Subgroups — #25257069

Order 11008.

2422 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	#19137685	C₂	1	4	yes	maximal, complemented
2	#19137655	C₂	1	4	yes	maximal, complemented
3	#19137472	C₂	1	4	yes	maximal
4	Q₈×C₂²⋊Dic₄₃	C₂	1	4	yes	maximal
5	#19137344	C₂	1	4	yes	maximal, complemented
6	#19137213	C₂	1	2	yes	maximal
7	C₄⋊Q₈×Dic₄₃	C₂	1	4	yes	maximal, complemented
8	#19137002	C₂	1	1	yes	maximal, characteristic
9	#19136952	C₂	1	2	yes	maximal
10	C₄×#13063284	C₂	1	1	yes	maximal, characteristic
11	C₂²×C₄⋊Q₈×C₄₃	C₂	1	1	yes	maximal, characteristic
12	C₂×Q₈×Dic₄₃	C₂²	1	8	yes	—
13	C₂×#13063284	C₂²	1	1	yes	characteristic
14	C₂×#13063284	C₂²	1	2	yes	—
15	C₂×#13063284	C₂²	1	1	yes	characteristic
16	#14582806	C₂²	1	16	yes	—
17	#14582806	C₂²	1	8	yes	—
18	#14582798	C₂²	1	8	yes	—
19	#14582798	C₂²	1	8	yes	—
20	#14582798	C₂²	1	8	yes	—
21	#14582785	C₂²	1	16	yes	—
22	#14582769	C₂²	1	2	yes	—
23	#14582765	C₂²	1	2	yes	—
24	#14582759	C₂²	1	2	yes	—
25	#14582759	C₂²	1	8	yes	—
26	#14582759	C₂²	1	2	yes	—
27	C₄⋊C₄×Dic₄₃	C₂²	1	8	yes	—
28	C₄⋊C₄×Dic₄₃	C₂²	1	8	yes	—
29	C₄⋊C₄×Dic₄₃	C₂²	1	8	yes	—
30	C₄×C₄⋊Dic₄₃	C₂²	1	2	yes	—
31	C₄×C₄⋊Dic₄₃	C₂²	1	2	yes	—
32	C₄×C₄⋊Dic₄₃	C₂²	1	2	yes	—
33	C₄×C₄⋊Dic₄₃	C₂²	1	2	yes	—
34	C₄×C₂²⋊Dic₄₃	C₂²	1	2	yes	—
35	C₄×C₂²⋊Dic₄₃	C₂²	1	8	yes	—
36	C₄×C₂²⋊Dic₄₃	C₂²	1	2	yes	—
37	#14582745	C₂²	1	2	yes	—
38	C₄²×Dic₄₃	C₂²	1	2	yes	—
39	C₂³×Q₈×C₄₃	C₂²	1	2	yes	—
40	C₂×C₄⋊Q₈×C₄₃	C₄	1	16	yes	complemented
41	C₂×C₄⋊Q₈×C₄₃	C₂²	1	2	yes	—
42	C₂×C₄⋊Q₈×C₄₃	C₂²	1	2	yes	—
43	C₂×C₄⋊Q₈×C₄₃	C₂²	1	2	yes	—
44	C₂×C₄⋊Q₈×C₄₃	C₂²	1	2	yes	—
45	C₂²×C₄⋊C₄×C₄₃	C₂²	1	2	yes	—
46	C₂²×C₄⋊C₄×C₄₃	C₂²	1	2	yes	—
47	C₂²×C₄²×C₄₃	C₂²	1	1	yes	characteristic
48	Q₈×Dic₄₃	—	4	16	no	—
49	#13063284	—	2	4	no	—
50	#13063284	—	2	8	no	—
51	#13063284	Q₈	1	8	yes	complemented
52	C₂×C₄⋊Dic₄₃	C₂³	1	2	yes	—
53	C₂×C₄⋊Dic₄₃	C₂³	1	4	yes	—
54	C₂×C₄⋊Dic₄₃	C₂³	1	4	yes	—
55	C₂×C₄⋊Dic₄₃	C₂³	1	4	yes	—
56	C₂×C₄⋊Dic₄₃	C₂³	1	16	yes	—
57	C₂×C₄⋊Dic₄₃	C₂³	1	2	yes	—
58	C₂×C₂²⋊Dic₄₃	C₂³	1	2	yes	—
59	C₂×C₂²⋊Dic₄₃	C₂³	1	4	yes	—
60	C₂×C₂²⋊Dic₄₃	C₂³	1	2	yes	—
61	C₂×C₄×Dic₄₃	C₂³	1	2	yes	—
62	C₂×C₄×Dic₄₃	C₂³	1	4	yes	—
63	C₂×C₄×Dic₄₃	C₂³	1	4	yes	—
64	C₂×C₄×Dic₄₃	C₂³	1	4	yes	—
65	C₂×C₄×Dic₄₃	C₂³	1	16	yes	—
66	C₂×C₄×Dic₄₃	C₂³	1	2	yes	—
67	C₄₃⋊#95	C₂³	1	4	yes	—
68	C₄₃⋊#95	C₂³	1	4	yes	—
69	C₄₃⋊#95	C₂³	1	16	yes	—
70	C₄₃⋊#95	C₂³	1	16	yes	—
71	C₄₃⋊#95	C₂³	1	4	yes	—
72	C₄₃⋊#95	C₂³	1	4	yes	—
73	C₂²×Q₈×C₄₃	—	4	8	no	—
74	C₂²×Q₈×C₄₃	C₂×C₄	1	16	yes	—
75	C₂²×Q₈×C₄₃	C₂³	1	4	yes	—
76	C₂²×Q₈×C₄₃	C₂³	1	4	yes	—
77	C₂³×C₄×C₄₃	C₂³	1	1	yes	characteristic
78	C₂³×C₄×C₄₃	C₂³	1	1	yes	characteristic
79	C₂³×C₄×C₄₃	C₂³	1	4	yes	—
80	C₂³×C₄×C₄₃	C₂³	1	1	yes	characteristic
81	C₄⋊Q₈×C₄₃	C₂×C₄	1	16	yes	—
82	C₄⋊Q₈×C₄₃	C₂×C₄	1	16	yes	—
83	C₄⋊Q₈×C₄₃	C₂×C₄	1	16	yes	—
84	C₄⋊Q₈×C₄₃	C₂×C₄	1	16	yes	—
85	C₂×C₄⋊C₄×C₄₃	C₂×C₄	1	16	yes	—
86	C₂×C₄⋊C₄×C₄₃	C₂×C₄	1	16	yes	—
87	C₂×C₄⋊C₄×C₄₃	C₂³	1	4	yes	—
88	C₂×C₄⋊C₄×C₄₃	C₂³	1	4	yes	—
89	C₂×C₄⋊C₄×C₄₃	C₂³	1	4	yes	—
90	C₂×C₄⋊C₄×C₄₃	C₂³	1	4	yes	—
91	C₂×C₄²×C₄₃	C₂×C₄	1	8	yes	—
92	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
93	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
94	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
95	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
96	C₂⁴×C₄₃	C₂⁴	1	1	yes	characteristic
97	C₂×Q₈×C₄₃	—	2	16	no	—
98	C₂×Q₈×C₄₃	—	4	8	no	—
99	C₂×Q₈×C₄₃	—	4	32	no	—
100	C₂×Q₈×C₄₃	C₂²×C₄	1	16	yes	—
101	C₂×Q₈×C₄₃	C₂²×C₄	1	16	yes	—
102	C₂²×C₄×C₄₃	—	2	4	no	—
103	C₂²×C₄×C₄₃	—	2	4	no	—
104	C₂²×C₄×C₄₃	—	4	8	no	—
105	C₂²×C₄×C₄₃	C₂²×C₄	1	4	yes	—
106	C₂²×C₄×C₄₃	C₂²×C₄	1	4	yes	—
107	C₂²×C₄×C₄₃	C₂²×C₄	1	16	yes	—
108	C₂²×C₄×C₄₃	C₂²×C₄	1	4	yes	—
109	C₂²×C₄×C₄₃	C₂×Q₈	1	4	yes	—
110	C₂²×C₄×C₄₃	#41	1	4	yes	—
111	C₂²×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
112	C₂²×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
113	C₂²×C₄×C₄₃	C₂⁴	1	8	yes	—
114	C₂²×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
115	C₂²×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
116	C₂²×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
117	C₂²×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
118	C₂²×Dic₄₃	C₂⁴	1	4	yes	—
119	C₂²×Dic₄₃	C₂⁴	1	8	yes	—
120	C₂²×Dic₄₃	C₂⁴	1	4	yes	—
121	C₄⋊C₄×C₄₃	C₂²×C₄	1	16	yes	—
122	C₄⋊C₄×C₄₃	C₂²×C₄	1	16	yes	—
123	C₄⋊C₄×C₄₃	C₂²×C₄	1	16	yes	—
124	C₄⋊C₄×C₄₃	C₂²×C₄	1	16	yes	—
125	C₄²×C₄₃	C₂²×C₄	1	4	yes	—
126	C₄²×C₄₃	C₂²×C₄	1	4	yes	—
127	C₄²×C₄₃	C₂²×C₄	1	4	yes	—
128	C₄²×C₄₃	C₂²×C₄	1	4	yes	—
129	C₂²⋊Dic₄₃	—	2	4	no	—
130	C₂²⋊Dic₄₃	—	2	8	no	—
131	C₂²⋊Dic₄₃	C₂×Q₈	1	8	yes	—
132	C₄⋊Dic₄₃	—	2	4	no	—
133	C₄⋊Dic₄₃	—	2	8	no	—
134	C₄⋊Dic₄₃	—	2	8	no	—
135	C₄⋊Dic₄₃	—	2	8	no	—
136	C₄⋊Dic₄₃	—	4	16	no	—
137	C₄⋊Dic₄₃	C₂×Q₈	1	8	yes	complemented
138	C₄×Dic₄₃	—	2	8	no	—
139	C₄×Dic₄₃	—	2	4	no	—
140	C₄×Dic₄₃	—	2	8	no	—
141	C₄×Dic₄₃	—	2	8	no	—
142	C₄×Dic₄₃	—	4	16	no	—
143	C₄×Dic₄₃	C₂×Q₈	1	8	yes	complemented
144	C₂³×C₄₃	—	2	2	no	—
145	C₂³×C₄₃	—	2	2	no	—
146	C₂³×C₄₃	C₂³×C₄	1	2	yes	—
147	C₂³×C₄₃	C₂²×Q₈	1	2	yes	—
148	C₂³×C₄₃	C₂×#41	1	2	yes	—
149	C₂³×C₄₃	C₂⁵	1	1	yes	characteristic
150	Q₈×C₄₃	—	2	32	no	—
151	Q₈×C₄₃	—	4	16	no	—
152	C₂×C₄×C₄₃	—	2	16	no	—
153	C₂×C₄×C₄₃	—	2	2	no	—
154	C₂×C₄×C₄₃	—	2	2	no	—
155	C₂×C₄×C₄₃	—	2	8	no	—
156	C₂×C₄×C₄₃	—	2	8	no	—
157	C₂×C₄×C₄₃	—	4	16	no	—
158	C₂×C₄×C₄₃	C₄×Q₈	1	16	yes	complemented
159	C₂×C₄×C₄₃	C₂³×C₄	1	2	yes	—
160	C₂×C₄×C₄₃	C₂³×C₄	1	2	yes	—
161	C₂×C₄×C₄₃	C₂³×C₄	1	16	yes	—
162	C₂×C₄×C₄₃	C₂³×C₄	1	2	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	C₂²×Q₈	1	2	yes	—
167	C₂×C₄×C₄₃	C₂²×Q₈	1	2	yes	—
168	C₂×C₄×C₄₃	C₂×#41	1	2	yes	—
169	C₂×C₄×C₄₃	C₂×#41	1	2	yes	—
170	C₂×C₄×C₄₃	H(5,𝔽₂)	1	4	yes	—
171	C₂×C₄×C₄₃	2₋¹⁺⁴	1	4	yes	—
172	C₂×Dic₄₃	—	2	4	no	—
173	C₂×Dic₄₃	—	2	4	no	—
174	C₂×Dic₄₃	—	2	4	no	—
175	C₂×Dic₄₃	—	2	8	no	—
176	C₂×Dic₄₃	—	2	4	no	—
177	C₂×Dic₄₃	—	2	8	no	—
178	C₂×Dic₄₃	—	2	4	no	—
179	C₂×Dic₄₃	—	2	8	no	—
180	C₂×Dic₄₃	C₂²×Q₈	1	8	yes	—
181	#34216	—	43	1	no	maximal, Sylow
182	C₂²×C₄₃	—	2	2	no	—
183	C₂²×C₄₃	—	2	2	no	—
184	C₂²×C₄₃	—	2	4	no	—
185	C₂²×C₄₃	—	2	4	no	—
186	C₂²×C₄₃	C₂×C₄×Q₈	1	4	yes	—
187	C₂²×C₄₃	C₂⁴×C₄	1	1	yes	characteristic
188	C₂²×C₄₃	C₂³×Q₈	1	1	yes	characteristic
189	C₂²×C₄₃	C₂²×#41	1	1	yes	characteristic
190	C₂²×C₄₃	C₂×H(5,𝔽₂)	1	2	yes	—
191	C₂²×C₄₃	C₂×2₋¹⁺⁴	1	2	yes	—
192	C₄×C₄₃	—	2	2	no	—
193	C₄×C₄₃	—	2	16	no	—
194	C₄×C₄₃	—	2	2	no	—
195	C₄×C₄₃	C₂×C₄×Q₈	1	4	yes	—
196	C₄×C₄₃	C₂×C₄×Q₈	1	4	yes	—
197	C₄×C₄₃	#518	1	4	yes	—
198	C₄×C₄₃	#519	1	4	yes	—
199	Dic₄₃	—	2	8	no	—
200	Dic₄₃	—	4	4	no	—
201	Dic₄₃	—	4	8	no	—
202	C₂²×C₄⋊Q₈	D₄₃	1	1	yes	characteristic
203	#2369	—	43	4	no	—
204	#2365	—	43	4	no	—
205	#2345	—	43	4	no	—
206	Q₈×C₂²⋊C₄	—	43	4	no	—
207	#2331	—	43	4	no	—
208	#2316	—	43	2	no	—
209	C₄×C₄⋊Q₈	—	43	4	no	—
210	#2285	—	43	1	no	—
211	#2274	—	43	2	no	—
212	C₄×#117	—	43	1	no	—
213	C₂×C₄₃	—	2	4	no	—
214	C₂×C₄₃	C₂²×C₄×Q₈	1	1	yes	characteristic
215	C₂×C₄₃	C₂×#518	1	1	yes	characteristic
216	C₂×C₄₃	C₂×#519	1	1	yes	characteristic
217	C₂×C₄₃	#3503	1	2	yes	—
218	C₂×C₄₃	#3511	1	2	yes	—
219	C₂³×Q₈	C₂×D₄₃	1	2	yes	—
220	C₂×C₄⋊Q₈	Dic₄₃	1	16	yes	complemented
221	C₂×C₄⋊Q₈	C₂×D₄₃	1	2	yes	—
222	C₂×C₄⋊Q₈	C₂×D₄₃	1	2	yes	—
223	C₂×C₄⋊Q₈	C₂×D₄₃	1	2	yes	—
224	C₂×C₄⋊Q₈	C₂×D₄₃	1	2	yes	—
225	C₂×C₄×Q₈	—	43	8	no	—
226	C₂×#117	—	43	1	no	—
227	C₂×#117	—	43	1	no	—
228	C₂×#117	—	43	2	no	—
229	C₂²×C₄⋊C₄	C₂×D₄₃	1	2	yes	—
230	C₂²×C₄⋊C₄	C₂×D₄₃	1	2	yes	—
231	C₂²×C₄²	C₂×D₄₃	1	1	yes	characteristic
232	#391	—	43	8	no	—
233	#391	—	43	16	no	—
234	#389	—	43	8	no	—
235	#389	—	43	8	no	—
236	#389	—	43	8	no	—
237	#387	—	43	16	no	—
238	#384	—	43	2	no	—
239	#382	—	43	2	no	—
240	#380	—	43	8	no	—
241	#380	—	43	2	no	—
242	#380	—	43	2	no	—
243	C₄×C₄⋊C₄	—	43	8	no	—
244	C₄×C₄⋊C₄	—	43	8	no	—
245	C₄×C₄⋊C₄	—	43	8	no	—
246	C₄×C₄⋊C₄	—	43	2	no	—
247	C₄×C₄⋊C₄	—	43	2	no	—
248	C₄×C₄⋊C₄	—	43	2	no	—
249	C₄×C₄⋊C₄	—	43	2	no	—
250	C₄×C₂²⋊C₄	—	43	2	no	—
251	C₄×C₂²⋊C₄	—	43	8	no	—
252	C₄×C₂²⋊C₄	—	43	2	no	—
253	#376	—	43	2	no	—
254	C₄³	—	43	2	no	—
255	C₄₃	#34216	1	1	yes	characteristic, complemented, Sylow
256	C₂²×Q₈	—	4	8	no	—
257	C₂²×Q₈	C₂×Dic₄₃	1	16	yes	—
258	C₂²×Q₈	C₂²×D₄₃	1	4	yes	—
259	C₂²×Q₈	C₂²×D₄₃	1	4	yes	—
260	C₂³×C₄	C₂²×D₄₃	1	1	yes	characteristic
261	C₂³×C₄	C₂²×D₄₃	1	1	yes	characteristic
262	C₂³×C₄	C₂²×D₄₃	1	4	yes	—
263	C₂³×C₄	C₂²×D₄₃	1	1	yes	characteristic
264	C₄⋊Q₈	C₂×Dic₄₃	1	16	yes	—
265	C₄⋊Q₈	C₂×Dic₄₃	1	16	yes	—
266	C₄⋊Q₈	C₂×Dic₄₃	1	16	yes	—
267	C₄⋊Q₈	C₂×Dic₄₃	1	16	yes	—
268	C₄×Q₈	—	172	16	no	—
269	#117	—	43	8	no	—
270	#117	—	86	4	no	—
271	#117	—	86	8	no	—
272	C₂×C₄⋊C₄	—	43	2	no	—
273	C₂×C₄⋊C₄	—	43	4	no	—
274	C₂×C₄⋊C₄	—	43	2	no	—
275	C₂×C₄⋊C₄	—	43	4	no	—
276	C₂×C₄⋊C₄	—	43	4	no	—
277	C₂×C₄⋊C₄	—	43	16	no	—
278	C₂×C₄⋊C₄	C₂×Dic₄₃	1	16	yes	—
279	C₂×C₄⋊C₄	C₂×Dic₄₃	1	16	yes	—
280	C₂×C₄⋊C₄	C₂²×D₄₃	1	4	yes	—
281	C₂×C₄⋊C₄	C₂²×D₄₃	1	4	yes	—
282	C₂×C₄⋊C₄	C₂²×D₄₃	1	4	yes	—
283	C₂×C₄⋊C₄	C₂²×D₄₃	1	4	yes	—
284	C₂×C₂²⋊C₄	—	43	2	no	—
285	C₂×C₂²⋊C₄	—	43	2	no	—
286	C₂×C₂²⋊C₄	—	43	4	no	—
287	C₂×C₄²	—	43	2	no	—
288	C₂×C₄²	—	43	2	no	—
289	C₂×C₄²	—	43	4	no	—
290	C₂×C₄²	—	43	4	no	—
291	C₂×C₄²	—	43	4	no	—
292	C₂×C₄²	—	43	16	no	—
293	C₂×C₄²	C₂×Dic₄₃	1	8	yes	—
294	C₂×C₄²	C₂²×D₄₃	1	1	yes	characteristic
295	C₂×C₄²	C₂²×D₄₃	1	1	yes	characteristic
296	C₂×C₄²	C₂²×D₄₃	1	1	yes	characteristic
297	C₂×C₄²	C₂²×D₄₃	1	1	yes	characteristic
298	#95	—	43	4	no	—
299	#95	—	43	4	no	—
300	#95	—	43	16	no	—
301	#95	—	43	4	no	—
302	#95	—	43	4	no	—
303	#95	—	43	16	no	—
304	C₂⁴	C₂³×D₄₃	1	1	yes	characteristic
305	C₂×Q₈	—	2	16	no	—
306	C₂×Q₈	—	4	8	no	—
307	C₂×Q₈	—	4	32	no	—
308	C₂×Q₈	C₂²×Dic₄₃	1	16	yes	—
309	C₂×Q₈	C₂²×Dic₄₃	1	16	yes	—
310	C₂²×C₄	—	2	4	no	—
311	C₂²×C₄	—	2	4	no	—
312	C₂²×C₄	—	4	8	no	—
313	C₂²×C₄	—	43	4	no	—
314	C₂²×C₄	—	43	4	no	—
315	C₂²×C₄	—	43	8	no	—
316	C₂²×C₄	Q₈×D₄₃	1	4	yes	—
317	C₂²×C₄	#10621902	1	4	yes	—
318	C₂²×C₄	C₂²×Dic₄₃	1	4	yes	—
319	C₂²×C₄	C₂²×Dic₄₃	1	4	yes	—
320	C₂²×C₄	C₂²×Dic₄₃	1	16	yes	—
321	C₂²×C₄	C₂²×Dic₄₃	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	8	yes	—
325	C₂²×C₄	C₂³×D₄₃	1	1	yes	characteristic
326	C₂²×C₄	C₂³×D₄₃	1	1	yes	characteristic
327	C₂²×C₄	C₂³×D₄₃	1	1	yes	characteristic
328	C₂²×C₄	C₂³×D₄₃	1	1	yes	characteristic
329	C₄⋊C₄	—	43	8	no	—
330	C₄⋊C₄	—	86	4	no	—
331	C₄⋊C₄	—	86	8	no	—
332	C₄⋊C₄	—	86	8	no	—
333	C₄⋊C₄	—	86	8	no	—
334	C₄⋊C₄	—	172	16	no	—
335	C₄⋊C₄	C₂²×Dic₄₃	1	16	yes	—
336	C₄⋊C₄	C₂²×Dic₄₃	1	16	yes	—
337	C₄⋊C₄	C₂²×Dic₄₃	1	16	yes	—
338	C₄⋊C₄	C₂²×Dic₄₃	1	16	yes	—
339	C₂²⋊C₄	—	43	8	no	—
340	C₂²⋊C₄	—	86	4	no	—
341	C₂²⋊C₄	—	86	8	no	—
342	C₄²	—	43	8	no	—
343	C₄²	—	86	8	no	—
344	C₄²	—	86	4	no	—
345	C₄²	—	86	8	no	—
346	C₄²	—	86	8	no	—
347	C₄²	—	172	16	no	—
348	C₄²	C₂²×Dic₄₃	1	4	yes	—
349	C₄²	C₂²×Dic₄₃	1	4	yes	—
350	C₄²	C₂²×Dic₄₃	1	4	yes	—
351	C₄²	C₂²×Dic₄₃	1	4	yes	—
352	C₂³	—	2	2	no	—
353	C₂³	—	2	2	no	—
354	C₂³	C₂³×Dic₄₃	1	2	yes	—
355	C₂³	C₂×Q₈×D₄₃	1	2	yes	—
356	C₂³	C₂×#10621902	1	2	yes	—
357	C₂³	C₂⁴×D₄₃	1	1	yes	characteristic
358	Q₈	—	2	32	no	—
359	Q₈	—	4	16	no	—
360	C₂×C₄	—	2	16	no	—
361	C₂×C₄	—	2	2	no	—
362	C₂×C₄	—	2	2	no	—
363	C₂×C₄	—	2	8	no	—
364	C₂×C₄	—	2	8	no	—
365	C₂×C₄	—	4	16	no	—
366	C₂×C₄	—	43	8	no	—
367	C₂×C₄	—	86	4	no	—
368	C₂×C₄	—	86	4	no	—
369	C₂×C₄	—	86	4	no	—
370	C₂×C₄	—	86	8	no	—
371	C₂×C₄	—	86	4	no	—
372	C₂×C₄	—	86	8	no	—
373	C₂×C₄	—	86	4	no	—
374	C₂×C₄	—	86	8	no	—
375	C₂×C₄	Q₈×Dic₄₃	1	16	yes	complemented
376	C₂×C₄	C₂³×Dic₄₃	1	2	yes	—
377	C₂×C₄	C₂³×Dic₄₃	1	2	yes	—
378	C₂×C₄	C₂³×Dic₄₃	1	16	yes	—
379	C₂×C₄	C₂³×Dic₄₃	1	2	yes	—
380	C₂×C₄	C₂³×Dic₄₃	1	2	yes	—
381	C₂×C₄	C₂³×Dic₄₃	1	2	yes	—
382	C₂×C₄	C₂³×Dic₄₃	1	2	yes	—
383	C₂×C₄	C₂×Q₈×D₄₃	1	2	yes	—
384	C₂×C₄	C₂×Q₈×D₄₃	1	2	yes	—
385	C₂×C₄	C₂×#10621902	1	2	yes	—
386	C₂×C₄	C₂×#10621902	1	2	yes	—
387	C₂×C₄	#13063370	1	4	yes	—
388	C₂×C₄	#13063373	1	4	yes	—
389	C₂²	—	2	2	no	—
390	C₂²	—	2	2	no	—
391	C₂²	—	2	4	no	—
392	C₂²	—	2	4	no	—
393	C₂²	C₂×Q₈×Dic₄₃	1	4	yes	—
394	C₂²	C₂⁴×Dic₄₃	1	1	yes	characteristic
395	C₂²	C₂²×Q₈×D₄₃	1	1	yes	characteristic
396	C₂²	C₂²×#10621902	1	1	yes	characteristic
397	C₂²	C₂×#13063370	1	2	yes	—
398	C₂²	C₂×#13063373	1	2	yes	—
399	C₄	—	2	2	no	—
400	C₄	—	2	16	no	—
401	C₄	—	2	2	no	—
402	C₄	—	86	8	no	—
403	C₄	—	172	4	no	—
404	C₄	—	172	8	no	—
405	C₄	C₂×Q₈×Dic₄₃	1	4	yes	—
406	C₄	C₂×Q₈×Dic₄₃	1	4	yes	—
407	C₄	#14583374	1	4	yes	—
408	C₄	#14583377	1	4	yes	—
409	C₂	—	2	4	no	—
410	C₂	C₂²×Q₈×Dic₄₃	1	1	yes	characteristic
411	C₂	C₂×#14583374	1	1	yes	characteristic
412	C₂	C₂×#14583377	1	1	yes	characteristic
413	C₂	#19148411	1	2	yes	—
414	C₂	#19148508	1	2	yes	—

	subgroup	G/H
center, Frattini	C₂³	C₂⁴×D₄₃
commutator	C₂²×C₄₃	C₂⁴×C₄
Fitting	C₂²×C₄⋊Q₈×C₄₃	C₂
socle, cosocle	C₂³×C₄₃	C₂⁵
prime radical	C₂⁴×C₄₃	C₂⁴
hypercenter	C₂²×C₄⋊Q₈	D₄₃
hypocenter	C₄₃	#34216
LCS	G ▷ C₂²×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂³ ◁ C₂²×C₄⋊Q₈

Complements

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

N	H ≅ G/N	type
1. #19137685	C₂	semidirect
2. #19137655	C₂	semidirect
5. #19137344	C₂	semidirect
7. C₄⋊Q₈×Dic₄₃	C₂	semidirect
40. C₂×C₄⋊Q₈×C₄₃	C₄	semidirect
51. #13063284	Q₈	semidirect
137. C₄⋊Dic₄₃	C₂×Q₈	semidirect
143. C₄×Dic₄₃	C₂×Q₈	semidirect
158. C₂×C₄×C₄₃	C₄×Q₈	semidirect
220. C₂×C₄⋊Q₈	Dic₄₃	semidirect
255. C₄₃	#34216	semidirect
375. C₂×C₄	Q₈×Dic₄₃	semidirect

Maximal subgroups

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

subgroup	index
#19137685	2
#19137655	2
#19137472	2
Q₈×C₂²⋊Dic₄₃	2
#19137344	2
#19137213	2
C₄⋊Q₈×Dic₄₃	2
#19137002	2
#19136952	2
C₄×#13063284	2
C₂²×C₄⋊Q₈×C₄₃	2
#34216	43