Subgroups — C₇×#23146 #13200362

Order 1792.

820 conjugacy classes of subgroups.

The subgroup lattice has 462 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×#3050	C₂	1	1	yes	maximal, characteristic
2	C₇×#2933	C₂	1	2	yes	maximal, complemented
3	C₇×#1937	C₂	1	2	yes	maximal, complemented
4	C₇×#1922	C₂	1	2	yes	maximal, complemented
5	C₇×#1876	C₂	1	2	yes	maximal, complemented
6	C₇×#1871	C₂	1	2	yes	maximal, complemented
7	C₇×#1764	C₂	1	2	yes	maximal, complemented
8	C₇×C₈×C₂²⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×C₇×#341	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×C₇×#135	C₂²	1	1	yes	characteristic
11	C₂×C₇×#131	C₂²	1	2	yes	—
12	C₂²×C₇×M₁₆	C₂²	1	2	yes	—
13	C₂³×C₇×C₈	C₂²	1	1	yes	characteristic
14	C₇×#525	C₂²	1	2	yes	—
15	C₇×#467	C₄	1	1	yes	characteristic, complemented
16	C₇×#467	C₄	1	1	yes	characteristic, complemented
17	C₇×#466	C₄	1	1	yes	characteristic, complemented
18	C₇×#466	C₄	1	1	yes	characteristic, complemented
19	C₇×#465	C₄	1	2	yes	complemented
20	C₇×#465	C₄	1	2	yes	complemented
21	C₇×#436	—	2	2	no	—
22	C₇×#435	—	2	2	no	—
23	C₇×#435	—	2	2	no	—
24	C₇×C₈×D₄	—	2	2	no	—
25	C₇×#427	C₂²	1	1	yes	characteristic
26	C₇×#424	C₂²	1	2	yes	—
27	C₂×C₇×#104	C₂²	1	2	yes	—
28	C₂×C₇×#104	C₂²	1	2	yes	—
29	C₇×#416	C₂²	1	2	yes	—
30	C₇×#408	C₂²	1	2	yes	—
31	C₂×C₇×C₂²⋊C₈	C₂²	1	1	yes	characteristic
32	C₇×#405	C₂²	1	2	yes	—
33	C₂×C₄×C₇×C₈	C₂²	1	2	yes	—
34	C₄×C₇×C₂²⋊C₄	C₂²	1	1	yes	characteristic
35	C₇×#341	C₂²	1	1	yes	characteristic
36	C₇×#341	C₂²	1	2	yes	—
37	C₇×#341	C₂²	1	1	yes	characteristic
38	C₇×#339	C₂²	1	2	yes	—
39	C₇×#339	C₂²	1	2	yes	—
40	C₇×#336	C₂²	1	2	yes	—
41	#23146	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
42	C₂×C₇×#41	C₂³	1	2	yes	—
43	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
44	C₇×#135	—	4	2	no	—
45	C₂×C₇×Q₁₆	C₂×C₄	1	1	yes	characteristic
46	C₂×C₇×SD₁₆	C₂×C₄	1	2	yes	—
47	C₂×C₇×D₈	C₂×C₄	1	1	yes	characteristic
48	C₇×#131	—	2	4	no	—
49	C₇×#131	—	4	2	no	—
50	C₂×C₇×M₁₆	—	2	2	no	—
51	C₂×C₇×M₁₆	—	2	2	no	—
52	C₂×C₇×M₁₆	—	2	4	no	—
53	C₂×C₇×M₁₆	—	4	2	no	—
54	C₂×C₇×M₁₆	C₂³	1	2	yes	—
55	C₂×C₇×M₁₆	C₂³	1	2	yes	—
56	C₂²×C₇×C₈	—	2	2	no	—
57	C₂²×C₇×C₈	—	2	2	no	—
58	C₂²×C₇×C₈	—	4	2	no	—
59	C₂²×C₇×C₈	C₂×C₄	1	1	yes	characteristic
60	C₂²×C₇×C₈	C₂×C₄	1	1	yes	characteristic
61	C₂²×C₇×C₈	C₂×C₄	1	1	yes	characteristic
62	C₂²×C₇×C₈	C₂×C₄	1	1	yes	characteristic
63	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
64	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
65	C₂²×C₇×C₈	C₂³	1	2	yes	—
66	C₇×#123	—	2	2	no	—
67	C₇×C₂²⋊Q₈	C₂×C₄	1	2	yes	—
68	C₇×C₂²⋊Q₈	C₂×C₄	1	2	yes	—
69	C₇×#121	C₂×C₄	1	2	yes	—
70	C₇×#121	C₂×C₄	1	2	yes	—
71	C₇×#120	—	2	2	no	—
72	C₄×C₇×D₄	—	2	2	no	—
73	C₄×C₇×D₄	—	2	2	no	—
74	C₇×#117	C₂³	1	2	yes	—
75	C₂×C₇×C₂²⋊C₄	—	2	1	no	—
76	C₂×C₄²×C₇	C₂³	1	2	yes	—
77	C₇×#107	C₂×C₄	1	1	yes	characteristic
78	C₇×#107	C₂×C₄	1	1	yes	characteristic
79	C₇×#106	C₂×C₄	1	2	yes	—
80	C₇×C₄⋊C₈	—	2	2	no	—
81	C₇×C₄⋊C₈	—	2	2	no	—
82	C₇×#104	—	2	4	no	—
83	C₇×#104	—	4	2	no	—
84	C₇×#103	C₂×C₄	1	2	yes	—
85	C₇×#103	C₂×C₄	1	2	yes	—
86	C₇×#102	C₂×C₄	1	2	yes	—
87	C₇×#102	C₂×C₄	1	2	yes	—
88	C₇×C₂²⋊C₈	—	2	2	no	—
89	C₇×C₂²⋊C₈	—	2	2	no	—
90	C₇×C₂²⋊C₈	D₄	1	1	yes	characteristic
91	C₇×C₂²⋊C₈	D₄	1	1	yes	characteristic
92	C₇×C₂²⋊C₈	D₄	1	2	yes	—
93	C₇×#97	—	2	2	no	—
94	C₄×C₇×C₈	—	2	2	no	—
95	C₄×C₇×C₈	—	4	2	no	—
96	C₇×#95	—	2	1	no	—
97	#3050	C₂×C₇	1	1	yes	characteristic
98	#2933	C₂×C₇	1	2	yes	complemented
99	#1937	C₂×C₇	1	2	yes	complemented
100	#1922	C₂×C₇	1	2	yes	complemented
101	#1876	C₂×C₇	1	2	yes	complemented
102	#1871	C₂×C₇	1	2	yes	complemented
103	#1764	C₂×C₇	1	2	yes	complemented
104	C₈×C₂²⋊C₄	C₂×C₇	1	1	yes	characteristic, complemented
105	C₂×#341	C₂×C₇	1	1	yes	characteristic, complemented
106	C₂⁴×C₇	#41	1	1	yes	characteristic
107	C₇×#41	—	2	2	no	—
108	C₇×#41	—	2	2	no	—
109	C₇×#41	—	2	2	no	—
110	C₇×#41	—	2	2	no	—
111	C₂×C₇×Q₈	C₂²×C₄	1	2	yes	—
112	C₂×C₇×D₄	—	2	2	no	—
113	C₂×C₇×D₄	—	2	2	no	—
114	C₂×C₇×D₄	—	2	2	no	—
115	C₂×C₇×D₄	C₂²×C₄	1	2	yes	—
116	C₂²×C₄×C₇	—	2	2	no	—
117	C₂²×C₄×C₇	—	2	2	no	—
118	C₂²×C₄×C₇	—	2	2	no	—
119	C₂²×C₄×C₇	—	2	2	no	—
120	C₂²×C₄×C₇	C₂²×C₄	1	1	yes	characteristic
121	C₂²×C₄×C₇	C₂²×C₄	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	#41	1	1	yes	characteristic
125	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
126	C₇×Q₁₆	—	4	1	no	—
127	C₇×SD₁₆	—	4	2	no	—
128	C₇×D₈	—	4	1	no	—
129	C₇×M₁₆	—	2	2	no	—
130	C₇×M₁₆	—	2	2	no	—
131	C₇×M₁₆	—	2	2	no	—
132	C₇×M₁₆	—	4	4	no	—
133	C₇×M₁₆	—	4	4	no	—
134	C₇×M₁₆	#41	1	4	yes	—
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	—	2	2	no	—
140	C₂×C₇×C₈	—	2	2	no	—
141	C₂×C₇×C₈	—	4	1	no	—
142	C₂×C₇×C₈	—	4	1	no	—
143	C₂×C₇×C₈	—	4	1	no	—
144	C₂×C₇×C₈	—	4	1	no	—
145	C₂×C₇×C₈	—	4	4	no	—
146	C₂×C₇×C₈	—	4	4	no	—
147	C₂×C₇×C₈	C₂²×C₄	1	1	yes	characteristic
148	C₂×C₇×C₈	C₂²×C₄	1	1	yes	characteristic
149	C₂×C₇×C₈	C₂²×C₄	1	1	yes	characteristic
150	C₂×C₇×C₈	C₂²×C₄	1	1	yes	characteristic
151	C₂×C₇×C₈	C₂×D₄	1	2	yes	—
152	C₂×C₇×C₈	C₂×D₄	1	2	yes	—
153	C₇×C₄⋊C₄	—	2	2	no	—
154	C₇×C₄⋊C₄	—	2	2	no	—
155	C₇×C₄⋊C₄	C₂²×C₄	1	2	yes	—
156	C₇×C₄⋊C₄	C₂²×C₄	1	2	yes	—
157	C₇×C₂²⋊C₄	—	2	4	no	—
158	C₇×C₂²⋊C₄	—	2	2	no	—
159	C₇×C₂²⋊C₄	—	2	2	no	—
160	C₇×C₂²⋊C₄	—	2	2	no	—
161	C₇×C₂²⋊C₄	—	2	2	no	—
162	C₇×C₂²⋊C₄	—	2	2	no	—
163	C₄²×C₇	—	2	2	no	—
164	C₄²×C₇	—	2	2	no	—
165	C₄²×C₇	—	2	2	no	—
166	C₂×#135	C₂²×C₇	1	1	yes	characteristic
167	C₂×#131	C₂²×C₇	1	2	yes	—
168	C₂²×M₁₆	C₂²×C₇	1	2	yes	—
169	C₂³×C₈	C₂²×C₇	1	1	yes	characteristic
170	#525	C₂²×C₇	1	2	yes	—
171	#467	C₄×C₇	1	1	yes	characteristic, complemented
172	#467	C₄×C₇	1	1	yes	characteristic, complemented
173	#466	C₄×C₇	1	1	yes	characteristic, complemented
174	#466	C₄×C₇	1	1	yes	characteristic, complemented
175	#465	C₄×C₇	1	2	yes	complemented
176	#465	C₄×C₇	1	2	yes	complemented
177	#436	—	2	2	no	—
178	#435	—	2	2	no	—
179	#435	—	2	2	no	—
180	C₈×D₄	—	2	2	no	—
181	#427	C₂²×C₇	1	1	yes	characteristic
182	#424	C₂²×C₇	1	2	yes	—
183	C₂×#104	C₂²×C₇	1	2	yes	—
184	C₂×#104	C₂²×C₇	1	2	yes	—
185	#416	C₂²×C₇	1	2	yes	—
186	#408	C₂²×C₇	1	2	yes	—
187	C₂×C₂²⋊C₈	C₂²×C₇	1	1	yes	characteristic
188	#405	C₂²×C₇	1	2	yes	—
189	C₂×C₄×C₈	C₂²×C₇	1	2	yes	—
190	C₄×C₂²⋊C₄	C₂²×C₇	1	1	yes	characteristic
191	#341	C₂²×C₇	1	2	yes	—
192	#341	C₂²×C₇	1	1	yes	characteristic
193	#341	C₂²×C₇	1	1	yes	characteristic
194	#339	C₂²×C₇	1	2	yes	—
195	#339	C₂²×C₇	1	2	yes	—
196	#336	C₂²×C₇	1	2	yes	—
197	C₂³×C₇	—	2	2	no	—
198	C₂³×C₇	—	2	2	no	—
199	C₂³×C₇	—	2	2	no	—
200	C₂³×C₇	—	4	1	no	—
201	C₂³×C₇	C₄×D₄	1	1	yes	characteristic
202	C₂³×C₇	C₄×D₄	1	1	yes	characteristic
203	C₂³×C₇	C₂×#41	1	1	yes	characteristic
204	C₇×Q₈	—	2	2	no	—
205	C₇×Q₈	—	2	2	no	—
206	C₇×D₄	—	2	2	no	—
207	C₇×D₄	—	2	2	no	—
208	C₇×D₄	—	4	2	no	—
209	C₇×D₄	—	4	2	no	—
210	C₇×D₄	—	4	4	no	—
211	C₇×D₄	—	8	2	no	—
212	C₂×C₄×C₇	—	2	2	no	—
213	C₂×C₄×C₇	—	2	1	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	2	no	—
218	C₂×C₄×C₇	—	2	2	no	—
219	C₂×C₄×C₇	—	2	4	no	—
220	C₂×C₄×C₇	—	2	2	no	—
221	C₂×C₄×C₇	—	2	2	no	—
222	C₂×C₄×C₇	—	2	2	no	—
223	C₂×C₄×C₇	—	4	2	no	—
224	C₂×C₄×C₇	—	4	2	no	—
225	C₂×C₄×C₇	—	4	2	no	—
226	C₂×C₄×C₇	—	4	2	no	—
227	C₂×C₄×C₇	C₄×D₄	1	1	yes	characteristic
228	C₂×C₄×C₇	C₄×D₄	1	1	yes	characteristic
229	C₂×C₄×C₇	C₂³×C₄	1	1	yes	characteristic
230	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
231	C₂×C₄×C₇	C₂×#41	1	2	yes	—
232	C₂×C₄×C₇	H(5,𝔽₂)	1	2	yes	—
233	C₇×C₈	—	2	1	no	—
234	C₇×C₈	—	2	1	no	—
235	C₇×C₈	—	2	1	no	—
236	C₇×C₈	—	2	1	no	—
237	C₇×C₈	—	2	2	no	—
238	C₇×C₈	—	2	2	no	—
239	C₇×C₈	—	2	4	no	—
240	C₇×C₈	—	4	2	no	—
241	C₂×#41	C₂³×C₇	1	2	yes	—
242	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
243	#135	—	4	2	no	—
244	C₂×Q₁₆	C₂×C₄×C₇	1	1	yes	characteristic
245	C₂×SD₁₆	C₂×C₄×C₇	1	2	yes	—
246	C₂×D₈	C₂×C₄×C₇	1	1	yes	characteristic
247	#131	—	2	4	no	—
248	#131	—	4	2	no	—
249	C₂×M₁₆	—	2	2	no	—
250	C₂×M₁₆	—	2	2	no	—
251	C₂×M₁₆	—	2	4	no	—
252	C₂×M₁₆	—	4	2	no	—
253	C₂×M₁₆	C₂³×C₇	1	2	yes	—
254	C₂×M₁₆	C₂³×C₇	1	2	yes	—
255	C₂²×C₈	—	2	2	no	—
256	C₂²×C₈	—	2	2	no	—
257	C₂²×C₈	—	4	2	no	—
258	C₂²×C₈	C₂×C₄×C₇	1	1	yes	characteristic
259	C₂²×C₈	C₂×C₄×C₇	1	1	yes	characteristic
260	C₂²×C₈	C₂×C₄×C₇	1	1	yes	characteristic
261	C₂²×C₈	C₂×C₄×C₇	1	1	yes	characteristic
262	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
263	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
264	C₂²×C₈	C₂³×C₇	1	2	yes	—
265	#123	—	2	2	no	—
266	C₂²⋊Q₈	C₂×C₄×C₇	1	2	yes	—
267	C₂²⋊Q₈	C₂×C₄×C₇	1	2	yes	—
268	#121	C₂×C₄×C₇	1	2	yes	—
269	#121	C₂×C₄×C₇	1	2	yes	—
270	#120	—	2	2	no	—
271	C₄×D₄	—	2	2	no	—
272	C₄×D₄	—	2	2	no	—
273	#117	C₂³×C₇	1	2	yes	—
274	C₂×C₂²⋊C₄	—	2	1	no	—
275	C₂×C₄²	C₂³×C₇	1	2	yes	—
276	#107	C₂×C₄×C₇	1	1	yes	characteristic
277	#107	C₂×C₄×C₇	1	1	yes	characteristic
278	#106	C₂×C₄×C₇	1	2	yes	—
279	C₄⋊C₈	—	2	2	no	—
280	C₄⋊C₈	—	2	2	no	—
281	#104	—	2	4	no	—
282	#104	—	4	2	no	—
283	#103	C₂×C₄×C₇	1	2	yes	—
284	#103	C₂×C₄×C₇	1	2	yes	—
285	#102	C₂×C₄×C₇	1	2	yes	—
286	#102	C₂×C₄×C₇	1	2	yes	—
287	C₂²⋊C₈	—	2	2	no	—
288	C₂²⋊C₈	—	2	2	no	—
289	C₂²⋊C₈	C₇×D₄	1	1	yes	characteristic
290	C₂²⋊C₈	C₇×D₄	1	1	yes	characteristic
291	C₂²⋊C₈	C₇×D₄	1	2	yes	—
292	#97	—	2	2	no	—
293	C₄×C₈	—	2	2	no	—
294	C₄×C₈	—	4	2	no	—
295	#95	—	2	1	no	—
296	C₂²×C₇	—	2	1	no	—
297	C₂²×C₇	—	2	1	no	—
298	C₂²×C₇	—	2	1	no	—
299	C₂²×C₇	—	2	1	no	—
300	C₂²×C₇	—	2	1	no	—
301	C₂²×C₇	—	2	1	no	—
302	C₂²×C₇	—	2	1	no	—
303	C₂²×C₇	—	4	4	no	—
304	C₂²×C₇	—	4	2	no	—
305	C₂²×C₇	—	4	2	no	—
306	C₂²×C₇	—	4	2	no	—
307	C₂²×C₇	#443	1	2	yes	—
308	C₂²×C₇	C₂×C₄×D₄	1	1	yes	characteristic
309	C₂²×C₇	#553	1	2	yes	—
310	C₄×C₇	—	2	1	no	—
311	C₄×C₇	—	2	1	no	—
312	C₄×C₇	—	4	4	no	—
313	C₄×C₇	—	4	2	no	—
314	C₄×C₇	—	4	2	no	—
315	C₄×C₇	—	4	2	no	—
316	C₄×C₇	C₄×#41	1	1	yes	characteristic
317	C₄×C₇	#518	1	1	yes	characteristic
318	C₄×C₇	#546	1	2	yes	—
319	C₂⁴	C₇×#41	1	1	yes	characteristic
320	#41	—	2	2	no	—
321	#41	—	2	2	no	—
322	#41	—	2	2	no	—
323	#41	—	2	2	no	—
324	C₂×Q₈	C₂²×C₄×C₇	1	2	yes	—
325	C₂×D₄	—	2	2	no	—
326	C₂×D₄	—	2	2	no	—
327	C₂×D₄	—	2	2	no	—
328	C₂×D₄	C₂²×C₄×C₇	1	2	yes	—
329	C₂²×C₄	—	2	2	no	—
330	C₂²×C₄	—	2	2	no	—
331	C₂²×C₄	—	2	2	no	—
332	C₂²×C₄	—	2	2	no	—
333	C₂²×C₄	C₂²×C₄×C₇	1	1	yes	characteristic
334	C₂²×C₄	C₂²×C₄×C₇	1	1	yes	characteristic
335	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
336	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
337	C₂²×C₄	C₇×#41	1	1	yes	characteristic
338	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
339	Q₁₆	—	4	1	no	—
340	SD₁₆	—	4	2	no	—
341	D₈	—	4	1	no	—
342	M₁₆	—	2	2	no	—
343	M₁₆	—	2	2	no	—
344	M₁₆	—	2	2	no	—
345	M₁₆	—	4	4	no	—
346	M₁₆	—	4	4	no	—
347	M₁₆	C₇×#41	1	4	yes	—
348	C₂×C₈	—	2	2	no	—
349	C₂×C₈	—	2	2	no	—
350	C₂×C₈	—	2	2	no	—
351	C₂×C₈	—	2	2	no	—
352	C₂×C₈	—	2	2	no	—
353	C₂×C₈	—	2	2	no	—
354	C₂×C₈	—	4	1	no	—
355	C₂×C₈	—	4	1	no	—
356	C₂×C₈	—	4	1	no	—
357	C₂×C₈	—	4	1	no	—
358	C₂×C₈	—	4	4	no	—
359	C₂×C₈	—	4	4	no	—
360	C₂×C₈	C₂²×C₄×C₇	1	1	yes	characteristic
361	C₂×C₈	C₂²×C₄×C₇	1	1	yes	characteristic
362	C₂×C₈	C₂²×C₄×C₇	1	1	yes	characteristic
363	C₂×C₈	C₂²×C₄×C₇	1	1	yes	characteristic
364	C₂×C₈	C₂×C₇×D₄	1	2	yes	—
365	C₂×C₈	C₂×C₇×D₄	1	2	yes	—
366	C₄⋊C₄	—	2	2	no	—
367	C₄⋊C₄	—	2	2	no	—
368	C₄⋊C₄	C₂²×C₄×C₇	1	2	yes	—
369	C₄⋊C₄	C₂²×C₄×C₇	1	2	yes	—
370	C₂²⋊C₄	—	2	4	no	—
371	C₂²⋊C₄	—	2	2	no	—
372	C₂²⋊C₄	—	2	2	no	—
373	C₂²⋊C₄	—	2	2	no	—
374	C₂²⋊C₄	—	2	2	no	—
375	C₂²⋊C₄	—	2	2	no	—
376	C₄²	—	2	2	no	—
377	C₄²	—	2	2	no	—
378	C₄²	—	2	2	no	—
379	C₂×C₇	—	2	2	no	—
380	C₂×C₇	—	2	2	no	—
381	C₂×C₇	—	4	1	no	—
382	C₂×C₇	—	8	2	no	—
383	C₂×C₇	#2364	1	1	yes	characteristic
384	C₂×C₇	C₂×#443	1	1	yes	characteristic
385	C₂×C₇	#2957	1	1	yes	characteristic
386	C₂³	—	2	2	no	—
387	C₂³	—	2	2	no	—
388	C₂³	—	2	2	no	—
389	C₂³	—	4	1	no	—
390	C₂³	C₄×C₇×D₄	1	1	yes	characteristic
391	C₂³	C₄×C₇×D₄	1	1	yes	characteristic
392	C₂³	C₂×C₇×#41	1	1	yes	characteristic
393	Q₈	—	2	2	no	—
394	Q₈	—	2	2	no	—
395	D₄	—	2	2	no	—
396	D₄	—	2	2	no	—
397	D₄	—	4	2	no	—
398	D₄	—	4	2	no	—
399	D₄	—	4	4	no	—
400	D₄	—	8	2	no	—
401	C₂×C₄	—	2	2	no	—
402	C₂×C₄	—	2	1	no	—
403	C₂×C₄	—	2	1	no	—
404	C₂×C₄	—	2	1	no	—
405	C₂×C₄	—	2	1	no	—
406	C₂×C₄	—	2	2	no	—
407	C₂×C₄	—	2	2	no	—
408	C₂×C₄	—	2	4	no	—
409	C₂×C₄	—	2	2	no	—
410	C₂×C₄	—	2	2	no	—
411	C₂×C₄	—	2	2	no	—
412	C₂×C₄	—	4	2	no	—
413	C₂×C₄	—	4	2	no	—
414	C₂×C₄	—	4	2	no	—
415	C₂×C₄	—	4	2	no	—
416	C₂×C₄	C₄×C₇×D₄	1	1	yes	characteristic
417	C₂×C₄	C₄×C₇×D₄	1	1	yes	characteristic
418	C₂×C₄	C₂³×C₄×C₇	1	1	yes	characteristic
419	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
420	C₂×C₄	C₂×C₇×#41	1	2	yes	—
421	C₂×C₄	C₇×H(5,𝔽₂)	1	2	yes	—
422	C₈	—	2	1	no	—
423	C₈	—	2	1	no	—
424	C₈	—	2	1	no	—
425	C₈	—	2	1	no	—
426	C₈	—	2	2	no	—
427	C₈	—	2	2	no	—
428	C₈	—	2	4	no	—
429	C₈	—	4	2	no	—
430	C₇	#23146	1	1	yes	characteristic, direct product factor, Sylow
431	C₂²	—	2	1	no	—
432	C₂²	—	2	1	no	—
433	C₂²	—	2	1	no	—
434	C₂²	—	2	1	no	—
435	C₂²	—	2	1	no	—
436	C₂²	—	2	1	no	—
437	C₂²	—	2	1	no	—
438	C₂²	—	4	4	no	—
439	C₂²	—	4	2	no	—
440	C₂²	—	4	2	no	—
441	C₂²	—	4	2	no	—
442	C₂²	C₇×#443	1	2	yes	—
443	C₂²	C₂×C₄×C₇×D₄	1	1	yes	characteristic
444	C₂²	C₇×#553	1	2	yes	—
445	C₄	—	2	1	no	—
446	C₄	—	2	1	no	—
447	C₄	—	4	4	no	—
448	C₄	—	4	2	no	—
449	C₄	—	4	2	no	—
450	C₄	—	4	2	no	—
451	C₄	C₄×C₇×#41	1	1	yes	characteristic
452	C₄	C₇×#518	1	1	yes	characteristic
453	C₄	C₇×#546	1	2	yes	—
454	C₂	—	2	2	no	—
455	C₂	—	2	2	no	—
456	C₂	—	4	1	no	—
457	C₂	—	8	2	no	—
458	C₂	C₇×#2364	1	1	yes	characteristic
459	C₂	C₂×C₇×#443	1	1	yes	characteristic
460	C₂	C₇×#2957	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₇	C₂²×D₄
commutator	C₂×C₄	C₂³×C₄×C₇
Frattini, cosocle	C₂²×C₄	C₂⁴×C₇
socle	C₂²×C₇	C₂×C₄×D₄
prime radical	C₇×#3050	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₇ ◁ C₂×C₇×C₂²⋊C₈ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₇×#2933	C₂	semidirect
3. C₇×#1937	C₂	semidirect
4. C₇×#1922	C₂	semidirect
5. C₇×#1876	C₂	semidirect
6. C₇×#1871	C₂	semidirect
7. C₇×#1764	C₂	semidirect
8. C₇×C₈×C₂²⋊C₄	C₂	semidirect
9. C₂×C₇×#341	C₂	semidirect
15. C₇×#467	C₄	semidirect
16. C₇×#467	C₄	semidirect
17. C₇×#466	C₄	semidirect
18. C₇×#466	C₄	semidirect
19. C₇×#465	C₄	semidirect
20. C₇×#465	C₄	semidirect
41. #23146	C₇	direct (N × H)
98. #2933	C₂×C₇	semidirect
99. #1937	C₂×C₇	semidirect
100. #1922	C₂×C₇	semidirect
101. #1876	C₂×C₇	semidirect
102. #1871	C₂×C₇	semidirect
103. #1764	C₂×C₇	semidirect
104. C₈×C₂²⋊C₄	C₂×C₇	semidirect
105. C₂×#341	C₂×C₇	semidirect
171. #467	C₄×C₇	semidirect
172. #467	C₄×C₇	semidirect
173. #466	C₄×C₇	semidirect
174. #466	C₄×C₇	semidirect
175. #465	C₄×C₇	semidirect
176. #465	C₄×C₇	semidirect
430. C₇	#23146	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×#3050	2
C₇×#2933	2
C₇×#1937	2
C₇×#1922	2
C₇×#1876	2
C₇×#1871	2
C₇×#1764	2
C₇×C₈×C₂²⋊C₄	2
C₂×C₇×#341	2
#23146	7

Subgroups — C7×#23146 #13200362

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×#23146 #13200362