Subgroups — C₇×#21466 #13198682

Order 1792.

1354 conjugacy classes of subgroups.

The subgroup lattice has 630 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₇×#131	C₂	1	1	yes	maximal, characteristic, complemented
2	C₇×#3002	C₂	1	1	yes	maximal, characteristic
3	C₂×C₇×#443	C₂	1	2	yes	maximal, complemented
4	C₇×#2929	C₂	1	1	yes	maximal, characteristic, complemented
5	C₇×#1876	C₂	1	2	yes	maximal, complemented
6	C₇×#1871	C₂	1	1	yes	maximal, characteristic, complemented
7	C₇×#1866	C₂	1	2	yes	maximal, complemented
8	C₇×#1855	C₂	1	1	yes	maximal, characteristic, complemented
9	C₇×#1789	C₂	1	1	yes	maximal, characteristic, complemented
10	C₇×#1764	C₂	1	2	yes	maximal, complemented
11	C₇×C₈×C₂²⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×C₇×#41	C₂²	1	1	yes	characteristic
13	C₂×C₇×#135	C₂²	1	2	yes	—
14	C₂×C₇×#131	—	2	8	no	—
15	C₂×C₇×#131	—	2	1	no	—
16	C₂×C₇×#131	—	2	1	no	—
17	C₂×C₇×#131	C₂²	1	2	yes	—
18	C₂×C₇×#131	C₂²	1	2	yes	—
19	C₂×C₇×#131	C₂²	1	1	yes	characteristic, complemented
20	C₂²×C₇×M₁₆	—	2	1	no	—
21	C₂²×C₇×M₁₆	C₂²	1	1	yes	characteristic
22	C₂³×C₇×C₈	—	2	1	no	—
23	C₂³×C₇×C₈	C₂²	1	1	yes	characteristic
24	C₇×#525	C₂²	1	1	yes	characteristic
25	C₇×#452	C₄	1	2	yes	complemented
26	C₇×#451	C₄	1	1	yes	characteristic, complemented
27	C₇×#450	C₄	1	1	yes	characteristic, complemented
28	C₇×#449	C₄	1	2	yes	complemented
29	C₇×#448	C₄	1	1	yes	characteristic, complemented
30	C₇×#447	C₄	1	1	yes	characteristic, complemented
31	C₇×#443	—	2	8	no	—
32	C₇×#435	—	2	1	no	—
33	C₇×#435	—	2	1	no	—
34	C₇×C₈×D₄	—	2	1	no	—
35	C₇×C₈×D₄	—	2	1	no	—
36	C₂×C₇×#108	C₂²	1	2	yes	complemented
37	C₇×#424	C₂²	1	1	yes	characteristic, complemented
38	C₂×C₇×#104	C₂²	1	2	yes	—
39	C₂×C₇×#104	C₂²	1	2	yes	—
40	C₂×C₇×#104	C₂²	1	2	yes	complemented
41	C₇×#416	C₂²	1	2	yes	—
42	C₇×#408	C₂²	1	1	yes	characteristic, complemented
43	C₇×#407	C₂²	1	1	yes	characteristic
44	C₂×C₇×C₂²⋊C₈	C₂²	1	1	yes	characteristic
45	C₇×#405	C₂²	1	1	yes	characteristic, complemented
46	C₂×C₄×C₇×C₈	C₂²	1	2	yes	complemented
47	C₄×C₇×C₂²⋊C₄	C₂²	1	1	yes	characteristic
48	C₇×#341	C₂²	1	2	yes	complemented
49	C₇×#339	C₂²	1	2	yes	complemented
50	C₇×#336	C₂²	1	2	yes	complemented
51	#21466	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
52	C₂×C₇×#41	—	2	4	no	—
53	C₂×C₇×#41	—	2	4	no	—
54	C₂×C₇×#41	—	2	1	no	—
55	C₂×C₇×#41	—	2	1	no	—
56	C₂×C₇×#41	C₂×C₄	1	2	yes	—
57	C₂×C₇×#41	C₂³	1	1	yes	characteristic
58	C₂×C₇×#41	C₂³	1	2	yes	—
59	C₂²×C₇×Q₈	C₂×C₄	1	1	yes	characteristic
60	C₂²×C₇×D₄	—	2	1	no	—
61	C₂²×C₇×D₄	C₂×C₄	1	1	yes	characteristic
62	C₂³×C₄×C₇	—	2	1	no	—
63	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
64	C₇×#135	—	2	4	no	—
65	C₇×#135	—	2	4	no	—
66	C₂×C₇×Q₁₆	C₂×C₄	1	2	yes	—
67	C₂×C₇×SD₁₆	C₂×C₄	1	2	yes	—
68	C₂×C₇×SD₁₆	C₂×C₄	1	2	yes	—
69	C₂×C₇×D₈	C₂×C₄	1	2	yes	—
70	C₇×#131	—	2	8	no	—
71	C₇×#131	—	2	8	no	—
72	C₇×#131	—	2	4	no	—
73	C₇×#131	—	2	4	no	—
74	C₇×#131	—	2	4	no	—
75	C₇×#131	—	2	4	no	—
76	C₇×#131	D₄	1	8	yes	complemented
77	C₂×C₇×M₁₆	—	2	8	no	—
78	C₂×C₇×M₁₆	—	2	1	no	—
79	C₂×C₇×M₁₆	—	2	4	no	—
80	C₂×C₇×M₁₆	—	2	2	no	—
81	C₂×C₇×M₁₆	—	2	2	no	—
82	C₂×C₇×M₁₆	—	2	1	no	—
83	C₂×C₇×M₁₆	C₂³	1	1	yes	characteristic
84	C₂×C₇×M₁₆	C₂³	1	1	yes	characteristic
85	C₂×C₇×M₁₆	C₂³	1	2	yes	—
86	C₂²×C₇×C₈	—	2	8	no	—
87	C₂²×C₇×C₈	—	2	1	no	—
88	C₂²×C₇×C₈	—	2	2	no	—
89	C₂²×C₇×C₈	—	2	4	no	—
90	C₂²×C₇×C₈	—	2	2	no	—
91	C₂²×C₇×C₈	—	2	1	no	—
92	C₂²×C₇×C₈	D₄	1	1	yes	characteristic
93	C₂²×C₇×C₈	D₄	1	1	yes	characteristic
94	C₂²×C₇×C₈	D₄	1	1	yes	characteristic
95	C₂²×C₇×C₈	D₄	1	1	yes	characteristic
96	C₂²×C₇×C₈	C₂³	1	2	yes	—
97	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
98	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
99	C₇×#123	—	2	1	no	—
100	C₇×C₂²⋊Q₈	C₂×C₄	1	1	yes	characteristic
101	C₇×C₂²⋊Q₈	C₂×C₄	1	1	yes	characteristic
102	C₇×#121	C₂×C₄	1	1	yes	characteristic
103	C₇×#121	C₂×C₄	1	1	yes	characteristic
104	C₇×#120	—	2	1	no	—
105	C₄×C₇×D₄	—	2	1	no	—
106	C₄×C₇×D₄	—	2	1	no	—
107	C₇×#117	C₂³	1	1	yes	characteristic
108	C₂×C₇×C₂²⋊C₄	—	2	1	no	—
109	C₂×C₄²×C₇	C₂³	1	2	yes	—
110	C₇×#108	—	2	4	no	—
111	C₇×C₄⋊C₈	—	2	1	no	—
112	C₇×C₄⋊C₈	—	2	1	no	—
113	C₇×#104	—	2	4	no	—
114	C₇×#104	—	2	4	no	—
115	C₇×#104	—	2	4	no	—
116	C₇×#103	C₂×C₄	1	2	yes	—
117	C₇×#103	C₂×C₄	1	2	yes	—
118	C₇×#102	C₂×C₄	1	2	yes	—
119	C₇×#102	C₂×C₄	1	2	yes	—
120	C₇×C₂²⋊C₈	—	2	1	no	—
121	C₇×C₂²⋊C₈	—	2	1	no	—
122	C₇×C₂²⋊C₈	—	2	1	no	—
123	C₇×C₂²⋊C₈	—	2	1	no	—
124	C₇×C₂²⋊C₈	C₂×C₄	1	1	yes	characteristic
125	C₇×C₂²⋊C₈	C₂×C₄	1	1	yes	characteristic
126	C₇×C₂²⋊C₈	C₂×C₄	1	2	yes	—
127	C₇×#97	—	2	1	no	—
128	C₄×C₇×C₈	—	2	4	no	—
129	C₄×C₇×C₈	—	2	1	no	—
130	C₇×#95	—	2	1	no	—
131	C₂²×#131	C₂×C₇	1	1	yes	characteristic, complemented
132	#3002	C₂×C₇	1	1	yes	characteristic
133	C₂×#443	C₂×C₇	1	2	yes	complemented
134	#2929	C₂×C₇	1	1	yes	characteristic, complemented
135	#1876	C₂×C₇	1	2	yes	complemented
136	#1871	C₂×C₇	1	1	yes	characteristic, complemented
137	#1866	C₂×C₇	1	2	yes	complemented
138	#1855	C₂×C₇	1	1	yes	characteristic, complemented
139	#1789	C₂×C₇	1	1	yes	characteristic, complemented
140	#1764	C₂×C₇	1	2	yes	complemented
141	C₈×C₂²⋊C₄	C₂×C₇	1	1	yes	characteristic, complemented
142	C₂⁴×C₇	—	2	1	no	—
143	C₂⁴×C₇	#41	1	1	yes	characteristic
144	C₇×#41	—	2	4	no	—
145	C₇×#41	—	2	8	no	—
146	C₇×#41	—	2	4	no	—
147	C₇×#41	—	2	4	no	—
148	C₇×#41	—	2	4	no	—
149	C₇×#41	—	2	2	no	—
150	C₇×#41	—	2	2	no	—
151	C₇×#41	—	2	2	no	—
152	C₇×#41	—	2	2	no	—
153	C₇×#41	C₂×D₄	1	4	yes	—
154	C₇×#41	#41	1	4	yes	—
155	C₂×C₇×Q₈	—	2	4	no	—
156	C₂×C₇×Q₈	—	2	1	no	—
157	C₂×C₇×Q₈	C₂²×C₄	1	1	yes	characteristic
158	C₂×C₇×Q₈	C₂²×C₄	1	2	yes	—
159	C₂×C₇×D₄	—	2	8	no	—
160	C₂×C₇×D₄	—	2	2	no	—
161	C₂×C₇×D₄	—	2	2	no	—
162	C₂×C₇×D₄	—	2	4	no	—
163	C₂×C₇×D₄	—	2	1	no	—
164	C₂×C₇×D₄	—	2	1	no	—
165	C₂×C₇×D₄	—	2	1	no	—
166	C₂×C₇×D₄	—	2	1	no	—
167	C₂×C₇×D₄	C₂²×C₄	1	1	yes	characteristic
168	C₂×C₇×D₄	C₂²×C₄	1	2	yes	—
169	C₂²×C₄×C₇	—	2	4	no	—
170	C₂²×C₄×C₇	—	2	4	no	—
171	C₂²×C₄×C₇	—	2	1	no	—
172	C₂²×C₄×C₇	—	2	2	no	—
173	C₂²×C₄×C₇	—	2	2	no	—
174	C₂²×C₄×C₇	—	2	2	no	—
175	C₂²×C₄×C₇	—	2	2	no	—
176	C₂²×C₄×C₇	—	2	2	no	—
177	C₂²×C₄×C₇	—	2	1	no	—
178	C₂²×C₄×C₇	C₂²×C₄	1	1	yes	characteristic
179	C₂²×C₄×C₇	C₂²×C₄	1	1	yes	characteristic
180	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
181	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
182	C₂²×C₄×C₇	#41	1	1	yes	characteristic
183	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
184	C₇×Q₁₆	—	2	4	no	—
185	C₇×SD₁₆	—	2	4	no	—
186	C₇×SD₁₆	—	2	4	no	—
187	C₇×D₈	—	2	4	no	—
188	C₇×M₁₆	—	2	4	no	—
189	C₇×M₁₆	—	2	8	no	—
190	C₇×M₁₆	—	2	2	no	—
191	C₇×M₁₆	—	2	8	no	—
192	C₇×M₁₆	—	2	2	no	—
193	C₇×M₁₆	—	2	2	no	—
194	C₇×M₁₆	—	4	2	no	—
195	C₇×M₁₆	C₂×D₄	1	4	yes	—
196	C₂×C₇×C₈	—	2	4	no	—
197	C₂×C₇×C₈	—	2	8	no	—
198	C₂×C₇×C₈	—	2	2	no	—
199	C₂×C₇×C₈	—	2	2	no	—
200	C₂×C₇×C₈	—	2	2	no	—
201	C₂×C₇×C₈	—	2	2	no	—
202	C₂×C₇×C₈	—	2	2	no	—
203	C₂×C₇×C₈	—	2	8	no	—
204	C₂×C₇×C₈	—	2	2	no	—
205	C₂×C₇×C₈	—	2	2	no	—
206	C₂×C₇×C₈	—	2	2	no	—
207	C₂×C₇×C₈	—	2	1	no	—
208	C₂×C₇×C₈	—	2	1	no	—
209	C₂×C₇×C₈	—	4	2	no	—
210	C₂×C₇×C₈	C₂²×C₄	1	2	yes	—
211	C₂×C₇×C₈	C₂²×C₄	1	2	yes	—
212	C₂×C₇×C₈	C₂×D₄	1	1	yes	characteristic
213	C₂×C₇×C₈	C₂×D₄	1	1	yes	characteristic
214	C₂×C₇×C₈	C₂×D₄	1	4	yes	—
215	C₂×C₇×C₈	C₂×D₄	1	1	yes	characteristic
216	C₂×C₇×C₈	C₂×D₄	1	1	yes	characteristic
217	C₇×C₄⋊C₄	—	2	1	no	—
218	C₇×C₄⋊C₄	—	2	1	no	—
219	C₇×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
220	C₇×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
221	C₇×C₂²⋊C₄	—	2	4	no	—
222	C₇×C₂²⋊C₄	—	2	1	no	—
223	C₇×C₂²⋊C₄	—	2	1	no	—
224	C₇×C₂²⋊C₄	—	2	1	no	—
225	C₇×C₂²⋊C₄	—	2	1	no	—
226	C₇×C₂²⋊C₄	—	2	1	no	—
227	C₄²×C₇	—	2	1	no	—
228	C₄²×C₇	—	2	2	no	—
229	C₄²×C₇	—	2	2	no	—
230	C₂²×#41	C₂²×C₇	1	1	yes	characteristic
231	C₂×#135	C₂²×C₇	1	2	yes	—
232	C₂×#131	—	2	8	no	—
233	C₂×#131	—	2	1	no	—
234	C₂×#131	—	2	1	no	—
235	C₂×#131	C₂²×C₇	1	2	yes	—
236	C₂×#131	C₂²×C₇	1	2	yes	—
237	C₂×#131	C₂²×C₇	1	1	yes	characteristic, complemented
238	C₂²×M₁₆	—	2	1	no	—
239	C₂²×M₁₆	C₂²×C₇	1	1	yes	characteristic
240	C₂³×C₈	—	2	1	no	—
241	C₂³×C₈	C₂²×C₇	1	1	yes	characteristic
242	#525	C₂²×C₇	1	1	yes	characteristic
243	#452	C₄×C₇	1	2	yes	complemented
244	#451	C₄×C₇	1	1	yes	characteristic, complemented
245	#450	C₄×C₇	1	1	yes	characteristic, complemented
246	#449	C₄×C₇	1	2	yes	complemented
247	#448	C₄×C₇	1	1	yes	characteristic, complemented
248	#447	C₄×C₇	1	1	yes	characteristic, complemented
249	#443	—	2	8	no	—
250	#435	—	2	1	no	—
251	#435	—	2	1	no	—
252	C₈×D₄	—	2	1	no	—
253	C₈×D₄	—	2	1	no	—
254	C₂×#108	C₂²×C₇	1	2	yes	complemented
255	#424	C₂²×C₇	1	1	yes	characteristic, complemented
256	C₂×#104	C₂²×C₇	1	2	yes	—
257	C₂×#104	C₂²×C₇	1	2	yes	—
258	C₂×#104	C₂²×C₇	1	2	yes	complemented
259	#416	C₂²×C₇	1	2	yes	—
260	#408	C₂²×C₇	1	1	yes	characteristic, complemented
261	#407	C₂²×C₇	1	1	yes	characteristic
262	C₂×C₂²⋊C₈	C₂²×C₇	1	1	yes	characteristic
263	#405	C₂²×C₇	1	1	yes	characteristic, complemented
264	C₂×C₄×C₈	C₂²×C₇	1	2	yes	complemented
265	C₄×C₂²⋊C₄	C₂²×C₇	1	1	yes	characteristic
266	#341	C₂²×C₇	1	2	yes	complemented
267	#339	C₂²×C₇	1	2	yes	complemented
268	#336	C₂²×C₇	1	2	yes	complemented
269	C₂³×C₇	—	2	4	no	—
270	C₂³×C₇	—	2	2	no	—
271	C₂³×C₇	—	2	2	no	—
272	C₂³×C₇	—	2	2	no	—
273	C₂³×C₇	—	2	1	no	—
274	C₂³×C₇	—	4	1	no	—
275	C₂³×C₇	—	4	2	no	—
276	C₂³×C₇	—	4	2	no	—
277	C₂³×C₇	C₄×D₄	1	1	yes	characteristic
278	C₂³×C₇	C₄×D₄	1	1	yes	characteristic
279	C₂³×C₇	C₂×#41	1	1	yes	characteristic
280	C₇×Q₈	—	2	4	no	—
281	C₇×Q₈	—	2	2	no	—
282	C₇×Q₈	—	2	2	no	—
283	C₇×Q₈	C₄×D₄	1	4	yes	—
284	C₇×D₄	—	2	8	no	—
285	C₇×D₄	—	2	4	no	—
286	C₇×D₄	—	2	4	no	—
287	C₇×D₄	—	2	4	no	—
288	C₇×D₄	—	2	2	no	—
289	C₇×D₄	—	2	2	no	—
290	C₇×D₄	—	4	2	no	—
291	C₇×D₄	—	4	2	no	—
292	C₇×D₄	—	4	2	no	—
293	C₇×D₄	C₄×D₄	1	4	yes	—
294	C₂×C₄×C₇	—	2	4	no	—
295	C₂×C₄×C₇	—	2	8	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	1	no	—
301	C₂×C₄×C₇	—	2	4	no	—
302	C₂×C₄×C₇	—	2	1	no	—
303	C₂×C₄×C₇	—	2	1	no	—
304	C₂×C₄×C₇	—	2	4	no	—
305	C₂×C₄×C₇	—	2	1	no	—
306	C₂×C₄×C₇	—	2	4	no	—
307	C₂×C₄×C₇	—	2	1	no	—
308	C₂×C₄×C₇	—	2	1	no	—
309	C₂×C₄×C₇	—	2	1	no	—
310	C₂×C₄×C₇	—	4	2	no	—
311	C₂×C₄×C₇	—	4	2	no	—
312	C₂×C₄×C₇	—	4	1	no	—
313	C₂×C₄×C₇	—	4	1	no	—
314	C₂×C₄×C₇	C₄×D₄	1	1	yes	characteristic
315	C₂×C₄×C₇	C₄×D₄	1	1	yes	characteristic
316	C₂×C₄×C₇	C₂³×C₄	1	1	yes	characteristic
317	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
318	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
319	C₂×C₄×C₇	C₂×#41	1	2	yes	—
320	C₇×C₈	—	2	2	no	—
321	C₇×C₈	—	2	2	no	—
322	C₇×C₈	—	2	1	no	—
323	C₇×C₈	—	2	4	no	—
324	C₇×C₈	—	2	1	no	—
325	C₇×C₈	—	4	1	no	—
326	C₇×C₈	—	4	1	no	—
327	C₇×C₈	#120	1	2	yes	—
328	C₇×C₈	#120	1	2	yes	—
329	C₂×#41	—	2	4	no	—
330	C₂×#41	—	2	4	no	—
331	C₂×#41	—	2	1	no	—
332	C₂×#41	—	2	1	no	—
333	C₂×#41	C₂×C₄×C₇	1	2	yes	—
334	C₂×#41	C₂³×C₇	1	1	yes	characteristic
335	C₂×#41	C₂³×C₇	1	2	yes	—
336	C₂²×Q₈	C₂×C₄×C₇	1	1	yes	characteristic
337	C₂²×D₄	—	2	1	no	—
338	C₂²×D₄	C₂×C₄×C₇	1	1	yes	characteristic
339	C₂³×C₄	—	2	1	no	—
340	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
341	#135	—	2	4	no	—
342	#135	—	2	4	no	—
343	C₂×Q₁₆	C₂×C₄×C₇	1	2	yes	—
344	C₂×SD₁₆	C₂×C₄×C₇	1	2	yes	—
345	C₂×SD₁₆	C₂×C₄×C₇	1	2	yes	—
346	C₂×D₈	C₂×C₄×C₇	1	2	yes	—
347	#131	—	2	8	no	—
348	#131	—	2	8	no	—
349	#131	—	2	4	no	—
350	#131	—	2	4	no	—
351	#131	—	2	4	no	—
352	#131	—	2	4	no	—
353	#131	C₇×D₄	1	8	yes	complemented
354	C₂×M₁₆	—	2	8	no	—
355	C₂×M₁₆	—	2	1	no	—
356	C₂×M₁₆	—	2	4	no	—
357	C₂×M₁₆	—	2	2	no	—
358	C₂×M₁₆	—	2	2	no	—
359	C₂×M₁₆	—	2	1	no	—
360	C₂×M₁₆	C₂³×C₇	1	1	yes	characteristic
361	C₂×M₁₆	C₂³×C₇	1	1	yes	characteristic
362	C₂×M₁₆	C₂³×C₇	1	2	yes	—
363	C₂²×C₈	—	2	8	no	—
364	C₂²×C₈	—	2	1	no	—
365	C₂²×C₈	—	2	2	no	—
366	C₂²×C₈	—	2	2	no	—
367	C₂²×C₈	—	2	4	no	—
368	C₂²×C₈	—	2	1	no	—
369	C₂²×C₈	C₇×D₄	1	1	yes	characteristic
370	C₂²×C₈	C₇×D₄	1	1	yes	characteristic
371	C₂²×C₈	C₇×D₄	1	1	yes	characteristic
372	C₂²×C₈	C₇×D₄	1	1	yes	characteristic
373	C₂²×C₈	C₂³×C₇	1	2	yes	—
374	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
375	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
376	#123	—	2	1	no	—
377	C₂²⋊Q₈	C₂×C₄×C₇	1	1	yes	characteristic
378	C₂²⋊Q₈	C₂×C₄×C₇	1	1	yes	characteristic
379	#121	C₂×C₄×C₇	1	1	yes	characteristic
380	#121	C₂×C₄×C₇	1	1	yes	characteristic
381	#120	—	2	1	no	—
382	C₄×D₄	—	2	1	no	—
383	C₄×D₄	—	2	1	no	—
384	#117	C₂³×C₇	1	1	yes	characteristic
385	C₂×C₂²⋊C₄	—	2	1	no	—
386	C₂×C₄²	C₂³×C₇	1	2	yes	—
387	#108	—	2	4	no	—
388	C₄⋊C₈	—	2	1	no	—
389	C₄⋊C₈	—	2	1	no	—
390	#104	—	2	4	no	—
391	#104	—	2	4	no	—
392	#104	—	2	4	no	—
393	#103	C₂×C₄×C₇	1	2	yes	—
394	#103	C₂×C₄×C₇	1	2	yes	—
395	#102	C₂×C₄×C₇	1	2	yes	—
396	#102	C₂×C₄×C₇	1	2	yes	—
397	C₂²⋊C₈	—	2	1	no	—
398	C₂²⋊C₈	—	2	1	no	—
399	C₂²⋊C₈	—	2	1	no	—
400	C₂²⋊C₈	—	2	1	no	—
401	C₂²⋊C₈	C₂×C₄×C₇	1	1	yes	characteristic
402	C₂²⋊C₈	C₂×C₄×C₇	1	1	yes	characteristic
403	C₂²⋊C₈	C₂×C₄×C₇	1	2	yes	—
404	#97	—	2	1	no	—
405	C₄×C₈	—	2	4	no	—
406	C₄×C₈	—	2	1	no	—
407	#95	—	2	1	no	—
408	C₂²×C₇	—	2	1	no	—
409	C₂²×C₇	—	2	1	no	—
410	C₂²×C₇	—	2	1	no	—
411	C₂²×C₇	—	2	1	no	—
412	C₂²×C₇	—	2	1	no	—
413	C₂²×C₇	—	2	1	no	—
414	C₂²×C₇	—	2	1	no	—
415	C₂²×C₇	—	2	4	no	—
416	C₂²×C₇	—	4	4	no	—
417	C₂²×C₇	—	4	8	no	—
418	C₂²×C₇	—	4	2	no	—
419	C₂²×C₇	—	4	2	no	—
420	C₂²×C₇	—	4	1	no	—
421	C₂²×C₇	—	4	1	no	—
422	C₂²×C₇	—	4	1	no	—
423	C₂²×C₇	#443	1	2	yes	complemented
424	C₂²×C₇	C₂×C₄×D₄	1	1	yes	characteristic
425	C₂²×C₇	#525	1	2	yes	—
426	C₄×C₇	—	2	1	no	—
427	C₄×C₇	—	2	4	no	—
428	C₄×C₇	—	2	1	no	—
429	C₄×C₇	—	4	4	no	—
430	C₄×C₇	—	4	1	no	—
431	C₄×C₇	—	4	1	no	—
432	C₄×C₇	—	4	1	no	—
433	C₄×C₇	C₂×C₄×D₄	1	2	yes	—
434	C₄×C₇	C₂×#120	1	1	yes	characteristic
435	C₄×C₇	#525	1	1	yes	characteristic
436	C₂⁴	—	2	1	no	—
437	C₂⁴	C₇×#41	1	1	yes	characteristic
438	#41	—	2	4	no	—
439	#41	—	2	8	no	—
440	#41	—	2	4	no	—
441	#41	—	2	4	no	—
442	#41	—	2	4	no	—
443	#41	—	2	2	no	—
444	#41	—	2	2	no	—
445	#41	—	2	2	no	—
446	#41	—	2	2	no	—
447	#41	C₂×C₇×D₄	1	4	yes	—
448	#41	C₇×#41	1	4	yes	—
449	C₂×Q₈	—	2	4	no	—
450	C₂×Q₈	—	2	1	no	—
451	C₂×Q₈	C₂²×C₄×C₇	1	1	yes	characteristic
452	C₂×Q₈	C₂²×C₄×C₇	1	2	yes	—
453	C₂×D₄	—	2	8	no	—
454	C₂×D₄	—	2	2	no	—
455	C₂×D₄	—	2	2	no	—
456	C₂×D₄	—	2	4	no	—
457	C₂×D₄	—	2	1	no	—
458	C₂×D₄	—	2	1	no	—
459	C₂×D₄	—	2	1	no	—
460	C₂×D₄	—	2	1	no	—
461	C₂×D₄	C₂²×C₄×C₇	1	1	yes	characteristic
462	C₂×D₄	C₂²×C₄×C₇	1	2	yes	—
463	C₂²×C₄	—	2	4	no	—
464	C₂²×C₄	—	2	4	no	—
465	C₂²×C₄	—	2	1	no	—
466	C₂²×C₄	—	2	2	no	—
467	C₂²×C₄	—	2	2	no	—
468	C₂²×C₄	—	2	2	no	—
469	C₂²×C₄	—	2	2	no	—
470	C₂²×C₄	—	2	2	no	—
471	C₂²×C₄	—	2	1	no	—
472	C₂²×C₄	C₂²×C₄×C₇	1	1	yes	characteristic
473	C₂²×C₄	C₂²×C₄×C₇	1	1	yes	characteristic
474	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
475	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
476	C₂²×C₄	C₇×#41	1	1	yes	characteristic
477	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
478	Q₁₆	—	2	4	no	—
479	SD₁₆	—	2	4	no	—
480	SD₁₆	—	2	4	no	—
481	D₈	—	2	4	no	—
482	M₁₆	—	2	4	no	—
483	M₁₆	—	2	8	no	—
484	M₁₆	—	2	2	no	—
485	M₁₆	—	2	8	no	—
486	M₁₆	—	2	2	no	—
487	M₁₆	—	2	2	no	—
488	M₁₆	—	4	2	no	—
489	M₁₆	C₂×C₇×D₄	1	4	yes	—
490	C₂×C₈	—	2	4	no	—
491	C₂×C₈	—	2	8	no	—
492	C₂×C₈	—	2	2	no	—
493	C₂×C₈	—	2	2	no	—
494	C₂×C₈	—	2	2	no	—
495	C₂×C₈	—	2	2	no	—
496	C₂×C₈	—	2	2	no	—
497	C₂×C₈	—	2	8	no	—
498	C₂×C₈	—	2	2	no	—
499	C₂×C₈	—	2	2	no	—
500	C₂×C₈	—	2	2	no	—
501	C₂×C₈	—	2	1	no	—
502	C₂×C₈	—	2	1	no	—
503	C₂×C₈	—	4	2	no	—
504	C₂×C₈	C₂²×C₄×C₇	1	2	yes	—
505	C₂×C₈	C₂²×C₄×C₇	1	2	yes	—
506	C₂×C₈	C₂×C₇×D₄	1	1	yes	characteristic
507	C₂×C₈	C₂×C₇×D₄	1	1	yes	characteristic
508	C₂×C₈	C₂×C₇×D₄	1	4	yes	—
509	C₂×C₈	C₂×C₇×D₄	1	1	yes	characteristic
510	C₂×C₈	C₂×C₇×D₄	1	1	yes	characteristic
511	C₄⋊C₄	—	2	1	no	—
512	C₄⋊C₄	—	2	1	no	—
513	C₄⋊C₄	C₂²×C₄×C₇	1	1	yes	characteristic
514	C₄⋊C₄	C₂²×C₄×C₇	1	1	yes	characteristic
515	C₂²⋊C₄	—	2	4	no	—
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	C₄²	—	2	1	no	—
522	C₄²	—	2	2	no	—
523	C₄²	—	2	2	no	—
524	C₂×C₇	—	2	2	no	—
525	C₂×C₇	—	2	2	no	—
526	C₂×C₇	—	4	1	no	—
527	C₂×C₇	—	4	4	no	—
528	C₂×C₇	—	8	1	no	—
529	C₂×C₇	C₄×#120	1	1	yes	characteristic
530	C₂×C₇	C₂×#443	1	1	yes	characteristic
531	C₂×C₇	#2955	1	1	yes	characteristic
532	C₂³	—	2	4	no	—
533	C₂³	—	2	2	no	—
534	C₂³	—	2	2	no	—
535	C₂³	—	2	2	no	—
536	C₂³	—	2	1	no	—
537	C₂³	—	4	1	no	—
538	C₂³	—	4	2	no	—
539	C₂³	—	4	2	no	—
540	C₂³	C₄×C₇×D₄	1	1	yes	characteristic
541	C₂³	C₄×C₇×D₄	1	1	yes	characteristic
542	C₂³	C₂×C₇×#41	1	1	yes	characteristic
543	Q₈	—	2	4	no	—
544	Q₈	—	2	2	no	—
545	Q₈	—	2	2	no	—
546	Q₈	C₄×C₇×D₄	1	4	yes	—
547	D₄	—	2	8	no	—
548	D₄	—	2	4	no	—
549	D₄	—	2	4	no	—
550	D₄	—	2	4	no	—
551	D₄	—	2	2	no	—
552	D₄	—	2	2	no	—
553	D₄	—	4	2	no	—
554	D₄	—	4	2	no	—
555	D₄	—	4	2	no	—
556	D₄	C₄×C₇×D₄	1	4	yes	—
557	C₂×C₄	—	2	4	no	—
558	C₂×C₄	—	2	8	no	—
559	C₂×C₄	—	2	2	no	—
560	C₂×C₄	—	2	2	no	—
561	C₂×C₄	—	2	2	no	—
562	C₂×C₄	—	2	2	no	—
563	C₂×C₄	—	2	1	no	—
564	C₂×C₄	—	2	4	no	—
565	C₂×C₄	—	2	1	no	—
566	C₂×C₄	—	2	1	no	—
567	C₂×C₄	—	2	4	no	—
568	C₂×C₄	—	2	1	no	—
569	C₂×C₄	—	2	4	no	—
570	C₂×C₄	—	2	1	no	—
571	C₂×C₄	—	2	1	no	—
572	C₂×C₄	—	2	1	no	—
573	C₂×C₄	—	4	2	no	—
574	C₂×C₄	—	4	2	no	—
575	C₂×C₄	—	4	1	no	—
576	C₂×C₄	—	4	1	no	—
577	C₂×C₄	C₄×C₇×D₄	1	1	yes	characteristic
578	C₂×C₄	C₄×C₇×D₄	1	1	yes	characteristic
579	C₂×C₄	C₂³×C₄×C₇	1	1	yes	characteristic
580	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
581	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
582	C₂×C₄	C₂×C₇×#41	1	2	yes	—
583	C₈	—	2	2	no	—
584	C₈	—	2	2	no	—
585	C₈	—	2	1	no	—
586	C₈	—	2	4	no	—
587	C₈	—	2	1	no	—
588	C₈	—	4	1	no	—
589	C₈	—	4	1	no	—
590	C₈	C₇×#120	1	2	yes	—
591	C₈	C₇×#120	1	2	yes	—
592	C₇	#21466	1	1	yes	characteristic, direct product factor, Sylow
593	C₂²	—	2	1	no	—
594	C₂²	—	2	1	no	—
595	C₂²	—	2	1	no	—
596	C₂²	—	2	1	no	—
597	C₂²	—	2	1	no	—
598	C₂²	—	2	1	no	—
599	C₂²	—	2	1	no	—
600	C₂²	—	2	4	no	—
601	C₂²	—	4	4	no	—
602	C₂²	—	4	8	no	—
603	C₂²	—	4	2	no	—
604	C₂²	—	4	2	no	—
605	C₂²	—	4	1	no	—
606	C₂²	—	4	1	no	—
607	C₂²	—	4	1	no	—
608	C₂²	C₇×#443	1	2	yes	complemented
609	C₂²	C₂×C₄×C₇×D₄	1	1	yes	characteristic
610	C₂²	C₇×#525	1	2	yes	—
611	C₄	—	2	1	no	—
612	C₄	—	2	4	no	—
613	C₄	—	2	1	no	—
614	C₄	—	4	4	no	—
615	C₄	—	4	1	no	—
616	C₄	—	4	1	no	—
617	C₄	—	4	1	no	—
618	C₄	C₂×C₄×C₇×D₄	1	2	yes	—
619	C₄	C₂×C₇×#120	1	1	yes	characteristic
620	C₄	C₇×#525	1	1	yes	characteristic
621	C₂	—	2	2	no	—
622	C₂	—	2	2	no	—
623	C₂	—	4	1	no	—
624	C₂	—	4	4	no	—
625	C₂	—	8	1	no	—
626	C₂	C₄×C₇×#120	1	1	yes	characteristic
627	C₂	C₂×C₇×#443	1	1	yes	characteristic
628	C₂	C₇×#2955	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₇×C₈	C₂×D₄
commutator	C₂×C₄	C₂³×C₄×C₇
Frattini, cosocle	C₂²×C₄	C₂⁴×C₇
socle	C₂²×C₇	C₂×C₄×D₄
prime radical	C₇×#3002	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₇×C₈ ◁ C₂³×C₇×C₈ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂²×C₇×#131	C₂	semidirect
3. C₂×C₇×#443	C₂	semidirect
4. C₇×#2929	C₂	semidirect
5. C₇×#1876	C₂	semidirect
6. C₇×#1871	C₂	semidirect
7. C₇×#1866	C₂	semidirect
8. C₇×#1855	C₂	semidirect
9. C₇×#1789	C₂	semidirect
10. C₇×#1764	C₂	semidirect
11. C₇×C₈×C₂²⋊C₄	C₂	semidirect
19. C₂×C₇×#131	C₂²	semidirect
25. C₇×#452	C₄	semidirect
26. C₇×#451	C₄	semidirect
27. C₇×#450	C₄	semidirect
28. C₇×#449	C₄	semidirect
29. C₇×#448	C₄	semidirect
30. C₇×#447	C₄	semidirect
36. C₂×C₇×#108	C₂²	semidirect
37. C₇×#424	C₂²	semidirect
40. C₂×C₇×#104	C₂²	semidirect
42. C₇×#408	C₂²	semidirect
45. C₇×#405	C₂²	semidirect
46. C₂×C₄×C₇×C₈	C₂²	semidirect
48. C₇×#341	C₂²	semidirect
49. C₇×#339	C₂²	semidirect
50. C₇×#336	C₂²	semidirect
51. #21466	C₇	direct (N × H)
76. C₇×#131	D₄	semidirect
131. C₂²×#131	C₂×C₇	semidirect
133. C₂×#443	C₂×C₇	semidirect
134. #2929	C₂×C₇	semidirect
135. #1876	C₂×C₇	semidirect
136. #1871	C₂×C₇	semidirect
137. #1866	C₂×C₇	semidirect
138. #1855	C₂×C₇	semidirect
139. #1789	C₂×C₇	semidirect
140. #1764	C₂×C₇	semidirect
141. C₈×C₂²⋊C₄	C₂×C₇	semidirect
237. C₂×#131	C₂²×C₇	semidirect
243. #452	C₄×C₇	semidirect
244. #451	C₄×C₇	semidirect
245. #450	C₄×C₇	semidirect
246. #449	C₄×C₇	semidirect
247. #448	C₄×C₇	semidirect
248. #447	C₄×C₇	semidirect
254. C₂×#108	C₂²×C₇	semidirect
255. #424	C₂²×C₇	semidirect
258. C₂×#104	C₂²×C₇	semidirect
260. #408	C₂²×C₇	semidirect
263. #405	C₂²×C₇	semidirect
264. C₂×C₄×C₈	C₂²×C₇	semidirect
266. #341	C₂²×C₇	semidirect
267. #339	C₂²×C₇	semidirect
268. #336	C₂²×C₇	semidirect
353. #131	C₇×D₄	semidirect
423. C₂²×C₇	#443	semidirect
592. C₇	#21466	direct (N × H)
608. C₂²	C₇×#443	semidirect

Maximal subgroups

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

subgroup	index
C₂²×C₇×#131	2
C₇×#3002	2
C₂×C₇×#443	2
C₇×#2929	2
C₇×#1876	2
C₇×#1871	2
C₇×#1866	2
C₇×#1855	2
C₇×#1789	2
C₇×#1764	2
C₇×C₈×C₂²⋊C₄	2
#21466	7

Subgroups — C7×#21466 #13198682

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×#21466 #13198682