Subgroups — C₇×#22765 #13199981

Order 1792.

830 conjugacy classes of subgroups.

The subgroup lattice has 446 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×#2357	C₂	1	1	yes	maximal, characteristic
3	C₇×#2351	C₂	1	1	yes	maximal, characteristic, complemented
4	C₇×#1936	C₂	1	2	yes	maximal
5	C₇×#1920	C₂	1	2	yes	maximal, complemented
6	C₇×#1880	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×#1763	C₂	1	2	yes	maximal, complemented
12	C₂²×C₇×SD₁₆	C₂²	1	1	yes	characteristic
13	C₂×C₄×C₇×Q₈	C₂²	1	2	yes	—
14	C₂×C₄×C₇×Q₈	C₂²	1	1	yes	characteristic
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×#390	C₂²	1	2	yes	—
26	C₇×#389	—	2	2	no	—
27	C₇×#389	C₂²	1	2	yes	—
28	C₇×#388	—	2	2	no	—
29	C₇×#382	—	2	1	no	—
30	C₇×#382	C₂²	1	1	yes	characteristic
31	C₇×#382	C₂²	1	1	yes	characteristic
32	C₇×#381	—	2	1	no	—
33	C₄×C₇×C₄⋊C₄	—	2	1	no	—
34	C₄×C₇×C₄⋊C₄	C₂²	1	2	yes	—
35	C₄×C₇×C₄⋊C₄	C₂²	1	1	yes	characteristic
36	C₄×C₇×C₂²⋊C₄	—	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	#22765	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	C₂×C₇×SD₁₆	—	2	2	no	—
47	C₂×C₇×SD₁₆	—	2	2	no	—
48	C₂×C₇×SD₁₆	C₂×C₄	1	4	yes	—
49	C₂²×C₇×C₈	C₂³	1	2	yes	—
50	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
51	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
52	C₄×C₇×Q₈	—	2	2	no	—
53	C₄×C₇×Q₈	—	2	4	no	—
54	C₄×C₇×Q₈	—	4	2	no	—
55	C₄×C₇×Q₈	C₂×C₄	1	4	yes	—
56	C₄×C₇×D₄	—	2	2	no	—
57	C₄×C₇×D₄	C₂×C₄	1	4	yes	—
58	C₂×C₇×C₄⋊C₄	—	2	1	no	—
59	C₂×C₇×C₄⋊C₄	—	2	2	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×C₇×C₂²⋊C₄	—	2	2	no	—
69	C₂×C₄²×C₇	—	2	1	no	—
70	C₂×C₄²×C₇	—	2	2	no	—
71	C₂×C₄²×C₇	—	2	2	no	—
72	C₂×C₄²×C₇	C₂³	1	2	yes	—
73	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
74	C₇×#106	C₂×C₄	1	4	yes	—
75	C₇×C₄⋊C₈	—	2	2	no	—
76	C₇×#103	—	2	4	no	—
77	C₇×#103	C₂×C₄	1	4	yes	—
78	C₇×#102	—	4	2	no	—
79	C₇×#102	C₂×C₄	1	4	yes	—
80	C₇×#97	—	4	2	no	—
81	C₄×C₇×C₈	C₂×C₄	1	4	yes	—
82	C₇×#95	—	2	1	no	—
83	C₇×#95	—	2	1	no	—
84	C₇×#95	—	2	2	no	—
85	C₇×#95	—	2	2	no	—
86	C₇×#95	—	2	1	no	—
87	C₇×#95	—	2	1	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	#2357	C₂×C₇	1	1	yes	characteristic
92	#2351	C₂×C₇	1	1	yes	characteristic, complemented
93	#1936	C₂×C₇	1	2	yes	—
94	#1920	C₂×C₇	1	2	yes	complemented
95	#1880	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	#1763	C₂×C₇	1	2	yes	complemented
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	C₂²×C₄	1	2	yes	—
106	C₂×C₇×Q₈	#41	1	2	yes	—
107	C₂×C₇×Q₈	#41	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	—	2	1	no	—
112	C₂×C₇×D₄	—	2	1	no	—
113	C₂×C₇×D₄	C₂²×C₄	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	—	8	2	no	—
121	C₂²×C₄×C₇	C₂×D₄	1	2	yes	—
122	C₂²×C₄×C₇	C₂×D₄	1	2	yes	—
123	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
124	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
125	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
126	C₇×SD₁₆	—	2	8	no	—
127	C₂×C₇×C₈	—	2	1	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	2	no	—
132	C₂×C₇×C₈	—	2	2	no	—
133	C₂×C₇×C₈	—	2	2	no	—
134	C₂×C₇×C₈	C₂²×C₄	1	2	yes	—
135	C₂×C₇×C₈	C₂²×C₄	1	2	yes	—
136	C₇×C₄⋊C₄	—	2	4	no	—
137	C₇×C₄⋊C₄	—	2	1	no	—
138	C₇×C₄⋊C₄	—	2	1	no	—
139	C₇×C₄⋊C₄	—	2	2	no	—
140	C₇×C₄⋊C₄	—	2	2	no	—
141	C₇×C₄⋊C₄	—	2	2	no	—
142	C₇×C₄⋊C₄	—	2	2	no	—
143	C₇×C₄⋊C₄	—	4	2	no	—
144	C₇×C₄⋊C₄	—	4	4	no	—
145	C₇×C₄⋊C₄	—	4	4	no	—
146	C₇×C₄⋊C₄	C₂²×C₄	1	2	yes	—
147	C₇×C₄⋊C₄	C₂²×C₄	1	2	yes	—
148	C₇×C₂²⋊C₄	—	2	4	no	—
149	C₇×C₂²⋊C₄	—	4	4	no	—
150	C₇×C₂²⋊C₄	—	8	2	no	—
151	C₄²×C₇	—	2	4	no	—
152	C₄²×C₇	—	2	2	no	—
153	C₄²×C₇	—	2	2	no	—
154	C₄²×C₇	—	4	4	no	—
155	C₄²×C₇	—	8	2	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	2	yes	—
160	C₂×C₄×Q₈	C₂²×C₇	1	1	yes	characteristic
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	#390	C₂²×C₇	1	2	yes	—
172	#389	—	2	2	no	—
173	#389	C₂²×C₇	1	2	yes	—
174	#388	—	2	2	no	—
175	#382	—	2	1	no	—
176	#382	C₂²×C₇	1	1	yes	characteristic
177	#382	C₂²×C₇	1	1	yes	characteristic
178	#381	—	2	1	no	—
179	C₄×C₄⋊C₄	—	2	1	no	—
180	C₄×C₄⋊C₄	C₂²×C₇	1	2	yes	—
181	C₄×C₄⋊C₄	C₂²×C₇	1	1	yes	characteristic
182	C₄×C₂²⋊C₄	—	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	—	4	1	no	—
190	C₂³×C₇	—	4	1	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	—	2	2	no	—
197	C₇×Q₈	#117	1	4	yes	—
198	C₇×D₄	—	2	2	no	—
199	C₇×D₄	—	2	2	no	—
200	C₇×D₄	—	4	1	no	—
201	C₇×D₄	—	4	1	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	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	—	2	2	no	—
214	C₂×C₄×C₇	—	2	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	—	4	2	no	—
223	C₂×C₄×C₇	—	8	4	no	—
224	C₂×C₄×C₇	C₄×D₄	1	2	yes	—
225	C₂×C₄×C₇	C₄×D₄	1	2	yes	—
226	C₂×C₄×C₇	C₂³×C₄	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	C₂×C₄×C₇	H(5,𝔽₂)	1	1	yes	characteristic
231	C₂×C₄×C₇	2₋¹⁺⁴	1	1	yes	characteristic
232	C₇×C₈	—	2	2	no	—
233	C₇×C₈	—	2	2	no	—
234	C₇×C₈	—	4	2	no	—
235	C₂²×Q₈	C₂³×C₇	1	1	yes	characteristic
236	C₂²×D₄	C₂³×C₇	1	1	yes	characteristic
237	C₂³×C₄	—	2	1	no	—
238	C₂×SD₁₆	—	2	2	no	—
239	C₂×SD₁₆	—	2	2	no	—
240	C₂×SD₁₆	C₂×C₄×C₇	1	4	yes	—
241	C₂²×C₈	C₂³×C₇	1	2	yes	—
242	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
243	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
244	C₄×Q₈	—	2	2	no	—
245	C₄×Q₈	—	2	4	no	—
246	C₄×Q₈	—	4	2	no	—
247	C₄×Q₈	C₂×C₄×C₇	1	4	yes	—
248	C₄×D₄	—	2	2	no	—
249	C₄×D₄	C₂×C₄×C₇	1	4	yes	—
250	C₂×C₄⋊C₄	—	2	1	no	—
251	C₂×C₄⋊C₄	—	2	2	no	—
252	C₂×C₄⋊C₄	—	2	2	no	—
253	C₂×C₄⋊C₄	C₇×D₄	1	2	yes	—
254	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
255	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
256	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
257	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
258	C₂×C₂²⋊C₄	—	2	1	no	—
259	C₂×C₂²⋊C₄	—	2	2	no	—
260	C₂×C₂²⋊C₄	—	2	2	no	—
261	C₂×C₄²	—	2	1	no	—
262	C₂×C₄²	—	2	2	no	—
263	C₂×C₄²	—	2	2	no	—
264	C₂×C₄²	C₂³×C₇	1	2	yes	—
265	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
266	#106	C₂×C₄×C₇	1	4	yes	—
267	C₄⋊C₈	—	2	2	no	—
268	#103	—	2	4	no	—
269	#103	C₂×C₄×C₇	1	4	yes	—
270	#102	—	4	2	no	—
271	#102	C₂×C₄×C₇	1	4	yes	—
272	#97	—	4	2	no	—
273	C₄×C₈	C₂×C₄×C₇	1	4	yes	—
274	#95	—	2	1	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	C₇×D₄	1	1	yes	characteristic
281	#95	C₇×D₄	1	1	yes	characteristic
282	C₂²×C₇	—	4	2	no	—
283	C₂²×C₇	—	4	2	no	—
284	C₂²×C₇	—	4	2	no	—
285	C₂²×C₇	—	8	2	no	—
286	C₂²×C₇	—	8	2	no	—
287	C₂²×C₇	C₂×C₄×D₄	1	1	yes	characteristic
288	C₂²×C₇	#546	1	1	yes	characteristic
289	C₂²×C₇	#548	1	1	yes	characteristic
290	C₂²×C₇	#575	1	2	yes	—
291	C₂²×C₇	#577	1	2	yes	—
292	C₄×C₇	—	2	4	no	—
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	—	8	2	no	—
300	C₄×C₇	—	8	2	no	—
301	C₄×C₇	C₂×#117	1	1	yes	characteristic
302	C₄×C₇	#520	1	1	yes	characteristic
303	C₄×C₇	#552	1	1	yes	characteristic
304	C₄×C₇	#553	1	1	yes	characteristic
305	C₂⁴	—	2	1	no	—
306	C₂×Q₈	—	2	1	no	—
307	C₂×Q₈	—	2	1	no	—
308	C₂×Q₈	—	2	1	no	—
309	C₂×Q₈	C₂²×C₄×C₇	1	2	yes	—
310	C₂×Q₈	C₇×#41	1	2	yes	—
311	C₂×Q₈	C₇×#41	1	2	yes	—
312	C₂×D₄	—	2	1	no	—
313	C₂×D₄	—	2	1	no	—
314	C₂×D₄	—	2	1	no	—
315	C₂×D₄	—	2	1	no	—
316	C₂×D₄	—	2	1	no	—
317	C₂×D₄	C₂²×C₄×C₇	1	2	yes	—
318	C₂²×C₄	—	2	1	no	—
319	C₂²×C₄	—	2	1	no	—
320	C₂²×C₄	—	2	1	no	—
321	C₂²×C₄	—	2	4	no	—
322	C₂²×C₄	—	2	2	no	—
323	C₂²×C₄	—	2	2	no	—
324	C₂²×C₄	—	8	2	no	—
325	C₂²×C₄	C₂×C₇×D₄	1	2	yes	—
326	C₂²×C₄	C₂×C₇×D₄	1	2	yes	—
327	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
328	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
329	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
330	SD₁₆	—	2	8	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	—	2	2	no	—
336	C₂×C₈	—	2	2	no	—
337	C₂×C₈	—	2	2	no	—
338	C₂×C₈	C₂²×C₄×C₇	1	2	yes	—
339	C₂×C₈	C₂²×C₄×C₇	1	2	yes	—
340	C₄⋊C₄	—	2	4	no	—
341	C₄⋊C₄	—	2	1	no	—
342	C₄⋊C₄	—	2	1	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	—	4	2	no	—
348	C₄⋊C₄	—	4	4	no	—
349	C₄⋊C₄	—	4	4	no	—
350	C₄⋊C₄	C₂²×C₄×C₇	1	2	yes	—
351	C₄⋊C₄	C₂²×C₄×C₇	1	2	yes	—
352	C₂²⋊C₄	—	2	4	no	—
353	C₂²⋊C₄	—	4	4	no	—
354	C₂²⋊C₄	—	8	2	no	—
355	C₄²	—	2	4	no	—
356	C₄²	—	2	2	no	—
357	C₄²	—	2	2	no	—
358	C₄²	—	4	4	no	—
359	C₄²	—	8	2	no	—
360	C₄²	C₂²×C₄×C₇	1	2	yes	—
361	C₄²	C₇×#41	1	2	yes	—
362	C₂×C₇	—	8	2	no	—
363	C₂×C₇	#2352	1	1	yes	characteristic
364	C₂×C₇	#2943	1	1	yes	characteristic
365	C₂×C₇	#2949	1	1	yes	characteristic
366	C₂×C₇	#3326	1	2	yes	—
367	C₂×C₇	#3371	1	2	yes	—
368	C₂³	—	2	2	no	—
369	C₂³	—	4	1	no	—
370	C₂³	—	4	1	no	—
371	C₂³	—	4	2	no	—
372	C₂³	—	4	2	no	—
373	C₂³	C₂²×C₇×D₄	1	1	yes	characteristic
374	Q₈	—	2	2	no	—
375	Q₈	—	2	2	no	—
376	Q₈	—	2	2	no	—
377	Q₈	C₇×#117	1	4	yes	—
378	D₄	—	2	2	no	—
379	D₄	—	2	2	no	—
380	D₄	—	4	1	no	—
381	D₄	—	4	1	no	—
382	C₂×C₄	—	2	2	no	—
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	—	2	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	—	4	2	no	—
400	C₂×C₄	—	4	2	no	—
401	C₂×C₄	—	4	2	no	—
402	C₂×C₄	—	4	2	no	—
403	C₂×C₄	—	8	4	no	—
404	C₂×C₄	C₄×C₇×D₄	1	2	yes	—
405	C₂×C₄	C₄×C₇×D₄	1	2	yes	—
406	C₂×C₄	C₂³×C₄×C₇	1	1	yes	characteristic
407	C₂×C₄	C₂×C₇×#41	1	1	yes	characteristic
408	C₂×C₄	C₂×C₇×#41	1	1	yes	characteristic
409	C₂×C₄	C₂×C₇×#41	1	1	yes	characteristic
410	C₂×C₄	C₇×H(5,𝔽₂)	1	1	yes	characteristic
411	C₂×C₄	C₇×2₋¹⁺⁴	1	1	yes	characteristic
412	C₈	—	2	2	no	—
413	C₈	—	2	2	no	—
414	C₈	—	4	2	no	—
415	C₇	#22765	1	1	yes	characteristic, direct product factor, Sylow
416	C₂²	—	4	2	no	—
417	C₂²	—	4	2	no	—
418	C₂²	—	4	2	no	—
419	C₂²	—	8	2	no	—
420	C₂²	—	8	2	no	—
421	C₂²	C₂×C₄×C₇×D₄	1	1	yes	characteristic
422	C₂²	C₇×#546	1	1	yes	characteristic
423	C₂²	C₇×#548	1	1	yes	characteristic
424	C₂²	C₇×#575	1	2	yes	—
425	C₂²	C₇×#577	1	2	yes	—
426	C₄	—	2	2	no	—
427	C₄	—	2	2	no	—
428	C₄	—	2	4	no	—
429	C₄	—	4	2	no	—
430	C₄	—	4	2	no	—
431	C₄	—	4	2	no	—
432	C₄	—	4	2	no	—
433	C₄	—	8	2	no	—
434	C₄	—	8	2	no	—
435	C₄	C₂×C₇×#117	1	1	yes	characteristic
436	C₄	C₇×#520	1	1	yes	characteristic
437	C₄	C₇×#552	1	1	yes	characteristic
438	C₄	C₇×#553	1	1	yes	characteristic
439	C₂	—	8	2	no	—
440	C₂	C₇×#2352	1	1	yes	characteristic
441	C₂	C₇×#2943	1	1	yes	characteristic
442	C₂	C₇×#2949	1	1	yes	characteristic
443	C₂	C₇×#3326	1	2	yes	—
444	C₂	C₇×#3371	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
3. C₇×#2351	C₂	semidirect
5. C₇×#1920	C₂	semidirect
7. C₇×#1835	C₂	semidirect
8. C₇×#1805	C₂	semidirect
10. C₇×#1770	C₂	semidirect
11. C₇×#1763	C₂	semidirect
16. C₄×C₇×SD₁₆	C₄	semidirect
42. #22765	C₇	direct (N × H)
92. #2351	C₂×C₇	semidirect
94. #1920	C₂×C₇	semidirect
96. #1835	C₂×C₇	semidirect
97. #1805	C₂×C₇	semidirect
99. #1770	C₂×C₇	semidirect
100. #1763	C₂×C₇	semidirect
162. C₄×SD₁₆	C₄×C₇	semidirect
415. C₇	#22765	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×#2357	2
C₇×#2351	2
C₇×#1936	2
C₇×#1920	2
C₇×#1880	2
C₇×#1835	2
C₇×#1805	2
C₇×#1804	2
C₇×#1770	2
C₇×#1763	2
#22765	7

Subgroups — C7×#22765 #13199981

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×#22765 #13199981