Subgroups — C₄×#13063310 #19137121

Order 5504.

688 conjugacy classes of subgroups.

The subgroup lattice has 414 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#13063310	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄×D₁₇₂	C₂	1	1	yes	maximal, characteristic
3	C₂×C₄²×D₄₃	C₂	1	1	yes	maximal, characteristic, complemented
4	#14582789	C₂	1	1	yes	maximal, characteristic, complemented
5	#14582788	C₂	1	1	yes	maximal, characteristic, complemented
6	#14582786	C₂	1	1	yes	maximal, characteristic, complemented
7	#14582785	C₂	1	1	yes	maximal, characteristic, complemented
8	#14582777	C₂	1	1	yes	maximal, characteristic
9	#14582770	C₂	1	1	yes	maximal, characteristic, complemented
10	#14582761	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄×Dic₄₃⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
12	C₄×(C₂×D₄₃)⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
13	C₄×(C₂×D₄₃)⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
14	C₄×(C₂×D₄₃)⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
15	C₄×C₄⋊C₄×C₄₃	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×D₁₇₂	C₂²	1	1	yes	characteristic
17	C₂²×C₄×D₄₃	C₂²	1	1	yes	characteristic
18	C₂²×C₄×D₄₃	C₂²	1	1	yes	characteristic
19	C₂²×C₄×D₄₃	C₂²	1	1	yes	characteristic
20	C₂²×C₄×D₄₃	C₂²	1	1	yes	characteristic
21	#13063310	C₄	1	8	yes	direct product factor
22	C₄×D₁₇₂	—	2	4	no	—
23	C₂×C₄⋊Dic₄₃	C₂²	1	1	yes	characteristic
24	C₂×Dic₄₃⋊C₄	C₂²	1	1	yes	characteristic
25	C₂×Dic₄₃⋊C₄	C₂²	1	1	yes	characteristic
26	C₂×(C₂×D₄₃)⋊C₄	C₂²	1	1	yes	characteristic
27	C₂×(C₂×D₄₃)⋊C₄	C₂²	1	1	yes	characteristic
28	C₂×(C₂×D₄₃)⋊C₄	C₂²	1	1	yes	characteristic
29	C₂×(C₂×D₄₃)⋊C₄	C₂²	1	1	yes	characteristic
30	C₂×(C₂×D₄₃)⋊C₄	C₂²	1	1	yes	characteristic
31	C₂×(C₂×D₄₃)⋊C₄	C₂²	1	1	yes	characteristic
32	C₂×(C₂×D₄₃)⋊C₄	C₂²	1	1	yes	characteristic
33	C₂×(C₂×D₄₃)⋊C₄	C₂²	1	1	yes	characteristic
34	C₂×C₄×Dic₄₃	C₂²	1	1	yes	characteristic
35	C₂×C₄×Dic₄₃	C₂²	1	1	yes	characteristic
36	C₂×C₄×Dic₄₃	C₂²	1	1	yes	characteristic
37	C₂×C₄×Dic₄₃	C₂²	1	1	yes	characteristic
38	C₄²×D₄₃	—	2	4	no	—
39	C₄₃⋊#95	C₂²	1	1	yes	characteristic
40	C₄₃⋊#95	C₂²	1	1	yes	characteristic
41	C₄₃⋊#95	C₂²	1	1	yes	characteristic
42	C₄₃⋊#95	C₂²	1	1	yes	characteristic
43	C₄₃⋊#95	C₂²	1	1	yes	characteristic
44	C₄₃⋊#95	C₂²	1	1	yes	characteristic
45	C₄₃⋊#95	C₂²	1	1	yes	characteristic
46	C₄₃⋊#95	C₂²	1	1	yes	characteristic
47	C₂×C₄⋊C₄×C₄₃	C₂²	1	1	yes	characteristic
48	C₂×C₄⋊C₄×C₄₃	C₂²	1	1	yes	characteristic
49	C₂×C₄²×C₄₃	C₂²	1	1	yes	characteristic
50	C₂×C₄²×C₄₃	C₂²	1	1	yes	characteristic
51	C₂×C₄²×C₄₃	C₂²	1	1	yes	characteristic
52	#95×C₄₃	C₂²	1	1	yes	characteristic
53	#95×C₄₃	C₂²	1	1	yes	characteristic
54	C₂³×D₄₃	C₂³	1	1	yes	characteristic
55	C₂³×D₄₃	C₂³	1	1	yes	characteristic
56	C₂²×C₄×C₄₃	C₂³	1	1	yes	characteristic
57	C₂²×C₄×C₄₃	C₂³	1	1	yes	characteristic
58	C₂²×C₄×C₄₃	C₂³	1	1	yes	characteristic
59	C₂²×C₄×C₄₃	C₂³	1	1	yes	characteristic
60	C₂²×C₄×C₄₃	C₂³	1	1	yes	characteristic
61	C₂²×C₄×C₄₃	C₂³	1	1	yes	characteristic
62	C₂²×C₄×C₄₃	C₂³	1	1	yes	characteristic
63	C₂²×Dic₄₃	C₂³	1	1	yes	characteristic
64	C₂²×Dic₄₃	C₂³	1	1	yes	characteristic
65	C₂²×Dic₄₃	C₂³	1	1	yes	characteristic
66	C₂²×Dic₄₃	C₂³	1	1	yes	characteristic
67	C₂²×Dic₄₃	C₂³	1	1	yes	characteristic
68	C₂²×Dic₄₃	C₂³	1	1	yes	characteristic
69	C₂×D₁₇₂	—	2	2	no	—
70	C₂×D₁₇₂	—	2	2	no	—
71	C₂×D₁₇₂	C₂×C₄	1	4	yes	—
72	C₂×C₄×D₄₃	—	2	2	no	—
73	C₂×C₄×D₄₃	—	2	2	no	—
74	C₂×C₄×D₄₃	—	2	2	no	—
75	C₂×C₄×D₄₃	—	2	2	no	—
76	C₂×C₄×D₄₃	—	2	2	no	—
77	C₂×C₄×D₄₃	—	2	2	no	—
78	C₂×C₄×D₄₃	—	2	2	no	—
79	C₂×C₄×D₄₃	—	2	2	no	—
80	C₂×C₄×D₄₃	—	2	2	no	—
81	C₂×C₄×D₄₃	—	2	2	no	—
82	C₂×C₄×D₄₃	C₂×C₄	1	4	yes	complemented
83	C₂×C₄×D₄₃	D₄	1	4	yes	—
84	C₄⋊C₄×C₄₃	—	2	2	no	—
85	C₄⋊C₄×C₄₃	C₂×C₄	1	4	yes	complemented
86	C₄²×C₄₃	—	2	2	no	—
87	C₄²×C₄₃	—	2	2	no	—
88	C₄²×C₄₃	—	2	2	no	—
89	(C₂×D₄₃)⋊C₄	—	2	2	no	—
90	(C₂×D₄₃)⋊C₄	—	2	2	no	—
91	(C₂×D₄₃)⋊C₄	—	2	2	no	—
92	(C₂×D₄₃)⋊C₄	—	2	2	no	—
93	(C₂×D₄₃)⋊C₄	—	2	2	no	—
94	(C₂×D₄₃)⋊C₄	C₂×C₄	1	4	yes	complemented
95	(C₂×D₄₃)⋊C₄	C₂×C₄	1	4	yes	complemented
96	(C₂×D₄₃)⋊C₄	C₂×C₄	1	4	yes	complemented
97	C₄⋊Dic₄₃	—	2	2	no	—
98	Dic₄₃⋊C₄	—	2	2	no	—
99	Dic₄₃⋊C₄	C₂×C₄	1	4	yes	complemented
100	C₄×Dic₄₃	—	2	2	no	—
101	C₄×Dic₄₃	—	2	2	no	—
102	C₄×Dic₄₃	—	2	2	no	—
103	C₄×Dic₄₃	—	2	2	no	—
104	C₂³×C₄₃	C₂⁴	1	1	yes	characteristic
105	C₂²×D₄₃	—	2	1	no	—
106	C₂²×D₄₃	—	2	1	no	—
107	C₂²×D₄₃	—	2	1	no	—
108	C₂²×D₄₃	—	2	1	no	—
109	C₂²×D₄₃	—	2	1	no	—
110	C₂²×D₄₃	—	2	1	no	—
111	C₂²×D₄₃	—	2	1	no	—
112	C₂²×D₄₃	—	2	1	no	—
113	C₂²×D₄₃	—	2	1	no	—
114	C₂²×D₄₃	—	2	1	no	—
115	C₂²×D₄₃	C₂²×C₄	1	2	yes	—
116	C₂²×D₄₃	C₂²×C₄	1	2	yes	—
117	C₂²×D₄₃	C₂×D₄	1	2	yes	—
118	C₂²×D₄₃	#41	1	2	yes	—
119	C₂×C₄×C₄₃	—	2	1	no	—
120	C₂×C₄×C₄₃	—	2	1	no	—
121	C₂×C₄×C₄₃	—	2	1	no	—
122	C₂×C₄×C₄₃	—	2	1	no	—
123	C₂×C₄×C₄₃	—	2	1	no	—
124	C₂×C₄×C₄₃	—	2	1	no	—
125	C₂×C₄×C₄₃	—	2	1	no	—
126	C₂×C₄×C₄₃	—	2	1	no	—
127	C₂×C₄×C₄₃	—	2	1	no	—
128	C₂×C₄×C₄₃	—	2	1	no	—
129	C₂×C₄×C₄₃	—	2	1	no	—
130	C₂×C₄×C₄₃	—	2	1	no	—
131	C₂×C₄×C₄₃	—	2	1	no	—
132	C₂×C₄×C₄₃	—	2	1	no	—
133	C₂×C₄×C₄₃	C₂²×C₄	1	2	yes	—
134	C₂×C₄×C₄₃	C₂²×C₄	1	2	yes	—
135	C₂×C₄×C₄₃	C₂²×C₄	1	2	yes	—
136	C₂×C₄×C₄₃	C₂×D₄	1	2	yes	—
137	C₂×C₄×C₄₃	#41	1	2	yes	—
138	C₂×C₄×C₄₃	#41	1	2	yes	—
139	C₂×C₄×C₄₃	#41	1	2	yes	—
140	C₂×Dic₄₃	—	2	1	no	—
141	C₂×Dic₄₃	—	2	1	no	—
142	C₂×Dic₄₃	—	2	1	no	—
143	C₂×Dic₄₃	—	2	1	no	—
144	C₂×Dic₄₃	—	2	1	no	—
145	C₂×Dic₄₃	—	2	1	no	—
146	C₂×Dic₄₃	—	2	1	no	—
147	C₂×Dic₄₃	—	2	1	no	—
148	C₂×Dic₄₃	—	2	1	no	—
149	C₂×Dic₄₃	—	2	1	no	—
150	C₂×Dic₄₃	—	2	1	no	—
151	C₂×Dic₄₃	—	2	1	no	—
152	C₂×Dic₄₃	—	2	1	no	—
153	C₂×Dic₄₃	—	2	1	no	—
154	C₂×Dic₄₃	C₂²×C₄	1	2	yes	—
155	C₂×Dic₄₃	C₂²×C₄	1	2	yes	—
156	C₂×Dic₄₃	C₂×D₄	1	2	yes	—
157	C₂×Dic₄₃	#41	1	2	yes	—
158	D₁₇₂	—	2	8	no	—
159	C₄×D₄₃	—	2	8	no	—
160	C₄×D₄₃	—	2	8	no	—
161	C₄×D₄₃	—	2	8	no	—
162	C₄×D₄₃	—	4	4	no	—
163	C₂²×C₄₃	C₂³×C₄	1	1	yes	characteristic
164	C₂²×C₄₃	C₂²×D₄	1	1	yes	characteristic
165	C₂²×C₄₃	C₂×#41	1	1	yes	characteristic
166	C₂²×C₄₃	C₂×#41	1	1	yes	characteristic
167	C₂²×C₄₃	C₂×#41	1	1	yes	characteristic
168	C₂²×C₄₃	C₂×#41	1	1	yes	characteristic
169	C₂²×C₄₃	C₂×#41	1	1	yes	characteristic
170	C₂×D₄₃	—	2	2	no	—
171	C₂×D₄₃	—	2	2	no	—
172	C₂×D₄₃	—	2	2	no	—
173	C₂×D₄₃	—	2	2	no	—
174	C₂×D₄₃	—	2	2	no	—
175	C₂×D₄₃	—	2	2	no	—
176	C₂×D₄₃	—	2	2	no	—
177	C₂×D₄₃	—	2	2	no	—
178	C₂×D₄₃	—	2	2	no	—
179	C₂×D₄₃	—	4	1	no	—
180	C₂×D₄₃	—	4	1	no	—
181	C₂×D₄₃	—	4	1	no	—
182	C₂×D₄₃	—	4	1	no	—
183	C₂×D₄₃	C₄×D₄	1	4	yes	—
184	C₄×C₄₃	—	2	2	no	—
185	C₄×C₄₃	—	2	2	no	—
186	C₄×C₄₃	—	2	2	no	—
187	C₄×C₄₃	—	2	2	no	—
188	C₄×C₄₃	—	4	1	no	—
189	C₄×C₄₃	—	4	1	no	—
190	C₄×C₄₃	#123	1	4	yes	complemented
191	Dic₄₃	—	2	2	no	—
192	Dic₄₃	—	2	2	no	—
193	Dic₄₃	—	2	2	no	—
194	Dic₄₃	—	2	2	no	—
195	Dic₄₃	—	4	1	no	—
196	Dic₄₃	—	4	1	no	—
197	C₄×#123	—	43	1	no	maximal, Sylow
198	C₂×C₄₃	C₂×C₄×D₄	1	1	yes	characteristic
199	C₂×C₄₃	C₄×#41	1	1	yes	characteristic
200	C₂×C₄₃	C₄×#41	1	1	yes	characteristic
201	C₂×C₄₃	C₂×#123	1	1	yes	characteristic
202	C₂×C₄₃	#525	1	1	yes	characteristic
203	C₂×C₄₃	#529	1	1	yes	characteristic
204	C₂×C₄₃	#529	1	1	yes	characteristic
205	D₄₃	—	2	4	no	—
206	D₄₃	—	4	2	no	—
207	C₂×#123	—	43	1	no	—
208	C₂×C₄×D₄	—	43	1	no	—
209	C₂²×C₄²	—	43	1	no	—
210	#388	—	43	1	no	—
211	#388	—	43	1	no	—
212	#387	—	43	1	no	—
213	#387	—	43	1	no	—
214	#386	—	43	1	no	—
215	#385	—	43	1	no	—
216	#381	—	43	1	no	—
217	C₄×C₄⋊C₄	—	43	1	no	—
218	C₄×C₄⋊C₄	D₄₃	1	1	yes	characteristic, complemented
219	C₄×C₂²⋊C₄	—	43	1	no	—
220	C₄×C₂²⋊C₄	—	43	1	no	—
221	C₄×C₂²⋊C₄	—	43	1	no	—
222	C₄₃	C₄×#123	1	1	yes	characteristic, complemented, Sylow
223	C₂²×D₄	—	43	1	no	—
224	C₂³×C₄	—	43	1	no	—
225	C₂³×C₄	—	43	1	no	—
226	C₂³×C₄	—	43	1	no	—
227	C₂³×C₄	—	43	1	no	—
228	#123	—	43	8	no	—
229	C₄×D₄	—	86	4	no	—
230	C₂×C₄⋊C₄	—	43	1	no	—
231	C₂×C₄⋊C₄	—	43	1	no	—
232	C₂×C₄⋊C₄	—	43	1	no	—
233	C₂×C₄⋊C₄	C₂×D₄₃	1	1	yes	characteristic
234	C₂×C₄⋊C₄	C₂×D₄₃	1	1	yes	characteristic
235	C₂×C₂²⋊C₄	—	43	1	no	—
236	C₂×C₂²⋊C₄	—	43	1	no	—
237	C₂×C₂²⋊C₄	—	43	1	no	—
238	C₂×C₂²⋊C₄	—	43	1	no	—
239	C₂×C₂²⋊C₄	—	43	1	no	—
240	C₂×C₂²⋊C₄	—	43	1	no	—
241	C₂×C₂²⋊C₄	—	43	1	no	—
242	C₂×C₂²⋊C₄	—	43	1	no	—
243	C₂×C₄²	—	43	1	no	—
244	C₂×C₄²	—	43	1	no	—
245	C₂×C₄²	—	43	1	no	—
246	C₂×C₄²	—	43	1	no	—
247	C₂×C₄²	—	86	4	no	—
248	C₂×C₄²	C₂×D₄₃	1	1	yes	characteristic
249	C₂×C₄²	C₂×D₄₃	1	1	yes	characteristic
250	C₂×C₄²	C₂×D₄₃	1	1	yes	characteristic
251	#95	—	43	1	no	—
252	#95	—	43	1	no	—
253	#95	—	43	1	no	—
254	#95	—	43	1	no	—
255	#95	—	43	1	no	—
256	#95	—	43	1	no	—
257	#95	—	43	1	no	—
258	#95	—	43	1	no	—
259	#95	C₂×D₄₃	1	1	yes	characteristic
260	#95	C₂×D₄₃	1	1	yes	characteristic
261	C₂⁴	—	43	1	no	—
262	C₂⁴	—	43	1	no	—
263	C₂×D₄	—	43	4	no	—
264	C₂×D₄	—	86	2	no	—
265	C₂×D₄	—	86	2	no	—
266	C₂²×C₄	—	43	1	no	—
267	C₂²×C₄	—	43	1	no	—
268	C₂²×C₄	—	43	1	no	—
269	C₂²×C₄	—	43	1	no	—
270	C₂²×C₄	—	43	4	no	—
271	C₂²×C₄	—	43	4	no	—
272	C₂²×C₄	—	43	1	no	—
273	C₂²×C₄	—	43	1	no	—
274	C₂²×C₄	—	86	2	no	—
275	C₂²×C₄	—	86	2	no	—
276	C₂²×C₄	—	86	2	no	—
277	C₂²×C₄	—	86	2	no	—
278	C₂²×C₄	—	86	2	no	—
279	C₂²×C₄	—	86	2	no	—
280	C₂²×C₄	—	86	2	no	—
281	C₂²×C₄	—	86	2	no	—
282	C₂²×C₄	—	86	2	no	—
283	C₂²×C₄	—	86	2	no	—
284	C₂²×C₄	C₂²×D₄₃	1	1	yes	characteristic
285	C₂²×C₄	C₂²×D₄₃	1	1	yes	characteristic
286	C₂²×C₄	C₂²×D₄₃	1	1	yes	characteristic
287	C₂²×C₄	C₂²×D₄₃	1	1	yes	characteristic
288	C₂²×C₄	C₂²×D₄₃	1	1	yes	characteristic
289	C₂²×C₄	C₂²×D₄₃	1	1	yes	characteristic
290	C₂²×C₄	C₂²×D₄₃	1	1	yes	characteristic
291	C₄⋊C₄	—	2	2	no	—
292	C₄⋊C₄	—	43	4	no	—
293	C₄⋊C₄	—	86	2	no	—
294	C₄⋊C₄	—	86	2	no	—
295	C₄⋊C₄	C₄×D₄₃	1	4	yes	complemented
296	C₂²⋊C₄	—	43	4	no	—
297	C₂²⋊C₄	—	43	4	no	—
298	C₂²⋊C₄	—	43	4	no	—
299	C₂²⋊C₄	—	86	2	no	—
300	C₂²⋊C₄	—	86	2	no	—
301	C₂²⋊C₄	—	86	2	no	—
302	C₂²⋊C₄	—	86	2	no	—
303	C₂²⋊C₄	—	86	2	no	—
304	C₄²	—	2	2	no	—
305	C₄²	—	2	2	no	—
306	C₄²	—	2	2	no	—
307	C₄²	—	86	2	no	—
308	C₄²	—	86	2	no	—
309	C₄²	—	86	2	no	—
310	C₄²	—	86	2	no	—
311	C₂³	—	43	2	no	—
312	C₂³	—	43	2	no	—
313	C₂³	—	43	2	no	—
314	C₂³	—	43	2	no	—
315	C₂³	—	86	1	no	—
316	C₂³	—	86	1	no	—
317	C₂³	—	86	1	no	—
318	C₂³	—	86	1	no	—
319	C₂³	—	86	1	no	—
320	C₂³	—	86	1	no	—
321	C₂³	—	86	1	no	—
322	C₂³	—	86	1	no	—
323	C₂³	—	86	1	no	—
324	C₂³	—	86	1	no	—
325	C₂³	C₂³×D₄₃	1	1	yes	characteristic
326	D₄	—	86	8	no	—
327	C₂×C₄	—	2	1	no	—
328	C₂×C₄	—	2	1	no	—
329	C₂×C₄	—	2	1	no	—
330	C₂×C₄	—	2	1	no	—
331	C₂×C₄	—	2	1	no	—
332	C₂×C₄	—	2	1	no	—
333	C₂×C₄	—	2	1	no	—
334	C₂×C₄	—	2	1	no	—
335	C₂×C₄	—	2	1	no	—
336	C₂×C₄	—	2	1	no	—
337	C₂×C₄	—	2	1	no	—
338	C₂×C₄	—	2	1	no	—
339	C₂×C₄	—	2	1	no	—
340	C₂×C₄	—	2	1	no	—
341	C₂×C₄	—	43	2	no	—
342	C₂×C₄	—	43	2	no	—
343	C₂×C₄	—	43	2	no	—
344	C₂×C₄	—	43	2	no	—
345	C₂×C₄	—	86	8	no	—
346	C₂×C₄	—	86	8	no	—
347	C₂×C₄	—	86	1	no	—
348	C₂×C₄	—	86	1	no	—
349	C₂×C₄	—	86	1	no	—
350	C₂×C₄	—	86	1	no	—
351	C₂×C₄	—	86	1	no	—
352	C₂×C₄	—	86	1	no	—
353	C₂×C₄	—	86	1	no	—
354	C₂×C₄	—	86	1	no	—
355	C₂×C₄	—	86	8	no	—
356	C₂×C₄	—	86	1	no	—
357	C₂×C₄	—	86	1	no	—
358	C₂×C₄	—	86	1	no	—
359	C₂×C₄	—	86	1	no	—
360	C₂×C₄	—	86	1	no	—
361	C₂×C₄	—	86	1	no	—
362	C₂×C₄	—	172	4	no	—
363	C₂×C₄	C₂×C₄×D₄₃	1	2	yes	—
364	C₂×C₄	C₂×C₄×D₄₃	1	2	yes	—
365	C₂×C₄	C₂×C₄×D₄₃	1	2	yes	—
366	C₂×C₄	#10621898	1	2	yes	—
367	C₂×C₄	#10621898	1	2	yes	—
368	C₂×C₄	D₄×D₄₃	1	2	yes	—
369	C₂×C₄	#10621902	1	2	yes	—
370	C₂²	—	43	4	no	—
371	C₂²	—	86	2	no	—
372	C₂²	—	86	2	no	—
373	C₂²	—	86	2	no	—
374	C₂²	—	86	2	no	—
375	C₂²	—	86	2	no	—
376	C₂²	—	86	2	no	—
377	C₂²	—	86	2	no	—
378	C₂²	—	86	2	no	—
379	C₂²	—	86	2	no	—
380	C₂²	—	172	1	no	—
381	C₂²	—	172	1	no	—
382	C₂²	—	172	1	no	—
383	C₂²	—	172	1	no	—
384	C₂²	C₂²×C₄×D₄₃	1	1	yes	characteristic
385	C₂²	C₂×D₄×D₄₃	1	1	yes	characteristic
386	C₂²	#41×D₄₃	1	1	yes	characteristic
387	C₂²	#41×D₄₃	1	1	yes	characteristic
388	C₂²	C₂×#10621898	1	1	yes	characteristic
389	C₂²	C₂×#10621898	1	1	yes	characteristic
390	C₂²	C₂×#10621902	1	1	yes	characteristic
391	C₄	—	2	2	no	—
392	C₄	—	2	2	no	—
393	C₄	—	2	2	no	—
394	C₄	—	2	2	no	—
395	C₄	—	4	1	no	—
396	C₄	—	4	1	no	—
397	C₄	—	86	2	no	—
398	C₄	—	86	2	no	—
399	C₄	—	86	2	no	—
400	C₄	—	86	2	no	—
401	C₄	—	172	1	no	—
402	C₄	—	172	1	no	—
403	C₄	#13063310	1	4	yes	direct product factor
404	C₂	—	86	4	no	—
405	C₂	—	172	2	no	—
406	C₂	C₄×D₄×D₄₃	1	1	yes	characteristic
407	C₂	C₄×#10621898	1	1	yes	characteristic
408	C₂	C₄×#10621902	1	1	yes	characteristic
409	C₂	C₂×#13063310	1	1	yes	characteristic
410	C₂	#14583408	1	1	yes	characteristic
411	C₂	#14583427	1	1	yes	characteristic
412	C₂	#14583436	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄	C₂²×D₄₃
commutator	C₂²×C₄₃	C₂³×C₄
Frattini	C₂³	C₂³×D₄₃
Fitting	C₄×C₄⋊C₄×C₄₃	C₂
socle	C₂³×C₄₃	C₂⁴
hypercenter	C₄×C₄⋊C₄	D₄₃
hypocenter	C₄₃	C₄×#123
LCS	G ▷ C₂²×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂²×C₄ ◁ C₄×C₄⋊C₄

Complements

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

N	H ≅ G/N	type
3. C₂×C₄²×D₄₃	C₂	semidirect
4. #14582789	C₂	semidirect
5. #14582788	C₂	semidirect
6. #14582786	C₂	semidirect
7. #14582785	C₂	semidirect
9. #14582770	C₂	semidirect
10. #14582761	C₂	semidirect
11. C₄×Dic₄₃⋊C₄	C₂	semidirect
12. C₄×(C₂×D₄₃)⋊C₄	C₂	semidirect
13. C₄×(C₂×D₄₃)⋊C₄	C₂	semidirect
14. C₄×(C₂×D₄₃)⋊C₄	C₂	semidirect
15. C₄×C₄⋊C₄×C₄₃	C₂	semidirect
21. #13063310	C₄	direct (N × H)
82. C₂×C₄×D₄₃	C₂×C₄	semidirect
85. C₄⋊C₄×C₄₃	C₂×C₄	semidirect
94. (C₂×D₄₃)⋊C₄	C₂×C₄	semidirect
95. (C₂×D₄₃)⋊C₄	C₂×C₄	semidirect
96. (C₂×D₄₃)⋊C₄	C₂×C₄	semidirect
99. Dic₄₃⋊C₄	C₂×C₄	semidirect
190. C₄×C₄₃	#123	semidirect
218. C₄×C₄⋊C₄	D₄₃	semidirect
222. C₄₃	C₄×#123	semidirect
295. C₄⋊C₄	C₄×D₄₃	semidirect
403. C₄	#13063310	direct (N × H)

Subgroups — C4×#13063310 #19137121

Conjugacy classes of subgroups

Complements

Subgroups — C₄×#13063310 #19137121