Subgroups — #13323025

Order 1792.

610 conjugacy classes of subgroups.

The subgroup lattice has 572 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#11736779	C₂	1	1	yes	maximal, characteristic
2	#11736730	C₂	1	1	yes	maximal, characteristic
3	#11736721	C₂	1	1	yes	maximal, characteristic
4	C₇×#1572	C₂	1	1	yes	maximal, characteristic, complemented
5	#11728548	C₂	1	1	yes	maximal, characteristic, complemented
6	#11728505	C₂	1	1	yes	maximal, characteristic, complemented
7	#11728499	C₂	1	1	yes	maximal, characteristic, complemented
8	#11726326	C₂	1	1	yes	maximal, characteristic, complemented
9	#11726326	C₂	1	1	yes	maximal, characteristic, complemented
10	#11726324	C₂	1	1	yes	maximal, characteristic, complemented
11	#11726321	C₂	1	1	yes	maximal, characteristic, complemented
12	#11726287	C₂	1	1	yes	maximal, characteristic, complemented
13	#11726287	C₂	1	1	yes	maximal, characteristic, complemented
14	#11726283	C₂	1	1	yes	maximal, characteristic, complemented
15	D₇×#334	C₂	1	1	yes	maximal, characteristic, complemented
16	C₄×#1157	C₂²	1	1	yes	characteristic
17	C₇×#432	C₂²	1	1	yes	characteristic
18	C₇×#431	C₂²	1	1	yes	characteristic
19	C₇×#431	C₂²	1	1	yes	characteristic
20	#89698	C₂²	1	1	yes	characteristic
21	#89697	C₂²	1	1	yes	characteristic
22	C₂×C₄×C₇⋊C₈	C₂²	1	1	yes	characteristic
23	#89609	C₂²	1	1	yes	characteristic
24	#89609	C₂²	1	1	yes	characteristic
25	#89607	C₂²	1	1	yes	characteristic
26	#89607	C₂²	1	1	yes	characteristic
27	#89606	C₄	1	1	yes	characteristic
28	#89606	C₄	1	1	yes	characteristic
29	#89605	C₂²	1	1	yes	characteristic
30	#89605	C₂²	1	1	yes	characteristic
31	D₇×C₄⋊C₈	C₂²	1	1	yes	characteristic
32	D₇×C₄⋊C₈	C₂²	1	1	yes	characteristic
33	#89602	C₄	1	1	yes	characteristic
34	#89602	C₄	1	1	yes	characteristic
35	#89499	—	2	1	no	—
36	#89499	—	2	1	no	—
37	(C₂²⋊D₇)⋊C₈	C₄	1	1	yes	characteristic
38	(C₂²⋊D₇)⋊C₈	C₄	1	1	yes	characteristic
39	(C₂²⋊D₇)⋊C₈	C₄	1	1	yes	characteristic
40	(C₂²⋊D₇)⋊C₈	C₄	1	1	yes	characteristic
41	#89492	—	2	1	no	—
42	#89492	—	2	1	no	—
43	#89481	—	2	1	no	—
44	#89480	—	2	1	no	—
45	#89462	—	2	1	no	—
46	#89461	—	2	1	no	—
47	#89457	C₂²	1	1	yes	characteristic
48	#89457	C₂²	1	1	yes	characteristic
49	C₄×C₈×D₇	C₂²	1	1	yes	characteristic
50	C₄×C₈×D₇	C₂²	1	1	yes	characteristic
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	#89275	C₂²	1	1	yes	characteristic
56	#89275	C₂²	1	1	yes	characteristic
57	#89275	C₂²	1	1	yes	characteristic
58	#89275	C₂²	1	1	yes	characteristic
59	#89274	C₂²	1	1	yes	characteristic
60	#89274	C₂²	1	1	yes	characteristic
61	#89274	C₂²	1	1	yes	characteristic
62	#89274	C₂²	1	1	yes	characteristic
63	#89253	C₂²	1	1	yes	characteristic
64	#89253	C₂²	1	1	yes	characteristic
65	#89252	C₂²	1	1	yes	characteristic
66	#89252	C₂²	1	1	yes	characteristic
67	#17827	—	7	1	no	maximal, Sylow
68	C₂×#1157	D₄	1	1	yes	characteristic
69	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
70	C₄×C₂²⋊D₇	C₂×C₄	1	1	yes	characteristic
71	C₄×C₂²⋊D₇	C₂×C₄	1	1	yes	characteristic
72	C₄×C₂²⋊D₇	Q₈	1	1	yes	characteristic
73	C₄×C₂²⋊D₇	Q₈	1	1	yes	characteristic
74	#6489	D₄	1	1	yes	characteristic
75	C₂²×C₇⋊C₈	C₂×C₄	1	1	yes	characteristic
76	C₂²×C₇⋊C₈	C₂×C₄	1	1	yes	characteristic
77	C₂×#1131	—	2	1	no	—
78	C₂×#1131	—	2	1	no	—
79	C₂×C₈×D₇	—	2	1	no	—
80	C₂×C₈×D₇	—	2	1	no	—
81	C₂×C₈×D₇	C₂×C₄	1	1	yes	characteristic
82	C₂×C₈×D₇	C₂×C₄	1	1	yes	characteristic
83	C₂×C₈×D₇	C₂×C₄	1	1	yes	characteristic
84	C₂×C₈×D₇	C₂×C₄	1	1	yes	characteristic
85	C₄×D₂₈	C₂×C₄	1	1	yes	characteristic
86	C₄×D₂₈	Q₈	1	1	yes	characteristic
87	#6435	D₄	1	1	yes	characteristic
88	#6435	D₄	1	1	yes	characteristic
89	C₄²×D₇	C₂³	1	1	yes	characteristic
90	C₄²×D₇	C₂³	1	1	yes	characteristic
91	C₄×Dic₁₄	C₂×C₄	1	1	yes	characteristic
92	C₄×Dic₁₄	Q₈	1	1	yes	characteristic
93	C₇×C₄⋊C₈	C₂×C₄	1	1	yes	characteristic
94	C₇×C₄⋊C₈	C₂×C₄	1	1	yes	characteristic
95	C₇×C₄⋊C₈	C₂³	1	1	yes	characteristic
96	C₇×C₄⋊C₈	C₂³	1	1	yes	characteristic
97	C₇×C₄⋊C₈	C₂³	1	1	yes	characteristic
98	C₇×C₄⋊C₈	C₂³	1	1	yes	characteristic
99	C₇×C₂²⋊C₈	—	2	1	no	—
100	C₇×C₂²⋊C₈	—	2	1	no	—
101	C₇×C₂²⋊C₈	C₂×C₄	1	1	yes	characteristic
102	C₇×C₂²⋊C₈	C₂×C₄	1	1	yes	characteristic
103	C₇×#97	—	2	1	no	—
104	C₄×C₇×C₈	—	2	1	no	—
105	C₄×C₇×C₈	C₂³	1	1	yes	characteristic
106	C₄×C₇×C₈	C₂³	1	1	yes	characteristic
107	C₂²⋊(C₇⋊C₈)	—	2	1	no	—
108	C₂²⋊(C₇⋊C₈)	—	2	1	no	—
109	(C₂×D₇)⋊C₈	—	2	1	no	—
110	(C₂×D₇)⋊C₈	—	2	1	no	—
111	(C₂×D₇)⋊C₈	—	2	1	no	—
112	(C₂×D₇)⋊C₈	—	2	1	no	—
113	(C₂×D₇)⋊C₈	C₂×C₄	1	1	yes	characteristic
114	(C₂×D₇)⋊C₈	C₂×C₄	1	1	yes	characteristic
115	(C₂×D₇)⋊C₈	C₂×C₄	1	1	yes	characteristic
116	(C₂×D₇)⋊C₈	C₂×C₄	1	1	yes	characteristic
117	#6389	—	2	1	no	—
118	#6389	—	2	1	no	—
119	Dic₇⋊C₈	—	2	1	no	—
120	Dic₇⋊C₈	—	2	1	no	—
121	Dic₇⋊C₈	—	2	1	no	—
122	Dic₇⋊C₈	—	2	1	no	—
123	Dic₇⋊C₈	C₂×C₄	1	1	yes	characteristic
124	Dic₇⋊C₈	C₂×C₄	1	1	yes	characteristic
125	Dic₇⋊C₈	C₂×C₄	1	1	yes	characteristic
126	Dic₇⋊C₈	C₂×C₄	1	1	yes	characteristic
127	C₈×Dic₇	—	2	1	no	—
128	C₈×Dic₇	—	2	1	no	—
129	C₈×Dic₇	C₂×C₄	1	1	yes	characteristic
130	C₈×Dic₇	C₂×C₄	1	1	yes	characteristic
131	C₈×Dic₇	C₂×C₄	1	1	yes	characteristic
132	C₈×Dic₇	C₂×C₄	1	1	yes	characteristic
133	C₄⋊(C₇⋊C₈)	C₂³	1	1	yes	characteristic
134	C₄⋊(C₇⋊C₈)	C₂³	1	1	yes	characteristic
135	C₄⋊(C₇⋊C₈)	C₂³	1	1	yes	characteristic
136	C₄⋊(C₇⋊C₈)	C₂³	1	1	yes	characteristic
137	#6377	—	2	1	no	—
138	C₄×C₇⋊C₈	—	2	1	no	—
139	C₄×C₇⋊C₈	C₂×C₄	1	1	yes	characteristic
140	C₄×C₇⋊C₈	C₂×C₄	1	1	yes	characteristic
141	C₄×C₇⋊C₈	C₂³	1	1	yes	characteristic
142	C₄×C₇⋊C₈	C₂³	1	1	yes	characteristic
143	C₈×#41	—	7	1	no	—
144	#2925	—	7	1	no	—
145	#2925	—	7	1	no	—
146	#1572	—	7	1	no	—
147	#1572	—	7	1	no	—
148	#1572	—	7	1	no	—
149	#1572	D₇	1	1	yes	characteristic, complemented
150	#1571	—	7	1	no	—
151	#1571	—	7	1	no	—
152	#1568	—	7	1	no	—
153	#1568	—	7	1	no	—
154	#1566	—	7	1	no	—
155	#1564	—	7	1	no	—
156	#1564	—	7	1	no	—
157	C₂×#334	—	7	1	no	—
158	C₂²×C₄×C₇	C₂²×C₄	1	1	yes	characteristic
159	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
160	C₂²×C₄×C₇	C₂×Q₈	1	1	yes	characteristic
161	C₂×C₂²⋊D₇	C₄⋊C₄	1	1	yes	characteristic
162	C₂×C₂²⋊D₇	C₄⋊C₄	1	1	yes	characteristic
163	#1157	—	2	2	no	—
164	#1157	—	2	2	no	—
165	C₂×D₂₈	C₄⋊C₄	1	1	yes	characteristic
166	C₂×C₄×D₇	C₂²×C₄	1	1	yes	characteristic
167	C₂×C₄×D₇	C₂²×C₄	1	1	yes	characteristic
168	C₂×C₄×D₇	C₂×D₄	1	1	yes	characteristic
169	C₂×C₄×D₇	C₂×D₄	1	1	yes	characteristic
170	C₂×C₄×D₇	C₂×Q₈	1	1	yes	characteristic
171	C₂×C₄×D₇	C₂×Q₈	1	1	yes	characteristic
172	C₂×Dic₁₄	C₄⋊C₄	1	1	yes	characteristic
173	C₂×C₇×C₈	—	2	1	no	—
174	C₂×C₇×C₈	—	2	1	no	—
175	C₂×C₇×C₈	—	2	1	no	—
176	C₂×C₇×C₈	—	2	1	no	—
177	C₂×C₇×C₈	C₂²×C₄	1	1	yes	characteristic
178	C₂×C₇×C₈	C₂²×C₄	1	1	yes	characteristic
179	C₂×C₇×C₈	C₂²×C₄	1	1	yes	characteristic
180	C₂×C₇×C₈	C₂²×C₄	1	1	yes	characteristic
181	C₄²×C₇	C₂²×C₄	1	1	yes	characteristic
182	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
183	C₄²×C₇	C₂×Q₈	1	1	yes	characteristic
184	C₄²×C₇	C₂⁴	1	1	yes	characteristic
185	C₂²⋊Dic₇	C₄⋊C₄	1	1	yes	characteristic
186	C₂²⋊Dic₇	C₄⋊C₄	1	1	yes	characteristic
187	(C₂×D₇)⋊C₄	C₄⋊C₄	1	1	yes	characteristic
188	(C₂×D₇)⋊C₄	C₄⋊C₄	1	1	yes	characteristic
189	(C₂×D₇)⋊C₄	C₄⋊C₄	1	1	yes	characteristic
190	(C₂×D₇)⋊C₄	C₄⋊C₄	1	1	yes	characteristic
191	C₄⋊Dic₇	C₄⋊C₄	1	1	yes	characteristic
192	C₄⋊Dic₇	C₄⋊C₄	1	1	yes	characteristic
193	Dic₇⋊C₄	C₄⋊C₄	1	1	yes	characteristic
194	Dic₇⋊C₄	C₄⋊C₄	1	1	yes	characteristic
195	Dic₇⋊C₄	C₄⋊C₄	1	1	yes	characteristic
196	Dic₇⋊C₄	C₄⋊C₄	1	1	yes	characteristic
197	C₄×Dic₇	C₂²×C₄	1	1	yes	characteristic
198	C₄×Dic₇	C₂²×C₄	1	1	yes	characteristic
199	C₄×Dic₇	C₂×D₄	1	1	yes	characteristic
200	C₄×Dic₇	C₂×D₄	1	1	yes	characteristic
201	C₄×Dic₇	C₂×Q₈	1	1	yes	characteristic
202	C₄×Dic₇	C₂×Q₈	1	1	yes	characteristic
203	C₂×C₇⋊C₈	—	2	2	no	—
204	C₂×C₇⋊C₈	—	2	1	no	—
205	C₂×C₇⋊C₈	—	2	1	no	—
206	C₂×C₇⋊C₈	—	2	1	no	—
207	C₂×C₇⋊C₈	—	2	1	no	—
208	C₂×C₇⋊C₈	—	4	1	no	—
209	C₂×C₇⋊C₈	C₂²×C₄	1	1	yes	characteristic
210	C₂×C₇⋊C₈	C₂²×C₄	1	1	yes	characteristic
211	C₂×C₇⋊C₈	C₂²×C₄	1	1	yes	characteristic
212	C₂×C₇⋊C₈	C₂²×C₄	1	1	yes	characteristic
213	#1131	—	4	2	no	—
214	#1131	—	4	2	no	—
215	C₈×D₇	—	2	2	no	—
216	C₈×D₇	—	2	2	no	—
217	C₈×D₇	—	4	1	no	—
218	C₈×D₇	—	4	1	no	—
219	C₈×D₇	—	4	2	no	—
220	C₈×D₇	—	4	2	no	—
221	C₄×#41	—	7	1	no	—
222	C₈×Q₈	—	7	1	no	—
223	C₈×Q₈	—	7	1	no	—
224	C₈×D₄	—	7	1	no	—
225	C₈×D₄	—	7	1	no	—
226	C₈×D₄	—	7	1	no	—
227	C₈×D₄	—	7	1	no	—
228	C₈×D₄	—	7	1	no	—
229	C₈×D₄	—	7	1	no	—
230	#433	—	14	1	no	—
231	#433	—	14	1	no	—
232	#433	—	14	1	no	—
233	#433	—	14	1	no	—
234	#432	—	7	1	no	—
235	#432	—	7	1	no	—
236	#432	—	7	1	no	—
237	#432	C₂×D₇	1	1	yes	characteristic
238	#431	—	7	1	no	—
239	#431	—	7	1	no	—
240	#431	—	7	1	no	—
241	#431	—	7	1	no	—
242	#431	—	7	1	no	—
243	#431	C₂×D₇	1	1	yes	characteristic
244	#431	C₂×D₇	1	1	yes	characteristic
245	#423	—	7	1	no	—
246	#423	—	7	1	no	—
247	C₂×C₄⋊C₈	—	7	1	no	—
248	C₂×C₄⋊C₈	—	7	1	no	—
249	#408	—	14	1	no	—
250	#408	—	14	1	no	—
251	#405	—	14	1	no	—
252	#405	—	14	1	no	—
253	C₂×C₄×C₈	—	7	1	no	—
254	C₂×C₄×C₈	—	7	1	no	—
255	C₂×C₄×C₈	—	7	1	no	—
256	#335	—	7	1	no	—
257	#335	—	7	1	no	—
258	#335	—	7	1	no	—
259	#335	—	7	1	no	—
260	#335	—	7	1	no	—
261	#335	—	7	1	no	—
262	#335	C₂×D₇	1	1	yes	characteristic
263	#335	C₂×D₇	1	1	yes	characteristic
264	#334	—	7	1	no	—
265	#334	—	7	1	no	—
266	#334	—	7	1	no	—
267	#334	—	7	1	no	—
268	#334	—	7	1	no	—
269	#334	—	7	1	no	—
270	#334	C₂×D₇	1	1	yes	characteristic
271	#334	C₂×D₇	1	1	yes	characteristic
272	C₂³×C₇	C₂×C₄⋊C₄	1	1	yes	characteristic
273	C₂²×D₇	C₂×C₄⋊C₄	1	1	yes	characteristic
274	C₂²×D₇	C₂×C₄⋊C₄	1	1	yes	characteristic
275	C₂×C₄×C₇	—	2	1	no	—
276	C₂×C₄×C₇	—	2	1	no	—
277	C₂×C₄×C₇	—	2	1	no	—
278	C₂×C₄×C₇	—	2	1	no	—
279	C₂×C₄×C₇	—	4	1	no	—
280	C₂×C₄×C₇	C₂×C₄⋊C₄	1	1	yes	characteristic
281	C₂×C₄×C₇	C₂×C₄⋊C₄	1	1	yes	characteristic
282	C₂×C₄×C₇	C₂×C₄⋊C₄	1	1	yes	characteristic
283	C₂×C₄×C₇	C₂³×C₄	1	1	yes	characteristic
284	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
285	C₂×C₄×C₇	C₂²×Q₈	1	1	yes	characteristic
286	C₂²⋊D₇	—	2	2	no	—
287	C₂²⋊D₇	—	2	2	no	—
288	C₂×Dic₇	C₂×C₄⋊C₄	1	1	yes	characteristic
289	C₂×Dic₇	C₂×C₄⋊C₄	1	1	yes	characteristic
290	C₂×Dic₇	C₂×C₄⋊C₄	1	1	yes	characteristic
291	C₂×Dic₇	C₂×C₄⋊C₄	1	1	yes	characteristic
292	C₂×Dic₇	C₂×C₄⋊C₄	1	1	yes	characteristic
293	C₂×Dic₇	C₂×C₄⋊C₄	1	1	yes	characteristic
294	D₂₈	—	2	2	no	—
295	C₄×D₇	—	2	1	no	—
296	C₄×D₇	—	2	1	no	—
297	C₄×D₇	—	2	1	no	—
298	C₄×D₇	—	2	1	no	—
299	C₄×D₇	—	2	1	no	—
300	C₄×D₇	—	2	1	no	—
301	C₄×D₇	—	4	1	no	—
302	C₄×D₇	—	4	1	no	—
303	C₄×D₇	#135	1	2	yes	—
304	C₄×D₇	#135	1	2	yes	—
305	Dic₁₄	—	2	2	no	—
306	C₇×C₈	—	2	1	no	—
307	C₇×C₈	—	2	1	no	—
308	C₇×C₈	—	2	1	no	—
309	C₇×C₈	—	2	1	no	—
310	C₇×C₈	—	4	1	no	—
311	C₇×C₈	—	4	1	no	—
312	C₇×C₈	—	4	1	no	—
313	C₇×C₈	—	4	1	no	—
314	C₇⋊C₈	—	2	1	no	—
315	C₇⋊C₈	—	2	1	no	—
316	C₇⋊C₈	—	2	1	no	—
317	C₇⋊C₈	—	4	1	no	—
318	C₇⋊C₈	—	4	1	no	—
319	C₇⋊C₈	—	4	1	no	—
320	C₇⋊C₈	—	4	1	no	—
321	C₇⋊C₈	#131	1	2	yes	—
322	C₂×#41	—	7	1	no	—
323	C₂×M₁₆	—	14	1	no	—
324	C₂×M₁₆	—	14	1	no	—
325	C₂²×C₈	—	7	1	no	—
326	C₂²×C₈	—	7	1	no	—
327	C₂²×C₈	—	7	1	no	—
328	C₂²×C₈	—	7	1	no	—
329	C₂²×C₈	—	7	1	no	—
330	C₂²×C₈	—	7	1	no	—
331	C₂²×C₈	—	14	1	no	—
332	C₂²×C₈	—	14	1	no	—
333	C₄×Q₈	—	7	1	no	—
334	C₄×Q₈	—	7	1	no	—
335	C₄×D₄	—	7	1	no	—
336	C₄×D₄	—	7	1	no	—
337	C₄×D₄	—	7	1	no	—
338	C₄×D₄	—	7	1	no	—
339	C₄×D₄	—	7	1	no	—
340	C₄×D₄	—	7	1	no	—
341	#117	—	7	1	no	—
342	#117	—	7	1	no	—
343	#117	—	7	1	no	—
344	C₂×C₄²	—	7	1	no	—
345	C₂×C₄²	—	7	1	no	—
346	C₂×C₄²	C₂²×D₇	1	1	yes	characteristic
347	C₄⋊C₈	—	7	1	no	—
348	C₄⋊C₈	—	7	1	no	—
349	C₄⋊C₈	—	7	1	no	—
350	C₄⋊C₈	—	7	1	no	—
351	C₄⋊C₈	—	7	1	no	—
352	C₄⋊C₈	—	7	1	no	—
353	C₄⋊C₈	—	7	1	no	—
354	C₄⋊C₈	—	7	1	no	—
355	C₄⋊C₈	—	14	1	no	—
356	C₄⋊C₈	—	14	1	no	—
357	C₄⋊C₈	—	14	1	no	—
358	C₄⋊C₈	—	14	1	no	—
359	C₄⋊C₈	C₄×D₇	1	1	yes	characteristic
360	C₄⋊C₈	C₄×D₇	1	1	yes	characteristic
361	C₄⋊C₈	C₂²×D₇	1	1	yes	characteristic
362	C₄⋊C₈	C₂²×D₇	1	1	yes	characteristic
363	C₄⋊C₈	C₂²×D₇	1	1	yes	characteristic
364	C₄⋊C₈	C₂²×D₇	1	1	yes	characteristic
365	C₂²⋊C₈	—	2	1	no	—
366	C₂²⋊C₈	—	2	1	no	—
367	C₂²⋊C₈	—	7	1	no	—
368	C₂²⋊C₈	—	7	1	no	—
369	C₂²⋊C₈	—	7	1	no	—
370	C₂²⋊C₈	—	7	1	no	—
371	C₂²⋊C₈	—	14	1	no	—
372	C₂²⋊C₈	—	14	1	no	—
373	C₂²⋊C₈	—	14	1	no	—
374	C₂²⋊C₈	—	14	1	no	—
375	C₂²⋊C₈	—	14	1	no	—
376	C₂²⋊C₈	—	14	1	no	—
377	C₂²⋊C₈	C₄×D₇	1	1	yes	characteristic
378	C₂²⋊C₈	C₄×D₇	1	1	yes	characteristic
379	#97	—	2	1	no	—
380	#97	—	14	1	no	—
381	#97	—	14	1	no	—
382	#97	—	14	1	no	—
383	C₄×C₈	—	2	1	no	—
384	C₄×C₈	—	7	1	no	—
385	C₄×C₈	—	7	1	no	—
386	C₄×C₈	—	7	1	no	—
387	C₄×C₈	—	7	1	no	—
388	C₄×C₈	—	7	1	no	—
389	C₄×C₈	—	7	1	no	—
390	C₄×C₈	—	7	1	no	—
391	C₄×C₈	—	7	1	no	—
392	C₄×C₈	—	14	1	no	—
393	C₄×C₈	—	14	1	no	—
394	C₄×C₈	—	14	1	no	—
395	C₄×C₈	C₂²×D₇	1	1	yes	characteristic
396	C₄×C₈	C₂²×D₇	1	1	yes	characteristic
397	C₂²×C₇	—	2	1	no	—
398	C₂²×C₇	—	2	1	no	—
399	C₂²×C₇	—	2	1	no	—
400	C₂²×C₇	C₂²×C₄⋊C₄	1	1	yes	characteristic
401	C₂×D₇	—	2	1	no	—
402	C₂×D₇	—	2	1	no	—
403	C₂×D₇	—	2	1	no	—
404	C₂×D₇	—	2	1	no	—
405	C₂×D₇	—	2	1	no	—
406	C₂×D₇	#427	1	2	yes	—
407	C₄×C₇	—	2	1	no	—
408	C₄×C₇	—	2	1	no	—
409	C₄×C₇	—	2	1	no	—
410	C₄×C₇	—	2	1	no	—
411	C₄×C₇	C₂×#131	1	1	yes	characteristic
412	C₄×C₇	#568	1	1	yes	characteristic
413	C₄×C₇	C₂×#135	1	1	yes	characteristic
414	C₄×C₇	C₂×#135	1	1	yes	characteristic
415	Dic₇	—	2	1	no	—
416	Dic₇	—	2	1	no	—
417	Dic₇	—	2	1	no	—
418	Dic₇	—	2	1	no	—
419	Dic₇	—	2	1	no	—
420	Dic₇	#427	1	2	yes	—
421	#41	—	14	2	no	—
422	#41	—	14	2	no	—
423	C₂×Q₈	—	7	1	no	—
424	C₂×D₄	—	7	1	no	—
425	C₂×D₄	—	7	1	no	—
426	C₂×D₄	—	7	1	no	—
427	C₂²×C₄	—	7	1	no	—
428	C₂²×C₄	—	7	1	no	—
429	C₂²×C₄	—	7	1	no	—
430	C₂²×C₄	—	7	1	no	—
431	C₂²×C₄	—	7	1	no	—
432	C₂²×C₄	—	7	1	no	—
433	C₂²×C₄	C₂×C₄×D₇	1	1	yes	characteristic
434	C₂²×C₄	D₄×D₇	1	1	yes	characteristic
435	C₂²×C₄	Q₈×D₇	1	1	yes	characteristic
436	M₁₆	—	28	2	no	—
437	M₁₆	—	28	2	no	—
438	C₂×C₈	—	2	1	no	—
439	C₂×C₈	—	2	1	no	—
440	C₂×C₈	—	2	1	no	—
441	C₂×C₈	—	2	1	no	—
442	C₂×C₈	—	7	1	no	—
443	C₂×C₈	—	7	1	no	—
444	C₂×C₈	—	7	1	no	—
445	C₂×C₈	—	7	1	no	—
446	C₂×C₈	—	14	2	no	—
447	C₂×C₈	—	14	2	no	—
448	C₂×C₈	—	14	2	no	—
449	C₂×C₈	—	14	1	no	—
450	C₂×C₈	—	14	1	no	—
451	C₂×C₈	—	14	1	no	—
452	C₂×C₈	—	14	1	no	—
453	C₂×C₈	—	28	1	no	—
454	C₂×C₈	—	28	1	no	—
455	C₂×C₈	—	28	2	no	—
456	C₂×C₈	—	28	2	no	—
457	C₂×C₈	—	28	1	no	—
458	C₂×C₈	C₂×C₄×D₇	1	1	yes	characteristic
459	C₂×C₈	C₂×C₄×D₇	1	1	yes	characteristic
460	C₂×C₈	C₂×C₄×D₇	1	1	yes	characteristic
461	C₂×C₈	C₂×C₄×D₇	1	1	yes	characteristic
462	C₄⋊C₄	—	7	1	no	—
463	C₄⋊C₄	—	7	1	no	—
464	C₄⋊C₄	—	7	1	no	—
465	C₄⋊C₄	—	7	1	no	—
466	C₄⋊C₄	—	7	1	no	—
467	C₄⋊C₄	—	7	1	no	—
468	C₂²⋊C₄	—	7	1	no	—
469	C₂²⋊C₄	—	7	1	no	—
470	C₂²⋊C₄	—	7	1	no	—
471	C₂²⋊C₄	—	7	1	no	—
472	C₂²⋊C₄	—	7	1	no	—
473	C₂²⋊C₄	—	7	1	no	—
474	C₄²	—	7	1	no	—
475	C₄²	—	7	1	no	—
476	C₄²	—	7	1	no	—
477	C₄²	—	7	1	no	—
478	C₄²	—	7	1	no	—
479	C₄²	—	7	1	no	—
480	C₄²	C₂×C₄×D₇	1	1	yes	characteristic
481	C₄²	D₄×D₇	1	1	yes	characteristic
482	C₄²	Q₈×D₇	1	1	yes	characteristic
483	C₄²	C₂³×D₇	1	1	yes	characteristic
484	C₂×C₇	—	4	1	no	—
485	C₂×C₇	#2906	1	1	yes	characteristic
486	C₂×C₇	C₂×#427	1	1	yes	characteristic
487	C₂×C₇	#2916	1	1	yes	characteristic
488	D₇	—	2	2	no	—
489	D₇	—	4	1	no	—
490	C₂³	—	7	1	no	—
491	C₂³	—	7	1	no	—
492	C₂³	D₇×C₄⋊C₄	1	1	yes	characteristic
493	Q₈	—	14	2	no	—
494	D₄	—	14	2	no	—
495	D₄	—	14	2	no	—
496	D₄	—	14	2	no	—
497	C₂×C₄	—	2	1	no	—
498	C₂×C₄	—	2	1	no	—
499	C₂×C₄	—	2	1	no	—
500	C₂×C₄	—	2	1	no	—
501	C₂×C₄	—	4	1	no	—
502	C₂×C₄	—	7	1	no	—
503	C₂×C₄	—	7	2	no	—
504	C₂×C₄	—	7	2	no	—
505	C₂×C₄	—	7	1	no	—
506	C₂×C₄	—	7	1	no	—
507	C₂×C₄	—	7	1	no	—
508	C₂×C₄	—	7	1	no	—
509	C₂×C₄	—	7	1	no	—
510	C₂×C₄	—	14	1	no	—
511	C₂×C₄	—	14	1	no	—
512	C₂×C₄	—	14	1	no	—
513	C₂×C₄	—	14	1	no	—
514	C₂×C₄	—	14	1	no	—
515	C₂×C₄	—	14	1	no	—
516	C₂×C₄	—	28	1	no	—
517	C₂×C₄	—	28	1	no	—
518	C₂×C₄	D₇×C₄⋊C₄	1	1	yes	characteristic
519	C₂×C₄	D₇×C₄⋊C₄	1	1	yes	characteristic
520	C₂×C₄	D₇×C₄⋊C₄	1	1	yes	characteristic
521	C₂×C₄	C₂²×C₄×D₇	1	1	yes	characteristic
522	C₂×C₄	C₂×D₄×D₇	1	1	yes	characteristic
523	C₂×C₄	C₂×Q₈×D₇	1	1	yes	characteristic
524	C₈	—	2	1	no	—
525	C₈	—	2	1	no	—
526	C₈	—	2	1	no	—
527	C₈	—	2	1	no	—
528	C₈	—	4	1	no	—
529	C₈	—	4	1	no	—
530	C₈	—	4	1	no	—
531	C₈	—	4	1	no	—
532	C₈	—	7	2	no	—
533	C₈	—	14	1	no	—
534	C₈	—	14	1	no	—
535	C₈	—	14	1	no	—
536	C₈	—	28	1	no	—
537	C₈	—	28	1	no	—
538	C₈	—	28	1	no	—
539	C₈	—	28	1	no	—
540	C₇	#17827	1	1	yes	characteristic, complemented, Sylow
541	C₂²	—	2	1	no	—
542	C₂²	—	2	1	no	—
543	C₂²	—	2	1	no	—
544	C₂²	—	7	2	no	—
545	C₂²	—	14	1	no	—
546	C₂²	—	14	1	no	—
547	C₂²	—	14	1	no	—
548	C₂²	—	14	1	no	—
549	C₂²	—	14	1	no	—
550	C₂²	C₂×D₇×C₄⋊C₄	1	1	yes	characteristic
551	C₄	—	2	1	no	—
552	C₄	—	2	1	no	—
553	C₄	—	2	1	no	—
554	C₄	—	2	1	no	—
555	C₄	—	7	2	no	—
556	C₄	—	14	1	no	—
557	C₄	—	14	1	no	—
558	C₄	—	14	1	no	—
559	C₄	—	14	1	no	—
560	C₄	—	14	1	no	—
561	C₄	D₇×#131	1	1	yes	characteristic
562	C₄	#90441	1	1	yes	characteristic
563	C₄	D₇×#135	1	1	yes	characteristic
564	C₄	D₇×#135	1	1	yes	characteristic
565	C₂	—	4	1	no	—
566	C₂	—	14	2	no	—
567	C₂	—	28	1	no	—
568	C₂	#11736526	1	1	yes	characteristic
569	C₂	D₇×#427	1	1	yes	characteristic
570	C₂	#11736705	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	C₂²×C₄⋊C₄
prime radical	C₂×#1157	D₄
cosocle	C₄²×C₇	C₂⁴
hypercenter	#1572	D₇
hypocenter	C₇	#17827
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
4. C₇×#1572	C₂	semidirect
5. #11728548	C₂	semidirect
6. #11728505	C₂	semidirect
7. #11728499	C₂	semidirect
8. #11726326	C₂	semidirect
9. #11726326	C₂	semidirect
10. #11726324	C₂	semidirect
11. #11726321	C₂	semidirect
12. #11726287	C₂	semidirect
13. #11726287	C₂	semidirect
14. #11726283	C₂	semidirect
15. D₇×#334	C₂	semidirect
149. #1572	D₇	semidirect
540. C₇	#17827	semidirect

Maximal subgroups

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

subgroup	index
#11736779	2
#11736730	2
#11736721	2
C₇×#1572	2
#11728548	2
#11728505	2
#11728499	2
#11726326	2
#11726324	2
#11726321	2
#11726287	2
#11726283	2
D₇×#334	2
#17827	7