Subgroups — C₇×#21896 #13199112

Order 1792.

1078 conjugacy classes of subgroups.

The subgroup lattice has 710 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₇×#542	C₂	1	1	yes	maximal, characteristic
2	C₂×C₇×#424	C₂	1	1	yes	maximal, characteristic, complemented
3	C₇×#2314	C₂	1	1	yes	maximal, characteristic, complemented
4	C₇×#1988	C₂	1	1	yes	maximal, characteristic, complemented
5	C₇×#1987	C₂	1	1	yes	maximal, characteristic, complemented
6	C₇×#1983	C₂	1	1	yes	maximal, characteristic, complemented
7	C₇×#1983	C₂	1	1	yes	maximal, characteristic, complemented
8	C₇×#1895	C₂	1	1	yes	maximal, characteristic
9	C₇×#1894	C₂	1	1	yes	maximal, characteristic, complemented
10	C₇×#1893	C₂	1	1	yes	maximal, characteristic
11	C₇×#1892	C₂	1	1	yes	maximal, characteristic, complemented
12	C₇×#1805	C₂	1	1	yes	maximal, characteristic, complemented
13	C₇×#1804	C₂	1	1	yes	maximal, characteristic, complemented
14	C₇×#1803	C₂	1	1	yes	maximal, characteristic, complemented
15	C₇×#1802	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×C₇×M₁₆	C₂²	1	1	yes	characteristic
17	C₂³×C₇×C₈	C₂²	1	1	yes	characteristic
18	C₇×#542	—	2	4	no	—
19	C₇×#542	C₄	1	8	yes	complemented
20	C₂×C₇×C₄⋊Q₈	C₂²	1	1	yes	characteristic
21	C₂×C₇×#126	—	2	1	no	—
22	C₂×C₇×#124	—	2	1	no	—
23	C₂×C₇×#124	C₂²	1	1	yes	characteristic
24	C₂×C₇×#123	—	2	1	no	—
25	C₂×C₇×C₂²⋊Q₈	—	2	1	no	—
26	C₂×C₇×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
27	C₂×C₇×#121	C₂²	1	1	yes	characteristic
28	C₂×C₄×C₇×Q₈	C₂²	1	1	yes	characteristic
29	C₂×C₄×C₇×D₄	C₂²	1	1	yes	characteristic
30	C₂×C₇×#117	C₂²	1	1	yes	characteristic
31	C₇×#424	—	2	4	no	—
32	C₂×C₇×C₄⋊C₈	C₂²	1	1	yes	characteristic
33	C₂×C₇×C₄⋊C₈	C₂²	1	1	yes	characteristic
34	C₂×C₇×C₄⋊C₈	C₂²	1	1	yes	characteristic
35	C₂×C₇×C₄⋊C₈	C₂²	1	1	yes	characteristic
36	C₂×C₇×#103	C₂²	1	1	yes	characteristic
37	C₂×C₇×#103	C₂²	1	1	yes	characteristic
38	C₂×C₇×#103	C₂²	1	1	yes	characteristic
39	C₂×C₇×#103	C₂²	1	1	yes	characteristic
40	C₂×C₇×#102	C₂²	1	1	yes	characteristic
41	C₂×C₇×#102	C₂²	1	1	yes	characteristic
42	C₂×C₇×#102	C₂²	1	1	yes	characteristic
43	C₂×C₇×#102	C₂²	1	1	yes	characteristic
44	C₇×#388	—	2	1	no	—
45	C₇×#388	—	2	1	no	—
46	C₇×#387	—	2	1	no	—
47	C₇×#387	—	2	1	no	—
48	C₇×#384	C₂²	1	1	yes	characteristic
49	C₇×#382	C₂²	1	1	yes	characteristic
50	C₇×#380	C₂²	1	1	yes	characteristic
51	C₇×#380	C₂²	1	1	yes	characteristic
52	C₄×C₇×C₄⋊C₄	C₂²	1	1	yes	characteristic
53	C₄×C₇×C₄⋊C₄	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×#340	C₂²	1	1	yes	characteristic
59	C₇×#340	C₂²	1	1	yes	characteristic
60	C₇×#340	C₂²	1	1	yes	characteristic
61	C₇×#340	C₂²	1	1	yes	characteristic
62	#21896	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
63	C₂²×C₇×Q₈	—	2	1	no	—
64	C₂²×C₇×Q₈	C₂³	1	1	yes	characteristic
65	C₂²×C₇×D₄	—	2	1	no	—
66	C₂²×C₇×D₄	C₂³	1	1	yes	characteristic
67	C₂³×C₄×C₇	—	2	1	no	—
68	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
69	C₂×C₇×M₁₆	—	2	2	no	—
70	C₂×C₇×M₁₆	—	4	1	no	—
71	C₂×C₇×M₁₆	—	4	1	no	—
72	C₂²×C₇×C₈	—	2	2	no	—
73	C₂²×C₇×C₈	—	4	1	no	—
74	C₂²×C₇×C₈	—	4	1	no	—
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	—
81	C₇×#126	—	2	8	no	—
82	C₇×#124	—	2	8	no	—
83	C₇×#124	—	2	2	no	—
84	C₇×#124	C₂×C₄	1	4	yes	—
85	C₇×#123	—	2	8	no	—
86	C₇×C₂²⋊Q₈	—	2	2	no	—
87	C₇×C₂²⋊Q₈	—	2	8	no	—
88	C₇×C₂²⋊Q₈	C₂×C₄	1	4	yes	—
89	C₇×#121	—	2	2	no	—
90	C₇×#121	C₂×C₄	1	4	yes	—
91	C₄×C₇×Q₈	—	2	2	no	—
92	C₄×C₇×Q₈	C₂×C₄	1	4	yes	—
93	C₄×C₇×D₄	—	2	2	no	—
94	C₄×C₇×D₄	C₂×C₄	1	4	yes	—
95	C₇×#117	C₂×C₄	1	4	yes	—
96	C₇×#117	D₄	1	4	yes	—
97	C₂×C₇×C₄⋊C₄	—	2	1	no	—
98	C₂×C₇×C₄⋊C₄	—	2	1	no	—
99	C₂×C₇×C₄⋊C₄	—	2	1	no	—
100	C₂×C₇×C₄⋊C₄	—	2	1	no	—
101	C₂×C₇×C₄⋊C₄	—	2	1	no	—
102	C₂×C₇×C₄⋊C₄	D₄	1	1	yes	characteristic
103	C₂×C₇×C₄⋊C₄	D₄	1	1	yes	characteristic
104	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
105	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
106	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
107	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
108	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
109	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
110	C₂×C₇×C₂²⋊C₄	—	2	1	no	—
111	C₂×C₇×C₂²⋊C₄	—	2	1	no	—
112	C₂×C₇×C₂²⋊C₄	—	2	1	no	—
113	C₂×C₇×C₂²⋊C₄	—	2	1	no	—
114	C₂×C₇×C₂²⋊C₄	—	2	1	no	—
115	C₂×C₇×C₂²⋊C₄	—	2	1	no	—
116	C₂×C₇×C₂²⋊C₄	—	2	1	no	—
117	C₂×C₇×C₂²⋊C₄	D₄	1	1	yes	characteristic
118	C₂×C₇×C₂²⋊C₄	D₄	1	1	yes	characteristic
119	C₂×C₄²×C₇	—	2	1	no	—
120	C₂×C₄²×C₇	—	2	1	no	—
121	C₂×C₄²×C₇	—	2	1	no	—
122	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
123	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
124	C₇×C₄⋊C₈	—	2	2	no	—
125	C₇×C₄⋊C₈	—	2	2	no	—
126	C₇×C₄⋊C₈	—	2	2	no	—
127	C₇×C₄⋊C₈	—	2	2	no	—
128	C₇×#103	—	4	1	no	—
129	C₇×#103	—	4	1	no	—
130	C₇×#103	—	4	1	no	—
131	C₇×#103	—	4	1	no	—
132	C₇×#102	—	4	1	no	—
133	C₇×#102	—	4	1	no	—
134	C₇×#102	—	4	1	no	—
135	C₇×#102	—	4	1	no	—
136	C₇×#95	—	2	1	no	—
137	C₇×#95	—	2	1	no	—
138	C₇×#95	—	2	1	no	—
139	C₇×#95	—	2	1	no	—
140	C₇×#95	—	2	1	no	—
141	C₇×#95	—	2	1	no	—
142	C₂×#542	C₂×C₇	1	1	yes	characteristic
143	C₂×#424	C₂×C₇	1	1	yes	characteristic, complemented
144	#2314	C₂×C₇	1	1	yes	characteristic, complemented
145	#1988	C₂×C₇	1	1	yes	characteristic, complemented
146	#1987	C₂×C₇	1	1	yes	characteristic, complemented
147	#1983	C₂×C₇	1	1	yes	characteristic, complemented
148	#1983	C₂×C₇	1	1	yes	characteristic, complemented
149	#1895	C₂×C₇	1	1	yes	characteristic
150	#1894	C₂×C₇	1	1	yes	characteristic, complemented
151	#1893	C₂×C₇	1	1	yes	characteristic
152	#1892	C₂×C₇	1	1	yes	characteristic, complemented
153	#1805	C₂×C₇	1	1	yes	characteristic, complemented
154	#1804	C₂×C₇	1	1	yes	characteristic, complemented
155	#1803	C₂×C₇	1	1	yes	characteristic, complemented
156	#1802	C₂×C₇	1	1	yes	characteristic, complemented
157	C₂⁴×C₇	—	2	1	no	—
158	C₂⁴×C₇	C₂×D₄	1	1	yes	characteristic
159	C₂×C₇×Q₈	—	2	4	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	—	8	1	no	—
166	C₂×C₇×Q₈	—	8	1	no	—
167	C₂×C₇×Q₈	C₂²×C₄	1	2	yes	—
168	C₂×C₇×D₄	—	2	4	no	—
169	C₂×C₇×D₄	—	2	1	no	—
170	C₂×C₇×D₄	—	2	1	no	—
171	C₂×C₇×D₄	—	2	1	no	—
172	C₂×C₇×D₄	—	2	1	no	—
173	C₂×C₇×D₄	—	2	1	no	—
174	C₂×C₇×D₄	—	8	1	no	—
175	C₂×C₇×D₄	—	8	1	no	—
176	C₂×C₇×D₄	C₂²×C₄	1	2	yes	—
177	C₂²×C₄×C₇	—	2	1	no	—
178	C₂²×C₄×C₇	—	2	1	no	—
179	C₂²×C₄×C₇	—	2	1	no	—
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	—	8	1	no	—
190	C₂²×C₄×C₇	—	8	1	no	—
191	C₂²×C₄×C₇	C₂²×C₄	1	2	yes	—
192	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
193	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
194	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
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	2	yes	—
198	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
199	C₇×M₁₆	—	4	4	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	—	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	—	4	4	no	—
213	C₇×C₄⋊C₄	—	2	4	no	—
214	C₇×C₄⋊C₄	—	2	4	no	—
215	C₇×C₄⋊C₄	—	2	4	no	—
216	C₇×C₄⋊C₄	—	2	1	no	—
217	C₇×C₄⋊C₄	—	2	1	no	—
218	C₇×C₄⋊C₄	—	2	1	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	—	8	1	no	—
227	C₇×C₄⋊C₄	—	8	1	no	—
228	C₇×C₄⋊C₄	C₂²⋊C₄	1	4	yes	—
229	C₇×C₄⋊C₄	C₂²⋊C₄	1	4	yes	—
230	C₇×C₄⋊C₄	C₂²×C₄	1	2	yes	—
231	C₇×C₄⋊C₄	C₂²×C₄	1	2	yes	—
232	C₇×C₂²⋊C₄	—	2	4	no	—
233	C₇×C₂²⋊C₄	—	2	4	no	—
234	C₇×C₂²⋊C₄	—	2	4	no	—
235	C₇×C₂²⋊C₄	—	2	4	no	—
236	C₇×C₂²⋊C₄	—	2	4	no	—
237	C₇×C₂²⋊C₄	—	8	1	no	—
238	C₇×C₂²⋊C₄	—	8	1	no	—
239	C₇×C₂²⋊C₄	C₂²⋊C₄	1	4	yes	—
240	C₇×C₂²⋊C₄	C₂²⋊C₄	1	4	yes	—
241	C₄²×C₇	—	2	4	no	—
242	C₄²×C₇	—	8	1	no	—
243	C₄²×C₇	—	8	1	no	—
244	C₄²×C₇	C₂²×C₄	1	2	yes	—
245	C₄²×C₇	C₂²×C₄	1	2	yes	—
246	C₄²×C₇	C₂×D₄	1	2	yes	—
247	C₄²×C₇	C₂×D₄	1	2	yes	—
248	C₂²×M₁₆	C₂²×C₇	1	1	yes	characteristic
249	C₂³×C₈	C₂²×C₇	1	1	yes	characteristic
250	#542	—	2	4	no	—
251	#542	C₄×C₇	1	8	yes	complemented
252	C₂×C₄⋊Q₈	C₂²×C₇	1	1	yes	characteristic
253	C₂×#126	—	2	1	no	—
254	C₂×#124	—	2	1	no	—
255	C₂×#124	C₂²×C₇	1	1	yes	characteristic
256	C₂×#123	—	2	1	no	—
257	C₂×C₂²⋊Q₈	—	2	1	no	—
258	C₂×C₂²⋊Q₈	C₂²×C₇	1	1	yes	characteristic
259	C₂×#121	C₂²×C₇	1	1	yes	characteristic
260	C₂×C₄×Q₈	C₂²×C₇	1	1	yes	characteristic
261	C₂×C₄×D₄	C₂²×C₇	1	1	yes	characteristic
262	C₂×#117	C₂²×C₇	1	1	yes	characteristic
263	#424	—	2	4	no	—
264	C₂×C₄⋊C₈	C₂²×C₇	1	1	yes	characteristic
265	C₂×C₄⋊C₈	C₂²×C₇	1	1	yes	characteristic
266	C₂×C₄⋊C₈	C₂²×C₇	1	1	yes	characteristic
267	C₂×C₄⋊C₈	C₂²×C₇	1	1	yes	characteristic
268	C₂×#103	C₂²×C₇	1	1	yes	characteristic
269	C₂×#103	C₂²×C₇	1	1	yes	characteristic
270	C₂×#103	C₂²×C₇	1	1	yes	characteristic
271	C₂×#103	C₂²×C₇	1	1	yes	characteristic
272	C₂×#102	C₂²×C₇	1	1	yes	characteristic
273	C₂×#102	C₂²×C₇	1	1	yes	characteristic
274	C₂×#102	C₂²×C₇	1	1	yes	characteristic
275	C₂×#102	C₂²×C₇	1	1	yes	characteristic
276	#388	—	2	1	no	—
277	#388	—	2	1	no	—
278	#387	—	2	1	no	—
279	#387	—	2	1	no	—
280	#384	C₂²×C₇	1	1	yes	characteristic
281	#382	C₂²×C₇	1	1	yes	characteristic
282	#380	C₂²×C₇	1	1	yes	characteristic
283	#380	C₂²×C₇	1	1	yes	characteristic
284	C₄×C₄⋊C₄	C₂²×C₇	1	1	yes	characteristic
285	C₄×C₄⋊C₄	C₂²×C₇	1	1	yes	characteristic
286	#340	C₂²×C₇	1	1	yes	characteristic
287	#340	C₂²×C₇	1	1	yes	characteristic
288	#340	C₂²×C₇	1	1	yes	characteristic
289	#340	C₂²×C₇	1	1	yes	characteristic
290	#340	C₂²×C₇	1	1	yes	characteristic
291	#340	C₂²×C₇	1	1	yes	characteristic
292	#340	C₂²×C₇	1	1	yes	characteristic
293	#340	C₂²×C₇	1	1	yes	characteristic
294	C₂³×C₇	—	2	1	no	—
295	C₂³×C₇	—	2	1	no	—
296	C₂³×C₇	—	2	1	no	—
297	C₂³×C₇	—	2	1	no	—
298	C₂³×C₇	—	2	1	no	—
299	C₂³×C₇	—	2	1	no	—
300	C₂³×C₇	—	2	2	no	—
301	C₂³×C₇	—	4	1	no	—
302	C₂³×C₇	—	4	1	no	—
303	C₂³×C₇	—	4	1	no	—
304	C₂³×C₇	—	4	1	no	—
305	C₂³×C₇	—	4	1	no	—
306	C₂³×C₇	—	4	1	no	—
307	C₂³×C₇	C₂×C₂²⋊C₄	1	2	yes	—
308	C₂³×C₇	C₂²×D₄	1	1	yes	characteristic
309	C₇×Q₈	—	2	2	no	—
310	C₇×Q₈	—	2	2	no	—
311	C₇×Q₈	—	4	1	no	—
312	C₇×Q₈	—	4	1	no	—
313	C₇×Q₈	—	8	4	no	—
314	C₇×D₄	—	2	2	no	—
315	C₇×D₄	—	2	2	no	—
316	C₇×D₄	—	4	1	no	—
317	C₇×D₄	—	4	1	no	—
318	C₇×D₄	—	8	4	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	—	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	—	2	1	no	—
329	C₂×C₄×C₇	—	2	2	no	—
330	C₂×C₄×C₇	—	2	2	no	—
331	C₂×C₄×C₇	—	2	2	no	—
332	C₂×C₄×C₇	—	2	2	no	—
333	C₂×C₄×C₇	—	2	2	no	—
334	C₂×C₄×C₇	—	2	2	no	—
335	C₂×C₄×C₇	—	2	2	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	—	4	1	no	—
352	C₂×C₄×C₇	—	4	1	no	—
353	C₂×C₄×C₇	—	4	1	no	—
354	C₂×C₄×C₇	—	8	4	no	—
355	C₂×C₄×C₇	C₂×C₂²⋊C₄	1	2	yes	—
356	C₂×C₄×C₇	C₂×C₂²⋊C₄	1	2	yes	—
357	C₂×C₄×C₇	C₂×C₂²⋊C₄	1	2	yes	—
358	C₂×C₄×C₇	C₂×C₂²⋊C₄	1	2	yes	—
359	C₂×C₄×C₇	C₂×C₂²⋊C₄	1	2	yes	—
360	C₂×C₄×C₇	C₂³×C₄	1	1	yes	characteristic
361	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
362	C₂×C₄×C₇	H(5,𝔽₂)	1	1	yes	characteristic
363	C₂×C₄×C₇	H(5,𝔽₂)	1	1	yes	characteristic
364	C₂×C₄×C₇	2₋¹⁺⁴	1	1	yes	characteristic
365	C₂×C₄×C₇	2₋¹⁺⁴	1	1	yes	characteristic
366	C₇×C₈	—	4	1	no	—
367	C₇×C₈	—	4	1	no	—
368	C₇×C₈	—	4	1	no	—
369	C₇×C₈	—	4	1	no	—
370	C₂²×Q₈	—	2	1	no	—
371	C₂²×Q₈	C₂³×C₇	1	1	yes	characteristic
372	C₂²×D₄	—	2	1	no	—
373	C₂²×D₄	C₂³×C₇	1	1	yes	characteristic
374	C₂³×C₄	—	2	1	no	—
375	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
376	C₂×M₁₆	—	2	2	no	—
377	C₂×M₁₆	—	4	1	no	—
378	C₂×M₁₆	—	4	1	no	—
379	C₂²×C₈	—	2	2	no	—
380	C₂²×C₈	—	4	1	no	—
381	C₂²×C₈	—	4	1	no	—
382	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
383	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
384	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
385	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
386	C₄⋊Q₈	—	2	2	no	—
387	C₄⋊Q₈	C₂×C₄×C₇	1	4	yes	—
388	#126	—	2	8	no	—
389	#124	—	2	8	no	—
390	#124	—	2	2	no	—
391	#124	C₂×C₄×C₇	1	4	yes	—
392	#123	—	2	8	no	—
393	C₂²⋊Q₈	—	2	2	no	—
394	C₂²⋊Q₈	—	2	8	no	—
395	C₂²⋊Q₈	C₂×C₄×C₇	1	4	yes	—
396	#121	—	2	2	no	—
397	#121	C₂×C₄×C₇	1	4	yes	—
398	C₄×Q₈	—	2	2	no	—
399	C₄×Q₈	C₂×C₄×C₇	1	4	yes	—
400	C₄×D₄	—	2	2	no	—
401	C₄×D₄	C₂×C₄×C₇	1	4	yes	—
402	#117	C₂×C₄×C₇	1	4	yes	—
403	#117	C₇×D₄	1	4	yes	—
404	C₂×C₄⋊C₄	—	2	1	no	—
405	C₂×C₄⋊C₄	—	2	1	no	—
406	C₂×C₄⋊C₄	—	2	1	no	—
407	C₂×C₄⋊C₄	—	2	1	no	—
408	C₂×C₄⋊C₄	—	2	1	no	—
409	C₂×C₄⋊C₄	C₇×D₄	1	1	yes	characteristic
410	C₂×C₄⋊C₄	C₇×D₄	1	1	yes	characteristic
411	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
412	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
413	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
414	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
415	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
416	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
417	C₂×C₂²⋊C₄	—	2	1	no	—
418	C₂×C₂²⋊C₄	—	2	1	no	—
419	C₂×C₂²⋊C₄	—	2	1	no	—
420	C₂×C₂²⋊C₄	—	2	1	no	—
421	C₂×C₂²⋊C₄	—	2	1	no	—
422	C₂×C₂²⋊C₄	—	2	1	no	—
423	C₂×C₂²⋊C₄	—	2	1	no	—
424	C₂×C₂²⋊C₄	C₇×D₄	1	1	yes	characteristic
425	C₂×C₂²⋊C₄	C₇×D₄	1	1	yes	characteristic
426	C₂×C₄²	—	2	1	no	—
427	C₂×C₄²	—	2	1	no	—
428	C₂×C₄²	—	2	1	no	—
429	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
430	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
431	C₄⋊C₈	—	2	2	no	—
432	C₄⋊C₈	—	2	2	no	—
433	C₄⋊C₈	—	2	2	no	—
434	C₄⋊C₈	—	2	2	no	—
435	#103	—	4	1	no	—
436	#103	—	4	1	no	—
437	#103	—	4	1	no	—
438	#103	—	4	1	no	—
439	#102	—	4	1	no	—
440	#102	—	4	1	no	—
441	#102	—	4	1	no	—
442	#102	—	4	1	no	—
443	#95	—	2	1	no	—
444	#95	—	2	1	no	—
445	#95	—	2	1	no	—
446	#95	—	2	1	no	—
447	#95	—	2	1	no	—
448	#95	—	2	1	no	—
449	C₂²×C₇	—	2	2	no	—
450	C₂²×C₇	—	2	2	no	—
451	C₂²×C₇	—	2	2	no	—
452	C₂²×C₇	—	4	1	no	—
453	C₂²×C₇	—	4	1	no	—
454	C₂²×C₇	—	4	1	no	—
455	C₂²×C₇	—	4	1	no	—
456	C₂²×C₇	—	4	2	no	—
457	C₂²×C₇	—	4	2	no	—
458	C₂²×C₇	—	4	2	no	—
459	C₂²×C₇	—	8	1	no	—
460	C₂²×C₇	—	8	1	no	—
461	C₂²×C₇	—	8	1	no	—
462	C₂²×C₇	—	8	1	no	—
463	C₂²×C₇	C₂²×C₂²⋊C₄	1	1	yes	characteristic
464	C₂²×C₇	#537	1	1	yes	characteristic
465	C₂²×C₇	#537	1	1	yes	characteristic
466	C₂²×C₇	#576	1	1	yes	characteristic
467	C₂²×C₇	#577	1	1	yes	characteristic
468	C₂²×C₇	#577	1	1	yes	characteristic
469	C₂²×C₇	#578	1	1	yes	characteristic
470	C₄×C₇	—	2	2	no	—
471	C₄×C₇	—	2	2	no	—
472	C₄×C₇	—	2	2	no	—
473	C₄×C₇	—	2	2	no	—
474	C₄×C₇	—	2	2	no	—
475	C₄×C₇	—	4	2	no	—
476	C₄×C₇	—	4	2	no	—
477	C₄×C₇	—	4	2	no	—
478	C₄×C₇	—	8	1	no	—
479	C₄×C₇	—	8	1	no	—
480	C₄×C₇	—	8	1	no	—
481	C₄×C₇	—	8	1	no	—
482	C₄×C₇	#520	1	1	yes	characteristic
483	C₄×C₇	#520	1	1	yes	characteristic
484	C₄×C₇	#535	1	1	yes	characteristic
485	C₄×C₇	#536	1	1	yes	characteristic
486	C₂⁴	—	2	1	no	—
487	C₂⁴	C₂×C₇×D₄	1	1	yes	characteristic
488	C₂×Q₈	—	2	4	no	—
489	C₂×Q₈	—	2	1	no	—
490	C₂×Q₈	—	2	1	no	—
491	C₂×Q₈	—	2	1	no	—
492	C₂×Q₈	—	2	1	no	—
493	C₂×Q₈	—	2	1	no	—
494	C₂×Q₈	—	8	1	no	—
495	C₂×Q₈	—	8	1	no	—
496	C₂×Q₈	C₂²×C₄×C₇	1	2	yes	—
497	C₂×D₄	—	2	4	no	—
498	C₂×D₄	—	2	1	no	—
499	C₂×D₄	—	2	1	no	—
500	C₂×D₄	—	2	1	no	—
501	C₂×D₄	—	2	1	no	—
502	C₂×D₄	—	2	1	no	—
503	C₂×D₄	—	8	1	no	—
504	C₂×D₄	—	8	1	no	—
505	C₂×D₄	C₂²×C₄×C₇	1	2	yes	—
506	C₂²×C₄	—	2	1	no	—
507	C₂²×C₄	—	2	1	no	—
508	C₂²×C₄	—	2	1	no	—
509	C₂²×C₄	—	2	1	no	—
510	C₂²×C₄	—	2	1	no	—
511	C₂²×C₄	—	2	1	no	—
512	C₂²×C₄	—	2	1	no	—
513	C₂²×C₄	—	2	4	no	—
514	C₂²×C₄	—	2	1	no	—
515	C₂²×C₄	—	2	1	no	—
516	C₂²×C₄	—	2	1	no	—
517	C₂²×C₄	—	2	1	no	—
518	C₂²×C₄	—	8	1	no	—
519	C₂²×C₄	—	8	1	no	—
520	C₂²×C₄	C₂²×C₄×C₇	1	2	yes	—
521	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
522	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
523	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
524	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
525	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
526	C₂²×C₄	C₂×C₇×D₄	1	2	yes	—
527	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
528	M₁₆	—	4	4	no	—
529	C₂×C₈	—	2	1	no	—
530	C₂×C₈	—	2	1	no	—
531	C₂×C₈	—	2	1	no	—
532	C₂×C₈	—	2	1	no	—
533	C₂×C₈	—	2	1	no	—
534	C₂×C₈	—	2	1	no	—
535	C₂×C₈	—	2	1	no	—
536	C₂×C₈	—	2	1	no	—
537	C₂×C₈	—	2	1	no	—
538	C₂×C₈	—	2	1	no	—
539	C₂×C₈	—	2	1	no	—
540	C₂×C₈	—	2	1	no	—
541	C₂×C₈	—	4	4	no	—
542	C₄⋊C₄	—	2	4	no	—
543	C₄⋊C₄	—	2	4	no	—
544	C₄⋊C₄	—	2	4	no	—
545	C₄⋊C₄	—	2	1	no	—
546	C₄⋊C₄	—	2	1	no	—
547	C₄⋊C₄	—	2	1	no	—
548	C₄⋊C₄	—	2	1	no	—
549	C₄⋊C₄	—	2	1	no	—
550	C₄⋊C₄	—	2	1	no	—
551	C₄⋊C₄	—	2	1	no	—
552	C₄⋊C₄	—	2	1	no	—
553	C₄⋊C₄	—	2	1	no	—
554	C₄⋊C₄	—	2	1	no	—
555	C₄⋊C₄	—	8	1	no	—
556	C₄⋊C₄	—	8	1	no	—
557	C₄⋊C₄	C₇×C₂²⋊C₄	1	4	yes	—
558	C₄⋊C₄	C₇×C₂²⋊C₄	1	4	yes	—
559	C₄⋊C₄	C₂²×C₄×C₇	1	2	yes	—
560	C₄⋊C₄	C₂²×C₄×C₇	1	2	yes	—
561	C₂²⋊C₄	—	2	4	no	—
562	C₂²⋊C₄	—	2	4	no	—
563	C₂²⋊C₄	—	2	4	no	—
564	C₂²⋊C₄	—	2	4	no	—
565	C₂²⋊C₄	—	2	4	no	—
566	C₂²⋊C₄	—	8	1	no	—
567	C₂²⋊C₄	—	8	1	no	—
568	C₂²⋊C₄	C₇×C₂²⋊C₄	1	4	yes	—
569	C₂²⋊C₄	C₇×C₂²⋊C₄	1	4	yes	—
570	C₄²	—	2	4	no	—
571	C₄²	—	8	1	no	—
572	C₄²	—	8	1	no	—
573	C₄²	C₂²×C₄×C₇	1	2	yes	—
574	C₄²	C₂²×C₄×C₇	1	2	yes	—
575	C₄²	C₂×C₇×D₄	1	2	yes	—
576	C₄²	C₂×C₇×D₄	1	2	yes	—
577	C₂×C₇	—	4	2	no	—
578	C₂×C₇	—	8	2	no	—
579	C₂×C₇	#2311	1	1	yes	characteristic
580	C₂×C₇	#2897	1	1	yes	characteristic
581	C₂×C₇	#2898	1	1	yes	characteristic
582	C₂×C₇	#3257	1	1	yes	characteristic
583	C₂×C₇	#3258	1	1	yes	characteristic
584	C₂×C₇	#3262	1	1	yes	characteristic
585	C₂×C₇	#3263	1	1	yes	characteristic
586	C₂³	—	2	1	no	—
587	C₂³	—	2	1	no	—
588	C₂³	—	2	1	no	—
589	C₂³	—	2	1	no	—
590	C₂³	—	2	1	no	—
591	C₂³	—	2	1	no	—
592	C₂³	—	2	2	no	—
593	C₂³	—	4	1	no	—
594	C₂³	—	4	1	no	—
595	C₂³	—	4	1	no	—
596	C₂³	—	4	1	no	—
597	C₂³	—	4	1	no	—
598	C₂³	—	4	1	no	—
599	C₂³	C₂×C₇×C₂²⋊C₄	1	2	yes	—
600	C₂³	C₂²×C₇×D₄	1	1	yes	characteristic
601	Q₈	—	2	2	no	—
602	Q₈	—	2	2	no	—
603	Q₈	—	4	1	no	—
604	Q₈	—	4	1	no	—
605	Q₈	—	8	4	no	—
606	D₄	—	2	2	no	—
607	D₄	—	2	2	no	—
608	D₄	—	4	1	no	—
609	D₄	—	4	1	no	—
610	D₄	—	8	4	no	—
611	C₂×C₄	—	2	1	no	—
612	C₂×C₄	—	2	1	no	—
613	C₂×C₄	—	2	1	no	—
614	C₂×C₄	—	2	1	no	—
615	C₂×C₄	—	2	1	no	—
616	C₂×C₄	—	2	1	no	—
617	C₂×C₄	—	2	1	no	—
618	C₂×C₄	—	2	1	no	—
619	C₂×C₄	—	2	1	no	—
620	C₂×C₄	—	2	1	no	—
621	C₂×C₄	—	2	2	no	—
622	C₂×C₄	—	2	2	no	—
623	C₂×C₄	—	2	2	no	—
624	C₂×C₄	—	2	2	no	—
625	C₂×C₄	—	2	2	no	—
626	C₂×C₄	—	2	2	no	—
627	C₂×C₄	—	2	2	no	—
628	C₂×C₄	—	4	1	no	—
629	C₂×C₄	—	4	1	no	—
630	C₂×C₄	—	4	1	no	—
631	C₂×C₄	—	4	1	no	—
632	C₂×C₄	—	4	1	no	—
633	C₂×C₄	—	4	1	no	—
634	C₂×C₄	—	4	1	no	—
635	C₂×C₄	—	4	1	no	—
636	C₂×C₄	—	4	1	no	—
637	C₂×C₄	—	4	1	no	—
638	C₂×C₄	—	4	1	no	—
639	C₂×C₄	—	4	1	no	—
640	C₂×C₄	—	4	1	no	—
641	C₂×C₄	—	4	1	no	—
642	C₂×C₄	—	4	1	no	—
643	C₂×C₄	—	4	1	no	—
644	C₂×C₄	—	4	1	no	—
645	C₂×C₄	—	4	1	no	—
646	C₂×C₄	—	8	4	no	—
647	C₂×C₄	C₂×C₇×C₂²⋊C₄	1	2	yes	—
648	C₂×C₄	C₂×C₇×C₂²⋊C₄	1	2	yes	—
649	C₂×C₄	C₂×C₇×C₂²⋊C₄	1	2	yes	—
650	C₂×C₄	C₂×C₇×C₂²⋊C₄	1	2	yes	—
651	C₂×C₄	C₂×C₇×C₂²⋊C₄	1	2	yes	—
652	C₂×C₄	C₂³×C₄×C₇	1	1	yes	characteristic
653	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
654	C₂×C₄	C₇×H(5,𝔽₂)	1	1	yes	characteristic
655	C₂×C₄	C₇×H(5,𝔽₂)	1	1	yes	characteristic
656	C₂×C₄	C₇×2₋¹⁺⁴	1	1	yes	characteristic
657	C₂×C₄	C₇×2₋¹⁺⁴	1	1	yes	characteristic
658	C₈	—	4	1	no	—
659	C₈	—	4	1	no	—
660	C₈	—	4	1	no	—
661	C₈	—	4	1	no	—
662	C₇	#21896	1	1	yes	characteristic, direct product factor, Sylow
663	C₂²	—	2	2	no	—
664	C₂²	—	2	2	no	—
665	C₂²	—	2	2	no	—
666	C₂²	—	4	1	no	—
667	C₂²	—	4	1	no	—
668	C₂²	—	4	1	no	—
669	C₂²	—	4	1	no	—
670	C₂²	—	4	2	no	—
671	C₂²	—	4	2	no	—
672	C₂²	—	4	2	no	—
673	C₂²	—	8	1	no	—
674	C₂²	—	8	1	no	—
675	C₂²	—	8	1	no	—
676	C₂²	—	8	1	no	—
677	C₂²	C₂²×C₇×C₂²⋊C₄	1	1	yes	characteristic
678	C₂²	C₇×#537	1	1	yes	characteristic
679	C₂²	C₇×#537	1	1	yes	characteristic
680	C₂²	C₇×#576	1	1	yes	characteristic
681	C₂²	C₇×#577	1	1	yes	characteristic
682	C₂²	C₇×#577	1	1	yes	characteristic
683	C₂²	C₇×#578	1	1	yes	characteristic
684	C₄	—	2	2	no	—
685	C₄	—	2	2	no	—
686	C₄	—	2	2	no	—
687	C₄	—	2	2	no	—
688	C₄	—	2	2	no	—
689	C₄	—	4	2	no	—
690	C₄	—	4	2	no	—
691	C₄	—	4	2	no	—
692	C₄	—	8	1	no	—
693	C₄	—	8	1	no	—
694	C₄	—	8	1	no	—
695	C₄	—	8	1	no	—
696	C₄	C₇×#520	1	1	yes	characteristic
697	C₄	C₇×#520	1	1	yes	characteristic
698	C₄	C₇×#535	1	1	yes	characteristic
699	C₄	C₇×#536	1	1	yes	characteristic
700	C₂	—	4	2	no	—
701	C₂	—	8	2	no	—
702	C₂	C₇×#2311	1	1	yes	characteristic
703	C₂	C₇×#2897	1	1	yes	characteristic
704	C₂	C₇×#2898	1	1	yes	characteristic
705	C₂	C₇×#3257	1	1	yes	characteristic
706	C₂	C₇×#3258	1	1	yes	characteristic
707	C₂	C₇×#3262	1	1	yes	characteristic
708	C₂	C₇×#3263	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	C₂×C₇×#121	C₂²
LCS	G ▷ C₂×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
2. C₂×C₇×#424	C₂	semidirect
3. C₇×#2314	C₂	semidirect
4. C₇×#1988	C₂	semidirect
5. C₇×#1987	C₂	semidirect
6. C₇×#1983	C₂	semidirect
7. C₇×#1983	C₂	semidirect
9. C₇×#1894	C₂	semidirect
11. C₇×#1892	C₂	semidirect
12. C₇×#1805	C₂	semidirect
13. C₇×#1804	C₂	semidirect
14. C₇×#1803	C₂	semidirect
15. C₇×#1802	C₂	semidirect
19. C₇×#542	C₄	semidirect
62. #21896	C₇	direct (N × H)
143. C₂×#424	C₂×C₇	semidirect
144. #2314	C₂×C₇	semidirect
145. #1988	C₂×C₇	semidirect
146. #1987	C₂×C₇	semidirect
147. #1983	C₂×C₇	semidirect
148. #1983	C₂×C₇	semidirect
150. #1894	C₂×C₇	semidirect
152. #1892	C₂×C₇	semidirect
153. #1805	C₂×C₇	semidirect
154. #1804	C₂×C₇	semidirect
155. #1803	C₂×C₇	semidirect
156. #1802	C₂×C₇	semidirect
251. #542	C₄×C₇	semidirect
662. C₇	#21896	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×#542	2
C₂×C₇×#424	2
C₇×#2314	2
C₇×#1988	2
C₇×#1987	2
C₇×#1983	2
C₇×#1895	2
C₇×#1894	2
C₇×#1893	2
C₇×#1892	2
C₇×#1805	2
C₇×#1804	2
C₇×#1803	2
C₇×#1802	2
#21896	7

Subgroups — C7×#21896 #13199112

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×#21896 #13199112