Subgroups — C₇×#23046 #13200262

Order 1792.

896 conjugacy classes of subgroups.

The subgroup lattice has 488 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₇×#472	C₂	1	1	yes	maximal, characteristic
2	C₇×#2948	C₂	1	1	yes	maximal, characteristic, complemented
3	C₇×#2946	C₂	1	2	yes	maximal, complemented
4	C₇×#2913	C₂	1	1	yes	maximal, characteristic, complemented
5	C₇×#1970	C₂	1	1	yes	maximal, characteristic, complemented
6	C₇×#1952	C₂	1	1	yes	maximal, characteristic, complemented
7	C₇×#1931	C₂	1	2	yes	maximal, complemented
8	C₇×#1883	C₂	1	2	yes	maximal, complemented
9	C₇×#1856	C₂	1	2	yes	maximal, complemented
10	C₇×#1772	C₂	1	1	yes	maximal, characteristic, complemented
11	C₇×#1764	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₇×AGL(1,ℤ/8)	C₂²	1	2	yes	—
13	C₂²×C₇×D₈	C₂²	1	1	yes	characteristic
14	C₂×C₇×#131	C₂²	1	1	yes	characteristic
15	C₇×#520	C₂²	1	2	yes	—
16	C₇×#518	C₂²	1	2	yes	—
17	C₇×#472	C₄	1	8	yes	complemented
18	C₇×#442	—	2	2	no	—
19	C₇×#442	—	2	2	no	—
20	C₇×#440	—	2	2	no	—
21	C₄×C₇×SD₁₆	—	2	2	no	—
22	C₄×C₇×D₈	—	2	1	no	—
23	C₄×C₇×D₈	—	2	1	no	—
24	C₄×C₇×D₈	—	2	2	no	—
25	C₂×C₇×#108	C₂²	1	1	yes	characteristic
26	C₇×#428	—	2	2	no	—
27	C₇×#428	C₂²	1	2	yes	—
28	C₇×#428	C₂²	1	2	yes	—
29	C₇×#427	—	2	1	no	—
30	C₇×#427	C₂²	1	1	yes	characteristic
31	C₂×C₇×#107	—	2	1	no	—
32	C₂×C₇×#107	C₂²	1	1	yes	characteristic
33	C₂×C₇×#104	C₂²	1	1	yes	characteristic
34	C₇×#418	C₂²	1	2	yes	—
35	C₇×#416	C₂²	1	1	yes	characteristic
36	C₂×C₇×#102	C₂²	1	2	yes	—
37	C₂×C₇×#100	C₂²	1	2	yes	—
38	C₇×#405	C₂²	1	2	yes	—
39	C₇×#405	C₂²	1	1	yes	characteristic
40	C₂×C₄×C₇×C₈	C₂²	1	1	yes	characteristic
41	C₇×#390	C₂²	1	2	yes	—
42	C₇×#343	C₂²	1	2	yes	—
43	C₇×#341	C₂²	1	1	yes	characteristic
44	C₇×#339	C₂²	1	1	yes	characteristic
45	C₇×#339	C₂²	1	2	yes	—
46	#23046	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
47	C₂×C₇×#41	C₂³	1	1	yes	characteristic
48	C₂²×C₇×D₄	C₂³	1	2	yes	—
49	C₇×AGL(1,ℤ/8)	—	2	4	no	—
50	C₇×AGL(1,ℤ/8)	C₂×C₄	1	8	yes	complemented
51	C₂×C₇×SD₁₆	—	2	2	no	—
52	C₂×C₇×D₈	—	2	2	no	—
53	C₂×C₇×D₈	—	2	1	no	—
54	C₂×C₇×D₈	—	2	1	no	—
55	C₂×C₇×D₈	—	2	2	no	—
56	C₂×C₇×D₈	C₂×C₄	1	4	yes	complemented
57	C₇×#131	—	2	2	no	—
58	C₇×#131	C₂×C₄	1	4	yes	complemented
59	C₂×C₇×M₁₆	—	2	1	no	—
60	C₂×C₇×M₁₆	C₂³	1	1	yes	characteristic
61	C₂×C₇×M₁₆	C₂³	1	1	yes	characteristic
62	C₂×C₇×M₁₆	C₂³	1	2	yes	—
63	C₂²×C₇×C₈	—	2	1	no	—
64	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
65	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
66	C₄×C₇×Q₈	—	2	2	no	—
67	C₄×C₇×D₄	—	2	2	no	—
68	C₄×C₇×D₄	—	2	2	no	—
69	C₄×C₇×D₄	—	2	2	no	—
70	C₄×C₇×D₄	—	2	2	no	—
71	C₄×C₇×D₄	—	2	2	no	—
72	C₄×C₇×D₄	—	4	2	no	—
73	C₇×#117	—	2	2	no	—
74	C₇×#117	C₂³	1	1	yes	characteristic
75	C₇×#117	C₂³	1	2	yes	—
76	C₂×C₇×C₄⋊C₄	—	2	2	no	—
77	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
78	C₂×C₇×C₂²⋊C₄	—	4	2	no	—
79	C₂×C₇×C₂²⋊C₄	—	4	2	no	—
80	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
81	C₇×#108	C₂×C₄	1	4	yes	complemented
82	C₇×#107	—	2	1	no	—
83	C₇×#107	—	2	1	no	—
84	C₇×#107	—	2	2	no	—
85	C₇×#107	—	2	2	no	—
86	C₇×#107	D₄	1	1	yes	characteristic
87	C₇×#107	D₄	1	1	yes	characteristic
88	C₇×#106	—	2	2	no	—
89	C₇×#106	—	2	2	no	—
90	C₇×#106	D₄	1	2	yes	—
91	C₇×#104	—	2	2	no	—
92	C₇×#103	D₄	1	1	yes	characteristic
93	C₇×#103	D₄	1	1	yes	characteristic
94	C₇×#102	—	2	2	no	—
95	C₇×#102	—	2	2	no	—
96	C₇×#102	—	2	2	no	—
97	C₇×#102	—	2	2	no	—
98	C₇×#102	D₄	1	1	yes	characteristic
99	C₇×#102	D₄	1	1	yes	characteristic
100	C₇×#100	C₂×C₄	1	8	yes	complemented
101	C₇×#97	—	2	2	no	—
102	C₇×#97	—	2	1	no	—
103	C₄×C₇×C₈	—	2	1	no	—
104	C₄×C₇×C₈	—	2	2	no	—
105	C₄×C₇×C₈	—	2	2	no	—
106	C₂×#472	C₂×C₇	1	1	yes	characteristic
107	#2948	C₂×C₇	1	1	yes	characteristic, complemented
108	#2946	C₂×C₇	1	2	yes	complemented
109	#2913	C₂×C₇	1	1	yes	characteristic, complemented
110	#1970	C₂×C₇	1	1	yes	characteristic, complemented
111	#1952	C₂×C₇	1	1	yes	characteristic, complemented
112	#1931	C₂×C₇	1	2	yes	complemented
113	#1883	C₂×C₇	1	2	yes	complemented
114	#1856	C₂×C₇	1	2	yes	complemented
115	#1772	C₂×C₇	1	1	yes	characteristic, complemented
116	#1764	C₂×C₇	1	1	yes	characteristic, complemented
117	C₂⁴×C₇	—	2	2	no	—
118	C₇×#41	—	2	1	no	—
119	C₇×#41	—	2	1	no	—
120	C₇×#41	C₂²×C₄	1	2	yes	—
121	C₇×#41	#41	1	2	yes	—
122	C₂×C₇×Q₈	C₂×D₄	1	1	yes	characteristic
123	C₂×C₇×D₄	—	2	1	no	—
124	C₂×C₇×D₄	—	2	2	no	—
125	C₂×C₇×D₄	—	2	2	no	—
126	C₂×C₇×D₄	—	2	2	no	—
127	C₂×C₇×D₄	—	2	2	no	—
128	C₂×C₇×D₄	—	2	2	no	—
129	C₂×C₇×D₄	C₂²×C₄	1	4	yes	—
130	C₂×C₇×D₄	C₂×D₄	1	1	yes	characteristic
131	C₂²×C₄×C₇	—	2	1	no	—
132	C₂²×C₄×C₇	—	2	1	no	—
133	C₂²×C₄×C₇	—	2	2	no	—
134	C₂²×C₄×C₇	—	4	2	no	—
135	C₂²×C₄×C₇	—	4	2	no	—
136	C₂²×C₄×C₇	—	4	2	no	—
137	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
138	C₇×SD₁₆	—	2	8	no	—
139	C₇×D₈	—	2	8	no	—
140	C₇×D₈	—	2	4	no	—
141	C₇×D₈	—	2	4	no	—
142	C₇×M₁₆	—	2	1	no	—
143	C₇×M₁₆	—	2	2	no	—
144	C₇×M₁₆	—	2	4	no	—
145	C₇×M₁₆	—	2	1	no	—
146	C₇×M₁₆	—	2	1	no	—
147	C₇×M₁₆	C₂²×C₄	1	2	yes	—
148	C₇×M₁₆	C₂²×C₄	1	4	yes	—
149	C₂×C₇×C₈	—	2	2	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	4	no	—
154	C₂×C₇×C₈	—	2	1	no	—
155	C₂×C₇×C₈	C₂²×C₄	1	2	yes	—
156	C₂×C₇×C₈	C₂×D₄	1	1	yes	characteristic
157	C₂×C₇×C₈	C₂×D₄	1	1	yes	characteristic
158	C₂×C₇×C₈	C₂×D₄	1	1	yes	characteristic
159	C₂×C₇×C₈	C₂×D₄	1	1	yes	characteristic
160	C₂×C₇×C₈	#41	1	2	yes	—
161	C₇×C₄⋊C₄	—	2	2	no	—
162	C₇×C₄⋊C₄	—	2	2	no	—
163	C₇×C₄⋊C₄	—	4	2	no	—
164	C₇×C₄⋊C₄	C₂×D₄	1	2	yes	—
165	C₇×C₄⋊C₄	C₂×D₄	1	2	yes	—
166	C₇×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
167	C₇×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
168	C₇×C₂²⋊C₄	—	2	1	no	—
169	C₇×C₂²⋊C₄	—	2	2	no	—
170	C₇×C₂²⋊C₄	—	4	2	no	—
171	C₇×C₂²⋊C₄	—	4	2	no	—
172	C₇×C₂²⋊C₄	—	4	2	no	—
173	C₇×C₂²⋊C₄	—	8	4	no	—
174	C₄²×C₇	—	2	1	no	—
175	C₄²×C₇	—	2	2	no	—
176	C₄²×C₇	—	2	1	no	—
177	C₄²×C₇	—	2	1	no	—
178	C₄²×C₇	—	4	2	no	—
179	C₂×AGL(1,ℤ/8)	C₂²×C₇	1	2	yes	—
180	C₂²×D₈	C₂²×C₇	1	1	yes	characteristic
181	C₂×#131	C₂²×C₇	1	1	yes	characteristic
182	#520	C₂²×C₇	1	2	yes	—
183	#518	C₂²×C₇	1	2	yes	—
184	#472	C₄×C₇	1	8	yes	complemented
185	#442	—	2	2	no	—
186	#442	—	2	2	no	—
187	#440	—	2	2	no	—
188	C₄×SD₁₆	—	2	2	no	—
189	C₄×D₈	—	2	1	no	—
190	C₄×D₈	—	2	1	no	—
191	C₄×D₈	—	2	2	no	—
192	C₂×#108	C₂²×C₇	1	1	yes	characteristic
193	#428	—	2	2	no	—
194	#428	C₂²×C₇	1	2	yes	—
195	#428	C₂²×C₇	1	2	yes	—
196	#427	—	2	1	no	—
197	#427	C₂²×C₇	1	1	yes	characteristic
198	C₂×#107	—	2	1	no	—
199	C₂×#107	C₂²×C₇	1	1	yes	characteristic
200	C₂×#104	C₂²×C₇	1	1	yes	characteristic
201	#418	C₂²×C₇	1	2	yes	—
202	#416	C₂²×C₇	1	1	yes	characteristic
203	C₂×#102	C₂²×C₇	1	2	yes	—
204	C₂×#100	C₂²×C₇	1	2	yes	—
205	#405	C₂²×C₇	1	2	yes	—
206	#405	C₂²×C₇	1	1	yes	characteristic
207	C₂×C₄×C₈	C₂²×C₇	1	1	yes	characteristic
208	#390	C₂²×C₇	1	2	yes	—
209	#343	C₂²×C₇	1	2	yes	—
210	#341	C₂²×C₇	1	1	yes	characteristic
211	#339	C₂²×C₇	1	1	yes	characteristic
212	#339	C₂²×C₇	1	2	yes	—
213	C₂³×C₇	—	2	1	no	—
214	C₂³×C₇	—	2	4	no	—
215	C₂³×C₇	—	4	2	no	—
216	C₂³×C₇	—	4	2	no	—
217	C₂³×C₇	—	8	2	no	—
218	C₂³×C₇	—	8	2	no	—
219	C₂³×C₇	H(5,𝔽₂)	1	1	yes	characteristic
220	C₇×Q₈	—	2	1	no	—
221	C₇×Q₈	C₄×D₄	1	2	yes	—
222	C₇×D₄	—	2	2	no	—
223	C₇×D₄	—	2	2	no	—
224	C₇×D₄	—	2	4	no	—
225	C₇×D₄	—	2	4	no	—
226	C₇×D₄	—	2	1	no	—
227	C₇×D₄	—	4	2	no	—
228	C₇×D₄	—	4	2	no	—
229	C₇×D₄	C₄×D₄	1	2	yes	—
230	C₂×C₄×C₇	—	2	1	no	—
231	C₂×C₄×C₇	—	2	2	no	—
232	C₂×C₄×C₇	—	2	2	no	—
233	C₂×C₄×C₇	—	2	2	no	—
234	C₂×C₄×C₇	—	2	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	—	4	1	no	—
239	C₂×C₄×C₇	—	4	1	no	—
240	C₂×C₄×C₇	—	4	2	no	—
241	C₂×C₄×C₇	—	8	2	no	—
242	C₂×C₄×C₇	—	16	2	no	—
243	C₂×C₄×C₇	—	16	2	no	—
244	C₂×C₄×C₇	—	16	2	no	—
245	C₂×C₄×C₇	C₂³×C₄	1	1	yes	characteristic
246	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
247	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
248	C₂×C₄×C₇	C₂×#41	1	1	yes	characteristic
249	C₂×C₄×C₇	C₂×#41	1	1	yes	characteristic
250	C₂×C₄×C₇	2₋¹⁺⁴	1	1	yes	characteristic
251	C₇×C₈	—	2	2	no	—
252	C₇×C₈	—	2	4	no	—
253	C₇×C₈	—	2	1	no	—
254	C₇×C₈	—	2	1	no	—
255	C₇×C₈	—	4	1	no	—
256	C₇×C₈	C₄×D₄	1	2	yes	—
257	C₇×C₈	C₄×D₄	1	2	yes	—
258	C₂×#41	C₂³×C₇	1	1	yes	characteristic
259	C₂²×D₄	C₂³×C₇	1	2	yes	—
260	AGL(1,ℤ/8)	—	2	4	no	—
261	AGL(1,ℤ/8)	C₂×C₄×C₇	1	8	yes	complemented
262	C₂×SD₁₆	—	2	2	no	—
263	C₂×D₈	—	2	2	no	—
264	C₂×D₈	—	2	1	no	—
265	C₂×D₈	—	2	1	no	—
266	C₂×D₈	—	2	2	no	—
267	C₂×D₈	C₂×C₄×C₇	1	4	yes	complemented
268	#131	—	2	2	no	—
269	#131	C₂×C₄×C₇	1	4	yes	complemented
270	C₂×M₁₆	—	2	1	no	—
271	C₂×M₁₆	C₂³×C₇	1	1	yes	characteristic
272	C₂×M₁₆	C₂³×C₇	1	1	yes	characteristic
273	C₂×M₁₆	C₂³×C₇	1	2	yes	—
274	C₂²×C₈	—	2	1	no	—
275	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
276	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
277	C₄×Q₈	—	2	2	no	—
278	C₄×D₄	—	2	2	no	—
279	C₄×D₄	—	2	2	no	—
280	C₄×D₄	—	2	2	no	—
281	C₄×D₄	—	2	2	no	—
282	C₄×D₄	—	2	2	no	—
283	C₄×D₄	—	4	2	no	—
284	#117	—	2	2	no	—
285	#117	C₂³×C₇	1	1	yes	characteristic
286	#117	C₂³×C₇	1	2	yes	—
287	C₂×C₄⋊C₄	—	2	2	no	—
288	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
289	C₂×C₂²⋊C₄	—	4	2	no	—
290	C₂×C₂²⋊C₄	—	4	2	no	—
291	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
292	#108	C₂×C₄×C₇	1	4	yes	complemented
293	#107	—	2	1	no	—
294	#107	—	2	1	no	—
295	#107	—	2	2	no	—
296	#107	—	2	2	no	—
297	#107	C₇×D₄	1	1	yes	characteristic
298	#107	C₇×D₄	1	1	yes	characteristic
299	#106	—	2	2	no	—
300	#106	—	2	2	no	—
301	#106	C₇×D₄	1	2	yes	—
302	#104	—	2	2	no	—
303	#103	C₇×D₄	1	1	yes	characteristic
304	#103	C₇×D₄	1	1	yes	characteristic
305	#102	—	2	2	no	—
306	#102	—	2	2	no	—
307	#102	—	2	2	no	—
308	#102	—	2	2	no	—
309	#102	C₇×D₄	1	1	yes	characteristic
310	#102	C₇×D₄	1	1	yes	characteristic
311	#100	C₂×C₄×C₇	1	8	yes	complemented
312	#97	—	2	2	no	—
313	#97	—	2	1	no	—
314	C₄×C₈	—	2	1	no	—
315	C₄×C₈	—	2	2	no	—
316	C₄×C₈	—	2	2	no	—
317	C₂²×C₇	—	2	1	no	—
318	C₂²×C₇	—	2	1	no	—
319	C₂²×C₇	—	2	2	no	—
320	C₂²×C₇	—	4	1	no	—
321	C₂²×C₇	—	4	1	no	—
322	C₂²×C₇	—	4	4	no	—
323	C₂²×C₇	—	8	4	no	—
324	C₂²×C₇	—	8	2	no	—
325	C₂²×C₇	—	8	2	no	—
326	C₂²×C₇	—	16	2	no	—
327	C₂²×C₇	#520	1	1	yes	characteristic
328	C₂²×C₇	D₄²	1	1	yes	characteristic
329	C₂²×C₇	#553	1	1	yes	characteristic
330	C₄×C₇	—	2	2	no	—
331	C₄×C₇	—	4	2	no	—
332	C₄×C₇	—	4	2	no	—
333	C₄×C₇	—	4	1	no	—
334	C₄×C₇	—	4	1	no	—
335	C₄×C₇	—	4	2	no	—
336	C₄×C₇	—	8	2	no	—
337	C₄×C₇	C₂×C₄×D₄	1	1	yes	characteristic
338	C₄×C₇	C₂×C₄×D₄	1	1	yes	characteristic
339	C₄×C₇	#547	1	1	yes	characteristic
340	C₄×C₇	#548	1	1	yes	characteristic
341	C₂⁴	—	2	2	no	—
342	#41	—	2	1	no	—
343	#41	—	2	1	no	—
344	#41	C₂²×C₄×C₇	1	2	yes	—
345	#41	C₇×#41	1	2	yes	—
346	C₂×Q₈	C₂×C₇×D₄	1	1	yes	characteristic
347	C₂×D₄	—	2	1	no	—
348	C₂×D₄	—	2	2	no	—
349	C₂×D₄	—	2	2	no	—
350	C₂×D₄	—	2	2	no	—
351	C₂×D₄	—	2	2	no	—
352	C₂×D₄	—	2	2	no	—
353	C₂×D₄	C₂²×C₄×C₇	1	4	yes	—
354	C₂×D₄	C₂×C₇×D₄	1	1	yes	characteristic
355	C₂²×C₄	—	2	1	no	—
356	C₂²×C₄	—	2	1	no	—
357	C₂²×C₄	—	2	2	no	—
358	C₂²×C₄	—	4	2	no	—
359	C₂²×C₄	—	4	2	no	—
360	C₂²×C₄	—	4	2	no	—
361	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
362	SD₁₆	—	2	8	no	—
363	D₈	—	2	8	no	—
364	D₈	—	2	4	no	—
365	D₈	—	2	4	no	—
366	M₁₆	—	2	1	no	—
367	M₁₆	—	2	2	no	—
368	M₁₆	—	2	4	no	—
369	M₁₆	—	2	1	no	—
370	M₁₆	—	2	1	no	—
371	M₁₆	C₂²×C₄×C₇	1	2	yes	—
372	M₁₆	C₂²×C₄×C₇	1	4	yes	—
373	C₂×C₈	—	2	2	no	—
374	C₂×C₈	—	2	1	no	—
375	C₂×C₈	—	2	1	no	—
376	C₂×C₈	—	2	1	no	—
377	C₂×C₈	—	2	4	no	—
378	C₂×C₈	—	2	1	no	—
379	C₂×C₈	C₂²×C₄×C₇	1	2	yes	—
380	C₂×C₈	C₂×C₇×D₄	1	1	yes	characteristic
381	C₂×C₈	C₂×C₇×D₄	1	1	yes	characteristic
382	C₂×C₈	C₂×C₇×D₄	1	1	yes	characteristic
383	C₂×C₈	C₂×C₇×D₄	1	1	yes	characteristic
384	C₂×C₈	C₇×#41	1	2	yes	—
385	C₄⋊C₄	—	2	2	no	—
386	C₄⋊C₄	—	2	2	no	—
387	C₄⋊C₄	—	4	2	no	—
388	C₄⋊C₄	C₂×C₇×D₄	1	2	yes	—
389	C₄⋊C₄	C₂×C₇×D₄	1	2	yes	—
390	C₄⋊C₄	C₂×C₇×D₄	1	1	yes	characteristic
391	C₄⋊C₄	C₂×C₇×D₄	1	1	yes	characteristic
392	C₂²⋊C₄	—	2	1	no	—
393	C₂²⋊C₄	—	2	2	no	—
394	C₂²⋊C₄	—	4	2	no	—
395	C₂²⋊C₄	—	4	2	no	—
396	C₂²⋊C₄	—	4	2	no	—
397	C₂²⋊C₄	—	8	4	no	—
398	C₄²	—	2	1	no	—
399	C₄²	—	2	2	no	—
400	C₄²	—	2	1	no	—
401	C₄²	—	2	1	no	—
402	C₄²	—	4	2	no	—
403	C₂×C₇	—	2	1	no	—
404	C₂×C₇	—	2	1	no	—
405	C₂×C₇	—	4	2	no	—
406	C₂×C₇	—	8	4	no	—
407	C₂×C₇	#2361	1	1	yes	characteristic
408	C₂×C₇	#3290	1	1	yes	characteristic
409	C₂×C₇	#3292	1	1	yes	characteristic
410	C₂³	—	2	1	no	—
411	C₂³	—	2	4	no	—
412	C₂³	—	4	2	no	—
413	C₂³	—	4	2	no	—
414	C₂³	—	8	2	no	—
415	C₂³	—	8	2	no	—
416	C₂³	C₇×H(5,𝔽₂)	1	1	yes	characteristic
417	Q₈	—	2	1	no	—
418	Q₈	C₄×C₇×D₄	1	2	yes	—
419	D₄	—	2	2	no	—
420	D₄	—	2	2	no	—
421	D₄	—	2	4	no	—
422	D₄	—	2	4	no	—
423	D₄	—	2	1	no	—
424	D₄	—	4	2	no	—
425	D₄	—	4	2	no	—
426	D₄	C₄×C₇×D₄	1	2	yes	—
427	C₂×C₄	—	2	1	no	—
428	C₂×C₄	—	2	2	no	—
429	C₂×C₄	—	2	2	no	—
430	C₂×C₄	—	2	2	no	—
431	C₂×C₄	—	2	2	no	—
432	C₂×C₄	—	2	1	no	—
433	C₂×C₄	—	2	1	no	—
434	C₂×C₄	—	2	2	no	—
435	C₂×C₄	—	4	1	no	—
436	C₂×C₄	—	4	1	no	—
437	C₂×C₄	—	4	2	no	—
438	C₂×C₄	—	8	2	no	—
439	C₂×C₄	—	16	2	no	—
440	C₂×C₄	—	16	2	no	—
441	C₂×C₄	—	16	2	no	—
442	C₂×C₄	C₂³×C₄×C₇	1	1	yes	characteristic
443	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
444	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
445	C₂×C₄	C₂×C₇×#41	1	1	yes	characteristic
446	C₂×C₄	C₂×C₇×#41	1	1	yes	characteristic
447	C₂×C₄	C₇×2₋¹⁺⁴	1	1	yes	characteristic
448	C₈	—	2	2	no	—
449	C₈	—	2	4	no	—
450	C₈	—	2	1	no	—
451	C₈	—	2	1	no	—
452	C₈	—	4	1	no	—
453	C₈	C₄×C₇×D₄	1	2	yes	—
454	C₈	C₄×C₇×D₄	1	2	yes	—
455	C₇	#23046	1	1	yes	characteristic, direct product factor, Sylow
456	C₂²	—	2	1	no	—
457	C₂²	—	2	1	no	—
458	C₂²	—	2	2	no	—
459	C₂²	—	4	1	no	—
460	C₂²	—	4	1	no	—
461	C₂²	—	4	4	no	—
462	C₂²	—	8	4	no	—
463	C₂²	—	8	2	no	—
464	C₂²	—	8	2	no	—
465	C₂²	—	16	2	no	—
466	C₂²	C₇×#520	1	1	yes	characteristic
467	C₂²	C₇×D₄²	1	1	yes	characteristic
468	C₂²	C₇×#553	1	1	yes	characteristic
469	C₄	—	2	2	no	—
470	C₄	—	4	2	no	—
471	C₄	—	4	1	no	—
472	C₄	—	4	2	no	—
473	C₄	—	4	1	no	—
474	C₄	—	4	2	no	—
475	C₄	—	8	2	no	—
476	C₄	C₂×C₄×C₇×D₄	1	1	yes	characteristic
477	C₄	C₂×C₄×C₇×D₄	1	1	yes	characteristic
478	C₄	C₇×#547	1	1	yes	characteristic
479	C₄	C₇×#548	1	1	yes	characteristic
480	C₂	—	2	1	no	—
481	C₂	—	2	1	no	—
482	C₂	—	4	2	no	—
483	C₂	—	8	4	no	—
484	C₂	C₇×#2361	1	1	yes	characteristic
485	C₂	C₇×#3290	1	1	yes	characteristic
486	C₂	C₇×#3292	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₇	D₄²
commutator	C₂×C₄	C₂³×C₄×C₇
Frattini, cosocle	C₂²×C₄	C₂⁴×C₇
prime radical	C₂×C₇×#472	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₇ ◁ C₂²×C₄×C₇ ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
2. C₇×#2948	C₂	semidirect
3. C₇×#2946	C₂	semidirect
4. C₇×#2913	C₂	semidirect
5. C₇×#1970	C₂	semidirect
6. C₇×#1952	C₂	semidirect
7. C₇×#1931	C₂	semidirect
8. C₇×#1883	C₂	semidirect
9. C₇×#1856	C₂	semidirect
10. C₇×#1772	C₂	semidirect
11. C₇×#1764	C₂	semidirect
17. C₇×#472	C₄	semidirect
46. #23046	C₇	direct (N × H)
50. C₇×AGL(1,ℤ/8)	C₂×C₄	semidirect
56. C₂×C₇×D₈	C₂×C₄	semidirect
58. C₇×#131	C₂×C₄	semidirect
81. C₇×#108	C₂×C₄	semidirect
100. C₇×#100	C₂×C₄	semidirect
107. #2948	C₂×C₇	semidirect
108. #2946	C₂×C₇	semidirect
109. #2913	C₂×C₇	semidirect
110. #1970	C₂×C₇	semidirect
111. #1952	C₂×C₇	semidirect
112. #1931	C₂×C₇	semidirect
113. #1883	C₂×C₇	semidirect
114. #1856	C₂×C₇	semidirect
115. #1772	C₂×C₇	semidirect
116. #1764	C₂×C₇	semidirect
184. #472	C₄×C₇	semidirect
261. AGL(1,ℤ/8)	C₂×C₄×C₇	semidirect
267. C₂×D₈	C₂×C₄×C₇	semidirect
269. #131	C₂×C₄×C₇	semidirect
292. #108	C₂×C₄×C₇	semidirect
311. #100	C₂×C₄×C₇	semidirect
455. C₇	#23046	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂×C₇×#472	2
C₇×#2948	2
C₇×#2946	2
C₇×#2913	2
C₇×#1970	2
C₇×#1952	2
C₇×#1931	2
C₇×#1883	2
C₇×#1856	2
C₇×#1772	2
C₇×#1764	2
#23046	7

Subgroups — C7×#23046 #13200262

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×#23046 #13200262