Subgroups — #13507316

Order 1792.

558 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	C₈×#1159	C₂	1	1	yes	maximal, characteristic
2	C₇×#2168	C₂	1	1	yes	maximal, characteristic, complemented
3	#11729184	C₂	1	1	yes	maximal, characteristic, complemented
4	Dic₇×M₃₂	C₂	1	1	yes	maximal, characteristic, complemented
5	#11729161	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×C₁₆×Dic₇	C₂	1	1	yes	maximal, characteristic, complemented
7	#11728611	C₂	1	1	yes	maximal, characteristic, complemented
8	#11727036	C₂	1	1	yes	maximal, characteristic, complemented
9	#11727028	C₂	1	1	yes	maximal, characteristic, complemented
10	#11726858	C₂	1	1	yes	maximal, characteristic, complemented
11	#11726856	C₂	1	1	yes	maximal, characteristic, complemented
12	#11726846	C₂	1	1	yes	maximal, characteristic, complemented
13	#11726846	C₂	1	1	yes	maximal, characteristic, complemented
14	#11726825	C₂	1	1	yes	maximal, characteristic, complemented
15	#11726822	C₂	1	1	yes	maximal, characteristic, complemented
16	C₄×#1159	C₄	1	1	yes	characteristic
17	C₂×C₇×M₃₂	C₂²	1	1	yes	characteristic
18	C₂²×C₇×C₁₆	C₂²	1	1	yes	characteristic
19	C₇×C₈×D₄	C₂²	1	1	yes	characteristic
20	C₈×C₂²⋊D₇	C₂²	1	1	yes	characteristic
21	C₈×C₂²⋊D₇	C₂²	1	1	yes	characteristic
22	C₂×C₈×Dic₇	C₂²	1	1	yes	characteristic
23	C₂×C₈×Dic₇	C₂²	1	1	yes	characteristic
24	C₂×#6386	C₂²	1	1	yes	characteristic
25	C₂²×C₇⋊C₁₆	C₂²	1	1	yes	characteristic
26	D₄×C₇⋊C₈	C₄	1	1	yes	characteristic
27	C₂×#6372	C₂²	1	1	yes	characteristic
28	C₂×#6372	C₂²	1	1	yes	characteristic
29	#89605	C₄	1	1	yes	characteristic
30	#89602	C₄	1	1	yes	characteristic
31	(C₂²⋊D₇)⋊C₈	C₄	1	1	yes	characteristic
32	(C₂²⋊D₇)⋊C₈	C₄	1	1	yes	characteristic
33	#89490	C₄	1	1	yes	characteristic
34	#89490	C₄	1	1	yes	characteristic
35	C₄×C₈×D₇	C₂²	1	1	yes	characteristic
36	C₈×Dic₁₄	C₂²	1	1	yes	characteristic
37	C₇×C₄⋊C₁₆	C₂²	1	1	yes	characteristic
38	C₇×C₂²⋊C₁₆	C₂²	1	1	yes	characteristic
39	C₇×C₂²⋊C₁₆	C₂²	1	1	yes	characteristic
40	C₇×#346	C₂²	1	1	yes	characteristic
41	C₂²⋊(C₇⋊C₁₆)	C₂²	1	1	yes	characteristic
42	C₂²⋊(C₇⋊C₁₆)	C₂²	1	1	yes	characteristic
43	(C₂×D₇)⋊C₁₆	C₂²	1	1	yes	characteristic
44	(C₂×D₇)⋊C₁₆	C₂²	1	1	yes	characteristic
45	#89297	C₂²	1	1	yes	characteristic
46	#89297	C₂²	1	1	yes	characteristic
47	Dic₇⋊C₁₆	C₂²	1	1	yes	characteristic
48	Dic₇⋊C₁₆	C₂²	1	1	yes	characteristic
49	Dic₇⋊C₁₆	C₂²	1	1	yes	characteristic
50	Dic₇⋊C₁₆	C₂²	1	1	yes	characteristic
51	C₁₆×Dic₇	C₂²	1	1	yes	characteristic
52	C₁₆×Dic₇	C₂²	1	1	yes	characteristic
53	C₁₆×Dic₇	C₂²	1	1	yes	characteristic
54	C₁₆×Dic₇	C₂²	1	1	yes	characteristic
55	C₁₆×Dic₇	C₂²	1	1	yes	characteristic
56	C₁₆×Dic₇	C₂²	1	1	yes	characteristic
57	C₄⋊(C₇⋊C₁₆)	C₂²	1	1	yes	characteristic
58	#89256	C₂²	1	1	yes	characteristic
59	#33479	—	7	1	no	maximal, Sylow
60	C₂×#1159	C₈	1	1	yes	characteristic
61	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
62	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
63	C₄×C₇×D₄	C₂×C₄	1	1	yes	characteristic
64	D₄×Dic₇	C₈	1	1	yes	characteristic
65	C₄×C₂²⋊D₇	C₂×C₄	1	1	yes	characteristic
66	C₄×C₂²⋊D₇	C₂×C₄	1	1	yes	characteristic
67	C₂×C₄×Dic₇	C₂×C₄	1	1	yes	characteristic
68	C₂×C₄×Dic₇	C₂×C₄	1	1	yes	characteristic
69	C₂²×C₇⋊C₈	C₂×C₄	1	1	yes	characteristic
70	C₂²×C₇⋊C₈	C₂×C₄	1	1	yes	characteristic
71	C₂×C₈×D₇	C₂×C₄	1	1	yes	characteristic
72	C₂×C₈×D₇	C₂³	1	1	yes	characteristic
73	#6455	C₈	1	1	yes	characteristic
74	#6450	C₈	1	1	yes	characteristic
75	(C₂²⋊D₇)⋊C₄	C₈	1	1	yes	characteristic
76	(C₂²⋊D₇)⋊C₄	C₈	1	1	yes	characteristic
77	#6440	C₈	1	1	yes	characteristic
78	#6440	C₈	1	1	yes	characteristic
79	C₄²×D₇	C₂×C₄	1	1	yes	characteristic
80	C₄×Dic₁₄	C₂×C₄	1	1	yes	characteristic
81	C₇×M₃₂	—	2	2	no	—
82	C₂×C₇×C₁₆	—	2	2	no	—
83	C₂×C₇×C₁₆	C₂³	1	1	yes	characteristic
84	C₂×C₇×C₁₆	C₂³	1	1	yes	characteristic
85	C₂×C₇×C₁₆	C₂³	1	1	yes	characteristic
86	C₂×C₇×C₁₆	C₂³	1	1	yes	characteristic
87	C₇×C₄⋊C₈	C₂×C₄	1	1	yes	characteristic
88	C₇×C₂²⋊C₈	C₂×C₄	1	1	yes	characteristic
89	C₇×C₂²⋊C₈	C₂×C₄	1	1	yes	characteristic
90	C₄×C₇×C₈	C₂³	1	1	yes	characteristic
91	C₂²⋊(C₇⋊C₈)	C₂×C₄	1	1	yes	characteristic
92	C₂²⋊(C₇⋊C₈)	C₂×C₄	1	1	yes	characteristic
93	(C₂×D₇)⋊C₈	C₂×C₄	1	1	yes	characteristic
94	(C₂×D₇)⋊C₈	C₂×C₄	1	1	yes	characteristic
95	Dic₇⋊C₈	C₂×C₄	1	1	yes	characteristic
96	Dic₇⋊C₈	C₂×C₄	1	1	yes	characteristic
97	Dic₇⋊C₈	C₂×C₄	1	1	yes	characteristic
98	Dic₇⋊C₈	C₂×C₄	1	1	yes	characteristic
99	C₈×Dic₇	C₂×C₄	1	1	yes	characteristic
100	C₈×Dic₇	C₂×C₄	1	1	yes	characteristic
101	C₈×Dic₇	C₂×C₄	1	1	yes	characteristic
102	C₈×Dic₇	C₂×C₄	1	1	yes	characteristic
103	C₈×Dic₇	C₂×C₄	1	1	yes	characteristic
104	C₈×Dic₇	C₂³	1	1	yes	characteristic
105	C₈×Dic₇	C₂³	1	1	yes	characteristic
106	C₈×Dic₇	C₂³	1	1	yes	characteristic
107	#6386	—	2	2	no	—
108	C₂×C₇⋊C₁₆	—	2	2	no	—
109	C₂×C₇⋊C₁₆	C₂³	1	1	yes	characteristic
110	C₂×C₇⋊C₁₆	C₂³	1	1	yes	characteristic
111	C₂×C₇⋊C₁₆	C₂³	1	1	yes	characteristic
112	C₂×C₇⋊C₁₆	C₂³	1	1	yes	characteristic
113	C₄⋊(C₇⋊C₈)	C₂×C₄	1	1	yes	characteristic
114	C₄×C₇⋊C₈	C₂×C₄	1	1	yes	characteristic
115	#6372	—	2	2	no	—
116	#6372	—	2	2	no	—
117	C₈×#41	—	7	1	no	—
118	#2183	—	7	1	no	—
119	#2183	—	7	1	no	—
120	#2169	—	7	1	no	—
121	#2169	—	7	1	no	—
122	#2168	—	7	1	no	—
123	#2168	—	7	1	no	—
124	#2168	—	7	1	no	—
125	#2168	D₇	1	1	yes	characteristic, complemented
126	#2162	—	7	1	no	—
127	#2162	—	7	1	no	—
128	#2162	—	7	1	no	—
129	C₄×M₃₂	—	7	1	no	—
130	C₄×M₃₂	—	7	1	no	—
131	C₂×C₄×C₁₆	—	7	1	no	—
132	C₂×C₇×D₄	C₂×C₈	1	1	yes	characteristic
133	C₂²×C₄×C₇	C₂²×C₄	1	1	yes	characteristic
134	C₂²×C₄×C₇	C₂²×C₄	1	1	yes	characteristic
135	C₂×C₂²⋊D₇	C₂×C₈	1	1	yes	characteristic
136	C₂×C₂²⋊D₇	C₂×C₈	1	1	yes	characteristic
137	C₂²×Dic₇	C₂×C₈	1	1	yes	characteristic
138	C₂²×Dic₇	C₂×C₈	1	1	yes	characteristic
139	C₂²×Dic₇	C₂×C₈	1	1	yes	characteristic
140	C₂²×Dic₇	C₂×C₈	1	1	yes	characteristic
141	#1159	—	2	4	no	—
142	C₂×C₄×D₇	C₂×C₈	1	1	yes	characteristic
143	C₂×C₄×D₇	C₂×C₈	1	1	yes	characteristic
144	C₂×C₄×D₇	C₂²×C₄	1	1	yes	characteristic
145	C₂×Dic₁₄	C₂×C₈	1	1	yes	characteristic
146	C₂×C₇×C₈	—	2	1	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	C₂²×C₄	1	1	yes	characteristic
151	C₂×C₇×C₈	C₂²×C₄	1	1	yes	characteristic
152	C₂×C₇×C₈	C₂²×C₄	1	1	yes	characteristic
153	C₂×C₇×C₈	C₂⁴	1	1	yes	characteristic
154	C₇×C₄⋊C₄	C₂×C₈	1	1	yes	characteristic
155	C₇×C₂²⋊C₄	C₂×C₈	1	1	yes	characteristic
156	C₇×C₂²⋊C₄	C₂×C₈	1	1	yes	characteristic
157	C₄²×C₇	C₂²×C₄	1	1	yes	characteristic
158	C₂²⋊Dic₇	C₂×C₈	1	1	yes	characteristic
159	C₂²⋊Dic₇	C₂×C₈	1	1	yes	characteristic
160	(C₂×D₇)⋊C₄	C₂×C₈	1	1	yes	characteristic
161	(C₂×D₇)⋊C₄	C₂×C₈	1	1	yes	characteristic
162	C₄⋊Dic₇	C₂×C₈	1	1	yes	characteristic
163	Dic₇⋊C₄	C₂×C₈	1	1	yes	characteristic
164	Dic₇⋊C₄	C₂×C₈	1	1	yes	characteristic
165	Dic₇⋊C₄	C₂×C₈	1	1	yes	characteristic
166	Dic₇⋊C₄	C₂×C₈	1	1	yes	characteristic
167	C₄×Dic₇	C₂×C₈	1	1	yes	characteristic
168	C₄×Dic₇	C₂×C₈	1	1	yes	characteristic
169	C₄×Dic₇	C₂×C₈	1	1	yes	characteristic
170	C₄×Dic₇	C₂×C₈	1	1	yes	characteristic
171	C₄×Dic₇	C₂×C₈	1	1	yes	characteristic
172	C₄×Dic₇	C₂×C₈	1	1	yes	characteristic
173	C₄×Dic₇	C₂²×C₄	1	1	yes	characteristic
174	C₄×Dic₇	C₂²×C₄	1	1	yes	characteristic
175	C₄×Dic₇	C₂²×C₄	1	1	yes	characteristic
176	C₂×C₇⋊C₈	—	2	2	no	—
177	C₂×C₇⋊C₈	—	2	2	no	—
178	C₂×C₇⋊C₈	C₂²×C₄	1	1	yes	characteristic
179	C₂×C₇⋊C₈	C₂²×C₄	1	1	yes	characteristic
180	C₂×C₇⋊C₈	C₂²×C₄	1	1	yes	characteristic
181	C₂×C₇⋊C₈	C₂²×C₄	1	1	yes	characteristic
182	C₈×D₇	—	2	1	no	—
183	C₈×D₇	—	2	1	no	—
184	C₈×D₇	—	2	2	no	—
185	C₇×C₁₆	—	2	1	no	—
186	C₇×C₁₆	—	2	1	no	—
187	C₇×C₁₆	—	2	1	no	—
188	C₇×C₁₆	#41	1	2	yes	complemented
189	C₇⋊C₁₆	—	2	1	no	—
190	C₇⋊C₁₆	—	2	1	no	—
191	C₇⋊C₁₆	—	2	1	no	—
192	C₇⋊C₁₆	#41	1	2	yes	complemented
193	C₄×#41	—	7	1	no	—
194	C₂×M₃₂	—	7	1	no	—
195	C₂×M₃₂	—	7	1	no	—
196	C₂×M₃₂	—	7	1	no	—
197	C₂×M₃₂	C₂×D₇	1	1	yes	characteristic
198	C₂²×C₁₆	—	7	1	no	—
199	C₂²×C₁₆	C₂×D₇	1	1	yes	characteristic
200	C₈×Q₈	—	7	1	no	—
201	C₈×Q₈	—	7	1	no	—
202	C₈×D₄	—	7	1	no	—
203	C₈×D₄	—	7	1	no	—
204	C₈×D₄	—	7	1	no	—
205	C₈×D₄	—	7	1	no	—
206	C₈×D₄	—	7	1	no	—
207	C₈×D₄	C₂×D₇	1	1	yes	characteristic
208	#431	—	7	1	no	—
209	#431	—	7	1	no	—
210	#431	—	7	1	no	—
211	C₂×C₄×C₈	—	7	1	no	—
212	C₂×C₄×C₈	—	7	1	no	—
213	C₂×C₄×C₈	—	7	1	no	—
214	C₄⋊C₁₆	—	7	1	no	—
215	C₄⋊C₁₆	—	7	1	no	—
216	C₄⋊C₁₆	—	7	1	no	—
217	C₄⋊C₁₆	—	7	1	no	—
218	C₄⋊C₁₆	—	7	1	no	—
219	C₄⋊C₁₆	C₂×D₇	1	1	yes	characteristic
220	C₂²⋊C₁₆	—	7	1	no	—
221	C₂²⋊C₁₆	—	7	1	no	—
222	C₂²⋊C₁₆	—	7	1	no	—
223	C₂²⋊C₁₆	—	7	1	no	—
224	C₂²⋊C₁₆	C₂×D₇	1	1	yes	characteristic
225	C₂²⋊C₁₆	C₂×D₇	1	1	yes	characteristic
226	#346	—	7	1	no	—
227	#346	—	7	1	no	—
228	#346	—	7	1	no	—
229	#346	C₂×D₇	1	1	yes	characteristic
230	C₄×C₁₆	—	7	1	no	—
231	C₄×C₁₆	—	7	1	no	—
232	C₄×C₁₆	—	7	1	no	—
233	C₄×C₁₆	—	7	1	no	—
234	C₄×C₁₆	—	7	1	no	—
235	C₄×C₁₆	—	7	1	no	—
236	C₂³×C₇	C₂²×C₈	1	1	yes	characteristic
237	C₂³×C₇	C₂²×C₈	1	1	yes	characteristic
238	C₂²×D₇	C₂²×C₈	1	1	yes	characteristic
239	C₇×D₄	—	2	2	no	—
240	C₂×C₄×C₇	—	2	1	no	—
241	C₂×C₄×C₇	—	2	1	no	—
242	C₂×C₄×C₇	—	2	1	no	—
243	C₂×C₄×C₇	—	2	1	no	—
244	C₂×C₄×C₇	C₂²×C₈	1	1	yes	characteristic
245	C₂×C₄×C₇	C₂²×C₈	1	1	yes	characteristic
246	C₂×C₄×C₇	C₂²×C₈	1	1	yes	characteristic
247	C₂×C₄×C₇	C₂²×C₈	1	1	yes	characteristic
248	C₂×C₄×C₇	C₂³×C₄	1	1	yes	characteristic
249	C₂²⋊D₇	—	2	2	no	—
250	C₂²⋊D₇	—	2	2	no	—
251	C₂×Dic₇	—	2	2	no	—
252	C₂×Dic₇	—	2	2	no	—
253	C₂×Dic₇	—	2	2	no	—
254	C₂×Dic₇	M₃₂	1	4	yes	complemented
255	C₂×Dic₇	C₂²×C₈	1	1	yes	characteristic
256	C₂×Dic₇	C₂²×C₈	1	1	yes	characteristic
257	C₂×Dic₇	C₂²×C₈	1	1	yes	characteristic
258	C₂×Dic₇	C₂²×C₈	1	1	yes	characteristic
259	C₂×Dic₇	C₂²×C₈	1	1	yes	characteristic
260	C₂×Dic₇	C₂²×C₈	1	1	yes	characteristic
261	C₂×Dic₇	C₂²×C₈	1	1	yes	characteristic
262	C₄×D₇	—	2	1	no	—
263	C₄×D₇	—	2	1	no	—
264	C₄×D₇	—	2	2	no	—
265	C₄×D₇	—	2	2	no	—
266	Dic₁₄	—	2	2	no	—
267	C₇×C₈	—	2	1	no	—
268	C₇×C₈	—	2	1	no	—
269	C₇×C₈	—	2	1	no	—
270	C₇×C₈	C₂×#41	1	1	yes	characteristic
271	C₇×C₈	C₂×#41	1	1	yes	characteristic
272	C₇⋊C₈	—	2	1	no	—
273	C₇⋊C₈	—	2	1	no	—
274	C₇⋊C₈	—	2	1	no	—
275	C₇⋊C₈	#131	1	2	yes	—
276	C₂×#41	—	7	1	no	—
277	C₂²×C₈	—	7	1	no	—
278	C₂²×C₈	—	7	1	no	—
279	C₂²×C₈	—	7	1	no	—
280	C₂²×C₈	—	7	1	no	—
281	C₂²×C₈	C₂²×D₇	1	1	yes	characteristic
282	C₂²×C₈	C₂²×D₇	1	1	yes	characteristic
283	C₄×Q₈	—	7	1	no	—
284	C₄×Q₈	—	7	1	no	—
285	C₄×D₄	—	7	1	no	—
286	C₄×D₄	—	7	1	no	—
287	C₄×D₄	—	7	1	no	—
288	C₄×D₄	—	7	1	no	—
289	C₄×D₄	—	7	1	no	—
290	C₄×D₄	C₄×D₇	1	1	yes	characteristic
291	#117	—	7	1	no	—
292	#117	—	7	1	no	—
293	#117	—	7	1	no	—
294	C₂×C₄²	—	7	1	no	—
295	C₂×C₄²	—	7	1	no	—
296	C₂×C₄²	—	7	1	no	—
297	M₃₂	—	2	2	no	—
298	M₃₂	—	14	2	no	—
299	M₃₂	—	14	2	no	—
300	M₃₂	—	14	2	no	—
301	C₂×C₁₆	—	2	2	no	—
302	C₂×C₁₆	—	7	1	no	—
303	C₂×C₁₆	—	7	1	no	—
304	C₂×C₁₆	—	7	1	no	—
305	C₂×C₁₆	—	7	1	no	—
306	C₂×C₁₆	—	14	2	no	—
307	C₂×C₁₆	C₂²×D₇	1	1	yes	characteristic
308	C₂×C₁₆	C₂²×D₇	1	1	yes	characteristic
309	C₂×C₁₆	C₂²×D₇	1	1	yes	characteristic
310	C₂×C₁₆	C₂²×D₇	1	1	yes	characteristic
311	C₄⋊C₈	—	7	1	no	—
312	C₄⋊C₈	—	7	1	no	—
313	C₄⋊C₈	—	7	1	no	—
314	C₄⋊C₈	—	7	1	no	—
315	C₄⋊C₈	—	7	1	no	—
316	C₄⋊C₈	C₄×D₇	1	1	yes	characteristic
317	C₂²⋊C₈	—	7	1	no	—
318	C₂²⋊C₈	—	7	1	no	—
319	C₂²⋊C₈	—	7	1	no	—
320	C₂²⋊C₈	—	7	1	no	—
321	C₂²⋊C₈	C₄×D₇	1	1	yes	characteristic
322	C₂²⋊C₈	C₄×D₇	1	1	yes	characteristic
323	C₄×C₈	—	7	1	no	—
324	C₄×C₈	—	7	1	no	—
325	C₄×C₈	—	7	1	no	—
326	C₄×C₈	—	7	1	no	—
327	C₄×C₈	—	7	1	no	—
328	C₄×C₈	—	7	1	no	—
329	C₄×C₈	—	7	1	no	—
330	C₄×C₈	—	7	1	no	—
331	C₄×C₈	—	7	1	no	—
332	C₄×C₈	C₂²×D₇	1	1	yes	characteristic
333	C₂²×C₇	—	2	1	no	—
334	C₂²×C₇	—	2	1	no	—
335	C₂²×C₇	—	2	1	no	—
336	C₂²×C₇	—	2	1	no	—
337	C₂²×C₇	—	2	1	no	—
338	C₂²×C₇	C₂×M₃₂	1	2	yes	—
339	C₂²×C₇	C₂³×C₈	1	1	yes	characteristic
340	C₂×D₇	—	2	1	no	—
341	C₂×D₇	—	2	1	no	—
342	C₂×D₇	—	2	1	no	—
343	C₄×C₇	—	2	1	no	—
344	C₄×C₇	—	2	1	no	—
345	C₄×C₇	—	2	1	no	—
346	C₄×C₇	—	2	1	no	—
347	C₄×C₇	C₄×#41	1	1	yes	characteristic
348	C₄×C₇	C₂×#131	1	1	yes	characteristic
349	Dic₇	—	2	1	no	—
350	Dic₇	—	2	1	no	—
351	Dic₇	—	2	1	no	—
352	Dic₇	—	2	1	no	—
353	Dic₇	C₂×M₃₂	1	2	yes	—
354	Dic₇	C₂×M₃₂	1	2	yes	—
355	Dic₇	#504	1	2	yes	—
356	#41	—	14	4	no	—
357	C₂×Q₈	—	7	1	no	—
358	C₂×D₄	—	7	1	no	—
359	C₂×D₄	—	7	1	no	—
360	C₂×D₄	C₈×D₇	1	1	yes	characteristic
361	C₂²×C₄	—	7	1	no	—
362	C₂²×C₄	—	7	1	no	—
363	C₂²×C₄	—	7	1	no	—
364	C₂²×C₄	—	7	1	no	—
365	C₂²×C₄	—	7	1	no	—
366	C₂²×C₄	—	7	1	no	—
367	C₂²×C₄	—	7	1	no	—
368	C₂²×C₄	C₂×C₄×D₇	1	1	yes	characteristic
369	C₂²×C₄	C₂×C₄×D₇	1	1	yes	characteristic
370	C₂×C₈	—	2	1	no	—
371	C₂×C₈	—	2	1	no	—
372	C₂×C₈	—	2	1	no	—
373	C₂×C₈	—	2	1	no	—
374	C₂×C₈	—	7	1	no	—
375	C₂×C₈	—	7	1	no	—
376	C₂×C₈	—	7	1	no	—
377	C₂×C₈	—	7	1	no	—
378	C₂×C₈	—	14	2	no	—
379	C₂×C₈	—	14	2	no	—
380	C₂×C₈	—	14	2	no	—
381	C₂×C₈	—	14	1	no	—
382	C₂×C₈	—	14	1	no	—
383	C₂×C₈	C₂×C₄×D₇	1	1	yes	characteristic
384	C₂×C₈	C₂×C₄×D₇	1	1	yes	characteristic
385	C₂×C₈	C₂×C₄×D₇	1	1	yes	characteristic
386	C₂×C₈	C₂³×D₇	1	1	yes	characteristic
387	C₄⋊C₄	—	7	1	no	—
388	C₄⋊C₄	—	7	1	no	—
389	C₄⋊C₄	—	7	1	no	—
390	C₄⋊C₄	—	7	1	no	—
391	C₄⋊C₄	—	7	1	no	—
392	C₄⋊C₄	C₈×D₇	1	1	yes	characteristic
393	C₂²⋊C₄	—	7	1	no	—
394	C₂²⋊C₄	—	7	1	no	—
395	C₂²⋊C₄	—	7	1	no	—
396	C₂²⋊C₄	—	7	1	no	—
397	C₂²⋊C₄	C₈×D₇	1	1	yes	characteristic
398	C₂²⋊C₄	C₈×D₇	1	1	yes	characteristic
399	C₄²	—	7	1	no	—
400	C₄²	—	7	1	no	—
401	C₄²	—	7	1	no	—
402	C₄²	—	7	1	no	—
403	C₄²	—	7	1	no	—
404	C₄²	—	7	1	no	—
405	C₄²	—	7	1	no	—
406	C₄²	—	7	1	no	—
407	C₄²	—	7	1	no	—
408	C₄²	C₂×C₄×D₇	1	1	yes	characteristic
409	C₁₆	—	2	1	no	—
410	C₁₆	—	2	1	no	—
411	C₁₆	—	2	1	no	—
412	C₁₆	—	7	2	no	—
413	C₁₆	—	14	1	no	—
414	C₁₆	—	14	1	no	—
415	C₁₆	—	14	1	no	—
416	C₁₆	#1159	1	2	yes	complemented
417	C₂×C₇	—	2	2	no	—
418	C₂×C₇	—	4	1	no	—
419	C₂×C₇	C₈×#41	1	1	yes	characteristic
420	C₂×C₇	C₂²×M₃₂	1	1	yes	characteristic
421	C₂×C₇	C₂×#504	1	1	yes	characteristic
422	D₇	—	4	1	no	—
423	C₂³	—	7	1	no	—
424	C₂³	C₂×C₈×D₇	1	1	yes	characteristic
425	C₂³	C₂×C₈×D₇	1	1	yes	characteristic
426	Q₈	—	14	2	no	—
427	D₄	—	2	2	no	—
428	D₄	—	14	2	no	—
429	D₄	—	14	2	no	—
430	C₂×C₄	—	2	1	no	—
431	C₂×C₄	—	2	1	no	—
432	C₂×C₄	—	2	1	no	—
433	C₂×C₄	—	2	1	no	—
434	C₂×C₄	—	7	1	no	—
435	C₂×C₄	—	7	1	no	—
436	C₂×C₄	—	7	1	no	—
437	C₂×C₄	—	7	4	no	—
438	C₂×C₄	—	7	1	no	—
439	C₂×C₄	—	7	1	no	—
440	C₂×C₄	—	7	1	no	—
441	C₂×C₄	—	7	1	no	—
442	C₂×C₄	—	14	2	no	—
443	C₂×C₄	—	14	2	no	—
444	C₂×C₄	—	14	2	no	—
445	C₂×C₄	—	14	2	no	—
446	C₂×C₄	—	14	2	no	—
447	C₂×C₄	—	14	1	no	—
448	C₂×C₄	—	14	1	no	—
449	C₂×C₄	C₂×C₈×D₇	1	1	yes	characteristic
450	C₂×C₄	C₂×C₈×D₇	1	1	yes	characteristic
451	C₂×C₄	C₂×C₈×D₇	1	1	yes	characteristic
452	C₂×C₄	C₂×C₈×D₇	1	1	yes	characteristic
453	C₂×C₄	C₂²×C₄×D₇	1	1	yes	characteristic
454	C₈	—	2	1	no	—
455	C₈	—	2	1	no	—
456	C₈	—	2	1	no	—
457	C₈	—	7	2	no	—
458	C₈	—	14	1	no	—
459	C₈	—	14	1	no	—
460	C₈	—	14	1	no	—
461	C₈	C₂×#1159	1	1	yes	characteristic
462	C₈	D₇×#41	1	1	yes	characteristic
463	C₇	#33479	1	1	yes	characteristic, complemented, Sylow
464	C₂²	—	2	1	no	—
465	C₂²	—	2	1	no	—
466	C₂²	—	2	1	no	—
467	C₂²	—	2	1	no	—
468	C₂²	—	2	1	no	—
469	C₂²	—	14	1	no	—
470	C₂²	—	14	1	no	—
471	C₂²	—	14	1	no	—
472	C₂²	D₇×M₃₂	1	2	yes	—
473	C₂²	C₂²×C₈×D₇	1	1	yes	characteristic
474	C₄	—	2	1	no	—
475	C₄	—	2	1	no	—
476	C₄	—	2	1	no	—
477	C₄	—	2	1	no	—
478	C₄	—	7	2	no	—
479	C₄	—	7	2	no	—
480	C₄	—	7	2	no	—
481	C₄	—	14	1	no	—
482	C₄	—	14	1	no	—
483	C₄	—	14	1	no	—
484	C₄	—	14	1	no	—
485	C₄	C₄×#1159	1	1	yes	characteristic
486	C₄	D₇×#131	1	1	yes	characteristic
487	C₂	—	2	2	no	—
488	C₂	—	4	1	no	—
489	C₂	—	28	1	no	—
490	C₂	C₈×#1159	1	1	yes	characteristic
491	C₂	C₂×D₇×M₃₂	1	1	yes	characteristic
492	C₂	D₇×#504	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂×C₈	C₂³×D₇
commutator, socle	C₂²×C₇	C₂³×C₈
Fitting	C₇×#2168	C₂
prime radical	C₂×#1159	C₈
cosocle	C₂×C₇×C₈	C₂⁴
hypercenter	#2168	D₇
hypocenter	C₇	#33479
LCS	G ▷ C₂²×C₇ ▷ C₇
UCS	C₁ ◁ C₂×C₈ ◁ #2168

Complements

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

N	H ≅ G/N	type
2. C₇×#2168	C₂	semidirect
3. #11729184	C₂	semidirect
4. Dic₇×M₃₂	C₂	semidirect
5. #11729161	C₂	semidirect
6. C₂×C₁₆×Dic₇	C₂	semidirect
7. #11728611	C₂	semidirect
8. #11727036	C₂	semidirect
9. #11727028	C₂	semidirect
10. #11726858	C₂	semidirect
11. #11726856	C₂	semidirect
12. #11726846	C₂	semidirect
13. #11726846	C₂	semidirect
14. #11726825	C₂	semidirect
15. #11726822	C₂	semidirect
125. #2168	D₇	semidirect
188. C₇×C₁₆	#41	semidirect
192. C₇⋊C₁₆	#41	semidirect
254. C₂×Dic₇	M₃₂	semidirect
416. C₁₆	#1159	semidirect
463. C₇	#33479	semidirect

Maximal subgroups

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

subgroup	index
C₈×#1159	2
C₇×#2168	2
#11729184	2
Dic₇×M₃₂	2
#11729161	2
C₂×C₁₆×Dic₇	2
#11728611	2
#11727036	2
#11727028	2
#11726858	2
#11726856	2
#11726846	2
#11726825	2
#11726822	2
#33479	7