Subgroups — C₇×#22095 #13199311

Order 1792.

738 conjugacy classes of subgroups.

The subgroup lattice has 518 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×#3091	C₂	1	1	yes	maximal, characteristic
2	C₇×#2929	C₂	1	1	yes	maximal, characteristic
3	C₂×C₇×#424	C₂	1	1	yes	maximal, characteristic, complemented
4	C₇×#1945	C₂	1	2	yes	maximal, complemented
5	C₇×#1937	C₂	1	2	yes	maximal, complemented
6	C₇×#1922	C₂	1	2	yes	maximal, complemented
7	C₇×#1871	C₂	1	1	yes	maximal, characteristic
8	C₇×#1866	C₂	1	2	yes	maximal, complemented
9	C₇×#1855	C₂	1	1	yes	maximal, characteristic, complemented
10	C₇×#1826	C₂	1	1	yes	maximal, characteristic, complemented
11	C₇×C₈×C₂²⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₇×#131	C₂²	1	1	yes	characteristic
13	C₂²×C₇×M₁₆	C₂²	1	1	yes	characteristic
14	C₂³×C₇×C₈	C₂²	1	1	yes	characteristic
15	C₇×#525	C₂²	1	1	yes	characteristic
16	C₂×C₇×#117	C₂²	1	1	yes	characteristic
17	C₇×#485	C₄	1	2	yes	complemented
18	C₇×#484	C₄	1	1	yes	characteristic, complemented
19	C₇×#483	C₄	1	1	yes	characteristic, complemented
20	C₇×#482	C₄	1	2	yes	complemented
21	C₇×#481	C₄	1	1	yes	characteristic, complemented
22	C₇×#480	C₄	1	1	yes	characteristic, complemented
23	C₇×#435	—	2	1	no	—
24	C₇×#435	—	2	1	no	—
25	C₇×C₈×D₄	—	2	1	no	—
26	C₇×C₈×D₄	—	2	1	no	—
27	C₂×C₇×#108	C₂²	1	2	yes	—
28	C₇×#427	C₂²	1	2	yes	—
29	C₇×#424	—	2	1	no	—
30	C₇×#424	—	2	1	no	—
31	C₇×#424	C₂²	1	2	yes	—
32	C₇×#424	C₂²	1	2	yes	—
33	C₇×#424	C₂²	1	1	yes	characteristic
34	C₂×C₇×C₄⋊C₈	—	2	1	no	—
35	C₂×C₇×C₄⋊C₈	—	2	1	no	—
36	C₂×C₇×#104	C₂²	1	2	yes	—
37	C₇×#416	C₂²	1	2	yes	—
38	C₇×#408	C₂²	1	1	yes	characteristic
39	C₇×#407	C₂²	1	1	yes	characteristic
40	C₂×C₇×C₂²⋊C₈	C₂²	1	1	yes	characteristic
41	C₇×#405	C₂²	1	1	yes	characteristic
42	C₂×C₄×C₇×C₈	C₂²	1	2	yes	—
43	C₄×C₇×C₂²⋊C₄	C₂²	1	1	yes	characteristic
44	C₇×#341	C₂²	1	2	yes	—
45	C₇×#339	C₂²	1	2	yes	—
46	C₇×#339	C₂²	1	2	yes	—
47	C₇×#339	C₂²	1	2	yes	—
48	C₇×#336	C₂²	1	2	yes	—
49	#22095	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
50	C₂×C₇×#41	C₂³	1	1	yes	characteristic
51	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
52	C₇×#131	—	4	2	no	—
53	C₂×C₇×M₁₆	—	2	1	no	—
54	C₂×C₇×M₁₆	—	2	1	no	—
55	C₂×C₇×M₁₆	—	4	2	no	—
56	C₂×C₇×M₁₆	C₂³	1	1	yes	characteristic
57	C₂×C₇×M₁₆	C₂³	1	1	yes	characteristic
58	C₂×C₇×M₁₆	C₂³	1	2	yes	—
59	C₂²×C₇×C₈	—	2	1	no	—
60	C₂²×C₇×C₈	—	2	1	no	—
61	C₂²×C₇×C₈	—	4	2	no	—
62	C₂²×C₇×C₈	D₄	1	1	yes	characteristic
63	C₂²×C₇×C₈	D₄	1	1	yes	characteristic
64	C₂²×C₇×C₈	D₄	1	1	yes	characteristic
65	C₂²×C₇×C₈	D₄	1	1	yes	characteristic
66	C₂²×C₇×C₈	C₂³	1	2	yes	—
67	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
68	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
69	C₇×#123	—	2	1	no	—
70	C₇×C₂²⋊Q₈	C₂×C₄	1	1	yes	characteristic
71	C₇×C₂²⋊Q₈	C₂×C₄	1	1	yes	characteristic
72	C₇×#121	C₂×C₄	1	1	yes	characteristic
73	C₇×#121	C₂×C₄	1	1	yes	characteristic
74	C₇×#120	—	2	1	no	—
75	C₄×C₇×D₄	—	2	1	no	—
76	C₄×C₇×D₄	—	2	1	no	—
77	C₇×#117	—	2	1	no	—
78	C₇×#117	—	2	1	no	—
79	C₇×#117	C₂×C₄	1	2	yes	—
80	C₇×#117	C₂³	1	2	yes	—
81	C₇×#117	C₂³	1	1	yes	characteristic
82	C₂×C₇×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
83	C₂×C₇×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
84	C₂×C₇×C₂²⋊C₄	—	2	1	no	—
85	C₂×C₇×C₂²⋊C₄	—	2	1	no	—
86	C₂×C₄²×C₇	—	2	1	no	—
87	C₂×C₄²×C₇	C₂³	1	2	yes	—
88	C₇×#108	—	4	2	no	—
89	C₇×#107	C₂×C₄	1	2	yes	—
90	C₇×#107	C₂×C₄	1	2	yes	—
91	C₇×#106	C₂×C₄	1	2	yes	—
92	C₇×#106	C₂×C₄	1	2	yes	—
93	C₇×C₄⋊C₈	—	2	2	no	—
94	C₇×C₄⋊C₈	—	2	2	no	—
95	C₇×C₄⋊C₈	—	2	2	no	—
96	C₇×C₄⋊C₈	—	2	2	no	—
97	C₇×C₄⋊C₈	—	2	1	no	—
98	C₇×C₄⋊C₈	—	2	1	no	—
99	C₇×#104	—	4	2	no	—
100	C₇×#103	C₂×C₄	1	2	yes	—
101	C₇×#103	C₂×C₄	1	2	yes	—
102	C₇×#102	C₂×C₄	1	2	yes	—
103	C₇×#102	C₂×C₄	1	2	yes	—
104	C₇×C₂²⋊C₈	—	2	1	no	—
105	C₇×C₂²⋊C₈	—	2	1	no	—
106	C₇×C₂²⋊C₈	—	2	1	no	—
107	C₇×C₂²⋊C₈	—	2	1	no	—
108	C₇×C₂²⋊C₈	C₂×C₄	1	1	yes	characteristic
109	C₇×C₂²⋊C₈	C₂×C₄	1	1	yes	characteristic
110	C₇×C₂²⋊C₈	C₂×C₄	1	2	yes	—
111	C₇×#97	—	2	1	no	—
112	C₄×C₇×C₈	—	2	1	no	—
113	C₄×C₇×C₈	—	4	2	no	—
114	C₇×#95	—	2	1	no	—
115	#3091	C₂×C₇	1	1	yes	characteristic
116	#2929	C₂×C₇	1	1	yes	characteristic
117	C₂×#424	C₂×C₇	1	1	yes	characteristic, complemented
118	#1945	C₂×C₇	1	2	yes	complemented
119	#1937	C₂×C₇	1	2	yes	complemented
120	#1922	C₂×C₇	1	2	yes	complemented
121	#1871	C₂×C₇	1	1	yes	characteristic
122	#1866	C₂×C₇	1	2	yes	complemented
123	#1855	C₂×C₇	1	1	yes	characteristic, complemented
124	#1826	C₂×C₇	1	1	yes	characteristic, complemented
125	C₈×C₂²⋊C₄	C₂×C₇	1	1	yes	characteristic, complemented
126	C₂⁴×C₇	#41	1	1	yes	characteristic
127	C₇×#41	—	2	2	no	—
128	C₇×#41	—	2	2	no	—
129	C₂×C₇×Q₈	C₂²×C₄	1	1	yes	characteristic
130	C₂×C₇×D₄	—	2	1	no	—
131	C₂×C₇×D₄	—	2	1	no	—
132	C₂×C₇×D₄	—	2	1	no	—
133	C₂×C₇×D₄	C₂²×C₄	1	1	yes	characteristic
134	C₂²×C₄×C₇	—	2	2	no	—
135	C₂²×C₄×C₇	—	2	2	no	—
136	C₂²×C₄×C₇	—	2	1	no	—
137	C₂²×C₄×C₇	—	2	1	no	—
138	C₂²×C₄×C₇	—	2	2	no	—
139	C₂²×C₄×C₇	—	2	1	no	—
140	C₂²×C₄×C₇	C₂²×C₄	1	1	yes	characteristic
141	C₂²×C₄×C₇	C₂²×C₄	1	1	yes	characteristic
142	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
143	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
144	C₂²×C₄×C₇	#41	1	1	yes	characteristic
145	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
146	C₇×M₁₆	—	2	2	no	—
147	C₇×M₁₆	—	2	2	no	—
148	C₇×M₁₆	—	2	2	no	—
149	C₇×M₁₆	—	2	2	no	—
150	C₇×M₁₆	—	4	2	no	—
151	C₇×M₁₆	—	4	2	no	—
152	C₂×C₇×C₈	—	2	2	no	—
153	C₂×C₇×C₈	—	2	2	no	—
154	C₂×C₇×C₈	—	2	2	no	—
155	C₂×C₇×C₈	—	2	2	no	—
156	C₂×C₇×C₈	—	2	1	no	—
157	C₂×C₇×C₈	—	2	1	no	—
158	C₂×C₇×C₈	—	2	2	no	—
159	C₂×C₇×C₈	—	4	1	no	—
160	C₂×C₇×C₈	—	4	1	no	—
161	C₂×C₇×C₈	—	4	1	no	—
162	C₂×C₇×C₈	—	4	1	no	—
163	C₂×C₇×C₈	—	4	2	no	—
164	C₂×C₇×C₈	—	4	2	no	—
165	C₂×C₇×C₈	C₂²×C₄	1	2	yes	—
166	C₂×C₇×C₈	C₂²×C₄	1	2	yes	—
167	C₂×C₇×C₈	C₂×D₄	1	1	yes	characteristic
168	C₂×C₇×C₈	C₂×D₄	1	1	yes	characteristic
169	C₂×C₇×C₈	C₂×D₄	1	1	yes	characteristic
170	C₂×C₇×C₈	C₂×D₄	1	1	yes	characteristic
171	C₇×C₄⋊C₄	—	2	1	no	—
172	C₇×C₄⋊C₄	—	2	1	no	—
173	C₇×C₄⋊C₄	—	2	1	no	—
174	C₇×C₄⋊C₄	—	2	1	no	—
175	C₇×C₄⋊C₄	C₂²×C₄	1	2	yes	—
176	C₇×C₄⋊C₄	C₂²×C₄	1	2	yes	—
177	C₇×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
178	C₇×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
179	C₇×C₂²⋊C₄	—	2	4	no	—
180	C₇×C₂²⋊C₄	—	2	2	no	—
181	C₇×C₂²⋊C₄	—	2	1	no	—
182	C₇×C₂²⋊C₄	—	2	1	no	—
183	C₇×C₂²⋊C₄	—	2	2	no	—
184	C₇×C₂²⋊C₄	—	2	1	no	—
185	C₇×C₂²⋊C₄	—	2	1	no	—
186	C₇×C₂²⋊C₄	—	2	1	no	—
187	C₄²×C₇	—	2	2	no	—
188	C₄²×C₇	—	2	1	no	—
189	C₄²×C₇	—	2	2	no	—
190	C₄²×C₇	—	2	2	no	—
191	C₄²×C₇	—	2	2	no	—
192	C₂×#131	C₂²×C₇	1	1	yes	characteristic
193	C₂²×M₁₆	C₂²×C₇	1	1	yes	characteristic
194	C₂³×C₈	C₂²×C₇	1	1	yes	characteristic
195	#525	C₂²×C₇	1	1	yes	characteristic
196	C₂×#117	C₂²×C₇	1	1	yes	characteristic
197	#485	C₄×C₇	1	2	yes	complemented
198	#484	C₄×C₇	1	1	yes	characteristic, complemented
199	#483	C₄×C₇	1	1	yes	characteristic, complemented
200	#482	C₄×C₇	1	2	yes	complemented
201	#481	C₄×C₇	1	1	yes	characteristic, complemented
202	#480	C₄×C₇	1	1	yes	characteristic, complemented
203	#435	—	2	1	no	—
204	#435	—	2	1	no	—
205	C₈×D₄	—	2	1	no	—
206	C₈×D₄	—	2	1	no	—
207	C₂×#108	C₂²×C₇	1	2	yes	—
208	#427	C₂²×C₇	1	2	yes	—
209	#424	—	2	1	no	—
210	#424	—	2	1	no	—
211	#424	C₂²×C₇	1	2	yes	—
212	#424	C₂²×C₇	1	2	yes	—
213	#424	C₂²×C₇	1	1	yes	characteristic
214	C₂×C₄⋊C₈	—	2	1	no	—
215	C₂×C₄⋊C₈	—	2	1	no	—
216	C₂×#104	C₂²×C₇	1	2	yes	—
217	#416	C₂²×C₇	1	2	yes	—
218	#408	C₂²×C₇	1	1	yes	characteristic
219	#407	C₂²×C₇	1	1	yes	characteristic
220	C₂×C₂²⋊C₈	C₂²×C₇	1	1	yes	characteristic
221	#405	C₂²×C₇	1	1	yes	characteristic
222	C₂×C₄×C₈	C₂²×C₇	1	2	yes	—
223	C₄×C₂²⋊C₄	C₂²×C₇	1	1	yes	characteristic
224	#341	C₂²×C₇	1	2	yes	—
225	#339	C₂²×C₇	1	2	yes	—
226	#339	C₂²×C₇	1	2	yes	—
227	#339	C₂²×C₇	1	2	yes	—
228	#336	C₂²×C₇	1	2	yes	—
229	C₂³×C₇	—	2	2	no	—
230	C₂³×C₇	—	2	2	no	—
231	C₂³×C₇	—	2	1	no	—
232	C₂³×C₇	—	4	1	no	—
233	C₂³×C₇	C₄×D₄	1	1	yes	characteristic
234	C₂³×C₇	C₄×D₄	1	1	yes	characteristic
235	C₂³×C₇	C₂×#41	1	1	yes	characteristic
236	C₇×Q₈	—	2	2	no	—
237	C₇×D₄	—	2	2	no	—
238	C₇×D₄	—	4	2	no	—
239	C₇×D₄	—	4	2	no	—
240	C₇×D₄	—	4	2	no	—
241	C₂×C₄×C₇	—	2	2	no	—
242	C₂×C₄×C₇	—	2	2	no	—
243	C₂×C₄×C₇	—	2	2	no	—
244	C₂×C₄×C₇	—	2	1	no	—
245	C₂×C₄×C₇	—	2	1	no	—
246	C₂×C₄×C₇	—	2	1	no	—
247	C₂×C₄×C₇	—	2	1	no	—
248	C₂×C₄×C₇	—	2	4	no	—
249	C₂×C₄×C₇	—	2	2	no	—
250	C₂×C₄×C₇	—	2	2	no	—
251	C₂×C₄×C₇	—	2	1	no	—
252	C₂×C₄×C₇	—	2	1	no	—
253	C₂×C₄×C₇	—	2	1	no	—
254	C₂×C₄×C₇	—	4	2	no	—
255	C₂×C₄×C₇	—	4	2	no	—
256	C₂×C₄×C₇	—	4	2	no	—
257	C₂×C₄×C₇	—	4	2	no	—
258	C₂×C₄×C₇	—	4	1	no	—
259	C₂×C₄×C₇	—	4	1	no	—
260	C₂×C₄×C₇	C₄×D₄	1	1	yes	characteristic
261	C₂×C₄×C₇	C₄×D₄	1	1	yes	characteristic
262	C₂×C₄×C₇	C₂³×C₄	1	1	yes	characteristic
263	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
264	C₂×C₄×C₇	H(5,𝔽₂)	1	2	yes	—
265	C₂×C₄×C₇	2₋¹⁺⁴	1	2	yes	—
266	C₇×C₈	—	2	2	no	—
267	C₇×C₈	—	2	2	no	—
268	C₇×C₈	—	2	1	no	—
269	C₇×C₈	—	2	1	no	—
270	C₇×C₈	—	2	1	no	—
271	C₇×C₈	—	2	1	no	—
272	C₇×C₈	—	4	1	no	—
273	C₇×C₈	—	4	2	no	—
274	C₇×C₈	—	4	1	no	—
275	C₂×#41	C₂³×C₇	1	1	yes	characteristic
276	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
277	#131	—	4	2	no	—
278	C₂×M₁₆	—	2	1	no	—
279	C₂×M₁₆	—	2	1	no	—
280	C₂×M₁₆	—	4	2	no	—
281	C₂×M₁₆	C₂³×C₇	1	2	yes	—
282	C₂×M₁₆	C₂³×C₇	1	1	yes	characteristic
283	C₂×M₁₆	C₂³×C₇	1	1	yes	characteristic
284	C₂²×C₈	—	2	1	no	—
285	C₂²×C₈	—	2	1	no	—
286	C₂²×C₈	—	4	2	no	—
287	C₂²×C₈	C₇×D₄	1	1	yes	characteristic
288	C₂²×C₈	C₇×D₄	1	1	yes	characteristic
289	C₂²×C₈	C₇×D₄	1	1	yes	characteristic
290	C₂²×C₈	C₇×D₄	1	1	yes	characteristic
291	C₂²×C₈	C₂³×C₇	1	2	yes	—
292	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
293	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
294	#123	—	2	1	no	—
295	C₂²⋊Q₈	C₂×C₄×C₇	1	1	yes	characteristic
296	C₂²⋊Q₈	C₂×C₄×C₇	1	1	yes	characteristic
297	#121	C₂×C₄×C₇	1	1	yes	characteristic
298	#121	C₂×C₄×C₇	1	1	yes	characteristic
299	#120	—	2	1	no	—
300	C₄×D₄	—	2	1	no	—
301	C₄×D₄	—	2	1	no	—
302	#117	—	2	1	no	—
303	#117	—	2	1	no	—
304	#117	C₂×C₄×C₇	1	2	yes	—
305	#117	C₂³×C₇	1	2	yes	—
306	#117	C₂³×C₇	1	1	yes	characteristic
307	C₂×C₄⋊C₄	C₂×C₄×C₇	1	1	yes	characteristic
308	C₂×C₄⋊C₄	C₂×C₄×C₇	1	1	yes	characteristic
309	C₂×C₂²⋊C₄	—	2	1	no	—
310	C₂×C₂²⋊C₄	—	2	1	no	—
311	C₂×C₄²	—	2	1	no	—
312	C₂×C₄²	C₂³×C₇	1	2	yes	—
313	#108	—	4	2	no	—
314	#107	C₂×C₄×C₇	1	2	yes	—
315	#107	C₂×C₄×C₇	1	2	yes	—
316	#106	C₂×C₄×C₇	1	2	yes	—
317	#106	C₂×C₄×C₇	1	2	yes	—
318	C₄⋊C₈	—	2	2	no	—
319	C₄⋊C₈	—	2	2	no	—
320	C₄⋊C₈	—	2	2	no	—
321	C₄⋊C₈	—	2	2	no	—
322	C₄⋊C₈	—	2	1	no	—
323	C₄⋊C₈	—	2	1	no	—
324	#104	—	4	2	no	—
325	#103	C₂×C₄×C₇	1	2	yes	—
326	#103	C₂×C₄×C₇	1	2	yes	—
327	#102	C₂×C₄×C₇	1	2	yes	—
328	#102	C₂×C₄×C₇	1	2	yes	—
329	C₂²⋊C₈	—	2	1	no	—
330	C₂²⋊C₈	—	2	1	no	—
331	C₂²⋊C₈	—	2	1	no	—
332	C₂²⋊C₈	—	2	1	no	—
333	C₂²⋊C₈	C₂×C₄×C₇	1	1	yes	characteristic
334	C₂²⋊C₈	C₂×C₄×C₇	1	1	yes	characteristic
335	C₂²⋊C₈	C₂×C₄×C₇	1	2	yes	—
336	#97	—	2	1	no	—
337	C₄×C₈	—	2	1	no	—
338	C₄×C₈	—	4	2	no	—
339	#95	—	2	1	no	—
340	C₂²×C₇	—	2	1	no	—
341	C₂²×C₇	—	2	1	no	—
342	C₂²×C₇	—	2	1	no	—
343	C₂²×C₇	—	2	1	no	—
344	C₂²×C₇	—	2	1	no	—
345	C₂²×C₇	—	2	1	no	—
346	C₂²×C₇	—	2	1	no	—
347	C₂²×C₇	—	4	4	no	—
348	C₂²×C₇	—	4	1	no	—
349	C₂²×C₇	—	4	1	no	—
350	C₂²×C₇	—	4	1	no	—
351	C₂²×C₇	#443	1	2	yes	—
352	C₂²×C₇	C₂×C₄×D₄	1	1	yes	characteristic
353	C₂²×C₇	#539	1	2	yes	—
354	C₄×C₇	—	2	1	no	—
355	C₄×C₇	—	2	1	no	—
356	C₄×C₇	—	4	4	no	—
357	C₄×C₇	—	4	1	no	—
358	C₄×C₇	—	4	2	no	—
359	C₄×C₇	—	4	1	no	—
360	C₄×C₇	—	4	2	no	—
361	C₄×C₇	—	4	1	no	—
362	C₄×C₇	#520	1	2	yes	—
363	C₄×C₇	#534	1	1	yes	characteristic
364	C₄×C₇	#536	1	1	yes	characteristic
365	C₂⁴	C₇×#41	1	1	yes	characteristic
366	#41	—	2	2	no	—
367	#41	—	2	2	no	—
368	C₂×Q₈	C₂²×C₄×C₇	1	1	yes	characteristic
369	C₂×D₄	—	2	1	no	—
370	C₂×D₄	—	2	1	no	—
371	C₂×D₄	—	2	1	no	—
372	C₂×D₄	C₂²×C₄×C₇	1	1	yes	characteristic
373	C₂²×C₄	—	2	2	no	—
374	C₂²×C₄	—	2	2	no	—
375	C₂²×C₄	—	2	1	no	—
376	C₂²×C₄	—	2	1	no	—
377	C₂²×C₄	—	2	2	no	—
378	C₂²×C₄	—	2	1	no	—
379	C₂²×C₄	C₂²×C₄×C₇	1	1	yes	characteristic
380	C₂²×C₄	C₂²×C₄×C₇	1	1	yes	characteristic
381	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
382	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
383	C₂²×C₄	C₇×#41	1	1	yes	characteristic
384	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
385	M₁₆	—	2	2	no	—
386	M₁₆	—	2	2	no	—
387	M₁₆	—	2	2	no	—
388	M₁₆	—	2	2	no	—
389	M₁₆	—	4	2	no	—
390	M₁₆	—	4	2	no	—
391	C₂×C₈	—	2	2	no	—
392	C₂×C₈	—	2	2	no	—
393	C₂×C₈	—	2	2	no	—
394	C₂×C₈	—	2	2	no	—
395	C₂×C₈	—	2	1	no	—
396	C₂×C₈	—	2	1	no	—
397	C₂×C₈	—	2	2	no	—
398	C₂×C₈	—	4	1	no	—
399	C₂×C₈	—	4	1	no	—
400	C₂×C₈	—	4	1	no	—
401	C₂×C₈	—	4	1	no	—
402	C₂×C₈	—	4	2	no	—
403	C₂×C₈	—	4	2	no	—
404	C₂×C₈	C₂²×C₄×C₇	1	2	yes	—
405	C₂×C₈	C₂²×C₄×C₇	1	2	yes	—
406	C₂×C₈	C₂×C₇×D₄	1	1	yes	characteristic
407	C₂×C₈	C₂×C₇×D₄	1	1	yes	characteristic
408	C₂×C₈	C₂×C₇×D₄	1	1	yes	characteristic
409	C₂×C₈	C₂×C₇×D₄	1	1	yes	characteristic
410	C₄⋊C₄	—	2	1	no	—
411	C₄⋊C₄	—	2	1	no	—
412	C₄⋊C₄	—	2	1	no	—
413	C₄⋊C₄	—	2	1	no	—
414	C₄⋊C₄	C₂²×C₄×C₇	1	2	yes	—
415	C₄⋊C₄	C₂²×C₄×C₇	1	2	yes	—
416	C₄⋊C₄	C₂²×C₄×C₇	1	1	yes	characteristic
417	C₄⋊C₄	C₂²×C₄×C₇	1	1	yes	characteristic
418	C₂²⋊C₄	—	2	4	no	—
419	C₂²⋊C₄	—	2	2	no	—
420	C₂²⋊C₄	—	2	1	no	—
421	C₂²⋊C₄	—	2	1	no	—
422	C₂²⋊C₄	—	2	2	no	—
423	C₂²⋊C₄	—	2	1	no	—
424	C₂²⋊C₄	—	2	1	no	—
425	C₂²⋊C₄	—	2	1	no	—
426	C₄²	—	2	2	no	—
427	C₄²	—	2	1	no	—
428	C₄²	—	2	2	no	—
429	C₄²	—	2	2	no	—
430	C₄²	—	2	2	no	—
431	C₂×C₇	—	2	2	no	—
432	C₂×C₇	—	2	2	no	—
433	C₂×C₇	—	4	1	no	—
434	C₂×C₇	—	8	1	no	—
435	C₂×C₇	#2322	1	1	yes	characteristic
436	C₂×C₇	C₂×#443	1	1	yes	characteristic
437	C₂×C₇	#2955	1	1	yes	characteristic
438	C₂³	—	2	2	no	—
439	C₂³	—	2	2	no	—
440	C₂³	—	2	1	no	—
441	C₂³	—	4	1	no	—
442	C₂³	C₄×C₇×D₄	1	1	yes	characteristic
443	C₂³	C₄×C₇×D₄	1	1	yes	characteristic
444	C₂³	C₂×C₇×#41	1	1	yes	characteristic
445	Q₈	—	2	2	no	—
446	D₄	—	2	2	no	—
447	D₄	—	4	2	no	—
448	D₄	—	4	2	no	—
449	D₄	—	4	2	no	—
450	C₂×C₄	—	2	2	no	—
451	C₂×C₄	—	2	2	no	—
452	C₂×C₄	—	2	2	no	—
453	C₂×C₄	—	2	1	no	—
454	C₂×C₄	—	2	1	no	—
455	C₂×C₄	—	2	1	no	—
456	C₂×C₄	—	2	1	no	—
457	C₂×C₄	—	2	4	no	—
458	C₂×C₄	—	2	2	no	—
459	C₂×C₄	—	2	2	no	—
460	C₂×C₄	—	2	1	no	—
461	C₂×C₄	—	2	1	no	—
462	C₂×C₄	—	2	1	no	—
463	C₂×C₄	—	4	2	no	—
464	C₂×C₄	—	4	2	no	—
465	C₂×C₄	—	4	2	no	—
466	C₂×C₄	—	4	2	no	—
467	C₂×C₄	—	4	1	no	—
468	C₂×C₄	—	4	1	no	—
469	C₂×C₄	C₄×C₇×D₄	1	1	yes	characteristic
470	C₂×C₄	C₄×C₇×D₄	1	1	yes	characteristic
471	C₂×C₄	C₂³×C₄×C₇	1	1	yes	characteristic
472	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
473	C₂×C₄	C₇×H(5,𝔽₂)	1	2	yes	—
474	C₂×C₄	C₇×2₋¹⁺⁴	1	2	yes	—
475	C₈	—	2	2	no	—
476	C₈	—	2	2	no	—
477	C₈	—	2	1	no	—
478	C₈	—	2	1	no	—
479	C₈	—	2	1	no	—
480	C₈	—	2	1	no	—
481	C₈	—	4	1	no	—
482	C₈	—	4	2	no	—
483	C₈	—	4	1	no	—
484	C₇	#22095	1	1	yes	characteristic, direct product factor, Sylow
485	C₂²	—	2	1	no	—
486	C₂²	—	2	1	no	—
487	C₂²	—	2	1	no	—
488	C₂²	—	2	1	no	—
489	C₂²	—	2	1	no	—
490	C₂²	—	2	1	no	—
491	C₂²	—	2	1	no	—
492	C₂²	—	4	4	no	—
493	C₂²	—	4	1	no	—
494	C₂²	—	4	1	no	—
495	C₂²	—	4	1	no	—
496	C₂²	C₇×#443	1	2	yes	—
497	C₂²	C₂×C₄×C₇×D₄	1	1	yes	characteristic
498	C₂²	C₇×#539	1	2	yes	—
499	C₄	—	2	1	no	—
500	C₄	—	2	1	no	—
501	C₄	—	4	4	no	—
502	C₄	—	4	2	no	—
503	C₄	—	4	1	no	—
504	C₄	—	4	2	no	—
505	C₄	—	4	1	no	—
506	C₄	—	4	1	no	—
507	C₄	C₇×#520	1	2	yes	—
508	C₄	C₇×#534	1	1	yes	characteristic
509	C₄	C₇×#536	1	1	yes	characteristic
510	C₂	—	2	2	no	—
511	C₂	—	2	2	no	—
512	C₂	—	4	1	no	—
513	C₂	—	8	1	no	—
514	C₂	C₇×#2322	1	1	yes	characteristic
515	C₂	C₂×C₇×#443	1	1	yes	characteristic
516	C₂	C₇×#2955	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₇	C₂²×D₄
commutator	C₂×C₄	C₂³×C₄×C₇
Frattini, cosocle	C₂²×C₄	C₂⁴×C₇
socle	C₂²×C₇	C₂×C₄×D₄
prime radical	C₇×#525	C₂²
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₇ ◁ C₂³×C₇×C₈ ◁ G

Complements

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

N	H ≅ G/N	type
3. C₂×C₇×#424	C₂	semidirect
4. C₇×#1945	C₂	semidirect
5. C₇×#1937	C₂	semidirect
6. C₇×#1922	C₂	semidirect
8. C₇×#1866	C₂	semidirect
9. C₇×#1855	C₂	semidirect
10. C₇×#1826	C₂	semidirect
11. C₇×C₈×C₂²⋊C₄	C₂	semidirect
17. C₇×#485	C₄	semidirect
18. C₇×#484	C₄	semidirect
19. C₇×#483	C₄	semidirect
20. C₇×#482	C₄	semidirect
21. C₇×#481	C₄	semidirect
22. C₇×#480	C₄	semidirect
49. #22095	C₇	direct (N × H)
117. C₂×#424	C₂×C₇	semidirect
118. #1945	C₂×C₇	semidirect
119. #1937	C₂×C₇	semidirect
120. #1922	C₂×C₇	semidirect
122. #1866	C₂×C₇	semidirect
123. #1855	C₂×C₇	semidirect
124. #1826	C₂×C₇	semidirect
125. C₈×C₂²⋊C₄	C₂×C₇	semidirect
197. #485	C₄×C₇	semidirect
198. #484	C₄×C₇	semidirect
199. #483	C₄×C₇	semidirect
200. #482	C₄×C₇	semidirect
201. #481	C₄×C₇	semidirect
202. #480	C₄×C₇	semidirect
484. C₇	#22095	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×#3091	2
C₇×#2929	2
C₂×C₇×#424	2
C₇×#1945	2
C₇×#1937	2
C₇×#1922	2
C₇×#1871	2
C₇×#1866	2
C₇×#1855	2
C₇×#1826	2
C₇×C₈×C₂²⋊C₄	2
#22095	7

Subgroups — C7×#22095 #13199311

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×#22095 #13199311