Subgroups — C₄×#14583140 #25103104

Order 11008.

1054 conjugacy classes of subgroups.

The subgroup lattice has 496 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#14583140	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄×Dic₁₇₂	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄×#13063304	C₂	1	2	yes	maximal
4	#19135456	C₂	1	1	yes	maximal, characteristic, complemented
5	#19135328	C₂	1	1	yes	maximal, characteristic, complemented
6	#19135271	C₂	1	2	yes	maximal, complemented
7	#19135018	C₂	1	2	yes	maximal
8	#19134624	C₂	1	1	yes	maximal, characteristic
9	C₄×#13063259	C₂	1	1	yes	maximal, characteristic, complemented
10	C₄×#13063250	C₂	1	2	yes	maximal, complemented
11	C₂²×C₄×C₈×C₄₃	C₂	1	1	yes	maximal, characteristic
12	C₂²×Dic₁₇₂	C₂²	1	1	yes	characteristic
13	C₂×#13063304	C₂²	1	2	yes	—
14	C₂×C₄×Dic₈₆	C₂²	1	2	yes	—
15	#14583140	C₄	1	8	yes	direct product factor
16	C₄×Dic₁₇₂	—	2	4	no	—
17	C₂×#13063259	C₂²	1	1	yes	characteristic
18	C₂×#13063259	C₂²	1	1	yes	characteristic
19	C₂×#13063259	C₂²	1	1	yes	characteristic
20	C₂×#13063250	C₂²	1	2	yes	—
21	C₂×#13063250	C₂²	1	2	yes	—
22	C₂×#13063250	C₂²	1	2	yes	—
23	#14582805	C₂²	1	2	yes	—
24	#14582797	C₂²	1	2	yes	—
25	#14582783	—	2	2	no	—
26	#14582772	—	2	2	no	—
27	#14582759	C₂²	1	2	yes	—
28	C₄×Dic₄₃⋊C₄	—	2	2	no	—
29	C₄×C₄⋊Dic₄₃	C₂²	1	2	yes	—
30	C₄×C₂²⋊Dic₄₃	—	2	2	no	—
31	#14582662	C₂²	1	2	yes	—
32	#14582662	C₂²	1	2	yes	—
33	#14582662	C₂²	1	2	yes	—
34	C₂³×C₈×C₄₃	C₂²	1	1	yes	characteristic
35	C₂³×C₈×C₄₃	C₂²	1	1	yes	characteristic
36	C₂²×C₄²×C₄₃	C₂²	1	1	yes	characteristic
37	C₂×C₄×C₈×C₄₃	—	2	4	no	—
38	C₂×C₄×C₈×C₄₃	C₂²	1	1	yes	characteristic
39	C₂×C₄×C₈×C₄₃	C₂²	1	1	yes	characteristic
40	C₂×C₄×C₈×C₄₃	C₂²	1	1	yes	characteristic
41	C₂×C₄×C₈×C₄₃	C₂²	1	1	yes	characteristic
42	C₂²×Dic₈₆	C₂³	1	2	yes	—
43	C₂×Dic₁₇₂	—	2	2	no	—
44	C₂×Dic₁₇₂	—	2	2	no	—
45	C₂×Dic₁₇₂	C₂×C₄	1	4	yes	complemented
46	#13063304	—	2	4	no	—
47	#13063304	C₂×C₄	1	8	yes	—
48	C₄×Dic₈₆	—	2	4	no	—
49	C₄×Dic₈₆	—	2	4	no	—
50	C₂×C₄⋊Dic₄₃	C₂³	1	2	yes	—
51	C₂×C₄⋊Dic₄₃	C₂³	1	2	yes	—
52	C₂×C₄⋊Dic₄₃	C₂³	1	2	yes	—
53	C₂×Dic₄₃⋊C₄	—	2	2	no	—
54	C₂×Dic₄₃⋊C₄	—	2	2	no	—
55	C₂×Dic₄₃⋊C₄	—	2	2	no	—
56	C₂×C₂²⋊Dic₄₃	—	2	2	no	—
57	C₂×C₂²⋊Dic₄₃	—	2	2	no	—
58	C₂×C₄×Dic₄₃	—	2	2	no	—
59	C₂×C₄×Dic₄₃	—	2	2	no	—
60	#13063259	—	2	2	no	—
61	#13063259	—	2	2	no	—
62	#13063259	C₂×C₄	1	4	yes	complemented
63	#13063250	—	2	4	no	—
64	#13063250	—	2	4	no	—
65	#13063250	C₂×C₄	1	8	yes	complemented
66	C₄₃⋊#95	—	2	2	no	—
67	C₄₃⋊#95	—	2	2	no	—
68	C₄₃⋊#95	—	2	2	no	—
69	C₄₃⋊#95	—	2	2	no	—
70	C₄₃⋊#95	—	2	2	no	—
71	C₂³×C₄×C₄₃	D₄	1	1	yes	characteristic
72	C₂³×C₄×C₄₃	D₄	1	1	yes	characteristic
73	C₂³×C₄×C₄₃	C₂³	1	1	yes	characteristic
74	C₂²×C₈×C₄₃	—	2	2	no	—
75	C₂²×C₈×C₄₃	—	2	2	no	—
76	C₂²×C₈×C₄₃	—	2	2	no	—
77	C₂²×C₈×C₄₃	—	2	2	no	—
78	C₂²×C₈×C₄₃	—	2	2	no	—
79	C₂²×C₈×C₄₃	C₂×C₄	1	4	yes	—
80	C₂²×C₈×C₄₃	C₂³	1	1	yes	characteristic
81	C₂²×C₈×C₄₃	C₂³	1	1	yes	characteristic
82	C₂²×C₈×C₄₃	C₂³	1	1	yes	characteristic
83	C₂²×C₈×C₄₃	C₂³	1	1	yes	characteristic
84	C₂×C₄²×C₄₃	—	2	2	no	—
85	C₂×C₄²×C₄₃	—	2	2	no	—
86	C₂×C₄²×C₄₃	D₄	1	1	yes	characteristic
87	C₂×C₄²×C₄₃	D₄	1	1	yes	characteristic
88	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
89	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
90	C₄×C₈×C₄₃	—	2	2	no	—
91	C₄×C₈×C₄₃	—	2	2	no	—
92	C₄×C₈×C₄₃	—	2	2	no	—
93	C₄×C₈×C₄₃	D₄	1	4	yes	—
94	C₂⁴×C₄₃	C₂×D₄	1	1	yes	characteristic
95	C₂²×C₄×C₄₃	—	2	2	no	—
96	C₂²×C₄×C₄₃	—	2	2	no	—
97	C₂²×C₄×C₄₃	—	2	2	no	—
98	C₂²×C₄×C₄₃	—	2	2	no	—
99	C₂²×C₄×C₄₃	—	2	1	no	—
100	C₂²×C₄×C₄₃	—	2	1	no	—
101	C₂²×C₄×C₄₃	—	2	1	no	—
102	C₂²×C₄×C₄₃	—	2	1	no	—
103	C₂²×C₄×C₄₃	—	2	2	no	—
104	C₂²×C₄×C₄₃	Q₁₆	1	4	yes	complemented
105	C₂²×C₄×C₄₃	C₂²×C₄	1	2	yes	—
106	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
107	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
108	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
109	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
110	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
111	C₂²×C₄×C₄₃	#41	1	2	yes	—
112	C₂²×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
113	C₂²×Dic₄₃	—	2	2	no	—
114	C₂²×Dic₄₃	—	2	2	no	—
115	C₂²×Dic₄₃	—	2	2	no	—
116	C₂²×Dic₄₃	—	2	2	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×C₈×C₄₃	—	2	8	no	—
124	C₂×C₈×C₄₃	—	2	1	no	—
125	C₂×C₈×C₄₃	—	2	1	no	—
126	C₂×C₈×C₄₃	—	2	1	no	—
127	C₂×C₈×C₄₃	—	2	1	no	—
128	C₂×C₈×C₄₃	—	2	1	no	—
129	C₂×C₈×C₄₃	—	2	1	no	—
130	C₂×C₈×C₄₃	—	2	8	no	—
131	C₂×C₈×C₄₃	C₂²×C₄	1	2	yes	—
132	C₂×C₈×C₄₃	C₂²×C₄	1	2	yes	—
133	C₂×C₈×C₄₃	C₂×D₄	1	2	yes	—
134	C₂×C₈×C₄₃	C₂×D₄	1	2	yes	—
135	C₂×C₈×C₄₃	#41	1	2	yes	—
136	C₂×C₈×C₄₃	#41	1	2	yes	—
137	C₄²×C₄₃	—	2	2	no	—
138	C₄²×C₄₃	—	2	2	no	—
139	C₄²×C₄₃	—	2	1	no	—
140	C₄²×C₄₃	—	2	1	no	—
141	C₄²×C₄₃	C₂×D₄	1	2	yes	—
142	C₄²×C₄₃	#41	1	2	yes	—
143	C₂²⋊Dic₄₃	—	2	8	no	—
144	C₂²⋊Dic₄₃	—	4	4	no	—
145	C₄⋊Dic₄₃	—	2	2	no	—
146	C₄⋊Dic₄₃	—	2	2	no	—
147	C₄⋊Dic₄₃	—	2	2	no	—
148	C₄⋊Dic₄₃	—	2	2	no	—
149	C₄⋊Dic₄₃	—	2	2	no	—
150	C₄⋊Dic₄₃	C₂²×C₄	1	4	yes	—
151	Dic₄₃⋊C₄	—	2	8	no	—
152	Dic₄₃⋊C₄	—	4	4	no	—
153	Dic₄₃⋊C₄	—	4	4	no	—
154	C₄×Dic₄₃	—	4	4	no	—
155	C₄×Dic₄₃	—	4	4	no	—
156	Dic₁₇₂	—	2	8	no	—
157	C₂³×C₄₃	—	2	1	no	—
158	C₂³×C₄₃	—	2	1	no	—
159	C₂³×C₄₃	—	2	1	no	—
160	C₂³×C₄₃	—	2	1	no	—
161	C₂³×C₄₃	C₄×D₄	1	2	yes	—
162	C₂³×C₄₃	C₂×Q₁₆	1	2	yes	—
163	C₂³×C₄₃	#135	1	2	yes	—
164	C₂³×C₄₃	C₂²×D₄	1	1	yes	characteristic
165	C₂×C₄×C₄₃	—	2	8	no	—
166	C₂×C₄×C₄₃	—	2	1	no	—
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	2	no	—
175	C₂×C₄×C₄₃	—	2	2	no	—
176	C₂×C₄×C₄₃	—	2	2	no	—
177	C₂×C₄×C₄₃	—	2	2	no	—
178	C₂×C₄×C₄₃	—	2	8	no	—
179	C₂×C₄×C₄₃	C₄×D₄	1	2	yes	—
180	C₂×C₄×C₄₃	#121	1	2	yes	—
181	C₂×C₄×C₄₃	#121	1	2	yes	—
182	C₂×C₄×C₄₃	C₂×Q₁₆	1	2	yes	—
183	C₂×C₄×C₄₃	C₂×Q₁₆	1	2	yes	—
184	C₂×C₄×C₄₃	#135	1	2	yes	—
185	C₂×C₄×C₄₃	#135	1	2	yes	—
186	C₂×C₄×C₄₃	C₂³×C₄	1	1	yes	characteristic
187	C₂×C₄×C₄₃	C₂²×D₄	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×C₄×C₄₃	C₂×#41	1	1	yes	characteristic
192	C₂×Dic₄₃	—	2	4	no	—
193	C₂×Dic₄₃	—	2	4	no	—
194	C₂×Dic₄₃	—	4	2	no	—
195	C₂×Dic₄₃	—	4	2	no	—
196	C₂×Dic₄₃	—	4	2	no	—
197	C₂×Dic₄₃	—	4	2	no	—
198	C₂×Dic₄₃	—	4	2	no	—
199	C₂×Dic₄₃	—	4	2	no	—
200	C₂×Dic₄₃	—	4	2	no	—
201	C₂×Dic₄₃	—	4	2	no	—
202	C₂×Dic₄₃	—	4	2	no	—
203	C₂×Dic₄₃	—	4	2	no	—
204	Dic₈₆	—	2	4	no	—
205	Dic₈₆	—	2	4	no	—
206	Dic₈₆	—	4	2	no	—
207	Dic₈₆	—	4	2	no	—
208	C₈×C₄₃	—	2	2	no	—
209	C₈×C₄₃	—	2	2	no	—
210	C₈×C₄₃	—	2	2	no	—
211	C₈×C₄₃	C₄×D₄	1	4	yes	—
212	C₄×#467	—	43	1	no	maximal, Sylow
213	C₂²×C₄₃	—	2	2	no	—
214	C₂²×C₄₃	—	2	2	no	—
215	C₂²×C₄₃	—	2	2	no	—
216	C₂²×C₄₃	—	2	2	no	—
217	C₂²×C₄₃	—	2	2	no	—
218	C₂²×C₄₃	—	2	2	no	—
219	C₂²×C₄₃	C₄×Q₁₆	1	4	yes	complemented
220	C₂²×C₄₃	C₂×C₄×D₄	1	1	yes	characteristic
221	C₂²×C₄₃	C₂×#121	1	1	yes	characteristic
222	C₂²×C₄₃	#532	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×#135	1	1	yes	characteristic
226	C₂²×C₄₃	C₂×#135	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	—	2	2	no	—
231	C₄×C₄₃	#467	1	4	yes	complemented
232	C₄×C₄₃	C₂×C₄×D₄	1	1	yes	characteristic
233	C₄×C₄₃	C₄×#41	1	1	yes	characteristic
234	C₄×C₄₃	#525	1	1	yes	characteristic
235	C₄×C₄₃	#529	1	1	yes	characteristic
236	Dic₄₃	—	4	4	no	—
237	Dic₄₃	—	4	4	no	—
238	Dic₄₃	—	8	2	no	—
239	Dic₄₃	—	8	2	no	—
240	C₂×#467	—	43	1	no	—
241	C₂×C₄×Q₁₆	—	43	1	no	—
242	C₂²×C₄×C₈	D₄₃	1	1	yes	characteristic
243	C₄×C₂²⋊Q₈	—	43	2	no	—
244	#1969	—	43	1	no	—
245	#1942	—	43	1	no	—
246	#1933	—	43	2	no	—
247	#1892	—	43	2	no	—
248	#1808	—	43	1	no	—
249	C₄×#107	—	43	1	no	—
250	C₄×#103	—	43	2	no	—
251	C₂×C₄₃	—	2	4	no	—
252	C₂×C₄₃	C₄×#121	1	1	yes	characteristic
253	C₂×C₄₃	C₂×C₄×Q₁₆	1	1	yes	characteristic
254	C₂×C₄₃	C₄×#135	1	1	yes	characteristic
255	C₂×C₄₃	C₂×#467	1	1	yes	characteristic
256	C₂×C₄₃	#3050	1	1	yes	characteristic
257	C₂×C₄₃	#3168	1	1	yes	characteristic
258	C₂×C₄₃	#3170	1	1	yes	characteristic
259	C₂²×Q₁₆	—	43	1	no	—
260	C₂³×C₈	C₂×D₄₃	1	1	yes	characteristic
261	C₂³×C₈	C₂×D₄₃	1	1	yes	characteristic
262	C₂×C₂²⋊Q₈	—	43	2	no	—
263	C₂×C₄×Q₈	—	43	2	no	—
264	C₂²×C₄²	C₂×D₄₃	1	1	yes	characteristic
265	#467	—	43	8	no	—
266	C₄×Q₁₆	—	86	4	no	—
267	C₂×#107	—	43	1	no	—
268	C₂×#107	—	43	1	no	—
269	C₂×#107	—	43	1	no	—
270	C₂×#103	—	43	2	no	—
271	C₂×#103	—	43	2	no	—
272	C₂×#103	—	43	2	no	—
273	C₂×C₄×C₈	—	2	4	no	—
274	C₂×C₄×C₈	C₂×D₄₃	1	1	yes	characteristic
275	C₂×C₄×C₈	C₂×D₄₃	1	1	yes	characteristic
276	C₂×C₄×C₈	C₂×D₄₃	1	1	yes	characteristic
277	C₂×C₄×C₈	C₂×D₄₃	1	1	yes	characteristic
278	#391	—	43	2	no	—
279	#389	—	43	2	no	—
280	#387	—	86	2	no	—
281	#385	—	86	2	no	—
282	#380	—	43	2	no	—
283	C₄×C₄⋊C₄	—	43	2	no	—
284	C₄×C₄⋊C₄	—	86	2	no	—
285	C₄×C₂²⋊C₄	—	86	2	no	—
286	#340	—	43	2	no	—
287	#340	—	43	2	no	—
288	#340	—	43	2	no	—
289	C₄₃	C₄×#467	1	1	yes	characteristic, complemented, Sylow
290	C₂²×Q₈	—	43	2	no	—
291	C₂³×C₄	D₁₇₂	1	1	yes	characteristic
292	C₂³×C₄	D₁₇₂	1	1	yes	characteristic
293	C₂³×C₄	C₂²×D₄₃	1	1	yes	characteristic
294	C₂×Q₁₆	—	43	4	no	—
295	C₂×Q₁₆	—	86	2	no	—
296	C₂×Q₁₆	—	86	2	no	—
297	C₂²×C₈	—	2	2	no	—
298	C₂²×C₈	—	2	2	no	—
299	C₂²×C₈	—	2	2	no	—
300	C₂²×C₈	—	2	2	no	—
301	C₂²×C₈	—	2	2	no	—
302	C₂²×C₈	C₄×D₄₃	1	4	yes	—
303	C₂²×C₈	C₂²×D₄₃	1	1	yes	characteristic
304	C₂²×C₈	C₂²×D₄₃	1	1	yes	characteristic
305	C₂²×C₈	C₂²×D₄₃	1	1	yes	characteristic
306	C₂²×C₈	C₂²×D₄₃	1	1	yes	characteristic
307	C₂²⋊Q₈	—	43	8	no	—
308	C₂²⋊Q₈	—	86	4	no	—
309	C₄×Q₈	—	86	4	no	—
310	C₄×Q₈	—	86	4	no	—
311	C₂×C₄⋊C₄	—	43	2	no	—
312	C₂×C₄⋊C₄	—	43	2	no	—
313	C₂×C₄⋊C₄	—	43	2	no	—
314	C₂×C₄⋊C₄	—	86	2	no	—
315	C₂×C₄⋊C₄	—	86	2	no	—
316	C₂×C₄⋊C₄	—	86	2	no	—
317	C₂×C₂²⋊C₄	—	86	2	no	—
318	C₂×C₂²⋊C₄	—	86	2	no	—
319	C₂×C₄²	—	2	2	no	—
320	C₂×C₄²	—	2	2	no	—
321	C₂×C₄²	—	86	2	no	—
322	C₂×C₄²	—	86	2	no	—
323	C₂×C₄²	D₁₇₂	1	1	yes	characteristic
324	C₂×C₄²	D₁₇₂	1	1	yes	characteristic
325	C₂×C₄²	C₂²×D₄₃	1	1	yes	characteristic
326	C₂×C₄²	C₂²×D₄₃	1	1	yes	characteristic
327	#107	—	43	4	no	—
328	#107	—	86	2	no	—
329	#107	—	86	2	no	—
330	#103	—	43	8	no	—
331	#103	—	86	4	no	—
332	#103	—	86	4	no	—
333	C₄×C₈	—	2	2	no	—
334	C₄×C₈	—	2	2	no	—
335	C₄×C₈	—	2	2	no	—
336	C₄×C₈	C₂²⋊D₄₃	1	4	yes	—
337	#95	—	86	2	no	—
338	#95	—	86	2	no	—
339	#95	—	86	2	no	—
340	#95	—	86	2	no	—
341	#95	—	86	2	no	—
342	C₂⁴	C₂×D₁₇₂	1	1	yes	characteristic
343	C₂×Q₈	—	43	4	no	—
344	C₂×Q₈	—	86	2	no	—
345	C₂×Q₈	—	86	2	no	—
346	C₂×Q₈	—	86	2	no	—
347	C₂×Q₈	—	86	2	no	—
348	C₂×Q₈	—	86	2	no	—
349	C₂²×C₄	—	2	2	no	—
350	C₂²×C₄	—	2	2	no	—
351	C₂²×C₄	—	2	2	no	—
352	C₂²×C₄	—	2	2	no	—
353	C₂²×C₄	—	2	2	no	—
354	C₂²×C₄	—	2	1	no	—
355	C₂²×C₄	—	2	1	no	—
356	C₂²×C₄	—	2	1	no	—
357	C₂²×C₄	—	2	1	no	—
358	C₂²×C₄	—	86	2	no	—
359	C₂²×C₄	—	86	2	no	—
360	C₂²×C₄	—	86	2	no	—
361	C₂²×C₄	—	86	2	no	—
362	C₂²×C₄	Dic₁₇₂	1	4	yes	complemented
363	C₂²×C₄	C₂×C₄×D₄₃	1	2	yes	—
364	C₂²×C₄	C₂×D₁₇₂	1	1	yes	characteristic
365	C₂²×C₄	C₂×D₁₇₂	1	1	yes	characteristic
366	C₂²×C₄	C₂×D₁₇₂	1	1	yes	characteristic
367	C₂²×C₄	C₂×D₁₇₂	1	1	yes	characteristic
368	C₂²×C₄	C₂×D₁₇₂	1	1	yes	characteristic
369	C₂²×C₄	#10621898	1	2	yes	—
370	C₂²×C₄	C₂³×D₄₃	1	1	yes	characteristic
371	Q₁₆	—	86	8	no	—
372	C₂×C₈	—	2	8	no	—
373	C₂×C₈	—	2	1	no	—
374	C₂×C₈	—	2	1	no	—
375	C₂×C₈	—	2	1	no	—
376	C₂×C₈	—	2	1	no	—
377	C₂×C₈	—	2	1	no	—
378	C₂×C₈	—	2	1	no	—
379	C₂×C₈	—	2	8	no	—
380	C₂×C₈	C₂×C₄×D₄₃	1	2	yes	—
381	C₂×C₈	C₂×C₄×D₄₃	1	2	yes	—
382	C₂×C₈	#10621898	1	2	yes	—
383	C₂×C₈	#10621898	1	2	yes	—
384	C₂×C₈	C₂×C₂²⋊D₄₃	1	2	yes	—
385	C₂×C₈	C₂×C₂²⋊D₄₃	1	2	yes	—
386	C₄⋊C₄	—	43	4	no	—
387	C₄⋊C₄	—	86	8	no	—
388	C₄⋊C₄	—	86	2	no	—
389	C₄⋊C₄	—	86	2	no	—
390	C₄⋊C₄	—	86	2	no	—
391	C₄⋊C₄	—	86	2	no	—
392	C₄⋊C₄	—	86	2	no	—
393	C₄⋊C₄	—	172	4	no	—
394	C₄⋊C₄	—	172	4	no	—
395	C₂²⋊C₄	—	86	8	no	—
396	C₂²⋊C₄	—	172	4	no	—
397	C₄²	—	2	2	no	—
398	C₄²	—	2	2	no	—
399	C₄²	—	2	1	no	—
400	C₄²	—	2	1	no	—
401	C₄²	—	172	4	no	—
402	C₄²	—	172	4	no	—
403	C₄²	#10621898	1	2	yes	—
404	C₄²	C₂×C₂²⋊D₄₃	1	2	yes	—
405	C₂³	—	2	1	no	—
406	C₂³	—	2	1	no	—
407	C₂³	—	2	1	no	—
408	C₂³	—	2	1	no	—
409	C₂³	C₄×D₁₇₂	1	2	yes	—
410	C₂³	C₂×Dic₁₇₂	1	2	yes	—
411	C₂³	#13063347	1	2	yes	—
412	C₂³	C₂²×D₁₇₂	1	1	yes	characteristic
413	Q₈	—	86	4	no	—
414	Q₈	—	86	4	no	—
415	Q₈	—	172	2	no	—
416	Q₈	—	172	2	no	—
417	C₂×C₄	—	2	8	no	—
418	C₂×C₄	—	2	1	no	—
419	C₂×C₄	—	2	1	no	—
420	C₂×C₄	—	2	1	no	—
421	C₂×C₄	—	2	1	no	—
422	C₂×C₄	—	2	1	no	—
423	C₂×C₄	—	2	1	no	—
424	C₂×C₄	—	2	1	no	—
425	C₂×C₄	—	2	1	no	—
426	C₂×C₄	—	2	2	no	—
427	C₂×C₄	—	2	2	no	—
428	C₂×C₄	—	2	8	no	—
429	C₂×C₄	—	2	2	no	—
430	C₂×C₄	—	2	2	no	—
431	C₂×C₄	—	86	4	no	—
432	C₂×C₄	—	86	4	no	—
433	C₂×C₄	—	172	2	no	—
434	C₂×C₄	—	172	2	no	—
435	C₂×C₄	—	172	2	no	—
436	C₂×C₄	—	172	2	no	—
437	C₂×C₄	—	172	2	no	—
438	C₂×C₄	—	172	2	no	—
439	C₂×C₄	—	172	2	no	—
440	C₂×C₄	—	172	2	no	—
441	C₂×C₄	—	172	2	no	—
442	C₂×C₄	—	172	2	no	—
443	C₂×C₄	C₄×D₁₇₂	1	2	yes	—
444	C₂×C₄	#13063299	1	2	yes	—
445	C₂×C₄	#13063299	1	2	yes	—
446	C₂×C₄	C₂×Dic₁₇₂	1	2	yes	—
447	C₂×C₄	C₂×Dic₁₇₂	1	2	yes	—
448	C₂×C₄	#13063347	1	2	yes	—
449	C₂×C₄	#13063347	1	2	yes	—
450	C₂×C₄	C₂²×C₄×D₄₃	1	1	yes	characteristic
451	C₂×C₄	C₂²×C₂²⋊D₄₃	1	1	yes	characteristic
452	C₂×C₄	C₂×#10621898	1	1	yes	characteristic
453	C₂×C₄	C₂×#10621898	1	1	yes	characteristic
454	C₂×C₄	C₂×#10621898	1	1	yes	characteristic
455	C₂×C₄	C₂×#10621898	1	1	yes	characteristic
456	C₈	—	2	2	no	—
457	C₈	—	2	2	no	—
458	C₈	—	2	2	no	—
459	C₈	C₄×C₂²⋊D₄₃	1	4	yes	—
460	C₂²	—	2	2	no	—
461	C₂²	—	2	2	no	—
462	C₂²	—	2	2	no	—
463	C₂²	—	2	2	no	—
464	C₂²	—	2	2	no	—
465	C₂²	—	2	2	no	—
466	C₂²	C₄×Dic₁₇₂	1	4	yes	complemented
467	C₂²	C₂×C₄×D₁₇₂	1	1	yes	characteristic
468	C₂²	C₂×#13063299	1	1	yes	characteristic
469	C₂²	#14583449	1	1	yes	characteristic
470	C₂²	C₂²×Dic₁₇₂	1	1	yes	characteristic
471	C₂²	C₂×#13063347	1	1	yes	characteristic
472	C₂²	C₂×#13063347	1	1	yes	characteristic
473	C₂²	C₂×#13063347	1	1	yes	characteristic
474	C₄	—	2	2	no	—
475	C₄	—	2	2	no	—
476	C₄	—	2	2	no	—
477	C₄	—	2	2	no	—
478	C₄	—	344	2	no	—
479	C₄	—	344	2	no	—
480	C₄	—	172	4	no	—
481	C₄	—	172	4	no	—
482	C₄	#14583140	1	4	yes	direct product factor
483	C₄	C₂×C₄×C₂²⋊D₄₃	1	1	yes	characteristic
484	C₄	C₄×#10621898	1	1	yes	characteristic
485	C₄	#14583410	1	1	yes	characteristic
486	C₄	#14583433	1	1	yes	characteristic
487	C₂	—	2	4	no	—
488	C₂	C₄×#13063299	1	1	yes	characteristic
489	C₂	C₂×C₄×Dic₁₇₂	1	1	yes	characteristic
490	C₂	C₄×#13063347	1	1	yes	characteristic
491	C₂	C₂×#14583140	1	1	yes	characteristic
492	C₂	#19144176	1	1	yes	characteristic
493	C₂	#19145165	1	1	yes	characteristic
494	C₂	#19145181	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄	C₂×D₁₇₂
commutator	C₂×C₄×C₄₃	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₄₃
Fitting	C₂²×C₄×C₈×C₄₃	C₂
socle	C₂³×C₄₃	C₂²×D₄
prime radical	C₂⁴×C₄₃	C₂×D₄
cosocle	C₂²×C₄×C₄₃	C₂⁴
hypercenter	C₂²×C₄×C₈	D₄₃
hypocenter	C₄₃	C₄×#467
LCS	G ▷ C₂×C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂²×C₄ ◁ C₂²×C₄² ◁ C₂²×C₄×C₈

Complements

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

N	H ≅ G/N	type
2. C₂×C₄×Dic₁₇₂	C₂	semidirect
4. #19135456	C₂	semidirect
5. #19135328	C₂	semidirect
6. #19135271	C₂	semidirect
9. C₄×#13063259	C₂	semidirect
10. C₄×#13063250	C₂	semidirect
15. #14583140	C₄	direct (N × H)
45. C₂×Dic₁₇₂	C₂×C₄	semidirect
62. #13063259	C₂×C₄	semidirect
65. #13063250	C₂×C₄	semidirect
104. C₂²×C₄×C₄₃	Q₁₆	semidirect
219. C₂²×C₄₃	C₄×Q₁₆	semidirect
231. C₄×C₄₃	#467	semidirect
289. C₄₃	C₄×#467	semidirect
362. C₂²×C₄	Dic₁₇₂	semidirect
466. C₂²	C₄×Dic₁₇₂	semidirect
482. C₄	#14583140	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×#14583140	2
C₂×C₄×Dic₁₇₂	2
C₄×#13063304	2
#19135456	2
#19135328	2
#19135271	2
#19135018	2
#19134624	2
C₄×#13063259	2
C₄×#13063250	2
C₂²×C₄×C₈×C₄₃	2
C₄×#467	43

Subgroups — C4×#14583140 #25103104

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄×#14583140 #25103104