Subgroups — C₇×#24969 #13202185

Order 1792.

842 conjugacy classes of subgroups.

The subgroup lattice has 484 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×#2538	C₂	1	1	yes	maximal, characteristic
2	C₇×D₄×C₄⋊C₄	C₂	1	1	yes	maximal, characteristic
3	C₇×#2077	C₂	1	2	yes	maximal, complemented
4	C₇×#2035	C₂	1	2	yes	maximal, complemented
5	C₇×#1954	C₂	1	1	yes	maximal, characteristic
6	C₇×#1948	C₂	1	1	yes	maximal, characteristic, complemented
7	C₇×#1872	C₂	1	2	yes	maximal, complemented
8	C₇×#1834	C₂	1	1	yes	maximal, characteristic, complemented
9	C₇×#1823	C₂	1	2	yes	maximal, complemented
10	C₇×#1803	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄×C₇×#103	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₇×C₂²⋊Q₈	C₂²	1	2	yes	—
13	C₂×C₄×C₇×Q₈	C₂²	1	1	yes	characteristic
14	C₂×C₄×C₇×D₄	—	2	1	no	—
15	C₂×C₄×C₇×D₄	C₂²	1	1	yes	characteristic
16	C₂²×C₇×C₄⋊C₄	C₂²	1	2	yes	—
17	C₂×C₇×#106	C₂²	1	2	yes	—
18	C₂×C₇×C₄⋊C₈	C₂²	1	1	yes	characteristic
19	C₂×C₇×#103	C₂²	1	1	yes	characteristic
20	C₂×C₇×#103	C₂²	1	1	yes	characteristic
21	C₂×C₇×#103	C₂²	1	2	yes	—
22	C₂×C₇×C₂²⋊C₈	C₂²	1	2	yes	—
23	C₂×C₇×C₂²⋊C₈	C₂²	1	2	yes	—
24	C₂×C₄×C₇×C₈	C₂²	1	1	yes	characteristic
25	C₇×#396	—	2	2	no	—
26	C₇×#390	—	2	1	no	—
27	C₇×#389	—	2	1	no	—
28	C₇×#389	—	2	1	no	—
29	C₇×#385	—	2	2	no	—
30	C₇×#384	C₂²	1	1	yes	characteristic
31	C₇×#384	C₂²	1	1	yes	characteristic
32	C₇×#380	C₂²	1	2	yes	—
33	C₇×#380	C₂²	1	2	yes	—
34	C₄×C₇×C₄⋊C₄	C₂²	1	1	yes	characteristic
35	C₇×#340	C₂²	1	1	yes	characteristic
36	C₇×#340	C₂²	1	1	yes	characteristic
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	#24969	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
42	C₂²×C₇×Q₈	C₂³	1	1	yes	characteristic
43	C₂²×C₇×D₄	D₄	1	1	yes	characteristic
44	C₂³×C₄×C₇	—	2	2	no	—
45	C₂³×C₄×C₇	C₂³	1	2	yes	—
46	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
47	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
48	C₂²×C₇×C₈	C₂³	1	2	yes	—
49	C₇×C₂²⋊Q₈	—	2	4	no	—
50	C₇×C₂²⋊Q₈	—	4	2	no	—
51	C₄×C₇×Q₈	—	2	2	no	—
52	C₄×C₇×Q₈	—	2	2	no	—
53	C₄×C₇×D₄	—	2	2	no	—
54	C₄×C₇×D₄	—	2	2	no	—
55	C₄×C₇×D₄	—	4	4	no	—
56	C₂×C₇×C₄⋊C₄	—	2	4	no	—
57	C₂×C₇×C₄⋊C₄	—	2	2	no	—
58	C₂×C₇×C₄⋊C₄	—	2	1	no	—
59	C₂×C₇×C₄⋊C₄	—	2	1	no	—
60	C₂×C₇×C₄⋊C₄	—	2	1	no	—
61	C₂×C₇×C₄⋊C₄	—	2	2	no	—
62	C₂×C₇×C₄⋊C₄	—	2	1	no	—
63	C₂×C₇×C₄⋊C₄	—	2	1	no	—
64	C₂×C₇×C₄⋊C₄	—	4	2	no	—
65	C₂×C₇×C₄⋊C₄	D₄	1	1	yes	characteristic
66	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
67	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
68	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
69	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
70	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
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	D₄	1	2	yes	—
75	C₂×C₄²×C₇	—	2	1	no	—
76	C₂×C₄²×C₇	—	2	1	no	—
77	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
78	C₇×#106	—	4	2	no	—
79	C₇×C₄⋊C₈	—	2	2	no	—
80	C₇×#103	—	2	2	no	—
81	C₇×#103	—	2	2	no	—
82	C₇×#103	—	4	2	no	—
83	C₇×C₂²⋊C₈	—	4	2	no	—
84	C₇×C₂²⋊C₈	—	4	2	no	—
85	C₄×C₇×C₈	—	2	2	no	—
86	C₇×#95	—	2	1	no	—
87	C₇×#95	—	2	2	no	—
88	C₇×#95	—	2	2	no	—
89	#2538	C₂×C₇	1	1	yes	characteristic
90	D₄×C₄⋊C₄	C₂×C₇	1	1	yes	characteristic
91	#2077	C₂×C₇	1	2	yes	complemented
92	#2035	C₂×C₇	1	2	yes	complemented
93	#1954	C₂×C₇	1	1	yes	characteristic
94	#1948	C₂×C₇	1	1	yes	characteristic, complemented
95	#1872	C₂×C₇	1	2	yes	complemented
96	#1834	C₂×C₇	1	1	yes	characteristic, complemented
97	#1823	C₂×C₇	1	2	yes	complemented
98	#1803	C₂×C₇	1	1	yes	characteristic, complemented
99	C₄×#103	C₂×C₇	1	1	yes	characteristic, complemented
100	C₂⁴×C₇	C₂×D₄	1	2	yes	—
101	C₂×C₇×Q₈	—	2	1	no	—
102	C₂×C₇×Q₈	—	2	1	no	—
103	C₂×C₇×Q₈	—	2	1	no	—
104	C₂×C₇×Q₈	—	2	1	no	—
105	C₂×C₇×Q₈	—	2	1	no	—
106	C₂×C₇×Q₈	#41	1	2	yes	—
107	C₂×C₇×D₄	—	2	2	no	—
108	C₂×C₇×D₄	—	2	2	no	—
109	C₂×C₇×D₄	SD₁₆	1	4	yes	—
110	C₂²×C₄×C₇	—	2	1	no	—
111	C₂²×C₄×C₇	—	2	1	no	—
112	C₂²×C₄×C₇	—	2	2	no	—
113	C₂²×C₄×C₇	—	2	2	no	—
114	C₂²×C₄×C₇	—	2	2	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	1	no	—
119	C₂²×C₄×C₇	—	2	1	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	—	4	4	no	—
124	C₂²×C₄×C₇	—	8	2	no	—
125	C₂²×C₄×C₇	C₂×D₄	1	2	yes	—
126	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
127	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
128	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
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	2	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	C₇×C₄⋊C₄	—	2	2	no	—
139	C₇×C₄⋊C₄	—	2	1	no	—
140	C₇×C₄⋊C₄	—	2	1	no	—
141	C₇×C₄⋊C₄	—	2	2	no	—
142	C₇×C₄⋊C₄	—	2	1	no	—
143	C₇×C₄⋊C₄	—	2	1	no	—
144	C₇×C₄⋊C₄	—	2	2	no	—
145	C₇×C₄⋊C₄	—	2	2	no	—
146	C₇×C₄⋊C₄	—	2	1	no	—
147	C₇×C₄⋊C₄	—	2	2	no	—
148	C₇×C₄⋊C₄	—	4	4	no	—
149	C₇×C₄⋊C₄	—	4	4	no	—
150	C₇×C₄⋊C₄	—	4	2	no	—
151	C₇×C₄⋊C₄	—	4	2	no	—
152	C₇×C₄⋊C₄	—	4	2	no	—
153	C₇×C₄⋊C₄	—	8	1	no	—
154	C₇×C₄⋊C₄	—	8	1	no	—
155	C₇×C₄⋊C₄	#41	1	2	yes	—
156	C₇×C₂²⋊C₄	—	2	4	no	—
157	C₇×C₂²⋊C₄	—	4	4	no	—
158	C₇×C₂²⋊C₄	—	4	4	no	—
159	C₇×C₂²⋊C₄	—	8	2	no	—
160	C₄²×C₇	—	4	2	no	—
161	C₄²×C₇	—	4	2	no	—
162	C₄²×C₇	#41	1	2	yes	—
163	C₄²×C₇	#41	1	2	yes	—
164	C₂×C₂²⋊Q₈	C₂²×C₇	1	2	yes	—
165	C₂×C₄×Q₈	C₂²×C₇	1	1	yes	characteristic
166	C₂×C₄×D₄	—	2	1	no	—
167	C₂×C₄×D₄	C₂²×C₇	1	1	yes	characteristic
168	C₂²×C₄⋊C₄	C₂²×C₇	1	2	yes	—
169	C₂×#106	C₂²×C₇	1	2	yes	—
170	C₂×C₄⋊C₈	C₂²×C₇	1	1	yes	characteristic
171	C₂×#103	C₂²×C₇	1	1	yes	characteristic
172	C₂×#103	C₂²×C₇	1	1	yes	characteristic
173	C₂×#103	C₂²×C₇	1	2	yes	—
174	C₂×C₂²⋊C₈	C₂²×C₇	1	2	yes	—
175	C₂×C₂²⋊C₈	C₂²×C₇	1	2	yes	—
176	C₂×C₄×C₈	C₂²×C₇	1	1	yes	characteristic
177	#396	—	2	2	no	—
178	#390	—	2	1	no	—
179	#389	—	2	1	no	—
180	#389	—	2	1	no	—
181	#385	—	2	2	no	—
182	#384	C₂²×C₇	1	1	yes	characteristic
183	#384	C₂²×C₇	1	1	yes	characteristic
184	#380	C₂²×C₇	1	2	yes	—
185	#380	C₂²×C₇	1	2	yes	—
186	C₄×C₄⋊C₄	C₂²×C₇	1	1	yes	characteristic
187	#340	C₂²×C₇	1	2	yes	—
188	#340	C₂²×C₇	1	1	yes	characteristic
189	#340	C₂²×C₇	1	2	yes	—
190	#340	C₂²×C₇	1	1	yes	characteristic
191	#340	C₂²×C₇	1	2	yes	—
192	#340	C₂²×C₇	1	2	yes	—
193	C₂³×C₇	—	2	2	no	—
194	C₂³×C₇	—	2	2	no	—
195	C₂³×C₇	—	2	2	no	—
196	C₂³×C₇	—	2	2	no	—
197	C₂³×C₇	—	2	2	no	—
198	C₂³×C₇	—	2	2	no	—
199	C₂³×C₇	C₂×SD₁₆	1	4	yes	—
200	C₂³×C₇	C₂²×D₄	1	1	yes	characteristic
201	C₇×Q₈	—	2	2	no	—
202	C₇×Q₈	—	2	2	no	—
203	C₇×Q₈	—	4	1	no	—
204	C₇×Q₈	—	4	1	no	—
205	C₇×D₄	—	2	8	no	—
206	C₂×C₄×C₇	—	2	1	no	—
207	C₂×C₄×C₇	—	2	1	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	—	4	1	no	—
214	C₂×C₄×C₇	—	4	1	no	—
215	C₂×C₄×C₇	—	4	1	no	—
216	C₂×C₄×C₇	—	4	1	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	1	no	—
222	C₂×C₄×C₇	—	4	2	no	—
223	C₂×C₄×C₇	—	4	2	no	—
224	C₂×C₄×C₇	—	4	1	no	—
225	C₂×C₄×C₇	—	4	1	no	—
226	C₂×C₄×C₇	—	4	2	no	—
227	C₂×C₄×C₇	—	4	2	no	—
228	C₂×C₄×C₇	—	4	1	no	—
229	C₂×C₄×C₇	—	4	2	no	—
230	C₂×C₄×C₇	—	4	2	no	—
231	C₂×C₄×C₇	—	4	1	no	—
232	C₂×C₄×C₇	—	4	1	no	—
233	C₂×C₄×C₇	—	8	8	no	—
234	C₂×C₄×C₇	#123	1	2	yes	—
235	C₂×C₄×C₇	#123	1	2	yes	—
236	C₂×C₄×C₇	C₂×SD₁₆	1	2	yes	—
237	C₂×C₄×C₇	#137	1	2	yes	—
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	C₂×C₄×C₇	H(5,𝔽₂)	1	1	yes	characteristic
243	C₂×C₄×C₇	H(5,𝔽₂)	1	1	yes	characteristic
244	C₇×C₈	—	4	2	no	—
245	C₇×C₈	—	4	1	no	—
246	C₇×C₈	—	4	1	no	—
247	C₂²×Q₈	C₂³×C₇	1	1	yes	characteristic
248	C₂²×D₄	C₇×D₄	1	1	yes	characteristic
249	C₂³×C₄	—	2	2	no	—
250	C₂³×C₄	C₂³×C₇	1	2	yes	—
251	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
252	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
253	C₂²×C₈	C₂³×C₇	1	2	yes	—
254	C₂²⋊Q₈	—	2	4	no	—
255	C₂²⋊Q₈	—	4	2	no	—
256	C₄×Q₈	—	2	2	no	—
257	C₄×Q₈	—	2	2	no	—
258	C₄×D₄	—	2	2	no	—
259	C₄×D₄	—	2	2	no	—
260	C₄×D₄	—	4	4	no	—
261	C₂×C₄⋊C₄	—	2	4	no	—
262	C₂×C₄⋊C₄	—	2	2	no	—
263	C₂×C₄⋊C₄	—	2	1	no	—
264	C₂×C₄⋊C₄	—	2	1	no	—
265	C₂×C₄⋊C₄	—	2	2	no	—
266	C₂×C₄⋊C₄	—	2	1	no	—
267	C₂×C₄⋊C₄	—	2	1	no	—
268	C₂×C₄⋊C₄	—	2	1	no	—
269	C₂×C₄⋊C₄	—	4	2	no	—
270	C₂×C₄⋊C₄	C₇×D₄	1	1	yes	characteristic
271	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
272	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
273	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
274	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
275	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
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	1	no	—
281	C₂×C₄²	—	2	1	no	—
282	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
283	#106	—	4	2	no	—
284	C₄⋊C₈	—	2	2	no	—
285	#103	—	2	2	no	—
286	#103	—	2	2	no	—
287	#103	—	4	2	no	—
288	C₂²⋊C₈	—	4	2	no	—
289	C₂²⋊C₈	—	4	2	no	—
290	C₄×C₈	—	2	2	no	—
291	#95	—	2	1	no	—
292	#95	—	2	2	no	—
293	#95	—	2	2	no	—
294	C₂²×C₇	—	2	4	no	—
295	C₂²×C₇	—	2	4	no	—
296	C₂²×C₇	—	2	4	no	—
297	C₂²×C₇	—	4	2	no	—
298	C₂²×C₇	—	4	2	no	—
299	C₂²×C₇	—	4	2	no	—
300	C₂²×C₇	—	4	2	no	—
301	C₂²×C₇	C₂×#123	1	1	yes	characteristic
302	C₂²×C₇	#546	1	1	yes	characteristic
303	C₂²×C₇	#546	1	1	yes	characteristic
304	C₂²×C₇	C₂²×SD₁₆	1	1	yes	characteristic
305	C₂²×C₇	C₂×#137	1	1	yes	characteristic
306	C₂²×C₇	#576	1	1	yes	characteristic
307	C₂²×C₇	#578	1	1	yes	characteristic
308	C₄×C₇	—	2	2	no	—
309	C₄×C₇	—	4	2	no	—
310	C₄×C₇	—	4	2	no	—
311	C₄×C₇	—	4	2	no	—
312	C₄×C₇	—	8	2	no	—
313	C₄×C₇	—	8	1	no	—
314	C₄×C₇	—	8	2	no	—
315	C₄×C₇	—	8	1	no	—
316	C₄×C₇	#483	1	4	yes	—
317	C₄×C₇	#529	1	1	yes	characteristic
318	C₄×C₇	#540	1	1	yes	characteristic
319	C₄×C₇	#553	1	1	yes	characteristic
320	C₄×C₇	#555	1	1	yes	characteristic
321	C₂⁴	C₂×C₇×D₄	1	2	yes	—
322	C₂×Q₈	—	2	1	no	—
323	C₂×Q₈	—	2	1	no	—
324	C₂×Q₈	—	2	1	no	—
325	C₂×Q₈	—	2	1	no	—
326	C₂×Q₈	—	2	1	no	—
327	C₂×Q₈	C₇×#41	1	2	yes	—
328	C₂×D₄	—	2	2	no	—
329	C₂×D₄	—	2	2	no	—
330	C₂×D₄	C₇×SD₁₆	1	4	yes	—
331	C₂²×C₄	—	2	1	no	—
332	C₂²×C₄	—	2	1	no	—
333	C₂²×C₄	—	2	2	no	—
334	C₂²×C₄	—	2	2	no	—
335	C₂²×C₄	—	2	2	no	—
336	C₂²×C₄	—	2	2	no	—
337	C₂²×C₄	—	2	2	no	—
338	C₂²×C₄	—	2	2	no	—
339	C₂²×C₄	—	2	1	no	—
340	C₂²×C₄	—	2	1	no	—
341	C₂²×C₄	—	2	2	no	—
342	C₂²×C₄	—	2	2	no	—
343	C₂²×C₄	—	4	4	no	—
344	C₂²×C₄	—	4	4	no	—
345	C₂²×C₄	—	8	2	no	—
346	C₂²×C₄	C₂×C₇×D₄	1	2	yes	—
347	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
348	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
349	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
350	C₂×C₈	—	2	1	no	—
351	C₂×C₈	—	2	1	no	—
352	C₂×C₈	—	2	1	no	—
353	C₂×C₈	—	2	1	no	—
354	C₂×C₈	—	2	2	no	—
355	C₂×C₈	—	2	1	no	—
356	C₂×C₈	—	2	1	no	—
357	C₂×C₈	—	2	2	no	—
358	C₂×C₈	—	2	2	no	—
359	C₄⋊C₄	—	2	2	no	—
360	C₄⋊C₄	—	2	1	no	—
361	C₄⋊C₄	—	2	1	no	—
362	C₄⋊C₄	—	2	2	no	—
363	C₄⋊C₄	—	2	1	no	—
364	C₄⋊C₄	—	2	1	no	—
365	C₄⋊C₄	—	2	2	no	—
366	C₄⋊C₄	—	2	2	no	—
367	C₄⋊C₄	—	2	1	no	—
368	C₄⋊C₄	—	2	2	no	—
369	C₄⋊C₄	—	4	4	no	—
370	C₄⋊C₄	—	4	4	no	—
371	C₄⋊C₄	—	4	2	no	—
372	C₄⋊C₄	—	4	2	no	—
373	C₄⋊C₄	—	4	2	no	—
374	C₄⋊C₄	—	8	1	no	—
375	C₄⋊C₄	—	8	1	no	—
376	C₄⋊C₄	C₇×#41	1	2	yes	—
377	C₂²⋊C₄	—	2	4	no	—
378	C₂²⋊C₄	—	4	4	no	—
379	C₂²⋊C₄	—	4	4	no	—
380	C₂²⋊C₄	—	8	2	no	—
381	C₄²	—	4	2	no	—
382	C₄²	—	4	2	no	—
383	C₄²	C₇×#41	1	2	yes	—
384	C₄²	C₇×#41	1	2	yes	—
385	C₂×C₇	—	4	4	no	—
386	C₂×C₇	#2420	1	1	yes	characteristic
387	C₂×C₇	C₂×#483	1	1	yes	characteristic
388	C₂×C₇	#3098	1	1	yes	characteristic
389	C₂×C₇	#3295	1	1	yes	characteristic
390	C₂×C₇	#3298	1	1	yes	characteristic
391	C₂×C₇	#3328	1	1	yes	characteristic
392	C₂×C₇	#3333	1	1	yes	characteristic
393	C₂³	—	2	2	no	—
394	C₂³	—	2	2	no	—
395	C₂³	—	2	2	no	—
396	C₂³	—	2	2	no	—
397	C₂³	—	2	2	no	—
398	C₂³	—	2	2	no	—
399	C₂³	C₂×C₇×SD₁₆	1	4	yes	—
400	C₂³	C₂²×C₇×D₄	1	1	yes	characteristic
401	Q₈	—	2	2	no	—
402	Q₈	—	2	2	no	—
403	Q₈	—	4	1	no	—
404	Q₈	—	4	1	no	—
405	D₄	—	2	8	no	—
406	C₂×C₄	—	2	1	no	—
407	C₂×C₄	—	2	1	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	—	2	2	no	—
413	C₂×C₄	—	4	1	no	—
414	C₂×C₄	—	4	1	no	—
415	C₂×C₄	—	4	1	no	—
416	C₂×C₄	—	4	1	no	—
417	C₂×C₄	—	4	2	no	—
418	C₂×C₄	—	4	2	no	—
419	C₂×C₄	—	4	2	no	—
420	C₂×C₄	—	4	2	no	—
421	C₂×C₄	—	4	1	no	—
422	C₂×C₄	—	4	2	no	—
423	C₂×C₄	—	4	2	no	—
424	C₂×C₄	—	4	1	no	—
425	C₂×C₄	—	4	1	no	—
426	C₂×C₄	—	4	2	no	—
427	C₂×C₄	—	4	2	no	—
428	C₂×C₄	—	4	1	no	—
429	C₂×C₄	—	4	2	no	—
430	C₂×C₄	—	4	2	no	—
431	C₂×C₄	—	4	1	no	—
432	C₂×C₄	—	4	1	no	—
433	C₂×C₄	—	8	8	no	—
434	C₂×C₄	C₇×#123	1	2	yes	—
435	C₂×C₄	C₇×#123	1	2	yes	—
436	C₂×C₄	C₂×C₇×SD₁₆	1	2	yes	—
437	C₂×C₄	C₇×#137	1	2	yes	—
438	C₂×C₄	C₂×C₇×#41	1	1	yes	characteristic
439	C₂×C₄	C₂×C₇×#41	1	1	yes	characteristic
440	C₂×C₄	C₂×C₇×#41	1	1	yes	characteristic
441	C₂×C₄	C₂×C₇×#41	1	1	yes	characteristic
442	C₂×C₄	C₇×H(5,𝔽₂)	1	1	yes	characteristic
443	C₂×C₄	C₇×H(5,𝔽₂)	1	1	yes	characteristic
444	C₈	—	4	2	no	—
445	C₈	—	4	1	no	—
446	C₈	—	4	1	no	—
447	C₇	#24969	1	1	yes	characteristic, direct product factor, Sylow
448	C₂²	—	2	4	no	—
449	C₂²	—	2	4	no	—
450	C₂²	—	2	4	no	—
451	C₂²	—	4	2	no	—
452	C₂²	—	4	2	no	—
453	C₂²	—	4	2	no	—
454	C₂²	—	4	2	no	—
455	C₂²	C₂×C₇×#123	1	1	yes	characteristic
456	C₂²	C₇×#546	1	1	yes	characteristic
457	C₂²	C₇×#546	1	1	yes	characteristic
458	C₂²	C₂²×C₇×SD₁₆	1	1	yes	characteristic
459	C₂²	C₂×C₇×#137	1	1	yes	characteristic
460	C₂²	C₇×#576	1	1	yes	characteristic
461	C₂²	C₇×#578	1	1	yes	characteristic
462	C₄	—	2	2	no	—
463	C₄	—	4	2	no	—
464	C₄	—	4	2	no	—
465	C₄	—	4	2	no	—
466	C₄	—	8	2	no	—
467	C₄	—	8	1	no	—
468	C₄	—	8	2	no	—
469	C₄	—	8	1	no	—
470	C₄	C₇×#483	1	4	yes	—
471	C₄	C₇×#529	1	1	yes	characteristic
472	C₄	C₇×#540	1	1	yes	characteristic
473	C₄	C₇×#553	1	1	yes	characteristic
474	C₄	C₇×#555	1	1	yes	characteristic
475	C₂	—	4	4	no	—
476	C₂	C₇×#2420	1	1	yes	characteristic
477	C₂	C₂×C₇×#483	1	1	yes	characteristic
478	C₂	C₇×#3098	1	1	yes	characteristic
479	C₂	C₇×#3295	1	1	yes	characteristic
480	C₂	C₇×#3298	1	1	yes	characteristic
481	C₂	C₇×#3328	1	1	yes	characteristic
482	C₂	C₇×#3333	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
3. C₇×#2077	C₂	semidirect
4. C₇×#2035	C₂	semidirect
6. C₇×#1948	C₂	semidirect
7. C₇×#1872	C₂	semidirect
8. C₇×#1834	C₂	semidirect
9. C₇×#1823	C₂	semidirect
10. C₇×#1803	C₂	semidirect
11. C₄×C₇×#103	C₂	semidirect
41. #24969	C₇	direct (N × H)
91. #2077	C₂×C₇	semidirect
92. #2035	C₂×C₇	semidirect
94. #1948	C₂×C₇	semidirect
95. #1872	C₂×C₇	semidirect
96. #1834	C₂×C₇	semidirect
97. #1823	C₂×C₇	semidirect
98. #1803	C₂×C₇	semidirect
99. C₄×#103	C₂×C₇	semidirect
447. C₇	#24969	direct (N × H)

Maximal subgroups

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

subgroup	index
C₇×#2538	2
C₇×D₄×C₄⋊C₄	2
C₇×#2077	2
C₇×#2035	2
C₇×#1954	2
C₇×#1948	2
C₇×#1872	2
C₇×#1834	2
C₇×#1823	2
C₇×#1803	2
C₄×C₇×#103	2
#24969	7

Subgroups — C7×#24969 #13202185

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×#24969 #13202185