Subgroups — #27095046

Order 12032.

1842 conjugacy classes of subgroups.

The subgroup lattice has 678 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20256952	C₂	1	2	yes	maximal, complemented
2	#20256016	C₂	1	2	yes	maximal, complemented
3	#20256005	C₂	1	2	yes	maximal, complemented
4	#20255995	C₂	1	2	yes	maximal, complemented
5	#20255985	C₂	1	2	yes	maximal, complemented
6	#20255974	C₂	1	2	yes	maximal, complemented
7	#20255964	C₂	1	2	yes	maximal, complemented
8	#20255953	C₂	1	4	yes	maximal, complemented
9	#20253902	C₂	1	1	yes	maximal, characteristic, complemented
10	#20253299	C₂	1	4	yes	maximal, complemented
11	#20253176	C₂	1	2	yes	maximal, complemented
12	#20252993	C₂	1	2	yes	maximal, complemented
13	C₂×#15689202	C₂	1	1	yes	maximal, characteristic, complemented
14	#20251976	C₂	1	2	yes	maximal, complemented
15	C₄×#135×C₄₇	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×#10625324	C₂²	1	2	yes	—
17	#15689846	C₂²	1	2	yes	—
18	#15689838	C₂²	1	2	yes	—
19	#15689833	C₂²	1	2	yes	—
20	#15689823	C₂²	1	4	yes	—
21	#15689814	C₂²	1	4	yes	—
22	#15689813	—	2	2	no	—
23	#15689802	—	2	4	no	—
24	#15689778	C₂²	1	2	yes	—
25	#15689769	—	2	2	no	—
26	#15689680	C₂²	1	2	yes	—
27	#15689657	—	2	2	no	—
28	#15689651	—	2	4	no	—
29	#15689630	C₂²	1	4	yes	—
30	C₄×#10625350	—	2	2	no	—
31	C₂×C₄×D₁₈₈	C₂²	1	1	yes	characteristic
32	#117×D₄₇	C₂²	1	4	yes	—
33	#15689528	C₂²	1	1	yes	characteristic, complemented
34	#15689528	C₂²	1	1	yes	characteristic, complemented
35	#15689525	C₂²	1	2	yes	complemented
36	#15689525	C₂²	1	2	yes	complemented
37	#15689521	C₂²	1	2	yes	complemented
38	#15689463	C₂²	1	4	yes	complemented
39	#15689462	C₂²	1	4	yes	complemented
40	#15689457	C₂²	1	4	yes	complemented
41	#15689452	C₂²	1	4	yes	complemented
42	#15689446	C₂²	1	4	yes	complemented
43	#15689445	C₂²	1	4	yes	complemented
44	#15689440	C₂²	1	4	yes	complemented
45	#15689435	C₂²	1	4	yes	complemented
46	#15689430	C₂²	1	4	yes	complemented
47	#15689423	C₂²	1	4	yes	complemented
48	#15689418	C₂²	1	2	yes	complemented
49	#15689413	C₂²	1	2	yes	complemented
50	#15689408	C₂²	1	2	yes	complemented
51	#15689403	C₂²	1	2	yes	complemented
52	#15689378	C₂²	1	4	yes	complemented
53	#15689373	C₂²	1	4	yes	complemented
54	#15689366	C₂²	1	4	yes	complemented
55	#15689366	C₂²	1	4	yes	complemented
56	#15689202	C₂²	1	2	yes	—
57	#15689202	C₂²	1	2	yes	—
58	#15689202	C₂²	1	2	yes	—
59	#15689202	C₂²	1	2	yes	—
60	#15689164	C₂²	1	4	yes	complemented
61	#15689164	C₂²	1	4	yes	complemented
62	#15689162	C₂²	1	4	yes	complemented
63	#15689162	C₂²	1	4	yes	complemented
64	#15689161	C₂²	1	2	yes	—
65	#15689161	C₂²	1	2	yes	—
66	#15689159	C₂²	1	4	yes	—
67	C₂×C₄⋊(C₄₇⋊C₈)	C₂²	1	1	yes	characteristic
68	#15689119	C₂²	1	4	yes	—
69	C₂×(C₂×D₄₇)⋊C₈	C₂²	1	2	yes	—
70	C₂×#135×C₄₇	C₂²	1	1	yes	characteristic
71	C₄×#41×C₄₇	C₂²	1	2	yes	—
72	C₄×Q₁₆×C₄₇	C₂²	1	1	yes	characteristic, complemented
73	C₄×Q₁₆×C₄₇	C₂²	1	1	yes	characteristic, complemented
74	C₄×SD₁₆×C₄₇	C₂²	1	2	yes	complemented
75	C₄×SD₁₆×C₄₇	C₂²	1	2	yes	complemented
76	C₄×D₈×C₄₇	C₂²	1	1	yes	characteristic, complemented
77	C₄×D₈×C₄₇	C₂²	1	1	yes	characteristic, complemented
78	C₄₇×#427	C₂²	1	1	yes	characteristic
79	C₄₇×#416	C₂²	1	2	yes	—
80	C₂×C₄×C₈×C₄₇	C₂²	1	1	yes	characteristic
81	C₂×#10625350	—	2	2	no	—
82	C₂²×D₁₈₈	D₄	1	1	yes	characteristic
83	C₂²×C₄×D₄₇	C₂³	1	2	yes	—
84	C₂×#10625324	—	2	8	no	—
85	C₂×#10625324	C₂³	1	4	yes	—
86	C₂×#10625324	C₂³	1	4	yes	—
87	C₂²×C₄₇⋊C₈	C₂³	1	2	yes	—
88	#13094024	C₂³	1	2	yes	—
89	#13094024	C₂³	1	2	yes	—
90	#13094019	—	2	4	no	—
91	#13094018	—	2	4	no	—
92	#13094017	—	2	4	no	—
93	#13094016	—	2	2	no	—
94	#13094016	C₂³	1	4	yes	—
95	#13094014	—	2	4	no	—
96	#13094012	—	2	2	no	—
97	#13094010	—	2	4	no	—
98	#13094009	—	2	4	no	—
99	#13094007	—	2	4	no	—
100	#13094006	—	2	4	no	—
101	#13094005	—	2	4	no	—
102	#13094003	—	2	2	no	—
103	#13094003	—	2	2	no	—
104	#13094003	—	2	2	no	—
105	#13094002	—	2	4	no	—
106	#13094000	C₂³	1	4	yes	—
107	#13094000	C₂³	1	4	yes	—
108	#13093998	—	2	2	no	—
109	#13093997	—	2	4	no	—
110	#13093995	C₂³	1	4	yes	—
111	#13093995	C₂³	1	4	yes	—
112	#13093992	—	2	4	no	—
113	C₄×Dic₉₄	—	2	2	no	—
114	C₄×Dic₉₄	—	2	2	no	—
115	C₄×Dic₉₄	—	2	2	no	—
116	C₄×D₁₈₈	—	2	2	no	—
117	C₄×D₁₈₈	D₄	1	2	yes	—
118	C₄×D₁₈₈	D₄	1	2	yes	—
119	C₄×D₁₈₈	C₂³	1	2	yes	—
120	C₄×D₁₈₈	C₂³	1	2	yes	—
121	C₄×C₂²⋊D₄₇	—	2	4	no	—
122	C₄×C₂²⋊D₄₇	—	2	4	no	—
123	C₄×C₂²⋊D₄₇	—	2	4	no	—
124	#13093983	—	2	2	no	—
125	#13093983	C₂³	1	4	yes	—
126	#13093982	C₂³	1	4	yes	—
127	#13093982	C₂³	1	4	yes	—
128	#13093981	—	2	4	no	—
129	#13093981	—	2	4	no	—
130	#13093980	—	2	4	no	—
131	C₂×C₄⋊Dic₄₇	D₄	1	1	yes	characteristic
132	C₄⋊C₄×D₄₇	C₂³	1	4	yes	—
133	C₄⋊C₄×D₄₇	C₂³	1	4	yes	—
134	C₂×(C₂×D₄₇)⋊C₄	D₄	1	2	yes	—
135	C₂²⋊C₄×D₄₇	—	2	4	no	—
136	C₄²×D₄₇	—	2	4	no	—
137	#13093958	C₂³	1	2	yes	—
138	#13093958	C₂³	1	2	yes	—
139	#13093958	C₂³	1	2	yes	—
140	#13093958	C₂³	1	2	yes	—
141	#13093957	C₂³	1	4	yes	—
142	#13093957	C₂³	1	4	yes	—
143	#13093956	C₂³	1	4	yes	—
144	#13093956	C₂³	1	4	yes	—
145	#13093955	C₂³	1	4	yes	—
146	#13093955	C₂³	1	4	yes	—
147	C₄⋊(C₄₇⋊C₈)	C₂³	1	2	yes	—
148	C₄⋊(C₄₇⋊C₈)	C₂³	1	2	yes	—
149	#13093948	C₂³	1	4	yes	—
150	#13093948	C₂³	1	4	yes	—
151	#13093945	C₂³	1	4	yes	—
152	#13093945	C₂³	1	4	yes	—
153	(C₂×D₄₇)⋊C₈	C₂³	1	4	yes	—
154	(C₂×D₄₇)⋊C₈	C₂³	1	4	yes	—
155	C₂×#41×C₄₇	C₂³	1	2	yes	—
156	#135×C₄₇	—	2	4	no	—
157	C₂×Q₁₆×C₄₇	C₂³	1	1	yes	characteristic
158	C₂×SD₁₆×C₄₇	C₂³	1	2	yes	—
159	C₂×D₈×C₄₇	C₂³	1	1	yes	characteristic
160	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
161	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
162	C₄×Q₈×C₄₇	C₂³	1	2	yes	—
163	C₄×Q₈×C₄₇	C₂³	1	2	yes	—
164	C₄×D₄×C₄₇	—	2	2	no	—
165	C₄×D₄×C₄₇	—	2	2	no	—
166	C₄×D₄×C₄₇	C₂³	1	2	yes	—
167	C₄×D₄×C₄₇	C₂³	1	2	yes	—
168	#117×C₄₇	—	2	2	no	—
169	#117×C₄₇	C₂³	1	2	yes	—
170	C₂×C₄²×C₄₇	—	2	2	no	—
171	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
172	#107×C₄₇	C₂³	1	1	yes	characteristic
173	#107×C₄₇	C₂³	1	1	yes	characteristic
174	#106×C₄₇	C₂³	1	2	yes	—
175	#103×C₄₇	C₂³	1	2	yes	—
176	#103×C₄₇	C₂³	1	2	yes	—
177	#102×C₄₇	C₂³	1	2	yes	—
178	#102×C₄₇	C₂³	1	2	yes	—
179	C₄×C₈×C₄₇	C₂³	1	1	yes	characteristic
180	C₄×C₈×C₄₇	C₂³	1	1	yes	characteristic
181	C₄×C₈×C₄₇	C₂³	1	1	yes	characteristic
182	C₄×C₈×C₄₇	C₂³	1	1	yes	characteristic
183	C₂³×D₄₇	C₂×D₄	1	2	yes	—
184	#41×C₄₇	—	2	4	no	—
185	#41×C₄₇	—	2	4	no	—
186	C₂×Q₈×C₄₇	C₂⁴	1	2	yes	—
187	C₂×D₄×C₄₇	—	2	2	no	—
188	C₂×D₄×C₄₇	C₂⁴	1	2	yes	—
189	C₂²×C₄×C₄₇	—	2	2	no	—
190	C₂²×C₄×C₄₇	—	2	2	no	—
191	C₂²×C₄×C₄₇	—	2	2	no	—
192	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
193	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
194	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
195	C₂×C₂²⋊D₄₇	—	2	4	no	—
196	C₂×C₂²⋊D₄₇	—	2	4	no	—
197	C₂²×Dic₄₇	C₂×D₄	1	2	yes	—
198	#10625350	—	4	8	no	—
199	C₂×D₁₈₈	—	4	2	no	—
200	C₂×D₁₈₈	C₂×D₄	1	2	yes	—
201	C₂×D₁₈₈	C₂×D₄	1	2	yes	—
202	C₂×C₄×D₄₇	—	2	4	no	—
203	C₂×C₄×D₄₇	—	2	4	no	—
204	C₂×C₄×D₄₇	—	2	4	no	—
205	C₂×C₄×D₄₇	—	2	4	no	—
206	C₂×C₄×D₄₇	C₂×D₄	1	4	yes	—
207	C₂×C₄×D₄₇	C₂⁴	1	4	yes	—
208	C₂×Dic₉₄	—	2	2	no	—
209	C₂×Dic₉₄	—	2	2	no	—
210	Q₁₆×C₄₇	—	2	2	no	—
211	SD₁₆×C₄₇	—	2	4	no	—
212	D₈×C₄₇	—	2	2	no	—
213	C₂×C₈×C₄₇	—	2	2	no	—
214	C₂×C₈×C₄₇	#41	1	4	yes	complemented
215	C₂×C₈×C₄₇	C₂⁴	1	1	yes	characteristic
216	C₂×C₈×C₄₇	C₂⁴	1	1	yes	characteristic
217	C₂×C₈×C₄₇	C₂⁴	1	1	yes	characteristic
218	C₂×C₈×C₄₇	C₂⁴	1	1	yes	characteristic
219	C₄⋊C₄×C₄₇	—	2	2	no	—
220	C₄⋊C₄×C₄₇	—	2	2	no	—
221	C₄⋊C₄×C₄₇	C₂⁴	1	2	yes	—
222	C₄⋊C₄×C₄₇	C₂⁴	1	2	yes	—
223	C₂²⋊C₄×C₄₇	—	2	2	no	—
224	C₂²⋊C₄×C₄₇	—	2	2	no	—
225	C₂²⋊C₄×C₄₇	—	2	2	no	—
226	C₄²×C₄₇	—	2	2	no	—
227	C₄²×C₄₇	—	2	2	no	—
228	C₄²×C₄₇	—	2	2	no	—
229	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
230	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
231	C₄²×C₄₇	C₂⁴	1	1	yes	characteristic
232	C₄²×C₄₇	C₂⁴	1	1	yes	characteristic
233	C₂²⋊Dic₄₇	—	2	4	no	—
234	C₂²⋊Dic₄₇	—	2	4	no	—
235	C₂²⋊Dic₄₇	—	2	4	no	—
236	(C₂×D₄₇)⋊C₄	—	2	4	no	—
237	(C₂×D₄₇)⋊C₄	—	2	4	no	—
238	(C₂×D₄₇)⋊C₄	—	2	4	no	—
239	(C₂×D₄₇)⋊C₄	—	2	4	no	—
240	(C₂×D₄₇)⋊C₄	C₂×D₄	1	4	yes	—
241	(C₂×D₄₇)⋊C₄	C₂×D₄	1	4	yes	—
242	C₄⋊Dic₄₇	—	2	2	no	—
243	C₄⋊Dic₄₇	—	2	2	no	—
244	C₄⋊Dic₄₇	C₂×D₄	1	2	yes	—
245	C₄⋊Dic₄₇	C₂×D₄	1	2	yes	—
246	C₄⋊Dic₄₇	C₂⁴	1	4	yes	—
247	C₄⋊Dic₄₇	C₂⁴	1	4	yes	—
248	Dic₄₇⋊C₄	—	2	4	no	—
249	Dic₄₇⋊C₄	—	2	4	no	—
250	Dic₄₇⋊C₄	—	2	4	no	—
251	Dic₄₇⋊C₄	—	2	4	no	—
252	Dic₄₇⋊C₄	—	2	4	no	—
253	Dic₄₇⋊C₄	—	2	4	no	—
254	C₄×Dic₄₇	—	2	4	no	—
255	C₄×Dic₄₇	—	2	4	no	—
256	C₄×Dic₄₇	—	2	4	no	—
257	C₂×C₄₇⋊C₈	—	2	4	no	—
258	C₂×C₄₇⋊C₈	C₂⁴	1	4	yes	—
259	#10625324	—	2	8	no	—
260	#10625324	—	2	8	no	—
261	C₂³×C₄₇	—	2	2	no	—
262	C₂³×C₄₇	C₂²×D₄	1	1	yes	characteristic
263	C₂²×D₄₇	—	2	4	no	—
264	C₂²×D₄₇	—	4	2	no	—
265	C₂²×D₄₇	—	4	2	no	—
266	C₂²×D₄₇	C₂²×D₄	1	4	yes	—
267	Q₈×C₄₇	—	2	2	no	—
268	Q₈×C₄₇	—	2	2	no	—
269	D₄×C₄₇	—	2	2	no	—
270	D₄×C₄₇	—	2	2	no	—
271	D₄×C₄₇	—	4	4	no	—
272	C₂×C₄×C₄₇	—	2	2	no	—
273	C₂×C₄×C₄₇	—	2	2	no	—
274	C₂×C₄×C₄₇	—	2	2	no	—
275	C₂×C₄×C₄₇	—	2	2	no	—
276	C₂×C₄×C₄₇	—	4	1	no	—
277	C₂×C₄×C₄₇	—	4	4	no	—
278	C₂×C₄×C₄₇	—	4	4	no	—
279	C₂×C₄×C₄₇	—	8	2	no	—
280	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
281	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
282	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
283	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
284	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
285	C₂×C₄×C₄₇	C₂×#41	1	2	yes	—
286	C₂×C₄×C₄₇	2₋¹⁺⁴	1	2	yes	—
287	C₂×C₄×C₄₇	C₂⁵	1	1	yes	characteristic
288	C₂²⋊D₄₇	—	4	8	no	—
289	C₂²⋊D₄₇	—	8	4	no	—
290	C₂×Dic₄₇	—	2	4	no	—
291	C₂×Dic₄₇	—	2	4	no	—
292	C₂×Dic₄₇	—	2	4	no	—
293	C₂×Dic₄₇	C₂²×D₄	1	4	yes	—
294	D₁₈₈	—	2	4	no	—
295	D₁₈₈	—	4	2	no	—
296	C₄×D₄₇	—	2	8	no	—
297	C₄×D₄₇	—	2	4	no	—
298	C₄×D₄₇	—	2	4	no	—
299	C₄×D₄₇	—	4	8	no	—
300	C₄×D₄₇	—	8	4	no	—
301	Dic₉₄	—	4	4	no	—
302	Dic₉₄	—	8	2	no	—
303	C₈×C₄₇	—	2	1	no	—
304	C₈×C₄₇	—	2	1	no	—
305	C₈×C₄₇	C₂×#41	1	2	yes	—
306	C₈×C₄₇	C₂×#41	1	2	yes	—
307	C₄₇⋊C₈	—	2	4	no	—
308	#61251	—	47	1	no	maximal, Sylow
309	C₂²×C₄₇	—	2	1	no	—
310	C₂²×C₄₇	—	2	1	no	—
311	C₂²×C₄₇	—	4	2	no	—
312	C₂²×C₄₇	—	4	2	no	—
313	C₂²×C₄₇	—	4	2	no	—
314	C₂²×C₄₇	#547	1	2	yes	—
315	C₂²×C₄₇	C₂³×D₄	1	1	yes	characteristic
316	C₂×D₄₇	—	2	4	no	—
317	C₂×D₄₇	—	2	4	no	—
318	C₂×D₄₇	—	2	4	no	—
319	C₂×D₄₇	—	8	4	no	—
320	C₄×C₄₇	—	2	1	no	—
321	C₄×C₄₇	—	2	1	no	—
322	C₄×C₄₇	—	2	1	no	—
323	C₄×C₄₇	—	4	2	no	—
324	C₄×C₄₇	—	4	2	no	—
325	C₄×C₄₇	—	4	2	no	—
326	C₄×C₄₇	#547	1	2	yes	—
327	C₄×C₄₇	#575	1	2	yes	—
328	C₄×C₄₇	C₂²×#41	1	1	yes	characteristic
329	C₄×C₄₇	C₂×2₋¹⁺⁴	1	1	yes	characteristic
330	Dic₄₇	—	2	4	no	—
331	Dic₄₇	—	4	4	no	—
332	Dic₄₇	—	4	4	no	—
333	#3475	—	47	2	no	—
334	#3357	—	47	2	no	—
335	#3356	—	47	2	no	—
336	#3355	—	47	2	no	—
337	#3354	—	47	2	no	—
338	#3353	—	47	2	no	—
339	#3352	—	47	2	no	—
340	#3351	—	47	4	no	—
341	#3160	—	47	1	no	—
342	#3091	—	47	4	no	—
343	#3076	—	47	2	no	—
344	#3054	—	47	2	no	—
345	C₄×#135	D₄₇	1	1	yes	characteristic, complemented
346	C₂×#436	—	47	1	no	—
347	#2911	—	47	2	no	—
348	C₂×C₄₇	—	2	2	no	—
349	C₂×C₄₇	—	8	2	no	—
350	C₂×C₄₇	C₂×#547	1	1	yes	characteristic
351	C₂×C₄₇	C₂×#575	1	1	yes	characteristic
352	C₂×C₄₇	#3584	1	1	yes	characteristic
353	D₄₇	—	4	4	no	—
354	C₂×#135	C₂×D₄₇	1	1	yes	characteristic
355	C₂²×M₁₆	—	47	2	no	—
356	#556	—	47	2	no	—
357	#555	—	47	2	no	—
358	#554	—	47	2	no	—
359	#553	—	47	4	no	—
360	#552	—	47	4	no	—
361	#552	—	94	2	no	—
362	#551	—	94	4	no	—
363	#547	—	47	2	no	—
364	#546	—	94	2	no	—
365	#533	—	47	2	no	—
366	#529	—	94	2	no	—
367	#529	—	94	4	no	—
368	#525	—	47	4	no	—
369	C₄×#41	—	94	2	no	—
370	C₄×#41	C₂×D₄₇	1	2	yes	—
371	C₂×C₄×D₄	—	47	1	no	—
372	C₂×#117	—	47	4	no	—
373	#500	—	47	1	no	—
374	#500	—	47	1	no	—
375	#499	—	47	2	no	—
376	#499	—	47	2	no	—
377	#498	—	47	2	no	—
378	#485	—	47	4	no	—
379	#485	—	47	4	no	—
380	#484	—	47	4	no	—
381	#483	—	47	4	no	—
382	#482	—	47	4	no	—
383	#482	—	47	4	no	—
384	#481	—	47	4	no	—
385	#480	—	47	4	no	—
386	#479	—	47	4	no	—
387	#478	—	47	4	no	—
388	#477	—	47	2	no	—
389	#476	—	47	2	no	—
390	#475	—	47	2	no	—
391	#474	—	47	2	no	—
392	#470	—	47	4	no	—
393	#469	—	47	4	no	—
394	#468	—	47	4	no	—
395	#468	—	47	4	no	—
396	C₄×Q₁₆	C₂×D₄₇	1	1	yes	characteristic, complemented
397	C₄×Q₁₆	C₂×D₄₇	1	1	yes	characteristic, complemented
398	C₄×SD₁₆	C₂×D₄₇	1	2	yes	complemented
399	C₄×SD₁₆	C₂×D₄₇	1	2	yes	complemented
400	C₄×D₈	C₂×D₄₇	1	1	yes	characteristic, complemented
401	C₄×D₈	C₂×D₄₇	1	1	yes	characteristic, complemented
402	#436	—	47	2	no	—
403	#436	—	47	2	no	—
404	#436	—	47	2	no	—
405	#436	—	47	2	no	—
406	#428	—	47	4	no	—
407	#428	—	47	4	no	—
408	#428	—	47	4	no	—
409	#428	—	47	4	no	—
410	#427	—	47	2	no	—
411	#427	—	47	2	no	—
412	#427	—	47	4	no	—
413	#427	C₂×D₄₇	1	1	yes	characteristic
414	C₂×C₄⋊C₈	—	47	1	no	—
415	#416	—	47	4	no	—
416	#416	C₂×D₄₇	1	2	yes	—
417	C₂×C₂²⋊C₈	—	47	2	no	—
418	C₂×C₄×C₈	C₂×D₄₇	1	1	yes	characteristic
419	C₄₇	#61251	1	1	yes	characteristic, complemented, Sylow
420	C₂×#41	—	94	2	no	—
421	C₂×#41	C₂²×D₄₇	1	2	yes	—
422	C₂²×D₄	—	47	1	no	—
423	C₂³×C₄	—	47	2	no	—
424	#135	—	2	4	no	—
425	C₂×Q₁₆	C₂²×D₄₇	1	1	yes	characteristic
426	C₂×SD₁₆	C₂²×D₄₇	1	2	yes	—
427	C₂×D₈	C₂²×D₄₇	1	1	yes	characteristic
428	C₂×M₁₆	—	47	4	no	—
429	C₂×M₁₆	—	47	4	no	—
430	C₂×M₁₆	—	94	8	no	—
431	C₂²×C₈	—	47	2	no	—
432	C₂²×C₈	C₂²×D₄₇	1	1	yes	characteristic
433	C₂²×C₈	C₂²×D₄₇	1	1	yes	characteristic
434	C₄⋊Q₈	—	47	2	no	—
435	C₄⋊Q₈	—	47	2	no	—
436	#126	—	94	4	no	—
437	#126	—	94	4	no	—
438	#126	—	94	4	no	—
439	#125	—	47	4	no	—
440	#125	—	94	2	no	—
441	#125	—	94	4	no	—
442	#124	—	94	2	no	—
443	#124	—	94	4	no	—
444	#123	—	94	4	no	—
445	#123	—	94	4	no	—
446	#123	—	94	4	no	—
447	#123	—	94	4	no	—
448	C₂²⋊Q₈	—	47	4	no	—
449	C₂²⋊Q₈	—	47	4	no	—
450	C₂²⋊Q₈	—	94	4	no	—
451	C₂²⋊Q₈	—	94	2	no	—
452	C₂²⋊Q₈	—	94	2	no	—
453	C₂²⋊Q₈	—	94	2	no	—
454	#121	—	47	4	no	—
455	#121	—	47	4	no	—
456	#121	—	94	4	no	—
457	#121	—	94	2	no	—
458	#120	—	94	4	no	—
459	C₄×Q₈	—	94	2	no	—
460	C₄×Q₈	—	94	2	no	—
461	C₄×Q₈	—	94	2	no	—
462	C₄×Q₈	C₂²×D₄₇	1	2	yes	—
463	C₄×Q₈	C₂²×D₄₇	1	2	yes	—
464	C₄×D₄	—	2	2	no	—
465	C₄×D₄	—	2	2	no	—
466	C₄×D₄	—	47	2	no	—
467	C₄×D₄	—	47	2	no	—
468	C₄×D₄	—	47	2	no	—
469	C₄×D₄	—	47	2	no	—
470	C₄×D₄	—	94	2	no	—
471	C₄×D₄	—	94	4	no	—
472	C₄×D₄	—	94	4	no	—
473	C₄×D₄	—	94	4	no	—
474	C₄×D₄	C₂²×D₄₇	1	2	yes	—
475	C₄×D₄	C₂²×D₄₇	1	2	yes	—
476	#117	—	2	2	no	—
477	#117	—	47	4	no	—
478	#117	—	47	4	no	—
479	#117	—	47	4	no	—
480	#117	—	94	4	no	—
481	#117	—	94	4	no	—
482	#117	—	94	4	no	—
483	#117	—	94	2	no	—
484	#117	C₂²×D₄₇	1	2	yes	—
485	C₂×C₄⋊C₄	—	47	1	no	—
486	C₂×C₄⋊C₄	—	47	4	no	—
487	C₂×C₄⋊C₄	—	47	4	no	—
488	C₂×C₂²⋊C₄	—	47	2	no	—
489	C₂×C₂²⋊C₄	—	94	4	no	—
490	C₂×C₄²	—	2	2	no	—
491	C₂×C₄²	—	94	4	no	—
492	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
493	#107	—	47	2	no	—
494	#107	—	47	2	no	—
495	#107	—	47	2	no	—
496	#107	—	47	2	no	—
497	#107	—	47	4	no	—
498	#107	—	47	4	no	—
499	#107	C₂²×D₄₇	1	1	yes	characteristic
500	#107	C₂²×D₄₇	1	1	yes	characteristic
501	#106	—	47	4	no	—
502	#106	—	47	4	no	—
503	#106	—	47	4	no	—
504	#106	—	47	4	no	—
505	#106	C₂²×D₄₇	1	2	yes	—
506	C₄⋊C₈	—	47	2	no	—
507	C₄⋊C₈	—	47	2	no	—
508	#103	—	47	4	no	—
509	#103	—	47	4	no	—
510	#103	C₂²×D₄₇	1	2	yes	—
511	#103	C₂²×D₄₇	1	2	yes	—
512	#102	—	47	4	no	—
513	#102	—	47	4	no	—
514	#102	C₂²×D₄₇	1	2	yes	—
515	#102	C₂²×D₄₇	1	2	yes	—
516	C₂²⋊C₈	—	47	4	no	—
517	C₂²⋊C₈	—	47	4	no	—
518	C₄×C₈	C₂²×D₄₇	1	1	yes	characteristic
519	C₄×C₈	C₂²×D₄₇	1	1	yes	characteristic
520	C₄×C₈	C₂²×D₄₇	1	1	yes	characteristic
521	C₄×C₈	C₂²×D₄₇	1	1	yes	characteristic
522	C₂⁴	—	47	2	no	—
523	#41	—	2	4	no	—
524	#41	—	2	4	no	—
525	#41	—	188	8	no	—
526	C₂×Q₈	—	94	2	no	—
527	C₂×Q₈	—	94	2	no	—
528	C₂×Q₈	C₂³×D₄₇	1	2	yes	—
529	C₂×D₄	—	2	2	no	—
530	C₂×D₄	—	47	2	no	—
531	C₂×D₄	—	47	2	no	—
532	C₂×D₄	—	94	4	no	—
533	C₂×D₄	—	94	4	no	—
534	C₂×D₄	—	188	2	no	—
535	C₂×D₄	C₂³×D₄₇	1	2	yes	—
536	C₂²×C₄	—	2	2	no	—
537	C₂²×C₄	—	2	2	no	—
538	C₂²×C₄	—	2	2	no	—
539	C₂²×C₄	—	47	2	no	—
540	C₂²×C₄	—	47	4	no	—
541	C₂²×C₄	—	47	4	no	—
542	C₂²×C₄	—	94	4	no	—
543	C₂²×C₄	—	94	4	no	—
544	C₂²×C₄	—	94	4	no	—
545	C₂²×C₄	—	94	4	no	—
546	C₂²×C₄	D₄×D₄₇	1	1	yes	characteristic
547	C₂²×C₄	D₄×D₄₇	1	1	yes	characteristic
548	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
549	Q₁₆	—	2	2	no	—
550	SD₁₆	—	2	4	no	—
551	D₈	—	2	2	no	—
552	M₁₆	—	94	8	no	—
553	M₁₆	—	94	8	no	—
554	C₂×C₈	—	2	2	no	—
555	C₂×C₈	—	47	4	no	—
556	C₂×C₈	—	94	4	no	—
557	C₂×C₈	#10625350	1	4	yes	complemented
558	C₂×C₈	C₂³×D₄₇	1	1	yes	characteristic
559	C₂×C₈	C₂³×D₄₇	1	1	yes	characteristic
560	C₂×C₈	C₂³×D₄₇	1	1	yes	characteristic
561	C₂×C₈	C₂³×D₄₇	1	1	yes	characteristic
562	C₄⋊C₄	—	2	2	no	—
563	C₄⋊C₄	—	2	2	no	—
564	C₄⋊C₄	—	47	2	no	—
565	C₄⋊C₄	—	47	2	no	—
566	C₄⋊C₄	—	47	4	no	—
567	C₄⋊C₄	—	47	4	no	—
568	C₄⋊C₄	—	94	4	no	—
569	C₄⋊C₄	—	94	4	no	—
570	C₄⋊C₄	—	94	4	no	—
571	C₄⋊C₄	—	94	4	no	—
572	C₄⋊C₄	—	94	4	no	—
573	C₄⋊C₄	—	94	4	no	—
574	C₄⋊C₄	—	94	2	no	—
575	C₄⋊C₄	—	94	2	no	—
576	C₄⋊C₄	C₂³×D₄₇	1	2	yes	—
577	C₄⋊C₄	C₂³×D₄₇	1	2	yes	—
578	C₂²⋊C₄	—	2	2	no	—
579	C₂²⋊C₄	—	2	2	no	—
580	C₂²⋊C₄	—	2	2	no	—
581	C₂²⋊C₄	—	47	4	no	—
582	C₂²⋊C₄	—	47	4	no	—
583	C₂²⋊C₄	—	94	4	no	—
584	C₂²⋊C₄	—	94	4	no	—
585	C₂²⋊C₄	—	94	4	no	—
586	C₂²⋊C₄	—	94	4	no	—
587	C₂²⋊C₄	—	94	4	no	—
588	C₂²⋊C₄	—	94	4	no	—
589	C₂²⋊C₄	—	94	4	no	—
590	C₄²	—	2	2	no	—
591	C₄²	—	2	2	no	—
592	C₄²	—	2	2	no	—
593	C₄²	—	94	4	no	—
594	C₄²	—	94	4	no	—
595	C₄²	—	94	4	no	—
596	C₄²	D₄×D₄₇	1	1	yes	characteristic
597	C₄²	D₄×D₄₇	1	1	yes	characteristic
598	C₄²	C₂³×D₄₇	1	1	yes	characteristic
599	C₄²	C₂³×D₄₇	1	1	yes	characteristic
600	C₂³	—	2	2	no	—
601	C₂³	—	47	4	no	—
602	C₂³	—	94	4	no	—
603	C₂³	—	188	2	no	—
604	C₂³	—	188	2	no	—
605	C₂³	C₂×D₄×D₄₇	1	1	yes	characteristic
606	Q₈	—	2	2	no	—
607	Q₈	—	2	2	no	—
608	Q₈	—	376	2	no	—
609	Q₈	—	188	4	no	—
610	D₄	—	2	2	no	—
611	D₄	—	2	2	no	—
612	D₄	—	4	4	no	—
613	D₄	—	94	4	no	—
614	D₄	—	376	4	no	—
615	D₄	—	188	2	no	—
616	D₄	—	188	8	no	—
617	C₂×C₄	—	2	2	no	—
618	C₂×C₄	—	2	2	no	—
619	C₂×C₄	—	2	2	no	—
620	C₂×C₄	—	2	2	no	—
621	C₂×C₄	—	4	1	no	—
622	C₂×C₄	—	4	4	no	—
623	C₂×C₄	—	4	4	no	—
624	C₂×C₄	—	8	2	no	—
625	C₂×C₄	—	47	4	no	—
626	C₂×C₄	—	94	4	no	—
627	C₂×C₄	—	94	8	no	—
628	C₂×C₄	—	94	4	no	—
629	C₂×C₄	—	94	4	no	—
630	C₂×C₄	—	94	4	no	—
631	C₂×C₄	—	94	4	no	—
632	C₂×C₄	—	376	4	no	—
633	C₂×C₄	—	188	8	no	—
634	C₂×C₄	C₂×D₄×D₄₇	1	1	yes	characteristic
635	C₂×C₄	C₂×D₄×D₄₇	1	1	yes	characteristic
636	C₂×C₄	C₂×D₄×D₄₇	1	1	yes	characteristic
637	C₂×C₄	C₂×D₄×D₄₇	1	1	yes	characteristic
638	C₂×C₄	C₂×D₄×D₄₇	1	1	yes	characteristic
639	C₂×C₄	C₂×#10625350	1	2	yes	—
640	C₂×C₄	#13094071	1	2	yes	—
641	C₂×C₄	C₂⁴×D₄₇	1	1	yes	characteristic
642	C₈	—	2	1	no	—
643	C₈	—	2	1	no	—
644	C₈	—	94	4	no	—
645	C₈	C₂×#10625350	1	2	yes	—
646	C₈	C₂×#10625350	1	2	yes	—
647	C₂²	—	2	1	no	—
648	C₂²	—	2	1	no	—
649	C₂²	—	4	2	no	—
650	C₂²	—	4	2	no	—
651	C₂²	—	4	2	no	—
652	C₂²	—	94	4	no	—
653	C₂²	—	94	4	no	—
654	C₂²	—	94	4	no	—
655	C₂²	—	376	4	no	—
656	C₂²	#15689778	1	2	yes	—
657	C₂²	C₂²×D₄×D₄₇	1	1	yes	characteristic
658	C₄	—	2	1	no	—
659	C₄	—	2	1	no	—
660	C₄	—	2	1	no	—
661	C₄	—	4	2	no	—
662	C₄	—	4	2	no	—
663	C₄	—	4	2	no	—
664	C₄	—	94	4	no	—
665	C₄	—	188	4	no	—
666	C₄	—	188	4	no	—
667	C₄	#15689778	1	2	yes	—
668	C₄	#15689920	1	2	yes	—
669	C₄	C₂²×#10625350	1	1	yes	characteristic
670	C₄	C₂×#13094071	1	1	yes	characteristic
671	C₂	—	2	2	no	—
672	C₂	—	8	2	no	—
673	C₂	—	188	4	no	—
674	C₂	C₂×#15689778	1	1	yes	characteristic
675	C₂	C₂×#15689920	1	1	yes	characteristic
676	C₂	#20258157	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂×D₄×D₄₇
commutator, cosocle	C₂×C₄×C₄₇	C₂⁵
Frattini	C₂×C₄	C₂⁴×D₄₇
Fitting	C₄×#135×C₄₇	C₂
socle	C₂²×C₄₇	C₂³×D₄
hypercenter	C₄×#135	D₄₇
hypocenter	C₄₇	#61251
LCS	G ▷ C₂×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ C₄×#135

Complements

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

N	H ≅ G/N	type
1. #20256952	C₂	semidirect
2. #20256016	C₂	semidirect
3. #20256005	C₂	semidirect
4. #20255995	C₂	semidirect
5. #20255985	C₂	semidirect
6. #20255974	C₂	semidirect
7. #20255964	C₂	semidirect
8. #20255953	C₂	semidirect
9. #20253902	C₂	semidirect
10. #20253299	C₂	semidirect
11. #20253176	C₂	semidirect
12. #20252993	C₂	semidirect
13. C₂×#15689202	C₂	semidirect
14. #20251976	C₂	semidirect
15. C₄×#135×C₄₇	C₂	semidirect
33. #15689528	C₂²	semidirect
34. #15689528	C₂²	semidirect
35. #15689525	C₂²	semidirect
36. #15689525	C₂²	semidirect
37. #15689521	C₂²	semidirect
38. #15689463	C₂²	semidirect
39. #15689462	C₂²	semidirect
40. #15689457	C₂²	semidirect
41. #15689452	C₂²	semidirect
42. #15689446	C₂²	semidirect
43. #15689445	C₂²	semidirect
44. #15689440	C₂²	semidirect
45. #15689435	C₂²	semidirect
46. #15689430	C₂²	semidirect
47. #15689423	C₂²	semidirect
48. #15689418	C₂²	semidirect
49. #15689413	C₂²	semidirect
50. #15689408	C₂²	semidirect
51. #15689403	C₂²	semidirect
52. #15689378	C₂²	semidirect
53. #15689373	C₂²	semidirect
54. #15689366	C₂²	semidirect
55. #15689366	C₂²	semidirect
60. #15689164	C₂²	semidirect
61. #15689164	C₂²	semidirect
62. #15689162	C₂²	semidirect
63. #15689162	C₂²	semidirect
72. C₄×Q₁₆×C₄₇	C₂²	semidirect
73. C₄×Q₁₆×C₄₇	C₂²	semidirect
74. C₄×SD₁₆×C₄₇	C₂²	semidirect
75. C₄×SD₁₆×C₄₇	C₂²	semidirect
76. C₄×D₈×C₄₇	C₂²	semidirect
77. C₄×D₈×C₄₇	C₂²	semidirect
214. C₂×C₈×C₄₇	#41	semidirect
345. C₄×#135	D₄₇	semidirect
396. C₄×Q₁₆	C₂×D₄₇	semidirect
397. C₄×Q₁₆	C₂×D₄₇	semidirect
398. C₄×SD₁₆	C₂×D₄₇	semidirect
399. C₄×SD₁₆	C₂×D₄₇	semidirect
400. C₄×D₈	C₂×D₄₇	semidirect
401. C₄×D₈	C₂×D₄₇	semidirect
419. C₄₇	#61251	semidirect
557. C₂×C₈	#10625350	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
#20256952	2
#20256016	2
#20256005	2
#20255995	2
#20255985	2
#20255974	2
#20255964	2
#20255953	2
#20253902	2
#20253299	2
#20253176	2
#20252993	2
C₂×#15689202	2
#20251976	2
C₄×#135×C₄₇	2
#61251	47