Subgroups — #20257654

Order 6016.

1058 conjugacy classes of subgroups.

The subgroup lattice has 430 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#15689866	C₂	1	2	yes	maximal, complemented
2	#15689860	C₂	1	2	yes	maximal, complemented
3	#15689859	C₂	1	2	yes	maximal, complemented
4	#15689841	C₂	1	2	yes	maximal, complemented
5	#15689837	C₂	1	2	yes	maximal, complemented
6	#15689804	C₂	1	2	yes	maximal, complemented
7	#15689779	C₂	1	2	yes	maximal, complemented
8	#15689767	C₂	1	2	yes	maximal, complemented
9	#15689740	C₂	1	2	yes	maximal, complemented
10	#15689737	C₂	1	4	yes	maximal, complemented
11	#15689708	C₂	1	4	yes	maximal, complemented
12	#15689694	C₂	1	1	yes	maximal, characteristic, complemented
13	#15689633	C₂	1	2	yes	maximal, complemented
14	#15689630	C₂	1	1	yes	maximal, characteristic, complemented
15	C₄₇×#535	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×#10625352	C₂²	1	2	yes	—
17	C₂²×Dic₉₄	C₂²	1	1	yes	characteristic, complemented
18	C₂²×C₄×D₄₇	C₂²	1	1	yes	characteristic, complemented
19	#13094023	C₂²	1	2	yes	complemented
20	#13094022	C₂²	1	2	yes	complemented
21	#13094018	C₂²	1	4	yes	complemented
22	#13094017	C₂²	1	4	yes	complemented
23	#13094017	C₂²	1	4	yes	complemented
24	#13094011	C₂²	1	2	yes	—
25	#13094011	C₂²	1	2	yes	complemented
26	#13094011	C₂²	1	4	yes	complemented
27	#13094011	C₂²	1	4	yes	complemented
28	#13094010	C₂²	1	4	yes	—
29	#13094010	C₂²	1	4	yes	complemented
30	#13094010	C₂²	1	4	yes	complemented
31	#13094006	C₂²	1	4	yes	complemented
32	#13094005	C₂²	1	1	yes	characteristic
33	#13094005	C₂²	1	4	yes	complemented
34	#13094005	C₂²	1	4	yes	complemented
35	#13094005	C₂²	1	1	yes	characteristic, complemented
36	#13094005	C₂²	1	2	yes	complemented
37	#13094005	C₂²	1	2	yes	complemented
38	#13094004	C₂²	1	2	yes	complemented
39	#13094003	C₂²	1	2	yes	complemented
40	#13094003	C₂²	1	2	yes	complemented
41	#13094001	C₂²	1	4	yes	complemented
42	#13094001	C₂²	1	4	yes	complemented
43	#13094000	C₂²	1	2	yes	complemented
44	#13093996	C₂²	1	4	yes	—
45	#13093996	C₂²	1	4	yes	complemented
46	#13093996	C₂²	1	4	yes	complemented
47	#13093995	C₂²	1	2	yes	—
48	#13093995	C₂²	1	2	yes	—
49	#13093993	C₂²	1	4	yes	—
50	#13093992	C₂²	1	1	yes	characteristic
51	#13093992	C₂²	1	1	yes	characteristic, complemented
52	#13093992	C₂²	1	4	yes	complemented
53	C₄×Dic₉₄	C₂²	1	4	yes	complemented
54	#13093989	C₂²	1	2	yes	complemented
55	D₄×Dic₄₇	C₂²	1	2	yes	complemented
56	D₄×Dic₄₇	C₂²	1	4	yes	complemented
57	D₄×Dic₄₇	C₂²	1	4	yes	complemented
58	C₄×C₂²⋊D₄₇	C₂²	1	2	yes	—
59	C₄×C₂²⋊D₄₇	C₂²	1	2	yes	complemented
60	(C₂²⋊D₄₇)⋊C₄	C₂²	1	4	yes	complemented
61	#13093983	C₂²	1	1	yes	characteristic, complemented
62	#13093983	C₂²	1	1	yes	characteristic, complemented
63	#13093982	C₂²	1	2	yes	complemented
64	#13093980	C₂²	1	4	yes	complemented
65	C₂×C₂²⋊Dic₄₇	C₂²	1	4	yes	complemented
66	C₂×#41×C₄₇	C₂²	1	1	yes	characteristic
67	C₂²×D₄×C₄₇	C₂²	1	1	yes	characteristic, complemented
68	#127×C₄₇	C₂²	1	2	yes	—
69	#124×C₄₇	C₂²	1	2	yes	complemented
70	#121×C₄₇	C₂²	1	2	yes	—
71	#121×C₄₇	C₂²	1	2	yes	complemented
72	#120×C₄₇	C₂²	1	2	yes	—
73	#120×C₄₇	C₂²	1	2	yes	complemented
74	#117×C₄₇	C₂²	1	1	yes	characteristic, complemented
75	C₂⁴×C₄₇	C₂³	1	2	yes	—
76	C₂³×D₄₇	C₂³	1	1	yes	characteristic
77	#41×C₄₇	—	4	2	no	—
78	C₂×Q₈×C₄₇	C₂³	1	1	yes	characteristic
79	C₂×D₄×C₄₇	—	4	2	no	—
80	C₂×D₄×C₄₇	C₂³	1	2	yes	—
81	C₂×D₄×C₄₇	C₂³	1	1	yes	characteristic
82	C₂×D₄×C₄₇	C₂³	1	4	yes	—
83	C₂×D₄×C₄₇	C₂³	1	1	yes	characteristic
84	C₂×D₄×C₄₇	C₂³	1	4	yes	—
85	C₂×D₄×C₄₇	C₂³	1	2	yes	—
86	C₂×D₄×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	C₂²×C₄×C₄₇	C₂³	1	1	yes	characteristic
90	C₂×C₂²⋊D₄₇	C₂³	1	4	yes	—
91	C₂×C₂²⋊D₄₇	C₂³	1	2	yes	—
92	C₂×C₂²⋊D₄₇	C₂³	1	2	yes	—
93	C₂×C₂²⋊D₄₇	C₂³	1	4	yes	—
94	C₂²×Dic₄₇	C₂³	1	4	yes	—
95	C₂²×Dic₄₇	C₂³	1	4	yes	—
96	C₂²×Dic₄₇	C₂³	1	1	yes	characteristic
97	C₂²×Dic₄₇	C₂³	1	2	yes	—
98	#10625352	—	4	4	no	—
99	C₂×C₄×D₄₇	—	4	2	no	—
100	C₂×C₄×D₄₇	C₂³	1	2	yes	—
101	C₂×C₄×D₄₇	C₂³	1	2	yes	—
102	C₂×Dic₉₄	—	4	2	no	—
103	C₂×Dic₉₄	C₂³	1	2	yes	—
104	C₂×Dic₉₄	C₂³	1	4	yes	—
105	C₂×Dic₉₄	C₂³	1	2	yes	—
106	C₄⋊C₄×C₄₇	C₂³	1	2	yes	—
107	C₂²⋊C₄×C₄₇	C₂³	1	2	yes	—
108	C₂²⋊C₄×C₄₇	C₂³	1	4	yes	—
109	C₂²⋊C₄×C₄₇	C₂³	1	4	yes	—
110	C₄²×C₄₇	C₂³	1	2	yes	—
111	C₂²⋊Dic₄₇	C₂³	1	2	yes	—
112	C₂²⋊Dic₄₇	C₂³	1	4	yes	—
113	C₂²⋊Dic₄₇	C₂³	1	4	yes	—
114	C₂²⋊Dic₄₇	C₂³	1	4	yes	—
115	C₂²⋊Dic₄₇	C₂³	1	1	yes	characteristic
116	C₂²⋊Dic₄₇	C₂³	1	1	yes	characteristic
117	C₂²⋊Dic₄₇	C₂³	1	2	yes	—
118	C₂²⋊Dic₄₇	C₂³	1	2	yes	—
119	C₂²⋊Dic₄₇	C₂³	1	4	yes	—
120	C₂²⋊Dic₄₇	C₂³	1	4	yes	—
121	C₂²⋊Dic₄₇	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	2	yes	—
125	(C₂×D₄₇)⋊C₄	C₂³	1	2	yes	—
126	C₄⋊Dic₄₇	C₂³	1	2	yes	—
127	C₄⋊Dic₄₇	C₂³	1	2	yes	—
128	C₄⋊Dic₄₇	C₂³	1	4	yes	—
129	Dic₄₇⋊C₄	C₂³	1	2	yes	—
130	Dic₄₇⋊C₄	C₂³	1	4	yes	—
131	Dic₄₇⋊C₄	C₂³	1	4	yes	—
132	Dic₄₇⋊C₄	C₂³	1	2	yes	—
133	Dic₄₇⋊C₄	C₂³	1	4	yes	—
134	Dic₄₇⋊C₄	C₂³	1	4	yes	—
135	C₄×Dic₄₇	C₂³	1	2	yes	—
136	C₄×Dic₄₇	C₂³	1	4	yes	—
137	C₄×Dic₄₇	C₂³	1	2	yes	—
138	C₄×Dic₄₇	C₂³	1	4	yes	—
139	C₂³×C₄₇	—	4	2	no	—
140	C₂³×C₄₇	—	4	4	no	—
141	C₂³×C₄₇	C₂⁴	1	1	yes	characteristic
142	C₂³×C₄₇	C₂⁴	1	1	yes	characteristic
143	C₂³×C₄₇	C₂⁴	1	4	yes	—
144	C₂³×C₄₇	C₂⁴	1	1	yes	characteristic
145	C₂²×D₄₇	—	4	1	no	—
146	C₂²×D₄₇	—	4	2	no	—
147	C₂²×D₄₇	C₂⁴	1	2	yes	—
148	Q₈×C₄₇	—	4	1	no	—
149	D₄×C₄₇	—	2	4	no	—
150	D₄×C₄₇	—	4	2	no	—
151	D₄×C₄₇	—	4	4	no	—
152	D₄×C₄₇	—	4	4	no	—
153	D₄×C₄₇	—	4	1	no	—
154	D₄×C₄₇	—	4	1	no	—
155	D₄×C₄₇	—	4	1	no	—
156	C₂×C₄×C₄₇	—	2	2	no	—
157	C₂×C₄×C₄₇	—	2	2	no	—
158	C₂×C₄×C₄₇	—	2	2	no	—
159	C₂×C₄×C₄₇	C₂⁴	1	4	yes	—
160	C₂×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
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	C₂²⋊D₄₇	—	4	4	no	—
165	C₂²⋊D₄₇	—	4	2	no	—
166	C₂²⋊D₄₇	—	4	4	no	—
167	C₂²⋊D₄₇	—	4	2	no	—
168	C₂×Dic₄₇	—	4	2	no	—
169	C₂×Dic₄₇	—	4	1	no	—
170	C₂×Dic₄₇	—	4	4	no	—
171	C₂×Dic₄₇	—	4	4	no	—
172	C₂×Dic₄₇	C₂⁴	1	2	yes	—
173	C₂×Dic₄₇	C₂⁴	1	4	yes	—
174	C₂×Dic₄₇	C₂⁴	1	2	yes	—
175	C₂×Dic₄₇	C₂⁴	1	2	yes	—
176	C₂×Dic₄₇	C₂⁴	1	4	yes	—
177	C₄×D₄₇	—	2	4	no	—
178	C₄×D₄₇	—	4	2	no	—
179	Dic₉₄	—	2	4	no	—
180	Dic₉₄	—	4	2	no	—
181	Dic₉₄	—	4	4	no	—
182	C₂²×C₄₇	—	2	1	no	—
183	C₂²×C₄₇	—	2	4	no	—
184	C₂²×C₄₇	—	2	1	no	—
185	C₂²×C₄₇	—	2	1	no	—
186	C₂²×C₄₇	—	2	4	no	—
187	C₂²×C₄₇	—	2	2	no	—
188	C₂²×C₄₇	—	2	4	no	—
189	C₂²×C₄₇	—	2	2	no	—
190	C₂²×C₄₇	—	2	2	no	—
191	C₂²×C₄₇	—	8	4	no	—
192	C₂²×C₄₇	C₂⁵	1	1	yes	characteristic
193	C₂×D₄₇	—	2	2	no	—
194	C₂×D₄₇	—	2	2	no	—
195	C₂×D₄₇	—	2	2	no	—
196	C₂×D₄₇	—	4	4	no	—
197	C₄×C₄₇	—	2	1	no	—
198	C₄×C₄₇	—	2	1	no	—
199	C₄×C₄₇	—	2	1	no	—
200	C₄×C₄₇	—	2	4	no	—
201	C₄×C₄₇	H(5,𝔽₂)	1	2	yes	—
202	Dic₄₇	—	2	4	no	—
203	Dic₄₇	—	2	2	no	—
204	Dic₄₇	—	2	2	no	—
205	Dic₄₇	—	2	4	no	—
206	Dic₄₇	—	2	2	no	—
207	#3540	—	47	1	no	maximal, Sylow
208	C₂×C₄₇	—	4	1	no	—
209	C₂×C₄₇	—	4	1	no	—
210	C₂×C₄₇	—	4	4	no	—
211	C₂×C₄₇	—	4	1	no	—
212	C₂×C₄₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
213	C₂×C₄₇	#585	1	2	yes	—
214	D₄₇	—	4	2	no	—
215	H(3,𝔽₄)	—	47	2	no	—
216	#560	—	47	2	no	—
217	#559	—	47	2	no	—
218	#556	—	47	2	no	—
219	#555	—	47	2	no	—
220	#551	—	47	2	no	—
221	#548	—	47	2	no	—
222	#546	—	47	2	no	—
223	#542	—	47	4	no	—
224	#542	—	47	2	no	—
225	#538	—	47	4	no	—
226	#536	—	47	1	no	—
227	#535	D₄₇	1	1	yes	characteristic, complemented
228	#525	—	47	1	no	—
229	#525	—	47	2	no	—
230	C₄₇	#3540	1	1	yes	characteristic, complemented, Sylow
231	C₂×#41	—	47	2	no	—
232	C₂×#41	C₂×D₄₇	1	1	yes	characteristic
233	C₂²×Q₈	—	47	1	no	—
234	C₂²×D₄	C₂×D₄₇	1	1	yes	characteristic, complemented
235	C₂³×C₄	—	47	1	no	—
236	C₄⋊Q₈	—	47	2	no	—
237	C₄⋊Q₈	—	47	2	no	—
238	#127	C₂×D₄₇	1	2	yes	—
239	#126	—	47	4	no	—
240	#126	—	47	4	no	—
241	#126	—	47	4	no	—
242	#124	—	47	2	no	—
243	#124	—	47	4	no	—
244	#124	—	47	2	no	—
245	#124	—	47	4	no	—
246	#124	—	47	4	no	—
247	#124	—	47	4	no	—
248	#124	—	47	4	no	—
249	#124	C₂×D₄₇	1	2	yes	complemented
250	#123	—	47	1	no	—
251	#123	—	47	1	no	—
252	#123	—	47	2	no	—
253	#123	—	47	2	no	—
254	#123	—	47	4	no	—
255	#123	—	47	4	no	—
256	#123	—	47	4	no	—
257	C₂²⋊Q₈	—	47	2	no	—
258	C₂²⋊Q₈	—	47	2	no	—
259	C₂²⋊Q₈	—	47	2	no	—
260	C₂²⋊Q₈	—	47	2	no	—
261	C₂²⋊Q₈	—	47	4	no	—
262	C₂²⋊Q₈	—	47	4	no	—
263	#121	—	47	2	no	—
264	#121	—	47	2	no	—
265	#121	—	47	4	no	—
266	#121	—	47	4	no	—
267	#121	—	47	4	no	—
268	#121	C₂×D₄₇	1	2	yes	—
269	#121	C₂×D₄₇	1	2	yes	complemented
270	#120	—	47	4	no	—
271	#120	—	47	1	no	—
272	#120	—	47	4	no	—
273	#120	—	47	1	no	—
274	#120	C₂×D₄₇	1	2	yes	—
275	#120	C₂×D₄₇	1	2	yes	complemented
276	C₄×Q₈	—	47	2	no	—
277	C₄×Q₈	—	47	4	no	—
278	C₄×D₄	—	47	4	no	—
279	C₄×D₄	—	47	4	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	#117	—	47	1	no	—
285	#117	—	47	1	no	—
286	#117	—	47	2	no	—
287	#117	—	47	4	no	—
288	#117	C₂×D₄₇	1	1	yes	characteristic, complemented
289	C₂×C₂²⋊C₄	—	47	4	no	—
290	C₂⁴	—	47	1	no	—
291	C₂⁴	C₂²×D₄₇	1	2	yes	—
292	#41	—	4	2	no	—
293	#41	—	188	4	no	—
294	C₂×Q₈	—	47	2	no	—
295	C₂×Q₈	—	47	4	no	—
296	C₂×Q₈	—	47	2	no	—
297	C₂×Q₈	—	188	2	no	—
298	C₂×Q₈	C₂²×D₄₇	1	1	yes	characteristic
299	C₂×D₄	—	4	2	no	—
300	C₂×D₄	—	47	2	no	—
301	C₂×D₄	—	47	4	no	—
302	C₂×D₄	—	47	2	no	—
303	C₂×D₄	—	47	4	no	—
304	C₂×D₄	C₂²×D₄₇	1	2	yes	—
305	C₂×D₄	C₂²×D₄₇	1	4	yes	—
306	C₂×D₄	C₂²×D₄₇	1	4	yes	—
307	C₂×D₄	C₂²×D₄₇	1	1	yes	characteristic
308	C₂×D₄	C₂²×D₄₇	1	1	yes	characteristic
309	C₂×D₄	C₂²×D₄₇	1	1	yes	characteristic
310	C₂×D₄	C₂²×D₄₇	1	2	yes	—
311	C₂²×C₄	—	47	4	no	—
312	C₂²×C₄	—	47	4	no	—
313	C₂²×C₄	—	47	1	no	—
314	C₂²×C₄	—	47	2	no	—
315	C₂²×C₄	—	47	2	no	—
316	C₂²×C₄	—	47	2	no	—
317	C₂²×C₄	—	188	2	no	—
318	C₂²×C₄	C₂²×D₄₇	1	1	yes	characteristic
319	C₂²×C₄	C₂²×D₄₇	1	1	yes	characteristic
320	C₂²×C₄	C₂²×D₄₇	1	1	yes	characteristic
321	C₄⋊C₄	—	47	2	no	—
322	C₄⋊C₄	—	47	4	no	—
323	C₄⋊C₄	—	47	2	no	—
324	C₄⋊C₄	—	47	4	no	—
325	C₄⋊C₄	—	47	4	no	—
326	C₄⋊C₄	—	47	4	no	—
327	C₄⋊C₄	—	47	2	no	—
328	C₄⋊C₄	—	47	2	no	—
329	C₄⋊C₄	—	47	4	no	—
330	C₄⋊C₄	C₂²×D₄₇	1	2	yes	—
331	C₂²⋊C₄	—	47	2	no	—
332	C₂²⋊C₄	—	47	4	no	—
333	C₂²⋊C₄	—	47	4	no	—
334	C₂²⋊C₄	—	47	4	no	—
335	C₂²⋊C₄	—	47	1	no	—
336	C₂²⋊C₄	—	47	1	no	—
337	C₂²⋊C₄	—	47	2	no	—
338	C₂²⋊C₄	—	47	2	no	—
339	C₂²⋊C₄	—	47	4	no	—
340	C₂²⋊C₄	—	47	4	no	—
341	C₂²⋊C₄	—	47	4	no	—
342	C₂²⋊C₄	—	47	4	no	—
343	C₂²⋊C₄	—	47	2	no	—
344	C₂²⋊C₄	—	47	4	no	—
345	C₂²⋊C₄	—	47	2	no	—
346	C₂²⋊C₄	C₂²×D₄₇	1	4	yes	—
347	C₂²⋊C₄	C₂²×D₄₇	1	2	yes	—
348	C₂²⋊C₄	C₂²×D₄₇	1	4	yes	—
349	C₄²	—	47	2	no	—
350	C₄²	—	47	4	no	—
351	C₄²	—	47	2	no	—
352	C₄²	—	47	4	no	—
353	C₄²	C₂²×D₄₇	1	2	yes	—
354	C₂³	—	4	2	no	—
355	C₂³	—	4	4	no	—
356	C₂³	—	47	2	no	—
357	C₂³	—	188	1	no	—
358	C₂³	—	188	2	no	—
359	C₂³	C₂³×D₄₇	1	1	yes	characteristic
360	C₂³	C₂³×D₄₇	1	1	yes	characteristic
361	C₂³	C₂³×D₄₇	1	4	yes	—
362	C₂³	C₂³×D₄₇	1	1	yes	characteristic
363	Q₈	—	4	1	no	—
364	Q₈	—	94	4	no	—
365	Q₈	—	188	4	no	—
366	Q₈	—	188	2	no	—
367	D₄	—	2	4	no	—
368	D₄	—	4	2	no	—
369	D₄	—	4	4	no	—
370	D₄	—	4	4	no	—
371	D₄	—	4	1	no	—
372	D₄	—	4	1	no	—
373	D₄	—	4	1	no	—
374	D₄	—	188	2	no	—
375	D₄	—	188	4	no	—
376	D₄	—	188	2	no	—
377	D₄	—	188	4	no	—
378	C₂×C₄	—	2	2	no	—
379	C₂×C₄	—	2	2	no	—
380	C₂×C₄	—	2	2	no	—
381	C₂×C₄	—	47	2	no	—
382	C₂×C₄	—	47	4	no	—
383	C₂×C₄	—	47	2	no	—
384	C₂×C₄	—	47	2	no	—
385	C₂×C₄	—	47	4	no	—
386	C₂×C₄	—	94	4	no	—
387	C₂×C₄	—	188	2	no	—
388	C₂×C₄	—	188	4	no	—
389	C₂×C₄	—	188	1	no	—
390	C₂×C₄	—	188	2	no	—
391	C₂×C₄	—	188	4	no	—
392	C₂×C₄	C₂³×D₄₇	1	4	yes	—
393	C₂×C₄	C₂³×D₄₇	1	1	yes	characteristic
394	C₂×C₄	C₂³×D₄₇	1	1	yes	characteristic
395	C₂×C₄	C₂³×D₄₇	1	1	yes	characteristic
396	C₂×C₄	C₂³×D₄₇	1	1	yes	characteristic
397	C₂²	—	2	1	no	—
398	C₂²	—	2	1	no	—
399	C₂²	—	2	1	no	—
400	C₂²	—	2	4	no	—
401	C₂²	—	2	4	no	—
402	C₂²	—	2	2	no	—
403	C₂²	—	2	2	no	—
404	C₂²	—	2	4	no	—
405	C₂²	—	2	2	no	—
406	C₂²	—	8	4	no	—
407	C₂²	—	94	2	no	—
408	C₂²	—	94	2	no	—
409	C₂²	—	94	2	no	—
410	C₂²	—	188	4	no	—
411	C₂²	C₂⁴×D₄₇	1	1	yes	characteristic
412	C₄	—	2	1	no	—
413	C₄	—	2	1	no	—
414	C₄	—	2	1	no	—
415	C₄	—	2	4	no	—
416	C₄	—	94	2	no	—
417	C₄	—	94	4	no	—
418	C₄	—	94	2	no	—
419	C₄	—	94	4	no	—
420	C₄	—	94	2	no	—
421	C₄	#13094069	1	2	yes	—
422	C₂	—	4	1	no	—
423	C₂	—	4	4	no	—
424	C₂	—	4	1	no	—
425	C₂	—	4	1	no	—
426	C₂	—	188	2	no	—
427	C₂	C₂×#13094069	1	1	yes	characteristic
428	C₂	#15689958	1	2	yes	—

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₄₇
commutator, socle	C₂²×C₄₇	C₂⁵
Fitting	C₄₇×#535	C₂
hypercenter	#535	D₄₇
hypocenter	C₄₇	#3540
LCS	G ▷ C₂²×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂² ◁ #535

Complements

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

N	H ≅ G/N	type
1. #15689866	C₂	semidirect
2. #15689860	C₂	semidirect
3. #15689859	C₂	semidirect
4. #15689841	C₂	semidirect
5. #15689837	C₂	semidirect
6. #15689804	C₂	semidirect
7. #15689779	C₂	semidirect
8. #15689767	C₂	semidirect
9. #15689740	C₂	semidirect
10. #15689737	C₂	semidirect
11. #15689708	C₂	semidirect
12. #15689694	C₂	semidirect
13. #15689633	C₂	semidirect
14. #15689630	C₂	semidirect
15. C₄₇×#535	C₂	semidirect
17. C₂²×Dic₉₄	C₂²	semidirect
18. C₂²×C₄×D₄₇	C₂²	semidirect
19. #13094023	C₂²	semidirect
20. #13094022	C₂²	semidirect
21. #13094018	C₂²	semidirect
22. #13094017	C₂²	semidirect
23. #13094017	C₂²	semidirect
25. #13094011	C₂²	semidirect
26. #13094011	C₂²	semidirect
27. #13094011	C₂²	semidirect
29. #13094010	C₂²	semidirect
30. #13094010	C₂²	semidirect
31. #13094006	C₂²	semidirect
33. #13094005	C₂²	semidirect
34. #13094005	C₂²	semidirect
35. #13094005	C₂²	semidirect
36. #13094005	C₂²	semidirect
37. #13094005	C₂²	semidirect
38. #13094004	C₂²	semidirect
39. #13094003	C₂²	semidirect
40. #13094003	C₂²	semidirect
41. #13094001	C₂²	semidirect
42. #13094001	C₂²	semidirect
43. #13094000	C₂²	semidirect
45. #13093996	C₂²	semidirect
46. #13093996	C₂²	semidirect
51. #13093992	C₂²	semidirect
52. #13093992	C₂²	semidirect
53. C₄×Dic₉₄	C₂²	semidirect
54. #13093989	C₂²	semidirect
55. D₄×Dic₄₇	C₂²	semidirect
56. D₄×Dic₄₇	C₂²	semidirect
57. D₄×Dic₄₇	C₂²	semidirect
59. C₄×C₂²⋊D₄₇	C₂²	semidirect
60. (C₂²⋊D₄₇)⋊C₄	C₂²	semidirect
61. #13093983	C₂²	semidirect
62. #13093983	C₂²	semidirect
63. #13093982	C₂²	semidirect
64. #13093980	C₂²	semidirect
65. C₂×C₂²⋊Dic₄₇	C₂²	semidirect
67. C₂²×D₄×C₄₇	C₂²	semidirect
69. #124×C₄₇	C₂²	semidirect
71. #121×C₄₇	C₂²	semidirect
73. #120×C₄₇	C₂²	semidirect
74. #117×C₄₇	C₂²	semidirect
227. #535	D₄₇	semidirect
230. C₄₇	#3540	semidirect
234. C₂²×D₄	C₂×D₄₇	semidirect
249. #124	C₂×D₄₇	semidirect
269. #121	C₂×D₄₇	semidirect
275. #120	C₂×D₄₇	semidirect
288. #117	C₂×D₄₇	semidirect