Subgroups — C₇×#23817 #13201033

Order 1792.

810 conjugacy classes of subgroups.

The subgroup lattice has 474 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×C₇×C₄⋊Q₈	C₂	1	1	yes	maximal, characteristic, complemented
2	C₄×C₇×#124	C₂	1	1	yes	maximal, characteristic
3	C₇×#2101	C₂	1	2	yes	maximal, complemented
4	C₇×#2072	C₂	1	1	yes	maximal, characteristic, complemented
5	C₇×#2071	C₂	1	1	yes	maximal, characteristic
6	C₇×#2042	C₂	1	2	yes	maximal
7	C₇×#2024	C₂	1	1	yes	maximal, characteristic, complemented
8	C₇×#2023	C₂	1	1	yes	maximal, characteristic
9	C₄×C₇×#103	C₂	1	2	yes	maximal, complemented
10	C₄×C₇×#102	C₂	1	2	yes	maximal
11	C₇×#1744	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₇×C₄⋊Q₈	C₂²	1	1	yes	characteristic
13	C₂×C₇×#124	C₂²	1	1	yes	characteristic
14	C₂×C₄×C₇×Q₈	—	2	1	no	—
15	C₂×C₄×C₇×Q₈	C₂²	1	1	yes	characteristic
16	C₂×C₄×C₇×D₄	C₂²	1	1	yes	characteristic
17	C₂×C₇×#103	C₂²	1	2	yes	—
18	C₂×C₇×#103	C₂²	1	2	yes	—
19	C₂×C₇×#102	C₂²	1	2	yes	—
20	C₂×C₇×#102	C₂²	1	2	yes	—
21	C₂×C₄×C₇×C₈	C₂²	1	2	yes	—
22	C₇×#391	—	2	1	no	—
23	C₇×#391	C₂²	1	1	yes	characteristic
24	C₇×#390	C₂²	1	1	yes	characteristic
25	C₇×#389	—	2	1	no	—
26	C₇×#389	C₂²	1	2	yes	—
27	C₇×#388	—	2	1	no	—
28	C₇×#388	—	2	1	no	—
29	C₇×#384	C₂²	1	1	yes	characteristic
30	C₇×#382	C₂²	1	1	yes	characteristic
31	C₄×C₇×C₄⋊C₄	—	2	1	no	—
32	C₄×C₇×C₄⋊C₄	C₂²	1	2	yes	—
33	C₄×C₇×C₂²⋊C₄	—	2	1	no	—
34	C₄×C₇×C₂²⋊C₄	—	2	1	no	—
35	C₄³×C₇	C₂²	1	1	yes	characteristic
36	C₇×#340	C₂²	1	2	yes	—
37	C₇×#340	C₂²	1	2	yes	—
38	C₇×#340	C₂²	1	2	yes	—
39	C₇×#340	C₂²	1	2	yes	—
40	C₇×#336	C₂²	1	1	yes	characteristic
41	C₇×#336	C₂²	1	1	yes	characteristic
42	C₇×#336	C₂²	1	2	yes	—
43	#23817	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
44	C₂²×C₇×Q₈	—	2	1	no	—
45	C₂²×C₇×Q₈	C₂³	1	1	yes	characteristic
46	C₂²×C₇×D₄	C₂³	1	1	yes	characteristic
47	C₂³×C₄×C₇	—	2	1	no	—
48	C₂²×C₇×C₈	C₂³	1	2	yes	—
49	C₂²×C₇×C₈	C₂³	1	2	yes	—
50	C₇×C₄⋊Q₈	—	2	4	no	—
51	C₇×#124	—	2	2	no	—
52	C₇×#124	—	2	2	no	—
53	C₄×C₇×Q₈	—	2	4	no	—
54	C₄×C₇×Q₈	—	4	4	no	—
55	C₄×C₇×D₄	—	2	4	no	—
56	C₂×C₇×C₄⋊C₄	—	2	1	no	—
57	C₂×C₇×C₄⋊C₄	—	2	1	no	—
58	C₂×C₇×C₄⋊C₄	—	2	1	no	—
59	C₂×C₇×C₄⋊C₄	—	2	2	no	—
60	C₂×C₇×C₄⋊C₄	—	2	1	no	—
61	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
62	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
63	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
64	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
65	C₂×C₇×C₂²⋊C₄	—	2	1	no	—
66	C₂×C₇×C₂²⋊C₄	—	2	1	no	—
67	C₂×C₇×C₂²⋊C₄	—	2	1	no	—
68	C₂×C₇×C₂²⋊C₄	—	2	1	no	—
69	C₂×C₇×C₂²⋊C₄	—	2	1	no	—
70	C₂×C₄²×C₇	—	2	1	no	—
71	C₂×C₄²×C₇	—	2	2	no	—
72	C₂×C₄²×C₇	D₄	1	1	yes	characteristic
73	C₂×C₄²×C₇	D₄	1	1	yes	characteristic
74	C₂×C₄²×C₇	D₄	1	1	yes	characteristic
75	C₂×C₄²×C₇	D₄	1	1	yes	characteristic
76	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
77	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
78	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
79	C₇×#103	—	2	4	no	—
80	C₇×#103	—	2	4	no	—
81	C₇×#102	—	2	4	no	—
82	C₇×#102	—	2	4	no	—
83	C₄×C₇×C₈	—	2	4	no	—
84	C₇×#95	—	2	1	no	—
85	C₇×#95	—	2	1	no	—
86	C₇×#95	—	2	1	no	—
87	C₇×#95	—	2	1	no	—
88	C₇×#95	—	2	2	no	—
89	C₇×#95	—	2	2	no	—
90	C₄×C₄⋊Q₈	C₂×C₇	1	1	yes	characteristic, complemented
91	C₄×#124	C₂×C₇	1	1	yes	characteristic
92	#2101	C₂×C₇	1	2	yes	complemented
93	#2072	C₂×C₇	1	1	yes	characteristic, complemented
94	#2071	C₂×C₇	1	1	yes	characteristic
95	#2042	C₂×C₇	1	2	yes	—
96	#2024	C₂×C₇	1	1	yes	characteristic, complemented
97	#2023	C₂×C₇	1	1	yes	characteristic
98	C₄×#103	C₂×C₇	1	2	yes	complemented
99	C₄×#102	C₂×C₇	1	2	yes	—
100	#1744	C₂×C₇	1	1	yes	characteristic, complemented
101	C₂⁴×C₇	—	2	1	no	—
102	C₂×C₇×Q₈	—	2	4	no	—
103	C₂×C₇×Q₈	—	2	1	no	—
104	C₂×C₇×Q₈	—	2	2	no	—
105	C₂×C₇×Q₈	—	2	2	no	—
106	C₂×C₇×Q₈	—	4	2	no	—
107	C₂×C₇×Q₈	—	4	2	no	—
108	C₂×C₇×Q₈	#41	1	2	yes	—
109	C₂×C₇×D₄	—	2	2	no	—
110	C₂×C₇×D₄	—	2	2	no	—
111	C₂×C₇×D₄	—	2	1	no	—
112	C₂×C₇×D₄	#41	1	2	yes	—
113	C₂²×C₄×C₇	—	2	1	no	—
114	C₂²×C₄×C₇	—	2	2	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	—	4	2	no	—
119	C₂²×C₄×C₇	—	4	2	no	—
120	C₂²×C₄×C₇	—	4	2	no	—
121	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
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	C₂⁴	1	1	yes	characteristic
128	C₂×C₇×C₈	—	2	2	no	—
129	C₂×C₇×C₈	—	2	2	no	—
130	C₂×C₇×C₈	—	2	2	no	—
131	C₂×C₇×C₈	—	2	2	no	—
132	C₂×C₇×C₈	—	2	2	no	—
133	C₂×C₇×C₈	—	2	2	no	—
134	C₇×C₄⋊C₄	—	2	4	no	—
135	C₇×C₄⋊C₄	—	2	2	no	—
136	C₇×C₄⋊C₄	—	2	2	no	—
137	C₇×C₄⋊C₄	—	2	2	no	—
138	C₇×C₄⋊C₄	—	2	2	no	—
139	C₇×C₄⋊C₄	—	2	2	no	—
140	C₇×C₄⋊C₄	—	4	2	no	—
141	C₇×C₄⋊C₄	—	4	4	no	—
142	C₇×C₄⋊C₄	—	4	2	no	—
143	C₇×C₄⋊C₄	—	4	2	no	—
144	C₇×C₄⋊C₄	#41	1	4	yes	—
145	C₇×C₂²⋊C₄	—	2	4	no	—
146	C₇×C₂²⋊C₄	—	2	4	no	—
147	C₇×C₂²⋊C₄	—	4	2	no	—
148	C₇×C₂²⋊C₄	—	4	2	no	—
149	C₇×C₂²⋊C₄	—	4	2	no	—
150	C₄²×C₇	—	2	2	no	—
151	C₄²×C₇	—	2	2	no	—
152	C₄²×C₇	—	2	2	no	—
153	C₄²×C₇	—	2	2	no	—
154	C₄²×C₇	—	2	1	no	—
155	C₄²×C₇	—	2	1	no	—
156	C₄²×C₇	—	2	2	no	—
157	C₄²×C₇	—	4	2	no	—
158	C₄²×C₇	—	4	4	no	—
159	C₄²×C₇	#41	1	4	yes	—
160	C₂×C₄⋊Q₈	C₂²×C₇	1	1	yes	characteristic
161	C₂×#124	C₂²×C₇	1	1	yes	characteristic
162	C₂×C₄×Q₈	—	2	1	no	—
163	C₂×C₄×Q₈	C₂²×C₇	1	1	yes	characteristic
164	C₂×C₄×D₄	C₂²×C₇	1	1	yes	characteristic
165	C₂×#103	C₂²×C₇	1	2	yes	—
166	C₂×#103	C₂²×C₇	1	2	yes	—
167	C₂×#102	C₂²×C₇	1	2	yes	—
168	C₂×#102	C₂²×C₇	1	2	yes	—
169	C₂×C₄×C₈	C₂²×C₇	1	2	yes	—
170	#391	—	2	1	no	—
171	#391	C₂²×C₇	1	1	yes	characteristic
172	#390	C₂²×C₇	1	1	yes	characteristic
173	#389	—	2	1	no	—
174	#389	C₂²×C₇	1	2	yes	—
175	#388	—	2	1	no	—
176	#388	—	2	1	no	—
177	#384	C₂²×C₇	1	1	yes	characteristic
178	#382	C₂²×C₇	1	1	yes	characteristic
179	C₄×C₄⋊C₄	—	2	1	no	—
180	C₄×C₄⋊C₄	C₂²×C₇	1	2	yes	—
181	C₄×C₂²⋊C₄	—	2	1	no	—
182	C₄×C₂²⋊C₄	—	2	1	no	—
183	C₄³	C₂²×C₇	1	1	yes	characteristic
184	#340	C₂²×C₇	1	2	yes	—
185	#340	C₂²×C₇	1	2	yes	—
186	#340	C₂²×C₇	1	2	yes	—
187	#340	C₂²×C₇	1	2	yes	—
188	#336	C₂²×C₇	1	1	yes	characteristic
189	#336	C₂²×C₇	1	1	yes	characteristic
190	#336	C₂²×C₇	1	2	yes	—
191	C₂³×C₇	—	2	2	no	—
192	C₂³×C₇	—	4	1	no	—
193	C₂³×C₇	—	4	1	no	—
194	C₂³×C₇	—	4	1	no	—
195	C₂³×C₇	—	4	1	no	—
196	C₂³×C₇	—	4	1	no	—
197	C₂³×C₇	—	4	1	no	—
198	C₂³×C₇	C₂²×D₄	1	1	yes	characteristic
199	C₇×Q₈	—	2	4	no	—
200	C₇×Q₈	—	4	8	no	—
201	C₇×Q₈	—	4	2	no	—
202	C₇×D₄	—	2	4	no	—
203	C₇×D₄	—	4	2	no	—
204	C₂×C₄×C₇	—	2	1	no	—
205	C₂×C₄×C₇	—	2	1	no	—
206	C₂×C₄×C₇	—	2	1	no	—
207	C₂×C₄×C₇	—	2	1	no	—
208	C₂×C₄×C₇	—	2	1	no	—
209	C₂×C₄×C₇	—	2	1	no	—
210	C₂×C₄×C₇	—	2	1	no	—
211	C₂×C₄×C₇	—	2	1	no	—
212	C₂×C₄×C₇	—	2	2	no	—
213	C₂×C₄×C₇	—	2	4	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	—	4	1	no	—
219	C₂×C₄×C₇	—	4	1	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	1	no	—
224	C₂×C₄×C₇	—	4	1	no	—
225	C₂×C₄×C₇	—	4	1	no	—
226	C₂×C₄×C₇	—	4	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	—	8	4	no	—
232	C₂×C₄×C₇	#124	1	2	yes	—
233	C₂×C₄×C₇	#124	1	2	yes	—
234	C₂×C₄×C₇	#135	1	2	yes	—
235	C₂×C₄×C₇	#135	1	2	yes	—
236	C₂×C₄×C₇	AGL(1,ℤ/8)	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	2	yes	—
241	C₂×C₄×C₇	C₂×#41	1	2	yes	—
242	C₇×C₈	—	4	2	no	—
243	C₇×C₈	—	4	2	no	—
244	C₂²×Q₈	—	2	1	no	—
245	C₂²×Q₈	C₂³×C₇	1	1	yes	characteristic
246	C₂²×D₄	C₂³×C₇	1	1	yes	characteristic
247	C₂³×C₄	—	2	1	no	—
248	C₂²×C₈	C₂³×C₇	1	2	yes	—
249	C₂²×C₈	C₂³×C₇	1	2	yes	—
250	C₄⋊Q₈	—	2	4	no	—
251	#124	—	2	2	no	—
252	#124	—	2	2	no	—
253	C₄×Q₈	—	2	4	no	—
254	C₄×Q₈	—	4	4	no	—
255	C₄×D₄	—	2	4	no	—
256	C₂×C₄⋊C₄	—	2	1	no	—
257	C₂×C₄⋊C₄	—	2	1	no	—
258	C₂×C₄⋊C₄	—	2	2	no	—
259	C₂×C₄⋊C₄	—	2	1	no	—
260	C₂×C₄⋊C₄	—	2	1	no	—
261	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
262	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
263	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
264	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
265	C₂×C₂²⋊C₄	—	2	1	no	—
266	C₂×C₂²⋊C₄	—	2	1	no	—
267	C₂×C₂²⋊C₄	—	2	1	no	—
268	C₂×C₂²⋊C₄	—	2	1	no	—
269	C₂×C₂²⋊C₄	—	2	1	no	—
270	C₂×C₄²	—	2	2	no	—
271	C₂×C₄²	—	2	1	no	—
272	C₂×C₄²	C₇×D₄	1	1	yes	characteristic
273	C₂×C₄²	C₇×D₄	1	1	yes	characteristic
274	C₂×C₄²	C₇×D₄	1	1	yes	characteristic
275	C₂×C₄²	C₇×D₄	1	1	yes	characteristic
276	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
277	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
278	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
279	#103	—	2	4	no	—
280	#103	—	2	4	no	—
281	#102	—	2	4	no	—
282	#102	—	2	4	no	—
283	C₄×C₈	—	2	4	no	—
284	#95	—	2	1	no	—
285	#95	—	2	1	no	—
286	#95	—	2	1	no	—
287	#95	—	2	1	no	—
288	#95	—	2	2	no	—
289	#95	—	2	2	no	—
290	C₂²×C₇	—	4	2	no	—
291	C₂²×C₇	—	4	2	no	—
292	C₂²×C₇	—	4	2	no	—
293	C₂²×C₇	—	8	1	no	—
294	C₂²×C₇	—	8	1	no	—
295	C₂²×C₇	—	8	1	no	—
296	C₂²×C₇	—	8	1	no	—
297	C₂²×C₇	#525	1	1	yes	characteristic
298	C₂²×C₇	#525	1	1	yes	characteristic
299	C₂²×C₇	C₂×#124	1	1	yes	characteristic
300	C₂²×C₇	C₂×#135	1	1	yes	characteristic
301	C₂²×C₇	C₂×#135	1	1	yes	characteristic
302	C₂²×C₇	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
303	C₂²×C₇	C₂×#137	1	1	yes	characteristic
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	2	no	—
311	C₄×C₇	—	8	2	no	—
312	C₄×C₇	—	8	1	no	—
313	C₄×C₇	—	8	1	no	—
314	C₄×C₇	#489	1	4	yes	—
315	C₄×C₇	#529	1	2	yes	—
316	C₄×C₇	#529	1	2	yes	—
317	C₂⁴	—	2	1	no	—
318	C₂×Q₈	—	2	4	no	—
319	C₂×Q₈	—	2	1	no	—
320	C₂×Q₈	—	2	2	no	—
321	C₂×Q₈	—	2	2	no	—
322	C₂×Q₈	—	4	2	no	—
323	C₂×Q₈	—	4	2	no	—
324	C₂×Q₈	C₇×#41	1	2	yes	—
325	C₂×D₄	—	2	2	no	—
326	C₂×D₄	—	2	2	no	—
327	C₂×D₄	—	2	1	no	—
328	C₂×D₄	C₇×#41	1	2	yes	—
329	C₂²×C₄	—	2	1	no	—
330	C₂²×C₄	—	2	2	no	—
331	C₂²×C₄	—	2	1	no	—
332	C₂²×C₄	—	2	1	no	—
333	C₂²×C₄	—	2	2	no	—
334	C₂²×C₄	—	4	2	no	—
335	C₂²×C₄	—	4	2	no	—
336	C₂²×C₄	—	4	2	no	—
337	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
338	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
339	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
340	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
341	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
342	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
343	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
344	C₂×C₈	—	2	2	no	—
345	C₂×C₈	—	2	2	no	—
346	C₂×C₈	—	2	2	no	—
347	C₂×C₈	—	2	2	no	—
348	C₂×C₈	—	2	2	no	—
349	C₂×C₈	—	2	2	no	—
350	C₄⋊C₄	—	2	4	no	—
351	C₄⋊C₄	—	2	2	no	—
352	C₄⋊C₄	—	2	2	no	—
353	C₄⋊C₄	—	2	2	no	—
354	C₄⋊C₄	—	2	2	no	—
355	C₄⋊C₄	—	2	2	no	—
356	C₄⋊C₄	—	4	2	no	—
357	C₄⋊C₄	—	4	4	no	—
358	C₄⋊C₄	—	4	2	no	—
359	C₄⋊C₄	—	4	2	no	—
360	C₄⋊C₄	C₇×#41	1	4	yes	—
361	C₂²⋊C₄	—	2	4	no	—
362	C₂²⋊C₄	—	2	4	no	—
363	C₂²⋊C₄	—	4	2	no	—
364	C₂²⋊C₄	—	4	2	no	—
365	C₂²⋊C₄	—	4	2	no	—
366	C₄²	—	2	2	no	—
367	C₄²	—	2	2	no	—
368	C₄²	—	2	2	no	—
369	C₄²	—	2	2	no	—
370	C₄²	—	2	1	no	—
371	C₄²	—	2	1	no	—
372	C₄²	—	2	2	no	—
373	C₄²	—	4	2	no	—
374	C₄²	—	4	4	no	—
375	C₄²	C₇×#41	1	4	yes	—
376	C₂×C₇	—	8	2	no	—
377	C₂×C₇	#2398	1	1	yes	characteristic
378	C₂×C₇	#3105	1	1	yes	characteristic
379	C₂×C₇	#3106	1	1	yes	characteristic
380	C₂×C₇	#3107	1	1	yes	characteristic
381	C₂×C₇	#3108	1	1	yes	characteristic
382	C₂×C₇	#3131	1	1	yes	characteristic
383	C₂×C₇	C₂×#489	1	1	yes	characteristic
384	C₂³	—	2	2	no	—
385	C₂³	—	4	1	no	—
386	C₂³	—	4	1	no	—
387	C₂³	—	4	1	no	—
388	C₂³	—	4	1	no	—
389	C₂³	—	4	1	no	—
390	C₂³	—	4	1	no	—
391	C₂³	C₂²×C₇×D₄	1	1	yes	characteristic
392	Q₈	—	2	4	no	—
393	Q₈	—	4	8	no	—
394	Q₈	—	4	2	no	—
395	D₄	—	2	4	no	—
396	D₄	—	4	2	no	—
397	C₂×C₄	—	2	1	no	—
398	C₂×C₄	—	2	1	no	—
399	C₂×C₄	—	2	1	no	—
400	C₂×C₄	—	2	1	no	—
401	C₂×C₄	—	2	1	no	—
402	C₂×C₄	—	2	1	no	—
403	C₂×C₄	—	2	1	no	—
404	C₂×C₄	—	2	1	no	—
405	C₂×C₄	—	2	2	no	—
406	C₂×C₄	—	2	4	no	—
407	C₂×C₄	—	2	1	no	—
408	C₂×C₄	—	2	1	no	—
409	C₂×C₄	—	2	1	no	—
410	C₂×C₄	—	2	1	no	—
411	C₂×C₄	—	4	1	no	—
412	C₂×C₄	—	4	1	no	—
413	C₂×C₄	—	4	2	no	—
414	C₂×C₄	—	4	2	no	—
415	C₂×C₄	—	4	2	no	—
416	C₂×C₄	—	4	1	no	—
417	C₂×C₄	—	4	1	no	—
418	C₂×C₄	—	4	1	no	—
419	C₂×C₄	—	4	1	no	—
420	C₂×C₄	—	4	2	no	—
421	C₂×C₄	—	4	2	no	—
422	C₂×C₄	—	4	1	no	—
423	C₂×C₄	—	4	1	no	—
424	C₂×C₄	—	8	4	no	—
425	C₂×C₄	C₇×#124	1	2	yes	—
426	C₂×C₄	C₇×#124	1	2	yes	—
427	C₂×C₄	C₇×#135	1	2	yes	—
428	C₂×C₄	C₇×#135	1	2	yes	—
429	C₂×C₄	C₇×AGL(1,ℤ/8)	1	2	yes	—
430	C₂×C₄	C₇×#137	1	2	yes	—
431	C₂×C₄	C₂×C₇×#41	1	1	yes	characteristic
432	C₂×C₄	C₂×C₇×#41	1	1	yes	characteristic
433	C₂×C₄	C₂×C₇×#41	1	2	yes	—
434	C₂×C₄	C₂×C₇×#41	1	2	yes	—
435	C₈	—	4	2	no	—
436	C₈	—	4	2	no	—
437	C₇	#23817	1	1	yes	characteristic, direct product factor, Sylow
438	C₂²	—	4	2	no	—
439	C₂²	—	4	2	no	—
440	C₂²	—	4	2	no	—
441	C₂²	—	8	1	no	—
442	C₂²	—	8	1	no	—
443	C₂²	—	8	1	no	—
444	C₂²	—	8	1	no	—
445	C₂²	C₇×#525	1	1	yes	characteristic
446	C₂²	C₇×#525	1	1	yes	characteristic
447	C₂²	C₂×C₇×#124	1	1	yes	characteristic
448	C₂²	C₂×C₇×#135	1	1	yes	characteristic
449	C₂²	C₂×C₇×#135	1	1	yes	characteristic
450	C₂²	C₂×C₇×AGL(1,ℤ/8)	1	1	yes	characteristic
451	C₂²	C₂×C₇×#137	1	1	yes	characteristic
452	C₄	—	2	2	no	—
453	C₄	—	2	2	no	—
454	C₄	—	2	2	no	—
455	C₄	—	4	2	no	—
456	C₄	—	4	4	no	—
457	C₄	—	4	1	no	—
458	C₄	—	4	1	no	—
459	C₄	—	8	2	no	—
460	C₄	—	8	1	no	—
461	C₄	—	8	1	no	—
462	C₄	C₇×#489	1	4	yes	—
463	C₄	C₇×#529	1	2	yes	—
464	C₄	C₇×#529	1	2	yes	—
465	C₂	—	8	2	no	—
466	C₂	C₇×#2398	1	1	yes	characteristic
467	C₂	C₇×#3105	1	1	yes	characteristic
468	C₂	C₇×#3106	1	1	yes	characteristic
469	C₂	C₇×#3107	1	1	yes	characteristic
470	C₂	C₇×#3108	1	1	yes	characteristic
471	C₂	C₇×#3131	1	1	yes	characteristic
472	C₂	C₂×C₇×#489	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
1. C₄×C₇×C₄⋊Q₈	C₂	semidirect
3. C₇×#2101	C₂	semidirect
4. C₇×#2072	C₂	semidirect
7. C₇×#2024	C₂	semidirect
9. C₄×C₇×#103	C₂	semidirect
11. C₇×#1744	C₂	semidirect
43. #23817	C₇	direct (N × H)
90. C₄×C₄⋊Q₈	C₂×C₇	semidirect
92. #2101	C₂×C₇	semidirect
93. #2072	C₂×C₇	semidirect
96. #2024	C₂×C₇	semidirect
98. C₄×#103	C₂×C₇	semidirect
100. #1744	C₂×C₇	semidirect
437. C₇	#23817	direct (N × H)

Maximal subgroups

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

subgroup	index
C₄×C₇×C₄⋊Q₈	2
C₄×C₇×#124	2
C₇×#2101	2
C₇×#2072	2
C₇×#2071	2
C₇×#2042	2
C₇×#2024	2
C₇×#2023	2
C₄×C₇×#103	2
C₄×C₇×#102	2
C₇×#1744	2
#23817	7

Subgroups — C7×#23817 #13201033

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×#23817 #13201033