Subgroups — C₇×#21537 #13198753

Order 1792.

954 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×#470	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄×C₇×Q₁₆	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₇×#405	C₂	1	1	yes	maximal, characteristic
4	C₇×#2323	C₂	1	2	yes	maximal
5	C₇×#1971	C₂	1	1	yes	maximal, characteristic, complemented
6	C₇×#1944	C₂	1	1	yes	maximal, characteristic, complemented
7	C₇×#1933	C₂	1	2	yes	maximal, complemented
8	C₇×#1892	C₂	1	2	yes	maximal
9	C₇×#1809	C₂	1	1	yes	maximal, characteristic
10	C₄×C₇×#106	C₂	1	1	yes	maximal, characteristic, complemented
11	C₇×#1763	C₂	1	2	yes	maximal, complemented
12	C₂²×C₇×Q₁₆	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×C₂²⋊Q₈	C₂²	1	2	yes	—
16	C₂×C₄×C₇×Q₈	C₂²	1	2	yes	—
17	C₂×C₇×#117	C₂²	1	1	yes	characteristic
18	C₇×#470	C₄	1	8	yes	complemented
19	C₄×C₇×Q₁₆	—	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×#103	C₂²	1	2	yes	—
24	C₂×C₇×#103	C₂²	1	2	yes	—
25	C₂×C₇×#103	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×#391	C₂²	1	2	yes	—
32	C₇×#389	—	2	2	no	—
33	C₇×#389	C₂²	1	2	yes	—
34	C₇×#388	—	2	2	no	—
35	C₇×#388	—	2	2	no	—
36	C₇×#387	—	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	#21537	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
43	C₂²×C₇×Q₈	C₂³	1	2	yes	—
44	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
45	C₂×C₇×Q₁₆	—	2	2	no	—
46	C₂×C₇×Q₁₆	—	2	2	no	—
47	C₂×C₇×Q₁₆	C₂×C₄	1	4	yes	—
48	C₂×C₇×M₁₆	—	2	2	no	—
49	C₂×C₇×M₁₆	—	2	2	no	—
50	C₂×C₇×M₁₆	C₂×C₄	1	4	yes	—
51	C₂²×C₇×C₈	—	2	2	no	—
52	C₂²×C₇×C₈	—	2	2	no	—
53	C₂²×C₇×C₈	—	2	2	no	—
54	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
55	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
56	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
57	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
58	C₇×C₂²⋊Q₈	—	2	4	no	—
59	C₇×C₂²⋊Q₈	C₂×C₄	1	8	yes	—
60	C₄×C₇×Q₈	—	2	4	no	—
61	C₄×C₇×Q₈	—	2	4	no	—
62	C₇×#117	—	2	2	no	—
63	C₇×#117	—	2	2	no	—
64	C₂×C₇×C₄⋊C₄	—	2	2	no	—
65	C₂×C₇×C₄⋊C₄	—	2	2	no	—
66	C₂×C₇×C₄⋊C₄	—	2	2	no	—
67	C₂×C₇×C₄⋊C₄	D₄	1	1	yes	characteristic
68	C₂×C₇×C₄⋊C₄	D₄	1	1	yes	characteristic
69	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
70	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
71	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
72	C₂×C₇×C₂²⋊C₄	—	2	2	no	—
73	C₂×C₇×C₂²⋊C₄	—	2	2	no	—
74	C₂×C₇×C₂²⋊C₄	D₄	1	1	yes	characteristic
75	C₂×C₇×C₂²⋊C₄	D₄	1	1	yes	characteristic
76	C₂×C₄²×C₇	—	2	2	no	—
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	—
83	C₇×#103	—	2	4	no	—
84	C₇×#103	—	2	4	no	—
85	C₇×#103	C₂×C₄	1	8	yes	—
86	C₇×#97	—	2	2	no	—
87	C₇×#97	—	2	2	no	—
88	C₄×C₇×C₈	—	2	2	no	—
89	C₄×C₇×C₈	D₄	1	4	yes	—
90	C₇×#95	—	2	2	no	—
91	C₇×#95	—	2	2	no	—
92	C₇×#95	—	2	2	no	—
93	C₇×#95	—	2	2	no	—
94	C₇×#95	—	2	2	no	—
95	C₂×#470	C₂×C₇	1	1	yes	characteristic
96	C₂×C₄×Q₁₆	C₂×C₇	1	1	yes	characteristic, complemented
97	C₂×#405	C₂×C₇	1	1	yes	characteristic
98	#2323	C₂×C₇	1	2	yes	—
99	#1971	C₂×C₇	1	1	yes	characteristic, complemented
100	#1944	C₂×C₇	1	1	yes	characteristic, complemented
101	#1933	C₂×C₇	1	2	yes	complemented
102	#1892	C₂×C₇	1	2	yes	—
103	#1809	C₂×C₇	1	1	yes	characteristic
104	C₄×#106	C₂×C₇	1	1	yes	characteristic, complemented
105	#1763	C₂×C₇	1	2	yes	complemented
106	C₂⁴×C₇	C₂×D₄	1	1	yes	characteristic
107	C₂×C₇×Q₈	—	2	2	no	—
108	C₂×C₇×Q₈	—	2	2	no	—
109	C₂×C₇×Q₈	—	2	2	no	—
110	C₂×C₇×Q₈	—	2	2	no	—
111	C₂×C₇×Q₈	—	2	2	no	—
112	C₂×C₇×Q₈	C₂²×C₄	1	4	yes	—
113	C₂²×C₄×C₇	—	2	1	no	—
114	C₂²×C₄×C₇	—	2	1	no	—
115	C₂²×C₄×C₇	—	2	1	no	—
116	C₂²×C₄×C₇	—	2	1	no	—
117	C₂²×C₄×C₇	—	2	2	no	—
118	C₂²×C₄×C₇	—	2	2	no	—
119	C₂²×C₄×C₇	—	2	2	no	—
120	C₂²×C₄×C₇	—	2	2	no	—
121	C₂²×C₄×C₇	C₂²×C₄	1	2	yes	—
122	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
123	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
124	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
125	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
126	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
127	C₂²×C₄×C₇	#41	1	2	yes	—
128	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
129	C₇×Q₁₆	—	2	8	no	—
130	C₇×M₁₆	—	2	8	no	—
131	C₂×C₇×C₈	—	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	1	no	—
137	C₂×C₇×C₈	—	2	1	no	—
138	C₂×C₇×C₈	C₂²×C₄	1	2	yes	—
139	C₂×C₇×C₈	C₂²×C₄	1	2	yes	—
140	C₂×C₇×C₈	C₂×D₄	1	2	yes	—
141	C₂×C₇×C₈	C₂×D₄	1	2	yes	—
142	C₂×C₇×C₈	#41	1	2	yes	—
143	C₂×C₇×C₈	#41	1	2	yes	—
144	C₇×C₄⋊C₄	—	2	8	no	—
145	C₇×C₄⋊C₄	—	2	2	no	—
146	C₇×C₄⋊C₄	—	2	2	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	—	4	4	no	—
153	C₇×C₄⋊C₄	—	8	2	no	—
154	C₇×C₄⋊C₄	C₂²×C₄	1	4	yes	—
155	C₇×C₂²⋊C₄	—	2	8	no	—
156	C₇×C₂²⋊C₄	—	2	2	no	—
157	C₇×C₂²⋊C₄	—	2	2	no	—
158	C₇×C₂²⋊C₄	—	8	2	no	—
159	C₄²×C₇	—	2	1	no	—
160	C₄²×C₇	—	2	1	no	—
161	C₄²×C₇	—	4	4	no	—
162	C₄²×C₇	—	8	2	no	—
163	C₄²×C₇	C₂×D₄	1	2	yes	—
164	C₄²×C₇	#41	1	2	yes	—
165	C₂²×Q₁₆	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×C₂²⋊Q₈	C₂²×C₇	1	2	yes	—
169	C₂×C₄×Q₈	C₂²×C₇	1	2	yes	—
170	C₂×#117	C₂²×C₇	1	1	yes	characteristic
171	#470	C₄×C₇	1	8	yes	complemented
172	C₄×Q₁₆	—	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×#103	C₂²×C₇	1	2	yes	—
177	C₂×#103	C₂²×C₇	1	2	yes	—
178	C₂×#103	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	#391	C₂²×C₇	1	2	yes	—
185	#389	—	2	2	no	—
186	#389	C₂²×C₇	1	2	yes	—
187	#388	—	2	2	no	—
188	#388	—	2	2	no	—
189	#387	—	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	C₄×D₄	1	2	yes	—
200	C₂³×C₇	C₂²×D₄	1	1	yes	characteristic
201	C₇×Q₈	—	2	4	no	—
202	C₇×Q₈	—	2	4	no	—
203	C₇×Q₈	—	4	2	no	—
204	C₇×Q₈	—	4	2	no	—
205	C₂×C₄×C₇	—	2	1	no	—
206	C₂×C₄×C₇	—	2	1	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	—	2	2	no	—
213	C₂×C₄×C₇	—	2	4	no	—
214	C₂×C₄×C₇	—	2	4	no	—
215	C₂×C₄×C₇	—	2	1	no	—
216	C₂×C₄×C₇	—	2	1	no	—
217	C₂×C₄×C₇	—	2	2	no	—
218	C₂×C₄×C₇	—	2	2	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	—	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	C₄×D₄	1	2	yes	—
230	C₂×C₄×C₇	#121	1	2	yes	—
231	C₂×C₄×C₇	#121	1	2	yes	—
232	C₂×C₄×C₇	C₂³×C₄	1	1	yes	characteristic
233	C₂×C₄×C₇	C₂²×D₄	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	C₂×#41	1	1	yes	characteristic
238	C₇×C₈	—	2	2	no	—
239	C₇×C₈	—	2	2	no	—
240	C₇×C₈	—	2	2	no	—
241	C₇×C₈	C₄×D₄	1	4	yes	—
242	C₂²×Q₈	C₂³×C₇	1	2	yes	—
243	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
244	C₂×Q₁₆	—	2	2	no	—
245	C₂×Q₁₆	—	2	2	no	—
246	C₂×Q₁₆	C₂×C₄×C₇	1	4	yes	—
247	C₂×M₁₆	—	2	2	no	—
248	C₂×M₁₆	—	2	2	no	—
249	C₂×M₁₆	C₂×C₄×C₇	1	4	yes	—
250	C₂²×C₈	—	2	2	no	—
251	C₂²×C₈	—	2	2	no	—
252	C₂²×C₈	—	2	2	no	—
253	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
254	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
255	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
256	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
257	C₂²⋊Q₈	—	2	4	no	—
258	C₂²⋊Q₈	C₂×C₄×C₇	1	8	yes	—
259	C₄×Q₈	—	2	4	no	—
260	C₄×Q₈	—	2	4	no	—
261	#117	—	2	2	no	—
262	#117	—	2	2	no	—
263	C₂×C₄⋊C₄	—	2	2	no	—
264	C₂×C₄⋊C₄	—	2	2	no	—
265	C₂×C₄⋊C₄	—	2	2	no	—
266	C₂×C₄⋊C₄	C₇×D₄	1	1	yes	characteristic
267	C₂×C₄⋊C₄	C₇×D₄	1	1	yes	characteristic
268	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
269	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
270	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
271	C₂×C₂²⋊C₄	—	2	2	no	—
272	C₂×C₂²⋊C₄	—	2	2	no	—
273	C₂×C₂²⋊C₄	C₇×D₄	1	1	yes	characteristic
274	C₂×C₂²⋊C₄	C₇×D₄	1	1	yes	characteristic
275	C₂×C₄²	—	2	2	no	—
276	C₂×C₄²	—	2	2	no	—
277	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
278	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
279	#107	—	2	2	no	—
280	#106	—	2	2	no	—
281	#106	C₂×C₄×C₇	1	4	yes	—
282	#103	—	2	4	no	—
283	#103	—	2	4	no	—
284	#103	C₂×C₄×C₇	1	8	yes	—
285	#97	—	2	2	no	—
286	#97	—	2	2	no	—
287	C₄×C₈	—	2	2	no	—
288	C₄×C₈	C₇×D₄	1	4	yes	—
289	#95	—	2	2	no	—
290	#95	—	2	2	no	—
291	#95	—	2	2	no	—
292	#95	—	2	2	no	—
293	#95	—	2	2	no	—
294	C₂²×C₇	—	2	4	no	—
295	C₂²×C₇	—	2	2	no	—
296	C₂²×C₇	—	4	2	no	—
297	C₂²×C₇	—	4	1	no	—
298	C₂²×C₇	—	4	1	no	—
299	C₂²×C₇	C₂×C₄×D₄	1	1	yes	characteristic
300	C₂²×C₇	C₂×#121	1	1	yes	characteristic
301	C₂²×C₇	#532	1	1	yes	characteristic
302	C₂²×C₇	#577	1	2	yes	—
303	C₂²×C₇	#578	1	2	yes	—
304	C₄×C₇	—	2	2	no	—
305	C₄×C₇	—	2	2	no	—
306	C₄×C₇	—	2	2	no	—
307	C₄×C₇	—	4	4	no	—
308	C₄×C₇	—	4	1	no	—
309	C₄×C₇	—	4	1	no	—
310	C₄×C₇	—	4	4	no	—
311	C₄×C₇	—	8	2	no	—
312	C₄×C₇	—	8	2	no	—
313	C₄×C₇	C₂×C₄×D₄	1	1	yes	characteristic
314	C₄×C₇	C₄×#41	1	1	yes	characteristic
315	C₄×C₇	#525	1	1	yes	characteristic
316	C₄×C₇	#529	1	1	yes	characteristic
317	C₂⁴	C₂×C₇×D₄	1	1	yes	characteristic
318	C₂×Q₈	—	2	2	no	—
319	C₂×Q₈	—	2	2	no	—
320	C₂×Q₈	—	2	2	no	—
321	C₂×Q₈	—	2	2	no	—
322	C₂×Q₈	—	2	2	no	—
323	C₂×Q₈	C₂²×C₄×C₇	1	4	yes	—
324	C₂²×C₄	—	2	1	no	—
325	C₂²×C₄	—	2	1	no	—
326	C₂²×C₄	—	2	1	no	—
327	C₂²×C₄	—	2	1	no	—
328	C₂²×C₄	—	2	2	no	—
329	C₂²×C₄	—	2	2	no	—
330	C₂²×C₄	—	2	2	no	—
331	C₂²×C₄	—	2	2	no	—
332	C₂²×C₄	C₂²×C₄×C₇	1	2	yes	—
333	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
334	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
335	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
336	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
337	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
338	C₂²×C₄	C₇×#41	1	2	yes	—
339	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
340	Q₁₆	—	2	8	no	—
341	M₁₆	—	2	8	no	—
342	C₂×C₈	—	2	8	no	—
343	C₂×C₈	—	2	1	no	—
344	C₂×C₈	—	2	1	no	—
345	C₂×C₈	—	2	1	no	—
346	C₂×C₈	—	2	1	no	—
347	C₂×C₈	—	2	1	no	—
348	C₂×C₈	—	2	1	no	—
349	C₂×C₈	C₂²×C₄×C₇	1	2	yes	—
350	C₂×C₈	C₂²×C₄×C₇	1	2	yes	—
351	C₂×C₈	C₂×C₇×D₄	1	2	yes	—
352	C₂×C₈	C₂×C₇×D₄	1	2	yes	—
353	C₂×C₈	C₇×#41	1	2	yes	—
354	C₂×C₈	C₇×#41	1	2	yes	—
355	C₄⋊C₄	—	2	8	no	—
356	C₄⋊C₄	—	2	2	no	—
357	C₄⋊C₄	—	2	2	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	—	2	2	no	—
363	C₄⋊C₄	—	4	4	no	—
364	C₄⋊C₄	—	8	2	no	—
365	C₄⋊C₄	C₂²×C₄×C₇	1	4	yes	—
366	C₂²⋊C₄	—	2	8	no	—
367	C₂²⋊C₄	—	2	2	no	—
368	C₂²⋊C₄	—	2	2	no	—
369	C₂²⋊C₄	—	8	2	no	—
370	C₄²	—	2	1	no	—
371	C₄²	—	2	1	no	—
372	C₄²	—	4	4	no	—
373	C₄²	—	8	2	no	—
374	C₄²	C₂×C₇×D₄	1	2	yes	—
375	C₄²	C₇×#41	1	2	yes	—
376	C₂×C₇	—	4	2	no	—
377	C₂×C₇	C₄×#121	1	1	yes	characteristic
378	C₂×C₇	#2947	1	2	yes	—
379	C₂×C₇	#3059	1	1	yes	characteristic
380	C₂×C₇	#3060	1	1	yes	characteristic
381	C₂×C₇	#3178	1	2	yes	—
382	C₂³	—	2	1	no	—
383	C₂³	—	2	1	no	—
384	C₂³	—	2	2	no	—
385	C₂³	—	2	2	no	—
386	C₂³	C₄×C₇×D₄	1	2	yes	—
387	C₂³	C₂²×C₇×D₄	1	1	yes	characteristic
388	Q₈	—	2	4	no	—
389	Q₈	—	2	4	no	—
390	Q₈	—	4	2	no	—
391	Q₈	—	4	2	no	—
392	C₂×C₄	—	2	1	no	—
393	C₂×C₄	—	2	1	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	4	no	—
401	C₂×C₄	—	2	4	no	—
402	C₂×C₄	—	2	1	no	—
403	C₂×C₄	—	2	1	no	—
404	C₂×C₄	—	2	2	no	—
405	C₂×C₄	—	2	2	no	—
406	C₂×C₄	—	4	2	no	—
407	C₂×C₄	—	4	2	no	—
408	C₂×C₄	—	4	2	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	—	4	2	no	—
416	C₂×C₄	C₄×C₇×D₄	1	2	yes	—
417	C₂×C₄	C₇×#121	1	2	yes	—
418	C₂×C₄	C₇×#121	1	2	yes	—
419	C₂×C₄	C₂³×C₄×C₇	1	1	yes	characteristic
420	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
421	C₂×C₄	C₂×C₇×#41	1	1	yes	characteristic
422	C₂×C₄	C₂×C₇×#41	1	1	yes	characteristic
423	C₂×C₄	C₂×C₇×#41	1	1	yes	characteristic
424	C₂×C₄	C₂×C₇×#41	1	1	yes	characteristic
425	C₈	—	2	2	no	—
426	C₈	—	2	2	no	—
427	C₈	—	2	2	no	—
428	C₈	C₄×C₇×D₄	1	4	yes	—
429	C₇	#21537	1	1	yes	characteristic, direct product factor, Sylow
430	C₂²	—	2	4	no	—
431	C₂²	—	2	2	no	—
432	C₂²	—	4	2	no	—
433	C₂²	—	4	1	no	—
434	C₂²	—	4	1	no	—
435	C₂²	C₂×C₄×C₇×D₄	1	1	yes	characteristic
436	C₂²	C₂×C₇×#121	1	1	yes	characteristic
437	C₂²	C₇×#532	1	1	yes	characteristic
438	C₂²	C₇×#577	1	2	yes	—
439	C₂²	C₇×#578	1	2	yes	—
440	C₄	—	2	2	no	—
441	C₄	—	2	2	no	—
442	C₄	—	2	2	no	—
443	C₄	—	4	4	no	—
444	C₄	—	4	1	no	—
445	C₄	—	4	1	no	—
446	C₄	—	4	4	no	—
447	C₄	—	8	2	no	—
448	C₄	—	8	2	no	—
449	C₄	C₂×C₄×C₇×D₄	1	1	yes	characteristic
450	C₄	C₄×C₇×#41	1	1	yes	characteristic
451	C₄	C₇×#525	1	1	yes	characteristic
452	C₄	C₇×#529	1	1	yes	characteristic
453	C₂	—	4	2	no	—
454	C₂	C₄×C₇×#121	1	1	yes	characteristic
455	C₂	C₇×#2947	1	2	yes	—
456	C₂	C₇×#3059	1	1	yes	characteristic
457	C₂	C₇×#3060	1	1	yes	characteristic
458	C₂	C₇×#3178	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	C₂⁴×C₇	C₂×D₄
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×C₄×C₇×Q₁₆	C₂	semidirect
5. C₇×#1971	C₂	semidirect
6. C₇×#1944	C₂	semidirect
7. C₇×#1933	C₂	semidirect
10. C₄×C₇×#106	C₂	semidirect
11. C₇×#1763	C₂	semidirect
18. C₇×#470	C₄	semidirect
42. #21537	C₇	direct (N × H)
96. C₂×C₄×Q₁₆	C₂×C₇	semidirect
99. #1971	C₂×C₇	semidirect
100. #1944	C₂×C₇	semidirect
101. #1933	C₂×C₇	semidirect
104. C₄×#106	C₂×C₇	semidirect
105. #1763	C₂×C₇	semidirect
171. #470	C₄×C₇	semidirect
429. C₇	#21537	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×#470	2
C₂×C₄×C₇×Q₁₆	2
C₂×C₇×#405	2
C₇×#2323	2
C₇×#1971	2
C₇×#1944	2
C₇×#1933	2
C₇×#1892	2
C₇×#1809	2
C₄×C₇×#106	2
C₇×#1763	2
#21537	7

Subgroups — C7×#21537 #13198753

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×#21537 #13198753