Subgroups — C₇×#24536 #13201752

Order 1792.

1006 conjugacy classes of subgroups.

The subgroup lattice has 722 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₇×#452	C₂	1	1	yes	maximal, characteristic
2	C₂×C₇×#416	C₂	1	1	yes	maximal, characteristic
3	C₇×#2499	C₂	1	1	yes	maximal, characteristic, complemented
4	C₇×#2339	C₂	1	1	yes	maximal, characteristic
5	C₇×#2074	C₂	1	1	yes	maximal, characteristic, complemented
6	C₇×#2072	C₂	1	1	yes	maximal, characteristic, complemented
7	C₇×#2056	C₂	1	1	yes	maximal, characteristic, complemented
8	C₇×#2056	C₂	1	1	yes	maximal, characteristic, complemented
9	C₇×#1892	C₂	1	1	yes	maximal, characteristic, complemented
10	C₇×#1877	C₂	1	1	yes	maximal, characteristic, complemented
11	C₇×#1877	C₂	1	1	yes	maximal, characteristic, complemented
12	C₇×#1850	C₂	1	1	yes	maximal, characteristic, complemented
13	C₇×#1825	C₂	1	1	yes	maximal, characteristic, complemented
14	C₇×#1804	C₂	1	1	yes	maximal, characteristic, complemented
15	C₇×#1802	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×C₇×#41	C₂²	1	1	yes	characteristic
17	C₂²×C₇×Q₁₆	C₂²	1	1	yes	characteristic
18	C₂²×C₇×SD₁₆	C₂²	1	1	yes	characteristic
19	C₂³×C₇×C₈	C₂²	1	1	yes	characteristic
20	C₂×C₇×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
21	C₂×C₄×C₇×D₄	C₂²	1	1	yes	characteristic
22	C₂×C₄×C₇×D₄	C₂²	1	1	yes	characteristic
23	C₂×C₇×#117	C₂²	1	1	yes	characteristic
24	C₇×#452	—	2	4	no	—
25	C₂×C₇×C₄⋊C₈	C₂²	1	1	yes	characteristic
26	C₂×C₇×C₄⋊C₈	C₂²	1	1	yes	characteristic
27	C₇×#416	—	2	4	no	—
28	C₂×C₇×#103	C₂²	1	1	yes	characteristic
29	C₂×C₇×#103	C₂²	1	1	yes	characteristic
30	C₂×C₇×#103	C₂²	1	1	yes	characteristic
31	C₂×C₇×#103	C₂²	1	1	yes	characteristic
32	C₂×C₇×#103	C₂²	1	1	yes	characteristic
33	C₂×C₇×#102	C₂²	1	1	yes	characteristic
34	C₂×C₇×#102	C₂²	1	1	yes	characteristic
35	C₂×C₇×#102	C₂²	1	1	yes	characteristic
36	C₂×C₇×C₂²⋊C₈	C₂²	1	1	yes	characteristic
37	C₇×#397	—	2	1	no	—
38	C₇×#397	—	2	1	no	—
39	C₇×#391	C₂²	1	1	yes	characteristic
40	C₇×#391	C₂²	1	1	yes	characteristic
41	C₇×#391	C₂²	1	1	yes	characteristic
42	C₇×#391	C₂²	1	1	yes	characteristic
43	C₇×#387	—	2	1	no	—
44	C₇×#387	—	2	1	no	—
45	C₇×#386	—	2	1	no	—
46	C₇×#386	—	2	1	no	—
47	C₇×#384	C₂²	1	1	yes	characteristic
48	C₇×#382	C₂²	1	1	yes	characteristic
49	C₇×#381	—	2	1	no	—
50	C₇×#380	C₂²	1	1	yes	characteristic
51	C₄×C₇×C₂²⋊C₄	C₂²	1	1	yes	characteristic
52	C₂×C₇×#95	—	2	1	no	—
53	C₇×#340	C₂²	1	1	yes	characteristic
54	C₇×#340	C₂²	1	1	yes	characteristic
55	C₇×#340	C₂²	1	1	yes	characteristic
56	C₇×#340	C₂²	1	1	yes	characteristic
57	C₇×#340	C₂²	1	1	yes	characteristic
58	C₇×#340	C₂²	1	1	yes	characteristic
59	C₇×#336	C₂²	1	1	yes	characteristic
60	C₇×#336	C₂²	1	1	yes	characteristic
61	#24536	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
62	C₂×C₇×#41	—	2	2	no	—
63	C₂×C₇×#41	—	2	2	no	—
64	C₂×C₇×#41	—	2	2	no	—
65	C₂×C₇×#41	—	4	1	no	—
66	C₂×C₇×#41	—	4	1	no	—
67	C₂×C₇×#41	D₄	1	4	yes	—
68	C₂²×C₇×Q₈	C₂³	1	1	yes	characteristic
69	C₂²×C₇×Q₈	C₂³	1	1	yes	characteristic
70	C₂²×C₇×D₄	—	2	1	no	—
71	C₂²×C₇×D₄	C₂³	1	1	yes	characteristic
72	C₂³×C₄×C₇	—	2	1	no	—
73	C₂³×C₄×C₇	—	2	1	no	—
74	C₂³×C₄×C₇	—	2	1	no	—
75	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
76	C₂×C₇×Q₁₆	—	2	2	no	—
77	C₂×C₇×Q₁₆	—	4	1	no	—
78	C₂×C₇×Q₁₆	—	4	1	no	—
79	C₂×C₇×SD₁₆	—	2	2	no	—
80	C₂×C₇×SD₁₆	—	2	2	no	—
81	C₂×C₇×SD₁₆	—	2	2	no	—
82	C₂²×C₇×C₈	—	2	2	no	—
83	C₂²×C₇×C₈	—	4	1	no	—
84	C₂²×C₇×C₈	—	4	1	no	—
85	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
86	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
87	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
88	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
89	C₇×C₂²⋊Q₈	—	2	2	no	—
90	C₇×C₂²⋊Q₈	—	2	2	no	—
91	C₄×C₇×D₄	—	2	2	no	—
92	C₄×C₇×D₄	—	2	2	no	—
93	C₄×C₇×D₄	—	4	1	no	—
94	C₄×C₇×D₄	—	4	1	no	—
95	C₇×#117	—	2	2	no	—
96	C₇×#117	—	2	2	no	—
97	C₂×C₇×C₄⋊C₄	—	2	1	no	—
98	C₂×C₇×C₄⋊C₄	—	2	1	no	—
99	C₂×C₇×C₄⋊C₄	—	2	1	no	—
100	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
101	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
102	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
103	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
104	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
105	C₂×C₇×C₂²⋊C₄	—	2	1	no	—
106	C₂×C₇×C₂²⋊C₄	—	2	1	no	—
107	C₂×C₇×C₂²⋊C₄	—	2	1	no	—
108	C₂×C₇×C₂²⋊C₄	—	2	1	no	—
109	C₂×C₇×C₂²⋊C₄	—	2	1	no	—
110	C₂×C₇×C₂²⋊C₄	D₄	1	1	yes	characteristic
111	C₂×C₇×C₂²⋊C₄	D₄	1	1	yes	characteristic
112	C₂×C₄²×C₇	—	2	1	no	—
113	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
114	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
115	C₇×C₄⋊C₈	—	4	1	no	—
116	C₇×C₄⋊C₈	—	4	1	no	—
117	C₇×#103	—	2	2	no	—
118	C₇×#103	—	2	2	no	—
119	C₇×#103	—	2	2	no	—
120	C₇×#103	—	4	1	no	—
121	C₇×#103	—	4	1	no	—
122	C₇×#102	—	2	2	no	—
123	C₇×#102	—	2	2	no	—
124	C₇×#102	—	2	2	no	—
125	C₇×C₂²⋊C₈	—	2	2	no	—
126	C₇×#95	—	2	1	no	—
127	C₇×#95	—	2	1	no	—
128	C₇×#95	—	2	1	no	—
129	C₇×#95	—	2	1	no	—
130	C₇×#95	—	2	1	no	—
131	C₇×#95	—	2	1	no	—
132	C₇×#95	—	2	1	no	—
133	C₇×#95	—	2	1	no	—
134	C₇×#95	—	2	1	no	—
135	C₇×#95	—	2	1	no	—
136	C₇×#95	—	2	1	no	—
137	C₇×#95	D₄	1	1	yes	characteristic
138	C₇×#95	D₄	1	1	yes	characteristic
139	C₂×#452	C₂×C₇	1	1	yes	characteristic
140	C₂×#416	C₂×C₇	1	1	yes	characteristic
141	#2499	C₂×C₇	1	1	yes	characteristic, complemented
142	#2339	C₂×C₇	1	1	yes	characteristic
143	#2074	C₂×C₇	1	1	yes	characteristic, complemented
144	#2072	C₂×C₇	1	1	yes	characteristic, complemented
145	#2056	C₂×C₇	1	1	yes	characteristic, complemented
146	#2056	C₂×C₇	1	1	yes	characteristic, complemented
147	#1892	C₂×C₇	1	1	yes	characteristic, complemented
148	#1877	C₂×C₇	1	1	yes	characteristic, complemented
149	#1877	C₂×C₇	1	1	yes	characteristic, complemented
150	#1850	C₂×C₇	1	1	yes	characteristic, complemented
151	#1825	C₂×C₇	1	1	yes	characteristic, complemented
152	#1804	C₂×C₇	1	1	yes	characteristic, complemented
153	#1802	C₂×C₇	1	1	yes	characteristic, complemented
154	C₂⁴×C₇	—	2	1	no	—
155	C₂⁴×C₇	C₂×D₄	1	1	yes	characteristic
156	C₇×#41	—	2	8	no	—
157	C₇×#41	—	4	4	no	—
158	C₇×#41	—	4	4	no	—
159	C₇×#41	—	4	4	no	—
160	C₂×C₇×Q₈	—	2	1	no	—
161	C₂×C₇×Q₈	—	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×D₄	—	2	4	no	—
173	C₂×C₇×D₄	—	2	1	no	—
174	C₂×C₇×D₄	—	2	1	no	—
175	C₂×C₇×D₄	—	2	1	no	—
176	C₂×C₇×D₄	—	4	2	no	—
177	C₂×C₇×D₄	—	4	2	no	—
178	C₂×C₇×D₄	C₂×D₄	1	2	yes	—
179	C₂×C₇×D₄	#41	1	2	yes	—
180	C₂×C₇×D₄	#41	1	2	yes	—
181	C₂²×C₄×C₇	—	2	1	no	—
182	C₂²×C₄×C₇	—	2	1	no	—
183	C₂²×C₄×C₇	—	2	1	no	—
184	C₂²×C₄×C₇	—	2	1	no	—
185	C₂²×C₄×C₇	—	2	1	no	—
186	C₂²×C₄×C₇	—	2	4	no	—
187	C₂²×C₄×C₇	—	2	1	no	—
188	C₂²×C₄×C₇	—	2	1	no	—
189	C₂²×C₄×C₇	—	2	1	no	—
190	C₂²×C₄×C₇	—	2	1	no	—
191	C₂²×C₄×C₇	—	2	1	no	—
192	C₂²×C₄×C₇	—	2	1	no	—
193	C₂²×C₄×C₇	—	4	2	no	—
194	C₂²×C₄×C₇	—	4	2	no	—
195	C₂²×C₄×C₇	—	4	2	no	—
196	C₂²×C₄×C₇	—	4	2	no	—
197	C₂²×C₄×C₇	—	4	2	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	2	yes	—
206	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
207	C₂²×C₄×C₇	#41	1	2	yes	—
208	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
209	C₇×Q₁₆	—	4	4	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	—	2	1	no	—
223	C₂×C₇×C₈	—	4	4	no	—
224	C₇×C₄⋊C₄	—	2	1	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	—	2	1	no	—
233	C₇×C₄⋊C₄	—	2	1	no	—
234	C₇×C₄⋊C₄	—	4	2	no	—
235	C₇×C₄⋊C₄	—	4	2	no	—
236	C₇×C₄⋊C₄	—	4	2	no	—
237	C₇×C₂²⋊C₄	—	2	2	no	—
238	C₇×C₂²⋊C₄	—	4	1	no	—
239	C₇×C₂²⋊C₄	—	4	2	no	—
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	—	8	1	no	—
244	C₄²×C₇	—	2	1	no	—
245	C₄²×C₇	—	2	1	no	—
246	C₄²×C₇	—	2	1	no	—
247	C₄²×C₇	—	2	1	no	—
248	C₄²×C₇	—	4	2	no	—
249	C₂²×#41	C₂²×C₇	1	1	yes	characteristic
250	C₂²×Q₁₆	C₂²×C₇	1	1	yes	characteristic
251	C₂²×SD₁₆	C₂²×C₇	1	1	yes	characteristic
252	C₂³×C₈	C₂²×C₇	1	1	yes	characteristic
253	C₂×C₂²⋊Q₈	C₂²×C₇	1	1	yes	characteristic
254	C₂×C₄×D₄	C₂²×C₇	1	1	yes	characteristic
255	C₂×C₄×D₄	C₂²×C₇	1	1	yes	characteristic
256	C₂×#117	C₂²×C₇	1	1	yes	characteristic
257	#452	—	2	4	no	—
258	C₂×C₄⋊C₈	C₂²×C₇	1	1	yes	characteristic
259	C₂×C₄⋊C₈	C₂²×C₇	1	1	yes	characteristic
260	#416	—	2	4	no	—
261	C₂×#103	C₂²×C₇	1	1	yes	characteristic
262	C₂×#103	C₂²×C₇	1	1	yes	characteristic
263	C₂×#103	C₂²×C₇	1	1	yes	characteristic
264	C₂×#103	C₂²×C₇	1	1	yes	characteristic
265	C₂×#103	C₂²×C₇	1	1	yes	characteristic
266	C₂×#102	C₂²×C₇	1	1	yes	characteristic
267	C₂×#102	C₂²×C₇	1	1	yes	characteristic
268	C₂×#102	C₂²×C₇	1	1	yes	characteristic
269	C₂×C₂²⋊C₈	C₂²×C₇	1	1	yes	characteristic
270	#397	—	2	1	no	—
271	#397	—	2	1	no	—
272	#391	C₂²×C₇	1	1	yes	characteristic
273	#391	C₂²×C₇	1	1	yes	characteristic
274	#391	C₂²×C₇	1	1	yes	characteristic
275	#391	C₂²×C₇	1	1	yes	characteristic
276	#387	—	2	1	no	—
277	#387	—	2	1	no	—
278	#386	—	2	1	no	—
279	#386	—	2	1	no	—
280	#384	C₂²×C₇	1	1	yes	characteristic
281	#382	C₂²×C₇	1	1	yes	characteristic
282	#381	—	2	1	no	—
283	#380	C₂²×C₇	1	1	yes	characteristic
284	C₄×C₂²⋊C₄	C₂²×C₇	1	1	yes	characteristic
285	C₂×#95	—	2	1	no	—
286	#340	C₂²×C₇	1	1	yes	characteristic
287	#340	C₂²×C₇	1	1	yes	characteristic
288	#340	C₂²×C₇	1	1	yes	characteristic
289	#340	C₂²×C₇	1	1	yes	characteristic
290	#340	C₂²×C₇	1	1	yes	characteristic
291	#340	C₂²×C₇	1	1	yes	characteristic
292	#336	C₂²×C₇	1	1	yes	characteristic
293	#336	C₂²×C₇	1	1	yes	characteristic
294	C₂³×C₇	—	2	2	no	—
295	C₂³×C₇	—	2	2	no	—
296	C₂³×C₇	—	2	2	no	—
297	C₂³×C₇	—	2	1	no	—
298	C₂³×C₇	—	2	1	no	—
299	C₂³×C₇	—	2	1	no	—
300	C₂³×C₇	—	2	1	no	—
301	C₂³×C₇	—	2	1	no	—
302	C₂³×C₇	—	2	1	no	—
303	C₂³×C₇	—	4	1	no	—
304	C₂³×C₇	—	4	1	no	—
305	C₂³×C₇	—	4	1	no	—
306	C₂³×C₇	—	4	1	no	—
307	C₂³×C₇	#121	1	2	yes	—
308	C₂³×C₇	C₂²×D₄	1	1	yes	characteristic
309	C₇×Q₈	—	2	2	no	—
310	C₇×Q₈	—	2	2	no	—
311	C₇×Q₈	—	4	1	no	—
312	C₇×Q₈	—	4	1	no	—
313	C₇×Q₈	—	4	1	no	—
314	C₇×Q₈	—	4	1	no	—
315	C₇×Q₈	—	4	1	no	—
316	C₇×Q₈	—	4	1	no	—
317	C₇×D₄	—	2	2	no	—
318	C₇×D₄	—	2	2	no	—
319	C₇×D₄	—	2	2	no	—
320	C₇×D₄	—	4	8	no	—
321	C₇×D₄	#123	1	4	yes	—
322	C₂×C₄×C₇	—	2	1	no	—
323	C₂×C₄×C₇	—	2	1	no	—
324	C₂×C₄×C₇	—	2	1	no	—
325	C₂×C₄×C₇	—	2	1	no	—
326	C₂×C₄×C₇	—	2	2	no	—
327	C₂×C₄×C₇	—	2	2	no	—
328	C₂×C₄×C₇	—	2	2	no	—
329	C₂×C₄×C₇	—	2	2	no	—
330	C₂×C₄×C₇	—	2	2	no	—
331	C₂×C₄×C₇	—	2	1	no	—
332	C₂×C₄×C₇	—	2	1	no	—
333	C₂×C₄×C₇	—	2	1	no	—
334	C₂×C₄×C₇	—	2	1	no	—
335	C₂×C₄×C₇	—	2	1	no	—
336	C₂×C₄×C₇	—	2	1	no	—
337	C₂×C₄×C₇	—	2	1	no	—
338	C₂×C₄×C₇	—	2	1	no	—
339	C₂×C₄×C₇	—	2	1	no	—
340	C₂×C₄×C₇	—	4	8	no	—
341	C₂×C₄×C₇	—	4	1	no	—
342	C₂×C₄×C₇	—	4	1	no	—
343	C₂×C₄×C₇	—	4	1	no	—
344	C₂×C₄×C₇	—	4	1	no	—
345	C₂×C₄×C₇	—	4	1	no	—
346	C₂×C₄×C₇	—	4	1	no	—
347	C₂×C₄×C₇	—	4	1	no	—
348	C₂×C₄×C₇	—	4	1	no	—
349	C₂×C₄×C₇	—	4	1	no	—
350	C₂×C₄×C₇	—	4	1	no	—
351	C₂×C₄×C₇	—	4	1	no	—
352	C₂×C₄×C₇	—	4	1	no	—
353	C₂×C₄×C₇	—	4	1	no	—
354	C₂×C₄×C₇	—	4	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	—	8	4	no	—
362	C₂×C₄×C₇	—	8	4	no	—
363	C₂×C₄×C₇	#121	1	2	yes	—
364	C₂×C₄×C₇	#135	1	2	yes	—
365	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
366	C₂×C₄×C₇	C₂×#41	1	1	yes	characteristic
367	C₂×C₄×C₇	C₂×#41	1	1	yes	characteristic
368	C₂×C₄×C₇	C₂×#41	1	1	yes	characteristic
369	C₂×C₄×C₇	H(5,𝔽₂)	1	1	yes	characteristic
370	C₂×C₄×C₇	H(5,𝔽₂)	1	1	yes	characteristic
371	C₇×C₈	—	4	1	no	—
372	C₇×C₈	—	4	1	no	—
373	C₇×C₈	—	4	1	no	—
374	C₇×C₈	—	4	1	no	—
375	C₂×#41	—	2	2	no	—
376	C₂×#41	—	2	2	no	—
377	C₂×#41	—	2	2	no	—
378	C₂×#41	—	4	1	no	—
379	C₂×#41	—	4	1	no	—
380	C₂×#41	C₇×D₄	1	4	yes	—
381	C₂²×Q₈	C₂³×C₇	1	1	yes	characteristic
382	C₂²×Q₈	C₂³×C₇	1	1	yes	characteristic
383	C₂²×D₄	—	2	1	no	—
384	C₂²×D₄	C₂³×C₇	1	1	yes	characteristic
385	C₂³×C₄	—	2	1	no	—
386	C₂³×C₄	—	2	1	no	—
387	C₂³×C₄	—	2	1	no	—
388	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
389	C₂×Q₁₆	—	2	2	no	—
390	C₂×Q₁₆	—	4	1	no	—
391	C₂×Q₁₆	—	4	1	no	—
392	C₂×SD₁₆	—	2	2	no	—
393	C₂×SD₁₆	—	2	2	no	—
394	C₂×SD₁₆	—	2	2	no	—
395	C₂²×C₈	—	2	2	no	—
396	C₂²×C₈	—	4	1	no	—
397	C₂²×C₈	—	4	1	no	—
398	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
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⋊Q₈	—	2	2	no	—
403	C₂²⋊Q₈	—	2	2	no	—
404	C₄×D₄	—	2	2	no	—
405	C₄×D₄	—	2	2	no	—
406	C₄×D₄	—	4	1	no	—
407	C₄×D₄	—	4	1	no	—
408	#117	—	2	2	no	—
409	#117	—	2	2	no	—
410	C₂×C₄⋊C₄	—	2	1	no	—
411	C₂×C₄⋊C₄	—	2	1	no	—
412	C₂×C₄⋊C₄	—	2	1	no	—
413	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
414	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
415	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
416	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
417	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
418	C₂×C₂²⋊C₄	—	2	1	no	—
419	C₂×C₂²⋊C₄	—	2	1	no	—
420	C₂×C₂²⋊C₄	—	2	1	no	—
421	C₂×C₂²⋊C₄	—	2	1	no	—
422	C₂×C₂²⋊C₄	—	2	1	no	—
423	C₂×C₂²⋊C₄	C₇×D₄	1	1	yes	characteristic
424	C₂×C₂²⋊C₄	C₇×D₄	1	1	yes	characteristic
425	C₂×C₄²	—	2	1	no	—
426	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
427	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
428	C₄⋊C₈	—	4	1	no	—
429	C₄⋊C₈	—	4	1	no	—
430	#103	—	2	2	no	—
431	#103	—	2	2	no	—
432	#103	—	2	2	no	—
433	#103	—	4	1	no	—
434	#103	—	4	1	no	—
435	#102	—	2	2	no	—
436	#102	—	2	2	no	—
437	#102	—	2	2	no	—
438	C₂²⋊C₈	—	2	2	no	—
439	#95	—	2	1	no	—
440	#95	—	2	1	no	—
441	#95	—	2	1	no	—
442	#95	—	2	1	no	—
443	#95	—	2	1	no	—
444	#95	—	2	1	no	—
445	#95	—	2	1	no	—
446	#95	—	2	1	no	—
447	#95	—	2	1	no	—
448	#95	—	2	1	no	—
449	#95	—	2	1	no	—
450	#95	C₇×D₄	1	1	yes	characteristic
451	#95	C₇×D₄	1	1	yes	characteristic
452	C₂²×C₇	—	2	2	no	—
453	C₂²×C₇	—	2	4	no	—
454	C₂²×C₇	—	2	2	no	—
455	C₂²×C₇	—	2	2	no	—
456	C₂²×C₇	—	4	2	no	—
457	C₂²×C₇	—	4	2	no	—
458	C₂²×C₇	—	4	1	no	—
459	C₂²×C₇	—	4	2	no	—
460	C₂²×C₇	—	4	1	no	—
461	C₂²×C₇	—	4	2	no	—
462	C₂²×C₇	—	4	2	no	—
463	C₂²×C₇	—	4	1	no	—
464	C₂²×C₇	—	4	1	no	—
465	C₂²×C₇	—	4	2	no	—
466	C₂²×C₇	C₂×#121	1	1	yes	characteristic
467	C₂²×C₇	#546	1	1	yes	characteristic
468	C₂²×C₇	#546	1	1	yes	characteristic
469	C₂²×C₇	C₂×#135	1	1	yes	characteristic
470	C₂²×C₇	#575	1	1	yes	characteristic
471	C₂²×C₇	#577	1	1	yes	characteristic
472	C₂²×C₇	#578	1	1	yes	characteristic
473	C₄×C₇	—	2	2	no	—
474	C₄×C₇	—	2	2	no	—
475	C₄×C₇	—	4	2	no	—
476	C₄×C₇	—	4	1	no	—
477	C₄×C₇	—	4	1	no	—
478	C₄×C₇	—	4	1	no	—
479	C₄×C₇	—	8	1	no	—
480	C₄×C₇	—	8	1	no	—
481	C₄×C₇	—	8	1	no	—
482	C₄×C₇	—	8	1	no	—
483	C₄×C₇	—	8	1	no	—
484	C₄×C₇	—	8	1	no	—
485	C₄×C₇	C₂×#123	1	1	yes	characteristic
486	C₄×C₇	#534	1	1	yes	characteristic
487	C₄×C₇	#551	1	1	yes	characteristic
488	C₄×C₇	#551	1	1	yes	characteristic
489	C₂⁴	—	2	1	no	—
490	C₂⁴	C₂×C₇×D₄	1	1	yes	characteristic
491	#41	—	2	8	no	—
492	#41	—	4	4	no	—
493	#41	—	4	4	no	—
494	#41	—	4	4	no	—
495	C₂×Q₈	—	2	1	no	—
496	C₂×Q₈	—	2	1	no	—
497	C₂×Q₈	—	2	1	no	—
498	C₂×Q₈	—	2	1	no	—
499	C₂×Q₈	—	2	1	no	—
500	C₂×Q₈	—	2	1	no	—
501	C₂×Q₈	—	2	1	no	—
502	C₂×Q₈	—	2	1	no	—
503	C₂×Q₈	—	2	1	no	—
504	C₂×Q₈	—	2	1	no	—
505	C₂×Q₈	—	2	1	no	—
506	C₂×Q₈	C₂×C₇×D₄	1	2	yes	—
507	C₂×D₄	—	2	4	no	—
508	C₂×D₄	—	2	1	no	—
509	C₂×D₄	—	2	1	no	—
510	C₂×D₄	—	2	1	no	—
511	C₂×D₄	—	4	2	no	—
512	C₂×D₄	—	4	2	no	—
513	C₂×D₄	C₂×C₇×D₄	1	2	yes	—
514	C₂×D₄	C₇×#41	1	2	yes	—
515	C₂×D₄	C₇×#41	1	2	yes	—
516	C₂²×C₄	—	2	1	no	—
517	C₂²×C₄	—	2	1	no	—
518	C₂²×C₄	—	2	1	no	—
519	C₂²×C₄	—	2	1	no	—
520	C₂²×C₄	—	2	1	no	—
521	C₂²×C₄	—	2	4	no	—
522	C₂²×C₄	—	2	1	no	—
523	C₂²×C₄	—	2	1	no	—
524	C₂²×C₄	—	2	1	no	—
525	C₂²×C₄	—	2	1	no	—
526	C₂²×C₄	—	2	1	no	—
527	C₂²×C₄	—	2	1	no	—
528	C₂²×C₄	—	4	2	no	—
529	C₂²×C₄	—	4	2	no	—
530	C₂²×C₄	—	4	2	no	—
531	C₂²×C₄	—	4	2	no	—
532	C₂²×C₄	—	4	2	no	—
533	C₂²×C₄	—	4	2	no	—
534	C₂²×C₄	—	8	1	no	—
535	C₂²×C₄	—	8	1	no	—
536	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
537	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
538	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
539	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
540	C₂²×C₄	C₂×C₇×D₄	1	2	yes	—
541	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
542	C₂²×C₄	C₇×#41	1	2	yes	—
543	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
544	Q₁₆	—	4	4	no	—
545	SD₁₆	—	4	4	no	—
546	C₂×C₈	—	2	1	no	—
547	C₂×C₈	—	2	1	no	—
548	C₂×C₈	—	2	1	no	—
549	C₂×C₈	—	2	1	no	—
550	C₂×C₈	—	2	1	no	—
551	C₂×C₈	—	2	1	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	—	4	4	no	—
559	C₄⋊C₄	—	2	1	no	—
560	C₄⋊C₄	—	2	1	no	—
561	C₄⋊C₄	—	2	1	no	—
562	C₄⋊C₄	—	2	1	no	—
563	C₄⋊C₄	—	2	1	no	—
564	C₄⋊C₄	—	2	1	no	—
565	C₄⋊C₄	—	2	1	no	—
566	C₄⋊C₄	—	2	1	no	—
567	C₄⋊C₄	—	2	1	no	—
568	C₄⋊C₄	—	2	1	no	—
569	C₄⋊C₄	—	4	2	no	—
570	C₄⋊C₄	—	4	2	no	—
571	C₄⋊C₄	—	4	2	no	—
572	C₂²⋊C₄	—	2	2	no	—
573	C₂²⋊C₄	—	4	1	no	—
574	C₂²⋊C₄	—	4	2	no	—
575	C₂²⋊C₄	—	4	2	no	—
576	C₂²⋊C₄	—	4	2	no	—
577	C₂²⋊C₄	—	4	2	no	—
578	C₂²⋊C₄	—	8	1	no	—
579	C₄²	—	2	1	no	—
580	C₄²	—	2	1	no	—
581	C₄²	—	2	1	no	—
582	C₄²	—	2	1	no	—
583	C₄²	—	4	2	no	—
584	C₂×C₇	—	4	2	no	—
585	C₂×C₇	—	4	4	no	—
586	C₂×C₇	#2412	1	1	yes	characteristic
587	C₂×C₇	#3035	1	1	yes	characteristic
588	C₂×C₇	#3046	1	1	yes	characteristic
589	C₂×C₇	#3296	1	1	yes	characteristic
590	C₂×C₇	#3302	1	1	yes	characteristic
591	C₂×C₇	#3311	1	1	yes	characteristic
592	C₂×C₇	#3315	1	1	yes	characteristic
593	C₂³	—	2	2	no	—
594	C₂³	—	2	2	no	—
595	C₂³	—	2	2	no	—
596	C₂³	—	2	1	no	—
597	C₂³	—	2	1	no	—
598	C₂³	—	2	1	no	—
599	C₂³	—	2	1	no	—
600	C₂³	—	2	1	no	—
601	C₂³	—	2	1	no	—
602	C₂³	—	4	1	no	—
603	C₂³	—	4	1	no	—
604	C₂³	—	4	1	no	—
605	C₂³	—	4	1	no	—
606	C₂³	C₇×#121	1	2	yes	—
607	C₂³	C₂²×C₇×D₄	1	1	yes	characteristic
608	Q₈	—	2	2	no	—
609	Q₈	—	2	2	no	—
610	Q₈	—	4	1	no	—
611	Q₈	—	4	1	no	—
612	Q₈	—	4	1	no	—
613	Q₈	—	4	1	no	—
614	Q₈	—	4	1	no	—
615	Q₈	—	4	1	no	—
616	D₄	—	2	2	no	—
617	D₄	—	2	2	no	—
618	D₄	—	2	2	no	—
619	D₄	—	4	8	no	—
620	D₄	C₇×#123	1	4	yes	—
621	C₂×C₄	—	2	1	no	—
622	C₂×C₄	—	2	1	no	—
623	C₂×C₄	—	2	1	no	—
624	C₂×C₄	—	2	1	no	—
625	C₂×C₄	—	2	2	no	—
626	C₂×C₄	—	2	2	no	—
627	C₂×C₄	—	2	2	no	—
628	C₂×C₄	—	2	2	no	—
629	C₂×C₄	—	2	2	no	—
630	C₂×C₄	—	2	1	no	—
631	C₂×C₄	—	2	1	no	—
632	C₂×C₄	—	2	1	no	—
633	C₂×C₄	—	2	1	no	—
634	C₂×C₄	—	2	1	no	—
635	C₂×C₄	—	2	1	no	—
636	C₂×C₄	—	2	1	no	—
637	C₂×C₄	—	2	1	no	—
638	C₂×C₄	—	2	1	no	—
639	C₂×C₄	—	4	8	no	—
640	C₂×C₄	—	4	1	no	—
641	C₂×C₄	—	4	1	no	—
642	C₂×C₄	—	4	1	no	—
643	C₂×C₄	—	4	1	no	—
644	C₂×C₄	—	4	1	no	—
645	C₂×C₄	—	4	1	no	—
646	C₂×C₄	—	4	1	no	—
647	C₂×C₄	—	4	1	no	—
648	C₂×C₄	—	4	1	no	—
649	C₂×C₄	—	4	1	no	—
650	C₂×C₄	—	4	1	no	—
651	C₂×C₄	—	4	1	no	—
652	C₂×C₄	—	4	1	no	—
653	C₂×C₄	—	4	1	no	—
654	C₂×C₄	—	4	1	no	—
655	C₂×C₄	—	4	1	no	—
656	C₂×C₄	—	4	1	no	—
657	C₂×C₄	—	4	1	no	—
658	C₂×C₄	—	4	1	no	—
659	C₂×C₄	—	4	1	no	—
660	C₂×C₄	—	8	4	no	—
661	C₂×C₄	—	8	4	no	—
662	C₂×C₄	C₇×#121	1	2	yes	—
663	C₂×C₄	C₇×#135	1	2	yes	—
664	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
665	C₂×C₄	C₂×C₇×#41	1	1	yes	characteristic
666	C₂×C₄	C₂×C₇×#41	1	1	yes	characteristic
667	C₂×C₄	C₂×C₇×#41	1	1	yes	characteristic
668	C₂×C₄	C₇×H(5,𝔽₂)	1	1	yes	characteristic
669	C₂×C₄	C₇×H(5,𝔽₂)	1	1	yes	characteristic
670	C₈	—	4	1	no	—
671	C₈	—	4	1	no	—
672	C₈	—	4	1	no	—
673	C₈	—	4	1	no	—
674	C₇	#24536	1	1	yes	characteristic, direct product factor, Sylow
675	C₂²	—	2	2	no	—
676	C₂²	—	2	4	no	—
677	C₂²	—	2	2	no	—
678	C₂²	—	2	2	no	—
679	C₂²	—	4	2	no	—
680	C₂²	—	4	2	no	—
681	C₂²	—	4	1	no	—
682	C₂²	—	4	2	no	—
683	C₂²	—	4	1	no	—
684	C₂²	—	4	2	no	—
685	C₂²	—	4	2	no	—
686	C₂²	—	4	1	no	—
687	C₂²	—	4	1	no	—
688	C₂²	—	4	2	no	—
689	C₂²	C₂×C₇×#121	1	1	yes	characteristic
690	C₂²	C₇×#546	1	1	yes	characteristic
691	C₂²	C₇×#546	1	1	yes	characteristic
692	C₂²	C₂×C₇×#135	1	1	yes	characteristic
693	C₂²	C₇×#575	1	1	yes	characteristic
694	C₂²	C₇×#577	1	1	yes	characteristic
695	C₂²	C₇×#578	1	1	yes	characteristic
696	C₄	—	2	2	no	—
697	C₄	—	2	2	no	—
698	C₄	—	4	2	no	—
699	C₄	—	4	1	no	—
700	C₄	—	4	1	no	—
701	C₄	—	4	1	no	—
702	C₄	—	8	1	no	—
703	C₄	—	8	1	no	—
704	C₄	—	8	1	no	—
705	C₄	—	8	1	no	—
706	C₄	—	8	1	no	—
707	C₄	—	8	1	no	—
708	C₄	C₂×C₇×#123	1	1	yes	characteristic
709	C₄	C₇×#534	1	1	yes	characteristic
710	C₄	C₇×#551	1	1	yes	characteristic
711	C₄	C₇×#551	1	1	yes	characteristic
712	C₂	—	4	2	no	—
713	C₂	—	4	4	no	—
714	C₂	C₇×#2412	1	1	yes	characteristic
715	C₂	C₇×#3035	1	1	yes	characteristic
716	C₂	C₇×#3046	1	1	yes	characteristic
717	C₂	C₇×#3296	1	1	yes	characteristic
718	C₂	C₇×#3302	1	1	yes	characteristic
719	C₂	C₇×#3311	1	1	yes	characteristic
720	C₂	C₇×#3315	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₇	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₇
prime radical	C₂²×C₇×#41	C₂²
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₇ ◁ C₄×C₇×C₂²⋊C₄ ◁ G

Complements

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

N	H ≅ G/N	type
3. C₇×#2499	C₂	semidirect
5. C₇×#2074	C₂	semidirect
6. C₇×#2072	C₂	semidirect
7. C₇×#2056	C₂	semidirect
8. C₇×#2056	C₂	semidirect
9. C₇×#1892	C₂	semidirect
10. C₇×#1877	C₂	semidirect
11. C₇×#1877	C₂	semidirect
12. C₇×#1850	C₂	semidirect
13. C₇×#1825	C₂	semidirect
14. C₇×#1804	C₂	semidirect
15. C₇×#1802	C₂	semidirect
61. #24536	C₇	direct (N × H)
141. #2499	C₂×C₇	semidirect
143. #2074	C₂×C₇	semidirect
144. #2072	C₂×C₇	semidirect
145. #2056	C₂×C₇	semidirect
146. #2056	C₂×C₇	semidirect
147. #1892	C₂×C₇	semidirect
148. #1877	C₂×C₇	semidirect
149. #1877	C₂×C₇	semidirect
150. #1850	C₂×C₇	semidirect
151. #1825	C₂×C₇	semidirect
152. #1804	C₂×C₇	semidirect
153. #1802	C₂×C₇	semidirect
674. C₇	#24536	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×#452	2
C₂×C₇×#416	2
C₇×#2499	2
C₇×#2339	2
C₇×#2074	2
C₇×#2072	2
C₇×#2056	2
C₇×#1892	2
C₇×#1877	2
C₇×#1850	2
C₇×#1825	2
C₇×#1804	2
C₇×#1802	2
#24536	7

Subgroups — C7×#24536 #13201752

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×#24536 #13201752