Subgroups — #13323256

Order 1792.

730 conjugacy classes of subgroups.

The subgroup lattice has 604 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#11737365	C₂	1	1	yes	maximal, characteristic, complemented
2	C₄×D₇×SD₁₆	C₂	1	1	yes	maximal, characteristic
3	#11736871	C₂	1	1	yes	maximal, characteristic
4	C₇×C₈×SD₁₆	C₂	1	1	yes	maximal, characteristic, complemented
5	#11728691	C₂	1	1	yes	maximal, characteristic, complemented
6	SD₁₆×C₇⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
7	#11728593	C₂	1	1	yes	maximal, characteristic, complemented
8	#11726281	C₂	1	1	yes	maximal, characteristic, complemented
9	#11726270	C₂	1	1	yes	maximal, characteristic, complemented
10	#11725985	C₂	1	1	yes	maximal, characteristic, complemented
11	#11725968	C₂	1	1	yes	maximal, characteristic, complemented
12	#11725921	C₂	1	1	yes	maximal, characteristic
13	#11725904	C₂	1	1	yes	maximal, characteristic, complemented
14	C₈×#1132	C₂	1	1	yes	maximal, characteristic, complemented
15	#11725801	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×D₇×SD₁₆	C₄	1	1	yes	characteristic
17	C₄×Q₈×D₇	C₂²	1	1	yes	characteristic
18	C₄×D₄×D₇	C₂²	1	1	yes	characteristic
19	C₇×C₈×Q₈	C₂²	1	1	yes	characteristic, complemented
20	C₄×C₇×SD₁₆	C₂²	1	1	yes	characteristic
21	C₇×C₈×D₄	C₂²	1	1	yes	characteristic
22	SD₁₆×Dic₇	C₄	1	1	yes	characteristic
23	C₈×C₂²⋊D₇	—	2	1	no	—
24	C₂×(C₂×D₇)⋊C₈	—	2	1	no	—
25	C₄×#1143	C₂²	1	1	yes	characteristic
26	Q₈×C₇⋊C₈	C₂²	1	1	yes	characteristic, complemented
27	C₄×#1142	C₂²	1	1	yes	characteristic
28	D₄×C₇⋊C₈	C₂²	1	1	yes	characteristic
29	D₇×#106	C₄	1	1	yes	characteristic
30	#89624	C₄	1	1	yes	characteristic
31	#89606	C₂²	1	1	yes	characteristic
32	#89605	—	2	1	no	—
33	#89605	C₂²	1	1	yes	characteristic
34	#89605	C₂²	1	1	yes	characteristic
35	#89602	—	2	1	no	—
36	#89602	C₂²	1	1	yes	characteristic, complemented
37	D₇×#103	C₄	1	1	yes	characteristic
38	#89560	C₄	1	1	yes	characteristic
39	D₇×#102	C₄	1	1	yes	characteristic
40	#89530	C₄	1	1	yes	characteristic
41	(C₂²⋊D₇)⋊C₈	—	2	1	no	—
42	D₇×C₂²⋊C₈	—	2	1	no	—
43	C₄×#1132	C₂²	1	1	yes	characteristic
44	C₈×D₂₈	C₂²	1	1	yes	characteristic
45	#89457	—	2	1	no	—
46	#89457	C₂²	1	1	yes	characteristic
47	#89457	C₂²	1	1	yes	characteristic
48	C₄×C₈×D₇	C₂²	1	1	yes	characteristic
49	C₈×Dic₁₄	—	2	1	no	—
50	C₈×Dic₁₄	C₂²	1	1	yes	characteristic, complemented
51	C₇×#334	C₂²	1	1	yes	characteristic, complemented
52	C₇×Q₈⋊C₈	C₂²	1	1	yes	characteristic, complemented
53	C₇×D₄⋊C₈	C₂²	1	1	yes	characteristic
54	C₇×C₈²	C₂²	1	1	yes	characteristic, complemented
55	Q₈⋊(C₇⋊C₈)	C₂²	1	1	yes	characteristic, complemented
56	D₄⋊(C₇⋊C₈)	C₂²	1	1	yes	characteristic
57	#89279	C₂²	1	1	yes	characteristic, complemented
58	#89278	C₂²	1	1	yes	characteristic
59	#89274	C₂²	1	1	yes	characteristic, complemented
60	#89274	C₂²	1	1	yes	characteristic, complemented
61	#89254	C₂²	1	1	yes	characteristic
62	#89252	C₂²	1	1	yes	characteristic, complemented
63	#89251	C₂²	1	1	yes	characteristic, complemented
64	#89249	C₂²	1	1	yes	characteristic, complemented
65	#89249	C₂²	1	1	yes	characteristic, complemented
66	C₈×C₇⋊C₈	C₂²	1	1	yes	characteristic, complemented
67	#17855	—	7	1	no	maximal, Sylow
68	C₂×Q₈×D₇	C₂×C₄	1	1	yes	characteristic
69	C₂×D₄×D₇	C₂×C₄	1	1	yes	characteristic
70	C₂²×C₄×D₇	—	2	1	no	—
71	C₂×C₇×SD₁₆	C₂×C₄	1	1	yes	characteristic
72	C₂²×C₇×C₈	—	2	1	no	—
73	C₄×C₇×Q₈	C₂³	1	1	yes	characteristic
74	C₄×C₇×D₄	C₂³	1	1	yes	characteristic
75	Q₈×Dic₇	C₂×C₄	1	1	yes	characteristic
76	C₂×#1143	C₂×C₄	1	1	yes	characteristic
77	D₄×Dic₇	C₂×C₄	1	1	yes	characteristic
78	C₂×#1142	C₂×C₄	1	1	yes	characteristic
79	C₄×C₂²⋊D₇	—	2	1	no	—
80	C₂²×C₇⋊C₈	—	2	1	no	—
81	D₇×SD₁₆	C₈	1	8	yes	complemented
82	C₂×#1132	C₂×C₄	1	1	yes	characteristic
83	C₂×C₈×D₇	—	2	1	no	—
84	C₂×C₈×D₇	—	2	1	no	—
85	C₂×C₈×D₇	C₂×C₄	1	1	yes	characteristic
86	C₂×C₈×D₇	C₂×C₄	1	1	yes	characteristic
87	#6456	C₂×C₄	1	1	yes	characteristic
88	D₇×C₄⋊C₄	—	2	1	no	—
89	D₇×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
90	D₇×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
91	#6450	—	2	1	no	—
92	#6450	C₂×C₄	1	1	yes	characteristic
93	(C₂²⋊D₇)⋊C₄	—	2	1	no	—
94	D₇×C₂²⋊C₄	—	2	1	no	—
95	C₄×D₂₈	C₂³	1	1	yes	characteristic
96	C₄²×D₇	—	2	1	no	—
97	C₄²×D₇	C₂³	1	1	yes	characteristic
98	C₄×Dic₁₄	—	2	1	no	—
99	C₄×Dic₁₄	C₂³	1	1	yes	characteristic
100	C₇×#106	C₂×C₄	1	1	yes	characteristic
101	C₇×C₄⋊C₈	—	2	1	no	—
102	C₇×C₄⋊C₈	C₂³	1	1	yes	characteristic
103	C₇×C₄⋊C₈	C₂³	1	1	yes	characteristic
104	C₇×#103	C₂×C₄	1	1	yes	characteristic
105	C₇×#102	C₂×C₄	1	1	yes	characteristic
106	C₇×C₂²⋊C₈	—	2	1	no	—
107	C₄×C₇×C₈	—	2	1	no	—
108	C₄×C₇×C₈	C₂³	1	1	yes	characteristic
109	C₄×C₇×C₈	C₂³	1	1	yes	characteristic
110	C₄×C₇×C₈	C₂³	1	1	yes	characteristic
111	#6409	C₂×C₄	1	1	yes	characteristic
112	#6406	C₂×C₄	1	1	yes	characteristic
113	C₂²⋊(C₇⋊C₈)	—	2	1	no	—
114	#6395	C₂×C₄	1	1	yes	characteristic
115	(C₂×D₇)⋊C₈	—	2	1	no	—
116	(C₂×D₇)⋊C₈	—	2	1	no	—
117	(C₂×D₇)⋊C₈	—	2	1	no	—
118	(C₂×D₇)⋊C₈	—	2	1	no	—
119	(C₂×D₇)⋊C₈	—	2	1	no	—
120	(C₂×D₇)⋊C₈	D₄	1	1	yes	characteristic
121	(C₂×D₇)⋊C₈	D₄	1	1	yes	characteristic
122	#6391	C₂×C₄	1	1	yes	characteristic
123	#6390	C₂×C₄	1	1	yes	characteristic
124	Dic₇⋊C₈	—	2	1	no	—
125	Dic₇⋊C₈	—	2	1	no	—
126	Dic₇⋊C₈	—	2	1	no	—
127	Dic₇⋊C₈	D₄	1	1	yes	characteristic
128	Dic₇⋊C₈	D₄	1	1	yes	characteristic
129	C₈×Dic₇	—	2	1	no	—
130	C₈×Dic₇	—	2	1	no	—
131	C₈×Dic₇	—	2	1	no	—
132	C₈×Dic₇	—	2	1	no	—
133	C₈×Dic₇	C₂×C₄	1	1	yes	characteristic
134	C₈×Dic₇	C₂×C₄	1	1	yes	characteristic
135	#6384	C₂×C₄	1	1	yes	characteristic
136	#6383	C₂×C₄	1	1	yes	characteristic
137	#6382	C₂×C₄	1	1	yes	characteristic
138	#6382	C₂×C₄	1	1	yes	characteristic
139	C₄⋊(C₇⋊C₈)	—	2	1	no	—
140	C₄⋊(C₇⋊C₈)	C₂³	1	1	yes	characteristic
141	C₄⋊(C₇⋊C₈)	C₂³	1	1	yes	characteristic
142	C₄×C₇⋊C₈	—	2	1	no	—
143	C₄×C₇⋊C₈	C₂³	1	1	yes	characteristic
144	C₄×C₇⋊C₈	C₂³	1	1	yes	characteristic
145	C₄×C₇⋊C₈	C₂³	1	1	yes	characteristic
146	#2982	—	7	1	no	—
147	#2972	—	7	1	no	—
148	C₂×C₄×SD₁₆	—	7	1	no	—
149	SD₁₆⋊C₈	—	7	1	no	—
150	SD₁₆⋊C₈	—	7	1	no	—
151	SD₁₆⋊C₈	—	7	1	no	—
152	SD₁₆⋊C₈	—	7	1	no	—
153	C₈×SD₁₆	—	7	1	no	—
154	C₈×SD₁₆	—	7	1	no	—
155	C₈×SD₁₆	—	7	1	no	—
156	C₈×SD₁₆	D₇	1	1	yes	characteristic, complemented
157	#1564	—	7	1	no	—
158	#1479	—	7	1	no	—
159	#1478	—	7	1	no	—
160	#1450	—	7	1	no	—
161	C₂³×D₇	—	2	1	no	—
162	C₂×C₇×Q₈	C₂²×C₄	1	1	yes	characteristic
163	C₂×C₇×D₄	C₂²×C₄	1	1	yes	characteristic
164	C₂²×C₄×C₇	—	2	1	no	—
165	C₂×C₂²⋊D₇	—	2	1	no	—
166	C₂²×Dic₇	—	2	1	no	—
167	Q₈×D₇	—	2	2	no	—
168	Q₈×D₇	C₂×C₈	1	4	yes	complemented
169	D₄×D₇	—	2	2	no	—
170	D₄×D₇	C₂×C₈	1	4	yes	—
171	C₂×D₂₈	C₂²×C₄	1	1	yes	characteristic
172	C₂×C₄×D₇	—	2	1	no	—
173	C₂×C₄×D₇	—	2	1	no	—
174	C₂×C₄×D₇	—	2	1	no	—
175	C₂×C₄×D₇	—	2	1	no	—
176	C₂×C₄×D₇	—	2	1	no	—
177	C₂×C₄×D₇	—	8	1	no	—
178	C₂×C₄×D₇	—	8	1	no	—
179	C₂×C₄×D₇	C₂²×C₄	1	1	yes	characteristic
180	C₂×C₄×D₇	C₂×D₄	1	1	yes	characteristic
181	C₂×C₄×D₇	#41	1	1	yes	characteristic
182	C₂×Dic₁₄	—	2	1	no	—
183	C₂×Dic₁₄	C₂²×C₄	1	1	yes	characteristic
184	C₇×SD₁₆	C₂×C₈	1	4	yes	complemented
185	C₂×C₇×C₈	—	2	1	no	—
186	C₂×C₇×C₈	—	2	1	no	—
187	C₂×C₇×C₈	—	2	1	no	—
188	C₂×C₇×C₈	—	8	1	no	—
189	C₂×C₇×C₈	C₂²×C₄	1	1	yes	characteristic
190	C₂×C₇×C₈	C₂²×C₄	1	1	yes	characteristic
191	C₂×C₇×C₈	C₂×D₄	1	1	yes	characteristic
192	C₂×C₇×C₈	C₂×D₄	1	1	yes	characteristic
193	C₇×C₄⋊C₄	—	2	1	no	—
194	C₇×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
195	C₇×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
196	C₇×C₂²⋊C₄	—	2	1	no	—
197	C₄²×C₇	—	2	1	no	—
198	C₄²×C₇	C₂⁴	1	1	yes	characteristic
199	C₂²⋊Dic₇	—	2	1	no	—
200	#1143	C₂×C₈	1	4	yes	complemented
201	#1142	C₂×C₈	1	4	yes	complemented
202	(C₂×D₇)⋊C₄	—	2	1	no	—
203	(C₂×D₇)⋊C₄	—	2	1	no	—
204	C₄⋊Dic₇	—	2	1	no	—
205	C₄⋊Dic₇	C₂²×C₄	1	1	yes	characteristic
206	C₄⋊Dic₇	C₂²×C₄	1	1	yes	characteristic
207	Dic₇⋊C₄	—	2	1	no	—
208	Dic₇⋊C₄	—	2	1	no	—
209	Dic₇⋊C₄	—	2	1	no	—
210	Dic₇⋊C₄	—	2	1	no	—
211	C₄×Dic₇	—	2	1	no	—
212	C₄×Dic₇	—	2	1	no	—
213	C₄×Dic₇	—	2	1	no	—
214	C₄×Dic₇	C₂²×C₄	1	1	yes	characteristic
215	C₄×Dic₇	C₂×D₄	1	1	yes	characteristic
216	C₄×Dic₇	#41	1	1	yes	characteristic
217	C₂×C₇⋊C₈	—	2	1	no	—
218	C₂×C₇⋊C₈	—	2	1	no	—
219	C₂×C₇⋊C₈	—	2	1	no	—
220	C₂×C₇⋊C₈	—	8	1	no	—
221	C₂×C₇⋊C₈	C₂²×C₄	1	1	yes	characteristic
222	C₂×C₇⋊C₈	C₂²×C₄	1	1	yes	characteristic
223	C₂×C₇⋊C₈	C₂×D₄	1	1	yes	characteristic
224	C₂×C₇⋊C₈	C₂×D₄	1	1	yes	characteristic
225	#1132	C₂×C₈	1	4	yes	complemented
226	C₈×D₇	—	2	2	no	—
227	C₈×D₇	—	8	1	no	—
228	C₈×D₇	—	8	1	no	—
229	C₈×D₇	C₂×C₈	1	4	yes	complemented
230	C₂²×SD₁₆	—	7	1	no	—
231	C₂×C₄×Q₈	—	7	1	no	—
232	C₂×C₄×D₄	—	7	1	no	—
233	C₈×Q₈	—	7	1	no	—
234	C₈×Q₈	—	7	1	no	—
235	C₈×Q₈	—	7	1	no	—
236	C₈×Q₈	—	14	1	no	—
237	C₈×Q₈	—	14	1	no	—
238	C₈×Q₈	C₂×D₇	1	1	yes	characteristic, complemented
239	C₄×SD₁₆	—	7	1	no	—
240	C₄×SD₁₆	—	7	1	no	—
241	C₄×SD₁₆	—	7	1	no	—
242	C₄×SD₁₆	—	7	1	no	—
243	C₄×SD₁₆	—	7	1	no	—
244	C₄×SD₁₆	—	7	1	no	—
245	C₄×SD₁₆	—	7	1	no	—
246	C₄×SD₁₆	C₂×D₇	1	1	yes	characteristic
247	C₈×D₄	—	7	1	no	—
248	C₈×D₄	—	7	1	no	—
249	C₈×D₄	—	7	1	no	—
250	C₈×D₄	—	14	1	no	—
251	C₈×D₄	—	14	1	no	—
252	C₈×D₄	C₂×D₇	1	1	yes	characteristic
253	#431	—	7	1	no	—
254	#431	—	7	1	no	—
255	#431	—	7	1	no	—
256	#431	—	7	1	no	—
257	#431	—	14	1	no	—
258	#431	—	14	1	no	—
259	C₂×#106	—	7	1	no	—
260	C₂×#103	—	7	1	no	—
261	C₂×#102	—	7	1	no	—
262	C₂×C₂²⋊C₈	—	14	1	no	—
263	C₂×C₂²⋊C₈	—	14	1	no	—
264	C₂×C₄×C₈	—	7	1	no	—
265	#335	—	7	1	no	—
266	#335	—	7	1	no	—
267	#334	—	7	1	no	—
268	#334	C₂×D₇	1	1	yes	characteristic, complemented
269	Q₈⋊C₈	—	7	1	no	—
270	Q₈⋊C₈	—	7	1	no	—
271	Q₈⋊C₈	—	7	1	no	—
272	Q₈⋊C₈	C₂×D₇	1	1	yes	characteristic, complemented
273	D₄⋊C₈	—	7	1	no	—
274	D₄⋊C₈	—	7	1	no	—
275	D₄⋊C₈	—	7	1	no	—
276	D₄⋊C₈	C₂×D₇	1	1	yes	characteristic
277	#322	—	7	1	no	—
278	#322	—	7	1	no	—
279	C₈²	—	7	1	no	—
280	C₈²	C₂×D₇	1	1	yes	characteristic, complemented
281	C₂³×C₇	—	2	1	no	—
282	C₂²×D₇	—	2	1	no	—
283	C₂²×D₇	—	2	4	no	—
284	C₂²×D₇	—	8	1	no	—
285	C₂²×D₇	—	8	1	no	—
286	C₂²×D₇	C₄×D₄	1	1	yes	characteristic
287	C₇×Q₈	—	2	1	no	—
288	C₇×Q₈	C₂²×C₈	1	2	yes	—
289	C₇×D₄	—	2	1	no	—
290	C₇×D₄	C₂²×C₈	1	2	yes	—
291	C₂×C₄×C₇	—	2	1	no	—
292	C₂×C₄×C₇	—	2	1	no	—
293	C₂×C₄×C₇	—	2	1	no	—
294	C₂×C₄×C₇	—	4	1	no	—
295	C₂×C₄×C₇	—	4	1	no	—
296	C₂×C₄×C₇	C₂³×C₄	1	1	yes	characteristic
297	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
298	C₂×C₄×C₇	C₂×#41	1	1	yes	characteristic
299	C₂²⋊D₇	—	2	4	no	—
300	C₂×Dic₇	—	2	1	no	—
301	C₂×Dic₇	—	2	1	no	—
302	C₂×Dic₇	—	2	1	no	—
303	C₂×Dic₇	—	8	1	no	—
304	C₂×Dic₇	C₄×D₄	1	1	yes	characteristic
305	C₂×Dic₇	C₄×D₄	1	1	yes	characteristic
306	C₂×Dic₇	C₄×D₄	1	1	yes	characteristic
307	D₂₈	—	2	1	no	—
308	D₂₈	C₂²×C₈	1	2	yes	—
309	C₄×D₇	—	2	4	no	—
310	C₄×D₇	—	2	1	no	—
311	C₄×D₇	—	2	1	no	—
312	C₄×D₇	—	4	1	no	—
313	C₄×D₇	—	4	1	no	—
314	C₄×D₇	—	4	1	no	—
315	C₄×D₇	—	8	1	no	—
316	C₄×D₇	—	8	1	no	—
317	C₄×D₇	—	8	1	no	—
318	C₄×D₇	C₂²×C₈	1	2	yes	—
319	C₄×D₇	#131	1	2	yes	—
320	Dic₁₄	—	2	1	no	—
321	Dic₁₄	—	2	4	no	—
322	Dic₁₄	C₂²×C₈	1	2	yes	—
323	C₇×C₈	—	2	1	no	—
324	C₇×C₈	—	2	1	no	—
325	C₇×C₈	—	2	1	no	—
326	C₇×C₈	—	4	1	no	—
327	C₇×C₈	—	4	1	no	—
328	C₇×C₈	—	4	1	no	—
329	C₇×C₈	C₂²×C₈	1	2	yes	—
330	C₇⋊C₈	—	2	1	no	—
331	C₇⋊C₈	—	2	1	no	—
332	C₇⋊C₈	—	2	1	no	—
333	C₇⋊C₈	—	4	1	no	—
334	C₇⋊C₈	—	4	1	no	—
335	C₇⋊C₈	—	4	1	no	—
336	C₇⋊C₈	C₂²×C₈	1	2	yes	—
337	C₂²×Q₈	—	7	1	no	—
338	C₂²×D₄	—	7	1	no	—
339	C₂³×C₄	—	14	1	no	—
340	C₂×SD₁₆	—	7	1	no	—
341	C₂×SD₁₆	—	7	1	no	—
342	C₂×SD₁₆	—	7	8	no	—
343	C₂×SD₁₆	—	7	1	no	—
344	C₂×SD₁₆	C₄×D₇	1	1	yes	characteristic
345	C₂²×C₈	—	2	1	no	—
346	C₂²×C₈	—	7	1	no	—
347	C₂²×C₈	—	7	1	no	—
348	C₂²×C₈	—	14	1	no	—
349	C₂²×C₈	—	14	1	no	—
350	C₂²×C₈	—	14	1	no	—
351	C₄×Q₈	—	7	1	no	—
352	C₄×Q₈	—	7	1	no	—
353	C₄×Q₈	—	7	1	no	—
354	C₄×Q₈	—	14	1	no	—
355	C₄×Q₈	—	14	1	no	—
356	C₄×Q₈	C₂²×D₇	1	1	yes	characteristic
357	C₄×D₄	—	7	1	no	—
358	C₄×D₄	—	7	1	no	—
359	C₄×D₄	—	7	1	no	—
360	C₄×D₄	—	14	1	no	—
361	C₄×D₄	—	14	1	no	—
362	C₄×D₄	C₂²×D₇	1	1	yes	characteristic
363	C₂×C₄⋊C₄	—	7	1	no	—
364	C₂×C₄⋊C₄	—	7	1	no	—
365	C₂×C₄⋊C₄	—	14	1	no	—
366	C₂×C₂²⋊C₄	—	14	1	no	—
367	C₂×C₄²	—	7	1	no	—
368	C₂×C₄²	—	14	1	no	—
369	#106	—	7	1	no	—
370	#106	—	7	1	no	—
371	#106	—	7	1	no	—
372	#106	C₄×D₇	1	1	yes	characteristic
373	C₄⋊C₈	—	2	1	no	—
374	C₄⋊C₈	—	7	1	no	—
375	C₄⋊C₈	—	7	1	no	—
376	C₄⋊C₈	—	7	1	no	—
377	C₄⋊C₈	—	7	1	no	—
378	C₄⋊C₈	—	14	1	no	—
379	C₄⋊C₈	—	14	1	no	—
380	C₄⋊C₈	—	14	1	no	—
381	C₄⋊C₈	—	14	1	no	—
382	C₄⋊C₈	C₂²×D₇	1	1	yes	characteristic
383	C₄⋊C₈	C₂²×D₇	1	1	yes	characteristic
384	#103	—	7	1	no	—
385	#103	—	7	1	no	—
386	#103	—	7	1	no	—
387	#103	C₄×D₇	1	1	yes	characteristic
388	#102	—	7	1	no	—
389	#102	—	7	1	no	—
390	#102	—	7	1	no	—
391	#102	C₄×D₇	1	1	yes	characteristic
392	C₂²⋊C₈	—	2	1	no	—
393	C₂²⋊C₈	—	7	1	no	—
394	C₂²⋊C₈	—	7	1	no	—
395	C₂²⋊C₈	—	14	1	no	—
396	C₂²⋊C₈	—	14	1	no	—
397	C₂²⋊C₈	—	14	1	no	—
398	C₂²⋊C₈	—	14	1	no	—
399	C₂²⋊C₈	—	14	1	no	—
400	C₂²⋊C₈	—	14	1	no	—
401	C₄×C₈	—	2	1	no	—
402	C₄×C₈	—	7	1	no	—
403	C₄×C₈	—	7	1	no	—
404	C₄×C₈	—	7	1	no	—
405	C₄×C₈	—	7	1	no	—
406	C₄×C₈	—	7	1	no	—
407	C₄×C₈	—	14	1	no	—
408	C₄×C₈	—	14	1	no	—
409	C₄×C₈	—	14	1	no	—
410	C₄×C₈	—	14	1	no	—
411	C₄×C₈	—	14	1	no	—
412	C₄×C₈	C₂²×D₇	1	1	yes	characteristic
413	C₄×C₈	C₂²×D₇	1	1	yes	characteristic
414	C₄×C₈	C₂²×D₇	1	1	yes	characteristic
415	C₂²×C₇	—	2	2	no	—
416	C₂²×C₇	—	4	1	no	—
417	C₂²×C₇	—	4	1	no	—
418	C₂²×C₇	C₂×C₄×D₄	1	1	yes	characteristic
419	C₂×D₇	—	2	1	no	—
420	C₂×D₇	—	2	1	no	—
421	C₂×D₇	—	2	2	no	—
422	C₂×D₇	—	4	1	no	—
423	C₂×D₇	—	4	1	no	—
424	C₂×D₇	—	8	4	no	—
425	C₂×D₇	C₈×D₄	1	2	yes	—
426	C₄×C₇	—	2	2	no	—
427	C₄×C₇	—	2	1	no	—
428	C₄×C₇	—	4	1	no	—
429	C₄×C₇	—	4	1	no	—
430	C₄×C₇	C₂³×C₈	1	1	yes	characteristic
431	C₄×C₇	C₂×#131	1	1	yes	characteristic
432	C₄×C₇	#577	1	1	yes	characteristic
433	C₄×C₇	#577	1	1	yes	characteristic
434	Dic₇	—	2	2	no	—
435	Dic₇	—	2	1	no	—
436	Dic₇	—	2	1	no	—
437	Dic₇	—	4	1	no	—
438	Dic₇	—	4	1	no	—
439	Dic₇	C₈×D₄	1	2	yes	—
440	C₂⁴	—	14	1	no	—
441	C₂×Q₈	—	7	4	no	—
442	C₂×Q₈	—	7	1	no	—
443	C₂×Q₈	—	14	1	no	—
444	C₂×Q₈	—	14	2	no	—
445	C₂×Q₈	C₂×C₄×D₇	1	1	yes	characteristic
446	C₂×D₄	—	7	4	no	—
447	C₂×D₄	—	7	1	no	—
448	C₂×D₄	—	14	2	no	—
449	C₂×D₄	—	14	1	no	—
450	C₂×D₄	C₂×C₄×D₇	1	1	yes	characteristic
451	C₂²×C₄	—	2	1	no	—
452	C₂²×C₄	—	7	1	no	—
453	C₂²×C₄	—	7	1	no	—
454	C₂²×C₄	—	7	1	no	—
455	C₂²×C₄	—	14	1	no	—
456	C₂²×C₄	—	14	1	no	—
457	C₂²×C₄	—	14	1	no	—
458	C₂²×C₄	—	14	1	no	—
459	C₂²×C₄	—	14	1	no	—
460	C₂²×C₄	—	14	1	no	—
461	C₂²×C₄	—	56	1	no	—
462	C₂²×C₄	—	56	1	no	—
463	SD₁₆	—	7	4	no	—
464	SD₁₆	—	7	4	no	—
465	SD₁₆	—	7	4	no	—
466	SD₁₆	C₈×D₇	1	4	yes	complemented
467	C₂×C₈	—	2	1	no	—
468	C₂×C₈	—	2	1	no	—
469	C₂×C₈	—	2	1	no	—
470	C₂×C₈	—	7	1	no	—
471	C₂×C₈	—	7	4	no	—
472	C₂×C₈	—	7	1	no	—
473	C₂×C₈	—	7	1	no	—
474	C₂×C₈	—	7	1	no	—
475	C₂×C₈	—	8	1	no	—
476	C₂×C₈	—	14	2	no	—
477	C₂×C₈	—	14	1	no	—
478	C₂×C₈	—	14	1	no	—
479	C₂×C₈	—	14	1	no	—
480	C₂×C₈	—	56	1	no	—
481	C₂×C₈	—	56	1	no	—
482	C₂×C₈	—	56	1	no	—
483	C₂×C₈	C₂×C₄×D₇	1	1	yes	characteristic
484	C₂×C₈	C₂×C₄×D₇	1	1	yes	characteristic
485	C₂×C₈	D₄×D₇	1	1	yes	characteristic
486	C₂×C₈	D₄×D₇	1	1	yes	characteristic
487	C₄⋊C₄	—	2	1	no	—
488	C₄⋊C₄	—	7	1	no	—
489	C₄⋊C₄	—	7	1	no	—
490	C₄⋊C₄	—	14	1	no	—
491	C₄⋊C₄	—	14	1	no	—
492	C₄⋊C₄	—	14	1	no	—
493	C₄⋊C₄	—	14	1	no	—
494	C₄⋊C₄	—	14	1	no	—
495	C₄⋊C₄	C₂×C₄×D₇	1	1	yes	characteristic
496	C₄⋊C₄	C₂×C₄×D₇	1	1	yes	characteristic
497	C₂²⋊C₄	—	2	1	no	—
498	C₂²⋊C₄	—	14	1	no	—
499	C₂²⋊C₄	—	14	1	no	—
500	C₂²⋊C₄	—	14	1	no	—
501	C₄²	—	2	1	no	—
502	C₄²	—	7	1	no	—
503	C₄²	—	7	1	no	—
504	C₄²	—	7	1	no	—
505	C₄²	—	14	1	no	—
506	C₄²	—	14	1	no	—
507	C₄²	—	14	1	no	—
508	C₄²	C₂³×D₇	1	1	yes	characteristic
509	C₂×C₇	—	4	2	no	—
510	C₂×C₇	C₂×C₈×D₄	1	1	yes	characteristic
511	C₂×C₇	#2949	1	1	yes	characteristic
512	C₂×C₇	#2957	1	1	yes	characteristic
513	D₇	—	2	2	no	—
514	D₇	—	4	2	no	—
515	C₂³	—	2	1	no	—
516	C₂³	—	7	1	no	—
517	C₂³	—	14	4	no	—
518	C₂³	—	14	1	no	—
519	C₂³	—	56	1	no	—
520	C₂³	—	56	1	no	—
521	Q₈	—	2	1	no	—
522	Q₈	—	7	2	no	—
523	Q₈	—	14	4	no	—
524	Q₈	—	14	1	no	—
525	Q₈	C₂×C₈×D₇	1	2	yes	—
526	D₄	—	2	1	no	—
527	D₄	—	7	2	no	—
528	D₄	—	14	4	no	—
529	D₄	—	14	1	no	—
530	D₄	C₂×C₈×D₇	1	2	yes	—
531	C₂×C₄	—	2	1	no	—
532	C₂×C₄	—	2	1	no	—
533	C₂×C₄	—	2	1	no	—
534	C₂×C₄	—	4	1	no	—
535	C₂×C₄	—	4	1	no	—
536	C₂×C₄	—	7	1	no	—
537	C₂×C₄	—	7	2	no	—
538	C₂×C₄	—	7	2	no	—
539	C₂×C₄	—	7	1	no	—
540	C₂×C₄	—	7	1	no	—
541	C₂×C₄	—	14	4	no	—
542	C₂×C₄	—	14	1	no	—
543	C₂×C₄	—	14	1	no	—
544	C₂×C₄	—	14	1	no	—
545	C₂×C₄	—	14	1	no	—
546	C₂×C₄	—	14	1	no	—
547	C₂×C₄	—	28	1	no	—
548	C₂×C₄	—	28	1	no	—
549	C₂×C₄	—	28	1	no	—
550	C₂×C₄	—	56	1	no	—
551	C₂×C₄	—	56	1	no	—
552	C₂×C₄	—	56	1	no	—
553	C₂×C₄	—	56	1	no	—
554	C₂×C₄	C₂²×C₄×D₇	1	1	yes	characteristic
555	C₂×C₄	C₂×D₄×D₇	1	1	yes	characteristic
556	C₂×C₄	D₇×#41	1	1	yes	characteristic
557	C₈	—	2	1	no	—
558	C₈	—	2	1	no	—
559	C₈	—	2	1	no	—
560	C₈	—	4	1	no	—
561	C₈	—	4	1	no	—
562	C₈	—	4	1	no	—
563	C₈	—	7	2	no	—
564	C₈	—	14	1	no	—
565	C₈	—	14	1	no	—
566	C₈	—	14	1	no	—
567	C₈	—	28	1	no	—
568	C₈	—	28	1	no	—
569	C₈	—	28	1	no	—
570	C₈	C₂×C₈×D₇	1	2	yes	—
571	C₇	#17855	1	1	yes	characteristic, complemented, Sylow
572	C₂²	—	2	2	no	—
573	C₂²	—	4	1	no	—
574	C₂²	—	4	1	no	—
575	C₂²	—	7	2	no	—
576	C₂²	—	14	1	no	—
577	C₂²	—	14	1	no	—
578	C₂²	—	14	2	no	—
579	C₂²	—	28	1	no	—
580	C₂²	—	28	1	no	—
581	C₂²	—	56	4	no	—
582	C₂²	C₄×D₄×D₇	1	1	yes	characteristic
583	C₄	—	2	2	no	—
584	C₄	—	2	1	no	—
585	C₄	—	4	1	no	—
586	C₄	—	4	1	no	—
587	C₄	—	7	2	no	—
588	C₄	—	14	1	no	—
589	C₄	—	14	2	no	—
590	C₄	—	14	1	no	—
591	C₄	—	28	1	no	—
592	C₄	—	28	1	no	—
593	C₄	C₂²×C₈×D₇	1	1	yes	characteristic
594	C₄	D₇×#131	1	1	yes	characteristic
595	C₄	#90453	1	1	yes	characteristic
596	C₄	#90461	1	1	yes	characteristic
597	C₂	—	4	2	no	—
598	C₂	—	14	2	no	—
599	C₂	—	28	2	no	—
600	C₂	C₈×D₄×D₇	1	1	yes	characteristic
601	C₂	#11737094	1	1	yes	characteristic
602	C₂	#11737335	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂×D₄×D₇
commutator	C₄×C₇	C₂³×C₈
Frattini	C₄²	C₂³×D₇
Fitting	C₇×C₈×SD₁₆	C₂
socle	C₂²×C₇	C₂×C₄×D₄
prime radical	C₂×D₄×D₇	C₂×C₄
cosocle	C₄²×C₇	C₂⁴
hypercenter	C₈×SD₁₆	D₇
hypocenter	C₇	#17855
LCS	G ▷ C₄×C₇ ▷ C₂×C₇ ▷ C₇
UCS	C₁ ◁ C₂×C₄ ◁ C₄×C₈ ◁ C₈×SD₁₆

Complements

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

N	H ≅ G/N	type
1. #11737365	C₂	semidirect
4. C₇×C₈×SD₁₆	C₂	semidirect
5. #11728691	C₂	semidirect
6. SD₁₆×C₇⋊C₈	C₂	semidirect
7. #11728593	C₂	semidirect
8. #11726281	C₂	semidirect
9. #11726270	C₂	semidirect
10. #11725985	C₂	semidirect
11. #11725968	C₂	semidirect
13. #11725904	C₂	semidirect
14. C₈×#1132	C₂	semidirect
15. #11725801	C₂	semidirect
19. C₇×C₈×Q₈	C₂²	semidirect
26. Q₈×C₇⋊C₈	C₂²	semidirect
36. #89602	C₂²	semidirect
50. C₈×Dic₁₄	C₂²	semidirect
51. C₇×#334	C₂²	semidirect
52. C₇×Q₈⋊C₈	C₂²	semidirect
54. C₇×C₈²	C₂²	semidirect
55. Q₈⋊(C₇⋊C₈)	C₂²	semidirect
57. #89279	C₂²	semidirect
59. #89274	C₂²	semidirect
60. #89274	C₂²	semidirect
62. #89252	C₂²	semidirect
63. #89251	C₂²	semidirect
64. #89249	C₂²	semidirect
65. #89249	C₂²	semidirect
66. C₈×C₇⋊C₈	C₂²	semidirect
81. D₇×SD₁₆	C₈	semidirect
156. C₈×SD₁₆	D₇	semidirect
168. Q₈×D₇	C₂×C₈	semidirect
184. C₇×SD₁₆	C₂×C₈	semidirect
200. #1143	C₂×C₈	semidirect
201. #1142	C₂×C₈	semidirect
225. #1132	C₂×C₈	semidirect
229. C₈×D₇	C₂×C₈	semidirect
238. C₈×Q₈	C₂×D₇	semidirect
268. #334	C₂×D₇	semidirect
272. Q₈⋊C₈	C₂×D₇	semidirect
280. C₈²	C₂×D₇	semidirect
466. SD₁₆	C₈×D₇	semidirect
571. C₇	#17855	semidirect

Maximal subgroups

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

subgroup	index
#11737365	2
C₄×D₇×SD₁₆	2
#11736871	2
C₇×C₈×SD₁₆	2
#11728691	2
SD₁₆×C₇⋊C₈	2
#11728593	2
#11726281	2
#11726270	2
#11725985	2
#11725968	2
#11725921	2
#11725904	2
C₈×#1132	2
#11725801	2
#17855	7