Subgroups — C₄×#13063311 #19137135

Order 5504.

652 conjugacy classes of subgroups.

The subgroup lattice has 412 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#13063311	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄×Dic₈₆	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₄×C₂²⋊D₄₃	C₂	1	1	yes	maximal, characteristic
4	#14582803	C₂	1	1	yes	maximal, characteristic, complemented
5	#14582799	C₂	1	1	yes	maximal, characteristic
6	#14582792	C₂	1	1	yes	maximal, characteristic, complemented
7	#14582791	C₂	1	1	yes	maximal, characteristic, complemented
8	#14582788	C₂	1	1	yes	maximal, characteristic, complemented
9	#14582787	C₂	1	1	yes	maximal, characteristic, complemented
10	#14582763	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄×(C₂×D₄₃)⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
12	C₄×(C₂×D₄₃)⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
13	C₄×C₂²⋊Dic₄₃	C₂	1	1	yes	maximal, characteristic, complemented
14	C₄²×Dic₄₃	C₂	1	1	yes	maximal, characteristic, complemented
15	C₄×C₂²⋊C₄×C₄₃	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×Dic₈₆	C₂²	1	1	yes	characteristic
17	C₂²×C₂²⋊D₄₃	C₂²	1	1	yes	characteristic
18	C₂²×C₄×D₄₃	C₂²	1	1	yes	characteristic
19	#13063311	C₄	1	8	yes	direct product factor
20	C₄×Dic₈₆	—	2	4	no	—
21	C₄×C₂²⋊D₄₃	—	2	4	no	—
22	C₂×C₄⋊Dic₄₃	C₂²	1	1	yes	characteristic
23	C₂×Dic₄₃⋊C₄	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×C₂²⋊Dic₄₃	C₂²	1	1	yes	characteristic
27	C₂×C₂²⋊Dic₄₃	C₂²	1	1	yes	characteristic
28	C₂×C₂²⋊Dic₄₃	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	C₂×C₄×Dic₄₃	C₂²	1	1	yes	characteristic
39	C₂×C₄×Dic₄₃	C₂²	1	1	yes	characteristic
40	C₂×C₄×Dic₄₃	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	C₂³×C₄×C₄₃	C₂²	1	1	yes	characteristic
48	C₂×C₂²⋊C₄×C₄₃	C₂²	1	1	yes	characteristic
49	C₂×C₂²⋊C₄×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	C₂⁴×C₄₃	C₂³	1	1	yes	characteristic
55	C₂³×D₄₃	C₂³	1	1	yes	characteristic
56	C₂²×C₄×C₄₃	—	2	2	no	—
57	C₂²×C₄×C₄₃	—	2	2	no	—
58	C₂²×C₄×C₄₃	—	2	2	no	—
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×C₄×C₄₃	C₂³	1	1	yes	characteristic
64	C₂²×C₄×C₄₃	C₂³	1	1	yes	characteristic
65	C₂×C₂²⋊D₄₃	—	2	2	no	—
66	C₂×C₂²⋊D₄₃	—	2	2	no	—
67	C₂×C₂²⋊D₄₃	C₂×C₄	1	4	yes	—
68	C₂²×Dic₄₃	C₂³	1	1	yes	characteristic
69	C₂²×Dic₄₃	C₂³	1	1	yes	characteristic
70	C₂²×Dic₄₃	C₂³	1	1	yes	characteristic
71	C₂²×Dic₄₃	C₂³	1	1	yes	characteristic
72	C₂²×Dic₄₃	C₂³	1	1	yes	characteristic
73	C₂²×Dic₄₃	C₂³	1	1	yes	characteristic
74	C₂²×Dic₄₃	C₂³	1	1	yes	characteristic
75	C₂×C₄×D₄₃	—	2	2	no	—
76	C₂×C₄×D₄₃	—	2	2	no	—
77	C₂×C₄×D₄₃	—	2	2	no	—
78	C₂×Dic₈₆	—	2	2	no	—
79	C₂×Dic₈₆	—	2	2	no	—
80	C₂×Dic₈₆	C₂×C₄	1	4	yes	complemented
81	C₂²⋊C₄×C₄₃	—	2	2	no	—
82	C₂²⋊C₄×C₄₃	C₂×C₄	1	4	yes	complemented
83	C₄²×C₄₃	—	2	2	no	—
84	C₄²×C₄₃	—	2	2	no	—
85	C₂²⋊Dic₄₃	—	2	2	no	—
86	C₂²⋊Dic₄₃	—	2	2	no	—
87	C₂²⋊Dic₄₃	C₂×C₄	1	4	yes	complemented
88	(C₂×D₄₃)⋊C₄	—	2	2	no	—
89	(C₂×D₄₃)⋊C₄	—	2	2	no	—
90	(C₂×D₄₃)⋊C₄	—	2	2	no	—
91	(C₂×D₄₃)⋊C₄	C₂×C₄	1	4	yes	complemented
92	(C₂×D₄₃)⋊C₄	C₂×C₄	1	4	yes	complemented
93	C₄⋊Dic₄₃	—	2	2	no	—
94	Dic₄₃⋊C₄	—	2	2	no	—
95	Dic₄₃⋊C₄	—	2	2	no	—
96	Dic₄₃⋊C₄	—	2	2	no	—
97	C₄×Dic₄₃	—	2	2	no	—
98	C₄×Dic₄₃	—	2	2	no	—
99	C₄×Dic₄₃	—	2	2	no	—
100	C₄×Dic₄₃	—	2	2	no	—
101	C₄×Dic₄₃	—	2	2	no	—
102	C₄×Dic₄₃	C₂×C₄	1	4	yes	complemented
103	C₄×Dic₄₃	D₄	1	4	yes	—
104	C₂³×C₄₃	—	2	1	no	—
105	C₂³×C₄₃	—	2	1	no	—
106	C₂³×C₄₃	—	2	1	no	—
107	C₂³×C₄₃	—	2	1	no	—
108	C₂³×C₄₃	—	2	1	no	—
109	C₂³×C₄₃	—	2	1	no	—
110	C₂³×C₄₃	C₂²×C₄	1	2	yes	—
111	C₂³×C₄₃	C₂⁴	1	1	yes	characteristic
112	C₂²×D₄₃	—	2	1	no	—
113	C₂²×D₄₃	—	2	1	no	—
114	C₂²×D₄₃	—	2	1	no	—
115	C₂²×D₄₃	—	2	1	no	—
116	C₂²×D₄₃	—	2	1	no	—
117	C₂²×D₄₃	—	2	1	no	—
118	C₂²×D₄₃	C₂²×C₄	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	—	4	4	no	—
132	C₂×C₄×C₄₃	C₂²×C₄	1	2	yes	—
133	C₂×C₄×C₄₃	C₂²×C₄	1	2	yes	—
134	C₂×C₄×C₄₃	C₂×D₄	1	2	yes	—
135	C₂×C₄×C₄₃	#41	1	2	yes	—
136	C₂×C₄×C₄₃	#41	1	2	yes	—
137	C₂×C₄×C₄₃	#41	1	2	yes	—
138	C₂²⋊D₄₃	—	2	8	no	—
139	C₂×Dic₄₃	—	2	1	no	—
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	C₂²×C₄	1	2	yes	—
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	C₂×D₄	1	2	yes	—
158	C₂×Dic₄₃	#41	1	2	yes	—
159	C₂×Dic₄₃	#41	1	2	yes	—
160	C₄×D₄₃	—	4	4	no	—
161	Dic₈₆	—	2	8	no	—
162	C₂²×C₄₃	—	2	2	no	—
163	C₂²×C₄₃	—	2	2	no	—
164	C₂²×C₄₃	—	2	2	no	—
165	C₂²×C₄₃	—	4	1	no	—
166	C₂²×C₄₃	—	4	1	no	—
167	C₂²×C₄₃	—	4	1	no	—
168	C₂²×C₄₃	—	4	1	no	—
169	C₂²×C₄₃	C₂³×C₄	1	1	yes	characteristic
170	C₂²×C₄₃	C₂²×D₄	1	1	yes	characteristic
171	C₂²×C₄₃	C₂×#41	1	1	yes	characteristic
172	C₂²×C₄₃	C₂×#41	1	1	yes	characteristic
173	C₂²×C₄₃	C₂×#41	1	1	yes	characteristic
174	C₂²×C₄₃	C₂×#41	1	1	yes	characteristic
175	C₂²×C₄₃	C₂×#41	1	1	yes	characteristic
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	C₄×C₄₃	—	2	2	no	—
184	C₄×C₄₃	—	2	2	no	—
185	C₄×C₄₃	—	2	2	no	—
186	C₄×C₄₃	—	4	1	no	—
187	C₄×C₄₃	—	4	1	no	—
188	C₄×C₄₃	#124	1	4	yes	complemented
189	Dic₄₃	—	2	2	no	—
190	Dic₄₃	—	2	2	no	—
191	Dic₄₃	—	2	2	no	—
192	Dic₄₃	—	2	2	no	—
193	Dic₄₃	—	4	1	no	—
194	Dic₄₃	—	4	1	no	—
195	Dic₄₃	C₄×D₄	1	4	yes	—
196	C₄×#124	—	43	1	no	maximal, Sylow
197	C₂×C₄₃	—	4	2	no	—
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×#124	1	1	yes	characteristic
202	C₂×C₄₃	#529	1	1	yes	characteristic
203	C₂×C₄₃	#529	1	1	yes	characteristic
204	C₂×C₄₃	#532	1	1	yes	characteristic
205	D₄₃	—	4	2	no	—
206	C₂×#124	—	43	1	no	—
207	C₂×C₄×Q₈	—	43	1	no	—
208	C₂×C₄×D₄	—	43	1	no	—
209	#391	—	43	1	no	—
210	#390	—	43	1	no	—
211	#388	—	43	1	no	—
212	#388	—	43	1	no	—
213	#388	—	43	1	no	—
214	#388	—	43	1	no	—
215	#382	—	43	1	no	—
216	C₄×C₂²⋊C₄	—	43	1	no	—
217	C₄×C₂²⋊C₄	—	43	1	no	—
218	C₄×C₂²⋊C₄	—	43	1	no	—
219	C₄×C₂²⋊C₄	D₄₃	1	1	yes	characteristic, complemented
220	C₄³	—	43	1	no	—
221	C₄₃	C₄×#124	1	1	yes	characteristic, complemented, Sylow
222	C₂²×Q₈	—	43	1	no	—
223	C₂²×D₄	—	43	1	no	—
224	C₂³×C₄	—	43	1	no	—
225	C₂³×C₄	C₂×D₄₃	1	1	yes	characteristic
226	#124	—	43	8	no	—
227	C₄×Q₈	—	86	4	no	—
228	C₄×D₄	—	86	4	no	—
229	C₂×C₄⋊C₄	—	43	1	no	—
230	C₂×C₄⋊C₄	—	43	1	no	—
231	C₂×C₄⋊C₄	—	43	1	no	—
232	C₂×C₄⋊C₄	—	43	1	no	—
233	C₂×C₂²⋊C₄	—	43	1	no	—
234	C₂×C₂²⋊C₄	—	43	1	no	—
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	C₂×D₄₃	1	1	yes	characteristic
242	C₂×C₂²⋊C₄	C₂×D₄₃	1	1	yes	characteristic
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	—	43	1	no	—
248	C₂×C₄²	—	43	1	no	—
249	C₂×C₄²	—	43	1	no	—
250	C₂×C₄²	C₂×D₄₃	1	1	yes	characteristic
251	C₂×C₄²	C₂×D₄₃	1	1	yes	characteristic
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	C₂×D₄₃	1	1	yes	characteristic
259	#95	C₂×D₄₃	1	1	yes	characteristic
260	C₂⁴	—	43	1	no	—
261	C₂⁴	C₂²×D₄₃	1	1	yes	characteristic
262	C₂×Q₈	—	43	4	no	—
263	C₂×Q₈	—	86	2	no	—
264	C₂×Q₈	—	86	2	no	—
265	C₂×D₄	—	43	4	no	—
266	C₂×D₄	—	86	2	no	—
267	C₂×D₄	—	86	2	no	—
268	C₂²×C₄	—	2	2	no	—
269	C₂²×C₄	—	2	2	no	—
270	C₂²×C₄	—	2	2	no	—
271	C₂²×C₄	—	43	1	no	—
272	C₂²×C₄	—	43	1	no	—
273	C₂²×C₄	—	43	1	no	—
274	C₂²×C₄	—	43	1	no	—
275	C₂²×C₄	—	43	1	no	—
276	C₂²×C₄	—	43	1	no	—
277	C₂²×C₄	—	43	1	no	—
278	C₂²×C₄	—	86	2	no	—
279	C₂²×C₄	—	86	2	no	—
280	C₂²×C₄	—	86	2	no	—
281	C₂²×C₄	C₂²×D₄₃	1	1	yes	characteristic
282	C₂²×C₄	C₂²×D₄₃	1	1	yes	characteristic
283	C₂²×C₄	C₂²×D₄₃	1	1	yes	characteristic
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	C₄⋊C₄	—	86	2	no	—
288	C₄⋊C₄	—	86	2	no	—
289	C₄⋊C₄	—	86	2	no	—
290	C₄⋊C₄	—	86	2	no	—
291	C₂²⋊C₄	—	2	2	no	—
292	C₂²⋊C₄	—	43	4	no	—
293	C₂²⋊C₄	—	43	4	no	—
294	C₂²⋊C₄	—	43	4	no	—
295	C₂²⋊C₄	—	86	2	no	—
296	C₂²⋊C₄	—	86	2	no	—
297	C₂²⋊C₄	—	86	2	no	—
298	C₂²⋊C₄	—	86	2	no	—
299	C₂²⋊C₄	—	86	2	no	—
300	C₂²⋊C₄	C₄×D₄₃	1	4	yes	complemented
301	C₄²	—	2	2	no	—
302	C₄²	—	2	2	no	—
303	C₄²	—	43	4	no	—
304	C₄²	—	43	4	no	—
305	C₄²	—	86	2	no	—
306	C₄²	—	86	2	no	—
307	C₄²	—	86	2	no	—
308	C₄²	—	86	2	no	—
309	C₄²	—	86	2	no	—
310	C₂³	—	2	1	no	—
311	C₂³	—	2	1	no	—
312	C₂³	—	2	1	no	—
313	C₂³	—	2	1	no	—
314	C₂³	—	2	1	no	—
315	C₂³	—	2	1	no	—
316	C₂³	—	43	2	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	C₂×C₄×D₄₃	1	2	yes	—
324	C₂³	C₂³×D₄₃	1	1	yes	characteristic
325	Q₈	—	86	8	no	—
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	—	4	4	no	—
340	C₂×C₄	—	43	2	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	—	43	2	no	—
346	C₂×C₄	—	43	2	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	1	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	—	172	4	no	—
362	C₂×C₄	C₂×C₄×D₄₃	1	2	yes	—
363	C₂×C₄	C₂×C₄×D₄₃	1	2	yes	—
364	C₂×C₄	#10621898	1	2	yes	—
365	C₂×C₄	#10621898	1	2	yes	—
366	C₂×C₄	D₄×D₄₃	1	2	yes	—
367	C₂×C₄	#10621900	1	2	yes	—
368	C₂²	—	2	2	no	—
369	C₂²	—	2	2	no	—
370	C₂²	—	2	2	no	—
371	C₂²	—	4	1	no	—
372	C₂²	—	4	1	no	—
373	C₂²	—	4	1	no	—
374	C₂²	—	4	1	no	—
375	C₂²	—	86	2	no	—
376	C₂²	—	86	2	no	—
377	C₂²	—	86	2	no	—
378	C₂²	—	172	1	no	—
379	C₂²	—	172	1	no	—
380	C₂²	—	172	1	no	—
381	C₂²	—	172	1	no	—
382	C₂²	C₂²×C₄×D₄₃	1	1	yes	characteristic
383	C₂²	C₂×D₄×D₄₃	1	1	yes	characteristic
384	C₂²	#41×D₄₃	1	1	yes	characteristic
385	C₂²	#41×D₄₃	1	1	yes	characteristic
386	C₂²	C₂×#10621900	1	1	yes	characteristic
387	C₂²	C₂×#10621898	1	1	yes	characteristic
388	C₂²	C₂×#10621898	1	1	yes	characteristic
389	C₄	—	2	2	no	—
390	C₄	—	2	2	no	—
391	C₄	—	2	2	no	—
392	C₄	—	4	1	no	—
393	C₄	—	4	1	no	—
394	C₄	—	43	4	no	—
395	C₄	—	86	2	no	—
396	C₄	—	86	2	no	—
397	C₄	—	86	2	no	—
398	C₄	—	86	2	no	—
399	C₄	—	172	1	no	—
400	C₄	—	172	1	no	—
401	C₄	#13063311	1	4	yes	direct product factor
402	C₂	—	4	2	no	—
403	C₂	—	172	2	no	—
404	C₂	C₄×D₄×D₄₃	1	1	yes	characteristic
405	C₂	C₄×#10621900	1	1	yes	characteristic
406	C₂	C₄×#10621898	1	1	yes	characteristic
407	C₂	C₂×#13063311	1	1	yes	characteristic
408	C₂	#14583427	1	1	yes	characteristic
409	C₂	#14583429	1	1	yes	characteristic
410	C₂	#14583446	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄	C₂²×D₄₃
commutator	C₂²×C₄₃	C₂³×C₄
Frattini	C₂³	C₂³×D₄₃
Fitting	C₄×C₂²⋊C₄×C₄₃	C₂
socle	C₂³×C₄₃	C₂⁴
hypercenter	C₄×C₂²⋊C₄	D₄₃
hypocenter	C₄₃	C₄×#124
LCS	G ▷ C₂²×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂²×C₄ ◁ C₄×C₂²⋊C₄

Complements

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

N	H ≅ G/N	type
2. C₂×C₄×Dic₈₆	C₂	semidirect
4. #14582803	C₂	semidirect
6. #14582792	C₂	semidirect
7. #14582791	C₂	semidirect
8. #14582788	C₂	semidirect
9. #14582787	C₂	semidirect
10. #14582763	C₂	semidirect
11. C₄×(C₂×D₄₃)⋊C₄	C₂	semidirect
12. C₄×(C₂×D₄₃)⋊C₄	C₂	semidirect
13. C₄×C₂²⋊Dic₄₃	C₂	semidirect
14. C₄²×Dic₄₃	C₂	semidirect
15. C₄×C₂²⋊C₄×C₄₃	C₂	semidirect
19. #13063311	C₄	direct (N × H)
80. C₂×Dic₈₆	C₂×C₄	semidirect
82. C₂²⋊C₄×C₄₃	C₂×C₄	semidirect
87. C₂²⋊Dic₄₃	C₂×C₄	semidirect
91. (C₂×D₄₃)⋊C₄	C₂×C₄	semidirect
92. (C₂×D₄₃)⋊C₄	C₂×C₄	semidirect
102. C₄×Dic₄₃	C₂×C₄	semidirect
188. C₄×C₄₃	#124	semidirect
219. C₄×C₂²⋊C₄	D₄₃	semidirect
221. C₄₃	C₄×#124	semidirect
300. C₂²⋊C₄	C₄×D₄₃	semidirect
401. C₄	#13063311	direct (N × H)

Subgroups — C4×#13063311 #19137135

Conjugacy classes of subgroups

Complements

Subgroups — C₄×#13063311 #19137135