Subgroups — #19148390

Order 5504.

1100 conjugacy classes of subgroups.

The subgroup lattice has 452 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14583610	C₂	1	2	yes	maximal, complemented
2	#14583609	C₂	1	1	yes	maximal, characteristic, complemented
3	#14583608	C₂	1	2	yes	maximal, complemented
4	#14583607	C₂	1	2	yes	maximal, complemented
5	#14583606	C₂	1	1	yes	maximal, characteristic, complemented
6	#14583603	C₂	1	4	yes	maximal, complemented
7	#14583564	C₂	1	1	yes	maximal, characteristic, complemented
8	Q₈×C₂²⋊D₄₃	C₂	1	2	yes	maximal, complemented
9	#14583526	C₂	1	2	yes	maximal, complemented
10	#14583524	C₂	1	4	yes	maximal, complemented
11	#14583454	C₂	1	1	yes	maximal, characteristic, complemented
12	#14583453	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂×#13063301	C₂	1	2	yes	maximal, complemented
14	C₂²⋊Q₈×D₄₃	C₂	1	2	yes	maximal, complemented
15	#14583371	C₂	1	2	yes	maximal
16	C₄×D₄×D₄₃	C₂	1	1	yes	maximal, characteristic
17	D₄×Q₈×C₄₃	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂×Q₈×D₄₃	C₂²	1	2	yes	complemented
19	C₂×D₄×D₄₃	C₂²	1	1	yes	characteristic
20	C₂²×C₄×D₄₃	C₂²	1	2	yes	—
21	#13063325	C₂²	1	1	yes	characteristic, complemented
22	#13063324	C₂²	1	2	yes	complemented
23	#13063324	C₂²	1	1	yes	characteristic, complemented
24	#13063323	C₂²	1	1	yes	characteristic, complemented
25	#13063323	C₂²	1	4	yes	complemented
26	#13063317	C₂²	1	2	yes	complemented
27	#13063316	C₂²	1	2	yes	complemented
28	#13063316	C₂²	1	2	yes	complemented
29	#13063315	C₂²	1	2	yes	complemented
30	#13063315	C₂²	1	4	yes	complemented
31	#13063305	C₂²	1	1	yes	characteristic
32	#13063305	C₂²	1	2	yes	—
33	#13063305	C₂²	1	4	yes	complemented
34	#13063304	C₂²	1	2	yes	complemented
35	#13063304	C₂²	1	4	yes	complemented
36	#13063303	C₂²	1	4	yes	—
37	#13063303	C₂²	1	2	yes	—
38	#13063303	C₂²	1	4	yes	complemented
39	#13063303	C₂²	1	4	yes	complemented
40	#13063302	C₂²	1	4	yes	complemented
41	#13063302	C₂²	1	4	yes	complemented
42	#13063302	C₂²	1	4	yes	complemented
43	#13063301	C₂²	1	2	yes	—
44	#13063301	C₂²	1	1	yes	characteristic
45	#13063301	C₂²	1	4	yes	—
46	#13063301	C₂²	1	2	yes	complemented
47	#13063301	C₂²	1	4	yes	complemented
48	#13063301	C₂²	1	2	yes	complemented
49	#13063301	C₂²	1	4	yes	complemented
50	Q₈×Dic₄₃	C₂²	1	2	yes	complemented
51	C₄×Dic₈₆	C₂²	1	1	yes	characteristic, complemented
52	C₄×Dic₈₆	C₂²	1	2	yes	complemented
53	#13063290	C₂²	1	2	yes	complemented
54	C₄×D₁₇₂	C₂²	1	1	yes	characteristic
55	C₄×D₁₇₂	C₂²	1	2	yes	—
56	D₄×Dic₄₃	C₂²	1	2	yes	—
57	D₄×Dic₄₃	C₂²	1	1	yes	characteristic
58	#13063287	C₂²	1	2	yes	—
59	#13063287	C₂²	1	1	yes	characteristic
60	C₄×C₂²⋊D₄₃	C₂²	1	4	yes	—
61	C₄×C₂²⋊D₄₃	C₂²	1	2	yes	—
62	(C₂²⋊D₄₃)⋊C₄	C₂²	1	2	yes	—
63	(C₂²⋊D₄₃)⋊C₄	C₂²	1	4	yes	—
64	#13063283	C₂²	1	2	yes	—
65	#13063282	C₂²	1	2	yes	—
66	C₂×C₄⋊Dic₄₃	C₂²	1	2	yes	complemented
67	C₂×Dic₄₃⋊C₄	C₂²	1	4	yes	complemented
68	C₄⋊C₄×D₄₃	C₂²	1	1	yes	characteristic
69	C₄⋊C₄×D₄₃	C₂²	1	4	yes	complemented
70	C₄⋊C₄×D₄₃	C₂²	1	2	yes	complemented
71	C₂×(C₂×D₄₃)⋊C₄	C₂²	1	4	yes	—
72	C₂²⋊C₄×D₄₃	C₂²	1	2	yes	—
73	C₂²⋊C₄×D₄₃	C₂²	1	4	yes	—
74	C₄²×D₄₃	C₂²	1	1	yes	characteristic
75	C₂²×Q₈×C₄₃	C₂²	1	2	yes	complemented
76	C₄⋊Q₈×C₄₃	C₂²	1	1	yes	characteristic, complemented
77	C₄⋊Q₈×C₄₃	C₂²	1	2	yes	complemented
78	C₂²⋊Q₈×C₄₃	C₂²	1	4	yes	complemented
79	C₂²⋊Q₈×C₄₃	C₂²	1	2	yes	complemented
80	C₄×Q₈×C₄₃	C₂²	1	1	yes	characteristic, complemented
81	C₄×D₄×C₄₃	C₂²	1	1	yes	characteristic
82	C₄×D₄×C₄₃	C₂²	1	2	yes	—
83	C₂³×D₄₃	C₂³	1	2	yes	—
84	C₂×Q₈×C₄₃	—	4	4	no	—
85	C₂×Q₈×C₄₃	C₂³	1	1	yes	characteristic
86	C₂×Q₈×C₄₃	C₂³	1	2	yes	—
87	C₂×Q₈×C₄₃	C₂³	1	4	yes	—
88	C₂×D₄×C₄₃	C₂³	1	1	yes	characteristic
89	C₂²×C₄×C₄₃	C₂³	1	2	yes	—
90	C₂²×C₄×C₄₃	C₂³	1	4	yes	—
91	C₂×C₂²⋊D₄₃	C₂³	1	2	yes	—
92	C₂²×Dic₄₃	C₂³	1	4	yes	—
93	C₂²×Dic₄₃	C₂³	1	2	yes	—
94	Q₈×D₄₃	—	4	4	no	—
95	D₄×D₄₃	Q₈	1	8	yes	complemented
96	C₂×D₁₇₂	C₂³	1	1	yes	characteristic
97	C₂×C₄×D₄₃	—	4	4	no	—
98	C₂×C₄×D₄₃	C₂³	1	1	yes	characteristic
99	C₂×C₄×D₄₃	C₂³	1	2	yes	—
100	C₂×C₄×D₄₃	C₂³	1	1	yes	characteristic
101	C₂×C₄×D₄₃	C₂³	1	2	yes	—
102	C₂×C₄×D₄₃	C₂³	1	4	yes	—
103	C₂×C₄×D₄₃	C₂³	1	4	yes	—
104	C₂×C₄×D₄₃	C₂³	1	2	yes	—
105	C₂×C₄×D₄₃	C₂³	1	1	yes	characteristic
106	C₂×Dic₈₆	C₂³	1	1	yes	characteristic
107	C₂×Dic₈₆	C₂³	1	2	yes	—
108	C₂×Dic₈₆	C₂³	1	2	yes	—
109	C₂×Dic₈₆	C₂³	1	4	yes	—
110	C₄⋊C₄×C₄₃	C₂³	1	1	yes	characteristic
111	C₄⋊C₄×C₄₃	C₂³	1	2	yes	—
112	C₄⋊C₄×C₄₃	C₂³	1	1	yes	characteristic
113	C₄⋊C₄×C₄₃	C₂³	1	2	yes	—
114	C₄⋊C₄×C₄₃	C₂³	1	4	yes	—
115	C₄⋊C₄×C₄₃	C₂³	1	2	yes	—
116	C₂²⋊C₄×C₄₃	C₂³	1	4	yes	—
117	C₂²⋊C₄×C₄₃	C₂³	1	2	yes	—
118	C₄²×C₄₃	C₂³	1	1	yes	characteristic
119	C₄²×C₄₃	C₂³	1	2	yes	—
120	C₂²⋊Dic₄₃	C₂³	1	2	yes	—
121	C₂²⋊Dic₄₃	C₂³	1	4	yes	—
122	(C₂×D₄₃)⋊C₄	C₂³	1	2	yes	—
123	(C₂×D₄₃)⋊C₄	C₂³	1	4	yes	—
124	(C₂×D₄₃)⋊C₄	C₂³	1	2	yes	—
125	(C₂×D₄₃)⋊C₄	C₂³	1	2	yes	—
126	(C₂×D₄₃)⋊C₄	C₂³	1	2	yes	—
127	(C₂×D₄₃)⋊C₄	C₂³	1	4	yes	—
128	(C₂×D₄₃)⋊C₄	C₂³	1	4	yes	—
129	C₄⋊Dic₄₃	C₂³	1	1	yes	characteristic
130	C₄⋊Dic₄₃	C₂³	1	2	yes	—
131	C₄⋊Dic₄₃	C₂³	1	2	yes	—
132	C₄⋊Dic₄₃	C₂³	1	1	yes	characteristic
133	C₄⋊Dic₄₃	C₂³	1	4	yes	—
134	C₄⋊Dic₄₃	C₂³	1	2	yes	—
135	C₄⋊Dic₄₃	C₂³	1	4	yes	—
136	Dic₄₃⋊C₄	C₂³	1	2	yes	—
137	Dic₄₃⋊C₄	C₂³	1	4	yes	—
138	Dic₄₃⋊C₄	C₂³	1	4	yes	—
139	Dic₄₃⋊C₄	C₂³	1	4	yes	—
140	Dic₄₃⋊C₄	C₂³	1	2	yes	—
141	Dic₄₃⋊C₄	C₂³	1	4	yes	—
142	Dic₄₃⋊C₄	C₂³	1	4	yes	—
143	Dic₄₃⋊C₄	C₂³	1	2	yes	—
144	Dic₄₃⋊C₄	C₂³	1	2	yes	—
145	Dic₄₃⋊C₄	C₂³	1	2	yes	—
146	Dic₄₃⋊C₄	C₂³	1	2	yes	—
147	C₄×Dic₄₃	C₂³	1	1	yes	characteristic
148	C₄×Dic₄₃	C₂³	1	1	yes	characteristic
149	C₄×Dic₄₃	C₂³	1	1	yes	characteristic
150	C₄×Dic₄₃	C₂³	1	2	yes	—
151	C₄×Dic₄₃	C₂³	1	4	yes	—
152	C₂³×C₄₃	C₂⁴	1	2	yes	—
153	C₂²×D₄₃	—	4	2	no	—
154	C₂²×D₄₃	—	4	2	no	—
155	C₂²×D₄₃	C₂×Q₈	1	8	yes	complemented
156	C₂²×D₄₃	C₂⁴	1	1	yes	characteristic
157	C₂²×D₄₃	C₂⁴	1	2	yes	—
158	Q₈×C₄₃	—	2	4	no	—
159	Q₈×C₄₃	—	2	2	no	—
160	Q₈×C₄₃	—	4	4	no	—
161	D₄×C₄₃	C₂×Q₈	1	4	yes	complemented
162	C₂×C₄×C₄₃	—	2	4	no	—
163	C₂×C₄×C₄₃	—	4	4	no	—
164	C₂×C₄×C₄₃	C₂⁴	1	4	yes	—
165	C₂×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
166	C₂×C₄×C₄₃	C₂⁴	1	2	yes	—
167	C₂×C₄×C₄₃	C₂⁴	1	2	yes	—
168	C₂×C₄×C₄₃	C₂⁴	1	2	yes	—
169	C₂×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
170	C₂×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
171	C₂²⋊D₄₃	C₂×Q₈	1	8	yes	complemented
172	C₂×Dic₄₃	—	4	2	no	—
173	C₂×Dic₄₃	—	4	4	no	—
174	C₂×Dic₄₃	C₂⁴	1	1	yes	characteristic
175	C₂×Dic₄₃	C₂⁴	1	1	yes	characteristic
176	C₂×Dic₄₃	C₂⁴	1	2	yes	—
177	C₂×Dic₄₃	C₂⁴	1	2	yes	—
178	C₂×Dic₄₃	C₂⁴	1	4	yes	—
179	C₂×Dic₄₃	C₂⁴	1	2	yes	—
180	C₂×Dic₄₃	C₂⁴	1	1	yes	characteristic
181	D₁₇₂	C₂×Q₈	1	4	yes	complemented
182	C₄×D₄₃	—	2	2	no	—
183	C₄×D₄₃	—	2	4	no	—
184	C₄×D₄₃	—	4	2	no	—
185	C₄×D₄₃	—	4	2	no	—
186	C₄×D₄₃	—	4	1	no	—
187	C₄×D₄₃	—	4	4	no	—
188	C₄×D₄₃	—	4	4	no	—
189	C₄×D₄₃	C₂×Q₈	1	4	yes	complemented
190	Dic₈₆	—	2	2	no	—
191	Dic₈₆	—	4	2	no	—
192	Dic₈₆	—	4	2	no	—
193	Dic₈₆	—	4	4	no	—
194	C₂²×C₄₃	—	2	2	no	—
195	C₂²×C₄₃	—	2	2	no	—
196	C₂²×C₄₃	C₂²×Q₈	1	4	yes	—
197	C₂²×C₄₃	C₂⁵	1	1	yes	characteristic
198	C₂×D₄₃	—	2	1	no	—
199	C₂×D₄₃	—	2	2	no	—
200	C₂×D₄₃	—	2	1	no	—
201	C₂×D₄₃	—	2	2	no	—
202	C₂×D₄₃	—	4	8	no	—
203	C₂×D₄₃	C₂²×Q₈	1	2	yes	—
204	C₂×D₄₃	C₂²×Q₈	1	4	yes	—
205	C₄×C₄₃	—	2	4	no	—
206	C₄×C₄₃	—	2	2	no	—
207	C₄×C₄₃	—	2	2	no	—
208	C₄×C₄₃	—	2	1	no	—
209	C₄×C₄₃	—	2	2	no	—
210	C₄×C₄₃	C₂²×Q₈	1	2	yes	—
211	C₄×C₄₃	H(5,𝔽₂)	1	2	yes	—
212	Dic₄₃	—	2	2	no	—
213	Dic₄₃	—	2	2	no	—
214	Dic₄₃	—	2	1	no	—
215	Dic₄₃	—	2	1	no	—
216	Dic₄₃	—	2	4	no	—
217	Dic₄₃	—	2	2	no	—
218	Dic₄₃	C₂²×Q₈	1	2	yes	—
219	#3501	—	43	1	no	maximal, Sylow
220	C₂×C₄₃	—	2	4	no	—
221	C₂×C₄₃	C₂³×Q₈	1	1	yes	characteristic
222	C₂×C₄₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
223	C₂×C₄₃	#585	1	1	yes	characteristic
224	D₄₃	—	2	2	no	—
225	D₄₃	—	2	4	no	—
226	#554	—	43	2	no	—
227	#554	—	43	4	no	—
228	#554	—	43	2	no	—
229	#554	—	43	1	no	—
230	#554	—	43	1	no	—
231	#554	—	43	2	no	—
232	D₄×Q₈	—	43	2	no	—
233	D₄×Q₈	—	43	1	no	—
234	D₄×Q₈	D₄₃	1	1	yes	characteristic, complemented
235	#544	—	43	2	no	—
236	#543	—	43	4	no	—
237	#533	—	43	1	no	—
238	#533	—	43	1	no	—
239	C₂×C₂²⋊Q₈	—	43	2	no	—
240	C₂×C₂²⋊Q₈	—	43	2	no	—
241	#518	—	43	2	no	—
242	C₂×C₄×D₄	—	43	1	no	—
243	C₄₃	#3501	1	1	yes	characteristic, complemented, Sylow
244	C₂²×Q₈	—	43	2	no	—
245	C₂²×Q₈	C₂×D₄₃	1	2	yes	complemented
246	C₂²×D₄	—	43	1	no	—
247	C₂³×C₄	—	43	2	no	—
248	C₄⋊Q₈	—	43	1	no	—
249	C₄⋊Q₈	—	43	4	no	—
250	C₄⋊Q₈	—	43	1	no	—
251	C₄⋊Q₈	—	43	2	no	—
252	C₄⋊Q₈	—	43	1	no	—
253	C₄⋊Q₈	C₂×D₄₃	1	1	yes	characteristic, complemented
254	C₄⋊Q₈	C₂×D₄₃	1	2	yes	complemented
255	#125	—	43	2	no	—
256	#125	—	43	2	no	—
257	#125	—	43	4	no	—
258	#125	—	43	2	no	—
259	#125	—	43	2	no	—
260	C₂²⋊Q₈	—	43	2	no	—
261	C₂²⋊Q₈	—	43	1	no	—
262	C₂²⋊Q₈	—	43	4	no	—
263	C₂²⋊Q₈	—	43	2	no	—
264	C₂²⋊Q₈	—	43	2	no	—
265	C₂²⋊Q₈	—	43	4	no	—
266	C₂²⋊Q₈	—	43	4	no	—
267	C₂²⋊Q₈	—	43	2	no	—
268	C₂²⋊Q₈	—	43	4	no	—
269	C₂²⋊Q₈	—	43	1	no	—
270	C₂²⋊Q₈	—	43	4	no	—
271	C₂²⋊Q₈	—	43	2	no	—
272	C₂²⋊Q₈	—	43	2	no	—
273	C₂²⋊Q₈	—	43	4	no	—
274	C₂²⋊Q₈	—	43	4	no	—
275	C₂²⋊Q₈	—	43	4	no	—
276	C₂²⋊Q₈	—	43	4	no	—
277	C₂²⋊Q₈	—	43	4	no	—
278	C₂²⋊Q₈	—	43	4	no	—
279	C₂²⋊Q₈	C₂×D₄₃	1	2	yes	complemented
280	C₂²⋊Q₈	C₂×D₄₃	1	4	yes	complemented
281	C₄×Q₈	—	43	2	no	—
282	C₄×Q₈	—	43	2	no	—
283	C₄×Q₈	—	43	1	no	—
284	C₄×Q₈	—	43	2	no	—
285	C₄×Q₈	C₂×D₄₃	1	1	yes	characteristic, complemented
286	C₄×D₄	—	43	1	no	—
287	C₄×D₄	—	43	2	no	—
288	C₄×D₄	—	43	2	no	—
289	C₄×D₄	—	43	4	no	—
290	C₄×D₄	—	43	1	no	—
291	C₄×D₄	—	43	2	no	—
292	C₄×D₄	—	43	2	no	—
293	C₄×D₄	—	43	4	no	—
294	C₄×D₄	—	43	1	no	—
295	C₄×D₄	—	43	2	no	—
296	C₄×D₄	C₂×D₄₃	1	1	yes	characteristic
297	C₄×D₄	C₂×D₄₃	1	2	yes	—
298	#117	—	43	2	no	—
299	#117	—	43	2	no	—
300	C₂×C₄⋊C₄	—	43	4	no	—
301	C₂×C₄⋊C₄	—	43	2	no	—
302	C₂×C₄⋊C₄	—	43	1	no	—
303	C₂×C₄⋊C₄	—	43	4	no	—
304	C₂×C₄⋊C₄	—	43	2	no	—
305	C₂×C₂²⋊C₄	—	43	4	no	—
306	C₂×C₂²⋊C₄	—	43	2	no	—
307	C₂×C₂²⋊C₄	—	43	4	no	—
308	C₂×C₄²	—	43	1	no	—
309	C₂⁴	—	43	2	no	—
310	C₂×Q₈	—	4	4	no	—
311	C₂×Q₈	—	43	1	no	—
312	C₂×Q₈	—	43	2	no	—
313	C₂×Q₈	—	43	2	no	—
314	C₂×Q₈	—	43	4	no	—
315	C₂×Q₈	—	172	4	no	—
316	C₂×Q₈	C₂²×D₄₃	1	2	yes	—
317	C₂×Q₈	C₂²×D₄₃	1	1	yes	characteristic
318	C₂×Q₈	C₂²×D₄₃	1	4	yes	—
319	C₂×D₄	—	43	2	no	—
320	C₂×D₄	—	43	8	no	—
321	C₂×D₄	—	43	1	no	—
322	C₂×D₄	C₂²×D₄₃	1	1	yes	characteristic
323	C₂²×C₄	—	43	1	no	—
324	C₂²×C₄	—	43	4	no	—
325	C₂²×C₄	—	43	2	no	—
326	C₂²×C₄	—	43	1	no	—
327	C₂²×C₄	—	43	2	no	—
328	C₂²×C₄	—	43	1	no	—
329	C₂²×C₄	—	43	4	no	—
330	C₂²×C₄	—	43	4	no	—
331	C₂²×C₄	—	43	2	no	—
332	C₂²×C₄	—	43	2	no	—
333	C₂²×C₄	—	172	4	no	—
334	C₂²×C₄	C₂²×D₄₃	1	2	yes	—
335	C₂²×C₄	C₂²×D₄₃	1	4	yes	—
336	C₄⋊C₄	—	43	4	no	—
337	C₄⋊C₄	—	43	2	no	—
338	C₄⋊C₄	—	43	2	no	—
339	C₄⋊C₄	—	43	1	no	—
340	C₄⋊C₄	—	43	2	no	—
341	C₄⋊C₄	—	43	2	no	—
342	C₄⋊C₄	—	43	1	no	—
343	C₄⋊C₄	—	43	4	no	—
344	C₄⋊C₄	—	43	4	no	—
345	C₄⋊C₄	—	43	4	no	—
346	C₄⋊C₄	—	43	4	no	—
347	C₄⋊C₄	—	43	4	no	—
348	C₄⋊C₄	—	43	2	no	—
349	C₄⋊C₄	—	43	2	no	—
350	C₄⋊C₄	—	43	2	no	—
351	C₄⋊C₄	—	43	2	no	—
352	C₄⋊C₄	—	43	4	no	—
353	C₄⋊C₄	—	43	2	no	—
354	C₄⋊C₄	C₂²×D₄₃	1	1	yes	characteristic
355	C₄⋊C₄	C₂²×D₄₃	1	1	yes	characteristic
356	C₄⋊C₄	C₂²×D₄₃	1	4	yes	—
357	C₄⋊C₄	C₂²×D₄₃	1	2	yes	—
358	C₄⋊C₄	C₂²×D₄₃	1	2	yes	—
359	C₄⋊C₄	C₂²×D₄₃	1	2	yes	—
360	C₂²⋊C₄	—	43	2	no	—
361	C₂²⋊C₄	—	43	4	no	—
362	C₂²⋊C₄	—	43	4	no	—
363	C₂²⋊C₄	—	43	2	no	—
364	C₂²⋊C₄	—	43	2	no	—
365	C₂²⋊C₄	—	43	2	no	—
366	C₂²⋊C₄	—	43	4	no	—
367	C₂²⋊C₄	—	43	4	no	—
368	C₂²⋊C₄	—	43	2	no	—
369	C₂²⋊C₄	C₂²×D₄₃	1	2	yes	—
370	C₂²⋊C₄	C₂²×D₄₃	1	4	yes	—
371	C₄²	—	43	1	no	—
372	C₄²	—	43	1	no	—
373	C₄²	—	43	1	no	—
374	C₄²	—	43	4	no	—
375	C₄²	—	43	2	no	—
376	C₄²	C₂²×D₄₃	1	1	yes	characteristic
377	C₄²	C₂²×D₄₃	1	2	yes	—
378	C₂³	—	43	1	no	—
379	C₂³	—	43	2	no	—
380	C₂³	—	43	8	no	—
381	C₂³	—	172	2	no	—
382	C₂³	—	172	2	no	—
383	C₂³	C₂³×D₄₃	1	2	yes	—
384	Q₈	—	2	2	no	—
385	Q₈	—	2	4	no	—
386	Q₈	—	4	4	no	—
387	Q₈	—	86	2	no	—
388	Q₈	—	172	4	no	—
389	Q₈	—	172	2	no	—
390	Q₈	—	172	2	no	—
391	D₄	—	43	8	no	—
392	D₄	—	43	4	no	—
393	D₄	Q₈×D₄₃	1	4	yes	complemented
394	C₂×C₄	—	2	4	no	—
395	C₂×C₄	—	4	4	no	—
396	C₂×C₄	—	43	1	no	—
397	C₂×C₄	—	43	4	no	—
398	C₂×C₄	—	43	1	no	—
399	C₂×C₄	—	43	1	no	—
400	C₂×C₄	—	43	4	no	—
401	C₂×C₄	—	43	2	no	—
402	C₂×C₄	—	43	2	no	—
403	C₂×C₄	—	43	2	no	—
404	C₂×C₄	—	86	2	no	—
405	C₂×C₄	—	86	4	no	—
406	C₂×C₄	—	172	2	no	—
407	C₂×C₄	—	172	2	no	—
408	C₂×C₄	—	172	4	no	—
409	C₂×C₄	—	172	4	no	—
410	C₂×C₄	—	172	1	no	—
411	C₂×C₄	—	172	2	no	—
412	C₂×C₄	—	172	4	no	—
413	C₂×C₄	C₂³×D₄₃	1	1	yes	characteristic
414	C₂×C₄	C₂³×D₄₃	1	4	yes	—
415	C₂×C₄	C₂³×D₄₃	1	2	yes	—
416	C₂×C₄	C₂³×D₄₃	1	2	yes	—
417	C₂×C₄	C₂³×D₄₃	1	2	yes	—
418	C₂×C₄	C₂³×D₄₃	1	1	yes	characteristic
419	C₂×C₄	C₂³×D₄₃	1	1	yes	characteristic
420	C₂²	—	2	2	no	—
421	C₂²	—	2	2	no	—
422	C₂²	—	43	2	no	—
423	C₂²	—	43	4	no	—
424	C₂²	—	86	2	no	—
425	C₂²	—	86	1	no	—
426	C₂²	—	86	2	no	—
427	C₂²	—	86	1	no	—
428	C₂²	—	172	8	no	—
429	C₂²	C₂×Q₈×D₄₃	1	4	yes	—
430	C₂²	C₂⁴×D₄₃	1	1	yes	characteristic
431	C₄	—	2	2	no	—
432	C₄	—	2	2	no	—
433	C₄	—	2	4	no	—
434	C₄	—	2	2	no	—
435	C₄	—	2	1	no	—
436	C₄	—	43	2	no	—
437	C₄	—	86	1	no	—
438	C₄	—	86	2	no	—
439	C₄	—	86	2	no	—
440	C₄	—	86	4	no	—
441	C₄	—	86	2	no	—
442	C₄	—	86	1	no	—
443	C₄	C₂×Q₈×D₄₃	1	2	yes	—
444	C₄	#13063370	1	2	yes	—
445	C₂	—	2	4	no	—
446	C₂	—	86	2	no	—
447	C₂	—	86	4	no	—
448	C₂	C₂²×Q₈×D₄₃	1	1	yes	characteristic
449	C₂	C₂×#13063370	1	1	yes	characteristic
450	C₂	#14583736	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₄₃
commutator, socle	C₂²×C₄₃	C₂⁵
Fitting	D₄×Q₈×C₄₃	C₂
hypercenter	D₄×Q₈	D₄₃
hypocenter	C₄₃	#3501
LCS	G ▷ C₂²×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂² ◁ D₄×Q₈

Complements

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

N	H ≅ G/N	type
1. #14583610	C₂	semidirect
2. #14583609	C₂	semidirect
3. #14583608	C₂	semidirect
4. #14583607	C₂	semidirect
5. #14583606	C₂	semidirect
6. #14583603	C₂	semidirect
7. #14583564	C₂	semidirect
8. Q₈×C₂²⋊D₄₃	C₂	semidirect
9. #14583526	C₂	semidirect
10. #14583524	C₂	semidirect
11. #14583454	C₂	semidirect
12. #14583453	C₂	semidirect
13. C₂×#13063301	C₂	semidirect
14. C₂²⋊Q₈×D₄₃	C₂	semidirect
17. D₄×Q₈×C₄₃	C₂	semidirect
18. C₂×Q₈×D₄₃	C₂²	semidirect
21. #13063325	C₂²	semidirect
22. #13063324	C₂²	semidirect
23. #13063324	C₂²	semidirect
24. #13063323	C₂²	semidirect
25. #13063323	C₂²	semidirect
26. #13063317	C₂²	semidirect
27. #13063316	C₂²	semidirect
28. #13063316	C₂²	semidirect
29. #13063315	C₂²	semidirect
30. #13063315	C₂²	semidirect
33. #13063305	C₂²	semidirect
34. #13063304	C₂²	semidirect
35. #13063304	C₂²	semidirect
38. #13063303	C₂²	semidirect
39. #13063303	C₂²	semidirect
40. #13063302	C₂²	semidirect
41. #13063302	C₂²	semidirect
42. #13063302	C₂²	semidirect
46. #13063301	C₂²	semidirect
47. #13063301	C₂²	semidirect
48. #13063301	C₂²	semidirect
49. #13063301	C₂²	semidirect
50. Q₈×Dic₄₃	C₂²	semidirect
51. C₄×Dic₈₆	C₂²	semidirect
52. C₄×Dic₈₆	C₂²	semidirect
53. #13063290	C₂²	semidirect
66. C₂×C₄⋊Dic₄₃	C₂²	semidirect
67. C₂×Dic₄₃⋊C₄	C₂²	semidirect
69. C₄⋊C₄×D₄₃	C₂²	semidirect
70. C₄⋊C₄×D₄₃	C₂²	semidirect
75. C₂²×Q₈×C₄₃	C₂²	semidirect
76. C₄⋊Q₈×C₄₃	C₂²	semidirect
77. C₄⋊Q₈×C₄₃	C₂²	semidirect
78. C₂²⋊Q₈×C₄₃	C₂²	semidirect
79. C₂²⋊Q₈×C₄₃	C₂²	semidirect
80. C₄×Q₈×C₄₃	C₂²	semidirect
95. D₄×D₄₃	Q₈	semidirect
155. C₂²×D₄₃	C₂×Q₈	semidirect
161. D₄×C₄₃	C₂×Q₈	semidirect
171. C₂²⋊D₄₃	C₂×Q₈	semidirect
181. D₁₇₂	C₂×Q₈	semidirect
189. C₄×D₄₃	C₂×Q₈	semidirect
234. D₄×Q₈	D₄₃	semidirect
243. C₄₃	#3501	semidirect
245. C₂²×Q₈	C₂×D₄₃	semidirect
253. C₄⋊Q₈	C₂×D₄₃	semidirect
254. C₄⋊Q₈	C₂×D₄₃	semidirect
279. C₂²⋊Q₈	C₂×D₄₃	semidirect
280. C₂²⋊Q₈	C₂×D₄₃	semidirect
285. C₄×Q₈	C₂×D₄₃	semidirect
393. D₄	Q₈×D₄₃	semidirect