Subgroups — #13323751

Order 1792.

626 conjugacy classes of subgroups.

The subgroup lattice has 580 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#11736770	C₂	1	1	yes	maximal, characteristic, complemented
2	#11736744	C₂	1	1	yes	maximal, characteristic
3	#11736721	C₂	1	1	yes	maximal, characteristic, complemented
4	C₇×#1572	C₂	1	1	yes	maximal, characteristic, complemented
5	#11728552	C₂	1	1	yes	maximal, characteristic, complemented
6	#11728513	C₂	1	1	yes	maximal, characteristic, complemented
7	#11728496	C₂	1	1	yes	maximal, characteristic, complemented
8	#11726316	C₂	1	1	yes	maximal, characteristic, complemented
9	#11726315	C₂	1	1	yes	maximal, characteristic, complemented
10	#11726312	C₂	1	1	yes	maximal, characteristic, complemented
11	#11726312	C₂	1	1	yes	maximal, characteristic, complemented
12	#11726276	C₂	1	1	yes	maximal, characteristic, complemented
13	#11726275	C₂	1	1	yes	maximal, characteristic, complemented
14	#11726272	C₂	1	1	yes	maximal, characteristic, complemented
15	#11726271	C₂	1	1	yes	maximal, characteristic, complemented
16	#90170	C₂²	1	1	yes	characteristic
17	C₄×#1157	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	C₂×C₄×C₇⋊C₈	C₂²	1	1	yes	characteristic
23	#89619	C₄	1	1	yes	characteristic
24	#89617	C₄	1	1	yes	characteristic
25	#89616	C₄	1	1	yes	characteristic
26	#89610	C₂²	1	1	yes	characteristic
27	#89606	C₂²	1	1	yes	characteristic
28	#89606	C₂²	1	1	yes	characteristic
29	#89606	C₂²	1	1	yes	characteristic
30	#89603	C₂²	1	1	yes	characteristic
31	#89602	C₂²	1	1	yes	characteristic
32	#89602	C₂²	1	1	yes	characteristic
33	#89602	C₂²	1	1	yes	characteristic
34	#89601	C₄	1	1	yes	characteristic
35	#89509	C₄	1	1	yes	characteristic
36	#89506	C₄	1	1	yes	characteristic
37	#89505	C₄	1	1	yes	characteristic
38	#89502	—	2	1	no	—
39	(C₂²⋊D₇)⋊C₈	—	2	1	no	—
40	(C₂²⋊D₇)⋊C₈	—	2	1	no	—
41	(C₂²⋊D₇)⋊C₈	—	2	1	no	—
42	#89495	C₄	1	1	yes	characteristic
43	#89481	—	2	1	no	—
44	#89480	—	2	1	no	—
45	C₄×Dic₂₈	C₂²	1	1	yes	characteristic
46	C₄×D₅₆	C₂²	1	1	yes	characteristic
47	C₄×#1132	C₂²	1	1	yes	characteristic
48	C₄×#1132	C₂²	1	1	yes	characteristic
49	#89457	—	2	1	no	—
50	C₄×C₈×D₇	—	2	1	no	—
51	C₇×#335	C₂²	1	1	yes	characteristic
52	C₇×#335	C₂²	1	1	yes	characteristic
53	C₇×#334	C₂²	1	1	yes	characteristic
54	C₇×#334	C₂²	1	1	yes	characteristic
55	#89279	C₂²	1	1	yes	characteristic
56	#89279	C₂²	1	1	yes	characteristic
57	#89279	C₂²	1	1	yes	characteristic
58	#89279	C₂²	1	1	yes	characteristic
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
64	#89250	C₂²	1	1	yes	characteristic
65	#89249	C₂²	1	1	yes	characteristic
66	#89249	C₂²	1	1	yes	characteristic
67	#17909	—	7	1	no	maximal, Sylow
68	C₂×#1157	C₂×C₄	1	1	yes	characteristic
69	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
70	#6493	C₂×C₄	1	1	yes	characteristic
71	#6492	—	2	1	no	—
72	C₄×C₂²⋊D₇	—	2	1	no	—
73	C₄×C₂²⋊D₇	—	2	1	no	—
74	C₄×C₂²⋊D₇	—	2	1	no	—
75	#6489	C₂×C₄	1	1	yes	characteristic
76	#6487	C₂×C₄	1	1	yes	characteristic
77	C₂²×C₇⋊C₈	D₄	1	1	yes	characteristic
78	C₂²×C₇⋊C₈	D₄	1	1	yes	characteristic
79	C₂×Dic₂₈	C₂×C₄	1	1	yes	characteristic
80	C₂×D₅₆	C₂×C₄	1	1	yes	characteristic
81	C₂×#1132	C₂×C₄	1	1	yes	characteristic
82	C₂×#1132	C₂×C₄	1	1	yes	characteristic
83	C₂×#1131	—	2	1	no	—
84	C₂×C₈×D₇	—	2	1	no	—
85	C₂×C₈×D₇	—	2	1	no	—
86	C₂×C₈×D₇	—	2	1	no	—
87	#6439	—	2	1	no	—
88	#6438	C₂×C₄	1	1	yes	characteristic
89	C₄×D₂₈	C₂×C₄	1	1	yes	characteristic
90	C₄×D₂₈	C₂³	1	1	yes	characteristic
91	C₄×D₂₈	C₂³	1	1	yes	characteristic
92	#6435	—	2	1	no	—
93	#6435	—	2	1	no	—
94	C₄²×D₇	—	2	1	no	—
95	#6433	C₂×C₄	1	1	yes	characteristic
96	C₄×Dic₁₄	C₂×C₄	1	1	yes	characteristic
97	C₄×Dic₁₄	C₂³	1	1	yes	characteristic
98	C₄×Dic₁₄	C₂³	1	1	yes	characteristic
99	C₇×C₄⋊C₈	C₂×C₄	1	1	yes	characteristic
100	C₇×C₄⋊C₈	C₂×C₄	1	1	yes	characteristic
101	C₇×C₄⋊C₈	C₂³	1	1	yes	characteristic
102	C₇×C₄⋊C₈	C₂³	1	1	yes	characteristic
103	C₇×C₄⋊C₈	C₂³	1	1	yes	characteristic
104	C₇×C₄⋊C₈	C₂³	1	1	yes	characteristic
105	C₇×C₂²⋊C₈	—	2	1	no	—
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	—	2	1	no	—
110	C₄×C₇×C₈	—	2	1	no	—
111	C₄×C₇×C₈	C₂³	1	1	yes	characteristic
112	C₄×C₇×C₈	C₂³	1	1	yes	characteristic
113	C₂²⋊(C₇⋊C₈)	—	2	1	no	—
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	#6392	C₂×C₄	1	1	yes	characteristic
123	#6392	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	Dic₇⋊C₈	—	2	1	no	—
132	Dic₇⋊C₈	—	2	1	no	—
133	Dic₇⋊C₈	—	2	1	no	—
134	Dic₇⋊C₈	—	2	1	no	—
135	C₈×Dic₇	—	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	#3102	—	7	1	no	—
146	#2966	—	7	1	no	—
147	C₈×#41	—	7	1	no	—
148	#1588	—	7	1	no	—
149	#1587	—	7	1	no	—
150	#1586	—	7	1	no	—
151	#1585	—	7	1	no	—
152	#1580	—	7	1	no	—
153	#1579	—	7	1	no	—
154	SD₁₆⋊C₈	—	7	1	no	—
155	SD₁₆⋊C₈	—	7	1	no	—
156	#1572	D₇	1	1	yes	characteristic, complemented
157	#1488	—	7	1	no	—
158	#1482	—	7	1	no	—
159	#1452	—	7	1	no	—
160	C₂²×C₄×C₇	C₂²×C₄	1	1	yes	characteristic
161	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
162	C₂²×C₄×C₇	#41	1	1	yes	characteristic
163	C₂×C₂²⋊D₇	—	2	1	no	—
164	C₂×C₂²⋊D₇	—	2	1	no	—
165	#1157	—	2	2	no	—
166	#1157	—	2	2	no	—
167	C₂×D₂₈	C₂²×C₄	1	1	yes	characteristic
168	C₂×D₂₈	C₂²×C₄	1	1	yes	characteristic
169	C₂×C₄×D₇	—	2	1	no	—
170	C₂×C₄×D₇	—	2	1	no	—
171	C₂×C₄×D₇	—	2	1	no	—
172	C₂×C₄×D₇	—	2	1	no	—
173	C₂×Dic₁₄	C₂²×C₄	1	1	yes	characteristic
174	C₂×Dic₁₄	C₂²×C₄	1	1	yes	characteristic
175	C₂×C₇×C₈	—	2	1	no	—
176	C₂×C₇×C₈	—	2	1	no	—
177	C₂×C₇×C₈	—	2	1	no	—
178	C₂×C₇×C₈	—	2	1	no	—
179	C₂×C₇×C₈	C₂²×C₄	1	1	yes	characteristic
180	C₂×C₇×C₈	C₂²×C₄	1	1	yes	characteristic
181	C₂×C₇×C₈	C₂²×C₄	1	1	yes	characteristic
182	C₂×C₇×C₈	C₂²×C₄	1	1	yes	characteristic
183	C₄²×C₇	C₂²×C₄	1	1	yes	characteristic
184	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
185	C₄²×C₇	#41	1	1	yes	characteristic
186	C₄²×C₇	C₂⁴	1	1	yes	characteristic
187	C₂²⋊Dic₇	—	2	1	no	—
188	C₂²⋊Dic₇	—	2	1	no	—
189	(C₂×D₇)⋊C₄	—	2	1	no	—
190	(C₂×D₇)⋊C₄	—	2	1	no	—
191	(C₂×D₇)⋊C₄	—	2	1	no	—
192	(C₂×D₇)⋊C₄	—	2	1	no	—
193	(C₂×D₇)⋊C₄	—	2	1	no	—
194	(C₂×D₇)⋊C₄	—	2	1	no	—
195	C₄⋊Dic₇	C₂²×C₄	1	1	yes	characteristic
196	C₄⋊Dic₇	C₂²×C₄	1	1	yes	characteristic
197	C₄⋊Dic₇	C₂²×C₄	1	1	yes	characteristic
198	C₄⋊Dic₇	C₂²×C₄	1	1	yes	characteristic
199	Dic₇⋊C₄	—	2	1	no	—
200	Dic₇⋊C₄	—	2	1	no	—
201	Dic₇⋊C₄	—	2	1	no	—
202	Dic₇⋊C₄	—	2	1	no	—
203	Dic₇⋊C₄	—	2	1	no	—
204	Dic₇⋊C₄	—	2	1	no	—
205	C₄×Dic₇	—	2	1	no	—
206	C₄×Dic₇	—	2	1	no	—
207	C₄×Dic₇	—	2	1	no	—
208	C₄×Dic₇	—	2	1	no	—
209	C₂×C₇⋊C₈	—	2	1	no	—
210	C₂×C₇⋊C₈	—	2	1	no	—
211	C₂×C₇⋊C₈	—	4	1	no	—
212	C₂×C₇⋊C₈	—	4	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	Dic₂₈	—	2	2	no	—
218	D₅₆	—	2	2	no	—
219	#1132	—	2	2	no	—
220	#1132	—	2	2	no	—
221	#1131	—	4	2	no	—
222	C₈×D₇	—	4	2	no	—
223	C₈×D₇	—	4	2	no	—
224	C₈×D₇	—	4	2	no	—
225	#529	—	7	1	no	—
226	C₄×#41	—	7	1	no	—
227	#485	—	7	1	no	—
228	#482	—	7	1	no	—
229	#479	—	7	1	no	—
230	#478	—	7	1	no	—
231	#464	—	7	1	no	—
232	#463	—	7	1	no	—
233	#452	—	7	1	no	—
234	#449	—	7	1	no	—
235	#446	—	7	1	no	—
236	C₈×Q₈	—	7	1	no	—
237	C₈×Q₈	—	7	1	no	—
238	C₈×Q₈	—	7	1	no	—
239	C₄×Q₁₆	—	7	1	no	—
240	C₄×SD₁₆	—	7	1	no	—
241	C₄×SD₁₆	—	7	1	no	—
242	C₄×D₈	—	7	1	no	—
243	#436	—	7	1	no	—
244	#435	—	14	1	no	—
245	C₈×D₄	—	7	1	no	—
246	C₈×D₄	—	7	1	no	—
247	C₈×D₄	—	7	1	no	—
248	C₈×D₄	—	14	1	no	—
249	C₈×D₄	—	14	1	no	—
250	C₈×D₄	—	14	1	no	—
251	#433	—	14	1	no	—
252	#432	C₂×D₇	1	1	yes	characteristic
253	#431	—	7	1	no	—
254	#431	—	14	1	no	—
255	#431	C₂×D₇	1	1	yes	characteristic
256	#431	C₂×D₇	1	1	yes	characteristic
257	#405	—	14	1	no	—
258	C₂×C₄×C₈	—	7	1	no	—
259	C₂×C₄×C₈	—	14	1	no	—
260	#335	C₂×D₇	1	1	yes	characteristic
261	#335	C₂×D₇	1	1	yes	characteristic
262	#334	C₂×D₇	1	1	yes	characteristic
263	#334	C₂×D₇	1	1	yes	characteristic
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	#322	—	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	C₂×C₄×C₇	—	2	1	no	—
280	C₂×C₄×C₇	—	2	1	no	—
281	C₂×C₄×C₇	—	2	1	no	—
282	C₂×C₄×C₇	—	2	1	no	—
283	C₂×C₄×C₇	—	4	1	no	—
284	C₂×C₄×C₇	C₄×D₄	1	1	yes	characteristic
285	C₂×C₄×C₇	C₄×D₄	1	1	yes	characteristic
286	C₂×C₄×C₇	C₄×D₄	1	1	yes	characteristic
287	C₂×C₄×C₇	C₂³×C₄	1	1	yes	characteristic
288	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
289	C₂×C₄×C₇	C₂×#41	1	1	yes	characteristic
290	C₂²⋊D₇	—	2	4	no	—
291	C₂²⋊D₇	—	4	2	no	—
292	C₂×Dic₇	—	2	1	no	—
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	D₂₈	—	2	1	no	—
299	D₂₈	—	2	1	no	—
300	D₂₈	—	2	1	no	—
301	D₂₈	#131	1	2	yes	—
302	C₄×D₇	—	2	4	no	—
303	C₄×D₇	—	4	2	no	—
304	C₄×D₇	—	4	1	no	—
305	C₄×D₇	—	4	1	no	—
306	C₄×D₇	—	4	1	no	—
307	C₄×D₇	—	4	1	no	—
308	Dic₁₄	—	2	1	no	—
309	Dic₁₄	—	2	1	no	—
310	Dic₁₄	—	2	1	no	—
311	Dic₁₄	#131	1	2	yes	—
312	C₇×C₈	—	2	1	no	—
313	C₇×C₈	—	2	1	no	—
314	C₇×C₈	—	2	1	no	—
315	C₇×C₈	—	2	1	no	—
316	C₇×C₈	—	4	1	no	—
317	C₇×C₈	—	4	1	no	—
318	C₇×C₈	—	4	1	no	—
319	C₇×C₈	—	4	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	C₂×#41	—	7	1	no	—
327	C₂×Q₁₆	—	7	1	no	—
328	C₂×SD₁₆	—	7	1	no	—
329	C₂×SD₁₆	—	7	1	no	—
330	C₂×D₈	—	7	1	no	—
331	C₂×M₁₆	—	14	1	no	—
332	C₂²×C₈	—	7	1	no	—
333	C₂²×C₈	—	7	1	no	—
334	C₂²×C₈	—	14	1	no	—
335	C₂²×C₈	—	14	1	no	—
336	C₂²×C₈	—	14	1	no	—
337	#126	—	14	1	no	—
338	#125	—	7	1	no	—
339	#124	—	7	1	no	—
340	#123	—	14	1	no	—
341	C₂²⋊Q₈	—	7	1	no	—
342	#121	—	7	1	no	—
343	C₄×Q₈	—	7	1	no	—
344	C₄×Q₈	—	7	1	no	—
345	C₄×Q₈	—	7	1	no	—
346	C₄×D₄	—	7	1	no	—
347	C₄×D₄	—	7	1	no	—
348	C₄×D₄	—	7	1	no	—
349	C₄×D₄	—	14	1	no	—
350	C₄×D₄	—	14	1	no	—
351	C₄×D₄	—	14	1	no	—
352	#117	—	7	1	no	—
353	#117	—	14	1	no	—
354	#117	—	14	1	no	—
355	C₂×C₄²	—	14	1	no	—
356	C₂×C₄²	C₂²×D₇	1	1	yes	characteristic
357	#107	—	7	1	no	—
358	#107	—	7	1	no	—
359	#106	—	7	1	no	—
360	#106	—	7	1	no	—
361	C₄⋊C₈	—	14	1	no	—
362	C₄⋊C₈	—	14	1	no	—
363	C₄⋊C₈	—	14	1	no	—
364	C₄⋊C₈	—	14	1	no	—
365	C₄⋊C₈	—	14	1	no	—
366	C₄⋊C₈	C₄×D₇	1	1	yes	characteristic
367	C₄⋊C₈	C₄×D₇	1	1	yes	characteristic
368	C₄⋊C₈	C₂²×D₇	1	1	yes	characteristic
369	C₄⋊C₈	C₂²×D₇	1	1	yes	characteristic
370	C₄⋊C₈	C₂²×D₇	1	1	yes	characteristic
371	C₄⋊C₈	C₂²×D₇	1	1	yes	characteristic
372	#103	—	7	1	no	—
373	#103	—	7	1	no	—
374	#103	—	7	1	no	—
375	#103	—	7	1	no	—
376	#102	—	7	1	no	—
377	#102	—	7	1	no	—
378	#102	—	7	1	no	—
379	#102	—	7	1	no	—
380	C₂²⋊C₈	—	2	1	no	—
381	C₂²⋊C₈	—	2	1	no	—
382	C₂²⋊C₈	—	14	1	no	—
383	C₂²⋊C₈	—	14	1	no	—
384	C₂²⋊C₈	—	14	1	no	—
385	C₂²⋊C₈	—	14	1	no	—
386	C₂²⋊C₈	—	14	1	no	—
387	C₂²⋊C₈	C₄×D₇	1	1	yes	characteristic
388	C₂²⋊C₈	C₄×D₇	1	1	yes	characteristic
389	#97	—	2	1	no	—
390	#97	—	14	1	no	—
391	C₄×C₈	—	2	1	no	—
392	C₄×C₈	—	7	1	no	—
393	C₄×C₈	—	7	1	no	—
394	C₄×C₈	—	7	1	no	—
395	C₄×C₈	—	7	1	no	—
396	C₄×C₈	—	7	1	no	—
397	C₄×C₈	—	7	1	no	—
398	C₄×C₈	—	14	1	no	—
399	C₄×C₈	—	14	1	no	—
400	C₄×C₈	—	14	1	no	—
401	C₄×C₈	C₂²×D₇	1	1	yes	characteristic
402	C₄×C₈	C₂²×D₇	1	1	yes	characteristic
403	C₂²×C₇	—	2	1	no	—
404	C₂²×C₇	—	2	1	no	—
405	C₂²×C₇	—	2	1	no	—
406	C₂²×C₇	C₂×C₄×D₄	1	1	yes	characteristic
407	C₂×D₇	—	2	2	no	—
408	C₂×D₇	—	4	1	no	—
409	C₂×D₇	—	4	1	no	—
410	C₂×D₇	—	4	1	no	—
411	C₂×D₇	—	4	1	no	—
412	C₂×D₇	—	4	1	no	—
413	C₄×C₇	—	2	1	no	—
414	C₄×C₇	—	2	1	no	—
415	C₄×C₇	—	2	1	no	—
416	C₄×C₇	—	2	1	no	—
417	C₄×C₇	C₂×#131	1	1	yes	characteristic
418	C₄×C₇	C₂×#131	1	1	yes	characteristic
419	C₄×C₇	#575	1	1	yes	characteristic
420	C₄×C₇	#575	1	1	yes	characteristic
421	Dic₇	—	2	2	no	—
422	Dic₇	—	4	1	no	—
423	Dic₇	—	4	1	no	—
424	Dic₇	—	4	1	no	—
425	Dic₇	—	4	1	no	—
426	Dic₇	—	4	1	no	—
427	#41	—	14	2	no	—
428	#41	—	14	2	no	—
429	C₂×Q₈	—	7	1	no	—
430	C₂×Q₈	—	7	1	no	—
431	C₂×D₄	—	7	1	no	—
432	C₂×D₄	—	7	1	no	—
433	C₂×D₄	—	14	1	no	—
434	C₂×D₄	—	14	1	no	—
435	C₂²×C₄	—	14	1	no	—
436	C₂²×C₄	—	14	1	no	—
437	C₂²×C₄	—	14	1	no	—
438	C₂²×C₄	—	14	1	no	—
439	C₂²×C₄	C₂×C₄×D₇	1	1	yes	characteristic
440	C₂²×C₄	D₄×D₇	1	1	yes	characteristic
441	C₂²×C₄	#1161	1	1	yes	characteristic
442	Q₁₆	—	14	2	no	—
443	SD₁₆	—	14	2	no	—
444	SD₁₆	—	14	2	no	—
445	D₈	—	14	2	no	—
446	M₁₆	—	28	2	no	—
447	C₂×C₈	—	2	1	no	—
448	C₂×C₈	—	2	1	no	—
449	C₂×C₈	—	2	1	no	—
450	C₂×C₈	—	2	1	no	—
451	C₂×C₈	—	7	1	no	—
452	C₂×C₈	—	7	1	no	—
453	C₂×C₈	—	7	1	no	—
454	C₂×C₈	—	7	1	no	—
455	C₂×C₈	—	14	1	no	—
456	C₂×C₈	—	14	1	no	—
457	C₂×C₈	—	28	2	no	—
458	C₂×C₈	—	28	2	no	—
459	C₂×C₈	—	28	2	no	—
460	C₂×C₈	—	28	1	no	—
461	C₂×C₈	—	28	1	no	—
462	C₂×C₈	C₂×C₄×D₇	1	1	yes	characteristic
463	C₂×C₈	C₂×C₄×D₇	1	1	yes	characteristic
464	C₂×C₈	C₂×C₄×D₇	1	1	yes	characteristic
465	C₂×C₈	C₂×C₄×D₇	1	1	yes	characteristic
466	C₄⋊C₄	—	7	1	no	—
467	C₄⋊C₄	—	7	1	no	—
468	C₄⋊C₄	—	7	1	no	—
469	C₄⋊C₄	—	7	1	no	—
470	C₄⋊C₄	—	14	1	no	—
471	C₄⋊C₄	—	14	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	C₂²⋊C₄	—	14	1	no	—
477	C₂²⋊C₄	—	14	1	no	—
478	C₂²⋊C₄	—	14	1	no	—
479	C₂²⋊C₄	—	14	1	no	—
480	C₂²⋊C₄	—	14	1	no	—
481	C₂²⋊C₄	—	14	1	no	—
482	C₂²⋊C₄	—	14	1	no	—
483	C₂²⋊C₄	—	14	1	no	—
484	C₄²	—	14	1	no	—
485	C₄²	—	14	1	no	—
486	C₄²	—	14	1	no	—
487	C₄²	—	14	1	no	—
488	C₄²	C₂×C₄×D₇	1	1	yes	characteristic
489	C₄²	D₄×D₇	1	1	yes	characteristic
490	C₄²	#1161	1	1	yes	characteristic
491	C₄²	C₂³×D₇	1	1	yes	characteristic
492	C₂×C₇	—	4	1	no	—
493	C₂×C₇	#2929	1	1	yes	characteristic
494	C₂×C₇	#2943	1	1	yes	characteristic
495	C₂×C₇	#2955	1	1	yes	characteristic
496	D₇	—	4	2	no	—
497	D₇	—	8	1	no	—
498	C₂³	—	14	1	no	—
499	C₂³	—	14	1	no	—
500	C₂³	#6456	1	1	yes	characteristic
501	Q₈	—	7	2	no	—
502	Q₈	—	14	1	no	—
503	Q₈	—	14	1	no	—
504	Q₈	—	14	1	no	—
505	D₄	—	7	2	no	—
506	D₄	—	14	4	no	—
507	D₄	—	14	1	no	—
508	D₄	—	14	1	no	—
509	D₄	—	14	1	no	—
510	D₄	—	28	2	no	—
511	C₂×C₄	—	2	1	no	—
512	C₂×C₄	—	2	1	no	—
513	C₂×C₄	—	2	1	no	—
514	C₂×C₄	—	2	1	no	—
515	C₂×C₄	—	4	1	no	—
516	C₂×C₄	—	14	4	no	—
517	C₂×C₄	—	14	1	no	—
518	C₂×C₄	—	14	1	no	—
519	C₂×C₄	—	14	1	no	—
520	C₂×C₄	—	14	1	no	—
521	C₂×C₄	—	14	1	no	—
522	C₂×C₄	—	14	1	no	—
523	C₂×C₄	—	28	2	no	—
524	C₂×C₄	—	28	1	no	—
525	C₂×C₄	—	28	1	no	—
526	C₂×C₄	—	28	1	no	—
527	C₂×C₄	—	28	1	no	—
528	C₂×C₄	#6456	1	1	yes	characteristic
529	C₂×C₄	#6456	1	1	yes	characteristic
530	C₂×C₄	#6456	1	1	yes	characteristic
531	C₂×C₄	C₂²×C₄×D₇	1	1	yes	characteristic
532	C₂×C₄	C₂×D₄×D₇	1	1	yes	characteristic
533	C₂×C₄	C₂×#1161	1	1	yes	characteristic
534	C₈	—	2	1	no	—
535	C₈	—	2	1	no	—
536	C₈	—	2	1	no	—
537	C₈	—	2	1	no	—
538	C₈	—	4	1	no	—
539	C₈	—	4	1	no	—
540	C₈	—	4	1	no	—
541	C₈	—	4	1	no	—
542	C₈	—	14	1	no	—
543	C₈	—	14	1	no	—
544	C₈	—	14	1	no	—
545	C₈	—	14	1	no	—
546	C₈	—	28	1	no	—
547	C₈	—	28	1	no	—
548	C₇	#17909	1	1	yes	characteristic, complemented, Sylow
549	C₂²	—	2	1	no	—
550	C₂²	—	2	1	no	—
551	C₂²	—	2	1	no	—
552	C₂²	—	14	2	no	—
553	C₂²	—	28	1	no	—
554	C₂²	—	28	1	no	—
555	C₂²	—	28	1	no	—
556	C₂²	—	28	1	no	—
557	C₂²	—	28	1	no	—
558	C₂²	C₂×#6456	1	1	yes	characteristic
559	C₄	—	2	1	no	—
560	C₄	—	2	1	no	—
561	C₄	—	2	1	no	—
562	C₄	—	2	1	no	—
563	C₄	—	14	2	no	—
564	C₄	—	28	1	no	—
565	C₄	—	28	1	no	—
566	C₄	—	28	1	no	—
567	C₄	—	28	1	no	—
568	C₄	—	28	1	no	—
569	C₄	D₇×#131	1	1	yes	characteristic
570	C₄	D₇×#131	1	1	yes	characteristic
571	C₄	#90459	1	1	yes	characteristic
572	C₄	#90459	1	1	yes	characteristic
573	C₂	—	4	1	no	—
574	C₂	—	28	2	no	—
575	C₂	—	56	1	no	—
576	C₂	#11736518	1	1	yes	characteristic
577	C₂	#11736611	1	1	yes	characteristic
578	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	#89506	C₄
cosocle	C₄²×C₇	C₂⁴
hypercenter	#1572	D₇
hypocenter	C₇	#17909
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
1. #11736770	C₂	semidirect
3. #11736721	C₂	semidirect
4. C₇×#1572	C₂	semidirect
5. #11728552	C₂	semidirect
6. #11728513	C₂	semidirect
7. #11728496	C₂	semidirect
8. #11726316	C₂	semidirect
9. #11726315	C₂	semidirect
10. #11726312	C₂	semidirect
11. #11726312	C₂	semidirect
12. #11726276	C₂	semidirect
13. #11726275	C₂	semidirect
14. #11726272	C₂	semidirect
15. #11726271	C₂	semidirect
156. #1572	D₇	semidirect
548. C₇	#17909	semidirect

Maximal subgroups

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

subgroup	index
#11736770	2
#11736744	2
#11736721	2
C₇×#1572	2
#11728552	2
#11728513	2
#11728496	2
#11726316	2
#11726315	2
#11726312	2
#11726276	2
#11726275	2
#11726272	2
#11726271	2
#17909	7