Subgroups — #13323755

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	C₇×#3102	C₂	1	1	yes	maximal, characteristic
2	#11740571	C₂	1	1	yes	maximal, characteristic, complemented
3	#41×C₇⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
4	#11729504	C₂	1	1	yes	maximal, characteristic, complemented
5	#11729394	C₂	1	1	yes	maximal, characteristic, complemented
6	#11728658	C₂	1	1	yes	maximal, characteristic, complemented
7	#11728656	C₂	1	1	yes	maximal, characteristic, complemented
8	#11728652	C₂	1	1	yes	maximal, characteristic, complemented
9	#11728651	C₂	1	1	yes	maximal, characteristic, complemented
10	SD₁₆⋊(C₇⋊C₈)	C₂	1	1	yes	maximal, characteristic, complemented
11	SD₁₆⋊(C₇⋊C₈)	C₂	1	1	yes	maximal, characteristic, complemented
12	#11728634	C₂	1	1	yes	maximal, characteristic, complemented
13	#11728632	C₂	1	1	yes	maximal, characteristic, complemented
14	#11728505	C₂	1	1	yes	maximal, characteristic, complemented
15	#11728496	C₂	1	1	yes	maximal, characteristic, complemented
16	C₇×#529	C₂²	1	1	yes	characteristic
17	C₄×C₇×#41	C₂²	1	1	yes	characteristic
18	C₇×#485	C₄	1	1	yes	characteristic
19	C₇×#482	C₄	1	1	yes	characteristic
20	C₇×#479	C₄	1	1	yes	characteristic
21	C₇×#478	C₄	1	1	yes	characteristic
22	C₇×#464	C₄	1	1	yes	characteristic
23	C₇×#463	C₄	1	1	yes	characteristic
24	C₇×#452	C₄	1	1	yes	characteristic
25	C₇×#449	C₄	1	1	yes	characteristic
26	C₄×C₇×Q₁₆	C₂²	1	1	yes	characteristic
27	C₄×C₇×SD₁₆	C₂²	1	1	yes	characteristic
28	C₄×C₇×SD₁₆	C₂²	1	1	yes	characteristic
29	C₄×C₇×D₈	C₂²	1	1	yes	characteristic
30	C₇×#431	C₂²	1	1	yes	characteristic
31	#89796	C₂²	1	1	yes	characteristic
32	Q₈×C₇⋊C₈	C₂²	1	1	yes	characteristic
33	Q₈×C₇⋊C₈	C₂²	1	1	yes	characteristic
34	Q₈×C₇⋊C₈	C₂²	1	1	yes	characteristic
35	#89784	C₂²	1	1	yes	characteristic
36	#89783	—	2	1	no	—
37	D₄×C₇⋊C₈	—	2	1	no	—
38	D₄×C₇⋊C₈	—	2	1	no	—
39	D₄×C₇⋊C₈	—	2	1	no	—
40	D₄×C₇⋊C₈	C₂²	1	1	yes	characteristic
41	D₄×C₇⋊C₈	C₂²	1	1	yes	characteristic
42	D₄×C₇⋊C₈	C₂²	1	1	yes	characteristic
43	#89772	—	2	1	no	—
44	#89769	—	2	1	no	—
45	#89698	C₂²	1	1	yes	characteristic
46	#89697	—	2	1	no	—
47	#89697	C₂²	1	1	yes	characteristic
48	#89697	C₂²	1	1	yes	characteristic
49	C₂×C₄×C₇⋊C₈	—	2	1	no	—
50	C₂×C₄×C₇⋊C₈	C₂²	1	1	yes	characteristic
51	Q₈⋊(C₇⋊C₈)	C₂²	1	1	yes	characteristic
52	Q₈⋊(C₇⋊C₈)	C₂²	1	1	yes	characteristic
53	Q₈⋊(C₇⋊C₈)	C₂²	1	1	yes	characteristic
54	Q₈⋊(C₇⋊C₈)	C₂²	1	1	yes	characteristic
55	D₄⋊(C₇⋊C₈)	C₂²	1	1	yes	characteristic
56	D₄⋊(C₇⋊C₈)	C₂²	1	1	yes	characteristic
57	D₄⋊(C₇⋊C₈)	C₂²	1	1	yes	characteristic
58	D₄⋊(C₇⋊C₈)	C₂²	1	1	yes	characteristic
59	#89253	C₂²	1	1	yes	characteristic
60	#89253	C₂²	1	1	yes	characteristic
61	#89252	C₂²	1	1	yes	characteristic
62	#89252	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×C₇×#41	C₂×C₄	1	1	yes	characteristic
69	C₂×C₇×Q₁₆	C₂×C₄	1	1	yes	characteristic
70	C₂×C₇×SD₁₆	C₂×C₄	1	1	yes	characteristic
71	C₂×C₇×SD₁₆	C₂×C₄	1	1	yes	characteristic
72	C₂×C₇×D₈	C₂×C₄	1	1	yes	characteristic
73	C₇×#126	—	2	1	no	—
74	C₇×#125	C₂×C₄	1	1	yes	characteristic
75	C₇×#124	C₂×C₄	1	1	yes	characteristic
76	C₇×#123	—	2	1	no	—
77	C₇×C₂²⋊Q₈	C₂×C₄	1	1	yes	characteristic
78	C₇×#121	C₂×C₄	1	1	yes	characteristic
79	C₄×C₇×Q₈	C₂×C₄	1	1	yes	characteristic
80	C₄×C₇×Q₈	C₂³	1	1	yes	characteristic
81	C₄×C₇×Q₈	C₂³	1	1	yes	characteristic
82	C₄×C₇×D₄	—	2	1	no	—
83	C₄×C₇×D₄	—	2	1	no	—
84	C₄×C₇×D₄	—	2	1	no	—
85	C₄×C₇×D₄	C₂×C₄	1	1	yes	characteristic
86	C₄×C₇×D₄	C₂³	1	1	yes	characteristic
87	C₄×C₇×D₄	C₂³	1	1	yes	characteristic
88	C₇×#117	—	2	1	no	—
89	C₇×#117	—	2	1	no	—
90	C₇×#117	C₂×C₄	1	1	yes	characteristic
91	C₂×C₄²×C₇	—	2	1	no	—
92	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
93	C₂×#1136	—	2	1	no	—
94	C₂²×C₇⋊C₈	—	2	1	no	—
95	C₂²×C₇⋊C₈	—	2	1	no	—
96	C₂²×C₇⋊C₈	—	2	1	no	—
97	C₂²×C₇⋊C₈	D₄	1	1	yes	characteristic
98	C₂²×C₇⋊C₈	D₄	1	1	yes	characteristic
99	C₇×#107	C₂×C₄	1	1	yes	characteristic
100	C₇×#107	C₂×C₄	1	1	yes	characteristic
101	C₇×#106	C₂×C₄	1	1	yes	characteristic
102	C₇×#106	C₂×C₄	1	1	yes	characteristic
103	C₇×C₄⋊C₈	C₂×C₄	1	1	yes	characteristic
104	C₇×C₄⋊C₈	C₂×C₄	1	1	yes	characteristic
105	C₇×#103	C₂×C₄	1	1	yes	characteristic
106	C₇×#103	C₂×C₄	1	1	yes	characteristic
107	C₇×#103	C₂×C₄	1	1	yes	characteristic
108	C₇×#103	C₂×C₄	1	1	yes	characteristic
109	C₇×#102	C₂×C₄	1	1	yes	characteristic
110	C₇×#102	C₂×C₄	1	1	yes	characteristic
111	C₇×#102	C₂×C₄	1	1	yes	characteristic
112	C₇×#102	C₂×C₄	1	1	yes	characteristic
113	C₇×C₂²⋊C₈	C₂×C₄	1	1	yes	characteristic
114	C₇×C₂²⋊C₈	C₂×C₄	1	1	yes	characteristic
115	C₄×C₇×C₈	C₂³	1	1	yes	characteristic
116	C₄×C₇×C₈	C₂³	1	1	yes	characteristic
117	C₂²⋊(C₇⋊C₈)	—	2	1	no	—
118	C₂²⋊(C₇⋊C₈)	—	2	1	no	—
119	C₂²⋊(C₇⋊C₈)	—	2	1	no	—
120	C₂²⋊(C₇⋊C₈)	—	2	1	no	—
121	C₂²⋊(C₇⋊C₈)	—	2	1	no	—
122	C₂²⋊(C₇⋊C₈)	—	2	1	no	—
123	C₂²⋊(C₇⋊C₈)	—	2	1	no	—
124	C₄⋊(C₇⋊C₈)	—	2	1	no	—
125	C₄⋊(C₇⋊C₈)	—	2	1	no	—
126	C₄⋊(C₇⋊C₈)	—	2	1	no	—
127	C₄⋊(C₇⋊C₈)	—	2	1	no	—
128	C₄⋊(C₇⋊C₈)	—	2	1	no	—
129	C₄⋊(C₇⋊C₈)	C₂³	1	1	yes	characteristic
130	C₄⋊(C₇⋊C₈)	C₂³	1	1	yes	characteristic
131	C₄⋊(C₇⋊C₈)	C₂³	1	1	yes	characteristic
132	C₄⋊(C₇⋊C₈)	C₂³	1	1	yes	characteristic
133	#6377	—	2	1	no	—
134	#6377	—	2	1	no	—
135	C₄×C₇⋊C₈	—	2	1	no	—
136	C₄×C₇⋊C₈	—	2	1	no	—
137	C₄×C₇⋊C₈	—	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	D₇	1	1	yes	characteristic
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	—	7	1	no	—
157	#1488	—	7	1	no	—
158	#1482	—	7	1	no	—
159	#1452	—	7	1	no	—
160	C₇×#41	—	2	2	no	—
161	C₇×#41	—	2	2	no	—
162	C₂×C₇×Q₈	C₂²×C₄	1	1	yes	characteristic
163	C₂×C₇×Q₈	C₂²×C₄	1	1	yes	characteristic
164	C₂×C₇×D₄	—	2	1	no	—
165	C₂×C₇×D₄	—	2	1	no	—
166	C₂×C₇×D₄	C₂²×C₄	1	1	yes	characteristic
167	C₂×C₇×D₄	C₂²×C₄	1	1	yes	characteristic
168	C₂²×C₄×C₇	—	2	1	no	—
169	C₂²×C₄×C₇	—	2	1	no	—
170	C₂²×C₄×C₇	—	2	1	no	—
171	C₂²×C₄×C₇	—	2	1	no	—
172	C₂²×C₄×C₇	C₂²×C₄	1	1	yes	characteristic
173	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
174	C₂²×C₄×C₇	#41	1	1	yes	characteristic
175	C₇×Q₁₆	—	2	2	no	—
176	C₇×SD₁₆	—	2	2	no	—
177	C₇×SD₁₆	—	2	2	no	—
178	C₇×D₈	—	2	2	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	C₇×C₄⋊C₄	—	2	1	no	—
184	C₇×C₄⋊C₄	—	2	1	no	—
185	C₇×C₄⋊C₄	—	2	1	no	—
186	C₇×C₄⋊C₄	—	2	1	no	—
187	C₇×C₄⋊C₄	—	2	1	no	—
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×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
192	C₇×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
193	C₇×C₂²⋊C₄	—	2	1	no	—
194	C₇×C₂²⋊C₄	—	2	1	no	—
195	C₇×C₂²⋊C₄	—	2	1	no	—
196	C₇×C₂²⋊C₄	—	2	1	no	—
197	C₇×C₂²⋊C₄	—	2	1	no	—
198	C₇×C₂²⋊C₄	—	2	1	no	—
199	C₇×C₂²⋊C₄	—	2	1	no	—
200	C₇×C₂²⋊C₄	—	2	1	no	—
201	C₄²×C₇	—	2	1	no	—
202	C₄²×C₇	—	2	1	no	—
203	C₄²×C₇	—	2	1	no	—
204	C₄²×C₇	—	2	1	no	—
205	C₄²×C₇	C₂²×C₄	1	1	yes	characteristic
206	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
207	C₄²×C₇	#41	1	1	yes	characteristic
208	C₄²×C₇	C₂⁴	1	1	yes	characteristic
209	#1136	—	4	2	no	—
210	C₂×C₇⋊C₈	—	2	1	no	—
211	C₂×C₇⋊C₈	—	2	1	no	—
212	C₂×C₇⋊C₈	—	2	1	no	—
213	C₂×C₇⋊C₈	—	2	1	no	—
214	C₂×C₇⋊C₈	—	2	1	no	—
215	C₂×C₇⋊C₈	—	2	1	no	—
216	C₂×C₇⋊C₈	—	4	1	no	—
217	C₂×C₇⋊C₈	—	4	1	no	—
218	C₂×C₇⋊C₈	—	4	2	no	—
219	C₂×C₇⋊C₈	—	4	2	no	—
220	C₂×C₇⋊C₈	—	4	2	no	—
221	C₂×C₇⋊C₈	C₂×D₄	1	1	yes	characteristic
222	C₂×C₇⋊C₈	C₂×D₄	1	1	yes	characteristic
223	C₂×C₇⋊C₈	C₂×D₄	1	1	yes	characteristic
224	C₂×C₇⋊C₈	C₂×D₄	1	1	yes	characteristic
225	#529	C₂×D₇	1	1	yes	characteristic
226	C₄×#41	C₂×D₇	1	1	yes	characteristic
227	#485	Dic₇	1	1	yes	characteristic
228	#482	Dic₇	1	1	yes	characteristic
229	#479	Dic₇	1	1	yes	characteristic
230	#478	Dic₇	1	1	yes	characteristic
231	#464	Dic₇	1	1	yes	characteristic
232	#463	Dic₇	1	1	yes	characteristic
233	#452	Dic₇	1	1	yes	characteristic
234	#449	Dic₇	1	1	yes	characteristic
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	C₂×D₇	1	1	yes	characteristic
240	C₄×SD₁₆	C₂×D₇	1	1	yes	characteristic
241	C₄×SD₁₆	C₂×D₇	1	1	yes	characteristic
242	C₄×D₈	C₂×D₇	1	1	yes	characteristic
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	—	7	1	no	—
253	#431	—	7	1	no	—
254	#431	—	7	1	no	—
255	#431	—	14	1	no	—
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	—	7	1	no	—
261	#335	—	7	1	no	—
262	#334	—	7	1	no	—
263	#334	—	7	1	no	—
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	—	2	1	no	—
277	C₂³×C₇	—	2	1	no	—
278	C₂³×C₇	C₄×D₄	1	1	yes	characteristic
279	C₇×Q₈	—	2	1	no	—
280	C₇×Q₈	—	2	1	no	—
281	C₇×Q₈	—	2	1	no	—
282	C₇×Q₈	#131	1	2	yes	—
283	C₇×D₄	—	2	4	no	—
284	C₇×D₄	—	2	1	no	—
285	C₇×D₄	—	2	1	no	—
286	C₇×D₄	—	2	1	no	—
287	C₇×D₄	—	4	2	no	—
288	C₇×D₄	#131	1	2	yes	—
289	C₂×C₄×C₇	—	2	4	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	—	2	1	no	—
294	C₂×C₄×C₇	—	2	1	no	—
295	C₂×C₄×C₇	—	2	1	no	—
296	C₂×C₄×C₇	—	2	1	no	—
297	C₂×C₄×C₇	—	2	1	no	—
298	C₂×C₄×C₇	—	2	1	no	—
299	C₂×C₄×C₇	—	2	1	no	—
300	C₂×C₄×C₇	—	4	1	no	—
301	C₂×C₄×C₇	—	4	2	no	—
302	C₂×C₄×C₇	—	4	1	no	—
303	C₂×C₄×C₇	—	4	1	no	—
304	C₂×C₄×C₇	—	4	1	no	—
305	C₂×C₄×C₇	—	4	1	no	—
306	C₂×C₄×C₇	C₄×D₄	1	1	yes	characteristic
307	C₂×C₄×C₇	C₄×D₄	1	1	yes	characteristic
308	C₂×C₄×C₇	C₄×D₄	1	1	yes	characteristic
309	C₂×C₄×C₇	C₂³×C₄	1	1	yes	characteristic
310	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
311	C₂×C₄×C₇	C₂×#41	1	1	yes	characteristic
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	—	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	—	4	1	no	—
325	C₇⋊C₈	—	4	1	no	—
326	C₂×#41	C₂×Dic₇	1	1	yes	characteristic
327	C₂×Q₁₆	C₂×Dic₇	1	1	yes	characteristic
328	C₂×SD₁₆	C₂×Dic₇	1	1	yes	characteristic
329	C₂×SD₁₆	C₂×Dic₇	1	1	yes	characteristic
330	C₂×D₈	C₂×Dic₇	1	1	yes	characteristic
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	—	2	1	no	—
338	#125	C₂×Dic₇	1	1	yes	characteristic
339	#124	C₂×Dic₇	1	1	yes	characteristic
340	#123	—	2	1	no	—
341	C₂²⋊Q₈	C₂×Dic₇	1	1	yes	characteristic
342	#121	C₂×Dic₇	1	1	yes	characteristic
343	C₄×Q₈	C₂×Dic₇	1	1	yes	characteristic
344	C₄×Q₈	C₂²×D₇	1	1	yes	characteristic
345	C₄×Q₈	C₂²×D₇	1	1	yes	characteristic
346	C₄×D₄	—	2	1	no	—
347	C₄×D₄	—	2	1	no	—
348	C₄×D₄	—	2	1	no	—
349	C₄×D₄	C₂×Dic₇	1	1	yes	characteristic
350	C₄×D₄	C₂²×D₇	1	1	yes	characteristic
351	C₄×D₄	C₂²×D₇	1	1	yes	characteristic
352	#117	—	2	1	no	—
353	#117	—	2	1	no	—
354	#117	C₂×Dic₇	1	1	yes	characteristic
355	C₂×C₄²	—	2	1	no	—
356	C₂×C₄²	C₂²×D₇	1	1	yes	characteristic
357	#107	C₂×Dic₇	1	1	yes	characteristic
358	#107	C₂×Dic₇	1	1	yes	characteristic
359	#106	C₂×Dic₇	1	1	yes	characteristic
360	#106	C₂×Dic₇	1	1	yes	characteristic
361	C₄⋊C₈	—	7	1	no	—
362	C₄⋊C₈	—	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	C₂×Dic₇	1	1	yes	characteristic
371	C₄⋊C₈	C₂×Dic₇	1	1	yes	characteristic
372	#103	C₂×Dic₇	1	1	yes	characteristic
373	#103	C₂×Dic₇	1	1	yes	characteristic
374	#103	C₂×Dic₇	1	1	yes	characteristic
375	#103	C₂×Dic₇	1	1	yes	characteristic
376	#102	C₂×Dic₇	1	1	yes	characteristic
377	#102	C₂×Dic₇	1	1	yes	characteristic
378	#102	C₂×Dic₇	1	1	yes	characteristic
379	#102	C₂×Dic₇	1	1	yes	characteristic
380	C₂²⋊C₈	—	14	1	no	—
381	C₂²⋊C₈	—	14	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	C₂×Dic₇	1	1	yes	characteristic
388	C₂²⋊C₈	C₂×Dic₇	1	1	yes	characteristic
389	#97	—	14	1	no	—
390	#97	—	14	1	no	—
391	C₄×C₈	—	7	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	—	14	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	2	no	—
405	C₂²×C₇	—	2	1	no	—
406	C₂²×C₇	—	2	1	no	—
407	C₂²×C₇	—	4	1	no	—
408	C₂²×C₇	—	4	1	no	—
409	C₂²×C₇	—	4	1	no	—
410	C₂²×C₇	—	4	1	no	—
411	C₂²×C₇	—	4	1	no	—
412	C₂²×C₇	C₂×C₄×D₄	1	1	yes	characteristic
413	C₄×C₇	—	2	1	no	—
414	C₄×C₇	—	2	2	no	—
415	C₄×C₇	—	2	1	no	—
416	C₄×C₇	—	2	1	no	—
417	C₄×C₇	—	2	1	no	—
418	C₄×C₇	—	4	1	no	—
419	C₄×C₇	—	4	1	no	—
420	C₄×C₇	—	4	1	no	—
421	C₄×C₇	—	4	1	no	—
422	C₄×C₇	—	4	1	no	—
423	C₄×C₇	C₂×#131	1	1	yes	characteristic
424	C₄×C₇	C₂×#131	1	1	yes	characteristic
425	C₄×C₇	#575	1	1	yes	characteristic
426	C₄×C₇	#575	1	1	yes	characteristic
427	#41	—	2	2	no	—
428	#41	—	2	2	no	—
429	C₂×Q₈	C₂²×Dic₇	1	1	yes	characteristic
430	C₂×Q₈	C₂²×Dic₇	1	1	yes	characteristic
431	C₂×D₄	—	2	1	no	—
432	C₂×D₄	—	2	1	no	—
433	C₂×D₄	C₂²×Dic₇	1	1	yes	characteristic
434	C₂×D₄	C₂²×Dic₇	1	1	yes	characteristic
435	C₂²×C₄	—	2	1	no	—
436	C₂²×C₄	—	2	1	no	—
437	C₂²×C₄	—	2	1	no	—
438	C₂²×C₄	—	2	1	no	—
439	C₂²×C₄	D₄×D₇	1	1	yes	characteristic
440	C₂²×C₄	#1159	1	1	yes	characteristic
441	C₂²×C₄	C₂²×Dic₇	1	1	yes	characteristic
442	Q₁₆	—	2	2	no	—
443	SD₁₆	—	2	2	no	—
444	SD₁₆	—	2	2	no	—
445	D₈	—	2	2	no	—
446	M₁₆	—	28	2	no	—
447	C₂×C₈	—	7	1	no	—
448	C₂×C₈	—	7	1	no	—
449	C₂×C₈	—	7	1	no	—
450	C₂×C₈	—	7	1	no	—
451	C₂×C₈	—	14	1	no	—
452	C₂×C₈	—	14	1	no	—
453	C₂×C₈	—	14	1	no	—
454	C₂×C₈	—	14	1	no	—
455	C₂×C₈	—	14	1	no	—
456	C₂×C₈	—	14	1	no	—
457	C₂×C₈	—	28	1	no	—
458	C₂×C₈	—	28	1	no	—
459	C₂×C₈	—	28	2	no	—
460	C₂×C₈	—	28	2	no	—
461	C₂×C₈	—	28	2	no	—
462	C₂×C₈	C₂²×Dic₇	1	1	yes	characteristic
463	C₂×C₈	C₂²×Dic₇	1	1	yes	characteristic
464	C₂×C₈	C₂²×Dic₇	1	1	yes	characteristic
465	C₂×C₈	C₂²×Dic₇	1	1	yes	characteristic
466	C₄⋊C₄	—	2	1	no	—
467	C₄⋊C₄	—	2	1	no	—
468	C₄⋊C₄	—	2	1	no	—
469	C₄⋊C₄	—	2	1	no	—
470	C₄⋊C₄	—	2	1	no	—
471	C₄⋊C₄	—	2	1	no	—
472	C₄⋊C₄	C₂²×Dic₇	1	1	yes	characteristic
473	C₄⋊C₄	C₂²×Dic₇	1	1	yes	characteristic
474	C₄⋊C₄	C₂²×Dic₇	1	1	yes	characteristic
475	C₄⋊C₄	C₂²×Dic₇	1	1	yes	characteristic
476	C₂²⋊C₄	—	2	1	no	—
477	C₂²⋊C₄	—	2	1	no	—
478	C₂²⋊C₄	—	2	1	no	—
479	C₂²⋊C₄	—	2	1	no	—
480	C₂²⋊C₄	—	2	1	no	—
481	C₂²⋊C₄	—	2	1	no	—
482	C₂²⋊C₄	—	2	1	no	—
483	C₂²⋊C₄	—	2	1	no	—
484	C₄²	—	2	1	no	—
485	C₄²	—	2	1	no	—
486	C₄²	—	2	1	no	—
487	C₄²	—	2	1	no	—
488	C₄²	D₄×D₇	1	1	yes	characteristic
489	C₄²	#1159	1	1	yes	characteristic
490	C₄²	C₂²×Dic₇	1	1	yes	characteristic
491	C₄²	C₂³×D₇	1	1	yes	characteristic
492	C₂×C₇	—	4	1	no	—
493	C₂×C₇	—	4	2	no	—
494	C₂×C₇	—	8	1	no	—
495	C₂×C₇	#2929	1	1	yes	characteristic
496	C₂×C₇	#2943	1	1	yes	characteristic
497	C₂×C₇	#2955	1	1	yes	characteristic
498	C₂³	—	2	1	no	—
499	C₂³	—	2	1	no	—
500	C₂³	D₄×Dic₇	1	1	yes	characteristic
501	Q₈	—	2	1	no	—
502	Q₈	—	2	1	no	—
503	Q₈	—	2	1	no	—
504	Q₈	#6511	1	2	yes	—
505	D₄	—	2	4	no	—
506	D₄	—	2	1	no	—
507	D₄	—	2	1	no	—
508	D₄	—	2	1	no	—
509	D₄	—	4	2	no	—
510	D₄	#6511	1	2	yes	—
511	C₂×C₄	—	2	4	no	—
512	C₂×C₄	—	2	1	no	—
513	C₂×C₄	—	2	1	no	—
514	C₂×C₄	—	2	1	no	—
515	C₂×C₄	—	2	1	no	—
516	C₂×C₄	—	2	1	no	—
517	C₂×C₄	—	2	1	no	—
518	C₂×C₄	—	2	1	no	—
519	C₂×C₄	—	2	1	no	—
520	C₂×C₄	—	2	1	no	—
521	C₂×C₄	—	2	1	no	—
522	C₂×C₄	—	4	1	no	—
523	C₂×C₄	—	4	2	no	—
524	C₂×C₄	—	4	1	no	—
525	C₂×C₄	—	4	1	no	—
526	C₂×C₄	—	4	1	no	—
527	C₂×C₄	—	4	1	no	—
528	C₂×C₄	D₄×Dic₇	1	1	yes	characteristic
529	C₂×C₄	D₄×Dic₇	1	1	yes	characteristic
530	C₂×C₄	D₄×Dic₇	1	1	yes	characteristic
531	C₂×C₄	C₂×D₄×D₇	1	1	yes	characteristic
532	C₂×C₄	C₂×#1159	1	1	yes	characteristic
533	C₂×C₄	C₂³×Dic₇	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	—	14	1	no	—
539	C₈	—	14	1	no	—
540	C₈	—	14	1	no	—
541	C₈	—	14	1	no	—
542	C₈	—	28	1	no	—
543	C₈	—	28	1	no	—
544	C₈	—	28	1	no	—
545	C₈	—	28	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	—	2	2	no	—
553	C₂²	—	4	1	no	—
554	C₂²	—	4	1	no	—
555	C₂²	—	4	1	no	—
556	C₂²	—	4	1	no	—
557	C₂²	—	4	1	no	—
558	C₂²	C₂×D₄×Dic₇	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	—	2	2	no	—
564	C₄	—	4	1	no	—
565	C₄	—	4	1	no	—
566	C₄	—	4	1	no	—
567	C₄	—	4	1	no	—
568	C₄	—	4	1	no	—
569	C₄	#90459	1	1	yes	characteristic
570	C₄	#90459	1	1	yes	characteristic
571	C₄	C₂×#6511	1	1	yes	characteristic
572	C₄	C₂×#6511	1	1	yes	characteristic
573	C₂	—	4	1	no	—
574	C₂	—	4	2	no	—
575	C₂	—	8	1	no	—
576	C₂	#11740361	1	1	yes	characteristic
577	C₂	#11741342	1	1	yes	characteristic
578	C₂	#11741444	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×#3102	C₂
socle	C₂²×C₇	C₂×C₄×D₄
prime radical	C₇×#449	C₄
cosocle	C₄²×C₇	C₂⁴
hypercenter	#3102	D₇
hypocenter	C₇	#17909
LCS	G ▷ C₂×C₄×C₇ ▷ C₂×C₇ ▷ C₇
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #3102

Complements

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

N	H ≅ G/N	type
2. #11740571	C₂	semidirect
3. #41×C₇⋊C₈	C₂	semidirect
4. #11729504	C₂	semidirect
5. #11729394	C₂	semidirect
6. #11728658	C₂	semidirect
7. #11728656	C₂	semidirect
8. #11728652	C₂	semidirect
9. #11728651	C₂	semidirect
10. SD₁₆⋊(C₇⋊C₈)	C₂	semidirect
11. SD₁₆⋊(C₇⋊C₈)	C₂	semidirect
12. #11728634	C₂	semidirect
13. #11728632	C₂	semidirect
14. #11728505	C₂	semidirect
15. #11728496	C₂	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
C₇×#3102	2
#11740571	2
#41×C₇⋊C₈	2
#11729504	2
#11729394	2
#11728658	2
#11728656	2
#11728652	2
#11728651	2
SD₁₆⋊(C₇⋊C₈)	2
#11728634	2
#11728632	2
#11728505	2
#11728496	2
#17909	7