Subgroups — C₇×#23677 #13200893

Order 1792.

924 conjugacy classes of subgroups.

The subgroup lattice has 492 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄×C₇×SD₁₆	C₂	1	2	yes	maximal
2	C₄×C₇×C₄⋊Q₈	C₂	1	1	yes	maximal, characteristic, complemented
3	C₇×#2293	C₂	1	1	yes	maximal, characteristic
4	C₇×#2084	C₂	1	1	yes	maximal, characteristic, complemented
5	C₇×#2071	C₂	1	1	yes	maximal, characteristic
6	C₇×#2066	C₂	1	2	yes	maximal, complemented
7	C₇×#2055	C₂	1	2	yes	maximal
8	C₇×#2043	C₂	1	1	yes	maximal, characteristic, complemented
9	C₇×#2013	C₂	1	1	yes	maximal, characteristic
10	C₄×C₇×C₄⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄×C₇×#103	C₂	1	2	yes	maximal, complemented
12	C₂²×C₇×SD₁₆	C₂²	1	2	yes	—
13	C₂×C₇×C₄⋊Q₈	C₂²	1	1	yes	characteristic
14	C₂×C₄×C₇×Q₈	C₂²	1	2	yes	—
15	C₂×C₄×C₇×D₄	C₂²	1	1	yes	characteristic
16	C₂×C₇×#117	—	2	1	no	—
17	C₄×C₇×SD₁₆	—	2	8	no	—
18	C₂×C₇×#106	C₂²	1	2	yes	—
19	C₂×C₇×C₄⋊C₈	C₂²	1	2	yes	—
20	C₂×C₇×#103	C₂²	1	2	yes	—
21	C₂×C₇×#103	C₂²	1	2	yes	—
22	C₂×C₇×#103	C₂²	1	2	yes	—
23	C₂×C₇×#102	C₂²	1	2	yes	—
24	C₂×C₄×C₇×C₈	C₂²	1	2	yes	—
25	C₇×#391	C₂²	1	2	yes	—
26	C₇×#390	C₂²	1	1	yes	characteristic
27	C₇×#390	C₂²	1	1	yes	characteristic
28	C₇×#389	—	2	1	no	—
29	C₇×#389	—	2	1	no	—
30	C₇×#389	C₂²	1	1	yes	characteristic
31	C₇×#389	C₂²	1	1	yes	characteristic
32	C₇×#388	—	2	1	no	—
33	C₇×#388	—	2	1	no	—
34	C₇×#384	C₂²	1	1	yes	characteristic
35	C₄×C₇×C₄⋊C₄	—	2	1	no	—
36	C₄×C₇×C₄⋊C₄	—	2	1	no	—
37	C₄×C₇×C₄⋊C₄	C₂²	1	1	yes	characteristic
38	C₄×C₇×C₂²⋊C₄	—	2	1	no	—
39	C₄³×C₇	C₂²	1	1	yes	characteristic
40	C₇×#340	C₂²	1	2	yes	—
41	C₇×#340	C₂²	1	2	yes	—
42	C₇×#336	C₂²	1	1	yes	characteristic
43	C₇×#336	C₂²	1	1	yes	characteristic
44	#23677	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
45	C₂²×C₇×Q₈	C₂³	1	2	yes	—
46	C₂²×C₇×D₄	C₂³	1	1	yes	characteristic
47	C₂³×C₄×C₇	—	2	1	no	—
48	C₂×C₇×SD₁₆	—	2	4	no	—
49	C₂×C₇×SD₁₆	—	2	4	no	—
50	C₂×C₇×SD₁₆	—	2	4	no	—
51	C₂²×C₇×C₈	C₂³	1	2	yes	—
52	C₂²×C₇×C₈	C₂³	1	2	yes	—
53	C₇×C₄⋊Q₈	—	2	4	no	—
54	C₄×C₇×Q₈	—	2	4	no	—
55	C₄×C₇×Q₈	—	2	4	no	—
56	C₄×C₇×D₄	—	2	2	no	—
57	C₄×C₇×D₄	D₄	1	4	yes	—
58	C₇×#117	—	4	4	no	—
59	C₂×C₇×C₄⋊C₄	—	2	1	no	—
60	C₂×C₇×C₄⋊C₄	—	2	1	no	—
61	C₂×C₇×C₄⋊C₄	—	2	1	no	—
62	C₂×C₇×C₄⋊C₄	—	2	1	no	—
63	C₂×C₇×C₄⋊C₄	—	2	1	no	—
64	C₂×C₇×C₄⋊C₄	—	2	1	no	—
65	C₂×C₇×C₄⋊C₄	—	2	2	no	—
66	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
67	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
68	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
69	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
70	C₂×C₇×C₂²⋊C₄	—	2	1	no	—
71	C₂×C₇×C₂²⋊C₄	—	2	1	no	—
72	C₂×C₇×C₂²⋊C₄	—	2	1	no	—
73	C₂×C₇×C₂²⋊C₄	—	2	1	no	—
74	C₂×C₇×C₂²⋊C₄	—	2	1	no	—
75	C₂×C₄²×C₇	—	2	1	no	—
76	C₂×C₄²×C₇	—	2	2	no	—
77	C₂×C₄²×C₇	D₄	1	1	yes	characteristic
78	C₂×C₄²×C₇	D₄	1	1	yes	characteristic
79	C₂×C₄²×C₇	D₄	1	1	yes	characteristic
80	C₂×C₄²×C₇	D₄	1	1	yes	characteristic
81	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
82	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
83	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
84	C₇×#106	—	2	4	no	—
85	C₇×C₄⋊C₈	—	2	4	no	—
86	C₇×#103	—	2	4	no	—
87	C₇×#103	—	2	4	no	—
88	C₇×#103	—	2	4	no	—
89	C₇×#102	—	2	4	no	—
90	C₄×C₇×C₈	—	2	4	no	—
91	C₇×#95	—	2	1	no	—
92	C₇×#95	—	2	1	no	—
93	C₇×#95	—	2	2	no	—
94	C₇×#95	—	2	2	no	—
95	C₇×#95	—	2	1	no	—
96	C₂×C₄×SD₁₆	C₂×C₇	1	2	yes	—
97	C₄×C₄⋊Q₈	C₂×C₇	1	1	yes	characteristic, complemented
98	#2293	C₂×C₇	1	1	yes	characteristic
99	#2084	C₂×C₇	1	1	yes	characteristic, complemented
100	#2071	C₂×C₇	1	1	yes	characteristic
101	#2066	C₂×C₇	1	2	yes	complemented
102	#2055	C₂×C₇	1	2	yes	—
103	#2043	C₂×C₇	1	1	yes	characteristic, complemented
104	#2013	C₂×C₇	1	1	yes	characteristic
105	C₄×C₄⋊C₈	C₂×C₇	1	1	yes	characteristic, complemented
106	C₄×#103	C₂×C₇	1	2	yes	complemented
107	C₂⁴×C₇	—	2	1	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	—	2	2	no	—
113	C₂×C₇×Q₈	#41	1	4	yes	—
114	C₂×C₇×D₄	—	2	2	no	—
115	C₂×C₇×D₄	—	2	2	no	—
116	C₂×C₇×D₄	—	2	1	no	—
117	C₂×C₇×D₄	C₂×D₄	1	2	yes	—
118	C₂²×C₄×C₇	—	2	2	no	—
119	C₂²×C₄×C₇	—	2	1	no	—
120	C₂²×C₄×C₇	—	2	4	no	—
121	C₂²×C₄×C₇	—	2	1	no	—
122	C₂²×C₄×C₇	—	2	1	no	—
123	C₂²×C₄×C₇	—	2	2	no	—
124	C₂²×C₄×C₇	—	4	2	no	—
125	C₂²×C₄×C₇	—	4	2	no	—
126	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
127	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
128	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
129	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
130	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
131	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
132	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
133	C₇×SD₁₆	—	2	16	no	—
134	C₂×C₇×C₈	—	2	2	no	—
135	C₂×C₇×C₈	—	2	2	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	#41	1	4	yes	—
140	C₇×C₄⋊C₄	—	2	4	no	—
141	C₇×C₄⋊C₄	—	2	4	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	—	4	4	no	—
149	C₇×C₄⋊C₄	—	4	2	no	—
150	C₇×C₄⋊C₄	—	4	2	no	—
151	C₇×C₄⋊C₄	—	4	2	no	—
152	C₇×C₄⋊C₄	C₂×D₄	1	2	yes	—
153	C₇×C₂²⋊C₄	—	2	4	no	—
154	C₇×C₂²⋊C₄	—	4	2	no	—
155	C₇×C₂²⋊C₄	—	4	2	no	—
156	C₇×C₂²⋊C₄	—	4	2	no	—
157	C₇×C₂²⋊C₄	—	4	2	no	—
158	C₄²×C₇	—	2	2	no	—
159	C₄²×C₇	—	2	2	no	—
160	C₄²×C₇	—	2	2	no	—
161	C₄²×C₇	—	2	2	no	—
162	C₄²×C₇	—	4	1	no	—
163	C₄²×C₇	—	4	4	no	—
164	C₄²×C₇	—	4	2	no	—
165	C₄²×C₇	SD₁₆	1	4	yes	complemented
166	C₄²×C₇	C₂×D₄	1	2	yes	—
167	C₄²×C₇	#41	1	2	yes	—
168	C₂²×SD₁₆	C₂²×C₇	1	2	yes	—
169	C₂×C₄⋊Q₈	C₂²×C₇	1	1	yes	characteristic
170	C₂×C₄×Q₈	C₂²×C₇	1	2	yes	—
171	C₂×C₄×D₄	C₂²×C₇	1	1	yes	characteristic
172	C₂×#117	—	2	1	no	—
173	C₄×SD₁₆	—	2	8	no	—
174	C₂×#106	C₂²×C₇	1	2	yes	—
175	C₂×C₄⋊C₈	C₂²×C₇	1	2	yes	—
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	C₂×#102	C₂²×C₇	1	2	yes	—
180	C₂×C₄×C₈	C₂²×C₇	1	2	yes	—
181	#391	C₂²×C₇	1	2	yes	—
182	#390	C₂²×C₇	1	1	yes	characteristic
183	#390	C₂²×C₇	1	1	yes	characteristic
184	#389	—	2	1	no	—
185	#389	—	2	1	no	—
186	#389	C₂²×C₇	1	1	yes	characteristic
187	#389	C₂²×C₇	1	1	yes	characteristic
188	#388	—	2	1	no	—
189	#388	—	2	1	no	—
190	#384	C₂²×C₇	1	1	yes	characteristic
191	C₄×C₄⋊C₄	—	2	1	no	—
192	C₄×C₄⋊C₄	—	2	1	no	—
193	C₄×C₄⋊C₄	C₂²×C₇	1	1	yes	characteristic
194	C₄×C₂²⋊C₄	—	2	1	no	—
195	C₄³	C₂²×C₇	1	1	yes	characteristic
196	#340	C₂²×C₇	1	2	yes	—
197	#340	C₂²×C₇	1	2	yes	—
198	#336	C₂²×C₇	1	1	yes	characteristic
199	#336	C₂²×C₇	1	1	yes	characteristic
200	C₂³×C₇	—	2	2	no	—
201	C₂³×C₇	—	4	1	no	—
202	C₂³×C₇	—	4	1	no	—
203	C₂³×C₇	—	4	1	no	—
204	C₂³×C₇	—	4	1	no	—
205	C₂³×C₇	—	4	1	no	—
206	C₂³×C₇	—	4	1	no	—
207	C₂³×C₇	C₂²×D₄	1	1	yes	characteristic
208	C₇×Q₈	—	2	4	no	—
209	C₇×Q₈	—	2	4	no	—
210	C₇×Q₈	—	4	2	no	—
211	C₇×Q₈	—	4	2	no	—
212	C₇×D₄	—	2	4	no	—
213	C₇×D₄	—	4	2	no	—
214	C₂×C₄×C₇	—	2	1	no	—
215	C₂×C₄×C₇	—	2	1	no	—
216	C₂×C₄×C₇	—	2	1	no	—
217	C₂×C₄×C₇	—	2	1	no	—
218	C₂×C₄×C₇	—	2	1	no	—
219	C₂×C₄×C₇	—	2	1	no	—
220	C₂×C₄×C₇	—	2	1	no	—
221	C₂×C₄×C₇	—	2	1	no	—
222	C₂×C₄×C₇	—	2	2	no	—
223	C₂×C₄×C₇	—	2	4	no	—
224	C₂×C₄×C₇	—	2	1	no	—
225	C₂×C₄×C₇	—	2	1	no	—
226	C₂×C₄×C₇	—	2	1	no	—
227	C₂×C₄×C₇	—	4	2	no	—
228	C₂×C₄×C₇	—	4	2	no	—
229	C₂×C₄×C₇	—	4	1	no	—
230	C₂×C₄×C₇	—	4	1	no	—
231	C₂×C₄×C₇	—	4	8	no	—
232	C₂×C₄×C₇	—	4	2	no	—
233	C₂×C₄×C₇	—	4	1	no	—
234	C₂×C₄×C₇	—	4	1	no	—
235	C₂×C₄×C₇	—	4	1	no	—
236	C₂×C₄×C₇	—	4	1	no	—
237	C₂×C₄×C₇	—	4	1	no	—
238	C₂×C₄×C₇	—	4	2	no	—
239	C₂×C₄×C₇	—	4	1	no	—
240	C₂×C₄×C₇	—	4	2	no	—
241	C₂×C₄×C₇	#121	1	2	yes	—
242	C₂×C₄×C₇	#121	1	2	yes	—
243	C₂×C₄×C₇	C₂×SD₁₆	1	2	yes	—
244	C₂×C₄×C₇	C₂×SD₁₆	1	2	yes	—
245	C₂×C₄×C₇	C₂×SD₁₆	1	2	yes	—
246	C₂×C₄×C₇	#135	1	2	yes	—
247	C₂×C₄×C₇	#137	1	2	yes	—
248	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
249	C₂×C₄×C₇	C₂×#41	1	2	yes	—
250	C₂×C₄×C₇	C₂×#41	1	2	yes	—
251	C₂×C₄×C₇	C₂×#41	1	1	yes	characteristic
252	C₇×C₈	—	2	4	no	—
253	C₇×C₈	—	4	2	no	—
254	C₂²×Q₈	C₂³×C₇	1	2	yes	—
255	C₂²×D₄	C₂³×C₇	1	1	yes	characteristic
256	C₂³×C₄	—	2	1	no	—
257	C₂×SD₁₆	—	2	4	no	—
258	C₂×SD₁₆	—	2	4	no	—
259	C₂×SD₁₆	—	2	4	no	—
260	C₂²×C₈	C₂³×C₇	1	2	yes	—
261	C₂²×C₈	C₂³×C₇	1	2	yes	—
262	C₄⋊Q₈	—	2	4	no	—
263	C₄×Q₈	—	2	4	no	—
264	C₄×Q₈	—	2	4	no	—
265	C₄×D₄	—	2	2	no	—
266	C₄×D₄	C₇×D₄	1	4	yes	—
267	#117	—	4	4	no	—
268	C₂×C₄⋊C₄	—	2	1	no	—
269	C₂×C₄⋊C₄	—	2	1	no	—
270	C₂×C₄⋊C₄	—	2	1	no	—
271	C₂×C₄⋊C₄	—	2	1	no	—
272	C₂×C₄⋊C₄	—	2	2	no	—
273	C₂×C₄⋊C₄	—	2	1	no	—
274	C₂×C₄⋊C₄	—	2	1	no	—
275	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
276	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
277	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
278	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
279	C₂×C₂²⋊C₄	—	2	1	no	—
280	C₂×C₂²⋊C₄	—	2	1	no	—
281	C₂×C₂²⋊C₄	—	2	1	no	—
282	C₂×C₂²⋊C₄	—	2	1	no	—
283	C₂×C₂²⋊C₄	—	2	1	no	—
284	C₂×C₄²	—	2	1	no	—
285	C₂×C₄²	—	2	2	no	—
286	C₂×C₄²	C₇×D₄	1	1	yes	characteristic
287	C₂×C₄²	C₇×D₄	1	1	yes	characteristic
288	C₂×C₄²	C₇×D₄	1	1	yes	characteristic
289	C₂×C₄²	C₇×D₄	1	1	yes	characteristic
290	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
291	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
292	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
293	#106	—	2	4	no	—
294	C₄⋊C₈	—	2	4	no	—
295	#103	—	2	4	no	—
296	#103	—	2	4	no	—
297	#103	—	2	4	no	—
298	#102	—	2	4	no	—
299	C₄×C₈	—	2	4	no	—
300	#95	—	2	1	no	—
301	#95	—	2	1	no	—
302	#95	—	2	2	no	—
303	#95	—	2	2	no	—
304	#95	—	2	1	no	—
305	C₂²×C₇	—	4	2	no	—
306	C₂²×C₇	—	4	2	no	—
307	C₂²×C₇	—	4	2	no	—
308	C₂²×C₇	—	8	1	no	—
309	C₂²×C₇	—	8	1	no	—
310	C₂²×C₇	—	8	1	no	—
311	C₂²×C₇	—	8	1	no	—
312	C₂²×C₇	C₂×#121	1	1	yes	characteristic
313	C₂²×C₇	#525	1	1	yes	characteristic
314	C₂²×C₇	#532	1	1	yes	characteristic
315	C₂²×C₇	C₂²×SD₁₆	1	1	yes	characteristic
316	C₂²×C₇	C₂×#135	1	1	yes	characteristic
317	C₂²×C₇	C₂×#137	1	1	yes	characteristic
318	C₂²×C₇	#575	1	1	yes	characteristic
319	C₄×C₇	—	2	2	no	—
320	C₄×C₇	—	2	2	no	—
321	C₄×C₇	—	2	2	no	—
322	C₄×C₇	—	2	2	no	—
323	C₄×C₇	—	4	4	no	—
324	C₄×C₇	—	4	1	no	—
325	C₄×C₇	—	4	2	no	—
326	C₄×C₇	—	8	1	no	—
327	C₄×C₇	—	8	1	no	—
328	C₄×C₇	—	8	2	no	—
329	C₄×C₇	#461	1	4	yes	—
330	C₄×C₇	#525	1	2	yes	—
331	C₄×C₇	#529	1	2	yes	—
332	C₂⁴	—	2	1	no	—
333	C₂×Q₈	—	2	2	no	—
334	C₂×Q₈	—	2	2	no	—
335	C₂×Q₈	—	2	2	no	—
336	C₂×Q₈	—	2	2	no	—
337	C₂×Q₈	—	2	2	no	—
338	C₂×Q₈	C₇×#41	1	4	yes	—
339	C₂×D₄	—	2	2	no	—
340	C₂×D₄	—	2	2	no	—
341	C₂×D₄	—	2	1	no	—
342	C₂×D₄	C₂×C₇×D₄	1	2	yes	—
343	C₂²×C₄	—	2	2	no	—
344	C₂²×C₄	—	2	1	no	—
345	C₂²×C₄	—	2	4	no	—
346	C₂²×C₄	—	2	1	no	—
347	C₂²×C₄	—	2	1	no	—
348	C₂²×C₄	—	2	2	no	—
349	C₂²×C₄	—	4	2	no	—
350	C₂²×C₄	—	4	2	no	—
351	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
352	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
353	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
354	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
355	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
356	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
357	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
358	SD₁₆	—	2	16	no	—
359	C₂×C₈	—	2	2	no	—
360	C₂×C₈	—	2	2	no	—
361	C₂×C₈	—	2	2	no	—
362	C₂×C₈	—	2	2	no	—
363	C₂×C₈	—	2	2	no	—
364	C₂×C₈	C₇×#41	1	4	yes	—
365	C₄⋊C₄	—	2	4	no	—
366	C₄⋊C₄	—	2	4	no	—
367	C₄⋊C₄	—	2	1	no	—
368	C₄⋊C₄	—	2	2	no	—
369	C₄⋊C₄	—	2	2	no	—
370	C₄⋊C₄	—	2	2	no	—
371	C₄⋊C₄	—	2	2	no	—
372	C₄⋊C₄	—	4	2	no	—
373	C₄⋊C₄	—	4	4	no	—
374	C₄⋊C₄	—	4	2	no	—
375	C₄⋊C₄	—	4	2	no	—
376	C₄⋊C₄	—	4	2	no	—
377	C₄⋊C₄	C₂×C₇×D₄	1	2	yes	—
378	C₂²⋊C₄	—	2	4	no	—
379	C₂²⋊C₄	—	4	2	no	—
380	C₂²⋊C₄	—	4	2	no	—
381	C₂²⋊C₄	—	4	2	no	—
382	C₂²⋊C₄	—	4	2	no	—
383	C₄²	—	2	2	no	—
384	C₄²	—	2	2	no	—
385	C₄²	—	2	2	no	—
386	C₄²	—	2	2	no	—
387	C₄²	—	4	1	no	—
388	C₄²	—	4	4	no	—
389	C₄²	—	4	2	no	—
390	C₄²	C₇×SD₁₆	1	4	yes	complemented
391	C₄²	C₂×C₇×D₄	1	2	yes	—
392	C₄²	C₇×#41	1	2	yes	—
393	C₂×C₇	—	8	2	no	—
394	C₂×C₇	#2392	1	1	yes	characteristic
395	C₂×C₇	C₂×#461	1	1	yes	characteristic
396	C₂×C₇	#3035	1	1	yes	characteristic
397	C₂×C₇	#3103	1	1	yes	characteristic
398	C₂×C₇	#3108	1	1	yes	characteristic
399	C₂×C₇	#3167	1	1	yes	characteristic
400	C₂×C₇	#3172	1	1	yes	characteristic
401	C₂³	—	2	2	no	—
402	C₂³	—	4	1	no	—
403	C₂³	—	4	1	no	—
404	C₂³	—	4	1	no	—
405	C₂³	—	4	1	no	—
406	C₂³	—	4	1	no	—
407	C₂³	—	4	1	no	—
408	C₂³	C₂²×C₇×D₄	1	1	yes	characteristic
409	Q₈	—	2	4	no	—
410	Q₈	—	2	4	no	—
411	Q₈	—	4	2	no	—
412	Q₈	—	4	2	no	—
413	D₄	—	2	4	no	—
414	D₄	—	4	2	no	—
415	C₂×C₄	—	2	1	no	—
416	C₂×C₄	—	2	1	no	—
417	C₂×C₄	—	2	1	no	—
418	C₂×C₄	—	2	1	no	—
419	C₂×C₄	—	2	1	no	—
420	C₂×C₄	—	2	1	no	—
421	C₂×C₄	—	2	1	no	—
422	C₂×C₄	—	2	1	no	—
423	C₂×C₄	—	2	2	no	—
424	C₂×C₄	—	2	4	no	—
425	C₂×C₄	—	2	1	no	—
426	C₂×C₄	—	2	1	no	—
427	C₂×C₄	—	2	1	no	—
428	C₂×C₄	—	4	2	no	—
429	C₂×C₄	—	4	2	no	—
430	C₂×C₄	—	4	1	no	—
431	C₂×C₄	—	4	1	no	—
432	C₂×C₄	—	4	8	no	—
433	C₂×C₄	—	4	2	no	—
434	C₂×C₄	—	4	1	no	—
435	C₂×C₄	—	4	1	no	—
436	C₂×C₄	—	4	1	no	—
437	C₂×C₄	—	4	1	no	—
438	C₂×C₄	—	4	1	no	—
439	C₂×C₄	—	4	2	no	—
440	C₂×C₄	—	4	1	no	—
441	C₂×C₄	—	4	2	no	—
442	C₂×C₄	C₇×#121	1	2	yes	—
443	C₂×C₄	C₇×#121	1	2	yes	—
444	C₂×C₄	C₂×C₇×SD₁₆	1	2	yes	—
445	C₂×C₄	C₂×C₇×SD₁₆	1	2	yes	—
446	C₂×C₄	C₂×C₇×SD₁₆	1	2	yes	—
447	C₂×C₄	C₇×#135	1	2	yes	—
448	C₂×C₄	C₇×#137	1	2	yes	—
449	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
450	C₂×C₄	C₂×C₇×#41	1	2	yes	—
451	C₂×C₄	C₂×C₇×#41	1	2	yes	—
452	C₂×C₄	C₂×C₇×#41	1	1	yes	characteristic
453	C₈	—	2	4	no	—
454	C₈	—	4	2	no	—
455	C₇	#23677	1	1	yes	characteristic, direct product factor, Sylow
456	C₂²	—	4	2	no	—
457	C₂²	—	4	2	no	—
458	C₂²	—	4	2	no	—
459	C₂²	—	8	1	no	—
460	C₂²	—	8	1	no	—
461	C₂²	—	8	1	no	—
462	C₂²	—	8	1	no	—
463	C₂²	C₂×C₇×#121	1	1	yes	characteristic
464	C₂²	C₇×#525	1	1	yes	characteristic
465	C₂²	C₇×#532	1	1	yes	characteristic
466	C₂²	C₂²×C₇×SD₁₆	1	1	yes	characteristic
467	C₂²	C₂×C₇×#135	1	1	yes	characteristic
468	C₂²	C₂×C₇×#137	1	1	yes	characteristic
469	C₂²	C₇×#575	1	1	yes	characteristic
470	C₄	—	2	2	no	—
471	C₄	—	2	2	no	—
472	C₄	—	2	2	no	—
473	C₄	—	2	2	no	—
474	C₄	—	4	4	no	—
475	C₄	—	4	1	no	—
476	C₄	—	4	2	no	—
477	C₄	—	8	1	no	—
478	C₄	—	8	2	no	—
479	C₄	—	8	1	no	—
480	C₄	C₇×#461	1	4	yes	—
481	C₄	C₇×#525	1	2	yes	—
482	C₄	C₇×#529	1	2	yes	—
483	C₂	—	8	2	no	—
484	C₂	C₇×#2392	1	1	yes	characteristic
485	C₂	C₂×C₇×#461	1	1	yes	characteristic
486	C₂	C₇×#3035	1	1	yes	characteristic
487	C₂	C₇×#3103	1	1	yes	characteristic
488	C₂	C₇×#3108	1	1	yes	characteristic
489	C₂	C₇×#3167	1	1	yes	characteristic
490	C₂	C₇×#3172	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄×C₇	C₂×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₇
socle	C₂³×C₇	C₂²×D₄
prime radical	C₂²×C₇×D₄	C₂³
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₄×C₇ ◁ C₄³×C₇ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₄×C₇×C₄⋊Q₈	C₂	semidirect
4. C₇×#2084	C₂	semidirect
6. C₇×#2066	C₂	semidirect
8. C₇×#2043	C₂	semidirect
10. C₄×C₇×C₄⋊C₈	C₂	semidirect
11. C₄×C₇×#103	C₂	semidirect
44. #23677	C₇	direct (N × H)
97. C₄×C₄⋊Q₈	C₂×C₇	semidirect
99. #2084	C₂×C₇	semidirect
101. #2066	C₂×C₇	semidirect
103. #2043	C₂×C₇	semidirect
105. C₄×C₄⋊C₈	C₂×C₇	semidirect
106. C₄×#103	C₂×C₇	semidirect
165. C₄²×C₇	SD₁₆	semidirect
390. C₄²	C₇×SD₁₆	semidirect
455. C₇	#23677	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×SD₁₆	2
C₄×C₇×C₄⋊Q₈	2
C₇×#2293	2
C₇×#2084	2
C₇×#2071	2
C₇×#2066	2
C₇×#2055	2
C₇×#2043	2
C₇×#2013	2
C₄×C₇×C₄⋊C₈	2
C₄×C₇×#103	2
#23677	7

Subgroups — C7×#23677 #13200893

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×#23677 #13200893