Subgroups — #13323862

Order 1792.

648 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	#11740586	C₂	1	1	yes	maximal, characteristic
2	#11740576	C₂	1	1	yes	maximal, characteristic, complemented
3	#11736731	C₂	1	1	yes	maximal, characteristic, complemented
4	C₇×#1482	C₂	1	1	yes	maximal, characteristic, complemented
5	#11728516	C₂	1	1	yes	maximal, characteristic, complemented
6	#11728502	C₂	1	1	yes	maximal, characteristic, complemented
7	#11728498	C₂	1	1	yes	maximal, characteristic, complemented
8	#11725974	C₂	1	1	yes	maximal, characteristic, complemented
9	#11725970	C₂	1	1	yes	maximal, characteristic, complemented
10	#11725968	C₂	1	1	yes	maximal, characteristic, complemented
11	#11725966	C₂	1	1	yes	maximal, characteristic, complemented
12	#11725912	C₂	1	1	yes	maximal, characteristic, complemented
13	#11725907	C₂	1	1	yes	maximal, characteristic, complemented
14	#11725905	C₂	1	1	yes	maximal, characteristic, complemented
15	#11725902	C₂	1	1	yes	maximal, characteristic, complemented
16	C₇×#529	C₂²	1	1	yes	characteristic
17	C₂×C₄×D₂₈	C₂²	1	1	yes	characteristic
18	C₇×#431	C₂²	1	1	yes	characteristic
19	C₇×#431	C₂²	1	1	yes	characteristic
20	#89838	C₄	1	1	yes	characteristic
21	#89838	C₄	1	1	yes	characteristic
22	#89829	C₄	1	1	yes	characteristic
23	#89829	C₄	1	1	yes	characteristic
24	#89818	C₄	1	1	yes	characteristic
25	#89816	C₄	1	1	yes	characteristic
26	#89808	C₄	1	1	yes	characteristic
27	#89806	C₄	1	1	yes	characteristic
28	C₄×#1143	C₂²	1	1	yes	characteristic
29	C₄×#1143	C₂²	1	1	yes	characteristic
30	#89796	C₂²	1	1	yes	characteristic, complemented
31	Q₈×C₇⋊C₈	C₂²	1	1	yes	characteristic, complemented
32	C₄×#1141	C₂²	1	1	yes	characteristic
33	C₄×#1141	C₂²	1	1	yes	characteristic
34	#89784	—	2	1	no	—
35	#89784	C₂²	1	1	yes	characteristic, complemented
36	#89783	—	2	1	no	—
37	D₄×C₇⋊C₈	C₂²	1	1	yes	characteristic, complemented
38	#89772	—	2	1	no	—
39	#89771	—	2	1	no	—
40	#89697	C₂²	1	1	yes	characteristic
41	#89697	C₂²	1	1	yes	characteristic
42	#89696	C₂²	1	1	yes	characteristic
43	#89606	C₂²	1	1	yes	characteristic
44	#89606	C₂²	1	1	yes	characteristic
45	#89606	C₂²	1	1	yes	characteristic
46	#89606	C₂²	1	1	yes	characteristic
47	D₇×C₂²⋊C₈	—	2	1	no	—
48	D₇×C₂²⋊C₈	—	2	1	no	—
49	C₈×D₂₈	—	2	1	no	—
50	C₈×D₂₈	—	2	1	no	—
51	C₇×Q₈⋊C₈	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, complemented
54	C₇×D₄⋊C₈	C₂²	1	1	yes	characteristic, complemented
55	#89275	C₂²	1	1	yes	characteristic, complemented
56	#89275	C₂²	1	1	yes	characteristic, complemented
57	#89274	C₂²	1	1	yes	characteristic, complemented
58	#89274	C₂²	1	1	yes	characteristic, complemented
59	#89254	C₂²	1	1	yes	characteristic
60	#89254	C₂²	1	1	yes	characteristic
61	#89254	C₂²	1	1	yes	characteristic
62	#89254	C₂²	1	1	yes	characteristic
63	#89250	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	#17918	—	7	1	no	maximal, Sylow
68	C₂²×D₂₈	C₂×C₄	1	1	yes	characteristic
69	C₂²×C₄×D₇	—	2	1	no	—
70	C₇×#126	—	2	1	no	—
71	C₇×#125	C₂×C₄	1	1	yes	characteristic
72	C₇×#124	C₂×C₄	1	1	yes	characteristic
73	C₇×#123	—	2	1	no	—
74	C₇×C₂²⋊Q₈	C₂×C₄	1	1	yes	characteristic
75	C₇×#121	C₂×C₄	1	1	yes	characteristic
76	C₄×C₇×Q₈	C₂³	1	1	yes	characteristic
77	C₄×C₇×D₄	—	2	1	no	—
78	C₄×C₇×D₄	C₂³	1	1	yes	characteristic
79	C₇×#117	—	2	1	no	—
80	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
81	C₂×#1143	C₂×C₄	1	1	yes	characteristic
82	C₂×#1143	C₂×C₄	1	1	yes	characteristic
83	C₂×#1141	C₂×C₄	1	1	yes	characteristic
84	C₂×#1141	C₂×C₄	1	1	yes	characteristic
85	C₂×(C₂×D₇)⋊C₄	—	2	1	no	—
86	C₂×C₄⋊Dic₇	C₂×C₄	1	1	yes	characteristic
87	C₂×#1136	—	2	1	no	—
88	C₂×#1136	—	2	1	no	—
89	C₂²×C₇⋊C₈	—	2	1	no	—
90	C₂×C₈×D₇	—	2	1	no	—
91	C₂×C₈×D₇	—	2	1	no	—
92	C₂×C₈×D₇	—	2	1	no	—
93	C₂×C₈×D₇	—	2	1	no	—
94	C₄×D₂₈	—	2	1	no	—
95	C₄×D₂₈	—	2	1	no	—
96	C₄×D₂₈	C₂×C₄	1	1	yes	characteristic
97	C₄×D₂₈	C₂×C₄	1	1	yes	characteristic
98	C₄×D₂₈	C₂³	1	1	yes	characteristic
99	C₄×D₂₈	C₂³	1	1	yes	characteristic
100	C₇×C₄⋊C₈	—	2	1	no	—
101	C₇×C₄⋊C₈	C₂³	1	1	yes	characteristic
102	C₇×C₄⋊C₈	C₂³	1	1	yes	characteristic
103	C₇×C₂²⋊C₈	—	2	1	no	—
104	C₇×C₂²⋊C₈	—	2	1	no	—
105	C₄×C₇×C₈	—	2	1	no	—
106	C₄×C₇×C₈	C₂³	1	1	yes	characteristic
107	C₄×C₇×C₈	C₂³	1	1	yes	characteristic
108	#6409	C₂×C₄	1	1	yes	characteristic
109	#6409	C₂×C₄	1	1	yes	characteristic
110	#6406	C₂×C₄	1	1	yes	characteristic
111	#6406	C₂×C₄	1	1	yes	characteristic
112	C₂²⋊(C₇⋊C₈)	—	2	1	no	—
113	C₂²⋊(C₇⋊C₈)	—	2	1	no	—
114	C₂²⋊(C₇⋊C₈)	C₂×C₄	1	1	yes	characteristic
115	C₂²⋊(C₇⋊C₈)	C₂×C₄	1	1	yes	characteristic
116	C₂²⋊(C₇⋊C₈)	D₄	1	1	yes	characteristic
117	C₂²⋊(C₇⋊C₈)	D₄	1	1	yes	characteristic
118	(C₂×D₇)⋊C₈	—	2	1	no	—
119	(C₂×D₇)⋊C₈	—	2	1	no	—
120	(C₂×D₇)⋊C₈	—	2	1	no	—
121	(C₂×D₇)⋊C₈	—	2	1	no	—
122	#6383	C₂×C₄	1	1	yes	characteristic
123	#6383	C₂×C₄	1	1	yes	characteristic
124	#6383	C₂×C₄	1	1	yes	characteristic
125	#6383	C₂×C₄	1	1	yes	characteristic
126	#6382	C₂×C₄	1	1	yes	characteristic
127	#6382	C₂×C₄	1	1	yes	characteristic
128	#6381	C₂×C₄	1	1	yes	characteristic
129	#6381	C₂×C₄	1	1	yes	characteristic
130	C₄⋊(C₇⋊C₈)	—	2	1	no	—
131	C₄⋊(C₇⋊C₈)	—	2	1	no	—
132	C₄⋊(C₇⋊C₈)	—	2	1	no	—
133	C₄⋊(C₇⋊C₈)	C₂×C₄	1	1	yes	characteristic
134	C₄⋊(C₇⋊C₈)	C₂×C₄	1	1	yes	characteristic
135	C₄⋊(C₇⋊C₈)	D₄	1	1	yes	characteristic
136	C₄⋊(C₇⋊C₈)	D₄	1	1	yes	characteristic
137	C₄⋊(C₇⋊C₈)	C₂³	1	1	yes	characteristic
138	C₄⋊(C₇⋊C₈)	C₂³	1	1	yes	characteristic
139	#6377	—	2	1	no	—
140	C₄×C₇⋊C₈	—	2	1	no	—
141	C₄×C₇⋊C₈	C₂³	1	1	yes	characteristic
142	C₄×C₇⋊C₈	C₂³	1	1	yes	characteristic
143	C₄×C₇⋊C₈	C₂³	1	1	yes	characteristic
144	C₄×C₇⋊C₈	C₂³	1	1	yes	characteristic
145	#3105	—	7	1	no	—
146	#2993	—	7	1	no	—
147	#2972	—	7	1	no	—
148	#1586	—	7	1	no	—
149	#1585	—	7	1	no	—
150	#1582	—	7	1	no	—
151	#1581	—	7	1	no	—
152	#1580	—	7	1	no	—
153	SD₁₆⋊C₈	—	7	1	no	—
154	C₈×SD₁₆	—	7	1	no	—
155	C₈×D₈	—	7	1	no	—
156	#1574	—	7	1	no	—
157	#1486	—	7	1	no	—
158	#1482	D₇	1	1	yes	characteristic, complemented
159	#1454	—	7	1	no	—
160	C₂³×D₇	—	2	1	no	—
161	C₂×C₇×Q₈	C₂²×C₄	1	1	yes	characteristic
162	C₂×C₇×D₄	—	2	1	no	—
163	C₂×C₇×D₄	C₂²×C₄	1	1	yes	characteristic
164	C₂²×C₄×C₇	—	2	1	no	—
165	C₂²×C₄×C₇	C₂²×C₄	1	1	yes	characteristic
166	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
167	C₂²×C₄×C₇	#41	1	1	yes	characteristic
168	C₂²×Dic₇	—	2	1	no	—
169	C₂×D₂₈	—	2	1	no	—
170	C₂×D₂₈	—	2	2	no	—
171	C₂×D₂₈	—	2	2	no	—
172	C₂×D₂₈	C₂²×C₄	1	1	yes	characteristic
173	C₂×D₂₈	C₂²×C₄	1	1	yes	characteristic
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	—	2	1	no	—
178	C₂×C₄×D₇	—	8	1	no	—
179	C₂×C₄×D₇	—	8	1	no	—
180	C₂×C₇×C₈	—	2	1	no	—
181	C₂×C₇×C₈	—	2	1	no	—
182	C₂×C₇×C₈	—	2	1	no	—
183	C₂×C₇×C₈	—	2	1	no	—
184	C₇×C₄⋊C₄	—	2	1	no	—
185	C₇×C₄⋊C₄	—	2	1	no	—
186	C₇×C₄⋊C₄	—	2	1	no	—
187	C₇×C₄⋊C₄	—	2	1	no	—
188	C₇×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
189	C₇×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
190	C₇×C₂²⋊C₄	—	2	1	no	—
191	C₇×C₂²⋊C₄	—	2	1	no	—
192	C₇×C₂²⋊C₄	—	2	1	no	—
193	C₇×C₂²⋊C₄	—	2	1	no	—
194	C₇×C₂²⋊C₄	—	2	1	no	—
195	C₄²×C₇	—	2	1	no	—
196	C₄²×C₇	C₂²×C₄	1	1	yes	characteristic
197	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
198	C₄²×C₇	#41	1	1	yes	characteristic
199	C₄²×C₇	C₂⁴	1	1	yes	characteristic
200	#1143	—	2	2	no	—
201	#1143	—	2	2	no	—
202	#1141	—	2	2	no	—
203	#1141	—	2	2	no	—
204	(C₂×D₇)⋊C₄	—	2	1	no	—
205	(C₂×D₇)⋊C₄	—	2	1	no	—
206	(C₂×D₇)⋊C₄	—	2	1	no	—
207	(C₂×D₇)⋊C₄	—	2	1	no	—
208	C₄⋊Dic₇	—	2	1	no	—
209	C₄⋊Dic₇	C₂²×C₄	1	1	yes	characteristic
210	C₄⋊Dic₇	C₂²×C₄	1	1	yes	characteristic
211	#1136	—	8	1	no	—
212	#1136	—	8	1	no	—
213	C₂×C₇⋊C₈	—	2	1	no	—
214	C₂×C₇⋊C₈	—	2	1	no	—
215	C₂×C₇⋊C₈	—	8	1	no	—
216	C₂×C₇⋊C₈	C₂²×C₄	1	1	yes	characteristic
217	C₂×C₇⋊C₈	C₂²×C₄	1	1	yes	characteristic
218	C₂×C₇⋊C₈	C₂²×C₄	1	1	yes	characteristic
219	C₂×C₇⋊C₈	C₂²×C₄	1	1	yes	characteristic
220	C₂×C₇⋊C₈	C₂×D₄	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	C₂×C₇⋊C₈	C₂×D₄	1	1	yes	characteristic
224	C₈×D₇	—	8	1	no	—
225	C₈×D₇	—	8	1	no	—
226	C₈×D₇	—	8	1	no	—
227	C₈×D₇	—	8	1	no	—
228	#529	C₂×D₇	1	1	yes	characteristic
229	C₂×C₄×D₄	—	7	1	no	—
230	#484	—	7	1	no	—
231	#481	—	7	1	no	—
232	#478	—	7	1	no	—
233	#478	—	7	1	no	—
234	#463	—	7	1	no	—
235	#463	—	7	1	no	—
236	#450	—	7	1	no	—
237	#447	—	7	1	no	—
238	#446	—	7	1	no	—
239	C₈×Q₈	—	7	1	no	—
240	C₄×SD₁₆	—	7	1	no	—
241	C₄×SD₁₆	—	7	1	no	—
242	C₄×D₈	—	7	1	no	—
243	C₄×D₈	—	7	1	no	—
244	#436	—	7	1	no	—
245	#436	—	14	1	no	—
246	#435	—	14	1	no	—
247	C₈×D₄	—	7	1	no	—
248	C₈×D₄	—	7	1	no	—
249	C₈×D₄	—	7	1	no	—
250	C₈×D₄	—	7	1	no	—
251	C₈×D₄	—	7	1	no	—
252	C₈×D₄	—	14	1	no	—
253	C₈×D₄	—	14	1	no	—
254	#433	—	14	1	no	—
255	#431	—	7	1	no	—
256	#431	—	7	1	no	—
257	#431	C₂×D₇	1	1	yes	characteristic
258	#431	C₂×D₇	1	1	yes	characteristic
259	#424	—	14	1	no	—
260	#423	—	7	1	no	—
261	C₂×C₂²⋊C₈	—	14	1	no	—
262	C₂×C₂²⋊C₈	—	14	1	no	—
263	#335	—	7	1	no	—
264	#335	—	7	1	no	—
265	#334	—	7	1	no	—
266	#334	—	7	1	no	—
267	Q₈⋊C₈	C₂×D₇	1	1	yes	characteristic, complemented
268	Q₈⋊C₈	C₂×D₇	1	1	yes	characteristic, complemented
269	D₄⋊C₈	—	7	1	no	—
270	D₄⋊C₈	—	7	1	no	—
271	D₄⋊C₈	—	7	1	no	—
272	D₄⋊C₈	—	7	1	no	—
273	D₄⋊C₈	C₂×D₇	1	1	yes	characteristic, complemented
274	D₄⋊C₈	C₂×D₇	1	1	yes	characteristic, complemented
275	#322	—	7	1	no	—
276	#322	—	7	1	no	—
277	#322	—	7	1	no	—
278	C₈²	—	7	1	no	—
279	C₂³×C₇	—	2	1	no	—
280	C₂³×C₇	C₄×D₄	1	1	yes	characteristic
281	C₂²×D₇	—	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	C₇×Q₈	—	2	1	no	—
287	C₇×Q₈	—	2	1	no	—
288	C₇×D₄	—	2	1	no	—
289	C₇×D₄	—	2	1	no	—
290	C₇×D₄	—	8	1	no	—
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	—	2	1	no	—
295	C₂×C₄×C₇	—	2	1	no	—
296	C₂×C₄×C₇	—	2	1	no	—
297	C₂×C₄×C₇	—	2	1	no	—
298	C₂×C₄×C₇	—	4	1	no	—
299	C₂×C₄×C₇	—	4	1	no	—
300	C₂×C₄×C₇	—	4	1	no	—
301	C₂×C₄×C₇	C₄×D₄	1	1	yes	characteristic
302	C₂×C₄×C₇	C₄×D₄	1	1	yes	characteristic
303	C₂×C₄×C₇	C₄×D₄	1	1	yes	characteristic
304	C₂×C₄×C₇	C₂³×C₄	1	1	yes	characteristic
305	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
306	C₂×C₄×C₇	C₂×#41	1	1	yes	characteristic
307	C₂×Dic₇	—	2	1	no	—
308	C₂×Dic₇	—	2	1	no	—
309	C₂×Dic₇	—	8	1	no	—
310	D₂₈	—	2	4	no	—
311	D₂₈	—	2	1	no	—
312	D₂₈	—	2	1	no	—
313	D₂₈	#131	1	2	yes	—
314	D₂₈	#131	1	2	yes	—
315	C₄×D₇	—	4	1	no	—
316	C₄×D₇	—	4	1	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	C₇×C₈	—	4	1	no	—
322	C₇×C₈	—	4	1	no	—
323	C₇×C₈	—	4	1	no	—
324	C₇×C₈	—	4	1	no	—
325	C₇⋊C₈	—	2	1	no	—
326	C₇⋊C₈	—	2	1	no	—
327	C₇⋊C₈	—	2	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	—	2	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×D₈	—	7	1	no	—
340	C₂×D₈	—	7	1	no	—
341	C₂×M₁₆	—	14	1	no	—
342	C₂×M₁₆	—	14	1	no	—
343	C₂²×C₈	—	14	1	no	—
344	C₂²×C₈	—	14	1	no	—
345	C₂²×C₈	—	14	1	no	—
346	C₂²×C₈	—	14	1	no	—
347	C₂²×C₈	—	14	1	no	—
348	#126	—	2	1	no	—
349	#125	C₄×D₇	1	1	yes	characteristic
350	#124	C₄×D₇	1	1	yes	characteristic
351	#123	—	2	1	no	—
352	C₂²⋊Q₈	C₄×D₇	1	1	yes	characteristic
353	#121	C₄×D₇	1	1	yes	characteristic
354	C₄×Q₈	C₂²×D₇	1	1	yes	characteristic
355	C₄×D₄	—	2	1	no	—
356	C₄×D₄	—	7	1	no	—
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	#117	—	2	1	no	—
364	C₂×C₄⋊C₄	—	7	1	no	—
365	C₂×C₂²⋊C₄	—	14	1	no	—
366	C₂×C₄²	C₂²×D₇	1	1	yes	characteristic
367	#107	—	7	1	no	—
368	#107	—	7	1	no	—
369	#106	—	7	1	no	—
370	#106	—	7	1	no	—
371	C₄⋊C₈	—	2	1	no	—
372	C₄⋊C₈	—	7	1	no	—
373	C₄⋊C₈	—	7	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	C₂²×D₇	1	1	yes	characteristic
382	C₄⋊C₈	C₂²×D₇	1	1	yes	characteristic
383	#103	—	7	1	no	—
384	#103	—	7	1	no	—
385	#102	—	7	1	no	—
386	#102	—	7	1	no	—
387	#102	—	7	1	no	—
388	#102	—	7	1	no	—
389	#102	—	7	1	no	—
390	#102	—	7	1	no	—
391	C₂²⋊C₈	—	2	1	no	—
392	C₂²⋊C₈	—	2	1	no	—
393	C₂²⋊C₈	—	7	1	no	—
394	C₂²⋊C₈	—	7	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	C₂²⋊C₈	—	14	1	no	—
402	C₂²⋊C₈	—	14	1	no	—
403	#97	—	14	1	no	—
404	C₄×C₈	—	2	1	no	—
405	C₄×C₈	—	7	1	no	—
406	C₄×C₈	—	7	1	no	—
407	C₄×C₈	—	7	1	no	—
408	C₄×C₈	—	7	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	C₂²×C₇	—	2	1	no	—
413	C₂²×C₇	—	2	1	no	—
414	C₂²×C₇	—	2	1	no	—
415	C₂²×C₇	—	4	1	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	2	no	—
420	C₂×D₇	—	2	2	no	—
421	C₂×D₇	—	4	1	no	—
422	C₂×D₇	—	4	1	no	—
423	C₂×D₇	—	4	1	no	—
424	C₂×D₇	—	4	1	no	—
425	C₂×D₇	—	8	4	no	—
426	C₄×C₇	—	2	1	no	—
427	C₄×C₇	—	2	1	no	—
428	C₄×C₇	—	2	1	no	—
429	C₄×C₇	—	2	1	no	—
430	C₄×C₇	—	4	1	no	—
431	C₄×C₇	—	4	1	no	—
432	C₄×C₇	—	4	1	no	—
433	C₄×C₇	C₂×#131	1	1	yes	characteristic
434	C₄×C₇	C₂×#131	1	1	yes	characteristic
435	C₄×C₇	#576	1	1	yes	characteristic
436	C₄×C₇	#577	1	1	yes	characteristic
437	Dic₇	—	4	1	no	—
438	Dic₇	—	4	1	no	—
439	C₂⁴	—	14	1	no	—
440	C₂×Q₈	C₂×C₄×D₇	1	1	yes	characteristic
441	C₂×D₄	—	2	1	no	—
442	C₂×D₄	—	7	1	no	—
443	C₂×D₄	—	7	1	no	—
444	C₂×D₄	—	14	2	no	—
445	C₂×D₄	—	14	2	no	—
446	C₂×D₄	—	14	1	no	—
447	C₂×D₄	C₂×C₄×D₇	1	1	yes	characteristic
448	C₂²×C₄	—	2	1	no	—
449	C₂²×C₄	—	14	1	no	—
450	C₂²×C₄	—	14	1	no	—
451	C₂²×C₄	—	14	1	no	—
452	C₂²×C₄	—	14	1	no	—
453	C₂²×C₄	—	14	1	no	—
454	C₂²×C₄	—	56	1	no	—
455	C₂²×C₄	—	56	1	no	—
456	C₂²×C₄	C₂×C₄×D₇	1	1	yes	characteristic
457	C₂²×C₄	D₄×D₇	1	1	yes	characteristic
458	C₂²×C₄	#1159	1	1	yes	characteristic
459	SD₁₆	—	14	2	no	—
460	SD₁₆	—	14	2	no	—
461	D₈	—	14	2	no	—
462	D₈	—	14	2	no	—
463	M₁₆	—	56	1	no	—
464	M₁₆	—	56	1	no	—
465	C₂×C₈	—	2	1	no	—
466	C₂×C₈	—	2	1	no	—
467	C₂×C₈	—	2	1	no	—
468	C₂×C₈	—	2	1	no	—
469	C₂×C₈	—	7	1	no	—
470	C₂×C₈	—	7	1	no	—
471	C₂×C₈	—	7	1	no	—
472	C₂×C₈	—	7	1	no	—
473	C₂×C₈	—	7	1	no	—
474	C₂×C₈	—	7	1	no	—
475	C₂×C₈	—	7	1	no	—
476	C₂×C₈	—	7	1	no	—
477	C₂×C₈	—	14	1	no	—
478	C₂×C₈	—	14	1	no	—
479	C₂×C₈	—	56	1	no	—
480	C₂×C₈	—	56	1	no	—
481	C₂×C₈	—	56	1	no	—
482	C₂×C₈	—	56	1	no	—
483	C₂×C₈	—	56	1	no	—
484	C₄⋊C₄	—	2	1	no	—
485	C₄⋊C₄	—	2	1	no	—
486	C₄⋊C₄	—	2	1	no	—
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	C₂×C₄×D₇	1	1	yes	characteristic
492	C₄⋊C₄	C₂×C₄×D₇	1	1	yes	characteristic
493	C₂²⋊C₄	—	2	1	no	—
494	C₂²⋊C₄	—	2	1	no	—
495	C₂²⋊C₄	—	2	1	no	—
496	C₂²⋊C₄	—	2	1	no	—
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	C₂²⋊C₄	—	14	1	no	—
502	C₄²	—	2	1	no	—
503	C₄²	C₂×C₄×D₇	1	1	yes	characteristic
504	C₄²	D₄×D₇	1	1	yes	characteristic
505	C₄²	#1159	1	1	yes	characteristic
506	C₄²	C₂³×D₇	1	1	yes	characteristic
507	C₂×C₇	—	4	1	no	—
508	C₂×C₇	—	8	1	no	—
509	C₂×C₇	#2929	1	1	yes	characteristic
510	C₂×C₇	#2946	1	1	yes	characteristic
511	C₂×C₇	#2957	1	1	yes	characteristic
512	D₇	—	4	2	no	—
513	D₇	—	4	2	no	—
514	C₂³	—	2	1	no	—
515	C₂³	—	14	4	no	—
516	C₂³	—	14	1	no	—
517	C₂³	—	14	1	no	—
518	C₂³	—	56	1	no	—
519	C₂³	—	56	1	no	—
520	C₂³	(C₂²⋊D₇)⋊C₄	1	1	yes	characteristic
521	Q₈	—	2	1	no	—
522	Q₈	—	2	1	no	—
523	D₄	—	2	1	no	—
524	D₄	—	2	1	no	—
525	D₄	—	7	2	no	—
526	D₄	—	7	2	no	—
527	D₄	—	8	1	no	—
528	D₄	—	14	4	no	—
529	D₄	—	14	1	no	—
530	D₄	—	14	1	no	—
531	C₂×C₄	—	2	1	no	—
532	C₂×C₄	—	2	1	no	—
533	C₂×C₄	—	2	1	no	—
534	C₂×C₄	—	2	1	no	—
535	C₂×C₄	—	2	1	no	—
536	C₂×C₄	—	2	1	no	—
537	C₂×C₄	—	2	1	no	—
538	C₂×C₄	—	4	1	no	—
539	C₂×C₄	—	4	1	no	—
540	C₂×C₄	—	4	1	no	—
541	C₂×C₄	—	14	1	no	—
542	C₂×C₄	—	14	1	no	—
543	C₂×C₄	—	28	1	no	—
544	C₂×C₄	—	28	1	no	—
545	C₂×C₄	—	28	1	no	—
546	C₂×C₄	—	28	1	no	—
547	C₂×C₄	—	56	1	no	—
548	C₂×C₄	—	56	1	no	—
549	C₂×C₄	—	56	1	no	—
550	C₂×C₄	(C₂²⋊D₇)⋊C₄	1	1	yes	characteristic
551	C₂×C₄	(C₂²⋊D₇)⋊C₄	1	1	yes	characteristic
552	C₂×C₄	(C₂²⋊D₇)⋊C₄	1	1	yes	characteristic
553	C₂×C₄	C₂²×C₄×D₇	1	1	yes	characteristic
554	C₂×C₄	C₂×D₄×D₇	1	1	yes	characteristic
555	C₂×C₄	C₂×#1159	1	1	yes	characteristic
556	C₈	—	4	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	—	14	1	no	—
565	C₈	—	14	1	no	—
566	C₈	—	14	1	no	—
567	C₈	—	14	1	no	—
568	C₈	—	28	1	no	—
569	C₈	—	28	1	no	—
570	C₇	#17918	1	1	yes	characteristic, complemented, Sylow
571	C₂²	—	2	1	no	—
572	C₂²	—	2	1	no	—
573	C₂²	—	2	1	no	—
574	C₂²	—	4	1	no	—
575	C₂²	—	4	1	no	—
576	C₂²	—	4	1	no	—
577	C₂²	—	14	2	no	—
578	C₂²	—	14	2	no	—
579	C₂²	—	28	1	no	—
580	C₂²	—	28	1	no	—
581	C₂²	—	28	1	no	—
582	C₂²	—	28	1	no	—
583	C₂²	—	56	4	no	—
584	C₂²	C₂×(C₂²⋊D₇)⋊C₄	1	1	yes	characteristic
585	C₄	—	2	1	no	—
586	C₄	—	2	1	no	—
587	C₄	—	2	1	no	—
588	C₄	—	2	1	no	—
589	C₄	—	4	1	no	—
590	C₄	—	4	1	no	—
591	C₄	—	4	1	no	—
592	C₄	—	28	1	no	—
593	C₄	—	28	1	no	—
594	C₄	D₇×#131	1	1	yes	characteristic
595	C₄	D₇×#131	1	1	yes	characteristic
596	C₄	#90460	1	1	yes	characteristic
597	C₄	#90461	1	1	yes	characteristic
598	C₂	—	4	1	no	—
599	C₂	—	8	1	no	—
600	C₂	—	28	2	no	—
601	C₂	—	28	2	no	—
602	C₂	#11736100	1	1	yes	characteristic
603	C₂	#11736265	1	1	yes	characteristic
604	C₂	#11736435	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×#1482	C₂
socle	C₂²×C₇	C₂×C₄×D₄
prime radical	#89808	C₄
cosocle	C₄²×C₇	C₂⁴
hypercenter	#1482	D₇
hypocenter	C₇	#17918
LCS	G ▷ C₂×C₄×C₇ ▷ C₂×C₇ ▷ C₇
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #1482

Complements

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

N	H ≅ G/N	type
2. #11740576	C₂	semidirect
3. #11736731	C₂	semidirect
4. C₇×#1482	C₂	semidirect
5. #11728516	C₂	semidirect
6. #11728502	C₂	semidirect
7. #11728498	C₂	semidirect
8. #11725974	C₂	semidirect
9. #11725970	C₂	semidirect
10. #11725968	C₂	semidirect
11. #11725966	C₂	semidirect
12. #11725912	C₂	semidirect
13. #11725907	C₂	semidirect
14. #11725905	C₂	semidirect
15. #11725902	C₂	semidirect
30. #89796	C₂²	semidirect
31. Q₈×C₇⋊C₈	C₂²	semidirect
35. #89784	C₂²	semidirect
37. D₄×C₇⋊C₈	C₂²	semidirect
51. C₇×Q₈⋊C₈	C₂²	semidirect
52. C₇×Q₈⋊C₈	C₂²	semidirect
53. C₇×D₄⋊C₈	C₂²	semidirect
54. C₇×D₄⋊C₈	C₂²	semidirect
55. #89275	C₂²	semidirect
56. #89275	C₂²	semidirect
57. #89274	C₂²	semidirect
58. #89274	C₂²	semidirect
63. #89250	C₂²	semidirect
64. #89249	C₂²	semidirect
65. #89249	C₂²	semidirect
66. C₈×C₇⋊C₈	C₂²	semidirect
158. #1482	D₇	semidirect
267. Q₈⋊C₈	C₂×D₇	semidirect
268. Q₈⋊C₈	C₂×D₇	semidirect
273. D₄⋊C₈	C₂×D₇	semidirect
274. D₄⋊C₈	C₂×D₇	semidirect
570. C₇	#17918	semidirect

Maximal subgroups

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

subgroup	index
#11740586	2
#11740576	2
#11736731	2
C₇×#1482	2
#11728516	2
#11728502	2
#11728498	2
#11725974	2
#11725970	2
#11725968	2
#11725966	2
#11725912	2
#11725907	2
#11725905	2
#11725902	2
#17918	7