Subgroups — C₇×#24813 #13202029

Order 1792.

894 conjugacy classes of subgroups.

The subgroup lattice has 502 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₇×#475	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₄×C₇×SD₁₆	C₂	1	1	yes	maximal, characteristic
3	C₇×#2542	C₂	1	1	yes	maximal, characteristic
4	C₇×Q₈×C₄⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
5	C₇×#2084	C₂	1	2	yes	maximal, complemented
6	C₇×#2065	C₂	1	2	yes	maximal
7	C₇×#1990	C₂	1	1	yes	maximal, characteristic, complemented
8	C₇×#1939	C₂	1	1	yes	maximal, characteristic, complemented
9	C₇×#1880	C₂	1	2	yes	maximal
10	C₇×#1803	C₂	1	2	yes	maximal, complemented
11	C₇×#1802	C₂	1	1	yes	maximal, characteristic
12	C₂²×C₇×SD₁₆	C₂²	1	1	yes	characteristic
13	C₂×C₇×C₄⋊Q₈	C₂²	1	1	yes	characteristic
14	C₂×C₇×C₂²⋊Q₈	—	2	1	no	—
15	C₂×C₇×C₂²⋊Q₈	—	2	1	no	—
16	C₂×C₄×C₇×Q₈	C₂²	1	2	yes	—
17	C₂×C₄×C₇×Q₈	C₂²	1	1	yes	characteristic
18	C₂×C₄×C₇×D₄	C₂²	1	1	yes	characteristic
19	C₇×#475	—	2	4	no	—
20	C₄×C₇×SD₁₆	—	2	4	no	—
21	C₂×C₇×#106	C₂²	1	1	yes	characteristic
22	C₂×C₇×#106	C₂²	1	2	yes	—
23	C₂×C₇×C₄⋊C₈	C₂²	1	1	yes	characteristic
24	C₂×C₇×C₄⋊C₈	C₂²	1	2	yes	—
25	C₂×C₇×#103	C₂²	1	1	yes	characteristic
26	C₂×C₇×#103	C₂²	1	2	yes	—
27	C₂×C₇×#102	C₂²	1	1	yes	characteristic
28	C₂×C₇×#102	C₂²	1	2	yes	—
29	C₂×C₄×C₇×C₈	C₂²	1	1	yes	characteristic
30	C₇×#399	—	2	2	no	—
31	C₇×#390	C₂²	1	2	yes	—
32	C₇×#389	—	2	2	no	—
33	C₇×#389	C₂²	1	2	yes	—
34	C₇×#384	—	2	1	no	—
35	C₇×#384	C₂²	1	1	yes	characteristic
36	C₇×#384	C₂²	1	2	yes	—
37	C₄×C₇×C₄⋊C₄	—	2	1	no	—
38	C₄×C₇×C₄⋊C₄	C₂²	1	1	yes	characteristic
39	C₇×#340	C₂²	1	2	yes	—
40	C₇×#340	C₂²	1	2	yes	—
41	C₇×#340	C₂²	1	2	yes	—
42	C₇×#336	C₂²	1	2	yes	—
43	#24813	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
44	C₂²×C₇×Q₈	—	2	1	no	—
45	C₂²×C₇×Q₈	C₂³	1	1	yes	characteristic
46	C₂²×C₇×D₄	C₂³	1	1	yes	characteristic
47	C₂³×C₄×C₇	—	2	1	no	—
48	C₂×C₇×SD₁₆	—	2	2	no	—
49	C₂×C₇×SD₁₆	—	2	2	no	—
50	C₂×C₇×SD₁₆	Q₈	1	4	yes	complemented
51	C₂²×C₇×C₈	C₂³	1	2	yes	—
52	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
53	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
54	C₇×C₄⋊Q₈	—	2	2	no	—
55	C₇×C₄⋊Q₈	—	2	2	no	—
56	C₇×C₂²⋊Q₈	—	4	4	no	—
57	C₇×C₂²⋊Q₈	—	4	4	no	—
58	C₄×C₇×Q₈	—	2	2	no	—
59	C₄×C₇×Q₈	—	2	4	no	—
60	C₄×C₇×Q₈	—	4	2	no	—
61	C₄×C₇×Q₈	D₄	1	4	yes	—
62	C₄×C₇×D₄	—	2	2	no	—
63	C₄×C₇×D₄	—	2	2	no	—
64	C₂×C₇×C₄⋊C₄	—	2	1	no	—
65	C₂×C₇×C₄⋊C₄	—	2	1	no	—
66	C₂×C₇×C₄⋊C₄	—	2	2	no	—
67	C₂×C₇×C₄⋊C₄	—	2	2	no	—
68	C₂×C₇×C₄⋊C₄	—	2	2	no	—
69	C₂×C₇×C₄⋊C₄	—	2	1	no	—
70	C₂×C₇×C₄⋊C₄	—	2	2	no	—
71	C₂×C₇×C₄⋊C₄	—	2	1	no	—
72	C₂×C₇×C₄⋊C₄	D₄	1	1	yes	characteristic
73	C₂×C₇×C₄⋊C₄	D₄	1	1	yes	characteristic
74	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
75	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
76	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
77	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
78	C₂×C₇×C₂²⋊C₄	—	2	1	no	—
79	C₂×C₇×C₂²⋊C₄	—	2	2	no	—
80	C₂×C₇×C₂²⋊C₄	—	2	2	no	—
81	C₂×C₄²×C₇	—	2	1	no	—
82	C₂×C₄²×C₇	—	2	2	no	—
83	C₂×C₄²×C₇	C₂³	1	2	yes	—
84	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
85	C₇×#106	—	2	4	no	—
86	C₇×#106	—	2	2	no	—
87	C₇×C₄⋊C₈	—	2	2	no	—
88	C₇×C₄⋊C₈	—	4	2	no	—
89	C₇×#103	—	2	4	no	—
90	C₇×#103	—	2	2	no	—
91	C₇×#102	—	2	2	no	—
92	C₇×#102	—	4	2	no	—
93	C₄×C₇×C₈	—	2	2	no	—
94	C₇×#95	—	2	2	no	—
95	C₇×#95	D₄	1	2	yes	—
96	C₂×#475	C₂×C₇	1	1	yes	characteristic, complemented
97	C₂×C₄×SD₁₆	C₂×C₇	1	1	yes	characteristic
98	#2542	C₂×C₇	1	1	yes	characteristic
99	Q₈×C₄⋊C₄	C₂×C₇	1	1	yes	characteristic, complemented
100	#2084	C₂×C₇	1	2	yes	complemented
101	#2065	C₂×C₇	1	2	yes	—
102	#1990	C₂×C₇	1	1	yes	characteristic, complemented
103	#1939	C₂×C₇	1	1	yes	characteristic, complemented
104	#1880	C₂×C₇	1	2	yes	—
105	#1803	C₂×C₇	1	2	yes	complemented
106	#1802	C₂×C₇	1	1	yes	characteristic
107	C₂⁴×C₇	—	2	1	no	—
108	C₂×C₇×Q₈	—	2	1	no	—
109	C₂×C₇×Q₈	—	2	1	no	—
110	C₂×C₇×Q₈	—	2	1	no	—
111	C₂×C₇×Q₈	—	4	2	no	—
112	C₂×C₇×Q₈	—	4	2	no	—
113	C₂×C₇×Q₈	—	4	2	no	—
114	C₂×C₇×Q₈	C₂×D₄	1	2	yes	—
115	C₂×C₇×Q₈	C₂×Q₈	1	2	yes	—
116	C₂×C₇×Q₈	#41	1	2	yes	—
117	C₂×C₇×D₄	—	2	1	no	—
118	C₂×C₇×D₄	—	2	1	no	—
119	C₂×C₇×D₄	—	2	1	no	—
120	C₂×C₇×D₄	—	2	1	no	—
121	C₂×C₇×D₄	—	2	1	no	—
122	C₂×C₇×D₄	C₂×Q₈	1	2	yes	—
123	C₂²×C₄×C₇	—	2	1	no	—
124	C₂²×C₄×C₇	—	2	1	no	—
125	C₂²×C₄×C₇	—	2	2	no	—
126	C₂²×C₄×C₇	—	2	2	no	—
127	C₂²×C₄×C₇	—	2	1	no	—
128	C₂²×C₄×C₇	—	4	2	no	—
129	C₂²×C₄×C₇	—	4	2	no	—
130	C₂²×C₄×C₇	—	4	2	no	—
131	C₂²×C₄×C₇	C₂×D₄	1	2	yes	—
132	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
133	C₂²×C₄×C₇	C₂×D₄	1	2	yes	—
134	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
135	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
136	C₇×SD₁₆	—	2	8	no	—
137	C₂×C₇×C₈	—	2	1	no	—
138	C₂×C₇×C₈	—	2	1	no	—
139	C₂×C₇×C₈	—	2	1	no	—
140	C₂×C₇×C₈	—	2	2	no	—
141	C₂×C₇×C₈	—	2	2	no	—
142	C₂×C₇×C₈	—	2	1	no	—
143	C₂×C₇×C₈	—	2	2	no	—
144	C₂×C₇×C₈	—	2	1	no	—
145	C₂×C₇×C₈	C₂×Q₈	1	2	yes	—
146	C₇×C₄⋊C₄	—	2	4	no	—
147	C₇×C₄⋊C₄	—	2	2	no	—
148	C₇×C₄⋊C₄	—	2	1	no	—
149	C₇×C₄⋊C₄	—	2	1	no	—
150	C₇×C₄⋊C₄	—	2	2	no	—
151	C₇×C₄⋊C₄	—	2	1	no	—
152	C₇×C₄⋊C₄	—	2	2	no	—
153	C₇×C₄⋊C₄	—	2	2	no	—
154	C₇×C₄⋊C₄	—	2	2	no	—
155	C₇×C₄⋊C₄	—	4	4	no	—
156	C₇×C₄⋊C₄	—	4	4	no	—
157	C₇×C₄⋊C₄	—	4	2	no	—
158	C₇×C₄⋊C₄	—	4	4	no	—
159	C₇×C₄⋊C₄	—	4	2	no	—
160	C₇×C₄⋊C₄	—	8	1	no	—
161	C₇×C₄⋊C₄	—	8	2	no	—
162	C₇×C₄⋊C₄	SD₁₆	1	4	yes	complemented
163	C₇×C₄⋊C₄	C₂×D₄	1	2	yes	—
164	C₇×C₂²⋊C₄	—	4	4	no	—
165	C₇×C₂²⋊C₄	—	4	2	no	—
166	C₇×C₂²⋊C₄	—	4	4	no	—
167	C₄²×C₇	—	2	4	no	—
168	C₄²×C₇	—	2	2	no	—
169	C₄²×C₇	—	2	2	no	—
170	C₄²×C₇	—	4	4	no	—
171	C₄²×C₇	C₂×D₄	1	2	yes	—
172	C₄²×C₇	#41	1	2	yes	—
173	C₂²×SD₁₆	C₂²×C₇	1	1	yes	characteristic
174	C₂×C₄⋊Q₈	C₂²×C₇	1	1	yes	characteristic
175	C₂×C₂²⋊Q₈	—	2	1	no	—
176	C₂×C₂²⋊Q₈	—	2	1	no	—
177	C₂×C₄×Q₈	C₂²×C₇	1	2	yes	—
178	C₂×C₄×Q₈	C₂²×C₇	1	1	yes	characteristic
179	C₂×C₄×D₄	C₂²×C₇	1	1	yes	characteristic
180	#475	—	2	4	no	—
181	C₄×SD₁₆	—	2	4	no	—
182	C₂×#106	C₂²×C₇	1	2	yes	—
183	C₂×#106	C₂²×C₇	1	1	yes	characteristic
184	C₂×C₄⋊C₈	C₂²×C₇	1	1	yes	characteristic
185	C₂×C₄⋊C₈	C₂²×C₇	1	2	yes	—
186	C₂×#103	C₂²×C₇	1	2	yes	—
187	C₂×#103	C₂²×C₇	1	1	yes	characteristic
188	C₂×#102	C₂²×C₇	1	1	yes	characteristic
189	C₂×#102	C₂²×C₇	1	2	yes	—
190	C₂×C₄×C₈	C₂²×C₇	1	1	yes	characteristic
191	#399	—	2	2	no	—
192	#390	C₂²×C₇	1	2	yes	—
193	#389	—	2	2	no	—
194	#389	C₂²×C₇	1	2	yes	—
195	#384	—	2	1	no	—
196	#384	C₂²×C₇	1	1	yes	characteristic
197	#384	C₂²×C₇	1	2	yes	—
198	C₄×C₄⋊C₄	—	2	1	no	—
199	C₄×C₄⋊C₄	C₂²×C₇	1	1	yes	characteristic
200	#340	C₂²×C₇	1	2	yes	—
201	#340	C₂²×C₇	1	2	yes	—
202	#340	C₂²×C₇	1	2	yes	—
203	#336	C₂²×C₇	1	2	yes	—
204	C₂³×C₇	—	2	2	no	—
205	C₂³×C₇	—	4	1	no	—
206	C₂³×C₇	—	4	1	no	—
207	C₂³×C₇	—	4	1	no	—
208	C₂³×C₇	—	4	1	no	—
209	C₂³×C₇	—	4	1	no	—
210	C₂³×C₇	—	4	1	no	—
211	C₂³×C₇	C₂²×D₄	1	1	yes	characteristic
212	C₇×Q₈	—	2	2	no	—
213	C₇×Q₈	—	2	2	no	—
214	C₇×Q₈	—	2	2	no	—
215	C₇×Q₈	—	8	4	no	—
216	C₇×Q₈	C₂²⋊Q₈	1	4	yes	complemented
217	C₇×D₄	—	2	2	no	—
218	C₇×D₄	—	2	2	no	—
219	C₇×D₄	—	4	1	no	—
220	C₇×D₄	—	4	1	no	—
221	C₂×C₄×C₇	—	2	2	no	—
222	C₂×C₄×C₇	—	2	2	no	—
223	C₂×C₄×C₇	—	2	2	no	—
224	C₂×C₄×C₇	—	2	2	no	—
225	C₂×C₄×C₇	—	2	1	no	—
226	C₂×C₄×C₇	—	2	2	no	—
227	C₂×C₄×C₇	—	2	1	no	—
228	C₂×C₄×C₇	—	2	2	no	—
229	C₂×C₄×C₇	—	2	2	no	—
230	C₂×C₄×C₇	—	2	2	no	—
231	C₂×C₄×C₇	—	2	2	no	—
232	C₂×C₄×C₇	—	4	1	no	—
233	C₂×C₄×C₇	—	4	1	no	—
234	C₂×C₄×C₇	—	4	1	no	—
235	C₂×C₄×C₇	—	4	2	no	—
236	C₂×C₄×C₇	—	4	2	no	—
237	C₂×C₄×C₇	—	4	2	no	—
238	C₂×C₄×C₇	—	4	1	no	—
239	C₂×C₄×C₇	—	4	2	no	—
240	C₂×C₄×C₇	—	4	1	no	—
241	C₂×C₄×C₇	—	4	2	no	—
242	C₂×C₄×C₇	—	4	2	no	—
243	C₂×C₄×C₇	—	8	4	no	—
244	C₂×C₄×C₇	#121	1	2	yes	—
245	C₂×C₄×C₇	#121	1	2	yes	—
246	C₂×C₄×C₇	C₂×SD₁₆	1	4	yes	—
247	C₂×C₄×C₇	C₂×SD₁₆	1	2	yes	—
248	C₂×C₄×C₇	AGL(1,ℤ/8)	1	2	yes	—
249	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
250	C₂×C₄×C₇	C₂²×Q₈	1	1	yes	characteristic
251	C₂×C₄×C₇	C₂×#41	1	1	yes	characteristic
252	C₂×C₄×C₇	C₂×#41	1	1	yes	characteristic
253	C₂×C₄×C₇	H(5,𝔽₂)	1	1	yes	characteristic
254	C₂×C₄×C₇	2₋¹⁺⁴	1	1	yes	characteristic
255	C₇×C₈	—	2	2	no	—
256	C₇×C₈	—	4	1	no	—
257	C₇×C₈	—	4	2	no	—
258	C₂²×Q₈	—	2	1	no	—
259	C₂²×Q₈	C₂³×C₇	1	1	yes	characteristic
260	C₂²×D₄	C₂³×C₇	1	1	yes	characteristic
261	C₂³×C₄	—	2	1	no	—
262	C₂×SD₁₆	—	2	2	no	—
263	C₂×SD₁₆	—	2	2	no	—
264	C₂×SD₁₆	C₇×Q₈	1	4	yes	complemented
265	C₂²×C₈	C₂³×C₇	1	2	yes	—
266	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
267	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
268	C₄⋊Q₈	—	2	2	no	—
269	C₄⋊Q₈	—	2	2	no	—
270	C₂²⋊Q₈	—	4	4	no	—
271	C₂²⋊Q₈	—	4	4	no	—
272	C₄×Q₈	—	2	2	no	—
273	C₄×Q₈	—	2	4	no	—
274	C₄×Q₈	—	4	2	no	—
275	C₄×Q₈	C₇×D₄	1	4	yes	—
276	C₄×D₄	—	2	2	no	—
277	C₄×D₄	—	2	2	no	—
278	C₂×C₄⋊C₄	—	2	1	no	—
279	C₂×C₄⋊C₄	—	2	2	no	—
280	C₂×C₄⋊C₄	—	2	2	no	—
281	C₂×C₄⋊C₄	—	2	2	no	—
282	C₂×C₄⋊C₄	—	2	1	no	—
283	C₂×C₄⋊C₄	—	2	1	no	—
284	C₂×C₄⋊C₄	—	2	2	no	—
285	C₂×C₄⋊C₄	—	2	1	no	—
286	C₂×C₄⋊C₄	C₇×D₄	1	1	yes	characteristic
287	C₂×C₄⋊C₄	C₇×D₄	1	1	yes	characteristic
288	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
289	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
290	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
291	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
292	C₂×C₂²⋊C₄	—	2	1	no	—
293	C₂×C₂²⋊C₄	—	2	2	no	—
294	C₂×C₂²⋊C₄	—	2	2	no	—
295	C₂×C₄²	—	2	1	no	—
296	C₂×C₄²	—	2	2	no	—
297	C₂×C₄²	C₂³×C₇	1	2	yes	—
298	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
299	#106	—	2	2	no	—
300	#106	—	2	4	no	—
301	C₄⋊C₈	—	2	2	no	—
302	C₄⋊C₈	—	4	2	no	—
303	#103	—	2	2	no	—
304	#103	—	2	4	no	—
305	#102	—	2	2	no	—
306	#102	—	4	2	no	—
307	C₄×C₈	—	2	2	no	—
308	#95	—	2	2	no	—
309	#95	C₇×D₄	1	2	yes	—
310	C₂²×C₇	—	4	2	no	—
311	C₂²×C₇	—	4	2	no	—
312	C₂²×C₇	—	4	2	no	—
313	C₂²×C₇	—	8	1	no	—
314	C₂²×C₇	—	8	1	no	—
315	C₂²×C₇	—	8	1	no	—
316	C₂²×C₇	—	8	1	no	—
317	C₂²×C₇	C₂×#121	1	1	yes	characteristic
318	C₂²×C₇	#546	1	1	yes	characteristic
319	C₂²×C₇	D₄×Q₈	1	1	yes	characteristic
320	C₂²×C₇	C₂²×SD₁₆	1	1	yes	characteristic
321	C₂²×C₇	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
322	C₂²×C₇	#577	1	1	yes	characteristic
323	C₂²×C₇	#578	1	1	yes	characteristic
324	C₄×C₇	—	2	4	no	—
325	C₄×C₇	—	2	4	no	—
326	C₄×C₇	—	2	2	no	—
327	C₄×C₇	—	4	2	no	—
328	C₄×C₇	—	4	2	no	—
329	C₄×C₇	—	8	2	no	—
330	C₄×C₇	—	8	1	no	—
331	C₄×C₇	—	8	2	no	—
332	C₄×C₇	#460	1	4	yes	—
333	C₄×C₇	C₂×C₂²⋊Q₈	1	1	yes	characteristic
334	C₄×C₇	#537	1	1	yes	characteristic
335	C₄×C₇	#552	1	1	yes	characteristic
336	C₄×C₇	#554	1	1	yes	characteristic
337	C₂⁴	—	2	1	no	—
338	C₂×Q₈	—	2	1	no	—
339	C₂×Q₈	—	2	1	no	—
340	C₂×Q₈	—	2	1	no	—
341	C₂×Q₈	—	4	2	no	—
342	C₂×Q₈	—	4	2	no	—
343	C₂×Q₈	—	4	2	no	—
344	C₂×Q₈	C₂×C₇×D₄	1	2	yes	—
345	C₂×Q₈	C₂×C₇×Q₈	1	2	yes	—
346	C₂×Q₈	C₇×#41	1	2	yes	—
347	C₂×D₄	—	2	1	no	—
348	C₂×D₄	—	2	1	no	—
349	C₂×D₄	—	2	1	no	—
350	C₂×D₄	—	2	1	no	—
351	C₂×D₄	—	2	1	no	—
352	C₂×D₄	C₂×C₇×Q₈	1	2	yes	—
353	C₂²×C₄	—	2	1	no	—
354	C₂²×C₄	—	2	1	no	—
355	C₂²×C₄	—	2	2	no	—
356	C₂²×C₄	—	2	2	no	—
357	C₂²×C₄	—	2	1	no	—
358	C₂²×C₄	—	4	2	no	—
359	C₂²×C₄	—	4	2	no	—
360	C₂²×C₄	—	4	2	no	—
361	C₂²×C₄	C₂×C₇×D₄	1	2	yes	—
362	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
363	C₂²×C₄	C₂×C₇×D₄	1	2	yes	—
364	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
365	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
366	SD₁₆	—	2	8	no	—
367	C₂×C₈	—	2	1	no	—
368	C₂×C₈	—	2	1	no	—
369	C₂×C₈	—	2	1	no	—
370	C₂×C₈	—	2	2	no	—
371	C₂×C₈	—	2	2	no	—
372	C₂×C₈	—	2	1	no	—
373	C₂×C₈	—	2	2	no	—
374	C₂×C₈	—	2	1	no	—
375	C₂×C₈	C₂×C₇×Q₈	1	2	yes	—
376	C₄⋊C₄	—	2	4	no	—
377	C₄⋊C₄	—	2	2	no	—
378	C₄⋊C₄	—	2	1	no	—
379	C₄⋊C₄	—	2	1	no	—
380	C₄⋊C₄	—	2	2	no	—
381	C₄⋊C₄	—	2	1	no	—
382	C₄⋊C₄	—	2	2	no	—
383	C₄⋊C₄	—	2	2	no	—
384	C₄⋊C₄	—	2	2	no	—
385	C₄⋊C₄	—	4	4	no	—
386	C₄⋊C₄	—	4	4	no	—
387	C₄⋊C₄	—	4	2	no	—
388	C₄⋊C₄	—	4	4	no	—
389	C₄⋊C₄	—	4	2	no	—
390	C₄⋊C₄	—	8	1	no	—
391	C₄⋊C₄	—	8	2	no	—
392	C₄⋊C₄	C₇×SD₁₆	1	4	yes	complemented
393	C₄⋊C₄	C₂×C₇×D₄	1	2	yes	—
394	C₂²⋊C₄	—	4	4	no	—
395	C₂²⋊C₄	—	4	2	no	—
396	C₂²⋊C₄	—	4	4	no	—
397	C₄²	—	2	4	no	—
398	C₄²	—	2	2	no	—
399	C₄²	—	2	2	no	—
400	C₄²	—	4	4	no	—
401	C₄²	C₂×C₇×D₄	1	2	yes	—
402	C₄²	C₇×#41	1	2	yes	—
403	C₂×C₇	—	8	2	no	—
404	C₂×C₇	#2417	1	1	yes	characteristic
405	C₂×C₇	C₂×#460	1	1	yes	characteristic
406	C₂×C₇	#3046	1	1	yes	characteristic
407	C₂×C₇	#3298	1	1	yes	characteristic
408	C₂×C₇	#3332	1	1	yes	characteristic
409	C₂×C₇	Q₈×SD₁₆	1	1	yes	characteristic
410	C₂×C₇	#3386	1	1	yes	characteristic
411	C₂³	—	2	2	no	—
412	C₂³	—	4	1	no	—
413	C₂³	—	4	1	no	—
414	C₂³	—	4	1	no	—
415	C₂³	—	4	1	no	—
416	C₂³	—	4	1	no	—
417	C₂³	—	4	1	no	—
418	C₂³	C₂²×C₇×D₄	1	1	yes	characteristic
419	Q₈	—	2	2	no	—
420	Q₈	—	2	2	no	—
421	Q₈	—	2	2	no	—
422	Q₈	—	8	4	no	—
423	Q₈	C₇×C₂²⋊Q₈	1	4	yes	complemented
424	D₄	—	2	2	no	—
425	D₄	—	2	2	no	—
426	D₄	—	4	1	no	—
427	D₄	—	4	1	no	—
428	C₂×C₄	—	2	2	no	—
429	C₂×C₄	—	2	2	no	—
430	C₂×C₄	—	2	2	no	—
431	C₂×C₄	—	2	2	no	—
432	C₂×C₄	—	2	1	no	—
433	C₂×C₄	—	2	2	no	—
434	C₂×C₄	—	2	1	no	—
435	C₂×C₄	—	2	2	no	—
436	C₂×C₄	—	2	2	no	—
437	C₂×C₄	—	2	2	no	—
438	C₂×C₄	—	2	2	no	—
439	C₂×C₄	—	4	1	no	—
440	C₂×C₄	—	4	1	no	—
441	C₂×C₄	—	4	1	no	—
442	C₂×C₄	—	4	2	no	—
443	C₂×C₄	—	4	2	no	—
444	C₂×C₄	—	4	2	no	—
445	C₂×C₄	—	4	1	no	—
446	C₂×C₄	—	4	2	no	—
447	C₂×C₄	—	4	1	no	—
448	C₂×C₄	—	4	2	no	—
449	C₂×C₄	—	4	2	no	—
450	C₂×C₄	—	8	4	no	—
451	C₂×C₄	C₇×#121	1	2	yes	—
452	C₂×C₄	C₇×#121	1	2	yes	—
453	C₂×C₄	C₂×C₇×SD₁₆	1	4	yes	—
454	C₂×C₄	C₂×C₇×SD₁₆	1	2	yes	—
455	C₂×C₄	C₇×AGL(1,ℤ/8)	1	2	yes	—
456	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
457	C₂×C₄	C₂²×C₇×Q₈	1	1	yes	characteristic
458	C₂×C₄	C₂×C₇×#41	1	1	yes	characteristic
459	C₂×C₄	C₂×C₇×#41	1	1	yes	characteristic
460	C₂×C₄	C₇×H(5,𝔽₂)	1	1	yes	characteristic
461	C₂×C₄	C₇×2₋¹⁺⁴	1	1	yes	characteristic
462	C₈	—	2	2	no	—
463	C₈	—	4	1	no	—
464	C₈	—	4	2	no	—
465	C₇	#24813	1	1	yes	characteristic, direct product factor, Sylow
466	C₂²	—	4	2	no	—
467	C₂²	—	4	2	no	—
468	C₂²	—	4	2	no	—
469	C₂²	—	8	1	no	—
470	C₂²	—	8	1	no	—
471	C₂²	—	8	1	no	—
472	C₂²	—	8	1	no	—
473	C₂²	C₂×C₇×#121	1	1	yes	characteristic
474	C₂²	C₇×#546	1	1	yes	characteristic
475	C₂²	C₇×D₄×Q₈	1	1	yes	characteristic
476	C₂²	C₂²×C₇×SD₁₆	1	1	yes	characteristic
477	C₂²	C₂×C₇×AGL(1,ℤ/8)	1	1	yes	characteristic
478	C₂²	C₇×#577	1	1	yes	characteristic
479	C₂²	C₇×#578	1	1	yes	characteristic
480	C₄	—	2	4	no	—
481	C₄	—	2	4	no	—
482	C₄	—	2	2	no	—
483	C₄	—	4	2	no	—
484	C₄	—	4	2	no	—
485	C₄	—	8	1	no	—
486	C₄	—	8	2	no	—
487	C₄	—	8	2	no	—
488	C₄	C₇×#460	1	4	yes	—
489	C₄	C₂×C₇×C₂²⋊Q₈	1	1	yes	characteristic
490	C₄	C₇×#537	1	1	yes	characteristic
491	C₄	C₇×#552	1	1	yes	characteristic
492	C₄	C₇×#554	1	1	yes	characteristic
493	C₂	—	8	2	no	—
494	C₂	C₇×#2417	1	1	yes	characteristic
495	C₂	C₂×C₇×#460	1	1	yes	characteristic
496	C₂	C₇×#3046	1	1	yes	characteristic
497	C₂	C₇×#3298	1	1	yes	characteristic
498	C₂	C₇×#3332	1	1	yes	characteristic
499	C₂	C₇×Q₈×SD₁₆	1	1	yes	characteristic
500	C₂	C₇×#3386	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 ◁ C₄×C₇×C₄⋊C₄ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₇×#475	C₂	semidirect
4. C₇×Q₈×C₄⋊C₄	C₂	semidirect
5. C₇×#2084	C₂	semidirect
7. C₇×#1990	C₂	semidirect
8. C₇×#1939	C₂	semidirect
10. C₇×#1803	C₂	semidirect
43. #24813	C₇	direct (N × H)
50. C₂×C₇×SD₁₆	Q₈	semidirect
96. C₂×#475	C₂×C₇	semidirect
99. Q₈×C₄⋊C₄	C₂×C₇	semidirect
100. #2084	C₂×C₇	semidirect
102. #1990	C₂×C₇	semidirect
103. #1939	C₂×C₇	semidirect
105. #1803	C₂×C₇	semidirect
162. C₇×C₄⋊C₄	SD₁₆	semidirect
216. C₇×Q₈	C₂²⋊Q₈	semidirect
264. C₂×SD₁₆	C₇×Q₈	semidirect
392. C₄⋊C₄	C₇×SD₁₆	semidirect
423. Q₈	C₇×C₂²⋊Q₈	semidirect
465. C₇	#24813	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×#475	2
C₂×C₄×C₇×SD₁₆	2
C₇×#2542	2
C₇×Q₈×C₄⋊C₄	2
C₇×#2084	2
C₇×#2065	2
C₇×#1990	2
C₇×#1939	2
C₇×#1880	2
C₇×#1803	2
C₇×#1802	2
#24813	7

Subgroups — C7×#24813 #13202029

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×#24813 #13202029