Subgroups — #19148644

Order 5504.

1124 conjugacy classes of subgroups.

The subgroup lattice has 462 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14583619	C₂	1	1	yes	maximal, characteristic, complemented
2	#14583604	C₂	1	2	yes	maximal, complemented
3	#14583589	C₂	1	2	yes	maximal, complemented
4	#14583575	C₂	1	4	yes	maximal, complemented
5	D₄×Dic₈₆	C₂	1	1	yes	maximal, characteristic, complemented
6	#14583558	C₂	1	2	yes	maximal, complemented
7	#14583554	C₂	1	1	yes	maximal, characteristic, complemented
8	#14583553	C₂	1	1	yes	maximal, characteristic, complemented
9	#14583543	C₂	1	2	yes	maximal, complemented
10	#14583514	C₂	1	2	yes	maximal, complemented
11	#14583491	C₂	1	4	yes	maximal, complemented
12	#14583456	C₂	1	1	yes	maximal, characteristic, complemented
13	#14583433	C₂	1	1	yes	maximal, characteristic, complemented
14	#14583410	C₂	1	2	yes	maximal, complemented
15	C₂×#13063304	C₂	1	2	yes	maximal, complemented
16	#14583378	C₂	1	2	yes	maximal, complemented
17	C₂×C₄×D₄×C₄₃	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂×#10621898	C₂²	1	2	yes	complemented
19	C₂×#10621900	C₂²	1	2	yes	—
20	C₂²×Dic₈₆	C₂²	1	2	yes	complemented
21	#13063325	C₂²	1	1	yes	characteristic, complemented
22	#13063325	C₂²	1	1	yes	characteristic, complemented
23	#13063324	C₂²	1	2	yes	complemented
24	#13063319	C₂²	1	2	yes	complemented
25	#13063318	C₂²	1	4	yes	complemented
26	#13063318	C₂²	1	4	yes	complemented
27	#13063317	C₂²	1	1	yes	characteristic, complemented
28	#13063317	C₂²	1	2	yes	complemented
29	#13063315	C₂²	1	4	yes	complemented
30	#13063313	C₂²	1	1	yes	characteristic, complemented
31	#13063312	C₂²	1	2	yes	—
32	#13063311	C₂²	1	4	yes	complemented
33	#13063309	C₂²	1	4	yes	complemented
34	#13063308	C₂²	1	2	yes	—
35	#13063308	C₂²	1	4	yes	complemented
36	#13063307	C₂²	1	4	yes	complemented
37	#13063306	C₂²	1	4	yes	—
38	#13063305	C₂²	1	2	yes	complemented
39	#13063304	C₂²	1	4	yes	—
40	#13063304	C₂²	1	2	yes	—
41	#13063304	C₂²	1	1	yes	characteristic
42	#13063304	C₂²	1	2	yes	—
43	#13063304	C₂²	1	2	yes	complemented
44	#13063304	C₂²	1	2	yes	complemented
45	#13063304	C₂²	1	2	yes	complemented
46	#13063304	C₂²	1	4	yes	complemented
47	#13063303	C₂²	1	4	yes	complemented
48	#13063302	C₂²	1	4	yes	complemented
49	#13063299	C₂²	1	1	yes	characteristic
50	#13063299	C₂²	1	2	yes	complemented
51	#13063297	C₂²	1	4	yes	—
52	#13063296	C₂²	1	2	yes	—
53	#13063294	C₂²	1	4	yes	—
54	C₄×Dic₈₆	C₂²	1	2	yes	complemented
55	C₄×Dic₈₆	C₂²	1	1	yes	characteristic, complemented
56	C₄×Dic₈₆	C₂²	1	2	yes	complemented
57	#13063290	C₂²	1	2	yes	complemented
58	C₄×D₁₇₂	C₂²	1	1	yes	characteristic, complemented
59	D₄×Dic₄₃	C₂²	1	2	yes	—
60	C₄×C₂²⋊D₄₃	C₂²	1	4	yes	—
61	C₄×C₂²⋊D₄₃	C₂²	1	2	yes	—
62	C₄×C₂²⋊D₄₃	C₂²	1	4	yes	complemented
63	(C₂²⋊D₄₃)⋊C₄	C₂²	1	4	yes	complemented
64	#13063284	C₂²	1	2	yes	—
65	#13063284	C₂²	1	2	yes	complemented
66	#13063282	C₂²	1	2	yes	complemented
67	#13063281	C₂²	1	4	yes	complemented
68	C₂×C₄⋊Dic₄₃	C₂²	1	2	yes	complemented
69	C₂×Dic₄₃⋊C₄	C₂²	1	4	yes	complemented
70	C₄⋊C₄×D₄₃	C₂²	1	2	yes	complemented
71	C₂×C₂²⋊Dic₄₃	C₂²	1	4	yes	—
72	C₂²×D₄×C₄₃	C₂²	1	1	yes	characteristic
73	C₂³×C₄×C₄₃	C₂²	1	2	yes	—
74	C₄×D₄×C₄₃	C₂²	1	1	yes	characteristic
75	C₄×D₄×C₄₃	C₂²	1	1	yes	characteristic
76	C₄×D₄×C₄₃	C₂²	1	2	yes	—
77	C₄×D₄×C₄₃	C₂²	1	1	yes	characteristic
78	C₄×D₄×C₄₃	C₂²	1	2	yes	—
79	C₄×D₄×C₄₃	C₂²	1	1	yes	characteristic
80	C₂×C₄⋊C₄×C₄₃	C₂²	1	1	yes	characteristic
81	C₂×C₂²⋊C₄×C₄₃	C₂²	1	2	yes	—
82	C₂×C₄²×C₄₃	C₂²	1	1	yes	characteristic
83	C₂⁴×C₄₃	C₂³	1	2	yes	—
84	C₂×D₄×C₄₃	—	2	4	no	—
85	C₂×D₄×C₄₃	C₂³	1	1	yes	characteristic
86	C₂×D₄×C₄₃	C₂³	1	2	yes	—
87	C₂×D₄×C₄₃	C₂³	1	1	yes	characteristic
88	C₂²×C₄×C₄₃	—	4	4	no	—
89	C₂²×C₄×C₄₃	C₂³	1	1	yes	characteristic
90	C₂²×C₄×C₄₃	C₂³	1	1	yes	characteristic
91	C₂²×C₄×C₄₃	C₂³	1	1	yes	characteristic
92	C₂²×C₄×C₄₃	C₂³	1	2	yes	—
93	C₂²×C₄×C₄₃	C₂³	1	2	yes	—
94	C₂²×C₄×C₄₃	C₂³	1	2	yes	—
95	C₂²×C₄×C₄₃	C₂³	1	2	yes	—
96	C₂²×C₄×C₄₃	C₂³	1	2	yes	—
97	C₂×C₂²⋊D₄₃	C₂³	1	4	yes	—
98	C₂×C₂²⋊D₄₃	C₂³	1	2	yes	—
99	C₂×C₂²⋊D₄₃	C₂³	1	4	yes	—
100	C₂²×Dic₄₃	C₂³	1	4	yes	—
101	C₂²×Dic₄₃	C₂³	1	4	yes	—
102	#10621900	—	2	8	no	—
103	#10621898	—	4	4	no	—
104	C₂×D₁₇₂	C₂³	1	1	yes	characteristic
105	C₂×C₄×D₄₃	C₂³	1	2	yes	—
106	C₂×C₄×D₄₃	C₂³	1	4	yes	—
107	C₂×Dic₈₆	—	4	4	no	—
108	C₂×Dic₈₆	C₂³	1	2	yes	—
109	C₂×Dic₈₆	C₂³	1	1	yes	characteristic
110	C₂×Dic₈₆	C₂³	1	2	yes	—
111	C₂×Dic₈₆	C₂³	1	4	yes	—
112	C₄⋊C₄×C₄₃	C₂³	1	1	yes	characteristic
113	C₄⋊C₄×C₄₃	C₂³	1	2	yes	—
114	C₄⋊C₄×C₄₃	C₂³	1	1	yes	characteristic
115	C₂²⋊C₄×C₄₃	C₂³	1	2	yes	—
116	C₂²⋊C₄×C₄₃	C₂³	1	2	yes	—
117	C₂²⋊C₄×C₄₃	C₂³	1	2	yes	—
118	C₂²⋊C₄×C₄₃	C₂³	1	2	yes	—
119	C₄²×C₄₃	C₂³	1	1	yes	characteristic
120	C₄²×C₄₃	C₂³	1	1	yes	characteristic
121	C₄²×C₄₃	C₂³	1	1	yes	characteristic
122	C₄²×C₄₃	C₂³	1	1	yes	characteristic
123	C₂²⋊Dic₄₃	C₂³	1	2	yes	—
124	C₂²⋊Dic₄₃	C₂³	1	4	yes	—
125	C₂²⋊Dic₄₃	C₂³	1	4	yes	—
126	C₂²⋊Dic₄₃	C₂³	1	4	yes	—
127	C₂²⋊Dic₄₃	C₂³	1	4	yes	—
128	C₂²⋊Dic₄₃	C₂³	1	4	yes	—
129	(C₂×D₄₃)⋊C₄	C₂³	1	2	yes	—
130	(C₂×D₄₃)⋊C₄	C₂³	1	2	yes	—
131	(C₂×D₄₃)⋊C₄	C₂³	1	2	yes	—
132	(C₂×D₄₃)⋊C₄	C₂³	1	4	yes	—
133	(C₂×D₄₃)⋊C₄	C₂³	1	2	yes	—
134	C₄⋊Dic₄₃	C₂³	1	2	yes	—
135	C₄⋊Dic₄₃	C₂³	1	1	yes	characteristic
136	C₄⋊Dic₄₃	C₂³	1	2	yes	—
137	C₄⋊Dic₄₃	C₂³	1	4	yes	—
138	C₄⋊Dic₄₃	C₂³	1	2	yes	—
139	C₄⋊Dic₄₃	C₂³	1	2	yes	—
140	C₄⋊Dic₄₃	C₂³	1	1	yes	characteristic
141	Dic₄₃⋊C₄	C₂³	1	4	yes	—
142	Dic₄₃⋊C₄	C₂³	1	2	yes	—
143	Dic₄₃⋊C₄	C₂³	1	4	yes	—
144	Dic₄₃⋊C₄	C₂³	1	4	yes	—
145	Dic₄₃⋊C₄	C₂³	1	2	yes	—
146	Dic₄₃⋊C₄	C₂³	1	4	yes	—
147	Dic₄₃⋊C₄	C₂³	1	2	yes	—
148	Dic₄₃⋊C₄	C₂³	1	4	yes	—
149	Dic₄₃⋊C₄	C₂³	1	2	yes	—
150	C₄×Dic₄₃	C₂³	1	4	yes	—
151	C₄×Dic₄₃	C₂³	1	4	yes	—
152	C₄×Dic₄₃	C₂³	1	2	yes	—
153	C₂³×C₄₃	—	2	4	no	—
154	C₂³×C₄₃	—	2	4	no	—
155	C₂³×C₄₃	—	4	2	no	—
156	C₂³×C₄₃	C₂⁴	1	2	yes	—
157	C₂³×C₄₃	C₂⁴	1	2	yes	—
158	C₂³×C₄₃	C₂⁴	1	1	yes	characteristic
159	C₂²×D₄₃	C₂⁴	1	2	yes	—
160	D₄×C₄₃	—	2	4	no	—
161	D₄×C₄₃	—	2	2	no	—
162	D₄×C₄₃	#41	1	4	yes	complemented
163	C₂×C₄×C₄₃	—	2	2	no	—
164	C₂×C₄×C₄₃	—	2	2	no	—
165	C₂×C₄×C₄₃	—	2	4	no	—
166	C₂×C₄×C₄₃	—	2	4	no	—
167	C₂×C₄×C₄₃	—	2	2	no	—
168	C₂×C₄×C₄₃	—	4	2	no	—
169	C₂×C₄×C₄₃	—	4	2	no	—
170	C₂×C₄×C₄₃	—	4	2	no	—
171	C₂×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
172	C₂×C₄×C₄₃	C₂⁴	1	2	yes	—
173	C₂×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
174	C₂×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
175	C₂×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
176	C₂×C₄×C₄₃	C₂⁴	1	2	yes	—
177	C₂×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
178	C₂×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
179	C₂²⋊D₄₃	—	2	8	no	—
180	C₂²⋊D₄₃	—	2	4	no	—
181	C₂²⋊D₄₃	—	4	4	no	—
182	C₂×Dic₄₃	—	2	8	no	—
183	C₂×Dic₄₃	—	4	4	no	—
184	C₂×Dic₄₃	C₂⁴	1	2	yes	—
185	C₂×Dic₄₃	C₂⁴	1	4	yes	—
186	C₂×Dic₄₃	C₂⁴	1	4	yes	—
187	C₂×Dic₄₃	C₂⁴	1	2	yes	—
188	C₂×Dic₄₃	C₂⁴	1	2	yes	—
189	D₁₇₂	—	2	2	no	—
190	C₄×D₄₃	—	2	4	no	—
191	C₄×D₄₃	—	4	4	no	—
192	Dic₈₆	—	2	4	no	—
193	Dic₈₆	—	2	2	no	—
194	Dic₈₆	—	2	4	no	—
195	Dic₈₆	—	4	4	no	—
196	C₂²×C₄₃	—	2	1	no	—
197	C₂²×C₄₃	—	2	1	no	—
198	C₂²×C₄₃	—	2	2	no	—
199	C₂²×C₄₃	—	2	2	no	—
200	C₂²×C₄₃	—	2	2	no	—
201	C₂²×C₄₃	—	2	2	no	—
202	C₂²×C₄₃	—	2	2	no	—
203	C₂²×C₄₃	—	4	8	no	—
204	C₂²×C₄₃	C₂×#41	1	4	yes	—
205	C₂²×C₄₃	2₋¹⁺⁴	1	2	yes	—
206	C₂²×C₄₃	C₂⁵	1	1	yes	characteristic
207	C₂×D₄₃	—	2	2	no	—
208	C₂×D₄₃	—	2	2	no	—
209	C₂×D₄₃	—	2	2	no	—
210	C₄×C₄₃	—	2	1	no	—
211	C₄×C₄₃	—	2	2	no	—
212	C₄×C₄₃	—	2	2	no	—
213	C₄×C₄₃	—	2	1	no	—
214	C₄×C₄₃	—	2	1	no	—
215	C₄×C₄₃	—	2	1	no	—
216	C₄×C₄₃	C₂×#41	1	2	yes	—
217	C₄×C₄₃	H(5,𝔽₂)	1	2	yes	—
218	Dic₄₃	—	2	4	no	—
219	Dic₄₃	—	2	2	no	—
220	Dic₄₃	—	2	2	no	—
221	Dic₄₃	—	2	4	no	—
222	Dic₄₃	—	2	2	no	—
223	#3520	—	43	1	no	maximal, Sylow
224	C₂×C₄₃	—	2	2	no	—
225	C₂×C₄₃	—	2	4	no	—
226	C₂×C₄₃	—	4	2	no	—
227	C₂×C₄₃	C₂²×#41	1	1	yes	characteristic
228	C₂×C₄₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
229	C₂×C₄₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
230	D₄₃	—	4	2	no	—
231	#556	—	43	1	no	—
232	#554	—	43	2	no	—
233	#552	—	43	2	no	—
234	#551	—	43	4	no	—
235	D₄×Q₈	—	43	1	no	—
236	#548	—	43	2	no	—
237	#547	—	43	1	no	—
238	#547	—	43	1	no	—
239	#546	—	43	2	no	—
240	#542	—	43	2	no	—
241	#539	—	43	4	no	—
242	#533	—	43	1	no	—
243	#529	—	43	1	no	—
244	#525	—	43	2	no	—
245	C₂×C₂²⋊Q₈	—	43	2	no	—
246	#520	—	43	2	no	—
247	C₂×C₄×D₄	D₄₃	1	1	yes	characteristic, complemented
248	C₄₃	#3520	1	1	yes	characteristic, complemented, Sylow
249	C₂×#41	—	43	2	no	—
250	C₂×#41	—	43	2	no	—
251	C₂²×Q₈	—	43	2	no	—
252	C₂²×D₄	C₂×D₄₃	1	1	yes	characteristic
253	C₂³×C₄	C₂×D₄₃	1	2	yes	—
254	C₄⋊Q₈	—	43	2	no	—
255	C₄⋊Q₈	—	43	1	no	—
256	C₄⋊Q₈	—	43	1	no	—
257	#126	—	43	4	no	—
258	#126	—	43	4	no	—
259	#126	—	43	2	no	—
260	#125	—	43	4	no	—
261	#125	—	43	1	no	—
262	#125	—	43	2	no	—
263	#124	—	43	2	no	—
264	#124	—	43	4	no	—
265	#124	—	43	1	no	—
266	#123	—	43	4	no	—
267	#123	—	43	4	no	—
268	#123	—	43	2	no	—
269	#123	—	43	4	no	—
270	#123	—	43	4	no	—
271	C₂²⋊Q₈	—	43	1	no	—
272	C₂²⋊Q₈	—	43	2	no	—
273	C₂²⋊Q₈	—	43	4	no	—
274	C₂²⋊Q₈	—	43	2	no	—
275	C₂²⋊Q₈	—	43	2	no	—
276	C₂²⋊Q₈	—	43	4	no	—
277	C₂²⋊Q₈	—	43	2	no	—
278	C₂²⋊Q₈	—	43	2	no	—
279	C₂²⋊Q₈	—	43	4	no	—
280	C₂²⋊Q₈	—	43	2	no	—
281	C₂²⋊Q₈	—	43	4	no	—
282	#121	—	43	4	no	—
283	#121	—	43	2	no	—
284	#121	—	43	1	no	—
285	#121	—	43	2	no	—
286	#120	—	43	4	no	—
287	C₄×Q₈	—	43	2	no	—
288	C₄×Q₈	—	43	2	no	—
289	C₄×Q₈	—	43	1	no	—
290	C₄×Q₈	—	43	2	no	—
291	C₄×D₄	—	43	2	no	—
292	C₄×D₄	—	43	4	no	—
293	C₄×D₄	—	43	4	no	—
294	C₄×D₄	—	43	2	no	—
295	C₄×D₄	—	43	4	no	—
296	C₄×D₄	—	43	1	no	—
297	C₄×D₄	C₂×D₄₃	1	1	yes	characteristic
298	C₄×D₄	C₂×D₄₃	1	2	yes	—
299	C₄×D₄	C₂×D₄₃	1	1	yes	characteristic
300	C₄×D₄	C₂×D₄₃	1	1	yes	characteristic
301	C₄×D₄	C₂×D₄₃	1	1	yes	characteristic
302	C₄×D₄	C₂×D₄₃	1	2	yes	—
303	#117	—	43	2	no	—
304	#117	—	43	2	no	—
305	#117	—	43	4	no	—
306	#117	—	43	2	no	—
307	C₂×C₄⋊C₄	—	43	4	no	—
308	C₂×C₄⋊C₄	—	43	2	no	—
309	C₂×C₄⋊C₄	—	43	2	no	—
310	C₂×C₄⋊C₄	C₂×D₄₃	1	1	yes	characteristic
311	C₂×C₂²⋊C₄	—	43	4	no	—
312	C₂×C₂²⋊C₄	C₂×D₄₃	1	2	yes	—
313	C₂×C₄²	C₂×D₄₃	1	1	yes	characteristic
314	C₂⁴	C₂²×D₄₃	1	2	yes	—
315	#41	—	86	8	no	—
316	#41	—	172	4	no	—
317	C₂×Q₈	—	43	2	no	—
318	C₂×Q₈	—	43	1	no	—
319	C₂×Q₈	—	43	2	no	—
320	C₂×Q₈	—	43	4	no	—
321	C₂×Q₈	—	172	4	no	—
322	C₂×D₄	—	2	4	no	—
323	C₂×D₄	—	43	2	no	—
324	C₂×D₄	—	43	4	no	—
325	C₂×D₄	—	43	4	no	—
326	C₂×D₄	—	43	1	no	—
327	C₂×D₄	C₂²×D₄₃	1	2	yes	—
328	C₂×D₄	C₂²×D₄₃	1	1	yes	characteristic
329	C₂×D₄	C₂²×D₄₃	1	1	yes	characteristic
330	C₂²×C₄	—	4	4	no	—
331	C₂²×C₄	—	43	4	no	—
332	C₂²×C₄	—	43	4	no	—
333	C₂²×C₄	—	43	2	no	—
334	C₂²×C₄	—	43	4	no	—
335	C₂²×C₄	C₂²×D₄₃	1	1	yes	characteristic
336	C₂²×C₄	C₂²×D₄₃	1	1	yes	characteristic
337	C₂²×C₄	C₂²×D₄₃	1	1	yes	characteristic
338	C₂²×C₄	C₂²×D₄₃	1	2	yes	—
339	C₂²×C₄	C₂²×D₄₃	1	2	yes	—
340	C₂²×C₄	C₂²×D₄₃	1	2	yes	—
341	C₂²×C₄	C₂²×D₄₃	1	2	yes	—
342	C₂²×C₄	C₂²×D₄₃	1	2	yes	—
343	C₄⋊C₄	—	43	2	no	—
344	C₄⋊C₄	—	43	4	no	—
345	C₄⋊C₄	—	43	1	no	—
346	C₄⋊C₄	—	43	2	no	—
347	C₄⋊C₄	—	43	2	no	—
348	C₄⋊C₄	—	43	4	no	—
349	C₄⋊C₄	—	43	4	no	—
350	C₄⋊C₄	—	43	4	no	—
351	C₄⋊C₄	—	43	2	no	—
352	C₄⋊C₄	—	43	1	no	—
353	C₄⋊C₄	—	43	2	no	—
354	C₄⋊C₄	—	43	2	no	—
355	C₄⋊C₄	—	43	4	no	—
356	C₄⋊C₄	—	43	2	no	—
357	C₄⋊C₄	—	43	4	no	—
358	C₄⋊C₄	—	43	2	no	—
359	C₄⋊C₄	C₂²×D₄₃	1	1	yes	characteristic
360	C₄⋊C₄	C₂²×D₄₃	1	2	yes	—
361	C₄⋊C₄	C₂²×D₄₃	1	1	yes	characteristic
362	C₂²⋊C₄	—	43	2	no	—
363	C₂²⋊C₄	—	43	4	no	—
364	C₂²⋊C₄	—	43	4	no	—
365	C₂²⋊C₄	—	43	4	no	—
366	C₂²⋊C₄	—	43	4	no	—
367	C₂²⋊C₄	—	43	4	no	—
368	C₂²⋊C₄	—	43	2	no	—
369	C₂²⋊C₄	—	43	2	no	—
370	C₂²⋊C₄	—	43	2	no	—
371	C₂²⋊C₄	—	43	4	no	—
372	C₂²⋊C₄	—	43	2	no	—
373	C₂²⋊C₄	C₂²×D₄₃	1	2	yes	—
374	C₂²⋊C₄	C₂²×D₄₃	1	2	yes	—
375	C₂²⋊C₄	C₂²×D₄₃	1	2	yes	—
376	C₂²⋊C₄	C₂²×D₄₃	1	2	yes	—
377	C₄²	—	43	4	no	—
378	C₄²	—	43	4	no	—
379	C₄²	—	43	2	no	—
380	C₄²	C₂²×D₄₃	1	1	yes	characteristic
381	C₄²	C₂²×D₄₃	1	1	yes	characteristic
382	C₄²	C₂²×D₄₃	1	1	yes	characteristic
383	C₄²	C₂²×D₄₃	1	1	yes	characteristic
384	C₂³	—	2	4	no	—
385	C₂³	—	2	4	no	—
386	C₂³	—	4	2	no	—
387	C₂³	—	43	2	no	—
388	C₂³	C₂³×D₄₃	1	2	yes	—
389	C₂³	C₂³×D₄₃	1	2	yes	—
390	C₂³	C₂³×D₄₃	1	1	yes	characteristic
391	Q₈	—	86	4	no	—
392	Q₈	—	86	2	no	—
393	Q₈	—	86	4	no	—
394	Q₈	—	172	4	no	—
395	D₄	—	2	4	no	—
396	D₄	—	2	2	no	—
397	D₄	—	86	8	no	—
398	D₄	—	86	4	no	—
399	D₄	—	86	2	no	—
400	D₄	—	172	4	no	—
401	D₄	#10621898	1	4	yes	complemented
402	C₂×C₄	—	2	2	no	—
403	C₂×C₄	—	2	2	no	—
404	C₂×C₄	—	2	2	no	—
405	C₂×C₄	—	2	4	no	—
406	C₂×C₄	—	2	4	no	—
407	C₂×C₄	—	4	2	no	—
408	C₂×C₄	—	4	2	no	—
409	C₂×C₄	—	4	2	no	—
410	C₂×C₄	—	43	2	no	—
411	C₂×C₄	—	43	4	no	—
412	C₂×C₄	—	43	2	no	—
413	C₂×C₄	—	43	4	no	—
414	C₂×C₄	—	43	2	no	—
415	C₂×C₄	—	86	8	no	—
416	C₂×C₄	—	86	4	no	—
417	C₂×C₄	—	172	4	no	—
418	C₂×C₄	—	172	4	no	—
419	C₂×C₄	C₂³×D₄₃	1	1	yes	characteristic
420	C₂×C₄	C₂³×D₄₃	1	2	yes	—
421	C₂×C₄	C₂³×D₄₃	1	1	yes	characteristic
422	C₂×C₄	C₂³×D₄₃	1	1	yes	characteristic
423	C₂×C₄	C₂³×D₄₃	1	1	yes	characteristic
424	C₂×C₄	C₂³×D₄₃	1	2	yes	—
425	C₂×C₄	C₂³×D₄₃	1	1	yes	characteristic
426	C₂×C₄	C₂³×D₄₃	1	1	yes	characteristic
427	C₂²	—	2	1	no	—
428	C₂²	—	2	1	no	—
429	C₂²	—	2	2	no	—
430	C₂²	—	2	2	no	—
431	C₂²	—	2	2	no	—
432	C₂²	—	2	2	no	—
433	C₂²	—	2	2	no	—
434	C₂²	—	4	8	no	—
435	C₂²	—	86	2	no	—
436	C₂²	—	86	2	no	—
437	C₂²	—	86	2	no	—
438	C₂²	C₂×#10621898	1	4	yes	—
439	C₂²	#13063372	1	2	yes	—
440	C₂²	C₂⁴×D₄₃	1	1	yes	characteristic
441	C₄	—	2	1	no	—
442	C₄	—	2	1	no	—
443	C₄	—	2	2	no	—
444	C₄	—	2	2	no	—
445	C₄	—	2	1	no	—
446	C₄	—	2	1	no	—
447	C₄	—	86	2	no	—
448	C₄	—	86	4	no	—
449	C₄	—	86	4	no	—
450	C₄	—	86	2	no	—
451	C₄	—	86	2	no	—
452	C₄	C₂×#10621898	1	2	yes	—
453	C₄	#13063370	1	2	yes	—
454	C₂	—	2	2	no	—
455	C₂	—	2	4	no	—
456	C₂	—	4	2	no	—
457	C₂	—	172	2	no	—
458	C₂	C₂²×#10621898	1	1	yes	characteristic
459	C₂	C₂×#13063370	1	1	yes	characteristic
460	C₂	C₂×#13063372	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₄₃
commutator, socle	C₂²×C₄₃	C₂⁵
Fitting	C₂×C₄×D₄×C₄₃	C₂
hypercenter	C₂×C₄×D₄	D₄₃
hypocenter	C₄₃	#3520
LCS	G ▷ C₂²×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂² ◁ C₂×C₄×D₄

Complements

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

N	H ≅ G/N	type
1. #14583619	C₂	semidirect
2. #14583604	C₂	semidirect
3. #14583589	C₂	semidirect
4. #14583575	C₂	semidirect
5. D₄×Dic₈₆	C₂	semidirect
6. #14583558	C₂	semidirect
7. #14583554	C₂	semidirect
8. #14583553	C₂	semidirect
9. #14583543	C₂	semidirect
10. #14583514	C₂	semidirect
11. #14583491	C₂	semidirect
12. #14583456	C₂	semidirect
13. #14583433	C₂	semidirect
14. #14583410	C₂	semidirect
15. C₂×#13063304	C₂	semidirect
16. #14583378	C₂	semidirect
17. C₂×C₄×D₄×C₄₃	C₂	semidirect
18. C₂×#10621898	C₂²	semidirect
20. C₂²×Dic₈₆	C₂²	semidirect
21. #13063325	C₂²	semidirect
22. #13063325	C₂²	semidirect
23. #13063324	C₂²	semidirect
24. #13063319	C₂²	semidirect
25. #13063318	C₂²	semidirect
26. #13063318	C₂²	semidirect
27. #13063317	C₂²	semidirect
28. #13063317	C₂²	semidirect
29. #13063315	C₂²	semidirect
30. #13063313	C₂²	semidirect
32. #13063311	C₂²	semidirect
33. #13063309	C₂²	semidirect
35. #13063308	C₂²	semidirect
36. #13063307	C₂²	semidirect
38. #13063305	C₂²	semidirect
43. #13063304	C₂²	semidirect
44. #13063304	C₂²	semidirect
45. #13063304	C₂²	semidirect
46. #13063304	C₂²	semidirect
47. #13063303	C₂²	semidirect
48. #13063302	C₂²	semidirect
50. #13063299	C₂²	semidirect
54. C₄×Dic₈₆	C₂²	semidirect
55. C₄×Dic₈₆	C₂²	semidirect
56. C₄×Dic₈₆	C₂²	semidirect
57. #13063290	C₂²	semidirect
58. C₄×D₁₇₂	C₂²	semidirect
62. C₄×C₂²⋊D₄₃	C₂²	semidirect
63. (C₂²⋊D₄₃)⋊C₄	C₂²	semidirect
65. #13063284	C₂²	semidirect
66. #13063282	C₂²	semidirect
67. #13063281	C₂²	semidirect
68. C₂×C₄⋊Dic₄₃	C₂²	semidirect
69. C₂×Dic₄₃⋊C₄	C₂²	semidirect
70. C₄⋊C₄×D₄₃	C₂²	semidirect
162. D₄×C₄₃	#41	semidirect
247. C₂×C₄×D₄	D₄₃	semidirect
248. C₄₃	#3520	semidirect
401. D₄	#10621898	semidirect