Subgroups — C₇×#19623 #13196839

Order 1792.

848 conjugacy classes of subgroups.

The subgroup lattice has 456 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×#3208	C₂	1	1	yes	maximal, characteristic, complemented
2	C₇×#3206	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×#486	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×#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	C₂×C₇×AGL(1,ℤ/8)	—	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×#501	—	2	2	no	—
18	C₇×#500	C₂²	1	2	yes	complemented
19	C₇×#498	C₂²	1	2	yes	complemented
20	C₇×#498	C₂²	1	1	yes	characteristic, complemented
21	C₇×#496	—	2	2	no	—
22	C₇×#493	C₂²	1	2	yes	—
23	C₇×#492	C₂²	1	2	yes	—
24	C₇×#492	C₂²	1	2	yes	—
25	C₇×#492	C₂²	1	1	yes	characteristic, complemented
26	C₇×#492	C₂²	1	2	yes	complemented
27	C₇×#487	C₂²	1	1	yes	characteristic, complemented
28	C₇×#487	C₂²	1	2	yes	complemented
29	C₇×#486	—	2	2	no	—
30	C₇×#486	C₂²	1	2	yes	—
31	C₇×#486	C₂²	1	2	yes	—
32	C₇×#486	C₂²	1	2	yes	—
33	C₇×#486	C₂²	1	1	yes	characteristic, complemented
34	C₇×#465	—	2	2	no	—
35	C₇×#461	—	2	2	no	—
36	C₇×#460	—	2	2	no	—
37	C₇×#450	—	2	2	no	—
38	C₇×#448	—	2	2	no	—
39	C₄×C₇×SD₁₆	—	2	2	no	—
40	C₇×#431	C₂²	1	1	yes	characteristic
41	C₇×#428	—	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×C₈²	C₂²	1	2	yes	complemented
47	#19623	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	2	no	—
56	C₂×C₇×SD₁₆	—	2	4	no	—
57	C₂×C₇×SD₁₆	—	2	4	no	—
58	C₂×C₇×D₈	—	2	4	no	—
59	C₂×C₇×M₁₆	D₄	1	2	yes	—
60	C₂²×C₇×C₈	D₄	1	2	yes	—
61	C₇×C₄⋊Q₈	—	2	1	no	—
62	C₇×C₄⋊Q₈	—	2	1	no	—
63	C₇×C₄⋊Q₈	—	2	1	no	—
64	C₇×C₄⋊Q₈	C₂³	1	1	yes	characteristic
65	C₇×C₄⋊Q₈	C₂³	1	2	yes	—
66	C₇×C₄⋊Q₈	C₂³	1	1	yes	characteristic
67	C₇×C₄⋊Q₈	C₂³	1	1	yes	characteristic
68	C₇×#127	—	2	1	no	—
69	C₇×#127	—	2	1	no	—
70	C₇×#127	—	2	1	no	—
71	C₇×#127	C₂³	1	2	yes	—
72	C₇×#127	C₂³	1	1	yes	characteristic
73	C₇×#125	—	2	1	no	—
74	C₇×#124	—	2	1	no	—
75	C₇×C₂²⋊Q₈	—	2	1	no	—
76	C₇×C₂²⋊Q₈	—	2	1	no	—
77	C₇×#121	—	2	1	no	—
78	C₇×#121	—	2	1	no	—
79	C₄×C₇×Q₈	—	2	1	no	—
80	C₄×C₇×Q₈	—	2	1	no	—
81	C₄×C₇×D₄	—	2	1	no	—
82	C₄×C₇×D₄	—	2	1	no	—
83	C₇×#117	—	2	1	no	—
84	C₂×C₇×C₄⋊C₄	—	2	1	no	—
85	C₂×C₇×C₄⋊C₄	—	2	1	no	—
86	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
87	C₇×#107	—	2	4	no	—
88	C₇×#106	—	2	4	no	—
89	C₇×#106	—	2	2	no	—
90	C₇×C₄⋊C₈	D₄	1	2	yes	—
91	C₇×#103	—	2	2	no	—
92	C₇×#103	—	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	#3208	C₂×C₇	1	1	yes	characteristic, complemented
105	#3206	C₂×C₇	1	1	yes	characteristic, complemented
106	#3167	C₂×C₇	1	1	yes	characteristic, complemented
107	#3165	C₂×C₇	1	1	yes	characteristic, complemented
108	#3151	C₂×C₇	1	1	yes	characteristic
109	C₂×#486	C₂×C₇	1	1	yes	characteristic, complemented
110	#1715	C₂×C₇	1	2	yes	complemented
111	#1714	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	2	no	—
119	C₂×C₇×Q₈	—	2	1	no	—
120	C₂×C₇×Q₈	—	2	1	no	—
121	C₂×C₇×Q₈	—	4	1	no	—
122	C₂×C₇×Q₈	—	8	2	no	—
123	C₂×C₇×D₄	—	2	2	no	—
124	C₂×C₇×D₄	—	2	1	no	—
125	C₂×C₇×D₄	—	2	2	no	—
126	C₂×C₇×D₄	—	2	1	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	4	no	—
142	C₇×SD₁₆	—	4	8	no	—
143	C₇×SD₁₆	—	8	4	no	—
144	C₇×SD₁₆	—	8	4	no	—
145	C₇×D₈	—	4	8	no	—
146	C₇×M₁₆	SD₁₆	1	8	yes	complemented
147	C₂×C₇×C₈	—	4	2	no	—
148	C₂×C₇×C₈	C₂×D₄	1	2	yes	—
149	C₂×C₇×C₈	C₂×D₄	1	2	yes	—
150	C₂×C₇×C₈	C₂×D₄	1	4	yes	—
151	C₂×C₇×C₈	C₂×D₄	1	4	yes	—
152	C₇×C₄⋊C₄	—	2	2	no	—
153	C₇×C₄⋊C₄	—	2	1	no	—
154	C₇×C₄⋊C₄	—	2	1	no	—
155	C₇×C₄⋊C₄	—	2	1	no	—
156	C₇×C₄⋊C₄	—	2	1	no	—
157	C₇×C₄⋊C₄	—	2	1	no	—
158	C₇×C₄⋊C₄	—	2	2	no	—
159	C₇×C₄⋊C₄	—	2	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×C₄⋊C₄	—	4	1	no	—
164	C₇×C₂²⋊C₄	—	4	1	no	—
165	C₇×C₂²⋊C₄	—	4	1	no	—
166	C₇×C₂²⋊C₄	—	4	1	no	—
167	C₄²×C₇	—	4	1	no	—
168	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
169	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
170	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
171	C₄²×C₇	C₂⁴	1	1	yes	characteristic
172	C₂×AGL(1,ℤ/8)	—	2	2	no	—
173	#533	C₂²×C₇	1	1	yes	characteristic
174	#532	C₂²×C₇	1	1	yes	characteristic
175	C₂×C₄⋊Q₈	C₂²×C₇	1	1	yes	characteristic
176	C₂×#127	C₂²×C₇	1	1	yes	characteristic
177	#501	—	2	2	no	—
178	#500	C₂²×C₇	1	2	yes	complemented
179	#498	C₂²×C₇	1	2	yes	complemented
180	#498	C₂²×C₇	1	1	yes	characteristic, complemented
181	#496	—	2	2	no	—
182	#493	C₂²×C₇	1	2	yes	—
183	#492	C₂²×C₇	1	2	yes	—
184	#492	C₂²×C₇	1	2	yes	—
185	#492	C₂²×C₇	1	1	yes	characteristic, complemented
186	#492	C₂²×C₇	1	2	yes	complemented
187	#487	C₂²×C₇	1	1	yes	characteristic, complemented
188	#487	C₂²×C₇	1	2	yes	complemented
189	#486	—	2	2	no	—
190	#486	C₂²×C₇	1	2	yes	—
191	#486	C₂²×C₇	1	2	yes	—
192	#486	C₂²×C₇	1	2	yes	—
193	#486	C₂²×C₇	1	1	yes	characteristic, complemented
194	#465	—	2	2	no	—
195	#461	—	2	2	no	—
196	#460	—	2	2	no	—
197	#450	—	2	2	no	—
198	#448	—	2	2	no	—
199	C₄×SD₁₆	—	2	2	no	—
200	#431	C₂²×C₇	1	1	yes	characteristic
201	#428	—	2	2	no	—
202	C₂×#102	—	2	2	no	—
203	C₄×M₁₆	C₂²×C₇	1	1	yes	characteristic
204	C₂×C₄×C₈	C₂²×C₇	1	1	yes	characteristic
205	#322	C₂²×C₇	1	2	yes	complemented
206	C₈²	C₂²×C₇	1	2	yes	complemented
207	C₂³×C₇	—	4	1	no	—
208	C₂³×C₇	—	4	2	no	—
209	C₂³×C₇	—	8	2	no	—
210	C₂³×C₇	—	8	2	no	—
211	C₂³×C₇	—	8	2	no	—
212	C₂³×C₇	#127	1	1	yes	characteristic
213	C₇×Q₈	—	4	2	no	—
214	C₇×Q₈	—	4	2	no	—
215	C₇×Q₈	—	4	2	no	—
216	C₇×Q₈	—	4	4	no	—
217	C₇×Q₈	—	8	2	no	—
218	C₇×D₄	—	4	2	no	—
219	C₇×D₄	—	4	4	no	—
220	C₇×D₄	—	4	2	no	—
221	C₇×D₄	—	4	4	no	—
222	C₇×D₄	—	4	2	no	—
223	C₇×D₄	—	4	4	no	—
224	C₇×D₄	—	8	2	no	—
225	C₇×D₄	—	8	2	no	—
226	C₇×D₄	—	8	2	no	—
227	C₇×D₄	—	8	2	no	—
228	C₂×C₄×C₇	—	2	2	no	—
229	C₂×C₄×C₇	—	2	2	no	—
230	C₂×C₄×C₇	—	4	1	no	—
231	C₂×C₄×C₇	—	4	1	no	—
232	C₂×C₄×C₇	—	4	1	no	—
233	C₂×C₄×C₇	—	4	2	no	—
234	C₂×C₄×C₇	—	8	2	no	—
235	C₂×C₄×C₇	—	8	2	no	—
236	C₂×C₄×C₇	#127	1	1	yes	characteristic
237	C₂×C₄×C₇	#127	1	1	yes	characteristic
238	C₂×C₄×C₇	#127	1	1	yes	characteristic
239	C₂×C₄×C₇	C₂×SD₁₆	1	4	yes	—
240	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
241	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
242	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
243	C₇×C₈	—	2	2	no	—
244	C₇×C₈	—	2	2	no	—
245	C₇×C₈	—	2	4	no	—
246	C₇×C₈	C₂×SD₁₆	1	8	yes	—
247	C₂×#41	—	2	1	no	—
248	C₂²×Q₈	—	2	1	no	—
249	C₂²×D₄	—	2	1	no	—
250	C₂²×D₄	—	2	1	no	—
251	C₂²×D₄	—	2	1	no	—
252	AGL(1,ℤ/8)	—	4	8	no	—
253	C₂×SD₁₆	—	2	4	no	—
254	C₂×SD₁₆	—	2	2	no	—
255	C₂×SD₁₆	—	2	4	no	—
256	C₂×SD₁₆	—	2	4	no	—
257	C₂×D₈	—	2	4	no	—
258	C₂×M₁₆	C₇×D₄	1	2	yes	—
259	C₂²×C₈	C₇×D₄	1	2	yes	—
260	C₄⋊Q₈	—	2	1	no	—
261	C₄⋊Q₈	—	2	1	no	—
262	C₄⋊Q₈	—	2	1	no	—
263	C₄⋊Q₈	C₂³×C₇	1	2	yes	—
264	C₄⋊Q₈	C₂³×C₇	1	1	yes	characteristic
265	C₄⋊Q₈	C₂³×C₇	1	1	yes	characteristic
266	C₄⋊Q₈	C₂³×C₇	1	1	yes	characteristic
267	#127	—	2	1	no	—
268	#127	—	2	1	no	—
269	#127	—	2	1	no	—
270	#127	C₂³×C₇	1	2	yes	—
271	#127	C₂³×C₇	1	1	yes	characteristic
272	#125	—	2	1	no	—
273	#124	—	2	1	no	—
274	C₂²⋊Q₈	—	2	1	no	—
275	C₂²⋊Q₈	—	2	1	no	—
276	#121	—	2	1	no	—
277	#121	—	2	1	no	—
278	C₄×Q₈	—	2	1	no	—
279	C₄×Q₈	—	2	1	no	—
280	C₄×D₄	—	2	1	no	—
281	C₄×D₄	—	2	1	no	—
282	#117	—	2	1	no	—
283	C₂×C₄⋊C₄	—	2	1	no	—
284	C₂×C₄⋊C₄	—	2	1	no	—
285	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
286	#107	—	2	4	no	—
287	#106	—	2	4	no	—
288	#106	—	2	2	no	—
289	C₄⋊C₈	C₇×D₄	1	2	yes	—
290	#103	—	2	2	no	—
291	#103	—	2	4	no	—
292	#102	—	2	4	no	—
293	#102	—	2	4	no	—
294	#102	—	2	2	no	—
295	#102	—	2	4	no	—
296	C₂²⋊C₈	C₇×D₄	1	2	yes	—
297	#97	C₇×D₄	1	2	yes	—
298	C₄×C₈	C₇×D₄	1	2	yes	—
299	C₄×C₈	C₂³×C₇	1	1	yes	characteristic
300	C₄×C₈	C₂³×C₇	1	2	yes	—
301	C₄×C₈	C₂³×C₇	1	2	yes	—
302	C₄×C₈	C₂³×C₇	1	1	yes	characteristic
303	C₂²×C₇	—	2	1	no	—
304	C₂²×C₇	—	2	1	no	—
305	C₂²×C₇	—	8	1	no	—
306	C₂²×C₇	—	8	2	no	—
307	C₂²×C₇	—	8	2	no	—
308	C₂²×C₇	—	8	1	no	—
309	C₂²×C₇	—	8	2	no	—
310	C₂²×C₇	—	8	1	no	—
311	C₂²×C₇	—	16	4	no	—
312	C₂²×C₇	#492	1	2	yes	—
313	C₂²×C₇	C₂×#127	1	1	yes	characteristic
314	C₄×C₇	—	2	1	no	—
315	C₄×C₇	—	2	1	no	—
316	C₄×C₇	—	8	1	no	—
317	C₄×C₇	—	8	1	no	—
318	C₄×C₇	—	8	2	no	—
319	C₄×C₇	—	8	1	no	—
320	C₄×C₇	#492	1	2	yes	—
321	C₄×C₇	C₂²×SD₁₆	1	2	yes	—
322	C₄×C₇	#575	1	2	yes	—
323	C₄×C₇	#576	1	2	yes	—
324	C₂⁴	—	4	1	no	—
325	#41	—	4	4	no	—
326	C₂×Q₈	—	2	1	no	—
327	C₂×Q₈	—	2	2	no	—
328	C₂×Q₈	—	2	1	no	—
329	C₂×Q₈	—	2	1	no	—
330	C₂×Q₈	—	4	1	no	—
331	C₂×Q₈	—	8	2	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	1	no	—
337	C₂×D₄	—	2	2	no	—
338	C₂×D₄	—	4	4	no	—
339	C₂×D₄	—	4	1	no	—
340	C₂×D₄	—	4	1	no	—
341	C₂×D₄	—	4	1	no	—
342	C₂×D₄	—	4	1	no	—
343	C₂×D₄	—	4	4	no	—
344	C₂×D₄	—	8	2	no	—
345	C₂²×C₄	—	4	1	no	—
346	C₂²×C₄	—	4	1	no	—
347	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
348	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
349	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
350	SD₁₆	—	4	4	no	—
351	SD₁₆	—	4	8	no	—
352	SD₁₆	—	8	4	no	—
353	SD₁₆	—	8	4	no	—
354	D₈	—	4	8	no	—
355	M₁₆	C₇×SD₁₆	1	8	yes	complemented
356	C₂×C₈	—	4	2	no	—
357	C₂×C₈	C₂×C₇×D₄	1	2	yes	—
358	C₂×C₈	C₂×C₇×D₄	1	2	yes	—
359	C₂×C₈	C₂×C₇×D₄	1	4	yes	—
360	C₂×C₈	C₂×C₇×D₄	1	4	yes	—
361	C₄⋊C₄	—	2	2	no	—
362	C₄⋊C₄	—	2	1	no	—
363	C₄⋊C₄	—	2	1	no	—
364	C₄⋊C₄	—	2	1	no	—
365	C₄⋊C₄	—	2	1	no	—
366	C₄⋊C₄	—	2	1	no	—
367	C₄⋊C₄	—	2	2	no	—
368	C₄⋊C₄	—	2	1	no	—
369	C₄⋊C₄	—	4	1	no	—
370	C₄⋊C₄	—	4	1	no	—
371	C₄⋊C₄	—	4	1	no	—
372	C₄⋊C₄	—	4	1	no	—
373	C₂²⋊C₄	—	4	1	no	—
374	C₂²⋊C₄	—	4	1	no	—
375	C₂²⋊C₄	—	4	1	no	—
376	C₄²	—	4	1	no	—
377	C₄²	C₂×C₇×D₄	1	1	yes	characteristic
378	C₄²	C₂×C₇×D₄	1	1	yes	characteristic
379	C₄²	C₂×C₇×D₄	1	1	yes	characteristic
380	C₄²	C₂⁴×C₇	1	1	yes	characteristic
381	C₂×C₇	—	2	2	no	—
382	C₂×C₇	—	16	1	no	—
383	C₂×C₇	—	16	2	no	—
384	C₂×C₇	C₂×#492	1	1	yes	characteristic
385	C₂×C₇	#3153	1	1	yes	characteristic
386	C₂×C₇	#3155	1	1	yes	characteristic
387	C₂³	—	4	1	no	—
388	C₂³	—	4	2	no	—
389	C₂³	—	8	2	no	—
390	C₂³	—	8	2	no	—
391	C₂³	—	8	2	no	—
392	C₂³	C₇×#127	1	1	yes	characteristic
393	Q₈	—	4	2	no	—
394	Q₈	—	4	2	no	—
395	Q₈	—	4	2	no	—
396	Q₈	—	4	4	no	—
397	Q₈	—	8	2	no	—
398	D₄	—	4	2	no	—
399	D₄	—	4	4	no	—
400	D₄	—	4	2	no	—
401	D₄	—	4	4	no	—
402	D₄	—	4	2	no	—
403	D₄	—	4	4	no	—
404	D₄	—	8	2	no	—
405	D₄	—	8	2	no	—
406	D₄	—	8	2	no	—
407	D₄	—	8	2	no	—
408	C₂×C₄	—	2	2	no	—
409	C₂×C₄	—	2	2	no	—
410	C₂×C₄	—	4	1	no	—
411	C₂×C₄	—	4	1	no	—
412	C₂×C₄	—	4	1	no	—
413	C₂×C₄	—	4	2	no	—
414	C₂×C₄	—	8	2	no	—
415	C₂×C₄	—	8	2	no	—
416	C₂×C₄	C₇×#127	1	1	yes	characteristic
417	C₂×C₄	C₇×#127	1	1	yes	characteristic
418	C₂×C₄	C₇×#127	1	1	yes	characteristic
419	C₂×C₄	C₂×C₇×SD₁₆	1	4	yes	—
420	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
421	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
422	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
423	C₈	—	2	2	no	—
424	C₈	—	2	2	no	—
425	C₈	—	2	4	no	—
426	C₈	C₂×C₇×SD₁₆	1	8	yes	—
427	C₇	#19623	1	1	yes	characteristic, direct product factor, Sylow
428	C₂²	—	2	1	no	—
429	C₂²	—	2	1	no	—
430	C₂²	—	8	2	no	—
431	C₂²	—	8	1	no	—
432	C₂²	—	8	1	no	—
433	C₂²	—	8	2	no	—
434	C₂²	—	8	2	no	—
435	C₂²	—	8	1	no	—
436	C₂²	—	16	4	no	—
437	C₂²	C₇×#492	1	2	yes	—
438	C₂²	C₂×C₇×#127	1	1	yes	characteristic
439	C₄	—	2	1	no	—
440	C₄	—	2	1	no	—
441	C₄	—	8	2	no	—
442	C₄	—	8	1	no	—
443	C₄	—	8	1	no	—
444	C₄	—	8	1	no	—
445	C₄	C₇×#492	1	2	yes	—
446	C₄	C₂²×C₇×SD₁₆	1	2	yes	—
447	C₄	C₇×#575	1	2	yes	—
448	C₄	C₇×#576	1	2	yes	—
449	C₂	—	2	2	no	—
450	C₂	—	16	2	no	—
451	C₂	—	16	1	no	—
452	C₂	C₂×C₇×#492	1	1	yes	characteristic
453	C₂	C₇×#3153	1	1	yes	characteristic
454	C₂	C₇×#3155	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×#3208	C₂	semidirect
2. C₇×#3206	C₂	semidirect
3. C₇×#3167	C₂	semidirect
4. C₇×#3165	C₂	semidirect
6. C₂×C₇×#486	C₂	semidirect
7. C₇×#1715	C₂	semidirect
8. C₇×#1714	C₂	semidirect
9. C₇×#1708	C₂	semidirect
10. C₇×#1706	C₂	semidirect
11. C₇×C₈×M₁₆	C₂	semidirect
18. C₇×#500	C₂²	semidirect
19. C₇×#498	C₂²	semidirect
20. C₇×#498	C₂²	semidirect
25. C₇×#492	C₂²	semidirect
26. C₇×#492	C₂²	semidirect
27. C₇×#487	C₂²	semidirect
28. C₇×#487	C₂²	semidirect
33. C₇×#486	C₂²	semidirect
45. C₇×#322	C₂²	semidirect
46. C₇×C₈²	C₂²	semidirect
47. #19623	C₇	direct (N × H)
104. #3208	C₂×C₇	semidirect
105. #3206	C₂×C₇	semidirect
106. #3167	C₂×C₇	semidirect
107. #3165	C₂×C₇	semidirect
109. C₂×#486	C₂×C₇	semidirect
110. #1715	C₂×C₇	semidirect
111. #1714	C₂×C₇	semidirect
112. #1708	C₂×C₇	semidirect
113. #1706	C₂×C₇	semidirect
114. C₈×M₁₆	C₂×C₇	semidirect
146. C₇×M₁₆	SD₁₆	semidirect
178. #500	C₂²×C₇	semidirect
179. #498	C₂²×C₇	semidirect
180. #498	C₂²×C₇	semidirect
185. #492	C₂²×C₇	semidirect
186. #492	C₂²×C₇	semidirect
187. #487	C₂²×C₇	semidirect
188. #487	C₂²×C₇	semidirect
193. #486	C₂²×C₇	semidirect
205. #322	C₂²×C₇	semidirect
206. C₈²	C₂²×C₇	semidirect
355. M₁₆	C₇×SD₁₆	semidirect
427. C₇	#19623	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×#3208	2
C₇×#3206	2
C₇×#3167	2
C₇×#3165	2
C₇×#3151	2
C₂×C₇×#486	2
C₇×#1715	2
C₇×#1714	2
C₇×#1708	2
C₇×#1706	2
C₇×C₈×M₁₆	2
#19623	7

Subgroups — C7×#19623 #13196839

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×#19623 #13196839