Subgroups — C₄×#66694 #13059856

Order 1344.

852 conjugacy classes of subgroups.

The subgroup lattice has 516 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₄×D₂₁	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#66694	C₂	1	1	yes	maximal, characteristic
3	C₂×C₄×D₃×D₇	C₂	1	1	yes	maximal, characteristic, complemented
4	C₄×C₇×#67	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×C₄×C₂²⋊D₇	C₂	1	1	yes	maximal, characteristic, complemented
6	#10621123	C₂	1	1	yes	maximal, characteristic, complemented
7	#67⋊Dic₇	C₂	1	1	yes	maximal, characteristic, complemented
8	(C₂²⋊D₇)⋊Dic₃	C₂	1	1	yes	maximal, characteristic, complemented
9	#10621035	C₂	1	1	yes	maximal, characteristic, complemented
10	C₄×#4247	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄×#4246	C₂	1	1	yes	maximal, characteristic, complemented
12	#10620968	C₂	1	1	yes	maximal, characteristic, complemented
13	#10620966	C₂	1	1	yes	maximal, characteristic, complemented
14	C₄×D₂₁⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
15	#10620958	C₂	1	1	yes	maximal, characteristic, complemented
16	C₄×D₄×D₇	—	3	1	no	maximal, Hall
17	C₂³×D₂₁	C₂²	1	1	yes	characteristic
18	C₂²×D₃×D₇	C₂²	1	1	yes	characteristic
19	C₂²×C₃×C₄×C₇	C₂²	1	1	yes	characteristic, complemented
20	C₂²×Dic₂₁	C₂²	1	1	yes	characteristic, complemented
21	C₂×C₄×D₂₁	—	2	4	no	—
22	C₂×C₄×D₂₁	C₂²	1	1	yes	characteristic
23	C₂×C₄×D₂₁	C₂²	1	1	yes	characteristic
24	C₂×C₄×D₂₁	C₂²	1	1	yes	characteristic, complemented
25	C₂×C₄×D₂₁	C₂²	1	1	yes	characteristic, complemented
26	C₂×C₇×#67	C₂²	1	1	yes	characteristic
27	C₂×C₄×D₃×C₇	C₂²	1	1	yes	characteristic, complemented
28	C₂×C₃×C₂²⋊D₇	C₂²	1	1	yes	characteristic
29	C₂×C₃×C₄×D₇	C₂²	1	1	yes	characteristic, complemented
30	#66694	C₄	1	8	yes	direct product factor
31	C₂×#4247	C₂²	1	1	yes	characteristic
32	C₂×#4246	C₂²	1	1	yes	characteristic
33	C₂×D₂₁⋊C₄	C₂²	1	1	yes	characteristic
34	C₂×D₂₁⋊C₄	C₂²	1	1	yes	characteristic
35	C₂×D₂₁⋊C₄	C₂²	1	1	yes	characteristic
36	C₂×D₃×Dic₇	C₂²	1	1	yes	characteristic, complemented
37	C₂×Dic₃×D₇	C₂²	1	1	yes	characteristic, complemented
38	C₄×D₃×D₇	—	2	4	no	—
39	C₇×#217	C₂²	1	1	yes	characteristic, complemented
40	C₇×(C₂×D₃)⋊C₄	C₂²	1	1	yes	characteristic, complemented
41	C₇×Dic₃⋊C₄	C₂²	1	1	yes	characteristic, complemented
42	C₄×C₇×Dic₃	C₂²	1	1	yes	characteristic, complemented
43	C₃×C₂²⋊Dic₇	C₂²	1	1	yes	characteristic, complemented
44	C₃×(C₂×D₇)⋊C₄	C₂²	1	1	yes	characteristic, complemented
45	C₃×Dic₇⋊C₄	C₂²	1	1	yes	characteristic, complemented
46	C₃×C₄×Dic₇	C₂²	1	1	yes	characteristic, complemented
47	Dic₃⋊Dic₇	C₂²	1	1	yes	characteristic, complemented
48	Dic₇⋊Dic₃	C₂²	1	1	yes	characteristic, complemented
49	#66575	C₂²	1	1	yes	characteristic, complemented
50	#66575	C₂²	1	1	yes	characteristic, complemented
51	(C₂×D₃)⋊Dic₇	C₂²	1	1	yes	characteristic, complemented
52	(C₂×D₇)⋊Dic₃	C₂²	1	1	yes	characteristic, complemented
53	Dic₃×Dic₇	C₂²	1	1	yes	characteristic, complemented
54	Dic₃×Dic₇	C₂²	1	1	yes	characteristic, complemented
55	C₂×D₄×D₇	—	3	1	no	—
56	C₂²×C₄×D₇	—	3	1	no	—
57	C₂²×C₄×D₇	—	3	1	no	—
58	C₄×C₇×D₄	—	3	1	no	—
59	D₄×Dic₇	—	3	1	no	—
60	C₄×C₂²⋊D₇	—	3	1	no	—
61	C₄×C₂²⋊D₇	D₃	1	1	yes	characteristic, complemented
62	#6456	—	3	1	no	—
63	D₇×C₄⋊C₄	—	3	1	no	—
64	(C₂²⋊D₇)⋊C₄	—	3	1	no	—
65	(C₂²⋊D₇)⋊C₄	—	3	1	no	—
66	D₇×C₂²⋊C₄	—	3	1	no	—
67	D₇×C₂²⋊C₄	—	3	1	no	—
68	C₄×D₂₈	—	3	1	no	—
69	C₄²×D₇	—	3	1	no	—
70	C₄×D₃×D₄	—	7	1	no	maximal, Hall
71	C₂³×C₃×C₇	C₂³	1	1	yes	characteristic
72	C₂²×D₂₁	—	2	2	no	—
73	C₂²×D₂₁	—	2	2	no	—
74	C₂²×D₂₁	C₂×C₄	1	4	yes	complemented
75	C₂²×D₂₁	C₂³	1	1	yes	characteristic
76	C₂²×D₂₁	C₂³	1	1	yes	characteristic
77	C₂²×D₃×C₇	C₂³	1	1	yes	characteristic
78	C₂²×C₃×D₇	C₂³	1	1	yes	characteristic
79	C₂×D₃×D₇	—	2	2	no	—
80	C₂×D₃×D₇	—	2	2	no	—
81	C₂×D₃×D₇	C₂×C₄	1	4	yes	complemented
82	C₂×C₃×C₄×C₇	—	2	2	no	—
83	C₂×C₃×C₄×C₇	C₂³	1	1	yes	characteristic
84	C₂×C₃×C₄×C₇	C₂³	1	1	yes	characteristic
85	C₂×Dic₂₁	—	2	2	no	—
86	C₂×Dic₂₁	C₂³	1	1	yes	characteristic
87	C₂×Dic₂₁	C₂³	1	1	yes	characteristic
88	C₄×D₂₁	—	2	2	no	—
89	C₄×D₂₁	—	2	2	no	—
90	C₄×D₂₁	—	2	2	no	—
91	C₄×D₂₁	D₄	1	4	yes	complemented
92	C₇×#67	C₂×C₄	1	4	yes	complemented
93	C₂×C₇×Dic₃	C₂³	1	1	yes	characteristic
94	C₂×C₇×Dic₃	C₂³	1	1	yes	characteristic
95	C₂×C₇×Dic₃	C₂³	1	1	yes	characteristic
96	C₄×D₃×C₇	—	2	2	no	—
97	C₃×C₂²⋊D₇	C₂×C₄	1	4	yes	complemented
98	C₂×C₃×Dic₇	C₂³	1	1	yes	characteristic
99	C₂×C₃×Dic₇	C₂³	1	1	yes	characteristic
100	C₂×C₃×Dic₇	C₂³	1	1	yes	characteristic
101	C₃×C₄×D₇	—	2	2	no	—
102	#4247	C₂×C₄	1	4	yes	complemented
103	#4246	C₂×C₄	1	4	yes	complemented
104	D₂₁⋊C₄	—	2	2	no	—
105	D₂₁⋊C₄	—	2	2	no	—
106	D₂₁⋊C₄	C₂×C₄	1	4	yes	complemented
107	D₃×Dic₇	—	2	2	no	—
108	Dic₃×D₇	—	2	2	no	—
109	C₂³×D₇	—	3	1	no	—
110	C₂³×D₇	—	3	1	no	—
111	C₂×C₇×D₄	—	3	1	no	—
112	C₂²×C₄×C₇	—	3	1	no	—
113	C₂²×C₄×C₇	C₂×D₃	1	1	yes	characteristic, complemented
114	C₂×C₂²⋊D₇	—	3	1	no	—
115	C₂×C₂²⋊D₇	C₂×D₃	1	1	yes	characteristic
116	C₂²×Dic₇	—	3	1	no	—
117	C₂²×Dic₇	—	3	1	no	—
118	D₄×D₇	—	3	8	no	—
119	C₂×D₂₈	—	3	1	no	—
120	C₂×C₄×D₇	—	3	1	no	—
121	C₂×C₄×D₇	—	3	1	no	—
122	C₂×C₄×D₇	—	3	1	no	—
123	C₂×C₄×D₇	—	3	1	no	—
124	C₂×C₄×D₇	—	3	1	no	—
125	C₂×C₄×D₇	—	3	1	no	—
126	C₂×C₄×D₇	—	3	1	no	—
127	C₂×C₄×D₇	—	3	1	no	—
128	C₂×C₄×D₇	—	6	4	no	—
129	C₂×C₄×D₇	—	6	4	no	—
130	C₂×C₄×D₇	C₂×D₃	1	1	yes	characteristic, complemented
131	C₇×C₄⋊C₄	—	3	1	no	—
132	C₇×C₂²⋊C₄	—	3	1	no	—
133	C₇×C₂²⋊C₄	—	3	1	no	—
134	C₄²×C₇	—	3	1	no	—
135	C₂²⋊Dic₇	—	3	1	no	—
136	C₂²⋊Dic₇	C₂×D₃	1	1	yes	characteristic, complemented
137	(C₂×D₇)⋊C₄	—	3	1	no	—
138	(C₂×D₇)⋊C₄	—	3	1	no	—
139	(C₂×D₇)⋊C₄	—	3	1	no	—
140	(C₂×D₇)⋊C₄	C₂×D₃	1	1	yes	characteristic, complemented
141	C₄⋊Dic₇	—	3	1	no	—
142	Dic₇⋊C₄	—	3	1	no	—
143	Dic₇⋊C₄	C₂×D₃	1	1	yes	characteristic, complemented
144	C₄×Dic₇	—	3	1	no	—
145	C₄×Dic₇	—	3	1	no	—
146	C₄×Dic₇	C₂×D₃	1	1	yes	characteristic, complemented
147	C₂×D₃×D₄	—	7	1	no	—
148	C₂²×C₄×D₃	—	7	1	no	—
149	C₂²×C₄×D₃	—	7	1	no	—
150	C₃×C₄×D₄	—	7	1	no	—
151	D₄×Dic₃	—	7	1	no	—
152	C₄×#67	—	7	1	no	—
153	C₄×#67	D₇	1	1	yes	characteristic, complemented
154	#893	—	7	1	no	—
155	D₃×C₄⋊C₄	—	7	1	no	—
156	#67⋊C₄	—	7	1	no	—
157	#67⋊C₄	—	7	1	no	—
158	D₃×C₂²⋊C₄	—	7	1	no	—
159	D₃×C₂²⋊C₄	—	7	1	no	—
160	C₄×D₁₂	—	7	1	no	—
161	C₄²×D₃	—	7	1	no	—
162	C₂²×C₃×C₇	—	2	1	no	—
163	C₂²×C₃×C₇	—	2	1	no	—
164	C₂²×C₃×C₇	C₂²×C₄	1	2	yes	complemented
165	C₂²×C₃×C₇	C₂⁴	1	1	yes	characteristic
166	C₂×D₂₁	—	2	1	no	—
167	C₂×D₂₁	—	2	1	no	—
168	C₂×D₂₁	—	2	8	no	—
169	C₂×D₂₁	C₂²×C₄	1	2	yes	—
170	C₂×D₂₁	C₂²×C₄	1	2	yes	complemented
171	C₂×D₂₁	C₂×D₄	1	2	yes	—
172	C₂×D₂₁	#41	1	2	yes	—
173	C₂×D₃×C₇	—	2	1	no	—
174	C₂×D₃×C₇	—	2	1	no	—
175	C₂×D₃×C₇	C₂²×C₄	1	2	yes	complemented
176	C₂×C₃×D₇	—	2	1	no	—
177	C₂×C₃×D₇	—	2	1	no	—
178	C₂×C₃×D₇	C₂²×C₄	1	2	yes	complemented
179	D₃×D₇	—	2	8	no	—
180	C₃×C₄×C₇	—	2	1	no	—
181	C₃×C₄×C₇	C₂×D₄	1	2	yes	complemented
182	Dic₂₁	—	2	1	no	—
183	Dic₂₁	C₂×D₄	1	2	yes	complemented
184	C₃×Dic₇	—	2	1	no	—
185	C₃×Dic₇	—	2	1	no	—
186	C₃×Dic₇	C₂²×C₄	1	2	yes	complemented
187	C₇×Dic₃	—	2	1	no	—
188	C₇×Dic₃	—	2	1	no	—
189	C₇×Dic₃	C₂²×C₄	1	2	yes	complemented
190	C₂×C₄×D₄	—	21	1	no	Sylow
191	C₂³×C₇	—	3	1	no	—
192	C₂³×C₇	C₂²×D₃	1	1	yes	characteristic
193	C₂²×D₇	—	3	1	no	—
194	C₂²×D₇	—	3	4	no	—
195	C₂²×D₇	—	3	1	no	—
196	C₂²×D₇	—	3	4	no	—
197	C₂²×D₇	—	6	2	no	—
198	C₂²×D₇	—	6	2	no	—
199	C₂²×D₇	—	6	2	no	—
200	C₂²×D₇	—	6	2	no	—
201	C₂²×D₇	C₂²×D₃	1	1	yes	characteristic
202	C₇×D₄	—	3	4	no	—
203	C₂×C₄×C₇	—	2	2	no	—
204	C₂×C₄×C₇	—	3	1	no	—
205	C₂×C₄×C₇	—	3	1	no	—
206	C₂×C₄×C₇	—	3	1	no	—
207	C₂×C₄×C₇	—	6	2	no	—
208	C₂×C₄×C₇	C₂²×D₃	1	1	yes	characteristic
209	C₂×C₄×C₇	C₂²×D₃	1	1	yes	characteristic
210	C₂²⋊D₇	—	3	4	no	—
211	C₂²⋊D₇	C₄×D₃	1	4	yes	complemented
212	C₂×Dic₇	—	3	1	no	—
213	C₂×Dic₇	—	3	1	no	—
214	C₂×Dic₇	—	6	2	no	—
215	C₂×Dic₇	—	6	2	no	—
216	C₂×Dic₇	C₂²×D₃	1	1	yes	characteristic
217	C₂×Dic₇	C₂²×D₃	1	1	yes	characteristic
218	C₂×Dic₇	C₂²×D₃	1	1	yes	characteristic
219	D₂₈	—	3	4	no	—
220	C₄×D₇	—	2	2	no	—
221	C₄×D₇	—	3	4	no	—
222	C₄×D₇	—	3	4	no	—
223	C₄×D₇	—	6	2	no	—
224	C₄×D₇	—	6	2	no	—
225	C₄×D₇	—	6	2	no	—
226	C₄×D₇	—	6	2	no	—
227	C₄×D₇	—	6	2	no	—
228	C₄×D₇	—	6	2	no	—
229	C₂³×D₃	—	7	1	no	—
230	C₂³×D₃	—	7	1	no	—
231	C₂×C₃×D₄	—	7	1	no	—
232	C₂²×C₃×C₄	—	7	1	no	—
233	C₂²×C₃×C₄	C₂×D₇	1	1	yes	characteristic, complemented
234	C₂×#67	—	7	1	no	—
235	C₂×#67	C₂×D₇	1	1	yes	characteristic
236	C₂²×Dic₃	—	7	1	no	—
237	C₂²×Dic₃	—	7	1	no	—
238	D₃×D₄	—	7	8	no	—
239	C₂×D₁₂	—	7	1	no	—
240	C₂×C₄×D₃	—	7	1	no	—
241	C₂×C₄×D₃	—	7	1	no	—
242	C₂×C₄×D₃	—	7	1	no	—
243	C₂×C₄×D₃	—	7	1	no	—
244	C₂×C₄×D₃	—	7	1	no	—
245	C₂×C₄×D₃	—	7	1	no	—
246	C₂×C₄×D₃	—	7	1	no	—
247	C₂×C₄×D₃	—	7	1	no	—
248	C₂×C₄×D₃	—	14	4	no	—
249	C₂×C₄×D₃	—	14	4	no	—
250	C₂×C₄×D₃	C₂×D₇	1	1	yes	characteristic, complemented
251	C₃×C₄⋊C₄	—	7	1	no	—
252	C₃×C₂²⋊C₄	—	7	1	no	—
253	C₃×C₂²⋊C₄	—	7	1	no	—
254	C₃×C₄²	—	7	1	no	—
255	#217	—	7	1	no	—
256	#217	C₂×D₇	1	1	yes	characteristic, complemented
257	(C₂×D₃)⋊C₄	—	7	1	no	—
258	(C₂×D₃)⋊C₄	—	7	1	no	—
259	(C₂×D₃)⋊C₄	—	7	1	no	—
260	(C₂×D₃)⋊C₄	C₂×D₇	1	1	yes	characteristic, complemented
261	C₄⋊Dic₃	—	7	1	no	—
262	Dic₃⋊C₄	—	7	1	no	—
263	Dic₃⋊C₄	C₂×D₇	1	1	yes	characteristic, complemented
264	C₄×Dic₃	—	7	1	no	—
265	C₄×Dic₃	—	7	1	no	—
266	C₄×Dic₃	C₂×D₇	1	1	yes	characteristic, complemented
267	C₂×C₃×C₇	—	2	2	no	—
268	C₂×C₃×C₇	C₂³×C₄	1	1	yes	characteristic
269	C₂×C₃×C₇	C₂²×D₄	1	1	yes	characteristic
270	C₂×C₃×C₇	C₂×#41	1	1	yes	characteristic
271	D₂₁	—	2	2	no	—
272	D₂₁	C₄×D₄	1	4	yes	complemented
273	C₃×D₇	—	2	2	no	—
274	D₃×C₇	—	2	2	no	—
275	C₂²×D₄	—	21	1	no	—
276	C₂³×C₄	—	21	1	no	—
277	C₂³×C₄	—	21	1	no	—
278	C₄×D₄	—	3	1	no	—
279	C₄×D₄	—	7	1	no	—
280	C₄×D₄	—	21	1	no	—
281	C₄×D₄	—	21	1	no	—
282	C₄×D₄	—	21	1	no	—
283	C₄×D₄	—	21	1	no	—
284	C₄×D₄	—	21	1	no	—
285	C₄×D₄	—	21	1	no	—
286	C₂×C₄⋊C₄	—	21	1	no	—
287	C₂×C₂²⋊C₄	—	21	1	no	—
288	C₂×C₂²⋊C₄	—	21	1	no	—
289	C₂×C₄²	—	21	1	no	—
290	C₂²×C₇	—	2	1	no	—
291	C₂²×C₇	—	2	1	no	—
292	C₂²×C₇	—	3	2	no	—
293	C₂²×C₇	—	6	1	no	—
294	C₂²×C₇	—	6	1	no	—
295	C₂²×C₇	C₂×C₄×D₃	1	2	yes	complemented
296	C₂²×C₇	C₂³×D₃	1	1	yes	characteristic
297	C₂×D₇	—	2	1	no	—
298	C₂×D₇	—	2	1	no	—
299	C₂×D₇	—	3	2	no	—
300	C₂×D₇	—	3	2	no	—
301	C₂×D₇	—	3	2	no	—
302	C₂×D₇	—	3	2	no	—
303	C₂×D₇	—	6	8	no	—
304	C₂×D₇	—	6	8	no	—
305	C₂×D₇	—	6	1	no	—
306	C₂×D₇	—	6	1	no	—
307	C₂×D₇	C₂×C₄×D₃	1	2	yes	complemented
308	C₄×C₇	—	2	1	no	—
309	C₄×C₇	—	3	2	no	—
310	C₄×C₇	—	6	1	no	—
311	C₄×C₇	—	6	1	no	—
312	C₄×C₇	D₃×D₄	1	2	yes	complemented
313	Dic₇	—	2	1	no	—
314	Dic₇	—	2	1	no	—
315	Dic₇	—	3	2	no	—
316	Dic₇	—	6	1	no	—
317	Dic₇	C₂×C₄×D₃	1	2	yes	complemented
318	C₂³×C₃	—	7	1	no	—
319	C₂³×C₃	C₂²×D₇	1	1	yes	characteristic
320	C₂²×D₃	—	7	1	no	—
321	C₂²×D₃	—	7	4	no	—
322	C₂²×D₃	—	7	1	no	—
323	C₂²×D₃	—	7	4	no	—
324	C₂²×D₃	—	14	2	no	—
325	C₂²×D₃	—	14	2	no	—
326	C₂²×D₃	—	14	2	no	—
327	C₂²×D₃	—	14	2	no	—
328	C₂²×D₃	C₂²×D₇	1	1	yes	characteristic
329	C₃×D₄	—	7	4	no	—
330	C₂×C₃×C₄	—	2	2	no	—
331	C₂×C₃×C₄	—	7	1	no	—
332	C₂×C₃×C₄	—	7	1	no	—
333	C₂×C₃×C₄	—	7	1	no	—
334	C₂×C₃×C₄	—	14	2	no	—
335	C₂×C₃×C₄	C₂²×D₇	1	1	yes	characteristic
336	C₂×C₃×C₄	C₂²×D₇	1	1	yes	characteristic
337	#67	—	7	4	no	—
338	#67	C₄×D₇	1	4	yes	complemented
339	C₂×Dic₃	—	7	1	no	—
340	C₂×Dic₃	—	7	1	no	—
341	C₂×Dic₃	—	14	2	no	—
342	C₂×Dic₃	—	14	2	no	—
343	C₂×Dic₃	C₂²×D₇	1	1	yes	characteristic
344	C₂×Dic₃	C₂²×D₇	1	1	yes	characteristic
345	C₂×Dic₃	C₂²×D₇	1	1	yes	characteristic
346	D₁₂	—	7	4	no	—
347	C₄×D₃	—	2	2	no	—
348	C₄×D₃	—	7	4	no	—
349	C₄×D₃	—	7	4	no	—
350	C₄×D₃	—	14	2	no	—
351	C₄×D₃	—	14	2	no	—
352	C₄×D₃	—	14	2	no	—
353	C₄×D₃	—	14	2	no	—
354	C₄×D₃	—	14	2	no	—
355	C₄×D₃	—	14	2	no	—
356	C₃×C₇	C₂×C₄×D₄	1	1	yes	characteristic, complemented, Hall
357	C₂⁴	—	21	1	no	—
358	C₂⁴	—	21	1	no	—
359	C₂×D₄	—	3	1	no	—
360	C₂×D₄	—	7	1	no	—
361	C₂×D₄	—	21	1	no	—
362	C₂×D₄	—	21	1	no	—
363	C₂×D₄	—	21	8	no	—
364	C₂²×C₄	—	3	1	no	—
365	C₂²×C₄	—	7	1	no	—
366	C₂²×C₄	—	21	1	no	—
367	C₂²×C₄	—	21	1	no	—
368	C₂²×C₄	—	21	1	no	—
369	C₂²×C₄	—	21	1	no	—
370	C₂²×C₄	—	21	1	no	—
371	C₂²×C₄	—	21	1	no	—
372	C₂²×C₄	—	21	1	no	—
373	C₂²×C₄	—	21	1	no	—
374	C₂²×C₄	—	21	1	no	—
375	C₂²×C₄	—	21	1	no	—
376	C₂²×C₄	—	42	4	no	—
377	C₂²×C₄	—	42	4	no	—
378	C₂²×C₄	D₃×D₇	1	1	yes	characteristic, complemented
379	C₄⋊C₄	—	3	1	no	—
380	C₄⋊C₄	—	7	1	no	—
381	C₄⋊C₄	—	21	1	no	—
382	C₄⋊C₄	—	21	1	no	—
383	C₂²⋊C₄	—	3	1	no	—
384	C₂²⋊C₄	—	3	1	no	—
385	C₂²⋊C₄	—	7	1	no	—
386	C₂²⋊C₄	—	7	1	no	—
387	C₂²⋊C₄	—	21	1	no	—
388	C₂²⋊C₄	—	21	1	no	—
389	C₂²⋊C₄	—	21	1	no	—
390	C₂²⋊C₄	—	21	1	no	—
391	C₄²	—	3	1	no	—
392	C₄²	—	7	1	no	—
393	C₄²	—	21	1	no	—
394	C₄²	—	21	1	no	—
395	C₂×C₇	—	2	2	no	—
396	C₂×C₇	—	6	2	no	—
397	C₂×C₇	C₂²×C₄×D₃	1	1	yes	characteristic
398	C₂×C₇	C₂×D₃×D₄	1	1	yes	characteristic
399	C₂×C₇	D₃×#41	1	1	yes	characteristic
400	D₇	—	2	2	no	—
401	D₇	—	3	4	no	—
402	D₇	—	6	2	no	—
403	C₂²×C₃	—	2	1	no	—
404	C₂²×C₃	—	2	1	no	—
405	C₂²×C₃	—	7	2	no	—
406	C₂²×C₃	—	14	1	no	—
407	C₂²×C₃	—	14	1	no	—
408	C₂²×C₃	C₂×C₄×D₇	1	2	yes	complemented
409	C₂²×C₃	C₂³×D₇	1	1	yes	characteristic
410	C₂×D₃	—	2	1	no	—
411	C₂×D₃	—	2	1	no	—
412	C₂×D₃	—	7	2	no	—
413	C₂×D₃	—	7	2	no	—
414	C₂×D₃	—	7	2	no	—
415	C₂×D₃	—	7	2	no	—
416	C₂×D₃	—	14	8	no	—
417	C₂×D₃	—	14	8	no	—
418	C₂×D₃	—	14	1	no	—
419	C₂×D₃	—	14	1	no	—
420	C₂×D₃	C₂×C₄×D₇	1	2	yes	complemented
421	C₃×C₄	—	2	1	no	—
422	C₃×C₄	—	7	2	no	—
423	C₃×C₄	—	14	1	no	—
424	C₃×C₄	—	14	1	no	—
425	C₃×C₄	D₄×D₇	1	2	yes	complemented
426	Dic₃	—	2	1	no	—
427	Dic₃	—	2	1	no	—
428	Dic₃	—	7	2	no	—
429	Dic₃	—	14	1	no	—
430	Dic₃	C₂×C₄×D₇	1	2	yes	complemented
431	C₂³	—	3	1	no	—
432	C₂³	—	7	1	no	—
433	C₂³	—	21	4	no	—
434	C₂³	—	21	1	no	—
435	C₂³	—	21	4	no	—
436	C₂³	—	21	1	no	—
437	C₂³	—	42	2	no	—
438	C₂³	—	42	2	no	—
439	C₂³	—	42	2	no	—
440	C₂³	—	42	2	no	—
441	C₂³	C₂×D₃×D₇	1	1	yes	characteristic
442	D₄	—	3	4	no	—
443	D₄	—	7	4	no	—
444	D₄	—	21	4	no	—
445	D₄	—	21	4	no	—
446	C₂×C₄	—	2	2	no	—
447	C₂×C₄	—	3	1	no	—
448	C₂×C₄	—	3	1	no	—
449	C₂×C₄	—	3	1	no	—
450	C₂×C₄	—	6	2	no	—
451	C₂×C₄	—	7	1	no	—
452	C₂×C₄	—	7	1	no	—
453	C₂×C₄	—	7	1	no	—
454	C₂×C₄	—	14	2	no	—
455	C₂×C₄	—	21	4	no	—
456	C₂×C₄	—	21	1	no	—
457	C₂×C₄	—	21	4	no	—
458	C₂×C₄	—	21	1	no	—
459	C₂×C₄	—	42	2	no	—
460	C₂×C₄	—	42	2	no	—
461	C₂×C₄	—	42	2	no	—
462	C₂×C₄	—	42	2	no	—
463	C₂×C₄	—	42	2	no	—
464	C₂×C₄	—	42	2	no	—
465	C₂×C₄	—	42	2	no	—
466	C₂×C₄	—	42	2	no	—
467	C₂×C₄	C₂×D₃×D₇	1	1	yes	characteristic
468	C₂×C₄	C₂×D₃×D₇	1	1	yes	characteristic
469	C₇	C₄×D₃×D₄	1	1	yes	characteristic, complemented, Sylow
470	C₂×C₃	—	2	2	no	—
471	C₂×C₃	—	14	2	no	—
472	C₂×C₃	C₂²×C₄×D₇	1	1	yes	characteristic
473	C₂×C₃	C₂×D₄×D₇	1	1	yes	characteristic
474	C₂×C₃	D₇×#41	1	1	yes	characteristic
475	D₃	—	2	2	no	—
476	D₃	—	7	4	no	—
477	D₃	—	14	2	no	—
478	C₂²	—	2	1	no	—
479	C₂²	—	2	1	no	—
480	C₂²	—	3	2	no	—
481	C₂²	—	6	1	no	—
482	C₂²	—	6	1	no	—
483	C₂²	—	7	2	no	—
484	C₂²	—	14	1	no	—
485	C₂²	—	14	1	no	—
486	C₂²	—	21	2	no	—
487	C₂²	—	21	2	no	—
488	C₂²	—	21	2	no	—
489	C₂²	—	21	2	no	—
490	C₂²	—	42	8	no	—
491	C₂²	—	42	8	no	—
492	C₂²	—	42	1	no	—
493	C₂²	—	42	1	no	—
494	C₂²	C₄×D₃×D₇	1	2	yes	complemented
495	C₂²	C₂²×D₃×D₇	1	1	yes	characteristic
496	C₄	—	2	1	no	—
497	C₄	—	3	2	no	—
498	C₄	—	6	1	no	—
499	C₄	—	6	1	no	—
500	C₄	—	7	2	no	—
501	C₄	—	14	1	no	—
502	C₄	—	14	1	no	—
503	C₄	—	21	2	no	—
504	C₄	—	42	1	no	—
505	C₄	#66694	1	2	yes	direct product factor
506	C₃	C₄×D₄×D₇	1	1	yes	characteristic, complemented, Sylow
507	C₂	—	2	2	no	—
508	C₂	—	6	2	no	—
509	C₂	—	14	2	no	—
510	C₂	—	21	4	no	—
511	C₂	—	42	2	no	—
512	C₂	C₂×C₄×D₃×D₇	1	1	yes	characteristic
513	C₂	#10621563	1	1	yes	characteristic
514	C₂	C₂×#66694	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂×D₃×D₇
commutator	C₂×C₃×C₇	C₂³×C₄
Frattini	C₂²	C₂²×D₃×D₇
Fitting	C₂²×C₃×C₄×C₇	C₂²
socle, cosocle	C₂²×C₃×C₇	C₂⁴
prime radical	C₂×#66694	C₂
hypercenter	C₂²×C₄	D₃×D₇
hypocenter	C₃×C₇	C₂×C₄×D₄
LCS	G ▷ C₂×C₃×C₇ ▷ C₃×C₇
UCS	C₁ ◁ C₂×C₄ ◁ C₂²×C₄

Complements

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

N	H ≅ G/N	type
1. C₂²×C₄×D₂₁	C₂	semidirect
3. C₂×C₄×D₃×D₇	C₂	semidirect
4. C₄×C₇×#67	C₂	semidirect
5. C₃×C₄×C₂²⋊D₇	C₂	semidirect
6. #10621123	C₂	semidirect
7. #67⋊Dic₇	C₂	semidirect
8. (C₂²⋊D₇)⋊Dic₃	C₂	semidirect
9. #10621035	C₂	semidirect
10. C₄×#4247	C₂	semidirect
11. C₄×#4246	C₂	semidirect
12. #10620968	C₂	semidirect
13. #10620966	C₂	semidirect
14. C₄×D₂₁⋊C₄	C₂	semidirect
15. #10620958	C₂	semidirect
19. C₂²×C₃×C₄×C₇	C₂²	semidirect
20. C₂²×Dic₂₁	C₂²	semidirect
24. C₂×C₄×D₂₁	C₂²	semidirect
25. C₂×C₄×D₂₁	C₂²	semidirect
27. C₂×C₄×D₃×C₇	C₂²	semidirect
29. C₂×C₃×C₄×D₇	C₂²	semidirect
30. #66694	C₄	direct (N × H)
36. C₂×D₃×Dic₇	C₂²	semidirect
37. C₂×Dic₃×D₇	C₂²	semidirect
39. C₇×#217	C₂²	semidirect
40. C₇×(C₂×D₃)⋊C₄	C₂²	semidirect
41. C₇×Dic₃⋊C₄	C₂²	semidirect
42. C₄×C₇×Dic₃	C₂²	semidirect
43. C₃×C₂²⋊Dic₇	C₂²	semidirect
44. C₃×(C₂×D₇)⋊C₄	C₂²	semidirect
45. C₃×Dic₇⋊C₄	C₂²	semidirect
46. C₃×C₄×Dic₇	C₂²	semidirect
47. Dic₃⋊Dic₇	C₂²	semidirect
48. Dic₇⋊Dic₃	C₂²	semidirect
49. #66575	C₂²	semidirect
50. #66575	C₂²	semidirect
51. (C₂×D₃)⋊Dic₇	C₂²	semidirect
52. (C₂×D₇)⋊Dic₃	C₂²	semidirect
53. Dic₃×Dic₇	C₂²	semidirect
54. Dic₃×Dic₇	C₂²	semidirect
61. C₄×C₂²⋊D₇	D₃	semidirect
74. C₂²×D₂₁	C₂×C₄	semidirect
81. C₂×D₃×D₇	C₂×C₄	semidirect
91. C₄×D₂₁	D₄	semidirect
92. C₇×#67	C₂×C₄	semidirect
97. C₃×C₂²⋊D₇	C₂×C₄	semidirect
102. #4247	C₂×C₄	semidirect
103. #4246	C₂×C₄	semidirect
106. D₂₁⋊C₄	C₂×C₄	semidirect
113. C₂²×C₄×C₇	C₂×D₃	semidirect
130. C₂×C₄×D₇	C₂×D₃	semidirect
136. C₂²⋊Dic₇	C₂×D₃	semidirect
140. (C₂×D₇)⋊C₄	C₂×D₃	semidirect
143. Dic₇⋊C₄	C₂×D₃	semidirect
146. C₄×Dic₇	C₂×D₃	semidirect
153. C₄×#67	D₇	semidirect
164. C₂²×C₃×C₇	C₂²×C₄	semidirect
170. C₂×D₂₁	C₂²×C₄	semidirect
175. C₂×D₃×C₇	C₂²×C₄	semidirect
178. C₂×C₃×D₇	C₂²×C₄	semidirect
181. C₃×C₄×C₇	C₂×D₄	semidirect
183. Dic₂₁	C₂×D₄	semidirect
186. C₃×Dic₇	C₂²×C₄	semidirect
189. C₇×Dic₃	C₂²×C₄	semidirect
211. C₂²⋊D₇	C₄×D₃	semidirect
233. C₂²×C₃×C₄	C₂×D₇	semidirect
250. C₂×C₄×D₃	C₂×D₇	semidirect
256. #217	C₂×D₇	semidirect
260. (C₂×D₃)⋊C₄	C₂×D₇	semidirect
263. Dic₃⋊C₄	C₂×D₇	semidirect
266. C₄×Dic₃	C₂×D₇	semidirect
272. D₂₁	C₄×D₄	semidirect
295. C₂²×C₇	C₂×C₄×D₃	semidirect
307. C₂×D₇	C₂×C₄×D₃	semidirect
312. C₄×C₇	D₃×D₄	semidirect
317. Dic₇	C₂×C₄×D₃	semidirect
338. #67	C₄×D₇	semidirect
356. C₃×C₇	C₂×C₄×D₄	semidirect
378. C₂²×C₄	D₃×D₇	semidirect
408. C₂²×C₃	C₂×C₄×D₇	semidirect
420. C₂×D₃	C₂×C₄×D₇	semidirect
425. C₃×C₄	D₄×D₇	semidirect
430. Dic₃	C₂×C₄×D₇	semidirect
469. C₇	C₄×D₃×D₄	semidirect
494. C₂²	C₄×D₃×D₇	semidirect
505. C₄	#66694	direct (N × H)
506. C₃	C₄×D₄×D₇	semidirect

Maximal subgroups

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

subgroup	index
C₂²×C₄×D₂₁	2
C₂×#66694	2
C₂×C₄×D₃×D₇	2
C₄×C₇×#67	2
C₃×C₄×C₂²⋊D₇	2
#10621123	2
#67⋊Dic₇	2
(C₂²⋊D₇)⋊Dic₃	2
#10621035	2
C₄×#4247	2
C₄×#4246	2
#10620968	2
#10620966	2
C₄×D₂₁⋊C₄	2
#10620958	2
C₄×D₄×D₇	3
C₄×D₃×D₄	7

Subgroups — C4×#66694 #13059856

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄×#66694 #13059856