Subgroups — C₇×#24329 #13201545

Order 1792.

1102 conjugacy classes of subgroups.

The subgroup lattice has 530 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₇×Q₈²	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₇×#476	C₂	1	1	yes	maximal, characteristic
3	C₂×C₄×C₇×SD₁₆	C₂	1	1	yes	maximal, characteristic
4	C₇×#2538	C₂	1	1	yes	maximal, characteristic
5	C₇×#2058	C₂	1	2	yes	maximal, complemented
6	C₇×#2023	C₂	1	2	yes	maximal
7	C₇×#1990	C₂	1	1	yes	maximal, characteristic, complemented
8	C₇×#1984	C₂	1	1	yes	maximal, characteristic, complemented
9	C₇×#1880	C₂	1	2	yes	maximal
10	C₇×#1865	C₂	1	2	yes	maximal, complemented
11	C₇×#1803	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×C₇×SD₁₆	C₂²	1	1	yes	characteristic
13	C₇×Q₈²	—	2	4	no	—
14	C₇×Q₈²	—	2	4	no	—
15	C₂×C₇×C₄⋊Q₈	—	2	1	no	—
16	C₂×C₇×C₄⋊Q₈	—	2	2	no	—
17	C₂×C₇×C₄⋊Q₈	C₂²	1	2	yes	—
18	C₂×C₇×C₄⋊Q₈	C₂²	1	1	yes	characteristic
19	C₂×C₇×C₂²⋊Q₈	—	2	1	no	—
20	C₂×C₄×C₇×Q₈	—	2	1	no	—
21	C₂×C₄×C₇×Q₈	C₂²	1	2	yes	—
22	C₂×C₄×C₇×Q₈	C₂²	1	1	yes	characteristic
23	C₂×C₄×C₇×Q₈	C₂²	1	1	yes	characteristic
24	C₂×C₄×C₇×D₄	C₂²	1	1	yes	characteristic
25	C₇×#476	—	2	4	no	—
26	C₄×C₇×SD₁₆	—	2	4	no	—
27	C₂×C₇×#106	C₂²	1	1	yes	characteristic
28	C₂×C₇×#106	C₂²	1	2	yes	—
29	C₂×C₇×C₄⋊C₈	C₂²	1	1	yes	characteristic
30	C₂×C₇×#103	C₂²	1	1	yes	characteristic
31	C₂×C₇×#103	C₂²	1	2	yes	—
32	C₂×C₇×#102	C₂²	1	1	yes	characteristic
33	C₂×C₇×#102	C₂²	1	2	yes	—
34	C₂×C₄×C₇×C₈	C₂²	1	1	yes	characteristic
35	C₇×#396	—	2	2	no	—
36	C₇×#390	C₂²	1	2	yes	—
37	C₇×#389	C₂²	1	2	yes	—
38	C₇×#384	C₂²	1	1	yes	characteristic
39	C₇×#380	—	2	1	no	—
40	C₇×#340	C₂²	1	2	yes	—
41	C₇×#340	C₂²	1	2	yes	—
42	C₇×#340	C₂²	1	2	yes	—
43	C₇×#336	C₂²	1	2	yes	—
44	C₇×#336	C₂²	1	2	yes	—
45	#24329	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
46	C₂²×C₇×Q₈	—	2	2	no	—
47	C₂²×C₇×Q₈	—	2	1	no	—
48	C₂²×C₇×Q₈	D₄	1	1	yes	characteristic
49	C₂²×C₇×Q₈	C₂³	1	1	yes	characteristic
50	C₂²×C₇×D₄	C₂³	1	1	yes	characteristic
51	C₂³×C₄×C₇	—	2	1	no	—
52	C₂×C₇×SD₁₆	—	2	2	no	—
53	C₂×C₇×SD₁₆	—	2	2	no	—
54	C₂×C₇×SD₁₆	Q₈	1	4	yes	complemented
55	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
56	C₂²×C₇×C₈	C₂³	1	2	yes	—
57	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
58	C₇×C₄⋊Q₈	—	2	16	no	—
59	C₇×C₄⋊Q₈	—	2	8	no	—
60	C₇×C₄⋊Q₈	—	2	4	no	—
61	C₇×C₄⋊Q₈	—	2	4	no	—
62	C₇×C₄⋊Q₈	—	2	2	no	—
63	C₇×C₄⋊Q₈	D₄	1	4	yes	—
64	C₇×C₂²⋊Q₈	—	4	4	no	—
65	C₄×C₇×Q₈	—	2	8	no	—
66	C₄×C₇×Q₈	—	2	4	no	—
67	C₄×C₇×Q₈	—	2	4	no	—
68	C₄×C₇×Q₈	—	2	2	no	—
69	C₄×C₇×Q₈	—	2	2	no	—
70	C₄×C₇×Q₈	—	2	2	no	—
71	C₄×C₇×Q₈	D₄	1	4	yes	—
72	C₄×C₇×D₄	—	2	2	no	—
73	C₄×C₇×D₄	—	2	2	no	—
74	C₂×C₇×C₄⋊C₄	—	2	2	no	—
75	C₂×C₇×C₄⋊C₄	—	2	1	no	—
76	C₂×C₇×C₄⋊C₄	—	2	2	no	—
77	C₂×C₇×C₄⋊C₄	—	2	1	no	—
78	C₂×C₇×C₄⋊C₄	—	2	1	no	—
79	C₂×C₇×C₄⋊C₄	—	2	2	no	—
80	C₂×C₇×C₄⋊C₄	—	2	1	no	—
81	C₂×C₇×C₄⋊C₄	D₄	1	1	yes	characteristic
82	C₂×C₇×C₄⋊C₄	D₄	1	2	yes	—
83	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
84	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
85	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
86	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
87	C₂×C₇×C₂²⋊C₄	—	2	1	no	—
88	C₂×C₇×C₂²⋊C₄	—	2	2	no	—
89	C₂×C₇×C₂²⋊C₄	—	2	2	no	—
90	C₂×C₄²×C₇	—	2	2	no	—
91	C₂×C₄²×C₇	—	2	1	no	—
92	C₂×C₄²×C₇	C₂³	1	2	yes	—
93	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
94	C₇×#106	—	2	4	no	—
95	C₇×#106	—	2	2	no	—
96	C₇×C₄⋊C₈	—	2	2	no	—
97	C₇×#103	—	2	2	no	—
98	C₇×#103	—	2	4	no	—
99	C₇×#102	—	2	4	no	—
100	C₇×#102	—	2	2	no	—
101	C₄×C₇×C₈	—	2	2	no	—
102	C₇×#95	—	2	2	no	—
103	C₂×Q₈²	C₂×C₇	1	1	yes	characteristic, complemented
104	C₂×#476	C₂×C₇	1	1	yes	characteristic
105	C₂×C₄×SD₁₆	C₂×C₇	1	1	yes	characteristic
106	#2538	C₂×C₇	1	1	yes	characteristic
107	#2058	C₂×C₇	1	2	yes	complemented
108	#2023	C₂×C₇	1	2	yes	—
109	#1990	C₂×C₇	1	1	yes	characteristic, complemented
110	#1984	C₂×C₇	1	1	yes	characteristic, complemented
111	#1880	C₂×C₇	1	2	yes	—
112	#1865	C₂×C₇	1	2	yes	complemented
113	#1803	C₂×C₇	1	1	yes	characteristic, complemented
114	C₂⁴×C₇	—	2	1	no	—
115	C₂×C₇×Q₈	—	2	8	no	—
116	C₂×C₇×Q₈	—	2	2	no	—
117	C₂×C₇×Q₈	—	2	4	no	—
118	C₂×C₇×Q₈	—	2	2	no	—
119	C₂×C₇×Q₈	—	2	1	no	—
120	C₂×C₇×Q₈	—	2	1	no	—
121	C₂×C₇×Q₈	—	2	1	no	—
122	C₂×C₇×Q₈	—	8	1	no	—
123	C₂×C₇×Q₈	—	8	1	no	—
124	C₂×C₇×Q₈	—	8	2	no	—
125	C₂×C₇×Q₈	—	8	2	no	—
126	C₂×C₇×Q₈	SD₁₆	1	4	yes	complemented
127	C₂×C₇×Q₈	C₂×D₄	1	2	yes	—
128	C₂×C₇×Q₈	C₂×Q₈	1	2	yes	—
129	C₂×C₇×Q₈	#41	1	2	yes	—
130	C₂×C₇×D₄	—	2	1	no	—
131	C₂×C₇×D₄	—	2	1	no	—
132	C₂×C₇×D₄	—	2	1	no	—
133	C₂×C₇×D₄	—	2	1	no	—
134	C₂×C₇×D₄	—	2	1	no	—
135	C₂×C₇×D₄	C₂×Q₈	1	2	yes	—
136	C₂²×C₄×C₇	—	2	1	no	—
137	C₂²×C₄×C₇	—	2	2	no	—
138	C₂²×C₄×C₇	—	2	1	no	—
139	C₂²×C₄×C₇	—	2	1	no	—
140	C₂²×C₄×C₇	—	2	2	no	—
141	C₂²×C₄×C₇	—	4	2	no	—
142	C₂²×C₄×C₇	—	4	2	no	—
143	C₂²×C₄×C₇	—	4	2	no	—
144	C₂²×C₄×C₇	C₂×D₄	1	2	yes	—
145	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
146	C₂²×C₄×C₇	C₂×D₄	1	2	yes	—
147	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
148	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
149	C₇×SD₁₆	—	2	8	no	—
150	C₂×C₇×C₈	—	2	1	no	—
151	C₂×C₇×C₈	—	2	1	no	—
152	C₂×C₇×C₈	—	2	1	no	—
153	C₂×C₇×C₈	—	2	2	no	—
154	C₂×C₇×C₈	—	2	2	no	—
155	C₂×C₇×C₈	—	2	1	no	—
156	C₂×C₇×C₈	—	2	1	no	—
157	C₂×C₇×C₈	—	2	2	no	—
158	C₂×C₇×C₈	C₂×Q₈	1	2	yes	—
159	C₇×C₄⋊C₄	—	2	8	no	—
160	C₇×C₄⋊C₄	—	2	8	no	—
161	C₇×C₄⋊C₄	—	2	4	no	—
162	C₇×C₄⋊C₄	—	2	4	no	—
163	C₇×C₄⋊C₄	—	2	4	no	—
164	C₇×C₄⋊C₄	—	2	2	no	—
165	C₇×C₄⋊C₄	—	2	2	no	—
166	C₇×C₄⋊C₄	—	2	1	no	—
167	C₇×C₄⋊C₄	—	2	1	no	—
168	C₇×C₄⋊C₄	—	2	1	no	—
169	C₇×C₄⋊C₄	—	2	2	no	—
170	C₇×C₄⋊C₄	—	2	2	no	—
171	C₇×C₄⋊C₄	—	4	2	no	—
172	C₇×C₄⋊C₄	—	4	4	no	—
173	C₇×C₄⋊C₄	—	8	1	no	—
174	C₇×C₄⋊C₄	C₂×D₄	1	4	yes	—
175	C₇×C₄⋊C₄	C₂×D₄	1	2	yes	—
176	C₇×C₂²⋊C₄	—	4	2	no	—
177	C₇×C₂²⋊C₄	—	4	4	no	—
178	C₇×C₂²⋊C₄	—	8	2	no	—
179	C₄²×C₇	—	2	8	no	—
180	C₄²×C₇	—	2	4	no	—
181	C₄²×C₇	—	2	2	no	—
182	C₄²×C₇	—	2	2	no	—
183	C₄²×C₇	C₂×D₄	1	2	yes	—
184	C₄²×C₇	C₂×D₄	1	2	yes	—
185	C₂²×SD₁₆	C₂²×C₇	1	1	yes	characteristic
186	Q₈²	—	2	4	no	—
187	Q₈²	—	2	4	no	—
188	C₂×C₄⋊Q₈	—	2	1	no	—
189	C₂×C₄⋊Q₈	—	2	2	no	—
190	C₂×C₄⋊Q₈	C₂²×C₇	1	2	yes	—
191	C₂×C₄⋊Q₈	C₂²×C₇	1	1	yes	characteristic
192	C₂×C₂²⋊Q₈	—	2	1	no	—
193	C₂×C₄×Q₈	—	2	1	no	—
194	C₂×C₄×Q₈	C₂²×C₇	1	2	yes	—
195	C₂×C₄×Q₈	C₂²×C₇	1	1	yes	characteristic
196	C₂×C₄×Q₈	C₂²×C₇	1	1	yes	characteristic
197	C₂×C₄×D₄	C₂²×C₇	1	1	yes	characteristic
198	#476	—	2	4	no	—
199	C₄×SD₁₆	—	2	4	no	—
200	C₂×#106	C₂²×C₇	1	1	yes	characteristic
201	C₂×#106	C₂²×C₇	1	2	yes	—
202	C₂×C₄⋊C₈	C₂²×C₇	1	1	yes	characteristic
203	C₂×#103	C₂²×C₇	1	2	yes	—
204	C₂×#103	C₂²×C₇	1	1	yes	characteristic
205	C₂×#102	C₂²×C₇	1	2	yes	—
206	C₂×#102	C₂²×C₇	1	1	yes	characteristic
207	C₂×C₄×C₈	C₂²×C₇	1	1	yes	characteristic
208	#396	—	2	2	no	—
209	#390	C₂²×C₇	1	2	yes	—
210	#389	C₂²×C₇	1	2	yes	—
211	#384	C₂²×C₇	1	1	yes	characteristic
212	#380	—	2	1	no	—
213	#340	C₂²×C₇	1	2	yes	—
214	#340	C₂²×C₇	1	2	yes	—
215	#340	C₂²×C₇	1	2	yes	—
216	#336	C₂²×C₇	1	2	yes	—
217	#336	C₂²×C₇	1	2	yes	—
218	C₂³×C₇	—	2	2	no	—
219	C₂³×C₇	—	4	1	no	—
220	C₂³×C₇	—	4	1	no	—
221	C₂³×C₇	—	4	1	no	—
222	C₂³×C₇	—	4	1	no	—
223	C₂³×C₇	—	4	1	no	—
224	C₂³×C₇	—	4	1	no	—
225	C₂³×C₇	C₂²×D₄	1	1	yes	characteristic
226	C₇×Q₈	—	2	2	no	—
227	C₇×Q₈	—	2	2	no	—
228	C₇×Q₈	—	2	2	no	—
229	C₇×Q₈	—	2	8	no	—
230	C₇×Q₈	—	8	4	no	—
231	C₇×Q₈	—	8	8	no	—
232	C₇×Q₈	C₂²⋊Q₈	1	4	yes	complemented
233	C₇×D₄	—	2	2	no	—
234	C₇×D₄	—	2	2	no	—
235	C₇×D₄	—	4	1	no	—
236	C₇×D₄	—	4	1	no	—
237	C₂×C₄×C₇	—	2	2	no	—
238	C₂×C₄×C₇	—	2	2	no	—
239	C₂×C₄×C₇	—	2	2	no	—
240	C₂×C₄×C₇	—	2	2	no	—
241	C₂×C₄×C₇	—	2	2	no	—
242	C₂×C₄×C₇	—	2	1	no	—
243	C₂×C₄×C₇	—	2	1	no	—
244	C₂×C₄×C₇	—	2	2	no	—
245	C₂×C₄×C₇	—	2	4	no	—
246	C₂×C₄×C₇	—	2	2	no	—
247	C₂×C₄×C₇	—	2	2	no	—
248	C₂×C₄×C₇	—	2	2	no	—
249	C₂×C₄×C₇	—	4	2	no	—
250	C₂×C₄×C₇	—	4	1	no	—
251	C₂×C₄×C₇	—	4	2	no	—
252	C₂×C₄×C₇	—	4	1	no	—
253	C₂×C₄×C₇	—	4	1	no	—
254	C₂×C₄×C₇	—	4	2	no	—
255	C₂×C₄×C₇	—	4	2	no	—
256	C₂×C₄×C₇	—	4	1	no	—
257	C₂×C₄×C₇	—	4	1	no	—
258	C₂×C₄×C₇	—	4	2	no	—
259	C₂×C₄×C₇	—	8	4	no	—
260	C₂×C₄×C₇	#120	1	2	yes	—
261	C₂×C₄×C₇	#120	1	2	yes	—
262	C₂×C₄×C₇	C₂×SD₁₆	1	4	yes	—
263	C₂×C₄×C₇	C₂×SD₁₆	1	2	yes	—
264	C₂×C₄×C₇	#137	1	2	yes	—
265	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
266	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
267	C₂×C₄×C₇	C₂²×Q₈	1	1	yes	characteristic
268	C₂×C₄×C₇	C₂×#41	1	1	yes	characteristic
269	C₂×C₄×C₇	2₋¹⁺⁴	1	1	yes	characteristic
270	C₂×C₄×C₇	2₋¹⁺⁴	1	1	yes	characteristic
271	C₇×C₈	—	2	2	no	—
272	C₇×C₈	—	4	1	no	—
273	C₇×C₈	—	4	2	no	—
274	C₂²×Q₈	—	2	2	no	—
275	C₂²×Q₈	—	2	1	no	—
276	C₂²×Q₈	C₇×D₄	1	1	yes	characteristic
277	C₂²×Q₈	C₂³×C₇	1	1	yes	characteristic
278	C₂²×D₄	C₂³×C₇	1	1	yes	characteristic
279	C₂³×C₄	—	2	1	no	—
280	C₂×SD₁₆	—	2	2	no	—
281	C₂×SD₁₆	—	2	2	no	—
282	C₂×SD₁₆	C₇×Q₈	1	4	yes	complemented
283	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
284	C₂²×C₈	C₂³×C₇	1	2	yes	—
285	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
286	C₄⋊Q₈	—	2	16	no	—
287	C₄⋊Q₈	—	2	8	no	—
288	C₄⋊Q₈	—	2	4	no	—
289	C₄⋊Q₈	—	2	4	no	—
290	C₄⋊Q₈	—	2	2	no	—
291	C₄⋊Q₈	C₇×D₄	1	4	yes	—
292	C₂²⋊Q₈	—	4	4	no	—
293	C₄×Q₈	—	2	8	no	—
294	C₄×Q₈	—	2	4	no	—
295	C₄×Q₈	—	2	4	no	—
296	C₄×Q₈	—	2	2	no	—
297	C₄×Q₈	—	2	2	no	—
298	C₄×Q₈	—	2	2	no	—
299	C₄×Q₈	C₇×D₄	1	4	yes	—
300	C₄×D₄	—	2	2	no	—
301	C₄×D₄	—	2	2	no	—
302	C₂×C₄⋊C₄	—	2	2	no	—
303	C₂×C₄⋊C₄	—	2	1	no	—
304	C₂×C₄⋊C₄	—	2	2	no	—
305	C₂×C₄⋊C₄	—	2	1	no	—
306	C₂×C₄⋊C₄	—	2	1	no	—
307	C₂×C₄⋊C₄	—	2	2	no	—
308	C₂×C₄⋊C₄	—	2	1	no	—
309	C₂×C₄⋊C₄	C₇×D₄	1	1	yes	characteristic
310	C₂×C₄⋊C₄	C₇×D₄	1	2	yes	—
311	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
312	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
313	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
314	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
315	C₂×C₂²⋊C₄	—	2	1	no	—
316	C₂×C₂²⋊C₄	—	2	2	no	—
317	C₂×C₂²⋊C₄	—	2	2	no	—
318	C₂×C₄²	—	2	2	no	—
319	C₂×C₄²	—	2	1	no	—
320	C₂×C₄²	C₂³×C₇	1	2	yes	—
321	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
322	#106	—	2	2	no	—
323	#106	—	2	4	no	—
324	C₄⋊C₈	—	2	2	no	—
325	#103	—	2	2	no	—
326	#103	—	2	4	no	—
327	#102	—	2	2	no	—
328	#102	—	2	4	no	—
329	C₄×C₈	—	2	2	no	—
330	#95	—	2	2	no	—
331	C₂²×C₇	—	4	2	no	—
332	C₂²×C₇	—	4	2	no	—
333	C₂²×C₇	—	4	2	no	—
334	C₂²×C₇	—	8	1	no	—
335	C₂²×C₇	—	8	1	no	—
336	C₂²×C₇	—	8	1	no	—
337	C₂²×C₇	—	8	1	no	—
338	C₂²×C₇	C₂×#120	1	1	yes	characteristic
339	C₂²×C₇	#548	1	1	yes	characteristic
340	C₂²×C₇	D₄×Q₈	1	1	yes	characteristic
341	C₂²×C₇	C₂²×SD₁₆	1	1	yes	characteristic
342	C₂²×C₇	C₂×#137	1	1	yes	characteristic
343	C₂²×C₇	#576	1	1	yes	characteristic
344	C₂²×C₇	#577	1	1	yes	characteristic
345	C₄×C₇	—	2	4	no	—
346	C₄×C₇	—	2	4	no	—
347	C₄×C₇	—	2	2	no	—
348	C₄×C₇	—	4	2	no	—
349	C₄×C₇	—	4	4	no	—
350	C₄×C₇	—	4	2	no	—
351	C₄×C₇	—	8	2	no	—
352	C₄×C₇	—	8	1	no	—
353	C₄×C₇	#448	1	4	yes	—
354	C₄×C₇	C₂×C₂²⋊Q₈	1	1	yes	characteristic
355	C₄×C₇	#536	1	1	yes	characteristic
356	C₄×C₇	#548	1	1	yes	characteristic
357	C₄×C₇	D₄×Q₈	1	1	yes	characteristic
358	C₂⁴	—	2	1	no	—
359	C₂×Q₈	—	2	8	no	—
360	C₂×Q₈	—	2	2	no	—
361	C₂×Q₈	—	2	4	no	—
362	C₂×Q₈	—	2	2	no	—
363	C₂×Q₈	—	2	1	no	—
364	C₂×Q₈	—	2	1	no	—
365	C₂×Q₈	—	2	1	no	—
366	C₂×Q₈	—	8	1	no	—
367	C₂×Q₈	—	8	1	no	—
368	C₂×Q₈	—	8	2	no	—
369	C₂×Q₈	—	8	2	no	—
370	C₂×Q₈	C₇×SD₁₆	1	4	yes	complemented
371	C₂×Q₈	C₂×C₇×D₄	1	2	yes	—
372	C₂×Q₈	C₂×C₇×Q₈	1	2	yes	—
373	C₂×Q₈	C₇×#41	1	2	yes	—
374	C₂×D₄	—	2	1	no	—
375	C₂×D₄	—	2	1	no	—
376	C₂×D₄	—	2	1	no	—
377	C₂×D₄	—	2	1	no	—
378	C₂×D₄	—	2	1	no	—
379	C₂×D₄	C₂×C₇×Q₈	1	2	yes	—
380	C₂²×C₄	—	2	1	no	—
381	C₂²×C₄	—	2	2	no	—
382	C₂²×C₄	—	2	1	no	—
383	C₂²×C₄	—	2	1	no	—
384	C₂²×C₄	—	2	2	no	—
385	C₂²×C₄	—	4	2	no	—
386	C₂²×C₄	—	4	2	no	—
387	C₂²×C₄	—	4	2	no	—
388	C₂²×C₄	C₂×C₇×D₄	1	2	yes	—
389	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
390	C₂²×C₄	C₂×C₇×D₄	1	2	yes	—
391	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
392	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
393	SD₁₆	—	2	8	no	—
394	C₂×C₈	—	2	1	no	—
395	C₂×C₈	—	2	1	no	—
396	C₂×C₈	—	2	1	no	—
397	C₂×C₈	—	2	2	no	—
398	C₂×C₈	—	2	2	no	—
399	C₂×C₈	—	2	1	no	—
400	C₂×C₈	—	2	1	no	—
401	C₂×C₈	—	2	2	no	—
402	C₂×C₈	C₂×C₇×Q₈	1	2	yes	—
403	C₄⋊C₄	—	2	8	no	—
404	C₄⋊C₄	—	2	8	no	—
405	C₄⋊C₄	—	2	4	no	—
406	C₄⋊C₄	—	2	4	no	—
407	C₄⋊C₄	—	2	4	no	—
408	C₄⋊C₄	—	2	2	no	—
409	C₄⋊C₄	—	2	2	no	—
410	C₄⋊C₄	—	2	1	no	—
411	C₄⋊C₄	—	2	1	no	—
412	C₄⋊C₄	—	2	1	no	—
413	C₄⋊C₄	—	2	2	no	—
414	C₄⋊C₄	—	2	2	no	—
415	C₄⋊C₄	—	4	2	no	—
416	C₄⋊C₄	—	4	4	no	—
417	C₄⋊C₄	—	8	1	no	—
418	C₄⋊C₄	C₂×C₇×D₄	1	4	yes	—
419	C₄⋊C₄	C₂×C₇×D₄	1	2	yes	—
420	C₂²⋊C₄	—	4	2	no	—
421	C₂²⋊C₄	—	4	4	no	—
422	C₂²⋊C₄	—	8	2	no	—
423	C₄²	—	2	8	no	—
424	C₄²	—	2	4	no	—
425	C₄²	—	2	2	no	—
426	C₄²	—	2	2	no	—
427	C₄²	C₂×C₇×D₄	1	2	yes	—
428	C₄²	C₂×C₇×D₄	1	2	yes	—
429	C₂×C₇	—	8	2	no	—
430	C₂×C₇	#2409	1	1	yes	characteristic
431	C₂×C₇	C₂×#448	1	1	yes	characteristic
432	C₂×C₇	#3012	1	1	yes	characteristic
433	C₂×C₇	#3362	1	1	yes	characteristic
434	C₂×C₇	#3369	1	1	yes	characteristic
435	C₂×C₇	Q₈×SD₁₆	1	1	yes	characteristic
436	C₂×C₇	#3385	1	1	yes	characteristic
437	C₂³	—	2	2	no	—
438	C₂³	—	4	1	no	—
439	C₂³	—	4	1	no	—
440	C₂³	—	4	1	no	—
441	C₂³	—	4	1	no	—
442	C₂³	—	4	1	no	—
443	C₂³	—	4	1	no	—
444	C₂³	C₂²×C₇×D₄	1	1	yes	characteristic
445	Q₈	—	2	2	no	—
446	Q₈	—	2	2	no	—
447	Q₈	—	2	2	no	—
448	Q₈	—	2	8	no	—
449	Q₈	—	8	4	no	—
450	Q₈	—	8	8	no	—
451	Q₈	C₇×C₂²⋊Q₈	1	4	yes	complemented
452	D₄	—	2	2	no	—
453	D₄	—	2	2	no	—
454	D₄	—	4	1	no	—
455	D₄	—	4	1	no	—
456	C₂×C₄	—	2	2	no	—
457	C₂×C₄	—	2	2	no	—
458	C₂×C₄	—	2	2	no	—
459	C₂×C₄	—	2	2	no	—
460	C₂×C₄	—	2	2	no	—
461	C₂×C₄	—	2	1	no	—
462	C₂×C₄	—	2	1	no	—
463	C₂×C₄	—	2	2	no	—
464	C₂×C₄	—	2	4	no	—
465	C₂×C₄	—	2	2	no	—
466	C₂×C₄	—	2	2	no	—
467	C₂×C₄	—	2	2	no	—
468	C₂×C₄	—	4	2	no	—
469	C₂×C₄	—	4	1	no	—
470	C₂×C₄	—	4	2	no	—
471	C₂×C₄	—	4	1	no	—
472	C₂×C₄	—	4	1	no	—
473	C₂×C₄	—	4	2	no	—
474	C₂×C₄	—	4	2	no	—
475	C₂×C₄	—	4	1	no	—
476	C₂×C₄	—	4	1	no	—
477	C₂×C₄	—	4	2	no	—
478	C₂×C₄	—	8	4	no	—
479	C₂×C₄	C₇×#120	1	2	yes	—
480	C₂×C₄	C₇×#120	1	2	yes	—
481	C₂×C₄	C₂×C₇×SD₁₆	1	4	yes	—
482	C₂×C₄	C₂×C₇×SD₁₆	1	2	yes	—
483	C₂×C₄	C₇×#137	1	2	yes	—
484	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
485	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
486	C₂×C₄	C₂²×C₇×Q₈	1	1	yes	characteristic
487	C₂×C₄	C₂×C₇×#41	1	1	yes	characteristic
488	C₂×C₄	C₇×2₋¹⁺⁴	1	1	yes	characteristic
489	C₂×C₄	C₇×2₋¹⁺⁴	1	1	yes	characteristic
490	C₈	—	2	2	no	—
491	C₈	—	4	1	no	—
492	C₈	—	4	2	no	—
493	C₇	#24329	1	1	yes	characteristic, direct product factor, Sylow
494	C₂²	—	4	2	no	—
495	C₂²	—	4	2	no	—
496	C₂²	—	4	2	no	—
497	C₂²	—	8	1	no	—
498	C₂²	—	8	1	no	—
499	C₂²	—	8	1	no	—
500	C₂²	—	8	1	no	—
501	C₂²	C₂×C₇×#120	1	1	yes	characteristic
502	C₂²	C₇×#548	1	1	yes	characteristic
503	C₂²	C₇×D₄×Q₈	1	1	yes	characteristic
504	C₂²	C₂²×C₇×SD₁₆	1	1	yes	characteristic
505	C₂²	C₂×C₇×#137	1	1	yes	characteristic
506	C₂²	C₇×#576	1	1	yes	characteristic
507	C₂²	C₇×#577	1	1	yes	characteristic
508	C₄	—	2	4	no	—
509	C₄	—	2	4	no	—
510	C₄	—	2	2	no	—
511	C₄	—	4	2	no	—
512	C₄	—	4	4	no	—
513	C₄	—	4	2	no	—
514	C₄	—	8	1	no	—
515	C₄	—	8	2	no	—
516	C₄	C₇×#448	1	4	yes	—
517	C₄	C₂×C₇×C₂²⋊Q₈	1	1	yes	characteristic
518	C₄	C₇×#536	1	1	yes	characteristic
519	C₄	C₇×#548	1	1	yes	characteristic
520	C₄	C₇×D₄×Q₈	1	1	yes	characteristic
521	C₂	—	8	2	no	—
522	C₂	C₇×#2409	1	1	yes	characteristic
523	C₂	C₂×C₇×#448	1	1	yes	characteristic
524	C₂	C₇×#3012	1	1	yes	characteristic
525	C₂	C₇×#3362	1	1	yes	characteristic
526	C₂	C₇×#3369	1	1	yes	characteristic
527	C₂	C₇×Q₈×SD₁₆	1	1	yes	characteristic
528	C₂	C₇×#3385	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₇	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₇
prime radical	C₂²×C₇×D₄	C₂³
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₇ ◁ C₂×C₄×C₇×Q₈ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₇×Q₈²	C₂	semidirect
5. C₇×#2058	C₂	semidirect
7. C₇×#1990	C₂	semidirect
8. C₇×#1984	C₂	semidirect
10. C₇×#1865	C₂	semidirect
11. C₇×#1803	C₂	semidirect
45. #24329	C₇	direct (N × H)
54. C₂×C₇×SD₁₆	Q₈	semidirect
103. C₂×Q₈²	C₂×C₇	semidirect
107. #2058	C₂×C₇	semidirect
109. #1990	C₂×C₇	semidirect
110. #1984	C₂×C₇	semidirect
112. #1865	C₂×C₇	semidirect
113. #1803	C₂×C₇	semidirect
126. C₂×C₇×Q₈	SD₁₆	semidirect
232. C₇×Q₈	C₂²⋊Q₈	semidirect
282. C₂×SD₁₆	C₇×Q₈	semidirect
370. C₂×Q₈	C₇×SD₁₆	semidirect
451. Q₈	C₇×C₂²⋊Q₈	semidirect
493. C₇	#24329	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₇×Q₈²	2
C₂×C₇×#476	2
C₂×C₄×C₇×SD₁₆	2
C₇×#2538	2
C₇×#2058	2
C₇×#2023	2
C₇×#1990	2
C₇×#1984	2
C₇×#1880	2
C₇×#1865	2
C₇×#1803	2
#24329	7

Subgroups — C7×#24329 #13201545

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×#24329 #13201545