Subgroups — C₇×#19231 #13196447

Order 1792.

726 conjugacy classes of subgroups.

The subgroup lattice has 472 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×#3245	C₂	1	1	yes	maximal, characteristic
2	C₇×#3226	C₂	1	1	yes	maximal, characteristic, complemented
3	C₇×#3152	C₂	1	1	yes	maximal, characteristic, complemented
4	C₇×#2935	C₂	1	1	yes	maximal, characteristic, complemented
5	C₇×#1689	C₂	1	2	yes	maximal, complemented
6	C₇×#1685	C₂	1	2	yes	maximal, complemented
7	C₇×#1669	C₂	1	2	yes	maximal, complemented
8	C₇×#1665	C₂	1	2	yes	maximal, complemented
9	C₇×#1565	C₂	1	1	yes	maximal, characteristic, complemented
10	C₇×#1540	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×C₇×#332	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₇×#137	—	2	1	no	—
13	C₂×C₇×#137	—	2	1	no	—
14	C₂×C₇×#131	—	2	1	no	—
15	C₇×#532	C₂²	1	1	yes	characteristic
16	C₇×#532	C₂²	1	1	yes	characteristic
17	C₂×C₇×C₄⋊Q₈	C₂²	1	1	yes	characteristic
18	C₇×#500	—	2	1	no	—
19	C₇×#497	—	2	2	no	—
20	C₇×#494	C₂²	1	2	yes	—
21	C₇×#492	C₂²	1	2	yes	—
22	C₇×#486	—	2	1	no	—
23	C₇×#480	—	2	2	no	—
24	C₇×#474	—	2	1	no	—
25	C₇×#474	C₂²	1	2	yes	—
26	C₇×#474	C₂²	1	2	yes	—
27	C₇×#474	C₂²	1	2	yes	—
28	C₇×#466	—	2	2	no	—
29	C₇×#459	—	2	1	no	—
30	C₇×#459	C₂²	1	2	yes	—
31	C₇×#436	C₂²	1	2	yes	—
32	C₇×#435	—	2	2	no	—
33	C₇×C₈×D₄	C₂²	1	2	yes	—
34	C₇×#431	C₂²	1	1	yes	characteristic
35	C₂×C₇×C₄⋊C₈	C₂²	1	1	yes	characteristic
36	C₂×C₇×C₄⋊C₈	C₂²	1	1	yes	characteristic
37	C₇×#408	—	2	1	no	—
38	C₄×C₇×M₁₆	C₂²	1	1	yes	characteristic
39	C₇×#335	C₂²	1	2	yes	—
40	C₇×#334	C₂²	1	2	yes	—
41	C₇×#332	C₂²	1	2	yes	—
42	C₇×#332	C₂²	1	2	yes	—
43	C₇×#332	C₂²	1	1	yes	characteristic
44	C₇×#332	C₂²	1	1	yes	characteristic
45	C₇×#331	C₂²	1	1	yes	characteristic
46	C₇×#331	C₂²	1	1	yes	characteristic
47	#19231	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
48	C₂×C₇×#41	—	2	1	no	—
49	C₂×C₇×#41	—	2	1	no	—
50	C₂²×C₇×Q₈	—	2	1	no	—
51	C₇×#137	—	4	4	no	—
52	C₇×#137	—	4	4	no	—
53	C₂×C₇×Q₁₆	—	2	2	no	—
54	C₂×C₇×Q₁₆	—	2	2	no	—
55	C₂×C₇×SD₁₆	—	2	2	no	—
56	C₂×C₇×SD₁₆	—	2	2	no	—
57	C₂×C₇×D₈	—	2	2	no	—
58	C₇×#131	—	4	4	no	—
59	C₂×C₇×M₁₆	—	2	2	no	—
60	C₂×C₇×M₁₆	D₄	1	1	yes	characteristic
61	C₂×C₇×M₁₆	D₄	1	1	yes	characteristic
62	C₂²×C₇×C₈	—	2	1	no	—
63	C₂²×C₇×C₈	—	2	1	no	—
64	C₂²×C₇×C₈	—	2	2	no	—
65	C₇×C₄⋊Q₈	—	2	1	no	—
66	C₇×C₄⋊Q₈	—	2	1	no	—
67	C₇×C₄⋊Q₈	—	2	1	no	—
68	C₇×C₄⋊Q₈	D₄	1	1	yes	characteristic
69	C₇×C₄⋊Q₈	C₂³	1	2	yes	—
70	C₇×C₄⋊Q₈	C₂³	1	1	yes	characteristic
71	C₇×#127	D₄	1	1	yes	characteristic
72	C₇×#127	C₂³	1	1	yes	characteristic
73	C₇×#124	—	2	1	no	—
74	C₇×#124	—	2	1	no	—
75	C₇×#121	—	2	1	no	—
76	C₇×#121	—	2	1	no	—
77	C₇×#121	—	2	1	no	—
78	C₇×#121	D₄	1	2	yes	—
79	C₄×C₇×D₄	—	2	1	no	—
80	C₄×C₇×D₄	—	2	1	no	—
81	C₄×C₇×D₄	—	2	1	no	—
82	C₄×C₇×D₄	C₂³	1	2	yes	—
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	2	no	—
87	C₇×#107	—	2	2	no	—
88	C₇×#107	—	2	2	no	—
89	C₇×C₄⋊C₈	—	2	1	no	—
90	C₇×C₄⋊C₈	—	2	1	no	—
91	C₇×C₄⋊C₈	C₂³	1	1	yes	characteristic
92	C₇×C₄⋊C₈	C₂³	1	1	yes	characteristic
93	C₇×C₄⋊C₈	C₂³	1	2	yes	—
94	C₇×C₄⋊C₈	C₂³	1	1	yes	characteristic
95	C₇×C₄⋊C₈	C₂³	1	1	yes	characteristic
96	C₇×#102	—	2	2	no	—
97	C₇×#102	—	2	2	no	—
98	C₇×#102	—	2	2	no	—
99	C₇×#102	—	2	2	no	—
100	C₇×C₂²⋊C₈	—	2	1	no	—
101	C₇×C₂²⋊C₈	—	2	2	no	—
102	C₇×C₂²⋊C₈	—	2	2	no	—
103	C₇×#97	D₄	1	2	yes	—
104	C₄×C₇×C₈	—	2	1	no	—
105	C₄×C₇×C₈	C₂³	1	2	yes	—
106	#3245	C₂×C₇	1	1	yes	characteristic
107	#3226	C₂×C₇	1	1	yes	characteristic, complemented
108	#3152	C₂×C₇	1	1	yes	characteristic, complemented
109	#2935	C₂×C₇	1	1	yes	characteristic, complemented
110	#1689	C₂×C₇	1	2	yes	complemented
111	#1685	C₂×C₇	1	2	yes	complemented
112	#1669	C₂×C₇	1	2	yes	complemented
113	#1665	C₂×C₇	1	2	yes	complemented
114	#1565	C₂×C₇	1	1	yes	characteristic, complemented
115	#1540	C₂×C₇	1	1	yes	characteristic, complemented
116	C₂×#332	C₂×C₇	1	1	yes	characteristic, complemented
117	C₇×#41	—	4	2	no	—
118	C₇×#41	—	4	2	no	—
119	C₇×#41	—	4	2	no	—
120	C₇×#41	—	4	2	no	—
121	C₂×C₇×Q₈	—	2	1	no	—
122	C₂×C₇×Q₈	—	2	1	no	—
123	C₂×C₇×Q₈	—	2	2	no	—
124	C₂×C₇×Q₈	—	4	1	no	—
125	C₂×C₇×Q₈	—	4	2	no	—
126	C₂×C₇×Q₈	—	4	2	no	—
127	C₂×C₇×D₄	—	2	2	no	—
128	C₂×C₇×D₄	—	2	1	no	—
129	C₂×C₇×D₄	—	2	1	no	—
130	C₂×C₇×D₄	—	2	1	no	—
131	C₂×C₇×D₄	—	2	1	no	—
132	C₂×C₇×D₄	—	2	1	no	—
133	C₂×C₇×D₄	—	4	1	no	—
134	C₂×C₇×D₄	C₂×D₄	1	2	yes	—
135	C₂²×C₄×C₇	—	2	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	#41	1	1	yes	characteristic
141	C₇×Q₁₆	—	4	4	no	—
142	C₇×Q₁₆	—	4	4	no	—
143	C₇×SD₁₆	—	4	4	no	—
144	C₇×SD₁₆	—	4	4	no	—
145	C₇×D₈	—	8	2	no	—
146	C₇×M₁₆	—	2	2	no	—
147	C₇×M₁₆	—	4	4	no	—
148	C₇×M₁₆	D₈	1	4	yes	complemented
149	C₂×C₇×C₈	—	2	1	no	—
150	C₂×C₇×C₈	—	2	1	no	—
151	C₂×C₇×C₈	—	2	1	no	—
152	C₂×C₇×C₈	—	2	1	no	—
153	C₂×C₇×C₈	—	2	2	no	—
154	C₂×C₇×C₈	—	4	2	no	—
155	C₂×C₇×C₈	—	4	4	no	—
156	C₂×C₇×C₈	—	8	1	no	—
157	C₂×C₇×C₈	C₂×D₄	1	2	yes	—
158	C₂×C₇×C₈	C₂×D₄	1	2	yes	—
159	C₇×C₄⋊C₄	—	2	1	no	—
160	C₇×C₄⋊C₄	—	2	2	no	—
161	C₇×C₄⋊C₄	—	2	1	no	—
162	C₇×C₄⋊C₄	—	2	2	no	—
163	C₇×C₄⋊C₄	—	2	1	no	—
164	C₇×C₄⋊C₄	—	4	1	no	—
165	C₇×C₄⋊C₄	—	4	1	no	—
166	C₇×C₄⋊C₄	C₂×D₄	1	2	yes	—
167	C₇×C₂²⋊C₄	—	2	2	no	—
168	C₇×C₂²⋊C₄	—	2	2	no	—
169	C₇×C₂²⋊C₄	—	4	1	no	—
170	C₇×C₂²⋊C₄	—	4	1	no	—
171	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
172	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
173	C₄²×C₇	#41	1	1	yes	characteristic
174	C₄²×C₇	C₂⁴	1	1	yes	characteristic
175	C₂×#137	—	2	1	no	—
176	C₂×#137	—	2	1	no	—
177	C₂×#131	—	2	1	no	—
178	#532	C₂²×C₇	1	1	yes	characteristic
179	#532	C₂²×C₇	1	1	yes	characteristic
180	C₂×C₄⋊Q₈	C₂²×C₇	1	1	yes	characteristic
181	#500	—	2	1	no	—
182	#497	—	2	2	no	—
183	#494	C₂²×C₇	1	2	yes	—
184	#492	C₂²×C₇	1	2	yes	—
185	#486	—	2	1	no	—
186	#480	—	2	2	no	—
187	#474	—	2	1	no	—
188	#474	C₂²×C₇	1	2	yes	—
189	#474	C₂²×C₇	1	2	yes	—
190	#474	C₂²×C₇	1	2	yes	—
191	#466	—	2	2	no	—
192	#459	—	2	1	no	—
193	#459	C₂²×C₇	1	2	yes	—
194	#436	C₂²×C₇	1	2	yes	—
195	#435	—	2	2	no	—
196	C₈×D₄	C₂²×C₇	1	2	yes	—
197	#431	C₂²×C₇	1	1	yes	characteristic
198	C₂×C₄⋊C₈	C₂²×C₇	1	1	yes	characteristic
199	C₂×C₄⋊C₈	C₂²×C₇	1	1	yes	characteristic
200	#408	—	2	1	no	—
201	C₄×M₁₆	C₂²×C₇	1	1	yes	characteristic
202	#335	C₂²×C₇	1	2	yes	—
203	#334	C₂²×C₇	1	2	yes	—
204	#332	C₂²×C₇	1	2	yes	—
205	#332	C₂²×C₇	1	2	yes	—
206	#332	C₂²×C₇	1	1	yes	characteristic
207	#332	C₂²×C₇	1	1	yes	characteristic
208	#331	C₂²×C₇	1	1	yes	characteristic
209	#331	C₂²×C₇	1	1	yes	characteristic
210	C₂³×C₇	—	2	2	no	—
211	C₂³×C₇	—	4	1	no	—
212	C₂³×C₇	#121	1	1	yes	characteristic
213	C₇×Q₈	—	4	2	no	—
214	C₇×Q₈	—	4	2	no	—
215	C₇×Q₈	—	4	1	no	—
216	C₇×Q₈	—	4	2	no	—
217	C₇×Q₈	—	4	1	no	—
218	C₇×Q₈	—	8	2	no	—
219	C₇×D₄	—	2	2	no	—
220	C₇×D₄	—	2	2	no	—
221	C₇×D₄	—	4	4	no	—
222	C₇×D₄	—	4	1	no	—
223	C₇×D₄	—	4	1	no	—
224	C₇×D₄	—	4	1	no	—
225	C₇×D₄	—	4	1	no	—
226	C₇×D₄	—	4	2	no	—
227	C₇×D₄	—	8	1	no	—
228	C₇×D₄	—	8	1	no	—
229	C₇×D₄	—	8	2	no	—
230	C₂×C₄×C₇	—	2	1	no	—
231	C₂×C₄×C₇	—	2	1	no	—
232	C₂×C₄×C₇	—	2	2	no	—
233	C₂×C₄×C₇	—	4	1	no	—
234	C₂×C₄×C₇	—	4	2	no	—
235	C₂×C₄×C₇	—	4	2	no	—
236	C₂×C₄×C₇	—	4	1	no	—
237	C₂×C₄×C₇	—	4	2	no	—
238	C₂×C₄×C₇	—	8	2	no	—
239	C₂×C₄×C₇	—	8	2	no	—
240	C₂×C₄×C₇	#121	1	1	yes	characteristic
241	C₂×C₄×C₇	#121	1	1	yes	characteristic
242	C₂×C₄×C₇	#121	1	1	yes	characteristic
243	C₂×C₄×C₇	C₂×D₈	1	2	yes	—
244	C₂×C₄×C₇	AGL(1,ℤ/8)	1	2	yes	—
245	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
246	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
247	C₂×C₄×C₇	C₂×#41	1	1	yes	characteristic
248	C₇×C₈	—	2	2	no	—
249	C₇×C₈	—	4	1	no	—
250	C₇×C₈	—	4	1	no	—
251	C₇×C₈	—	4	1	no	—
252	C₇×C₈	—	4	2	no	—
253	C₇×C₈	—	4	1	no	—
254	C₇×C₈	C₂×D₈	1	4	yes	—
255	C₂×#41	—	2	1	no	—
256	C₂×#41	—	2	1	no	—
257	C₂²×Q₈	—	2	1	no	—
258	#137	—	4	4	no	—
259	#137	—	4	4	no	—
260	C₂×Q₁₆	—	2	2	no	—
261	C₂×Q₁₆	—	2	2	no	—
262	C₂×SD₁₆	—	2	2	no	—
263	C₂×SD₁₆	—	2	2	no	—
264	C₂×D₈	—	2	2	no	—
265	#131	—	4	4	no	—
266	C₂×M₁₆	—	2	2	no	—
267	C₂×M₁₆	C₇×D₄	1	1	yes	characteristic
268	C₂×M₁₆	C₇×D₄	1	1	yes	characteristic
269	C₂²×C₈	—	2	1	no	—
270	C₂²×C₈	—	2	1	no	—
271	C₂²×C₈	—	2	2	no	—
272	C₄⋊Q₈	—	2	1	no	—
273	C₄⋊Q₈	—	2	1	no	—
274	C₄⋊Q₈	—	2	1	no	—
275	C₄⋊Q₈	C₇×D₄	1	1	yes	characteristic
276	C₄⋊Q₈	C₂³×C₇	1	2	yes	—
277	C₄⋊Q₈	C₂³×C₇	1	1	yes	characteristic
278	#127	C₇×D₄	1	1	yes	characteristic
279	#127	C₂³×C₇	1	1	yes	characteristic
280	#124	—	2	1	no	—
281	#124	—	2	1	no	—
282	#121	—	2	1	no	—
283	#121	—	2	1	no	—
284	#121	—	2	1	no	—
285	#121	C₇×D₄	1	2	yes	—
286	C₄×D₄	—	2	1	no	—
287	C₄×D₄	—	2	1	no	—
288	C₄×D₄	—	2	1	no	—
289	C₄×D₄	C₂³×C₇	1	2	yes	—
290	C₂×C₄⋊C₄	—	2	1	no	—
291	C₂×C₄⋊C₄	—	2	1	no	—
292	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
293	#107	—	2	2	no	—
294	#107	—	2	2	no	—
295	#107	—	2	2	no	—
296	C₄⋊C₈	—	2	1	no	—
297	C₄⋊C₈	—	2	1	no	—
298	C₄⋊C₈	C₂³×C₇	1	1	yes	characteristic
299	C₄⋊C₈	C₂³×C₇	1	1	yes	characteristic
300	C₄⋊C₈	C₂³×C₇	1	1	yes	characteristic
301	C₄⋊C₈	C₂³×C₇	1	1	yes	characteristic
302	C₄⋊C₈	C₂³×C₇	1	2	yes	—
303	#102	—	2	2	no	—
304	#102	—	2	2	no	—
305	#102	—	2	2	no	—
306	#102	—	2	2	no	—
307	C₂²⋊C₈	—	2	1	no	—
308	C₂²⋊C₈	—	2	2	no	—
309	C₂²⋊C₈	—	2	2	no	—
310	#97	C₇×D₄	1	2	yes	—
311	C₄×C₈	—	2	1	no	—
312	C₄×C₈	C₂³×C₇	1	2	yes	—
313	C₂²×C₇	—	2	1	no	—
314	C₂²×C₇	—	2	1	no	—
315	C₂²×C₇	—	4	2	no	—
316	C₂²×C₇	—	4	2	no	—
317	C₂²×C₇	—	4	2	no	—
318	C₂²×C₇	—	8	1	no	—
319	C₂²×C₇	—	8	1	no	—
320	C₂²×C₇	—	8	1	no	—
321	C₂²×C₇	#459	1	2	yes	—
322	C₂²×C₇	C₂×#121	1	1	yes	characteristic
323	C₄×C₇	—	2	1	no	—
324	C₄×C₇	—	2	1	no	—
325	C₄×C₇	—	2	1	no	—
326	C₄×C₇	—	4	2	no	—
327	C₄×C₇	—	8	1	no	—
328	C₄×C₇	—	8	2	no	—
329	C₄×C₇	#459	1	2	yes	—
330	C₄×C₇	C₂²×D₈	1	1	yes	characteristic
331	C₄×C₇	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
332	C₄×C₇	#577	1	1	yes	characteristic
333	C₄×C₇	#578	1	1	yes	characteristic
334	#41	—	4	2	no	—
335	#41	—	4	2	no	—
336	#41	—	4	2	no	—
337	#41	—	4	2	no	—
338	C₂×Q₈	—	2	1	no	—
339	C₂×Q₈	—	2	1	no	—
340	C₂×Q₈	—	2	2	no	—
341	C₂×Q₈	—	4	1	no	—
342	C₂×Q₈	—	4	2	no	—
343	C₂×Q₈	—	4	2	no	—
344	C₂×D₄	—	2	2	no	—
345	C₂×D₄	—	2	1	no	—
346	C₂×D₄	—	2	1	no	—
347	C₂×D₄	—	2	1	no	—
348	C₂×D₄	—	2	1	no	—
349	C₂×D₄	—	2	1	no	—
350	C₂×D₄	—	4	1	no	—
351	C₂×D₄	C₂×C₇×D₄	1	2	yes	—
352	C₂²×C₄	—	2	2	no	—
353	C₂²×C₄	—	4	1	no	—
354	C₂²×C₄	—	4	1	no	—
355	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
356	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
357	C₂²×C₄	C₇×#41	1	1	yes	characteristic
358	Q₁₆	—	4	4	no	—
359	Q₁₆	—	4	4	no	—
360	SD₁₆	—	4	4	no	—
361	SD₁₆	—	4	4	no	—
362	D₈	—	8	2	no	—
363	M₁₆	—	2	2	no	—
364	M₁₆	—	4	4	no	—
365	M₁₆	C₇×D₈	1	4	yes	complemented
366	C₂×C₈	—	2	1	no	—
367	C₂×C₈	—	2	1	no	—
368	C₂×C₈	—	2	1	no	—
369	C₂×C₈	—	2	1	no	—
370	C₂×C₈	—	2	2	no	—
371	C₂×C₈	—	4	2	no	—
372	C₂×C₈	—	4	4	no	—
373	C₂×C₈	—	8	1	no	—
374	C₂×C₈	C₂×C₇×D₄	1	2	yes	—
375	C₂×C₈	C₂×C₇×D₄	1	2	yes	—
376	C₄⋊C₄	—	2	1	no	—
377	C₄⋊C₄	—	2	2	no	—
378	C₄⋊C₄	—	2	1	no	—
379	C₄⋊C₄	—	2	2	no	—
380	C₄⋊C₄	—	2	1	no	—
381	C₄⋊C₄	—	4	1	no	—
382	C₄⋊C₄	—	4	1	no	—
383	C₄⋊C₄	C₂×C₇×D₄	1	2	yes	—
384	C₂²⋊C₄	—	2	2	no	—
385	C₂²⋊C₄	—	2	2	no	—
386	C₂²⋊C₄	—	4	1	no	—
387	C₂²⋊C₄	—	4	1	no	—
388	C₄²	C₂×C₇×D₄	1	1	yes	characteristic
389	C₄²	C₂×C₇×D₄	1	1	yes	characteristic
390	C₄²	C₇×#41	1	1	yes	characteristic
391	C₄²	C₂⁴×C₇	1	1	yes	characteristic
392	C₂×C₇	—	2	2	no	—
393	C₂×C₇	—	8	2	no	—
394	C₂×C₇	—	16	1	no	—
395	C₂×C₇	C₂×#459	1	1	yes	characteristic
396	C₂×C₇	#3063	1	1	yes	characteristic
397	C₂×C₇	#3069	1	1	yes	characteristic
398	C₂³	—	2	2	no	—
399	C₂³	—	4	1	no	—
400	C₂³	C₇×#121	1	1	yes	characteristic
401	Q₈	—	4	2	no	—
402	Q₈	—	4	2	no	—
403	Q₈	—	4	1	no	—
404	Q₈	—	4	2	no	—
405	Q₈	—	4	1	no	—
406	Q₈	—	8	2	no	—
407	D₄	—	2	2	no	—
408	D₄	—	2	2	no	—
409	D₄	—	4	4	no	—
410	D₄	—	4	1	no	—
411	D₄	—	4	1	no	—
412	D₄	—	4	1	no	—
413	D₄	—	4	1	no	—
414	D₄	—	4	2	no	—
415	D₄	—	8	1	no	—
416	D₄	—	8	1	no	—
417	D₄	—	8	2	no	—
418	C₂×C₄	—	2	1	no	—
419	C₂×C₄	—	2	1	no	—
420	C₂×C₄	—	2	2	no	—
421	C₂×C₄	—	4	1	no	—
422	C₂×C₄	—	4	2	no	—
423	C₂×C₄	—	4	2	no	—
424	C₂×C₄	—	4	1	no	—
425	C₂×C₄	—	4	2	no	—
426	C₂×C₄	—	8	2	no	—
427	C₂×C₄	—	8	2	no	—
428	C₂×C₄	C₇×#121	1	1	yes	characteristic
429	C₂×C₄	C₇×#121	1	1	yes	characteristic
430	C₂×C₄	C₇×#121	1	1	yes	characteristic
431	C₂×C₄	C₂×C₇×D₈	1	2	yes	—
432	C₂×C₄	C₇×AGL(1,ℤ/8)	1	2	yes	—
433	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
434	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
435	C₂×C₄	C₂×C₇×#41	1	1	yes	characteristic
436	C₈	—	2	2	no	—
437	C₈	—	4	1	no	—
438	C₈	—	4	1	no	—
439	C₈	—	4	1	no	—
440	C₈	—	4	2	no	—
441	C₈	—	4	1	no	—
442	C₈	C₂×C₇×D₈	1	4	yes	—
443	C₇	#19231	1	1	yes	characteristic, direct product factor, Sylow
444	C₂²	—	2	1	no	—
445	C₂²	—	2	1	no	—
446	C₂²	—	4	2	no	—
447	C₂²	—	4	2	no	—
448	C₂²	—	4	2	no	—
449	C₂²	—	8	1	no	—
450	C₂²	—	8	1	no	—
451	C₂²	—	8	1	no	—
452	C₂²	C₇×#459	1	2	yes	—
453	C₂²	C₂×C₇×#121	1	1	yes	characteristic
454	C₄	—	2	1	no	—
455	C₄	—	2	1	no	—
456	C₄	—	2	1	no	—
457	C₄	—	4	2	no	—
458	C₄	—	8	1	no	—
459	C₄	—	8	2	no	—
460	C₄	C₇×#459	1	2	yes	—
461	C₄	C₂²×C₇×D₈	1	1	yes	characteristic
462	C₄	C₂×C₇×AGL(1,ℤ/8)	1	1	yes	characteristic
463	C₄	C₇×#577	1	1	yes	characteristic
464	C₄	C₇×#578	1	1	yes	characteristic
465	C₂	—	2	2	no	—
466	C₂	—	8	2	no	—
467	C₂	—	16	1	no	—
468	C₂	C₂×C₇×#459	1	1	yes	characteristic
469	C₂	C₇×#3063	1	1	yes	characteristic
470	C₂	C₇×#3069	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₇	C₂×#121
commutator, Frattini, cosocle	C₄²	C₂⁴×C₇
prime radical	C₇×#3245	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
2. C₇×#3226	C₂	semidirect
3. C₇×#3152	C₂	semidirect
4. C₇×#2935	C₂	semidirect
5. C₇×#1689	C₂	semidirect
6. C₇×#1685	C₂	semidirect
7. C₇×#1669	C₂	semidirect
8. C₇×#1665	C₂	semidirect
9. C₇×#1565	C₂	semidirect
10. C₇×#1540	C₂	semidirect
11. C₂×C₇×#332	C₂	semidirect
47. #19231	C₇	direct (N × H)
107. #3226	C₂×C₇	semidirect
108. #3152	C₂×C₇	semidirect
109. #2935	C₂×C₇	semidirect
110. #1689	C₂×C₇	semidirect
111. #1685	C₂×C₇	semidirect
112. #1669	C₂×C₇	semidirect
113. #1665	C₂×C₇	semidirect
114. #1565	C₂×C₇	semidirect
115. #1540	C₂×C₇	semidirect
116. C₂×#332	C₂×C₇	semidirect
148. C₇×M₁₆	D₈	semidirect
365. M₁₆	C₇×D₈	semidirect
443. C₇	#19231	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×#3245	2
C₇×#3226	2
C₇×#3152	2
C₇×#2935	2
C₇×#1689	2
C₇×#1685	2
C₇×#1669	2
C₇×#1665	2
C₇×#1565	2
C₇×#1540	2
C₂×C₇×#332	2
#19231	7

Subgroups — C7×#19231 #13196447

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×#19231 #13196447