Subgroups — #20257421

Order 6016.

1252 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	#15689839	C₂	1	1	yes	maximal, characteristic, complemented
2	#15689826	C₂	1	2	yes	maximal, complemented
3	#15689821	C₂	1	2	yes	maximal, complemented
4	#15689795	C₂	1	1	yes	maximal, characteristic, complemented
5	#15689764	C₂	1	2	yes	maximal, complemented
6	#15689764	C₂	1	4	yes	maximal, complemented
7	D₄×D₁₈₈	C₂	1	1	yes	maximal, characteristic, complemented
8	D₄×D₁₈₈	C₂	1	2	yes	maximal, complemented
9	#15689729	C₂	1	2	yes	maximal, complemented
10	#15689713	C₂	1	4	yes	maximal, complemented
11	#15689674	C₂	1	1	yes	maximal, characteristic, complemented
12	#15689660	C₂	1	1	yes	maximal, characteristic, complemented
13	#15689636	C₂	1	2	yes	maximal, complemented
14	C₂×#13093999	C₂	1	2	yes	maximal, complemented
15	#15689595	C₂	1	2	yes	maximal, complemented
16	C₄×D₄×D₄₇	C₂	1	1	yes	maximal, characteristic, complemented
17	C₄₇×#554	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂×#10625354	C₂²	1	2	yes	complemented
19	C₂×#10625354	C₂²	1	2	yes	complemented
20	C₂²×D₁₈₈	C₂²	1	2	yes	complemented
21	C₂²×D₁₈₈	C₂²	1	4	yes	complemented
22	C₂×D₄×D₄₇	C₂²	1	1	yes	characteristic
23	C₂×D₄×D₄₇	C₂²	1	2	yes	—
24	C₂²×C₄×D₄₇	C₂²	1	2	yes	complemented
25	#13094021	C₂²	1	2	yes	complemented
26	#13094021	C₂²	1	1	yes	characteristic, complemented
27	#13094019	C₂²	1	4	yes	complemented
28	#13094019	C₂²	1	2	yes	complemented
29	#13094015	C₂²	1	1	yes	characteristic, complemented
30	#13094013	C₂²	1	1	yes	characteristic, complemented
31	#13094013	C₂²	1	4	yes	complemented
32	#13094013	C₂²	1	2	yes	complemented
33	#13094009	C₂²	1	4	yes	complemented
34	#13094009	C₂²	1	4	yes	complemented
35	#13094009	C₂²	1	2	yes	complemented
36	#13094009	C₂²	1	4	yes	complemented
37	#13094000	C₂²	1	1	yes	characteristic, complemented
38	#13093999	C₂²	1	1	yes	characteristic
39	#13093999	C₂²	1	2	yes	complemented
40	#13093999	C₂²	1	2	yes	complemented
41	#13093999	C₂²	1	4	yes	complemented
42	#13093999	C₂²	1	4	yes	complemented
43	#13093999	C₂²	1	2	yes	complemented
44	#13093999	C₂²	1	4	yes	complemented
45	#13093999	C₂²	1	4	yes	complemented
46	#13093999	C₂²	1	2	yes	complemented
47	#13093999	C₂²	1	2	yes	complemented
48	#13093999	C₂²	1	2	yes	complemented
49	#13093998	C₂²	1	2	yes	complemented
50	#13093998	C₂²	1	4	yes	complemented
51	#13093994	C₂²	1	4	yes	complemented
52	#13093994	C₂²	1	4	yes	complemented
53	#13093994	C₂²	1	4	yes	complemented
54	C₄×D₁₈₈	C₂²	1	2	yes	complemented
55	C₄×D₁₈₈	C₂²	1	1	yes	characteristic, complemented
56	C₄×D₁₈₈	C₂²	1	2	yes	complemented
57	C₄×D₁₈₈	C₂²	1	1	yes	characteristic, complemented
58	D₄×Dic₄₇	C₂²	1	1	yes	characteristic
59	#13093986	C₂²	1	1	yes	characteristic, complemented
60	#13093986	C₂²	1	2	yes	complemented
61	#13093986	C₂²	1	2	yes	complemented
62	#13093986	C₂²	1	4	yes	complemented
63	C₄×C₂²⋊D₄₇	C₂²	1	2	yes	complemented
64	C₄×C₂²⋊D₄₇	C₂²	1	4	yes	complemented
65	(C₂²⋊D₄₇)⋊C₄	C₂²	1	2	yes	complemented
66	(C₂²⋊D₄₇)⋊C₄	C₂²	1	4	yes	complemented
67	#13093982	C₂²	1	2	yes	complemented
68	#13093982	C₂²	1	2	yes	complemented
69	#13093981	C₂²	1	2	yes	complemented
70	C₄⋊C₄×D₄₇	C₂²	1	1	yes	characteristic, complemented
71	C₂×(C₂×D₄₇)⋊C₄	C₂²	1	4	yes	complemented
72	C₂²⋊C₄×D₄₇	C₂²	1	2	yes	complemented
73	C₂²⋊C₄×D₄₇	C₂²	1	4	yes	complemented
74	C₄²×D₄₇	C₂²	1	1	yes	characteristic, complemented
75	C₄⋊Q₈×C₄₇	C₂²	1	1	yes	characteristic, complemented
76	#125×C₄₇	C₂²	1	2	yes	complemented
77	C₂²⋊Q₈×C₄₇	C₂²	1	2	yes	complemented
78	C₂²⋊Q₈×C₄₇	C₂²	1	4	yes	complemented
79	C₄×Q₈×C₄₇	C₂²	1	1	yes	characteristic, complemented
80	C₄×D₄×C₄₇	C₂²	1	1	yes	characteristic
81	C₄×D₄×C₄₇	C₂²	1	2	yes	—
82	C₂×C₄⋊C₄×C₄₇	C₂²	1	2	yes	complemented
83	C₂³×D₄₇	C₂³	1	2	yes	—
84	C₂³×D₄₇	C₂³	1	4	yes	—
85	C₂×Q₈×C₄₇	C₂³	1	1	yes	characteristic
86	C₂×Q₈×C₄₇	C₂³	1	2	yes	—
87	C₂×D₄×C₄₇	C₂³	1	1	yes	characteristic
88	C₂²×C₄×C₄₇	C₂³	1	2	yes	—
89	C₂²×C₄×C₄₇	C₂³	1	4	yes	—
90	C₂×C₂²⋊D₄₇	C₂³	1	2	yes	—
91	C₂×C₂²⋊D₄₇	C₂³	1	4	yes	—
92	C₂²×Dic₄₇	C₂³	1	2	yes	—
93	#10625354	—	4	4	no	—
94	#10625354	—	4	4	no	—
95	D₄×D₄₇	—	2	4	no	—
96	D₄×D₄₇	—	2	8	no	—
97	C₂×D₁₈₈	—	4	4	no	—
98	C₂×D₁₈₈	—	4	8	no	—
99	C₂×D₁₈₈	C₂³	1	1	yes	characteristic
100	C₂×D₁₈₈	C₂³	1	2	yes	—
101	C₂×D₁₈₈	C₂³	1	4	yes	—
102	C₂×D₁₈₈	C₂³	1	2	yes	—
103	C₂×D₁₈₈	C₂³	1	2	yes	—
104	C₂×D₁₈₈	C₂³	1	1	yes	characteristic
105	C₂×D₁₈₈	C₂³	1	4	yes	—
106	C₂×D₁₈₈	C₂³	1	2	yes	—
107	C₂×D₁₈₈	C₂³	1	4	yes	—
108	C₂×D₁₈₈	C₂³	1	4	yes	—
109	C₂×D₁₈₈	C₂³	1	4	yes	—
110	C₂×C₄×D₄₇	—	4	4	no	—
111	C₂×C₄×D₄₇	C₂³	1	1	yes	characteristic
112	C₂×C₄×D₄₇	C₂³	1	1	yes	characteristic
113	C₂×C₄×D₄₇	C₂³	1	1	yes	characteristic
114	C₂×C₄×D₄₇	C₂³	1	2	yes	—
115	C₂×C₄×D₄₇	C₂³	1	2	yes	—
116	C₂×C₄×D₄₇	C₂³	1	2	yes	—
117	C₂×C₄×D₄₇	C₂³	1	4	yes	—
118	C₂×C₄×D₄₇	C₂³	1	4	yes	—
119	C₂×C₄×D₄₇	C₂³	1	2	yes	—
120	C₄⋊C₄×C₄₇	C₂³	1	1	yes	characteristic
121	C₄⋊C₄×C₄₇	C₂³	1	4	yes	—
122	C₄⋊C₄×C₄₇	C₂³	1	2	yes	—
123	C₄⋊C₄×C₄₇	C₂³	1	1	yes	characteristic
124	C₄⋊C₄×C₄₇	C₂³	1	2	yes	—
125	C₄⋊C₄×C₄₇	C₂³	1	2	yes	—
126	C₄⋊C₄×C₄₇	C₂³	1	4	yes	—
127	C₂²⋊C₄×C₄₇	C₂³	1	2	yes	—
128	C₂²⋊C₄×C₄₇	C₂³	1	4	yes	—
129	C₄²×C₄₇	C₂³	1	2	yes	—
130	C₄²×C₄₇	C₂³	1	1	yes	characteristic
131	C₂²⋊Dic₄₇	C₂³	1	2	yes	—
132	(C₂×D₄₇)⋊C₄	C₂³	1	2	yes	—
133	(C₂×D₄₇)⋊C₄	C₂³	1	4	yes	—
134	(C₂×D₄₇)⋊C₄	C₂³	1	2	yes	—
135	(C₂×D₄₇)⋊C₄	C₂³	1	2	yes	—
136	(C₂×D₄₇)⋊C₄	C₂³	1	2	yes	—
137	(C₂×D₄₇)⋊C₄	C₂³	1	4	yes	—
138	(C₂×D₄₇)⋊C₄	C₂³	1	4	yes	—
139	(C₂×D₄₇)⋊C₄	C₂³	1	4	yes	—
140	(C₂×D₄₇)⋊C₄	C₂³	1	2	yes	—
141	(C₂×D₄₇)⋊C₄	C₂³	1	4	yes	—
142	(C₂×D₄₇)⋊C₄	C₂³	1	4	yes	—
143	(C₂×D₄₇)⋊C₄	C₂³	1	2	yes	—
144	(C₂×D₄₇)⋊C₄	C₂³	1	2	yes	—
145	C₄⋊Dic₄₇	C₂³	1	1	yes	characteristic
146	C₄⋊Dic₄₇	C₂³	1	1	yes	characteristic
147	C₄⋊Dic₄₇	C₂³	1	2	yes	—
148	Dic₄₇⋊C₄	C₂³	1	2	yes	—
149	Dic₄₇⋊C₄	C₂³	1	2	yes	—
150	Dic₄₇⋊C₄	C₂³	1	2	yes	—
151	C₄×Dic₄₇	C₂³	1	1	yes	characteristic
152	C₄×Dic₄₇	C₂³	1	1	yes	characteristic
153	C₄×Dic₄₇	C₂³	1	1	yes	characteristic
154	C₄×Dic₄₇	C₂³	1	4	yes	—
155	C₂³×C₄₇	C₂⁴	1	2	yes	—
156	C₂²×D₄₇	—	2	4	no	—
157	C₂²×D₄₇	—	2	8	no	—
158	C₂²×D₄₇	—	2	4	no	—
159	C₂²×D₄₇	—	4	2	no	—
160	C₂²×D₄₇	—	4	4	no	—
161	C₂²×D₄₇	—	4	4	no	—
162	C₂²×D₄₇	C₂⁴	1	2	yes	—
163	C₂²×D₄₇	C₂⁴	1	2	yes	—
164	C₂²×D₄₇	C₂⁴	1	4	yes	—
165	C₂²×D₄₇	C₂⁴	1	1	yes	characteristic
166	Q₈×C₄₇	—	2	2	no	—
167	Q₈×C₄₇	—	4	2	no	—
168	D₄×C₄₇	#41	1	4	yes	complemented
169	C₂×C₄×C₄₇	—	2	4	no	—
170	C₂×C₄×C₄₇	—	4	4	no	—
171	C₂×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
172	C₂×C₄×C₄₇	C₂⁴	1	4	yes	—
173	C₂×C₄×C₄₇	C₂⁴	1	2	yes	—
174	C₂×C₄×C₄₇	C₂⁴	1	2	yes	—
175	C₂×C₄×C₄₇	C₂⁴	1	2	yes	—
176	C₂×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
177	C₂×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
178	C₂²⋊D₄₇	—	2	4	no	—
179	C₂²⋊D₄₇	—	2	8	no	—
180	C₂×Dic₄₇	—	4	2	no	—
181	C₂×Dic₄₇	C₂⁴	1	1	yes	characteristic
182	C₂×Dic₄₇	C₂⁴	1	2	yes	—
183	C₂×Dic₄₇	C₂⁴	1	1	yes	characteristic
184	C₂×Dic₄₇	C₂⁴	1	1	yes	characteristic
185	C₂×Dic₄₇	C₂⁴	1	2	yes	—
186	D₁₈₈	—	2	4	no	—
187	D₁₈₈	—	2	8	no	—
188	D₁₈₈	—	2	2	no	—
189	D₁₈₈	—	2	4	no	—
190	D₁₈₈	—	2	2	no	—
191	D₁₈₈	—	2	4	no	—
192	D₁₈₈	—	4	4	no	—
193	D₁₈₈	—	4	4	no	—
194	D₁₈₈	—	4	4	no	—
195	D₁₈₈	—	4	2	no	—
196	D₁₈₈	—	4	4	no	—
197	C₄×D₄₇	—	2	2	no	—
198	C₄×D₄₇	—	2	2	no	—
199	C₄×D₄₇	—	2	4	no	—
200	C₄×D₄₇	—	2	2	no	—
201	C₄×D₄₇	—	2	4	no	—
202	C₄×D₄₇	—	4	2	no	—
203	C₄×D₄₇	—	4	2	no	—
204	C₄×D₄₇	—	4	4	no	—
205	C₄×D₄₇	—	4	4	no	—
206	C₂²×C₄₇	—	2	2	no	—
207	C₂²×C₄₇	—	2	2	no	—
208	C₂²×C₄₇	C₂×#41	1	4	yes	—
209	C₂²×C₄₇	C₂⁵	1	1	yes	characteristic
210	C₂×D₄₇	—	2	1	no	—
211	C₂×D₄₇	—	2	1	no	—
212	C₂×D₄₇	—	2	2	no	—
213	C₂×D₄₇	—	2	2	no	—
214	C₂×D₄₇	—	2	4	no	—
215	C₂×D₄₇	—	2	2	no	—
216	C₂×D₄₇	—	2	4	no	—
217	C₂×D₄₇	—	2	4	no	—
218	C₂×D₄₇	—	2	2	no	—
219	C₂×D₄₇	—	2	2	no	—
220	C₂×D₄₇	—	2	2	no	—
221	C₂×D₄₇	—	4	8	no	—
222	C₂×D₄₇	—	8	8	no	—
223	C₂×D₄₇	H(5,𝔽₂)	1	2	yes	—
224	C₄×C₄₇	—	2	1	no	—
225	C₄×C₄₇	—	2	2	no	—
226	C₄×C₄₇	—	2	2	no	—
227	C₄×C₄₇	—	2	4	no	—
228	C₄×C₄₇	—	2	2	no	—
229	C₄×C₄₇	C₂×#41	1	2	yes	—
230	C₄×C₄₇	H(5,𝔽₂)	1	2	yes	—
231	Dic₄₇	—	2	1	no	—
232	Dic₄₇	—	2	2	no	—
233	Dic₄₇	—	2	1	no	—
234	Dic₄₇	—	2	2	no	—
235	Dic₄₇	—	2	1	no	—
236	#3519	—	47	1	no	maximal, Sylow
237	C₂×C₄₇	—	2	4	no	—
238	C₂×C₄₇	C₂²×#41	1	1	yes	characteristic
239	C₂×C₄₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
240	C₂×C₄₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
241	D₄₇	—	2	2	no	—
242	D₄₇	—	4	2	no	—
243	D₄₇	—	4	4	no	—
244	D₄₇	—	4	2	no	—
245	#555	—	47	1	no	—
246	#554	D₄₇	1	1	yes	characteristic, complemented
247	#553	—	47	2	no	—
248	#553	—	47	2	no	—
249	#550	—	47	1	no	—
250	#546	—	47	4	no	—
251	#546	—	47	2	no	—
252	D₄²	—	47	2	no	—
253	D₄²	—	47	1	no	—
254	#540	—	47	2	no	—
255	#538	—	47	4	no	—
256	#532	—	47	1	no	—
257	#529	—	47	1	no	—
258	#525	—	47	2	no	—
259	C₂×#121	—	47	2	no	—
260	#518	—	47	2	no	—
261	C₂×C₄×D₄	—	47	1	no	—
262	C₄₇	#3519	1	1	yes	characteristic, complemented, Sylow
263	C₂×#41	—	47	2	no	—
264	C₂×#41	—	47	2	no	—
265	C₂²×D₄	—	47	1	no	—
266	C₂²×D₄	—	47	2	no	—
267	C₂²×D₄	—	47	2	no	—
268	C₂²×D₄	—	47	4	no	—
269	C₂³×C₄	—	47	2	no	—
270	C₄⋊Q₈	C₂×D₄₇	1	1	yes	characteristic, complemented
271	#127	—	47	1	no	—
272	#127	—	47	2	no	—
273	#126	—	47	2	no	—
274	#126	—	47	4	no	—
275	#125	—	47	1	no	—
276	#125	C₂×D₄₇	1	2	yes	complemented
277	#124	—	47	1	no	—
278	#124	—	47	2	no	—
279	#124	—	47	4	no	—
280	#123	—	47	4	no	—
281	#123	—	47	2	no	—
282	#123	—	47	4	no	—
283	#123	—	47	4	no	—
284	C₂²⋊Q₈	—	47	1	no	—
285	C₂²⋊Q₈	C₂×D₄₇	1	2	yes	complemented
286	C₂²⋊Q₈	C₂×D₄₇	1	4	yes	complemented
287	#121	—	47	2	no	—
288	#121	—	47	4	no	—
289	#121	—	47	1	no	—
290	#121	—	47	2	no	—
291	#121	—	47	4	no	—
292	#121	—	47	4	no	—
293	#121	—	47	2	no	—
294	#121	—	47	2	no	—
295	#121	—	47	2	no	—
296	#121	—	47	4	no	—
297	#121	—	47	2	no	—
298	#121	—	47	2	no	—
299	#121	—	47	4	no	—
300	#120	—	47	4	no	—
301	#120	—	47	4	no	—
302	#120	—	47	4	no	—
303	C₄×Q₈	C₂×D₄₇	1	1	yes	characteristic, complemented
304	C₄×D₄	—	47	1	no	—
305	C₄×D₄	—	47	2	no	—
306	C₄×D₄	—	47	4	no	—
307	C₄×D₄	—	47	1	no	—
308	C₄×D₄	—	47	2	no	—
309	C₄×D₄	—	47	4	no	—
310	C₄×D₄	—	47	2	no	—
311	C₄×D₄	—	47	2	no	—
312	C₄×D₄	—	47	4	no	—
313	C₄×D₄	—	47	1	no	—
314	C₄×D₄	—	47	2	no	—
315	C₄×D₄	—	47	2	no	—
316	C₄×D₄	—	47	1	no	—
317	C₄×D₄	C₂×D₄₇	1	1	yes	characteristic
318	C₄×D₄	C₂×D₄₇	1	2	yes	—
319	#117	—	47	2	no	—
320	#117	—	47	2	no	—
321	#117	—	47	2	no	—
322	C₂×C₄⋊C₄	—	47	1	no	—
323	C₂×C₄⋊C₄	C₂×D₄₇	1	2	yes	complemented
324	C₂×C₂²⋊C₄	—	47	4	no	—
325	C₂×C₂²⋊C₄	—	47	2	no	—
326	C₂×C₂²⋊C₄	—	47	4	no	—
327	C₂×C₄²	—	47	1	no	—
328	C₂⁴	—	47	2	no	—
329	C₂⁴	—	47	4	no	—
330	#41	—	188	4	no	—
331	#41	—	188	4	no	—
332	C₂×Q₈	C₂²×D₄₇	1	1	yes	characteristic
333	C₂×Q₈	C₂²×D₄₇	1	2	yes	—
334	C₂×D₄	—	47	2	no	—
335	C₂×D₄	—	47	4	no	—
336	C₂×D₄	—	47	1	no	—
337	C₂×D₄	—	47	2	no	—
338	C₂×D₄	—	47	4	no	—
339	C₂×D₄	—	47	2	no	—
340	C₂×D₄	—	47	1	no	—
341	C₂×D₄	—	47	2	no	—
342	C₂×D₄	—	47	4	no	—
343	C₂×D₄	—	47	2	no	—
344	C₂×D₄	—	47	4	no	—
345	C₂×D₄	—	47	4	no	—
346	C₂×D₄	—	47	4	no	—
347	C₂×D₄	—	94	8	no	—
348	C₂×D₄	—	94	4	no	—
349	C₂×D₄	—	188	4	no	—
350	C₂×D₄	—	188	8	no	—
351	C₂×D₄	C₂²×D₄₇	1	1	yes	characteristic
352	C₂²×C₄	—	47	2	no	—
353	C₂²×C₄	—	47	1	no	—
354	C₂²×C₄	—	47	1	no	—
355	C₂²×C₄	—	47	1	no	—
356	C₂²×C₄	—	47	2	no	—
357	C₂²×C₄	—	47	2	no	—
358	C₂²×C₄	—	47	2	no	—
359	C₂²×C₄	—	47	4	no	—
360	C₂²×C₄	—	47	4	no	—
361	C₂²×C₄	—	47	2	no	—
362	C₂²×C₄	—	188	4	no	—
363	C₂²×C₄	C₂²×D₄₇	1	2	yes	—
364	C₂²×C₄	C₂²×D₄₇	1	4	yes	—
365	C₄⋊C₄	—	47	2	no	—
366	C₄⋊C₄	—	47	2	no	—
367	C₄⋊C₄	—	47	2	no	—
368	C₄⋊C₄	—	47	1	no	—
369	C₄⋊C₄	—	47	1	no	—
370	C₄⋊C₄	—	47	2	no	—
371	C₄⋊C₄	C₂²×D₄₇	1	1	yes	characteristic
372	C₄⋊C₄	C₂²×D₄₇	1	1	yes	characteristic
373	C₄⋊C₄	C₂²×D₄₇	1	2	yes	—
374	C₄⋊C₄	C₂²×D₄₇	1	4	yes	—
375	C₄⋊C₄	C₂²×D₄₇	1	2	yes	—
376	C₄⋊C₄	C₂²×D₄₇	1	4	yes	—
377	C₄⋊C₄	C₂²×D₄₇	1	2	yes	—
378	C₂²⋊C₄	—	47	2	no	—
379	C₂²⋊C₄	—	47	2	no	—
380	C₂²⋊C₄	—	47	4	no	—
381	C₂²⋊C₄	—	47	2	no	—
382	C₂²⋊C₄	—	47	4	no	—
383	C₂²⋊C₄	—	47	2	no	—
384	C₂²⋊C₄	—	47	4	no	—
385	C₂²⋊C₄	—	47	2	no	—
386	C₂²⋊C₄	—	47	4	no	—
387	C₂²⋊C₄	—	47	2	no	—
388	C₂²⋊C₄	—	47	2	no	—
389	C₂²⋊C₄	—	47	2	no	—
390	C₂²⋊C₄	—	47	4	no	—
391	C₂²⋊C₄	—	47	4	no	—
392	C₂²⋊C₄	C₂²×D₄₇	1	2	yes	—
393	C₂²⋊C₄	C₂²×D₄₇	1	4	yes	—
394	C₄²	—	47	1	no	—
395	C₄²	—	47	1	no	—
396	C₄²	—	47	1	no	—
397	C₄²	—	47	4	no	—
398	C₄²	C₂²×D₄₇	1	1	yes	characteristic
399	C₄²	C₂²×D₄₇	1	2	yes	—
400	C₂³	—	47	1	no	—
401	C₂³	—	47	2	no	—
402	C₂³	—	47	4	no	—
403	C₂³	—	47	2	no	—
404	C₂³	—	94	4	no	—
405	C₂³	—	94	8	no	—
406	C₂³	—	94	4	no	—
407	C₂³	—	188	4	no	—
408	C₂³	—	188	4	no	—
409	C₂³	—	188	2	no	—
410	C₂³	C₂³×D₄₇	1	2	yes	—
411	Q₈	—	2	2	no	—
412	Q₈	—	4	2	no	—
413	D₄	—	94	4	no	—
414	D₄	—	94	8	no	—
415	D₄	—	94	8	no	—
416	D₄	—	94	4	no	—
417	D₄	—	94	4	no	—
418	D₄	—	94	2	no	—
419	D₄	—	94	2	no	—
420	D₄	—	94	4	no	—
421	D₄	—	188	4	no	—
422	D₄	—	188	4	no	—
423	D₄	—	188	4	no	—
424	D₄	—	188	2	no	—
425	D₄	—	188	4	no	—
426	D₄	#10625354	1	4	yes	complemented
427	C₂×C₄	—	2	4	no	—
428	C₂×C₄	—	4	4	no	—
429	C₂×C₄	—	47	1	no	—
430	C₂×C₄	—	47	2	no	—
431	C₂×C₄	—	47	1	no	—
432	C₂×C₄	—	47	1	no	—
433	C₂×C₄	—	47	2	no	—
434	C₂×C₄	—	94	2	no	—
435	C₂×C₄	—	94	2	no	—
436	C₂×C₄	—	94	4	no	—
437	C₂×C₄	—	94	2	no	—
438	C₂×C₄	—	94	4	no	—
439	C₂×C₄	—	188	2	no	—
440	C₂×C₄	—	188	2	no	—
441	C₂×C₄	—	188	4	no	—
442	C₂×C₄	—	188	4	no	—
443	C₂×C₄	—	188	2	no	—
444	C₂×C₄	C₂³×D₄₇	1	1	yes	characteristic
445	C₂×C₄	C₂³×D₄₇	1	4	yes	—
446	C₂×C₄	C₂³×D₄₇	1	2	yes	—
447	C₂×C₄	C₂³×D₄₇	1	2	yes	—
448	C₂×C₄	C₂³×D₄₇	1	2	yes	—
449	C₂×C₄	C₂³×D₄₇	1	1	yes	characteristic
450	C₂×C₄	C₂³×D₄₇	1	1	yes	characteristic
451	C₂²	—	2	2	no	—
452	C₂²	—	2	2	no	—
453	C₂²	—	47	2	no	—
454	C₂²	—	94	1	no	—
455	C₂²	—	94	1	no	—
456	C₂²	—	94	2	no	—
457	C₂²	—	94	4	no	—
458	C₂²	—	94	2	no	—
459	C₂²	—	94	4	no	—
460	C₂²	—	94	2	no	—
461	C₂²	—	94	2	no	—
462	C₂²	—	94	2	no	—
463	C₂²	—	94	4	no	—
464	C₂²	—	94	2	no	—
465	C₂²	—	376	8	no	—
466	C₂²	—	188	8	no	—
467	C₂²	C₂×#10625354	1	4	yes	—
468	C₂²	C₂⁴×D₄₇	1	1	yes	characteristic
469	C₄	—	2	2	no	—
470	C₄	—	2	4	no	—
471	C₄	—	2	1	no	—
472	C₄	—	2	2	no	—
473	C₄	—	2	2	no	—
474	C₄	—	94	1	no	—
475	C₄	—	94	2	no	—
476	C₄	—	94	1	no	—
477	C₄	—	94	1	no	—
478	C₄	—	94	2	no	—
479	C₄	C₂×#10625354	1	2	yes	—
480	C₄	#13094070	1	2	yes	—
481	C₂	—	2	4	no	—
482	C₂	—	94	2	no	—
483	C₂	—	188	2	no	—
484	C₂	—	188	4	no	—
485	C₂	—	188	2	no	—
486	C₂	C₂²×#10625354	1	1	yes	characteristic
487	C₂	H(5,𝔽₂)×D₄₇	1	1	yes	characteristic
488	C₂	C₂×#13094070	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₄₇
commutator, socle	C₂²×C₄₇	C₂⁵
Fitting	C₄₇×#554	C₂
hypercenter	#554	D₄₇
hypocenter	C₄₇	#3519
LCS	G ▷ C₂²×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂² ◁ #554

Complements

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

N	H ≅ G/N	type
1. #15689839	C₂	semidirect
2. #15689826	C₂	semidirect
3. #15689821	C₂	semidirect
4. #15689795	C₂	semidirect
5. #15689764	C₂	semidirect
6. #15689764	C₂	semidirect
7. D₄×D₁₈₈	C₂	semidirect
8. D₄×D₁₈₈	C₂	semidirect
9. #15689729	C₂	semidirect
10. #15689713	C₂	semidirect
11. #15689674	C₂	semidirect
12. #15689660	C₂	semidirect
13. #15689636	C₂	semidirect
14. C₂×#13093999	C₂	semidirect
15. #15689595	C₂	semidirect
16. C₄×D₄×D₄₇	C₂	semidirect
17. C₄₇×#554	C₂	semidirect
18. C₂×#10625354	C₂²	semidirect
19. C₂×#10625354	C₂²	semidirect
20. C₂²×D₁₈₈	C₂²	semidirect
21. C₂²×D₁₈₈	C₂²	semidirect
24. C₂²×C₄×D₄₇	C₂²	semidirect
25. #13094021	C₂²	semidirect
26. #13094021	C₂²	semidirect
27. #13094019	C₂²	semidirect
28. #13094019	C₂²	semidirect
29. #13094015	C₂²	semidirect
30. #13094013	C₂²	semidirect
31. #13094013	C₂²	semidirect
32. #13094013	C₂²	semidirect
33. #13094009	C₂²	semidirect
34. #13094009	C₂²	semidirect
35. #13094009	C₂²	semidirect
36. #13094009	C₂²	semidirect
37. #13094000	C₂²	semidirect
39. #13093999	C₂²	semidirect
40. #13093999	C₂²	semidirect
41. #13093999	C₂²	semidirect
42. #13093999	C₂²	semidirect
43. #13093999	C₂²	semidirect
44. #13093999	C₂²	semidirect
45. #13093999	C₂²	semidirect
46. #13093999	C₂²	semidirect
47. #13093999	C₂²	semidirect
48. #13093999	C₂²	semidirect
49. #13093998	C₂²	semidirect
50. #13093998	C₂²	semidirect
51. #13093994	C₂²	semidirect
52. #13093994	C₂²	semidirect
53. #13093994	C₂²	semidirect
54. C₄×D₁₈₈	C₂²	semidirect
55. C₄×D₁₈₈	C₂²	semidirect
56. C₄×D₁₈₈	C₂²	semidirect
57. C₄×D₁₈₈	C₂²	semidirect
59. #13093986	C₂²	semidirect
60. #13093986	C₂²	semidirect
61. #13093986	C₂²	semidirect
62. #13093986	C₂²	semidirect
63. C₄×C₂²⋊D₄₇	C₂²	semidirect
64. C₄×C₂²⋊D₄₇	C₂²	semidirect
65. (C₂²⋊D₄₇)⋊C₄	C₂²	semidirect
66. (C₂²⋊D₄₇)⋊C₄	C₂²	semidirect
67. #13093982	C₂²	semidirect
68. #13093982	C₂²	semidirect
69. #13093981	C₂²	semidirect
70. C₄⋊C₄×D₄₇	C₂²	semidirect
71. C₂×(C₂×D₄₇)⋊C₄	C₂²	semidirect
72. C₂²⋊C₄×D₄₇	C₂²	semidirect
73. C₂²⋊C₄×D₄₇	C₂²	semidirect
74. C₄²×D₄₇	C₂²	semidirect
75. C₄⋊Q₈×C₄₇	C₂²	semidirect
76. #125×C₄₇	C₂²	semidirect
77. C₂²⋊Q₈×C₄₇	C₂²	semidirect
78. C₂²⋊Q₈×C₄₇	C₂²	semidirect
79. C₄×Q₈×C₄₇	C₂²	semidirect
82. C₂×C₄⋊C₄×C₄₇	C₂²	semidirect
168. D₄×C₄₇	#41	semidirect
246. #554	D₄₇	semidirect
262. C₄₇	#3519	semidirect
270. C₄⋊Q₈	C₂×D₄₇	semidirect
276. #125	C₂×D₄₇	semidirect
285. C₂²⋊Q₈	C₂×D₄₇	semidirect
286. C₂²⋊Q₈	C₂×D₄₇	semidirect
303. C₄×Q₈	C₂×D₄₇	semidirect
323. C₂×C₄⋊C₄	C₂×D₄₇	semidirect
426. D₄	#10625354	semidirect