Subgroups — C₇×#23048 #13200264

Order 1792.

892 conjugacy classes of subgroups.

The subgroup lattice has 466 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×#2912	C₂	1	1	yes	maximal, characteristic, complemented
5	C₇×#1972	C₂	1	1	yes	maximal, characteristic, complemented
6	C₇×#1951	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×#1773	C₂	1	1	yes	maximal, characteristic, complemented
11	C₇×#1765	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	1	no	—
19	C₇×#442	—	2	1	no	—
20	C₇×#442	—	2	2	no	—
21	C₇×#440	—	2	2	no	—
22	C₄×C₇×SD₁₆	—	2	2	no	—
23	C₄×C₇×D₈	—	2	2	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×#106	—	2	1	no	—
32	C₂×C₇×#106	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×C₇×#97	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	#23048	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	2	no	—
83	C₇×#107	—	2	2	no	—
84	C₇×#107	D₄	1	2	yes	—
85	C₇×#106	—	2	1	no	—
86	C₇×#106	—	2	1	no	—
87	C₇×#106	—	2	2	no	—
88	C₇×#106	—	2	2	no	—
89	C₇×#106	D₄	1	1	yes	characteristic
90	C₇×#106	D₄	1	1	yes	characteristic
91	C₇×#104	—	2	2	no	—
92	C₇×#103	D₄	1	2	yes	—
93	C₇×#102	—	2	2	no	—
94	C₇×#102	—	2	2	no	—
95	C₇×#102	—	2	2	no	—
96	C₇×#102	—	2	2	no	—
97	C₇×#102	D₄	1	2	yes	—
98	C₇×#100	C₂×C₄	1	8	yes	complemented
99	C₇×#97	—	2	2	no	—
100	C₇×#97	—	2	1	no	—
101	C₇×#97	—	2	2	no	—
102	C₄×C₇×C₈	—	2	1	no	—
103	C₄×C₇×C₈	—	2	2	no	—
104	C₂×#472	C₂×C₇	1	1	yes	characteristic
105	#2948	C₂×C₇	1	1	yes	characteristic, complemented
106	#2946	C₂×C₇	1	2	yes	complemented
107	#2912	C₂×C₇	1	1	yes	characteristic, complemented
108	#1972	C₂×C₇	1	1	yes	characteristic, complemented
109	#1951	C₂×C₇	1	1	yes	characteristic, complemented
110	#1931	C₂×C₇	1	2	yes	complemented
111	#1883	C₂×C₇	1	2	yes	complemented
112	#1856	C₂×C₇	1	2	yes	complemented
113	#1773	C₂×C₇	1	1	yes	characteristic, complemented
114	#1765	C₂×C₇	1	1	yes	characteristic, complemented
115	C₂⁴×C₇	—	2	2	no	—
116	C₇×#41	—	2	1	no	—
117	C₇×#41	—	2	1	no	—
118	C₇×#41	C₂²×C₄	1	2	yes	—
119	C₇×#41	#41	1	2	yes	—
120	C₂×C₇×Q₈	C₂×D₄	1	1	yes	characteristic
121	C₂×C₇×D₄	—	2	1	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	—	2	2	no	—
126	C₂×C₇×D₄	—	2	2	no	—
127	C₂×C₇×D₄	C₂²×C₄	1	4	yes	—
128	C₂×C₇×D₄	C₂×D₄	1	1	yes	characteristic
129	C₂²×C₄×C₇	—	2	1	no	—
130	C₂²×C₄×C₇	—	2	1	no	—
131	C₂²×C₄×C₇	—	2	2	no	—
132	C₂²×C₄×C₇	—	4	2	no	—
133	C₂²×C₄×C₇	—	4	2	no	—
134	C₂²×C₄×C₇	—	4	2	no	—
135	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
136	C₇×SD₁₆	—	2	8	no	—
137	C₇×D₈	—	2	8	no	—
138	C₇×D₈	—	2	4	no	—
139	C₇×D₈	—	2	4	no	—
140	C₇×M₁₆	—	2	1	no	—
141	C₇×M₁₆	—	2	2	no	—
142	C₇×M₁₆	—	2	4	no	—
143	C₇×M₁₆	—	2	1	no	—
144	C₇×M₁₆	—	2	1	no	—
145	C₇×M₁₆	C₂²×C₄	1	2	yes	—
146	C₇×M₁₆	C₂²×C₄	1	4	yes	—
147	C₂×C₇×C₈	—	2	2	no	—
148	C₂×C₇×C₈	—	2	1	no	—
149	C₂×C₇×C₈	—	2	1	no	—
150	C₂×C₇×C₈	—	2	1	no	—
151	C₂×C₇×C₈	—	2	4	no	—
152	C₂×C₇×C₈	—	2	1	no	—
153	C₂×C₇×C₈	C₂²×C₄	1	2	yes	—
154	C₂×C₇×C₈	C₂×D₄	1	2	yes	—
155	C₂×C₇×C₈	C₂×D₄	1	1	yes	characteristic
156	C₂×C₇×C₈	C₂×D₄	1	1	yes	characteristic
157	C₂×C₇×C₈	#41	1	2	yes	—
158	C₇×C₄⋊C₄	—	2	2	no	—
159	C₇×C₄⋊C₄	—	2	2	no	—
160	C₇×C₄⋊C₄	—	4	2	no	—
161	C₇×C₄⋊C₄	C₂×D₄	1	2	yes	—
162	C₇×C₄⋊C₄	C₂×D₄	1	2	yes	—
163	C₇×C₄⋊C₄	C₂×D₄	1	2	yes	—
164	C₇×C₂²⋊C₄	—	2	1	no	—
165	C₇×C₂²⋊C₄	—	2	2	no	—
166	C₇×C₂²⋊C₄	—	4	2	no	—
167	C₇×C₂²⋊C₄	—	4	2	no	—
168	C₇×C₂²⋊C₄	—	4	2	no	—
169	C₇×C₂²⋊C₄	—	8	4	no	—
170	C₄²×C₇	—	2	1	no	—
171	C₄²×C₇	—	2	2	no	—
172	C₄²×C₇	—	2	1	no	—
173	C₄²×C₇	—	2	1	no	—
174	C₄²×C₇	—	4	2	no	—
175	C₂×AGL(1,ℤ/8)	C₂²×C₇	1	2	yes	—
176	C₂²×D₈	C₂²×C₇	1	1	yes	characteristic
177	C₂×#131	C₂²×C₇	1	1	yes	characteristic
178	#520	C₂²×C₇	1	2	yes	—
179	#518	C₂²×C₇	1	2	yes	—
180	#472	C₄×C₇	1	8	yes	complemented
181	#442	—	2	1	no	—
182	#442	—	2	1	no	—
183	#442	—	2	2	no	—
184	#440	—	2	2	no	—
185	C₄×SD₁₆	—	2	2	no	—
186	C₄×D₈	—	2	2	no	—
187	C₄×D₈	—	2	2	no	—
188	C₂×#108	C₂²×C₇	1	1	yes	characteristic
189	#428	—	2	2	no	—
190	#428	C₂²×C₇	1	2	yes	—
191	#428	C₂²×C₇	1	2	yes	—
192	#427	—	2	1	no	—
193	#427	C₂²×C₇	1	1	yes	characteristic
194	C₂×#106	—	2	1	no	—
195	C₂×#106	C₂²×C₇	1	1	yes	characteristic
196	C₂×#104	C₂²×C₇	1	1	yes	characteristic
197	#418	C₂²×C₇	1	2	yes	—
198	#416	C₂²×C₇	1	1	yes	characteristic
199	C₂×#102	C₂²×C₇	1	2	yes	—
200	C₂×#100	C₂²×C₇	1	2	yes	—
201	#405	C₂²×C₇	1	2	yes	—
202	#405	C₂²×C₇	1	1	yes	characteristic
203	C₂×#97	C₂²×C₇	1	1	yes	characteristic
204	#390	C₂²×C₇	1	2	yes	—
205	#343	C₂²×C₇	1	2	yes	—
206	#341	C₂²×C₇	1	1	yes	characteristic
207	#339	C₂²×C₇	1	1	yes	characteristic
208	#339	C₂²×C₇	1	2	yes	—
209	C₂³×C₇	—	2	1	no	—
210	C₂³×C₇	—	2	4	no	—
211	C₂³×C₇	—	4	2	no	—
212	C₂³×C₇	—	4	2	no	—
213	C₂³×C₇	—	8	2	no	—
214	C₂³×C₇	—	8	2	no	—
215	C₂³×C₇	H(5,𝔽₂)	1	1	yes	characteristic
216	C₇×Q₈	—	2	1	no	—
217	C₇×Q₈	C₄×D₄	1	2	yes	—
218	C₇×D₄	—	2	2	no	—
219	C₇×D₄	—	2	2	no	—
220	C₇×D₄	—	2	4	no	—
221	C₇×D₄	—	2	4	no	—
222	C₇×D₄	—	2	1	no	—
223	C₇×D₄	—	4	2	no	—
224	C₇×D₄	—	4	2	no	—
225	C₇×D₄	C₄×D₄	1	2	yes	—
226	C₂×C₄×C₇	—	2	1	no	—
227	C₂×C₄×C₇	—	2	2	no	—
228	C₂×C₄×C₇	—	2	2	no	—
229	C₂×C₄×C₇	—	2	2	no	—
230	C₂×C₄×C₇	—	2	2	no	—
231	C₂×C₄×C₇	—	2	2	no	—
232	C₂×C₄×C₇	—	4	2	no	—
233	C₂×C₄×C₇	—	4	2	no	—
234	C₂×C₄×C₇	—	4	1	no	—
235	C₂×C₄×C₇	—	8	2	no	—
236	C₂×C₄×C₇	—	16	2	no	—
237	C₂×C₄×C₇	—	16	2	no	—
238	C₂×C₄×C₇	—	16	2	no	—
239	C₂×C₄×C₇	C₂³×C₄	1	1	yes	characteristic
240	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
241	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
242	C₂×C₄×C₇	C₂×#41	1	1	yes	characteristic
243	C₂×C₄×C₇	C₂×#41	1	1	yes	characteristic
244	C₂×C₄×C₇	2₋¹⁺⁴	1	1	yes	characteristic
245	C₇×C₈	—	2	2	no	—
246	C₇×C₈	—	2	4	no	—
247	C₇×C₈	—	2	2	no	—
248	C₇×C₈	—	4	1	no	—
249	C₇×C₈	C₄×D₄	1	2	yes	—
250	C₇×C₈	C₄×D₄	1	2	yes	—
251	C₂×#41	C₂³×C₇	1	1	yes	characteristic
252	C₂²×D₄	C₂³×C₇	1	2	yes	—
253	AGL(1,ℤ/8)	—	2	4	no	—
254	AGL(1,ℤ/8)	C₂×C₄×C₇	1	8	yes	complemented
255	C₂×SD₁₆	—	2	2	no	—
256	C₂×D₈	—	2	2	no	—
257	C₂×D₈	—	2	1	no	—
258	C₂×D₈	—	2	1	no	—
259	C₂×D₈	—	2	2	no	—
260	C₂×D₈	C₂×C₄×C₇	1	4	yes	complemented
261	#131	—	2	2	no	—
262	#131	C₂×C₄×C₇	1	4	yes	complemented
263	C₂×M₁₆	—	2	1	no	—
264	C₂×M₁₆	C₂³×C₇	1	1	yes	characteristic
265	C₂×M₁₆	C₂³×C₇	1	1	yes	characteristic
266	C₂×M₁₆	C₂³×C₇	1	2	yes	—
267	C₂²×C₈	—	2	1	no	—
268	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
269	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
270	C₄×Q₈	—	2	2	no	—
271	C₄×D₄	—	2	2	no	—
272	C₄×D₄	—	2	2	no	—
273	C₄×D₄	—	2	2	no	—
274	C₄×D₄	—	2	2	no	—
275	C₄×D₄	—	2	2	no	—
276	C₄×D₄	—	4	2	no	—
277	#117	—	2	2	no	—
278	#117	C₂³×C₇	1	1	yes	characteristic
279	#117	C₂³×C₇	1	2	yes	—
280	C₂×C₄⋊C₄	—	2	2	no	—
281	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
282	C₂×C₂²⋊C₄	—	4	2	no	—
283	C₂×C₂²⋊C₄	—	4	2	no	—
284	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
285	#108	C₂×C₄×C₇	1	4	yes	complemented
286	#107	—	2	2	no	—
287	#107	—	2	2	no	—
288	#107	C₇×D₄	1	2	yes	—
289	#106	—	2	1	no	—
290	#106	—	2	1	no	—
291	#106	—	2	2	no	—
292	#106	—	2	2	no	—
293	#106	C₇×D₄	1	1	yes	characteristic
294	#106	C₇×D₄	1	1	yes	characteristic
295	#104	—	2	2	no	—
296	#103	C₇×D₄	1	2	yes	—
297	#102	—	2	2	no	—
298	#102	—	2	2	no	—
299	#102	—	2	2	no	—
300	#102	—	2	2	no	—
301	#102	C₇×D₄	1	2	yes	—
302	#100	C₂×C₄×C₇	1	8	yes	complemented
303	#97	—	2	2	no	—
304	#97	—	2	1	no	—
305	#97	—	2	2	no	—
306	C₄×C₈	—	2	1	no	—
307	C₄×C₈	—	2	2	no	—
308	C₂²×C₇	—	2	2	no	—
309	C₂²×C₇	—	2	2	no	—
310	C₂²×C₇	—	4	2	no	—
311	C₂²×C₇	—	4	4	no	—
312	C₂²×C₇	—	8	4	no	—
313	C₂²×C₇	—	8	2	no	—
314	C₂²×C₇	—	8	2	no	—
315	C₂²×C₇	—	16	2	no	—
316	C₂²×C₇	#520	1	1	yes	characteristic
317	C₂²×C₇	D₄²	1	1	yes	characteristic
318	C₂²×C₇	#553	1	1	yes	characteristic
319	C₄×C₇	—	2	2	no	—
320	C₄×C₇	—	4	2	no	—
321	C₄×C₇	—	4	2	no	—
322	C₄×C₇	—	4	2	no	—
323	C₄×C₇	—	8	1	no	—
324	C₄×C₇	—	8	2	no	—
325	C₄×C₇	C₂×C₄×D₄	1	1	yes	characteristic
326	C₄×C₇	C₂×C₄×D₄	1	1	yes	characteristic
327	C₄×C₇	#547	1	1	yes	characteristic
328	C₄×C₇	#548	1	1	yes	characteristic
329	C₂⁴	—	2	2	no	—
330	#41	—	2	1	no	—
331	#41	—	2	1	no	—
332	#41	C₂²×C₄×C₇	1	2	yes	—
333	#41	C₇×#41	1	2	yes	—
334	C₂×Q₈	C₂×C₇×D₄	1	1	yes	characteristic
335	C₂×D₄	—	2	1	no	—
336	C₂×D₄	—	2	2	no	—
337	C₂×D₄	—	2	2	no	—
338	C₂×D₄	—	2	2	no	—
339	C₂×D₄	—	2	2	no	—
340	C₂×D₄	—	2	2	no	—
341	C₂×D₄	C₂²×C₄×C₇	1	4	yes	—
342	C₂×D₄	C₂×C₇×D₄	1	1	yes	characteristic
343	C₂²×C₄	—	2	1	no	—
344	C₂²×C₄	—	2	1	no	—
345	C₂²×C₄	—	2	2	no	—
346	C₂²×C₄	—	4	2	no	—
347	C₂²×C₄	—	4	2	no	—
348	C₂²×C₄	—	4	2	no	—
349	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
350	SD₁₆	—	2	8	no	—
351	D₈	—	2	8	no	—
352	D₈	—	2	4	no	—
353	D₈	—	2	4	no	—
354	M₁₆	—	2	1	no	—
355	M₁₆	—	2	2	no	—
356	M₁₆	—	2	4	no	—
357	M₁₆	—	2	1	no	—
358	M₁₆	—	2	1	no	—
359	M₁₆	C₂²×C₄×C₇	1	2	yes	—
360	M₁₆	C₂²×C₄×C₇	1	4	yes	—
361	C₂×C₈	—	2	2	no	—
362	C₂×C₈	—	2	1	no	—
363	C₂×C₈	—	2	1	no	—
364	C₂×C₈	—	2	1	no	—
365	C₂×C₈	—	2	4	no	—
366	C₂×C₈	—	2	1	no	—
367	C₂×C₈	C₂²×C₄×C₇	1	2	yes	—
368	C₂×C₈	C₂×C₇×D₄	1	2	yes	—
369	C₂×C₈	C₂×C₇×D₄	1	1	yes	characteristic
370	C₂×C₈	C₂×C₇×D₄	1	1	yes	characteristic
371	C₂×C₈	C₇×#41	1	2	yes	—
372	C₄⋊C₄	—	2	2	no	—
373	C₄⋊C₄	—	2	2	no	—
374	C₄⋊C₄	—	4	2	no	—
375	C₄⋊C₄	C₂×C₇×D₄	1	2	yes	—
376	C₄⋊C₄	C₂×C₇×D₄	1	2	yes	—
377	C₄⋊C₄	C₂×C₇×D₄	1	2	yes	—
378	C₂²⋊C₄	—	2	1	no	—
379	C₂²⋊C₄	—	2	2	no	—
380	C₂²⋊C₄	—	4	2	no	—
381	C₂²⋊C₄	—	4	2	no	—
382	C₂²⋊C₄	—	4	2	no	—
383	C₂²⋊C₄	—	8	4	no	—
384	C₄²	—	2	1	no	—
385	C₄²	—	2	2	no	—
386	C₄²	—	2	1	no	—
387	C₄²	—	2	1	no	—
388	C₄²	—	4	2	no	—
389	C₂×C₇	—	2	1	no	—
390	C₂×C₇	—	2	1	no	—
391	C₂×C₇	—	4	2	no	—
392	C₂×C₇	—	8	4	no	—
393	C₂×C₇	#2361	1	1	yes	characteristic
394	C₂×C₇	#3288	1	2	yes	—
395	C₂³	—	2	1	no	—
396	C₂³	—	2	4	no	—
397	C₂³	—	4	2	no	—
398	C₂³	—	4	2	no	—
399	C₂³	—	8	2	no	—
400	C₂³	—	8	2	no	—
401	C₂³	C₇×H(5,𝔽₂)	1	1	yes	characteristic
402	Q₈	—	2	1	no	—
403	Q₈	C₄×C₇×D₄	1	2	yes	—
404	D₄	—	2	2	no	—
405	D₄	—	2	2	no	—
406	D₄	—	2	4	no	—
407	D₄	—	2	4	no	—
408	D₄	—	2	1	no	—
409	D₄	—	4	2	no	—
410	D₄	—	4	2	no	—
411	D₄	C₄×C₇×D₄	1	2	yes	—
412	C₂×C₄	—	2	1	no	—
413	C₂×C₄	—	2	2	no	—
414	C₂×C₄	—	2	2	no	—
415	C₂×C₄	—	2	2	no	—
416	C₂×C₄	—	2	2	no	—
417	C₂×C₄	—	2	2	no	—
418	C₂×C₄	—	4	2	no	—
419	C₂×C₄	—	4	2	no	—
420	C₂×C₄	—	4	1	no	—
421	C₂×C₄	—	8	2	no	—
422	C₂×C₄	—	16	2	no	—
423	C₂×C₄	—	16	2	no	—
424	C₂×C₄	—	16	2	no	—
425	C₂×C₄	C₂³×C₄×C₇	1	1	yes	characteristic
426	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
427	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
428	C₂×C₄	C₂×C₇×#41	1	1	yes	characteristic
429	C₂×C₄	C₂×C₇×#41	1	1	yes	characteristic
430	C₂×C₄	C₇×2₋¹⁺⁴	1	1	yes	characteristic
431	C₈	—	2	2	no	—
432	C₈	—	2	4	no	—
433	C₈	—	2	2	no	—
434	C₈	—	4	1	no	—
435	C₈	C₄×C₇×D₄	1	2	yes	—
436	C₈	C₄×C₇×D₄	1	2	yes	—
437	C₇	#23048	1	1	yes	characteristic, direct product factor, Sylow
438	C₂²	—	2	2	no	—
439	C₂²	—	2	2	no	—
440	C₂²	—	4	2	no	—
441	C₂²	—	4	4	no	—
442	C₂²	—	8	4	no	—
443	C₂²	—	8	2	no	—
444	C₂²	—	8	2	no	—
445	C₂²	—	16	2	no	—
446	C₂²	C₇×#520	1	1	yes	characteristic
447	C₂²	C₇×D₄²	1	1	yes	characteristic
448	C₂²	C₇×#553	1	1	yes	characteristic
449	C₄	—	2	2	no	—
450	C₄	—	4	2	no	—
451	C₄	—	4	2	no	—
452	C₄	—	4	2	no	—
453	C₄	—	8	1	no	—
454	C₄	—	8	2	no	—
455	C₄	C₂×C₄×C₇×D₄	1	1	yes	characteristic
456	C₄	C₂×C₄×C₇×D₄	1	1	yes	characteristic
457	C₄	C₇×#547	1	1	yes	characteristic
458	C₄	C₇×#548	1	1	yes	characteristic
459	C₂	—	2	1	no	—
460	C₂	—	2	1	no	—
461	C₂	—	4	2	no	—
462	C₂	—	8	4	no	—
463	C₂	C₇×#2361	1	1	yes	characteristic
464	C₂	C₇×#3288	1	2	yes	—

	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×#2912	C₂	semidirect
5. C₇×#1972	C₂	semidirect
6. C₇×#1951	C₂	semidirect
7. C₇×#1931	C₂	semidirect
8. C₇×#1883	C₂	semidirect
9. C₇×#1856	C₂	semidirect
10. C₇×#1773	C₂	semidirect
11. C₇×#1765	C₂	semidirect
17. C₇×#472	C₄	semidirect
46. #23048	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
98. C₇×#100	C₂×C₄	semidirect
105. #2948	C₂×C₇	semidirect
106. #2946	C₂×C₇	semidirect
107. #2912	C₂×C₇	semidirect
108. #1972	C₂×C₇	semidirect
109. #1951	C₂×C₇	semidirect
110. #1931	C₂×C₇	semidirect
111. #1883	C₂×C₇	semidirect
112. #1856	C₂×C₇	semidirect
113. #1773	C₂×C₇	semidirect
114. #1765	C₂×C₇	semidirect
180. #472	C₄×C₇	semidirect
254. AGL(1,ℤ/8)	C₂×C₄×C₇	semidirect
260. C₂×D₈	C₂×C₄×C₇	semidirect
262. #131	C₂×C₄×C₇	semidirect
285. #108	C₂×C₄×C₇	semidirect
302. #100	C₂×C₄×C₇	semidirect
437. C₇	#23048	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×#2912	2
C₇×#1972	2
C₇×#1951	2
C₇×#1931	2
C₇×#1883	2
C₇×#1856	2
C₇×#1773	2
C₇×#1765	2
#23048	7

Subgroups — C7×#23048 #13200264

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×#23048 #13200264