Subgroups — C₂×#19135261 #25099175

Order 11008.

1046 conjugacy classes of subgroups.

The subgroup lattice has 636 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#14582947	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#14582916	C₂	1	1	yes	maximal, characteristic
3	C₂×#14582883	C₂	1	1	yes	maximal, characteristic
4	C₂×C₄×#10621877	C₂	1	1	yes	maximal, characteristic, complemented
5	#19135261	C₂	1	8	yes	maximal, direct product factor
6	C₂×#14582670	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×#14582659	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂²×#104×C₄₃	C₂	1	1	yes	maximal, characteristic
9	C₂²×#10621877	C₂²	1	1	yes	characteristic
10	C₂²×#10621877	C₂²	1	1	yes	characteristic
11	C₂²×#10621877	C₂²	1	1	yes	characteristic
12	C₂×#13063284	C₂²	1	1	yes	characteristic
13	#14582947	—	2	2	no	—
14	#14582947	C₂²	1	4	yes	complemented
15	C₂×#13063260	—	2	2	no	—
16	#14582916	—	2	2	no	—
17	#14582916	C₂²	1	4	yes	—
18	C₂×#13063252	—	2	2	no	—
19	#14582883	C₄	1	4	yes	complemented
20	#14582883	C₂²	1	4	yes	—
21	C₂×#13063244	C₄	1	2	yes	complemented
22	C₂×#13063242	C₄	1	2	yes	complemented
23	C₄×#10621877	—	2	2	no	—
24	C₄×#10621877	C₂²	1	4	yes	complemented
25	C₂×#13063236	—	2	1	no	—
26	C₂×C₄×C₄₃⋊C₈	—	2	1	no	—
27	#14582670	C₂²	1	4	yes	complemented
28	#14582659	C₂²	1	4	yes	complemented
29	C₂²×#41×C₄₃	C₂²	1	1	yes	characteristic
30	C₂²×M₁₆×C₄₃	C₂²	1	1	yes	characteristic
31	C₂²×C₄²×C₄₃	C₂²	1	1	yes	characteristic
32	C₂×#104×C₄₃	—	2	1	no	—
33	C₂×#104×C₄₃	—	2	1	no	—
34	C₂×#104×C₄₃	—	2	2	no	—
35	C₂×#104×C₄₃	C₂²	1	4	yes	—
36	C₂×#10621877	—	2	1	no	—
37	C₂×#10621877	—	2	1	no	—
38	C₂×#10621877	—	2	1	no	—
39	C₂×#10621877	—	2	1	no	—
40	C₂×#10621877	—	2	1	no	—
41	C₂×#10621877	—	2	1	no	—
42	C₂×#10621877	—	2	1	no	—
43	C₂×#10621877	—	2	1	no	—
44	C₂×#10621877	—	2	1	no	—
45	C₂×#10621877	C₂×C₄	1	2	yes	—
46	C₂×#10621877	C₂×C₄	1	2	yes	—
47	C₂×#10621877	C₂×C₄	1	2	yes	—
48	C₂×#10621877	C₂×C₄	1	2	yes	—
49	C₂×#10621877	D₄	1	2	yes	—
50	C₂×#10621877	D₄	1	2	yes	—
51	C₂×#10621877	C₂³	1	2	yes	—
52	C₂×#10621877	C₂³	1	2	yes	—
53	C₂×#10621877	C₂³	1	2	yes	—
54	C₂²×C₄₃⋊C₈	—	2	1	no	—
55	C₂²×C₄₃⋊C₈	—	2	1	no	—
56	C₂²×C₄₃⋊C₈	—	2	1	no	—
57	#13063284	—	2	1	no	—
58	#13063284	—	2	1	no	—
59	#13063284	—	2	1	no	—
60	#13063284	C₂³	1	2	yes	—
61	C₂×C₄⋊Dic₄₃	—	2	1	no	—
62	C₂×C₂²⋊Dic₄₃	—	2	1	no	—
63	C₂×C₄×Dic₄₃	—	2	1	no	—
64	#13063260	—	2	8	no	—
65	#13063252	—	2	8	no	—
66	#13063244	C₂×C₄	1	8	yes	complemented
67	#13063242	C₂×C₄	1	8	yes	complemented
68	#13063236	—	2	4	no	—
69	C₄×C₄₃⋊C₈	—	2	4	no	—
70	C₂×#41×C₄₃	—	2	1	no	—
71	C₂×#41×C₄₃	—	2	1	no	—
72	C₂×#41×C₄₃	—	2	1	no	—
73	C₂×#41×C₄₃	—	2	1	no	—
74	C₂×#41×C₄₃	—	2	1	no	—
75	C₂×#41×C₄₃	—	2	1	no	—
76	C₂×#41×C₄₃	—	2	1	no	—
77	C₂×#41×C₄₃	—	2	1	no	—
78	C₂×#41×C₄₃	—	2	1	no	—
79	C₂×#41×C₄₃	—	2	1	no	—
80	C₂×#41×C₄₃	C₂×C₄	1	2	yes	—
81	C₂×#41×C₄₃	C₂³	1	2	yes	—
82	C₂²×Q₈×C₄₃	C₂×C₄	1	1	yes	characteristic
83	C₂²×D₄×C₄₃	—	2	1	no	—
84	C₂²×D₄×C₄₃	C₂×C₄	1	1	yes	characteristic
85	C₂³×C₄×C₄₃	—	2	1	no	—
86	C₂³×C₄×C₄₃	—	2	1	no	—
87	C₂³×C₄×C₄₃	C₂³	1	1	yes	characteristic
88	C₂×M₁₆×C₄₃	—	2	1	no	—
89	C₂×M₁₆×C₄₃	—	2	1	no	—
90	C₂×M₁₆×C₄₃	—	2	1	no	—
91	C₂×M₁₆×C₄₃	—	2	1	no	—
92	C₂×M₁₆×C₄₃	—	2	1	no	—
93	C₂×M₁₆×C₄₃	C₂³	1	2	yes	—
94	C₂²×C₈×C₄₃	—	2	1	no	—
95	C₂×C₄²×C₄₃	—	2	1	no	—
96	C₂×C₄²×C₄₃	—	2	1	no	—
97	C₂×C₄²×C₄₃	—	2	1	no	—
98	C₂×C₄²×C₄₃	D₄	1	1	yes	characteristic
99	C₂×C₄²×C₄₃	D₄	1	1	yes	characteristic
100	C₂×C₄²×C₄₃	D₄	1	2	yes	—
101	C₂×C₄²×C₄₃	C₂³	1	2	yes	—
102	#104×C₄₃	—	2	4	no	—
103	#104×C₄₃	—	2	4	no	—
104	C₂⁴×C₄₃	—	2	1	no	—
105	C₂⁴×C₄₃	#41	1	1	yes	characteristic
106	#41×C₄₃	—	2	2	no	—
107	#41×C₄₃	—	2	2	no	—
108	#41×C₄₃	—	2	2	no	—
109	#41×C₄₃	—	2	2	no	—
110	#41×C₄₃	—	2	2	no	—
111	#41×C₄₃	—	2	2	no	—
112	#41×C₄₃	—	2	2	no	—
113	#41×C₄₃	—	2	2	no	—
114	#41×C₄₃	—	4	1	no	—
115	#41×C₄₃	—	4	1	no	—
116	#41×C₄₃	—	4	1	no	—
117	#41×C₄₃	—	4	1	no	—
118	#41×C₄₃	—	4	1	no	—
119	#41×C₄₃	—	4	1	no	—
120	#41×C₄₃	—	4	1	no	—
121	#41×C₄₃	—	4	1	no	—
122	C₂×Q₈×C₄₃	—	2	1	no	—
123	C₂×Q₈×C₄₃	—	2	1	no	—
124	C₂×Q₈×C₄₃	—	2	1	no	—
125	C₂×Q₈×C₄₃	—	2	1	no	—
126	C₂×Q₈×C₄₃	—	2	1	no	—
127	C₂×Q₈×C₄₃	C₂²×C₄	1	2	yes	—
128	C₂×D₄×C₄₃	—	2	1	no	—
129	C₂×D₄×C₄₃	—	2	2	no	—
130	C₂×D₄×C₄₃	—	2	2	no	—
131	C₂×D₄×C₄₃	—	2	1	no	—
132	C₂×D₄×C₄₃	—	2	1	no	—
133	C₂×D₄×C₄₃	—	2	1	no	—
134	C₂×D₄×C₄₃	—	2	1	no	—
135	C₂×D₄×C₄₃	—	4	1	no	—
136	C₂×D₄×C₄₃	—	4	1	no	—
137	C₂×D₄×C₄₃	—	4	1	no	—
138	C₂×D₄×C₄₃	—	4	1	no	—
139	C₂×D₄×C₄₃	C₂²×C₄	1	2	yes	—
140	C₂²×C₄×C₄₃	—	2	2	no	—
141	C₂²×C₄×C₄₃	—	2	2	no	—
142	C₂²×C₄×C₄₃	—	2	1	no	—
143	C₂²×C₄×C₄₃	—	2	1	no	—
144	C₂²×C₄×C₄₃	—	2	1	no	—
145	C₂²×C₄×C₄₃	—	2	2	no	—
146	C₂²×C₄×C₄₃	—	2	2	no	—
147	C₂²×C₄×C₄₃	—	4	4	no	—
148	C₂²×C₄×C₄₃	—	4	1	no	—
149	C₂²×C₄×C₄₃	—	4	1	no	—
150	C₂²×C₄×C₄₃	—	4	1	no	—
151	C₂²×C₄×C₄₃	—	4	1	no	—
152	C₂²×C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
153	C₂²×C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
154	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
155	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
156	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
157	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
158	C₂²×C₄×C₄₃	#41	1	1	yes	characteristic
159	C₂²×C₄×C₄₃	#41	1	1	yes	characteristic
160	C₂²×C₄×C₄₃	#41	1	1	yes	characteristic
161	C₂²×C₄×C₄₃	#41	1	1	yes	characteristic
162	C₂²×C₄×C₄₃	#41	1	1	yes	characteristic
163	C₂²×C₄×C₄₃	#41	1	1	yes	characteristic
164	C₂²×C₄×C₄₃	#41	1	1	yes	characteristic
165	C₂²×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
166	C₂²×Dic₄₃	—	4	1	no	—
167	M₁₆×C₄₃	—	2	2	no	—
168	M₁₆×C₄₃	—	2	2	no	—
169	M₁₆×C₄₃	—	4	1	no	—
170	M₁₆×C₄₃	—	4	1	no	—
171	C₂×C₈×C₄₃	—	2	2	no	—
172	C₂×C₈×C₄₃	—	4	1	no	—
173	C₂×C₈×C₄₃	—	4	1	no	—
174	C₄²×C₄₃	—	2	1	no	—
175	C₄²×C₄₃	—	2	2	no	—
176	C₄²×C₄₃	—	2	1	no	—
177	C₄²×C₄₃	—	2	2	no	—
178	C₄²×C₄₃	C₂×D₄	1	2	yes	—
179	C₄²×C₄₃	C₂×D₄	1	2	yes	—
180	C₂²⋊Dic₄₃	—	2	2	no	—
181	C₂²⋊Dic₄₃	—	4	1	no	—
182	C₄⋊Dic₄₃	—	2	2	no	—
183	C₄⋊Dic₄₃	—	4	1	no	—
184	C₄×Dic₄₃	—	2	2	no	—
185	C₄×Dic₄₃	—	4	1	no	—
186	#10621877	—	2	2	no	—
187	#10621877	—	2	2	no	—
188	#10621877	—	2	2	no	—
189	#10621877	—	2	2	no	—
190	#10621877	—	2	2	no	—
191	#10621877	—	2	2	no	—
192	#10621877	—	2	2	no	—
193	#10621877	—	2	2	no	—
194	#10621877	—	2	2	no	—
195	#10621877	C₂²×C₄	1	4	yes	—
196	#10621877	C₂²×C₄	1	4	yes	—
197	#10621877	C₂×D₄	1	4	yes	—
198	C₂×C₄₃⋊C₈	—	2	2	no	—
199	C₂×C₄₃⋊C₈	—	2	2	no	—
200	C₂×C₄₃⋊C₈	—	2	2	no	—
201	C₂×C₄₃⋊C₈	—	2	2	no	—
202	C₂×C₄₃⋊C₈	—	2	2	no	—
203	C₂×C₄₃⋊C₈	—	2	2	no	—
204	C₂×C₄₃⋊C₈	—	2	2	no	—
205	C₂×C₄₃⋊C₈	—	2	2	no	—
206	C₂×C₄₃⋊C₈	—	2	2	no	—
207	C₂³×C₄₃	—	2	2	no	—
208	C₂³×C₄₃	—	4	2	no	—
209	C₂³×C₄₃	—	4	1	no	—
210	C₂³×C₄₃	—	4	1	no	—
211	C₂³×C₄₃	—	8	2	no	—
212	C₂³×C₄₃	#117	1	1	yes	characteristic
213	C₂³×C₄₃	#117	1	1	yes	characteristic
214	C₂³×C₄₃	#123	1	1	yes	characteristic
215	C₂³×C₄₃	#123	1	1	yes	characteristic
216	C₂³×C₄₃	#124	1	1	yes	characteristic
217	C₂³×C₄₃	#124	1	1	yes	characteristic
218	C₂³×C₄₃	C₂×#41	1	1	yes	characteristic
219	Q₈×C₄₃	—	2	2	no	—
220	Q₈×C₄₃	—	2	2	no	—
221	Q₈×C₄₃	—	4	1	no	—
222	Q₈×C₄₃	—	4	1	no	—
223	D₄×C₄₃	—	2	2	no	—
224	D₄×C₄₃	—	2	2	no	—
225	D₄×C₄₃	—	4	2	no	—
226	D₄×C₄₃	—	4	2	no	—
227	D₄×C₄₃	—	4	2	no	—
228	D₄×C₄₃	—	4	2	no	—
229	D₄×C₄₃	—	4	1	no	—
230	D₄×C₄₃	—	4	1	no	—
231	C₂×C₄×C₄₃	—	2	4	no	—
232	C₂×C₄×C₄₃	—	2	2	no	—
233	C₂×C₄×C₄₃	—	2	2	no	—
234	C₂×C₄×C₄₃	—	2	2	no	—
235	C₂×C₄×C₄₃	—	4	4	no	—
236	C₂×C₄×C₄₃	—	4	4	no	—
237	C₂×C₄×C₄₃	—	4	2	no	—
238	C₂×C₄×C₄₃	—	4	1	no	—
239	C₂×C₄×C₄₃	—	4	1	no	—
240	C₂×C₄×C₄₃	—	4	2	no	—
241	C₂×C₄×C₄₃	—	4	2	no	—
242	C₂×C₄×C₄₃	—	4	2	no	—
243	C₂×C₄×C₄₃	—	4	2	no	—
244	C₂×C₄×C₄₃	#117	1	1	yes	characteristic
245	C₂×C₄×C₄₃	#117	1	1	yes	characteristic
246	C₂×C₄×C₄₃	C₄×D₄	1	1	yes	characteristic
247	C₂×C₄×C₄₃	C₄×D₄	1	1	yes	characteristic
248	C₂×C₄×C₄₃	C₄×D₄	1	1	yes	characteristic
249	C₂×C₄×C₄₃	C₄×D₄	1	1	yes	characteristic
250	C₂×C₄×C₄₃	C₄×D₄	1	1	yes	characteristic
251	C₂×C₄×C₄₃	C₄×D₄	1	1	yes	characteristic
252	C₂×C₄×C₄₃	C₄×D₄	1	1	yes	characteristic
253	C₂×C₄×C₄₃	C₄×D₄	1	1	yes	characteristic
254	C₂×C₄×C₄₃	#121	1	1	yes	characteristic
255	C₂×C₄×C₄₃	#121	1	1	yes	characteristic
256	C₂×C₄×C₄₃	#121	1	1	yes	characteristic
257	C₂×C₄×C₄₃	#121	1	1	yes	characteristic
258	C₂×C₄×C₄₃	#123	1	1	yes	characteristic
259	C₂×C₄×C₄₃	#123	1	1	yes	characteristic
260	C₂×C₄×C₄₃	#124	1	1	yes	characteristic
261	C₂×C₄×C₄₃	#124	1	1	yes	characteristic
262	C₂×C₄×C₄₃	#126	1	1	yes	characteristic
263	C₂×C₄×C₄₃	#126	1	1	yes	characteristic
264	C₂×C₄×C₄₃	#126	1	1	yes	characteristic
265	C₂×C₄×C₄₃	#126	1	1	yes	characteristic
266	C₂×C₄×C₄₃	C₂³×C₄	1	1	yes	characteristic
267	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
268	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
269	C₂×C₄×C₄₃	C₂×#41	1	1	yes	characteristic
270	C₂×C₄×C₄₃	C₂×#41	1	1	yes	characteristic
271	C₂×C₄×C₄₃	C₂×#41	1	1	yes	characteristic
272	C₂×Dic₄₃	—	4	2	no	—
273	C₂×Dic₄₃	—	8	2	no	—
274	C₈×C₄₃	—	4	2	no	—
275	C₄₃⋊C₈	—	2	4	no	—
276	C₄₃⋊C₈	—	2	4	no	—
277	C₄₃⋊C₈	—	2	4	no	—
278	C₂×#1932	—	43	1	no	maximal, Sylow
279	C₂²×C₄₃	—	2	2	no	—
280	C₂²×C₄₃	—	2	2	no	—
281	C₂²×C₄₃	—	2	2	no	—
282	C₂²×C₄₃	—	4	1	no	—
283	C₂²×C₄₃	—	4	1	no	—
284	C₂²×C₄₃	—	4	1	no	—
285	C₂²×C₄₃	—	4	1	no	—
286	C₂²×C₄₃	—	4	2	no	—
287	C₂²×C₄₃	—	8	2	no	—
288	C₂²×C₄₃	—	8	2	no	—
289	C₂²×C₄₃	—	8	2	no	—
290	C₂²×C₄₃	#388	1	1	yes	characteristic
291	C₂²×C₄₃	#388	1	1	yes	characteristic
292	C₂²×C₄₃	#388	1	1	yes	characteristic
293	C₂²×C₄₃	#388	1	1	yes	characteristic
294	C₂²×C₄₃	C₂×#117	1	1	yes	characteristic
295	C₂²×C₄₃	C₂×#123	1	1	yes	characteristic
296	C₂²×C₄₃	C₂×#124	1	1	yes	characteristic
297	C₄×C₄₃	—	2	4	no	—
298	C₄×C₄₃	—	4	2	no	—
299	C₄×C₄₃	—	4	2	no	—
300	C₄×C₄₃	#388	1	1	yes	characteristic
301	C₄×C₄₃	#388	1	1	yes	characteristic
302	C₄×C₄₃	#388	1	1	yes	characteristic
303	C₄×C₄₃	#388	1	1	yes	characteristic
304	C₄×C₄₃	C₂×C₄×D₄	1	1	yes	characteristic
305	C₄×C₄₃	C₂×C₄×D₄	1	1	yes	characteristic
306	C₄×C₄₃	C₂×#121	1	1	yes	characteristic
307	C₄×C₄₃	C₂×#126	1	1	yes	characteristic
308	Dic₄₃	—	8	2	no	—
309	C₂×#430	—	43	1	no	—
310	C₂×#421	—	43	1	no	—
311	C₂²×#104	D₄₃	1	1	yes	characteristic
312	C₂×#413	—	43	1	no	—
313	C₂×C₄×M₁₆	—	43	1	no	—
314	#1932	—	43	8	no	—
315	C₂×#344	—	43	1	no	—
316	C₂×#339	—	43	1	no	—
317	C₂×C₄₃	—	2	1	no	—
318	C₂×C₄₃	—	2	1	no	—
319	C₂×C₄₃	—	2	1	no	—
320	C₂×C₄₃	—	2	1	no	—
321	C₂×C₄₃	—	2	1	no	—
322	C₂×C₄₃	—	2	1	no	—
323	C₂×C₄₃	—	8	2	no	—
324	C₂×C₄₃	#1932	1	2	yes	complemented
325	C₂×C₄₃	C₂×#388	1	1	yes	characteristic
326	C₂²×#41	C₂×D₄₃	1	1	yes	characteristic
327	C₂²×M₁₆	—	43	1	no	—
328	C₂²×M₁₆	—	43	1	no	—
329	C₂²×M₁₆	—	43	1	no	—
330	C₂²×M₁₆	C₂×D₄₃	1	1	yes	characteristic
331	C₂×#117	—	43	1	no	—
332	C₂²×C₄²	C₂×D₄₃	1	1	yes	characteristic
333	#430	—	43	4	no	—
334	#430	—	86	2	no	—
335	C₂×#108	—	86	2	no	—
336	#421	—	43	4	no	—
337	#421	—	86	2	no	—
338	C₂×#104	—	2	1	no	—
339	C₂×#104	—	2	1	no	—
340	C₂×#104	—	2	2	no	—
341	C₂×#104	—	86	2	no	—
342	C₂×#104	C₂×D₄₃	1	4	yes	—
343	#413	—	43	4	no	—
344	#413	—	43	4	no	—
345	C₂×#101	—	43	2	no	—
346	C₂×#100	—	43	2	no	—
347	C₄×M₁₆	—	43	4	no	—
348	C₄×M₁₆	—	86	2	no	—
349	C₂×#97	—	86	1	no	—
350	C₂×C₄×C₈	—	86	1	no	—
351	#344	—	43	4	no	—
352	#339	—	43	4	no	—
353	C₄₃	C₂×#1932	1	1	yes	characteristic, complemented, Sylow
354	C₂×#41	—	2	1	no	—
355	C₂×#41	—	2	1	no	—
356	C₂×#41	—	2	1	no	—
357	C₂×#41	—	2	1	no	—
358	C₂×#41	—	2	1	no	—
359	C₂×#41	—	2	1	no	—
360	C₂×#41	—	2	1	no	—
361	C₂×#41	—	2	1	no	—
362	C₂×#41	—	2	1	no	—
363	C₂×#41	—	2	1	no	—
364	C₂×#41	C₄×D₄₃	1	2	yes	—
365	C₂×#41	C₂²×D₄₃	1	2	yes	—
366	C₂²×Q₈	C₄×D₄₃	1	1	yes	characteristic
367	C₂²×D₄	—	2	1	no	—
368	C₂²×D₄	C₄×D₄₃	1	1	yes	characteristic
369	C₂³×C₄	—	2	1	no	—
370	C₂³×C₄	—	2	1	no	—
371	C₂³×C₄	C₂²×D₄₃	1	1	yes	characteristic
372	C₂×M₁₆	—	2	1	no	—
373	C₂×M₁₆	—	2	1	no	—
374	C₂×M₁₆	—	2	1	no	—
375	C₂×M₁₆	—	2	1	no	—
376	C₂×M₁₆	—	2	1	no	—
377	C₂×M₁₆	—	43	2	no	—
378	C₂×M₁₆	—	43	2	no	—
379	C₂×M₁₆	—	43	2	no	—
380	C₂×M₁₆	—	43	2	no	—
381	C₂×M₁₆	—	43	2	no	—
382	C₂×M₁₆	—	43	2	no	—
383	C₂×M₁₆	—	43	2	no	—
384	C₂×M₁₆	—	43	2	no	—
385	C₂×M₁₆	—	43	2	no	—
386	C₂×M₁₆	—	86	1	no	—
387	C₂×M₁₆	—	86	1	no	—
388	C₂×M₁₆	—	86	1	no	—
389	C₂×M₁₆	—	86	1	no	—
390	C₂×M₁₆	—	86	1	no	—
391	C₂×M₁₆	—	86	1	no	—
392	C₂×M₁₆	—	86	1	no	—
393	C₂×M₁₆	—	86	1	no	—
394	C₂×M₁₆	—	86	1	no	—
395	C₂×M₁₆	C₂²×D₄₃	1	2	yes	—
396	C₂²×C₈	—	2	1	no	—
397	C₂²×C₈	—	86	1	no	—
398	C₂²×C₈	—	86	1	no	—
399	C₂²×C₈	—	86	1	no	—
400	#117	—	43	2	no	—
401	#117	—	86	1	no	—
402	#117	—	86	1	no	—
403	#117	—	86	1	no	—
404	C₂×C₄⋊C₄	—	86	1	no	—
405	C₂×C₂²⋊C₄	—	86	1	no	—
406	C₂×C₄²	—	2	1	no	—
407	C₂×C₄²	—	2	1	no	—
408	C₂×C₄²	—	2	1	no	—
409	C₂×C₄²	—	86	1	no	—
410	C₂×C₄²	C₂²⋊D₄₃	1	1	yes	characteristic
411	C₂×C₄²	C₂²⋊D₄₃	1	1	yes	characteristic
412	C₂×C₄²	C₂²⋊D₄₃	1	2	yes	—
413	C₂×C₄²	C₂²×D₄₃	1	2	yes	—
414	#108	—	86	8	no	—
415	#104	—	2	4	no	—
416	#104	—	2	4	no	—
417	#104	—	86	8	no	—
418	#101	—	43	8	no	—
419	#100	—	43	8	no	—
420	#97	—	86	4	no	—
421	C₄×C₈	—	86	4	no	—
422	C₂⁴	—	2	1	no	—
423	C₂⁴	#10621900	1	1	yes	characteristic
424	#41	—	2	2	no	—
425	#41	—	2	2	no	—
426	#41	—	2	2	no	—
427	#41	—	2	2	no	—
428	#41	—	2	2	no	—
429	#41	—	2	2	no	—
430	#41	—	2	2	no	—
431	#41	—	2	2	no	—
432	#41	—	4	1	no	—
433	#41	—	4	1	no	—
434	#41	—	4	1	no	—
435	#41	—	4	1	no	—
436	#41	—	4	1	no	—
437	#41	—	4	1	no	—
438	#41	—	4	1	no	—
439	#41	—	4	1	no	—
440	C₂×Q₈	—	2	1	no	—
441	C₂×Q₈	—	2	1	no	—
442	C₂×Q₈	—	2	1	no	—
443	C₂×Q₈	—	2	1	no	—
444	C₂×Q₈	—	2	1	no	—
445	C₂×Q₈	C₂×C₄×D₄₃	1	2	yes	—
446	C₂×D₄	—	2	2	no	—
447	C₂×D₄	—	2	2	no	—
448	C₂×D₄	—	2	1	no	—
449	C₂×D₄	—	2	1	no	—
450	C₂×D₄	—	2	1	no	—
451	C₂×D₄	—	2	1	no	—
452	C₂×D₄	—	2	1	no	—
453	C₂×D₄	—	4	1	no	—
454	C₂×D₄	—	4	1	no	—
455	C₂×D₄	—	4	1	no	—
456	C₂×D₄	—	4	1	no	—
457	C₂×D₄	C₂×C₄×D₄₃	1	2	yes	—
458	C₂²×C₄	—	2	1	no	—
459	C₂²×C₄	—	2	1	no	—
460	C₂²×C₄	—	2	2	no	—
461	C₂²×C₄	—	2	1	no	—
462	C₂²×C₄	—	2	2	no	—
463	C₂²×C₄	—	2	2	no	—
464	C₂²×C₄	—	2	2	no	—
465	C₂²×C₄	—	4	4	no	—
466	C₂²×C₄	—	4	1	no	—
467	C₂²×C₄	—	4	1	no	—
468	C₂²×C₄	—	4	1	no	—
469	C₂²×C₄	—	4	1	no	—
470	C₂²×C₄	—	172	1	no	—
471	C₂²×C₄	C₂×C₄×D₄₃	1	1	yes	characteristic
472	C₂²×C₄	C₂×C₄×D₄₃	1	1	yes	characteristic
473	C₂²×C₄	#10621898	1	1	yes	characteristic
474	C₂²×C₄	#10621898	1	1	yes	characteristic
475	C₂²×C₄	D₄×D₄₃	1	1	yes	characteristic
476	C₂²×C₄	D₄×D₄₃	1	1	yes	characteristic
477	C₂²×C₄	#10621900	1	1	yes	characteristic
478	C₂²×C₄	#10621900	1	1	yes	characteristic
479	C₂²×C₄	#10621900	1	1	yes	characteristic
480	C₂²×C₄	#10621900	1	1	yes	characteristic
481	C₂²×C₄	#10621900	1	1	yes	characteristic
482	C₂²×C₄	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
483	C₂²×C₄	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
484	C₂²×C₄	C₂³×D₄₃	1	1	yes	characteristic
485	M₁₆	—	2	2	no	—
486	M₁₆	—	2	2	no	—
487	M₁₆	—	4	1	no	—
488	M₁₆	—	4	1	no	—
489	M₁₆	—	43	4	no	—
490	M₁₆	—	43	4	no	—
491	M₁₆	—	43	4	no	—
492	M₁₆	—	86	2	no	—
493	M₁₆	—	86	2	no	—
494	M₁₆	—	86	2	no	—
495	M₁₆	—	86	2	no	—
496	M₁₆	—	86	2	no	—
497	M₁₆	—	86	2	no	—
498	M₁₆	—	86	2	no	—
499	M₁₆	—	86	2	no	—
500	M₁₆	—	86	2	no	—
501	C₂×C₈	—	2	2	no	—
502	C₂×C₈	—	4	1	no	—
503	C₂×C₈	—	4	1	no	—
504	C₂×C₈	—	86	2	no	—
505	C₂×C₈	—	86	2	no	—
506	C₂×C₈	—	86	2	no	—
507	C₂×C₈	—	86	2	no	—
508	C₂×C₈	—	86	2	no	—
509	C₂×C₈	—	86	2	no	—
510	C₂×C₈	—	86	2	no	—
511	C₂×C₈	—	86	2	no	—
512	C₂×C₈	—	86	2	no	—
513	C₄⋊C₄	—	86	2	no	—
514	C₄⋊C₄	—	172	1	no	—
515	C₂²⋊C₄	—	86	2	no	—
516	C₂²⋊C₄	—	172	1	no	—
517	C₄²	—	2	1	no	—
518	C₄²	—	2	2	no	—
519	C₄²	—	2	1	no	—
520	C₄²	—	2	2	no	—
521	C₄²	—	86	2	no	—
522	C₄²	—	172	1	no	—
523	C₄²	C₂×C₂²⋊D₄₃	1	2	yes	—
524	C₄²	C₂×C₂²⋊D₄₃	1	2	yes	—
525	C₂³	—	2	2	no	—
526	C₂³	—	4	2	no	—
527	C₂³	—	4	1	no	—
528	C₂³	—	4	1	no	—
529	C₂³	—	8	2	no	—
530	C₂³	#13063281	1	1	yes	characteristic
531	C₂³	#13063281	1	1	yes	characteristic
532	C₂³	#13063306	1	1	yes	characteristic
533	C₂³	#13063306	1	1	yes	characteristic
534	C₂³	#13063311	1	1	yes	characteristic
535	C₂³	#13063311	1	1	yes	characteristic
536	C₂³	C₂×#10621900	1	1	yes	characteristic
537	Q₈	—	2	2	no	—
538	Q₈	—	2	2	no	—
539	Q₈	—	4	1	no	—
540	Q₈	—	4	1	no	—
541	D₄	—	2	2	no	—
542	D₄	—	2	2	no	—
543	D₄	—	4	2	no	—
544	D₄	—	4	2	no	—
545	D₄	—	4	2	no	—
546	D₄	—	4	2	no	—
547	D₄	—	4	1	no	—
548	D₄	—	4	1	no	—
549	C₂×C₄	—	2	4	no	—
550	C₂×C₄	—	2	2	no	—
551	C₂×C₄	—	2	2	no	—
552	C₂×C₄	—	2	2	no	—
553	C₂×C₄	—	4	4	no	—
554	C₂×C₄	—	4	4	no	—
555	C₂×C₄	—	4	2	no	—
556	C₂×C₄	—	4	1	no	—
557	C₂×C₄	—	4	1	no	—
558	C₂×C₄	—	4	2	no	—
559	C₂×C₄	—	4	2	no	—
560	C₂×C₄	—	4	2	no	—
561	C₂×C₄	—	4	2	no	—
562	C₂×C₄	—	344	2	no	—
563	C₂×C₄	—	172	2	no	—
564	C₂×C₄	#13063281	1	1	yes	characteristic
565	C₂×C₄	#13063281	1	1	yes	characteristic
566	C₂×C₄	(C₂²⋊D₄₃)⋊C₄	1	1	yes	characteristic
567	C₂×C₄	(C₂²⋊D₄₃)⋊C₄	1	1	yes	characteristic
568	C₂×C₄	(C₂²⋊D₄₃)⋊C₄	1	1	yes	characteristic
569	C₂×C₄	(C₂²⋊D₄₃)⋊C₄	1	1	yes	characteristic
570	C₂×C₄	C₄×C₂²⋊D₄₃	1	1	yes	characteristic
571	C₂×C₄	C₄×C₂²⋊D₄₃	1	1	yes	characteristic
572	C₂×C₄	C₄×C₂²⋊D₄₃	1	1	yes	characteristic
573	C₂×C₄	C₄×C₂²⋊D₄₃	1	1	yes	characteristic
574	C₂×C₄	#13063296	1	1	yes	characteristic
575	C₂×C₄	#13063296	1	1	yes	characteristic
576	C₂×C₄	#13063296	1	1	yes	characteristic
577	C₂×C₄	#13063296	1	1	yes	characteristic
578	C₂×C₄	#13063306	1	1	yes	characteristic
579	C₂×C₄	#13063306	1	1	yes	characteristic
580	C₂×C₄	#13063311	1	1	yes	characteristic
581	C₂×C₄	#13063311	1	1	yes	characteristic
582	C₂×C₄	#13063318	1	1	yes	characteristic
583	C₂×C₄	#13063318	1	1	yes	characteristic
584	C₂×C₄	#13063318	1	1	yes	characteristic
585	C₂×C₄	#13063318	1	1	yes	characteristic
586	C₂×C₄	C₂²×C₄×D₄₃	1	1	yes	characteristic
587	C₂×C₄	C₂×D₄×D₄₃	1	1	yes	characteristic
588	C₂×C₄	C₂²×C₂²⋊D₄₃	1	1	yes	characteristic
589	C₂×C₄	C₂×#10621900	1	1	yes	characteristic
590	C₂×C₄	C₂×#10621900	1	1	yes	characteristic
591	C₂×C₄	C₂×#10621898	1	1	yes	characteristic
592	C₈	—	4	2	no	—
593	C₈	—	86	4	no	—
594	C₈	—	86	4	no	—
595	C₈	—	86	4	no	—
596	C₂²	—	2	2	no	—
597	C₂²	—	2	2	no	—
598	C₂²	—	2	2	no	—
599	C₂²	—	4	1	no	—
600	C₂²	—	4	1	no	—
601	C₂²	—	4	1	no	—
602	C₂²	—	4	1	no	—
603	C₂²	—	4	2	no	—
604	C₂²	—	8	2	no	—
605	C₂²	—	8	2	no	—
606	C₂²	—	8	2	no	—
607	C₂²	#14582787	1	1	yes	characteristic
608	C₂²	#14582787	1	1	yes	characteristic
609	C₂²	#14582787	1	1	yes	characteristic
610	C₂²	#14582787	1	1	yes	characteristic
611	C₂²	C₂×#13063281	1	1	yes	characteristic
612	C₂²	C₂×#13063306	1	1	yes	characteristic
613	C₂²	C₂×#13063311	1	1	yes	characteristic
614	C₄	—	2	4	no	—
615	C₄	—	4	2	no	—
616	C₄	—	4	2	no	—
617	C₄	—	344	2	no	—
618	C₄	#14582787	1	1	yes	characteristic
619	C₄	#14582787	1	1	yes	characteristic
620	C₄	#14582787	1	1	yes	characteristic
621	C₄	#14582787	1	1	yes	characteristic
622	C₄	C₂×(C₂²⋊D₄₃)⋊C₄	1	1	yes	characteristic
623	C₄	C₂×C₄×C₂²⋊D₄₃	1	1	yes	characteristic
624	C₄	C₂×#13063296	1	1	yes	characteristic
625	C₄	C₂×#13063318	1	1	yes	characteristic
626	C₂	—	2	1	no	—
627	C₂	—	2	1	no	—
628	C₂	—	2	1	no	—
629	C₂	—	2	1	no	—
630	C₂	—	2	1	no	—
631	C₂	—	2	1	no	—
632	C₂	—	8	2	no	—
633	C₂	#19135261	1	2	yes	direct product factor
634	C₂	C₂×#14582787	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	#13063296
commutator	C₂×C₄×C₄₃	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₄₃
Fitting	C₂²×#104×C₄₃	C₂
socle	C₂²×C₄₃	#388
prime radical	C₂²×#41×C₄₃	C₂²
cosocle	C₂²×C₄×C₄₃	C₂⁴
hypercenter	C₂²×#104	D₄₃
hypocenter	C₄₃	C₂×#1932
LCS	G ▷ C₂×C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂×C₄ ◁ C₂³×C₄ ◁ C₂²×#104

Complements

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

N	H ≅ G/N	type
1. C₂×#14582947	C₂	semidirect
4. C₂×C₄×#10621877	C₂	semidirect
5. #19135261	C₂	direct (N × H)
6. C₂×#14582670	C₂	semidirect
7. C₂×#14582659	C₂	semidirect
14. #14582947	C₂²	semidirect
19. #14582883	C₄	semidirect
21. C₂×#13063244	C₄	semidirect
22. C₂×#13063242	C₄	semidirect
24. C₄×#10621877	C₂²	semidirect
27. #14582670	C₂²	semidirect
28. #14582659	C₂²	semidirect
66. #13063244	C₂×C₄	semidirect
67. #13063242	C₂×C₄	semidirect
324. C₂×C₄₃	#1932	semidirect
353. C₄₃	C₂×#1932	semidirect
633. C₂	#19135261	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×#14582947	2
C₂×#14582916	2
C₂×#14582883	2
C₂×C₄×#10621877	2
#19135261	2
C₂×#14582670	2
C₂×#14582659	2
C₂²×#104×C₄₃	2
C₂×#1932	43

Subgroups — C2×#19135261 #25099175

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#19135261 #25099175