Subgroups — C₇×#19238 #13196454

Order 1792.

722 conjugacy classes of subgroups.

The subgroup lattice has 478 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×#3246	C₂	1	1	yes	maximal, characteristic, complemented
2	C₇×#3208	C₂	1	1	yes	maximal, characteristic, complemented
3	C₇×#3151	C₂	1	1	yes	maximal, characteristic
4	C₇×#2962	C₂	1	1	yes	maximal, characteristic, complemented
5	C₇×#1688	C₂	1	2	yes	maximal, complemented
6	C₇×#1686	C₂	1	2	yes	maximal, complemented
7	C₇×#1668	C₂	1	2	yes	maximal, complemented
8	C₇×#1666	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×#331	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₇×AGL(1,ℤ/8)	—	2	1	no	—
13	C₂×C₇×AGL(1,ℤ/8)	—	2	1	no	—
14	C₇×#533	C₂²	1	1	yes	characteristic
15	C₇×#532	C₂²	1	1	yes	characteristic
16	C₂×C₇×#127	C₂²	1	1	yes	characteristic
17	C₇×#496	—	2	2	no	—
18	C₇×#493	C₂²	1	2	yes	—
19	C₇×#492	—	2	1	no	—
20	C₇×#492	C₂²	1	2	yes	—
21	C₇×#486	—	2	1	no	—
22	C₇×#476	—	2	1	no	—
23	C₇×#475	C₂²	1	2	yes	complemented
24	C₇×#465	—	2	2	no	—
25	C₇×#461	—	2	1	no	—
26	C₇×#460	C₂²	1	2	yes	—
27	C₇×#460	C₂²	1	2	yes	—
28	C₇×#460	C₂²	1	2	yes	complemented
29	C₇×#450	—	2	2	no	—
30	C₇×#446	—	2	2	no	—
31	C₇×#446	C₂²	1	2	yes	complemented
32	C₇×C₈×Q₈	C₂²	1	2	yes	complemented
33	C₇×#431	C₂²	1	1	yes	characteristic
34	C₇×#424	—	2	1	no	—
35	C₂×C₇×C₄⋊C₈	C₂²	1	1	yes	characteristic
36	C₂×C₇×C₄⋊C₈	C₂²	1	1	yes	characteristic
37	C₇×#405	—	2	1	no	—
38	C₄×C₇×M₁₆	C₂²	1	1	yes	characteristic
39	C₇×#335	C₂²	1	2	yes	complemented
40	C₇×#334	C₂²	1	2	yes	complemented
41	C₇×#332	C₂²	1	1	yes	characteristic, complemented
42	C₇×#332	C₂²	1	1	yes	characteristic, complemented
43	C₇×#331	C₂²	1	2	yes	—
44	C₇×#331	C₂²	1	2	yes	—
45	C₇×#331	C₂²	1	1	yes	characteristic, complemented
46	C₇×#331	C₂²	1	1	yes	characteristic, complemented
47	#19238	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
48	C₂×C₇×#41	—	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	C₇×AGL(1,ℤ/8)	—	4	4	no	—
53	C₇×AGL(1,ℤ/8)	—	4	4	no	—
54	C₂×C₇×SD₁₆	—	2	2	no	—
55	C₂×C₇×SD₁₆	—	2	2	no	—
56	C₂×C₇×SD₁₆	—	2	2	no	—
57	C₂×C₇×SD₁₆	—	2	2	no	—
58	C₂×C₇×SD₁₆	—	2	2	no	—
59	C₂×C₇×D₈	—	2	2	no	—
60	C₂×C₇×D₈	—	2	2	no	—
61	C₂×C₇×M₁₆	D₄	1	1	yes	characteristic
62	C₂×C₇×M₁₆	D₄	1	1	yes	characteristic
63	C₂²×C₇×C₈	—	2	1	no	—
64	C₂²×C₇×C₈	—	2	1	no	—
65	C₇×C₄⋊Q₈	D₄	1	1	yes	characteristic
66	C₇×C₄⋊Q₈	D₄	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	D₄	1	2	yes	—
77	C₇×#121	—	2	1	no	—
78	C₇×#121	—	2	1	no	—
79	C₄×C₇×Q₈	—	2	1	no	—
80	C₄×C₇×Q₈	C₂³	1	2	yes	—
81	C₄×C₇×D₄	—	2	1	no	—
82	C₄×C₇×D₄	—	2	1	no	—
83	C₇×#117	—	2	1	no	—
84	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
85	C₇×#106	—	2	2	no	—
86	C₇×C₄⋊C₈	—	2	2	no	—
87	C₇×C₄⋊C₈	—	2	2	no	—
88	C₇×C₄⋊C₈	—	2	1	no	—
89	C₇×C₄⋊C₈	—	2	1	no	—
90	C₇×C₄⋊C₈	C₂³	1	2	yes	—
91	C₇×C₄⋊C₈	C₂³	1	1	yes	characteristic
92	C₇×C₄⋊C₈	C₂³	1	1	yes	characteristic
93	C₇×C₄⋊C₈	C₂³	1	1	yes	characteristic
94	C₇×C₄⋊C₈	C₂³	1	1	yes	characteristic
95	C₇×#103	—	2	2	no	—
96	C₇×#102	—	2	2	no	—
97	C₇×#102	—	2	2	no	—
98	C₇×#102	—	2	2	no	—
99	C₇×C₂²⋊C₈	—	2	1	no	—
100	C₇×#97	—	2	2	no	—
101	C₇×#97	D₄	1	2	yes	—
102	C₄×C₇×C₈	—	2	2	no	—
103	C₄×C₇×C₈	—	2	1	no	—
104	C₄×C₇×C₈	C₂³	1	2	yes	—
105	#3246	C₂×C₇	1	1	yes	characteristic, complemented
106	#3208	C₂×C₇	1	1	yes	characteristic, complemented
107	#3151	C₂×C₇	1	1	yes	characteristic
108	#2962	C₂×C₇	1	1	yes	characteristic, complemented
109	#1688	C₂×C₇	1	2	yes	complemented
110	#1686	C₂×C₇	1	2	yes	complemented
111	#1668	C₂×C₇	1	2	yes	complemented
112	#1666	C₂×C₇	1	2	yes	complemented
113	#1565	C₂×C₇	1	1	yes	characteristic, complemented
114	#1540	C₂×C₇	1	1	yes	characteristic, complemented
115	C₂×#331	C₂×C₇	1	1	yes	characteristic, complemented
116	C₂⁴×C₇	—	4	1	no	—
117	C₇×#41	—	4	2	no	—
118	C₇×#41	—	4	2	no	—
119	C₂×C₇×Q₈	—	2	1	no	—
120	C₂×C₇×Q₈	—	2	1	no	—
121	C₂×C₇×Q₈	C₂×D₄	1	2	yes	—
122	C₂×C₇×D₄	—	2	1	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	2	no	—
128	C₂×C₇×D₄	—	4	1	no	—
129	C₂×C₇×D₄	—	4	1	no	—
130	C₂×C₇×D₄	—	4	1	no	—
131	C₂×C₇×D₄	—	4	1	no	—
132	C₂×C₇×D₄	—	4	2	no	—
133	C₂×C₇×D₄	—	4	2	no	—
134	C₂×C₇×D₄	—	8	1	no	—
135	C₂×C₇×D₄	—	8	1	no	—
136	C₂×C₇×D₄	—	8	2	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×SD₁₆	—	4	4	no	—
142	C₇×SD₁₆	—	4	4	no	—
143	C₇×SD₁₆	—	8	2	no	—
144	C₇×SD₁₆	—	8	2	no	—
145	C₇×SD₁₆	—	8	2	no	—
146	C₇×D₈	—	4	4	no	—
147	C₇×D₈	—	4	4	no	—
148	C₇×M₁₆	—	2	2	no	—
149	C₇×M₁₆	SD₁₆	1	4	yes	complemented
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	1	no	—
154	C₂×C₇×C₈	—	2	2	no	—
155	C₂×C₇×C₈	—	4	2	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	1	no	—
161	C₇×C₄⋊C₄	—	2	1	no	—
162	C₇×C₄⋊C₄	—	2	2	no	—
163	C₇×C₄⋊C₄	—	2	2	no	—
164	C₇×C₄⋊C₄	—	2	1	no	—
165	C₇×C₄⋊C₄	—	2	1	no	—
166	C₇×C₄⋊C₄	C₂×D₄	1	2	yes	—
167	C₇×C₂²⋊C₄	—	2	2	no	—
168	C₇×C₂²⋊C₄	—	4	1	no	—
169	C₇×C₂²⋊C₄	—	4	1	no	—
170	C₄²×C₇	—	2	2	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×AGL(1,ℤ/8)	—	2	1	no	—
176	C₂×AGL(1,ℤ/8)	—	2	1	no	—
177	#533	C₂²×C₇	1	1	yes	characteristic
178	#532	C₂²×C₇	1	1	yes	characteristic
179	C₂×#127	C₂²×C₇	1	1	yes	characteristic
180	#496	—	2	2	no	—
181	#493	C₂²×C₇	1	2	yes	—
182	#492	—	2	1	no	—
183	#492	C₂²×C₇	1	2	yes	—
184	#486	—	2	1	no	—
185	#476	—	2	1	no	—
186	#475	C₂²×C₇	1	2	yes	complemented
187	#465	—	2	2	no	—
188	#461	—	2	1	no	—
189	#460	C₂²×C₇	1	2	yes	—
190	#460	C₂²×C₇	1	2	yes	—
191	#460	C₂²×C₇	1	2	yes	complemented
192	#450	—	2	2	no	—
193	#446	—	2	2	no	—
194	#446	C₂²×C₇	1	2	yes	complemented
195	C₈×Q₈	C₂²×C₇	1	2	yes	complemented
196	#431	C₂²×C₇	1	1	yes	characteristic
197	#424	—	2	1	no	—
198	C₂×C₄⋊C₈	C₂²×C₇	1	1	yes	characteristic
199	C₂×C₄⋊C₈	C₂²×C₇	1	1	yes	characteristic
200	#405	—	2	1	no	—
201	C₄×M₁₆	C₂²×C₇	1	1	yes	characteristic
202	#335	C₂²×C₇	1	2	yes	complemented
203	#334	C₂²×C₇	1	2	yes	complemented
204	#332	C₂²×C₇	1	1	yes	characteristic, complemented
205	#332	C₂²×C₇	1	1	yes	characteristic, complemented
206	#331	C₂²×C₇	1	2	yes	—
207	#331	C₂²×C₇	1	2	yes	—
208	#331	C₂²×C₇	1	1	yes	characteristic, complemented
209	#331	C₂²×C₇	1	1	yes	characteristic, complemented
210	C₂³×C₇	—	4	1	no	—
211	C₂³×C₇	—	4	2	no	—
212	C₂³×C₇	—	8	2	no	—
213	C₂³×C₇	—	8	2	no	—
214	C₂³×C₇	—	8	2	no	—
215	C₂³×C₇	#121	1	1	yes	characteristic
216	C₇×Q₈	—	2	2	no	—
217	C₇×Q₈	—	2	2	no	—
218	C₇×Q₈	—	4	1	no	—
219	C₇×Q₈	—	4	1	no	—
220	C₇×Q₈	—	8	1	no	—
221	C₇×D₄	—	4	1	no	—
222	C₇×D₄	—	4	2	no	—
223	C₇×D₄	—	4	1	no	—
224	C₇×D₄	—	4	2	no	—
225	C₇×D₄	—	4	1	no	—
226	C₇×D₄	—	4	2	no	—
227	C₇×D₄	—	4	2	no	—
228	C₇×D₄	—	4	1	no	—
229	C₇×D₄	—	8	1	no	—
230	C₇×D₄	—	8	2	no	—
231	C₇×D₄	—	8	2	no	—
232	C₇×D₄	—	8	2	no	—
233	C₇×D₄	—	8	2	no	—
234	C₇×D₄	—	8	2	no	—
235	C₂×C₄×C₇	—	2	1	no	—
236	C₂×C₄×C₇	—	2	1	no	—
237	C₂×C₄×C₇	—	2	2	no	—
238	C₂×C₄×C₇	—	2	2	no	—
239	C₂×C₄×C₇	—	4	1	no	—
240	C₂×C₄×C₇	—	4	1	no	—
241	C₂×C₄×C₇	—	8	2	no	—
242	C₂×C₄×C₇	#121	1	1	yes	characteristic
243	C₂×C₄×C₇	#121	1	1	yes	characteristic
244	C₂×C₄×C₇	#121	1	1	yes	characteristic
245	C₂×C₄×C₇	C₂×SD₁₆	1	2	yes	—
246	C₂×C₄×C₇	AGL(1,ℤ/8)	1	2	yes	—
247	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
248	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
249	C₂×C₄×C₇	C₂×#41	1	1	yes	characteristic
250	C₇×C₈	—	2	2	no	—
251	C₇×C₈	—	4	1	no	—
252	C₇×C₈	—	4	1	no	—
253	C₇×C₈	—	4	2	no	—
254	C₇×C₈	—	4	1	no	—
255	C₇×C₈	—	4	1	no	—
256	C₇×C₈	C₂×SD₁₆	1	4	yes	—
257	C₂×#41	—	2	1	no	—
258	C₂²×D₄	—	2	1	no	—
259	C₂²×D₄	—	2	1	no	—
260	C₂²×D₄	—	2	1	no	—
261	AGL(1,ℤ/8)	—	4	4	no	—
262	AGL(1,ℤ/8)	—	4	4	no	—
263	C₂×SD₁₆	—	2	2	no	—
264	C₂×SD₁₆	—	2	2	no	—
265	C₂×SD₁₆	—	2	2	no	—
266	C₂×SD₁₆	—	2	2	no	—
267	C₂×SD₁₆	—	2	2	no	—
268	C₂×D₈	—	2	2	no	—
269	C₂×D₈	—	2	2	no	—
270	C₂×M₁₆	C₇×D₄	1	1	yes	characteristic
271	C₂×M₁₆	C₇×D₄	1	1	yes	characteristic
272	C₂²×C₈	—	2	1	no	—
273	C₂²×C₈	—	2	1	no	—
274	C₄⋊Q₈	C₇×D₄	1	1	yes	characteristic
275	C₄⋊Q₈	C₇×D₄	1	1	yes	characteristic
276	C₄⋊Q₈	C₂³×C₇	1	1	yes	characteristic
277	#127	—	2	1	no	—
278	#127	—	2	1	no	—
279	#127	—	2	1	no	—
280	#127	C₂³×C₇	1	2	yes	—
281	#127	C₂³×C₇	1	1	yes	characteristic
282	#125	—	2	1	no	—
283	#124	—	2	1	no	—
284	C₂²⋊Q₈	—	2	1	no	—
285	C₂²⋊Q₈	C₇×D₄	1	2	yes	—
286	#121	—	2	1	no	—
287	#121	—	2	1	no	—
288	C₄×Q₈	—	2	1	no	—
289	C₄×Q₈	C₂³×C₇	1	2	yes	—
290	C₄×D₄	—	2	1	no	—
291	C₄×D₄	—	2	1	no	—
292	#117	—	2	1	no	—
293	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
294	#106	—	2	2	no	—
295	C₄⋊C₈	—	2	2	no	—
296	C₄⋊C₈	—	2	2	no	—
297	C₄⋊C₈	—	2	1	no	—
298	C₄⋊C₈	—	2	1	no	—
299	C₄⋊C₈	C₂³×C₇	1	1	yes	characteristic
300	C₄⋊C₈	C₂³×C₇	1	1	yes	characteristic
301	C₄⋊C₈	C₂³×C₇	1	2	yes	—
302	C₄⋊C₈	C₂³×C₇	1	1	yes	characteristic
303	C₄⋊C₈	C₂³×C₇	1	1	yes	characteristic
304	#103	—	2	2	no	—
305	#102	—	2	2	no	—
306	#102	—	2	2	no	—
307	#102	—	2	2	no	—
308	C₂²⋊C₈	—	2	1	no	—
309	#97	—	2	2	no	—
310	#97	C₇×D₄	1	2	yes	—
311	C₄×C₈	—	2	2	no	—
312	C₄×C₈	—	2	1	no	—
313	C₄×C₈	C₂³×C₇	1	2	yes	—
314	C₂²×C₇	—	2	1	no	—
315	C₂²×C₇	—	2	1	no	—
316	C₂²×C₇	—	8	1	no	—
317	C₂²×C₇	—	8	2	no	—
318	C₂²×C₇	—	8	2	no	—
319	C₂²×C₇	—	8	1	no	—
320	C₂²×C₇	—	8	2	no	—
321	C₂²×C₇	—	8	1	no	—
322	C₂²×C₇	—	16	4	no	—
323	C₂²×C₇	#460	1	2	yes	—
324	C₂²×C₇	C₂×#121	1	1	yes	characteristic
325	C₄×C₇	—	2	1	no	—
326	C₄×C₇	—	2	1	no	—
327	C₄×C₇	—	2	1	no	—
328	C₄×C₇	—	4	2	no	—
329	C₄×C₇	—	4	2	no	—
330	C₄×C₇	—	8	1	no	—
331	C₄×C₇	#460	1	2	yes	—
332	C₄×C₇	C₂²×SD₁₆	1	1	yes	characteristic
333	C₄×C₇	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
334	C₄×C₇	#576	1	1	yes	characteristic
335	C₄×C₇	#577	1	1	yes	characteristic
336	C₂⁴	—	4	1	no	—
337	#41	—	4	2	no	—
338	#41	—	4	2	no	—
339	C₂×Q₈	—	2	1	no	—
340	C₂×Q₈	—	2	1	no	—
341	C₂×Q₈	C₂×C₇×D₄	1	2	yes	—
342	C₂×D₄	—	2	1	no	—
343	C₂×D₄	—	2	2	no	—
344	C₂×D₄	—	2	1	no	—
345	C₂×D₄	—	2	2	no	—
346	C₂×D₄	—	2	1	no	—
347	C₂×D₄	—	2	2	no	—
348	C₂×D₄	—	4	1	no	—
349	C₂×D₄	—	4	1	no	—
350	C₂×D₄	—	4	1	no	—
351	C₂×D₄	—	4	1	no	—
352	C₂×D₄	—	4	2	no	—
353	C₂×D₄	—	4	2	no	—
354	C₂×D₄	—	8	1	no	—
355	C₂×D₄	—	8	1	no	—
356	C₂×D₄	—	8	2	no	—
357	C₂²×C₄	—	4	1	no	—
358	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
359	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
360	C₂²×C₄	C₇×#41	1	1	yes	characteristic
361	SD₁₆	—	4	4	no	—
362	SD₁₆	—	4	4	no	—
363	SD₁₆	—	8	2	no	—
364	SD₁₆	—	8	2	no	—
365	SD₁₆	—	8	2	no	—
366	D₈	—	4	4	no	—
367	D₈	—	4	4	no	—
368	M₁₆	—	2	2	no	—
369	M₁₆	C₇×SD₁₆	1	4	yes	complemented
370	C₂×C₈	—	2	1	no	—
371	C₂×C₈	—	2	1	no	—
372	C₂×C₈	—	2	1	no	—
373	C₂×C₈	—	2	1	no	—
374	C₂×C₈	—	2	2	no	—
375	C₂×C₈	—	4	2	no	—
376	C₂×C₈	—	8	1	no	—
377	C₂×C₈	C₂×C₇×D₄	1	2	yes	—
378	C₂×C₈	C₂×C₇×D₄	1	2	yes	—
379	C₄⋊C₄	—	2	1	no	—
380	C₄⋊C₄	—	2	1	no	—
381	C₄⋊C₄	—	2	1	no	—
382	C₄⋊C₄	—	2	2	no	—
383	C₄⋊C₄	—	2	2	no	—
384	C₄⋊C₄	—	2	1	no	—
385	C₄⋊C₄	—	2	1	no	—
386	C₄⋊C₄	C₂×C₇×D₄	1	2	yes	—
387	C₂²⋊C₄	—	2	2	no	—
388	C₂²⋊C₄	—	4	1	no	—
389	C₂²⋊C₄	—	4	1	no	—
390	C₄²	—	2	2	no	—
391	C₄²	C₂×C₇×D₄	1	1	yes	characteristic
392	C₄²	C₂×C₇×D₄	1	1	yes	characteristic
393	C₄²	C₇×#41	1	1	yes	characteristic
394	C₄²	C₂⁴×C₇	1	1	yes	characteristic
395	C₂×C₇	—	2	2	no	—
396	C₂×C₇	—	16	1	no	—
397	C₂×C₇	—	16	2	no	—
398	C₂×C₇	C₂×#460	1	1	yes	characteristic
399	C₂×C₇	#3062	1	1	yes	characteristic
400	C₂×C₇	#3068	1	1	yes	characteristic
401	C₂³	—	4	1	no	—
402	C₂³	—	4	2	no	—
403	C₂³	—	8	2	no	—
404	C₂³	—	8	2	no	—
405	C₂³	—	8	2	no	—
406	C₂³	C₇×#121	1	1	yes	characteristic
407	Q₈	—	2	2	no	—
408	Q₈	—	2	2	no	—
409	Q₈	—	4	1	no	—
410	Q₈	—	4	1	no	—
411	Q₈	—	8	1	no	—
412	D₄	—	4	1	no	—
413	D₄	—	4	2	no	—
414	D₄	—	4	1	no	—
415	D₄	—	4	2	no	—
416	D₄	—	4	1	no	—
417	D₄	—	4	2	no	—
418	D₄	—	4	2	no	—
419	D₄	—	4	1	no	—
420	D₄	—	8	1	no	—
421	D₄	—	8	2	no	—
422	D₄	—	8	2	no	—
423	D₄	—	8	2	no	—
424	D₄	—	8	2	no	—
425	D₄	—	8	2	no	—
426	C₂×C₄	—	2	1	no	—
427	C₂×C₄	—	2	1	no	—
428	C₂×C₄	—	2	2	no	—
429	C₂×C₄	—	2	2	no	—
430	C₂×C₄	—	4	1	no	—
431	C₂×C₄	—	4	1	no	—
432	C₂×C₄	—	8	2	no	—
433	C₂×C₄	C₇×#121	1	1	yes	characteristic
434	C₂×C₄	C₇×#121	1	1	yes	characteristic
435	C₂×C₄	C₇×#121	1	1	yes	characteristic
436	C₂×C₄	C₂×C₇×SD₁₆	1	2	yes	—
437	C₂×C₄	C₇×AGL(1,ℤ/8)	1	2	yes	—
438	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
439	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
440	C₂×C₄	C₂×C₇×#41	1	1	yes	characteristic
441	C₈	—	2	2	no	—
442	C₈	—	4	1	no	—
443	C₈	—	4	1	no	—
444	C₈	—	4	2	no	—
445	C₈	—	4	1	no	—
446	C₈	—	4	1	no	—
447	C₈	C₂×C₇×SD₁₆	1	4	yes	—
448	C₇	#19238	1	1	yes	characteristic, direct product factor, Sylow
449	C₂²	—	2	1	no	—
450	C₂²	—	2	1	no	—
451	C₂²	—	8	1	no	—
452	C₂²	—	8	2	no	—
453	C₂²	—	8	2	no	—
454	C₂²	—	8	1	no	—
455	C₂²	—	8	2	no	—
456	C₂²	—	8	1	no	—
457	C₂²	—	16	4	no	—
458	C₂²	C₇×#460	1	2	yes	—
459	C₂²	C₂×C₇×#121	1	1	yes	characteristic
460	C₄	—	2	1	no	—
461	C₄	—	2	1	no	—
462	C₄	—	2	1	no	—
463	C₄	—	4	2	no	—
464	C₄	—	4	2	no	—
465	C₄	—	8	1	no	—
466	C₄	C₇×#460	1	2	yes	—
467	C₄	C₂²×C₇×SD₁₆	1	1	yes	characteristic
468	C₄	C₂×C₇×AGL(1,ℤ/8)	1	1	yes	characteristic
469	C₄	C₇×#576	1	1	yes	characteristic
470	C₄	C₇×#577	1	1	yes	characteristic
471	C₂	—	2	2	no	—
472	C₂	—	16	2	no	—
473	C₂	—	16	1	no	—
474	C₂	C₂×C₇×#460	1	1	yes	characteristic
475	C₂	C₇×#3062	1	1	yes	characteristic
476	C₂	C₇×#3068	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₇	C₂×#121
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×#3246	C₂	semidirect
2. C₇×#3208	C₂	semidirect
4. C₇×#2962	C₂	semidirect
5. C₇×#1688	C₂	semidirect
6. C₇×#1686	C₂	semidirect
7. C₇×#1668	C₂	semidirect
8. C₇×#1666	C₂	semidirect
9. C₇×#1565	C₂	semidirect
10. C₇×#1540	C₂	semidirect
11. C₂×C₇×#331	C₂	semidirect
23. C₇×#475	C₂²	semidirect
28. C₇×#460	C₂²	semidirect
31. C₇×#446	C₂²	semidirect
32. C₇×C₈×Q₈	C₂²	semidirect
39. C₇×#335	C₂²	semidirect
40. C₇×#334	C₂²	semidirect
41. C₇×#332	C₂²	semidirect
42. C₇×#332	C₂²	semidirect
45. C₇×#331	C₂²	semidirect
46. C₇×#331	C₂²	semidirect
47. #19238	C₇	direct (N × H)
105. #3246	C₂×C₇	semidirect
106. #3208	C₂×C₇	semidirect
108. #2962	C₂×C₇	semidirect
109. #1688	C₂×C₇	semidirect
110. #1686	C₂×C₇	semidirect
111. #1668	C₂×C₇	semidirect
112. #1666	C₂×C₇	semidirect
113. #1565	C₂×C₇	semidirect
114. #1540	C₂×C₇	semidirect
115. C₂×#331	C₂×C₇	semidirect
149. C₇×M₁₆	SD₁₆	semidirect
186. #475	C₂²×C₇	semidirect
191. #460	C₂²×C₇	semidirect
194. #446	C₂²×C₇	semidirect
195. C₈×Q₈	C₂²×C₇	semidirect
202. #335	C₂²×C₇	semidirect
203. #334	C₂²×C₇	semidirect
204. #332	C₂²×C₇	semidirect
205. #332	C₂²×C₇	semidirect
208. #331	C₂²×C₇	semidirect
209. #331	C₂²×C₇	semidirect
369. M₁₆	C₇×SD₁₆	semidirect
448. C₇	#19238	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×#3246	2
C₇×#3208	2
C₇×#3151	2
C₇×#2962	2
C₇×#1688	2
C₇×#1686	2
C₇×#1668	2
C₇×#1666	2
C₇×#1565	2
C₇×#1540	2
C₂×C₇×#331	2
#19238	7

Subgroups — C7×#19238 #13196454

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×#19238 #13196454