Subgroups — C₇×#26065 #13203281

Order 1792.

894 conjugacy classes of subgroups.

The subgroup lattice has 460 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₇×#500	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×C₇×#107	C₂	1	1	yes	maximal, characteristic
3	C₇×#2440	C₂	1	2	yes	maximal
4	C₇×#2083	C₂	1	2	yes	maximal, complemented
5	C₇×#2057	C₂	1	2	yes	maximal, complemented
6	C₇×#1942	C₂	1	1	yes	maximal, characteristic, complemented
7	C₇×#1942	C₂	1	1	yes	maximal, characteristic, complemented
8	C₇×#1852	C₂	1	2	yes	maximal
9	C₇×#1845	C₂	1	1	yes	maximal, characteristic, complemented
10	C₇×#1808	C₂	1	1	yes	maximal, characteristic
11	C₇×C₈×C₂²⋊C₄	C₂	1	1	yes	maximal, characteristic
12	C₂³×C₇×C₈	C₂²	1	1	yes	characteristic
13	C₂×C₇×C₄⋊Q₈	C₂²	1	2	yes	—
14	C₂×C₇×C₂²⋊Q₈	—	2	2	no	—
15	C₂²×C₇×C₄⋊C₄	C₂²	1	2	yes	—
16	C₇×#500	—	2	4	no	—
17	C₂×C₇×#107	—	2	4	no	—
18	C₂×C₇×#107	C₂²	1	1	yes	characteristic
19	C₂×C₇×#107	C₂²	1	2	yes	—
20	C₂×C₇×#107	C₂²	1	2	yes	—
21	C₂×C₇×#107	C₂²	1	1	yes	characteristic
22	C₂×C₇×#107	C₂²	1	1	yes	characteristic
23	C₂×C₇×#107	C₂²	1	2	yes	—
24	C₂×C₇×#107	C₂²	1	1	yes	characteristic
25	C₂×C₇×C₂²⋊C₈	C₂²	1	1	yes	characteristic
26	C₂×C₄×C₇×C₈	C₂²	1	1	yes	characteristic
27	C₂×C₄×C₇×C₈	C₂²	1	1	yes	characteristic
28	C₇×#398	—	2	2	no	—
29	C₇×#395	—	2	2	no	—
30	C₇×#389	C₂²	1	2	yes	—
31	C₇×#389	C₂²	1	2	yes	—
32	C₇×#385	—	2	2	no	—
33	C₇×#384	C₂²	1	2	yes	—
34	C₇×#380	C₂²	1	2	yes	—
35	C₄×C₇×C₂²⋊C₄	C₂²	1	1	yes	characteristic
36	C₇×#340	C₂²	1	2	yes	—
37	C₇×#340	C₂²	1	2	yes	—
38	C₇×#340	C₂²	1	2	yes	—
39	C₇×#336	C₂²	1	1	yes	characteristic
40	C₇×#336	C₂²	1	1	yes	characteristic
41	#26065	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
42	C₂²×C₇×Q₈	—	2	2	no	—
43	C₂³×C₄×C₇	—	2	2	no	—
44	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
45	C₂²×C₇×C₈	—	2	2	no	—
46	C₂²×C₇×C₈	—	2	2	no	—
47	C₂²×C₇×C₈	Q₈	1	4	yes	complemented
48	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
49	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
50	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
51	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
52	C₇×C₄⋊Q₈	—	2	4	no	—
53	C₇×C₄⋊Q₈	—	4	2	no	—
54	C₇×C₂²⋊Q₈	—	4	8	no	—
55	C₂×C₇×C₄⋊C₄	—	2	4	no	—
56	C₂×C₇×C₄⋊C₄	—	2	2	no	—
57	C₂×C₇×C₄⋊C₄	—	2	2	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	2	no	—
62	C₂×C₇×C₄⋊C₄	—	4	2	no	—
63	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
64	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
65	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
66	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
67	C₂×C₇×C₂²⋊C₄	—	2	2	no	—
68	C₂×C₇×C₂²⋊C₄	D₄	1	1	yes	characteristic
69	C₂×C₇×C₂²⋊C₄	D₄	1	1	yes	characteristic
70	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
71	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
72	C₇×#107	—	2	2	no	—
73	C₇×#107	—	2	2	no	—
74	C₇×#107	—	2	2	no	—
75	C₇×#107	—	2	4	no	—
76	C₇×#107	—	2	4	no	—
77	C₇×#107	—	4	2	no	—
78	C₇×#107	D₄	1	4	yes	—
79	C₇×C₂²⋊C₈	Q₈	1	4	yes	complemented
80	C₄×C₇×C₈	—	2	2	no	—
81	C₄×C₇×C₈	—	2	2	no	—
82	C₇×#95	—	2	2	no	—
83	C₇×#95	—	2	2	no	—
84	C₇×#95	—	2	2	no	—
85	C₇×#95	D₄	1	1	yes	characteristic
86	C₇×#95	D₄	1	1	yes	characteristic
87	C₂×#500	C₂×C₇	1	1	yes	characteristic, complemented
88	C₂²×#107	C₂×C₇	1	1	yes	characteristic
89	#2440	C₂×C₇	1	2	yes	—
90	#2083	C₂×C₇	1	2	yes	complemented
91	#2057	C₂×C₇	1	2	yes	complemented
92	#1942	C₂×C₇	1	1	yes	characteristic, complemented
93	#1942	C₂×C₇	1	1	yes	characteristic, complemented
94	#1852	C₂×C₇	1	2	yes	—
95	#1845	C₂×C₇	1	1	yes	characteristic, complemented
96	#1808	C₂×C₇	1	1	yes	characteristic
97	C₈×C₂²⋊C₄	C₂×C₇	1	1	yes	characteristic
98	C₂⁴×C₇	C₂×D₄	1	1	yes	characteristic
99	C₂×C₇×Q₈	—	4	4	no	—
100	C₂×C₇×Q₈	—	4	4	no	—
101	C₂×C₇×Q₈	—	8	2	no	—
102	C₂²×C₄×C₇	—	2	1	no	—
103	C₂²×C₄×C₇	—	2	1	no	—
104	C₂²×C₄×C₇	—	2	1	no	—
105	C₂²×C₄×C₇	—	2	1	no	—
106	C₂²×C₄×C₇	—	2	2	no	—
107	C₂²×C₄×C₇	—	2	2	no	—
108	C₂²×C₄×C₇	—	2	2	no	—
109	C₂²×C₄×C₇	—	2	2	no	—
110	C₂²×C₄×C₇	—	4	4	no	—
111	C₂²×C₄×C₇	—	4	4	no	—
112	C₂²×C₄×C₇	—	8	2	no	—
113	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
114	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
115	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
116	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
117	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
118	C₂²×C₄×C₇	C₂×Q₈	1	2	yes	—
119	C₂²×C₄×C₇	C₂×Q₈	1	2	yes	—
120	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
121	C₂×C₇×C₈	—	2	1	no	—
122	C₂×C₇×C₈	—	2	1	no	—
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	8	no	—
128	C₂×C₇×C₈	C₂×D₄	1	2	yes	—
129	C₂×C₇×C₈	C₂×Q₈	1	2	yes	—
130	C₂×C₇×C₈	C₂×Q₈	1	2	yes	—
131	C₂×C₇×C₈	C₂×Q₈	1	2	yes	—
132	C₂×C₇×C₈	C₂×Q₈	1	2	yes	—
133	C₂×C₇×C₈	#41	1	2	yes	—
134	C₇×C₄⋊C₄	—	2	2	no	—
135	C₇×C₄⋊C₄	—	2	2	no	—
136	C₇×C₄⋊C₄	—	2	2	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	4	no	—
145	C₇×C₄⋊C₄	—	4	4	no	—
146	C₇×C₄⋊C₄	—	8	2	no	—
147	C₇×C₄⋊C₄	C₂×D₄	1	4	yes	—
148	C₇×C₂²⋊C₄	—	4	4	no	—
149	C₇×C₂²⋊C₄	D₈	1	4	yes	—
150	C₇×C₂²⋊C₄	Q₁₆	1	4	yes	—
151	C₄²×C₇	—	2	1	no	—
152	C₄²×C₇	—	2	1	no	—
153	C₄²×C₇	—	2	1	no	—
154	C₄²×C₇	—	2	1	no	—
155	C₂³×C₈	C₂²×C₇	1	1	yes	characteristic
156	C₂×C₄⋊Q₈	C₂²×C₇	1	2	yes	—
157	C₂×C₂²⋊Q₈	—	2	2	no	—
158	C₂²×C₄⋊C₄	C₂²×C₇	1	2	yes	—
159	#500	—	2	4	no	—
160	C₂×#107	—	2	4	no	—
161	C₂×#107	C₂²×C₇	1	2	yes	—
162	C₂×#107	C₂²×C₇	1	1	yes	characteristic
163	C₂×#107	C₂²×C₇	1	1	yes	characteristic
164	C₂×#107	C₂²×C₇	1	2	yes	—
165	C₂×#107	C₂²×C₇	1	1	yes	characteristic
166	C₂×#107	C₂²×C₇	1	2	yes	—
167	C₂×#107	C₂²×C₇	1	1	yes	characteristic
168	C₂×C₂²⋊C₈	C₂²×C₇	1	1	yes	characteristic
169	C₂×C₄×C₈	C₂²×C₇	1	1	yes	characteristic
170	C₂×C₄×C₈	C₂²×C₇	1	1	yes	characteristic
171	#398	—	2	2	no	—
172	#395	—	2	2	no	—
173	#389	C₂²×C₇	1	2	yes	—
174	#389	C₂²×C₇	1	2	yes	—
175	#385	—	2	2	no	—
176	#384	C₂²×C₇	1	2	yes	—
177	#380	C₂²×C₇	1	2	yes	—
178	C₄×C₂²⋊C₄	C₂²×C₇	1	1	yes	characteristic
179	#340	C₂²×C₇	1	2	yes	—
180	#340	C₂²×C₇	1	2	yes	—
181	#340	C₂²×C₇	1	2	yes	—
182	#336	C₂²×C₇	1	1	yes	characteristic
183	#336	C₂²×C₇	1	1	yes	characteristic
184	C₂³×C₇	—	2	1	no	—
185	C₂³×C₇	—	2	1	no	—
186	C₂³×C₇	—	2	1	no	—
187	C₂³×C₇	—	2	1	no	—
188	C₂³×C₇	C₄⋊Q₈	1	2	yes	—
189	C₂³×C₇	C₂×D₈	1	2	yes	—
190	C₂³×C₇	C₂×Q₁₆	1	2	yes	—
191	C₂³×C₇	C₂²×D₄	1	1	yes	characteristic
192	C₇×Q₈	—	8	8	no	—
193	C₂×C₄×C₇	—	2	1	no	—
194	C₂×C₄×C₇	—	2	1	no	—
195	C₂×C₄×C₇	—	2	1	no	—
196	C₂×C₄×C₇	—	2	1	no	—
197	C₂×C₄×C₇	—	2	1	no	—
198	C₂×C₄×C₇	—	2	1	no	—
199	C₂×C₄×C₇	—	2	1	no	—
200	C₂×C₄×C₇	—	2	1	no	—
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	4	no	—
208	C₂×C₄×C₇	—	4	2	no	—
209	C₂×C₄×C₇	—	4	2	no	—
210	C₂×C₄×C₇	—	4	2	no	—
211	C₂×C₄×C₇	—	4	2	no	—
212	C₂×C₄×C₇	—	4	2	no	—
213	C₂×C₄×C₇	—	4	2	no	—
214	C₂×C₄×C₇	—	4	2	no	—
215	C₂×C₄×C₇	—	4	2	no	—
216	C₂×C₄×C₇	—	4	2	no	—
217	C₂×C₄×C₇	—	4	2	no	—
218	C₂×C₄×C₇	—	4	2	no	—
219	C₂×C₄×C₇	—	8	8	no	—
220	C₂×C₄×C₇	C₄⋊Q₈	1	2	yes	—
221	C₂×C₄×C₇	C₂×D₈	1	2	yes	—
222	C₂×C₄×C₇	C₂×D₈	1	2	yes	—
223	C₂×C₄×C₇	C₂×Q₁₆	1	2	yes	—
224	C₂×C₄×C₇	C₂×Q₁₆	1	2	yes	—
225	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
226	C₂×C₄×C₇	C₂²×Q₈	1	1	yes	characteristic
227	C₂×C₄×C₇	C₂²×Q₈	1	1	yes	characteristic
228	C₂×C₄×C₇	C₂×#41	1	1	yes	characteristic
229	C₂×C₄×C₇	H(5,𝔽₂)	1	1	yes	characteristic
230	C₂×C₄×C₇	2₋¹⁺⁴	1	1	yes	characteristic
231	C₇×C₈	—	2	2	no	—
232	C₇×C₈	—	2	2	no	—
233	C₇×C₈	—	2	2	no	—
234	C₇×C₈	C₂²⋊Q₈	1	4	yes	complemented
235	C₂²×Q₈	—	2	2	no	—
236	C₂³×C₄	—	2	2	no	—
237	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
238	C₂²×C₈	—	2	2	no	—
239	C₂²×C₈	—	2	2	no	—
240	C₂²×C₈	C₇×Q₈	1	4	yes	complemented
241	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
242	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
243	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
244	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
245	C₄⋊Q₈	—	2	4	no	—
246	C₄⋊Q₈	—	4	2	no	—
247	C₂²⋊Q₈	—	4	8	no	—
248	C₂×C₄⋊C₄	—	2	4	no	—
249	C₂×C₄⋊C₄	—	2	2	no	—
250	C₂×C₄⋊C₄	—	2	2	no	—
251	C₂×C₄⋊C₄	—	2	2	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	—	4	2	no	—
256	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
257	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
258	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
259	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
260	C₂×C₂²⋊C₄	—	2	2	no	—
261	C₂×C₂²⋊C₄	C₇×D₄	1	1	yes	characteristic
262	C₂×C₂²⋊C₄	C₇×D₄	1	1	yes	characteristic
263	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
264	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
265	#107	—	2	2	no	—
266	#107	—	2	2	no	—
267	#107	—	2	2	no	—
268	#107	—	2	4	no	—
269	#107	—	2	4	no	—
270	#107	—	4	2	no	—
271	#107	C₇×D₄	1	4	yes	—
272	C₂²⋊C₈	C₇×Q₈	1	4	yes	complemented
273	C₄×C₈	—	2	2	no	—
274	C₄×C₈	—	2	2	no	—
275	#95	—	2	2	no	—
276	#95	—	2	2	no	—
277	#95	—	2	2	no	—
278	#95	C₇×D₄	1	1	yes	characteristic
279	#95	C₇×D₄	1	1	yes	characteristic
280	C₂²×C₇	—	2	2	no	—
281	C₂²×C₇	—	2	2	no	—
282	C₂²×C₇	—	2	2	no	—
283	C₂²×C₇	—	2	2	no	—
284	C₂²×C₇	—	2	2	no	—
285	C₂²×C₇	—	2	2	no	—
286	C₂²×C₇	#500	1	4	yes	complemented
287	C₂²×C₇	C₂×C₄⋊Q₈	1	1	yes	characteristic
288	C₂²×C₇	D₄²	1	1	yes	characteristic
289	C₂²×C₇	#547	1	1	yes	characteristic
290	C₂²×C₇	C₂²×D₈	1	1	yes	characteristic
291	C₂²×C₇	C₂²×Q₁₆	1	1	yes	characteristic
292	C₂²×C₇	#576	1	1	yes	characteristic
293	C₂²×C₇	#578	1	1	yes	characteristic
294	C₄×C₇	—	2	2	no	—
295	C₄×C₇	—	2	2	no	—
296	C₄×C₇	—	2	2	no	—
297	C₄×C₇	—	2	2	no	—
298	C₄×C₇	—	2	2	no	—
299	C₄×C₇	—	4	4	no	—
300	C₄×C₇	—	8	2	no	—
301	C₄×C₇	—	8	2	no	—
302	C₄×C₇	—	8	2	no	—
303	C₄×C₇	C₂×C₂²⋊Q₈	1	1	yes	characteristic
304	C₄×C₇	#544	1	1	yes	characteristic
305	C₄×C₇	D₄×Q₈	1	1	yes	characteristic
306	C₄×C₇	#554	1	1	yes	characteristic
307	C₂⁴	C₂×C₇×D₄	1	1	yes	characteristic
308	C₂×Q₈	—	4	4	no	—
309	C₂×Q₈	—	4	4	no	—
310	C₂×Q₈	—	8	2	no	—
311	C₂²×C₄	—	2	1	no	—
312	C₂²×C₄	—	2	1	no	—
313	C₂²×C₄	—	2	1	no	—
314	C₂²×C₄	—	2	1	no	—
315	C₂²×C₄	—	2	2	no	—
316	C₂²×C₄	—	2	2	no	—
317	C₂²×C₄	—	2	2	no	—
318	C₂²×C₄	—	2	2	no	—
319	C₂²×C₄	—	4	4	no	—
320	C₂²×C₄	—	4	4	no	—
321	C₂²×C₄	—	8	2	no	—
322	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
323	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
324	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
325	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
326	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
327	C₂²×C₄	C₂×C₇×Q₈	1	2	yes	—
328	C₂²×C₄	C₂×C₇×Q₈	1	2	yes	—
329	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
330	C₂×C₈	—	2	1	no	—
331	C₂×C₈	—	2	1	no	—
332	C₂×C₈	—	2	1	no	—
333	C₂×C₈	—	2	1	no	—
334	C₂×C₈	—	2	1	no	—
335	C₂×C₈	—	2	1	no	—
336	C₂×C₈	—	2	8	no	—
337	C₂×C₈	C₂×C₇×D₄	1	2	yes	—
338	C₂×C₈	C₂×C₇×Q₈	1	2	yes	—
339	C₂×C₈	C₂×C₇×Q₈	1	2	yes	—
340	C₂×C₈	C₂×C₇×Q₈	1	2	yes	—
341	C₂×C₈	C₂×C₇×Q₈	1	2	yes	—
342	C₂×C₈	C₇×#41	1	2	yes	—
343	C₄⋊C₄	—	2	2	no	—
344	C₄⋊C₄	—	2	2	no	—
345	C₄⋊C₄	—	2	2	no	—
346	C₄⋊C₄	—	2	2	no	—
347	C₄⋊C₄	—	2	2	no	—
348	C₄⋊C₄	—	2	2	no	—
349	C₄⋊C₄	—	2	2	no	—
350	C₄⋊C₄	—	4	4	no	—
351	C₄⋊C₄	—	4	4	no	—
352	C₄⋊C₄	—	4	4	no	—
353	C₄⋊C₄	—	4	4	no	—
354	C₄⋊C₄	—	4	4	no	—
355	C₄⋊C₄	—	8	2	no	—
356	C₄⋊C₄	C₂×C₇×D₄	1	4	yes	—
357	C₂²⋊C₄	—	4	4	no	—
358	C₂²⋊C₄	C₇×D₈	1	4	yes	—
359	C₂²⋊C₄	C₇×Q₁₆	1	4	yes	—
360	C₄²	—	2	1	no	—
361	C₄²	—	2	1	no	—
362	C₄²	—	2	1	no	—
363	C₄²	—	2	1	no	—
364	C₂×C₇	—	2	4	no	—
365	C₂×C₇	#2440	1	1	yes	characteristic
366	C₂×C₇	C₂×#500	1	1	yes	characteristic
367	C₂×C₇	#3164	1	1	yes	characteristic
368	C₂×C₇	D₄×D₈	1	1	yes	characteristic
369	C₂×C₇	D₄×Q₁₆	1	1	yes	characteristic
370	C₂×C₇	#3334	1	1	yes	characteristic
371	C₂×C₇	#3338	1	1	yes	characteristic
372	C₂³	—	2	1	no	—
373	C₂³	—	2	1	no	—
374	C₂³	—	2	1	no	—
375	C₂³	—	2	1	no	—
376	C₂³	C₇×C₄⋊Q₈	1	2	yes	—
377	C₂³	C₂×C₇×D₈	1	2	yes	—
378	C₂³	C₂×C₇×Q₁₆	1	2	yes	—
379	C₂³	C₂²×C₇×D₄	1	1	yes	characteristic
380	Q₈	—	8	8	no	—
381	C₂×C₄	—	2	1	no	—
382	C₂×C₄	—	2	1	no	—
383	C₂×C₄	—	2	1	no	—
384	C₂×C₄	—	2	1	no	—
385	C₂×C₄	—	2	1	no	—
386	C₂×C₄	—	2	1	no	—
387	C₂×C₄	—	2	1	no	—
388	C₂×C₄	—	2	1	no	—
389	C₂×C₄	—	2	1	no	—
390	C₂×C₄	—	2	1	no	—
391	C₂×C₄	—	2	2	no	—
392	C₂×C₄	—	2	2	no	—
393	C₂×C₄	—	2	2	no	—
394	C₂×C₄	—	2	2	no	—
395	C₂×C₄	—	2	4	no	—
396	C₂×C₄	—	4	2	no	—
397	C₂×C₄	—	4	2	no	—
398	C₂×C₄	—	4	2	no	—
399	C₂×C₄	—	4	2	no	—
400	C₂×C₄	—	4	2	no	—
401	C₂×C₄	—	4	2	no	—
402	C₂×C₄	—	4	2	no	—
403	C₂×C₄	—	4	2	no	—
404	C₂×C₄	—	4	2	no	—
405	C₂×C₄	—	4	2	no	—
406	C₂×C₄	—	4	2	no	—
407	C₂×C₄	—	8	8	no	—
408	C₂×C₄	C₇×C₄⋊Q₈	1	2	yes	—
409	C₂×C₄	C₂×C₇×D₈	1	2	yes	—
410	C₂×C₄	C₂×C₇×D₈	1	2	yes	—
411	C₂×C₄	C₂×C₇×Q₁₆	1	2	yes	—
412	C₂×C₄	C₂×C₇×Q₁₆	1	2	yes	—
413	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
414	C₂×C₄	C₂²×C₇×Q₈	1	1	yes	characteristic
415	C₂×C₄	C₂²×C₇×Q₈	1	1	yes	characteristic
416	C₂×C₄	C₂×C₇×#41	1	1	yes	characteristic
417	C₂×C₄	C₇×H(5,𝔽₂)	1	1	yes	characteristic
418	C₂×C₄	C₇×2₋¹⁺⁴	1	1	yes	characteristic
419	C₈	—	2	2	no	—
420	C₈	—	2	2	no	—
421	C₈	—	2	2	no	—
422	C₈	C₇×C₂²⋊Q₈	1	4	yes	complemented
423	C₇	#26065	1	1	yes	characteristic, direct product factor, Sylow
424	C₂²	—	2	2	no	—
425	C₂²	—	2	2	no	—
426	C₂²	—	2	2	no	—
427	C₂²	—	2	2	no	—
428	C₂²	—	2	2	no	—
429	C₂²	—	2	2	no	—
430	C₂²	C₇×#500	1	4	yes	complemented
431	C₂²	C₂×C₇×C₄⋊Q₈	1	1	yes	characteristic
432	C₂²	C₇×D₄²	1	1	yes	characteristic
433	C₂²	C₇×#547	1	1	yes	characteristic
434	C₂²	C₂²×C₇×D₈	1	1	yes	characteristic
435	C₂²	C₂²×C₇×Q₁₆	1	1	yes	characteristic
436	C₂²	C₇×#576	1	1	yes	characteristic
437	C₂²	C₇×#578	1	1	yes	characteristic
438	C₄	—	2	2	no	—
439	C₄	—	2	2	no	—
440	C₄	—	2	2	no	—
441	C₄	—	2	2	no	—
442	C₄	—	2	2	no	—
443	C₄	—	4	4	no	—
444	C₄	—	8	2	no	—
445	C₄	—	8	2	no	—
446	C₄	—	8	2	no	—
447	C₄	C₂×C₇×C₂²⋊Q₈	1	1	yes	characteristic
448	C₄	C₇×#544	1	1	yes	characteristic
449	C₄	C₇×D₄×Q₈	1	1	yes	characteristic
450	C₄	C₇×#554	1	1	yes	characteristic
451	C₂	—	2	4	no	—
452	C₂	C₇×#2440	1	1	yes	characteristic
453	C₂	C₂×C₇×#500	1	1	yes	characteristic
454	C₂	C₇×#3164	1	1	yes	characteristic
455	C₂	C₇×D₄×D₈	1	1	yes	characteristic
456	C₂	C₇×D₄×Q₁₆	1	1	yes	characteristic
457	C₂	C₇×#3334	1	1	yes	characteristic
458	C₂	C₇×#3338	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
1. C₂×C₇×#500	C₂	semidirect
4. C₇×#2083	C₂	semidirect
5. C₇×#2057	C₂	semidirect
6. C₇×#1942	C₂	semidirect
7. C₇×#1942	C₂	semidirect
9. C₇×#1845	C₂	semidirect
41. #26065	C₇	direct (N × H)
47. C₂²×C₇×C₈	Q₈	semidirect
79. C₇×C₂²⋊C₈	Q₈	semidirect
87. C₂×#500	C₂×C₇	semidirect
90. #2083	C₂×C₇	semidirect
91. #2057	C₂×C₇	semidirect
92. #1942	C₂×C₇	semidirect
93. #1942	C₂×C₇	semidirect
95. #1845	C₂×C₇	semidirect
234. C₇×C₈	C₂²⋊Q₈	semidirect
240. C₂²×C₈	C₇×Q₈	semidirect
272. C₂²⋊C₈	C₇×Q₈	semidirect
286. C₂²×C₇	#500	semidirect
422. C₈	C₇×C₂²⋊Q₈	semidirect
423. C₇	#26065	direct (N × H)
430. C₂²	C₇×#500	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₇×#500	2
C₂²×C₇×#107	2
C₇×#2440	2
C₇×#2083	2
C₇×#2057	2
C₇×#1942	2
C₇×#1852	2
C₇×#1845	2
C₇×#1808	2
C₇×C₈×C₂²⋊C₄	2
#26065	7

Subgroups — C7×#26065 #13203281

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×#26065 #13203281