Subgroups — #25960998

Order 11008.

1882 conjugacy classes of subgroups.

The subgroup lattice has 416 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#14583456	C₂	1	1	yes	maximal, characteristic
2	M₁₆×Dic₈₆	C₂	1	8	yes	maximal, complemented
3	#19143542	C₂	1	8	yes	maximal, complemented
4	#19143535	C₂	1	4	yes	maximal, complemented
5	#19143529	C₂	1	4	yes	maximal, complemented
6	#19143158	C₂	1	2	yes	maximal
7	C₂×#14582923	C₂	1	1	yes	maximal, characteristic
8	#19143013	C₂	1	2	yes	maximal
9	C₂×C₄×M₁₆×C₄₃	C₂	1	1	yes	maximal, characteristic
10	C₂²×#10621877	C₂²	1	2	yes	—
11	#14583456	C₄	1	2	yes	—
12	#14583456	C₄	1	4	yes	—
13	#14583456	C₄	1	2	yes	—
14	#14583456	C₂²	1	2	yes	—
15	#14583456	C₂²	1	2	yes	—
16	#14583456	C₂²	1	4	yes	—
17	C₂×#13063325	C₄	1	2	yes	—
18	C₂×#13063317	C₄	1	2	yes	—
19	C₂×#13063304	C₄	1	4	yes	—
20	C₂×C₄×Dic₈₆	C₂²	1	4	yes	—
21	C₂×#13063284	C₂²	1	2	yes	—
22	#14583029	C₂²	1	16	yes	complemented
23	#14583027	C₂²	1	32	yes	complemented
24	C₈×Dic₈₆	C₂²	1	16	yes	complemented
25	#14582927	C₂²	1	8	yes	—
26	#14582925	C₂²	1	8	yes	—
27	#14582923	C₂²	1	2	yes	—
28	#14582923	C₂²	1	2	yes	—
29	#14582923	C₂²	1	4	yes	—
30	#14582922	C₂²	1	8	yes	—
31	C₂×C₄⋊(C₄₃⋊C₈)	C₂²	1	4	yes	—
32	#14582857	C₂²	1	8	yes	—
33	#14582854	C₂²	1	8	yes	—
34	M₁₆×Dic₄₃	C₂²	1	8	yes	—
35	C₂²×M₁₆×C₄₃	C₂²	1	1	yes	characteristic
36	C₂²×M₁₆×C₄₃	C₂²	1	1	yes	characteristic
37	C₂²×C₄²×C₄₃	C₂²	1	1	yes	characteristic
38	C₄×M₁₆×C₄₃	C₂²	1	4	yes	—
39	C₄×M₁₆×C₄₃	C₂²	1	4	yes	—
40	C₂×#97×C₄₃	C₂²	1	2	yes	—
41	C₂×C₄×C₈×C₄₃	C₂²	1	2	yes	—
42	C₂²×Dic₈₆	C₂×C₄	1	4	yes	—
43	C₂×#10621877	—	2	8	no	—
44	C₂×#10621877	C₂³	1	4	yes	—
45	C₂×#10621877	C₂³	1	4	yes	—
46	C₂²×C₄₃⋊C₈	C₂³	1	4	yes	—
47	#13063325	C₂×C₄	1	4	yes	—
48	#13063325	C₂×C₄	1	4	yes	—
49	#13063325	C₂×C₄	1	4	yes	—
50	#13063325	C₂×C₄	1	4	yes	—
51	#13063317	C₂×C₄	1	4	yes	—
52	#13063317	C₂×C₄	1	4	yes	—
53	#13063317	C₂×C₄	1	8	yes	—
54	#13063304	C₂×C₄	1	8	yes	—
55	#13063304	C₂×C₄	1	8	yes	—
56	#13063304	C₂×C₄	1	8	yes	—
57	#13063304	C₂×C₄	1	8	yes	—
58	C₄×Dic₈₆	C₂×C₄	1	8	yes	—
59	C₄×Dic₈₆	C₂×C₄	1	8	yes	—
60	C₄×Dic₈₆	C₂³	1	8	yes	—
61	C₄×Dic₈₆	C₂³	1	8	yes	—
62	#13063284	C₂×C₄	1	4	yes	—
63	#13063284	C₂×C₄	1	4	yes	—
64	#13063284	C₂³	1	4	yes	—
65	#13063284	C₂³	1	4	yes	—
66	C₂×C₄⋊Dic₄₃	C₂×C₄	1	4	yes	—
67	C₂×C₄⋊Dic₄₃	C₂×C₄	1	4	yes	—
68	C₂×Dic₄₃⋊C₄	C₂×C₄	1	8	yes	—
69	C₂×C₂²⋊Dic₄₃	C₂×C₄	1	4	yes	—
70	C₂×C₄×Dic₄₃	C₂³	1	4	yes	—
71	C₄⋊(C₄₃⋊C₈)	C₂³	1	8	yes	—
72	C₄⋊(C₄₃⋊C₈)	C₂³	1	8	yes	—
73	Dic₄₃⋊C₈	C₂³	1	32	yes	—
74	#13063235	C₂³	1	16	yes	—
75	C₈×Dic₄₃	C₂³	1	16	yes	—
76	C₂³×C₄×C₄₃	C₂×C₄	1	2	yes	—
77	C₂³×C₄×C₄₃	C₂³	1	1	yes	characteristic
78	C₂×M₁₆×C₄₃	—	2	4	no	—
79	C₂×M₁₆×C₄₃	Q₈	1	8	yes	complemented
80	C₂×M₁₆×C₄₃	C₂³	1	2	yes	—
81	C₂×M₁₆×C₄₃	C₂³	1	2	yes	—
82	C₂×M₁₆×C₄₃	C₂³	1	2	yes	—
83	C₂×M₁₆×C₄₃	C₂³	1	2	yes	—
84	C₂²×C₈×C₄₃	C₂³	1	2	yes	—
85	C₂²×C₈×C₄₃	C₂³	1	2	yes	—
86	C₂×C₄²×C₄₃	C₂×C₄	1	1	yes	characteristic
87	C₂×C₄²×C₄₃	C₂×C₄	1	1	yes	characteristic
88	C₂×C₄²×C₄₃	C₂×C₄	1	1	yes	characteristic
89	C₂×C₄²×C₄₃	C₂×C₄	1	2	yes	—
90	C₂×C₄²×C₄₃	C₂×C₄	1	1	yes	characteristic
91	C₂×C₄²×C₄₃	C₂³	1	2	yes	—
92	C₂×C₄²×C₄₃	C₂³	1	2	yes	—
93	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
94	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
95	#97×C₄₃	C₂³	1	8	yes	—
96	C₄×C₈×C₄₃	C₂³	1	8	yes	—
97	C₂⁴×C₄₃	C₂²×C₄	1	1	yes	characteristic
98	C₂²×C₄×C₄₃	—	4	4	no	—
99	C₂²×C₄×C₄₃	C₂²×C₄	1	2	yes	—
100	C₂²×C₄×C₄₃	C₂²×C₄	1	2	yes	—
101	C₂²×C₄×C₄₃	C₂²×C₄	1	2	yes	—
102	C₂²×C₄×C₄₃	C₂²×C₄	1	2	yes	—
103	C₂²×C₄×C₄₃	C₂²×C₄	1	2	yes	—
104	C₂²×C₄×C₄₃	C₂²×C₄	1	2	yes	—
105	C₂²×C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
106	C₂²×C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
107	C₂²×C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
108	C₂²×C₄×C₄₃	C₂×Q₈	1	4	yes	—
109	C₂²×C₄×C₄₃	#41	1	4	yes	—
110	C₂²×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
111	C₂²×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
112	C₂²×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
113	C₂²×Dic₄₃	C₂²×C₄	1	8	yes	—
114	C₂×Dic₈₆	—	4	8	no	—
115	C₂×Dic₈₆	C₂²×C₄	1	8	yes	—
116	C₂×Dic₈₆	C₂²×C₄	1	8	yes	—
117	M₁₆×C₄₃	—	2	4	no	—
118	M₁₆×C₄₃	—	2	4	no	—
119	M₁₆×C₄₃	C₂×Q₈	1	8	yes	—
120	M₁₆×C₄₃	C₂×Q₈	1	8	yes	complemented
121	C₂×C₈×C₄₃	—	2	4	no	—
122	C₂×C₈×C₄₃	C₂×Q₈	1	8	yes	complemented
123	C₂×C₈×C₄₃	C₂⁴	1	4	yes	—
124	C₂×C₈×C₄₃	C₂⁴	1	4	yes	—
125	C₄²×C₄₃	C₂²×C₄	1	2	yes	—
126	C₄²×C₄₃	C₂²×C₄	1	2	yes	—
127	C₄²×C₄₃	C₂²×C₄	1	2	yes	—
128	C₄²×C₄₃	C₂²×C₄	1	1	yes	characteristic
129	C₄²×C₄₃	C₂²×C₄	1	1	yes	characteristic
130	C₄²×C₄₃	C₂²×C₄	1	1	yes	characteristic
131	C₄²×C₄₃	C₂²×C₄	1	2	yes	—
132	C₄²×C₄₃	C₂²×C₄	1	1	yes	characteristic
133	C₄²×C₄₃	C₂⁴	1	2	yes	—
134	C₄²×C₄₃	C₂⁴	1	2	yes	—
135	C₂²⋊Dic₄₃	C₂²×C₄	1	8	yes	—
136	C₂²⋊Dic₄₃	C₂²×C₄	1	8	yes	—
137	C₄⋊Dic₄₃	C₂²×C₄	1	8	yes	—
138	C₄⋊Dic₄₃	C₂²×C₄	1	8	yes	—
139	C₄⋊Dic₄₃	C₂²×C₄	1	8	yes	—
140	C₄⋊Dic₄₃	C₂²×C₄	1	8	yes	—
141	Dic₄₃⋊C₄	C₂²×C₄	1	16	yes	—
142	Dic₄₃⋊C₄	C₂²×C₄	1	16	yes	—
143	C₄×Dic₄₃	C₂²×C₄	1	8	yes	—
144	C₄×Dic₄₃	C₂⁴	1	8	yes	—
145	#10621877	—	2	8	no	—
146	#10621877	—	2	8	no	—
147	C₂×C₄₃⋊C₈	—	2	8	no	—
148	C₂×C₄₃⋊C₈	C₂⁴	1	8	yes	—
149	C₂³×C₄₃	—	4	2	no	—
150	C₂³×C₄₃	C₄×Q₈	1	4	yes	—
151	C₂³×C₄₃	C₂³×C₄	1	1	yes	characteristic
152	C₂³×C₄₃	C₂³×C₄	1	1	yes	characteristic
153	C₂³×C₄₃	C₂³×C₄	1	1	yes	characteristic
154	C₂×C₄×C₄₃	—	2	4	no	—
155	C₂×C₄×C₄₃	—	2	4	no	—
156	C₂×C₄×C₄₃	—	2	4	no	—
157	C₂×C₄×C₄₃	—	4	2	no	—
158	C₂×C₄×C₄₃	—	4	2	no	—
159	C₂×C₄×C₄₃	—	4	2	no	—
160	C₂×C₄×C₄₃	C₄×Q₈	1	4	yes	—
161	C₂×C₄×C₄₃	C₄×Q₈	1	4	yes	—
162	C₂×C₄×C₄₃	C₄×Q₈	1	4	yes	—
163	C₂×C₄×C₄₃	C₂³×C₄	1	2	yes	—
164	C₂×C₄×C₄₃	C₂³×C₄	1	2	yes	—
165	C₂×C₄×C₄₃	C₂³×C₄	1	2	yes	—
166	C₂×C₄×C₄₃	C₂³×C₄	1	1	yes	characteristic
167	C₂×C₄×C₄₃	C₂³×C₄	1	1	yes	characteristic
168	C₂×C₄×C₄₃	C₂³×C₄	1	1	yes	characteristic
169	C₂×C₄×C₄₃	C₂³×C₄	1	2	yes	—
170	C₂×C₄×C₄₃	C₂²×Q₈	1	2	yes	—
171	C₂×C₄×C₄₃	C₂²×Q₈	1	2	yes	—
172	C₂×C₄×C₄₃	C₂²×Q₈	1	2	yes	—
173	C₂×C₄×C₄₃	C₂×#41	1	2	yes	—
174	C₂×C₄×C₄₃	C₂×#41	1	2	yes	—
175	C₂×C₄×C₄₃	C₂×#41	1	2	yes	—
176	C₂×C₄×C₄₃	C₂⁵	1	1	yes	characteristic
177	C₂×Dic₄₃	—	4	8	no	—
178	C₂×Dic₄₃	C₂³×C₄	1	16	yes	—
179	Dic₈₆	—	2	16	no	—
180	Dic₈₆	—	4	8	no	—
181	C₈×C₄₃	—	2	4	no	—
182	C₈×C₄₃	C₂²×Q₈	1	8	yes	—
183	C₄₃⋊C₈	—	2	8	no	—
184	#60192	—	43	1	no	maximal, Sylow
185	C₂²×C₄₃	—	2	2	no	—
186	C₂²×C₄₃	—	2	2	no	—
187	C₂²×C₄₃	—	2	2	no	—
188	C₂²×C₄₃	—	4	4	no	—
189	C₂²×C₄₃	C₂×C₄×Q₈	1	2	yes	—
190	C₂²×C₄₃	C₂×C₄×Q₈	1	2	yes	—
191	C₂²×C₄₃	C₂×C₄×Q₈	1	2	yes	—
192	C₂²×C₄₃	C₂⁴×C₄	1	1	yes	characteristic
193	C₄×C₄₃	—	2	2	no	—
194	C₄×C₄₃	—	2	2	no	—
195	C₄×C₄₃	—	2	2	no	—
196	C₄×C₄₃	C₂×C₄×Q₈	1	2	yes	—
197	C₄×C₄₃	C₂×C₄×Q₈	1	2	yes	—
198	C₄×C₄₃	C₂×C₄×Q₈	1	2	yes	—
199	C₄×C₄₃	#568	1	4	yes	—
200	C₄×C₄₃	C₂³×Q₈	1	1	yes	characteristic
201	C₄×C₄₃	C₂²×#41	1	1	yes	characteristic
202	Dic₄₃	—	2	16	no	—
203	C₂×#533	—	43	1	no	—
204	Q₈×M₁₆	—	43	8	no	—
205	#2962	—	43	8	no	—
206	#2961	—	43	4	no	—
207	#2960	—	43	4	no	—
208	#2905	—	43	2	no	—
209	C₂×#423	—	43	1	no	—
210	#2873	—	43	2	no	—
211	C₂×C₄×M₁₆	D₄₃	1	1	yes	characteristic
212	C₂×C₄₃	—	2	2	no	—
213	C₂×C₄₃	—	2	2	no	—
214	C₂×C₄₃	—	2	2	no	—
215	C₂×C₄₃	C₂²×C₄×Q₈	1	1	yes	characteristic
216	C₂×C₄₃	C₂×#568	1	2	yes	—
217	C₂²×M₁₆	—	43	2	no	—
218	C₂²×M₁₆	C₂×D₄₃	1	1	yes	characteristic
219	C₂²×M₁₆	C₂×D₄₃	1	1	yes	characteristic
220	#533	—	43	2	no	—
221	#533	—	43	2	no	—
222	#533	—	43	4	no	—
223	#533	—	43	2	no	—
224	#533	—	43	4	no	—
225	#533	—	43	2	no	—
226	C₂×C₄⋊Q₈	—	43	2	no	—
227	C₂×#125	—	43	2	no	—
228	C₂×C₂²⋊Q₈	—	43	4	no	—
229	C₂×C₄×Q₈	—	43	4	no	—
230	C₂×#117	—	43	2	no	—
231	C₂²×C₄²	C₂×D₄₃	1	1	yes	characteristic
232	#446	—	43	32	no	—
233	#446	—	43	16	no	—
234	C₈×Q₈	—	43	16	no	—
235	#424	—	43	8	no	—
236	#424	—	43	8	no	—
237	#423	—	43	8	no	—
238	#423	—	43	2	no	—
239	#423	—	43	2	no	—
240	#423	—	43	4	no	—
241	C₂×C₄⋊C₈	—	43	4	no	—
242	#405	—	43	8	no	—
243	#405	—	43	8	no	—
244	C₄×M₁₆	—	43	8	no	—
245	C₄×M₁₆	C₂×D₄₃	1	4	yes	—
246	C₄×M₁₆	C₂×D₄₃	1	4	yes	—
247	C₂×#97	C₂×D₄₃	1	2	yes	—
248	C₂×C₄×C₈	C₂×D₄₃	1	2	yes	—
249	C₄₃	#60192	1	1	yes	characteristic, complemented, Sylow
250	C₂²×Q₈	—	43	4	no	—
251	C₂³×C₄	C₄×D₄₃	1	2	yes	—
252	C₂³×C₄	C₂²×D₄₃	1	1	yes	characteristic
253	C₂×M₁₆	—	2	4	no	—
254	C₂×M₁₆	—	43	4	no	—
255	C₂×M₁₆	—	43	4	no	—
256	C₂×M₁₆	—	86	8	no	—
257	C₂×M₁₆	Dic₈₆	1	8	yes	complemented
258	C₂×M₁₆	C₂²×D₄₃	1	2	yes	—
259	C₂×M₁₆	C₂²×D₄₃	1	2	yes	—
260	C₂×M₁₆	C₂²×D₄₃	1	2	yes	—
261	C₂×M₁₆	C₂²×D₄₃	1	2	yes	—
262	C₂²×C₈	—	43	4	no	—
263	C₂²×C₈	C₂²×D₄₃	1	2	yes	—
264	C₂²×C₈	C₂²×D₄₃	1	2	yes	—
265	C₄⋊Q₈	—	43	4	no	—
266	C₄⋊Q₈	—	43	4	no	—
267	C₄⋊Q₈	—	43	4	no	—
268	C₄⋊Q₈	—	43	4	no	—
269	#125	—	43	4	no	—
270	#125	—	43	4	no	—
271	#125	—	43	8	no	—
272	C₂²⋊Q₈	—	43	8	no	—
273	C₂²⋊Q₈	—	43	8	no	—
274	C₂²⋊Q₈	—	43	8	no	—
275	C₂²⋊Q₈	—	43	8	no	—
276	C₄×Q₈	—	43	8	no	—
277	C₄×Q₈	—	43	8	no	—
278	C₄×Q₈	—	43	8	no	—
279	C₄×Q₈	—	43	8	no	—
280	#117	—	43	4	no	—
281	#117	—	43	4	no	—
282	#117	—	43	4	no	—
283	#117	—	43	4	no	—
284	C₂×C₄⋊C₄	—	43	4	no	—
285	C₂×C₄⋊C₄	—	43	8	no	—
286	C₂×C₄⋊C₄	—	43	4	no	—
287	C₂×C₂²⋊C₄	—	43	4	no	—
288	C₂×C₄²	—	43	4	no	—
289	C₂×C₄²	C₄×D₄₃	1	1	yes	characteristic
290	C₂×C₄²	C₄×D₄₃	1	1	yes	characteristic
291	C₂×C₄²	C₄×D₄₃	1	1	yes	characteristic
292	C₂×C₄²	C₄×D₄₃	1	2	yes	—
293	C₂×C₄²	C₄×D₄₃	1	1	yes	characteristic
294	C₂×C₄²	C₂²×D₄₃	1	2	yes	—
295	C₂×C₄²	C₂²×D₄₃	1	1	yes	characteristic
296	C₂×C₄²	C₂²×D₄₃	1	1	yes	characteristic
297	C₂×C₄²	C₂²×D₄₃	1	2	yes	—
298	C₄⋊C₈	—	43	32	no	—
299	C₄⋊C₈	—	43	8	no	—
300	C₄⋊C₈	—	43	8	no	—
301	#97	—	43	16	no	—
302	#97	C₂²×D₄₃	1	8	yes	—
303	C₄×C₈	—	43	16	no	—
304	C₄×C₈	C₂²×D₄₃	1	8	yes	—
305	C₂⁴	C₂×C₄×D₄₃	1	1	yes	characteristic
306	C₂×Q₈	—	43	8	no	—
307	C₂×Q₈	—	43	8	no	—
308	C₂×Q₈	—	172	8	no	—
309	C₂²×C₄	—	4	4	no	—
310	C₂²×C₄	—	43	8	no	—
311	C₂²×C₄	C₂×Dic₈₆	1	4	yes	—
312	C₂²×C₄	C₂×C₄×D₄₃	1	2	yes	—
313	C₂²×C₄	C₂×C₄×D₄₃	1	2	yes	—
314	C₂²×C₄	C₂×C₄×D₄₃	1	2	yes	—
315	C₂²×C₄	C₂×C₄×D₄₃	1	2	yes	—
316	C₂²×C₄	C₂×C₄×D₄₃	1	2	yes	—
317	C₂²×C₄	C₂×C₄×D₄₃	1	2	yes	—
318	C₂²×C₄	C₂×C₄×D₄₃	1	1	yes	characteristic
319	C₂²×C₄	C₂×C₄×D₄₃	1	1	yes	characteristic
320	C₂²×C₄	C₂×C₄×D₄₃	1	1	yes	characteristic
321	C₂²×C₄	#10621898	1	4	yes	—
322	C₂²×C₄	C₂³×D₄₃	1	1	yes	characteristic
323	C₂²×C₄	C₂³×D₄₃	1	1	yes	characteristic
324	C₂²×C₄	C₂³×D₄₃	1	1	yes	characteristic
325	M₁₆	—	2	4	no	—
326	M₁₆	—	2	4	no	—
327	M₁₆	—	86	8	no	—
328	M₁₆	—	86	8	no	—
329	M₁₆	C₂×Dic₈₆	1	8	yes	—
330	M₁₆	C₂×Dic₈₆	1	8	yes	complemented
331	C₂×C₈	—	2	4	no	—
332	C₂×C₈	—	43	8	no	—
333	C₂×C₈	—	86	8	no	—
334	C₂×C₈	C₂×Dic₈₆	1	8	yes	complemented
335	C₂×C₈	C₂³×D₄₃	1	4	yes	—
336	C₂×C₈	C₂³×D₄₃	1	4	yes	—
337	C₄⋊C₄	—	43	8	no	—
338	C₄⋊C₄	—	43	8	no	—
339	C₄⋊C₄	—	43	16	no	—
340	C₄⋊C₄	—	43	16	no	—
341	C₄⋊C₄	—	43	8	no	—
342	C₄⋊C₄	—	43	8	no	—
343	C₂²⋊C₄	—	43	8	no	—
344	C₂²⋊C₄	—	43	8	no	—
345	C₄²	—	43	8	no	—
346	C₄²	—	43	8	no	—
347	C₄²	C₂×C₄×D₄₃	1	2	yes	—
348	C₄²	C₂×C₄×D₄₃	1	2	yes	—
349	C₄²	C₂×C₄×D₄₃	1	1	yes	characteristic
350	C₄²	C₂×C₄×D₄₃	1	1	yes	characteristic
351	C₄²	C₂×C₄×D₄₃	1	2	yes	—
352	C₄²	C₂×C₄×D₄₃	1	1	yes	characteristic
353	C₄²	C₂×C₄×D₄₃	1	2	yes	—
354	C₄²	C₂×C₄×D₄₃	1	1	yes	characteristic
355	C₄²	C₂³×D₄₃	1	2	yes	—
356	C₄²	C₂³×D₄₃	1	2	yes	—
357	C₂³	—	4	2	no	—
358	C₂³	C₄×Dic₈₆	1	4	yes	—
359	C₂³	C₂²×C₄×D₄₃	1	1	yes	characteristic
360	C₂³	C₂²×C₄×D₄₃	1	1	yes	characteristic
361	C₂³	C₂²×C₄×D₄₃	1	1	yes	characteristic
362	Q₈	—	86	16	no	—
363	Q₈	—	172	8	no	—
364	C₂×C₄	—	2	4	no	—
365	C₂×C₄	—	2	4	no	—
366	C₂×C₄	—	2	4	no	—
367	C₂×C₄	—	4	2	no	—
368	C₂×C₄	—	4	2	no	—
369	C₂×C₄	—	4	2	no	—
370	C₂×C₄	—	43	16	no	—
371	C₂×C₄	—	172	8	no	—
372	C₂×C₄	C₄×Dic₈₆	1	4	yes	—
373	C₂×C₄	C₄×Dic₈₆	1	4	yes	—
374	C₂×C₄	C₄×Dic₈₆	1	4	yes	—
375	C₂×C₄	C₂²×C₄×D₄₃	1	2	yes	—
376	C₂×C₄	C₂²×C₄×D₄₃	1	2	yes	—
377	C₂×C₄	C₂²×C₄×D₄₃	1	2	yes	—
378	C₂×C₄	C₂²×C₄×D₄₃	1	1	yes	characteristic
379	C₂×C₄	C₂²×C₄×D₄₃	1	1	yes	characteristic
380	C₂×C₄	C₂²×C₄×D₄₃	1	1	yes	characteristic
381	C₂×C₄	C₂²×C₄×D₄₃	1	2	yes	—
382	C₂×C₄	C₂²×Dic₈₆	1	2	yes	—
383	C₂×C₄	C₂²×Dic₈₆	1	2	yes	—
384	C₂×C₄	C₂²×Dic₈₆	1	2	yes	—
385	C₂×C₄	C₂×#10621898	1	2	yes	—
386	C₂×C₄	C₂×#10621898	1	2	yes	—
387	C₂×C₄	C₂×#10621898	1	2	yes	—
388	C₂×C₄	C₂⁴×D₄₃	1	1	yes	characteristic
389	C₈	—	2	4	no	—
390	C₈	—	86	8	no	—
391	C₈	C₂²×Dic₈₆	1	8	yes	—
392	C₂²	—	2	2	no	—
393	C₂²	—	2	2	no	—
394	C₂²	—	2	2	no	—
395	C₂²	—	4	4	no	—
396	C₂²	C₂×C₄×Dic₈₆	1	2	yes	—
397	C₂²	C₂×C₄×Dic₈₆	1	2	yes	—
398	C₂²	C₂×C₄×Dic₈₆	1	2	yes	—
399	C₂²	C₂³×C₄×D₄₃	1	1	yes	characteristic
400	C₄	—	2	2	no	—
401	C₄	—	2	2	no	—
402	C₄	—	2	2	no	—
403	C₄	—	86	16	no	—
404	C₄	C₂×C₄×Dic₈₆	1	2	yes	—
405	C₄	C₂×C₄×Dic₈₆	1	2	yes	—
406	C₄	C₂×C₄×Dic₈₆	1	2	yes	—
407	C₄	#14583665	1	4	yes	—
408	C₄	C₂³×Dic₈₆	1	1	yes	characteristic
409	C₄	C₂²×#10621898	1	1	yes	characteristic
410	C₂	—	2	2	no	—
411	C₂	—	2	2	no	—
412	C₂	—	2	2	no	—
413	C₂	C₂²×C₄×Dic₈₆	1	1	yes	characteristic
414	C₂	C₂×#14583665	1	2	yes	—

	subgroup	G/H
center, Frattini	C₂×C₄	C₂⁴×D₄₃
commutator, socle	C₂²×C₄₃	C₂⁴×C₄
Fitting	C₂×C₄×M₁₆×C₄₃	C₂
prime radical	C₂⁴×C₄₃	C₂²×C₄
cosocle	C₂×C₄×C₄₃	C₂⁵
hypercenter	C₂×C₄×M₁₆	D₄₃
hypocenter	C₄₃	#60192
LCS	G ▷ C₂²×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄×M₁₆

Complements

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

N	H ≅ G/N	type
2. M₁₆×Dic₈₆	C₂	semidirect
3. #19143542	C₂	semidirect
4. #19143535	C₂	semidirect
5. #19143529	C₂	semidirect
22. #14583029	C₂²	semidirect
23. #14583027	C₂²	semidirect
24. C₈×Dic₈₆	C₂²	semidirect
79. C₂×M₁₆×C₄₃	Q₈	semidirect
120. M₁₆×C₄₃	C₂×Q₈	semidirect
122. C₂×C₈×C₄₃	C₂×Q₈	semidirect
249. C₄₃	#60192	semidirect
257. C₂×M₁₆	Dic₈₆	semidirect
330. M₁₆	C₂×Dic₈₆	semidirect
334. C₂×C₈	C₂×Dic₈₆	semidirect

Maximal subgroups

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

subgroup	index
C₂×#14583456	2
M₁₆×Dic₈₆	2
#19143542	2
#19143535	2
#19143529	2
#19143158	2
C₂×#14582923	2
#19143013	2
C₂×C₄×M₁₆×C₄₃	2
#60192	43