Subgroups — C₂×#19143396 #25960651

Order 11008.

2854 conjugacy classes of subgroups.

The subgroup lattice has 394 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#41×Dic₄₃	C₂	1	2	yes	maximal, complemented
2	#19143396	C₂	1	16	yes	maximal, direct product factor
3	C₂×#14583011	C₂	1	2	yes	maximal, complemented
4	C₂×#14583006	C₂	1	2	yes	maximal, complemented
5	C₂×#14583000	C₂	1	4	yes	maximal, complemented
6	C₂×#14582937	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×#14582895	C₂	1	2	yes	maximal, complemented
8	C₂²×#13063235	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂²×#135×C₄₃	C₂	1	1	yes	maximal, characteristic
10	C₂³×C₄₃⋊C₈	C₂²	1	1	yes	characteristic
11	#41×Dic₄₃	—	2	8	no	—
12	#41×Dic₄₃	C₂²	1	16	yes	complemented
13	C₂×Q₈×Dic₄₃	C₂²	1	4	yes	—
14	C₂×D₄×Dic₄₃	—	2	4	no	—
15	C₂×D₄×Dic₄₃	C₂²	1	4	yes	—
16	C₂×#13063284	—	2	2	no	—
17	C₂×#13063284	C₂²	1	2	yes	—
18	C₂²×C₄×Dic₄₃	—	2	2	no	—
19	C₂²×C₄×Dic₄₃	C₂²	1	1	yes	characteristic
20	#14583011	C₂²	1	16	yes	complemented
21	#14583006	C₂²	1	16	yes	complemented
22	#14583000	C₂²	1	32	yes	complemented
23	#14582937	C₂²	1	8	yes	complemented
24	C₂×#13063259	C₂²	1	2	yes	—
25	C₂×#13063257	C₂²	1	2	yes	—
26	#14582895	C₂²	1	16	yes	complemented
27	C₂×#13063249	C₂²	1	4	yes	—
28	C₂×#13063246	C₂²	1	4	yes	—
29	C₂×#13063235	C₂²	1	2	yes	—
30	C₂×#13063235	C₂²	1	2	yes	—
31	C₂×#13063235	C₂²	1	8	yes	complemented
32	C₂²×#41×C₄₃	C₂²	1	2	yes	—
33	C₂×#135×C₄₃	C₄	1	16	yes	complemented
34	C₂×#135×C₄₃	C₂²	1	8	yes	—
35	C₂²×Q₁₆×C₄₃	C₂²	1	1	yes	characteristic
36	C₂²×SD₁₆×C₄₃	C₂²	1	2	yes	—
37	C₂²×D₈×C₄₃	C₂²	1	1	yes	characteristic
38	C₂³×C₈×C₄₃	C₂²	1	1	yes	characteristic
39	C₂³×Dic₄₃	—	2	4	no	—
40	C₂³×Dic₄₃	D₄	1	2	yes	—
41	C₂²×C₄₃⋊C₈	—	2	4	no	—
42	C₂²×C₄₃⋊C₈	C₂³	1	2	yes	—
43	C₂²×C₄₃⋊C₈	C₂³	1	4	yes	—
44	Q₈×Dic₄₃	—	2	8	no	—
45	Q₈×Dic₄₃	C₂³	1	16	yes	—
46	D₄×Dic₄₃	—	2	32	no	—
47	D₄×Dic₄₃	—	2	8	no	—
48	D₄×Dic₄₃	C₂³	1	16	yes	—
49	#13063284	—	2	4	no	—
50	#13063284	—	2	16	no	—
51	#13063284	C₂³	1	8	yes	—
52	C₂×C₄⋊Dic₄₃	—	2	4	no	—
53	C₂×C₄⋊Dic₄₃	C₂³	1	4	yes	—
54	C₂×C₂²⋊Dic₄₃	—	2	2	no	—
55	C₂×C₂²⋊Dic₄₃	—	2	4	no	—
56	C₂×C₄×Dic₄₃	—	2	2	no	—
57	C₂×C₄×Dic₄₃	—	2	4	no	—
58	C₂×C₄×Dic₄₃	—	2	16	no	—
59	C₂×C₄×Dic₄₃	D₄	1	2	yes	—
60	C₂×C₄×Dic₄₃	D₄	1	4	yes	—
61	C₂×C₄×Dic₄₃	C₂³	1	2	yes	—
62	C₂×C₄×Dic₄₃	C₂³	1	4	yes	—
63	#13063259	C₂³	1	8	yes	—
64	#13063257	C₂³	1	8	yes	—
65	#13063249	C₂³	1	16	yes	—
66	#13063246	C₂³	1	16	yes	—
67	#13063235	C₂³	1	8	yes	—
68	#13063235	C₂³	1	8	yes	—
69	C₂×#41×C₄₃	—	2	4	no	—
70	C₂×#41×C₄₃	—	2	8	no	—
71	C₂×#41×C₄₃	C₂×C₄	1	16	yes	complemented
72	C₂×#41×C₄₃	C₂³	1	8	yes	—
73	C₂²×Q₈×C₄₃	C₂³	1	2	yes	—
74	C₂²×D₄×C₄₃	—	2	2	no	—
75	C₂²×D₄×C₄₃	C₂³	1	2	yes	—
76	C₂³×C₄×C₄₃	—	2	2	no	—
77	C₂³×C₄×C₄₃	C₂³	1	1	yes	characteristic
78	#135×C₄₃	C₂×C₄	1	64	yes	complemented
79	C₂×Q₁₆×C₄₃	C₂×C₄	1	8	yes	complemented
80	C₂×Q₁₆×C₄₃	C₂³	1	4	yes	—
81	C₂×SD₁₆×C₄₃	C₂×C₄	1	16	yes	complemented
82	C₂×SD₁₆×C₄₃	C₂³	1	8	yes	—
83	C₂×D₈×C₄₃	C₂×C₄	1	8	yes	complemented
84	C₂×D₈×C₄₃	C₂³	1	4	yes	—
85	C₂²×C₈×C₄₃	C₂×C₄	1	8	yes	complemented
86	C₂²×C₈×C₄₃	C₂³	1	1	yes	characteristic
87	C₂²×C₈×C₄₃	C₂³	1	1	yes	characteristic
88	C₂²×C₈×C₄₃	C₂³	1	4	yes	—
89	C₂⁴×C₄₃	—	2	2	no	—
90	C₂⁴×C₄₃	C₂×D₄	1	1	yes	characteristic
91	#41×C₄₃	—	2	32	no	—
92	#41×C₄₃	—	2	16	no	—
93	#41×C₄₃	C₂²×C₄	1	32	yes	complemented
94	C₂×Q₈×C₄₃	—	2	2	no	—
95	C₂×Q₈×C₄₃	—	2	4	no	—
96	C₂×Q₈×C₄₃	C₂²×C₄	1	8	yes	—
97	C₂×Q₈×C₄₃	C₂⁴	1	4	yes	—
98	C₂×D₄×C₄₃	—	2	2	no	—
99	C₂×D₄×C₄₃	—	2	4	no	—
100	C₂×D₄×C₄₃	—	2	16	no	—
101	C₂×D₄×C₄₃	—	2	8	no	—
102	C₂×D₄×C₄₃	C₂²×C₄	1	8	yes	—
103	C₂×D₄×C₄₃	C₂⁴	1	4	yes	—
104	C₂²×C₄×C₄₃	—	2	16	no	—
105	C₂²×C₄×C₄₃	—	2	8	no	—
106	C₂²×C₄×C₄₃	—	2	2	no	—
107	C₂²×C₄×C₄₃	C₂²×C₄	1	4	yes	—
108	C₂²×C₄×C₄₃	C₂×D₄	1	2	yes	—
109	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
110	C₂²×C₄×C₄₃	#41	1	4	yes	—
111	C₂²×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
112	C₂²×C₄×C₄₃	C₂⁴	1	2	yes	—
113	C₂²×Dic₄₃	—	2	16	no	—
114	C₂²×Dic₄₃	—	2	4	no	—
115	C₂²×Dic₄₃	—	4	4	no	—
116	C₂²×Dic₄₃	—	4	16	no	—
117	C₂²×Dic₄₃	C₂×D₄	1	4	yes	—
118	C₂²×Dic₄₃	C₂×D₄	1	8	yes	—
119	Q₁₆×C₄₃	C₂²×C₄	1	16	yes	complemented
120	SD₁₆×C₄₃	C₂²×C₄	1	32	yes	complemented
121	D₈×C₄₃	C₂²×C₄	1	16	yes	complemented
122	C₂×C₈×C₄₃	C₂²×C₄	1	4	yes	—
123	C₂×C₈×C₄₃	C₂²×C₄	1	4	yes	—
124	C₂×C₈×C₄₃	C₂²×C₄	1	16	yes	complemented
125	C₂×C₈×C₄₃	C₂⁴	1	2	yes	—
126	C₂×C₈×C₄₃	C₂⁴	1	2	yes	—
127	C₂²⋊Dic₄₃	—	2	16	no	—
128	C₂²⋊Dic₄₃	—	2	8	no	—
129	C₄⋊Dic₄₃	—	2	4	no	—
130	C₄⋊Dic₄₃	—	2	16	no	—
131	C₄⋊Dic₄₃	C₂⁴	1	8	yes	—
132	C₄×Dic₄₃	—	2	8	no	—
133	C₄×Dic₄₃	—	2	16	no	—
134	C₄×Dic₄₃	C₂×D₄	1	8	yes	—
135	C₄×Dic₄₃	C₂×D₄	1	4	yes	—
136	C₄×Dic₄₃	C₂⁴	1	4	yes	—
137	C₂×C₄₃⋊C₈	—	2	4	no	—
138	C₂×C₄₃⋊C₈	—	2	8	no	—
139	C₂×C₄₃⋊C₈	C₂⁴	1	4	yes	—
140	C₂³×C₄₃	—	2	4	no	—
141	C₂³×C₄₃	—	2	8	no	—
142	C₂³×C₄₃	—	2	4	no	—
143	C₂³×C₄₃	—	4	8	no	—
144	C₂³×C₄₃	C₄×D₄	1	4	yes	—
145	C₂³×C₄₃	C₂²×D₄	1	2	yes	—
146	C₂³×C₄₃	C₂²×D₄	1	1	yes	characteristic
147	Q₈×C₄₃	—	2	8	no	—
148	Q₈×C₄₃	—	2	4	no	—
149	Q₈×C₄₃	C₂³×C₄	1	8	yes	—
150	D₄×C₄₃	—	2	32	no	—
151	D₄×C₄₃	—	2	8	no	—
152	D₄×C₄₃	—	2	4	no	—
153	D₄×C₄₃	C₂³×C₄	1	8	yes	—
154	C₂×C₄×C₄₃	—	2	8	no	—
155	C₂×C₄×C₄₃	—	2	4	no	—
156	C₂×C₄×C₄₃	—	2	32	no	—
157	C₂×C₄×C₄₃	C₄×D₄	1	4	yes	—
158	C₂×C₄×C₄₃	C₄×D₄	1	8	yes	—
159	C₂×C₄×C₄₃	C₂³×C₄	1	2	yes	—
160	C₂×C₄×C₄₃	C₂³×C₄	1	4	yes	—
161	C₂×C₄×C₄₃	C₂²×D₄	1	2	yes	—
162	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
163	C₂×C₄×C₄₃	C₂×#41	1	2	yes	—
164	C₂×C₄×C₄₃	C₂×#41	1	4	yes	—
165	C₂×C₄×C₄₃	C₂⁵	1	1	yes	characteristic
166	C₂×Dic₄₃	—	2	8	no	—
167	C₂×Dic₄₃	—	2	8	no	—
168	C₂×Dic₄₃	—	4	8	no	—
169	C₂×Dic₄₃	—	4	32	no	—
170	C₂×Dic₄₃	—	4	8	no	—
171	C₂×Dic₄₃	C₂²×D₄	1	8	yes	—
172	C₈×C₄₃	C₂³×C₄	1	4	yes	—
173	C₈×C₄₃	C₂³×C₄	1	4	yes	—
174	C₄₃⋊C₈	—	2	4	no	—
175	C₂×#2943	—	43	1	no	maximal, Sylow
176	C₂²×C₄₃	—	2	8	no	—
177	C₂²×C₄₃	—	2	4	no	—
178	C₂²×C₄₃	—	2	8	no	—
179	C₂²×C₄₃	—	4	16	no	—
180	C₂²×C₄₃	—	4	8	no	—
181	C₂²×C₄₃	C₂×C₄×D₄	1	4	yes	—
182	C₂²×C₄₃	C₂×C₄×D₄	1	2	yes	—
183	C₂²×C₄₃	#575	1	4	yes	—
184	C₂²×C₄₃	C₂³×D₄	1	1	yes	characteristic
185	C₄×C₄₃	—	2	8	no	—
186	C₄×C₄₃	C₂×C₄×D₄	1	4	yes	—
187	C₄×C₄₃	C₂×C₄×D₄	1	2	yes	—
188	C₄×C₄₃	C₂⁴×C₄	1	1	yes	characteristic
189	C₄×C₄₃	C₂²×#41	1	1	yes	characteristic
190	Dic₄₃	—	2	8	no	—
191	Dic₄₃	—	4	8	no	—
192	C₂²×#135	D₄₃	1	1	yes	characteristic
193	C₂×C₄×#41	—	43	2	no	—
194	#2943	—	43	16	no	—
195	C₂×#442	—	43	2	no	—
196	C₂×#441	—	43	2	no	—
197	C₂×#440	—	43	4	no	—
198	C₂×#427	—	43	1	no	—
199	C₂×#416	—	43	2	no	—
200	C₂²×#97	—	43	1	no	—
201	C₂×C₄₃	—	2	4	no	—
202	C₂×C₄₃	—	4	8	no	—
203	C₂×C₄₃	#2943	1	4	yes	complemented
204	C₂×C₄₃	C₂²×C₄×D₄	1	1	yes	characteristic
205	C₂×C₄₃	C₂×#575	1	2	yes	—
206	C₂²×#41	C₂×D₄₃	1	2	yes	—
207	C₂×#135	Dic₄₃	1	16	yes	complemented
208	C₂×#135	C₂×D₄₃	1	8	yes	—
209	C₂²×Q₁₆	C₂×D₄₃	1	1	yes	characteristic
210	C₂²×SD₁₆	C₂×D₄₃	1	2	yes	—
211	C₂²×D₈	C₂×D₄₃	1	1	yes	characteristic
212	C₂³×C₈	—	43	1	no	—
213	C₂³×C₈	C₂×D₄₃	1	1	yes	characteristic
214	C₄×#41	—	43	16	no	—
215	C₄×#41	—	86	8	no	—
216	C₂×C₄×Q₈	—	43	4	no	—
217	C₂×C₄×D₄	—	43	4	no	—
218	C₂×C₄×D₄	—	86	4	no	—
219	C₂×#117	—	43	2	no	—
220	C₂×#117	—	86	2	no	—
221	C₂²×C₄²	—	43	1	no	—
222	C₂²×C₄²	—	86	2	no	—
223	#442	—	43	16	no	—
224	#441	—	43	16	no	—
225	#440	—	43	32	no	—
226	#427	—	43	8	no	—
227	C₂×#107	—	43	2	no	—
228	C₂×#106	—	43	2	no	—
229	#416	—	43	16	no	—
230	C₂×#103	—	43	4	no	—
231	C₂×#102	—	43	4	no	—
232	C₂×#97	—	43	2	no	—
233	C₂×#97	—	43	2	no	—
234	C₂×#97	—	43	8	no	—
235	C₄₃	C₂×#2943	1	1	yes	characteristic, complemented, Sylow
236	C₂×#41	—	2	4	no	—
237	C₂×#41	—	2	8	no	—
238	C₂×#41	C₂×Dic₄₃	1	16	yes	complemented
239	C₂×#41	C₂²×D₄₃	1	8	yes	—
240	C₂²×Q₈	C₂²×D₄₃	1	2	yes	—
241	C₂²×D₄	—	2	2	no	—
242	C₂²×D₄	C₂²×D₄₃	1	2	yes	—
243	C₂³×C₄	—	2	2	no	—
244	C₂³×C₄	—	43	2	no	—
245	C₂³×C₄	—	86	4	no	—
246	C₂³×C₄	C₂²×D₄₃	1	1	yes	characteristic
247	#135	C₂×Dic₄₃	1	64	yes	complemented
248	C₂×Q₁₆	C₂×Dic₄₃	1	8	yes	complemented
249	C₂×Q₁₆	C₂²×D₄₃	1	4	yes	—
250	C₂×SD₁₆	C₂×Dic₄₃	1	16	yes	complemented
251	C₂×SD₁₆	C₂²×D₄₃	1	8	yes	—
252	C₂×D₈	C₂×Dic₄₃	1	8	yes	complemented
253	C₂×D₈	C₂²×D₄₃	1	4	yes	—
254	C₂²×C₈	—	43	2	no	—
255	C₂²×C₈	—	43	4	no	—
256	C₂²×C₈	—	86	4	no	—
257	C₂²×C₈	C₂×Dic₄₃	1	8	yes	complemented
258	C₂²×C₈	C₂²×D₄₃	1	1	yes	characteristic
259	C₂²×C₈	C₂²×D₄₃	1	1	yes	characteristic
260	C₂²×C₈	C₂²×D₄₃	1	4	yes	—
261	C₄×Q₈	—	43	16	no	—
262	C₄×Q₈	—	86	8	no	—
263	C₄×D₄	—	43	16	no	—
264	C₄×D₄	—	86	8	no	—
265	C₄×D₄	—	86	32	no	—
266	#117	—	43	8	no	—
267	#117	—	86	16	no	—
268	#117	—	86	4	no	—
269	C₂×C₄⋊C₄	—	43	4	no	—
270	C₂×C₄⋊C₄	—	86	4	no	—
271	C₂×C₂²⋊C₄	—	86	4	no	—
272	C₂×C₂²⋊C₄	—	86	2	no	—
273	C₂×C₄²	—	43	4	no	—
274	C₂×C₄²	—	43	2	no	—
275	C₂×C₄²	—	43	2	no	—
276	C₂×C₄²	—	43	4	no	—
277	C₂×C₄²	—	86	16	no	—
278	C₂×C₄²	—	86	4	no	—
279	C₂×C₄²	—	86	2	no	—
280	#107	—	43	8	no	—
281	#106	—	43	8	no	—
282	#103	—	43	16	no	—
283	#102	—	43	16	no	—
284	#97	—	43	8	no	—
285	#97	—	43	8	no	—
286	C₂⁴	—	2	2	no	—
287	C₂⁴	D₄×D₄₃	1	1	yes	characteristic
288	#41	—	2	32	no	—
289	#41	—	2	16	no	—
290	#41	C₂²×Dic₄₃	1	32	yes	complemented
291	C₂×Q₈	—	2	2	no	—
292	C₂×Q₈	—	2	4	no	—
293	C₂×Q₈	C₂²×Dic₄₃	1	8	yes	—
294	C₂×Q₈	C₂³×D₄₃	1	4	yes	—
295	C₂×D₄	—	2	16	no	—
296	C₂×D₄	—	2	8	no	—
297	C₂×D₄	—	2	2	no	—
298	C₂×D₄	—	2	4	no	—
299	C₂×D₄	C₂²×Dic₄₃	1	8	yes	—
300	C₂×D₄	C₂³×D₄₃	1	4	yes	—
301	C₂²×C₄	—	2	2	no	—
302	C₂²×C₄	—	2	16	no	—
303	C₂²×C₄	—	2	8	no	—
304	C₂²×C₄	—	43	4	no	—
305	C₂²×C₄	—	43	8	no	—
306	C₂²×C₄	—	86	16	no	—
307	C₂²×C₄	—	86	4	no	—
308	C₂²×C₄	—	172	4	no	—
309	C₂²×C₄	—	172	16	no	—
310	C₂²×C₄	D₄×D₄₃	1	2	yes	—
311	C₂²×C₄	D₄×D₄₃	1	1	yes	characteristic
312	C₂²×C₄	#10621900	1	4	yes	—
313	C₂²×C₄	C₂²×Dic₄₃	1	4	yes	—
314	C₂²×C₄	C₂³×D₄₃	1	1	yes	characteristic
315	C₂²×C₄	C₂³×D₄₃	1	2	yes	—
316	Q₁₆	C₂²×Dic₄₃	1	16	yes	complemented
317	SD₁₆	C₂²×Dic₄₃	1	32	yes	complemented
318	D₈	C₂²×Dic₄₃	1	16	yes	complemented
319	C₂×C₈	—	43	4	no	—
320	C₂×C₈	—	86	4	no	—
321	C₂×C₈	—	86	8	no	—
322	C₂×C₈	C₂²×Dic₄₃	1	4	yes	—
323	C₂×C₈	C₂²×Dic₄₃	1	4	yes	—
324	C₂×C₈	C₂²×Dic₄₃	1	16	yes	complemented
325	C₂×C₈	C₂³×D₄₃	1	2	yes	—
326	C₂×C₈	C₂³×D₄₃	1	2	yes	—
327	C₄⋊C₄	—	43	8	no	—
328	C₄⋊C₄	—	86	16	no	—
329	C₄⋊C₄	—	86	4	no	—
330	C₂²⋊C₄	—	86	16	no	—
331	C₂²⋊C₄	—	86	8	no	—
332	C₄²	—	43	8	no	—
333	C₄²	—	43	4	no	—
334	C₄²	—	43	4	no	—
335	C₄²	—	86	16	no	—
336	C₄²	—	86	8	no	—
337	C₂³	—	2	4	no	—
338	C₂³	—	2	8	no	—
339	C₂³	—	2	4	no	—
340	C₂³	—	4	8	no	—
341	C₂³	D₄×Dic₄₃	1	4	yes	—
342	C₂³	C₂×D₄×D₄₃	1	2	yes	—
343	C₂³	C₂×D₄×D₄₃	1	1	yes	characteristic
344	Q₈	—	2	8	no	—
345	Q₈	—	2	4	no	—
346	Q₈	C₂³×Dic₄₃	1	8	yes	—
347	D₄	—	2	32	no	—
348	D₄	—	2	8	no	—
349	D₄	—	2	4	no	—
350	D₄	C₂³×Dic₄₃	1	8	yes	—
351	C₂×C₄	—	2	8	no	—
352	C₂×C₄	—	2	4	no	—
353	C₂×C₄	—	2	32	no	—
354	C₂×C₄	—	43	8	no	—
355	C₂×C₄	—	86	8	no	—
356	C₂×C₄	—	86	8	no	—
357	C₂×C₄	—	172	8	no	—
358	C₂×C₄	—	172	32	no	—
359	C₂×C₄	—	172	8	no	—
360	C₂×C₄	D₄×Dic₄₃	1	4	yes	—
361	C₂×C₄	D₄×Dic₄₃	1	8	yes	—
362	C₂×C₄	C₂³×Dic₄₃	1	2	yes	—
363	C₂×C₄	C₂³×Dic₄₃	1	4	yes	—
364	C₂×C₄	C₂×D₄×D₄₃	1	2	yes	—
365	C₂×C₄	C₂×D₄×D₄₃	1	1	yes	characteristic
366	C₂×C₄	C₂×#10621900	1	2	yes	—
367	C₂×C₄	C₂×#10621900	1	4	yes	—
368	C₂×C₄	C₂⁴×D₄₃	1	1	yes	characteristic
369	C₈	—	86	4	no	—
370	C₈	C₂³×Dic₄₃	1	4	yes	—
371	C₈	C₂³×Dic₄₃	1	4	yes	—
372	C₂²	—	2	4	no	—
373	C₂²	—	2	8	no	—
374	C₂²	—	2	8	no	—
375	C₂²	—	4	8	no	—
376	C₂²	—	4	16	no	—
377	C₂²	C₂×D₄×Dic₄₃	1	4	yes	—
378	C₂²	C₂×D₄×Dic₄₃	1	2	yes	—
379	C₂²	#14583696	1	4	yes	—
380	C₂²	C₂²×D₄×D₄₃	1	1	yes	characteristic
381	C₄	—	2	8	no	—
382	C₄	—	86	8	no	—
383	C₄	—	172	8	no	—
384	C₄	C₂×D₄×Dic₄₃	1	4	yes	—
385	C₄	C₂×D₄×Dic₄₃	1	2	yes	—
386	C₄	C₂⁴×Dic₄₃	1	1	yes	characteristic
387	C₄	C₂²×#10621900	1	1	yes	characteristic
388	C₂	—	2	4	no	—
389	C₂	—	4	8	no	—
390	C₂	#19143396	1	4	yes	direct product factor
391	C₂	C₂²×D₄×Dic₄₃	1	1	yes	characteristic
392	C₂	C₂×#14583696	1	2	yes	—

	subgroup	G/H
center	C₂²×C₄	D₄×D₄₃
commutator	C₄×C₄₃	C₂⁴×C₄
Frattini	C₂×C₄	C₂⁴×D₄₃
Fitting, prime radical	C₂²×#135×C₄₃	C₂
socle	C₂³×C₄₃	C₂²×D₄
cosocle	C₂×C₄×C₄₃	C₂⁵
hypercenter	C₂²×#135	D₄₃
hypocenter	C₄₃	C₂×#2943
LCS	G ▷ C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂²×C₄ ◁ C₂³×C₄ ◁ C₂²×#135

Complements

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

N	H ≅ G/N	type
1. C₂×#41×Dic₄₃	C₂	semidirect
2. #19143396	C₂	direct (N × H)
3. C₂×#14583011	C₂	semidirect
4. C₂×#14583006	C₂	semidirect
5. C₂×#14583000	C₂	semidirect
6. C₂×#14582937	C₂	semidirect
7. C₂×#14582895	C₂	semidirect
8. C₂²×#13063235	C₂	semidirect
12. #41×Dic₄₃	C₂²	semidirect
20. #14583011	C₂²	semidirect
21. #14583006	C₂²	semidirect
22. #14583000	C₂²	semidirect
23. #14582937	C₂²	semidirect
26. #14582895	C₂²	semidirect
31. C₂×#13063235	C₂²	semidirect
33. C₂×#135×C₄₃	C₄	semidirect
71. C₂×#41×C₄₃	C₂×C₄	semidirect
78. #135×C₄₃	C₂×C₄	semidirect
79. C₂×Q₁₆×C₄₃	C₂×C₄	semidirect
81. C₂×SD₁₆×C₄₃	C₂×C₄	semidirect
83. C₂×D₈×C₄₃	C₂×C₄	semidirect
85. C₂²×C₈×C₄₃	C₂×C₄	semidirect
93. #41×C₄₃	C₂²×C₄	semidirect
119. Q₁₆×C₄₃	C₂²×C₄	semidirect
120. SD₁₆×C₄₃	C₂²×C₄	semidirect
121. D₈×C₄₃	C₂²×C₄	semidirect
124. C₂×C₈×C₄₃	C₂²×C₄	semidirect
203. C₂×C₄₃	#2943	semidirect
207. C₂×#135	Dic₄₃	semidirect
235. C₄₃	C₂×#2943	semidirect
238. C₂×#41	C₂×Dic₄₃	semidirect
247. #135	C₂×Dic₄₃	semidirect
248. C₂×Q₁₆	C₂×Dic₄₃	semidirect
250. C₂×SD₁₆	C₂×Dic₄₃	semidirect
252. C₂×D₈	C₂×Dic₄₃	semidirect
257. C₂²×C₈	C₂×Dic₄₃	semidirect
290. #41	C₂²×Dic₄₃	semidirect
316. Q₁₆	C₂²×Dic₄₃	semidirect
317. SD₁₆	C₂²×Dic₄₃	semidirect
318. D₈	C₂²×Dic₄₃	semidirect
324. C₂×C₈	C₂²×Dic₄₃	semidirect
390. C₂	#19143396	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×#41×Dic₄₃	2
#19143396	2
C₂×#14583011	2
C₂×#14583006	2
C₂×#14583000	2
C₂×#14582937	2
C₂×#14582895	2
C₂²×#13063235	2
C₂²×#135×C₄₃	2
C₂×#2943	43

Subgroups — C2×#19143396 #25960651

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#19143396 #25960651