Subgroups — #13323433

Order 1792.

648 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	#11737365	C₂	1	1	yes	maximal, characteristic, complemented
2	C₄×#6478	C₂	1	1	yes	maximal, characteristic
3	#11736968	C₂	1	1	yes	maximal, characteristic
4	C₇×#1588	C₂	1	1	yes	maximal, characteristic, complemented
5	#11728688	C₂	1	1	yes	maximal, characteristic, complemented
6	#11728650	C₂	1	1	yes	maximal, characteristic, complemented
7	#11728618	C₂	1	1	yes	maximal, characteristic, complemented
8	#11726322	C₂	1	1	yes	maximal, characteristic, complemented
9	#11726314	C₂	1	1	yes	maximal, characteristic, complemented
10	D₇×Q₈⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
11	#11725975	C₂	1	1	yes	maximal, characteristic, complemented
12	#11725919	C₂	1	1	yes	maximal, characteristic
13	#11725913	C₂	1	1	yes	maximal, characteristic, complemented
14	#11725841	C₂	1	1	yes	maximal, characteristic, complemented
15	#11725823	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×#6478	C₄	1	1	yes	characteristic
17	C₄×Q₈×D₇	C₂²	1	1	yes	characteristic
18	C₄×#1159	C₂²	1	1	yes	characteristic
19	C₇×C₈×Q₈	C₂²	1	1	yes	characteristic
20	C₄×C₇×SD₁₆	C₂²	1	1	yes	characteristic
21	C₇×#436	C₂²	1	1	yes	characteristic
22	#89936	C₄	1	1	yes	characteristic
23	#89899	—	2	1	no	—
24	#89890	—	2	1	no	—
25	C₄×#1144	C₂²	1	1	yes	characteristic
26	Q₈×C₇⋊C₈	C₂²	1	1	yes	characteristic
27	C₄×#1142	C₂²	1	1	yes	characteristic
28	#89784	C₂²	1	1	yes	characteristic
29	#89633	C₄	1	1	yes	characteristic
30	#89625	C₄	1	1	yes	characteristic
31	#89605	—	2	1	no	—
32	#89605	C₂²	1	1	yes	characteristic
33	D₇×C₄⋊C₈	C₂²	1	1	yes	characteristic
34	#89603	C₂²	1	1	yes	characteristic
35	#89602	—	2	1	no	—
36	#89602	C₂²	1	1	yes	characteristic
37	#89574	C₄	1	1	yes	characteristic
38	#89561	C₄	1	1	yes	characteristic
39	#89543	C₄	1	1	yes	characteristic
40	#89529	C₄	1	1	yes	characteristic
41	#89500	—	2	1	no	—
42	#89491	—	2	1	no	—
43	C₄×Dic₂₈	C₂²	1	1	yes	characteristic
44	C₄×#1131	C₂²	1	1	yes	characteristic
45	#89457	—	2	1	no	—
46	#89457	C₂²	1	1	yes	characteristic
47	C₄×C₈×D₇	C₂²	1	1	yes	characteristic
48	#89451	C₂²	1	1	yes	characteristic
49	C₈×Dic₁₄	—	2	1	no	—
50	C₈×Dic₁₄	C₂²	1	1	yes	characteristic
51	C₇×#335	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	#89279	C₂²	1	1	yes	characteristic
59	#89275	C₂²	1	1	yes	characteristic
60	#89274	C₂²	1	1	yes	characteristic
61	#89252	C₂²	1	1	yes	characteristic
62	#89251	C₂²	1	1	yes	characteristic
63	#89251	C₂²	1	1	yes	characteristic
64	#89250	C₂²	1	1	yes	characteristic
65	#89250	C₂²	1	1	yes	characteristic
66	#89249	C₂²	1	1	yes	characteristic
67	#17874	—	7	1	no	maximal, Sylow
68	C₂×Q₈×D₇	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	C₂×C₇×M₁₆	—	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×#1142	C₂×C₄	1	1	yes	characteristic
78	C₄×C₂²⋊D₇	—	2	1	no	—
79	C₂×C₄×Dic₇	—	2	1	no	—
80	C₂×#1136	—	2	1	no	—
81	#6478	—	2	4	no	—
82	C₂×Dic₂₈	C₂×C₄	1	1	yes	characteristic
83	C₂×#1131	C₂×C₄	1	1	yes	characteristic
84	C₂×#1131	C₂×C₄	1	1	yes	characteristic
85	C₂×C₈×D₇	—	2	1	no	—
86	C₂×C₈×D₇	—	2	1	no	—
87	#6455	C₂×C₄	1	1	yes	characteristic
88	D₇×C₄⋊C₄	—	2	1	no	—
89	D₇×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
90	#6450	—	2	1	no	—
91	#6450	C₂×C₄	1	1	yes	characteristic
92	#6450	C₂×C₄	1	1	yes	characteristic
93	(C₂²⋊D₇)⋊C₄	—	2	1	no	—
94	#6440	—	2	1	no	—
95	C₄²×D₇	—	2	1	no	—
96	C₄²×D₇	C₂³	1	1	yes	characteristic
97	C₄×Dic₁₄	—	2	1	no	—
98	C₄×Dic₁₄	C₂³	1	1	yes	characteristic
99	C₄×Dic₁₄	C₂³	1	1	yes	characteristic
100	C₇×#106	C₂×C₄	1	1	yes	characteristic
101	C₇×C₄⋊C₈	—	2	1	no	—
102	C₇×C₄⋊C₈	C₂³	1	1	yes	characteristic
103	C₇×C₄⋊C₈	C₂³	1	1	yes	characteristic
104	C₇×#103	C₂×C₄	1	1	yes	characteristic
105	C₇×#102	C₂×C₄	1	1	yes	characteristic
106	C₇×C₂²⋊C₈	—	2	1	no	—
107	C₄×C₇×C₈	—	2	1	no	—
108	C₄×C₇×C₈	C₂³	1	1	yes	characteristic
109	C₄×C₇×C₈	C₂³	1	1	yes	characteristic
110	C₄×C₇×C₈	C₂³	1	1	yes	characteristic
111	#6409	C₂×C₄	1	1	yes	characteristic
112	#6406	C₂×C₄	1	1	yes	characteristic
113	C₂²⋊(C₇⋊C₈)	—	2	1	no	—
114	(C₂×D₇)⋊C₈	—	2	1	no	—
115	(C₂×D₇)⋊C₈	D₄	1	1	yes	characteristic
116	(C₂×D₇)⋊C₈	D₄	1	1	yes	characteristic
117	#6392	C₂×C₄	1	1	yes	characteristic
118	#6390	C₂×C₄	1	1	yes	characteristic
119	#6390	C₂×C₄	1	1	yes	characteristic
120	#6389	—	2	1	no	—
121	#6389	—	2	1	no	—
122	#6389	C₂×C₄	1	1	yes	characteristic
123	#6389	C₂×C₄	1	1	yes	characteristic
124	Dic₇⋊C₈	—	2	1	no	—
125	Dic₇⋊C₈	—	2	1	no	—
126	Dic₇⋊C₈	—	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	—	2	1	no	—
132	C₈×Dic₇	—	2	1	no	—
133	C₈×Dic₇	—	2	1	no	—
134	C₈×Dic₇	—	2	1	no	—
135	#6384	C₂×C₄	1	1	yes	characteristic
136	#6384	C₂×C₄	1	1	yes	characteristic
137	#6382	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	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	#2989	—	7	1	no	—
147	#2982	—	7	1	no	—
148	C₄×#137	—	7	1	no	—
149	#1588	—	7	1	no	—
150	#1588	D₇	1	1	yes	characteristic, complemented
151	#1587	—	7	1	no	—
152	#1587	—	7	1	no	—
153	#1584	—	7	1	no	—
154	#1584	—	7	1	no	—
155	#1583	—	7	1	no	—
156	#1583	—	7	1	no	—
157	#1565	—	7	1	no	—
158	#1476	—	7	1	no	—
159	C₂×Q₈⋊C₈	—	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	Q₈×D₇	—	2	2	no	—
168	Q₈×D₇	M₁₆	1	4	yes	complemented
169	#1159	—	2	2	no	—
170	#1159	—	2	2	no	—
171	C₂×C₄×D₇	—	2	1	no	—
172	C₂×C₄×D₇	—	2	1	no	—
173	C₂×C₄×D₇	C₂²×C₄	1	1	yes	characteristic
174	C₂×C₄×D₇	C₂×D₄	1	1	yes	characteristic
175	C₂×C₄×D₇	#41	1	1	yes	characteristic
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	C₇×SD₁₆	—	2	2	no	—
180	C₇×M₁₆	—	8	1	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	C₂²×C₄	1	1	yes	characteristic
190	C₇×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
191	C₇×C₂²⋊C₄	—	2	1	no	—
192	C₄²×C₇	—	2	1	no	—
193	C₄²×C₇	C₂⁴	1	1	yes	characteristic
194	C₂²⋊Dic₇	—	2	1	no	—
195	#1144	—	2	2	no	—
196	#1142	—	2	2	no	—
197	(C₂×D₇)⋊C₄	—	2	1	no	—
198	C₄⋊Dic₇	—	2	1	no	—
199	C₄⋊Dic₇	C₂²×C₄	1	1	yes	characteristic
200	C₄⋊Dic₇	C₂²×C₄	1	1	yes	characteristic
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	Dic₇⋊C₄	—	2	1	no	—
206	C₄×Dic₇	—	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	#1136	—	8	1	no	—
216	C₂×C₇⋊C₈	—	2	1	no	—
217	C₂×C₇⋊C₈	—	2	1	no	—
218	C₂×C₇⋊C₈	—	2	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	Dic₂₈	—	2	2	no	—
224	#1131	—	2	2	no	—
225	#1131	—	2	2	no	—
226	C₈×D₇	—	4	2	no	—
227	C₈×D₇	—	8	1	no	—
228	C₂×#137	—	7	1	no	—
229	C₄×#41	—	7	1	no	—
230	C₂×C₄×Q₈	—	7	1	no	—
231	#446	—	7	1	no	—
232	#446	—	7	1	no	—
233	C₈×Q₈	—	7	1	no	—
234	C₈×Q₈	—	7	1	no	—
235	C₈×Q₈	—	7	1	no	—
236	C₈×Q₈	—	14	1	no	—
237	C₈×Q₈	—	14	1	no	—
238	C₈×Q₈	C₂×D₇	1	1	yes	characteristic
239	#441	—	7	1	no	—
240	#441	—	7	1	no	—
241	#440	—	7	1	no	—
242	#440	—	7	1	no	—
243	C₄×Q₁₆	—	7	1	no	—
244	C₄×Q₁₆	—	7	1	no	—
245	C₄×SD₁₆	—	7	1	no	—
246	C₄×SD₁₆	C₂×D₇	1	1	yes	characteristic
247	#436	—	7	1	no	—
248	#436	C₂×D₇	1	1	yes	characteristic
249	#435	—	14	1	no	—
250	#435	—	14	1	no	—
251	#432	—	14	1	no	—
252	#431	—	7	1	no	—
253	#431	—	7	1	no	—
254	#431	—	14	1	no	—
255	#431	—	14	1	no	—
256	#428	—	7	1	no	—
257	#423	—	14	1	no	—
258	C₂×C₄⋊C₈	—	7	1	no	—
259	#419	—	7	1	no	—
260	#417	—	7	1	no	—
261	C₄×M₁₆	—	7	1	no	—
262	C₂×C₄×C₈	—	7	1	no	—
263	#335	—	7	1	no	—
264	#335	C₂×D₇	1	1	yes	characteristic
265	#334	—	7	1	no	—
266	#334	—	7	1	no	—
267	Q₈⋊C₈	—	7	1	no	—
268	Q₈⋊C₈	—	7	1	no	—
269	Q₈⋊C₈	—	7	1	no	—
270	Q₈⋊C₈	—	7	1	no	—
271	Q₈⋊C₈	—	7	1	no	—
272	Q₈⋊C₈	C₂×D₇	1	1	yes	characteristic
273	D₄⋊C₈	—	7	1	no	—
274	D₄⋊C₈	C₂×D₇	1	1	yes	characteristic
275	#322	—	7	1	no	—
276	#322	—	7	1	no	—
277	#322	—	7	1	no	—
278	#322	C₂×D₇	1	1	yes	characteristic
279	C₂³×C₇	—	2	1	no	—
280	C₂²×D₇	C₄×D₄	1	1	yes	characteristic
281	C₇×Q₈	—	2	1	no	—
282	C₇×Q₈	C₂×M₁₆	1	2	yes	—
283	C₇×D₄	—	2	1	no	—
284	C₇×D₄	—	2	1	no	—
285	C₂×C₄×C₇	—	2	1	no	—
286	C₂×C₄×C₇	—	2	1	no	—
287	C₂×C₄×C₇	—	2	1	no	—
288	C₂×C₄×C₇	—	4	1	no	—
289	C₂×C₄×C₇	—	4	1	no	—
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	C₂²⋊D₇	—	4	2	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	—	4	2	no	—
299	C₂×Dic₇	—	8	1	no	—
300	C₂×Dic₇	C₄×D₄	1	1	yes	characteristic
301	C₂×Dic₇	C₄×D₄	1	1	yes	characteristic
302	C₂×Dic₇	C₄×D₄	1	1	yes	characteristic
303	C₄×D₇	—	2	4	no	—
304	C₄×D₇	—	2	1	no	—
305	C₄×D₇	—	2	1	no	—
306	C₄×D₇	—	4	1	no	—
307	C₄×D₇	—	8	1	no	—
308	C₄×D₇	C₂×M₁₆	1	2	yes	—
309	C₄×D₇	#131	1	2	yes	—
310	Dic₁₄	—	2	1	no	—
311	Dic₁₄	—	2	4	no	—
312	Dic₁₄	—	2	1	no	—
313	Dic₁₄	—	2	1	no	—
314	Dic₁₄	C₂×M₁₆	1	2	yes	—
315	C₇×C₈	—	2	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	—	2	1	no	—
323	C₇⋊C₈	—	2	1	no	—
324	C₇⋊C₈	—	2	1	no	—
325	C₇⋊C₈	—	2	1	no	—
326	C₇⋊C₈	—	4	1	no	—
327	C₇⋊C₈	—	4	1	no	—
328	C₇⋊C₈	—	4	1	no	—
329	C₂×#41	—	7	1	no	—
330	C₂²×Q₈	—	7	1	no	—
331	#137	—	14	4	no	—
332	C₂×Q₁₆	—	7	1	no	—
333	C₂×Q₁₆	—	7	1	no	—
334	C₂×SD₁₆	—	7	1	no	—
335	C₂×SD₁₆	C₄×D₇	1	1	yes	characteristic
336	C₂×M₁₆	—	2	1	no	—
337	C₂×M₁₆	—	7	1	no	—
338	C₂×M₁₆	—	7	1	no	—
339	C₂×M₁₆	—	14	1	no	—
340	C₂²×C₈	—	14	1	no	—
341	C₂²×C₈	—	14	1	no	—
342	C₄×Q₈	—	7	1	no	—
343	C₄×Q₈	—	7	1	no	—
344	C₄×Q₈	—	7	1	no	—
345	C₄×Q₈	—	7	1	no	—
346	C₄×Q₈	—	7	1	no	—
347	C₄×Q₈	—	14	1	no	—
348	C₄×Q₈	—	14	1	no	—
349	C₄×Q₈	C₂²×D₇	1	1	yes	characteristic
350	C₄×D₄	—	7	1	no	—
351	C₄×D₄	—	14	1	no	—
352	C₄×D₄	—	14	1	no	—
353	C₄×D₄	C₂²×D₇	1	1	yes	characteristic
354	#117	—	7	1	no	—
355	#117	—	14	1	no	—
356	C₂×C₄⋊C₄	—	7	1	no	—
357	C₂×C₄⋊C₄	—	14	1	no	—
358	C₂×C₄²	—	7	1	no	—
359	C₂×C₄²	—	14	1	no	—
360	C₂×C₄²	—	14	1	no	—
361	#107	—	7	1	no	—
362	#107	—	7	1	no	—
363	#106	—	7	1	no	—
364	#106	C₄×D₇	1	1	yes	characteristic
365	C₄⋊C₈	—	2	1	no	—
366	C₄⋊C₈	—	7	1	no	—
367	C₄⋊C₈	—	7	1	no	—
368	C₄⋊C₈	—	7	1	no	—
369	C₄⋊C₈	—	7	1	no	—
370	C₄⋊C₈	—	14	1	no	—
371	C₄⋊C₈	—	14	1	no	—
372	C₄⋊C₈	—	14	1	no	—
373	C₄⋊C₈	—	14	1	no	—
374	C₄⋊C₈	—	14	1	no	—
375	C₄⋊C₈	—	14	1	no	—
376	C₄⋊C₈	C₂²×D₇	1	1	yes	characteristic
377	C₄⋊C₈	C₂²×D₇	1	1	yes	characteristic
378	#103	—	7	1	no	—
379	#103	—	7	1	no	—
380	#103	—	7	1	no	—
381	#103	—	7	1	no	—
382	#103	—	7	1	no	—
383	#103	C₄×D₇	1	1	yes	characteristic
384	#102	—	7	1	no	—
385	#102	C₄×D₇	1	1	yes	characteristic
386	C₂²⋊C₈	—	2	1	no	—
387	C₂²⋊C₈	—	7	1	no	—
388	C₂²⋊C₈	—	7	1	no	—
389	C₂²⋊C₈	—	14	1	no	—
390	C₂²⋊C₈	—	14	1	no	—
391	#97	—	7	1	no	—
392	#97	—	7	1	no	—
393	#97	—	14	1	no	—
394	#97	—	14	1	no	—
395	C₄×C₈	—	2	1	no	—
396	C₄×C₈	—	7	1	no	—
397	C₄×C₈	—	7	1	no	—
398	C₄×C₈	—	7	1	no	—
399	C₄×C₈	—	14	1	no	—
400	C₄×C₈	—	14	1	no	—
401	C₄×C₈	—	14	1	no	—
402	C₄×C₈	—	14	1	no	—
403	C₄×C₈	—	14	1	no	—
404	C₄×C₈	C₂²×D₇	1	1	yes	characteristic
405	C₄×C₈	C₂²×D₇	1	1	yes	characteristic
406	C₄×C₈	C₂²×D₇	1	1	yes	characteristic
407	C₂²×C₇	—	4	1	no	—
408	C₂²×C₇	—	4	1	no	—
409	C₂²×C₇	—	4	1	no	—
410	C₂²×C₇	C₂×C₄×D₄	1	1	yes	characteristic
411	C₂×D₇	—	2	1	no	—
412	C₂×D₇	—	2	1	no	—
413	C₂×D₇	#435	1	2	yes	—
414	C₄×C₇	—	2	2	no	—
415	C₄×C₇	—	2	1	no	—
416	C₄×C₇	—	4	1	no	—
417	C₄×C₇	—	4	1	no	—
418	C₄×C₇	C₂²×M₁₆	1	1	yes	characteristic
419	C₄×C₇	C₂×#131	1	1	yes	characteristic
420	C₄×C₇	#577	1	1	yes	characteristic
421	C₄×C₇	#578	1	1	yes	characteristic
422	Dic₇	—	2	2	no	—
423	Dic₇	—	2	1	no	—
424	Dic₇	—	2	1	no	—
425	Dic₇	—	4	1	no	—
426	Dic₇	—	4	1	no	—
427	Dic₇	—	4	1	no	—
428	Dic₇	#435	1	2	yes	—
429	#41	—	14	2	no	—
430	#41	—	14	2	no	—
431	C₂×Q₈	—	7	4	no	—
432	C₂×Q₈	—	7	1	no	—
433	C₂×Q₈	—	7	1	no	—
434	C₂×Q₈	—	14	1	no	—
435	C₂×Q₈	—	14	2	no	—
436	C₂×Q₈	C₂×C₄×D₇	1	1	yes	characteristic
437	C₂×D₄	—	14	1	no	—
438	C₂×D₄	C₂×C₄×D₇	1	1	yes	characteristic
439	C₂²×C₄	—	2	1	no	—
440	C₂²×C₄	—	7	1	no	—
441	C₂²×C₄	—	7	1	no	—
442	C₂²×C₄	—	7	1	no	—
443	C₂²×C₄	—	14	1	no	—
444	C₂²×C₄	—	14	1	no	—
445	C₂²×C₄	—	14	1	no	—
446	C₂²×C₄	—	14	1	no	—
447	Q₁₆	—	14	2	no	—
448	Q₁₆	—	14	2	no	—
449	SD₁₆	—	2	2	no	—
450	SD₁₆	—	14	2	no	—
451	M₁₆	—	8	1	no	—
452	M₁₆	—	14	2	no	—
453	M₁₆	—	14	2	no	—
454	M₁₆	—	56	1	no	—
455	C₂×C₈	—	2	1	no	—
456	C₂×C₈	—	2	1	no	—
457	C₂×C₈	—	2	1	no	—
458	C₂×C₈	—	7	1	no	—
459	C₂×C₈	—	7	1	no	—
460	C₂×C₈	—	7	1	no	—
461	C₂×C₈	—	7	1	no	—
462	C₂×C₈	—	14	1	no	—
463	C₂×C₈	—	14	1	no	—
464	C₂×C₈	—	14	1	no	—
465	C₂×C₈	—	28	2	no	—
466	C₂×C₈	—	56	1	no	—
467	C₂×C₈	C₂×C₄×D₇	1	1	yes	characteristic
468	C₂×C₈	C₂×C₄×D₇	1	1	yes	characteristic
469	C₂×C₈	D₄×D₇	1	1	yes	characteristic
470	C₂×C₈	D₄×D₇	1	1	yes	characteristic
471	C₄⋊C₄	—	2	1	no	—
472	C₄⋊C₄	—	7	1	no	—
473	C₄⋊C₄	—	7	1	no	—
474	C₄⋊C₄	—	14	1	no	—
475	C₄⋊C₄	—	14	1	no	—
476	C₄⋊C₄	—	14	1	no	—
477	C₄⋊C₄	—	14	1	no	—
478	C₄⋊C₄	—	14	1	no	—
479	C₄⋊C₄	—	14	1	no	—
480	C₄⋊C₄	C₂×C₄×D₇	1	1	yes	characteristic
481	C₄⋊C₄	C₂×C₄×D₇	1	1	yes	characteristic
482	C₂²⋊C₄	—	2	1	no	—
483	C₂²⋊C₄	—	14	1	no	—
484	C₂²⋊C₄	—	14	1	no	—
485	C₄²	—	2	1	no	—
486	C₄²	—	7	1	no	—
487	C₄²	—	7	1	no	—
488	C₄²	—	7	1	no	—
489	C₄²	—	14	1	no	—
490	C₄²	—	14	1	no	—
491	C₄²	—	14	1	no	—
492	C₄²	—	14	1	no	—
493	C₄²	—	14	1	no	—
494	C₄²	—	14	1	no	—
495	C₄²	C₂³×D₇	1	1	yes	characteristic
496	C₂×C₇	—	8	1	no	—
497	C₂×C₇	C₂×#435	1	1	yes	characteristic
498	C₂×C₇	#2947	1	1	yes	characteristic
499	C₂×C₇	#2956	1	1	yes	characteristic
500	D₇	—	2	2	no	—
501	C₂³	—	2	1	no	—
502	C₂³	—	7	1	no	—
503	Q₈	—	2	1	no	—
504	Q₈	—	7	2	no	—
505	Q₈	—	14	4	no	—
506	Q₈	—	14	1	no	—
507	Q₈	—	14	1	no	—
508	Q₈	—	14	1	no	—
509	Q₈	D₇×M₁₆	1	2	yes	—
510	D₄	—	2	1	no	—
511	D₄	—	2	1	no	—
512	D₄	—	28	2	no	—
513	C₂×C₄	—	2	1	no	—
514	C₂×C₄	—	2	1	no	—
515	C₂×C₄	—	2	1	no	—
516	C₂×C₄	—	4	1	no	—
517	C₂×C₄	—	4	1	no	—
518	C₂×C₄	—	7	1	no	—
519	C₂×C₄	—	7	2	no	—
520	C₂×C₄	—	7	2	no	—
521	C₂×C₄	—	7	1	no	—
522	C₂×C₄	—	7	1	no	—
523	C₂×C₄	—	14	4	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	2	no	—
532	C₂×C₄	—	56	1	no	—
533	C₂×C₄	—	56	1	no	—
534	C₂×C₄	C₂²×C₄×D₇	1	1	yes	characteristic
535	C₂×C₄	C₂×D₄×D₇	1	1	yes	characteristic
536	C₂×C₄	D₇×#41	1	1	yes	characteristic
537	C₈	—	2	2	no	—
538	C₈	—	2	1	no	—
539	C₈	—	2	1	no	—
540	C₈	—	2	1	no	—
541	C₈	—	2	1	no	—
542	C₈	—	4	1	no	—
543	C₈	—	4	1	no	—
544	C₈	—	14	1	no	—
545	C₈	—	14	1	no	—
546	C₈	—	14	1	no	—
547	C₈	—	14	1	no	—
548	C₈	—	28	1	no	—
549	C₈	—	28	1	no	—
550	C₈	—	28	1	no	—
551	C₇	#17874	1	1	yes	characteristic, complemented, Sylow
552	C₂²	—	4	1	no	—
553	C₂²	—	4	1	no	—
554	C₂²	—	4	1	no	—
555	C₂²	—	7	2	no	—
556	C₂²	—	14	1	no	—
557	C₂²	—	14	1	no	—
558	C₂²	C₄×D₄×D₇	1	1	yes	characteristic
559	C₄	—	2	2	no	—
560	C₄	—	2	1	no	—
561	C₄	—	4	1	no	—
562	C₄	—	4	1	no	—
563	C₄	—	7	2	no	—
564	C₄	—	14	2	no	—
565	C₄	—	14	1	no	—
566	C₄	—	14	1	no	—
567	C₄	—	28	1	no	—
568	C₄	—	28	1	no	—
569	C₄	—	28	1	no	—
570	C₄	C₂×D₇×M₁₆	1	1	yes	characteristic
571	C₄	D₇×#131	1	1	yes	characteristic
572	C₄	#90466	1	1	yes	characteristic
573	C₄	#90470	1	1	yes	characteristic
574	C₂	—	8	1	no	—
575	C₂	—	14	2	no	—
576	C₂	D₇×#435	1	1	yes	characteristic
577	C₂	#11737221	1	1	yes	characteristic
578	C₂	#11737334	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×#1588	C₂
socle	C₂²×C₇	C₂×C₄×D₄
prime radical	C₂×#1159	C₂×C₄
cosocle	C₄²×C₇	C₂⁴
hypercenter	#1588	D₇
hypocenter	C₇	#17874
LCS	G ▷ C₂×C₄×C₇ ▷ C₂×C₇ ▷ C₇
UCS	C₁ ◁ C₂×C₄ ◁ C₄×C₈ ◁ #1588

Complements

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

N	H ≅ G/N	type
1. #11737365	C₂	semidirect
4. C₇×#1588	C₂	semidirect
5. #11728688	C₂	semidirect
6. #11728650	C₂	semidirect
7. #11728618	C₂	semidirect
8. #11726322	C₂	semidirect
9. #11726314	C₂	semidirect
10. D₇×Q₈⋊C₈	C₂	semidirect
11. #11725975	C₂	semidirect
13. #11725913	C₂	semidirect
14. #11725841	C₂	semidirect
15. #11725823	C₂	semidirect
150. #1588	D₇	semidirect
168. Q₈×D₇	M₁₆	semidirect
551. C₇	#17874	semidirect

Maximal subgroups

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

subgroup	index
#11737365	2
C₄×#6478	2
#11736968	2
C₇×#1588	2
#11728688	2
#11728650	2
#11728618	2
#11726322	2
#11726314	2
D₇×Q₈⋊C₈	2
#11725975	2
#11725919	2
#11725913	2
#11725841	2
#11725823	2
#17874	7