Subgroups — C₇×#22147 #13199363

Order 1792.

988 conjugacy classes of subgroups.

The subgroup lattice has 530 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₇×#460	C₂	1	1	yes	maximal, characteristic
2	C₄×C₇×#127	C₂	1	1	yes	maximal, characteristic
3	C₇×#2295	C₂	1	1	yes	maximal, characteristic, complemented
4	C₇×#1982	C₂	1	1	yes	maximal, characteristic
5	C₇×#1968	C₂	1	2	yes	maximal, complemented
6	C₇×#1948	C₂	1	1	yes	maximal, characteristic, complemented
7	C₇×#1934	C₂	1	2	yes	maximal, complemented
8	C₇×#1877	C₂	1	2	yes	maximal, complemented
9	C₇×#1864	C₂	1	2	yes	maximal, complemented
10	C₇×#1803	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄×C₇×C₄⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×C₇×SD₁₆	C₂²	1	2	yes	—
13	C₂×C₇×#127	C₂²	1	1	yes	characteristic
14	C₂×C₄×C₇×Q₈	C₂²	1	1	yes	characteristic
15	C₂×C₄×C₇×D₄	—	2	1	no	—
16	C₂×C₄×C₇×D₄	—	2	1	no	—
17	C₂×C₄×C₇×D₄	C₂²	1	2	yes	—
18	C₇×#460	C₄	1	8	yes	complemented
19	C₂×C₇×#106	C₂²	1	2	yes	—
20	C₂×C₇×C₄⋊C₈	C₂²	1	1	yes	characteristic
21	C₂×C₇×C₄⋊C₈	C₂²	1	1	yes	characteristic
22	C₂×C₇×#103	C₂²	1	2	yes	—
23	C₂×C₇×#102	C₂²	1	2	yes	—
24	C₂×C₇×#102	C₂²	1	2	yes	—
25	C₂×C₇×#102	C₂²	1	2	yes	—
26	C₂×C₄×C₇×C₈	C₂²	1	2	yes	—
27	C₇×#391	C₂²	1	1	yes	characteristic
28	C₇×#391	C₂²	1	1	yes	characteristic
29	C₇×#390	—	2	1	no	—
30	C₇×#390	—	2	1	no	—
31	C₇×#390	C₂²	1	2	yes	—
32	C₇×#389	C₂²	1	1	yes	characteristic
33	C₇×#389	C₂²	1	1	yes	characteristic
34	C₇×#387	—	2	1	no	—
35	C₇×#387	—	2	1	no	—
36	C₇×#384	C₂²	1	1	yes	characteristic
37	C₄×C₇×C₄⋊C₄	—	2	1	no	—
38	C₄×C₇×C₄⋊C₄	C₂²	1	1	yes	characteristic
39	C₇×#376	—	2	1	no	—
40	C₄³×C₇	C₂²	1	1	yes	characteristic
41	C₇×#340	C₂²	1	2	yes	—
42	C₇×#340	C₂²	1	2	yes	—
43	C₇×#336	C₂²	1	2	yes	—
44	#22147	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
45	C₂²×C₇×Q₈	C₂³	1	1	yes	characteristic
46	C₂²×C₇×D₄	—	2	1	no	—
47	C₂²×C₇×D₄	—	2	1	no	—
48	C₂²×C₇×D₄	C₂³	1	2	yes	—
49	C₂³×C₄×C₇	—	2	2	no	—
50	C₂×C₇×SD₁₆	—	4	2	no	—
51	C₂×C₇×SD₁₆	—	4	2	no	—
52	C₂×C₇×SD₁₆	C₂×C₄	1	8	yes	complemented
53	C₂²×C₇×C₈	C₂³	1	2	yes	—
54	C₂²×C₇×C₈	C₂³	1	2	yes	—
55	C₇×#127	—	2	2	no	—
56	C₇×#127	C₂×C₄	1	4	yes	—
57	C₄×C₇×Q₈	—	2	2	no	—
58	C₄×C₇×Q₈	C₂×C₄	1	4	yes	complemented
59	C₄×C₇×D₄	—	4	2	no	—
60	C₄×C₇×D₄	—	4	2	no	—
61	C₄×C₇×D₄	—	4	4	no	—
62	C₄×C₇×D₄	—	4	4	no	—
63	C₂×C₇×C₄⋊C₄	—	2	1	no	—
64	C₂×C₇×C₄⋊C₄	—	2	1	no	—
65	C₂×C₇×C₄⋊C₄	—	2	1	no	—
66	C₂×C₇×C₄⋊C₄	—	2	1	no	—
67	C₂×C₇×C₄⋊C₄	—	2	1	no	—
68	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
69	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
70	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
71	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
72	C₂×C₇×C₂²⋊C₄	—	2	2	no	—
73	C₂×C₇×C₂²⋊C₄	—	2	2	no	—
74	C₂×C₇×C₂²⋊C₄	—	2	2	no	—
75	C₂×C₄²×C₇	—	2	1	no	—
76	C₂×C₄²×C₇	—	2	1	no	—
77	C₂×C₄²×C₇	D₄	1	1	yes	characteristic
78	C₂×C₄²×C₇	D₄	1	1	yes	characteristic
79	C₂×C₄²×C₇	D₄	1	1	yes	characteristic
80	C₂×C₄²×C₇	D₄	1	1	yes	characteristic
81	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
82	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
83	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
84	C₇×#106	—	4	2	no	—
85	C₇×C₄⋊C₈	—	2	2	no	—
86	C₇×C₄⋊C₈	C₂×C₄	1	4	yes	complemented
87	C₇×#103	—	4	2	no	—
88	C₇×#102	—	4	2	no	—
89	C₇×#102	—	4	2	no	—
90	C₇×#102	C₂×C₄	1	8	yes	complemented
91	C₄×C₇×C₈	—	4	2	no	—
92	C₇×#95	—	2	1	no	—
93	C₇×#95	—	2	1	no	—
94	C₇×#95	—	2	1	no	—
95	C₇×#95	—	2	1	no	—
96	C₇×#95	—	2	1	no	—
97	C₇×#95	—	2	1	no	—
98	C₇×#95	—	2	1	no	—
99	C₂×#460	C₂×C₇	1	1	yes	characteristic
100	C₄×#127	C₂×C₇	1	1	yes	characteristic
101	#2295	C₂×C₇	1	1	yes	characteristic, complemented
102	#1982	C₂×C₇	1	1	yes	characteristic
103	#1968	C₂×C₇	1	2	yes	complemented
104	#1948	C₂×C₇	1	1	yes	characteristic, complemented
105	#1934	C₂×C₇	1	2	yes	complemented
106	#1877	C₂×C₇	1	2	yes	complemented
107	#1864	C₂×C₇	1	2	yes	complemented
108	#1803	C₂×C₇	1	1	yes	characteristic, complemented
109	C₄×C₄⋊C₈	C₂×C₇	1	1	yes	characteristic, complemented
110	C₂⁴×C₇	—	2	2	no	—
111	C₂×C₇×Q₈	—	2	1	no	—
112	C₂×C₇×Q₈	—	2	1	no	—
113	C₂×C₇×Q₈	—	2	1	no	—
114	C₂×C₇×Q₈	—	2	1	no	—
115	C₂×C₇×Q₈	—	2	1	no	—
116	C₂×C₇×Q₈	C₂²×C₄	1	2	yes	—
117	C₂×C₇×D₄	—	2	4	no	—
118	C₂×C₇×D₄	—	2	4	no	—
119	C₂×C₇×D₄	—	2	2	no	—
120	C₂×C₇×D₄	—	2	2	no	—
121	C₂×C₇×D₄	—	2	2	no	—
122	C₂×C₇×D₄	—	2	2	no	—
123	C₂×C₇×D₄	—	2	2	no	—
124	C₂×C₇×D₄	—	4	2	no	—
125	C₂×C₇×D₄	—	4	2	no	—
126	C₂×C₇×D₄	—	4	2	no	—
127	C₂×C₇×D₄	—	4	2	no	—
128	C₂×C₇×D₄	C₂²×C₄	1	4	yes	—
129	C₂²×C₄×C₇	—	2	1	no	—
130	C₂²×C₄×C₇	—	2	1	no	—
131	C₂²×C₄×C₇	—	2	1	no	—
132	C₂²×C₄×C₇	—	2	1	no	—
133	C₂²×C₄×C₇	—	2	2	no	—
134	C₂²×C₄×C₇	—	4	4	no	—
135	C₂²×C₄×C₇	—	4	4	no	—
136	C₂²×C₄×C₇	—	4	4	no	—
137	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
138	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
139	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
140	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
141	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
142	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
143	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
144	C₇×SD₁₆	—	4	8	no	—
145	C₂×C₇×C₈	—	2	2	no	—
146	C₂×C₇×C₈	—	2	2	no	—
147	C₂×C₇×C₈	—	2	2	no	—
148	C₂×C₇×C₈	—	2	2	no	—
149	C₂×C₇×C₈	—	2	2	no	—
150	C₂×C₇×C₈	C₂²×C₄	1	4	yes	—
151	C₇×C₄⋊C₄	—	2	4	no	—
152	C₇×C₄⋊C₄	—	2	1	no	—
153	C₇×C₄⋊C₄	—	2	1	no	—
154	C₇×C₄⋊C₄	—	2	1	no	—
155	C₇×C₄⋊C₄	—	2	2	no	—
156	C₇×C₄⋊C₄	—	2	1	no	—
157	C₇×C₄⋊C₄	—	2	2	no	—
158	C₇×C₄⋊C₄	—	2	1	no	—
159	C₇×C₄⋊C₄	—	4	2	no	—
160	C₇×C₄⋊C₄	—	4	2	no	—
161	C₇×C₄⋊C₄	—	4	2	no	—
162	C₇×C₄⋊C₄	—	4	2	no	—
163	C₇×C₄⋊C₄	C₂²×C₄	1	2	yes	—
164	C₇×C₂²⋊C₄	—	4	4	no	—
165	C₇×C₂²⋊C₄	—	4	4	no	—
166	C₇×C₂²⋊C₄	—	4	4	no	—
167	C₄²×C₇	—	2	4	no	—
168	C₄²×C₇	—	2	2	no	—
169	C₄²×C₇	—	2	2	no	—
170	C₄²×C₇	—	2	1	no	—
171	C₄²×C₇	—	2	1	no	—
172	C₄²×C₇	—	2	1	no	—
173	C₄²×C₇	—	2	1	no	—
174	C₄²×C₇	—	4	1	no	—
175	C₄²×C₇	—	4	2	no	—
176	C₄²×C₇	SD₁₆	1	4	yes	complemented
177	C₄²×C₇	C₂²×C₄	1	2	yes	—
178	C₄²×C₇	#41	1	2	yes	—
179	C₂²×SD₁₆	C₂²×C₇	1	2	yes	—
180	C₂×#127	C₂²×C₇	1	1	yes	characteristic
181	C₂×C₄×Q₈	C₂²×C₇	1	1	yes	characteristic
182	C₂×C₄×D₄	—	2	1	no	—
183	C₂×C₄×D₄	—	2	1	no	—
184	C₂×C₄×D₄	C₂²×C₇	1	2	yes	—
185	#460	C₄×C₇	1	8	yes	complemented
186	C₂×#106	C₂²×C₇	1	2	yes	—
187	C₂×C₄⋊C₈	C₂²×C₇	1	1	yes	characteristic
188	C₂×C₄⋊C₈	C₂²×C₇	1	1	yes	characteristic
189	C₂×#103	C₂²×C₇	1	2	yes	—
190	C₂×#102	C₂²×C₇	1	2	yes	—
191	C₂×#102	C₂²×C₇	1	2	yes	—
192	C₂×#102	C₂²×C₇	1	2	yes	—
193	C₂×C₄×C₈	C₂²×C₇	1	2	yes	—
194	#391	C₂²×C₇	1	1	yes	characteristic
195	#391	C₂²×C₇	1	1	yes	characteristic
196	#390	—	2	1	no	—
197	#390	—	2	1	no	—
198	#390	C₂²×C₇	1	2	yes	—
199	#389	C₂²×C₇	1	1	yes	characteristic
200	#389	C₂²×C₇	1	1	yes	characteristic
201	#387	—	2	1	no	—
202	#387	—	2	1	no	—
203	#384	C₂²×C₇	1	1	yes	characteristic
204	C₄×C₄⋊C₄	—	2	1	no	—
205	C₄×C₄⋊C₄	C₂²×C₇	1	1	yes	characteristic
206	#376	—	2	1	no	—
207	C₄³	C₂²×C₇	1	1	yes	characteristic
208	#340	C₂²×C₇	1	2	yes	—
209	#340	C₂²×C₇	1	2	yes	—
210	#336	C₂²×C₇	1	2	yes	—
211	C₂³×C₇	—	2	4	no	—
212	C₂³×C₇	—	4	2	no	—
213	C₂³×C₇	—	4	2	no	—
214	C₂³×C₇	—	4	2	no	—
215	C₂³×C₇	—	4	2	no	—
216	C₂³×C₇	—	4	2	no	—
217	C₂³×C₇	—	4	2	no	—
218	C₂³×C₇	C₂²×D₄	1	1	yes	characteristic
219	C₇×Q₈	—	2	2	no	—
220	C₇×Q₈	—	2	2	no	—
221	C₇×Q₈	—	4	1	no	—
222	C₇×Q₈	—	4	1	no	—
223	C₇×D₄	—	2	4	no	—
224	C₇×D₄	—	2	4	no	—
225	C₇×D₄	—	4	8	no	—
226	C₇×D₄	—	4	2	no	—
227	C₇×D₄	—	4	2	no	—
228	C₇×D₄	—	4	8	no	—
229	C₂×C₄×C₇	—	2	1	no	—
230	C₂×C₄×C₇	—	2	1	no	—
231	C₂×C₄×C₇	—	2	1	no	—
232	C₂×C₄×C₇	—	2	1	no	—
233	C₂×C₄×C₇	—	2	1	no	—
234	C₂×C₄×C₇	—	2	1	no	—
235	C₂×C₄×C₇	—	2	1	no	—
236	C₂×C₄×C₇	—	2	1	no	—
237	C₂×C₄×C₇	—	2	2	no	—
238	C₂×C₄×C₇	—	2	2	no	—
239	C₂×C₄×C₇	—	2	1	no	—
240	C₂×C₄×C₇	—	2	1	no	—
241	C₂×C₄×C₇	—	2	1	no	—
242	C₂×C₄×C₇	—	4	1	no	—
243	C₂×C₄×C₇	—	4	1	no	—
244	C₂×C₄×C₇	—	4	1	no	—
245	C₂×C₄×C₇	—	4	1	no	—
246	C₂×C₄×C₇	—	4	2	no	—
247	C₂×C₄×C₇	—	4	1	no	—
248	C₂×C₄×C₇	—	4	1	no	—
249	C₂×C₄×C₇	—	4	2	no	—
250	C₂×C₄×C₇	—	4	1	no	—
251	C₂×C₄×C₇	—	4	1	no	—
252	C₂×C₄×C₇	—	4	2	no	—
253	C₂×C₄×C₇	—	4	1	no	—
254	C₂×C₄×C₇	—	4	1	no	—
255	C₂×C₄×C₇	—	8	8	no	—
256	C₂×C₄×C₇	C₄×D₄	1	2	yes	—
257	C₂×C₄×C₇	C₄×D₄	1	2	yes	—
258	C₂×C₄×C₇	C₂×SD₁₆	1	2	yes	—
259	C₂×C₄×C₇	C₂×SD₁₆	1	2	yes	—
260	C₂×C₄×C₇	C₂×SD₁₆	1	2	yes	—
261	C₂×C₄×C₇	#135	1	2	yes	—
262	C₂×C₄×C₇	AGL(1,ℤ/8)	1	2	yes	—
263	C₂×C₄×C₇	C₂³×C₄	1	1	yes	characteristic
264	C₂×C₄×C₇	C₂×#41	1	1	yes	characteristic
265	C₂×C₄×C₇	H(5,𝔽₂)	1	1	yes	characteristic
266	C₂×C₄×C₇	H(5,𝔽₂)	1	1	yes	characteristic
267	C₂×C₄×C₇	H(5,𝔽₂)	1	1	yes	characteristic
268	C₂×C₄×C₇	2₋¹⁺⁴	1	1	yes	characteristic
269	C₇×C₈	—	2	4	no	—
270	C₇×C₈	—	4	2	no	—
271	C₂²×Q₈	C₂³×C₇	1	1	yes	characteristic
272	C₂²×D₄	—	2	1	no	—
273	C₂²×D₄	—	2	1	no	—
274	C₂²×D₄	C₂³×C₇	1	2	yes	—
275	C₂³×C₄	—	2	2	no	—
276	C₂×SD₁₆	—	4	2	no	—
277	C₂×SD₁₆	—	4	2	no	—
278	C₂×SD₁₆	C₂×C₄×C₇	1	8	yes	complemented
279	C₂²×C₈	C₂³×C₇	1	2	yes	—
280	C₂²×C₈	C₂³×C₇	1	2	yes	—
281	#127	—	2	2	no	—
282	#127	C₂×C₄×C₇	1	4	yes	—
283	C₄×Q₈	—	2	2	no	—
284	C₄×Q₈	C₂×C₄×C₇	1	4	yes	complemented
285	C₄×D₄	—	4	2	no	—
286	C₄×D₄	—	4	2	no	—
287	C₄×D₄	—	4	4	no	—
288	C₄×D₄	—	4	4	no	—
289	C₂×C₄⋊C₄	—	2	1	no	—
290	C₂×C₄⋊C₄	—	2	1	no	—
291	C₂×C₄⋊C₄	—	2	1	no	—
292	C₂×C₄⋊C₄	—	2	1	no	—
293	C₂×C₄⋊C₄	—	2	1	no	—
294	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
295	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
296	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
297	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
298	C₂×C₂²⋊C₄	—	2	2	no	—
299	C₂×C₂²⋊C₄	—	2	2	no	—
300	C₂×C₂²⋊C₄	—	2	2	no	—
301	C₂×C₄²	—	2	1	no	—
302	C₂×C₄²	—	2	1	no	—
303	C₂×C₄²	C₇×D₄	1	1	yes	characteristic
304	C₂×C₄²	C₇×D₄	1	1	yes	characteristic
305	C₂×C₄²	C₇×D₄	1	1	yes	characteristic
306	C₂×C₄²	C₇×D₄	1	1	yes	characteristic
307	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
308	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
309	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
310	#106	—	4	2	no	—
311	C₄⋊C₈	—	2	2	no	—
312	C₄⋊C₈	C₂×C₄×C₇	1	4	yes	complemented
313	#103	—	4	2	no	—
314	#102	—	4	2	no	—
315	#102	—	4	2	no	—
316	#102	C₂×C₄×C₇	1	8	yes	complemented
317	C₄×C₈	—	4	2	no	—
318	#95	—	2	1	no	—
319	#95	—	2	1	no	—
320	#95	—	2	1	no	—
321	#95	—	2	1	no	—
322	#95	—	2	1	no	—
323	#95	—	2	1	no	—
324	#95	—	2	1	no	—
325	C₂²×C₇	—	4	4	no	—
326	C₂²×C₇	—	4	4	no	—
327	C₂²×C₇	—	4	4	no	—
328	C₂²×C₇	—	8	2	no	—
329	C₂²×C₇	—	8	2	no	—
330	C₂²×C₇	—	8	2	no	—
331	C₂²×C₇	—	8	2	no	—
332	C₂²×C₇	C₂×C₄×D₄	1	1	yes	characteristic
333	C₂²×C₇	#535	1	1	yes	characteristic
334	C₂²×C₇	#537	1	1	yes	characteristic
335	C₂²×C₇	C₂²×SD₁₆	1	1	yes	characteristic
336	C₂²×C₇	C₂×#135	1	1	yes	characteristic
337	C₂²×C₇	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
338	C₂²×C₇	#575	1	1	yes	characteristic
339	C₄×C₇	—	2	2	no	—
340	C₄×C₇	—	2	2	no	—
341	C₄×C₇	—	2	2	no	—
342	C₄×C₇	—	2	2	no	—
343	C₄×C₇	—	4	2	no	—
344	C₄×C₇	—	4	2	no	—
345	C₄×C₇	—	4	1	no	—
346	C₄×C₇	—	8	2	no	—
347	C₄×C₇	—	8	1	no	—
348	C₄×C₇	—	8	1	no	—
349	C₄×C₇	C₄×SD₁₆	1	4	yes	—
350	C₄×C₇	#518	1	1	yes	characteristic
351	C₄×C₇	#520	1	1	yes	characteristic
352	C₄×C₇	#540	1	1	yes	characteristic
353	C₄×C₇	#542	1	1	yes	characteristic
354	C₂⁴	—	2	2	no	—
355	C₂×Q₈	—	2	1	no	—
356	C₂×Q₈	—	2	1	no	—
357	C₂×Q₈	—	2	1	no	—
358	C₂×Q₈	—	2	1	no	—
359	C₂×Q₈	—	2	1	no	—
360	C₂×Q₈	C₂²×C₄×C₇	1	2	yes	—
361	C₂×D₄	—	2	4	no	—
362	C₂×D₄	—	2	4	no	—
363	C₂×D₄	—	2	2	no	—
364	C₂×D₄	—	2	2	no	—
365	C₂×D₄	—	2	2	no	—
366	C₂×D₄	—	2	2	no	—
367	C₂×D₄	—	2	2	no	—
368	C₂×D₄	—	4	2	no	—
369	C₂×D₄	—	4	2	no	—
370	C₂×D₄	—	4	2	no	—
371	C₂×D₄	—	4	2	no	—
372	C₂×D₄	C₂²×C₄×C₇	1	4	yes	—
373	C₂²×C₄	—	2	1	no	—
374	C₂²×C₄	—	2	1	no	—
375	C₂²×C₄	—	2	1	no	—
376	C₂²×C₄	—	2	1	no	—
377	C₂²×C₄	—	2	2	no	—
378	C₂²×C₄	—	4	4	no	—
379	C₂²×C₄	—	4	4	no	—
380	C₂²×C₄	—	4	4	no	—
381	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
382	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
383	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
384	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
385	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
386	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
387	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
388	SD₁₆	—	4	8	no	—
389	C₂×C₈	—	2	2	no	—
390	C₂×C₈	—	2	2	no	—
391	C₂×C₈	—	2	2	no	—
392	C₂×C₈	—	2	2	no	—
393	C₂×C₈	—	2	2	no	—
394	C₂×C₈	C₂²×C₄×C₇	1	4	yes	—
395	C₄⋊C₄	—	2	4	no	—
396	C₄⋊C₄	—	2	1	no	—
397	C₄⋊C₄	—	2	1	no	—
398	C₄⋊C₄	—	2	1	no	—
399	C₄⋊C₄	—	2	2	no	—
400	C₄⋊C₄	—	2	1	no	—
401	C₄⋊C₄	—	2	2	no	—
402	C₄⋊C₄	—	2	1	no	—
403	C₄⋊C₄	—	4	2	no	—
404	C₄⋊C₄	—	4	2	no	—
405	C₄⋊C₄	—	4	2	no	—
406	C₄⋊C₄	—	4	2	no	—
407	C₄⋊C₄	C₂²×C₄×C₇	1	2	yes	—
408	C₂²⋊C₄	—	4	4	no	—
409	C₂²⋊C₄	—	4	4	no	—
410	C₂²⋊C₄	—	4	4	no	—
411	C₄²	—	2	4	no	—
412	C₄²	—	2	2	no	—
413	C₄²	—	2	2	no	—
414	C₄²	—	2	1	no	—
415	C₄²	—	2	1	no	—
416	C₄²	—	2	1	no	—
417	C₄²	—	2	1	no	—
418	C₄²	—	4	1	no	—
419	C₄²	—	4	2	no	—
420	C₄²	C₇×SD₁₆	1	4	yes	complemented
421	C₄²	C₂²×C₄×C₇	1	2	yes	—
422	C₄²	C₇×#41	1	2	yes	—
423	C₂×C₇	—	8	4	no	—
424	C₂×C₇	#2324	1	1	yes	characteristic
425	C₂×C₇	C₂×C₄×SD₁₆	1	1	yes	characteristic
426	C₂×C₇	C₄×AGL(1,ℤ/8)	1	1	yes	characteristic
427	C₂×C₇	#3208	1	1	yes	characteristic
428	C₂×C₇	#3212	1	1	yes	characteristic
429	C₂×C₇	#3246	1	1	yes	characteristic
430	C₂×C₇	#3247	1	1	yes	characteristic
431	C₂³	—	2	4	no	—
432	C₂³	—	4	2	no	—
433	C₂³	—	4	2	no	—
434	C₂³	—	4	2	no	—
435	C₂³	—	4	2	no	—
436	C₂³	—	4	2	no	—
437	C₂³	—	4	2	no	—
438	C₂³	C₂²×C₇×D₄	1	1	yes	characteristic
439	Q₈	—	2	2	no	—
440	Q₈	—	2	2	no	—
441	Q₈	—	4	1	no	—
442	Q₈	—	4	1	no	—
443	D₄	—	2	4	no	—
444	D₄	—	2	4	no	—
445	D₄	—	4	8	no	—
446	D₄	—	4	2	no	—
447	D₄	—	4	2	no	—
448	D₄	—	4	8	no	—
449	C₂×C₄	—	2	1	no	—
450	C₂×C₄	—	2	1	no	—
451	C₂×C₄	—	2	1	no	—
452	C₂×C₄	—	2	1	no	—
453	C₂×C₄	—	2	1	no	—
454	C₂×C₄	—	2	1	no	—
455	C₂×C₄	—	2	1	no	—
456	C₂×C₄	—	2	1	no	—
457	C₂×C₄	—	2	2	no	—
458	C₂×C₄	—	2	2	no	—
459	C₂×C₄	—	2	1	no	—
460	C₂×C₄	—	2	1	no	—
461	C₂×C₄	—	2	1	no	—
462	C₂×C₄	—	4	1	no	—
463	C₂×C₄	—	4	1	no	—
464	C₂×C₄	—	4	1	no	—
465	C₂×C₄	—	4	1	no	—
466	C₂×C₄	—	4	2	no	—
467	C₂×C₄	—	4	1	no	—
468	C₂×C₄	—	4	1	no	—
469	C₂×C₄	—	4	2	no	—
470	C₂×C₄	—	4	1	no	—
471	C₂×C₄	—	4	1	no	—
472	C₂×C₄	—	4	2	no	—
473	C₂×C₄	—	4	1	no	—
474	C₂×C₄	—	4	1	no	—
475	C₂×C₄	—	8	8	no	—
476	C₂×C₄	C₄×C₇×D₄	1	2	yes	—
477	C₂×C₄	C₄×C₇×D₄	1	2	yes	—
478	C₂×C₄	C₂×C₇×SD₁₆	1	2	yes	—
479	C₂×C₄	C₂×C₇×SD₁₆	1	2	yes	—
480	C₂×C₄	C₂×C₇×SD₁₆	1	2	yes	—
481	C₂×C₄	C₇×#135	1	2	yes	—
482	C₂×C₄	C₇×AGL(1,ℤ/8)	1	2	yes	—
483	C₂×C₄	C₂³×C₄×C₇	1	1	yes	characteristic
484	C₂×C₄	C₂×C₇×#41	1	1	yes	characteristic
485	C₂×C₄	C₇×H(5,𝔽₂)	1	1	yes	characteristic
486	C₂×C₄	C₇×H(5,𝔽₂)	1	1	yes	characteristic
487	C₂×C₄	C₇×H(5,𝔽₂)	1	1	yes	characteristic
488	C₂×C₄	C₇×2₋¹⁺⁴	1	1	yes	characteristic
489	C₈	—	2	4	no	—
490	C₈	—	4	2	no	—
491	C₇	#22147	1	1	yes	characteristic, direct product factor, Sylow
492	C₂²	—	4	4	no	—
493	C₂²	—	4	4	no	—
494	C₂²	—	4	4	no	—
495	C₂²	—	8	2	no	—
496	C₂²	—	8	2	no	—
497	C₂²	—	8	2	no	—
498	C₂²	—	8	2	no	—
499	C₂²	C₂×C₄×C₇×D₄	1	1	yes	characteristic
500	C₂²	C₇×#535	1	1	yes	characteristic
501	C₂²	C₇×#537	1	1	yes	characteristic
502	C₂²	C₂²×C₇×SD₁₆	1	1	yes	characteristic
503	C₂²	C₂×C₇×#135	1	1	yes	characteristic
504	C₂²	C₂×C₇×AGL(1,ℤ/8)	1	1	yes	characteristic
505	C₂²	C₇×#575	1	1	yes	characteristic
506	C₄	—	2	2	no	—
507	C₄	—	2	2	no	—
508	C₄	—	2	2	no	—
509	C₄	—	2	2	no	—
510	C₄	—	4	2	no	—
511	C₄	—	4	1	no	—
512	C₄	—	4	2	no	—
513	C₄	—	8	2	no	—
514	C₄	—	8	1	no	—
515	C₄	—	8	1	no	—
516	C₄	C₄×C₇×SD₁₆	1	4	yes	—
517	C₄	C₇×#518	1	1	yes	characteristic
518	C₄	C₇×#520	1	1	yes	characteristic
519	C₄	C₇×#540	1	1	yes	characteristic
520	C₄	C₇×#542	1	1	yes	characteristic
521	C₂	—	8	4	no	—
522	C₂	C₇×#2324	1	1	yes	characteristic
523	C₂	C₂×C₄×C₇×SD₁₆	1	1	yes	characteristic
524	C₂	C₄×C₇×AGL(1,ℤ/8)	1	1	yes	characteristic
525	C₂	C₇×#3208	1	1	yes	characteristic
526	C₂	C₇×#3212	1	1	yes	characteristic
527	C₂	C₇×#3246	1	1	yes	characteristic
528	C₂	C₇×#3247	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₇	C₂²×D₄
commutator	C₂×C₄	C₂³×C₄×C₇
Frattini, cosocle	C₂²×C₄	C₂⁴×C₇
prime radical	C₂×C₇×#127	C₂²
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₇ ◁ C₄³×C₇ ◁ G

Complements

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

N	H ≅ G/N	type
3. C₇×#2295	C₂	semidirect
5. C₇×#1968	C₂	semidirect
6. C₇×#1948	C₂	semidirect
7. C₇×#1934	C₂	semidirect
8. C₇×#1877	C₂	semidirect
9. C₇×#1864	C₂	semidirect
10. C₇×#1803	C₂	semidirect
11. C₄×C₇×C₄⋊C₈	C₂	semidirect
18. C₇×#460	C₄	semidirect
44. #22147	C₇	direct (N × H)
52. C₂×C₇×SD₁₆	C₂×C₄	semidirect
58. C₄×C₇×Q₈	C₂×C₄	semidirect
86. C₇×C₄⋊C₈	C₂×C₄	semidirect
90. C₇×#102	C₂×C₄	semidirect
101. #2295	C₂×C₇	semidirect
103. #1968	C₂×C₇	semidirect
104. #1948	C₂×C₇	semidirect
105. #1934	C₂×C₇	semidirect
106. #1877	C₂×C₇	semidirect
107. #1864	C₂×C₇	semidirect
108. #1803	C₂×C₇	semidirect
109. C₄×C₄⋊C₈	C₂×C₇	semidirect
176. C₄²×C₇	SD₁₆	semidirect
185. #460	C₄×C₇	semidirect
278. C₂×SD₁₆	C₂×C₄×C₇	semidirect
284. C₄×Q₈	C₂×C₄×C₇	semidirect
312. C₄⋊C₈	C₂×C₄×C₇	semidirect
316. #102	C₂×C₄×C₇	semidirect
420. C₄²	C₇×SD₁₆	semidirect
491. C₇	#22147	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×#460	2
C₄×C₇×#127	2
C₇×#2295	2
C₇×#1982	2
C₇×#1968	2
C₇×#1948	2
C₇×#1934	2
C₇×#1877	2
C₇×#1864	2
C₇×#1803	2
C₄×C₇×C₄⋊C₈	2
#22147	7

Subgroups — C7×#22147 #13199363

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×#22147 #13199363