Subgroups — C₇×#22077 #13199293

Order 1792.

824 conjugacy classes of subgroups.

The subgroup lattice has 624 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₇×#485	C₂	1	1	yes	maximal, characteristic
2	C₄×C₇×C₂²⋊Q₈	C₂	1	1	yes	maximal, characteristic
3	C₇×#2296	C₂	1	1	yes	maximal, characteristic
4	C₇×#1942	C₂	1	1	yes	maximal, characteristic, complemented
5	C₇×#1941	C₂	1	1	yes	maximal, characteristic, complemented
6	C₇×#1933	C₂	1	1	yes	maximal, characteristic, complemented
7	C₇×#1933	C₂	1	1	yes	maximal, characteristic, complemented
8	C₇×#1920	C₂	1	1	yes	maximal, characteristic, complemented
9	C₇×#1918	C₂	1	1	yes	maximal, characteristic, complemented
10	C₇×#1873	C₂	1	1	yes	maximal, characteristic
11	C₇×#1865	C₂	1	1	yes	maximal, characteristic, complemented
12	C₇×#1863	C₂	1	1	yes	maximal, characteristic, complemented
13	C₇×#1854	C₂	1	1	yes	maximal, characteristic
14	C₇×#1825	C₂	1	1	yes	maximal, characteristic
15	C₄×C₇×C₂²⋊C₈	C₂	1	1	yes	maximal, characteristic
16	C₂×C₇×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
17	C₂×C₄×C₇×Q₈	C₂²	1	1	yes	characteristic
18	C₂×C₇×#117	C₂²	1	1	yes	characteristic
19	C₂×C₇×#117	C₂²	1	1	yes	characteristic
20	C₂²×C₄²×C₇	C₂²	1	1	yes	characteristic
21	C₇×#485	C₄	1	8	yes	complemented
22	C₂×C₇×#107	C₂²	1	1	yes	characteristic
23	C₂×C₇×#107	C₂²	1	1	yes	characteristic
24	C₂×C₇×#106	C₂²	1	1	yes	characteristic
25	C₂×C₇×#106	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×C₂²⋊C₈	C₂²	1	1	yes	characteristic
31	C₂×C₇×C₂²⋊C₈	C₂²	1	1	yes	characteristic
32	C₂×C₄×C₇×C₈	C₂²	1	1	yes	characteristic
33	C₂×C₄×C₇×C₈	C₂²	1	1	yes	characteristic
34	C₇×#391	C₂²	1	1	yes	characteristic
35	C₇×#389	C₂²	1	1	yes	characteristic
36	C₇×#389	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×#387	—	2	1	no	—
41	C₇×#385	—	2	1	no	—
42	C₇×#385	—	2	1	no	—
43	C₇×#385	—	2	1	no	—
44	C₇×#380	C₂²	1	1	yes	characteristic
45	C₄×C₇×C₄⋊C₄	—	2	1	no	—
46	C₄×C₇×C₄⋊C₄	—	2	1	no	—
47	C₄×C₇×C₄⋊C₄	—	2	1	no	—
48	C₄×C₇×C₄⋊C₄	C₂²	1	1	yes	characteristic
49	C₄×C₇×C₂²⋊C₄	—	2	1	no	—
50	C₇×#340	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×#340	C₂²	1	1	yes	characteristic
58	C₇×#336	C₂²	1	1	yes	characteristic
59	C₇×#336	C₂²	1	1	yes	characteristic
60	#22077	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
61	C₂²×C₇×Q₈	C₂³	1	1	yes	characteristic
62	C₂³×C₄×C₇	D₄	1	1	yes	characteristic
63	C₂³×C₄×C₇	D₄	1	1	yes	characteristic
64	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
65	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
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	C₇×C₂²⋊Q₈	—	2	2	no	—
70	C₇×C₂²⋊Q₈	C₂×C₄	1	4	yes	—
71	C₄×C₇×Q₈	—	4	1	no	—
72	C₄×C₇×Q₈	—	4	1	no	—
73	C₇×#117	—	2	2	no	—
74	C₇×#117	—	4	1	no	—
75	C₇×#117	—	4	1	no	—
76	C₇×#117	C₂×C₄	1	4	yes	—
77	C₂×C₇×C₄⋊C₄	—	2	1	no	—
78	C₂×C₇×C₄⋊C₄	—	2	1	no	—
79	C₂×C₇×C₄⋊C₄	—	2	1	no	—
80	C₂×C₇×C₄⋊C₄	—	2	1	no	—
81	C₂×C₇×C₄⋊C₄	—	2	1	no	—
82	C₂×C₇×C₄⋊C₄	—	2	1	no	—
83	C₂×C₇×C₄⋊C₄	—	2	1	no	—
84	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
85	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
86	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
87	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
88	C₂×C₇×C₄⋊C₄	C₂³	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×C₂²⋊C₄	—	2	1	no	—
92	C₂×C₇×C₂²⋊C₄	—	2	1	no	—
93	C₂×C₇×C₂²⋊C₄	—	2	1	no	—
94	C₂×C₇×C₂²⋊C₄	—	2	1	no	—
95	C₂×C₄²×C₇	—	2	1	no	—
96	C₂×C₄²×C₇	—	2	1	no	—
97	C₂×C₄²×C₇	—	2	1	no	—
98	C₂×C₄²×C₇	—	2	1	no	—
99	C₂×C₄²×C₇	—	4	1	no	—
100	C₂×C₄²×C₇	—	4	1	no	—
101	C₂×C₄²×C₇	D₄	1	1	yes	characteristic
102	C₂×C₄²×C₇	D₄	1	1	yes	characteristic
103	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
104	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
105	C₇×#107	—	4	1	no	—
106	C₇×#107	C₂×C₄	1	4	yes	complemented
107	C₇×#106	—	4	1	no	—
108	C₇×#106	C₂×C₄	1	4	yes	complemented
109	C₇×#103	—	4	1	no	—
110	C₇×#103	—	4	1	no	—
111	C₇×#103	C₂×C₄	1	4	yes	complemented
112	C₇×#103	C₂×C₄	1	4	yes	complemented
113	C₇×C₂²⋊C₈	—	2	2	no	—
114	C₇×C₂²⋊C₈	C₂×C₄	1	4	yes	—
115	C₄×C₇×C₈	—	4	1	no	—
116	C₄×C₇×C₈	—	4	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	C₇×#95	—	2	1	no	—
123	C₇×#95	—	2	1	no	—
124	C₇×#95	—	2	1	no	—
125	C₇×#95	—	2	1	no	—
126	C₂×#485	C₂×C₇	1	1	yes	characteristic
127	C₄×C₂²⋊Q₈	C₂×C₇	1	1	yes	characteristic
128	#2296	C₂×C₇	1	1	yes	characteristic
129	#1942	C₂×C₇	1	1	yes	characteristic, complemented
130	#1941	C₂×C₇	1	1	yes	characteristic, complemented
131	#1933	C₂×C₇	1	1	yes	characteristic, complemented
132	#1933	C₂×C₇	1	1	yes	characteristic, complemented
133	#1920	C₂×C₇	1	1	yes	characteristic, complemented
134	#1918	C₂×C₇	1	1	yes	characteristic, complemented
135	#1873	C₂×C₇	1	1	yes	characteristic
136	#1865	C₂×C₇	1	1	yes	characteristic, complemented
137	#1863	C₂×C₇	1	1	yes	characteristic, complemented
138	#1854	C₂×C₇	1	1	yes	characteristic
139	#1825	C₂×C₇	1	1	yes	characteristic
140	C₄×C₂²⋊C₈	C₂×C₇	1	1	yes	characteristic
141	C₂⁴×C₇	C₂×D₄	1	1	yes	characteristic
142	C₂×C₇×Q₈	—	2	1	no	—
143	C₂×C₇×Q₈	—	2	1	no	—
144	C₂×C₇×Q₈	—	2	1	no	—
145	C₂×C₇×Q₈	—	2	1	no	—
146	C₂×C₇×Q₈	—	2	1	no	—
147	C₂×C₇×Q₈	C₂²×C₄	1	2	yes	—
148	C₂²×C₄×C₇	—	2	1	no	—
149	C₂²×C₄×C₇	—	2	1	no	—
150	C₂²×C₄×C₇	—	2	1	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	2	no	—
157	C₂²×C₄×C₇	—	2	2	no	—
158	C₂²×C₄×C₇	—	2	2	no	—
159	C₂²×C₄×C₇	—	2	1	no	—
160	C₂²×C₄×C₇	—	2	1	no	—
161	C₂²×C₄×C₇	—	2	1	no	—
162	C₂²×C₄×C₇	—	2	1	no	—
163	C₂²×C₄×C₇	—	4	1	no	—
164	C₂²×C₄×C₇	—	4	1	no	—
165	C₂²×C₄×C₇	—	4	1	no	—
166	C₂²×C₄×C₇	C₂²×C₄	1	2	yes	—
167	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
168	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
169	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
170	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
171	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
172	C₂²×C₄×C₇	#41	1	2	yes	—
173	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
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	—	2	1	no	—
179	C₂×C₇×C₈	—	2	1	no	—
180	C₂×C₇×C₈	—	2	1	no	—
181	C₂×C₇×C₈	—	2	1	no	—
182	C₂×C₇×C₈	—	2	1	no	—
183	C₂×C₇×C₈	—	2	1	no	—
184	C₂×C₇×C₈	C₂²×C₄	1	2	yes	—
185	C₂×C₇×C₈	C₂²×C₄	1	2	yes	—
186	C₇×C₄⋊C₄	—	2	4	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	—	2	1	no	—
192	C₇×C₄⋊C₄	—	2	1	no	—
193	C₇×C₄⋊C₄	—	2	1	no	—
194	C₇×C₄⋊C₄	—	2	1	no	—
195	C₇×C₄⋊C₄	—	2	1	no	—
196	C₇×C₄⋊C₄	—	2	1	no	—
197	C₇×C₄⋊C₄	—	2	1	no	—
198	C₇×C₄⋊C₄	—	4	2	no	—
199	C₇×C₄⋊C₄	—	4	2	no	—
200	C₇×C₄⋊C₄	—	4	2	no	—
201	C₇×C₄⋊C₄	—	4	2	no	—
202	C₇×C₄⋊C₄	—	4	2	no	—
203	C₇×C₄⋊C₄	—	4	2	no	—
204	C₇×C₄⋊C₄	C₂²×C₄	1	2	yes	—
205	C₇×C₄⋊C₄	C₂²×C₄	1	2	yes	—
206	C₇×C₄⋊C₄	C₂²×C₄	1	2	yes	—
207	C₇×C₂²⋊C₄	—	2	4	no	—
208	C₇×C₂²⋊C₄	—	2	4	no	—
209	C₇×C₂²⋊C₄	—	4	2	no	—
210	C₇×C₂²⋊C₄	—	4	2	no	—
211	C₄²×C₇	—	2	4	no	—
212	C₄²×C₇	—	2	1	no	—
213	C₄²×C₇	—	2	1	no	—
214	C₄²×C₇	—	2	1	no	—
215	C₄²×C₇	—	2	1	no	—
216	C₄²×C₇	—	4	1	no	—
217	C₄²×C₇	—	4	1	no	—
218	C₄²×C₇	—	4	2	no	—
219	C₄²×C₇	—	4	2	no	—
220	C₄²×C₇	—	4	2	no	—
221	C₂×C₂²⋊Q₈	C₂²×C₇	1	1	yes	characteristic
222	C₂×C₄×Q₈	C₂²×C₇	1	1	yes	characteristic
223	C₂×#117	C₂²×C₇	1	1	yes	characteristic
224	C₂×#117	C₂²×C₇	1	1	yes	characteristic
225	C₂²×C₄²	C₂²×C₇	1	1	yes	characteristic
226	#485	C₄×C₇	1	8	yes	complemented
227	C₂×#107	C₂²×C₇	1	1	yes	characteristic
228	C₂×#107	C₂²×C₇	1	1	yes	characteristic
229	C₂×#106	C₂²×C₇	1	1	yes	characteristic
230	C₂×#106	C₂²×C₇	1	1	yes	characteristic
231	C₂×#103	C₂²×C₇	1	1	yes	characteristic
232	C₂×#103	C₂²×C₇	1	1	yes	characteristic
233	C₂×#103	C₂²×C₇	1	1	yes	characteristic
234	C₂×#103	C₂²×C₇	1	1	yes	characteristic
235	C₂×C₂²⋊C₈	C₂²×C₇	1	1	yes	characteristic
236	C₂×C₂²⋊C₈	C₂²×C₇	1	1	yes	characteristic
237	C₂×C₄×C₈	C₂²×C₇	1	1	yes	characteristic
238	C₂×C₄×C₈	C₂²×C₇	1	1	yes	characteristic
239	#391	C₂²×C₇	1	1	yes	characteristic
240	#389	C₂²×C₇	1	1	yes	characteristic
241	#389	C₂²×C₇	1	1	yes	characteristic
242	#389	C₂²×C₇	1	1	yes	characteristic
243	#389	C₂²×C₇	1	1	yes	characteristic
244	#389	C₂²×C₇	1	1	yes	characteristic
245	#387	—	2	1	no	—
246	#385	—	2	1	no	—
247	#385	—	2	1	no	—
248	#385	—	2	1	no	—
249	#380	C₂²×C₇	1	1	yes	characteristic
250	C₄×C₄⋊C₄	—	2	1	no	—
251	C₄×C₄⋊C₄	—	2	1	no	—
252	C₄×C₄⋊C₄	—	2	1	no	—
253	C₄×C₄⋊C₄	C₂²×C₇	1	1	yes	characteristic
254	C₄×C₂²⋊C₄	—	2	1	no	—
255	#340	C₂²×C₇	1	1	yes	characteristic
256	#340	C₂²×C₇	1	1	yes	characteristic
257	#340	C₂²×C₇	1	1	yes	characteristic
258	#340	C₂²×C₇	1	1	yes	characteristic
259	#340	C₂²×C₇	1	1	yes	characteristic
260	#340	C₂²×C₇	1	1	yes	characteristic
261	#340	C₂²×C₇	1	1	yes	characteristic
262	#340	C₂²×C₇	1	1	yes	characteristic
263	#336	C₂²×C₇	1	1	yes	characteristic
264	#336	C₂²×C₇	1	1	yes	characteristic
265	C₂³×C₇	—	2	1	no	—
266	C₂³×C₇	—	2	1	no	—
267	C₂³×C₇	—	2	1	no	—
268	C₂³×C₇	—	2	1	no	—
269	C₂³×C₇	—	2	1	no	—
270	C₂³×C₇	—	2	1	no	—
271	C₂³×C₇	C₄×D₄	1	2	yes	—
272	C₂³×C₇	C₂²×D₄	1	1	yes	characteristic
273	C₇×Q₈	—	2	2	no	—
274	C₇×Q₈	—	2	2	no	—
275	C₇×Q₈	—	4	1	no	—
276	C₇×Q₈	—	4	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	1	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	2	no	—
286	C₂×C₄×C₇	—	2	2	no	—
287	C₂×C₄×C₇	—	2	2	no	—
288	C₂×C₄×C₇	—	2	2	no	—
289	C₂×C₄×C₇	—	2	2	no	—
290	C₂×C₄×C₇	—	2	2	no	—
291	C₂×C₄×C₇	—	2	2	no	—
292	C₂×C₄×C₇	—	2	2	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	—	4	4	no	—
297	C₂×C₄×C₇	—	4	4	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	—	4	1	no	—
309	C₂×C₄×C₇	—	4	1	no	—
310	C₂×C₄×C₇	—	4	1	no	—
311	C₂×C₄×C₇	—	4	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	C₄×D₄	1	2	yes	—
319	C₂×C₄×C₇	#135	1	2	yes	—
320	C₂×C₄×C₇	#135	1	2	yes	—
321	C₂×C₄×C₇	#137	1	2	yes	—
322	C₂×C₄×C₇	C₂³×C₄	1	1	yes	characteristic
323	C₂×C₄×C₇	C₂×#41	1	1	yes	characteristic
324	C₂×C₄×C₇	H(5,𝔽₂)	1	1	yes	characteristic
325	C₂×C₄×C₇	H(5,𝔽₂)	1	1	yes	characteristic
326	C₂×C₄×C₇	2₋¹⁺⁴	1	1	yes	characteristic
327	C₂×C₄×C₇	2₋¹⁺⁴	1	1	yes	characteristic
328	C₇×C₈	—	2	2	no	—
329	C₇×C₈	—	2	2	no	—
330	C₇×C₈	—	4	1	no	—
331	C₇×C₈	—	4	1	no	—
332	C₂²×Q₈	C₂³×C₇	1	1	yes	characteristic
333	C₂³×C₄	C₇×D₄	1	1	yes	characteristic
334	C₂³×C₄	C₇×D₄	1	1	yes	characteristic
335	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
336	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
337	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
338	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
339	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
340	C₂²⋊Q₈	—	2	2	no	—
341	C₂²⋊Q₈	C₂×C₄×C₇	1	4	yes	—
342	C₄×Q₈	—	4	1	no	—
343	C₄×Q₈	—	4	1	no	—
344	#117	—	2	2	no	—
345	#117	—	4	1	no	—
346	#117	—	4	1	no	—
347	#117	C₂×C₄×C₇	1	4	yes	—
348	C₂×C₄⋊C₄	—	2	1	no	—
349	C₂×C₄⋊C₄	—	2	1	no	—
350	C₂×C₄⋊C₄	—	2	1	no	—
351	C₂×C₄⋊C₄	—	2	1	no	—
352	C₂×C₄⋊C₄	—	2	1	no	—
353	C₂×C₄⋊C₄	—	2	1	no	—
354	C₂×C₄⋊C₄	—	2	1	no	—
355	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
356	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
357	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
358	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
359	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
360	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
361	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
362	C₂×C₂²⋊C₄	—	2	1	no	—
363	C₂×C₂²⋊C₄	—	2	1	no	—
364	C₂×C₂²⋊C₄	—	2	1	no	—
365	C₂×C₂²⋊C₄	—	2	1	no	—
366	C₂×C₄²	—	2	1	no	—
367	C₂×C₄²	—	2	1	no	—
368	C₂×C₄²	—	2	1	no	—
369	C₂×C₄²	—	2	1	no	—
370	C₂×C₄²	—	4	1	no	—
371	C₂×C₄²	—	4	1	no	—
372	C₂×C₄²	C₇×D₄	1	1	yes	characteristic
373	C₂×C₄²	C₇×D₄	1	1	yes	characteristic
374	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
375	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
376	#107	—	4	1	no	—
377	#107	C₂×C₄×C₇	1	4	yes	complemented
378	#106	—	4	1	no	—
379	#106	C₂×C₄×C₇	1	4	yes	complemented
380	#103	—	4	1	no	—
381	#103	—	4	1	no	—
382	#103	C₂×C₄×C₇	1	4	yes	complemented
383	#103	C₂×C₄×C₇	1	4	yes	complemented
384	C₂²⋊C₈	—	2	2	no	—
385	C₂²⋊C₈	C₂×C₄×C₇	1	4	yes	—
386	C₄×C₈	—	4	1	no	—
387	C₄×C₈	—	4	1	no	—
388	#95	—	2	1	no	—
389	#95	—	2	1	no	—
390	#95	—	2	1	no	—
391	#95	—	2	1	no	—
392	#95	—	2	1	no	—
393	#95	—	2	1	no	—
394	#95	—	2	1	no	—
395	#95	—	2	1	no	—
396	#95	—	2	1	no	—
397	C₂²×C₇	—	2	2	no	—
398	C₂²×C₇	—	2	2	no	—
399	C₂²×C₇	—	2	2	no	—
400	C₂²×C₇	—	4	1	no	—
401	C₂²×C₇	—	4	1	no	—
402	C₂²×C₇	—	4	1	no	—
403	C₂²×C₇	—	4	1	no	—
404	C₂²×C₇	C₂×C₄×D₄	1	1	yes	characteristic
405	C₂²×C₇	#534	1	1	yes	characteristic
406	C₂²×C₇	#536	1	1	yes	characteristic
407	C₂²×C₇	C₂×#135	1	1	yes	characteristic
408	C₂²×C₇	C₂×#135	1	1	yes	characteristic
409	C₂²×C₇	C₂×#137	1	1	yes	characteristic
410	C₂²×C₇	#575	1	1	yes	characteristic
411	C₄×C₇	—	2	2	no	—
412	C₄×C₇	—	2	2	no	—
413	C₄×C₇	—	2	2	no	—
414	C₄×C₇	—	2	2	no	—
415	C₄×C₇	—	4	2	no	—
416	C₄×C₇	—	4	1	no	—
417	C₄×C₇	—	4	2	no	—
418	C₄×C₇	—	4	2	no	—
419	C₄×C₇	—	4	2	no	—
420	C₄×C₇	—	8	1	no	—
421	C₄×C₇	—	8	1	no	—
422	C₄×C₇	—	8	1	no	—
423	C₄×C₇	—	8	1	no	—
424	C₄×C₇	#520	1	1	yes	characteristic
425	C₄×C₇	#520	1	1	yes	characteristic
426	C₄×C₇	#539	1	1	yes	characteristic
427	C₄×C₇	#539	1	1	yes	characteristic
428	C₂⁴	C₂×C₇×D₄	1	1	yes	characteristic
429	C₂×Q₈	—	2	1	no	—
430	C₂×Q₈	—	2	1	no	—
431	C₂×Q₈	—	2	1	no	—
432	C₂×Q₈	—	2	1	no	—
433	C₂×Q₈	—	2	1	no	—
434	C₂×Q₈	C₂²×C₄×C₇	1	2	yes	—
435	C₂²×C₄	—	2	1	no	—
436	C₂²×C₄	—	2	1	no	—
437	C₂²×C₄	—	2	1	no	—
438	C₂²×C₄	—	2	1	no	—
439	C₂²×C₄	—	2	1	no	—
440	C₂²×C₄	—	2	1	no	—
441	C₂²×C₄	—	2	1	no	—
442	C₂²×C₄	—	2	1	no	—
443	C₂²×C₄	—	2	2	no	—
444	C₂²×C₄	—	2	2	no	—
445	C₂²×C₄	—	2	2	no	—
446	C₂²×C₄	—	2	1	no	—
447	C₂²×C₄	—	2	1	no	—
448	C₂²×C₄	—	2	1	no	—
449	C₂²×C₄	—	2	1	no	—
450	C₂²×C₄	—	4	1	no	—
451	C₂²×C₄	—	4	1	no	—
452	C₂²×C₄	—	4	1	no	—
453	C₂²×C₄	C₂²×C₄×C₇	1	2	yes	—
454	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
455	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
456	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
457	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
458	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
459	C₂²×C₄	C₇×#41	1	2	yes	—
460	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
461	C₂×C₈	—	2	1	no	—
462	C₂×C₈	—	2	1	no	—
463	C₂×C₈	—	2	1	no	—
464	C₂×C₈	—	2	1	no	—
465	C₂×C₈	—	2	1	no	—
466	C₂×C₈	—	2	1	no	—
467	C₂×C₈	—	2	1	no	—
468	C₂×C₈	—	2	1	no	—
469	C₂×C₈	—	2	1	no	—
470	C₂×C₈	—	2	1	no	—
471	C₂×C₈	C₂²×C₄×C₇	1	2	yes	—
472	C₂×C₈	C₂²×C₄×C₇	1	2	yes	—
473	C₄⋊C₄	—	2	4	no	—
474	C₄⋊C₄	—	2	1	no	—
475	C₄⋊C₄	—	2	1	no	—
476	C₄⋊C₄	—	2	1	no	—
477	C₄⋊C₄	—	2	1	no	—
478	C₄⋊C₄	—	2	1	no	—
479	C₄⋊C₄	—	2	1	no	—
480	C₄⋊C₄	—	2	1	no	—
481	C₄⋊C₄	—	2	1	no	—
482	C₄⋊C₄	—	2	1	no	—
483	C₄⋊C₄	—	2	1	no	—
484	C₄⋊C₄	—	2	1	no	—
485	C₄⋊C₄	—	4	2	no	—
486	C₄⋊C₄	—	4	2	no	—
487	C₄⋊C₄	—	4	2	no	—
488	C₄⋊C₄	—	4	2	no	—
489	C₄⋊C₄	—	4	2	no	—
490	C₄⋊C₄	—	4	2	no	—
491	C₄⋊C₄	C₂²×C₄×C₇	1	2	yes	—
492	C₄⋊C₄	C₂²×C₄×C₇	1	2	yes	—
493	C₄⋊C₄	C₂²×C₄×C₇	1	2	yes	—
494	C₂²⋊C₄	—	2	4	no	—
495	C₂²⋊C₄	—	2	4	no	—
496	C₂²⋊C₄	—	4	2	no	—
497	C₂²⋊C₄	—	4	2	no	—
498	C₄²	—	2	4	no	—
499	C₄²	—	2	1	no	—
500	C₄²	—	2	1	no	—
501	C₄²	—	2	1	no	—
502	C₄²	—	2	1	no	—
503	C₄²	—	4	1	no	—
504	C₄²	—	4	1	no	—
505	C₄²	—	4	2	no	—
506	C₄²	—	4	2	no	—
507	C₄²	—	4	2	no	—
508	C₂×C₇	—	4	2	no	—
509	C₂×C₇	#2322	1	1	yes	characteristic
510	C₂×C₇	C₄×#135	1	1	yes	characteristic
511	C₂×C₇	C₄×#137	1	1	yes	characteristic
512	C₂×C₇	#3190	1	1	yes	characteristic
513	C₂×C₇	#3191	1	1	yes	characteristic
514	C₂×C₇	#3231	1	1	yes	characteristic
515	C₂×C₇	#3233	1	1	yes	characteristic
516	C₂³	—	2	1	no	—
517	C₂³	—	2	1	no	—
518	C₂³	—	2	1	no	—
519	C₂³	—	2	1	no	—
520	C₂³	—	2	1	no	—
521	C₂³	—	2	1	no	—
522	C₂³	C₄×C₇×D₄	1	2	yes	—
523	C₂³	C₂²×C₇×D₄	1	1	yes	characteristic
524	Q₈	—	2	2	no	—
525	Q₈	—	2	2	no	—
526	Q₈	—	4	1	no	—
527	Q₈	—	4	1	no	—
528	C₂×C₄	—	2	1	no	—
529	C₂×C₄	—	2	1	no	—
530	C₂×C₄	—	2	1	no	—
531	C₂×C₄	—	2	1	no	—
532	C₂×C₄	—	2	1	no	—
533	C₂×C₄	—	2	1	no	—
534	C₂×C₄	—	2	1	no	—
535	C₂×C₄	—	2	1	no	—
536	C₂×C₄	—	2	2	no	—
537	C₂×C₄	—	2	2	no	—
538	C₂×C₄	—	2	2	no	—
539	C₂×C₄	—	2	2	no	—
540	C₂×C₄	—	2	2	no	—
541	C₂×C₄	—	2	2	no	—
542	C₂×C₄	—	2	2	no	—
543	C₂×C₄	—	2	2	no	—
544	C₂×C₄	—	2	1	no	—
545	C₂×C₄	—	2	1	no	—
546	C₂×C₄	—	2	1	no	—
547	C₂×C₄	—	4	4	no	—
548	C₂×C₄	—	4	4	no	—
549	C₂×C₄	—	4	1	no	—
550	C₂×C₄	—	4	1	no	—
551	C₂×C₄	—	4	1	no	—
552	C₂×C₄	—	4	1	no	—
553	C₂×C₄	—	4	1	no	—
554	C₂×C₄	—	4	1	no	—
555	C₂×C₄	—	4	1	no	—
556	C₂×C₄	—	4	1	no	—
557	C₂×C₄	—	4	1	no	—
558	C₂×C₄	—	4	1	no	—
559	C₂×C₄	—	4	1	no	—
560	C₂×C₄	—	4	1	no	—
561	C₂×C₄	—	4	1	no	—
562	C₂×C₄	—	4	1	no	—
563	C₂×C₄	—	4	1	no	—
564	C₂×C₄	—	4	1	no	—
565	C₂×C₄	—	4	1	no	—
566	C₂×C₄	—	4	1	no	—
567	C₂×C₄	—	4	1	no	—
568	C₂×C₄	—	4	1	no	—
569	C₂×C₄	C₄×C₇×D₄	1	2	yes	—
570	C₂×C₄	C₇×#135	1	2	yes	—
571	C₂×C₄	C₇×#135	1	2	yes	—
572	C₂×C₄	C₇×#137	1	2	yes	—
573	C₂×C₄	C₂³×C₄×C₇	1	1	yes	characteristic
574	C₂×C₄	C₂×C₇×#41	1	1	yes	characteristic
575	C₂×C₄	C₇×H(5,𝔽₂)	1	1	yes	characteristic
576	C₂×C₄	C₇×H(5,𝔽₂)	1	1	yes	characteristic
577	C₂×C₄	C₇×2₋¹⁺⁴	1	1	yes	characteristic
578	C₂×C₄	C₇×2₋¹⁺⁴	1	1	yes	characteristic
579	C₈	—	2	2	no	—
580	C₈	—	2	2	no	—
581	C₈	—	4	1	no	—
582	C₈	—	4	1	no	—
583	C₇	#22077	1	1	yes	characteristic, direct product factor, Sylow
584	C₂²	—	2	2	no	—
585	C₂²	—	2	2	no	—
586	C₂²	—	2	2	no	—
587	C₂²	—	4	1	no	—
588	C₂²	—	4	1	no	—
589	C₂²	—	4	1	no	—
590	C₂²	—	4	1	no	—
591	C₂²	C₂×C₄×C₇×D₄	1	1	yes	characteristic
592	C₂²	C₇×#534	1	1	yes	characteristic
593	C₂²	C₇×#536	1	1	yes	characteristic
594	C₂²	C₂×C₇×#135	1	1	yes	characteristic
595	C₂²	C₂×C₇×#135	1	1	yes	characteristic
596	C₂²	C₂×C₇×#137	1	1	yes	characteristic
597	C₂²	C₇×#575	1	1	yes	characteristic
598	C₄	—	2	2	no	—
599	C₄	—	2	2	no	—
600	C₄	—	2	2	no	—
601	C₄	—	2	2	no	—
602	C₄	—	4	1	no	—
603	C₄	—	4	2	no	—
604	C₄	—	4	2	no	—
605	C₄	—	4	2	no	—
606	C₄	—	4	2	no	—
607	C₄	—	8	1	no	—
608	C₄	—	8	1	no	—
609	C₄	—	8	1	no	—
610	C₄	—	8	1	no	—
611	C₄	C₇×#520	1	1	yes	characteristic
612	C₄	C₇×#520	1	1	yes	characteristic
613	C₄	C₇×#539	1	1	yes	characteristic
614	C₄	C₇×#539	1	1	yes	characteristic
615	C₂	—	4	2	no	—
616	C₂	C₇×#2322	1	1	yes	characteristic
617	C₂	C₄×C₇×#135	1	1	yes	characteristic
618	C₂	C₄×C₇×#137	1	1	yes	characteristic
619	C₂	C₇×#3190	1	1	yes	characteristic
620	C₂	C₇×#3191	1	1	yes	characteristic
621	C₂	C₇×#3231	1	1	yes	characteristic
622	C₂	C₇×#3233	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	C₂⁴×C₇	C₂×D₄
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₇ ◁ C₂²×C₄²×C₇ ◁ G

Complements

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

N	H ≅ G/N	type
4. C₇×#1942	C₂	semidirect
5. C₇×#1941	C₂	semidirect
6. C₇×#1933	C₂	semidirect
7. C₇×#1933	C₂	semidirect
8. C₇×#1920	C₂	semidirect
9. C₇×#1918	C₂	semidirect
11. C₇×#1865	C₂	semidirect
12. C₇×#1863	C₂	semidirect
21. C₇×#485	C₄	semidirect
60. #22077	C₇	direct (N × H)
106. C₇×#107	C₂×C₄	semidirect
108. C₇×#106	C₂×C₄	semidirect
111. C₇×#103	C₂×C₄	semidirect
112. C₇×#103	C₂×C₄	semidirect
129. #1942	C₂×C₇	semidirect
130. #1941	C₂×C₇	semidirect
131. #1933	C₂×C₇	semidirect
132. #1933	C₂×C₇	semidirect
133. #1920	C₂×C₇	semidirect
134. #1918	C₂×C₇	semidirect
136. #1865	C₂×C₇	semidirect
137. #1863	C₂×C₇	semidirect
226. #485	C₄×C₇	semidirect
377. #107	C₂×C₄×C₇	semidirect
379. #106	C₂×C₄×C₇	semidirect
382. #103	C₂×C₄×C₇	semidirect
383. #103	C₂×C₄×C₇	semidirect
583. C₇	#22077	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×#485	2
C₄×C₇×C₂²⋊Q₈	2
C₇×#2296	2
C₇×#1942	2
C₇×#1941	2
C₇×#1933	2
C₇×#1920	2
C₇×#1918	2
C₇×#1873	2
C₇×#1865	2
C₇×#1863	2
C₇×#1854	2
C₇×#1825	2
C₄×C₇×C₂²⋊C₈	2
#22077	7

Subgroups — C7×#22077 #13199293

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×#22077 #13199293