Subgroups — #25098762

Order 11008.

926 conjugacy classes of subgroups.

The subgroup lattice has 448 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#19137079	C₂	1	1	yes	maximal, characteristic
2	#117×Dic₄₃	C₂	1	1	yes	maximal, characteristic
3	#19135189	C₂	1	2	yes	maximal, complemented
4	#19135182	C₂	1	2	yes	maximal, complemented
5	#19135175	C₂	1	2	yes	maximal, complemented
6	#19135168	C₂	1	2	yes	maximal, complemented
7	#19134312	C₂	1	1	yes	maximal, characteristic
8	#19134311	C₂	1	1	yes	maximal, characteristic
9	#19134311	C₂	1	1	yes	maximal, characteristic
10	C₂×#14582653	C₂	1	1	yes	maximal, characteristic
11	C₂×C₄₃×#427	C₂	1	1	yes	maximal, characteristic
12	C₂³×C₄₃⋊C₈	C₂²	1	1	yes	characteristic
13	C₂×#13063284	C₂²	1	1	yes	characteristic
14	C₂×#13063284	C₂²	1	1	yes	characteristic
15	C₂²×C₄×Dic₄₃	C₂²	1	1	yes	characteristic
16	#14582798	C₂²	1	2	yes	—
17	#14582798	C₂²	1	2	yes	—
18	#14582774	—	2	2	no	—
19	C₄⋊C₄×Dic₄₃	C₂²	1	2	yes	—
20	C₄⋊C₄×Dic₄₃	C₂²	1	2	yes	—
21	C₄×C₄⋊Dic₄₃	—	2	1	no	—
22	C₄×C₄⋊Dic₄₃	—	2	1	no	—
23	C₂²⋊C₄×Dic₄₃	—	2	2	no	—
24	#14582745	—	2	1	no	—
25	C₄²×Dic₄₃	—	2	1	no	—
26	#14582662	C₂²	1	2	yes	—
27	#14582662	C₂²	1	2	yes	—
28	#14582661	C₂²	1	2	yes	—
29	#14582661	C₂²	1	2	yes	—
30	#14582661	C₂²	1	2	yes	—
31	#14582661	C₂²	1	2	yes	—
32	#14582653	C₂²	1	2	yes	—
33	#14582653	C₂²	1	2	yes	—
34	C₂³×C₈×C₄₃	C₂²	1	1	yes	characteristic
35	C₂×#117×C₄₃	C₂²	1	1	yes	characteristic
36	C₂×#117×C₄₃	C₂²	1	1	yes	characteristic
37	C₄₃×#427	C₄	1	8	yes	complemented
38	C₂×#107×C₄₃	C₂²	1	1	yes	characteristic
39	C₂×#107×C₄₃	C₂²	1	1	yes	characteristic
40	C₂×#106×C₄₃	C₂²	1	1	yes	characteristic
41	C₂×#106×C₄₃	C₂²	1	1	yes	characteristic
42	C₂³×Dic₄₃	D₄	1	2	yes	—
43	C₂²×C₄₃⋊C₈	—	2	2	no	—
44	C₂²×C₄₃⋊C₈	—	2	2	no	—
45	C₂²×C₄₃⋊C₈	—	2	2	no	—
46	C₂²×C₄₃⋊C₈	C₂³	1	2	yes	—
47	#13063284	—	2	2	no	—
48	#13063284	—	2	2	no	—
49	#13063284	—	2	2	no	—
50	#13063284	Q₈	1	4	yes	—
51	C₂×C₄⋊Dic₄₃	—	2	2	no	—
52	C₂×C₄⋊Dic₄₃	—	2	2	no	—
53	C₂×C₄⋊Dic₄₃	C₂³	1	2	yes	—
54	C₂×C₄⋊Dic₄₃	C₂³	1	2	yes	—
55	C₂×C₂²⋊Dic₄₃	—	2	1	no	—
56	C₂×C₂²⋊Dic₄₃	—	2	1	no	—
57	C₂×C₄×Dic₄₃	—	2	1	no	—
58	C₂×C₄×Dic₄₃	—	2	2	no	—
59	C₂×C₄×Dic₄₃	—	2	2	no	—
60	C₂×C₄×Dic₄₃	—	2	1	no	—
61	C₂×C₄×Dic₄₃	—	2	2	no	—
62	C₂×C₄×Dic₄₃	—	2	2	no	—
63	C₂×C₄×Dic₄₃	D₄	1	1	yes	characteristic
64	C₂×C₄×Dic₄₃	D₄	1	1	yes	characteristic
65	C₂×C₄×Dic₄₃	C₂³	1	2	yes	—
66	C₄₃⋊#95	—	2	2	no	—
67	C₄₃⋊#95	—	2	2	no	—
68	C₄₃⋊#95	—	2	2	no	—
69	C₄₃⋊#95	—	2	2	no	—
70	C₂³×C₄×C₄₃	C₂³	1	1	yes	characteristic
71	C₂²×C₈×C₄₃	—	2	2	no	—
72	C₂²×C₈×C₄₃	—	2	2	no	—
73	C₂²×C₈×C₄₃	C₂×C₄	1	4	yes	—
74	C₂²×C₈×C₄₃	C₂³	1	1	yes	characteristic
75	C₂²×C₈×C₄₃	C₂³	1	1	yes	characteristic
76	#117×C₄₃	—	2	2	no	—
77	#117×C₄₃	—	2	2	no	—
78	#117×C₄₃	C₂×C₄	1	4	yes	—
79	#117×C₄₃	C₂×C₄	1	4	yes	—
80	C₂×C₄⋊C₄×C₄₃	C₂³	1	1	yes	characteristic
81	C₂×C₄⋊C₄×C₄₃	C₂³	1	1	yes	characteristic
82	C₂×C₄⋊C₄×C₄₃	C₂³	1	1	yes	characteristic
83	C₂×C₄⋊C₄×C₄₃	C₂³	1	1	yes	characteristic
84	C₂×C₂²⋊C₄×C₄₃	—	2	1	no	—
85	C₂×C₂²⋊C₄×C₄₃	—	2	1	no	—
86	C₂×C₄²×C₄₃	—	2	1	no	—
87	C₂×C₄²×C₄₃	—	2	1	no	—
88	#107×C₄₃	C₂×C₄	1	4	yes	complemented
89	#107×C₄₃	C₂×C₄	1	4	yes	complemented
90	#106×C₄₃	C₂×C₄	1	4	yes	complemented
91	#106×C₄₃	C₂×C₄	1	4	yes	complemented
92	C₂⁴×C₄₃	C₂×D₄	1	1	yes	characteristic
93	C₂²×C₄×C₄₃	—	2	1	no	—
94	C₂²×C₄×C₄₃	—	2	1	no	—
95	C₂²×C₄×C₄₃	—	2	1	no	—
96	C₂²×C₄×C₄₃	—	2	1	no	—
97	C₂²×C₄×C₄₃	C₂²×C₄	1	2	yes	—
98	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
99	C₂²×C₄×C₄₃	C₂×Q₈	1	2	yes	—
100	C₂²×C₄×C₄₃	#41	1	2	yes	—
101	C₂²×C₄×C₄₃	#41	1	2	yes	—
102	C₂²×C₄×C₄₃	#41	1	2	yes	—
103	C₂²×C₄×C₄₃	#41	1	2	yes	—
104	C₂²×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
105	C₂²×Dic₄₃	—	2	4	no	—
106	C₂²×Dic₄₃	—	2	4	no	—
107	C₂²×Dic₄₃	—	2	2	no	—
108	C₂²×Dic₄₃	—	2	2	no	—
109	C₂²×Dic₄₃	—	4	2	no	—
110	C₂²×Dic₄₃	C₂×D₄	1	2	yes	—
111	C₂²×Dic₄₃	C₂×D₄	1	2	yes	—
112	C₂×C₈×C₄₃	—	2	8	no	—
113	C₂×C₈×C₄₃	—	2	1	no	—
114	C₂×C₈×C₄₃	—	2	1	no	—
115	C₂×C₈×C₄₃	—	2	1	no	—
116	C₂×C₈×C₄₃	—	2	1	no	—
117	C₂×C₈×C₄₃	C₂²×C₄	1	2	yes	—
118	C₂×C₈×C₄₃	C₂²×C₄	1	2	yes	—
119	C₄⋊C₄×C₄₃	—	2	1	no	—
120	C₄⋊C₄×C₄₃	—	2	1	no	—
121	C₄⋊C₄×C₄₃	—	2	1	no	—
122	C₄⋊C₄×C₄₃	—	2	1	no	—
123	C₄⋊C₄×C₄₃	C₂²×C₄	1	2	yes	—
124	C₄⋊C₄×C₄₃	C₂²×C₄	1	2	yes	—
125	C₄⋊C₄×C₄₃	C₂²×C₄	1	2	yes	—
126	C₄⋊C₄×C₄₃	C₂²×C₄	1	2	yes	—
127	C₂²⋊C₄×C₄₃	—	2	4	no	—
128	C₂²⋊C₄×C₄₃	—	2	4	no	—
129	C₄²×C₄₃	—	2	4	no	—
130	C₄²×C₄₃	—	2	4	no	—
131	C₂²⋊Dic₄₃	—	2	4	no	—
132	C₂²⋊Dic₄₃	—	4	2	no	—
133	C₄⋊Dic₄₃	—	2	2	no	—
134	C₄⋊Dic₄₃	—	2	2	no	—
135	C₄⋊Dic₄₃	—	2	2	no	—
136	C₄⋊Dic₄₃	—	4	4	no	—
137	C₄⋊Dic₄₃	—	4	4	no	—
138	C₄⋊Dic₄₃	C₂×Q₈	1	4	yes	—
139	C₄×Dic₄₃	—	2	4	no	—
140	C₄×Dic₄₃	—	2	2	no	—
141	C₄×Dic₄₃	—	2	2	no	—
142	C₄×Dic₄₃	—	2	2	no	—
143	C₄×Dic₄₃	—	2	2	no	—
144	C₄×Dic₄₃	—	4	4	no	—
145	C₄×Dic₄₃	—	4	2	no	—
146	C₄×Dic₄₃	—	4	4	no	—
147	C₂×C₄₃⋊C₈	—	2	2	no	—
148	C₂×C₄₃⋊C₈	—	2	2	no	—
149	C₂×C₄₃⋊C₈	—	2	2	no	—
150	C₂×C₄₃⋊C₈	—	4	4	no	—
151	C₂³×C₄₃	—	2	2	no	—
152	C₂³×C₄₃	—	2	2	no	—
153	C₂³×C₄₃	C₄×D₄	1	2	yes	—
154	C₂³×C₄₃	C₂²⋊Q₈	1	2	yes	—
155	C₂³×C₄₃	#123	1	2	yes	—
156	C₂³×C₄₃	C₂²×D₄	1	1	yes	characteristic
157	C₂×C₄×C₄₃	—	2	2	no	—
158	C₂×C₄×C₄₃	—	2	2	no	—
159	C₂×C₄×C₄₃	—	2	2	no	—
160	C₂×C₄×C₄₃	—	2	2	no	—
161	C₂×C₄×C₄₃	—	4	2	no	—
162	C₂×C₄×C₄₃	—	4	2	no	—
163	C₂×C₄×C₄₃	—	4	2	no	—
164	C₂×C₄×C₄₃	—	4	2	no	—
165	C₂×C₄×C₄₃	#117	1	4	yes	—
166	C₂×C₄×C₄₃	C₄×D₄	1	2	yes	—
167	C₂×C₄×C₄₃	C₄×Q₈	1	4	yes	—
168	C₂×C₄×C₄₃	C₂²⋊Q₈	1	2	yes	—
169	C₂×C₄×C₄₃	#123	1	2	yes	—
170	C₂×C₄×C₄₃	#125	1	4	yes	—
171	C₂×C₄×C₄₃	#126	1	4	yes	—
172	C₂×C₄×C₄₃	C₂³×C₄	1	1	yes	characteristic
173	C₂×C₄×C₄₃	C₂²×Q₈	1	1	yes	characteristic
174	C₂×C₄×C₄₃	C₂×#41	1	1	yes	characteristic
175	C₂×C₄×C₄₃	C₂×#41	1	1	yes	characteristic
176	C₂×C₄×C₄₃	C₂×#41	1	1	yes	characteristic
177	C₂×C₄×C₄₃	C₂×#41	1	1	yes	characteristic
178	C₂×Dic₄₃	—	2	2	no	—
179	C₂×Dic₄₃	—	2	2	no	—
180	C₂×Dic₄₃	—	2	4	no	—
181	C₂×Dic₄₃	—	2	2	no	—
182	C₂×Dic₄₃	—	2	2	no	—
183	C₂×Dic₄₃	—	2	2	no	—
184	C₂×Dic₄₃	—	4	8	no	—
185	C₂×Dic₄₃	—	4	2	no	—
186	C₂×Dic₄₃	—	4	2	no	—
187	C₂×Dic₄₃	—	4	2	no	—
188	C₂×Dic₄₃	—	4	2	no	—
189	C₂×Dic₄₃	—	4	2	no	—
190	C₂×Dic₄₃	#135	1	4	yes	—
191	C₈×C₄₃	—	2	2	no	—
192	C₈×C₄₃	—	2	2	no	—
193	C₄₃⋊C₈	—	4	2	no	—
194	#21032	—	43	1	no	maximal, Sylow
195	C₂²×C₄₃	—	2	4	no	—
196	C₂²×C₄₃	—	2	4	no	—
197	C₂²×C₄₃	—	2	2	no	—
198	C₂²×C₄₃	—	2	2	no	—
199	C₂²×C₄₃	#387	1	4	yes	—
200	C₂²×C₄₃	C₂×C₄×D₄	1	1	yes	characteristic
201	C₂²×C₄₃	C₂×C₂²⋊Q₈	1	1	yes	characteristic
202	C₂²×C₄₃	C₂×#123	1	1	yes	characteristic
203	C₂²×C₄₃	C₂×#135	1	2	yes	—
204	C₂²×C₄₃	#575	1	2	yes	—
205	C₄×C₄₃	—	4	2	no	—
206	C₄×C₄₃	—	4	2	no	—
207	C₄×C₄₃	—	4	2	no	—
208	C₄×C₄₃	—	4	2	no	—
209	C₄×C₄₃	#387	1	4	yes	—
210	C₄×C₄₃	C₂×#117	1	1	yes	characteristic
211	C₄×C₄₃	C₂×C₄×Q₈	1	1	yes	characteristic
212	C₄×C₄₃	C₂×#125	1	1	yes	characteristic
213	C₄×C₄₃	C₂×#126	1	1	yes	characteristic
214	Dic₄₃	—	2	4	no	—
215	Dic₄₃	—	4	4	no	—
216	Dic₄₃	—	4	2	no	—
217	Dic₄₃	—	8	2	no	—
218	C₂×#427	D₄₃	1	1	yes	characteristic
219	#2296	—	43	1	no	—
220	C₄×#117	—	43	1	no	—
221	#1921	—	43	2	no	—
222	#1920	—	43	2	no	—
223	#1919	—	43	2	no	—
224	#1918	—	43	2	no	—
225	#1735	—	43	1	no	—
226	#1735	—	43	1	no	—
227	#1735	—	43	1	no	—
228	C₂×#336	—	43	1	no	—
229	C₂×C₄₃	—	2	4	no	—
230	C₂×C₄₃	C₂×#387	1	1	yes	characteristic
231	C₂×C₄₃	C₄×#135	1	1	yes	characteristic
232	C₂×C₄₃	#2943	1	1	yes	characteristic
233	C₂×C₄₃	#3076	1	2	yes	—
234	C₂×C₄₃	#3091	1	2	yes	—
235	C₂³×C₈	—	43	1	no	—
236	C₂³×C₈	C₂×D₄₃	1	1	yes	characteristic
237	C₂×#117	—	43	1	no	—
238	C₂×#117	—	43	1	no	—
239	C₂×#117	C₂×D₄₃	1	1	yes	characteristic
240	C₂×#117	C₂×D₄₃	1	1	yes	characteristic
241	C₂²×C₄²	—	43	1	no	—
242	#427	Dic₄₃	1	8	yes	complemented
243	C₂×#107	C₂×D₄₃	1	1	yes	characteristic
244	C₂×#107	C₂×D₄₃	1	1	yes	characteristic
245	C₂×#106	C₂×D₄₃	1	1	yes	characteristic
246	C₂×#106	C₂×D₄₃	1	1	yes	characteristic
247	#389	—	43	2	no	—
248	#389	—	43	2	no	—
249	#385	—	86	2	no	—
250	C₄×C₄⋊C₄	—	43	2	no	—
251	C₄×C₄⋊C₄	—	43	2	no	—
252	C₄×C₄⋊C₄	—	86	1	no	—
253	C₄×C₄⋊C₄	—	86	1	no	—
254	C₄×C₂²⋊C₄	—	86	2	no	—
255	#376	—	86	1	no	—
256	C₄³	—	86	1	no	—
257	#340	—	43	2	no	—
258	#340	—	43	2	no	—
259	#340	—	43	2	no	—
260	#340	—	43	2	no	—
261	#340	—	43	2	no	—
262	#340	—	43	2	no	—
263	#336	—	43	2	no	—
264	#336	—	43	2	no	—
265	C₄₃	#21032	1	1	yes	characteristic, complemented, Sylow
266	C₂³×C₄	—	43	2	no	—
267	C₂³×C₄	C₂²×D₄₃	1	1	yes	characteristic
268	C₂²×C₈	—	2	2	no	—
269	C₂²×C₈	—	2	2	no	—
270	C₂²×C₈	—	43	2	no	—
271	C₂²×C₈	—	86	2	no	—
272	C₂²×C₈	—	86	2	no	—
273	C₂²×C₈	—	86	2	no	—
274	C₂²×C₈	C₂×Dic₄₃	1	4	yes	—
275	C₂²×C₈	C₂²×D₄₃	1	1	yes	characteristic
276	C₂²×C₈	C₂²×D₄₃	1	1	yes	characteristic
277	#117	—	2	2	no	—
278	#117	—	2	2	no	—
279	#117	—	43	4	no	—
280	#117	—	86	2	no	—
281	#117	—	86	2	no	—
282	#117	—	86	2	no	—
283	#117	C₂×Dic₄₃	1	4	yes	—
284	#117	C₂×Dic₄₃	1	4	yes	—
285	C₂×C₄⋊C₄	—	43	2	no	—
286	C₂×C₄⋊C₄	—	43	2	no	—
287	C₂×C₄⋊C₄	—	86	2	no	—
288	C₂×C₄⋊C₄	—	86	2	no	—
289	C₂×C₄⋊C₄	C₂²×D₄₃	1	1	yes	characteristic
290	C₂×C₄⋊C₄	C₂²×D₄₃	1	1	yes	characteristic
291	C₂×C₄⋊C₄	C₂²×D₄₃	1	1	yes	characteristic
292	C₂×C₄⋊C₄	C₂²×D₄₃	1	1	yes	characteristic
293	C₂×C₂²⋊C₄	—	2	1	no	—
294	C₂×C₂²⋊C₄	—	2	1	no	—
295	C₂×C₂²⋊C₄	—	86	1	no	—
296	C₂×C₂²⋊C₄	—	86	1	no	—
297	C₂×C₄²	—	2	1	no	—
298	C₂×C₄²	—	2	1	no	—
299	C₂×C₄²	—	43	1	no	—
300	C₂×C₄²	—	43	1	no	—
301	C₂×C₄²	—	43	2	no	—
302	C₂×C₄²	—	86	2	no	—
303	C₂×C₄²	—	86	1	no	—
304	C₂×C₄²	—	86	2	no	—
305	C₂×C₄²	—	86	2	no	—
306	C₂×C₄²	—	86	2	no	—
307	C₂×C₄²	—	86	1	no	—
308	#107	C₂×Dic₄₃	1	4	yes	complemented
309	#107	C₂×Dic₄₃	1	4	yes	complemented
310	#106	C₂×Dic₄₃	1	4	yes	complemented
311	#106	C₂×Dic₄₃	1	4	yes	complemented
312	#95	—	86	2	no	—
313	#95	—	86	2	no	—
314	#95	—	86	2	no	—
315	#95	—	86	2	no	—
316	C₂⁴	D₄×D₄₃	1	1	yes	characteristic
317	C₂²×C₄	—	2	1	no	—
318	C₂²×C₄	—	2	1	no	—
319	C₂²×C₄	—	2	1	no	—
320	C₂²×C₄	—	2	1	no	—
321	C₂²×C₄	—	43	2	no	—
322	C₂²×C₄	—	43	2	no	—
323	C₂²×C₄	—	86	4	no	—
324	C₂²×C₄	—	86	4	no	—
325	C₂²×C₄	—	86	2	no	—
326	C₂²×C₄	—	86	2	no	—
327	C₂²×C₄	—	172	2	no	—
328	C₂²×C₄	#10621898	1	2	yes	—
329	C₂²×C₄	#10621898	1	2	yes	—
330	C₂²×C₄	D₄×D₄₃	1	1	yes	characteristic
331	C₂²×C₄	#10621900	1	2	yes	—
332	C₂²×C₄	Q₈×D₄₃	1	2	yes	—
333	C₂²×C₄	#10621902	1	2	yes	—
334	C₂²×C₄	C₂²×Dic₄₃	1	2	yes	—
335	C₂²×C₄	C₂³×D₄₃	1	1	yes	characteristic
336	C₂×C₈	—	2	8	no	—
337	C₂×C₈	—	2	1	no	—
338	C₂×C₈	—	2	1	no	—
339	C₂×C₈	—	2	1	no	—
340	C₂×C₈	—	2	1	no	—
341	C₂×C₈	—	86	2	no	—
342	C₂×C₈	—	86	2	no	—
343	C₂×C₈	—	86	2	no	—
344	C₂×C₈	—	172	4	no	—
345	C₂×C₈	C₂²×Dic₄₃	1	2	yes	—
346	C₂×C₈	C₂²×Dic₄₃	1	2	yes	—
347	C₄⋊C₄	—	2	1	no	—
348	C₄⋊C₄	—	2	1	no	—
349	C₄⋊C₄	—	2	1	no	—
350	C₄⋊C₄	—	2	1	no	—
351	C₄⋊C₄	—	43	4	no	—
352	C₄⋊C₄	—	86	2	no	—
353	C₄⋊C₄	—	86	2	no	—
354	C₄⋊C₄	—	86	2	no	—
355	C₄⋊C₄	—	172	4	no	—
356	C₄⋊C₄	—	172	4	no	—
357	C₄⋊C₄	C₂²×Dic₄₃	1	2	yes	—
358	C₄⋊C₄	C₂²×Dic₄₃	1	2	yes	—
359	C₄⋊C₄	C₂²×Dic₄₃	1	2	yes	—
360	C₄⋊C₄	C₂²×Dic₄₃	1	2	yes	—
361	C₂²⋊C₄	—	2	4	no	—
362	C₂²⋊C₄	—	2	4	no	—
363	C₂²⋊C₄	—	86	4	no	—
364	C₂²⋊C₄	—	172	2	no	—
365	C₄²	—	2	4	no	—
366	C₄²	—	2	4	no	—
367	C₄²	—	86	4	no	—
368	C₄²	—	86	2	no	—
369	C₄²	—	86	2	no	—
370	C₄²	—	86	2	no	—
371	C₄²	—	86	2	no	—
372	C₄²	—	172	4	no	—
373	C₄²	—	172	4	no	—
374	C₄²	—	172	2	no	—
375	C₂³	—	2	2	no	—
376	C₂³	—	2	2	no	—
377	C₂³	D₄×Dic₄₃	1	2	yes	—
378	C₂³	#13063303	1	2	yes	—
379	C₂³	#13063310	1	2	yes	—
380	C₂³	C₂×D₄×D₄₃	1	1	yes	characteristic
381	C₂×C₄	—	2	2	no	—
382	C₂×C₄	—	2	2	no	—
383	C₂×C₄	—	2	2	no	—
384	C₂×C₄	—	2	2	no	—
385	C₂×C₄	—	4	2	no	—
386	C₂×C₄	—	4	2	no	—
387	C₂×C₄	—	4	2	no	—
388	C₂×C₄	—	4	2	no	—
389	C₂×C₄	—	43	4	no	—
390	C₂×C₄	—	86	2	no	—
391	C₂×C₄	—	86	2	no	—
392	C₂×C₄	—	86	4	no	—
393	C₂×C₄	—	86	2	no	—
394	C₂×C₄	—	86	2	no	—
395	C₂×C₄	—	86	2	no	—
396	C₂×C₄	—	172	8	no	—
397	C₂×C₄	—	172	2	no	—
398	C₂×C₄	—	172	2	no	—
399	C₂×C₄	—	172	2	no	—
400	C₂×C₄	—	172	2	no	—
401	C₂×C₄	—	172	2	no	—
402	C₂×C₄	#13063284	1	4	yes	—
403	C₂×C₄	D₄×Dic₄₃	1	2	yes	—
404	C₂×C₄	Q₈×Dic₄₃	1	4	yes	—
405	C₂×C₄	#13063303	1	2	yes	—
406	C₂×C₄	#13063310	1	2	yes	—
407	C₂×C₄	#13063315	1	4	yes	—
408	C₂×C₄	#13063320	1	4	yes	—
409	C₂×C₄	C₂³×Dic₄₃	1	1	yes	characteristic
410	C₂×C₄	C₂×Q₈×D₄₃	1	1	yes	characteristic
411	C₂×C₄	C₂×#10621900	1	1	yes	characteristic
412	C₂×C₄	C₂×#10621898	1	1	yes	characteristic
413	C₂×C₄	C₂×#10621898	1	1	yes	characteristic
414	C₂×C₄	C₂×#10621902	1	1	yes	characteristic
415	C₈	—	2	2	no	—
416	C₈	—	2	2	no	—
417	C₈	—	172	2	no	—
418	C₂²	—	2	4	no	—
419	C₂²	—	2	4	no	—
420	C₂²	—	2	2	no	—
421	C₂²	—	2	2	no	—
422	C₂²	#14582785	1	4	yes	—
423	C₂²	C₂×D₄×Dic₄₃	1	1	yes	characteristic
424	C₂²	C₂×#13063303	1	1	yes	characteristic
425	C₂²	C₂×#13063310	1	1	yes	characteristic
426	C₂²	#135×D₄₃	1	2	yes	—
427	C₂²	#14583696	1	2	yes	—
428	C₄	—	4	2	no	—
429	C₄	—	4	2	no	—
430	C₄	—	4	2	no	—
431	C₄	—	4	2	no	—
432	C₄	—	86	4	no	—
433	C₄	—	344	2	no	—
434	C₄	—	172	2	no	—
435	C₄	—	172	4	no	—
436	C₄	#14582785	1	4	yes	—
437	C₄	C₂×#13063284	1	1	yes	characteristic
438	C₄	C₂×Q₈×Dic₄₃	1	1	yes	characteristic
439	C₄	C₂×#13063315	1	1	yes	characteristic
440	C₄	C₂×#13063320	1	1	yes	characteristic
441	C₂	—	2	4	no	—
442	C₂	C₂×#14582785	1	1	yes	characteristic
443	C₂	#135×Dic₄₃	1	1	yes	characteristic
444	C₂	#19143396	1	1	yes	characteristic
445	C₂	#19144381	1	2	yes	—
446	C₂	#19144512	1	2	yes	—

	subgroup	G/H
center	C₂²×C₄	D₄×D₄₃
commutator	C₂×C₄×C₄₃	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₄₃
Fitting	C₂×C₄₃×#427	C₂
socle	C₂³×C₄₃	C₂²×D₄
prime radical	C₂⁴×C₄₃	C₂×D₄
cosocle	C₂²×C₄×C₄₃	C₂⁴
hypercenter	C₂×#427	D₄₃
hypocenter	C₄₃	#21032
LCS	G ▷ C₂×C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂²×C₄ ◁ C₂³×C₄ ◁ C₂×#427

Complements

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

N	H ≅ G/N	type
3. #19135189	C₂	semidirect
4. #19135182	C₂	semidirect
5. #19135175	C₂	semidirect
6. #19135168	C₂	semidirect
37. C₄₃×#427	C₄	semidirect
88. #107×C₄₃	C₂×C₄	semidirect
89. #107×C₄₃	C₂×C₄	semidirect
90. #106×C₄₃	C₂×C₄	semidirect
91. #106×C₄₃	C₂×C₄	semidirect
242. #427	Dic₄₃	semidirect
265. C₄₃	#21032	semidirect
308. #107	C₂×Dic₄₃	semidirect
309. #107	C₂×Dic₄₃	semidirect
310. #106	C₂×Dic₄₃	semidirect
311. #106	C₂×Dic₄₃	semidirect

Maximal subgroups

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

subgroup	index
#19137079	2
#117×Dic₄₃	2
#19135189	2
#19135182	2
#19135175	2
#19135168	2
#19134312	2
#19134311	2
C₂×#14582653	2
C₂×C₄₃×#427	2
#21032	43