Subgroups — #20257617

Order 6016.

1134 conjugacy classes of subgroups.

The subgroup lattice has 452 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#15689869	C₂	1	4	yes	maximal, complemented
2	#15689831	C₂	1	2	yes	maximal, complemented
3	#15689784	C₂	1	2	yes	maximal, complemented
4	#15689774	C₂	1	2	yes	maximal, complemented
5	#15689764	C₂	1	2	yes	maximal, complemented
6	#15689763	C₂	1	4	yes	maximal, complemented
7	#15689748	C₂	1	2	yes	maximal, complemented
8	#15689746	C₂	1	2	yes	maximal, complemented
9	#15689720	C₂	1	2	yes	maximal, complemented
10	#15689713	C₂	1	2	yes	maximal, complemented
11	#15689704	C₂	1	2	yes	maximal, complemented
12	#15689703	C₂	1	2	yes	maximal, complemented
13	#15689634	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂×#13093998	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂×C₂²⋊Q₈×C₄₇	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×#10625354	C₂²	1	2	yes	complemented
17	C₂×#10625350	C₂²	1	4	yes	complemented
18	C₂×#10625350	C₂²	1	1	yes	characteristic, complemented
19	C₂²×D₁₈₈	C₂²	1	1	yes	characteristic
20	C₂²×C₂²⋊D₄₇	C₂²	1	2	yes	—
21	#13094023	C₂²	1	2	yes	complemented
22	#13094019	C₂²	1	4	yes	complemented
23	#13094014	C₂²	1	4	yes	complemented
24	#13094013	C₂²	1	2	yes	complemented
25	#13094013	C₂²	1	4	yes	complemented
26	#13094010	C₂²	1	4	yes	complemented
27	#13094009	C₂²	1	4	yes	complemented
28	#13094009	C₂²	1	4	yes	complemented
29	#13094007	C₂²	1	4	yes	complemented
30	#13094007	C₂²	1	2	yes	complemented
31	#13094006	C₂²	1	4	yes	complemented
32	#13094004	C₂²	1	4	yes	complemented
33	#13094004	C₂²	1	4	yes	complemented
34	#13094003	C₂²	1	1	yes	characteristic
35	#13094003	C₂²	1	1	yes	characteristic, complemented
36	#13094002	C₂²	1	4	yes	complemented
37	#13094002	C₂²	1	4	yes	complemented
38	#13094001	C₂²	1	4	yes	—
39	#13094000	C₂²	1	4	yes	complemented
40	#13094000	C₂²	1	2	yes	complemented
41	#13093999	C₂²	1	2	yes	complemented
42	#13093999	C₂²	1	4	yes	complemented
43	#13093999	C₂²	1	4	yes	complemented
44	#13093998	C₂²	1	2	yes	—
45	#13093998	C₂²	1	2	yes	—
46	#13093998	C₂²	1	2	yes	—
47	#13093998	C₂²	1	2	yes	—
48	#13093998	C₂²	1	1	yes	characteristic
49	#13093998	C₂²	1	4	yes	complemented
50	#13093998	C₂²	1	1	yes	characteristic, complemented
51	#13093997	C₂²	1	4	yes	complemented
52	#13093997	C₂²	1	4	yes	complemented
53	#13093994	C₂²	1	4	yes	—
54	#13093993	C₂²	1	2	yes	—
55	Q₈×Dic₄₇	C₂²	1	2	yes	complemented
56	#13093986	C₂²	1	2	yes	complemented
57	C₄×C₂²⋊D₄₇	C₂²	1	2	yes	—
58	C₄×C₂²⋊D₄₇	C₂²	1	4	yes	complemented
59	C₄×C₂²⋊D₄₇	C₂²	1	2	yes	complemented
60	(C₂²⋊D₄₇)⋊C₄	C₂²	1	4	yes	—
61	#13093983	C₂²	1	1	yes	characteristic, complemented
62	C₂×C₄⋊Dic₄₇	C₂²	1	1	yes	characteristic
63	C₄⋊C₄×D₄₇	C₂²	1	2	yes	complemented
64	C₂×(C₂×D₄₇)⋊C₄	C₂²	1	2	yes	—
65	C₂²⋊C₄×D₄₇	C₂²	1	4	yes	—
66	C₂²×Q₈×C₄₇	C₂²	1	1	yes	characteristic, complemented
67	C₂³×C₄×C₄₇	C₂²	1	1	yes	characteristic
68	C₂²⋊Q₈×C₄₇	C₂²	1	2	yes	—
69	C₂²⋊Q₈×C₄₇	C₂²	1	2	yes	—
70	C₂²⋊Q₈×C₄₇	C₂²	1	2	yes	complemented
71	C₂²⋊Q₈×C₄₇	C₂²	1	2	yes	complemented
72	C₂×C₄⋊C₄×C₄₇	C₂²	1	1	yes	characteristic, complemented
73	C₂×C₄⋊C₄×C₄₇	C₂²	1	2	yes	complemented
74	C₂×C₂²⋊C₄×C₄₇	C₂²	1	2	yes	—
75	C₂⁴×C₄₇	C₂³	1	1	yes	characteristic
76	C₂³×D₄₇	C₂³	1	2	yes	—
77	C₂×Q₈×C₄₇	—	4	2	no	—
78	C₂×Q₈×C₄₇	C₂³	1	2	yes	—
79	C₂×Q₈×C₄₇	C₂³	1	2	yes	—
80	C₂²×C₄×C₄₇	—	4	2	no	—
81	C₂²×C₄×C₄₇	C₂³	1	2	yes	—
82	C₂²×C₄×C₄₇	C₂³	1	1	yes	characteristic
83	C₂²×C₄×C₄₇	C₂³	1	1	yes	characteristic
84	C₂²×C₄×C₄₇	C₂³	1	1	yes	characteristic
85	C₂²×C₄×C₄₇	C₂³	1	2	yes	—
86	C₂²×C₄×C₄₇	C₂³	1	1	yes	characteristic
87	C₂²×C₄×C₄₇	C₂³	1	1	yes	characteristic
88	C₂²×C₄×C₄₇	C₂³	1	1	yes	characteristic
89	C₂×C₂²⋊D₄₇	—	4	4	no	—
90	C₂×C₂²⋊D₄₇	C₂³	1	2	yes	—
91	C₂×C₂²⋊D₄₇	C₂³	1	2	yes	—
92	C₂×C₂²⋊D₄₇	C₂³	1	4	yes	—
93	C₂×C₂²⋊D₄₇	C₂³	1	2	yes	—
94	C₂×C₂²⋊D₄₇	C₂³	1	4	yes	—
95	C₂²×Dic₄₇	C₂³	1	2	yes	—
96	#10625354	—	4	4	no	—
97	#10625350	—	4	2	no	—
98	#10625350	—	4	8	no	—
99	C₂×D₁₈₈	—	4	2	no	—
100	C₂×D₁₈₈	C₂³	1	2	yes	—
101	C₂×D₁₈₈	C₂³	1	4	yes	—
102	C₂×D₁₈₈	C₂³	1	4	yes	—
103	C₂×D₁₈₈	C₂³	1	2	yes	—
104	C₂×D₁₈₈	C₂³	1	1	yes	characteristic
105	C₂×C₄×D₄₇	C₂³	1	2	yes	—
106	C₂×C₄×D₄₇	C₂³	1	4	yes	—
107	C₂×C₄×D₄₇	C₂³	1	4	yes	—
108	C₂×C₄×D₄₇	C₂³	1	4	yes	—
109	C₂×Dic₉₄	C₂³	1	4	yes	—
110	C₂×Dic₉₄	C₂³	1	1	yes	characteristic
111	C₄⋊C₄×C₄₇	C₂³	1	2	yes	—
112	C₄⋊C₄×C₄₇	C₂³	1	4	yes	—
113	C₄⋊C₄×C₄₇	C₂³	1	4	yes	—
114	C₄⋊C₄×C₄₇	C₂³	1	2	yes	—
115	C₂²⋊C₄×C₄₇	C₂³	1	4	yes	—
116	C₂²⋊C₄×C₄₇	C₂³	1	4	yes	—
117	C₂²⋊Dic₄₇	C₂³	1	2	yes	—
118	C₂²⋊Dic₄₇	C₂³	1	2	yes	—
119	C₂²⋊Dic₄₇	C₂³	1	2	yes	—
120	(C₂×D₄₇)⋊C₄	C₂³	1	4	yes	—
121	(C₂×D₄₇)⋊C₄	C₂³	1	4	yes	—
122	(C₂×D₄₇)⋊C₄	C₂³	1	4	yes	—
123	(C₂×D₄₇)⋊C₄	C₂³	1	4	yes	—
124	(C₂×D₄₇)⋊C₄	C₂³	1	4	yes	—
125	(C₂×D₄₇)⋊C₄	C₂³	1	2	yes	—
126	(C₂×D₄₇)⋊C₄	C₂³	1	4	yes	—
127	(C₂×D₄₇)⋊C₄	C₂³	1	2	yes	—
128	(C₂×D₄₇)⋊C₄	C₂³	1	4	yes	—
129	C₄⋊Dic₄₇	C₂³	1	2	yes	—
130	C₄⋊Dic₄₇	C₂³	1	2	yes	—
131	C₄⋊Dic₄₇	C₂³	1	1	yes	characteristic
132	C₄⋊Dic₄₇	C₂³	1	1	yes	characteristic
133	C₄⋊Dic₄₇	C₂³	1	4	yes	—
134	Dic₄₇⋊C₄	C₂³	1	4	yes	—
135	Dic₄₇⋊C₄	C₂³	1	4	yes	—
136	Dic₄₇⋊C₄	C₂³	1	2	yes	—
137	Dic₄₇⋊C₄	C₂³	1	4	yes	—
138	Dic₄₇⋊C₄	C₂³	1	2	yes	—
139	C₄×Dic₄₇	C₂³	1	2	yes	—
140	C₄×Dic₄₇	C₂³	1	4	yes	—
141	C₂³×C₄₇	—	2	2	no	—
142	C₂³×C₄₇	—	2	2	no	—
143	C₂³×C₄₇	—	4	1	no	—
144	C₂³×C₄₇	C₂⁴	1	1	yes	characteristic
145	C₂³×C₄₇	C₂⁴	1	1	yes	characteristic
146	C₂³×C₄₇	C₂⁴	1	1	yes	characteristic
147	C₂²×D₄₇	—	2	4	no	—
148	C₂²×D₄₇	—	4	2	no	—
149	C₂²×D₄₇	—	4	2	no	—
150	C₂²×D₄₇	C₂⁴	1	4	yes	—
151	C₂²×D₄₇	C₂⁴	1	2	yes	—
152	Q₈×C₄₇	—	2	4	no	—
153	Q₈×C₄₇	—	4	2	no	—
154	C₂×C₄×C₄₇	—	2	4	no	—
155	C₂×C₄×C₄₇	—	2	2	no	—
156	C₂×C₄×C₄₇	—	2	2	no	—
157	C₂×C₄×C₄₇	—	2	2	no	—
158	C₂×C₄×C₄₇	—	4	1	no	—
159	C₂×C₄×C₄₇	—	4	1	no	—
160	C₂×C₄×C₄₇	—	4	1	no	—
161	C₂×C₄×C₄₇	—	4	2	no	—
162	C₂×C₄×C₄₇	C₂⁴	1	4	yes	—
163	C₂×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
164	C₂×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
165	C₂×C₄×C₄₇	C₂⁴	1	4	yes	—
166	C₂×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
167	C₂×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
168	C₂²⋊D₄₇	—	2	4	no	—
169	C₂²⋊D₄₇	—	2	8	no	—
170	C₂²⋊D₄₇	—	2	4	no	—
171	C₂²⋊D₄₇	—	4	2	no	—
172	C₂²⋊D₄₇	—	4	4	no	—
173	C₂×Dic₄₇	—	4	2	no	—
174	C₂×Dic₄₇	C₂⁴	1	2	yes	—
175	C₂×Dic₄₇	C₂⁴	1	4	yes	—
176	C₂×Dic₄₇	C₂⁴	1	2	yes	—
177	C₂×Dic₄₇	C₂⁴	1	2	yes	—
178	D₁₈₈	—	2	4	no	—
179	D₁₈₈	—	4	2	no	—
180	D₁₈₈	—	4	4	no	—
181	D₁₈₈	—	4	1	no	—
182	D₁₈₈	—	4	4	no	—
183	C₄×D₄₇	—	2	4	no	—
184	C₄×D₄₇	—	4	4	no	—
185	C₄×D₄₇	—	4	4	no	—
186	C₄×D₄₇	—	4	4	no	—
187	Dic₉₄	—	4	4	no	—
188	Dic₉₄	—	4	1	no	—
189	C₂²×C₄₇	—	2	1	no	—
190	C₂²×C₄₇	—	2	1	no	—
191	C₂²×C₄₇	—	2	1	no	—
192	C₂²×C₄₇	—	2	1	no	—
193	C₂²×C₄₇	—	2	1	no	—
194	C₂²×C₄₇	—	2	1	no	—
195	C₂²×C₄₇	—	2	1	no	—
196	C₂²×C₄₇	—	4	4	no	—
197	C₂²×C₄₇	H(5,𝔽₂)	1	2	yes	—
198	C₂²×C₄₇	2₋¹⁺⁴	1	2	yes	—
199	C₂²×C₄₇	C₂⁵	1	1	yes	characteristic
200	C₂×D₄₇	—	2	2	no	—
201	C₂×D₄₇	—	2	2	no	—
202	C₂×D₄₇	—	2	4	no	—
203	C₂×D₄₇	—	2	4	no	—
204	C₂×D₄₇	—	2	2	no	—
205	C₂×D₄₇	—	2	4	no	—
206	C₂×D₄₇	—	8	4	no	—
207	C₄×C₄₇	—	2	4	no	—
208	C₄×C₄₇	—	2	1	no	—
209	C₄×C₄₇	—	2	4	no	—
210	C₄×C₄₇	—	2	1	no	—
211	C₄×C₄₇	—	2	1	no	—
212	C₄×C₄₇	H(5,𝔽₂)	1	2	yes	—
213	Dic₄₇	—	2	2	no	—
214	Dic₄₇	—	2	2	no	—
215	Dic₄₇	—	2	4	no	—
216	Dic₄₇	—	2	2	no	—
217	#3536	—	47	1	no	maximal, Sylow
218	C₂×C₄₇	—	2	2	no	—
219	C₂×C₄₇	—	2	2	no	—
220	C₂×C₄₇	—	4	1	no	—
221	C₂×C₄₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
222	C₂×C₄₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
223	C₂×C₄₇	C₂×2₋¹⁺⁴	1	1	yes	characteristic
224	D₄₇	—	4	2	no	—
225	D₄₇	—	4	4	no	—
226	#562	—	47	4	no	—
227	#554	—	47	2	no	—
228	#548	—	47	2	no	—
229	#547	—	47	2	no	—
230	#546	—	47	2	no	—
231	#546	—	47	4	no	—
232	#543	—	47	2	no	—
233	#542	—	47	2	no	—
234	#539	—	47	2	no	—
235	#538	—	47	2	no	—
236	#537	—	47	2	no	—
237	#537	—	47	2	no	—
238	#525	—	47	1	no	—
239	C₂×C₂²⋊Q₈	D₄₇	1	1	yes	characteristic, complemented
240	C₂×#121	—	47	1	no	—
241	C₄₇	#3536	1	1	yes	characteristic, complemented, Sylow
242	C₂×#41	—	47	2	no	—
243	C₂×#41	—	47	1	no	—
244	C₂×#41	—	47	4	no	—
245	C₂²×Q₈	C₂×D₄₇	1	1	yes	characteristic, complemented
246	C₂²×D₄	—	47	2	no	—
247	C₂²×D₄	—	47	1	no	—
248	C₂³×C₄	C₂×D₄₇	1	1	yes	characteristic
249	C₄⋊Q₈	—	47	2	no	—
250	#126	—	47	4	no	—
251	#125	—	47	4	no	—
252	#124	—	47	4	no	—
253	#124	—	47	2	no	—
254	#124	—	47	4	no	—
255	#123	—	47	2	no	—
256	#123	—	47	4	no	—
257	#123	—	47	4	no	—
258	#123	—	47	4	no	—
259	#123	—	47	4	no	—
260	C₂²⋊Q₈	—	47	2	no	—
261	C₂²⋊Q₈	—	47	4	no	—
262	C₂²⋊Q₈	—	47	1	no	—
263	C₂²⋊Q₈	—	47	1	no	—
264	C₂²⋊Q₈	—	47	4	no	—
265	C₂²⋊Q₈	—	47	4	no	—
266	C₂²⋊Q₈	—	47	4	no	—
267	C₂²⋊Q₈	—	47	4	no	—
268	C₂²⋊Q₈	—	47	4	no	—
269	C₂²⋊Q₈	C₂×D₄₇	1	2	yes	—
270	C₂²⋊Q₈	C₂×D₄₇	1	2	yes	—
271	C₂²⋊Q₈	C₂×D₄₇	1	2	yes	complemented
272	C₂²⋊Q₈	C₂×D₄₇	1	2	yes	complemented
273	#121	—	47	2	no	—
274	#121	—	47	2	no	—
275	#121	—	47	2	no	—
276	#121	—	47	2	no	—
277	#121	—	47	1	no	—
278	#121	—	47	1	no	—
279	#121	—	47	4	no	—
280	#121	—	47	4	no	—
281	#121	—	47	2	no	—
282	#121	—	47	4	no	—
283	#121	—	47	4	no	—
284	#121	—	47	4	no	—
285	#120	—	47	2	no	—
286	#120	—	47	4	no	—
287	C₄×Q₈	—	47	2	no	—
288	C₄×D₄	—	47	2	no	—
289	C₄×D₄	—	47	2	no	—
290	C₄×D₄	—	47	4	no	—
291	C₄×D₄	—	47	2	no	—
292	C₄×D₄	—	47	4	no	—
293	#117	—	47	1	no	—
294	C₂×C₄⋊C₄	—	47	1	no	—
295	C₂×C₄⋊C₄	—	47	2	no	—
296	C₂×C₄⋊C₄	C₂×D₄₇	1	2	yes	complemented
297	C₂×C₄⋊C₄	C₂×D₄₇	1	1	yes	characteristic, complemented
298	C₂×C₂²⋊C₄	—	47	2	no	—
299	C₂×C₂²⋊C₄	—	47	4	no	—
300	C₂×C₂²⋊C₄	C₂×D₄₇	1	2	yes	—
301	C₂⁴	—	47	2	no	—
302	C₂⁴	C₂²×D₄₇	1	1	yes	characteristic
303	#41	—	188	2	no	—
304	#41	—	188	8	no	—
305	#41	—	188	4	no	—
306	C₂×Q₈	—	4	2	no	—
307	C₂×Q₈	—	47	1	no	—
308	C₂×Q₈	—	47	4	no	—
309	C₂×Q₈	C₂²×D₄₇	1	2	yes	—
310	C₂×Q₈	C₂²×D₄₇	1	2	yes	—
311	C₂×D₄	—	47	2	no	—
312	C₂×D₄	—	47	2	no	—
313	C₂×D₄	—	47	4	no	—
314	C₂×D₄	—	47	2	no	—
315	C₂×D₄	—	47	4	no	—
316	C₂×D₄	—	47	2	no	—
317	C₂×D₄	—	47	4	no	—
318	C₂×D₄	—	47	4	no	—
319	C₂×D₄	—	47	1	no	—
320	C₂×D₄	—	47	2	no	—
321	C₂×D₄	—	188	2	no	—
322	C₂×D₄	—	188	4	no	—
323	C₂²×C₄	—	4	2	no	—
324	C₂²×C₄	—	47	2	no	—
325	C₂²×C₄	—	47	2	no	—
326	C₂²×C₄	—	47	4	no	—
327	C₂²×C₄	—	47	4	no	—
328	C₂²×C₄	—	47	4	no	—
329	C₂²×C₄	C₂²×D₄₇	1	2	yes	—
330	C₂²×C₄	C₂²×D₄₇	1	1	yes	characteristic
331	C₂²×C₄	C₂²×D₄₇	1	1	yes	characteristic
332	C₂²×C₄	C₂²×D₄₇	1	1	yes	characteristic
333	C₂²×C₄	C₂²×D₄₇	1	1	yes	characteristic
334	C₂²×C₄	C₂²×D₄₇	1	2	yes	—
335	C₂²×C₄	C₂²×D₄₇	1	1	yes	characteristic
336	C₂²×C₄	C₂²×D₄₇	1	1	yes	characteristic
337	C₄⋊C₄	—	47	4	no	—
338	C₄⋊C₄	—	47	4	no	—
339	C₄⋊C₄	—	47	2	no	—
340	C₄⋊C₄	—	47	2	no	—
341	C₄⋊C₄	—	47	4	no	—
342	C₄⋊C₄	—	47	2	no	—
343	C₄⋊C₄	—	47	2	no	—
344	C₄⋊C₄	—	47	1	no	—
345	C₄⋊C₄	—	47	1	no	—
346	C₄⋊C₄	—	47	4	no	—
347	C₄⋊C₄	C₂²×D₄₇	1	2	yes	—
348	C₄⋊C₄	C₂²×D₄₇	1	4	yes	—
349	C₄⋊C₄	C₂²×D₄₇	1	4	yes	—
350	C₄⋊C₄	C₂²×D₄₇	1	2	yes	—
351	C₂²⋊C₄	—	47	2	no	—
352	C₂²⋊C₄	—	47	2	no	—
353	C₂²⋊C₄	—	47	2	no	—
354	C₂²⋊C₄	—	47	4	no	—
355	C₂²⋊C₄	—	47	4	no	—
356	C₂²⋊C₄	—	47	4	no	—
357	C₂²⋊C₄	—	47	4	no	—
358	C₂²⋊C₄	—	47	4	no	—
359	C₂²⋊C₄	—	47	4	no	—
360	C₂²⋊C₄	—	47	2	no	—
361	C₂²⋊C₄	—	47	4	no	—
362	C₂²⋊C₄	—	47	2	no	—
363	C₂²⋊C₄	C₂²×D₄₇	1	4	yes	—
364	C₂²⋊C₄	C₂²×D₄₇	1	4	yes	—
365	C₄²	—	47	2	no	—
366	C₄²	—	47	4	no	—
367	C₂³	—	2	2	no	—
368	C₂³	—	2	2	no	—
369	C₂³	—	4	1	no	—
370	C₂³	—	47	4	no	—
371	C₂³	—	47	2	no	—
372	C₂³	—	94	4	no	—
373	C₂³	—	188	2	no	—
374	C₂³	—	188	2	no	—
375	C₂³	C₂³×D₄₇	1	1	yes	characteristic
376	C₂³	C₂³×D₄₇	1	1	yes	characteristic
377	C₂³	C₂³×D₄₇	1	1	yes	characteristic
378	Q₈	—	2	4	no	—
379	Q₈	—	4	2	no	—
380	Q₈	—	188	1	no	—
381	Q₈	—	188	4	no	—
382	D₄	—	94	8	no	—
383	D₄	—	94	4	no	—
384	D₄	—	94	4	no	—
385	D₄	—	94	4	no	—
386	D₄	—	188	2	no	—
387	D₄	—	188	1	no	—
388	D₄	—	188	4	no	—
389	D₄	—	188	4	no	—
390	D₄	—	188	4	no	—
391	D₄	—	188	2	no	—
392	C₂×C₄	—	2	4	no	—
393	C₂×C₄	—	2	2	no	—
394	C₂×C₄	—	2	2	no	—
395	C₂×C₄	—	2	2	no	—
396	C₂×C₄	—	4	1	no	—
397	C₂×C₄	—	4	1	no	—
398	C₂×C₄	—	4	1	no	—
399	C₂×C₄	—	4	2	no	—
400	C₂×C₄	—	47	2	no	—
401	C₂×C₄	—	47	2	no	—
402	C₂×C₄	—	47	4	no	—
403	C₂×C₄	—	47	2	no	—
404	C₂×C₄	—	94	4	no	—
405	C₂×C₄	—	188	4	no	—
406	C₂×C₄	—	188	4	no	—
407	C₂×C₄	—	188	4	no	—
408	C₂×C₄	—	188	2	no	—
409	C₂×C₄	C₂³×D₄₇	1	4	yes	—
410	C₂×C₄	C₂³×D₄₇	1	1	yes	characteristic
411	C₂×C₄	C₂³×D₄₇	1	1	yes	characteristic
412	C₂×C₄	C₂³×D₄₇	1	4	yes	—
413	C₂×C₄	C₂³×D₄₇	1	1	yes	characteristic
414	C₂×C₄	C₂³×D₄₇	1	1	yes	characteristic
415	C₂²	—	2	1	no	—
416	C₂²	—	2	1	no	—
417	C₂²	—	2	1	no	—
418	C₂²	—	2	1	no	—
419	C₂²	—	2	1	no	—
420	C₂²	—	2	1	no	—
421	C₂²	—	2	1	no	—
422	C₂²	—	4	4	no	—
423	C₂²	—	94	2	no	—
424	C₂²	—	94	4	no	—
425	C₂²	—	94	2	no	—
426	C₂²	—	94	4	no	—
427	C₂²	—	94	2	no	—
428	C₂²	—	94	4	no	—
429	C₂²	—	376	4	no	—
430	C₂²	#13094070	1	2	yes	—
431	C₂²	#13094072	1	2	yes	—
432	C₂²	C₂⁴×D₄₇	1	1	yes	characteristic
433	C₄	—	2	1	no	—
434	C₄	—	2	1	no	—
435	C₄	—	2	1	no	—
436	C₄	—	2	4	no	—
437	C₄	—	2	4	no	—
438	C₄	—	94	2	no	—
439	C₄	—	94	4	no	—
440	C₄	—	94	2	no	—
441	C₄	—	94	2	no	—
442	C₄	#13094069	1	2	yes	—
443	C₂	—	2	2	no	—
444	C₂	—	2	2	no	—
445	C₂	—	4	1	no	—
446	C₂	—	188	4	no	—
447	C₂	—	188	2	no	—
448	C₂	C₂×#13094069	1	1	yes	characteristic
449	C₂	C₂×#13094070	1	1	yes	characteristic
450	C₂	C₂×#13094072	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₄₇
commutator, socle	C₂²×C₄₇	C₂⁵
Fitting	C₂×C₂²⋊Q₈×C₄₇	C₂
hypercenter	C₂×C₂²⋊Q₈	D₄₇
hypocenter	C₄₇	#3536
LCS	G ▷ C₂²×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂² ◁ C₂×C₂²⋊Q₈

Complements

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

N	H ≅ G/N	type
1. #15689869	C₂	semidirect
2. #15689831	C₂	semidirect
3. #15689784	C₂	semidirect
4. #15689774	C₂	semidirect
5. #15689764	C₂	semidirect
6. #15689763	C₂	semidirect
7. #15689748	C₂	semidirect
8. #15689746	C₂	semidirect
9. #15689720	C₂	semidirect
10. #15689713	C₂	semidirect
11. #15689704	C₂	semidirect
12. #15689703	C₂	semidirect
13. #15689634	C₂	semidirect
14. C₂×#13093998	C₂	semidirect
15. C₂×C₂²⋊Q₈×C₄₇	C₂	semidirect
16. C₂×#10625354	C₂²	semidirect
17. C₂×#10625350	C₂²	semidirect
18. C₂×#10625350	C₂²	semidirect
21. #13094023	C₂²	semidirect
22. #13094019	C₂²	semidirect
23. #13094014	C₂²	semidirect
24. #13094013	C₂²	semidirect
25. #13094013	C₂²	semidirect
26. #13094010	C₂²	semidirect
27. #13094009	C₂²	semidirect
28. #13094009	C₂²	semidirect
29. #13094007	C₂²	semidirect
30. #13094007	C₂²	semidirect
31. #13094006	C₂²	semidirect
32. #13094004	C₂²	semidirect
33. #13094004	C₂²	semidirect
35. #13094003	C₂²	semidirect
36. #13094002	C₂²	semidirect
37. #13094002	C₂²	semidirect
39. #13094000	C₂²	semidirect
40. #13094000	C₂²	semidirect
41. #13093999	C₂²	semidirect
42. #13093999	C₂²	semidirect
43. #13093999	C₂²	semidirect
49. #13093998	C₂²	semidirect
50. #13093998	C₂²	semidirect
51. #13093997	C₂²	semidirect
52. #13093997	C₂²	semidirect
55. Q₈×Dic₄₇	C₂²	semidirect
56. #13093986	C₂²	semidirect
58. C₄×C₂²⋊D₄₇	C₂²	semidirect
59. C₄×C₂²⋊D₄₇	C₂²	semidirect
61. #13093983	C₂²	semidirect
63. C₄⋊C₄×D₄₇	C₂²	semidirect
66. C₂²×Q₈×C₄₇	C₂²	semidirect
70. C₂²⋊Q₈×C₄₇	C₂²	semidirect
71. C₂²⋊Q₈×C₄₇	C₂²	semidirect
72. C₂×C₄⋊C₄×C₄₇	C₂²	semidirect
73. C₂×C₄⋊C₄×C₄₇	C₂²	semidirect
239. C₂×C₂²⋊Q₈	D₄₇	semidirect
241. C₄₇	#3536	semidirect
245. C₂²×Q₈	C₂×D₄₇	semidirect
271. C₂²⋊Q₈	C₂×D₄₇	semidirect
272. C₂²⋊Q₈	C₂×D₄₇	semidirect
296. C₂×C₄⋊C₄	C₂×D₄₇	semidirect
297. C₂×C₄⋊C₄	C₂×D₄₇	semidirect