Subgroups — #13324866

Order 1792.

670 conjugacy classes of subgroups.

The subgroup lattice has 612 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#11736745	C₂	1	1	yes	maximal, characteristic
2	M₁₆×D₂₈	C₂	1	1	yes	maximal, characteristic, complemented
3	#11735956	C₂	1	1	yes	maximal, characteristic, complemented
4	C₇×#1453	C₂	1	1	yes	maximal, characteristic, complemented
5	#11728518	C₂	1	1	yes	maximal, characteristic, complemented
6	#11728511	C₂	1	1	yes	maximal, characteristic, complemented
7	#11728507	C₂	1	1	yes	maximal, characteristic, complemented
8	#11725839	C₂	1	1	yes	maximal, characteristic, complemented
9	#11725836	C₂	1	1	yes	maximal, characteristic, complemented
10	#11725835	C₂	1	1	yes	maximal, characteristic, complemented
11	#11725834	C₂	1	1	yes	maximal, characteristic, complemented
12	#11725832	C₂	1	1	yes	maximal, characteristic, complemented
13	#11725831	C₂	1	1	yes	maximal, characteristic, complemented
14	C₈×#1132	C₂	1	1	yes	maximal, characteristic, complemented
15	#11725806	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×D₇×M₁₆	—	2	1	no	—
17	#90170	C₂²	1	1	yes	characteristic
18	C₂×C₄×D₂₈	C₂²	1	1	yes	characteristic
19	C₇×#431	C₂²	1	1	yes	characteristic
20	C₇×#431	C₂²	1	1	yes	characteristic
21	C₄×C₇×M₁₆	C₂²	1	1	yes	characteristic
22	#89900	—	2	1	no	—
23	#89899	—	2	1	no	—
24	#89898	—	2	1	no	—
25	#89697	C₂²	1	1	yes	characteristic
26	#89696	C₂²	1	1	yes	characteristic
27	#89619	C₄	1	1	yes	characteristic
28	#89619	C₄	1	1	yes	characteristic
29	#89616	C₄	1	1	yes	characteristic
30	#89616	C₄	1	1	yes	characteristic
31	#89507	C₄	1	1	yes	characteristic
32	#89504	C₄	1	1	yes	characteristic
33	#89503	C₄	1	1	yes	characteristic
34	#89494	C₄	1	1	yes	characteristic
35	#89481	—	2	1	no	—
36	#89480	—	2	1	no	—
37	#89478	—	2	1	no	—
38	#89478	—	2	1	no	—
39	C₄×D₅₆	C₂²	1	1	yes	characteristic
40	C₄×D₅₆	C₂²	1	1	yes	characteristic
41	C₄×#1132	C₂²	1	1	yes	characteristic
42	C₄×#1132	C₂²	1	1	yes	characteristic
43	#89460	C₂²	1	1	yes	characteristic
44	#89460	C₂²	1	1	yes	characteristic
45	#89460	C₂²	1	1	yes	characteristic, complemented
46	C₈×D₂₈	C₂²	1	1	yes	characteristic
47	C₈×D₂₈	C₂²	1	1	yes	characteristic
48	C₈×D₂₈	C₂²	1	1	yes	characteristic, complemented
49	#89451	C₂²	1	1	yes	characteristic, complemented
50	C₈×Dic₁₄	C₂²	1	1	yes	characteristic, complemented
51	C₇×#322	C₂²	1	1	yes	characteristic, complemented
52	C₇×#322	C₂²	1	1	yes	characteristic, complemented
53	C₇×#322	C₂²	1	1	yes	characteristic, complemented
54	C₇×C₈²	C₂²	1	1	yes	characteristic, complemented
55	#89254	C₂²	1	1	yes	characteristic
56	#89254	C₂²	1	1	yes	characteristic
57	#89254	C₂²	1	1	yes	characteristic
58	#89254	C₂²	1	1	yes	characteristic
59	#89254	C₂²	1	1	yes	characteristic, complemented
60	#89254	C₂²	1	1	yes	characteristic, complemented
61	#89253	C₂²	1	1	yes	characteristic, complemented
62	#89253	C₂²	1	1	yes	characteristic, complemented
63	#89252	C₂²	1	1	yes	characteristic, complemented
64	#89252	C₂²	1	1	yes	characteristic, complemented
65	#89251	C₂²	1	1	yes	characteristic, complemented
66	#89251	C₂²	1	1	yes	characteristic, complemented
67	#18008	—	7	1	no	maximal, Sylow
68	C₂²×D₂₈	C₂×C₄	1	1	yes	characteristic
69	C₂²×C₄×D₇	—	2	1	no	—
70	C₂×C₇×M₁₆	D₄	1	1	yes	characteristic
71	C₂×C₇×M₁₆	D₄	1	1	yes	characteristic
72	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
73	#6493	C₂×C₄	1	1	yes	characteristic
74	#6492	—	2	1	no	—
75	C₄×C₂²⋊D₇	—	2	1	no	—
76	C₂×(C₂×D₇)⋊C₄	—	2	1	no	—
77	C₂×C₄⋊Dic₇	C₂×C₄	1	1	yes	characteristic
78	#6487	C₂×C₄	1	1	yes	characteristic
79	C₂×#1136	—	2	1	no	—
80	D₇×M₁₆	—	4	4	no	—
81	C₂×D₅₆	C₂×C₄	1	1	yes	characteristic
82	C₂×D₅₆	C₂×C₄	1	1	yes	characteristic
83	C₂×#1132	C₂×C₄	1	1	yes	characteristic
84	C₂×#1132	C₂×C₄	1	1	yes	characteristic
85	C₂×#1131	—	2	1	no	—
86	C₂×#1131	—	2	1	no	—
87	C₂×#1131	—	2	1	no	—
88	C₂×C₈×D₇	—	2	1	no	—
89	C₂×C₈×D₇	—	2	1	no	—
90	C₂×C₈×D₇	—	2	1	no	—
91	#6439	—	2	1	no	—
92	#6438	C₂×C₄	1	1	yes	characteristic
93	C₄×D₂₈	—	2	1	no	—
94	C₄×D₂₈	—	2	1	no	—
95	C₄×D₂₈	C₂×C₄	1	1	yes	characteristic
96	C₄×D₂₈	C₂×C₄	1	1	yes	characteristic
97	C₄×D₂₈	C₂³	1	1	yes	characteristic
98	C₄×D₂₈	C₂³	1	1	yes	characteristic
99	C₄×D₂₈	C₂³	1	1	yes	characteristic
100	#6435	—	2	1	no	—
101	#6433	C₂×C₄	1	1	yes	characteristic
102	C₄×Dic₁₄	C₂³	1	1	yes	characteristic
103	C₇×C₄⋊C₈	—	2	1	no	—
104	C₇×C₄⋊C₈	C₂×C₄	1	1	yes	characteristic
105	C₇×C₄⋊C₈	C₂×C₄	1	1	yes	characteristic
106	C₇×C₂²⋊C₈	—	2	1	no	—
107	C₇×C₂²⋊C₈	C₂×C₄	1	1	yes	characteristic
108	C₇×C₂²⋊C₈	C₂×C₄	1	1	yes	characteristic
109	C₇×#97	D₄	1	1	yes	characteristic
110	C₇×#97	D₄	1	1	yes	characteristic
111	C₄×C₇×C₈	C₂³	1	1	yes	characteristic
112	C₄×C₇×C₈	C₂³	1	1	yes	characteristic
113	C₄×C₇×C₈	C₂³	1	1	yes	characteristic
114	C₄×C₇×C₈	C₂³	1	1	yes	characteristic
115	C₄×C₇×C₈	C₂³	1	1	yes	characteristic
116	C₄×C₇×C₈	C₂³	1	1	yes	characteristic
117	C₂²⋊(C₇⋊C₈)	—	2	1	no	—
118	#6395	C₂×C₄	1	1	yes	characteristic
119	#6395	C₂×C₄	1	1	yes	characteristic
120	#6395	C₂×C₄	1	1	yes	characteristic
121	#6395	C₂×C₄	1	1	yes	characteristic
122	#6395	C₂×C₄	1	1	yes	characteristic
123	#6395	C₂×C₄	1	1	yes	characteristic
124	(C₂×D₇)⋊C₈	—	2	1	no	—
125	(C₂×D₇)⋊C₈	—	2	1	no	—
126	(C₂×D₇)⋊C₈	—	2	1	no	—
127	(C₂×D₇)⋊C₈	—	2	1	no	—
128	(C₂×D₇)⋊C₈	—	2	1	no	—
129	(C₂×D₇)⋊C₈	—	2	1	no	—
130	#6392	C₂×C₄	1	1	yes	characteristic
131	#6392	C₂×C₄	1	1	yes	characteristic
132	#6391	C₂×C₄	1	1	yes	characteristic
133	#6391	C₂×C₄	1	1	yes	characteristic
134	#6390	C₂×C₄	1	1	yes	characteristic
135	#6390	C₂×C₄	1	1	yes	characteristic
136	#6389	—	2	1	no	—
137	Dic₇⋊C₈	—	2	1	no	—
138	Dic₇⋊C₈	—	2	1	no	—
139	C₈×Dic₇	—	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	C₄×C₇⋊C₈	—	2	1	no	—
146	#3105	—	7	1	no	—
147	#2969	—	7	1	no	—
148	D₄×M₁₆	—	7	1	no	—
149	#1592	—	7	1	no	—
150	#1589	—	7	1	no	—
151	#1586	—	7	1	no	—
152	#1585	—	7	1	no	—
153	#1583	—	7	1	no	—
154	#1581	—	7	1	no	—
155	#1580	—	7	1	no	—
156	C₈×SD₁₆	—	7	1	no	—
157	#1574	—	7	1	no	—
158	#1495	—	7	1	no	—
159	#1478	—	7	1	no	—
160	#1453	D₇	1	1	yes	characteristic, complemented
161	C₂³×D₇	—	2	1	no	—
162	C₂²×C₄×C₇	C₂²×C₄	1	1	yes	characteristic
163	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
164	C₂²×C₄×C₇	#41	1	1	yes	characteristic
165	C₂×C₂²⋊D₇	—	2	1	no	—
166	C₂²×Dic₇	—	2	1	no	—
167	C₂×D₂₈	—	2	2	no	—
168	C₂×D₂₈	—	2	1	no	—
169	C₂×D₂₈	—	4	1	no	—
170	C₂×D₂₈	C₂²×C₄	1	1	yes	characteristic
171	C₂×D₂₈	C₂²×C₄	1	1	yes	characteristic
172	C₂×D₂₈	C₂²×C₄	1	1	yes	characteristic
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	—	2	1	no	—
178	C₂×C₄×D₇	—	4	2	no	—
179	C₂×C₄×D₇	—	4	2	no	—
180	C₂×Dic₁₄	C₂²×C₄	1	1	yes	characteristic
181	C₇×M₁₆	—	2	2	no	—
182	C₇×M₁₆	—	4	1	no	—
183	C₂×C₇×C₈	—	2	1	no	—
184	C₂×C₇×C₈	—	2	1	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	C₂²×C₄	1	1	yes	characteristic
188	C₂×C₇×C₈	C₂²×C₄	1	1	yes	characteristic
189	C₂×C₇×C₈	C₂×D₄	1	1	yes	characteristic
190	C₂×C₇×C₈	C₂×D₄	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	C₄²×C₇	C₂²×C₄	1	1	yes	characteristic
194	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
195	C₄²×C₇	#41	1	1	yes	characteristic
196	C₄²×C₇	C₂⁴	1	1	yes	characteristic
197	C₂²⋊Dic₇	—	2	1	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	(C₂×D₇)⋊C₄	—	2	1	no	—
203	(C₂×D₇)⋊C₄	—	2	1	no	—
204	(C₂×D₇)⋊C₄	—	2	1	no	—
205	(C₂×D₇)⋊C₄	—	2	1	no	—
206	C₄⋊Dic₇	—	2	1	no	—
207	C₄⋊Dic₇	C₂²×C₄	1	1	yes	characteristic
208	C₄⋊Dic₇	C₂²×C₄	1	1	yes	characteristic
209	C₄⋊Dic₇	C₂²×C₄	1	1	yes	characteristic
210	C₄⋊Dic₇	C₂²×C₄	1	1	yes	characteristic
211	Dic₇⋊C₄	—	2	1	no	—
212	Dic₇⋊C₄	—	2	1	no	—
213	Dic₇⋊C₄	—	2	1	no	—
214	Dic₇⋊C₄	—	2	1	no	—
215	C₄×Dic₇	—	2	1	no	—
216	#1136	—	4	2	no	—
217	C₂×C₇⋊C₈	—	2	1	no	—
218	C₂×C₇⋊C₈	—	2	1	no	—
219	C₂×C₇⋊C₈	—	2	1	no	—
220	C₂×C₇⋊C₈	—	2	1	no	—
221	D₅₆	—	2	2	no	—
222	D₅₆	—	4	1	no	—
223	#1132	—	2	2	no	—
224	#1132	—	4	1	no	—
225	#1131	—	4	2	no	—
226	#1131	—	4	2	no	—
227	#1131	—	4	2	no	—
228	C₈×D₇	—	4	2	no	—
229	C₈×D₇	—	4	2	no	—
230	C₈×D₇	—	4	2	no	—
231	C₂²×M₁₆	—	14	1	no	—
232	#529	—	7	1	no	—
233	C₂×C₄×D₄	—	7	1	no	—
234	#484	—	7	1	no	—
235	#481	—	7	1	no	—
236	#478	—	7	1	no	—
237	#478	—	7	1	no	—
238	#463	—	7	1	no	—
239	#463	—	7	1	no	—
240	#450	—	7	1	no	—
241	#447	—	7	1	no	—
242	#446	—	7	1	no	—
243	C₈×Q₈	—	7	1	no	—
244	C₄×SD₁₆	—	7	1	no	—
245	C₄×SD₁₆	—	7	1	no	—
246	C₄×D₈	—	7	1	no	—
247	C₄×D₈	—	7	1	no	—
248	#436	—	7	1	no	—
249	#436	—	7	1	no	—
250	#436	—	7	1	no	—
251	#436	—	14	1	no	—
252	#435	—	14	1	no	—
253	#435	—	14	1	no	—
254	#435	—	14	1	no	—
255	C₈×D₄	—	7	1	no	—
256	C₈×D₄	—	7	1	no	—
257	C₈×D₄	—	7	1	no	—
258	#433	—	14	1	no	—
259	#431	—	7	1	no	—
260	#431	C₂×D₇	1	1	yes	characteristic
261	#431	C₂×D₇	1	1	yes	characteristic
262	#423	—	7	1	no	—
263	#407	—	14	1	no	—
264	#405	—	14	1	no	—
265	C₄×M₁₆	C₂×D₇	1	1	yes	characteristic
266	#335	—	7	1	no	—
267	#335	—	7	1	no	—
268	#334	—	7	1	no	—
269	#334	—	7	1	no	—
270	Q₈⋊C₈	—	7	1	no	—
271	Q₈⋊C₈	—	7	1	no	—
272	D₄⋊C₈	—	7	1	no	—
273	D₄⋊C₈	—	7	1	no	—
274	D₄⋊C₈	—	7	1	no	—
275	D₄⋊C₈	—	7	1	no	—
276	D₄⋊C₈	—	7	1	no	—
277	D₄⋊C₈	—	7	1	no	—
278	#322	C₂×D₇	1	1	yes	characteristic, complemented
279	#322	C₂×D₇	1	1	yes	characteristic, complemented
280	#322	C₂×D₇	1	1	yes	characteristic, complemented
281	C₈²	C₂×D₇	1	1	yes	characteristic, complemented
282	C₂³×C₇	C₄×D₄	1	1	yes	characteristic
283	C₂²×D₇	—	2	1	no	—
284	C₂²×D₇	—	2	1	no	—
285	C₂²×D₇	—	2	1	no	—
286	C₂²×D₇	—	4	2	no	—
287	C₂²×D₇	—	4	2	no	—
288	C₂²×D₇	—	8	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	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	—	8	1	no	—
301	C₂×Dic₇	—	2	1	no	—
302	C₂×Dic₇	—	2	1	no	—
303	C₂×Dic₇	—	2	1	no	—
304	C₂×Dic₇	—	2	1	no	—
305	C₂×Dic₇	—	2	1	no	—
306	C₂×Dic₇	—	4	2	no	—
307	D₂₈	—	2	1	no	—
308	D₂₈	—	2	1	no	—
309	D₂₈	—	2	1	no	—
310	D₂₈	—	2	1	no	—
311	D₂₈	—	2	1	no	—
312	D₂₈	—	4	2	no	—
313	D₂₈	#131	1	2	yes	—
314	C₄×D₇	—	4	2	no	—
315	C₄×D₇	—	4	2	no	—
316	C₄×D₇	—	4	1	no	—
317	C₄×D₇	—	4	1	no	—
318	C₄×D₇	—	4	1	no	—
319	C₄×D₇	—	4	1	no	—
320	C₄×D₇	—	4	1	no	—
321	C₄×D₇	—	4	1	no	—
322	Dic₁₄	—	2	1	no	—
323	Dic₁₄	—	2	1	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	—	2	1	no	—
329	C₇×C₈	—	2	1	no	—
330	C₇×C₈	—	2	1	no	—
331	C₇×C₈	—	4	1	no	—
332	C₇×C₈	—	4	1	no	—
333	C₇×C₈	AGL(1,ℤ/8)	1	2	yes	—
334	C₇⋊C₈	—	4	1	no	—
335	C₇⋊C₈	—	4	1	no	—
336	C₇⋊C₈	—	4	1	no	—
337	C₇⋊C₈	—	4	1	no	—
338	C₂²×D₄	—	7	1	no	—
339	C₂³×C₄	—	14	1	no	—
340	C₂×SD₁₆	—	7	1	no	—
341	C₂×SD₁₆	—	7	1	no	—
342	C₂×D₈	—	7	1	no	—
343	C₂×D₈	—	7	1	no	—
344	C₂×M₁₆	—	14	1	no	—
345	C₂×M₁₆	—	14	1	no	—
346	C₂×M₁₆	—	14	1	no	—
347	C₂×M₁₆	—	14	1	no	—
348	C₂×M₁₆	—	28	4	no	—
349	C₂×M₁₆	D₂₈	1	1	yes	characteristic
350	C₂×M₁₆	D₂₈	1	1	yes	characteristic
351	C₂²×C₈	—	14	1	no	—
352	C₂²×C₈	—	14	1	no	—
353	C₂²×C₈	—	14	1	no	—
354	#126	—	14	1	no	—
355	#125	—	7	1	no	—
356	#124	—	7	1	no	—
357	#123	—	14	1	no	—
358	C₂²⋊Q₈	—	7	1	no	—
359	#121	—	7	1	no	—
360	C₄×Q₈	—	7	1	no	—
361	C₄×D₄	—	7	1	no	—
362	C₄×D₄	—	7	1	no	—
363	C₄×D₄	—	7	1	no	—
364	C₄×D₄	—	7	1	no	—
365	C₄×D₄	—	7	1	no	—
366	C₄×D₄	—	14	1	no	—
367	C₄×D₄	—	14	1	no	—
368	C₄×D₄	—	14	1	no	—
369	#117	—	14	1	no	—
370	C₂×C₄⋊C₄	—	7	1	no	—
371	C₂×C₂²⋊C₄	—	14	1	no	—
372	C₂×C₄²	C₂²×D₇	1	1	yes	characteristic
373	#107	—	7	1	no	—
374	#107	—	7	1	no	—
375	#106	—	7	1	no	—
376	#106	—	7	1	no	—
377	C₄⋊C₈	—	2	1	no	—
378	C₄⋊C₈	—	7	1	no	—
379	C₄⋊C₈	—	7	1	no	—
380	C₄⋊C₈	—	7	1	no	—
381	C₄⋊C₈	—	7	1	no	—
382	C₄⋊C₈	—	14	1	no	—
383	C₄⋊C₈	—	14	1	no	—
384	C₄⋊C₈	—	14	1	no	—
385	C₄⋊C₈	C₄×D₇	1	1	yes	characteristic
386	C₄⋊C₈	C₄×D₇	1	1	yes	characteristic
387	#103	—	7	1	no	—
388	#103	—	7	1	no	—
389	#102	—	7	1	no	—
390	#102	—	7	1	no	—
391	#102	—	7	1	no	—
392	#102	—	7	1	no	—
393	#102	—	7	1	no	—
394	#102	—	7	1	no	—
395	C₂²⋊C₈	—	2	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	C₂²⋊C₈	—	14	1	no	—
402	C₂²⋊C₈	—	14	1	no	—
403	C₂²⋊C₈	C₄×D₇	1	1	yes	characteristic
404	C₂²⋊C₈	C₄×D₇	1	1	yes	characteristic
405	#97	—	14	1	no	—
406	#97	D₂₈	1	1	yes	characteristic
407	#97	D₂₈	1	1	yes	characteristic
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	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	—	2	1	no	—
417	C₂²×C₇	—	2	1	no	—
418	C₂²×C₇	—	2	1	no	—
419	C₂²×C₇	C₂×C₄×D₄	1	1	yes	characteristic
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	—	4	1	no	—
426	C₂×D₇	—	4	1	no	—
427	C₂×D₇	—	4	1	no	—
428	C₂×D₇	—	4	1	no	—
429	C₂×D₇	—	8	4	no	—
430	C₄×C₇	—	2	1	no	—
431	C₄×C₇	—	2	1	no	—
432	C₄×C₇	—	2	1	no	—
433	C₄×C₇	—	2	1	no	—
434	C₄×C₇	C₂×#131	1	1	yes	characteristic
435	C₄×C₇	#568	1	1	yes	characteristic
436	C₄×C₇	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
437	C₄×C₇	#575	1	1	yes	characteristic
438	Dic₇	—	4	1	no	—
439	Dic₇	—	4	1	no	—
440	Dic₇	—	4	1	no	—
441	Dic₇	—	4	1	no	—
442	Dic₇	—	4	1	no	—
443	C₂⁴	—	14	1	no	—
444	C₂×Q₈	—	7	1	no	—
445	C₂×D₄	—	7	1	no	—
446	C₂×D₄	—	7	1	no	—
447	C₂×D₄	—	7	1	no	—
448	C₂×D₄	—	14	2	no	—
449	C₂×D₄	—	14	1	no	—
450	C₂×D₄	—	14	1	no	—
451	C₂×D₄	—	28	1	no	—
452	C₂²×C₄	—	14	1	no	—
453	C₂²×C₄	—	14	1	no	—
454	C₂²×C₄	—	14	1	no	—
455	C₂²×C₄	—	14	1	no	—
456	C₂²×C₄	—	14	1	no	—
457	C₂²×C₄	—	14	1	no	—
458	C₂²×C₄	—	28	2	no	—
459	C₂²×C₄	—	28	2	no	—
460	C₂²×C₄	C₂×C₄×D₇	1	1	yes	characteristic
461	C₂²×C₄	C₂×D₂₈	1	1	yes	characteristic
462	C₂²×C₄	#1157	1	1	yes	characteristic
463	SD₁₆	—	14	2	no	—
464	SD₁₆	—	28	1	no	—
465	D₈	—	14	2	no	—
466	D₈	—	28	1	no	—
467	M₁₆	—	2	2	no	—
468	M₁₆	—	4	1	no	—
469	M₁₆	—	28	2	no	—
470	M₁₆	—	28	2	no	—
471	M₁₆	—	28	2	no	—
472	M₁₆	—	28	2	no	—
473	C₂×C₈	—	2	1	no	—
474	C₂×C₈	—	2	1	no	—
475	C₂×C₈	—	14	1	no	—
476	C₂×C₈	—	14	1	no	—
477	C₂×C₈	—	14	1	no	—
478	C₂×C₈	—	14	1	no	—
479	C₂×C₈	—	28	2	no	—
480	C₂×C₈	—	28	2	no	—
481	C₂×C₈	—	28	2	no	—
482	C₂×C₈	C₂×C₄×D₇	1	1	yes	characteristic
483	C₂×C₈	C₂×C₄×D₇	1	1	yes	characteristic
484	C₂×C₈	C₂×C₄×D₇	1	1	yes	characteristic
485	C₂×C₈	C₂×C₄×D₇	1	1	yes	characteristic
486	C₂×C₈	C₂×D₂₈	1	1	yes	characteristic
487	C₂×C₈	C₂×D₂₈	1	1	yes	characteristic
488	C₂×C₈	C₂×D₂₈	1	1	yes	characteristic
489	C₂×C₈	C₂×D₂₈	1	1	yes	characteristic
490	C₄⋊C₄	—	7	1	no	—
491	C₄⋊C₄	—	7	1	no	—
492	C₄⋊C₄	—	7	1	no	—
493	C₄⋊C₄	—	7	1	no	—
494	C₄⋊C₄	—	14	1	no	—
495	C₄⋊C₄	—	14	1	no	—
496	C₄⋊C₄	—	14	1	no	—
497	C₄⋊C₄	—	14	1	no	—
498	C₄⋊C₄	—	14	1	no	—
499	C₂²⋊C₄	—	14	1	no	—
500	C₂²⋊C₄	—	14	1	no	—
501	C₂²⋊C₄	—	14	1	no	—
502	C₂²⋊C₄	—	14	1	no	—
503	C₂²⋊C₄	—	14	1	no	—
504	C₂²⋊C₄	—	14	1	no	—
505	C₂²⋊C₄	—	14	1	no	—
506	C₂²⋊C₄	—	14	1	no	—
507	C₂²⋊C₄	—	14	1	no	—
508	C₄²	—	14	1	no	—
509	C₄²	C₂×C₄×D₇	1	1	yes	characteristic
510	C₄²	C₂×D₂₈	1	1	yes	characteristic
511	C₄²	#1157	1	1	yes	characteristic
512	C₄²	C₂³×D₇	1	1	yes	characteristic
513	C₂×C₇	—	4	1	no	—
514	C₂×C₇	#2933	1	1	yes	characteristic
515	C₂×C₇	C₄×AGL(1,ℤ/8)	1	1	yes	characteristic
516	C₂×C₇	#2957	1	1	yes	characteristic
517	D₇	—	4	2	no	—
518	D₇	—	8	1	no	—
519	D₇	—	8	1	no	—
520	C₂³	—	14	1	no	—
521	C₂³	—	14	1	no	—
522	C₂³	—	14	1	no	—
523	C₂³	—	28	2	no	—
524	C₂³	—	28	2	no	—
525	C₂³	—	56	1	no	—
526	C₂³	C₄×D₂₈	1	1	yes	characteristic
527	Q₈	—	14	1	no	—
528	Q₈	—	14	1	no	—
529	D₄	—	7	2	no	—
530	D₄	—	14	1	no	—
531	D₄	—	14	1	no	—
532	D₄	—	14	1	no	—
533	D₄	—	14	1	no	—
534	D₄	—	14	1	no	—
535	D₄	—	28	2	no	—
536	D₄	—	56	1	no	—
537	C₂×C₄	—	2	1	no	—
538	C₂×C₄	—	2	1	no	—
539	C₂×C₄	—	2	1	no	—
540	C₂×C₄	—	2	1	no	—
541	C₂×C₄	—	4	1	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	—	28	2	no	—
548	C₂×C₄	—	28	2	no	—
549	C₂×C₄	—	28	2	no	—
550	C₂×C₄	—	28	1	no	—
551	C₂×C₄	—	28	1	no	—
552	C₂×C₄	—	28	1	no	—
553	C₂×C₄	—	28	1	no	—
554	C₂×C₄	—	28	1	no	—
555	C₂×C₄	—	28	1	no	—
556	C₂×C₄	C₄×D₂₈	1	1	yes	characteristic
557	C₂×C₄	C₄×D₂₈	1	1	yes	characteristic
558	C₂×C₄	C₄×D₂₈	1	1	yes	characteristic
559	C₂×C₄	C₂²×C₄×D₇	1	1	yes	characteristic
560	C₂×C₄	C₂²×D₂₈	1	1	yes	characteristic
561	C₂×C₄	C₂×#1157	1	1	yes	characteristic
562	C₈	—	2	1	no	—
563	C₈	—	2	1	no	—
564	C₈	—	2	1	no	—
565	C₈	—	2	1	no	—
566	C₈	—	2	1	no	—
567	C₈	—	2	1	no	—
568	C₈	—	2	1	no	—
569	C₈	—	4	1	no	—
570	C₈	—	4	1	no	—
571	C₈	—	28	1	no	—
572	C₈	—	28	1	no	—
573	C₈	—	28	1	no	—
574	C₈	—	28	1	no	—
575	C₈	#6471	1	2	yes	—
576	C₇	#18008	1	1	yes	characteristic, complemented, Sylow
577	C₂²	—	2	1	no	—
578	C₂²	—	2	1	no	—
579	C₂²	—	2	1	no	—
580	C₂²	—	14	2	no	—
581	C₂²	—	28	1	no	—
582	C₂²	—	28	1	no	—
583	C₂²	—	28	1	no	—
584	C₂²	—	28	1	no	—
585	C₂²	—	28	1	no	—
586	C₂²	—	28	1	no	—
587	C₂²	—	28	1	no	—
588	C₂²	—	28	1	no	—
589	C₂²	—	56	4	no	—
590	C₂²	C₂×C₄×D₂₈	1	1	yes	characteristic
591	C₄	—	2	1	no	—
592	C₄	—	2	1	no	—
593	C₄	—	2	1	no	—
594	C₄	—	2	1	no	—
595	C₄	—	28	1	no	—
596	C₄	—	28	1	no	—
597	C₄	—	28	1	no	—
598	C₄	—	28	1	no	—
599	C₄	—	28	1	no	—
600	C₄	C₂×#6471	1	1	yes	characteristic
601	C₄	#90439	1	1	yes	characteristic
602	C₄	D₇×#131	1	1	yes	characteristic
603	C₄	#90441	1	1	yes	characteristic
604	C₂	—	4	1	no	—
605	C₂	—	28	2	no	—
606	C₂	—	56	1	no	—
607	C₂	—	56	1	no	—
608	C₂	C₄×#6471	1	1	yes	characteristic
609	C₂	#11736000	1	1	yes	characteristic
610	C₂	#11736025	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂²×D₂₈
commutator	C₂×C₄×C₇	C₂³×C₄
Frattini	C₄²	C₂³×D₇
Fitting	C₇×#1453	C₂
socle	C₂²×C₇	C₂×C₄×D₄
prime radical	#89504	C₄
cosocle	C₄²×C₇	C₂⁴
hypercenter	#1453	D₇
hypocenter	C₇	#18008
LCS	G ▷ C₂×C₄×C₇ ▷ C₂×C₇ ▷ C₇
UCS	C₁ ◁ C₂×C₄ ◁ C₄×M₁₆ ◁ #1453

Complements

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

N	H ≅ G/N	type
2. M₁₆×D₂₈	C₂	semidirect
3. #11735956	C₂	semidirect
4. C₇×#1453	C₂	semidirect
5. #11728518	C₂	semidirect
6. #11728511	C₂	semidirect
7. #11728507	C₂	semidirect
8. #11725839	C₂	semidirect
9. #11725836	C₂	semidirect
10. #11725835	C₂	semidirect
11. #11725834	C₂	semidirect
12. #11725832	C₂	semidirect
13. #11725831	C₂	semidirect
14. C₈×#1132	C₂	semidirect
15. #11725806	C₂	semidirect
45. #89460	C₂²	semidirect
48. C₈×D₂₈	C₂²	semidirect
49. #89451	C₂²	semidirect
50. C₈×Dic₁₄	C₂²	semidirect
51. C₇×#322	C₂²	semidirect
52. C₇×#322	C₂²	semidirect
53. C₇×#322	C₂²	semidirect
54. C₇×C₈²	C₂²	semidirect
59. #89254	C₂²	semidirect
60. #89254	C₂²	semidirect
61. #89253	C₂²	semidirect
62. #89253	C₂²	semidirect
63. #89252	C₂²	semidirect
64. #89252	C₂²	semidirect
65. #89251	C₂²	semidirect
66. #89251	C₂²	semidirect
160. #1453	D₇	semidirect
278. #322	C₂×D₇	semidirect
279. #322	C₂×D₇	semidirect
280. #322	C₂×D₇	semidirect
281. C₈²	C₂×D₇	semidirect
576. C₇	#18008	semidirect

Maximal subgroups

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

subgroup	index
#11736745	2
M₁₆×D₂₈	2
#11735956	2
C₇×#1453	2
#11728518	2
#11728511	2
#11728507	2
#11725839	2
#11725836	2
#11725835	2
#11725834	2
#11725832	2
#11725831	2
C₈×#1132	2
#11725806	2
#18008	7