Subgroups — C₇×#22764 #13199980

Order 1792.

906 conjugacy classes of subgroups.

The subgroup lattice has 470 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄×C₇×D₈	C₂	1	1	yes	maximal, characteristic
2	C₇×#2357	C₂	1	1	yes	maximal, characteristic, complemented
3	C₇×#2349	C₂	1	1	yes	maximal, characteristic, complemented
4	C₇×#1936	C₂	1	2	yes	maximal, complemented
5	C₇×#1918	C₂	1	2	yes	maximal, complemented
6	C₇×#1879	C₂	1	2	yes	maximal
7	C₇×#1835	C₂	1	1	yes	maximal, characteristic, complemented
8	C₇×#1804	C₂	1	1	yes	maximal, characteristic, complemented
9	C₇×#1804	C₂	1	1	yes	maximal, characteristic, complemented
10	C₇×#1770	C₂	1	1	yes	maximal, characteristic, complemented
11	C₇×#1762	C₂	1	2	yes	maximal, complemented
12	C₂²×C₇×D₈	C₂²	1	1	yes	characteristic
13	C₂×C₄×C₇×D₄	C₂²	1	2	yes	—
14	C₂×C₄×C₇×D₄	C₂²	1	1	yes	characteristic
15	C₂×C₄×C₇×D₄	C₂²	1	1	yes	characteristic
16	C₄×C₇×D₈	C₄	1	8	yes	complemented
17	C₂×C₇×#107	C₂²	1	1	yes	characteristic
18	C₂×C₇×C₄⋊C₈	C₂²	1	1	yes	characteristic
19	C₂×C₇×#102	C₂²	1	2	yes	—
20	C₂×C₇×#102	C₂²	1	2	yes	—
21	C₂×C₇×#102	C₂²	1	1	yes	characteristic
22	C₂×C₇×#102	C₂²	1	1	yes	characteristic
23	C₂×C₇×#97	C₂²	1	2	yes	—
24	C₂×C₄×C₇×C₈	C₂²	1	1	yes	characteristic
25	C₇×#390	C₂²	1	2	yes	—
26	C₇×#389	C₂²	1	2	yes	—
27	C₇×#388	—	2	2	no	—
28	C₇×#385	—	2	2	no	—
29	C₇×#382	C₂²	1	1	yes	characteristic
30	C₇×#382	C₂²	1	1	yes	characteristic
31	C₇×#381	—	2	1	no	—
32	C₇×#380	—	2	1	no	—
33	C₄×C₇×C₄⋊C₄	C₂²	1	2	yes	—
34	C₄×C₇×C₄⋊C₄	C₂²	1	1	yes	characteristic
35	C₄×C₇×C₂²⋊C₄	—	2	1	no	—
36	C₂×C₇×#95	—	2	1	no	—
37	C₇×#340	C₂²	1	2	yes	—
38	C₇×#340	C₂²	1	2	yes	—
39	C₇×#340	C₂²	1	2	yes	—
40	C₇×#340	C₂²	1	2	yes	—
41	C₇×#336	C₂²	1	2	yes	—
42	#22764	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
43	C₂²×C₇×D₄	C₂³	1	1	yes	characteristic
44	C₂²×C₇×D₄	C₂³	1	1	yes	characteristic
45	C₂³×C₄×C₇	—	2	1	no	—
46	C₂³×C₄×C₇	—	2	1	no	—
47	C₂³×C₄×C₇	—	2	2	no	—
48	C₂×C₇×D₈	—	2	2	no	—
49	C₂×C₇×D₈	—	2	2	no	—
50	C₂×C₇×D₈	C₂×C₄	1	4	yes	—
51	C₂²×C₇×C₈	C₂³	1	2	yes	—
52	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
53	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
54	C₄×C₇×D₄	—	2	4	no	—
55	C₄×C₇×D₄	—	2	2	no	—
56	C₄×C₇×D₄	—	2	2	no	—
57	C₄×C₇×D₄	—	4	2	no	—
58	C₄×C₇×D₄	C₂×C₄	1	4	yes	—
59	C₄×C₇×D₄	C₂×C₄	1	4	yes	complemented
60	C₂×C₇×C₄⋊C₄	—	2	2	no	—
61	C₂×C₇×C₄⋊C₄	D₄	1	2	yes	—
62	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
63	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
64	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
65	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
66	C₂×C₇×C₂²⋊C₄	—	2	1	no	—
67	C₂×C₇×C₂²⋊C₄	—	2	1	no	—
68	C₂×C₇×C₂²⋊C₄	—	2	2	no	—
69	C₂×C₇×C₂²⋊C₄	—	2	2	no	—
70	C₂×C₇×C₂²⋊C₄	—	2	2	no	—
71	C₂×C₄²×C₇	—	2	2	no	—
72	C₂×C₄²×C₇	C₂³	1	2	yes	—
73	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
74	C₇×#107	C₂×C₄	1	4	yes	complemented
75	C₇×C₄⋊C₈	—	2	2	no	—
76	C₇×#102	—	2	4	no	—
77	C₇×#102	—	4	2	no	—
78	C₇×#102	C₂×C₄	1	4	yes	—
79	C₇×#102	C₂×C₄	1	4	yes	complemented
80	C₇×#97	—	4	2	no	—
81	C₄×C₇×C₈	C₂×C₄	1	4	yes	complemented
82	C₇×#95	—	2	1	no	—
83	C₇×#95	—	2	2	no	—
84	C₇×#95	—	2	1	no	—
85	C₇×#95	—	2	2	no	—
86	C₇×#95	—	2	1	no	—
87	C₇×#95	—	2	1	no	—
88	C₇×#95	D₄	1	1	yes	characteristic
89	C₇×#95	D₄	1	1	yes	characteristic
90	C₂×C₄×D₈	C₂×C₇	1	1	yes	characteristic
91	#2357	C₂×C₇	1	1	yes	characteristic, complemented
92	#2349	C₂×C₇	1	1	yes	characteristic, complemented
93	#1936	C₂×C₇	1	2	yes	complemented
94	#1918	C₂×C₇	1	2	yes	complemented
95	#1879	C₂×C₇	1	2	yes	—
96	#1835	C₂×C₇	1	1	yes	characteristic, complemented
97	#1804	C₂×C₇	1	1	yes	characteristic, complemented
98	#1804	C₂×C₇	1	1	yes	characteristic, complemented
99	#1770	C₂×C₇	1	1	yes	characteristic, complemented
100	#1762	C₂×C₇	1	2	yes	complemented
101	C₂⁴×C₇	—	2	1	no	—
102	C₂⁴×C₇	—	2	1	no	—
103	C₂×C₇×D₄	—	2	1	no	—
104	C₂×C₇×D₄	—	2	1	no	—
105	C₂×C₇×D₄	—	2	1	no	—
106	C₂×C₇×D₄	—	2	1	no	—
107	C₂×C₇×D₄	—	2	1	no	—
108	C₂×C₇×D₄	—	2	1	no	—
109	C₂×C₇×D₄	—	2	1	no	—
110	C₂×C₇×D₄	—	2	1	no	—
111	C₂×C₇×D₄	C₂²×C₄	1	2	yes	—
112	C₂×C₇×D₄	C₂²×C₄	1	2	yes	—
113	C₂×C₇×D₄	#41	1	2	yes	—
114	C₂×C₇×D₄	#41	1	2	yes	—
115	C₂²×C₄×C₇	—	2	1	no	—
116	C₂²×C₄×C₇	—	2	1	no	—
117	C₂²×C₄×C₇	—	2	4	no	—
118	C₂²×C₄×C₇	—	2	4	no	—
119	C₂²×C₄×C₇	—	2	2	no	—
120	C₂²×C₄×C₇	—	2	2	no	—
121	C₂²×C₄×C₇	—	4	4	no	—
122	C₂²×C₄×C₇	—	4	4	no	—
123	C₂²×C₄×C₇	—	8	2	no	—
124	C₂²×C₄×C₇	—	8	2	no	—
125	C₂²×C₄×C₇	—	8	2	no	—
126	C₂²×C₄×C₇	C₂×D₄	1	2	yes	—
127	C₂²×C₄×C₇	C₂×D₄	1	2	yes	—
128	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
129	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
130	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
131	C₇×D₈	—	2	8	no	—
132	C₂×C₇×C₈	—	2	1	no	—
133	C₂×C₇×C₈	—	2	1	no	—
134	C₂×C₇×C₈	—	2	1	no	—
135	C₂×C₇×C₈	—	2	1	no	—
136	C₂×C₇×C₈	—	2	2	no	—
137	C₂×C₇×C₈	—	2	2	no	—
138	C₂×C₇×C₈	—	2	2	no	—
139	C₂×C₇×C₈	C₂²×C₄	1	2	yes	—
140	C₂×C₇×C₈	C₂²×C₄	1	2	yes	—
141	C₇×C₄⋊C₄	—	2	1	no	—
142	C₇×C₄⋊C₄	—	2	1	no	—
143	C₇×C₄⋊C₄	—	2	2	no	—
144	C₇×C₄⋊C₄	—	2	2	no	—
145	C₇×C₄⋊C₄	—	2	2	no	—
146	C₇×C₄⋊C₄	—	2	2	no	—
147	C₇×C₄⋊C₄	—	4	2	no	—
148	C₇×C₄⋊C₄	—	8	2	no	—
149	C₇×C₄⋊C₄	C₂²×C₄	1	2	yes	—
150	C₇×C₄⋊C₄	C₂²×C₄	1	2	yes	—
151	C₇×C₂²⋊C₄	—	2	4	no	—
152	C₇×C₂²⋊C₄	—	2	4	no	—
153	C₇×C₂²⋊C₄	—	4	4	no	—
154	C₇×C₂²⋊C₄	—	4	4	no	—
155	C₇×C₂²⋊C₄	—	8	2	no	—
156	C₄²×C₇	—	2	2	no	—
157	C₄²×C₇	—	2	2	no	—
158	C₄²×C₇	—	8	2	no	—
159	C₄²×C₇	C₂²×C₄	1	2	yes	—
160	C₄²×C₇	#41	1	2	yes	—
161	C₂²×D₈	C₂²×C₇	1	1	yes	characteristic
162	C₂×C₄×D₄	C₂²×C₇	1	2	yes	—
163	C₂×C₄×D₄	C₂²×C₇	1	1	yes	characteristic
164	C₂×C₄×D₄	C₂²×C₇	1	1	yes	characteristic
165	C₄×D₈	C₄×C₇	1	8	yes	complemented
166	C₂×#107	C₂²×C₇	1	1	yes	characteristic
167	C₂×C₄⋊C₈	C₂²×C₇	1	1	yes	characteristic
168	C₂×#102	C₂²×C₇	1	2	yes	—
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×#97	C₂²×C₇	1	2	yes	—
173	C₂×C₄×C₈	C₂²×C₇	1	1	yes	characteristic
174	#390	C₂²×C₇	1	2	yes	—
175	#389	C₂²×C₇	1	2	yes	—
176	#388	—	2	2	no	—
177	#385	—	2	2	no	—
178	#382	C₂²×C₇	1	1	yes	characteristic
179	#382	C₂²×C₇	1	1	yes	characteristic
180	#381	—	2	1	no	—
181	#380	—	2	1	no	—
182	C₄×C₄⋊C₄	C₂²×C₇	1	2	yes	—
183	C₄×C₄⋊C₄	C₂²×C₇	1	1	yes	characteristic
184	C₄×C₂²⋊C₄	—	2	1	no	—
185	C₂×#95	—	2	1	no	—
186	#340	C₂²×C₇	1	2	yes	—
187	#340	C₂²×C₇	1	2	yes	—
188	#340	C₂²×C₇	1	2	yes	—
189	#340	C₂²×C₇	1	2	yes	—
190	#336	C₂²×C₇	1	2	yes	—
191	C₂³×C₇	—	2	2	no	—
192	C₂³×C₇	—	2	2	no	—
193	C₂³×C₇	—	2	2	no	—
194	C₂³×C₇	—	2	2	no	—
195	C₂³×C₇	—	4	2	no	—
196	C₂³×C₇	—	4	2	no	—
197	C₂³×C₇	—	4	1	no	—
198	C₂³×C₇	—	4	1	no	—
199	C₂³×C₇	—	4	2	no	—
200	C₂³×C₇	—	4	2	no	—
201	C₂³×C₇	C₂²×D₄	1	1	yes	characteristic
202	C₇×D₄	—	2	2	no	—
203	C₇×D₄	—	2	2	no	—
204	C₇×D₄	—	2	2	no	—
205	C₇×D₄	—	2	2	no	—
206	C₇×D₄	—	2	2	no	—
207	C₇×D₄	—	4	1	no	—
208	C₇×D₄	—	4	1	no	—
209	C₇×D₄	#117	1	4	yes	—
210	C₂×C₄×C₇	—	2	2	no	—
211	C₂×C₄×C₇	—	2	2	no	—
212	C₂×C₄×C₇	—	2	2	no	—
213	C₂×C₄×C₇	—	2	2	no	—
214	C₂×C₄×C₇	—	2	2	no	—
215	C₂×C₄×C₇	—	2	2	no	—
216	C₂×C₄×C₇	—	2	2	no	—
217	C₂×C₄×C₇	—	2	2	no	—
218	C₂×C₄×C₇	—	2	2	no	—
219	C₂×C₄×C₇	—	2	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	—	4	2	no	—
226	C₂×C₄×C₇	—	4	2	no	—
227	C₂×C₄×C₇	—	4	2	no	—
228	C₂×C₄×C₇	—	8	4	no	—
229	C₂×C₄×C₇	—	8	4	no	—
230	C₂×C₄×C₇	—	8	8	no	—
231	C₂×C₄×C₇	C₄×D₄	1	2	yes	—
232	C₂×C₄×C₇	C₄×D₄	1	2	yes	—
233	C₂×C₄×C₇	C₂³×C₄	1	1	yes	characteristic
234	C₂×C₄×C₇	C₂×#41	1	1	yes	characteristic
235	C₂×C₄×C₇	C₂×#41	1	1	yes	characteristic
236	C₂×C₄×C₇	C₂×#41	1	1	yes	characteristic
237	C₂×C₄×C₇	H(5,𝔽₂)	1	1	yes	characteristic
238	C₂×C₄×C₇	2₋¹⁺⁴	1	1	yes	characteristic
239	C₇×C₈	—	2	2	no	—
240	C₇×C₈	—	2	2	no	—
241	C₇×C₈	—	4	2	no	—
242	C₂²×D₄	C₂³×C₇	1	1	yes	characteristic
243	C₂²×D₄	C₂³×C₇	1	1	yes	characteristic
244	C₂³×C₄	—	2	1	no	—
245	C₂³×C₄	—	2	1	no	—
246	C₂³×C₄	—	2	2	no	—
247	C₂×D₈	—	2	2	no	—
248	C₂×D₈	—	2	2	no	—
249	C₂×D₈	C₂×C₄×C₇	1	4	yes	—
250	C₂²×C₈	C₂³×C₇	1	2	yes	—
251	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
252	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
253	C₄×D₄	—	2	4	no	—
254	C₄×D₄	—	2	2	no	—
255	C₄×D₄	—	2	2	no	—
256	C₄×D₄	—	4	2	no	—
257	C₄×D₄	C₂×C₄×C₇	1	4	yes	—
258	C₄×D₄	C₂×C₄×C₇	1	4	yes	complemented
259	C₂×C₄⋊C₄	—	2	2	no	—
260	C₂×C₄⋊C₄	C₇×D₄	1	2	yes	—
261	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
262	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
263	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
264	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
265	C₂×C₂²⋊C₄	—	2	1	no	—
266	C₂×C₂²⋊C₄	—	2	1	no	—
267	C₂×C₂²⋊C₄	—	2	2	no	—
268	C₂×C₂²⋊C₄	—	2	2	no	—
269	C₂×C₂²⋊C₄	—	2	2	no	—
270	C₂×C₄²	—	2	2	no	—
271	C₂×C₄²	C₂³×C₇	1	2	yes	—
272	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
273	#107	C₂×C₄×C₇	1	4	yes	complemented
274	C₄⋊C₈	—	2	2	no	—
275	#102	—	2	4	no	—
276	#102	—	4	2	no	—
277	#102	C₂×C₄×C₇	1	4	yes	—
278	#102	C₂×C₄×C₇	1	4	yes	complemented
279	#97	—	4	2	no	—
280	C₄×C₈	C₂×C₄×C₇	1	4	yes	complemented
281	#95	—	2	1	no	—
282	#95	—	2	2	no	—
283	#95	—	2	1	no	—
284	#95	—	2	2	no	—
285	#95	—	2	1	no	—
286	#95	—	2	1	no	—
287	#95	C₇×D₄	1	1	yes	characteristic
288	#95	C₇×D₄	1	1	yes	characteristic
289	C₂²×C₇	—	2	4	no	—
290	C₂²×C₇	—	4	4	no	—
291	C₂²×C₇	—	4	2	no	—
292	C₂²×C₇	—	4	2	no	—
293	C₂²×C₇	—	4	4	no	—
294	C₂²×C₇	—	4	2	no	—
295	C₂²×C₇	—	4	2	no	—
296	C₂²×C₇	—	4	2	no	—
297	C₂²×C₇	—	8	2	no	—
298	C₂²×C₇	—	8	2	no	—
299	C₂²×C₇	C₂×C₄×D₄	1	1	yes	characteristic
300	C₂²×C₇	#546	1	1	yes	characteristic
301	C₂²×C₇	#548	1	1	yes	characteristic
302	C₂²×C₇	#575	1	2	yes	—
303	C₂²×C₇	#576	1	2	yes	—
304	C₄×C₇	—	2	2	no	—
305	C₄×C₇	—	2	2	no	—
306	C₄×C₇	—	4	2	no	—
307	C₄×C₇	—	4	2	no	—
308	C₄×C₇	—	4	2	no	—
309	C₄×C₇	—	4	2	no	—
310	C₄×C₇	—	8	2	no	—
311	C₄×C₇	—	8	2	no	—
312	C₄×C₇	C₂×#117	1	1	yes	characteristic
313	C₄×C₇	#520	1	1	yes	characteristic
314	C₄×C₇	#552	1	1	yes	characteristic
315	C₄×C₇	#553	1	1	yes	characteristic
316	C₂⁴	—	2	1	no	—
317	C₂⁴	—	2	1	no	—
318	C₂×D₄	—	2	1	no	—
319	C₂×D₄	—	2	1	no	—
320	C₂×D₄	—	2	1	no	—
321	C₂×D₄	—	2	1	no	—
322	C₂×D₄	—	2	1	no	—
323	C₂×D₄	—	2	1	no	—
324	C₂×D₄	—	2	1	no	—
325	C₂×D₄	—	2	1	no	—
326	C₂×D₄	C₂²×C₄×C₇	1	2	yes	—
327	C₂×D₄	C₂²×C₄×C₇	1	2	yes	—
328	C₂×D₄	C₇×#41	1	2	yes	—
329	C₂×D₄	C₇×#41	1	2	yes	—
330	C₂²×C₄	—	2	1	no	—
331	C₂²×C₄	—	2	1	no	—
332	C₂²×C₄	—	2	4	no	—
333	C₂²×C₄	—	2	4	no	—
334	C₂²×C₄	—	2	2	no	—
335	C₂²×C₄	—	2	2	no	—
336	C₂²×C₄	—	4	4	no	—
337	C₂²×C₄	—	4	4	no	—
338	C₂²×C₄	—	8	2	no	—
339	C₂²×C₄	—	8	2	no	—
340	C₂²×C₄	—	8	2	no	—
341	C₂²×C₄	C₂×C₇×D₄	1	2	yes	—
342	C₂²×C₄	C₂×C₇×D₄	1	2	yes	—
343	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
344	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
345	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
346	D₈	—	2	8	no	—
347	C₂×C₈	—	2	1	no	—
348	C₂×C₈	—	2	1	no	—
349	C₂×C₈	—	2	1	no	—
350	C₂×C₈	—	2	1	no	—
351	C₂×C₈	—	2	2	no	—
352	C₂×C₈	—	2	2	no	—
353	C₂×C₈	—	2	2	no	—
354	C₂×C₈	C₂²×C₄×C₇	1	2	yes	—
355	C₂×C₈	C₂²×C₄×C₇	1	2	yes	—
356	C₄⋊C₄	—	2	1	no	—
357	C₄⋊C₄	—	2	1	no	—
358	C₄⋊C₄	—	2	2	no	—
359	C₄⋊C₄	—	2	2	no	—
360	C₄⋊C₄	—	2	2	no	—
361	C₄⋊C₄	—	2	2	no	—
362	C₄⋊C₄	—	4	2	no	—
363	C₄⋊C₄	—	8	2	no	—
364	C₄⋊C₄	C₂²×C₄×C₇	1	2	yes	—
365	C₄⋊C₄	C₂²×C₄×C₇	1	2	yes	—
366	C₂²⋊C₄	—	2	4	no	—
367	C₂²⋊C₄	—	2	4	no	—
368	C₂²⋊C₄	—	4	4	no	—
369	C₂²⋊C₄	—	4	4	no	—
370	C₂²⋊C₄	—	8	2	no	—
371	C₄²	—	2	2	no	—
372	C₄²	—	2	2	no	—
373	C₄²	—	8	2	no	—
374	C₄²	C₂²×C₄×C₇	1	2	yes	—
375	C₄²	C₇×#41	1	2	yes	—
376	C₂×C₇	—	4	4	no	—
377	C₂×C₇	—	8	2	no	—
378	C₂×C₇	#2352	1	1	yes	characteristic
379	C₂×C₇	#2943	1	1	yes	characteristic
380	C₂×C₇	#2948	1	1	yes	characteristic
381	C₂×C₇	#3322	1	2	yes	—
382	C₂×C₇	#3370	1	2	yes	—
383	C₂³	—	2	2	no	—
384	C₂³	—	2	2	no	—
385	C₂³	—	2	2	no	—
386	C₂³	—	2	2	no	—
387	C₂³	—	4	2	no	—
388	C₂³	—	4	2	no	—
389	C₂³	—	4	1	no	—
390	C₂³	—	4	1	no	—
391	C₂³	—	4	2	no	—
392	C₂³	—	4	2	no	—
393	C₂³	C₂²×C₇×D₄	1	1	yes	characteristic
394	D₄	—	2	2	no	—
395	D₄	—	2	2	no	—
396	D₄	—	2	2	no	—
397	D₄	—	2	2	no	—
398	D₄	—	2	2	no	—
399	D₄	—	4	1	no	—
400	D₄	—	4	1	no	—
401	D₄	C₇×#117	1	4	yes	—
402	C₂×C₄	—	2	2	no	—
403	C₂×C₄	—	2	2	no	—
404	C₂×C₄	—	2	2	no	—
405	C₂×C₄	—	2	2	no	—
406	C₂×C₄	—	2	2	no	—
407	C₂×C₄	—	2	2	no	—
408	C₂×C₄	—	2	2	no	—
409	C₂×C₄	—	2	2	no	—
410	C₂×C₄	—	2	2	no	—
411	C₂×C₄	—	2	2	no	—
412	C₂×C₄	—	4	2	no	—
413	C₂×C₄	—	4	2	no	—
414	C₂×C₄	—	4	2	no	—
415	C₂×C₄	—	4	2	no	—
416	C₂×C₄	—	4	2	no	—
417	C₂×C₄	—	4	2	no	—
418	C₂×C₄	—	4	2	no	—
419	C₂×C₄	—	4	2	no	—
420	C₂×C₄	—	8	4	no	—
421	C₂×C₄	—	8	4	no	—
422	C₂×C₄	—	8	8	no	—
423	C₂×C₄	C₄×C₇×D₄	1	2	yes	—
424	C₂×C₄	C₄×C₇×D₄	1	2	yes	—
425	C₂×C₄	C₂³×C₄×C₇	1	1	yes	characteristic
426	C₂×C₄	C₂×C₇×#41	1	1	yes	characteristic
427	C₂×C₄	C₂×C₇×#41	1	1	yes	characteristic
428	C₂×C₄	C₂×C₇×#41	1	1	yes	characteristic
429	C₂×C₄	C₇×H(5,𝔽₂)	1	1	yes	characteristic
430	C₂×C₄	C₇×2₋¹⁺⁴	1	1	yes	characteristic
431	C₈	—	2	2	no	—
432	C₈	—	2	2	no	—
433	C₈	—	4	2	no	—
434	C₇	#22764	1	1	yes	characteristic, direct product factor, Sylow
435	C₂²	—	2	4	no	—
436	C₂²	—	4	2	no	—
437	C₂²	—	4	2	no	—
438	C₂²	—	4	4	no	—
439	C₂²	—	4	4	no	—
440	C₂²	—	4	2	no	—
441	C₂²	—	4	2	no	—
442	C₂²	—	4	2	no	—
443	C₂²	—	8	2	no	—
444	C₂²	—	8	2	no	—
445	C₂²	C₂×C₄×C₇×D₄	1	1	yes	characteristic
446	C₂²	C₇×#546	1	1	yes	characteristic
447	C₂²	C₇×#548	1	1	yes	characteristic
448	C₂²	C₇×#575	1	2	yes	—
449	C₂²	C₇×#576	1	2	yes	—
450	C₄	—	2	2	no	—
451	C₄	—	2	2	no	—
452	C₄	—	4	2	no	—
453	C₄	—	4	2	no	—
454	C₄	—	4	2	no	—
455	C₄	—	4	2	no	—
456	C₄	—	8	2	no	—
457	C₄	—	8	2	no	—
458	C₄	C₂×C₇×#117	1	1	yes	characteristic
459	C₄	C₇×#520	1	1	yes	characteristic
460	C₄	C₇×#552	1	1	yes	characteristic
461	C₄	C₇×#553	1	1	yes	characteristic
462	C₂	—	4	4	no	—
463	C₂	—	8	2	no	—
464	C₂	C₇×#2352	1	1	yes	characteristic
465	C₂	C₇×#2943	1	1	yes	characteristic
466	C₂	C₇×#2948	1	1	yes	characteristic
467	C₂	C₇×#3322	1	2	yes	—
468	C₂	C₇×#3370	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₇	C₂²×D₄
commutator	C₂×C₄	C₂³×C₄×C₇
Frattini, cosocle	C₂²×C₄	C₂⁴×C₇
prime radical	C₂²×C₇×D₈	C₂²
LCS	G ▷ C₂×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×#2357	C₂	semidirect
3. C₇×#2349	C₂	semidirect
4. C₇×#1936	C₂	semidirect
5. C₇×#1918	C₂	semidirect
7. C₇×#1835	C₂	semidirect
8. C₇×#1804	C₂	semidirect
9. C₇×#1804	C₂	semidirect
10. C₇×#1770	C₂	semidirect
11. C₇×#1762	C₂	semidirect
16. C₄×C₇×D₈	C₄	semidirect
42. #22764	C₇	direct (N × H)
59. C₄×C₇×D₄	C₂×C₄	semidirect
74. C₇×#107	C₂×C₄	semidirect
79. C₇×#102	C₂×C₄	semidirect
81. C₄×C₇×C₈	C₂×C₄	semidirect
91. #2357	C₂×C₇	semidirect
92. #2349	C₂×C₇	semidirect
93. #1936	C₂×C₇	semidirect
94. #1918	C₂×C₇	semidirect
96. #1835	C₂×C₇	semidirect
97. #1804	C₂×C₇	semidirect
98. #1804	C₂×C₇	semidirect
99. #1770	C₂×C₇	semidirect
100. #1762	C₂×C₇	semidirect
165. C₄×D₈	C₄×C₇	semidirect
258. C₄×D₄	C₂×C₄×C₇	semidirect
273. #107	C₂×C₄×C₇	semidirect
278. #102	C₂×C₄×C₇	semidirect
280. C₄×C₈	C₂×C₄×C₇	semidirect
434. C₇	#22764	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×C₄×C₇×D₈	2
C₇×#2357	2
C₇×#2349	2
C₇×#1936	2
C₇×#1918	2
C₇×#1879	2
C₇×#1835	2
C₇×#1804	2
C₇×#1770	2
C₇×#1762	2
#22764	7

Subgroups — C7×#22764 #13199980

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×#22764 #13199980