Subgroups — #25107135

Order 11008.

850 conjugacy classes of subgroups.

The subgroup lattice has 406 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#19137002	C₂	1	1	yes	maximal, characteristic
2	#19137002	C₂	1	1	yes	maximal, characteristic
3	#19135365	C₂	1	4	yes	maximal, complemented
4	#19134796	C₂	1	4	yes	maximal
5	#19134755	C₂	1	1	yes	maximal, characteristic, complemented
6	#19134752	C₂	1	1	yes	maximal, characteristic, complemented
7	#19134723	C₂	1	1	yes	maximal, characteristic, complemented
8	#19134723	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×C₄₃×#431	C₂	1	1	yes	maximal, characteristic
10	C₂×#13063284	—	2	1	no	—
11	C₂×#13063284	C₂²	1	2	yes	—
12	C₂×#13063259	C₂²	1	4	yes	—
13	C₂×#13063257	C₂²	1	4	yes	—
14	#14582769	C₂²	1	1	yes	characteristic
15	#14582769	C₂²	1	1	yes	characteristic
16	#14582769	C₂²	1	1	yes	characteristic
17	#14582769	C₂²	1	1	yes	characteristic
18	#14582765	—	2	1	no	—
19	#14582765	C₂²	1	2	yes	—
20	#14582759	—	2	1	no	—
21	#14582759	—	2	1	no	—
22	#14582759	—	2	1	no	—
23	#14582759	C₂²	1	2	yes	—
24	C₄×C₄⋊Dic₄₃	—	2	1	no	—
25	C₄×C₄⋊Dic₄₃	—	2	1	no	—
26	C₄×C₄⋊Dic₄₃	—	2	1	no	—
27	C₄×C₄⋊Dic₄₃	C₂²	1	2	yes	—
28	#14582662	C₂²	1	4	yes	—
29	#14582662	C₂²	1	4	yes	—
30	C₂²×C₄²×C₄₃	C₂²	1	1	yes	characteristic
31	C₄₃×#431	C₄	1	8	yes	complemented
32	C₂×C₄⋊C₈×C₄₃	C₂²	1	2	yes	—
33	C₂×C₂²⋊C₈×C₄₃	C₂²	1	2	yes	—
34	C₂×C₄×C₈×C₄₃	C₂²	1	1	yes	characteristic
35	C₂×C₄×C₈×C₄₃	C₂²	1	1	yes	characteristic
36	#13063284	—	4	4	no	—
37	#13063284	—	4	4	no	—
38	C₂×C₄⋊Dic₄₃	—	2	1	no	—
39	C₂×C₄⋊Dic₄₃	—	2	1	no	—
40	C₂×C₄⋊Dic₄₃	—	2	1	no	—
41	C₂×C₄⋊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	C₂³	1	2	yes	—
47	C₂×C₄⋊Dic₄₃	C₂³	1	2	yes	—
48	C₂×C₄⋊Dic₄₃	C₂³	1	2	yes	—
49	C₂×C₄⋊Dic₄₃	C₂³	1	2	yes	—
50	C₂×C₂²⋊Dic₄₃	—	2	2	no	—
51	C₂×C₂²⋊Dic₄₃	—	2	2	no	—
52	C₂×C₄×Dic₄₃	—	2	2	no	—
53	C₂×C₄×Dic₄₃	—	2	2	no	—
54	#13063259	—	4	4	no	—
55	#13063257	—	4	4	no	—
56	C₄₃⋊#95	—	2	2	no	—
57	C₄₃⋊#95	—	2	2	no	—
58	C₄₃⋊#95	—	2	2	no	—
59	C₄₃⋊#95	—	2	2	no	—
60	C₂³×C₄×C₄₃	D₄	1	1	yes	characteristic
61	C₂³×C₄×C₄₃	D₄	1	1	yes	characteristic
62	C₂³×C₄×C₄₃	C₂³	1	1	yes	characteristic
63	C₂²×C₈×C₄₃	C₂³	1	2	yes	—
64	C₂²×C₈×C₄₃	C₂³	1	2	yes	—
65	C₂×C₄²×C₄₃	C₂×C₄	1	4	yes	—
66	C₂×C₄²×C₄₃	D₄	1	1	yes	characteristic
67	C₂×C₄²×C₄₃	D₄	1	1	yes	characteristic
68	C₂×C₄²×C₄₃	Q₈	1	4	yes	—
69	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
70	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
71	C₄⋊C₈×C₄₃	C₂×C₄	1	8	yes	—
72	C₂²⋊C₈×C₄₃	C₂×C₄	1	8	yes	—
73	C₄×C₈×C₄₃	C₂×C₄	1	4	yes	—
74	C₄×C₈×C₄₃	C₂×C₄	1	4	yes	—
75	C₂⁴×C₄₃	C₂×D₄	1	1	yes	characteristic
76	C₂²×C₄×C₄₃	—	2	2	no	—
77	C₂²×C₄×C₄₃	—	2	2	no	—
78	C₂²×C₄×C₄₃	—	2	2	no	—
79	C₂²×C₄×C₄₃	—	2	2	no	—
80	C₂²×C₄×C₄₃	—	2	2	no	—
81	C₂²×C₄×C₄₃	—	2	2	no	—
82	C₂²×C₄×C₄₃	C₄⋊C₄	1	4	yes	—
83	C₂²×C₄×C₄₃	C₄⋊C₄	1	4	yes	—
84	C₂²×C₄×C₄₃	C₂²×C₄	1	2	yes	—
85	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
86	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
87	C₂²×C₄×C₄₃	C₂×D₄	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×Q₈	1	2	yes	—
91	C₂²×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
92	C₂²×Dic₄₃	—	2	2	no	—
93	C₂²×Dic₄₃	—	2	2	no	—
94	C₂²×Dic₄₃	—	2	2	no	—
95	C₂²×Dic₄₃	—	2	2	no	—
96	C₂×C₈×C₄₃	—	2	2	no	—
97	C₂×C₈×C₄₃	—	2	2	no	—
98	C₂×C₈×C₄₃	—	2	2	no	—
99	C₂×C₈×C₄₃	—	2	2	no	—
100	C₂×C₈×C₄₃	C₂²×C₄	1	4	yes	—
101	C₂×C₈×C₄₃	C₂²×C₄	1	4	yes	—
102	C₄²×C₄₃	C₄⋊C₄	1	4	yes	—
103	C₄²×C₄₃	C₄⋊C₄	1	4	yes	—
104	C₄²×C₄₃	C₂²×C₄	1	2	yes	—
105	C₄²×C₄₃	C₂²×C₄	1	2	yes	—
106	C₄²×C₄₃	C₂×Q₈	1	2	yes	—
107	C₄²×C₄₃	C₂×Q₈	1	2	yes	—
108	C₂²⋊Dic₄₃	—	4	4	no	—
109	C₂²⋊Dic₄₃	—	4	4	no	—
110	C₄⋊Dic₄₃	—	2	4	no	—
111	C₄⋊Dic₄₃	—	2	4	no	—
112	C₄⋊Dic₄₃	—	2	4	no	—
113	C₄⋊Dic₄₃	—	2	4	no	—
114	C₄⋊Dic₄₃	—	4	2	no	—
115	C₄⋊Dic₄₃	—	4	2	no	—
116	C₄⋊Dic₄₃	—	4	2	no	—
117	C₄⋊Dic₄₃	—	4	2	no	—
118	C₄⋊Dic₄₃	—	4	2	no	—
119	C₄⋊Dic₄₃	—	4	2	no	—
120	C₄⋊Dic₄₃	—	4	2	no	—
121	C₄⋊Dic₄₃	—	4	2	no	—
122	C₄×Dic₄₃	—	4	4	no	—
123	C₄×Dic₄₃	—	4	4	no	—
124	C₂³×C₄₃	—	2	1	no	—
125	C₂³×C₄₃	—	2	1	no	—
126	C₂³×C₄₃	—	2	1	no	—
127	C₂³×C₄₃	—	2	1	no	—
128	C₂³×C₄₃	—	2	1	no	—
129	C₂³×C₄₃	—	2	1	no	—
130	C₂³×C₄₃	C₂×C₄⋊C₄	1	2	yes	—
131	C₂³×C₄₃	C₂²×D₄	1	1	yes	characteristic
132	C₂×C₄×C₄₃	—	2	1	no	—
133	C₂×C₄×C₄₃	—	2	1	no	—
134	C₂×C₄×C₄₃	—	2	1	no	—
135	C₂×C₄×C₄₃	—	2	1	no	—
136	C₂×C₄×C₄₃	—	2	1	no	—
137	C₂×C₄×C₄₃	—	2	1	no	—
138	C₂×C₄×C₄₃	—	2	4	no	—
139	C₂×C₄×C₄₃	—	2	4	no	—
140	C₂×C₄×C₄₃	—	2	8	no	—
141	C₂×C₄×C₄₃	—	2	8	no	—
142	C₂×C₄×C₄₃	C₂×C₄⋊C₄	1	2	yes	—
143	C₂×C₄×C₄₃	C₂×C₄⋊C₄	1	2	yes	—
144	C₂×C₄×C₄₃	C₂×C₄⋊C₄	1	2	yes	—
145	C₂×C₄×C₄₃	C₂×C₄⋊C₄	1	2	yes	—
146	C₂×C₄×C₄₃	C₂×C₄⋊C₄	1	2	yes	—
147	C₂×C₄×C₄₃	#135	1	2	yes	—
148	C₂×C₄×C₄₃	#135	1	2	yes	—
149	C₂×C₄×C₄₃	AGL(1,ℤ/8)	1	2	yes	—
150	C₂×C₄×C₄₃	#137	1	2	yes	—
151	C₂×C₄×C₄₃	C₂³×C₄	1	1	yes	characteristic
152	C₂×C₄×C₄₃	C₂²×Q₈	1	1	yes	characteristic
153	C₂×C₄×C₄₃	H(5,𝔽₂)	1	2	yes	—
154	C₂×C₄×C₄₃	2₋¹⁺⁴	1	2	yes	—
155	C₂×Dic₄₃	—	4	2	no	—
156	C₂×Dic₄₃	—	4	2	no	—
157	C₂×Dic₄₃	—	4	2	no	—
158	C₂×Dic₄₃	—	4	2	no	—
159	C₂×Dic₄₃	—	4	2	no	—
160	C₂×Dic₄₃	—	4	2	no	—
161	C₂×Dic₄₃	—	4	2	no	—
162	C₂×Dic₄₃	—	4	2	no	—
163	C₂×Dic₄₃	—	4	2	no	—
164	C₂×Dic₄₃	—	4	2	no	—
165	C₂×Dic₄₃	—	4	2	no	—
166	C₂×Dic₄₃	—	4	2	no	—
167	C₈×C₄₃	—	2	4	no	—
168	C₈×C₄₃	—	2	4	no	—
169	#21984	—	43	1	no	maximal, Sylow
170	C₂²×C₄₃	—	2	2	no	—
171	C₂²×C₄₃	—	2	2	no	—
172	C₂²×C₄₃	—	2	2	no	—
173	C₂²×C₄₃	—	4	1	no	—
174	C₂²×C₄₃	—	4	1	no	—
175	C₂²×C₄₃	—	4	1	no	—
176	C₂²×C₄₃	—	4	1	no	—
177	C₂²×C₄₃	C₂²×C₄⋊C₄	1	1	yes	characteristic
178	C₂²×C₄₃	#535	1	1	yes	characteristic
179	C₂²×C₄₃	#536	1	1	yes	characteristic
180	C₂²×C₄₃	C₂×#135	1	1	yes	characteristic
181	C₂²×C₄₃	C₂×#135	1	1	yes	characteristic
182	C₂²×C₄₃	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
183	C₂²×C₄₃	C₂×#137	1	1	yes	characteristic
184	C₄×C₄₃	—	2	2	no	—
185	C₄×C₄₃	—	2	2	no	—
186	C₄×C₄₃	—	2	2	no	—
187	C₄×C₄₃	#427	1	4	yes	—
188	C₄×C₄₃	#428	1	4	yes	—
189	C₄×C₄₃	#520	1	2	yes	—
190	C₄×C₄₃	#544	1	2	yes	—
191	Dic₄₃	—	8	2	no	—
192	Dic₄₃	—	8	2	no	—
193	Dic₄₃	—	8	2	no	—
194	Dic₄₃	—	8	2	no	—
195	C₂×#431	D₄₃	1	1	yes	characteristic
196	#2285	—	43	1	no	—
197	#2285	—	43	1	no	—
198	#1949	—	43	4	no	—
199	#1854	—	43	4	no	—
200	#1845	—	43	1	no	—
201	#1844	—	43	1	no	—
202	#1834	—	43	1	no	—
203	#1834	—	43	1	no	—
204	C₂×C₄₃	—	4	2	no	—
205	C₂×C₄₃	#2317	1	1	yes	characteristic
206	C₂×C₄₃	C₂×#427	1	1	yes	characteristic
207	C₂×C₄₃	C₂×#428	1	1	yes	characteristic
208	C₂×C₄₃	#3207	1	1	yes	characteristic
209	C₂×C₄₃	#3210	1	1	yes	characteristic
210	C₂×C₄₃	#3228	1	1	yes	characteristic
211	C₂×C₄₃	#3231	1	1	yes	characteristic
212	C₂×#117	—	43	2	no	—
213	C₂×#117	—	86	1	no	—
214	C₂²×C₄²	C₂×D₄₃	1	1	yes	characteristic
215	#431	Dic₄₃	1	8	yes	complemented
216	C₂×#107	—	43	4	no	—
217	C₂×#106	—	43	4	no	—
218	C₂×C₄⋊C₈	C₂×D₄₃	1	2	yes	—
219	C₂×C₂²⋊C₈	C₂×D₄₃	1	2	yes	—
220	C₂×C₄×C₈	C₂×D₄₃	1	1	yes	characteristic
221	C₂×C₄×C₈	C₂×D₄₃	1	1	yes	characteristic
222	#384	—	43	1	no	—
223	#384	—	43	1	no	—
224	#384	—	43	1	no	—
225	#384	—	43	1	no	—
226	#382	—	43	2	no	—
227	#382	—	86	1	no	—
228	#380	—	43	2	no	—
229	#380	—	86	1	no	—
230	#380	—	86	1	no	—
231	#380	—	86	1	no	—
232	C₄×C₄⋊C₄	—	43	2	no	—
233	C₄×C₄⋊C₄	—	86	1	no	—
234	C₄×C₄⋊C₄	—	86	1	no	—
235	C₄×C₄⋊C₄	—	86	1	no	—
236	#340	—	43	4	no	—
237	#340	—	43	4	no	—
238	C₄₃	#21984	1	1	yes	characteristic, complemented, Sylow
239	C₂³×C₄	D₁₇₂	1	1	yes	characteristic
240	C₂³×C₄	D₁₇₂	1	1	yes	characteristic
241	C₂³×C₄	C₂²×D₄₃	1	1	yes	characteristic
242	C₂²×C₈	C₂²×D₄₃	1	2	yes	—
243	C₂²×C₈	C₂²×D₄₃	1	2	yes	—
244	#117	—	172	4	no	—
245	#117	—	172	4	no	—
246	C₂×C₄⋊C₄	—	43	2	no	—
247	C₂×C₄⋊C₄	—	43	2	no	—
248	C₂×C₄⋊C₄	—	43	2	no	—
249	C₂×C₄⋊C₄	—	43	2	no	—
250	C₂×C₄⋊C₄	—	86	1	no	—
251	C₂×C₄⋊C₄	—	86	1	no	—
252	C₂×C₄⋊C₄	—	86	1	no	—
253	C₂×C₄⋊C₄	—	86	1	no	—
254	C₂×C₄⋊C₄	—	86	1	no	—
255	C₂×C₄⋊C₄	—	86	1	no	—
256	C₂×C₄⋊C₄	—	86	1	no	—
257	C₂×C₄⋊C₄	—	86	1	no	—
258	C₂×C₂²⋊C₄	—	86	2	no	—
259	C₂×C₂²⋊C₄	—	86	2	no	—
260	C₂×C₄²	—	86	2	no	—
261	C₂×C₄²	—	86	2	no	—
262	C₂×C₄²	Dic₈₆	1	4	yes	—
263	C₂×C₄²	D₁₇₂	1	1	yes	characteristic
264	C₂×C₄²	D₁₇₂	1	1	yes	characteristic
265	C₂×C₄²	C₂×Dic₄₃	1	4	yes	—
266	C₂×C₄²	C₂²×D₄₃	1	1	yes	characteristic
267	C₂×C₄²	C₂²×D₄₃	1	1	yes	characteristic
268	#107	—	172	4	no	—
269	#106	—	172	4	no	—
270	C₄⋊C₈	C₂×Dic₄₃	1	8	yes	—
271	C₂²⋊C₈	C₂×Dic₄₃	1	8	yes	—
272	C₄×C₈	C₂×Dic₄₃	1	4	yes	—
273	C₄×C₈	C₂×Dic₄₃	1	4	yes	—
274	#95	—	86	2	no	—
275	#95	—	86	2	no	—
276	#95	—	86	2	no	—
277	#95	—	86	2	no	—
278	C₂⁴	C₂×D₁₇₂	1	1	yes	characteristic
279	C₂²×C₄	—	2	2	no	—
280	C₂²×C₄	—	2	2	no	—
281	C₂²×C₄	—	2	2	no	—
282	C₂²×C₄	—	2	2	no	—
283	C₂²×C₄	—	2	2	no	—
284	C₂²×C₄	—	2	2	no	—
285	C₂²×C₄	—	86	2	no	—
286	C₂²×C₄	—	86	2	no	—
287	C₂²×C₄	—	86	2	no	—
288	C₂²×C₄	—	86	2	no	—
289	C₂²×C₄	C₄⋊Dic₄₃	1	4	yes	—
290	C₂²×C₄	C₄⋊Dic₄₃	1	4	yes	—
291	C₂²×C₄	C₂×Dic₈₆	1	2	yes	—
292	C₂²×C₄	C₂×D₁₇₂	1	1	yes	characteristic
293	C₂²×C₄	C₂×D₁₇₂	1	1	yes	characteristic
294	C₂²×C₄	C₂×D₁₇₂	1	1	yes	characteristic
295	C₂²×C₄	C₂×D₁₇₂	1	1	yes	characteristic
296	C₂²×C₄	C₂×D₁₇₂	1	1	yes	characteristic
297	C₂²×C₄	C₂²×Dic₄₃	1	2	yes	—
298	C₂²×C₄	C₂³×D₄₃	1	1	yes	characteristic
299	C₂×C₈	—	2	2	no	—
300	C₂×C₈	—	2	2	no	—
301	C₂×C₈	—	2	2	no	—
302	C₂×C₈	—	2	2	no	—
303	C₂×C₈	C₂²×Dic₄₃	1	4	yes	—
304	C₂×C₈	C₂²×Dic₄₃	1	4	yes	—
305	C₄⋊C₄	—	86	4	no	—
306	C₄⋊C₄	—	86	4	no	—
307	C₄⋊C₄	—	86	4	no	—
308	C₄⋊C₄	—	86	4	no	—
309	C₄⋊C₄	—	172	2	no	—
310	C₄⋊C₄	—	172	2	no	—
311	C₄⋊C₄	—	172	2	no	—
312	C₄⋊C₄	—	172	2	no	—
313	C₄⋊C₄	—	172	2	no	—
314	C₄⋊C₄	—	172	2	no	—
315	C₄⋊C₄	—	172	2	no	—
316	C₄⋊C₄	—	172	2	no	—
317	C₂²⋊C₄	—	172	4	no	—
318	C₂²⋊C₄	—	172	4	no	—
319	C₄²	—	172	4	no	—
320	C₄²	—	172	4	no	—
321	C₄²	C₄⋊Dic₄₃	1	4	yes	—
322	C₄²	C₄⋊Dic₄₃	1	4	yes	—
323	C₄²	C₂×Dic₈₆	1	2	yes	—
324	C₄²	C₂×Dic₈₆	1	2	yes	—
325	C₄²	C₂²×Dic₄₃	1	2	yes	—
326	C₄²	C₂²×Dic₄₃	1	2	yes	—
327	C₂³	—	2	1	no	—
328	C₂³	—	2	1	no	—
329	C₂³	—	2	1	no	—
330	C₂³	—	2	1	no	—
331	C₂³	—	2	1	no	—
332	C₂³	—	2	1	no	—
333	C₂³	C₂×C₄⋊Dic₄₃	1	2	yes	—
334	C₂³	C₂²×D₁₇₂	1	1	yes	characteristic
335	C₂×C₄	—	2	1	no	—
336	C₂×C₄	—	2	1	no	—
337	C₂×C₄	—	2	1	no	—
338	C₂×C₄	—	2	1	no	—
339	C₂×C₄	—	2	1	no	—
340	C₂×C₄	—	2	1	no	—
341	C₂×C₄	—	2	4	no	—
342	C₂×C₄	—	2	8	no	—
343	C₂×C₄	—	2	8	no	—
344	C₂×C₄	—	2	4	no	—
345	C₂×C₄	—	172	2	no	—
346	C₂×C₄	—	172	2	no	—
347	C₂×C₄	—	172	2	no	—
348	C₂×C₄	—	172	2	no	—
349	C₂×C₄	—	172	2	no	—
350	C₂×C₄	—	172	2	no	—
351	C₂×C₄	—	172	2	no	—
352	C₂×C₄	—	172	2	no	—
353	C₂×C₄	—	172	2	no	—
354	C₂×C₄	—	172	2	no	—
355	C₂×C₄	—	172	2	no	—
356	C₂×C₄	—	172	2	no	—
357	C₂×C₄	C₂×C₄⋊Dic₄₃	1	2	yes	—
358	C₂×C₄	C₂×C₄⋊Dic₄₃	1	2	yes	—
359	C₂×C₄	C₂×C₄⋊Dic₄₃	1	2	yes	—
360	C₂×C₄	C₂×C₄⋊Dic₄₃	1	2	yes	—
361	C₂×C₄	C₂×C₄⋊Dic₄₃	1	2	yes	—
362	C₂×C₄	#13063347	1	2	yes	—
363	C₂×C₄	#13063347	1	2	yes	—
364	C₂×C₄	#13063353	1	2	yes	—
365	C₂×C₄	#13063358	1	2	yes	—
366	C₂×C₄	C₂³×Dic₄₃	1	1	yes	characteristic
367	C₂×C₄	C₂²×Dic₈₆	1	1	yes	characteristic
368	C₂×C₄	#13063371	1	2	yes	—
369	C₂×C₄	#13063372	1	2	yes	—
370	C₈	—	2	4	no	—
371	C₈	—	2	4	no	—
372	C₂²	—	2	2	no	—
373	C₂²	—	2	2	no	—
374	C₂²	—	2	2	no	—
375	C₂²	—	4	1	no	—
376	C₂²	—	4	1	no	—
377	C₂²	—	4	1	no	—
378	C₂²	—	4	1	no	—
379	C₂²	C₂²×C₄⋊Dic₄₃	1	1	yes	characteristic
380	C₂²	#14583468	1	1	yes	characteristic
381	C₂²	#14583475	1	1	yes	characteristic
382	C₂²	C₂×#13063347	1	1	yes	characteristic
383	C₂²	C₂×#13063347	1	1	yes	characteristic
384	C₂²	C₂×#13063353	1	1	yes	characteristic
385	C₂²	C₂×#13063358	1	1	yes	characteristic
386	C₄	—	2	2	no	—
387	C₄	—	2	2	no	—
388	C₄	—	2	2	no	—
389	C₄	—	344	2	no	—
390	C₄	—	344	2	no	—
391	C₄	—	344	2	no	—
392	C₄	—	344	2	no	—
393	C₄	#14582937	1	4	yes	—
394	C₄	#14582941	1	4	yes	—
395	C₄	#14583382	1	2	yes	—
396	C₄	#14583527	1	2	yes	—
397	C₂	—	4	2	no	—
398	C₂	#19137218	1	1	yes	characteristic
399	C₂	C₂×#14582937	1	1	yes	characteristic
400	C₂	C₂×#14582941	1	1	yes	characteristic
401	C₂	#19145530	1	1	yes	characteristic
402	C₂	#19145553	1	1	yes	characteristic
403	C₂	#19145733	1	1	yes	characteristic
404	C₂	#19145756	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	C₂²×D₁₇₂
commutator	C₂×C₄×C₄₃	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₄₃
Fitting	C₂×C₄₃×#431	C₂
socle	C₂³×C₄₃	C₂²×D₄
prime radical	C₂⁴×C₄₃	C₂×D₄
cosocle	C₂²×C₄×C₄₃	C₂⁴
hypercenter	C₂×#431	D₄₃
hypocenter	C₄₃	#21984
LCS	G ▷ C₂×C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂³ ◁ C₂²×C₄² ◁ C₂×#431

Complements

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

N	H ≅ G/N	type
3. #19135365	C₂	semidirect
5. #19134755	C₂	semidirect
6. #19134752	C₂	semidirect
7. #19134723	C₂	semidirect
8. #19134723	C₂	semidirect
31. C₄₃×#431	C₄	semidirect
215. #431	Dic₄₃	semidirect
238. C₄₃	#21984	semidirect

Maximal subgroups

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

subgroup	index
#19137002	2
#19135365	2
#19134796	2
#19134755	2
#19134752	2
#19134723	2
C₂×C₄₃×#431	2
#21984	43