Subgroups — C₇×#22953 #13200169

Order 1792.

868 conjugacy classes of subgroups.

The subgroup lattice has 488 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₇×C₈×Q₈	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₇×#423	C₂	1	1	yes	maximal, characteristic
3	C₄×C₇×C₂²⋊Q₈	C₂	1	1	yes	maximal, characteristic
4	C₇×#1984	C₂	1	1	yes	maximal, characteristic, complemented
5	C₇×#1940	C₂	1	2	yes	maximal, complemented
6	C₇×#1939	C₂	1	1	yes	maximal, characteristic, complemented
7	C₇×#1916	C₂	1	2	yes	maximal, complemented
8	C₇×#1851	C₂	1	2	yes	maximal
9	C₇×#1770	C₂	1	1	yes	maximal, characteristic, complemented
10	C₇×#1753	C₂	1	2	yes	maximal
11	C₄×C₇×C₂²⋊C₈	C₂	1	1	yes	maximal, characteristic
12	C₂²×C₇×M₁₆	C₂²	1	2	yes	—
13	C₂×C₇×C₂²⋊Q₈	C₄	1	1	yes	characteristic
14	C₂×C₄×C₇×Q₈	C₂²	1	1	yes	characteristic
15	C₂²×C₄²×C₇	C₂²	1	1	yes	characteristic
16	C₇×C₈×Q₈	—	2	4	no	—
17	C₇×#423	—	2	4	no	—
18	C₂×C₇×C₄⋊C₈	C₂²	1	1	yes	characteristic
19	C₂×C₇×C₄⋊C₈	C₂²	1	2	yes	—
20	C₂×C₇×C₄⋊C₈	C₂²	1	2	yes	—
21	C₂×C₇×C₄⋊C₈	C₂²	1	2	yes	—
22	C₂×C₇×C₄⋊C₈	C₂²	1	1	yes	characteristic
23	C₂×C₇×C₂²⋊C₈	C₂²	1	1	yes	characteristic
24	C₂×C₇×C₂²⋊C₈	C₂²	1	1	yes	characteristic
25	C₂×C₇×#97	C₂²	1	2	yes	—
26	C₂×C₄×C₇×C₈	C₂²	1	1	yes	characteristic
27	C₂×C₄×C₇×C₈	C₂²	1	1	yes	characteristic
28	C₂×C₄×C₇×C₈	C₂²	1	2	yes	—
29	C₇×#391	C₄	1	1	yes	characteristic
30	C₇×#389	C₄	1	1	yes	characteristic
31	C₇×#387	C₄	1	2	yes	—
32	C₇×#385	C₄	1	2	yes	—
33	C₇×#380	C₄	1	1	yes	characteristic
34	C₄×C₇×C₄⋊C₄	C₂²	1	1	yes	characteristic
35	C₄×C₇×C₄⋊C₄	C₂²	1	2	yes	—
36	C₄×C₇×C₂²⋊C₄	C₂²	1	2	yes	—
37	C₇×#336	C₂²	1	2	yes	—
38	C₇×#336	C₂²	1	2	yes	—
39	C₇×#336	C₂²	1	1	yes	characteristic
40	C₇×#336	C₂²	1	1	yes	characteristic
41	C₇×#336	C₂²	1	2	yes	—
42	C₇×#336	C₂²	1	2	yes	—
43	#22953	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
44	C₂²×C₇×Q₈	C₂×C₄	1	1	yes	characteristic
45	C₂³×C₄×C₇	C₂×C₄	1	1	yes	characteristic
46	C₂³×C₄×C₇	C₂×C₄	1	1	yes	characteristic
47	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
48	C₂×C₇×M₁₆	—	2	4	no	—
49	C₂×C₇×M₁₆	—	2	4	no	—
50	C₂×C₇×M₁₆	—	4	2	no	—
51	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
52	C₂²×C₇×C₈	C₂³	1	2	yes	—
53	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
54	C₂²×C₇×C₈	C₂³	1	2	yes	—
55	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
56	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
57	C₇×C₂²⋊Q₈	—	2	4	no	—
58	C₄×C₇×Q₈	—	2	2	no	—
59	C₄×C₇×Q₈	—	2	2	no	—
60	C₂×C₇×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
61	C₂×C₇×C₄⋊C₄	C₂×C₄	1	2	yes	—
62	C₂×C₇×C₄⋊C₄	C₂×C₄	1	2	yes	—
63	C₂×C₇×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
64	C₂×C₇×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
65	C₂×C₇×C₄⋊C₄	C₂×C₄	1	2	yes	—
66	C₂×C₇×C₂²⋊C₄	C₂×C₄	1	2	yes	—
67	C₂×C₇×C₂²⋊C₄	C₂×C₄	1	2	yes	—
68	C₂×C₄²×C₇	—	2	2	no	—
69	C₂×C₄²×C₇	—	2	2	no	—
70	C₂×C₄²×C₇	C₂×C₄	1	1	yes	characteristic
71	C₂×C₄²×C₇	C₂×C₄	1	1	yes	characteristic
72	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
73	C₂×C₄²×C₇	C₂³	1	2	yes	—
74	C₂×C₄²×C₇	C₂³	1	2	yes	—
75	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
76	C₇×C₄⋊C₈	—	2	4	no	—
77	C₇×C₄⋊C₈	—	2	4	no	—
78	C₇×C₄⋊C₈	—	2	2	no	—
79	C₇×C₄⋊C₈	—	4	2	no	—
80	C₇×C₄⋊C₈	D₄	1	4	yes	—
81	C₇×C₂²⋊C₈	—	2	2	no	—
82	C₇×C₂²⋊C₈	Q₈	1	4	yes	complemented
83	C₇×#97	—	4	2	no	—
84	C₄×C₇×C₈	—	2	4	no	—
85	C₄×C₇×C₈	—	2	2	no	—
86	C₄×C₇×C₈	—	2	2	no	—
87	C₇×#95	C₂×C₄	1	2	yes	—
88	C₇×#95	C₂×C₄	1	2	yes	—
89	C₇×#95	C₂×C₄	1	2	yes	—
90	C₇×#95	C₂×C₄	1	2	yes	—
91	C₇×#95	C₂×C₄	1	2	yes	—
92	C₂×C₈×Q₈	C₂×C₇	1	1	yes	characteristic, complemented
93	C₂×#423	C₂×C₇	1	1	yes	characteristic
94	C₄×C₂²⋊Q₈	C₂×C₇	1	1	yes	characteristic
95	#1984	C₂×C₇	1	1	yes	characteristic, complemented
96	#1940	C₂×C₇	1	2	yes	complemented
97	#1939	C₂×C₇	1	1	yes	characteristic, complemented
98	#1916	C₂×C₇	1	2	yes	complemented
99	#1851	C₂×C₇	1	2	yes	—
100	#1770	C₂×C₇	1	1	yes	characteristic, complemented
101	#1753	C₂×C₇	1	2	yes	—
102	C₄×C₂²⋊C₈	C₂×C₇	1	1	yes	characteristic
103	C₂⁴×C₇	C₂²×C₄	1	1	yes	characteristic
104	C₂×C₇×Q₈	—	2	2	no	—
105	C₂×C₇×Q₈	—	2	2	no	—
106	C₂×C₇×Q₈	M₁₆	1	4	yes	complemented
107	C₂²×C₄×C₇	—	2	1	no	—
108	C₂²×C₄×C₇	—	2	1	no	—
109	C₂²×C₄×C₇	—	2	1	no	—
110	C₂²×C₄×C₇	—	2	1	no	—
111	C₂²×C₄×C₇	—	2	2	no	—
112	C₂²×C₄×C₇	—	2	2	no	—
113	C₂²×C₄×C₇	—	2	2	no	—
114	C₂²×C₄×C₇	—	2	2	no	—
115	C₂²×C₄×C₇	—	2	2	no	—
116	C₂²×C₄×C₇	—	4	1	no	—
117	C₂²×C₄×C₇	C₂²×C₄	1	2	yes	—
118	C₂²×C₄×C₇	C₂²×C₄	1	1	yes	characteristic
119	C₂²×C₄×C₇	C₂²×C₄	1	2	yes	—
120	C₂²×C₄×C₇	C₂²×C₄	1	2	yes	—
121	C₂²×C₄×C₇	C₂²×C₄	1	1	yes	characteristic
122	C₂²×C₄×C₇	C₂²×C₄	1	1	yes	characteristic
123	C₂²×C₄×C₇	C₂²×C₄	1	2	yes	—
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×Q₈	1	2	yes	—
127	C₂²×C₄×C₇	#41	1	2	yes	—
128	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
129	C₇×M₁₆	—	4	8	no	—
130	C₂×C₇×C₈	—	2	1	no	—
131	C₂×C₇×C₈	—	2	1	no	—
132	C₂×C₇×C₈	—	2	2	no	—
133	C₂×C₇×C₈	—	2	1	no	—
134	C₂×C₇×C₈	—	2	2	no	—
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	1	no	—
139	C₂×C₇×C₈	—	2	1	no	—
140	C₂×C₇×C₈	—	2	1	no	—
141	C₂×C₇×C₈	—	2	2	no	—
142	C₂×C₇×C₈	—	2	1	no	—
143	C₂×C₇×C₈	—	2	2	no	—
144	C₂×C₇×C₈	—	2	1	no	—
145	C₂×C₇×C₈	C₂×D₄	1	4	yes	—
146	C₂×C₇×C₈	C₂×Q₈	1	2	yes	—
147	C₂×C₇×C₈	C₂×Q₈	1	2	yes	—
148	C₇×C₄⋊C₄	—	2	4	no	—
149	C₇×C₄⋊C₄	—	2	2	no	—
150	C₇×C₄⋊C₄	—	2	2	no	—
151	C₇×C₄⋊C₄	—	2	4	no	—
152	C₇×C₄⋊C₄	—	2	4	no	—
153	C₇×C₄⋊C₄	—	2	2	no	—
154	C₇×C₂²⋊C₄	—	2	4	no	—
155	C₇×C₂²⋊C₄	—	4	2	no	—
156	C₄²×C₇	—	2	2	no	—
157	C₄²×C₇	—	2	2	no	—
158	C₄²×C₇	—	2	2	no	—
159	C₄²×C₇	—	2	1	no	—
160	C₄²×C₇	—	2	1	no	—
161	C₄²×C₇	—	2	2	no	—
162	C₄²×C₇	—	2	2	no	—
163	C₄²×C₇	—	2	2	no	—
164	C₄²×C₇	C₂×D₄	1	2	yes	—
165	C₄²×C₇	#41	1	2	yes	—
166	C₂²×M₁₆	C₂²×C₇	1	2	yes	—
167	C₂×C₂²⋊Q₈	C₄×C₇	1	1	yes	characteristic
168	C₂×C₄×Q₈	C₂²×C₇	1	1	yes	characteristic
169	C₂²×C₄²	C₂²×C₇	1	1	yes	characteristic
170	C₈×Q₈	—	2	4	no	—
171	#423	—	2	4	no	—
172	C₂×C₄⋊C₈	C₂²×C₇	1	2	yes	—
173	C₂×C₄⋊C₈	C₂²×C₇	1	2	yes	—
174	C₂×C₄⋊C₈	C₂²×C₇	1	1	yes	characteristic
175	C₂×C₄⋊C₈	C₂²×C₇	1	2	yes	—
176	C₂×C₄⋊C₈	C₂²×C₇	1	1	yes	characteristic
177	C₂×C₂²⋊C₈	C₂²×C₇	1	1	yes	characteristic
178	C₂×C₂²⋊C₈	C₂²×C₇	1	1	yes	characteristic
179	C₂×#97	C₂²×C₇	1	2	yes	—
180	C₂×C₄×C₈	C₂²×C₇	1	2	yes	—
181	C₂×C₄×C₈	C₂²×C₇	1	1	yes	characteristic
182	C₂×C₄×C₈	C₂²×C₇	1	1	yes	characteristic
183	#391	C₄×C₇	1	1	yes	characteristic
184	#389	C₄×C₇	1	1	yes	characteristic
185	#387	C₄×C₇	1	2	yes	—
186	#385	C₄×C₇	1	2	yes	—
187	#380	C₄×C₇	1	1	yes	characteristic
188	C₄×C₄⋊C₄	C₂²×C₇	1	2	yes	—
189	C₄×C₄⋊C₄	C₂²×C₇	1	1	yes	characteristic
190	C₄×C₂²⋊C₄	C₂²×C₇	1	2	yes	—
191	#336	C₂²×C₇	1	2	yes	—
192	#336	C₂²×C₇	1	2	yes	—
193	#336	C₂²×C₇	1	1	yes	characteristic
194	#336	C₂²×C₇	1	2	yes	—
195	#336	C₂²×C₇	1	1	yes	characteristic
196	#336	C₂²×C₇	1	2	yes	—
197	C₂³×C₇	—	2	1	no	—
198	C₂³×C₇	—	2	1	no	—
199	C₂³×C₇	—	2	1	no	—
200	C₂³×C₇	—	2	1	no	—
201	C₂³×C₇	—	2	1	no	—
202	C₂³×C₇	—	2	1	no	—
203	C₂³×C₇	C₄×Q₈	1	2	yes	—
204	C₂³×C₇	C₂³×C₄	1	1	yes	characteristic
205	C₇×Q₈	—	2	8	no	—
206	C₂×C₄×C₇	—	2	1	no	—
207	C₂×C₄×C₇	—	2	1	no	—
208	C₂×C₄×C₇	—	2	2	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	1	no	—
213	C₂×C₄×C₇	—	2	1	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	1	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	—	2	2	no	—
223	C₂×C₄×C₇	—	2	1	no	—
224	C₂×C₄×C₇	—	2	2	no	—
225	C₂×C₄×C₇	—	2	2	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	2	no	—
230	C₂×C₄×C₇	—	4	4	no	—
231	C₂×C₄×C₇	—	4	4	no	—
232	C₂×C₄×C₇	C₄×D₄	1	2	yes	—
233	C₂×C₄×C₇	C₄×D₄	1	2	yes	—
234	C₂×C₄×C₇	C₄×Q₈	1	2	yes	—
235	C₂×C₄×C₇	C₂×M₁₆	1	4	yes	—
236	C₂×C₄×C₇	C₂×M₁₆	1	2	yes	—
237	C₂×C₄×C₇	#131	1	2	yes	—
238	C₂×C₄×C₇	#131	1	2	yes	—
239	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
240	C₂×C₄×C₇	C₂²×Q₈	1	1	yes	characteristic
241	C₂×C₄×C₇	C₂×#41	1	1	yes	characteristic
242	C₂×C₄×C₇	C₂×#41	1	1	yes	characteristic
243	C₂×C₄×C₇	H(5,𝔽₂)	1	1	yes	characteristic
244	C₂×C₄×C₇	2₋¹⁺⁴	1	1	yes	characteristic
245	C₇×C₈	—	2	4	no	—
246	C₇×C₈	—	2	2	no	—
247	C₇×C₈	—	2	2	no	—
248	C₇×C₈	—	4	1	no	—
249	C₇×C₈	—	4	2	no	—
250	C₇×C₈	—	4	1	no	—
251	C₂²×Q₈	C₂×C₄×C₇	1	1	yes	characteristic
252	C₂³×C₄	C₂×C₄×C₇	1	1	yes	characteristic
253	C₂³×C₄	C₂×C₄×C₇	1	1	yes	characteristic
254	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
255	C₂×M₁₆	—	2	4	no	—
256	C₂×M₁₆	—	2	4	no	—
257	C₂×M₁₆	—	4	2	no	—
258	C₂²×C₈	C₂³×C₇	1	2	yes	—
259	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
260	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
261	C₂²×C₈	C₂³×C₇	1	2	yes	—
262	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
263	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
264	C₂²⋊Q₈	—	2	4	no	—
265	C₄×Q₈	—	2	2	no	—
266	C₄×Q₈	—	2	2	no	—
267	C₂×C₄⋊C₄	C₂×C₄×C₇	1	1	yes	characteristic
268	C₂×C₄⋊C₄	C₂×C₄×C₇	1	2	yes	—
269	C₂×C₄⋊C₄	C₂×C₄×C₇	1	2	yes	—
270	C₂×C₄⋊C₄	C₂×C₄×C₇	1	1	yes	characteristic
271	C₂×C₄⋊C₄	C₂×C₄×C₇	1	1	yes	characteristic
272	C₂×C₄⋊C₄	C₂×C₄×C₇	1	2	yes	—
273	C₂×C₂²⋊C₄	C₂×C₄×C₇	1	2	yes	—
274	C₂×C₂²⋊C₄	C₂×C₄×C₇	1	2	yes	—
275	C₂×C₄²	—	2	2	no	—
276	C₂×C₄²	—	2	2	no	—
277	C₂×C₄²	C₂×C₄×C₇	1	1	yes	characteristic
278	C₂×C₄²	C₂×C₄×C₇	1	1	yes	characteristic
279	C₂×C₄²	C₂³×C₇	1	2	yes	—
280	C₂×C₄²	C₂³×C₇	1	2	yes	—
281	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
282	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
283	C₄⋊C₈	—	2	4	no	—
284	C₄⋊C₈	—	2	4	no	—
285	C₄⋊C₈	—	2	2	no	—
286	C₄⋊C₈	—	4	2	no	—
287	C₄⋊C₈	C₇×D₄	1	4	yes	—
288	C₂²⋊C₈	—	2	2	no	—
289	C₂²⋊C₈	C₇×Q₈	1	4	yes	complemented
290	#97	—	4	2	no	—
291	C₄×C₈	—	2	4	no	—
292	C₄×C₈	—	2	2	no	—
293	C₄×C₈	—	2	2	no	—
294	#95	C₂×C₄×C₇	1	2	yes	—
295	#95	C₂×C₄×C₇	1	2	yes	—
296	#95	C₂×C₄×C₇	1	2	yes	—
297	#95	C₂×C₄×C₇	1	2	yes	—
298	#95	C₂×C₄×C₇	1	2	yes	—
299	C₂²×C₇	—	2	2	no	—
300	C₂²×C₇	—	2	2	no	—
301	C₂²×C₇	—	2	2	no	—
302	C₂²×C₇	—	4	1	no	—
303	C₂²×C₇	—	4	1	no	—
304	C₂²×C₇	—	4	1	no	—
305	C₂²×C₇	—	4	1	no	—
306	C₂²×C₇	C₂×C₄×D₄	1	1	yes	characteristic
307	C₂²×C₇	C₂×C₄×Q₈	1	1	yes	characteristic
308	C₂²×C₇	#520	1	1	yes	characteristic
309	C₂²×C₇	C₂²×M₁₆	1	1	yes	characteristic
310	C₂²×C₇	C₂×#131	1	1	yes	characteristic
311	C₂²×C₇	C₂×#131	1	1	yes	characteristic
312	C₂²×C₇	#568	1	1	yes	characteristic
313	C₄×C₇	—	2	2	no	—
314	C₄×C₇	—	2	4	no	—
315	C₄×C₇	—	2	2	no	—
316	C₄×C₇	—	2	2	no	—
317	C₄×C₇	—	4	1	no	—
318	C₄×C₇	—	4	2	no	—
319	C₄×C₇	—	4	2	no	—
320	C₄×C₇	—	4	2	no	—
321	C₄×C₇	#435	1	4	yes	—
322	C₄×C₇	#546	1	1	yes	characteristic
323	C₄×C₇	D₄×Q₈	1	1	yes	characteristic
324	C₄×C₇	#552	1	1	yes	characteristic
325	C₄×C₇	#554	1	1	yes	characteristic
326	C₂⁴	C₂²×C₄×C₇	1	1	yes	characteristic
327	C₂×Q₈	—	2	2	no	—
328	C₂×Q₈	—	2	2	no	—
329	C₂×Q₈	C₇×M₁₆	1	4	yes	complemented
330	C₂²×C₄	—	2	1	no	—
331	C₂²×C₄	—	2	1	no	—
332	C₂²×C₄	—	2	1	no	—
333	C₂²×C₄	—	2	1	no	—
334	C₂²×C₄	—	2	2	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	1	no	—
340	C₂²×C₄	C₂²×C₄×C₇	1	2	yes	—
341	C₂²×C₄	C₂²×C₄×C₇	1	1	yes	characteristic
342	C₂²×C₄	C₂²×C₄×C₇	1	2	yes	—
343	C₂²×C₄	C₂²×C₄×C₇	1	2	yes	—
344	C₂²×C₄	C₂²×C₄×C₇	1	1	yes	characteristic
345	C₂²×C₄	C₂²×C₄×C₇	1	1	yes	characteristic
346	C₂²×C₄	C₂²×C₄×C₇	1	2	yes	—
347	C₂²×C₄	C₂²×C₄×C₇	1	1	yes	characteristic
348	C₂²×C₄	C₂²×C₄×C₇	1	1	yes	characteristic
349	C₂²×C₄	C₂×C₇×Q₈	1	2	yes	—
350	C₂²×C₄	C₇×#41	1	2	yes	—
351	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
352	M₁₆	—	4	8	no	—
353	C₂×C₈	—	2	1	no	—
354	C₂×C₈	—	2	1	no	—
355	C₂×C₈	—	2	2	no	—
356	C₂×C₈	—	2	1	no	—
357	C₂×C₈	—	2	2	no	—
358	C₂×C₈	—	2	1	no	—
359	C₂×C₈	—	2	1	no	—
360	C₂×C₈	—	2	2	no	—
361	C₂×C₈	—	2	1	no	—
362	C₂×C₈	—	2	1	no	—
363	C₂×C₈	—	2	1	no	—
364	C₂×C₈	—	2	2	no	—
365	C₂×C₈	—	2	1	no	—
366	C₂×C₈	—	2	2	no	—
367	C₂×C₈	—	2	1	no	—
368	C₂×C₈	C₂×C₇×D₄	1	4	yes	—
369	C₂×C₈	C₂×C₇×Q₈	1	2	yes	—
370	C₂×C₈	C₂×C₇×Q₈	1	2	yes	—
371	C₄⋊C₄	—	2	4	no	—
372	C₄⋊C₄	—	2	2	no	—
373	C₄⋊C₄	—	2	2	no	—
374	C₄⋊C₄	—	2	4	no	—
375	C₄⋊C₄	—	2	4	no	—
376	C₄⋊C₄	—	2	2	no	—
377	C₂²⋊C₄	—	2	4	no	—
378	C₂²⋊C₄	—	4	2	no	—
379	C₄²	—	2	2	no	—
380	C₄²	—	2	2	no	—
381	C₄²	—	2	2	no	—
382	C₄²	—	2	1	no	—
383	C₄²	—	2	1	no	—
384	C₄²	—	2	2	no	—
385	C₄²	—	2	2	no	—
386	C₄²	—	2	2	no	—
387	C₄²	C₂×C₇×D₄	1	2	yes	—
388	C₄²	C₇×#41	1	2	yes	—
389	C₂×C₇	—	4	2	no	—
390	C₂×C₇	#2360	1	1	yes	characteristic
391	C₂×C₇	C₂×#435	1	1	yes	characteristic
392	C₂×C₇	#2933	1	1	yes	characteristic
393	C₂×C₇	#2960	1	1	yes	characteristic
394	C₂×C₇	Q₈×M₁₆	1	1	yes	characteristic
395	C₂×C₇	#2991	1	1	yes	characteristic
396	C₂×C₇	#2993	1	1	yes	characteristic
397	C₂³	—	2	1	no	—
398	C₂³	—	2	1	no	—
399	C₂³	—	2	1	no	—
400	C₂³	—	2	1	no	—
401	C₂³	—	2	1	no	—
402	C₂³	—	2	1	no	—
403	C₂³	C₄×C₇×Q₈	1	2	yes	—
404	C₂³	C₂³×C₄×C₇	1	1	yes	characteristic
405	Q₈	—	2	8	no	—
406	C₂×C₄	—	2	1	no	—
407	C₂×C₄	—	2	1	no	—
408	C₂×C₄	—	2	2	no	—
409	C₂×C₄	—	2	1	no	—
410	C₂×C₄	—	2	1	no	—
411	C₂×C₄	—	2	2	no	—
412	C₂×C₄	—	2	1	no	—
413	C₂×C₄	—	2	1	no	—
414	C₂×C₄	—	2	2	no	—
415	C₂×C₄	—	2	2	no	—
416	C₂×C₄	—	2	2	no	—
417	C₂×C₄	—	2	2	no	—
418	C₂×C₄	—	2	1	no	—
419	C₂×C₄	—	2	2	no	—
420	C₂×C₄	—	2	2	no	—
421	C₂×C₄	—	2	2	no	—
422	C₂×C₄	—	2	2	no	—
423	C₂×C₄	—	2	1	no	—
424	C₂×C₄	—	2	2	no	—
425	C₂×C₄	—	2	2	no	—
426	C₂×C₄	—	2	2	no	—
427	C₂×C₄	—	2	1	no	—
428	C₂×C₄	—	2	2	no	—
429	C₂×C₄	—	2	2	no	—
430	C₂×C₄	—	4	4	no	—
431	C₂×C₄	—	4	4	no	—
432	C₂×C₄	C₄×C₇×D₄	1	2	yes	—
433	C₂×C₄	C₄×C₇×D₄	1	2	yes	—
434	C₂×C₄	C₄×C₇×Q₈	1	2	yes	—
435	C₂×C₄	C₂×C₇×M₁₆	1	4	yes	—
436	C₂×C₄	C₂×C₇×M₁₆	1	2	yes	—
437	C₂×C₄	C₇×#131	1	2	yes	—
438	C₂×C₄	C₇×#131	1	2	yes	—
439	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
440	C₂×C₄	C₂²×C₇×Q₈	1	1	yes	characteristic
441	C₂×C₄	C₂×C₇×#41	1	1	yes	characteristic
442	C₂×C₄	C₂×C₇×#41	1	1	yes	characteristic
443	C₂×C₄	C₇×H(5,𝔽₂)	1	1	yes	characteristic
444	C₂×C₄	C₇×2₋¹⁺⁴	1	1	yes	characteristic
445	C₈	—	2	4	no	—
446	C₈	—	2	2	no	—
447	C₈	—	2	2	no	—
448	C₈	—	4	1	no	—
449	C₈	—	4	2	no	—
450	C₈	—	4	1	no	—
451	C₇	#22953	1	1	yes	characteristic, direct product factor, Sylow
452	C₂²	—	2	2	no	—
453	C₂²	—	2	2	no	—
454	C₂²	—	2	2	no	—
455	C₂²	—	4	1	no	—
456	C₂²	—	4	1	no	—
457	C₂²	—	4	1	no	—
458	C₂²	—	4	1	no	—
459	C₂²	C₂×C₄×C₇×D₄	1	1	yes	characteristic
460	C₂²	C₂×C₄×C₇×Q₈	1	1	yes	characteristic
461	C₂²	C₇×#520	1	1	yes	characteristic
462	C₂²	C₂²×C₇×M₁₆	1	1	yes	characteristic
463	C₂²	C₂×C₇×#131	1	1	yes	characteristic
464	C₂²	C₂×C₇×#131	1	1	yes	characteristic
465	C₂²	C₇×#568	1	1	yes	characteristic
466	C₄	—	2	4	no	—
467	C₄	—	2	2	no	—
468	C₄	—	2	2	no	—
469	C₄	—	2	2	no	—
470	C₄	—	4	1	no	—
471	C₄	—	4	2	no	—
472	C₄	—	4	2	no	—
473	C₄	—	4	2	no	—
474	C₄	C₇×#435	1	4	yes	—
475	C₄	C₇×#546	1	1	yes	characteristic
476	C₄	C₇×D₄×Q₈	1	1	yes	characteristic
477	C₄	C₇×#552	1	1	yes	characteristic
478	C₄	C₇×#554	1	1	yes	characteristic
479	C₂	—	4	2	no	—
480	C₂	C₇×#2360	1	1	yes	characteristic
481	C₂	C₂×C₇×#435	1	1	yes	characteristic
482	C₂	C₇×#2933	1	1	yes	characteristic
483	C₂	C₇×#2960	1	1	yes	characteristic
484	C₂	C₇×Q₈×M₁₆	1	1	yes	characteristic
485	C₂	C₇×#2991	1	1	yes	characteristic
486	C₂	C₇×#2993	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄×C₇	C₂⁴
commutator	C₂³	C₂³×C₄×C₇
Frattini, cosocle	C₂²×C₄	C₂⁴×C₇
socle	C₂³×C₇	C₂³×C₄
prime radical	C₂⁴×C₇	C₂²×C₄
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂²×C₄×C₇ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₇×C₈×Q₈	C₂	semidirect
4. C₇×#1984	C₂	semidirect
5. C₇×#1940	C₂	semidirect
6. C₇×#1939	C₂	semidirect
7. C₇×#1916	C₂	semidirect
9. C₇×#1770	C₂	semidirect
43. #22953	C₇	direct (N × H)
82. C₇×C₂²⋊C₈	Q₈	semidirect
92. C₂×C₈×Q₈	C₂×C₇	semidirect
95. #1984	C₂×C₇	semidirect
96. #1940	C₂×C₇	semidirect
97. #1939	C₂×C₇	semidirect
98. #1916	C₂×C₇	semidirect
100. #1770	C₂×C₇	semidirect
106. C₂×C₇×Q₈	M₁₆	semidirect
289. C₂²⋊C₈	C₇×Q₈	semidirect
329. C₂×Q₈	C₇×M₁₆	semidirect
451. C₇	#22953	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×C₇×C₈×Q₈	2
C₂×C₇×#423	2
C₄×C₇×C₂²⋊Q₈	2
C₇×#1984	2
C₇×#1940	2
C₇×#1939	2
C₇×#1916	2
C₇×#1851	2
C₇×#1770	2
C₇×#1753	2
C₄×C₇×C₂²⋊C₈	2
#22953	7

Subgroups — C7×#22953 #13200169

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×#22953 #13200169