Subgroups — #13325160

Order 1792.

606 conjugacy classes of subgroups.

The subgroup lattice has 588 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×#2984	C₂	1	1	yes	maximal, characteristic, complemented
2	#11739887	C₂	1	1	yes	maximal, characteristic
3	#11736734	C₂	1	1	yes	maximal, characteristic
4	#11729375	C₂	1	1	yes	maximal, characteristic, complemented
5	#11728709	C₂	1	1	yes	maximal, characteristic, complemented
6	#11728708	C₂	1	1	yes	maximal, characteristic, complemented
7	#11728707	C₂	1	1	yes	maximal, characteristic, complemented
8	#11728704	C₂	1	1	yes	maximal, characteristic, complemented
9	#11728691	C₂	1	1	yes	maximal, characteristic, complemented
10	#11728690	C₂	1	1	yes	maximal, characteristic, complemented
11	#11728687	C₂	1	1	yes	maximal, characteristic, complemented
12	C₈×#1143	C₂	1	1	yes	maximal, characteristic, complemented
13	#11728555	C₂	1	1	yes	maximal, characteristic
14	#11728550	C₂	1	1	yes	maximal, characteristic, complemented
15	#11728498	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×C₄×C₇×Q₈	C₂²	1	1	yes	characteristic
17	#90168	C₂²	1	1	yes	characteristic
18	C₇×#446	—	2	1	no	—
19	C₇×#446	—	2	1	no	—
20	C₇×#446	C₂²	1	1	yes	characteristic
21	C₇×#446	C₂²	1	1	yes	characteristic
22	C₇×C₈×Q₈	C₂²	1	1	yes	characteristic
23	C₇×C₈×Q₈	C₂²	1	1	yes	characteristic
24	C₇×#432	—	2	1	no	—
25	C₇×#432	C₂²	1	1	yes	characteristic
26	C₇×#431	—	2	1	no	—
27	C₇×#431	C₂²	1	1	yes	characteristic
28	#89999	C₄	1	1	yes	characteristic
29	#89999	C₄	1	1	yes	characteristic
30	#89799	C₄	1	1	yes	characteristic
31	#89799	C₄	1	1	yes	characteristic
32	C₄×#1143	C₂²	1	1	yes	characteristic
33	C₄×#1143	C₂²	1	1	yes	characteristic
34	C₄×#1143	C₂²	1	1	yes	characteristic
35	C₄×#1143	C₂²	1	1	yes	characteristic
36	#89792	C₄	1	1	yes	characteristic
37	#89792	C₄	1	1	yes	characteristic
38	#89740	C₄	1	1	yes	characteristic
39	#89740	C₄	1	1	yes	characteristic
40	#89697	C₂²	1	1	yes	characteristic
41	#89697	C₂²	1	1	yes	characteristic
42	#89697	C₂²	1	1	yes	characteristic
43	#89610	—	2	1	no	—
44	#89606	—	2	1	no	—
45	#89499	—	2	1	no	—
46	#89499	—	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
52	Q₈⋊(C₇⋊C₈)	C₂²	1	1	yes	characteristic
53	Q₈⋊(C₇⋊C₈)	C₂²	1	1	yes	characteristic
54	Q₈⋊(C₇⋊C₈)	C₂²	1	1	yes	characteristic
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
60	#89275	C₂²	1	1	yes	characteristic
61	#89274	C₂²	1	1	yes	characteristic
62	#89274	C₂²	1	1	yes	characteristic
63	#89250	C₂²	1	1	yes	characteristic
64	#89249	C₂²	1	1	yes	characteristic
65	#89249	C₂²	1	1	yes	characteristic
66	C₈×C₇⋊C₈	C₂²	1	1	yes	characteristic
67	#18030	—	7	1	no	maximal, Sylow
68	C₂²×C₇×Q₈	C₂×C₄	1	1	yes	characteristic
69	C₂×#1157	—	2	1	no	—
70	C₄×C₇×Q₈	—	2	1	no	—
71	C₄×C₇×Q₈	—	2	1	no	—
72	C₄×C₇×Q₈	C₂×C₄	1	1	yes	characteristic
73	C₄×C₇×Q₈	C₂×C₄	1	1	yes	characteristic
74	C₄×C₇×Q₈	C₂³	1	1	yes	characteristic
75	C₄×C₇×Q₈	C₂³	1	1	yes	characteristic
76	C₂×C₇×C₄⋊C₄	—	2	1	no	—
77	C₂×C₇×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
78	C₂×C₄²×C₇	—	2	1	no	—
79	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
80	C₂×#1143	C₂×C₄	1	1	yes	characteristic
81	C₂×#1143	C₂×C₄	1	1	yes	characteristic
82	C₂×#1143	C₂×C₄	1	1	yes	characteristic
83	C₂×#1143	C₂×C₄	1	1	yes	characteristic
84	#6493	—	2	1	no	—
85	#6493	C₂×C₄	1	1	yes	characteristic
86	#6493	C₂×C₄	1	1	yes	characteristic
87	C₂×#1131	—	2	1	no	—
88	C₂×#1131	—	2	1	no	—
89	C₂×C₈×D₇	—	2	1	no	—
90	C₂×C₈×D₇	—	2	1	no	—
91	#6438	—	2	1	no	—
92	#6437	C₂×C₄	1	1	yes	characteristic
93	C₄×D₂₈	—	2	1	no	—
94	C₄×D₂₈	C₂³	1	1	yes	characteristic
95	C₄×D₂₈	C₂³	1	1	yes	characteristic
96	#6432	C₂×C₄	1	1	yes	characteristic
97	C₇×C₄⋊C₈	—	2	1	no	—
98	C₇×C₄⋊C₈	—	2	1	no	—
99	C₇×C₄⋊C₈	—	2	1	no	—
100	C₇×C₄⋊C₈	—	2	1	no	—
101	C₇×C₄⋊C₈	D₄	1	1	yes	characteristic
102	C₇×C₄⋊C₈	D₄	1	1	yes	characteristic
103	C₇×C₄⋊C₈	C₂³	1	1	yes	characteristic
104	C₇×C₄⋊C₈	C₂³	1	1	yes	characteristic
105	C₇×C₂²⋊C₈	—	2	1	no	—
106	C₇×C₂²⋊C₈	D₄	1	1	yes	characteristic
107	C₇×C₂²⋊C₈	D₄	1	1	yes	characteristic
108	C₇×#97	—	2	1	no	—
109	C₇×#97	—	2	1	no	—
110	C₇×#97	—	2	1	no	—
111	C₄×C₇×C₈	—	2	1	no	—
112	C₄×C₇×C₈	—	2	1	no	—
113	C₄×C₇×C₈	C₂³	1	1	yes	characteristic
114	C₄×C₇×C₈	C₂³	1	1	yes	characteristic
115	#6409	C₂×C₄	1	1	yes	characteristic
116	#6409	C₂×C₄	1	1	yes	characteristic
117	#6409	C₂×C₄	1	1	yes	characteristic
118	#6409	C₂×C₄	1	1	yes	characteristic
119	C₂²⋊(C₇⋊C₈)	—	2	1	no	—
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	#6382	C₂×C₄	1	1	yes	characteristic
134	#6382	C₂×C₄	1	1	yes	characteristic
135	C₄⋊(C₇⋊C₈)	—	2	1	no	—
136	C₄⋊(C₇⋊C₈)	C₂×C₄	1	1	yes	characteristic
137	C₄⋊(C₇⋊C₈)	C₂×C₄	1	1	yes	characteristic
138	C₄⋊(C₇⋊C₈)	C₂³	1	1	yes	characteristic
139	C₄⋊(C₇⋊C₈)	C₂³	1	1	yes	characteristic
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	#3103	—	7	1	no	—
146	#2984	D₇	1	1	yes	characteristic, complemented
147	#2979	—	7	1	no	—
148	#1592	—	7	1	no	—
149	#1590	—	7	1	no	—
150	#1588	—	7	1	no	—
151	#1585	—	7	1	no	—
152	#1583	—	7	1	no	—
153	#1582	—	7	1	no	—
154	SD₁₆⋊C₈	—	7	1	no	—
155	C₈×SD₁₆	—	7	1	no	—
156	#1572	—	7	1	no	—
157	#1496	—	7	1	no	—
158	#1479	—	7	1	no	—
159	#1454	—	7	1	no	—
160	C₂×C₇×Q₈	—	2	1	no	—
161	C₂×C₇×Q₈	—	2	2	no	—
162	C₂×C₇×Q₈	—	4	1	no	—
163	C₂×C₇×Q₈	C₂²×C₄	1	1	yes	characteristic
164	C₂×C₇×Q₈	C₂²×C₄	1	1	yes	characteristic
165	C₂²×C₄×C₇	—	2	1	no	—
166	C₂²×C₄×C₇	—	2	1	no	—
167	C₂²×C₄×C₇	C₂²×C₄	1	1	yes	characteristic
168	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
169	C₂²×C₄×C₇	#41	1	1	yes	characteristic
170	C₂×C₂²⋊D₇	—	2	1	no	—
171	C₂×C₂²⋊D₇	—	2	1	no	—
172	#1157	—	8	1	no	—
173	#1157	—	8	1	no	—
174	C₂×D₂₈	—	2	1	no	—
175	C₂×D₂₈	—	2	1	no	—
176	C₂×D₂₈	C₂²×C₄	1	1	yes	characteristic
177	C₂×D₂₈	C₂²×C₄	1	1	yes	characteristic
178	C₂×C₄×D₇	—	2	1	no	—
179	C₂×C₄×D₇	—	2	1	no	—
180	C₂×Dic₁₄	—	2	1	no	—
181	C₂×C₇×C₈	—	2	1	no	—
182	C₂×C₇×C₈	—	2	1	no	—
183	C₂×C₇×C₈	C₂×D₄	1	1	yes	characteristic
184	C₂×C₇×C₈	C₂×D₄	1	1	yes	characteristic
185	C₂×C₇×C₈	C₂×D₄	1	1	yes	characteristic
186	C₂×C₇×C₈	C₂×D₄	1	1	yes	characteristic
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	—	2	1	no	—
191	C₇×C₄⋊C₄	—	2	1	no	—
192	C₇×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
193	C₇×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
194	C₄²×C₇	—	2	1	no	—
195	C₄²×C₇	—	2	1	no	—
196	C₄²×C₇	—	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	—	2	2	no	—
204	#1143	—	4	1	no	—
205	#1143	—	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	C₂×C₇⋊C₈	—	2	1	no	—
214	C₂×C₇⋊C₈	—	2	1	no	—
215	C₂×C₇⋊C₈	—	2	1	no	—
216	C₂×C₇⋊C₈	—	2	1	no	—
217	C₂×C₇⋊C₈	C₂²×C₄	1	1	yes	characteristic
218	C₂×C₇⋊C₈	C₂²×C₄	1	1	yes	characteristic
219	C₂×C₇⋊C₈	C₂²×C₄	1	1	yes	characteristic
220	C₂×C₇⋊C₈	C₂²×C₄	1	1	yes	characteristic
221	#1131	—	8	1	no	—
222	#1131	—	8	1	no	—
223	C₈×D₇	—	8	1	no	—
224	C₈×D₇	—	8	1	no	—
225	#532	—	7	1	no	—
226	C₂×C₄×Q₈	C₂×D₇	1	1	yes	characteristic
227	#481	—	7	1	no	—
228	#481	—	7	1	no	—
229	#475	—	7	1	no	—
230	#475	—	7	1	no	—
231	#460	—	7	1	no	—
232	#460	—	7	1	no	—
233	#448	—	7	1	no	—
234	#448	—	7	1	no	—
235	#446	—	2	1	no	—
236	#446	—	2	1	no	—
237	#446	C₂×D₇	1	1	yes	characteristic
238	#446	C₂×D₇	1	1	yes	characteristic
239	C₈×Q₈	C₂×D₇	1	1	yes	characteristic
240	C₈×Q₈	C₂×D₇	1	1	yes	characteristic
241	C₄×SD₁₆	—	7	1	no	—
242	C₄×SD₁₆	—	7	1	no	—
243	C₄×SD₁₆	—	7	1	no	—
244	C₄×SD₁₆	—	7	1	no	—
245	#436	—	7	1	no	—
246	#436	—	7	1	no	—
247	#436	—	14	1	no	—
248	C₈×D₄	—	7	1	no	—
249	C₈×D₄	—	7	1	no	—
250	C₈×D₄	—	14	1	no	—
251	#432	—	2	1	no	—
252	#432	C₂×D₇	1	1	yes	characteristic
253	#431	—	2	1	no	—
254	#431	—	7	1	no	—
255	#431	—	7	1	no	—
256	#431	—	7	1	no	—
257	#431	C₂×D₇	1	1	yes	characteristic
258	#408	—	14	1	no	—
259	#408	—	14	1	no	—
260	#335	—	7	1	no	—
261	#335	—	7	1	no	—
262	#334	—	7	1	no	—
263	#334	—	7	1	no	—
264	Q₈⋊C₈	—	7	1	no	—
265	Q₈⋊C₈	—	7	1	no	—
266	Q₈⋊C₈	—	7	1	no	—
267	Q₈⋊C₈	—	7	1	no	—
268	D₄⋊C₈	—	7	1	no	—
269	D₄⋊C₈	—	7	1	no	—
270	D₄⋊C₈	—	7	1	no	—
271	D₄⋊C₈	—	7	1	no	—
272	#322	—	7	1	no	—
273	#322	—	7	1	no	—
274	#322	—	7	1	no	—
275	C₈²	—	7	1	no	—
276	C₂³×C₇	C₄×D₄	1	1	yes	characteristic
277	C₂²×D₇	—	2	1	no	—
278	C₂²×D₇	—	2	1	no	—
279	C₇×Q₈	—	2	1	no	—
280	C₇×Q₈	—	2	1	no	—
281	C₇×Q₈	—	2	1	no	—
282	C₇×Q₈	—	4	2	no	—
283	C₇×Q₈	#131	1	2	yes	—
284	C₂×C₄×C₇	—	2	1	no	—
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	—	2	1	no	—
290	C₂×C₄×C₇	—	2	1	no	—
291	C₂×C₄×C₇	—	2	1	no	—
292	C₂×C₄×C₇	—	4	1	no	—
293	C₂×C₄×C₇	—	4	2	no	—
294	C₂×C₄×C₇	—	4	2	no	—
295	C₂×C₄×C₇	C₄×D₄	1	1	yes	characteristic
296	C₂×C₄×C₇	C₄×D₄	1	1	yes	characteristic
297	C₂×C₄×C₇	C₄×D₄	1	1	yes	characteristic
298	C₂×C₄×C₇	C₂³×C₄	1	1	yes	characteristic
299	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
300	C₂×C₄×C₇	C₂×#41	1	1	yes	characteristic
301	C₂²⋊D₇	—	8	1	no	—
302	C₂²⋊D₇	—	8	1	no	—
303	C₂×Dic₇	—	2	1	no	—
304	C₂×Dic₇	—	2	1	no	—
305	D₂₈	—	2	1	no	—
306	D₂₈	—	2	1	no	—
307	D₂₈	—	2	1	no	—
308	D₂₈	—	2	1	no	—
309	D₂₈	—	4	2	no	—
310	D₂₈	—	8	1	no	—
311	C₄×D₇	—	4	1	no	—
312	C₄×D₇	—	4	1	no	—
313	C₄×D₇	—	4	1	no	—
314	C₄×D₇	—	4	1	no	—
315	Dic₁₄	—	8	1	no	—
316	C₇×C₈	—	2	1	no	—
317	C₇×C₈	—	2	1	no	—
318	C₇×C₈	—	2	1	no	—
319	C₇×C₈	—	2	1	no	—
320	C₇×C₈	—	4	1	no	—
321	C₇×C₈	—	4	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	—	4	1	no	—
329	C₇⋊C₈	—	4	1	no	—
330	C₂×#41	—	14	1	no	—
331	C₂²×Q₈	C₄×D₇	1	1	yes	characteristic
332	C₂×SD₁₆	—	7	1	no	—
333	C₂×SD₁₆	—	7	1	no	—
334	C₂×SD₁₆	—	7	1	no	—
335	C₂×SD₁₆	—	7	1	no	—
336	C₂×M₁₆	—	14	1	no	—
337	C₂×M₁₆	—	14	1	no	—
338	C₂²×C₈	—	14	1	no	—
339	C₂²×C₈	—	14	1	no	—
340	C₄⋊Q₈	—	7	1	no	—
341	#127	—	7	1	no	—
342	#124	—	14	1	no	—
343	#121	—	7	1	no	—
344	#121	—	7	1	no	—
345	#121	—	14	1	no	—
346	C₄×Q₈	—	2	1	no	—
347	C₄×Q₈	—	2	1	no	—
348	C₄×Q₈	C₄×D₇	1	1	yes	characteristic
349	C₄×Q₈	C₄×D₇	1	1	yes	characteristic
350	C₄×Q₈	C₂²×D₇	1	1	yes	characteristic
351	C₄×Q₈	C₂²×D₇	1	1	yes	characteristic
352	C₄×D₄	—	7	1	no	—
353	C₄×D₄	—	7	1	no	—
354	C₄×D₄	—	14	1	no	—
355	C₂×C₄⋊C₄	—	2	1	no	—
356	C₂×C₄⋊C₄	C₄×D₇	1	1	yes	characteristic
357	C₂×C₄²	—	2	1	no	—
358	C₂×C₄²	C₂²×D₇	1	1	yes	characteristic
359	#106	—	7	1	no	—
360	#106	—	7	1	no	—
361	#106	—	7	1	no	—
362	#106	—	7	1	no	—
363	C₄⋊C₈	—	2	1	no	—
364	C₄⋊C₈	—	2	1	no	—
365	C₄⋊C₈	—	2	1	no	—
366	C₄⋊C₈	—	2	1	no	—
367	C₄⋊C₈	—	7	1	no	—
368	C₄⋊C₈	—	7	1	no	—
369	C₄⋊C₈	—	7	1	no	—
370	C₄⋊C₈	—	7	1	no	—
371	C₄⋊C₈	—	14	1	no	—
372	C₄⋊C₈	C₂²⋊D₇	1	1	yes	characteristic
373	C₄⋊C₈	C₂²⋊D₇	1	1	yes	characteristic
374	C₄⋊C₈	C₂²×D₇	1	1	yes	characteristic
375	C₄⋊C₈	C₂²×D₇	1	1	yes	characteristic
376	#103	—	7	1	no	—
377	#103	—	7	1	no	—
378	#103	—	7	1	no	—
379	#103	—	7	1	no	—
380	#102	—	7	1	no	—
381	#102	—	7	1	no	—
382	#102	—	7	1	no	—
383	#102	—	7	1	no	—
384	C₂²⋊C₈	—	2	1	no	—
385	C₂²⋊C₈	—	7	1	no	—
386	C₂²⋊C₈	—	7	1	no	—
387	C₂²⋊C₈	—	14	1	no	—
388	C₂²⋊C₈	—	14	1	no	—
389	C₂²⋊C₈	—	14	1	no	—
390	C₂²⋊C₈	—	14	1	no	—
391	C₂²⋊C₈	—	14	1	no	—
392	C₂²⋊C₈	—	14	1	no	—
393	C₂²⋊C₈	C₂²⋊D₇	1	1	yes	characteristic
394	C₂²⋊C₈	C₂²⋊D₇	1	1	yes	characteristic
395	#97	—	2	1	no	—
396	#97	—	2	1	no	—
397	#97	—	2	1	no	—
398	C₄×C₈	—	2	1	no	—
399	C₄×C₈	—	2	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	—	14	1	no	—
405	C₄×C₈	C₂²×D₇	1	1	yes	characteristic
406	C₄×C₈	C₂²×D₇	1	1	yes	characteristic
407	C₂²×C₇	—	2	1	no	—
408	C₂²×C₇	—	2	1	no	—
409	C₂²×C₇	—	2	1	no	—
410	C₂²×C₇	C₂×C₄×D₄	1	1	yes	characteristic
411	C₂×D₇	—	4	1	no	—
412	C₂×D₇	—	4	1	no	—
413	C₂×D₇	—	4	1	no	—
414	C₂×D₇	—	4	1	no	—
415	C₂×D₇	—	4	1	no	—
416	C₂×D₇	—	4	1	no	—
417	C₄×C₇	—	2	1	no	—
418	C₄×C₇	—	2	2	no	—
419	C₄×C₇	—	2	1	no	—
420	C₄×C₇	—	2	1	no	—
421	C₄×C₇	—	2	1	no	—
422	C₄×C₇	—	4	1	no	—
423	C₄×C₇	—	4	1	no	—
424	C₄×C₇	—	4	1	no	—
425	C₄×C₇	C₂×#131	1	1	yes	characteristic
426	C₄×C₇	#568	1	1	yes	characteristic
427	C₄×C₇	#577	1	1	yes	characteristic
428	C₄×C₇	#577	1	1	yes	characteristic
429	Dic₇	—	4	1	no	—
430	Dic₇	—	4	1	no	—
431	#41	—	56	1	no	—
432	#41	—	56	1	no	—
433	C₂×Q₈	—	2	1	no	—
434	C₂×Q₈	—	2	2	no	—
435	C₂×Q₈	—	4	1	no	—
436	C₂×Q₈	—	14	1	no	—
437	C₂×Q₈	C₂×C₄×D₇	1	1	yes	characteristic
438	C₂×Q₈	C₂×C₄×D₇	1	1	yes	characteristic
439	C₂×D₄	—	7	1	no	—
440	C₂×D₄	—	7	1	no	—
441	C₂×D₄	—	14	1	no	—
442	C₂×D₄	—	14	1	no	—
443	C₂×D₄	—	14	1	no	—
444	C₂×D₄	—	14	1	no	—
445	C₂²×C₄	—	2	1	no	—
446	C₂²×C₄	—	2	1	no	—
447	C₂²×C₄	—	14	1	no	—
448	C₂²×C₄	—	14	1	no	—
449	C₂²×C₄	C₂×C₄×D₇	1	1	yes	characteristic
450	C₂²×C₄	#1157	1	1	yes	characteristic
451	C₂²×C₄	C₂×C₂²⋊D₇	1	1	yes	characteristic
452	SD₁₆	—	14	2	no	—
453	SD₁₆	—	14	2	no	—
454	SD₁₆	—	28	1	no	—
455	SD₁₆	—	28	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	—	7	1	no	—
461	C₂×C₈	—	7	1	no	—
462	C₂×C₈	—	7	1	no	—
463	C₂×C₈	—	7	1	no	—
464	C₂×C₈	—	14	1	no	—
465	C₂×C₈	—	14	1	no	—
466	C₂×C₈	—	14	1	no	—
467	C₂×C₈	—	14	1	no	—
468	C₂×C₈	—	56	1	no	—
469	C₂×C₈	—	56	1	no	—
470	C₂×C₈	C₂×C₂²⋊D₇	1	1	yes	characteristic
471	C₂×C₈	C₂×C₂²⋊D₇	1	1	yes	characteristic
472	C₂×C₈	C₂×C₂²⋊D₇	1	1	yes	characteristic
473	C₂×C₈	C₂×C₂²⋊D₇	1	1	yes	characteristic
474	C₄⋊C₄	—	2	1	no	—
475	C₄⋊C₄	—	2	1	no	—
476	C₄⋊C₄	—	2	1	no	—
477	C₄⋊C₄	—	2	1	no	—
478	C₄⋊C₄	—	2	1	no	—
479	C₄⋊C₄	—	7	1	no	—
480	C₄⋊C₄	—	7	1	no	—
481	C₄⋊C₄	—	14	1	no	—
482	C₄⋊C₄	C₂×C₄×D₇	1	1	yes	characteristic
483	C₄⋊C₄	C₂×C₄×D₇	1	1	yes	characteristic
484	C₂²⋊C₄	—	14	1	no	—
485	C₂²⋊C₄	—	14	1	no	—
486	C₂²⋊C₄	—	14	1	no	—
487	C₂²⋊C₄	—	14	1	no	—
488	C₄²	—	2	1	no	—
489	C₄²	—	2	1	no	—
490	C₄²	—	2	1	no	—
491	C₄²	—	2	1	no	—
492	C₄²	C₂×C₄×D₇	1	1	yes	characteristic
493	C₄²	#1157	1	1	yes	characteristic
494	C₄²	C₂×C₂²⋊D₇	1	1	yes	characteristic
495	C₄²	C₂³×D₇	1	1	yes	characteristic
496	C₂×C₇	—	4	1	no	—
497	C₂×C₇	#2933	1	1	yes	characteristic
498	C₂×C₇	#2949	1	1	yes	characteristic
499	C₂×C₇	#2955	1	1	yes	characteristic
500	D₇	—	8	1	no	—
501	D₇	—	8	1	no	—
502	C₂³	—	14	1	no	—
503	C₂³	—	14	1	no	—
504	C₂³	C₄×C₂²⋊D₇	1	1	yes	characteristic
505	Q₈	—	2	1	no	—
506	Q₈	—	2	1	no	—
507	Q₈	—	2	1	no	—
508	Q₈	—	4	2	no	—
509	Q₈	—	56	1	no	—
510	Q₈	#6470	1	2	yes	—
511	D₄	—	14	1	no	—
512	D₄	—	14	1	no	—
513	D₄	—	14	1	no	—
514	D₄	—	14	1	no	—
515	D₄	—	28	2	no	—
516	D₄	—	56	1	no	—
517	D₄	—	56	1	no	—
518	D₄	—	56	1	no	—
519	C₂×C₄	—	2	1	no	—
520	C₂×C₄	—	2	1	no	—
521	C₂×C₄	—	2	1	no	—
522	C₂×C₄	—	2	1	no	—
523	C₂×C₄	—	2	1	no	—
524	C₂×C₄	—	2	1	no	—
525	C₂×C₄	—	2	1	no	—
526	C₂×C₄	—	2	1	no	—
527	C₂×C₄	—	4	1	no	—
528	C₂×C₄	—	4	2	no	—
529	C₂×C₄	—	4	2	no	—
530	C₂×C₄	—	14	1	no	—
531	C₂×C₄	—	14	1	no	—
532	C₂×C₄	—	28	1	no	—
533	C₂×C₄	—	28	1	no	—
534	C₂×C₄	—	28	1	no	—
535	C₂×C₄	—	28	1	no	—
536	C₂×C₄	C₄×C₂²⋊D₇	1	1	yes	characteristic
537	C₂×C₄	C₄×C₂²⋊D₇	1	1	yes	characteristic
538	C₂×C₄	C₄×C₂²⋊D₇	1	1	yes	characteristic
539	C₂×C₄	C₂²×C₄×D₇	1	1	yes	characteristic
540	C₂×C₄	C₂×#1157	1	1	yes	characteristic
541	C₂×C₄	C₂²×C₂²⋊D₇	1	1	yes	characteristic
542	C₈	—	2	1	no	—
543	C₈	—	2	1	no	—
544	C₈	—	2	1	no	—
545	C₈	—	2	1	no	—
546	C₈	—	4	1	no	—
547	C₈	—	4	1	no	—
548	C₈	—	14	1	no	—
549	C₈	—	14	1	no	—
550	C₈	—	14	1	no	—
551	C₈	—	14	1	no	—
552	C₈	—	28	1	no	—
553	C₈	—	28	1	no	—
554	C₈	—	28	1	no	—
555	C₈	—	28	1	no	—
556	C₇	#18030	1	1	yes	characteristic, complemented, Sylow
557	C₂²	—	2	1	no	—
558	C₂²	—	2	1	no	—
559	C₂²	—	2	1	no	—
560	C₂²	—	28	1	no	—
561	C₂²	—	28	1	no	—
562	C₂²	—	28	1	no	—
563	C₂²	—	28	1	no	—
564	C₂²	—	28	1	no	—
565	C₂²	—	28	1	no	—
566	C₂²	C₂×C₄×C₂²⋊D₇	1	1	yes	characteristic
567	C₄	—	2	1	no	—
568	C₄	—	2	2	no	—
569	C₄	—	2	1	no	—
570	C₄	—	2	1	no	—
571	C₄	—	2	1	no	—
572	C₄	—	4	1	no	—
573	C₄	—	4	1	no	—
574	C₄	—	4	1	no	—
575	C₄	—	28	1	no	—
576	C₄	—	28	1	no	—
577	C₄	C₂×#6470	1	1	yes	characteristic
578	C₄	#90436	1	1	yes	characteristic
579	C₄	#90528	1	1	yes	characteristic
580	C₄	#90528	1	1	yes	characteristic
581	C₂	—	4	1	no	—
582	C₂	—	56	1	no	—
583	C₂	—	56	1	no	—
584	C₂	#11739993	1	1	yes	characteristic
585	C₂	#11741202	1	1	yes	characteristic
586	C₂	#11741237	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×#2984	C₂
socle	C₂²×C₇	C₂×C₄×D₄
prime radical	#90168	C₂²
cosocle	C₄²×C₇	C₂⁴
hypercenter	#2984	D₇
hypocenter	C₇	#18030
LCS	G ▷ C₂×C₄×C₇ ▷ C₂×C₇ ▷ C₇
UCS	C₁ ◁ C₂×C₄ ◁ #431 ◁ #2984

Complements

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

N	H ≅ G/N	type
1. C₇×#2984	C₂	semidirect
4. #11729375	C₂	semidirect
5. #11728709	C₂	semidirect
6. #11728708	C₂	semidirect
7. #11728707	C₂	semidirect
8. #11728704	C₂	semidirect
9. #11728691	C₂	semidirect
10. #11728690	C₂	semidirect
11. #11728687	C₂	semidirect
12. C₈×#1143	C₂	semidirect
14. #11728550	C₂	semidirect
15. #11728498	C₂	semidirect
146. #2984	D₇	semidirect
556. C₇	#18030	semidirect

Maximal subgroups

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

subgroup	index
C₇×#2984	2
#11739887	2
#11736734	2
#11729375	2
#11728709	2
#11728708	2
#11728707	2
#11728704	2
#11728691	2
#11728690	2
#11728687	2
C₈×#1143	2
#11728555	2
#11728550	2
#11728498	2
#18030	7