₂²	1	2	yes	—
40	C₂×C₄×C₄₇⋊C₈	C₂²	1	1	yes	characteristic
41	#15688887	C₂²	1	2	yes	—
42	#15688883	C₂²	1	2	yes	—
43	#15688878	C₂²	1	2	yes	—
44	C₄₇×#533	C₂²	1	1	yes	characteristic
45	C₄×M₁₆×C₄₇	C₂²	1	1	yes	characteristic
46	C₄×C₄⋊C₄×C₄₇	C₂²	1	1	yes	characteristic
47	C₄₇×#339	C₂²	1	2	yes	—
48	C₄₇×#339	C₂²	1	2	yes	—
49	C₂×#10625350	C₂³	1	1	yes	characteristic
50	C₂×#10625329	C₂³	1	2	yes	—
51	C₂²×C₄₇⋊C₈	C₂³	1	2	yes	—
52	C₂²×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
53	C₂²×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
54	C₄×Dic₉₄	C₂×C₄	1	1	yes	characteristic
55	C₄×Dic₉₄	C₂×C₄	1	1	yes	characteristic
56	C₄×D₁₈₈	C₂×C₄	1	1	yes	characteristic
57	C₄×D₁₈₈	C₂×C₄	1	1	yes	characteristic
58	C₄×C₂²⋊D₄₇	—	2	1	no	—
59	C₄×C₂²⋊D₄₇	—	2	1	no	—
60	#13093983	C₂³	1	1	yes	characteristic
61	#13093981	—	2	1	no	—
62	C₄²×D₄₇	—	2	1	no	—
63	#13093959	—	4	2	no	—
64	#13093957	C₂×C₄	1	2	yes	—
65	#13093957	C₂×C₄	1	2	yes	—
66	#13093955	C₂×C₄	1	2	yes	—
67	#13093955	C₂×C₄	1	2	yes	—
68	C₄⋊(C₄₇⋊C₈)	—	2	1	no	—
69	C₄⋊(C₄₇⋊C₈)	—	2	1	no	—
70	C₄⋊(C₄₇⋊C₈)	—	2	2	no	—
71	C₄⋊(C₄₇⋊C₈)	—	2	2	no	—
72	C₄⋊(C₄₇⋊C₈)	C₂×C₄	1	1	yes	characteristic
73	C₄⋊(C₄₇⋊C₈)	C₂×C₄	1	1	yes	characteristic
74	C₄⋊(C₄₇⋊C₈)	C₂×C₄	1	2	yes	—
75	Dic₄₇⋊C₈	—	2	1	no	—
76	Dic₄₇⋊C₈	—	2	1	no	—
77	Dic₄₇⋊C₈	—	2	1	no	—
78	Dic₄₇⋊C₈	—	2	1	no	—
79	#13093952	—	4	2	no	—
80	#13093947	C₂×C₄	1	2	yes	—
81	#13093947	C₂×C₄	1	2	yes	—
82	#13093944	C₂×C₄	1	2	yes	—
83	#13093944	C₂×C₄	1	2	yes	—
84	(C₂×D₄₇)⋊C₈	—	2	1	no	—
85	(C₂×D₄₇)⋊C₈	—	2	1	no	—
86	(C₂×D₄₇)⋊C₈	—	2	1	no	—
87	(C₂×D₄₇)⋊C₈	—	2	1	no	—
88	#13093935	—	2	2	no	—
89	C₄×C₄₇⋊C₈	—	2	2	no	—
90	C₄×C₄₇⋊C₈	—	4	2	no	—
91	C₄×C₄₇⋊C₈	D₄	1	1	yes	characteristic
92	C₄×C₄₇⋊C₈	D₄	1	1	yes	characteristic
93	C₄×C₄₇⋊C₈	D₄	1	1	yes	characteristic
94	C₄×C₄₇⋊C₈	D₄	1	1	yes	characteristic
95	C₂×M₁₆×C₄₇	C₂³	1	1	yes	characteristic
96	C₂×M₁₆×C₄₇	C₂³	1	1	yes	characteristic
97	C₄⋊Q₈×C₄₇	C₂×C₄	1	1	yes	characteristic
98	C₄⋊Q₈×C₄₇	C₂×C₄	1	1	yes	characteristic
99	#125×C₄₇	C₂×C₄	1	2	yes	—
100	C₂²⋊Q₈×C₄₇	—	2	1	no	—
101	C₂²⋊Q₈×C₄₇	—	2	1	no	—
102	C₄×Q₈×C₄₇	—	2	1	no	—
103	C₄×Q₈×C₄₇	—	2	1	no	—
104	#117×C₄₇	C₂³	1	2	yes	—
105	C₂×C₄⋊C₄×C₄₇	—	2	1	no	—
106	C₂×C₄²×C₄₇	C₂³	1	2	yes	—
107	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
108	#97×C₄₇	—	2	1	no	—
109	C₄×C₈×C₄₇	—	2	1	no	—
110	#95×C₄₇	—	2	1	no	—
111	C₂×Q₈×C₄₇	—	2	1	no	—
112	C₂×Q₈×C₄₇	—	2	1	no	—
113	C₂²×C₄×C₄₇	—	2	2	no	—
114	C₂²×C₄×C₄₇	#41	1	1	yes	characteristic
115	C₂²×C₄×C₄₇	#41	1	1	yes	characteristic
116	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
117	C₂×C₂²⋊D₄₇	—	2	1	no	—
118	#10625350	—	2	1	no	—
119	#10625350	—	2	1	no	—
120	#10625350	—	2	1	no	—
121	#10625350	—	2	1	no	—
122	C₂×D₁₈₈	C₂²×C₄	1	1	yes	characteristic
123	C₂×C₄×D₄₇	—	2	1	no	—
124	C₂×C₄×D₄₇	—	2	1	no	—
125	C₂×C₄×D₄₇	—	2	1	no	—
126	C₂×Dic₉₄	C₂²×C₄	1	1	yes	characteristic
127	M₁₆×C₄₇	—	2	1	no	—
128	M₁₆×C₄₇	—	2	1	no	—
129	M₁₆×C₄₇	—	2	1	no	—
130	M₁₆×C₄₇	—	2	1	no	—
131	C₂×C₈×C₄₇	—	2	1	no	—
132	C₂×C₈×C₄₇	—	2	1	no	—
133	C₄⋊C₄×C₄₇	—	2	4	no	—
134	C₄⋊C₄×C₄₇	—	2	2	no	—
135	C₄⋊C₄×C₄₇	—	2	2	no	—
136	C₄⋊C₄×C₄₇	—	2	1	no	—
137	C₄⋊C₄×C₄₇	—	2	1	no	—
138	C₄⋊C₄×C₄₇	C₂²×C₄	1	2	yes	—
139	C₄⋊C₄×C₄₇	C₂²×C₄	1	2	yes	—
140	C₂²⋊C₄×C₄₇	—	2	2	no	—
141	C₄²×C₄₇	—	2	2	no	—
142	C₄²×C₄₇	—	2	2	no	—
143	C₄²×C₄₇	—	2	2	no	—
144	C₄²×C₄₇	C₂²×C₄	1	1	yes	characteristic
145	C₄²×C₄₇	C₂²×C₄	1	1	yes	characteristic
146	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
147	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
148	C₂²⋊Dic₄₇	—	2	1	no	—
149	(C₂×D₄₇)⋊C₄	—	2	1	no	—
150	(C₂×D₄₇)⋊C₄	—	2	1	no	—
151	C₄⋊Dic₄₇	C₂²×C₄	1	1	yes	characteristic
152	C₄⋊Dic₄₇	C₂²×C₄	1	1	yes	characteristic
153	Dic₄₇⋊C₄	—	2	1	no	—
154	Dic₄₇⋊C₄	—	2	1	no	—
155	C₄×Dic₄₇	—	2	1	no	—
156	C₄×Dic₄₇	—	2	1	no	—
157	C₄×Dic₄₇	—	2	1	no	—
158	#10625329	—	2	2	no	—
159	#10625329	—	2	2	no	—
160	C₂×C₄₇⋊C₈	—	2	1	no	—
161	C₂×C₄₇⋊C₈	—	2	2	no	—
162	C₂×C₄₇⋊C₈	—	2	2	no	—
163	C₂×C₄₇⋊C₈	—	2	1	no	—
164	C₂×C₄₇⋊C₈	—	2	1	no	—
165	C₂×C₄₇⋊C₈	—	2	1	no	—
166	C₂×C₄₇⋊C₈	—	2	2	no	—
167	C₂×C₄₇⋊C₈	C₂²×C₄	1	2	yes	—
168	C₂×C₄₇⋊C₈	C₂²×C₄	1	2	yes	—
169	C₂×C₄₇⋊C₈	C₂×D₄	1	1	yes	characteristic
170	C₂×C₄₇⋊C₈	C₂×D₄	1	1	yes	characteristic
171	C₂×C₄₇⋊C₈	C₂×D₄	1	1	yes	characteristic
172	C₂×C₄₇⋊C₈	C₂×D₄	1	1	yes	characteristic
173	C₂³×C₄₇	C₂×#41	1	1	yes	characteristic
174	C₂²×D₄₇	—	2	1	no	—
175	Q₈×C₄₇	—	4	2	no	—
176	Q₈×C₄₇	—	4	2	no	—
177	C₂×C₄×C₄₇	—	2	2	no	—
178	C₂×C₄×C₄₇	—	2	4	no	—
179	C₂×C₄×C₄₇	—	2	2	no	—
180	C₂×C₄×C₄₇	—	2	2	no	—
181	C₂×C₄×C₄₇	—	4	1	no	—
182	C₂×C₄×C₄₇	—	4	2	no	—
183	C₂×C₄×C₄₇	—	4	2	no	—
184	C₂×C₄×C₄₇	C₄×D₄	1	1	yes	characteristic
185	C₂×C₄×C₄₇	C₄×D₄	1	1	yes	characteristic
186	C₂×C₄×C₄₇	C₄×D₄	1	1	yes	characteristic
187	C₂×C₄×C₄₇	C₄×D₄	1	1	yes	characteristic
188	C₂×C₄×C₄₇	C₂³×C₄	1	1	yes	characteristic
189	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
190	C₂×C₄×C₄₇	H(5,𝔽₂)	1	1	yes	characteristic
191	C₂×C₄×C₄₇	2₋¹⁺⁴	1	1	yes	characteristic
192	C₂×C₄×C₄₇	2₋¹⁺⁴	1	1	yes	characteristic
193	C₂×C₄×C₄₇	2₋¹⁺⁴	1	1	yes	characteristic
194	C₂²⋊D₄₇	—	4	1	no	—
195	C₂²⋊D₄₇	—	4	1	no	—
196	C₂×Dic₄₇	—	2	1	no	—
197	C₂×Dic₄₇	—	2	1	no	—
198	C₂×Dic₄₇	—	2	1	no	—
199	D₁₈₈	—	2	1	no	—
200	D₁₈₈	—	2	1	no	—
201	C₄×D₄₇	—	4	2	no	—
202	C₄×D₄₇	—	4	1	no	—
203	C₄×D₄₇	—	4	1	no	—
204	C₄×D₄₇	—	4	2	no	—
205	Dic₉₄	—	2	1	no	—
206	Dic₉₄	—	2	1	no	—
207	C₈×C₄₇	—	4	1	no	—
208	C₈×C₄₇	—	4	1	no	—
209	C₄₇⋊C₈	—	2	2	no	—
210	C₄₇⋊C₈	—	2	2	no	—
211	C₄₇⋊C₈	—	2	1	no	—
212	C₄₇⋊C₈	—	2	1	no	—
213	C₄₇⋊C₈	—	2	1	no	—
214	C₄₇⋊C₈	—	2	1	no	—
215	C₄₇⋊C₈	—	4	2	no	—
216	#22130	—	47	1	no	maximal, Sylow
217	C₂²×C₄₇	—	2	1	no	—
218	C₂²×C₄₇	—	2	1	no	—
219	C₂²×C₄₇	C₂×C₄×D₄	1	1	yes	characteristic
220	C₂²×C₄₇	#541	1	1	yes	characteristic
221	C₂²×C₄₇	#542	1	1	yes	characteristic
222	C₂×D₄₇	—	4	1	no	—
223	C₂×D₄₇	—	4	1	no	—
224	C₂×D₄₇	—	4	1	no	—
225	C₄×C₄₇	—	2	1	no	—
226	C₄×C₄₇	—	2	1	no	—
227	C₄×C₄₇	—	2	1	no	—
228	C₄×C₄₇	—	4	4	no	—
229	C₄×C₄₇	—	4	2	no	—
230	C₄×C₄₇	—	4	2	no	—
231	C₄×C₄₇	#443	1	2	yes	—
232	C₄×C₄₇	#519	1	1	yes	characteristic
233	C₄×C₄₇	#520	1	1	yes	characteristic
234	C₄×C₄₇	#536	1	1	yes	characteristic
235	C₄×C₄₇	#537	1	1	yes	characteristic
236	Dic₄₇	—	4	1	no	—
237	Dic₄₇	—	4	1	no	—
238	Dic₄₇	—	4	1	no	—
239	#3076	—	47	1	no	—
240	#2960	—	47	1	no	—
241	#2922	—	47	1	no	—
242	#1986	D₄₇	1	1	yes	characteristic, complemented
243	#1950	—	47	1	no	—
244	#1945	—	47	2	no	—
245	#1937	—	47	2	no	—
246	#1929	—	47	2	no	—
247	#1922	—	47	2	no	—
248	#1806	—	47	1	no	—
249	C₈×C₄⋊C₄	—	47	1	no	—
250	C₂×C₄₇	—	2	1	no	—
251	C₂×C₄₇	—	2	1	no	—
252	C₂×C₄₇	#2323	1	1	yes	characteristic
253	C₂×C₄₇	C₂×#443	1	1	yes	characteristic
254	C₂×C₄₇	#2955	1	1	yes	characteristic
255	D₄₇	—	8	1	no	—
256	#533	C₂×D₄₇	1	1	yes	characteristic
257	C₄×#41	—	47	1	no	—
258	#479	—	47	2	no	—
259	#478	—	47	2	no	—
260	#477	—	47	1	no	—
261	#476	—	47	1	no	—
262	#475	—	47	1	no	—
263	#474	—	47	1	no	—
264	#446	—	94	1	no	—
265	#446	—	94	1	no	—
266	C₈×Q₈	—	94	1	no	—
267	C₈×Q₈	—	94	1	no	—
268	#433	—	94	1	no	—
269	#433	—	94	1	no	—
270	#431	—	94	1	no	—
271	#431	—	94	1	no	—
272	C₂×#108	—	47	2	no	—
273	#427	—	47	2	no	—
274	#424	—	47	1	no	—
275	#424	—	47	1	no	—
276	#424	—	47	2	no	—
277	#423	—	47	1	no	—
278	C₂×C₄⋊C₈	—	47	1	no	—
279	C₂×#104	—	47	2	no	—
280	#416	—	47	2	no	—
281	#408	—	47	1	no	—
282	#408	—	47	1	no	—
283	#405	—	47	2	no	—
284	C₄×M₁₆	C₂×D₄₇	1	1	yes	characteristic
285	C₂×C₄×C₈	—	47	1	no	—
286	C₂×C₄×C₈	—	47	2	no	—
287	C₄×C₄⋊C₄	C₂×D₄₇	1	1	yes	characteristic
288	#341	—	47	2	no	—
289	#339	—	47	2	no	—
290	#339	C₂×D₄₇	1	2	yes	—
291	#339	C₂×D₄₇	1	2	yes	—
292	#336	—	47	2	no	—
293	C₄₇	#22130	1	1	yes	characteristic, complemented, Sylow
294	C₂×#41	—	47	1	no	—
295	C₂×M₁₆	—	47	2	no	—
296	C₂×M₁₆	C₂²×D₄₇	1	1	yes	characteristic
297	C₂×M₁₆	C₂²×D₄₇	1	1	yes	characteristic
298	C₂²×C₈	—	47	1	no	—
299	C₂²×C₈	—	47	2	no	—
300	C₂²×C₈	—	47	1	no	—
301	C₄⋊Q₈	C₄×D₄₇	1	1	yes	characteristic
302	C₄⋊Q₈	C₄×D₄₇	1	1	yes	characteristic
303	#125	C₄×D₄₇	1	2	yes	—
304	C₂²⋊Q₈	—	2	1	no	—
305	C₂²⋊Q₈	—	2	1	no	—
306	C₄×Q₈	—	2	1	no	—
307	C₄×Q₈	—	2	1	no	—
308	C₄×Q₈	—	47	1	no	—
309	C₄×Q₈	—	47	1	no	—
310	C₄×D₄	—	47	1	no	—
311	C₄×D₄	—	47	1	no	—
312	C₄×D₄	—	94	1	no	—
313	C₄×D₄	—	94	1	no	—
314	#117	—	47	1	no	—
315	#117	—	94	1	no	—
316	#117	C₂²×D₄₇	1	2	yes	—
317	C₂×C₄⋊C₄	—	2	1	no	—
318	C₂×C₄²	—	94	1	no	—
319	C₂×C₄²	C₂²×D₄₇	1	2	yes	—
320	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
321	#108	—	188	2	no	—
322	#107	—	47	2	no	—
323	#107	—	47	2	no	—
324	#106	—	47	2	no	—
325	#106	—	47	2	no	—
326	C₄⋊C₈	—	47	1	no	—
327	C₄⋊C₈	—	47	1	no	—
328	C₄⋊C₈	—	47	2	no	—
329	C₄⋊C₈	—	94	2	no	—
330	C₄⋊C₈	—	94	2	no	—
331	C₄⋊C₈	—	94	1	no	—
332	C₄⋊C₈	—	94	1	no	—
333	C₄⋊C₈	—	94	1	no	—
334	C₄⋊C₈	—	94	1	no	—
335	C₄⋊C₈	—	94	1	no	—
336	C₄⋊C₈	—	94	1	no	—
337	#104	—	188	2	no	—
338	#103	—	47	2	no	—
339	#103	—	47	2	no	—
340	#102	—	47	2	no	—
341	#102	—	47	2	no	—
342	C₂²⋊C₈	—	94	1	no	—
343	C₂²⋊C₈	—	94	1	no	—
344	C₂²⋊C₈	—	94	1	no	—
345	C₂²⋊C₈	—	94	1	no	—
346	#97	—	2	1	no	—
347	#97	—	94	2	no	—
348	C₄×C₈	—	2	1	no	—
349	C₄×C₈	—	47	1	no	—
350	C₄×C₈	—	47	1	no	—
351	C₄×C₈	—	47	1	no	—
352	C₄×C₈	—	47	1	no	—
353	C₄×C₈	—	94	2	no	—
354	C₄×C₈	—	188	2	no	—
355	#95	—	2	1	no	—
356	#41	—	94	1	no	—
357	#41	—	94	1	no	—
358	#41	—	94	1	no	—
359	#41	—	94	1	no	—
360	C₂×Q₈	—	2	1	no	—
361	C₂×Q₈	—	2	1	no	—
362	C₂×Q₈	—	47	1	no	—
363	C₂×D₄	—	47	1	no	—
364	C₂×D₄	—	94	1	no	—
365	C₂²×C₄	—	2	2	no	—
366	C₂²×C₄	—	94	1	no	—
367	C₂²×C₄	—	94	1	no	—
368	C₂²×C₄	—	94	1	no	—
369	C₂²×C₄	#10625352	1	1	yes	characteristic
370	C₂²×C₄	#10625352	1	1	yes	characteristic
371	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
372	M₁₆	—	2	1	no	—
373	M₁₆	—	2	1	no	—
374	M₁₆	—	2	1	no	—
375	M₁₆	—	2	1	no	—
376	M₁₆	—	94	2	no	—
377	M₁₆	—	94	2	no	—
378	C₂×C₈	—	2	1	no	—
379	C₂×C₈	—	2	1	no	—
380	C₂×C₈	—	47	2	no	—
381	C₂×C₈	—	47	2	no	—
382	C₂×C₈	—	47	1	no	—
383	C₂×C₈	—	47	1	no	—
384	C₂×C₈	—	47	1	no	—
385	C₂×C₈	—	47	1	no	—
386	C₂×C₈	—	94	1	no	—
387	C₂×C₈	—	94	2	no	—
388	C₂×C₈	—	94	1	no	—
389	C₂×C₈	—	94	2	no	—
390	C₂×C₈	—	94	1	no	—
391	C₂×C₈	—	94	1	no	—
392	C₂×C₈	—	94	2	no	—
393	C₄⋊C₄	—	2	4	no	—
394	C₄⋊C₄	—	2	2	no	—
395	C₄⋊C₄	—	2	2	no	—
396	C₄⋊C₄	—	2	1	no	—
397	C₄⋊C₄	—	2	1	no	—
398	C₄⋊C₄	—	47	1	no	—
399	C₄⋊C₄	—	47	1	no	—
400	C₄⋊C₄	—	94	1	no	—
401	C₄⋊C₄	—	94	1	no	—
402	C₄⋊C₄	C₂×C₄×D₄₇	1	2	yes	—
403	C₄⋊C₄	C₂×C₄×D₄₇	1	2	yes	—
404	C₂²⋊C₄	—	2	2	no	—
405	C₂²⋊C₄	—	94	1	no	—
406	C₂²⋊C₄	—	94	1	no	—
407	C₂²⋊C₄	—	94	1	no	—
408	C₄²	—	2	2	no	—
409	C₄²	—	2	2	no	—
410	C₄²	—	2	2	no	—
411	C₄²	—	94	1	no	—
412	C₄²	—	94	1	no	—
413	C₄²	—	94	1	no	—
414	C₄²	C₂×C₄×D₄₇	1	1	yes	characteristic
415	C₄²	C₂×C₄×D₄₇	1	1	yes	characteristic
416	C₄²	D₄×D₄₇	1	1	yes	characteristic
417	C₄²	D₄×D₄₇	1	1	yes	characteristic
418	C₂³	—	94	1	no	—
419	C₂³	C₂×#10625352	1	1	yes	characteristic
420	Q₈	—	4	2	no	—
421	Q₈	—	4	2	no	—
422	Q₈	—	94	1	no	—
423	Q₈	—	94	1	no	—
424	D₄	—	94	1	no	—
425	D₄	—	94	1	no	—
426	D₄	—	188	1	no	—
427	D₄	—	188	1	no	—
428	C₂×C₄	—	2	2	no	—
429	C₂×C₄	—	2	4	no	—
430	C₂×C₄	—	2	2	no	—
431	C₂×C₄	—	2	2	no	—
432	C₂×C₄	—	4	1	no	—
433	C₂×C₄	—	4	2	no	—
434	C₂×C₄	—	4	2	no	—
435	C₂×C₄	—	94	1	no	—
436	C₂×C₄	—	94	1	no	—
437	C₂×C₄	—	94	1	no	—
438	C₂×C₄	—	188	2	no	—
439	C₂×C₄	—	188	2	no	—
440	C₂×C₄	—	188	1	no	—
441	C₂×C₄	—	188	1	no	—
442	C₂×C₄	(C₂²⋊D₄₇)⋊C₄	1	1	yes	characteristic
443	C₂×C₄	(C₂²⋊D₄₇)⋊C₄	1	1	yes	characteristic
444	C₂×C₄	(C₂²⋊D₄₇)⋊C₄	1	1	yes	characteristic
445	C₂×C₄	(C₂²⋊D₄₇)⋊C₄	1	1	yes	characteristic
446	C₂×C₄	C₂²×C₄×D₄₇	1	1	yes	characteristic
447	C₂×C₄	C₂×D₄×D₄₇	1	1	yes	characteristic
448	C₂×C₄	#13094070	1	1	yes	characteristic
449	C₂×C₄	#13094071	1	1	yes	characteristic
450	C₂×C₄	#13094072	1	1	yes	characteristic
451	C₂×C₄	#13094072	1	1	yes	characteristic
452	C₈	—	4	1	no	—
453	C₈	—	4	1	no	—
454	C₈	—	94	2	no	—
455	C₈	—	94	2	no	—
456	C₈	—	94	1	no	—
457	C₈	—	94	1	no	—
458	C₈	—	94	1	no	—
459	C₈	—	94	1	no	—
460	C₈	—	188	2	no	—
461	C₂²	—	2	1	no	—
462	C₂²	—	2	1	no	—
463	C₂²	—	188	1	no	—
464	C₂²	—	188	1	no	—
465	C₂²	—	188	1	no	—
466	C₂²	C₂×(C₂²⋊D₄₇)⋊C₄	1	1	yes	characteristic
467	C₂²	#15689734	1	1	yes	characteristic
468	C₂²	#15689742	1	1	yes	characteristic
469	C₄	—	2	1	no	—
470	C₄	—	2	1	no	—
471	C₄	—	2	1	no	—
472	C₄	—	4	4	no	—
473	C₄	—	4	2	no	—
474	C₄	—	4	2	no	—
475	C₄	—	188	1	no	—
476	C₄	—	188	1	no	—
477	C₄	—	188	1	no	—
478	C₄	#15689237	1	2	yes	—
479	C₄	#15689599	1	1	yes	characteristic
480	C₄	#15689605	1	1	yes	characteristic
481	C₄	#15689696	1	1	yes	characteristic
482	C₄	#15689703	1	1	yes	characteristic
483	C₂	—	2	1	no	—
484	C₂	—	2	1	no	—
485	C₂	—	376	1	no	—
486	C₂	#20246073	1	1	yes	characteristic
487	C₂	C₂×#15689237	1	1	yes	characteristic
488	C₂	#20252287	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂×D₄×D₄₇
commutator	C₂×C₄×C₄₇	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₄₇
Fitting	C₄₇×#1986	C₂
socle	C₂²×C₄₇	C₂×C₄×D₄
prime radical	C₂×#10625350	C₂³
cosocle	C₂²×C₄×C₄₇	C₂⁴
hypercenter	#1986	D₄₇
hypocenter	C₄₇	#22130
LCS	G ▷ C₂×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #1986

Complements

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

N	H ≅ G/N	type
2. #20252323	C₂	semidirect
4. #20244163	C₂	semidirect
5. #20244135	C₂	semidirect
8. #20243985	C₂	semidirect
10. C₄⋊C₄×C₄₇⋊C₈	C₂	semidirect
11. C₄₇×#1986	C₂	semidirect
13. #15689427	C₄	semidirect
14. #15689420	C₄	semidirect
15. #15689415	C₄	semidirect
16. #15689410	C₄	semidirect
17. #15689405	C₄	semidirect
18. #15689400	C₄	semidirect
242. #1986	D₄₇	semidirect
293. C₄₇	#22130	semidirect

Maximal subgroups

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

subgroup	index
#20253170	2
#20252323	2
#20252033	2
#20244163	2
#20244135	2
#20244093	2
#20244034	2
#20243985	2
#20243409	2
C₄⋊C₄×C₄₇⋊C₈	2
C₄₇×#1986	2
#22130	47