Subgroups — C₇×#23809 #13201025

Order 1792.

974 conjugacy classes of subgroups.

The subgroup lattice has 604 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₇×#441	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₇×#440	C₂	1	1	yes	maximal, characteristic
3	C₂×C₄×C₇×Q₁₆	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₄×C₇×SD₁₆	C₂	1	1	yes	maximal, characteristic
5	C₇×#2327	C₂	1	1	yes	maximal, characteristic, complemented
6	C₇×#2326	C₂	1	1	yes	maximal, characteristic
7	C₇×#2097	C₂	1	1	yes	maximal, characteristic, complemented
8	C₇×#2096	C₂	1	1	yes	maximal, characteristic, complemented
9	C₇×#2095	C₂	1	1	yes	maximal, characteristic, complemented
10	C₇×#2092	C₂	1	1	yes	maximal, characteristic
11	C₇×#2016	C₂	1	1	yes	maximal, characteristic, complemented
12	C₇×#2015	C₂	1	1	yes	maximal, characteristic
13	C₇×#2015	C₂	1	1	yes	maximal, characteristic
14	C₇×#2013	C₂	1	1	yes	maximal, characteristic
15	C₇×#1746	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×C₇×Q₁₆	C₂²	1	1	yes	characteristic
17	C₂²×C₇×Q₁₆	C₂²	1	1	yes	characteristic
18	C₂²×C₇×SD₁₆	C₂²	1	1	yes	characteristic
19	C₂²×C₇×SD₁₆	C₂²	1	1	yes	characteristic
20	C₂×C₇×C₄⋊Q₈	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×#441	—	2	4	no	—
27	C₇×#440	—	2	4	no	—
28	C₄×C₇×Q₁₆	—	2	4	no	—
29	C₄×C₇×SD₁₆	—	2	4	no	—
30	C₂×C₇×#107	C₂²	1	1	yes	characteristic
31	C₂×C₇×#107	C₂²	1	1	yes	characteristic
32	C₂×C₇×#106	C₂²	1	1	yes	characteristic
33	C₂×C₇×#106	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×#103	C₂²	1	1	yes	characteristic
39	C₂×C₇×#103	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×#97	C₂²	1	1	yes	characteristic
43	C₂×C₄×C₇×C₈	C₂²	1	1	yes	characteristic
44	C₇×#391	C₂²	1	1	yes	characteristic
45	C₇×#391	C₂²	1	1	yes	characteristic
46	C₇×#391	C₂²	1	1	yes	characteristic
47	C₇×#390	C₂²	1	1	yes	characteristic
48	C₇×#388	—	2	2	no	—
49	C₇×#387	—	2	2	no	—
50	C₇×#387	—	2	2	no	—
51	C₇×#385	—	2	2	no	—
52	C₇×#384	C₂²	1	1	yes	characteristic
53	C₇×#382	C₂²	1	1	yes	characteristic
54	C₇×#376	C₂²	1	1	yes	characteristic
55	C₇×#336	C₂²	1	1	yes	characteristic
56	C₇×#336	C₂²	1	1	yes	characteristic
57	C₇×#336	C₂²	1	1	yes	characteristic
58	C₇×#336	C₂²	1	1	yes	characteristic
59	#23809	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
60	C₂²×C₇×Q₈	C₂³	1	1	yes	characteristic
61	C₂²×C₇×Q₈	C₂³	1	1	yes	characteristic
62	C₂²×C₇×Q₈	C₂³	1	1	yes	characteristic
63	C₂²×C₇×D₄	C₂³	1	1	yes	characteristic
64	C₂³×C₄×C₇	—	2	1	no	—
65	C₂×C₇×Q₁₆	—	2	2	no	—
66	C₂×C₇×Q₁₆	—	2	2	no	—
67	C₂×C₇×Q₁₆	—	2	2	no	—
68	C₂×C₇×Q₁₆	—	2	2	no	—
69	C₂×C₇×Q₁₆	—	2	2	no	—
70	C₂×C₇×Q₁₆	—	2	2	no	—
71	C₂×C₇×SD₁₆	—	2	2	no	—
72	C₂×C₇×SD₁₆	—	2	2	no	—
73	C₂×C₇×SD₁₆	—	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	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
78	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
79	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
80	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
81	C₇×C₄⋊Q₈	—	2	2	no	—
82	C₇×C₄⋊Q₈	—	2	2	no	—
83	C₇×#124	—	2	2	no	—
84	C₇×#124	—	2	2	no	—
85	C₄×C₇×Q₈	—	2	2	no	—
86	C₄×C₇×Q₈	—	2	2	no	—
87	C₄×C₇×Q₈	—	2	2	no	—
88	C₄×C₇×Q₈	—	2	2	no	—
89	C₄×C₇×Q₈	—	2	2	no	—
90	C₄×C₇×Q₈	—	2	2	no	—
91	C₄×C₇×D₄	—	2	2	no	—
92	C₄×C₇×D₄	—	2	2	no	—
93	C₂×C₇×C₄⋊C₄	—	2	2	no	—
94	C₂×C₇×C₄⋊C₄	—	2	1	no	—
95	C₂×C₇×C₄⋊C₄	—	2	1	no	—
96	C₂×C₇×C₄⋊C₄	—	2	1	no	—
97	C₂×C₇×C₄⋊C₄	—	2	2	no	—
98	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
99	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
100	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
101	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
102	C₂×C₇×C₂²⋊C₄	—	2	2	no	—
103	C₂×C₇×C₂²⋊C₄	—	2	1	no	—
104	C₂×C₇×C₂²⋊C₄	—	2	2	no	—
105	C₂×C₄²×C₇	—	2	1	no	—
106	C₂×C₄²×C₇	—	2	1	no	—
107	C₂×C₄²×C₇	—	2	1	no	—
108	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
109	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
110	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
111	C₇×#107	—	2	2	no	—
112	C₇×#107	—	2	2	no	—
113	C₇×#106	—	2	2	no	—
114	C₇×#106	—	2	2	no	—
115	C₇×#103	—	2	2	no	—
116	C₇×#103	—	2	2	no	—
117	C₇×#103	—	2	2	no	—
118	C₇×#103	—	2	2	no	—
119	C₇×#103	—	2	2	no	—
120	C₇×#103	—	2	2	no	—
121	C₇×#102	—	2	2	no	—
122	C₇×#102	—	2	2	no	—
123	C₇×#97	D₄	1	4	yes	—
124	C₄×C₇×C₈	D₄	1	4	yes	—
125	C₇×#95	—	2	2	no	—
126	C₇×#95	—	2	2	no	—
127	C₇×#95	—	2	2	no	—
128	C₇×#95	—	2	2	no	—
129	C₇×#95	D₄	1	2	yes	—
130	C₇×#95	D₄	1	2	yes	—
131	C₂×#441	C₂×C₇	1	1	yes	characteristic, complemented
132	C₂×#440	C₂×C₇	1	1	yes	characteristic
133	C₂×C₄×Q₁₆	C₂×C₇	1	1	yes	characteristic, complemented
134	C₂×C₄×SD₁₆	C₂×C₇	1	1	yes	characteristic
135	#2327	C₂×C₇	1	1	yes	characteristic, complemented
136	#2326	C₂×C₇	1	1	yes	characteristic
137	#2097	C₂×C₇	1	1	yes	characteristic, complemented
138	#2096	C₂×C₇	1	1	yes	characteristic, complemented
139	#2095	C₂×C₇	1	1	yes	characteristic, complemented
140	#2092	C₂×C₇	1	1	yes	characteristic
141	#2016	C₂×C₇	1	1	yes	characteristic, complemented
142	#2015	C₂×C₇	1	1	yes	characteristic
143	#2015	C₂×C₇	1	1	yes	characteristic
144	#2013	C₂×C₇	1	1	yes	characteristic
145	#1746	C₂×C₇	1	1	yes	characteristic, complemented
146	C₂⁴×C₇	—	2	1	no	—
147	C₂×C₇×Q₈	—	2	1	no	—
148	C₂×C₇×Q₈	—	2	1	no	—
149	C₂×C₇×Q₈	—	2	1	no	—
150	C₂×C₇×Q₈	—	2	1	no	—
151	C₂×C₇×Q₈	—	2	1	no	—
152	C₂×C₇×Q₈	—	2	1	no	—
153	C₂×C₇×Q₈	—	2	1	no	—
154	C₂×C₇×Q₈	—	2	1	no	—
155	C₂×C₇×Q₈	—	2	1	no	—
156	C₂×C₇×Q₈	—	2	1	no	—
157	C₂×C₇×Q₈	—	2	1	no	—
158	C₂×C₇×Q₈	—	2	1	no	—
159	C₂×C₇×Q₈	—	2	1	no	—
160	C₂×C₇×Q₈	—	2	1	no	—
161	C₂×C₇×Q₈	—	2	1	no	—
162	C₂×C₇×Q₈	#41	1	2	yes	—
163	C₂×C₇×Q₈	#41	1	2	yes	—
164	C₂×C₇×Q₈	#41	1	2	yes	—
165	C₂×C₇×D₄	—	2	1	no	—
166	C₂×C₇×D₄	—	2	1	no	—
167	C₂×C₇×D₄	—	2	1	no	—
168	C₂×C₇×D₄	—	2	1	no	—
169	C₂×C₇×D₄	—	2	1	no	—
170	C₂×C₇×D₄	#41	1	2	yes	—
171	C₂²×C₄×C₇	—	2	1	no	—
172	C₂²×C₄×C₇	—	2	1	no	—
173	C₂²×C₄×C₇	—	2	1	no	—
174	C₂²×C₄×C₇	—	2	1	no	—
175	C₂²×C₄×C₇	—	2	1	no	—
176	C₂²×C₄×C₇	—	2	1	no	—
177	C₂²×C₄×C₇	—	2	1	no	—
178	C₂²×C₄×C₇	—	4	2	no	—
179	C₂²×C₄×C₇	—	8	2	no	—
180	C₂²×C₄×C₇	C₂×D₄	1	2	yes	—
181	C₂²×C₄×C₇	C₂×D₄	1	2	yes	—
182	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
183	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
184	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
185	C₇×Q₁₆	—	2	8	no	—
186	C₇×Q₁₆	—	2	8	no	—
187	C₇×SD₁₆	—	2	8	no	—
188	C₇×SD₁₆	—	2	8	no	—
189	C₂×C₇×C₈	—	2	1	no	—
190	C₂×C₇×C₈	—	2	1	no	—
191	C₂×C₇×C₈	—	2	1	no	—
192	C₂×C₇×C₈	—	2	1	no	—
193	C₂×C₇×C₈	—	2	1	no	—
194	C₂×C₇×C₈	—	2	1	no	—
195	C₂×C₇×C₈	—	2	1	no	—
196	C₂×C₇×C₈	—	2	1	no	—
197	C₂×C₇×C₈	C₂×D₄	1	2	yes	—
198	C₂×C₇×C₈	C₂×D₄	1	2	yes	—
199	C₂×C₇×C₈	C₂×D₄	1	2	yes	—
200	C₂×C₇×C₈	C₂×D₄	1	2	yes	—
201	C₇×C₄⋊C₄	—	2	8	no	—
202	C₇×C₄⋊C₄	—	2	1	no	—
203	C₇×C₄⋊C₄	—	2	1	no	—
204	C₇×C₄⋊C₄	—	2	1	no	—
205	C₇×C₄⋊C₄	—	2	1	no	—
206	C₇×C₄⋊C₄	—	2	1	no	—
207	C₇×C₄⋊C₄	—	2	1	no	—
208	C₇×C₄⋊C₄	—	2	1	no	—
209	C₇×C₄⋊C₄	—	2	1	no	—
210	C₇×C₄⋊C₄	—	4	2	no	—
211	C₇×C₄⋊C₄	—	4	2	no	—
212	C₇×C₄⋊C₄	—	4	2	no	—
213	C₇×C₄⋊C₄	—	8	2	no	—
214	C₇×C₂²⋊C₄	—	2	8	no	—
215	C₇×C₂²⋊C₄	—	4	2	no	—
216	C₇×C₂²⋊C₄	—	8	2	no	—
217	C₄²×C₇	—	2	1	no	—
218	C₄²×C₇	—	2	1	no	—
219	C₄²×C₇	—	2	1	no	—
220	C₄²×C₇	—	2	1	no	—
221	C₄²×C₇	—	4	2	no	—
222	C₄²×C₇	—	4	2	no	—
223	C₄²×C₇	—	4	2	no	—
224	C₄²×C₇	C₂×D₄	1	2	yes	—
225	C₄²×C₇	C₂×D₄	1	2	yes	—
226	C₂²×Q₁₆	C₂²×C₇	1	1	yes	characteristic
227	C₂²×Q₁₆	C₂²×C₇	1	1	yes	characteristic
228	C₂²×SD₁₆	C₂²×C₇	1	1	yes	characteristic
229	C₂²×SD₁₆	C₂²×C₇	1	1	yes	characteristic
230	C₂×C₄⋊Q₈	C₂²×C₇	1	1	yes	characteristic
231	C₂×#124	C₂²×C₇	1	1	yes	characteristic
232	C₂×C₄×Q₈	C₂²×C₇	1	1	yes	characteristic
233	C₂×C₄×Q₈	C₂²×C₇	1	1	yes	characteristic
234	C₂×C₄×Q₈	C₂²×C₇	1	1	yes	characteristic
235	C₂×C₄×D₄	C₂²×C₇	1	1	yes	characteristic
236	#441	—	2	4	no	—
237	#440	—	2	4	no	—
238	C₄×Q₁₆	—	2	4	no	—
239	C₄×SD₁₆	—	2	4	no	—
240	C₂×#107	C₂²×C₇	1	1	yes	characteristic
241	C₂×#107	C₂²×C₇	1	1	yes	characteristic
242	C₂×#106	C₂²×C₇	1	1	yes	characteristic
243	C₂×#106	C₂²×C₇	1	1	yes	characteristic
244	C₂×#103	C₂²×C₇	1	1	yes	characteristic
245	C₂×#103	C₂²×C₇	1	1	yes	characteristic
246	C₂×#103	C₂²×C₇	1	1	yes	characteristic
247	C₂×#103	C₂²×C₇	1	1	yes	characteristic
248	C₂×#103	C₂²×C₇	1	1	yes	characteristic
249	C₂×#103	C₂²×C₇	1	1	yes	characteristic
250	C₂×#102	C₂²×C₇	1	1	yes	characteristic
251	C₂×#102	C₂²×C₇	1	1	yes	characteristic
252	C₂×#97	C₂²×C₇	1	1	yes	characteristic
253	C₂×C₄×C₈	C₂²×C₇	1	1	yes	characteristic
254	#391	C₂²×C₇	1	1	yes	characteristic
255	#391	C₂²×C₇	1	1	yes	characteristic
256	#391	C₂²×C₇	1	1	yes	characteristic
257	#390	C₂²×C₇	1	1	yes	characteristic
258	#388	—	2	2	no	—
259	#387	—	2	2	no	—
260	#387	—	2	2	no	—
261	#385	—	2	2	no	—
262	#384	C₂²×C₇	1	1	yes	characteristic
263	#382	C₂²×C₇	1	1	yes	characteristic
264	#376	C₂²×C₇	1	1	yes	characteristic
265	#336	C₂²×C₇	1	1	yes	characteristic
266	#336	C₂²×C₇	1	1	yes	characteristic
267	#336	C₂²×C₇	1	1	yes	characteristic
268	#336	C₂²×C₇	1	1	yes	characteristic
269	C₂³×C₇	—	2	2	no	—
270	C₂³×C₇	—	4	1	no	—
271	C₂³×C₇	—	4	1	no	—
272	C₂³×C₇	—	4	2	no	—
273	C₂³×C₇	—	4	2	no	—
274	C₂³×C₇	C₂²×D₄	1	1	yes	characteristic
275	C₇×Q₈	—	2	2	no	—
276	C₇×Q₈	—	2	2	no	—
277	C₇×Q₈	—	2	2	no	—
278	C₇×Q₈	—	2	2	no	—
279	C₇×Q₈	—	2	2	no	—
280	C₇×Q₈	—	2	2	no	—
281	C₇×Q₈	—	4	1	no	—
282	C₇×Q₈	—	4	1	no	—
283	C₇×Q₈	—	4	1	no	—
284	C₇×Q₈	—	4	1	no	—
285	C₇×Q₈	—	4	1	no	—
286	C₇×Q₈	—	4	1	no	—
287	C₇×D₄	—	2	2	no	—
288	C₇×D₄	—	2	2	no	—
289	C₇×D₄	—	4	1	no	—
290	C₇×D₄	—	4	1	no	—
291	C₂×C₄×C₇	—	2	2	no	—
292	C₂×C₄×C₇	—	2	2	no	—
293	C₂×C₄×C₇	—	2	2	no	—
294	C₂×C₄×C₇	—	2	2	no	—
295	C₂×C₄×C₇	—	2	2	no	—
296	C₂×C₄×C₇	—	2	2	no	—
297	C₂×C₄×C₇	—	2	2	no	—
298	C₂×C₄×C₇	—	2	2	no	—
299	C₂×C₄×C₇	—	2	2	no	—
300	C₂×C₄×C₇	—	2	2	no	—
301	C₂×C₄×C₇	—	2	2	no	—
302	C₂×C₄×C₇	—	4	1	no	—
303	C₂×C₄×C₇	—	4	1	no	—
304	C₂×C₄×C₇	—	4	1	no	—
305	C₂×C₄×C₇	—	4	1	no	—
306	C₂×C₄×C₇	—	4	1	no	—
307	C₂×C₄×C₇	—	4	1	no	—
308	C₂×C₄×C₇	—	4	1	no	—
309	C₂×C₄×C₇	—	4	1	no	—
310	C₂×C₄×C₇	—	4	1	no	—
311	C₂×C₄×C₇	—	4	1	no	—
312	C₂×C₄×C₇	—	4	2	no	—
313	C₂×C₄×C₇	—	4	2	no	—
314	C₂×C₄×C₇	—	4	2	no	—
315	C₂×C₄×C₇	—	4	2	no	—
316	C₂×C₄×C₇	—	8	4	no	—
317	C₂×C₄×C₇	#127	1	2	yes	—
318	C₂×C₄×C₇	#127	1	2	yes	—
319	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
320	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
321	C₂×C₄×C₇	C₂×#41	1	1	yes	characteristic
322	C₂×C₄×C₇	C₂×#41	1	1	yes	characteristic
323	C₂×C₄×C₇	C₂×#41	1	1	yes	characteristic
324	C₂×C₄×C₇	C₂×#41	1	1	yes	characteristic
325	C₇×C₈	—	2	2	no	—
326	C₇×C₈	—	2	2	no	—
327	C₇×C₈	—	2	2	no	—
328	C₇×C₈	—	2	2	no	—
329	C₂²×Q₈	C₂³×C₇	1	1	yes	characteristic
330	C₂²×Q₈	C₂³×C₇	1	1	yes	characteristic
331	C₂²×Q₈	C₂³×C₇	1	1	yes	characteristic
332	C₂²×D₄	C₂³×C₇	1	1	yes	characteristic
333	C₂³×C₄	—	2	1	no	—
334	C₂×Q₁₆	—	2	2	no	—
335	C₂×Q₁₆	—	2	2	no	—
336	C₂×Q₁₆	—	2	2	no	—
337	C₂×Q₁₆	—	2	2	no	—
338	C₂×Q₁₆	—	2	2	no	—
339	C₂×Q₁₆	—	2	2	no	—
340	C₂×SD₁₆	—	2	2	no	—
341	C₂×SD₁₆	—	2	2	no	—
342	C₂×SD₁₆	—	2	2	no	—
343	C₂×SD₁₆	—	2	2	no	—
344	C₂×SD₁₆	—	2	2	no	—
345	C₂×SD₁₆	—	2	2	no	—
346	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
347	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
348	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
349	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
350	C₄⋊Q₈	—	2	2	no	—
351	C₄⋊Q₈	—	2	2	no	—
352	#124	—	2	2	no	—
353	#124	—	2	2	no	—
354	C₄×Q₈	—	2	2	no	—
355	C₄×Q₈	—	2	2	no	—
356	C₄×Q₈	—	2	2	no	—
357	C₄×Q₈	—	2	2	no	—
358	C₄×Q₈	—	2	2	no	—
359	C₄×Q₈	—	2	2	no	—
360	C₄×D₄	—	2	2	no	—
361	C₄×D₄	—	2	2	no	—
362	C₂×C₄⋊C₄	—	2	2	no	—
363	C₂×C₄⋊C₄	—	2	1	no	—
364	C₂×C₄⋊C₄	—	2	1	no	—
365	C₂×C₄⋊C₄	—	2	1	no	—
366	C₂×C₄⋊C₄	—	2	2	no	—
367	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
368	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
369	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
370	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
371	C₂×C₂²⋊C₄	—	2	2	no	—
372	C₂×C₂²⋊C₄	—	2	1	no	—
373	C₂×C₂²⋊C₄	—	2	2	no	—
374	C₂×C₄²	—	2	1	no	—
375	C₂×C₄²	—	2	1	no	—
376	C₂×C₄²	—	2	1	no	—
377	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
378	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
379	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
380	#107	—	2	2	no	—
381	#107	—	2	2	no	—
382	#106	—	2	2	no	—
383	#106	—	2	2	no	—
384	#103	—	2	2	no	—
385	#103	—	2	2	no	—
386	#103	—	2	2	no	—
387	#103	—	2	2	no	—
388	#103	—	2	2	no	—
389	#103	—	2	2	no	—
390	#102	—	2	2	no	—
391	#102	—	2	2	no	—
392	#97	C₇×D₄	1	4	yes	—
393	C₄×C₈	C₇×D₄	1	4	yes	—
394	#95	—	2	2	no	—
395	#95	—	2	2	no	—
396	#95	—	2	2	no	—
397	#95	—	2	2	no	—
398	#95	C₇×D₄	1	2	yes	—
399	#95	C₇×D₄	1	2	yes	—
400	C₂²×C₇	—	4	4	no	—
401	C₂²×C₇	—	4	2	no	—
402	C₂²×C₇	—	8	2	no	—
403	C₂²×C₇	—	8	1	no	—
404	C₂²×C₇	—	8	1	no	—
405	C₂²×C₇	#525	1	1	yes	characteristic
406	C₂²×C₇	#525	1	1	yes	characteristic
407	C₂²×C₇	C₂×#127	1	1	yes	characteristic
408	C₂²×C₇	#577	1	2	yes	—
409	C₂²×C₇	#578	1	2	yes	—
410	C₄×C₇	—	2	2	no	—
411	C₄×C₇	—	2	2	no	—
412	C₄×C₇	—	4	2	no	—
413	C₄×C₇	—	4	2	no	—
414	C₄×C₇	—	4	2	no	—
415	C₄×C₇	—	4	2	no	—
416	C₄×C₇	—	4	2	no	—
417	C₄×C₇	—	8	1	no	—
418	C₄×C₇	—	8	1	no	—
419	C₄×C₇	—	8	1	no	—
420	C₄×C₇	—	8	1	no	—
421	C₄×C₇	#525	1	1	yes	characteristic
422	C₄×C₇	#525	1	1	yes	characteristic
423	C₄×C₇	#525	1	1	yes	characteristic
424	C₄×C₇	#525	1	1	yes	characteristic
425	C₂⁴	—	2	1	no	—
426	C₂×Q₈	—	2	1	no	—
427	C₂×Q₈	—	2	1	no	—
428	C₂×Q₈	—	2	1	no	—
429	C₂×Q₈	—	2	1	no	—
430	C₂×Q₈	—	2	1	no	—
431	C₂×Q₈	—	2	1	no	—
432	C₂×Q₈	—	2	1	no	—
433	C₂×Q₈	—	2	1	no	—
434	C₂×Q₈	—	2	1	no	—
435	C₂×Q₈	—	2	1	no	—
436	C₂×Q₈	—	2	1	no	—
437	C₂×Q₈	—	2	1	no	—
438	C₂×Q₈	—	2	1	no	—
439	C₂×Q₈	—	2	1	no	—
440	C₂×Q₈	—	2	1	no	—
441	C₂×Q₈	C₇×#41	1	2	yes	—
442	C₂×Q₈	C₇×#41	1	2	yes	—
443	C₂×Q₈	C₇×#41	1	2	yes	—
444	C₂×D₄	—	2	1	no	—
445	C₂×D₄	—	2	1	no	—
446	C₂×D₄	—	2	1	no	—
447	C₂×D₄	—	2	1	no	—
448	C₂×D₄	—	2	1	no	—
449	C₂×D₄	C₇×#41	1	2	yes	—
450	C₂²×C₄	—	2	1	no	—
451	C₂²×C₄	—	2	1	no	—
452	C₂²×C₄	—	2	1	no	—
453	C₂²×C₄	—	2	1	no	—
454	C₂²×C₄	—	2	1	no	—
455	C₂²×C₄	—	2	1	no	—
456	C₂²×C₄	—	2	1	no	—
457	C₂²×C₄	—	4	2	no	—
458	C₂²×C₄	—	8	2	no	—
459	C₂²×C₄	C₂×C₇×D₄	1	2	yes	—
460	C₂²×C₄	C₂×C₇×D₄	1	2	yes	—
461	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
462	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
463	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
464	Q₁₆	—	2	8	no	—
465	Q₁₆	—	2	8	no	—
466	SD₁₆	—	2	8	no	—
467	SD₁₆	—	2	8	no	—
468	C₂×C₈	—	2	1	no	—
469	C₂×C₈	—	2	1	no	—
470	C₂×C₈	—	2	1	no	—
471	C₂×C₈	—	2	1	no	—
472	C₂×C₈	—	2	1	no	—
473	C₂×C₈	—	2	1	no	—
474	C₂×C₈	—	2	1	no	—
475	C₂×C₈	—	2	1	no	—
476	C₂×C₈	C₂×C₇×D₄	1	2	yes	—
477	C₂×C₈	C₂×C₇×D₄	1	2	yes	—
478	C₂×C₈	C₂×C₇×D₄	1	2	yes	—
479	C₂×C₈	C₂×C₇×D₄	1	2	yes	—
480	C₄⋊C₄	—	2	8	no	—
481	C₄⋊C₄	—	2	1	no	—
482	C₄⋊C₄	—	2	1	no	—
483	C₄⋊C₄	—	2	1	no	—
484	C₄⋊C₄	—	2	1	no	—
485	C₄⋊C₄	—	2	1	no	—
486	C₄⋊C₄	—	2	1	no	—
487	C₄⋊C₄	—	2	1	no	—
488	C₄⋊C₄	—	2	1	no	—
489	C₄⋊C₄	—	4	2	no	—
490	C₄⋊C₄	—	4	2	no	—
491	C₄⋊C₄	—	4	2	no	—
492	C₄⋊C₄	—	8	2	no	—
493	C₂²⋊C₄	—	2	8	no	—
494	C₂²⋊C₄	—	4	2	no	—
495	C₂²⋊C₄	—	8	2	no	—
496	C₄²	—	2	1	no	—
497	C₄²	—	2	1	no	—
498	C₄²	—	2	1	no	—
499	C₄²	—	2	1	no	—
500	C₄²	—	4	2	no	—
501	C₄²	—	4	2	no	—
502	C₄²	—	4	2	no	—
503	C₄²	C₂×C₇×D₄	1	2	yes	—
504	C₄²	C₂×C₇×D₄	1	2	yes	—
505	C₂×C₇	—	8	2	no	—
506	C₂×C₇	#2397	1	1	yes	characteristic
507	C₂×C₇	#3120	1	2	yes	—
508	C₂×C₇	#3121	1	2	yes	—
509	C₂×C₇	#3154	1	1	yes	characteristic
510	C₂×C₇	#3156	1	1	yes	characteristic
511	C₂³	—	2	2	no	—
512	C₂³	—	4	1	no	—
513	C₂³	—	4	1	no	—
514	C₂³	—	4	2	no	—
515	C₂³	—	4	2	no	—
516	C₂³	C₂²×C₇×D₄	1	1	yes	characteristic
517	Q₈	—	2	2	no	—
518	Q₈	—	2	2	no	—
519	Q₈	—	2	2	no	—
520	Q₈	—	2	2	no	—
521	Q₈	—	2	2	no	—
522	Q₈	—	2	2	no	—
523	Q₈	—	4	1	no	—
524	Q₈	—	4	1	no	—
525	Q₈	—	4	1	no	—
526	Q₈	—	4	1	no	—
527	Q₈	—	4	1	no	—
528	Q₈	—	4	1	no	—
529	D₄	—	2	2	no	—
530	D₄	—	2	2	no	—
531	D₄	—	4	1	no	—
532	D₄	—	4	1	no	—
533	C₂×C₄	—	2	2	no	—
534	C₂×C₄	—	2	2	no	—
535	C₂×C₄	—	2	2	no	—
536	C₂×C₄	—	2	2	no	—
537	C₂×C₄	—	2	2	no	—
538	C₂×C₄	—	2	2	no	—
539	C₂×C₄	—	2	2	no	—
540	C₂×C₄	—	2	2	no	—
541	C₂×C₄	—	2	2	no	—
542	C₂×C₄	—	2	2	no	—
543	C₂×C₄	—	2	2	no	—
544	C₂×C₄	—	4	1	no	—
545	C₂×C₄	—	4	1	no	—
546	C₂×C₄	—	4	1	no	—
547	C₂×C₄	—	4	1	no	—
548	C₂×C₄	—	4	1	no	—
549	C₂×C₄	—	4	1	no	—
550	C₂×C₄	—	4	1	no	—
551	C₂×C₄	—	4	1	no	—
552	C₂×C₄	—	4	1	no	—
553	C₂×C₄	—	4	1	no	—
554	C₂×C₄	—	4	2	no	—
555	C₂×C₄	—	4	2	no	—
556	C₂×C₄	—	4	2	no	—
557	C₂×C₄	—	4	2	no	—
558	C₂×C₄	—	8	4	no	—
559	C₂×C₄	C₇×#127	1	2	yes	—
560	C₂×C₄	C₇×#127	1	2	yes	—
561	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
562	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
563	C₂×C₄	C₂×C₇×#41	1	1	yes	characteristic
564	C₂×C₄	C₂×C₇×#41	1	1	yes	characteristic
565	C₂×C₄	C₂×C₇×#41	1	1	yes	characteristic
566	C₂×C₄	C₂×C₇×#41	1	1	yes	characteristic
567	C₈	—	2	2	no	—
568	C₈	—	2	2	no	—
569	C₈	—	2	2	no	—
570	C₈	—	2	2	no	—
571	C₇	#23809	1	1	yes	characteristic, direct product factor, Sylow
572	C₂²	—	4	2	no	—
573	C₂²	—	4	4	no	—
574	C₂²	—	8	1	no	—
575	C₂²	—	8	2	no	—
576	C₂²	—	8	1	no	—
577	C₂²	C₇×#525	1	1	yes	characteristic
578	C₂²	C₇×#525	1	1	yes	characteristic
579	C₂²	C₂×C₇×#127	1	1	yes	characteristic
580	C₂²	C₇×#577	1	2	yes	—
581	C₂²	C₇×#578	1	2	yes	—
582	C₄	—	2	2	no	—
583	C₄	—	2	2	no	—
584	C₄	—	4	2	no	—
585	C₄	—	4	2	no	—
586	C₄	—	4	2	no	—
587	C₄	—	4	2	no	—
588	C₄	—	4	2	no	—
589	C₄	—	8	1	no	—
590	C₄	—	8	1	no	—
591	C₄	—	8	1	no	—
592	C₄	—	8	1	no	—
593	C₄	C₇×#525	1	1	yes	characteristic
594	C₄	C₇×#525	1	1	yes	characteristic
595	C₄	C₇×#525	1	1	yes	characteristic
596	C₄	C₇×#525	1	1	yes	characteristic
597	C₂	—	8	2	no	—
598	C₂	C₇×#2397	1	1	yes	characteristic
599	C₂	C₇×#3120	1	2	yes	—
600	C₂	C₇×#3121	1	2	yes	—
601	C₂	C₇×#3154	1	1	yes	characteristic
602	C₂	C₇×#3156	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 ◁ C₇×#376 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₇×#441	C₂	semidirect
3. C₂×C₄×C₇×Q₁₆	C₂	semidirect
5. C₇×#2327	C₂	semidirect
7. C₇×#2097	C₂	semidirect
8. C₇×#2096	C₂	semidirect
9. C₇×#2095	C₂	semidirect
11. C₇×#2016	C₂	semidirect
15. C₇×#1746	C₂	semidirect
59. #23809	C₇	direct (N × H)
131. C₂×#441	C₂×C₇	semidirect
133. C₂×C₄×Q₁₆	C₂×C₇	semidirect
135. #2327	C₂×C₇	semidirect
137. #2097	C₂×C₇	semidirect
138. #2096	C₂×C₇	semidirect
139. #2095	C₂×C₇	semidirect
141. #2016	C₂×C₇	semidirect
145. #1746	C₂×C₇	semidirect
571. C₇	#23809	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×#441	2
C₂×C₇×#440	2
C₂×C₄×C₇×Q₁₆	2
C₂×C₄×C₇×SD₁₆	2
C₇×#2327	2
C₇×#2326	2
C₇×#2097	2
C₇×#2096	2
C₇×#2095	2
C₇×#2092	2
C₇×#2016	2
C₇×#2015	2
C₇×#2013	2
C₇×#1746	2
#23809	7

Subgroups — C7×#23809 #13201025

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×#23809 #13201025