Subgroups — C₇×#23107 #13200323

Order 1792.

854 conjugacy classes of subgroups.

The subgroup lattice has 646 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₇×#464	C₂	1	1	yes	maximal, characteristic
2	C₇×#2367	C₂	1	1	yes	maximal, characteristic
3	C₇×#2355	C₂	1	1	yes	maximal, characteristic, complemented
4	C₇×#1971	C₂	1	1	yes	maximal, characteristic, complemented
5	C₇×#1968	C₂	1	1	yes	maximal, characteristic
6	C₇×#1959	C₂	1	1	yes	maximal, characteristic
7	C₇×#1948	C₂	1	1	yes	maximal, characteristic, complemented
8	C₇×#1927	C₂	1	1	yes	maximal, characteristic, complemented
9	C₇×#1926	C₂	1	1	yes	maximal, characteristic
10	C₇×#1878	C₂	1	1	yes	maximal, characteristic, complemented
11	C₇×#1877	C₂	1	1	yes	maximal, characteristic
12	C₇×#1771	C₂	1	1	yes	maximal, characteristic, complemented
13	C₇×#1763	C₂	1	1	yes	maximal, characteristic, complemented
14	C₇×#1762	C₂	1	1	yes	maximal, characteristic
15	C₄×C₇×#103	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×C₇×Q₁₆	C₂²	1	1	yes	characteristic
17	C₂²×C₇×SD₁₆	C₂²	1	1	yes	characteristic
18	C₂×C₇×#124	C₂²	1	1	yes	characteristic
19	C₂×C₄×C₇×Q₈	C₂²	1	1	yes	characteristic
20	C₂×C₄×C₇×Q₈	C₂²	1	1	yes	characteristic
21	C₂×C₄×C₇×D₄	C₂²	1	1	yes	characteristic
22	C₇×#464	C₄	1	8	yes	complemented
23	C₂×C₇×#106	C₂²	1	1	yes	characteristic
24	C₂×C₇×#106	C₂²	1	1	yes	characteristic
25	C₂×C₇×C₄⋊C₈	C₂²	1	1	yes	characteristic
26	C₂×C₇×#103	C₂²	1	1	yes	characteristic
27	C₂×C₇×#103	C₂²	1	1	yes	characteristic
28	C₂×C₇×#103	C₂²	1	1	yes	characteristic
29	C₂×C₇×#103	C₂²	1	1	yes	characteristic
30	C₂×C₇×#103	C₂²	1	1	yes	characteristic
31	C₂×C₇×#102	C₂²	1	1	yes	characteristic
32	C₂×C₇×#102	C₂²	1	1	yes	characteristic
33	C₂×C₇×#102	C₂²	1	1	yes	characteristic
34	C₂×C₇×#97	C₂²	1	1	yes	characteristic
35	C₂×C₇×#97	C₂²	1	1	yes	characteristic
36	C₂×C₄×C₇×C₈	C₂²	1	1	yes	characteristic
37	C₇×#391	C₂²	1	1	yes	characteristic
38	C₇×#391	C₂²	1	1	yes	characteristic
39	C₇×#391	C₂²	1	1	yes	characteristic
40	C₇×#390	C₂²	1	1	yes	characteristic
41	C₇×#388	—	2	1	no	—
42	C₇×#388	—	2	1	no	—
43	C₇×#387	—	2	1	no	—
44	C₇×#387	—	2	1	no	—
45	C₇×#385	—	2	1	no	—
46	C₇×#384	C₂²	1	1	yes	characteristic
47	C₇×#382	—	2	1	no	—
48	C₄×C₇×C₄⋊C₄	—	2	1	no	—
49	C₄×C₇×C₄⋊C₄	C₂²	1	1	yes	characteristic
50	C₄×C₇×C₄⋊C₄	C₂²	1	1	yes	characteristic
51	C₄×C₇×C₄⋊C₄	C₂²	1	1	yes	characteristic
52	C₄×C₇×C₄⋊C₄	C₂²	1	1	yes	characteristic
53	C₄×C₇×C₂²⋊C₄	—	2	1	no	—
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×#340	C₂²	1	1	yes	characteristic
58	C₇×#336	C₂²	1	1	yes	characteristic
59	C₇×#336	C₂²	1	1	yes	characteristic
60	#23107	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
61	C₂²×C₇×Q₈	C₂³	1	1	yes	characteristic
62	C₂²×C₇×Q₈	C₂³	1	1	yes	characteristic
63	C₂²×C₇×D₄	C₂³	1	1	yes	characteristic
64	C₂³×C₄×C₇	—	2	1	no	—
65	C₂×C₇×Q₁₆	—	4	1	no	—
66	C₂×C₇×Q₁₆	—	4	1	no	—
67	C₂×C₇×Q₁₆	C₂×C₄	1	4	yes	complemented
68	C₂×C₇×SD₁₆	—	4	1	no	—
69	C₂×C₇×SD₁₆	—	4	1	no	—
70	C₂×C₇×SD₁₆	C₂×C₄	1	4	yes	—
71	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
72	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
73	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
74	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
75	C₇×#124	—	2	2	no	—
76	C₇×#124	C₂×C₄	1	4	yes	—
77	C₄×C₇×Q₈	—	2	2	no	—
78	C₄×C₇×Q₈	—	2	2	no	—
79	C₄×C₇×Q₈	—	4	1	no	—
80	C₄×C₇×Q₈	C₂×C₄	1	4	yes	complemented
81	C₄×C₇×D₄	—	2	2	no	—
82	C₄×C₇×D₄	—	4	1	no	—
83	C₂×C₇×C₄⋊C₄	—	2	1	no	—
84	C₂×C₇×C₄⋊C₄	—	2	1	no	—
85	C₂×C₇×C₄⋊C₄	—	2	1	no	—
86	C₂×C₇×C₄⋊C₄	—	2	1	no	—
87	C₂×C₇×C₄⋊C₄	D₄	1	1	yes	characteristic
88	C₂×C₇×C₄⋊C₄	D₄	1	1	yes	characteristic
89	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
90	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
91	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
92	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
93	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
94	C₂×C₇×C₂²⋊C₄	—	2	1	no	—
95	C₂×C₇×C₂²⋊C₄	—	2	1	no	—
96	C₂×C₇×C₂²⋊C₄	—	2	1	no	—
97	C₂×C₇×C₂²⋊C₄	—	2	1	no	—
98	C₂×C₇×C₂²⋊C₄	—	2	1	no	—
99	C₂×C₄²×C₇	—	2	1	no	—
100	C₂×C₄²×C₇	—	2	1	no	—
101	C₂×C₄²×C₇	—	2	1	no	—
102	C₂×C₄²×C₇	—	2	1	no	—
103	C₂×C₄²×C₇	—	2	1	no	—
104	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
105	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
106	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
107	C₇×#106	—	4	1	no	—
108	C₇×#106	—	4	1	no	—
109	C₇×C₄⋊C₈	C₂×C₄	1	4	yes	complemented
110	C₇×#103	—	2	2	no	—
111	C₇×#103	—	2	2	no	—
112	C₇×#103	—	2	2	no	—
113	C₇×#103	—	4	1	no	—
114	C₇×#103	C₂×C₄	1	4	yes	complemented
115	C₇×#102	—	2	2	no	—
116	C₇×#102	—	4	1	no	—
117	C₇×#102	C₂×C₄	1	4	yes	—
118	C₇×#97	—	2	2	no	—
119	C₇×#97	—	4	1	no	—
120	C₄×C₇×C₈	—	4	1	no	—
121	C₇×#95	—	2	1	no	—
122	C₇×#95	—	2	1	no	—
123	C₇×#95	—	2	1	no	—
124	C₇×#95	—	2	1	no	—
125	C₇×#95	—	2	1	no	—
126	C₇×#95	—	2	1	no	—
127	C₇×#95	—	2	1	no	—
128	C₇×#95	—	2	1	no	—
129	C₇×#95	—	2	1	no	—
130	C₇×#95	D₄	1	1	yes	characteristic
131	C₇×#95	D₄	1	1	yes	characteristic
132	C₂×#464	C₂×C₇	1	1	yes	characteristic
133	#2367	C₂×C₇	1	1	yes	characteristic
134	#2355	C₂×C₇	1	1	yes	characteristic, complemented
135	#1971	C₂×C₇	1	1	yes	characteristic, complemented
136	#1968	C₂×C₇	1	1	yes	characteristic
137	#1959	C₂×C₇	1	1	yes	characteristic
138	#1948	C₂×C₇	1	1	yes	characteristic, complemented
139	#1927	C₂×C₇	1	1	yes	characteristic, complemented
140	#1926	C₂×C₇	1	1	yes	characteristic
141	#1878	C₂×C₇	1	1	yes	characteristic, complemented
142	#1877	C₂×C₇	1	1	yes	characteristic
143	#1771	C₂×C₇	1	1	yes	characteristic, complemented
144	#1763	C₂×C₇	1	1	yes	characteristic, complemented
145	#1762	C₂×C₇	1	1	yes	characteristic
146	C₄×#103	C₂×C₇	1	1	yes	characteristic, complemented
147	C₂⁴×C₇	—	2	1	no	—
148	C₂×C₇×Q₈	—	2	1	no	—
149	C₂×C₇×Q₈	—	2	1	no	—
150	C₂×C₇×Q₈	—	2	1	no	—
151	C₂×C₇×Q₈	—	2	1	no	—
152	C₂×C₇×Q₈	—	2	1	no	—
153	C₂×C₇×Q₈	—	2	1	no	—
154	C₂×C₇×Q₈	—	2	1	no	—
155	C₂×C₇×Q₈	—	2	1	no	—
156	C₂×C₇×Q₈	—	2	1	no	—
157	C₂×C₇×Q₈	—	2	1	no	—
158	C₂×C₇×Q₈	C₂²×C₄	1	2	yes	—
159	C₂×C₇×Q₈	C₂²×C₄	1	2	yes	—
160	C₂×C₇×D₄	—	2	1	no	—
161	C₂×C₇×D₄	—	2	1	no	—
162	C₂×C₇×D₄	—	2	1	no	—
163	C₂×C₇×D₄	—	2	1	no	—
164	C₂×C₇×D₄	—	2	1	no	—
165	C₂×C₇×D₄	C₂²×C₄	1	2	yes	—
166	C₂²×C₄×C₇	—	2	1	no	—
167	C₂²×C₄×C₇	—	2	1	no	—
168	C₂²×C₄×C₇	—	2	1	no	—
169	C₂²×C₄×C₇	—	2	1	no	—
170	C₂²×C₄×C₇	—	2	1	no	—
171	C₂²×C₄×C₇	—	2	1	no	—
172	C₂²×C₄×C₇	—	2	1	no	—
173	C₂²×C₄×C₇	—	4	2	no	—
174	C₂²×C₄×C₇	—	4	2	no	—
175	C₂²×C₄×C₇	—	8	1	no	—
176	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
177	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
178	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
179	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
180	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
181	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
182	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
183	C₇×Q₁₆	—	4	4	no	—
184	C₇×SD₁₆	—	4	4	no	—
185	C₂×C₇×C₈	—	2	1	no	—
186	C₂×C₇×C₈	—	2	1	no	—
187	C₂×C₇×C₈	—	2	1	no	—
188	C₂×C₇×C₈	—	2	1	no	—
189	C₂×C₇×C₈	—	2	1	no	—
190	C₂×C₇×C₈	—	2	1	no	—
191	C₂×C₇×C₈	—	2	1	no	—
192	C₂×C₇×C₈	—	2	1	no	—
193	C₂×C₇×C₈	—	2	1	no	—
194	C₂×C₇×C₈	C₂²×C₄	1	2	yes	—
195	C₂×C₇×C₈	C₂²×C₄	1	2	yes	—
196	C₂×C₇×C₈	#41	1	2	yes	—
197	C₇×C₄⋊C₄	—	2	4	no	—
198	C₇×C₄⋊C₄	—	2	2	no	—
199	C₇×C₄⋊C₄	—	2	1	no	—
200	C₇×C₄⋊C₄	—	2	1	no	—
201	C₇×C₄⋊C₄	—	2	1	no	—
202	C₇×C₄⋊C₄	—	2	1	no	—
203	C₇×C₄⋊C₄	—	2	1	no	—
204	C₇×C₄⋊C₄	—	2	1	no	—
205	C₇×C₄⋊C₄	—	2	1	no	—
206	C₇×C₄⋊C₄	—	2	1	no	—
207	C₇×C₄⋊C₄	—	4	1	no	—
208	C₇×C₄⋊C₄	—	4	2	no	—
209	C₇×C₄⋊C₄	—	4	2	no	—
210	C₇×C₄⋊C₄	—	8	1	no	—
211	C₇×C₄⋊C₄	C₂²×C₄	1	2	yes	—
212	C₇×C₄⋊C₄	#41	1	2	yes	—
213	C₇×C₂²⋊C₄	—	2	4	no	—
214	C₇×C₂²⋊C₄	—	2	4	no	—
215	C₇×C₂²⋊C₄	—	4	2	no	—
216	C₇×C₂²⋊C₄	—	4	2	no	—
217	C₇×C₂²⋊C₄	—	8	1	no	—
218	C₄²×C₇	—	2	4	no	—
219	C₄²×C₇	—	2	1	no	—
220	C₄²×C₇	—	2	1	no	—
221	C₄²×C₇	—	2	1	no	—
222	C₄²×C₇	—	2	1	no	—
223	C₄²×C₇	—	4	2	no	—
224	C₄²×C₇	—	8	1	no	—
225	C₄²×C₇	—	8	1	no	—
226	C₄²×C₇	—	8	1	no	—
227	C₄²×C₇	C₂²×C₄	1	2	yes	—
228	C₄²×C₇	#41	1	2	yes	—
229	C₂²×Q₁₆	C₂²×C₇	1	1	yes	characteristic
230	C₂²×SD₁₆	C₂²×C₇	1	1	yes	characteristic
231	C₂×#124	C₂²×C₇	1	1	yes	characteristic
232	C₂×C₄×Q₈	C₂²×C₇	1	1	yes	characteristic
233	C₂×C₄×Q₈	C₂²×C₇	1	1	yes	characteristic
234	C₂×C₄×D₄	C₂²×C₇	1	1	yes	characteristic
235	#464	C₄×C₇	1	8	yes	complemented
236	C₂×#106	C₂²×C₇	1	1	yes	characteristic
237	C₂×#106	C₂²×C₇	1	1	yes	characteristic
238	C₂×C₄⋊C₈	C₂²×C₇	1	1	yes	characteristic
239	C₂×#103	C₂²×C₇	1	1	yes	characteristic
240	C₂×#103	C₂²×C₇	1	1	yes	characteristic
241	C₂×#103	C₂²×C₇	1	1	yes	characteristic
242	C₂×#103	C₂²×C₇	1	1	yes	characteristic
243	C₂×#103	C₂²×C₇	1	1	yes	characteristic
244	C₂×#102	C₂²×C₇	1	1	yes	characteristic
245	C₂×#102	C₂²×C₇	1	1	yes	characteristic
246	C₂×#102	C₂²×C₇	1	1	yes	characteristic
247	C₂×#97	C₂²×C₇	1	1	yes	characteristic
248	C₂×#97	C₂²×C₇	1	1	yes	characteristic
249	C₂×C₄×C₈	C₂²×C₇	1	1	yes	characteristic
250	#391	C₂²×C₇	1	1	yes	characteristic
251	#391	C₂²×C₇	1	1	yes	characteristic
252	#391	C₂²×C₇	1	1	yes	characteristic
253	#390	C₂²×C₇	1	1	yes	characteristic
254	#388	—	2	1	no	—
255	#388	—	2	1	no	—
256	#387	—	2	1	no	—
257	#387	—	2	1	no	—
258	#385	—	2	1	no	—
259	#384	C₂²×C₇	1	1	yes	characteristic
260	#382	—	2	1	no	—
261	C₄×C₄⋊C₄	—	2	1	no	—
262	C₄×C₄⋊C₄	C₂²×C₇	1	1	yes	characteristic
263	C₄×C₄⋊C₄	C₂²×C₇	1	1	yes	characteristic
264	C₄×C₄⋊C₄	C₂²×C₇	1	1	yes	characteristic
265	C₄×C₄⋊C₄	C₂²×C₇	1	1	yes	characteristic
266	C₄×C₂²⋊C₄	—	2	1	no	—
267	#340	C₂²×C₇	1	1	yes	characteristic
268	#340	C₂²×C₇	1	1	yes	characteristic
269	#340	C₂²×C₇	1	1	yes	characteristic
270	#340	C₂²×C₇	1	1	yes	characteristic
271	#336	C₂²×C₇	1	1	yes	characteristic
272	#336	C₂²×C₇	1	1	yes	characteristic
273	C₂³×C₇	—	2	2	no	—
274	C₂³×C₇	—	4	1	no	—
275	C₂³×C₇	—	4	1	no	—
276	C₂³×C₇	—	4	1	no	—
277	C₂³×C₇	—	4	1	no	—
278	C₂³×C₇	—	4	1	no	—
279	C₂³×C₇	—	4	1	no	—
280	C₂³×C₇	C₂²×D₄	1	1	yes	characteristic
281	C₇×Q₈	—	2	2	no	—
282	C₇×Q₈	—	2	2	no	—
283	C₇×Q₈	—	2	2	no	—
284	C₇×Q₈	—	2	2	no	—
285	C₇×Q₈	—	4	1	no	—
286	C₇×Q₈	—	4	1	no	—
287	C₇×Q₈	—	4	1	no	—
288	C₇×Q₈	—	4	1	no	—
289	C₇×D₄	—	2	2	no	—
290	C₇×D₄	—	2	2	no	—
291	C₇×D₄	—	4	1	no	—
292	C₇×D₄	—	4	1	no	—
293	C₂×C₄×C₇	—	2	1	no	—
294	C₂×C₄×C₇	—	2	1	no	—
295	C₂×C₄×C₇	—	2	1	no	—
296	C₂×C₄×C₇	—	2	1	no	—
297	C₂×C₄×C₇	—	2	1	no	—
298	C₂×C₄×C₇	—	2	1	no	—
299	C₂×C₄×C₇	—	2	2	no	—
300	C₂×C₄×C₇	—	2	2	no	—
301	C₂×C₄×C₇	—	2	2	no	—
302	C₂×C₄×C₇	—	2	1	no	—
303	C₂×C₄×C₇	—	2	1	no	—
304	C₂×C₄×C₇	—	2	1	no	—
305	C₂×C₄×C₇	—	2	2	no	—
306	C₂×C₄×C₇	—	2	1	no	—
307	C₂×C₄×C₇	—	2	1	no	—
308	C₂×C₄×C₇	—	2	1	no	—
309	C₂×C₄×C₇	—	2	1	no	—
310	C₂×C₄×C₇	—	2	1	no	—
311	C₂×C₄×C₇	—	2	1	no	—
312	C₂×C₄×C₇	—	4	1	no	—
313	C₂×C₄×C₇	—	4	1	no	—
314	C₂×C₄×C₇	—	4	1	no	—
315	C₂×C₄×C₇	—	4	1	no	—
316	C₂×C₄×C₇	—	4	1	no	—
317	C₂×C₄×C₇	—	4	1	no	—
318	C₂×C₄×C₇	—	4	1	no	—
319	C₂×C₄×C₇	—	4	1	no	—
320	C₂×C₄×C₇	—	4	1	no	—
321	C₂×C₄×C₇	—	4	1	no	—
322	C₂×C₄×C₇	—	4	1	no	—
323	C₂×C₄×C₇	—	4	1	no	—
324	C₂×C₄×C₇	—	4	1	no	—
325	C₂×C₄×C₇	—	4	1	no	—
326	C₂×C₄×C₇	—	4	1	no	—
327	C₂×C₄×C₇	—	4	1	no	—
328	C₂×C₄×C₇	—	4	1	no	—
329	C₂×C₄×C₇	—	8	4	no	—
330	C₂×C₄×C₇	C₄×D₄	1	2	yes	—
331	C₂×C₄×C₇	C₄×D₄	1	2	yes	—
332	C₂×C₄×C₇	#137	1	2	yes	—
333	C₂×C₄×C₇	C₂³×C₄	1	1	yes	characteristic
334	C₂×C₄×C₇	C₂×#41	1	1	yes	characteristic
335	C₂×C₄×C₇	C₂×#41	1	1	yes	characteristic
336	C₂×C₄×C₇	C₂×#41	1	1	yes	characteristic
337	C₂×C₄×C₇	H(5,𝔽₂)	1	1	yes	characteristic
338	C₂×C₄×C₇	H(5,𝔽₂)	1	1	yes	characteristic
339	C₇×C₈	—	2	2	no	—
340	C₇×C₈	—	2	2	no	—
341	C₇×C₈	—	2	2	no	—
342	C₇×C₈	—	4	1	no	—
343	C₂²×Q₈	C₂³×C₇	1	1	yes	characteristic
344	C₂²×Q₈	C₂³×C₇	1	1	yes	characteristic
345	C₂²×D₄	C₂³×C₇	1	1	yes	characteristic
346	C₂³×C₄	—	2	1	no	—
347	C₂×Q₁₆	—	4	1	no	—
348	C₂×Q₁₆	—	4	1	no	—
349	C₂×Q₁₆	C₂×C₄×C₇	1	4	yes	complemented
350	C₂×SD₁₆	—	4	1	no	—
351	C₂×SD₁₆	—	4	1	no	—
352	C₂×SD₁₆	C₂×C₄×C₇	1	4	yes	—
353	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
354	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
355	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
356	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
357	#124	—	2	2	no	—
358	#124	C₂×C₄×C₇	1	4	yes	—
359	C₄×Q₈	—	2	2	no	—
360	C₄×Q₈	—	2	2	no	—
361	C₄×Q₈	—	4	1	no	—
362	C₄×Q₈	C₂×C₄×C₇	1	4	yes	complemented
363	C₄×D₄	—	2	2	no	—
364	C₄×D₄	—	4	1	no	—
365	C₂×C₄⋊C₄	—	2	1	no	—
366	C₂×C₄⋊C₄	—	2	1	no	—
367	C₂×C₄⋊C₄	—	2	1	no	—
368	C₂×C₄⋊C₄	—	2	1	no	—
369	C₂×C₄⋊C₄	C₇×D₄	1	1	yes	characteristic
370	C₂×C₄⋊C₄	C₇×D₄	1	1	yes	characteristic
371	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
372	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
373	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
374	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
375	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
376	C₂×C₂²⋊C₄	—	2	1	no	—
377	C₂×C₂²⋊C₄	—	2	1	no	—
378	C₂×C₂²⋊C₄	—	2	1	no	—
379	C₂×C₂²⋊C₄	—	2	1	no	—
380	C₂×C₂²⋊C₄	—	2	1	no	—
381	C₂×C₄²	—	2	1	no	—
382	C₂×C₄²	—	2	1	no	—
383	C₂×C₄²	—	2	1	no	—
384	C₂×C₄²	—	2	1	no	—
385	C₂×C₄²	—	2	1	no	—
386	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
387	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
388	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
389	#106	—	4	1	no	—
390	#106	—	4	1	no	—
391	C₄⋊C₈	C₂×C₄×C₇	1	4	yes	complemented
392	#103	—	2	2	no	—
393	#103	—	2	2	no	—
394	#103	—	2	2	no	—
395	#103	—	4	1	no	—
396	#103	C₂×C₄×C₇	1	4	yes	complemented
397	#102	—	2	2	no	—
398	#102	—	4	1	no	—
399	#102	C₂×C₄×C₇	1	4	yes	—
400	#97	—	2	2	no	—
401	#97	—	4	1	no	—
402	C₄×C₈	—	4	1	no	—
403	#95	—	2	1	no	—
404	#95	—	2	1	no	—
405	#95	—	2	1	no	—
406	#95	—	2	1	no	—
407	#95	—	2	1	no	—
408	#95	—	2	1	no	—
409	#95	—	2	1	no	—
410	#95	—	2	1	no	—
411	#95	—	2	1	no	—
412	#95	C₇×D₄	1	1	yes	characteristic
413	#95	C₇×D₄	1	1	yes	characteristic
414	C₂²×C₇	—	4	2	no	—
415	C₂²×C₇	—	4	2	no	—
416	C₂²×C₇	—	4	2	no	—
417	C₂²×C₇	—	8	1	no	—
418	C₂²×C₇	—	8	1	no	—
419	C₂²×C₇	—	8	1	no	—
420	C₂²×C₇	—	8	1	no	—
421	C₂²×C₇	C₂×C₄×D₄	1	1	yes	characteristic
422	C₂²×C₇	#546	1	1	yes	characteristic
423	C₂²×C₇	#550	1	1	yes	characteristic
424	C₂²×C₇	C₂×#137	1	1	yes	characteristic
425	C₂²×C₇	#575	1	1	yes	characteristic
426	C₂²×C₇	#577	1	1	yes	characteristic
427	C₂²×C₇	#577	1	1	yes	characteristic
428	C₄×C₇	—	2	2	no	—
429	C₄×C₇	—	2	2	no	—
430	C₄×C₇	—	2	2	no	—
431	C₄×C₇	—	4	2	no	—
432	C₄×C₇	—	4	2	no	—
433	C₄×C₇	—	4	2	no	—
434	C₄×C₇	—	4	1	no	—
435	C₄×C₇	—	4	1	no	—
436	C₄×C₇	—	4	2	no	—
437	C₄×C₇	—	4	1	no	—
438	C₄×C₇	—	8	1	no	—
439	C₄×C₇	—	8	1	no	—
440	C₄×C₇	—	8	1	no	—
441	C₄×C₇	C₄×#41	1	1	yes	characteristic
442	C₄×C₇	#518	1	1	yes	characteristic
443	C₄×C₇	#553	1	1	yes	characteristic
444	C₄×C₇	#555	1	1	yes	characteristic
445	C₂⁴	—	2	1	no	—
446	C₂×Q₈	—	2	1	no	—
447	C₂×Q₈	—	2	1	no	—
448	C₂×Q₈	—	2	1	no	—
449	C₂×Q₈	—	2	1	no	—
450	C₂×Q₈	—	2	1	no	—
451	C₂×Q₈	—	2	1	no	—
452	C₂×Q₈	—	2	1	no	—
453	C₂×Q₈	—	2	1	no	—
454	C₂×Q₈	—	2	1	no	—
455	C₂×Q₈	—	2	1	no	—
456	C₂×Q₈	C₂²×C₄×C₇	1	2	yes	—
457	C₂×Q₈	C₂²×C₄×C₇	1	2	yes	—
458	C₂×D₄	—	2	1	no	—
459	C₂×D₄	—	2	1	no	—
460	C₂×D₄	—	2	1	no	—
461	C₂×D₄	—	2	1	no	—
462	C₂×D₄	—	2	1	no	—
463	C₂×D₄	C₂²×C₄×C₇	1	2	yes	—
464	C₂²×C₄	—	2	1	no	—
465	C₂²×C₄	—	2	1	no	—
466	C₂²×C₄	—	2	1	no	—
467	C₂²×C₄	—	2	1	no	—
468	C₂²×C₄	—	2	1	no	—
469	C₂²×C₄	—	2	1	no	—
470	C₂²×C₄	—	2	1	no	—
471	C₂²×C₄	—	4	2	no	—
472	C₂²×C₄	—	4	2	no	—
473	C₂²×C₄	—	8	1	no	—
474	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
475	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
476	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
477	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
478	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
479	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
480	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
481	Q₁₆	—	4	4	no	—
482	SD₁₆	—	4	4	no	—
483	C₂×C₈	—	2	1	no	—
484	C₂×C₈	—	2	1	no	—
485	C₂×C₈	—	2	1	no	—
486	C₂×C₈	—	2	1	no	—
487	C₂×C₈	—	2	1	no	—
488	C₂×C₈	—	2	1	no	—
489	C₂×C₈	—	2	1	no	—
490	C₂×C₈	—	2	1	no	—
491	C₂×C₈	—	2	1	no	—
492	C₂×C₈	C₂²×C₄×C₇	1	2	yes	—
493	C₂×C₈	C₂²×C₄×C₇	1	2	yes	—
494	C₂×C₈	C₇×#41	1	2	yes	—
495	C₄⋊C₄	—	2	4	no	—
496	C₄⋊C₄	—	2	2	no	—
497	C₄⋊C₄	—	2	1	no	—
498	C₄⋊C₄	—	2	1	no	—
499	C₄⋊C₄	—	2	1	no	—
500	C₄⋊C₄	—	2	1	no	—
501	C₄⋊C₄	—	2	1	no	—
502	C₄⋊C₄	—	2	1	no	—
503	C₄⋊C₄	—	2	1	no	—
504	C₄⋊C₄	—	2	1	no	—
505	C₄⋊C₄	—	4	1	no	—
506	C₄⋊C₄	—	4	2	no	—
507	C₄⋊C₄	—	4	2	no	—
508	C₄⋊C₄	—	8	1	no	—
509	C₄⋊C₄	C₂²×C₄×C₇	1	2	yes	—
510	C₄⋊C₄	C₇×#41	1	2	yes	—
511	C₂²⋊C₄	—	2	4	no	—
512	C₂²⋊C₄	—	2	4	no	—
513	C₂²⋊C₄	—	4	2	no	—
514	C₂²⋊C₄	—	4	2	no	—
515	C₂²⋊C₄	—	8	1	no	—
516	C₄²	—	2	4	no	—
517	C₄²	—	2	1	no	—
518	C₄²	—	2	1	no	—
519	C₄²	—	2	1	no	—
520	C₄²	—	2	1	no	—
521	C₄²	—	4	2	no	—
522	C₄²	—	8	1	no	—
523	C₄²	—	8	1	no	—
524	C₄²	—	8	1	no	—
525	C₄²	C₂²×C₄×C₇	1	2	yes	—
526	C₄²	C₇×#41	1	2	yes	—
527	C₂×C₇	—	8	2	no	—
528	C₂×C₇	#2363	1	1	yes	characteristic
529	C₂×C₇	C₄×#137	1	1	yes	characteristic
530	C₂×C₇	#2952	1	1	yes	characteristic
531	C₂×C₇	#3311	1	1	yes	characteristic
532	C₂×C₇	#3316	1	1	yes	characteristic
533	C₂×C₇	#3400	1	1	yes	characteristic
534	C₂×C₇	#3401	1	1	yes	characteristic
535	C₂³	—	2	2	no	—
536	C₂³	—	4	1	no	—
537	C₂³	—	4	1	no	—
538	C₂³	—	4	1	no	—
539	C₂³	—	4	1	no	—
540	C₂³	—	4	1	no	—
541	C₂³	—	4	1	no	—
542	C₂³	C₂²×C₇×D₄	1	1	yes	characteristic
543	Q₈	—	2	2	no	—
544	Q₈	—	2	2	no	—
545	Q₈	—	2	2	no	—
546	Q₈	—	2	2	no	—
547	Q₈	—	4	1	no	—
548	Q₈	—	4	1	no	—
549	Q₈	—	4	1	no	—
550	Q₈	—	4	1	no	—
551	D₄	—	2	2	no	—
552	D₄	—	2	2	no	—
553	D₄	—	4	1	no	—
554	D₄	—	4	1	no	—
555	C₂×C₄	—	2	1	no	—
556	C₂×C₄	—	2	1	no	—
557	C₂×C₄	—	2	1	no	—
558	C₂×C₄	—	2	1	no	—
559	C₂×C₄	—	2	1	no	—
560	C₂×C₄	—	2	1	no	—
561	C₂×C₄	—	2	2	no	—
562	C₂×C₄	—	2	2	no	—
563	C₂×C₄	—	2	2	no	—
564	C₂×C₄	—	2	1	no	—
565	C₂×C₄	—	2	1	no	—
566	C₂×C₄	—	2	1	no	—
567	C₂×C₄	—	2	2	no	—
568	C₂×C₄	—	2	1	no	—
569	C₂×C₄	—	2	1	no	—
570	C₂×C₄	—	2	1	no	—
571	C₂×C₄	—	2	1	no	—
572	C₂×C₄	—	2	1	no	—
573	C₂×C₄	—	2	1	no	—
574	C₂×C₄	—	4	1	no	—
575	C₂×C₄	—	4	1	no	—
576	C₂×C₄	—	4	1	no	—
577	C₂×C₄	—	4	1	no	—
578	C₂×C₄	—	4	1	no	—
579	C₂×C₄	—	4	1	no	—
580	C₂×C₄	—	4	1	no	—
581	C₂×C₄	—	4	1	no	—
582	C₂×C₄	—	4	1	no	—
583	C₂×C₄	—	4	1	no	—
584	C₂×C₄	—	4	1	no	—
585	C₂×C₄	—	4	1	no	—
586	C₂×C₄	—	4	1	no	—
587	C₂×C₄	—	4	1	no	—
588	C₂×C₄	—	4	1	no	—
589	C₂×C₄	—	4	1	no	—
590	C₂×C₄	—	4	1	no	—
591	C₂×C₄	—	8	4	no	—
592	C₂×C₄	C₄×C₇×D₄	1	2	yes	—
593	C₂×C₄	C₄×C₇×D₄	1	2	yes	—
594	C₂×C₄	C₇×#137	1	2	yes	—
595	C₂×C₄	C₂³×C₄×C₇	1	1	yes	characteristic
596	C₂×C₄	C₂×C₇×#41	1	1	yes	characteristic
597	C₂×C₄	C₂×C₇×#41	1	1	yes	characteristic
598	C₂×C₄	C₂×C₇×#41	1	1	yes	characteristic
599	C₂×C₄	C₇×H(5,𝔽₂)	1	1	yes	characteristic
600	C₂×C₄	C₇×H(5,𝔽₂)	1	1	yes	characteristic
601	C₈	—	2	2	no	—
602	C₈	—	2	2	no	—
603	C₈	—	2	2	no	—
604	C₈	—	4	1	no	—
605	C₇	#23107	1	1	yes	characteristic, direct product factor, Sylow
606	C₂²	—	4	2	no	—
607	C₂²	—	4	2	no	—
608	C₂²	—	4	2	no	—
609	C₂²	—	8	1	no	—
610	C₂²	—	8	1	no	—
611	C₂²	—	8	1	no	—
612	C₂²	—	8	1	no	—
613	C₂²	C₂×C₄×C₇×D₄	1	1	yes	characteristic
614	C₂²	C₇×#546	1	1	yes	characteristic
615	C₂²	C₇×#550	1	1	yes	characteristic
616	C₂²	C₂×C₇×#137	1	1	yes	characteristic
617	C₂²	C₇×#575	1	1	yes	characteristic
618	C₂²	C₇×#577	1	1	yes	characteristic
619	C₂²	C₇×#577	1	1	yes	characteristic
620	C₄	—	2	2	no	—
621	C₄	—	2	2	no	—
622	C₄	—	2	2	no	—
623	C₄	—	4	2	no	—
624	C₄	—	4	1	no	—
625	C₄	—	4	1	no	—
626	C₄	—	4	2	no	—
627	C₄	—	4	1	no	—
628	C₄	—	4	2	no	—
629	C₄	—	4	2	no	—
630	C₄	—	8	1	no	—
631	C₄	—	8	1	no	—
632	C₄	—	8	1	no	—
633	C₄	C₄×C₇×#41	1	1	yes	characteristic
634	C₄	C₇×#518	1	1	yes	characteristic
635	C₄	C₇×#553	1	1	yes	characteristic
636	C₄	C₇×#555	1	1	yes	characteristic
637	C₂	—	8	2	no	—
638	C₂	C₇×#2363	1	1	yes	characteristic
639	C₂	C₄×C₇×#137	1	1	yes	characteristic
640	C₂	C₇×#2952	1	1	yes	characteristic
641	C₂	C₇×#3311	1	1	yes	characteristic
642	C₂	C₇×#3316	1	1	yes	characteristic
643	C₂	C₇×#3400	1	1	yes	characteristic
644	C₂	C₇×#3401	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	C₂²×C₇×D₄	C₂³
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₇ ◁ C₄×C₇×C₄⋊C₄ ◁ G

Complements

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

N	H ≅ G/N	type
3. C₇×#2355	C₂	semidirect
4. C₇×#1971	C₂	semidirect
7. C₇×#1948	C₂	semidirect
8. C₇×#1927	C₂	semidirect
10. C₇×#1878	C₂	semidirect
12. C₇×#1771	C₂	semidirect
13. C₇×#1763	C₂	semidirect
15. C₄×C₇×#103	C₂	semidirect
22. C₇×#464	C₄	semidirect
60. #23107	C₇	direct (N × H)
67. C₂×C₇×Q₁₆	C₂×C₄	semidirect
80. C₄×C₇×Q₈	C₂×C₄	semidirect
109. C₇×C₄⋊C₈	C₂×C₄	semidirect
114. C₇×#103	C₂×C₄	semidirect
134. #2355	C₂×C₇	semidirect
135. #1971	C₂×C₇	semidirect
138. #1948	C₂×C₇	semidirect
139. #1927	C₂×C₇	semidirect
141. #1878	C₂×C₇	semidirect
143. #1771	C₂×C₇	semidirect
144. #1763	C₂×C₇	semidirect
146. C₄×#103	C₂×C₇	semidirect
235. #464	C₄×C₇	semidirect
349. C₂×Q₁₆	C₂×C₄×C₇	semidirect
362. C₄×Q₈	C₂×C₄×C₇	semidirect
391. C₄⋊C₈	C₂×C₄×C₇	semidirect
396. #103	C₂×C₄×C₇	semidirect
605. C₇	#23107	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×#464	2
C₇×#2367	2
C₇×#2355	2
C₇×#1971	2
C₇×#1968	2
C₇×#1959	2
C₇×#1948	2
C₇×#1927	2
C₇×#1926	2
C₇×#1878	2
C₇×#1877	2
C₇×#1771	2
C₇×#1763	2
C₇×#1762	2
C₄×C₇×#103	2
#23107	7

Subgroups — C7×#23107 #13200323

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×#23107 #13200323