Subgroups — #13325022

Order 1792.

642 conjugacy classes of subgroups.

The subgroup lattice has 608 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×#2994	C₂	1	1	yes	maximal, characteristic, complemented
2	#11740586	C₂	1	1	yes	maximal, characteristic
3	#11736732	C₂	1	1	yes	maximal, characteristic, complemented
4	#11729506	C₂	1	1	yes	maximal, characteristic, complemented
5	#11728709	C₂	1	1	yes	maximal, characteristic, complemented
6	#11728707	C₂	1	1	yes	maximal, characteristic, complemented
7	#11728691	C₂	1	1	yes	maximal, characteristic, complemented
8	#11728687	C₂	1	1	yes	maximal, characteristic, complemented
9	#11728616	C₂	1	1	yes	maximal, characteristic, complemented
10	#11728615	C₂	1	1	yes	maximal, characteristic, complemented
11	#11728595	C₂	1	1	yes	maximal, characteristic, complemented
12	#11728594	C₂	1	1	yes	maximal, characteristic, complemented
13	#11728496	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂×#89278	C₂	1	1	yes	maximal, characteristic, complemented
15	#11728177	C₂	1	1	yes	maximal, characteristic, complemented
16	C₇×#529	C₂²	1	1	yes	characteristic
17	C₂×C₄×D₂₈	C₂²	1	1	yes	characteristic
18	C₇×#446	C₂²	1	1	yes	characteristic, complemented
19	C₇×C₈×Q₈	C₂²	1	1	yes	characteristic, complemented
20	C₇×#436	C₂²	1	1	yes	characteristic, complemented
21	C₇×#435	—	2	1	no	—
22	C₇×C₈×D₄	—	2	1	no	—
23	C₇×C₈×D₄	C₂²	1	1	yes	characteristic, complemented
24	C₇×#433	—	2	1	no	—
25	C₇×#431	C₂²	1	1	yes	characteristic
26	C₇×#424	—	2	1	no	—
27	C₂×C₇×C₄⋊C₈	C₂²	1	1	yes	characteristic
28	#89838	C₄	1	1	yes	characteristic
29	#89838	C₄	1	1	yes	characteristic
30	#89829	C₄	1	1	yes	characteristic
31	#89829	C₄	1	1	yes	characteristic
32	#89818	C₄	1	1	yes	characteristic
33	#89816	C₄	1	1	yes	characteristic
34	#89808	C₄	1	1	yes	characteristic
35	#89806	C₄	1	1	yes	characteristic
36	C₄×#1143	C₂²	1	1	yes	characteristic
37	C₄×#1143	C₂²	1	1	yes	characteristic
38	C₄×#1141	C₂²	1	1	yes	characteristic
39	C₄×#1141	C₂²	1	1	yes	characteristic
40	#89698	C₂²	1	1	yes	characteristic
41	#89697	C₂²	1	1	yes	characteristic
42	C₂×C₄×C₇⋊C₈	C₂²	1	1	yes	characteristic
43	#89608	—	2	1	no	—
44	#89608	—	2	1	no	—
45	#89498	—	2	1	no	—
46	D₇×C₂²⋊C₈	—	2	1	no	—
47	#89460	C₂²	1	1	yes	characteristic
48	#89460	C₂²	1	1	yes	characteristic
49	C₈×D₂₈	C₂²	1	1	yes	characteristic
50	C₈×D₂₈	C₂²	1	1	yes	characteristic
51	Q₈⋊(C₇⋊C₈)	C₂²	1	1	yes	characteristic, complemented
52	Q₈⋊(C₇⋊C₈)	C₂²	1	1	yes	characteristic, complemented
53	D₄⋊(C₇⋊C₈)	C₂²	1	1	yes	characteristic, complemented
54	D₄⋊(C₇⋊C₈)	C₂²	1	1	yes	characteristic, complemented
55	#89278	C₂²	1	1	yes	characteristic
56	#89278	C₂²	1	1	yes	characteristic
57	#89278	C₂²	1	1	yes	characteristic
58	#89278	C₂²	1	1	yes	characteristic
59	#89275	C₂²	1	1	yes	characteristic, complemented
60	#89275	C₂²	1	1	yes	characteristic, complemented
61	#89274	C₂²	1	1	yes	characteristic, complemented
62	#89274	C₂²	1	1	yes	characteristic, complemented
63	#89250	C₂²	1	1	yes	characteristic, complemented
64	#89250	C₂²	1	1	yes	characteristic, complemented
65	#89249	C₂²	1	1	yes	characteristic, complemented
66	#89249	C₂²	1	1	yes	characteristic, complemented
67	#18020	—	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	C₂²×C₇×C₈	—	2	1	no	—
72	C₂²×C₇×C₈	—	2	1	no	—
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	C₂³	1	1	yes	characteristic
80	C₄×C₇×D₄	—	2	1	no	—
81	C₄×C₇×D₄	C₂³	1	1	yes	characteristic
82	C₇×#117	—	2	1	no	—
83	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
84	C₂×#1143	C₂×C₄	1	1	yes	characteristic
85	C₂×#1143	C₂×C₄	1	1	yes	characteristic
86	C₂×#1141	C₂×C₄	1	1	yes	characteristic
87	C₂×#1141	C₂×C₄	1	1	yes	characteristic
88	C₂×(C₂×D₇)⋊C₄	—	2	1	no	—
89	C₂×C₄⋊Dic₇	C₂×C₄	1	1	yes	characteristic
90	C₂²×C₇⋊C₈	—	2	1	no	—
91	C₂×#1131	—	2	1	no	—
92	C₂×#1131	—	2	1	no	—
93	C₂×C₈×D₇	—	2	1	no	—
94	C₂×C₈×D₇	—	2	1	no	—
95	C₄×D₂₈	—	2	1	no	—
96	C₄×D₂₈	—	2	1	no	—
97	C₄×D₂₈	C₂×C₄	1	1	yes	characteristic
98	C₄×D₂₈	C₂×C₄	1	1	yes	characteristic
99	C₄×D₂₈	C₂³	1	1	yes	characteristic
100	C₄×D₂₈	C₂³	1	1	yes	characteristic
101	C₇×C₄⋊C₈	—	2	1	no	—
102	C₇×C₄⋊C₈	—	2	1	no	—
103	C₇×C₄⋊C₈	—	2	1	no	—
104	C₇×C₄⋊C₈	D₄	1	1	yes	characteristic
105	C₇×C₄⋊C₈	D₄	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×C₂²⋊C₈	—	2	1	no	—
110	C₇×C₂²⋊C₈	D₄	1	1	yes	characteristic
111	C₇×C₂²⋊C₈	D₄	1	1	yes	characteristic
112	C₇×#97	—	2	1	no	—
113	C₄×C₇×C₈	—	2	1	no	—
114	C₄×C₇×C₈	C₂³	1	1	yes	characteristic
115	C₄×C₇×C₈	C₂³	1	1	yes	characteristic
116	#6409	C₂×C₄	1	1	yes	characteristic
117	#6409	C₂×C₄	1	1	yes	characteristic
118	#6406	C₂×C₄	1	1	yes	characteristic
119	#6406	C₂×C₄	1	1	yes	characteristic
120	C₂²⋊(C₇⋊C₈)	—	2	1	no	—
121	C₂²⋊(C₇⋊C₈)	C₂×C₄	1	1	yes	characteristic
122	C₂²⋊(C₇⋊C₈)	C₂×C₄	1	1	yes	characteristic
123	(C₂×D₇)⋊C₈	—	2	1	no	—
124	(C₂×D₇)⋊C₈	—	2	1	no	—
125	(C₂×D₇)⋊C₈	—	2	1	no	—
126	(C₂×D₇)⋊C₈	—	2	1	no	—
127	#6383	C₂×C₄	1	1	yes	characteristic
128	#6383	C₂×C₄	1	1	yes	characteristic
129	#6383	C₂×C₄	1	1	yes	characteristic
130	#6383	C₂×C₄	1	1	yes	characteristic
131	#6382	C₂×C₄	1	1	yes	characteristic
132	#6382	C₂×C₄	1	1	yes	characteristic
133	#6381	C₂×C₄	1	1	yes	characteristic
134	#6381	C₂×C₄	1	1	yes	characteristic
135	C₄⋊(C₇⋊C₈)	C₂×C₄	1	1	yes	characteristic
136	C₄⋊(C₇⋊C₈)	C₂×C₄	1	1	yes	characteristic
137	C₄⋊(C₇⋊C₈)	C₂³	1	1	yes	characteristic
138	C₄⋊(C₇⋊C₈)	C₂³	1	1	yes	characteristic
139	#6377	—	2	1	no	—
140	C₄×C₇⋊C₈	—	2	1	no	—
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	#3105	—	7	1	no	—
146	#2994	D₇	1	1	yes	characteristic, complemented
147	#2974	—	7	1	no	—
148	#1594	—	7	1	no	—
149	#1592	—	7	1	no	—
150	#1583	—	7	1	no	—
151	#1582	—	7	1	no	—
152	#1581	—	7	1	no	—
153	#1581	—	7	1	no	—
154	#1580	—	7	1	no	—
155	SD₁₆⋊C₈	—	7	1	no	—
156	#1573	—	7	1	no	—
157	#1494	—	7	1	no	—
158	C₂×D₄⋊C₈	—	7	1	no	—
159	#1452	—	7	1	no	—
160	C₂³×D₇	—	2	1	no	—
161	C₂×C₇×Q₈	C₂²×C₄	1	1	yes	characteristic
162	C₂×C₇×D₄	—	2	1	no	—
163	C₂×C₇×D₄	C₂²×C₄	1	1	yes	characteristic
164	C₂²×C₄×C₇	—	2	1	no	—
165	C₂²×C₄×C₇	C₂²×C₄	1	1	yes	characteristic
166	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
167	C₂²×C₄×C₇	#41	1	1	yes	characteristic
168	C₂²×Dic₇	—	2	1	no	—
169	C₂×D₂₈	—	2	2	no	—
170	C₂×D₂₈	—	2	1	no	—
171	C₂×D₂₈	—	4	1	no	—
172	C₂×D₂₈	C₂²×C₄	1	1	yes	characteristic
173	C₂×D₂₈	C₂²×C₄	1	1	yes	characteristic
174	C₂×C₄×D₇	—	2	1	no	—
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	—	8	1	no	—
179	C₂×C₄×D₇	—	8	1	no	—
180	C₇×M₁₆	—	8	1	no	—
181	C₂×C₇×C₈	—	2	1	no	—
182	C₂×C₇×C₈	—	2	1	no	—
183	C₂×C₇×C₈	—	8	1	no	—
184	C₂×C₇×C₈	—	8	1	no	—
185	C₂×C₇×C₈	C₂×D₄	1	1	yes	characteristic
186	C₂×C₇×C₈	C₂×D₄	1	1	yes	characteristic
187	C₂×C₇×C₈	C₂×D₄	1	1	yes	characteristic
188	C₂×C₇×C₈	C₂×D₄	1	1	yes	characteristic
189	C₇×C₄⋊C₄	—	2	1	no	—
190	C₇×C₄⋊C₄	—	2	1	no	—
191	C₇×C₄⋊C₄	—	2	1	no	—
192	C₇×C₄⋊C₄	—	2	1	no	—
193	C₇×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
194	C₇×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
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	C₄²×C₇	—	2	1	no	—
201	C₄²×C₇	C₂²×C₄	1	1	yes	characteristic
202	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
203	C₄²×C₇	#41	1	1	yes	characteristic
204	C₄²×C₇	C₂⁴	1	1	yes	characteristic
205	#1143	—	2	2	no	—
206	#1143	—	4	1	no	—
207	#1141	—	2	2	no	—
208	#1141	—	4	1	no	—
209	(C₂×D₇)⋊C₄	—	2	1	no	—
210	(C₂×D₇)⋊C₄	—	2	1	no	—
211	(C₂×D₇)⋊C₄	—	2	1	no	—
212	(C₂×D₇)⋊C₄	—	2	1	no	—
213	C₄⋊Dic₇	—	2	1	no	—
214	C₄⋊Dic₇	C₂²×C₄	1	1	yes	characteristic
215	C₄⋊Dic₇	C₂²×C₄	1	1	yes	characteristic
216	C₂×C₇⋊C₈	—	2	1	no	—
217	C₂×C₇⋊C₈	—	2	1	no	—
218	C₂×C₇⋊C₈	—	2	1	no	—
219	C₂×C₇⋊C₈	—	2	1	no	—
220	C₂×C₇⋊C₈	—	4	2	no	—
221	C₂×C₇⋊C₈	C₂²×C₄	1	1	yes	characteristic
222	C₂×C₇⋊C₈	C₂²×C₄	1	1	yes	characteristic
223	C₂×C₇⋊C₈	C₂²×C₄	1	1	yes	characteristic
224	C₂×C₇⋊C₈	C₂²×C₄	1	1	yes	characteristic
225	#1131	—	8	1	no	—
226	#1131	—	8	1	no	—
227	C₈×D₇	—	8	1	no	—
228	C₈×D₇	—	8	1	no	—
229	#529	C₂×D₇	1	1	yes	characteristic
230	C₂×C₄×D₄	—	7	1	no	—
231	#484	—	7	1	no	—
232	#481	—	7	1	no	—
233	#478	—	7	1	no	—
234	#478	—	7	1	no	—
235	#463	—	7	1	no	—
236	#463	—	7	1	no	—
237	#450	—	7	1	no	—
238	#447	—	7	1	no	—
239	#446	C₂×D₇	1	1	yes	characteristic, complemented
240	C₈×Q₈	C₂×D₇	1	1	yes	characteristic, complemented
241	C₄×SD₁₆	—	7	1	no	—
242	C₄×SD₁₆	—	7	1	no	—
243	C₄×D₈	—	7	1	no	—
244	C₄×D₈	—	7	1	no	—
245	#436	—	7	1	no	—
246	#436	—	7	1	no	—
247	#436	C₂×D₇	1	1	yes	characteristic, complemented
248	#435	—	2	1	no	—
249	#435	—	14	1	no	—
250	#435	—	14	1	no	—
251	C₈×D₄	—	2	1	no	—
252	C₈×D₄	—	7	1	no	—
253	C₈×D₄	—	7	1	no	—
254	C₈×D₄	C₂×D₇	1	1	yes	characteristic, complemented
255	#433	—	2	1	no	—
256	#432	—	7	1	no	—
257	#431	—	7	1	no	—
258	#431	C₂×D₇	1	1	yes	characteristic
259	#424	—	2	1	no	—
260	C₂×C₄⋊C₈	C₂×D₇	1	1	yes	characteristic
261	#407	—	14	1	no	—
262	C₂×C₂²⋊C₈	—	14	1	no	—
263	C₂×C₄×C₈	—	7	1	no	—
264	#335	—	7	1	no	—
265	#335	—	7	1	no	—
266	#334	—	7	1	no	—
267	#334	—	7	1	no	—
268	Q₈⋊C₈	—	7	1	no	—
269	Q₈⋊C₈	—	7	1	no	—
270	D₄⋊C₈	—	7	1	no	—
271	D₄⋊C₈	—	7	1	no	—
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	#322	—	7	1	no	—
277	#322	—	7	1	no	—
278	#322	—	7	1	no	—
279	#322	—	7	1	no	—
280	C₂³×C₇	—	2	1	no	—
281	C₂³×C₇	C₄×D₄	1	1	yes	characteristic
282	C₂²×D₇	—	2	1	no	—
283	C₂²×D₇	—	2	1	no	—
284	C₂²×D₇	—	4	2	no	—
285	C₂²×D₇	—	4	2	no	—
286	C₂²×D₇	—	8	1	no	—
287	C₇×Q₈	—	2	1	no	—
288	C₇×Q₈	—	2	1	no	—
289	C₇×D₄	—	2	1	no	—
290	C₇×D₄	—	2	1	no	—
291	C₇×D₄	—	4	2	no	—
292	C₂×C₄×C₇	—	2	2	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	1	no	—
302	C₂×C₄×C₇	C₄×D₄	1	1	yes	characteristic
303	C₂×C₄×C₇	C₄×D₄	1	1	yes	characteristic
304	C₂×C₄×C₇	C₄×D₄	1	1	yes	characteristic
305	C₂×C₄×C₇	C₂³×C₄	1	1	yes	characteristic
306	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
307	C₂×C₄×C₇	C₂×#41	1	1	yes	characteristic
308	C₂×Dic₇	—	2	1	no	—
309	C₂×Dic₇	—	2	1	no	—
310	C₂×Dic₇	—	8	1	no	—
311	D₂₈	—	2	1	no	—
312	D₂₈	—	2	1	no	—
313	D₂₈	—	2	1	no	—
314	D₂₈	—	4	2	no	—
315	D₂₈	#131	1	2	yes	—
316	C₄×D₇	—	4	1	no	—
317	C₄×D₇	—	4	1	no	—
318	C₄×D₇	—	4	1	no	—
319	C₄×D₇	—	4	1	no	—
320	C₄×D₇	—	8	1	no	—
321	C₄×D₇	—	8	1	no	—
322	C₇×C₈	—	2	1	no	—
323	C₇×C₈	—	2	1	no	—
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	—	2	1	no	—
329	C₇⋊C₈	—	2	1	no	—
330	C₇⋊C₈	—	2	1	no	—
331	C₇⋊C₈	—	2	1	no	—
332	C₇⋊C₈	—	4	1	no	—
333	C₇⋊C₈	—	4	1	no	—
334	C₇⋊C₈	—	4	1	no	—
335	C₇⋊C₈	—	4	1	no	—
336	C₂²×D₄	—	7	1	no	—
337	C₂³×C₄	—	14	1	no	—
338	C₂×SD₁₆	—	7	1	no	—
339	C₂×SD₁₆	—	7	1	no	—
340	C₂×D₈	—	7	1	no	—
341	C₂×D₈	—	7	1	no	—
342	C₂×M₁₆	—	2	1	no	—
343	C₂×M₁₆	—	14	1	no	—
344	C₂×M₁₆	—	14	1	no	—
345	C₂²×C₈	—	2	1	no	—
346	C₂²×C₈	—	2	1	no	—
347	C₂²×C₈	—	14	1	no	—
348	C₂²×C₈	—	14	1	no	—
349	C₂²×C₈	—	14	1	no	—
350	#126	—	2	1	no	—
351	#125	C₄×D₇	1	1	yes	characteristic
352	#124	C₄×D₇	1	1	yes	characteristic
353	#123	—	2	1	no	—
354	C₂²⋊Q₈	C₄×D₇	1	1	yes	characteristic
355	#121	C₄×D₇	1	1	yes	characteristic
356	C₄×Q₈	C₂²×D₇	1	1	yes	characteristic
357	C₄×D₄	—	2	1	no	—
358	C₄×D₄	—	7	1	no	—
359	C₄×D₄	—	7	1	no	—
360	C₄×D₄	—	7	1	no	—
361	C₄×D₄	—	7	1	no	—
362	C₄×D₄	—	14	1	no	—
363	C₄×D₄	—	14	1	no	—
364	C₄×D₄	C₂²×D₇	1	1	yes	characteristic
365	#117	—	2	1	no	—
366	C₂×C₄⋊C₄	—	7	1	no	—
367	C₂×C₂²⋊C₄	—	14	1	no	—
368	C₂×C₄²	C₂²×D₇	1	1	yes	characteristic
369	#107	—	7	1	no	—
370	#107	—	7	1	no	—
371	#106	—	7	1	no	—
372	#106	—	7	1	no	—
373	C₄⋊C₈	—	2	1	no	—
374	C₄⋊C₈	—	2	1	no	—
375	C₄⋊C₈	—	2	1	no	—
376	C₄⋊C₈	—	7	1	no	—
377	C₄⋊C₈	—	7	1	no	—
378	C₄⋊C₈	—	7	1	no	—
379	C₄⋊C₈	—	7	1	no	—
380	C₄⋊C₈	C₂²⋊D₇	1	1	yes	characteristic
381	C₄⋊C₈	C₂²⋊D₇	1	1	yes	characteristic
382	C₄⋊C₈	C₂²×D₇	1	1	yes	characteristic
383	C₄⋊C₈	C₂²×D₇	1	1	yes	characteristic
384	#103	—	7	1	no	—
385	#103	—	7	1	no	—
386	#102	—	7	1	no	—
387	#102	—	7	1	no	—
388	#102	—	7	1	no	—
389	#102	—	7	1	no	—
390	#102	—	7	1	no	—
391	#102	—	7	1	no	—
392	C₂²⋊C₈	—	2	1	no	—
393	C₂²⋊C₈	—	2	1	no	—
394	C₂²⋊C₈	—	7	1	no	—
395	C₂²⋊C₈	—	7	1	no	—
396	C₂²⋊C₈	—	14	1	no	—
397	C₂²⋊C₈	—	14	1	no	—
398	C₂²⋊C₈	—	14	1	no	—
399	C₂²⋊C₈	—	14	1	no	—
400	C₂²⋊C₈	—	14	1	no	—
401	C₂²⋊C₈	C₂²⋊D₇	1	1	yes	characteristic
402	C₂²⋊C₈	C₂²⋊D₇	1	1	yes	characteristic
403	#97	—	2	1	no	—
404	#97	—	14	1	no	—
405	C₄×C₈	—	2	1	no	—
406	C₄×C₈	—	7	1	no	—
407	C₄×C₈	—	7	1	no	—
408	C₄×C₈	—	7	1	no	—
409	C₄×C₈	—	7	1	no	—
410	C₄×C₈	—	14	1	no	—
411	C₄×C₈	C₂²×D₇	1	1	yes	characteristic
412	C₄×C₈	C₂²×D₇	1	1	yes	characteristic
413	C₂²×C₇	—	2	1	no	—
414	C₂²×C₇	—	2	1	no	—
415	C₂²×C₇	—	4	1	no	—
416	C₂²×C₇	—	4	1	no	—
417	C₂²×C₇	—	4	1	no	—
418	C₂²×C₇	#444	1	2	yes	—
419	C₂²×C₇	C₂×C₄×D₄	1	1	yes	characteristic
420	C₂×D₇	—	2	2	no	—
421	C₂×D₇	—	4	1	no	—
422	C₂×D₇	—	4	1	no	—
423	C₂×D₇	—	4	1	no	—
424	C₂×D₇	—	4	1	no	—
425	C₂×D₇	—	4	1	no	—
426	C₂×D₇	—	8	4	no	—
427	C₄×C₇	—	2	1	no	—
428	C₄×C₇	—	2	1	no	—
429	C₄×C₇	—	2	1	no	—
430	C₄×C₇	—	2	1	no	—
431	C₄×C₇	—	4	1	no	—
432	C₄×C₇	—	4	1	no	—
433	C₄×C₇	—	4	1	no	—
434	C₄×C₇	C₂×#131	1	1	yes	characteristic
435	C₄×C₇	#568	1	1	yes	characteristic
436	C₄×C₇	#576	1	1	yes	characteristic
437	C₄×C₇	#577	1	1	yes	characteristic
438	Dic₇	—	4	1	no	—
439	Dic₇	—	4	1	no	—
440	C₂⁴	—	14	1	no	—
441	C₂×Q₈	C₂×C₄×D₇	1	1	yes	characteristic
442	C₂×D₄	—	2	1	no	—
443	C₂×D₄	—	7	1	no	—
444	C₂×D₄	—	7	1	no	—
445	C₂×D₄	—	14	2	no	—
446	C₂×D₄	—	14	1	no	—
447	C₂×D₄	—	28	1	no	—
448	C₂×D₄	C₂×C₄×D₇	1	1	yes	characteristic
449	C₂²×C₄	—	2	1	no	—
450	C₂²×C₄	—	14	1	no	—
451	C₂²×C₄	—	14	1	no	—
452	C₂²×C₄	—	14	1	no	—
453	C₂²×C₄	—	14	1	no	—
454	C₂²×C₄	—	14	1	no	—
455	C₂²×C₄	—	56	1	no	—
456	C₂²×C₄	—	56	1	no	—
457	C₂²×C₄	C₂×C₄×D₇	1	1	yes	characteristic
458	C₂²×C₄	#1157	1	1	yes	characteristic
459	C₂²×C₄	C₂×C₂²⋊D₇	1	1	yes	characteristic
460	SD₁₆	—	14	2	no	—
461	SD₁₆	—	28	1	no	—
462	D₈	—	14	2	no	—
463	D₈	—	28	1	no	—
464	M₁₆	—	8	1	no	—
465	M₁₆	—	56	1	no	—
466	M₁₆	—	56	1	no	—
467	C₂×C₈	—	2	1	no	—
468	C₂×C₈	—	2	1	no	—
469	C₂×C₈	—	7	1	no	—
470	C₂×C₈	—	7	1	no	—
471	C₂×C₈	—	7	1	no	—
472	C₂×C₈	—	7	1	no	—
473	C₂×C₈	—	8	1	no	—
474	C₂×C₈	—	8	1	no	—
475	C₂×C₈	—	14	1	no	—
476	C₂×C₈	—	14	1	no	—
477	C₂×C₈	—	14	1	no	—
478	C₂×C₈	—	14	1	no	—
479	C₂×C₈	—	28	2	no	—
480	C₂×C₈	—	56	1	no	—
481	C₂×C₈	—	56	1	no	—
482	C₂×C₈	C₂×C₂²⋊D₇	1	1	yes	characteristic
483	C₂×C₈	C₂×C₂²⋊D₇	1	1	yes	characteristic
484	C₂×C₈	C₂×C₂²⋊D₇	1	1	yes	characteristic
485	C₂×C₈	C₂×C₂²⋊D₇	1	1	yes	characteristic
486	C₄⋊C₄	—	2	1	no	—
487	C₄⋊C₄	—	2	1	no	—
488	C₄⋊C₄	—	2	1	no	—
489	C₄⋊C₄	—	2	1	no	—
490	C₄⋊C₄	—	7	1	no	—
491	C₄⋊C₄	—	7	1	no	—
492	C₄⋊C₄	—	14	1	no	—
493	C₄⋊C₄	C₂×C₄×D₇	1	1	yes	characteristic
494	C₄⋊C₄	C₂×C₄×D₇	1	1	yes	characteristic
495	C₂²⋊C₄	—	2	1	no	—
496	C₂²⋊C₄	—	2	1	no	—
497	C₂²⋊C₄	—	2	1	no	—
498	C₂²⋊C₄	—	2	1	no	—
499	C₂²⋊C₄	—	2	1	no	—
500	C₂²⋊C₄	—	14	1	no	—
501	C₂²⋊C₄	—	14	1	no	—
502	C₂²⋊C₄	—	14	1	no	—
503	C₂²⋊C₄	—	14	1	no	—
504	C₄²	—	2	1	no	—
505	C₄²	C₂×C₄×D₇	1	1	yes	characteristic
506	C₄²	#1157	1	1	yes	characteristic
507	C₄²	C₂×C₂²⋊D₇	1	1	yes	characteristic
508	C₄²	C₂³×D₇	1	1	yes	characteristic
509	C₂×C₇	—	2	2	no	—
510	C₂×C₇	—	8	1	no	—
511	C₂×C₇	#2933	1	1	yes	characteristic
512	C₂×C₇	#2946	1	1	yes	characteristic
513	C₂×C₇	C₂×#444	1	1	yes	characteristic
514	D₇	—	4	2	no	—
515	D₇	—	8	1	no	—
516	C₂³	—	2	1	no	—
517	C₂³	—	14	1	no	—
518	C₂³	—	14	1	no	—
519	C₂³	—	28	2	no	—
520	C₂³	—	28	2	no	—
521	C₂³	—	56	1	no	—
522	C₂³	C₄×C₂²⋊D₇	1	1	yes	characteristic
523	Q₈	—	2	1	no	—
524	Q₈	—	2	1	no	—
525	D₄	—	2	1	no	—
526	D₄	—	2	1	no	—
527	D₄	—	4	2	no	—
528	D₄	—	7	2	no	—
529	D₄	—	14	1	no	—
530	D₄	—	14	1	no	—
531	D₄	—	14	1	no	—
532	D₄	—	28	2	no	—
533	C₂×C₄	—	2	2	no	—
534	C₂×C₄	—	2	1	no	—
535	C₂×C₄	—	2	1	no	—
536	C₂×C₄	—	2	1	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	—	4	1	no	—
542	C₂×C₄	—	4	1	no	—
543	C₂×C₄	—	14	1	no	—
544	C₂×C₄	—	14	1	no	—
545	C₂×C₄	—	28	1	no	—
546	C₂×C₄	—	28	1	no	—
547	C₂×C₄	—	28	1	no	—
548	C₂×C₄	—	28	1	no	—
549	C₂×C₄	—	56	1	no	—
550	C₂×C₄	—	56	1	no	—
551	C₂×C₄	—	56	1	no	—
552	C₂×C₄	C₄×C₂²⋊D₇	1	1	yes	characteristic
553	C₂×C₄	C₄×C₂²⋊D₇	1	1	yes	characteristic
554	C₂×C₄	C₄×C₂²⋊D₇	1	1	yes	characteristic
555	C₂×C₄	C₂²×C₄×D₇	1	1	yes	characteristic
556	C₂×C₄	C₂×#1157	1	1	yes	characteristic
557	C₂×C₄	C₂²×C₂²⋊D₇	1	1	yes	characteristic
558	C₈	—	2	1	no	—
559	C₈	—	2	1	no	—
560	C₈	—	2	1	no	—
561	C₈	—	2	1	no	—
562	C₈	—	4	1	no	—
563	C₈	—	4	1	no	—
564	C₈	—	14	1	no	—
565	C₈	—	14	1	no	—
566	C₈	—	14	1	no	—
567	C₈	—	14	1	no	—
568	C₈	—	28	1	no	—
569	C₈	—	28	1	no	—
570	C₈	—	28	1	no	—
571	C₈	—	28	1	no	—
572	C₇	#18020	1	1	yes	characteristic, complemented, Sylow
573	C₂²	—	2	1	no	—
574	C₂²	—	2	1	no	—
575	C₂²	—	4	1	no	—
576	C₂²	—	4	1	no	—
577	C₂²	—	4	1	no	—
578	C₂²	—	14	2	no	—
579	C₂²	—	28	1	no	—
580	C₂²	—	28	1	no	—
581	C₂²	—	28	1	no	—
582	C₂²	—	28	1	no	—
583	C₂²	—	28	1	no	—
584	C₂²	—	56	4	no	—
585	C₂²	#89917	1	2	yes	—
586	C₂²	C₂×C₄×C₂²⋊D₇	1	1	yes	characteristic
587	C₄	—	2	1	no	—
588	C₄	—	2	1	no	—
589	C₄	—	2	1	no	—
590	C₄	—	2	1	no	—
591	C₄	—	4	1	no	—
592	C₄	—	4	1	no	—
593	C₄	—	4	1	no	—
594	C₄	—	28	1	no	—
595	C₄	—	28	1	no	—
596	C₄	D₇×#131	1	1	yes	characteristic
597	C₄	#90441	1	1	yes	characteristic
598	C₄	#90526	1	1	yes	characteristic
599	C₄	#90528	1	1	yes	characteristic
600	C₂	—	2	2	no	—
601	C₂	—	8	1	no	—
602	C₂	—	28	2	no	—
603	C₂	—	56	1	no	—
604	C₂	#11740009	1	1	yes	characteristic
605	C₂	C₂×#89917	1	1	yes	characteristic
606	C₂	#11741241	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂²×C₂²⋊D₇
commutator	C₂×C₄×C₇	C₂³×C₄
Frattini	C₄²	C₂³×D₇
Fitting	C₇×#2994	C₂
socle	C₂²×C₇	C₂×C₄×D₄
prime radical	#89808	C₄
cosocle	C₄²×C₇	C₂⁴
hypercenter	#2994	D₇
hypocenter	C₇	#18020
LCS	G ▷ C₂×C₄×C₇ ▷ C₂×C₇ ▷ C₇
UCS	C₁ ◁ C₂×C₄ ◁ #431 ◁ #2994

Complements

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

N	H ≅ G/N	type
1. C₇×#2994	C₂	semidirect
3. #11736732	C₂	semidirect
4. #11729506	C₂	semidirect
5. #11728709	C₂	semidirect
6. #11728707	C₂	semidirect
7. #11728691	C₂	semidirect
8. #11728687	C₂	semidirect
9. #11728616	C₂	semidirect
10. #11728615	C₂	semidirect
11. #11728595	C₂	semidirect
12. #11728594	C₂	semidirect
13. #11728496	C₂	semidirect
14. C₂×#89278	C₂	semidirect
15. #11728177	C₂	semidirect
18. C₇×#446	C₂²	semidirect
19. C₇×C₈×Q₈	C₂²	semidirect
20. C₇×#436	C₂²	semidirect
23. C₇×C₈×D₄	C₂²	semidirect
51. Q₈⋊(C₇⋊C₈)	C₂²	semidirect
52. Q₈⋊(C₇⋊C₈)	C₂²	semidirect
53. D₄⋊(C₇⋊C₈)	C₂²	semidirect
54. D₄⋊(C₇⋊C₈)	C₂²	semidirect
59. #89275	C₂²	semidirect
60. #89275	C₂²	semidirect
61. #89274	C₂²	semidirect
62. #89274	C₂²	semidirect
63. #89250	C₂²	semidirect
64. #89250	C₂²	semidirect
65. #89249	C₂²	semidirect
66. #89249	C₂²	semidirect
146. #2994	D₇	semidirect
239. #446	C₂×D₇	semidirect
240. C₈×Q₈	C₂×D₇	semidirect
247. #436	C₂×D₇	semidirect
254. C₈×D₄	C₂×D₇	semidirect
572. C₇	#18020	semidirect

Maximal subgroups

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

subgroup	index
C₇×#2994	2
#11740586	2
#11736732	2
#11729506	2
#11728709	2
#11728707	2
#11728691	2
#11728687	2
#11728616	2
#11728615	2
#11728595	2
#11728594	2
#11728496	2
C₂×#89278	2
#11728177	2
#18020	7