Subgroups — #13325499

Order 1792.

668 conjugacy classes of subgroups.

The subgroup lattice has 606 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#11737366	C₂	1	1	yes	maximal, characteristic, complemented
2	C₄×D₇×SD₁₆	C₂	1	1	yes	maximal, characteristic
3	#11736987	C₂	1	1	yes	maximal, characteristic
4	C₇×#1583	C₂	1	1	yes	maximal, characteristic, complemented
5	#11728691	C₂	1	1	yes	maximal, characteristic, complemented
6	#11728650	C₂	1	1	yes	maximal, characteristic, complemented
7	#11728614	C₂	1	1	yes	maximal, characteristic, complemented
8	#11726284	C₂	1	1	yes	maximal, characteristic, complemented
9	#11726273	C₂	1	1	yes	maximal, characteristic, complemented
10	#11725993	C₂	1	1	yes	maximal, characteristic, complemented
11	#11725968	C₂	1	1	yes	maximal, characteristic, complemented
12	#11725929	C₂	1	1	yes	maximal, characteristic
13	#11725916	C₂	1	1	yes	maximal, characteristic, complemented
14	#11725833	C₂	1	1	yes	maximal, characteristic, complemented
15	#11725824	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×#436	C₂²	1	1	yes	characteristic
22	SD₁₆×Dic₇	C₄	1	1	yes	characteristic
23	#89899	—	2	1	no	—
24	#89898	—	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	#89784	C₂²	1	1	yes	characteristic
29	D₇×#106	C₄	1	1	yes	characteristic
30	#89624	C₄	1	1	yes	characteristic
31	#89607	—	2	1	no	—
32	#89607	C₂²	1	1	yes	characteristic
33	#89607	C₂²	1	1	yes	characteristic
34	#89606	C₂²	1	1	yes	characteristic
35	#89603	—	2	1	no	—
36	#89603	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	#89500	—	2	1	no	—
42	D₇×C₂²⋊C₈	—	2	1	no	—
43	C₄×#1132	C₂²	1	1	yes	characteristic
44	C₄×#1131	C₂²	1	1	yes	characteristic
45	C₈×D₂₈	C₂²	1	1	yes	characteristic
46	#89457	—	2	1	no	—
47	#89457	C₂²	1	1	yes	characteristic
48	C₄×C₈×D₇	C₂²	1	1	yes	characteristic
49	#89451	—	2	1	no	—
50	#89451	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×#322	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	#89249	C₂²	1	1	yes	characteristic, complemented
67	#18060	—	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	C₂×C₇×M₁₆	—	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	C₂×#1136	—	2	1	no	—
81	D₇×SD₁₆	—	2	4	no	—
82	C₂×#1132	C₂×C₄	1	1	yes	characteristic
83	C₂×#1131	—	2	1	no	—
84	C₂×C₈×D₇	—	2	1	no	—
85	C₂×C₈×D₇	—	2	1	no	—
86	C₂×C₈×D₇	C₂×C₄	1	1	yes	characteristic
87	C₂×C₈×D₇	C₂×C₄	1	1	yes	characteristic
88	#6456	C₂×C₄	1	1	yes	characteristic
89	D₇×C₄⋊C₄	—	2	1	no	—
90	D₇×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
91	D₇×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
92	#6450	—	2	1	no	—
93	#6450	C₂×C₄	1	1	yes	characteristic
94	(C₂²⋊D₇)⋊C₄	—	2	1	no	—
95	D₇×C₂²⋊C₄	—	2	1	no	—
96	C₄×D₂₈	C₂³	1	1	yes	characteristic
97	C₄²×D₇	—	2	1	no	—
98	C₄²×D₇	C₂³	1	1	yes	characteristic
99	C₄×Dic₁₄	—	2	1	no	—
100	C₄×Dic₁₄	C₂³	1	1	yes	characteristic
101	C₇×#106	C₂×C₄	1	1	yes	characteristic
102	C₇×C₄⋊C₈	—	2	1	no	—
103	C₇×C₄⋊C₈	C₂³	1	1	yes	characteristic
104	C₇×C₄⋊C₈	C₂³	1	1	yes	characteristic
105	C₇×#103	C₂×C₄	1	1	yes	characteristic
106	C₇×#102	C₂×C₄	1	1	yes	characteristic
107	C₇×C₂²⋊C₈	—	2	1	no	—
108	C₄×C₇×C₈	—	2	1	no	—
109	C₄×C₇×C₈	C₂³	1	1	yes	characteristic
110	C₄×C₇×C₈	C₂³	1	1	yes	characteristic
111	C₄×C₇×C₈	C₂³	1	1	yes	characteristic
112	#6409	C₂×C₄	1	1	yes	characteristic
113	#6406	C₂×C₄	1	1	yes	characteristic
114	C₂²⋊(C₇⋊C₈)	—	2	1	no	—
115	#6395	C₂×C₄	1	1	yes	characteristic
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	#6389	—	2	1	no	—
125	#6389	—	2	1	no	—
126	#6389	—	2	1	no	—
127	#6389	—	2	1	no	—
128	#6389	—	2	1	no	—
129	Dic₇⋊C₈	—	2	1	no	—
130	Dic₇⋊C₈	—	2	1	no	—
131	Dic₇⋊C₈	D₄	1	1	yes	characteristic
132	Dic₇⋊C₈	D₄	1	1	yes	characteristic
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	#2984	—	7	1	no	—
147	#2974	—	7	1	no	—
148	C₂×C₄×SD₁₆	—	7	1	no	—
149	#1592	—	7	1	no	—
150	#1592	—	7	1	no	—
151	#1583	—	7	1	no	—
152	#1583	D₇	1	1	yes	characteristic, complemented
153	#1582	—	7	1	no	—
154	#1582	—	7	1	no	—
155	SD₁₆⋊C₈	—	7	1	no	—
156	SD₁₆⋊C₈	—	7	1	no	—
157	#1568	—	7	1	no	—
158	#1491	—	7	1	no	—
159	#1490	—	7	1	no	—
160	#1451	—	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	—	4	1	no	—
169	D₄×D₇	—	2	2	no	—
170	D₄×D₇	—	4	1	no	—
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	—	2	2	no	—
185	C₇×M₁₆	—	8	1	no	—
186	C₂×C₇×C₈	—	2	1	no	—
187	C₂×C₇×C₈	—	2	1	no	—
188	C₂×C₇×C₈	—	2	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	M₁₆	1	4	yes	complemented
201	#1142	—	2	2	no	—
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	#1136	—	8	1	no	—
218	C₂×C₇⋊C₈	—	2	1	no	—
219	C₂×C₇⋊C₈	—	2	1	no	—
220	C₂×C₇⋊C₈	—	2	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	—	2	2	no	—
226	#1131	—	4	2	no	—
227	C₈×D₇	—	2	2	no	—
228	C₈×D₇	—	4	1	no	—
229	C₈×D₇	—	8	1	no	—
230	C₈×D₇	—	8	1	no	—
231	C₂²×SD₁₆	—	7	1	no	—
232	C₂×C₄×Q₈	—	7	1	no	—
233	C₂×C₄×D₄	—	7	1	no	—
234	#446	—	7	1	no	—
235	#446	—	7	1	no	—
236	#446	—	14	1	no	—
237	#446	—	14	1	no	—
238	C₈×Q₈	—	7	1	no	—
239	C₈×Q₈	C₂×D₇	1	1	yes	characteristic, complemented
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	—	7	1	no	—
247	C₄×SD₁₆	C₂×D₇	1	1	yes	characteristic
248	#436	—	7	1	no	—
249	#436	C₂×D₇	1	1	yes	characteristic
250	#435	—	14	1	no	—
251	#435	—	14	1	no	—
252	C₈×D₄	—	7	1	no	—
253	C₈×D₄	—	7	1	no	—
254	#432	—	7	1	no	—
255	#432	—	7	1	no	—
256	#432	—	14	1	no	—
257	#431	—	7	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	#407	—	14	1	no	—
263	C₂×C₂²⋊C₈	—	14	1	no	—
264	C₄×M₁₆	—	7	1	no	—
265	C₂×C₄×C₈	—	7	1	no	—
266	#335	—	7	1	no	—
267	#335	—	7	1	no	—
268	#334	—	7	1	no	—
269	#334	C₂×D₇	1	1	yes	characteristic, complemented
270	Q₈⋊C₈	—	7	1	no	—
271	Q₈⋊C₈	—	7	1	no	—
272	Q₈⋊C₈	—	7	1	no	—
273	Q₈⋊C₈	C₂×D₇	1	1	yes	characteristic, complemented
274	D₄⋊C₈	—	7	1	no	—
275	D₄⋊C₈	—	7	1	no	—
276	D₄⋊C₈	—	7	1	no	—
277	D₄⋊C₈	C₂×D₇	1	1	yes	characteristic
278	#322	—	7	1	no	—
279	#322	—	7	1	no	—
280	#322	—	7	1	no	—
281	#322	C₂×D₇	1	1	yes	characteristic, complemented
282	C₂³×C₇	—	2	1	no	—
283	C₂²×D₇	—	2	1	no	—
284	C₂²×D₇	—	4	2	no	—
285	C₂²×D₇	—	4	2	no	—
286	C₂²×D₇	—	8	1	no	—
287	C₂²×D₇	C₄×D₄	1	1	yes	characteristic
288	C₇×Q₈	—	2	1	no	—
289	C₇×Q₈	C₂×M₁₆	1	2	yes	—
290	C₇×D₄	—	2	1	no	—
291	C₇×D₄	—	2	1	no	—
292	C₂×C₄×C₇	—	2	1	no	—
293	C₂×C₄×C₇	—	2	1	no	—
294	C₂×C₄×C₇	—	2	1	no	—
295	C₂×C₄×C₇	—	4	1	no	—
296	C₂×C₄×C₇	—	4	1	no	—
297	C₂×C₄×C₇	C₂³×C₄	1	1	yes	characteristic
298	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
299	C₂×C₄×C₇	C₂×#41	1	1	yes	characteristic
300	C₂²⋊D₇	—	4	2	no	—
301	C₂×Dic₇	—	2	1	no	—
302	C₂×Dic₇	—	2	1	no	—
303	C₂×Dic₇	—	2	1	no	—
304	C₂×Dic₇	—	8	1	no	—
305	C₂×Dic₇	C₄×D₄	1	1	yes	characteristic
306	C₂×Dic₇	C₄×D₄	1	1	yes	characteristic
307	C₂×Dic₇	C₄×D₄	1	1	yes	characteristic
308	D₂₈	—	2	1	no	—
309	D₂₈	C₂×M₁₆	1	2	yes	—
310	C₄×D₇	—	2	2	no	—
311	C₄×D₇	—	2	1	no	—
312	C₄×D₇	—	2	1	no	—
313	C₄×D₇	—	2	1	no	—
314	C₄×D₇	—	2	1	no	—
315	C₄×D₇	—	4	2	no	—
316	C₄×D₇	—	4	2	no	—
317	C₄×D₇	—	4	1	no	—
318	C₄×D₇	—	4	1	no	—
319	C₄×D₇	—	8	1	no	—
320	C₄×D₇	—	8	1	no	—
321	Dic₁₄	—	2	1	no	—
322	Dic₁₄	—	2	1	no	—
323	Dic₁₄	—	4	2	no	—
324	C₇×C₈	—	2	1	no	—
325	C₇×C₈	—	2	1	no	—
326	C₇×C₈	—	2	1	no	—
327	C₇×C₈	—	2	1	no	—
328	C₇×C₈	—	4	1	no	—
329	C₇×C₈	—	4	1	no	—
330	C₇×C₈	—	4	1	no	—
331	C₇⋊C₈	—	2	1	no	—
332	C₇⋊C₈	—	2	1	no	—
333	C₇⋊C₈	—	2	1	no	—
334	C₇⋊C₈	—	4	1	no	—
335	C₇⋊C₈	—	4	1	no	—
336	C₇⋊C₈	—	4	1	no	—
337	C₇⋊C₈	C₂×M₁₆	1	2	yes	—
338	C₂²×Q₈	—	7	1	no	—
339	C₂²×D₄	—	7	1	no	—
340	C₂³×C₄	—	14	1	no	—
341	C₂×SD₁₆	—	7	1	no	—
342	C₂×SD₁₆	—	7	1	no	—
343	C₂×SD₁₆	—	7	1	no	—
344	C₂×SD₁₆	—	14	4	no	—
345	C₂×SD₁₆	C₄×D₇	1	1	yes	characteristic
346	C₂×M₁₆	—	2	1	no	—
347	C₂×M₁₆	—	14	1	no	—
348	C₂×M₁₆	—	14	1	no	—
349	C₂²×C₈	—	7	1	no	—
350	C₂²×C₈	—	7	1	no	—
351	C₂²×C₈	—	14	1	no	—
352	C₂²×C₈	—	14	1	no	—
353	C₄×Q₈	—	7	1	no	—
354	C₄×Q₈	—	7	1	no	—
355	C₄×Q₈	—	7	1	no	—
356	C₄×Q₈	—	14	1	no	—
357	C₄×Q₈	—	14	1	no	—
358	C₄×Q₈	C₂²×D₇	1	1	yes	characteristic
359	C₄×D₄	—	7	1	no	—
360	C₄×D₄	—	7	1	no	—
361	C₄×D₄	—	7	1	no	—
362	C₄×D₄	—	14	1	no	—
363	C₄×D₄	—	14	1	no	—
364	C₄×D₄	C₂²×D₇	1	1	yes	characteristic
365	C₂×C₄⋊C₄	—	7	1	no	—
366	C₂×C₄⋊C₄	—	7	1	no	—
367	C₂×C₄⋊C₄	—	14	1	no	—
368	C₂×C₂²⋊C₄	—	14	1	no	—
369	C₂×C₄²	—	7	1	no	—
370	C₂×C₄²	—	14	1	no	—
371	#106	—	7	1	no	—
372	#106	—	7	1	no	—
373	#106	—	7	1	no	—
374	#106	C₄×D₇	1	1	yes	characteristic
375	C₄⋊C₈	—	2	1	no	—
376	C₄⋊C₈	—	7	1	no	—
377	C₄⋊C₈	—	7	1	no	—
378	C₄⋊C₈	—	7	1	no	—
379	C₄⋊C₈	—	7	1	no	—
380	C₄⋊C₈	—	14	1	no	—
381	C₄⋊C₈	—	14	1	no	—
382	C₄⋊C₈	—	14	1	no	—
383	C₄⋊C₈	C₂²×D₇	1	1	yes	characteristic
384	C₄⋊C₈	C₂²×D₇	1	1	yes	characteristic
385	#103	—	7	1	no	—
386	#103	—	7	1	no	—
387	#103	—	7	1	no	—
388	#103	C₄×D₇	1	1	yes	characteristic
389	#102	—	7	1	no	—
390	#102	—	7	1	no	—
391	#102	—	7	1	no	—
392	#102	C₄×D₇	1	1	yes	characteristic
393	C₂²⋊C₈	—	2	1	no	—
394	C₂²⋊C₈	—	7	1	no	—
395	C₂²⋊C₈	—	7	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	#97	—	14	1	no	—
402	#97	—	14	1	no	—
403	#97	—	14	1	no	—
404	#97	—	14	1	no	—
405	#97	—	14	1	no	—
406	C₄×C₈	—	2	1	no	—
407	C₄×C₈	—	7	1	no	—
408	C₄×C₈	—	7	1	no	—
409	C₄×C₈	—	7	1	no	—
410	C₄×C₈	—	7	1	no	—
411	C₄×C₈	—	7	1	no	—
412	C₄×C₈	—	14	1	no	—
413	C₄×C₈	C₂²×D₇	1	1	yes	characteristic
414	C₄×C₈	C₂²×D₇	1	1	yes	characteristic
415	C₄×C₈	C₂²×D₇	1	1	yes	characteristic
416	C₂²×C₇	—	4	1	no	—
417	C₂²×C₇	—	4	1	no	—
418	C₂²×C₇	—	4	1	no	—
419	C₂²×C₇	C₂×C₄×D₄	1	1	yes	characteristic
420	C₂×D₇	—	2	1	no	—
421	C₂×D₇	—	2	1	no	—
422	C₂×D₇	—	2	2	no	—
423	C₂×D₇	—	4	1	no	—
424	C₂×D₇	—	4	1	no	—
425	C₂×D₇	—	8	4	no	—
426	C₂×D₇	#444	1	2	yes	—
427	C₄×C₇	—	2	2	no	—
428	C₄×C₇	—	2	1	no	—
429	C₄×C₇	—	4	1	no	—
430	C₄×C₇	—	4	1	no	—
431	C₄×C₇	C₂²×M₁₆	1	1	yes	characteristic
432	C₄×C₇	#568	1	1	yes	characteristic
433	C₄×C₇	#577	1	1	yes	characteristic
434	C₄×C₇	#577	1	1	yes	characteristic
435	Dic₇	—	2	1	no	—
436	Dic₇	—	2	1	no	—
437	Dic₇	—	2	1	no	—
438	Dic₇	—	4	1	no	—
439	Dic₇	—	4	1	no	—
440	Dic₇	—	4	1	no	—
441	C₂⁴	—	14	1	no	—
442	C₂×Q₈	—	7	1	no	—
443	C₂×Q₈	—	14	1	no	—
444	C₂×Q₈	—	14	2	no	—
445	C₂×Q₈	—	28	1	no	—
446	C₂×Q₈	C₂×C₄×D₇	1	1	yes	characteristic
447	C₂×D₄	—	7	1	no	—
448	C₂×D₄	—	14	1	no	—
449	C₂×D₄	—	14	2	no	—
450	C₂×D₄	—	28	1	no	—
451	C₂×D₄	C₂×C₄×D₇	1	1	yes	characteristic
452	C₂²×C₄	—	2	1	no	—
453	C₂²×C₄	—	7	1	no	—
454	C₂²×C₄	—	7	1	no	—
455	C₂²×C₄	—	7	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	—	14	1	no	—
462	C₂²×C₄	—	56	1	no	—
463	C₂²×C₄	—	56	1	no	—
464	SD₁₆	—	2	2	no	—
465	SD₁₆	—	7	4	no	—
466	SD₁₆	—	14	2	no	—
467	SD₁₆	—	14	2	no	—
468	M₁₆	—	8	1	no	—
469	M₁₆	—	28	2	no	—
470	M₁₆	—	56	1	no	—
471	C₂×C₈	—	2	1	no	—
472	C₂×C₈	—	2	1	no	—
473	C₂×C₈	—	2	1	no	—
474	C₂×C₈	—	7	1	no	—
475	C₂×C₈	—	7	1	no	—
476	C₂×C₈	—	7	1	no	—
477	C₂×C₈	—	7	1	no	—
478	C₂×C₈	—	14	2	no	—
479	C₂×C₈	—	14	1	no	—
480	C₂×C₈	—	14	1	no	—
481	C₂×C₈	—	14	1	no	—
482	C₂×C₈	—	28	1	no	—
483	C₂×C₈	—	56	1	no	—
484	C₂×C₈	—	56	1	no	—
485	C₂×C₈	C₂×C₄×D₇	1	1	yes	characteristic
486	C₂×C₈	C₂×C₄×D₇	1	1	yes	characteristic
487	C₂×C₈	D₄×D₇	1	1	yes	characteristic
488	C₂×C₈	D₄×D₇	1	1	yes	characteristic
489	C₄⋊C₄	—	2	1	no	—
490	C₄⋊C₄	—	7	1	no	—
491	C₄⋊C₄	—	7	1	no	—
492	C₄⋊C₄	—	14	1	no	—
493	C₄⋊C₄	—	14	1	no	—
494	C₄⋊C₄	—	14	1	no	—
495	C₄⋊C₄	—	14	1	no	—
496	C₄⋊C₄	—	14	1	no	—
497	C₄⋊C₄	C₂×C₄×D₇	1	1	yes	characteristic
498	C₄⋊C₄	C₂×C₄×D₇	1	1	yes	characteristic
499	C₂²⋊C₄	—	2	1	no	—
500	C₂²⋊C₄	—	14	1	no	—
501	C₂²⋊C₄	—	14	1	no	—
502	C₂²⋊C₄	—	14	1	no	—
503	C₄²	—	2	1	no	—
504	C₄²	—	7	1	no	—
505	C₄²	—	7	1	no	—
506	C₄²	—	7	1	no	—
507	C₄²	—	14	1	no	—
508	C₄²	—	14	1	no	—
509	C₄²	—	14	1	no	—
510	C₄²	C₂³×D₇	1	1	yes	characteristic
511	C₂×C₇	—	8	1	no	—
512	C₂×C₇	D₄×M₁₆	1	1	yes	characteristic
513	C₂×C₇	#2949	1	1	yes	characteristic
514	C₂×C₇	C₂×#444	1	1	yes	characteristic
515	D₇	—	2	2	no	—
516	D₇	—	4	2	no	—
517	C₂³	—	2	1	no	—
518	C₂³	—	7	1	no	—
519	C₂³	—	14	1	no	—
520	C₂³	—	28	2	no	—
521	C₂³	—	28	2	no	—
522	C₂³	—	56	1	no	—
523	Q₈	—	2	1	no	—
524	Q₈	—	14	1	no	—
525	Q₈	—	14	1	no	—
526	Q₈	—	28	2	no	—
527	Q₈	D₇×M₁₆	1	2	yes	—
528	D₄	—	2	1	no	—
529	D₄	—	2	1	no	—
530	D₄	—	7	2	no	—
531	D₄	—	14	1	no	—
532	D₄	—	28	2	no	—
533	C₂×C₄	—	2	1	no	—
534	C₂×C₄	—	2	1	no	—
535	C₂×C₄	—	2	1	no	—
536	C₂×C₄	—	4	1	no	—
537	C₂×C₄	—	4	1	no	—
538	C₂×C₄	—	7	1	no	—
539	C₂×C₄	—	7	1	no	—
540	C₂×C₄	—	7	1	no	—
541	C₂×C₄	—	14	2	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	—	14	1	no	—
548	C₂×C₄	—	14	1	no	—
549	C₂×C₄	—	28	2	no	—
550	C₂×C₄	—	28	2	no	—
551	C₂×C₄	—	28	1	no	—
552	C₂×C₄	—	28	1	no	—
553	C₂×C₄	—	56	1	no	—
554	C₂×C₄	—	56	1	no	—
555	C₂×C₄	—	56	1	no	—
556	C₂×C₄	C₂²×C₄×D₇	1	1	yes	characteristic
557	C₂×C₄	C₂×D₄×D₇	1	1	yes	characteristic
558	C₂×C₄	D₇×#41	1	1	yes	characteristic
559	C₈	—	2	1	no	—
560	C₈	—	2	1	no	—
561	C₈	—	2	1	no	—
562	C₈	—	2	1	no	—
563	C₈	—	4	1	no	—
564	C₈	—	4	1	no	—
565	C₈	—	4	1	no	—
566	C₈	—	7	2	no	—
567	C₈	—	14	1	no	—
568	C₈	—	14	1	no	—
569	C₈	—	14	1	no	—
570	C₈	—	28	1	no	—
571	C₈	—	28	1	no	—
572	C₈	—	28	1	no	—
573	C₇	#18060	1	1	yes	characteristic, complemented, Sylow
574	C₂²	—	4	1	no	—
575	C₂²	—	4	1	no	—
576	C₂²	—	4	1	no	—
577	C₂²	—	7	2	no	—
578	C₂²	—	14	1	no	—
579	C₂²	—	14	1	no	—
580	C₂²	—	14	2	no	—
581	C₂²	—	28	1	no	—
582	C₂²	—	28	1	no	—
583	C₂²	—	56	4	no	—
584	C₂²	C₄×D₄×D₇	1	1	yes	characteristic
585	C₄	—	2	2	no	—
586	C₄	—	2	1	no	—
587	C₄	—	4	1	no	—
588	C₄	—	4	1	no	—
589	C₄	—	14	1	no	—
590	C₄	—	14	1	no	—
591	C₄	—	14	1	no	—
592	C₄	—	28	1	no	—
593	C₄	—	28	1	no	—
594	C₄	—	28	1	no	—
595	C₄	C₂×D₇×M₁₆	1	1	yes	characteristic
596	C₄	#90441	1	1	yes	characteristic
597	C₄	#90453	1	1	yes	characteristic
598	C₄	#90461	1	1	yes	characteristic
599	C₂	—	8	1	no	—
600	C₂	—	14	2	no	—
601	C₂	—	28	2	no	—
602	C₂	#11736928	1	1	yes	characteristic
603	C₂	#11737094	1	1	yes	characteristic
604	C₂	D₇×#444	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂×D₄×D₇
commutator	C₂×C₄×C₇	C₂³×C₄
Frattini	C₄²	C₂³×D₇
Fitting	C₇×#1583	C₂
socle	C₂²×C₇	C₂×C₄×D₄
prime radical	C₂×D₄×D₇	C₂×C₄
cosocle	C₄²×C₇	C₂⁴
hypercenter	#1583	D₇
hypocenter	C₇	#18060
LCS	G ▷ C₂×C₄×C₇ ▷ C₂×C₇ ▷ C₇
UCS	C₁ ◁ C₂×C₄ ◁ C₄×C₈ ◁ #1583

Complements

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

N	H ≅ G/N	type
1. #11737366	C₂	semidirect
4. C₇×#1583	C₂	semidirect
5. #11728691	C₂	semidirect
6. #11728650	C₂	semidirect
7. #11728614	C₂	semidirect
8. #11726284	C₂	semidirect
9. #11726273	C₂	semidirect
10. #11725993	C₂	semidirect
11. #11725968	C₂	semidirect
13. #11725916	C₂	semidirect
14. #11725833	C₂	semidirect
15. #11725824	C₂	semidirect
19. C₇×C₈×Q₈	C₂²	semidirect
26. Q₈×C₇⋊C₈	C₂²	semidirect
36. #89603	C₂²	semidirect
50. #89451	C₂²	semidirect
51. C₇×#334	C₂²	semidirect
52. C₇×Q₈⋊C₈	C₂²	semidirect
54. C₇×#322	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. #89249	C₂²	semidirect
152. #1583	D₇	semidirect
200. #1143	M₁₆	semidirect
239. C₈×Q₈	C₂×D₇	semidirect
269. #334	C₂×D₇	semidirect
273. Q₈⋊C₈	C₂×D₇	semidirect
281. #322	C₂×D₇	semidirect
573. C₇	#18060	semidirect

Maximal subgroups

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

subgroup	index
#11737366	2
C₄×D₇×SD₁₆	2
#11736987	2
C₇×#1583	2
#11728691	2
#11728650	2
#11728614	2
#11726284	2
#11726273	2
#11725993	2
#11725968	2
#11725929	2
#11725916	2
#11725833	2
#11725824	2
#18060	7