Subgroups — C₇×#21514 #13198730

Order 1792.

1008 conjugacy classes of subgroups.

The subgroup lattice has 666 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₇×#461	C₂	1	1	yes	maximal, characteristic
2	C₂×C₇×#440	C₂	1	1	yes	maximal, characteristic
3	C₂×C₄×C₇×SD₁₆	C₂	1	1	yes	maximal, characteristic
4	C₇×#2327	C₂	1	1	yes	maximal, characteristic, complemented
5	C₇×#2275	C₂	1	1	yes	maximal, characteristic
6	C₇×#1981	C₂	1	1	yes	maximal, characteristic, complemented
7	C₇×#1949	C₂	1	1	yes	maximal, characteristic, complemented
8	C₇×#1928	C₂	1	1	yes	maximal, characteristic, complemented
9	C₇×#1927	C₂	1	1	yes	maximal, characteristic, complemented
10	C₇×#1877	C₂	1	1	yes	maximal, characteristic
11	C₇×#1877	C₂	1	1	yes	maximal, characteristic
12	C₇×#1804	C₂	1	1	yes	maximal, characteristic
13	C₇×#1768	C₂	1	1	yes	maximal, characteristic, complemented
14	C₇×#1763	C₂	1	1	yes	maximal, characteristic, complemented
15	C₄×C₇×#103	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×C₇×SD₁₆	C₂²	1	1	yes	characteristic
17	C₂²×C₇×SD₁₆	C₂²	1	1	yes	characteristic
18	C₂×C₇×C₄⋊Q₈	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	C₂×C₄×C₇×D₄	C₂²	1	1	yes	characteristic
23	C₂×C₄×C₇×D₄	C₂²	1	1	yes	characteristic
24	C₇×#461	C₄	1	8	yes	complemented
25	C₇×#440	—	2	4	no	—
26	C₄×C₇×SD₁₆	—	2	4	no	—
27	C₂×C₇×#107	C₂²	1	1	yes	characteristic
28	C₂×C₇×#106	C₂²	1	1	yes	characteristic
29	C₂×C₇×C₄⋊C₈	C₂²	1	1	yes	characteristic
30	C₂×C₇×C₄⋊C₈	C₂²	1	1	yes	characteristic
31	C₂×C₇×#103	C₂²	1	1	yes	characteristic
32	C₂×C₇×#103	C₂²	1	1	yes	characteristic
33	C₂×C₇×#103	C₂²	1	1	yes	characteristic
34	C₂×C₇×#103	C₂²	1	1	yes	characteristic
35	C₂×C₇×#103	C₂²	1	1	yes	characteristic
36	C₂×C₇×#103	C₂²	1	1	yes	characteristic
37	C₂×C₇×#102	C₂²	1	1	yes	characteristic
38	C₂×C₇×#102	C₂²	1	1	yes	characteristic
39	C₂×C₇×#97	C₂²	1	1	yes	characteristic
40	C₂×C₄×C₇×C₈	C₂²	1	1	yes	characteristic
41	C₇×#391	C₂²	1	1	yes	characteristic
42	C₇×#391	C₂²	1	1	yes	characteristic
43	C₇×#387	—	2	1	no	—
44	C₇×#387	—	2	1	no	—
45	C₇×#387	—	2	1	no	—
46	C₇×#387	—	2	1	no	—
47	C₇×#382	C₂²	1	1	yes	characteristic
48	C₄×C₇×C₄⋊C₄	C₂²	1	1	yes	characteristic
49	C₄×C₇×C₄⋊C₄	C₂²	1	1	yes	characteristic
50	C₄×C₇×C₄⋊C₄	C₂²	1	1	yes	characteristic
51	C₄×C₇×C₂²⋊C₄	—	2	1	no	—
52	C₄×C₇×C₂²⋊C₄	—	2	1	no	—
53	C₄×C₇×C₂²⋊C₄	—	2	1	no	—
54	C₇×#376	C₂²	1	1	yes	characteristic
55	C₂×C₇×#95	—	2	1	no	—
56	C₇×#340	C₂²	1	1	yes	characteristic
57	C₇×#340	C₂²	1	1	yes	characteristic
58	C₇×#340	C₂²	1	1	yes	characteristic
59	C₇×#340	C₂²	1	1	yes	characteristic
60	C₇×#336	C₂²	1	1	yes	characteristic
61	C₇×#336	C₂²	1	1	yes	characteristic
62	#21514	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
63	C₂²×C₇×Q₈	C₂³	1	1	yes	characteristic
64	C₂²×C₇×Q₈	C₂³	1	1	yes	characteristic
65	C₂²×C₇×D₄	C₂³	1	1	yes	characteristic
66	C₂³×C₄×C₇	—	2	1	no	—
67	C₂³×C₄×C₇	—	2	1	no	—
68	C₂³×C₄×C₇	—	2	1	no	—
69	C₂×C₇×SD₁₆	—	2	2	no	—
70	C₂×C₇×SD₁₆	—	2	2	no	—
71	C₂×C₇×SD₁₆	—	2	2	no	—
72	C₂×C₇×SD₁₆	—	2	2	no	—
73	C₂×C₇×SD₁₆	C₂×C₄	1	4	yes	—
74	C₂×C₇×SD₁₆	C₂×C₄	1	4	yes	—
75	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
76	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
77	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
78	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
79	C₇×C₄⋊Q₈	—	2	2	no	—
80	C₇×C₄⋊Q₈	C₂×C₄	1	4	yes	complemented
81	C₄×C₇×Q₈	—	2	2	no	—
82	C₄×C₇×Q₈	—	2	2	no	—
83	C₄×C₇×Q₈	—	2	2	no	—
84	C₄×C₇×Q₈	—	2	2	no	—
85	C₄×C₇×D₄	—	2	2	no	—
86	C₄×C₇×D₄	—	2	2	no	—
87	C₄×C₇×D₄	—	2	2	no	—
88	C₄×C₇×D₄	—	2	2	no	—
89	C₄×C₇×D₄	C₂×C₄	1	4	yes	—
90	C₄×C₇×D₄	D₄	1	4	yes	—
91	C₂×C₇×C₄⋊C₄	—	2	1	no	—
92	C₂×C₇×C₄⋊C₄	—	2	1	no	—
93	C₂×C₇×C₄⋊C₄	—	2	1	no	—
94	C₂×C₇×C₄⋊C₄	—	2	1	no	—
95	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
96	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
97	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
98	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
99	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
100	C₂×C₇×C₂²⋊C₄	—	2	1	no	—
101	C₂×C₇×C₂²⋊C₄	—	2	1	no	—
102	C₂×C₇×C₂²⋊C₄	—	2	1	no	—
103	C₂×C₄²×C₇	—	2	1	no	—
104	C₂×C₄²×C₇	—	2	1	no	—
105	C₂×C₄²×C₇	—	2	1	no	—
106	C₂×C₄²×C₇	—	2	1	no	—
107	C₂×C₄²×C₇	—	2	1	no	—
108	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
109	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
110	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
111	C₇×#107	—	2	2	no	—
112	C₇×#106	—	2	2	no	—
113	C₇×C₄⋊C₈	—	2	2	no	—
114	C₇×C₄⋊C₈	C₂×C₄	1	4	yes	complemented
115	C₇×#103	—	2	2	no	—
116	C₇×#103	—	2	2	no	—
117	C₇×#103	—	2	2	no	—
118	C₇×#103	—	2	2	no	—
119	C₇×#103	C₂×C₄	1	4	yes	complemented
120	C₇×#103	C₂×C₄	1	4	yes	complemented
121	C₇×#102	—	2	2	no	—
122	C₇×#102	—	2	2	no	—
123	C₇×#97	—	2	2	no	—
124	C₄×C₇×C₈	—	2	2	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	—	2	1	no	—
131	C₇×#95	—	2	1	no	—
132	C₇×#95	—	2	1	no	—
133	C₇×#95	—	2	1	no	—
134	C₇×#95	D₄	1	1	yes	characteristic
135	C₇×#95	D₄	1	1	yes	characteristic
136	C₇×#95	D₄	1	1	yes	characteristic
137	C₇×#95	D₄	1	1	yes	characteristic
138	C₂×#461	C₂×C₇	1	1	yes	characteristic
139	C₂×#440	C₂×C₇	1	1	yes	characteristic
140	C₂×C₄×SD₁₆	C₂×C₇	1	1	yes	characteristic
141	#2327	C₂×C₇	1	1	yes	characteristic, complemented
142	#2275	C₂×C₇	1	1	yes	characteristic
143	#1981	C₂×C₇	1	1	yes	characteristic, complemented
144	#1949	C₂×C₇	1	1	yes	characteristic, complemented
145	#1928	C₂×C₇	1	1	yes	characteristic, complemented
146	#1927	C₂×C₇	1	1	yes	characteristic, complemented
147	#1877	C₂×C₇	1	1	yes	characteristic
148	#1877	C₂×C₇	1	1	yes	characteristic
149	#1804	C₂×C₇	1	1	yes	characteristic
150	#1768	C₂×C₇	1	1	yes	characteristic, complemented
151	#1763	C₂×C₇	1	1	yes	characteristic, complemented
152	C₄×#103	C₂×C₇	1	1	yes	characteristic, complemented
153	C₂⁴×C₇	—	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	—	2	1	no	—
159	C₂×C₇×Q₈	—	2	1	no	—
160	C₂×C₇×Q₈	—	2	1	no	—
161	C₂×C₇×Q₈	—	2	1	no	—
162	C₂×C₇×Q₈	—	2	1	no	—
163	C₂×C₇×Q₈	—	2	1	no	—
164	C₂×C₇×Q₈	C₂²×C₄	1	2	yes	—
165	C₂×C₇×Q₈	C₂²×C₄	1	2	yes	—
166	C₂×C₇×D₄	—	2	1	no	—
167	C₂×C₇×D₄	—	2	1	no	—
168	C₂×C₇×D₄	—	2	1	no	—
169	C₂×C₇×D₄	C₂²×C₄	1	2	yes	—
170	C₂×C₇×D₄	C₂×D₄	1	2	yes	—
171	C₂×C₇×D₄	#41	1	2	yes	—
172	C₂²×C₄×C₇	—	2	1	no	—
173	C₂²×C₄×C₇	—	2	1	no	—
174	C₂²×C₄×C₇	—	2	1	no	—
175	C₂²×C₄×C₇	—	2	1	no	—
176	C₂²×C₄×C₇	—	2	1	no	—
177	C₂²×C₄×C₇	—	2	4	no	—
178	C₂²×C₄×C₇	—	2	4	no	—
179	C₂²×C₄×C₇	—	2	4	no	—
180	C₂²×C₄×C₇	—	2	1	no	—
181	C₂²×C₄×C₇	—	2	1	no	—
182	C₂²×C₄×C₇	—	8	1	no	—
183	C₂²×C₄×C₇	—	8	1	no	—
184	C₂²×C₄×C₇	—	8	1	no	—
185	C₂²×C₄×C₇	—	8	1	no	—
186	C₂²×C₄×C₇	—	8	1	no	—
187	C₂²×C₄×C₇	—	8	1	no	—
188	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
189	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
190	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
191	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
192	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
193	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
194	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
195	C₇×SD₁₆	—	2	8	no	—
196	C₇×SD₁₆	—	2	8	no	—
197	C₂×C₇×C₈	—	2	1	no	—
198	C₂×C₇×C₈	—	2	1	no	—
199	C₂×C₇×C₈	—	2	1	no	—
200	C₂×C₇×C₈	—	2	1	no	—
201	C₂×C₇×C₈	—	2	1	no	—
202	C₂×C₇×C₈	—	2	1	no	—
203	C₂×C₇×C₈	—	2	1	no	—
204	C₂×C₇×C₈	—	2	1	no	—
205	C₂×C₇×C₈	—	2	1	no	—
206	C₂×C₇×C₈	—	2	1	no	—
207	C₂×C₇×C₈	C₂²×C₄	1	2	yes	—
208	C₂×C₇×C₈	C₂²×C₄	1	2	yes	—
209	C₇×C₄⋊C₄	—	2	4	no	—
210	C₇×C₄⋊C₄	—	2	4	no	—
211	C₇×C₄⋊C₄	—	2	1	no	—
212	C₇×C₄⋊C₄	—	2	1	no	—
213	C₇×C₄⋊C₄	—	2	1	no	—
214	C₇×C₄⋊C₄	—	2	1	no	—
215	C₇×C₄⋊C₄	—	2	1	no	—
216	C₇×C₄⋊C₄	—	2	1	no	—
217	C₇×C₄⋊C₄	—	2	1	no	—
218	C₇×C₄⋊C₄	—	4	2	no	—
219	C₇×C₄⋊C₄	—	4	2	no	—
220	C₇×C₄⋊C₄	C₂²×C₄	1	2	yes	—
221	C₇×C₄⋊C₄	C₂×D₄	1	2	yes	—
222	C₇×C₄⋊C₄	#41	1	2	yes	—
223	C₇×C₂²⋊C₄	—	2	4	no	—
224	C₇×C₂²⋊C₄	—	2	4	no	—
225	C₇×C₂²⋊C₄	—	2	4	no	—
226	C₄²×C₇	—	2	1	no	—
227	C₄²×C₇	—	2	1	no	—
228	C₄²×C₇	—	4	2	no	—
229	C₄²×C₇	—	4	2	no	—
230	C₄²×C₇	—	8	1	no	—
231	C₄²×C₇	—	8	1	no	—
232	C₄²×C₇	—	8	1	no	—
233	C₄²×C₇	C₂²×C₄	1	2	yes	—
234	C₄²×C₇	C₂×D₄	1	2	yes	—
235	C₄²×C₇	#41	1	2	yes	—
236	C₄²×C₇	#41	1	2	yes	—
237	C₂²×SD₁₆	C₂²×C₇	1	1	yes	characteristic
238	C₂²×SD₁₆	C₂²×C₇	1	1	yes	characteristic
239	C₂×C₄⋊Q₈	C₂²×C₇	1	1	yes	characteristic
240	C₂×C₄×Q₈	C₂²×C₇	1	1	yes	characteristic
241	C₂×C₄×Q₈	C₂²×C₇	1	1	yes	characteristic
242	C₂×C₄×D₄	C₂²×C₇	1	1	yes	characteristic
243	C₂×C₄×D₄	C₂²×C₇	1	1	yes	characteristic
244	C₂×C₄×D₄	C₂²×C₇	1	1	yes	characteristic
245	#461	C₄×C₇	1	8	yes	complemented
246	#440	—	2	4	no	—
247	C₄×SD₁₆	—	2	4	no	—
248	C₂×#107	C₂²×C₇	1	1	yes	characteristic
249	C₂×#106	C₂²×C₇	1	1	yes	characteristic
250	C₂×C₄⋊C₈	C₂²×C₇	1	1	yes	characteristic
251	C₂×C₄⋊C₈	C₂²×C₇	1	1	yes	characteristic
252	C₂×#103	C₂²×C₇	1	1	yes	characteristic
253	C₂×#103	C₂²×C₇	1	1	yes	characteristic
254	C₂×#103	C₂²×C₇	1	1	yes	characteristic
255	C₂×#103	C₂²×C₇	1	1	yes	characteristic
256	C₂×#103	C₂²×C₇	1	1	yes	characteristic
257	C₂×#103	C₂²×C₇	1	1	yes	characteristic
258	C₂×#102	C₂²×C₇	1	1	yes	characteristic
259	C₂×#102	C₂²×C₇	1	1	yes	characteristic
260	C₂×#97	C₂²×C₇	1	1	yes	characteristic
261	C₂×C₄×C₈	C₂²×C₇	1	1	yes	characteristic
262	#391	C₂²×C₇	1	1	yes	characteristic
263	#391	C₂²×C₇	1	1	yes	characteristic
264	#387	—	2	1	no	—
265	#387	—	2	1	no	—
266	#387	—	2	1	no	—
267	#387	—	2	1	no	—
268	#382	C₂²×C₇	1	1	yes	characteristic
269	C₄×C₄⋊C₄	C₂²×C₇	1	1	yes	characteristic
270	C₄×C₄⋊C₄	C₂²×C₇	1	1	yes	characteristic
271	C₄×C₄⋊C₄	C₂²×C₇	1	1	yes	characteristic
272	C₄×C₂²⋊C₄	—	2	1	no	—
273	C₄×C₂²⋊C₄	—	2	1	no	—
274	C₄×C₂²⋊C₄	—	2	1	no	—
275	#376	C₂²×C₇	1	1	yes	characteristic
276	C₂×#95	—	2	1	no	—
277	#340	C₂²×C₇	1	1	yes	characteristic
278	#340	C₂²×C₇	1	1	yes	characteristic
279	#340	C₂²×C₇	1	1	yes	characteristic
280	#340	C₂²×C₇	1	1	yes	characteristic
281	#336	C₂²×C₇	1	1	yes	characteristic
282	#336	C₂²×C₇	1	1	yes	characteristic
283	C₂³×C₇	—	2	2	no	—
284	C₂³×C₇	—	2	2	no	—
285	C₂³×C₇	—	2	2	no	—
286	C₂³×C₇	—	4	1	no	—
287	C₂³×C₇	—	4	1	no	—
288	C₂³×C₇	—	4	1	no	—
289	C₂³×C₇	—	4	1	no	—
290	C₂³×C₇	C₂²×D₄	1	1	yes	characteristic
291	C₇×Q₈	—	2	2	no	—
292	C₇×Q₈	—	2	2	no	—
293	C₇×Q₈	—	2	2	no	—
294	C₇×Q₈	—	2	2	no	—
295	C₇×Q₈	—	4	1	no	—
296	C₇×Q₈	—	4	1	no	—
297	C₇×Q₈	—	4	1	no	—
298	C₇×Q₈	—	4	1	no	—
299	C₇×D₄	—	2	2	no	—
300	C₇×D₄	—	2	2	no	—
301	C₇×D₄	—	2	2	no	—
302	C₇×D₄	C₄×D₄	1	4	yes	—
303	C₂×C₄×C₇	—	2	1	no	—
304	C₂×C₄×C₇	—	2	1	no	—
305	C₂×C₄×C₇	—	2	1	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	2	no	—
312	C₂×C₄×C₇	—	2	2	no	—
313	C₂×C₄×C₇	—	2	2	no	—
314	C₂×C₄×C₇	—	2	2	no	—
315	C₂×C₄×C₇	—	2	1	no	—
316	C₂×C₄×C₇	—	2	1	no	—
317	C₂×C₄×C₇	—	2	2	no	—
318	C₂×C₄×C₇	—	2	1	no	—
319	C₂×C₄×C₇	—	2	1	no	—
320	C₂×C₄×C₇	—	2	1	no	—
321	C₂×C₄×C₇	—	2	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	—	4	1	no	—
330	C₂×C₄×C₇	—	4	1	no	—
331	C₂×C₄×C₇	—	4	1	no	—
332	C₂×C₄×C₇	—	4	1	no	—
333	C₂×C₄×C₇	—	4	1	no	—
334	C₂×C₄×C₇	—	4	1	no	—
335	C₂×C₄×C₇	—	4	1	no	—
336	C₂×C₄×C₇	—	4	1	no	—
337	C₂×C₄×C₇	—	4	1	no	—
338	C₂×C₄×C₇	—	8	4	no	—
339	C₂×C₄×C₇	—	8	4	no	—
340	C₂×C₄×C₇	—	8	4	no	—
341	C₂×C₄×C₇	C₄×D₄	1	2	yes	—
342	C₂×C₄×C₇	C₄×D₄	1	2	yes	—
343	C₂×C₄×C₇	#121	1	2	yes	—
344	C₂×C₄×C₇	#121	1	2	yes	—
345	C₂×C₄×C₇	C₂³×C₄	1	1	yes	characteristic
346	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
347	C₂×C₄×C₇	C₂×#41	1	1	yes	characteristic
348	C₂×C₄×C₇	C₂×#41	1	1	yes	characteristic
349	C₂×C₄×C₇	C₂×#41	1	1	yes	characteristic
350	C₂×C₄×C₇	C₂×#41	1	1	yes	characteristic
351	C₇×C₈	—	2	2	no	—
352	C₇×C₈	—	2	2	no	—
353	C₇×C₈	—	4	1	no	—
354	C₇×C₈	—	4	1	no	—
355	C₂²×Q₈	C₂³×C₇	1	1	yes	characteristic
356	C₂²×Q₈	C₂³×C₇	1	1	yes	characteristic
357	C₂²×D₄	C₂³×C₇	1	1	yes	characteristic
358	C₂³×C₄	—	2	1	no	—
359	C₂³×C₄	—	2	1	no	—
360	C₂³×C₄	—	2	1	no	—
361	C₂×SD₁₆	—	2	2	no	—
362	C₂×SD₁₆	—	2	2	no	—
363	C₂×SD₁₆	—	2	2	no	—
364	C₂×SD₁₆	—	2	2	no	—
365	C₂×SD₁₆	C₂×C₄×C₇	1	4	yes	—
366	C₂×SD₁₆	C₂×C₄×C₇	1	4	yes	—
367	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
368	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
369	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
370	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
371	C₄⋊Q₈	—	2	2	no	—
372	C₄⋊Q₈	C₂×C₄×C₇	1	4	yes	complemented
373	C₄×Q₈	—	2	2	no	—
374	C₄×Q₈	—	2	2	no	—
375	C₄×Q₈	—	2	2	no	—
376	C₄×Q₈	—	2	2	no	—
377	C₄×D₄	—	2	2	no	—
378	C₄×D₄	—	2	2	no	—
379	C₄×D₄	—	2	2	no	—
380	C₄×D₄	—	2	2	no	—
381	C₄×D₄	C₂×C₄×C₇	1	4	yes	—
382	C₄×D₄	C₇×D₄	1	4	yes	—
383	C₂×C₄⋊C₄	—	2	1	no	—
384	C₂×C₄⋊C₄	—	2	1	no	—
385	C₂×C₄⋊C₄	—	2	1	no	—
386	C₂×C₄⋊C₄	—	2	1	no	—
387	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
388	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
389	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
390	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
391	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
392	C₂×C₂²⋊C₄	—	2	1	no	—
393	C₂×C₂²⋊C₄	—	2	1	no	—
394	C₂×C₂²⋊C₄	—	2	1	no	—
395	C₂×C₄²	—	2	1	no	—
396	C₂×C₄²	—	2	1	no	—
397	C₂×C₄²	—	2	1	no	—
398	C₂×C₄²	—	2	1	no	—
399	C₂×C₄²	—	2	1	no	—
400	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
401	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
402	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
403	#107	—	2	2	no	—
404	#106	—	2	2	no	—
405	C₄⋊C₈	—	2	2	no	—
406	C₄⋊C₈	C₂×C₄×C₇	1	4	yes	complemented
407	#103	—	2	2	no	—
408	#103	—	2	2	no	—
409	#103	—	2	2	no	—
410	#103	—	2	2	no	—
411	#103	C₂×C₄×C₇	1	4	yes	complemented
412	#103	C₂×C₄×C₇	1	4	yes	complemented
413	#102	—	2	2	no	—
414	#102	—	2	2	no	—
415	#97	—	2	2	no	—
416	C₄×C₈	—	2	2	no	—
417	#95	—	2	1	no	—
418	#95	—	2	1	no	—
419	#95	—	2	1	no	—
420	#95	—	2	1	no	—
421	#95	—	2	1	no	—
422	#95	—	2	1	no	—
423	#95	—	2	1	no	—
424	#95	—	2	1	no	—
425	#95	—	2	1	no	—
426	#95	C₇×D₄	1	1	yes	characteristic
427	#95	C₇×D₄	1	1	yes	characteristic
428	#95	C₇×D₄	1	1	yes	characteristic
429	#95	C₇×D₄	1	1	yes	characteristic
430	C₂²×C₇	—	2	4	no	—
431	C₂²×C₇	—	4	2	no	—
432	C₂²×C₇	—	4	2	no	—
433	C₂²×C₇	—	4	2	no	—
434	C₂²×C₇	—	4	2	no	—
435	C₂²×C₇	—	4	2	no	—
436	C₂²×C₇	—	4	2	no	—
437	C₂²×C₇	C₂×C₄×D₄	1	1	yes	characteristic
438	C₂²×C₇	C₂×#121	1	1	yes	characteristic
439	C₂²×C₇	#525	1	1	yes	characteristic
440	C₂²×C₇	#577	1	1	yes	characteristic
441	C₂²×C₇	#577	1	1	yes	characteristic
442	C₂²×C₇	#577	1	1	yes	characteristic
443	C₂²×C₇	#578	1	1	yes	characteristic
444	C₄×C₇	—	2	2	no	—
445	C₄×C₇	—	2	2	no	—
446	C₄×C₇	—	2	2	no	—
447	C₄×C₇	—	2	2	no	—
448	C₄×C₇	—	4	1	no	—
449	C₄×C₇	—	4	1	no	—
450	C₄×C₇	—	4	2	no	—
451	C₄×C₇	—	4	2	no	—
452	C₄×C₇	—	4	2	no	—
453	C₄×C₇	—	4	2	no	—
454	C₄×C₇	—	4	2	no	—
455	C₄×C₇	—	8	1	no	—
456	C₄×C₇	—	8	1	no	—
457	C₄×C₇	C₂×C₄×D₄	1	1	yes	characteristic
458	C₄×C₇	C₄×#41	1	1	yes	characteristic
459	C₄×C₇	#529	1	1	yes	characteristic
460	C₄×C₇	#532	1	1	yes	characteristic
461	C₂⁴	—	2	1	no	—
462	C₂×Q₈	—	2	1	no	—
463	C₂×Q₈	—	2	1	no	—
464	C₂×Q₈	—	2	1	no	—
465	C₂×Q₈	—	2	1	no	—
466	C₂×Q₈	—	2	1	no	—
467	C₂×Q₈	—	2	1	no	—
468	C₂×Q₈	—	2	1	no	—
469	C₂×Q₈	—	2	1	no	—
470	C₂×Q₈	—	2	1	no	—
471	C₂×Q₈	—	2	1	no	—
472	C₂×Q₈	C₂²×C₄×C₇	1	2	yes	—
473	C₂×Q₈	C₂²×C₄×C₇	1	2	yes	—
474	C₂×D₄	—	2	1	no	—
475	C₂×D₄	—	2	1	no	—
476	C₂×D₄	—	2	1	no	—
477	C₂×D₄	C₂²×C₄×C₇	1	2	yes	—
478	C₂×D₄	C₂×C₇×D₄	1	2	yes	—
479	C₂×D₄	C₇×#41	1	2	yes	—
480	C₂²×C₄	—	2	1	no	—
481	C₂²×C₄	—	2	1	no	—
482	C₂²×C₄	—	2	1	no	—
483	C₂²×C₄	—	2	1	no	—
484	C₂²×C₄	—	2	1	no	—
485	C₂²×C₄	—	2	4	no	—
486	C₂²×C₄	—	2	4	no	—
487	C₂²×C₄	—	2	4	no	—
488	C₂²×C₄	—	2	1	no	—
489	C₂²×C₄	—	2	1	no	—
490	C₂²×C₄	—	8	1	no	—
491	C₂²×C₄	—	8	1	no	—
492	C₂²×C₄	—	8	1	no	—
493	C₂²×C₄	—	8	1	no	—
494	C₂²×C₄	—	8	1	no	—
495	C₂²×C₄	—	8	1	no	—
496	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
497	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
498	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
499	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
500	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
501	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
502	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
503	SD₁₆	—	2	8	no	—
504	SD₁₆	—	2	8	no	—
505	C₂×C₈	—	2	1	no	—
506	C₂×C₈	—	2	1	no	—
507	C₂×C₈	—	2	1	no	—
508	C₂×C₈	—	2	1	no	—
509	C₂×C₈	—	2	1	no	—
510	C₂×C₈	—	2	1	no	—
511	C₂×C₈	—	2	1	no	—
512	C₂×C₈	—	2	1	no	—
513	C₂×C₈	—	2	1	no	—
514	C₂×C₈	—	2	1	no	—
515	C₂×C₈	C₂²×C₄×C₇	1	2	yes	—
516	C₂×C₈	C₂²×C₄×C₇	1	2	yes	—
517	C₄⋊C₄	—	2	4	no	—
518	C₄⋊C₄	—	2	4	no	—
519	C₄⋊C₄	—	2	1	no	—
520	C₄⋊C₄	—	2	1	no	—
521	C₄⋊C₄	—	2	1	no	—
522	C₄⋊C₄	—	2	1	no	—
523	C₄⋊C₄	—	2	1	no	—
524	C₄⋊C₄	—	2	1	no	—
525	C₄⋊C₄	—	2	1	no	—
526	C₄⋊C₄	—	4	2	no	—
527	C₄⋊C₄	—	4	2	no	—
528	C₄⋊C₄	C₂²×C₄×C₇	1	2	yes	—
529	C₄⋊C₄	C₂×C₇×D₄	1	2	yes	—
530	C₄⋊C₄	C₇×#41	1	2	yes	—
531	C₂²⋊C₄	—	2	4	no	—
532	C₂²⋊C₄	—	2	4	no	—
533	C₂²⋊C₄	—	2	4	no	—
534	C₄²	—	2	1	no	—
535	C₄²	—	2	1	no	—
536	C₄²	—	4	2	no	—
537	C₄²	—	4	2	no	—
538	C₄²	—	8	1	no	—
539	C₄²	—	8	1	no	—
540	C₄²	—	8	1	no	—
541	C₄²	C₂²×C₄×C₇	1	2	yes	—
542	C₄²	C₂×C₇×D₄	1	2	yes	—
543	C₄²	C₇×#41	1	2	yes	—
544	C₄²	C₇×#41	1	2	yes	—
545	C₂×C₇	—	4	4	no	—
546	C₂×C₇	C₄×#121	1	1	yes	characteristic
547	C₂×C₇	#2947	1	1	yes	characteristic
548	C₂×C₇	#2949	1	1	yes	characteristic
549	C₂×C₇	#3042	1	1	yes	characteristic
550	C₂×C₇	#3046	1	1	yes	characteristic
551	C₂×C₇	#3120	1	1	yes	characteristic
552	C₂×C₇	#3123	1	1	yes	characteristic
553	C₂³	—	2	2	no	—
554	C₂³	—	2	2	no	—
555	C₂³	—	2	2	no	—
556	C₂³	—	4	1	no	—
557	C₂³	—	4	1	no	—
558	C₂³	—	4	1	no	—
559	C₂³	—	4	1	no	—
560	C₂³	C₂²×C₇×D₄	1	1	yes	characteristic
561	Q₈	—	2	2	no	—
562	Q₈	—	2	2	no	—
563	Q₈	—	2	2	no	—
564	Q₈	—	2	2	no	—
565	Q₈	—	4	1	no	—
566	Q₈	—	4	1	no	—
567	Q₈	—	4	1	no	—
568	Q₈	—	4	1	no	—
569	D₄	—	2	2	no	—
570	D₄	—	2	2	no	—
571	D₄	—	2	2	no	—
572	D₄	C₄×C₇×D₄	1	4	yes	—
573	C₂×C₄	—	2	1	no	—
574	C₂×C₄	—	2	1	no	—
575	C₂×C₄	—	2	1	no	—
576	C₂×C₄	—	2	1	no	—
577	C₂×C₄	—	2	1	no	—
578	C₂×C₄	—	2	1	no	—
579	C₂×C₄	—	2	1	no	—
580	C₂×C₄	—	2	1	no	—
581	C₂×C₄	—	2	2	no	—
582	C₂×C₄	—	2	2	no	—
583	C₂×C₄	—	2	2	no	—
584	C₂×C₄	—	2	2	no	—
585	C₂×C₄	—	2	1	no	—
586	C₂×C₄	—	2	1	no	—
587	C₂×C₄	—	2	2	no	—
588	C₂×C₄	—	2	1	no	—
589	C₂×C₄	—	2	1	no	—
590	C₂×C₄	—	2	1	no	—
591	C₂×C₄	—	2	1	no	—
592	C₂×C₄	—	4	1	no	—
593	C₂×C₄	—	4	1	no	—
594	C₂×C₄	—	4	1	no	—
595	C₂×C₄	—	4	1	no	—
596	C₂×C₄	—	4	1	no	—
597	C₂×C₄	—	4	1	no	—
598	C₂×C₄	—	4	1	no	—
599	C₂×C₄	—	4	1	no	—
600	C₂×C₄	—	4	1	no	—
601	C₂×C₄	—	4	1	no	—
602	C₂×C₄	—	4	1	no	—
603	C₂×C₄	—	4	1	no	—
604	C₂×C₄	—	4	1	no	—
605	C₂×C₄	—	4	1	no	—
606	C₂×C₄	—	4	1	no	—
607	C₂×C₄	—	4	1	no	—
608	C₂×C₄	—	8	4	no	—
609	C₂×C₄	—	8	4	no	—
610	C₂×C₄	—	8	4	no	—
611	C₂×C₄	C₄×C₇×D₄	1	2	yes	—
612	C₂×C₄	C₄×C₇×D₄	1	2	yes	—
613	C₂×C₄	C₇×#121	1	2	yes	—
614	C₂×C₄	C₇×#121	1	2	yes	—
615	C₂×C₄	C₂³×C₄×C₇	1	1	yes	characteristic
616	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
617	C₂×C₄	C₂×C₇×#41	1	1	yes	characteristic
618	C₂×C₄	C₂×C₇×#41	1	1	yes	characteristic
619	C₂×C₄	C₂×C₇×#41	1	1	yes	characteristic
620	C₂×C₄	C₂×C₇×#41	1	1	yes	characteristic
621	C₈	—	2	2	no	—
622	C₈	—	2	2	no	—
623	C₈	—	4	1	no	—
624	C₈	—	4	1	no	—
625	C₇	#21514	1	1	yes	characteristic, direct product factor, Sylow
626	C₂²	—	2	4	no	—
627	C₂²	—	4	2	no	—
628	C₂²	—	4	2	no	—
629	C₂²	—	4	2	no	—
630	C₂²	—	4	2	no	—
631	C₂²	—	4	2	no	—
632	C₂²	—	4	2	no	—
633	C₂²	C₂×C₄×C₇×D₄	1	1	yes	characteristic
634	C₂²	C₂×C₇×#121	1	1	yes	characteristic
635	C₂²	C₇×#525	1	1	yes	characteristic
636	C₂²	C₇×#577	1	1	yes	characteristic
637	C₂²	C₇×#577	1	1	yes	characteristic
638	C₂²	C₇×#577	1	1	yes	characteristic
639	C₂²	C₇×#578	1	1	yes	characteristic
640	C₄	—	2	2	no	—
641	C₄	—	2	2	no	—
642	C₄	—	2	2	no	—
643	C₄	—	2	2	no	—
644	C₄	—	4	2	no	—
645	C₄	—	4	2	no	—
646	C₄	—	4	2	no	—
647	C₄	—	4	2	no	—
648	C₄	—	4	1	no	—
649	C₄	—	4	1	no	—
650	C₄	—	4	2	no	—
651	C₄	—	8	1	no	—
652	C₄	—	8	1	no	—
653	C₄	C₂×C₄×C₇×D₄	1	1	yes	characteristic
654	C₄	C₄×C₇×#41	1	1	yes	characteristic
655	C₄	C₇×#529	1	1	yes	characteristic
656	C₄	C₇×#532	1	1	yes	characteristic
657	C₂	—	4	4	no	—
658	C₂	C₄×C₇×#121	1	1	yes	characteristic
659	C₂	C₇×#2947	1	1	yes	characteristic
660	C₂	C₇×#2949	1	1	yes	characteristic
661	C₂	C₇×#3042	1	1	yes	characteristic
662	C₂	C₇×#3046	1	1	yes	characteristic
663	C₂	C₇×#3120	1	1	yes	characteristic
664	C₂	C₇×#3123	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 ◁ C₇×#376 ◁ G

Complements

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

N	H ≅ G/N	type
4. C₇×#2327	C₂	semidirect
6. C₇×#1981	C₂	semidirect
7. C₇×#1949	C₂	semidirect
8. C₇×#1928	C₂	semidirect
9. C₇×#1927	C₂	semidirect
13. C₇×#1768	C₂	semidirect
14. C₇×#1763	C₂	semidirect
15. C₄×C₇×#103	C₂	semidirect
24. C₇×#461	C₄	semidirect
62. #21514	C₇	direct (N × H)
80. C₇×C₄⋊Q₈	C₂×C₄	semidirect
114. C₇×C₄⋊C₈	C₂×C₄	semidirect
119. C₇×#103	C₂×C₄	semidirect
120. C₇×#103	C₂×C₄	semidirect
141. #2327	C₂×C₇	semidirect
143. #1981	C₂×C₇	semidirect
144. #1949	C₂×C₇	semidirect
145. #1928	C₂×C₇	semidirect
146. #1927	C₂×C₇	semidirect
150. #1768	C₂×C₇	semidirect
151. #1763	C₂×C₇	semidirect
152. C₄×#103	C₂×C₇	semidirect
245. #461	C₄×C₇	semidirect
372. C₄⋊Q₈	C₂×C₄×C₇	semidirect
406. C₄⋊C₈	C₂×C₄×C₇	semidirect
411. #103	C₂×C₄×C₇	semidirect
412. #103	C₂×C₄×C₇	semidirect
625. C₇	#21514	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×#461	2
C₂×C₇×#440	2
C₂×C₄×C₇×SD₁₆	2
C₇×#2327	2
C₇×#2275	2
C₇×#1981	2
C₇×#1949	2
C₇×#1928	2
C₇×#1927	2
C₇×#1877	2
C₇×#1804	2
C₇×#1768	2
C₇×#1763	2
C₄×C₇×#103	2
#21514	7

Subgroups — C7×#21514 #13198730

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×#21514 #13198730