Subgroups — #25105110

Order 11008.

1110 conjugacy classes of subgroups.

The subgroup lattice has 428 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#14583283	C₂	1	1	yes	maximal, characteristic
2	C₂×#14583001	C₂	1	2	yes	maximal, complemented
3	C₂×C₄×Dic₁₇₂	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₄×D₃₄₄	C₂	1	1	yes	maximal, characteristic
5	#19137306	C₂	1	2	yes	maximal, complemented
6	#19135476	C₂	1	2	yes	maximal, complemented
7	#19135461	C₂	1	1	yes	maximal, characteristic
8	#19135456	C₂	1	1	yes	maximal, characteristic, complemented
9	#19135411	C₂	1	2	yes	maximal, complemented
10	#19134755	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄₃×#1726	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×Dic₁₇₂	C₂²	1	1	yes	characteristic
13	C₂²×#10621873	C₂²	1	2	yes	—
14	C₂²×D₃₄₄	C₂²	1	1	yes	characteristic
15	C₂×#13063313	C₂²	1	2	yes	—
16	C₂×C₄×Dic₈₆	C₂²	1	2	yes	—
17	C₂×C₄×D₁₇₂	C₂²	1	2	yes	—
18	#14583283	C₄	1	8	yes	complemented
19	#14583001	—	2	8	no	—
20	C₄×Dic₁₇₂	—	2	4	no	—
21	C₄×D₃₄₄	—	2	4	no	—
22	C₂×#13063259	C₂²	1	1	yes	characteristic
23	C₂×#13063259	C₂²	1	1	yes	characteristic
24	C₂×#13063259	C₂²	1	2	yes	—
25	C₂×#13063250	C₂²	1	2	yes	—
26	C₂×#13063250	C₂²	1	2	yes	—
27	C₂×#13063247	C₂²	1	2	yes	—
28	C₂×#13063247	C₂²	1	2	yes	—
29	#14582805	C₂²	1	2	yes	—
30	#14582801	C₂²	1	2	yes	—
31	#14582791	—	2	4	no	—
32	#14582773	—	2	4	no	—
33	#14582769	C₂²	1	2	yes	—
34	C₂×#97×C₄₃	C₂²	1	1	yes	characteristic
35	C₂×#97×C₄₃	C₂²	1	1	yes	characteristic
36	C₂×#97×C₄₃	C₂²	1	1	yes	characteristic
37	C₂×C₄×C₈×C₄₃	C₂²	1	1	yes	characteristic
38	C₂×C₄×C₈×C₄₃	C₂²	1	1	yes	characteristic
39	C₂×C₄×C₈×C₄₃	C₂²	1	1	yes	characteristic
40	C₄₃×#376	C₂²	1	1	yes	characteristic
41	C₂²×Dic₈₆	C₂³	1	2	yes	—
42	C₂²×D₁₇₂	C₂³	1	2	yes	—
43	C₂²×C₄×D₄₃	—	2	2	no	—
44	C₂×Dic₁₇₂	—	2	2	no	—
45	C₂×Dic₁₇₂	—	2	2	no	—
46	C₂×Dic₁₇₂	C₂×C₄	1	4	yes	complemented
47	C₂×#10621873	—	2	4	no	—
48	C₂×#10621873	—	2	4	no	—
49	C₂×#10621873	C₂×C₄	1	8	yes	complemented
50	C₂×D₃₄₄	—	2	2	no	—
51	C₂×D₃₄₄	—	2	2	no	—
52	C₂×D₃₄₄	C₂×C₄	1	4	yes	—
53	#13063313	—	2	4	no	—
54	#13063313	C₂×C₄	1	8	yes	complemented
55	C₄×Dic₈₆	—	2	4	no	—
56	C₄×Dic₈₆	—	2	4	no	—
57	C₄×D₁₇₂	—	2	4	no	—
58	C₄×D₁₇₂	—	2	4	no	—
59	C₂×C₄⋊Dic₄₃	—	2	4	no	—
60	C₂×C₄⋊Dic₄₃	C₂³	1	2	yes	—
61	C₂×C₄⋊Dic₄₃	C₂³	1	2	yes	—
62	C₂×Dic₄₃⋊C₄	—	2	2	no	—
63	C₂×(C₂×D₄₃)⋊C₄	—	2	4	no	—
64	C₂×(C₂×D₄₃)⋊C₄	—	2	2	no	—
65	C₂×(C₂×D₄₃)⋊C₄	—	2	4	no	—
66	C₂×C₄×Dic₄₃	—	2	2	no	—
67	#13063259	—	2	2	no	—
68	#13063259	—	2	2	no	—
69	#13063259	—	2	4	no	—
70	#13063250	—	2	4	no	—
71	#13063250	—	2	4	no	—
72	#13063247	—	2	4	no	—
73	#13063247	—	2	4	no	—
74	C₄₃⋊#95	—	2	4	no	—
75	C₂²×C₈×C₄₃	C₂³	1	1	yes	characteristic
76	C₂²×C₈×C₄₃	C₂³	1	1	yes	characteristic
77	C₂²×C₈×C₄₃	C₂³	1	1	yes	characteristic
78	C₂²×C₈×C₄₃	C₂³	1	1	yes	characteristic
79	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
80	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
81	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
82	#97×C₄₃	—	2	2	no	—
83	#97×C₄₃	—	2	2	no	—
84	#97×C₄₃	D₄	1	4	yes	—
85	C₄×C₈×C₄₃	—	2	2	no	—
86	C₄×C₈×C₄₃	C₂×C₄	1	4	yes	complemented
87	C₄×C₈×C₄₃	D₄	1	4	yes	—
88	#95×C₄₃	D₄	1	2	yes	—
89	#95×C₄₃	D₄	1	2	yes	—
90	C₂³×D₄₃	—	2	2	no	—
91	C₂²×C₄×C₄₃	C₂×D₄	1	2	yes	—
92	C₂²×C₄×C₄₃	C₂×D₄	1	2	yes	—
93	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
94	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
95	C₂²×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
96	C₂²×Dic₄₃	—	2	2	no	—
97	C₂²×Dic₄₃	—	2	2	no	—
98	C₂²×Dic₄₃	—	2	2	no	—
99	C₂×D₁₇₂	—	2	2	no	—
100	C₂×D₁₇₂	—	2	2	no	—
101	C₂×D₁₇₂	—	2	2	no	—
102	C₂×D₁₇₂	—	2	2	no	—
103	C₂×D₁₇₂	—	2	2	no	—
104	C₂×D₁₇₂	C₂²×C₄	1	4	yes	—
105	C₂×C₄×D₄₃	—	4	4	no	—
106	C₂×C₄×D₄₃	—	8	4	no	—
107	C₂×Dic₈₆	—	2	2	no	—
108	C₂×Dic₈₆	—	2	2	no	—
109	C₂×Dic₈₆	—	2	2	no	—
110	C₂×Dic₈₆	—	2	2	no	—
111	C₂×Dic₈₆	—	2	2	no	—
112	C₂×Dic₈₆	C₂²×C₄	1	4	yes	—
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	C₂×C₈×C₄₃	C₂×D₄	1	2	yes	—
120	C₂×C₈×C₄₃	C₂×D₄	1	2	yes	—
121	C₂×C₈×C₄₃	C₂×D₄	1	2	yes	—
122	C₂×C₈×C₄₃	C₂×D₄	1	2	yes	—
123	C₂×C₈×C₄₃	#41	1	2	yes	—
124	C₂×C₈×C₄₃	#41	1	2	yes	—
125	C₄²×C₄₃	—	2	1	no	—
126	C₄²×C₄₃	—	2	1	no	—
127	C₄²×C₄₃	C₂²×C₄	1	2	yes	—
128	C₄²×C₄₃	C₂×D₄	1	2	yes	—
129	C₄²×C₄₃	C₂×D₄	1	2	yes	—
130	C₄²×C₄₃	#41	1	2	yes	—
131	(C₂×D₄₃)⋊C₄	—	2	16	no	—
132	(C₂×D₄₃)⋊C₄	—	4	4	no	—
133	(C₂×D₄₃)⋊C₄	—	8	4	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	—	8	4	no	—
139	Dic₄₃⋊C₄	—	4	4	no	—
140	C₄×Dic₄₃	—	4	4	no	—
141	Dic₁₇₂	—	2	8	no	—
142	D₃₄₄	—	2	8	no	—
143	#10621873	—	2	16	no	—
144	C₂³×C₄₃	C₂²×D₄	1	1	yes	characteristic
145	C₂²×D₄₃	—	2	4	no	—
146	C₂²×D₄₃	—	4	2	no	—
147	C₂²×D₄₃	—	4	2	no	—
148	C₂²×D₄₃	—	4	4	no	—
149	C₂²×D₄₃	—	4	4	no	—
150	C₂×C₄×C₄₃	—	2	2	no	—
151	C₂×C₄×C₄₃	—	2	2	no	—
152	C₂×C₄×C₄₃	—	2	2	no	—
153	C₂×C₄×C₄₃	—	2	2	no	—
154	C₂×C₄×C₄₃	—	2	2	no	—
155	C₂×C₄×C₄₃	—	2	2	no	—
156	C₂×C₄×C₄₃	—	2	2	no	—
157	C₂×C₄×C₄₃	C₄×D₄	1	4	yes	—
158	C₂×C₄×C₄₃	#127	1	2	yes	—
159	C₂×C₄×C₄₃	#127	1	2	yes	—
160	C₂×C₄×C₄₃	C₂³×C₄	1	1	yes	characteristic
161	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
162	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
163	C₂×C₄×C₄₃	C₂×#41	1	1	yes	characteristic
164	C₂×C₄×C₄₃	C₂×#41	1	1	yes	characteristic
165	C₂×C₄×C₄₃	C₂×#41	1	1	yes	characteristic
166	C₂×Dic₄₃	—	2	4	no	—
167	C₂×Dic₄₃	—	4	2	no	—
168	C₂×Dic₄₃	—	4	2	no	—
169	C₂×Dic₄₃	—	4	2	no	—
170	C₂×Dic₄₃	—	4	2	no	—
171	C₂×Dic₄₃	—	4	4	no	—
172	C₂×Dic₄₃	—	4	4	no	—
173	D₁₇₂	—	2	4	no	—
174	D₁₇₂	—	2	4	no	—
175	D₁₇₂	—	4	2	no	—
176	D₁₇₂	—	4	2	no	—
177	C₄×D₄₃	—	8	8	no	—
178	Dic₈₆	—	2	4	no	—
179	Dic₈₆	—	2	4	no	—
180	Dic₈₆	—	4	2	no	—
181	Dic₈₆	—	4	2	no	—
182	C₈×C₄₃	—	2	2	no	—
183	C₈×C₄₃	—	2	2	no	—
184	C₈×C₄₃	C₄×D₄	1	4	yes	—
185	C₈×C₄₃	C₄×D₄	1	4	yes	—
186	#21696	—	43	1	no	maximal, Sylow
187	C₂²×C₄₃	C₂×C₄×D₄	1	1	yes	characteristic
188	C₂²×C₄₃	C₂×#127	1	1	yes	characteristic
189	C₂²×C₄₃	#532	1	1	yes	characteristic
190	C₂²×C₄₃	#576	1	2	yes	—
191	C₂²×C₄₃	#578	1	2	yes	—
192	C₂×D₄₃	—	4	4	no	—
193	C₂×D₄₃	—	4	8	no	—
194	C₂×D₄₃	—	8	2	no	—
195	C₂×D₄₃	—	8	2	no	—
196	C₂×D₄₃	—	8	4	no	—
197	C₄×C₄₃	—	2	2	no	—
198	C₄×C₄₃	—	2	2	no	—
199	C₄×C₄₃	—	2	4	no	—
200	C₄×C₄₃	—	4	2	no	—
201	C₄×C₄₃	C₂×C₄×D₄	1	1	yes	characteristic
202	C₄×C₄₃	C₂×C₄×D₄	1	1	yes	characteristic
203	C₄×C₄₃	#532	1	1	yes	characteristic
204	C₄×C₄₃	#532	1	1	yes	characteristic
205	Dic₄₃	—	4	4	no	—
206	Dic₄₃	—	8	2	no	—
207	Dic₄₃	—	8	2	no	—
208	C₂×#495	—	43	1	no	—
209	C₂×#440	—	43	2	no	—
210	C₂×C₄×Q₁₆	—	43	1	no	—
211	C₂×C₄×D₈	—	43	1	no	—
212	#2326	—	43	2	no	—
213	#1973	—	43	2	no	—
214	#1970	—	43	1	no	—
215	#1969	—	43	1	no	—
216	#1959	—	43	2	no	—
217	#1845	—	43	1	no	—
218	#1726	D₄₃	1	1	yes	characteristic, complemented
219	C₂×C₄₃	C₄×#127	1	1	yes	characteristic
220	C₂×C₄₃	#2951	1	2	yes	—
221	C₂×C₄₃	#3155	1	1	yes	characteristic
222	C₂×C₄₃	#3156	1	1	yes	characteristic
223	C₂×C₄₃	#3175	1	2	yes	—
224	D₄₃	—	8	4	no	—
225	C₂²×Q₁₆	—	43	1	no	—
226	C₂²×SD₁₆	—	43	2	no	—
227	C₂²×D₈	—	43	1	no	—
228	C₂×#124	—	43	2	no	—
229	C₂×C₄×Q₈	—	43	2	no	—
230	C₂×C₄×D₄	—	43	2	no	—
231	#495	—	43	8	no	—
232	#440	—	86	8	no	—
233	C₄×Q₁₆	—	86	4	no	—
234	C₄×D₈	—	86	4	no	—
235	C₂×#107	—	43	1	no	—
236	C₂×#107	—	43	1	no	—
237	C₂×#107	—	43	2	no	—
238	C₂×#103	—	43	2	no	—
239	C₂×#103	—	43	2	no	—
240	C₂×#102	—	43	2	no	—
241	C₂×#102	—	43	2	no	—
242	C₂×#97	C₂×D₄₃	1	1	yes	characteristic
243	C₂×#97	C₂×D₄₃	1	1	yes	characteristic
244	C₂×#97	C₂×D₄₃	1	1	yes	characteristic
245	C₂×C₄×C₈	C₂×D₄₃	1	1	yes	characteristic
246	C₂×C₄×C₈	C₂×D₄₃	1	1	yes	characteristic
247	C₂×C₄×C₈	C₂×D₄₃	1	1	yes	characteristic
248	#391	—	43	2	no	—
249	#390	—	43	2	no	—
250	#388	—	86	4	no	—
251	#385	—	86	4	no	—
252	#384	—	43	2	no	—
253	#376	C₂×D₄₃	1	1	yes	characteristic
254	C₄₃	#21696	1	1	yes	characteristic, complemented, Sylow
255	C₂²×Q₈	—	43	2	no	—
256	C₂²×D₄	—	43	2	no	—
257	C₂³×C₄	—	86	2	no	—
258	C₂×Q₁₆	—	43	4	no	—
259	C₂×Q₁₆	—	86	2	no	—
260	C₂×Q₁₆	—	86	2	no	—
261	C₂×SD₁₆	—	43	8	no	—
262	C₂×SD₁₆	—	86	4	no	—
263	C₂×SD₁₆	—	86	4	no	—
264	C₂×D₈	—	43	4	no	—
265	C₂×D₈	—	86	2	no	—
266	C₂×D₈	—	86	2	no	—
267	C₂²×C₈	C₂²×D₄₃	1	1	yes	characteristic
268	C₂²×C₈	C₂²×D₄₃	1	1	yes	characteristic
269	C₂²×C₈	C₂²×D₄₃	1	1	yes	characteristic
270	C₂²×C₈	C₂²×D₄₃	1	1	yes	characteristic
271	#124	—	43	8	no	—
272	#124	—	86	4	no	—
273	C₄×Q₈	—	86	4	no	—
274	C₄×Q₈	—	86	4	no	—
275	C₄×D₄	—	86	4	no	—
276	C₄×D₄	—	86	4	no	—
277	C₂×C₄⋊C₄	—	43	2	no	—
278	C₂×C₄⋊C₄	—	43	2	no	—
279	C₂×C₄⋊C₄	—	86	4	no	—
280	C₂×C₄⋊C₄	—	86	2	no	—
281	C₂×C₂²⋊C₄	—	86	4	no	—
282	C₂×C₂²⋊C₄	—	86	4	no	—
283	C₂×C₂²⋊C₄	—	86	2	no	—
284	C₂×C₄²	—	86	2	no	—
285	C₂×C₄²	C₂²×D₄₃	1	1	yes	characteristic
286	C₂×C₄²	C₂²×D₄₃	1	1	yes	characteristic
287	C₂×C₄²	C₂²×D₄₃	1	1	yes	characteristic
288	#107	—	86	2	no	—
289	#107	—	86	2	no	—
290	#107	—	86	4	no	—
291	#103	—	86	4	no	—
292	#103	—	86	4	no	—
293	#102	—	86	4	no	—
294	#102	—	86	4	no	—
295	#97	—	2	2	no	—
296	#97	—	2	2	no	—
297	#97	D₁₇₂	1	4	yes	—
298	C₄×C₈	—	2	2	no	—
299	C₄×C₈	C₄×D₄₃	1	4	yes	complemented
300	C₄×C₈	D₁₇₂	1	4	yes	—
301	#95	—	86	4	no	—
302	#95	D₁₇₂	1	2	yes	—
303	#95	D₁₇₂	1	2	yes	—
304	C₂⁴	—	86	2	no	—
305	C₂×Q₈	—	43	4	no	—
306	C₂×Q₈	—	86	2	no	—
307	C₂×Q₈	—	86	2	no	—
308	C₂×Q₈	—	86	2	no	—
309	C₂×Q₈	—	86	2	no	—
310	C₂×Q₈	—	86	2	no	—
311	C₂×D₄	—	43	4	no	—
312	C₂×D₄	—	86	2	no	—
313	C₂×D₄	—	86	2	no	—
314	C₂×D₄	—	86	2	no	—
315	C₂×D₄	—	86	2	no	—
316	C₂×D₄	—	86	2	no	—
317	C₂²×C₄	—	86	2	no	—
318	C₂²×C₄	—	86	2	no	—
319	C₂²×C₄	—	86	2	no	—
320	C₂²×C₄	—	344	4	no	—
321	C₂²×C₄	—	172	4	no	—
322	C₂²×C₄	C₂×D₁₇₂	1	2	yes	—
323	C₂²×C₄	C₂×D₁₇₂	1	2	yes	—
324	C₂²×C₄	C₂×D₁₇₂	1	1	yes	characteristic
325	C₂²×C₄	C₂×D₁₇₂	1	1	yes	characteristic
326	C₂²×C₄	C₂³×D₄₃	1	1	yes	characteristic
327	Q₁₆	—	86	8	no	—
328	SD₁₆	—	86	16	no	—
329	D₈	—	86	8	no	—
330	C₂×C₈	—	2	1	no	—
331	C₂×C₈	—	2	1	no	—
332	C₂×C₈	—	2	1	no	—
333	C₂×C₈	—	2	1	no	—
334	C₂×C₈	C₂×C₄×D₄₃	1	2	yes	—
335	C₂×C₈	C₂×C₄×D₄₃	1	2	yes	—
336	C₂×C₈	C₂×D₁₇₂	1	2	yes	—
337	C₂×C₈	C₂×D₁₇₂	1	2	yes	—
338	C₂×C₈	C₂×D₁₇₂	1	2	yes	—
339	C₂×C₈	C₂×D₁₇₂	1	2	yes	—
340	C₂×C₈	#10621898	1	2	yes	—
341	C₂×C₈	#10621898	1	2	yes	—
342	C₄⋊C₄	—	86	2	no	—
343	C₄⋊C₄	—	86	2	no	—
344	C₄⋊C₄	—	86	2	no	—
345	C₄⋊C₄	—	86	2	no	—
346	C₄⋊C₄	—	344	4	no	—
347	C₄⋊C₄	—	172	4	no	—
348	C₂²⋊C₄	—	86	16	no	—
349	C₂²⋊C₄	—	344	4	no	—
350	C₂²⋊C₄	—	172	4	no	—
351	C₄²	—	2	1	no	—
352	C₄²	—	2	1	no	—
353	C₄²	—	172	4	no	—
354	C₄²	C₂×C₄×D₄₃	1	2	yes	—
355	C₄²	C₂×D₁₇₂	1	2	yes	—
356	C₄²	C₂×D₁₇₂	1	2	yes	—
357	C₄²	#10621898	1	2	yes	—
358	C₂³	—	86	4	no	—
359	C₂³	—	172	2	no	—
360	C₂³	—	172	4	no	—
361	C₂³	—	172	2	no	—
362	C₂³	—	172	4	no	—
363	C₂³	C₂²×D₁₇₂	1	1	yes	characteristic
364	Q₈	—	86	4	no	—
365	Q₈	—	86	4	no	—
366	Q₈	—	172	2	no	—
367	Q₈	—	172	2	no	—
368	D₄	—	86	4	no	—
369	D₄	—	86	4	no	—
370	D₄	—	172	2	no	—
371	D₄	—	172	2	no	—
372	C₂×C₄	—	2	2	no	—
373	C₂×C₄	—	2	2	no	—
374	C₂×C₄	—	2	2	no	—
375	C₂×C₄	—	2	2	no	—
376	C₂×C₄	—	2	2	no	—
377	C₂×C₄	—	2	2	no	—
378	C₂×C₄	—	2	2	no	—
379	C₂×C₄	—	86	4	no	—
380	C₂×C₄	—	344	8	no	—
381	C₂×C₄	—	172	2	no	—
382	C₂×C₄	—	172	2	no	—
383	C₂×C₄	—	172	4	no	—
384	C₂×C₄	—	172	4	no	—
385	C₂×C₄	—	172	2	no	—
386	C₂×C₄	—	172	2	no	—
387	C₂×C₄	C₄×D₁₇₂	1	4	yes	—
388	C₂×C₄	#13063322	1	2	yes	—
389	C₂×C₄	#13063322	1	2	yes	—
390	C₂×C₄	C₂²×C₄×D₄₃	1	1	yes	characteristic
391	C₂×C₄	C₂²×D₁₇₂	1	1	yes	characteristic
392	C₂×C₄	C₂²×D₁₇₂	1	1	yes	characteristic
393	C₂×C₄	C₂×#10621898	1	1	yes	characteristic
394	C₂×C₄	C₂×#10621898	1	1	yes	characteristic
395	C₂×C₄	C₂×#10621898	1	1	yes	characteristic
396	C₈	—	2	2	no	—
397	C₈	—	2	2	no	—
398	C₈	C₄×D₁₇₂	1	4	yes	—
399	C₈	C₄×D₁₇₂	1	4	yes	—
400	C₂²	—	344	4	no	—
401	C₂²	—	344	2	no	—
402	C₂²	—	344	2	no	—
403	C₂²	—	172	8	no	—
404	C₂²	—	172	4	no	—
405	C₂²	C₂×C₄×D₁₇₂	1	1	yes	characteristic
406	C₂²	C₂×#13063322	1	1	yes	characteristic
407	C₂²	#14583449	1	1	yes	characteristic
408	C₂²	#14583704	1	2	yes	—
409	C₂²	#14583716	1	2	yes	—
410	C₄	—	2	4	no	—
411	C₄	—	2	2	no	—
412	C₄	—	2	2	no	—
413	C₄	—	4	2	no	—
414	C₄	—	344	2	no	—
415	C₄	—	344	2	no	—
416	C₄	—	172	4	no	—
417	C₄	C₂×C₄×D₁₇₂	1	1	yes	characteristic
418	C₄	C₂×C₄×D₁₇₂	1	1	yes	characteristic
419	C₄	#14583449	1	1	yes	characteristic
420	C₄	#14583449	1	1	yes	characteristic
421	C₂	—	344	4	no	—
422	C₂	C₄×#13063322	1	1	yes	characteristic
423	C₂	#19143472	1	2	yes	—
424	C₂	#19145081	1	1	yes	characteristic
425	C₂	#19145089	1	1	yes	characteristic
426	C₂	#19145234	1	2	yes	—

	subgroup	G/H
center	C₂³	C₂²×D₁₇₂
commutator	C₂×C₄×C₄₃	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₄₃
Fitting	C₄₃×#1726	C₂
socle	C₂³×C₄₃	C₂²×D₄
prime radical	C₂²×D₃₄₄	C₂²
cosocle	C₂²×C₄×C₄₃	C₂⁴
hypercenter	#1726	D₄₃
hypocenter	C₄₃	#21696
LCS	G ▷ C₂×C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂³ ◁ #376 ◁ #1726

Complements

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

N	H ≅ G/N	type
2. C₂×#14583001	C₂	semidirect
3. C₂×C₄×Dic₁₇₂	C₂	semidirect
5. #19137306	C₂	semidirect
6. #19135476	C₂	semidirect
8. #19135456	C₂	semidirect
9. #19135411	C₂	semidirect
10. #19134755	C₂	semidirect
11. C₄₃×#1726	C₂	semidirect
18. #14583283	C₄	semidirect
46. C₂×Dic₁₇₂	C₂×C₄	semidirect
49. C₂×#10621873	C₂×C₄	semidirect
54. #13063313	C₂×C₄	semidirect
86. C₄×C₈×C₄₃	C₂×C₄	semidirect
218. #1726	D₄₃	semidirect
254. C₄₃	#21696	semidirect
299. C₄×C₈	C₄×D₄₃	semidirect

Maximal subgroups

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

subgroup	index
C₂×#14583283	2
C₂×#14583001	2
C₂×C₄×Dic₁₇₂	2
C₂×C₄×D₃₄₄	2
#19137306	2
#19135476	2
#19135461	2
#19135456	2
#19135411	2
#19134755	2
C₄₃×#1726	2
#21696	43