Subgroups — C₄×#14583110 #25102808

Order 11008.

984 conjugacy classes of subgroups.

The subgroup lattice has 500 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#14583110	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄×Dic₁₇₂	C₂	1	2	yes	maximal
3	C₄×#13063325	C₂	1	1	yes	maximal, characteristic
4	C₄²×Dic₈₆	C₂	1	1	yes	maximal, characteristic
5	#19135517	C₂	1	1	yes	maximal, characteristic
6	#19135354	C₂	1	1	yes	maximal, characteristic
7	#19135237	C₂	1	2	yes	maximal
8	#19134935	C₂	1	2	yes	maximal
9	#19134601	C₂	1	1	yes	maximal, characteristic
10	C₄×#13063250	C₂	1	2	yes	maximal
11	C₄×C₄⋊C₈×C₄₃	C₂	1	1	yes	maximal, characteristic
12	C₂²×Dic₁₇₂	C₂²	1	2	yes	—
13	C₂×#13063325	C₂²	1	1	yes	characteristic
14	C₂×C₄×Dic₈₆	C₂²	1	2	yes	—
15	C₂×C₄×Dic₈₆	C₂²	1	1	yes	characteristic
16	C₂×C₄×Dic₈₆	C₂²	1	1	yes	characteristic
17	C₂×C₄×Dic₈₆	C₂²	1	1	yes	characteristic
18	#14583110	C₄	1	8	yes	direct product factor
19	C₄×Dic₁₇₂	—	2	8	no	—
20	C₂×#13063259	C₂²	1	2	yes	—
21	C₂×#13063250	C₂²	1	2	yes	—
22	C₂×#13063250	C₂²	1	2	yes	—
23	C₂×#13063250	C₂²	1	2	yes	—
24	C₂×#13063250	C₂²	1	2	yes	—
25	#14582805	C₂²	1	2	yes	—
26	#14582797	—	2	1	no	—
27	#14582797	—	2	1	no	—
28	#14582769	C₂²	1	1	yes	characteristic
29	C₄×Dic₄₃⋊C₄	—	2	1	no	—
30	C₄×Dic₄₃⋊C₄	—	2	1	no	—
31	C₄×Dic₄₃⋊C₄	—	2	1	no	—
32	C₄×C₄⋊Dic₄₃	—	2	1	no	—
33	C₄×C₄⋊Dic₄₃	—	2	1	no	—
34	C₄×C₄⋊Dic₄₃	C₂²	1	1	yes	characteristic
35	C₄×C₄⋊Dic₄₃	C₂²	1	1	yes	characteristic
36	C₄×C₄⋊Dic₄₃	C₂²	1	1	yes	characteristic
37	C₄²×Dic₄₃	—	2	1	no	—
38	#14582662	C₂²	1	2	yes	—
39	#14582662	C₂²	1	2	yes	—
40	C₂×C₄⋊C₈×C₄₃	C₂²	1	1	yes	characteristic
41	C₂×C₄⋊C₈×C₄₃	C₂²	1	1	yes	characteristic
42	C₂×C₄×C₈×C₄₃	C₂²	1	2	yes	—
43	C₄³×C₄₃	C₂²	1	1	yes	characteristic
44	C₄₃×#336	C₂²	1	2	yes	—
45	C₂²×Dic₈₆	C₂³	1	2	yes	—
46	C₂²×Dic₈₆	C₂³	1	1	yes	characteristic
47	C₂×Dic₁₇₂	—	2	4	no	—
48	C₂×Dic₁₇₂	—	2	4	no	—
49	C₂×Dic₁₇₂	C₂×C₄	1	8	yes	—
50	#13063325	—	2	2	no	—
51	#13063325	C₂×C₄	1	4	yes	—
52	C₄×Dic₈₆	—	2	2	no	—
53	C₄×Dic₈₆	—	2	2	no	—
54	C₄×Dic₈₆	—	2	2	no	—
55	C₄×Dic₈₆	—	2	2	no	—
56	C₄×Dic₈₆	—	2	4	no	—
57	C₄×Dic₈₆	—	2	4	no	—
58	C₄×Dic₈₆	C₂×C₄	1	4	yes	—
59	C₄×Dic₈₆	D₄	1	4	yes	—
60	C₂×C₄⋊Dic₄₃	—	2	1	no	—
61	C₂×C₄⋊Dic₄₃	—	2	1	no	—
62	C₂×C₄⋊Dic₄₃	—	2	1	no	—
63	C₂×C₄⋊Dic₄₃	—	2	1	no	—
64	C₂×C₄⋊Dic₄₃	C₂³	1	2	yes	—
65	C₂×C₄⋊Dic₄₃	C₂³	1	1	yes	characteristic
66	C₂×C₄⋊Dic₄₃	C₂³	1	1	yes	characteristic
67	C₂×C₄⋊Dic₄₃	C₂³	1	1	yes	characteristic
68	C₂×Dic₄₃⋊C₄	—	2	1	no	—
69	C₂×Dic₄₃⋊C₄	—	2	1	no	—
70	C₂×Dic₄₃⋊C₄	—	2	1	no	—
71	C₂×Dic₄₃⋊C₄	—	2	2	no	—
72	C₂×C₄×Dic₄₃	—	2	1	no	—
73	C₂×C₄×Dic₄₃	—	2	1	no	—
74	C₂×C₄×Dic₄₃	—	2	1	no	—
75	C₂×C₄×Dic₄₃	—	2	2	no	—
76	C₂×C₄×Dic₄₃	—	2	1	no	—
77	C₂×C₄×Dic₄₃	—	2	1	no	—
78	C₂×C₄×Dic₄₃	—	2	1	no	—
79	#13063259	—	2	4	no	—
80	#13063250	—	2	4	no	—
81	#13063250	—	2	4	no	—
82	#13063250	—	2	4	no	—
83	#13063250	C₂×C₄	1	8	yes	—
84	C₄₃⋊#95	—	2	2	no	—
85	C₄₃⋊#95	—	2	2	no	—
86	C₄₃⋊#95	—	2	1	no	—
87	C₄₃⋊#95	—	2	1	no	—
88	C₄₃⋊#95	—	2	1	no	—
89	C₂²×C₈×C₄₃	C₂³	1	2	yes	—
90	C₂²×C₈×C₄₃	C₂³	1	2	yes	—
91	C₂×C₄²×C₄₃	D₄	1	1	yes	characteristic
92	C₂×C₄²×C₄₃	D₄	1	1	yes	characteristic
93	C₂×C₄²×C₄₃	D₄	1	1	yes	characteristic
94	C₂×C₄²×C₄₃	D₄	1	1	yes	characteristic
95	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
96	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
97	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
98	C₄⋊C₈×C₄₃	—	2	2	no	—
99	C₄⋊C₈×C₄₃	C₂×C₄	1	4	yes	—
100	C₄×C₈×C₄₃	—	2	4	no	—
101	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
102	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
103	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
104	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
105	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
106	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
107	C₂²×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
108	C₂²×Dic₄₃	—	2	1	no	—
109	C₂²×Dic₄₃	—	2	1	no	—
110	C₂²×Dic₄₃	—	2	1	no	—
111	C₂²×Dic₄₃	—	2	1	no	—
112	C₂²×Dic₄₃	—	2	2	no	—
113	C₂²×Dic₄₃	—	2	2	no	—
114	C₂×Dic₈₆	—	2	1	no	—
115	C₂×Dic₈₆	—	2	1	no	—
116	C₂×Dic₈₆	—	2	1	no	—
117	C₂×Dic₈₆	—	2	2	no	—
118	C₂×Dic₈₆	—	2	2	no	—
119	C₂×Dic₈₆	—	2	2	no	—
120	C₂×Dic₈₆	—	2	2	no	—
121	C₂×Dic₈₆	—	2	2	no	—
122	C₂×Dic₈₆	C₂²×C₄	1	4	yes	—
123	C₂×Dic₈₆	C₂²×C₄	1	2	yes	—
124	C₂×Dic₈₆	C₂×D₄	1	2	yes	—
125	C₂×Dic₈₆	#41	1	2	yes	—
126	C₂×C₈×C₄₃	—	2	2	no	—
127	C₂×C₈×C₄₃	—	2	2	no	—
128	C₂×C₈×C₄₃	—	2	2	no	—
129	C₂×C₈×C₄₃	—	2	2	no	—
130	C₂×C₈×C₄₃	—	2	2	no	—
131	C₂×C₈×C₄₃	C₂²×C₄	1	4	yes	—
132	C₄²×C₄₃	—	2	2	no	—
133	C₄²×C₄₃	—	2	2	no	—
134	C₄²×C₄₃	—	2	1	no	—
135	C₄²×C₄₃	—	2	1	no	—
136	C₄²×C₄₃	—	4	1	no	—
137	C₄²×C₄₃	Q₁₆	1	4	yes	complemented
138	C₄²×C₄₃	C₂²×C₄	1	2	yes	—
139	C₄²×C₄₃	C₂×D₄	1	2	yes	—
140	C₄²×C₄₃	#41	1	2	yes	—
141	C₄²×C₄₃	#41	1	2	yes	—
142	C₄⋊Dic₄₃	—	2	4	no	—
143	C₄⋊Dic₄₃	—	2	4	no	—
144	C₄⋊Dic₄₃	—	2	1	no	—
145	C₄⋊Dic₄₃	—	2	1	no	—
146	C₄⋊Dic₄₃	—	2	1	no	—
147	C₄⋊Dic₄₃	—	2	2	no	—
148	C₄⋊Dic₄₃	—	2	2	no	—
149	C₄⋊Dic₄₃	—	4	2	no	—
150	C₄⋊Dic₄₃	—	4	2	no	—
151	C₄⋊Dic₄₃	C₂²×C₄	1	2	yes	—
152	C₄⋊Dic₄₃	C₂×D₄	1	2	yes	—
153	C₄⋊Dic₄₃	#41	1	2	yes	—
154	Dic₄₃⋊C₄	—	2	4	no	—
155	Dic₄₃⋊C₄	—	2	4	no	—
156	Dic₄₃⋊C₄	—	2	4	no	—
157	Dic₄₃⋊C₄	—	4	4	no	—
158	C₄×Dic₄₃	—	2	4	no	—
159	C₄×Dic₄₃	—	2	4	no	—
160	C₄×Dic₄₃	—	2	4	no	—
161	C₄×Dic₄₃	—	4	2	no	—
162	C₄×Dic₄₃	—	4	4	no	—
163	C₄×Dic₄₃	—	4	2	no	—
164	C₄×Dic₄₃	—	4	2	no	—
165	Dic₁₇₂	—	2	16	no	—
166	C₂³×C₄₃	C₂²×D₄	1	1	yes	characteristic
167	C₂×C₄×C₄₃	—	2	1	no	—
168	C₂×C₄×C₄₃	—	2	1	no	—
169	C₂×C₄×C₄₃	—	2	1	no	—
170	C₂×C₄×C₄₃	—	2	1	no	—
171	C₂×C₄×C₄₃	—	2	1	no	—
172	C₂×C₄×C₄₃	—	2	1	no	—
173	C₂×C₄×C₄₃	—	2	1	no	—
174	C₂×C₄×C₄₃	—	2	1	no	—
175	C₂×C₄×C₄₃	—	2	1	no	—
176	C₂×C₄×C₄₃	C₄×D₄	1	2	yes	—
177	C₂×C₄×C₄₃	C₄×D₄	1	2	yes	—
178	C₂×C₄×C₄₃	#121	1	2	yes	—
179	C₂×C₄×C₄₃	#121	1	2	yes	—
180	C₂×C₄×C₄₃	C₂×Q₁₆	1	2	yes	—
181	C₂×C₄×C₄₃	C₂×Q₁₆	1	2	yes	—
182	C₂×C₄×C₄₃	C₂×Q₁₆	1	2	yes	—
183	C₂×C₄×C₄₃	#135	1	2	yes	—
184	C₂×C₄×C₄₃	#137	1	2	yes	—
185	C₂×C₄×C₄₃	C₂³×C₄	1	1	yes	characteristic
186	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
187	C₂×C₄×C₄₃	C₂×#41	1	1	yes	characteristic
188	C₂×C₄×C₄₃	C₂×#41	1	1	yes	characteristic
189	C₂×C₄×C₄₃	C₂×#41	1	1	yes	characteristic
190	C₂×C₄×C₄₃	C₂×#41	1	1	yes	characteristic
191	C₂×Dic₄₃	—	2	2	no	—
192	C₂×Dic₄₃	—	2	2	no	—
193	C₂×Dic₄₃	—	2	2	no	—
194	C₂×Dic₄₃	—	2	2	no	—
195	C₂×Dic₄₃	—	2	4	no	—
196	C₂×Dic₄₃	—	2	2	no	—
197	C₂×Dic₄₃	—	2	2	no	—
198	C₂×Dic₄₃	—	4	2	no	—
199	C₂×Dic₄₃	—	4	2	no	—
200	C₂×Dic₄₃	—	4	1	no	—
201	C₂×Dic₄₃	—	4	1	no	—
202	C₂×Dic₄₃	—	4	1	no	—
203	C₂×Dic₄₃	—	4	1	no	—
204	C₂×Dic₄₃	—	4	1	no	—
205	C₂×Dic₄₃	—	4	1	no	—
206	C₂×Dic₄₃	—	4	2	no	—
207	C₂×Dic₄₃	—	4	2	no	—
208	C₂×Dic₄₃	—	4	2	no	—
209	Dic₈₆	—	2	2	no	—
210	Dic₈₆	—	2	2	no	—
211	Dic₈₆	—	2	2	no	—
212	Dic₈₆	—	2	4	no	—
213	Dic₈₆	—	2	4	no	—
214	Dic₈₆	—	4	2	no	—
215	Dic₈₆	—	4	2	no	—
216	Dic₈₆	C₄×D₄	1	4	yes	—
217	C₈×C₄₃	—	2	4	no	—
218	C₈×C₄₃	—	4	2	no	—
219	C₄×#462	—	43	1	no	maximal, Sylow
220	C₂²×C₄₃	C₂×C₄×D₄	1	1	yes	characteristic
221	C₂²×C₄₃	C₂×#121	1	1	yes	characteristic
222	C₂²×C₄₃	#525	1	1	yes	characteristic
223	C₂²×C₄₃	C₂²×Q₁₆	1	1	yes	characteristic
224	C₂²×C₄₃	C₂×#135	1	1	yes	characteristic
225	C₂²×C₄₃	C₂×#137	1	1	yes	characteristic
226	C₂²×C₄₃	#575	1	1	yes	characteristic
227	C₄×C₄₃	—	2	2	no	—
228	C₄×C₄₃	—	2	2	no	—
229	C₄×C₄₃	—	2	2	no	—
230	C₄×C₄₃	—	4	1	no	—
231	C₄×C₄₃	C₄×Q₁₆	1	4	yes	complemented
232	C₄×C₄₃	#462	1	4	yes	complemented
233	C₄×C₄₃	C₂×C₄×D₄	1	1	yes	characteristic
234	C₄×C₄₃	C₄×#41	1	1	yes	characteristic
235	C₄×C₄₃	#529	1	1	yes	characteristic
236	C₄×C₄₃	#532	1	1	yes	characteristic
237	Dic₄₃	—	2	4	no	—
238	Dic₄₃	—	4	2	no	—
239	Dic₄₃	—	4	2	no	—
240	Dic₄₃	—	4	2	no	—
241	Dic₄₃	—	4	4	no	—
242	Dic₄₃	—	8	2	no	—
243	C₂×#462	—	43	1	no	—
244	C₂×C₄×Q₁₆	—	43	2	no	—
245	C₄×C₄⋊Q₈	—	43	1	no	—
246	C₄²×Q₈	—	43	1	no	—
247	#1981	—	43	1	no	—
248	#1947	—	43	1	no	—
249	#1928	—	43	2	no	—
250	#1878	—	43	2	no	—
251	#1803	—	43	1	no	—
252	C₄×C₄⋊C₈	D₄₃	1	1	yes	characteristic
253	C₄×#103	—	43	2	no	—
254	C₂×C₄₃	C₄×#121	1	1	yes	characteristic
255	C₂×C₄₃	C₂×C₄×Q₁₆	1	1	yes	characteristic
256	C₂×C₄₃	C₄×#137	1	1	yes	characteristic
257	C₂×C₄₃	C₂×#462	1	1	yes	characteristic
258	C₂×C₄₃	#3035	1	1	yes	characteristic
259	C₂×C₄₃	#3104	1	1	yes	characteristic
260	C₂×C₄₃	#3107	1	1	yes	characteristic
261	C₂²×Q₁₆	—	43	2	no	—
262	C₂×C₄⋊Q₈	—	43	1	no	—
263	C₂×C₄×Q₈	—	43	1	no	—
264	C₂×C₄×Q₈	—	43	1	no	—
265	C₂×C₄×Q₈	—	43	2	no	—
266	C₂×C₄×Q₈	—	43	1	no	—
267	#462	—	43	8	no	—
268	C₄×Q₁₆	—	86	8	no	—
269	C₂×#107	—	43	2	no	—
270	C₂×C₄⋊C₈	C₂×D₄₃	1	1	yes	characteristic
271	C₂×C₄⋊C₈	C₂×D₄₃	1	1	yes	characteristic
272	C₂×#103	—	43	2	no	—
273	C₂×#103	—	43	2	no	—
274	C₂×#103	—	43	2	no	—
275	C₂×#103	—	43	2	no	—
276	C₂×C₄×C₈	C₂×D₄₃	1	2	yes	—
277	#391	—	43	2	no	—
278	#389	—	86	1	no	—
279	#389	—	86	1	no	—
280	#384	—	43	1	no	—
281	C₄×C₄⋊C₄	—	43	1	no	—
282	C₄×C₄⋊C₄	—	43	1	no	—
283	C₄×C₄⋊C₄	—	43	1	no	—
284	C₄×C₄⋊C₄	—	86	1	no	—
285	C₄×C₄⋊C₄	—	86	1	no	—
286	C₄×C₄⋊C₄	—	86	1	no	—
287	C₄×C₄⋊C₄	—	86	1	no	—
288	C₄×C₄⋊C₄	—	86	1	no	—
289	C₄³	—	86	1	no	—
290	C₄³	C₂×D₄₃	1	1	yes	characteristic
291	#340	—	43	2	no	—
292	#340	—	43	2	no	—
293	#336	C₂×D₄₃	1	2	yes	—
294	C₄₃	C₄×#462	1	1	yes	characteristic, complemented, Sylow
295	C₂²×Q₈	—	43	1	no	—
296	C₂²×Q₈	—	43	2	no	—
297	C₂×Q₁₆	—	43	8	no	—
298	C₂×Q₁₆	—	86	4	no	—
299	C₂×Q₁₆	—	86	4	no	—
300	C₂²×C₈	C₂²×D₄₃	1	2	yes	—
301	C₂²×C₈	C₂²×D₄₃	1	2	yes	—
302	C₄⋊Q₈	—	43	4	no	—
303	C₄⋊Q₈	—	86	2	no	—
304	C₄×Q₈	—	43	4	no	—
305	C₄×Q₈	—	43	4	no	—
306	C₄×Q₈	—	86	2	no	—
307	C₄×Q₈	—	86	2	no	—
308	C₄×Q₈	—	86	2	no	—
309	C₄×Q₈	—	86	2	no	—
310	C₄×Q₈	—	86	4	no	—
311	C₄×Q₈	—	86	4	no	—
312	C₂×C₄⋊C₄	—	43	1	no	—
313	C₂×C₄⋊C₄	—	43	1	no	—
314	C₂×C₄⋊C₄	—	43	1	no	—
315	C₂×C₄⋊C₄	—	43	2	no	—
316	C₂×C₄⋊C₄	—	86	1	no	—
317	C₂×C₄⋊C₄	—	86	1	no	—
318	C₂×C₄⋊C₄	—	86	1	no	—
319	C₂×C₄⋊C₄	—	86	1	no	—
320	C₂×C₄⋊C₄	—	86	1	no	—
321	C₂×C₄⋊C₄	—	86	2	no	—
322	C₂×C₄⋊C₄	—	86	1	no	—
323	C₂×C₄⋊C₄	—	86	1	no	—
324	C₂×C₄²	—	86	1	no	—
325	C₂×C₄²	—	86	1	no	—
326	C₂×C₄²	—	86	1	no	—
327	C₂×C₄²	—	86	1	no	—
328	C₂×C₄²	—	86	1	no	—
329	C₂×C₄²	—	86	2	no	—
330	C₂×C₄²	—	86	1	no	—
331	C₂×C₄²	D₁₇₂	1	1	yes	characteristic
332	C₂×C₄²	D₁₇₂	1	1	yes	characteristic
333	C₂×C₄²	D₁₇₂	1	1	yes	characteristic
334	C₂×C₄²	D₁₇₂	1	1	yes	characteristic
335	C₂×C₄²	C₂²×D₄₃	1	1	yes	characteristic
336	C₂×C₄²	C₂²×D₄₃	1	1	yes	characteristic
337	C₂×C₄²	C₂²×D₄₃	1	1	yes	characteristic
338	#107	—	86	4	no	—
339	C₄⋊C₈	—	2	2	no	—
340	C₄⋊C₈	C₄×D₄₃	1	4	yes	—
341	#103	—	43	8	no	—
342	#103	—	86	4	no	—
343	#103	—	86	4	no	—
344	#103	—	86	4	no	—
345	C₄×C₈	—	2	4	no	—
346	#95	—	86	1	no	—
347	#95	—	86	1	no	—
348	#95	—	86	1	no	—
349	#95	—	86	2	no	—
350	#95	—	86	2	no	—
351	C₂×Q₈	—	43	2	no	—
352	C₂×Q₈	—	43	4	no	—
353	C₂×Q₈	—	43	2	no	—
354	C₂×Q₈	—	43	2	no	—
355	C₂×Q₈	—	86	1	no	—
356	C₂×Q₈	—	86	1	no	—
357	C₂×Q₈	—	86	2	no	—
358	C₂×Q₈	—	86	1	no	—
359	C₂×Q₈	—	86	2	no	—
360	C₂×Q₈	—	86	2	no	—
361	C₂×Q₈	—	86	2	no	—
362	C₂×Q₈	—	86	2	no	—
363	C₂²×C₄	—	86	1	no	—
364	C₂²×C₄	—	86	1	no	—
365	C₂²×C₄	—	86	1	no	—
366	C₂²×C₄	—	86	1	no	—
367	C₂²×C₄	—	86	2	no	—
368	C₂²×C₄	—	86	2	no	—
369	C₂²×C₄	C₂×D₁₇₂	1	1	yes	characteristic
370	C₂²×C₄	C₂×D₁₇₂	1	1	yes	characteristic
371	C₂²×C₄	C₂×D₁₇₂	1	1	yes	characteristic
372	C₂²×C₄	C₂×D₁₇₂	1	1	yes	characteristic
373	C₂²×C₄	C₂×D₁₇₂	1	1	yes	characteristic
374	C₂²×C₄	C₂×D₁₇₂	1	1	yes	characteristic
375	C₂²×C₄	C₂³×D₄₃	1	1	yes	characteristic
376	Q₁₆	—	86	16	no	—
377	C₂×C₈	—	2	2	no	—
378	C₂×C₈	—	2	2	no	—
379	C₂×C₈	—	2	2	no	—
380	C₂×C₈	—	2	2	no	—
381	C₂×C₈	—	2	2	no	—
382	C₂×C₈	C₂×C₄×D₄₃	1	4	yes	—
383	C₄⋊C₄	—	43	2	no	—
384	C₄⋊C₄	—	43	2	no	—
385	C₄⋊C₄	—	43	2	no	—
386	C₄⋊C₄	—	86	4	no	—
387	C₄⋊C₄	—	86	4	no	—
388	C₄⋊C₄	—	86	4	no	—
389	C₄⋊C₄	—	86	4	no	—
390	C₄⋊C₄	—	86	4	no	—
391	C₄⋊C₄	—	86	1	no	—
392	C₄⋊C₄	—	86	1	no	—
393	C₄⋊C₄	—	86	1	no	—
394	C₄⋊C₄	—	86	2	no	—
395	C₄⋊C₄	—	86	2	no	—
396	C₄⋊C₄	—	172	2	no	—
397	C₄⋊C₄	—	172	4	no	—
398	C₄⋊C₄	—	172	2	no	—
399	C₄²	—	2	2	no	—
400	C₄²	—	2	2	no	—
401	C₄²	—	2	1	no	—
402	C₄²	—	2	1	no	—
403	C₄²	—	4	1	no	—
404	C₄²	—	86	4	no	—
405	C₄²	—	86	4	no	—
406	C₄²	—	86	4	no	—
407	C₄²	—	172	2	no	—
408	C₄²	—	172	4	no	—
409	C₄²	—	172	2	no	—
410	C₄²	—	172	2	no	—
411	C₄²	Dic₁₇₂	1	4	yes	complemented
412	C₄²	C₂×C₄×D₄₃	1	2	yes	—
413	C₄²	#10621898	1	2	yes	—
414	C₄²	D₄×D₄₃	1	2	yes	—
415	C₄²	#10621902	1	2	yes	—
416	C₂³	C₂²×D₁₇₂	1	1	yes	characteristic
417	Q₈	—	43	4	no	—
418	Q₈	—	86	2	no	—
419	Q₈	—	86	2	no	—
420	Q₈	—	86	2	no	—
421	Q₈	—	86	4	no	—
422	Q₈	—	86	4	no	—
423	Q₈	—	172	2	no	—
424	Q₈	—	172	2	no	—
425	C₂×C₄	—	2	1	no	—
426	C₂×C₄	—	2	1	no	—
427	C₂×C₄	—	2	1	no	—
428	C₂×C₄	—	2	1	no	—
429	C₂×C₄	—	2	1	no	—
430	C₂×C₄	—	2	1	no	—
431	C₂×C₄	—	2	1	no	—
432	C₂×C₄	—	2	1	no	—
433	C₂×C₄	—	2	1	no	—
434	C₂×C₄	—	86	2	no	—
435	C₂×C₄	—	86	2	no	—
436	C₂×C₄	—	86	2	no	—
437	C₂×C₄	—	86	2	no	—
438	C₂×C₄	—	86	4	no	—
439	C₂×C₄	—	86	2	no	—
440	C₂×C₄	—	86	2	no	—
441	C₂×C₄	—	172	2	no	—
442	C₂×C₄	—	172	2	no	—
443	C₂×C₄	—	172	2	no	—
444	C₂×C₄	—	172	2	no	—
445	C₂×C₄	—	172	2	no	—
446	C₂×C₄	—	172	1	no	—
447	C₂×C₄	—	172	1	no	—
448	C₂×C₄	—	172	1	no	—
449	C₂×C₄	—	172	1	no	—
450	C₂×C₄	—	172	1	no	—
451	C₂×C₄	—	172	1	no	—
452	C₂×C₄	C₄×D₁₇₂	1	2	yes	—
453	C₂×C₄	C₄×D₁₇₂	1	2	yes	—
454	C₂×C₄	#13063300	1	2	yes	—
455	C₂×C₄	#13063300	1	2	yes	—
456	C₂×C₄	C₂×Dic₁₇₂	1	2	yes	—
457	C₂×C₄	C₂×Dic₁₇₂	1	2	yes	—
458	C₂×C₄	C₂×Dic₁₇₂	1	2	yes	—
459	C₂×C₄	#13063347	1	2	yes	—
460	C₂×C₄	#13063358	1	2	yes	—
461	C₂×C₄	C₂²×C₄×D₄₃	1	1	yes	characteristic
462	C₂×C₄	C₂×D₄×D₄₃	1	1	yes	characteristic
463	C₂×C₄	#41×D₄₃	1	1	yes	characteristic
464	C₂×C₄	#41×D₄₃	1	1	yes	characteristic
465	C₂×C₄	C₂×#10621898	1	1	yes	characteristic
466	C₂×C₄	C₂×#10621902	1	1	yes	characteristic
467	C₈	—	2	4	no	—
468	C₈	—	4	2	no	—
469	C₂²	C₂×C₄×D₁₇₂	1	1	yes	characteristic
470	C₂²	C₂×#13063300	1	1	yes	characteristic
471	C₂²	#14583411	1	1	yes	characteristic
472	C₂²	C₂²×Dic₁₇₂	1	1	yes	characteristic
473	C₂²	C₂×#13063347	1	1	yes	characteristic
474	C₂²	C₂×#13063358	1	1	yes	characteristic
475	C₂²	#14583699	1	1	yes	characteristic
476	C₄	—	2	2	no	—
477	C₄	—	2	2	no	—
478	C₄	—	2	2	no	—
479	C₄	—	4	1	no	—
480	C₄	—	86	4	no	—
481	C₄	—	344	2	no	—
482	C₄	—	172	4	no	—
483	C₄	—	172	2	no	—
484	C₄	—	172	2	no	—
485	C₄	—	172	2	no	—
486	C₄	C₄×Dic₁₇₂	1	4	yes	complemented
487	C₄	#14583110	1	4	yes	direct product factor
488	C₄	C₄×D₄×D₄₃	1	1	yes	characteristic
489	C₄	C₄×#10621902	1	1	yes	characteristic
490	C₄	#14583436	1	1	yes	characteristic
491	C₄	#14583446	1	1	yes	characteristic
492	C₂	C₄×#13063300	1	1	yes	characteristic
493	C₂	C₂×C₄×Dic₁₇₂	1	1	yes	characteristic
494	C₂	C₄×#13063358	1	1	yes	characteristic
495	C₂	C₂×#14583110	1	1	yes	characteristic
496	C₂	#19144052	1	1	yes	characteristic
497	C₂	#19144635	1	1	yes	characteristic
498	C₂	#19144667	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄	C₂×D₁₇₂
commutator	C₂×C₄×C₄₃	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₄₃
Fitting	C₄×C₄⋊C₈×C₄₃	C₂
socle, prime radical	C₂³×C₄₃	C₂²×D₄
cosocle	C₂²×C₄×C₄₃	C₂⁴
hypercenter	C₄×C₄⋊C₈	D₄₃
hypocenter	C₄₃	C₄×#462
LCS	G ▷ C₂×C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂²×C₄ ◁ C₄³ ◁ C₄×C₄⋊C₈

Complements

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

N	H ≅ G/N	type
18. #14583110	C₄	direct (N × H)
137. C₄²×C₄₃	Q₁₆	semidirect
231. C₄×C₄₃	C₄×Q₁₆	semidirect
232. C₄×C₄₃	#462	semidirect
294. C₄₃	C₄×#462	semidirect
411. C₄²	Dic₁₇₂	semidirect
486. C₄	C₄×Dic₁₇₂	semidirect
487. C₄	#14583110	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×#14583110	2
C₂×C₄×Dic₁₇₂	2
C₄×#13063325	2
C₄²×Dic₈₆	2
#19135517	2
#19135354	2
#19135237	2
#19134935	2
#19134601	2
C₄×#13063250	2
C₄×C₄⋊C₈×C₄₃	2
C₄×#462	43

Subgroups — C4×#14583110 #25102808

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄×#14583110 #25102808