Subgroups — #25079464

Order 11008.

682 conjugacy classes of subgroups.

The subgroup lattice has 490 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#19145054	C₂	1	1	yes	maximal, characteristic
2	#19144626	C₂	1	1	yes	maximal, characteristic
3	C₂×#14583184	C₂	1	1	yes	maximal, characteristic, complemented
4	#19134089	C₂	1	2	yes	maximal, complemented
5	#19134067	C₂	1	2	yes	maximal, complemented
6	#19133965	C₂	1	2	yes	maximal, complemented
7	#19133943	C₂	1	2	yes	maximal, complemented
8	#19133347	C₂	1	1	yes	maximal, characteristic, complemented
9	#19133273	C₂	1	1	yes	maximal, characteristic
10	#19133268	C₂	1	1	yes	maximal, characteristic, complemented
11	Q₈×M₁₆×C₄₃	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#13063358	—	2	1	no	—
13	C₂×#13063358	—	2	1	no	—
14	#14583449	C₂²	1	1	yes	characteristic
15	C₂×#13063325	C₂²	1	1	yes	characteristic
16	#14583293	—	2	2	no	—
17	#14583279	C₂²	1	2	yes	—
18	#14583272	C₂²	1	2	yes	—
19	#14583217	—	2	1	no	—
20	#14583184	—	2	1	no	—
21	#14583184	—	2	1	no	—
22	#14583184	C₂²	1	1	yes	characteristic
23	#14583184	C₂²	1	2	yes	—
24	#14583184	C₂²	1	2	yes	—
25	#14583184	C₂²	1	1	yes	characteristic
26	#14583099	C₂²	1	1	yes	characteristic
27	#14583099	C₂²	1	1	yes	characteristic
28	#14583038	—	2	1	no	—
29	C₄×#10621884	—	2	1	no	—
30	C₄×#10621884	—	2	1	no	—
31	#14582952	C₂²	1	1	yes	characteristic
32	C₂×#13063256	—	2	1	no	—
33	C₂×C₄⋊(C₄₃⋊C₈)	C₂²	1	1	yes	characteristic
34	C₂×#13063249	—	2	1	no	—
35	#14582652	C₂²	1	2	yes	—
36	#14582650	C₂²	1	2	yes	—
37	#14582646	C₂²	1	2	yes	—
38	#14582646	C₂²	1	2	yes	—
39	#14582646	C₂²	1	2	yes	—
40	#14582642	C₂²	1	2	yes	—
41	C₂×C₄×Q₈×C₄₃	C₂²	1	1	yes	characteristic
42	C₄₃×#446	—	2	2	no	—
43	C₄₃×#446	C₂²	1	2	yes	—
44	C₈×Q₈×C₄₃	C₂²	1	2	yes	—
45	C₄₃×#423	—	2	1	no	—
46	C₄₃×#423	C₂²	1	1	yes	characteristic
47	C₄×M₁₆×C₄₃	—	2	1	no	—
48	C₄×M₁₆×C₄₃	C₂²	1	1	yes	characteristic
49	C₂×#10621898	—	2	1	no	—
50	C₂²×Dic₈₆	—	2	1	no	—
51	#13063358	—	4	4	no	—
52	#13063358	—	4	4	no	—
53	C₂×Dic₁₇₂	—	2	2	no	—
54	C₂×Dic₁₇₂	—	2	2	no	—
55	C₂×#10621873	—	2	2	no	—
56	C₂×#10621873	—	2	2	no	—
57	C₂×#10621884	—	2	1	no	—
58	C₂×#10621884	—	2	1	no	—
59	C₂²×C₄₃⋊C₈	—	2	1	no	—
60	#13063325	—	2	1	no	—
61	#13063325	—	2	1	no	—
62	#13063325	—	2	1	no	—
63	#13063325	C₂³	1	2	yes	—
64	#13063325	C₂³	1	1	yes	characteristic
65	#13063322	C₂³	1	1	yes	characteristic
66	#13063313	—	2	1	no	—
67	#13063299	—	2	1	no	—
68	#13063299	—	2	1	no	—
69	C₄×D₁₇₂	—	2	1	no	—
70	C₄×D₁₇₂	—	2	1	no	—
71	C₂×C₄⋊Dic₄₃	—	2	1	no	—
72	C₂×C₄⋊Dic₄₃	—	2	1	no	—
73	#13063256	—	2	2	no	—
74	#13063256	—	2	2	no	—
75	#13063256	—	2	1	no	—
76	#13063256	—	2	1	no	—
77	C₄⋊(C₄₃⋊C₈)	—	2	1	no	—
78	C₄⋊(C₄₃⋊C₈)	C₂³	1	1	yes	characteristic
79	C₄⋊(C₄₃⋊C₈)	C₂³	1	1	yes	characteristic
80	C₄⋊(C₄₃⋊C₈)	C₂³	1	2	yes	—
81	#13063249	—	2	2	no	—
82	#13063249	—	2	2	no	—
83	#13063249	—	2	1	no	—
84	#13063249	—	2	1	no	—
85	#13063245	—	2	1	no	—
86	#13063245	—	2	1	no	—
87	C₂²⋊(C₄₃⋊C₈)	—	2	1	no	—
88	C₄×C₄₃⋊C₈	—	2	1	no	—
89	C₂²×Q₈×C₄₃	D₄	1	1	yes	characteristic
90	C₂×M₁₆×C₄₃	—	2	1	no	—
91	C₂×M₁₆×C₄₃	D₄	1	1	yes	characteristic
92	C₂×M₁₆×C₄₃	D₄	1	1	yes	characteristic
93	C₄×Q₈×C₄₃	—	2	1	no	—
94	C₄×Q₈×C₄₃	—	2	1	no	—
95	C₄×Q₈×C₄₃	D₄	1	1	yes	characteristic
96	C₄×Q₈×C₄₃	D₄	1	1	yes	characteristic
97	C₄×Q₈×C₄₃	C₂³	1	1	yes	characteristic
98	C₄×Q₈×C₄₃	C₂³	1	1	yes	characteristic
99	C₂×C₄⋊C₄×C₄₃	—	2	1	no	—
100	C₂×C₄⋊C₄×C₄₃	D₄	1	1	yes	characteristic
101	C₂×C₄²×C₄₃	—	2	1	no	—
102	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
103	C₄⋊C₈×C₄₃	—	2	2	no	—
104	C₄⋊C₈×C₄₃	—	2	2	no	—
105	C₄⋊C₈×C₄₃	—	2	1	no	—
106	C₄⋊C₈×C₄₃	C₂³	1	2	yes	—
107	#97×C₄₃	—	2	2	no	—
108	#97×C₄₃	D₄	1	2	yes	—
109	C₄×C₈×C₄₃	—	2	2	no	—
110	C₄×C₈×C₄₃	C₂³	1	2	yes	—
111	C₂×Q₈×C₄₃	—	2	1	no	—
112	C₂×Q₈×C₄₃	—	2	2	no	—
113	C₂×Q₈×C₄₃	—	4	1	no	—
114	C₂×Q₈×C₄₃	C₂×D₄	1	1	yes	characteristic
115	C₂×Q₈×C₄₃	C₂×D₄	1	1	yes	characteristic
116	C₂²×C₄×C₄₃	—	2	1	no	—
117	C₂²×C₄×C₄₃	—	2	1	no	—
118	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
119	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
120	C₂²×C₄×C₄₃	#41	1	1	yes	characteristic
121	C₂×C₂²⋊D₄₃	—	4	1	no	—
122	C₂²×Dic₄₃	—	4	1	no	—
123	#10621898	—	4	2	no	—
124	#10621898	—	4	2	no	—
125	C₂×D₁₇₂	—	2	1	no	—
126	C₂×D₁₇₂	—	2	1	no	—
127	C₂×D₁₇₂	—	2	1	no	—
128	C₂×C₄×D₄₃	—	4	1	no	—
129	C₂×Dic₈₆	—	2	1	no	—
130	C₂×Dic₈₆	—	2	2	no	—
131	C₂×Dic₈₆	—	4	2	no	—
132	C₂×Dic₈₆	—	4	2	no	—
133	C₂×Dic₈₆	—	4	1	no	—
134	M₁₆×C₄₃	—	2	2	no	—
135	M₁₆×C₄₃	—	4	2	no	—
136	M₁₆×C₄₃	SD₁₆	1	4	yes	complemented
137	C₂×C₈×C₄₃	—	2	2	no	—
138	C₂×C₈×C₄₃	C₂×D₄	1	2	yes	—
139	C₂×C₈×C₄₃	C₂×D₄	1	2	yes	—
140	C₄⋊C₄×C₄₃	—	2	1	no	—
141	C₄⋊C₄×C₄₃	—	2	1	no	—
142	C₄⋊C₄×C₄₃	—	2	1	no	—
143	C₄⋊C₄×C₄₃	—	2	1	no	—
144	C₄⋊C₄×C₄₃	—	2	1	no	—
145	C₄⋊C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
146	C₄⋊C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
147	C₄²×C₄₃	—	2	1	no	—
148	C₄²×C₄₃	—	2	1	no	—
149	C₄²×C₄₃	—	2	1	no	—
150	C₄²×C₄₃	—	2	1	no	—
151	C₄²×C₄₃	C₂×D₄	1	1	yes	characteristic
152	C₄²×C₄₃	C₂×D₄	1	1	yes	characteristic
153	C₄²×C₄₃	#41	1	1	yes	characteristic
154	C₄²×C₄₃	C₂⁴	1	1	yes	characteristic
155	#10621884	—	4	2	no	—
156	#10621884	—	4	2	no	—
157	(C₂×D₄₃)⋊C₄	—	4	1	no	—
158	(C₂×D₄₃)⋊C₄	—	4	1	no	—
159	C₄⋊Dic₄₃	—	2	2	no	—
160	C₄⋊Dic₄₃	—	2	1	no	—
161	C₄⋊Dic₄₃	—	2	2	no	—
162	C₄⋊Dic₄₃	—	2	1	no	—
163	C₄⋊Dic₄₃	—	4	1	no	—
164	C₄⋊Dic₄₃	—	4	1	no	—
165	C₂×C₄₃⋊C₈	—	2	1	no	—
166	C₂×C₄₃⋊C₈	—	2	1	no	—
167	C₂×C₄₃⋊C₈	—	2	2	no	—
168	C₂×C₄₃⋊C₈	—	4	2	no	—
169	Dic₁₇₂	—	4	4	no	—
170	Dic₁₇₂	—	4	4	no	—
171	#10621873	—	4	4	no	—
172	#10621873	—	4	4	no	—
173	C₂³×C₄₃	#121	1	1	yes	characteristic
174	C₂²×D₄₃	—	4	1	no	—
175	Q₈×C₄₃	—	2	1	no	—
176	Q₈×C₄₃	—	2	1	no	—
177	Q₈×C₄₃	—	2	1	no	—
178	Q₈×C₄₃	—	4	2	no	—
179	Q₈×C₄₃	#137	1	2	yes	complemented
180	C₂×C₄×C₄₃	—	2	1	no	—
181	C₂×C₄×C₄₃	—	2	1	no	—
182	C₂×C₄×C₄₃	—	2	1	no	—
183	C₂×C₄×C₄₃	—	2	1	no	—
184	C₂×C₄×C₄₃	—	2	1	no	—
185	C₂×C₄×C₄₃	—	2	1	no	—
186	C₂×C₄×C₄₃	—	4	1	no	—
187	C₂×C₄×C₄₃	—	4	2	no	—
188	C₂×C₄×C₄₃	—	8	1	no	—
189	C₂×C₄×C₄₃	#121	1	1	yes	characteristic
190	C₂×C₄×C₄₃	#121	1	1	yes	characteristic
191	C₂×C₄×C₄₃	#121	1	1	yes	characteristic
192	C₂×C₄×C₄₃	C₂×SD₁₆	1	2	yes	—
193	C₂×C₄×C₄₃	AGL(1,ℤ/8)	1	2	yes	—
194	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
195	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
196	C₂×C₄×C₄₃	C₂×#41	1	1	yes	characteristic
197	C₂²⋊D₄₃	—	8	2	no	—
198	C₂×Dic₄₃	—	4	2	no	—
199	C₂×Dic₄₃	—	4	1	no	—
200	C₂×Dic₄₃	—	8	2	no	—
201	D₁₇₂	—	4	1	no	—
202	D₁₇₂	—	4	1	no	—
203	D₁₇₂	—	4	1	no	—
204	D₁₇₂	—	4	1	no	—
205	D₁₇₂	—	8	1	no	—
206	C₄×D₄₃	—	8	2	no	—
207	Dic₈₆	—	4	2	no	—
208	Dic₈₆	—	4	1	no	—
209	Dic₈₆	—	4	2	no	—
210	Dic₈₆	—	4	1	no	—
211	Dic₈₆	—	8	2	no	—
212	C₈×C₄₃	—	2	2	no	—
213	C₈×C₄₃	—	4	2	no	—
214	C₈×C₄₃	C₂×SD₁₆	1	4	yes	—
215	C₄₃⋊C₈	—	4	1	no	—
216	C₄₃⋊C₈	—	4	2	no	—
217	C₄₃⋊C₈	—	4	1	no	—
218	#19171	—	43	1	no	maximal, Sylow
219	C₂²×C₄₃	—	2	1	no	—
220	C₂²×C₄₃	—	2	1	no	—
221	C₂²×C₄₃	#460	1	2	yes	—
222	C₂²×C₄₃	C₂×#121	1	1	yes	characteristic
223	C₂×D₄₃	—	8	1	no	—
224	C₂×D₄₃	—	8	1	no	—
225	C₂×D₄₃	—	8	1	no	—
226	C₄×C₄₃	—	2	1	no	—
227	C₄×C₄₃	—	2	2	no	—
228	C₄×C₄₃	—	2	1	no	—
229	C₄×C₄₃	—	2	1	no	—
230	C₄×C₄₃	—	4	1	no	—
231	C₄×C₄₃	—	4	1	no	—
232	C₄×C₄₃	—	4	1	no	—
233	C₄×C₄₃	#460	1	2	yes	—
234	C₄×C₄₃	C₂²×SD₁₆	1	1	yes	characteristic
235	C₄×C₄₃	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
236	C₄×C₄₃	C₂×#137	1	1	yes	characteristic
237	C₄×C₄₃	#575	1	1	yes	characteristic
238	Dic₄₃	—	8	2	no	—
239	Dic₄₃	—	8	1	no	—
240	#3152	—	43	1	no	—
241	#3103	—	43	1	no	—
242	C₂×#475	—	43	1	no	—
243	Q₈×M₁₆	D₄₃	1	1	yes	characteristic, complemented
244	#1690	—	43	2	no	—
245	#1686	—	43	2	no	—
246	#1670	—	43	2	no	—
247	#1666	—	43	2	no	—
248	#1565	—	43	1	no	—
249	#1547	—	43	1	no	—
250	#1546	—	43	1	no	—
251	C₂×C₄₃	—	2	2	no	—
252	C₂×C₄₃	C₂×#460	1	1	yes	characteristic
253	C₂×C₄₃	#3056	1	1	yes	characteristic
254	C₂×C₄₃	#3069	1	1	yes	characteristic
255	D₄₃	—	16	1	no	—
256	C₂×#137	—	86	1	no	—
257	C₂×#137	—	86	1	no	—
258	#532	—	43	1	no	—
259	C₂×C₄⋊Q₈	—	43	1	no	—
260	C₂×C₄×Q₈	C₂×D₄₃	1	1	yes	characteristic
261	#497	—	86	2	no	—
262	#494	—	43	2	no	—
263	#492	—	43	2	no	—
264	#481	—	86	1	no	—
265	#475	—	43	2	no	—
266	#475	—	43	2	no	—
267	#475	—	43	1	no	—
268	#475	—	43	1	no	—
269	#475	—	86	1	no	—
270	#475	—	86	1	no	—
271	#460	—	43	1	no	—
272	#460	—	43	1	no	—
273	#448	—	86	1	no	—
274	#446	—	2	2	no	—
275	#446	C₂×D₄₃	1	2	yes	—
276	C₈×Q₈	C₂×D₄₃	1	2	yes	—
277	C₄×SD₁₆	—	86	1	no	—
278	C₄×SD₁₆	—	86	1	no	—
279	#431	—	43	1	no	—
280	C₂×#106	—	86	1	no	—
281	#423	—	2	1	no	—
282	#423	C₂×D₄₃	1	1	yes	characteristic
283	C₂×C₄⋊C₈	—	43	1	no	—
284	C₂×#103	—	86	1	no	—
285	C₄×M₁₆	—	2	1	no	—
286	C₄×M₁₆	C₂×D₄₃	1	1	yes	characteristic
287	#335	—	43	2	no	—
288	#334	—	43	2	no	—
289	#332	—	43	2	no	—
290	#332	—	43	2	no	—
291	#332	—	43	2	no	—
292	#331	—	43	2	no	—
293	C₄₃	#19171	1	1	yes	characteristic, complemented, Sylow
294	C₂×#41	—	86	1	no	—
295	C₂²×Q₈	—	86	1	no	—
296	C₂²×Q₈	D₁₇₂	1	1	yes	characteristic
297	#137	—	172	4	no	—
298	#137	—	172	4	no	—
299	C₂×Q₁₆	—	86	2	no	—
300	C₂×Q₁₆	—	86	2	no	—
301	C₂×SD₁₆	—	86	1	no	—
302	C₂×SD₁₆	—	86	1	no	—
303	C₂×SD₁₆	—	86	2	no	—
304	C₂×SD₁₆	—	86	2	no	—
305	C₂×M₁₆	—	2	1	no	—
306	C₂×M₁₆	C₂²⋊D₄₃	1	1	yes	characteristic
307	C₂×M₁₆	C₂²⋊D₄₃	1	1	yes	characteristic
308	C₂²×C₈	—	86	1	no	—
309	C₄⋊Q₈	—	43	2	no	—
310	C₄⋊Q₈	—	43	1	no	—
311	C₄⋊Q₈	—	86	1	no	—
312	C₄⋊Q₈	—	86	1	no	—
313	C₄⋊Q₈	—	86	1	no	—
314	#127	—	43	1	no	—
315	#124	—	86	1	no	—
316	#121	—	86	1	no	—
317	#121	—	86	1	no	—
318	C₄×Q₈	—	2	1	no	—
319	C₄×Q₈	—	2	1	no	—
320	C₄×Q₈	D₁₇₂	1	1	yes	characteristic
321	C₄×Q₈	D₁₇₂	1	1	yes	characteristic
322	C₄×Q₈	C₂²×D₄₃	1	1	yes	characteristic
323	C₄×Q₈	C₂²×D₄₃	1	1	yes	characteristic
324	C₄×D₄	—	86	1	no	—
325	C₄×D₄	—	86	1	no	—
326	C₂×C₄⋊C₄	—	2	1	no	—
327	C₂×C₄⋊C₄	—	86	1	no	—
328	C₂×C₄⋊C₄	—	86	1	no	—
329	C₂×C₄⋊C₄	D₁₇₂	1	1	yes	characteristic
330	C₂×C₄²	—	2	1	no	—
331	C₂×C₄²	C₂²×D₄₃	1	1	yes	characteristic
332	#106	—	86	2	no	—
333	#106	—	86	2	no	—
334	#106	—	86	1	no	—
335	#106	—	86	1	no	—
336	C₄⋊C₈	—	2	2	no	—
337	C₄⋊C₈	—	2	2	no	—
338	C₄⋊C₈	—	2	1	no	—
339	C₄⋊C₈	—	43	2	no	—
340	C₄⋊C₈	—	43	1	no	—
341	C₄⋊C₈	—	43	1	no	—
342	C₄⋊C₈	—	86	1	no	—
343	C₄⋊C₈	C₂²×D₄₃	1	2	yes	—
344	#103	—	86	2	no	—
345	#103	—	86	2	no	—
346	#103	—	86	1	no	—
347	#103	—	86	1	no	—
348	#102	—	86	1	no	—
349	#102	—	86	1	no	—
350	C₂²⋊C₈	—	86	1	no	—
351	#97	—	2	2	no	—
352	#97	C₂²⋊D₄₃	1	2	yes	—
353	C₄×C₈	—	2	2	no	—
354	C₄×C₈	—	86	1	no	—
355	C₄×C₈	C₂²×D₄₃	1	2	yes	—
356	#41	—	172	2	no	—
357	#41	—	172	2	no	—
358	C₂×Q₈	—	2	1	no	—
359	C₂×Q₈	—	2	2	no	—
360	C₂×Q₈	—	4	1	no	—
361	C₂×Q₈	—	86	1	no	—
362	C₂×Q₈	—	86	2	no	—
363	C₂×Q₈	—	172	2	no	—
364	C₂×Q₈	—	172	2	no	—
365	C₂×Q₈	—	172	1	no	—
366	C₂×Q₈	C₂×D₁₇₂	1	1	yes	characteristic
367	C₂×Q₈	C₂×D₁₇₂	1	1	yes	characteristic
368	C₂×D₄	—	86	1	no	—
369	C₂×D₄	—	86	1	no	—
370	C₂×D₄	—	86	1	no	—
371	C₂×D₄	—	172	1	no	—
372	C₂²×C₄	—	2	1	no	—
373	C₂²×C₄	—	2	1	no	—
374	C₂²×C₄	—	172	1	no	—
375	C₂²×C₄	—	172	1	no	—
376	C₂²×C₄	C₂×D₁₇₂	1	1	yes	characteristic
377	C₂²×C₄	#10621898	1	1	yes	characteristic
378	C₂²×C₄	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
379	Q₁₆	—	172	4	no	—
380	Q₁₆	—	172	4	no	—
381	SD₁₆	—	172	4	no	—
382	SD₁₆	—	172	2	no	—
383	SD₁₆	—	172	2	no	—
384	SD₁₆	—	172	4	no	—
385	M₁₆	—	2	2	no	—
386	M₁₆	—	4	2	no	—
387	M₁₆	#10621884	1	4	yes	complemented
388	C₂×C₈	—	2	2	no	—
389	C₂×C₈	—	86	1	no	—
390	C₂×C₈	—	86	1	no	—
391	C₂×C₈	—	86	2	no	—
392	C₂×C₈	—	172	2	no	—
393	C₂×C₈	C₂×C₂²⋊D₄₃	1	2	yes	—
394	C₂×C₈	C₂×C₂²⋊D₄₃	1	2	yes	—
395	C₄⋊C₄	—	2	1	no	—
396	C₄⋊C₄	—	2	1	no	—
397	C₄⋊C₄	—	2	1	no	—
398	C₄⋊C₄	—	2	1	no	—
399	C₄⋊C₄	—	2	1	no	—
400	C₄⋊C₄	—	86	2	no	—
401	C₄⋊C₄	—	86	1	no	—
402	C₄⋊C₄	—	86	2	no	—
403	C₄⋊C₄	—	86	1	no	—
404	C₄⋊C₄	—	172	1	no	—
405	C₄⋊C₄	—	172	1	no	—
406	C₄⋊C₄	C₂×D₁₇₂	1	1	yes	characteristic
407	C₄⋊C₄	C₂×D₁₇₂	1	1	yes	characteristic
408	C₂²⋊C₄	—	172	1	no	—
409	C₂²⋊C₄	—	172	1	no	—
410	C₄²	—	2	1	no	—
411	C₄²	—	2	1	no	—
412	C₄²	—	2	1	no	—
413	C₄²	—	2	1	no	—
414	C₄²	C₂×D₁₇₂	1	1	yes	characteristic
415	C₄²	#10621898	1	1	yes	characteristic
416	C₄²	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
417	C₄²	C₂³×D₄₃	1	1	yes	characteristic
418	C₂³	—	172	1	no	—
419	C₂³	#13063299	1	1	yes	characteristic
420	Q₈	—	2	1	no	—
421	Q₈	—	2	1	no	—
422	Q₈	—	2	1	no	—
423	Q₈	—	4	2	no	—
424	Q₈	—	344	2	no	—
425	Q₈	—	172	2	no	—
426	Q₈	—	172	1	no	—
427	Q₈	—	172	2	no	—
428	Q₈	—	172	1	no	—
429	Q₈	#13063358	1	2	yes	complemented
430	D₄	—	344	1	no	—
431	D₄	—	344	2	no	—
432	D₄	—	172	1	no	—
433	D₄	—	172	1	no	—
434	D₄	—	172	1	no	—
435	D₄	—	172	1	no	—
436	C₂×C₄	—	2	1	no	—
437	C₂×C₄	—	2	1	no	—
438	C₂×C₄	—	2	1	no	—
439	C₂×C₄	—	2	1	no	—
440	C₂×C₄	—	2	1	no	—
441	C₂×C₄	—	2	1	no	—
442	C₂×C₄	—	4	1	no	—
443	C₂×C₄	—	4	2	no	—
444	C₂×C₄	—	8	1	no	—
445	C₂×C₄	—	344	2	no	—
446	C₂×C₄	—	344	2	no	—
447	C₂×C₄	—	172	1	no	—
448	C₂×C₄	—	172	2	no	—
449	C₂×C₄	#13063299	1	1	yes	characteristic
450	C₂×C₄	#13063299	1	1	yes	characteristic
451	C₂×C₄	#13063299	1	1	yes	characteristic
452	C₂×C₄	C₂×#10621884	1	2	yes	—
453	C₂×C₄	#13063350	1	2	yes	—
454	C₂×C₄	C₂²×C₂²⋊D₄₃	1	1	yes	characteristic
455	C₂×C₄	C₂²×D₁₇₂	1	1	yes	characteristic
456	C₂×C₄	C₂×#10621898	1	1	yes	characteristic
457	C₈	—	2	2	no	—
458	C₈	—	4	2	no	—
459	C₈	—	172	1	no	—
460	C₈	—	172	2	no	—
461	C₈	—	172	1	no	—
462	C₈	C₂×#10621884	1	4	yes	—
463	C₂²	—	2	1	no	—
464	C₂²	—	2	1	no	—
465	C₂²	—	344	1	no	—
466	C₂²	—	344	1	no	—
467	C₂²	—	344	1	no	—
468	C₂²	#14583099	1	2	yes	—
469	C₂²	C₂×#13063299	1	1	yes	characteristic
470	C₄	—	2	1	no	—
471	C₄	—	2	2	no	—
472	C₄	—	2	1	no	—
473	C₄	—	2	1	no	—
474	C₄	—	4	1	no	—
475	C₄	—	4	1	no	—
476	C₄	—	4	1	no	—
477	C₄	—	344	1	no	—
478	C₄	—	344	2	no	—
479	C₄	#14583099	1	2	yes	—
480	C₄	C₂²×#10621884	1	1	yes	characteristic
481	C₄	C₂×#13063350	1	1	yes	characteristic
482	C₄	C₂×#13063358	1	1	yes	characteristic
483	C₄	#14583699	1	1	yes	characteristic
484	C₂	—	2	2	no	—
485	C₂	—	688	1	no	—
486	C₂	C₂×#14583099	1	1	yes	characteristic
487	C₂	#19144225	1	1	yes	characteristic
488	C₂	#19144332	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂×#13063299
commutator, cosocle	C₄²×C₄₃	C₂⁴
Frattini	C₄²	C₂³×D₄₃
Fitting	Q₈×M₁₆×C₄₃	C₂
socle	C₂²×C₄₃	C₂×#121
prime radical	#14583449	C₂²
hypercenter	Q₈×M₁₆	D₄₃
hypocenter	C₄₃	#19171
LCS	G ▷ C₄²×C₄₃ ▷ C₂²×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ Q₈×M₁₆

Complements

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

N	H ≅ G/N	type
3. C₂×#14583184	C₂	semidirect
4. #19134089	C₂	semidirect
5. #19134067	C₂	semidirect
6. #19133965	C₂	semidirect
7. #19133943	C₂	semidirect
8. #19133347	C₂	semidirect
10. #19133268	C₂	semidirect
11. Q₈×M₁₆×C₄₃	C₂	semidirect
136. M₁₆×C₄₃	SD₁₆	semidirect
179. Q₈×C₄₃	#137	semidirect
243. Q₈×M₁₆	D₄₃	semidirect
293. C₄₃	#19171	semidirect
387. M₁₆	#10621884	semidirect
429. Q₈	#13063358	semidirect

Maximal subgroups

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

subgroup	index
#19145054	2
#19144626	2
C₂×#14583184	2
#19134089	2
#19134067	2
#19133965	2
#19133943	2
#19133347	2
#19133273	2
#19133268	2
Q₈×M₁₆×C₄₃	2
#19171	43