Subgroups — #13322845

Order 1792.

666 conjugacy classes of subgroups.

The subgroup lattice has 592 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#11736784	C₂	1	1	yes	maximal, characteristic
2	#11736495	C₂	1	1	yes	maximal, characteristic
3	C₄×#6470	C₂	1	1	yes	maximal, characteristic
4	C₇×#1569	C₂	1	1	yes	maximal, characteristic, complemented
5	#11728548	C₂	1	1	yes	maximal, characteristic, complemented
6	#11728245	C₂	1	1	yes	maximal, characteristic, complemented
7	#11727605	C₂	1	1	yes	maximal, characteristic, complemented
8	#11726325	C₂	1	1	yes	maximal, characteristic, complemented
9	#11726323	C₂	1	1	yes	maximal, characteristic, complemented
10	#11726322	C₂	1	1	yes	maximal, characteristic, complemented
11	D₇×#335	C₂	1	1	yes	maximal, characteristic, complemented
12	#11726285	C₂	1	1	yes	maximal, characteristic, complemented
13	#11726284	C₂	1	1	yes	maximal, characteristic, complemented
14	#11726282	C₂	1	1	yes	maximal, characteristic, complemented
15	#11726281	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×#6470	C₄	1	1	yes	characteristic
17	C₂×#6470	C₄	1	1	yes	characteristic
18	C₄×#1157	C₂²	1	1	yes	characteristic
19	C₇×#432	C₂²	1	1	yes	characteristic
20	C₇×#423	C₂²	1	1	yes	characteristic
21	C₄×C₇×M₁₆	C₂²	1	1	yes	characteristic
22	#89900	—	2	1	no	—
23	#89899	—	2	1	no	—
24	#89894	C₄	1	1	yes	characteristic
25	#89894	C₄	1	1	yes	characteristic
26	#89698	C₂²	1	1	yes	characteristic
27	#89696	C₂²	1	1	yes	characteristic
28	C₂×C₄×C₇⋊C₈	C₂²	1	1	yes	characteristic
29	#89609	C₂²	1	1	yes	characteristic
30	#89609	C₂²	1	1	yes	characteristic
31	#89608	—	2	1	no	—
32	#89607	C₂²	1	1	yes	characteristic
33	#89607	C₂²	1	1	yes	characteristic
34	#89605	C₂²	1	1	yes	characteristic
35	#89605	C₂²	1	1	yes	characteristic
36	D₇×C₄⋊C₈	C₂²	1	1	yes	characteristic
37	D₇×C₄⋊C₈	C₂²	1	1	yes	characteristic
38	#89600	—	2	1	no	—
39	#89501	—	2	1	no	—
40	#89500	—	2	1	no	—
41	#89480	C₄	1	1	yes	characteristic
42	#89480	C₄	1	1	yes	characteristic
43	#89480	C₄	1	1	yes	characteristic
44	#89480	C₄	1	1	yes	characteristic
45	#89478	—	2	1	no	—
46	#89473	—	2	1	no	—
47	C₄×#1131	C₂²	1	1	yes	characteristic
48	C₄×#1131	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	#89274	C₂²	1	1	yes	characteristic
58	#89274	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	#17799	—	7	1	no	maximal, Sylow
68	C₂×#1157	C₂×C₄	1	1	yes	characteristic
69	C₂×C₇×M₁₆	—	2	1	no	—
70	C₂×C₇×M₁₆	C₂×C₄	1	1	yes	characteristic
71	C₂×C₇×M₁₆	C₂×C₄	1	1	yes	characteristic
72	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
73	C₄×C₂²⋊D₇	D₄	1	1	yes	characteristic
74	C₄×C₂²⋊D₇	D₄	1	1	yes	characteristic
75	C₄×C₂²⋊D₇	Q₈	1	1	yes	characteristic
76	C₄×C₂²⋊D₇	Q₈	1	1	yes	characteristic
77	#6489	C₂×C₄	1	1	yes	characteristic
78	C₂×#1136	—	2	1	no	—
79	C₂²×C₇⋊C₈	C₂×C₄	1	1	yes	characteristic
80	C₂²×C₇⋊C₈	C₂×C₄	1	1	yes	characteristic
81	#6470	—	2	4	no	—
82	#6470	—	2	4	no	—
83	C₂×#1131	—	2	1	no	—
84	C₂×#1131	—	2	1	no	—
85	C₂×#1131	C₂×C₄	1	1	yes	characteristic
86	C₂×#1131	C₂×C₄	1	1	yes	characteristic
87	C₂×#1131	C₂×C₄	1	1	yes	characteristic
88	C₂×#1131	C₂×C₄	1	1	yes	characteristic
89	C₂×C₈×D₇	—	2	1	no	—
90	C₂×C₈×D₇	—	2	1	no	—
91	C₂×C₈×D₇	C₂×C₄	1	1	yes	characteristic
92	C₂×C₈×D₇	C₂×C₄	1	1	yes	characteristic
93	C₂×C₈×D₇	C₂×C₄	1	1	yes	characteristic
94	C₂×C₈×D₇	C₂×C₄	1	1	yes	characteristic
95	C₄×D₂₈	D₄	1	1	yes	characteristic
96	C₄×D₂₈	Q₈	1	1	yes	characteristic
97	#6435	C₂×C₄	1	1	yes	characteristic
98	#6435	C₂×C₄	1	1	yes	characteristic
99	C₄²×D₇	C₂³	1	1	yes	characteristic
100	C₄²×D₇	C₂³	1	1	yes	characteristic
101	C₄×Dic₁₄	D₄	1	1	yes	characteristic
102	C₄×Dic₁₄	Q₈	1	1	yes	characteristic
103	C₇×C₄⋊C₈	—	2	1	no	—
104	C₇×C₄⋊C₈	C₂³	1	1	yes	characteristic
105	C₇×C₄⋊C₈	C₂³	1	1	yes	characteristic
106	C₇×C₄⋊C₈	C₂³	1	1	yes	characteristic
107	C₇×C₄⋊C₈	C₂³	1	1	yes	characteristic
108	C₇×C₂²⋊C₈	—	2	1	no	—
109	C₇×#97	—	2	1	no	—
110	C₇×#97	C₂×C₄	1	1	yes	characteristic
111	C₇×#97	C₂×C₄	1	1	yes	characteristic
112	C₄×C₇×C₈	C₂³	1	1	yes	characteristic
113	C₄×C₇×C₈	C₂³	1	1	yes	characteristic
114	C₂²⋊(C₇⋊C₈)	—	2	1	no	—
115	(C₂×D₇)⋊C₈	—	2	1	no	—
116	(C₂×D₇)⋊C₈	—	2	1	no	—
117	(C₂×D₇)⋊C₈	—	2	1	no	—
118	(C₂×D₇)⋊C₈	—	2	1	no	—
119	#6389	—	2	1	no	—
120	#6389	—	2	1	no	—
121	#6389	C₂×C₄	1	1	yes	characteristic
122	#6389	C₂×C₄	1	1	yes	characteristic
123	#6389	C₂×C₄	1	1	yes	characteristic
124	#6389	C₂×C₄	1	1	yes	characteristic
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	C₈×Dic₇	—	2	1	no	—
130	C₈×Dic₇	—	2	1	no	—
131	C₈×Dic₇	C₂×C₄	1	1	yes	characteristic
132	C₈×Dic₇	C₂×C₄	1	1	yes	characteristic
133	C₈×Dic₇	C₂×C₄	1	1	yes	characteristic
134	C₈×Dic₇	C₂×C₄	1	1	yes	characteristic
135	C₄⋊(C₇⋊C₈)	—	2	1	no	—
136	C₄⋊(C₇⋊C₈)	C₂³	1	1	yes	characteristic
137	C₄⋊(C₇⋊C₈)	C₂³	1	1	yes	characteristic
138	C₄⋊(C₇⋊C₈)	C₂³	1	1	yes	characteristic
139	C₄⋊(C₇⋊C₈)	C₂³	1	1	yes	characteristic
140	#6377	—	2	1	no	—
141	C₄×C₇⋊C₈	C₂×C₄	1	1	yes	characteristic
142	C₄×C₇⋊C₈	C₂×C₄	1	1	yes	characteristic
143	C₄×C₇⋊C₈	C₂³	1	1	yes	characteristic
144	C₄×C₇⋊C₈	C₂³	1	1	yes	characteristic
145	#2989	—	7	1	no	—
146	#2989	—	7	1	no	—
147	C₄×#131	—	7	1	no	—
148	#1569	—	7	1	no	—
149	#1569	—	7	1	no	—
150	#1569	—	7	1	no	—
151	#1569	D₇	1	1	yes	characteristic, complemented
152	#1568	—	7	1	no	—
153	#1568	—	7	1	no	—
154	#1567	—	7	1	no	—
155	#1567	—	7	1	no	—
156	#1565	—	7	1	no	—
157	#1565	—	7	1	no	—
158	#1564	—	7	1	no	—
159	C₂×#335	—	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	C₂×Q₈	1	1	yes	characteristic
163	C₂×C₂²⋊D₇	C₄⋊C₄	1	1	yes	characteristic
164	C₂×C₂²⋊D₇	C₄⋊C₄	1	1	yes	characteristic
165	#1157	—	2	2	no	—
166	#1157	—	2	2	no	—
167	C₂×D₂₈	C₄⋊C₄	1	1	yes	characteristic
168	C₂×C₄×D₇	C₂²×C₄	1	1	yes	characteristic
169	C₂×C₄×D₇	C₂²×C₄	1	1	yes	characteristic
170	C₂×C₄×D₇	C₂×D₄	1	1	yes	characteristic
171	C₂×C₄×D₇	C₂×D₄	1	1	yes	characteristic
172	C₂×C₄×D₇	C₂×Q₈	1	1	yes	characteristic
173	C₂×C₄×D₇	C₂×Q₈	1	1	yes	characteristic
174	C₂×Dic₁₄	C₄⋊C₄	1	1	yes	characteristic
175	C₇×M₁₆	—	2	2	no	—
176	C₇×M₁₆	—	2	2	no	—
177	C₇×M₁₆	—	8	1	no	—
178	C₂×C₇×C₈	—	2	1	no	—
179	C₂×C₇×C₈	—	2	1	no	—
180	C₂×C₇×C₈	—	2	1	no	—
181	C₂×C₇×C₈	—	2	1	no	—
182	C₂×C₇×C₈	C₂²×C₄	1	1	yes	characteristic
183	C₂×C₇×C₈	C₂²×C₄	1	1	yes	characteristic
184	C₂×C₇×C₈	C₂²×C₄	1	1	yes	characteristic
185	C₂×C₇×C₈	C₂²×C₄	1	1	yes	characteristic
186	C₄²×C₇	C₂²×C₄	1	1	yes	characteristic
187	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
188	C₄²×C₇	C₂×Q₈	1	1	yes	characteristic
189	C₄²×C₇	C₂⁴	1	1	yes	characteristic
190	C₂²⋊Dic₇	C₄⋊C₄	1	1	yes	characteristic
191	C₂²⋊Dic₇	C₄⋊C₄	1	1	yes	characteristic
192	(C₂×D₇)⋊C₄	C₄⋊C₄	1	1	yes	characteristic
193	(C₂×D₇)⋊C₄	C₄⋊C₄	1	1	yes	characteristic
194	(C₂×D₇)⋊C₄	C₄⋊C₄	1	1	yes	characteristic
195	(C₂×D₇)⋊C₄	C₄⋊C₄	1	1	yes	characteristic
196	C₄⋊Dic₇	C₄⋊C₄	1	1	yes	characteristic
197	C₄⋊Dic₇	C₄⋊C₄	1	1	yes	characteristic
198	Dic₇⋊C₄	C₄⋊C₄	1	1	yes	characteristic
199	Dic₇⋊C₄	C₄⋊C₄	1	1	yes	characteristic
200	Dic₇⋊C₄	C₄⋊C₄	1	1	yes	characteristic
201	Dic₇⋊C₄	C₄⋊C₄	1	1	yes	characteristic
202	C₄×Dic₇	C₂²×C₄	1	1	yes	characteristic
203	C₄×Dic₇	C₂²×C₄	1	1	yes	characteristic
204	C₄×Dic₇	C₂×D₄	1	1	yes	characteristic
205	C₄×Dic₇	C₂×D₄	1	1	yes	characteristic
206	C₄×Dic₇	C₂×Q₈	1	1	yes	characteristic
207	C₄×Dic₇	C₂×Q₈	1	1	yes	characteristic
208	#1136	—	8	1	no	—
209	C₂×C₇⋊C₈	—	2	2	no	—
210	C₂×C₇⋊C₈	—	2	2	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	C₂²×C₄	1	1	yes	characteristic
216	C₂×C₇⋊C₈	C₂²×C₄	1	1	yes	characteristic
217	C₂×C₇⋊C₈	C₂²×C₄	1	1	yes	characteristic
218	C₂×C₇⋊C₈	C₂²×C₄	1	1	yes	characteristic
219	#1131	—	2	2	no	—
220	#1131	—	2	2	no	—
221	#1131	—	2	2	no	—
222	#1131	—	8	1	no	—
223	#1131	—	8	1	no	—
224	#1131	M₁₆	1	4	yes	complemented
225	C₈×D₇	—	2	2	no	—
226	C₈×D₇	—	2	2	no	—
227	C₈×D₇	—	2	2	no	—
228	C₈×D₇	—	8	1	no	—
229	C₈×D₇	—	8	1	no	—
230	C₈×D₇	M₁₆	1	4	yes	complemented
231	C₂×#131	—	7	1	no	—
232	C₂×#131	—	7	1	no	—
233	C₄×#41	—	7	1	no	—
234	#446	—	14	1	no	—
235	#446	—	14	1	no	—
236	#436	—	14	1	no	—
237	#436	—	14	1	no	—
238	#435	—	14	1	no	—
239	#435	—	14	1	no	—
240	#435	—	14	1	no	—
241	#435	—	14	1	no	—
242	#432	—	7	1	no	—
243	#432	—	7	1	no	—
244	#432	—	7	1	no	—
245	#432	C₂×D₇	1	1	yes	characteristic
246	#431	—	7	1	no	—
247	#431	—	7	1	no	—
248	#423	—	7	1	no	—
249	#423	—	7	1	no	—
250	#423	—	7	1	no	—
251	#423	C₂×D₇	1	1	yes	characteristic
252	C₂×C₄⋊C₈	—	7	1	no	—
253	C₂×C₄⋊C₈	—	7	1	no	—
254	#405	—	7	1	no	—
255	#405	—	7	1	no	—
256	#405	—	7	1	no	—
257	#405	—	7	1	no	—
258	#405	—	7	1	no	—
259	#405	—	7	1	no	—
260	C₄×M₁₆	—	7	1	no	—
261	C₄×M₁₆	—	7	1	no	—
262	C₄×M₁₆	C₂×D₇	1	1	yes	characteristic
263	C₂×C₄×C₈	—	7	1	no	—
264	C₂×C₄×C₈	—	7	1	no	—
265	C₂×C₄×C₈	—	7	1	no	—
266	#335	—	7	1	no	—
267	#335	—	7	1	no	—
268	#335	—	7	1	no	—
269	#335	—	7	1	no	—
270	#335	—	7	1	no	—
271	#335	—	7	1	no	—
272	#335	—	7	1	no	—
273	#335	—	7	1	no	—
274	#335	C₂×D₇	1	1	yes	characteristic
275	#335	C₂×D₇	1	1	yes	characteristic
276	#334	—	7	1	no	—
277	#334	—	7	1	no	—
278	#334	—	7	1	no	—
279	#334	—	7	1	no	—
280	#334	C₂×D₇	1	1	yes	characteristic
281	#334	C₂×D₇	1	1	yes	characteristic
282	C₂³×C₇	C₂×C₄⋊C₄	1	1	yes	characteristic
283	C₂²×D₇	C₂×C₄⋊C₄	1	1	yes	characteristic
284	C₂²×D₇	C₂×C₄⋊C₄	1	1	yes	characteristic
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	—	2	1	no	—
289	C₂×C₄×C₇	—	4	1	no	—
290	C₂×C₄×C₇	C₂×C₄⋊C₄	1	1	yes	characteristic
291	C₂×C₄×C₇	C₂×C₄⋊C₄	1	1	yes	characteristic
292	C₂×C₄×C₇	C₂×C₄⋊C₄	1	1	yes	characteristic
293	C₂×C₄×C₇	C₂³×C₄	1	1	yes	characteristic
294	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
295	C₂×C₄×C₇	C₂²×Q₈	1	1	yes	characteristic
296	C₂²⋊D₇	—	2	2	no	—
297	C₂²⋊D₇	—	2	2	no	—
298	C₂×Dic₇	C₂×C₄⋊C₄	1	1	yes	characteristic
299	C₂×Dic₇	C₂×C₄⋊C₄	1	1	yes	characteristic
300	C₂×Dic₇	C₂×C₄⋊C₄	1	1	yes	characteristic
301	C₂×Dic₇	C₂×C₄⋊C₄	1	1	yes	characteristic
302	C₂×Dic₇	C₂×C₄⋊C₄	1	1	yes	characteristic
303	C₂×Dic₇	C₂×C₄⋊C₄	1	1	yes	characteristic
304	D₂₈	—	2	2	no	—
305	C₄×D₇	—	2	1	no	—
306	C₄×D₇	—	2	1	no	—
307	C₄×D₇	—	2	1	no	—
308	C₄×D₇	—	2	1	no	—
309	C₄×D₇	—	2	1	no	—
310	C₄×D₇	—	2	1	no	—
311	C₄×D₇	—	4	1	no	—
312	C₄×D₇	—	4	1	no	—
313	C₄×D₇	C₂×M₁₆	1	2	yes	—
314	C₄×D₇	C₂×M₁₆	1	2	yes	—
315	Dic₁₄	—	2	2	no	—
316	C₇×C₈	—	2	1	no	—
317	C₇×C₈	—	2	1	no	—
318	C₇×C₈	—	4	1	no	—
319	C₇×C₈	—	4	1	no	—
320	C₇×C₈	—	4	1	no	—
321	C₇×C₈	—	4	1	no	—
322	C₇×C₈	C₂×M₁₆	1	2	yes	—
323	C₇×C₈	C₂×M₁₆	1	2	yes	—
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	C₇⋊C₈	—	4	1	no	—
330	C₇⋊C₈	C₂×M₁₆	1	2	yes	—
331	C₇⋊C₈	C₂×M₁₆	1	2	yes	—
332	C₂×#41	—	7	1	no	—
333	#131	—	14	4	no	—
334	#131	—	14	4	no	—
335	C₂×M₁₆	—	2	1	no	—
336	C₂×M₁₆	—	7	1	no	—
337	C₂×M₁₆	—	7	1	no	—
338	C₂×M₁₆	—	7	1	no	—
339	C₂×M₁₆	—	7	1	no	—
340	C₂×M₁₆	—	14	1	no	—
341	C₂×M₁₆	—	14	1	no	—
342	C₂×M₁₆	—	14	1	no	—
343	C₂×M₁₆	C₄×D₇	1	1	yes	characteristic
344	C₂×M₁₆	C₄×D₇	1	1	yes	characteristic
345	C₂²×C₈	—	7	1	no	—
346	C₂²×C₈	—	7	1	no	—
347	C₂²×C₈	—	7	1	no	—
348	C₂²×C₈	—	7	1	no	—
349	C₂²×C₈	—	7	1	no	—
350	C₂²×C₈	—	7	1	no	—
351	C₂²×C₈	—	14	1	no	—
352	C₂²×C₈	—	14	1	no	—
353	C₄×Q₈	—	7	1	no	—
354	C₄×Q₈	—	7	1	no	—
355	C₄×D₄	—	7	1	no	—
356	C₄×D₄	—	7	1	no	—
357	C₄×D₄	—	7	1	no	—
358	C₄×D₄	—	7	1	no	—
359	C₄×D₄	—	7	1	no	—
360	C₄×D₄	—	7	1	no	—
361	#117	—	7	1	no	—
362	#117	—	7	1	no	—
363	#117	—	7	1	no	—
364	C₂×C₄²	—	7	1	no	—
365	C₂×C₄²	—	7	1	no	—
366	C₂×C₄²	C₂²×D₇	1	1	yes	characteristic
367	C₄⋊C₈	—	2	1	no	—
368	C₄⋊C₈	—	7	1	no	—
369	C₄⋊C₈	—	7	1	no	—
370	C₄⋊C₈	—	7	1	no	—
371	C₄⋊C₈	—	7	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	—	14	1	no	—
377	C₄⋊C₈	C₂²×D₇	1	1	yes	characteristic
378	C₄⋊C₈	C₂²×D₇	1	1	yes	characteristic
379	C₄⋊C₈	C₂²×D₇	1	1	yes	characteristic
380	C₄⋊C₈	C₂²×D₇	1	1	yes	characteristic
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	#97	—	2	1	no	—
388	#97	—	7	1	no	—
389	#97	—	7	1	no	—
390	#97	—	7	1	no	—
391	#97	—	7	1	no	—
392	#97	—	14	1	no	—
393	#97	—	14	1	no	—
394	#97	—	14	1	no	—
395	#97	C₄×D₇	1	1	yes	characteristic
396	#97	C₄×D₇	1	1	yes	characteristic
397	C₄×C₈	—	7	1	no	—
398	C₄×C₈	—	7	1	no	—
399	C₄×C₈	—	7	1	no	—
400	C₄×C₈	—	7	1	no	—
401	C₄×C₈	—	7	1	no	—
402	C₄×C₈	—	7	1	no	—
403	C₄×C₈	—	7	1	no	—
404	C₄×C₈	—	7	1	no	—
405	C₄×C₈	—	14	1	no	—
406	C₄×C₈	—	14	1	no	—
407	C₄×C₈	C₂²×D₇	1	1	yes	characteristic
408	C₄×C₈	C₂²×D₇	1	1	yes	characteristic
409	C₂²×C₇	—	2	1	no	—
410	C₂²×C₇	—	2	1	no	—
411	C₂²×C₇	—	2	1	no	—
412	C₂²×C₇	C₂²×C₄⋊C₄	1	1	yes	characteristic
413	C₂×D₇	—	2	1	no	—
414	C₂×D₇	—	2	1	no	—
415	C₂×D₇	—	2	1	no	—
416	C₂×D₇	—	2	1	no	—
417	C₂×D₇	—	2	1	no	—
418	C₂×D₇	#423	1	2	yes	—
419	C₄×C₇	—	2	1	no	—
420	C₄×C₇	—	2	1	no	—
421	C₄×C₇	—	2	1	no	—
422	C₄×C₇	—	2	1	no	—
423	C₄×C₇	C₂²×M₁₆	1	1	yes	characteristic
424	C₄×C₇	C₂²×M₁₆	1	1	yes	characteristic
425	C₄×C₇	#576	1	1	yes	characteristic
426	C₄×C₇	#578	1	1	yes	characteristic
427	Dic₇	—	2	1	no	—
428	Dic₇	—	2	1	no	—
429	Dic₇	—	2	1	no	—
430	Dic₇	—	2	1	no	—
431	Dic₇	—	2	1	no	—
432	Dic₇	#423	1	2	yes	—
433	#41	—	14	2	no	—
434	#41	—	14	2	no	—
435	C₂×Q₈	—	7	1	no	—
436	C₂×D₄	—	7	1	no	—
437	C₂×D₄	—	7	1	no	—
438	C₂×D₄	—	7	1	no	—
439	C₂²×C₄	—	7	1	no	—
440	C₂²×C₄	—	7	1	no	—
441	C₂²×C₄	—	7	1	no	—
442	C₂²×C₄	—	7	1	no	—
443	C₂²×C₄	—	7	1	no	—
444	C₂²×C₄	—	7	1	no	—
445	C₂²×C₄	C₂×C₄×D₇	1	1	yes	characteristic
446	C₂²×C₄	D₄×D₇	1	1	yes	characteristic
447	C₂²×C₄	Q₈×D₇	1	1	yes	characteristic
448	M₁₆	—	2	2	no	—
449	M₁₆	—	2	2	no	—
450	M₁₆	—	7	4	no	—
451	M₁₆	—	8	1	no	—
452	M₁₆	—	14	2	no	—
453	M₁₆	—	14	2	no	—
454	M₁₆	—	14	2	no	—
455	M₁₆	—	56	1	no	—
456	M₁₆	—	56	1	no	—
457	M₁₆	—	56	1	no	—
458	C₂×C₈	—	2	1	no	—
459	C₂×C₈	—	2	1	no	—
460	C₂×C₈	—	2	1	no	—
461	C₂×C₈	—	2	1	no	—
462	C₂×C₈	—	7	1	no	—
463	C₂×C₈	—	7	1	no	—
464	C₂×C₈	—	7	4	no	—
465	C₂×C₈	—	7	1	no	—
466	C₂×C₈	—	7	1	no	—
467	C₂×C₈	—	14	2	no	—
468	C₂×C₈	—	14	2	no	—
469	C₂×C₈	—	14	2	no	—
470	C₂×C₈	—	14	2	no	—
471	C₂×C₈	—	14	2	no	—
472	C₂×C₈	—	14	1	no	—
473	C₂×C₈	—	14	1	no	—
474	C₂×C₈	—	14	1	no	—
475	C₂×C₈	—	14	1	no	—
476	C₂×C₈	—	56	1	no	—
477	C₂×C₈	—	56	1	no	—
478	C₂×C₈	C₂×C₄×D₇	1	1	yes	characteristic
479	C₂×C₈	C₂×C₄×D₇	1	1	yes	characteristic
480	C₂×C₈	C₂×C₄×D₇	1	1	yes	characteristic
481	C₂×C₈	C₂×C₄×D₇	1	1	yes	characteristic
482	C₄⋊C₄	—	7	1	no	—
483	C₄⋊C₄	—	7	1	no	—
484	C₄⋊C₄	—	7	1	no	—
485	C₄⋊C₄	—	7	1	no	—
486	C₄⋊C₄	—	7	1	no	—
487	C₄⋊C₄	—	7	1	no	—
488	C₂²⋊C₄	—	7	1	no	—
489	C₂²⋊C₄	—	7	1	no	—
490	C₂²⋊C₄	—	7	1	no	—
491	C₂²⋊C₄	—	7	1	no	—
492	C₂²⋊C₄	—	7	1	no	—
493	C₂²⋊C₄	—	7	1	no	—
494	C₄²	—	7	1	no	—
495	C₄²	—	7	1	no	—
496	C₄²	—	7	1	no	—
497	C₄²	—	7	1	no	—
498	C₄²	—	7	1	no	—
499	C₄²	—	7	1	no	—
500	C₄²	C₂×C₄×D₇	1	1	yes	characteristic
501	C₄²	D₄×D₇	1	1	yes	characteristic
502	C₄²	Q₈×D₇	1	1	yes	characteristic
503	C₄²	C₂³×D₇	1	1	yes	characteristic
504	C₂×C₇	—	4	1	no	—
505	C₂×C₇	C₂×#423	1	1	yes	characteristic
506	C₂×C₇	#2913	1	1	yes	characteristic
507	C₂×C₇	#2916	1	1	yes	characteristic
508	D₇	—	2	2	no	—
509	D₇	—	4	1	no	—
510	C₂³	—	7	1	no	—
511	C₂³	—	7	1	no	—
512	C₂³	D₇×C₄⋊C₄	1	1	yes	characteristic
513	Q₈	—	14	2	no	—
514	D₄	—	14	2	no	—
515	D₄	—	14	2	no	—
516	D₄	—	14	2	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	—	4	1	no	—
522	C₂×C₄	—	7	1	no	—
523	C₂×C₄	—	7	2	no	—
524	C₂×C₄	—	7	2	no	—
525	C₂×C₄	—	7	1	no	—
526	C₂×C₄	—	7	1	no	—
527	C₂×C₄	—	7	1	no	—
528	C₂×C₄	—	7	1	no	—
529	C₂×C₄	—	7	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	—	28	1	no	—
537	C₂×C₄	—	28	1	no	—
538	C₂×C₄	D₇×C₄⋊C₄	1	1	yes	characteristic
539	C₂×C₄	D₇×C₄⋊C₄	1	1	yes	characteristic
540	C₂×C₄	D₇×C₄⋊C₄	1	1	yes	characteristic
541	C₂×C₄	C₂²×C₄×D₇	1	1	yes	characteristic
542	C₂×C₄	C₂×D₄×D₇	1	1	yes	characteristic
543	C₂×C₄	C₂×Q₈×D₇	1	1	yes	characteristic
544	C₈	—	2	1	no	—
545	C₈	—	2	1	no	—
546	C₈	—	4	1	no	—
547	C₈	—	4	1	no	—
548	C₈	—	4	1	no	—
549	C₈	—	4	1	no	—
550	C₈	—	7	2	no	—
551	C₈	—	7	2	no	—
552	C₈	—	14	1	no	—
553	C₈	—	14	1	no	—
554	C₈	—	28	1	no	—
555	C₈	—	28	1	no	—
556	C₈	—	28	1	no	—
557	C₈	—	28	1	no	—
558	C₈	D₇×M₁₆	1	2	yes	—
559	C₈	D₇×M₁₆	1	2	yes	—
560	C₇	#17799	1	1	yes	characteristic, complemented, Sylow
561	C₂²	—	2	1	no	—
562	C₂²	—	2	1	no	—
563	C₂²	—	2	1	no	—
564	C₂²	—	7	2	no	—
565	C₂²	—	14	1	no	—
566	C₂²	—	14	1	no	—
567	C₂²	—	14	1	no	—
568	C₂²	—	14	1	no	—
569	C₂²	—	14	1	no	—
570	C₂²	C₂×D₇×C₄⋊C₄	1	1	yes	characteristic
571	C₄	—	2	1	no	—
572	C₄	—	2	1	no	—
573	C₄	—	2	1	no	—
574	C₄	—	2	1	no	—
575	C₄	—	7	2	no	—
576	C₄	—	14	1	no	—
577	C₄	—	14	1	no	—
578	C₄	—	14	1	no	—
579	C₄	—	14	1	no	—
580	C₄	—	14	1	no	—
581	C₄	C₂×D₇×M₁₆	1	1	yes	characteristic
582	C₄	C₂×D₇×M₁₆	1	1	yes	characteristic
583	C₄	#90465	1	1	yes	characteristic
584	C₄	#90470	1	1	yes	characteristic
585	C₂	—	4	1	no	—
586	C₂	—	14	2	no	—
587	C₂	—	28	1	no	—
588	C₂	D₇×#423	1	1	yes	characteristic
589	C₂	#11736655	1	1	yes	characteristic
590	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×#1569	C₂
socle	C₂²×C₇	C₂²×C₄⋊C₄
prime radical	C₂×#1157	C₂×C₄
cosocle	C₄²×C₇	C₂⁴
hypercenter	#1569	D₇
hypocenter	C₇	#17799
LCS	G ▷ C₂×C₄×C₇ ▷ C₂×C₇ ▷ C₇
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #1569

Complements

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

N	H ≅ G/N	type
4. C₇×#1569	C₂	semidirect
5. #11728548	C₂	semidirect
6. #11728245	C₂	semidirect
7. #11727605	C₂	semidirect
8. #11726325	C₂	semidirect
9. #11726323	C₂	semidirect
10. #11726322	C₂	semidirect
11. D₇×#335	C₂	semidirect
12. #11726285	C₂	semidirect
13. #11726284	C₂	semidirect
14. #11726282	C₂	semidirect
15. #11726281	C₂	semidirect
151. #1569	D₇	semidirect
224. #1131	M₁₆	semidirect
230. C₈×D₇	M₁₆	semidirect
560. C₇	#17799	semidirect

Maximal subgroups

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

subgroup	index
#11736784	2
#11736495	2
C₄×#6470	2
C₇×#1569	2
#11728548	2
#11728245	2
#11727605	2
#11726325	2
#11726323	2
#11726322	2
D₇×#335	2
#11726285	2
#11726284	2
#11726282	2
#11726281	2
#17799	7