Subgroups — #25966618

Order 11008.

1978 conjugacy classes of subgroups.

The subgroup lattice has 776 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#19148011	C₂	1	2	yes	maximal, complemented
2	#19145278	C₂	1	4	yes	maximal, complemented
3	#19145245	C₂	1	2	yes	maximal, complemented
4	#19145234	C₂	1	2	yes	maximal, complemented
5	#19145190	C₂	1	4	yes	maximal, complemented
6	#19145174	C₂	1	2	yes	maximal, complemented
7	#19145165	C₂	1	2	yes	maximal, complemented
8	#19145134	C₂	1	1	yes	maximal, characteristic, complemented
9	#19145081	C₂	1	1	yes	maximal, characteristic, complemented
10	#19144951	C₂	1	2	yes	maximal, complemented
11	#19144275	C₂	1	2	yes	maximal, complemented
12	#19144265	C₂	1	1	yes	maximal, characteristic, complemented
13	#19144243	C₂	1	1	yes	maximal, characteristic, complemented
14	C₄×#13063353	C₂	1	2	yes	maximal, complemented
15	C₄×#13063347	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×C₄×D₃₄₄	C₂	1	1	yes	maximal, characteristic, complemented
17	C₄×#131×C₄₃	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂×#13063353	C₂²	1	2	yes	—
19	C₂×#13063347	C₂²	1	1	yes	characteristic
20	C₂²×D₃₄₄	C₂²	1	1	yes	characteristic
21	#14583527	C₂²	1	2	yes	—
22	#14583521	—	2	2	no	—
23	#14583520	C₂²	1	4	yes	complemented
24	#14583504	C₂²	1	4	yes	complemented
25	#14583500	—	2	2	no	—
26	#14583482	—	2	4	no	—
27	#14583477	C₂²	1	2	yes	—
28	#14583468	C₂²	1	2	yes	—
29	#14583463	C₂²	1	2	yes	—
30	#14583449	C₂²	1	4	yes	complemented
31	#14583446	—	2	2	no	—
32	#14583436	—	2	2	no	—
33	#14583433	C₂²	1	4	yes	complemented
34	#14583408	—	2	4	no	—
35	C₄×#10621898	C₂²	1	2	yes	—
36	C₂×C₄×D₁₇₂	C₂²	1	2	yes	—
37	#14583308	C₂²	1	4	yes	complemented
38	#14583304	C₂²	1	2	yes	complemented
39	#14583301	C₂²	1	2	yes	complemented
40	#14583288	C₂²	1	4	yes	—
41	#14583283	C₂²	1	2	yes	—
42	#14583276	C₂²	1	2	yes	—
43	#14583264	C₂²	1	4	yes	complemented
44	#14583259	C₂²	1	4	yes	complemented
45	#14583254	C₂²	1	4	yes	complemented
46	#14583246	C₂²	1	4	yes	complemented
47	#14583152	C₂²	1	4	yes	—
48	#14583152	C₂²	1	4	yes	complemented
49	#14583145	C₂²	1	4	yes	complemented
50	#14583145	C₂²	1	4	yes	complemented
51	#14583140	C₂²	1	2	yes	complemented
52	#14583135	C₂²	1	2	yes	—
53	#14583135	C₂²	1	2	yes	—
54	#14583135	C₂²	1	2	yes	complemented
55	#14583135	C₂²	1	4	yes	complemented
56	#14583128	C₂²	1	4	yes	complemented
57	#14583012	C₂²	1	4	yes	complemented
58	#14583001	C₂²	1	4	yes	complemented
59	C₄×Dic₁₇₂	C₂²	1	1	yes	characteristic, complemented
60	C₄×Dic₁₇₂	C₂²	1	1	yes	characteristic, complemented
61	C₄×#10621873	C₂²	1	2	yes	complemented
62	C₄×#10621873	C₂²	1	2	yes	complemented
63	C₄×#10621873	C₂²	1	4	yes	complemented
64	C₄×D₃₄₄	C₂²	1	2	yes	—
65	C₄×D₃₄₄	C₂²	1	2	yes	—
66	C₄×D₃₄₄	C₂²	1	2	yes	—
67	C₄×D₃₄₄	C₂²	1	2	yes	—
68	C₄×D₃₄₄	C₂²	1	1	yes	characteristic, complemented
69	C₄×D₃₄₄	C₂²	1	1	yes	characteristic, complemented
70	C₄×D₃₄₄	C₂²	1	4	yes	complemented
71	#14582941	C₂²	1	2	yes	—
72	#14582937	C₂²	1	1	yes	characteristic
73	C₂×#13063259	C₂²	1	1	yes	characteristic
74	#14582905	C₂²	1	2	yes	—
75	#14582901	C₂²	1	2	yes	—
76	#14582896	C₂²	1	2	yes	—
77	C₂×#13063247	C₂²	1	2	yes	—
78	C₂×#131×C₄₃	C₂²	1	1	yes	characteristic
79	C₂×#131×C₄₃	C₂²	1	1	yes	characteristic
80	C₄×#41×C₄₃	C₂²	1	1	yes	characteristic
81	C₄₃×#405	C₂²	1	1	yes	characteristic
82	C₄₃×#405	C₂²	1	1	yes	characteristic
83	C₄₃×#405	C₂²	1	2	yes	complemented
84	C₄₃×#405	C₂²	1	2	yes	complemented
85	C₄×M₁₆×C₄₃	C₂²	1	1	yes	characteristic
86	C₄×M₁₆×C₄₃	C₂²	1	2	yes	complemented
87	C₂×C₄×C₈×C₄₃	C₂²	1	1	yes	characteristic
88	C₂×C₄×C₈×C₄₃	C₂²	1	2	yes	complemented
89	C₂×#10621898	—	2	4	no	—
90	C₂×#10621898	C₂³	1	2	yes	—
91	C₂²×D₁₇₂	C₂³	1	2	yes	—
92	C₂²×C₄×D₄₃	—	2	2	no	—
93	#13063353	—	2	8	no	—
94	#13063347	—	2	4	no	—
95	C₂×Dic₁₇₂	C₂³	1	1	yes	characteristic
96	C₂×#10621873	C₂³	1	4	yes	—
97	C₂×#10621873	C₂³	1	2	yes	—
98	C₂×D₃₄₄	—	2	4	no	—
99	C₂×D₃₄₄	C₂³	1	2	yes	—
100	C₂×D₃₄₄	C₂³	1	1	yes	characteristic
101	C₂×D₃₄₄	C₂³	1	4	yes	—
102	C₂×D₃₄₄	C₂³	1	2	yes	—
103	#13063325	C₂³	1	4	yes	—
104	#13063324	—	2	2	no	—
105	#13063322	C₂³	1	4	yes	—
106	#13063321	—	2	2	no	—
107	#13063320	—	2	4	no	—
108	#13063319	—	2	4	no	—
109	#13063317	C₂³	1	4	yes	—
110	#13063316	—	2	2	no	—
111	#13063314	—	2	2	no	—
112	#13063313	—	2	4	no	—
113	#13063313	C₂³	1	4	yes	—
114	#13063311	—	2	4	no	—
115	#13063310	—	2	4	no	—
116	#13063310	—	2	4	no	—
117	#13063308	—	2	4	no	—
118	#13063307	—	2	4	no	—
119	#13063304	C₂³	1	4	yes	—
120	#13063303	—	2	4	no	—
121	#13063302	—	2	4	no	—
122	#13063301	—	2	2	no	—
123	#13063300	—	2	2	no	—
124	#13063300	—	2	2	no	—
125	#13063299	—	2	4	no	—
126	#13063299	C₂³	1	4	yes	—
127	#13063299	C₂³	1	4	yes	—
128	#13063299	C₂³	1	4	yes	—
129	#13063298	—	2	4	no	—
130	#13063298	—	2	4	no	—
131	#13063297	—	2	4	no	—
132	#13063296	—	2	2	no	—
133	#13063295	—	2	4	no	—
134	#13063293	—	2	4	no	—
135	C₄×Dic₈₆	C₂³	1	2	yes	—
136	C₄×Dic₈₆	C₂³	1	2	yes	—
137	C₄×D₁₇₂	—	2	2	no	—
138	C₄×D₁₇₂	—	2	2	no	—
139	C₄×D₁₇₂	—	2	4	no	—
140	C₄×D₁₇₂	C₂³	1	4	yes	—
141	C₄×D₁₇₂	C₂³	1	4	yes	—
142	C₄×D₁₇₂	C₂³	1	2	yes	—
143	C₄×D₁₇₂	C₂³	1	2	yes	—
144	C₄×C₂²⋊D₄₃	—	2	2	no	—
145	C₄×C₂²⋊D₄₃	—	2	2	no	—
146	C₄×C₂²⋊D₄₃	—	2	4	no	—
147	#13063284	C₂³	1	2	yes	—
148	#13063282	—	2	2	no	—
149	#13063282	—	2	4	no	—
150	C₂×C₄⋊Dic₄₃	C₂³	1	2	yes	—
151	C₂×(C₂×D₄₃)⋊C₄	—	2	2	no	—
152	C₄²×D₄₃	—	2	2	no	—
153	#13063259	C₂³	1	1	yes	characteristic
154	#13063259	C₂³	1	2	yes	—
155	#13063259	C₂³	1	1	yes	characteristic
156	#13063259	C₂³	1	4	yes	—
157	#13063259	C₂³	1	2	yes	—
158	#13063257	C₂³	1	4	yes	—
159	#13063257	C₂³	1	2	yes	—
160	#13063250	C₂³	1	2	yes	—
161	#13063250	C₂³	1	4	yes	—
162	#13063250	C₂³	1	2	yes	—
163	#13063247	C₂³	1	4	yes	—
164	#13063247	C₂³	1	4	yes	—
165	#13063247	C₂³	1	4	yes	—
166	#13063247	C₂³	1	2	yes	—
167	#13063247	C₂³	1	4	yes	—
168	#13063247	C₂³	1	4	yes	—
169	#13063247	C₂³	1	2	yes	—
170	C₂×#41×C₄₃	C₂³	1	1	yes	characteristic
171	#131×C₄₃	—	2	4	no	—
172	#131×C₄₃	—	2	4	no	—
173	C₂×M₁₆×C₄₃	C₂³	1	2	yes	—
174	C₂×M₁₆×C₄₃	C₂³	1	2	yes	—
175	C₂×M₁₆×C₄₃	C₂³	1	1	yes	characteristic
176	C₂×M₁₆×C₄₃	C₂³	1	1	yes	characteristic
177	C₂²×C₈×C₄₃	C₂³	1	2	yes	—
178	C₂²×C₈×C₄₃	C₂³	1	2	yes	—
179	C₂²×C₈×C₄₃	C₂³	1	1	yes	characteristic
180	C₂²×C₈×C₄₃	C₂³	1	1	yes	characteristic
181	C₄×Q₈×C₄₃	D₄	1	1	yes	characteristic
182	C₄×Q₈×C₄₃	D₄	1	1	yes	characteristic
183	C₄×D₄×C₄₃	D₄	1	2	yes	—
184	C₄×D₄×C₄₃	D₄	1	1	yes	characteristic
185	C₄×D₄×C₄₃	D₄	1	2	yes	—
186	C₄×D₄×C₄₃	D₄	1	1	yes	characteristic
187	#117×C₄₃	C₂³	1	1	yes	characteristic
188	#117×C₄₃	C₂³	1	2	yes	—
189	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
190	C₂×C₄²×C₄₃	C₂³	1	2	yes	—
191	#97×C₄₃	C₂³	1	2	yes	—
192	#97×C₄₃	C₂³	1	2	yes	—
193	#97×C₄₃	C₂³	1	2	yes	—
194	C₄×C₈×C₄₃	C₂³	1	2	yes	—
195	C₄×C₈×C₄₃	C₂³	1	1	yes	characteristic
196	C₄×C₈×C₄₃	C₂³	1	1	yes	characteristic
197	C₄×C₈×C₄₃	C₂³	1	1	yes	characteristic
198	C₄×C₈×C₄₃	C₂³	1	1	yes	characteristic
199	C₄×C₈×C₄₃	C₂³	1	2	yes	—
200	C₄×C₈×C₄₃	C₂³	1	2	yes	—
201	C₂³×D₄₃	—	2	2	no	—
202	#41×C₄₃	—	2	2	no	—
203	#41×C₄₃	—	2	2	no	—
204	C₂×Q₈×C₄₃	C₂×D₄	1	1	yes	characteristic
205	C₂×D₄×C₄₃	C₂×D₄	1	2	yes	—
206	C₂×D₄×C₄₃	C₂×D₄	1	1	yes	characteristic
207	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
208	C₂²×C₄×C₄₃	C₂×D₄	1	2	yes	—
209	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
210	C₂²×C₄×C₄₃	C₂×D₄	1	2	yes	—
211	C₂²×C₄×C₄₃	C₂⁴	1	2	yes	—
212	C₂²×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
213	C₂×C₂²⋊D₄₃	—	2	2	no	—
214	C₂×C₂²⋊D₄₃	—	2	4	no	—
215	C₂×C₂²⋊D₄₃	—	2	4	no	—
216	C₂×C₂²⋊D₄₃	—	2	4	no	—
217	C₂²×Dic₄₃	—	2	2	no	—
218	#10621898	—	2	4	no	—
219	#10621898	—	2	4	no	—
220	#10621898	—	8	8	no	—
221	C₂×D₁₇₂	—	2	2	no	—
222	C₂×D₁₇₂	—	2	4	no	—
223	C₂×D₁₇₂	—	2	4	no	—
224	C₂×D₁₇₂	—	2	4	no	—
225	C₂×D₁₇₂	—	2	4	no	—
226	C₂×D₁₇₂	C₂⁴	1	4	yes	—
227	C₂×D₁₇₂	C₂⁴	1	2	yes	—
228	C₂×C₄×D₄₃	—	2	2	no	—
229	C₂×C₄×D₄₃	—	2	2	no	—
230	C₂×C₄×D₄₃	—	2	4	no	—
231	C₂×C₄×D₄₃	—	2	2	no	—
232	C₂×C₄×D₄₃	—	2	4	no	—
233	C₂×C₄×D₄₃	—	8	4	no	—
234	C₂×Dic₈₆	—	2	4	no	—
235	C₂×Dic₈₆	C₂⁴	1	2	yes	—
236	M₁₆×C₄₃	—	2	2	no	—
237	M₁₆×C₄₃	—	2	4	no	—
238	M₁₆×C₄₃	—	2	4	no	—
239	M₁₆×C₄₃	#41	1	4	yes	complemented
240	C₂×C₈×C₄₃	—	2	2	no	—
241	C₂×C₈×C₄₃	—	2	4	no	—
242	C₂×C₈×C₄₃	—	2	4	no	—
243	C₂×C₈×C₄₃	#41	1	4	yes	complemented
244	C₂×C₈×C₄₃	C₂⁴	1	1	yes	characteristic
245	C₂×C₈×C₄₃	C₂⁴	1	1	yes	characteristic
246	C₂×C₈×C₄₃	C₂⁴	1	2	yes	—
247	C₂×C₈×C₄₃	C₂⁴	1	1	yes	characteristic
248	C₂×C₈×C₄₃	C₂⁴	1	2	yes	—
249	C₂×C₈×C₄₃	C₂⁴	1	1	yes	characteristic
250	C₄⋊C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
251	C₄⋊C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
252	C₄⋊C₄×C₄₃	C₂×D₄	1	2	yes	—
253	C₄⋊C₄×C₄₃	C₂×D₄	1	2	yes	—
254	C₂²⋊C₄×C₄₃	C₂×D₄	1	2	yes	—
255	C₂²⋊C₄×C₄₃	C₂×D₄	1	2	yes	—
256	C₂²⋊C₄×C₄₃	C₂×D₄	1	2	yes	—
257	C₄²×C₄₃	C₂×D₄	1	1	yes	characteristic
258	C₄²×C₄₃	C₂×D₄	1	1	yes	characteristic
259	C₄²×C₄₃	C₂×D₄	1	2	yes	—
260	C₄²×C₄₃	C₂×D₄	1	2	yes	—
261	C₄²×C₄₃	C₂⁴	1	1	yes	characteristic
262	C₄²×C₄₃	C₂⁴	1	1	yes	characteristic
263	C₄²×C₄₃	C₂⁴	1	2	yes	—
264	C₂²⋊Dic₄₃	—	2	2	no	—
265	C₂²⋊Dic₄₃	—	2	4	no	—
266	(C₂×D₄₃)⋊C₄	—	2	4	no	—
267	(C₂×D₄₃)⋊C₄	—	2	4	no	—
268	(C₂×D₄₃)⋊C₄	—	2	2	no	—
269	(C₂×D₄₃)⋊C₄	—	2	2	no	—
270	(C₂×D₄₃)⋊C₄	—	2	4	no	—
271	(C₂×D₄₃)⋊C₄	—	2	4	no	—
272	(C₂×D₄₃)⋊C₄	—	2	4	no	—
273	(C₂×D₄₃)⋊C₄	—	2	4	no	—
274	(C₂×D₄₃)⋊C₄	—	2	4	no	—
275	C₄⋊Dic₄₃	—	2	2	no	—
276	C₄⋊Dic₄₃	—	2	4	no	—
277	C₄⋊Dic₄₃	C₂⁴	1	2	yes	—
278	C₄⋊Dic₄₃	C₂⁴	1	4	yes	—
279	C₄⋊Dic₄₃	C₂⁴	1	2	yes	—
280	Dic₄₃⋊C₄	—	2	2	no	—
281	Dic₄₃⋊C₄	—	2	2	no	—
282	Dic₄₃⋊C₄	—	2	4	no	—
283	Dic₄₃⋊C₄	—	2	4	no	—
284	Dic₄₃⋊C₄	—	2	4	no	—
285	C₄×Dic₄₃	—	2	2	no	—
286	C₄×Dic₄₃	—	2	2	no	—
287	C₄×Dic₄₃	—	2	2	no	—
288	Dic₁₇₂	—	2	2	no	—
289	D₃₄₄	—	2	4	no	—
290	D₃₄₄	—	2	4	no	—
291	D₃₄₄	—	2	2	no	—
292	D₃₄₄	—	2	8	no	—
293	#10621873	—	2	4	no	—
294	#10621873	—	2	8	no	—
295	C₂³×C₄₃	C₂²×D₄	1	2	yes	—
296	C₂³×C₄₃	C₂²×D₄	1	1	yes	characteristic
297	C₂²×D₄₃	—	2	4	no	—
298	C₂²×D₄₃	—	2	2	no	—
299	C₂²×D₄₃	—	4	4	no	—
300	C₂²×D₄₃	—	8	2	no	—
301	C₂²×D₄₃	—	8	2	no	—
302	Q₈×C₄₃	—	2	2	no	—
303	D₄×C₄₃	—	2	4	no	—
304	D₄×C₄₃	—	2	2	no	—
305	C₂×C₄×C₄₃	—	2	2	no	—
306	C₂×C₄×C₄₃	—	2	4	no	—
307	C₂×C₄×C₄₃	—	2	2	no	—
308	C₂×C₄×C₄₃	—	2	2	no	—
309	C₂×C₄×C₄₃	—	4	1	no	—
310	C₂×C₄×C₄₃	—	4	2	no	—
311	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
312	C₂×C₄×C₄₃	C₂²×D₄	1	2	yes	—
313	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
314	C₂×C₄×C₄₃	C₂²×D₄	1	2	yes	—
315	C₂×C₄×C₄₃	C₂²×D₄	1	2	yes	—
316	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
317	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
318	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
319	C₂×C₄×C₄₃	C₂×#41	1	2	yes	—
320	C₂×C₄×C₄₃	C₂×#41	1	2	yes	—
321	C₂×C₄×C₄₃	C₂⁵	1	1	yes	characteristic
322	C₂²⋊D₄₃	—	4	4	no	—
323	C₂²⋊D₄₃	—	8	4	no	—
324	C₂²⋊D₄₃	—	8	4	no	—
325	C₂²⋊D₄₃	—	8	4	no	—
326	C₂×Dic₄₃	—	2	2	no	—
327	C₂×Dic₄₃	—	2	2	no	—
328	C₂×Dic₄₃	—	2	2	no	—
329	C₂×Dic₄₃	—	2	4	no	—
330	C₂×Dic₄₃	—	8	2	no	—
331	D₁₇₂	—	2	4	no	—
332	D₁₇₂	—	2	2	no	—
333	D₁₇₂	—	2	4	no	—
334	D₁₇₂	—	2	2	no	—
335	D₁₇₂	—	4	4	no	—
336	D₁₇₂	—	8	4	no	—
337	D₁₇₂	—	8	4	no	—
338	C₄×D₄₃	—	4	4	no	—
339	C₄×D₄₃	—	4	8	no	—
340	C₄×D₄₃	—	4	4	no	—
341	C₄×D₄₃	—	8	2	no	—
342	C₄×D₄₃	—	8	4	no	—
343	Dic₈₆	—	2	2	no	—
344	Dic₈₆	—	2	2	no	—
345	Dic₈₆	—	8	4	no	—
346	C₈×C₄₃	—	2	1	no	—
347	C₈×C₄₃	—	2	1	no	—
348	C₈×C₄₃	—	2	2	no	—
349	C₈×C₄₃	C₂×#41	1	4	yes	—
350	C₈×C₄₃	C₂×#41	1	2	yes	—
351	C₈×C₄₃	C₂×#41	1	2	yes	—
352	#60695	—	43	1	no	maximal, Sylow
353	C₂²×C₄₃	—	2	1	no	—
354	C₂²×C₄₃	—	2	1	no	—
355	C₂²×C₄₃	—	2	2	no	—
356	C₂²×C₄₃	—	2	2	no	—
357	C₂²×C₄₃	—	2	2	no	—
358	C₂²×C₄₃	#532	1	2	yes	—
359	C₂²×C₄₃	C₂³×D₄	1	1	yes	characteristic
360	C₂×D₄₃	—	4	4	no	—
361	C₂×D₄₃	—	4	2	no	—
362	C₂×D₄₃	—	4	4	no	—
363	C₂×D₄₃	—	4	2	no	—
364	C₂×D₄₃	—	4	4	no	—
365	C₂×D₄₃	—	4	2	no	—
366	C₂×D₄₃	—	8	8	no	—
367	C₄×C₄₃	—	2	1	no	—
368	C₄×C₄₃	—	2	2	no	—
369	C₄×C₄₃	—	2	1	no	—
370	C₄×C₄₃	—	2	2	no	—
371	C₄×C₄₃	—	2	2	no	—
372	C₄×C₄₃	—	2	1	no	—
373	C₄×C₄₃	#532	1	2	yes	—
374	C₄×C₄₃	#576	1	2	yes	—
375	C₄×C₄₃	C₂²×#41	1	1	yes	characteristic
376	C₄×C₄₃	C₂²×#41	1	1	yes	characteristic
377	Dic₄₃	—	4	2	no	—
378	Dic₄₃	—	4	2	no	—
379	Dic₄₃	—	4	2	no	—
380	Dic₄₃	—	4	4	no	—
381	#3460	—	43	2	no	—
382	#3179	—	43	4	no	—
383	#3176	—	43	2	no	—
384	#3175	—	43	2	no	—
385	#3171	—	43	4	no	—
386	#3169	—	43	2	no	—
387	#3168	—	43	2	no	—
388	#3164	—	43	1	no	—
389	#3155	—	43	1	no	—
390	#3136	—	43	2	no	—
391	#3062	—	43	2	no	—
392	#3061	—	43	1	no	—
393	#3058	—	43	1	no	—
394	C₄×AGL(1,ℤ/8)	—	43	2	no	—
395	C₄×#135	—	43	1	no	—
396	C₂×C₄×D₈	—	43	1	no	—
397	C₄×#131	D₄₃	1	1	yes	characteristic, complemented
398	C₂×C₄₃	—	2	2	no	—
399	C₂×C₄₃	—	4	2	no	—
400	C₂×C₄₃	C₂×#532	1	1	yes	characteristic
401	C₂×C₄₃	C₂×#576	1	1	yes	characteristic
402	C₂×C₄₃	#3584	1	1	yes	characteristic
403	D₄₃	—	8	2	no	—
404	D₄₃	—	8	4	no	—
405	C₂×AGL(1,ℤ/8)	—	43	2	no	—
406	C₂×#135	—	43	1	no	—
407	C₂²×D₈	—	43	1	no	—
408	C₂×#131	C₂×D₄₃	1	1	yes	characteristic
409	C₂×#131	C₂×D₄₃	1	1	yes	characteristic
410	#544	—	43	2	no	—
411	#542	—	43	4	no	—
412	#542	—	86	2	no	—
413	#540	—	43	4	no	—
414	#540	—	86	2	no	—
415	#538	—	86	4	no	—
416	#537	—	43	2	no	—
417	#535	—	43	2	no	—
418	#535	—	43	2	no	—
419	#532	—	43	4	no	—
420	#532	—	86	2	no	—
421	#529	—	43	4	no	—
422	#529	—	86	2	no	—
423	#525	—	86	4	no	—
424	C₄×#41	—	43	2	no	—
425	C₄×#41	C₂×D₄₃	1	1	yes	characteristic
426	C₂×C₄×D₄	—	43	2	no	—
427	#501	—	43	4	no	—
428	#500	—	43	2	no	—
429	#499	—	43	2	no	—
430	#496	—	43	4	no	—
431	#495	—	43	2	no	—
432	#493	—	43	2	no	—
433	#490	—	43	4	no	—
434	#489	—	43	4	no	—
435	#488	—	43	4	no	—
436	#486	—	43	4	no	—
437	#469	—	43	4	no	—
438	#469	—	43	4	no	—
439	#468	—	43	4	no	—
440	#468	—	43	4	no	—
441	#467	—	43	2	no	—
442	#466	—	43	2	no	—
443	#466	—	43	2	no	—
444	#466	—	43	2	no	—
445	#466	—	43	4	no	—
446	#465	—	43	4	no	—
447	#442	—	43	4	no	—
448	#440	—	43	4	no	—
449	C₄×Q₁₆	—	43	1	no	—
450	C₄×Q₁₆	—	43	1	no	—
451	C₄×SD₁₆	—	43	4	no	—
452	C₄×SD₁₆	—	43	2	no	—
453	C₄×SD₁₆	—	43	2	no	—
454	C₄×D₈	—	43	2	no	—
455	C₄×D₈	—	43	1	no	—
456	C₄×D₈	—	43	4	no	—
457	C₄×D₈	—	43	2	no	—
458	C₄×D₈	—	43	2	no	—
459	C₄×D₈	—	43	1	no	—
460	C₄×D₈	—	43	2	no	—
461	#428	—	43	2	no	—
462	#427	—	43	1	no	—
463	C₂×#107	—	43	1	no	—
464	#418	—	43	2	no	—
465	#417	—	43	2	no	—
466	#416	—	43	2	no	—
467	C₂×#102	—	43	2	no	—
468	#405	C₂×D₄₃	1	1	yes	characteristic
469	#405	C₂×D₄₃	1	1	yes	characteristic
470	#405	C₂×D₄₃	1	2	yes	complemented
471	#405	C₂×D₄₃	1	2	yes	complemented
472	C₄×M₁₆	C₂×D₄₃	1	1	yes	characteristic
473	C₄×M₁₆	C₂×D₄₃	1	2	yes	complemented
474	C₂×C₄×C₈	C₂×D₄₃	1	1	yes	characteristic
475	C₂×C₄×C₈	C₂×D₄₃	1	2	yes	complemented
476	C₄₃	#60695	1	1	yes	characteristic, complemented, Sylow
477	C₂×#41	—	43	2	no	—
478	C₂×#41	—	86	4	no	—
479	C₂×#41	C₂²×D₄₃	1	1	yes	characteristic
480	C₂²×D₄	—	43	2	no	—
481	C₂³×C₄	—	86	2	no	—
482	AGL(1,ℤ/8)	—	86	8	no	—
483	#135	—	86	4	no	—
484	C₂×Q₁₆	—	43	1	no	—
485	C₂×SD₁₆	—	43	2	no	—
486	C₂×SD₁₆	—	43	4	no	—
487	C₂×D₈	—	43	2	no	—
488	C₂×D₈	—	43	2	no	—
489	C₂×D₈	—	43	1	no	—
490	C₂×D₈	—	43	4	no	—
491	C₂×D₈	—	86	4	no	—
492	#131	—	2	4	no	—
493	#131	—	2	4	no	—
494	C₂×M₁₆	C₂²×D₄₃	1	1	yes	characteristic
495	C₂×M₁₆	C₂²×D₄₃	1	2	yes	—
496	C₂×M₁₆	C₂²×D₄₃	1	2	yes	—
497	C₂×M₁₆	C₂²×D₄₃	1	1	yes	characteristic
498	C₂²×C₈	C₂²×D₄₃	1	1	yes	characteristic
499	C₂²×C₈	C₂²×D₄₃	1	2	yes	—
500	C₂²×C₈	C₂²×D₄₃	1	2	yes	—
501	C₂²×C₈	C₂²×D₄₃	1	1	yes	characteristic
502	C₄⋊Q₈	—	43	4	no	—
503	C₄⋊Q₈	—	86	2	no	—
504	#127	—	43	4	no	—
505	#127	—	86	2	no	—
506	#126	—	86	4	no	—
507	#126	—	86	4	no	—
508	#125	—	43	4	no	—
509	#125	—	86	2	no	—
510	#124	—	43	4	no	—
511	#124	—	86	2	no	—
512	#124	—	86	4	no	—
513	#124	—	86	4	no	—
514	#123	—	86	4	no	—
515	#123	—	86	4	no	—
516	#123	—	86	4	no	—
517	#123	—	86	4	no	—
518	C₂²⋊Q₈	—	43	4	no	—
519	C₂²⋊Q₈	—	86	2	no	—
520	C₂²⋊Q₈	—	86	4	no	—
521	C₂²⋊Q₈	—	86	4	no	—
522	#121	—	43	4	no	—
523	#121	—	43	4	no	—
524	#121	—	43	4	no	—
525	#121	—	86	4	no	—
526	#121	—	86	2	no	—
527	#121	—	86	4	no	—
528	#121	—	86	2	no	—
529	#121	—	86	2	no	—
530	#121	—	86	4	no	—
531	#121	—	86	4	no	—
532	#120	—	86	4	no	—
533	#120	—	86	4	no	—
534	C₄×Q₈	—	43	2	no	—
535	C₄×Q₈	—	43	2	no	—
536	C₄×Q₈	D₁₇₂	1	1	yes	characteristic
537	C₄×Q₈	D₁₇₂	1	1	yes	characteristic
538	C₄×D₄	—	43	4	no	—
539	C₄×D₄	—	43	4	no	—
540	C₄×D₄	—	43	2	no	—
541	C₄×D₄	—	43	2	no	—
542	C₄×D₄	—	86	2	no	—
543	C₄×D₄	—	86	2	no	—
544	C₄×D₄	—	86	4	no	—
545	C₄×D₄	—	86	2	no	—
546	C₄×D₄	—	86	2	no	—
547	C₄×D₄	—	86	4	no	—
548	C₄×D₄	D₁₇₂	1	2	yes	—
549	C₄×D₄	D₁₇₂	1	1	yes	characteristic
550	C₄×D₄	D₁₇₂	1	2	yes	—
551	C₄×D₄	D₁₇₂	1	1	yes	characteristic
552	#117	—	43	2	no	—
553	#117	—	86	2	no	—
554	#117	—	86	4	no	—
555	#117	C₂²×D₄₃	1	1	yes	characteristic
556	#117	C₂²×D₄₃	1	2	yes	—
557	C₂×C₄⋊C₄	—	43	2	no	—
558	C₂×C₂²⋊C₄	—	86	2	no	—
559	C₂×C₄²	—	86	2	no	—
560	C₂×C₄²	C₂²×D₄₃	1	1	yes	characteristic
561	C₂×C₄²	C₂²×D₄₃	1	2	yes	—
562	#107	—	43	2	no	—
563	#107	—	43	2	no	—
564	#107	—	43	1	no	—
565	#107	—	43	1	no	—
566	#107	—	43	4	no	—
567	#106	—	43	2	no	—
568	#106	—	43	4	no	—
569	#103	—	43	2	no	—
570	#103	—	43	2	no	—
571	#103	—	43	4	no	—
572	#102	—	43	4	no	—
573	#102	—	43	4	no	—
574	#102	—	43	2	no	—
575	#102	—	43	2	no	—
576	#102	—	43	4	no	—
577	#102	—	43	4	no	—
578	#102	—	43	4	no	—
579	#97	C₂²×D₄₃	1	2	yes	—
580	#97	C₂²×D₄₃	1	2	yes	—
581	#97	C₂²×D₄₃	1	2	yes	—
582	C₄×C₈	C₂²×D₄₃	1	1	yes	characteristic
583	C₄×C₈	C₂²×D₄₃	1	1	yes	characteristic
584	C₄×C₈	C₂²×D₄₃	1	1	yes	characteristic
585	C₄×C₈	C₂²×D₄₃	1	1	yes	characteristic
586	C₄×C₈	C₂²×D₄₃	1	2	yes	—
587	C₄×C₈	C₂²×D₄₃	1	2	yes	—
588	C₄×C₈	C₂²×D₄₃	1	2	yes	—
589	C₂⁴	—	86	2	no	—
590	#41	—	2	2	no	—
591	#41	—	2	2	no	—
592	#41	—	86	4	no	—
593	#41	—	86	4	no	—
594	#41	—	344	8	no	—
595	C₂×Q₈	—	43	2	no	—
596	C₂×Q₈	—	86	4	no	—
597	C₂×Q₈	C₂×D₁₇₂	1	1	yes	characteristic
598	C₂×D₄	—	43	4	no	—
599	C₂×D₄	—	43	2	no	—
600	C₂×D₄	—	86	4	no	—
601	C₂×D₄	—	86	4	no	—
602	C₂×D₄	—	86	4	no	—
603	C₂×D₄	—	86	2	no	—
604	C₂×D₄	—	86	4	no	—
605	C₂×D₄	—	86	4	no	—
606	C₂×D₄	—	86	2	no	—
607	C₂×D₄	—	86	4	no	—
608	C₂×D₄	—	86	4	no	—
609	C₂×D₄	C₂×D₁₇₂	1	2	yes	—
610	C₂×D₄	C₂×D₁₇₂	1	1	yes	characteristic
611	C₂²×C₄	—	86	2	no	—
612	C₂²×C₄	—	86	2	no	—
613	C₂²×C₄	—	86	4	no	—
614	C₂²×C₄	—	86	2	no	—
615	C₂²×C₄	—	86	2	no	—
616	C₂²×C₄	—	86	4	no	—
617	C₂²×C₄	—	344	4	no	—
618	C₂²×C₄	C₂×D₁₇₂	1	1	yes	characteristic
619	C₂²×C₄	C₂×D₁₇₂	1	2	yes	—
620	C₂²×C₄	C₂×D₁₇₂	1	1	yes	characteristic
621	C₂²×C₄	C₂×D₁₇₂	1	2	yes	—
622	C₂²×C₄	C₂³×D₄₃	1	2	yes	—
623	C₂²×C₄	C₂³×D₄₃	1	1	yes	characteristic
624	Q₁₆	—	86	2	no	—
625	SD₁₆	—	86	4	no	—
626	SD₁₆	—	86	8	no	—
627	D₈	—	86	4	no	—
628	D₈	—	86	4	no	—
629	D₈	—	86	2	no	—
630	D₈	—	86	8	no	—
631	M₁₆	—	2	2	no	—
632	M₁₆	—	2	4	no	—
633	M₁₆	—	2	4	no	—
634	M₁₆	#10621898	1	4	yes	complemented
635	C₂×C₈	—	2	2	no	—
636	C₂×C₈	—	2	4	no	—
637	C₂×C₈	—	2	4	no	—
638	C₂×C₈	#10621898	1	4	yes	complemented
639	C₂×C₈	C₂³×D₄₃	1	1	yes	characteristic
640	C₂×C₈	C₂³×D₄₃	1	1	yes	characteristic
641	C₂×C₈	C₂³×D₄₃	1	2	yes	—
642	C₂×C₈	C₂³×D₄₃	1	1	yes	characteristic
643	C₂×C₈	C₂³×D₄₃	1	2	yes	—
644	C₂×C₈	C₂³×D₄₃	1	1	yes	characteristic
645	C₄⋊C₄	—	43	2	no	—
646	C₄⋊C₄	—	43	4	no	—
647	C₄⋊C₄	—	43	2	no	—
648	C₄⋊C₄	—	86	2	no	—
649	C₄⋊C₄	—	86	2	no	—
650	C₄⋊C₄	—	86	2	no	—
651	C₄⋊C₄	—	86	4	no	—
652	C₄⋊C₄	—	86	4	no	—
653	C₄⋊C₄	—	86	4	no	—
654	C₄⋊C₄	—	86	4	no	—
655	C₄⋊C₄	C₂×D₁₇₂	1	1	yes	characteristic
656	C₄⋊C₄	C₂×D₁₇₂	1	1	yes	characteristic
657	C₄⋊C₄	C₂×D₁₇₂	1	2	yes	—
658	C₄⋊C₄	C₂×D₁₇₂	1	2	yes	—
659	C₂²⋊C₄	—	86	2	no	—
660	C₂²⋊C₄	—	86	4	no	—
661	C₂²⋊C₄	—	86	4	no	—
662	C₂²⋊C₄	—	86	4	no	—
663	C₂²⋊C₄	—	86	2	no	—
664	C₂²⋊C₄	—	86	2	no	—
665	C₂²⋊C₄	—	86	4	no	—
666	C₂²⋊C₄	—	86	4	no	—
667	C₂²⋊C₄	—	86	4	no	—
668	C₂²⋊C₄	—	86	4	no	—
669	C₂²⋊C₄	—	86	4	no	—
670	C₂²⋊C₄	C₂×D₁₇₂	1	2	yes	—
671	C₂²⋊C₄	C₂×D₁₇₂	1	2	yes	—
672	C₂²⋊C₄	C₂×D₁₇₂	1	2	yes	—
673	C₄²	—	86	2	no	—
674	C₄²	—	86	2	no	—
675	C₄²	—	86	2	no	—
676	C₄²	C₂×D₁₇₂	1	1	yes	characteristic
677	C₄²	C₂×D₁₇₂	1	2	yes	—
678	C₄²	C₂×D₁₇₂	1	1	yes	characteristic
679	C₄²	C₂×D₁₇₂	1	2	yes	—
680	C₄²	C₂³×D₄₃	1	1	yes	characteristic
681	C₄²	C₂³×D₄₃	1	2	yes	—
682	C₄²	C₂³×D₄₃	1	1	yes	characteristic
683	C₂³	—	86	4	no	—
684	C₂³	—	86	2	no	—
685	C₂³	—	344	2	no	—
686	C₂³	—	344	2	no	—
687	C₂³	—	172	4	no	—
688	C₂³	C₂²×D₁₇₂	1	2	yes	—
689	C₂³	C₂²×D₁₇₂	1	1	yes	characteristic
690	Q₈	—	2	2	no	—
691	Q₈	—	86	2	no	—
692	Q₈	—	86	2	no	—
693	Q₈	—	344	4	no	—
694	D₄	—	2	4	no	—
695	D₄	—	2	2	no	—
696	D₄	—	86	4	no	—
697	D₄	—	86	2	no	—
698	D₄	—	86	4	no	—
699	D₄	—	86	2	no	—
700	D₄	—	344	4	no	—
701	D₄	—	344	4	no	—
702	D₄	—	344	4	no	—
703	D₄	—	344	4	no	—
704	D₄	—	344	4	no	—
705	D₄	—	172	4	no	—
706	D₄	—	172	4	no	—
707	C₂×C₄	—	2	2	no	—
708	C₂×C₄	—	2	4	no	—
709	C₂×C₄	—	2	2	no	—
710	C₂×C₄	—	2	2	no	—
711	C₂×C₄	—	4	1	no	—
712	C₂×C₄	—	4	2	no	—
713	C₂×C₄	—	86	2	no	—
714	C₂×C₄	—	86	2	no	—
715	C₂×C₄	—	86	2	no	—
716	C₂×C₄	—	86	4	no	—
717	C₂×C₄	—	344	4	no	—
718	C₂×C₄	—	344	2	no	—
719	C₂×C₄	—	344	2	no	—
720	C₂×C₄	—	172	8	no	—
721	C₂×C₄	—	172	4	no	—
722	C₂×C₄	—	172	4	no	—
723	C₂×C₄	C₂²×D₁₇₂	1	1	yes	characteristic
724	C₂×C₄	C₂²×D₁₇₂	1	1	yes	characteristic
725	C₂×C₄	C₂²×D₁₇₂	1	2	yes	—
726	C₂×C₄	C₂²×D₁₇₂	1	2	yes	—
727	C₂×C₄	C₂²×D₁₇₂	1	1	yes	characteristic
728	C₂×C₄	C₂²×D₁₇₂	1	2	yes	—
729	C₂×C₄	C₂²×D₁₇₂	1	1	yes	characteristic
730	C₂×C₄	C₂²×D₁₇₂	1	1	yes	characteristic
731	C₂×C₄	C₂×#10621898	1	2	yes	—
732	C₂×C₄	C₂×#10621898	1	2	yes	—
733	C₂×C₄	C₂⁴×D₄₃	1	1	yes	characteristic
734	C₈	—	2	1	no	—
735	C₈	—	2	1	no	—
736	C₈	—	2	2	no	—
737	C₈	C₂×#10621898	1	2	yes	—
738	C₈	C₂×#10621898	1	4	yes	—
739	C₈	C₂×#10621898	1	2	yes	—
740	C₂²	—	2	1	no	—
741	C₂²	—	2	1	no	—
742	C₂²	—	2	2	no	—
743	C₂²	—	2	2	no	—
744	C₂²	—	2	2	no	—
745	C₂²	—	344	8	no	—
746	C₂²	—	172	4	no	—
747	C₂²	—	172	2	no	—
748	C₂²	—	172	2	no	—
749	C₂²	—	172	4	no	—
750	C₂²	—	172	2	no	—
751	C₂²	—	172	4	no	—
752	C₂²	#14583449	1	2	yes	—
753	C₂²	C₂³×D₁₇₂	1	1	yes	characteristic
754	C₄	—	2	1	no	—
755	C₄	—	2	2	no	—
756	C₄	—	2	1	no	—
757	C₄	—	2	1	no	—
758	C₄	—	2	2	no	—
759	C₄	—	2	2	no	—
760	C₄	—	172	4	no	—
761	C₄	—	172	2	no	—
762	C₄	—	172	2	no	—
763	C₄	—	172	2	no	—
764	C₄	#14583449	1	2	yes	—
765	C₄	#14583704	1	2	yes	—
766	C₄	C₂²×#10621898	1	1	yes	characteristic
767	C₄	C₂²×#10621898	1	1	yes	characteristic
768	C₂	—	2	2	no	—
769	C₂	—	4	2	no	—
770	C₂	—	344	4	no	—
771	C₂	—	344	2	no	—
772	C₂	C₂×#14583449	1	1	yes	characteristic
773	C₂	C₂×#14583704	1	1	yes	characteristic
774	C₂	#19149369	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂²×D₁₇₂
commutator, cosocle	C₂×C₄×C₄₃	C₂⁵
Frattini	C₂×C₄	C₂⁴×D₄₃
Fitting	C₄×#131×C₄₃	C₂
socle	C₂²×C₄₃	C₂³×D₄
hypercenter	C₄×#131	D₄₃
hypocenter	C₄₃	#60695
LCS	G ▷ C₂×C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂×C₄ ◁ C₄×#41 ◁ C₄×#131

Complements

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

N	H ≅ G/N	type
1. #19148011	C₂	semidirect
2. #19145278	C₂	semidirect
3. #19145245	C₂	semidirect
4. #19145234	C₂	semidirect
5. #19145190	C₂	semidirect
6. #19145174	C₂	semidirect
7. #19145165	C₂	semidirect
8. #19145134	C₂	semidirect
9. #19145081	C₂	semidirect
10. #19144951	C₂	semidirect
11. #19144275	C₂	semidirect
12. #19144265	C₂	semidirect
13. #19144243	C₂	semidirect
14. C₄×#13063353	C₂	semidirect
15. C₄×#13063347	C₂	semidirect
16. C₂×C₄×D₃₄₄	C₂	semidirect
17. C₄×#131×C₄₃	C₂	semidirect
23. #14583520	C₂²	semidirect
24. #14583504	C₂²	semidirect
30. #14583449	C₂²	semidirect
33. #14583433	C₂²	semidirect
37. #14583308	C₂²	semidirect
38. #14583304	C₂²	semidirect
39. #14583301	C₂²	semidirect
43. #14583264	C₂²	semidirect
44. #14583259	C₂²	semidirect
45. #14583254	C₂²	semidirect
46. #14583246	C₂²	semidirect
48. #14583152	C₂²	semidirect
49. #14583145	C₂²	semidirect
50. #14583145	C₂²	semidirect
51. #14583140	C₂²	semidirect
54. #14583135	C₂²	semidirect
55. #14583135	C₂²	semidirect
56. #14583128	C₂²	semidirect
57. #14583012	C₂²	semidirect
58. #14583001	C₂²	semidirect
59. C₄×Dic₁₇₂	C₂²	semidirect
60. C₄×Dic₁₇₂	C₂²	semidirect
61. C₄×#10621873	C₂²	semidirect
62. C₄×#10621873	C₂²	semidirect
63. C₄×#10621873	C₂²	semidirect
68. C₄×D₃₄₄	C₂²	semidirect
69. C₄×D₃₄₄	C₂²	semidirect
70. C₄×D₃₄₄	C₂²	semidirect
83. C₄₃×#405	C₂²	semidirect
84. C₄₃×#405	C₂²	semidirect
86. C₄×M₁₆×C₄₃	C₂²	semidirect
88. C₂×C₄×C₈×C₄₃	C₂²	semidirect
239. M₁₆×C₄₃	#41	semidirect
243. C₂×C₈×C₄₃	#41	semidirect
397. C₄×#131	D₄₃	semidirect
470. #405	C₂×D₄₃	semidirect
471. #405	C₂×D₄₃	semidirect
473. C₄×M₁₆	C₂×D₄₃	semidirect
475. C₂×C₄×C₈	C₂×D₄₃	semidirect
476. C₄₃	#60695	semidirect
634. M₁₆	#10621898	semidirect
638. C₂×C₈	#10621898	semidirect

Maximal subgroups

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

subgroup	index
#19148011	2
#19145278	2
#19145245	2
#19145234	2
#19145190	2
#19145174	2
#19145165	2
#19145134	2
#19145081	2
#19144951	2
#19144275	2
#19144265	2
#19144243	2
C₄×#13063353	2
C₄×#13063347	2
C₂×C₄×D₃₄₄	2
C₄×#131×C₄₃	2
#60695	43