Subgroups — #20257955

Order 6016.

1032 conjugacy classes of subgroups.

The subgroup lattice has 578 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#15689874	C₂	1	2	yes	maximal, complemented
2	#15689869	C₂	1	2	yes	maximal, complemented
3	#15689844	C₂	1	2	yes	maximal, complemented
4	#15689800	C₂	1	2	yes	maximal, complemented
5	#15689799	C₂	1	2	yes	maximal, complemented
6	#15689786	C₂	1	2	yes	maximal, complemented
7	#15689783	C₂	1	2	yes	maximal, complemented
8	#15689763	C₂	1	2	yes	maximal, complemented
9	#15689748	C₂	1	1	yes	maximal, characteristic, complemented
10	#15689746	C₂	1	2	yes	maximal, complemented
11	#15689743	C₂	1	2	yes	maximal, complemented
12	#15689743	C₂	1	2	yes	maximal, complemented
13	#15689713	C₂	1	1	yes	maximal, characteristic, complemented
14	#15689711	C₂	1	1	yes	maximal, characteristic, complemented
15	#15689696	C₂	1	2	yes	maximal, complemented
16	#15689675	C₂	1	1	yes	maximal, characteristic, complemented
17	#15689659	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂×#13094010	C₂	1	1	yes	maximal, characteristic, complemented
19	C₄₇×#543	C₂	1	1	yes	maximal, characteristic, complemented
20	C₂×#10625350	C₂²	1	2	yes	—
21	C₂²×Dic₉₄	C₂²	1	1	yes	characteristic
22	C₂×Q₈×D₄₇	C₂²	1	2	yes	complemented
23	C₂²×C₂²⋊D₄₇	C₂²	1	1	yes	characteristic
24	#13094023	C₂²	1	2	yes	complemented
25	#13094023	C₂²	1	2	yes	complemented
26	#13094023	C₂²	1	1	yes	characteristic, complemented
27	#13094022	C₂²	1	1	yes	characteristic, complemented
28	#13094022	C₂²	1	2	yes	complemented
29	#13094019	C₂²	1	2	yes	complemented
30	#13094019	C₂²	1	2	yes	complemented
31	#13094019	C₂²	1	2	yes	complemented
32	#13094019	C₂²	1	2	yes	complemented
33	#13094017	C₂²	1	2	yes	complemented
34	#13094017	C₂²	1	2	yes	complemented
35	#13094017	C₂²	1	2	yes	complemented
36	#13094015	C₂²	1	1	yes	characteristic, complemented
37	#13094014	C₂²	1	2	yes	complemented
38	#13094013	C₂²	1	2	yes	complemented
39	#13094013	C₂²	1	2	yes	complemented
40	#13094013	C₂²	1	1	yes	characteristic, complemented
41	#13094010	C₂²	1	2	yes	—
42	#13094010	C₂²	1	2	yes	—
43	#13094010	C₂²	1	2	yes	—
44	#13094010	C₂²	1	2	yes	—
45	#13094010	C₂²	1	2	yes	—
46	#13094010	C₂²	1	2	yes	complemented
47	#13094010	C₂²	1	2	yes	complemented
48	#13094009	C₂²	1	2	yes	complemented
49	#13094009	C₂²	1	2	yes	complemented
50	#13094009	C₂²	1	2	yes	complemented
51	#13094008	C₂²	1	2	yes	—
52	#13094007	C₂²	1	2	yes	—
53	#13094007	C₂²	1	2	yes	complemented
54	#13094006	C₂²	1	2	yes	—
55	#13094006	C₂²	1	2	yes	complemented
56	#13094006	C₂²	1	2	yes	complemented
57	#13094004	C₂²	1	2	yes	complemented
58	#13094004	C₂²	1	2	yes	complemented
59	#13094003	C₂²	1	1	yes	characteristic
60	#13094003	C₂²	1	2	yes	complemented
61	#13094002	C₂²	1	2	yes	complemented
62	#13094002	C₂²	1	2	yes	complemented
63	#13094002	C₂²	1	2	yes	complemented
64	#13094002	C₂²	1	2	yes	complemented
65	#13094001	C₂²	1	2	yes	—
66	#13094001	C₂²	1	2	yes	—
67	#13094000	C₂²	1	2	yes	complemented
68	#13094000	C₂²	1	2	yes	complemented
69	#13093999	C₂²	1	2	yes	complemented
70	#13093998	C₂²	1	2	yes	—
71	#13093998	C₂²	1	1	yes	characteristic
72	#13093997	C₂²	1	2	yes	—
73	#13093997	C₂²	1	2	yes	—
74	#13093997	C₂²	1	2	yes	complemented
75	#13093994	C₂²	1	2	yes	—
76	#13093993	C₂²	1	2	yes	—
77	Q₈×Dic₄₇	C₂²	1	1	yes	characteristic, complemented
78	Q₈×Dic₄₇	C₂²	1	1	yes	characteristic, complemented
79	#13093989	C₂²	1	1	yes	characteristic, complemented
80	#13093989	C₂²	1	2	yes	complemented
81	#13093989	C₂²	1	2	yes	complemented
82	#13093986	C₂²	1	2	yes	complemented
83	#13093986	C₂²	1	1	yes	characteristic, complemented
84	C₄×C₂²⋊D₄₇	C₂²	1	2	yes	—
85	C₄×C₂²⋊D₄₇	C₂²	1	2	yes	—
86	C₄×C₂²⋊D₄₇	C₂²	1	2	yes	complemented
87	(C₂²⋊D₄₇)⋊C₄	C₂²	1	2	yes	—
88	(C₂²⋊D₄₇)⋊C₄	C₂²	1	2	yes	—
89	#13093983	C₂²	1	2	yes	complemented
90	#13093982	C₂²	1	2	yes	complemented
91	#13093982	C₂²	1	2	yes	complemented
92	#13093980	C₂²	1	2	yes	—
93	C₂×C₂²⋊Dic₄₇	C₂²	1	1	yes	characteristic
94	C₂×(C₂×D₄₇)⋊C₄	C₂²	1	1	yes	characteristic
95	C₂×(C₂×D₄₇)⋊C₄	C₂²	1	1	yes	characteristic
96	C₂²⋊C₄×D₄₇	C₂²	1	2	yes	—
97	C₂×C₄×Dic₄₇	C₂²	1	1	yes	characteristic
98	C₂²⋊Q₈×C₄₇	C₂²	1	1	yes	characteristic
99	C₂²⋊Q₈×C₄₇	C₂²	1	2	yes	—
100	C₂²⋊Q₈×C₄₇	C₂²	1	1	yes	characteristic
101	C₂²⋊Q₈×C₄₇	C₂²	1	2	yes	complemented
102	C₂²⋊Q₈×C₄₇	C₂²	1	2	yes	complemented
103	C₂²⋊Q₈×C₄₇	C₂²	1	2	yes	complemented
104	C₂²⋊Q₈×C₄₇	C₂²	1	2	yes	complemented
105	C₂×C₂²⋊C₄×C₄₇	C₂²	1	2	yes	—
106	C₂×C₂²⋊C₄×C₄₇	C₂²	1	1	yes	characteristic
107	C₂⁴×C₄₇	C₂³	1	1	yes	characteristic
108	C₂³×D₄₇	C₂³	1	1	yes	characteristic
109	C₂×Q₈×C₄₇	C₂³	1	1	yes	characteristic
110	C₂×Q₈×C₄₇	C₂³	1	1	yes	characteristic
111	C₂×Q₈×C₄₇	C₂³	1	2	yes	—
112	C₂²×C₄×C₄₇	C₂³	1	1	yes	characteristic
113	C₂²×C₄×C₄₇	C₂³	1	1	yes	characteristic
114	C₂²×C₄×C₄₇	C₂³	1	2	yes	—
115	C₂²×C₄×C₄₇	C₂³	1	2	yes	—
116	C₂×C₂²⋊D₄₇	—	4	2	no	—
117	C₂×C₂²⋊D₄₇	C₂³	1	2	yes	—
118	C₂×C₂²⋊D₄₇	C₂³	1	2	yes	—
119	C₂×C₂²⋊D₄₇	C₂³	1	2	yes	—
120	C₂×C₂²⋊D₄₇	C₂³	1	2	yes	—
121	C₂×C₂²⋊D₄₇	C₂³	1	2	yes	—
122	C₂²×Dic₄₇	C₂³	1	1	yes	characteristic
123	C₂²×Dic₄₇	C₂³	1	1	yes	characteristic
124	C₂²×Dic₄₇	C₂³	1	1	yes	characteristic
125	Q₈×D₄₇	—	4	4	no	—
126	#10625350	—	4	4	no	—
127	C₂×D₁₈₈	C₂³	1	2	yes	—
128	C₂×D₁₈₈	C₂³	1	1	yes	characteristic
129	C₂×D₁₈₈	C₂³	1	2	yes	—
130	C₂×C₄×D₄₇	C₂³	1	2	yes	—
131	C₂×C₄×D₄₇	C₂³	1	2	yes	—
132	C₂×C₄×D₄₇	C₂³	1	2	yes	—
133	C₂×C₄×D₄₇	C₂³	1	2	yes	—
134	C₂×C₄×D₄₇	C₂³	1	2	yes	—
135	C₂×Dic₉₄	—	4	2	no	—
136	C₂×Dic₉₄	C₂³	1	2	yes	—
137	C₂×Dic₉₄	C₂³	1	2	yes	—
138	C₂×Dic₉₄	C₂³	1	1	yes	characteristic
139	C₂×Dic₉₄	C₂³	1	2	yes	—
140	C₂×Dic₉₄	C₂³	1	2	yes	—
141	C₄⋊C₄×C₄₇	C₂³	1	2	yes	—
142	C₄⋊C₄×C₄₇	C₂³	1	2	yes	—
143	C₄⋊C₄×C₄₇	C₂³	1	1	yes	characteristic
144	C₄⋊C₄×C₄₇	C₂³	1	2	yes	—
145	C₄⋊C₄×C₄₇	C₂³	1	2	yes	—
146	C₄⋊C₄×C₄₇	C₂³	1	2	yes	—
147	C₄⋊C₄×C₄₇	C₂³	1	1	yes	characteristic
148	C₂²⋊C₄×C₄₇	C₂³	1	2	yes	—
149	C₂²⋊C₄×C₄₇	C₂³	1	2	yes	—
150	C₂²⋊C₄×C₄₇	C₂³	1	2	yes	—
151	C₂²⋊C₄×C₄₇	C₂³	1	2	yes	—
152	C₂²⋊C₄×C₄₇	C₂³	1	2	yes	—
153	C₂²⋊C₄×C₄₇	C₂³	1	2	yes	—
154	C₂²⋊Dic₄₇	C₂³	1	2	yes	—
155	C₂²⋊Dic₄₇	C₂³	1	2	yes	—
156	C₂²⋊Dic₄₇	C₂³	1	2	yes	—
157	C₂²⋊Dic₄₇	C₂³	1	2	yes	—
158	C₂²⋊Dic₄₇	C₂³	1	2	yes	—
159	(C₂×D₄₇)⋊C₄	C₂³	1	2	yes	—
160	(C₂×D₄₇)⋊C₄	C₂³	1	2	yes	—
161	(C₂×D₄₇)⋊C₄	C₂³	1	2	yes	—
162	(C₂×D₄₇)⋊C₄	C₂³	1	2	yes	—
163	(C₂×D₄₇)⋊C₄	C₂³	1	2	yes	—
164	(C₂×D₄₇)⋊C₄	C₂³	1	2	yes	—
165	(C₂×D₄₇)⋊C₄	C₂³	1	2	yes	—
166	(C₂×D₄₇)⋊C₄	C₂³	1	2	yes	—
167	(C₂×D₄₇)⋊C₄	C₂³	1	2	yes	—
168	(C₂×D₄₇)⋊C₄	C₂³	1	2	yes	—
169	(C₂×D₄₇)⋊C₄	C₂³	1	2	yes	—
170	(C₂×D₄₇)⋊C₄	C₂³	1	2	yes	—
171	(C₂×D₄₇)⋊C₄	C₂³	1	2	yes	—
172	(C₂×D₄₇)⋊C₄	C₂³	1	2	yes	—
173	C₄⋊Dic₄₇	C₂³	1	2	yes	—
174	C₄⋊Dic₄₇	C₂³	1	2	yes	—
175	C₄⋊Dic₄₇	C₂³	1	2	yes	—
176	C₄⋊Dic₄₇	C₂³	1	2	yes	—
177	C₄⋊Dic₄₇	C₂³	1	1	yes	characteristic
178	C₄⋊Dic₄₇	C₂³	1	1	yes	characteristic
179	Dic₄₇⋊C₄	C₂³	1	2	yes	—
180	Dic₄₇⋊C₄	C₂³	1	2	yes	—
181	Dic₄₇⋊C₄	C₂³	1	2	yes	—
182	Dic₄₇⋊C₄	C₂³	1	2	yes	—
183	Dic₄₇⋊C₄	C₂³	1	2	yes	—
184	Dic₄₇⋊C₄	C₂³	1	2	yes	—
185	Dic₄₇⋊C₄	C₂³	1	2	yes	—
186	Dic₄₇⋊C₄	C₂³	1	2	yes	—
187	Dic₄₇⋊C₄	C₂³	1	2	yes	—
188	Dic₄₇⋊C₄	C₂³	1	2	yes	—
189	C₄×Dic₄₇	C₂³	1	1	yes	characteristic
190	C₄×Dic₄₇	C₂³	1	1	yes	characteristic
191	C₄×Dic₄₇	C₂³	1	1	yes	characteristic
192	C₄×Dic₄₇	C₂³	1	1	yes	characteristic
193	C₄×Dic₄₇	C₂³	1	2	yes	—
194	C₄×Dic₄₇	C₂³	1	2	yes	—
195	C₄×Dic₄₇	C₂³	1	2	yes	—
196	C₄×Dic₄₇	C₂³	1	2	yes	—
197	C₄×Dic₄₇	C₂³	1	2	yes	—
198	C₂³×C₄₇	—	2	2	no	—
199	C₂³×C₄₇	—	4	1	no	—
200	C₂³×C₄₇	—	4	1	no	—
201	C₂³×C₄₇	C₂⁴	1	2	yes	—
202	C₂³×C₄₇	C₂⁴	1	1	yes	characteristic
203	C₂²×D₄₇	—	2	2	no	—
204	C₂²×D₄₇	—	4	1	no	—
205	C₂²×D₄₇	—	4	1	no	—
206	C₂²×D₄₇	C₂⁴	1	2	yes	—
207	C₂²×D₄₇	C₂⁴	1	2	yes	—
208	Q₈×C₄₇	—	4	2	no	—
209	Q₈×C₄₇	—	4	1	no	—
210	Q₈×C₄₇	—	4	1	no	—
211	C₂×C₄×C₄₇	—	4	1	no	—
212	C₂×C₄×C₄₇	—	4	2	no	—
213	C₂×C₄×C₄₇	—	4	1	no	—
214	C₂×C₄×C₄₇	—	4	2	no	—
215	C₂×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
216	C₂×C₄×C₄₇	C₂⁴	1	2	yes	—
217	C₂×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
218	C₂×C₄×C₄₇	C₂⁴	1	2	yes	—
219	C₂×C₄×C₄₇	C₂⁴	1	2	yes	—
220	C₂×C₄×C₄₇	C₂⁴	1	2	yes	—
221	C₂×C₄×C₄₇	C₂⁴	1	2	yes	—
222	C₂²⋊D₄₇	—	2	4	no	—
223	C₂²⋊D₄₇	—	2	4	no	—
224	C₂²⋊D₄₇	—	4	2	no	—
225	C₂²⋊D₄₇	—	4	2	no	—
226	C₂²⋊D₄₇	—	4	2	no	—
227	C₂×Dic₄₇	—	2	2	no	—
228	C₂×Dic₄₇	—	2	2	no	—
229	C₂×Dic₄₇	—	4	1	no	—
230	C₂×Dic₄₇	C₂⁴	1	1	yes	characteristic
231	C₂×Dic₄₇	C₂⁴	1	2	yes	—
232	C₂×Dic₄₇	C₂⁴	1	2	yes	—
233	C₂×Dic₄₇	C₂⁴	1	1	yes	characteristic
234	C₂×Dic₄₇	C₂⁴	1	1	yes	characteristic
235	C₂×Dic₄₇	C₂⁴	1	2	yes	—
236	C₂×Dic₄₇	C₂⁴	1	2	yes	—
237	C₂×Dic₄₇	C₂⁴	1	1	yes	characteristic
238	D₁₈₈	—	4	2	no	—
239	D₁₈₈	—	4	1	no	—
240	D₁₈₈	—	4	2	no	—
241	C₄×D₄₇	—	2	4	no	—
242	C₄×D₄₇	—	4	2	no	—
243	C₄×D₄₇	—	4	2	no	—
244	C₄×D₄₇	—	4	2	no	—
245	C₄×D₄₇	—	4	2	no	—
246	Dic₉₄	—	2	4	no	—
247	Dic₉₄	—	2	4	no	—
248	Dic₉₄	—	4	2	no	—
249	Dic₉₄	—	4	1	no	—
250	Dic₉₄	—	4	2	no	—
251	C₂²×C₄₇	—	2	1	no	—
252	C₂²×C₄₇	—	2	1	no	—
253	C₂²×C₄₇	—	2	2	no	—
254	C₂²×C₄₇	—	2	2	no	—
255	C₂²×C₄₇	—	2	2	no	—
256	C₂²×C₄₇	—	8	2	no	—
257	C₂²×C₄₇	2₋¹⁺⁴	1	2	yes	—
258	C₂²×C₄₇	C₂⁵	1	1	yes	characteristic
259	C₂×D₄₇	—	2	2	no	—
260	C₂×D₄₇	—	2	2	no	—
261	C₂×D₄₇	—	2	2	no	—
262	C₂×D₄₇	—	2	2	no	—
263	C₂×D₄₇	—	2	2	no	—
264	C₂×D₄₇	—	2	2	no	—
265	C₂×D₄₇	—	8	2	no	—
266	C₄×C₄₇	—	2	2	no	—
267	C₄×C₄₇	—	2	2	no	—
268	C₄×C₄₇	—	2	2	no	—
269	C₄×C₄₇	—	2	1	no	—
270	C₄×C₄₇	—	2	2	no	—
271	C₄×C₄₇	—	2	2	no	—
272	C₄×C₄₇	—	2	1	no	—
273	Dic₄₇	—	2	2	no	—
274	Dic₄₇	—	2	2	no	—
275	Dic₄₇	—	2	1	no	—
276	Dic₄₇	—	2	1	no	—
277	Dic₄₇	—	2	1	no	—
278	Dic₄₇	—	2	2	no	—
279	Dic₄₇	—	2	2	no	—
280	Dic₄₇	H(5,𝔽₂)	1	2	yes	—
281	#3561	—	47	1	no	maximal, Sylow
282	C₂×C₄₇	—	2	2	no	—
283	C₂×C₄₇	—	4	2	no	—
284	C₂×C₄₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
285	C₂×C₄₇	C₂×2₋¹⁺⁴	1	1	yes	characteristic
286	C₂×C₄₇	#585	1	1	yes	characteristic
287	D₄₇	—	4	2	no	—
288	D₄₇	—	4	2	no	—
289	#563	—	47	2	no	—
290	#562	—	47	2	no	—
291	#556	—	47	2	no	—
292	#551	—	47	2	no	—
293	#551	—	47	2	no	—
294	D₄×Q₈	—	47	2	no	—
295	#548	—	47	2	no	—
296	#546	—	47	2	no	—
297	#543	—	47	1	no	—
298	#543	D₄₇	1	1	yes	characteristic, complemented
299	#542	—	47	2	no	—
300	#542	—	47	2	no	—
301	#542	—	47	2	no	—
302	#538	—	47	1	no	—
303	#538	—	47	1	no	—
304	#536	—	47	2	no	—
305	#533	—	47	1	no	—
306	#529	—	47	1	no	—
307	C₂×#124	—	47	1	no	—
308	C₄₇	#3561	1	1	yes	characteristic, complemented, Sylow
309	C₂×#41	—	47	2	no	—
310	C₂²×Q₈	—	47	2	no	—
311	C₂²×Q₈	—	47	1	no	—
312	C₂²×D₄	—	47	1	no	—
313	C₄⋊Q₈	—	47	1	no	—
314	C₄⋊Q₈	—	47	2	no	—
315	C₄⋊Q₈	—	47	1	no	—
316	C₄⋊Q₈	—	47	2	no	—
317	C₄⋊Q₈	—	47	2	no	—
318	#126	—	47	2	no	—
319	#126	—	47	2	no	—
320	#126	—	47	2	no	—
321	#126	—	47	2	no	—
322	#126	—	47	2	no	—
323	#126	—	47	2	no	—
324	#126	—	47	2	no	—
325	#125	—	47	1	no	—
326	#125	—	47	2	no	—
327	#124	—	47	1	no	—
328	#124	—	47	2	no	—
329	#124	—	47	2	no	—
330	#124	—	47	2	no	—
331	#124	—	47	2	no	—
332	#124	—	47	2	no	—
333	#124	—	47	2	no	—
334	#124	—	47	2	no	—
335	#124	—	47	2	no	—
336	#124	—	47	2	no	—
337	#123	—	47	2	no	—
338	#123	—	47	2	no	—
339	#123	—	47	2	no	—
340	#123	—	47	2	no	—
341	#123	—	47	2	no	—
342	#123	—	47	2	no	—
343	#123	—	47	2	no	—
344	#123	—	47	2	no	—
345	#123	—	47	2	no	—
346	C₂²⋊Q₈	—	47	2	no	—
347	C₂²⋊Q₈	—	47	2	no	—
348	C₂²⋊Q₈	—	47	1	no	—
349	C₂²⋊Q₈	—	47	2	no	—
350	C₂²⋊Q₈	—	47	2	no	—
351	C₂²⋊Q₈	—	47	2	no	—
352	C₂²⋊Q₈	—	47	2	no	—
353	C₂²⋊Q₈	—	47	2	no	—
354	C₂²⋊Q₈	—	47	2	no	—
355	C₂²⋊Q₈	—	47	2	no	—
356	C₂²⋊Q₈	—	47	2	no	—
357	C₂²⋊Q₈	—	47	2	no	—
358	C₂²⋊Q₈	C₂×D₄₇	1	1	yes	characteristic
359	C₂²⋊Q₈	C₂×D₄₇	1	1	yes	characteristic
360	C₂²⋊Q₈	C₂×D₄₇	1	2	yes	—
361	C₂²⋊Q₈	C₂×D₄₇	1	2	yes	complemented
362	C₂²⋊Q₈	C₂×D₄₇	1	2	yes	complemented
363	C₂²⋊Q₈	C₂×D₄₇	1	2	yes	complemented
364	C₂²⋊Q₈	C₂×D₄₇	1	2	yes	complemented
365	#121	—	47	1	no	—
366	#121	—	47	2	no	—
367	#121	—	47	2	no	—
368	#121	—	47	2	no	—
369	#121	—	47	2	no	—
370	#121	—	47	2	no	—
371	#120	—	47	2	no	—
372	#120	—	47	2	no	—
373	C₄×Q₈	—	47	1	no	—
374	C₄×Q₈	—	47	1	no	—
375	C₄×Q₈	—	47	1	no	—
376	C₄×Q₈	—	47	2	no	—
377	C₄×Q₈	—	47	2	no	—
378	C₄×D₄	—	47	2	no	—
379	C₄×D₄	—	47	2	no	—
380	C₄×D₄	—	47	2	no	—
381	C₄×D₄	—	47	1	no	—
382	C₄×D₄	—	47	2	no	—
383	C₄×D₄	—	47	2	no	—
384	C₄×D₄	—	47	2	no	—
385	#117	—	47	2	no	—
386	#117	—	47	2	no	—
387	#117	—	47	2	no	—
388	#117	—	47	2	no	—
389	C₂×C₂²⋊C₄	—	47	1	no	—
390	C₂×C₂²⋊C₄	—	47	1	no	—
391	C₂×C₂²⋊C₄	—	47	1	no	—
392	C₂×C₂²⋊C₄	—	47	2	no	—
393	C₂×C₂²⋊C₄	C₂×D₄₇	1	1	yes	characteristic
394	C₂×C₂²⋊C₄	C₂×D₄₇	1	2	yes	—
395	C₂×C₄²	—	47	1	no	—
396	C₂⁴	—	47	1	no	—
397	C₂⁴	C₂²×D₄₇	1	1	yes	characteristic
398	#41	—	188	4	no	—
399	C₂×Q₈	—	47	2	no	—
400	C₂×Q₈	—	47	2	no	—
401	C₂×Q₈	—	47	1	no	—
402	C₂×Q₈	—	47	2	no	—
403	C₂×Q₈	—	47	2	no	—
404	C₂×Q₈	—	188	2	no	—
405	C₂×Q₈	—	188	4	no	—
406	C₂×Q₈	C₂²×D₄₇	1	1	yes	characteristic
407	C₂×Q₈	C₂²×D₄₇	1	1	yes	characteristic
408	C₂×Q₈	C₂²×D₄₇	1	2	yes	—
409	C₂×D₄	—	47	2	no	—
410	C₂×D₄	—	47	2	no	—
411	C₂×D₄	—	47	2	no	—
412	C₂×D₄	—	47	2	no	—
413	C₂×D₄	—	47	2	no	—
414	C₂×D₄	—	47	2	no	—
415	C₂×D₄	—	47	1	no	—
416	C₂×D₄	—	47	2	no	—
417	C₂×D₄	—	188	2	no	—
418	C₂²×C₄	—	47	1	no	—
419	C₂²×C₄	—	47	1	no	—
420	C₂²×C₄	—	47	1	no	—
421	C₂²×C₄	—	47	2	no	—
422	C₂²×C₄	—	47	2	no	—
423	C₂²×C₄	—	47	2	no	—
424	C₂²×C₄	—	47	2	no	—
425	C₂²×C₄	—	47	2	no	—
426	C₂²×C₄	C₂²×D₄₇	1	1	yes	characteristic
427	C₂²×C₄	C₂²×D₄₇	1	1	yes	characteristic
428	C₂²×C₄	C₂²×D₄₇	1	2	yes	—
429	C₂²×C₄	C₂²×D₄₇	1	2	yes	—
430	C₄⋊C₄	—	47	2	no	—
431	C₄⋊C₄	—	47	2	no	—
432	C₄⋊C₄	—	47	2	no	—
433	C₄⋊C₄	—	47	2	no	—
434	C₄⋊C₄	—	47	2	no	—
435	C₄⋊C₄	—	47	2	no	—
436	C₄⋊C₄	—	47	2	no	—
437	C₄⋊C₄	—	47	2	no	—
438	C₄⋊C₄	—	47	2	no	—
439	C₄⋊C₄	—	47	2	no	—
440	C₄⋊C₄	—	47	2	no	—
441	C₄⋊C₄	—	47	2	no	—
442	C₄⋊C₄	—	47	2	no	—
443	C₄⋊C₄	—	47	2	no	—
444	C₄⋊C₄	—	47	1	no	—
445	C₄⋊C₄	—	47	1	no	—
446	C₄⋊C₄	C₂²×D₄₇	1	2	yes	—
447	C₄⋊C₄	C₂²×D₄₇	1	2	yes	—
448	C₄⋊C₄	C₂²×D₄₇	1	1	yes	characteristic
449	C₄⋊C₄	C₂²×D₄₇	1	2	yes	—
450	C₄⋊C₄	C₂²×D₄₇	1	2	yes	—
451	C₄⋊C₄	C₂²×D₄₇	1	2	yes	—
452	C₄⋊C₄	C₂²×D₄₇	1	1	yes	characteristic
453	C₂²⋊C₄	—	47	2	no	—
454	C₂²⋊C₄	—	47	2	no	—
455	C₂²⋊C₄	—	47	2	no	—
456	C₂²⋊C₄	—	47	2	no	—
457	C₂²⋊C₄	—	47	2	no	—
458	C₂²⋊C₄	—	47	2	no	—
459	C₂²⋊C₄	—	47	2	no	—
460	C₂²⋊C₄	—	47	2	no	—
461	C₂²⋊C₄	—	47	2	no	—
462	C₂²⋊C₄	—	47	2	no	—
463	C₂²⋊C₄	—	47	2	no	—
464	C₂²⋊C₄	—	47	2	no	—
465	C₂²⋊C₄	—	47	2	no	—
466	C₂²⋊C₄	—	47	2	no	—
467	C₂²⋊C₄	—	47	2	no	—
468	C₂²⋊C₄	—	47	2	no	—
469	C₂²⋊C₄	—	47	2	no	—
470	C₂²⋊C₄	—	47	2	no	—
471	C₂²⋊C₄	—	47	2	no	—
472	C₂²⋊C₄	C₂²×D₄₇	1	2	yes	—
473	C₂²⋊C₄	C₂²×D₄₇	1	2	yes	—
474	C₂²⋊C₄	C₂²×D₄₇	1	2	yes	—
475	C₂²⋊C₄	C₂²×D₄₇	1	2	yes	—
476	C₂²⋊C₄	C₂²×D₄₇	1	2	yes	—
477	C₂²⋊C₄	C₂²×D₄₇	1	2	yes	—
478	C₄²	—	47	1	no	—
479	C₄²	—	47	1	no	—
480	C₄²	—	47	1	no	—
481	C₄²	—	47	1	no	—
482	C₄²	—	47	2	no	—
483	C₄²	—	47	2	no	—
484	C₄²	—	47	2	no	—
485	C₄²	—	47	2	no	—
486	C₄²	—	47	2	no	—
487	C₂³	—	2	2	no	—
488	C₂³	—	4	1	no	—
489	C₂³	—	4	1	no	—
490	C₂³	—	47	2	no	—
491	C₂³	—	47	2	no	—
492	C₂³	—	94	2	no	—
493	C₂³	—	188	1	no	—
494	C₂³	—	188	1	no	—
495	C₂³	C₂³×D₄₇	1	2	yes	—
496	C₂³	C₂³×D₄₇	1	1	yes	characteristic
497	Q₈	—	4	2	no	—
498	Q₈	—	4	1	no	—
499	Q₈	—	4	1	no	—
500	Q₈	—	94	4	no	—
501	Q₈	—	94	4	no	—
502	Q₈	—	188	1	no	—
503	Q₈	—	188	2	no	—
504	Q₈	—	188	2	no	—
505	D₄	—	94	4	no	—
506	D₄	—	94	4	no	—
507	D₄	—	188	2	no	—
508	D₄	—	188	1	no	—
509	D₄	—	188	2	no	—
510	D₄	—	188	2	no	—
511	D₄	—	188	2	no	—
512	D₄	—	188	2	no	—
513	C₂×C₄	—	4	2	no	—
514	C₂×C₄	—	4	1	no	—
515	C₂×C₄	—	4	1	no	—
516	C₂×C₄	—	4	2	no	—
517	C₂×C₄	—	47	1	no	—
518	C₂×C₄	—	47	1	no	—
519	C₂×C₄	—	47	2	no	—
520	C₂×C₄	—	47	1	no	—
521	C₂×C₄	—	47	2	no	—
522	C₂×C₄	—	47	1	no	—
523	C₂×C₄	—	47	2	no	—
524	C₂×C₄	—	47	2	no	—
525	C₂×C₄	—	94	4	no	—
526	C₂×C₄	—	94	2	no	—
527	C₂×C₄	—	94	2	no	—
528	C₂×C₄	—	188	2	no	—
529	C₂×C₄	—	188	2	no	—
530	C₂×C₄	—	188	2	no	—
531	C₂×C₄	—	188	2	no	—
532	C₂×C₄	—	188	1	no	—
533	C₂×C₄	C₂³×D₄₇	1	1	yes	characteristic
534	C₂×C₄	C₂³×D₄₇	1	1	yes	characteristic
535	C₂×C₄	C₂³×D₄₇	1	2	yes	—
536	C₂×C₄	C₂³×D₄₇	1	2	yes	—
537	C₂×C₄	C₂³×D₄₇	1	2	yes	—
538	C₂×C₄	C₂³×D₄₇	1	2	yes	—
539	C₂×C₄	C₂³×D₄₇	1	2	yes	—
540	C₂²	—	2	1	no	—
541	C₂²	—	2	1	no	—
542	C₂²	—	2	2	no	—
543	C₂²	—	2	2	no	—
544	C₂²	—	2	2	no	—
545	C₂²	—	8	2	no	—
546	C₂²	—	94	2	no	—
547	C₂²	—	94	2	no	—
548	C₂²	—	94	2	no	—
549	C₂²	—	94	2	no	—
550	C₂²	—	94	2	no	—
551	C₂²	—	94	2	no	—
552	C₂²	—	376	2	no	—
553	C₂²	#13094072	1	2	yes	—
554	C₂²	C₂⁴×D₄₇	1	1	yes	characteristic
555	C₄	—	2	2	no	—
556	C₄	—	2	2	no	—
557	C₄	—	2	2	no	—
558	C₄	—	2	2	no	—
559	C₄	—	2	2	no	—
560	C₄	—	2	1	no	—
561	C₄	—	2	1	no	—
562	C₄	—	47	2	no	—
563	C₄	—	94	1	no	—
564	C₄	—	94	2	no	—
565	C₄	—	94	2	no	—
566	C₄	—	94	1	no	—
567	C₄	—	94	1	no	—
568	C₄	—	94	2	no	—
569	C₄	—	94	2	no	—
570	C₂	—	2	2	no	—
571	C₂	—	4	2	no	—
572	C₂	—	188	2	no	—
573	C₂	—	188	2	no	—
574	C₂	H(5,𝔽₂)×D₄₇	1	1	yes	characteristic
575	C₂	C₂×#13094072	1	1	yes	characteristic
576	C₂	#15689958	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₄₇
commutator, socle	C₂²×C₄₇	C₂⁵
Fitting	C₄₇×#543	C₂
hypercenter	#543	D₄₇
hypocenter	C₄₇	#3561
LCS	G ▷ C₂²×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂² ◁ #543

Complements

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

N	H ≅ G/N	type
1. #15689874	C₂	semidirect
2. #15689869	C₂	semidirect
3. #15689844	C₂	semidirect
4. #15689800	C₂	semidirect
5. #15689799	C₂	semidirect
6. #15689786	C₂	semidirect
7. #15689783	C₂	semidirect
8. #15689763	C₂	semidirect
9. #15689748	C₂	semidirect
10. #15689746	C₂	semidirect
11. #15689743	C₂	semidirect
12. #15689743	C₂	semidirect
13. #15689713	C₂	semidirect
14. #15689711	C₂	semidirect
15. #15689696	C₂	semidirect
16. #15689675	C₂	semidirect
17. #15689659	C₂	semidirect
18. C₂×#13094010	C₂	semidirect
19. C₄₇×#543	C₂	semidirect
22. C₂×Q₈×D₄₇	C₂²	semidirect
24. #13094023	C₂²	semidirect
25. #13094023	C₂²	semidirect
26. #13094023	C₂²	semidirect
27. #13094022	C₂²	semidirect
28. #13094022	C₂²	semidirect
29. #13094019	C₂²	semidirect
30. #13094019	C₂²	semidirect
31. #13094019	C₂²	semidirect
32. #13094019	C₂²	semidirect
33. #13094017	C₂²	semidirect
34. #13094017	C₂²	semidirect
35. #13094017	C₂²	semidirect
36. #13094015	C₂²	semidirect
37. #13094014	C₂²	semidirect
38. #13094013	C₂²	semidirect
39. #13094013	C₂²	semidirect
40. #13094013	C₂²	semidirect
46. #13094010	C₂²	semidirect
47. #13094010	C₂²	semidirect
48. #13094009	C₂²	semidirect
49. #13094009	C₂²	semidirect
50. #13094009	C₂²	semidirect
53. #13094007	C₂²	semidirect
55. #13094006	C₂²	semidirect
56. #13094006	C₂²	semidirect
57. #13094004	C₂²	semidirect
58. #13094004	C₂²	semidirect
60. #13094003	C₂²	semidirect
61. #13094002	C₂²	semidirect
62. #13094002	C₂²	semidirect
63. #13094002	C₂²	semidirect
64. #13094002	C₂²	semidirect
67. #13094000	C₂²	semidirect
68. #13094000	C₂²	semidirect
69. #13093999	C₂²	semidirect
74. #13093997	C₂²	semidirect
77. Q₈×Dic₄₇	C₂²	semidirect
78. Q₈×Dic₄₇	C₂²	semidirect
79. #13093989	C₂²	semidirect
80. #13093989	C₂²	semidirect
81. #13093989	C₂²	semidirect
82. #13093986	C₂²	semidirect
83. #13093986	C₂²	semidirect
86. C₄×C₂²⋊D₄₇	C₂²	semidirect
89. #13093983	C₂²	semidirect
90. #13093982	C₂²	semidirect
91. #13093982	C₂²	semidirect
101. C₂²⋊Q₈×C₄₇	C₂²	semidirect
102. C₂²⋊Q₈×C₄₇	C₂²	semidirect
103. C₂²⋊Q₈×C₄₇	C₂²	semidirect
104. C₂²⋊Q₈×C₄₇	C₂²	semidirect
298. #543	D₄₇	semidirect
308. C₄₇	#3561	semidirect
361. C₂²⋊Q₈	C₂×D₄₇	semidirect
362. C₂²⋊Q₈	C₂×D₄₇	semidirect
363. C₂²⋊Q₈	C₂×D₄₇	semidirect
364. C₂²⋊Q₈	C₂×D₄₇	semidirect