Subgroups — C₇×#22668 #13199884

Order 1792.

868 conjugacy classes of subgroups.

The subgroup lattice has 494 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×D₄×M₁₆	C₂	1	2	yes	maximal
2	C₂×C₇×#435	C₂	1	1	yes	maximal, characteristic
3	C₂×C₇×#430	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂²×C₇×#108	C₂	1	1	yes	maximal, characteristic, complemented
5	C₇×#1950	C₂	1	2	yes	maximal, complemented
6	C₇×#1855	C₂	1	2	yes	maximal, complemented
7	C₇×#1855	C₂	1	2	yes	maximal, complemented
8	C₇×#1849	C₂	1	1	yes	maximal, characteristic, complemented
9	C₇×#1811	C₂	1	1	yes	maximal, characteristic, complemented
10	C₇×#1810	C₂	1	1	yes	maximal, characteristic, complemented
11	C₇×#1778	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×C₇×M₁₆	C₂²	1	2	yes	—
13	C₂²×C₇×M₁₆	C₂²	1	2	yes	—
14	C₂²×C₇×M₁₆	C₂²	1	1	yes	characteristic
15	C₂³×C₇×C₈	C₂²	1	1	yes	characteristic
16	C₂×C₄×C₇×D₄	C₂²	1	1	yes	characteristic
17	C₇×#436	—	2	2	no	—
18	C₇×#435	—	2	2	no	—
19	C₇×#435	—	2	2	no	—
20	C₇×#435	C₄	1	4	yes	—
21	C₇×#435	C₄	1	4	yes	—
22	C₇×C₈×D₄	—	2	2	no	—
23	C₇×#430	—	2	4	no	—
24	C₂×C₇×#108	—	2	4	no	—
25	C₂×C₇×#108	C₂²	1	1	yes	characteristic
26	C₂×C₇×#108	C₂²	1	2	yes	—
27	C₂×C₇×#108	C₂²	1	1	yes	characteristic
28	C₂×C₇×#108	C₂²	1	2	yes	—
29	C₂×C₇×#108	C₂²	1	1	yes	characteristic
30	C₂×C₇×#108	C₂²	1	2	yes	—
31	C₂×C₇×#108	C₂²	1	1	yes	characteristic
32	C₇×#423	C₂²	1	2	yes	—
33	C₂×C₇×C₄⋊C₈	C₂²	1	1	yes	characteristic
34	C₇×#407	C₂²	1	2	yes	—
35	C₇×#407	C₂²	1	2	yes	—
36	C₂×C₇×C₂²⋊C₈	C₂²	1	1	yes	characteristic
37	C₂×C₇×C₂²⋊C₈	C₂²	1	1	yes	characteristic
38	C₄×C₇×M₁₆	C₂²	1	2	yes	—
39	C₂×C₇×#97	C₂²	1	1	yes	characteristic
40	C₇×#341	C₂²	1	2	yes	—
41	C₇×#341	C₂²	1	2	yes	—
42	C₇×#341	C₂²	1	2	yes	—
43	#22668	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
44	C₂²×C₇×D₄	Q₈	1	1	yes	characteristic
45	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
46	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
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	2	no	—
51	C₂×C₇×M₁₆	—	2	4	no	—
52	C₂×C₇×M₁₆	—	2	4	no	—
53	C₂×C₇×M₁₆	—	4	2	no	—
54	C₂×C₇×M₁₆	—	4	2	no	—
55	C₂×C₇×M₁₆	C₂×C₄	1	4	yes	—
56	C₂×C₇×M₁₆	C₂³	1	2	yes	—
57	C₂×C₇×M₁₆	C₂³	1	2	yes	—
58	C₂×C₇×M₁₆	C₂³	1	2	yes	—
59	C₂×C₇×M₁₆	C₂³	1	2	yes	—
60	C₂²×C₇×C₈	—	2	2	no	—
61	C₂²×C₇×C₈	—	2	2	no	—
62	C₂²×C₇×C₈	—	2	2	no	—
63	C₂²×C₇×C₈	—	2	2	no	—
64	C₂²×C₇×C₈	C₂×C₄	1	2	yes	—
65	C₂²×C₇×C₈	C₂×C₄	1	2	yes	—
66	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
67	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
68	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
69	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
70	C₄×C₇×D₄	C₂×C₄	1	2	yes	—
71	C₄×C₇×D₄	C₂×C₄	1	2	yes	—
72	C₄×C₇×D₄	D₄	1	2	yes	—
73	C₄×C₇×D₄	D₄	1	2	yes	—
74	C₂×C₇×C₄⋊C₄	Q₈	1	1	yes	characteristic
75	C₂×C₇×C₂²⋊C₄	Q₈	1	1	yes	characteristic
76	C₂×C₇×C₂²⋊C₄	Q₈	1	1	yes	characteristic
77	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
78	C₇×#108	—	2	4	no	—
79	C₇×#108	—	2	4	no	—
80	C₇×#108	—	2	2	no	—
81	C₇×#108	—	2	2	no	—
82	C₇×#108	—	2	2	no	—
83	C₇×#108	—	4	2	no	—
84	C₇×#108	D₄	1	4	yes	complemented
85	C₇×C₄⋊C₈	—	2	2	no	—
86	C₇×C₄⋊C₈	—	2	2	no	—
87	C₇×C₄⋊C₈	C₂×C₄	1	4	yes	—
88	C₇×C₂²⋊C₈	—	2	2	no	—
89	C₇×C₂²⋊C₈	—	2	2	no	—
90	C₇×C₂²⋊C₈	—	2	2	no	—
91	C₇×C₂²⋊C₈	—	2	2	no	—
92	C₇×C₂²⋊C₈	C₂×C₄	1	4	yes	—
93	C₇×C₂²⋊C₈	C₂×C₄	1	2	yes	—
94	C₇×C₂²⋊C₈	C₂×C₄	1	2	yes	—
95	C₇×#97	—	2	2	no	—
96	C₇×#97	C₂×C₄	1	4	yes	—
97	C₄×C₇×C₈	—	2	2	no	—
98	D₄×M₁₆	C₂×C₇	1	2	yes	—
99	C₂×#435	C₂×C₇	1	1	yes	characteristic
100	C₂×#430	C₂×C₇	1	1	yes	characteristic, complemented
101	C₂²×#108	C₂×C₇	1	1	yes	characteristic, complemented
102	#1950	C₂×C₇	1	2	yes	complemented
103	#1855	C₂×C₇	1	2	yes	complemented
104	#1855	C₂×C₇	1	2	yes	complemented
105	#1849	C₂×C₇	1	1	yes	characteristic, complemented
106	#1811	C₂×C₇	1	1	yes	characteristic, complemented
107	#1810	C₂×C₇	1	1	yes	characteristic, complemented
108	#1778	C₂×C₇	1	1	yes	characteristic, complemented
109	C₂⁴×C₇	C₂×Q₈	1	1	yes	characteristic
110	C₂⁴×C₇	C₂×Q₈	1	1	yes	characteristic
111	C₂×C₇×D₄	—	4	2	no	—
112	C₂×C₇×D₄	C₄⋊C₄	1	2	yes	—
113	C₂×C₇×D₄	C₄⋊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	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	C₂²×C₄	1	1	yes	characteristic
123	C₂²×C₄×C₇	C₂²×C₄	1	1	yes	characteristic
124	C₂²×C₄×C₇	C₂²×C₄	1	2	yes	—
125	C₂²×C₄×C₇	C₂×D₄	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×Q₈	1	1	yes	characteristic
129	C₂²×C₄×C₇	C₂×Q₈	1	1	yes	characteristic
130	C₂²×C₄×C₇	C₂×Q₈	1	1	yes	characteristic
131	C₂²×C₄×C₇	C₂×Q₈	1	1	yes	characteristic
132	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
133	C₇×M₁₆	—	2	2	no	—
134	C₇×M₁₆	—	2	8	no	—
135	C₇×M₁₆	—	2	2	no	—
136	C₇×M₁₆	—	2	2	no	—
137	C₇×M₁₆	—	2	2	no	—
138	C₇×M₁₆	—	2	2	no	—
139	C₇×M₁₆	—	2	2	no	—
140	C₇×M₁₆	—	2	2	no	—
141	C₇×M₁₆	—	4	4	no	—
142	C₇×M₁₆	—	4	4	no	—
143	C₇×M₁₆	C₂×D₄	1	4	yes	—
144	C₂×C₇×C₈	—	2	1	no	—
145	C₂×C₇×C₈	—	2	1	no	—
146	C₂×C₇×C₈	—	2	2	no	—
147	C₂×C₇×C₈	—	2	1	no	—
148	C₂×C₇×C₈	—	2	1	no	—
149	C₂×C₇×C₈	—	2	1	no	—
150	C₂×C₇×C₈	—	2	1	no	—
151	C₂×C₇×C₈	—	2	4	no	—
152	C₂×C₇×C₈	—	2	4	no	—
153	C₂×C₇×C₈	—	2	2	no	—
154	C₂×C₇×C₈	—	2	2	no	—
155	C₂×C₇×C₈	—	2	2	no	—
156	C₂×C₇×C₈	—	4	4	no	—
157	C₂×C₇×C₈	—	4	4	no	—
158	C₂×C₇×C₈	C₂²×C₄	1	2	yes	—
159	C₂×C₇×C₈	C₂²×C₄	1	2	yes	—
160	C₂×C₇×C₈	C₂²×C₄	1	2	yes	—
161	C₂×C₇×C₈	C₂²×C₄	1	2	yes	—
162	C₂×C₇×C₈	C₂×D₄	1	2	yes	—
163	C₂×C₇×C₈	#41	1	2	yes	—
164	C₇×C₄⋊C₄	C₄⋊C₄	1	2	yes	—
165	C₇×C₄⋊C₄	C₄⋊C₄	1	2	yes	—
166	C₇×C₂²⋊C₄	C₄⋊C₄	1	2	yes	—
167	C₇×C₂²⋊C₄	C₄⋊C₄	1	2	yes	—
168	C₇×C₂²⋊C₄	C₄⋊C₄	1	2	yes	—
169	C₇×C₂²⋊C₄	C₄⋊C₄	1	2	yes	—
170	C₄²×C₇	C₂²×C₄	1	2	yes	—
171	C₄²×C₇	C₂×D₄	1	2	yes	—
172	C₂²×M₁₆	C₂²×C₇	1	2	yes	—
173	C₂²×M₁₆	C₂²×C₇	1	2	yes	—
174	C₂²×M₁₆	C₂²×C₇	1	1	yes	characteristic
175	C₂³×C₈	C₂²×C₇	1	1	yes	characteristic
176	C₂×C₄×D₄	C₂²×C₇	1	1	yes	characteristic
177	#436	—	2	2	no	—
178	#435	—	2	2	no	—
179	#435	—	2	2	no	—
180	#435	C₄×C₇	1	4	yes	—
181	#435	C₄×C₇	1	4	yes	—
182	C₈×D₄	—	2	2	no	—
183	#430	—	2	4	no	—
184	C₂×#108	—	2	4	no	—
185	C₂×#108	C₂²×C₇	1	1	yes	characteristic
186	C₂×#108	C₂²×C₇	1	1	yes	characteristic
187	C₂×#108	C₂²×C₇	1	1	yes	characteristic
188	C₂×#108	C₂²×C₇	1	2	yes	—
189	C₂×#108	C₂²×C₇	1	2	yes	—
190	C₂×#108	C₂²×C₇	1	2	yes	—
191	C₂×#108	C₂²×C₇	1	1	yes	characteristic
192	#423	C₂²×C₇	1	2	yes	—
193	C₂×C₄⋊C₈	C₂²×C₇	1	1	yes	characteristic
194	#407	C₂²×C₇	1	2	yes	—
195	#407	C₂²×C₇	1	2	yes	—
196	C₂×C₂²⋊C₈	C₂²×C₇	1	1	yes	characteristic
197	C₂×C₂²⋊C₈	C₂²×C₇	1	1	yes	characteristic
198	C₄×M₁₆	C₂²×C₇	1	2	yes	—
199	C₂×#97	C₂²×C₇	1	1	yes	characteristic
200	#341	C₂²×C₇	1	2	yes	—
201	#341	C₂²×C₇	1	2	yes	—
202	#341	C₂²×C₇	1	2	yes	—
203	C₂³×C₇	—	2	1	no	—
204	C₂³×C₇	—	2	1	no	—
205	C₂³×C₇	—	2	2	no	—
206	C₂³×C₇	—	2	1	no	—
207	C₂³×C₇	—	2	1	no	—
208	C₂³×C₇	—	4	1	no	—
209	C₂³×C₇	—	4	1	no	—
210	C₂³×C₇	—	4	1	no	—
211	C₂³×C₇	C₂×C₄⋊C₄	1	2	yes	—
212	C₂³×C₇	C₂×C₄⋊C₄	1	1	yes	characteristic
213	C₂³×C₇	C₂×C₄⋊C₄	1	1	yes	characteristic
214	C₂³×C₇	C₂²×Q₈	1	1	yes	characteristic
215	C₇×D₄	—	2	4	no	—
216	C₇×D₄	—	4	2	no	—
217	C₂×C₄×C₇	—	2	1	no	—
218	C₂×C₄×C₇	—	2	1	no	—
219	C₂×C₄×C₇	—	2	1	no	—
220	C₂×C₄×C₇	—	2	1	no	—
221	C₂×C₄×C₇	—	2	1	no	—
222	C₂×C₄×C₇	—	2	1	no	—
223	C₂×C₄×C₇	—	2	2	no	—
224	C₂×C₄×C₇	—	2	1	no	—
225	C₂×C₄×C₇	—	2	1	no	—
226	C₂×C₄×C₇	—	2	2	no	—
227	C₂×C₄×C₇	—	2	1	no	—
228	C₂×C₄×C₇	—	2	2	no	—
229	C₂×C₄×C₇	—	2	1	no	—
230	C₂×C₄×C₇	—	2	1	no	—
231	C₂×C₄×C₇	—	2	1	no	—
232	C₂×C₄×C₇	—	2	2	no	—
233	C₂×C₄×C₇	—	4	1	no	—
234	C₂×C₄×C₇	—	4	1	no	—
235	C₂×C₄×C₇	C₂×C₄⋊C₄	1	2	yes	—
236	C₂×C₄×C₇	C₂×C₄⋊C₄	1	2	yes	—
237	C₂×C₄×C₇	C₂×C₄⋊C₄	1	1	yes	characteristic
238	C₂×C₄×C₇	C₂×C₄⋊C₄	1	1	yes	characteristic
239	C₂×C₄×C₇	C₂×C₄⋊C₄	1	2	yes	—
240	C₂×C₄×C₇	C₂³×C₄	1	1	yes	characteristic
241	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
242	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
243	C₂×C₄×C₇	C₂×#41	1	1	yes	characteristic
244	C₂×C₄×C₇	H(5,𝔽₂)	1	1	yes	characteristic
245	C₂×C₄×C₇	2₋¹⁺⁴	1	1	yes	characteristic
246	C₇×C₈	—	2	2	no	—
247	C₇×C₈	—	2	2	no	—
248	C₇×C₈	—	2	2	no	—
249	C₇×C₈	—	2	4	no	—
250	C₇×C₈	—	4	2	no	—
251	C₇×C₈	—	4	2	no	—
252	C₇×C₈	—	4	2	no	—
253	C₇×C₈	C₄×D₄	1	4	yes	—
254	C₂²×D₄	C₇×Q₈	1	1	yes	characteristic
255	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
256	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
257	C₂×M₁₆	—	2	2	no	—
258	C₂×M₁₆	—	2	2	no	—
259	C₂×M₁₆	—	2	2	no	—
260	C₂×M₁₆	—	2	2	no	—
261	C₂×M₁₆	—	2	4	no	—
262	C₂×M₁₆	—	2	4	no	—
263	C₂×M₁₆	—	4	2	no	—
264	C₂×M₁₆	—	4	2	no	—
265	C₂×M₁₆	C₂×C₄×C₇	1	4	yes	—
266	C₂×M₁₆	C₂³×C₇	1	2	yes	—
267	C₂×M₁₆	C₂³×C₇	1	2	yes	—
268	C₂×M₁₆	C₂³×C₇	1	2	yes	—
269	C₂×M₁₆	C₂³×C₇	1	2	yes	—
270	C₂²×C₈	—	2	2	no	—
271	C₂²×C₈	—	2	2	no	—
272	C₂²×C₈	—	2	2	no	—
273	C₂²×C₈	—	2	2	no	—
274	C₂²×C₈	C₂×C₄×C₇	1	2	yes	—
275	C₂²×C₈	C₂×C₄×C₇	1	2	yes	—
276	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
277	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
278	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
279	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
280	C₄×D₄	C₂×C₄×C₇	1	2	yes	—
281	C₄×D₄	C₂×C₄×C₇	1	2	yes	—
282	C₄×D₄	C₇×D₄	1	2	yes	—
283	C₄×D₄	C₇×D₄	1	2	yes	—
284	C₂×C₄⋊C₄	C₇×Q₈	1	1	yes	characteristic
285	C₂×C₂²⋊C₄	C₇×Q₈	1	1	yes	characteristic
286	C₂×C₂²⋊C₄	C₇×Q₈	1	1	yes	characteristic
287	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
288	#108	—	2	4	no	—
289	#108	—	2	4	no	—
290	#108	—	2	2	no	—
291	#108	—	2	2	no	—
292	#108	—	2	2	no	—
293	#108	—	4	2	no	—
294	#108	C₇×D₄	1	4	yes	complemented
295	C₄⋊C₈	—	2	2	no	—
296	C₄⋊C₈	—	2	2	no	—
297	C₄⋊C₈	C₂×C₄×C₇	1	4	yes	—
298	C₂²⋊C₈	—	2	2	no	—
299	C₂²⋊C₈	—	2	2	no	—
300	C₂²⋊C₈	—	2	2	no	—
301	C₂²⋊C₈	—	2	2	no	—
302	C₂²⋊C₈	C₂×C₄×C₇	1	4	yes	—
303	C₂²⋊C₈	C₂×C₄×C₇	1	2	yes	—
304	C₂²⋊C₈	C₂×C₄×C₇	1	2	yes	—
305	#97	—	2	2	no	—
306	#97	C₂×C₄×C₇	1	4	yes	—
307	C₄×C₈	—	2	2	no	—
308	C₂²×C₇	—	2	1	no	—
309	C₂²×C₇	—	2	1	no	—
310	C₂²×C₇	—	2	1	no	—
311	C₂²×C₇	—	2	1	no	—
312	C₂²×C₇	—	2	1	no	—
313	C₂²×C₇	—	2	2	no	—
314	C₂²×C₇	—	2	2	no	—
315	C₂²×C₇	—	2	1	no	—
316	C₂²×C₇	—	2	1	no	—
317	C₂²×C₇	—	2	2	no	—
318	C₂²×C₇	—	4	2	no	—
319	C₂²×C₇	—	4	2	no	—
320	C₂²×C₇	—	8	1	no	—
321	C₂²×C₇	—	8	1	no	—
322	C₂²×C₇	#430	1	2	yes	complemented
323	C₂²×C₇	C₂²×C₄⋊C₄	1	1	yes	characteristic
324	C₂²×C₇	D₄×Q₈	1	1	yes	characteristic
325	C₂²×C₇	#554	1	1	yes	characteristic
326	C₄×C₇	—	2	1	no	—
327	C₄×C₇	—	2	1	no	—
328	C₄×C₇	—	2	2	no	—
329	C₄×C₇	—	2	2	no	—
330	C₄×C₇	—	2	2	no	—
331	C₄×C₇	C₂×C₄×D₄	1	1	yes	characteristic
332	C₄×C₇	#520	1	1	yes	characteristic
333	C₄×C₇	D₄²	1	1	yes	characteristic
334	C₄×C₇	#547	1	1	yes	characteristic
335	C₂⁴	C₂×C₇×Q₈	1	1	yes	characteristic
336	C₂⁴	C₂×C₇×Q₈	1	1	yes	characteristic
337	C₂×D₄	—	4	2	no	—
338	C₂×D₄	C₇×C₄⋊C₄	1	2	yes	—
339	C₂×D₄	C₇×C₄⋊C₄	1	2	yes	—
340	C₂²×C₄	—	2	1	no	—
341	C₂²×C₄	—	2	1	no	—
342	C₂²×C₄	—	2	1	no	—
343	C₂²×C₄	—	2	1	no	—
344	C₂²×C₄	—	2	1	no	—
345	C₂²×C₄	—	2	1	no	—
346	C₂²×C₄	—	2	1	no	—
347	C₂²×C₄	—	2	1	no	—
348	C₂²×C₄	C₂²×C₄×C₇	1	1	yes	characteristic
349	C₂²×C₄	C₂²×C₄×C₇	1	1	yes	characteristic
350	C₂²×C₄	C₂²×C₄×C₇	1	2	yes	—
351	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
352	C₂²×C₄	C₂×C₇×D₄	1	2	yes	—
353	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
354	C₂²×C₄	C₂×C₇×Q₈	1	1	yes	characteristic
355	C₂²×C₄	C₂×C₇×Q₈	1	1	yes	characteristic
356	C₂²×C₄	C₂×C₇×Q₈	1	1	yes	characteristic
357	C₂²×C₄	C₂×C₇×Q₈	1	1	yes	characteristic
358	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
359	M₁₆	—	2	2	no	—
360	M₁₆	—	2	8	no	—
361	M₁₆	—	2	2	no	—
362	M₁₆	—	2	2	no	—
363	M₁₆	—	2	2	no	—
364	M₁₆	—	2	2	no	—
365	M₁₆	—	2	2	no	—
366	M₁₆	—	2	2	no	—
367	M₁₆	—	4	4	no	—
368	M₁₆	—	4	4	no	—
369	M₁₆	C₂×C₇×D₄	1	4	yes	—
370	C₂×C₈	—	2	2	no	—
371	C₂×C₈	—	2	1	no	—
372	C₂×C₈	—	2	1	no	—
373	C₂×C₈	—	2	1	no	—
374	C₂×C₈	—	2	1	no	—
375	C₂×C₈	—	2	1	no	—
376	C₂×C₈	—	2	1	no	—
377	C₂×C₈	—	2	4	no	—
378	C₂×C₈	—	2	4	no	—
379	C₂×C₈	—	2	2	no	—
380	C₂×C₈	—	2	2	no	—
381	C₂×C₈	—	2	2	no	—
382	C₂×C₈	—	4	4	no	—
383	C₂×C₈	—	4	4	no	—
384	C₂×C₈	C₂²×C₄×C₇	1	2	yes	—
385	C₂×C₈	C₂²×C₄×C₇	1	2	yes	—
386	C₂×C₈	C₂²×C₄×C₇	1	2	yes	—
387	C₂×C₈	C₂²×C₄×C₇	1	2	yes	—
388	C₂×C₈	C₂×C₇×D₄	1	2	yes	—
389	C₂×C₈	C₇×#41	1	2	yes	—
390	C₄⋊C₄	C₇×C₄⋊C₄	1	2	yes	—
391	C₄⋊C₄	C₇×C₄⋊C₄	1	2	yes	—
392	C₂²⋊C₄	C₇×C₄⋊C₄	1	2	yes	—
393	C₂²⋊C₄	C₇×C₄⋊C₄	1	2	yes	—
394	C₂²⋊C₄	C₇×C₄⋊C₄	1	2	yes	—
395	C₂²⋊C₄	C₇×C₄⋊C₄	1	2	yes	—
396	C₄²	C₂²×C₄×C₇	1	2	yes	—
397	C₄²	C₂×C₇×D₄	1	2	yes	—
398	C₂×C₇	—	2	1	no	—
399	C₂×C₇	—	2	1	no	—
400	C₂×C₇	—	2	2	no	—
401	C₂×C₇	—	4	1	no	—
402	C₂×C₇	—	4	2	no	—
403	C₂×C₇	D₄×C₄⋊C₄	1	1	yes	characteristic
404	C₂×C₇	C₂×#430	1	1	yes	characteristic
405	C₂×C₇	#2916	1	1	yes	characteristic
406	C₂³	—	2	1	no	—
407	C₂³	—	2	1	no	—
408	C₂³	—	2	2	no	—
409	C₂³	—	2	1	no	—
410	C₂³	—	2	1	no	—
411	C₂³	—	4	1	no	—
412	C₂³	—	4	1	no	—
413	C₂³	—	4	1	no	—
414	C₂³	C₂×C₇×C₄⋊C₄	1	2	yes	—
415	C₂³	C₂×C₇×C₄⋊C₄	1	1	yes	characteristic
416	C₂³	C₂×C₇×C₄⋊C₄	1	1	yes	characteristic
417	C₂³	C₂²×C₇×Q₈	1	1	yes	characteristic
418	D₄	—	2	4	no	—
419	D₄	—	4	2	no	—
420	C₂×C₄	—	2	1	no	—
421	C₂×C₄	—	2	1	no	—
422	C₂×C₄	—	2	1	no	—
423	C₂×C₄	—	2	1	no	—
424	C₂×C₄	—	2	1	no	—
425	C₂×C₄	—	2	1	no	—
426	C₂×C₄	—	2	2	no	—
427	C₂×C₄	—	2	1	no	—
428	C₂×C₄	—	2	1	no	—
429	C₂×C₄	—	2	2	no	—
430	C₂×C₄	—	2	1	no	—
431	C₂×C₄	—	2	2	no	—
432	C₂×C₄	—	2	1	no	—
433	C₂×C₄	—	2	1	no	—
434	C₂×C₄	—	2	1	no	—
435	C₂×C₄	—	2	2	no	—
436	C₂×C₄	—	4	1	no	—
437	C₂×C₄	—	4	1	no	—
438	C₂×C₄	C₂×C₇×C₄⋊C₄	1	2	yes	—
439	C₂×C₄	C₂×C₇×C₄⋊C₄	1	2	yes	—
440	C₂×C₄	C₂×C₇×C₄⋊C₄	1	1	yes	characteristic
441	C₂×C₄	C₂×C₇×C₄⋊C₄	1	1	yes	characteristic
442	C₂×C₄	C₂×C₇×C₄⋊C₄	1	2	yes	—
443	C₂×C₄	C₂³×C₄×C₇	1	1	yes	characteristic
444	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
445	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
446	C₂×C₄	C₂×C₇×#41	1	1	yes	characteristic
447	C₂×C₄	C₇×H(5,𝔽₂)	1	1	yes	characteristic
448	C₂×C₄	C₇×2₋¹⁺⁴	1	1	yes	characteristic
449	C₈	—	2	2	no	—
450	C₈	—	2	2	no	—
451	C₈	—	2	2	no	—
452	C₈	—	2	4	no	—
453	C₈	—	4	2	no	—
454	C₈	—	4	2	no	—
455	C₈	—	4	2	no	—
456	C₈	C₄×C₇×D₄	1	4	yes	—
457	C₇	#22668	1	1	yes	characteristic, direct product factor, Sylow
458	C₂²	—	2	1	no	—
459	C₂²	—	2	1	no	—
460	C₂²	—	2	1	no	—
461	C₂²	—	2	1	no	—
462	C₂²	—	2	2	no	—
463	C₂²	—	2	1	no	—
464	C₂²	—	2	1	no	—
465	C₂²	—	2	2	no	—
466	C₂²	—	2	1	no	—
467	C₂²	—	2	2	no	—
468	C₂²	—	4	2	no	—
469	C₂²	—	4	2	no	—
470	C₂²	—	8	1	no	—
471	C₂²	—	8	1	no	—
472	C₂²	C₇×#430	1	2	yes	complemented
473	C₂²	C₂²×C₇×C₄⋊C₄	1	1	yes	characteristic
474	C₂²	C₇×D₄×Q₈	1	1	yes	characteristic
475	C₂²	C₇×#554	1	1	yes	characteristic
476	C₄	—	2	2	no	—
477	C₄	—	2	2	no	—
478	C₄	—	2	1	no	—
479	C₄	—	2	1	no	—
480	C₄	—	2	2	no	—
481	C₄	C₂×C₄×C₇×D₄	1	1	yes	characteristic
482	C₄	C₇×#520	1	1	yes	characteristic
483	C₄	C₇×D₄²	1	1	yes	characteristic
484	C₄	C₇×#547	1	1	yes	characteristic
485	C₂	—	2	1	no	—
486	C₂	—	2	1	no	—
487	C₂	—	2	2	no	—
488	C₂	—	4	1	no	—
489	C₂	—	4	2	no	—
490	C₂	C₇×D₄×C₄⋊C₄	1	1	yes	characteristic
491	C₂	C₂×C₇×#430	1	1	yes	characteristic
492	C₂	C₇×#2916	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	C₂²×C₄⋊C₄
prime radical	C₂²×C₇×D₄	Q₈
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₇ ◁ C₂×C₄×C₇×D₄ ◁ G

Complements

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

N	H ≅ G/N	type
3. C₂×C₇×#430	C₂	semidirect
4. C₂²×C₇×#108	C₂	semidirect
5. C₇×#1950	C₂	semidirect
6. C₇×#1855	C₂	semidirect
7. C₇×#1855	C₂	semidirect
8. C₇×#1849	C₂	semidirect
9. C₇×#1811	C₂	semidirect
10. C₇×#1810	C₂	semidirect
11. C₇×#1778	C₂	semidirect
43. #22668	C₇	direct (N × H)
84. C₇×#108	D₄	semidirect
100. C₂×#430	C₂×C₇	semidirect
101. C₂²×#108	C₂×C₇	semidirect
102. #1950	C₂×C₇	semidirect
103. #1855	C₂×C₇	semidirect
104. #1855	C₂×C₇	semidirect
105. #1849	C₂×C₇	semidirect
106. #1811	C₂×C₇	semidirect
107. #1810	C₂×C₇	semidirect
108. #1778	C₂×C₇	semidirect
294. #108	C₇×D₄	semidirect
322. C₂²×C₇	#430	semidirect
457. C₇	#22668	direct (N × H)
472. C₂²	C₇×#430	semidirect

Maximal subgroups

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

subgroup	index
C₇×D₄×M₁₆	2
C₂×C₇×#435	2
C₂×C₇×#430	2
C₂²×C₇×#108	2
C₇×#1950	2
C₇×#1855	2
C₇×#1849	2
C₇×#1811	2
C₇×#1810	2
C₇×#1778	2
#22668	7

Subgroups — C7×#22668 #13199884

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×#22668 #13199884