Subgroups — C₇×#21547 #13198763

Order 1792.

906 conjugacy classes of subgroups.

The subgroup lattice has 444 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	C₂×C₇×#444	C₂	1	1	yes	maximal, characteristic, complemented
3	C₇×#2930	C₂	1	2	yes	maximal, complemented
4	C₂×C₇×#405	C₂	1	1	yes	maximal, characteristic, complemented
5	C₇×#1975	C₂	1	1	yes	maximal, characteristic, complemented
6	C₇×#1946	C₂	1	1	yes	maximal, characteristic, complemented
7	C₇×#1937	C₂	1	2	yes	maximal, complemented
8	C₇×#1897	C₂	1	2	yes	maximal, complemented
9	C₇×#1810	C₂	1	1	yes	maximal, characteristic, complemented
10	C₇×#1773	C₂	1	1	yes	maximal, characteristic, complemented
11	C₇×#1764	C₂	1	2	yes	maximal, complemented
12	C₂×C₇×#135	C₂²	1	1	yes	characteristic
13	C₂×C₇×#131	C₂²	1	2	yes	—
14	C₂²×C₇×M₁₆	C₂²	1	1	yes	characteristic
15	C₂³×C₇×C₈	C₂²	1	1	yes	characteristic
16	C₇×#525	C₂²	1	2	yes	—
17	C₂×C₇×#117	C₂²	1	1	yes	characteristic
18	C₇×#467	C₄	1	2	yes	complemented
19	C₇×#466	C₄	1	2	yes	complemented
20	C₇×#465	C₄	1	4	yes	complemented
21	C₇×#444	—	2	4	no	—
22	C₇×#436	—	2	4	no	—
23	C₇×#435	—	2	4	no	—
24	C₂×C₇×#108	C₂²	1	1	yes	characteristic
25	C₂×C₇×#108	C₂²	1	1	yes	characteristic
26	C₇×#427	C₂²	1	1	yes	characteristic
27	C₇×#424	C₂²	1	2	yes	—
28	C₂×C₇×#104	C₂²	1	2	yes	—
29	C₂×C₇×#104	C₂²	1	2	yes	—
30	C₇×#416	C₂²	1	2	yes	—
31	C₇×#408	C₂²	1	2	yes	—
32	C₇×#407	C₂²	1	2	yes	—
33	C₇×#405	—	2	4	no	—
34	C₇×#405	C₂²	1	2	yes	—
35	C₂×C₇×#97	C₂²	1	1	yes	characteristic
36	C₂×C₇×#97	C₂²	1	1	yes	characteristic
37	C₂×C₄×C₇×C₈	C₂²	1	1	yes	characteristic
38	C₂×C₄×C₇×C₈	C₂²	1	1	yes	characteristic
39	C₇×#341	C₂²	1	2	yes	—
40	C₇×#339	C₂²	1	2	yes	—
41	C₇×#339	C₂²	1	2	yes	—
42	#21547	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
43	C₂×C₇×#41	C₂³	1	2	yes	—
44	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
45	C₇×#135	—	2	2	no	—
46	C₇×#135	—	2	2	no	—
47	C₂×C₇×Q₁₆	C₂×C₄	1	1	yes	characteristic
48	C₂×C₇×SD₁₆	C₂×C₄	1	2	yes	—
49	C₂×C₇×D₈	C₂×C₄	1	1	yes	characteristic
50	C₇×#131	—	2	4	no	—
51	C₇×#131	—	2	4	no	—
52	C₂×C₇×M₁₆	—	2	2	no	—
53	C₂×C₇×M₁₆	—	2	2	no	—
54	C₂×C₇×M₁₆	—	2	2	no	—
55	C₂×C₇×M₁₆	D₄	1	4	yes	—
56	C₂×C₇×M₁₆	C₂³	1	2	yes	—
57	C₂×C₇×M₁₆	C₂³	1	2	yes	—
58	C₂²×C₇×C₈	—	2	2	no	—
59	C₂²×C₇×C₈	—	2	2	no	—
60	C₂²×C₇×C₈	—	2	2	no	—
61	C₂²×C₇×C₈	C₂×C₄	1	2	yes	—
62	C₂²×C₇×C₈	C₂×C₄	1	2	yes	—
63	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
64	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
65	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
66	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
67	C₇×#123	—	2	2	no	—
68	C₇×C₂²⋊Q₈	C₂×C₄	1	4	yes	—
69	C₇×#121	C₂×C₄	1	4	yes	—
70	C₇×#120	—	2	2	no	—
71	C₄×C₇×D₄	—	2	4	no	—
72	C₇×#117	—	2	2	no	—
73	C₇×#117	—	2	2	no	—
74	C₇×#117	C₂³	1	2	yes	—
75	C₂×C₇×C₄⋊C₄	—	2	1	no	—
76	C₂×C₇×C₂²⋊C₄	—	2	1	no	—
77	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
78	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
79	C₇×#108	—	2	2	no	—
80	C₇×#108	—	2	2	no	—
81	C₇×#107	C₂×C₄	1	2	yes	—
82	C₇×#106	C₂×C₄	1	2	yes	—
83	C₇×C₄⋊C₈	—	2	4	no	—
84	C₇×#104	—	2	4	no	—
85	C₇×#104	—	2	4	no	—
86	C₇×#103	C₂×C₄	1	4	yes	—
87	C₇×#102	C₂×C₄	1	4	yes	—
88	C₇×C₂²⋊C₈	—	2	4	no	—
89	C₇×C₂²⋊C₈	—	2	4	no	—
90	C₇×#97	—	2	2	no	—
91	C₇×#97	—	2	2	no	—
92	C₇×#97	D₄	1	4	yes	complemented
93	C₄×C₇×C₈	—	2	2	no	—
94	C₄×C₇×C₈	—	2	2	no	—
95	C₄×C₇×C₈	—	2	2	no	—
96	#3050	C₂×C₇	1	1	yes	characteristic
97	C₂×#444	C₂×C₇	1	1	yes	characteristic, complemented
98	#2930	C₂×C₇	1	2	yes	complemented
99	C₂×#405	C₂×C₇	1	1	yes	characteristic, complemented
100	#1975	C₂×C₇	1	1	yes	characteristic, complemented
101	#1946	C₂×C₇	1	1	yes	characteristic, complemented
102	#1937	C₂×C₇	1	2	yes	complemented
103	#1897	C₂×C₇	1	2	yes	complemented
104	#1810	C₂×C₇	1	1	yes	characteristic, complemented
105	#1773	C₂×C₇	1	1	yes	characteristic, complemented
106	#1764	C₂×C₇	1	2	yes	complemented
107	C₂⁴×C₇	#41	1	1	yes	characteristic
108	C₇×#41	—	2	2	no	—
109	C₇×#41	—	2	2	no	—
110	C₇×#41	—	2	2	no	—
111	C₇×#41	—	2	2	no	—
112	C₂×C₇×Q₈	C₂²×C₄	1	2	yes	—
113	C₂×C₇×D₄	—	2	2	no	—
114	C₂×C₇×D₄	—	2	4	no	—
115	C₂×C₇×D₄	C₂²×C₄	1	2	yes	—
116	C₂²×C₄×C₇	—	2	1	no	—
117	C₂²×C₄×C₇	—	2	1	no	—
118	C₂²×C₄×C₇	—	2	1	no	—
119	C₂²×C₄×C₇	—	2	1	no	—
120	C₂²×C₄×C₇	—	2	1	no	—
121	C₂²×C₄×C₇	—	2	1	no	—
122	C₂²×C₄×C₇	—	2	2	no	—
123	C₂²×C₄×C₇	C₂²×C₄	1	2	yes	—
124	C₂²×C₄×C₇	C₂×D₄	1	2	yes	—
125	C₂²×C₄×C₇	#41	1	1	yes	characteristic
126	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
127	C₇×Q₁₆	—	2	2	no	—
128	C₇×SD₁₆	—	2	4	no	—
129	C₇×D₈	—	2	2	no	—
130	C₇×M₁₆	—	2	8	no	—
131	C₇×M₁₆	—	2	2	no	—
132	C₇×M₁₆	—	2	2	no	—
133	C₇×M₁₆	—	2	2	no	—
134	C₇×M₁₆	—	2	2	no	—
135	C₇×M₁₆	—	4	4	no	—
136	C₂×C₇×C₈	—	2	1	no	—
137	C₂×C₇×C₈	—	2	1	no	—
138	C₂×C₇×C₈	—	2	1	no	—
139	C₂×C₇×C₈	—	2	1	no	—
140	C₂×C₇×C₈	—	2	4	no	—
141	C₂×C₇×C₈	—	2	4	no	—
142	C₂×C₇×C₈	—	2	2	no	—
143	C₂×C₇×C₈	—	2	2	no	—
144	C₂×C₇×C₈	—	4	4	no	—
145	C₂×C₇×C₈	C₂²×C₄	1	2	yes	—
146	C₂×C₇×C₈	C₂²×C₄	1	1	yes	characteristic
147	C₂×C₇×C₈	C₂²×C₄	1	1	yes	characteristic
148	C₂×C₇×C₈	C₂×D₄	1	2	yes	—
149	C₂×C₇×C₈	C₂×D₄	1	2	yes	—
150	C₂×C₇×C₈	C₂×D₄	1	2	yes	—
151	C₂×C₇×C₈	C₂×D₄	1	2	yes	—
152	C₂×C₇×C₈	#41	1	2	yes	—
153	C₂×C₇×C₈	#41	1	2	yes	—
154	C₇×C₄⋊C₄	—	2	4	no	—
155	C₇×C₄⋊C₄	—	2	4	no	—
156	C₇×C₄⋊C₄	C₂²×C₄	1	4	yes	—
157	C₇×C₂²⋊C₄	—	2	4	no	—
158	C₇×C₂²⋊C₄	—	2	4	no	—
159	C₇×C₂²⋊C₄	—	2	2	no	—
160	C₇×C₂²⋊C₄	—	2	4	no	—
161	C₄²×C₇	—	2	1	no	—
162	C₄²×C₇	—	2	2	no	—
163	C₄²×C₇	—	2	1	no	—
164	C₄²×C₇	C₂×D₄	1	2	yes	—
165	C₄²×C₇	#41	1	2	yes	—
166	C₂×#135	C₂²×C₇	1	1	yes	characteristic
167	C₂×#131	C₂²×C₇	1	2	yes	—
168	C₂²×M₁₆	C₂²×C₇	1	1	yes	characteristic
169	C₂³×C₈	C₂²×C₇	1	1	yes	characteristic
170	#525	C₂²×C₇	1	2	yes	—
171	C₂×#117	C₂²×C₇	1	1	yes	characteristic
172	#467	C₄×C₇	1	2	yes	complemented
173	#466	C₄×C₇	1	2	yes	complemented
174	#465	C₄×C₇	1	4	yes	complemented
175	#444	—	2	4	no	—
176	#436	—	2	4	no	—
177	#435	—	2	4	no	—
178	C₂×#108	C₂²×C₇	1	1	yes	characteristic
179	C₂×#108	C₂²×C₇	1	1	yes	characteristic
180	#427	C₂²×C₇	1	1	yes	characteristic
181	#424	C₂²×C₇	1	2	yes	—
182	C₂×#104	C₂²×C₇	1	2	yes	—
183	C₂×#104	C₂²×C₇	1	2	yes	—
184	#416	C₂²×C₇	1	2	yes	—
185	#408	C₂²×C₇	1	2	yes	—
186	#407	C₂²×C₇	1	2	yes	—
187	#405	—	2	4	no	—
188	#405	C₂²×C₇	1	2	yes	—
189	C₂×#97	C₂²×C₇	1	1	yes	characteristic
190	C₂×#97	C₂²×C₇	1	1	yes	characteristic
191	C₂×C₄×C₈	C₂²×C₇	1	1	yes	characteristic
192	C₂×C₄×C₈	C₂²×C₇	1	1	yes	characteristic
193	#341	C₂²×C₇	1	2	yes	—
194	#339	C₂²×C₇	1	2	yes	—
195	#339	C₂²×C₇	1	2	yes	—
196	C₂³×C₇	—	2	1	no	—
197	C₂³×C₇	—	2	1	no	—
198	C₂³×C₇	—	2	2	no	—
199	C₂³×C₇	—	4	2	no	—
200	C₂³×C₇	C₄×D₄	1	2	yes	—
201	C₂³×C₇	C₂×#41	1	1	yes	characteristic
202	C₇×Q₈	—	2	2	no	—
203	C₇×Q₈	—	2	2	no	—
204	C₇×D₄	—	2	2	no	—
205	C₇×D₄	—	2	2	no	—
206	C₇×D₄	—	4	2	no	—
207	C₇×D₄	—	4	2	no	—
208	C₇×D₄	—	8	4	no	—
209	C₂×C₄×C₇	—	2	1	no	—
210	C₂×C₄×C₇	—	2	1	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	—	2	4	no	—
216	C₂×C₄×C₇	—	2	2	no	—
217	C₂×C₄×C₇	—	2	2	no	—
218	C₂×C₄×C₇	—	2	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	C₄×D₄	1	2	yes	—
224	C₂×C₄×C₇	C₂³×C₄	1	1	yes	characteristic
225	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
226	C₂×C₄×C₇	C₂²×D₄	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	C₇×C₈	—	2	2	no	—
231	C₇×C₈	—	2	2	no	—
232	C₇×C₈	—	4	2	no	—
233	C₇×C₈	—	4	2	no	—
234	C₇×C₈	C₄×D₄	1	2	yes	—
235	C₇×C₈	C₄×D₄	1	2	yes	—
236	C₇×C₈	#121	1	4	yes	—
237	C₂×#41	C₂³×C₇	1	2	yes	—
238	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
239	#135	—	2	2	no	—
240	#135	—	2	2	no	—
241	C₂×Q₁₆	C₂×C₄×C₇	1	1	yes	characteristic
242	C₂×SD₁₆	C₂×C₄×C₇	1	2	yes	—
243	C₂×D₈	C₂×C₄×C₇	1	1	yes	characteristic
244	#131	—	2	4	no	—
245	#131	—	2	4	no	—
246	C₂×M₁₆	—	2	2	no	—
247	C₂×M₁₆	—	2	2	no	—
248	C₂×M₁₆	—	2	2	no	—
249	C₂×M₁₆	C₇×D₄	1	4	yes	—
250	C₂×M₁₆	C₂³×C₇	1	2	yes	—
251	C₂×M₁₆	C₂³×C₇	1	2	yes	—
252	C₂²×C₈	—	2	2	no	—
253	C₂²×C₈	—	2	2	no	—
254	C₂²×C₈	—	2	2	no	—
255	C₂²×C₈	C₂×C₄×C₇	1	2	yes	—
256	C₂²×C₈	C₂×C₄×C₇	1	2	yes	—
257	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
258	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
259	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
260	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
261	#123	—	2	2	no	—
262	C₂²⋊Q₈	C₂×C₄×C₇	1	4	yes	—
263	#121	C₂×C₄×C₇	1	4	yes	—
264	#120	—	2	2	no	—
265	C₄×D₄	—	2	4	no	—
266	#117	—	2	2	no	—
267	#117	—	2	2	no	—
268	#117	C₂³×C₇	1	2	yes	—
269	C₂×C₄⋊C₄	—	2	1	no	—
270	C₂×C₂²⋊C₄	—	2	1	no	—
271	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
272	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
273	#108	—	2	2	no	—
274	#108	—	2	2	no	—
275	#107	C₂×C₄×C₇	1	2	yes	—
276	#106	C₂×C₄×C₇	1	2	yes	—
277	C₄⋊C₈	—	2	4	no	—
278	#104	—	2	4	no	—
279	#104	—	2	4	no	—
280	#103	C₂×C₄×C₇	1	4	yes	—
281	#102	C₂×C₄×C₇	1	4	yes	—
282	C₂²⋊C₈	—	2	4	no	—
283	C₂²⋊C₈	—	2	4	no	—
284	#97	—	2	2	no	—
285	#97	—	2	2	no	—
286	#97	C₇×D₄	1	4	yes	complemented
287	C₄×C₈	—	2	2	no	—
288	C₄×C₈	—	2	2	no	—
289	C₄×C₈	—	2	2	no	—
290	C₂²×C₇	—	2	2	no	—
291	C₂²×C₇	—	2	2	no	—
292	C₂²×C₇	—	2	2	no	—
293	C₂²×C₇	—	2	2	no	—
294	C₂²×C₇	—	4	2	no	—
295	C₂²×C₇	—	4	2	no	—
296	C₂²×C₇	—	4	4	no	—
297	C₂²×C₇	—	4	2	no	—
298	C₂²×C₇	C₂×C₄×D₄	1	1	yes	characteristic
299	C₂²×C₇	#525	1	1	yes	characteristic
300	C₂²×C₇	#529	1	1	yes	characteristic
301	C₄×C₇	—	2	2	no	—
302	C₄×C₇	—	4	2	no	—
303	C₄×C₇	—	4	2	no	—
304	C₄×C₇	—	4	4	no	—
305	C₄×C₇	—	4	2	no	—
306	C₄×C₇	C₂×C₄×D₄	1	1	yes	characteristic
307	C₄×C₇	C₄×#41	1	1	yes	characteristic
308	C₄×C₇	C₂×#121	1	1	yes	characteristic
309	C₄×C₇	#532	1	1	yes	characteristic
310	C₂⁴	C₇×#41	1	1	yes	characteristic
311	#41	—	2	2	no	—
312	#41	—	2	2	no	—
313	#41	—	2	2	no	—
314	#41	—	2	2	no	—
315	C₂×Q₈	C₂²×C₄×C₇	1	2	yes	—
316	C₂×D₄	—	2	2	no	—
317	C₂×D₄	—	2	4	no	—
318	C₂×D₄	C₂²×C₄×C₇	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	1	no	—
323	C₂²×C₄	—	2	1	no	—
324	C₂²×C₄	—	2	1	no	—
325	C₂²×C₄	—	2	2	no	—
326	C₂²×C₄	C₂²×C₄×C₇	1	2	yes	—
327	C₂²×C₄	C₂×C₇×D₄	1	2	yes	—
328	C₂²×C₄	C₇×#41	1	1	yes	characteristic
329	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
330	Q₁₆	—	2	2	no	—
331	SD₁₆	—	2	4	no	—
332	D₈	—	2	2	no	—
333	M₁₆	—	2	8	no	—
334	M₁₆	—	2	2	no	—
335	M₁₆	—	2	2	no	—
336	M₁₆	—	2	2	no	—
337	M₁₆	—	2	2	no	—
338	M₁₆	—	4	4	no	—
339	C₂×C₈	—	2	1	no	—
340	C₂×C₈	—	2	1	no	—
341	C₂×C₈	—	2	1	no	—
342	C₂×C₈	—	2	1	no	—
343	C₂×C₈	—	2	4	no	—
344	C₂×C₈	—	2	4	no	—
345	C₂×C₈	—	2	2	no	—
346	C₂×C₈	—	2	2	no	—
347	C₂×C₈	—	4	4	no	—
348	C₂×C₈	C₂²×C₄×C₇	1	2	yes	—
349	C₂×C₈	C₂²×C₄×C₇	1	1	yes	characteristic
350	C₂×C₈	C₂²×C₄×C₇	1	1	yes	characteristic
351	C₂×C₈	C₂×C₇×D₄	1	2	yes	—
352	C₂×C₈	C₂×C₇×D₄	1	2	yes	—
353	C₂×C₈	C₂×C₇×D₄	1	2	yes	—
354	C₂×C₈	C₂×C₇×D₄	1	2	yes	—
355	C₂×C₈	C₇×#41	1	2	yes	—
356	C₂×C₈	C₇×#41	1	2	yes	—
357	C₄⋊C₄	—	2	4	no	—
358	C₄⋊C₄	—	2	4	no	—
359	C₄⋊C₄	C₂²×C₄×C₇	1	4	yes	—
360	C₂²⋊C₄	—	2	4	no	—
361	C₂²⋊C₄	—	2	4	no	—
362	C₂²⋊C₄	—	2	2	no	—
363	C₂²⋊C₄	—	2	4	no	—
364	C₄²	—	2	1	no	—
365	C₄²	—	2	2	no	—
366	C₄²	—	2	1	no	—
367	C₄²	C₂×C₇×D₄	1	2	yes	—
368	C₄²	C₇×#41	1	2	yes	—
369	C₂×C₇	—	2	1	no	—
370	C₂×C₇	—	2	1	no	—
371	C₂×C₇	—	4	2	no	—
372	C₂×C₇	—	8	2	no	—
373	C₂×C₇	C₄×#121	1	1	yes	characteristic
374	C₂×C₇	#2957	1	2	yes	—
375	C₂³	—	2	1	no	—
376	C₂³	—	2	1	no	—
377	C₂³	—	2	2	no	—
378	C₂³	—	4	2	no	—
379	C₂³	C₄×C₇×D₄	1	2	yes	—
380	C₂³	C₂×C₇×#41	1	1	yes	characteristic
381	Q₈	—	2	2	no	—
382	Q₈	—	2	2	no	—
383	D₄	—	2	2	no	—
384	D₄	—	2	2	no	—
385	D₄	—	4	2	no	—
386	D₄	—	4	2	no	—
387	D₄	—	8	4	no	—
388	C₂×C₄	—	2	1	no	—
389	C₂×C₄	—	2	1	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	4	no	—
395	C₂×C₄	—	2	2	no	—
396	C₂×C₄	—	2	2	no	—
397	C₂×C₄	—	2	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	C₄×C₇×D₄	1	2	yes	—
403	C₂×C₄	C₂³×C₄×C₇	1	1	yes	characteristic
404	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
405	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
406	C₂×C₄	C₂×C₇×#41	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	C₈	—	2	2	no	—
410	C₈	—	2	2	no	—
411	C₈	—	4	2	no	—
412	C₈	—	4	2	no	—
413	C₈	C₄×C₇×D₄	1	2	yes	—
414	C₈	C₄×C₇×D₄	1	2	yes	—
415	C₈	C₇×#121	1	4	yes	—
416	C₇	#21547	1	1	yes	characteristic, direct product factor, Sylow
417	C₂²	—	2	2	no	—
418	C₂²	—	2	2	no	—
419	C₂²	—	2	2	no	—
420	C₂²	—	2	2	no	—
421	C₂²	—	4	2	no	—
422	C₂²	—	4	2	no	—
423	C₂²	—	4	4	no	—
424	C₂²	—	4	2	no	—
425	C₂²	C₂×C₄×C₇×D₄	1	1	yes	characteristic
426	C₂²	C₇×#525	1	1	yes	characteristic
427	C₂²	C₇×#529	1	1	yes	characteristic
428	C₄	—	2	2	no	—
429	C₄	—	4	2	no	—
430	C₄	—	4	2	no	—
431	C₄	—	4	4	no	—
432	C₄	—	4	2	no	—
433	C₄	C₂×C₄×C₇×D₄	1	1	yes	characteristic
434	C₄	C₄×C₇×#41	1	1	yes	characteristic
435	C₄	C₂×C₇×#121	1	1	yes	characteristic
436	C₄	C₇×#532	1	1	yes	characteristic
437	C₂	—	2	1	no	—
438	C₂	—	2	1	no	—
439	C₂	—	4	2	no	—
440	C₂	—	8	2	no	—
441	C₂	C₄×C₇×#121	1	1	yes	characteristic
442	C₂	C₇×#2957	1	2	yes	—

	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 ◁ C₂²×C₇×M₁₆ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₇×#444	C₂	semidirect
3. C₇×#2930	C₂	semidirect
4. C₂×C₇×#405	C₂	semidirect
5. C₇×#1975	C₂	semidirect
6. C₇×#1946	C₂	semidirect
7. C₇×#1937	C₂	semidirect
8. C₇×#1897	C₂	semidirect
9. C₇×#1810	C₂	semidirect
10. C₇×#1773	C₂	semidirect
11. C₇×#1764	C₂	semidirect
18. C₇×#467	C₄	semidirect
19. C₇×#466	C₄	semidirect
20. C₇×#465	C₄	semidirect
42. #21547	C₇	direct (N × H)
92. C₇×#97	D₄	semidirect
97. C₂×#444	C₂×C₇	semidirect
98. #2930	C₂×C₇	semidirect
99. C₂×#405	C₂×C₇	semidirect
100. #1975	C₂×C₇	semidirect
101. #1946	C₂×C₇	semidirect
102. #1937	C₂×C₇	semidirect
103. #1897	C₂×C₇	semidirect
104. #1810	C₂×C₇	semidirect
105. #1773	C₂×C₇	semidirect
106. #1764	C₂×C₇	semidirect
172. #467	C₄×C₇	semidirect
173. #466	C₄×C₇	semidirect
174. #465	C₄×C₇	semidirect
286. #97	C₇×D₄	semidirect
416. C₇	#21547	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
C₂×C₇×#444	2
C₇×#2930	2
C₂×C₇×#405	2
C₇×#1975	2
C₇×#1946	2
C₇×#1937	2
C₇×#1897	2
C₇×#1810	2
C₇×#1773	2
C₇×#1764	2
#21547	7

Subgroups — C7×#21547 #13198763

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×#21547 #13198763