Subgroups — #13325510

Order 1792.

650 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	#11737352	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄×#6482	C₂	1	1	yes	maximal, characteristic
4	C₇×#1584	C₂	1	1	yes	maximal, characteristic, complemented
5	#11728709	C₂	1	1	yes	maximal, characteristic, complemented
6	#11728691	C₂	1	1	yes	maximal, characteristic, complemented
7	#11728657	C₂	1	1	yes	maximal, characteristic, complemented
8	#11726323	C₂	1	1	yes	maximal, characteristic, complemented
9	#11726313	C₂	1	1	yes	maximal, characteristic, complemented
10	#11725992	C₂	1	1	yes	maximal, characteristic, complemented
11	#11725992	C₂	1	1	yes	maximal, characteristic, complemented
12	#11725980	C₂	1	1	yes	maximal, characteristic, complemented
13	#11725968	C₂	1	1	yes	maximal, characteristic, complemented
14	#11725832	C₂	1	1	yes	maximal, characteristic, complemented
15	#11725824	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×#6482	C₄	1	1	yes	characteristic
17	C₄×#1161	C₂²	1	1	yes	characteristic
18	C₄×#1161	C₂²	1	1	yes	characteristic
19	C₇×#446	C₂²	1	1	yes	characteristic
20	C₇×C₈×Q₈	C₂²	1	1	yes	characteristic
21	C₄×C₇×Q₁₆	C₂²	1	1	yes	characteristic
22	Q₁₆×Dic₇	C₄	1	1	yes	characteristic
23	C₄×#1143	C₂²	1	1	yes	characteristic
24	C₄×#1143	C₂²	1	1	yes	characteristic
25	#89796	C₂²	1	1	yes	characteristic
26	Q₈×C₇⋊C₈	C₂²	1	1	yes	characteristic
27	#89652	C₄	1	1	yes	characteristic
28	#89644	C₄	1	1	yes	characteristic
29	#89610	—	2	1	no	—
30	#89610	C₂²	1	1	yes	characteristic
31	#89609	—	2	1	no	—
32	#89609	C₂²	1	1	yes	characteristic
33	#89609	C₂²	1	1	yes	characteristic
34	#89608	—	2	1	no	—
35	#89606	C₂²	1	1	yes	characteristic
36	D₇×C₄⋊C₈	—	2	1	no	—
37	#89576	C₄	1	1	yes	characteristic
38	#89576	C₄	1	1	yes	characteristic
39	#89560	C₄	1	1	yes	characteristic
40	#89560	C₄	1	1	yes	characteristic
41	#89478	—	2	1	no	—
42	#89477	—	2	1	no	—
43	C₄×D₅₆	C₂²	1	1	yes	characteristic
44	#89460	—	2	1	no	—
45	#89460	C₂²	1	1	yes	characteristic
46	C₄×#1131	C₂²	1	1	yes	characteristic
47	C₈×D₂₈	C₂²	1	1	yes	characteristic
48	#89457	—	2	1	no	—
49	#89457	C₂²	1	1	yes	characteristic
50	C₄×C₈×D₇	C₂²	1	1	yes	characteristic
51	C₇×#335	C₂²	1	1	yes	characteristic
52	C₇×Q₈⋊C₈	C₂²	1	1	yes	characteristic
53	C₇×Q₈⋊C₈	C₂²	1	1	yes	characteristic
54	C₇×#322	C₂²	1	1	yes	characteristic
55	Q₈⋊(C₇⋊C₈)	C₂²	1	1	yes	characteristic
56	Q₈⋊(C₇⋊C₈)	C₂²	1	1	yes	characteristic
57	#89278	C₂²	1	1	yes	characteristic
58	#89278	C₂²	1	1	yes	characteristic
59	#89274	C₂²	1	1	yes	characteristic
60	#89274	C₂²	1	1	yes	characteristic
61	#89254	C₂²	1	1	yes	characteristic
62	#89254	C₂²	1	1	yes	characteristic
63	#89253	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	#18061	—	7	1	no	maximal, Sylow
68	C₂×#1161	C₂×C₄	1	1	yes	characteristic
69	C₂×#1161	C₂×C₄	1	1	yes	characteristic
70	C₂×C₇×Q₁₆	C₂×C₄	1	1	yes	characteristic
71	C₄×C₇×Q₈	C₂³	1	1	yes	characteristic
72	C₄×C₇×Q₈	C₂³	1	1	yes	characteristic
73	Q₈×Dic₇	C₂×C₄	1	1	yes	characteristic
74	Q₈×Dic₇	C₂×C₄	1	1	yes	characteristic
75	C₂×#1143	C₂×C₄	1	1	yes	characteristic
76	C₂×#1143	C₂×C₄	1	1	yes	characteristic
77	#6482	—	2	4	no	—
78	C₂×D₅₆	C₂×C₄	1	1	yes	characteristic
79	C₂×#1131	—	2	1	no	—
80	C₂×#1131	—	2	1	no	—
81	C₂×#1131	—	2	1	no	—
82	C₂×#1131	—	2	1	no	—
83	C₂×#1131	—	2	1	no	—
84	C₂×C₈×D₇	—	2	1	no	—
85	C₂×C₈×D₇	—	2	1	no	—
86	C₂×C₈×D₇	C₂×C₄	1	1	yes	characteristic
87	C₂×C₈×D₇	C₂×C₄	1	1	yes	characteristic
88	#6456	—	2	1	no	—
89	#6456	—	2	1	no	—
90	#6456	C₂×C₄	1	1	yes	characteristic
91	#6456	C₂×C₄	1	1	yes	characteristic
92	#6455	—	2	1	no	—
93	#6455	—	2	1	no	—
94	#6455	C₂×C₄	1	1	yes	characteristic
95	#6455	C₂×C₄	1	1	yes	characteristic
96	C₄×D₂₈	—	2	1	no	—
97	C₄×D₂₈	—	2	1	no	—
98	C₄×D₂₈	C₂³	1	1	yes	characteristic
99	C₄×D₂₈	C₂³	1	1	yes	characteristic
100	C₄²×D₇	—	2	1	no	—
101	C₄²×D₇	—	2	1	no	—
102	C₄²×D₇	C₂³	1	1	yes	characteristic
103	C₇×#107	C₂×C₄	1	1	yes	characteristic
104	C₇×C₄⋊C₈	—	2	1	no	—
105	C₇×C₄⋊C₈	—	2	1	no	—
106	C₇×C₄⋊C₈	C₂³	1	1	yes	characteristic
107	C₇×C₄⋊C₈	C₂³	1	1	yes	characteristic
108	C₇×#103	C₂×C₄	1	1	yes	characteristic
109	C₇×#103	C₂×C₄	1	1	yes	characteristic
110	C₇×#97	—	2	1	no	—
111	C₄×C₇×C₈	—	2	1	no	—
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	#6409	C₂×C₄	1	1	yes	characteristic
116	#6409	C₂×C₄	1	1	yes	characteristic
117	#6395	C₂×C₄	1	1	yes	characteristic
118	#6395	C₂×C₄	1	1	yes	characteristic
119	(C₂×D₇)⋊C₈	—	2	1	no	—
120	(C₂×D₇)⋊C₈	—	2	1	no	—
121	(C₂×D₇)⋊C₈	—	2	1	no	—
122	(C₂×D₇)⋊C₈	—	2	1	no	—
123	(C₂×D₇)⋊C₈	D₄	1	1	yes	characteristic
124	(C₂×D₇)⋊C₈	D₄	1	1	yes	characteristic
125	#6392	C₂×C₄	1	1	yes	characteristic
126	#6389	—	2	1	no	—
127	Dic₇⋊C₈	—	2	1	no	—
128	Dic₇⋊C₈	—	2	1	no	—
129	Dic₇⋊C₈	D₄	1	1	yes	characteristic
130	Dic₇⋊C₈	D₄	1	1	yes	characteristic
131	C₈×Dic₇	C₂×C₄	1	1	yes	characteristic
132	C₈×Dic₇	C₂×C₄	1	1	yes	characteristic
133	#6383	C₂×C₄	1	1	yes	characteristic
134	#6383	C₂×C₄	1	1	yes	characteristic
135	#6382	C₂×C₄	1	1	yes	characteristic
136	#6382	C₂×C₄	1	1	yes	characteristic
137	C₄⋊(C₇⋊C₈)	—	2	1	no	—
138	C₄⋊(C₇⋊C₈)	—	2	1	no	—
139	C₄⋊(C₇⋊C₈)	C₂³	1	1	yes	characteristic
140	C₄⋊(C₇⋊C₈)	C₂³	1	1	yes	characteristic
141	#6377	—	2	1	no	—
142	C₄×C₇⋊C₈	—	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	#2991	—	7	1	no	—
147	#2990	—	7	1	no	—
148	C₄×#135	—	7	1	no	—
149	#1592	—	7	1	no	—
150	#1592	—	7	1	no	—
151	#1584	—	7	1	no	—
152	#1584	D₇	1	1	yes	characteristic, complemented
153	#1581	—	7	1	no	—
154	#1581	—	7	1	no	—
155	SD₁₆⋊C₈	—	7	1	no	—
156	SD₁₆⋊C₈	—	7	1	no	—
157	#1567	—	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×Q₈	C₂²×C₄	1	1	yes	characteristic
163	#1161	—	2	2	no	—
164	#1161	—	2	2	no	—
165	#1161	—	4	1	no	—
166	#1161	—	4	1	no	—
167	C₂×D₂₈	—	2	1	no	—
168	C₂×D₂₈	—	2	1	no	—
169	C₂×D₂₈	C₂²×C₄	1	1	yes	characteristic
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×C₄×D₇	—	2	1	no	—
175	C₂×C₄×D₇	—	2	1	no	—
176	C₂×C₄×D₇	—	2	1	no	—
177	C₂×C₄×D₇	C₂²×C₄	1	1	yes	characteristic
178	C₂×C₄×D₇	C₂×D₄	1	1	yes	characteristic
179	C₂×C₄×D₇	#41	1	1	yes	characteristic
180	C₇×Q₁₆	—	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	C₂²×C₄	1	1	yes	characteristic
185	C₂×C₇×C₈	C₂²×C₄	1	1	yes	characteristic
186	C₂×C₇×C₈	C₂×D₄	1	1	yes	characteristic
187	C₂×C₇×C₈	C₂×D₄	1	1	yes	characteristic
188	C₇×C₄⋊C₄	—	2	1	no	—
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	C₄²×C₇	—	2	1	no	—
193	C₄²×C₇	—	2	1	no	—
194	C₄²×C₇	C₂⁴	1	1	yes	characteristic
195	#1143	—	2	2	no	—
196	#1143	M₁₆	1	4	yes	complemented
197	(C₂×D₇)⋊C₄	—	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	C₄⋊Dic₇	—	2	1	no	—
204	C₄⋊Dic₇	—	2	1	no	—
205	C₄⋊Dic₇	C₂²×C₄	1	1	yes	characteristic
206	C₄⋊Dic₇	C₂²×C₄	1	1	yes	characteristic
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	C₂²×C₄	1	1	yes	characteristic
212	C₄×Dic₇	C₂×D₄	1	1	yes	characteristic
213	C₄×Dic₇	#41	1	1	yes	characteristic
214	C₂×C₇⋊C₈	—	2	1	no	—
215	C₂×C₇⋊C₈	—	2	1	no	—
216	C₂×C₇⋊C₈	—	2	1	no	—
217	C₂×C₇⋊C₈	C₂²×C₄	1	1	yes	characteristic
218	C₂×C₇⋊C₈	C₂²×C₄	1	1	yes	characteristic
219	C₂×C₇⋊C₈	C₂×D₄	1	1	yes	characteristic
220	C₂×C₇⋊C₈	C₂×D₄	1	1	yes	characteristic
221	D₅₆	—	2	2	no	—
222	#1131	—	4	2	no	—
223	#1131	—	8	1	no	—
224	#1131	—	8	1	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	C₂×D₇	1	1	yes	characteristic
236	C₈×Q₈	—	7	1	no	—
237	C₈×Q₈	C₂×D₇	1	1	yes	characteristic
238	C₄×Q₁₆	—	7	1	no	—
239	C₄×Q₁₆	C₂×D₇	1	1	yes	characteristic
240	C₄×SD₁₆	—	7	1	no	—
241	C₄×SD₁₆	—	7	1	no	—
242	C₄×SD₁₆	—	7	1	no	—
243	C₄×SD₁₆	—	7	1	no	—
244	C₄×D₈	—	7	1	no	—
245	C₄×D₈	—	7	1	no	—
246	#436	—	7	1	no	—
247	#436	—	7	1	no	—
248	#436	—	14	1	no	—
249	#436	—	14	1	no	—
250	#435	—	14	1	no	—
251	#435	—	14	1	no	—
252	C₈×D₄	—	7	1	no	—
253	C₈×D₄	—	7	1	no	—
254	#432	—	14	1	no	—
255	#431	—	7	1	no	—
256	#431	—	14	1	no	—
257	#427	—	7	1	no	—
258	#423	—	7	1	no	—
259	#423	—	7	1	no	—
260	#423	—	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	#335	—	7	1	no	—
267	#335	—	7	1	no	—
268	#335	—	7	1	no	—
269	#335	C₂×D₇	1	1	yes	characteristic
270	Q₈⋊C₈	—	7	1	no	—
271	Q₈⋊C₈	—	7	1	no	—
272	Q₈⋊C₈	C₂×D₇	1	1	yes	characteristic
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	—	7	1	no	—
278	#322	—	7	1	no	—
279	#322	—	7	1	no	—
280	#322	—	7	1	no	—
281	#322	C₂×D₇	1	1	yes	characteristic
282	C₂²×D₇	—	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×Q₈	—	2	1	no	—
288	C₇×Q₈	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	—	2	1	no	—
293	C₂×C₄×C₇	C₂³×C₄	1	1	yes	characteristic
294	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
295	C₂×C₄×C₇	C₂×#41	1	1	yes	characteristic
296	C₂×Dic₇	—	2	1	no	—
297	C₂×Dic₇	—	2	1	no	—
298	C₂×Dic₇	C₄×D₄	1	1	yes	characteristic
299	C₂×Dic₇	C₄×D₄	1	1	yes	characteristic
300	C₂×Dic₇	C₄×D₄	1	1	yes	characteristic
301	D₂₈	—	2	1	no	—
302	D₂₈	—	2	1	no	—
303	D₂₈	—	2	1	no	—
304	D₂₈	—	4	2	no	—
305	D₂₈	—	4	2	no	—
306	D₂₈	C₂×M₁₆	1	2	yes	—
307	C₄×D₇	—	2	1	no	—
308	C₄×D₇	—	2	1	no	—
309	C₄×D₇	—	2	1	no	—
310	C₄×D₇	—	2	1	no	—
311	C₄×D₇	—	2	2	no	—
312	C₄×D₇	—	4	2	no	—
313	C₄×D₇	—	4	2	no	—
314	C₄×D₇	—	4	1	no	—
315	C₄×D₇	—	4	1	no	—
316	C₄×D₇	—	4	1	no	—
317	C₄×D₇	—	4	1	no	—
318	C₄×D₇	—	4	2	no	—
319	C₄×D₇	—	4	2	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	C₄×D₇	1	1	yes	characteristic
338	C₂×SD₁₆	—	7	1	no	—
339	C₂×SD₁₆	—	7	1	no	—
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	C₂×M₁₆	—	14	1	no	—
345	C₂×M₁₆	—	14	1	no	—
346	C₂²×C₈	—	7	1	no	—
347	C₂²×C₈	—	7	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	C₂²×D₇	1	1	yes	characteristic
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	—	7	1	no	—
358	C₄×D₄	—	14	1	no	—
359	C₄×D₄	—	14	1	no	—
360	C₄×D₄	—	14	1	no	—
361	C₄×D₄	—	14	1	no	—
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	C₄×D₇	1	1	yes	characteristic
371	#106	—	7	1	no	—
372	#106	—	7	1	no	—
373	C₄⋊C₈	—	2	1	no	—
374	C₄⋊C₈	—	2	1	no	—
375	C₄⋊C₈	—	7	1	no	—
376	C₄⋊C₈	—	7	1	no	—
377	C₄⋊C₈	—	7	1	no	—
378	C₄⋊C₈	—	7	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	C₄×D₇	1	1	yes	characteristic
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	—	7	1	no	—
393	C₂²⋊C₈	—	7	1	no	—
394	C₂²⋊C₈	—	7	1	no	—
395	C₂²⋊C₈	—	14	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	C₄×C₈	—	2	1	no	—
403	C₄×C₈	—	7	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	—	14	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	C₂×C₄×D₄	1	1	yes	characteristic
413	C₂×D₇	—	2	1	no	—
414	C₂×D₇	—	2	2	no	—
415	C₂×D₇	—	2	1	no	—
416	C₂×D₇	—	2	1	no	—
417	C₂×D₇	—	4	1	no	—
418	C₂×D₇	—	4	1	no	—
419	C₂×D₇	—	4	1	no	—
420	C₂×D₇	—	4	1	no	—
421	C₂×D₇	—	4	1	no	—
422	C₄×C₇	—	2	2	no	—
423	C₄×C₇	—	2	1	no	—
424	C₄×C₇	—	4	1	no	—
425	C₄×C₇	—	4	1	no	—
426	C₄×C₇	—	4	1	no	—
427	C₄×C₇	C₂²×M₁₆	1	1	yes	characteristic
428	C₄×C₇	#568	1	1	yes	characteristic
429	C₄×C₇	#576	1	1	yes	characteristic
430	C₄×C₇	#578	1	1	yes	characteristic
431	Dic₇	—	2	1	no	—
432	Dic₇	—	2	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	C₂×C₄×D₇	1	1	yes	characteristic
441	C₂×Q₈	C₂×C₄×D₇	1	1	yes	characteristic
442	C₂×D₄	—	7	1	no	—
443	C₂×D₄	—	7	1	no	—
444	C₂×D₄	—	14	1	no	—
445	C₂×D₄	—	14	1	no	—
446	C₂²×C₄	—	7	1	no	—
447	C₂²×C₄	—	7	1	no	—
448	C₂²×C₄	—	7	1	no	—
449	C₂²×C₄	—	14	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	—	2	2	no	—
456	SD₁₆	—	7	4	no	—
457	SD₁₆	—	14	2	no	—
458	D₈	—	14	2	no	—
459	M₁₆	—	28	2	no	—
460	M₁₆	—	56	1	no	—
461	M₁₆	—	56	1	no	—
462	M₁₆	—	56	1	no	—
463	M₁₆	—	56	1	no	—
464	C₂×C₈	—	2	1	no	—
465	C₂×C₈	—	2	1	no	—
466	C₂×C₈	—	2	1	no	—
467	C₂×C₈	—	7	1	no	—
468	C₂×C₈	—	7	1	no	—
469	C₂×C₈	—	7	1	no	—
470	C₂×C₈	—	7	1	no	—
471	C₂×C₈	—	14	2	no	—
472	C₂×C₈	—	14	1	no	—
473	C₂×C₈	—	14	1	no	—
474	C₂×C₈	—	14	1	no	—
475	C₂×C₈	—	28	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	—	2	1	no	—
484	C₄⋊C₄	—	7	1	no	—
485	C₄⋊C₄	—	7	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	—	14	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	—	2	1	no	—
498	C₄²	—	7	1	no	—
499	C₄²	—	7	1	no	—
500	C₄²	—	7	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	D₄×M₁₆	1	1	yes	characteristic
507	C₂×C₇	#2951	1	1	yes	characteristic
508	C₂×C₇	C₂×#444	1	1	yes	characteristic
509	D₇	—	4	1	no	—
510	D₇	—	4	2	no	—
511	D₇	—	8	1	no	—
512	C₂³	—	7	1	no	—
513	C₂³	—	14	1	no	—
514	C₂³	—	14	1	no	—
515	Q₈	—	2	1	no	—
516	Q₈	—	2	1	no	—
517	Q₈	—	2	1	no	—
518	Q₈	D₇×M₁₆	1	2	yes	—
519	D₄	—	7	2	no	—
520	D₄	—	14	1	no	—
521	D₄	—	14	1	no	—
522	D₄	—	14	1	no	—
523	D₄	—	28	2	no	—
524	D₄	—	28	2	no	—
525	C₂×C₄	—	2	1	no	—
526	C₂×C₄	—	2	1	no	—
527	C₂×C₄	—	2	1	no	—
528	C₂×C₄	—	2	1	no	—
529	C₂×C₄	—	7	1	no	—
530	C₂×C₄	—	7	1	no	—
531	C₂×C₄	—	7	1	no	—
532	C₂×C₄	—	14	2	no	—
533	C₂×C₄	—	14	1	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	—	28	2	no	—
540	C₂×C₄	—	28	2	no	—
541	C₂×C₄	—	28	2	no	—
542	C₂×C₄	—	28	2	no	—
543	C₂×C₄	—	28	1	no	—
544	C₂×C₄	—	28	1	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	#18061	1	1	yes	characteristic, complemented, Sylow
565	C₂²	—	14	1	no	—
566	C₂²	—	14	1	no	—
567	C₂²	—	14	2	no	—
568	C₂²	—	14	1	no	—
569	C₂²	—	28	1	no	—
570	C₂²	—	28	1	no	—
571	C₂²	—	28	1	no	—
572	C₂²	—	28	1	no	—
573	C₂²	—	28	1	no	—
574	C₂²	C₄×D₄×D₇	1	1	yes	characteristic
575	C₄	—	2	2	no	—
576	C₄	—	2	1	no	—
577	C₄	—	4	1	no	—
578	C₄	—	4	1	no	—
579	C₄	—	4	1	no	—
580	C₄	—	7	2	no	—
581	C₄	—	14	1	no	—
582	C₄	—	14	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	#90457	1	1	yes	characteristic
588	C₄	#90460	1	1	yes	characteristic
589	C₂	—	28	1	no	—
590	C₂	—	28	2	no	—
591	C₂	—	56	1	no	—
592	C₂	#11736928	1	1	yes	characteristic
593	C₂	#11737166	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×#1584	C₂
socle	C₂²×C₇	C₂×C₄×D₄
prime radical	C₂×#6482	C₄
cosocle	C₄²×C₇	C₂⁴
hypercenter	#1584	D₇
hypocenter	C₇	#18061
LCS	G ▷ C₂×C₄×C₇ ▷ C₂×C₇ ▷ C₇
UCS	C₁ ◁ C₂×C₄ ◁ C₄×C₈ ◁ #1584

Complements

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

N	H ≅ G/N	type
1. #11737390	C₂	semidirect
2. #11737352	C₂	semidirect
4. C₇×#1584	C₂	semidirect
5. #11728709	C₂	semidirect
6. #11728691	C₂	semidirect
7. #11728657	C₂	semidirect
8. #11726323	C₂	semidirect
9. #11726313	C₂	semidirect
10. #11725992	C₂	semidirect
11. #11725992	C₂	semidirect
12. #11725980	C₂	semidirect
13. #11725968	C₂	semidirect
14. #11725832	C₂	semidirect
15. #11725824	C₂	semidirect
152. #1584	D₇	semidirect
196. #1143	M₁₆	semidirect
564. C₇	#18061	semidirect

Maximal subgroups

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

subgroup	index
#11737390	2
#11737352	2
C₄×#6482	2
C₇×#1584	2
#11728709	2
#11728691	2
#11728657	2
#11726323	2
#11726313	2
#11725992	2
#11725980	2
#11725968	2
#11725832	2
#11725824	2
#18061	7