Subgroups — #13323749

Order 1792.

626 conjugacy classes of subgroups.

The subgroup lattice has 580 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×#2966	C₂	1	1	yes	maximal, characteristic, complemented
2	#11740585	C₂	1	1	yes	maximal, characteristic
3	C₈×#1157	C₂	1	1	yes	maximal, characteristic, complemented
4	#11729504	C₂	1	1	yes	maximal, characteristic, complemented
5	#11728711	C₂	1	1	yes	maximal, characteristic, complemented
6	#11728708	C₂	1	1	yes	maximal, characteristic, complemented
7	#11728691	C₂	1	1	yes	maximal, characteristic, complemented
8	#11728686	C₂	1	1	yes	maximal, characteristic, complemented
9	#11728619	C₂	1	1	yes	maximal, characteristic, complemented
10	#11728617	C₂	1	1	yes	maximal, characteristic, complemented
11	#11728594	C₂	1	1	yes	maximal, characteristic, complemented
12	#11728593	C₂	1	1	yes	maximal, characteristic, complemented
13	#11728552	C₂	1	1	yes	maximal, characteristic, complemented
14	#11728550	C₂	1	1	yes	maximal, characteristic, complemented
15	#11727480	C₂	1	1	yes	maximal, characteristic, complemented
16	C₇×#529	C₂²	1	1	yes	characteristic
17	C₄×#1157	C₂²	1	1	yes	characteristic
18	C₇×#446	C₂²	1	1	yes	characteristic
19	C₇×C₈×Q₈	C₂²	1	1	yes	characteristic
20	C₇×#436	C₂²	1	1	yes	characteristic
21	C₇×#435	—	2	1	no	—
22	C₇×C₈×D₄	—	2	1	no	—
23	C₇×C₈×D₄	C₂²	1	1	yes	characteristic
24	C₇×#433	—	2	1	no	—
25	C₇×#432	C₂²	1	1	yes	characteristic
26	C₇×#405	—	2	1	no	—
27	C₂×C₄×C₇×C₈	C₂²	1	1	yes	characteristic
28	C₈×C₂²⋊D₇	—	2	1	no	—
29	C₈×C₂²⋊D₇	—	2	1	no	—
30	#89838	C₄	1	1	yes	characteristic
31	#89835	C₄	1	1	yes	characteristic
32	#89829	C₄	1	1	yes	characteristic
33	#89826	C₄	1	1	yes	characteristic
34	#89819	C₄	1	1	yes	characteristic
35	#89817	C₄	1	1	yes	characteristic
36	#89809	C₄	1	1	yes	characteristic
37	#89807	C₄	1	1	yes	characteristic
38	C₄×#1144	C₂²	1	1	yes	characteristic
39	C₄×#1143	C₂²	1	1	yes	characteristic
40	C₄×#1142	C₂²	1	1	yes	characteristic
41	C₄×#1141	C₂²	1	1	yes	characteristic
42	#89697	C₂²	1	1	yes	characteristic
43	#89697	C₂²	1	1	yes	characteristic
44	#89697	C₂²	1	1	yes	characteristic
45	C₈×D₂₈	C₂²	1	1	yes	characteristic
46	C₈×D₂₈	C₂²	1	1	yes	characteristic
47	#89457	—	2	1	no	—
48	C₄×C₈×D₇	—	2	1	no	—
49	C₈×Dic₁₄	C₂²	1	1	yes	characteristic
50	C₈×Dic₁₄	C₂²	1	1	yes	characteristic
51	Q₈⋊(C₇⋊C₈)	C₂²	1	1	yes	characteristic
52	Q₈⋊(C₇⋊C₈)	C₂²	1	1	yes	characteristic
53	D₄⋊(C₇⋊C₈)	C₂²	1	1	yes	characteristic
54	D₄⋊(C₇⋊C₈)	C₂²	1	1	yes	characteristic
55	#89279	C₂²	1	1	yes	characteristic
56	#89279	C₂²	1	1	yes	characteristic
57	#89278	C₂²	1	1	yes	characteristic
58	#89278	C₂²	1	1	yes	characteristic
59	#89275	C₂²	1	1	yes	characteristic
60	#89275	C₂²	1	1	yes	characteristic
61	#89274	C₂²	1	1	yes	characteristic
62	#89274	C₂²	1	1	yes	characteristic
63	#89249	C₂²	1	1	yes	characteristic
64	#89249	C₂²	1	1	yes	characteristic
65	#89249	C₂²	1	1	yes	characteristic
66	#89249	C₂²	1	1	yes	characteristic
67	#17909	—	7	1	no	maximal, Sylow
68	C₂×#1157	C₂×C₄	1	1	yes	characteristic
69	C₂×C₇×M₁₆	—	2	1	no	—
70	C₂²×C₇×C₈	—	2	1	no	—
71	C₂²×C₇×C₈	D₄	1	1	yes	characteristic
72	C₂²×C₇×C₈	D₄	1	1	yes	characteristic
73	C₇×#126	—	2	1	no	—
74	C₇×#125	C₂×C₄	1	1	yes	characteristic
75	C₇×#124	C₂×C₄	1	1	yes	characteristic
76	C₇×#123	—	2	1	no	—
77	C₇×C₂²⋊Q₈	C₂×C₄	1	1	yes	characteristic
78	C₇×#121	C₂×C₄	1	1	yes	characteristic
79	C₄×C₇×Q₈	C₂³	1	1	yes	characteristic
80	C₄×C₇×D₄	—	2	1	no	—
81	C₄×C₇×D₄	C₂³	1	1	yes	characteristic
82	C₇×#117	—	2	1	no	—
83	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
84	C₂×#1144	C₂×C₄	1	1	yes	characteristic
85	C₂×#1143	C₂×C₄	1	1	yes	characteristic
86	C₂×#1142	C₂×C₄	1	1	yes	characteristic
87	C₂×#1141	C₂×C₄	1	1	yes	characteristic
88	C₄×C₂²⋊D₇	—	2	1	no	—
89	C₄×C₂²⋊D₇	—	2	1	no	—
90	#6489	C₂×C₄	1	1	yes	characteristic
91	C₂×C₈×D₇	—	2	1	no	—
92	C₂×C₈×D₇	—	2	1	no	—
93	C₄×D₂₈	C₂×C₄	1	1	yes	characteristic
94	C₄×D₂₈	C₂³	1	1	yes	characteristic
95	#6435	—	2	1	no	—
96	C₄²×D₇	—	2	1	no	—
97	C₄×Dic₁₄	C₂×C₄	1	1	yes	characteristic
98	C₄×Dic₁₄	C₂³	1	1	yes	characteristic
99	C₇×C₄⋊C₈	—	2	1	no	—
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	C₇×C₂²⋊C₈	—	2	1	no	—
106	C₇×#97	—	2	1	no	—
107	C₇×#97	—	2	1	no	—
108	C₄×C₇×C₈	—	2	1	no	—
109	C₄×C₇×C₈	D₄	1	1	yes	characteristic
110	C₄×C₇×C₈	D₄	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	#6409	C₂×C₄	1	1	yes	characteristic
115	#6406	C₂×C₄	1	1	yes	characteristic
116	#6406	C₂×C₄	1	1	yes	characteristic
117	C₂²⋊(C₇⋊C₈)	—	2	1	no	—
118	C₂²⋊(C₇⋊C₈)	—	2	1	no	—
119	C₂²⋊(C₇⋊C₈)	C₂×C₄	1	1	yes	characteristic
120	C₂²⋊(C₇⋊C₈)	C₂×C₄	1	1	yes	characteristic
121	(C₂×D₇)⋊C₈	—	2	1	no	—
122	(C₂×D₇)⋊C₈	—	2	1	no	—
123	Dic₇⋊C₈	—	2	1	no	—
124	Dic₇⋊C₈	—	2	1	no	—
125	C₈×Dic₇	—	2	1	no	—
126	C₈×Dic₇	—	2	1	no	—
127	#6384	C₂×C₄	1	1	yes	characteristic
128	#6384	C₂×C₄	1	1	yes	characteristic
129	#6383	C₂×C₄	1	1	yes	characteristic
130	#6383	C₂×C₄	1	1	yes	characteristic
131	#6382	C₂×C₄	1	1	yes	characteristic
132	#6382	C₂×C₄	1	1	yes	characteristic
133	#6381	C₂×C₄	1	1	yes	characteristic
134	#6381	C₂×C₄	1	1	yes	characteristic
135	C₄⋊(C₇⋊C₈)	—	2	1	no	—
136	C₄⋊(C₇⋊C₈)	C₂×C₄	1	1	yes	characteristic
137	C₄⋊(C₇⋊C₈)	C₂×C₄	1	1	yes	characteristic
138	C₄⋊(C₇⋊C₈)	C₂³	1	1	yes	characteristic
139	C₄⋊(C₇⋊C₈)	C₂³	1	1	yes	characteristic
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	#3102	—	7	1	no	—
146	#2966	D₇	1	1	yes	characteristic, complemented
147	C₈×#41	—	7	1	no	—
148	#1588	—	7	1	no	—
149	#1587	—	7	1	no	—
150	#1586	—	7	1	no	—
151	#1585	—	7	1	no	—
152	#1580	—	7	1	no	—
153	#1579	—	7	1	no	—
154	SD₁₆⋊C₈	—	7	1	no	—
155	SD₁₆⋊C₈	—	7	1	no	—
156	#1572	—	7	1	no	—
157	#1488	—	7	1	no	—
158	#1482	—	7	1	no	—
159	#1452	—	7	1	no	—
160	C₂×C₇×Q₈	C₂²×C₄	1	1	yes	characteristic
161	C₂×C₇×D₄	—	2	1	no	—
162	C₂×C₇×D₄	C₂²×C₄	1	1	yes	characteristic
163	C₂²×C₄×C₇	—	2	1	no	—
164	C₂²×C₄×C₇	C₂²×C₄	1	1	yes	characteristic
165	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
166	C₂²×C₄×C₇	#41	1	1	yes	characteristic
167	C₂×C₂²⋊D₇	—	2	1	no	—
168	#1157	—	2	2	no	—
169	#1157	—	2	2	no	—
170	C₂×D₂₈	C₂²×C₄	1	1	yes	characteristic
171	C₂×C₄×D₇	—	2	1	no	—
172	C₂×C₄×D₇	—	2	1	no	—
173	C₂×C₄×D₇	—	2	1	no	—
174	C₂×Dic₁₄	C₂²×C₄	1	1	yes	characteristic
175	C₇×M₁₆	—	4	2	no	—
176	C₂×C₇×C₈	—	2	1	no	—
177	C₂×C₇×C₈	—	2	1	no	—
178	C₂×C₇×C₈	—	4	1	no	—
179	C₂×C₇×C₈	—	4	1	no	—
180	C₂×C₇×C₈	—	4	2	no	—
181	C₂×C₇×C₈	C₂×D₄	1	1	yes	characteristic
182	C₂×C₇×C₈	C₂×D₄	1	1	yes	characteristic
183	C₂×C₇×C₈	C₂×D₄	1	1	yes	characteristic
184	C₂×C₇×C₈	C₂×D₄	1	1	yes	characteristic
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	—	2	1	no	—
189	C₇×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
190	C₇×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
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	C₇×C₂²⋊C₄	—	2	1	no	—
196	C₄²×C₇	—	2	1	no	—
197	C₄²×C₇	C₂²×C₄	1	1	yes	characteristic
198	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
199	C₄²×C₇	#41	1	1	yes	characteristic
200	C₄²×C₇	C₂⁴	1	1	yes	characteristic
201	C₂²⋊Dic₇	—	2	1	no	—
202	#1144	—	2	2	no	—
203	#1143	—	2	2	no	—
204	#1142	—	2	2	no	—
205	#1141	—	2	2	no	—
206	(C₂×D₇)⋊C₄	—	2	1	no	—
207	(C₂×D₇)⋊C₄	—	2	1	no	—
208	C₄⋊Dic₇	C₂²×C₄	1	1	yes	characteristic
209	C₄⋊Dic₇	C₂²×C₄	1	1	yes	characteristic
210	Dic₇⋊C₄	—	2	1	no	—
211	Dic₇⋊C₄	—	2	1	no	—
212	C₄×Dic₇	—	2	1	no	—
213	C₄×Dic₇	—	2	1	no	—
214	C₄×Dic₇	—	2	1	no	—
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	—	2	1	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	C₂²×C₄	1	1	yes	characteristic
222	C₂×C₇⋊C₈	C₂²×C₄	1	1	yes	characteristic
223	C₈×D₇	—	4	2	no	—
224	C₈×D₇	—	4	2	no	—
225	#529	C₂×D₇	1	1	yes	characteristic
226	C₄×#41	—	7	1	no	—
227	#485	—	7	1	no	—
228	#482	—	7	1	no	—
229	#479	—	7	1	no	—
230	#478	—	7	1	no	—
231	#464	—	7	1	no	—
232	#463	—	7	1	no	—
233	#452	—	7	1	no	—
234	#449	—	7	1	no	—
235	#446	C₂×D₇	1	1	yes	characteristic
236	C₈×Q₈	—	7	1	no	—
237	C₈×Q₈	—	7	1	no	—
238	C₈×Q₈	C₂×D₇	1	1	yes	characteristic
239	C₄×Q₁₆	—	7	1	no	—
240	C₄×SD₁₆	—	7	1	no	—
241	C₄×SD₁₆	—	7	1	no	—
242	C₄×D₈	—	7	1	no	—
243	#436	C₂×D₇	1	1	yes	characteristic
244	#435	—	2	1	no	—
245	C₈×D₄	—	2	1	no	—
246	C₈×D₄	—	7	1	no	—
247	C₈×D₄	—	7	1	no	—
248	C₈×D₄	—	14	1	no	—
249	C₈×D₄	—	14	1	no	—
250	C₈×D₄	C₂×D₇	1	1	yes	characteristic
251	#433	—	2	1	no	—
252	#432	C₂×D₇	1	1	yes	characteristic
253	#431	—	7	1	no	—
254	#431	—	7	1	no	—
255	#431	—	7	1	no	—
256	#431	—	14	1	no	—
257	#405	—	2	1	no	—
258	C₂×C₄×C₈	—	14	1	no	—
259	C₂×C₄×C₈	C₂×D₇	1	1	yes	characteristic
260	#335	—	7	1	no	—
261	#335	—	7	1	no	—
262	#334	—	7	1	no	—
263	#334	—	7	1	no	—
264	Q₈⋊C₈	—	7	1	no	—
265	Q₈⋊C₈	—	7	1	no	—
266	Q₈⋊C₈	—	7	1	no	—
267	Q₈⋊C₈	—	7	1	no	—
268	D₄⋊C₈	—	7	1	no	—
269	D₄⋊C₈	—	7	1	no	—
270	D₄⋊C₈	—	7	1	no	—
271	D₄⋊C₈	—	7	1	no	—
272	#322	—	7	1	no	—
273	#322	—	7	1	no	—
274	#322	—	7	1	no	—
275	#322	—	7	1	no	—
276	C₂³×C₇	—	2	1	no	—
277	C₂³×C₇	C₄×D₄	1	1	yes	characteristic
278	C₂²×D₇	—	2	1	no	—
279	C₇×Q₈	—	2	1	no	—
280	C₇×Q₈	—	2	1	no	—
281	C₇×D₄	—	2	1	no	—
282	C₇×D₄	—	2	1	no	—
283	C₇×D₄	—	4	2	no	—
284	C₂×C₄×C₇	—	2	1	no	—
285	C₂×C₄×C₇	—	2	1	no	—
286	C₂×C₄×C₇	—	2	1	no	—
287	C₂×C₄×C₇	—	2	1	no	—
288	C₂×C₄×C₇	—	2	1	no	—
289	C₂×C₄×C₇	—	2	1	no	—
290	C₂×C₄×C₇	—	2	1	no	—
291	C₂×C₄×C₇	—	4	1	no	—
292	C₂×C₄×C₇	—	4	1	no	—
293	C₂×C₄×C₇	—	4	1	no	—
294	C₂×C₄×C₇	C₄×D₄	1	1	yes	characteristic
295	C₂×C₄×C₇	C₄×D₄	1	1	yes	characteristic
296	C₂×C₄×C₇	C₄×D₄	1	1	yes	characteristic
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	—	2	4	no	—
301	C₂×Dic₇	—	2	1	no	—
302	C₂×Dic₇	—	2	1	no	—
303	C₂×Dic₇	—	2	1	no	—
304	D₂₈	—	2	1	no	—
305	D₂₈	#131	1	2	yes	—
306	C₄×D₇	—	2	4	no	—
307	C₄×D₇	—	4	2	no	—
308	C₄×D₇	—	4	1	no	—
309	C₄×D₇	—	4	1	no	—
310	Dic₁₄	—	2	1	no	—
311	Dic₁₄	#131	1	2	yes	—
312	C₇×C₈	—	2	1	no	—
313	C₇×C₈	—	2	1	no	—
314	C₇×C₈	—	2	1	no	—
315	C₇×C₈	—	2	1	no	—
316	C₇×C₈	—	4	1	no	—
317	C₇×C₈	—	4	1	no	—
318	C₇⋊C₈	—	2	1	no	—
319	C₇⋊C₈	—	2	1	no	—
320	C₇⋊C₈	—	2	1	no	—
321	C₇⋊C₈	—	2	1	no	—
322	C₇⋊C₈	—	4	1	no	—
323	C₇⋊C₈	—	4	1	no	—
324	C₇⋊C₈	—	4	1	no	—
325	C₇⋊C₈	—	4	1	no	—
326	C₂×#41	—	7	1	no	—
327	C₂×Q₁₆	—	7	1	no	—
328	C₂×SD₁₆	—	7	1	no	—
329	C₂×SD₁₆	—	7	1	no	—
330	C₂×D₈	—	7	1	no	—
331	C₂×M₁₆	—	2	1	no	—
332	C₂²×C₈	—	2	1	no	—
333	C₂²×C₈	—	14	1	no	—
334	C₂²×C₈	—	14	1	no	—
335	C₂²×C₈	C₂²⋊D₇	1	1	yes	characteristic
336	C₂²×C₈	C₂²⋊D₇	1	1	yes	characteristic
337	#126	—	2	1	no	—
338	#125	C₄×D₇	1	1	yes	characteristic
339	#124	C₄×D₇	1	1	yes	characteristic
340	#123	—	2	1	no	—
341	C₂²⋊Q₈	C₄×D₇	1	1	yes	characteristic
342	#121	C₄×D₇	1	1	yes	characteristic
343	C₄×Q₈	—	7	1	no	—
344	C₄×Q₈	—	7	1	no	—
345	C₄×Q₈	C₂²×D₇	1	1	yes	characteristic
346	C₄×D₄	—	2	1	no	—
347	C₄×D₄	—	7	1	no	—
348	C₄×D₄	—	7	1	no	—
349	C₄×D₄	—	14	1	no	—
350	C₄×D₄	—	14	1	no	—
351	C₄×D₄	C₂²×D₇	1	1	yes	characteristic
352	#117	—	2	1	no	—
353	#117	—	7	1	no	—
354	#117	—	14	1	no	—
355	C₂×C₄²	—	14	1	no	—
356	C₂×C₄²	C₂²×D₇	1	1	yes	characteristic
357	#107	—	7	1	no	—
358	#107	—	7	1	no	—
359	#106	—	7	1	no	—
360	#106	—	7	1	no	—
361	C₄⋊C₈	—	2	1	no	—
362	C₄⋊C₈	—	2	1	no	—
363	C₄⋊C₈	—	7	1	no	—
364	C₄⋊C₈	—	7	1	no	—
365	C₄⋊C₈	—	7	1	no	—
366	C₄⋊C₈	—	7	1	no	—
367	C₄⋊C₈	—	14	1	no	—
368	C₄⋊C₈	—	14	1	no	—
369	C₄⋊C₈	—	14	1	no	—
370	C₄⋊C₈	C₂²×D₇	1	1	yes	characteristic
371	C₄⋊C₈	C₂²×D₇	1	1	yes	characteristic
372	#103	—	7	1	no	—
373	#103	—	7	1	no	—
374	#103	—	7	1	no	—
375	#103	—	7	1	no	—
376	#102	—	7	1	no	—
377	#102	—	7	1	no	—
378	#102	—	7	1	no	—
379	#102	—	7	1	no	—
380	C₂²⋊C₈	—	2	1	no	—
381	C₂²⋊C₈	—	2	1	no	—
382	C₂²⋊C₈	—	2	1	no	—
383	C₂²⋊C₈	—	7	1	no	—
384	C₂²⋊C₈	—	7	1	no	—
385	C₂²⋊C₈	—	14	1	no	—
386	C₂²⋊C₈	—	14	1	no	—
387	C₂²⋊C₈	—	14	1	no	—
388	C₂²⋊C₈	—	14	1	no	—
389	#97	—	2	1	no	—
390	#97	—	2	1	no	—
391	C₄×C₈	—	2	1	no	—
392	C₄×C₈	—	7	1	no	—
393	C₄×C₈	—	7	1	no	—
394	C₄×C₈	—	7	1	no	—
395	C₄×C₈	—	7	1	no	—
396	C₄×C₈	—	14	1	no	—
397	C₄×C₈	—	14	1	no	—
398	C₄×C₈	—	14	1	no	—
399	C₄×C₈	C₂²⋊D₇	1	1	yes	characteristic
400	C₄×C₈	C₂²⋊D₇	1	1	yes	characteristic
401	C₄×C₈	C₂²×D₇	1	1	yes	characteristic
402	C₄×C₈	C₂²×D₇	1	1	yes	characteristic
403	C₂²×C₇	—	2	1	no	—
404	C₂²×C₇	—	2	1	no	—
405	C₂²×C₇	—	2	1	no	—
406	C₂²×C₇	—	4	1	no	—
407	C₂²×C₇	—	4	1	no	—
408	C₂²×C₇	—	4	1	no	—
409	C₂²×C₇	C₂×C₄×D₄	1	1	yes	characteristic
410	C₂×D₇	—	2	2	no	—
411	C₂×D₇	—	4	1	no	—
412	C₂×D₇	—	4	1	no	—
413	C₄×C₇	—	2	1	no	—
414	C₄×C₇	—	2	1	no	—
415	C₄×C₇	—	2	1	no	—
416	C₄×C₇	—	2	1	no	—
417	C₄×C₇	—	4	1	no	—
418	C₄×C₇	—	4	1	no	—
419	C₄×C₇	—	4	1	no	—
420	C₄×C₇	C₂×#131	1	1	yes	characteristic
421	C₄×C₇	C₂×#131	1	1	yes	characteristic
422	C₄×C₇	#575	1	1	yes	characteristic
423	C₄×C₇	#575	1	1	yes	characteristic
424	Dic₇	—	2	2	no	—
425	Dic₇	—	4	1	no	—
426	Dic₇	—	4	1	no	—
427	#41	—	14	2	no	—
428	#41	—	14	2	no	—
429	C₂×Q₈	—	7	1	no	—
430	C₂×Q₈	C₂×C₄×D₇	1	1	yes	characteristic
431	C₂×D₄	—	2	1	no	—
432	C₂×D₄	—	7	1	no	—
433	C₂×D₄	—	14	1	no	—
434	C₂×D₄	C₂×C₄×D₇	1	1	yes	characteristic
435	C₂²×C₄	—	2	1	no	—
436	C₂²×C₄	—	14	1	no	—
437	C₂²×C₄	—	14	1	no	—
438	C₂²×C₄	—	14	1	no	—
439	C₂²×C₄	C₂×C₄×D₇	1	1	yes	characteristic
440	C₂²×C₄	#1157	1	1	yes	characteristic
441	C₂²×C₄	C₂×C₂²⋊D₇	1	1	yes	characteristic
442	Q₁₆	—	14	2	no	—
443	SD₁₆	—	14	2	no	—
444	SD₁₆	—	14	2	no	—
445	D₈	—	14	2	no	—
446	M₁₆	—	4	2	no	—
447	C₂×C₈	—	2	1	no	—
448	C₂×C₈	—	2	1	no	—
449	C₂×C₈	—	4	1	no	—
450	C₂×C₈	—	4	1	no	—
451	C₂×C₈	—	4	2	no	—
452	C₂×C₈	—	7	1	no	—
453	C₂×C₈	—	7	1	no	—
454	C₂×C₈	—	7	1	no	—
455	C₂×C₈	—	7	1	no	—
456	C₂×C₈	—	14	1	no	—
457	C₂×C₈	—	14	1	no	—
458	C₂×C₈	—	14	1	no	—
459	C₂×C₈	—	14	1	no	—
460	C₂×C₈	—	28	2	no	—
461	C₂×C₈	—	28	2	no	—
462	C₂×C₈	C₂×C₂²⋊D₇	1	1	yes	characteristic
463	C₂×C₈	C₂×C₂²⋊D₇	1	1	yes	characteristic
464	C₂×C₈	C₂×C₂²⋊D₇	1	1	yes	characteristic
465	C₂×C₈	C₂×C₂²⋊D₇	1	1	yes	characteristic
466	C₄⋊C₄	—	2	1	no	—
467	C₄⋊C₄	—	2	1	no	—
468	C₄⋊C₄	—	2	1	no	—
469	C₄⋊C₄	—	2	1	no	—
470	C₄⋊C₄	—	7	1	no	—
471	C₄⋊C₄	—	7	1	no	—
472	C₄⋊C₄	—	14	1	no	—
473	C₄⋊C₄	—	14	1	no	—
474	C₄⋊C₄	C₂×C₄×D₇	1	1	yes	characteristic
475	C₄⋊C₄	C₂×C₄×D₇	1	1	yes	characteristic
476	C₂²⋊C₄	—	2	1	no	—
477	C₂²⋊C₄	—	2	1	no	—
478	C₂²⋊C₄	—	2	1	no	—
479	C₂²⋊C₄	—	2	1	no	—
480	C₂²⋊C₄	—	2	1	no	—
481	C₂²⋊C₄	—	14	1	no	—
482	C₂²⋊C₄	—	14	1	no	—
483	C₂²⋊C₄	—	14	1	no	—
484	C₄²	—	2	1	no	—
485	C₄²	—	14	1	no	—
486	C₄²	—	14	1	no	—
487	C₄²	—	14	1	no	—
488	C₄²	C₂×C₄×D₇	1	1	yes	characteristic
489	C₄²	#1157	1	1	yes	characteristic
490	C₄²	C₂×C₂²⋊D₇	1	1	yes	characteristic
491	C₄²	C₂³×D₇	1	1	yes	characteristic
492	C₂×C₇	—	4	1	no	—
493	C₂×C₇	—	8	1	no	—
494	C₂×C₇	#2929	1	1	yes	characteristic
495	C₂×C₇	#2943	1	1	yes	characteristic
496	C₂×C₇	#2955	1	1	yes	characteristic
497	D₇	—	4	2	no	—
498	C₂³	—	2	1	no	—
499	C₂³	—	14	1	no	—
500	C₂³	C₄×C₂²⋊D₇	1	1	yes	characteristic
501	Q₈	—	2	1	no	—
502	Q₈	—	2	1	no	—
503	Q₈	—	7	2	no	—
504	Q₈	—	14	1	no	—
505	D₄	—	2	1	no	—
506	D₄	—	2	1	no	—
507	D₄	—	4	2	no	—
508	D₄	—	7	2	no	—
509	D₄	—	14	4	no	—
510	D₄	—	14	1	no	—
511	C₂×C₄	—	2	1	no	—
512	C₂×C₄	—	2	1	no	—
513	C₂×C₄	—	2	1	no	—
514	C₂×C₄	—	2	1	no	—
515	C₂×C₄	—	2	1	no	—
516	C₂×C₄	—	2	1	no	—
517	C₂×C₄	—	2	1	no	—
518	C₂×C₄	—	4	1	no	—
519	C₂×C₄	—	4	1	no	—
520	C₂×C₄	—	4	1	no	—
521	C₂×C₄	—	14	4	no	—
522	C₂×C₄	—	14	1	no	—
523	C₂×C₄	—	14	1	no	—
524	C₂×C₄	—	14	1	no	—
525	C₂×C₄	—	28	2	no	—
526	C₂×C₄	—	28	1	no	—
527	C₂×C₄	—	28	1	no	—
528	C₂×C₄	C₄×C₂²⋊D₇	1	1	yes	characteristic
529	C₂×C₄	C₄×C₂²⋊D₇	1	1	yes	characteristic
530	C₂×C₄	C₄×C₂²⋊D₇	1	1	yes	characteristic
531	C₂×C₄	C₂²×C₄×D₇	1	1	yes	characteristic
532	C₂×C₄	C₂×#1157	1	1	yes	characteristic
533	C₂×C₄	C₂²×C₂²⋊D₇	1	1	yes	characteristic
534	C₈	—	2	1	no	—
535	C₈	—	2	1	no	—
536	C₈	—	2	1	no	—
537	C₈	—	2	1	no	—
538	C₈	—	4	1	no	—
539	C₈	—	4	1	no	—
540	C₈	—	14	1	no	—
541	C₈	—	14	1	no	—
542	C₈	—	14	1	no	—
543	C₈	—	14	1	no	—
544	C₈	—	28	1	no	—
545	C₈	—	28	1	no	—
546	C₈	—	28	1	no	—
547	C₈	—	28	1	no	—
548	C₇	#17909	1	1	yes	characteristic, complemented, Sylow
549	C₂²	—	2	1	no	—
550	C₂²	—	2	1	no	—
551	C₂²	—	2	1	no	—
552	C₂²	—	4	1	no	—
553	C₂²	—	4	1	no	—
554	C₂²	—	4	1	no	—
555	C₂²	—	14	2	no	—
556	C₂²	—	28	1	no	—
557	C₂²	—	28	1	no	—
558	C₂²	C₂×C₄×C₂²⋊D₇	1	1	yes	characteristic
559	C₄	—	2	1	no	—
560	C₄	—	2	1	no	—
561	C₄	—	2	1	no	—
562	C₄	—	2	1	no	—
563	C₄	—	4	1	no	—
564	C₄	—	4	1	no	—
565	C₄	—	4	1	no	—
566	C₄	—	14	2	no	—
567	C₄	—	28	1	no	—
568	C₄	—	28	1	no	—
569	C₄	D₇×#131	1	1	yes	characteristic
570	C₄	D₇×#131	1	1	yes	characteristic
571	C₄	#90513	1	1	yes	characteristic
572	C₄	#90513	1	1	yes	characteristic
573	C₂	—	4	1	no	—
574	C₂	—	8	1	no	—
575	C₂	—	28	2	no	—
576	C₂	#11739951	1	1	yes	characteristic
577	C₂	#11741237	1	1	yes	characteristic
578	C₂	#11741239	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂²×C₂²⋊D₇
commutator	C₂×C₄×C₇	C₂³×C₄
Frattini	C₄²	C₂³×D₇
Fitting	C₇×#2966	C₂
socle	C₂²×C₇	C₂×C₄×D₄
prime radical	#89809	C₄
cosocle	C₄²×C₇	C₂⁴
hypercenter	#2966	D₇
hypocenter	C₇	#17909
LCS	G ▷ C₂×C₄×C₇ ▷ C₂×C₇ ▷ C₇
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄×C₈ ◁ #2966

Complements

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

N	H ≅ G/N	type
1. C₇×#2966	C₂	semidirect
3. C₈×#1157	C₂	semidirect
4. #11729504	C₂	semidirect
5. #11728711	C₂	semidirect
6. #11728708	C₂	semidirect
7. #11728691	C₂	semidirect
8. #11728686	C₂	semidirect
9. #11728619	C₂	semidirect
10. #11728617	C₂	semidirect
11. #11728594	C₂	semidirect
12. #11728593	C₂	semidirect
13. #11728552	C₂	semidirect
14. #11728550	C₂	semidirect
15. #11727480	C₂	semidirect
146. #2966	D₇	semidirect
548. C₇	#17909	semidirect

Maximal subgroups

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

subgroup	index
C₇×#2966	2
#11740585	2
C₈×#1157	2
#11729504	2
#11728711	2
#11728708	2
#11728691	2
#11728686	2
#11728619	2
#11728617	2
#11728594	2
#11728593	2
#11728552	2
#11728550	2
#11727480	2
#17909	7