Subgroups — C₇×#17969 #13195185

Order 1792.

582 conjugacy classes of subgroups.

The subgroup lattice has 562 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×#3172	C₂	1	1	yes	maximal, characteristic
2	C₇×#2993	C₂	1	1	yes	maximal, characteristic
3	C₇×#2985	C₂	1	1	yes	maximal, characteristic, complemented
4	C₇×#1593	C₂	1	1	yes	maximal, characteristic, complemented
5	C₇×#1592	C₂	1	1	yes	maximal, characteristic, complemented
6	C₇×#1591	C₂	1	1	yes	maximal, characteristic, complemented
7	C₇×#1590	C₂	1	1	yes	maximal, characteristic, complemented
8	C₇×#1579	C₂	1	1	yes	maximal, characteristic, complemented
9	C₇×SD₁₆⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
10	C₇×C₈×Q₁₆	C₂	1	1	yes	maximal, characteristic, complemented
11	C₇×C₈×SD₁₆	C₂	1	1	yes	maximal, characteristic, complemented
12	C₇×#1569	C₂	1	1	yes	maximal, characteristic, complemented
13	C₇×#1494	C₂	1	1	yes	maximal, characteristic
14	C₇×#1493	C₂	1	1	yes	maximal, characteristic, complemented
15	C₇×C₈×M₁₆	C₂	1	1	yes	maximal, characteristic, complemented
16	C₇×#533	C₂²	1	1	yes	characteristic
17	C₇×#529	C₂²	1	1	yes	characteristic
18	C₇×#501	C₄	1	1	yes	characteristic
19	C₇×#497	C₄	1	1	yes	characteristic
20	C₇×#491	C₄	1	1	yes	characteristic
21	C₇×#489	C₄	1	1	yes	characteristic
22	C₇×#470	C₄	1	1	yes	characteristic
23	C₇×#470	C₄	1	1	yes	characteristic
24	C₇×#468	C₄	1	1	yes	characteristic
25	C₇×#468	C₄	1	1	yes	characteristic
26	C₇×#446	—	2	1	no	—
27	C₇×#446	—	2	1	no	—
28	C₇×#446	C₂²	1	1	yes	characteristic
29	C₇×#446	C₂²	1	1	yes	characteristic
30	C₇×#446	C₂²	1	1	yes	characteristic
31	C₇×C₈×Q₈	C₂²	1	1	yes	characteristic
32	C₇×C₈×Q₈	C₂²	1	1	yes	characteristic
33	C₇×C₈×Q₈	C₂²	1	1	yes	characteristic
34	C₄×C₇×Q₁₆	C₂²	1	1	yes	characteristic
35	C₄×C₇×Q₁₆	C₂²	1	1	yes	characteristic
36	C₄×C₇×SD₁₆	C₂²	1	1	yes	characteristic
37	C₄×C₇×SD₁₆	C₂²	1	1	yes	characteristic
38	C₇×#436	—	2	1	no	—
39	C₇×#436	C₂²	1	1	yes	characteristic
40	C₇×#435	—	2	1	no	—
41	C₇×C₈×D₄	C₂²	1	1	yes	characteristic
42	C₇×#433	—	2	1	no	—
43	C₇×#433	—	2	1	no	—
44	C₇×#433	—	2	1	no	—
45	C₇×#432	C₂²	1	1	yes	characteristic
46	C₇×#431	C₂²	1	1	yes	characteristic
47	C₇×#424	—	2	1	no	—
48	C₇×#423	C₂²	1	1	yes	characteristic
49	C₄×C₇×M₁₆	C₂²	1	1	yes	characteristic
50	C₂×C₄×C₇×C₈	C₂²	1	1	yes	characteristic
51	C₇×#335	C₂²	1	1	yes	characteristic
52	C₇×#335	C₂²	1	1	yes	characteristic
53	C₇×#334	C₂²	1	1	yes	characteristic
54	C₇×#334	C₂²	1	1	yes	characteristic
55	C₇×Q₈⋊C₈	C₂²	1	1	yes	characteristic
56	C₇×Q₈⋊C₈	C₂²	1	1	yes	characteristic
57	C₇×Q₈⋊C₈	C₂²	1	1	yes	characteristic
58	C₇×Q₈⋊C₈	C₂²	1	1	yes	characteristic
59	C₇×Q₈⋊C₈	C₂²	1	1	yes	characteristic
60	C₇×Q₈⋊C₈	C₂²	1	1	yes	characteristic
61	C₇×D₄⋊C₈	C₂²	1	1	yes	characteristic
62	C₇×D₄⋊C₈	C₂²	1	1	yes	characteristic
63	C₇×#322	C₂²	1	1	yes	characteristic
64	C₇×#322	C₂²	1	1	yes	characteristic
65	C₇×C₈²	C₂²	1	1	yes	characteristic
66	C₇×C₈²	C₂²	1	1	yes	characteristic
67	#17969	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
68	C₂×C₇×Q₁₆	C₂×C₄	1	1	yes	characteristic
69	C₂×C₇×Q₁₆	C₂×C₄	1	1	yes	characteristic
70	C₂×C₇×SD₁₆	C₂×C₄	1	1	yes	characteristic
71	C₂×C₇×SD₁₆	C₂×C₄	1	1	yes	characteristic
72	C₂×C₇×M₁₆	—	2	1	no	—
73	C₂×C₇×M₁₆	—	2	1	no	—
74	C₂×C₇×M₁₆	C₂×C₄	1	1	yes	characteristic
75	C₂×C₇×M₁₆	C₂×C₄	1	1	yes	characteristic
76	C₂²×C₇×C₈	—	2	1	no	—
77	C₂²×C₇×C₈	—	2	1	no	—
78	C₇×C₄⋊Q₈	C₂×C₄	1	1	yes	characteristic
79	C₇×C₄⋊Q₈	C₂×C₄	1	1	yes	characteristic
80	C₇×#126	—	2	1	no	—
81	C₇×#125	—	2	1	no	—
82	C₇×#125	C₂×C₄	1	1	yes	characteristic
83	C₇×#124	C₂×C₄	1	1	yes	characteristic
84	C₇×#123	—	2	1	no	—
85	C₇×C₂²⋊Q₈	—	2	1	no	—
86	C₇×C₂²⋊Q₈	C₂×C₄	1	1	yes	characteristic
87	C₇×C₂²⋊Q₈	C₂×C₄	1	1	yes	characteristic
88	C₇×C₂²⋊Q₈	C₂×C₄	1	1	yes	characteristic
89	C₇×#121	C₂×C₄	1	1	yes	characteristic
90	C₄×C₇×Q₈	—	2	1	no	—
91	C₄×C₇×Q₈	C₂³	1	1	yes	characteristic
92	C₄×C₇×Q₈	C₂³	1	1	yes	characteristic
93	C₄×C₇×Q₈	C₂³	1	1	yes	characteristic
94	C₄×C₇×D₄	—	2	1	no	—
95	C₄×C₇×D₄	C₂³	1	1	yes	characteristic
96	C₇×#117	—	2	1	no	—
97	C₇×#117	—	2	1	no	—
98	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
99	C₇×#107	C₂×C₄	1	1	yes	characteristic
100	C₇×#107	C₂×C₄	1	1	yes	characteristic
101	C₇×#106	C₂×C₄	1	1	yes	characteristic
102	C₇×#106	C₂×C₄	1	1	yes	characteristic
103	C₇×C₄⋊C₈	—	2	1	no	—
104	C₇×C₄⋊C₈	—	2	1	no	—
105	C₇×C₄⋊C₈	—	2	1	no	—
106	C₇×C₄⋊C₈	—	2	1	no	—
107	C₇×C₄⋊C₈	—	2	1	no	—
108	C₇×C₄⋊C₈	—	2	1	no	—
109	C₇×C₄⋊C₈	—	2	1	no	—
110	C₇×C₄⋊C₈	D₄	1	1	yes	characteristic
111	C₇×C₄⋊C₈	D₄	1	1	yes	characteristic
112	C₇×C₄⋊C₈	C₂³	1	1	yes	characteristic
113	C₇×C₄⋊C₈	C₂³	1	1	yes	characteristic
114	C₇×C₄⋊C₈	C₂³	1	1	yes	characteristic
115	C₇×C₄⋊C₈	C₂³	1	1	yes	characteristic
116	C₇×#103	C₂×C₄	1	1	yes	characteristic
117	C₇×#103	C₂×C₄	1	1	yes	characteristic
118	C₇×#103	C₂×C₄	1	1	yes	characteristic
119	C₇×#103	C₂×C₄	1	1	yes	characteristic
120	C₇×#103	C₂×C₄	1	1	yes	characteristic
121	C₇×#103	C₂×C₄	1	1	yes	characteristic
122	C₇×#102	C₂×C₄	1	1	yes	characteristic
123	C₇×#102	C₂×C₄	1	1	yes	characteristic
124	C₇×C₂²⋊C₈	—	2	1	no	—
125	C₇×C₂²⋊C₈	—	2	1	no	—
126	C₇×C₂²⋊C₈	—	2	1	no	—
127	C₇×C₂²⋊C₈	D₄	1	1	yes	characteristic
128	C₇×C₂²⋊C₈	D₄	1	1	yes	characteristic
129	C₇×#97	—	2	1	no	—
130	C₇×#97	—	2	1	no	—
131	C₇×#97	—	2	1	no	—
132	C₇×#97	—	2	1	no	—
133	C₇×#97	C₂×C₄	1	1	yes	characteristic
134	C₇×#97	C₂×C₄	1	1	yes	characteristic
135	C₄×C₇×C₈	—	2	1	no	—
136	C₄×C₇×C₈	—	2	1	no	—
137	C₄×C₇×C₈	—	2	1	no	—
138	C₄×C₇×C₈	—	2	1	no	—
139	C₄×C₇×C₈	C₂³	1	1	yes	characteristic
140	C₄×C₇×C₈	C₂³	1	1	yes	characteristic
141	C₄×C₇×C₈	C₂³	1	1	yes	characteristic
142	C₄×C₇×C₈	C₂³	1	1	yes	characteristic
143	C₄×C₇×C₈	C₂³	1	1	yes	characteristic
144	C₄×C₇×C₈	C₂³	1	1	yes	characteristic
145	#3172	C₂×C₇	1	1	yes	characteristic
146	#2993	C₂×C₇	1	1	yes	characteristic
147	#2985	C₂×C₇	1	1	yes	characteristic, complemented
148	#1593	C₂×C₇	1	1	yes	characteristic, complemented
149	#1592	C₂×C₇	1	1	yes	characteristic, complemented
150	#1591	C₂×C₇	1	1	yes	characteristic, complemented
151	#1590	C₂×C₇	1	1	yes	characteristic, complemented
152	#1579	C₂×C₇	1	1	yes	characteristic, complemented
153	SD₁₆⋊C₈	C₂×C₇	1	1	yes	characteristic, complemented
154	C₈×Q₁₆	C₂×C₇	1	1	yes	characteristic, complemented
155	C₈×SD₁₆	C₂×C₇	1	1	yes	characteristic, complemented
156	#1569	C₂×C₇	1	1	yes	characteristic, complemented
157	#1494	C₂×C₇	1	1	yes	characteristic
158	#1493	C₂×C₇	1	1	yes	characteristic, complemented
159	C₈×M₁₆	C₂×C₇	1	1	yes	characteristic, complemented
160	C₂×C₇×Q₈	—	2	1	no	—
161	C₂×C₇×Q₈	C₂²×C₄	1	1	yes	characteristic
162	C₂×C₇×Q₈	C₂²×C₄	1	1	yes	characteristic
163	C₂×C₇×Q₈	C₂²×C₄	1	1	yes	characteristic
164	C₂×C₇×D₄	—	2	1	no	—
165	C₂×C₇×D₄	C₂²×C₄	1	1	yes	characteristic
166	C₂²×C₄×C₇	—	2	1	no	—
167	C₂²×C₄×C₇	C₂²×C₄	1	1	yes	characteristic
168	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
169	C₂²×C₄×C₇	#41	1	1	yes	characteristic
170	C₇×Q₁₆	—	2	2	no	—
171	C₇×Q₁₆	—	2	2	no	—
172	C₇×SD₁₆	—	2	2	no	—
173	C₇×SD₁₆	—	2	2	no	—
174	C₇×M₁₆	—	2	2	no	—
175	C₇×M₁₆	—	2	2	no	—
176	C₇×M₁₆	—	8	1	no	—
177	C₇×M₁₆	—	8	1	no	—
178	C₂×C₇×C₈	—	2	1	no	—
179	C₂×C₇×C₈	—	2	1	no	—
180	C₂×C₇×C₈	—	2	1	no	—
181	C₂×C₇×C₈	—	2	1	no	—
182	C₂×C₇×C₈	—	2	1	no	—
183	C₂×C₇×C₈	—	2	1	no	—
184	C₂×C₇×C₈	—	4	2	no	—
185	C₂×C₇×C₈	—	8	1	no	—
186	C₂×C₇×C₈	C₂²×C₄	1	1	yes	characteristic
187	C₂×C₇×C₈	C₂²×C₄	1	1	yes	characteristic
188	C₂×C₇×C₈	C₂²×C₄	1	1	yes	characteristic
189	C₂×C₇×C₈	C₂²×C₄	1	1	yes	characteristic
190	C₂×C₇×C₈	C₂×D₄	1	1	yes	characteristic
191	C₂×C₇×C₈	C₂×D₄	1	1	yes	characteristic
192	C₂×C₇×C₈	C₂×D₄	1	1	yes	characteristic
193	C₂×C₇×C₈	C₂×D₄	1	1	yes	characteristic
194	C₇×C₄⋊C₄	—	2	1	no	—
195	C₇×C₄⋊C₄	—	2	1	no	—
196	C₇×C₄⋊C₄	—	2	1	no	—
197	C₇×C₄⋊C₄	—	2	1	no	—
198	C₇×C₄⋊C₄	—	2	1	no	—
199	C₇×C₄⋊C₄	—	2	1	no	—
200	C₇×C₄⋊C₄	—	2	1	no	—
201	C₇×C₄⋊C₄	—	2	1	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	C₂²×C₄	1	1	yes	characteristic
206	C₇×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
207	C₇×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
208	C₇×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
209	C₇×C₂²⋊C₄	—	2	1	no	—
210	C₇×C₂²⋊C₄	—	2	1	no	—
211	C₇×C₂²⋊C₄	—	2	1	no	—
212	C₇×C₂²⋊C₄	—	2	1	no	—
213	C₇×C₂²⋊C₄	—	2	1	no	—
214	C₇×C₂²⋊C₄	—	2	1	no	—
215	C₇×C₂²⋊C₄	—	2	1	no	—
216	C₄²×C₇	—	2	1	no	—
217	C₄²×C₇	—	2	1	no	—
218	C₄²×C₇	—	2	1	no	—
219	C₄²×C₇	C₂²×C₄	1	1	yes	characteristic
220	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
221	C₄²×C₇	#41	1	1	yes	characteristic
222	C₄²×C₇	C₂⁴	1	1	yes	characteristic
223	#533	C₂²×C₇	1	1	yes	characteristic
224	#529	C₂²×C₇	1	1	yes	characteristic
225	#501	C₄×C₇	1	1	yes	characteristic
226	#497	C₄×C₇	1	1	yes	characteristic
227	#491	C₄×C₇	1	1	yes	characteristic
228	#489	C₄×C₇	1	1	yes	characteristic
229	#470	C₄×C₇	1	1	yes	characteristic
230	#470	C₄×C₇	1	1	yes	characteristic
231	#468	C₄×C₇	1	1	yes	characteristic
232	#468	C₄×C₇	1	1	yes	characteristic
233	#446	—	2	1	no	—
234	#446	—	2	1	no	—
235	#446	C₂²×C₇	1	1	yes	characteristic
236	#446	C₂²×C₇	1	1	yes	characteristic
237	#446	C₂²×C₇	1	1	yes	characteristic
238	C₈×Q₈	C₂²×C₇	1	1	yes	characteristic
239	C₈×Q₈	C₂²×C₇	1	1	yes	characteristic
240	C₈×Q₈	C₂²×C₇	1	1	yes	characteristic
241	C₄×Q₁₆	C₂²×C₇	1	1	yes	characteristic
242	C₄×Q₁₆	C₂²×C₇	1	1	yes	characteristic
243	C₄×SD₁₆	C₂²×C₇	1	1	yes	characteristic
244	C₄×SD₁₆	C₂²×C₇	1	1	yes	characteristic
245	#436	—	2	1	no	—
246	#436	C₂²×C₇	1	1	yes	characteristic
247	#435	—	2	1	no	—
248	C₈×D₄	C₂²×C₇	1	1	yes	characteristic
249	#433	—	2	1	no	—
250	#433	—	2	1	no	—
251	#433	—	2	1	no	—
252	#432	C₂²×C₇	1	1	yes	characteristic
253	#431	C₂²×C₇	1	1	yes	characteristic
254	#424	—	2	1	no	—
255	#423	C₂²×C₇	1	1	yes	characteristic
256	C₄×M₁₆	C₂²×C₇	1	1	yes	characteristic
257	C₂×C₄×C₈	C₂²×C₇	1	1	yes	characteristic
258	#335	C₂²×C₇	1	1	yes	characteristic
259	#335	C₂²×C₇	1	1	yes	characteristic
260	#334	C₂²×C₇	1	1	yes	characteristic
261	#334	C₂²×C₇	1	1	yes	characteristic
262	Q₈⋊C₈	C₂²×C₇	1	1	yes	characteristic
263	Q₈⋊C₈	C₂²×C₇	1	1	yes	characteristic
264	Q₈⋊C₈	C₂²×C₇	1	1	yes	characteristic
265	Q₈⋊C₈	C₂²×C₇	1	1	yes	characteristic
266	Q₈⋊C₈	C₂²×C₇	1	1	yes	characteristic
267	Q₈⋊C₈	C₂²×C₇	1	1	yes	characteristic
268	D₄⋊C₈	C₂²×C₇	1	1	yes	characteristic
269	D₄⋊C₈	C₂²×C₇	1	1	yes	characteristic
270	#322	C₂²×C₇	1	1	yes	characteristic
271	#322	C₂²×C₇	1	1	yes	characteristic
272	C₈²	C₂²×C₇	1	1	yes	characteristic
273	C₈²	C₂²×C₇	1	1	yes	characteristic
274	C₂³×C₇	—	2	1	no	—
275	C₂³×C₇	C₄×D₄	1	1	yes	characteristic
276	C₇×Q₈	—	2	1	no	—
277	C₇×Q₈	—	2	1	no	—
278	C₇×Q₈	—	2	1	no	—
279	C₇×Q₈	—	2	1	no	—
280	C₇×Q₈	—	2	1	no	—
281	C₇×Q₈	—	2	1	no	—
282	C₇×Q₈	—	8	1	no	—
283	C₇×D₄	—	2	1	no	—
284	C₇×D₄	—	2	1	no	—
285	C₇×D₄	—	8	1	no	—
286	C₂×C₄×C₇	—	2	1	no	—
287	C₂×C₄×C₇	—	2	1	no	—
288	C₂×C₄×C₇	—	2	1	no	—
289	C₂×C₄×C₇	—	2	1	no	—
290	C₂×C₄×C₇	—	2	1	no	—
291	C₂×C₄×C₇	—	2	1	no	—
292	C₂×C₄×C₇	—	2	1	no	—
293	C₂×C₄×C₇	—	2	1	no	—
294	C₂×C₄×C₇	—	2	1	no	—
295	C₂×C₄×C₇	—	2	1	no	—
296	C₂×C₄×C₇	—	2	1	no	—
297	C₂×C₄×C₇	—	4	1	no	—
298	C₂×C₄×C₇	—	4	1	no	—
299	C₂×C₄×C₇	—	4	1	no	—
300	C₂×C₄×C₇	C₄×D₄	1	1	yes	characteristic
301	C₂×C₄×C₇	C₄×D₄	1	1	yes	characteristic
302	C₂×C₄×C₇	C₄×D₄	1	1	yes	characteristic
303	C₂×C₄×C₇	C₂³×C₄	1	1	yes	characteristic
304	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
305	C₂×C₄×C₇	C₂×#41	1	1	yes	characteristic
306	C₇×C₈	—	2	2	no	—
307	C₇×C₈	—	2	1	no	—
308	C₇×C₈	—	2	1	no	—
309	C₇×C₈	—	2	1	no	—
310	C₇×C₈	—	2	1	no	—
311	C₇×C₈	—	2	1	no	—
312	C₇×C₈	—	2	1	no	—
313	C₇×C₈	—	4	1	no	—
314	C₇×C₈	—	4	1	no	—
315	C₇×C₈	—	4	1	no	—
316	C₇×C₈	—	4	1	no	—
317	C₇×C₈	—	4	1	no	—
318	C₇×C₈	#131	1	2	yes	—
319	C₇×C₈	#131	1	2	yes	—
320	C₂×Q₁₆	C₂×C₄×C₇	1	1	yes	characteristic
321	C₂×Q₁₆	C₂×C₄×C₇	1	1	yes	characteristic
322	C₂×SD₁₆	C₂×C₄×C₇	1	1	yes	characteristic
323	C₂×SD₁₆	C₂×C₄×C₇	1	1	yes	characteristic
324	C₂×M₁₆	—	2	1	no	—
325	C₂×M₁₆	—	2	1	no	—
326	C₂×M₁₆	C₂×C₄×C₇	1	1	yes	characteristic
327	C₂×M₁₆	C₂×C₄×C₇	1	1	yes	characteristic
328	C₂²×C₈	—	2	1	no	—
329	C₂²×C₈	—	2	1	no	—
330	C₄⋊Q₈	C₂×C₄×C₇	1	1	yes	characteristic
331	C₄⋊Q₈	C₂×C₄×C₇	1	1	yes	characteristic
332	#126	—	2	1	no	—
333	#125	—	2	1	no	—
334	#125	C₂×C₄×C₇	1	1	yes	characteristic
335	#124	C₂×C₄×C₇	1	1	yes	characteristic
336	#123	—	2	1	no	—
337	C₂²⋊Q₈	—	2	1	no	—
338	C₂²⋊Q₈	C₂×C₄×C₇	1	1	yes	characteristic
339	C₂²⋊Q₈	C₂×C₄×C₇	1	1	yes	characteristic
340	C₂²⋊Q₈	C₂×C₄×C₇	1	1	yes	characteristic
341	#121	C₂×C₄×C₇	1	1	yes	characteristic
342	C₄×Q₈	—	2	1	no	—
343	C₄×Q₈	C₂³×C₇	1	1	yes	characteristic
344	C₄×Q₈	C₂³×C₇	1	1	yes	characteristic
345	C₄×Q₈	C₂³×C₇	1	1	yes	characteristic
346	C₄×D₄	—	2	1	no	—
347	C₄×D₄	C₂³×C₇	1	1	yes	characteristic
348	#117	—	2	1	no	—
349	#117	—	2	1	no	—
350	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
351	#107	C₂×C₄×C₇	1	1	yes	characteristic
352	#107	C₂×C₄×C₇	1	1	yes	characteristic
353	#106	C₂×C₄×C₇	1	1	yes	characteristic
354	#106	C₂×C₄×C₇	1	1	yes	characteristic
355	C₄⋊C₈	—	2	1	no	—
356	C₄⋊C₈	—	2	1	no	—
357	C₄⋊C₈	—	2	1	no	—
358	C₄⋊C₈	—	2	1	no	—
359	C₄⋊C₈	—	2	1	no	—
360	C₄⋊C₈	—	2	1	no	—
361	C₄⋊C₈	—	2	1	no	—
362	C₄⋊C₈	C₇×D₄	1	1	yes	characteristic
363	C₄⋊C₈	C₇×D₄	1	1	yes	characteristic
364	C₄⋊C₈	C₂³×C₇	1	1	yes	characteristic
365	C₄⋊C₈	C₂³×C₇	1	1	yes	characteristic
366	C₄⋊C₈	C₂³×C₇	1	1	yes	characteristic
367	C₄⋊C₈	C₂³×C₇	1	1	yes	characteristic
368	#103	C₂×C₄×C₇	1	1	yes	characteristic
369	#103	C₂×C₄×C₇	1	1	yes	characteristic
370	#103	C₂×C₄×C₇	1	1	yes	characteristic
371	#103	C₂×C₄×C₇	1	1	yes	characteristic
372	#103	C₂×C₄×C₇	1	1	yes	characteristic
373	#103	C₂×C₄×C₇	1	1	yes	characteristic
374	#102	C₂×C₄×C₇	1	1	yes	characteristic
375	#102	C₂×C₄×C₇	1	1	yes	characteristic
376	C₂²⋊C₈	—	2	1	no	—
377	C₂²⋊C₈	—	2	1	no	—
378	C₂²⋊C₈	—	2	1	no	—
379	C₂²⋊C₈	C₇×D₄	1	1	yes	characteristic
380	C₂²⋊C₈	C₇×D₄	1	1	yes	characteristic
381	#97	—	2	1	no	—
382	#97	—	2	1	no	—
383	#97	—	2	1	no	—
384	#97	—	2	1	no	—
385	#97	C₂×C₄×C₇	1	1	yes	characteristic
386	#97	C₂×C₄×C₇	1	1	yes	characteristic
387	C₄×C₈	—	2	1	no	—
388	C₄×C₈	—	2	1	no	—
389	C₄×C₈	—	2	1	no	—
390	C₄×C₈	—	2	1	no	—
391	C₄×C₈	C₂³×C₇	1	1	yes	characteristic
392	C₄×C₈	C₂³×C₇	1	1	yes	characteristic
393	C₄×C₈	C₂³×C₇	1	1	yes	characteristic
394	C₄×C₈	C₂³×C₇	1	1	yes	characteristic
395	C₄×C₈	C₂³×C₇	1	1	yes	characteristic
396	C₄×C₈	C₂³×C₇	1	1	yes	characteristic
397	C₂²×C₇	—	2	1	no	—
398	C₂²×C₇	—	2	1	no	—
399	C₂²×C₇	—	2	1	no	—
400	C₂²×C₇	—	4	1	no	—
401	C₂²×C₇	—	4	1	no	—
402	C₂²×C₇	—	4	1	no	—
403	C₂²×C₇	C₂×C₄×D₄	1	1	yes	characteristic
404	C₄×C₇	—	2	1	no	—
405	C₄×C₇	—	2	1	no	—
406	C₄×C₇	—	2	1	no	—
407	C₄×C₇	—	2	1	no	—
408	C₄×C₇	—	4	1	no	—
409	C₄×C₇	—	4	1	no	—
410	C₄×C₇	—	4	1	no	—
411	C₄×C₇	—	4	1	no	—
412	C₄×C₇	—	4	1	no	—
413	C₄×C₇	—	4	1	no	—
414	C₄×C₇	—	4	1	no	—
415	C₄×C₇	C₂×#131	1	1	yes	characteristic
416	C₄×C₇	C₂×#131	1	1	yes	characteristic
417	C₄×C₇	#577	1	1	yes	characteristic
418	C₄×C₇	#578	1	1	yes	characteristic
419	C₂×Q₈	—	2	1	no	—
420	C₂×Q₈	C₂²×C₄×C₇	1	1	yes	characteristic
421	C₂×Q₈	C₂²×C₄×C₇	1	1	yes	characteristic
422	C₂×Q₈	C₂²×C₄×C₇	1	1	yes	characteristic
423	C₂×D₄	—	2	1	no	—
424	C₂×D₄	C₂²×C₄×C₇	1	1	yes	characteristic
425	C₂²×C₄	—	2	1	no	—
426	C₂²×C₄	C₂²×C₄×C₇	1	1	yes	characteristic
427	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
428	C₂²×C₄	C₇×#41	1	1	yes	characteristic
429	Q₁₆	—	2	2	no	—
430	Q₁₆	—	2	2	no	—
431	SD₁₆	—	2	2	no	—
432	SD₁₆	—	2	2	no	—
433	M₁₆	—	2	2	no	—
434	M₁₆	—	2	2	no	—
435	M₁₆	—	8	1	no	—
436	M₁₆	—	8	1	no	—
437	C₂×C₈	—	2	1	no	—
438	C₂×C₈	—	2	1	no	—
439	C₂×C₈	—	2	1	no	—
440	C₂×C₈	—	2	1	no	—
441	C₂×C₈	—	2	1	no	—
442	C₂×C₈	—	2	1	no	—
443	C₂×C₈	—	4	2	no	—
444	C₂×C₈	—	8	1	no	—
445	C₂×C₈	C₂²×C₄×C₇	1	1	yes	characteristic
446	C₂×C₈	C₂²×C₄×C₇	1	1	yes	characteristic
447	C₂×C₈	C₂²×C₄×C₇	1	1	yes	characteristic
448	C₂×C₈	C₂²×C₄×C₇	1	1	yes	characteristic
449	C₂×C₈	C₂×C₇×D₄	1	1	yes	characteristic
450	C₂×C₈	C₂×C₇×D₄	1	1	yes	characteristic
451	C₂×C₈	C₂×C₇×D₄	1	1	yes	characteristic
452	C₂×C₈	C₂×C₇×D₄	1	1	yes	characteristic
453	C₄⋊C₄	—	2	1	no	—
454	C₄⋊C₄	—	2	1	no	—
455	C₄⋊C₄	—	2	1	no	—
456	C₄⋊C₄	—	2	1	no	—
457	C₄⋊C₄	—	2	1	no	—
458	C₄⋊C₄	—	2	1	no	—
459	C₄⋊C₄	—	2	1	no	—
460	C₄⋊C₄	—	2	1	no	—
461	C₄⋊C₄	—	2	1	no	—
462	C₄⋊C₄	—	2	1	no	—
463	C₄⋊C₄	—	2	1	no	—
464	C₄⋊C₄	C₂²×C₄×C₇	1	1	yes	characteristic
465	C₄⋊C₄	C₂²×C₄×C₇	1	1	yes	characteristic
466	C₄⋊C₄	C₂²×C₄×C₇	1	1	yes	characteristic
467	C₄⋊C₄	C₂²×C₄×C₇	1	1	yes	characteristic
468	C₂²⋊C₄	—	2	1	no	—
469	C₂²⋊C₄	—	2	1	no	—
470	C₂²⋊C₄	—	2	1	no	—
471	C₂²⋊C₄	—	2	1	no	—
472	C₂²⋊C₄	—	2	1	no	—
473	C₂²⋊C₄	—	2	1	no	—
474	C₂²⋊C₄	—	2	1	no	—
475	C₄²	—	2	1	no	—
476	C₄²	—	2	1	no	—
477	C₄²	—	2	1	no	—
478	C₄²	C₂²×C₄×C₇	1	1	yes	characteristic
479	C₄²	C₂×C₇×D₄	1	1	yes	characteristic
480	C₄²	C₇×#41	1	1	yes	characteristic
481	C₄²	C₂⁴×C₇	1	1	yes	characteristic
482	C₂×C₇	—	4	1	no	—
483	C₂×C₇	—	8	1	no	—
484	C₂×C₇	#2931	1	1	yes	characteristic
485	C₂×C₇	#2947	1	1	yes	characteristic
486	C₂×C₇	#2956	1	1	yes	characteristic
487	C₂³	—	2	1	no	—
488	C₂³	C₄×C₇×D₄	1	1	yes	characteristic
489	Q₈	—	2	1	no	—
490	Q₈	—	2	1	no	—
491	Q₈	—	2	1	no	—
492	Q₈	—	2	1	no	—
493	Q₈	—	2	1	no	—
494	Q₈	—	2	1	no	—
495	Q₈	—	8	1	no	—
496	D₄	—	2	1	no	—
497	D₄	—	2	1	no	—
498	D₄	—	8	1	no	—
499	C₂×C₄	—	2	1	no	—
500	C₂×C₄	—	2	1	no	—
501	C₂×C₄	—	2	1	no	—
502	C₂×C₄	—	2	1	no	—
503	C₂×C₄	—	2	1	no	—
504	C₂×C₄	—	2	1	no	—
505	C₂×C₄	—	2	1	no	—
506	C₂×C₄	—	2	1	no	—
507	C₂×C₄	—	2	1	no	—
508	C₂×C₄	—	2	1	no	—
509	C₂×C₄	—	2	1	no	—
510	C₂×C₄	—	4	1	no	—
511	C₂×C₄	—	4	1	no	—
512	C₂×C₄	—	4	1	no	—
513	C₂×C₄	C₄×C₇×D₄	1	1	yes	characteristic
514	C₂×C₄	C₄×C₇×D₄	1	1	yes	characteristic
515	C₂×C₄	C₄×C₇×D₄	1	1	yes	characteristic
516	C₂×C₄	C₂³×C₄×C₇	1	1	yes	characteristic
517	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
518	C₂×C₄	C₂×C₇×#41	1	1	yes	characteristic
519	C₈	—	2	2	no	—
520	C₈	—	2	1	no	—
521	C₈	—	2	1	no	—
522	C₈	—	2	1	no	—
523	C₈	—	2	1	no	—
524	C₈	—	2	1	no	—
525	C₈	—	2	1	no	—
526	C₈	—	4	1	no	—
527	C₈	—	4	1	no	—
528	C₈	—	4	1	no	—
529	C₈	—	4	1	no	—
530	C₈	—	4	1	no	—
531	C₈	C₇×#131	1	2	yes	—
532	C₈	C₇×#131	1	2	yes	—
533	C₇	#17969	1	1	yes	characteristic, direct product factor, Sylow
534	C₂²	—	2	1	no	—
535	C₂²	—	2	1	no	—
536	C₂²	—	2	1	no	—
537	C₂²	—	4	1	no	—
538	C₂²	—	4	1	no	—
539	C₂²	—	4	1	no	—
540	C₂²	C₂×C₄×C₇×D₄	1	1	yes	characteristic
541	C₄	—	2	1	no	—
542	C₄	—	2	1	no	—
543	C₄	—	2	1	no	—
544	C₄	—	2	1	no	—
545	C₄	—	4	1	no	—
546	C₄	—	4	1	no	—
547	C₄	—	4	1	no	—
548	C₄	—	4	1	no	—
549	C₄	—	4	1	no	—
550	C₄	—	4	1	no	—
551	C₄	—	4	1	no	—
552	C₄	C₂×C₇×#131	1	1	yes	characteristic
553	C₄	C₂×C₇×#131	1	1	yes	characteristic
554	C₄	C₇×#577	1	1	yes	characteristic
555	C₄	C₇×#578	1	1	yes	characteristic
556	C₂	—	4	1	no	—
557	C₂	—	8	1	no	—
558	C₂	C₇×#2931	1	1	yes	characteristic
559	C₂	C₇×#2947	1	1	yes	characteristic
560	C₂	C₇×#2956	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₇	C₂²×D₄
commutator	C₂×C₄	C₂³×C₄×C₇
Frattini, cosocle	C₄²	C₂⁴×C₇
socle	C₂²×C₇	C₂×C₄×D₄
prime radical	C₇×#121	C₂×C₄
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₇ ◁ C₇×#431 ◁ G

Complements

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

N	H ≅ G/N	type
3. C₇×#2985	C₂	semidirect
4. C₇×#1593	C₂	semidirect
5. C₇×#1592	C₂	semidirect
6. C₇×#1591	C₂	semidirect
7. C₇×#1590	C₂	semidirect
8. C₇×#1579	C₂	semidirect
9. C₇×SD₁₆⋊C₈	C₂	semidirect
10. C₇×C₈×Q₁₆	C₂	semidirect
11. C₇×C₈×SD₁₆	C₂	semidirect
12. C₇×#1569	C₂	semidirect
14. C₇×#1493	C₂	semidirect
15. C₇×C₈×M₁₆	C₂	semidirect
67. #17969	C₇	direct (N × H)
147. #2985	C₂×C₇	semidirect
148. #1593	C₂×C₇	semidirect
149. #1592	C₂×C₇	semidirect
150. #1591	C₂×C₇	semidirect
151. #1590	C₂×C₇	semidirect
152. #1579	C₂×C₇	semidirect
153. SD₁₆⋊C₈	C₂×C₇	semidirect
154. C₈×Q₁₆	C₂×C₇	semidirect
155. C₈×SD₁₆	C₂×C₇	semidirect
156. #1569	C₂×C₇	semidirect
158. #1493	C₂×C₇	semidirect
159. C₈×M₁₆	C₂×C₇	semidirect
533. C₇	#17969	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₇×#3172	2
C₇×#2993	2
C₇×#2985	2
C₇×#1593	2
C₇×#1592	2
C₇×#1591	2
C₇×#1590	2
C₇×#1579	2
C₇×SD₁₆⋊C₈	2
C₇×C₈×Q₁₆	2
C₇×C₈×SD₁₆	2
C₇×#1569	2
C₇×#1494	2
C₇×#1493	2
C₇×C₈×M₁₆	2
#17969	7

Subgroups — C7×#17969 #13195185

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×#17969 #13195185