Subgroups — C₇×#22683 #13199899

Order 1792.

986 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	C₂×C₄×C₇×SD₁₆	C₂	1	2	yes	maximal
2	C₂×C₄×C₇×SD₁₆	C₂	1	1	yes	maximal, characteristic
3	C₇×#2351	C₂	1	1	yes	maximal, characteristic, complemented
4	C₇×#2349	C₂	1	1	yes	maximal, characteristic
5	C₇×#1941	C₂	1	2	yes	maximal, complemented
6	C₇×#1863	C₂	1	2	yes	maximal, complemented
7	C₇×#1862	C₂	1	2	yes	maximal
8	C₇×#1846	C₂	1	1	yes	maximal, characteristic, complemented
9	C₇×#1805	C₂	1	1	yes	maximal, characteristic, complemented
10	C₇×#1804	C₂	1	1	yes	maximal, characteristic
11	C₇×C₈×C₄⋊C₄	C₂	1	1	yes	maximal, characteristic, 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	2	yes	—
16	C₂×C₄×C₇×D₄	C₂²	1	1	yes	characteristic
17	C₄×C₇×SD₁₆	—	2	8	no	—
18	C₄×C₇×SD₁₆	C₄	1	8	yes	complemented
19	C₂×C₇×#107	C₂²	1	2	yes	—
20	C₂×C₇×#106	C₂²	1	2	yes	—
21	C₂×C₇×#106	C₂²	1	1	yes	characteristic
22	C₂×C₇×C₄⋊C₈	C₂²	1	1	yes	characteristic
23	C₂×C₇×#103	C₂²	1	2	yes	—
24	C₂×C₇×#103	C₂²	1	1	yes	characteristic
25	C₂×C₇×#102	C₂²	1	2	yes	—
26	C₂×C₇×#102	C₂²	1	1	yes	characteristic
27	C₂×C₄×C₇×C₈	C₂²	1	2	yes	—
28	C₂×C₄×C₇×C₈	C₂²	1	1	yes	characteristic
29	C₇×#389	—	2	2	no	—
30	C₇×#389	C₂²	1	2	yes	—
31	C₇×#389	C₂²	1	2	yes	—
32	C₇×#385	—	2	2	no	—
33	C₇×#382	—	2	1	no	—
34	C₇×#382	C₂²	1	1	yes	characteristic
35	C₇×#382	C₂²	1	1	yes	characteristic
36	C₇×#380	—	2	1	no	—
37	C₄×C₇×C₄⋊C₄	—	2	1	no	—
38	C₄×C₇×C₄⋊C₄	C₂²	1	1	yes	characteristic
39	C₂×C₇×#95	—	2	1	no	—
40	C₇×#340	C₂²	1	2	yes	—
41	C₇×#340	C₂²	1	2	yes	—
42	C₇×#336	C₂²	1	2	yes	—
43	#22683	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
44	C₂²×C₇×Q₈	C₂³	1	1	yes	characteristic
45	C₂²×C₇×D₄	C₂³	1	1	yes	characteristic
46	C₂³×C₄×C₇	—	2	1	no	—
47	C₂³×C₄×C₇	—	2	2	no	—
48	C₂×C₇×SD₁₆	C₂×C₄	1	4	yes	—
49	C₂×C₇×SD₁₆	D₄	1	4	yes	—
50	C₂×C₇×SD₁₆	Q₈	1	4	yes	—
51	C₂²×C₇×C₈	C₂³	1	2	yes	—
52	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
53	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
54	C₄×C₇×Q₈	—	2	2	no	—
55	C₄×C₇×Q₈	—	2	4	no	—
56	C₄×C₇×Q₈	—	4	2	no	—
57	C₄×C₇×Q₈	C₂×C₄	1	4	yes	complemented
58	C₄×C₇×D₄	—	2	4	no	—
59	C₄×C₇×D₄	—	2	2	no	—
60	C₄×C₇×D₄	—	4	2	no	—
61	C₄×C₇×D₄	C₂×C₄	1	4	yes	—
62	C₂×C₇×C₄⋊C₄	—	2	1	no	—
63	C₂×C₇×C₄⋊C₄	—	2	2	no	—
64	C₂×C₇×C₄⋊C₄	—	2	2	no	—
65	C₂×C₇×C₄⋊C₄	—	2	2	no	—
66	C₂×C₇×C₄⋊C₄	D₄	1	2	yes	—
67	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
68	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
69	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
70	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
71	C₂×C₇×C₂²⋊C₄	—	2	1	no	—
72	C₂×C₇×C₂²⋊C₄	—	2	2	no	—
73	C₂×C₄²×C₇	—	2	1	no	—
74	C₂×C₄²×C₇	—	2	2	no	—
75	C₂×C₄²×C₇	C₂³	1	2	yes	—
76	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
77	C₇×#107	—	4	2	no	—
78	C₇×#106	—	2	4	no	—
79	C₇×#106	C₂×C₄	1	4	yes	complemented
80	C₇×C₄⋊C₈	—	2	2	no	—
81	C₇×#103	—	2	4	no	—
82	C₇×#103	C₂×C₄	1	4	yes	complemented
83	C₇×#102	—	2	4	no	—
84	C₇×#102	C₂×C₄	1	4	yes	—
85	C₄×C₇×C₈	—	2	4	no	—
86	C₄×C₇×C₈	C₂×C₄	1	4	yes	complemented
87	C₇×#95	—	2	1	no	—
88	C₇×#95	—	2	2	no	—
89	C₇×#95	—	2	1	no	—
90	C₇×#95	—	2	2	no	—
91	C₇×#95	—	2	1	no	—
92	C₇×#95	—	2	1	no	—
93	C₇×#95	D₄	1	1	yes	characteristic
94	C₇×#95	D₄	1	1	yes	characteristic
95	C₂×C₄×SD₁₆	C₂×C₇	1	2	yes	—
96	C₂×C₄×SD₁₆	C₂×C₇	1	1	yes	characteristic
97	#2351	C₂×C₇	1	1	yes	characteristic, complemented
98	#2349	C₂×C₇	1	1	yes	characteristic
99	#1941	C₂×C₇	1	2	yes	complemented
100	#1863	C₂×C₇	1	2	yes	complemented
101	#1862	C₂×C₇	1	2	yes	—
102	#1846	C₂×C₇	1	1	yes	characteristic, complemented
103	#1805	C₂×C₇	1	1	yes	characteristic, complemented
104	#1804	C₂×C₇	1	1	yes	characteristic
105	C₈×C₄⋊C₄	C₂×C₇	1	1	yes	characteristic, complemented
106	C₂⁴×C₇	—	2	1	no	—
107	C₂×C₇×Q₈	—	2	1	no	—
108	C₂×C₇×Q₈	—	2	1	no	—
109	C₂×C₇×Q₈	—	2	1	no	—
110	C₂×C₇×Q₈	C₂²×C₄	1	2	yes	—
111	C₂×C₇×Q₈	C₂×D₄	1	2	yes	—
112	C₂×C₇×Q₈	C₂×Q₈	1	2	yes	—
113	C₂×C₇×D₄	—	2	1	no	—
114	C₂×C₇×D₄	—	2	1	no	—
115	C₂×C₇×D₄	—	2	1	no	—
116	C₂×C₇×D₄	C₂²×C₄	1	2	yes	—
117	C₂×C₇×D₄	C₂×D₄	1	2	yes	—
118	C₂×C₇×D₄	C₂×Q₈	1	2	yes	—
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	4	no	—
123	C₂²×C₄×C₇	—	2	2	no	—
124	C₂²×C₄×C₇	—	2	2	no	—
125	C₂²×C₄×C₇	—	4	4	no	—
126	C₂²×C₄×C₇	—	4	4	no	—
127	C₂²×C₄×C₇	—	8	2	no	—
128	C₂²×C₄×C₇	—	8	2	no	—
129	C₂²×C₄×C₇	C₂×D₄	1	2	yes	—
130	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
131	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
132	C₂²×C₄×C₇	C₂×D₄	1	2	yes	—
133	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
134	C₇×SD₁₆	C₄⋊C₄	1	16	yes	complemented
135	C₂×C₇×C₈	—	2	1	no	—
136	C₂×C₇×C₈	—	2	1	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	C₂²×C₄	1	2	yes	—
141	C₂×C₇×C₈	C₂²×C₄	1	2	yes	—
142	C₂×C₇×C₈	C₂×D₄	1	2	yes	—
143	C₂×C₇×C₈	C₂×Q₈	1	2	yes	—
144	C₇×C₄⋊C₄	—	2	4	no	—
145	C₇×C₄⋊C₄	—	2	4	no	—
146	C₇×C₄⋊C₄	—	2	1	no	—
147	C₇×C₄⋊C₄	—	2	1	no	—
148	C₇×C₄⋊C₄	—	2	2	no	—
149	C₇×C₄⋊C₄	—	2	2	no	—
150	C₇×C₄⋊C₄	—	2	2	no	—
151	C₇×C₄⋊C₄	—	2	2	no	—
152	C₇×C₄⋊C₄	—	4	4	no	—
153	C₇×C₄⋊C₄	—	4	4	no	—
154	C₇×C₄⋊C₄	—	8	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	—	4	4	no	—
159	C₄²×C₇	—	2	4	no	—
160	C₄²×C₇	—	2	2	no	—
161	C₄²×C₇	—	2	2	no	—
162	C₄²×C₇	—	4	4	no	—
163	C₄²×C₇	C₂²×C₄	1	2	yes	—
164	C₄²×C₇	#41	1	2	yes	—
165	C₂²×SD₁₆	C₂²×C₇	1	1	yes	characteristic
166	C₂×C₄×Q₈	C₂²×C₇	1	2	yes	—
167	C₂×C₄×Q₈	C₂²×C₇	1	1	yes	characteristic
168	C₂×C₄×D₄	C₂²×C₇	1	2	yes	—
169	C₂×C₄×D₄	C₂²×C₇	1	1	yes	characteristic
170	C₄×SD₁₆	—	2	8	no	—
171	C₄×SD₁₆	C₄×C₇	1	8	yes	complemented
172	C₂×#107	C₂²×C₇	1	2	yes	—
173	C₂×#106	C₂²×C₇	1	2	yes	—
174	C₂×#106	C₂²×C₇	1	1	yes	characteristic
175	C₂×C₄⋊C₈	C₂²×C₇	1	1	yes	characteristic
176	C₂×#103	C₂²×C₇	1	2	yes	—
177	C₂×#103	C₂²×C₇	1	1	yes	characteristic
178	C₂×#102	C₂²×C₇	1	2	yes	—
179	C₂×#102	C₂²×C₇	1	1	yes	characteristic
180	C₂×C₄×C₈	C₂²×C₇	1	2	yes	—
181	C₂×C₄×C₈	C₂²×C₇	1	1	yes	characteristic
182	#389	—	2	2	no	—
183	#389	C₂²×C₇	1	2	yes	—
184	#389	C₂²×C₇	1	2	yes	—
185	#385	—	2	2	no	—
186	#382	—	2	1	no	—
187	#382	C₂²×C₇	1	1	yes	characteristic
188	#382	C₂²×C₇	1	1	yes	characteristic
189	#380	—	2	1	no	—
190	C₄×C₄⋊C₄	—	2	1	no	—
191	C₄×C₄⋊C₄	C₂²×C₇	1	1	yes	characteristic
192	C₂×#95	—	2	1	no	—
193	#340	C₂²×C₇	1	2	yes	—
194	#340	C₂²×C₇	1	2	yes	—
195	#336	C₂²×C₇	1	2	yes	—
196	C₂³×C₇	—	2	2	no	—
197	C₂³×C₇	—	2	2	no	—
198	C₂³×C₇	—	2	2	no	—
199	C₂³×C₇	—	4	2	no	—
200	C₂³×C₇	—	4	2	no	—
201	C₂³×C₇	C₂²×D₄	1	1	yes	characteristic
202	C₇×Q₈	—	2	2	no	—
203	C₇×Q₈	—	2	2	no	—
204	C₇×Q₈	—	2	2	no	—
205	C₇×Q₈	C₂×C₄⋊C₄	1	4	yes	—
206	C₇×D₄	—	2	2	no	—
207	C₇×D₄	—	2	2	no	—
208	C₇×D₄	—	2	2	no	—
209	C₇×D₄	C₂×C₄⋊C₄	1	4	yes	—
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	—	2	2	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	—	2	2	no	—
220	C₂×C₄×C₇	—	2	2	no	—
221	C₂×C₄×C₇	—	2	2	no	—
222	C₂×C₄×C₇	—	4	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	—	4	2	no	—
228	C₂×C₄×C₇	—	4	2	no	—
229	C₂×C₄×C₇	—	4	2	no	—
230	C₂×C₄×C₇	—	8	4	no	—
231	C₂×C₄×C₇	—	8	8	no	—
232	C₂×C₄×C₇	C₄×D₄	1	2	yes	—
233	C₂×C₄×C₇	C₄×D₄	1	2	yes	—
234	C₂×C₄×C₇	#135	1	4	yes	—
235	C₂×C₄×C₇	C₂³×C₄	1	1	yes	characteristic
236	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
237	C₂×C₄×C₇	C₂²×Q₈	1	1	yes	characteristic
238	C₂×C₄×C₇	C₂×#41	1	1	yes	characteristic
239	C₂×C₄×C₇	H(5,𝔽₂)	1	1	yes	characteristic
240	C₂×C₄×C₇	2₋¹⁺⁴	1	1	yes	characteristic
241	C₇×C₈	—	2	2	no	—
242	C₇×C₈	—	4	2	no	—
243	C₇×C₈	C₂×C₄⋊C₄	1	4	yes	—
244	C₂²×Q₈	C₂³×C₇	1	1	yes	characteristic
245	C₂²×D₄	C₂³×C₇	1	1	yes	characteristic
246	C₂³×C₄	—	2	1	no	—
247	C₂³×C₄	—	2	2	no	—
248	C₂×SD₁₆	C₂×C₄×C₇	1	4	yes	—
249	C₂×SD₁₆	C₇×D₄	1	4	yes	—
250	C₂×SD₁₆	C₇×Q₈	1	4	yes	—
251	C₂²×C₈	C₂³×C₇	1	2	yes	—
252	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
253	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
254	C₄×Q₈	—	2	2	no	—
255	C₄×Q₈	—	2	4	no	—
256	C₄×Q₈	—	4	2	no	—
257	C₄×Q₈	C₂×C₄×C₇	1	4	yes	complemented
258	C₄×D₄	—	2	4	no	—
259	C₄×D₄	—	2	2	no	—
260	C₄×D₄	—	4	2	no	—
261	C₄×D₄	C₂×C₄×C₇	1	4	yes	—
262	C₂×C₄⋊C₄	—	2	1	no	—
263	C₂×C₄⋊C₄	—	2	2	no	—
264	C₂×C₄⋊C₄	—	2	2	no	—
265	C₂×C₄⋊C₄	—	2	2	no	—
266	C₂×C₄⋊C₄	C₇×D₄	1	2	yes	—
267	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
268	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
269	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
270	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
271	C₂×C₂²⋊C₄	—	2	1	no	—
272	C₂×C₂²⋊C₄	—	2	2	no	—
273	C₂×C₄²	—	2	1	no	—
274	C₂×C₄²	—	2	2	no	—
275	C₂×C₄²	C₂³×C₇	1	2	yes	—
276	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
277	#107	—	4	2	no	—
278	#106	—	2	4	no	—
279	#106	C₂×C₄×C₇	1	4	yes	complemented
280	C₄⋊C₈	—	2	2	no	—
281	#103	—	2	4	no	—
282	#103	C₂×C₄×C₇	1	4	yes	complemented
283	#102	—	2	4	no	—
284	#102	C₂×C₄×C₇	1	4	yes	—
285	C₄×C₈	—	2	4	no	—
286	C₄×C₈	C₂×C₄×C₇	1	4	yes	complemented
287	#95	—	2	1	no	—
288	#95	—	2	2	no	—
289	#95	—	2	1	no	—
290	#95	—	2	2	no	—
291	#95	—	2	1	no	—
292	#95	—	2	1	no	—
293	#95	C₇×D₄	1	1	yes	characteristic
294	#95	C₇×D₄	1	1	yes	characteristic
295	C₂²×C₇	—	2	4	no	—
296	C₂²×C₇	—	4	4	no	—
297	C₂²×C₇	—	4	2	no	—
298	C₂²×C₇	—	4	2	no	—
299	C₂²×C₇	—	4	4	no	—
300	C₂²×C₇	C₂×C₄×D₄	1	1	yes	characteristic
301	C₂²×C₇	D₄²	1	1	yes	characteristic
302	C₂²×C₇	D₄×Q₈	1	1	yes	characteristic
303	C₂²×C₇	C₂×#135	1	2	yes	—
304	C₂²×C₇	#577	1	2	yes	—
305	C₄×C₇	—	2	4	no	—
306	C₄×C₇	—	2	2	no	—
307	C₄×C₇	—	2	2	no	—
308	C₄×C₇	—	2	4	no	—
309	C₄×C₇	—	4	2	no	—
310	C₄×C₇	—	4	2	no	—
311	C₄×C₇	—	4	2	no	—
312	C₄×C₇	—	8	2	no	—
313	C₄×C₇	—	8	2	no	—
314	C₄×C₇	C₂²×C₄⋊C₄	1	1	yes	characteristic
315	C₄×C₇	#520	1	1	yes	characteristic
316	C₄×C₇	#547	1	1	yes	characteristic
317	C₄×C₇	#554	1	1	yes	characteristic
318	C₂⁴	—	2	1	no	—
319	C₂×Q₈	—	2	1	no	—
320	C₂×Q₈	—	2	1	no	—
321	C₂×Q₈	—	2	1	no	—
322	C₂×Q₈	C₂²×C₄×C₇	1	2	yes	—
323	C₂×Q₈	C₂×C₇×D₄	1	2	yes	—
324	C₂×Q₈	C₂×C₇×Q₈	1	2	yes	—
325	C₂×D₄	—	2	1	no	—
326	C₂×D₄	—	2	1	no	—
327	C₂×D₄	—	2	1	no	—
328	C₂×D₄	C₂²×C₄×C₇	1	2	yes	—
329	C₂×D₄	C₂×C₇×D₄	1	2	yes	—
330	C₂×D₄	C₂×C₇×Q₈	1	2	yes	—
331	C₂²×C₄	—	2	1	no	—
332	C₂²×C₄	—	2	1	no	—
333	C₂²×C₄	—	2	1	no	—
334	C₂²×C₄	—	2	4	no	—
335	C₂²×C₄	—	2	2	no	—
336	C₂²×C₄	—	2	2	no	—
337	C₂²×C₄	—	4	4	no	—
338	C₂²×C₄	—	4	4	no	—
339	C₂²×C₄	—	8	2	no	—
340	C₂²×C₄	—	8	2	no	—
341	C₂²×C₄	C₂×C₇×D₄	1	2	yes	—
342	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
343	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
344	C₂²×C₄	C₂×C₇×D₄	1	2	yes	—
345	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
346	SD₁₆	C₇×C₄⋊C₄	1	16	yes	complemented
347	C₂×C₈	—	2	1	no	—
348	C₂×C₈	—	2	1	no	—
349	C₂×C₈	—	2	2	no	—
350	C₂×C₈	—	2	2	no	—
351	C₂×C₈	—	2	2	no	—
352	C₂×C₈	C₂²×C₄×C₇	1	2	yes	—
353	C₂×C₈	C₂²×C₄×C₇	1	2	yes	—
354	C₂×C₈	C₂×C₇×D₄	1	2	yes	—
355	C₂×C₈	C₂×C₇×Q₈	1	2	yes	—
356	C₄⋊C₄	—	2	4	no	—
357	C₄⋊C₄	—	2	4	no	—
358	C₄⋊C₄	—	2	1	no	—
359	C₄⋊C₄	—	2	1	no	—
360	C₄⋊C₄	—	2	2	no	—
361	C₄⋊C₄	—	2	2	no	—
362	C₄⋊C₄	—	2	2	no	—
363	C₄⋊C₄	—	2	2	no	—
364	C₄⋊C₄	—	4	4	no	—
365	C₄⋊C₄	—	4	4	no	—
366	C₄⋊C₄	—	8	2	no	—
367	C₄⋊C₄	C₂²×C₄×C₇	1	2	yes	—
368	C₄⋊C₄	C₂²×C₄×C₇	1	2	yes	—
369	C₂²⋊C₄	—	2	4	no	—
370	C₂²⋊C₄	—	4	4	no	—
371	C₄²	—	2	4	no	—
372	C₄²	—	2	2	no	—
373	C₄²	—	2	2	no	—
374	C₄²	—	4	4	no	—
375	C₄²	C₂²×C₄×C₇	1	2	yes	—
376	C₄²	C₇×#41	1	2	yes	—
377	C₂×C₇	—	4	4	no	—
378	C₂×C₇	D₄×C₄⋊C₄	1	1	yes	characteristic
379	C₂×C₇	C₄×#135	1	1	yes	characteristic
380	C₂×C₇	#2949	1	1	yes	characteristic
381	C₂×C₇	#3282	1	2	yes	—
382	C₂×C₇	#3381	1	2	yes	—
383	C₂³	—	2	2	no	—
384	C₂³	—	2	2	no	—
385	C₂³	—	2	2	no	—
386	C₂³	—	4	2	no	—
387	C₂³	—	4	2	no	—
388	C₂³	C₂²×C₇×D₄	1	1	yes	characteristic
389	Q₈	—	2	2	no	—
390	Q₈	—	2	2	no	—
391	Q₈	—	2	2	no	—
392	Q₈	C₂×C₇×C₄⋊C₄	1	4	yes	—
393	D₄	—	2	2	no	—
394	D₄	—	2	2	no	—
395	D₄	—	2	2	no	—
396	D₄	C₂×C₇×C₄⋊C₄	1	4	yes	—
397	C₂×C₄	—	2	2	no	—
398	C₂×C₄	—	2	2	no	—
399	C₂×C₄	—	2	2	no	—
400	C₂×C₄	—	2	2	no	—
401	C₂×C₄	—	2	2	no	—
402	C₂×C₄	—	2	2	no	—
403	C₂×C₄	—	2	2	no	—
404	C₂×C₄	—	2	2	no	—
405	C₂×C₄	—	2	2	no	—
406	C₂×C₄	—	2	2	no	—
407	C₂×C₄	—	2	2	no	—
408	C₂×C₄	—	2	2	no	—
409	C₂×C₄	—	4	2	no	—
410	C₂×C₄	—	4	2	no	—
411	C₂×C₄	—	4	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	—	4	2	no	—
417	C₂×C₄	—	8	4	no	—
418	C₂×C₄	—	8	8	no	—
419	C₂×C₄	C₄×C₇×D₄	1	2	yes	—
420	C₂×C₄	C₄×C₇×D₄	1	2	yes	—
421	C₂×C₄	C₇×#135	1	4	yes	—
422	C₂×C₄	C₂³×C₄×C₇	1	1	yes	characteristic
423	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
424	C₂×C₄	C₂²×C₇×Q₈	1	1	yes	characteristic
425	C₂×C₄	C₂×C₇×#41	1	1	yes	characteristic
426	C₂×C₄	C₇×H(5,𝔽₂)	1	1	yes	characteristic
427	C₂×C₄	C₇×2₋¹⁺⁴	1	1	yes	characteristic
428	C₈	—	2	2	no	—
429	C₈	—	4	2	no	—
430	C₈	C₂×C₇×C₄⋊C₄	1	4	yes	—
431	C₇	#22683	1	1	yes	characteristic, direct product factor, Sylow
432	C₂²	—	2	4	no	—
433	C₂²	—	4	2	no	—
434	C₂²	—	4	2	no	—
435	C₂²	—	4	4	no	—
436	C₂²	—	4	4	no	—
437	C₂²	C₂×C₄×C₇×D₄	1	1	yes	characteristic
438	C₂²	C₇×D₄²	1	1	yes	characteristic
439	C₂²	C₇×D₄×Q₈	1	1	yes	characteristic
440	C₂²	C₂×C₇×#135	1	2	yes	—
441	C₂²	C₇×#577	1	2	yes	—
442	C₄	—	2	2	no	—
443	C₄	—	2	2	no	—
444	C₄	—	2	4	no	—
445	C₄	—	2	4	no	—
446	C₄	—	4	2	no	—
447	C₄	—	4	2	no	—
448	C₄	—	4	2	no	—
449	C₄	—	8	2	no	—
450	C₄	—	8	2	no	—
451	C₄	C₂²×C₇×C₄⋊C₄	1	1	yes	characteristic
452	C₄	C₇×#520	1	1	yes	characteristic
453	C₄	C₇×#547	1	1	yes	characteristic
454	C₄	C₇×#554	1	1	yes	characteristic
455	C₂	—	4	4	no	—
456	C₂	C₇×D₄×C₄⋊C₄	1	1	yes	characteristic
457	C₂	C₄×C₇×#135	1	1	yes	characteristic
458	C₂	C₇×#2949	1	1	yes	characteristic
459	C₂	C₇×#3282	1	2	yes	—
460	C₂	C₇×#3381	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×#1941	C₂	semidirect
6. C₇×#1863	C₂	semidirect
8. C₇×#1846	C₂	semidirect
9. C₇×#1805	C₂	semidirect
11. C₇×C₈×C₄⋊C₄	C₂	semidirect
18. C₄×C₇×SD₁₆	C₄	semidirect
43. #22683	C₇	direct (N × H)
57. C₄×C₇×Q₈	C₂×C₄	semidirect
79. C₇×#106	C₂×C₄	semidirect
82. C₇×#103	C₂×C₄	semidirect
86. C₄×C₇×C₈	C₂×C₄	semidirect
97. #2351	C₂×C₇	semidirect
99. #1941	C₂×C₇	semidirect
100. #1863	C₂×C₇	semidirect
102. #1846	C₂×C₇	semidirect
103. #1805	C₂×C₇	semidirect
105. C₈×C₄⋊C₄	C₂×C₇	semidirect
134. C₇×SD₁₆	C₄⋊C₄	semidirect
171. C₄×SD₁₆	C₄×C₇	semidirect
257. C₄×Q₈	C₂×C₄×C₇	semidirect
279. #106	C₂×C₄×C₇	semidirect
282. #103	C₂×C₄×C₇	semidirect
286. C₄×C₈	C₂×C₄×C₇	semidirect
346. SD₁₆	C₇×C₄⋊C₄	semidirect
431. C₇	#22683	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×#2351	2
C₇×#2349	2
C₇×#1941	2
C₇×#1863	2
C₇×#1862	2
C₇×#1846	2
C₇×#1805	2
C₇×#1804	2
C₇×C₈×C₄⋊C₄	2
#22683	7

Subgroups — C7×#22683 #13199899

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×#22683 #13199899