Subgroups — D₄×#14268646 #28404056

Order 14464.

1648 conjugacy classes of subgroups.

The subgroup lattice has 512 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#14268646	C₂	1	2	yes	maximal, complemented
2	#20299268	C₂	1	1	yes	maximal, characteristic, complemented
3	D₄×Dic₂₂₆	C₂	1	1	yes	maximal, characteristic, complemented
4	#20299254	C₂	1	2	yes	maximal, complemented
5	#20299252	C₂	1	1	yes	maximal, characteristic, complemented
6	#20299248	C₂	1	2	yes	maximal, complemented
7	#20299242	C₂	1	2	yes	maximal, complemented
8	#20299235	C₂	1	4	yes	maximal, complemented
9	D₄×C₂²⋊D₁₁₃	C₂	1	2	yes	maximal, complemented
10	#20299146	C₂	1	1	yes	maximal, characteristic, complemented
11	#20299143	C₂	1	2	yes	maximal, complemented
12	#20299108	C₂	1	2	yes	maximal, complemented
13	#20299104	C₂	1	4	yes	maximal, complemented
14	C₄×#14268646	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂×D₄×Dic₁₁₃	C₂	1	2	yes	maximal, complemented
16	C₄×D₄×D₁₁₃	C₂	1	1	yes	maximal, characteristic, complemented
17	D₄²×C₁₁₃	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂×#14268646	—	2	16	no	—
19	C₂×#14268646	C₂²	1	1	yes	characteristic
20	C₂×#14268646	C₂²	1	2	yes	complemented
21	C₂×#14268646	C₂²	1	4	yes	complemented
22	C₂×#14268646	C₂²	1	2	yes	complemented
23	C₂×#14268646	C₂²	1	4	yes	complemented
24	C₂×#14268646	C₂²	1	2	yes	complemented
25	C₂²×Dic₂₂₆	C₂²	1	2	yes	complemented
26	C₂²×C₂²⋊D₁₁₃	C₂²	1	4	yes	complemented
27	C₂×D₄×D₁₁₃	C₂²	1	1	yes	characteristic
28	C₂³×Dic₁₁₃	C₂²	1	4	yes	complemented
29	C₂²×C₄×D₁₁₃	C₂²	1	2	yes	complemented
30	#16813622	C₂²	1	1	yes	characteristic, complemented
31	#16813621	C₂²	1	2	yes	complemented
32	#16813618	C₂²	1	2	yes	complemented
33	#16813609	C₂²	1	2	yes	complemented
34	#16813608	C₂²	1	4	yes	complemented
35	#16813606	C₂²	1	4	yes	complemented
36	#16813604	C₂²	1	4	yes	complemented
37	#16813603	C₂²	1	4	yes	complemented
38	#16813602	C₂²	1	2	yes	complemented
39	#16813601	C₂²	1	2	yes	complemented
40	#16813599	C₂²	1	4	yes	complemented
41	#16813599	C₂²	1	4	yes	complemented
42	#16813596	C₂²	1	2	yes	complemented
43	#16813594	C₂²	1	4	yes	complemented
44	#16813594	C₂²	1	4	yes	complemented
45	#16813594	C₂²	1	4	yes	complemented
46	#16813593	C₂²	1	2	yes	complemented
47	#16813593	C₂²	1	2	yes	complemented
48	#16813593	C₂²	1	2	yes	complemented
49	#16813591	C₂²	1	4	yes	complemented
50	#16813590	C₂²	1	4	yes	complemented
51	C₄×Dic₂₂₆	C₂²	1	1	yes	characteristic, complemented
52	#16813587	C₂²	1	1	yes	characteristic, complemented
53	C₄×D₄₅₂	C₂²	1	1	yes	characteristic, complemented
54	D₄×Dic₁₁₃	C₂²	1	2	yes	—
55	D₄×Dic₁₁₃	C₂²	1	1	yes	characteristic
56	D₄×Dic₁₁₃	C₂²	1	2	yes	complemented
57	D₄×Dic₁₁₃	C₂²	1	4	yes	complemented
58	D₄×Dic₁₁₃	C₂²	1	2	yes	complemented
59	D₄×Dic₁₁₃	C₂²	1	4	yes	complemented
60	D₄×Dic₁₁₃	C₂²	1	1	yes	characteristic, complemented
61	D₄×Dic₁₁₃	C₂²	1	2	yes	complemented
62	#16813584	C₂²	1	1	yes	characteristic, complemented
63	C₄×C₂²⋊D₁₁₃	C₂²	1	2	yes	complemented
64	C₄×C₂²⋊D₁₁₃	C₂²	1	2	yes	complemented
65	#16813582	C₂²	1	2	yes	complemented
66	#16813582	C₂²	1	2	yes	complemented
67	#16813582	C₂²	1	4	yes	complemented
68	#16813580	C₂²	1	1	yes	characteristic, complemented
69	#16813578	C₂²	1	2	yes	complemented
70	C₂×C₄⋊Dic₁₁₃	C₂²	1	2	yes	complemented
71	C₄⋊C₄×D₁₁₃	C₂²	1	1	yes	characteristic, complemented
72	C₂×C₂²⋊Dic₁₁₃	C₂²	1	4	yes	complemented
73	C₂²⋊C₄×D₁₁₃	C₂²	1	2	yes	complemented
74	C₂×C₄×Dic₁₁₃	C₂²	1	2	yes	complemented
75	C₄²×D₁₁₃	C₂²	1	1	yes	characteristic, complemented
76	C₂²×D₄×C₁₁₃	C₂²	1	2	yes	—
77	C₂²×D₄×C₁₁₃	C₂²	1	2	yes	complemented
78	#127×C₁₁₃	C₂²	1	1	yes	characteristic, complemented
79	#121×C₁₁₃	C₂²	1	2	yes	complemented
80	#121×C₁₁₃	C₂²	1	2	yes	complemented
81	#120×C₁₁₃	C₂²	1	4	yes	complemented
82	C₄×D₄×C₁₁₃	C₂²	1	1	yes	characteristic
83	C₄×D₄×C₁₁₃	C₂²	1	1	yes	characteristic, complemented
84	C₂³×D₁₁₃	C₂³	1	2	yes	—
85	#14268646	—	2	8	no	—
86	#14268646	—	2	16	no	—
87	#14268646	—	2	16	no	—
88	#14268646	—	2	8	no	—
89	#14268646	—	2	8	no	—
90	#14268646	D₄	1	8	yes	direct product factor
91	C₂×Dic₂₂₆	—	2	8	no	—
92	C₂×Dic₂₂₆	C₂³	1	4	yes	—
93	C₂×Dic₂₂₆	C₂³	1	2	yes	—
94	C₂×Dic₂₂₆	C₂³	1	1	yes	characteristic
95	C₂×D₄₅₂	C₂³	1	1	yes	characteristic
96	C₂×C₂²⋊D₁₁₃	—	2	16	no	—
97	C₂×C₂²⋊D₁₁₃	C₂³	1	2	yes	—
98	C₂×C₂²⋊D₁₁₃	C₂³	1	4	yes	—
99	C₂×C₂²⋊D₁₁₃	C₂³	1	4	yes	—
100	C₂×C₂²⋊D₁₁₃	C₂³	1	4	yes	—
101	C₂×C₂²⋊D₁₁₃	C₂³	1	4	yes	—
102	C₂×C₂²⋊D₁₁₃	C₂³	1	2	yes	—
103	D₄×D₁₁₃	—	2	4	no	—
104	C₂²×Dic₁₁₃	—	2	16	no	—
105	C₂²×Dic₁₁₃	C₂³	1	4	yes	—
106	C₂²×Dic₁₁₃	C₂³	1	2	yes	—
107	C₂²×Dic₁₁₃	C₂³	1	4	yes	—
108	C₂²×Dic₁₁₃	C₂³	1	4	yes	—
109	C₂²×Dic₁₁₃	C₂³	1	4	yes	—
110	C₂²×Dic₁₁₃	C₂³	1	2	yes	—
111	C₂²×Dic₁₁₃	C₂³	1	2	yes	—
112	C₂×C₄×D₁₁₃	—	2	8	no	—
113	C₂×C₄×D₁₁₃	C₂³	1	1	yes	characteristic
114	C₂×C₄×D₁₁₃	C₂³	1	2	yes	—
115	C₂×C₄×D₁₁₃	C₂³	1	2	yes	—
116	C₂×C₄×D₁₁₃	C₂³	1	2	yes	—
117	C₂×C₄×D₁₁₃	C₂³	1	1	yes	characteristic
118	C₂×C₄×D₁₁₃	C₂³	1	1	yes	characteristic
119	C₄⋊Dic₁₁₃	C₂³	1	1	yes	characteristic
120	C₄⋊Dic₁₁₃	C₂³	1	2	yes	—
121	C₄⋊Dic₁₁₃	C₂³	1	4	yes	—
122	C₄⋊Dic₁₁₃	C₂³	1	1	yes	characteristic
123	C₄⋊Dic₁₁₃	C₂³	1	2	yes	—
124	#14268626	C₂³	1	2	yes	—
125	#14268626	C₂³	1	2	yes	—
126	#14268626	C₂³	1	2	yes	—
127	#14268626	C₂³	1	4	yes	—
128	C₂²⋊Dic₁₁₃	C₂³	1	2	yes	—
129	C₂²⋊Dic₁₁₃	C₂³	1	4	yes	—
130	C₂²⋊Dic₁₁₃	C₂³	1	4	yes	—
131	C₂²⋊Dic₁₁₃	C₂³	1	4	yes	—
132	C₂²⋊Dic₁₁₃	C₂³	1	2	yes	—
133	C₂²⋊Dic₁₁₃	C₂³	1	4	yes	—
134	#14268624	C₂³	1	2	yes	—
135	#14268624	C₂³	1	2	yes	—
136	#14268624	C₂³	1	2	yes	—
137	#14268624	C₂³	1	4	yes	—
138	C₄×Dic₁₁₃	C₂³	1	1	yes	characteristic
139	C₄×Dic₁₁₃	C₂³	1	1	yes	characteristic
140	C₄×Dic₁₁₃	C₂³	1	1	yes	characteristic
141	C₄×Dic₁₁₃	C₂³	1	2	yes	—
142	C₄×Dic₁₁₃	C₂³	1	2	yes	—
143	C₄×Dic₁₁₃	C₂³	1	2	yes	—
144	C₂⁴×C₁₁₃	C₂³	1	4	yes	—
145	C₂×D₄×C₁₁₃	—	2	8	no	—
146	C₂×D₄×C₁₁₃	—	2	8	no	—
147	C₂×D₄×C₁₁₃	C₂³	1	4	yes	—
148	C₂×D₄×C₁₁₃	C₂³	1	2	yes	—
149	C₂×D₄×C₁₁₃	C₂³	1	2	yes	—
150	C₂×D₄×C₁₁₃	C₂³	1	4	yes	—
151	C₂×D₄×C₁₁₃	C₂³	1	2	yes	—
152	C₂×D₄×C₁₁₃	C₂³	1	1	yes	characteristic
153	C₂×D₄×C₁₁₃	C₂³	1	1	yes	characteristic
154	C₂²×C₄×C₁₁₃	C₂³	1	2	yes	—
155	C₂²×C₄×C₁₁₃	C₂³	1	2	yes	—
156	C₄⋊C₄×C₁₁₃	C₂³	1	1	yes	characteristic
157	C₄⋊C₄×C₁₁₃	C₂³	1	1	yes	characteristic
158	C₂²⋊C₄×C₁₁₃	C₂³	1	2	yes	—
159	C₂²⋊C₄×C₁₁₃	C₂³	1	2	yes	—
160	C₂²⋊C₄×C₁₁₃	C₂³	1	4	yes	—
161	C₄²×C₁₁₃	C₂³	1	1	yes	characteristic
162	C₂³×C₁₁₃	—	2	8	no	—
163	C₂³×C₁₁₃	—	2	8	no	—
164	C₂³×C₁₁₃	—	4	4	no	—
165	C₂³×C₁₁₃	C₂⁴	1	4	yes	—
166	C₂³×C₁₁₃	C₂⁴	1	2	yes	—
167	C₂³×C₁₁₃	C₂⁴	1	2	yes	—
168	C₂²×D₁₁₃	—	2	4	no	—
169	C₂²×D₁₁₃	—	2	4	no	—
170	C₂²×D₁₁₃	—	4	2	no	—
171	C₂²×D₁₁₃	C₂⁴	1	2	yes	—
172	C₂²×D₁₁₃	C₂⁴	1	1	yes	characteristic
173	D₄×C₁₁₃	—	2	8	no	—
174	D₄×C₁₁₃	—	2	8	no	—
175	D₄×C₁₁₃	—	2	4	no	—
176	D₄×C₁₁₃	—	2	4	no	—
177	D₄×C₁₁₃	—	4	2	no	—
178	D₄×C₁₁₃	C₂×D₄	1	4	yes	complemented
179	D₄×C₁₁₃	#41	1	4	yes	complemented
180	C₂×C₄×C₁₁₃	—	2	4	no	—
181	C₂×C₄×C₁₁₃	—	2	4	no	—
182	C₂×C₄×C₁₁₃	C₂⁴	1	1	yes	characteristic
183	C₂×C₄×C₁₁₃	C₂⁴	1	2	yes	—
184	C₂×C₄×C₁₁₃	C₂⁴	1	2	yes	—
185	C₂×C₄×C₁₁₃	C₂⁴	1	1	yes	characteristic
186	C₂×C₄×C₁₁₃	C₂⁴	1	1	yes	characteristic
187	C₂²⋊D₁₁₃	—	2	8	no	—
188	C₂²⋊D₁₁₃	—	2	4	no	—
189	C₂²⋊D₁₁₃	—	2	8	no	—
190	C₂²⋊D₁₁₃	—	2	8	no	—
191	C₂²⋊D₁₁₃	—	4	4	no	—
192	C₂²⋊D₁₁₃	C₂×D₄	1	8	yes	complemented
193	C₂×Dic₁₁₃	—	2	8	no	—
194	C₂×Dic₁₁₃	—	2	4	no	—
195	C₂×Dic₁₁₃	—	2	8	no	—
196	C₂×Dic₁₁₃	—	2	8	no	—
197	C₂×Dic₁₁₃	—	2	8	no	—
198	C₂×Dic₁₁₃	—	4	2	no	—
199	C₂×Dic₁₁₃	C₂×D₄	1	8	yes	complemented
200	C₂×Dic₁₁₃	C₂⁴	1	1	yes	characteristic
201	C₂×Dic₁₁₃	C₂⁴	1	2	yes	—
202	C₂×Dic₁₁₃	C₂⁴	1	1	yes	characteristic
203	C₂×Dic₁₁₃	C₂⁴	1	2	yes	—
204	C₂×Dic₁₁₃	C₂⁴	1	4	yes	—
205	C₂×Dic₁₁₃	C₂⁴	1	1	yes	characteristic
206	C₂×Dic₁₁₃	C₂⁴	1	2	yes	—
207	D₄₅₂	—	2	2	no	—
208	C₄×D₁₁₃	—	2	4	no	—
209	C₄×D₁₁₃	—	2	4	no	—
210	C₄×D₁₁₃	—	2	2	no	—
211	C₄×D₁₁₃	—	2	4	no	—
212	C₄×D₁₁₃	—	4	1	no	—
213	C₄×D₁₁₃	C₂×D₄	1	4	yes	complemented
214	Dic₂₂₆	—	2	4	no	—
215	Dic₂₂₆	—	2	8	no	—
216	Dic₂₂₆	C₂×D₄	1	4	yes	complemented
217	C₂²×C₁₁₃	—	2	2	no	—
218	C₂²×C₁₁₃	—	2	2	no	—
219	C₂²×C₁₁₃	—	2	2	no	—
220	C₂²×C₁₁₃	—	2	2	no	—
221	C₂²×C₁₁₃	—	2	4	no	—
222	C₂²×C₁₁₃	—	2	4	no	—
223	C₂²×C₁₁₃	—	2	4	no	—
224	C₂²×C₁₁₃	—	4	16	no	—
225	C₂²×C₁₁₃	C₂²×D₄	1	4	yes	—
226	C₂²×C₁₁₃	C₂×#41	1	4	yes	complemented
227	C₂²×C₁₁₃	C₂⁵	1	1	yes	characteristic
228	C₂×D₁₁₃	—	2	1	no	—
229	C₂×D₁₁₃	—	2	1	no	—
230	C₂×D₁₁₃	—	2	2	no	—
231	C₂×D₁₁₃	—	2	2	no	—
232	C₂×D₁₁₃	—	2	2	no	—
233	C₂×D₁₁₃	—	4	8	no	—
234	C₂×D₁₁₃	C₂²×D₄	1	2	yes	—
235	C₄×C₁₁₃	—	2	2	no	—
236	C₄×C₁₁₃	—	2	2	no	—
237	C₄×C₁₁₃	—	2	1	no	—
238	C₄×C₁₁₃	C₂²×D₄	1	2	yes	—
239	C₄×C₁₁₃	C₂×#41	1	2	yes	complemented
240	Dic₁₁₃	—	2	4	no	—
241	Dic₁₁₃	—	2	2	no	—
242	Dic₁₁₃	—	2	1	no	—
243	Dic₁₁₃	—	2	1	no	—
244	Dic₁₁₃	—	2	2	no	—
245	Dic₁₁₃	C₂²×D₄	1	4	yes	—
246	Dic₁₁₃	C₂²×D₄	1	2	yes	—
247	C₂×C₁₁₃	—	2	4	no	—
248	C₂×C₁₁₃	—	2	4	no	—
249	C₂×C₁₁₃	—	4	4	no	—
250	C₂×C₁₁₃	C₂³×D₄	1	1	yes	characteristic
251	C₂×C₁₁₃	C₂²×#41	1	1	yes	characteristic
252	C₂×C₁₁₃	#585	1	1	yes	characteristic
253	D₁₁₃	—	2	2	no	—
254	D₁₁₃	—	4	2	no	—
255	D₄×#41	—	113	1	no	maximal, Sylow
256	C₁₁₃	D₄×#41	1	1	yes	characteristic, complemented, Sylow
257	C₂²×#41	—	113	2	no	—
258	#550	—	113	1	no	—
259	D₄×Q₈	—	113	1	no	—
260	#548	—	113	2	no	—
261	#547	—	113	2	no	—
262	#547	—	113	1	no	—
263	#546	—	113	2	no	—
264	#546	—	113	4	no	—
265	D₄²	—	113	2	no	—
266	D₄²	D₁₁₃	1	1	yes	characteristic, complemented
267	#532	—	113	1	no	—
268	#532	—	113	2	no	—
269	#525	—	113	2	no	—
270	#525	—	113	4	no	—
271	C₄×#41	—	113	1	no	—
272	C₂×C₄×D₄	—	113	2	no	—
273	C₂×C₄×D₄	—	113	1	no	—
274	C₂×#41	—	113	1	no	—
275	C₂×#41	—	113	4	no	—
276	C₂×#41	—	113	2	no	—
277	C₂×#41	—	113	2	no	—
278	C₂×#41	—	113	4	no	—
279	C₂×#41	—	113	2	no	—
280	C₂×#41	—	226	16	no	—
281	C₂²×Q₈	—	113	2	no	—
282	C₂²×D₄	—	113	4	no	—
283	C₂²×D₄	—	113	1	no	—
284	C₂²×D₄	C₂×D₁₁₃	1	2	yes	—
285	C₂²×D₄	C₂×D₁₁₃	1	2	yes	complemented
286	C₂³×C₄	—	113	4	no	—
287	C₂³×C₄	—	113	2	no	—
288	C₄⋊Q₈	—	113	2	no	—
289	C₄⋊Q₈	—	113	1	no	—
290	#127	—	113	2	no	—
291	#127	C₂×D₁₁₃	1	1	yes	characteristic, complemented
292	#124	—	113	2	no	—
293	#124	—	113	4	no	—
294	#123	—	113	4	no	—
295	#123	—	113	4	no	—
296	#123	—	113	4	no	—
297	C₂²⋊Q₈	—	113	2	no	—
298	C₂²⋊Q₈	—	113	2	no	—
299	C₂²⋊Q₈	—	113	4	no	—
300	C₂²⋊Q₈	—	113	4	no	—
301	#121	—	113	2	no	—
302	#121	—	113	4	no	—
303	#121	—	113	4	no	—
304	#121	—	113	2	no	—
305	#121	—	113	2	no	—
306	#121	—	113	4	no	—
307	#121	—	113	2	no	—
308	#121	C₂×D₁₁₃	1	2	yes	complemented
309	#121	C₂×D₁₁₃	1	2	yes	complemented
310	#120	—	113	4	no	—
311	#120	—	113	4	no	—
312	#120	C₂×D₁₁₃	1	4	yes	complemented
313	C₄×Q₈	—	113	1	no	—
314	C₄×Q₈	—	113	1	no	—
315	C₄×D₄	—	113	1	no	—
316	C₄×D₄	—	113	4	no	—
317	C₄×D₄	—	113	2	no	—
318	C₄×D₄	—	113	2	no	—
319	C₄×D₄	—	113	4	no	—
320	C₄×D₄	—	113	2	no	—
321	C₄×D₄	—	113	1	no	—
322	C₄×D₄	—	113	2	no	—
323	C₄×D₄	—	113	2	no	—
324	C₄×D₄	—	113	2	no	—
325	C₄×D₄	—	113	1	no	—
326	C₄×D₄	—	113	2	no	—
327	C₄×D₄	—	113	2	no	—
328	C₄×D₄	—	113	4	no	—
329	C₄×D₄	—	113	1	no	—
330	C₄×D₄	C₂×D₁₁₃	1	1	yes	characteristic
331	C₄×D₄	C₂×D₁₁₃	1	1	yes	characteristic, complemented
332	#117	—	113	1	no	—
333	#117	—	113	2	no	—
334	C₂×C₄⋊C₄	—	113	2	no	—
335	C₂×C₄⋊C₄	—	113	1	no	—
336	C₂×C₂²⋊C₄	—	113	4	no	—
337	C₂×C₂²⋊C₄	—	113	2	no	—
338	C₂×C₄²	—	113	2	no	—
339	C₂×C₄²	—	113	1	no	—
340	C₂⁴	—	113	2	no	—
341	C₂⁴	C₂²×D₁₁₃	1	4	yes	—
342	#41	—	113	8	no	—
343	#41	—	226	16	no	—
344	#41	—	226	8	no	—
345	#41	—	226	16	no	—
346	#41	—	226	8	no	—
347	#41	—	226	8	no	—
348	C₂×Q₈	—	113	1	no	—
349	C₂×Q₈	—	113	4	no	—
350	C₂×Q₈	—	113	2	no	—
351	C₂×Q₈	—	226	8	no	—
352	C₂×D₄	—	2	8	no	—
353	C₂×D₄	—	2	8	no	—
354	C₂×D₄	—	113	2	no	—
355	C₂×D₄	—	113	4	no	—
356	C₂×D₄	—	113	2	no	—
357	C₂×D₄	—	113	4	no	—
358	C₂×D₄	—	113	4	no	—
359	C₂×D₄	—	113	4	no	—
360	C₂×D₄	—	113	1	no	—
361	C₂×D₄	—	226	16	no	—
362	C₂×D₄	—	226	4	no	—
363	C₂×D₄	C₂²×D₁₁₃	1	4	yes	—
364	C₂×D₄	C₂²×D₁₁₃	1	2	yes	—
365	C₂×D₄	C₂²×D₁₁₃	1	4	yes	—
366	C₂×D₄	C₂²×D₁₁₃	1	2	yes	—
367	C₂×D₄	C₂²×D₁₁₃	1	2	yes	—
368	C₂×D₄	C₂²×D₁₁₃	1	1	yes	characteristic
369	C₂×D₄	C₂²×D₁₁₃	1	1	yes	characteristic
370	C₂²×C₄	—	113	2	no	—
371	C₂²×C₄	—	113	1	no	—
372	C₂²×C₄	—	113	2	no	—
373	C₂²×C₄	—	113	4	no	—
374	C₂²×C₄	—	113	2	no	—
375	C₂²×C₄	—	113	4	no	—
376	C₂²×C₄	—	113	4	no	—
377	C₂²×C₄	—	113	4	no	—
378	C₂²×C₄	—	113	1	no	—
379	C₂²×C₄	—	113	1	no	—
380	C₂²×C₄	—	113	2	no	—
381	C₂²×C₄	—	113	2	no	—
382	C₂²×C₄	—	113	2	no	—
383	C₂²×C₄	—	226	8	no	—
384	C₂²×C₄	—	226	16	no	—
385	C₂²×C₄	C₂²×D₁₁₃	1	2	yes	—
386	C₂²×C₄	C₂²×D₁₁₃	1	2	yes	—
387	C₄⋊C₄	—	113	1	no	—
388	C₄⋊C₄	—	113	2	no	—
389	C₄⋊C₄	—	113	2	no	—
390	C₄⋊C₄	—	113	4	no	—
391	C₄⋊C₄	—	113	2	no	—
392	C₄⋊C₄	—	113	2	no	—
393	C₄⋊C₄	—	113	1	no	—
394	C₄⋊C₄	—	113	4	no	—
395	C₄⋊C₄	—	113	2	no	—
396	C₄⋊C₄	C₂²×D₁₁₃	1	1	yes	characteristic
397	C₄⋊C₄	C₂²×D₁₁₃	1	1	yes	characteristic
398	C₂²⋊C₄	—	113	2	no	—
399	C₂²⋊C₄	—	113	4	no	—
400	C₂²⋊C₄	—	113	4	no	—
401	C₂²⋊C₄	—	113	4	no	—
402	C₂²⋊C₄	—	113	2	no	—
403	C₂²⋊C₄	—	113	4	no	—
404	C₂²⋊C₄	—	113	2	no	—
405	C₂²⋊C₄	—	113	2	no	—
406	C₂²⋊C₄	—	113	2	no	—
407	C₂²⋊C₄	—	113	4	no	—
408	C₂²⋊C₄	C₂²×D₁₁₃	1	2	yes	—
409	C₂²⋊C₄	C₂²×D₁₁₃	1	2	yes	—
410	C₂²⋊C₄	C₂²×D₁₁₃	1	4	yes	—
411	C₄²	—	113	1	no	—
412	C₄²	—	113	2	no	—
413	C₄²	—	113	1	no	—
414	C₄²	—	113	2	no	—
415	C₄²	—	113	1	no	—
416	C₄²	—	113	2	no	—
417	C₄²	C₂²×D₁₁₃	1	1	yes	characteristic
418	C₂³	—	2	8	no	—
419	C₂³	—	2	8	no	—
420	C₂³	—	4	4	no	—
421	C₂³	—	113	1	no	—
422	C₂³	—	113	2	no	—
423	C₂³	—	452	2	no	—
424	C₂³	—	226	4	no	—
425	C₂³	—	226	4	no	—
426	C₂³	C₂³×D₁₁₃	1	4	yes	—
427	C₂³	C₂³×D₁₁₃	1	2	yes	—
428	C₂³	C₂³×D₁₁₃	1	2	yes	—
429	Q₈	—	113	4	no	—
430	Q₈	—	226	8	no	—
431	Q₈	—	226	4	no	—
432	D₄	—	2	8	no	—
433	D₄	—	2	8	no	—
434	D₄	—	2	4	no	—
435	D₄	—	2	4	no	—
436	D₄	—	4	2	no	—
437	D₄	—	113	8	no	—
438	D₄	—	452	4	no	—
439	D₄	—	226	8	no	—
440	D₄	—	226	8	no	—
441	D₄	—	226	8	no	—
442	D₄	—	226	4	no	—
443	D₄	—	226	2	no	—
444	D₄	D₄×D₁₁₃	1	4	yes	complemented
445	D₄	#14268646	1	4	yes	direct product factor
446	C₂×C₄	—	2	4	no	—
447	C₂×C₄	—	2	4	no	—
448	C₂×C₄	—	113	8	no	—
449	C₂×C₄	—	113	1	no	—
450	C₂×C₄	—	113	2	no	—
451	C₂×C₄	—	113	4	no	—
452	C₂×C₄	—	113	1	no	—
453	C₂×C₄	—	113	1	no	—
454	C₂×C₄	—	113	2	no	—
455	C₂×C₄	—	113	2	no	—
456	C₂×C₄	—	113	4	no	—
457	C₂×C₄	—	452	1	no	—
458	C₂×C₄	—	452	2	no	—
459	C₂×C₄	—	226	4	no	—
460	C₂×C₄	—	226	4	no	—
461	C₂×C₄	—	226	4	no	—
462	C₂×C₄	—	226	8	no	—
463	C₂×C₄	—	226	8	no	—
464	C₂×C₄	—	226	8	no	—
465	C₂×C₄	—	226	8	no	—
466	C₂×C₄	—	226	4	no	—
467	C₂×C₄	—	226	2	no	—
468	C₂×C₄	C₂³×D₁₁₃	1	2	yes	—
469	C₂×C₄	C₂³×D₁₁₃	1	1	yes	characteristic
470	C₂×C₄	C₂³×D₁₁₃	1	2	yes	—
471	C₂×C₄	C₂³×D₁₁₃	1	1	yes	characteristic
472	C₂×C₄	C₂³×D₁₁₃	1	1	yes	characteristic
473	C₂²	—	2	2	no	—
474	C₂²	—	2	2	no	—
475	C₂²	—	2	2	no	—
476	C₂²	—	2	2	no	—
477	C₂²	—	2	4	no	—
478	C₂²	—	2	4	no	—
479	C₂²	—	2	4	no	—
480	C₂²	—	4	16	no	—
481	C₂²	—	113	2	no	—
482	C₂²	—	452	8	no	—
483	C₂²	—	226	2	no	—
484	C₂²	—	226	2	no	—
485	C₂²	—	226	2	no	—
486	C₂²	—	226	1	no	—
487	C₂²	—	226	1	no	—
488	C₂²	C₂×D₄×D₁₁₃	1	4	yes	—
489	C₂²	C₂×#14268646	1	4	yes	complemented
490	C₂²	C₂⁴×D₁₁₃	1	1	yes	characteristic
491	C₄	—	2	2	no	—
492	C₄	—	2	2	no	—
493	C₄	—	2	1	no	—
494	C₄	—	113	2	no	—
495	C₄	—	113	4	no	—
496	C₄	—	226	2	no	—
497	C₄	—	226	4	no	—
498	C₄	—	226	1	no	—
499	C₄	—	226	1	no	—
500	C₄	—	226	2	no	—
501	C₄	C₂×D₄×D₁₁₃	1	2	yes	—
502	C₄	C₂×#14268646	1	2	yes	complemented
503	C₂	—	2	4	no	—
504	C₂	—	2	4	no	—
505	C₂	—	4	4	no	—
506	C₂	—	452	2	no	—
507	C₂	—	226	2	no	—
508	C₂	C₂²×D₄×D₁₁₃	1	1	yes	characteristic
509	C₂	C₂²×#14268646	1	1	yes	characteristic
510	C₂	#20299433	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₁₁₃
commutator, socle, cosocle	C₂²×C₁₁₃	C₂⁵
Fitting	D₄²×C₁₁₃	C₂
hypercenter	D₄²	D₁₁₃
hypocenter	C₁₁₃	D₄×#41
LCS	G ▷ C₂²×C₁₁₃ ▷ C₁₁₃
UCS	C₁ ◁ C₂² ◁ D₄²

Complements

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

N	H ≅ G/N	type
1. C₂²×#14268646	C₂	semidirect
2. #20299268	C₂	semidirect
3. D₄×Dic₂₂₆	C₂	semidirect
4. #20299254	C₂	semidirect
5. #20299252	C₂	semidirect
6. #20299248	C₂	semidirect
7. #20299242	C₂	semidirect
8. #20299235	C₂	semidirect
9. D₄×C₂²⋊D₁₁₃	C₂	semidirect
10. #20299146	C₂	semidirect
11. #20299143	C₂	semidirect
12. #20299108	C₂	semidirect
13. #20299104	C₂	semidirect
14. C₄×#14268646	C₂	semidirect
15. C₂×D₄×Dic₁₁₃	C₂	semidirect
16. C₄×D₄×D₁₁₃	C₂	semidirect
17. D₄²×C₁₁₃	C₂	semidirect
20. C₂×#14268646	C₂²	semidirect
21. C₂×#14268646	C₂²	semidirect
22. C₂×#14268646	C₂²	semidirect
23. C₂×#14268646	C₂²	semidirect
24. C₂×#14268646	C₂²	semidirect
25. C₂²×Dic₂₂₆	C₂²	semidirect
26. C₂²×C₂²⋊D₁₁₃	C₂²	semidirect
28. C₂³×Dic₁₁₃	C₂²	semidirect
29. C₂²×C₄×D₁₁₃	C₂²	semidirect
30. #16813622	C₂²	semidirect
31. #16813621	C₂²	semidirect
32. #16813618	C₂²	semidirect
33. #16813609	C₂²	semidirect
34. #16813608	C₂²	semidirect
35. #16813606	C₂²	semidirect
36. #16813604	C₂²	semidirect
37. #16813603	C₂²	semidirect
38. #16813602	C₂²	semidirect
39. #16813601	C₂²	semidirect
40. #16813599	C₂²	semidirect
41. #16813599	C₂²	semidirect
42. #16813596	C₂²	semidirect
43. #16813594	C₂²	semidirect
44. #16813594	C₂²	semidirect
45. #16813594	C₂²	semidirect
46. #16813593	C₂²	semidirect
47. #16813593	C₂²	semidirect
48. #16813593	C₂²	semidirect
49. #16813591	C₂²	semidirect
50. #16813590	C₂²	semidirect
51. C₄×Dic₂₂₆	C₂²	semidirect
52. #16813587	C₂²	semidirect
53. C₄×D₄₅₂	C₂²	semidirect
56. D₄×Dic₁₁₃	C₂²	semidirect
57. D₄×Dic₁₁₃	C₂²	semidirect
58. D₄×Dic₁₁₃	C₂²	semidirect
59. D₄×Dic₁₁₃	C₂²	semidirect
60. D₄×Dic₁₁₃	C₂²	semidirect
61. D₄×Dic₁₁₃	C₂²	semidirect
62. #16813584	C₂²	semidirect
63. C₄×C₂²⋊D₁₁₃	C₂²	semidirect
64. C₄×C₂²⋊D₁₁₃	C₂²	semidirect
65. #16813582	C₂²	semidirect
66. #16813582	C₂²	semidirect
67. #16813582	C₂²	semidirect
68. #16813580	C₂²	semidirect
69. #16813578	C₂²	semidirect
70. C₂×C₄⋊Dic₁₁₃	C₂²	semidirect
71. C₄⋊C₄×D₁₁₃	C₂²	semidirect
72. C₂×C₂²⋊Dic₁₁₃	C₂²	semidirect
73. C₂²⋊C₄×D₁₁₃	C₂²	semidirect
74. C₂×C₄×Dic₁₁₃	C₂²	semidirect
75. C₄²×D₁₁₃	C₂²	semidirect
77. C₂²×D₄×C₁₁₃	C₂²	semidirect
78. #127×C₁₁₃	C₂²	semidirect
79. #121×C₁₁₃	C₂²	semidirect
80. #121×C₁₁₃	C₂²	semidirect
81. #120×C₁₁₃	C₂²	semidirect
83. C₄×D₄×C₁₁₃	C₂²	semidirect
90. #14268646	D₄	direct (N × H)
178. D₄×C₁₁₃	C₂×D₄	semidirect
179. D₄×C₁₁₃	#41	semidirect
192. C₂²⋊D₁₁₃	C₂×D₄	semidirect
199. C₂×Dic₁₁₃	C₂×D₄	semidirect
213. C₄×D₁₁₃	C₂×D₄	semidirect
216. Dic₂₂₆	C₂×D₄	semidirect
226. C₂²×C₁₁₃	C₂×#41	semidirect
239. C₄×C₁₁₃	C₂×#41	semidirect
256. C₁₁₃	D₄×#41	semidirect
266. D₄²	D₁₁₃	semidirect
285. C₂²×D₄	C₂×D₁₁₃	semidirect
291. #127	C₂×D₁₁₃	semidirect
308. #121	C₂×D₁₁₃	semidirect
309. #121	C₂×D₁₁₃	semidirect
312. #120	C₂×D₁₁₃	semidirect
331. C₄×D₄	C₂×D₁₁₃	semidirect
444. D₄	D₄×D₁₁₃	semidirect
445. D₄	#14268646	direct (N × H)
489. C₂²	C₂×#14268646	semidirect
502. C₄	C₂×#14268646	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂²×#14268646	2
#20299268	2
D₄×Dic₂₂₆	2
#20299254	2
#20299252	2
#20299248	2
#20299242	2
#20299235	2
D₄×C₂²⋊D₁₁₃	2
#20299146	2
#20299143	2
#20299108	2
#20299104	2
C₄×#14268646	2
C₂×D₄×Dic₁₁₃	2
C₄×D₄×D₁₁₃	2
D₄²×C₁₁₃	2
D₄×#41	113

Subgroups — D4×#14268646 #28404056

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₄×#14268646 #28404056