Subgroups — C₇×#22775 #13199991

Order 1792.

838 conjugacy classes of subgroups.

The subgroup lattice has 622 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₇×#440	C₂	1	1	yes	maximal, characteristic
2	C₇×#2357	C₂	1	1	yes	maximal, characteristic
3	C₇×Q₈×C₄⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
4	C₇×#1936	C₂	1	1	yes	maximal, characteristic
5	C₇×#1934	C₂	1	1	yes	maximal, characteristic
6	C₇×#1921	C₂	1	1	yes	maximal, characteristic, complemented
7	C₇×#1918	C₂	1	1	yes	maximal, characteristic, complemented
8	C₇×#1880	C₂	1	1	yes	maximal, characteristic
9	C₇×#1880	C₂	1	1	yes	maximal, characteristic
10	C₇×#1836	C₂	1	1	yes	maximal, characteristic, complemented
11	C₇×#1805	C₂	1	1	yes	maximal, characteristic, complemented
12	C₇×#1802	C₂	1	1	yes	maximal, characteristic
13	C₇×#1771	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	C₂×C₄×C₇×Q₈	C₂²	1	1	yes	characteristic
18	C₂×C₄×C₇×Q₈	C₂²	1	1	yes	characteristic
19	C₂×C₄×C₇×Q₈	C₂²	1	1	yes	characteristic
20	C₂×C₄×C₇×D₄	C₂²	1	1	yes	characteristic
21	C₇×#440	C₄	1	8	yes	complemented
22	C₂×C₇×#107	C₂²	1	1	yes	characteristic
23	C₂×C₇×C₄⋊C₈	C₂²	1	1	yes	characteristic
24	C₂×C₇×#103	C₂²	1	1	yes	characteristic
25	C₂×C₇×#103	C₂²	1	1	yes	characteristic
26	C₂×C₇×#103	C₂²	1	1	yes	characteristic
27	C₂×C₇×#102	C₂²	1	1	yes	characteristic
28	C₂×C₇×#102	C₂²	1	1	yes	characteristic
29	C₂×C₇×#102	C₂²	1	1	yes	characteristic
30	C₂×C₇×#97	C₂²	1	1	yes	characteristic
31	C₂×C₇×#97	C₂²	1	1	yes	characteristic
32	C₂×C₄×C₇×C₈	C₂²	1	1	yes	characteristic
33	C₇×#390	C₂²	1	1	yes	characteristic
34	C₇×#390	C₂²	1	1	yes	characteristic
35	C₇×#389	—	2	1	no	—
36	C₇×#389	—	2	1	no	—
37	C₇×#389	C₂²	1	1	yes	characteristic
38	C₇×#389	C₂²	1	1	yes	characteristic
39	C₇×#388	—	2	1	no	—
40	C₇×#388	—	2	1	no	—
41	C₇×#384	—	2	1	no	—
42	C₇×#384	C₂²	1	1	yes	characteristic
43	C₇×#382	C₂²	1	1	yes	characteristic
44	C₇×#381	—	2	1	no	—
45	C₄×C₇×C₄⋊C₄	—	2	1	no	—
46	C₄×C₇×C₄⋊C₄	C₂²	1	1	yes	characteristic
47	C₄×C₇×C₄⋊C₄	C₂²	1	1	yes	characteristic
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	#22775	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
61	C₂²×C₇×Q₈	C₂³	1	1	yes	characteristic
62	C₂²×C₇×D₄	C₂³	1	1	yes	characteristic
63	C₂³×C₄×C₇	—	2	1	no	—
64	C₂×C₇×SD₁₆	—	2	2	no	—
65	C₂×C₇×SD₁₆	—	2	2	no	—
66	C₂×C₇×SD₁₆	C₂×C₄	1	4	yes	—
67	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
68	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
69	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
70	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
71	C₄×C₇×Q₈	—	2	2	no	—
72	C₄×C₇×Q₈	—	2	2	no	—
73	C₄×C₇×Q₈	—	2	2	no	—
74	C₄×C₇×Q₈	—	4	1	no	—
75	C₄×C₇×Q₈	—	4	1	no	—
76	C₄×C₇×Q₈	C₂×C₄	1	4	yes	—
77	C₄×C₇×D₄	—	2	2	no	—
78	C₄×C₇×D₄	C₂×C₄	1	4	yes	—
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	—	2	1	no	—
85	C₂×C₇×C₄⋊C₄	—	2	1	no	—
86	C₂×C₇×C₄⋊C₄	D₄	1	1	yes	characteristic
87	C₂×C₇×C₄⋊C₄	D₄	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×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×#107	C₂×C₄	1	4	yes	—
108	C₇×C₄⋊C₈	—	2	2	no	—
109	C₇×#103	—	2	2	no	—
110	C₇×#103	—	2	2	no	—
111	C₇×#103	C₂×C₄	1	4	yes	—
112	C₇×#102	—	4	1	no	—
113	C₇×#102	—	4	1	no	—
114	C₇×#102	C₂×C₄	1	4	yes	—
115	C₇×#97	—	4	1	no	—
116	C₇×#97	C₂×C₄	1	4	yes	—
117	C₄×C₇×C₈	—	4	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	D₄	1	1	yes	characteristic
125	C₇×#95	D₄	1	1	yes	characteristic
126	C₂×#440	C₂×C₇	1	1	yes	characteristic
127	#2357	C₂×C₇	1	1	yes	characteristic
128	Q₈×C₄⋊C₄	C₂×C₇	1	1	yes	characteristic, complemented
129	#1936	C₂×C₇	1	1	yes	characteristic
130	#1934	C₂×C₇	1	1	yes	characteristic
131	#1921	C₂×C₇	1	1	yes	characteristic, complemented
132	#1918	C₂×C₇	1	1	yes	characteristic, complemented
133	#1880	C₂×C₇	1	1	yes	characteristic
134	#1880	C₂×C₇	1	1	yes	characteristic
135	#1836	C₂×C₇	1	1	yes	characteristic, complemented
136	#1805	C₂×C₇	1	1	yes	characteristic, complemented
137	#1802	C₂×C₇	1	1	yes	characteristic
138	#1771	C₂×C₇	1	1	yes	characteristic, complemented
139	#1763	C₂×C₇	1	1	yes	characteristic, complemented
140	C₄×#103	C₂×C₇	1	1	yes	characteristic, complemented
141	C₂⁴×C₇	—	2	1	no	—
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	C₂²×C₄	1	2	yes	—
146	C₂×C₇×Q₈	#41	1	2	yes	—
147	C₂×C₇×Q₈	#41	1	2	yes	—
148	C₂×C₇×D₄	—	2	1	no	—
149	C₂×C₇×D₄	—	2	1	no	—
150	C₂×C₇×D₄	—	2	1	no	—
151	C₂×C₇×D₄	—	2	1	no	—
152	C₂×C₇×D₄	—	2	1	no	—
153	C₂×C₇×D₄	C₂²×C₄	1	2	yes	—
154	C₂²×C₄×C₇	—	2	1	no	—
155	C₂²×C₄×C₇	—	2	1	no	—
156	C₂²×C₄×C₇	—	2	1	no	—
157	C₂²×C₄×C₇	—	2	4	no	—
158	C₂²×C₄×C₇	—	2	1	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	—	8	1	no	—
163	C₂²×C₄×C₇	—	8	1	no	—
164	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
165	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
166	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
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	C₂⁴	1	1	yes	characteristic
171	C₇×SD₁₆	—	2	8	no	—
172	C₂×C₇×C₈	—	2	1	no	—
173	C₂×C₇×C₈	—	2	1	no	—
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	C₂²×C₄	1	2	yes	—
183	C₂×C₇×C₈	C₂²×C₄	1	2	yes	—
184	C₇×C₄⋊C₄	—	2	4	no	—
185	C₇×C₄⋊C₄	—	2	2	no	—
186	C₇×C₄⋊C₄	—	2	1	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	—	4	1	no	—
197	C₇×C₄⋊C₄	—	4	2	no	—
198	C₇×C₄⋊C₄	—	4	2	no	—
199	C₇×C₄⋊C₄	—	4	2	no	—
200	C₇×C₄⋊C₄	—	8	1	no	—
201	C₇×C₄⋊C₄	—	8	1	no	—
202	C₇×C₄⋊C₄	—	8	1	no	—
203	C₇×C₄⋊C₄	C₂²×C₄	1	2	yes	—
204	C₇×C₄⋊C₄	C₂²×C₄	1	2	yes	—
205	C₇×C₂²⋊C₄	—	2	4	no	—
206	C₇×C₂²⋊C₄	—	4	2	no	—
207	C₇×C₂²⋊C₄	—	4	2	no	—
208	C₇×C₂²⋊C₄	—	8	1	no	—
209	C₇×C₂²⋊C₄	—	8	1	no	—
210	C₄²×C₇	—	2	4	no	—
211	C₄²×C₇	—	2	1	no	—
212	C₄²×C₇	—	2	1	no	—
213	C₄²×C₇	—	2	1	no	—
214	C₄²×C₇	—	2	1	no	—
215	C₄²×C₇	—	4	2	no	—
216	C₄²×C₇	—	4	2	no	—
217	C₄²×C₇	—	8	1	no	—
218	C₄²×C₇	—	8	1	no	—
219	C₄²×C₇	C₂²×C₄	1	2	yes	—
220	C₄²×C₇	#41	1	2	yes	—
221	C₂²×SD₁₆	C₂²×C₇	1	1	yes	characteristic
222	C₂×C₄×Q₈	C₂²×C₇	1	1	yes	characteristic
223	C₂×C₄×Q₈	C₂²×C₇	1	1	yes	characteristic
224	C₂×C₄×Q₈	C₂²×C₇	1	1	yes	characteristic
225	C₂×C₄×D₄	C₂²×C₇	1	1	yes	characteristic
226	#440	C₄×C₇	1	8	yes	complemented
227	C₂×#107	C₂²×C₇	1	1	yes	characteristic
228	C₂×C₄⋊C₈	C₂²×C₇	1	1	yes	characteristic
229	C₂×#103	C₂²×C₇	1	1	yes	characteristic
230	C₂×#103	C₂²×C₇	1	1	yes	characteristic
231	C₂×#103	C₂²×C₇	1	1	yes	characteristic
232	C₂×#102	C₂²×C₇	1	1	yes	characteristic
233	C₂×#102	C₂²×C₇	1	1	yes	characteristic
234	C₂×#102	C₂²×C₇	1	1	yes	characteristic
235	C₂×#97	C₂²×C₇	1	1	yes	characteristic
236	C₂×#97	C₂²×C₇	1	1	yes	characteristic
237	C₂×C₄×C₈	C₂²×C₇	1	1	yes	characteristic
238	#390	C₂²×C₇	1	1	yes	characteristic
239	#390	C₂²×C₇	1	1	yes	characteristic
240	#389	—	2	1	no	—
241	#389	—	2	1	no	—
242	#389	C₂²×C₇	1	1	yes	characteristic
243	#389	C₂²×C₇	1	1	yes	characteristic
244	#388	—	2	1	no	—
245	#388	—	2	1	no	—
246	#384	—	2	1	no	—
247	#384	C₂²×C₇	1	1	yes	characteristic
248	#382	C₂²×C₇	1	1	yes	characteristic
249	#381	—	2	1	no	—
250	C₄×C₄⋊C₄	—	2	1	no	—
251	C₄×C₄⋊C₄	C₂²×C₇	1	1	yes	characteristic
252	C₄×C₄⋊C₄	C₂²×C₇	1	1	yes	characteristic
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	2	no	—
266	C₂³×C₇	—	4	1	no	—
267	C₂³×C₇	—	4	1	no	—
268	C₂³×C₇	—	4	1	no	—
269	C₂³×C₇	—	4	1	no	—
270	C₂³×C₇	—	4	1	no	—
271	C₂³×C₇	—	4	1	no	—
272	C₂³×C₇	C₂²×D₄	1	1	yes	characteristic
273	C₇×Q₈	—	2	2	no	—
274	C₇×Q₈	—	2	2	no	—
275	C₇×Q₈	—	2	2	no	—
276	C₇×Q₈	#117	1	4	yes	—
277	C₇×D₄	—	2	2	no	—
278	C₇×D₄	—	2	2	no	—
279	C₇×D₄	—	4	1	no	—
280	C₇×D₄	—	4	1	no	—
281	C₂×C₄×C₇	—	2	2	no	—
282	C₂×C₄×C₇	—	2	1	no	—
283	C₂×C₄×C₇	—	2	2	no	—
284	C₂×C₄×C₇	—	2	2	no	—
285	C₂×C₄×C₇	—	2	1	no	—
286	C₂×C₄×C₇	—	2	1	no	—
287	C₂×C₄×C₇	—	2	1	no	—
288	C₂×C₄×C₇	—	2	1	no	—
289	C₂×C₄×C₇	—	2	1	no	—
290	C₂×C₄×C₇	—	2	2	no	—
291	C₂×C₄×C₇	—	2	2	no	—
292	C₂×C₄×C₇	—	2	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	1	no	—
300	C₂×C₄×C₇	—	2	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	—	8	4	no	—
318	C₂×C₄×C₇	C₄×D₄	1	2	yes	—
319	C₂×C₄×C₇	C₄×D₄	1	2	yes	—
320	C₂×C₄×C₇	#137	1	2	yes	—
321	C₂×C₄×C₇	C₂³×C₄	1	1	yes	characteristic
322	C₂×C₄×C₇	C₂×#41	1	1	yes	characteristic
323	C₂×C₄×C₇	C₂×#41	1	1	yes	characteristic
324	C₂×C₄×C₇	C₂×#41	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	C₇×C₈	—	2	2	no	—
328	C₇×C₈	—	2	2	no	—
329	C₇×C₈	—	4	1	no	—
330	C₇×C₈	—	4	1	no	—
331	C₂²×Q₈	C₂³×C₇	1	1	yes	characteristic
332	C₂²×D₄	C₂³×C₇	1	1	yes	characteristic
333	C₂³×C₄	—	2	1	no	—
334	C₂×SD₁₆	—	2	2	no	—
335	C₂×SD₁₆	—	2	2	no	—
336	C₂×SD₁₆	C₂×C₄×C₇	1	4	yes	—
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×C₈	C₂³×C₇	1	1	yes	characteristic
341	C₄×Q₈	—	2	2	no	—
342	C₄×Q₈	—	2	2	no	—
343	C₄×Q₈	—	2	2	no	—
344	C₄×Q₈	—	4	1	no	—
345	C₄×Q₈	—	4	1	no	—
346	C₄×Q₈	C₂×C₄×C₇	1	4	yes	—
347	C₄×D₄	—	2	2	no	—
348	C₄×D₄	C₂×C₄×C₇	1	4	yes	—
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	—	2	1	no	—
356	C₂×C₄⋊C₄	C₇×D₄	1	1	yes	characteristic
357	C₂×C₄⋊C₄	C₇×D₄	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×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
363	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
364	C₂×C₂²⋊C₄	—	2	1	no	—
365	C₂×C₂²⋊C₄	—	2	1	no	—
366	C₂×C₂²⋊C₄	—	2	1	no	—
367	C₂×C₂²⋊C₄	—	2	1	no	—
368	C₂×C₂²⋊C₄	—	2	1	no	—
369	C₂×C₄²	—	2	1	no	—
370	C₂×C₄²	—	2	1	no	—
371	C₂×C₄²	—	2	1	no	—
372	C₂×C₄²	—	2	1	no	—
373	C₂×C₄²	—	2	1	no	—
374	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
375	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
376	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
377	#107	C₂×C₄×C₇	1	4	yes	—
378	C₄⋊C₈	—	2	2	no	—
379	#103	—	2	2	no	—
380	#103	—	2	2	no	—
381	#103	C₂×C₄×C₇	1	4	yes	—
382	#102	—	4	1	no	—
383	#102	—	4	1	no	—
384	#102	C₂×C₄×C₇	1	4	yes	—
385	#97	—	4	1	no	—
386	#97	C₂×C₄×C₇	1	4	yes	—
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	C₇×D₄	1	1	yes	characteristic
395	#95	C₇×D₄	1	1	yes	characteristic
396	C₂²×C₇	—	4	2	no	—
397	C₂²×C₇	—	4	2	no	—
398	C₂²×C₇	—	4	2	no	—
399	C₂²×C₇	—	8	1	no	—
400	C₂²×C₇	—	8	1	no	—
401	C₂²×C₇	—	8	1	no	—
402	C₂²×C₇	—	8	1	no	—
403	C₂²×C₇	C₂×C₄×D₄	1	1	yes	characteristic
404	C₂²×C₇	#546	1	1	yes	characteristic
405	C₂²×C₇	#548	1	1	yes	characteristic
406	C₂²×C₇	C₂×#137	1	1	yes	characteristic
407	C₂²×C₇	#575	1	1	yes	characteristic
408	C₂²×C₇	#576	1	1	yes	characteristic
409	C₂²×C₇	#577	1	1	yes	characteristic
410	C₄×C₇	—	2	4	no	—
411	C₄×C₇	—	2	2	no	—
412	C₄×C₇	—	2	2	no	—
413	C₄×C₇	—	2	2	no	—
414	C₄×C₇	—	4	2	no	—
415	C₄×C₇	—	4	2	no	—
416	C₄×C₇	—	4	1	no	—
417	C₄×C₇	—	4	1	no	—
418	C₄×C₇	—	4	1	no	—
419	C₄×C₇	—	8	1	no	—
420	C₄×C₇	—	8	1	no	—
421	C₄×C₇	—	8	1	no	—
422	C₄×C₇	—	8	1	no	—
423	C₄×C₇	C₂×#117	1	1	yes	characteristic
424	C₄×C₇	#520	1	1	yes	characteristic
425	C₄×C₇	#552	1	1	yes	characteristic
426	C₄×C₇	#553	1	1	yes	characteristic
427	C₂⁴	—	2	1	no	—
428	C₂×Q₈	—	2	1	no	—
429	C₂×Q₈	—	2	1	no	—
430	C₂×Q₈	—	2	1	no	—
431	C₂×Q₈	C₂²×C₄×C₇	1	2	yes	—
432	C₂×Q₈	C₇×#41	1	2	yes	—
433	C₂×Q₈	C₇×#41	1	2	yes	—
434	C₂×D₄	—	2	1	no	—
435	C₂×D₄	—	2	1	no	—
436	C₂×D₄	—	2	1	no	—
437	C₂×D₄	—	2	1	no	—
438	C₂×D₄	—	2	1	no	—
439	C₂×D₄	C₂²×C₄×C₇	1	2	yes	—
440	C₂²×C₄	—	2	1	no	—
441	C₂²×C₄	—	2	1	no	—
442	C₂²×C₄	—	2	1	no	—
443	C₂²×C₄	—	2	4	no	—
444	C₂²×C₄	—	2	1	no	—
445	C₂²×C₄	—	2	1	no	—
446	C₂²×C₄	—	2	1	no	—
447	C₂²×C₄	—	2	1	no	—
448	C₂²×C₄	—	8	1	no	—
449	C₂²×C₄	—	8	1	no	—
450	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
451	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
452	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
453	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
454	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
455	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
456	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
457	SD₁₆	—	2	8	no	—
458	C₂×C₈	—	2	1	no	—
459	C₂×C₈	—	2	1	no	—
460	C₂×C₈	—	2	1	no	—
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	C₂²×C₄×C₇	1	2	yes	—
469	C₂×C₈	C₂²×C₄×C₇	1	2	yes	—
470	C₄⋊C₄	—	2	4	no	—
471	C₄⋊C₄	—	2	2	no	—
472	C₄⋊C₄	—	2	1	no	—
473	C₄⋊C₄	—	2	1	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	—	4	1	no	—
483	C₄⋊C₄	—	4	2	no	—
484	C₄⋊C₄	—	4	2	no	—
485	C₄⋊C₄	—	4	2	no	—
486	C₄⋊C₄	—	8	1	no	—
487	C₄⋊C₄	—	8	1	no	—
488	C₄⋊C₄	—	8	1	no	—
489	C₄⋊C₄	C₂²×C₄×C₇	1	2	yes	—
490	C₄⋊C₄	C₂²×C₄×C₇	1	2	yes	—
491	C₂²⋊C₄	—	2	4	no	—
492	C₂²⋊C₄	—	4	2	no	—
493	C₂²⋊C₄	—	4	2	no	—
494	C₂²⋊C₄	—	8	1	no	—
495	C₂²⋊C₄	—	8	1	no	—
496	C₄²	—	2	4	no	—
497	C₄²	—	2	1	no	—
498	C₄²	—	2	1	no	—
499	C₄²	—	2	1	no	—
500	C₄²	—	2	1	no	—
501	C₄²	—	4	2	no	—
502	C₄²	—	4	2	no	—
503	C₄²	—	8	1	no	—
504	C₄²	—	8	1	no	—
505	C₄²	C₂²×C₄×C₇	1	2	yes	—
506	C₄²	C₇×#41	1	2	yes	—
507	C₂×C₇	—	8	2	no	—
508	C₂×C₇	#2352	1	1	yes	characteristic
509	C₂×C₇	C₄×#137	1	1	yes	characteristic
510	C₂×C₇	#2946	1	1	yes	characteristic
511	C₂×C₇	#3309	1	1	yes	characteristic
512	C₂×C₇	#3320	1	1	yes	characteristic
513	C₂×C₇	#3371	1	1	yes	characteristic
514	C₂×C₇	#3375	1	1	yes	characteristic
515	C₂³	—	2	2	no	—
516	C₂³	—	4	1	no	—
517	C₂³	—	4	1	no	—
518	C₂³	—	4	1	no	—
519	C₂³	—	4	1	no	—
520	C₂³	—	4	1	no	—
521	C₂³	—	4	1	no	—
522	C₂³	C₂²×C₇×D₄	1	1	yes	characteristic
523	Q₈	—	2	2	no	—
524	Q₈	—	2	2	no	—
525	Q₈	—	2	2	no	—
526	Q₈	C₇×#117	1	4	yes	—
527	D₄	—	2	2	no	—
528	D₄	—	2	2	no	—
529	D₄	—	4	1	no	—
530	D₄	—	4	1	no	—
531	C₂×C₄	—	2	2	no	—
532	C₂×C₄	—	2	1	no	—
533	C₂×C₄	—	2	2	no	—
534	C₂×C₄	—	2	2	no	—
535	C₂×C₄	—	2	1	no	—
536	C₂×C₄	—	2	1	no	—
537	C₂×C₄	—	2	1	no	—
538	C₂×C₄	—	2	1	no	—
539	C₂×C₄	—	2	1	no	—
540	C₂×C₄	—	2	2	no	—
541	C₂×C₄	—	2	2	no	—
542	C₂×C₄	—	2	1	no	—
543	C₂×C₄	—	2	1	no	—
544	C₂×C₄	—	2	1	no	—
545	C₂×C₄	—	2	1	no	—
546	C₂×C₄	—	2	1	no	—
547	C₂×C₄	—	2	1	no	—
548	C₂×C₄	—	2	1	no	—
549	C₂×C₄	—	2	1	no	—
550	C₂×C₄	—	2	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	—	8	4	no	—
568	C₂×C₄	C₄×C₇×D₄	1	2	yes	—
569	C₂×C₄	C₄×C₇×D₄	1	2	yes	—
570	C₂×C₄	C₇×#137	1	2	yes	—
571	C₂×C₄	C₂³×C₄×C₇	1	1	yes	characteristic
572	C₂×C₄	C₂×C₇×#41	1	1	yes	characteristic
573	C₂×C₄	C₂×C₇×#41	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	C₇×2₋¹⁺⁴	1	1	yes	characteristic
577	C₈	—	2	2	no	—
578	C₈	—	2	2	no	—
579	C₈	—	4	1	no	—
580	C₈	—	4	1	no	—
581	C₇	#22775	1	1	yes	characteristic, direct product factor, Sylow
582	C₂²	—	4	2	no	—
583	C₂²	—	4	2	no	—
584	C₂²	—	4	2	no	—
585	C₂²	—	8	1	no	—
586	C₂²	—	8	1	no	—
587	C₂²	—	8	1	no	—
588	C₂²	—	8	1	no	—
589	C₂²	C₂×C₄×C₇×D₄	1	1	yes	characteristic
590	C₂²	C₇×#546	1	1	yes	characteristic
591	C₂²	C₇×#548	1	1	yes	characteristic
592	C₂²	C₂×C₇×#137	1	1	yes	characteristic
593	C₂²	C₇×#575	1	1	yes	characteristic
594	C₂²	C₇×#576	1	1	yes	characteristic
595	C₂²	C₇×#577	1	1	yes	characteristic
596	C₄	—	2	2	no	—
597	C₄	—	2	2	no	—
598	C₄	—	2	2	no	—
599	C₄	—	2	4	no	—
600	C₄	—	4	2	no	—
601	C₄	—	4	2	no	—
602	C₄	—	4	1	no	—
603	C₄	—	4	1	no	—
604	C₄	—	4	1	no	—
605	C₄	—	8	1	no	—
606	C₄	—	8	1	no	—
607	C₄	—	8	1	no	—
608	C₄	—	8	1	no	—
609	C₄	C₂×C₇×#117	1	1	yes	characteristic
610	C₄	C₇×#520	1	1	yes	characteristic
611	C₄	C₇×#552	1	1	yes	characteristic
612	C₄	C₇×#553	1	1	yes	characteristic
613	C₂	—	8	2	no	—
614	C₂	C₇×#2352	1	1	yes	characteristic
615	C₂	C₄×C₇×#137	1	1	yes	characteristic
616	C₂	C₇×#2946	1	1	yes	characteristic
617	C₂	C₇×#3309	1	1	yes	characteristic
618	C₂	C₇×#3320	1	1	yes	characteristic
619	C₂	C₇×#3371	1	1	yes	characteristic
620	C₂	C₇×#3375	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×Q₈×C₄⋊C₄	C₂	semidirect
6. C₇×#1921	C₂	semidirect
7. C₇×#1918	C₂	semidirect
10. C₇×#1836	C₂	semidirect
11. C₇×#1805	C₂	semidirect
13. C₇×#1771	C₂	semidirect
14. C₇×#1763	C₂	semidirect
15. C₄×C₇×#103	C₂	semidirect
21. C₇×#440	C₄	semidirect
60. #22775	C₇	direct (N × H)
128. Q₈×C₄⋊C₄	C₂×C₇	semidirect
131. #1921	C₂×C₇	semidirect
132. #1918	C₂×C₇	semidirect
135. #1836	C₂×C₇	semidirect
136. #1805	C₂×C₇	semidirect
138. #1771	C₂×C₇	semidirect
139. #1763	C₂×C₇	semidirect
140. C₄×#103	C₂×C₇	semidirect
226. #440	C₄×C₇	semidirect
581. C₇	#22775	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×#440	2
C₇×#2357	2
C₇×Q₈×C₄⋊C₄	2
C₇×#1936	2
C₇×#1934	2
C₇×#1921	2
C₇×#1918	2
C₇×#1880	2
C₇×#1836	2
C₇×#1805	2
C₇×#1802	2
C₇×#1771	2
C₇×#1763	2
C₄×C₇×#103	2
#22775	7

Subgroups — C7×#22775 #13199991

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×#22775 #13199991