Subgroups — #25115444

Order 11008.

750 conjugacy classes of subgroups.

The subgroup lattice has 402 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₈×Dic₈₆	C₂	1	1	yes	maximal, characteristic
2	#19137553	C₂	1	2	yes	maximal
3	#19135363	C₂	1	2	yes	maximal
4	#19135362	C₂	1	2	yes	maximal
5	#19135357	C₂	1	2	yes	maximal
6	#19134759	C₂	1	1	yes	maximal, characteristic
7	#19134758	C₂	1	1	yes	maximal, characteristic
8	#19134753	C₂	1	1	yes	maximal, characteristic
9	#107×Dic₄₃	C₂	1	1	yes	maximal, characteristic
10	#107×Dic₄₃	C₂	1	1	yes	maximal, characteristic
11	C₄×#107×C₄₃	C₂	1	1	yes	maximal, characteristic
12	C₂×C₄×Dic₈₆	C₂²	1	1	yes	characteristic
13	C₈×Dic₈₆	C₄	1	8	yes	complemented
14	C₂×#13063259	C₂²	1	1	yes	characteristic
15	C₂×#13063259	C₂²	1	1	yes	characteristic
16	C₂×#13063258	C₂²	1	2	yes	—
17	C₂×#13063257	C₂²	1	2	yes	—
18	C₂×#13063256	C₂²	1	2	yes	—
19	C₂×C₄⋊(C₄₃⋊C₈)	C₂²	1	1	yes	characteristic
20	C₂×Dic₄₃⋊C₈	C₂²	1	1	yes	characteristic
21	C₂×Dic₄₃⋊C₈	C₂²	1	1	yes	characteristic
22	C₂×C₈×Dic₄₃	C₂²	1	1	yes	characteristic
23	C₂×C₈×Dic₄₃	C₂²	1	1	yes	characteristic
24	#14582803	—	2	2	no	—
25	#14582783	—	2	2	no	—
26	#14582782	—	2	2	no	—
27	#14582768	C₂²	1	2	yes	—
28	#14582765	C₂²	1	2	yes	—
29	#14582764	C₂²	1	2	yes	—
30	C₄⋊C₄×Dic₄₃	C₂²	1	2	yes	—
31	C₄⋊C₄×Dic₄₃	C₂²	1	2	yes	—
32	C₄×Dic₄₃⋊C₄	—	2	2	no	—
33	#14582661	C₂²	1	2	yes	—
34	#14582661	C₂²	1	2	yes	—
35	C₂×#107×C₄₃	C₂²	1	1	yes	characteristic
36	C₂×#107×C₄₃	C₂²	1	1	yes	characteristic
37	C₂×C₄×C₈×C₄₃	C₂²	1	1	yes	characteristic
38	C₄×C₄⋊C₄×C₄₃	C₂²	1	2	yes	—
39	C₄₃×#340	C₂²	1	2	yes	—
40	C₂²×Dic₈₆	D₄	1	1	yes	characteristic
41	C₂²×C₄₃⋊C₈	C₂³	1	1	yes	characteristic
42	C₂²×C₄₃⋊C₈	C₂³	1	1	yes	characteristic
43	C₄×Dic₈₆	C₂×C₄	1	4	yes	—
44	C₄×Dic₈₆	Q₈	1	4	yes	—
45	C₂×C₄⋊Dic₄₃	D₄	1	1	yes	characteristic
46	C₂×C₄⋊Dic₄₃	C₂³	1	2	yes	—
47	C₂×C₄⋊Dic₄₃	C₂³	1	2	yes	—
48	C₂×Dic₄₃⋊C₄	—	2	2	no	—
49	C₂×Dic₄₃⋊C₄	—	2	2	no	—
50	C₂×Dic₄₃⋊C₄	D₄	1	1	yes	characteristic
51	C₂×Dic₄₃⋊C₄	D₄	1	1	yes	characteristic
52	C₂×C₄×Dic₄₃	—	2	2	no	—
53	C₂×C₄×Dic₄₃	—	2	2	no	—
54	C₂×C₄×Dic₄₃	C₂³	1	1	yes	characteristic
55	C₂×C₄×Dic₄₃	C₂³	1	1	yes	characteristic
56	#13063259	—	2	2	no	—
57	#13063259	—	2	2	no	—
58	#13063258	—	4	2	no	—
59	#13063257	—	4	2	no	—
60	#13063256	—	4	2	no	—
61	C₄⋊(C₄₃⋊C₈)	C₂×C₄	1	4	yes	—
62	Dic₄₃⋊C₈	C₂×C₄	1	4	yes	—
63	Dic₄₃⋊C₈	C₂×C₄	1	4	yes	—
64	C₈×Dic₄₃	C₂×C₄	1	4	yes	—
65	C₈×Dic₄₃	C₂×C₄	1	4	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	C₄₃⋊#95	—	2	2	no	—
71	C₄₃⋊#95	—	2	2	no	—
72	C₂²×C₈×C₄₃	C₂³	1	1	yes	characteristic
73	C₂²×C₈×C₄₃	C₂³	1	1	yes	characteristic
74	C₂×C₄⋊C₄×C₄₃	C₂³	1	2	yes	—
75	C₂×C₄⋊C₄×C₄₃	C₂³	1	2	yes	—
76	C₂×C₄²×C₄₃	—	2	2	no	—
77	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
78	#107×C₄₃	—	2	2	no	—
79	#107×C₄₃	Q₈	1	4	yes	complemented
80	C₄×C₈×C₄₃	C₂×C₄	1	4	yes	—
81	#95×C₄₃	—	2	2	no	—
82	C₂²×C₄×C₄₃	—	2	2	no	—
83	C₂²×C₄×C₄₃	—	2	2	no	—
84	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
85	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
86	C₂²×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
87	C₂²×Dic₄₃	—	2	2	no	—
88	C₂²×Dic₄₃	—	2	2	no	—
89	C₂²×Dic₄₃	C₂×D₄	1	1	yes	characteristic
90	C₂²×Dic₄₃	C₂×D₄	1	1	yes	characteristic
91	C₂²×Dic₄₃	C₂×D₄	1	1	yes	characteristic
92	C₂²×Dic₄₃	C₂×D₄	1	1	yes	characteristic
93	C₂×Dic₈₆	—	2	2	no	—
94	C₂×Dic₈₆	—	2	2	no	—
95	C₂×Dic₈₆	C₄⋊C₄	1	4	yes	—
96	C₂×C₈×C₄₃	—	2	1	no	—
97	C₂×C₈×C₄₃	—	2	1	no	—
98	C₂×C₈×C₄₃	C₂²×C₄	1	2	yes	—
99	C₂×C₈×C₄₃	C₂²×C₄	1	2	yes	—
100	C₂×C₈×C₄₃	C₂×Q₈	1	2	yes	—
101	C₂×C₈×C₄₃	#41	1	2	yes	—
102	C₄⋊C₄×C₄₃	—	2	2	no	—
103	C₄⋊C₄×C₄₃	—	2	2	no	—
104	C₄⋊C₄×C₄₃	—	2	2	no	—
105	C₄⋊C₄×C₄₃	C₂×Q₈	1	4	yes	—
106	C₄²×C₄₃	—	8	2	no	—
107	C₄²×C₄₃	C₂²×C₄	1	2	yes	—
108	C₄²×C₄₃	C₂×Q₈	1	2	yes	—
109	C₄⋊Dic₄₃	—	2	2	no	—
110	C₄⋊Dic₄₃	—	2	2	no	—
111	C₄⋊Dic₄₃	—	2	2	no	—
112	C₄⋊Dic₄₃	—	2	2	no	—
113	C₄⋊Dic₄₃	C₄⋊C₄	1	4	yes	—
114	Dic₄₃⋊C₄	—	4	4	no	—
115	Dic₄₃⋊C₄	—	8	2	no	—
116	Dic₄₃⋊C₄	C₄⋊C₄	1	4	yes	—
117	Dic₄₃⋊C₄	C₄⋊C₄	1	4	yes	—
118	C₄×Dic₄₃	—	4	4	no	—
119	C₄×Dic₄₃	—	8	2	no	—
120	C₄×Dic₄₃	C₂²×C₄	1	2	yes	—
121	C₄×Dic₄₃	C₂²×C₄	1	2	yes	—
122	C₄×Dic₄₃	C₂×Q₈	1	2	yes	—
123	C₄×Dic₄₃	C₂×Q₈	1	2	yes	—
124	C₂×C₄₃⋊C₈	—	2	1	no	—
125	C₂×C₄₃⋊C₈	—	2	1	no	—
126	C₂×C₄₃⋊C₈	—	2	1	no	—
127	C₂×C₄₃⋊C₈	—	2	1	no	—
128	C₂×C₄₃⋊C₈	C₂²×C₄	1	2	yes	—
129	C₂×C₄₃⋊C₈	C₂²×C₄	1	2	yes	—
130	C₂³×C₄₃	C₂²×D₄	1	1	yes	characteristic
131	C₂×C₄×C₄₃	—	2	1	no	—
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	4	no	—
136	C₂×C₄×C₄₃	—	4	2	no	—
137	C₂×C₄×C₄₃	—	4	2	no	—
138	C₂×C₄×C₄₃	—	4	2	no	—
139	C₂×C₄×C₄₃	—	4	2	no	—
140	C₂×C₄×C₄₃	—	4	2	no	—
141	C₂×C₄×C₄₃	C₂×C₄⋊C₄	1	2	yes	—
142	C₂×C₄×C₄₃	C₂×C₄⋊C₄	1	2	yes	—
143	C₂×C₄×C₄₃	C₂³×C₄	1	1	yes	characteristic
144	C₂×C₄×C₄₃	C₂²×Q₈	1	1	yes	characteristic
145	C₂×C₄×C₄₃	C₂²×Q₈	1	1	yes	characteristic
146	C₂×C₄×C₄₃	C₂×#41	1	1	yes	characteristic
147	C₂×C₄×C₄₃	H(5,𝔽₂)	1	1	yes	characteristic
148	C₂×C₄×C₄₃	2₋¹⁺⁴	1	1	yes	characteristic
149	C₂×Dic₄₃	—	2	1	no	—
150	C₂×Dic₄₃	—	2	1	no	—
151	C₂×Dic₄₃	—	2	1	no	—
152	C₂×Dic₄₃	—	2	1	no	—
153	C₂×Dic₄₃	—	2	1	no	—
154	C₂×Dic₄₃	—	2	1	no	—
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	C₂×C₄⋊C₄	1	2	yes	—
162	C₂×Dic₄₃	C₂×C₄⋊C₄	1	2	yes	—
163	C₂×Dic₄₃	C₂×C₄⋊C₄	1	2	yes	—
164	C₂×Dic₄₃	C₂×C₄⋊C₄	1	2	yes	—
165	C₂×Dic₄₃	#135	1	2	yes	—
166	C₂×Dic₄₃	#135	1	2	yes	—
167	Dic₈₆	—	2	8	no	—
168	C₈×C₄₃	—	2	2	no	—
169	C₈×C₄₃	C₄×Q₈	1	4	yes	—
170	C₄₃⋊C₈	—	2	2	no	—
171	C₄₃⋊C₈	—	2	2	no	—
172	#22727	—	43	1	no	maximal, Sylow
173	C₂²×C₄₃	C₂²×C₄⋊C₄	1	1	yes	characteristic
174	C₂²×C₄₃	D₄×Q₈	1	1	yes	characteristic
175	C₂²×C₄₃	#550	1	1	yes	characteristic
176	C₂²×C₄₃	C₂×#135	1	1	yes	characteristic
177	C₂²×C₄₃	C₂×#135	1	1	yes	characteristic
178	C₂²×C₄₃	#576	1	1	yes	characteristic
179	C₂²×C₄₃	#578	1	1	yes	characteristic
180	C₄×C₄₃	—	2	2	no	—
181	C₄×C₄₃	—	2	2	no	—
182	C₄×C₄₃	—	4	4	no	—
183	C₄×C₄₃	—	8	2	no	—
184	C₄×C₄₃	C₂×C₄×Q₈	1	1	yes	characteristic
185	C₄×C₄₃	#520	1	1	yes	characteristic
186	C₄×C₄₃	#557	1	1	yes	characteristic
187	C₄×C₄₃	Q₈²	1	1	yes	characteristic
188	Dic₄₃	—	2	2	no	—
189	Dic₄₃	—	2	2	no	—
190	Dic₄₃	—	2	2	no	—
191	Dic₄₃	—	8	2	no	—
192	Dic₄₃	—	8	2	no	—
193	Dic₄₃	#427	1	4	yes	—
194	C₂×C₈×Q₈	—	43	1	no	—
195	#2355	—	43	2	no	—
196	#1949	—	43	2	no	—
197	#1949	—	43	2	no	—
198	#1948	—	43	2	no	—
199	#1846	—	43	1	no	—
200	#1846	—	43	1	no	—
201	#1845	—	43	1	no	—
202	C₄×#107	—	43	1	no	—
203	C₄×#107	—	43	1	no	—
204	C₄×#107	D₄₃	1	1	yes	characteristic
205	C₂×C₄₃	Q₈×C₄⋊C₄	1	1	yes	characteristic
206	C₂×C₄₃	C₂×#427	1	1	yes	characteristic
207	C₂×C₄₃	#2913	1	1	yes	characteristic
208	C₂×C₄₃	#3380	1	1	yes	characteristic
209	C₂×C₄₃	#3383	1	1	yes	characteristic
210	C₂×C₄₃	#3393	1	1	yes	characteristic
211	C₂×C₄₃	#3396	1	1	yes	characteristic
212	C₂×C₄×Q₈	—	43	1	no	—
213	C₈×Q₈	—	43	8	no	—
214	C₂×#107	—	43	1	no	—
215	C₂×#107	—	43	1	no	—
216	C₂×#107	—	43	2	no	—
217	C₂×#107	C₂×D₄₃	1	1	yes	characteristic
218	C₂×#107	C₂×D₄₃	1	1	yes	characteristic
219	C₂×#106	—	43	2	no	—
220	C₂×#106	—	43	2	no	—
221	C₂×C₄⋊C₈	—	43	1	no	—
222	C₂×C₄⋊C₈	—	43	1	no	—
223	C₂×C₄⋊C₈	—	43	1	no	—
224	C₂×C₄×C₈	—	43	1	no	—
225	C₂×C₄×C₈	—	43	1	no	—
226	C₂×C₄×C₈	C₂×D₄₃	1	1	yes	characteristic
227	#391	—	86	2	no	—
228	#387	—	86	2	no	—
229	#387	—	86	2	no	—
230	#384	—	43	2	no	—
231	#382	—	43	2	no	—
232	#382	—	43	2	no	—
233	C₄×C₄⋊C₄	—	43	2	no	—
234	C₄×C₄⋊C₄	—	43	2	no	—
235	C₄×C₄⋊C₄	—	86	2	no	—
236	C₄×C₄⋊C₄	C₂×D₄₃	1	2	yes	—
237	#340	—	43	2	no	—
238	#340	—	43	2	no	—
239	#340	C₂×D₄₃	1	2	yes	—
240	C₄₃	#22727	1	1	yes	characteristic, complemented, Sylow
241	C₂²×Q₈	—	43	1	no	—
242	C₂²×C₈	—	43	1	no	—
243	C₂²×C₈	—	43	1	no	—
244	C₂²×C₈	C₂²×D₄₃	1	1	yes	characteristic
245	C₂²×C₈	C₂²×D₄₃	1	1	yes	characteristic
246	C₄×Q₈	—	43	4	no	—
247	C₄×Q₈	—	43	4	no	—
248	C₂×C₄⋊C₄	—	43	1	no	—
249	C₂×C₄⋊C₄	—	43	1	no	—
250	C₂×C₄⋊C₄	—	43	1	no	—
251	C₂×C₄⋊C₄	—	43	2	no	—
252	C₂×C₄⋊C₄	—	43	2	no	—
253	C₂×C₄⋊C₄	—	86	2	no	—
254	C₂×C₄⋊C₄	—	86	2	no	—
255	C₂×C₄⋊C₄	C₂²×D₄₃	1	2	yes	—
256	C₂×C₄⋊C₄	C₂²×D₄₃	1	2	yes	—
257	C₂×C₄²	—	2	2	no	—
258	C₂×C₄²	—	43	1	no	—
259	C₂×C₄²	—	43	1	no	—
260	C₂×C₄²	—	86	2	no	—
261	C₂×C₄²	—	86	2	no	—
262	C₂×C₄²	C₂²×D₄₃	1	1	yes	characteristic
263	#107	—	2	2	no	—
264	#107	—	86	2	no	—
265	#107	—	86	2	no	—
266	#107	—	172	2	no	—
267	#107	Dic₈₆	1	4	yes	complemented
268	#106	—	172	2	no	—
269	#106	—	172	2	no	—
270	C₄⋊C₈	—	43	4	no	—
271	C₄⋊C₈	—	43	4	no	—
272	C₄⋊C₈	—	43	4	no	—
273	C₄×C₈	—	43	4	no	—
274	C₄×C₈	—	43	4	no	—
275	C₄×C₈	C₄×D₄₃	1	4	yes	—
276	#95	—	2	2	no	—
277	#95	—	86	2	no	—
278	#95	—	86	2	no	—
279	#95	—	86	2	no	—
280	#95	—	86	2	no	—
281	#95	—	86	2	no	—
282	#95	—	86	2	no	—
283	C₂×Q₈	—	43	4	no	—
284	C₂×Q₈	—	86	2	no	—
285	C₂×Q₈	—	86	2	no	—
286	C₂²×C₄	—	2	2	no	—
287	C₂²×C₄	—	2	2	no	—
288	C₂²×C₄	—	43	1	no	—
289	C₂²×C₄	—	43	1	no	—
290	C₂²×C₄	—	43	1	no	—
291	C₂²×C₄	—	43	1	no	—
292	C₂²×C₄	—	86	2	no	—
293	C₂²×C₄	—	86	2	no	—
294	C₂²×C₄	D₄×D₄₃	1	1	yes	characteristic
295	C₂²×C₄	D₄×D₄₃	1	1	yes	characteristic
296	C₂²×C₄	C₂³×D₄₃	1	1	yes	characteristic
297	C₂×C₈	—	2	1	no	—
298	C₂×C₈	—	2	1	no	—
299	C₂×C₈	—	43	2	no	—
300	C₂×C₈	—	43	2	no	—
301	C₂×C₈	—	86	1	no	—
302	C₂×C₈	—	86	1	no	—
303	C₂×C₈	—	86	1	no	—
304	C₂×C₈	—	86	1	no	—
305	C₂×C₈	C₂×Dic₈₆	1	2	yes	—
306	C₂×C₈	C₂×C₄×D₄₃	1	2	yes	—
307	C₂×C₈	C₂×C₄×D₄₃	1	2	yes	—
308	C₂×C₈	#10621898	1	2	yes	—
309	C₄⋊C₄	—	2	2	no	—
310	C₄⋊C₄	—	2	2	no	—
311	C₄⋊C₄	—	2	2	no	—
312	C₄⋊C₄	—	43	4	no	—
313	C₄⋊C₄	—	43	4	no	—
314	C₄⋊C₄	—	43	4	no	—
315	C₄⋊C₄	—	86	2	no	—
316	C₄⋊C₄	—	86	2	no	—
317	C₄⋊C₄	—	86	2	no	—
318	C₄⋊C₄	—	86	2	no	—
319	C₄⋊C₄	—	344	2	no	—
320	C₄⋊C₄	—	172	4	no	—
321	C₄⋊C₄	C₂×Dic₈₆	1	4	yes	—
322	C₄²	—	8	2	no	—
323	C₄²	—	43	2	no	—
324	C₄²	—	43	2	no	—
325	C₄²	—	43	2	no	—
326	C₄²	—	43	2	no	—
327	C₄²	—	344	2	no	—
328	C₄²	—	172	4	no	—
329	C₄²	C₂×C₄×D₄₃	1	2	yes	—
330	C₄²	Q₈×D₄₃	1	2	yes	—
331	C₂³	C₂×D₄×D₄₃	1	1	yes	characteristic
332	Q₈	—	86	8	no	—
333	C₂×C₄	—	2	1	no	—
334	C₂×C₄	—	2	1	no	—
335	C₂×C₄	—	2	1	no	—
336	C₂×C₄	—	2	1	no	—
337	C₂×C₄	—	2	4	no	—
338	C₂×C₄	—	4	2	no	—
339	C₂×C₄	—	4	2	no	—
340	C₂×C₄	—	4	2	no	—
341	C₂×C₄	—	4	2	no	—
342	C₂×C₄	—	4	2	no	—
343	C₂×C₄	—	43	2	no	—
344	C₂×C₄	—	43	2	no	—
345	C₂×C₄	—	43	2	no	—
346	C₂×C₄	—	43	2	no	—
347	C₂×C₄	—	43	2	no	—
348	C₂×C₄	—	43	2	no	—
349	C₂×C₄	—	86	1	no	—
350	C₂×C₄	—	86	1	no	—
351	C₂×C₄	—	86	1	no	—
352	C₂×C₄	—	86	1	no	—
353	C₂×C₄	—	86	1	no	—
354	C₂×C₄	—	86	1	no	—
355	C₂×C₄	—	172	2	no	—
356	C₂×C₄	—	172	2	no	—
357	C₂×C₄	—	172	2	no	—
358	C₂×C₄	—	172	2	no	—
359	C₂×C₄	—	172	2	no	—
360	C₂×C₄	—	172	2	no	—
361	C₂×C₄	C₄⋊C₄×D₄₃	1	2	yes	—
362	C₂×C₄	C₄⋊C₄×D₄₃	1	2	yes	—
363	C₂×C₄	C₂²×C₄×D₄₃	1	1	yes	characteristic
364	C₂×C₄	C₂×Q₈×D₄₃	1	1	yes	characteristic
365	C₂×C₄	C₂²×Dic₈₆	1	1	yes	characteristic
366	C₂×C₄	C₂×#10621898	1	1	yes	characteristic
367	C₂×C₄	#13063371	1	1	yes	characteristic
368	C₂×C₄	#13063372	1	1	yes	characteristic
369	C₈	—	2	2	no	—
370	C₈	—	86	2	no	—
371	C₈	—	86	2	no	—
372	C₈	C₄×Dic₈₆	1	4	yes	—
373	C₂²	C₂×C₄⋊C₄×D₄₃	1	1	yes	characteristic
374	C₂²	D₄×Dic₈₆	1	1	yes	characteristic
375	C₂²	#14583570	1	1	yes	characteristic
376	C₂²	#135×D₄₃	1	1	yes	characteristic
377	C₂²	#135×D₄₃	1	1	yes	characteristic
378	C₂²	#14583700	1	1	yes	characteristic
379	C₂²	#14583712	1	1	yes	characteristic
380	C₄	—	2	2	no	—
381	C₄	—	2	2	no	—
382	C₄	—	4	4	no	—
383	C₄	—	8	2	no	—
384	C₄	—	43	4	no	—
385	C₄	—	86	2	no	—
386	C₄	—	86	2	no	—
387	C₄	—	86	2	no	—
388	C₄	—	344	2	no	—
389	C₄	—	344	2	no	—
390	C₄	C₂×C₄×Dic₈₆	1	1	yes	characteristic
391	C₄	#14583379	1	1	yes	characteristic
392	C₄	#14583627	1	1	yes	characteristic
393	C₄	Q₈×Dic₈₆	1	1	yes	characteristic
394	C₂	C₄⋊C₄×Dic₈₆	1	1	yes	characteristic
395	C₂	#427×D₄₃	1	1	yes	characteristic
396	C₂	#19143191	1	1	yes	characteristic
397	C₂	#19147462	1	1	yes	characteristic
398	C₂	#19147486	1	1	yes	characteristic
399	C₂	#19147583	1	1	yes	characteristic
400	C₂	#19147607	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	C₂×D₄×D₄₃
commutator	C₂×C₄×C₄₃	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₄₃
Fitting	C₄×#107×C₄₃	C₂
socle, prime radical	C₂³×C₄₃	C₂²×D₄
cosocle	C₂²×C₄×C₄₃	C₂⁴
hypercenter	C₄×#107	D₄₃
hypocenter	C₄₃	#22727
LCS	G ▷ C₂×C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ C₄×#107

Complements

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

N	H ≅ G/N	type
13. C₈×Dic₈₆	C₄	semidirect
79. #107×C₄₃	Q₈	semidirect
240. C₄₃	#22727	semidirect
267. #107	Dic₈₆	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₈×Dic₈₆	2
#19137553	2
#19135363	2
#19135362	2
#19135357	2
#19134759	2
#19134758	2
#19134753	2
#107×Dic₄₃	2
C₄×#107×C₄₃	2
#22727	43