Subgroups — C₇×#21072 #13198288

Order 1792.

1018 conjugacy classes of subgroups.

The subgroup lattice has 468 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₇×#108	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₇×#421	C₂	1	1	yes	maximal, characteristic
3	C₂×C₇×#416	C₂	1	1	yes	maximal, characteristic
4	C₇×#2879	C₂	1	1	yes	maximal, characteristic
5	C₇×#2873	C₂	1	1	yes	maximal, characteristic, complemented
6	C₇×#1929	C₂	1	8	yes	maximal, complemented
7	C₇×#1733	C₂	1	1	yes	maximal, characteristic, complemented
8	C₇×#1729	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂²×C₇×#41	C₂²	1	1	yes	characteristic
10	C₂²×C₇×M₁₆	C₂²	1	1	yes	characteristic
11	C₂²×C₇×M₁₆	C₂²	1	1	yes	characteristic
12	C₂²×C₇×M₁₆	C₂²	1	1	yes	characteristic
13	C₂³×C₇×C₈	C₂²	1	1	yes	characteristic
14	C₂×C₇×#117	C₂²	1	1	yes	characteristic
15	C₂×C₇×#117	C₂²	1	1	yes	characteristic
16	C₂×C₇×#108	—	2	4	no	—
17	C₂×C₇×#108	C₂²	1	4	yes	complemented
18	C₇×#421	—	2	4	no	—
19	C₂×C₇×#104	C₂²	1	4	yes	—
20	C₇×#416	C₄	1	4	yes	complemented
21	C₇×#416	C₂²	1	4	yes	—
22	C₂×C₇×#103	C₄	1	2	yes	complemented
23	C₂×C₇×#102	C₄	1	2	yes	complemented
24	C₇×#408	—	2	2	no	—
25	C₇×#408	C₂²	1	4	yes	—
26	C₇×#407	—	2	2	no	—
27	C₇×#405	—	2	2	no	—
28	C₇×#405	C₂²	1	4	yes	complemented
29	C₄×C₇×M₁₆	—	2	2	no	—
30	C₇×#339	C₂²	1	4	yes	complemented
31	C₇×#336	C₂²	1	4	yes	complemented
32	#21072	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
33	C₂×C₇×#41	—	2	1	no	—
34	C₂×C₇×#41	—	2	1	no	—
35	C₂×C₇×#41	—	2	2	no	—
36	C₂×C₇×#41	—	2	2	no	—
37	C₂×C₇×#41	—	2	2	no	—
38	C₂×C₇×#41	—	2	2	no	—
39	C₂×C₇×#41	C₂×C₄	1	2	yes	—
40	C₂×C₇×#41	C₂³	1	2	yes	—
41	C₂²×C₇×Q₈	C₂×C₄	1	1	yes	characteristic
42	C₂²×C₇×D₄	—	2	1	no	—
43	C₂²×C₇×D₄	C₂×C₄	1	1	yes	characteristic
44	C₂³×C₄×C₇	—	2	1	no	—
45	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
46	C₂×C₇×M₁₆	—	2	1	no	—
47	C₂×C₇×M₁₆	—	2	2	no	—
48	C₂×C₇×M₁₆	—	2	2	no	—
49	C₂×C₇×M₁₆	—	2	2	no	—
50	C₂×C₇×M₁₆	—	2	1	no	—
51	C₂×C₇×M₁₆	—	2	2	no	—
52	C₂×C₇×M₁₆	—	2	2	no	—
53	C₂×C₇×M₁₆	D₄	1	4	yes	—
54	C₂×C₇×M₁₆	D₄	1	2	yes	—
55	C₂×C₇×M₁₆	D₄	1	2	yes	—
56	C₂×C₇×M₁₆	C₂³	1	2	yes	—
57	C₂×C₇×M₁₆	C₂³	1	2	yes	—
58	C₂²×C₇×C₈	—	2	1	no	—
59	C₂²×C₇×C₈	—	2	2	no	—
60	C₂²×C₇×C₈	—	2	2	no	—
61	C₂²×C₇×C₈	—	2	1	no	—
62	C₂²×C₇×C₈	C₂×C₄	1	2	yes	—
63	C₂²×C₇×C₈	C₂×C₄	1	2	yes	—
64	C₂²×C₇×C₈	C₂³	1	2	yes	—
65	C₂²×C₇×C₈	C₂³	1	2	yes	—
66	C₇×#117	—	2	1	no	—
67	C₇×#117	—	2	1	no	—
68	C₇×#117	—	2	2	no	—
69	C₇×#117	—	2	2	no	—
70	C₇×#117	C₂×C₄	1	2	yes	—
71	C₇×#117	C₂³	1	2	yes	—
72	C₂×C₇×C₄⋊C₄	—	2	1	no	—
73	C₂×C₇×C₄⋊C₄	C₂×C₄	1	2	yes	—
74	C₂×C₇×C₂²⋊C₄	—	2	1	no	—
75	C₂×C₇×C₂²⋊C₄	—	2	1	no	—
76	C₂×C₄²×C₇	—	2	1	no	—
77	C₂×C₄²×C₇	C₂³	1	2	yes	—
78	C₇×#108	—	2	8	no	—
79	C₇×#104	—	2	8	no	—
80	C₇×#103	C₂×C₄	1	8	yes	—
81	C₇×#102	C₂×C₄	1	8	yes	—
82	C₇×C₂²⋊C₈	—	2	8	no	—
83	C₇×#97	—	2	4	no	—
84	C₄×C₇×C₈	—	2	4	no	—
85	C₂²×#108	C₂×C₇	1	1	yes	characteristic, complemented
86	C₂×#421	C₂×C₇	1	1	yes	characteristic
87	C₂×#416	C₂×C₇	1	1	yes	characteristic
88	#2879	C₂×C₇	1	1	yes	characteristic
89	#2873	C₂×C₇	1	1	yes	characteristic, complemented
90	#1929	C₂×C₇	1	8	yes	complemented
91	#1733	C₂×C₇	1	1	yes	characteristic, complemented
92	#1729	C₂×C₇	1	1	yes	characteristic, complemented
93	C₂⁴×C₇	—	2	1	no	—
94	C₂⁴×C₇	#41	1	1	yes	characteristic
95	C₇×#41	—	2	4	no	—
96	C₇×#41	—	2	4	no	—
97	C₇×#41	—	2	2	no	—
98	C₇×#41	—	2	2	no	—
99	C₇×#41	—	2	2	no	—
100	C₇×#41	—	2	2	no	—
101	C₇×#41	—	4	2	no	—
102	C₇×#41	—	4	2	no	—
103	C₇×#41	—	4	2	no	—
104	C₇×#41	—	4	2	no	—
105	C₂×C₇×Q₈	—	2	1	no	—
106	C₂×C₇×Q₈	—	2	2	no	—
107	C₂×C₇×Q₈	—	2	2	no	—
108	C₂×C₇×Q₈	C₂²×C₄	1	2	yes	—
109	C₂×C₇×D₄	—	2	2	no	—
110	C₂×C₇×D₄	—	2	2	no	—
111	C₂×C₇×D₄	—	2	2	no	—
112	C₂×C₇×D₄	—	2	2	no	—
113	C₂×C₇×D₄	—	2	1	no	—
114	C₂×C₇×D₄	—	4	2	no	—
115	C₂×C₇×D₄	—	4	2	no	—
116	C₂×C₇×D₄	C₂²×C₄	1	2	yes	—
117	C₂²×C₄×C₇	—	2	1	no	—
118	C₂²×C₄×C₇	—	2	2	no	—
119	C₂²×C₄×C₇	—	2	2	no	—
120	C₂²×C₄×C₇	—	2	2	no	—
121	C₂²×C₄×C₇	—	2	2	no	—
122	C₂²×C₄×C₇	—	4	2	no	—
123	C₂²×C₄×C₇	—	4	2	no	—
124	C₂²×C₄×C₇	C₂²×C₄	1	1	yes	characteristic
125	C₂²×C₄×C₇	C₂²×C₄	1	1	yes	characteristic
126	C₂²×C₄×C₇	C₂×D₄	1	2	yes	—
127	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
128	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
129	C₂²×C₄×C₇	#41	1	2	yes	—
130	C₂²×C₄×C₇	#41	1	2	yes	—
131	C₂²×C₄×C₇	#41	1	2	yes	—
132	C₂²×C₄×C₇	#41	1	1	yes	characteristic
133	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
134	C₇×M₁₆	—	2	4	no	—
135	C₇×M₁₆	—	2	4	no	—
136	C₇×M₁₆	—	2	4	no	—
137	C₇×M₁₆	—	2	2	no	—
138	C₇×M₁₆	—	2	2	no	—
139	C₇×M₁₆	—	2	2	no	—
140	C₇×M₁₆	—	4	2	no	—
141	C₇×M₁₆	C₂×D₄	1	4	yes	—
142	C₂×C₇×C₈	—	2	4	no	—
143	C₂×C₇×C₈	—	2	4	no	—
144	C₂×C₇×C₈	—	2	4	no	—
145	C₂×C₇×C₈	—	2	2	no	—
146	C₂×C₇×C₈	—	2	2	no	—
147	C₂×C₇×C₈	—	2	2	no	—
148	C₂×C₇×C₈	—	2	2	no	—
149	C₂×C₇×C₈	—	2	2	no	—
150	C₂×C₇×C₈	—	2	2	no	—
151	C₂×C₇×C₈	—	4	2	no	—
152	C₂×C₇×C₈	C₂²×C₄	1	4	yes	—
153	C₂×C₇×C₈	C₂×D₄	1	4	yes	—
154	C₇×C₄⋊C₄	—	2	2	no	—
155	C₇×C₄⋊C₄	—	4	2	no	—
156	C₇×C₄⋊C₄	C₂²×C₄	1	4	yes	—
157	C₇×C₂²⋊C₄	—	2	2	no	—
158	C₇×C₂²⋊C₄	—	2	2	no	—
159	C₇×C₂²⋊C₄	—	4	2	no	—
160	C₄²×C₇	—	2	2	no	—
161	C₄²×C₇	—	2	2	no	—
162	C₄²×C₇	—	2	2	no	—
163	C₄²×C₇	—	2	2	no	—
164	C₂²×#41	C₂²×C₇	1	1	yes	characteristic
165	C₂²×M₁₆	C₂²×C₇	1	1	yes	characteristic
166	C₂²×M₁₆	C₂²×C₇	1	1	yes	characteristic
167	C₂²×M₁₆	C₂²×C₇	1	1	yes	characteristic
168	C₂³×C₈	C₂²×C₇	1	1	yes	characteristic
169	C₂×#117	C₂²×C₇	1	1	yes	characteristic
170	C₂×#117	C₂²×C₇	1	1	yes	characteristic
171	C₂×#108	—	2	4	no	—
172	C₂×#108	C₂²×C₇	1	4	yes	complemented
173	#421	—	2	4	no	—
174	C₂×#104	C₂²×C₇	1	4	yes	—
175	#416	C₄×C₇	1	4	yes	complemented
176	#416	C₂²×C₇	1	4	yes	—
177	C₂×#103	C₄×C₇	1	2	yes	complemented
178	C₂×#102	C₄×C₇	1	2	yes	complemented
179	#408	—	2	2	no	—
180	#408	C₂²×C₇	1	4	yes	—
181	#407	—	2	2	no	—
182	#405	—	2	2	no	—
183	#405	C₂²×C₇	1	4	yes	complemented
184	C₄×M₁₆	—	2	2	no	—
185	#339	C₂²×C₇	1	4	yes	complemented
186	#336	C₂²×C₇	1	4	yes	complemented
187	C₂³×C₇	—	2	2	no	—
188	C₂³×C₇	—	4	2	no	—
189	C₂³×C₇	—	4	2	no	—
190	C₂³×C₇	—	8	2	no	—
191	C₂³×C₇	C₄×D₄	1	1	yes	characteristic
192	C₂³×C₇	C₄×D₄	1	1	yes	characteristic
193	C₂³×C₇	#124	1	2	yes	—
194	C₂³×C₇	#126	1	2	yes	—
195	C₂³×C₇	C₂×#41	1	1	yes	characteristic
196	C₇×Q₈	—	2	2	no	—
197	C₇×Q₈	—	2	2	no	—
198	C₇×Q₈	—	4	2	no	—
199	C₇×D₄	—	2	2	no	—
200	C₇×D₄	—	2	2	no	—
201	C₇×D₄	—	4	2	no	—
202	C₇×D₄	—	4	2	no	—
203	C₇×D₄	—	4	4	no	—
204	C₇×D₄	—	4	2	no	—
205	C₂×C₄×C₇	—	2	4	no	—
206	C₂×C₄×C₇	—	2	2	no	—
207	C₂×C₄×C₇	—	4	2	no	—
208	C₂×C₄×C₇	—	4	2	no	—
209	C₂×C₄×C₇	—	4	2	no	—
210	C₂×C₄×C₇	—	4	4	no	—
211	C₂×C₄×C₇	—	4	4	no	—
212	C₂×C₄×C₇	—	4	2	no	—
213	C₂×C₄×C₇	—	8	2	no	—
214	C₂×C₄×C₇	#117	1	2	yes	—
215	C₂×C₄×C₇	#117	1	2	yes	—
216	C₂×C₄×C₇	C₄×D₄	1	2	yes	—
217	C₂×C₄×C₇	C₄×D₄	1	2	yes	—
218	C₂×C₄×C₇	C₄×D₄	1	1	yes	characteristic
219	C₂×C₄×C₇	C₄×D₄	1	1	yes	characteristic
220	C₂×C₄×C₇	#121	1	2	yes	—
221	C₂×C₄×C₇	#121	1	2	yes	—
222	C₂×C₄×C₇	#123	1	2	yes	—
223	C₂×C₄×C₇	#123	1	2	yes	—
224	C₂×C₄×C₇	#124	1	2	yes	—
225	C₂×C₄×C₇	#126	1	2	yes	—
226	C₂×C₄×C₇	C₂³×C₄	1	1	yes	characteristic
227	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
228	C₂×C₄×C₇	C₂²×D₄	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	C₂×#41	1	1	yes	characteristic
232	C₇×C₈	—	2	4	no	—
233	C₇×C₈	—	2	4	no	—
234	C₇×C₈	—	2	4	no	—
235	C₇×C₈	—	4	2	no	—
236	C₂×#41	—	2	1	no	—
237	C₂×#41	—	2	1	no	—
238	C₂×#41	—	2	2	no	—
239	C₂×#41	—	2	2	no	—
240	C₂×#41	—	2	2	no	—
241	C₂×#41	—	2	2	no	—
242	C₂×#41	C₂×C₄×C₇	1	2	yes	—
243	C₂×#41	C₂³×C₇	1	2	yes	—
244	C₂²×Q₈	C₂×C₄×C₇	1	1	yes	characteristic
245	C₂²×D₄	—	2	1	no	—
246	C₂²×D₄	C₂×C₄×C₇	1	1	yes	characteristic
247	C₂³×C₄	—	2	1	no	—
248	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
249	C₂×M₁₆	—	2	1	no	—
250	C₂×M₁₆	—	2	2	no	—
251	C₂×M₁₆	—	2	2	no	—
252	C₂×M₁₆	—	2	2	no	—
253	C₂×M₁₆	—	2	1	no	—
254	C₂×M₁₆	—	2	2	no	—
255	C₂×M₁₆	—	2	2	no	—
256	C₂×M₁₆	C₇×D₄	1	4	yes	—
257	C₂×M₁₆	C₇×D₄	1	2	yes	—
258	C₂×M₁₆	C₇×D₄	1	2	yes	—
259	C₂×M₁₆	C₂³×C₇	1	2	yes	—
260	C₂×M₁₆	C₂³×C₇	1	2	yes	—
261	C₂²×C₈	—	2	2	no	—
262	C₂²×C₈	—	2	1	no	—
263	C₂²×C₈	—	2	2	no	—
264	C₂²×C₈	—	2	1	no	—
265	C₂²×C₈	C₂×C₄×C₇	1	2	yes	—
266	C₂²×C₈	C₂×C₄×C₇	1	2	yes	—
267	C₂²×C₈	C₂³×C₇	1	2	yes	—
268	C₂²×C₈	C₂³×C₇	1	2	yes	—
269	#117	—	2	1	no	—
270	#117	—	2	1	no	—
271	#117	—	2	2	no	—
272	#117	—	2	2	no	—
273	#117	C₂×C₄×C₇	1	2	yes	—
274	#117	C₂³×C₇	1	2	yes	—
275	C₂×C₄⋊C₄	—	2	1	no	—
276	C₂×C₄⋊C₄	C₂×C₄×C₇	1	2	yes	—
277	C₂×C₂²⋊C₄	—	2	1	no	—
278	C₂×C₂²⋊C₄	—	2	1	no	—
279	C₂×C₄²	—	2	1	no	—
280	C₂×C₄²	C₂³×C₇	1	2	yes	—
281	#108	—	2	8	no	—
282	#104	—	2	8	no	—
283	#103	C₂×C₄×C₇	1	8	yes	—
284	#102	C₂×C₄×C₇	1	8	yes	—
285	C₂²⋊C₈	—	2	8	no	—
286	#97	—	2	4	no	—
287	C₄×C₈	—	2	4	no	—
288	C₂²×C₇	—	2	2	no	—
289	C₂²×C₇	—	2	2	no	—
290	C₂²×C₇	—	2	2	no	—
291	C₂²×C₇	—	4	2	no	—
292	C₂²×C₇	—	4	2	no	—
293	C₂²×C₇	—	4	4	no	—
294	C₂²×C₇	—	4	2	no	—
295	C₂²×C₇	—	8	4	no	—
296	C₂²×C₇	#388	1	2	yes	—
297	C₂²×C₇	#388	1	2	yes	—
298	C₂²×C₇	C₂×C₄×D₄	1	1	yes	characteristic
299	C₂²×C₇	C₂×#124	1	1	yes	characteristic
300	C₂²×C₇	C₂×#126	1	1	yes	characteristic
301	C₄×C₇	—	4	4	no	—
302	C₄×C₇	—	4	2	no	—
303	C₄×C₇	—	8	2	no	—
304	C₄×C₇	#388	1	2	yes	—
305	C₄×C₇	#388	1	2	yes	—
306	C₄×C₇	C₂×#117	1	1	yes	characteristic
307	C₄×C₇	C₂×C₄×D₄	1	1	yes	characteristic
308	C₄×C₇	C₂×#121	1	1	yes	characteristic
309	C₄×C₇	C₂×#123	1	1	yes	characteristic
310	C₂⁴	—	2	1	no	—
311	C₂⁴	C₇×#41	1	1	yes	characteristic
312	#41	—	2	4	no	—
313	#41	—	2	4	no	—
314	#41	—	2	2	no	—
315	#41	—	2	2	no	—
316	#41	—	2	2	no	—
317	#41	—	2	2	no	—
318	#41	—	4	2	no	—
319	#41	—	4	2	no	—
320	#41	—	4	2	no	—
321	#41	—	4	2	no	—
322	C₂×Q₈	—	2	1	no	—
323	C₂×Q₈	—	2	2	no	—
324	C₂×Q₈	—	2	2	no	—
325	C₂×Q₈	C₂²×C₄×C₇	1	2	yes	—
326	C₂×D₄	—	2	2	no	—
327	C₂×D₄	—	2	2	no	—
328	C₂×D₄	—	2	2	no	—
329	C₂×D₄	—	2	2	no	—
330	C₂×D₄	—	2	1	no	—
331	C₂×D₄	—	4	2	no	—
332	C₂×D₄	—	4	2	no	—
333	C₂×D₄	C₂²×C₄×C₇	1	2	yes	—
334	C₂²×C₄	—	2	1	no	—
335	C₂²×C₄	—	2	2	no	—
336	C₂²×C₄	—	2	2	no	—
337	C₂²×C₄	—	2	2	no	—
338	C₂²×C₄	—	2	2	no	—
339	C₂²×C₄	—	4	2	no	—
340	C₂²×C₄	—	4	2	no	—
341	C₂²×C₄	C₂²×C₄×C₇	1	1	yes	characteristic
342	C₂²×C₄	C₂²×C₄×C₇	1	1	yes	characteristic
343	C₂²×C₄	C₂×C₇×D₄	1	2	yes	—
344	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
345	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
346	C₂²×C₄	C₇×#41	1	2	yes	—
347	C₂²×C₄	C₇×#41	1	2	yes	—
348	C₂²×C₄	C₇×#41	1	2	yes	—
349	C₂²×C₄	C₇×#41	1	1	yes	characteristic
350	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
351	M₁₆	—	2	4	no	—
352	M₁₆	—	2	4	no	—
353	M₁₆	—	2	4	no	—
354	M₁₆	—	2	2	no	—
355	M₁₆	—	2	2	no	—
356	M₁₆	—	2	2	no	—
357	M₁₆	—	4	2	no	—
358	M₁₆	C₂×C₇×D₄	1	4	yes	—
359	C₂×C₈	—	2	4	no	—
360	C₂×C₈	—	2	4	no	—
361	C₂×C₈	—	2	4	no	—
362	C₂×C₈	—	2	2	no	—
363	C₂×C₈	—	2	2	no	—
364	C₂×C₈	—	2	2	no	—
365	C₂×C₈	—	2	2	no	—
366	C₂×C₈	—	2	2	no	—
367	C₂×C₈	—	2	2	no	—
368	C₂×C₈	—	4	2	no	—
369	C₂×C₈	C₂²×C₄×C₇	1	4	yes	—
370	C₂×C₈	C₂×C₇×D₄	1	4	yes	—
371	C₄⋊C₄	—	2	2	no	—
372	C₄⋊C₄	—	4	2	no	—
373	C₄⋊C₄	C₂²×C₄×C₇	1	4	yes	—
374	C₂²⋊C₄	—	2	2	no	—
375	C₂²⋊C₄	—	2	2	no	—
376	C₂²⋊C₄	—	4	2	no	—
377	C₄²	—	2	2	no	—
378	C₄²	—	2	2	no	—
379	C₄²	—	2	2	no	—
380	C₄²	—	2	2	no	—
381	C₂×C₇	—	2	1	no	—
382	C₂×C₇	—	2	2	no	—
383	C₂×C₇	—	2	1	no	—
384	C₂×C₇	—	2	2	no	—
385	C₂×C₇	—	8	2	no	—
386	C₂×C₇	C₂×#388	1	1	yes	characteristic
387	C₂×C₇	#2957	1	2	yes	—
388	C₂³	—	2	2	no	—
389	C₂³	—	4	2	no	—
390	C₂³	—	4	2	no	—
391	C₂³	—	8	2	no	—
392	C₂³	C₄×C₇×D₄	1	1	yes	characteristic
393	C₂³	C₄×C₇×D₄	1	1	yes	characteristic
394	C₂³	C₇×#124	1	2	yes	—
395	C₂³	C₇×#126	1	2	yes	—
396	C₂³	C₂×C₇×#41	1	1	yes	characteristic
397	Q₈	—	2	2	no	—
398	Q₈	—	2	2	no	—
399	Q₈	—	4	2	no	—
400	D₄	—	2	2	no	—
401	D₄	—	2	2	no	—
402	D₄	—	4	4	no	—
403	D₄	—	4	2	no	—
404	D₄	—	4	2	no	—
405	D₄	—	4	2	no	—
406	C₂×C₄	—	2	4	no	—
407	C₂×C₄	—	2	2	no	—
408	C₂×C₄	—	4	2	no	—
409	C₂×C₄	—	4	2	no	—
410	C₂×C₄	—	4	2	no	—
411	C₂×C₄	—	4	4	no	—
412	C₂×C₄	—	4	4	no	—
413	C₂×C₄	—	4	2	no	—
414	C₂×C₄	—	8	2	no	—
415	C₂×C₄	C₇×#117	1	2	yes	—
416	C₂×C₄	C₇×#117	1	2	yes	—
417	C₂×C₄	C₄×C₇×D₄	1	2	yes	—
418	C₂×C₄	C₄×C₇×D₄	1	2	yes	—
419	C₂×C₄	C₄×C₇×D₄	1	1	yes	characteristic
420	C₂×C₄	C₄×C₇×D₄	1	1	yes	characteristic
421	C₂×C₄	C₇×#121	1	2	yes	—
422	C₂×C₄	C₇×#121	1	2	yes	—
423	C₂×C₄	C₇×#123	1	2	yes	—
424	C₂×C₄	C₇×#123	1	2	yes	—
425	C₂×C₄	C₇×#124	1	2	yes	—
426	C₂×C₄	C₇×#126	1	2	yes	—
427	C₂×C₄	C₂³×C₄×C₇	1	1	yes	characteristic
428	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
429	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
430	C₂×C₄	C₂×C₇×#41	1	1	yes	characteristic
431	C₂×C₄	C₂×C₇×#41	1	1	yes	characteristic
432	C₂×C₄	C₂×C₇×#41	1	1	yes	characteristic
433	C₈	—	2	4	no	—
434	C₈	—	2	4	no	—
435	C₈	—	2	4	no	—
436	C₈	—	4	2	no	—
437	C₇	#21072	1	1	yes	characteristic, direct product factor, Sylow
438	C₂²	—	2	2	no	—
439	C₂²	—	2	2	no	—
440	C₂²	—	2	2	no	—
441	C₂²	—	4	2	no	—
442	C₂²	—	4	2	no	—
443	C₂²	—	4	4	no	—
444	C₂²	—	4	2	no	—
445	C₂²	—	8	4	no	—
446	C₂²	C₇×#388	1	2	yes	—
447	C₂²	C₇×#388	1	2	yes	—
448	C₂²	C₂×C₄×C₇×D₄	1	1	yes	characteristic
449	C₂²	C₂×C₇×#124	1	1	yes	characteristic
450	C₂²	C₂×C₇×#126	1	1	yes	characteristic
451	C₄	—	4	4	no	—
452	C₄	—	4	2	no	—
453	C₄	—	8	2	no	—
454	C₄	C₇×#388	1	2	yes	—
455	C₄	C₇×#388	1	2	yes	—
456	C₄	C₂×C₇×#117	1	1	yes	characteristic
457	C₄	C₂×C₄×C₇×D₄	1	1	yes	characteristic
458	C₄	C₂×C₇×#121	1	1	yes	characteristic
459	C₄	C₂×C₇×#123	1	1	yes	characteristic
460	C₂	—	2	1	no	—
461	C₂	—	2	2	no	—
462	C₂	—	2	2	no	—
463	C₂	—	2	1	no	—
464	C₂	—	8	2	no	—
465	C₂	C₂×C₇×#388	1	1	yes	characteristic
466	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	C₂²×C₇×#41	C₂²
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
1. C₂²×C₇×#108	C₂	semidirect
5. C₇×#2873	C₂	semidirect
6. C₇×#1929	C₂	semidirect
7. C₇×#1733	C₂	semidirect
8. C₇×#1729	C₂	semidirect
17. C₂×C₇×#108	C₂²	semidirect
20. C₇×#416	C₄	semidirect
22. C₂×C₇×#103	C₄	semidirect
23. C₂×C₇×#102	C₄	semidirect
28. C₇×#405	C₂²	semidirect
30. C₇×#339	C₂²	semidirect
31. C₇×#336	C₂²	semidirect
32. #21072	C₇	direct (N × H)
85. C₂²×#108	C₂×C₇	semidirect
89. #2873	C₂×C₇	semidirect
90. #1929	C₂×C₇	semidirect
91. #1733	C₂×C₇	semidirect
92. #1729	C₂×C₇	semidirect
172. C₂×#108	C₂²×C₇	semidirect
175. #416	C₄×C₇	semidirect
177. C₂×#103	C₄×C₇	semidirect
178. C₂×#102	C₄×C₇	semidirect
183. #405	C₂²×C₇	semidirect
185. #339	C₂²×C₇	semidirect
186. #336	C₂²×C₇	semidirect
437. C₇	#21072	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×C₇×#108	2
C₂×C₇×#421	2
C₂×C₇×#416	2
C₇×#2879	2
C₇×#2873	2
C₇×#1929	2
C₇×#1733	2
C₇×#1729	2
#21072	7

Subgroups — C7×#21072 #13198288

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×#21072 #13198288