Subgroups — C₇×#21900 #13199116

Order 1792.

1106 conjugacy classes of subgroups.

The subgroup lattice has 638 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×#3444	C₂	1	1	yes	maximal, characteristic
2	C₇×#2920	C₂	1	1	yes	maximal, characteristic, complemented
3	C₇×#2285	C₂	1	1	yes	maximal, characteristic, complemented
4	C₇×#1986	C₂	1	2	yes	maximal, complemented
5	C₇×#1980	C₂	1	2	yes	maximal, complemented
6	C₇×#1897	C₂	1	4	yes	maximal, complemented
7	C₇×#1806	C₂	1	4	yes	maximal, complemented
8	C₇×#533	C₄	1	1	yes	characteristic, complemented
9	C₇×#533	C₄	1	1	yes	characteristic, complemented
10	C₇×#533	C₂²	1	1	yes	characteristic
11	C₇×#532	C₄	1	1	yes	characteristic, complemented
12	C₇×#532	C₄	1	1	yes	characteristic, complemented
13	C₇×#532	C₂²	1	1	yes	characteristic
14	C₇×#529	—	2	1	no	—
15	C₇×#529	—	2	1	no	—
16	C₇×#529	—	2	1	no	—
17	C₇×#529	—	2	1	no	—
18	C₇×#529	C₄	1	2	yes	complemented
19	C₇×#529	C₄	1	2	yes	complemented
20	C₇×#525	—	2	1	no	—
21	C₇×#525	—	2	1	no	—
22	C₇×#525	C₂²	1	2	yes	—
23	C₄×C₇×#41	—	2	1	no	—
24	C₄×C₇×#41	—	2	1	no	—
25	C₄×C₇×#41	C₂²	1	2	yes	—
26	C₂×C₇×#117	C₂²	1	2	yes	—
27	C₂²×C₄²×C₇	C₂²	1	1	yes	characteristic
28	C₇×#432	—	2	1	no	—
29	C₇×#432	—	2	1	no	—
30	C₇×#431	—	2	1	no	—
31	C₇×#431	—	2	1	no	—
32	C₇×#423	C₂²	1	2	yes	—
33	C₂×C₇×#104	C₂²	1	8	yes	—
34	C₇×#407	C₂²	1	2	yes	—
35	C₄×C₇×M₁₆	C₂²	1	2	yes	—
36	C₇×#384	—	2	1	no	—
37	C₇×#382	—	2	1	no	—
38	C₇×#380	—	2	1	no	—
39	C₇×#380	—	2	1	no	—
40	C₄×C₇×C₄⋊C₄	C₂²	1	2	yes	—
41	C₄×C₇×C₄⋊C₄	C₂²	1	2	yes	—
42	C₇×#339	C₂²	1	8	yes	—
43	#21900	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
44	C₂×C₇×#41	—	2	1	no	—
45	C₂×C₇×#41	—	2	1	no	—
46	C₂×C₇×#41	C₂³	1	2	yes	—
47	C₂³×C₄×C₇	D₄	1	1	yes	characteristic
48	C₂³×C₄×C₇	D₄	1	1	yes	characteristic
49	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
50	C₂×C₇×M₁₆	C₂³	1	4	yes	—
51	C₇×C₄⋊Q₈	C₂×C₄	1	1	yes	characteristic
52	C₇×C₄⋊Q₈	C₂×C₄	1	1	yes	characteristic
53	C₇×C₄⋊Q₈	C₂×C₄	1	1	yes	characteristic
54	C₇×#127	C₂×C₄	1	1	yes	characteristic
55	C₇×#126	—	2	2	no	—
56	C₇×#126	—	2	2	no	—
57	C₇×#125	—	2	1	no	—
58	C₇×#125	—	2	1	no	—
59	C₇×#125	C₂×C₄	1	2	yes	—
60	C₇×#124	—	2	1	no	—
61	C₇×#124	—	2	1	no	—
62	C₇×#124	C₂×C₄	1	2	yes	—
63	C₇×#123	—	2	2	no	—
64	C₇×#123	—	2	2	no	—
65	C₇×#123	—	2	2	no	—
66	C₇×C₂²⋊Q₈	—	2	1	no	—
67	C₇×C₂²⋊Q₈	—	2	1	no	—
68	C₇×C₂²⋊Q₈	—	2	1	no	—
69	C₇×C₂²⋊Q₈	—	2	1	no	—
70	C₇×C₂²⋊Q₈	C₂×C₄	1	2	yes	—
71	C₇×C₂²⋊Q₈	C₂×C₄	1	2	yes	—
72	C₇×#121	—	2	1	no	—
73	C₇×#121	—	2	1	no	—
74	C₇×#121	—	2	1	no	—
75	C₇×#121	—	2	1	no	—
76	C₇×#121	C₂×C₄	1	2	yes	—
77	C₇×#121	C₂×C₄	1	2	yes	—
78	C₇×#120	—	2	2	no	—
79	C₄×C₇×Q₈	—	2	1	no	—
80	C₄×C₇×Q₈	—	2	1	no	—
81	C₄×C₇×Q₈	—	2	1	no	—
82	C₄×C₇×Q₈	—	2	1	no	—
83	C₄×C₇×Q₈	C₂×C₄	1	2	yes	—
84	C₄×C₇×Q₈	C₂×C₄	1	2	yes	—
85	C₄×C₇×D₄	—	2	2	no	—
86	C₄×C₇×D₄	—	2	2	no	—
87	C₄×C₇×D₄	—	2	2	no	—
88	C₄×C₇×D₄	—	2	2	no	—
89	C₄×C₇×D₄	—	2	2	no	—
90	C₄×C₇×D₄	—	2	2	no	—
91	C₄×C₇×D₄	—	2	1	no	—
92	C₄×C₇×D₄	—	2	1	no	—
93	C₄×C₇×D₄	—	2	1	no	—
94	C₄×C₇×D₄	—	2	1	no	—
95	C₄×C₇×D₄	C₂×C₄	1	2	yes	—
96	C₄×C₇×D₄	C₂×C₄	1	2	yes	—
97	C₇×#117	—	2	1	no	—
98	C₇×#117	—	2	1	no	—
99	C₇×#117	—	2	2	no	—
100	C₇×#117	—	2	2	no	—
101	C₇×#117	—	2	2	no	—
102	C₇×#117	—	4	4	no	—
103	C₇×#117	C₂³	1	2	yes	—
104	C₂×C₇×C₄⋊C₄	—	2	2	no	—
105	C₂×C₇×C₄⋊C₄	—	2	2	no	—
106	C₂×C₇×C₄⋊C₄	—	2	2	no	—
107	C₂×C₇×C₂²⋊C₄	—	2	2	no	—
108	C₂×C₄²×C₇	—	2	2	no	—
109	C₂×C₄²×C₇	C₂×C₄	1	1	yes	characteristic
110	C₂×C₄²×C₇	C₂×C₄	1	1	yes	characteristic
111	C₂×C₄²×C₇	C₂×C₄	1	1	yes	characteristic
112	C₂×C₄²×C₇	C₂×C₄	1	1	yes	characteristic
113	C₂×C₄²×C₇	D₄	1	1	yes	characteristic
114	C₂×C₄²×C₇	D₄	1	1	yes	characteristic
115	C₂×C₄²×C₇	D₄	1	1	yes	characteristic
116	C₂×C₄²×C₇	D₄	1	1	yes	characteristic
117	C₂×C₄²×C₇	D₄	1	1	yes	characteristic
118	C₂×C₄²×C₇	D₄	1	1	yes	characteristic
119	C₂×C₄²×C₇	C₂³	1	4	yes	—
120	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
121	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
122	C₇×C₄⋊C₈	—	2	2	no	—
123	C₇×C₄⋊C₈	—	2	2	no	—
124	C₇×#104	—	4	8	no	—
125	C₇×C₂²⋊C₈	—	2	2	no	—
126	C₇×C₂²⋊C₈	—	2	2	no	—
127	C₇×#97	—	2	2	no	—
128	C₄×C₇×C₈	—	2	2	no	—
129	C₇×#95	—	2	2	no	—
130	C₇×#95	—	2	2	no	—
131	#3444	C₂×C₇	1	1	yes	characteristic
132	#2920	C₂×C₇	1	1	yes	characteristic, complemented
133	#2285	C₂×C₇	1	1	yes	characteristic, complemented
134	#1986	C₂×C₇	1	2	yes	complemented
135	#1980	C₂×C₇	1	2	yes	complemented
136	#1897	C₂×C₇	1	4	yes	complemented
137	#1806	C₂×C₇	1	4	yes	complemented
138	C₂⁴×C₇	C₂×D₄	1	1	yes	characteristic
139	C₇×#41	—	2	4	no	—
140	C₇×#41	—	2	4	no	—
141	C₇×#41	—	4	4	no	—
142	C₇×#41	—	4	4	no	—
143	C₂×C₇×Q₈	—	2	1	no	—
144	C₂×C₇×Q₈	—	2	1	no	—
145	C₂×C₇×Q₈	C₂²×C₄	1	2	yes	—
146	C₂×C₇×D₄	—	2	2	no	—
147	C₂×C₇×D₄	—	2	2	no	—
148	C₂×C₇×D₄	—	2	2	no	—
149	C₂×C₇×D₄	—	2	1	no	—
150	C₂×C₇×D₄	—	2	1	no	—
151	C₂×C₇×D₄	C₂²×C₄	1	2	yes	—
152	C₂²×C₄×C₇	—	2	2	no	—
153	C₂²×C₄×C₇	—	2	2	no	—
154	C₂²×C₄×C₇	—	2	2	no	—
155	C₂²×C₄×C₇	—	2	2	no	—
156	C₂²×C₄×C₇	—	2	2	no	—
157	C₂²×C₄×C₇	—	2	4	no	—
158	C₂²×C₄×C₇	—	4	2	no	—
159	C₂²×C₄×C₇	—	4	2	no	—
160	C₂²×C₄×C₇	C₂²⋊C₄	1	1	yes	characteristic
161	C₂²×C₄×C₇	C₂²⋊C₄	1	1	yes	characteristic
162	C₂²×C₄×C₇	C₂²⋊C₄	1	1	yes	characteristic
163	C₂²×C₄×C₇	C₂²⋊C₄	1	1	yes	characteristic
164	C₂²×C₄×C₇	C₂²⋊C₄	1	1	yes	characteristic
165	C₂²×C₄×C₇	C₂²⋊C₄	1	1	yes	characteristic
166	C₂²×C₄×C₇	C₂²⋊C₄	1	1	yes	characteristic
167	C₂²×C₄×C₇	C₂²⋊C₄	1	1	yes	characteristic
168	C₂²×C₄×C₇	C₂²×C₄	1	1	yes	characteristic
169	C₂²×C₄×C₇	C₂²×C₄	1	1	yes	characteristic
170	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
171	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
172	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
173	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
174	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
175	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
176	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
177	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
178	C₇×M₁₆	—	2	4	no	—
179	C₇×M₁₆	—	2	4	no	—
180	C₂×C₇×C₈	—	2	4	no	—
181	C₇×C₄⋊C₄	—	2	1	no	—
182	C₇×C₄⋊C₄	—	2	1	no	—
183	C₇×C₄⋊C₄	—	2	1	no	—
184	C₇×C₄⋊C₄	—	2	1	no	—
185	C₇×C₄⋊C₄	—	2	2	no	—
186	C₇×C₄⋊C₄	—	2	2	no	—
187	C₇×C₄⋊C₄	—	2	2	no	—
188	C₇×C₄⋊C₄	—	2	2	no	—
189	C₇×C₄⋊C₄	—	2	2	no	—
190	C₇×C₄⋊C₄	—	2	2	no	—
191	C₇×C₄⋊C₄	—	4	4	no	—
192	C₇×C₄⋊C₄	—	4	4	no	—
193	C₇×C₄⋊C₄	—	4	4	no	—
194	C₇×C₄⋊C₄	C₂²×C₄	1	2	yes	—
195	C₇×C₄⋊C₄	C₂²×C₄	1	2	yes	—
196	C₇×C₂²⋊C₄	—	2	2	no	—
197	C₇×C₂²⋊C₄	—	2	2	no	—
198	C₇×C₂²⋊C₄	—	2	2	no	—
199	C₇×C₂²⋊C₄	—	2	2	no	—
200	C₇×C₂²⋊C₄	—	2	2	no	—
201	C₇×C₂²⋊C₄	—	2	2	no	—
202	C₇×C₂²⋊C₄	—	2	2	no	—
203	C₇×C₂²⋊C₄	—	2	2	no	—
204	C₇×C₂²⋊C₄	—	2	2	no	—
205	C₇×C₂²⋊C₄	—	4	4	no	—
206	C₄²×C₇	—	2	2	no	—
207	C₄²×C₇	—	2	2	no	—
208	C₄²×C₇	—	2	2	no	—
209	C₄²×C₇	—	2	8	no	—
210	C₄²×C₇	C₂²⋊C₄	1	1	yes	characteristic
211	C₄²×C₇	C₂²⋊C₄	1	1	yes	characteristic
212	C₄²×C₇	C₂²⋊C₄	1	1	yes	characteristic
213	C₄²×C₇	C₂²⋊C₄	1	1	yes	characteristic
214	C₄²×C₇	C₂²⋊C₄	1	1	yes	characteristic
215	C₄²×C₇	C₂²⋊C₄	1	1	yes	characteristic
216	C₄²×C₇	C₂²⋊C₄	1	1	yes	characteristic
217	C₄²×C₇	C₂²⋊C₄	1	1	yes	characteristic
218	C₄²×C₇	C₂²×C₄	1	1	yes	characteristic
219	C₄²×C₇	C₂²×C₄	1	1	yes	characteristic
220	C₄²×C₇	C₂²×C₄	1	1	yes	characteristic
221	C₄²×C₇	C₂²×C₄	1	1	yes	characteristic
222	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
223	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
224	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
225	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
226	#533	C₄×C₇	1	1	yes	characteristic, complemented
227	#533	C₄×C₇	1	1	yes	characteristic, complemented
228	#533	C₂²×C₇	1	1	yes	characteristic
229	#532	C₄×C₇	1	1	yes	characteristic, complemented
230	#532	C₄×C₇	1	1	yes	characteristic, complemented
231	#532	C₂²×C₇	1	1	yes	characteristic
232	#529	—	2	1	no	—
233	#529	—	2	1	no	—
234	#529	—	2	1	no	—
235	#529	—	2	1	no	—
236	#529	C₄×C₇	1	2	yes	complemented
237	#529	C₄×C₇	1	2	yes	complemented
238	#525	—	2	1	no	—
239	#525	—	2	1	no	—
240	#525	C₂²×C₇	1	2	yes	—
241	C₄×#41	—	2	1	no	—
242	C₄×#41	—	2	1	no	—
243	C₄×#41	C₂²×C₇	1	2	yes	—
244	C₂×#117	C₂²×C₇	1	2	yes	—
245	C₂²×C₄²	C₂²×C₇	1	1	yes	characteristic
246	#432	—	2	1	no	—
247	#432	—	2	1	no	—
248	#431	—	2	1	no	—
249	#431	—	2	1	no	—
250	#423	C₂²×C₇	1	2	yes	—
251	C₂×#104	C₂²×C₇	1	8	yes	—
252	#407	C₂²×C₇	1	2	yes	—
253	C₄×M₁₆	C₂²×C₇	1	2	yes	—
254	#384	—	2	1	no	—
255	#382	—	2	1	no	—
256	#380	—	2	1	no	—
257	#380	—	2	1	no	—
258	C₄×C₄⋊C₄	C₂²×C₇	1	2	yes	—
259	C₄×C₄⋊C₄	C₂²×C₇	1	2	yes	—
260	#339	C₂²×C₇	1	8	yes	—
261	C₂³×C₇	—	2	1	no	—
262	C₂³×C₇	—	2	1	no	—
263	C₂³×C₇	—	2	2	no	—
264	C₂³×C₇	—	4	1	no	—
265	C₂³×C₇	—	4	1	no	—
266	C₂³×C₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
267	C₂³×C₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
268	C₂³×C₇	C₂²×D₄	1	1	yes	characteristic
269	C₇×Q₈	—	2	4	no	—
270	C₇×Q₈	—	4	2	no	—
271	C₇×Q₈	—	4	2	no	—
272	C₇×D₄	—	2	4	no	—
273	C₇×D₄	—	4	2	no	—
274	C₇×D₄	—	4	4	no	—
275	C₇×D₄	—	4	4	no	—
276	C₇×D₄	—	4	2	no	—
277	C₇×D₄	—	4	2	no	—
278	C₇×D₄	—	4	2	no	—
279	C₂×C₄×C₇	—	2	1	no	—
280	C₂×C₄×C₇	—	2	1	no	—
281	C₂×C₄×C₇	—	2	2	no	—
282	C₂×C₄×C₇	—	2	2	no	—
283	C₂×C₄×C₇	—	2	2	no	—
284	C₂×C₄×C₇	—	2	2	no	—
285	C₂×C₄×C₇	—	2	2	no	—
286	C₂×C₄×C₇	—	2	2	no	—
287	C₂×C₄×C₇	—	2	2	no	—
288	C₂×C₄×C₇	—	2	2	no	—
289	C₂×C₄×C₇	—	2	2	no	—
290	C₂×C₄×C₇	—	2	2	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	—	4	1	no	—
295	C₂×C₄×C₇	—	4	1	no	—
296	C₂×C₄×C₇	—	4	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	—	4	4	no	—
301	C₂×C₄×C₇	—	4	4	no	—
302	C₂×C₄×C₇	—	4	4	no	—
303	C₂×C₄×C₇	—	4	4	no	—
304	C₂×C₄×C₇	—	4	4	no	—
305	C₂×C₄×C₇	—	4	4	no	—
306	C₂×C₄×C₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
307	C₂×C₄×C₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
308	C₂×C₄×C₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
309	C₂×C₄×C₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
310	C₂×C₄×C₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
311	C₂×C₄×C₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
312	C₂×C₄×C₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
313	C₂×C₄×C₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
314	C₂×C₄×C₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
315	C₂×C₄×C₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
316	C₂×C₄×C₇	C₂³×C₄	1	1	yes	characteristic
317	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
318	C₂×C₄×C₇	H(5,𝔽₂)	1	2	yes	—
319	C₂×C₄×C₇	2₋¹⁺⁴	1	2	yes	—
320	C₇×C₈	—	4	4	no	—
321	C₂×#41	—	2	1	no	—
322	C₂×#41	—	2	1	no	—
323	C₂×#41	C₂³×C₇	1	2	yes	—
324	C₂³×C₄	C₇×D₄	1	1	yes	characteristic
325	C₂³×C₄	C₇×D₄	1	1	yes	characteristic
326	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
327	C₂×M₁₆	C₂³×C₇	1	4	yes	—
328	C₄⋊Q₈	C₂×C₄×C₇	1	1	yes	characteristic
329	C₄⋊Q₈	C₂×C₄×C₇	1	1	yes	characteristic
330	C₄⋊Q₈	C₂×C₄×C₇	1	1	yes	characteristic
331	#127	C₂×C₄×C₇	1	1	yes	characteristic
332	#126	—	2	2	no	—
333	#126	—	2	2	no	—
334	#125	—	2	1	no	—
335	#125	—	2	1	no	—
336	#125	C₂×C₄×C₇	1	2	yes	—
337	#124	—	2	1	no	—
338	#124	—	2	1	no	—
339	#124	C₂×C₄×C₇	1	2	yes	—
340	#123	—	2	2	no	—
341	#123	—	2	2	no	—
342	#123	—	2	2	no	—
343	C₂²⋊Q₈	—	2	1	no	—
344	C₂²⋊Q₈	—	2	1	no	—
345	C₂²⋊Q₈	—	2	1	no	—
346	C₂²⋊Q₈	—	2	1	no	—
347	C₂²⋊Q₈	C₂×C₄×C₇	1	2	yes	—
348	C₂²⋊Q₈	C₂×C₄×C₇	1	2	yes	—
349	#121	—	2	1	no	—
350	#121	—	2	1	no	—
351	#121	—	2	1	no	—
352	#121	—	2	1	no	—
353	#121	C₂×C₄×C₇	1	2	yes	—
354	#121	C₂×C₄×C₇	1	2	yes	—
355	#120	—	2	2	no	—
356	C₄×Q₈	—	2	1	no	—
357	C₄×Q₈	—	2	1	no	—
358	C₄×Q₈	—	2	1	no	—
359	C₄×Q₈	—	2	1	no	—
360	C₄×Q₈	C₂×C₄×C₇	1	2	yes	—
361	C₄×Q₈	C₂×C₄×C₇	1	2	yes	—
362	C₄×D₄	—	2	2	no	—
363	C₄×D₄	—	2	2	no	—
364	C₄×D₄	—	2	2	no	—
365	C₄×D₄	—	2	2	no	—
366	C₄×D₄	—	2	2	no	—
367	C₄×D₄	—	2	2	no	—
368	C₄×D₄	—	2	1	no	—
369	C₄×D₄	—	2	1	no	—
370	C₄×D₄	—	2	1	no	—
371	C₄×D₄	—	2	1	no	—
372	C₄×D₄	C₂×C₄×C₇	1	2	yes	—
373	C₄×D₄	C₂×C₄×C₇	1	2	yes	—
374	#117	—	2	1	no	—
375	#117	—	2	1	no	—
376	#117	—	2	2	no	—
377	#117	—	2	2	no	—
378	#117	—	2	2	no	—
379	#117	—	4	4	no	—
380	#117	C₂³×C₇	1	2	yes	—
381	C₂×C₄⋊C₄	—	2	2	no	—
382	C₂×C₄⋊C₄	—	2	2	no	—
383	C₂×C₄⋊C₄	—	2	2	no	—
384	C₂×C₂²⋊C₄	—	2	2	no	—
385	C₂×C₄²	—	2	2	no	—
386	C₂×C₄²	C₂×C₄×C₇	1	1	yes	characteristic
387	C₂×C₄²	C₂×C₄×C₇	1	1	yes	characteristic
388	C₂×C₄²	C₂×C₄×C₇	1	1	yes	characteristic
389	C₂×C₄²	C₂×C₄×C₇	1	1	yes	characteristic
390	C₂×C₄²	C₇×D₄	1	1	yes	characteristic
391	C₂×C₄²	C₇×D₄	1	1	yes	characteristic
392	C₂×C₄²	C₇×D₄	1	1	yes	characteristic
393	C₂×C₄²	C₇×D₄	1	1	yes	characteristic
394	C₂×C₄²	C₇×D₄	1	1	yes	characteristic
395	C₂×C₄²	C₇×D₄	1	1	yes	characteristic
396	C₂×C₄²	C₂³×C₇	1	4	yes	—
397	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
398	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
399	C₄⋊C₈	—	2	2	no	—
400	C₄⋊C₈	—	2	2	no	—
401	#104	—	4	8	no	—
402	C₂²⋊C₈	—	2	2	no	—
403	C₂²⋊C₈	—	2	2	no	—
404	#97	—	2	2	no	—
405	C₄×C₈	—	2	2	no	—
406	#95	—	2	2	no	—
407	#95	—	2	2	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	1	no	—
416	C₂²×C₇	—	4	2	no	—
417	C₂²×C₇	—	4	2	no	—
418	C₂²×C₇	—	4	2	no	—
419	C₂²×C₇	—	4	2	no	—
420	C₂²×C₇	—	4	2	no	—
421	C₂²×C₇	C₂²×C₂²⋊C₄	1	1	yes	characteristic
422	C₂²×C₇	#535	1	1	yes	characteristic
423	C₂²×C₇	#536	1	1	yes	characteristic
424	C₄×C₇	—	2	1	no	—
425	C₄×C₇	—	2	1	no	—
426	C₄×C₇	—	2	1	no	—
427	C₄×C₇	—	2	1	no	—
428	C₄×C₇	—	2	1	no	—
429	C₄×C₇	—	2	1	no	—
430	C₄×C₇	—	2	1	no	—
431	C₄×C₇	—	2	1	no	—
432	C₄×C₇	—	4	2	no	—
433	C₄×C₇	—	4	2	no	—
434	C₄×C₇	—	4	2	no	—
435	C₄×C₇	—	8	4	no	—
436	C₄×C₇	#421	1	2	yes	—
437	C₄×C₇	#421	1	2	yes	—
438	C₄×C₇	#520	1	2	yes	—
439	C₄×C₇	#537	1	2	yes	—
440	C₂⁴	C₂×C₇×D₄	1	1	yes	characteristic
441	#41	—	2	4	no	—
442	#41	—	2	4	no	—
443	#41	—	4	4	no	—
444	#41	—	4	4	no	—
445	C₂×Q₈	—	2	1	no	—
446	C₂×Q₈	—	2	1	no	—
447	C₂×Q₈	C₂²×C₄×C₇	1	2	yes	—
448	C₂×D₄	—	2	2	no	—
449	C₂×D₄	—	2	2	no	—
450	C₂×D₄	—	2	2	no	—
451	C₂×D₄	—	2	1	no	—
452	C₂×D₄	—	2	1	no	—
453	C₂×D₄	C₂²×C₄×C₇	1	2	yes	—
454	C₂²×C₄	—	2	2	no	—
455	C₂²×C₄	—	2	2	no	—
456	C₂²×C₄	—	2	2	no	—
457	C₂²×C₄	—	2	2	no	—
458	C₂²×C₄	—	2	2	no	—
459	C₂²×C₄	—	2	4	no	—
460	C₂²×C₄	—	4	2	no	—
461	C₂²×C₄	—	4	2	no	—
462	C₂²×C₄	C₇×C₂²⋊C₄	1	1	yes	characteristic
463	C₂²×C₄	C₇×C₂²⋊C₄	1	1	yes	characteristic
464	C₂²×C₄	C₇×C₂²⋊C₄	1	1	yes	characteristic
465	C₂²×C₄	C₇×C₂²⋊C₄	1	1	yes	characteristic
466	C₂²×C₄	C₇×C₂²⋊C₄	1	1	yes	characteristic
467	C₂²×C₄	C₇×C₂²⋊C₄	1	1	yes	characteristic
468	C₂²×C₄	C₇×C₂²⋊C₄	1	1	yes	characteristic
469	C₂²×C₄	C₇×C₂²⋊C₄	1	1	yes	characteristic
470	C₂²×C₄	C₂²×C₄×C₇	1	1	yes	characteristic
471	C₂²×C₄	C₂²×C₄×C₇	1	1	yes	characteristic
472	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
473	C₂²×C₄	C₂×C₇×D₄	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	C₂×C₇×D₄	1	1	yes	characteristic
477	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
478	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
479	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
480	M₁₆	—	2	4	no	—
481	M₁₆	—	2	4	no	—
482	C₂×C₈	—	2	4	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	2	no	—
488	C₄⋊C₄	—	2	2	no	—
489	C₄⋊C₄	—	2	2	no	—
490	C₄⋊C₄	—	2	2	no	—
491	C₄⋊C₄	—	2	2	no	—
492	C₄⋊C₄	—	2	2	no	—
493	C₄⋊C₄	—	4	4	no	—
494	C₄⋊C₄	—	4	4	no	—
495	C₄⋊C₄	—	4	4	no	—
496	C₄⋊C₄	C₂²×C₄×C₇	1	2	yes	—
497	C₄⋊C₄	C₂²×C₄×C₇	1	2	yes	—
498	C₂²⋊C₄	—	2	2	no	—
499	C₂²⋊C₄	—	2	2	no	—
500	C₂²⋊C₄	—	2	2	no	—
501	C₂²⋊C₄	—	2	2	no	—
502	C₂²⋊C₄	—	2	2	no	—
503	C₂²⋊C₄	—	2	2	no	—
504	C₂²⋊C₄	—	2	2	no	—
505	C₂²⋊C₄	—	2	2	no	—
506	C₂²⋊C₄	—	2	2	no	—
507	C₂²⋊C₄	—	4	4	no	—
508	C₄²	—	2	2	no	—
509	C₄²	—	2	2	no	—
510	C₄²	—	2	2	no	—
511	C₄²	—	2	8	no	—
512	C₄²	C₇×C₂²⋊C₄	1	1	yes	characteristic
513	C₄²	C₇×C₂²⋊C₄	1	1	yes	characteristic
514	C₄²	C₇×C₂²⋊C₄	1	1	yes	characteristic
515	C₄²	C₇×C₂²⋊C₄	1	1	yes	characteristic
516	C₄²	C₇×C₂²⋊C₄	1	1	yes	characteristic
517	C₄²	C₇×C₂²⋊C₄	1	1	yes	characteristic
518	C₄²	C₇×C₂²⋊C₄	1	1	yes	characteristic
519	C₄²	C₇×C₂²⋊C₄	1	1	yes	characteristic
520	C₄²	C₂²×C₄×C₇	1	1	yes	characteristic
521	C₄²	C₂²×C₄×C₇	1	1	yes	characteristic
522	C₄²	C₂²×C₄×C₇	1	1	yes	characteristic
523	C₄²	C₂²×C₄×C₇	1	1	yes	characteristic
524	C₄²	C₂×C₇×D₄	1	1	yes	characteristic
525	C₄²	C₂×C₇×D₄	1	1	yes	characteristic
526	C₄²	C₂×C₇×D₄	1	1	yes	characteristic
527	C₄²	C₂×C₇×D₄	1	1	yes	characteristic
528	C₂×C₇	—	2	1	no	—
529	C₂×C₇	—	2	1	no	—
530	C₂×C₇	—	4	1	no	—
531	C₂×C₇	—	4	1	no	—
532	C₂×C₇	—	8	2	no	—
533	C₂×C₇	#2311	1	1	yes	characteristic
534	C₂×C₇	C₂×#421	1	1	yes	characteristic
535	C₂×C₇	C₂×#421	1	1	yes	characteristic
536	C₂³	—	2	1	no	—
537	C₂³	—	2	1	no	—
538	C₂³	—	2	2	no	—
539	C₂³	—	4	1	no	—
540	C₂³	—	4	1	no	—
541	C₂³	C₂×C₇×C₂²⋊C₄	1	1	yes	characteristic
542	C₂³	C₂×C₇×C₂²⋊C₄	1	1	yes	characteristic
543	C₂³	C₂²×C₇×D₄	1	1	yes	characteristic
544	Q₈	—	2	4	no	—
545	Q₈	—	4	2	no	—
546	Q₈	—	4	2	no	—
547	D₄	—	2	4	no	—
548	D₄	—	4	2	no	—
549	D₄	—	4	4	no	—
550	D₄	—	4	4	no	—
551	D₄	—	4	2	no	—
552	D₄	—	4	2	no	—
553	D₄	—	4	2	no	—
554	C₂×C₄	—	2	1	no	—
555	C₂×C₄	—	2	1	no	—
556	C₂×C₄	—	2	2	no	—
557	C₂×C₄	—	2	2	no	—
558	C₂×C₄	—	2	2	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	2	no	—
564	C₂×C₄	—	2	2	no	—
565	C₂×C₄	—	2	2	no	—
566	C₂×C₄	—	2	2	no	—
567	C₂×C₄	—	2	2	no	—
568	C₂×C₄	—	2	2	no	—
569	C₂×C₄	—	4	1	no	—
570	C₂×C₄	—	4	1	no	—
571	C₂×C₄	—	4	1	no	—
572	C₂×C₄	—	4	1	no	—
573	C₂×C₄	—	4	1	no	—
574	C₂×C₄	—	4	1	no	—
575	C₂×C₄	—	4	4	no	—
576	C₂×C₄	—	4	4	no	—
577	C₂×C₄	—	4	4	no	—
578	C₂×C₄	—	4	4	no	—
579	C₂×C₄	—	4	4	no	—
580	C₂×C₄	—	4	4	no	—
581	C₂×C₄	C₂×C₇×C₂²⋊C₄	1	1	yes	characteristic
582	C₂×C₄	C₂×C₇×C₂²⋊C₄	1	1	yes	characteristic
583	C₂×C₄	C₂×C₇×C₂²⋊C₄	1	1	yes	characteristic
584	C₂×C₄	C₂×C₇×C₂²⋊C₄	1	1	yes	characteristic
585	C₂×C₄	C₂×C₇×C₂²⋊C₄	1	1	yes	characteristic
586	C₂×C₄	C₂×C₇×C₂²⋊C₄	1	1	yes	characteristic
587	C₂×C₄	C₂×C₇×C₂²⋊C₄	1	1	yes	characteristic
588	C₂×C₄	C₂×C₇×C₂²⋊C₄	1	1	yes	characteristic
589	C₂×C₄	C₂×C₇×C₂²⋊C₄	1	1	yes	characteristic
590	C₂×C₄	C₂×C₇×C₂²⋊C₄	1	1	yes	characteristic
591	C₂×C₄	C₂³×C₄×C₇	1	1	yes	characteristic
592	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
593	C₂×C₄	C₇×H(5,𝔽₂)	1	2	yes	—
594	C₂×C₄	C₇×2₋¹⁺⁴	1	2	yes	—
595	C₈	—	4	4	no	—
596	C₇	#21900	1	1	yes	characteristic, direct product factor, Sylow
597	C₂²	—	2	1	no	—
598	C₂²	—	2	1	no	—
599	C₂²	—	2	1	no	—
600	C₂²	—	2	1	no	—
601	C₂²	—	2	1	no	—
602	C₂²	—	2	1	no	—
603	C₂²	—	2	1	no	—
604	C₂²	—	2	1	no	—
605	C₂²	—	4	2	no	—
606	C₂²	—	4	2	no	—
607	C₂²	—	4	2	no	—
608	C₂²	—	4	2	no	—
609	C₂²	—	4	2	no	—
610	C₂²	C₂²×C₇×C₂²⋊C₄	1	1	yes	characteristic
611	C₂²	C₇×#535	1	1	yes	characteristic
612	C₂²	C₇×#536	1	1	yes	characteristic
613	C₄	—	2	1	no	—
614	C₄	—	2	1	no	—
615	C₄	—	2	1	no	—
616	C₄	—	2	1	no	—
617	C₄	—	2	1	no	—
618	C₄	—	2	1	no	—
619	C₄	—	2	1	no	—
620	C₄	—	2	1	no	—
621	C₄	—	4	2	no	—
622	C₄	—	4	2	no	—
623	C₄	—	4	2	no	—
624	C₄	—	8	4	no	—
625	C₄	C₇×#421	1	2	yes	—
626	C₄	C₇×#421	1	2	yes	—
627	C₄	C₇×#520	1	2	yes	—
628	C₄	C₇×#537	1	2	yes	—
629	C₂	—	2	1	no	—
630	C₂	—	2	1	no	—
631	C₂	—	4	1	no	—
632	C₂	—	4	1	no	—
633	C₂	—	8	2	no	—
634	C₂	C₇×#2311	1	1	yes	characteristic
635	C₂	C₂×C₇×#421	1	1	yes	characteristic
636	C₂	C₂×C₇×#421	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	C₂²×C₂²⋊C₄
prime radical	C₇×#3444	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₇ ◁ C₂²×C₄²×C₇ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₇×#2920	C₂	semidirect
3. C₇×#2285	C₂	semidirect
4. C₇×#1986	C₂	semidirect
5. C₇×#1980	C₂	semidirect
6. C₇×#1897	C₂	semidirect
7. C₇×#1806	C₂	semidirect
8. C₇×#533	C₄	semidirect
9. C₇×#533	C₄	semidirect
11. C₇×#532	C₄	semidirect
12. C₇×#532	C₄	semidirect
18. C₇×#529	C₄	semidirect
19. C₇×#529	C₄	semidirect
43. #21900	C₇	direct (N × H)
132. #2920	C₂×C₇	semidirect
133. #2285	C₂×C₇	semidirect
134. #1986	C₂×C₇	semidirect
135. #1980	C₂×C₇	semidirect
136. #1897	C₂×C₇	semidirect
137. #1806	C₂×C₇	semidirect
226. #533	C₄×C₇	semidirect
227. #533	C₄×C₇	semidirect
229. #532	C₄×C₇	semidirect
230. #532	C₄×C₇	semidirect
236. #529	C₄×C₇	semidirect
237. #529	C₄×C₇	semidirect
596. C₇	#21900	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×#3444	2
C₇×#2920	2
C₇×#2285	2
C₇×#1986	2
C₇×#1980	2
C₇×#1897	2
C₇×#1806	2
#21900	7

Subgroups — C7×#21900 #13199116

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×#21900 #13199116