Subgroups — C₇×#26045 #13203261

Order 1792.

862 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×#478	C₂	1	2	yes	maximal
2	C₇×#2552	C₂	1	1	yes	maximal, characteristic, complemented
3	C₇×D₄×C₄⋊C₄	C₂	1	1	yes	maximal, characteristic
4	C₇×#2088	C₂	1	2	yes	maximal, complemented
5	C₇×#2059	C₂	1	2	yes	maximal, complemented
6	C₇×#1947	C₂	1	1	yes	maximal, characteristic, complemented
7	C₇×#1939	C₂	1	1	yes	maximal, characteristic, complemented
8	C₇×#1864	C₂	1	2	yes	maximal
9	C₇×#1844	C₂	1	1	yes	maximal, characteristic, complemented
10	C₇×#1802	C₂	1	1	yes	maximal, characteristic
11	C₄×C₇×#102	C₂	1	1	yes	maximal, characteristic
12	C₂×C₇×#125	C₂²	1	2	yes	—
13	C₂×C₄×C₇×D₄	C₂²	1	2	yes	—
14	C₂×C₄×C₇×D₄	C₂²	1	1	yes	characteristic
15	C₂²×C₇×C₄⋊C₄	—	2	1	no	—
16	C₇×#478	—	2	8	no	—
17	C₂×C₇×#107	C₂²	1	2	yes	—
18	C₂×C₇×#106	C₂²	1	2	yes	—
19	C₂×C₇×#106	C₂²	1	2	yes	—
20	C₂×C₇×C₄⋊C₈	C₂²	1	1	yes	characteristic
21	C₂×C₇×C₄⋊C₈	C₂²	1	2	yes	—
22	C₂×C₇×#102	C₂²	1	2	yes	—
23	C₂×C₇×#102	C₂²	1	1	yes	characteristic
24	C₂×C₇×#102	C₂²	1	1	yes	characteristic
25	C₂×C₄×C₇×C₈	C₂²	1	1	yes	characteristic
26	C₇×#398	—	2	2	no	—
27	C₇×#389	—	2	1	no	—
28	C₇×#389	C₂²	1	2	yes	—
29	C₇×#389	C₂²	1	2	yes	—
30	C₇×#385	—	2	2	no	—
31	C₇×#384	—	2	1	no	—
32	C₇×#384	C₂²	1	1	yes	characteristic
33	C₇×#384	C₂²	1	1	yes	characteristic
34	C₇×#380	—	2	1	no	—
35	C₄×C₇×C₄⋊C₄	C₂²	1	1	yes	characteristic
36	C₄×C₇×C₄⋊C₄	C₂²	1	1	yes	characteristic
37	C₇×#340	C₂²	1	1	yes	characteristic
38	C₇×#340	C₂²	1	1	yes	characteristic
39	C₇×#340	C₂²	1	2	yes	—
40	C₇×#340	C₂²	1	2	yes	—
41	C₇×#336	C₂²	1	2	yes	—
42	#26045	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
43	C₂²×C₇×D₄	C₂³	1	1	yes	characteristic
44	C₂³×C₄×C₇	—	2	1	no	—
45	C₂³×C₄×C₇	—	2	2	no	—
46	C₂²×C₇×C₈	C₂³	1	2	yes	—
47	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
48	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
49	C₇×#125	—	2	4	no	—
50	C₇×#125	—	4	2	no	—
51	C₄×C₇×D₄	—	2	4	no	—
52	C₄×C₇×D₄	—	2	2	no	—
53	C₄×C₇×D₄	—	4	2	no	—
54	C₄×C₇×D₄	Q₈	1	4	yes	—
55	C₂×C₇×C₄⋊C₄	—	2	1	no	—
56	C₂×C₇×C₄⋊C₄	—	2	2	no	—
57	C₂×C₇×C₄⋊C₄	—	2	1	no	—
58	C₂×C₇×C₄⋊C₄	—	2	2	no	—
59	C₂×C₇×C₄⋊C₄	—	2	2	no	—
60	C₂×C₇×C₄⋊C₄	—	2	2	no	—
61	C₂×C₇×C₄⋊C₄	—	2	1	no	—
62	C₂×C₇×C₄⋊C₄	—	2	1	no	—
63	C₂×C₇×C₄⋊C₄	—	4	4	no	—
64	C₂×C₇×C₄⋊C₄	D₄	1	1	yes	characteristic
65	C₂×C₇×C₄⋊C₄	D₄	1	1	yes	characteristic
66	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
67	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
68	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
69	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
70	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
71	C₂×C₇×C₂²⋊C₄	—	2	1	no	—
72	C₂×C₇×C₂²⋊C₄	—	2	2	no	—
73	C₂×C₄²×C₇	—	2	1	no	—
74	C₂×C₄²×C₇	C₂³	1	2	yes	—
75	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
76	C₇×#107	—	2	4	no	—
77	C₇×#106	—	2	4	no	—
78	C₇×#106	—	4	2	no	—
79	C₇×C₄⋊C₈	—	2	4	no	—
80	C₇×C₄⋊C₈	—	2	2	no	—
81	C₇×#102	—	2	4	no	—
82	C₇×#102	D₄	1	4	yes	—
83	C₇×#102	Q₈	1	4	yes	—
84	C₄×C₇×C₈	—	2	2	no	—
85	C₇×#95	—	2	1	no	—
86	C₇×#95	—	2	2	no	—
87	C₇×#95	—	2	2	no	—
88	C₇×#95	D₄	1	2	yes	—
89	C₂×#478	C₂×C₇	1	2	yes	—
90	#2552	C₂×C₇	1	1	yes	characteristic, complemented
91	D₄×C₄⋊C₄	C₂×C₇	1	1	yes	characteristic
92	#2088	C₂×C₇	1	2	yes	complemented
93	#2059	C₂×C₇	1	2	yes	complemented
94	#1947	C₂×C₇	1	1	yes	characteristic, complemented
95	#1939	C₂×C₇	1	1	yes	characteristic, complemented
96	#1864	C₂×C₇	1	2	yes	—
97	#1844	C₂×C₇	1	1	yes	characteristic, complemented
98	#1802	C₂×C₇	1	1	yes	characteristic
99	C₄×#102	C₂×C₇	1	1	yes	characteristic
100	C₂⁴×C₇	—	2	1	no	—
101	C₂×C₇×D₄	—	2	1	no	—
102	C₂×C₇×D₄	—	2	1	no	—
103	C₂×C₇×D₄	—	2	1	no	—
104	C₂×C₇×D₄	C₂×D₄	1	2	yes	—
105	C₂×C₇×D₄	C₂×Q₈	1	2	yes	—
106	C₂×C₇×D₄	C₂×Q₈	1	2	yes	—
107	C₂²×C₄×C₇	—	2	1	no	—
108	C₂²×C₄×C₇	—	2	1	no	—
109	C₂²×C₄×C₇	—	2	1	no	—
110	C₂²×C₄×C₇	—	2	4	no	—
111	C₂²×C₄×C₇	—	2	2	no	—
112	C₂²×C₄×C₇	—	2	2	no	—
113	C₂²×C₄×C₇	—	4	4	no	—
114	C₂²×C₄×C₇	—	4	4	no	—
115	C₂²×C₄×C₇	—	4	2	no	—
116	C₂²×C₄×C₇	—	4	2	no	—
117	C₂²×C₄×C₇	—	8	2	no	—
118	C₂²×C₄×C₇	C₂×D₄	1	2	yes	—
119	C₂²×C₄×C₇	C₂×D₄	1	2	yes	—
120	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
121	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
122	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
123	C₂×C₇×C₈	—	2	1	no	—
124	C₂×C₇×C₈	—	2	1	no	—
125	C₂×C₇×C₈	—	2	1	no	—
126	C₂×C₇×C₈	—	2	1	no	—
127	C₂×C₇×C₈	—	2	2	no	—
128	C₂×C₇×C₈	—	2	2	no	—
129	C₂×C₇×C₈	—	2	2	no	—
130	C₂×C₇×C₈	C₂×D₄	1	2	yes	—
131	C₂×C₇×C₈	C₂×Q₈	1	2	yes	—
132	C₇×C₄⋊C₄	—	2	2	no	—
133	C₇×C₄⋊C₄	—	2	2	no	—
134	C₇×C₄⋊C₄	—	2	1	no	—
135	C₇×C₄⋊C₄	—	2	1	no	—
136	C₇×C₄⋊C₄	—	2	1	no	—
137	C₇×C₄⋊C₄	—	2	2	no	—
138	C₇×C₄⋊C₄	—	2	2	no	—
139	C₇×C₄⋊C₄	—	2	2	no	—
140	C₇×C₄⋊C₄	—	2	2	no	—
141	C₇×C₄⋊C₄	—	4	4	no	—
142	C₇×C₄⋊C₄	—	4	4	no	—
143	C₇×C₄⋊C₄	—	4	4	no	—
144	C₇×C₄⋊C₄	—	4	2	no	—
145	C₇×C₄⋊C₄	—	4	2	no	—
146	C₇×C₄⋊C₄	—	8	1	no	—
147	C₇×C₄⋊C₄	—	8	1	no	—
148	C₇×C₄⋊C₄	—	8	2	no	—
149	C₇×C₄⋊C₄	C₂×D₄	1	2	yes	—
150	C₇×C₄⋊C₄	C₂×Q₈	1	2	yes	—
151	C₇×C₄⋊C₄	C₂×Q₈	1	2	yes	—
152	C₇×C₂²⋊C₄	—	2	4	no	—
153	C₇×C₂²⋊C₄	—	4	4	no	—
154	C₄²×C₇	—	2	2	no	—
155	C₄²×C₇	—	2	2	no	—
156	C₄²×C₇	—	4	2	no	—
157	C₄²×C₇	C₂×Q₈	1	2	yes	—
158	C₄²×C₇	#41	1	2	yes	—
159	C₂×#125	C₂²×C₇	1	2	yes	—
160	C₂×C₄×D₄	C₂²×C₇	1	2	yes	—
161	C₂×C₄×D₄	C₂²×C₇	1	1	yes	characteristic
162	C₂²×C₄⋊C₄	—	2	1	no	—
163	#478	—	2	8	no	—
164	C₂×#107	C₂²×C₇	1	2	yes	—
165	C₂×#106	C₂²×C₇	1	2	yes	—
166	C₂×#106	C₂²×C₇	1	2	yes	—
167	C₂×C₄⋊C₈	C₂²×C₇	1	2	yes	—
168	C₂×C₄⋊C₈	C₂²×C₇	1	1	yes	characteristic
169	C₂×#102	C₂²×C₇	1	2	yes	—
170	C₂×#102	C₂²×C₇	1	1	yes	characteristic
171	C₂×#102	C₂²×C₇	1	1	yes	characteristic
172	C₂×C₄×C₈	C₂²×C₇	1	1	yes	characteristic
173	#398	—	2	2	no	—
174	#389	—	2	1	no	—
175	#389	C₂²×C₇	1	2	yes	—
176	#389	C₂²×C₇	1	2	yes	—
177	#385	—	2	2	no	—
178	#384	—	2	1	no	—
179	#384	C₂²×C₇	1	1	yes	characteristic
180	#384	C₂²×C₇	1	1	yes	characteristic
181	#380	—	2	1	no	—
182	C₄×C₄⋊C₄	C₂²×C₇	1	1	yes	characteristic
183	C₄×C₄⋊C₄	C₂²×C₇	1	1	yes	characteristic
184	#340	C₂²×C₇	1	2	yes	—
185	#340	C₂²×C₇	1	1	yes	characteristic
186	#340	C₂²×C₇	1	1	yes	characteristic
187	#340	C₂²×C₇	1	2	yes	—
188	#336	C₂²×C₇	1	2	yes	—
189	C₂³×C₇	—	2	2	no	—
190	C₂³×C₇	—	2	2	no	—
191	C₂³×C₇	—	2	2	no	—
192	C₂³×C₇	—	4	1	no	—
193	C₂³×C₇	—	4	1	no	—
194	C₂³×C₇	—	4	1	no	—
195	C₂³×C₇	—	4	1	no	—
196	C₂³×C₇	C₂²×D₄	1	1	yes	characteristic
197	C₇×D₄	—	2	2	no	—
198	C₇×D₄	—	2	2	no	—
199	C₇×D₄	—	2	2	no	—
200	C₇×D₄	C₄⋊Q₈	1	4	yes	—
201	C₂×C₄×C₇	—	2	1	no	—
202	C₂×C₄×C₇	—	2	1	no	—
203	C₂×C₄×C₇	—	2	2	no	—
204	C₂×C₄×C₇	—	2	2	no	—
205	C₂×C₄×C₇	—	2	2	no	—
206	C₂×C₄×C₇	—	2	2	no	—
207	C₂×C₄×C₇	—	2	2	no	—
208	C₂×C₄×C₇	—	2	2	no	—
209	C₂×C₄×C₇	—	2	2	no	—
210	C₂×C₄×C₇	—	2	2	no	—
211	C₂×C₄×C₇	—	2	2	no	—
212	C₂×C₄×C₇	—	4	1	no	—
213	C₂×C₄×C₇	—	4	1	no	—
214	C₂×C₄×C₇	—	4	1	no	—
215	C₂×C₄×C₇	—	4	1	no	—
216	C₂×C₄×C₇	—	4	1	no	—
217	C₂×C₄×C₇	—	4	1	no	—
218	C₂×C₄×C₇	—	4	8	no	—
219	C₂×C₄×C₇	—	4	2	no	—
220	C₂×C₄×C₇	—	4	2	no	—
221	C₂×C₄×C₇	—	4	2	no	—
222	C₂×C₄×C₇	—	4	2	no	—
223	C₂×C₄×C₇	—	4	2	no	—
224	C₂×C₄×C₇	—	4	2	no	—
225	C₂×C₄×C₇	—	8	8	no	—
226	C₂×C₄×C₇	C₂²⋊Q₈	1	2	yes	—
227	C₂×C₄×C₇	C₂²⋊Q₈	1	2	yes	—
228	C₂×C₄×C₇	#135	1	2	yes	—
229	C₂×C₄×C₇	AGL(1,ℤ/8)	1	2	yes	—
230	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
231	C₂×C₄×C₇	C₂²×Q₈	1	1	yes	characteristic
232	C₂×C₄×C₇	C₂²×Q₈	1	1	yes	characteristic
233	C₂×C₄×C₇	C₂×#41	1	1	yes	characteristic
234	C₂×C₄×C₇	H(5,𝔽₂)	1	1	yes	characteristic
235	C₂×C₄×C₇	2₋¹⁺⁴	1	1	yes	characteristic
236	C₇×C₈	—	2	2	no	—
237	C₇×C₈	—	2	2	no	—
238	C₇×C₈	—	4	2	no	—
239	C₂²×D₄	C₂³×C₇	1	1	yes	characteristic
240	C₂³×C₄	—	2	1	no	—
241	C₂³×C₄	—	2	2	no	—
242	C₂²×C₈	C₂³×C₇	1	2	yes	—
243	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
244	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
245	#125	—	2	4	no	—
246	#125	—	4	2	no	—
247	C₄×D₄	—	2	4	no	—
248	C₄×D₄	—	2	2	no	—
249	C₄×D₄	—	4	2	no	—
250	C₄×D₄	C₇×Q₈	1	4	yes	—
251	C₂×C₄⋊C₄	—	2	1	no	—
252	C₂×C₄⋊C₄	—	2	2	no	—
253	C₂×C₄⋊C₄	—	2	2	no	—
254	C₂×C₄⋊C₄	—	2	2	no	—
255	C₂×C₄⋊C₄	—	2	1	no	—
256	C₂×C₄⋊C₄	—	2	2	no	—
257	C₂×C₄⋊C₄	—	2	1	no	—
258	C₂×C₄⋊C₄	—	2	1	no	—
259	C₂×C₄⋊C₄	—	4	4	no	—
260	C₂×C₄⋊C₄	C₇×D₄	1	1	yes	characteristic
261	C₂×C₄⋊C₄	C₇×D₄	1	1	yes	characteristic
262	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
263	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
264	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
265	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
266	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
267	C₂×C₂²⋊C₄	—	2	1	no	—
268	C₂×C₂²⋊C₄	—	2	2	no	—
269	C₂×C₄²	—	2	1	no	—
270	C₂×C₄²	C₂³×C₇	1	2	yes	—
271	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
272	#107	—	2	4	no	—
273	#106	—	2	4	no	—
274	#106	—	4	2	no	—
275	C₄⋊C₈	—	2	4	no	—
276	C₄⋊C₈	—	2	2	no	—
277	#102	—	2	4	no	—
278	#102	C₇×D₄	1	4	yes	—
279	#102	C₇×Q₈	1	4	yes	—
280	C₄×C₈	—	2	2	no	—
281	#95	—	2	1	no	—
282	#95	—	2	2	no	—
283	#95	—	2	2	no	—
284	#95	C₇×D₄	1	2	yes	—
285	C₂²×C₇	—	2	4	no	—
286	C₂²×C₇	—	4	2	no	—
287	C₂²×C₇	—	4	2	no	—
288	C₂²×C₇	—	4	2	no	—
289	C₂²×C₇	—	4	2	no	—
290	C₂²×C₇	—	4	2	no	—
291	C₂²×C₇	—	4	2	no	—
292	C₂²×C₇	C₂×C₂²⋊Q₈	1	1	yes	characteristic
293	C₂²×C₇	D₄²	1	1	yes	characteristic
294	C₂²×C₇	D₄×Q₈	1	1	yes	characteristic
295	C₂²×C₇	C₂×#135	1	1	yes	characteristic
296	C₂²×C₇	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
297	C₂²×C₇	#577	1	1	yes	characteristic
298	C₂²×C₇	#577	1	1	yes	characteristic
299	C₄×C₇	—	2	2	no	—
300	C₄×C₇	—	4	2	no	—
301	C₄×C₇	—	4	2	no	—
302	C₄×C₇	—	4	2	no	—
303	C₄×C₇	—	4	2	no	—
304	C₄×C₇	—	4	2	no	—
305	C₄×C₇	—	8	2	no	—
306	C₄×C₇	—	8	2	no	—
307	C₄×C₇	#478	1	4	yes	complemented
308	C₄×C₇	C₂×C₄⋊Q₈	1	1	yes	characteristic
309	C₄×C₇	#544	1	1	yes	characteristic
310	C₄×C₇	#547	1	1	yes	characteristic
311	C₄×C₇	#554	1	1	yes	characteristic
312	C₂⁴	—	2	1	no	—
313	C₂×D₄	—	2	1	no	—
314	C₂×D₄	—	2	1	no	—
315	C₂×D₄	—	2	1	no	—
316	C₂×D₄	C₂×C₇×D₄	1	2	yes	—
317	C₂×D₄	C₂×C₇×Q₈	1	2	yes	—
318	C₂×D₄	C₂×C₇×Q₈	1	2	yes	—
319	C₂²×C₄	—	2	1	no	—
320	C₂²×C₄	—	2	1	no	—
321	C₂²×C₄	—	2	1	no	—
322	C₂²×C₄	—	2	4	no	—
323	C₂²×C₄	—	2	2	no	—
324	C₂²×C₄	—	2	2	no	—
325	C₂²×C₄	—	4	4	no	—
326	C₂²×C₄	—	4	4	no	—
327	C₂²×C₄	—	4	2	no	—
328	C₂²×C₄	—	4	2	no	—
329	C₂²×C₄	—	8	2	no	—
330	C₂²×C₄	C₂×C₇×D₄	1	2	yes	—
331	C₂²×C₄	C₂×C₇×D₄	1	2	yes	—
332	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
333	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
334	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
335	C₂×C₈	—	2	1	no	—
336	C₂×C₈	—	2	1	no	—
337	C₂×C₈	—	2	1	no	—
338	C₂×C₈	—	2	1	no	—
339	C₂×C₈	—	2	2	no	—
340	C₂×C₈	—	2	2	no	—
341	C₂×C₈	—	2	2	no	—
342	C₂×C₈	C₂×C₇×D₄	1	2	yes	—
343	C₂×C₈	C₂×C₇×Q₈	1	2	yes	—
344	C₄⋊C₄	—	2	2	no	—
345	C₄⋊C₄	—	2	2	no	—
346	C₄⋊C₄	—	2	1	no	—
347	C₄⋊C₄	—	2	1	no	—
348	C₄⋊C₄	—	2	1	no	—
349	C₄⋊C₄	—	2	2	no	—
350	C₄⋊C₄	—	2	2	no	—
351	C₄⋊C₄	—	2	2	no	—
352	C₄⋊C₄	—	2	2	no	—
353	C₄⋊C₄	—	4	4	no	—
354	C₄⋊C₄	—	4	4	no	—
355	C₄⋊C₄	—	4	4	no	—
356	C₄⋊C₄	—	4	2	no	—
357	C₄⋊C₄	—	4	2	no	—
358	C₄⋊C₄	—	8	1	no	—
359	C₄⋊C₄	—	8	1	no	—
360	C₄⋊C₄	—	8	2	no	—
361	C₄⋊C₄	C₂×C₇×D₄	1	2	yes	—
362	C₄⋊C₄	C₂×C₇×Q₈	1	2	yes	—
363	C₄⋊C₄	C₂×C₇×Q₈	1	2	yes	—
364	C₂²⋊C₄	—	2	4	no	—
365	C₂²⋊C₄	—	4	4	no	—
366	C₄²	—	2	2	no	—
367	C₄²	—	2	2	no	—
368	C₄²	—	4	2	no	—
369	C₄²	C₂×C₇×Q₈	1	2	yes	—
370	C₄²	C₇×#41	1	2	yes	—
371	C₂×C₇	—	4	4	no	—
372	C₂×C₇	#2440	1	1	yes	characteristic
373	C₂×C₇	C₂×#478	1	1	yes	characteristic
374	C₂×C₇	#3084	1	1	yes	characteristic
375	C₂×C₇	#3272	1	1	yes	characteristic
376	C₂×C₇	#3284	1	1	yes	characteristic
377	C₂×C₇	#3381	1	1	yes	characteristic
378	C₂×C₇	#3384	1	1	yes	characteristic
379	C₂³	—	2	2	no	—
380	C₂³	—	2	2	no	—
381	C₂³	—	2	2	no	—
382	C₂³	—	4	1	no	—
383	C₂³	—	4	1	no	—
384	C₂³	—	4	1	no	—
385	C₂³	—	4	1	no	—
386	C₂³	C₂²×C₇×D₄	1	1	yes	characteristic
387	D₄	—	2	2	no	—
388	D₄	—	2	2	no	—
389	D₄	—	2	2	no	—
390	D₄	C₇×C₄⋊Q₈	1	4	yes	—
391	C₂×C₄	—	2	1	no	—
392	C₂×C₄	—	2	1	no	—
393	C₂×C₄	—	2	2	no	—
394	C₂×C₄	—	2	2	no	—
395	C₂×C₄	—	2	2	no	—
396	C₂×C₄	—	2	2	no	—
397	C₂×C₄	—	2	2	no	—
398	C₂×C₄	—	2	2	no	—
399	C₂×C₄	—	2	2	no	—
400	C₂×C₄	—	2	2	no	—
401	C₂×C₄	—	2	2	no	—
402	C₂×C₄	—	4	1	no	—
403	C₂×C₄	—	4	1	no	—
404	C₂×C₄	—	4	1	no	—
405	C₂×C₄	—	4	1	no	—
406	C₂×C₄	—	4	1	no	—
407	C₂×C₄	—	4	1	no	—
408	C₂×C₄	—	4	8	no	—
409	C₂×C₄	—	4	2	no	—
410	C₂×C₄	—	4	2	no	—
411	C₂×C₄	—	4	2	no	—
412	C₂×C₄	—	4	2	no	—
413	C₂×C₄	—	4	2	no	—
414	C₂×C₄	—	4	2	no	—
415	C₂×C₄	—	8	8	no	—
416	C₂×C₄	C₇×C₂²⋊Q₈	1	2	yes	—
417	C₂×C₄	C₇×C₂²⋊Q₈	1	2	yes	—
418	C₂×C₄	C₇×#135	1	2	yes	—
419	C₂×C₄	C₇×AGL(1,ℤ/8)	1	2	yes	—
420	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
421	C₂×C₄	C₂²×C₇×Q₈	1	1	yes	characteristic
422	C₂×C₄	C₂²×C₇×Q₈	1	1	yes	characteristic
423	C₂×C₄	C₂×C₇×#41	1	1	yes	characteristic
424	C₂×C₄	C₇×H(5,𝔽₂)	1	1	yes	characteristic
425	C₂×C₄	C₇×2₋¹⁺⁴	1	1	yes	characteristic
426	C₈	—	2	2	no	—
427	C₈	—	2	2	no	—
428	C₈	—	4	2	no	—
429	C₇	#26045	1	1	yes	characteristic, direct product factor, Sylow
430	C₂²	—	2	4	no	—
431	C₂²	—	4	2	no	—
432	C₂²	—	4	2	no	—
433	C₂²	—	4	2	no	—
434	C₂²	—	4	2	no	—
435	C₂²	—	4	2	no	—
436	C₂²	—	4	2	no	—
437	C₂²	C₂×C₇×C₂²⋊Q₈	1	1	yes	characteristic
438	C₂²	C₇×D₄²	1	1	yes	characteristic
439	C₂²	C₇×D₄×Q₈	1	1	yes	characteristic
440	C₂²	C₂×C₇×#135	1	1	yes	characteristic
441	C₂²	C₂×C₇×AGL(1,ℤ/8)	1	1	yes	characteristic
442	C₂²	C₇×#577	1	1	yes	characteristic
443	C₂²	C₇×#577	1	1	yes	characteristic
444	C₄	—	2	2	no	—
445	C₄	—	4	2	no	—
446	C₄	—	4	2	no	—
447	C₄	—	4	2	no	—
448	C₄	—	4	2	no	—
449	C₄	—	4	2	no	—
450	C₄	—	8	2	no	—
451	C₄	—	8	2	no	—
452	C₄	C₇×#478	1	4	yes	complemented
453	C₄	C₂×C₇×C₄⋊Q₈	1	1	yes	characteristic
454	C₄	C₇×#544	1	1	yes	characteristic
455	C₄	C₇×#547	1	1	yes	characteristic
456	C₄	C₇×#554	1	1	yes	characteristic
457	C₂	—	4	4	no	—
458	C₂	C₇×#2440	1	1	yes	characteristic
459	C₂	C₂×C₇×#478	1	1	yes	characteristic
460	C₂	C₇×#3084	1	1	yes	characteristic
461	C₂	C₇×#3272	1	1	yes	characteristic
462	C₂	C₇×#3284	1	1	yes	characteristic
463	C₂	C₇×#3381	1	1	yes	characteristic
464	C₂	C₇×#3384	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₇	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₇
prime radical	C₂²×C₇×D₄	C₂³
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₇ ◁ C₄×C₇×C₄⋊C₄ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₇×#2552	C₂	semidirect
4. C₇×#2088	C₂	semidirect
5. C₇×#2059	C₂	semidirect
6. C₇×#1947	C₂	semidirect
7. C₇×#1939	C₂	semidirect
9. C₇×#1844	C₂	semidirect
42. #26045	C₇	direct (N × H)
90. #2552	C₂×C₇	semidirect
92. #2088	C₂×C₇	semidirect
93. #2059	C₂×C₇	semidirect
94. #1947	C₂×C₇	semidirect
95. #1939	C₂×C₇	semidirect
97. #1844	C₂×C₇	semidirect
307. C₄×C₇	#478	semidirect
429. C₇	#26045	direct (N × H)
452. C₄	C₇×#478	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₇×#478	2
C₇×#2552	2
C₇×D₄×C₄⋊C₄	2
C₇×#2088	2
C₇×#2059	2
C₇×#1947	2
C₇×#1939	2
C₇×#1864	2
C₇×#1844	2
C₇×#1802	2
C₄×C₇×#102	2
#26045	7

Subgroups — C7×#26045 #13203261

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×#26045 #13203261