Subgroups — C₇×#21816 #13199032

Order 1792.

1352 conjugacy classes of subgroups.

The subgroup lattice has 566 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₇×#532	C₂	1	1	yes	maximal, characteristic
2	C₇×#2920	C₂	1	1	yes	maximal, characteristic, complemented
3	C₇×#2283	C₂	1	1	yes	maximal, characteristic, complemented
4	C₇×#1980	C₂	1	4	yes	maximal, complemented
5	C₇×#1963	C₂	1	4	yes	maximal, complemented
6	C₇×#1789	C₂	1	4	yes	maximal, complemented
7	C₂²×C₇×#41	C₂²	1	2	yes	—
8	C₇×#532	—	2	1	no	—
9	C₇×#532	—	2	1	no	—
10	C₇×#532	—	2	1	no	—
11	C₇×#532	—	2	1	no	—
12	C₇×#532	C₄	1	2	yes	complemented
13	C₇×#532	C₄	1	2	yes	complemented
14	C₇×#532	C₂²	1	2	yes	—
15	C₇×#532	C₂²	1	2	yes	—
16	C₂×C₇×C₄⋊Q₈	C₄	1	1	yes	characteristic, complemented
17	C₂×C₇×#127	C₄	1	1	yes	characteristic, complemented
18	C₂×C₇×#124	C₄	1	2	yes	complemented
19	C₂×C₇×#121	—	2	1	no	—
20	C₂×C₇×#121	—	2	1	no	—
21	C₂×C₄×C₇×D₄	—	2	1	no	—
22	C₂×C₄×C₇×D₄	—	2	1	no	—
23	C₂²×C₄²×C₇	C₂²	1	1	yes	characteristic
24	C₇×#432	—	2	1	no	—
25	C₇×#432	—	2	1	no	—
26	C₇×#431	—	2	1	no	—
27	C₇×#431	—	2	1	no	—
28	C₇×#423	C₂²	1	2	yes	complemented
29	C₂×C₇×#104	C₂²	1	16	yes	complemented
30	C₇×#407	C₂²	1	2	yes	—
31	C₄×C₇×M₁₆	C₂²	1	2	yes	complemented
32	C₇×#383	—	2	1	no	—
33	C₇×#382	—	2	1	no	—
34	C₇×#381	—	2	1	no	—
35	C₇×#380	—	2	1	no	—
36	C₄×C₇×C₄⋊C₄	C₂²	1	2	yes	complemented
37	C₄×C₇×C₂²⋊C₄	C₂²	1	2	yes	—
38	C₇×#376	C₂²	1	2	yes	complemented
39	#21816	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
40	C₂×C₇×#41	—	2	2	no	—
41	C₂×C₇×#41	—	2	2	no	—
42	C₂×C₇×#41	—	4	8	no	—
43	C₂×C₇×#41	C₂×C₄	1	4	yes	—
44	C₂×C₇×#41	C₂³	1	4	yes	—
45	C₂²×C₇×Q₈	C₂×C₄	1	2	yes	—
46	C₂²×C₇×D₄	—	2	2	no	—
47	C₂²×C₇×D₄	—	2	1	no	—
48	C₂²×C₇×D₄	—	2	1	no	—
49	C₂²×C₇×D₄	C₂×C₄	1	2	yes	—
50	C₂³×C₄×C₇	—	2	2	no	—
51	C₂³×C₄×C₇	D₄	1	1	yes	characteristic
52	C₂³×C₄×C₇	D₄	1	1	yes	characteristic
53	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
54	C₂×C₇×M₁₆	C₂³	1	4	yes	—
55	C₇×C₄⋊Q₈	—	2	1	no	—
56	C₇×C₄⋊Q₈	—	2	1	no	—
57	C₇×C₄⋊Q₈	C₂×C₄	1	2	yes	—
58	C₇×C₄⋊Q₈	C₂×C₄	1	2	yes	—
59	C₇×#127	—	2	1	no	—
60	C₇×#127	—	2	1	no	—
61	C₇×#127	C₂×C₄	1	2	yes	—
62	C₇×#127	C₂×C₄	1	2	yes	—
63	C₇×#124	—	2	2	no	—
64	C₇×#124	—	2	2	no	—
65	C₇×#124	C₂×C₄	1	4	yes	—
66	C₇×#124	C₂×C₄	1	4	yes	—
67	C₇×#121	—	2	2	no	—
68	C₇×#121	—	2	2	no	—
69	C₇×#121	—	2	2	no	—
70	C₇×#121	—	2	2	no	—
71	C₇×#121	—	2	2	no	—
72	C₇×#121	—	2	2	no	—
73	C₇×#121	—	2	2	no	—
74	C₇×#121	—	2	2	no	—
75	C₄×C₇×D₄	—	2	2	no	—
76	C₄×C₇×D₄	—	2	2	no	—
77	C₄×C₇×D₄	—	2	2	no	—
78	C₄×C₇×D₄	—	2	2	no	—
79	C₄×C₇×D₄	—	2	2	no	—
80	C₄×C₇×D₄	—	2	2	no	—
81	C₄×C₇×D₄	—	2	2	no	—
82	C₄×C₇×D₄	—	2	2	no	—
83	C₂×C₇×C₄⋊C₄	—	2	1	no	—
84	C₂×C₇×C₄⋊C₄	—	2	1	no	—
85	C₂×C₇×C₄⋊C₄	—	2	2	no	—
86	C₂×C₇×C₂²⋊C₄	—	2	2	no	—
87	C₂×C₇×C₂²⋊C₄	—	2	2	no	—
88	C₂×C₇×C₂²⋊C₄	—	2	2	no	—
89	C₂×C₄²×C₇	C₂×C₄	1	1	yes	characteristic
90	C₂×C₄²×C₇	C₂×C₄	1	1	yes	characteristic
91	C₂×C₄²×C₇	C₂×C₄	1	1	yes	characteristic
92	C₂×C₄²×C₇	C₂×C₄	1	1	yes	characteristic
93	C₂×C₄²×C₇	D₄	1	1	yes	characteristic
94	C₂×C₄²×C₇	D₄	1	1	yes	characteristic
95	C₂×C₄²×C₇	D₄	1	1	yes	characteristic
96	C₂×C₄²×C₇	D₄	1	1	yes	characteristic
97	C₂×C₄²×C₇	D₄	1	1	yes	characteristic
98	C₂×C₄²×C₇	D₄	1	1	yes	characteristic
99	C₂×C₄²×C₇	C₂³	1	4	yes	—
100	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
101	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
102	C₇×C₄⋊C₈	—	2	2	no	—
103	C₇×C₄⋊C₈	—	2	2	no	—
104	C₇×#104	—	4	16	no	—
105	C₇×C₂²⋊C₈	—	2	2	no	—
106	C₇×C₂²⋊C₈	—	2	2	no	—
107	C₇×#97	—	2	2	no	—
108	C₄×C₇×C₈	—	2	2	no	—
109	C₇×#95	—	2	2	no	—
110	C₇×#95	—	2	2	no	—
111	C₇×#95	—	2	2	no	—
112	C₇×#95	—	2	2	no	—
113	C₂×#532	C₂×C₇	1	1	yes	characteristic
114	#2920	C₂×C₇	1	1	yes	characteristic, complemented
115	#2283	C₂×C₇	1	1	yes	characteristic, complemented
116	#1980	C₂×C₇	1	4	yes	complemented
117	#1963	C₂×C₇	1	4	yes	complemented
118	#1789	C₂×C₇	1	4	yes	complemented
119	C₂⁴×C₇	—	2	2	no	—
120	C₂⁴×C₇	C₂×D₄	1	1	yes	characteristic
121	C₇×#41	—	2	16	no	—
122	C₇×#41	—	4	8	no	—
123	C₇×#41	—	4	8	no	—
124	C₇×#41	—	4	8	no	—
125	C₂×C₇×Q₈	—	2	2	no	—
126	C₂×C₇×Q₈	—	4	4	no	—
127	C₂×C₇×Q₈	C₂²×C₄	1	4	yes	—
128	C₂×C₇×D₄	—	2	4	no	—
129	C₂×C₇×D₄	—	2	4	no	—
130	C₂×C₇×D₄	—	2	2	no	—
131	C₂×C₇×D₄	—	2	2	no	—
132	C₂×C₇×D₄	—	2	2	no	—
133	C₂×C₇×D₄	—	2	2	no	—
134	C₂×C₇×D₄	—	2	2	no	—
135	C₂×C₇×D₄	—	4	4	no	—
136	C₂×C₇×D₄	—	4	4	no	—
137	C₂×C₇×D₄	—	4	4	no	—
138	C₂×C₇×D₄	—	4	8	no	—
139	C₂×C₇×D₄	C₂²×C₄	1	4	yes	—
140	C₂²×C₄×C₇	—	2	4	no	—
141	C₂²×C₄×C₇	—	2	2	no	—
142	C₂²×C₄×C₇	—	2	4	no	—
143	C₂²×C₄×C₇	—	2	4	no	—
144	C₂²×C₄×C₇	—	2	4	no	—
145	C₂²×C₄×C₇	—	4	2	no	—
146	C₂²×C₄×C₇	—	4	2	no	—
147	C₂²×C₄×C₇	—	4	8	no	—
148	C₂²×C₄×C₇	C₂²⋊C₄	1	1	yes	characteristic
149	C₂²×C₄×C₇	C₂²⋊C₄	1	1	yes	characteristic
150	C₂²×C₄×C₇	C₂²⋊C₄	1	1	yes	characteristic
151	C₂²×C₄×C₇	C₂²⋊C₄	1	1	yes	characteristic
152	C₂²×C₄×C₇	C₂²⋊C₄	1	1	yes	characteristic
153	C₂²×C₄×C₇	C₂²⋊C₄	1	1	yes	characteristic
154	C₂²×C₄×C₇	C₂²⋊C₄	1	1	yes	characteristic
155	C₂²×C₄×C₇	C₂²⋊C₄	1	1	yes	characteristic
156	C₂²×C₄×C₇	C₂²×C₄	1	1	yes	characteristic
157	C₂²×C₄×C₇	C₂²×C₄	1	1	yes	characteristic
158	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
159	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
160	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
161	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
162	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
163	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
164	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
165	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
166	C₇×M₁₆	—	2	8	no	—
167	C₂×C₇×C₈	—	2	4	no	—
168	C₇×C₄⋊C₄	—	2	2	no	—
169	C₇×C₄⋊C₄	—	2	2	no	—
170	C₇×C₄⋊C₄	—	2	2	no	—
171	C₇×C₄⋊C₄	—	2	2	no	—
172	C₇×C₄⋊C₄	—	4	4	no	—
173	C₇×C₂²⋊C₄	—	2	4	no	—
174	C₇×C₂²⋊C₄	—	2	4	no	—
175	C₇×C₂²⋊C₄	—	2	4	no	—
176	C₇×C₂²⋊C₄	—	2	4	no	—
177	C₇×C₂²⋊C₄	—	4	4	no	—
178	C₄²×C₇	—	2	8	no	—
179	C₄²×C₇	C₂²⋊C₄	1	1	yes	characteristic
180	C₄²×C₇	C₂²⋊C₄	1	1	yes	characteristic
181	C₄²×C₇	C₂²⋊C₄	1	1	yes	characteristic
182	C₄²×C₇	C₂²⋊C₄	1	1	yes	characteristic
183	C₄²×C₇	C₂²⋊C₄	1	1	yes	characteristic
184	C₄²×C₇	C₂²⋊C₄	1	1	yes	characteristic
185	C₄²×C₇	C₂²⋊C₄	1	1	yes	characteristic
186	C₄²×C₇	C₂²⋊C₄	1	1	yes	characteristic
187	C₄²×C₇	C₂²×C₄	1	1	yes	characteristic
188	C₄²×C₇	C₂²×C₄	1	1	yes	characteristic
189	C₄²×C₇	C₂²×C₄	1	1	yes	characteristic
190	C₄²×C₇	C₂²×C₄	1	1	yes	characteristic
191	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
192	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
193	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
194	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
195	C₂²×#41	C₂²×C₇	1	2	yes	—
196	#532	—	2	1	no	—
197	#532	—	2	1	no	—
198	#532	—	2	1	no	—
199	#532	—	2	1	no	—
200	#532	C₄×C₇	1	2	yes	complemented
201	#532	C₄×C₇	1	2	yes	complemented
202	#532	C₂²×C₇	1	2	yes	—
203	#532	C₂²×C₇	1	2	yes	—
204	C₂×C₄⋊Q₈	C₄×C₇	1	1	yes	characteristic, complemented
205	C₂×#127	C₄×C₇	1	1	yes	characteristic, complemented
206	C₂×#124	C₄×C₇	1	2	yes	complemented
207	C₂×#121	—	2	1	no	—
208	C₂×#121	—	2	1	no	—
209	C₂×C₄×D₄	—	2	1	no	—
210	C₂×C₄×D₄	—	2	1	no	—
211	C₂²×C₄²	C₂²×C₇	1	1	yes	characteristic
212	#432	—	2	1	no	—
213	#432	—	2	1	no	—
214	#431	—	2	1	no	—
215	#431	—	2	1	no	—
216	#423	C₂²×C₇	1	2	yes	complemented
217	C₂×#104	C₂²×C₇	1	16	yes	complemented
218	#407	C₂²×C₇	1	2	yes	—
219	C₄×M₁₆	C₂²×C₇	1	2	yes	complemented
220	#383	—	2	1	no	—
221	#382	—	2	1	no	—
222	#381	—	2	1	no	—
223	#380	—	2	1	no	—
224	C₄×C₄⋊C₄	C₂²×C₇	1	2	yes	complemented
225	C₄×C₂²⋊C₄	C₂²×C₇	1	2	yes	—
226	#376	C₂²×C₇	1	2	yes	complemented
227	C₂³×C₇	—	2	2	no	—
228	C₂³×C₇	—	2	2	no	—
229	C₂³×C₇	—	2	4	no	—
230	C₂³×C₇	—	4	1	no	—
231	C₂³×C₇	—	4	4	no	—
232	C₂³×C₇	—	4	4	no	—
233	C₂³×C₇	—	4	4	no	—
234	C₂³×C₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
235	C₂³×C₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
236	C₂³×C₇	C₂²×D₄	1	1	yes	characteristic
237	C₇×Q₈	—	2	8	no	—
238	C₇×Q₈	—	4	4	no	—
239	C₇×D₄	—	2	8	no	—
240	C₇×D₄	—	4	4	no	—
241	C₇×D₄	—	4	4	no	—
242	C₇×D₄	—	4	4	no	—
243	C₇×D₄	—	4	4	no	—
244	C₇×D₄	—	4	8	no	—
245	C₇×D₄	—	4	8	no	—
246	C₇×D₄	—	4	4	no	—
247	C₂×C₄×C₇	—	2	2	no	—
248	C₂×C₄×C₇	—	2	2	no	—
249	C₂×C₄×C₇	—	2	2	no	—
250	C₂×C₄×C₇	—	2	2	no	—
251	C₂×C₄×C₇	—	2	2	no	—
252	C₂×C₄×C₇	—	2	2	no	—
253	C₂×C₄×C₇	—	2	2	no	—
254	C₂×C₄×C₇	—	2	2	no	—
255	C₂×C₄×C₇	—	2	2	no	—
256	C₂×C₄×C₇	—	2	2	no	—
257	C₂×C₄×C₇	—	2	4	no	—
258	C₂×C₄×C₇	—	4	1	no	—
259	C₂×C₄×C₇	—	4	1	no	—
260	C₂×C₄×C₇	—	4	1	no	—
261	C₂×C₄×C₇	—	4	1	no	—
262	C₂×C₄×C₇	—	4	1	no	—
263	C₂×C₄×C₇	—	4	1	no	—
264	C₂×C₄×C₇	—	4	1	no	—
265	C₂×C₄×C₇	—	4	8	no	—
266	C₂×C₄×C₇	—	4	4	no	—
267	C₂×C₄×C₇	—	4	8	no	—
268	C₂×C₄×C₇	—	4	4	no	—
269	C₂×C₄×C₇	—	4	4	no	—
270	C₂×C₄×C₇	—	4	4	no	—
271	C₂×C₄×C₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
272	C₂×C₄×C₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
273	C₂×C₄×C₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
274	C₂×C₄×C₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
275	C₂×C₄×C₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
276	C₂×C₄×C₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
277	C₂×C₄×C₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
278	C₂×C₄×C₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
279	C₂×C₄×C₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
280	C₂×C₄×C₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
281	C₂×C₄×C₇	C₂³×C₄	1	1	yes	characteristic
282	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
283	C₂×C₄×C₇	H(5,𝔽₂)	1	4	yes	—
284	C₇×C₈	—	4	4	no	—
285	C₂×#41	—	2	2	no	—
286	C₂×#41	—	2	2	no	—
287	C₂×#41	—	4	8	no	—
288	C₂×#41	C₂×C₄×C₇	1	4	yes	—
289	C₂×#41	C₂³×C₇	1	4	yes	—
290	C₂²×Q₈	C₂×C₄×C₇	1	2	yes	—
291	C₂²×D₄	—	2	2	no	—
292	C₂²×D₄	—	2	1	no	—
293	C₂²×D₄	—	2	1	no	—
294	C₂²×D₄	C₂×C₄×C₇	1	2	yes	—
295	C₂³×C₄	—	2	2	no	—
296	C₂³×C₄	C₇×D₄	1	1	yes	characteristic
297	C₂³×C₄	C₇×D₄	1	1	yes	characteristic
298	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
299	C₂×M₁₆	C₂³×C₇	1	4	yes	—
300	C₄⋊Q₈	—	2	1	no	—
301	C₄⋊Q₈	—	2	1	no	—
302	C₄⋊Q₈	C₂×C₄×C₇	1	2	yes	—
303	C₄⋊Q₈	C₂×C₄×C₇	1	2	yes	—
304	#127	—	2	1	no	—
305	#127	—	2	1	no	—
306	#127	C₂×C₄×C₇	1	2	yes	—
307	#127	C₂×C₄×C₇	1	2	yes	—
308	#124	—	2	2	no	—
309	#124	—	2	2	no	—
310	#124	C₂×C₄×C₇	1	4	yes	—
311	#124	C₂×C₄×C₇	1	4	yes	—
312	#121	—	2	2	no	—
313	#121	—	2	2	no	—
314	#121	—	2	2	no	—
315	#121	—	2	2	no	—
316	#121	—	2	2	no	—
317	#121	—	2	2	no	—
318	#121	—	2	2	no	—
319	#121	—	2	2	no	—
320	C₄×D₄	—	2	2	no	—
321	C₄×D₄	—	2	2	no	—
322	C₄×D₄	—	2	2	no	—
323	C₄×D₄	—	2	2	no	—
324	C₄×D₄	—	2	2	no	—
325	C₄×D₄	—	2	2	no	—
326	C₄×D₄	—	2	2	no	—
327	C₄×D₄	—	2	2	no	—
328	C₂×C₄⋊C₄	—	2	1	no	—
329	C₂×C₄⋊C₄	—	2	1	no	—
330	C₂×C₄⋊C₄	—	2	2	no	—
331	C₂×C₂²⋊C₄	—	2	2	no	—
332	C₂×C₂²⋊C₄	—	2	2	no	—
333	C₂×C₂²⋊C₄	—	2	2	no	—
334	C₂×C₄²	C₂×C₄×C₇	1	1	yes	characteristic
335	C₂×C₄²	C₂×C₄×C₇	1	1	yes	characteristic
336	C₂×C₄²	C₂×C₄×C₇	1	1	yes	characteristic
337	C₂×C₄²	C₂×C₄×C₇	1	1	yes	characteristic
338	C₂×C₄²	C₇×D₄	1	1	yes	characteristic
339	C₂×C₄²	C₇×D₄	1	1	yes	characteristic
340	C₂×C₄²	C₇×D₄	1	1	yes	characteristic
341	C₂×C₄²	C₇×D₄	1	1	yes	characteristic
342	C₂×C₄²	C₇×D₄	1	1	yes	characteristic
343	C₂×C₄²	C₇×D₄	1	1	yes	characteristic
344	C₂×C₄²	C₂³×C₇	1	4	yes	—
345	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
346	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
347	C₄⋊C₈	—	2	2	no	—
348	C₄⋊C₈	—	2	2	no	—
349	#104	—	4	16	no	—
350	C₂²⋊C₈	—	2	2	no	—
351	C₂²⋊C₈	—	2	2	no	—
352	#97	—	2	2	no	—
353	C₄×C₈	—	2	2	no	—
354	#95	—	2	2	no	—
355	#95	—	2	2	no	—
356	#95	—	2	2	no	—
357	#95	—	2	2	no	—
358	C₂²×C₇	—	2	1	no	—
359	C₂²×C₇	—	2	1	no	—
360	C₂²×C₇	—	2	1	no	—
361	C₂²×C₇	—	2	1	no	—
362	C₂²×C₇	—	2	1	no	—
363	C₂²×C₇	—	2	1	no	—
364	C₂²×C₇	—	2	1	no	—
365	C₂²×C₇	—	4	4	no	—
366	C₂²×C₇	—	4	4	no	—
367	C₂²×C₇	—	4	4	no	—
368	C₂²×C₇	—	4	4	no	—
369	C₂²×C₇	—	8	8	no	—
370	C₂²×C₇	#421	1	2	yes	—
371	C₂²×C₇	C₂²×C₂²⋊C₄	1	1	yes	characteristic
372	C₂²×C₇	#535	1	2	yes	—
373	C₄×C₇	—	2	1	no	—
374	C₄×C₇	—	2	1	no	—
375	C₄×C₇	—	2	1	no	—
376	C₄×C₇	—	2	1	no	—
377	C₄×C₇	—	2	1	no	—
378	C₄×C₇	—	2	1	no	—
379	C₄×C₇	—	2	1	no	—
380	C₄×C₇	—	2	1	no	—
381	C₄×C₇	—	2	1	no	—
382	C₄×C₇	—	4	4	no	—
383	C₄×C₇	—	8	4	no	—
384	C₄×C₇	#421	1	2	yes	—
385	C₄×C₇	#518	1	2	yes	—
386	C₄×C₇	#535	1	2	yes	—
387	C₂⁴	—	2	2	no	—
388	C₂⁴	C₂×C₇×D₄	1	1	yes	characteristic
389	#41	—	2	16	no	—
390	#41	—	4	8	no	—
391	#41	—	4	8	no	—
392	#41	—	4	8	no	—
393	C₂×Q₈	—	2	2	no	—
394	C₂×Q₈	—	4	4	no	—
395	C₂×Q₈	C₂²×C₄×C₇	1	4	yes	—
396	C₂×D₄	—	2	4	no	—
397	C₂×D₄	—	2	4	no	—
398	C₂×D₄	—	2	2	no	—
399	C₂×D₄	—	2	2	no	—
400	C₂×D₄	—	2	2	no	—
401	C₂×D₄	—	2	2	no	—
402	C₂×D₄	—	2	2	no	—
403	C₂×D₄	—	4	4	no	—
404	C₂×D₄	—	4	4	no	—
405	C₂×D₄	—	4	4	no	—
406	C₂×D₄	—	4	8	no	—
407	C₂×D₄	C₂²×C₄×C₇	1	4	yes	—
408	C₂²×C₄	—	2	4	no	—
409	C₂²×C₄	—	2	2	no	—
410	C₂²×C₄	—	2	4	no	—
411	C₂²×C₄	—	2	4	no	—
412	C₂²×C₄	—	2	4	no	—
413	C₂²×C₄	—	4	2	no	—
414	C₂²×C₄	—	4	2	no	—
415	C₂²×C₄	—	4	8	no	—
416	C₂²×C₄	C₇×C₂²⋊C₄	1	1	yes	characteristic
417	C₂²×C₄	C₇×C₂²⋊C₄	1	1	yes	characteristic
418	C₂²×C₄	C₇×C₂²⋊C₄	1	1	yes	characteristic
419	C₂²×C₄	C₇×C₂²⋊C₄	1	1	yes	characteristic
420	C₂²×C₄	C₇×C₂²⋊C₄	1	1	yes	characteristic
421	C₂²×C₄	C₇×C₂²⋊C₄	1	1	yes	characteristic
422	C₂²×C₄	C₇×C₂²⋊C₄	1	1	yes	characteristic
423	C₂²×C₄	C₇×C₂²⋊C₄	1	1	yes	characteristic
424	C₂²×C₄	C₂²×C₄×C₇	1	1	yes	characteristic
425	C₂²×C₄	C₂²×C₄×C₇	1	1	yes	characteristic
426	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
427	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
428	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
429	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
430	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
431	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
432	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
433	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
434	M₁₆	—	2	8	no	—
435	C₂×C₈	—	2	4	no	—
436	C₄⋊C₄	—	2	2	no	—
437	C₄⋊C₄	—	2	2	no	—
438	C₄⋊C₄	—	2	2	no	—
439	C₄⋊C₄	—	2	2	no	—
440	C₄⋊C₄	—	4	4	no	—
441	C₂²⋊C₄	—	2	4	no	—
442	C₂²⋊C₄	—	2	4	no	—
443	C₂²⋊C₄	—	2	4	no	—
444	C₂²⋊C₄	—	2	4	no	—
445	C₂²⋊C₄	—	4	4	no	—
446	C₄²	—	2	8	no	—
447	C₄²	C₇×C₂²⋊C₄	1	1	yes	characteristic
448	C₄²	C₇×C₂²⋊C₄	1	1	yes	characteristic
449	C₄²	C₇×C₂²⋊C₄	1	1	yes	characteristic
450	C₄²	C₇×C₂²⋊C₄	1	1	yes	characteristic
451	C₄²	C₇×C₂²⋊C₄	1	1	yes	characteristic
452	C₄²	C₇×C₂²⋊C₄	1	1	yes	characteristic
453	C₄²	C₇×C₂²⋊C₄	1	1	yes	characteristic
454	C₄²	C₇×C₂²⋊C₄	1	1	yes	characteristic
455	C₄²	C₂²×C₄×C₇	1	1	yes	characteristic
456	C₄²	C₂²×C₄×C₇	1	1	yes	characteristic
457	C₄²	C₂²×C₄×C₇	1	1	yes	characteristic
458	C₄²	C₂²×C₄×C₇	1	1	yes	characteristic
459	C₄²	C₂×C₇×D₄	1	1	yes	characteristic
460	C₄²	C₂×C₇×D₄	1	1	yes	characteristic
461	C₄²	C₂×C₇×D₄	1	1	yes	characteristic
462	C₄²	C₂×C₇×D₄	1	1	yes	characteristic
463	C₂×C₇	—	2	2	no	—
464	C₂×C₇	—	2	2	no	—
465	C₂×C₇	—	4	1	no	—
466	C₂×C₇	—	8	4	no	—
467	C₂×C₇	#2309	1	1	yes	characteristic
468	C₂×C₇	C₂×#421	1	1	yes	characteristic
469	C₂×C₇	C₂×#421	1	1	yes	characteristic
470	C₂³	—	2	2	no	—
471	C₂³	—	2	2	no	—
472	C₂³	—	2	4	no	—
473	C₂³	—	4	1	no	—
474	C₂³	—	4	4	no	—
475	C₂³	—	4	4	no	—
476	C₂³	—	4	4	no	—
477	C₂³	C₂×C₇×C₂²⋊C₄	1	1	yes	characteristic
478	C₂³	C₂×C₇×C₂²⋊C₄	1	1	yes	characteristic
479	C₂³	C₂²×C₇×D₄	1	1	yes	characteristic
480	Q₈	—	2	8	no	—
481	Q₈	—	4	4	no	—
482	D₄	—	2	8	no	—
483	D₄	—	4	4	no	—
484	D₄	—	4	4	no	—
485	D₄	—	4	4	no	—
486	D₄	—	4	4	no	—
487	D₄	—	4	8	no	—
488	D₄	—	4	8	no	—
489	D₄	—	4	4	no	—
490	C₂×C₄	—	2	2	no	—
491	C₂×C₄	—	2	2	no	—
492	C₂×C₄	—	2	2	no	—
493	C₂×C₄	—	2	2	no	—
494	C₂×C₄	—	2	2	no	—
495	C₂×C₄	—	2	2	no	—
496	C₂×C₄	—	2	2	no	—
497	C₂×C₄	—	2	2	no	—
498	C₂×C₄	—	2	2	no	—
499	C₂×C₄	—	2	2	no	—
500	C₂×C₄	—	2	4	no	—
501	C₂×C₄	—	4	1	no	—
502	C₂×C₄	—	4	1	no	—
503	C₂×C₄	—	4	1	no	—
504	C₂×C₄	—	4	1	no	—
505	C₂×C₄	—	4	1	no	—
506	C₂×C₄	—	4	1	no	—
507	C₂×C₄	—	4	1	no	—
508	C₂×C₄	—	4	8	no	—
509	C₂×C₄	—	4	4	no	—
510	C₂×C₄	—	4	8	no	—
511	C₂×C₄	—	4	4	no	—
512	C₂×C₄	—	4	4	no	—
513	C₂×C₄	—	4	4	no	—
514	C₂×C₄	C₂×C₇×C₂²⋊C₄	1	1	yes	characteristic
515	C₂×C₄	C₂×C₇×C₂²⋊C₄	1	1	yes	characteristic
516	C₂×C₄	C₂×C₇×C₂²⋊C₄	1	1	yes	characteristic
517	C₂×C₄	C₂×C₇×C₂²⋊C₄	1	1	yes	characteristic
518	C₂×C₄	C₂×C₇×C₂²⋊C₄	1	1	yes	characteristic
519	C₂×C₄	C₂×C₇×C₂²⋊C₄	1	1	yes	characteristic
520	C₂×C₄	C₂×C₇×C₂²⋊C₄	1	1	yes	characteristic
521	C₂×C₄	C₂×C₇×C₂²⋊C₄	1	1	yes	characteristic
522	C₂×C₄	C₂×C₇×C₂²⋊C₄	1	1	yes	characteristic
523	C₂×C₄	C₂×C₇×C₂²⋊C₄	1	1	yes	characteristic
524	C₂×C₄	C₂³×C₄×C₇	1	1	yes	characteristic
525	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
526	C₂×C₄	C₇×H(5,𝔽₂)	1	4	yes	—
527	C₈	—	4	4	no	—
528	C₇	#21816	1	1	yes	characteristic, direct product factor, Sylow
529	C₂²	—	2	1	no	—
530	C₂²	—	2	1	no	—
531	C₂²	—	2	1	no	—
532	C₂²	—	2	1	no	—
533	C₂²	—	2	1	no	—
534	C₂²	—	2	1	no	—
535	C₂²	—	2	1	no	—
536	C₂²	—	4	4	no	—
537	C₂²	—	4	4	no	—
538	C₂²	—	4	4	no	—
539	C₂²	—	4	4	no	—
540	C₂²	—	8	8	no	—
541	C₂²	C₇×#421	1	2	yes	—
542	C₂²	C₂²×C₇×C₂²⋊C₄	1	1	yes	characteristic
543	C₂²	C₇×#535	1	2	yes	—
544	C₄	—	2	1	no	—
545	C₄	—	2	1	no	—
546	C₄	—	2	1	no	—
547	C₄	—	2	1	no	—
548	C₄	—	2	1	no	—
549	C₄	—	2	1	no	—
550	C₄	—	2	1	no	—
551	C₄	—	2	1	no	—
552	C₄	—	2	1	no	—
553	C₄	—	4	4	no	—
554	C₄	—	8	4	no	—
555	C₄	C₇×#421	1	2	yes	—
556	C₄	C₇×#518	1	2	yes	—
557	C₄	C₇×#535	1	2	yes	—
558	C₂	—	2	2	no	—
559	C₂	—	2	2	no	—
560	C₂	—	4	1	no	—
561	C₂	—	8	4	no	—
562	C₂	C₇×#2309	1	1	yes	characteristic
563	C₂	C₂×C₇×#421	1	1	yes	characteristic
564	C₂	C₂×C₇×#421	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₇	C₂²×D₄
commutator	C₂×C₄	C₂³×C₄×C₇
Frattini, cosocle	C₂²×C₄	C₂⁴×C₇
socle	C₂²×C₇	C₂²×C₂²⋊C₄
prime radical	C₂×C₇×#532	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₇ ◁ C₂²×C₄²×C₇ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₇×#2920	C₂	semidirect
3. C₇×#2283	C₂	semidirect
4. C₇×#1980	C₂	semidirect
5. C₇×#1963	C₂	semidirect
6. C₇×#1789	C₂	semidirect
12. C₇×#532	C₄	semidirect
13. C₇×#532	C₄	semidirect
16. C₂×C₇×C₄⋊Q₈	C₄	semidirect
17. C₂×C₇×#127	C₄	semidirect
18. C₂×C₇×#124	C₄	semidirect
28. C₇×#423	C₂²	semidirect
29. C₂×C₇×#104	C₂²	semidirect
31. C₄×C₇×M₁₆	C₂²	semidirect
36. C₄×C₇×C₄⋊C₄	C₂²	semidirect
38. C₇×#376	C₂²	semidirect
39. #21816	C₇	direct (N × H)
114. #2920	C₂×C₇	semidirect
115. #2283	C₂×C₇	semidirect
116. #1980	C₂×C₇	semidirect
117. #1963	C₂×C₇	semidirect
118. #1789	C₂×C₇	semidirect
200. #532	C₄×C₇	semidirect
201. #532	C₄×C₇	semidirect
204. C₂×C₄⋊Q₈	C₄×C₇	semidirect
205. C₂×#127	C₄×C₇	semidirect
206. C₂×#124	C₄×C₇	semidirect
216. #423	C₂²×C₇	semidirect
217. C₂×#104	C₂²×C₇	semidirect
219. C₄×M₁₆	C₂²×C₇	semidirect
224. C₄×C₄⋊C₄	C₂²×C₇	semidirect
226. #376	C₂²×C₇	semidirect
528. C₇	#21816	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×C₇×#532	2
C₇×#2920	2
C₇×#2283	2
C₇×#1980	2
C₇×#1963	2
C₇×#1789	2
#21816	7

Subgroups — C7×#21816 #13199032

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×#21816 #13199032