Subgroups — #20256966

Order 6016.

1068 conjugacy classes of subgroups.

The subgroup lattice has 432 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#15689853	C₂	1	1	yes	maximal, characteristic, complemented
2	#15689850	C₂	1	2	yes	maximal, complemented
3	#15689848	C₂	1	1	yes	maximal, characteristic, complemented
4	#15689834	C₂	1	1	yes	maximal, characteristic, complemented
5	#15689831	C₂	1	2	yes	maximal, complemented
6	#15689829	C₂	1	2	yes	maximal, complemented
7	#15689827	C₂	1	4	yes	maximal, complemented
8	#15689788	C₂	1	1	yes	maximal, characteristic, complemented
9	#15689786	C₂	1	2	yes	maximal, complemented
10	#15689677	C₂	1	2	yes	maximal, complemented
11	#15689677	C₂	1	4	yes	maximal, complemented
12	#15689676	C₂	1	2	yes	maximal, complemented
13	C₄×#10625350	C₂	1	1	yes	maximal, characteristic
14	#15689591	C₂	1	2	yes	maximal
15	C₂×C₄×Dic₉₄	C₂	1	1	yes	maximal, characteristic, complemented
16	C₄×Q₈×D₄₇	C₂	1	2	yes	maximal, complemented
17	C₄₇×#533	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂×#10625350	C₂²	1	1	yes	characteristic
19	C₂²×Dic₉₄	C₂²	1	1	yes	characteristic
20	C₂×Q₈×D₄₇	C₂²	1	2	yes	—
21	#13094023	C₂²	1	4	yes	—
22	#13094023	C₂²	1	2	yes	—
23	#13094023	C₂²	1	2	yes	—
24	#13094023	C₂²	1	2	yes	—
25	#13094022	C₂²	1	2	yes	—
26	#13094022	C₂²	1	4	yes	—
27	#13094015	C₂²	1	2	yes	—
28	#13094015	C₂²	1	2	yes	—
29	#13094014	C₂²	1	4	yes	—
30	#13094014	C₂²	1	4	yes	—
31	#13094014	C₂²	1	4	yes	—
32	#13094004	C₂²	1	2	yes	—
33	#13094004	C₂²	1	4	yes	—
34	#13094002	C₂²	1	4	yes	—
35	#13094002	C₂²	1	4	yes	—
36	#13094002	C₂²	1	4	yes	—
37	#13094001	C₂²	1	4	yes	—
38	#13094001	C₂²	1	4	yes	—
39	#13094000	C₂²	1	2	yes	—
40	#13094000	C₂²	1	4	yes	—
41	Q₈×Dic₄₇	C₂²	1	2	yes	—
42	C₄×Dic₉₄	C₂²	1	1	yes	characteristic
43	C₄×Dic₉₄	C₂²	1	2	yes	—
44	C₄×Dic₉₄	C₂²	1	1	yes	characteristic
45	C₄×Dic₉₄	C₂²	1	1	yes	characteristic
46	C₄×Dic₉₄	C₂²	1	4	yes	—
47	C₄×Dic₉₄	C₂²	1	2	yes	—
48	C₄×Dic₉₄	C₂²	1	1	yes	characteristic
49	C₄×Dic₉₄	C₂²	1	1	yes	characteristic
50	C₄×Dic₉₄	C₂²	1	1	yes	characteristic
51	C₄×Dic₉₄	C₂²	1	4	yes	—
52	#13093989	C₂²	1	2	yes	—
53	#13093989	C₂²	1	4	yes	—
54	#13093989	C₂²	1	2	yes	—
55	#13093989	C₂²	1	2	yes	—
56	C₄×D₁₈₈	C₂²	1	1	yes	characteristic
57	C₄×D₁₈₈	C₂²	1	1	yes	characteristic
58	#13093986	C₂²	1	2	yes	—
59	#13093986	C₂²	1	2	yes	—
60	C₄×C₂²⋊D₄₇	C₂²	1	2	yes	—
61	C₄×C₂²⋊D₄₇	C₂²	1	2	yes	—
62	(C₂²⋊D₄₇)⋊C₄	C₂²	1	4	yes	—
63	(C₂²⋊D₄₇)⋊C₄	C₂²	1	4	yes	—
64	#13093983	C₂²	1	1	yes	characteristic
65	#13093981	C₂²	1	4	yes	—
66	#13093981	C₂²	1	2	yes	—
67	C₂×C₄⋊Dic₄₇	C₂²	1	1	yes	characteristic
68	C₂×Dic₄₇⋊C₄	C₂²	1	2	yes	—
69	C₄⋊C₄×D₄₇	C₂²	1	4	yes	—
70	C₄⋊C₄×D₄₇	C₂²	1	2	yes	—
71	C₂×C₄×Dic₄₇	C₂²	1	2	yes	—
72	C₄²×D₄₇	C₂²	1	4	yes	—
73	C₄²×D₄₇	C₂²	1	2	yes	—
74	C₄⋊Q₈×C₄₇	C₂²	1	1	yes	characteristic
75	C₄⋊Q₈×C₄₇	C₂²	1	1	yes	characteristic
76	#125×C₄₇	C₂²	1	2	yes	—
77	C₂²⋊Q₈×C₄₇	C₂²	1	2	yes	—
78	C₂²⋊Q₈×C₄₇	C₂²	1	2	yes	—
79	C₄×Q₈×C₄₇	C₂²	1	2	yes	—
80	C₄×Q₈×C₄₇	C₂²	1	2	yes	—
81	#117×C₄₇	C₂²	1	2	yes	—
82	C₂×C₄²×C₄₇	C₂²	1	1	yes	characteristic
83	C₂×Q₈×C₄₇	C₂³	1	2	yes	—
84	C₂×Q₈×C₄₇	C₂³	1	2	yes	—
85	C₂²×C₄×C₄₇	C₂³	1	1	yes	characteristic
86	C₂²×C₄×C₄₇	C₂³	1	1	yes	characteristic
87	C₂²×C₄×C₄₇	C₂³	1	1	yes	characteristic
88	C₂×C₂²⋊D₄₇	C₂³	1	2	yes	—
89	C₂²×Dic₄₇	C₂³	1	2	yes	—
90	C₂²×Dic₄₇	C₂³	1	2	yes	—
91	Q₈×D₄₇	—	2	8	no	—
92	#10625350	Q₈	1	8	yes	complemented
93	C₂×D₁₈₈	C₂³	1	1	yes	characteristic
94	C₂×C₄×D₄₇	C₂³	1	4	yes	—
95	C₂×C₄×D₄₇	C₂³	1	2	yes	—
96	C₂×C₄×D₄₇	C₂³	1	4	yes	—
97	C₂×C₄×D₄₇	C₂³	1	2	yes	—
98	C₂×C₄×D₄₇	C₂³	1	2	yes	—
99	C₂×Dic₉₄	—	2	4	no	—
100	C₂×Dic₉₄	C₂³	1	4	yes	—
101	C₂×Dic₉₄	C₂³	1	2	yes	—
102	C₂×Dic₉₄	C₂³	1	1	yes	characteristic
103	C₂×Dic₉₄	C₂³	1	4	yes	—
104	C₂×Dic₉₄	C₂³	1	1	yes	characteristic
105	C₂×Dic₉₄	C₂³	1	1	yes	characteristic
106	C₄⋊C₄×C₄₇	C₂³	1	2	yes	—
107	C₄⋊C₄×C₄₇	C₂³	1	2	yes	—
108	C₄⋊C₄×C₄₇	C₂³	1	4	yes	—
109	C₄⋊C₄×C₄₇	C₂³	1	4	yes	—
110	C₄⋊C₄×C₄₇	C₂³	1	2	yes	—
111	C₄⋊C₄×C₄₇	C₂³	1	2	yes	—
112	C₂²⋊C₄×C₄₇	C₂³	1	4	yes	—
113	C₄²×C₄₇	C₂³	1	1	yes	characteristic
114	C₄²×C₄₇	C₂³	1	1	yes	characteristic
115	C₄²×C₄₇	C₂³	1	1	yes	characteristic
116	C₄²×C₄₇	C₂³	1	1	yes	characteristic
117	C₄²×C₄₇	C₂³	1	4	yes	—
118	C₂²⋊Dic₄₇	C₂³	1	2	yes	—
119	(C₂×D₄₇)⋊C₄	C₂³	1	4	yes	—
120	(C₂×D₄₇)⋊C₄	C₂³	1	4	yes	—
121	(C₂×D₄₇)⋊C₄	C₂³	1	2	yes	—
122	(C₂×D₄₇)⋊C₄	C₂³	1	2	yes	—
123	C₄⋊Dic₄₇	C₂³	1	1	yes	characteristic
124	C₄⋊Dic₄₇	C₂³	1	4	yes	—
125	C₄⋊Dic₄₇	C₂³	1	1	yes	characteristic
126	C₄⋊Dic₄₇	C₂³	1	2	yes	—
127	C₄⋊Dic₄₇	C₂³	1	1	yes	characteristic
128	C₄⋊Dic₄₇	C₂³	1	1	yes	characteristic
129	C₄⋊Dic₄₇	C₂³	1	4	yes	—
130	Dic₄₇⋊C₄	C₂³	1	2	yes	—
131	Dic₄₇⋊C₄	C₂³	1	4	yes	—
132	Dic₄₇⋊C₄	C₂³	1	4	yes	—
133	Dic₄₇⋊C₄	C₂³	1	2	yes	—
134	Dic₄₇⋊C₄	C₂³	1	2	yes	—
135	Dic₄₇⋊C₄	C₂³	1	2	yes	—
136	Dic₄₇⋊C₄	C₂³	1	4	yes	—
137	Dic₄₇⋊C₄	C₂³	1	4	yes	—
138	Dic₄₇⋊C₄	C₂³	1	2	yes	—
139	Dic₄₇⋊C₄	C₂³	1	2	yes	—
140	Dic₄₇⋊C₄	C₂³	1	4	yes	—
141	Dic₄₇⋊C₄	C₂³	1	4	yes	—
142	C₄×Dic₄₇	C₂³	1	2	yes	—
143	C₄×Dic₄₇	C₂³	1	2	yes	—
144	C₄×Dic₄₇	C₂³	1	4	yes	—
145	C₄×Dic₄₇	C₂³	1	4	yes	—
146	C₄×Dic₄₇	C₂³	1	2	yes	—
147	C₄×Dic₄₇	C₂³	1	2	yes	—
148	C₄×Dic₄₇	C₂³	1	2	yes	—
149	C₄×Dic₄₇	C₂³	1	2	yes	—
150	C₄×Dic₄₇	C₂³	1	2	yes	—
151	C₂³×C₄₇	C₂⁴	1	1	yes	characteristic
152	C₂²×D₄₇	C₂⁴	1	2	yes	—
153	Q₈×C₄₇	—	2	4	no	—
154	Q₈×C₄₇	—	4	2	no	—
155	C₂×C₄×C₄₇	—	2	2	no	—
156	C₂×C₄×C₄₇	—	4	1	no	—
157	C₂×C₄×C₄₇	C₂×Q₈	1	4	yes	complemented
158	C₂×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
159	C₂×C₄×C₄₇	C₂⁴	1	4	yes	—
160	C₂×C₄×C₄₇	C₂⁴	1	4	yes	—
161	C₂×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
162	C₂×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
163	C₂×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
164	C₂×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
165	C₂×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
166	C₂²⋊D₄₇	C₂×Q₈	1	8	yes	complemented
167	C₂×Dic₄₇	—	2	4	no	—
168	C₂×Dic₄₇	—	4	2	no	—
169	C₂×Dic₄₇	C₂⁴	1	2	yes	—
170	C₂×Dic₄₇	C₂⁴	1	2	yes	—
171	C₂×Dic₄₇	C₂⁴	1	2	yes	—
172	C₂×Dic₄₇	C₂⁴	1	2	yes	—
173	C₂×Dic₄₇	C₂⁴	1	2	yes	—
174	C₂×Dic₄₇	C₂⁴	1	2	yes	—
175	C₂×Dic₄₇	C₂⁴	1	2	yes	—
176	D₁₈₈	C₂×Q₈	1	4	yes	complemented
177	C₄×D₄₇	—	2	4	no	—
178	C₄×D₄₇	—	2	8	no	—
179	C₄×D₄₇	—	4	2	no	—
180	C₄×D₄₇	—	4	4	no	—
181	C₄×D₄₇	C₂×Q₈	1	8	yes	complemented
182	Dic₉₄	—	2	2	no	—
183	Dic₉₄	—	2	4	no	—
184	Dic₉₄	—	2	8	no	—
185	Dic₉₄	—	4	4	no	—
186	Dic₉₄	C₂×Q₈	1	4	yes	complemented
187	Dic₉₄	#41	1	4	yes	complemented
188	C₂²×C₄₇	—	2	1	no	—
189	C₂²×C₄₇	—	2	1	no	—
190	C₂²×C₄₇	C₂²×Q₈	1	2	yes	—
191	C₂²×C₄₇	C₂⁵	1	1	yes	characteristic
192	C₂×D₄₇	—	2	2	no	—
193	C₂×D₄₇	—	2	2	no	—
194	C₂×D₄₇	C₂²×Q₈	1	4	yes	—
195	C₄×C₄₇	—	2	1	no	—
196	C₄×C₄₇	—	2	4	no	—
197	C₄×C₄₇	—	2	4	no	—
198	C₄×C₄₇	—	2	1	no	—
199	C₄×C₄₇	—	2	1	no	—
200	C₄×C₄₇	C₂²×Q₈	1	2	yes	—
201	C₄×C₄₇	C₂²×Q₈	1	2	yes	—
202	C₄×C₄₇	C₂×#41	1	2	yes	—
203	Dic₄₇	—	2	2	no	—
204	Dic₄₇	—	2	2	no	—
205	Dic₄₇	—	2	2	no	—
206	Dic₄₇	—	2	2	no	—
207	Dic₄₇	—	2	2	no	—
208	Dic₄₇	C₂²×Q₈	1	4	yes	—
209	Dic₄₇	C₂×#41	1	4	yes	—
210	Q₈×#41	—	47	1	no	maximal, Sylow
211	C₂×C₄₇	—	2	2	no	—
212	C₂×C₄₇	C₂³×Q₈	1	1	yes	characteristic
213	C₂×C₄₇	C₂²×#41	1	1	yes	characteristic
214	C₂×C₄₇	#585	1	1	yes	characteristic
215	D₄₇	—	2	4	no	—
216	Q₈²	—	47	1	no	—
217	#557	—	47	1	no	—
218	#557	—	47	2	no	—
219	#554	—	47	1	no	—
220	#554	—	47	2	no	—
221	#554	—	47	4	no	—
222	#554	—	47	2	no	—
223	D₄×Q₈	—	47	1	no	—
224	D₄×Q₈	—	47	2	no	—
225	#533	—	47	4	no	—
226	#533	—	47	2	no	—
227	#533	—	47	2	no	—
228	#533	D₄₇	1	1	yes	characteristic, complemented
229	C₄×#41	—	47	2	no	—
230	C₄×#41	—	47	1	no	—
231	C₂×C₄×Q₈	—	47	2	no	—
232	C₂×C₄×Q₈	—	47	1	no	—
233	C₄₇	Q₈×#41	1	1	yes	characteristic, complemented, Sylow
234	C₂×#41	—	47	1	no	—
235	C₂²×Q₈	—	47	2	no	—
236	C₂²×Q₈	—	47	1	no	—
237	C₄⋊Q₈	—	47	2	no	—
238	C₄⋊Q₈	—	47	4	no	—
239	C₄⋊Q₈	—	47	4	no	—
240	C₄⋊Q₈	—	47	2	no	—
241	C₄⋊Q₈	—	47	2	no	—
242	C₄⋊Q₈	—	47	2	no	—
243	C₄⋊Q₈	C₂×D₄₇	1	1	yes	characteristic
244	C₄⋊Q₈	C₂×D₄₇	1	1	yes	characteristic
245	#125	—	47	4	no	—
246	#125	—	47	4	no	—
247	#125	—	47	4	no	—
248	#125	—	47	2	no	—
249	#125	—	47	2	no	—
250	#125	C₂×D₄₇	1	2	yes	—
251	C₂²⋊Q₈	—	47	2	no	—
252	C₂²⋊Q₈	—	47	4	no	—
253	C₂²⋊Q₈	—	47	4	no	—
254	C₂²⋊Q₈	—	47	4	no	—
255	C₂²⋊Q₈	—	47	2	no	—
256	C₂²⋊Q₈	—	47	4	no	—
257	C₂²⋊Q₈	—	47	4	no	—
258	C₂²⋊Q₈	—	47	4	no	—
259	C₂²⋊Q₈	—	47	4	no	—
260	C₂²⋊Q₈	C₂×D₄₇	1	2	yes	—
261	C₂²⋊Q₈	C₂×D₄₇	1	2	yes	—
262	C₄×Q₈	—	47	2	no	—
263	C₄×Q₈	—	47	2	no	—
264	C₄×Q₈	—	47	4	no	—
265	C₄×Q₈	—	47	2	no	—
266	C₄×Q₈	—	47	2	no	—
267	C₄×Q₈	—	47	1	no	—
268	C₄×Q₈	—	47	4	no	—
269	C₄×Q₈	—	47	2	no	—
270	C₄×Q₈	—	47	1	no	—
271	C₄×Q₈	—	47	1	no	—
272	C₄×Q₈	—	47	1	no	—
273	C₄×Q₈	—	47	2	no	—
274	C₄×Q₈	—	47	1	no	—
275	C₄×Q₈	—	47	1	no	—
276	C₄×Q₈	—	47	4	no	—
277	C₄×Q₈	C₂×D₄₇	1	2	yes	—
278	C₄×Q₈	C₂×D₄₇	1	2	yes	—
279	C₄×D₄	—	47	2	no	—
280	C₄×D₄	—	47	2	no	—
281	C₄×D₄	—	47	2	no	—
282	C₄×D₄	—	47	2	no	—
283	C₄×D₄	—	47	4	no	—
284	C₄×D₄	—	47	4	no	—
285	C₄×D₄	—	47	1	no	—
286	C₄×D₄	—	47	1	no	—
287	#117	—	47	1	no	—
288	#117	—	47	4	no	—
289	#117	—	47	2	no	—
290	#117	C₂×D₄₇	1	2	yes	—
291	C₂×C₄⋊C₄	—	47	2	no	—
292	C₂×C₄⋊C₄	—	47	1	no	—
293	C₂×C₄⋊C₄	—	47	4	no	—
294	C₂×C₄⋊C₄	—	47	2	no	—
295	C₂×C₄²	—	47	2	no	—
296	C₂×C₄²	—	47	4	no	—
297	C₂×C₄²	—	47	2	no	—
298	C₂×C₄²	C₂×D₄₇	1	1	yes	characteristic
299	#41	—	47	8	no	—
300	C₂×Q₈	—	47	1	no	—
301	C₂×Q₈	—	47	1	no	—
302	C₂×Q₈	—	47	4	no	—
303	C₂×Q₈	—	47	2	no	—
304	C₂×Q₈	—	47	1	no	—
305	C₂×Q₈	—	47	4	no	—
306	C₂×Q₈	—	94	4	no	—
307	C₂×Q₈	—	94	8	no	—
308	C₂×Q₈	C₂²×D₄₇	1	2	yes	—
309	C₂×Q₈	C₂²×D₄₇	1	2	yes	—
310	C₂×D₄	—	47	2	no	—
311	C₂×D₄	—	47	1	no	—
312	C₂²×C₄	—	47	2	no	—
313	C₂²×C₄	—	47	2	no	—
314	C₂²×C₄	—	47	2	no	—
315	C₂²×C₄	—	47	4	no	—
316	C₂²×C₄	—	47	2	no	—
317	C₂²×C₄	—	47	4	no	—
318	C₂²×C₄	—	47	2	no	—
319	C₂²×C₄	C₂²×D₄₇	1	1	yes	characteristic
320	C₂²×C₄	C₂²×D₄₇	1	1	yes	characteristic
321	C₂²×C₄	C₂²×D₄₇	1	1	yes	characteristic
322	C₄⋊C₄	—	47	2	no	—
323	C₄⋊C₄	—	47	4	no	—
324	C₄⋊C₄	—	47	2	no	—
325	C₄⋊C₄	—	47	2	no	—
326	C₄⋊C₄	—	47	4	no	—
327	C₄⋊C₄	—	47	2	no	—
328	C₄⋊C₄	—	47	4	no	—
329	C₄⋊C₄	—	47	4	no	—
330	C₄⋊C₄	—	47	2	no	—
331	C₄⋊C₄	—	47	2	no	—
332	C₄⋊C₄	—	47	4	no	—
333	C₄⋊C₄	—	47	4	no	—
334	C₄⋊C₄	—	47	1	no	—
335	C₄⋊C₄	—	47	4	no	—
336	C₄⋊C₄	—	47	2	no	—
337	C₄⋊C₄	—	47	1	no	—
338	C₄⋊C₄	—	47	1	no	—
339	C₄⋊C₄	—	47	1	no	—
340	C₄⋊C₄	—	47	4	no	—
341	C₄⋊C₄	C₂²×D₄₇	1	4	yes	—
342	C₄⋊C₄	C₂²×D₄₇	1	2	yes	—
343	C₄⋊C₄	C₂²×D₄₇	1	2	yes	—
344	C₄⋊C₄	C₂²×D₄₇	1	2	yes	—
345	C₄⋊C₄	C₂²×D₄₇	1	2	yes	—
346	C₄⋊C₄	C₂²×D₄₇	1	4	yes	—
347	C₂²⋊C₄	—	47	2	no	—
348	C₂²⋊C₄	—	47	4	no	—
349	C₂²⋊C₄	—	47	4	no	—
350	C₂²⋊C₄	—	47	2	no	—
351	C₂²⋊C₄	—	47	2	no	—
352	C₂²⋊C₄	C₂²×D₄₇	1	4	yes	—
353	C₄²	—	47	4	no	—
354	C₄²	—	47	2	no	—
355	C₄²	—	47	2	no	—
356	C₄²	—	47	4	no	—
357	C₄²	—	47	2	no	—
358	C₄²	—	47	2	no	—
359	C₄²	—	47	2	no	—
360	C₄²	—	47	2	no	—
361	C₄²	—	47	2	no	—
362	C₄²	C₂²×D₄₇	1	1	yes	characteristic
363	C₄²	C₂²×D₄₇	1	1	yes	characteristic
364	C₄²	C₂²×D₄₇	1	1	yes	characteristic
365	C₄²	C₂²×D₄₇	1	4	yes	—
366	C₄²	C₂²×D₄₇	1	1	yes	characteristic
367	C₂³	—	47	2	no	—
368	C₂³	C₂³×D₄₇	1	1	yes	characteristic
369	Q₈	—	2	4	no	—
370	Q₈	—	4	2	no	—
371	Q₈	—	47	4	no	—
372	Q₈	—	47	4	no	—
373	Q₈	—	94	4	no	—
374	Q₈	—	94	8	no	—
375	Q₈	—	94	2	no	—
376	Q₈	—	188	4	no	—
377	D₄	—	47	8	no	—
378	D₄	—	47	4	no	—
379	C₂×C₄	—	2	2	no	—
380	C₂×C₄	—	4	1	no	—
381	C₂×C₄	—	47	2	no	—
382	C₂×C₄	—	47	2	no	—
383	C₂×C₄	—	47	8	no	—
384	C₂×C₄	—	47	2	no	—
385	C₂×C₄	—	47	2	no	—
386	C₂×C₄	—	47	2	no	—
387	C₂×C₄	—	47	2	no	—
388	C₂×C₄	—	47	2	no	—
389	C₂×C₄	—	94	8	no	—
390	C₂×C₄	—	94	4	no	—
391	C₂×C₄	—	94	4	no	—
392	C₂×C₄	—	188	2	no	—
393	C₂×C₄	—	188	4	no	—
394	C₂×C₄	—	188	2	no	—
395	C₂×C₄	Q₈×D₄₇	1	4	yes	complemented
396	C₂×C₄	C₂³×D₄₇	1	1	yes	characteristic
397	C₂×C₄	C₂³×D₄₇	1	4	yes	—
398	C₂×C₄	C₂³×D₄₇	1	4	yes	—
399	C₂×C₄	C₂³×D₄₇	1	1	yes	characteristic
400	C₂×C₄	C₂³×D₄₇	1	1	yes	characteristic
401	C₂×C₄	C₂³×D₄₇	1	1	yes	characteristic
402	C₂×C₄	C₂³×D₄₇	1	1	yes	characteristic
403	C₂×C₄	C₂³×D₄₇	1	1	yes	characteristic
404	C₂²	—	2	1	no	—
405	C₂²	—	2	1	no	—
406	C₂²	—	47	4	no	—
407	C₂²	—	94	2	no	—
408	C₂²	—	94	2	no	—
409	C₂²	C₂×Q₈×D₄₇	1	2	yes	—
410	C₂²	C₂⁴×D₄₇	1	1	yes	characteristic
411	C₄	—	2	1	no	—
412	C₄	—	2	4	no	—
413	C₄	—	2	1	no	—
414	C₄	—	2	1	no	—
415	C₄	—	2	4	no	—
416	C₄	—	47	4	no	—
417	C₄	—	47	4	no	—
418	C₄	—	94	2	no	—
419	C₄	—	94	2	no	—
420	C₄	—	94	2	no	—
421	C₄	—	94	2	no	—
422	C₄	—	94	2	no	—
423	C₄	C₂×Q₈×D₄₇	1	2	yes	—
424	C₄	C₂×Q₈×D₄₇	1	2	yes	—
425	C₄	#41×D₄₇	1	2	yes	—
426	C₂	—	2	2	no	—
427	C₂	—	94	4	no	—
428	C₂	C₂²×Q₈×D₄₇	1	1	yes	characteristic
429	C₂	C₂×#41×D₄₇	1	1	yes	characteristic
430	C₂	#15689959	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂³×D₄₇
commutator, socle	C₂²×C₄₇	C₂⁵
Frattini	C₂²	C₂⁴×D₄₇
Fitting	C₄₇×#533	C₂
hypercenter	#533	D₄₇
hypocenter	C₄₇	Q₈×#41
LCS	G ▷ C₂²×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂×C₄ ◁ #533

Complements

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

N	H ≅ G/N	type
1. #15689853	C₂	semidirect
2. #15689850	C₂	semidirect
3. #15689848	C₂	semidirect
4. #15689834	C₂	semidirect
5. #15689831	C₂	semidirect
6. #15689829	C₂	semidirect
7. #15689827	C₂	semidirect
8. #15689788	C₂	semidirect
9. #15689786	C₂	semidirect
10. #15689677	C₂	semidirect
11. #15689677	C₂	semidirect
12. #15689676	C₂	semidirect
15. C₂×C₄×Dic₉₄	C₂	semidirect
16. C₄×Q₈×D₄₇	C₂	semidirect
17. C₄₇×#533	C₂	semidirect
92. #10625350	Q₈	semidirect
157. C₂×C₄×C₄₇	C₂×Q₈	semidirect
166. C₂²⋊D₄₇	C₂×Q₈	semidirect
176. D₁₈₈	C₂×Q₈	semidirect
181. C₄×D₄₇	C₂×Q₈	semidirect
186. Dic₉₄	C₂×Q₈	semidirect
187. Dic₉₄	#41	semidirect
228. #533	D₄₇	semidirect
233. C₄₇	Q₈×#41	semidirect
395. C₂×C₄	Q₈×D₄₇	semidirect