Subgroups — #20257436

Order 6016.

1124 conjugacy classes of subgroups.

The subgroup lattice has 462 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#15689833	C₂	1	2	yes	maximal, complemented
2	#15689812	C₂	1	2	yes	maximal, complemented
3	#15689798	C₂	1	4	yes	maximal, complemented
4	Q₈×D₁₈₈	C₂	1	1	yes	maximal, characteristic, complemented
5	#15689783	C₂	1	2	yes	maximal, complemented
6	#15689778	C₂	1	1	yes	maximal, characteristic, complemented
7	#15689776	C₂	1	1	yes	maximal, characteristic, complemented
8	#15689766	C₂	1	2	yes	maximal, complemented
9	#15689742	C₂	1	2	yes	maximal, complemented
10	#15689714	C₂	1	4	yes	maximal, complemented
11	#15689678	C₂	1	1	yes	maximal, characteristic, complemented
12	#15689660	C₂	1	1	yes	maximal, characteristic, complemented
13	#15689635	C₂	1	2	yes	maximal, complemented
14	C₂²⋊Q₈×D₄₇	C₂	1	2	yes	maximal, complemented
15	#15689605	C₂	1	2	yes	maximal, complemented
16	C₄×D₄×D₄₇	C₂	1	1	yes	maximal, characteristic, complemented
17	C₄₇×#556	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂×#10625354	C₂²	1	2	yes	—
19	C₂×#10625350	C₂²	1	2	yes	complemented
20	C₂×Q₈×D₄₇	C₂²	1	2	yes	complemented
21	C₂×D₄×D₄₇	C₂²	1	1	yes	characteristic
22	C₂²×C₄×D₄₇	C₂²	1	2	yes	—
23	#13094024	C₂²	1	2	yes	complemented
24	#13094024	C₂²	1	1	yes	characteristic, complemented
25	#13094019	C₂²	1	2	yes	complemented
26	#13094017	C₂²	1	4	yes	complemented
27	#13094016	C₂²	1	4	yes	complemented
28	#13094015	C₂²	1	1	yes	characteristic, complemented
29	#13094015	C₂²	1	2	yes	complemented
30	#13094013	C₂²	1	1	yes	characteristic, complemented
31	#13094010	C₂²	1	4	yes	complemented
32	#13094009	C₂²	1	2	yes	—
33	#13094009	C₂²	1	4	yes	complemented
34	#13094008	C₂²	1	4	yes	complemented
35	#13094006	C₂²	1	4	yes	—
36	#13094006	C₂²	1	4	yes	complemented
37	#13094004	C₂²	1	2	yes	—
38	#13094004	C₂²	1	4	yes	complemented
39	#13094004	C₂²	1	2	yes	complemented
40	#13094003	C₂²	1	2	yes	complemented
41	#13094002	C₂²	1	4	yes	—
42	#13094002	C₂²	1	4	yes	complemented
43	#13094001	C₂²	1	4	yes	complemented
44	#13094000	C₂²	1	2	yes	—
45	#13094000	C₂²	1	1	yes	characteristic
46	#13094000	C₂²	1	2	yes	complemented
47	#13093999	C₂²	1	1	yes	characteristic
48	#13093999	C₂²	1	2	yes	complemented
49	#13093997	C₂²	1	4	yes	—
50	#13093995	C₂²	1	2	yes	—
51	#13093994	C₂²	1	4	yes	—
52	Q₈×Dic₄₇	C₂²	1	2	yes	complemented
53	#13093989	C₂²	1	2	yes	complemented
54	C₄×D₁₈₈	C₂²	1	2	yes	—
55	C₄×D₁₈₈	C₂²	1	2	yes	—
56	C₄×D₁₈₈	C₂²	1	1	yes	characteristic
57	C₄×D₁₈₈	C₂²	1	4	yes	—
58	C₄×D₁₈₈	C₂²	1	1	yes	characteristic, complemented
59	C₄×D₁₈₈	C₂²	1	4	yes	complemented
60	D₄×Dic₄₇	C₂²	1	1	yes	characteristic
61	#13093986	C₂²	1	1	yes	characteristic
62	#13093986	C₂²	1	4	yes	complemented
63	C₄×C₂²⋊D₄₇	C₂²	1	2	yes	—
64	(C₂²⋊D₄₇)⋊C₄	C₂²	1	2	yes	—
65	#13093982	C₂²	1	2	yes	—
66	#13093981	C₂²	1	2	yes	complemented
67	#13093981	C₂²	1	4	yes	complemented
68	C₄⋊C₄×D₄₇	C₂²	1	1	yes	characteristic
69	C₄⋊C₄×D₄₇	C₂²	1	2	yes	complemented
70	C₄⋊C₄×D₄₇	C₂²	1	2	yes	complemented
71	C₄⋊C₄×D₄₇	C₂²	1	4	yes	complemented
72	C₂²⋊C₄×D₄₇	C₂²	1	4	yes	—
73	C₂²⋊C₄×D₄₇	C₂²	1	2	yes	—
74	C₄²×D₄₇	C₂²	1	1	yes	characteristic
75	C₄⋊Q₈×C₄₇	C₂²	1	1	yes	characteristic, complemented
76	#126×C₄₇	C₂²	1	4	yes	complemented
77	#124×C₄₇	C₂²	1	2	yes	—
78	C₂²⋊Q₈×C₄₇	C₂²	1	2	yes	complemented
79	C₄×Q₈×C₄₇	C₂²	1	1	yes	characteristic, complemented
80	C₄×Q₈×C₄₇	C₂²	1	2	yes	complemented
81	C₄×D₄×C₄₇	C₂²	1	1	yes	characteristic
82	#117×C₄₇	C₂²	1	2	yes	complemented
83	C₂³×D₄₇	C₂³	1	2	yes	—
84	C₂×Q₈×C₄₇	C₂³	1	1	yes	characteristic
85	C₂×Q₈×C₄₇	C₂³	1	2	yes	—
86	C₂×D₄×C₄₇	C₂³	1	1	yes	characteristic
87	C₂²×C₄×C₄₇	C₂³	1	2	yes	—
88	C₂×C₂²⋊D₄₇	C₂³	1	2	yes	—
89	C₂×C₂²⋊D₄₇	C₂³	1	4	yes	—
90	C₂²×Dic₄₇	C₂³	1	2	yes	—
91	#10625354	—	2	8	no	—
92	Q₈×D₄₇	—	4	4	no	—
93	D₄×D₄₇	—	2	4	no	—
94	#10625350	—	4	4	no	—
95	C₂×D₁₈₈	C₂³	1	4	yes	—
96	C₂×D₁₈₈	C₂³	1	2	yes	—
97	C₂×D₁₈₈	C₂³	1	1	yes	characteristic
98	C₂×D₁₈₈	C₂³	1	1	yes	characteristic
99	C₂×C₄×D₄₇	—	4	4	no	—
100	C₂×C₄×D₄₇	C₂³	1	1	yes	characteristic
101	C₂×C₄×D₄₇	C₂³	1	1	yes	characteristic
102	C₂×C₄×D₄₇	C₂³	1	1	yes	characteristic
103	C₂×C₄×D₄₇	C₂³	1	4	yes	—
104	C₂×C₄×D₄₇	C₂³	1	2	yes	—
105	C₂×C₄×D₄₇	C₂³	1	2	yes	—
106	C₂×C₄×D₄₇	C₂³	1	2	yes	—
107	C₂×C₄×D₄₇	C₂³	1	4	yes	—
108	C₂×C₄×D₄₇	C₂³	1	2	yes	—
109	C₂×C₄×D₄₇	C₂³	1	4	yes	—
110	C₂×Dic₉₄	C₂³	1	2	yes	—
111	C₂×Dic₉₄	C₂³	1	4	yes	—
112	C₄⋊C₄×C₄₇	C₂³	1	1	yes	characteristic
113	C₄⋊C₄×C₄₇	C₂³	1	2	yes	—
114	C₄⋊C₄×C₄₇	C₂³	1	1	yes	characteristic
115	C₄⋊C₄×C₄₇	C₂³	1	4	yes	—
116	C₄⋊C₄×C₄₇	C₂³	1	2	yes	—
117	C₄⋊C₄×C₄₇	C₂³	1	2	yes	—
118	C₂²⋊C₄×C₄₇	C₂³	1	4	yes	—
119	C₂²⋊C₄×C₄₇	C₂³	1	2	yes	—
120	C₂²⋊C₄×C₄₇	C₂³	1	4	yes	—
121	C₄²×C₄₇	C₂³	1	4	yes	—
122	C₄²×C₄₇	C₂³	1	1	yes	characteristic
123	C₄²×C₄₇	C₂³	1	2	yes	—
124	C₂²⋊Dic₄₇	C₂³	1	2	yes	—
125	C₂²⋊Dic₄₇	C₂³	1	4	yes	—
126	(C₂×D₄₇)⋊C₄	C₂³	1	2	yes	—
127	(C₂×D₄₇)⋊C₄	C₂³	1	2	yes	—
128	(C₂×D₄₇)⋊C₄	C₂³	1	4	yes	—
129	(C₂×D₄₇)⋊C₄	C₂³	1	2	yes	—
130	(C₂×D₄₇)⋊C₄	C₂³	1	2	yes	—
131	(C₂×D₄₇)⋊C₄	C₂³	1	4	yes	—
132	(C₂×D₄₇)⋊C₄	C₂³	1	2	yes	—
133	(C₂×D₄₇)⋊C₄	C₂³	1	2	yes	—
134	(C₂×D₄₇)⋊C₄	C₂³	1	4	yes	—
135	(C₂×D₄₇)⋊C₄	C₂³	1	2	yes	—
136	C₄⋊Dic₄₇	C₂³	1	1	yes	characteristic
137	C₄⋊Dic₄₇	C₂³	1	1	yes	characteristic
138	C₄⋊Dic₄₇	C₂³	1	2	yes	—
139	C₄⋊Dic₄₇	C₂³	1	4	yes	—
140	C₄⋊Dic₄₇	C₂³	1	2	yes	—
141	C₄⋊Dic₄₇	C₂³	1	4	yes	—
142	C₄⋊Dic₄₇	C₂³	1	2	yes	—
143	Dic₄₇⋊C₄	C₂³	1	2	yes	—
144	Dic₄₇⋊C₄	C₂³	1	2	yes	—
145	Dic₄₇⋊C₄	C₂³	1	4	yes	—
146	Dic₄₇⋊C₄	C₂³	1	4	yes	—
147	Dic₄₇⋊C₄	C₂³	1	2	yes	—
148	Dic₄₇⋊C₄	C₂³	1	4	yes	—
149	C₄×Dic₄₇	C₂³	1	1	yes	characteristic
150	C₄×Dic₄₇	C₂³	1	1	yes	characteristic
151	C₄×Dic₄₇	C₂³	1	1	yes	characteristic
152	C₄×Dic₄₇	C₂³	1	4	yes	—
153	C₂³×C₄₇	C₂⁴	1	2	yes	—
154	C₂²×D₄₇	—	2	4	no	—
155	C₂²×D₄₇	—	2	4	no	—
156	C₂²×D₄₇	—	4	2	no	—
157	C₂²×D₄₇	C₂⁴	1	2	yes	—
158	C₂²×D₄₇	C₂⁴	1	2	yes	—
159	C₂²×D₄₇	C₂⁴	1	1	yes	characteristic
160	Q₈×C₄₇	—	2	4	no	—
161	Q₈×C₄₇	—	2	2	no	—
162	D₄×C₄₇	—	2	2	no	—
163	C₂×C₄×C₄₇	—	2	4	no	—
164	C₂×C₄×C₄₇	C₂⁴	1	4	yes	—
165	C₂×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
166	C₂×C₄×C₄₇	C₂⁴	1	2	yes	—
167	C₂×C₄×C₄₇	C₂⁴	1	2	yes	—
168	C₂×C₄×C₄₇	C₂⁴	1	2	yes	—
169	C₂×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
170	C₂×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
171	C₂²⋊D₄₇	—	2	4	no	—
172	C₂²⋊D₄₇	—	4	4	no	—
173	C₂×Dic₄₇	—	4	2	no	—
174	C₂×Dic₄₇	C₂⁴	1	1	yes	characteristic
175	C₂×Dic₄₇	C₂⁴	1	1	yes	characteristic
176	C₂×Dic₄₇	C₂⁴	1	1	yes	characteristic
177	C₂×Dic₄₇	C₂⁴	1	4	yes	—
178	C₂×Dic₄₇	C₂⁴	1	2	yes	—
179	C₂×Dic₄₇	C₂⁴	1	2	yes	—
180	D₁₈₈	—	2	8	no	—
181	D₁₈₈	—	2	4	no	—
182	D₁₈₈	—	2	2	no	—
183	D₁₈₈	#41	1	4	yes	complemented
184	C₄×D₄₇	—	2	8	no	—
185	C₄×D₄₇	—	2	2	no	—
186	C₄×D₄₇	—	2	2	no	—
187	C₄×D₄₇	—	2	4	no	—
188	C₄×D₄₇	—	2	2	no	—
189	C₄×D₄₇	—	2	4	no	—
190	C₄×D₄₇	—	4	2	no	—
191	C₄×D₄₇	—	4	2	no	—
192	C₄×D₄₇	—	4	4	no	—
193	C₄×D₄₇	—	4	4	no	—
194	Dic₉₄	—	2	4	no	—
195	Dic₉₄	—	4	4	no	—
196	C₂²×C₄₇	—	2	2	no	—
197	C₂²×C₄₇	—	2	2	no	—
198	C₂²×C₄₇	—	2	2	no	—
199	C₂²×C₄₇	C₂⁵	1	1	yes	characteristic
200	C₂×D₄₇	—	2	1	no	—
201	C₂×D₄₇	—	2	2	no	—
202	C₂×D₄₇	—	2	1	no	—
203	C₂×D₄₇	—	2	2	no	—
204	C₂×D₄₇	—	2	2	no	—
205	C₂×D₄₇	—	2	2	no	—
206	C₂×D₄₇	—	2	2	no	—
207	C₂×D₄₇	—	4	8	no	—
208	C₂×D₄₇	C₂×#41	1	4	yes	—
209	C₂×D₄₇	2₋¹⁺⁴	1	2	yes	—
210	C₄×C₄₇	—	2	4	no	—
211	C₄×C₄₇	—	2	2	no	—
212	C₄×C₄₇	—	2	2	no	—
213	C₄×C₄₇	—	2	1	no	—
214	C₄×C₄₇	—	2	2	no	—
215	C₄×C₄₇	C₂×#41	1	2	yes	—
216	C₄×C₄₇	H(5,𝔽₂)	1	2	yes	—
217	Dic₄₇	—	2	2	no	—
218	Dic₄₇	—	2	1	no	—
219	Dic₄₇	—	2	4	no	—
220	Dic₄₇	—	2	2	no	—
221	Dic₄₇	—	2	1	no	—
222	Dic₄₇	—	2	1	no	—
223	#3520	—	47	1	no	maximal, Sylow
224	C₂×C₄₇	—	4	2	no	—
225	C₂×C₄₇	C₂²×#41	1	1	yes	characteristic
226	C₂×C₄₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
227	C₂×C₄₇	C₂×2₋¹⁺⁴	1	1	yes	characteristic
228	D₄₇	—	2	2	no	—
229	D₄₇	—	2	4	no	—
230	D₄₇	—	4	2	no	—
231	#556	D₄₇	1	1	yes	characteristic, complemented
232	#554	—	47	2	no	—
233	#552	—	47	2	no	—
234	#551	—	47	4	no	—
235	D₄×Q₈	—	47	1	no	—
236	#548	—	47	2	no	—
237	#547	—	47	1	no	—
238	#547	—	47	1	no	—
239	#546	—	47	2	no	—
240	#542	—	47	2	no	—
241	#539	—	47	4	no	—
242	#533	—	47	1	no	—
243	#529	—	47	1	no	—
244	#525	—	47	2	no	—
245	C₂×C₂²⋊Q₈	—	47	2	no	—
246	#520	—	47	2	no	—
247	C₂×C₄×D₄	—	47	1	no	—
248	C₄₇	#3520	1	1	yes	characteristic, complemented, Sylow
249	C₂×#41	—	47	2	no	—
250	C₂×#41	—	47	2	no	—
251	C₂²×Q₈	—	47	2	no	—
252	C₂²×D₄	—	47	1	no	—
253	C₂³×C₄	—	47	2	no	—
254	C₄⋊Q₈	—	47	1	no	—
255	C₄⋊Q₈	—	47	2	no	—
256	C₄⋊Q₈	C₂×D₄₇	1	1	yes	characteristic, complemented
257	#126	—	47	2	no	—
258	#126	—	47	4	no	—
259	#126	C₂×D₄₇	1	4	yes	complemented
260	#125	—	47	1	no	—
261	#125	—	47	2	no	—
262	#125	—	47	4	no	—
263	#124	—	47	1	no	—
264	#124	—	47	4	no	—
265	#124	C₂×D₄₇	1	2	yes	—
266	#123	—	47	2	no	—
267	#123	—	47	4	no	—
268	#123	—	47	4	no	—
269	#123	—	47	4	no	—
270	#123	—	47	4	no	—
271	C₂²⋊Q₈	—	47	1	no	—
272	C₂²⋊Q₈	—	47	2	no	—
273	C₂²⋊Q₈	—	47	2	no	—
274	C₂²⋊Q₈	—	47	2	no	—
275	C₂²⋊Q₈	—	47	2	no	—
276	C₂²⋊Q₈	—	47	4	no	—
277	C₂²⋊Q₈	—	47	2	no	—
278	C₂²⋊Q₈	—	47	4	no	—
279	C₂²⋊Q₈	—	47	4	no	—
280	C₂²⋊Q₈	—	47	4	no	—
281	C₂²⋊Q₈	C₂×D₄₇	1	2	yes	complemented
282	#121	—	47	2	no	—
283	#121	—	47	1	no	—
284	#121	—	47	2	no	—
285	#121	—	47	4	no	—
286	#120	—	47	4	no	—
287	C₄×Q₈	—	47	2	no	—
288	C₄×Q₈	—	47	2	no	—
289	C₄×Q₈	C₂×D₄₇	1	2	yes	complemented
290	C₄×Q₈	C₂×D₄₇	1	1	yes	characteristic, complemented
291	C₄×D₄	—	47	1	no	—
292	C₄×D₄	—	47	2	no	—
293	C₄×D₄	—	47	1	no	—
294	C₄×D₄	—	47	4	no	—
295	C₄×D₄	—	47	2	no	—
296	C₄×D₄	—	47	1	no	—
297	C₄×D₄	—	47	4	no	—
298	C₄×D₄	—	47	2	no	—
299	C₄×D₄	—	47	4	no	—
300	C₄×D₄	—	47	2	no	—
301	C₄×D₄	—	47	1	no	—
302	C₄×D₄	C₂×D₄₇	1	1	yes	characteristic
303	#117	—	47	2	no	—
304	#117	—	47	2	no	—
305	#117	—	47	4	no	—
306	#117	C₂×D₄₇	1	2	yes	complemented
307	C₂×C₄⋊C₄	—	47	1	no	—
308	C₂×C₄⋊C₄	—	47	4	no	—
309	C₂×C₄⋊C₄	—	47	2	no	—
310	C₂×C₄⋊C₄	—	47	2	no	—
311	C₂×C₂²⋊C₄	—	47	2	no	—
312	C₂×C₂²⋊C₄	—	47	4	no	—
313	C₂×C₄²	—	47	1	no	—
314	C₂⁴	—	47	2	no	—
315	#41	—	94	8	no	—
316	#41	—	188	4	no	—
317	C₂×Q₈	—	47	2	no	—
318	C₂×Q₈	—	47	4	no	—
319	C₂×Q₈	—	188	4	no	—
320	C₂×Q₈	C₂²×D₄₇	1	2	yes	—
321	C₂×Q₈	C₂²×D₄₇	1	1	yes	characteristic
322	C₂×D₄	—	47	2	no	—
323	C₂×D₄	—	47	4	no	—
324	C₂×D₄	—	47	1	no	—
325	C₂×D₄	—	47	2	no	—
326	C₂×D₄	—	47	4	no	—
327	C₂×D₄	—	47	1	no	—
328	C₂×D₄	—	94	4	no	—
329	C₂×D₄	C₂²×D₄₇	1	1	yes	characteristic
330	C₂²×C₄	—	47	2	no	—
331	C₂²×C₄	—	47	1	no	—
332	C₂²×C₄	—	47	1	no	—
333	C₂²×C₄	—	47	1	no	—
334	C₂²×C₄	—	47	4	no	—
335	C₂²×C₄	—	47	2	no	—
336	C₂²×C₄	—	47	2	no	—
337	C₂²×C₄	—	47	4	no	—
338	C₂²×C₄	—	47	2	no	—
339	C₂²×C₄	—	47	2	no	—
340	C₂²×C₄	—	47	4	no	—
341	C₂²×C₄	—	188	4	no	—
342	C₂²×C₄	C₂²×D₄₇	1	2	yes	—
343	C₄⋊C₄	—	47	2	no	—
344	C₄⋊C₄	—	47	4	no	—
345	C₄⋊C₄	—	47	2	no	—
346	C₄⋊C₄	—	47	4	no	—
347	C₄⋊C₄	—	47	2	no	—
348	C₄⋊C₄	—	47	4	no	—
349	C₄⋊C₄	—	47	1	no	—
350	C₄⋊C₄	—	47	1	no	—
351	C₄⋊C₄	—	47	2	no	—
352	C₄⋊C₄	—	47	4	no	—
353	C₄⋊C₄	—	47	2	no	—
354	C₄⋊C₄	—	47	4	no	—
355	C₄⋊C₄	—	47	2	no	—
356	C₄⋊C₄	C₂²×D₄₇	1	1	yes	characteristic
357	C₄⋊C₄	C₂²×D₄₇	1	2	yes	—
358	C₄⋊C₄	C₂²×D₄₇	1	4	yes	—
359	C₄⋊C₄	C₂²×D₄₇	1	2	yes	—
360	C₄⋊C₄	C₂²×D₄₇	1	1	yes	characteristic
361	C₄⋊C₄	C₂²×D₄₇	1	2	yes	—
362	C₂²⋊C₄	—	47	2	no	—
363	C₂²⋊C₄	—	47	4	no	—
364	C₂²⋊C₄	—	47	2	no	—
365	C₂²⋊C₄	—	47	2	no	—
366	C₂²⋊C₄	—	47	4	no	—
367	C₂²⋊C₄	—	47	2	no	—
368	C₂²⋊C₄	—	47	4	no	—
369	C₂²⋊C₄	—	47	2	no	—
370	C₂²⋊C₄	—	47	2	no	—
371	C₂²⋊C₄	—	47	2	no	—
372	C₂²⋊C₄	—	47	4	no	—
373	C₂²⋊C₄	—	47	2	no	—
374	C₂²⋊C₄	C₂²×D₄₇	1	2	yes	—
375	C₂²⋊C₄	C₂²×D₄₇	1	4	yes	—
376	C₂²⋊C₄	C₂²×D₄₇	1	4	yes	—
377	C₄²	—	47	1	no	—
378	C₄²	—	47	1	no	—
379	C₄²	—	47	1	no	—
380	C₄²	—	47	4	no	—
381	C₄²	C₂²×D₄₇	1	1	yes	characteristic
382	C₄²	C₂²×D₄₇	1	4	yes	—
383	C₄²	C₂²×D₄₇	1	2	yes	—
384	C₂³	—	47	1	no	—
385	C₂³	—	47	2	no	—
386	C₂³	—	47	2	no	—
387	C₂³	—	94	4	no	—
388	C₂³	—	94	4	no	—
389	C₂³	—	188	2	no	—
390	C₂³	C₂³×D₄₇	1	2	yes	—
391	Q₈	—	2	4	no	—
392	Q₈	—	2	2	no	—
393	Q₈	—	94	4	no	—
394	Q₈	—	188	4	no	—
395	D₄	—	2	2	no	—
396	D₄	—	47	4	no	—
397	D₄	—	94	4	no	—
398	D₄	—	94	8	no	—
399	D₄	—	94	4	no	—
400	D₄	—	94	2	no	—
401	D₄	—	188	4	no	—
402	C₂×C₄	—	2	4	no	—
403	C₂×C₄	—	47	1	no	—
404	C₂×C₄	—	47	1	no	—
405	C₂×C₄	—	47	1	no	—
406	C₂×C₄	—	47	4	no	—
407	C₂×C₄	—	47	2	no	—
408	C₂×C₄	—	47	2	no	—
409	C₂×C₄	—	94	2	no	—
410	C₂×C₄	—	94	8	no	—
411	C₂×C₄	—	94	2	no	—
412	C₂×C₄	—	94	4	no	—
413	C₂×C₄	—	94	2	no	—
414	C₂×C₄	—	94	4	no	—
415	C₂×C₄	—	188	2	no	—
416	C₂×C₄	—	188	2	no	—
417	C₂×C₄	—	188	4	no	—
418	C₂×C₄	—	188	4	no	—
419	C₂×C₄	—	188	2	no	—
420	C₂×C₄	C₂³×D₄₇	1	1	yes	characteristic
421	C₂×C₄	C₂³×D₄₇	1	4	yes	—
422	C₂×C₄	C₂³×D₄₇	1	2	yes	—
423	C₂×C₄	C₂³×D₄₇	1	2	yes	—
424	C₂×C₄	C₂³×D₄₇	1	2	yes	—
425	C₂×C₄	C₂³×D₄₇	1	1	yes	characteristic
426	C₂×C₄	C₂³×D₄₇	1	1	yes	characteristic
427	C₂²	—	2	2	no	—
428	C₂²	—	2	2	no	—
429	C₂²	—	2	2	no	—
430	C₂²	—	47	4	no	—
431	C₂²	—	47	2	no	—
432	C₂²	—	94	1	no	—
433	C₂²	—	94	2	no	—
434	C₂²	—	94	1	no	—
435	C₂²	—	94	2	no	—
436	C₂²	—	94	2	no	—
437	C₂²	—	94	2	no	—
438	C₂²	—	94	2	no	—
439	C₂²	—	188	8	no	—
440	C₂²	C₂⁴×D₄₇	1	1	yes	characteristic
441	C₄	—	2	4	no	—
442	C₄	—	2	2	no	—
443	C₄	—	2	2	no	—
444	C₄	—	2	1	no	—
445	C₄	—	2	2	no	—
446	C₄	—	94	2	no	—
447	C₄	—	94	1	no	—
448	C₄	—	94	1	no	—
449	C₄	—	94	2	no	—
450	C₄	—	94	4	no	—
451	C₄	—	94	1	no	—
452	C₄	#41×D₄₇	1	2	yes	—
453	C₄	#13094070	1	2	yes	—
454	C₂	—	4	2	no	—
455	C₂	—	94	2	no	—
456	C₂	—	94	4	no	—
457	C₂	—	188	2	no	—
458	C₂	C₂×#41×D₄₇	1	1	yes	characteristic
459	C₂	C₂×#13094070	1	1	yes	characteristic
460	C₂	2₋¹⁺⁴×D₄₇	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₄₇
commutator, socle	C₂²×C₄₇	C₂⁵
Fitting	C₄₇×#556	C₂
hypercenter	#556	D₄₇
hypocenter	C₄₇	#3520
LCS	G ▷ C₂²×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂² ◁ #556

Complements

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

N	H ≅ G/N	type
1. #15689833	C₂	semidirect
2. #15689812	C₂	semidirect
3. #15689798	C₂	semidirect
4. Q₈×D₁₈₈	C₂	semidirect
5. #15689783	C₂	semidirect
6. #15689778	C₂	semidirect
7. #15689776	C₂	semidirect
8. #15689766	C₂	semidirect
9. #15689742	C₂	semidirect
10. #15689714	C₂	semidirect
11. #15689678	C₂	semidirect
12. #15689660	C₂	semidirect
13. #15689635	C₂	semidirect
14. C₂²⋊Q₈×D₄₇	C₂	semidirect
15. #15689605	C₂	semidirect
16. C₄×D₄×D₄₇	C₂	semidirect
17. C₄₇×#556	C₂	semidirect
19. C₂×#10625350	C₂²	semidirect
20. C₂×Q₈×D₄₇	C₂²	semidirect
23. #13094024	C₂²	semidirect
24. #13094024	C₂²	semidirect
25. #13094019	C₂²	semidirect
26. #13094017	C₂²	semidirect
27. #13094016	C₂²	semidirect
28. #13094015	C₂²	semidirect
29. #13094015	C₂²	semidirect
30. #13094013	C₂²	semidirect
31. #13094010	C₂²	semidirect
33. #13094009	C₂²	semidirect
34. #13094008	C₂²	semidirect
36. #13094006	C₂²	semidirect
38. #13094004	C₂²	semidirect
39. #13094004	C₂²	semidirect
40. #13094003	C₂²	semidirect
42. #13094002	C₂²	semidirect
43. #13094001	C₂²	semidirect
46. #13094000	C₂²	semidirect
48. #13093999	C₂²	semidirect
52. Q₈×Dic₄₇	C₂²	semidirect
53. #13093989	C₂²	semidirect
58. C₄×D₁₈₈	C₂²	semidirect
59. C₄×D₁₈₈	C₂²	semidirect
62. #13093986	C₂²	semidirect
66. #13093981	C₂²	semidirect
67. #13093981	C₂²	semidirect
69. C₄⋊C₄×D₄₇	C₂²	semidirect
70. C₄⋊C₄×D₄₇	C₂²	semidirect
71. C₄⋊C₄×D₄₇	C₂²	semidirect
75. C₄⋊Q₈×C₄₇	C₂²	semidirect
76. #126×C₄₇	C₂²	semidirect
78. C₂²⋊Q₈×C₄₇	C₂²	semidirect
79. C₄×Q₈×C₄₇	C₂²	semidirect
80. C₄×Q₈×C₄₇	C₂²	semidirect
82. #117×C₄₇	C₂²	semidirect
183. D₁₈₈	#41	semidirect
231. #556	D₄₇	semidirect
248. C₄₇	#3520	semidirect
256. C₄⋊Q₈	C₂×D₄₇	semidirect
259. #126	C₂×D₄₇	semidirect
281. C₂²⋊Q₈	C₂×D₄₇	semidirect
289. C₄×Q₈	C₂×D₄₇	semidirect
290. C₄×Q₈	C₂×D₄₇	semidirect
306. #117	C₂×D₄₇	semidirect