Subgroups — C₇×#21541 #13198757

Order 1792.

1066 conjugacy classes of subgroups.

The subgroup lattice has 478 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₇×#469	C₂	1	1	yes	maximal, characteristic
2	C₂×C₇×#442	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₇×#405	C₂	1	1	yes	maximal, characteristic, complemented
4	C₇×#2324	C₂	1	2	yes	maximal, complemented
5	C₇×#1970	C₂	1	1	yes	maximal, characteristic, complemented
6	C₇×#1941	C₂	1	1	yes	maximal, characteristic, complemented
7	C₇×#1936	C₂	1	2	yes	maximal, complemented
8	C₇×#1893	C₂	1	2	yes	maximal, complemented
9	C₇×#1809	C₂	1	1	yes	maximal, characteristic, complemented
10	C₇×#1776	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄×C₇×#102	C₂	1	2	yes	maximal, complemented
12	C₂²×C₇×D₈	C₂²	1	1	yes	characteristic
13	C₂²×C₇×M₁₆	C₂²	1	1	yes	characteristic
14	C₂³×C₇×C₈	C₂²	1	1	yes	characteristic
15	C₂×C₇×#121	C₂²	1	2	yes	—
16	C₂×C₄×C₇×D₄	C₂²	1	2	yes	—
17	C₂×C₇×#117	C₂²	1	1	yes	characteristic
18	C₇×#469	C₄	1	8	yes	complemented
19	C₇×#442	—	2	4	no	—
20	C₂×C₇×#107	C₂²	1	1	yes	characteristic
21	C₂×C₇×#106	C₂²	1	1	yes	characteristic
22	C₂×C₇×#106	C₂²	1	1	yes	characteristic
23	C₂×C₇×#102	C₂²	1	2	yes	—
24	C₂×C₇×#102	C₂²	1	2	yes	—
25	C₂×C₇×#102	C₂²	1	2	yes	—
26	C₇×#405	—	2	4	no	—
27	C₂×C₇×#97	C₂²	1	1	yes	characteristic
28	C₂×C₇×#97	C₂²	1	1	yes	characteristic
29	C₂×C₄×C₇×C₈	C₂²	1	1	yes	characteristic
30	C₂×C₄×C₇×C₈	C₂²	1	1	yes	characteristic
31	C₇×#390	—	2	2	no	—
32	C₇×#390	C₂²	1	2	yes	—
33	C₇×#389	C₂²	1	2	yes	—
34	C₇×#388	—	2	2	no	—
35	C₇×#386	—	2	2	no	—
36	C₇×#385	—	2	2	no	—
37	C₇×#380	C₂²	1	2	yes	—
38	C₄×C₇×C₄⋊C₄	C₂²	1	2	yes	—
39	C₇×#340	C₂²	1	2	yes	—
40	C₇×#340	C₂²	1	2	yes	—
41	C₇×#340	C₂²	1	2	yes	—
42	#21541	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
43	C₂²×C₇×D₄	—	2	2	no	—
44	C₂²×C₇×D₄	C₂³	1	2	yes	—
45	C₂³×C₄×C₇	—	2	2	no	—
46	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
47	C₂×C₇×D₈	—	2	2	no	—
48	C₂×C₇×D₈	—	2	2	no	—
49	C₂×C₇×D₈	C₂×C₄	1	4	yes	—
50	C₂×C₇×M₁₆	—	2	2	no	—
51	C₂×C₇×M₁₆	—	2	2	no	—
52	C₂×C₇×M₁₆	C₂×C₄	1	4	yes	complemented
53	C₂²×C₇×C₈	—	2	2	no	—
54	C₂²×C₇×C₈	—	2	2	no	—
55	C₂²×C₇×C₈	—	2	2	no	—
56	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
57	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
58	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
59	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
60	C₇×#121	—	2	4	no	—
61	C₇×#121	C₂×C₄	1	8	yes	complemented
62	C₄×C₇×D₄	—	2	4	no	—
63	C₄×C₇×D₄	—	2	4	no	—
64	C₇×#117	—	2	2	no	—
65	C₇×#117	—	2	2	no	—
66	C₂×C₇×C₄⋊C₄	—	2	2	no	—
67	C₂×C₇×C₄⋊C₄	D₄	1	2	yes	—
68	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
69	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
70	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
71	C₂×C₇×C₂²⋊C₄	—	2	2	no	—
72	C₂×C₇×C₂²⋊C₄	—	2	2	no	—
73	C₂×C₇×C₂²⋊C₄	—	2	2	no	—
74	C₂×C₇×C₂²⋊C₄	—	2	2	no	—
75	C₂×C₇×C₂²⋊C₄	—	2	2	no	—
76	C₂×C₇×C₂²⋊C₄	D₄	1	2	yes	—
77	C₂×C₄²×C₇	—	2	2	no	—
78	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
79	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
80	C₇×#107	—	2	2	no	—
81	C₇×#106	—	2	2	no	—
82	C₇×#106	C₂×C₄	1	4	yes	complemented
83	C₇×#102	—	2	4	no	—
84	C₇×#102	—	2	4	no	—
85	C₇×#102	C₂×C₄	1	8	yes	complemented
86	C₇×#97	—	2	2	no	—
87	C₇×#97	D₄	1	4	yes	complemented
88	C₄×C₇×C₈	—	2	2	no	—
89	C₄×C₇×C₈	—	2	2	no	—
90	C₇×#95	—	2	2	no	—
91	C₇×#95	—	2	2	no	—
92	C₇×#95	—	2	2	no	—
93	C₂×#469	C₂×C₇	1	1	yes	characteristic
94	C₂×#442	C₂×C₇	1	1	yes	characteristic, complemented
95	C₂×#405	C₂×C₇	1	1	yes	characteristic, complemented
96	#2324	C₂×C₇	1	2	yes	complemented
97	#1970	C₂×C₇	1	1	yes	characteristic, complemented
98	#1941	C₂×C₇	1	1	yes	characteristic, complemented
99	#1936	C₂×C₇	1	2	yes	complemented
100	#1893	C₂×C₇	1	2	yes	complemented
101	#1809	C₂×C₇	1	1	yes	characteristic, complemented
102	#1776	C₂×C₇	1	1	yes	characteristic, complemented
103	C₄×#102	C₂×C₇	1	2	yes	complemented
104	C₂⁴×C₇	—	2	2	no	—
105	C₂⁴×C₇	C₂×D₄	1	1	yes	characteristic
106	C₂×C₇×D₄	—	2	8	no	—
107	C₂×C₇×D₄	—	2	2	no	—
108	C₂×C₇×D₄	—	2	2	no	—
109	C₂×C₇×D₄	—	2	2	no	—
110	C₂×C₇×D₄	—	2	2	no	—
111	C₂×C₇×D₄	—	2	2	no	—
112	C₂×C₇×D₄	—	8	2	no	—
113	C₂×C₇×D₄	—	8	2	no	—
114	C₂×C₇×D₄	C₂²×C₄	1	4	yes	—
115	C₂²×C₄×C₇	—	2	1	no	—
116	C₂²×C₄×C₇	—	2	1	no	—
117	C₂²×C₄×C₇	—	2	1	no	—
118	C₂²×C₄×C₇	—	2	1	no	—
119	C₂²×C₄×C₇	—	2	2	no	—
120	C₂²×C₄×C₇	—	2	2	no	—
121	C₂²×C₄×C₇	—	2	2	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	C₂²×C₄	1	2	yes	—
126	C₂²×C₄×C₇	C₂×D₄	1	2	yes	—
127	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
128	C₂²×C₄×C₇	C₂×D₄	1	2	yes	—
129	C₂²×C₄×C₇	#41	1	2	yes	—
130	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
131	C₇×D₈	—	2	8	no	—
132	C₇×M₁₆	—	2	8	no	—
133	C₂×C₇×C₈	—	2	8	no	—
134	C₂×C₇×C₈	—	2	1	no	—
135	C₂×C₇×C₈	—	2	1	no	—
136	C₂×C₇×C₈	—	2	1	no	—
137	C₂×C₇×C₈	—	2	1	no	—
138	C₂×C₇×C₈	—	2	1	no	—
139	C₂×C₇×C₈	—	2	1	no	—
140	C₂×C₇×C₈	C₂²×C₄	1	2	yes	—
141	C₂×C₇×C₈	C₂²×C₄	1	2	yes	—
142	C₂×C₇×C₈	C₂×D₄	1	2	yes	—
143	C₂×C₇×C₈	C₂×D₄	1	2	yes	—
144	C₂×C₇×C₈	#41	1	2	yes	—
145	C₂×C₇×C₈	#41	1	2	yes	—
146	C₇×C₄⋊C₄	—	2	4	no	—
147	C₇×C₄⋊C₄	—	2	2	no	—
148	C₇×C₄⋊C₄	—	2	2	no	—
149	C₇×C₄⋊C₄	—	2	2	no	—
150	C₇×C₄⋊C₄	—	2	2	no	—
151	C₇×C₄⋊C₄	—	2	2	no	—
152	C₇×C₄⋊C₄	—	8	2	no	—
153	C₇×C₄⋊C₄	C₂²×C₄	1	4	yes	—
154	C₇×C₂²⋊C₄	—	2	8	no	—
155	C₇×C₂²⋊C₄	—	2	4	no	—
156	C₇×C₂²⋊C₄	—	4	4	no	—
157	C₇×C₂²⋊C₄	—	8	2	no	—
158	C₇×C₂²⋊C₄	—	8	2	no	—
159	C₇×C₂²⋊C₄	—	8	2	no	—
160	C₄²×C₇	—	2	1	no	—
161	C₄²×C₇	—	2	1	no	—
162	C₄²×C₇	—	8	2	no	—
163	C₄²×C₇	C₂×D₄	1	2	yes	—
164	C₄²×C₇	#41	1	2	yes	—
165	C₂²×D₈	C₂²×C₇	1	1	yes	characteristic
166	C₂²×M₁₆	C₂²×C₇	1	1	yes	characteristic
167	C₂³×C₈	C₂²×C₇	1	1	yes	characteristic
168	C₂×#121	C₂²×C₇	1	2	yes	—
169	C₂×C₄×D₄	C₂²×C₇	1	2	yes	—
170	C₂×#117	C₂²×C₇	1	1	yes	characteristic
171	#469	C₄×C₇	1	8	yes	complemented
172	#442	—	2	4	no	—
173	C₂×#107	C₂²×C₇	1	1	yes	characteristic
174	C₂×#106	C₂²×C₇	1	1	yes	characteristic
175	C₂×#106	C₂²×C₇	1	1	yes	characteristic
176	C₂×#102	C₂²×C₇	1	2	yes	—
177	C₂×#102	C₂²×C₇	1	2	yes	—
178	C₂×#102	C₂²×C₇	1	2	yes	—
179	#405	—	2	4	no	—
180	C₂×#97	C₂²×C₇	1	1	yes	characteristic
181	C₂×#97	C₂²×C₇	1	1	yes	characteristic
182	C₂×C₄×C₈	C₂²×C₇	1	1	yes	characteristic
183	C₂×C₄×C₈	C₂²×C₇	1	1	yes	characteristic
184	#390	—	2	2	no	—
185	#390	C₂²×C₇	1	2	yes	—
186	#389	C₂²×C₇	1	2	yes	—
187	#388	—	2	2	no	—
188	#386	—	2	2	no	—
189	#385	—	2	2	no	—
190	#380	C₂²×C₇	1	2	yes	—
191	C₄×C₄⋊C₄	C₂²×C₇	1	2	yes	—
192	#340	C₂²×C₇	1	2	yes	—
193	#340	C₂²×C₇	1	2	yes	—
194	#340	C₂²×C₇	1	2	yes	—
195	C₂³×C₇	—	2	1	no	—
196	C₂³×C₇	—	2	1	no	—
197	C₂³×C₇	—	2	2	no	—
198	C₂³×C₇	—	2	2	no	—
199	C₂³×C₇	—	2	4	no	—
200	C₂³×C₇	—	4	2	no	—
201	C₂³×C₇	—	4	2	no	—
202	C₂³×C₇	—	4	2	no	—
203	C₂³×C₇	—	4	2	no	—
204	C₂³×C₇	—	4	2	no	—
205	C₂³×C₇	—	4	2	no	—
206	C₂³×C₇	C₄×D₄	1	2	yes	—
207	C₂³×C₇	C₂²×D₄	1	1	yes	characteristic
208	C₇×D₄	—	2	4	no	—
209	C₇×D₄	—	2	4	no	—
210	C₇×D₄	—	4	2	no	—
211	C₇×D₄	—	4	2	no	—
212	C₇×D₄	—	8	8	no	—
213	C₂×C₄×C₇	—	2	1	no	—
214	C₂×C₄×C₇	—	2	1	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	—	2	2	no	—
221	C₂×C₄×C₇	—	2	4	no	—
222	C₂×C₄×C₇	—	2	2	no	—
223	C₂×C₄×C₇	—	2	2	no	—
224	C₂×C₄×C₇	—	2	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	—	4	2	no	—
229	C₂×C₄×C₇	—	4	2	no	—
230	C₂×C₄×C₇	—	4	2	no	—
231	C₂×C₄×C₇	—	4	2	no	—
232	C₂×C₄×C₇	—	4	2	no	—
233	C₂×C₄×C₇	—	8	8	no	—
234	C₂×C₄×C₇	C₄×D₄	1	2	yes	—
235	C₂×C₄×C₇	#121	1	4	yes	—
236	C₂×C₄×C₇	C₂³×C₄	1	1	yes	characteristic
237	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
238	C₂×C₄×C₇	C₂×#41	1	1	yes	characteristic
239	C₂×C₄×C₇	C₂×#41	1	1	yes	characteristic
240	C₂×C₄×C₇	C₂×#41	1	1	yes	characteristic
241	C₂×C₄×C₇	C₂×#41	1	1	yes	characteristic
242	C₇×C₈	—	2	2	no	—
243	C₇×C₈	—	2	2	no	—
244	C₇×C₈	—	2	2	no	—
245	C₇×C₈	C₄×D₄	1	4	yes	—
246	C₂²×D₄	—	2	2	no	—
247	C₂²×D₄	C₂³×C₇	1	2	yes	—
248	C₂³×C₄	—	2	2	no	—
249	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
250	C₂×D₈	—	2	2	no	—
251	C₂×D₈	—	2	2	no	—
252	C₂×D₈	C₂×C₄×C₇	1	4	yes	—
253	C₂×M₁₆	—	2	2	no	—
254	C₂×M₁₆	—	2	2	no	—
255	C₂×M₁₆	C₂×C₄×C₇	1	4	yes	complemented
256	C₂²×C₈	—	2	2	no	—
257	C₂²×C₈	—	2	2	no	—
258	C₂²×C₈	—	2	2	no	—
259	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
260	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
261	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
262	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
263	#121	—	2	4	no	—
264	#121	C₂×C₄×C₇	1	8	yes	complemented
265	C₄×D₄	—	2	4	no	—
266	C₄×D₄	—	2	4	no	—
267	#117	—	2	2	no	—
268	#117	—	2	2	no	—
269	C₂×C₄⋊C₄	—	2	2	no	—
270	C₂×C₄⋊C₄	C₇×D₄	1	2	yes	—
271	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
272	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
273	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
274	C₂×C₂²⋊C₄	—	2	2	no	—
275	C₂×C₂²⋊C₄	—	2	2	no	—
276	C₂×C₂²⋊C₄	—	2	2	no	—
277	C₂×C₂²⋊C₄	—	2	2	no	—
278	C₂×C₂²⋊C₄	—	2	2	no	—
279	C₂×C₂²⋊C₄	C₇×D₄	1	2	yes	—
280	C₂×C₄²	—	2	2	no	—
281	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
282	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
283	#107	—	2	2	no	—
284	#106	—	2	2	no	—
285	#106	C₂×C₄×C₇	1	4	yes	complemented
286	#102	—	2	4	no	—
287	#102	—	2	4	no	—
288	#102	C₂×C₄×C₇	1	8	yes	complemented
289	#97	—	2	2	no	—
290	#97	C₇×D₄	1	4	yes	complemented
291	C₄×C₈	—	2	2	no	—
292	C₄×C₈	—	2	2	no	—
293	#95	—	2	2	no	—
294	#95	—	2	2	no	—
295	#95	—	2	2	no	—
296	C₂²×C₇	—	2	4	no	—
297	C₂²×C₇	—	2	2	no	—
298	C₂²×C₇	—	4	1	no	—
299	C₂²×C₇	—	4	1	no	—
300	C₂²×C₇	—	4	2	no	—
301	C₂²×C₇	—	4	4	no	—
302	C₂²×C₇	—	4	4	no	—
303	C₂²×C₇	—	4	4	no	—
304	C₂²×C₇	—	8	2	no	—
305	C₂²×C₇	—	8	2	no	—
306	C₂²×C₇	—	8	2	no	—
307	C₂²×C₇	—	8	2	no	—
308	C₂²×C₇	C₂×C₄×D₄	1	1	yes	characteristic
309	C₂²×C₇	C₂×#121	1	1	yes	characteristic
310	C₂²×C₇	#532	1	1	yes	characteristic
311	C₂²×C₇	#576	1	2	yes	—
312	C₂²×C₇	#577	1	2	yes	—
313	C₄×C₇	—	2	4	no	—
314	C₄×C₇	—	2	2	no	—
315	C₄×C₇	—	4	4	no	—
316	C₄×C₇	—	4	2	no	—
317	C₄×C₇	—	8	2	no	—
318	C₄×C₇	—	8	2	no	—
319	C₄×C₇	C₂×C₄×D₄	1	1	yes	characteristic
320	C₄×C₇	C₄×#41	1	1	yes	characteristic
321	C₄×C₇	#525	1	1	yes	characteristic
322	C₄×C₇	#529	1	1	yes	characteristic
323	C₂⁴	—	2	2	no	—
324	C₂⁴	C₂×C₇×D₄	1	1	yes	characteristic
325	C₂×D₄	—	2	8	no	—
326	C₂×D₄	—	2	2	no	—
327	C₂×D₄	—	2	2	no	—
328	C₂×D₄	—	2	2	no	—
329	C₂×D₄	—	2	2	no	—
330	C₂×D₄	—	2	2	no	—
331	C₂×D₄	—	8	2	no	—
332	C₂×D₄	—	8	2	no	—
333	C₂×D₄	C₂²×C₄×C₇	1	4	yes	—
334	C₂²×C₄	—	2	1	no	—
335	C₂²×C₄	—	2	1	no	—
336	C₂²×C₄	—	2	1	no	—
337	C₂²×C₄	—	2	1	no	—
338	C₂²×C₄	—	2	2	no	—
339	C₂²×C₄	—	2	2	no	—
340	C₂²×C₄	—	2	2	no	—
341	C₂²×C₄	—	4	4	no	—
342	C₂²×C₄	—	8	2	no	—
343	C₂²×C₄	—	8	2	no	—
344	C₂²×C₄	C₂²×C₄×C₇	1	2	yes	—
345	C₂²×C₄	C₂×C₇×D₄	1	2	yes	—
346	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
347	C₂²×C₄	C₂×C₇×D₄	1	2	yes	—
348	C₂²×C₄	C₇×#41	1	2	yes	—
349	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
350	D₈	—	2	8	no	—
351	M₁₆	—	2	8	no	—
352	C₂×C₈	—	2	8	no	—
353	C₂×C₈	—	2	1	no	—
354	C₂×C₈	—	2	1	no	—
355	C₂×C₈	—	2	1	no	—
356	C₂×C₈	—	2	1	no	—
357	C₂×C₈	—	2	1	no	—
358	C₂×C₈	—	2	1	no	—
359	C₂×C₈	C₂²×C₄×C₇	1	2	yes	—
360	C₂×C₈	C₂²×C₄×C₇	1	2	yes	—
361	C₂×C₈	C₂×C₇×D₄	1	2	yes	—
362	C₂×C₈	C₂×C₇×D₄	1	2	yes	—
363	C₂×C₈	C₇×#41	1	2	yes	—
364	C₂×C₈	C₇×#41	1	2	yes	—
365	C₄⋊C₄	—	2	4	no	—
366	C₄⋊C₄	—	2	2	no	—
367	C₄⋊C₄	—	2	2	no	—
368	C₄⋊C₄	—	2	2	no	—
369	C₄⋊C₄	—	2	2	no	—
370	C₄⋊C₄	—	2	2	no	—
371	C₄⋊C₄	—	8	2	no	—
372	C₄⋊C₄	C₂²×C₄×C₇	1	4	yes	—
373	C₂²⋊C₄	—	2	8	no	—
374	C₂²⋊C₄	—	2	4	no	—
375	C₂²⋊C₄	—	4	4	no	—
376	C₂²⋊C₄	—	8	2	no	—
377	C₂²⋊C₄	—	8	2	no	—
378	C₂²⋊C₄	—	8	2	no	—
379	C₄²	—	2	1	no	—
380	C₄²	—	2	1	no	—
381	C₄²	—	8	2	no	—
382	C₄²	C₂×C₇×D₄	1	2	yes	—
383	C₄²	C₇×#41	1	2	yes	—
384	C₂×C₇	—	4	2	no	—
385	C₂×C₇	—	8	4	no	—
386	C₂×C₇	C₄×#121	1	1	yes	characteristic
387	C₂×C₇	#2946	1	2	yes	—
388	C₂×C₇	#3062	1	2	yes	—
389	C₂×C₇	#3173	1	1	yes	characteristic
390	C₂×C₇	#3176	1	1	yes	characteristic
391	C₂³	—	2	1	no	—
392	C₂³	—	2	1	no	—
393	C₂³	—	2	2	no	—
394	C₂³	—	2	2	no	—
395	C₂³	—	2	4	no	—
396	C₂³	—	4	2	no	—
397	C₂³	—	4	2	no	—
398	C₂³	—	4	2	no	—
399	C₂³	—	4	2	no	—
400	C₂³	—	4	2	no	—
401	C₂³	—	4	2	no	—
402	C₂³	C₄×C₇×D₄	1	2	yes	—
403	C₂³	C₂²×C₇×D₄	1	1	yes	characteristic
404	D₄	—	2	4	no	—
405	D₄	—	2	4	no	—
406	D₄	—	4	2	no	—
407	D₄	—	4	2	no	—
408	D₄	—	8	8	no	—
409	C₂×C₄	—	2	1	no	—
410	C₂×C₄	—	2	1	no	—
411	C₂×C₄	—	2	2	no	—
412	C₂×C₄	—	2	2	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	4	no	—
418	C₂×C₄	—	2	2	no	—
419	C₂×C₄	—	2	2	no	—
420	C₂×C₄	—	2	2	no	—
421	C₂×C₄	—	4	2	no	—
422	C₂×C₄	—	4	2	no	—
423	C₂×C₄	—	4	2	no	—
424	C₂×C₄	—	4	2	no	—
425	C₂×C₄	—	4	2	no	—
426	C₂×C₄	—	4	2	no	—
427	C₂×C₄	—	4	2	no	—
428	C₂×C₄	—	4	2	no	—
429	C₂×C₄	—	8	8	no	—
430	C₂×C₄	C₄×C₇×D₄	1	2	yes	—
431	C₂×C₄	C₇×#121	1	4	yes	—
432	C₂×C₄	C₂³×C₄×C₇	1	1	yes	characteristic
433	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
434	C₂×C₄	C₂×C₇×#41	1	1	yes	characteristic
435	C₂×C₄	C₂×C₇×#41	1	1	yes	characteristic
436	C₂×C₄	C₂×C₇×#41	1	1	yes	characteristic
437	C₂×C₄	C₂×C₇×#41	1	1	yes	characteristic
438	C₈	—	2	2	no	—
439	C₈	—	2	2	no	—
440	C₈	—	2	2	no	—
441	C₈	C₄×C₇×D₄	1	4	yes	—
442	C₇	#21541	1	1	yes	characteristic, direct product factor, Sylow
443	C₂²	—	2	4	no	—
444	C₂²	—	2	2	no	—
445	C₂²	—	4	1	no	—
446	C₂²	—	4	1	no	—
447	C₂²	—	4	2	no	—
448	C₂²	—	4	4	no	—
449	C₂²	—	4	4	no	—
450	C₂²	—	4	4	no	—
451	C₂²	—	8	2	no	—
452	C₂²	—	8	2	no	—
453	C₂²	—	8	2	no	—
454	C₂²	—	8	2	no	—
455	C₂²	C₂×C₄×C₇×D₄	1	1	yes	characteristic
456	C₂²	C₂×C₇×#121	1	1	yes	characteristic
457	C₂²	C₇×#532	1	1	yes	characteristic
458	C₂²	C₇×#576	1	2	yes	—
459	C₂²	C₇×#577	1	2	yes	—
460	C₄	—	2	4	no	—
461	C₄	—	2	2	no	—
462	C₄	—	4	4	no	—
463	C₄	—	4	2	no	—
464	C₄	—	8	2	no	—
465	C₄	—	8	2	no	—
466	C₄	C₂×C₄×C₇×D₄	1	1	yes	characteristic
467	C₄	C₄×C₇×#41	1	1	yes	characteristic
468	C₄	C₇×#525	1	1	yes	characteristic
469	C₄	C₇×#529	1	1	yes	characteristic
470	C₂	—	4	2	no	—
471	C₂	—	8	4	no	—
472	C₂	C₄×C₇×#121	1	1	yes	characteristic
473	C₂	C₇×#2946	1	2	yes	—
474	C₂	C₇×#3062	1	2	yes	—
475	C₂	C₇×#3173	1	1	yes	characteristic
476	C₂	C₇×#3176	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₇	C₂²×D₄
commutator	C₂×C₄	C₂³×C₄×C₇
Frattini, cosocle	C₂²×C₄	C₂⁴×C₇
prime radical	C₂×C₇×#469	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₇ ◁ C₂×C₇×#117 ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₇×#442	C₂	semidirect
3. C₂×C₇×#405	C₂	semidirect
4. C₇×#2324	C₂	semidirect
5. C₇×#1970	C₂	semidirect
6. C₇×#1941	C₂	semidirect
7. C₇×#1936	C₂	semidirect
8. C₇×#1893	C₂	semidirect
9. C₇×#1809	C₂	semidirect
10. C₇×#1776	C₂	semidirect
11. C₄×C₇×#102	C₂	semidirect
18. C₇×#469	C₄	semidirect
42. #21541	C₇	direct (N × H)
52. C₂×C₇×M₁₆	C₂×C₄	semidirect
61. C₇×#121	C₂×C₄	semidirect
82. C₇×#106	C₂×C₄	semidirect
85. C₇×#102	C₂×C₄	semidirect
87. C₇×#97	D₄	semidirect
94. C₂×#442	C₂×C₇	semidirect
95. C₂×#405	C₂×C₇	semidirect
96. #2324	C₂×C₇	semidirect
97. #1970	C₂×C₇	semidirect
98. #1941	C₂×C₇	semidirect
99. #1936	C₂×C₇	semidirect
100. #1893	C₂×C₇	semidirect
101. #1809	C₂×C₇	semidirect
102. #1776	C₂×C₇	semidirect
103. C₄×#102	C₂×C₇	semidirect
171. #469	C₄×C₇	semidirect
255. C₂×M₁₆	C₂×C₄×C₇	semidirect
264. #121	C₂×C₄×C₇	semidirect
285. #106	C₂×C₄×C₇	semidirect
288. #102	C₂×C₄×C₇	semidirect
290. #97	C₇×D₄	semidirect
442. C₇	#21541	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×#469	2
C₂×C₇×#442	2
C₂×C₇×#405	2
C₇×#2324	2
C₇×#1970	2
C₇×#1941	2
C₇×#1936	2
C₇×#1893	2
C₇×#1809	2
C₇×#1776	2
C₄×C₇×#102	2
#21541	7

Subgroups — C7×#21541 #13198757

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×#21541 #13198757