Subgroups — C₇×#21542 #13198758

Order 1792.

954 conjugacy classes of subgroups.

The subgroup lattice has 440 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×C₇×#441	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×#1969	C₂	1	1	yes	maximal, characteristic, complemented
6	C₇×#1941	C₂	1	1	yes	maximal, characteristic, complemented
7	C₇×#1935	C₂	1	2	yes	maximal, complemented
8	C₇×#1892	C₂	1	2	yes	maximal
9	C₇×#1809	C₂	1	1	yes	maximal, characteristic
10	C₇×#1776	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄×C₇×#103	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	C₇×#441	—	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	#21542	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	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	D₄	1	2	yes	—
74	C₂×C₄²×C₇	—	2	2	no	—
75	C₂×C₄²×C₇	—	2	2	no	—
76	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
77	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
78	C₇×#107	—	2	2	no	—
79	C₇×#106	—	2	2	no	—
80	C₇×#106	C₂×C₄	1	4	yes	—
81	C₇×#103	—	2	4	no	—
82	C₇×#103	—	2	4	no	—
83	C₇×#103	C₂×C₄	1	8	yes	—
84	C₇×#97	—	2	2	no	—
85	C₇×#97	D₄	1	4	yes	—
86	C₄×C₇×C₈	—	2	2	no	—
87	C₄×C₇×C₈	—	2	2	no	—
88	C₇×#95	—	2	2	no	—
89	C₇×#95	—	2	2	no	—
90	C₇×#95	—	2	2	no	—
91	C₇×#95	—	2	2	no	—
92	C₇×#95	—	2	2	no	—
93	C₂×#470	C₂×C₇	1	1	yes	characteristic
94	C₂×#441	C₂×C₇	1	1	yes	characteristic, complemented
95	C₂×#405	C₂×C₇	1	1	yes	characteristic
96	#2323	C₂×C₇	1	2	yes	—
97	#1969	C₂×C₇	1	1	yes	characteristic, complemented
98	#1941	C₂×C₇	1	1	yes	characteristic, complemented
99	#1935	C₂×C₇	1	2	yes	complemented
100	#1892	C₂×C₇	1	2	yes	—
101	#1809	C₂×C₇	1	1	yes	characteristic
102	#1776	C₂×C₇	1	1	yes	characteristic, complemented
103	C₄×#103	C₂×C₇	1	2	yes	complemented
104	C₂⁴×C₇	C₂×D₄	1	1	yes	characteristic
105	C₂×C₇×Q₈	—	2	2	no	—
106	C₂×C₇×Q₈	—	2	2	no	—
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	C₂²×C₄	1	4	yes	—
111	C₂²×C₄×C₇	—	2	1	no	—
112	C₂²×C₄×C₇	—	2	1	no	—
113	C₂²×C₄×C₇	—	2	1	no	—
114	C₂²×C₄×C₇	—	2	1	no	—
115	C₂²×C₄×C₇	—	2	2	no	—
116	C₂²×C₄×C₇	—	2	2	no	—
117	C₂²×C₄×C₇	—	2	2	no	—
118	C₂²×C₄×C₇	—	2	2	no	—
119	C₂²×C₄×C₇	C₂²×C₄	1	2	yes	—
120	C₂²×C₄×C₇	C₂×D₄	1	2	yes	—
121	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
122	C₂²×C₄×C₇	C₂×D₄	1	2	yes	—
123	C₂²×C₄×C₇	#41	1	2	yes	—
124	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
125	C₇×Q₁₆	—	2	8	no	—
126	C₇×M₁₆	—	2	8	no	—
127	C₂×C₇×C₈	—	2	8	no	—
128	C₂×C₇×C₈	—	2	1	no	—
129	C₂×C₇×C₈	—	2	1	no	—
130	C₂×C₇×C₈	—	2	1	no	—
131	C₂×C₇×C₈	—	2	1	no	—
132	C₂×C₇×C₈	—	2	1	no	—
133	C₂×C₇×C₈	—	2	1	no	—
134	C₂×C₇×C₈	C₂²×C₄	1	2	yes	—
135	C₂×C₇×C₈	C₂²×C₄	1	2	yes	—
136	C₂×C₇×C₈	C₂×D₄	1	2	yes	—
137	C₂×C₇×C₈	C₂×D₄	1	2	yes	—
138	C₂×C₇×C₈	#41	1	2	yes	—
139	C₂×C₇×C₈	#41	1	2	yes	—
140	C₇×C₄⋊C₄	—	2	8	no	—
141	C₇×C₄⋊C₄	—	2	4	no	—
142	C₇×C₄⋊C₄	—	2	2	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	4	no	—
148	C₇×C₄⋊C₄	—	8	2	no	—
149	C₇×C₄⋊C₄	C₂²×C₄	1	4	yes	—
150	C₇×C₂²⋊C₄	—	2	8	no	—
151	C₇×C₂²⋊C₄	—	2	4	no	—
152	C₇×C₂²⋊C₄	—	8	2	no	—
153	C₄²×C₇	—	2	1	no	—
154	C₄²×C₇	—	2	1	no	—
155	C₄²×C₇	—	4	4	no	—
156	C₄²×C₇	—	8	2	no	—
157	C₄²×C₇	C₂×D₄	1	2	yes	—
158	C₄²×C₇	#41	1	2	yes	—
159	C₂²×Q₁₆	C₂²×C₇	1	1	yes	characteristic
160	C₂²×M₁₆	C₂²×C₇	1	1	yes	characteristic
161	C₂³×C₈	C₂²×C₇	1	1	yes	characteristic
162	C₂×C₂²⋊Q₈	C₂²×C₇	1	2	yes	—
163	C₂×C₄×Q₈	C₂²×C₇	1	2	yes	—
164	C₂×#117	C₂²×C₇	1	1	yes	characteristic
165	#470	C₄×C₇	1	8	yes	complemented
166	#441	—	2	4	no	—
167	C₂×#107	C₂²×C₇	1	1	yes	characteristic
168	C₂×#106	C₂²×C₇	1	1	yes	characteristic
169	C₂×#106	C₂²×C₇	1	1	yes	characteristic
170	C₂×#103	C₂²×C₇	1	2	yes	—
171	C₂×#103	C₂²×C₇	1	2	yes	—
172	C₂×#103	C₂²×C₇	1	2	yes	—
173	#405	—	2	4	no	—
174	C₂×#97	C₂²×C₇	1	1	yes	characteristic
175	C₂×#97	C₂²×C₇	1	1	yes	characteristic
176	C₂×C₄×C₈	C₂²×C₇	1	1	yes	characteristic
177	C₂×C₄×C₈	C₂²×C₇	1	1	yes	characteristic
178	#391	C₂²×C₇	1	2	yes	—
179	#389	—	2	2	no	—
180	#389	C₂²×C₇	1	2	yes	—
181	#388	—	2	2	no	—
182	#388	—	2	2	no	—
183	#387	—	2	2	no	—
184	#380	C₂²×C₇	1	2	yes	—
185	C₄×C₄⋊C₄	C₂²×C₇	1	2	yes	—
186	#340	C₂²×C₇	1	2	yes	—
187	#340	C₂²×C₇	1	2	yes	—
188	#340	C₂²×C₇	1	2	yes	—
189	C₂³×C₇	—	2	1	no	—
190	C₂³×C₇	—	2	1	no	—
191	C₂³×C₇	—	2	2	no	—
192	C₂³×C₇	—	2	2	no	—
193	C₂³×C₇	C₄×D₄	1	2	yes	—
194	C₂³×C₇	C₂²×D₄	1	1	yes	characteristic
195	C₇×Q₈	—	2	4	no	—
196	C₇×Q₈	—	2	4	no	—
197	C₇×Q₈	—	4	2	no	—
198	C₇×Q₈	—	4	2	no	—
199	C₂×C₄×C₇	—	2	1	no	—
200	C₂×C₄×C₇	—	2	1	no	—
201	C₂×C₄×C₇	—	2	2	no	—
202	C₂×C₄×C₇	—	2	2	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	—	2	4	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	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	—	4	2	no	—
220	C₂×C₄×C₇	—	4	2	no	—
221	C₂×C₄×C₇	—	4	2	no	—
222	C₂×C₄×C₇	C₄×D₄	1	2	yes	—
223	C₂×C₄×C₇	#121	1	4	yes	—
224	C₂×C₄×C₇	C₂³×C₄	1	1	yes	characteristic
225	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
226	C₂×C₄×C₇	C₂×#41	1	1	yes	characteristic
227	C₂×C₄×C₇	C₂×#41	1	1	yes	characteristic
228	C₂×C₄×C₇	C₂×#41	1	1	yes	characteristic
229	C₂×C₄×C₇	C₂×#41	1	1	yes	characteristic
230	C₇×C₈	—	2	2	no	—
231	C₇×C₈	—	2	2	no	—
232	C₇×C₈	—	2	2	no	—
233	C₇×C₈	C₄×D₄	1	4	yes	—
234	C₂²×Q₈	C₂³×C₇	1	2	yes	—
235	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
236	C₂×Q₁₆	—	2	2	no	—
237	C₂×Q₁₆	—	2	2	no	—
238	C₂×Q₁₆	C₂×C₄×C₇	1	4	yes	—
239	C₂×M₁₆	—	2	2	no	—
240	C₂×M₁₆	—	2	2	no	—
241	C₂×M₁₆	C₂×C₄×C₇	1	4	yes	—
242	C₂²×C₈	—	2	2	no	—
243	C₂²×C₈	—	2	2	no	—
244	C₂²×C₈	—	2	2	no	—
245	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
246	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
247	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
248	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
249	C₂²⋊Q₈	—	2	4	no	—
250	C₂²⋊Q₈	C₂×C₄×C₇	1	8	yes	—
251	C₄×Q₈	—	2	4	no	—
252	C₄×Q₈	—	2	4	no	—
253	#117	—	2	2	no	—
254	#117	—	2	2	no	—
255	C₂×C₄⋊C₄	—	2	2	no	—
256	C₂×C₄⋊C₄	—	2	2	no	—
257	C₂×C₄⋊C₄	—	2	2	no	—
258	C₂×C₄⋊C₄	C₇×D₄	1	2	yes	—
259	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
260	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
261	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
262	C₂×C₂²⋊C₄	—	2	2	no	—
263	C₂×C₂²⋊C₄	—	2	2	no	—
264	C₂×C₂²⋊C₄	C₇×D₄	1	2	yes	—
265	C₂×C₄²	—	2	2	no	—
266	C₂×C₄²	—	2	2	no	—
267	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
268	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
269	#107	—	2	2	no	—
270	#106	—	2	2	no	—
271	#106	C₂×C₄×C₇	1	4	yes	—
272	#103	—	2	4	no	—
273	#103	—	2	4	no	—
274	#103	C₂×C₄×C₇	1	8	yes	—
275	#97	—	2	2	no	—
276	#97	C₇×D₄	1	4	yes	—
277	C₄×C₈	—	2	2	no	—
278	C₄×C₈	—	2	2	no	—
279	#95	—	2	2	no	—
280	#95	—	2	2	no	—
281	#95	—	2	2	no	—
282	#95	—	2	2	no	—
283	#95	—	2	2	no	—
284	C₂²×C₇	—	2	4	no	—
285	C₂²×C₇	—	2	2	no	—
286	C₂²×C₇	—	4	1	no	—
287	C₂²×C₇	—	4	1	no	—
288	C₂²×C₇	—	4	2	no	—
289	C₂²×C₇	C₂×C₄×D₄	1	1	yes	characteristic
290	C₂²×C₇	C₂×#121	1	1	yes	characteristic
291	C₂²×C₇	#532	1	1	yes	characteristic
292	C₂²×C₇	#577	1	2	yes	—
293	C₂²×C₇	#578	1	2	yes	—
294	C₄×C₇	—	2	4	no	—
295	C₄×C₇	—	2	2	no	—
296	C₄×C₇	—	4	4	no	—
297	C₄×C₇	—	4	2	no	—
298	C₄×C₇	—	4	4	no	—
299	C₄×C₇	—	8	2	no	—
300	C₄×C₇	—	8	2	no	—
301	C₄×C₇	C₂×C₄×D₄	1	1	yes	characteristic
302	C₄×C₇	C₄×#41	1	1	yes	characteristic
303	C₄×C₇	#525	1	1	yes	characteristic
304	C₄×C₇	#529	1	1	yes	characteristic
305	C₂⁴	C₂×C₇×D₄	1	1	yes	characteristic
306	C₂×Q₈	—	2	2	no	—
307	C₂×Q₈	—	2	2	no	—
308	C₂×Q₈	—	2	2	no	—
309	C₂×Q₈	—	2	2	no	—
310	C₂×Q₈	—	2	2	no	—
311	C₂×Q₈	C₂²×C₄×C₇	1	4	yes	—
312	C₂²×C₄	—	2	1	no	—
313	C₂²×C₄	—	2	1	no	—
314	C₂²×C₄	—	2	1	no	—
315	C₂²×C₄	—	2	1	no	—
316	C₂²×C₄	—	2	2	no	—
317	C₂²×C₄	—	2	2	no	—
318	C₂²×C₄	—	2	2	no	—
319	C₂²×C₄	—	2	2	no	—
320	C₂²×C₄	C₂²×C₄×C₇	1	2	yes	—
321	C₂²×C₄	C₂×C₇×D₄	1	2	yes	—
322	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
323	C₂²×C₄	C₂×C₇×D₄	1	2	yes	—
324	C₂²×C₄	C₇×#41	1	2	yes	—
325	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
326	Q₁₆	—	2	8	no	—
327	M₁₆	—	2	8	no	—
328	C₂×C₈	—	2	8	no	—
329	C₂×C₈	—	2	1	no	—
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	C₂²×C₄×C₇	1	2	yes	—
336	C₂×C₈	C₂²×C₄×C₇	1	2	yes	—
337	C₂×C₈	C₂×C₇×D₄	1	2	yes	—
338	C₂×C₈	C₂×C₇×D₄	1	2	yes	—
339	C₂×C₈	C₇×#41	1	2	yes	—
340	C₂×C₈	C₇×#41	1	2	yes	—
341	C₄⋊C₄	—	2	8	no	—
342	C₄⋊C₄	—	2	4	no	—
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	—	4	4	no	—
349	C₄⋊C₄	—	8	2	no	—
350	C₄⋊C₄	C₂²×C₄×C₇	1	4	yes	—
351	C₂²⋊C₄	—	2	8	no	—
352	C₂²⋊C₄	—	2	4	no	—
353	C₂²⋊C₄	—	8	2	no	—
354	C₄²	—	2	1	no	—
355	C₄²	—	2	1	no	—
356	C₄²	—	4	4	no	—
357	C₄²	—	8	2	no	—
358	C₄²	C₂×C₇×D₄	1	2	yes	—
359	C₄²	C₇×#41	1	2	yes	—
360	C₂×C₇	—	4	2	no	—
361	C₂×C₇	C₄×#121	1	1	yes	characteristic
362	C₂×C₇	#2947	1	2	yes	—
363	C₂×C₇	#3063	1	2	yes	—
364	C₂×C₇	#3173	1	1	yes	characteristic
365	C₂×C₇	#3177	1	1	yes	characteristic
366	C₂³	—	2	1	no	—
367	C₂³	—	2	1	no	—
368	C₂³	—	2	2	no	—
369	C₂³	—	2	2	no	—
370	C₂³	C₄×C₇×D₄	1	2	yes	—
371	C₂³	C₂²×C₇×D₄	1	1	yes	characteristic
372	Q₈	—	2	4	no	—
373	Q₈	—	2	4	no	—
374	Q₈	—	4	2	no	—
375	Q₈	—	4	2	no	—
376	C₂×C₄	—	2	1	no	—
377	C₂×C₄	—	2	1	no	—
378	C₂×C₄	—	2	2	no	—
379	C₂×C₄	—	2	2	no	—
380	C₂×C₄	—	2	2	no	—
381	C₂×C₄	—	2	2	no	—
382	C₂×C₄	—	2	2	no	—
383	C₂×C₄	—	2	2	no	—
384	C₂×C₄	—	2	4	no	—
385	C₂×C₄	—	2	4	no	—
386	C₂×C₄	—	2	2	no	—
387	C₂×C₄	—	2	2	no	—
388	C₂×C₄	—	2	2	no	—
389	C₂×C₄	—	4	2	no	—
390	C₂×C₄	—	4	2	no	—
391	C₂×C₄	—	4	2	no	—
392	C₂×C₄	—	4	2	no	—
393	C₂×C₄	—	4	2	no	—
394	C₂×C₄	—	4	2	no	—
395	C₂×C₄	—	4	2	no	—
396	C₂×C₄	—	4	2	no	—
397	C₂×C₄	—	4	2	no	—
398	C₂×C₄	—	4	2	no	—
399	C₂×C₄	C₄×C₇×D₄	1	2	yes	—
400	C₂×C₄	C₇×#121	1	4	yes	—
401	C₂×C₄	C₂³×C₄×C₇	1	1	yes	characteristic
402	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
403	C₂×C₄	C₂×C₇×#41	1	1	yes	characteristic
404	C₂×C₄	C₂×C₇×#41	1	1	yes	characteristic
405	C₂×C₄	C₂×C₇×#41	1	1	yes	characteristic
406	C₂×C₄	C₂×C₇×#41	1	1	yes	characteristic
407	C₈	—	2	2	no	—
408	C₈	—	2	2	no	—
409	C₈	—	2	2	no	—
410	C₈	C₄×C₇×D₄	1	4	yes	—
411	C₇	#21542	1	1	yes	characteristic, direct product factor, Sylow
412	C₂²	—	2	4	no	—
413	C₂²	—	2	2	no	—
414	C₂²	—	4	1	no	—
415	C₂²	—	4	1	no	—
416	C₂²	—	4	2	no	—
417	C₂²	C₂×C₄×C₇×D₄	1	1	yes	characteristic
418	C₂²	C₂×C₇×#121	1	1	yes	characteristic
419	C₂²	C₇×#532	1	1	yes	characteristic
420	C₂²	C₇×#577	1	2	yes	—
421	C₂²	C₇×#578	1	2	yes	—
422	C₄	—	2	4	no	—
423	C₄	—	2	2	no	—
424	C₄	—	4	4	no	—
425	C₄	—	4	2	no	—
426	C₄	—	4	4	no	—
427	C₄	—	8	2	no	—
428	C₄	—	8	2	no	—
429	C₄	C₂×C₄×C₇×D₄	1	1	yes	characteristic
430	C₄	C₄×C₇×#41	1	1	yes	characteristic
431	C₄	C₇×#525	1	1	yes	characteristic
432	C₄	C₇×#529	1	1	yes	characteristic
433	C₂	—	4	2	no	—
434	C₂	C₄×C₇×#121	1	1	yes	characteristic
435	C₂	C₇×#2947	1	2	yes	—
436	C₂	C₇×#3063	1	2	yes	—
437	C₂	C₇×#3173	1	1	yes	characteristic
438	C₂	C₇×#3177	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	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×C₇×#441	C₂	semidirect
5. C₇×#1969	C₂	semidirect
6. C₇×#1941	C₂	semidirect
7. C₇×#1935	C₂	semidirect
10. C₇×#1776	C₂	semidirect
11. C₄×C₇×#103	C₂	semidirect
18. C₇×#470	C₄	semidirect
42. #21542	C₇	direct (N × H)
94. C₂×#441	C₂×C₇	semidirect
97. #1969	C₂×C₇	semidirect
98. #1941	C₂×C₇	semidirect
99. #1935	C₂×C₇	semidirect
102. #1776	C₂×C₇	semidirect
103. C₄×#103	C₂×C₇	semidirect
165. #470	C₄×C₇	semidirect
411. C₇	#21542	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×C₇×#441	2
C₂×C₇×#405	2
C₇×#2323	2
C₇×#1969	2
C₇×#1941	2
C₇×#1935	2
C₇×#1892	2
C₇×#1809	2
C₇×#1776	2
C₄×C₇×#103	2
#21542	7

Subgroups — C7×#21542 #13198758

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×#21542 #13198758