Subgroups — #25113209

Order 11008.

1010 conjugacy classes of subgroups.

The subgroup lattice has 456 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#14583628	C₂	1	1	yes	maximal, characteristic
2	C₂×C₈×Dic₈₆	C₂	1	1	yes	maximal, characteristic
3	#19137550	C₂	1	1	yes	maximal, characteristic
4	#19135558	C₂	1	2	yes	maximal
5	#19135556	C₂	1	1	yes	maximal, characteristic
6	#19135549	C₂	1	2	yes	maximal
7	#19135547	C₂	1	1	yes	maximal, characteristic
8	#19134608	C₂	1	2	yes	maximal
9	#19134600	C₂	1	1	yes	maximal, characteristic
10	#103×Dic₄₃	C₂	1	2	yes	maximal
11	C₄×#103×C₄₃	C₂	1	1	yes	maximal, characteristic
12	#14583628	—	2	4	no	—
13	#14583628	C₄	1	8	yes	complemented
14	C₂×#13063325	—	2	1	no	—
15	C₂×#13063325	C₂²	1	1	yes	characteristic
16	C₂×#13063316	—	2	2	no	—
17	C₂×#13063316	C₂²	1	2	yes	—
18	C₂×Q₈×Dic₄₃	C₂²	1	2	yes	—
19	C₂×C₄×Dic₈₆	—	2	1	no	—
20	C₂×C₄×Dic₈₆	C₂²	1	1	yes	characteristic
21	C₈×Dic₈₆	—	2	4	no	—
22	C₂×C₄⋊(C₄₃⋊C₈)	C₂²	1	1	yes	characteristic
23	C₂×Dic₄₃⋊C₈	C₂²	1	2	yes	—
24	C₂×#13063249	C₂²	1	2	yes	—
25	C₂×C₈×Dic₄₃	C₂²	1	2	yes	—
26	#14582805	—	2	1	no	—
27	#14582786	—	2	2	no	—
28	#14582769	C₂²	1	1	yes	characteristic
29	#14582764	C₂²	1	2	yes	—
30	C₄⋊C₄×Dic₄₃	C₂²	1	2	yes	—
31	C₄×C₄⋊Dic₄₃	—	2	1	no	—
32	#14582662	C₂²	1	2	yes	—
33	#14582662	C₂²	1	2	yes	—
34	#14582661	C₂²	1	2	yes	—
35	#14582661	C₂²	1	2	yes	—
36	#14582661	C₂²	1	2	yes	—
37	C₂×C₄×Q₈×C₄₃	C₂²	1	1	yes	characteristic
38	C₂×#103×C₄₃	C₂²	1	1	yes	characteristic
39	C₂×#103×C₄₃	C₂²	1	1	yes	characteristic
40	C₂×C₄×C₈×C₄₃	C₂²	1	1	yes	characteristic
41	C₄×C₄⋊C₄×C₄₃	C₂²	1	1	yes	characteristic
42	C₄₃×#340	C₂²	1	1	yes	characteristic
43	C₄₃×#340	C₂²	1	1	yes	characteristic
44	C₂²×Dic₈₆	—	2	1	no	—
45	C₂²×Dic₈₆	D₄	1	1	yes	characteristic
46	C₂²×C₄₃⋊C₈	C₂³	1	2	yes	—
47	#13063325	—	2	8	no	—
48	#13063325	—	2	2	no	—
49	#13063325	C₂×C₄	1	4	yes	—
50	#13063316	—	2	16	no	—
51	#13063316	—	2	4	no	—
52	#13063316	C₂×C₄	1	8	yes	—
53	Q₈×Dic₄₃	—	2	4	no	—
54	Q₈×Dic₄₃	C₂×C₄	1	8	yes	—
55	C₄×Dic₈₆	—	2	8	no	—
56	C₄×Dic₈₆	C₂×C₄	1	4	yes	—
57	C₄×Dic₈₆	D₄	1	4	yes	—
58	C₂×C₄⋊Dic₄₃	—	2	1	no	—
59	C₂×C₄⋊Dic₄₃	—	2	2	no	—
60	C₂×C₄⋊Dic₄₃	—	2	2	no	—
61	C₂×C₄⋊Dic₄₃	—	2	1	no	—
62	C₂×C₄⋊Dic₄₃	—	2	1	no	—
63	C₂×C₄⋊Dic₄₃	D₄	1	1	yes	characteristic
64	C₂×C₄⋊Dic₄₃	C₂³	1	2	yes	—
65	C₂×C₄⋊Dic₄₃	C₂³	1	2	yes	—
66	C₂×Dic₄₃⋊C₄	—	2	2	no	—
67	C₂×Dic₄₃⋊C₄	D₄	1	2	yes	—
68	C₂×C₄×Dic₄₃	—	2	2	no	—
69	C₂×C₄×Dic₄₃	—	2	2	no	—
70	C₂×C₄×Dic₄₃	C₂³	1	2	yes	—
71	C₄⋊(C₄₃⋊C₈)	—	2	2	no	—
72	Dic₄₃⋊C₈	—	2	4	no	—
73	#13063249	—	2	4	no	—
74	C₈×Dic₄₃	—	2	4	no	—
75	C₄₃⋊#95	—	2	2	no	—
76	C₄₃⋊#95	—	2	2	no	—
77	C₄₃⋊#95	—	2	2	no	—
78	C₂²×Q₈×C₄₃	C₂³	1	1	yes	characteristic
79	C₂²×C₈×C₄₃	C₂³	1	1	yes	characteristic
80	C₂²×C₈×C₄₃	C₂³	1	1	yes	characteristic
81	C₄×Q₈×C₄₃	—	2	2	no	—
82	C₄×Q₈×C₄₃	C₂×C₄	1	4	yes	—
83	C₂×C₄⋊C₄×C₄₃	—	2	1	no	—
84	C₂×C₄⋊C₄×C₄₃	C₂³	1	1	yes	characteristic
85	C₂×C₄⋊C₄×C₄₃	C₂³	1	1	yes	characteristic
86	C₂×C₄⋊C₄×C₄₃	C₂³	1	1	yes	characteristic
87	C₂×C₄²×C₄₃	—	2	1	no	—
88	C₂×C₄²×C₄₃	—	2	1	no	—
89	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
90	#103×C₄₃	—	2	2	no	—
91	#103×C₄₃	Q₈	1	4	yes	complemented
92	C₄×C₈×C₄₃	—	2	2	no	—
93	#95×C₄₃	—	2	1	no	—
94	C₂×Q₈×C₄₃	—	2	1	no	—
95	C₂×Q₈×C₄₃	—	2	1	no	—
96	C₂×Q₈×C₄₃	—	2	1	no	—
97	C₂×Q₈×C₄₃	C₂²×C₄	1	2	yes	—
98	C₂×Q₈×C₄₃	C₂×Q₈	1	2	yes	—
99	C₂×Q₈×C₄₃	#41	1	2	yes	—
100	C₂²×C₄×C₄₃	—	2	1	no	—
101	C₂²×C₄×C₄₃	—	2	1	no	—
102	C₂²×C₄×C₄₃	—	2	1	no	—
103	C₂²×C₄×C₄₃	—	2	1	no	—
104	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
105	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
106	C₂²×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
107	C₂²×Dic₄₃	—	2	2	no	—
108	C₂²×Dic₄₃	—	2	2	no	—
109	C₂²×Dic₄₃	C₂×D₄	1	2	yes	—
110	C₂²×Dic₄₃	C₂×D₄	1	2	yes	—
111	C₂×Dic₈₆	—	2	2	no	—
112	C₂×Dic₈₆	—	2	2	no	—
113	C₂×Dic₈₆	—	2	4	no	—
114	C₂×Dic₈₆	—	4	2	no	—
115	C₂×Dic₈₆	—	4	2	no	—
116	C₂×Dic₈₆	C₂²⋊C₄	1	4	yes	—
117	C₂×C₈×C₄₃	—	2	1	no	—
118	C₂×C₈×C₄₃	—	2	1	no	—
119	C₂×C₈×C₄₃	—	2	1	no	—
120	C₂×C₈×C₄₃	—	2	1	no	—
121	C₂×C₈×C₄₃	—	2	1	no	—
122	C₂×C₈×C₄₃	C₂×Q₈	1	2	yes	—
123	C₄⋊C₄×C₄₃	—	2	4	no	—
124	C₄⋊C₄×C₄₃	—	2	1	no	—
125	C₄⋊C₄×C₄₃	—	2	1	no	—
126	C₄⋊C₄×C₄₃	—	2	1	no	—
127	C₄⋊C₄×C₄₃	—	2	1	no	—
128	C₄⋊C₄×C₄₃	C₂²×C₄	1	2	yes	—
129	C₄⋊C₄×C₄₃	C₂×Q₈	1	2	yes	—
130	C₄²×C₄₃	—	2	4	no	—
131	C₄²×C₄₃	—	4	2	no	—
132	C₄²×C₄₃	C₂²×C₄	1	2	yes	—
133	C₄²×C₄₃	C₂×D₄	1	2	yes	—
134	C₄⋊Dic₄₃	—	2	4	no	—
135	C₄⋊Dic₄₃	—	2	2	no	—
136	C₄⋊Dic₄₃	—	2	8	no	—
137	C₄⋊Dic₄₃	—	2	8	no	—
138	C₄⋊Dic₄₃	—	2	2	no	—
139	C₄⋊Dic₄₃	—	2	2	no	—
140	C₄⋊Dic₄₃	—	4	2	no	—
141	C₄⋊Dic₄₃	—	8	1	no	—
142	C₄⋊Dic₄₃	C₂²⋊C₄	1	4	yes	—
143	C₄⋊Dic₄₃	C₂²×C₄	1	4	yes	—
144	Dic₄₃⋊C₄	—	2	8	no	—
145	Dic₄₃⋊C₄	C₂²⋊C₄	1	8	yes	—
146	C₄×Dic₄₃	—	2	8	no	—
147	C₄×Dic₄₃	—	8	2	no	—
148	C₄×Dic₄₃	C₂²×C₄	1	4	yes	—
149	C₄×Dic₄₃	C₂×D₄	1	4	yes	—
150	C₂×C₄₃⋊C₈	—	2	2	no	—
151	C₂×C₄₃⋊C₈	—	2	2	no	—
152	C₂×C₄₃⋊C₈	—	2	2	no	—
153	C₂³×C₄₃	C₂²×D₄	1	1	yes	characteristic
154	Q₈×C₄₃	—	2	2	no	—
155	Q₈×C₄₃	—	2	2	no	—
156	Q₈×C₄₃	—	2	2	no	—
157	Q₈×C₄₃	C₄×Q₈	1	4	yes	—
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	—	2	1	no	—
162	C₂×C₄×C₄₃	—	2	1	no	—
163	C₂×C₄×C₄₃	—	2	2	no	—
164	C₂×C₄×C₄₃	—	2	2	no	—
165	C₂×C₄×C₄₃	—	4	1	no	—
166	C₂×C₄×C₄₃	—	4	1	no	—
167	C₂×C₄×C₄₃	—	4	1	no	—
168	C₂×C₄×C₄₃	—	4	1	no	—
169	C₂×C₄×C₄₃	—	4	1	no	—
170	C₂×C₄×C₄₃	—	4	1	no	—
171	C₂×C₄×C₄₃	—	4	1	no	—
172	C₂×C₄×C₄₃	C₂×C₂²⋊C₄	1	2	yes	—
173	C₂×C₄×C₄₃	C₂×C₂²⋊C₄	1	2	yes	—
174	C₂×C₄×C₄₃	#135	1	2	yes	—
175	C₂×C₄×C₄₃	#135	1	2	yes	—
176	C₂×C₄×C₄₃	C₂³×C₄	1	1	yes	characteristic
177	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
178	C₂×C₄×C₄₃	C₂²×Q₈	1	1	yes	characteristic
179	C₂×C₄×C₄₃	C₂×#41	1	1	yes	characteristic
180	C₂×C₄×C₄₃	2₋¹⁺⁴	1	1	yes	characteristic
181	C₂×C₄×C₄₃	2₋¹⁺⁴	1	1	yes	characteristic
182	C₂×Dic₄₃	—	2	2	no	—
183	C₂×Dic₄₃	—	2	2	no	—
184	C₂×Dic₄₃	—	2	2	no	—
185	C₂×Dic₄₃	—	2	2	no	—
186	C₂×Dic₄₃	—	2	4	no	—
187	C₂×Dic₄₃	—	4	2	no	—
188	C₂×Dic₄₃	—	4	2	no	—
189	C₂×Dic₄₃	—	4	2	no	—
190	C₂×Dic₄₃	—	4	2	no	—
191	C₂×Dic₄₃	—	4	2	no	—
192	C₂×Dic₄₃	C₂×C₂²⋊C₄	1	4	yes	—
193	C₂×Dic₄₃	C₂×C₂²⋊C₄	1	4	yes	—
194	Dic₈₆	—	2	8	no	—
195	Dic₈₆	—	4	8	no	—
196	C₈×C₄₃	—	2	2	no	—
197	C₈×C₄₃	—	4	1	no	—
198	C₄₃⋊C₈	—	4	2	no	—
199	#22521	—	43	1	no	maximal, Sylow
200	C₂²×C₄₃	C₂²×C₂²⋊C₄	1	1	yes	characteristic
201	C₂²×C₄₃	#548	1	1	yes	characteristic
202	C₂²×C₄₃	D₄×Q₈	1	1	yes	characteristic
203	C₂²×C₄₃	C₂×#135	1	1	yes	characteristic
204	C₂²×C₄₃	C₂×#135	1	1	yes	characteristic
205	C₂²×C₄₃	#577	1	1	yes	characteristic
206	C₂²×C₄₃	#578	1	1	yes	characteristic
207	C₄×C₄₃	—	2	4	no	—
208	C₄×C₄₃	—	2	2	no	—
209	C₄×C₄₃	—	4	2	no	—
210	C₄×C₄₃	—	4	2	no	—
211	C₄×C₄₃	—	8	1	no	—
212	C₄×C₄₃	#416	1	4	yes	—
213	C₄×C₄₃	C₂×C₄×Q₈	1	1	yes	characteristic
214	C₄×C₄₃	#519	1	1	yes	characteristic
215	C₄×C₄₃	#548	1	1	yes	characteristic
216	C₄×C₄₃	D₄×Q₈	1	1	yes	characteristic
217	Dic₄₃	—	2	4	no	—
218	Dic₄₃	—	2	4	no	—
219	Dic₄₃	—	4	4	no	—
220	Dic₄₃	—	8	2	no	—
221	C₂×#557	—	43	1	no	—
222	C₂×C₈×Q₈	—	43	1	no	—
223	#2355	—	43	1	no	—
224	#1991	—	43	2	no	—
225	#1990	—	43	1	no	—
226	#1989	—	43	2	no	—
227	#1988	—	43	1	no	—
228	#1805	—	43	2	no	—
229	#1803	—	43	1	no	—
230	C₄×#103	—	43	2	no	—
231	C₄×#103	D₄₃	1	1	yes	characteristic
232	C₂×C₄₃	Q₈×C₂²⋊C₄	1	1	yes	characteristic
233	C₂×C₄₃	C₂×#416	1	1	yes	characteristic
234	C₂×C₄₃	#2898	1	1	yes	characteristic
235	C₂×C₄₃	#3364	1	1	yes	characteristic
236	C₂×C₄₃	#3365	1	1	yes	characteristic
237	C₂×C₄₃	#3381	1	1	yes	characteristic
238	C₂×C₄₃	#3383	1	1	yes	characteristic
239	#557	—	43	8	no	—
240	#557	—	86	4	no	—
241	C₂×C₄⋊Q₈	—	43	1	no	—
242	C₂×C₄⋊Q₈	—	86	1	no	—
243	C₂×#125	—	43	2	no	—
244	C₂×#125	—	86	2	no	—
245	C₂×C₄×Q₈	—	43	1	no	—
246	C₂×C₄×Q₈	—	43	2	no	—
247	C₂×C₄×Q₈	—	86	1	no	—
248	C₂×C₄×Q₈	C₂×D₄₃	1	1	yes	characteristic
249	C₈×Q₈	—	86	4	no	—
250	C₂×C₄⋊C₈	—	43	2	no	—
251	C₂×C₄⋊C₈	—	43	1	no	—
252	C₂×#103	—	43	2	no	—
253	C₂×#103	C₂×D₄₃	1	1	yes	characteristic
254	C₂×#103	C₂×D₄₃	1	1	yes	characteristic
255	C₂×C₄×C₈	—	43	2	no	—
256	C₂×C₄×C₈	C₂×D₄₃	1	1	yes	characteristic
257	#391	—	86	1	no	—
258	#387	—	86	2	no	—
259	#384	—	43	1	no	—
260	#382	—	43	2	no	—
261	C₄×C₄⋊C₄	—	43	2	no	—
262	C₄×C₄⋊C₄	—	86	1	no	—
263	C₄×C₄⋊C₄	C₂×D₄₃	1	1	yes	characteristic
264	#340	—	43	2	no	—
265	#340	—	43	2	no	—
266	#340	—	43	2	no	—
267	#340	—	43	2	no	—
268	#340	—	43	2	no	—
269	#340	C₂×D₄₃	1	1	yes	characteristic
270	#340	C₂×D₄₃	1	1	yes	characteristic
271	C₄₃	#22521	1	1	yes	characteristic, complemented, Sylow
272	C₂²×Q₈	—	43	1	no	—
273	C₂²×Q₈	—	86	1	no	—
274	C₂²×Q₈	C₂²×D₄₃	1	1	yes	characteristic
275	C₂²×C₈	—	43	2	no	—
276	C₂²×C₈	C₂²×D₄₃	1	1	yes	characteristic
277	C₂²×C₈	C₂²×D₄₃	1	1	yes	characteristic
278	C₄⋊Q₈	—	43	4	no	—
279	C₄⋊Q₈	—	86	8	no	—
280	C₄⋊Q₈	—	86	2	no	—
281	#125	—	43	8	no	—
282	#125	—	86	4	no	—
283	#125	—	86	16	no	—
284	C₄×Q₈	—	2	2	no	—
285	C₄×Q₈	—	43	4	no	—
286	C₄×Q₈	—	43	4	no	—
287	C₄×Q₈	—	43	8	no	—
288	C₄×Q₈	—	86	8	no	—
289	C₄×Q₈	—	86	4	no	—
290	C₄×Q₈	C₄×D₄₃	1	4	yes	—
291	C₂×C₄⋊C₄	—	2	1	no	—
292	C₂×C₄⋊C₄	—	43	1	no	—
293	C₂×C₄⋊C₄	—	43	2	no	—
294	C₂×C₄⋊C₄	—	43	2	no	—
295	C₂×C₄⋊C₄	—	43	2	no	—
296	C₂×C₄⋊C₄	—	86	2	no	—
297	C₂×C₄⋊C₄	—	86	2	no	—
298	C₂×C₄⋊C₄	—	86	2	no	—
299	C₂×C₄⋊C₄	—	86	1	no	—
300	C₂×C₄⋊C₄	—	86	1	no	—
301	C₂×C₄⋊C₄	—	86	1	no	—
302	C₂×C₄⋊C₄	C₂²×D₄₃	1	1	yes	characteristic
303	C₂×C₄⋊C₄	C₂²×D₄₃	1	1	yes	characteristic
304	C₂×C₄⋊C₄	C₂²×D₄₃	1	1	yes	characteristic
305	C₂×C₄²	—	2	1	no	—
306	C₂×C₄²	—	2	1	no	—
307	C₂×C₄²	—	43	2	no	—
308	C₂×C₄²	—	86	2	no	—
309	C₂×C₄²	—	86	2	no	—
310	C₂×C₄²	C₂²×D₄₃	1	1	yes	characteristic
311	C₄⋊C₈	—	86	4	no	—
312	C₄⋊C₈	—	86	2	no	—
313	#103	—	2	2	no	—
314	#103	—	86	4	no	—
315	#103	Dic₈₆	1	4	yes	complemented
316	C₄×C₈	—	2	2	no	—
317	C₄×C₈	—	86	4	no	—
318	#95	—	2	1	no	—
319	#95	—	86	2	no	—
320	#95	—	86	2	no	—
321	#95	—	86	2	no	—
322	C₂×Q₈	—	2	1	no	—
323	C₂×Q₈	—	2	1	no	—
324	C₂×Q₈	—	2	1	no	—
325	C₂×Q₈	—	43	4	no	—
326	C₂×Q₈	—	86	4	no	—
327	C₂×Q₈	—	86	2	no	—
328	C₂×Q₈	—	86	2	no	—
329	C₂×Q₈	—	172	2	no	—
330	C₂×Q₈	—	172	2	no	—
331	C₂×Q₈	C₂×Dic₈₆	1	2	yes	—
332	C₂×Q₈	C₂×C₄×D₄₃	1	2	yes	—
333	C₂×Q₈	#10621898	1	2	yes	—
334	C₂²×C₄	—	2	1	no	—
335	C₂²×C₄	—	2	1	no	—
336	C₂²×C₄	—	2	1	no	—
337	C₂²×C₄	—	2	1	no	—
338	C₂²×C₄	—	43	2	no	—
339	C₂²×C₄	—	43	2	no	—
340	C₂²×C₄	—	86	2	no	—
341	C₂²×C₄	—	86	2	no	—
342	C₂²×C₄	D₄×D₄₃	1	1	yes	characteristic
343	C₂²×C₄	D₄×D₄₃	1	1	yes	characteristic
344	C₂²×C₄	C₂³×D₄₃	1	1	yes	characteristic
345	C₂×C₈	—	2	1	no	—
346	C₂×C₈	—	2	1	no	—
347	C₂×C₈	—	2	1	no	—
348	C₂×C₈	—	2	1	no	—
349	C₂×C₈	—	2	1	no	—
350	C₂×C₈	—	86	2	no	—
351	C₂×C₈	—	86	2	no	—
352	C₂×C₈	—	86	2	no	—
353	C₂×C₈	C₂×Dic₈₆	1	2	yes	—
354	C₄⋊C₄	—	2	4	no	—
355	C₄⋊C₄	—	2	1	no	—
356	C₄⋊C₄	—	2	1	no	—
357	C₄⋊C₄	—	2	1	no	—
358	C₄⋊C₄	—	2	1	no	—
359	C₄⋊C₄	—	43	4	no	—
360	C₄⋊C₄	—	43	8	no	—
361	C₄⋊C₄	—	43	4	no	—
362	C₄⋊C₄	—	86	8	no	—
363	C₄⋊C₄	—	86	8	no	—
364	C₄⋊C₄	—	86	8	no	—
365	C₄⋊C₄	—	86	4	no	—
366	C₄⋊C₄	—	86	2	no	—
367	C₄⋊C₄	—	86	2	no	—
368	C₄⋊C₄	—	86	2	no	—
369	C₄⋊C₄	—	344	1	no	—
370	C₄⋊C₄	—	172	2	no	—
371	C₄⋊C₄	C₂×Dic₈₆	1	2	yes	—
372	C₄⋊C₄	C₂×C₄×D₄₃	1	2	yes	—
373	C₄²	—	2	4	no	—
374	C₄²	—	4	2	no	—
375	C₄²	—	43	4	no	—
376	C₄²	—	43	4	no	—
377	C₄²	—	86	8	no	—
378	C₄²	—	344	2	no	—
379	C₄²	C₂×C₄×D₄₃	1	2	yes	—
380	C₄²	D₄×D₄₃	1	2	yes	—
381	C₂³	C₂×D₄×D₄₃	1	1	yes	characteristic
382	Q₈	—	2	2	no	—
383	Q₈	—	2	2	no	—
384	Q₈	—	2	2	no	—
385	Q₈	—	86	8	no	—
386	Q₈	—	172	8	no	—
387	Q₈	C₄×Dic₈₆	1	4	yes	—
388	C₂×C₄	—	2	2	no	—
389	C₂×C₄	—	2	2	no	—
390	C₂×C₄	—	2	2	no	—
391	C₂×C₄	—	2	1	no	—
392	C₂×C₄	—	2	1	no	—
393	C₂×C₄	—	2	2	no	—
394	C₂×C₄	—	2	2	no	—
395	C₂×C₄	—	4	1	no	—
396	C₂×C₄	—	4	1	no	—
397	C₂×C₄	—	4	1	no	—
398	C₂×C₄	—	4	1	no	—
399	C₂×C₄	—	4	1	no	—
400	C₂×C₄	—	4	1	no	—
401	C₂×C₄	—	4	1	no	—
402	C₂×C₄	—	43	4	no	—
403	C₂×C₄	—	43	4	no	—
404	C₂×C₄	—	86	2	no	—
405	C₂×C₄	—	86	2	no	—
406	C₂×C₄	—	86	2	no	—
407	C₂×C₄	—	86	2	no	—
408	C₂×C₄	—	86	4	no	—
409	C₂×C₄	—	172	2	no	—
410	C₂×C₄	—	172	2	no	—
411	C₂×C₄	—	172	2	no	—
412	C₂×C₄	—	172	2	no	—
413	C₂×C₄	—	172	2	no	—
414	C₂×C₄	C₂²⋊C₄×D₄₃	1	2	yes	—
415	C₂×C₄	C₂²⋊C₄×D₄₃	1	2	yes	—
416	C₂×C₄	#13063346	1	2	yes	—
417	C₂×C₄	#13063348	1	2	yes	—
418	C₂×C₄	C₂²×C₄×D₄₃	1	1	yes	characteristic
419	C₂×C₄	C₂×D₄×D₄₃	1	1	yes	characteristic
420	C₂×C₄	C₂²×Dic₈₆	1	1	yes	characteristic
421	C₂×C₄	C₂×#10621898	1	1	yes	characteristic
422	C₂×C₄	#13063372	1	1	yes	characteristic
423	C₂×C₄	#13063372	1	1	yes	characteristic
424	C₈	—	2	2	no	—
425	C₈	—	4	1	no	—
426	C₈	—	172	2	no	—
427	C₂²	C₂×C₂²⋊C₄×D₄₃	1	1	yes	characteristic
428	C₂²	#14583558	1	1	yes	characteristic
429	C₂²	D₄×Dic₈₆	1	1	yes	characteristic
430	C₂²	C₂×#13063346	1	1	yes	characteristic
431	C₂²	C₂×#13063348	1	1	yes	characteristic
432	C₂²	#14583706	1	1	yes	characteristic
433	C₂²	#14583713	1	1	yes	characteristic
434	C₄	—	2	4	no	—
435	C₄	—	2	2	no	—
436	C₄	—	4	2	no	—
437	C₄	—	4	2	no	—
438	C₄	—	8	1	no	—
439	C₄	—	86	4	no	—
440	C₄	—	86	4	no	—
441	C₄	—	344	2	no	—
442	C₄	—	172	4	no	—
443	C₄	#14582894	1	4	yes	—
444	C₄	C₂×C₄×Dic₈₆	1	1	yes	characteristic
445	C₄	#14583376	1	1	yes	characteristic
446	C₄	#14583558	1	1	yes	characteristic
447	C₄	D₄×Dic₈₆	1	1	yes	characteristic
448	C₂	C₂²⋊C₄×Dic₈₆	1	1	yes	characteristic
449	C₂	C₂×#14582894	1	1	yes	characteristic
450	C₂	#19143124	1	1	yes	characteristic
451	C₂	#19147278	1	1	yes	characteristic
452	C₂	#19147289	1	1	yes	characteristic
453	C₂	#19147468	1	1	yes	characteristic
454	C₂	#19147484	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×#103×C₄₃	C₂
socle, prime radical	C₂³×C₄₃	C₂²×D₄
cosocle	C₂²×C₄×C₄₃	C₂⁴
hypercenter	C₄×#103	D₄₃
hypocenter	C₄₃	#22521
LCS	G ▷ C₂×C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ C₄×#103

Complements

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

N	H ≅ G/N	type
13. #14583628	C₄	semidirect
91. #103×C₄₃	Q₈	semidirect
271. C₄₃	#22521	semidirect
315. #103	Dic₈₆	semidirect

Maximal subgroups

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

subgroup	index
C₂×#14583628	2
C₂×C₈×Dic₈₆	2
#19137550	2
#19135558	2
#19135556	2
#19135549	2
#19135547	2
#19134608	2
#19134600	2
#103×Dic₄₃	2
C₄×#103×C₄₃	2
#22521	43