Subgroups — #25100552

Order 11008.

1466 conjugacy classes of subgroups.

The subgroup lattice has 480 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#13063261	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#14582916	C₂	1	2	yes	maximal, complemented
3	#19143040	C₂	1	2	yes	maximal, complemented
4	C₂×#14582854	C₂	1	1	yes	maximal, characteristic, complemented
5	#19135489	C₂	1	4	yes	maximal, complemented
6	#19135484	C₂	1	4	yes	maximal, complemented
7	C₂²×#135×C₄₃	C₂	1	1	yes	maximal, characteristic
8	C₂²×#10621877	C₂²	1	2	yes	—
9	C₂²×#10621877	C₂²	1	1	yes	characteristic
10	C₂×#13063284	C₂²	1	1	yes	characteristic
11	C₂×#13063261	—	2	4	no	—
12	C₂×#13063261	C₂²	1	2	yes	complemented
13	C₂×#13063261	C₂²	1	2	yes	complemented
14	#14582916	—	2	8	no	—
15	C₂×#13063252	C₂²	1	8	yes	complemented
16	#14582866	—	2	4	no	—
17	#14582866	C₂²	1	8	yes	complemented
18	#14582863	—	2	4	no	—
19	#14582854	—	2	4	no	—
20	C₂×#13063235	C₂²	1	2	yes	complemented
21	C₂×C₈×Dic₄₃	C₂²	1	2	yes	complemented
22	C₂²×#41×C₄₃	C₂²	1	2	yes	—
23	C₂×#135×C₄₃	—	2	4	no	—
24	C₂×#135×C₄₃	—	2	4	no	—
25	C₂×#135×C₄₃	C₄	1	2	yes	complemented
26	C₂×#135×C₄₃	C₄	1	2	yes	complemented
27	C₂×#135×C₄₃	C₂²	1	2	yes	—
28	C₂×#135×C₄₃	C₂²	1	2	yes	—
29	C₂²×Q₁₆×C₄₃	C₄	1	1	yes	characteristic, complemented
30	C₂²×SD₁₆×C₄₃	C₄	1	2	yes	complemented
31	C₂²×D₈×C₄₃	C₄	1	1	yes	characteristic, complemented
32	C₂³×C₈×C₄₃	C₂²	1	1	yes	characteristic
33	C₂×#10621877	—	2	2	no	—
34	C₂×#10621877	—	2	2	no	—
35	C₂×#10621877	—	2	2	no	—
36	C₂×#10621877	—	2	4	no	—
37	C₂×#10621877	—	2	4	no	—
38	C₂×#10621877	D₄	1	2	yes	—
39	C₂×#10621877	D₄	1	2	yes	—
40	C₂×#10621877	C₂³	1	4	yes	—
41	C₂²×C₄₃⋊C₈	—	2	2	no	—
42	C₂²×C₄₃⋊C₈	C₂³	1	2	yes	—
43	#13063284	—	2	2	no	—
44	#13063284	D₄	1	4	yes	—
45	C₂×C₄⋊Dic₄₃	—	2	1	no	—
46	C₂×C₂²⋊Dic₄₃	—	2	1	no	—
47	C₂×C₄×Dic₄₃	C₂³	1	2	yes	—
48	#13063261	—	2	4	no	—
49	#13063261	—	2	4	no	—
50	#13063252	—	2	16	no	—
51	C₂²⋊(C₄₃⋊C₈)	—	2	16	no	—
52	#13063235	—	2	4	no	—
53	C₈×Dic₄₃	—	2	4	no	—
54	C₂×#41×C₄₃	—	2	2	no	—
55	C₂×#41×C₄₃	—	2	2	no	—
56	C₂×#41×C₄₃	—	2	4	no	—
57	C₂×#41×C₄₃	—	2	4	no	—
58	C₂×#41×C₄₃	—	2	4	no	—
59	C₂×#41×C₄₃	—	2	4	no	—
60	C₂×#41×C₄₃	C₂×C₄	1	4	yes	—
61	C₂×#41×C₄₃	C₂³	1	4	yes	—
62	C₂²×Q₈×C₄₃	C₂×C₄	1	2	yes	—
63	C₂²×D₄×C₄₃	—	2	2	no	—
64	C₂²×D₄×C₄₃	C₂×C₄	1	2	yes	—
65	C₂³×C₄×C₄₃	—	2	2	no	—
66	C₂³×C₄×C₄₃	C₂³	1	1	yes	characteristic
67	#135×C₄₃	—	2	8	no	—
68	#135×C₄₃	—	2	8	no	—
69	#135×C₄₃	—	2	4	no	—
70	#135×C₄₃	—	2	4	no	—
71	#135×C₄₃	—	2	4	no	—
72	#135×C₄₃	—	2	4	no	—
73	C₂×Q₁₆×C₄₃	—	2	4	no	—
74	C₂×Q₁₆×C₄₃	C₂×C₄	1	2	yes	—
75	C₂×Q₁₆×C₄₃	C₂×C₄	1	2	yes	—
76	C₂×SD₁₆×C₄₃	—	2	8	no	—
77	C₂×SD₁₆×C₄₃	C₂×C₄	1	4	yes	—
78	C₂×SD₁₆×C₄₃	C₂×C₄	1	4	yes	—
79	C₂×D₈×C₄₃	—	2	4	no	—
80	C₂×D₈×C₄₃	C₂×C₄	1	2	yes	—
81	C₂×D₈×C₄₃	C₂×C₄	1	2	yes	—
82	C₂²×C₈×C₄₃	C₂×C₄	1	1	yes	characteristic
83	C₂²×C₈×C₄₃	C₂×C₄	1	1	yes	characteristic
84	C₂²×C₈×C₄₃	C₂×C₄	1	1	yes	characteristic
85	C₂²×C₈×C₄₃	C₂×C₄	1	1	yes	characteristic
86	C₂²×C₈×C₄₃	D₄	1	4	yes	—
87	C₂²×C₈×C₄₃	D₄	1	4	yes	—
88	C₂²×C₈×C₄₃	C₂³	1	1	yes	characteristic
89	C₂²×C₈×C₄₃	C₂³	1	1	yes	characteristic
90	C₂⁴×C₄₃	—	2	2	no	—
91	C₂⁴×C₄₃	#41	1	1	yes	characteristic
92	#41×C₄₃	—	2	8	no	—
93	#41×C₄₃	—	2	8	no	—
94	#41×C₄₃	—	2	4	no	—
95	#41×C₄₃	—	2	4	no	—
96	#41×C₄₃	—	2	4	no	—
97	#41×C₄₃	—	2	4	no	—
98	#41×C₄₃	—	4	4	no	—
99	#41×C₄₃	—	4	4	no	—
100	#41×C₄₃	—	4	4	no	—
101	#41×C₄₃	—	4	4	no	—
102	C₂×Q₈×C₄₃	—	2	2	no	—
103	C₂×Q₈×C₄₃	—	2	4	no	—
104	C₂×Q₈×C₄₃	—	2	4	no	—
105	C₂×Q₈×C₄₃	C₂²×C₄	1	4	yes	—
106	C₂×D₄×C₄₃	—	2	2	no	—
107	C₂×D₄×C₄₃	—	2	4	no	—
108	C₂×D₄×C₄₃	—	2	4	no	—
109	C₂×D₄×C₄₃	—	2	4	no	—
110	C₂×D₄×C₄₃	—	2	4	no	—
111	C₂×D₄×C₄₃	—	4	4	no	—
112	C₂×D₄×C₄₃	—	4	4	no	—
113	C₂×D₄×C₄₃	C₂²×C₄	1	4	yes	—
114	C₂²×C₄×C₄₃	—	2	4	no	—
115	C₂²×C₄×C₄₃	—	2	4	no	—
116	C₂²×C₄×C₄₃	—	2	2	no	—
117	C₂²×C₄×C₄₃	—	4	4	no	—
118	C₂²×C₄×C₄₃	—	4	4	no	—
119	C₂²×C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
120	C₂²×C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
121	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
122	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
123	C₂²×C₄×C₄₃	C₂×D₄	1	2	yes	—
124	C₂²×C₄×C₄₃	C₂×D₄	1	2	yes	—
125	C₂²×C₄×C₄₃	C₂×D₄	1	2	yes	—
126	C₂²×C₄×C₄₃	#41	1	2	yes	—
127	C₂²×C₄×C₄₃	#41	1	1	yes	characteristic
128	C₂²×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
129	C₂²×Dic₄₃	—	2	2	no	—
130	Q₁₆×C₄₃	—	2	4	no	—
131	Q₁₆×C₄₃	—	2	4	no	—
132	SD₁₆×C₄₃	—	2	8	no	—
133	SD₁₆×C₄₃	—	2	8	no	—
134	D₈×C₄₃	—	2	4	no	—
135	D₈×C₄₃	—	2	4	no	—
136	C₂×C₈×C₄₃	C₂²⋊C₄	1	4	yes	—
137	C₂×C₈×C₄₃	C₂²⋊C₄	1	4	yes	—
138	C₂×C₈×C₄₃	C₂²⋊C₄	1	4	yes	—
139	C₂×C₈×C₄₃	C₂²⋊C₄	1	4	yes	—
140	C₂×C₈×C₄₃	C₂²×C₄	1	1	yes	characteristic
141	C₂×C₈×C₄₃	C₂²×C₄	1	1	yes	characteristic
142	C₂×C₈×C₄₃	C₂²×C₄	1	1	yes	characteristic
143	C₂×C₈×C₄₃	C₂²×C₄	1	1	yes	characteristic
144	C₂×C₈×C₄₃	C₂×D₄	1	2	yes	—
145	C₂×C₈×C₄₃	C₂×D₄	1	2	yes	—
146	C₂×C₈×C₄₃	C₂×D₄	1	2	yes	—
147	C₂×C₈×C₄₃	C₂×D₄	1	2	yes	—
148	C₂²⋊Dic₄₃	—	2	4	no	—
149	C₄⋊Dic₄₃	—	2	4	no	—
150	C₄×Dic₄₃	—	2	2	no	—
151	C₄×Dic₄₃	C₂×D₄	1	4	yes	—
152	#10621877	—	2	4	no	—
153	#10621877	—	2	4	no	—
154	#10621877	—	2	4	no	—
155	#10621877	—	2	4	no	—
156	#10621877	—	4	4	no	—
157	C₂×C₄₃⋊C₈	—	2	2	no	—
158	C₂×C₄₃⋊C₈	—	2	2	no	—
159	C₂×C₄₃⋊C₈	—	2	4	no	—
160	C₂×C₄₃⋊C₈	—	4	4	no	—
161	C₂×C₄₃⋊C₈	C₂×D₄	1	4	yes	—
162	C₂³×C₄₃	—	2	4	no	—
163	C₂³×C₄₃	—	4	2	no	—
164	C₂³×C₄₃	—	4	4	no	—
165	C₂³×C₄₃	—	8	4	no	—
166	C₂³×C₄₃	C₄×D₄	1	1	yes	characteristic
167	C₂³×C₄₃	C₄×D₄	1	1	yes	characteristic
168	C₂³×C₄₃	#121	1	2	yes	—
169	C₂³×C₄₃	#124	1	2	yes	—
170	C₂³×C₄₃	C₂×#41	1	1	yes	characteristic
171	Q₈×C₄₃	—	2	4	no	—
172	Q₈×C₄₃	—	2	4	no	—
173	Q₈×C₄₃	—	4	4	no	—
174	D₄×C₄₃	—	2	4	no	—
175	D₄×C₄₃	—	2	4	no	—
176	D₄×C₄₃	—	4	4	no	—
177	D₄×C₄₃	—	4	4	no	—
178	D₄×C₄₃	—	4	8	no	—
179	D₄×C₄₃	—	4	4	no	—
180	C₂×C₄×C₄₃	—	2	4	no	—
181	C₂×C₄×C₄₃	—	4	4	no	—
182	C₂×C₄×C₄₃	—	4	4	no	—
183	C₂×C₄×C₄₃	—	4	4	no	—
184	C₂×C₄×C₄₃	—	4	8	no	—
185	C₂×C₄×C₄₃	C₂×C₂²⋊C₄	1	2	yes	—
186	C₂×C₄×C₄₃	C₂×C₂²⋊C₄	1	2	yes	—
187	C₂×C₄×C₄₃	C₄×D₄	1	2	yes	—
188	C₂×C₄×C₄₃	C₄×D₄	1	2	yes	—
189	C₂×C₄×C₄₃	C₄×D₄	1	1	yes	characteristic
190	C₂×C₄×C₄₃	C₄×D₄	1	1	yes	characteristic
191	C₂×C₄×C₄₃	#121	1	2	yes	—
192	C₂×C₄×C₄₃	#121	1	2	yes	—
193	C₂×C₄×C₄₃	#121	1	2	yes	—
194	C₂×C₄×C₄₃	#124	1	2	yes	—
195	C₂×C₄×C₄₃	#127	1	2	yes	—
196	C₂×C₄×C₄₃	#127	1	2	yes	—
197	C₂×C₄×C₄₃	C₂³×C₄	1	1	yes	characteristic
198	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
199	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
200	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
201	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
202	C₂×C₄×C₄₃	C₂×#41	1	1	yes	characteristic
203	C₂×Dic₄₃	—	2	4	no	—
204	C₂×Dic₄₃	—	4	4	no	—
205	C₈×C₄₃	C₂×C₂²⋊C₄	1	2	yes	—
206	C₈×C₄₃	C₂×C₂²⋊C₄	1	2	yes	—
207	C₈×C₄₃	C₂×C₂²⋊C₄	1	2	yes	—
208	C₈×C₄₃	C₂×C₂²⋊C₄	1	2	yes	—
209	C₄₃⋊C₈	—	2	4	no	—
210	C₄₃⋊C₈	—	4	4	no	—
211	#21240	—	43	1	no	maximal, Sylow
212	C₂²×C₄₃	—	2	2	no	—
213	C₂²×C₄₃	—	2	2	no	—
214	C₂²×C₄₃	—	2	2	no	—
215	C₂²×C₄₃	—	4	2	no	—
216	C₂²×C₄₃	—	4	2	no	—
217	C₂²×C₄₃	—	4	8	no	—
218	C₂²×C₄₃	—	4	4	no	—
219	C₂²×C₄₃	—	8	8	no	—
220	C₂²×C₄₃	#390	1	2	yes	—
221	C₂²×C₄₃	#390	1	2	yes	—
222	C₂²×C₄₃	C₂×C₄×D₄	1	1	yes	characteristic
223	C₂²×C₄₃	C₂×#121	1	1	yes	characteristic
224	C₂²×C₄₃	C₂×#124	1	1	yes	characteristic
225	C₄×C₄₃	—	4	4	no	—
226	C₄×C₄₃	#390	1	2	yes	—
227	C₄×C₄₃	#390	1	2	yes	—
228	C₄×C₄₃	C₂²×C₂²⋊C₄	1	1	yes	characteristic
229	C₄×C₄₃	C₂×C₄×D₄	1	1	yes	characteristic
230	C₄×C₄₃	C₂×#121	1	1	yes	characteristic
231	C₄×C₄₃	C₂×#127	1	1	yes	characteristic
232	Dic₄₃	—	4	4	no	—
233	C₂²×#135	D₄₃	1	1	yes	characteristic
234	C₂²×#108	—	43	1	no	—
235	C₂×#421	—	43	2	no	—
236	#2879	—	43	2	no	—
237	C₂×#405	—	43	1	no	—
238	#1975	—	43	4	no	—
239	#1974	—	43	4	no	—
240	C₂×C₄₃	—	2	1	no	—
241	C₂×C₄₃	—	2	2	no	—
242	C₂×C₄₃	—	2	1	no	—
243	C₂×C₄₃	—	2	2	no	—
244	C₂×C₄₃	—	8	4	no	—
245	C₂×C₄₃	C₂×#390	1	1	yes	characteristic
246	C₂×C₄₃	#2957	1	2	yes	—
247	C₂²×#41	C₂×D₄₃	1	2	yes	—
248	C₂×#135	—	2	4	no	—
249	C₂×#135	—	2	4	no	—
250	C₂×#135	Dic₄₃	1	2	yes	complemented
251	C₂×#135	Dic₄₃	1	2	yes	complemented
252	C₂×#135	C₂×D₄₃	1	2	yes	—
253	C₂×#135	C₂×D₄₃	1	2	yes	—
254	C₂²×Q₁₆	Dic₄₃	1	1	yes	characteristic, complemented
255	C₂²×SD₁₆	Dic₄₃	1	2	yes	complemented
256	C₂²×D₈	Dic₄₃	1	1	yes	characteristic, complemented
257	C₂²×M₁₆	—	43	1	no	—
258	C₂²×M₁₆	—	43	2	no	—
259	C₂³×C₈	C₂×D₄₃	1	1	yes	characteristic
260	C₂×#117	—	43	1	no	—
261	C₂×#108	—	43	2	no	—
262	C₂×#108	—	43	2	no	—
263	C₂×#108	—	86	4	no	—
264	#421	—	86	8	no	—
265	C₂×#104	—	43	8	no	—
266	#408	—	43	8	no	—
267	#408	—	86	4	no	—
268	#407	—	86	4	no	—
269	#405	—	86	4	no	—
270	C₂×#97	—	43	2	no	—
271	C₂×C₄×C₈	—	43	2	no	—
272	C₄₃	#21240	1	1	yes	characteristic, complemented, Sylow
273	C₂×#41	—	2	2	no	—
274	C₂×#41	—	2	2	no	—
275	C₂×#41	—	2	4	no	—
276	C₂×#41	—	2	4	no	—
277	C₂×#41	—	2	4	no	—
278	C₂×#41	—	2	4	no	—
279	C₂×#41	C₂×Dic₄₃	1	4	yes	—
280	C₂×#41	C₂²×D₄₃	1	4	yes	—
281	C₂²×Q₈	C₂×Dic₄₃	1	2	yes	—
282	C₂²×D₄	—	2	2	no	—
283	C₂²×D₄	C₂×Dic₄₃	1	2	yes	—
284	C₂³×C₄	—	2	2	no	—
285	C₂³×C₄	C₂²×D₄₃	1	1	yes	characteristic
286	#135	—	2	8	no	—
287	#135	—	2	8	no	—
288	#135	—	2	4	no	—
289	#135	—	2	4	no	—
290	#135	—	2	4	no	—
291	#135	—	2	4	no	—
292	C₂×Q₁₆	—	2	4	no	—
293	C₂×Q₁₆	C₂×Dic₄₃	1	2	yes	—
294	C₂×Q₁₆	C₂×Dic₄₃	1	2	yes	—
295	C₂×SD₁₆	—	2	8	no	—
296	C₂×SD₁₆	C₂×Dic₄₃	1	4	yes	—
297	C₂×SD₁₆	C₂×Dic₄₃	1	4	yes	—
298	C₂×D₈	—	2	4	no	—
299	C₂×D₈	C₂×Dic₄₃	1	2	yes	—
300	C₂×D₈	C₂×Dic₄₃	1	2	yes	—
301	C₂×M₁₆	—	43	2	no	—
302	C₂×M₁₆	—	43	2	no	—
303	C₂×M₁₆	—	43	4	no	—
304	C₂×M₁₆	—	86	2	no	—
305	C₂×M₁₆	—	86	2	no	—
306	C₂×M₁₆	—	86	2	no	—
307	C₂×M₁₆	—	86	4	no	—
308	C₂×M₁₆	—	86	4	no	—
309	C₂²×C₈	—	43	2	no	—
310	C₂²×C₈	—	86	2	no	—
311	C₂²×C₈	C₂×Dic₄₃	1	1	yes	characteristic
312	C₂²×C₈	C₂×Dic₄₃	1	1	yes	characteristic
313	C₂²×C₈	C₂×Dic₄₃	1	1	yes	characteristic
314	C₂²×C₈	C₂×Dic₄₃	1	1	yes	characteristic
315	C₂²×C₈	C₂²⋊D₄₃	1	4	yes	—
316	C₂²×C₈	C₂²⋊D₄₃	1	4	yes	—
317	C₂²×C₈	C₂²×D₄₃	1	1	yes	characteristic
318	C₂²×C₈	C₂²×D₄₃	1	1	yes	characteristic
319	#117	—	43	4	no	—
320	#117	—	86	2	no	—
321	C₂×C₄⋊C₄	—	86	1	no	—
322	C₂×C₂²⋊C₄	—	86	1	no	—
323	C₂×C₄²	—	43	2	no	—
324	#108	—	86	4	no	—
325	#108	—	86	4	no	—
326	#104	—	86	16	no	—
327	C₂²⋊C₈	—	86	16	no	—
328	#97	—	86	4	no	—
329	C₄×C₈	—	86	4	no	—
330	C₂⁴	—	2	2	no	—
331	C₂⁴	#10621900	1	1	yes	characteristic
332	#41	—	2	8	no	—
333	#41	—	2	8	no	—
334	#41	—	2	4	no	—
335	#41	—	2	4	no	—
336	#41	—	2	4	no	—
337	#41	—	2	4	no	—
338	#41	—	4	4	no	—
339	#41	—	4	4	no	—
340	#41	—	4	4	no	—
341	#41	—	4	4	no	—
342	C₂×Q₈	—	2	2	no	—
343	C₂×Q₈	—	2	4	no	—
344	C₂×Q₈	—	2	4	no	—
345	C₂×Q₈	C₂²×Dic₄₃	1	4	yes	—
346	C₂×D₄	—	2	4	no	—
347	C₂×D₄	—	2	4	no	—
348	C₂×D₄	—	2	4	no	—
349	C₂×D₄	—	2	4	no	—
350	C₂×D₄	—	2	2	no	—
351	C₂×D₄	—	4	4	no	—
352	C₂×D₄	—	4	4	no	—
353	C₂×D₄	C₂²×Dic₄₃	1	4	yes	—
354	C₂²×C₄	—	2	2	no	—
355	C₂²×C₄	—	2	4	no	—
356	C₂²×C₄	—	2	4	no	—
357	C₂²×C₄	—	4	4	no	—
358	C₂²×C₄	—	4	4	no	—
359	C₂²×C₄	—	86	2	no	—
360	C₂²×C₄	D₄×D₄₃	1	2	yes	—
361	C₂²×C₄	D₄×D₄₃	1	1	yes	characteristic
362	C₂²×C₄	D₄×D₄₃	1	1	yes	characteristic
363	C₂²×C₄	#10621900	1	1	yes	characteristic
364	C₂²×C₄	#10621900	1	2	yes	—
365	C₂²×C₄	C₂²×Dic₄₃	1	1	yes	characteristic
366	C₂²×C₄	C₂²×Dic₄₃	1	1	yes	characteristic
367	C₂²×C₄	C₂×C₂²⋊D₄₃	1	2	yes	—
368	C₂²×C₄	C₂×C₂²⋊D₄₃	1	2	yes	—
369	C₂²×C₄	C₂³×D₄₃	1	1	yes	characteristic
370	Q₁₆	—	2	4	no	—
371	Q₁₆	—	2	4	no	—
372	SD₁₆	—	2	8	no	—
373	SD₁₆	—	2	8	no	—
374	D₈	—	2	4	no	—
375	D₈	—	2	4	no	—
376	M₁₆	—	86	4	no	—
377	M₁₆	—	86	4	no	—
378	M₁₆	—	86	4	no	—
379	M₁₆	—	86	4	no	—
380	M₁₆	—	172	4	no	—
381	C₂×C₈	—	43	4	no	—
382	C₂×C₈	—	86	2	no	—
383	C₂×C₈	—	86	2	no	—
384	C₂×C₈	—	86	4	no	—
385	C₂×C₈	—	172	4	no	—
386	C₂×C₈	C₂²⋊Dic₄₃	1	4	yes	—
387	C₂×C₈	C₂²⋊Dic₄₃	1	4	yes	—
388	C₂×C₈	C₂²⋊Dic₄₃	1	4	yes	—
389	C₂×C₈	C₂²⋊Dic₄₃	1	4	yes	—
390	C₂×C₈	C₂²×Dic₄₃	1	1	yes	characteristic
391	C₂×C₈	C₂²×Dic₄₃	1	1	yes	characteristic
392	C₂×C₈	C₂²×Dic₄₃	1	1	yes	characteristic
393	C₂×C₈	C₂²×Dic₄₃	1	1	yes	characteristic
394	C₂×C₈	C₂×C₂²⋊D₄₃	1	2	yes	—
395	C₂×C₈	C₂×C₂²⋊D₄₃	1	2	yes	—
396	C₂×C₈	C₂×C₂²⋊D₄₃	1	2	yes	—
397	C₂×C₈	C₂×C₂²⋊D₄₃	1	2	yes	—
398	C₄⋊C₄	—	86	4	no	—
399	C₂²⋊C₄	—	86	4	no	—
400	C₄²	—	43	4	no	—
401	C₄²	—	86	2	no	—
402	C₂³	—	2	4	no	—
403	C₂³	—	4	2	no	—
404	C₂³	—	4	4	no	—
405	C₂³	—	8	4	no	—
406	C₂³	D₄×Dic₄₃	1	1	yes	characteristic
407	C₂³	D₄×Dic₄₃	1	1	yes	characteristic
408	C₂³	#13063296	1	2	yes	—
409	C₂³	#13063312	1	2	yes	—
410	C₂³	C₂×#10621900	1	1	yes	characteristic
411	Q₈	—	2	4	no	—
412	Q₈	—	2	4	no	—
413	Q₈	—	4	4	no	—
414	D₄	—	2	4	no	—
415	D₄	—	2	4	no	—
416	D₄	—	4	8	no	—
417	D₄	—	4	4	no	—
418	D₄	—	4	4	no	—
419	D₄	—	4	4	no	—
420	C₂×C₄	—	2	4	no	—
421	C₂×C₄	—	4	4	no	—
422	C₂×C₄	—	4	8	no	—
423	C₂×C₄	—	4	4	no	—
424	C₂×C₄	—	4	4	no	—
425	C₂×C₄	—	86	4	no	—
426	C₂×C₄	—	172	4	no	—
427	C₂×C₄	C₂×C₂²⋊Dic₄₃	1	2	yes	—
428	C₂×C₄	C₂×C₂²⋊Dic₄₃	1	2	yes	—
429	C₂×C₄	D₄×Dic₄₃	1	1	yes	characteristic
430	C₂×C₄	D₄×Dic₄₃	1	1	yes	characteristic
431	C₂×C₄	D₄×Dic₄₃	1	2	yes	—
432	C₂×C₄	D₄×Dic₄₃	1	2	yes	—
433	C₂×C₄	#13063296	1	2	yes	—
434	C₂×C₄	#13063296	1	2	yes	—
435	C₂×C₄	#13063296	1	2	yes	—
436	C₂×C₄	#13063312	1	2	yes	—
437	C₂×C₄	#13063321	1	2	yes	—
438	C₂×C₄	#13063321	1	2	yes	—
439	C₂×C₄	C₂³×Dic₄₃	1	1	yes	characteristic
440	C₂×C₄	C₂×D₄×D₄₃	1	1	yes	characteristic
441	C₂×C₄	C₂×D₄×D₄₃	1	1	yes	characteristic
442	C₂×C₄	C₂²×C₂²⋊D₄₃	1	1	yes	characteristic
443	C₂×C₄	C₂²×C₂²⋊D₄₃	1	1	yes	characteristic
444	C₂×C₄	C₂×#10621900	1	1	yes	characteristic
445	C₈	—	86	4	no	—
446	C₈	—	172	4	no	—
447	C₈	C₂×C₂²⋊Dic₄₃	1	2	yes	—
448	C₈	C₂×C₂²⋊Dic₄₃	1	2	yes	—
449	C₈	C₂×C₂²⋊Dic₄₃	1	2	yes	—
450	C₈	C₂×C₂²⋊Dic₄₃	1	2	yes	—
451	C₂²	—	2	2	no	—
452	C₂²	—	2	2	no	—
453	C₂²	—	2	2	no	—
454	C₂²	—	4	2	no	—
455	C₂²	—	4	2	no	—
456	C₂²	—	4	4	no	—
457	C₂²	—	4	8	no	—
458	C₂²	—	8	8	no	—
459	C₂²	#14582802	1	2	yes	—
460	C₂²	#14582802	1	2	yes	—
461	C₂²	C₂×D₄×Dic₄₃	1	1	yes	characteristic
462	C₂²	C₂×#13063296	1	1	yes	characteristic
463	C₂²	C₂×#13063312	1	1	yes	characteristic
464	C₄	—	4	4	no	—
465	C₄	—	172	4	no	—
466	C₄	#14582802	1	2	yes	—
467	C₄	#14582802	1	2	yes	—
468	C₄	C₂²×C₂²⋊Dic₄₃	1	1	yes	characteristic
469	C₄	C₂×D₄×Dic₄₃	1	1	yes	characteristic
470	C₄	C₂×#13063296	1	1	yes	characteristic
471	C₄	C₂×#13063321	1	1	yes	characteristic
472	C₂	—	2	1	no	—
473	C₂	—	2	2	no	—
474	C₂	—	2	2	no	—
475	C₂	—	2	1	no	—
476	C₂	—	8	4	no	—
477	C₂	C₂×#14582802	1	1	yes	characteristic
478	C₂	#19143512	1	2	yes	—

	subgroup	G/H
center	C₂×C₄	C₂×D₄×D₄₃
commutator	C₂×C₄×C₄₃	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₄₃
Fitting, prime radical	C₂²×#135×C₄₃	C₂
socle	C₂²×C₄₃	C₂×C₄×D₄
cosocle	C₂²×C₄×C₄₃	C₂⁴
hypercenter	C₂²×#135	D₄₃
hypocenter	C₄₃	#21240
LCS	G ▷ C₂×C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂×C₄ ◁ C₂³×C₄ ◁ C₂²×#135

Complements

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

N	H ≅ G/N	type
1. C₂²×#13063261	C₂	semidirect
2. C₂×#14582916	C₂	semidirect
3. #19143040	C₂	semidirect
4. C₂×#14582854	C₂	semidirect
5. #19135489	C₂	semidirect
6. #19135484	C₂	semidirect
12. C₂×#13063261	C₂²	semidirect
13. C₂×#13063261	C₂²	semidirect
15. C₂×#13063252	C₂²	semidirect
17. #14582866	C₂²	semidirect
20. C₂×#13063235	C₂²	semidirect
21. C₂×C₈×Dic₄₃	C₂²	semidirect
25. C₂×#135×C₄₃	C₄	semidirect
26. C₂×#135×C₄₃	C₄	semidirect
29. C₂²×Q₁₆×C₄₃	C₄	semidirect
30. C₂²×SD₁₆×C₄₃	C₄	semidirect
31. C₂²×D₈×C₄₃	C₄	semidirect
250. C₂×#135	Dic₄₃	semidirect
251. C₂×#135	Dic₄₃	semidirect
254. C₂²×Q₁₆	Dic₄₃	semidirect
255. C₂²×SD₁₆	Dic₄₃	semidirect
256. C₂²×D₈	Dic₄₃	semidirect
272. C₄₃	#21240	semidirect

Maximal subgroups

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

subgroup	index
C₂²×#13063261	2
C₂×#14582916	2
#19143040	2
C₂×#14582854	2
#19135489	2
#19135484	2
C₂²×#135×C₄₃	2
#21240	43