Subgroups — C₇×#24514 #13201730

Order 1792.

896 conjugacy classes of subgroups.

The subgroup lattice has 682 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₇×#451	C₂	1	1	yes	maximal, characteristic
2	C₂×C₇×#433	C₂	1	1	yes	maximal, characteristic
3	C₇×#2625	C₂	1	1	yes	maximal, characteristic
4	C₇×#2310	C₂	1	1	yes	maximal, characteristic
5	C₇×#2068	C₂	1	1	yes	maximal, characteristic, complemented
6	C₇×#2066	C₂	1	1	yes	maximal, characteristic, complemented
7	C₇×#2056	C₂	1	1	yes	maximal, characteristic, complemented
8	C₇×#2056	C₂	1	1	yes	maximal, characteristic, complemented
9	C₇×#1971	C₂	1	1	yes	maximal, characteristic, complemented
10	C₇×#1969	C₂	1	1	yes	maximal, characteristic, complemented
11	C₇×#1935	C₂	1	1	yes	maximal, characteristic, complemented
12	C₇×#1933	C₂	1	1	yes	maximal, characteristic, complemented
13	C₇×#1873	C₂	1	1	yes	maximal, characteristic
14	C₇×#1854	C₂	1	1	yes	maximal, characteristic
15	C₇×#1787	C₂	1	1	yes	maximal, characteristic
16	C₂³×C₇×Q₈	C₂²	1	1	yes	characteristic
17	C₂²×C₇×Q₁₆	C₂²	1	1	yes	characteristic
18	C₂²×C₇×Q₁₆	C₂²	1	1	yes	characteristic
19	C₂×C₇×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
20	C₂×C₇×#117	C₂²	1	1	yes	characteristic
21	C₂×C₇×#117	C₂²	1	1	yes	characteristic
22	C₇×#451	—	2	4	no	—
23	C₇×#433	—	2	4	no	—
24	C₂×C₇×#107	C₂²	1	1	yes	characteristic
25	C₂×C₇×#106	C₂²	1	1	yes	characteristic
26	C₂×C₇×C₄⋊C₈	C₂²	1	1	yes	characteristic
27	C₂×C₇×C₄⋊C₈	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×#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×C₂²⋊C₈	C₂²	1	1	yes	characteristic
37	C₂×C₇×C₂²⋊C₈	C₂²	1	1	yes	characteristic
38	C₂×C₇×#97	C₂²	1	1	yes	characteristic
39	C₂×C₄×C₇×C₈	C₂²	1	1	yes	characteristic
40	C₇×#400	—	2	1	no	—
41	C₇×#398	—	2	1	no	—
42	C₇×#397	—	2	1	no	—
43	C₇×#397	—	2	1	no	—
44	C₇×#391	—	2	1	no	—
45	C₇×#391	—	2	1	no	—
46	C₇×#391	C₂²	1	1	yes	characteristic
47	C₇×#391	C₂²	1	1	yes	characteristic
48	C₇×#391	C₂²	1	1	yes	characteristic
49	C₇×#391	C₂²	1	1	yes	characteristic
50	C₇×#391	C₂²	1	1	yes	characteristic
51	C₇×#391	C₂²	1	1	yes	characteristic
52	C₇×#389	C₂²	1	1	yes	characteristic
53	C₇×#389	C₂²	1	1	yes	characteristic
54	C₇×#381	—	2	1	no	—
55	C₇×#381	—	2	1	no	—
56	C₇×#380	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×#340	C₂²	1	1	yes	characteristic
61	#24514	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
62	C₂²×C₇×Q₈	—	2	2	no	—
63	C₂²×C₇×Q₈	—	2	2	no	—
64	C₂²×C₇×Q₈	—	2	1	no	—
65	C₂²×C₇×Q₈	—	2	2	no	—
66	C₂²×C₇×Q₈	—	2	2	no	—
67	C₂²×C₇×Q₈	—	4	1	no	—
68	C₂²×C₇×Q₈	—	4	1	no	—
69	C₂²×C₇×Q₈	C₂³	1	1	yes	characteristic
70	C₂²×C₇×Q₈	C₂³	1	1	yes	characteristic
71	C₂²×C₇×Q₈	C₂³	1	1	yes	characteristic
72	C₂³×C₄×C₇	—	2	1	no	—
73	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
74	C₂×C₇×Q₁₆	—	2	2	no	—
75	C₂×C₇×Q₁₆	—	2	2	no	—
76	C₂×C₇×Q₁₆	—	2	2	no	—
77	C₂×C₇×Q₁₆	—	2	2	no	—
78	C₂×C₇×Q₁₆	—	4	1	no	—
79	C₂×C₇×Q₁₆	—	4	1	no	—
80	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
81	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
82	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
83	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
84	C₇×C₂²⋊Q₈	—	2	2	no	—
85	C₇×C₂²⋊Q₈	—	2	2	no	—
86	C₇×#117	—	2	2	no	—
87	C₇×#117	—	2	2	no	—
88	C₇×#117	—	4	1	no	—
89	C₇×#117	—	4	1	no	—
90	C₂×C₇×C₄⋊C₄	—	2	1	no	—
91	C₂×C₇×C₄⋊C₄	—	2	1	no	—
92	C₂×C₇×C₄⋊C₄	—	2	1	no	—
93	C₂×C₇×C₄⋊C₄	D₄	1	1	yes	characteristic
94	C₂×C₇×C₄⋊C₄	D₄	1	1	yes	characteristic
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×C₇×C₂²⋊C₄	D₄	1	1	yes	characteristic
104	C₂×C₇×C₂²⋊C₄	D₄	1	1	yes	characteristic
105	C₂×C₄²×C₇	—	2	1	no	—
106	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
107	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
108	C₇×#107	—	4	1	no	—
109	C₇×#106	—	4	1	no	—
110	C₇×C₄⋊C₈	—	2	2	no	—
111	C₇×C₄⋊C₈	—	2	2	no	—
112	C₇×#103	—	2	2	no	—
113	C₇×#103	—	2	2	no	—
114	C₇×#103	—	2	2	no	—
115	C₇×#103	—	2	2	no	—
116	C₇×#103	—	4	1	no	—
117	C₇×#103	—	4	1	no	—
118	C₇×#103	—	4	1	no	—
119	C₇×#103	—	4	1	no	—
120	C₇×C₂²⋊C₈	—	2	2	no	—
121	C₇×C₂²⋊C₈	D₄	1	4	yes	—
122	C₇×#97	—	2	2	no	—
123	C₄×C₇×C₈	—	2	2	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	—	2	1	no	—
131	C₇×#95	—	2	1	no	—
132	C₇×#95	—	2	1	no	—
133	C₇×#95	—	2	1	no	—
134	C₇×#95	—	2	1	no	—
135	C₇×#95	—	2	1	no	—
136	C₇×#95	—	2	1	no	—
137	C₇×#95	—	2	1	no	—
138	C₇×#95	—	2	1	no	—
139	C₂×#451	C₂×C₇	1	1	yes	characteristic
140	C₂×#433	C₂×C₇	1	1	yes	characteristic
141	#2625	C₂×C₇	1	1	yes	characteristic
142	#2310	C₂×C₇	1	1	yes	characteristic
143	#2068	C₂×C₇	1	1	yes	characteristic, complemented
144	#2066	C₂×C₇	1	1	yes	characteristic, complemented
145	#2056	C₂×C₇	1	1	yes	characteristic, complemented
146	#2056	C₂×C₇	1	1	yes	characteristic, complemented
147	#1971	C₂×C₇	1	1	yes	characteristic, complemented
148	#1969	C₂×C₇	1	1	yes	characteristic, complemented
149	#1935	C₂×C₇	1	1	yes	characteristic, complemented
150	#1933	C₂×C₇	1	1	yes	characteristic, complemented
151	#1873	C₂×C₇	1	1	yes	characteristic
152	#1854	C₂×C₇	1	1	yes	characteristic
153	#1787	C₂×C₇	1	1	yes	characteristic
154	C₂⁴×C₇	C₂×D₄	1	1	yes	characteristic
155	C₂×C₇×Q₈	—	2	4	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	—	2	1	no	—
165	C₂×C₇×Q₈	—	2	1	no	—
166	C₂×C₇×Q₈	—	2	1	no	—
167	C₂×C₇×Q₈	—	2	1	no	—
168	C₂×C₇×Q₈	—	2	1	no	—
169	C₂×C₇×Q₈	—	2	1	no	—
170	C₂×C₇×Q₈	—	2	1	no	—
171	C₂×C₇×Q₈	—	2	1	no	—
172	C₂×C₇×Q₈	—	4	4	no	—
173	C₂×C₇×Q₈	—	4	4	no	—
174	C₂×C₇×Q₈	—	4	4	no	—
175	C₂×C₇×Q₈	—	4	4	no	—
176	C₂×C₇×Q₈	—	4	2	no	—
177	C₂×C₇×Q₈	—	4	2	no	—
178	C₂×C₇×Q₈	#41	1	2	yes	—
179	C₂×C₇×Q₈	#41	1	2	yes	—
180	C₂²×C₄×C₇	—	2	1	no	—
181	C₂²×C₄×C₇	—	2	1	no	—
182	C₂²×C₄×C₇	—	2	1	no	—
183	C₂²×C₄×C₇	—	2	1	no	—
184	C₂²×C₄×C₇	—	2	4	no	—
185	C₂²×C₄×C₇	—	2	1	no	—
186	C₂²×C₄×C₇	—	2	1	no	—
187	C₂²×C₄×C₇	—	2	1	no	—
188	C₂²×C₄×C₇	—	2	1	no	—
189	C₂²×C₄×C₇	—	2	1	no	—
190	C₂²×C₄×C₇	—	2	1	no	—
191	C₂²×C₄×C₇	—	2	1	no	—
192	C₂²×C₄×C₇	—	2	1	no	—
193	C₂²×C₄×C₇	—	4	2	no	—
194	C₂²×C₄×C₇	—	4	2	no	—
195	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
196	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
197	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
198	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
199	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
200	C₂²×C₄×C₇	C₂×D₄	1	2	yes	—
201	C₂²×C₄×C₇	#41	1	2	yes	—
202	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
203	C₇×Q₁₆	—	4	4	no	—
204	C₇×Q₁₆	—	4	4	no	—
205	C₂×C₇×C₈	—	2	1	no	—
206	C₂×C₇×C₈	—	2	1	no	—
207	C₂×C₇×C₈	—	2	1	no	—
208	C₂×C₇×C₈	—	2	1	no	—
209	C₂×C₇×C₈	—	2	1	no	—
210	C₂×C₇×C₈	—	2	1	no	—
211	C₂×C₇×C₈	—	2	1	no	—
212	C₂×C₇×C₈	—	2	1	no	—
213	C₂×C₇×C₈	—	2	1	no	—
214	C₂×C₇×C₈	—	2	1	no	—
215	C₂×C₇×C₈	C₂×D₄	1	2	yes	—
216	C₂×C₇×C₈	C₂×D₄	1	2	yes	—
217	C₇×C₄⋊C₄	—	2	2	no	—
218	C₇×C₄⋊C₄	—	2	2	no	—
219	C₇×C₄⋊C₄	—	2	1	no	—
220	C₇×C₄⋊C₄	—	2	1	no	—
221	C₇×C₄⋊C₄	—	2	1	no	—
222	C₇×C₄⋊C₄	—	2	1	no	—
223	C₇×C₄⋊C₄	—	2	1	no	—
224	C₇×C₄⋊C₄	—	2	1	no	—
225	C₇×C₄⋊C₄	—	2	1	no	—
226	C₇×C₄⋊C₄	—	2	1	no	—
227	C₇×C₄⋊C₄	—	2	1	no	—
228	C₇×C₄⋊C₄	—	2	1	no	—
229	C₇×C₄⋊C₄	—	4	2	no	—
230	C₇×C₄⋊C₄	—	8	1	no	—
231	C₇×C₄⋊C₄	—	8	1	no	—
232	C₇×C₂²⋊C₄	—	2	2	no	—
233	C₇×C₂²⋊C₄	—	2	2	no	—
234	C₇×C₂²⋊C₄	—	4	2	no	—
235	C₇×C₂²⋊C₄	—	4	2	no	—
236	C₇×C₂²⋊C₄	—	8	1	no	—
237	C₄²×C₇	—	2	1	no	—
238	C₄²×C₇	—	2	1	no	—
239	C₄²×C₇	—	2	1	no	—
240	C₄²×C₇	—	2	1	no	—
241	C₄²×C₇	—	4	2	no	—
242	C₂³×Q₈	C₂²×C₇	1	1	yes	characteristic
243	C₂²×Q₁₆	C₂²×C₇	1	1	yes	characteristic
244	C₂²×Q₁₆	C₂²×C₇	1	1	yes	characteristic
245	C₂×C₂²⋊Q₈	C₂²×C₇	1	1	yes	characteristic
246	C₂×#117	C₂²×C₇	1	1	yes	characteristic
247	C₂×#117	C₂²×C₇	1	1	yes	characteristic
248	#451	—	2	4	no	—
249	#433	—	2	4	no	—
250	C₂×#107	C₂²×C₇	1	1	yes	characteristic
251	C₂×#106	C₂²×C₇	1	1	yes	characteristic
252	C₂×C₄⋊C₈	C₂²×C₇	1	1	yes	characteristic
253	C₂×C₄⋊C₈	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×#103	C₂²×C₇	1	1	yes	characteristic
259	C₂×#103	C₂²×C₇	1	1	yes	characteristic
260	C₂×#103	C₂²×C₇	1	1	yes	characteristic
261	C₂×#103	C₂²×C₇	1	1	yes	characteristic
262	C₂×C₂²⋊C₈	C₂²×C₇	1	1	yes	characteristic
263	C₂×C₂²⋊C₈	C₂²×C₇	1	1	yes	characteristic
264	C₂×#97	C₂²×C₇	1	1	yes	characteristic
265	C₂×C₄×C₈	C₂²×C₇	1	1	yes	characteristic
266	#400	—	2	1	no	—
267	#398	—	2	1	no	—
268	#397	—	2	1	no	—
269	#397	—	2	1	no	—
270	#391	—	2	1	no	—
271	#391	—	2	1	no	—
272	#391	C₂²×C₇	1	1	yes	characteristic
273	#391	C₂²×C₇	1	1	yes	characteristic
274	#391	C₂²×C₇	1	1	yes	characteristic
275	#391	C₂²×C₇	1	1	yes	characteristic
276	#391	C₂²×C₇	1	1	yes	characteristic
277	#391	C₂²×C₇	1	1	yes	characteristic
278	#389	C₂²×C₇	1	1	yes	characteristic
279	#389	C₂²×C₇	1	1	yes	characteristic
280	#381	—	2	1	no	—
281	#381	—	2	1	no	—
282	#380	C₂²×C₇	1	1	yes	characteristic
283	#340	C₂²×C₇	1	1	yes	characteristic
284	#340	C₂²×C₇	1	1	yes	characteristic
285	#340	C₂²×C₇	1	1	yes	characteristic
286	#340	C₂²×C₇	1	1	yes	characteristic
287	C₂³×C₇	—	2	1	no	—
288	C₂³×C₇	—	2	1	no	—
289	C₂³×C₇	—	2	1	no	—
290	C₂³×C₇	—	2	1	no	—
291	C₂³×C₇	—	2	1	no	—
292	C₂³×C₇	—	2	1	no	—
293	C₂³×C₇	#121	1	2	yes	—
294	C₂³×C₇	C₂²×D₄	1	1	yes	characteristic
295	C₇×Q₈	—	2	2	no	—
296	C₇×Q₈	—	2	2	no	—
297	C₇×Q₈	—	2	2	no	—
298	C₇×Q₈	—	2	2	no	—
299	C₇×Q₈	—	4	8	no	—
300	C₇×Q₈	—	4	1	no	—
301	C₇×Q₈	—	4	1	no	—
302	C₇×Q₈	—	4	1	no	—
303	C₇×Q₈	—	4	1	no	—
304	C₇×Q₈	—	4	1	no	—
305	C₇×Q₈	—	4	1	no	—
306	C₇×Q₈	—	4	1	no	—
307	C₇×Q₈	—	4	1	no	—
308	C₂×C₄×C₇	—	2	1	no	—
309	C₂×C₄×C₇	—	2	1	no	—
310	C₂×C₄×C₇	—	2	2	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	1	no	—
315	C₂×C₄×C₇	—	2	1	no	—
316	C₂×C₄×C₇	—	2	1	no	—
317	C₂×C₄×C₇	—	2	1	no	—
318	C₂×C₄×C₇	—	2	2	no	—
319	C₂×C₄×C₇	—	2	2	no	—
320	C₂×C₄×C₇	—	2	1	no	—
321	C₂×C₄×C₇	—	2	1	no	—
322	C₂×C₄×C₇	—	2	1	no	—
323	C₂×C₄×C₇	—	2	1	no	—
324	C₂×C₄×C₇	—	2	1	no	—
325	C₂×C₄×C₇	—	2	1	no	—
326	C₂×C₄×C₇	—	2	1	no	—
327	C₂×C₄×C₇	—	2	1	no	—
328	C₂×C₄×C₇	—	4	8	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	—	4	1	no	—
339	C₂×C₄×C₇	—	4	1	no	—
340	C₂×C₄×C₇	—	4	1	no	—
341	C₂×C₄×C₇	—	4	1	no	—
342	C₂×C₄×C₇	—	4	1	no	—
343	C₂×C₄×C₇	—	4	1	no	—
344	C₂×C₄×C₇	—	4	1	no	—
345	C₂×C₄×C₇	—	4	1	no	—
346	C₂×C₄×C₇	—	4	1	no	—
347	C₂×C₄×C₇	—	4	1	no	—
348	C₂×C₄×C₇	—	4	1	no	—
349	C₂×C₄×C₇	—	4	1	no	—
350	C₂×C₄×C₇	—	4	1	no	—
351	C₂×C₄×C₇	#121	1	2	yes	—
352	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
353	C₂×C₄×C₇	C₂×#41	1	1	yes	characteristic
354	C₂×C₄×C₇	C₂×#41	1	1	yes	characteristic
355	C₂×C₄×C₇	C₂×#41	1	1	yes	characteristic
356	C₂×C₄×C₇	H(5,𝔽₂)	1	1	yes	characteristic
357	C₂×C₄×C₇	H(5,𝔽₂)	1	1	yes	characteristic
358	C₇×C₈	—	2	2	no	—
359	C₇×C₈	—	2	2	no	—
360	C₇×C₈	—	4	1	no	—
361	C₇×C₈	—	4	1	no	—
362	C₂²×Q₈	—	2	2	no	—
363	C₂²×Q₈	—	2	2	no	—
364	C₂²×Q₈	—	2	1	no	—
365	C₂²×Q₈	—	2	2	no	—
366	C₂²×Q₈	—	2	2	no	—
367	C₂²×Q₈	—	4	1	no	—
368	C₂²×Q₈	—	4	1	no	—
369	C₂²×Q₈	C₂³×C₇	1	1	yes	characteristic
370	C₂²×Q₈	C₂³×C₇	1	1	yes	characteristic
371	C₂²×Q₈	C₂³×C₇	1	1	yes	characteristic
372	C₂³×C₄	—	2	1	no	—
373	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
374	C₂×Q₁₆	—	2	2	no	—
375	C₂×Q₁₆	—	2	2	no	—
376	C₂×Q₁₆	—	2	2	no	—
377	C₂×Q₁₆	—	2	2	no	—
378	C₂×Q₁₆	—	4	1	no	—
379	C₂×Q₁₆	—	4	1	no	—
380	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
381	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
382	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
383	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
384	C₂²⋊Q₈	—	2	2	no	—
385	C₂²⋊Q₈	—	2	2	no	—
386	#117	—	2	2	no	—
387	#117	—	2	2	no	—
388	#117	—	4	1	no	—
389	#117	—	4	1	no	—
390	C₂×C₄⋊C₄	—	2	1	no	—
391	C₂×C₄⋊C₄	—	2	1	no	—
392	C₂×C₄⋊C₄	—	2	1	no	—
393	C₂×C₄⋊C₄	C₇×D₄	1	1	yes	characteristic
394	C₂×C₄⋊C₄	C₇×D₄	1	1	yes	characteristic
395	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
396	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
397	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
398	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
399	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
400	C₂×C₂²⋊C₄	—	2	1	no	—
401	C₂×C₂²⋊C₄	—	2	1	no	—
402	C₂×C₂²⋊C₄	—	2	1	no	—
403	C₂×C₂²⋊C₄	C₇×D₄	1	1	yes	characteristic
404	C₂×C₂²⋊C₄	C₇×D₄	1	1	yes	characteristic
405	C₂×C₄²	—	2	1	no	—
406	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
407	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
408	#107	—	4	1	no	—
409	#106	—	4	1	no	—
410	C₄⋊C₈	—	2	2	no	—
411	C₄⋊C₈	—	2	2	no	—
412	#103	—	2	2	no	—
413	#103	—	2	2	no	—
414	#103	—	2	2	no	—
415	#103	—	2	2	no	—
416	#103	—	4	1	no	—
417	#103	—	4	1	no	—
418	#103	—	4	1	no	—
419	#103	—	4	1	no	—
420	C₂²⋊C₈	—	2	2	no	—
421	C₂²⋊C₈	C₇×D₄	1	4	yes	—
422	#97	—	2	2	no	—
423	C₄×C₈	—	2	2	no	—
424	#95	—	2	1	no	—
425	#95	—	2	1	no	—
426	#95	—	2	1	no	—
427	#95	—	2	1	no	—
428	#95	—	2	1	no	—
429	#95	—	2	1	no	—
430	#95	—	2	1	no	—
431	#95	—	2	1	no	—
432	#95	—	2	1	no	—
433	#95	—	2	1	no	—
434	#95	—	2	1	no	—
435	#95	—	2	1	no	—
436	#95	—	2	1	no	—
437	#95	—	2	1	no	—
438	#95	—	2	1	no	—
439	C₂²×C₇	—	2	2	no	—
440	C₂²×C₇	—	2	2	no	—
441	C₂²×C₇	—	2	2	no	—
442	C₂²×C₇	—	4	1	no	—
443	C₂²×C₇	—	4	1	no	—
444	C₂²×C₇	—	4	1	no	—
445	C₂²×C₇	—	4	1	no	—
446	C₂²×C₇	C₂×#121	1	1	yes	characteristic
447	C₂²×C₇	#525	1	1	yes	characteristic
448	C₂²×C₇	#535	1	1	yes	characteristic
449	C₂²×C₇	#577	1	1	yes	characteristic
450	C₂²×C₇	#578	1	1	yes	characteristic
451	C₂²×C₇	#578	1	1	yes	characteristic
452	C₂²×C₇	#578	1	1	yes	characteristic
453	C₄×C₇	—	2	2	no	—
454	C₄×C₇	—	4	2	no	—
455	C₄×C₇	—	4	2	no	—
456	C₄×C₇	—	4	1	no	—
457	C₄×C₇	—	4	1	no	—
458	C₄×C₇	—	4	1	no	—
459	C₄×C₇	—	4	1	no	—
460	C₄×C₇	—	8	1	no	—
461	C₄×C₇	—	8	1	no	—
462	C₄×C₇	—	8	1	no	—
463	C₄×C₇	—	8	1	no	—
464	C₄×C₇	—	8	1	no	—
465	C₄×C₇	—	8	1	no	—
466	C₄×C₇	#546	1	1	yes	characteristic
467	C₄×C₇	#546	1	1	yes	characteristic
468	C₄×C₇	#551	1	1	yes	characteristic
469	C₄×C₇	#551	1	1	yes	characteristic
470	C₂⁴	C₂×C₇×D₄	1	1	yes	characteristic
471	C₂×Q₈	—	2	4	no	—
472	C₂×Q₈	—	2	1	no	—
473	C₂×Q₈	—	2	1	no	—
474	C₂×Q₈	—	2	1	no	—
475	C₂×Q₈	—	2	1	no	—
476	C₂×Q₈	—	2	1	no	—
477	C₂×Q₈	—	2	1	no	—
478	C₂×Q₈	—	2	1	no	—
479	C₂×Q₈	—	2	1	no	—
480	C₂×Q₈	—	2	1	no	—
481	C₂×Q₈	—	2	1	no	—
482	C₂×Q₈	—	2	1	no	—
483	C₂×Q₈	—	2	1	no	—
484	C₂×Q₈	—	2	1	no	—
485	C₂×Q₈	—	2	1	no	—
486	C₂×Q₈	—	2	1	no	—
487	C₂×Q₈	—	2	1	no	—
488	C₂×Q₈	—	4	4	no	—
489	C₂×Q₈	—	4	4	no	—
490	C₂×Q₈	—	4	4	no	—
491	C₂×Q₈	—	4	4	no	—
492	C₂×Q₈	—	4	2	no	—
493	C₂×Q₈	—	4	2	no	—
494	C₂×Q₈	C₇×#41	1	2	yes	—
495	C₂×Q₈	C₇×#41	1	2	yes	—
496	C₂²×C₄	—	2	1	no	—
497	C₂²×C₄	—	2	1	no	—
498	C₂²×C₄	—	2	1	no	—
499	C₂²×C₄	—	2	1	no	—
500	C₂²×C₄	—	2	4	no	—
501	C₂²×C₄	—	2	1	no	—
502	C₂²×C₄	—	2	1	no	—
503	C₂²×C₄	—	2	1	no	—
504	C₂²×C₄	—	2	1	no	—
505	C₂²×C₄	—	2	1	no	—
506	C₂²×C₄	—	2	1	no	—
507	C₂²×C₄	—	2	1	no	—
508	C₂²×C₄	—	2	1	no	—
509	C₂²×C₄	—	4	2	no	—
510	C₂²×C₄	—	4	2	no	—
511	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
512	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
513	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
514	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
515	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
516	C₂²×C₄	C₂×C₇×D₄	1	2	yes	—
517	C₂²×C₄	C₇×#41	1	2	yes	—
518	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
519	Q₁₆	—	4	4	no	—
520	Q₁₆	—	4	4	no	—
521	C₂×C₈	—	2	1	no	—
522	C₂×C₈	—	2	1	no	—
523	C₂×C₈	—	2	1	no	—
524	C₂×C₈	—	2	1	no	—
525	C₂×C₈	—	2	1	no	—
526	C₂×C₈	—	2	1	no	—
527	C₂×C₈	—	2	1	no	—
528	C₂×C₈	—	2	1	no	—
529	C₂×C₈	—	2	1	no	—
530	C₂×C₈	—	2	1	no	—
531	C₂×C₈	C₂×C₇×D₄	1	2	yes	—
532	C₂×C₈	C₂×C₇×D₄	1	2	yes	—
533	C₄⋊C₄	—	2	2	no	—
534	C₄⋊C₄	—	2	2	no	—
535	C₄⋊C₄	—	2	1	no	—
536	C₄⋊C₄	—	2	1	no	—
537	C₄⋊C₄	—	2	1	no	—
538	C₄⋊C₄	—	2	1	no	—
539	C₄⋊C₄	—	2	1	no	—
540	C₄⋊C₄	—	2	1	no	—
541	C₄⋊C₄	—	2	1	no	—
542	C₄⋊C₄	—	2	1	no	—
543	C₄⋊C₄	—	2	1	no	—
544	C₄⋊C₄	—	2	1	no	—
545	C₄⋊C₄	—	4	2	no	—
546	C₄⋊C₄	—	8	1	no	—
547	C₄⋊C₄	—	8	1	no	—
548	C₂²⋊C₄	—	2	2	no	—
549	C₂²⋊C₄	—	2	2	no	—
550	C₂²⋊C₄	—	4	2	no	—
551	C₂²⋊C₄	—	4	2	no	—
552	C₂²⋊C₄	—	8	1	no	—
553	C₄²	—	2	1	no	—
554	C₄²	—	2	1	no	—
555	C₄²	—	2	1	no	—
556	C₄²	—	2	1	no	—
557	C₄²	—	4	2	no	—
558	C₂×C₇	—	4	2	no	—
559	C₂×C₇	#2411	1	1	yes	characteristic
560	C₂×C₇	#3059	1	1	yes	characteristic
561	C₂×C₇	#3063	1	1	yes	characteristic
562	C₂×C₇	#3121	1	1	yes	characteristic
563	C₂×C₇	#3127	1	1	yes	characteristic
564	C₂×C₇	#3223	1	1	yes	characteristic
565	C₂×C₇	#3225	1	1	yes	characteristic
566	C₂³	—	2	1	no	—
567	C₂³	—	2	1	no	—
568	C₂³	—	2	1	no	—
569	C₂³	—	2	1	no	—
570	C₂³	—	2	1	no	—
571	C₂³	—	2	1	no	—
572	C₂³	C₇×#121	1	2	yes	—
573	C₂³	C₂²×C₇×D₄	1	1	yes	characteristic
574	Q₈	—	2	2	no	—
575	Q₈	—	2	2	no	—
576	Q₈	—	2	2	no	—
577	Q₈	—	2	2	no	—
578	Q₈	—	4	8	no	—
579	Q₈	—	4	1	no	—
580	Q₈	—	4	1	no	—
581	Q₈	—	4	1	no	—
582	Q₈	—	4	1	no	—
583	Q₈	—	4	1	no	—
584	Q₈	—	4	1	no	—
585	Q₈	—	4	1	no	—
586	Q₈	—	4	1	no	—
587	C₂×C₄	—	2	1	no	—
588	C₂×C₄	—	2	1	no	—
589	C₂×C₄	—	2	2	no	—
590	C₂×C₄	—	2	2	no	—
591	C₂×C₄	—	2	2	no	—
592	C₂×C₄	—	2	2	no	—
593	C₂×C₄	—	2	1	no	—
594	C₂×C₄	—	2	1	no	—
595	C₂×C₄	—	2	1	no	—
596	C₂×C₄	—	2	1	no	—
597	C₂×C₄	—	2	2	no	—
598	C₂×C₄	—	2	2	no	—
599	C₂×C₄	—	2	1	no	—
600	C₂×C₄	—	2	1	no	—
601	C₂×C₄	—	2	1	no	—
602	C₂×C₄	—	2	1	no	—
603	C₂×C₄	—	2	1	no	—
604	C₂×C₄	—	2	1	no	—
605	C₂×C₄	—	2	1	no	—
606	C₂×C₄	—	2	1	no	—
607	C₂×C₄	—	4	8	no	—
608	C₂×C₄	—	4	1	no	—
609	C₂×C₄	—	4	1	no	—
610	C₂×C₄	—	4	1	no	—
611	C₂×C₄	—	4	1	no	—
612	C₂×C₄	—	4	1	no	—
613	C₂×C₄	—	4	1	no	—
614	C₂×C₄	—	4	1	no	—
615	C₂×C₄	—	4	1	no	—
616	C₂×C₄	—	4	1	no	—
617	C₂×C₄	—	4	1	no	—
618	C₂×C₄	—	4	1	no	—
619	C₂×C₄	—	4	1	no	—
620	C₂×C₄	—	4	1	no	—
621	C₂×C₄	—	4	1	no	—
622	C₂×C₄	—	4	1	no	—
623	C₂×C₄	—	4	1	no	—
624	C₂×C₄	—	4	1	no	—
625	C₂×C₄	—	4	1	no	—
626	C₂×C₄	—	4	1	no	—
627	C₂×C₄	—	4	1	no	—
628	C₂×C₄	—	4	1	no	—
629	C₂×C₄	—	4	1	no	—
630	C₂×C₄	C₇×#121	1	2	yes	—
631	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
632	C₂×C₄	C₂×C₇×#41	1	1	yes	characteristic
633	C₂×C₄	C₂×C₇×#41	1	1	yes	characteristic
634	C₂×C₄	C₂×C₇×#41	1	1	yes	characteristic
635	C₂×C₄	C₇×H(5,𝔽₂)	1	1	yes	characteristic
636	C₂×C₄	C₇×H(5,𝔽₂)	1	1	yes	characteristic
637	C₈	—	2	2	no	—
638	C₈	—	2	2	no	—
639	C₈	—	4	1	no	—
640	C₈	—	4	1	no	—
641	C₇	#24514	1	1	yes	characteristic, direct product factor, Sylow
642	C₂²	—	2	2	no	—
643	C₂²	—	2	2	no	—
644	C₂²	—	2	2	no	—
645	C₂²	—	4	1	no	—
646	C₂²	—	4	1	no	—
647	C₂²	—	4	1	no	—
648	C₂²	—	4	1	no	—
649	C₂²	C₂×C₇×#121	1	1	yes	characteristic
650	C₂²	C₇×#525	1	1	yes	characteristic
651	C₂²	C₇×#535	1	1	yes	characteristic
652	C₂²	C₇×#577	1	1	yes	characteristic
653	C₂²	C₇×#578	1	1	yes	characteristic
654	C₂²	C₇×#578	1	1	yes	characteristic
655	C₂²	C₇×#578	1	1	yes	characteristic
656	C₄	—	2	2	no	—
657	C₄	—	4	2	no	—
658	C₄	—	4	2	no	—
659	C₄	—	4	1	no	—
660	C₄	—	4	1	no	—
661	C₄	—	4	1	no	—
662	C₄	—	4	1	no	—
663	C₄	—	8	1	no	—
664	C₄	—	8	1	no	—
665	C₄	—	8	1	no	—
666	C₄	—	8	1	no	—
667	C₄	—	8	1	no	—
668	C₄	—	8	1	no	—
669	C₄	C₇×#546	1	1	yes	characteristic
670	C₄	C₇×#546	1	1	yes	characteristic
671	C₄	C₇×#551	1	1	yes	characteristic
672	C₄	C₇×#551	1	1	yes	characteristic
673	C₂	—	4	2	no	—
674	C₂	C₇×#2411	1	1	yes	characteristic
675	C₂	C₇×#3059	1	1	yes	characteristic
676	C₂	C₇×#3063	1	1	yes	characteristic
677	C₂	C₇×#3121	1	1	yes	characteristic
678	C₂	C₇×#3127	1	1	yes	characteristic
679	C₂	C₇×#3223	1	1	yes	characteristic
680	C₂	C₇×#3225	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₇	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₇
prime radical	C₂⁴×C₇	C₂×D₄
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₇ ◁ C₂×C₇×#117 ◁ G

Complements

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

N	H ≅ G/N	type
5. C₇×#2068	C₂	semidirect
6. C₇×#2066	C₂	semidirect
7. C₇×#2056	C₂	semidirect
8. C₇×#2056	C₂	semidirect
9. C₇×#1971	C₂	semidirect
10. C₇×#1969	C₂	semidirect
11. C₇×#1935	C₂	semidirect
12. C₇×#1933	C₂	semidirect
61. #24514	C₇	direct (N × H)
143. #2068	C₂×C₇	semidirect
144. #2066	C₂×C₇	semidirect
145. #2056	C₂×C₇	semidirect
146. #2056	C₂×C₇	semidirect
147. #1971	C₂×C₇	semidirect
148. #1969	C₂×C₇	semidirect
149. #1935	C₂×C₇	semidirect
150. #1933	C₂×C₇	semidirect
641. C₇	#24514	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×#451	2
C₂×C₇×#433	2
C₇×#2625	2
C₇×#2310	2
C₇×#2068	2
C₇×#2066	2
C₇×#2056	2
C₇×#1971	2
C₇×#1969	2
C₇×#1935	2
C₇×#1933	2
C₇×#1873	2
C₇×#1854	2
C₇×#1787	2
#24514	7

Subgroups — C7×#24514 #13201730

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×#24514 #13201730