Subgroups — #25148153

Order 11008.

892 conjugacy classes of subgroups.

The subgroup lattice has 534 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#19145082	C₂	1	1	yes	maximal, characteristic, complemented
2	#19144325	C₂	1	2	yes	maximal, complemented
3	C₂×#14583169	C₂	1	1	yes	maximal, characteristic, complemented
4	#19143512	C₂	1	1	yes	maximal, characteristic, complemented
5	#19135868	C₂	1	2	yes	maximal, complemented
6	#19135645	C₂	1	2	yes	maximal, complemented
7	#19135503	C₂	1	1	yes	maximal, characteristic, complemented
8	#19135383	C₂	1	1	yes	maximal, characteristic, complemented
9	#19135140	C₂	1	2	yes	maximal, complemented
10	#19134395	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄₃×#3067	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#13063350	C₂²	1	2	yes	—
13	C₂×#13063350	C₂²	1	2	yes	—
14	C₂²×D₃₄₄	C₂²	1	1	yes	characteristic
15	#14583666	C₂²	1	2	yes	—
16	#14583463	C₂²	1	2	yes	—
17	#14583285	—	2	2	no	—
18	#14583284	—	2	1	no	—
19	#14583274	—	2	1	no	—
20	#14583169	—	2	2	no	—
21	#14583169	—	2	2	no	—
22	#14583167	—	2	4	no	—
23	#14583164	—	2	4	no	—
24	#14583021	—	2	2	no	—
25	#14583016	—	2	2	no	—
26	#14582947	C₂²	1	2	yes	—
27	C₂×#13063261	C₂²	1	1	yes	characteristic
28	#14582916	C₂²	1	2	yes	—
29	#14582905	C₂²	1	2	yes	—
30	#14582883	C₂²	1	1	yes	characteristic
31	C₂×#13063241	C₂²	1	2	yes	—
32	C₂×#13063241	C₂²	1	2	yes	—
33	#14582873	C₂²	1	1	yes	characteristic
34	#14582854	C₂²	1	1	yes	characteristic
35	#14582854	C₂²	1	1	yes	characteristic
36	#14582670	C₂²	1	1	yes	characteristic
37	#14582670	C₂²	1	2	yes	—
38	#14582670	C₂²	1	1	yes	characteristic
39	C₄₃×#575	C₂²	1	2	yes	—
40	C₂×#135×C₄₃	C₂²	1	1	yes	characteristic
41	C₂×#131×C₄₃	C₂²	1	1	yes	characteristic
42	C₄₃×#473	—	2	1	no	—
43	C₄₃×#472	—	2	1	no	—
44	C₄₃×#471	—	2	2	no	—
45	C₂×#108×C₄₃	C₂²	1	1	yes	characteristic
46	C₄₃×#413	C₂²	1	2	yes	—
47	C₂²×D₁₇₂	C₂³	1	2	yes	—
48	#13063350	—	2	4	no	—
49	#13063350	—	2	4	no	—
50	#13063350	—	4	2	no	—
51	#13063350	—	4	2	no	—
52	C₂×#10621884	—	2	2	no	—
53	C₂×#10621884	—	2	2	no	—
54	C₂×D₃₄₄	—	2	1	no	—
55	C₂×D₃₄₄	—	2	1	no	—
56	C₂×D₃₄₄	—	2	1	no	—
57	C₂×D₃₄₄	—	2	1	no	—
58	C₂×D₃₄₄	—	2	1	no	—
59	C₂×D₃₄₄	—	2	1	no	—
60	C₂×#10621882	—	2	2	no	—
61	C₂×#10621882	—	2	2	no	—
62	#13063332	—	2	4	no	—
63	#13063332	—	2	4	no	—
64	C₂×#10621877	—	4	2	no	—
65	C₂×#10621877	C₂³	1	1	yes	characteristic
66	C₂×#10621877	C₂³	1	1	yes	characteristic
67	C₂×#10621877	C₂³	1	2	yes	—
68	#13063321	—	2	2	no	—
69	#13063314	—	2	2	no	—
70	#13063299	—	4	2	no	—
71	#13063293	—	2	4	no	—
72	#13063284	C₂³	1	1	yes	characteristic
73	#13063284	C₂³	1	1	yes	characteristic
74	#13063261	D₄	1	2	yes	complemented
75	#13063261	D₄	1	2	yes	complemented
76	#13063260	—	2	4	no	—
77	#13063252	—	2	4	no	—
78	#13063247	—	4	2	no	—
79	#13063244	D₄	1	2	yes	complemented
80	#13063242	D₄	1	2	yes	complemented
81	#13063241	—	2	4	no	—
82	#13063241	—	2	4	no	—
83	#13063240	—	2	2	no	—
84	#13063235	—	2	1	no	—
85	#13063235	—	2	1	no	—
86	C₈×Dic₄₃	—	2	1	no	—
87	C₈×Dic₄₃	—	2	1	no	—
88	C₂×#41×C₄₃	C₂³	1	1	yes	characteristic
89	C₂×#41×C₄₃	C₂³	1	2	yes	—
90	#137×C₄₃	—	2	2	no	—
91	#137×C₄₃	—	2	2	no	—
92	AGL(1,ℤ/8)×C₄₃	—	2	2	no	—
93	AGL(1,ℤ/8)×C₄₃	—	2	2	no	—
94	#135×C₄₃	—	2	1	no	—
95	#135×C₄₃	—	2	1	no	—
96	#135×C₄₃	—	2	1	no	—
97	#135×C₄₃	—	2	1	no	—
98	#135×C₄₃	—	4	2	no	—
99	C₂×Q₁₆×C₄₃	D₄	1	1	yes	characteristic
100	C₂×SD₁₆×C₄₃	D₄	1	2	yes	—
101	C₂×D₈×C₄₃	D₄	1	1	yes	characteristic
102	#131×C₄₃	—	2	1	no	—
103	#131×C₄₃	—	2	1	no	—
104	#131×C₄₃	—	2	1	no	—
105	#131×C₄₃	—	2	1	no	—
106	C₂×M₁₆×C₄₃	—	2	1	no	—
107	C₂×M₁₆×C₄₃	C₂³	1	1	yes	characteristic
108	C₂×M₁₆×C₄₃	C₂³	1	2	yes	—
109	C₂²×C₈×C₄₃	—	2	1	no	—
110	C₂²×C₈×C₄₃	C₂³	1	1	yes	characteristic
111	#108×C₄₃	—	2	1	no	—
112	#108×C₄₃	—	2	1	no	—
113	#101×C₄₃	—	2	2	no	—
114	#100×C₄₃	—	2	2	no	—
115	C₂³×D₄₃	—	2	2	no	—
116	#41×C₄₃	—	2	1	no	—
117	#41×C₄₃	—	2	1	no	—
118	#41×C₄₃	—	2	2	no	—
119	#41×C₄₃	—	2	2	no	—
120	#41×C₄₃	—	2	2	no	—
121	#41×C₄₃	—	2	1	no	—
122	#41×C₄₃	—	2	2	no	—
123	#41×C₄₃	—	2	1	no	—
124	C₂×Q₈×C₄₃	C₂×D₄	1	1	yes	characteristic
125	C₂×Q₈×C₄₃	C₂×D₄	1	2	yes	—
126	C₂×D₄×C₄₃	—	2	1	no	—
127	C₂×D₄×C₄₃	—	2	2	no	—
128	C₂×D₄×C₄₃	C₂×D₄	1	1	yes	characteristic
129	C₂×D₄×C₄₃	C₂×D₄	1	2	yes	—
130	C₂²×C₄×C₄₃	—	2	1	no	—
131	C₂²×C₄×C₄₃	—	2	2	no	—
132	C₂²×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
133	C₂×C₂²⋊D₄₃	—	4	4	no	—
134	C₂×D₁₇₂	—	2	2	no	—
135	C₂×D₁₇₂	—	2	2	no	—
136	C₂×D₁₇₂	—	2	2	no	—
137	C₂×D₁₇₂	—	2	2	no	—
138	C₂×D₁₇₂	—	2	2	no	—
139	C₂×D₁₇₂	—	2	2	no	—
140	Q₁₆×C₄₃	—	2	1	no	—
141	Q₁₆×C₄₃	—	2	1	no	—
142	Q₁₆×C₄₃	—	4	2	no	—
143	SD₁₆×C₄₃	—	2	2	no	—
144	SD₁₆×C₄₃	—	2	2	no	—
145	SD₁₆×C₄₃	—	4	2	no	—
146	SD₁₆×C₄₃	—	4	2	no	—
147	D₈×C₄₃	—	2	1	no	—
148	D₈×C₄₃	—	2	1	no	—
149	D₈×C₄₃	—	4	2	no	—
150	M₁₆×C₄₃	—	2	1	no	—
151	M₁₆×C₄₃	—	2	2	no	—
152	M₁₆×C₄₃	—	2	1	no	—
153	M₁₆×C₄₃	—	2	2	no	—
154	M₁₆×C₄₃	—	4	1	no	—
155	M₁₆×C₄₃	—	4	1	no	—
156	C₂×C₈×C₄₃	—	2	1	no	—
157	C₂×C₈×C₄₃	—	2	2	no	—
158	C₂×C₈×C₄₃	—	4	1	no	—
159	C₂×C₈×C₄₃	—	4	1	no	—
160	C₂×C₈×C₄₃	C₂×D₄	1	1	yes	characteristic
161	C₂×C₈×C₄₃	C₂×D₄	1	1	yes	characteristic
162	C₂×C₈×C₄₃	C₂×D₄	1	1	yes	characteristic
163	C₂×C₈×C₄₃	C₂×D₄	1	1	yes	characteristic
164	C₂×C₈×C₄₃	#41	1	1	yes	characteristic
165	C₂×C₈×C₄₃	#41	1	1	yes	characteristic
166	C₂²⋊Dic₄₃	—	2	1	no	—
167	C₂²⋊Dic₄₃	#41	1	2	yes	—
168	#10621884	—	4	4	no	—
169	#10621884	—	4	4	no	—
170	#10621882	—	4	4	no	—
171	#10621882	—	4	4	no	—
172	(C₂×D₄₃)⋊C₄	—	4	4	no	—
173	C₄⋊Dic₄₃	—	2	1	no	—
174	C₄⋊Dic₄₃	—	2	1	no	—
175	C₄×Dic₄₃	—	2	1	no	—
176	C₄×Dic₄₃	—	2	1	no	—
177	#10621877	—	2	1	no	—
178	#10621877	—	2	2	no	—
179	#10621877	—	2	1	no	—
180	#10621877	—	4	4	no	—
181	#10621877	C₂×D₄	1	2	yes	—
182	#10621877	C₂×D₄	1	4	yes	—
183	#10621877	C₂×D₄	1	2	yes	—
184	C₂×C₄₃⋊C₈	—	2	1	no	—
185	C₂×C₄₃⋊C₈	—	2	1	no	—
186	C₂×C₄₃⋊C₈	—	2	2	no	—
187	C₂×C₄₃⋊C₈	—	4	4	no	—
188	D₃₄₄	—	4	1	no	—
189	D₃₄₄	—	4	1	no	—
190	D₃₄₄	—	4	1	no	—
191	D₃₄₄	—	4	1	no	—
192	C₂³×C₄₃	—	2	1	no	—
193	C₂³×C₄₃	—	2	2	no	—
194	C₂³×C₄₃	C₂×#41	1	1	yes	characteristic
195	C₂²×D₄₃	—	4	2	no	—
196	C₂²×D₄₃	—	4	2	no	—
197	C₂²×D₄₃	—	4	2	no	—
198	C₂²×D₄₃	—	16	2	no	—
199	Q₈×C₄₃	—	2	2	no	—
200	Q₈×C₄₃	—	2	1	no	—
201	Q₈×C₄₃	—	2	2	no	—
202	Q₈×C₄₃	—	2	1	no	—
203	D₄×C₄₃	—	2	2	no	—
204	D₄×C₄₃	—	2	1	no	—
205	D₄×C₄₃	—	2	2	no	—
206	D₄×C₄₃	—	2	1	no	—
207	D₄×C₄₃	—	4	2	no	—
208	D₄×C₄₃	—	4	1	no	—
209	D₄×C₄₃	—	4	1	no	—
210	D₄×C₄₃	—	4	2	no	—
211	C₂×C₄×C₄₃	—	2	1	no	—
212	C₂×C₄×C₄₃	—	2	2	no	—
213	C₂×C₄×C₄₃	—	4	1	no	—
214	C₂×C₄×C₄₃	—	4	1	no	—
215	C₂×C₄×C₄₃	—	4	2	no	—
216	C₂×C₄×C₄₃	—	4	2	no	—
217	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
218	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
219	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
220	C₂×C₄×C₄₃	C₂×#41	1	1	yes	characteristic
221	C₂×C₄×C₄₃	H(5,𝔽₂)	1	1	yes	characteristic
222	C₂×C₄×C₄₃	H(5,𝔽₂)	1	1	yes	characteristic
223	C₂²⋊D₄₃	—	16	4	no	—
224	C₂×Dic₄₃	—	2	2	no	—
225	C₂×Dic₄₃	—	4	1	no	—
226	D₁₇₂	—	4	2	no	—
227	D₁₇₂	—	4	2	no	—
228	D₁₇₂	—	4	2	no	—
229	D₁₇₂	—	4	2	no	—
230	C₈×C₄₃	—	4	1	no	—
231	C₈×C₄₃	—	4	2	no	—
232	C₈×C₄₃	#121	1	1	yes	characteristic
233	C₈×C₄₃	#121	1	1	yes	characteristic
234	C₈×C₄₃	#121	1	1	yes	characteristic
235	C₈×C₄₃	#121	1	1	yes	characteristic
236	C₄₃⋊C₈	—	2	2	no	—
237	C₄₃⋊C₈	—	2	4	no	—
238	C₄₃⋊C₈	—	2	2	no	—
239	#25447	—	43	1	no	maximal, Sylow
240	C₂²×C₄₃	—	4	1	no	—
241	C₂²×C₄₃	—	4	1	no	—
242	C₂²×C₄₃	—	4	2	no	—
243	C₂²×C₄₃	—	8	1	no	—
244	C₂²×C₄₃	—	8	2	no	—
245	C₂²×C₄₃	#532	1	1	yes	characteristic
246	C₂²×C₄₃	#546	1	1	yes	characteristic
247	C₂²×C₄₃	#550	1	1	yes	characteristic
248	C₂×D₄₃	—	8	4	no	—
249	C₂×D₄₃	—	8	2	no	—
250	C₂×D₄₃	—	16	2	no	—
251	C₂×D₄₃	—	16	2	no	—
252	C₄×C₄₃	—	4	1	no	—
253	C₄×C₄₃	—	4	2	no	—
254	C₄×C₄₃	C₂×#121	1	1	yes	characteristic
255	C₄×C₄₃	#540	1	1	yes	characteristic
256	C₄×C₄₃	D₄²	1	1	yes	characteristic
257	C₄×C₄₃	D₄²	1	1	yes	characteristic
258	Dic₄₃	—	4	2	no	—
259	Dic₄₃	—	8	1	no	—
260	#3155	—	43	1	no	—
261	#3068	—	43	2	no	—
262	#3067	D₄₃	1	1	yes	characteristic, complemented
263	C₂×#472	—	43	1	no	—
264	#2957	—	43	1	no	—
265	#2048	—	43	2	no	—
266	#2008	—	43	2	no	—
267	#1978	—	43	1	no	—
268	#1953	—	43	1	no	—
269	#1914	—	43	2	no	—
270	#1757	—	43	1	no	—
271	C₂×C₄₃	—	2	1	no	—
272	C₂×C₄₃	—	2	1	no	—
273	C₂×C₄₃	—	2	1	no	—
274	C₂×C₄₃	—	8	1	no	—
275	C₂×C₄₃	—	8	2	no	—
276	C₂×C₄₃	#2428	1	1	yes	characteristic
277	D₄₃	—	16	2	no	—
278	#575	C₂×D₄₃	1	2	yes	—
279	C₂×AGL(1,ℤ/8)	—	43	2	no	—
280	C₂×AGL(1,ℤ/8)	—	43	2	no	—
281	C₂×#135	C₂×D₄₃	1	1	yes	characteristic
282	C₂²×D₈	—	43	1	no	—
283	#568	—	43	2	no	—
284	C₂×#131	C₂×D₄₃	1	1	yes	characteristic
285	#535	—	43	2	no	—
286	#496	—	86	2	no	—
287	#495	—	86	1	no	—
288	#493	—	86	1	no	—
289	#473	—	2	1	no	—
290	#472	—	2	1	no	—
291	#472	—	86	4	no	—
292	#472	—	86	2	no	—
293	#472	—	86	2	no	—
294	#471	—	2	2	no	—
295	#471	—	86	4	no	—
296	#444	—	86	2	no	—
297	#443	—	86	2	no	—
298	#430	—	43	2	no	—
299	C₂×#108	—	43	1	no	—
300	C₂×#108	C₂×D₄₃	1	1	yes	characteristic
301	#421	—	43	2	no	—
302	#418	—	43	2	no	—
303	#413	—	43	1	no	—
304	#413	C₂×D₄₃	1	2	yes	—
305	C₂×#100	—	43	2	no	—
306	C₂×#100	—	43	2	no	—
307	#410	—	43	1	no	—
308	#405	—	43	1	no	—
309	#405	—	43	1	no	—
310	#344	—	43	1	no	—
311	#344	—	43	1	no	—
312	#344	—	43	2	no	—
313	C₄₃	#25447	1	1	yes	characteristic, complemented, Sylow
314	C₂×#41	C₂²×D₄₃	1	1	yes	characteristic
315	C₂×#41	C₂²×D₄₃	1	2	yes	—
316	C₂²×D₄	—	43	2	no	—
317	#137	—	2	2	no	—
318	#137	—	2	2	no	—
319	AGL(1,ℤ/8)	—	2	2	no	—
320	AGL(1,ℤ/8)	—	2	2	no	—
321	AGL(1,ℤ/8)	—	86	4	no	—
322	AGL(1,ℤ/8)	—	86	4	no	—
323	AGL(1,ℤ/8)	—	172	2	no	—
324	AGL(1,ℤ/8)	—	172	2	no	—
325	#135	—	2	1	no	—
326	#135	—	2	1	no	—
327	#135	—	2	1	no	—
328	#135	—	2	1	no	—
329	#135	—	4	2	no	—
330	C₂×Q₁₆	C₂²⋊D₄₃	1	1	yes	characteristic
331	C₂×SD₁₆	—	86	2	no	—
332	C₂×SD₁₆	—	86	2	no	—
333	C₂×SD₁₆	C₂²⋊D₄₃	1	2	yes	—
334	C₂×D₈	—	86	2	no	—
335	C₂×D₈	—	86	2	no	—
336	C₂×D₈	—	86	1	no	—
337	C₂×D₈	—	86	1	no	—
338	C₂×D₈	—	86	1	no	—
339	C₂×D₈	—	86	1	no	—
340	C₂×D₈	—	86	1	no	—
341	C₂×D₈	—	86	1	no	—
342	C₂×D₈	C₂²⋊D₄₃	1	1	yes	characteristic
343	#131	—	2	1	no	—
344	#131	—	2	1	no	—
345	#131	—	2	1	no	—
346	#131	—	2	1	no	—
347	#131	—	86	4	no	—
348	#131	—	86	4	no	—
349	C₂×M₁₆	—	2	1	no	—
350	C₂×M₁₆	—	43	1	no	—
351	C₂×M₁₆	—	43	2	no	—
352	C₂×M₁₆	—	43	1	no	—
353	C₂×M₁₆	—	172	2	no	—
354	C₂×M₁₆	C₂²×D₄₃	1	1	yes	characteristic
355	C₂×M₁₆	C₂²×D₄₃	1	2	yes	—
356	C₂²×C₈	—	2	1	no	—
357	C₂²×C₈	C₂²×D₄₃	1	1	yes	characteristic
358	#127	—	86	2	no	—
359	#124	—	86	2	no	—
360	#121	—	172	2	no	—
361	#120	—	86	4	no	—
362	#117	—	43	1	no	—
363	#117	—	43	1	no	—
364	#108	—	2	1	no	—
365	#108	—	2	1	no	—
366	#108	—	43	2	no	—
367	#108	—	43	2	no	—
368	#108	—	86	4	no	—
369	#104	—	86	4	no	—
370	#102	—	172	2	no	—
371	#101	—	2	2	no	—
372	#101	—	43	2	no	—
373	#100	—	2	2	no	—
374	#100	—	43	2	no	—
375	#100	—	86	4	no	—
376	#100	—	86	4	no	—
377	#99	—	86	2	no	—
378	#97	—	86	1	no	—
379	#97	—	86	1	no	—
380	C₄×C₈	—	86	1	no	—
381	C₄×C₈	—	86	1	no	—
382	C₂⁴	—	86	2	no	—
383	#41	—	2	2	no	—
384	#41	—	2	1	no	—
385	#41	—	2	2	no	—
386	#41	—	2	1	no	—
387	#41	—	2	2	no	—
388	#41	—	2	1	no	—
389	#41	—	2	2	no	—
390	#41	—	2	1	no	—
391	C₂×Q₈	D₄×D₄₃	1	1	yes	characteristic
392	C₂×Q₈	C₂×C₂²⋊D₄₃	1	2	yes	—
393	C₂×D₄	—	2	1	no	—
394	C₂×D₄	—	2	2	no	—
395	C₂×D₄	—	86	2	no	—
396	C₂×D₄	—	86	2	no	—
397	C₂×D₄	—	86	2	no	—
398	C₂×D₄	—	86	2	no	—
399	C₂×D₄	—	86	2	no	—
400	C₂×D₄	—	86	2	no	—
401	C₂×D₄	—	172	4	no	—
402	C₂×D₄	D₄×D₄₃	1	1	yes	characteristic
403	C₂×D₄	C₂×C₂²⋊D₄₃	1	2	yes	—
404	C₂²×C₄	—	2	1	no	—
405	C₂²×C₄	—	2	2	no	—
406	C₂²×C₄	C₂³×D₄₃	1	1	yes	characteristic
407	Q₁₆	—	2	1	no	—
408	Q₁₆	—	2	1	no	—
409	Q₁₆	—	4	2	no	—
410	SD₁₆	—	2	2	no	—
411	SD₁₆	—	2	2	no	—
412	SD₁₆	—	4	2	no	—
413	SD₁₆	—	4	2	no	—
414	SD₁₆	—	172	4	no	—
415	SD₁₆	—	172	4	no	—
416	D₈	—	2	1	no	—
417	D₈	—	2	1	no	—
418	D₈	—	4	2	no	—
419	D₈	—	172	4	no	—
420	D₈	—	172	4	no	—
421	D₈	—	172	1	no	—
422	D₈	—	172	1	no	—
423	D₈	—	172	1	no	—
424	D₈	—	172	1	no	—
425	M₁₆	—	2	1	no	—
426	M₁₆	—	2	2	no	—
427	M₁₆	—	2	1	no	—
428	M₁₆	—	2	2	no	—
429	M₁₆	—	4	1	no	—
430	M₁₆	—	4	1	no	—
431	M₁₆	—	43	2	no	—
432	M₁₆	—	43	2	no	—
433	M₁₆	—	43	4	no	—
434	M₁₆	—	86	1	no	—
435	M₁₆	—	86	1	no	—
436	M₁₆	—	86	2	no	—
437	M₁₆	—	172	4	no	—
438	C₂×C₈	—	2	1	no	—
439	C₂×C₈	—	2	2	no	—
440	C₂×C₈	—	4	1	no	—
441	C₂×C₈	—	4	1	no	—
442	C₂×C₈	—	86	1	no	—
443	C₂×C₈	—	86	2	no	—
444	C₂×C₈	—	86	1	no	—
445	C₂×C₈	—	172	4	no	—
446	C₂×C₈	D₄×D₄₃	1	1	yes	characteristic
447	C₂×C₈	D₄×D₄₃	1	1	yes	characteristic
448	C₂×C₈	#10621900	1	1	yes	characteristic
449	C₂×C₈	#10621900	1	1	yes	characteristic
450	C₂×C₈	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
451	C₂×C₈	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
452	C₄⋊C₄	—	86	1	no	—
453	C₄⋊C₄	—	86	1	no	—
454	C₂²⋊C₄	—	43	2	no	—
455	C₂²⋊C₄	—	86	1	no	—
456	C₂²⋊C₄	—	172	4	no	—
457	C₄²	—	86	1	no	—
458	C₄²	—	86	1	no	—
459	C₂³	—	2	1	no	—
460	C₂³	—	2	2	no	—
461	C₂³	—	172	2	no	—
462	C₂³	—	172	2	no	—
463	C₂³	—	172	2	no	—
464	C₂³	—	688	2	no	—
465	C₂³	#41×D₄₃	1	1	yes	characteristic
466	Q₈	—	2	2	no	—
467	Q₈	—	2	1	no	—
468	Q₈	—	2	2	no	—
469	Q₈	—	2	1	no	—
470	D₄	—	2	2	no	—
471	D₄	—	2	1	no	—
472	D₄	—	2	2	no	—
473	D₄	—	2	1	no	—
474	D₄	—	4	1	no	—
475	D₄	—	4	2	no	—
476	D₄	—	4	2	no	—
477	D₄	—	4	1	no	—
478	D₄	—	172	2	no	—
479	D₄	—	172	2	no	—
480	D₄	—	172	2	no	—
481	D₄	—	172	2	no	—
482	D₄	—	688	4	no	—
483	C₂×C₄	—	2	1	no	—
484	C₂×C₄	—	2	2	no	—
485	C₂×C₄	—	4	1	no	—
486	C₂×C₄	—	4	1	no	—
487	C₂×C₄	—	4	2	no	—
488	C₂×C₄	—	4	2	no	—
489	C₂×C₄	—	86	2	no	—
490	C₂×C₄	—	172	1	no	—
491	C₂×C₄	C₂×D₄×D₄₃	1	1	yes	characteristic
492	C₂×C₄	C₂×D₄×D₄₃	1	1	yes	characteristic
493	C₂×C₄	C₂²×C₂²⋊D₄₃	1	1	yes	characteristic
494	C₂×C₄	C₂×#10621900	1	1	yes	characteristic
495	C₂×C₄	#13063370	1	1	yes	characteristic
496	C₂×C₄	#13063371	1	1	yes	characteristic
497	C₈	—	4	1	no	—
498	C₈	—	4	2	no	—
499	C₈	—	86	2	no	—
500	C₈	—	86	2	no	—
501	C₈	—	86	4	no	—
502	C₈	#13063297	1	1	yes	characteristic
503	C₈	#13063297	1	1	yes	characteristic
504	C₈	#13063297	1	1	yes	characteristic
505	C₈	#13063297	1	1	yes	characteristic
506	C₂²	—	4	1	no	—
507	C₂²	—	4	1	no	—
508	C₂²	—	4	2	no	—
509	C₂²	—	8	2	no	—
510	C₂²	—	8	1	no	—
511	C₂²	—	344	4	no	—
512	C₂²	—	344	2	no	—
513	C₂²	—	688	2	no	—
514	C₂²	—	688	2	no	—
515	C₂²	#14583444	1	1	yes	characteristic
516	C₂²	#14583537	1	1	yes	characteristic
517	C₂²	#14583567	1	1	yes	characteristic
518	C₄	—	4	1	no	—
519	C₄	—	4	2	no	—
520	C₄	—	344	1	no	—
521	C₄	—	172	2	no	—
522	C₄	C₂×#13063297	1	1	yes	characteristic
523	C₄	#14583502	1	1	yes	characteristic
524	C₄	D₄×C₂²⋊D₄₃	1	1	yes	characteristic
525	C₄	#14583533	1	1	yes	characteristic
526	C₂	—	2	1	no	—
527	C₂	—	2	1	no	—
528	C₂	—	2	1	no	—
529	C₂	—	8	2	no	—
530	C₂	—	8	1	no	—
531	C₂	—	688	2	no	—
532	C₂	#19138185	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#19138185
commutator, cosocle	C₂²×C₄×C₄₃	C₂⁴
Frattini	C₂²×C₄	C₂³×D₄₃
Fitting	C₄₃×#3067	C₂
socle	C₂×C₄₃	#2428
hypercenter	#3067	D₄₃
hypocenter	C₄₃	#25447
LCS	G ▷ C₂²×C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂ ◁ C₂²×C₄ ◁ #3067

Complements

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

N	H ≅ G/N	type
1. #19145082	C₂	semidirect
2. #19144325	C₂	semidirect
3. C₂×#14583169	C₂	semidirect
4. #19143512	C₂	semidirect
5. #19135868	C₂	semidirect
6. #19135645	C₂	semidirect
7. #19135503	C₂	semidirect
8. #19135383	C₂	semidirect
9. #19135140	C₂	semidirect
10. #19134395	C₂	semidirect
11. C₄₃×#3067	C₂	semidirect
74. #13063261	D₄	semidirect
75. #13063261	D₄	semidirect
79. #13063244	D₄	semidirect
80. #13063242	D₄	semidirect
262. #3067	D₄₃	semidirect
313. C₄₃	#25447	semidirect

Maximal subgroups

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

subgroup	index
#19145082	2
#19144325	2
C₂×#14583169	2
#19143512	2
#19135868	2
#19135645	2
#19135503	2
#19135383	2
#19135140	2
#19134395	2
C₄₃×#3067	2
#25447	43