Subgroups — #13324868

Order 1792.

670 conjugacy classes of subgroups.

The subgroup lattice has 612 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#11740586	C₂	1	1	yes	maximal, characteristic
2	#11740574	C₂	1	1	yes	maximal, characteristic, complemented
3	#11736488	C₂	1	1	yes	maximal, characteristic, complemented
4	C₇×#1495	C₂	1	1	yes	maximal, characteristic, complemented
5	#11728511	C₂	1	1	yes	maximal, characteristic, complemented
6	#11728497	C₂	1	1	yes	maximal, characteristic, complemented
7	#11728249	C₂	1	1	yes	maximal, characteristic, complemented
8	#11725980	C₂	1	1	yes	maximal, characteristic, complemented
9	#11725974	C₂	1	1	yes	maximal, characteristic, complemented
10	#11725971	C₂	1	1	yes	maximal, characteristic, complemented
11	#11725966	C₂	1	1	yes	maximal, characteristic, complemented
12	#11725914	C₂	1	1	yes	maximal, characteristic, complemented
13	#11725911	C₂	1	1	yes	maximal, characteristic, complemented
14	#11725907	C₂	1	1	yes	maximal, characteristic, complemented
15	#11725905	C₂	1	1	yes	maximal, characteristic, complemented
16	C₇×#529	C₂²	1	1	yes	characteristic
17	C₂×D₇×M₁₆	—	2	1	no	—
18	C₂×C₄×D₂₈	C₂²	1	1	yes	characteristic
19	C₇×#431	C₂²	1	1	yes	characteristic
20	C₇×#423	C₂²	1	1	yes	characteristic
21	#89898	—	2	1	no	—
22	#89838	C₄	1	1	yes	characteristic
23	#89838	C₄	1	1	yes	characteristic
24	#89829	C₄	1	1	yes	characteristic
25	#89829	C₄	1	1	yes	characteristic
26	#89818	C₄	1	1	yes	characteristic
27	#89816	C₄	1	1	yes	characteristic
28	#89808	C₄	1	1	yes	characteristic
29	#89806	C₄	1	1	yes	characteristic
30	C₄×#1143	C₂²	1	1	yes	characteristic
31	C₄×#1143	C₂²	1	1	yes	characteristic
32	#89796	C₂²	1	1	yes	characteristic, complemented
33	Q₈×C₇⋊C₈	C₂²	1	1	yes	characteristic, complemented
34	C₄×#1141	C₂²	1	1	yes	characteristic
35	C₄×#1141	C₂²	1	1	yes	characteristic
36	#89784	—	2	1	no	—
37	#89784	C₂²	1	1	yes	characteristic, complemented
38	#89783	—	2	1	no	—
39	D₄×C₇⋊C₈	C₂²	1	1	yes	characteristic, complemented
40	#89772	—	2	1	no	—
41	#89769	—	2	1	no	—
42	#89697	C₂²	1	1	yes	characteristic
43	#89697	C₂²	1	1	yes	characteristic
44	C₄×#1136	C₂²	1	1	yes	characteristic
45	#89610	C₂²	1	1	yes	characteristic
46	#89610	C₂²	1	1	yes	characteristic
47	#89608	—	2	1	no	—
48	#89608	—	2	1	no	—
49	#89606	C₂²	1	1	yes	characteristic
50	#89606	C₂²	1	1	yes	characteristic
51	C₇×Q₈⋊C₈	C₂²	1	1	yes	characteristic, complemented
52	C₇×Q₈⋊C₈	C₂²	1	1	yes	characteristic, complemented
53	C₇×D₄⋊C₈	C₂²	1	1	yes	characteristic, complemented
54	C₇×D₄⋊C₈	C₂²	1	1	yes	characteristic, complemented
55	#89275	C₂²	1	1	yes	characteristic, complemented
56	#89275	C₂²	1	1	yes	characteristic, complemented
57	#89274	C₂²	1	1	yes	characteristic, complemented
58	#89274	C₂²	1	1	yes	characteristic, complemented
59	#89254	C₂²	1	1	yes	characteristic
60	#89254	C₂²	1	1	yes	characteristic
61	#89254	C₂²	1	1	yes	characteristic
62	#89254	C₂²	1	1	yes	characteristic
63	#89250	C₂²	1	1	yes	characteristic, complemented
64	#89249	C₂²	1	1	yes	characteristic, complemented
65	#89249	C₂²	1	1	yes	characteristic, complemented
66	C₈×C₇⋊C₈	C₂²	1	1	yes	characteristic, complemented
67	#18008	—	7	1	no	maximal, Sylow
68	C₂²×D₂₈	C₂×C₄	1	1	yes	characteristic
69	C₂²×C₄×D₇	—	2	1	no	—
70	C₂×C₇×M₁₆	—	2	1	no	—
71	C₇×#126	—	2	1	no	—
72	C₇×#125	C₂×C₄	1	1	yes	characteristic
73	C₇×#124	C₂×C₄	1	1	yes	characteristic
74	C₇×#123	—	2	1	no	—
75	C₇×C₂²⋊Q₈	C₂×C₄	1	1	yes	characteristic
76	C₇×#121	C₂×C₄	1	1	yes	characteristic
77	C₄×C₇×Q₈	C₂³	1	1	yes	characteristic
78	C₄×C₇×D₄	—	2	1	no	—
79	C₄×C₇×D₄	C₂³	1	1	yes	characteristic
80	C₇×#117	—	2	1	no	—
81	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
82	C₂×#1143	C₂×C₄	1	1	yes	characteristic
83	C₂×#1143	C₂×C₄	1	1	yes	characteristic
84	C₂×#1141	C₂×C₄	1	1	yes	characteristic
85	C₂×#1141	C₂×C₄	1	1	yes	characteristic
86	C₂×(C₂×D₇)⋊C₄	—	2	1	no	—
87	C₂×C₄⋊Dic₇	C₂×C₄	1	1	yes	characteristic
88	C₂×#1136	—	2	1	no	—
89	C₂×#1136	D₄	1	1	yes	characteristic
90	C₂×#1136	D₄	1	1	yes	characteristic
91	C₂²×C₇⋊C₈	—	2	1	no	—
92	D₇×M₁₆	—	4	4	no	—
93	C₂×#1131	—	2	1	no	—
94	C₂×#1131	—	2	1	no	—
95	C₂×C₈×D₇	—	2	1	no	—
96	C₂×C₈×D₇	—	2	1	no	—
97	C₄×D₂₈	—	2	1	no	—
98	C₄×D₂₈	—	2	1	no	—
99	C₄×D₂₈	C₂×C₄	1	1	yes	characteristic
100	C₄×D₂₈	C₂×C₄	1	1	yes	characteristic
101	C₄×D₂₈	C₂³	1	1	yes	characteristic
102	C₄×D₂₈	C₂³	1	1	yes	characteristic
103	C₇×C₄⋊C₈	—	2	1	no	—
104	C₇×C₄⋊C₈	—	2	1	no	—
105	C₇×C₄⋊C₈	C₂³	1	1	yes	characteristic
106	C₇×C₄⋊C₈	C₂³	1	1	yes	characteristic
107	C₇×C₂²⋊C₈	—	2	1	no	—
108	C₄×C₇×C₈	C₂³	1	1	yes	characteristic
109	C₄×C₇×C₈	C₂³	1	1	yes	characteristic
110	#6409	C₂×C₄	1	1	yes	characteristic
111	#6409	C₂×C₄	1	1	yes	characteristic
112	#6406	C₂×C₄	1	1	yes	characteristic
113	#6406	C₂×C₄	1	1	yes	characteristic
114	C₂²⋊(C₇⋊C₈)	—	2	1	no	—
115	C₂²⋊(C₇⋊C₈)	—	2	1	no	—
116	C₂²⋊(C₇⋊C₈)	—	2	1	no	—
117	C₂²⋊(C₇⋊C₈)	C₂×C₄	1	1	yes	characteristic
118	C₂²⋊(C₇⋊C₈)	C₂×C₄	1	1	yes	characteristic
119	(C₂×D₇)⋊C₈	—	2	1	no	—
120	(C₂×D₇)⋊C₈	—	2	1	no	—
121	(C₂×D₇)⋊C₈	—	2	1	no	—
122	(C₂×D₇)⋊C₈	—	2	1	no	—
123	#6383	C₂×C₄	1	1	yes	characteristic
124	#6383	C₂×C₄	1	1	yes	characteristic
125	#6383	C₂×C₄	1	1	yes	characteristic
126	#6383	C₂×C₄	1	1	yes	characteristic
127	#6382	C₂×C₄	1	1	yes	characteristic
128	#6382	C₂×C₄	1	1	yes	characteristic
129	#6381	C₂×C₄	1	1	yes	characteristic
130	#6381	C₂×C₄	1	1	yes	characteristic
131	C₄⋊(C₇⋊C₈)	—	2	1	no	—
132	C₄⋊(C₇⋊C₈)	—	2	1	no	—
133	C₄⋊(C₇⋊C₈)	C₂×C₄	1	1	yes	characteristic
134	C₄⋊(C₇⋊C₈)	C₂×C₄	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	#6377	D₄	1	1	yes	characteristic
139	#6377	D₄	1	1	yes	characteristic
140	C₄×C₇⋊C₈	—	2	1	no	—
141	C₄×C₇⋊C₈	—	2	1	no	—
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	C₄×C₇⋊C₈	C₂³	1	1	yes	characteristic
146	#3105	—	7	1	no	—
147	#2969	—	7	1	no	—
148	D₄×M₁₆	—	7	1	no	—
149	#1592	—	7	1	no	—
150	#1589	—	7	1	no	—
151	#1586	—	7	1	no	—
152	#1585	—	7	1	no	—
153	#1583	—	7	1	no	—
154	#1581	—	7	1	no	—
155	#1580	—	7	1	no	—
156	C₈×SD₁₆	—	7	1	no	—
157	#1574	—	7	1	no	—
158	#1495	D₇	1	1	yes	characteristic, complemented
159	#1478	—	7	1	no	—
160	#1453	—	7	1	no	—
161	C₂³×D₇	—	2	1	no	—
162	C₂×C₇×Q₈	C₂²×C₄	1	1	yes	characteristic
163	C₂×C₇×D₄	—	2	1	no	—
164	C₂×C₇×D₄	C₂²×C₄	1	1	yes	characteristic
165	C₂²×C₄×C₇	—	2	1	no	—
166	C₂²×C₄×C₇	C₂²×C₄	1	1	yes	characteristic
167	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
168	C₂²×C₄×C₇	#41	1	1	yes	characteristic
169	C₂²×Dic₇	—	2	1	no	—
170	C₂×D₂₈	—	2	2	no	—
171	C₂×D₂₈	—	2	1	no	—
172	C₂×D₂₈	—	4	1	no	—
173	C₂×D₂₈	C₂²×C₄	1	1	yes	characteristic
174	C₂×D₂₈	C₂²×C₄	1	1	yes	characteristic
175	C₂×C₄×D₇	—	2	1	no	—
176	C₂×C₄×D₇	—	2	1	no	—
177	C₂×C₄×D₇	—	2	1	no	—
178	C₂×C₄×D₇	—	2	1	no	—
179	C₂×C₄×D₇	—	4	2	no	—
180	C₂×C₄×D₇	—	4	2	no	—
181	C₇×M₁₆	—	4	2	no	—
182	C₂×C₇×C₈	—	2	1	no	—
183	C₂×C₇×C₈	—	2	1	no	—
184	C₂×C₇×C₈	—	2	1	no	—
185	C₂×C₇×C₈	—	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	—	2	1	no	—
190	C₇×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
191	C₇×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
192	C₇×C₂²⋊C₄	—	2	1	no	—
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	C₄²×C₇	—	2	1	no	—
198	C₄²×C₇	C₂²×C₄	1	1	yes	characteristic
199	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
200	C₄²×C₇	#41	1	1	yes	characteristic
201	C₄²×C₇	C₂⁴	1	1	yes	characteristic
202	#1143	—	2	2	no	—
203	#1143	—	4	1	no	—
204	#1141	—	2	2	no	—
205	#1141	—	4	1	no	—
206	(C₂×D₇)⋊C₄	—	2	1	no	—
207	(C₂×D₇)⋊C₄	—	2	1	no	—
208	(C₂×D₇)⋊C₄	—	2	1	no	—
209	(C₂×D₇)⋊C₄	—	2	1	no	—
210	C₄⋊Dic₇	—	2	1	no	—
211	C₄⋊Dic₇	C₂²×C₄	1	1	yes	characteristic
212	C₄⋊Dic₇	C₂²×C₄	1	1	yes	characteristic
213	#1136	—	2	2	no	—
214	#1136	—	4	1	no	—
215	#1136	—	4	2	no	—
216	C₂×C₇⋊C₈	—	2	1	no	—
217	C₂×C₇⋊C₈	—	2	1	no	—
218	C₂×C₇⋊C₈	—	4	2	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	C₂²×C₄	1	1	yes	characteristic
222	C₂×C₇⋊C₈	C₂²×C₄	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	C₂×C₇⋊C₈	C₂×D₄	1	1	yes	characteristic
226	C₂×C₇⋊C₈	C₂×D₄	1	1	yes	characteristic
227	#1131	—	4	2	no	—
228	#1131	—	4	2	no	—
229	C₈×D₇	—	4	2	no	—
230	C₈×D₇	—	4	2	no	—
231	C₂²×M₁₆	—	14	1	no	—
232	#529	C₂×D₇	1	1	yes	characteristic
233	C₂×C₄×D₄	—	7	1	no	—
234	#484	—	7	1	no	—
235	#481	—	7	1	no	—
236	#478	—	7	1	no	—
237	#478	—	7	1	no	—
238	#463	—	7	1	no	—
239	#463	—	7	1	no	—
240	#450	—	7	1	no	—
241	#447	—	7	1	no	—
242	#446	—	7	1	no	—
243	C₈×Q₈	—	7	1	no	—
244	C₄×SD₁₆	—	7	1	no	—
245	C₄×SD₁₆	—	7	1	no	—
246	C₄×D₈	—	7	1	no	—
247	C₄×D₈	—	7	1	no	—
248	#436	—	7	1	no	—
249	#436	—	7	1	no	—
250	#436	—	7	1	no	—
251	#436	—	14	1	no	—
252	#435	—	14	1	no	—
253	#435	—	14	1	no	—
254	#435	—	14	1	no	—
255	C₈×D₄	—	7	1	no	—
256	C₈×D₄	—	7	1	no	—
257	C₈×D₄	—	7	1	no	—
258	#433	—	14	1	no	—
259	#431	—	7	1	no	—
260	#431	—	7	1	no	—
261	#431	C₂×D₇	1	1	yes	characteristic
262	#423	C₂×D₇	1	1	yes	characteristic
263	#407	—	14	1	no	—
264	#405	—	14	1	no	—
265	C₄×M₁₆	—	7	1	no	—
266	#335	—	7	1	no	—
267	#335	—	7	1	no	—
268	#334	—	7	1	no	—
269	#334	—	7	1	no	—
270	Q₈⋊C₈	C₂×D₇	1	1	yes	characteristic, complemented
271	Q₈⋊C₈	C₂×D₇	1	1	yes	characteristic, complemented
272	D₄⋊C₈	—	7	1	no	—
273	D₄⋊C₈	—	7	1	no	—
274	D₄⋊C₈	—	7	1	no	—
275	D₄⋊C₈	—	7	1	no	—
276	D₄⋊C₈	C₂×D₇	1	1	yes	characteristic, complemented
277	D₄⋊C₈	C₂×D₇	1	1	yes	characteristic, complemented
278	#322	—	7	1	no	—
279	#322	—	7	1	no	—
280	#322	—	7	1	no	—
281	C₈²	—	7	1	no	—
282	C₂³×C₇	—	2	1	no	—
283	C₂³×C₇	C₄×D₄	1	1	yes	characteristic
284	C₂²×D₇	—	2	1	no	—
285	C₂²×D₇	—	2	1	no	—
286	C₂²×D₇	—	4	2	no	—
287	C₂²×D₇	—	4	2	no	—
288	C₂²×D₇	—	8	1	no	—
289	C₇×Q₈	—	2	1	no	—
290	C₇×Q₈	—	2	1	no	—
291	C₇×D₄	—	2	1	no	—
292	C₇×D₄	—	2	1	no	—
293	C₇×D₄	—	8	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	—	2	1	no	—
301	C₂×C₄×C₇	—	4	1	no	—
302	C₂×C₄×C₇	—	4	1	no	—
303	C₂×C₄×C₇	—	4	1	no	—
304	C₂×C₄×C₇	C₄×D₄	1	1	yes	characteristic
305	C₂×C₄×C₇	C₄×D₄	1	1	yes	characteristic
306	C₂×C₄×C₇	C₄×D₄	1	1	yes	characteristic
307	C₂×C₄×C₇	C₂³×C₄	1	1	yes	characteristic
308	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
309	C₂×C₄×C₇	C₂×#41	1	1	yes	characteristic
310	C₂×Dic₇	—	2	1	no	—
311	C₂×Dic₇	—	2	1	no	—
312	C₂×Dic₇	—	4	2	no	—
313	D₂₈	—	2	1	no	—
314	D₂₈	—	2	1	no	—
315	D₂₈	—	2	1	no	—
316	D₂₈	—	4	2	no	—
317	D₂₈	#131	1	2	yes	—
318	C₄×D₇	—	4	2	no	—
319	C₄×D₇	—	4	2	no	—
320	C₄×D₇	—	4	1	no	—
321	C₄×D₇	—	4	1	no	—
322	C₄×D₇	—	4	1	no	—
323	C₄×D₇	—	4	1	no	—
324	C₇×C₈	—	4	1	no	—
325	C₇×C₈	—	4	1	no	—
326	C₇×C₈	—	4	1	no	—
327	C₇×C₈	—	4	1	no	—
328	C₇⋊C₈	—	2	1	no	—
329	C₇⋊C₈	—	2	1	no	—
330	C₇⋊C₈	—	2	1	no	—
331	C₇⋊C₈	—	2	1	no	—
332	C₇⋊C₈	—	2	1	no	—
333	C₇⋊C₈	—	2	1	no	—
334	C₇⋊C₈	—	2	1	no	—
335	C₇⋊C₈	—	4	1	no	—
336	C₇⋊C₈	—	4	1	no	—
337	C₇⋊C₈	AGL(1,ℤ/8)	1	2	yes	—
338	C₂²×D₄	—	7	1	no	—
339	C₂³×C₄	—	14	1	no	—
340	C₂×SD₁₆	—	7	1	no	—
341	C₂×SD₁₆	—	7	1	no	—
342	C₂×D₈	—	7	1	no	—
343	C₂×D₈	—	7	1	no	—
344	C₂×M₁₆	—	2	1	no	—
345	C₂×M₁₆	—	7	1	no	—
346	C₂×M₁₆	—	7	1	no	—
347	C₂×M₁₆	—	14	1	no	—
348	C₂×M₁₆	—	14	1	no	—
349	C₂×M₁₆	—	14	1	no	—
350	C₂×M₁₆	—	28	4	no	—
351	C₂²×C₈	—	14	1	no	—
352	C₂²×C₈	—	14	1	no	—
353	C₂²×C₈	—	14	1	no	—
354	#126	—	2	1	no	—
355	#125	C₄×D₇	1	1	yes	characteristic
356	#124	C₄×D₇	1	1	yes	characteristic
357	#123	—	2	1	no	—
358	C₂²⋊Q₈	C₄×D₇	1	1	yes	characteristic
359	#121	C₄×D₇	1	1	yes	characteristic
360	C₄×Q₈	C₂²×D₇	1	1	yes	characteristic
361	C₄×D₄	—	2	1	no	—
362	C₄×D₄	—	7	1	no	—
363	C₄×D₄	—	7	1	no	—
364	C₄×D₄	—	7	1	no	—
365	C₄×D₄	—	7	1	no	—
366	C₄×D₄	—	14	1	no	—
367	C₄×D₄	—	14	1	no	—
368	C₄×D₄	C₂²×D₇	1	1	yes	characteristic
369	#117	—	2	1	no	—
370	C₂×C₄⋊C₄	—	7	1	no	—
371	C₂×C₂²⋊C₄	—	14	1	no	—
372	C₂×C₄²	C₂²×D₇	1	1	yes	characteristic
373	#107	—	7	1	no	—
374	#107	—	7	1	no	—
375	#106	—	7	1	no	—
376	#106	—	7	1	no	—
377	C₄⋊C₈	—	2	1	no	—
378	C₄⋊C₈	—	2	1	no	—
379	C₄⋊C₈	—	7	1	no	—
380	C₄⋊C₈	—	7	1	no	—
381	C₄⋊C₈	—	7	1	no	—
382	C₄⋊C₈	—	7	1	no	—
383	C₄⋊C₈	—	14	1	no	—
384	C₄⋊C₈	—	14	1	no	—
385	C₄⋊C₈	C₂²×D₇	1	1	yes	characteristic
386	C₄⋊C₈	C₂²×D₇	1	1	yes	characteristic
387	#103	—	7	1	no	—
388	#103	—	7	1	no	—
389	#102	—	7	1	no	—
390	#102	—	7	1	no	—
391	#102	—	7	1	no	—
392	#102	—	7	1	no	—
393	#102	—	7	1	no	—
394	#102	—	7	1	no	—
395	C₂²⋊C₈	—	2	1	no	—
396	C₂²⋊C₈	—	7	1	no	—
397	C₂²⋊C₈	—	7	1	no	—
398	C₂²⋊C₈	—	14	1	no	—
399	C₂²⋊C₈	—	14	1	no	—
400	C₂²⋊C₈	—	14	1	no	—
401	C₂²⋊C₈	—	14	1	no	—
402	C₂²⋊C₈	—	14	1	no	—
403	C₂²⋊C₈	—	14	1	no	—
404	C₂²⋊C₈	—	14	1	no	—
405	#97	—	7	1	no	—
406	#97	—	7	1	no	—
407	#97	—	14	1	no	—
408	C₄×C₈	—	7	1	no	—
409	C₄×C₈	—	7	1	no	—
410	C₄×C₈	—	7	1	no	—
411	C₄×C₈	—	7	1	no	—
412	C₄×C₈	—	14	1	no	—
413	C₄×C₈	—	14	1	no	—
414	C₄×C₈	C₂²×D₇	1	1	yes	characteristic
415	C₄×C₈	C₂²×D₇	1	1	yes	characteristic
416	C₂²×C₇	—	2	1	no	—
417	C₂²×C₇	—	2	1	no	—
418	C₂²×C₇	—	2	1	no	—
419	C₂²×C₇	—	4	1	no	—
420	C₂²×C₇	—	4	1	no	—
421	C₂²×C₇	—	4	1	no	—
422	C₂²×C₇	C₂×C₄×D₄	1	1	yes	characteristic
423	C₂×D₇	—	2	2	no	—
424	C₂×D₇	—	4	1	no	—
425	C₂×D₇	—	4	1	no	—
426	C₂×D₇	—	4	1	no	—
427	C₂×D₇	—	4	1	no	—
428	C₂×D₇	—	4	1	no	—
429	C₂×D₇	—	8	4	no	—
430	C₄×C₇	—	2	1	no	—
431	C₄×C₇	—	2	1	no	—
432	C₄×C₇	—	2	1	no	—
433	C₄×C₇	—	2	1	no	—
434	C₄×C₇	—	4	1	no	—
435	C₄×C₇	—	4	1	no	—
436	C₄×C₇	—	4	1	no	—
437	C₄×C₇	C₂×#131	1	1	yes	characteristic
438	C₄×C₇	#568	1	1	yes	characteristic
439	C₄×C₇	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
440	C₄×C₇	#575	1	1	yes	characteristic
441	Dic₇	—	4	1	no	—
442	Dic₇	—	4	1	no	—
443	C₂⁴	—	14	1	no	—
444	C₂×Q₈	C₂×C₄×D₇	1	1	yes	characteristic
445	C₂×D₄	—	2	1	no	—
446	C₂×D₄	—	7	1	no	—
447	C₂×D₄	—	7	1	no	—
448	C₂×D₄	—	14	2	no	—
449	C₂×D₄	—	14	1	no	—
450	C₂×D₄	—	28	1	no	—
451	C₂×D₄	C₂×C₄×D₇	1	1	yes	characteristic
452	C₂²×C₄	—	2	1	no	—
453	C₂²×C₄	—	14	1	no	—
454	C₂²×C₄	—	14	1	no	—
455	C₂²×C₄	—	14	1	no	—
456	C₂²×C₄	—	14	1	no	—
457	C₂²×C₄	—	14	1	no	—
458	C₂²×C₄	—	28	2	no	—
459	C₂²×C₄	—	28	2	no	—
460	C₂²×C₄	C₂×C₄×D₇	1	1	yes	characteristic
461	C₂²×C₄	D₄×D₇	1	1	yes	characteristic
462	C₂²×C₄	#1159	1	1	yes	characteristic
463	SD₁₆	—	14	2	no	—
464	SD₁₆	—	28	1	no	—
465	D₈	—	14	2	no	—
466	D₈	—	28	1	no	—
467	M₁₆	—	4	2	no	—
468	M₁₆	—	14	2	no	—
469	M₁₆	—	28	2	no	—
470	M₁₆	—	28	2	no	—
471	M₁₆	—	28	2	no	—
472	M₁₆	—	28	1	no	—
473	C₂×C₈	—	2	1	no	—
474	C₂×C₈	—	2	1	no	—
475	C₂×C₈	—	2	1	no	—
476	C₂×C₈	—	2	1	no	—
477	C₂×C₈	—	7	1	no	—
478	C₂×C₈	—	7	1	no	—
479	C₂×C₈	—	7	1	no	—
480	C₂×C₈	—	7	1	no	—
481	C₂×C₈	—	7	1	no	—
482	C₂×C₈	—	7	1	no	—
483	C₂×C₈	—	7	1	no	—
484	C₂×C₈	—	7	1	no	—
485	C₂×C₈	—	14	1	no	—
486	C₂×C₈	—	14	1	no	—
487	C₂×C₈	—	28	2	no	—
488	C₂×C₈	—	28	2	no	—
489	C₂×C₈	—	28	2	no	—
490	C₄⋊C₄	—	2	1	no	—
491	C₄⋊C₄	—	2	1	no	—
492	C₄⋊C₄	—	2	1	no	—
493	C₄⋊C₄	—	2	1	no	—
494	C₄⋊C₄	—	7	1	no	—
495	C₄⋊C₄	—	7	1	no	—
496	C₄⋊C₄	—	14	1	no	—
497	C₄⋊C₄	C₂×C₄×D₇	1	1	yes	characteristic
498	C₄⋊C₄	C₂×C₄×D₇	1	1	yes	characteristic
499	C₂²⋊C₄	—	2	1	no	—
500	C₂²⋊C₄	—	2	1	no	—
501	C₂²⋊C₄	—	2	1	no	—
502	C₂²⋊C₄	—	2	1	no	—
503	C₂²⋊C₄	—	2	1	no	—
504	C₂²⋊C₄	—	14	1	no	—
505	C₂²⋊C₄	—	14	1	no	—
506	C₂²⋊C₄	—	14	1	no	—
507	C₂²⋊C₄	—	14	1	no	—
508	C₄²	—	2	1	no	—
509	C₄²	C₂×C₄×D₇	1	1	yes	characteristic
510	C₄²	D₄×D₇	1	1	yes	characteristic
511	C₄²	#1159	1	1	yes	characteristic
512	C₄²	C₂³×D₇	1	1	yes	characteristic
513	C₂×C₇	—	4	1	no	—
514	C₂×C₇	—	8	1	no	—
515	C₂×C₇	#2933	1	1	yes	characteristic
516	C₂×C₇	C₄×AGL(1,ℤ/8)	1	1	yes	characteristic
517	C₂×C₇	#2957	1	1	yes	characteristic
518	D₇	—	4	2	no	—
519	D₇	—	8	1	no	—
520	C₂³	—	2	1	no	—
521	C₂³	—	14	1	no	—
522	C₂³	—	14	1	no	—
523	C₂³	—	28	2	no	—
524	C₂³	—	28	2	no	—
525	C₂³	—	56	1	no	—
526	C₂³	(C₂²⋊D₇)⋊C₄	1	1	yes	characteristic
527	Q₈	—	2	1	no	—
528	Q₈	—	2	1	no	—
529	D₄	—	2	1	no	—
530	D₄	—	2	1	no	—
531	D₄	—	7	2	no	—
532	D₄	—	8	1	no	—
533	D₄	—	14	1	no	—
534	D₄	—	14	1	no	—
535	D₄	—	14	1	no	—
536	D₄	—	28	2	no	—
537	C₂×C₄	—	2	1	no	—
538	C₂×C₄	—	2	1	no	—
539	C₂×C₄	—	2	1	no	—
540	C₂×C₄	—	2	1	no	—
541	C₂×C₄	—	2	1	no	—
542	C₂×C₄	—	2	1	no	—
543	C₂×C₄	—	2	1	no	—
544	C₂×C₄	—	4	1	no	—
545	C₂×C₄	—	4	1	no	—
546	C₂×C₄	—	4	1	no	—
547	C₂×C₄	—	14	1	no	—
548	C₂×C₄	—	14	1	no	—
549	C₂×C₄	—	28	2	no	—
550	C₂×C₄	—	28	2	no	—
551	C₂×C₄	—	28	2	no	—
552	C₂×C₄	—	28	1	no	—
553	C₂×C₄	—	28	1	no	—
554	C₂×C₄	—	28	1	no	—
555	C₂×C₄	—	28	1	no	—
556	C₂×C₄	(C₂²⋊D₇)⋊C₄	1	1	yes	characteristic
557	C₂×C₄	(C₂²⋊D₇)⋊C₄	1	1	yes	characteristic
558	C₂×C₄	(C₂²⋊D₇)⋊C₄	1	1	yes	characteristic
559	C₂×C₄	C₂²×C₄×D₇	1	1	yes	characteristic
560	C₂×C₄	C₂×D₄×D₇	1	1	yes	characteristic
561	C₂×C₄	C₂×#1159	1	1	yes	characteristic
562	C₈	—	4	1	no	—
563	C₈	—	4	1	no	—
564	C₈	—	4	1	no	—
565	C₈	—	4	1	no	—
566	C₈	—	7	2	no	—
567	C₈	—	14	1	no	—
568	C₈	—	14	1	no	—
569	C₈	—	14	1	no	—
570	C₈	—	14	1	no	—
571	C₈	—	14	1	no	—
572	C₈	—	14	1	no	—
573	C₈	—	14	1	no	—
574	C₈	—	28	1	no	—
575	C₈	—	28	1	no	—
576	C₇	#18008	1	1	yes	characteristic, complemented, Sylow
577	C₂²	—	2	1	no	—
578	C₂²	—	2	1	no	—
579	C₂²	—	2	1	no	—
580	C₂²	—	4	1	no	—
581	C₂²	—	4	1	no	—
582	C₂²	—	4	1	no	—
583	C₂²	—	14	2	no	—
584	C₂²	—	28	1	no	—
585	C₂²	—	28	1	no	—
586	C₂²	—	28	1	no	—
587	C₂²	—	28	1	no	—
588	C₂²	—	28	1	no	—
589	C₂²	—	56	4	no	—
590	C₂²	C₂×(C₂²⋊D₇)⋊C₄	1	1	yes	characteristic
591	C₄	—	2	1	no	—
592	C₄	—	2	1	no	—
593	C₄	—	2	1	no	—
594	C₄	—	2	1	no	—
595	C₄	—	4	1	no	—
596	C₄	—	4	1	no	—
597	C₄	—	4	1	no	—
598	C₄	—	28	1	no	—
599	C₄	—	28	1	no	—
600	C₄	D₇×#131	1	1	yes	characteristic
601	C₄	#90441	1	1	yes	characteristic
602	C₄	D₇×AGL(1,ℤ/8)	1	1	yes	characteristic
603	C₄	#90468	1	1	yes	characteristic
604	C₂	—	4	1	no	—
605	C₂	—	8	1	no	—
606	C₂	—	28	2	no	—
607	C₂	—	56	1	no	—
608	C₂	#11736104	1	1	yes	characteristic
609	C₂	#11736311	1	1	yes	characteristic
610	C₂	#11736435	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×#1495	C₂
socle	C₂²×C₇	C₂×C₄×D₄
prime radical	#89808	C₄
cosocle	C₄²×C₇	C₂⁴
hypercenter	#1495	D₇
hypocenter	C₇	#18008
LCS	G ▷ C₂×C₄×C₇ ▷ C₂×C₇ ▷ C₇
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #1495

Complements

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

N	H ≅ G/N	type
2. #11740574	C₂	semidirect
3. #11736488	C₂	semidirect
4. C₇×#1495	C₂	semidirect
5. #11728511	C₂	semidirect
6. #11728497	C₂	semidirect
7. #11728249	C₂	semidirect
8. #11725980	C₂	semidirect
9. #11725974	C₂	semidirect
10. #11725971	C₂	semidirect
11. #11725966	C₂	semidirect
12. #11725914	C₂	semidirect
13. #11725911	C₂	semidirect
14. #11725907	C₂	semidirect
15. #11725905	C₂	semidirect
32. #89796	C₂²	semidirect
33. Q₈×C₇⋊C₈	C₂²	semidirect
37. #89784	C₂²	semidirect
39. D₄×C₇⋊C₈	C₂²	semidirect
51. C₇×Q₈⋊C₈	C₂²	semidirect
52. C₇×Q₈⋊C₈	C₂²	semidirect
53. C₇×D₄⋊C₈	C₂²	semidirect
54. C₇×D₄⋊C₈	C₂²	semidirect
55. #89275	C₂²	semidirect
56. #89275	C₂²	semidirect
57. #89274	C₂²	semidirect
58. #89274	C₂²	semidirect
63. #89250	C₂²	semidirect
64. #89249	C₂²	semidirect
65. #89249	C₂²	semidirect
66. C₈×C₇⋊C₈	C₂²	semidirect
158. #1495	D₇	semidirect
270. Q₈⋊C₈	C₂×D₇	semidirect
271. Q₈⋊C₈	C₂×D₇	semidirect
276. D₄⋊C₈	C₂×D₇	semidirect
277. D₄⋊C₈	C₂×D₇	semidirect
576. C₇	#18008	semidirect

Maximal subgroups

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

subgroup	index
#11740586	2
#11740574	2
#11736488	2
C₇×#1495	2
#11728511	2
#11728497	2
#11728249	2
#11725980	2
#11725974	2
#11725971	2
#11725966	2
#11725914	2
#11725911	2
#11725907	2
#11725905	2
#18008	7