Subgroups — C₇×#19621 #13196837

Order 1792.

900 conjugacy classes of subgroups.

The subgroup lattice has 460 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×#3227	C₂	1	1	yes	maximal, characteristic, complemented
2	C₇×#3208	C₂	1	1	yes	maximal, characteristic, complemented
3	C₇×#3167	C₂	1	1	yes	maximal, characteristic, complemented
4	C₇×#3165	C₂	1	1	yes	maximal, characteristic, complemented
5	C₇×#3151	C₂	1	1	yes	maximal, characteristic
6	C₂×C₇×#492	C₂	1	1	yes	maximal, characteristic, complemented
7	C₇×#1715	C₂	1	2	yes	maximal, complemented
8	C₇×#1714	C₂	1	2	yes	maximal, complemented
9	C₇×#1706	C₂	1	2	yes	maximal, complemented
10	C₇×#1705	C₂	1	2	yes	maximal, complemented
11	C₇×C₈×M₁₆	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₇×AGL(1,ℤ/8)	—	2	2	no	—
13	C₂²×C₇×SD₁₆	—	2	2	no	—
14	C₇×#533	C₂²	1	1	yes	characteristic
15	C₇×#532	C₂²	1	1	yes	characteristic
16	C₂×C₇×C₄⋊Q₈	C₂²	1	1	yes	characteristic
17	C₂×C₇×#127	C₂²	1	1	yes	characteristic
18	C₇×#501	—	2	2	no	—
19	C₇×#500	C₂²	1	2	yes	complemented
20	C₇×#498	C₂²	1	2	yes	complemented
21	C₇×#498	C₂²	1	2	yes	complemented
22	C₇×#498	C₂²	1	1	yes	characteristic, complemented
23	C₇×#496	—	2	2	no	—
24	C₇×#493	C₂²	1	2	yes	—
25	C₇×#492	—	2	2	no	—
26	C₇×#492	C₂²	1	2	yes	—
27	C₇×#492	C₂²	1	2	yes	—
28	C₇×#492	C₂²	1	2	yes	—
29	C₇×#492	C₂²	1	2	yes	—
30	C₇×#492	C₂²	1	1	yes	characteristic, complemented
31	C₇×#487	C₂²	1	1	yes	characteristic, complemented
32	C₇×#486	C₂²	1	2	yes	—
33	C₇×#486	C₂²	1	1	yes	characteristic, complemented
34	C₇×#486	C₂²	1	2	yes	complemented
35	C₇×#481	—	2	2	no	—
36	C₇×#476	—	2	2	no	—
37	C₇×#465	—	2	2	no	—
38	C₇×#460	—	2	2	no	—
39	C₇×#450	—	2	2	no	—
40	C₄×C₇×SD₁₆	—	2	2	no	—
41	C₇×#431	C₂²	1	1	yes	characteristic
42	C₇×#428	—	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	#19621	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	C₇×AGL(1,ℤ/8)	—	4	8	no	—
54	C₂×C₇×SD₁₆	—	2	4	no	—
55	C₂×C₇×SD₁₆	—	2	4	no	—
56	C₂×C₇×SD₁₆	—	2	4	no	—
57	C₂×C₇×SD₁₆	—	2	2	no	—
58	C₂×C₇×SD₁₆	—	2	4	no	—
59	C₂×C₇×SD₁₆	—	4	8	no	—
60	C₂×C₇×D₈	—	2	4	no	—
61	C₂×C₇×M₁₆	D₄	1	2	yes	—
62	C₂²×C₇×C₈	D₄	1	2	yes	—
63	C₇×C₄⋊Q₈	—	2	1	no	—
64	C₇×C₄⋊Q₈	—	2	1	no	—
65	C₇×C₄⋊Q₈	—	2	1	no	—
66	C₇×C₄⋊Q₈	C₂³	1	1	yes	characteristic
67	C₇×C₄⋊Q₈	C₂³	1	1	yes	characteristic
68	C₇×C₄⋊Q₈	C₂³	1	2	yes	—
69	C₇×C₄⋊Q₈	C₂³	1	1	yes	characteristic
70	C₇×#127	—	2	1	no	—
71	C₇×#127	—	2	1	no	—
72	C₇×#127	—	2	1	no	—
73	C₇×#127	C₂³	1	2	yes	—
74	C₇×#127	C₂³	1	1	yes	characteristic
75	C₇×#125	—	2	1	no	—
76	C₇×#124	—	2	1	no	—
77	C₇×C₂²⋊Q₈	—	2	1	no	—
78	C₇×C₂²⋊Q₈	—	2	1	no	—
79	C₇×#121	—	2	1	no	—
80	C₇×#121	—	2	1	no	—
81	C₄×C₇×Q₈	—	2	1	no	—
82	C₄×C₇×Q₈	—	2	1	no	—
83	C₄×C₇×D₄	—	2	1	no	—
84	C₄×C₇×D₄	—	2	1	no	—
85	C₇×#117	—	2	1	no	—
86	C₂×C₇×C₄⋊C₄	—	2	1	no	—
87	C₂×C₇×C₄⋊C₄	—	2	1	no	—
88	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
89	C₇×#107	—	2	4	no	—
90	C₇×#106	—	2	4	no	—
91	C₇×#106	—	2	4	no	—
92	C₇×#106	—	2	2	no	—
93	C₇×C₄⋊C₈	D₄	1	2	yes	—
94	C₇×#103	—	2	2	no	—
95	C₇×#102	—	2	4	no	—
96	C₇×#102	—	2	4	no	—
97	C₇×#102	—	2	2	no	—
98	C₇×C₂²⋊C₈	D₄	1	2	yes	—
99	C₇×#97	D₄	1	2	yes	—
100	C₄×C₇×C₈	D₄	1	2	yes	—
101	C₄×C₇×C₈	C₂³	1	1	yes	characteristic
102	C₄×C₇×C₈	C₂³	1	2	yes	—
103	C₄×C₇×C₈	C₂³	1	2	yes	—
104	C₄×C₇×C₈	C₂³	1	1	yes	characteristic
105	#3227	C₂×C₇	1	1	yes	characteristic, complemented
106	#3208	C₂×C₇	1	1	yes	characteristic, complemented
107	#3167	C₂×C₇	1	1	yes	characteristic, complemented
108	#3165	C₂×C₇	1	1	yes	characteristic, complemented
109	#3151	C₂×C₇	1	1	yes	characteristic
110	C₂×#492	C₂×C₇	1	1	yes	characteristic, complemented
111	#1715	C₂×C₇	1	2	yes	complemented
112	#1714	C₂×C₇	1	2	yes	complemented
113	#1706	C₂×C₇	1	2	yes	complemented
114	#1705	C₂×C₇	1	2	yes	complemented
115	C₈×M₁₆	C₂×C₇	1	1	yes	characteristic, complemented
116	C₂⁴×C₇	—	4	1	no	—
117	C₇×#41	—	4	4	no	—
118	C₂×C₇×Q₈	—	2	1	no	—
119	C₂×C₇×Q₈	—	2	1	no	—
120	C₂×C₇×Q₈	—	2	1	no	—
121	C₂×C₇×Q₈	—	2	2	no	—
122	C₂×C₇×Q₈	—	4	4	no	—
123	C₂×C₇×Q₈	—	4	1	no	—
124	C₂×C₇×D₄	—	2	1	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	—	2	2	no	—
130	C₂×C₇×D₄	—	4	4	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	1	no	—
135	C₂×C₇×D₄	—	4	4	no	—
136	C₂×C₇×D₄	—	8	2	no	—
137	C₂²×C₄×C₇	—	4	1	no	—
138	C₂²×C₄×C₇	—	4	1	no	—
139	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
140	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
141	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
142	C₇×SD₁₆	—	4	8	no	—
143	C₇×SD₁₆	—	4	8	no	—
144	C₇×SD₁₆	—	4	4	no	—
145	C₇×SD₁₆	—	4	8	no	—
146	C₇×SD₁₆	—	8	4	no	—
147	C₇×D₈	—	4	8	no	—
148	C₇×M₁₆	SD₁₆	1	8	yes	complemented
149	C₂×C₇×C₈	—	2	4	no	—
150	C₂×C₇×C₈	C₂×D₄	1	2	yes	—
151	C₂×C₇×C₈	C₂×D₄	1	4	yes	—
152	C₂×C₇×C₈	C₂×D₄	1	4	yes	—
153	C₂×C₇×C₈	C₂×D₄	1	2	yes	—
154	C₇×C₄⋊C₄	—	2	1	no	—
155	C₇×C₄⋊C₄	—	2	2	no	—
156	C₇×C₄⋊C₄	—	2	1	no	—
157	C₇×C₄⋊C₄	—	2	1	no	—
158	C₇×C₄⋊C₄	—	2	1	no	—
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	—	4	1	no	—
163	C₇×C₄⋊C₄	—	4	1	no	—
164	C₇×C₄⋊C₄	—	4	1	no	—
165	C₇×C₄⋊C₄	—	4	1	no	—
166	C₇×C₂²⋊C₄	—	4	1	no	—
167	C₇×C₂²⋊C₄	—	4	1	no	—
168	C₇×C₂²⋊C₄	—	4	1	no	—
169	C₄²×C₇	—	4	1	no	—
170	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
171	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
172	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
173	C₄²×C₇	C₂⁴	1	1	yes	characteristic
174	C₂×AGL(1,ℤ/8)	—	2	2	no	—
175	C₂²×SD₁₆	—	2	2	no	—
176	#533	C₂²×C₇	1	1	yes	characteristic
177	#532	C₂²×C₇	1	1	yes	characteristic
178	C₂×C₄⋊Q₈	C₂²×C₇	1	1	yes	characteristic
179	C₂×#127	C₂²×C₇	1	1	yes	characteristic
180	#501	—	2	2	no	—
181	#500	C₂²×C₇	1	2	yes	complemented
182	#498	C₂²×C₇	1	2	yes	complemented
183	#498	C₂²×C₇	1	1	yes	characteristic, complemented
184	#498	C₂²×C₇	1	2	yes	complemented
185	#496	—	2	2	no	—
186	#493	C₂²×C₇	1	2	yes	—
187	#492	—	2	2	no	—
188	#492	C₂²×C₇	1	2	yes	—
189	#492	C₂²×C₇	1	2	yes	—
190	#492	C₂²×C₇	1	2	yes	—
191	#492	C₂²×C₇	1	2	yes	—
192	#492	C₂²×C₇	1	1	yes	characteristic, complemented
193	#487	C₂²×C₇	1	1	yes	characteristic, complemented
194	#486	C₂²×C₇	1	2	yes	—
195	#486	C₂²×C₇	1	1	yes	characteristic, complemented
196	#486	C₂²×C₇	1	2	yes	complemented
197	#481	—	2	2	no	—
198	#476	—	2	2	no	—
199	#465	—	2	2	no	—
200	#460	—	2	2	no	—
201	#450	—	2	2	no	—
202	C₄×SD₁₆	—	2	2	no	—
203	#431	C₂²×C₇	1	1	yes	characteristic
204	#428	—	2	2	no	—
205	C₄×M₁₆	C₂²×C₇	1	1	yes	characteristic
206	C₂×C₄×C₈	C₂²×C₇	1	1	yes	characteristic
207	#322	C₂²×C₇	1	2	yes	complemented
208	C₈²	C₂²×C₇	1	2	yes	complemented
209	C₂³×C₇	—	4	1	no	—
210	C₂³×C₇	—	4	2	no	—
211	C₂³×C₇	—	8	2	no	—
212	C₂³×C₇	—	8	2	no	—
213	C₂³×C₇	—	8	2	no	—
214	C₂³×C₇	#127	1	1	yes	characteristic
215	C₇×Q₈	—	4	2	no	—
216	C₇×Q₈	—	4	4	no	—
217	C₇×Q₈	—	4	2	no	—
218	C₇×Q₈	—	4	2	no	—
219	C₇×Q₈	—	8	2	no	—
220	C₇×D₄	—	4	2	no	—
221	C₇×D₄	—	4	4	no	—
222	C₇×D₄	—	4	4	no	—
223	C₇×D₄	—	4	2	no	—
224	C₇×D₄	—	4	4	no	—
225	C₇×D₄	—	4	2	no	—
226	C₇×D₄	—	8	2	no	—
227	C₇×D₄	—	8	2	no	—
228	C₇×D₄	—	8	2	no	—
229	C₇×D₄	—	8	2	no	—
230	C₂×C₄×C₇	—	2	2	no	—
231	C₂×C₄×C₇	—	2	2	no	—
232	C₂×C₄×C₇	—	4	1	no	—
233	C₂×C₄×C₇	—	4	1	no	—
234	C₂×C₄×C₇	—	4	1	no	—
235	C₂×C₄×C₇	—	4	2	no	—
236	C₂×C₄×C₇	—	8	2	no	—
237	C₂×C₄×C₇	—	8	2	no	—
238	C₂×C₄×C₇	#127	1	1	yes	characteristic
239	C₂×C₄×C₇	#127	1	1	yes	characteristic
240	C₂×C₄×C₇	#127	1	1	yes	characteristic
241	C₂×C₄×C₇	C₂×SD₁₆	1	4	yes	—
242	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
243	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
244	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
245	C₇×C₈	—	2	2	no	—
246	C₇×C₈	—	2	4	no	—
247	C₇×C₈	C₂×SD₁₆	1	8	yes	complemented
248	C₇×C₈	AGL(1,ℤ/8)	1	4	yes	complemented
249	C₂×#41	—	2	1	no	—
250	C₂²×Q₈	—	2	1	no	—
251	C₂²×D₄	—	2	1	no	—
252	C₂²×D₄	—	2	1	no	—
253	C₂²×D₄	—	2	1	no	—
254	AGL(1,ℤ/8)	—	4	8	no	—
255	C₂×SD₁₆	—	2	4	no	—
256	C₂×SD₁₆	—	2	4	no	—
257	C₂×SD₁₆	—	2	4	no	—
258	C₂×SD₁₆	—	2	2	no	—
259	C₂×SD₁₆	—	2	4	no	—
260	C₂×SD₁₆	—	4	8	no	—
261	C₂×D₈	—	2	4	no	—
262	C₂×M₁₆	C₇×D₄	1	2	yes	—
263	C₂²×C₈	C₇×D₄	1	2	yes	—
264	C₄⋊Q₈	—	2	1	no	—
265	C₄⋊Q₈	—	2	1	no	—
266	C₄⋊Q₈	—	2	1	no	—
267	C₄⋊Q₈	C₂³×C₇	1	2	yes	—
268	C₄⋊Q₈	C₂³×C₇	1	1	yes	characteristic
269	C₄⋊Q₈	C₂³×C₇	1	1	yes	characteristic
270	C₄⋊Q₈	C₂³×C₇	1	1	yes	characteristic
271	#127	—	2	1	no	—
272	#127	—	2	1	no	—
273	#127	—	2	1	no	—
274	#127	C₂³×C₇	1	2	yes	—
275	#127	C₂³×C₇	1	1	yes	characteristic
276	#125	—	2	1	no	—
277	#124	—	2	1	no	—
278	C₂²⋊Q₈	—	2	1	no	—
279	C₂²⋊Q₈	—	2	1	no	—
280	#121	—	2	1	no	—
281	#121	—	2	1	no	—
282	C₄×Q₈	—	2	1	no	—
283	C₄×Q₈	—	2	1	no	—
284	C₄×D₄	—	2	1	no	—
285	C₄×D₄	—	2	1	no	—
286	#117	—	2	1	no	—
287	C₂×C₄⋊C₄	—	2	1	no	—
288	C₂×C₄⋊C₄	—	2	1	no	—
289	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
290	#107	—	2	4	no	—
291	#106	—	2	4	no	—
292	#106	—	2	2	no	—
293	#106	—	2	4	no	—
294	C₄⋊C₈	C₇×D₄	1	2	yes	—
295	#103	—	2	2	no	—
296	#102	—	2	2	no	—
297	#102	—	2	4	no	—
298	#102	—	2	4	no	—
299	C₂²⋊C₈	C₇×D₄	1	2	yes	—
300	#97	C₇×D₄	1	2	yes	—
301	C₄×C₈	C₇×D₄	1	2	yes	—
302	C₄×C₈	C₂³×C₇	1	1	yes	characteristic
303	C₄×C₈	C₂³×C₇	1	2	yes	—
304	C₄×C₈	C₂³×C₇	1	2	yes	—
305	C₄×C₈	C₂³×C₇	1	1	yes	characteristic
306	C₂²×C₇	—	2	1	no	—
307	C₂²×C₇	—	2	1	no	—
308	C₂²×C₇	—	8	1	no	—
309	C₂²×C₇	—	8	2	no	—
310	C₂²×C₇	—	8	2	no	—
311	C₂²×C₇	—	8	1	no	—
312	C₂²×C₇	—	8	2	no	—
313	C₂²×C₇	—	8	1	no	—
314	C₂²×C₇	—	16	4	no	—
315	C₂²×C₇	#492	1	2	yes	—
316	C₂²×C₇	C₂×#127	1	1	yes	characteristic
317	C₄×C₇	—	2	1	no	—
318	C₄×C₇	—	2	1	no	—
319	C₄×C₇	—	8	1	no	—
320	C₄×C₇	—	8	2	no	—
321	C₄×C₇	—	8	1	no	—
322	C₄×C₇	—	8	1	no	—
323	C₄×C₇	#492	1	2	yes	—
324	C₄×C₇	C₂²×SD₁₆	1	2	yes	—
325	C₄×C₇	C₂×AGL(1,ℤ/8)	1	2	yes	—
326	C₄×C₇	#577	1	2	yes	—
327	C₂⁴	—	4	1	no	—
328	#41	—	4	4	no	—
329	C₂×Q₈	—	2	1	no	—
330	C₂×Q₈	—	2	1	no	—
331	C₂×Q₈	—	2	1	no	—
332	C₂×Q₈	—	2	2	no	—
333	C₂×Q₈	—	4	4	no	—
334	C₂×Q₈	—	4	1	no	—
335	C₂×D₄	—	2	1	no	—
336	C₂×D₄	—	2	1	no	—
337	C₂×D₄	—	2	2	no	—
338	C₂×D₄	—	2	1	no	—
339	C₂×D₄	—	2	2	no	—
340	C₂×D₄	—	2	2	no	—
341	C₂×D₄	—	4	4	no	—
342	C₂×D₄	—	4	1	no	—
343	C₂×D₄	—	4	1	no	—
344	C₂×D₄	—	4	1	no	—
345	C₂×D₄	—	4	1	no	—
346	C₂×D₄	—	4	4	no	—
347	C₂×D₄	—	8	2	no	—
348	C₂²×C₄	—	4	1	no	—
349	C₂²×C₄	—	4	1	no	—
350	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
351	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
352	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
353	SD₁₆	—	4	8	no	—
354	SD₁₆	—	4	8	no	—
355	SD₁₆	—	4	4	no	—
356	SD₁₆	—	4	8	no	—
357	SD₁₆	—	8	4	no	—
358	D₈	—	4	8	no	—
359	M₁₆	C₇×SD₁₆	1	8	yes	complemented
360	C₂×C₈	—	2	4	no	—
361	C₂×C₈	C₂×C₇×D₄	1	2	yes	—
362	C₂×C₈	C₂×C₇×D₄	1	4	yes	—
363	C₂×C₈	C₂×C₇×D₄	1	4	yes	—
364	C₂×C₈	C₂×C₇×D₄	1	2	yes	—
365	C₄⋊C₄	—	2	1	no	—
366	C₄⋊C₄	—	2	2	no	—
367	C₄⋊C₄	—	2	1	no	—
368	C₄⋊C₄	—	2	1	no	—
369	C₄⋊C₄	—	2	1	no	—
370	C₄⋊C₄	—	2	1	no	—
371	C₄⋊C₄	—	2	2	no	—
372	C₄⋊C₄	—	2	1	no	—
373	C₄⋊C₄	—	4	1	no	—
374	C₄⋊C₄	—	4	1	no	—
375	C₄⋊C₄	—	4	1	no	—
376	C₄⋊C₄	—	4	1	no	—
377	C₂²⋊C₄	—	4	1	no	—
378	C₂²⋊C₄	—	4	1	no	—
379	C₂²⋊C₄	—	4	1	no	—
380	C₄²	—	4	1	no	—
381	C₄²	C₂×C₇×D₄	1	1	yes	characteristic
382	C₄²	C₂×C₇×D₄	1	1	yes	characteristic
383	C₄²	C₂×C₇×D₄	1	1	yes	characteristic
384	C₄²	C₂⁴×C₇	1	1	yes	characteristic
385	C₂×C₇	—	2	2	no	—
386	C₂×C₇	—	16	1	no	—
387	C₂×C₇	—	16	2	no	—
388	C₂×C₇	C₂×#492	1	1	yes	characteristic
389	C₂×C₇	#3151	1	1	yes	characteristic
390	C₂×C₇	#3154	1	1	yes	characteristic
391	C₂³	—	4	1	no	—
392	C₂³	—	4	2	no	—
393	C₂³	—	8	2	no	—
394	C₂³	—	8	2	no	—
395	C₂³	—	8	2	no	—
396	C₂³	C₇×#127	1	1	yes	characteristic
397	Q₈	—	4	2	no	—
398	Q₈	—	4	4	no	—
399	Q₈	—	4	2	no	—
400	Q₈	—	4	2	no	—
401	Q₈	—	8	2	no	—
402	D₄	—	4	2	no	—
403	D₄	—	4	4	no	—
404	D₄	—	4	4	no	—
405	D₄	—	4	2	no	—
406	D₄	—	4	4	no	—
407	D₄	—	4	2	no	—
408	D₄	—	8	2	no	—
409	D₄	—	8	2	no	—
410	D₄	—	8	2	no	—
411	D₄	—	8	2	no	—
412	C₂×C₄	—	2	2	no	—
413	C₂×C₄	—	2	2	no	—
414	C₂×C₄	—	4	1	no	—
415	C₂×C₄	—	4	1	no	—
416	C₂×C₄	—	4	1	no	—
417	C₂×C₄	—	4	2	no	—
418	C₂×C₄	—	8	2	no	—
419	C₂×C₄	—	8	2	no	—
420	C₂×C₄	C₇×#127	1	1	yes	characteristic
421	C₂×C₄	C₇×#127	1	1	yes	characteristic
422	C₂×C₄	C₇×#127	1	1	yes	characteristic
423	C₂×C₄	C₂×C₇×SD₁₆	1	4	yes	—
424	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
425	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
426	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
427	C₈	—	2	2	no	—
428	C₈	—	2	4	no	—
429	C₈	C₂×C₇×SD₁₆	1	8	yes	complemented
430	C₈	C₇×AGL(1,ℤ/8)	1	4	yes	complemented
431	C₇	#19621	1	1	yes	characteristic, direct product factor, Sylow
432	C₂²	—	2	1	no	—
433	C₂²	—	2	1	no	—
434	C₂²	—	8	1	no	—
435	C₂²	—	8	2	no	—
436	C₂²	—	8	2	no	—
437	C₂²	—	8	1	no	—
438	C₂²	—	8	2	no	—
439	C₂²	—	8	1	no	—
440	C₂²	—	16	4	no	—
441	C₂²	C₇×#492	1	2	yes	—
442	C₂²	C₂×C₇×#127	1	1	yes	characteristic
443	C₄	—	2	1	no	—
444	C₄	—	2	1	no	—
445	C₄	—	8	1	no	—
446	C₄	—	8	2	no	—
447	C₄	—	8	1	no	—
448	C₄	—	8	1	no	—
449	C₄	C₇×#492	1	2	yes	—
450	C₄	C₂²×C₇×SD₁₆	1	2	yes	—
451	C₄	C₂×C₇×AGL(1,ℤ/8)	1	2	yes	—
452	C₄	C₇×#577	1	2	yes	—
453	C₂	—	2	2	no	—
454	C₂	—	16	2	no	—
455	C₂	—	16	1	no	—
456	C₂	C₂×C₇×#492	1	1	yes	characteristic
457	C₂	C₇×#3151	1	1	yes	characteristic
458	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×#3151	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×#3227	C₂	semidirect
2. C₇×#3208	C₂	semidirect
3. C₇×#3167	C₂	semidirect
4. C₇×#3165	C₂	semidirect
6. C₂×C₇×#492	C₂	semidirect
7. C₇×#1715	C₂	semidirect
8. C₇×#1714	C₂	semidirect
9. C₇×#1706	C₂	semidirect
10. C₇×#1705	C₂	semidirect
11. C₇×C₈×M₁₆	C₂	semidirect
19. C₇×#500	C₂²	semidirect
20. C₇×#498	C₂²	semidirect
21. C₇×#498	C₂²	semidirect
22. C₇×#498	C₂²	semidirect
30. C₇×#492	C₂²	semidirect
31. C₇×#487	C₂²	semidirect
33. C₇×#486	C₂²	semidirect
34. C₇×#486	C₂²	semidirect
45. C₇×#322	C₂²	semidirect
46. C₇×C₈²	C₂²	semidirect
47. #19621	C₇	direct (N × H)
105. #3227	C₂×C₇	semidirect
106. #3208	C₂×C₇	semidirect
107. #3167	C₂×C₇	semidirect
108. #3165	C₂×C₇	semidirect
110. C₂×#492	C₂×C₇	semidirect
111. #1715	C₂×C₇	semidirect
112. #1714	C₂×C₇	semidirect
113. #1706	C₂×C₇	semidirect
114. #1705	C₂×C₇	semidirect
115. C₈×M₁₆	C₂×C₇	semidirect
148. C₇×M₁₆	SD₁₆	semidirect
181. #500	C₂²×C₇	semidirect
182. #498	C₂²×C₇	semidirect
183. #498	C₂²×C₇	semidirect
184. #498	C₂²×C₇	semidirect
192. #492	C₂²×C₇	semidirect
193. #487	C₂²×C₇	semidirect
195. #486	C₂²×C₇	semidirect
196. #486	C₂²×C₇	semidirect
207. #322	C₂²×C₇	semidirect
208. C₈²	C₂²×C₇	semidirect
247. C₇×C₈	C₂×SD₁₆	semidirect
248. C₇×C₈	AGL(1,ℤ/8)	semidirect
359. M₁₆	C₇×SD₁₆	semidirect
429. C₈	C₂×C₇×SD₁₆	semidirect
430. C₈	C₇×AGL(1,ℤ/8)	semidirect
431. C₇	#19621	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×#3227	2
C₇×#3208	2
C₇×#3167	2
C₇×#3165	2
C₇×#3151	2
C₂×C₇×#492	2
C₇×#1715	2
C₇×#1714	2
C₇×#1706	2
C₇×#1705	2
C₇×C₈×M₁₆	2
#19621	7

Subgroups — C7×#19621 #13196837

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×#19621 #13196837