Subgroups — #13323712

Order 1792.

698 conjugacy classes of subgroups.

The subgroup lattice has 600 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#11737403	C₂	1	1	yes	maximal, characteristic, complemented
2	#11737096	C₂	1	1	yes	maximal, characteristic
3	C₈×D₄×D₇	C₂	1	1	yes	maximal, characteristic
4	C₇×#1585	C₂	1	1	yes	maximal, characteristic, complemented
5	#11728708	C₂	1	1	yes	maximal, characteristic, complemented
6	SD₁₆⋊(C₇⋊C₈)	C₂	1	1	yes	maximal, characteristic, complemented
7	#11728597	C₂	1	1	yes	maximal, characteristic, complemented
8	#11726326	C₂	1	1	yes	maximal, characteristic, complemented
9	#11726312	C₂	1	1	yes	maximal, characteristic, complemented
10	#11725986	C₂	1	1	yes	maximal, characteristic, complemented
11	#11725968	C₂	1	1	yes	maximal, characteristic, complemented
12	#11725926	C₂	1	1	yes	maximal, characteristic
13	#11725904	C₂	1	1	yes	maximal, characteristic, complemented
14	#11725834	C₂	1	1	yes	maximal, characteristic, complemented
15	#11725825	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×C₈×D₇	—	2	1	no	—
17	#90269	C₂²	1	1	yes	characteristic
18	C₄×D₄×D₇	C₂²	1	1	yes	characteristic
19	C₇×#446	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	#89941	C₄	1	1	yes	characteristic
23	#89934	C₄	1	1	yes	characteristic
24	C₈×C₂²⋊D₇	—	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	#89642	C₄	1	1	yes	characteristic
30	#89634	C₄	1	1	yes	characteristic
31	#89611	—	2	1	no	—
32	#89609	C₂²	1	1	yes	characteristic
33	#89606	C₂²	1	1	yes	characteristic
34	D₇×C₄⋊C₈	C₂²	1	1	yes	characteristic
35	#89602	—	2	1	no	—
36	#89602	C₂²	1	1	yes	characteristic, complemented
37	#89590	C₄	1	1	yes	characteristic
38	#89577	C₄	1	1	yes	characteristic
39	#89548	C₄	1	1	yes	characteristic
40	#89533	C₄	1	1	yes	characteristic
41	(C₂²⋊D₇)⋊C₈	—	2	1	no	—
42	D₇×C₂²⋊C₈	—	2	1	no	—
43	#89480	—	2	1	no	—
44	#89473	—	2	1	no	—
45	C₄×#1132	C₂²	1	1	yes	characteristic
46	C₈×D₂₈	C₂²	1	1	yes	characteristic
47	#89457	C₂²	1	1	yes	characteristic
48	#89457	C₂²	1	1	yes	characteristic
49	C₄×C₈×D₇	C₂²	1	1	yes	characteristic
50	#89451	C₂²	1	1	yes	characteristic, complemented
51	C₇×#335	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	#89253	C₂²	1	1	yes	characteristic, complemented
63	#89251	C₂²	1	1	yes	characteristic, complemented
64	#89250	C₂²	1	1	yes	characteristic, complemented
65	#89249	C₂²	1	1	yes	characteristic, complemented
66	#89249	C₂²	1	1	yes	characteristic, complemented
67	#17905	—	7	1	no	maximal, Sylow
68	C₂×D₄×D₇	C₂×C₄	1	1	yes	characteristic
69	C₂²×C₄×D₇	—	2	1	no	—
70	C₂×C₇×SD₁₆	C₂×C₄	1	1	yes	characteristic
71	C₂²×C₇×C₈	—	2	1	no	—
72	C₄×C₇×Q₈	C₂³	1	1	yes	characteristic
73	C₄×C₇×D₄	C₂³	1	1	yes	characteristic
74	#6509	C₂×C₄	1	1	yes	characteristic
75	#6507	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	C₂×#1132	C₂×C₄	1	1	yes	characteristic
82	C₂×#1131	—	2	1	no	—
83	C₂×C₈×D₇	—	2	1	no	—
84	C₂×C₈×D₇	—	2	1	no	—
85	C₂×C₈×D₇	—	2	1	no	—
86	C₂×C₈×D₇	—	4	4	no	—
87	C₂×C₈×D₇	D₄	1	1	yes	characteristic
88	C₂×C₈×D₇	D₄	1	1	yes	characteristic
89	#6460	C₂×C₄	1	1	yes	characteristic
90	#6459	—	2	1	no	—
91	#6456	C₂×C₄	1	1	yes	characteristic
92	D₇×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
93	#6452	—	2	1	no	—
94	#6451	C₂×C₄	1	1	yes	characteristic
95	(C₂²⋊D₇)⋊C₄	—	2	1	no	—
96	D₇×C₂²⋊C₄	—	2	1	no	—
97	C₄×D₂₈	C₂³	1	1	yes	characteristic
98	#6435	—	2	1	no	—
99	C₄²×D₇	C₂³	1	1	yes	characteristic
100	C₄×Dic₁₄	—	2	1	no	—
101	C₄×Dic₁₄	C₂³	1	1	yes	characteristic
102	C₇×#106	C₂×C₄	1	1	yes	characteristic
103	C₇×C₄⋊C₈	—	2	1	no	—
104	C₇×C₄⋊C₈	C₂³	1	1	yes	characteristic
105	C₇×C₄⋊C₈	C₂³	1	1	yes	characteristic
106	C₇×#103	C₂×C₄	1	1	yes	characteristic
107	C₇×#102	C₂×C₄	1	1	yes	characteristic
108	C₇×C₂²⋊C₈	—	2	1	no	—
109	C₇×#97	—	2	1	no	—
110	C₄×C₇×C₈	C₂³	1	1	yes	characteristic
111	C₄×C₇×C₈	C₂³	1	1	yes	characteristic
112	C₄×C₇×C₈	C₂³	1	1	yes	characteristic
113	#6409	C₂×C₄	1	1	yes	characteristic
114	#6406	C₂×C₄	1	1	yes	characteristic
115	C₂²⋊(C₇⋊C₈)	—	2	1	no	—
116	#6395	C₂×C₄	1	1	yes	characteristic
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	C₂×C₄	1	1	yes	characteristic
121	(C₂×D₇)⋊C₈	C₂×C₄	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	Dic₇⋊C₈	—	2	1	no	—
126	Dic₇⋊C₈	—	2	1	no	—
127	Dic₇⋊C₈	—	2	1	no	—
128	Dic₇⋊C₈	—	2	1	no	—
129	Dic₇⋊C₈	—	2	1	no	—
130	Dic₇⋊C₈	C₂×C₄	1	1	yes	characteristic
131	Dic₇⋊C₈	C₂×C₄	1	1	yes	characteristic
132	C₈×Dic₇	—	2	1	no	—
133	C₈×Dic₇	D₄	1	1	yes	characteristic
134	C₈×Dic₇	D₄	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	#3101	—	7	1	no	—
147	#2960	—	7	1	no	—
148	C₂×C₈×D₄	—	7	1	no	—
149	#1585	—	7	1	no	—
150	#1585	—	7	1	no	—
151	#1585	—	7	1	no	—
152	#1585	D₇	1	1	yes	characteristic, complemented
153	SD₁₆⋊C₈	—	7	1	no	—
154	SD₁₆⋊C₈	—	7	1	no	—
155	SD₁₆⋊C₈	—	7	1	no	—
156	SD₁₆⋊C₈	—	7	1	no	—
157	#1571	—	7	1	no	—
158	#1486	—	7	1	no	—
159	#1481	—	7	1	no	—
160	#1452	—	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	D₄×D₇	—	2	2	no	—
168	D₄×D₇	—	2	2	no	—
169	C₂×D₂₈	C₂²×C₄	1	1	yes	characteristic
170	C₂×C₄×D₇	—	2	1	no	—
171	C₂×C₄×D₇	—	2	1	no	—
172	C₂×C₄×D₇	—	2	1	no	—
173	C₂×C₄×D₇	—	4	2	no	—
174	C₂×C₄×D₇	—	4	2	no	—
175	C₂×C₄×D₇	C₂²×C₄	1	1	yes	characteristic
176	C₂×C₄×D₇	C₂×D₄	1	1	yes	characteristic
177	C₂×C₄×D₇	#41	1	1	yes	characteristic
178	C₂×Dic₁₄	—	2	1	no	—
179	C₂×Dic₁₄	C₂²×C₄	1	1	yes	characteristic
180	C₇×SD₁₆	—	2	2	no	—
181	C₂×C₇×C₈	—	2	1	no	—
182	C₂×C₇×C₈	—	2	1	no	—
183	C₂×C₇×C₈	—	2	1	no	—
184	C₂×C₇×C₈	—	4	2	no	—
185	C₂×C₇×C₈	C₂²×C₄	1	1	yes	characteristic
186	C₂×C₇×C₈	C₂²×C₄	1	1	yes	characteristic
187	C₂×C₇×C₈	C₂×D₄	1	1	yes	characteristic
188	C₂×C₇×C₈	C₂×D₄	1	1	yes	characteristic
189	C₇×C₄⋊C₄	—	2	1	no	—
190	C₇×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
191	C₇×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
192	C₇×C₂²⋊C₄	—	2	1	no	—
193	C₄²×C₇	—	2	1	no	—
194	C₄²×C₇	C₂⁴	1	1	yes	characteristic
195	C₂²⋊Dic₇	—	2	1	no	—
196	#1143	—	2	2	no	—
197	#1142	—	2	2	no	—
198	(C₂×D₇)⋊C₄	—	2	1	no	—
199	(C₂×D₇)⋊C₄	—	2	1	no	—
200	(C₂×D₇)⋊C₄	—	2	1	no	—
201	(C₂×D₇)⋊C₄	—	2	1	no	—
202	C₄⋊Dic₇	—	2	1	no	—
203	C₄⋊Dic₇	C₂²×C₄	1	1	yes	characteristic
204	C₄⋊Dic₇	C₂²×C₄	1	1	yes	characteristic
205	Dic₇⋊C₄	—	2	1	no	—
206	Dic₇⋊C₄	—	2	1	no	—
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	C₂²×C₄	1	1	yes	characteristic
213	C₄×Dic₇	C₂×D₄	1	1	yes	characteristic
214	C₄×Dic₇	#41	1	1	yes	characteristic
215	C₂×C₇⋊C₈	—	2	1	no	—
216	C₂×C₇⋊C₈	—	2	1	no	—
217	C₂×C₇⋊C₈	—	2	1	no	—
218	C₂×C₇⋊C₈	—	4	2	no	—
219	C₂×C₇⋊C₈	C₂²×C₄	1	1	yes	characteristic
220	C₂×C₇⋊C₈	C₂²×C₄	1	1	yes	characteristic
221	C₂×C₇⋊C₈	C₂×D₄	1	1	yes	characteristic
222	C₂×C₇⋊C₈	C₂×D₄	1	1	yes	characteristic
223	#1132	—	2	2	no	—
224	#1131	—	4	2	no	—
225	C₈×D₇	—	2	2	no	—
226	C₈×D₇	—	2	2	no	—
227	C₈×D₇	—	4	2	no	—
228	C₈×D₇	—	4	2	no	—
229	C₈×D₇	—	4	2	no	—
230	C₂³×C₈	—	14	1	no	—
231	#533	—	7	1	no	—
232	C₂×C₄×D₄	—	7	1	no	—
233	#483	—	7	1	no	—
234	#483	—	7	1	no	—
235	#476	—	7	1	no	—
236	#476	—	7	1	no	—
237	#461	—	7	1	no	—
238	#461	—	7	1	no	—
239	#450	—	7	1	no	—
240	#450	—	7	1	no	—
241	#446	—	7	1	no	—
242	#446	—	14	1	no	—
243	#446	C₂×D₇	1	1	yes	characteristic, complemented
244	C₈×Q₈	—	7	1	no	—
245	C₈×Q₈	—	7	1	no	—
246	C₈×Q₈	—	14	1	no	—
247	C₄×SD₁₆	—	7	1	no	—
248	C₄×SD₁₆	—	7	1	no	—
249	C₄×SD₁₆	—	7	1	no	—
250	C₄×SD₁₆	C₂×D₇	1	1	yes	characteristic
251	C₈×D₄	—	7	1	no	—
252	C₈×D₄	—	7	1	no	—
253	C₈×D₄	—	7	1	no	—
254	C₈×D₄	—	14	1	no	—
255	C₈×D₄	—	14	1	no	—
256	C₈×D₄	C₂×D₇	1	1	yes	characteristic
257	#431	—	7	1	no	—
258	#431	—	7	1	no	—
259	#424	—	14	1	no	—
260	#423	—	7	1	no	—
261	C₂×C₄⋊C₈	—	7	1	no	—
262	C₂×C₂²⋊C₈	—	14	1	no	—
263	#405	—	14	1	no	—
264	C₂×C₄×C₈	—	7	1	no	—
265	#335	—	7	1	no	—
266	#335	—	7	1	no	—
267	#335	—	7	1	no	—
268	#335	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	#322	—	7	1	no	—
280	#322	C₂×D₇	1	1	yes	characteristic, complemented
281	C₂³×C₇	—	2	1	no	—
282	C₂²×D₇	—	2	4	no	—
283	C₂²×D₇	—	2	1	no	—
284	C₂²×D₇	—	4	2	no	—
285	C₂²×D₇	—	4	2	no	—
286	C₂²×D₇	C₄×D₄	1	1	yes	characteristic
287	C₇×Q₈	—	2	1	no	—
288	C₇×Q₈	—	2	1	no	—
289	C₇×D₄	—	2	1	no	—
290	C₇×D₄	#131	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	—	4	2	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	#131	1	2	yes	—
309	C₄×D₇	—	2	1	no	—
310	C₄×D₇	—	2	1	no	—
311	C₄×D₇	—	4	1	no	—
312	C₄×D₇	—	4	2	no	—
313	C₄×D₇	—	4	1	no	—
314	C₄×D₇	—	4	1	no	—
315	C₄×D₇	—	4	2	no	—
316	C₄×D₇	AGL(1,ℤ/8)	1	2	yes	—
317	C₄×D₇	#137	1	2	yes	—
318	Dic₁₄	—	2	1	no	—
319	Dic₁₄	—	2	1	no	—
320	Dic₁₄	—	4	2	no	—
321	C₇×C₈	—	2	1	no	—
322	C₇×C₈	—	2	1	no	—
323	C₇×C₈	—	2	1	no	—
324	C₇×C₈	—	2	1	no	—
325	C₇×C₈	—	4	1	no	—
326	C₇×C₈	—	4	1	no	—
327	C₇×C₈	—	4	1	no	—
328	C₇⋊C₈	—	2	1	no	—
329	C₇⋊C₈	—	2	1	no	—
330	C₇⋊C₈	—	2	1	no	—
331	C₇⋊C₈	—	2	1	no	—
332	C₇⋊C₈	—	4	1	no	—
333	C₇⋊C₈	—	4	1	no	—
334	C₇⋊C₈	—	4	1	no	—
335	C₂²×D₄	—	7	1	no	—
336	C₂³×C₄	—	14	1	no	—
337	C₂×SD₁₆	—	7	1	no	—
338	C₂×SD₁₆	—	7	1	no	—
339	C₂×SD₁₆	—	7	1	no	—
340	C₂×SD₁₆	C₄×D₇	1	1	yes	characteristic
341	C₂×M₁₆	—	14	1	no	—
342	C₂²×C₈	—	2	1	no	—
343	C₂²×C₈	—	7	1	no	—
344	C₂²×C₈	—	7	1	no	—
345	C₂²×C₈	—	14	1	no	—
346	C₂²×C₈	—	14	1	no	—
347	C₂²×C₈	—	14	1	no	—
348	C₂²×C₈	—	14	1	no	—
349	C₂²×C₈	—	28	4	no	—
350	C₄⋊Q₈	—	7	1	no	—
351	C₄⋊Q₈	—	7	1	no	—
352	#125	—	14	1	no	—
353	C₂²⋊Q₈	—	7	1	no	—
354	C₂²⋊Q₈	—	7	1	no	—
355	C₂²⋊Q₈	—	14	1	no	—
356	C₄×Q₈	—	7	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	#117	—	14	1	no	—
366	C₂×C₄⋊C₄	—	7	1	no	—
367	C₂×C₂²⋊C₄	—	14	1	no	—
368	C₂×C₄²	—	7	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	—	14	1	no	—
383	C₄⋊C₈	—	14	1	no	—
384	C₄⋊C₈	C₂²×D₇	1	1	yes	characteristic
385	C₄⋊C₈	C₂²×D₇	1	1	yes	characteristic
386	#103	—	7	1	no	—
387	#103	—	7	1	no	—
388	#103	—	7	1	no	—
389	#103	C₄×D₇	1	1	yes	characteristic
390	#102	—	7	1	no	—
391	#102	—	7	1	no	—
392	#102	—	7	1	no	—
393	#102	C₄×D₇	1	1	yes	characteristic
394	C₂²⋊C₈	—	2	1	no	—
395	C₂²⋊C₈	—	7	1	no	—
396	C₂²⋊C₈	—	7	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	—	2	1	no	—
402	#97	—	14	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	—	7	1	no	—
408	C₄×C₈	—	14	1	no	—
409	C₄×C₈	—	14	1	no	—
410	C₄×C₈	C₂²×D₇	1	1	yes	characteristic
411	C₄×C₈	C₂²×D₇	1	1	yes	characteristic
412	C₄×C₈	C₂²×D₇	1	1	yes	characteristic
413	C₂²×C₇	—	2	2	no	—
414	C₂²×C₇	—	4	1	no	—
415	C₂²×C₇	—	4	1	no	—
416	C₂²×C₇	C₂×C₄×D₄	1	1	yes	characteristic
417	C₂×D₇	—	2	1	no	—
418	C₂×D₇	—	2	1	no	—
419	C₂×D₇	—	2	2	no	—
420	C₂×D₇	—	4	8	no	—
421	C₂×D₇	—	4	1	no	—
422	C₂×D₇	—	4	1	no	—
423	C₂×D₇	#440	1	2	yes	—
424	C₄×C₇	—	2	1	no	—
425	C₄×C₇	—	4	1	no	—
426	C₄×C₇	—	4	1	no	—
427	C₄×C₇	—	4	1	no	—
428	C₄×C₇	C₂×#131	1	1	yes	characteristic
429	C₄×C₇	C₂×#131	1	1	yes	characteristic
430	C₄×C₇	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
431	C₄×C₇	C₂×#137	1	1	yes	characteristic
432	Dic₇	—	2	1	no	—
433	Dic₇	—	2	1	no	—
434	Dic₇	—	4	1	no	—
435	Dic₇	—	4	1	no	—
436	Dic₇	—	4	1	no	—
437	Dic₇	#440	1	2	yes	—
438	C₂⁴	—	14	1	no	—
439	C₂×Q₈	—	7	1	no	—
440	C₂×Q₈	—	14	1	no	—
441	C₂×Q₈	C₂×C₄×D₇	1	1	yes	characteristic
442	C₂×D₄	—	7	1	no	—
443	C₂×D₄	—	14	1	no	—
444	C₂×D₄	—	14	2	no	—
445	C₂×D₄	—	14	2	no	—
446	C₂×D₄	C₂×C₄×D₇	1	1	yes	characteristic
447	C₂²×C₄	—	2	1	no	—
448	C₂²×C₄	—	7	1	no	—
449	C₂²×C₄	—	7	1	no	—
450	C₂²×C₄	—	7	1	no	—
451	C₂²×C₄	—	14	1	no	—
452	C₂²×C₄	—	14	1	no	—
453	C₂²×C₄	—	14	1	no	—
454	C₂²×C₄	—	14	1	no	—
455	C₂²×C₄	—	28	2	no	—
456	C₂²×C₄	—	28	2	no	—
457	SD₁₆	—	2	2	no	—
458	SD₁₆	—	14	2	no	—
459	SD₁₆	—	14	2	no	—
460	SD₁₆	—	14	2	no	—
461	M₁₆	—	28	2	no	—
462	C₂×C₈	—	2	1	no	—
463	C₂×C₈	—	2	1	no	—
464	C₂×C₈	—	2	1	no	—
465	C₂×C₈	—	4	2	no	—
466	C₂×C₈	—	7	1	no	—
467	C₂×C₈	—	7	1	no	—
468	C₂×C₈	—	7	1	no	—
469	C₂×C₈	—	7	1	no	—
470	C₂×C₈	—	14	2	no	—
471	C₂×C₈	—	14	2	no	—
472	C₂×C₈	—	14	1	no	—
473	C₂×C₈	—	14	1	no	—
474	C₂×C₈	—	14	1	no	—
475	C₂×C₈	—	28	2	no	—
476	C₂×C₈	—	28	2	no	—
477	C₂×C₈	—	28	2	no	—
478	C₂×C₈	—	28	2	no	—
479	C₂×C₈	C₂×C₄×D₇	1	1	yes	characteristic
480	C₂×C₈	C₂×C₄×D₇	1	1	yes	characteristic
481	C₂×C₈	D₄×D₇	1	1	yes	characteristic
482	C₂×C₈	D₄×D₇	1	1	yes	characteristic
483	C₄⋊C₄	—	2	1	no	—
484	C₄⋊C₄	—	7	1	no	—
485	C₄⋊C₄	—	7	1	no	—
486	C₄⋊C₄	—	14	1	no	—
487	C₄⋊C₄	—	14	1	no	—
488	C₄⋊C₄	—	14	1	no	—
489	C₄⋊C₄	—	14	1	no	—
490	C₄⋊C₄	—	14	1	no	—
491	C₄⋊C₄	—	14	1	no	—
492	C₄⋊C₄	—	14	1	no	—
493	C₄⋊C₄	C₂×C₄×D₇	1	1	yes	characteristic
494	C₄⋊C₄	C₂×C₄×D₇	1	1	yes	characteristic
495	C₂²⋊C₄	—	2	1	no	—
496	C₂²⋊C₄	—	14	1	no	—
497	C₂²⋊C₄	—	14	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	C₂³×D₇	1	1	yes	characteristic
507	C₂×C₇	—	4	2	no	—
508	C₂×C₇	#2929	1	1	yes	characteristic
509	C₂×C₇	C₂×#440	1	1	yes	characteristic
510	C₂×C₇	#2955	1	1	yes	characteristic
511	D₇	—	2	2	no	—
512	D₇	—	4	2	no	—
513	C₂³	—	2	1	no	—
514	C₂³	—	7	1	no	—
515	C₂³	—	14	4	no	—
516	C₂³	—	14	1	no	—
517	C₂³	—	28	2	no	—
518	C₂³	—	28	2	no	—
519	Q₈	—	2	1	no	—
520	Q₈	—	2	1	no	—
521	Q₈	—	14	1	no	—
522	Q₈	—	14	1	no	—
523	Q₈	—	28	2	no	—
524	D₄	—	2	1	no	—
525	D₄	—	7	2	no	—
526	D₄	—	14	4	no	—
527	D₄	—	14	1	no	—
528	D₄	#6470	1	2	yes	—
529	C₂×C₄	—	2	1	no	—
530	C₂×C₄	—	2	1	no	—
531	C₂×C₄	—	2	1	no	—
532	C₂×C₄	—	4	1	no	—
533	C₂×C₄	—	4	1	no	—
534	C₂×C₄	—	7	1	no	—
535	C₂×C₄	—	7	2	no	—
536	C₂×C₄	—	7	2	no	—
537	C₂×C₄	—	7	1	no	—
538	C₂×C₄	—	7	1	no	—
539	C₂×C₄	—	14	1	no	—
540	C₂×C₄	—	14	1	no	—
541	C₂×C₄	—	14	1	no	—
542	C₂×C₄	—	14	1	no	—
543	C₂×C₄	—	14	1	no	—
544	C₂×C₄	—	28	1	no	—
545	C₂×C₄	—	28	2	no	—
546	C₂×C₄	—	28	2	no	—
547	C₂×C₄	—	28	2	no	—
548	C₂×C₄	—	28	1	no	—
549	C₂×C₄	—	28	1	no	—
550	C₂×C₄	C₂²×C₄×D₇	1	1	yes	characteristic
551	C₂×C₄	C₂×D₄×D₇	1	1	yes	characteristic
552	C₂×C₄	D₇×#41	1	1	yes	characteristic
553	C₈	—	2	1	no	—
554	C₈	—	2	1	no	—
555	C₈	—	2	1	no	—
556	C₈	—	2	1	no	—
557	C₈	—	4	1	no	—
558	C₈	—	4	1	no	—
559	C₈	—	4	1	no	—
560	C₈	—	14	1	no	—
561	C₈	—	14	1	no	—
562	C₈	—	14	1	no	—
563	C₈	—	14	1	no	—
564	C₈	—	28	1	no	—
565	C₈	—	28	1	no	—
566	C₈	—	28	1	no	—
567	C₇	#17905	1	1	yes	characteristic, complemented, Sylow
568	C₂²	—	2	2	no	—
569	C₂²	—	4	1	no	—
570	C₂²	—	4	1	no	—
571	C₂²	—	7	2	no	—
572	C₂²	—	14	1	no	—
573	C₂²	—	14	1	no	—
574	C₂²	—	14	2	no	—
575	C₂²	—	28	8	no	—
576	C₂²	—	28	1	no	—
577	C₂²	—	28	1	no	—
578	C₂²	C₄×D₄×D₇	1	1	yes	characteristic
579	C₄	—	2	1	no	—
580	C₄	—	4	1	no	—
581	C₄	—	4	1	no	—
582	C₄	—	4	1	no	—
583	C₄	—	7	2	no	—
584	C₄	—	14	1	no	—
585	C₄	—	14	1	no	—
586	C₄	—	28	1	no	—
587	C₄	—	28	1	no	—
588	C₄	—	28	1	no	—
589	C₄	C₂×#6470	1	1	yes	characteristic
590	C₄	D₇×#131	1	1	yes	characteristic
591	C₄	D₇×AGL(1,ℤ/8)	1	1	yes	characteristic
592	C₄	D₇×#137	1	1	yes	characteristic
593	C₂	—	4	2	no	—
594	C₂	—	14	2	no	—
595	C₂	—	28	2	no	—
596	C₂	#11736923	1	1	yes	characteristic
597	C₂	D₇×#440	1	1	yes	characteristic
598	C₂	#11737333	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×#1585	C₂
socle	C₂²×C₇	C₂×C₄×D₄
prime radical	C₂×D₄×D₇	C₂×C₄
cosocle	C₄²×C₇	C₂⁴
hypercenter	#1585	D₇
hypocenter	C₇	#17905
LCS	G ▷ C₂×C₄×C₇ ▷ C₂×C₇ ▷ C₇
UCS	C₁ ◁ C₂×C₄ ◁ C₄×C₈ ◁ #1585

Complements

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

N	H ≅ G/N	type
1. #11737403	C₂	semidirect
4. C₇×#1585	C₂	semidirect
5. #11728708	C₂	semidirect
6. SD₁₆⋊(C₇⋊C₈)	C₂	semidirect
7. #11728597	C₂	semidirect
8. #11726326	C₂	semidirect
9. #11726312	C₂	semidirect
10. #11725986	C₂	semidirect
11. #11725968	C₂	semidirect
13. #11725904	C₂	semidirect
14. #11725834	C₂	semidirect
15. #11725825	C₂	semidirect
19. C₇×#446	C₂²	semidirect
26. Q₈×C₇⋊C₈	C₂²	semidirect
36. #89602	C₂²	semidirect
50. #89451	C₂²	semidirect
51. C₇×#335	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. #89253	C₂²	semidirect
63. #89251	C₂²	semidirect
64. #89250	C₂²	semidirect
65. #89249	C₂²	semidirect
66. #89249	C₂²	semidirect
152. #1585	D₇	semidirect
243. #446	C₂×D₇	semidirect
268. #335	C₂×D₇	semidirect
272. Q₈⋊C₈	C₂×D₇	semidirect
280. #322	C₂×D₇	semidirect
567. C₇	#17905	semidirect

Maximal subgroups

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

subgroup	index
#11737403	2
#11737096	2
C₈×D₄×D₇	2
C₇×#1585	2
#11728708	2
SD₁₆⋊(C₇⋊C₈)	2
#11728597	2
#11726326	2
#11726312	2
#11725986	2
#11725968	2
#11725926	2
#11725904	2
#11725834	2
#11725825	2
#17905	7