Subgroups — #13325128

Order 1792.

616 conjugacy classes of subgroups.

The subgroup lattice has 590 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#11736781	C₂	1	1	yes	maximal, characteristic
2	#11736743	C₂	1	1	yes	maximal, characteristic
3	#11736712	C₂	1	1	yes	maximal, characteristic, complemented
4	C₇×#1572	C₂	1	1	yes	maximal, characteristic, complemented
5	#11728557	C₂	1	1	yes	maximal, characteristic, complemented
6	#11728510	C₂	1	1	yes	maximal, characteristic
7	#11728498	C₂	1	1	yes	maximal, characteristic, complemented
8	#11726319	C₂	1	1	yes	maximal, characteristic, complemented
9	#11726316	C₂	1	1	yes	maximal, characteristic, complemented
10	#11726315	C₂	1	1	yes	maximal, characteristic, complemented
11	#11726312	C₂	1	1	yes	maximal, characteristic, complemented
12	#11726277	C₂	1	1	yes	maximal, characteristic, complemented
13	#11726274	C₂	1	1	yes	maximal, characteristic, complemented
14	#11726273	C₂	1	1	yes	maximal, characteristic, complemented
15	#11726270	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×C₄×D₂₈	C₂²	1	1	yes	characteristic
17	#90161	C₂²	1	1	yes	characteristic
18	C₇×#432	C₂²	1	1	yes	characteristic
19	C₇×#431	C₂²	1	1	yes	characteristic
20	C₇×#431	C₂²	1	1	yes	characteristic
21	#89697	C₂²	1	1	yes	characteristic
22	#89697	C₂²	1	1	yes	characteristic
23	#89614	C₄	1	1	yes	characteristic
24	#89614	C₄	1	1	yes	characteristic
25	#89613	C₄	1	1	yes	characteristic
26	#89613	C₄	1	1	yes	characteristic
27	#89610	C₂²	1	1	yes	characteristic
28	#89610	C₂²	1	1	yes	characteristic
29	#89606	C₂²	1	1	yes	characteristic
30	#89606	C₂²	1	1	yes	characteristic
31	#89603	C₂²	1	1	yes	characteristic, complemented
32	#89603	C₂²	1	1	yes	characteristic, complemented
33	#89602	C₂²	1	1	yes	characteristic, complemented
34	#89602	C₂²	1	1	yes	characteristic, complemented
35	#89503	C₄	1	1	yes	characteristic
36	#89503	C₄	1	1	yes	characteristic
37	#89498	—	2	1	no	—
38	D₇×C₂²⋊C₈	—	2	1	no	—
39	#89493	C₄	1	1	yes	characteristic
40	#89493	C₄	1	1	yes	characteristic
41	#89492	—	2	1	no	—
42	#89492	—	2	1	no	—
43	#89478	—	2	1	no	—
44	#89478	—	2	1	no	—
45	C₄×#1132	C₂²	1	1	yes	characteristic
46	C₄×#1132	C₂²	1	1	yes	characteristic
47	C₄×#1132	C₂²	1	1	yes	characteristic
48	C₄×#1132	C₂²	1	1	yes	characteristic
49	#89451	—	2	1	no	—
50	C₈×Dic₁₄	—	2	1	no	—
51	C₇×#335	C₂²	1	1	yes	characteristic, complemented
52	C₇×#335	C₂²	1	1	yes	characteristic, complemented
53	C₇×#334	C₂²	1	1	yes	characteristic, complemented
54	C₇×#334	C₂²	1	1	yes	characteristic, complemented
55	#89279	C₂²	1	1	yes	characteristic, complemented
56	#89279	C₂²	1	1	yes	characteristic, complemented
57	#89279	C₂²	1	1	yes	characteristic, complemented
58	#89279	C₂²	1	1	yes	characteristic, complemented
59	#89278	C₂²	1	1	yes	characteristic
60	#89278	C₂²	1	1	yes	characteristic
61	#89278	C₂²	1	1	yes	characteristic
62	#89278	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	#18028	—	7	1	no	maximal, Sylow
68	C₂²×D₂₈	C₂×C₄	1	1	yes	characteristic
69	C₂²×C₄×D₇	—	2	1	no	—
70	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
71	C₂×(C₂×D₇)⋊C₄	—	2	1	no	—
72	#6489	—	2	1	no	—
73	C₂×C₄⋊Dic₇	C₂×C₄	1	1	yes	characteristic
74	#6487	—	2	1	no	—
75	#6487	C₂×C₄	1	1	yes	characteristic
76	#6487	C₂×C₄	1	1	yes	characteristic
77	C₂×#1132	C₂×C₄	1	1	yes	characteristic
78	C₂×#1132	C₂×C₄	1	1	yes	characteristic
79	C₂×#1132	C₂×C₄	1	1	yes	characteristic
80	C₂×#1132	C₂×C₄	1	1	yes	characteristic
81	C₂×#1131	—	2	1	no	—
82	C₂×#1131	—	2	1	no	—
83	C₂×C₈×D₇	—	2	1	no	—
84	C₂×C₈×D₇	—	2	1	no	—
85	C₄×D₂₈	—	2	1	no	—
86	C₄×D₂₈	—	2	1	no	—
87	C₄×D₂₈	C₂×C₄	1	1	yes	characteristic
88	C₄×D₂₈	C₂×C₄	1	1	yes	characteristic
89	C₄×D₂₈	C₂³	1	1	yes	characteristic
90	C₄×D₂₈	C₂³	1	1	yes	characteristic
91	#6433	—	2	1	no	—
92	#6432	C₂×C₄	1	1	yes	characteristic
93	#6432	C₂×C₄	1	1	yes	characteristic
94	C₄×Dic₁₄	—	2	1	no	—
95	C₄×Dic₁₄	C₂³	1	1	yes	characteristic
96	C₄×Dic₁₄	C₂³	1	1	yes	characteristic
97	C₇×C₄⋊C₈	C₂×C₄	1	1	yes	characteristic
98	C₇×C₄⋊C₈	C₂×C₄	1	1	yes	characteristic
99	C₇×C₄⋊C₈	C₂³	1	1	yes	characteristic
100	C₇×C₄⋊C₈	C₂³	1	1	yes	characteristic
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	C₂×C₄	1	1	yes	characteristic
106	C₇×C₂²⋊C₈	C₂×C₄	1	1	yes	characteristic
107	C₇×#97	—	2	1	no	—
108	C₄×C₇×C₈	—	2	1	no	—
109	C₄×C₇×C₈	C₂³	1	1	yes	characteristic
110	C₄×C₇×C₈	C₂³	1	1	yes	characteristic
111	C₂²⋊(C₇⋊C₈)	—	2	1	no	—
112	C₂²⋊(C₇⋊C₈)	D₄	1	1	yes	characteristic
113	C₂²⋊(C₇⋊C₈)	D₄	1	1	yes	characteristic
114	#6395	C₂×C₄	1	1	yes	characteristic
115	#6395	C₂×C₄	1	1	yes	characteristic
116	#6395	C₂×C₄	1	1	yes	characteristic
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	—	2	1	no	—
121	(C₂×D₇)⋊C₈	—	2	1	no	—
122	#6391	C₂×C₄	1	1	yes	characteristic
123	#6391	C₂×C₄	1	1	yes	characteristic
124	#6391	C₂×C₄	1	1	yes	characteristic
125	#6391	C₂×C₄	1	1	yes	characteristic
126	#6390	C₂×C₄	1	1	yes	characteristic
127	#6390	C₂×C₄	1	1	yes	characteristic
128	#6390	C₂×C₄	1	1	yes	characteristic
129	#6390	C₂×C₄	1	1	yes	characteristic
130	#6389	—	2	1	no	—
131	#6389	—	2	1	no	—
132	Dic₇⋊C₈	—	2	1	no	—
133	Dic₇⋊C₈	—	2	1	no	—
134	Dic₇⋊C₈	—	2	1	no	—
135	Dic₇⋊C₈	—	2	1	no	—
136	C₈×Dic₇	—	2	1	no	—
137	C₈×Dic₇	—	2	1	no	—
138	C₄⋊(C₇⋊C₈)	—	2	1	no	—
139	C₄⋊(C₇⋊C₈)	D₄	1	1	yes	characteristic
140	C₄⋊(C₇⋊C₈)	D₄	1	1	yes	characteristic
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	#3101	—	7	1	no	—
146	#2986	—	7	1	no	—
147	#2974	—	7	1	no	—
148	#1592	—	7	1	no	—
149	#1590	—	7	1	no	—
150	#1588	—	7	1	no	—
151	#1585	—	7	1	no	—
152	#1583	—	7	1	no	—
153	#1582	—	7	1	no	—
154	SD₁₆⋊C₈	—	7	1	no	—
155	C₈×SD₁₆	—	7	1	no	—
156	#1572	D₇	1	1	yes	characteristic, complemented
157	#1497	—	7	1	no	—
158	#1478	—	7	1	no	—
159	#1454	—	7	1	no	—
160	C₂³×D₇	—	2	1	no	—
161	C₂²×C₄×C₇	C₂²×C₄	1	1	yes	characteristic
162	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
163	C₂²×C₄×C₇	#41	1	1	yes	characteristic
164	C₂²×Dic₇	—	2	1	no	—
165	C₂×D₂₈	—	2	2	no	—
166	C₂×D₂₈	—	2	1	no	—
167	C₂×D₂₈	—	4	1	no	—
168	C₂×D₂₈	C₂²×C₄	1	1	yes	characteristic
169	C₂×D₂₈	C₂²×C₄	1	1	yes	characteristic
170	C₂×C₄×D₇	—	2	1	no	—
171	C₂×C₄×D₇	—	2	1	no	—
172	C₂×C₄×D₇	—	2	1	no	—
173	C₂×C₄×D₇	—	2	1	no	—
174	C₂×C₄×D₇	—	8	1	no	—
175	C₂×C₄×D₇	—	8	1	no	—
176	C₂×Dic₁₄	—	2	1	no	—
177	C₂×Dic₁₄	C₂²×C₄	1	1	yes	characteristic
178	C₂×Dic₁₄	C₂²×C₄	1	1	yes	characteristic
179	C₂×C₇×C₈	—	2	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	C₂²×C₄	1	1	yes	characteristic
184	C₂×C₇×C₈	C₂²×C₄	1	1	yes	characteristic
185	C₂×C₇×C₈	C₂²×C₄	1	1	yes	characteristic
186	C₂×C₇×C₈	C₂²×C₄	1	1	yes	characteristic
187	C₄²×C₇	C₂²×C₄	1	1	yes	characteristic
188	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
189	C₄²×C₇	#41	1	1	yes	characteristic
190	C₄²×C₇	C₂⁴	1	1	yes	characteristic
191	C₂²⋊Dic₇	—	2	1	no	—
192	C₂²⋊Dic₇	—	2	1	no	—
193	(C₂×D₇)⋊C₄	—	2	1	no	—
194	(C₂×D₇)⋊C₄	—	2	1	no	—
195	(C₂×D₇)⋊C₄	—	2	1	no	—
196	(C₂×D₇)⋊C₄	—	2	1	no	—
197	C₄⋊Dic₇	—	2	1	no	—
198	C₄⋊Dic₇	—	2	1	no	—
199	C₄⋊Dic₇	—	2	1	no	—
200	C₄⋊Dic₇	—	2	1	no	—
201	C₄⋊Dic₇	C₂²×C₄	1	1	yes	characteristic
202	C₄⋊Dic₇	C₂²×C₄	1	1	yes	characteristic
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	Dic₇⋊C₄	—	2	1	no	—
208	Dic₇⋊C₄	—	2	1	no	—
209	C₄×Dic₇	—	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	C₂×D₄	1	1	yes	characteristic
214	C₂×C₇⋊C₈	C₂×D₄	1	1	yes	characteristic
215	C₂×C₇⋊C₈	C₂×D₄	1	1	yes	characteristic
216	C₂×C₇⋊C₈	C₂×D₄	1	1	yes	characteristic
217	#1132	—	2	2	no	—
218	#1132	—	2	2	no	—
219	#1132	—	4	1	no	—
220	#1132	—	4	1	no	—
221	#1131	—	8	1	no	—
222	#1131	—	8	1	no	—
223	C₈×D₇	—	8	1	no	—
224	C₈×D₇	—	8	1	no	—
225	#533	—	7	1	no	—
226	C₂×C₄×D₄	—	7	1	no	—
227	#483	—	7	1	no	—
228	#483	—	7	1	no	—
229	#476	—	7	1	no	—
230	#476	—	7	1	no	—
231	#461	—	7	1	no	—
232	#461	—	7	1	no	—
233	#450	—	7	1	no	—
234	#450	—	7	1	no	—
235	#446	—	7	1	no	—
236	#446	—	7	1	no	—
237	#446	—	14	1	no	—
238	C₈×Q₈	—	7	1	no	—
239	C₈×Q₈	—	7	1	no	—
240	C₈×Q₈	—	14	1	no	—
241	C₄×SD₁₆	—	7	1	no	—
242	C₄×SD₁₆	—	7	1	no	—
243	C₄×SD₁₆	—	7	1	no	—
244	C₄×SD₁₆	—	7	1	no	—
245	#436	—	7	1	no	—
246	#436	—	7	1	no	—
247	#435	—	14	1	no	—
248	#435	—	14	1	no	—
249	C₈×D₄	—	7	1	no	—
250	C₈×D₄	—	7	1	no	—
251	#433	—	14	1	no	—
252	#433	—	14	1	no	—
253	#432	C₂×D₇	1	1	yes	characteristic
254	#431	—	7	1	no	—
255	#431	—	7	1	no	—
256	#431	C₂×D₇	1	1	yes	characteristic
257	#431	C₂×D₇	1	1	yes	characteristic
258	#407	—	14	1	no	—
259	C₂×C₂²⋊C₈	—	14	1	no	—
260	#335	C₂×D₇	1	1	yes	characteristic, complemented
261	#335	C₂×D₇	1	1	yes	characteristic, complemented
262	#334	C₂×D₇	1	1	yes	characteristic, complemented
263	#334	C₂×D₇	1	1	yes	characteristic, complemented
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	C₈²	—	7	1	no	—
276	C₂³×C₇	C₄×D₄	1	1	yes	characteristic
277	C₂²×D₇	—	2	1	no	—
278	C₂²×D₇	—	2	1	no	—
279	C₂²×D₇	—	4	2	no	—
280	C₂²×D₇	—	4	2	no	—
281	C₂²×D₇	—	8	1	no	—
282	C₂×C₄×C₇	—	2	1	no	—
283	C₂×C₄×C₇	—	2	1	no	—
284	C₂×C₄×C₇	—	2	1	no	—
285	C₂×C₄×C₇	—	2	1	no	—
286	C₂×C₄×C₇	—	4	1	no	—
287	C₂×C₄×C₇	C₄×D₄	1	1	yes	characteristic
288	C₂×C₄×C₇	C₄×D₄	1	1	yes	characteristic
289	C₂×C₄×C₇	C₄×D₄	1	1	yes	characteristic
290	C₂×C₄×C₇	C₂³×C₄	1	1	yes	characteristic
291	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
292	C₂×C₄×C₇	C₂×#41	1	1	yes	characteristic
293	C₂×Dic₇	—	2	1	no	—
294	C₂×Dic₇	—	2	1	no	—
295	C₂×Dic₇	—	2	1	no	—
296	C₂×Dic₇	—	2	1	no	—
297	C₂×Dic₇	—	2	1	no	—
298	C₂×Dic₇	—	2	1	no	—
299	C₂×Dic₇	—	8	1	no	—
300	D₂₈	—	2	1	no	—
301	D₂₈	—	2	1	no	—
302	D₂₈	—	2	1	no	—
303	D₂₈	—	4	2	no	—
304	D₂₈	#131	1	2	yes	—
305	C₄×D₇	—	4	1	no	—
306	C₄×D₇	—	4	1	no	—
307	C₄×D₇	—	4	1	no	—
308	C₄×D₇	—	4	1	no	—
309	C₄×D₇	—	8	1	no	—
310	C₄×D₇	—	8	1	no	—
311	Dic₁₄	—	2	1	no	—
312	Dic₁₄	—	2	1	no	—
313	Dic₁₄	—	2	1	no	—
314	Dic₁₄	—	2	1	no	—
315	Dic₁₄	—	4	2	no	—
316	C₇×C₈	—	2	1	no	—
317	C₇×C₈	—	2	1	no	—
318	C₇×C₈	—	2	1	no	—
319	C₇×C₈	—	2	1	no	—
320	C₇×C₈	—	4	1	no	—
321	C₇×C₈	—	4	1	no	—
322	C₇×C₈	—	4	1	no	—
323	C₇×C₈	—	4	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	—	4	1	no	—
329	C₇⋊C₈	—	4	1	no	—
330	C₂²×D₄	—	7	1	no	—
331	C₂³×C₄	—	14	1	no	—
332	C₂×SD₁₆	—	7	1	no	—
333	C₂×SD₁₆	—	7	1	no	—
334	C₂×SD₁₆	—	7	1	no	—
335	C₂×SD₁₆	—	7	1	no	—
336	C₂×M₁₆	—	14	1	no	—
337	C₂×M₁₆	—	14	1	no	—
338	C₂²×C₈	—	14	1	no	—
339	C₂²×C₈	—	14	1	no	—
340	C₄⋊Q₈	—	7	1	no	—
341	C₄⋊Q₈	—	7	1	no	—
342	#125	—	14	1	no	—
343	C₂²⋊Q₈	—	7	1	no	—
344	C₂²⋊Q₈	—	7	1	no	—
345	C₂²⋊Q₈	—	14	1	no	—
346	C₄×Q₈	—	7	1	no	—
347	C₄×Q₈	—	7	1	no	—
348	C₄×Q₈	—	14	1	no	—
349	C₄×D₄	—	7	1	no	—
350	C₄×D₄	—	7	1	no	—
351	C₄×D₄	—	7	1	no	—
352	C₄×D₄	—	7	1	no	—
353	C₄×D₄	—	14	1	no	—
354	C₄×D₄	—	14	1	no	—
355	#117	—	14	1	no	—
356	C₂×C₄⋊C₄	—	7	1	no	—
357	C₂×C₂²⋊C₄	—	14	1	no	—
358	C₂×C₄²	C₂²×D₇	1	1	yes	characteristic
359	#106	—	7	1	no	—
360	#106	—	7	1	no	—
361	#106	—	7	1	no	—
362	#106	—	7	1	no	—
363	C₄⋊C₈	—	7	1	no	—
364	C₄⋊C₈	—	7	1	no	—
365	C₄⋊C₈	—	14	1	no	—
366	C₄⋊C₈	—	14	1	no	—
367	C₄⋊C₈	—	14	1	no	—
368	C₄⋊C₈	—	14	1	no	—
369	C₄⋊C₈	—	14	1	no	—
370	C₄⋊C₈	C₄×D₇	1	1	yes	characteristic
371	C₄⋊C₈	C₄×D₇	1	1	yes	characteristic
372	C₄⋊C₈	C₂²×D₇	1	1	yes	characteristic
373	C₄⋊C₈	C₂²×D₇	1	1	yes	characteristic
374	C₄⋊C₈	C₂²×D₇	1	1	yes	characteristic
375	C₄⋊C₈	C₂²×D₇	1	1	yes	characteristic
376	#103	—	7	1	no	—
377	#103	—	7	1	no	—
378	#103	—	7	1	no	—
379	#103	—	7	1	no	—
380	#102	—	7	1	no	—
381	#102	—	7	1	no	—
382	#102	—	7	1	no	—
383	#102	—	7	1	no	—
384	C₂²⋊C₈	—	2	1	no	—
385	C₂²⋊C₈	—	2	1	no	—
386	C₂²⋊C₈	—	7	1	no	—
387	C₂²⋊C₈	—	7	1	no	—
388	C₂²⋊C₈	—	14	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	C₂²⋊C₈	C₄×D₇	1	1	yes	characteristic
394	C₂²⋊C₈	C₄×D₇	1	1	yes	characteristic
395	#97	—	2	1	no	—
396	#97	—	14	1	no	—
397	#97	—	14	1	no	—
398	C₄×C₈	—	2	1	no	—
399	C₄×C₈	—	7	1	no	—
400	C₄×C₈	—	7	1	no	—
401	C₄×C₈	—	7	1	no	—
402	C₄×C₈	—	7	1	no	—
403	C₄×C₈	—	14	1	no	—
404	C₄×C₈	—	14	1	no	—
405	C₄×C₈	C₂²×D₇	1	1	yes	characteristic
406	C₄×C₈	C₂²×D₇	1	1	yes	characteristic
407	C₂²×C₇	—	2	1	no	—
408	C₂²×C₇	—	2	1	no	—
409	C₂²×C₇	—	2	1	no	—
410	C₂²×C₇	C₂×C₄×D₄	1	1	yes	characteristic
411	C₂×D₇	—	2	2	no	—
412	C₂×D₇	—	4	1	no	—
413	C₂×D₇	—	4	1	no	—
414	C₂×D₇	—	4	1	no	—
415	C₂×D₇	—	4	1	no	—
416	C₂×D₇	—	4	1	no	—
417	C₂×D₇	—	8	4	no	—
418	C₄×C₇	—	2	1	no	—
419	C₄×C₇	—	2	1	no	—
420	C₄×C₇	—	2	1	no	—
421	C₄×C₇	—	2	1	no	—
422	C₄×C₇	C₂×#131	1	1	yes	characteristic
423	C₄×C₇	#568	1	1	yes	characteristic
424	C₄×C₇	#577	1	1	yes	characteristic
425	C₄×C₇	#577	1	1	yes	characteristic
426	Dic₇	—	4	1	no	—
427	Dic₇	—	4	1	no	—
428	Dic₇	—	4	1	no	—
429	Dic₇	—	4	1	no	—
430	Dic₇	—	4	1	no	—
431	Dic₇	—	4	1	no	—
432	C₂⁴	—	14	1	no	—
433	C₂×Q₈	—	7	1	no	—
434	C₂×Q₈	—	7	1	no	—
435	C₂×Q₈	—	14	1	no	—
436	C₂×D₄	—	7	1	no	—
437	C₂×D₄	—	7	1	no	—
438	C₂×D₄	—	14	2	no	—
439	C₂×D₄	—	14	1	no	—
440	C₂×D₄	—	28	1	no	—
441	C₂²×C₄	—	14	1	no	—
442	C₂²×C₄	—	14	1	no	—
443	C₂²×C₄	—	14	1	no	—
444	C₂²×C₄	—	14	1	no	—
445	C₂²×C₄	—	14	1	no	—
446	C₂²×C₄	—	56	1	no	—
447	C₂²×C₄	—	56	1	no	—
448	C₂²×C₄	C₂×C₄×D₇	1	1	yes	characteristic
449	C₂²×C₄	D₄×D₇	1	1	yes	characteristic
450	C₂²×C₄	#1161	1	1	yes	characteristic
451	SD₁₆	—	14	2	no	—
452	SD₁₆	—	14	2	no	—
453	SD₁₆	—	28	1	no	—
454	SD₁₆	—	28	1	no	—
455	M₁₆	—	56	1	no	—
456	M₁₆	—	56	1	no	—
457	C₂×C₈	—	2	1	no	—
458	C₂×C₈	—	2	1	no	—
459	C₂×C₈	—	2	1	no	—
460	C₂×C₈	—	2	1	no	—
461	C₂×C₈	—	7	1	no	—
462	C₂×C₈	—	7	1	no	—
463	C₂×C₈	—	7	1	no	—
464	C₂×C₈	—	7	1	no	—
465	C₂×C₈	—	14	1	no	—
466	C₂×C₈	—	14	1	no	—
467	C₂×C₈	—	56	1	no	—
468	C₂×C₈	—	56	1	no	—
469	C₂×C₈	C₂×C₄×D₇	1	1	yes	characteristic
470	C₂×C₈	C₂×C₄×D₇	1	1	yes	characteristic
471	C₂×C₈	C₂×C₄×D₇	1	1	yes	characteristic
472	C₂×C₈	C₂×C₄×D₇	1	1	yes	characteristic
473	C₄⋊C₄	—	7	1	no	—
474	C₄⋊C₄	—	7	1	no	—
475	C₄⋊C₄	—	7	1	no	—
476	C₄⋊C₄	—	7	1	no	—
477	C₄⋊C₄	—	14	1	no	—
478	C₄⋊C₄	—	14	1	no	—
479	C₄⋊C₄	—	14	1	no	—
480	C₄⋊C₄	—	14	1	no	—
481	C₄⋊C₄	—	14	1	no	—
482	C₄⋊C₄	—	14	1	no	—
483	C₄⋊C₄	—	14	1	no	—
484	C₄⋊C₄	—	14	1	no	—
485	C₂²⋊C₄	—	14	1	no	—
486	C₂²⋊C₄	—	14	1	no	—
487	C₂²⋊C₄	—	14	1	no	—
488	C₂²⋊C₄	—	14	1	no	—
489	C₂²⋊C₄	—	14	1	no	—
490	C₂²⋊C₄	—	14	1	no	—
491	C₄²	—	14	1	no	—
492	C₄²	—	14	1	no	—
493	C₄²	C₂×C₄×D₇	1	1	yes	characteristic
494	C₄²	D₄×D₇	1	1	yes	characteristic
495	C₄²	#1161	1	1	yes	characteristic
496	C₄²	C₂³×D₇	1	1	yes	characteristic
497	C₂×C₇	—	4	1	no	—
498	C₂×C₇	#2933	1	1	yes	characteristic
499	C₂×C₇	#2949	1	1	yes	characteristic
500	C₂×C₇	#2955	1	1	yes	characteristic
501	D₇	—	4	2	no	—
502	D₇	—	8	1	no	—
503	C₂³	—	14	1	no	—
504	C₂³	—	14	1	no	—
505	C₂³	—	28	2	no	—
506	C₂³	—	28	2	no	—
507	C₂³	—	56	1	no	—
508	C₂³	#6456	1	1	yes	characteristic
509	Q₈	—	14	1	no	—
510	Q₈	—	14	1	no	—
511	Q₈	—	14	1	no	—
512	Q₈	—	14	1	no	—
513	Q₈	—	28	2	no	—
514	D₄	—	7	2	no	—
515	D₄	—	14	1	no	—
516	D₄	—	14	1	no	—
517	D₄	—	14	1	no	—
518	D₄	—	28	2	no	—
519	C₂×C₄	—	2	1	no	—
520	C₂×C₄	—	2	1	no	—
521	C₂×C₄	—	2	1	no	—
522	C₂×C₄	—	2	1	no	—
523	C₂×C₄	—	4	1	no	—
524	C₂×C₄	—	14	1	no	—
525	C₂×C₄	—	14	1	no	—
526	C₂×C₄	—	14	1	no	—
527	C₂×C₄	—	14	1	no	—
528	C₂×C₄	—	14	1	no	—
529	C₂×C₄	—	14	1	no	—
530	C₂×C₄	—	28	1	no	—
531	C₂×C₄	—	28	1	no	—
532	C₂×C₄	—	28	1	no	—
533	C₂×C₄	—	28	1	no	—
534	C₂×C₄	—	56	1	no	—
535	C₂×C₄	—	56	1	no	—
536	C₂×C₄	—	56	1	no	—
537	C₂×C₄	#6456	1	1	yes	characteristic
538	C₂×C₄	#6456	1	1	yes	characteristic
539	C₂×C₄	#6456	1	1	yes	characteristic
540	C₂×C₄	C₂²×C₄×D₇	1	1	yes	characteristic
541	C₂×C₄	C₂×D₄×D₇	1	1	yes	characteristic
542	C₂×C₄	C₂×#1161	1	1	yes	characteristic
543	C₈	—	2	1	no	—
544	C₈	—	2	1	no	—
545	C₈	—	2	1	no	—
546	C₈	—	2	1	no	—
547	C₈	—	4	1	no	—
548	C₈	—	4	1	no	—
549	C₈	—	4	1	no	—
550	C₈	—	4	1	no	—
551	C₈	—	14	1	no	—
552	C₈	—	14	1	no	—
553	C₈	—	14	1	no	—
554	C₈	—	14	1	no	—
555	C₈	—	28	1	no	—
556	C₈	—	28	1	no	—
557	C₇	#18028	1	1	yes	characteristic, complemented, Sylow
558	C₂²	—	2	1	no	—
559	C₂²	—	2	1	no	—
560	C₂²	—	2	1	no	—
561	C₂²	—	14	2	no	—
562	C₂²	—	28	1	no	—
563	C₂²	—	28	1	no	—
564	C₂²	—	28	1	no	—
565	C₂²	—	28	1	no	—
566	C₂²	—	28	1	no	—
567	C₂²	—	56	4	no	—
568	C₂²	C₂×#6456	1	1	yes	characteristic
569	C₄	—	2	1	no	—
570	C₄	—	2	1	no	—
571	C₄	—	2	1	no	—
572	C₄	—	2	1	no	—
573	C₄	—	28	1	no	—
574	C₄	—	28	1	no	—
575	C₄	—	28	1	no	—
576	C₄	—	28	1	no	—
577	C₄	—	28	1	no	—
578	C₄	—	28	1	no	—
579	C₄	D₇×#131	1	1	yes	characteristic
580	C₄	#90441	1	1	yes	characteristic
581	C₄	#90461	1	1	yes	characteristic
582	C₄	#90461	1	1	yes	characteristic
583	C₂	—	4	1	no	—
584	C₂	—	28	2	no	—
585	C₂	—	56	1	no	—
586	C₂	#11736520	1	1	yes	characteristic
587	C₂	#11736613	1	1	yes	characteristic
588	C₂	#11736702	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×#1572	C₂
socle	C₂²×C₇	C₂×C₄×D₄
prime radical	C₂²×D₂₈	C₂×C₄
cosocle	C₄²×C₇	C₂⁴
hypercenter	#1572	D₇
hypocenter	C₇	#18028
LCS	G ▷ C₂×C₄×C₇ ▷ C₂×C₇ ▷ C₇
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #1572

Complements

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

N	H ≅ G/N	type
3. #11736712	C₂	semidirect
4. C₇×#1572	C₂	semidirect
5. #11728557	C₂	semidirect
7. #11728498	C₂	semidirect
8. #11726319	C₂	semidirect
9. #11726316	C₂	semidirect
10. #11726315	C₂	semidirect
11. #11726312	C₂	semidirect
12. #11726277	C₂	semidirect
13. #11726274	C₂	semidirect
14. #11726273	C₂	semidirect
15. #11726270	C₂	semidirect
31. #89603	C₂²	semidirect
32. #89603	C₂²	semidirect
33. #89602	C₂²	semidirect
34. #89602	C₂²	semidirect
51. C₇×#335	C₂²	semidirect
52. C₇×#335	C₂²	semidirect
53. C₇×#334	C₂²	semidirect
54. C₇×#334	C₂²	semidirect
55. #89279	C₂²	semidirect
56. #89279	C₂²	semidirect
57. #89279	C₂²	semidirect
58. #89279	C₂²	semidirect
63. #89250	C₂²	semidirect
64. #89249	C₂²	semidirect
65. #89249	C₂²	semidirect
66. C₈×C₇⋊C₈	C₂²	semidirect
156. #1572	D₇	semidirect
260. #335	C₂×D₇	semidirect
261. #335	C₂×D₇	semidirect
262. #334	C₂×D₇	semidirect
263. #334	C₂×D₇	semidirect
557. C₇	#18028	semidirect

Maximal subgroups

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

subgroup	index
#11736781	2
#11736743	2
#11736712	2
C₇×#1572	2
#11728557	2
#11728510	2
#11728498	2
#11726319	2
#11726316	2
#11726315	2
#11726312	2
#11726277	2
#11726274	2
#11726273	2
#11726270	2
#18028	7