Subgroups — #27083706

Order 12032.

2604 conjugacy classes of subgroups.

The subgroup lattice has 518 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20258175	C₂	1	1	yes	maximal, characteristic, complemented
2	#20258168	C₂	1	1	yes	maximal, characteristic, complemented
3	#20258099	C₂	1	1	yes	maximal, characteristic, complemented
4	#20253121	C₂	1	6	yes	maximal, complemented
5	#20253112	C₂	1	6	yes	maximal, complemented
6	#20253104	C₂	1	6	yes	maximal, complemented
7	C₂×#15689383	C₂	1	6	yes	maximal, complemented
8	#20251999	C₂	1	1	yes	maximal, characteristic, complemented
9	#20251871	C₂	1	1	yes	maximal, characteristic, complemented
10	#20251867	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×C₄₇×#577	C₂	1	1	yes	maximal, characteristic, complemented
12	#15689959	C₂²	1	1	yes	characteristic
13	#15689938	—	2	4	no	—
14	#15689934	—	2	4	no	—
15	#15689931	—	2	4	no	—
16	#15689926	—	2	4	no	—
17	#15689921	C₂²	1	6	yes	—
18	#15689921	C₂²	1	6	yes	complemented
19	C₂×#13094055	C₂²	1	6	yes	complemented
20	C₂×#13094050	C₂²	1	6	yes	—
21	#15689890	C₂²	1	1	yes	characteristic
22	#15689890	C₂²	1	1	yes	characteristic
23	#15689890	C₂²	1	1	yes	characteristic
24	#15689889	C₂²	1	6	yes	complemented
25	#15689888	—	2	4	no	—
26	C₂×#13094030	C₂²	1	6	yes	complemented
27	#131×D₄₇	—	2	4	no	—
28	#15689395	C₂²	1	12	yes	complemented
29	#15689390	C₂²	1	12	yes	complemented
30	#15689383	C₂²	1	12	yes	complemented
31	#15689383	C₂²	1	24	yes	complemented
32	#15689383	C₂²	1	4	yes	complemented
33	#15689172	C₂²	1	6	yes	complemented
34	C₂×#13093960	C₂²	1	6	yes	complemented
35	#15689107	C₂²	1	6	yes	complemented
36	#15689107	C₂²	1	6	yes	complemented
37	C₂×#13093943	C₂²	1	6	yes	complemented
38	C₂×#13093941	C₂²	1	6	yes	complemented
39	C₂×2₋¹⁺⁴×C₄₇	C₂²	1	1	yes	characteristic
40	C₂×H(5,𝔽₂)×C₄₇	C₂²	1	1	yes	characteristic
41	C₄₇×#577	—	2	4	no	—
42	C₄₇×#577	—	2	4	no	—
43	C₂×#137×C₄₇	C₂²	1	3	yes	complemented
44	C₂×AGL(1,ℤ/8)×C₄₇	C₂²	1	3	yes	complemented
45	C₂×#135×C₄₇	C₂²	1	3	yes	complemented
46	C₂²×SD₁₆×C₄₇	C₂²	1	3	yes	complemented
47	C₂×#131×C₄₇	C₂²	1	1	yes	characteristic
48	#13094072	—	2	1	no	—
49	#13094071	D₄	1	4	yes	—
50	#13094070	D₄	1	4	yes	—
51	#13094069	—	2	3	no	—
52	C₂×#10625350	C₂³	1	6	yes	—
53	#41×D₄₇	—	2	4	no	—
54	#13094055	—	2	12	no	—
55	#13094055	C₂³	1	12	yes	—
56	#13094055	C₂³	1	4	yes	—
57	#13094054	—	2	6	no	—
58	#13094054	—	2	6	no	—
59	#13094050	—	2	12	no	—
60	#13094050	C₂³	1	12	yes	—
61	#13094050	C₂³	1	4	yes	—
62	#13094049	—	2	6	no	—
63	#13094049	—	2	6	no	—
64	#13094044	—	2	12	no	—
65	#13094044	—	2	12	no	—
66	C₂×#10625337	—	2	6	no	—
67	C₂×#10625335	—	2	6	no	—
68	C₂×#10625336	—	2	6	no	—
69	C₂×#10625334	—	2	6	no	—
70	#13094032	—	2	12	no	—
71	#13094031	—	2	4	no	—
72	#13094031	—	2	4	no	—
73	#13094031	—	2	4	no	—
74	#13094030	—	2	6	no	—
75	#13094030	—	2	6	no	—
76	#13094030	C₂³	1	4	yes	—
77	#13094030	C₂³	1	12	yes	—
78	C₂×#10625329	C₂³	1	6	yes	—
79	C₂×#10625329	C₂³	1	6	yes	—
80	C₂×#10625329	C₂³	1	6	yes	—
81	C₂×#10625324	—	2	6	no	—
82	M₁₆×D₄₇	—	2	12	no	—
83	C₂×C₈×D₄₇	—	2	6	no	—
84	#13093960	C₂³	1	4	yes	—
85	#13093960	C₂³	1	12	yes	—
86	#13093943	C₂³	1	12	yes	—
87	#13093943	C₂³	1	4	yes	—
88	#13093941	C₂³	1	12	yes	—
89	#13093941	C₂³	1	4	yes	—
90	2₋¹⁺⁴×C₄₇	—	2	4	no	—
91	2₋¹⁺⁴×C₄₇	—	2	4	no	—
92	H(5,𝔽₂)×C₄₇	—	2	4	no	—
93	H(5,𝔽₂)×C₄₇	—	2	4	no	—
94	C₂×#41×C₄₇	—	2	1	no	—
95	C₂×#41×C₄₇	—	2	3	no	—
96	C₂×#41×C₄₇	C₂³	1	3	yes	—
97	C₂×#41×C₄₇	C₂³	1	3	yes	—
98	C₂×#41×C₄₇	C₂³	1	1	yes	characteristic
99	C₂²×Q₈×C₄₇	—	2	1	no	—
100	C₂²×Q₈×C₄₇	C₂³	1	3	yes	—
101	C₂²×D₄×C₄₇	—	2	3	no	—
102	C₂²×D₄×C₄₇	C₂³	1	3	yes	—
103	#137×C₄₇	—	2	12	no	—
104	AGL(1,ℤ/8)×C₄₇	—	2	12	no	—
105	#135×C₄₇	—	2	6	no	—
106	#135×C₄₇	—	2	6	no	—
107	C₂×Q₁₆×C₄₇	C₂³	1	3	yes	—
108	C₂×SD₁₆×C₄₇	—	2	6	no	—
109	C₂×SD₁₆×C₄₇	—	2	6	no	—
110	C₂×SD₁₆×C₄₇	C₂³	1	3	yes	—
111	C₂×SD₁₆×C₄₇	C₂³	1	6	yes	—
112	C₂×SD₁₆×C₄₇	C₂³	1	1	yes	characteristic
113	C₂×D₈×C₄₇	C₂³	1	3	yes	—
114	#131×C₄₇	D₄	1	4	yes	—
115	#131×C₄₇	D₄	1	4	yes	—
116	C₂×M₁₆×C₄₇	C₂³	1	3	yes	—
117	C₂²×C₈×C₄₇	C₂³	1	3	yes	—
118	C₂⁴×C₄₇	—	2	3	no	—
119	#41×C₄₇	—	2	6	no	—
120	#41×C₄₇	—	2	6	no	—
121	#41×C₄₇	—	2	6	no	—
122	#41×C₄₇	—	2	6	no	—
123	#41×C₄₇	—	4	4	no	—
124	#41×C₄₇	—	4	12	no	—
125	#41×C₄₇	C₂×D₄	1	4	yes	—
126	#41×C₄₇	C₂×D₄	1	4	yes	—
127	C₂×Q₈×C₄₇	—	2	3	no	—
128	C₂×Q₈×C₄₇	—	2	6	no	—
129	C₂×Q₈×C₄₇	—	2	6	no	—
130	C₂×Q₈×C₄₇	—	4	4	no	—
131	C₂×Q₈×C₄₇	#41	1	1	yes	characteristic
132	C₂×Q₈×C₄₇	C₂⁴	1	3	yes	—
133	C₂×Q₈×C₄₇	C₂⁴	1	1	yes	characteristic
134	C₂×D₄×C₄₇	—	2	3	no	—
135	C₂×D₄×C₄₇	—	2	3	no	—
136	C₂×D₄×C₄₇	—	2	6	no	—
137	C₂×D₄×C₄₇	—	2	6	no	—
138	C₂×D₄×C₄₇	—	2	3	no	—
139	C₂×D₄×C₄₇	—	4	12	no	—
140	C₂×D₄×C₄₇	#41	1	3	yes	—
141	C₂×D₄×C₄₇	C₂⁴	1	1	yes	characteristic
142	C₂×D₄×C₄₇	C₂⁴	1	3	yes	—
143	C₂²×C₄×C₄₇	—	2	3	no	—
144	C₂²×C₄×C₄₇	—	2	3	no	—
145	C₂²×C₄×C₄₇	—	2	3	no	—
146	C₂²×C₄×C₄₇	C₂⁴	1	3	yes	—
147	C₂×C₂²⋊D₄₇	—	2	6	no	—
148	#10625354	—	2	4	no	—
149	Q₈×D₄₇	—	2	4	no	—
150	#10625352	—	2	12	no	—
151	D₄×D₄₇	—	2	12	no	—
152	#10625350	—	2	6	no	—
153	#10625350	—	2	6	no	—
154	#10625350	C₂×D₄	1	12	yes	—
155	#10625350	C₂⁴	1	4	yes	—
156	C₂×D₁₈₈	C₂×D₄	1	6	yes	—
157	C₂×C₄×D₄₇	—	2	6	no	—
158	C₂×Dic₉₄	C₂×D₄	1	6	yes	—
159	Q₁₆×C₄₇	—	2	6	no	—
160	SD₁₆×C₄₇	—	2	3	no	—
161	SD₁₆×C₄₇	—	2	3	no	—
162	SD₁₆×C₄₇	—	2	12	no	—
163	SD₁₆×C₄₇	—	2	1	no	—
164	SD₁₆×C₄₇	—	2	1	no	—
165	D₈×C₄₇	—	2	6	no	—
166	M₁₆×C₄₇	C₂×D₄	1	12	yes	—
167	C₂×C₈×C₄₇	C₂×D₄	1	6	yes	—
168	C₂×C₈×C₄₇	C₂×D₄	1	6	yes	—
169	C₂×C₈×C₄₇	C₂⁴	1	1	yes	characteristic
170	C₂×C₈×C₄₇	C₂⁴	1	3	yes	—
171	#10625337	—	2	12	no	—
172	#10625337	—	2	4	no	—
173	#10625336	—	2	12	no	—
174	#10625336	—	2	4	no	—
175	#10625335	—	2	12	no	—
176	#10625335	—	2	4	no	—
177	#10625334	—	2	12	no	—
178	#10625334	—	2	4	no	—
179	#10625329	—	2	6	no	—
180	#10625329	—	2	6	no	—
181	#10625329	—	2	6	no	—
182	#10625329	C₂⁴	1	4	yes	—
183	#10625329	C₂⁴	1	4	yes	—
184	#10625329	C₂⁴	1	4	yes	—
185	C₂×C₄₇⋊C₈	—	2	6	no	—
186	C₂×C₄₇⋊C₈	—	2	6	no	—
187	C₂×C₄₇⋊C₈	—	2	6	no	—
188	#10625324	—	2	12	no	—
189	#10625324	—	2	4	no	—
190	C₈×D₄₇	—	2	4	no	—
191	C₈×D₄₇	—	2	12	no	—
192	C₂³×C₄₇	—	2	1	no	—
193	C₂³×C₄₇	—	2	3	no	—
194	C₂³×C₄₇	—	4	6	no	—
195	C₂³×C₄₇	—	16	3	no	—
196	C₂³×C₄₇	C₂×#41	1	3	yes	—
197	C₂²×D₄₇	—	2	6	no	—
198	Q₈×C₄₇	—	2	3	no	—
199	Q₈×C₄₇	—	2	1	no	—
200	Q₈×C₄₇	—	2	3	no	—
201	Q₈×C₄₇	—	2	1	no	—
202	Q₈×C₄₇	—	4	6	no	—
203	Q₈×C₄₇	#121	1	4	yes	—
204	D₄×C₄₇	—	2	3	no	—
205	D₄×C₄₇	—	2	1	no	—
206	D₄×C₄₇	—	2	1	no	—
207	D₄×C₄₇	—	2	3	no	—
208	D₄×C₄₇	—	4	6	no	—
209	D₄×C₄₇	—	4	6	no	—
210	D₄×C₄₇	—	4	6	no	—
211	D₄×C₄₇	#121	1	12	yes	—
212	C₂×C₄×C₄₇	—	2	1	no	—
213	C₂×C₄×C₄₇	—	2	3	no	—
214	C₂×C₄×C₄₇	—	4	6	no	—
215	C₂×C₄×C₄₇	—	4	6	no	—
216	C₂×C₄×C₄₇	—	4	6	no	—
217	C₂×C₄×C₄₇	C₂²×D₄	1	6	yes	—
218	C₂×C₄×C₄₇	C₂²×D₄	1	6	yes	—
219	C₂×C₄×C₄₇	C₂×#41	1	3	yes	—
220	C₂×C₄×C₄₇	C₂⁵	1	1	yes	characteristic
221	C₂²⋊D₄₇	—	2	12	no	—
222	C₂²⋊D₄₇	—	2	4	no	—
223	C₂×Dic₄₇	—	2	6	no	—
224	D₁₈₈	—	2	6	no	—
225	D₁₈₈	C₂²×D₄	1	4	yes	—
226	C₄×D₄₇	—	2	12	no	—
227	C₄×D₄₇	—	2	4	no	—
228	Dic₉₄	—	2	6	no	—
229	Dic₉₄	C₂²×D₄	1	4	yes	—
230	C₈×C₄₇	C₂²×D₄	1	1	yes	characteristic
231	C₈×C₄₇	C₂²×D₄	1	6	yes	—
232	C₈×C₄₇	C₂²×D₄	1	1	yes	characteristic
233	C₄₇⋊C₈	—	2	4	no	—
234	C₄₇⋊C₈	—	2	4	no	—
235	C₄₇⋊C₈	—	2	4	no	—
236	#60470	—	47	1	no	maximal, Sylow
237	C₂²×C₄₇	—	4	3	no	—
238	C₂²×C₄₇	—	4	1	no	—
239	C₂²×C₄₇	—	4	3	no	—
240	C₂²×C₄₇	—	8	1	no	—
241	C₂²×C₄₇	—	8	3	no	—
242	C₂²×C₄₇	—	16	6	no	—
243	C₂²×C₄₇	C₂×#121	1	6	yes	—
244	C₂²×C₄₇	C₂²×#41	1	1	yes	characteristic
245	C₂×D₄₇	—	2	4	no	—
246	C₂×D₄₇	—	8	6	no	—
247	C₄×C₄₇	—	4	1	no	—
248	C₄×C₄₇	—	4	3	no	—
249	C₄×C₄₇	C₂×#121	1	6	yes	—
250	C₄×C₄₇	C₂³×D₄	1	1	yes	characteristic
251	C₄×C₄₇	C₂³×D₄	1	1	yes	characteristic
252	Dic₄₇	—	2	4	no	—
253	#3586	—	47	1	no	—
254	#3585	—	47	1	no	—
255	C₂×#577	D₄₇	1	1	yes	characteristic, complemented
256	#3573	—	47	1	no	—
257	#3069	—	47	6	no	—
258	#3068	—	47	6	no	—
259	#3067	—	47	6	no	—
260	C₂×#471	—	47	6	no	—
261	#2916	—	47	1	no	—
262	#2889	—	47	1	no	—
263	#2888	—	47	1	no	—
264	C₂×C₄₇	—	2	6	no	—
265	C₂×C₄₇	—	2	1	no	—
266	C₂×C₄₇	—	8	1	no	—
267	C₂×C₄₇	—	8	3	no	—
268	C₂×C₄₇	C₂²×#121	1	1	yes	characteristic
269	D₄₇	—	4	4	no	—
270	#585	—	47	1	no	—
271	C₂×2₋¹⁺⁴	C₂×D₄₇	1	1	yes	characteristic
272	C₂×H(5,𝔽₂)	C₂×D₄₇	1	1	yes	characteristic
273	#578	—	94	4	no	—
274	#577	—	2	4	no	—
275	#577	—	2	4	no	—
276	#577	—	94	4	no	—
277	#577	—	94	4	no	—
278	#576	—	94	4	no	—
279	#575	—	47	6	no	—
280	#575	—	47	6	no	—
281	C₂×#137	—	47	6	no	—
282	C₂×#137	C₂×D₄₇	1	3	yes	complemented
283	C₂×AGL(1,ℤ/8)	—	47	6	no	—
284	C₂×AGL(1,ℤ/8)	C₂×D₄₇	1	3	yes	complemented
285	C₂×#135	C₂×D₄₇	1	3	yes	complemented
286	C₂²×SD₁₆	C₂×D₄₇	1	3	yes	complemented
287	#568	—	47	1	no	—
288	#568	—	47	1	no	—
289	#568	—	47	1	no	—
290	#568	—	47	6	no	—
291	#568	—	94	4	no	—
292	C₂×#131	—	47	6	no	—
293	C₂×#131	—	94	4	no	—
294	C₂×#131	C₂×D₄₇	1	1	yes	characteristic
295	#473	—	47	12	no	—
296	#472	—	47	12	no	—
297	#471	—	47	12	no	—
298	#471	—	47	24	no	—
299	#471	—	47	4	no	—
300	#430	—	47	6	no	—
301	C₂×#108	—	47	6	no	—
302	#413	—	47	6	no	—
303	#413	—	47	6	no	—
304	C₂×#101	—	47	6	no	—
305	C₂×#100	—	47	6	no	—
306	C₄₇	#60470	1	1	yes	characteristic, complemented, Sylow
307	2₋¹⁺⁴	—	2	4	no	—
308	2₋¹⁺⁴	—	2	4	no	—
309	2₋¹⁺⁴	—	47	4	no	—
310	2₋¹⁺⁴	—	94	1	no	—
311	H(5,𝔽₂)	—	2	4	no	—
312	H(5,𝔽₂)	—	2	4	no	—
313	H(5,𝔽₂)	—	47	4	no	—
314	H(5,𝔽₂)	—	94	3	no	—
315	C₂×#41	—	2	1	no	—
316	C₂×#41	—	2	3	no	—
317	C₂×#41	—	47	6	no	—
318	C₂×#41	—	94	4	no	—
319	C₂×#41	C₂²×D₄₇	1	3	yes	—
320	C₂×#41	C₂²×D₄₇	1	3	yes	—
321	C₂×#41	C₂²×D₄₇	1	1	yes	characteristic
322	C₂²×Q₈	—	2	1	no	—
323	C₂²×Q₈	C₂²×D₄₇	1	3	yes	—
324	C₂²×D₄	—	2	3	no	—
325	C₂²×D₄	C₂²×D₄₇	1	3	yes	—
326	#137	—	2	12	no	—
327	#137	—	47	12	no	—
328	#137	—	47	4	no	—
329	#137	—	94	12	no	—
330	#137	—	94	6	no	—
331	#137	—	94	6	no	—
332	AGL(1,ℤ/8)	—	2	12	no	—
333	AGL(1,ℤ/8)	—	47	12	no	—
334	AGL(1,ℤ/8)	—	47	4	no	—
335	AGL(1,ℤ/8)	—	94	12	no	—
336	AGL(1,ℤ/8)	—	94	6	no	—
337	AGL(1,ℤ/8)	—	94	6	no	—
338	#135	—	2	6	no	—
339	#135	—	2	6	no	—
340	#135	—	94	12	no	—
341	#135	—	94	12	no	—
342	C₂×Q₁₆	—	94	6	no	—
343	C₂×Q₁₆	C₂²×D₄₇	1	3	yes	—
344	C₂×SD₁₆	—	2	6	no	—
345	C₂×SD₁₆	—	2	6	no	—
346	C₂×SD₁₆	—	94	6	no	—
347	C₂×SD₁₆	—	94	6	no	—
348	C₂×SD₁₆	C₂²×D₄₇	1	3	yes	—
349	C₂×SD₁₆	C₂²×D₄₇	1	6	yes	—
350	C₂×SD₁₆	C₂²×D₄₇	1	1	yes	characteristic
351	C₂×D₈	—	94	6	no	—
352	C₂×D₈	C₂²×D₄₇	1	3	yes	—
353	#131	—	47	4	no	—
354	#131	—	47	12	no	—
355	#131	—	94	4	no	—
356	#131	—	94	4	no	—
357	#131	—	94	4	no	—
358	#131	—	94	12	no	—
359	#131	—	94	6	no	—
360	#131	—	94	6	no	—
361	#131	C₂²⋊D₄₇	1	4	yes	—
362	#131	C₂²⋊D₄₇	1	4	yes	—
363	C₂×M₁₆	—	47	6	no	—
364	C₂×M₁₆	—	47	6	no	—
365	C₂×M₁₆	—	47	6	no	—
366	C₂×M₁₆	—	94	12	no	—
367	C₂×M₁₆	—	94	6	no	—
368	C₂×M₁₆	C₂²×D₄₇	1	3	yes	—
369	C₂²×C₈	—	94	6	no	—
370	C₂²×C₈	C₂²×D₄₇	1	3	yes	—
371	#108	—	47	4	no	—
372	#108	—	47	12	no	—
373	#101	—	47	12	no	—
374	#101	—	47	4	no	—
375	#100	—	47	12	no	—
376	#100	—	47	4	no	—
377	C₂⁴	—	2	3	no	—
378	#41	—	2	6	no	—
379	#41	—	2	6	no	—
380	#41	—	2	6	no	—
381	#41	—	2	6	no	—
382	#41	—	4	4	no	—
383	#41	—	4	12	no	—
384	#41	—	47	12	no	—
385	#41	—	47	4	no	—
386	#41	—	94	4	no	—
387	#41	—	94	12	no	—
388	#41	—	94	6	no	—
389	#41	—	94	6	no	—
390	#41	D₄×D₄₇	1	4	yes	—
391	#41	C₂×C₂²⋊D₄₇	1	4	yes	—
392	C₂×Q₈	—	2	3	no	—
393	C₂×Q₈	—	2	6	no	—
394	C₂×Q₈	—	2	6	no	—
395	C₂×Q₈	—	4	4	no	—
396	C₂×Q₈	—	47	6	no	—
397	C₂×Q₈	—	94	4	no	—
398	C₂×Q₈	#10625352	1	1	yes	characteristic
399	C₂×Q₈	C₂³×D₄₇	1	3	yes	—
400	C₂×Q₈	C₂³×D₄₇	1	1	yes	characteristic
401	C₂×D₄	—	2	3	no	—
402	C₂×D₄	—	2	3	no	—
403	C₂×D₄	—	2	6	no	—
404	C₂×D₄	—	2	6	no	—
405	C₂×D₄	—	2	3	no	—
406	C₂×D₄	—	4	12	no	—
407	C₂×D₄	—	47	6	no	—
408	C₂×D₄	—	94	6	no	—
409	C₂×D₄	—	94	12	no	—
410	C₂×D₄	#10625352	1	3	yes	—
411	C₂×D₄	C₂³×D₄₇	1	1	yes	characteristic
412	C₂×D₄	C₂³×D₄₇	1	3	yes	—
413	C₂²×C₄	—	2	3	no	—
414	C₂²×C₄	—	2	3	no	—
415	C₂²×C₄	—	2	3	no	—
416	C₂²×C₄	—	94	6	no	—
417	C₂²×C₄	C₂³×D₄₇	1	3	yes	—
418	Q₁₆	—	2	6	no	—
419	Q₁₆	—	94	12	no	—
420	Q₁₆	—	94	4	no	—
421	SD₁₆	—	2	3	no	—
422	SD₁₆	—	2	3	no	—
423	SD₁₆	—	2	12	no	—
424	SD₁₆	—	2	1	no	—
425	SD₁₆	—	2	1	no	—
426	SD₁₆	—	94	12	no	—
427	SD₁₆	—	94	4	no	—
428	SD₁₆	—	94	12	no	—
429	SD₁₆	—	94	4	no	—
430	D₈	—	2	6	no	—
431	D₈	—	94	12	no	—
432	D₈	—	94	4	no	—
433	M₁₆	—	47	4	no	—
434	M₁₆	—	47	4	no	—
435	M₁₆	—	47	4	no	—
436	M₁₆	—	94	6	no	—
437	M₁₆	—	94	6	no	—
438	M₁₆	—	94	6	no	—
439	M₁₆	—	94	12	no	—
440	M₁₆	—	94	4	no	—
441	M₁₆	C₂×C₂²⋊D₄₇	1	12	yes	—
442	C₂×C₈	—	94	6	no	—
443	C₂×C₈	—	94	6	no	—
444	C₂×C₈	—	94	6	no	—
445	C₂×C₈	—	94	4	no	—
446	C₂×C₈	—	94	12	no	—
447	C₂×C₈	C₂×C₂²⋊D₄₇	1	6	yes	—
448	C₂×C₈	C₂×C₂²⋊D₄₇	1	6	yes	—
449	C₂×C₈	C₂³×D₄₇	1	1	yes	characteristic
450	C₂×C₈	C₂³×D₄₇	1	3	yes	—
451	C₂³	—	2	1	no	—
452	C₂³	—	2	3	no	—
453	C₂³	—	4	6	no	—
454	C₂³	—	16	3	no	—
455	C₂³	—	94	6	no	—
456	C₂³	C₂×#10625352	1	3	yes	—
457	Q₈	—	2	3	no	—
458	Q₈	—	2	1	no	—
459	Q₈	—	2	3	no	—
460	Q₈	—	2	1	no	—
461	Q₈	—	4	6	no	—
462	Q₈	—	47	4	no	—
463	Q₈	—	94	6	no	—
464	Q₈	#13093995	1	4	yes	—
465	D₄	—	2	3	no	—
466	D₄	—	2	1	no	—
467	D₄	—	2	1	no	—
468	D₄	—	2	3	no	—
469	D₄	—	4	6	no	—
470	D₄	—	4	6	no	—
471	D₄	—	4	6	no	—
472	D₄	—	47	4	no	—
473	D₄	—	94	12	no	—
474	D₄	—	94	4	no	—
475	D₄	—	94	6	no	—
476	D₄	#13093995	1	12	yes	—
477	C₂×C₄	—	2	1	no	—
478	C₂×C₄	—	2	3	no	—
479	C₂×C₄	—	4	6	no	—
480	C₂×C₄	—	4	6	no	—
481	C₂×C₄	—	4	6	no	—
482	C₂×C₄	—	94	6	no	—
483	C₂×C₄	—	94	12	no	—
484	C₂×C₄	—	94	4	no	—
485	C₂×C₄	C₂×D₄×D₄₇	1	6	yes	—
486	C₂×C₄	C₂²×C₂²⋊D₄₇	1	6	yes	—
487	C₂×C₄	C₂×#10625352	1	3	yes	—
488	C₂×C₄	C₂⁴×D₄₇	1	1	yes	characteristic
489	C₈	—	94	4	no	—
490	C₈	—	94	4	no	—
491	C₈	—	94	4	no	—
492	C₈	C₂²×C₂²⋊D₄₇	1	1	yes	characteristic
493	C₈	C₂²×C₂²⋊D₄₇	1	6	yes	—
494	C₈	C₂²×C₂²⋊D₄₇	1	1	yes	characteristic
495	C₂²	—	4	3	no	—
496	C₂²	—	4	1	no	—
497	C₂²	—	4	3	no	—
498	C₂²	—	8	3	no	—
499	C₂²	—	8	1	no	—
500	C₂²	—	16	6	no	—
501	C₂²	—	94	4	no	—
502	C₂²	—	376	6	no	—
503	C₂²	C₂×#13093995	1	6	yes	—
504	C₂²	C₂²×#10625352	1	1	yes	characteristic
505	C₄	—	4	1	no	—
506	C₄	—	4	3	no	—
507	C₄	—	94	4	no	—
508	C₄	C₂×#13093995	1	6	yes	—
509	C₄	C₂²×D₄×D₄₇	1	1	yes	characteristic
510	C₄	C₂³×C₂²⋊D₄₇	1	1	yes	characteristic
511	C₂	—	2	1	no	—
512	C₂	—	2	6	no	—
513	C₂	—	8	3	no	—
514	C₂	—	8	1	no	—
515	C₂	—	188	4	no	—
516	C₂	C₂²×#13093995	1	1	yes	characteristic

	subgroup	G/H
center	C₂	C₂²×#13093995
commutator, cosocle	C₂×C₄×C₄₇	C₂⁵
Frattini	C₂×C₄	C₂⁴×D₄₇
Fitting	C₂×C₄₇×#577	C₂
socle	C₂×C₄₇	C₂²×#121
hypercenter	C₂×#577	D₄₇
hypocenter	C₄₇	#60470
LCS	G ▷ C₂×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂ ◁ C₂×#41 ◁ C₂×#577

Complements

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

N	H ≅ G/N	type
1. #20258175	C₂	semidirect
2. #20258168	C₂	semidirect
3. #20258099	C₂	semidirect
4. #20253121	C₂	semidirect
5. #20253112	C₂	semidirect
6. #20253104	C₂	semidirect
7. C₂×#15689383	C₂	semidirect
8. #20251999	C₂	semidirect
9. #20251871	C₂	semidirect
10. #20251867	C₂	semidirect
11. C₂×C₄₇×#577	C₂	semidirect
18. #15689921	C₂²	semidirect
19. C₂×#13094055	C₂²	semidirect
24. #15689889	C₂²	semidirect
26. C₂×#13094030	C₂²	semidirect
28. #15689395	C₂²	semidirect
29. #15689390	C₂²	semidirect
30. #15689383	C₂²	semidirect
31. #15689383	C₂²	semidirect
32. #15689383	C₂²	semidirect
33. #15689172	C₂²	semidirect
34. C₂×#13093960	C₂²	semidirect
35. #15689107	C₂²	semidirect
36. #15689107	C₂²	semidirect
37. C₂×#13093943	C₂²	semidirect
38. C₂×#13093941	C₂²	semidirect
43. C₂×#137×C₄₇	C₂²	semidirect
44. C₂×AGL(1,ℤ/8)×C₄₇	C₂²	semidirect
45. C₂×#135×C₄₇	C₂²	semidirect
46. C₂²×SD₁₆×C₄₇	C₂²	semidirect
255. C₂×#577	D₄₇	semidirect
282. C₂×#137	C₂×D₄₇	semidirect
284. C₂×AGL(1,ℤ/8)	C₂×D₄₇	semidirect
285. C₂×#135	C₂×D₄₇	semidirect
286. C₂²×SD₁₆	C₂×D₄₇	semidirect
306. C₄₇	#60470	semidirect

Maximal subgroups

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

subgroup	index
#20258175	2
#20258168	2
#20258099	2
#20253121	2
#20253112	2
#20253104	2
C₂×#15689383	2
#20251999	2
#20251871	2
#20251867	2
C₂×C₄₇×#577	2
#60470	47