Subgroups — C₇×#24814 #13202030

Order 1792.

838 conjugacy classes of subgroups.

The subgroup lattice has 494 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₇×#477	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₄×C₇×SD₁₆	C₂	1	1	yes	maximal, characteristic
3	C₇×#2563	C₂	1	1	yes	maximal, characteristic
4	C₇×Q₈×C₄⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
5	C₇×#2085	C₂	1	2	yes	maximal, complemented
6	C₇×#2067	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×#1805	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×C₄×C₇×Q₈	C₂²	1	2	yes	—
15	C₂×C₄×C₇×Q₈	C₂²	1	1	yes	characteristic
16	C₂×C₄×C₇×D₄	C₂²	1	1	yes	characteristic
17	C₇×#477	—	2	4	no	—
18	C₄×C₇×SD₁₆	—	2	4	no	—
19	C₂×C₇×#107	C₂²	1	2	yes	—
20	C₂×C₇×#106	C₂²	1	1	yes	characteristic
21	C₂×C₇×C₄⋊C₈	C₂²	1	1	yes	characteristic
22	C₂×C₇×C₄⋊C₈	C₂²	1	2	yes	—
23	C₂×C₇×#103	C₂²	1	1	yes	characteristic
24	C₂×C₇×#103	C₂²	1	2	yes	—
25	C₂×C₇×#102	C₂²	1	1	yes	characteristic
26	C₂×C₇×#102	C₂²	1	2	yes	—
27	C₂×C₄×C₇×C₈	C₂²	1	1	yes	characteristic
28	C₇×#393	—	2	2	no	—
29	C₇×#390	C₂²	1	2	yes	—
30	C₇×#389	—	2	2	no	—
31	C₇×#389	C₂²	1	2	yes	—
32	C₇×#384	—	2	1	no	—
33	C₇×#384	C₂²	1	1	yes	characteristic
34	C₇×#382	C₂²	1	2	yes	—
35	C₇×#380	—	2	1	no	—
36	C₇×#380	—	2	1	no	—
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	#24814	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	C₄×C₇×Q₈	—	2	2	no	—
57	C₄×C₇×Q₈	—	2	4	no	—
58	C₄×C₇×Q₈	—	4	2	no	—
59	C₄×C₇×Q₈	D₄	1	4	yes	—
60	C₄×C₇×D₄	—	2	2	no	—
61	C₄×C₇×D₄	—	2	2	no	—
62	C₂×C₇×C₄⋊C₄	—	2	1	no	—
63	C₂×C₇×C₄⋊C₄	—	2	1	no	—
64	C₂×C₇×C₄⋊C₄	—	2	2	no	—
65	C₂×C₇×C₄⋊C₄	—	2	1	no	—
66	C₂×C₇×C₄⋊C₄	—	2	2	no	—
67	C₂×C₇×C₄⋊C₄	—	2	1	no	—
68	C₂×C₇×C₄⋊C₄	D₄	1	1	yes	characteristic
69	C₂×C₇×C₄⋊C₄	D₄	1	1	yes	characteristic
70	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
71	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
72	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
73	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
74	C₂×C₇×C₂²⋊C₄	—	2	1	no	—
75	C₂×C₇×C₂²⋊C₄	—	2	2	no	—
76	C₂×C₇×C₂²⋊C₄	—	2	2	no	—
77	C₂×C₄²×C₇	—	2	1	no	—
78	C₂×C₄²×C₇	—	2	2	no	—
79	C₂×C₄²×C₇	C₂³	1	2	yes	—
80	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
81	C₇×#107	—	2	4	no	—
82	C₇×#106	—	2	2	no	—
83	C₇×C₄⋊C₈	—	2	2	no	—
84	C₇×C₄⋊C₈	—	4	2	no	—
85	C₇×#103	—	2	4	no	—
86	C₇×#103	—	2	2	no	—
87	C₇×#102	—	2	2	no	—
88	C₇×#102	—	4	2	no	—
89	C₄×C₇×C₈	—	2	2	no	—
90	C₇×#95	—	2	2	no	—
91	C₇×#95	—	2	2	no	—
92	C₇×#95	—	2	2	no	—
93	C₇×#95	D₄	1	2	yes	—
94	C₂×#477	C₂×C₇	1	1	yes	characteristic, complemented
95	C₂×C₄×SD₁₆	C₂×C₇	1	1	yes	characteristic
96	#2563	C₂×C₇	1	1	yes	characteristic
97	Q₈×C₄⋊C₄	C₂×C₇	1	1	yes	characteristic, complemented
98	#2085	C₂×C₇	1	2	yes	complemented
99	#2067	C₂×C₇	1	2	yes	—
100	#1990	C₂×C₇	1	1	yes	characteristic, complemented
101	#1939	C₂×C₇	1	1	yes	characteristic, complemented
102	#1880	C₂×C₇	1	2	yes	—
103	#1805	C₂×C₇	1	2	yes	complemented
104	#1802	C₂×C₇	1	1	yes	characteristic
105	C₂⁴×C₇	—	2	1	no	—
106	C₂×C₇×Q₈	—	2	1	no	—
107	C₂×C₇×Q₈	—	2	1	no	—
108	C₂×C₇×Q₈	—	2	1	no	—
109	C₂×C₇×Q₈	—	4	2	no	—
110	C₂×C₇×Q₈	—	8	1	no	—
111	C₂×C₇×Q₈	—	8	1	no	—
112	C₂×C₇×Q₈	C₂×D₄	1	2	yes	—
113	C₂×C₇×Q₈	C₂×Q₈	1	2	yes	—
114	C₂×C₇×Q₈	#41	1	2	yes	—
115	C₂×C₇×D₄	—	2	1	no	—
116	C₂×C₇×D₄	—	2	1	no	—
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	C₂×Q₈	1	2	yes	—
121	C₂²×C₄×C₇	—	2	1	no	—
122	C₂²×C₄×C₇	—	2	1	no	—
123	C₂²×C₄×C₇	—	2	1	no	—
124	C₂²×C₄×C₇	—	2	2	no	—
125	C₂²×C₄×C₇	—	2	2	no	—
126	C₂²×C₄×C₇	—	4	2	no	—
127	C₂²×C₄×C₇	—	4	2	no	—
128	C₂²×C₄×C₇	—	4	2	no	—
129	C₂²×C₄×C₇	C₂×D₄	1	2	yes	—
130	C₂²×C₄×C₇	C₂×D₄	1	2	yes	—
131	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
132	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
133	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
134	C₇×SD₁₆	—	2	8	no	—
135	C₂×C₇×C₈	—	2	1	no	—
136	C₂×C₇×C₈	—	2	1	no	—
137	C₂×C₇×C₈	—	2	1	no	—
138	C₂×C₇×C₈	—	2	2	no	—
139	C₂×C₇×C₈	—	2	2	no	—
140	C₂×C₇×C₈	—	2	1	no	—
141	C₂×C₇×C₈	—	2	2	no	—
142	C₂×C₇×C₈	—	2	1	no	—
143	C₂×C₇×C₈	C₂×Q₈	1	2	yes	—
144	C₇×C₄⋊C₄	—	2	4	no	—
145	C₇×C₄⋊C₄	—	2	2	no	—
146	C₇×C₄⋊C₄	—	2	2	no	—
147	C₇×C₄⋊C₄	—	2	1	no	—
148	C₇×C₄⋊C₄	—	2	1	no	—
149	C₇×C₄⋊C₄	—	2	2	no	—
150	C₇×C₄⋊C₄	—	2	1	no	—
151	C₇×C₄⋊C₄	—	2	2	no	—
152	C₇×C₄⋊C₄	—	2	2	no	—
153	C₇×C₄⋊C₄	—	2	2	no	—
154	C₇×C₄⋊C₄	—	4	4	no	—
155	C₇×C₄⋊C₄	—	4	2	no	—
156	C₇×C₄⋊C₄	—	4	2	no	—
157	C₇×C₄⋊C₄	—	8	1	no	—
158	C₇×C₄⋊C₄	—	8	2	no	—
159	C₇×C₄⋊C₄	C₂×D₄	1	2	yes	—
160	C₇×C₂²⋊C₄	—	4	2	no	—
161	C₇×C₂²⋊C₄	—	8	2	no	—
162	C₇×C₂²⋊C₄	—	8	2	no	—
163	C₄²×C₇	—	2	4	no	—
164	C₄²×C₇	—	2	2	no	—
165	C₄²×C₇	—	2	2	no	—
166	C₄²×C₇	—	4	4	no	—
167	C₄²×C₇	C₂×D₄	1	2	yes	—
168	C₄²×C₇	#41	1	2	yes	—
169	C₂²×SD₁₆	C₂²×C₇	1	1	yes	characteristic
170	C₂×C₄⋊Q₈	C₂²×C₇	1	1	yes	characteristic
171	C₂×C₄×Q₈	C₂²×C₇	1	2	yes	—
172	C₂×C₄×Q₈	C₂²×C₇	1	1	yes	characteristic
173	C₂×C₄×D₄	C₂²×C₇	1	1	yes	characteristic
174	#477	—	2	4	no	—
175	C₄×SD₁₆	—	2	4	no	—
176	C₂×#107	C₂²×C₇	1	2	yes	—
177	C₂×#106	C₂²×C₇	1	1	yes	characteristic
178	C₂×C₄⋊C₈	C₂²×C₇	1	1	yes	characteristic
179	C₂×C₄⋊C₈	C₂²×C₇	1	2	yes	—
180	C₂×#103	C₂²×C₇	1	2	yes	—
181	C₂×#103	C₂²×C₇	1	1	yes	characteristic
182	C₂×#102	C₂²×C₇	1	1	yes	characteristic
183	C₂×#102	C₂²×C₇	1	2	yes	—
184	C₂×C₄×C₈	C₂²×C₇	1	1	yes	characteristic
185	#393	—	2	2	no	—
186	#390	C₂²×C₇	1	2	yes	—
187	#389	—	2	2	no	—
188	#389	C₂²×C₇	1	2	yes	—
189	#384	—	2	1	no	—
190	#384	C₂²×C₇	1	1	yes	characteristic
191	#382	C₂²×C₇	1	2	yes	—
192	#380	—	2	1	no	—
193	#380	—	2	1	no	—
194	C₄×C₄⋊C₄	—	2	1	no	—
195	C₄×C₄⋊C₄	C₂²×C₇	1	1	yes	characteristic
196	#340	C₂²×C₇	1	2	yes	—
197	#340	C₂²×C₇	1	2	yes	—
198	#340	C₂²×C₇	1	2	yes	—
199	#336	C₂²×C₇	1	2	yes	—
200	C₂³×C₇	—	2	2	no	—
201	C₂³×C₇	—	4	1	no	—
202	C₂³×C₇	—	4	1	no	—
203	C₂³×C₇	—	4	1	no	—
204	C₂³×C₇	—	4	1	no	—
205	C₂³×C₇	—	4	1	no	—
206	C₂³×C₇	—	4	1	no	—
207	C₂³×C₇	C₂²×D₄	1	1	yes	characteristic
208	C₇×Q₈	—	2	2	no	—
209	C₇×Q₈	—	2	2	no	—
210	C₇×Q₈	—	2	2	no	—
211	C₇×Q₈	—	8	4	no	—
212	C₇×Q₈	C₂²⋊Q₈	1	4	yes	—
213	C₇×D₄	—	2	2	no	—
214	C₇×D₄	—	2	2	no	—
215	C₇×D₄	—	4	1	no	—
216	C₇×D₄	—	4	1	no	—
217	C₂×C₄×C₇	—	2	2	no	—
218	C₂×C₄×C₇	—	2	2	no	—
219	C₂×C₄×C₇	—	2	2	no	—
220	C₂×C₄×C₇	—	2	1	no	—
221	C₂×C₄×C₇	—	2	1	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	2	no	—
226	C₂×C₄×C₇	—	2	2	no	—
227	C₂×C₄×C₇	—	2	2	no	—
228	C₂×C₄×C₇	—	2	2	no	—
229	C₂×C₄×C₇	—	4	1	no	—
230	C₂×C₄×C₇	—	4	1	no	—
231	C₂×C₄×C₇	—	4	1	no	—
232	C₂×C₄×C₇	—	4	2	no	—
233	C₂×C₄×C₇	—	4	2	no	—
234	C₂×C₄×C₇	—	4	2	no	—
235	C₂×C₄×C₇	—	4	1	no	—
236	C₂×C₄×C₇	—	4	1	no	—
237	C₂×C₄×C₇	—	4	2	no	—
238	C₂×C₄×C₇	—	4	2	no	—
239	C₂×C₄×C₇	—	4	2	no	—
240	C₂×C₄×C₇	—	8	4	no	—
241	C₂×C₄×C₇	#121	1	2	yes	—
242	C₂×C₄×C₇	#121	1	2	yes	—
243	C₂×C₄×C₇	#135	1	2	yes	—
244	C₂×C₄×C₇	#137	1	2	yes	—
245	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
246	C₂×C₄×C₇	C₂²×Q₈	1	1	yes	characteristic
247	C₂×C₄×C₇	C₂×#41	1	1	yes	characteristic
248	C₂×C₄×C₇	C₂×#41	1	1	yes	characteristic
249	C₂×C₄×C₇	H(5,𝔽₂)	1	1	yes	characteristic
250	C₂×C₄×C₇	2₋¹⁺⁴	1	1	yes	characteristic
251	C₇×C₈	—	2	2	no	—
252	C₇×C₈	—	4	1	no	—
253	C₇×C₈	—	4	2	no	—
254	C₂²×Q₈	—	2	1	no	—
255	C₂²×Q₈	C₂³×C₇	1	1	yes	characteristic
256	C₂²×D₄	C₂³×C₇	1	1	yes	characteristic
257	C₂³×C₄	—	2	1	no	—
258	C₂×SD₁₆	—	2	2	no	—
259	C₂×SD₁₆	—	2	2	no	—
260	C₂×SD₁₆	C₇×Q₈	1	4	yes	complemented
261	C₂²×C₈	C₂³×C₇	1	2	yes	—
262	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
263	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
264	C₄⋊Q₈	—	2	2	no	—
265	C₄⋊Q₈	—	2	2	no	—
266	C₄×Q₈	—	2	2	no	—
267	C₄×Q₈	—	2	4	no	—
268	C₄×Q₈	—	4	2	no	—
269	C₄×Q₈	C₇×D₄	1	4	yes	—
270	C₄×D₄	—	2	2	no	—
271	C₄×D₄	—	2	2	no	—
272	C₂×C₄⋊C₄	—	2	1	no	—
273	C₂×C₄⋊C₄	—	2	2	no	—
274	C₂×C₄⋊C₄	—	2	1	no	—
275	C₂×C₄⋊C₄	—	2	1	no	—
276	C₂×C₄⋊C₄	—	2	2	no	—
277	C₂×C₄⋊C₄	—	2	1	no	—
278	C₂×C₄⋊C₄	C₇×D₄	1	1	yes	characteristic
279	C₂×C₄⋊C₄	C₇×D₄	1	1	yes	characteristic
280	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
281	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
282	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
283	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
284	C₂×C₂²⋊C₄	—	2	1	no	—
285	C₂×C₂²⋊C₄	—	2	2	no	—
286	C₂×C₂²⋊C₄	—	2	2	no	—
287	C₂×C₄²	—	2	1	no	—
288	C₂×C₄²	—	2	2	no	—
289	C₂×C₄²	C₂³×C₇	1	2	yes	—
290	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
291	#107	—	2	4	no	—
292	#106	—	2	2	no	—
293	C₄⋊C₈	—	2	2	no	—
294	C₄⋊C₈	—	4	2	no	—
295	#103	—	2	2	no	—
296	#103	—	2	4	no	—
297	#102	—	2	2	no	—
298	#102	—	4	2	no	—
299	C₄×C₈	—	2	2	no	—
300	#95	—	2	2	no	—
301	#95	—	2	2	no	—
302	#95	—	2	2	no	—
303	#95	C₇×D₄	1	2	yes	—
304	C₂²×C₇	—	4	2	no	—
305	C₂²×C₇	—	4	2	no	—
306	C₂²×C₇	—	4	2	no	—
307	C₂²×C₇	—	8	1	no	—
308	C₂²×C₇	—	8	1	no	—
309	C₂²×C₇	—	8	1	no	—
310	C₂²×C₇	—	8	1	no	—
311	C₂²×C₇	C₂×#121	1	1	yes	characteristic
312	C₂²×C₇	#546	1	1	yes	characteristic
313	C₂²×C₇	D₄×Q₈	1	1	yes	characteristic
314	C₂²×C₇	C₂×#135	1	1	yes	characteristic
315	C₂²×C₇	C₂×#137	1	1	yes	characteristic
316	C₂²×C₇	#576	1	1	yes	characteristic
317	C₂²×C₇	#577	1	1	yes	characteristic
318	C₄×C₇	—	2	4	no	—
319	C₄×C₇	—	2	2	no	—
320	C₄×C₇	—	4	2	no	—
321	C₄×C₇	—	4	2	no	—
322	C₄×C₇	—	4	2	no	—
323	C₄×C₇	—	8	1	no	—
324	C₄×C₇	—	8	2	no	—
325	C₄×C₇	—	8	2	no	—
326	C₄×C₇	#464	1	4	yes	—
327	C₄×C₇	C₂×C₂²⋊Q₈	1	1	yes	characteristic
328	C₄×C₇	#537	1	1	yes	characteristic
329	C₄×C₇	#552	1	1	yes	characteristic
330	C₄×C₇	#554	1	1	yes	characteristic
331	C₂⁴	—	2	1	no	—
332	C₂×Q₈	—	2	1	no	—
333	C₂×Q₈	—	2	1	no	—
334	C₂×Q₈	—	2	1	no	—
335	C₂×Q₈	—	4	2	no	—
336	C₂×Q₈	—	8	1	no	—
337	C₂×Q₈	—	8	1	no	—
338	C₂×Q₈	C₂×C₇×D₄	1	2	yes	—
339	C₂×Q₈	C₂×C₇×Q₈	1	2	yes	—
340	C₂×Q₈	C₇×#41	1	2	yes	—
341	C₂×D₄	—	2	1	no	—
342	C₂×D₄	—	2	1	no	—
343	C₂×D₄	—	2	1	no	—
344	C₂×D₄	—	2	1	no	—
345	C₂×D₄	—	2	1	no	—
346	C₂×D₄	C₂×C₇×Q₈	1	2	yes	—
347	C₂²×C₄	—	2	1	no	—
348	C₂²×C₄	—	2	1	no	—
349	C₂²×C₄	—	2	1	no	—
350	C₂²×C₄	—	2	2	no	—
351	C₂²×C₄	—	2	2	no	—
352	C₂²×C₄	—	4	2	no	—
353	C₂²×C₄	—	4	2	no	—
354	C₂²×C₄	—	4	2	no	—
355	C₂²×C₄	C₂×C₇×D₄	1	2	yes	—
356	C₂²×C₄	C₂×C₇×D₄	1	2	yes	—
357	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
358	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
359	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
360	SD₁₆	—	2	8	no	—
361	C₂×C₈	—	2	1	no	—
362	C₂×C₈	—	2	1	no	—
363	C₂×C₈	—	2	1	no	—
364	C₂×C₈	—	2	2	no	—
365	C₂×C₈	—	2	2	no	—
366	C₂×C₈	—	2	1	no	—
367	C₂×C₈	—	2	2	no	—
368	C₂×C₈	—	2	1	no	—
369	C₂×C₈	C₂×C₇×Q₈	1	2	yes	—
370	C₄⋊C₄	—	2	4	no	—
371	C₄⋊C₄	—	2	2	no	—
372	C₄⋊C₄	—	2	2	no	—
373	C₄⋊C₄	—	2	1	no	—
374	C₄⋊C₄	—	2	1	no	—
375	C₄⋊C₄	—	2	2	no	—
376	C₄⋊C₄	—	2	1	no	—
377	C₄⋊C₄	—	2	2	no	—
378	C₄⋊C₄	—	2	2	no	—
379	C₄⋊C₄	—	2	2	no	—
380	C₄⋊C₄	—	4	4	no	—
381	C₄⋊C₄	—	4	2	no	—
382	C₄⋊C₄	—	4	2	no	—
383	C₄⋊C₄	—	8	1	no	—
384	C₄⋊C₄	—	8	2	no	—
385	C₄⋊C₄	C₂×C₇×D₄	1	2	yes	—
386	C₂²⋊C₄	—	4	2	no	—
387	C₂²⋊C₄	—	8	2	no	—
388	C₂²⋊C₄	—	8	2	no	—
389	C₄²	—	2	4	no	—
390	C₄²	—	2	2	no	—
391	C₄²	—	2	2	no	—
392	C₄²	—	4	4	no	—
393	C₄²	C₂×C₇×D₄	1	2	yes	—
394	C₄²	C₇×#41	1	2	yes	—
395	C₂×C₇	—	8	2	no	—
396	C₂×C₇	#2417	1	1	yes	characteristic
397	C₂×C₇	C₂×#464	1	1	yes	characteristic
398	C₂×C₇	#3045	1	1	yes	characteristic
399	C₂×C₇	#3305	1	1	yes	characteristic
400	C₂×C₇	#3329	1	1	yes	characteristic
401	C₂×C₇	#3381	1	1	yes	characteristic
402	C₂×C₇	#3385	1	1	yes	characteristic
403	C₂³	—	2	2	no	—
404	C₂³	—	4	1	no	—
405	C₂³	—	4	1	no	—
406	C₂³	—	4	1	no	—
407	C₂³	—	4	1	no	—
408	C₂³	—	4	1	no	—
409	C₂³	—	4	1	no	—
410	C₂³	C₂²×C₇×D₄	1	1	yes	characteristic
411	Q₈	—	2	2	no	—
412	Q₈	—	2	2	no	—
413	Q₈	—	2	2	no	—
414	Q₈	—	8	4	no	—
415	Q₈	C₇×C₂²⋊Q₈	1	4	yes	—
416	D₄	—	2	2	no	—
417	D₄	—	2	2	no	—
418	D₄	—	4	1	no	—
419	D₄	—	4	1	no	—
420	C₂×C₄	—	2	2	no	—
421	C₂×C₄	—	2	2	no	—
422	C₂×C₄	—	2	2	no	—
423	C₂×C₄	—	2	1	no	—
424	C₂×C₄	—	2	1	no	—
425	C₂×C₄	—	2	2	no	—
426	C₂×C₄	—	2	2	no	—
427	C₂×C₄	—	2	2	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	—	4	1	no	—
433	C₂×C₄	—	4	1	no	—
434	C₂×C₄	—	4	1	no	—
435	C₂×C₄	—	4	2	no	—
436	C₂×C₄	—	4	2	no	—
437	C₂×C₄	—	4	2	no	—
438	C₂×C₄	—	4	1	no	—
439	C₂×C₄	—	4	1	no	—
440	C₂×C₄	—	4	2	no	—
441	C₂×C₄	—	4	2	no	—
442	C₂×C₄	—	4	2	no	—
443	C₂×C₄	—	8	4	no	—
444	C₂×C₄	C₇×#121	1	2	yes	—
445	C₂×C₄	C₇×#121	1	2	yes	—
446	C₂×C₄	C₇×#135	1	2	yes	—
447	C₂×C₄	C₇×#137	1	2	yes	—
448	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
449	C₂×C₄	C₂²×C₇×Q₈	1	1	yes	characteristic
450	C₂×C₄	C₂×C₇×#41	1	1	yes	characteristic
451	C₂×C₄	C₂×C₇×#41	1	1	yes	characteristic
452	C₂×C₄	C₇×H(5,𝔽₂)	1	1	yes	characteristic
453	C₂×C₄	C₇×2₋¹⁺⁴	1	1	yes	characteristic
454	C₈	—	2	2	no	—
455	C₈	—	4	1	no	—
456	C₈	—	4	2	no	—
457	C₇	#24814	1	1	yes	characteristic, direct product factor, Sylow
458	C₂²	—	4	2	no	—
459	C₂²	—	4	2	no	—
460	C₂²	—	4	2	no	—
461	C₂²	—	8	1	no	—
462	C₂²	—	8	1	no	—
463	C₂²	—	8	1	no	—
464	C₂²	—	8	1	no	—
465	C₂²	C₂×C₇×#121	1	1	yes	characteristic
466	C₂²	C₇×#546	1	1	yes	characteristic
467	C₂²	C₇×D₄×Q₈	1	1	yes	characteristic
468	C₂²	C₂×C₇×#135	1	1	yes	characteristic
469	C₂²	C₂×C₇×#137	1	1	yes	characteristic
470	C₂²	C₇×#576	1	1	yes	characteristic
471	C₂²	C₇×#577	1	1	yes	characteristic
472	C₄	—	2	4	no	—
473	C₄	—	2	2	no	—
474	C₄	—	4	2	no	—
475	C₄	—	4	2	no	—
476	C₄	—	4	2	no	—
477	C₄	—	8	1	no	—
478	C₄	—	8	2	no	—
479	C₄	—	8	2	no	—
480	C₄	C₇×#464	1	4	yes	—
481	C₄	C₂×C₇×C₂²⋊Q₈	1	1	yes	characteristic
482	C₄	C₇×#537	1	1	yes	characteristic
483	C₄	C₇×#552	1	1	yes	characteristic
484	C₄	C₇×#554	1	1	yes	characteristic
485	C₂	—	8	2	no	—
486	C₂	C₇×#2417	1	1	yes	characteristic
487	C₂	C₂×C₇×#464	1	1	yes	characteristic
488	C₂	C₇×#3045	1	1	yes	characteristic
489	C₂	C₇×#3305	1	1	yes	characteristic
490	C₂	C₇×#3329	1	1	yes	characteristic
491	C₂	C₇×#3381	1	1	yes	characteristic
492	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 ◁ C₄×C₇×C₄⋊C₄ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₇×#477	C₂	semidirect
4. C₇×Q₈×C₄⋊C₄	C₂	semidirect
5. C₇×#2085	C₂	semidirect
7. C₇×#1990	C₂	semidirect
8. C₇×#1939	C₂	semidirect
10. C₇×#1805	C₂	semidirect
43. #24814	C₇	direct (N × H)
50. C₂×C₇×SD₁₆	Q₈	semidirect
94. C₂×#477	C₂×C₇	semidirect
97. Q₈×C₄⋊C₄	C₂×C₇	semidirect
98. #2085	C₂×C₇	semidirect
100. #1990	C₂×C₇	semidirect
101. #1939	C₂×C₇	semidirect
103. #1805	C₂×C₇	semidirect
260. C₂×SD₁₆	C₇×Q₈	semidirect
457. C₇	#24814	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×#477	2
C₂×C₄×C₇×SD₁₆	2
C₇×#2563	2
C₇×Q₈×C₄⋊C₄	2
C₇×#2085	2
C₇×#2067	2
C₇×#1990	2
C₇×#1939	2
C₇×#1880	2
C₇×#1805	2
C₇×#1802	2
#24814	7

Subgroups — C7×#24814 #13202030

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×#24814 #13202030