Subgroups — #25978034

Order 11008.

1890 conjugacy classes of subgroups.

The subgroup lattice has 752 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#19148159	C₂	1	2	yes	maximal, complemented
2	#19147584	C₂	1	1	yes	maximal, characteristic, complemented
3	#19147463	C₂	1	1	yes	maximal, characteristic, complemented
4	#19147246	C₂	1	2	yes	maximal, complemented
5	#19147018	C₂	1	1	yes	maximal, characteristic, complemented
6	#19146964	C₂	1	2	yes	maximal, complemented
7	#19146524	C₂	1	2	yes	maximal, complemented
8	#19146432	C₂	1	4	yes	maximal, complemented
9	#19146317	C₂	1	1	yes	maximal, characteristic, complemented
10	#19146282	C₂	1	2	yes	maximal, complemented
11	#19145181	C₂	1	1	yes	maximal, characteristic, complemented
12	#19145165	C₂	1	2	yes	maximal, complemented
13	#19144615	C₂	1	4	yes	maximal, complemented
14	#19144604	C₂	1	2	yes	maximal, complemented
15	C₄×#13063347	C₂	1	2	yes	maximal, complemented
16	C₂×C₄×D₃₄₄	C₂	1	1	yes	maximal, characteristic, complemented
17	C₈×#41×C₄₃	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂×#13063347	C₂²	1	2	yes	—
19	C₂²×D₃₄₄	C₂²	1	1	yes	characteristic
20	#14583622	C₂²	1	2	yes	complemented
21	#14583614	C₂²	1	2	yes	complemented
22	#14583609	C₂²	1	2	yes	complemented
23	#14583599	—	2	2	no	—
24	#14583590	—	2	2	no	—
25	#14583589	C₂²	1	4	yes	—
26	#14583578	—	2	4	no	—
27	#14583554	C₂²	1	2	yes	complemented
28	#14583545	C₂²	1	4	yes	—
29	#14583456	C₂²	1	2	yes	—
30	#14583433	C₂²	1	4	yes	complemented
31	#14583427	—	2	4	no	—
32	#14583406	—	2	2	no	—
33	C₄×#10621898	C₂²	1	4	yes	complemented
34	C₂×C₄×D₁₇₂	C₂²	1	2	yes	—
35	#117×D₄₃	—	2	2	no	—
36	#14583304	C₂²	1	1	yes	characteristic, complemented
37	#14583301	C₂²	1	2	yes	complemented
38	#14583283	C₂²	1	2	yes	—
39	#14583279	C₂²	1	1	yes	characteristic, complemented
40	#14583254	C₂²	1	4	yes	complemented
41	#14583250	C₂²	1	2	yes	complemented
42	#14583241	C₂²	1	4	yes	complemented
43	#14583230	C₂²	1	4	yes	—
44	#14583224	C₂²	1	4	yes	complemented
45	#14583207	C₂²	1	4	yes	complemented
46	#14583200	C₂²	1	4	yes	complemented
47	#14583190	C₂²	1	2	yes	complemented
48	#14583190	C₂²	1	2	yes	complemented
49	#14583140	C₂²	1	2	yes	—
50	#14583140	C₂²	1	2	yes	—
51	#14583140	C₂²	1	2	yes	complemented
52	#14583135	C₂²	1	2	yes	—
53	#14583128	C₂²	1	4	yes	complemented
54	#14583122	C₂²	1	4	yes	complemented
55	#14583115	C₂²	1	4	yes	—
56	#14583105	C₂²	1	2	yes	complemented
57	#14583105	C₂²	1	2	yes	complemented
58	#14583063	C₂²	1	4	yes	complemented
59	#14583052	C₂²	1	4	yes	—
60	#14583046	C₂²	1	4	yes	—
61	C₄×Dic₁₇₂	C₂²	1	2	yes	complemented
62	C₄×Dic₁₇₂	C₂²	1	2	yes	complemented
63	C₄×Dic₁₇₂	C₂²	1	2	yes	complemented
64	C₄×#10621873	C₂²	1	4	yes	complemented
65	C₄×#10621873	C₂²	1	4	yes	complemented
66	C₄×#10621873	C₂²	1	4	yes	complemented
67	C₄×D₃₄₄	C₂²	1	1	yes	characteristic
68	C₄×D₃₄₄	C₂²	1	2	yes	—
69	C₄×D₃₄₄	C₂²	1	2	yes	—
70	C₄×D₃₄₄	C₂²	1	1	yes	characteristic
71	C₄×D₃₄₄	C₂²	1	2	yes	—
72	C₄×D₃₄₄	C₂²	1	1	yes	characteristic
73	C₄×D₃₄₄	C₂²	1	1	yes	characteristic
74	#14582937	C₂²	1	2	yes	complemented
75	C₂×#13063259	C₂²	1	1	yes	characteristic
76	#14582896	C₂²	1	4	yes	complemented
77	C₂×#13063247	C₂²	1	2	yes	—
78	C₄×#41×C₄₃	C₂²	1	1	yes	characteristic
79	C₈×Q₈×C₄₃	C₂²	1	1	yes	characteristic, complemented
80	C₈×Q₈×C₄₃	C₂²	1	1	yes	characteristic, complemented
81	C₈×D₄×C₄₃	C₂²	1	2	yes	—
82	C₈×D₄×C₄₃	C₂²	1	2	yes	—
83	C₈×D₄×C₄₃	C₂²	1	1	yes	characteristic, complemented
84	C₈×D₄×C₄₃	C₂²	1	1	yes	characteristic, complemented
85	C₄₃×#431	C₂²	1	1	yes	characteristic
86	C₄₃×#431	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	C₂³	1	4	yes	—
90	C₂²×D₁₇₂	C₂³	1	2	yes	—
91	C₂²×C₄×D₄₃	—	2	2	no	—
92	#13063347	—	2	8	no	—
93	C₂×Dic₁₇₂	C₂³	1	2	yes	—
94	C₂×Dic₁₇₂	C₂³	1	2	yes	—
95	C₂×#10621873	C₂³	1	4	yes	—
96	C₂×#10621873	C₂³	1	4	yes	—
97	C₂×D₃₄₄	—	2	4	no	—
98	C₂×D₃₄₄	C₂³	1	2	yes	—
99	C₂×D₃₄₄	C₂³	1	1	yes	characteristic
100	C₂×D₃₄₄	C₂³	1	1	yes	characteristic
101	#13063325	C₂³	1	2	yes	—
102	#13063325	C₂³	1	2	yes	—
103	#13063320	—	2	4	no	—
104	#13063319	—	2	4	no	—
105	#13063318	—	2	4	no	—
106	#13063317	—	2	2	no	—
107	#13063317	C₂³	1	4	yes	—
108	#13063315	—	2	4	no	—
109	#13063313	C₂³	1	4	yes	—
110	#13063311	—	2	4	no	—
111	#13063310	—	2	4	no	—
112	#13063308	—	2	4	no	—
113	#13063307	—	2	4	no	—
114	#13063306	—	2	4	no	—
115	#13063304	—	2	2	no	—
116	#13063304	C₂³	1	4	yes	—
117	#13063304	C₂³	1	4	yes	—
118	#13063303	—	2	4	no	—
119	#13063301	—	2	2	no	—
120	#13063301	—	2	2	no	—
121	#13063299	C₂³	1	4	yes	—
122	#13063298	—	2	4	no	—
123	#13063296	—	2	2	no	—
124	#13063296	—	2	2	no	—
125	#13063293	—	2	4	no	—
126	C₄×Dic₈₆	—	2	2	no	—
127	C₄×Dic₈₆	C₂³	1	4	yes	—
128	C₄×Dic₈₆	C₂³	1	4	yes	—
129	C₄×D₁₇₂	—	2	2	no	—
130	C₄×D₁₇₂	—	2	2	no	—
131	C₄×D₁₇₂	C₂³	1	2	yes	—
132	C₄×D₁₇₂	C₂³	1	4	yes	—
133	C₄×D₁₇₂	C₂³	1	2	yes	—
134	C₄×D₁₇₂	C₂³	1	2	yes	—
135	C₄×D₁₇₂	C₂³	1	2	yes	—
136	C₄×C₂²⋊D₄₃	—	2	4	no	—
137	C₄×C₂²⋊D₄₃	—	2	4	no	—
138	C₄×C₂²⋊D₄₃	—	2	4	no	—
139	#13063284	—	2	2	no	—
140	#13063284	C₂³	1	4	yes	—
141	#13063283	—	2	2	no	—
142	#13063283	—	2	2	no	—
143	#13063282	—	2	4	no	—
144	#13063282	—	2	4	no	—
145	#13063281	—	2	4	no	—
146	C₂×C₄⋊Dic₄₃	C₂³	1	2	yes	—
147	C₄⋊C₄×D₄₃	—	2	2	no	—
148	C₄⋊C₄×D₄₃	—	2	2	no	—
149	C₂×(C₂×D₄₃)⋊C₄	—	2	2	no	—
150	C₂²⋊C₄×D₄₃	—	2	4	no	—
151	C₄²×D₄₃	—	2	4	no	—
152	#13063259	C₂³	1	1	yes	characteristic
153	#13063259	C₂³	1	2	yes	—
154	#13063259	C₂³	1	2	yes	—
155	#13063259	C₂³	1	1	yes	characteristic
156	#13063259	C₂³	1	2	yes	—
157	#13063257	C₂³	1	4	yes	—
158	#13063257	C₂³	1	4	yes	—
159	#13063250	C₂³	1	4	yes	—
160	#13063250	C₂³	1	4	yes	—
161	#13063250	C₂³	1	4	yes	—
162	#13063250	C₂³	1	4	yes	—
163	#13063247	C₂³	1	4	yes	—
164	#13063247	C₂³	1	4	yes	—
165	#13063247	C₂³	1	2	yes	—
166	#13063247	C₂³	1	2	yes	—
167	#13063247	C₂³	1	2	yes	—
168	#13063247	C₂³	1	2	yes	—
169	C₂×#41×C₄₃	D₄	1	1	yes	characteristic
170	C₂²×C₈×C₄₃	C₂³	1	2	yes	—
171	C₂²×C₈×C₄₃	C₂³	1	1	yes	characteristic
172	C₂²×C₈×C₄₃	C₂³	1	2	yes	—
173	C₂²×C₈×C₄₃	C₂³	1	1	yes	characteristic
174	C₄×Q₈×C₄₃	D₄	1	1	yes	characteristic
175	C₄×Q₈×C₄₃	C₂³	1	1	yes	characteristic
176	C₄×D₄×C₄₃	D₄	1	2	yes	—
177	C₄×D₄×C₄₃	D₄	1	1	yes	characteristic
178	C₄×D₄×C₄₃	C₂³	1	1	yes	characteristic
179	C₄×D₄×C₄₃	C₂³	1	2	yes	—
180	#117×C₄₃	D₄	1	1	yes	characteristic
181	#117×C₄₃	D₄	1	2	yes	—
182	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
183	C₂×C₄²×C₄₃	C₂³	1	2	yes	—
184	C₄⋊C₈×C₄₃	C₂³	1	1	yes	characteristic
185	C₄⋊C₈×C₄₃	C₂³	1	1	yes	characteristic
186	C₄⋊C₈×C₄₃	C₂³	1	2	yes	—
187	C₄⋊C₈×C₄₃	C₂³	1	2	yes	—
188	C₂²⋊C₈×C₄₃	C₂³	1	2	yes	—
189	C₂²⋊C₈×C₄₃	C₂³	1	2	yes	—
190	C₂²⋊C₈×C₄₃	C₂³	1	2	yes	—
191	C₄×C₈×C₄₃	C₂³	1	2	yes	—
192	C₄×C₈×C₄₃	C₂³	1	1	yes	characteristic
193	C₄×C₈×C₄₃	C₂³	1	1	yes	characteristic
194	C₄×C₈×C₄₃	C₂³	1	1	yes	characteristic
195	C₄×C₈×C₄₃	C₂³	1	1	yes	characteristic
196	C₄×C₈×C₄₃	C₂³	1	2	yes	—
197	C₄×C₈×C₄₃	C₂³	1	2	yes	—
198	C₂³×D₄₃	—	2	2	no	—
199	#41×C₄₃	—	2	4	no	—
200	C₂×Q₈×C₄₃	C₂×D₄	1	1	yes	characteristic
201	C₂×D₄×C₄₃	C₂×D₄	1	2	yes	—
202	C₂×D₄×C₄₃	C₂×D₄	1	1	yes	characteristic
203	C₂²×C₄×C₄₃	C₂×D₄	1	2	yes	—
204	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
205	C₂²×C₄×C₄₃	C₂×D₄	1	2	yes	—
206	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
207	C₂²×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
208	C₂²×C₄×C₄₃	C₂⁴	1	2	yes	—
209	C₂×C₂²⋊D₄₃	—	2	4	no	—
210	C₂×C₂²⋊D₄₃	—	2	4	no	—
211	C₂²×Dic₄₃	—	2	2	no	—
212	#10621898	—	2	8	no	—
213	#10621898	—	4	4	no	—
214	C₂×D₁₇₂	—	2	2	no	—
215	C₂×D₁₇₂	—	2	4	no	—
216	C₂×D₁₇₂	—	4	2	no	—
217	C₂×D₁₇₂	C₂⁴	1	2	yes	—
218	C₂×D₁₇₂	C₂⁴	1	2	yes	—
219	C₂×C₄×D₄₃	—	2	2	no	—
220	C₂×C₄×D₄₃	—	2	4	no	—
221	C₂×C₄×D₄₃	—	2	2	no	—
222	C₂×C₄×D₄₃	—	2	2	no	—
223	C₂×C₄×D₄₃	—	2	2	no	—
224	C₂×C₄×D₄₃	—	2	4	no	—
225	C₂×C₄×D₄₃	—	4	8	no	—
226	C₂×Dic₈₆	—	2	2	no	—
227	C₂×Dic₈₆	C₂⁴	1	4	yes	—
228	C₂×C₈×C₄₃	—	2	2	no	—
229	C₂×C₈×C₄₃	—	2	4	no	—
230	C₂×C₈×C₄₃	—	4	2	no	—
231	C₂×C₈×C₄₃	—	4	1	no	—
232	C₂×C₈×C₄₃	C₂⁴	1	1	yes	characteristic
233	C₂×C₈×C₄₃	C₂⁴	1	1	yes	characteristic
234	C₂×C₈×C₄₃	C₂⁴	1	2	yes	—
235	C₂×C₈×C₄₃	C₂⁴	1	2	yes	—
236	C₂×C₈×C₄₃	C₂⁴	1	1	yes	characteristic
237	C₂×C₈×C₄₃	C₂⁴	1	1	yes	characteristic
238	C₄⋊C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
239	C₄⋊C₄×C₄₃	C₂×D₄	1	2	yes	—
240	C₄⋊C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
241	C₄⋊C₄×C₄₃	C₂×D₄	1	2	yes	—
242	C₂²⋊C₄×C₄₃	C₂×D₄	1	2	yes	—
243	C₂²⋊C₄×C₄₃	C₂×D₄	1	2	yes	—
244	C₂²⋊C₄×C₄₃	C₂×D₄	1	2	yes	—
245	C₄²×C₄₃	C₂×D₄	1	2	yes	—
246	C₄²×C₄₃	C₂×D₄	1	1	yes	characteristic
247	C₄²×C₄₃	C₂×D₄	1	2	yes	—
248	C₄²×C₄₃	C₂×D₄	1	1	yes	characteristic
249	C₄²×C₄₃	C₂⁴	1	1	yes	characteristic
250	C₄²×C₄₃	C₂⁴	1	1	yes	characteristic
251	C₄²×C₄₃	C₂⁴	1	2	yes	—
252	C₂²⋊Dic₄₃	—	2	4	no	—
253	C₂²⋊Dic₄₃	—	2	4	no	—
254	C₂²⋊Dic₄₃	—	2	4	no	—
255	(C₂×D₄₃)⋊C₄	—	2	4	no	—
256	(C₂×D₄₃)⋊C₄	—	2	4	no	—
257	(C₂×D₄₃)⋊C₄	—	2	2	no	—
258	(C₂×D₄₃)⋊C₄	—	2	2	no	—
259	(C₂×D₄₃)⋊C₄	—	2	2	no	—
260	(C₂×D₄₃)⋊C₄	—	2	2	no	—
261	(C₂×D₄₃)⋊C₄	—	2	4	no	—
262	(C₂×D₄₃)⋊C₄	—	2	4	no	—
263	C₄⋊Dic₄₃	—	2	2	no	—
264	C₄⋊Dic₄₃	—	2	2	no	—
265	C₄⋊Dic₄₃	—	2	2	no	—
266	C₄⋊Dic₄₃	—	2	2	no	—
267	C₄⋊Dic₄₃	C₂⁴	1	2	yes	—
268	C₄⋊Dic₄₃	C₂⁴	1	2	yes	—
269	C₄⋊Dic₄₃	C₂⁴	1	4	yes	—
270	Dic₄₃⋊C₄	—	2	4	no	—
271	Dic₄₃⋊C₄	—	2	4	no	—
272	Dic₄₃⋊C₄	—	2	4	no	—
273	Dic₄₃⋊C₄	—	2	4	no	—
274	Dic₄₃⋊C₄	—	2	4	no	—
275	Dic₄₃⋊C₄	—	2	4	no	—
276	C₄×Dic₄₃	—	2	4	no	—
277	C₄×Dic₄₃	—	2	4	no	—
278	C₄×Dic₄₃	—	2	4	no	—
279	Dic₁₇₂	—	2	4	no	—
280	Dic₁₇₂	—	4	2	no	—
281	D₃₄₄	—	2	4	no	—
282	D₃₄₄	—	2	2	no	—
283	D₃₄₄	#41	1	4	yes	complemented
284	#10621873	—	2	8	no	—
285	#10621873	—	4	4	no	—
286	C₂³×C₄₃	C₂²×D₄	1	2	yes	—
287	C₂³×C₄₃	C₂²×D₄	1	1	yes	characteristic
288	C₂²×D₄₃	—	2	2	no	—
289	C₂²×D₄₃	—	2	2	no	—
290	C₂²×D₄₃	—	4	4	no	—
291	C₂²×D₄₃	—	4	4	no	—
292	C₂²×D₄₃	—	8	2	no	—
293	Q₈×C₄₃	—	2	2	no	—
294	D₄×C₄₃	—	2	4	no	—
295	D₄×C₄₃	—	2	2	no	—
296	C₂×C₄×C₄₃	—	2	4	no	—
297	C₂×C₄×C₄₃	—	2	1	no	—
298	C₂×C₄×C₄₃	—	2	2	no	—
299	C₂×C₄×C₄₃	—	2	1	no	—
300	C₂×C₄×C₄₃	—	2	2	no	—
301	C₂×C₄×C₄₃	—	4	1	no	—
302	C₂×C₄×C₄₃	—	4	2	no	—
303	C₂×C₄×C₄₃	#135	1	4	yes	complemented
304	C₂×C₄×C₄₃	C₂²×D₄	1	2	yes	—
305	C₂×C₄×C₄₃	C₂²×D₄	1	2	yes	—
306	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
307	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
308	C₂×C₄×C₄₃	C₂²×D₄	1	2	yes	—
309	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
310	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
311	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
312	C₂×C₄×C₄₃	C₂⁵	1	1	yes	characteristic
313	C₂²⋊D₄₃	—	4	8	no	—
314	C₂²⋊D₄₃	—	8	4	no	—
315	C₂×Dic₄₃	—	2	2	no	—
316	C₂×Dic₄₃	—	2	4	no	—
317	C₂×Dic₄₃	—	2	4	no	—
318	C₂×Dic₄₃	—	2	2	no	—
319	C₂×Dic₄₃	—	4	4	no	—
320	D₁₇₂	—	2	2	no	—
321	D₁₇₂	—	2	2	no	—
322	D₁₇₂	—	2	2	no	—
323	D₁₇₂	—	4	4	no	—
324	D₁₇₂	C₂×#41	1	4	yes	—
325	C₄×D₄₃	—	4	8	no	—
326	C₄×D₄₃	—	4	4	no	—
327	C₄×D₄₃	—	4	4	no	—
328	C₄×D₄₃	—	4	4	no	—
329	C₄×D₄₃	—	4	4	no	—
330	C₄×D₄₃	—	8	4	no	—
331	Dic₈₆	—	2	4	no	—
332	Dic₈₆	—	2	4	no	—
333	Dic₈₆	—	8	2	no	—
334	C₈×C₄₃	—	2	2	no	—
335	C₈×C₄₃	—	2	1	no	—
336	C₈×C₄₃	—	2	2	no	—
337	C₈×C₄₃	—	2	1	no	—
338	C₈×C₄₃	—	2	1	no	—
339	C₈×C₄₃	C₂×#41	1	2	yes	—
340	#61427	—	43	1	no	maximal, Sylow
341	C₂²×C₄₃	—	2	1	no	—
342	C₂²×C₄₃	—	2	1	no	—
343	C₂²×C₄₃	—	2	2	no	—
344	C₂²×C₄₃	—	2	2	no	—
345	C₂²×C₄₃	—	2	2	no	—
346	C₂²×C₄₃	C₂×#135	1	2	yes	—
347	C₂²×C₄₃	C₂³×D₄	1	1	yes	characteristic
348	C₂×D₄₃	—	2	4	no	—
349	C₂×D₄₃	—	4	2	no	—
350	C₂×D₄₃	—	4	2	no	—
351	C₂×D₄₃	—	4	2	no	—
352	C₂×D₄₃	—	4	2	no	—
353	C₂×D₄₃	—	4	2	no	—
354	C₂×D₄₃	—	8	8	no	—
355	C₄×C₄₃	—	2	1	no	—
356	C₄×C₄₃	—	2	2	no	—
357	C₄×C₄₃	—	2	1	no	—
358	C₄×C₄₃	—	2	2	no	—
359	C₄×C₄₃	—	2	1	no	—
360	C₄×C₄₃	—	2	2	no	—
361	C₄×C₄₃	C₂×#135	1	2	yes	—
362	C₄×C₄₃	C₂×#135	1	2	yes	—
363	C₄×C₄₃	C₂²×#41	1	1	yes	characteristic
364	C₄×C₄₃	#585	1	1	yes	characteristic
365	Dic₄₃	—	4	4	no	—
366	Dic₄₃	—	4	4	no	—
367	Dic₄₃	—	4	2	no	—
368	Dic₄₃	—	4	2	no	—
369	#3475	—	43	2	no	—
370	#3393	—	43	1	no	—
371	#3380	—	43	1	no	—
372	#3360	—	43	2	no	—
373	#3341	—	43	1	no	—
374	#3336	—	43	2	no	—
375	#3303	—	43	2	no	—
376	#3296	—	43	4	no	—
377	#3283	—	43	1	no	—
378	#3280	—	43	2	no	—
379	#3170	—	43	1	no	—
380	#3168	—	43	2	no	—
381	#3102	—	43	4	no	—
382	#3101	—	43	2	no	—
383	C₈×#41	D₄₃	1	1	yes	characteristic, complemented
384	C₄×#135	—	43	2	no	—
385	C₂×C₄×D₈	—	43	1	no	—
386	C₂×C₄₃	—	2	2	no	—
387	C₂×C₄₃	—	4	2	no	—
388	C₂×C₄₃	D₄×#41	1	1	yes	characteristic
389	C₂×C₄₃	C₂²×#135	1	1	yes	characteristic
390	C₂×C₄₃	#3584	1	1	yes	characteristic
391	D₄₃	—	4	4	no	—
392	D₄₃	—	8	2	no	—
393	C₂×#135	—	43	2	no	—
394	C₂²×D₈	—	43	1	no	—
395	#556	—	43	2	no	—
396	#555	—	43	2	no	—
397	#554	—	43	2	no	—
398	#553	—	86	2	no	—
399	#552	—	43	4	no	—
400	#552	—	86	2	no	—
401	#551	—	86	4	no	—
402	#547	—	43	2	no	—
403	#546	—	43	4	no	—
404	#533	—	43	2	no	—
405	#529	—	43	4	no	—
406	#529	—	86	4	no	—
407	#525	—	86	2	no	—
408	C₄×#41	—	43	4	no	—
409	C₄×#41	C₂×D₄₃	1	1	yes	characteristic
410	C₂×C₄×D₄	—	43	2	no	—
411	C₂×#117	—	86	2	no	—
412	#500	—	43	1	no	—
413	#499	—	43	2	no	—
414	#495	—	43	2	no	—
415	#494	—	43	1	no	—
416	#488	—	43	4	no	—
417	#487	—	43	2	no	—
418	#485	—	43	4	no	—
419	#483	—	43	4	no	—
420	#482	—	43	4	no	—
421	#479	—	43	4	no	—
422	#478	—	43	4	no	—
423	#476	—	43	2	no	—
424	#476	—	43	2	no	—
425	#467	—	43	2	no	—
426	#467	—	43	2	no	—
427	#467	—	43	2	no	—
428	#466	—	43	2	no	—
429	#465	—	43	4	no	—
430	#464	—	43	4	no	—
431	#463	—	43	4	no	—
432	#461	—	43	2	no	—
433	#461	—	43	2	no	—
434	#452	—	43	4	no	—
435	#450	—	43	4	no	—
436	#449	—	43	4	no	—
437	C₈×Q₈	C₂×D₄₃	1	1	yes	characteristic, complemented
438	C₈×Q₈	C₂×D₄₃	1	1	yes	characteristic, complemented
439	C₄×Q₁₆	—	43	2	no	—
440	C₄×Q₁₆	—	43	2	no	—
441	C₄×Q₁₆	—	43	2	no	—
442	C₄×SD₁₆	—	43	4	no	—
443	C₄×SD₁₆	—	43	4	no	—
444	C₄×SD₁₆	—	43	4	no	—
445	C₄×D₈	—	43	1	no	—
446	C₄×D₈	—	43	2	no	—
447	C₄×D₈	—	43	2	no	—
448	C₄×D₈	—	43	1	no	—
449	C₄×D₈	—	43	2	no	—
450	C₄×D₈	—	43	1	no	—
451	C₄×D₈	—	43	1	no	—
452	C₈×D₄	C₂×D₄₃	1	2	yes	—
453	C₈×D₄	C₂×D₄₃	1	2	yes	—
454	C₈×D₄	C₂×D₄₃	1	1	yes	characteristic, complemented
455	C₈×D₄	C₂×D₄₃	1	1	yes	characteristic, complemented
456	#431	C₂×D₄₃	1	1	yes	characteristic
457	#431	C₂×D₄₃	1	2	yes	complemented
458	#427	—	43	2	no	—
459	C₂×#107	—	43	1	no	—
460	#416	—	43	4	no	—
461	C₂×#102	—	43	2	no	—
462	C₂×C₄×C₈	C₂×D₄₃	1	1	yes	characteristic
463	C₂×C₄×C₈	C₂×D₄₃	1	2	yes	complemented
464	C₄₃	#61427	1	1	yes	characteristic, complemented, Sylow
465	C₂×#41	—	43	4	no	—
466	C₂×#41	D₁₇₂	1	1	yes	characteristic
467	C₂²×D₄	—	43	2	no	—
468	C₂³×C₄	—	86	2	no	—
469	#135	—	86	8	no	—
470	C₂×Q₁₆	—	43	2	no	—
471	C₂×Q₁₆	—	43	2	no	—
472	C₂×SD₁₆	—	43	4	no	—
473	C₂×SD₁₆	—	43	4	no	—
474	C₂×D₈	—	43	1	no	—
475	C₂×D₈	—	43	2	no	—
476	C₂×D₈	—	43	1	no	—
477	C₂×D₈	—	86	4	no	—
478	C₂²×C₈	C₂²×D₄₃	1	1	yes	characteristic
479	C₂²×C₈	C₂²×D₄₃	1	2	yes	—
480	C₂²×C₈	C₂²×D₄₃	1	1	yes	characteristic
481	C₂²×C₈	C₂²×D₄₃	1	2	yes	—
482	C₄⋊Q₈	—	43	2	no	—
483	C₄⋊Q₈	—	43	2	no	—
484	#126	—	86	4	no	—
485	#126	—	86	4	no	—
486	#126	—	86	4	no	—
487	#125	—	43	4	no	—
488	#125	—	86	4	no	—
489	#125	—	86	2	no	—
490	#124	—	43	4	no	—
491	#124	—	86	4	no	—
492	#123	—	86	4	no	—
493	#123	—	86	4	no	—
494	#123	—	86	4	no	—
495	#123	—	86	4	no	—
496	C₂²⋊Q₈	—	43	4	no	—
497	C₂²⋊Q₈	—	43	4	no	—
498	C₂²⋊Q₈	—	86	2	no	—
499	C₂²⋊Q₈	—	86	2	no	—
500	C₂²⋊Q₈	—	86	2	no	—
501	C₂²⋊Q₈	—	86	4	no	—
502	#121	—	43	4	no	—
503	#121	—	86	2	no	—
504	#121	—	86	2	no	—
505	#121	—	86	4	no	—
506	#120	—	86	4	no	—
507	C₄×Q₈	—	43	4	no	—
508	C₄×Q₈	—	43	4	no	—
509	C₄×Q₈	—	86	2	no	—
510	C₄×Q₈	D₁₇₂	1	1	yes	characteristic
511	C₄×Q₈	C₂²×D₄₃	1	1	yes	characteristic
512	C₄×D₄	—	43	2	no	—
513	C₄×D₄	—	43	2	no	—
514	C₄×D₄	—	43	2	no	—
515	C₄×D₄	—	43	2	no	—
516	C₄×D₄	—	43	4	no	—
517	C₄×D₄	—	86	4	no	—
518	C₄×D₄	—	86	4	no	—
519	C₄×D₄	—	86	4	no	—
520	C₄×D₄	—	86	2	no	—
521	C₄×D₄	—	86	2	no	—
522	C₄×D₄	D₁₇₂	1	2	yes	—
523	C₄×D₄	D₁₇₂	1	1	yes	characteristic
524	C₄×D₄	C₂²×D₄₃	1	2	yes	—
525	C₄×D₄	C₂²×D₄₃	1	1	yes	characteristic
526	#117	—	43	4	no	—
527	#117	—	86	2	no	—
528	#117	—	86	2	no	—
529	#117	—	86	2	no	—
530	#117	—	86	4	no	—
531	#117	—	86	4	no	—
532	#117	—	86	4	no	—
533	#117	D₁₇₂	1	1	yes	characteristic
534	#117	D₁₇₂	1	2	yes	—
535	C₂×C₄⋊C₄	—	43	2	no	—
536	C₂×C₄⋊C₄	—	86	2	no	—
537	C₂×C₄⋊C₄	—	86	2	no	—
538	C₂×C₂²⋊C₄	—	86	2	no	—
539	C₂×C₂²⋊C₄	—	86	4	no	—
540	C₂×C₄²	—	86	4	no	—
541	C₂×C₄²	C₂²×D₄₃	1	1	yes	characteristic
542	C₂×C₄²	C₂²×D₄₃	1	2	yes	—
543	#107	—	43	1	no	—
544	#107	—	43	1	no	—
545	#107	—	43	2	no	—
546	#107	—	43	2	no	—
547	#107	—	43	2	no	—
548	#106	—	43	4	no	—
549	#106	—	43	4	no	—
550	C₄⋊C₈	C₂²×D₄₃	1	1	yes	characteristic
551	C₄⋊C₈	C₂²×D₄₃	1	1	yes	characteristic
552	C₄⋊C₈	C₂²×D₄₃	1	2	yes	—
553	C₄⋊C₈	C₂²×D₄₃	1	2	yes	—
554	#103	—	43	4	no	—
555	#103	—	43	4	no	—
556	#103	—	43	4	no	—
557	#103	—	43	4	no	—
558	#102	—	43	2	no	—
559	#102	—	43	2	no	—
560	#102	—	43	2	no	—
561	#102	—	43	2	no	—
562	#102	—	43	4	no	—
563	#102	—	43	4	no	—
564	C₂²⋊C₈	C₂²×D₄₃	1	2	yes	—
565	C₂²⋊C₈	C₂²×D₄₃	1	2	yes	—
566	C₂²⋊C₈	C₂²×D₄₃	1	2	yes	—
567	C₄×C₈	C₂²×D₄₃	1	1	yes	characteristic
568	C₄×C₈	C₂²×D₄₃	1	1	yes	characteristic
569	C₄×C₈	C₂²×D₄₃	1	1	yes	characteristic
570	C₄×C₈	C₂²×D₄₃	1	1	yes	characteristic
571	C₄×C₈	C₂²×D₄₃	1	2	yes	—
572	C₄×C₈	C₂²×D₄₃	1	2	yes	—
573	C₄×C₈	C₂²×D₄₃	1	2	yes	—
574	C₂⁴	—	86	2	no	—
575	#41	—	2	4	no	—
576	#41	—	86	8	no	—
577	#41	—	172	4	no	—
578	C₂×Q₈	—	43	4	no	—
579	C₂×Q₈	—	86	2	no	—
580	C₂×Q₈	C₂×D₁₇₂	1	1	yes	characteristic
581	C₂×D₄	—	43	2	no	—
582	C₂×D₄	—	43	2	no	—
583	C₂×D₄	—	86	4	no	—
584	C₂×D₄	—	86	4	no	—
585	C₂×D₄	—	86	4	no	—
586	C₂×D₄	—	86	2	no	—
587	C₂×D₄	—	172	2	no	—
588	C₂×D₄	C₂×D₁₇₂	1	2	yes	—
589	C₂×D₄	C₂×D₁₇₂	1	1	yes	characteristic
590	C₂²×C₄	—	86	2	no	—
591	C₂²×C₄	—	86	4	no	—
592	C₂²×C₄	—	86	4	no	—
593	C₂²×C₄	—	86	2	no	—
594	C₂²×C₄	—	86	2	no	—
595	C₂²×C₄	—	86	2	no	—
596	C₂²×C₄	—	86	2	no	—
597	C₂²×C₄	—	172	8	no	—
598	C₂²×C₄	C₂×D₁₇₂	1	2	yes	—
599	C₂²×C₄	C₂×D₁₇₂	1	1	yes	characteristic
600	C₂²×C₄	C₂×D₁₇₂	1	2	yes	—
601	C₂²×C₄	C₂×D₁₇₂	1	1	yes	characteristic
602	C₂²×C₄	C₂³×D₄₃	1	1	yes	characteristic
603	C₂²×C₄	C₂³×D₄₃	1	2	yes	—
604	Q₁₆	—	86	4	no	—
605	Q₁₆	—	172	2	no	—
606	SD₁₆	—	86	8	no	—
607	SD₁₆	—	172	4	no	—
608	D₈	—	43	4	no	—
609	D₈	—	86	4	no	—
610	D₈	—	86	2	no	—
611	C₂×C₈	—	2	2	no	—
612	C₂×C₈	—	2	4	no	—
613	C₂×C₈	—	4	2	no	—
614	C₂×C₈	—	4	1	no	—
615	C₂×C₈	C₂³×D₄₃	1	1	yes	characteristic
616	C₂×C₈	C₂³×D₄₃	1	1	yes	characteristic
617	C₂×C₈	C₂³×D₄₃	1	2	yes	—
618	C₂×C₈	C₂³×D₄₃	1	2	yes	—
619	C₂×C₈	C₂³×D₄₃	1	1	yes	characteristic
620	C₂×C₈	C₂³×D₄₃	1	1	yes	characteristic
621	C₄⋊C₄	—	43	2	no	—
622	C₄⋊C₄	—	43	2	no	—
623	C₄⋊C₄	—	43	4	no	—
624	C₄⋊C₄	—	86	2	no	—
625	C₄⋊C₄	—	86	2	no	—
626	C₄⋊C₄	—	86	2	no	—
627	C₄⋊C₄	—	86	4	no	—
628	C₄⋊C₄	—	86	4	no	—
629	C₄⋊C₄	—	86	4	no	—
630	C₄⋊C₄	—	86	4	no	—
631	C₄⋊C₄	—	86	4	no	—
632	C₄⋊C₄	—	86	4	no	—
633	C₄⋊C₄	—	86	2	no	—
634	C₄⋊C₄	C₂×D₁₇₂	1	1	yes	characteristic
635	C₄⋊C₄	C₂×D₁₇₂	1	1	yes	characteristic
636	C₄⋊C₄	C₂×D₁₇₂	1	2	yes	—
637	C₄⋊C₄	C₂×D₁₇₂	1	2	yes	—
638	C₂²⋊C₄	—	86	4	no	—
639	C₂²⋊C₄	—	86	4	no	—
640	C₂²⋊C₄	—	86	4	no	—
641	C₂²⋊C₄	—	86	2	no	—
642	C₂²⋊C₄	—	86	4	no	—
643	C₂²⋊C₄	—	86	4	no	—
644	C₂²⋊C₄	—	86	2	no	—
645	C₂²⋊C₄	—	86	2	no	—
646	C₂²⋊C₄	—	86	2	no	—
647	C₂²⋊C₄	—	86	4	no	—
648	C₂²⋊C₄	—	86	4	no	—
649	C₂²⋊C₄	C₂×D₁₇₂	1	2	yes	—
650	C₂²⋊C₄	C₂×D₁₇₂	1	2	yes	—
651	C₂²⋊C₄	C₂×D₁₇₂	1	2	yes	—
652	C₄²	—	86	4	no	—
653	C₄²	—	86	4	no	—
654	C₄²	—	86	4	no	—
655	C₄²	C₂×D₁₇₂	1	2	yes	—
656	C₄²	C₂×D₁₇₂	1	1	yes	characteristic
657	C₄²	C₂×D₁₇₂	1	2	yes	—
658	C₄²	C₂×D₁₇₂	1	1	yes	characteristic
659	C₄²	C₂³×D₄₃	1	1	yes	characteristic
660	C₄²	C₂³×D₄₃	1	2	yes	—
661	C₄²	C₂³×D₄₃	1	1	yes	characteristic
662	C₂³	—	86	2	no	—
663	C₂³	—	86	2	no	—
664	C₂³	—	344	2	no	—
665	C₂³	—	172	4	no	—
666	C₂³	—	172	4	no	—
667	C₂³	C₂²×D₁₇₂	1	2	yes	—
668	C₂³	C₂²×D₁₇₂	1	1	yes	characteristic
669	Q₈	—	2	2	no	—
670	Q₈	—	86	4	no	—
671	Q₈	—	86	4	no	—
672	Q₈	—	344	2	no	—
673	D₄	—	2	4	no	—
674	D₄	—	2	2	no	—
675	D₄	—	43	4	no	—
676	D₄	—	86	2	no	—
677	D₄	—	86	2	no	—
678	D₄	—	86	2	no	—
679	D₄	—	344	4	no	—
680	D₄	—	172	4	no	—
681	D₄	—	172	8	no	—
682	C₂×C₄	—	2	4	no	—
683	C₂×C₄	—	2	1	no	—
684	C₂×C₄	—	2	2	no	—
685	C₂×C₄	—	2	1	no	—
686	C₂×C₄	—	2	2	no	—
687	C₂×C₄	—	4	2	no	—
688	C₂×C₄	—	4	1	no	—
689	C₂×C₄	—	86	2	no	—
690	C₂×C₄	—	86	4	no	—
691	C₂×C₄	—	86	4	no	—
692	C₂×C₄	—	86	2	no	—
693	C₂×C₄	—	344	4	no	—
694	C₂×C₄	—	172	8	no	—
695	C₂×C₄	—	172	4	no	—
696	C₂×C₄	—	172	4	no	—
697	C₂×C₄	—	172	4	no	—
698	C₂×C₄	—	172	4	no	—
699	C₂×C₄	—	172	4	no	—
700	C₂×C₄	#13063347	1	4	yes	complemented
701	C₂×C₄	C₂²×D₁₇₂	1	2	yes	—
702	C₂×C₄	C₂²×D₁₇₂	1	2	yes	—
703	C₂×C₄	C₂²×D₁₇₂	1	1	yes	characteristic
704	C₂×C₄	C₂²×D₁₇₂	1	1	yes	characteristic
705	C₂×C₄	C₂²×D₁₇₂	1	1	yes	characteristic
706	C₂×C₄	C₂²×D₁₇₂	1	2	yes	—
707	C₂×C₄	C₂²×D₁₇₂	1	1	yes	characteristic
708	C₂×C₄	C₂²×D₁₇₂	1	1	yes	characteristic
709	C₂×C₄	C₂⁴×D₄₃	1	1	yes	characteristic
710	C₈	—	2	1	no	—
711	C₈	—	2	2	no	—
712	C₈	—	2	1	no	—
713	C₈	—	2	2	no	—
714	C₈	—	2	1	no	—
715	C₈	#41×D₄₃	1	2	yes	—
716	C₂²	—	2	1	no	—
717	C₂²	—	2	1	no	—
718	C₂²	—	2	2	no	—
719	C₂²	—	2	2	no	—
720	C₂²	—	2	2	no	—
721	C₂²	—	86	4	no	—
722	C₂²	—	344	8	no	—
723	C₂²	—	172	2	no	—
724	C₂²	—	172	2	no	—
725	C₂²	—	172	2	no	—
726	C₂²	—	172	2	no	—
727	C₂²	—	172	2	no	—
728	C₂²	C₂×#13063347	1	2	yes	—
729	C₂²	C₂³×D₁₇₂	1	1	yes	characteristic
730	C₄	—	2	2	no	—
731	C₄	—	2	2	no	—
732	C₄	—	2	1	no	—
733	C₄	—	2	1	no	—
734	C₄	—	2	2	no	—
735	C₄	—	2	1	no	—
736	C₄	—	172	2	no	—
737	C₄	—	172	2	no	—
738	C₄	—	172	4	no	—
739	C₄	—	172	4	no	—
740	C₄	C₂×#13063347	1	2	yes	—
741	C₄	C₂×#13063347	1	2	yes	—
742	C₄	C₂×#41×D₄₃	1	1	yes	characteristic
743	C₄	#14583735	1	1	yes	characteristic
744	C₂	—	2	2	no	—
745	C₂	—	4	2	no	—
746	C₂	—	344	2	no	—
747	C₂	—	172	4	no	—
748	C₂	#41×D₁₇₂	1	1	yes	characteristic
749	C₂	C₂²×#13063347	1	1	yes	characteristic
750	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	C₈×#41×C₄₃	C₂
socle	C₂²×C₄₃	C₂³×D₄
hypercenter	C₈×#41	D₄₃
hypocenter	C₄₃	#61427
LCS	G ▷ C₂×C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂×C₄ ◁ C₄×#41 ◁ C₈×#41

Complements

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

N	H ≅ G/N	type
1. #19148159	C₂	semidirect
2. #19147584	C₂	semidirect
3. #19147463	C₂	semidirect
4. #19147246	C₂	semidirect
5. #19147018	C₂	semidirect
6. #19146964	C₂	semidirect
7. #19146524	C₂	semidirect
8. #19146432	C₂	semidirect
9. #19146317	C₂	semidirect
10. #19146282	C₂	semidirect
11. #19145181	C₂	semidirect
12. #19145165	C₂	semidirect
13. #19144615	C₂	semidirect
14. #19144604	C₂	semidirect
15. C₄×#13063347	C₂	semidirect
16. C₂×C₄×D₃₄₄	C₂	semidirect
17. C₈×#41×C₄₃	C₂	semidirect
20. #14583622	C₂²	semidirect
21. #14583614	C₂²	semidirect
22. #14583609	C₂²	semidirect
27. #14583554	C₂²	semidirect
30. #14583433	C₂²	semidirect
33. C₄×#10621898	C₂²	semidirect
36. #14583304	C₂²	semidirect
37. #14583301	C₂²	semidirect
39. #14583279	C₂²	semidirect
40. #14583254	C₂²	semidirect
41. #14583250	C₂²	semidirect
42. #14583241	C₂²	semidirect
44. #14583224	C₂²	semidirect
45. #14583207	C₂²	semidirect
46. #14583200	C₂²	semidirect
47. #14583190	C₂²	semidirect
48. #14583190	C₂²	semidirect
51. #14583140	C₂²	semidirect
53. #14583128	C₂²	semidirect
54. #14583122	C₂²	semidirect
56. #14583105	C₂²	semidirect
57. #14583105	C₂²	semidirect
58. #14583063	C₂²	semidirect
61. C₄×Dic₁₇₂	C₂²	semidirect
62. C₄×Dic₁₇₂	C₂²	semidirect
63. C₄×Dic₁₇₂	C₂²	semidirect
64. C₄×#10621873	C₂²	semidirect
65. C₄×#10621873	C₂²	semidirect
66. C₄×#10621873	C₂²	semidirect
74. #14582937	C₂²	semidirect
76. #14582896	C₂²	semidirect
79. C₈×Q₈×C₄₃	C₂²	semidirect
80. C₈×Q₈×C₄₃	C₂²	semidirect
83. C₈×D₄×C₄₃	C₂²	semidirect
84. C₈×D₄×C₄₃	C₂²	semidirect
86. C₄₃×#431	C₂²	semidirect
88. C₂×C₄×C₈×C₄₃	C₂²	semidirect
283. D₃₄₄	#41	semidirect
303. C₂×C₄×C₄₃	#135	semidirect
383. C₈×#41	D₄₃	semidirect
437. C₈×Q₈	C₂×D₄₃	semidirect
438. C₈×Q₈	C₂×D₄₃	semidirect
454. C₈×D₄	C₂×D₄₃	semidirect
455. C₈×D₄	C₂×D₄₃	semidirect
457. #431	C₂×D₄₃	semidirect
463. C₂×C₄×C₈	C₂×D₄₃	semidirect
464. C₄₃	#61427	semidirect
700. C₂×C₄	#13063347	semidirect

Maximal subgroups

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

subgroup	index
#19148159	2
#19147584	2
#19147463	2
#19147246	2
#19147018	2
#19146964	2
#19146524	2
#19146432	2
#19146317	2
#19146282	2
#19145181	2
#19145165	2
#19144615	2
#19144604	2
C₄×#13063347	2
C₂×C₄×D₃₄₄	2
C₈×#41×C₄₃	2
#61427	43