Subgroups — #13325543

Order 1792.

652 conjugacy classes of subgroups.

The subgroup lattice has 596 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#11737390	C₂	1	1	yes	maximal, characteristic, complemented
2	C₄×#6479	C₂	1	1	yes	maximal, characteristic
3	#11736851	C₂	1	1	yes	maximal, characteristic, complemented
4	C₇×#1582	C₂	1	1	yes	maximal, characteristic, complemented
5	#11728706	C₂	1	1	yes	maximal, characteristic, complemented
6	#11728649	C₂	1	1	yes	maximal, characteristic, complemented
7	#11728594	C₂	1	1	yes	maximal, characteristic, complemented
8	#11726283	C₂	1	1	yes	maximal, characteristic, complemented
9	#11726273	C₂	1	1	yes	maximal, characteristic, complemented
10	#11725992	C₂	1	1	yes	maximal, characteristic, complemented
11	#11725981	C₂	1	1	yes	maximal, characteristic, complemented
12	#11725928	C₂	1	1	yes	maximal, characteristic, complemented
13	#11725905	C₂	1	1	yes	maximal, characteristic, complemented
14	#11725833	C₂	1	1	yes	maximal, characteristic, complemented
15	#11725824	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×#6479	C₄	1	1	yes	characteristic
17	C₄×#1161	C₂²	1	1	yes	characteristic
18	C₄×#1159	C₂²	1	1	yes	characteristic
19	C₇×#446	C₂²	1	1	yes	characteristic
20	C₄×C₇×SD₁₆	C₂²	1	1	yes	characteristic
21	C₇×C₈×D₄	C₂²	1	1	yes	characteristic
22	SD₁₆×Dic₇	C₄	1	1	yes	characteristic
23	#89883	—	2	1	no	—
24	C₂×Dic₇⋊C₈	—	2	1	no	—
25	C₄×#1144	C₂²	1	1	yes	characteristic
26	#89796	C₂²	1	1	yes	characteristic
27	C₄×#1141	C₂²	1	1	yes	characteristic
28	D₄×C₇⋊C₈	C₂²	1	1	yes	characteristic
29	#89632	C₄	1	1	yes	characteristic
30	#89624	C₄	1	1	yes	characteristic
31	#89609	C₂²	1	1	yes	characteristic
32	#89609	C₂²	1	1	yes	characteristic
33	#89608	—	2	1	no	—
34	#89606	C₂²	1	1	yes	characteristic
35	D₇×C₄⋊C₈	—	2	1	no	—
36	#89603	C₂²	1	1	yes	characteristic
37	#89576	C₄	1	1	yes	characteristic
38	#89562	C₄	1	1	yes	characteristic
39	#89544	C₄	1	1	yes	characteristic
40	#89528	C₄	1	1	yes	characteristic
41	#89502	—	2	1	no	—
42	#89491	—	2	1	no	—
43	#89478	—	2	1	no	—
44	#89477	—	2	1	no	—
45	C₄×#1132	C₂²	1	1	yes	characteristic
46	C₄×#1131	C₂²	1	1	yes	characteristic
47	C₈×D₂₈	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
51	C₇×#334	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×#322	C₂²	1	1	yes	characteristic
55	Q₈⋊(C₇⋊C₈)	C₂²	1	1	yes	characteristic
56	D₄⋊(C₇⋊C₈)	C₂²	1	1	yes	characteristic
57	#89279	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	#89254	C₂²	1	1	yes	characteristic
62	#89252	C₂²	1	1	yes	characteristic
63	#89251	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	#18065	—	7	1	no	maximal, Sylow
68	C₂×#1161	C₂×C₄	1	1	yes	characteristic
69	C₂×#1159	C₂×C₄	1	1	yes	characteristic
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	Q₈×Dic₇	C₂×C₄	1	1	yes	characteristic
75	C₂×#1144	C₂×C₄	1	1	yes	characteristic
76	D₄×Dic₇	C₂×C₄	1	1	yes	characteristic
77	C₂×#1141	C₂×C₄	1	1	yes	characteristic
78	C₄×C₂²⋊D₇	—	2	1	no	—
79	C₂×C₄×Dic₇	—	2	1	no	—
80	C₂²×C₇⋊C₈	—	2	1	no	—
81	#6479	—	2	4	no	—
82	C₂×#1132	C₂×C₄	1	1	yes	characteristic
83	C₂×#1131	—	2	1	no	—
84	C₂×#1131	—	2	1	no	—
85	C₂×#1131	—	2	1	no	—
86	C₂×C₈×D₇	—	2	1	no	—
87	C₂×C₈×D₇	—	2	1	no	—
88	C₂×C₈×D₇	C₂×C₄	1	1	yes	characteristic
89	C₂×C₈×D₇	C₂×C₄	1	1	yes	characteristic
90	#6456	—	2	1	no	—
91	#6456	C₂×C₄	1	1	yes	characteristic
92	#6455	—	2	1	no	—
93	#6455	C₂×C₄	1	1	yes	characteristic
94	#6455	C₂×C₄	1	1	yes	characteristic
95	#6450	C₂×C₄	1	1	yes	characteristic
96	(C₂²⋊D₇)⋊C₄	—	2	1	no	—
97	#6440	—	2	1	no	—
98	C₄×D₂₈	—	2	1	no	—
99	C₄×D₂₈	C₂³	1	1	yes	characteristic
100	C₄²×D₇	—	2	1	no	—
101	C₄²×D₇	C₂³	1	1	yes	characteristic
102	C₄×Dic₁₄	C₂³	1	1	yes	characteristic
103	C₇×#106	C₂×C₄	1	1	yes	characteristic
104	C₇×C₄⋊C₈	—	2	1	no	—
105	C₇×C₄⋊C₈	C₂³	1	1	yes	characteristic
106	C₇×C₄⋊C₈	C₂³	1	1	yes	characteristic
107	C₇×#103	C₂×C₄	1	1	yes	characteristic
108	C₇×#102	C₂×C₄	1	1	yes	characteristic
109	C₇×C₂²⋊C₈	—	2	1	no	—
110	C₇×#97	—	2	1	no	—
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	#6409	C₂×C₄	1	1	yes	characteristic
115	#6406	C₂×C₄	1	1	yes	characteristic
116	C₂²⋊(C₇⋊C₈)	—	2	1	no	—
117	#6395	C₂×C₄	1	1	yes	characteristic
118	(C₂×D₇)⋊C₈	—	2	1	no	—
119	(C₂×D₇)⋊C₈	—	2	1	no	—
120	(C₂×D₇)⋊C₈	D₄	1	1	yes	characteristic
121	(C₂×D₇)⋊C₈	D₄	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	#6389	—	2	1	no	—
126	#6389	—	2	1	no	—
127	Dic₇⋊C₈	—	2	1	no	—
128	Dic₇⋊C₈	—	2	1	no	—
129	Dic₇⋊C₈	—	2	1	no	—
130	Dic₇⋊C₈	—	2	1	no	—
131	Dic₇⋊C₈	D₄	1	1	yes	characteristic
132	Dic₇⋊C₈	D₄	1	1	yes	characteristic
133	C₈×Dic₇	C₂×C₄	1	1	yes	characteristic
134	C₈×Dic₇	C₂×C₄	1	1	yes	characteristic
135	#6384	C₂×C₄	1	1	yes	characteristic
136	#6383	C₂×C₄	1	1	yes	characteristic
137	#6381	C₂×C₄	1	1	yes	characteristic
138	#6381	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	#6377	—	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	#2990	—	7	1	no	—
147	#2990	—	7	1	no	—
148	C₄×#135	—	7	1	no	—
149	#1593	—	7	1	no	—
150	#1593	—	7	1	no	—
151	#1582	—	7	1	no	—
152	#1582	—	7	1	no	—
153	#1582	—	7	1	no	—
154	#1582	D₇	1	1	yes	characteristic, complemented
155	#1580	—	7	1	no	—
156	#1580	—	7	1	no	—
157	#1566	—	7	1	no	—
158	#1489	—	7	1	no	—
159	#1489	—	7	1	no	—
160	#1451	—	7	1	no	—
161	C₂×C₇×Q₈	C₂²×C₄	1	1	yes	characteristic
162	C₂×C₇×D₄	C₂²×C₄	1	1	yes	characteristic
163	C₂²×C₄×C₇	—	2	1	no	—
164	C₂×C₂²⋊D₇	—	2	1	no	—
165	C₂²×Dic₇	—	2	1	no	—
166	C₂²×Dic₇	—	2	1	no	—
167	#1161	—	2	2	no	—
168	#1161	—	4	1	no	—
169	#1159	—	2	2	no	—
170	#1159	—	4	1	no	—
171	C₂×D₂₈	—	2	1	no	—
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	C₂²×C₄	1	1	yes	characteristic
177	C₂×C₄×D₇	C₂×D₄	1	1	yes	characteristic
178	C₂×C₄×D₇	#41	1	1	yes	characteristic
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	—	8	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	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	#1144	—	2	2	no	—
197	#1141	M₁₆	1	4	yes	complemented
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	C₄×Dic₇	—	2	1	no	—
208	C₄×Dic₇	—	2	1	no	—
209	C₄×Dic₇	—	2	1	no	—
210	C₄×Dic₇	—	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	—	8	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	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	#1131	—	8	1	no	—
226	#1131	—	8	1	no	—
227	C₈×D₇	—	2	2	no	—
228	C₈×D₇	—	4	1	no	—
229	C₈×D₇	—	8	1	no	—
230	C₈×D₇	—	8	1	no	—
231	C₂×#135	—	7	1	no	—
232	C₄×#41	—	7	1	no	—
233	C₄×#41	—	7	1	no	—
234	#446	—	7	1	no	—
235	#446	—	7	1	no	—
236	#446	—	7	1	no	—
237	#446	C₂×D₇	1	1	yes	characteristic
238	C₄×Q₁₆	—	7	1	no	—
239	C₄×Q₁₆	—	7	1	no	—
240	C₄×SD₁₆	—	7	1	no	—
241	C₄×SD₁₆	—	7	1	no	—
242	C₄×SD₁₆	—	7	1	no	—
243	C₄×SD₁₆	C₂×D₇	1	1	yes	characteristic
244	C₄×D₈	—	7	1	no	—
245	C₄×D₈	—	7	1	no	—
246	#435	—	14	1	no	—
247	#435	—	14	1	no	—
248	#435	—	14	1	no	—
249	#435	—	14	1	no	—
250	C₈×D₄	—	7	1	no	—
251	C₈×D₄	—	7	1	no	—
252	C₈×D₄	—	7	1	no	—
253	C₈×D₄	C₂×D₇	1	1	yes	characteristic
254	#432	—	14	1	no	—
255	#432	—	14	1	no	—
256	#431	—	7	1	no	—
257	#427	—	7	1	no	—
258	#423	—	7	1	no	—
259	#423	—	7	1	no	—
260	C₂×C₄⋊C₈	—	14	1	no	—
261	C₂×C₄⋊C₈	—	14	1	no	—
262	#416	—	7	1	no	—
263	#416	—	7	1	no	—
264	C₄×M₁₆	—	7	1	no	—
265	C₂×C₄×C₈	—	7	1	no	—
266	#334	—	7	1	no	—
267	#334	—	7	1	no	—
268	#334	—	7	1	no	—
269	#334	C₂×D₇	1	1	yes	characteristic
270	Q₈⋊C₈	—	7	1	no	—
271	Q₈⋊C₈	—	7	1	no	—
272	Q₈⋊C₈	—	7	1	no	—
273	Q₈⋊C₈	C₂×D₇	1	1	yes	characteristic
274	D₄⋊C₈	—	7	1	no	—
275	D₄⋊C₈	—	7	1	no	—
276	D₄⋊C₈	—	7	1	no	—
277	D₄⋊C₈	C₂×D₇	1	1	yes	characteristic
278	#322	—	7	1	no	—
279	#322	—	7	1	no	—
280	#322	—	7	1	no	—
281	#322	C₂×D₇	1	1	yes	characteristic
282	C₂³×C₇	—	2	1	no	—
283	C₂²×D₇	—	2	1	no	—
284	C₂²×D₇	C₄×D₄	1	1	yes	characteristic
285	C₇×Q₈	—	2	1	no	—
286	C₇×Q₈	—	2	1	no	—
287	C₇×D₄	—	2	1	no	—
288	C₇×D₄	C₂×M₁₆	1	2	yes	—
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	—	4	1	no	—
293	C₂×C₄×C₇	—	4	1	no	—
294	C₂×C₄×C₇	C₂³×C₄	1	1	yes	characteristic
295	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
296	C₂×C₄×C₇	C₂×#41	1	1	yes	characteristic
297	C₂²⋊D₇	—	4	2	no	—
298	C₂×Dic₇	—	2	1	no	—
299	C₂×Dic₇	—	2	1	no	—
300	C₂×Dic₇	—	2	1	no	—
301	C₂×Dic₇	—	4	2	no	—
302	C₂×Dic₇	—	4	2	no	—
303	C₂×Dic₇	C₄×D₄	1	1	yes	characteristic
304	C₂×Dic₇	C₄×D₄	1	1	yes	characteristic
305	C₂×Dic₇	C₄×D₄	1	1	yes	characteristic
306	D₂₈	—	2	1	no	—
307	D₂₈	—	4	2	no	—
308	D₂₈	C₂×M₁₆	1	2	yes	—
309	C₄×D₇	—	2	1	no	—
310	C₄×D₇	—	2	1	no	—
311	C₄×D₇	—	2	1	no	—
312	C₄×D₇	—	2	1	no	—
313	C₄×D₇	—	2	2	no	—
314	C₄×D₇	—	4	2	no	—
315	C₄×D₇	—	4	1	no	—
316	C₄×D₇	—	4	1	no	—
317	C₄×D₇	—	4	2	no	—
318	Dic₁₄	—	2	1	no	—
319	Dic₁₄	—	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	—	4	1	no	—
325	C₇×C₈	—	4	1	no	—
326	C₇×C₈	—	4	1	no	—
327	C₇⋊C₈	—	2	1	no	—
328	C₇⋊C₈	—	2	1	no	—
329	C₇⋊C₈	—	2	1	no	—
330	C₇⋊C₈	—	4	1	no	—
331	C₇⋊C₈	—	4	1	no	—
332	C₇⋊C₈	—	4	1	no	—
333	C₇⋊C₈	C₂×M₁₆	1	2	yes	—
334	C₂×#41	—	7	1	no	—
335	C₂×#41	—	7	1	no	—
336	#135	—	14	4	no	—
337	C₂×Q₁₆	—	7	1	no	—
338	C₂×SD₁₆	—	7	1	no	—
339	C₂×SD₁₆	C₄×D₇	1	1	yes	characteristic
340	C₂×D₈	—	7	1	no	—
341	C₂×M₁₆	—	14	1	no	—
342	C₂×M₁₆	—	14	1	no	—
343	C₂×M₁₆	—	14	1	no	—
344	C₂²×C₈	—	2	1	no	—
345	C₂²×C₈	—	7	1	no	—
346	C₂²×C₈	—	7	1	no	—
347	C₂²×C₈	—	14	1	no	—
348	C₂²×C₈	—	14	1	no	—
349	C₂²×C₈	—	14	1	no	—
350	C₄×Q₈	—	7	1	no	—
351	C₄×Q₈	—	7	1	no	—
352	C₄×Q₈	—	7	1	no	—
353	C₄×Q₈	C₂²×D₇	1	1	yes	characteristic
354	C₄×D₄	—	7	1	no	—
355	C₄×D₄	—	7	1	no	—
356	C₄×D₄	—	7	1	no	—
357	C₄×D₄	—	14	1	no	—
358	C₄×D₄	—	14	1	no	—
359	C₄×D₄	—	14	1	no	—
360	C₄×D₄	—	14	1	no	—
361	C₄×D₄	C₂²×D₇	1	1	yes	characteristic
362	#117	—	7	1	no	—
363	#117	—	7	1	no	—
364	#117	—	14	1	no	—
365	#117	—	14	1	no	—
366	C₂×C₄²	—	7	1	no	—
367	C₂×C₄²	—	14	1	no	—
368	C₂×C₄²	—	14	1	no	—
369	#107	—	7	1	no	—
370	#107	—	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	C₂²×D₇	1	1	yes	characteristic
384	C₄⋊C₈	C₂²×D₇	1	1	yes	characteristic
385	#103	—	7	1	no	—
386	#103	—	7	1	no	—
387	#103	—	7	1	no	—
388	#103	C₄×D₇	1	1	yes	characteristic
389	#102	—	7	1	no	—
390	#102	—	7	1	no	—
391	#102	—	7	1	no	—
392	#102	C₄×D₇	1	1	yes	characteristic
393	C₂²⋊C₈	—	2	1	no	—
394	C₂²⋊C₈	—	7	1	no	—
395	C₂²⋊C₈	—	7	1	no	—
396	C₂²⋊C₈	—	14	1	no	—
397	C₂²⋊C₈	—	14	1	no	—
398	C₂²⋊C₈	—	14	1	no	—
399	#97	—	2	1	no	—
400	#97	—	14	1	no	—
401	#97	—	14	1	no	—
402	#97	—	14	1	no	—
403	#97	—	14	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	—	7	1	no	—
409	C₄×C₈	C₂²×D₇	1	1	yes	characteristic
410	C₄×C₈	C₂²×D₇	1	1	yes	characteristic
411	C₄×C₈	C₂²×D₇	1	1	yes	characteristic
412	C₂²×C₇	—	2	2	no	—
413	C₂²×C₇	—	4	1	no	—
414	C₂²×C₇	—	4	1	no	—
415	C₂²×C₇	C₂×C₄×D₄	1	1	yes	characteristic
416	C₂×D₇	—	2	1	no	—
417	C₂×D₇	—	2	2	no	—
418	C₂×D₇	—	2	1	no	—
419	C₂×D₇	—	2	1	no	—
420	C₂×D₇	—	4	1	no	—
421	C₂×D₇	—	4	1	no	—
422	C₄×C₇	—	2	1	no	—
423	C₄×C₇	—	4	1	no	—
424	C₄×C₇	—	4	1	no	—
425	C₄×C₇	—	4	1	no	—
426	C₄×C₇	C₂²×M₁₆	1	1	yes	characteristic
427	C₄×C₇	#568	1	1	yes	characteristic
428	C₄×C₇	#577	1	1	yes	characteristic
429	C₄×C₇	#577	1	1	yes	characteristic
430	Dic₇	—	2	1	no	—
431	Dic₇	—	2	1	no	—
432	Dic₇	—	4	1	no	—
433	Dic₇	—	4	1	no	—
434	Dic₇	—	4	1	no	—
435	Dic₇	#444	1	2	yes	—
436	#41	—	14	2	no	—
437	#41	—	14	2	no	—
438	#41	—	28	1	no	—
439	#41	—	28	1	no	—
440	C₂×Q₈	—	7	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	1	no	—
445	C₂×D₄	C₂×C₄×D₇	1	1	yes	characteristic
446	C₂²×C₄	—	2	1	no	—
447	C₂²×C₄	—	7	1	no	—
448	C₂²×C₄	—	7	1	no	—
449	C₂²×C₄	—	7	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	—	14	1	no	—
455	Q₁₆	—	14	2	no	—
456	SD₁₆	—	2	2	no	—
457	SD₁₆	—	14	2	no	—
458	D₈	—	7	4	no	—
459	M₁₆	—	28	2	no	—
460	M₁₆	—	56	1	no	—
461	M₁₆	—	56	1	no	—
462	C₂×C₈	—	2	1	no	—
463	C₂×C₈	—	2	1	no	—
464	C₂×C₈	—	2	1	no	—
465	C₂×C₈	—	7	1	no	—
466	C₂×C₈	—	7	1	no	—
467	C₂×C₈	—	7	1	no	—
468	C₂×C₈	—	7	1	no	—
469	C₂×C₈	—	8	1	no	—
470	C₂×C₈	—	14	2	no	—
471	C₂×C₈	—	14	1	no	—
472	C₂×C₈	—	14	1	no	—
473	C₂×C₈	—	14	1	no	—
474	C₂×C₈	—	28	1	no	—
475	C₂×C₈	—	56	1	no	—
476	C₂×C₈	—	56	1	no	—
477	C₂×C₈	—	56	1	no	—
478	C₂×C₈	C₂×C₄×D₇	1	1	yes	characteristic
479	C₂×C₈	C₂×C₄×D₇	1	1	yes	characteristic
480	C₂×C₈	D₄×D₇	1	1	yes	characteristic
481	C₂×C₈	D₄×D₇	1	1	yes	characteristic
482	C₄⋊C₄	—	2	1	no	—
483	C₄⋊C₄	—	7	1	no	—
484	C₄⋊C₄	—	7	1	no	—
485	C₄⋊C₄	—	14	1	no	—
486	C₄⋊C₄	—	14	1	no	—
487	C₄⋊C₄	—	14	1	no	—
488	C₄⋊C₄	C₂×C₄×D₇	1	1	yes	characteristic
489	C₄⋊C₄	C₂×C₄×D₇	1	1	yes	characteristic
490	C₂²⋊C₄	—	2	1	no	—
491	C₂²⋊C₄	—	14	1	no	—
492	C₂²⋊C₄	—	14	1	no	—
493	C₂²⋊C₄	—	14	1	no	—
494	C₂²⋊C₄	—	14	1	no	—
495	C₂²⋊C₄	—	14	1	no	—
496	C₄²	—	2	1	no	—
497	C₄²	—	7	1	no	—
498	C₄²	—	7	1	no	—
499	C₄²	—	7	1	no	—
500	C₄²	—	14	1	no	—
501	C₄²	—	14	1	no	—
502	C₄²	—	14	1	no	—
503	C₄²	—	14	1	no	—
504	C₄²	—	14	1	no	—
505	C₄²	C₂³×D₇	1	1	yes	characteristic
506	C₂×C₇	—	4	2	no	—
507	C₂×C₇	D₄×M₁₆	1	1	yes	characteristic
508	C₂×C₇	#2952	1	1	yes	characteristic
509	C₂×C₇	C₂×#444	1	1	yes	characteristic
510	D₇	—	4	1	no	—
511	D₇	—	4	2	no	—
512	C₂³	—	2	1	no	—
513	C₂³	—	7	1	no	—
514	C₂³	—	14	1	no	—
515	Q₈	—	2	1	no	—
516	Q₈	—	2	1	no	—
517	Q₈	—	14	1	no	—
518	Q₈	—	14	1	no	—
519	D₄	—	2	1	no	—
520	D₄	—	7	2	no	—
521	D₄	—	14	1	no	—
522	D₄	—	28	2	no	—
523	D₄	—	28	2	no	—
524	D₄	D₇×M₁₆	1	2	yes	—
525	C₂×C₄	—	2	1	no	—
526	C₂×C₄	—	2	1	no	—
527	C₂×C₄	—	2	1	no	—
528	C₂×C₄	—	4	1	no	—
529	C₂×C₄	—	4	1	no	—
530	C₂×C₄	—	7	1	no	—
531	C₂×C₄	—	7	1	no	—
532	C₂×C₄	—	7	1	no	—
533	C₂×C₄	—	14	2	no	—
534	C₂×C₄	—	14	1	no	—
535	C₂×C₄	—	14	1	no	—
536	C₂×C₄	—	14	1	no	—
537	C₂×C₄	—	14	1	no	—
538	C₂×C₄	—	14	1	no	—
539	C₂×C₄	—	14	1	no	—
540	C₂×C₄	—	14	1	no	—
541	C₂×C₄	—	28	2	no	—
542	C₂×C₄	—	28	2	no	—
543	C₂×C₄	—	28	2	no	—
544	C₂×C₄	—	28	2	no	—
545	C₂×C₄	—	28	1	no	—
546	C₂×C₄	—	28	1	no	—
547	C₂×C₄	C₂²×C₄×D₇	1	1	yes	characteristic
548	C₂×C₄	C₂×D₄×D₇	1	1	yes	characteristic
549	C₂×C₄	D₇×#41	1	1	yes	characteristic
550	C₈	—	2	1	no	—
551	C₈	—	2	1	no	—
552	C₈	—	2	1	no	—
553	C₈	—	2	1	no	—
554	C₈	—	4	1	no	—
555	C₈	—	4	1	no	—
556	C₈	—	4	1	no	—
557	C₈	—	7	2	no	—
558	C₈	—	14	1	no	—
559	C₈	—	14	1	no	—
560	C₈	—	14	1	no	—
561	C₈	—	28	1	no	—
562	C₈	—	28	1	no	—
563	C₈	—	28	1	no	—
564	C₇	#18065	1	1	yes	characteristic, complemented, Sylow
565	C₂²	—	2	2	no	—
566	C₂²	—	4	1	no	—
567	C₂²	—	4	1	no	—
568	C₂²	—	14	1	no	—
569	C₂²	—	14	1	no	—
570	C₂²	—	14	2	no	—
571	C₂²	—	14	1	no	—
572	C₂²	—	28	1	no	—
573	C₂²	—	28	1	no	—
574	C₂²	C₄×D₄×D₇	1	1	yes	characteristic
575	C₄	—	2	1	no	—
576	C₄	—	4	1	no	—
577	C₄	—	4	1	no	—
578	C₄	—	4	1	no	—
579	C₄	—	7	2	no	—
580	C₄	—	14	1	no	—
581	C₄	—	14	1	no	—
582	C₄	—	28	1	no	—
583	C₄	—	28	1	no	—
584	C₄	—	28	1	no	—
585	C₄	C₂×D₇×M₁₆	1	1	yes	characteristic
586	C₄	#90441	1	1	yes	characteristic
587	C₄	#90453	1	1	yes	characteristic
588	C₄	#90461	1	1	yes	characteristic
589	C₂	—	4	2	no	—
590	C₂	—	28	1	no	—
591	C₂	—	28	2	no	—
592	C₂	#11736928	1	1	yes	characteristic
593	C₂	#11737095	1	1	yes	characteristic
594	C₂	D₇×#444	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×#1582	C₂
socle	C₂²×C₇	C₂×C₄×D₄
prime radical	C₂×#6479	C₄
cosocle	C₄²×C₇	C₂⁴
hypercenter	#1582	D₇
hypocenter	C₇	#18065
LCS	G ▷ C₂×C₄×C₇ ▷ C₂×C₇ ▷ C₇
UCS	C₁ ◁ C₂×C₄ ◁ C₄×C₈ ◁ #1582

Complements

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

N	H ≅ G/N	type
1. #11737390	C₂	semidirect
3. #11736851	C₂	semidirect
4. C₇×#1582	C₂	semidirect
5. #11728706	C₂	semidirect
6. #11728649	C₂	semidirect
7. #11728594	C₂	semidirect
8. #11726283	C₂	semidirect
9. #11726273	C₂	semidirect
10. #11725992	C₂	semidirect
11. #11725981	C₂	semidirect
12. #11725928	C₂	semidirect
13. #11725905	C₂	semidirect
14. #11725833	C₂	semidirect
15. #11725824	C₂	semidirect
154. #1582	D₇	semidirect
197. #1141	M₁₆	semidirect
564. C₇	#18065	semidirect

Maximal subgroups

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

subgroup	index
#11737390	2
C₄×#6479	2
#11736851	2
C₇×#1582	2
#11728706	2
#11728649	2
#11728594	2
#11726283	2
#11726273	2
#11725992	2
#11725981	2
#11725928	2
#11725905	2
#11725833	2
#11725824	2
#18065	7