Subgroups — #25002578

Order 11008.

846 conjugacy classes of subgroups.

The subgroup lattice has 476 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#19137077	C₂	1	1	yes	maximal, characteristic
2	C₂×#14582745	C₂	1	1	yes	maximal, characteristic
3	C₂×#14582660	C₂	1	1	yes	maximal, characteristic
4	C₂×#14582659	C₂	1	1	yes	maximal, characteristic
5	C₂×#14582658	C₂	1	1	yes	maximal, characteristic
6	#19134288	C₂	1	1	yes	maximal, characteristic
7	C₂×C₄₃×#339	C₂	1	1	yes	maximal, characteristic
8	C₂²×#10621877	C₂²	1	1	yes	characteristic
9	C₂×#13063284	C₂²	1	1	yes	characteristic
10	C₂²×C₄×Dic₄₃	C₂²	1	1	yes	characteristic
11	C₂²×C₄×Dic₄₃	C₂²	1	1	yes	characteristic
12	#14582795	C₄	1	4	yes	complemented
13	#14582771	—	2	2	no	—
14	C₄×Dic₄₃⋊C₄	—	2	2	no	—
15	#14582745	—	2	2	no	—
16	#14582745	—	2	2	no	—
17	C₂×C₄₃⋊#95	—	2	2	no	—
18	#14582660	C₄	1	4	yes	complemented
19	#14582659	C₄	1	4	yes	complemented
20	#14582658	—	2	2	no	—
21	#14582653	—	2	2	no	—
22	C₂²×M₁₆×C₄₃	C₂²	1	1	yes	characteristic
23	C₂×#117×C₄₃	C₂²	1	1	yes	characteristic
24	C₂²×C₄²×C₄₃	C₂²	1	1	yes	characteristic
25	C₄₃×#339	—	2	2	no	—
26	C₂³×Dic₄₃	—	2	1	no	—
27	C₂³×Dic₄₃	D₄	1	2	yes	—
28	C₂×#10621877	—	2	1	no	—
29	C₂×#10621877	—	2	1	no	—
30	C₂×#10621877	—	2	1	no	—
31	C₂×#10621877	—	2	1	no	—
32	C₂×#10621877	—	2	1	no	—
33	C₂×#10621877	C₂×C₄	1	2	yes	—
34	C₂²×C₄₃⋊C₈	—	2	1	no	—
35	#13063284	—	2	1	no	—
36	#13063284	—	2	1	no	—
37	#13063284	C₂×C₄	1	2	yes	—
38	#13063284	C₂×C₄	1	2	yes	—
39	C₂×C₄⋊Dic₄₃	C₂×C₄	1	2	yes	—
40	C₂×Dic₄₃⋊C₄	—	2	4	no	—
41	C₂×C₂²⋊Dic₄₃	—	2	1	no	—
42	C₂×C₄×Dic₄₃	—	2	1	no	—
43	C₂×C₄×Dic₄₃	—	2	1	no	—
44	C₂×C₄×Dic₄₃	—	2	1	no	—
45	C₂×C₄×Dic₄₃	—	2	1	no	—
46	C₂×C₄×Dic₄₃	—	2	1	no	—
47	C₂×C₄×Dic₄₃	—	2	1	no	—
48	C₂×C₄×Dic₄₃	—	2	1	no	—
49	C₂×C₄×Dic₄₃	—	2	1	no	—
50	C₂×C₄×Dic₄₃	C₂×C₄	1	2	yes	—
51	C₂×C₄×Dic₄₃	C₂×C₄	1	2	yes	—
52	C₂×C₄×Dic₄₃	D₄	1	2	yes	—
53	C₂×C₄×Dic₄₃	D₄	1	2	yes	—
54	C₂×C₄×Dic₄₃	Q₈	1	2	yes	—
55	C₄₃⋊#95	—	2	8	no	—
56	C₄₃⋊#95	—	2	4	no	—
57	C₂³×C₄×C₄₃	—	2	1	no	—
58	C₂³×C₄×C₄₃	C₂³	1	1	yes	characteristic
59	C₂×M₁₆×C₄₃	—	2	1	no	—
60	C₂×M₁₆×C₄₃	—	2	1	no	—
61	C₂×M₁₆×C₄₃	—	2	1	no	—
62	C₂×M₁₆×C₄₃	—	2	1	no	—
63	C₂×M₁₆×C₄₃	—	2	1	no	—
64	C₂×M₁₆×C₄₃	C₂×C₄	1	2	yes	—
65	C₂²×C₈×C₄₃	—	2	1	no	—
66	#117×C₄₃	—	2	1	no	—
67	#117×C₄₃	—	2	1	no	—
68	#117×C₄₃	—	2	1	no	—
69	#117×C₄₃	—	2	1	no	—
70	C₂×C₄⋊C₄×C₄₃	C₂×C₄	1	2	yes	—
71	C₂×C₂²⋊C₄×C₄₃	—	2	1	no	—
72	C₂×C₄²×C₄₃	—	2	1	no	—
73	C₂×C₄²×C₄₃	—	2	1	no	—
74	C₂×C₄²×C₄₃	—	2	1	no	—
75	C₂×C₄²×C₄₃	—	2	1	no	—
76	C₂×C₄²×C₄₃	C₂×C₄	1	2	yes	—
77	C₂×C₄²×C₄₃	D₄	1	2	yes	—
78	C₂×C₄²×C₄₃	Q₈	1	2	yes	—
79	C₂⁴×C₄₃	C₂×D₄	1	1	yes	characteristic
80	C₂²×C₄×C₄₃	—	2	2	no	—
81	C₂²×C₄×C₄₃	—	2	2	no	—
82	C₂²×C₄×C₄₃	—	2	2	no	—
83	C₂²×C₄×C₄₃	—	2	2	no	—
84	C₂²×C₄×C₄₃	—	4	4	no	—
85	C₂²×C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
86	C₂²×C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
87	C₂²×C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
88	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
89	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
90	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
91	C₂²×C₄×C₄₃	C₂×Q₈	1	1	yes	characteristic
92	C₂²×C₄×C₄₃	C₂×Q₈	1	1	yes	characteristic
93	C₂²×C₄×C₄₃	#41	1	1	yes	characteristic
94	C₂²×C₄×C₄₃	#41	1	1	yes	characteristic
95	C₂²×C₄×C₄₃	#41	1	1	yes	characteristic
96	C₂²×C₄×C₄₃	#41	1	1	yes	characteristic
97	C₂²×C₄×C₄₃	#41	1	1	yes	characteristic
98	C₂²×C₄×C₄₃	#41	1	1	yes	characteristic
99	C₂²×Dic₄₃	—	2	2	no	—
100	C₂²×Dic₄₃	—	2	2	no	—
101	C₂²×Dic₄₃	—	2	2	no	—
102	C₂²×Dic₄₃	—	2	2	no	—
103	C₂²×Dic₄₃	—	2	2	no	—
104	C₂²×Dic₄₃	—	2	2	no	—
105	C₂²×Dic₄₃	—	4	4	no	—
106	C₂²×Dic₄₃	—	4	4	no	—
107	C₂²×Dic₄₃	C₂²⋊C₄	1	4	yes	—
108	M₁₆×C₄₃	—	2	2	no	—
109	M₁₆×C₄₃	—	2	2	no	—
110	M₁₆×C₄₃	—	4	1	no	—
111	M₁₆×C₄₃	—	4	1	no	—
112	C₂×C₈×C₄₃	—	2	2	no	—
113	C₂×C₈×C₄₃	—	4	1	no	—
114	C₂×C₈×C₄₃	—	4	1	no	—
115	C₄⋊C₄×C₄₃	—	2	2	no	—
116	C₄⋊C₄×C₄₃	—	2	2	no	—
117	C₂²⋊C₄×C₄₃	—	4	1	no	—
118	C₂²⋊C₄×C₄₃	—	4	1	no	—
119	C₄²×C₄₃	—	2	2	no	—
120	C₄²×C₄₃	—	2	2	no	—
121	C₄²×C₄₃	—	2	2	no	—
122	C₄²×C₄₃	—	4	1	no	—
123	C₄²×C₄₃	—	4	1	no	—
124	C₄²×C₄₃	C₄⋊C₄	1	4	yes	complemented
125	C₂²⋊Dic₄₃	—	2	2	no	—
126	C₂²⋊Dic₄₃	—	2	2	no	—
127	C₄⋊Dic₄₃	—	2	2	no	—
128	C₄⋊Dic₄₃	C₄²	1	4	yes	—
129	Dic₄₃⋊C₄	—	4	8	no	—
130	C₄×Dic₄₃	—	2	2	no	—
131	C₄×Dic₄₃	—	2	2	no	—
132	C₄×Dic₄₃	—	2	2	no	—
133	C₄×Dic₄₃	—	2	2	no	—
134	C₄×Dic₄₃	—	2	2	no	—
135	C₄×Dic₄₃	—	2	2	no	—
136	C₄×Dic₄₃	—	2	2	no	—
137	C₄×Dic₄₃	—	2	2	no	—
138	C₄×Dic₄₃	—	2	2	no	—
139	C₄×Dic₄₃	C₄⋊C₄	1	4	yes	complemented
140	#10621877	—	2	2	no	—
141	#10621877	—	2	2	no	—
142	#10621877	—	4	1	no	—
143	#10621877	—	4	1	no	—
144	C₂×C₄₃⋊C₈	—	2	2	no	—
145	C₂×C₄₃⋊C₈	—	4	1	no	—
146	C₂×C₄₃⋊C₈	—	4	1	no	—
147	C₂³×C₄₃	—	2	4	no	—
148	C₂³×C₄₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
149	C₂³×C₄₃	C₄×D₄	1	1	yes	characteristic
150	C₂³×C₄₃	C₄×D₄	1	1	yes	characteristic
151	C₂³×C₄₃	#120	1	1	yes	characteristic
152	C₂³×C₄₃	C₂²⋊Q₈	1	1	yes	characteristic
153	C₂³×C₄₃	C₂²⋊Q₈	1	1	yes	characteristic
154	C₂³×C₄₃	#123	1	1	yes	characteristic
155	C₂×C₄×C₄₃	—	2	4	no	—
156	C₂×C₄×C₄₃	—	4	4	no	—
157	C₂×C₄×C₄₃	—	4	4	no	—
158	C₂×C₄×C₄₃	—	4	4	no	—
159	C₂×C₄×C₄₃	—	4	2	no	—
160	C₂×C₄×C₄₃	—	4	4	no	—
161	C₂×C₄×C₄₃	C₂×C₄²	1	1	yes	characteristic
162	C₂×C₄×C₄₃	C₂×C₄⋊C₄	1	1	yes	characteristic
163	C₂×C₄×C₄₃	C₂×C₄⋊C₄	1	1	yes	characteristic
164	C₂×C₄×C₄₃	#117	1	1	yes	characteristic
165	C₂×C₄×C₄₃	#117	1	1	yes	characteristic
166	C₂×C₄×C₄₃	#117	1	1	yes	characteristic
167	C₂×C₄×C₄₃	C₄×D₄	1	1	yes	characteristic
168	C₂×C₄×C₄₃	C₄×D₄	1	1	yes	characteristic
169	C₂×C₄×C₄₃	C₄×D₄	1	1	yes	characteristic
170	C₂×C₄×C₄₃	C₄×D₄	1	1	yes	characteristic
171	C₂×C₄×C₄₃	C₄×D₄	1	1	yes	characteristic
172	C₂×C₄×C₄₃	C₄×D₄	1	1	yes	characteristic
173	C₂×C₄×C₄₃	C₄×Q₈	1	1	yes	characteristic
174	C₂×C₄×C₄₃	C₄×Q₈	1	1	yes	characteristic
175	C₂×C₄×C₄₃	C₄×Q₈	1	1	yes	characteristic
176	C₂×C₄×C₄₃	C₄×Q₈	1	1	yes	characteristic
177	C₂×C₄×C₄₃	#121	1	1	yes	characteristic
178	C₂×C₄×C₄₃	#121	1	1	yes	characteristic
179	C₂×C₄×C₄₃	C₂²⋊Q₈	1	1	yes	characteristic
180	C₂×C₄×C₄₃	C₂²⋊Q₈	1	1	yes	characteristic
181	C₂×C₄×C₄₃	#123	1	1	yes	characteristic
182	C₂×C₄×C₄₃	#123	1	1	yes	characteristic
183	C₂×C₄×C₄₃	#124	1	1	yes	characteristic
184	C₂×C₄×C₄₃	#125	1	1	yes	characteristic
185	C₂×C₄×C₄₃	#125	1	1	yes	characteristic
186	C₂×C₄×C₄₃	#126	1	1	yes	characteristic
187	C₂×C₄×C₄₃	#126	1	1	yes	characteristic
188	C₂×C₄×C₄₃	C₄⋊Q₈	1	1	yes	characteristic
189	C₂×Dic₄₃	—	2	4	no	—
190	C₂×Dic₄₃	—	2	4	no	—
191	C₂×Dic₄₃	—	2	4	no	—
192	C₂×Dic₄₃	—	2	4	no	—
193	C₂×Dic₄₃	—	2	4	no	—
194	C₂×Dic₄₃	—	4	4	no	—
195	C₂×Dic₄₃	—	4	4	no	—
196	C₂×Dic₄₃	—	4	4	no	—
197	C₂×Dic₄₃	—	4	4	no	—
198	C₂×Dic₄₃	—	4	4	no	—
199	C₂×Dic₄₃	—	4	4	no	—
200	C₈×C₄₃	—	4	2	no	—
201	C₄₃⋊C₈	—	4	2	no	—
202	#10879	—	43	1	no	maximal, Sylow
203	C₂²×C₄₃	—	2	2	no	—
204	C₂²×C₄₃	—	2	2	no	—
205	C₂²×C₄₃	—	2	2	no	—
206	C₂²×C₄₃	—	2	2	no	—
207	C₂²×C₄₃	—	2	2	no	—
208	C₂²×C₄₃	—	2	2	no	—
209	C₂²×C₄₃	C₄×C₂²⋊C₄	1	1	yes	characteristic
210	C₂²×C₄₃	#385	1	1	yes	characteristic
211	C₂²×C₄₃	#385	1	1	yes	characteristic
212	C₂²×C₄₃	#386	1	1	yes	characteristic
213	C₂²×C₄₃	#387	1	1	yes	characteristic
214	C₂²×C₄₃	#387	1	1	yes	characteristic
215	C₂²×C₄₃	#391	1	1	yes	characteristic
216	C₂²×C₄₃	#421	1	4	yes	—
217	C₄×C₄₃	—	4	4	no	—
218	C₄×C₄₃	—	8	2	no	—
219	C₄×C₄₃	C₄×C₄⋊C₄	1	1	yes	characteristic
220	C₄×C₄₃	C₄×C₄⋊C₄	1	1	yes	characteristic
221	C₄×C₄₃	#387	1	1	yes	characteristic
222	C₄×C₄₃	#387	1	1	yes	characteristic
223	C₄×C₄₃	#388	1	1	yes	characteristic
224	C₄×C₄₃	#388	1	1	yes	characteristic
225	C₄×C₄₃	#389	1	1	yes	characteristic
226	C₄×C₄₃	#389	1	1	yes	characteristic
227	Dic₄₃	—	4	4	no	—
228	Dic₄₃	—	4	4	no	—
229	Dic₄₃	—	4	4	no	—
230	#2296	—	43	1	no	—
231	C₂×#376	—	43	1	no	—
232	C₂×#339	—	43	1	no	—
233	C₂×#339	—	43	1	no	—
234	C₂×#339	—	43	1	no	—
235	C₂×#339	D₄₃	1	1	yes	characteristic
236	#1728	—	43	1	no	—
237	C₂×C₄₃	—	2	1	no	—
238	C₂×C₄₃	—	2	1	no	—
239	C₂×C₄₃	—	2	1	no	—
240	C₂×C₄₃	—	2	1	no	—
241	C₂×C₄₃	#1436	1	1	yes	characteristic
242	C₂×C₄₃	#1759	1	2	yes	—
243	C₂×C₄₃	#1897	1	2	yes	—
244	C₂×C₄₃	#1995	1	2	yes	—
245	C₂²×M₁₆	—	43	1	no	—
246	C₂²×M₁₆	C₂×D₄₃	1	1	yes	characteristic
247	C₂×#117	—	43	1	no	—
248	C₂×#117	C₂×D₄₃	1	1	yes	characteristic
249	C₂²×C₄²	—	43	1	no	—
250	C₂²×C₄²	—	43	1	no	—
251	C₂²×C₄²	C₂×D₄₃	1	1	yes	characteristic
252	#389	—	43	4	no	—
253	#385	—	86	2	no	—
254	C₄×C₄⋊C₄	—	86	2	no	—
255	#376	—	86	2	no	—
256	#376	—	86	2	no	—
257	C₂×#95	—	86	2	no	—
258	#339	—	2	2	no	—
259	#339	—	43	4	no	—
260	#339	—	43	4	no	—
261	#339	—	86	2	no	—
262	#336	—	86	2	no	—
263	C₄₃	#10879	1	1	yes	characteristic, complemented, Sylow
264	C₂³×C₄	—	2	1	no	—
265	C₂³×C₄	—	43	2	no	—
266	C₂³×C₄	—	86	1	no	—
267	C₂³×C₄	C₂²×D₄₃	1	1	yes	characteristic
268	C₂×M₁₆	—	2	1	no	—
269	C₂×M₁₆	—	2	1	no	—
270	C₂×M₁₆	—	2	1	no	—
271	C₂×M₁₆	—	2	1	no	—
272	C₂×M₁₆	—	2	1	no	—
273	C₂×M₁₆	—	43	2	no	—
274	C₂×M₁₆	—	86	1	no	—
275	C₂×M₁₆	—	86	1	no	—
276	C₂×M₁₆	—	86	1	no	—
277	C₂×M₁₆	—	86	1	no	—
278	C₂×M₁₆	—	86	1	no	—
279	C₂×M₁₆	C₄×D₄₃	1	2	yes	—
280	C₂²×C₈	—	2	1	no	—
281	C₂²×C₈	—	86	1	no	—
282	#117	—	2	1	no	—
283	#117	—	2	1	no	—
284	#117	—	2	1	no	—
285	#117	—	2	1	no	—
286	#117	—	43	2	no	—
287	#117	—	43	2	no	—
288	#117	—	86	1	no	—
289	#117	—	86	1	no	—
290	C₂×C₄⋊C₄	—	43	2	no	—
291	C₂×C₄⋊C₄	—	86	4	no	—
292	C₂×C₄⋊C₄	C₄×D₄₃	1	2	yes	—
293	C₂×C₂²⋊C₄	—	2	1	no	—
294	C₂×C₂²⋊C₄	—	86	1	no	—
295	C₂×C₄²	—	2	1	no	—
296	C₂×C₄²	—	2	1	no	—
297	C₂×C₄²	—	2	1	no	—
298	C₂×C₄²	—	2	1	no	—
299	C₂×C₄²	—	43	2	no	—
300	C₂×C₄²	—	43	2	no	—
301	C₂×C₄²	—	43	2	no	—
302	C₂×C₄²	—	43	2	no	—
303	C₂×C₄²	—	43	2	no	—
304	C₂×C₄²	—	86	1	no	—
305	C₂×C₄²	—	86	1	no	—
306	C₂×C₄²	—	86	1	no	—
307	C₂×C₄²	—	86	1	no	—
308	C₂×C₄²	—	86	1	no	—
309	C₂×C₄²	—	86	1	no	—
310	C₂×C₄²	—	86	1	no	—
311	C₂×C₄²	—	86	1	no	—
312	C₂×C₄²	Dic₈₆	1	2	yes	—
313	C₂×C₄²	C₄×D₄₃	1	2	yes	—
314	C₂×C₄²	C₂²⋊D₄₃	1	2	yes	—
315	#95	—	86	4	no	—
316	#95	—	86	8	no	—
317	C₂⁴	D₄×D₄₃	1	1	yes	characteristic
318	C₂²×C₄	—	2	2	no	—
319	C₂²×C₄	—	2	2	no	—
320	C₂²×C₄	—	2	2	no	—
321	C₂²×C₄	—	2	2	no	—
322	C₂²×C₄	—	4	4	no	—
323	C₂²×C₄	—	43	4	no	—
324	C₂²×C₄	—	86	2	no	—
325	C₂²×C₄	—	86	2	no	—
326	C₂²×C₄	—	86	2	no	—
327	C₂²×C₄	—	86	2	no	—
328	C₂²×C₄	—	86	2	no	—
329	C₂²×C₄	—	86	2	no	—
330	C₂²×C₄	—	172	4	no	—
331	C₂²×C₄	—	172	4	no	—
332	C₂²×C₄	C₂×Dic₈₆	1	1	yes	characteristic
333	C₂²×C₄	C₂×C₄×D₄₃	1	1	yes	characteristic
334	C₂²×C₄	C₂×C₄×D₄₃	1	1	yes	characteristic
335	C₂²×C₄	C₂×C₄×D₄₃	1	1	yes	characteristic
336	C₂²×C₄	#10621898	1	1	yes	characteristic
337	C₂²×C₄	#10621898	1	1	yes	characteristic
338	C₂²×C₄	D₄×D₄₃	1	1	yes	characteristic
339	C₂²×C₄	D₄×D₄₃	1	1	yes	characteristic
340	C₂²×C₄	#10621900	1	1	yes	characteristic
341	C₂²×C₄	#10621900	1	1	yes	characteristic
342	C₂²×C₄	#10621900	1	1	yes	characteristic
343	C₂²×C₄	Q₈×D₄₃	1	1	yes	characteristic
344	C₂²×C₄	#10621902	1	1	yes	characteristic
345	C₂²×C₄	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
346	M₁₆	—	2	2	no	—
347	M₁₆	—	2	2	no	—
348	M₁₆	—	4	1	no	—
349	M₁₆	—	4	1	no	—
350	M₁₆	—	86	2	no	—
351	M₁₆	—	86	2	no	—
352	M₁₆	—	172	1	no	—
353	M₁₆	—	172	1	no	—
354	C₂×C₈	—	2	2	no	—
355	C₂×C₈	—	4	1	no	—
356	C₂×C₈	—	4	1	no	—
357	C₂×C₈	—	86	2	no	—
358	C₂×C₈	—	172	1	no	—
359	C₂×C₈	—	172	1	no	—
360	C₄⋊C₄	—	2	2	no	—
361	C₄⋊C₄	—	2	2	no	—
362	C₄⋊C₄	—	43	4	no	—
363	C₄⋊C₄	—	86	2	no	—
364	C₄⋊C₄	—	172	8	no	—
365	C₂²⋊C₄	—	4	1	no	—
366	C₂²⋊C₄	—	4	1	no	—
367	C₂²⋊C₄	—	86	2	no	—
368	C₂²⋊C₄	—	86	2	no	—
369	C₄²	—	2	2	no	—
370	C₄²	—	2	2	no	—
371	C₄²	—	2	2	no	—
372	C₄²	—	4	1	no	—
373	C₄²	—	4	1	no	—
374	C₄²	—	43	4	no	—
375	C₄²	—	86	2	no	—
376	C₄²	—	86	2	no	—
377	C₄²	—	86	2	no	—
378	C₄²	—	86	2	no	—
379	C₄²	—	86	2	no	—
380	C₄²	—	86	2	no	—
381	C₄²	—	86	2	no	—
382	C₄²	—	86	2	no	—
383	C₄²	—	86	2	no	—
384	C₄²	Dic₄₃⋊C₄	1	4	yes	complemented
385	C₂³	—	2	4	no	—
386	C₂³	C₂²⋊C₄×D₄₃	1	1	yes	characteristic
387	C₂³	(C₂²⋊D₄₃)⋊C₄	1	1	yes	characteristic
388	C₂³	#13063287	1	1	yes	characteristic
389	C₂³	#13063293	1	1	yes	characteristic
390	C₂³	#13063302	1	1	yes	characteristic
391	C₂³	#13063303	1	1	yes	characteristic
392	C₂³	#13063307	1	1	yes	characteristic
393	C₂×C₄	—	2	4	no	—
394	C₂×C₄	—	4	4	no	—
395	C₂×C₄	—	4	4	no	—
396	C₂×C₄	—	4	4	no	—
397	C₂×C₄	—	4	4	no	—
398	C₂×C₄	—	4	2	no	—
399	C₂×C₄	—	86	4	no	—
400	C₂×C₄	—	86	4	no	—
401	C₂×C₄	—	86	4	no	—
402	C₂×C₄	—	86	4	no	—
403	C₂×C₄	—	86	4	no	—
404	C₂×C₄	—	172	4	no	—
405	C₂×C₄	—	172	4	no	—
406	C₂×C₄	—	172	4	no	—
407	C₂×C₄	—	172	4	no	—
408	C₂×C₄	—	172	4	no	—
409	C₂×C₄	—	172	4	no	—
410	C₂×C₄	C₄²×D₄₃	1	1	yes	characteristic
411	C₂×C₄	C₄⋊C₄×D₄₃	1	1	yes	characteristic
412	C₂×C₄	C₂×Dic₄₃⋊C₄	1	1	yes	characteristic
413	C₂×C₄	#13063281	1	1	yes	characteristic
414	C₂×C₄	#13063282	1	1	yes	characteristic
415	C₂×C₄	#13063283	1	1	yes	characteristic
416	C₂×C₄	(C₂²⋊D₄₃)⋊C₄	1	1	yes	characteristic
417	C₂×C₄	(C₂²⋊D₄₃)⋊C₄	1	1	yes	characteristic
418	C₂×C₄	(C₂²⋊D₄₃)⋊C₄	1	1	yes	characteristic
419	C₂×C₄	C₄×C₂²⋊D₄₃	1	1	yes	characteristic
420	C₂×C₄	C₄×C₂²⋊D₄₃	1	1	yes	characteristic
421	C₂×C₄	#13063287	1	1	yes	characteristic
422	C₂×C₄	#13063290	1	1	yes	characteristic
423	C₂×C₄	#13063290	1	1	yes	characteristic
424	C₂×C₄	C₄×Dic₈₆	1	1	yes	characteristic
425	C₂×C₄	C₄×Dic₈₆	1	1	yes	characteristic
426	C₂×C₄	#13063296	1	1	yes	characteristic
427	C₂×C₄	#13063298	1	1	yes	characteristic
428	C₂×C₄	#13063301	1	1	yes	characteristic
429	C₂×C₄	#13063302	1	1	yes	characteristic
430	C₂×C₄	#13063306	1	1	yes	characteristic
431	C₂×C₄	#13063310	1	1	yes	characteristic
432	C₂×C₄	#13063311	1	1	yes	characteristic
433	C₂×C₄	#13063315	1	1	yes	characteristic
434	C₂×C₄	#13063316	1	1	yes	characteristic
435	C₂×C₄	#13063318	1	1	yes	characteristic
436	C₂×C₄	#13063320	1	1	yes	characteristic
437	C₂×C₄	#13063324	1	1	yes	characteristic
438	C₈	—	4	2	no	—
439	C₈	—	172	2	no	—
440	C₂²	—	2	2	no	—
441	C₂²	—	2	2	no	—
442	C₂²	—	2	2	no	—
443	C₂²	—	2	2	no	—
444	C₂²	—	2	2	no	—
445	C₂²	—	2	2	no	—
446	C₂²	#14582746	1	1	yes	characteristic
447	C₂²	#14582770	1	1	yes	characteristic
448	C₂²	#14582771	1	1	yes	characteristic
449	C₂²	#14582775	1	1	yes	characteristic
450	C₂²	#14582781	1	1	yes	characteristic
451	C₂²	#14582782	1	1	yes	characteristic
452	C₂²	#14582803	1	1	yes	characteristic
453	C₂²	#14582914	1	4	yes	—
454	C₄	—	4	4	no	—
455	C₄	—	8	2	no	—
456	C₄	—	172	4	no	—
457	C₄	—	172	4	no	—
458	C₄	—	172	4	no	—
459	C₄	#14582750	1	1	yes	characteristic
460	C₄	C₄×Dic₄₃⋊C₄	1	1	yes	characteristic
461	C₄	#14582780	1	1	yes	characteristic
462	C₄	#14582786	1	1	yes	characteristic
463	C₄	#14582787	1	1	yes	characteristic
464	C₄	#14582788	1	1	yes	characteristic
465	C₄	#14582795	1	1	yes	characteristic
466	C₄	#14582796	1	1	yes	characteristic
467	C₂	—	2	1	no	—
468	C₂	—	2	1	no	—
469	C₂	—	2	1	no	—
470	C₂	—	2	1	no	—
471	C₂	#19132826	1	1	yes	characteristic
472	C₂	#19134404	1	2	yes	—
473	C₂	#19135040	1	2	yes	—
474	C₂	#19135574	1	2	yes	—

	subgroup	G/H
center	C₂²×C₄	D₄×D₄₃
commutator	C₂×C₄×C₄₃	C₂×C₄²
Frattini	C₂³×C₄	C₂²×D₄₃
Fitting	C₂×C₄₃×#339	C₂
socle	C₂³×C₄₃	C₂×C₂²⋊C₄
prime radical	C₂⁴×C₄₃	C₂×D₄
cosocle	C₂³×C₄×C₄₃	C₂³
hypercenter	C₂×#339	D₄₃
hypocenter	C₄₃	#10879
LCS	G ▷ C₂×C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂²×C₄ ◁ C₂³×C₄ ◁ C₂×#339

Complements

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

N	H ≅ G/N	type
12. #14582795	C₄	semidirect
18. #14582660	C₄	semidirect
19. #14582659	C₄	semidirect
124. C₄²×C₄₃	C₄⋊C₄	semidirect
139. C₄×Dic₄₃	C₄⋊C₄	semidirect
263. C₄₃	#10879	semidirect
384. C₄²	Dic₄₃⋊C₄	semidirect

Maximal subgroups

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

subgroup	index
#19137077	2
C₂×#14582745	2
C₂×#14582660	2
C₂×#14582659	2
C₂×#14582658	2
#19134288	2
C₂×C₄₃×#339	2
#10879	43