Subgroups — C₂×#19136344 #25249558

Order 11008.

1154 conjugacy classes of subgroups.

The subgroup lattice has 492 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#13063265	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×#13063261	C₂	1	1	yes	maximal, characteristic, complemented
3	#19136344	C₂	1	8	yes	maximal, direct product factor
4	C₂×#14582715	C₂	1	2	yes	maximal, complemented
5	C₂×#14582712	C₂	1	2	yes	maximal, complemented
6	C₂²×#135×C₄₃	C₂	1	1	yes	maximal, characteristic
7	C₂²×#10621877	—	2	1	no	—
8	C₂×#13063265	—	2	1	no	—
9	C₂×#13063265	—	2	2	no	—
10	C₂×#13063265	C₂²	1	2	yes	—
11	C₂×#13063265	C₂²	1	4	yes	complemented
12	C₂²×C₄₃⋊C₁₆	—	2	1	no	—
13	C₂×#13063261	—	2	1	no	—
14	C₂×#13063261	—	2	2	no	—
15	C₂×#13063261	C₂²	1	2	yes	—
16	C₂×#13063261	C₂²	1	4	yes	complemented
17	#14582715	C₂²	1	8	yes	complemented
18	#14582712	C₂²	1	8	yes	complemented
19	C₂²×#41×C₄₃	—	2	1	no	—
20	C₂×#135×C₄₃	—	2	2	no	—
21	C₂×#135×C₄₃	—	2	1	no	—
22	C₂×#135×C₄₃	—	2	1	no	—
23	C₂×#135×C₄₃	—	2	2	no	—
24	C₂×#135×C₄₃	C₄	1	2	yes	—
25	C₂×#135×C₄₃	C₄	1	4	yes	—
26	C₂×#135×C₄₃	C₄	1	2	yes	—
27	C₂×#135×C₄₃	C₂²	1	4	yes	—
28	C₂²×Q₁₆×C₄₃	C₂²	1	1	yes	characteristic
29	C₂²×SD₁₆×C₄₃	—	2	1	no	—
30	C₂²×D₈×C₄₃	C₂²	1	1	yes	characteristic
31	C₂³×C₈×C₄₃	C₂²	1	1	yes	characteristic
32	C₂×#10621877	—	2	2	no	—
33	C₂×#10621877	—	2	4	no	—
34	C₂×#10621877	—	4	1	no	—
35	C₂×#10621877	—	4	2	no	—
36	C₂²×C₄₃⋊C₈	—	4	1	no	—
37	#13063265	—	2	2	no	—
38	#13063265	—	2	4	no	—
39	#13063265	C₂³	1	4	yes	—
40	C₂×C₄₃⋊C₁₆	—	2	2	no	—
41	C₂×C₄₃⋊C₁₆	—	2	4	no	—
42	#13063261	—	2	2	no	—
43	#13063261	—	2	4	no	—
44	#13063261	C₂³	1	4	yes	—
45	C₂×#41×C₄₃	—	2	2	no	—
46	C₂×#41×C₄₃	—	2	4	no	—
47	C₂×#41×C₄₃	—	2	2	no	—
48	C₂×#41×C₄₃	—	2	4	no	—
49	C₂×#41×C₄₃	—	4	1	no	—
50	C₂×#41×C₄₃	—	4	1	no	—
51	C₂×#41×C₄₃	—	4	2	no	—
52	C₂×#41×C₄₃	—	4	2	no	—
53	C₂²×Q₈×C₄₃	—	2	1	no	—
54	C₂²×D₄×C₄₃	—	2	1	no	—
55	C₂²×D₄×C₄₃	—	4	1	no	—
56	C₂³×C₄×C₄₃	—	4	1	no	—
57	C₂³×C₄×C₄₃	D₄	1	1	yes	characteristic
58	#135×C₄₃	—	2	4	no	—
59	#135×C₄₃	—	2	4	no	—
60	#135×C₄₃	—	2	4	no	—
61	#135×C₄₃	—	2	4	no	—
62	#135×C₄₃	—	2	4	no	—
63	#135×C₄₃	—	2	4	no	—
64	#135×C₄₃	C₂×C₄	1	8	yes	—
65	#135×C₄₃	C₂×C₄	1	8	yes	—
66	C₂×Q₁₆×C₄₃	—	2	1	no	—
67	C₂×Q₁₆×C₄₃	—	2	1	no	—
68	C₂×Q₁₆×C₄₃	—	2	1	no	—
69	C₂×Q₁₆×C₄₃	C₂×C₄	1	2	yes	—
70	C₂×Q₁₆×C₄₃	C₂×C₄	1	2	yes	—
71	C₂×Q₁₆×C₄₃	C₂³	1	2	yes	—
72	C₂×SD₁₆×C₄₃	—	2	2	no	—
73	C₂×SD₁₆×C₄₃	—	2	4	no	—
74	C₂×SD₁₆×C₄₃	—	2	2	no	—
75	C₂×SD₁₆×C₄₃	—	2	4	no	—
76	C₂×D₈×C₄₃	—	2	1	no	—
77	C₂×D₈×C₄₃	—	2	1	no	—
78	C₂×D₈×C₄₃	—	2	1	no	—
79	C₂×D₈×C₄₃	C₂×C₄	1	2	yes	—
80	C₂×D₈×C₄₃	C₂×C₄	1	2	yes	—
81	C₂×D₈×C₄₃	C₂³	1	2	yes	—
82	C₂²×C₈×C₄₃	C₂×C₄	1	1	yes	characteristic
83	C₂²×C₈×C₄₃	C₂×C₄	1	2	yes	—
84	C₂²×C₈×C₄₃	C₂×C₄	1	1	yes	characteristic
85	C₂²×C₈×C₄₃	D₄	1	1	yes	characteristic
86	C₂²×C₈×C₄₃	D₄	1	2	yes	—
87	C₂²×C₈×C₄₃	D₄	1	1	yes	characteristic
88	C₂²×C₈×C₄₃	D₄	1	1	yes	characteristic
89	C₂²×C₈×C₄₃	D₄	1	2	yes	—
90	C₂²×C₈×C₄₃	C₂³	1	1	yes	characteristic
91	C₂²×C₈×C₄₃	C₂³	1	2	yes	—
92	C₂⁴×C₄₃	—	4	1	no	—
93	C₂⁴×C₄₃	SD₁₆	1	1	yes	characteristic
94	#41×C₄₃	—	2	8	no	—
95	#41×C₄₃	—	2	8	no	—
96	#41×C₄₃	—	4	4	no	—
97	#41×C₄₃	—	4	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	2	no	—
104	C₂×Q₈×C₄₃	—	2	2	no	—
105	C₂×Q₈×C₄₃	—	4	1	no	—
106	C₂×Q₈×C₄₃	—	4	1	no	—
107	C₂×Q₈×C₄₃	—	4	1	no	—
108	C₂×D₄×C₄₃	—	2	2	no	—
109	C₂×D₄×C₄₃	—	2	2	no	—
110	C₂×D₄×C₄₃	—	2	2	no	—
111	C₂×D₄×C₄₃	—	4	1	no	—
112	C₂×D₄×C₄₃	—	4	1	no	—
113	C₂×D₄×C₄₃	—	4	1	no	—
114	C₂×D₄×C₄₃	—	4	2	no	—
115	C₂×D₄×C₄₃	—	4	2	no	—
116	C₂×D₄×C₄₃	—	4	4	no	—
117	C₂×D₄×C₄₃	—	4	4	no	—
118	C₂²×C₄×C₄₃	—	4	4	no	—
119	C₂²×C₄×C₄₃	—	4	2	no	—
120	C₂²×C₄×C₄₃	—	4	2	no	—
121	C₂²×C₄×C₄₃	—	4	4	no	—
122	C₂²×C₄×C₄₃	—	4	1	no	—
123	C₂²×C₄×C₄₃	C₂²⋊C₄	1	1	yes	characteristic
124	C₂²×C₄×C₄₃	C₂²⋊C₄	1	1	yes	characteristic
125	C₂²×C₄×C₄₃	C₂²⋊C₄	1	2	yes	—
126	C₂²×C₄×C₄₃	D₈	1	1	yes	characteristic
127	C₂²×C₄×C₄₃	D₈	1	1	yes	characteristic
128	C₂²×C₄×C₄₃	D₈	1	2	yes	—
129	C₂²×C₄×C₄₃	SD₁₆	1	1	yes	characteristic
130	C₂²×C₄×C₄₃	SD₁₆	1	2	yes	—
131	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
132	C₂²×C₄×C₄₃	C₂×D₄	1	2	yes	—
133	Q₁₆×C₄₃	—	2	2	no	—
134	Q₁₆×C₄₃	—	2	2	no	—
135	Q₁₆×C₄₃	—	2	2	no	—
136	Q₁₆×C₄₃	C₂²×C₄	1	4	yes	—
137	SD₁₆×C₄₃	—	2	8	no	—
138	SD₁₆×C₄₃	—	2	8	no	—
139	D₈×C₄₃	—	2	2	no	—
140	D₈×C₄₃	—	2	2	no	—
141	D₈×C₄₃	—	2	2	no	—
142	D₈×C₄₃	C₂²×C₄	1	4	yes	—
143	C₂×C₈×C₄₃	C₂²⋊C₄	1	1	yes	characteristic
144	C₂×C₈×C₄₃	C₂²⋊C₄	1	2	yes	—
145	C₂×C₈×C₄₃	C₂²⋊C₄	1	1	yes	characteristic
146	C₂×C₈×C₄₃	C₂²⋊C₄	1	2	yes	—
147	C₂×C₈×C₄₃	C₂²⋊C₄	1	2	yes	—
148	C₂×C₈×C₄₃	C₂²⋊C₄	1	2	yes	—
149	C₂×C₈×C₄₃	C₂²⋊C₄	1	2	yes	—
150	C₂×C₈×C₄₃	C₂²×C₄	1	1	yes	characteristic
151	C₂×C₈×C₄₃	C₂²×C₄	1	1	yes	characteristic
152	C₂×C₈×C₄₃	C₂²×C₄	1	2	yes	—
153	C₂×C₈×C₄₃	C₂²×C₄	1	2	yes	—
154	C₂×C₈×C₄₃	C₂×D₄	1	1	yes	characteristic
155	C₂×C₈×C₄₃	C₂×D₄	1	2	yes	—
156	C₂×C₈×C₄₃	C₂×D₄	1	1	yes	characteristic
157	C₂×C₈×C₄₃	C₂×D₄	1	1	yes	characteristic
158	C₂×C₈×C₄₃	C₂×D₄	1	2	yes	—
159	C₂×C₈×C₄₃	C₂×D₄	1	2	yes	—
160	C₂×C₈×C₄₃	C₂⁴	1	1	yes	characteristic
161	#10621877	—	2	4	no	—
162	#10621877	—	4	2	no	—
163	#10621877	—	4	4	no	—
164	C₂×C₄₃⋊C₈	—	4	2	no	—
165	C₂×C₄₃⋊C₈	—	4	4	no	—
166	C₄₃⋊C₁₆	—	2	4	no	—
167	C₂³×C₄₃	—	4	2	no	—
168	C₂³×C₄₃	—	4	2	no	—
169	C₂³×C₄₃	—	4	2	no	—
170	C₂³×C₄₃	—	4	2	no	—
171	C₂³×C₄₃	—	8	4	no	—
172	C₂³×C₄₃	#102	1	1	yes	characteristic
173	C₂³×C₄₃	#102	1	1	yes	characteristic
174	C₂³×C₄₃	#102	1	2	yes	—
175	C₂³×C₄₃	C₂×SD₁₆	1	1	yes	characteristic
176	C₂³×C₄₃	C₂×SD₁₆	1	2	yes	—
177	Q₈×C₄₃	—	2	4	no	—
178	Q₈×C₄₃	—	4	2	no	—
179	Q₈×C₄₃	—	4	2	no	—
180	Q₈×C₄₃	—	4	2	no	—
181	D₄×C₄₃	—	2	4	no	—
182	D₄×C₄₃	—	4	8	no	—
183	D₄×C₄₃	—	4	8	no	—
184	D₄×C₄₃	—	4	2	no	—
185	D₄×C₄₃	—	4	2	no	—
186	D₄×C₄₃	—	4	2	no	—
187	C₂×C₄×C₄₃	—	4	2	no	—
188	C₂×C₄×C₄₃	—	4	2	no	—
189	C₂×C₄×C₄₃	—	4	2	no	—
190	C₂×C₄×C₄₃	—	4	8	no	—
191	C₂×C₄×C₄₃	—	4	8	no	—
192	C₂×C₄×C₄₃	#102	1	2	yes	—
193	C₂×C₄×C₄₃	#102	1	1	yes	characteristic
194	C₂×C₄×C₄₃	#102	1	2	yes	—
195	C₂×C₄×C₄₃	#102	1	2	yes	—
196	C₂×C₄×C₄₃	#102	1	2	yes	—
197	C₂×C₄×C₄₃	#102	1	2	yes	—
198	C₂×C₄×C₄₃	#102	1	1	yes	characteristic
199	C₂×C₄×C₄₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
200	C₂×C₄×C₄₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
201	C₂×C₄×C₄₃	C₂×C₂²⋊C₄	1	2	yes	—
202	C₂×C₄×C₄₃	C₂×C₂²⋊C₄	1	2	yes	—
203	C₂×C₄×C₄₃	C₂×D₈	1	1	yes	characteristic
204	C₂×C₄×C₄₃	C₂×D₈	1	2	yes	—
205	C₂×C₄×C₄₃	C₂×D₈	1	1	yes	characteristic
206	C₂×C₄×C₄₃	C₂×D₈	1	2	yes	—
207	C₂×C₄×C₄₃	C₂×SD₁₆	1	2	yes	—
208	C₂×C₄×C₄₃	C₂×SD₁₆	1	1	yes	characteristic
209	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
210	C₈×C₄₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
211	C₈×C₄₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
212	C₈×C₄₃	C₂×C₂²⋊C₄	1	2	yes	—
213	C₈×C₄₃	C₂×C₂²⋊C₄	1	2	yes	—
214	C₈×C₄₃	C₂³×C₄	1	1	yes	characteristic
215	C₈×C₄₃	C₂²×D₄	1	1	yes	characteristic
216	C₄₃⋊C₈	—	4	4	no	—
217	C₂×#2148	—	43	1	no	maximal, Sylow
218	C₂²×C₄₃	—	2	2	no	—
219	C₂²×C₄₃	—	2	2	no	—
220	C₂²×C₄₃	—	2	2	no	—
221	C₂²×C₄₃	—	4	2	no	—
222	C₂²×C₄₃	—	4	2	no	—
223	C₂²×C₄₃	—	4	4	no	—
224	C₂²×C₄₃	—	8	4	no	—
225	C₂²×C₄₃	—	8	4	no	—
226	C₂²×C₄₃	—	8	4	no	—
227	C₂²×C₄₃	C₂×#102	1	1	yes	characteristic
228	C₂²×C₄₃	C₂×#102	1	2	yes	—
229	C₂²×C₄₃	C₂×#102	1	2	yes	—
230	C₂²×C₄₃	C₂×#102	1	1	yes	characteristic
231	C₂²×C₄₃	C₂²×SD₁₆	1	1	yes	characteristic
232	C₄×C₄₃	—	4	4	no	—
233	C₄×C₄₃	C₂×#102	1	2	yes	—
234	C₄×C₄₃	C₂×#102	1	2	yes	—
235	C₄×C₄₃	C₂×#102	1	1	yes	characteristic
236	C₄×C₄₃	C₂×#102	1	1	yes	characteristic
237	C₄×C₄₃	C₂²×C₂²⋊C₄	1	1	yes	characteristic
238	C₄×C₄₃	C₂²×D₈	1	1	yes	characteristic
239	C₂²×#135	D₄₃	1	1	yes	characteristic
240	C₂²×M₃₂	—	43	1	no	—
241	C₂²×#108	—	43	1	no	—
242	#2148	—	43	8	no	—
243	C₂×#362	—	43	2	no	—
244	C₂×#361	—	43	2	no	—
245	C₂×C₄₃	—	2	1	no	—
246	C₂×C₄₃	—	2	1	no	—
247	C₂×C₄₃	—	2	2	no	—
248	C₂×C₄₃	—	2	2	no	—
249	C₂×C₄₃	—	8	4	no	—
250	C₂×C₄₃	#2148	1	2	yes	complemented
251	C₂×C₄₃	C₂²×#102	1	1	yes	characteristic
252	C₂²×#41	—	2	1	no	—
253	C₂×#135	—	2	2	no	—
254	C₂×#135	—	2	1	no	—
255	C₂×#135	—	2	1	no	—
256	C₂×#135	—	2	2	no	—
257	C₂×#135	Dic₄₃	1	2	yes	—
258	C₂×#135	Dic₄₃	1	4	yes	—
259	C₂×#135	Dic₄₃	1	2	yes	—
260	C₂×#135	C₂×D₄₃	1	4	yes	—
261	C₂²×Q₁₆	C₂×D₄₃	1	1	yes	characteristic
262	C₂²×SD₁₆	—	2	1	no	—
263	C₂²×D₈	C₂×D₄₃	1	1	yes	characteristic
264	C₂²×M₁₆	—	86	1	no	—
265	C₂³×C₈	C₂×D₄₃	1	1	yes	characteristic
266	C₂×M₃₂	—	43	2	no	—
267	C₂×M₃₂	—	43	4	no	—
268	C₂×M₃₂	—	86	1	no	—
269	C₂×M₃₂	—	86	2	no	—
270	C₂²×C₁₆	—	86	1	no	—
271	C₂×#108	—	43	2	no	—
272	C₂×#108	—	43	4	no	—
273	C₂×#108	—	86	1	no	—
274	C₂×#108	—	86	2	no	—
275	#362	—	43	8	no	—
276	#361	—	43	8	no	—
277	C₄₃	C₂×#2148	1	1	yes	characteristic, complemented, Sylow
278	C₂×#41	—	2	2	no	—
279	C₂×#41	—	2	4	no	—
280	C₂×#41	—	2	2	no	—
281	C₂×#41	—	2	4	no	—
282	C₂×#41	—	4	1	no	—
283	C₂×#41	—	4	2	no	—
284	C₂×#41	—	4	1	no	—
285	C₂×#41	—	4	2	no	—
286	C₂²×Q₈	—	2	1	no	—
287	C₂²×D₄	—	2	1	no	—
288	C₂²×D₄	—	4	1	no	—
289	C₂³×C₄	—	4	1	no	—
290	C₂³×C₄	C₂²⋊D₄₃	1	1	yes	characteristic
291	#135	—	2	4	no	—
292	#135	—	2	4	no	—
293	#135	—	2	4	no	—
294	#135	—	2	4	no	—
295	#135	—	2	4	no	—
296	#135	—	2	4	no	—
297	#135	C₂×Dic₄₃	1	8	yes	—
298	#135	C₂×Dic₄₃	1	8	yes	—
299	C₂×Q₁₆	—	2	1	no	—
300	C₂×Q₁₆	—	2	1	no	—
301	C₂×Q₁₆	—	2	1	no	—
302	C₂×Q₁₆	C₂×Dic₄₃	1	2	yes	—
303	C₂×Q₁₆	C₂×Dic₄₃	1	2	yes	—
304	C₂×Q₁₆	C₂²×D₄₃	1	2	yes	—
305	C₂×SD₁₆	—	2	2	no	—
306	C₂×SD₁₆	—	2	4	no	—
307	C₂×SD₁₆	—	2	2	no	—
308	C₂×SD₁₆	—	2	4	no	—
309	C₂×D₈	—	2	1	no	—
310	C₂×D₈	—	2	1	no	—
311	C₂×D₈	—	2	1	no	—
312	C₂×D₈	C₂×Dic₄₃	1	2	yes	—
313	C₂×D₈	C₂×Dic₄₃	1	2	yes	—
314	C₂×D₈	C₂²×D₄₃	1	2	yes	—
315	C₂×M₁₆	—	86	2	no	—
316	C₂×M₁₆	—	86	4	no	—
317	C₂×M₁₆	—	172	1	no	—
318	C₂×M₁₆	—	172	2	no	—
319	C₂²×C₈	—	172	1	no	—
320	C₂²×C₈	C₂×Dic₄₃	1	1	yes	characteristic
321	C₂²×C₈	C₂×Dic₄₃	1	2	yes	—
322	C₂²×C₈	C₂×Dic₄₃	1	1	yes	characteristic
323	C₂²×C₈	C₂²⋊D₄₃	1	1	yes	characteristic
324	C₂²×C₈	C₂²⋊D₄₃	1	2	yes	—
325	C₂²×C₈	C₂²⋊D₄₃	1	1	yes	characteristic
326	C₂²×C₈	C₂²⋊D₄₃	1	1	yes	characteristic
327	C₂²×C₈	C₂²⋊D₄₃	1	2	yes	—
328	C₂²×C₈	C₂²×D₄₃	1	1	yes	characteristic
329	C₂²×C₈	C₂²×D₄₃	1	2	yes	—
330	M₃₂	—	43	4	no	—
331	M₃₂	—	86	2	no	—
332	M₃₂	—	86	4	no	—
333	C₂×C₁₆	—	86	2	no	—
334	C₂×C₁₆	—	86	4	no	—
335	#108	—	43	4	no	—
336	#108	—	86	2	no	—
337	#108	—	86	4	no	—
338	C₂⁴	—	4	1	no	—
339	C₂⁴	#10621883	1	1	yes	characteristic
340	#41	—	2	8	no	—
341	#41	—	2	8	no	—
342	#41	—	4	4	no	—
343	#41	—	4	4	no	—
344	#41	—	4	4	no	—
345	#41	—	4	4	no	—
346	#41	—	4	4	no	—
347	#41	—	4	4	no	—
348	C₂×Q₈	—	2	2	no	—
349	C₂×Q₈	—	2	2	no	—
350	C₂×Q₈	—	2	2	no	—
351	C₂×Q₈	—	4	1	no	—
352	C₂×Q₈	—	4	1	no	—
353	C₂×Q₈	—	4	1	no	—
354	C₂×D₄	—	2	2	no	—
355	C₂×D₄	—	2	2	no	—
356	C₂×D₄	—	2	2	no	—
357	C₂×D₄	—	4	2	no	—
358	C₂×D₄	—	4	2	no	—
359	C₂×D₄	—	4	4	no	—
360	C₂×D₄	—	4	4	no	—
361	C₂×D₄	—	4	1	no	—
362	C₂×D₄	—	4	1	no	—
363	C₂×D₄	—	4	1	no	—
364	C₂²×C₄	—	4	1	no	—
365	C₂²×C₄	—	4	4	no	—
366	C₂²×C₄	—	4	2	no	—
367	C₂²×C₄	—	4	2	no	—
368	C₂²×C₄	—	4	4	no	—
369	C₂²×C₄	#10621882	1	1	yes	characteristic
370	C₂²×C₄	#10621882	1	2	yes	—
371	C₂²×C₄	#10621882	1	1	yes	characteristic
372	C₂²×C₄	#10621883	1	2	yes	—
373	C₂²×C₄	#10621883	1	1	yes	characteristic
374	C₂²×C₄	C₂²⋊Dic₄₃	1	1	yes	characteristic
375	C₂²×C₄	C₂²⋊Dic₄₃	1	2	yes	—
376	C₂²×C₄	C₂²⋊Dic₄₃	1	1	yes	characteristic
377	C₂²×C₄	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
378	C₂²×C₄	C₂×C₂²⋊D₄₃	1	2	yes	—
379	Q₁₆	—	2	2	no	—
380	Q₁₆	—	2	2	no	—
381	Q₁₆	—	2	2	no	—
382	Q₁₆	C₂²×Dic₄₃	1	4	yes	—
383	SD₁₆	—	2	8	no	—
384	SD₁₆	—	2	8	no	—
385	D₈	—	2	2	no	—
386	D₈	—	2	2	no	—
387	D₈	—	2	2	no	—
388	D₈	C₂²×Dic₄₃	1	4	yes	—
389	M₁₆	—	86	4	no	—
390	M₁₆	—	172	2	no	—
391	M₁₆	—	172	4	no	—
392	C₂×C₈	—	172	2	no	—
393	C₂×C₈	—	172	4	no	—
394	C₂×C₈	C₂²⋊Dic₄₃	1	1	yes	characteristic
395	C₂×C₈	C₂²⋊Dic₄₃	1	2	yes	—
396	C₂×C₈	C₂²⋊Dic₄₃	1	1	yes	characteristic
397	C₂×C₈	C₂²⋊Dic₄₃	1	2	yes	—
398	C₂×C₈	C₂²⋊Dic₄₃	1	2	yes	—
399	C₂×C₈	C₂²⋊Dic₄₃	1	2	yes	—
400	C₂×C₈	C₂²⋊Dic₄₃	1	2	yes	—
401	C₂×C₈	C₂²×Dic₄₃	1	1	yes	characteristic
402	C₂×C₈	C₂²×Dic₄₃	1	1	yes	characteristic
403	C₂×C₈	C₂²×Dic₄₃	1	2	yes	—
404	C₂×C₈	C₂²×Dic₄₃	1	2	yes	—
405	C₂×C₈	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
406	C₂×C₈	C₂×C₂²⋊D₄₃	1	2	yes	—
407	C₂×C₈	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
408	C₂×C₈	C₂×C₂²⋊D₄₃	1	2	yes	—
409	C₂×C₈	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
410	C₂×C₈	C₂×C₂²⋊D₄₃	1	2	yes	—
411	C₂×C₈	C₂³×D₄₃	1	1	yes	characteristic
412	C₁₆	—	86	4	no	—
413	C₂³	—	4	2	no	—
414	C₂³	—	4	2	no	—
415	C₂³	—	4	2	no	—
416	C₂³	—	4	2	no	—
417	C₂³	—	8	4	no	—
418	C₂³	#13063246	1	1	yes	characteristic
419	C₂³	#13063246	1	1	yes	characteristic
420	C₂³	#13063246	1	2	yes	—
421	C₂³	C₂×#10621883	1	1	yes	characteristic
422	C₂³	C₂×#10621883	1	2	yes	—
423	Q₈	—	2	4	no	—
424	Q₈	—	4	2	no	—
425	Q₈	—	4	2	no	—
426	Q₈	—	4	2	no	—
427	D₄	—	2	4	no	—
428	D₄	—	4	8	no	—
429	D₄	—	4	8	no	—
430	D₄	—	4	2	no	—
431	D₄	—	4	2	no	—
432	D₄	—	4	2	no	—
433	C₂×C₄	—	4	2	no	—
434	C₂×C₄	—	4	2	no	—
435	C₂×C₄	—	4	2	no	—
436	C₂×C₄	—	4	8	no	—
437	C₂×C₄	—	4	8	no	—
438	C₂×C₄	#13063246	1	1	yes	characteristic
439	C₂×C₄	#13063246	1	2	yes	—
440	C₂×C₄	#13063246	1	2	yes	—
441	C₂×C₄	#13063246	1	2	yes	—
442	C₂×C₄	#13063246	1	2	yes	—
443	C₂×C₄	#13063246	1	2	yes	—
444	C₂×C₄	#13063246	1	1	yes	characteristic
445	C₂×C₄	C₂×C₂²⋊Dic₄₃	1	1	yes	characteristic
446	C₂×C₄	C₂×C₂²⋊Dic₄₃	1	1	yes	characteristic
447	C₂×C₄	C₂×C₂²⋊Dic₄₃	1	2	yes	—
448	C₂×C₄	C₂×C₂²⋊Dic₄₃	1	2	yes	—
449	C₂×C₄	C₂×#10621882	1	1	yes	characteristic
450	C₂×C₄	C₂×#10621882	1	2	yes	—
451	C₂×C₄	C₂×#10621882	1	1	yes	characteristic
452	C₂×C₄	C₂×#10621882	1	2	yes	—
453	C₂×C₄	C₂×#10621883	1	2	yes	—
454	C₂×C₄	C₂×#10621883	1	1	yes	characteristic
455	C₂×C₄	C₂²×C₂²⋊D₄₃	1	1	yes	characteristic
456	C₈	—	172	4	no	—
457	C₈	C₂×C₂²⋊Dic₄₃	1	1	yes	characteristic
458	C₈	C₂×C₂²⋊Dic₄₃	1	1	yes	characteristic
459	C₈	C₂×C₂²⋊Dic₄₃	1	2	yes	—
460	C₈	C₂×C₂²⋊Dic₄₃	1	2	yes	—
461	C₈	C₂³×Dic₄₃	1	1	yes	characteristic
462	C₈	C₂²×C₂²⋊D₄₃	1	1	yes	characteristic
463	C₂²	—	2	2	no	—
464	C₂²	—	2	2	no	—
465	C₂²	—	2	2	no	—
466	C₂²	—	4	2	no	—
467	C₂²	—	4	2	no	—
468	C₂²	—	4	4	no	—
469	C₂²	—	8	4	no	—
470	C₂²	—	8	4	no	—
471	C₂²	—	8	4	no	—
472	C₂²	C₂×#13063246	1	1	yes	characteristic
473	C₂²	C₂×#13063246	1	2	yes	—
474	C₂²	C₂×#13063246	1	2	yes	—
475	C₂²	C₂×#13063246	1	1	yes	characteristic
476	C₂²	C₂²×#10621883	1	1	yes	characteristic
477	C₄	—	4	4	no	—
478	C₄	C₂×#13063246	1	2	yes	—
479	C₄	C₂×#13063246	1	2	yes	—
480	C₄	C₂×#13063246	1	1	yes	characteristic
481	C₄	C₂×#13063246	1	1	yes	characteristic
482	C₄	C₂²×C₂²⋊Dic₄₃	1	1	yes	characteristic
483	C₄	C₂²×#10621882	1	1	yes	characteristic
484	C₂	—	2	1	no	—
485	C₂	—	2	1	no	—
486	C₂	—	2	2	no	—
487	C₂	—	2	2	no	—
488	C₂	—	8	4	no	—
489	C₂	#19136344	1	2	yes	direct product factor
490	C₂	C₂²×#13063246	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	#13063246
commutator	C₈×C₄₃	C₂³×C₄
Frattini	C₂×C₈	C₂³×D₄₃
Fitting, prime radical	C₂²×#135×C₄₃	C₂
socle	C₂²×C₄₃	C₂×#102
cosocle	C₂×C₈×C₄₃	C₂⁴
hypercenter	C₂²×#135	D₄₃
hypocenter	C₄₃	C₂×#2148
LCS	G ▷ C₈×C₄₃ ▷ C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂×C₄ ◁ C₂³×C₄ ◁ C₂³×C₈ ◁ C₂²×#135

Complements

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

N	H ≅ G/N	type
1. C₂²×#13063265	C₂	semidirect
2. C₂²×#13063261	C₂	semidirect
3. #19136344	C₂	direct (N × H)
4. C₂×#14582715	C₂	semidirect
5. C₂×#14582712	C₂	semidirect
11. C₂×#13063265	C₂²	semidirect
16. C₂×#13063261	C₂²	semidirect
17. #14582715	C₂²	semidirect
18. #14582712	C₂²	semidirect
250. C₂×C₄₃	#2148	semidirect
277. C₄₃	C₂×#2148	semidirect
489. C₂	#19136344	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×#13063265	2
C₂²×#13063261	2
#19136344	2
C₂×#14582715	2
C₂×#14582712	2
C₂²×#135×C₄₃	2
C₂×#2148	43

Subgroups — C2×#19136344 #25249558

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#19136344 #25249558