Subgroups — C₇×#22760 #13199976

Order 1792.

858 conjugacy classes of subgroups.

The subgroup lattice has 448 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	1	yes	maximal, characteristic
2	C₇×#2356	C₂	1	1	yes	maximal, characteristic, complemented
3	C₇×#2349	C₂	1	1	yes	maximal, characteristic
4	C₇×#1935	C₂	1	2	yes	maximal, complemented
5	C₇×#1919	C₂	1	2	yes	maximal, complemented
6	C₇×#1877	C₂	1	2	yes	maximal
7	C₇×#1835	C₂	1	1	yes	maximal, characteristic, complemented
8	C₇×#1805	C₂	1	1	yes	maximal, characteristic, complemented
9	C₇×#1804	C₂	1	1	yes	maximal, characteristic
10	C₇×#1770	C₂	1	1	yes	maximal, characteristic, complemented
11	C₇×#1762	C₂	1	2	yes	maximal
12	C₂²×C₇×SD₁₆	C₂²	1	1	yes	characteristic
13	C₂×C₄×C₇×Q₈	C₂²	1	1	yes	characteristic
14	C₂×C₄×C₇×D₄	C₂²	1	2	yes	—
15	C₂×C₄×C₇×D₄	C₂²	1	1	yes	characteristic
16	C₄×C₇×SD₁₆	C₄	1	8	yes	complemented
17	C₂×C₇×#106	C₂²	1	1	yes	characteristic
18	C₂×C₇×C₄⋊C₈	C₂²	1	1	yes	characteristic
19	C₂×C₇×#103	C₂²	1	2	yes	—
20	C₂×C₇×#103	C₂²	1	1	yes	characteristic
21	C₂×C₇×#102	C₂²	1	2	yes	—
22	C₂×C₇×#102	C₂²	1	1	yes	characteristic
23	C₂×C₇×#97	C₂²	1	2	yes	—
24	C₂×C₄×C₇×C₈	C₂²	1	1	yes	characteristic
25	C₇×#391	C₂²	1	2	yes	—
26	C₇×#389	C₂²	1	2	yes	—
27	C₇×#387	—	2	2	no	—
28	C₇×#385	—	2	2	no	—
29	C₇×#383	—	2	1	no	—
30	C₇×#382	C₂²	1	1	yes	characteristic
31	C₇×#382	C₂²	1	1	yes	characteristic
32	C₇×#380	—	2	1	no	—
33	C₄×C₇×C₄⋊C₄	C₂²	1	2	yes	—
34	C₄×C₇×C₄⋊C₄	C₂²	1	1	yes	characteristic
35	C₇×#376	—	2	1	no	—
36	C₂×C₇×#95	—	2	1	no	—
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	C₇×#336	C₂²	1	2	yes	—
42	#22760	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
43	C₂²×C₇×Q₈	C₂³	1	1	yes	characteristic
44	C₂²×C₇×D₄	C₂³	1	1	yes	characteristic
45	C₂³×C₄×C₇	—	2	1	no	—
46	C₂³×C₄×C₇	—	2	2	no	—
47	C₂×C₇×SD₁₆	—	2	2	no	—
48	C₂×C₇×SD₁₆	—	2	2	no	—
49	C₂×C₇×SD₁₆	C₂×C₄	1	4	yes	—
50	C₂²×C₇×C₈	C₂³	1	2	yes	—
51	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
52	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
53	C₄×C₇×Q₈	—	2	2	no	—
54	C₄×C₇×Q₈	C₂×C₄	1	4	yes	complemented
55	C₄×C₇×D₄	—	2	4	no	—
56	C₄×C₇×D₄	—	2	2	no	—
57	C₄×C₇×D₄	—	4	2	no	—
58	C₄×C₇×D₄	C₂×C₄	1	4	yes	—
59	C₂×C₇×C₄⋊C₄	—	2	1	no	—
60	C₂×C₇×C₄⋊C₄	—	2	2	no	—
61	C₂×C₇×C₄⋊C₄	D₄	1	2	yes	—
62	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
63	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
64	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
65	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
66	C₂×C₇×C₂²⋊C₄	—	2	1	no	—
67	C₂×C₇×C₂²⋊C₄	—	2	2	no	—
68	C₂×C₄²×C₇	—	2	1	no	—
69	C₂×C₄²×C₇	—	2	2	no	—
70	C₂×C₄²×C₇	C₂³	1	2	yes	—
71	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
72	C₇×#106	C₂×C₄	1	4	yes	complemented
73	C₇×C₄⋊C₈	—	2	2	no	—
74	C₇×#103	—	4	2	no	—
75	C₇×#103	C₂×C₄	1	4	yes	complemented
76	C₇×#102	—	2	4	no	—
77	C₇×#102	C₂×C₄	1	4	yes	—
78	C₇×#97	—	4	2	no	—
79	C₄×C₇×C₈	C₂×C₄	1	4	yes	complemented
80	C₇×#95	—	2	1	no	—
81	C₇×#95	—	2	2	no	—
82	C₇×#95	—	2	1	no	—
83	C₇×#95	—	2	2	no	—
84	C₇×#95	—	2	2	no	—
85	C₇×#95	—	2	1	no	—
86	C₇×#95	—	2	1	no	—
87	C₇×#95	—	2	2	no	—
88	C₇×#95	D₄	1	1	yes	characteristic
89	C₇×#95	D₄	1	1	yes	characteristic
90	C₂×C₄×SD₁₆	C₂×C₇	1	1	yes	characteristic
91	#2356	C₂×C₇	1	1	yes	characteristic, complemented
92	#2349	C₂×C₇	1	1	yes	characteristic
93	#1935	C₂×C₇	1	2	yes	complemented
94	#1919	C₂×C₇	1	2	yes	complemented
95	#1877	C₂×C₇	1	2	yes	—
96	#1835	C₂×C₇	1	1	yes	characteristic, complemented
97	#1805	C₂×C₇	1	1	yes	characteristic, complemented
98	#1804	C₂×C₇	1	1	yes	characteristic
99	#1770	C₂×C₇	1	1	yes	characteristic, complemented
100	#1762	C₂×C₇	1	2	yes	—
101	C₂⁴×C₇	—	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	—	2	1	no	—
107	C₂×C₇×Q₈	C₂²×C₄	1	2	yes	—
108	C₂×C₇×D₄	—	2	1	no	—
109	C₂×C₇×D₄	—	2	1	no	—
110	C₂×C₇×D₄	—	2	1	no	—
111	C₂×C₇×D₄	C₂²×C₄	1	2	yes	—
112	C₂×C₇×D₄	#41	1	2	yes	—
113	C₂×C₇×D₄	#41	1	2	yes	—
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	4	no	—
118	C₂²×C₄×C₇	—	2	2	no	—
119	C₂²×C₄×C₇	—	2	2	no	—
120	C₂²×C₄×C₇	—	4	4	no	—
121	C₂²×C₄×C₇	—	4	4	no	—
122	C₂²×C₄×C₇	—	8	2	no	—
123	C₂²×C₄×C₇	—	8	2	no	—
124	C₂²×C₄×C₇	C₂×D₄	1	2	yes	—
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	C₇×SD₁₆	—	2	8	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	—	2	2	no	—
135	C₂×C₇×C₈	—	2	2	no	—
136	C₂×C₇×C₈	—	2	2	no	—
137	C₂×C₇×C₈	C₂²×C₄	1	2	yes	—
138	C₂×C₇×C₈	C₂²×C₄	1	2	yes	—
139	C₇×C₄⋊C₄	—	2	4	no	—
140	C₇×C₄⋊C₄	—	2	1	no	—
141	C₇×C₄⋊C₄	—	2	1	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	—	4	2	no	—
147	C₇×C₄⋊C₄	—	8	2	no	—
148	C₇×C₄⋊C₄	C₂²×C₄	1	2	yes	—
149	C₇×C₄⋊C₄	C₂²×C₄	1	2	yes	—
150	C₇×C₂²⋊C₄	—	2	4	no	—
151	C₇×C₂²⋊C₄	—	4	4	no	—
152	C₄²×C₇	—	2	4	no	—
153	C₄²×C₇	—	2	2	no	—
154	C₄²×C₇	—	2	2	no	—
155	C₄²×C₇	—	4	4	no	—
156	C₄²×C₇	C₂²×C₄	1	2	yes	—
157	C₄²×C₇	#41	1	2	yes	—
158	C₂²×SD₁₆	C₂²×C₇	1	1	yes	characteristic
159	C₂×C₄×Q₈	C₂²×C₇	1	1	yes	characteristic
160	C₂×C₄×D₄	C₂²×C₇	1	2	yes	—
161	C₂×C₄×D₄	C₂²×C₇	1	1	yes	characteristic
162	C₄×SD₁₆	C₄×C₇	1	8	yes	complemented
163	C₂×#106	C₂²×C₇	1	1	yes	characteristic
164	C₂×C₄⋊C₈	C₂²×C₇	1	1	yes	characteristic
165	C₂×#103	C₂²×C₇	1	2	yes	—
166	C₂×#103	C₂²×C₇	1	1	yes	characteristic
167	C₂×#102	C₂²×C₇	1	2	yes	—
168	C₂×#102	C₂²×C₇	1	1	yes	characteristic
169	C₂×#97	C₂²×C₇	1	2	yes	—
170	C₂×C₄×C₈	C₂²×C₇	1	1	yes	characteristic
171	#391	C₂²×C₇	1	2	yes	—
172	#389	C₂²×C₇	1	2	yes	—
173	#387	—	2	2	no	—
174	#385	—	2	2	no	—
175	#383	—	2	1	no	—
176	#382	C₂²×C₇	1	1	yes	characteristic
177	#382	C₂²×C₇	1	1	yes	characteristic
178	#380	—	2	1	no	—
179	C₄×C₄⋊C₄	C₂²×C₇	1	2	yes	—
180	C₄×C₄⋊C₄	C₂²×C₇	1	1	yes	characteristic
181	#376	—	2	1	no	—
182	C₂×#95	—	2	1	no	—
183	#340	C₂²×C₇	1	2	yes	—
184	#340	C₂²×C₇	1	2	yes	—
185	#340	C₂²×C₇	1	2	yes	—
186	#340	C₂²×C₇	1	2	yes	—
187	#336	C₂²×C₇	1	2	yes	—
188	C₂³×C₇	—	2	2	no	—
189	C₂³×C₇	—	2	2	no	—
190	C₂³×C₇	—	2	2	no	—
191	C₂³×C₇	—	4	2	no	—
192	C₂³×C₇	—	4	2	no	—
193	C₂³×C₇	C₂²×D₄	1	1	yes	characteristic
194	C₇×Q₈	—	2	2	no	—
195	C₇×Q₈	—	2	2	no	—
196	C₇×Q₈	—	4	1	no	—
197	C₇×Q₈	—	4	1	no	—
198	C₇×D₄	—	2	2	no	—
199	C₇×D₄	—	2	2	no	—
200	C₇×D₄	—	2	2	no	—
201	C₇×D₄	#117	1	4	yes	—
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	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	—	4	1	no	—
214	C₂×C₄×C₇	—	4	1	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	—	4	2	no	—
223	C₂×C₄×C₇	—	8	4	no	—
224	C₂×C₄×C₇	—	8	8	no	—
225	C₂×C₄×C₇	C₄×D₄	1	2	yes	—
226	C₂×C₄×C₇	C₄×D₄	1	2	yes	—
227	C₂×C₄×C₇	C₂³×C₄	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	C₂×C₄×C₇	C₂×#41	1	1	yes	characteristic
231	C₂×C₄×C₇	H(5,𝔽₂)	1	1	yes	characteristic
232	C₂×C₄×C₇	2₋¹⁺⁴	1	1	yes	characteristic
233	C₇×C₈	—	2	2	no	—
234	C₇×C₈	—	2	2	no	—
235	C₇×C₈	—	4	2	no	—
236	C₂²×Q₈	C₂³×C₇	1	1	yes	characteristic
237	C₂²×D₄	C₂³×C₇	1	1	yes	characteristic
238	C₂³×C₄	—	2	1	no	—
239	C₂³×C₄	—	2	2	no	—
240	C₂×SD₁₆	—	2	2	no	—
241	C₂×SD₁₆	—	2	2	no	—
242	C₂×SD₁₆	C₂×C₄×C₇	1	4	yes	—
243	C₂²×C₈	C₂³×C₇	1	2	yes	—
244	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
245	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
246	C₄×Q₈	—	2	2	no	—
247	C₄×Q₈	C₂×C₄×C₇	1	4	yes	complemented
248	C₄×D₄	—	2	4	no	—
249	C₄×D₄	—	2	2	no	—
250	C₄×D₄	—	4	2	no	—
251	C₄×D₄	C₂×C₄×C₇	1	4	yes	—
252	C₂×C₄⋊C₄	—	2	1	no	—
253	C₂×C₄⋊C₄	—	2	2	no	—
254	C₂×C₄⋊C₄	C₇×D₄	1	2	yes	—
255	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
256	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
257	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
258	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
259	C₂×C₂²⋊C₄	—	2	1	no	—
260	C₂×C₂²⋊C₄	—	2	2	no	—
261	C₂×C₄²	—	2	1	no	—
262	C₂×C₄²	—	2	2	no	—
263	C₂×C₄²	C₂³×C₇	1	2	yes	—
264	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
265	#106	C₂×C₄×C₇	1	4	yes	complemented
266	C₄⋊C₈	—	2	2	no	—
267	#103	—	4	2	no	—
268	#103	C₂×C₄×C₇	1	4	yes	complemented
269	#102	—	2	4	no	—
270	#102	C₂×C₄×C₇	1	4	yes	—
271	#97	—	4	2	no	—
272	C₄×C₈	C₂×C₄×C₇	1	4	yes	complemented
273	#95	—	2	1	no	—
274	#95	—	2	2	no	—
275	#95	—	2	1	no	—
276	#95	—	2	2	no	—
277	#95	—	2	2	no	—
278	#95	—	2	1	no	—
279	#95	—	2	1	no	—
280	#95	—	2	2	no	—
281	#95	C₇×D₄	1	1	yes	characteristic
282	#95	C₇×D₄	1	1	yes	characteristic
283	C₂²×C₇	—	2	4	no	—
284	C₂²×C₇	—	4	4	no	—
285	C₂²×C₇	—	4	2	no	—
286	C₂²×C₇	—	4	2	no	—
287	C₂²×C₇	—	4	4	no	—
288	C₂²×C₇	C₂×C₄×D₄	1	1	yes	characteristic
289	C₂²×C₇	#546	1	1	yes	characteristic
290	C₂²×C₇	#548	1	1	yes	characteristic
291	C₂²×C₇	#575	1	2	yes	—
292	C₂²×C₇	#577	1	2	yes	—
293	C₄×C₇	—	2	2	no	—
294	C₄×C₇	—	2	2	no	—
295	C₄×C₇	—	4	2	no	—
296	C₄×C₇	—	4	2	no	—
297	C₄×C₇	—	4	2	no	—
298	C₄×C₇	—	4	2	no	—
299	C₄×C₇	—	4	2	no	—
300	C₄×C₇	—	8	2	no	—
301	C₄×C₇	—	8	2	no	—
302	C₄×C₇	C₂×#117	1	1	yes	characteristic
303	C₄×C₇	#520	1	1	yes	characteristic
304	C₄×C₇	#552	1	1	yes	characteristic
305	C₄×C₇	#553	1	1	yes	characteristic
306	C₂⁴	—	2	1	no	—
307	C₂×Q₈	—	2	1	no	—
308	C₂×Q₈	—	2	1	no	—
309	C₂×Q₈	—	2	1	no	—
310	C₂×Q₈	—	2	1	no	—
311	C₂×Q₈	—	2	1	no	—
312	C₂×Q₈	C₂²×C₄×C₇	1	2	yes	—
313	C₂×D₄	—	2	1	no	—
314	C₂×D₄	—	2	1	no	—
315	C₂×D₄	—	2	1	no	—
316	C₂×D₄	C₂²×C₄×C₇	1	2	yes	—
317	C₂×D₄	C₇×#41	1	2	yes	—
318	C₂×D₄	C₇×#41	1	2	yes	—
319	C₂²×C₄	—	2	1	no	—
320	C₂²×C₄	—	2	1	no	—
321	C₂²×C₄	—	2	1	no	—
322	C₂²×C₄	—	2	4	no	—
323	C₂²×C₄	—	2	2	no	—
324	C₂²×C₄	—	2	2	no	—
325	C₂²×C₄	—	4	4	no	—
326	C₂²×C₄	—	4	4	no	—
327	C₂²×C₄	—	8	2	no	—
328	C₂²×C₄	—	8	2	no	—
329	C₂²×C₄	C₂×C₇×D₄	1	2	yes	—
330	C₂²×C₄	C₂×C₇×D₄	1	2	yes	—
331	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
332	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
333	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
334	SD₁₆	—	2	8	no	—
335	C₂×C₈	—	2	1	no	—
336	C₂×C₈	—	2	1	no	—
337	C₂×C₈	—	2	1	no	—
338	C₂×C₈	—	2	1	no	—
339	C₂×C₈	—	2	2	no	—
340	C₂×C₈	—	2	2	no	—
341	C₂×C₈	—	2	2	no	—
342	C₂×C₈	C₂²×C₄×C₇	1	2	yes	—
343	C₂×C₈	C₂²×C₄×C₇	1	2	yes	—
344	C₄⋊C₄	—	2	4	no	—
345	C₄⋊C₄	—	2	1	no	—
346	C₄⋊C₄	—	2	1	no	—
347	C₄⋊C₄	—	2	2	no	—
348	C₄⋊C₄	—	2	2	no	—
349	C₄⋊C₄	—	2	2	no	—
350	C₄⋊C₄	—	2	2	no	—
351	C₄⋊C₄	—	4	2	no	—
352	C₄⋊C₄	—	8	2	no	—
353	C₄⋊C₄	C₂²×C₄×C₇	1	2	yes	—
354	C₄⋊C₄	C₂²×C₄×C₇	1	2	yes	—
355	C₂²⋊C₄	—	2	4	no	—
356	C₂²⋊C₄	—	4	4	no	—
357	C₄²	—	2	4	no	—
358	C₄²	—	2	2	no	—
359	C₄²	—	2	2	no	—
360	C₄²	—	4	4	no	—
361	C₄²	C₂²×C₄×C₇	1	2	yes	—
362	C₄²	C₇×#41	1	2	yes	—
363	C₂×C₇	—	4	4	no	—
364	C₂×C₇	#2352	1	1	yes	characteristic
365	C₂×C₇	#2943	1	1	yes	characteristic
366	C₂×C₇	#2949	1	1	yes	characteristic
367	C₂×C₇	#3323	1	2	yes	—
368	C₂×C₇	#3376	1	2	yes	—
369	C₂³	—	2	2	no	—
370	C₂³	—	2	2	no	—
371	C₂³	—	2	2	no	—
372	C₂³	—	4	2	no	—
373	C₂³	—	4	2	no	—
374	C₂³	C₂²×C₇×D₄	1	1	yes	characteristic
375	Q₈	—	2	2	no	—
376	Q₈	—	2	2	no	—
377	Q₈	—	4	1	no	—
378	Q₈	—	4	1	no	—
379	D₄	—	2	2	no	—
380	D₄	—	2	2	no	—
381	D₄	—	2	2	no	—
382	D₄	C₇×#117	1	4	yes	—
383	C₂×C₄	—	2	2	no	—
384	C₂×C₄	—	2	2	no	—
385	C₂×C₄	—	2	2	no	—
386	C₂×C₄	—	2	2	no	—
387	C₂×C₄	—	2	2	no	—
388	C₂×C₄	—	2	2	no	—
389	C₂×C₄	—	2	2	no	—
390	C₂×C₄	—	2	2	no	—
391	C₂×C₄	—	2	2	no	—
392	C₂×C₄	—	2	2	no	—
393	C₂×C₄	—	2	2	no	—
394	C₂×C₄	—	4	1	no	—
395	C₂×C₄	—	4	1	no	—
396	C₂×C₄	—	4	2	no	—
397	C₂×C₄	—	4	2	no	—
398	C₂×C₄	—	4	2	no	—
399	C₂×C₄	—	4	2	no	—
400	C₂×C₄	—	4	2	no	—
401	C₂×C₄	—	4	2	no	—
402	C₂×C₄	—	4	2	no	—
403	C₂×C₄	—	4	2	no	—
404	C₂×C₄	—	8	4	no	—
405	C₂×C₄	—	8	8	no	—
406	C₂×C₄	C₄×C₇×D₄	1	2	yes	—
407	C₂×C₄	C₄×C₇×D₄	1	2	yes	—
408	C₂×C₄	C₂³×C₄×C₇	1	1	yes	characteristic
409	C₂×C₄	C₂×C₇×#41	1	1	yes	characteristic
410	C₂×C₄	C₂×C₇×#41	1	1	yes	characteristic
411	C₂×C₄	C₂×C₇×#41	1	1	yes	characteristic
412	C₂×C₄	C₇×H(5,𝔽₂)	1	1	yes	characteristic
413	C₂×C₄	C₇×2₋¹⁺⁴	1	1	yes	characteristic
414	C₈	—	2	2	no	—
415	C₈	—	2	2	no	—
416	C₈	—	4	2	no	—
417	C₇	#22760	1	1	yes	characteristic, direct product factor, Sylow
418	C₂²	—	2	4	no	—
419	C₂²	—	4	2	no	—
420	C₂²	—	4	2	no	—
421	C₂²	—	4	4	no	—
422	C₂²	—	4	4	no	—
423	C₂²	C₂×C₄×C₇×D₄	1	1	yes	characteristic
424	C₂²	C₇×#546	1	1	yes	characteristic
425	C₂²	C₇×#548	1	1	yes	characteristic
426	C₂²	C₇×#575	1	2	yes	—
427	C₂²	C₇×#577	1	2	yes	—
428	C₄	—	2	2	no	—
429	C₄	—	2	2	no	—
430	C₄	—	4	2	no	—
431	C₄	—	4	2	no	—
432	C₄	—	4	2	no	—
433	C₄	—	4	2	no	—
434	C₄	—	4	2	no	—
435	C₄	—	8	2	no	—
436	C₄	—	8	2	no	—
437	C₄	C₂×C₇×#117	1	1	yes	characteristic
438	C₄	C₇×#520	1	1	yes	characteristic
439	C₄	C₇×#552	1	1	yes	characteristic
440	C₄	C₇×#553	1	1	yes	characteristic
441	C₂	—	4	4	no	—
442	C₂	C₇×#2352	1	1	yes	characteristic
443	C₂	C₇×#2943	1	1	yes	characteristic
444	C₂	C₇×#2949	1	1	yes	characteristic
445	C₂	C₇×#3323	1	2	yes	—
446	C₂	C₇×#3376	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	C₂²×C₇×D₄	C₂³
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₇ ◁ C₄×C₇×C₄⋊C₄ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₇×#2356	C₂	semidirect
4. C₇×#1935	C₂	semidirect
5. C₇×#1919	C₂	semidirect
7. C₇×#1835	C₂	semidirect
8. C₇×#1805	C₂	semidirect
10. C₇×#1770	C₂	semidirect
16. C₄×C₇×SD₁₆	C₄	semidirect
42. #22760	C₇	direct (N × H)
54. C₄×C₇×Q₈	C₂×C₄	semidirect
72. C₇×#106	C₂×C₄	semidirect
75. C₇×#103	C₂×C₄	semidirect
79. C₄×C₇×C₈	C₂×C₄	semidirect
91. #2356	C₂×C₇	semidirect
93. #1935	C₂×C₇	semidirect
94. #1919	C₂×C₇	semidirect
96. #1835	C₂×C₇	semidirect
97. #1805	C₂×C₇	semidirect
99. #1770	C₂×C₇	semidirect
162. C₄×SD₁₆	C₄×C₇	semidirect
247. C₄×Q₈	C₂×C₄×C₇	semidirect
265. #106	C₂×C₄×C₇	semidirect
268. #103	C₂×C₄×C₇	semidirect
272. C₄×C₈	C₂×C₄×C₇	semidirect
417. C₇	#22760	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
C₇×#2356	2
C₇×#2349	2
C₇×#1935	2
C₇×#1919	2
C₇×#1877	2
C₇×#1835	2
C₇×#1805	2
C₇×#1804	2
C₇×#1770	2
C₇×#1762	2
#22760	7

Subgroups — C7×#22760 #13199976

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×#22760 #13199976