Subgroups — C₇×#19682 #13196898

Order 1792.

754 conjugacy classes of subgroups.

The subgroup lattice has 434 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×#3209	C₂	1	1	yes	maximal, characteristic, complemented
2	C₇×#3208	C₂	1	1	yes	maximal, characteristic
3	C₇×#3170	C₂	1	1	yes	maximal, characteristic, complemented
4	C₇×#3165	C₂	1	1	yes	maximal, characteristic, complemented
5	C₇×#3138	C₂	1	1	yes	maximal, characteristic
6	C₂×C₇×#486	C₂	1	1	yes	maximal, characteristic
7	C₇×#1722	C₂	1	2	yes	maximal, complemented
8	C₇×#1720	C₂	1	2	yes	maximal, complemented
9	C₇×#1720	C₂	1	2	yes	maximal, complemented
10	C₇×#1719	C₂	1	2	yes	maximal, complemented
11	C₇×#1451	C₂	1	1	yes	maximal, characteristic, complemented
12	C₇×#533	C₂²	1	1	yes	characteristic
13	C₇×#533	C₂²	1	1	yes	characteristic
14	C₂×C₇×C₄⋊Q₈	C₂²	1	1	yes	characteristic
15	C₂×C₇×#127	C₂²	1	1	yes	characteristic
16	C₇×#501	—	2	2	no	—
17	C₇×#500	C₂²	1	2	yes	complemented
18	C₇×#500	C₂²	1	1	yes	characteristic, complemented
19	C₇×#498	C₂²	1	2	yes	complemented
20	C₇×#494	C₂²	1	1	yes	characteristic, complemented
21	C₇×#494	C₂²	1	2	yes	complemented
22	C₇×#492	C₂²	1	2	yes	—
23	C₇×#490	—	2	2	no	—
24	C₇×#487	C₂²	1	1	yes	characteristic, complemented
25	C₇×#487	C₂²	1	2	yes	complemented
26	C₇×#487	C₂²	1	1	yes	characteristic, complemented
27	C₇×#486	—	2	2	no	—
28	C₇×#486	C₂²	1	2	yes	—
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	2	yes	—
33	C₇×#467	—	2	2	no	—
34	C₇×#462	—	2	2	no	—
35	C₇×#460	—	2	2	no	—
36	C₇×#451	—	2	2	no	—
37	C₇×#450	—	2	2	no	—
38	C₄×C₇×Q₁₆	—	2	2	no	—
39	C₇×#431	C₂²	1	1	yes	characteristic
40	C₇×#428	—	2	2	no	—
41	C₇×#418	—	2	2	no	—
42	C₂×C₇×#102	—	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×#322	C₂²	1	2	yes	complemented
47	#19682	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
48	C₂²×C₇×Q₈	—	2	1	no	—
49	C₂²×C₇×D₄	—	2	1	no	—
50	C₂²×C₇×D₄	—	2	1	no	—
51	C₂²×C₇×D₄	—	2	1	no	—
52	C₂×C₇×Q₁₆	—	2	2	no	—
53	C₂×C₇×Q₁₆	—	2	4	no	—
54	C₂×C₇×SD₁₆	—	2	4	no	—
55	C₂×C₇×M₁₆	D₄	1	2	yes	—
56	C₂²×C₇×C₈	D₄	1	2	yes	—
57	C₇×C₄⋊Q₈	—	2	1	no	—
58	C₇×C₄⋊Q₈	—	2	1	no	—
59	C₇×C₄⋊Q₈	—	2	1	no	—
60	C₇×C₄⋊Q₈	C₂³	1	1	yes	characteristic
61	C₇×C₄⋊Q₈	C₂³	1	1	yes	characteristic
62	C₇×C₄⋊Q₈	C₂³	1	1	yes	characteristic
63	C₇×C₄⋊Q₈	C₂³	1	2	yes	—
64	C₇×C₄⋊Q₈	C₂³	1	1	yes	characteristic
65	C₇×#127	—	2	1	no	—
66	C₇×#127	—	2	1	no	—
67	C₇×#127	—	2	1	no	—
68	C₇×#127	C₂³	1	2	yes	—
69	C₇×#125	—	2	1	no	—
70	C₇×#125	—	2	1	no	—
71	C₇×C₂²⋊Q₈	—	2	1	no	—
72	C₇×C₂²⋊Q₈	—	2	1	no	—
73	C₇×C₂²⋊Q₈	—	2	1	no	—
74	C₇×C₂²⋊Q₈	—	2	1	no	—
75	C₄×C₇×Q₈	—	2	1	no	—
76	C₄×C₇×Q₈	—	2	1	no	—
77	C₄×C₇×Q₈	—	2	1	no	—
78	C₄×C₇×Q₈	—	2	1	no	—
79	C₇×#117	—	2	1	no	—
80	C₇×#117	—	2	1	no	—
81	C₂×C₇×C₄⋊C₄	—	2	1	no	—
82	C₂×C₇×C₄⋊C₄	—	2	1	no	—
83	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
84	C₇×#107	—	2	2	no	—
85	C₇×#107	—	2	4	no	—
86	C₇×#106	—	2	4	no	—
87	C₇×C₄⋊C₈	D₄	1	2	yes	—
88	C₇×#103	—	2	2	no	—
89	C₇×#103	—	2	2	no	—
90	C₇×#103	—	2	4	no	—
91	C₇×#102	—	2	4	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×C₂²⋊C₈	D₄	1	2	yes	—
97	C₇×#97	D₄	1	2	yes	—
98	C₄×C₇×C₈	D₄	1	2	yes	—
99	C₄×C₇×C₈	C₂³	1	1	yes	characteristic
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	#3209	C₂×C₇	1	1	yes	characteristic, complemented
104	#3208	C₂×C₇	1	1	yes	characteristic
105	#3170	C₂×C₇	1	1	yes	characteristic, complemented
106	#3165	C₂×C₇	1	1	yes	characteristic, complemented
107	#3138	C₂×C₇	1	1	yes	characteristic
108	C₂×#486	C₂×C₇	1	1	yes	characteristic
109	#1722	C₂×C₇	1	2	yes	complemented
110	#1720	C₂×C₇	1	2	yes	complemented
111	#1720	C₂×C₇	1	2	yes	complemented
112	#1719	C₂×C₇	1	2	yes	complemented
113	#1451	C₂×C₇	1	1	yes	characteristic, complemented
114	C₂⁴×C₇	—	4	1	no	—
115	C₂×C₇×Q₈	—	2	1	no	—
116	C₂×C₇×Q₈	—	2	1	no	—
117	C₂×C₇×Q₈	—	2	2	no	—
118	C₂×C₇×Q₈	—	2	1	no	—
119	C₂×C₇×Q₈	—	2	1	no	—
120	C₂×C₇×Q₈	—	4	1	no	—
121	C₂×C₇×Q₈	—	8	2	no	—
122	C₂×C₇×D₄	—	2	2	no	—
123	C₂×C₇×D₄	—	2	2	no	—
124	C₂×C₇×D₄	—	2	2	no	—
125	C₂×C₇×D₄	—	4	4	no	—
126	C₂×C₇×D₄	—	4	1	no	—
127	C₂×C₇×D₄	—	4	1	no	—
128	C₂×C₇×D₄	—	4	1	no	—
129	C₂×C₇×D₄	—	4	4	no	—
130	C₂×C₇×D₄	—	8	2	no	—
131	C₂²×C₄×C₇	—	4	1	no	—
132	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
133	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
134	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
135	C₇×Q₁₆	—	4	4	no	—
136	C₇×Q₁₆	—	8	4	no	—
137	C₇×SD₁₆	—	8	4	no	—
138	C₇×M₁₆	—	2	4	no	—
139	C₂×C₇×C₈	—	4	2	no	—
140	C₂×C₇×C₈	C₂×D₄	1	2	yes	—
141	C₂×C₇×C₈	C₂×D₄	1	2	yes	—
142	C₂×C₇×C₈	C₂×D₄	1	4	yes	—
143	C₂×C₇×C₈	C₂×D₄	1	4	yes	—
144	C₇×C₄⋊C₄	—	2	2	no	—
145	C₇×C₄⋊C₄	—	2	1	no	—
146	C₇×C₄⋊C₄	—	2	1	no	—
147	C₇×C₄⋊C₄	—	2	1	no	—
148	C₇×C₄⋊C₄	—	2	1	no	—
149	C₇×C₄⋊C₄	—	2	1	no	—
150	C₇×C₄⋊C₄	—	2	1	no	—
151	C₇×C₄⋊C₄	—	2	1	no	—
152	C₇×C₄⋊C₄	—	2	2	no	—
153	C₇×C₄⋊C₄	—	2	1	no	—
154	C₇×C₄⋊C₄	—	4	1	no	—
155	C₇×C₄⋊C₄	—	4	1	no	—
156	C₇×C₄⋊C₄	—	4	1	no	—
157	C₇×C₄⋊C₄	—	4	1	no	—
158	C₇×C₄⋊C₄	—	4	1	no	—
159	C₇×C₄⋊C₄	—	4	1	no	—
160	C₇×C₂²⋊C₄	—	4	1	no	—
161	C₇×C₂²⋊C₄	—	4	1	no	—
162	C₄²×C₇	—	4	1	no	—
163	C₄²×C₇	—	4	1	no	—
164	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
165	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
166	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
167	C₄²×C₇	C₂⁴	1	1	yes	characteristic
168	#533	C₂²×C₇	1	1	yes	characteristic
169	#533	C₂²×C₇	1	1	yes	characteristic
170	C₂×C₄⋊Q₈	C₂²×C₇	1	1	yes	characteristic
171	C₂×#127	C₂²×C₇	1	1	yes	characteristic
172	#501	—	2	2	no	—
173	#500	C₂²×C₇	1	2	yes	complemented
174	#500	C₂²×C₇	1	1	yes	characteristic, complemented
175	#498	C₂²×C₇	1	2	yes	complemented
176	#494	C₂²×C₇	1	1	yes	characteristic, complemented
177	#494	C₂²×C₇	1	2	yes	complemented
178	#492	C₂²×C₇	1	2	yes	—
179	#490	—	2	2	no	—
180	#487	C₂²×C₇	1	1	yes	characteristic, complemented
181	#487	C₂²×C₇	1	1	yes	characteristic, complemented
182	#487	C₂²×C₇	1	2	yes	complemented
183	#486	—	2	2	no	—
184	#486	C₂²×C₇	1	2	yes	—
185	#486	C₂²×C₇	1	2	yes	—
186	#486	C₂²×C₇	1	2	yes	—
187	#486	C₂²×C₇	1	2	yes	—
188	#486	C₂²×C₇	1	2	yes	—
189	#467	—	2	2	no	—
190	#462	—	2	2	no	—
191	#460	—	2	2	no	—
192	#451	—	2	2	no	—
193	#450	—	2	2	no	—
194	C₄×Q₁₆	—	2	2	no	—
195	#431	C₂²×C₇	1	1	yes	characteristic
196	#428	—	2	2	no	—
197	#418	—	2	2	no	—
198	C₂×#102	—	2	2	no	—
199	C₄×M₁₆	C₂²×C₇	1	1	yes	characteristic
200	C₂×C₄×C₈	C₂²×C₇	1	1	yes	characteristic
201	#322	C₂²×C₇	1	2	yes	complemented
202	#322	C₂²×C₇	1	2	yes	complemented
203	C₂³×C₇	—	4	2	no	—
204	C₂³×C₇	—	8	2	no	—
205	C₂³×C₇	—	8	2	no	—
206	C₂³×C₇	—	8	2	no	—
207	C₂³×C₇	#127	1	1	yes	characteristic
208	C₇×Q₈	—	4	2	no	—
209	C₇×Q₈	—	4	2	no	—
210	C₇×Q₈	—	4	2	no	—
211	C₇×Q₈	—	4	2	no	—
212	C₇×Q₈	—	4	4	no	—
213	C₇×Q₈	—	8	2	no	—
214	C₇×D₄	—	4	4	no	—
215	C₇×D₄	—	4	4	no	—
216	C₇×D₄	—	4	4	no	—
217	C₇×D₄	—	8	2	no	—
218	C₇×D₄	—	8	2	no	—
219	C₇×D₄	—	8	2	no	—
220	C₂×C₄×C₇	—	2	2	no	—
221	C₂×C₄×C₇	—	2	2	no	—
222	C₂×C₄×C₇	—	4	1	no	—
223	C₂×C₄×C₇	—	4	1	no	—
224	C₂×C₄×C₇	—	4	1	no	—
225	C₂×C₄×C₇	—	4	1	no	—
226	C₂×C₄×C₇	—	4	2	no	—
227	C₂×C₄×C₇	—	8	2	no	—
228	C₂×C₄×C₇	#127	1	1	yes	characteristic
229	C₂×C₄×C₇	#127	1	1	yes	characteristic
230	C₂×C₄×C₇	#127	1	1	yes	characteristic
231	C₂×C₄×C₇	#137	1	4	yes	—
232	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
233	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
234	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
235	C₇×C₈	—	2	4	no	—
236	C₇×C₈	—	2	2	no	—
237	C₇×C₈	—	2	2	no	—
238	C₇×C₈	—	2	4	no	—
239	C₂²×Q₈	—	2	1	no	—
240	C₂²×D₄	—	2	1	no	—
241	C₂²×D₄	—	2	1	no	—
242	C₂²×D₄	—	2	1	no	—
243	C₂×Q₁₆	—	2	2	no	—
244	C₂×Q₁₆	—	2	4	no	—
245	C₂×SD₁₆	—	2	4	no	—
246	C₂×M₁₆	C₇×D₄	1	2	yes	—
247	C₂²×C₈	C₇×D₄	1	2	yes	—
248	C₄⋊Q₈	—	2	1	no	—
249	C₄⋊Q₈	—	2	1	no	—
250	C₄⋊Q₈	—	2	1	no	—
251	C₄⋊Q₈	C₂³×C₇	1	2	yes	—
252	C₄⋊Q₈	C₂³×C₇	1	1	yes	characteristic
253	C₄⋊Q₈	C₂³×C₇	1	1	yes	characteristic
254	C₄⋊Q₈	C₂³×C₇	1	1	yes	characteristic
255	C₄⋊Q₈	C₂³×C₇	1	1	yes	characteristic
256	#127	—	2	1	no	—
257	#127	—	2	1	no	—
258	#127	—	2	1	no	—
259	#127	C₂³×C₇	1	2	yes	—
260	#125	—	2	1	no	—
261	#125	—	2	1	no	—
262	C₂²⋊Q₈	—	2	1	no	—
263	C₂²⋊Q₈	—	2	1	no	—
264	C₂²⋊Q₈	—	2	1	no	—
265	C₂²⋊Q₈	—	2	1	no	—
266	C₄×Q₈	—	2	1	no	—
267	C₄×Q₈	—	2	1	no	—
268	C₄×Q₈	—	2	1	no	—
269	C₄×Q₈	—	2	1	no	—
270	#117	—	2	1	no	—
271	#117	—	2	1	no	—
272	C₂×C₄⋊C₄	—	2	1	no	—
273	C₂×C₄⋊C₄	—	2	1	no	—
274	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
275	#107	—	2	4	no	—
276	#107	—	2	2	no	—
277	#106	—	2	4	no	—
278	C₄⋊C₈	C₇×D₄	1	2	yes	—
279	#103	—	2	2	no	—
280	#103	—	2	2	no	—
281	#103	—	2	4	no	—
282	#102	—	2	4	no	—
283	#102	—	2	4	no	—
284	#102	—	2	4	no	—
285	#102	—	2	4	no	—
286	#102	—	2	4	no	—
287	C₂²⋊C₈	C₇×D₄	1	2	yes	—
288	#97	C₇×D₄	1	2	yes	—
289	C₄×C₈	C₇×D₄	1	2	yes	—
290	C₄×C₈	C₂³×C₇	1	1	yes	characteristic
291	C₄×C₈	C₂³×C₇	1	1	yes	characteristic
292	C₄×C₈	C₂³×C₇	1	2	yes	—
293	C₄×C₈	C₂³×C₇	1	2	yes	—
294	C₂²×C₇	—	2	1	no	—
295	C₂²×C₇	—	2	1	no	—
296	C₂²×C₇	—	8	2	no	—
297	C₂²×C₇	—	8	2	no	—
298	C₂²×C₇	—	8	2	no	—
299	C₂²×C₇	—	16	4	no	—
300	C₂²×C₇	#497	1	2	yes	—
301	C₂²×C₇	C₂×#127	1	1	yes	characteristic
302	C₄×C₇	—	2	1	no	—
303	C₄×C₇	—	2	1	no	—
304	C₄×C₇	—	8	1	no	—
305	C₄×C₇	—	8	1	no	—
306	C₄×C₇	—	8	2	no	—
307	C₄×C₇	—	8	1	no	—
308	C₄×C₇	—	8	1	no	—
309	C₄×C₇	#497	1	2	yes	—
310	C₄×C₇	C₂×#137	1	2	yes	—
311	C₄×C₇	#575	1	2	yes	—
312	C₄×C₇	#576	1	2	yes	—
313	C₂⁴	—	4	1	no	—
314	C₂×Q₈	—	2	1	no	—
315	C₂×Q₈	—	2	1	no	—
316	C₂×Q₈	—	2	2	no	—
317	C₂×Q₈	—	2	1	no	—
318	C₂×Q₈	—	2	1	no	—
319	C₂×Q₈	—	4	1	no	—
320	C₂×Q₈	—	8	2	no	—
321	C₂×D₄	—	2	2	no	—
322	C₂×D₄	—	2	2	no	—
323	C₂×D₄	—	2	2	no	—
324	C₂×D₄	—	4	4	no	—
325	C₂×D₄	—	4	1	no	—
326	C₂×D₄	—	4	1	no	—
327	C₂×D₄	—	4	1	no	—
328	C₂×D₄	—	4	4	no	—
329	C₂×D₄	—	8	2	no	—
330	C₂²×C₄	—	4	1	no	—
331	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
332	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
333	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
334	Q₁₆	—	4	4	no	—
335	Q₁₆	—	8	4	no	—
336	SD₁₆	—	8	4	no	—
337	M₁₆	—	2	4	no	—
338	C₂×C₈	—	4	2	no	—
339	C₂×C₈	C₂×C₇×D₄	1	2	yes	—
340	C₂×C₈	C₂×C₇×D₄	1	2	yes	—
341	C₂×C₈	C₂×C₇×D₄	1	4	yes	—
342	C₂×C₈	C₂×C₇×D₄	1	4	yes	—
343	C₄⋊C₄	—	2	2	no	—
344	C₄⋊C₄	—	2	1	no	—
345	C₄⋊C₄	—	2	1	no	—
346	C₄⋊C₄	—	2	1	no	—
347	C₄⋊C₄	—	2	1	no	—
348	C₄⋊C₄	—	2	1	no	—
349	C₄⋊C₄	—	2	1	no	—
350	C₄⋊C₄	—	2	1	no	—
351	C₄⋊C₄	—	2	2	no	—
352	C₄⋊C₄	—	2	1	no	—
353	C₄⋊C₄	—	4	1	no	—
354	C₄⋊C₄	—	4	1	no	—
355	C₄⋊C₄	—	4	1	no	—
356	C₄⋊C₄	—	4	1	no	—
357	C₄⋊C₄	—	4	1	no	—
358	C₄⋊C₄	—	4	1	no	—
359	C₂²⋊C₄	—	4	1	no	—
360	C₂²⋊C₄	—	4	1	no	—
361	C₄²	—	4	1	no	—
362	C₄²	—	4	1	no	—
363	C₄²	C₂×C₇×D₄	1	1	yes	characteristic
364	C₄²	C₂×C₇×D₄	1	1	yes	characteristic
365	C₄²	C₂×C₇×D₄	1	1	yes	characteristic
366	C₄²	C₂⁴×C₇	1	1	yes	characteristic
367	C₂×C₇	—	2	2	no	—
368	C₂×C₇	—	16	2	no	—
369	C₂×C₇	C₂×#497	1	1	yes	characteristic
370	C₂×C₇	#3153	1	1	yes	characteristic
371	C₂×C₇	#3155	1	1	yes	characteristic
372	C₂³	—	4	2	no	—
373	C₂³	—	8	2	no	—
374	C₂³	—	8	2	no	—
375	C₂³	—	8	2	no	—
376	C₂³	C₇×#127	1	1	yes	characteristic
377	Q₈	—	4	2	no	—
378	Q₈	—	4	2	no	—
379	Q₈	—	4	2	no	—
380	Q₈	—	4	2	no	—
381	Q₈	—	4	4	no	—
382	Q₈	—	8	2	no	—
383	D₄	—	4	4	no	—
384	D₄	—	4	4	no	—
385	D₄	—	4	4	no	—
386	D₄	—	8	2	no	—
387	D₄	—	8	2	no	—
388	D₄	—	8	2	no	—
389	C₂×C₄	—	2	2	no	—
390	C₂×C₄	—	2	2	no	—
391	C₂×C₄	—	4	1	no	—
392	C₂×C₄	—	4	1	no	—
393	C₂×C₄	—	4	1	no	—
394	C₂×C₄	—	4	1	no	—
395	C₂×C₄	—	4	2	no	—
396	C₂×C₄	—	8	2	no	—
397	C₂×C₄	C₇×#127	1	1	yes	characteristic
398	C₂×C₄	C₇×#127	1	1	yes	characteristic
399	C₂×C₄	C₇×#127	1	1	yes	characteristic
400	C₂×C₄	C₇×#137	1	4	yes	—
401	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
402	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
403	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
404	C₈	—	2	4	no	—
405	C₈	—	2	2	no	—
406	C₈	—	2	2	no	—
407	C₈	—	2	4	no	—
408	C₇	#19682	1	1	yes	characteristic, direct product factor, Sylow
409	C₂²	—	2	1	no	—
410	C₂²	—	2	1	no	—
411	C₂²	—	8	2	no	—
412	C₂²	—	8	2	no	—
413	C₂²	—	8	2	no	—
414	C₂²	—	16	4	no	—
415	C₂²	C₇×#497	1	2	yes	—
416	C₂²	C₂×C₇×#127	1	1	yes	characteristic
417	C₄	—	2	1	no	—
418	C₄	—	2	1	no	—
419	C₄	—	8	2	no	—
420	C₄	—	8	1	no	—
421	C₄	—	8	1	no	—
422	C₄	—	8	1	no	—
423	C₄	—	8	1	no	—
424	C₄	C₇×#497	1	2	yes	—
425	C₄	C₂×C₇×#137	1	2	yes	—
426	C₄	C₇×#575	1	2	yes	—
427	C₄	C₇×#576	1	2	yes	—
428	C₂	—	2	2	no	—
429	C₂	—	16	2	no	—
430	C₂	C₂×C₇×#497	1	1	yes	characteristic
431	C₂	C₇×#3153	1	1	yes	characteristic
432	C₂	C₇×#3155	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₇	C₂×#127
commutator, Frattini, cosocle	C₄²	C₂⁴×C₇
prime radical	C₂×C₇×#127	C₂²
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×#3209	C₂	semidirect
3. C₇×#3170	C₂	semidirect
4. C₇×#3165	C₂	semidirect
7. C₇×#1722	C₂	semidirect
8. C₇×#1720	C₂	semidirect
9. C₇×#1720	C₂	semidirect
10. C₇×#1719	C₂	semidirect
11. C₇×#1451	C₂	semidirect
17. C₇×#500	C₂²	semidirect
18. C₇×#500	C₂²	semidirect
19. C₇×#498	C₂²	semidirect
20. C₇×#494	C₂²	semidirect
21. C₇×#494	C₂²	semidirect
24. C₇×#487	C₂²	semidirect
25. C₇×#487	C₂²	semidirect
26. C₇×#487	C₂²	semidirect
45. C₇×#322	C₂²	semidirect
46. C₇×#322	C₂²	semidirect
47. #19682	C₇	direct (N × H)
103. #3209	C₂×C₇	semidirect
105. #3170	C₂×C₇	semidirect
106. #3165	C₂×C₇	semidirect
109. #1722	C₂×C₇	semidirect
110. #1720	C₂×C₇	semidirect
111. #1720	C₂×C₇	semidirect
112. #1719	C₂×C₇	semidirect
113. #1451	C₂×C₇	semidirect
173. #500	C₂²×C₇	semidirect
174. #500	C₂²×C₇	semidirect
175. #498	C₂²×C₇	semidirect
176. #494	C₂²×C₇	semidirect
177. #494	C₂²×C₇	semidirect
180. #487	C₂²×C₇	semidirect
181. #487	C₂²×C₇	semidirect
182. #487	C₂²×C₇	semidirect
201. #322	C₂²×C₇	semidirect
202. #322	C₂²×C₇	semidirect
408. C₇	#19682	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×#3209	2
C₇×#3208	2
C₇×#3170	2
C₇×#3165	2
C₇×#3138	2
C₂×C₇×#486	2
C₇×#1722	2
C₇×#1720	2
C₇×#1719	2
C₇×#1451	2
#19682	7

Subgroups — C7×#19682 #13196898

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×#19682 #13196898