Subgroups — C₇×#29433 #13206649

Order 1792.

746 conjugacy classes of subgroups.

The subgroup lattice has 606 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×#2863	C₂	1	1	yes	maximal, characteristic, complemented
2	C₇×#2293	C₂	1	1	yes	maximal, characteristic
3	C₇×#2088	C₂	1	1	yes	maximal, characteristic, complemented
4	C₇×#2068	C₂	1	1	yes	maximal, characteristic, complemented
5	C₇×#2067	C₂	1	1	yes	maximal, characteristic
6	C₇×#2055	C₂	1	1	yes	maximal, characteristic
7	C₇×#1968	C₂	1	1	yes	maximal, characteristic
8	C₇×#1942	C₂	1	1	yes	maximal, characteristic, complemented
9	C₇×#1934	C₂	1	1	yes	maximal, characteristic
10	C₇×#1933	C₂	1	1	yes	maximal, characteristic, complemented
11	C₇×#1928	C₂	1	1	yes	maximal, characteristic, complemented
12	C₇×#1919	C₂	1	1	yes	maximal, characteristic, complemented
13	C₇×#1877	C₂	1	1	yes	maximal, characteristic
14	C₇×#1862	C₂	1	1	yes	maximal, characteristic
15	C₄×C₇×C₄⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×C₇×SD₁₆	C₂²	1	1	yes	characteristic
17	C₂×C₄×C₇×D₄	C₂²	1	1	yes	characteristic
18	C₂×C₇×#117	—	2	1	no	—
19	C₂×C₇×#107	C₂²	1	1	yes	characteristic
20	C₂×C₇×#107	C₂²	1	1	yes	characteristic
21	C₂×C₇×#106	C₂²	1	1	yes	characteristic
22	C₂×C₇×C₄⋊C₈	C₂²	1	1	yes	characteristic
23	C₂×C₇×C₄⋊C₈	C₂²	1	1	yes	characteristic
24	C₂×C₇×#103	C₂²	1	1	yes	characteristic
25	C₂×C₇×#103	C₂²	1	1	yes	characteristic
26	C₂×C₇×#103	C₂²	1	1	yes	characteristic
27	C₂×C₇×#102	C₂²	1	1	yes	characteristic
28	C₂×C₇×#102	C₂²	1	1	yes	characteristic
29	C₂×C₇×#102	C₂²	1	1	yes	characteristic
30	C₂×C₄×C₇×C₈	C₂²	1	1	yes	characteristic
31	C₂×C₄×C₇×C₈	C₂²	1	1	yes	characteristic
32	C₇×#391	C₂²	1	1	yes	characteristic
33	C₇×#391	C₂²	1	1	yes	characteristic
34	C₇×#391	C₂²	1	1	yes	characteristic
35	C₇×#390	C₂²	1	1	yes	characteristic
36	C₇×#390	C₂²	1	1	yes	characteristic
37	C₇×#389	C₂²	1	1	yes	characteristic
38	C₇×#389	C₂²	1	1	yes	characteristic
39	C₇×#389	C₂²	1	1	yes	characteristic
40	C₇×#389	C₂²	1	1	yes	characteristic
41	C₇×#389	C₂²	1	1	yes	characteristic
42	C₇×#388	—	2	1	no	—
43	C₇×#388	—	2	1	no	—
44	C₇×#387	—	2	1	no	—
45	C₇×#387	—	2	1	no	—
46	C₇×#387	—	2	1	no	—
47	C₇×#383	—	2	1	no	—
48	C₄×C₇×C₄⋊C₄	C₂²	1	1	yes	characteristic
49	C₄×C₇×C₂²⋊C₄	—	2	1	no	—
50	C₄³×C₇	C₂²	1	1	yes	characteristic
51	C₇×#340	C₂²	1	1	yes	characteristic
52	C₇×#340	C₂²	1	1	yes	characteristic
53	C₇×#340	C₂²	1	1	yes	characteristic
54	C₇×#340	C₂²	1	1	yes	characteristic
55	C₇×#340	C₂²	1	1	yes	characteristic
56	C₇×#340	C₂²	1	1	yes	characteristic
57	C₇×#336	C₂²	1	1	yes	characteristic
58	C₇×#336	C₂²	1	1	yes	characteristic
59	#29433	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
60	C₂²×C₇×Q₈	C₂³	1	1	yes	characteristic
61	C₂²×C₇×D₄	C₂³	1	1	yes	characteristic
62	C₂³×C₄×C₇	—	2	1	no	—
63	C₂×C₇×SD₁₆	—	2	2	no	—
64	C₂×C₇×SD₁₆	—	2	2	no	—
65	C₂×C₇×SD₁₆	—	4	1	no	—
66	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
67	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
68	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
69	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
70	C₄×C₇×D₄	—	2	2	no	—
71	C₄×C₇×D₄	—	2	2	no	—
72	C₇×#117	—	4	4	no	—
73	C₂×C₇×C₄⋊C₄	—	2	1	no	—
74	C₂×C₇×C₄⋊C₄	—	2	1	no	—
75	C₂×C₇×C₄⋊C₄	—	2	1	no	—
76	C₂×C₇×C₄⋊C₄	—	2	1	no	—
77	C₂×C₇×C₄⋊C₄	—	2	1	no	—
78	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
79	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
80	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
81	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
82	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
83	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
84	C₂×C₇×C₂²⋊C₄	—	2	1	no	—
85	C₂×C₇×C₂²⋊C₄	—	2	1	no	—
86	C₂×C₇×C₂²⋊C₄	—	2	1	no	—
87	C₂×C₇×C₂²⋊C₄	—	2	1	no	—
88	C₂×C₇×C₂²⋊C₄	—	2	1	no	—
89	C₂×C₄²×C₇	—	2	1	no	—
90	C₂×C₄²×C₇	D₄	1	1	yes	characteristic
91	C₂×C₄²×C₇	D₄	1	1	yes	characteristic
92	C₂×C₄²×C₇	D₄	1	1	yes	characteristic
93	C₂×C₄²×C₇	D₄	1	1	yes	characteristic
94	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
95	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
96	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
97	C₇×#107	—	2	2	no	—
98	C₇×#107	—	4	1	no	—
99	C₇×#106	—	2	2	no	—
100	C₇×C₄⋊C₈	—	2	2	no	—
101	C₇×C₄⋊C₈	—	2	2	no	—
102	C₇×#103	—	2	2	no	—
103	C₇×#103	—	2	2	no	—
104	C₇×#103	—	4	1	no	—
105	C₇×#102	—	2	2	no	—
106	C₇×#102	—	2	2	no	—
107	C₇×#102	—	4	1	no	—
108	C₄×C₇×C₈	—	4	1	no	—
109	C₄×C₇×C₈	—	4	1	no	—
110	C₇×#95	—	2	1	no	—
111	C₇×#95	—	2	1	no	—
112	C₇×#95	—	2	1	no	—
113	C₇×#95	—	2	1	no	—
114	C₇×#95	—	2	1	no	—
115	C₇×#95	—	2	1	no	—
116	C₇×#95	—	2	1	no	—
117	C₇×#95	—	2	1	no	—
118	C₇×#95	—	2	1	no	—
119	C₇×#95	—	2	1	no	—
120	C₇×#95	—	2	1	no	—
121	C₇×#95	—	2	1	no	—
122	#2863	C₂×C₇	1	1	yes	characteristic, complemented
123	#2293	C₂×C₇	1	1	yes	characteristic
124	#2088	C₂×C₇	1	1	yes	characteristic, complemented
125	#2068	C₂×C₇	1	1	yes	characteristic, complemented
126	#2067	C₂×C₇	1	1	yes	characteristic
127	#2055	C₂×C₇	1	1	yes	characteristic
128	#1968	C₂×C₇	1	1	yes	characteristic
129	#1942	C₂×C₇	1	1	yes	characteristic, complemented
130	#1934	C₂×C₇	1	1	yes	characteristic
131	#1933	C₂×C₇	1	1	yes	characteristic, complemented
132	#1928	C₂×C₇	1	1	yes	characteristic, complemented
133	#1919	C₂×C₇	1	1	yes	characteristic, complemented
134	#1877	C₂×C₇	1	1	yes	characteristic
135	#1862	C₂×C₇	1	1	yes	characteristic
136	C₄×C₄⋊C₈	C₂×C₇	1	1	yes	characteristic, complemented
137	C₂⁴×C₇	—	2	1	no	—
138	C₂×C₇×Q₈	—	2	1	no	—
139	C₂×C₇×Q₈	—	2	1	no	—
140	C₂×C₇×Q₈	—	2	1	no	—
141	C₂×C₇×Q₈	—	2	1	no	—
142	C₂×C₇×Q₈	—	2	1	no	—
143	C₂×C₇×Q₈	—	2	1	no	—
144	C₂×C₇×D₄	—	2	1	no	—
145	C₂×C₇×D₄	—	2	1	no	—
146	C₂×C₇×D₄	—	2	1	no	—
147	C₂×C₇×D₄	—	2	1	no	—
148	C₂×C₇×D₄	—	2	1	no	—
149	C₂×C₇×D₄	#41	1	2	yes	—
150	C₂²×C₄×C₇	—	2	4	no	—
151	C₂²×C₄×C₇	—	2	1	no	—
152	C₂²×C₄×C₇	—	2	1	no	—
153	C₂²×C₄×C₇	—	2	1	no	—
154	C₂²×C₄×C₇	—	2	1	no	—
155	C₂²×C₄×C₇	—	2	1	no	—
156	C₂²×C₄×C₇	—	2	1	no	—
157	C₂²×C₄×C₇	—	2	1	no	—
158	C₂²×C₄×C₇	—	4	2	no	—
159	C₂²×C₄×C₇	—	4	2	no	—
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	C₂×D₄	1	1	yes	characteristic
166	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
167	C₇×SD₁₆	—	4	4	no	—
168	C₂×C₇×C₈	—	2	1	no	—
169	C₂×C₇×C₈	—	2	1	no	—
170	C₂×C₇×C₈	—	2	1	no	—
171	C₂×C₇×C₈	—	2	1	no	—
172	C₂×C₇×C₈	—	2	1	no	—
173	C₂×C₇×C₈	—	2	1	no	—
174	C₂×C₇×C₈	—	2	1	no	—
175	C₂×C₇×C₈	—	2	1	no	—
176	C₂×C₇×C₈	—	2	1	no	—
177	C₂×C₇×C₈	—	2	1	no	—
178	C₂×C₇×C₈	#41	1	2	yes	—
179	C₂×C₇×C₈	#41	1	2	yes	—
180	C₇×C₄⋊C₄	—	2	1	no	—
181	C₇×C₄⋊C₄	—	2	1	no	—
182	C₇×C₄⋊C₄	—	2	1	no	—
183	C₇×C₄⋊C₄	—	2	1	no	—
184	C₇×C₄⋊C₄	—	2	1	no	—
185	C₇×C₄⋊C₄	—	2	1	no	—
186	C₇×C₄⋊C₄	—	2	1	no	—
187	C₇×C₄⋊C₄	—	2	1	no	—
188	C₇×C₄⋊C₄	—	2	1	no	—
189	C₇×C₄⋊C₄	—	2	1	no	—
190	C₇×C₄⋊C₄	—	2	1	no	—
191	C₇×C₄⋊C₄	—	4	2	no	—
192	C₇×C₄⋊C₄	—	4	2	no	—
193	C₇×C₄⋊C₄	—	4	2	no	—
194	C₇×C₄⋊C₄	—	4	2	no	—
195	C₇×C₄⋊C₄	—	4	2	no	—
196	C₇×C₄⋊C₄	#41	1	2	yes	—
197	C₇×C₂²⋊C₄	—	2	4	no	—
198	C₇×C₂²⋊C₄	—	4	2	no	—
199	C₇×C₂²⋊C₄	—	4	2	no	—
200	C₇×C₂²⋊C₄	—	4	2	no	—
201	C₇×C₂²⋊C₄	—	4	2	no	—
202	C₄²×C₇	—	2	2	no	—
203	C₄²×C₇	—	2	2	no	—
204	C₄²×C₇	—	2	2	no	—
205	C₄²×C₇	—	2	2	no	—
206	C₄²×C₇	—	2	1	no	—
207	C₄²×C₇	—	2	1	no	—
208	C₄²×C₇	—	2	1	no	—
209	C₄²×C₇	—	2	1	no	—
210	C₄²×C₇	—	2	1	no	—
211	C₄²×C₇	—	2	1	no	—
212	C₄²×C₇	—	4	2	no	—
213	C₂²×SD₁₆	C₂²×C₇	1	1	yes	characteristic
214	C₂×C₄×D₄	C₂²×C₇	1	1	yes	characteristic
215	C₂×#117	—	2	1	no	—
216	C₂×#107	C₂²×C₇	1	1	yes	characteristic
217	C₂×#107	C₂²×C₇	1	1	yes	characteristic
218	C₂×#106	C₂²×C₇	1	1	yes	characteristic
219	C₂×C₄⋊C₈	C₂²×C₇	1	1	yes	characteristic
220	C₂×C₄⋊C₈	C₂²×C₇	1	1	yes	characteristic
221	C₂×#103	C₂²×C₇	1	1	yes	characteristic
222	C₂×#103	C₂²×C₇	1	1	yes	characteristic
223	C₂×#103	C₂²×C₇	1	1	yes	characteristic
224	C₂×#102	C₂²×C₇	1	1	yes	characteristic
225	C₂×#102	C₂²×C₇	1	1	yes	characteristic
226	C₂×#102	C₂²×C₇	1	1	yes	characteristic
227	C₂×C₄×C₈	C₂²×C₇	1	1	yes	characteristic
228	C₂×C₄×C₈	C₂²×C₇	1	1	yes	characteristic
229	#391	C₂²×C₇	1	1	yes	characteristic
230	#391	C₂²×C₇	1	1	yes	characteristic
231	#391	C₂²×C₇	1	1	yes	characteristic
232	#390	C₂²×C₇	1	1	yes	characteristic
233	#390	C₂²×C₇	1	1	yes	characteristic
234	#389	C₂²×C₇	1	1	yes	characteristic
235	#389	C₂²×C₇	1	1	yes	characteristic
236	#389	C₂²×C₇	1	1	yes	characteristic
237	#389	C₂²×C₇	1	1	yes	characteristic
238	#389	C₂²×C₇	1	1	yes	characteristic
239	#388	—	2	1	no	—
240	#388	—	2	1	no	—
241	#387	—	2	1	no	—
242	#387	—	2	1	no	—
243	#387	—	2	1	no	—
244	#383	—	2	1	no	—
245	C₄×C₄⋊C₄	C₂²×C₇	1	1	yes	characteristic
246	C₄×C₂²⋊C₄	—	2	1	no	—
247	C₄³	C₂²×C₇	1	1	yes	characteristic
248	#340	C₂²×C₇	1	1	yes	characteristic
249	#340	C₂²×C₇	1	1	yes	characteristic
250	#340	C₂²×C₇	1	1	yes	characteristic
251	#340	C₂²×C₇	1	1	yes	characteristic
252	#340	C₂²×C₇	1	1	yes	characteristic
253	#340	C₂²×C₇	1	1	yes	characteristic
254	#336	C₂²×C₇	1	1	yes	characteristic
255	#336	C₂²×C₇	1	1	yes	characteristic
256	C₂³×C₇	—	2	2	no	—
257	C₂³×C₇	—	4	1	no	—
258	C₂³×C₇	—	4	1	no	—
259	C₂³×C₇	—	4	1	no	—
260	C₂³×C₇	—	4	1	no	—
261	C₂³×C₇	—	4	1	no	—
262	C₂³×C₇	—	4	1	no	—
263	C₂³×C₇	C₂²×D₄	1	1	yes	characteristic
264	C₇×Q₈	—	4	1	no	—
265	C₇×Q₈	—	4	1	no	—
266	C₇×Q₈	—	4	1	no	—
267	C₇×Q₈	—	4	1	no	—
268	C₇×D₄	—	2	2	no	—
269	C₇×D₄	—	2	2	no	—
270	C₇×D₄	—	4	1	no	—
271	C₇×D₄	—	4	1	no	—
272	C₂×C₄×C₇	—	2	1	no	—
273	C₂×C₄×C₇	—	2	1	no	—
274	C₂×C₄×C₇	—	2	1	no	—
275	C₂×C₄×C₇	—	2	1	no	—
276	C₂×C₄×C₇	—	2	1	no	—
277	C₂×C₄×C₇	—	2	1	no	—
278	C₂×C₄×C₇	—	2	1	no	—
279	C₂×C₄×C₇	—	2	1	no	—
280	C₂×C₄×C₇	—	2	1	no	—
281	C₂×C₄×C₇	—	2	2	no	—
282	C₂×C₄×C₇	—	2	1	no	—
283	C₂×C₄×C₇	—	2	1	no	—
284	C₂×C₄×C₇	—	2	1	no	—
285	C₂×C₄×C₇	—	2	1	no	—
286	C₂×C₄×C₇	—	2	1	no	—
287	C₂×C₄×C₇	—	4	8	no	—
288	C₂×C₄×C₇	—	4	1	no	—
289	C₂×C₄×C₇	—	4	1	no	—
290	C₂×C₄×C₇	—	4	1	no	—
291	C₂×C₄×C₇	—	4	1	no	—
292	C₂×C₄×C₇	—	4	1	no	—
293	C₂×C₄×C₇	—	4	1	no	—
294	C₂×C₄×C₇	—	4	1	no	—
295	C₂×C₄×C₇	—	4	1	no	—
296	C₂×C₄×C₇	—	4	1	no	—
297	C₂×C₄×C₇	—	4	1	no	—
298	C₂×C₄×C₇	—	4	1	no	—
299	C₂×C₄×C₇	—	4	1	no	—
300	C₂×C₄×C₇	—	4	1	no	—
301	C₂×C₄×C₇	—	4	1	no	—
302	C₂×C₄×C₇	—	4	1	no	—
303	C₂×C₄×C₇	—	4	1	no	—
304	C₂×C₄×C₇	—	4	1	no	—
305	C₂×C₄×C₇	—	4	1	no	—
306	C₂×C₄×C₇	—	4	1	no	—
307	C₂×C₄×C₇	—	4	1	no	—
308	C₂×C₄×C₇	#135	1	2	yes	—
309	C₂×C₄×C₇	#135	1	2	yes	—
310	C₂×C₄×C₇	AGL(1,ℤ/8)	1	2	yes	—
311	C₂×C₄×C₇	#137	1	2	yes	—
312	C₂×C₄×C₇	C₂×#41	1	1	yes	characteristic
313	C₂×C₄×C₇	C₂×#41	1	1	yes	characteristic
314	C₂×C₄×C₇	C₂×#41	1	1	yes	characteristic
315	C₂×C₄×C₇	C₂×#41	1	1	yes	characteristic
316	C₂×C₄×C₇	H(5,𝔽₂)	1	1	yes	characteristic
317	C₂×C₄×C₇	2₋¹⁺⁴	1	1	yes	characteristic
318	C₇×C₈	—	2	2	no	—
319	C₇×C₈	—	2	2	no	—
320	C₇×C₈	—	4	1	no	—
321	C₇×C₈	—	4	1	no	—
322	C₂²×Q₈	C₂³×C₇	1	1	yes	characteristic
323	C₂²×D₄	C₂³×C₇	1	1	yes	characteristic
324	C₂³×C₄	—	2	1	no	—
325	C₂×SD₁₆	—	2	2	no	—
326	C₂×SD₁₆	—	2	2	no	—
327	C₂×SD₁₆	—	4	1	no	—
328	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
329	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
330	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
331	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
332	C₄×D₄	—	2	2	no	—
333	C₄×D₄	—	2	2	no	—
334	#117	—	4	4	no	—
335	C₂×C₄⋊C₄	—	2	1	no	—
336	C₂×C₄⋊C₄	—	2	1	no	—
337	C₂×C₄⋊C₄	—	2	1	no	—
338	C₂×C₄⋊C₄	—	2	1	no	—
339	C₂×C₄⋊C₄	—	2	1	no	—
340	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
341	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
342	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
343	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
344	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
345	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
346	C₂×C₂²⋊C₄	—	2	1	no	—
347	C₂×C₂²⋊C₄	—	2	1	no	—
348	C₂×C₂²⋊C₄	—	2	1	no	—
349	C₂×C₂²⋊C₄	—	2	1	no	—
350	C₂×C₂²⋊C₄	—	2	1	no	—
351	C₂×C₄²	—	2	1	no	—
352	C₂×C₄²	C₇×D₄	1	1	yes	characteristic
353	C₂×C₄²	C₇×D₄	1	1	yes	characteristic
354	C₂×C₄²	C₇×D₄	1	1	yes	characteristic
355	C₂×C₄²	C₇×D₄	1	1	yes	characteristic
356	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
357	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
358	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
359	#107	—	2	2	no	—
360	#107	—	4	1	no	—
361	#106	—	2	2	no	—
362	C₄⋊C₈	—	2	2	no	—
363	C₄⋊C₈	—	2	2	no	—
364	#103	—	2	2	no	—
365	#103	—	2	2	no	—
366	#103	—	4	1	no	—
367	#102	—	2	2	no	—
368	#102	—	2	2	no	—
369	#102	—	4	1	no	—
370	C₄×C₈	—	4	1	no	—
371	C₄×C₈	—	4	1	no	—
372	#95	—	2	1	no	—
373	#95	—	2	1	no	—
374	#95	—	2	1	no	—
375	#95	—	2	1	no	—
376	#95	—	2	1	no	—
377	#95	—	2	1	no	—
378	#95	—	2	1	no	—
379	#95	—	2	1	no	—
380	#95	—	2	1	no	—
381	#95	—	2	1	no	—
382	#95	—	2	1	no	—
383	#95	—	2	1	no	—
384	C₂²×C₇	—	4	2	no	—
385	C₂²×C₇	—	4	2	no	—
386	C₂²×C₇	—	4	2	no	—
387	C₂²×C₇	—	8	1	no	—
388	C₂²×C₇	—	8	1	no	—
389	C₂²×C₇	—	8	1	no	—
390	C₂²×C₇	—	8	1	no	—
391	C₂²×C₇	#525	1	1	yes	characteristic
392	C₂²×C₇	#532	1	1	yes	characteristic
393	C₂²×C₇	#537	1	1	yes	characteristic
394	C₂²×C₇	C₂×#135	1	1	yes	characteristic
395	C₂²×C₇	C₂×#135	1	1	yes	characteristic
396	C₂²×C₇	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
397	C₂²×C₇	C₂×#137	1	1	yes	characteristic
398	C₄×C₇	—	2	2	no	—
399	C₄×C₇	—	2	2	no	—
400	C₄×C₇	—	2	2	no	—
401	C₄×C₇	—	2	2	no	—
402	C₄×C₇	—	4	2	no	—
403	C₄×C₇	—	4	1	no	—
404	C₄×C₇	—	4	1	no	—
405	C₄×C₇	—	8	1	no	—
406	C₄×C₇	—	8	1	no	—
407	C₄×C₇	—	8	1	no	—
408	C₄×C₇	—	8	1	no	—
409	C₄×C₇	—	8	1	no	—
410	C₄×C₇	—	8	1	no	—
411	C₄×C₇	#551	1	1	yes	characteristic
412	C₄×C₇	#552	1	1	yes	characteristic
413	C₄×C₇	#553	1	1	yes	characteristic
414	C₄×C₇	#556	1	1	yes	characteristic
415	C₂⁴	—	2	1	no	—
416	C₂×Q₈	—	2	1	no	—
417	C₂×Q₈	—	2	1	no	—
418	C₂×Q₈	—	2	1	no	—
419	C₂×Q₈	—	2	1	no	—
420	C₂×Q₈	—	2	1	no	—
421	C₂×Q₈	—	2	1	no	—
422	C₂×D₄	—	2	1	no	—
423	C₂×D₄	—	2	1	no	—
424	C₂×D₄	—	2	1	no	—
425	C₂×D₄	—	2	1	no	—
426	C₂×D₄	—	2	1	no	—
427	C₂×D₄	C₇×#41	1	2	yes	—
428	C₂²×C₄	—	2	4	no	—
429	C₂²×C₄	—	2	1	no	—
430	C₂²×C₄	—	2	1	no	—
431	C₂²×C₄	—	2	1	no	—
432	C₂²×C₄	—	2	1	no	—
433	C₂²×C₄	—	2	1	no	—
434	C₂²×C₄	—	2	1	no	—
435	C₂²×C₄	—	2	1	no	—
436	C₂²×C₄	—	4	2	no	—
437	C₂²×C₄	—	4	2	no	—
438	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
439	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
440	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
441	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
442	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
443	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
444	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
445	SD₁₆	—	4	4	no	—
446	C₂×C₈	—	2	1	no	—
447	C₂×C₈	—	2	1	no	—
448	C₂×C₈	—	2	1	no	—
449	C₂×C₈	—	2	1	no	—
450	C₂×C₈	—	2	1	no	—
451	C₂×C₈	—	2	1	no	—
452	C₂×C₈	—	2	1	no	—
453	C₂×C₈	—	2	1	no	—
454	C₂×C₈	—	2	1	no	—
455	C₂×C₈	—	2	1	no	—
456	C₂×C₈	C₇×#41	1	2	yes	—
457	C₂×C₈	C₇×#41	1	2	yes	—
458	C₄⋊C₄	—	2	1	no	—
459	C₄⋊C₄	—	2	1	no	—
460	C₄⋊C₄	—	2	1	no	—
461	C₄⋊C₄	—	2	1	no	—
462	C₄⋊C₄	—	2	1	no	—
463	C₄⋊C₄	—	2	1	no	—
464	C₄⋊C₄	—	2	1	no	—
465	C₄⋊C₄	—	2	1	no	—
466	C₄⋊C₄	—	2	1	no	—
467	C₄⋊C₄	—	2	1	no	—
468	C₄⋊C₄	—	2	1	no	—
469	C₄⋊C₄	—	4	2	no	—
470	C₄⋊C₄	—	4	2	no	—
471	C₄⋊C₄	—	4	2	no	—
472	C₄⋊C₄	—	4	2	no	—
473	C₄⋊C₄	—	4	2	no	—
474	C₄⋊C₄	C₇×#41	1	2	yes	—
475	C₂²⋊C₄	—	2	4	no	—
476	C₂²⋊C₄	—	4	2	no	—
477	C₂²⋊C₄	—	4	2	no	—
478	C₂²⋊C₄	—	4	2	no	—
479	C₂²⋊C₄	—	4	2	no	—
480	C₄²	—	2	2	no	—
481	C₄²	—	2	2	no	—
482	C₄²	—	2	2	no	—
483	C₄²	—	2	2	no	—
484	C₄²	—	2	1	no	—
485	C₄²	—	2	1	no	—
486	C₄²	—	2	1	no	—
487	C₄²	—	2	1	no	—
488	C₄²	—	2	1	no	—
489	C₄²	—	2	1	no	—
490	C₄²	—	4	2	no	—
491	C₂×C₇	—	8	2	no	—
492	C₂×C₇	#2601	1	1	yes	characteristic
493	C₂×C₇	#3105	1	1	yes	characteristic
494	C₂×C₇	#3107	1	1	yes	characteristic
495	C₂×C₇	#3168	1	1	yes	characteristic
496	C₂×C₇	#3182	1	1	yes	characteristic
497	C₂×C₇	#3247	1	1	yes	characteristic
498	C₂×C₇	#3248	1	1	yes	characteristic
499	C₂³	—	2	2	no	—
500	C₂³	—	4	1	no	—
501	C₂³	—	4	1	no	—
502	C₂³	—	4	1	no	—
503	C₂³	—	4	1	no	—
504	C₂³	—	4	1	no	—
505	C₂³	—	4	1	no	—
506	C₂³	C₂²×C₇×D₄	1	1	yes	characteristic
507	Q₈	—	4	1	no	—
508	Q₈	—	4	1	no	—
509	Q₈	—	4	1	no	—
510	Q₈	—	4	1	no	—
511	D₄	—	2	2	no	—
512	D₄	—	2	2	no	—
513	D₄	—	4	1	no	—
514	D₄	—	4	1	no	—
515	C₂×C₄	—	2	1	no	—
516	C₂×C₄	—	2	1	no	—
517	C₂×C₄	—	2	1	no	—
518	C₂×C₄	—	2	1	no	—
519	C₂×C₄	—	2	1	no	—
520	C₂×C₄	—	2	1	no	—
521	C₂×C₄	—	2	1	no	—
522	C₂×C₄	—	2	1	no	—
523	C₂×C₄	—	2	1	no	—
524	C₂×C₄	—	2	2	no	—
525	C₂×C₄	—	2	1	no	—
526	C₂×C₄	—	2	1	no	—
527	C₂×C₄	—	2	1	no	—
528	C₂×C₄	—	2	1	no	—
529	C₂×C₄	—	2	1	no	—
530	C₂×C₄	—	4	8	no	—
531	C₂×C₄	—	4	1	no	—
532	C₂×C₄	—	4	1	no	—
533	C₂×C₄	—	4	1	no	—
534	C₂×C₄	—	4	1	no	—
535	C₂×C₄	—	4	1	no	—
536	C₂×C₄	—	4	1	no	—
537	C₂×C₄	—	4	1	no	—
538	C₂×C₄	—	4	1	no	—
539	C₂×C₄	—	4	1	no	—
540	C₂×C₄	—	4	1	no	—
541	C₂×C₄	—	4	1	no	—
542	C₂×C₄	—	4	1	no	—
543	C₂×C₄	—	4	1	no	—
544	C₂×C₄	—	4	1	no	—
545	C₂×C₄	—	4	1	no	—
546	C₂×C₄	—	4	1	no	—
547	C₂×C₄	—	4	1	no	—
548	C₂×C₄	—	4	1	no	—
549	C₂×C₄	—	4	1	no	—
550	C₂×C₄	—	4	1	no	—
551	C₂×C₄	C₇×#135	1	2	yes	—
552	C₂×C₄	C₇×#135	1	2	yes	—
553	C₂×C₄	C₇×AGL(1,ℤ/8)	1	2	yes	—
554	C₂×C₄	C₇×#137	1	2	yes	—
555	C₂×C₄	C₂×C₇×#41	1	1	yes	characteristic
556	C₂×C₄	C₂×C₇×#41	1	1	yes	characteristic
557	C₂×C₄	C₂×C₇×#41	1	1	yes	characteristic
558	C₂×C₄	C₂×C₇×#41	1	1	yes	characteristic
559	C₂×C₄	C₇×H(5,𝔽₂)	1	1	yes	characteristic
560	C₂×C₄	C₇×2₋¹⁺⁴	1	1	yes	characteristic
561	C₈	—	2	2	no	—
562	C₈	—	2	2	no	—
563	C₈	—	4	1	no	—
564	C₈	—	4	1	no	—
565	C₇	#29433	1	1	yes	characteristic, direct product factor, Sylow
566	C₂²	—	4	2	no	—
567	C₂²	—	4	2	no	—
568	C₂²	—	4	2	no	—
569	C₂²	—	8	1	no	—
570	C₂²	—	8	1	no	—
571	C₂²	—	8	1	no	—
572	C₂²	—	8	1	no	—
573	C₂²	C₇×#525	1	1	yes	characteristic
574	C₂²	C₇×#532	1	1	yes	characteristic
575	C₂²	C₇×#537	1	1	yes	characteristic
576	C₂²	C₂×C₇×#135	1	1	yes	characteristic
577	C₂²	C₂×C₇×#135	1	1	yes	characteristic
578	C₂²	C₂×C₇×AGL(1,ℤ/8)	1	1	yes	characteristic
579	C₂²	C₂×C₇×#137	1	1	yes	characteristic
580	C₄	—	2	2	no	—
581	C₄	—	2	2	no	—
582	C₄	—	2	2	no	—
583	C₄	—	2	2	no	—
584	C₄	—	4	1	no	—
585	C₄	—	4	2	no	—
586	C₄	—	4	1	no	—
587	C₄	—	8	1	no	—
588	C₄	—	8	1	no	—
589	C₄	—	8	1	no	—
590	C₄	—	8	1	no	—
591	C₄	—	8	1	no	—
592	C₄	—	8	1	no	—
593	C₄	C₇×#551	1	1	yes	characteristic
594	C₄	C₇×#552	1	1	yes	characteristic
595	C₄	C₇×#553	1	1	yes	characteristic
596	C₄	C₇×#556	1	1	yes	characteristic
597	C₂	—	8	2	no	—
598	C₂	C₇×#2601	1	1	yes	characteristic
599	C₂	C₇×#3105	1	1	yes	characteristic
600	C₂	C₇×#3107	1	1	yes	characteristic
601	C₂	C₇×#3168	1	1	yes	characteristic
602	C₂	C₇×#3182	1	1	yes	characteristic
603	C₂	C₇×#3247	1	1	yes	characteristic
604	C₂	C₇×#3248	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₇	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₇
prime radical	C₂²×C₇×D₄	C₂³
LCS	G ▷ C₂²×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
1. C₇×#2863	C₂	semidirect
3. C₇×#2088	C₂	semidirect
4. C₇×#2068	C₂	semidirect
8. C₇×#1942	C₂	semidirect
10. C₇×#1933	C₂	semidirect
11. C₇×#1928	C₂	semidirect
12. C₇×#1919	C₂	semidirect
15. C₄×C₇×C₄⋊C₈	C₂	semidirect
59. #29433	C₇	direct (N × H)
122. #2863	C₂×C₇	semidirect
124. #2088	C₂×C₇	semidirect
125. #2068	C₂×C₇	semidirect
129. #1942	C₂×C₇	semidirect
131. #1933	C₂×C₇	semidirect
132. #1928	C₂×C₇	semidirect
133. #1919	C₂×C₇	semidirect
136. C₄×C₄⋊C₈	C₂×C₇	semidirect
565. C₇	#29433	direct (N × H)

Maximal subgroups

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

subgroup	index
C₇×#2863	2
C₇×#2293	2
C₇×#2088	2
C₇×#2068	2
C₇×#2067	2
C₇×#2055	2
C₇×#1968	2
C₇×#1942	2
C₇×#1934	2
C₇×#1933	2
C₇×#1928	2
C₇×#1919	2
C₇×#1877	2
C₇×#1862	2
C₄×C₇×C₄⋊C₈	2
#29433	7

Subgroups — C7×#29433 #13206649

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×#29433 #13206649