Subgroups — C₄×#14583189 #25104170

Order 11008.

1000 conjugacy classes of subgroups.

The subgroup lattice has 518 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#14583189	C₂	1	1	yes	maximal, characteristic
2	C₄×#13063325	C₂	1	1	yes	maximal, characteristic, complemented
3	#19135543	C₂	1	1	yes	maximal, characteristic, complemented
4	#19135358	C₂	1	1	yes	maximal, characteristic, complemented
5	#19135180	C₂	1	2	yes	maximal, complemented
6	#19134856	C₂	1	2	yes	maximal
7	#19134595	C₂	1	1	yes	maximal, characteristic
8	C₄×#13063256	C₂	1	2	yes	maximal, complemented
9	C₄×C₄⋊(C₄₃⋊C₈)	C₂	1	1	yes	maximal, characteristic, complemented
10	C₄×#13063246	C₂	1	2	yes	maximal
11	C₄²×D₄×C₄₃	C₂	1	1	yes	maximal, characteristic
12	C₂×#13063325	C₂²	1	1	yes	characteristic
13	C₂×C₄×Dic₈₆	—	2	1	no	—
14	#14583189	C₄	1	8	yes	direct product factor
15	C₂×#13063256	C₂²	1	2	yes	—
16	C₂×#13063256	C₂²	1	2	yes	—
17	C₂×C₄⋊(C₄₃⋊C₈)	C₂²	1	1	yes	characteristic
18	C₂×C₄⋊(C₄₃⋊C₈)	C₂²	1	1	yes	characteristic
19	C₂×#13063246	C₂²	1	2	yes	—
20	C₂×#13063246	C₂²	1	2	yes	—
21	C₂×C₄×C₄₃⋊C₈	C₂²	1	2	yes	—
22	#14582805	—	2	1	no	—
23	#14582797	—	2	1	no	—
24	#14582797	C₂²	1	2	yes	—
25	#14582769	C₂²	1	1	yes	characteristic
26	C₄×C₄⋊Dic₄₃	—	2	1	no	—
27	C₄×C₄⋊Dic₄₃	C₂²	1	2	yes	—
28	#14582661	C₂²	1	2	yes	—
29	#14582661	C₂²	1	2	yes	—
30	#14582661	C₂²	1	2	yes	—
31	#14582661	C₂²	1	2	yes	—
32	#14582654	C₂²	1	2	yes	—
33	C₂×C₄×D₄×C₄₃	C₂²	1	1	yes	characteristic
34	C₂×C₄×D₄×C₄₃	C₂²	1	1	yes	characteristic
35	C₂×C₄×D₄×C₄₃	C₂²	1	1	yes	characteristic
36	C₂²×C₄²×C₄₃	—	2	1	no	—
37	C₄×C₄⋊C₄×C₄₃	C₂²	1	1	yes	characteristic
38	C₄×C₄⋊C₄×C₄₃	C₂²	1	1	yes	characteristic
39	C₄×C₄⋊C₄×C₄₃	C₂²	1	1	yes	characteristic
40	C₄×C₂²⋊C₄×C₄₃	—	2	1	no	—
41	C₄×C₂²⋊C₄×C₄₃	—	2	1	no	—
42	C₄×C₂²⋊C₄×C₄₃	—	2	1	no	—
43	C₄³×C₄₃	C₂²	1	1	yes	characteristic
44	C₂²×Dic₈₆	—	2	1	no	—
45	C₂²×C₄₃⋊C₈	C₂³	1	2	yes	—
46	C₂²×C₄₃⋊C₈	C₂³	1	2	yes	—
47	#13063325	—	2	2	no	—
48	#13063325	C₂×C₄	1	4	yes	complemented
49	C₄×Dic₈₆	—	4	4	no	—
50	C₂×C₄⋊Dic₄₃	—	2	1	no	—
51	C₂×C₄⋊Dic₄₃	—	2	1	no	—
52	C₂×C₄⋊Dic₄₃	—	2	1	no	—
53	C₂×C₄⋊Dic₄₃	C₂³	1	2	yes	—
54	C₂×C₄⋊Dic₄₃	C₂³	1	2	yes	—
55	C₂×Dic₄₃⋊C₄	—	2	2	no	—
56	C₂×C₄×Dic₄₃	—	2	2	no	—
57	#13063256	—	2	4	no	—
58	#13063256	C₂×C₄	1	8	yes	complemented
59	C₄⋊(C₄₃⋊C₈)	—	2	2	no	—
60	C₄⋊(C₄₃⋊C₈)	C₂×C₄	1	4	yes	complemented
61	#13063246	—	2	4	no	—
62	#13063246	C₂×C₄	1	8	yes	—
63	C₄×C₄₃⋊C₈	—	2	4	no	—
64	C₄₃⋊#95	—	2	2	no	—
65	C₄₃⋊#95	—	2	2	no	—
66	C₂²×D₄×C₄₃	C₂³	1	1	yes	characteristic
67	C₂³×C₄×C₄₃	—	2	1	no	—
68	C₂³×C₄×C₄₃	—	2	1	no	—
69	C₂³×C₄×C₄₃	—	2	1	no	—
70	C₄×D₄×C₄₃	—	2	2	no	—
71	C₄×D₄×C₄₃	—	2	2	no	—
72	C₄×D₄×C₄₃	—	2	2	no	—
73	C₄×D₄×C₄₃	—	2	2	no	—
74	C₄×D₄×C₄₃	C₂×C₄	1	4	yes	—
75	C₄×D₄×C₄₃	Q₈	1	4	yes	complemented
76	C₂×C₄⋊C₄×C₄₃	C₂³	1	1	yes	characteristic
77	C₂×C₄⋊C₄×C₄₃	C₂³	1	1	yes	characteristic
78	C₂×C₄⋊C₄×C₄₃	C₂³	1	1	yes	characteristic
79	C₂×C₂²⋊C₄×C₄₃	—	2	1	no	—
80	C₂×C₂²⋊C₄×C₄₃	—	2	1	no	—
81	C₂×C₂²⋊C₄×C₄₃	—	2	1	no	—
82	C₂×C₄²×C₄₃	—	2	1	no	—
83	C₂×C₄²×C₄₃	—	2	1	no	—
84	C₂×C₄²×C₄₃	—	2	1	no	—
85	C₂×C₄²×C₄₃	—	4	4	no	—
86	C₂×C₄²×C₄₃	D₄	1	1	yes	characteristic
87	C₂×C₄²×C₄₃	D₄	1	1	yes	characteristic
88	C₂×C₄²×C₄₃	D₄	1	1	yes	characteristic
89	C₂×C₄²×C₄₃	D₄	1	1	yes	characteristic
90	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
91	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
92	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
93	#95×C₄₃	—	2	1	no	—
94	#95×C₄₃	—	2	1	no	—
95	#95×C₄₃	—	2	1	no	—
96	C₂⁴×C₄₃	—	2	1	no	—
97	C₂×D₄×C₄₃	—	2	1	no	—
98	C₂×D₄×C₄₃	—	2	1	no	—
99	C₂×D₄×C₄₃	—	2	1	no	—
100	C₂×D₄×C₄₃	C₂²×C₄	1	2	yes	—
101	C₂×D₄×C₄₃	C₂×Q₈	1	2	yes	—
102	C₂×D₄×C₄₃	#41	1	2	yes	—
103	C₂²×C₄×C₄₃	—	2	4	no	—
104	C₂²×C₄×C₄₃	—	2	4	no	—
105	C₂²×C₄×C₄₃	—	2	4	no	—
106	C₂²×C₄×C₄₃	—	2	1	no	—
107	C₂²×C₄×C₄₃	—	2	1	no	—
108	C₂²×C₄×C₄₃	—	2	1	no	—
109	C₂²×C₄×C₄₃	—	4	2	no	—
110	C₂²×C₄×C₄₃	—	4	2	no	—
111	C₂²×C₄×C₄₃	—	4	2	no	—
112	C₂²×C₄×C₄₃	—	4	2	no	—
113	C₂²×C₄×C₄₃	—	4	2	no	—
114	C₂²×C₄×C₄₃	—	4	2	no	—
115	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
116	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
117	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
118	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
119	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
120	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
121	C₂²×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
122	C₂²×Dic₄₃	—	2	2	no	—
123	C₂²×Dic₄₃	—	2	2	no	—
124	C₂×Dic₈₆	—	2	4	no	—
125	C₂×Dic₈₆	—	4	2	no	—
126	C₂×Dic₈₆	—	4	2	no	—
127	C₄⋊C₄×C₄₃	—	2	1	no	—
128	C₄⋊C₄×C₄₃	—	2	1	no	—
129	C₄⋊C₄×C₄₃	—	2	1	no	—
130	C₄⋊C₄×C₄₃	C₂²×C₄	1	2	yes	—
131	C₄⋊C₄×C₄₃	C₂×Q₈	1	2	yes	—
132	C₄⋊C₄×C₄₃	#41	1	2	yes	—
133	C₂²⋊C₄×C₄₃	—	2	4	no	—
134	C₂²⋊C₄×C₄₃	—	2	4	no	—
135	C₂²⋊C₄×C₄₃	—	2	4	no	—
136	C₄²×C₄₃	—	2	2	no	—
137	C₄²×C₄₃	—	2	2	no	—
138	C₄²×C₄₃	—	2	1	no	—
139	C₄²×C₄₃	—	2	1	no	—
140	C₄²×C₄₃	—	4	1	no	—
141	C₄²×C₄₃	—	4	2	no	—
142	C₄²×C₄₃	—	4	2	no	—
143	C₄²×C₄₃	—	4	2	no	—
144	C₄²×C₄₃	SD₁₆	1	4	yes	—
145	C₄²×C₄₃	C₂²×C₄	1	2	yes	—
146	C₄²×C₄₃	C₂×Q₈	1	2	yes	—
147	C₄²×C₄₃	#41	1	2	yes	—
148	C₄²×C₄₃	#41	1	2	yes	—
149	C₄⋊Dic₄₃	—	2	4	no	—
150	C₄⋊Dic₄₃	—	2	2	no	—
151	C₄⋊Dic₄₃	—	2	2	no	—
152	C₄⋊Dic₄₃	—	2	2	no	—
153	C₄⋊Dic₄₃	—	4	2	no	—
154	C₄⋊Dic₄₃	—	4	2	no	—
155	C₄⋊Dic₄₃	C₂²×C₄	1	4	yes	—
156	Dic₄₃⋊C₄	—	4	4	no	—
157	C₄×Dic₄₃	—	4	4	no	—
158	C₂×C₄₃⋊C₈	—	2	2	no	—
159	C₂×C₄₃⋊C₈	—	2	2	no	—
160	C₂×C₄₃⋊C₈	—	2	2	no	—
161	C₂×C₄₃⋊C₈	—	2	2	no	—
162	C₂×C₄₃⋊C₈	—	2	2	no	—
163	C₂×C₄₃⋊C₈	C₂²×C₄	1	4	yes	—
164	C₂³×C₄₃	—	2	2	no	—
165	C₂³×C₄₃	—	2	2	no	—
166	C₂³×C₄₃	—	2	2	no	—
167	C₂³×C₄₃	—	4	1	no	—
168	C₂³×C₄₃	—	4	1	no	—
169	C₂³×C₄₃	—	4	1	no	—
170	C₂³×C₄₃	—	4	1	no	—
171	C₂³×C₄₃	C₂²×D₄	1	1	yes	characteristic
172	D₄×C₄₃	—	2	2	no	—
173	D₄×C₄₃	—	2	2	no	—
174	D₄×C₄₃	—	2	2	no	—
175	D₄×C₄₃	C₄×Q₈	1	4	yes	complemented
176	C₂×C₄×C₄₃	—	2	1	no	—
177	C₂×C₄×C₄₃	—	2	1	no	—
178	C₂×C₄×C₄₃	—	2	1	no	—
179	C₂×C₄×C₄₃	—	2	1	no	—
180	C₂×C₄×C₄₃	—	2	1	no	—
181	C₂×C₄×C₄₃	—	2	1	no	—
182	C₂×C₄×C₄₃	—	2	2	no	—
183	C₂×C₄×C₄₃	—	2	2	no	—
184	C₂×C₄×C₄₃	—	2	1	no	—
185	C₂×C₄×C₄₃	—	2	2	no	—
186	C₂×C₄×C₄₃	—	2	1	no	—
187	C₂×C₄×C₄₃	—	2	1	no	—
188	C₂×C₄×C₄₃	—	4	8	no	—
189	C₂×C₄×C₄₃	—	4	1	no	—
190	C₂×C₄×C₄₃	—	4	1	no	—
191	C₂×C₄×C₄₃	—	4	1	no	—
192	C₂×C₄×C₄₃	—	4	1	no	—
193	C₂×C₄×C₄₃	—	4	1	no	—
194	C₂×C₄×C₄₃	—	4	1	no	—
195	C₂×C₄×C₄₃	—	4	8	no	—
196	C₂×C₄×C₄₃	—	4	8	no	—
197	C₂×C₄×C₄₃	C₄×D₄	1	2	yes	—
198	C₂×C₄×C₄₃	C₄×D₄	1	2	yes	—
199	C₂×C₄×C₄₃	C₂²⋊Q₈	1	2	yes	—
200	C₂×C₄×C₄₃	C₂²⋊Q₈	1	2	yes	—
201	C₂×C₄×C₄₃	C₂×SD₁₆	1	2	yes	—
202	C₂×C₄×C₄₃	C₂×SD₁₆	1	2	yes	—
203	C₂×C₄×C₄₃	C₂×SD₁₆	1	2	yes	—
204	C₂×C₄×C₄₃	#135	1	2	yes	—
205	C₂×C₄×C₄₃	AGL(1,ℤ/8)	1	2	yes	—
206	C₂×C₄×C₄₃	C₂³×C₄	1	1	yes	characteristic
207	C₂×C₄×C₄₃	C₂²×Q₈	1	1	yes	characteristic
208	C₂×C₄×C₄₃	C₂×#41	1	1	yes	characteristic
209	C₂×C₄×C₄₃	C₂×#41	1	1	yes	characteristic
210	C₂×C₄×C₄₃	C₂×#41	1	1	yes	characteristic
211	C₂×C₄×C₄₃	C₂×#41	1	1	yes	characteristic
212	C₂×Dic₄₃	—	2	4	no	—
213	C₂×Dic₄₃	—	4	2	no	—
214	C₂×Dic₄₃	—	4	2	no	—
215	C₂×Dic₄₃	—	4	2	no	—
216	C₂×Dic₄₃	—	4	2	no	—
217	C₂×Dic₄₃	—	4	2	no	—
218	Dic₈₆	—	4	8	no	—
219	C₄₃⋊C₈	—	2	4	no	—
220	C₄₃⋊C₈	—	4	2	no	—
221	C₄×#476	—	43	1	no	maximal, Sylow
222	C₂²×C₄₃	—	2	4	no	—
223	C₂²×C₄₃	—	4	2	no	—
224	C₂²×C₄₃	—	4	2	no	—
225	C₂²×C₄₃	—	4	2	no	—
226	C₂²×C₄₃	—	4	2	no	—
227	C₂²×C₄₃	—	4	2	no	—
228	C₂²×C₄₃	—	4	2	no	—
229	C₂²×C₄₃	C₂×C₄×D₄	1	1	yes	characteristic
230	C₂²×C₄₃	C₂×C₂²⋊Q₈	1	1	yes	characteristic
231	C₂²×C₄₃	#525	1	1	yes	characteristic
232	C₂²×C₄₃	C₂²×SD₁₆	1	1	yes	characteristic
233	C₂²×C₄₃	C₂×#135	1	1	yes	characteristic
234	C₂²×C₄₃	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
235	C₂²×C₄₃	#575	1	1	yes	characteristic
236	C₄×C₄₃	—	2	2	no	—
237	C₄×C₄₃	—	2	2	no	—
238	C₄×C₄₃	—	2	2	no	—
239	C₄×C₄₃	—	4	2	no	—
240	C₄×C₄₃	—	4	1	no	—
241	C₄×C₄₃	—	4	2	no	—
242	C₄×C₄₃	—	4	2	no	—
243	C₄×C₄₃	C₄×SD₁₆	1	4	yes	—
244	C₄×C₄₃	#476	1	4	yes	complemented
245	C₄×C₄₃	C₂×C₄×Q₈	1	1	yes	characteristic
246	C₄×C₄₃	C₄×#41	1	1	yes	characteristic
247	C₄×C₄₃	#529	1	1	yes	characteristic
248	C₄×C₄₃	#533	1	1	yes	characteristic
249	Dic₄₃	—	4	4	no	—
250	Dic₄₃	—	8	2	no	—
251	C₂×#476	—	43	1	no	—
252	C₄×C₄⋊Q₈	—	43	1	no	—
253	C₄²×D₄	D₄₃	1	1	yes	characteristic
254	#1987	—	43	1	no	—
255	#1948	—	43	1	no	—
256	#1920	—	43	2	no	—
257	#1864	—	43	2	no	—
258	#1802	—	43	1	no	—
259	C₄×#106	—	43	2	no	—
260	C₄×C₄⋊C₈	—	43	1	no	—
261	C₄×#102	—	43	2	no	—
262	C₂×C₄₃	—	4	4	no	—
263	C₂×C₄₃	C₄×C₂²⋊Q₈	1	1	yes	characteristic
264	C₂×C₄₃	C₂×C₄×SD₁₆	1	1	yes	characteristic
265	C₂×C₄₃	C₄×AGL(1,ℤ/8)	1	1	yes	characteristic
266	C₂×C₄₃	C₂×#476	1	1	yes	characteristic
267	C₂×C₄₃	#3076	1	1	yes	characteristic
268	C₂×C₄₃	#3101	1	1	yes	characteristic
269	C₂×C₄₃	#3106	1	1	yes	characteristic
270	C₂×C₄⋊Q₈	—	43	1	no	—
271	C₂×C₄×Q₈	—	86	1	no	—
272	C₂×C₄×D₄	C₂×D₄₃	1	1	yes	characteristic
273	C₂×C₄×D₄	C₂×D₄₃	1	1	yes	characteristic
274	C₂×C₄×D₄	C₂×D₄₃	1	1	yes	characteristic
275	C₂²×C₄²	—	2	1	no	—
276	#476	—	43	8	no	—
277	C₂×#106	—	43	2	no	—
278	C₂×#106	—	43	2	no	—
279	C₂×C₄⋊C₈	—	43	1	no	—
280	C₂×C₄⋊C₈	—	43	1	no	—
281	C₂×#102	—	43	2	no	—
282	C₂×#102	—	43	2	no	—
283	C₂×C₄×C₈	—	43	2	no	—
284	#391	—	86	1	no	—
285	#389	—	43	2	no	—
286	#389	—	86	1	no	—
287	#384	—	43	1	no	—
288	C₄×C₄⋊C₄	—	43	2	no	—
289	C₄×C₄⋊C₄	—	86	1	no	—
290	C₄×C₄⋊C₄	C₂×D₄₃	1	1	yes	characteristic
291	C₄×C₄⋊C₄	C₂×D₄₃	1	1	yes	characteristic
292	C₄×C₄⋊C₄	C₂×D₄₃	1	1	yes	characteristic
293	C₄×C₂²⋊C₄	—	2	1	no	—
294	C₄×C₂²⋊C₄	—	2	1	no	—
295	C₄×C₂²⋊C₄	—	2	1	no	—
296	C₄³	C₂×D₄₃	1	1	yes	characteristic
297	#340	—	43	2	no	—
298	#340	—	43	2	no	—
299	#340	—	43	2	no	—
300	#340	—	43	2	no	—
301	#336	—	43	2	no	—
302	C₄₃	C₄×#476	1	1	yes	characteristic, complemented, Sylow
303	C₂²×Q₈	—	86	1	no	—
304	C₂²×D₄	C₂²×D₄₃	1	1	yes	characteristic
305	C₂³×C₄	—	2	1	no	—
306	C₂³×C₄	—	2	1	no	—
307	C₂³×C₄	—	2	1	no	—
308	C₂²×C₈	—	43	2	no	—
309	C₂²×C₈	—	43	2	no	—
310	C₄⋊Q₈	—	43	4	no	—
311	C₄⋊Q₈	—	86	2	no	—
312	C₄×Q₈	—	172	4	no	—
313	C₄×D₄	—	2	2	no	—
314	C₄×D₄	—	2	2	no	—
315	C₄×D₄	—	2	2	no	—
316	C₄×D₄	—	2	2	no	—
317	C₄×D₄	Dic₈₆	1	4	yes	complemented
318	C₄×D₄	C₄×D₄₃	1	4	yes	—
319	C₂×C₄⋊C₄	—	43	2	no	—
320	C₂×C₄⋊C₄	—	43	2	no	—
321	C₂×C₄⋊C₄	—	86	1	no	—
322	C₂×C₄⋊C₄	—	86	2	no	—
323	C₂×C₄⋊C₄	—	86	1	no	—
324	C₂×C₄⋊C₄	—	86	1	no	—
325	C₂×C₄⋊C₄	C₂²×D₄₃	1	1	yes	characteristic
326	C₂×C₄⋊C₄	C₂²×D₄₃	1	1	yes	characteristic
327	C₂×C₄⋊C₄	C₂²×D₄₃	1	1	yes	characteristic
328	C₂×C₂²⋊C₄	—	2	1	no	—
329	C₂×C₂²⋊C₄	—	2	1	no	—
330	C₂×C₂²⋊C₄	—	2	1	no	—
331	C₂×C₄²	—	2	1	no	—
332	C₂×C₄²	—	2	1	no	—
333	C₂×C₄²	—	2	1	no	—
334	C₂×C₄²	—	4	4	no	—
335	C₂×C₄²	—	86	2	no	—
336	C₂×C₄²	C₂²⋊D₄₃	1	1	yes	characteristic
337	C₂×C₄²	C₂²⋊D₄₃	1	1	yes	characteristic
338	C₂×C₄²	C₂²⋊D₄₃	1	1	yes	characteristic
339	C₂×C₄²	C₂²⋊D₄₃	1	1	yes	characteristic
340	C₂×C₄²	C₂²×D₄₃	1	1	yes	characteristic
341	C₂×C₄²	C₂²×D₄₃	1	1	yes	characteristic
342	C₂×C₄²	C₂²×D₄₃	1	1	yes	characteristic
343	#106	—	43	8	no	—
344	#106	—	86	4	no	—
345	C₄⋊C₈	—	43	4	no	—
346	C₄⋊C₈	—	86	2	no	—
347	#102	—	43	8	no	—
348	#102	—	86	4	no	—
349	C₄×C₈	—	86	4	no	—
350	#95	—	2	1	no	—
351	#95	—	2	1	no	—
352	#95	—	2	1	no	—
353	#95	—	86	2	no	—
354	#95	—	86	2	no	—
355	C₂⁴	—	2	1	no	—
356	C₂×Q₈	—	86	4	no	—
357	C₂×Q₈	—	172	2	no	—
358	C₂×Q₈	—	172	2	no	—
359	C₂×D₄	—	2	1	no	—
360	C₂×D₄	—	2	1	no	—
361	C₂×D₄	—	2	1	no	—
362	C₂×D₄	C₂×Dic₈₆	1	2	yes	—
363	C₂×D₄	C₂×C₄×D₄₃	1	2	yes	—
364	C₂×D₄	#10621898	1	2	yes	—
365	C₂²×C₄	—	2	4	no	—
366	C₂²×C₄	—	2	1	no	—
367	C₂²×C₄	—	2	1	no	—
368	C₂²×C₄	—	2	1	no	—
369	C₂²×C₄	—	2	4	no	—
370	C₂²×C₄	—	2	4	no	—
371	C₂²×C₄	—	4	2	no	—
372	C₂²×C₄	—	4	2	no	—
373	C₂²×C₄	—	4	2	no	—
374	C₂²×C₄	—	4	2	no	—
375	C₂²×C₄	—	4	2	no	—
376	C₂²×C₄	—	4	2	no	—
377	C₂²×C₄	—	86	2	no	—
378	C₂²×C₄	—	86	2	no	—
379	C₂²×C₄	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
380	C₂²×C₄	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
381	C₂²×C₄	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
382	C₂²×C₄	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
383	C₂²×C₄	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
384	C₂²×C₄	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
385	C₂²×C₄	C₂³×D₄₃	1	1	yes	characteristic
386	C₂×C₈	—	43	4	no	—
387	C₂×C₈	—	86	2	no	—
388	C₂×C₈	—	86	2	no	—
389	C₂×C₈	—	86	2	no	—
390	C₂×C₈	—	86	2	no	—
391	C₂×C₈	—	86	2	no	—
392	C₄⋊C₄	—	2	1	no	—
393	C₄⋊C₄	—	2	1	no	—
394	C₄⋊C₄	—	2	1	no	—
395	C₄⋊C₄	—	43	4	no	—
396	C₄⋊C₄	—	86	4	no	—
397	C₄⋊C₄	—	86	2	no	—
398	C₄⋊C₄	—	86	2	no	—
399	C₄⋊C₄	—	86	2	no	—
400	C₄⋊C₄	—	172	4	no	—
401	C₄⋊C₄	—	172	2	no	—
402	C₄⋊C₄	—	172	2	no	—
403	C₄⋊C₄	C₂×Dic₈₆	1	2	yes	—
404	C₄⋊C₄	C₂×C₄×D₄₃	1	2	yes	—
405	C₄⋊C₄	#10621898	1	2	yes	—
406	C₂²⋊C₄	—	2	4	no	—
407	C₂²⋊C₄	—	2	4	no	—
408	C₂²⋊C₄	—	2	4	no	—
409	C₄²	—	2	2	no	—
410	C₄²	—	2	2	no	—
411	C₄²	—	2	1	no	—
412	C₄²	—	2	1	no	—
413	C₄²	—	4	1	no	—
414	C₄²	—	4	2	no	—
415	C₄²	—	4	2	no	—
416	C₄²	—	4	2	no	—
417	C₄²	—	172	4	no	—
418	C₄²	#10621883	1	4	yes	—
419	C₄²	C₂×Dic₈₆	1	2	yes	—
420	C₄²	C₂×C₄×D₄₃	1	2	yes	—
421	C₄²	#10621898	1	2	yes	—
422	C₄²	#10621898	1	2	yes	—
423	C₂³	—	2	2	no	—
424	C₂³	—	2	2	no	—
425	C₂³	—	2	2	no	—
426	C₂³	—	4	1	no	—
427	C₂³	—	4	1	no	—
428	C₂³	—	4	1	no	—
429	C₂³	—	4	1	no	—
430	C₂³	C₂²×C₂²⋊D₄₃	1	1	yes	characteristic
431	Q₈	—	172	8	no	—
432	D₄	—	2	2	no	—
433	D₄	—	2	2	no	—
434	D₄	—	2	2	no	—
435	D₄	C₄×Dic₈₆	1	4	yes	complemented
436	C₂×C₄	—	2	1	no	—
437	C₂×C₄	—	2	1	no	—
438	C₂×C₄	—	2	1	no	—
439	C₂×C₄	—	2	1	no	—
440	C₂×C₄	—	2	1	no	—
441	C₂×C₄	—	2	1	no	—
442	C₂×C₄	—	2	2	no	—
443	C₂×C₄	—	2	2	no	—
444	C₂×C₄	—	2	1	no	—
445	C₂×C₄	—	2	2	no	—
446	C₂×C₄	—	2	1	no	—
447	C₂×C₄	—	2	1	no	—
448	C₂×C₄	—	4	8	no	—
449	C₂×C₄	—	4	1	no	—
450	C₂×C₄	—	4	1	no	—
451	C₂×C₄	—	4	1	no	—
452	C₂×C₄	—	4	1	no	—
453	C₂×C₄	—	4	1	no	—
454	C₂×C₄	—	4	1	no	—
455	C₂×C₄	—	4	8	no	—
456	C₂×C₄	—	4	8	no	—
457	C₂×C₄	—	86	4	no	—
458	C₂×C₄	—	172	2	no	—
459	C₂×C₄	—	172	2	no	—
460	C₂×C₄	—	172	2	no	—
461	C₂×C₄	—	172	2	no	—
462	C₂×C₄	—	172	2	no	—
463	C₂×C₄	C₄×C₂²⋊D₄₃	1	2	yes	—
464	C₂×C₄	C₄×C₂²⋊D₄₃	1	2	yes	—
465	C₂×C₄	#13063304	1	2	yes	—
466	C₂×C₄	#13063304	1	2	yes	—
467	C₂×C₄	C₂×#10621883	1	2	yes	—
468	C₂×C₄	C₂×#10621883	1	2	yes	—
469	C₂×C₄	C₂×#10621883	1	2	yes	—
470	C₂×C₄	#13063345	1	2	yes	—
471	C₂×C₄	#13063350	1	2	yes	—
472	C₂×C₄	C₂²×C₄×D₄₃	1	1	yes	characteristic
473	C₂×C₄	C₂²×Dic₈₆	1	1	yes	characteristic
474	C₂×C₄	C₂×#10621898	1	1	yes	characteristic
475	C₂×C₄	C₂×#10621898	1	1	yes	characteristic
476	C₂×C₄	C₂×#10621898	1	1	yes	characteristic
477	C₂×C₄	C₂×#10621898	1	1	yes	characteristic
478	C₈	—	86	4	no	—
479	C₈	—	172	2	no	—
480	C₂²	—	2	4	no	—
481	C₂²	—	4	2	no	—
482	C₂²	—	4	2	no	—
483	C₂²	—	4	2	no	—
484	C₂²	—	4	2	no	—
485	C₂²	—	4	2	no	—
486	C₂²	—	4	2	no	—
487	C₂²	C₂×C₄×C₂²⋊D₄₃	1	1	yes	characteristic
488	C₂²	C₂×#13063304	1	1	yes	characteristic
489	C₂²	#14583410	1	1	yes	characteristic
490	C₂²	C₂²×#10621883	1	1	yes	characteristic
491	C₂²	C₂×#13063345	1	1	yes	characteristic
492	C₂²	C₂×#13063350	1	1	yes	characteristic
493	C₂²	#14583697	1	1	yes	characteristic
494	C₄	—	2	2	no	—
495	C₄	—	2	2	no	—
496	C₄	—	2	2	no	—
497	C₄	—	4	2	no	—
498	C₄	—	4	2	no	—
499	C₄	—	4	2	no	—
500	C₄	—	4	1	no	—
501	C₄	—	344	2	no	—
502	C₄	—	172	4	no	—
503	C₄	C₄×#10621883	1	4	yes	—
504	C₄	#14583189	1	4	yes	direct product factor
505	C₄	C₂×C₄×Dic₈₆	1	1	yes	characteristic
506	C₄	C₄×#10621898	1	1	yes	characteristic
507	C₄	#14583433	1	1	yes	characteristic
508	C₄	#14583456	1	1	yes	characteristic
509	C₂	—	4	4	no	—
510	C₂	C₄×#13063304	1	1	yes	characteristic
511	C₂	C₂×C₄×#10621883	1	1	yes	characteristic
512	C₂	C₄×#13063350	1	1	yes	characteristic
513	C₂	C₂×#14583189	1	1	yes	characteristic
514	C₂	#19144383	1	1	yes	characteristic
515	C₂	#19144603	1	1	yes	characteristic
516	C₂	#19144655	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄	C₂×C₂²⋊D₄₃
commutator	C₂×C₄×C₄₃	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₄₃
Fitting	C₄²×D₄×C₄₃	C₂
socle	C₂³×C₄₃	C₂²×D₄
prime radical	C₂²×D₄×C₄₃	C₂³
cosocle	C₂²×C₄×C₄₃	C₂⁴
hypercenter	C₄²×D₄	D₄₃
hypocenter	C₄₃	C₄×#476
LCS	G ▷ C₂×C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂²×C₄ ◁ C₄³ ◁ C₄²×D₄

Complements

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

N	H ≅ G/N	type
2. C₄×#13063325	C₂	semidirect
3. #19135543	C₂	semidirect
4. #19135358	C₂	semidirect
5. #19135180	C₂	semidirect
8. C₄×#13063256	C₂	semidirect
9. C₄×C₄⋊(C₄₃⋊C₈)	C₂	semidirect
14. #14583189	C₄	direct (N × H)
48. #13063325	C₂×C₄	semidirect
58. #13063256	C₂×C₄	semidirect
60. C₄⋊(C₄₃⋊C₈)	C₂×C₄	semidirect
75. C₄×D₄×C₄₃	Q₈	semidirect
175. D₄×C₄₃	C₄×Q₈	semidirect
244. C₄×C₄₃	#476	semidirect
302. C₄₃	C₄×#476	semidirect
317. C₄×D₄	Dic₈₆	semidirect
435. D₄	C₄×Dic₈₆	semidirect
504. C₄	#14583189	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×#14583189	2
C₄×#13063325	2
#19135543	2
#19135358	2
#19135180	2
#19134856	2
#19134595	2
C₄×#13063256	2
C₄×C₄⋊(C₄₃⋊C₈)	2
C₄×#13063246	2
C₄²×D₄×C₄₃	2
C₄×#476	43

Subgroups — C4×#14583189 #25104170

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄×#14583189 #25104170