Subgroups — C₇×#19625 #13196841

Order 1792.

836 conjugacy classes of subgroups.

The subgroup lattice has 454 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×#3230	C₂	1	1	yes	maximal, characteristic, complemented
2	C₇×#3205	C₂	1	1	yes	maximal, characteristic
3	C₇×#3167	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₇×#492	C₂	1	1	yes	maximal, characteristic, complemented
5	C₇×#3141	C₂	1	1	yes	maximal, characteristic, complemented
6	C₇×#3138	C₂	1	1	yes	maximal, characteristic, complemented
7	C₇×#1719	C₂	1	2	yes	maximal, complemented
8	C₇×#1717	C₂	1	2	yes	maximal, complemented
9	C₇×#1708	C₂	1	2	yes	maximal, complemented
10	C₇×#1706	C₂	1	2	yes	maximal, complemented
11	C₇×C₈×M₁₆	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×C₇×SD₁₆	—	2	2	no	—
13	C₇×#533	C₂²	1	1	yes	characteristic
14	C₇×#532	C₂²	1	1	yes	characteristic
15	C₂×C₇×C₄⋊Q₈	C₂²	1	1	yes	characteristic
16	C₂×C₇×#127	C₂²	1	1	yes	characteristic
17	C₇×#500	C₂²	1	2	yes	complemented
18	C₇×#498	C₂²	1	1	yes	characteristic, complemented
19	C₇×#493	C₂²	1	2	yes	—
20	C₇×#492	—	2	2	no	—
21	C₇×#492	C₂²	1	2	yes	—
22	C₇×#492	C₂²	1	2	yes	—
23	C₇×#492	C₂²	1	1	yes	characteristic, complemented
24	C₇×#490	—	2	2	no	—
25	C₇×#489	—	2	2	no	—
26	C₇×#487	C₂²	1	2	yes	complemented
27	C₇×#487	C₂²	1	2	yes	complemented
28	C₇×#487	C₂²	1	1	yes	characteristic, complemented
29	C₇×#486	C₂²	1	2	yes	—
30	C₇×#486	C₂²	1	2	yes	—
31	C₇×#486	C₂²	1	2	yes	—
32	C₇×#486	C₂²	1	1	yes	characteristic, complemented
33	C₇×#486	C₂²	1	2	yes	complemented
34	C₇×#484	—	2	2	no	—
35	C₇×#477	—	2	2	no	—
36	C₇×#465	—	2	2	no	—
37	C₇×#459	—	2	2	no	—
38	C₇×#447	—	2	2	no	—
39	C₄×C₇×SD₁₆	—	2	2	no	—
40	C₇×#431	C₂²	1	1	yes	characteristic
41	C₇×#418	—	2	2	no	—
42	C₇×#417	—	2	2	no	—
43	C₄×C₇×M₁₆	C₂²	1	1	yes	characteristic
44	C₂×C₄×C₇×C₈	C₂²	1	1	yes	characteristic
45	C₇×#322	C₂²	1	2	yes	complemented
46	C₇×C₈²	C₂²	1	2	yes	complemented
47	#19625	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
48	C₂×C₇×#41	—	2	1	no	—
49	C₂²×C₇×Q₈	—	2	1	no	—
50	C₂²×C₇×D₄	—	2	1	no	—
51	C₂²×C₇×D₄	—	2	1	no	—
52	C₂²×C₇×D₄	—	2	1	no	—
53	C₂×C₇×SD₁₆	—	2	4	no	—
54	C₂×C₇×SD₁₆	—	2	4	no	—
55	C₂×C₇×SD₁₆	—	2	2	no	—
56	C₂×C₇×SD₁₆	—	4	8	no	—
57	C₂×C₇×D₈	—	2	4	no	—
58	C₂×C₇×M₁₆	D₄	1	2	yes	—
59	C₂²×C₇×C₈	D₄	1	2	yes	—
60	C₇×C₄⋊Q₈	—	2	1	no	—
61	C₇×C₄⋊Q₈	—	2	1	no	—
62	C₇×C₄⋊Q₈	—	2	1	no	—
63	C₇×C₄⋊Q₈	C₂³	1	1	yes	characteristic
64	C₇×C₄⋊Q₈	C₂³	1	1	yes	characteristic
65	C₇×C₄⋊Q₈	C₂³	1	1	yes	characteristic
66	C₇×C₄⋊Q₈	C₂³	1	2	yes	—
67	C₇×#127	—	2	1	no	—
68	C₇×#127	—	2	1	no	—
69	C₇×#127	—	2	1	no	—
70	C₇×#127	C₂³	1	2	yes	—
71	C₇×#127	C₂³	1	1	yes	characteristic
72	C₇×#125	—	2	1	no	—
73	C₇×#124	—	2	1	no	—
74	C₇×C₂²⋊Q₈	—	2	1	no	—
75	C₇×C₂²⋊Q₈	—	2	1	no	—
76	C₇×#121	—	2	1	no	—
77	C₇×#121	—	2	1	no	—
78	C₄×C₇×Q₈	—	2	1	no	—
79	C₄×C₇×Q₈	—	2	1	no	—
80	C₄×C₇×D₄	—	2	1	no	—
81	C₄×C₇×D₄	—	2	1	no	—
82	C₇×#117	—	2	1	no	—
83	C₂×C₇×C₄⋊C₄	—	2	1	no	—
84	C₂×C₇×C₄⋊C₄	—	2	1	no	—
85	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
86	C₇×#107	—	2	4	no	—
87	C₇×#106	—	2	2	no	—
88	C₇×C₄⋊C₈	D₄	1	2	yes	—
89	C₇×#103	—	2	4	no	—
90	C₇×#103	—	2	4	no	—
91	C₇×#103	—	2	2	no	—
92	C₇×#102	—	2	4	no	—
93	C₇×#102	—	2	4	no	—
94	C₇×#102	—	2	4	no	—
95	C₇×#102	—	2	4	no	—
96	C₇×#102	—	2	2	no	—
97	C₇×C₂²⋊C₈	D₄	1	2	yes	—
98	C₇×#97	D₄	1	2	yes	—
99	C₄×C₇×C₈	D₄	1	2	yes	—
100	C₄×C₇×C₈	C₂³	1	1	yes	characteristic
101	C₄×C₇×C₈	C₂³	1	2	yes	—
102	C₄×C₇×C₈	C₂³	1	2	yes	—
103	C₄×C₇×C₈	C₂³	1	1	yes	characteristic
104	#3230	C₂×C₇	1	1	yes	characteristic, complemented
105	#3205	C₂×C₇	1	1	yes	characteristic
106	#3167	C₂×C₇	1	1	yes	characteristic, complemented
107	C₂×#492	C₂×C₇	1	1	yes	characteristic, complemented
108	#3141	C₂×C₇	1	1	yes	characteristic, complemented
109	#3138	C₂×C₇	1	1	yes	characteristic, complemented
110	#1719	C₂×C₇	1	2	yes	complemented
111	#1717	C₂×C₇	1	2	yes	complemented
112	#1708	C₂×C₇	1	2	yes	complemented
113	#1706	C₂×C₇	1	2	yes	complemented
114	C₈×M₁₆	C₂×C₇	1	1	yes	characteristic, complemented
115	C₂⁴×C₇	—	4	1	no	—
116	C₇×#41	—	4	4	no	—
117	C₂×C₇×Q₈	—	2	1	no	—
118	C₂×C₇×Q₈	—	2	1	no	—
119	C₂×C₇×Q₈	—	2	1	no	—
120	C₂×C₇×Q₈	—	2	2	no	—
121	C₂×C₇×Q₈	—	4	4	no	—
122	C₂×C₇×Q₈	—	4	1	no	—
123	C₂×C₇×D₄	—	2	1	no	—
124	C₂×C₇×D₄	—	2	2	no	—
125	C₂×C₇×D₄	—	2	1	no	—
126	C₂×C₇×D₄	—	2	2	no	—
127	C₂×C₇×D₄	—	2	1	no	—
128	C₂×C₇×D₄	—	2	2	no	—
129	C₂×C₇×D₄	—	4	4	no	—
130	C₂×C₇×D₄	—	4	1	no	—
131	C₂×C₇×D₄	—	4	1	no	—
132	C₂×C₇×D₄	—	4	1	no	—
133	C₂×C₇×D₄	—	4	1	no	—
134	C₂×C₇×D₄	—	4	4	no	—
135	C₂×C₇×D₄	—	8	2	no	—
136	C₂²×C₄×C₇	—	4	1	no	—
137	C₂²×C₄×C₇	—	4	1	no	—
138	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
139	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
140	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
141	C₇×SD₁₆	—	4	8	no	—
142	C₇×SD₁₆	—	4	4	no	—
143	C₇×SD₁₆	—	4	8	no	—
144	C₇×D₈	—	8	4	no	—
145	C₇×M₁₆	—	2	4	no	—
146	C₂×C₇×C₈	—	2	4	no	—
147	C₂×C₇×C₈	C₂×D₄	1	2	yes	—
148	C₂×C₇×C₈	C₂×D₄	1	4	yes	—
149	C₂×C₇×C₈	C₂×D₄	1	4	yes	—
150	C₂×C₇×C₈	C₂×D₄	1	2	yes	—
151	C₇×C₄⋊C₄	—	2	1	no	—
152	C₇×C₄⋊C₄	—	2	1	no	—
153	C₇×C₄⋊C₄	—	2	1	no	—
154	C₇×C₄⋊C₄	—	2	2	no	—
155	C₇×C₄⋊C₄	—	2	1	no	—
156	C₇×C₄⋊C₄	—	2	1	no	—
157	C₇×C₄⋊C₄	—	2	2	no	—
158	C₇×C₄⋊C₄	—	2	1	no	—
159	C₇×C₄⋊C₄	—	4	1	no	—
160	C₇×C₄⋊C₄	—	4	1	no	—
161	C₇×C₄⋊C₄	—	4	1	no	—
162	C₇×C₄⋊C₄	—	4	1	no	—
163	C₇×C₂²⋊C₄	—	4	1	no	—
164	C₇×C₂²⋊C₄	—	4	1	no	—
165	C₇×C₂²⋊C₄	—	4	1	no	—
166	C₄²×C₇	—	4	1	no	—
167	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
168	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
169	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
170	C₄²×C₇	C₂⁴	1	1	yes	characteristic
171	C₂²×SD₁₆	—	2	2	no	—
172	#533	C₂²×C₇	1	1	yes	characteristic
173	#532	C₂²×C₇	1	1	yes	characteristic
174	C₂×C₄⋊Q₈	C₂²×C₇	1	1	yes	characteristic
175	C₂×#127	C₂²×C₇	1	1	yes	characteristic
176	#500	C₂²×C₇	1	2	yes	complemented
177	#498	C₂²×C₇	1	1	yes	characteristic, complemented
178	#493	C₂²×C₇	1	2	yes	—
179	#492	—	2	2	no	—
180	#492	C₂²×C₇	1	2	yes	—
181	#492	C₂²×C₇	1	2	yes	—
182	#492	C₂²×C₇	1	1	yes	characteristic, complemented
183	#490	—	2	2	no	—
184	#489	—	2	2	no	—
185	#487	C₂²×C₇	1	2	yes	complemented
186	#487	C₂²×C₇	1	1	yes	characteristic, complemented
187	#487	C₂²×C₇	1	2	yes	complemented
188	#486	C₂²×C₇	1	2	yes	—
189	#486	C₂²×C₇	1	2	yes	—
190	#486	C₂²×C₇	1	2	yes	—
191	#486	C₂²×C₇	1	2	yes	complemented
192	#486	C₂²×C₇	1	1	yes	characteristic, complemented
193	#484	—	2	2	no	—
194	#477	—	2	2	no	—
195	#465	—	2	2	no	—
196	#459	—	2	2	no	—
197	#447	—	2	2	no	—
198	C₄×SD₁₆	—	2	2	no	—
199	#431	C₂²×C₇	1	1	yes	characteristic
200	#418	—	2	2	no	—
201	#417	—	2	2	no	—
202	C₄×M₁₆	C₂²×C₇	1	1	yes	characteristic
203	C₂×C₄×C₈	C₂²×C₇	1	1	yes	characteristic
204	#322	C₂²×C₇	1	2	yes	complemented
205	C₈²	C₂²×C₇	1	2	yes	complemented
206	C₂³×C₇	—	4	1	no	—
207	C₂³×C₇	—	4	2	no	—
208	C₂³×C₇	—	8	2	no	—
209	C₂³×C₇	—	8	2	no	—
210	C₂³×C₇	—	8	2	no	—
211	C₂³×C₇	#127	1	1	yes	characteristic
212	C₇×Q₈	—	4	2	no	—
213	C₇×Q₈	—	4	4	no	—
214	C₇×Q₈	—	4	2	no	—
215	C₇×Q₈	—	4	2	no	—
216	C₇×Q₈	—	8	2	no	—
217	C₇×D₄	—	4	4	no	—
218	C₇×D₄	—	4	2	no	—
219	C₇×D₄	—	4	4	no	—
220	C₇×D₄	—	4	2	no	—
221	C₇×D₄	—	4	2	no	—
222	C₇×D₄	—	4	4	no	—
223	C₇×D₄	—	8	2	no	—
224	C₇×D₄	—	8	2	no	—
225	C₇×D₄	—	8	2	no	—
226	C₇×D₄	—	8	2	no	—
227	C₂×C₄×C₇	—	2	2	no	—
228	C₂×C₄×C₇	—	2	2	no	—
229	C₂×C₄×C₇	—	4	1	no	—
230	C₂×C₄×C₇	—	4	1	no	—
231	C₂×C₄×C₇	—	4	1	no	—
232	C₂×C₄×C₇	—	4	2	no	—
233	C₂×C₄×C₇	—	8	2	no	—
234	C₂×C₄×C₇	—	8	2	no	—
235	C₂×C₄×C₇	#127	1	1	yes	characteristic
236	C₂×C₄×C₇	#127	1	1	yes	characteristic
237	C₂×C₄×C₇	#127	1	1	yes	characteristic
238	C₂×C₄×C₇	#135	1	4	yes	—
239	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
240	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
241	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
242	C₇×C₈	—	2	4	no	—
243	C₇×C₈	—	2	2	no	—
244	C₇×C₈	—	2	4	no	—
245	C₇×C₈	AGL(1,ℤ/8)	1	4	yes	—
246	C₂×#41	—	2	1	no	—
247	C₂²×Q₈	—	2	1	no	—
248	C₂²×D₄	—	2	1	no	—
249	C₂²×D₄	—	2	1	no	—
250	C₂²×D₄	—	2	1	no	—
251	C₂×SD₁₆	—	2	4	no	—
252	C₂×SD₁₆	—	2	4	no	—
253	C₂×SD₁₆	—	2	2	no	—
254	C₂×SD₁₆	—	4	8	no	—
255	C₂×D₈	—	2	4	no	—
256	C₂×M₁₆	C₇×D₄	1	2	yes	—
257	C₂²×C₈	C₇×D₄	1	2	yes	—
258	C₄⋊Q₈	—	2	1	no	—
259	C₄⋊Q₈	—	2	1	no	—
260	C₄⋊Q₈	—	2	1	no	—
261	C₄⋊Q₈	C₂³×C₇	1	2	yes	—
262	C₄⋊Q₈	C₂³×C₇	1	1	yes	characteristic
263	C₄⋊Q₈	C₂³×C₇	1	1	yes	characteristic
264	C₄⋊Q₈	C₂³×C₇	1	1	yes	characteristic
265	#127	—	2	1	no	—
266	#127	—	2	1	no	—
267	#127	—	2	1	no	—
268	#127	C₂³×C₇	1	2	yes	—
269	#127	C₂³×C₇	1	1	yes	characteristic
270	#125	—	2	1	no	—
271	#124	—	2	1	no	—
272	C₂²⋊Q₈	—	2	1	no	—
273	C₂²⋊Q₈	—	2	1	no	—
274	#121	—	2	1	no	—
275	#121	—	2	1	no	—
276	C₄×Q₈	—	2	1	no	—
277	C₄×Q₈	—	2	1	no	—
278	C₄×D₄	—	2	1	no	—
279	C₄×D₄	—	2	1	no	—
280	#117	—	2	1	no	—
281	C₂×C₄⋊C₄	—	2	1	no	—
282	C₂×C₄⋊C₄	—	2	1	no	—
283	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
284	#107	—	2	4	no	—
285	#106	—	2	2	no	—
286	C₄⋊C₈	C₇×D₄	1	2	yes	—
287	#103	—	2	4	no	—
288	#103	—	2	2	no	—
289	#103	—	2	4	no	—
290	#102	—	2	4	no	—
291	#102	—	2	4	no	—
292	#102	—	2	4	no	—
293	#102	—	2	2	no	—
294	#102	—	2	4	no	—
295	C₂²⋊C₈	C₇×D₄	1	2	yes	—
296	#97	C₇×D₄	1	2	yes	—
297	C₄×C₈	C₇×D₄	1	2	yes	—
298	C₄×C₈	C₂³×C₇	1	1	yes	characteristic
299	C₄×C₈	C₂³×C₇	1	2	yes	—
300	C₄×C₈	C₂³×C₇	1	2	yes	—
301	C₄×C₈	C₂³×C₇	1	1	yes	characteristic
302	C₂²×C₇	—	2	1	no	—
303	C₂²×C₇	—	2	1	no	—
304	C₂²×C₇	—	8	1	no	—
305	C₂²×C₇	—	8	2	no	—
306	C₂²×C₇	—	8	2	no	—
307	C₂²×C₇	—	8	1	no	—
308	C₂²×C₇	—	8	2	no	—
309	C₂²×C₇	—	8	1	no	—
310	C₂²×C₇	—	16	4	no	—
311	C₂²×C₇	#495	1	2	yes	—
312	C₂²×C₇	C₂×#127	1	1	yes	characteristic
313	C₄×C₇	—	2	1	no	—
314	C₄×C₇	—	2	1	no	—
315	C₄×C₇	—	8	1	no	—
316	C₄×C₇	—	8	2	no	—
317	C₄×C₇	—	8	1	no	—
318	C₄×C₇	—	8	1	no	—
319	C₄×C₇	#495	1	2	yes	—
320	C₄×C₇	C₂×#135	1	2	yes	—
321	C₄×C₇	C₂×AGL(1,ℤ/8)	1	2	yes	—
322	C₄×C₇	#577	1	2	yes	—
323	C₂⁴	—	4	1	no	—
324	#41	—	4	4	no	—
325	C₂×Q₈	—	2	1	no	—
326	C₂×Q₈	—	2	1	no	—
327	C₂×Q₈	—	2	1	no	—
328	C₂×Q₈	—	2	2	no	—
329	C₂×Q₈	—	4	4	no	—
330	C₂×Q₈	—	4	1	no	—
331	C₂×D₄	—	2	1	no	—
332	C₂×D₄	—	2	2	no	—
333	C₂×D₄	—	2	1	no	—
334	C₂×D₄	—	2	2	no	—
335	C₂×D₄	—	2	1	no	—
336	C₂×D₄	—	2	2	no	—
337	C₂×D₄	—	4	4	no	—
338	C₂×D₄	—	4	1	no	—
339	C₂×D₄	—	4	1	no	—
340	C₂×D₄	—	4	1	no	—
341	C₂×D₄	—	4	1	no	—
342	C₂×D₄	—	4	4	no	—
343	C₂×D₄	—	8	2	no	—
344	C₂²×C₄	—	4	1	no	—
345	C₂²×C₄	—	4	1	no	—
346	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
347	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
348	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
349	SD₁₆	—	4	8	no	—
350	SD₁₆	—	4	4	no	—
351	SD₁₆	—	4	8	no	—
352	D₈	—	8	4	no	—
353	M₁₆	—	2	4	no	—
354	C₂×C₈	—	2	4	no	—
355	C₂×C₈	C₂×C₇×D₄	1	2	yes	—
356	C₂×C₈	C₂×C₇×D₄	1	4	yes	—
357	C₂×C₈	C₂×C₇×D₄	1	4	yes	—
358	C₂×C₈	C₂×C₇×D₄	1	2	yes	—
359	C₄⋊C₄	—	2	1	no	—
360	C₄⋊C₄	—	2	1	no	—
361	C₄⋊C₄	—	2	1	no	—
362	C₄⋊C₄	—	2	2	no	—
363	C₄⋊C₄	—	2	1	no	—
364	C₄⋊C₄	—	2	1	no	—
365	C₄⋊C₄	—	2	2	no	—
366	C₄⋊C₄	—	2	1	no	—
367	C₄⋊C₄	—	4	1	no	—
368	C₄⋊C₄	—	4	1	no	—
369	C₄⋊C₄	—	4	1	no	—
370	C₄⋊C₄	—	4	1	no	—
371	C₂²⋊C₄	—	4	1	no	—
372	C₂²⋊C₄	—	4	1	no	—
373	C₂²⋊C₄	—	4	1	no	—
374	C₄²	—	4	1	no	—
375	C₄²	C₂×C₇×D₄	1	1	yes	characteristic
376	C₄²	C₂×C₇×D₄	1	1	yes	characteristic
377	C₄²	C₂×C₇×D₄	1	1	yes	characteristic
378	C₄²	C₂⁴×C₇	1	1	yes	characteristic
379	C₂×C₇	—	2	2	no	—
380	C₂×C₇	—	16	1	no	—
381	C₂×C₇	—	16	2	no	—
382	C₂×C₇	C₂×#495	1	1	yes	characteristic
383	C₂×C₇	#3151	1	1	yes	characteristic
384	C₂×C₇	#3154	1	1	yes	characteristic
385	C₂³	—	4	1	no	—
386	C₂³	—	4	2	no	—
387	C₂³	—	8	2	no	—
388	C₂³	—	8	2	no	—
389	C₂³	—	8	2	no	—
390	C₂³	C₇×#127	1	1	yes	characteristic
391	Q₈	—	4	2	no	—
392	Q₈	—	4	4	no	—
393	Q₈	—	4	2	no	—
394	Q₈	—	4	2	no	—
395	Q₈	—	8	2	no	—
396	D₄	—	4	4	no	—
397	D₄	—	4	2	no	—
398	D₄	—	4	4	no	—
399	D₄	—	4	2	no	—
400	D₄	—	4	2	no	—
401	D₄	—	4	4	no	—
402	D₄	—	8	2	no	—
403	D₄	—	8	2	no	—
404	D₄	—	8	2	no	—
405	D₄	—	8	2	no	—
406	C₂×C₄	—	2	2	no	—
407	C₂×C₄	—	2	2	no	—
408	C₂×C₄	—	4	1	no	—
409	C₂×C₄	—	4	1	no	—
410	C₂×C₄	—	4	1	no	—
411	C₂×C₄	—	4	2	no	—
412	C₂×C₄	—	8	2	no	—
413	C₂×C₄	—	8	2	no	—
414	C₂×C₄	C₇×#127	1	1	yes	characteristic
415	C₂×C₄	C₇×#127	1	1	yes	characteristic
416	C₂×C₄	C₇×#127	1	1	yes	characteristic
417	C₂×C₄	C₇×#135	1	4	yes	—
418	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
419	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
420	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
421	C₈	—	2	4	no	—
422	C₈	—	2	2	no	—
423	C₈	—	2	4	no	—
424	C₈	C₇×AGL(1,ℤ/8)	1	4	yes	—
425	C₇	#19625	1	1	yes	characteristic, direct product factor, Sylow
426	C₂²	—	2	1	no	—
427	C₂²	—	2	1	no	—
428	C₂²	—	8	1	no	—
429	C₂²	—	8	2	no	—
430	C₂²	—	8	2	no	—
431	C₂²	—	8	1	no	—
432	C₂²	—	8	2	no	—
433	C₂²	—	8	1	no	—
434	C₂²	—	16	4	no	—
435	C₂²	C₇×#495	1	2	yes	—
436	C₂²	C₂×C₇×#127	1	1	yes	characteristic
437	C₄	—	2	1	no	—
438	C₄	—	2	1	no	—
439	C₄	—	8	1	no	—
440	C₄	—	8	2	no	—
441	C₄	—	8	1	no	—
442	C₄	—	8	1	no	—
443	C₄	C₇×#495	1	2	yes	—
444	C₄	C₂×C₇×#135	1	2	yes	—
445	C₄	C₂×C₇×AGL(1,ℤ/8)	1	2	yes	—
446	C₄	C₇×#577	1	2	yes	—
447	C₂	—	2	2	no	—
448	C₂	—	16	2	no	—
449	C₂	—	16	1	no	—
450	C₂	C₂×C₇×#495	1	1	yes	characteristic
451	C₂	C₇×#3151	1	1	yes	characteristic
452	C₂	C₇×#3154	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₇	C₂×#127
commutator, Frattini, cosocle	C₄²	C₂⁴×C₇
prime radical	C₇×#3205	C₂
LCS	G ▷ C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₇ ◁ C₂×C₄²×C₇ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₇×#3230	C₂	semidirect
3. C₇×#3167	C₂	semidirect
4. C₂×C₇×#492	C₂	semidirect
5. C₇×#3141	C₂	semidirect
6. C₇×#3138	C₂	semidirect
7. C₇×#1719	C₂	semidirect
8. C₇×#1717	C₂	semidirect
9. C₇×#1708	C₂	semidirect
10. C₇×#1706	C₂	semidirect
11. C₇×C₈×M₁₆	C₂	semidirect
17. C₇×#500	C₂²	semidirect
18. C₇×#498	C₂²	semidirect
23. C₇×#492	C₂²	semidirect
26. C₇×#487	C₂²	semidirect
27. C₇×#487	C₂²	semidirect
28. C₇×#487	C₂²	semidirect
32. C₇×#486	C₂²	semidirect
33. C₇×#486	C₂²	semidirect
45. C₇×#322	C₂²	semidirect
46. C₇×C₈²	C₂²	semidirect
47. #19625	C₇	direct (N × H)
104. #3230	C₂×C₇	semidirect
106. #3167	C₂×C₇	semidirect
107. C₂×#492	C₂×C₇	semidirect
108. #3141	C₂×C₇	semidirect
109. #3138	C₂×C₇	semidirect
110. #1719	C₂×C₇	semidirect
111. #1717	C₂×C₇	semidirect
112. #1708	C₂×C₇	semidirect
113. #1706	C₂×C₇	semidirect
114. C₈×M₁₆	C₂×C₇	semidirect
176. #500	C₂²×C₇	semidirect
177. #498	C₂²×C₇	semidirect
182. #492	C₂²×C₇	semidirect
185. #487	C₂²×C₇	semidirect
186. #487	C₂²×C₇	semidirect
187. #487	C₂²×C₇	semidirect
191. #486	C₂²×C₇	semidirect
192. #486	C₂²×C₇	semidirect
204. #322	C₂²×C₇	semidirect
205. C₈²	C₂²×C₇	semidirect
425. C₇	#19625	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₇×#3230	2
C₇×#3205	2
C₇×#3167	2
C₂×C₇×#492	2
C₇×#3141	2
C₇×#3138	2
C₇×#1719	2
C₇×#1717	2
C₇×#1708	2
C₇×#1706	2
C₇×C₈×M₁₆	2
#19625	7

Subgroups — C7×#19625 #13196841

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×#19625 #13196841