Subgroups — C₇×#24739 #13201955

Order 1792.

990 conjugacy classes of subgroups.

The subgroup lattice has 734 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₇×#464	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₇×#464	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₇×#460	C₂	1	1	yes	maximal, characteristic
4	C₂×C₇×#440	C₂	1	1	yes	maximal, characteristic, complemented
5	C₇×#2544	C₂	1	1	yes	maximal, characteristic
6	C₇×Q₈×C₄⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
7	C₇×#2068	C₂	1	1	yes	maximal, characteristic, complemented
8	C₇×#2067	C₂	1	1	yes	maximal, characteristic, complemented
9	C₇×#2042	C₂	1	1	yes	maximal, characteristic, complemented
10	C₇×#2041	C₂	1	1	yes	maximal, characteristic
11	C₇×#1959	C₂	1	1	yes	maximal, characteristic, complemented
12	C₇×#1940	C₂	1	1	yes	maximal, characteristic, complemented
13	C₇×#1880	C₂	1	1	yes	maximal, characteristic, complemented
14	C₇×#1878	C₂	1	1	yes	maximal, characteristic, complemented
15	C₇×#1802	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×C₇×Q₁₆	C₂²	1	1	yes	characteristic
17	C₂²×C₇×SD₁₆	C₂²	1	1	yes	characteristic
18	C₂²×C₇×SD₁₆	C₂²	1	1	yes	characteristic
19	C₂×C₇×#127	C₂²	1	1	yes	characteristic
20	C₂×C₇×#124	C₂²	1	1	yes	characteristic
21	C₂×C₇×#124	C₂²	1	1	yes	characteristic
22	C₂×C₄×C₇×Q₈	C₂²	1	1	yes	characteristic
23	C₂×C₄×C₇×Q₈	C₂²	1	1	yes	characteristic
24	C₂×C₄×C₇×Q₈	C₂²	1	1	yes	characteristic
25	C₂×C₄×C₇×D₄	C₂²	1	1	yes	characteristic
26	C₇×#464	—	2	4	no	—
27	C₇×#464	—	2	4	no	—
28	C₇×#460	—	2	4	no	—
29	C₇×#440	—	2	4	no	—
30	C₂×C₇×#107	C₂²	1	1	yes	characteristic
31	C₂×C₇×C₄⋊C₈	C₂²	1	1	yes	characteristic
32	C₂×C₇×C₄⋊C₈	C₂²	1	1	yes	characteristic
33	C₂×C₇×C₄⋊C₈	C₂²	1	1	yes	characteristic
34	C₂×C₇×#103	C₂²	1	1	yes	characteristic
35	C₂×C₇×#103	C₂²	1	1	yes	characteristic
36	C₂×C₇×#103	C₂²	1	1	yes	characteristic
37	C₂×C₇×#103	C₂²	1	1	yes	characteristic
38	C₂×C₇×#102	C₂²	1	1	yes	characteristic
39	C₂×C₇×#102	C₂²	1	1	yes	characteristic
40	C₂×C₇×#102	C₂²	1	1	yes	characteristic
41	C₂×C₇×#102	C₂²	1	1	yes	characteristic
42	C₂×C₇×#102	C₂²	1	1	yes	characteristic
43	C₂×C₇×#102	C₂²	1	1	yes	characteristic
44	C₂×C₇×#97	C₂²	1	1	yes	characteristic
45	C₇×#394	—	2	1	no	—
46	C₇×#394	—	2	1	no	—
47	C₇×#391	C₂²	1	1	yes	characteristic
48	C₇×#390	C₂²	1	1	yes	characteristic
49	C₇×#389	—	2	1	no	—
50	C₇×#389	—	2	1	no	—
51	C₇×#389	C₂²	1	1	yes	characteristic
52	C₇×#389	C₂²	1	1	yes	characteristic
53	C₇×#386	—	2	1	no	—
54	C₇×#386	—	2	1	no	—
55	C₇×#384	—	2	1	no	—
56	C₇×#384	C₂²	1	1	yes	characteristic
57	C₄×C₇×C₄⋊C₄	—	2	1	no	—
58	C₄×C₇×C₄⋊C₄	C₂²	1	1	yes	characteristic
59	C₇×#340	C₂²	1	1	yes	characteristic
60	C₇×#340	C₂²	1	1	yes	characteristic
61	C₇×#336	C₂²	1	1	yes	characteristic
62	C₇×#336	C₂²	1	1	yes	characteristic
63	#24739	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
64	C₂²×C₇×Q₈	C₂³	1	1	yes	characteristic
65	C₂²×C₇×Q₈	C₂³	1	1	yes	characteristic
66	C₂²×C₇×D₄	—	2	1	no	—
67	C₂²×C₇×D₄	—	2	1	no	—
68	C₂²×C₇×D₄	C₂³	1	1	yes	characteristic
69	C₂²×C₇×D₄	C₂³	1	1	yes	characteristic
70	C₂³×C₄×C₇	—	2	1	no	—
71	C₂×C₇×Q₁₆	—	2	2	no	—
72	C₂×C₇×Q₁₆	—	2	2	no	—
73	C₂×C₇×Q₁₆	—	2	2	no	—
74	C₂×C₇×SD₁₆	—	2	2	no	—
75	C₂×C₇×SD₁₆	—	2	2	no	—
76	C₂×C₇×SD₁₆	—	2	2	no	—
77	C₂×C₇×SD₁₆	—	2	2	no	—
78	C₂×C₇×SD₁₆	—	2	2	no	—
79	C₂×C₇×SD₁₆	D₄	1	4	yes	—
80	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
81	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
82	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
83	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
84	C₇×#127	—	2	2	no	—
85	C₇×#127	—	4	1	no	—
86	C₇×#124	—	2	2	no	—
87	C₇×#124	—	2	2	no	—
88	C₇×#124	—	2	2	no	—
89	C₇×#124	—	4	1	no	—
90	C₄×C₇×Q₈	—	2	2	no	—
91	C₄×C₇×Q₈	—	2	2	no	—
92	C₄×C₇×Q₈	—	2	2	no	—
93	C₄×C₇×Q₈	—	4	1	no	—
94	C₄×C₇×Q₈	—	4	1	no	—
95	C₄×C₇×Q₈	D₄	1	4	yes	complemented
96	C₄×C₇×D₄	—	2	2	no	—
97	C₄×C₇×D₄	—	2	2	no	—
98	C₂×C₇×C₄⋊C₄	—	2	1	no	—
99	C₂×C₇×C₄⋊C₄	—	2	1	no	—
100	C₂×C₇×C₄⋊C₄	—	2	1	no	—
101	C₂×C₇×C₄⋊C₄	—	2	1	no	—
102	C₂×C₇×C₄⋊C₄	—	2	1	no	—
103	C₂×C₇×C₄⋊C₄	—	2	1	no	—
104	C₂×C₇×C₄⋊C₄	—	2	1	no	—
105	C₂×C₇×C₄⋊C₄	D₄	1	1	yes	characteristic
106	C₂×C₇×C₄⋊C₄	D₄	1	1	yes	characteristic
107	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
108	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
109	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
110	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
111	C₂×C₇×C₂²⋊C₄	—	2	1	no	—
112	C₂×C₇×C₂²⋊C₄	—	2	1	no	—
113	C₂×C₇×C₂²⋊C₄	—	2	1	no	—
114	C₂×C₇×C₂²⋊C₄	—	2	1	no	—
115	C₂×C₇×C₂²⋊C₄	—	2	1	no	—
116	C₂×C₇×C₂²⋊C₄	—	2	1	no	—
117	C₂×C₇×C₂²⋊C₄	—	2	1	no	—
118	C₂×C₄²×C₇	—	2	1	no	—
119	C₂×C₄²×C₇	—	2	1	no	—
120	C₂×C₄²×C₇	—	2	1	no	—
121	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
122	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
123	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
124	C₇×#107	—	2	2	no	—
125	C₇×C₄⋊C₈	—	2	2	no	—
126	C₇×C₄⋊C₈	—	2	2	no	—
127	C₇×C₄⋊C₈	—	2	2	no	—
128	C₇×#103	—	2	2	no	—
129	C₇×#103	—	2	2	no	—
130	C₇×#103	—	2	2	no	—
131	C₇×#103	—	4	1	no	—
132	C₇×#102	—	2	2	no	—
133	C₇×#102	—	2	2	no	—
134	C₇×#102	—	2	2	no	—
135	C₇×#102	—	2	2	no	—
136	C₇×#102	—	2	2	no	—
137	C₇×#102	—	4	1	no	—
138	C₇×#97	—	2	2	no	—
139	C₇×#95	—	2	1	no	—
140	C₇×#95	—	2	1	no	—
141	C₇×#95	—	2	1	no	—
142	C₇×#95	—	2	1	no	—
143	C₇×#95	D₄	1	1	yes	characteristic
144	C₇×#95	D₄	1	1	yes	characteristic
145	C₂×#464	C₂×C₇	1	1	yes	characteristic, complemented
146	C₂×#464	C₂×C₇	1	1	yes	characteristic, complemented
147	C₂×#460	C₂×C₇	1	1	yes	characteristic
148	C₂×#440	C₂×C₇	1	1	yes	characteristic, complemented
149	#2544	C₂×C₇	1	1	yes	characteristic
150	Q₈×C₄⋊C₄	C₂×C₇	1	1	yes	characteristic, complemented
151	#2068	C₂×C₇	1	1	yes	characteristic, complemented
152	#2067	C₂×C₇	1	1	yes	characteristic, complemented
153	#2042	C₂×C₇	1	1	yes	characteristic, complemented
154	#2041	C₂×C₇	1	1	yes	characteristic
155	#1959	C₂×C₇	1	1	yes	characteristic, complemented
156	#1940	C₂×C₇	1	1	yes	characteristic, complemented
157	#1880	C₂×C₇	1	1	yes	characteristic, complemented
158	#1878	C₂×C₇	1	1	yes	characteristic, complemented
159	#1802	C₂×C₇	1	1	yes	characteristic, complemented
160	C₂⁴×C₇	—	2	1	no	—
161	C₂⁴×C₇	—	2	1	no	—
162	C₂×C₇×Q₈	—	2	1	no	—
163	C₂×C₇×Q₈	—	2	1	no	—
164	C₂×C₇×Q₈	—	2	1	no	—
165	C₂×C₇×Q₈	—	2	1	no	—
166	C₂×C₇×Q₈	—	2	1	no	—
167	C₂×C₇×Q₈	—	2	1	no	—
168	C₂×C₇×Q₈	—	2	1	no	—
169	C₂×C₇×Q₈	—	2	1	no	—
170	C₂×C₇×Q₈	—	2	1	no	—
171	C₂×C₇×Q₈	C₂×D₄	1	2	yes	—
172	C₂×C₇×Q₈	C₂×D₄	1	2	yes	—
173	C₂×C₇×Q₈	#41	1	2	yes	—
174	C₂×C₇×D₄	—	2	1	no	—
175	C₂×C₇×D₄	—	2	1	no	—
176	C₂×C₇×D₄	—	2	1	no	—
177	C₂×C₇×D₄	—	2	1	no	—
178	C₂×C₇×D₄	—	2	1	no	—
179	C₂×C₇×D₄	—	2	1	no	—
180	C₂×C₇×D₄	—	2	1	no	—
181	C₂×C₇×D₄	—	2	1	no	—
182	C₂×C₇×D₄	—	2	1	no	—
183	C₂×C₇×D₄	—	2	1	no	—
184	C₂×C₇×D₄	—	2	1	no	—
185	C₂×C₇×D₄	—	4	2	no	—
186	C₂×C₇×D₄	—	4	2	no	—
187	C₂×C₇×D₄	—	4	2	no	—
188	C₂×C₇×D₄	—	4	2	no	—
189	C₂×C₇×D₄	—	8	1	no	—
190	C₂×C₇×D₄	—	8	1	no	—
191	C₂×C₇×D₄	C₂×D₄	1	2	yes	—
192	C₂²×C₄×C₇	—	2	1	no	—
193	C₂²×C₄×C₇	—	2	1	no	—
194	C₂²×C₄×C₇	—	2	1	no	—
195	C₂²×C₄×C₇	—	2	1	no	—
196	C₂²×C₄×C₇	—	2	1	no	—
197	C₂²×C₄×C₇	—	2	1	no	—
198	C₂²×C₄×C₇	—	4	2	no	—
199	C₂²×C₄×C₇	—	8	1	no	—
200	C₂²×C₄×C₇	—	8	1	no	—
201	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
202	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
203	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
204	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
205	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
206	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
207	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
208	C₇×Q₁₆	—	4	4	no	—
209	C₇×SD₁₆	—	2	8	no	—
210	C₇×SD₁₆	—	4	4	no	—
211	C₂×C₇×C₈	—	2	1	no	—
212	C₂×C₇×C₈	—	2	1	no	—
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	—	2	1	no	—
218	C₂×C₇×C₈	—	2	1	no	—
219	C₂×C₇×C₈	—	2	1	no	—
220	C₂×C₇×C₈	—	2	1	no	—
221	C₂×C₇×C₈	—	2	1	no	—
222	C₂×C₇×C₈	C₂×D₄	1	2	yes	—
223	C₇×C₄⋊C₄	—	2	4	no	—
224	C₇×C₄⋊C₄	—	2	2	no	—
225	C₇×C₄⋊C₄	—	2	1	no	—
226	C₇×C₄⋊C₄	—	2	1	no	—
227	C₇×C₄⋊C₄	—	2	1	no	—
228	C₇×C₄⋊C₄	—	2	1	no	—
229	C₇×C₄⋊C₄	—	2	1	no	—
230	C₇×C₄⋊C₄	—	2	1	no	—
231	C₇×C₄⋊C₄	—	2	1	no	—
232	C₇×C₄⋊C₄	—	4	1	no	—
233	C₇×C₄⋊C₄	—	4	2	no	—
234	C₇×C₄⋊C₄	—	4	2	no	—
235	C₇×C₄⋊C₄	—	4	2	no	—
236	C₇×C₄⋊C₄	—	8	1	no	—
237	C₇×C₄⋊C₄	—	8	1	no	—
238	C₇×C₄⋊C₄	—	8	1	no	—
239	C₇×C₄⋊C₄	C₂×D₄	1	2	yes	—
240	C₇×C₂²⋊C₄	—	4	2	no	—
241	C₇×C₂²⋊C₄	—	4	2	no	—
242	C₇×C₂²⋊C₄	—	4	2	no	—
243	C₇×C₂²⋊C₄	—	4	2	no	—
244	C₇×C₂²⋊C₄	—	4	2	no	—
245	C₇×C₂²⋊C₄	—	8	1	no	—
246	C₇×C₂²⋊C₄	—	8	1	no	—
247	C₄²×C₇	—	2	4	no	—
248	C₄²×C₇	—	2	1	no	—
249	C₄²×C₇	—	2	1	no	—
250	C₄²×C₇	—	2	1	no	—
251	C₄²×C₇	—	2	1	no	—
252	C₄²×C₇	—	4	2	no	—
253	C₄²×C₇	—	4	2	no	—
254	C₄²×C₇	C₂×D₄	1	2	yes	—
255	C₄²×C₇	#41	1	2	yes	—
256	C₂²×Q₁₆	C₂²×C₇	1	1	yes	characteristic
257	C₂²×SD₁₆	C₂²×C₇	1	1	yes	characteristic
258	C₂²×SD₁₆	C₂²×C₇	1	1	yes	characteristic
259	C₂×#127	C₂²×C₇	1	1	yes	characteristic
260	C₂×#124	C₂²×C₇	1	1	yes	characteristic
261	C₂×#124	C₂²×C₇	1	1	yes	characteristic
262	C₂×C₄×Q₈	C₂²×C₇	1	1	yes	characteristic
263	C₂×C₄×Q₈	C₂²×C₇	1	1	yes	characteristic
264	C₂×C₄×Q₈	C₂²×C₇	1	1	yes	characteristic
265	C₂×C₄×D₄	C₂²×C₇	1	1	yes	characteristic
266	#464	—	2	4	no	—
267	#464	—	2	4	no	—
268	#460	—	2	4	no	—
269	#440	—	2	4	no	—
270	C₂×#107	C₂²×C₇	1	1	yes	characteristic
271	C₂×C₄⋊C₈	C₂²×C₇	1	1	yes	characteristic
272	C₂×C₄⋊C₈	C₂²×C₇	1	1	yes	characteristic
273	C₂×C₄⋊C₈	C₂²×C₇	1	1	yes	characteristic
274	C₂×#103	C₂²×C₇	1	1	yes	characteristic
275	C₂×#103	C₂²×C₇	1	1	yes	characteristic
276	C₂×#103	C₂²×C₇	1	1	yes	characteristic
277	C₂×#103	C₂²×C₇	1	1	yes	characteristic
278	C₂×#102	C₂²×C₇	1	1	yes	characteristic
279	C₂×#102	C₂²×C₇	1	1	yes	characteristic
280	C₂×#102	C₂²×C₇	1	1	yes	characteristic
281	C₂×#102	C₂²×C₇	1	1	yes	characteristic
282	C₂×#102	C₂²×C₇	1	1	yes	characteristic
283	C₂×#102	C₂²×C₇	1	1	yes	characteristic
284	C₂×#97	C₂²×C₇	1	1	yes	characteristic
285	#394	—	2	1	no	—
286	#394	—	2	1	no	—
287	#391	C₂²×C₇	1	1	yes	characteristic
288	#390	C₂²×C₇	1	1	yes	characteristic
289	#389	—	2	1	no	—
290	#389	—	2	1	no	—
291	#389	C₂²×C₇	1	1	yes	characteristic
292	#389	C₂²×C₇	1	1	yes	characteristic
293	#386	—	2	1	no	—
294	#386	—	2	1	no	—
295	#384	—	2	1	no	—
296	#384	C₂²×C₇	1	1	yes	characteristic
297	C₄×C₄⋊C₄	—	2	1	no	—
298	C₄×C₄⋊C₄	C₂²×C₇	1	1	yes	characteristic
299	#340	C₂²×C₇	1	1	yes	characteristic
300	#340	C₂²×C₇	1	1	yes	characteristic
301	#336	C₂²×C₇	1	1	yes	characteristic
302	#336	C₂²×C₇	1	1	yes	characteristic
303	C₂³×C₇	—	2	2	no	—
304	C₂³×C₇	—	4	1	no	—
305	C₂³×C₇	—	4	1	no	—
306	C₂³×C₇	—	4	1	no	—
307	C₂³×C₇	—	4	1	no	—
308	C₂³×C₇	—	4	1	no	—
309	C₂³×C₇	—	4	1	no	—
310	C₂³×C₇	—	4	1	no	—
311	C₂³×C₇	—	4	1	no	—
312	C₂³×C₇	—	4	1	no	—
313	C₂³×C₇	—	4	1	no	—
314	C₂³×C₇	—	4	1	no	—
315	C₂³×C₇	—	4	1	no	—
316	C₂³×C₇	—	4	1	no	—
317	C₂³×C₇	C₂²×D₄	1	1	yes	characteristic
318	C₇×Q₈	—	2	2	no	—
319	C₇×Q₈	—	2	2	no	—
320	C₇×Q₈	—	2	2	no	—
321	C₇×Q₈	—	4	1	no	—
322	C₇×Q₈	—	4	1	no	—
323	C₇×Q₈	—	4	1	no	—
324	C₇×Q₈	—	4	1	no	—
325	C₇×Q₈	#121	1	4	yes	—
326	C₇×D₄	—	2	2	no	—
327	C₇×D₄	—	2	2	no	—
328	C₇×D₄	—	4	1	no	—
329	C₇×D₄	—	4	1	no	—
330	C₇×D₄	—	4	1	no	—
331	C₇×D₄	—	4	1	no	—
332	C₇×D₄	—	4	1	no	—
333	C₇×D₄	—	4	1	no	—
334	C₇×D₄	—	8	4	no	—
335	C₇×D₄	—	8	4	no	—
336	C₂×C₄×C₇	—	2	2	no	—
337	C₂×C₄×C₇	—	2	1	no	—
338	C₂×C₄×C₇	—	2	2	no	—
339	C₂×C₄×C₇	—	2	2	no	—
340	C₂×C₄×C₇	—	2	1	no	—
341	C₂×C₄×C₇	—	2	1	no	—
342	C₂×C₄×C₇	—	2	1	no	—
343	C₂×C₄×C₇	—	2	1	no	—
344	C₂×C₄×C₇	—	2	1	no	—
345	C₂×C₄×C₇	—	2	2	no	—
346	C₂×C₄×C₇	—	2	1	no	—
347	C₂×C₄×C₇	—	2	1	no	—
348	C₂×C₄×C₇	—	2	1	no	—
349	C₂×C₄×C₇	—	2	1	no	—
350	C₂×C₄×C₇	—	2	1	no	—
351	C₂×C₄×C₇	—	2	1	no	—
352	C₂×C₄×C₇	—	2	1	no	—
353	C₂×C₄×C₇	—	2	1	no	—
354	C₂×C₄×C₇	—	2	1	no	—
355	C₂×C₄×C₇	—	4	1	no	—
356	C₂×C₄×C₇	—	4	1	no	—
357	C₂×C₄×C₇	—	4	1	no	—
358	C₂×C₄×C₇	—	4	1	no	—
359	C₂×C₄×C₇	—	4	1	no	—
360	C₂×C₄×C₇	—	4	1	no	—
361	C₂×C₄×C₇	—	4	1	no	—
362	C₂×C₄×C₇	—	4	1	no	—
363	C₂×C₄×C₇	—	4	1	no	—
364	C₂×C₄×C₇	—	4	1	no	—
365	C₂×C₄×C₇	—	4	1	no	—
366	C₂×C₄×C₇	—	4	1	no	—
367	C₂×C₄×C₇	—	4	1	no	—
368	C₂×C₄×C₇	—	4	1	no	—
369	C₂×C₄×C₇	—	8	4	no	—
370	C₂×C₄×C₇	#121	1	2	yes	—
371	C₂×C₄×C₇	#121	1	2	yes	—
372	C₂×C₄×C₇	#137	1	2	yes	—
373	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
374	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
375	C₂×C₄×C₇	C₂×#41	1	1	yes	characteristic
376	C₂×C₄×C₇	C₂×#41	1	1	yes	characteristic
377	C₂×C₄×C₇	H(5,𝔽₂)	1	1	yes	characteristic
378	C₂×C₄×C₇	2₋¹⁺⁴	1	1	yes	characteristic
379	C₇×C₈	—	2	2	no	—
380	C₇×C₈	—	4	1	no	—
381	C₇×C₈	—	4	1	no	—
382	C₇×C₈	—	4	1	no	—
383	C₂²×Q₈	C₂³×C₇	1	1	yes	characteristic
384	C₂²×Q₈	C₂³×C₇	1	1	yes	characteristic
385	C₂²×D₄	—	2	1	no	—
386	C₂²×D₄	—	2	1	no	—
387	C₂²×D₄	C₂³×C₇	1	1	yes	characteristic
388	C₂²×D₄	C₂³×C₇	1	1	yes	characteristic
389	C₂³×C₄	—	2	1	no	—
390	C₂×Q₁₆	—	2	2	no	—
391	C₂×Q₁₆	—	2	2	no	—
392	C₂×Q₁₆	—	2	2	no	—
393	C₂×SD₁₆	—	2	2	no	—
394	C₂×SD₁₆	—	2	2	no	—
395	C₂×SD₁₆	—	2	2	no	—
396	C₂×SD₁₆	—	2	2	no	—
397	C₂×SD₁₆	—	2	2	no	—
398	C₂×SD₁₆	C₇×D₄	1	4	yes	—
399	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
400	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
401	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
402	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
403	#127	—	2	2	no	—
404	#127	—	4	1	no	—
405	#124	—	2	2	no	—
406	#124	—	2	2	no	—
407	#124	—	2	2	no	—
408	#124	—	4	1	no	—
409	C₄×Q₈	—	2	2	no	—
410	C₄×Q₈	—	2	2	no	—
411	C₄×Q₈	—	2	2	no	—
412	C₄×Q₈	—	4	1	no	—
413	C₄×Q₈	—	4	1	no	—
414	C₄×Q₈	C₇×D₄	1	4	yes	complemented
415	C₄×D₄	—	2	2	no	—
416	C₄×D₄	—	2	2	no	—
417	C₂×C₄⋊C₄	—	2	1	no	—
418	C₂×C₄⋊C₄	—	2	1	no	—
419	C₂×C₄⋊C₄	—	2	1	no	—
420	C₂×C₄⋊C₄	—	2	1	no	—
421	C₂×C₄⋊C₄	—	2	1	no	—
422	C₂×C₄⋊C₄	—	2	1	no	—
423	C₂×C₄⋊C₄	—	2	1	no	—
424	C₂×C₄⋊C₄	C₇×D₄	1	1	yes	characteristic
425	C₂×C₄⋊C₄	C₇×D₄	1	1	yes	characteristic
426	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
427	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
428	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
429	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
430	C₂×C₂²⋊C₄	—	2	1	no	—
431	C₂×C₂²⋊C₄	—	2	1	no	—
432	C₂×C₂²⋊C₄	—	2	1	no	—
433	C₂×C₂²⋊C₄	—	2	1	no	—
434	C₂×C₂²⋊C₄	—	2	1	no	—
435	C₂×C₂²⋊C₄	—	2	1	no	—
436	C₂×C₂²⋊C₄	—	2	1	no	—
437	C₂×C₄²	—	2	1	no	—
438	C₂×C₄²	—	2	1	no	—
439	C₂×C₄²	—	2	1	no	—
440	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
441	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
442	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
443	#107	—	2	2	no	—
444	C₄⋊C₈	—	2	2	no	—
445	C₄⋊C₈	—	2	2	no	—
446	C₄⋊C₈	—	2	2	no	—
447	#103	—	2	2	no	—
448	#103	—	2	2	no	—
449	#103	—	2	2	no	—
450	#103	—	4	1	no	—
451	#102	—	2	2	no	—
452	#102	—	2	2	no	—
453	#102	—	2	2	no	—
454	#102	—	2	2	no	—
455	#102	—	2	2	no	—
456	#102	—	4	1	no	—
457	#97	—	2	2	no	—
458	#95	—	2	1	no	—
459	#95	—	2	1	no	—
460	#95	—	2	1	no	—
461	#95	—	2	1	no	—
462	#95	C₇×D₄	1	1	yes	characteristic
463	#95	C₇×D₄	1	1	yes	characteristic
464	C₂²×C₇	—	4	2	no	—
465	C₂²×C₇	—	4	2	no	—
466	C₂²×C₇	—	4	2	no	—
467	C₂²×C₇	—	8	1	no	—
468	C₂²×C₇	—	8	1	no	—
469	C₂²×C₇	—	8	1	no	—
470	C₂²×C₇	—	8	1	no	—
471	C₂²×C₇	—	8	1	no	—
472	C₂²×C₇	—	8	1	no	—
473	C₂²×C₇	—	8	1	no	—
474	C₂²×C₇	—	8	1	no	—
475	C₂²×C₇	—	8	1	no	—
476	C₂²×C₇	—	8	1	no	—
477	C₂²×C₇	—	8	1	no	—
478	C₂²×C₇	C₂×#121	1	1	yes	characteristic
479	C₂²×C₇	D₄²	1	1	yes	characteristic
480	C₂²×C₇	#548	1	1	yes	characteristic
481	C₂²×C₇	C₂×#137	1	1	yes	characteristic
482	C₂²×C₇	#575	1	1	yes	characteristic
483	C₂²×C₇	#576	1	1	yes	characteristic
484	C₂²×C₇	#577	1	1	yes	characteristic
485	C₄×C₇	—	2	4	no	—
486	C₄×C₇	—	2	2	no	—
487	C₄×C₇	—	2	2	no	—
488	C₄×C₇	—	2	2	no	—
489	C₄×C₇	—	4	1	no	—
490	C₄×C₇	—	4	1	no	—
491	C₄×C₇	—	4	1	no	—
492	C₄×C₇	—	4	2	no	—
493	C₄×C₇	—	8	1	no	—
494	C₄×C₇	—	8	1	no	—
495	C₄×C₇	—	8	1	no	—
496	C₄×C₇	—	8	1	no	—
497	C₄×C₇	C₂×#121	1	1	yes	characteristic
498	C₄×C₇	#537	1	1	yes	characteristic
499	C₄×C₇	#547	1	1	yes	characteristic
500	C₄×C₇	#553	1	1	yes	characteristic
501	C₂⁴	—	2	1	no	—
502	C₂⁴	—	2	1	no	—
503	C₂×Q₈	—	2	1	no	—
504	C₂×Q₈	—	2	1	no	—
505	C₂×Q₈	—	2	1	no	—
506	C₂×Q₈	—	2	1	no	—
507	C₂×Q₈	—	2	1	no	—
508	C₂×Q₈	—	2	1	no	—
509	C₂×Q₈	—	2	1	no	—
510	C₂×Q₈	—	2	1	no	—
511	C₂×Q₈	—	2	1	no	—
512	C₂×Q₈	C₂×C₇×D₄	1	2	yes	—
513	C₂×Q₈	C₂×C₇×D₄	1	2	yes	—
514	C₂×Q₈	C₇×#41	1	2	yes	—
515	C₂×D₄	—	2	1	no	—
516	C₂×D₄	—	2	1	no	—
517	C₂×D₄	—	2	1	no	—
518	C₂×D₄	—	2	1	no	—
519	C₂×D₄	—	2	1	no	—
520	C₂×D₄	—	2	1	no	—
521	C₂×D₄	—	2	1	no	—
522	C₂×D₄	—	2	1	no	—
523	C₂×D₄	—	2	1	no	—
524	C₂×D₄	—	2	1	no	—
525	C₂×D₄	—	2	1	no	—
526	C₂×D₄	—	4	2	no	—
527	C₂×D₄	—	4	2	no	—
528	C₂×D₄	—	4	2	no	—
529	C₂×D₄	—	4	2	no	—
530	C₂×D₄	—	8	1	no	—
531	C₂×D₄	—	8	1	no	—
532	C₂×D₄	C₂×C₇×D₄	1	2	yes	—
533	C₂²×C₄	—	2	1	no	—
534	C₂²×C₄	—	2	1	no	—
535	C₂²×C₄	—	2	1	no	—
536	C₂²×C₄	—	2	1	no	—
537	C₂²×C₄	—	2	1	no	—
538	C₂²×C₄	—	2	1	no	—
539	C₂²×C₄	—	4	2	no	—
540	C₂²×C₄	—	8	1	no	—
541	C₂²×C₄	—	8	1	no	—
542	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
543	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
544	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
545	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
546	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
547	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
548	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
549	Q₁₆	—	4	4	no	—
550	SD₁₆	—	2	8	no	—
551	SD₁₆	—	4	4	no	—
552	C₂×C₈	—	2	1	no	—
553	C₂×C₈	—	2	1	no	—
554	C₂×C₈	—	2	1	no	—
555	C₂×C₈	—	2	1	no	—
556	C₂×C₈	—	2	1	no	—
557	C₂×C₈	—	2	1	no	—
558	C₂×C₈	—	2	1	no	—
559	C₂×C₈	—	2	1	no	—
560	C₂×C₈	—	2	1	no	—
561	C₂×C₈	—	2	1	no	—
562	C₂×C₈	—	2	1	no	—
563	C₂×C₈	C₂×C₇×D₄	1	2	yes	—
564	C₄⋊C₄	—	2	4	no	—
565	C₄⋊C₄	—	2	2	no	—
566	C₄⋊C₄	—	2	1	no	—
567	C₄⋊C₄	—	2	1	no	—
568	C₄⋊C₄	—	2	1	no	—
569	C₄⋊C₄	—	2	1	no	—
570	C₄⋊C₄	—	2	1	no	—
571	C₄⋊C₄	—	2	1	no	—
572	C₄⋊C₄	—	2	1	no	—
573	C₄⋊C₄	—	4	1	no	—
574	C₄⋊C₄	—	4	2	no	—
575	C₄⋊C₄	—	4	2	no	—
576	C₄⋊C₄	—	4	2	no	—
577	C₄⋊C₄	—	8	1	no	—
578	C₄⋊C₄	—	8	1	no	—
579	C₄⋊C₄	—	8	1	no	—
580	C₄⋊C₄	C₂×C₇×D₄	1	2	yes	—
581	C₂²⋊C₄	—	4	2	no	—
582	C₂²⋊C₄	—	4	2	no	—
583	C₂²⋊C₄	—	4	2	no	—
584	C₂²⋊C₄	—	4	2	no	—
585	C₂²⋊C₄	—	4	2	no	—
586	C₂²⋊C₄	—	8	1	no	—
587	C₂²⋊C₄	—	8	1	no	—
588	C₄²	—	2	4	no	—
589	C₄²	—	2	1	no	—
590	C₄²	—	2	1	no	—
591	C₄²	—	2	1	no	—
592	C₄²	—	2	1	no	—
593	C₄²	—	4	2	no	—
594	C₄²	—	4	2	no	—
595	C₄²	C₂×C₇×D₄	1	2	yes	—
596	C₄²	C₇×#41	1	2	yes	—
597	C₂×C₇	—	8	2	no	—
598	C₂×C₇	—	16	1	no	—
599	C₂×C₇	#2416	1	1	yes	characteristic
600	C₂×C₇	#3037	1	1	yes	characteristic
601	C₂×C₇	#3045	1	1	yes	characteristic
602	C₂×C₇	#3266	1	1	yes	characteristic
603	C₂×C₇	#3268	1	1	yes	characteristic
604	C₂×C₇	#3371	1	1	yes	characteristic
605	C₂×C₇	#3375	1	1	yes	characteristic
606	C₂³	—	2	2	no	—
607	C₂³	—	4	1	no	—
608	C₂³	—	4	1	no	—
609	C₂³	—	4	1	no	—
610	C₂³	—	4	1	no	—
611	C₂³	—	4	1	no	—
612	C₂³	—	4	1	no	—
613	C₂³	—	4	1	no	—
614	C₂³	—	4	1	no	—
615	C₂³	—	4	1	no	—
616	C₂³	—	4	1	no	—
617	C₂³	—	4	1	no	—
618	C₂³	—	4	1	no	—
619	C₂³	—	4	1	no	—
620	C₂³	C₂²×C₇×D₄	1	1	yes	characteristic
621	Q₈	—	2	2	no	—
622	Q₈	—	2	2	no	—
623	Q₈	—	2	2	no	—
624	Q₈	—	4	1	no	—
625	Q₈	—	4	1	no	—
626	Q₈	—	4	1	no	—
627	Q₈	—	4	1	no	—
628	Q₈	C₇×#121	1	4	yes	—
629	D₄	—	2	2	no	—
630	D₄	—	2	2	no	—
631	D₄	—	4	1	no	—
632	D₄	—	4	1	no	—
633	D₄	—	4	1	no	—
634	D₄	—	4	1	no	—
635	D₄	—	4	1	no	—
636	D₄	—	4	1	no	—
637	D₄	—	8	4	no	—
638	D₄	—	8	4	no	—
639	C₂×C₄	—	2	2	no	—
640	C₂×C₄	—	2	1	no	—
641	C₂×C₄	—	2	2	no	—
642	C₂×C₄	—	2	2	no	—
643	C₂×C₄	—	2	1	no	—
644	C₂×C₄	—	2	1	no	—
645	C₂×C₄	—	2	1	no	—
646	C₂×C₄	—	2	1	no	—
647	C₂×C₄	—	2	1	no	—
648	C₂×C₄	—	2	2	no	—
649	C₂×C₄	—	2	1	no	—
650	C₂×C₄	—	2	1	no	—
651	C₂×C₄	—	2	1	no	—
652	C₂×C₄	—	2	1	no	—
653	C₂×C₄	—	2	1	no	—
654	C₂×C₄	—	2	1	no	—
655	C₂×C₄	—	2	1	no	—
656	C₂×C₄	—	2	1	no	—
657	C₂×C₄	—	2	1	no	—
658	C₂×C₄	—	4	1	no	—
659	C₂×C₄	—	4	1	no	—
660	C₂×C₄	—	4	1	no	—
661	C₂×C₄	—	4	1	no	—
662	C₂×C₄	—	4	1	no	—
663	C₂×C₄	—	4	1	no	—
664	C₂×C₄	—	4	1	no	—
665	C₂×C₄	—	4	1	no	—
666	C₂×C₄	—	4	1	no	—
667	C₂×C₄	—	4	1	no	—
668	C₂×C₄	—	4	1	no	—
669	C₂×C₄	—	4	1	no	—
670	C₂×C₄	—	4	1	no	—
671	C₂×C₄	—	4	1	no	—
672	C₂×C₄	—	8	4	no	—
673	C₂×C₄	C₇×#121	1	2	yes	—
674	C₂×C₄	C₇×#121	1	2	yes	—
675	C₂×C₄	C₇×#137	1	2	yes	—
676	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
677	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
678	C₂×C₄	C₂×C₇×#41	1	1	yes	characteristic
679	C₂×C₄	C₂×C₇×#41	1	1	yes	characteristic
680	C₂×C₄	C₇×H(5,𝔽₂)	1	1	yes	characteristic
681	C₂×C₄	C₇×2₋¹⁺⁴	1	1	yes	characteristic
682	C₈	—	2	2	no	—
683	C₈	—	4	1	no	—
684	C₈	—	4	1	no	—
685	C₈	—	4	1	no	—
686	C₇	#24739	1	1	yes	characteristic, direct product factor, Sylow
687	C₂²	—	4	2	no	—
688	C₂²	—	4	2	no	—
689	C₂²	—	4	2	no	—
690	C₂²	—	8	1	no	—
691	C₂²	—	8	1	no	—
692	C₂²	—	8	1	no	—
693	C₂²	—	8	1	no	—
694	C₂²	—	8	1	no	—
695	C₂²	—	8	1	no	—
696	C₂²	—	8	1	no	—
697	C₂²	—	8	1	no	—
698	C₂²	—	8	1	no	—
699	C₂²	—	8	1	no	—
700	C₂²	—	8	1	no	—
701	C₂²	C₂×C₇×#121	1	1	yes	characteristic
702	C₂²	C₇×D₄²	1	1	yes	characteristic
703	C₂²	C₇×#548	1	1	yes	characteristic
704	C₂²	C₂×C₇×#137	1	1	yes	characteristic
705	C₂²	C₇×#575	1	1	yes	characteristic
706	C₂²	C₇×#576	1	1	yes	characteristic
707	C₂²	C₇×#577	1	1	yes	characteristic
708	C₄	—	2	4	no	—
709	C₄	—	2	2	no	—
710	C₄	—	2	2	no	—
711	C₄	—	2	2	no	—
712	C₄	—	4	1	no	—
713	C₄	—	4	1	no	—
714	C₄	—	4	1	no	—
715	C₄	—	4	2	no	—
716	C₄	—	8	1	no	—
717	C₄	—	8	1	no	—
718	C₄	—	8	1	no	—
719	C₄	—	8	1	no	—
720	C₄	C₂×C₇×#121	1	1	yes	characteristic
721	C₄	C₇×#537	1	1	yes	characteristic
722	C₄	C₇×#547	1	1	yes	characteristic
723	C₄	C₇×#553	1	1	yes	characteristic
724	C₂	—	8	2	no	—
725	C₂	—	16	1	no	—
726	C₂	C₇×#2416	1	1	yes	characteristic
727	C₂	C₇×#3037	1	1	yes	characteristic
728	C₂	C₇×#3045	1	1	yes	characteristic
729	C₂	C₇×#3266	1	1	yes	characteristic
730	C₂	C₇×#3268	1	1	yes	characteristic
731	C₂	C₇×#3371	1	1	yes	characteristic
732	C₂	C₇×#3375	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₇	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₇
prime radical	C₂×C₇×#127	C₂²
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×#464	C₂	semidirect
2. C₂×C₇×#464	C₂	semidirect
4. C₂×C₇×#440	C₂	semidirect
6. C₇×Q₈×C₄⋊C₄	C₂	semidirect
7. C₇×#2068	C₂	semidirect
8. C₇×#2067	C₂	semidirect
9. C₇×#2042	C₂	semidirect
11. C₇×#1959	C₂	semidirect
12. C₇×#1940	C₂	semidirect
13. C₇×#1880	C₂	semidirect
14. C₇×#1878	C₂	semidirect
15. C₇×#1802	C₂	semidirect
63. #24739	C₇	direct (N × H)
95. C₄×C₇×Q₈	D₄	semidirect
145. C₂×#464	C₂×C₇	semidirect
146. C₂×#464	C₂×C₇	semidirect
148. C₂×#440	C₂×C₇	semidirect
150. Q₈×C₄⋊C₄	C₂×C₇	semidirect
151. #2068	C₂×C₇	semidirect
152. #2067	C₂×C₇	semidirect
153. #2042	C₂×C₇	semidirect
155. #1959	C₂×C₇	semidirect
156. #1940	C₂×C₇	semidirect
157. #1880	C₂×C₇	semidirect
158. #1878	C₂×C₇	semidirect
159. #1802	C₂×C₇	semidirect
414. C₄×Q₈	C₇×D₄	semidirect
686. C₇	#24739	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×#464	2
C₂×C₇×#460	2
C₂×C₇×#440	2
C₇×#2544	2
C₇×Q₈×C₄⋊C₄	2
C₇×#2068	2
C₇×#2067	2
C₇×#2042	2
C₇×#2041	2
C₇×#1959	2
C₇×#1940	2
C₇×#1880	2
C₇×#1878	2
C₇×#1802	2
#24739	7

Subgroups — C7×#24739 #13201955

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×#24739 #13201955