Subgroups — #13362017

Order 1792.

718 conjugacy classes of subgroups.

The subgroup lattice has 600 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×#6461	C₂	1	1	yes	maximal, characteristic
2	C₇×#1916	C₂	1	1	yes	maximal, characteristic, complemented
3	#11728221	C₂	1	1	yes	maximal, characteristic, complemented
4	#11728204	C₂	1	1	yes	maximal, characteristic
5	#11727539	C₂	1	1	yes	maximal, characteristic
6	C₄×#6389	C₂	1	1	yes	maximal, characteristic, complemented
7	#11727232	C₂	1	1	yes	maximal, characteristic, complemented
8	#11726406	C₂	1	1	yes	maximal, characteristic, complemented
9	#11726402	C₂	1	1	yes	maximal, characteristic
10	#11726402	C₂	1	1	yes	maximal, characteristic
11	#11726401	C₂	1	1	yes	maximal, characteristic
12	#11726370	C₂	1	1	yes	maximal, characteristic
13	#11726368	C₂	1	1	yes	maximal, characteristic, complemented
14	#11726366	C₂	1	1	yes	maximal, characteristic, complemented
15	#11726361	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×C₈×D₇	C₂²	1	1	yes	characteristic
17	C₂×#6461	C₄	1	1	yes	characteristic
18	C₂×C₇×C₄⋊C₈	C₂²	1	1	yes	characteristic
19	C₂×C₄×C₇×C₈	C₂²	1	1	yes	characteristic
20	C₄×C₇×C₄⋊C₄	C₂²	1	1	yes	characteristic
21	C₂×(C₂×D₇)⋊C₈	C₂²	1	1	yes	characteristic
22	C₂×(C₂×D₇)⋊C₈	C₂²	1	1	yes	characteristic
23	C₂×(C₂×D₇)⋊C₈	C₂²	1	1	yes	characteristic
24	C₂×#6389	C₂²	1	1	yes	characteristic
25	C₂×#6389	C₂²	1	1	yes	characteristic
26	C₂×#6389	C₂²	1	1	yes	characteristic
27	C₂×#6389	C₂²	1	1	yes	characteristic
28	C₂×Dic₇⋊C₈	C₂²	1	1	yes	characteristic
29	C₂×C₈×Dic₇	C₂²	1	1	yes	characteristic
30	#89762	C₄	1	1	yes	characteristic
31	#89753	C₄	1	1	yes	characteristic
32	#89750	C₄	1	1	yes	characteristic
33	C₄×(C₂×D₇)⋊C₄	C₂²	1	1	yes	characteristic
34	C₄×(C₂×D₇)⋊C₄	C₂²	1	1	yes	characteristic
35	C₄×(C₂×D₇)⋊C₄	C₂²	1	1	yes	characteristic
36	C₄×C₄⋊Dic₇	C₂²	1	1	yes	characteristic
37	C₄×Dic₇⋊C₄	C₂²	1	1	yes	characteristic
38	C₄²×Dic₇	C₂²	1	1	yes	characteristic
39	C₂×C₄⋊(C₇⋊C₈)	C₂²	1	1	yes	characteristic
40	C₂×#6377	C₂²	1	1	yes	characteristic
41	C₂×#6377	C₂²	1	1	yes	characteristic
42	C₂×C₄×C₇⋊C₈	C₂²	1	1	yes	characteristic
43	#89442	C₄	1	1	yes	characteristic
44	#89441	C₄	1	1	yes	characteristic
45	#89426	C₄	1	1	yes	characteristic
46	#89423	C₄	1	1	yes	characteristic
47	C₇×#336	C₂²	1	1	yes	characteristic
48	C₇×#336	C₂²	1	1	yes	characteristic
49	C₇×#336	C₂²	1	1	yes	characteristic
50	C₇×#336	C₂²	1	1	yes	characteristic
51	#89345	C₂²	1	1	yes	characteristic
52	#89345	C₂²	1	1	yes	characteristic
53	#89345	C₂²	1	1	yes	characteristic
54	#89345	C₂²	1	1	yes	characteristic
55	#89345	C₂²	1	1	yes	characteristic
56	#89345	C₂²	1	1	yes	characteristic
57	#89319	C₂²	1	1	yes	characteristic
58	#89319	C₂²	1	1	yes	characteristic
59	#21665	—	7	1	no	maximal, Sylow
60	C₂²×C₄×D₇	C₂³	1	1	yes	characteristic
61	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
62	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
63	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
64	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
65	C₂×C₇×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
66	C₂×C₇×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
67	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
68	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
69	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
70	C₂×(C₂×D₇)⋊C₄	C₂×C₄	1	1	yes	characteristic
71	C₂×(C₂×D₇)⋊C₄	C₂×C₄	1	1	yes	characteristic
72	C₂×(C₂×D₇)⋊C₄	C₂×C₄	1	1	yes	characteristic
73	C₂×(C₂×D₇)⋊C₄	C₂×C₄	1	1	yes	characteristic
74	C₂×(C₂×D₇)⋊C₄	C₂×C₄	1	1	yes	characteristic
75	C₂×(C₂×D₇)⋊C₄	C₂×C₄	1	1	yes	characteristic
76	C₂×C₄⋊Dic₇	C₂×C₄	1	1	yes	characteristic
77	C₂×C₄⋊Dic₇	C₂×C₄	1	1	yes	characteristic
78	C₂×Dic₇⋊C₄	C₂×C₄	1	1	yes	characteristic
79	C₂×Dic₇⋊C₄	C₂×C₄	1	1	yes	characteristic
80	C₂×C₄×Dic₇	C₂×C₄	1	1	yes	characteristic
81	C₂×C₄×Dic₇	C₂×C₄	1	1	yes	characteristic
82	C₂×C₄×Dic₇	C₂×C₄	1	1	yes	characteristic
83	C₂×C₄×Dic₇	C₂×C₄	1	1	yes	characteristic
84	C₂×C₄×Dic₇	C₂³	1	1	yes	characteristic
85	C₂×C₄×Dic₇	C₂³	1	1	yes	characteristic
86	C₂×C₄×Dic₇	C₂³	1	1	yes	characteristic
87	C₂²×C₇⋊C₈	C₂³	1	1	yes	characteristic
88	C₂²×C₇⋊C₈	C₂³	1	1	yes	characteristic
89	C₂²×C₇⋊C₈	C₂³	1	1	yes	characteristic
90	C₂²×C₇⋊C₈	C₂³	1	1	yes	characteristic
91	C₂×C₈×D₇	—	2	2	no	—
92	C₂×C₈×D₇	—	2	2	no	—
93	C₂×C₈×D₇	—	2	2	no	—
94	#6461	—	2	4	no	—
95	C₇×C₄⋊C₈	—	2	2	no	—
96	C₄×C₇×C₈	—	2	2	no	—
97	C₇×#95	C₂×C₄	1	1	yes	characteristic
98	C₇×#95	C₂×C₄	1	1	yes	characteristic
99	C₇⋊#95	C₂×C₄	1	1	yes	characteristic
100	C₇⋊#95	C₂×C₄	1	1	yes	characteristic
101	C₇⋊#95	C₂×C₄	1	1	yes	characteristic
102	C₇⋊#95	C₂×C₄	1	1	yes	characteristic
103	C₇⋊#95	C₂×C₄	1	1	yes	characteristic
104	C₇⋊#95	C₂×C₄	1	1	yes	characteristic
105	C₇⋊#95	C₂×C₄	1	1	yes	characteristic
106	C₇⋊#95	C₂×C₄	1	1	yes	characteristic
107	C₇⋊#95	C₂×C₄	1	1	yes	characteristic
108	C₇⋊#95	C₂×C₄	1	1	yes	characteristic
109	(C₂×D₇)⋊C₈	—	2	2	no	—
110	(C₂×D₇)⋊C₈	—	2	2	no	—
111	(C₂×D₇)⋊C₈	—	2	2	no	—
112	#6389	—	2	2	no	—
113	#6389	—	2	2	no	—
114	#6389	—	2	2	no	—
115	#6389	—	2	2	no	—
116	Dic₇⋊C₈	—	2	2	no	—
117	C₈×Dic₇	—	2	2	no	—
118	C₄⋊(C₇⋊C₈)	—	2	2	no	—
119	#6377	—	2	2	no	—
120	#6377	—	2	2	no	—
121	C₄×C₇⋊C₈	—	2	2	no	—
122	C₄×#126	—	7	1	no	—
123	#1924	—	7	1	no	—
124	#1924	—	7	1	no	—
125	#1923	—	7	1	no	—
126	#1917	—	7	1	no	—
127	#1917	—	7	1	no	—
128	#1916	D₇	1	1	yes	characteristic, complemented
129	#1839	—	7	1	no	—
130	#1771	—	7	1	no	—
131	#1771	—	7	1	no	—
132	#1770	—	7	1	no	—
133	#1752	—	7	1	no	—
134	#1752	—	7	1	no	—
135	C₈×C₂²⋊C₄	—	7	1	no	—
136	C₄×#97	—	7	1	no	—
137	C₂³×D₇	C₂²×C₄	1	1	yes	characteristic
138	C₂²×C₄×C₇	C₂²×C₄	1	1	yes	characteristic
139	C₂²×C₄×C₇	C₂²×C₄	1	1	yes	characteristic
140	C₂²×C₄×C₇	C₂²×C₄	1	1	yes	characteristic
141	C₂²×C₄×C₇	C₂²×C₄	1	1	yes	characteristic
142	C₂²×C₄×C₇	C₂²×C₄	1	1	yes	characteristic
143	C₂²×C₄×C₇	C₂²×C₄	1	1	yes	characteristic
144	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
145	C₂²×Dic₇	C₂²×C₄	1	1	yes	characteristic
146	C₂²×Dic₇	C₂²×C₄	1	1	yes	characteristic
147	C₂²×Dic₇	C₂²×C₄	1	1	yes	characteristic
148	C₂²×Dic₇	C₂²×C₄	1	1	yes	characteristic
149	C₂²×Dic₇	C₂²×C₄	1	1	yes	characteristic
150	C₂²×Dic₇	C₂²×C₄	1	1	yes	characteristic
151	C₂²×Dic₇	C₂²×C₄	1	1	yes	characteristic
152	C₂×C₄×D₇	—	2	1	no	—
153	C₂×C₄×D₇	—	2	1	no	—
154	C₂×C₄×D₇	—	2	1	no	—
155	C₂×C₄×D₇	—	2	1	no	—
156	C₂×C₄×D₇	—	2	1	no	—
157	C₂×C₄×D₇	—	2	1	no	—
158	C₂×C₇×C₈	—	2	1	no	—
159	C₂×C₇×C₈	—	2	1	no	—
160	C₂×C₇×C₈	—	2	1	no	—
161	C₂×C₇×C₈	—	2	1	no	—
162	C₂×C₇×C₈	—	2	1	no	—
163	C₂×C₇×C₈	—	2	1	no	—
164	C₂×C₇×C₈	—	2	1	no	—
165	C₂×C₇×C₈	—	2	1	no	—
166	C₂×C₇×C₈	—	2	1	no	—
167	C₂×C₇×C₈	—	2	1	no	—
168	C₂×C₇×C₈	#41	1	2	yes	—
169	C₂×C₇×C₈	#41	1	2	yes	—
170	C₇×C₄⋊C₄	—	2	2	no	—
171	C₇×C₄⋊C₄	—	2	2	no	—
172	C₄²×C₇	—	2	1	no	—
173	C₄²×C₇	—	2	1	no	—
174	C₄²×C₇	—	2	1	no	—
175	C₄²×C₇	—	2	1	no	—
176	C₄²×C₇	—	2	1	no	—
177	C₄²×C₇	—	2	1	no	—
178	(C₂×D₇)⋊C₄	—	2	2	no	—
179	(C₂×D₇)⋊C₄	—	2	2	no	—
180	(C₂×D₇)⋊C₄	—	2	2	no	—
181	(C₂×D₇)⋊C₄	—	4	1	no	—
182	(C₂×D₇)⋊C₄	—	4	1	no	—
183	(C₂×D₇)⋊C₄	M₁₆	1	4	yes	—
184	C₄⋊Dic₇	—	2	2	no	—
185	C₄⋊Dic₇	—	4	1	no	—
186	Dic₇⋊C₄	—	2	2	no	—
187	Dic₇⋊C₄	—	4	1	no	—
188	C₄×Dic₇	—	2	2	no	—
189	C₄×Dic₇	—	2	2	no	—
190	C₄×Dic₇	—	2	1	no	—
191	C₄×Dic₇	—	2	1	no	—
192	C₄×Dic₇	—	2	1	no	—
193	C₄×Dic₇	—	2	1	no	—
194	C₄×Dic₇	—	2	1	no	—
195	C₄×Dic₇	—	2	1	no	—
196	C₄×Dic₇	—	4	1	no	—
197	C₄×Dic₇	—	4	1	no	—
198	C₂×C₇⋊C₈	—	2	1	no	—
199	C₂×C₇⋊C₈	—	2	1	no	—
200	C₂×C₇⋊C₈	—	2	1	no	—
201	C₂×C₇⋊C₈	—	2	1	no	—
202	C₂×C₇⋊C₈	—	2	1	no	—
203	C₂×C₇⋊C₈	—	2	1	no	—
204	C₂×C₇⋊C₈	—	2	1	no	—
205	C₂×C₇⋊C₈	—	2	1	no	—
206	C₂×C₇⋊C₈	#41	1	2	yes	—
207	C₂×C₇⋊C₈	#41	1	2	yes	—
208	C₂×C₇⋊C₈	#41	1	2	yes	—
209	C₂×C₇⋊C₈	#41	1	2	yes	—
210	C₈×D₇	—	4	4	no	—
211	C₂³×C₈	—	7	1	no	—
212	C₂×#126	—	7	1	no	—
213	C₂×C₄⋊C₈	—	7	1	no	—
214	C₂×C₄⋊C₈	—	7	1	no	—
215	C₂×C₄⋊C₈	C₂×D₇	1	1	yes	characteristic
216	C₂×C₂²⋊C₈	—	7	1	no	—
217	C₂×C₂²⋊C₈	—	7	1	no	—
218	C₂×C₂²⋊C₈	—	7	1	no	—
219	C₂×#97	—	7	1	no	—
220	C₂×#97	—	7	1	no	—
221	C₂×#97	—	7	1	no	—
222	C₂×#97	—	7	1	no	—
223	C₂×#97	—	7	1	no	—
224	C₂×#97	—	7	1	no	—
225	C₂×C₄×C₈	—	7	1	no	—
226	C₂×C₄×C₈	—	7	1	no	—
227	C₂×C₄×C₈	C₂×D₇	1	1	yes	characteristic
228	#388	—	7	1	no	—
229	#388	—	7	1	no	—
230	#388	—	7	1	no	—
231	#387	—	7	1	no	—
232	#387	—	7	1	no	—
233	#387	—	7	1	no	—
234	#383	—	7	1	no	—
235	C₄×C₄⋊C₄	—	7	1	no	—
236	C₄×C₄⋊C₄	—	7	1	no	—
237	C₄×C₄⋊C₄	C₂×D₇	1	1	yes	characteristic
238	C₄×C₂²⋊C₄	—	7	1	no	—
239	C₄×C₂²⋊C₄	—	7	1	no	—
240	C₄×C₂²⋊C₄	—	7	1	no	—
241	C₄³	—	7	1	no	—
242	#336	—	7	1	no	—
243	#336	—	7	1	no	—
244	#336	—	7	1	no	—
245	#336	—	7	1	no	—
246	#336	—	7	1	no	—
247	#336	—	7	1	no	—
248	#336	—	7	1	no	—
249	#336	—	7	1	no	—
250	#336	C₂×D₇	1	1	yes	characteristic
251	#336	C₂×D₇	1	1	yes	characteristic
252	#336	C₂×D₇	1	1	yes	characteristic
253	#336	C₂×D₇	1	1	yes	characteristic
254	C₂³×C₇	C₂³×C₄	1	1	yes	characteristic
255	C₂²×D₇	—	2	1	no	—
256	C₂²×D₇	—	2	1	no	—
257	C₂²×D₇	—	2	1	no	—
258	C₂²×D₇	—	2	1	no	—
259	C₂²×D₇	—	2	1	no	—
260	C₂²×D₇	—	2	1	no	—
261	C₂²×D₇	C₂×M₁₆	1	2	yes	—
262	C₂×C₄×C₇	—	2	1	no	—
263	C₂×C₄×C₇	—	2	1	no	—
264	C₂×C₄×C₇	—	2	1	no	—
265	C₂×C₄×C₇	—	2	1	no	—
266	C₂×C₄×C₇	—	2	1	no	—
267	C₂×C₄×C₇	—	2	1	no	—
268	C₂×C₄×C₇	—	2	1	no	—
269	C₂×C₄×C₇	—	2	1	no	—
270	C₂×C₄×C₇	—	2	1	no	—
271	C₂×C₄×C₇	—	2	1	no	—
272	C₂×C₄×C₇	—	2	1	no	—
273	C₂×C₄×C₇	—	2	1	no	—
274	C₂×C₄×C₇	—	2	1	no	—
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	C₂×M₁₆	1	2	yes	—
279	C₂×C₄×C₇	#131	1	2	yes	—
280	C₂×C₄×C₇	C₂×#41	1	1	yes	characteristic
281	C₂×C₄×C₇	C₂×#41	1	1	yes	characteristic
282	C₂×C₄×C₇	C₂×#41	1	1	yes	characteristic
283	C₂×C₄×C₇	C₂×#41	1	1	yes	characteristic
284	C₂×C₄×C₇	C₂×#41	1	1	yes	characteristic
285	C₂×C₄×C₇	C₂×#41	1	1	yes	characteristic
286	C₂×Dic₇	—	2	1	no	—
287	C₂×Dic₇	—	2	1	no	—
288	C₂×Dic₇	—	2	1	no	—
289	C₂×Dic₇	—	2	1	no	—
290	C₂×Dic₇	—	2	1	no	—
291	C₂×Dic₇	—	2	1	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	C₂×Dic₇	—	2	1	no	—
299	C₂×Dic₇	—	2	1	no	—
300	C₂×Dic₇	—	2	1	no	—
301	C₂×Dic₇	—	2	1	no	—
302	C₂×Dic₇	—	2	1	no	—
303	C₂×Dic₇	—	2	1	no	—
304	C₂×Dic₇	—	2	1	no	—
305	C₂×Dic₇	—	2	1	no	—
306	C₂×Dic₇	C₂×M₁₆	1	2	yes	—
307	C₄×D₇	—	4	1	no	—
308	C₄×D₇	—	4	1	no	—
309	C₄×D₇	—	4	1	no	—
310	C₄×D₇	—	4	1	no	—
311	C₇×C₈	—	2	2	no	—
312	C₇×C₈	—	2	2	no	—
313	C₇×C₈	—	4	1	no	—
314	C₇×C₈	—	4	1	no	—
315	C₇⋊C₈	—	2	2	no	—
316	C₇⋊C₈	—	4	1	no	—
317	C₇⋊C₈	—	4	1	no	—
318	C₇⋊C₈	#126	1	4	yes	complemented
319	C₂³×C₄	—	7	1	no	—
320	C₂²×C₈	—	7	1	no	—
321	C₂²×C₈	—	7	1	no	—
322	C₂²×C₈	—	7	1	no	—
323	C₂²×C₈	—	7	1	no	—
324	C₂²×C₈	—	14	2	no	—
325	C₂²×C₈	—	14	2	no	—
326	C₂²×C₈	—	14	2	no	—
327	C₂²×C₈	C₂²×D₇	1	1	yes	characteristic
328	C₂²×C₈	C₂²×D₇	1	1	yes	characteristic
329	C₂²×C₈	C₂²×D₇	1	1	yes	characteristic
330	C₂²×C₈	C₂²×D₇	1	1	yes	characteristic
331	#126	—	14	4	no	—
332	C₂×C₄⋊C₄	—	7	1	no	—
333	C₂×C₄⋊C₄	—	7	1	no	—
334	C₂×C₄⋊C₄	—	7	1	no	—
335	C₂×C₄⋊C₄	—	7	1	no	—
336	C₂×C₄⋊C₄	C₄×D₇	1	1	yes	characteristic
337	C₂×C₄⋊C₄	C₄×D₇	1	1	yes	characteristic
338	C₂×C₂²⋊C₄	—	7	1	no	—
339	C₂×C₂²⋊C₄	—	7	1	no	—
340	C₂×C₂²⋊C₄	—	7	1	no	—
341	C₂×C₂²⋊C₄	—	7	1	no	—
342	C₂×C₂²⋊C₄	—	7	1	no	—
343	C₂×C₂²⋊C₄	—	7	1	no	—
344	C₂×C₄²	—	7	1	no	—
345	C₂×C₄²	—	7	1	no	—
346	C₂×C₄²	—	7	1	no	—
347	C₂×C₄²	—	7	1	no	—
348	C₂×C₄²	—	7	1	no	—
349	C₂×C₄²	—	7	1	no	—
350	C₂×C₄²	—	7	1	no	—
351	C₂×C₄²	C₂²×D₇	1	1	yes	characteristic
352	C₂×C₄²	C₂²×D₇	1	1	yes	characteristic
353	C₂×C₄²	C₂²×D₇	1	1	yes	characteristic
354	C₄⋊C₈	—	2	2	no	—
355	C₄⋊C₈	—	14	2	no	—
356	C₄⋊C₈	—	14	2	no	—
357	C₂²⋊C₈	—	14	2	no	—
358	C₂²⋊C₈	—	14	2	no	—
359	C₂²⋊C₈	—	14	2	no	—
360	#97	—	14	2	no	—
361	#97	—	14	2	no	—
362	#97	—	14	2	no	—
363	#97	—	14	2	no	—
364	#97	—	14	2	no	—
365	#97	—	14	2	no	—
366	C₄×C₈	—	2	2	no	—
367	C₄×C₈	—	14	2	no	—
368	C₄×C₈	—	14	2	no	—
369	#95	—	7	1	no	—
370	#95	—	7	1	no	—
371	#95	—	7	1	no	—
372	#95	—	7	1	no	—
373	#95	—	7	1	no	—
374	#95	—	7	1	no	—
375	#95	—	7	1	no	—
376	#95	—	7	1	no	—
377	#95	—	7	1	no	—
378	#95	—	7	1	no	—
379	#95	C₄×D₇	1	1	yes	characteristic
380	#95	C₄×D₇	1	1	yes	characteristic
381	C₂²×C₇	C₄×#41	1	1	yes	characteristic
382	C₂²×C₇	C₄×#41	1	1	yes	characteristic
383	C₂²×C₇	C₄×#41	1	1	yes	characteristic
384	C₂²×C₇	C₂²×M₁₆	1	1	yes	characteristic
385	C₂²×C₇	C₂×#131	1	1	yes	characteristic
386	C₂²×C₇	#568	1	1	yes	characteristic
387	C₂²×C₇	#568	1	1	yes	characteristic
388	C₂×D₇	—	2	2	no	—
389	C₂×D₇	—	2	2	no	—
390	C₂×D₇	—	2	2	no	—
391	C₂×D₇	—	4	1	no	—
392	C₂×D₇	—	4	1	no	—
393	C₂×D₇	—	4	1	no	—
394	C₂×D₇	—	4	1	no	—
395	C₄×C₇	—	2	2	no	—
396	C₄×C₇	—	2	2	no	—
397	C₄×C₇	—	4	1	no	—
398	C₄×C₇	—	4	1	no	—
399	C₄×C₇	—	4	1	no	—
400	C₄×C₇	—	4	1	no	—
401	C₄×C₇	C₂×#126	1	1	yes	characteristic
402	C₄×C₇	#529	1	1	yes	characteristic
403	C₄×C₇	#529	1	1	yes	characteristic
404	C₄×C₇	#529	1	1	yes	characteristic
405	Dic₇	—	2	2	no	—
406	Dic₇	—	4	1	no	—
407	Dic₇	—	4	1	no	—
408	Dic₇	—	4	1	no	—
409	Dic₇	—	4	1	no	—
410	Dic₇	—	4	1	no	—
411	Dic₇	—	4	1	no	—
412	C₂⁴	—	7	1	no	—
413	C₂²×C₄	—	7	1	no	—
414	C₂²×C₄	—	7	1	no	—
415	C₂²×C₄	—	7	1	no	—
416	C₂²×C₄	—	7	1	no	—
417	C₂²×C₄	—	7	1	no	—
418	C₂²×C₄	—	7	1	no	—
419	C₂²×C₄	—	7	1	no	—
420	C₂²×C₄	—	14	1	no	—
421	C₂²×C₄	—	14	1	no	—
422	C₂²×C₄	—	14	1	no	—
423	C₂²×C₄	—	14	1	no	—
424	C₂²×C₄	—	14	1	no	—
425	C₂²×C₄	—	14	1	no	—
426	C₂²×C₄	C₂×C₄×D₇	1	1	yes	characteristic
427	C₂²×C₄	C₂×C₄×D₇	1	1	yes	characteristic
428	C₂²×C₄	C₂×C₄×D₇	1	1	yes	characteristic
429	C₂²×C₄	C₂×C₄×D₇	1	1	yes	characteristic
430	C₂²×C₄	C₂×C₄×D₇	1	1	yes	characteristic
431	C₂²×C₄	C₂×C₄×D₇	1	1	yes	characteristic
432	C₂²×C₄	C₂³×D₇	1	1	yes	characteristic
433	C₂×C₈	—	2	1	no	—
434	C₂×C₈	—	2	1	no	—
435	C₂×C₈	—	2	1	no	—
436	C₂×C₈	—	2	1	no	—
437	C₂×C₈	—	2	1	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	—	2	1	no	—
443	C₂×C₈	—	7	2	no	—
444	C₂×C₈	—	7	2	no	—
445	C₂×C₈	—	7	2	no	—
446	C₂×C₈	—	7	2	no	—
447	C₂×C₈	—	14	1	no	—
448	C₂×C₈	—	14	1	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	—	14	1	no	—
454	C₂×C₈	—	14	1	no	—
455	C₂×C₈	—	28	4	no	—
456	C₂×C₈	#1159	1	2	yes	—
457	C₂×C₈	#1161	1	2	yes	—
458	C₄⋊C₄	—	2	2	no	—
459	C₄⋊C₄	—	2	2	no	—
460	C₄⋊C₄	—	14	2	no	—
461	C₄⋊C₄	—	14	2	no	—
462	C₄⋊C₄	—	28	1	no	—
463	C₄⋊C₄	—	28	1	no	—
464	C₂²⋊C₄	—	7	4	no	—
465	C₂²⋊C₄	—	14	2	no	—
466	C₂²⋊C₄	—	14	2	no	—
467	C₂²⋊C₄	—	14	2	no	—
468	C₂²⋊C₄	—	28	1	no	—
469	C₂²⋊C₄	—	28	1	no	—
470	C₄²	—	2	1	no	—
471	C₄²	—	2	1	no	—
472	C₄²	—	2	1	no	—
473	C₄²	—	2	1	no	—
474	C₄²	—	2	1	no	—
475	C₄²	—	2	1	no	—
476	C₄²	—	14	2	no	—
477	C₄²	—	14	2	no	—
478	C₄²	—	14	1	no	—
479	C₄²	—	14	1	no	—
480	C₄²	—	14	1	no	—
481	C₄²	—	14	1	no	—
482	C₄²	—	14	1	no	—
483	C₄²	—	14	1	no	—
484	C₄²	—	28	1	no	—
485	C₄²	—	28	1	no	—
486	C₂×C₇	C₄×#126	1	1	yes	characteristic
487	C₂×C₇	#2965	1	1	yes	characteristic
488	C₂×C₇	#2967	1	1	yes	characteristic
489	C₂×C₇	#2968	1	1	yes	characteristic
490	C₂×C₇	#2969	1	1	yes	characteristic
491	C₂×C₇	#2970	1	1	yes	characteristic
492	C₂×C₇	#2970	1	1	yes	characteristic
493	D₇	—	4	2	no	—
494	C₂³	—	7	2	no	—
495	C₂³	—	14	1	no	—
496	C₂³	—	14	1	no	—
497	C₂³	—	14	1	no	—
498	C₂³	—	14	1	no	—
499	C₂³	—	14	1	no	—
500	C₂³	—	14	1	no	—
501	C₂³	C₂²×C₄×D₇	1	1	yes	characteristic
502	C₂×C₄	—	2	1	no	—
503	C₂×C₄	—	2	1	no	—
504	C₂×C₄	—	2	1	no	—
505	C₂×C₄	—	2	1	no	—
506	C₂×C₄	—	2	1	no	—
507	C₂×C₄	—	2	1	no	—
508	C₂×C₄	—	2	1	no	—
509	C₂×C₄	—	2	1	no	—
510	C₂×C₄	—	2	1	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	—	2	1	no	—
516	C₂×C₄	—	2	1	no	—
517	C₂×C₄	—	2	1	no	—
518	C₂×C₄	—	7	2	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	—	14	1	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	—	14	1	no	—
531	C₂×C₄	—	14	1	no	—
532	C₂×C₄	—	14	1	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	1	no	—
540	C₂×C₄	—	28	1	no	—
541	C₂×C₄	—	28	1	no	—
542	C₂×C₄	—	28	1	no	—
543	C₂×C₄	#6464	1	2	yes	—
544	C₂×C₄	D₇×M₁₆	1	2	yes	—
545	C₂×C₄	C₂×#1159	1	1	yes	characteristic
546	C₂×C₄	C₂×#1161	1	1	yes	characteristic
547	C₂×C₄	D₇×#41	1	1	yes	characteristic
548	C₂×C₄	D₇×#41	1	1	yes	characteristic
549	C₂×C₄	D₇×#41	1	1	yes	characteristic
550	C₂×C₄	D₇×#41	1	1	yes	characteristic
551	C₈	—	2	2	no	—
552	C₈	—	2	2	no	—
553	C₈	—	4	1	no	—
554	C₈	—	4	1	no	—
555	C₈	—	7	4	no	—
556	C₈	—	14	2	no	—
557	C₈	—	28	1	no	—
558	C₈	—	28	1	no	—
559	C₇	#21665	1	1	yes	characteristic, complemented, Sylow
560	C₂²	—	14	2	no	—
561	C₂²	—	14	2	no	—
562	C₂²	—	14	2	no	—
563	C₂²	—	28	1	no	—
564	C₂²	—	28	1	no	—
565	C₂²	—	28	1	no	—
566	C₂²	—	28	1	no	—
567	C₂²	#90213	1	1	yes	characteristic
568	C₂²	C₄×#1159	1	1	yes	characteristic
569	C₂²	C₄×#1161	1	1	yes	characteristic
570	C₂²	C₂×#6464	1	1	yes	characteristic
571	C₂²	C₂×D₇×M₁₆	1	1	yes	characteristic
572	C₂²	#90441	1	1	yes	characteristic
573	C₂²	#90441	1	1	yes	characteristic
574	C₄	—	2	2	no	—
575	C₄	—	2	2	no	—
576	C₄	—	4	1	no	—
577	C₄	—	4	1	no	—
578	C₄	—	4	1	no	—
579	C₄	—	4	1	no	—
580	C₄	—	14	2	no	—
581	C₄	—	28	1	no	—
582	C₄	—	28	1	no	—
583	C₄	—	28	1	no	—
584	C₄	—	28	1	no	—
585	C₄	—	28	1	no	—
586	C₄	—	28	1	no	—
587	C₄	#90315	1	1	yes	characteristic
588	C₄	#90340	1	1	yes	characteristic
589	C₄	#90382	1	1	yes	characteristic
590	C₄	D₇×#126	1	1	yes	characteristic
591	C₂	—	28	2	no	—
592	C₂	#11732387	1	1	yes	characteristic
593	C₂	#11736723	1	1	yes	characteristic
594	C₂	#11736812	1	1	yes	characteristic
595	C₂	#11736847	1	1	yes	characteristic
596	C₂	#11736905	1	1	yes	characteristic
597	C₂	#11737349	1	1	yes	characteristic
598	C₂	#11737388	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²×C₄	C₂³×D₇
commutator, socle	C₂³×C₇	C₂³×C₄
Fitting	C₇×#1916	C₂
prime radical	C₂³×D₇	C₂²×C₄
cosocle	C₂²×C₄×C₇	C₂⁴
hypercenter	#1916	D₇
hypocenter	C₇	#21665
LCS	G ▷ C₂³×C₇ ▷ C₇
UCS	C₁ ◁ C₂²×C₄ ◁ #1916

Complements

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

N	H ≅ G/N	type
2. C₇×#1916	C₂	semidirect
3. #11728221	C₂	semidirect
6. C₄×#6389	C₂	semidirect
7. #11727232	C₂	semidirect
8. #11726406	C₂	semidirect
13. #11726368	C₂	semidirect
14. #11726366	C₂	semidirect
15. #11726361	C₂	semidirect
128. #1916	D₇	semidirect
318. C₇⋊C₈	#126	semidirect
559. C₇	#21665	semidirect

Maximal subgroups

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

subgroup	index
C₄×#6461	2
C₇×#1916	2
#11728221	2
#11728204	2
#11727539	2
C₄×#6389	2
#11727232	2
#11726406	2
#11726402	2
#11726401	2
#11726370	2
#11726368	2
#11726366	2
#11726361	2
#21665	7