Subgroups — #13323954

Order 1792.

620 conjugacy classes of subgroups.

The subgroup lattice has 582 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#11739973	C₂	1	1	yes	maximal, characteristic
2	#11739965	C₂	1	1	yes	maximal, characteristic, complemented
3	#11736498	C₂	1	1	yes	maximal, characteristic, complemented
4	C₇×#1489	C₂	1	1	yes	maximal, characteristic, complemented
5	#11728248	C₂	1	1	yes	maximal, characteristic, complemented
6	#11727606	C₂	1	1	yes	maximal, characteristic, complemented
7	#11727602	C₂	1	1	yes	maximal, characteristic, complemented
8	#11725977	C₂	1	1	yes	maximal, characteristic, complemented
9	#11725972	C₂	1	1	yes	maximal, characteristic, complemented
10	#11725968	C₂	1	1	yes	maximal, characteristic, complemented
11	#11725967	C₂	1	1	yes	maximal, characteristic, complemented
12	#11725910	C₂	1	1	yes	maximal, characteristic, complemented
13	#11725906	C₂	1	1	yes	maximal, characteristic, complemented
14	#11725904	C₂	1	1	yes	maximal, characteristic, complemented
15	#11725902	C₂	1	1	yes	maximal, characteristic, complemented
16	C₄×C₇×#41	C₂²	1	1	yes	characteristic
17	#90170	C₂²	1	1	yes	characteristic
18	C₇×#423	C₂²	1	1	yes	characteristic
19	C₄×C₇×M₁₆	C₂²	1	1	yes	characteristic
20	#90011	C₄	1	1	yes	characteristic
21	#90010	C₄	1	1	yes	characteristic
22	#89900	—	2	1	no	—
23	#89899	—	2	1	no	—
24	C₄×#1144	C₂²	1	1	yes	characteristic
25	#89800	C₄	1	1	yes	characteristic
26	C₄×#1143	C₂²	1	1	yes	characteristic
27	Q₈×C₇⋊C₈	C₂²	1	1	yes	characteristic
28	Q₈×C₇⋊C₈	C₂²	1	1	yes	characteristic
29	#89794	C₄	1	1	yes	characteristic
30	C₄×#1142	C₂²	1	1	yes	characteristic
31	#89788	C₄	1	1	yes	characteristic
32	C₄×#1141	C₂²	1	1	yes	characteristic
33	D₄×C₇⋊C₈	—	2	1	no	—
34	D₄×C₇⋊C₈	—	2	1	no	—
35	D₄×C₇⋊C₈	C₂²	1	1	yes	characteristic
36	D₄×C₇⋊C₈	C₂²	1	1	yes	characteristic
37	#89781	C₄	1	1	yes	characteristic
38	#89775	C₄	1	1	yes	characteristic
39	#89768	C₄	1	1	yes	characteristic
40	#89697	—	2	1	no	—
41	#89697	C₂²	1	1	yes	characteristic
42	#89697	C₂²	1	1	yes	characteristic
43	C₂×C₄⋊(C₇⋊C₈)	—	2	1	no	—
44	C₂×C₄⋊(C₇⋊C₈)	C₂²	1	1	yes	characteristic
45	#89612	—	2	1	no	—
46	#89611	—	2	1	no	—
47	#89610	C₂²	1	1	yes	characteristic
48	#89606	C₂²	1	1	yes	characteristic
49	#89603	C₂²	1	1	yes	characteristic
50	#89602	C₂²	1	1	yes	characteristic
51	C₇×Q₈⋊C₈	C₂²	1	1	yes	characteristic
52	C₇×Q₈⋊C₈	C₂²	1	1	yes	characteristic
53	C₇×D₄⋊C₈	C₂²	1	1	yes	characteristic
54	C₇×D₄⋊C₈	C₂²	1	1	yes	characteristic
55	#89274	C₂²	1	1	yes	characteristic
56	#89274	C₂²	1	1	yes	characteristic
57	#89274	C₂²	1	1	yes	characteristic
58	#89274	C₂²	1	1	yes	characteristic
59	#89254	C₂²	1	1	yes	characteristic
60	#89254	C₂²	1	1	yes	characteristic
61	#89251	C₂²	1	1	yes	characteristic
62	#89251	C₂²	1	1	yes	characteristic
63	#89250	C₂²	1	1	yes	characteristic
64	#89249	C₂²	1	1	yes	characteristic
65	#89249	C₂²	1	1	yes	characteristic
66	C₈×C₇⋊C₈	C₂²	1	1	yes	characteristic
67	#17926	—	7	1	no	maximal, Sylow
68	C₂×C₇×#41	C₂×C₄	1	1	yes	characteristic
69	C₂×C₇×M₁₆	—	2	1	no	—
70	C₂×C₇×M₁₆	—	2	1	no	—
71	C₄×C₇×Q₈	C₂×C₄	1	1	yes	characteristic
72	C₄×C₇×Q₈	C₂³	1	1	yes	characteristic
73	C₄×C₇×D₄	—	2	1	no	—
74	C₄×C₇×D₄	—	2	1	no	—
75	C₄×C₇×D₄	C₂×C₄	1	1	yes	characteristic
76	C₄×C₇×D₄	C₂³	1	1	yes	characteristic
77	C₇×#117	—	2	1	no	—
78	C₇×#117	C₂×C₄	1	1	yes	characteristic
79	C₂×C₄²×C₇	—	2	1	no	—
80	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
81	C₂×#1144	C₂×C₄	1	1	yes	characteristic
82	C₂×#1143	C₂×C₄	1	1	yes	characteristic
83	C₂×#1142	C₂×C₄	1	1	yes	characteristic
84	C₂×#1141	C₂×C₄	1	1	yes	characteristic
85	#6493	C₂×C₄	1	1	yes	characteristic
86	#6492	—	2	1	no	—
87	C₄×C₂²⋊D₇	—	2	1	no	—
88	#6487	C₂×C₄	1	1	yes	characteristic
89	C₂²×C₇⋊C₈	—	2	1	no	—
90	C₂²×C₇⋊C₈	—	2	1	no	—
91	C₂²×C₇⋊C₈	—	2	1	no	—
92	C₂×#1131	—	2	1	no	—
93	C₂×C₈×D₇	—	2	1	no	—
94	#6439	—	2	1	no	—
95	#6438	C₂×C₄	1	1	yes	characteristic
96	C₄×D₂₈	C₂³	1	1	yes	characteristic
97	#6435	—	2	1	no	—
98	#6433	C₂×C₄	1	1	yes	characteristic
99	C₄×Dic₁₄	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×#97	—	2	1	no	—
104	C₄×C₇×C₈	C₂³	1	1	yes	characteristic
105	C₄×C₇×C₈	C₂³	1	1	yes	characteristic
106	#6409	C₂×C₄	1	1	yes	characteristic
107	#6409	C₂×C₄	1	1	yes	characteristic
108	#6406	C₂×C₄	1	1	yes	characteristic
109	#6406	C₂×C₄	1	1	yes	characteristic
110	C₂²⋊(C₇⋊C₈)	—	2	1	no	—
111	C₂²⋊(C₇⋊C₈)	—	2	1	no	—
112	C₂²⋊(C₇⋊C₈)	C₂×C₄	1	1	yes	characteristic
113	C₂²⋊(C₇⋊C₈)	C₂×C₄	1	1	yes	characteristic
114	C₂²⋊(C₇⋊C₈)	D₄	1	1	yes	characteristic
115	C₂²⋊(C₇⋊C₈)	D₄	1	1	yes	characteristic
116	(C₂×D₇)⋊C₈	—	2	1	no	—
117	(C₂×D₇)⋊C₈	—	2	1	no	—
118	#6389	—	2	1	no	—
119	Dic₇⋊C₈	—	2	1	no	—
120	Dic₇⋊C₈	—	2	1	no	—
121	C₈×Dic₇	—	2	1	no	—
122	#6384	C₂×C₄	1	1	yes	characteristic
123	#6384	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	C₄×C₇⋊C₈	—	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	#3102	—	7	1	no	—
146	#2993	—	7	1	no	—
147	#2988	—	7	1	no	—
148	#1588	—	7	1	no	—
149	#1585	—	7	1	no	—
150	#1584	—	7	1	no	—
151	#1581	—	7	1	no	—
152	SD₁₆⋊C₈	—	7	1	no	—
153	SD₁₆⋊C₈	—	7	1	no	—
154	C₈×Q₁₆	—	7	1	no	—
155	C₈×D₈	—	7	1	no	—
156	#1571	—	7	1	no	—
157	#1489	D₇	1	1	yes	characteristic, complemented
158	#1483	—	7	1	no	—
159	#1453	—	7	1	no	—
160	C₇×#41	—	2	2	no	—
161	C₇×#41	—	2	2	no	—
162	C₂×C₇×Q₈	C₂²×C₄	1	1	yes	characteristic
163	C₂×C₇×D₄	—	2	1	no	—
164	C₂×C₇×D₄	C₂²×C₄	1	1	yes	characteristic
165	C₂²×C₄×C₇	—	2	1	no	—
166	C₂²×C₄×C₇	—	2	1	no	—
167	C₂²×C₄×C₇	—	2	1	no	—
168	C₂²×C₄×C₇	C₂²×C₄	1	1	yes	characteristic
169	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
170	C₂²×C₄×C₇	#41	1	1	yes	characteristic
171	C₂×C₂²⋊D₇	—	2	1	no	—
172	C₂×D₂₈	C₂²×C₄	1	1	yes	characteristic
173	C₂×C₄×D₇	—	2	1	no	—
174	C₂×Dic₁₄	C₂²×C₄	1	1	yes	characteristic
175	C₇×M₁₆	—	4	2	no	—
176	C₇×M₁₆	—	8	1	no	—
177	C₂×C₇×C₈	—	2	1	no	—
178	C₂×C₇×C₈	—	2	1	no	—
179	C₂×C₇×C₈	—	2	1	no	—
180	C₂×C₇×C₈	—	2	1	no	—
181	C₇×C₄⋊C₄	—	2	1	no	—
182	C₇×C₄⋊C₄	—	2	1	no	—
183	C₇×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
184	C₇×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
185	C₇×C₂²⋊C₄	—	2	1	no	—
186	C₇×C₂²⋊C₄	—	2	1	no	—
187	C₇×C₂²⋊C₄	—	2	1	no	—
188	C₄²×C₇	—	2	1	no	—
189	C₄²×C₇	—	2	1	no	—
190	C₄²×C₇	—	2	1	no	—
191	C₄²×C₇	C₂²×C₄	1	1	yes	characteristic
192	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
193	C₄²×C₇	#41	1	1	yes	characteristic
194	C₄²×C₇	C₂⁴	1	1	yes	characteristic
195	C₂²⋊Dic₇	—	2	1	no	—
196	#1144	—	2	2	no	—
197	#1143	—	2	2	no	—
198	#1142	—	2	2	no	—
199	#1141	—	2	2	no	—
200	(C₂×D₇)⋊C₄	—	2	1	no	—
201	(C₂×D₇)⋊C₄	—	2	1	no	—
202	(C₂×D₇)⋊C₄	—	2	1	no	—
203	(C₂×D₇)⋊C₄	—	2	1	no	—
204	C₄⋊Dic₇	C₂²×C₄	1	1	yes	characteristic
205	C₄⋊Dic₇	C₂²×C₄	1	1	yes	characteristic
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	C₄×Dic₇	—	2	1	no	—
211	C₂×C₇⋊C₈	—	2	1	no	—
212	C₂×C₇⋊C₈	—	2	1	no	—
213	C₂×C₇⋊C₈	—	8	1	no	—
214	C₂×C₇⋊C₈	—	8	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	#1131	—	8	1	no	—
225	C₈×D₇	—	8	1	no	—
226	#529	—	7	1	no	—
227	C₄×#41	C₂×D₇	1	1	yes	characteristic
228	#485	—	7	1	no	—
229	#482	—	7	1	no	—
230	#479	—	7	1	no	—
231	#478	—	7	1	no	—
232	#464	—	7	1	no	—
233	#463	—	7	1	no	—
234	#452	—	7	1	no	—
235	#449	—	7	1	no	—
236	#446	—	7	1	no	—
237	C₈×Q₈	—	7	1	no	—
238	C₈×Q₈	—	7	1	no	—
239	C₈×Q₈	—	7	1	no	—
240	C₄×Q₁₆	—	7	1	no	—
241	C₄×SD₁₆	—	7	1	no	—
242	C₄×SD₁₆	—	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	—	14	1	no	—
251	C₈×D₄	—	14	1	no	—
252	#433	—	14	1	no	—
253	#431	—	7	1	no	—
254	#431	—	7	1	no	—
255	#431	—	14	1	no	—
256	#424	—	14	1	no	—
257	#423	C₂×D₇	1	1	yes	characteristic
258	C₂×C₄⋊C₈	—	7	1	no	—
259	C₂×C₄⋊C₈	—	14	1	no	—
260	C₄×M₁₆	C₂×D₇	1	1	yes	characteristic
261	#335	—	7	1	no	—
262	#335	—	7	1	no	—
263	#335	—	7	1	no	—
264	#335	—	7	1	no	—
265	Q₈⋊C₈	—	7	1	no	—
266	Q₈⋊C₈	—	7	1	no	—
267	Q₈⋊C₈	C₂×D₇	1	1	yes	characteristic
268	Q₈⋊C₈	C₂×D₇	1	1	yes	characteristic
269	D₄⋊C₈	—	7	1	no	—
270	D₄⋊C₈	—	7	1	no	—
271	D₄⋊C₈	C₂×D₇	1	1	yes	characteristic
272	D₄⋊C₈	C₂×D₇	1	1	yes	characteristic
273	#322	—	7	1	no	—
274	#322	—	7	1	no	—
275	#322	—	7	1	no	—
276	C₈²	—	7	1	no	—
277	C₂³×C₇	—	2	1	no	—
278	C₂³×C₇	C₄×D₄	1	1	yes	characteristic
279	C₂²×D₇	—	2	1	no	—
280	C₇×Q₈	—	2	1	no	—
281	C₇×Q₈	#131	1	2	yes	—
282	C₇×D₄	—	2	4	no	—
283	C₇×D₄	—	2	1	no	—
284	C₇×D₄	#131	1	2	yes	—
285	C₂×C₄×C₇	—	2	4	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	—	2	1	no	—
292	C₂×C₄×C₇	—	2	1	no	—
293	C₂×C₄×C₇	—	4	1	no	—
294	C₂×C₄×C₇	—	4	1	no	—
295	C₂×C₄×C₇	—	4	1	no	—
296	C₂×C₄×C₇	—	8	1	no	—
297	C₂×C₄×C₇	C₄×D₄	1	1	yes	characteristic
298	C₂×C₄×C₇	C₄×D₄	1	1	yes	characteristic
299	C₂×C₄×C₇	C₄×D₄	1	1	yes	characteristic
300	C₂×C₄×C₇	C₂³×C₄	1	1	yes	characteristic
301	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
302	C₂×C₄×C₇	C₂×#41	1	1	yes	characteristic
303	C₂²⋊D₇	—	8	1	no	—
304	C₂×Dic₇	—	2	1	no	—
305	C₂×Dic₇	—	2	1	no	—
306	C₂×Dic₇	—	2	1	no	—
307	D₂₈	—	2	1	no	—
308	D₂₈	—	2	1	no	—
309	C₄×D₇	—	4	1	no	—
310	C₄×D₇	—	4	1	no	—
311	Dic₁₄	—	2	1	no	—
312	Dic₁₄	—	2	1	no	—
313	C₇×C₈	—	2	2	no	—
314	C₇×C₈	—	4	1	no	—
315	C₇×C₈	—	4	1	no	—
316	C₇×C₈	—	4	1	no	—
317	C₇⋊C₈	—	2	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	—	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	C₂×#41	C₄×D₇	1	1	yes	characteristic
328	C₂×Q₁₆	—	7	1	no	—
329	C₂×SD₁₆	—	7	1	no	—
330	C₂×SD₁₆	—	7	1	no	—
331	C₂×D₈	—	7	1	no	—
332	C₂×M₁₆	—	2	1	no	—
333	C₂×M₁₆	—	2	1	no	—
334	C₂×M₁₆	—	14	1	no	—
335	C₂²×C₈	—	14	1	no	—
336	C₂²×C₈	—	14	1	no	—
337	C₂²×C₈	—	14	1	no	—
338	C₂²×C₈	—	14	1	no	—
339	#126	—	14	1	no	—
340	#125	—	7	1	no	—
341	#124	—	7	1	no	—
342	#123	—	14	1	no	—
343	C₂²⋊Q₈	—	7	1	no	—
344	#121	—	7	1	no	—
345	C₄×Q₈	—	7	1	no	—
346	C₄×Q₈	C₄×D₇	1	1	yes	characteristic
347	C₄×Q₈	C₂²×D₇	1	1	yes	characteristic
348	C₄×D₄	—	2	1	no	—
349	C₄×D₄	—	2	1	no	—
350	C₄×D₄	—	7	1	no	—
351	C₄×D₄	—	14	1	no	—
352	C₄×D₄	C₄×D₇	1	1	yes	characteristic
353	C₄×D₄	C₂²×D₇	1	1	yes	characteristic
354	#117	—	2	1	no	—
355	#117	—	14	1	no	—
356	#117	C₄×D₇	1	1	yes	characteristic
357	C₂×C₄²	—	2	1	no	—
358	C₂×C₄²	C₂²×D₇	1	1	yes	characteristic
359	#107	—	7	1	no	—
360	#107	—	7	1	no	—
361	#106	—	7	1	no	—
362	#106	—	7	1	no	—
363	C₄⋊C₈	—	2	1	no	—
364	C₄⋊C₈	—	7	1	no	—
365	C₄⋊C₈	—	7	1	no	—
366	C₄⋊C₈	—	7	1	no	—
367	C₄⋊C₈	—	7	1	no	—
368	C₄⋊C₈	—	7	1	no	—
369	C₄⋊C₈	—	7	1	no	—
370	C₄⋊C₈	—	14	1	no	—
371	C₄⋊C₈	—	14	1	no	—
372	C₄⋊C₈	—	14	1	no	—
373	C₄⋊C₈	—	14	1	no	—
374	C₄⋊C₈	—	14	1	no	—
375	C₄⋊C₈	C₂²×D₇	1	1	yes	characteristic
376	C₄⋊C₈	C₂²×D₇	1	1	yes	characteristic
377	#103	—	7	1	no	—
378	#103	—	7	1	no	—
379	#103	—	7	1	no	—
380	#103	—	7	1	no	—
381	#102	—	7	1	no	—
382	#102	—	7	1	no	—
383	#102	—	7	1	no	—
384	#102	—	7	1	no	—
385	C₂²⋊C₈	—	7	1	no	—
386	C₂²⋊C₈	—	7	1	no	—
387	C₂²⋊C₈	—	7	1	no	—
388	C₂²⋊C₈	—	7	1	no	—
389	C₂²⋊C₈	—	14	1	no	—
390	C₂²⋊C₈	—	14	1	no	—
391	C₂²⋊C₈	—	14	1	no	—
392	C₂²⋊C₈	—	14	1	no	—
393	#97	—	2	1	no	—
394	#97	—	14	1	no	—
395	C₄×C₈	—	7	1	no	—
396	C₄×C₈	—	7	1	no	—
397	C₄×C₈	—	7	1	no	—
398	C₄×C₈	—	7	1	no	—
399	C₄×C₈	—	14	1	no	—
400	C₄×C₈	—	14	1	no	—
401	C₄×C₈	—	14	1	no	—
402	C₄×C₈	C₂²×D₇	1	1	yes	characteristic
403	C₄×C₈	C₂²×D₇	1	1	yes	characteristic
404	C₂²×C₇	—	2	1	no	—
405	C₂²×C₇	—	2	2	no	—
406	C₂²×C₇	—	2	1	no	—
407	C₂²×C₇	—	2	1	no	—
408	C₂²×C₇	—	4	1	no	—
409	C₂²×C₇	—	4	1	no	—
410	C₂²×C₇	C₂×C₄×D₄	1	1	yes	characteristic
411	C₂×D₇	—	4	1	no	—
412	C₂×D₇	—	4	1	no	—
413	C₂×D₇	—	4	1	no	—
414	C₄×C₇	—	2	1	no	—
415	C₄×C₇	—	2	2	no	—
416	C₄×C₇	—	2	1	no	—
417	C₄×C₇	—	2	1	no	—
418	C₄×C₇	—	2	1	no	—
419	C₄×C₇	—	4	1	no	—
420	C₄×C₇	—	4	1	no	—
421	C₄×C₇	C₂×#131	1	1	yes	characteristic
422	C₄×C₇	C₂×#131	1	1	yes	characteristic
423	C₄×C₇	#576	1	1	yes	characteristic
424	C₄×C₇	#578	1	1	yes	characteristic
425	Dic₇	—	4	1	no	—
426	Dic₇	—	4	1	no	—
427	Dic₇	—	4	1	no	—
428	#41	—	2	2	no	—
429	#41	—	2	2	no	—
430	C₂×Q₈	—	7	1	no	—
431	C₂×Q₈	C₂×C₄×D₇	1	1	yes	characteristic
432	C₂×D₄	—	2	1	no	—
433	C₂×D₄	—	7	1	no	—
434	C₂×D₄	—	14	1	no	—
435	C₂×D₄	C₂×C₄×D₇	1	1	yes	characteristic
436	C₂²×C₄	—	2	1	no	—
437	C₂²×C₄	—	2	1	no	—
438	C₂²×C₄	—	2	1	no	—
439	C₂²×C₄	—	14	1	no	—
440	C₂²×C₄	C₂×C₄×D₇	1	1	yes	characteristic
441	C₂²×C₄	D₄×D₇	1	1	yes	characteristic
442	C₂²×C₄	#1159	1	1	yes	characteristic
443	Q₁₆	—	14	2	no	—
444	SD₁₆	—	14	2	no	—
445	SD₁₆	—	14	2	no	—
446	D₈	—	14	2	no	—
447	M₁₆	—	4	2	no	—
448	M₁₆	—	8	1	no	—
449	M₁₆	—	56	1	no	—
450	C₂×C₈	—	2	1	no	—
451	C₂×C₈	—	2	1	no	—
452	C₂×C₈	—	2	1	no	—
453	C₂×C₈	—	2	1	no	—
454	C₂×C₈	—	7	1	no	—
455	C₂×C₈	—	7	1	no	—
456	C₂×C₈	—	7	1	no	—
457	C₂×C₈	—	7	1	no	—
458	C₂×C₈	—	7	1	no	—
459	C₂×C₈	—	7	1	no	—
460	C₂×C₈	—	7	1	no	—
461	C₂×C₈	—	7	1	no	—
462	C₂×C₈	—	14	1	no	—
463	C₂×C₈	—	14	1	no	—
464	C₂×C₈	—	56	1	no	—
465	C₂×C₈	—	56	1	no	—
466	C₂×C₈	—	56	1	no	—
467	C₂×C₈	—	56	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	—	14	1	no	—
475	C₄⋊C₄	—	14	1	no	—
476	C₄⋊C₄	C₂×C₄×D₇	1	1	yes	characteristic
477	C₄⋊C₄	C₂×C₄×D₇	1	1	yes	characteristic
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	C₂²⋊C₄	—	14	1	no	—
485	C₂²⋊C₄	—	14	1	no	—
486	C₄²	—	2	1	no	—
487	C₄²	—	2	1	no	—
488	C₄²	—	2	1	no	—
489	C₄²	—	14	1	no	—
490	C₄²	C₂×C₄×D₇	1	1	yes	characteristic
491	C₄²	D₄×D₇	1	1	yes	characteristic
492	C₄²	#1159	1	1	yes	characteristic
493	C₄²	C₂³×D₇	1	1	yes	characteristic
494	C₂×C₇	—	4	1	no	—
495	C₂×C₇	—	4	2	no	—
496	C₂×C₇	#2929	1	1	yes	characteristic
497	C₂×C₇	#2951	1	1	yes	characteristic
498	C₂×C₇	#2956	1	1	yes	characteristic
499	D₇	—	8	1	no	—
500	C₂³	—	2	1	no	—
501	C₂³	—	14	1	no	—
502	C₂³	(C₂²⋊D₇)⋊C₄	1	1	yes	characteristic
503	Q₈	—	2	1	no	—
504	Q₈	—	14	1	no	—
505	Q₈	—	14	1	no	—
506	Q₈	#6470	1	2	yes	—
507	D₄	—	2	4	no	—
508	D₄	—	2	1	no	—
509	D₄	—	14	1	no	—
510	D₄	—	14	1	no	—
511	D₄	—	56	1	no	—
512	D₄	#6470	1	2	yes	—
513	C₂×C₄	—	2	4	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	—	2	1	no	—
519	C₂×C₄	—	2	1	no	—
520	C₂×C₄	—	2	1	no	—
521	C₂×C₄	—	4	1	no	—
522	C₂×C₄	—	4	1	no	—
523	C₂×C₄	—	4	1	no	—
524	C₂×C₄	—	8	1	no	—
525	C₂×C₄	—	14	1	no	—
526	C₂×C₄	—	14	1	no	—
527	C₂×C₄	—	14	1	no	—
528	C₂×C₄	—	28	1	no	—
529	C₂×C₄	—	28	1	no	—
530	C₂×C₄	(C₂²⋊D₇)⋊C₄	1	1	yes	characteristic
531	C₂×C₄	(C₂²⋊D₇)⋊C₄	1	1	yes	characteristic
532	C₂×C₄	(C₂²⋊D₇)⋊C₄	1	1	yes	characteristic
533	C₂×C₄	C₂²×C₄×D₇	1	1	yes	characteristic
534	C₂×C₄	C₂×D₄×D₇	1	1	yes	characteristic
535	C₂×C₄	C₂×#1159	1	1	yes	characteristic
536	C₈	—	2	2	no	—
537	C₈	—	4	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	—	14	1	no	—
545	C₈	—	14	1	no	—
546	C₈	—	14	1	no	—
547	C₈	—	14	1	no	—
548	C₈	—	28	1	no	—
549	C₈	—	28	1	no	—
550	C₇	#17926	1	1	yes	characteristic, complemented, Sylow
551	C₂²	—	2	1	no	—
552	C₂²	—	2	2	no	—
553	C₂²	—	2	1	no	—
554	C₂²	—	2	1	no	—
555	C₂²	—	4	1	no	—
556	C₂²	—	4	1	no	—
557	C₂²	—	28	1	no	—
558	C₂²	—	28	1	no	—
559	C₂²	—	28	1	no	—
560	C₂²	C₂×(C₂²⋊D₇)⋊C₄	1	1	yes	characteristic
561	C₄	—	2	1	no	—
562	C₄	—	2	2	no	—
563	C₄	—	2	1	no	—
564	C₄	—	2	1	no	—
565	C₄	—	2	1	no	—
566	C₄	—	4	1	no	—
567	C₄	—	4	1	no	—
568	C₄	—	28	1	no	—
569	C₄	—	28	1	no	—
570	C₄	—	28	1	no	—
571	C₄	C₂×#6470	1	1	yes	characteristic
572	C₄	C₂×#6470	1	1	yes	characteristic
573	C₄	#90465	1	1	yes	characteristic
574	C₄	#90470	1	1	yes	characteristic
575	C₂	—	4	1	no	—
576	C₂	—	4	2	no	—
577	C₂	—	56	1	no	—
578	C₂	#11736071	1	1	yes	characteristic
579	C₂	#11736313	1	1	yes	characteristic
580	C₂	#11736425	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×#1489	C₂
socle	C₂²×C₇	C₂×C₄×D₄
prime radical	#90010	C₄
cosocle	C₄²×C₇	C₂⁴
hypercenter	#1489	D₇
hypocenter	C₇	#17926
LCS	G ▷ C₂×C₄×C₇ ▷ C₂×C₇ ▷ C₇
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #1489

Complements

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

N	H ≅ G/N	type
2. #11739965	C₂	semidirect
3. #11736498	C₂	semidirect
4. C₇×#1489	C₂	semidirect
5. #11728248	C₂	semidirect
6. #11727606	C₂	semidirect
7. #11727602	C₂	semidirect
8. #11725977	C₂	semidirect
9. #11725972	C₂	semidirect
10. #11725968	C₂	semidirect
11. #11725967	C₂	semidirect
12. #11725910	C₂	semidirect
13. #11725906	C₂	semidirect
14. #11725904	C₂	semidirect
15. #11725902	C₂	semidirect
157. #1489	D₇	semidirect
550. C₇	#17926	semidirect

Maximal subgroups

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

subgroup	index
#11739973	2
#11739965	2
#11736498	2
C₇×#1489	2
#11728248	2
#11727606	2
#11727602	2
#11725977	2
#11725972	2
#11725968	2
#11725967	2
#11725910	2
#11725906	2
#11725904	2
#11725902	2
#17926	7