Subgroups — C₇×#22551 #13199767

Order 1792.

1058 conjugacy classes of subgroups.

The subgroup lattice has 692 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×#3480	C₂	1	1	yes	maximal, characteristic
2	C₇×Q₈×M₁₆	C₂	1	1	yes	maximal, characteristic, complemented
3	C₇×#2295	C₂	1	1	yes	maximal, characteristic, complemented
4	C₇×#1980	C₂	1	2	yes	maximal, complemented
5	C₇×#1980	C₂	1	1	yes	maximal, characteristic, complemented
6	C₇×#1963	C₂	1	2	yes	maximal, complemented
7	C₇×#1962	C₂	1	1	yes	maximal, characteristic, complemented
8	C₇×#1806	C₂	1	2	yes	maximal, complemented
9	C₇×#1806	C₂	1	1	yes	maximal, characteristic, complemented
10	C₇×#1759	C₂	1	2	yes	maximal, complemented
11	C₄×C₇×#104	C₂	1	1	yes	maximal, characteristic, complemented
12	C₇×#559	C₄	1	2	yes	complemented
13	C₇×#559	C₄	1	1	yes	characteristic, complemented
14	C₇×#557	C₄	1	1	yes	characteristic, complemented
15	C₇×#556	C₄	1	1	yes	characteristic, complemented
16	C₇×#556	C₄	1	2	yes	complemented
17	C₇×#553	—	2	2	no	—
18	C₇×#553	—	2	1	no	—
19	C₇×#550	C₄	1	1	yes	characteristic, complemented
20	C₇×#548	—	2	1	no	—
21	C₇×#532	C₂²	1	2	yes	—
22	C₇×#532	C₂²	1	1	yes	characteristic
23	C₇×#529	—	2	1	no	—
24	C₇×#529	—	2	2	no	—
25	C₄×C₇×#41	—	2	1	no	—
26	C₄×C₇×#41	C₂²	1	1	yes	characteristic
27	C₄×C₇×#41	C₂²	1	2	yes	—
28	C₂×C₄×C₇×Q₈	C₂²	1	1	yes	characteristic
29	C₇×#446	—	2	1	no	—
30	C₇×#446	—	2	2	no	—
31	C₇×C₈×Q₈	—	2	1	no	—
32	C₇×#423	C₂²	1	2	yes	—
33	C₇×#423	C₂²	1	1	yes	characteristic
34	C₂×C₇×#104	C₂²	1	1	yes	characteristic
35	C₂×C₇×#104	C₂²	1	2	yes	—
36	C₂×C₇×#104	C₂²	1	1	yes	characteristic
37	C₂×C₇×#104	C₂²	1	2	yes	—
38	C₂×C₇×#104	C₂²	1	2	yes	—
39	C₂×C₇×#104	C₂²	1	2	yes	—
40	C₂×C₇×#104	C₂²	1	2	yes	—
41	C₄×C₇×M₁₆	C₂²	1	1	yes	characteristic
42	C₄×C₇×M₁₆	C₂²	1	2	yes	—
43	C₇×#391	—	2	1	no	—
44	C₇×#389	—	2	1	no	—
45	C₇×#387	—	2	2	no	—
46	C₄×C₇×C₄⋊C₄	C₂²	1	1	yes	characteristic
47	C₄×C₇×C₄⋊C₄	C₂²	1	2	yes	—
48	C₇×#376	C₂²	1	2	yes	—
49	C₄³×C₇	C₂²	1	1	yes	characteristic
50	C₇×#339	C₂²	1	1	yes	characteristic
51	C₇×#339	C₂²	1	1	yes	characteristic
52	C₇×#339	C₂²	1	2	yes	—
53	#22551	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
54	C₂×C₇×#41	—	2	1	no	—
55	C₂×C₇×#41	C₂³	1	1	yes	characteristic
56	C₂×C₇×#41	C₂³	1	2	yes	—
57	C₂²×C₇×Q₈	D₄	1	1	yes	characteristic
58	C₂×C₇×M₁₆	C₂³	1	1	yes	characteristic
59	C₂×C₇×M₁₆	C₂³	1	2	yes	—
60	C₂×C₇×M₁₆	C₂³	1	1	yes	characteristic
61	C₇×C₄⋊Q₈	C₂×C₄	1	2	yes	—
62	C₇×C₄⋊Q₈	C₂×C₄	1	1	yes	characteristic
63	C₇×#127	C₂×C₄	1	2	yes	—
64	C₇×#127	C₂×C₄	1	1	yes	characteristic
65	C₇×#126	—	2	2	no	—
66	C₇×#126	—	2	2	no	—
67	C₇×#126	—	2	2	no	—
68	C₇×#125	—	2	2	no	—
69	C₇×#125	—	2	1	no	—
70	C₇×#124	—	2	1	no	—
71	C₇×#124	—	2	2	no	—
72	C₇×#124	C₂×C₄	1	2	yes	—
73	C₇×#124	C₂×C₄	1	2	yes	—
74	C₇×#124	C₂×C₄	1	2	yes	—
75	C₇×#123	—	2	2	no	—
76	C₇×#123	—	2	2	no	—
77	C₇×#123	—	2	2	no	—
78	C₇×C₂²⋊Q₈	—	2	1	no	—
79	C₇×C₂²⋊Q₈	—	2	2	no	—
80	C₇×#121	—	2	1	no	—
81	C₇×#121	—	2	2	no	—
82	C₇×#121	—	2	1	no	—
83	C₇×#121	—	2	2	no	—
84	C₇×#121	—	2	2	no	—
85	C₇×#121	—	2	1	no	—
86	C₄×C₇×Q₈	—	2	1	no	—
87	C₄×C₇×Q₈	C₂×C₄	1	1	yes	characteristic
88	C₄×C₇×Q₈	C₂×C₄	1	2	yes	—
89	C₄×C₇×Q₈	C₂×C₄	1	1	yes	characteristic
90	C₄×C₇×Q₈	C₂×C₄	1	2	yes	—
91	C₄×C₇×Q₈	C₂×C₄	1	1	yes	characteristic
92	C₄×C₇×Q₈	C₂×C₄	1	1	yes	characteristic
93	C₄×C₇×Q₈	C₂×C₄	1	2	yes	—
94	C₄×C₇×Q₈	D₄	1	1	yes	characteristic
95	C₄×C₇×Q₈	D₄	1	1	yes	characteristic
96	C₄×C₇×Q₈	D₄	1	2	yes	—
97	C₄×C₇×D₄	—	2	1	no	—
98	C₄×C₇×D₄	—	2	2	no	—
99	C₄×C₇×D₄	—	2	1	no	—
100	C₄×C₇×D₄	—	2	2	no	—
101	C₄×C₇×D₄	—	2	2	no	—
102	C₄×C₇×D₄	—	2	1	no	—
103	C₄×C₇×D₄	—	2	1	no	—
104	C₄×C₇×D₄	—	2	2	no	—
105	C₄×C₇×D₄	—	2	2	no	—
106	C₄×C₇×D₄	—	2	1	no	—
107	C₄×C₇×D₄	C₂×C₄	1	1	yes	characteristic
108	C₄×C₇×D₄	C₂×C₄	1	2	yes	—
109	C₄×C₇×D₄	C₂×C₄	1	1	yes	characteristic
110	C₄×C₇×D₄	C₂×C₄	1	2	yes	—
111	C₇×#117	—	2	2	no	—
112	C₇×#117	—	2	1	no	—
113	C₇×#117	—	2	2	no	—
114	C₇×#117	—	2	1	no	—
115	C₇×#117	C₂³	1	1	yes	characteristic
116	C₂×C₇×C₄⋊C₄	—	2	2	no	—
117	C₂×C₇×C₄⋊C₄	—	2	1	no	—
118	C₂×C₇×C₄⋊C₄	D₄	1	2	yes	—
119	C₂×C₇×C₄⋊C₄	D₄	1	1	yes	characteristic
120	C₂×C₄²×C₇	—	2	1	no	—
121	C₂×C₄²×C₇	—	2	2	no	—
122	C₂×C₄²×C₇	—	2	1	no	—
123	C₂×C₄²×C₇	—	2	1	no	—
124	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
125	C₂×C₄²×C₇	C₂³	1	2	yes	—
126	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
127	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
128	C₂×C₄²×C₇	C₂³	1	2	yes	—
129	C₇×C₄⋊C₈	—	2	1	no	—
130	C₇×C₄⋊C₈	—	2	2	no	—
131	C₇×C₄⋊C₈	—	2	2	no	—
132	C₇×C₄⋊C₈	—	2	1	no	—
133	C₇×#104	—	2	2	no	—
134	C₇×#104	—	2	4	no	—
135	C₇×#104	—	2	2	no	—
136	C₇×#104	—	2	4	no	—
137	C₇×#104	—	4	2	no	—
138	C₇×#104	—	4	2	no	—
139	C₇×#104	—	4	2	no	—
140	C₇×#97	—	2	2	no	—
141	C₇×#97	—	2	1	no	—
142	C₄×C₇×C₈	—	2	1	no	—
143	C₄×C₇×C₈	—	2	2	no	—
144	C₇×#95	—	2	2	no	—
145	C₇×#95	—	2	2	no	—
146	C₇×#95	—	2	1	no	—
147	C₇×#95	—	2	2	no	—
148	#3480	C₂×C₇	1	1	yes	characteristic
149	Q₈×M₁₆	C₂×C₇	1	1	yes	characteristic, complemented
150	#2295	C₂×C₇	1	1	yes	characteristic, complemented
151	#1980	C₂×C₇	1	1	yes	characteristic, complemented
152	#1980	C₂×C₇	1	2	yes	complemented
153	#1963	C₂×C₇	1	2	yes	complemented
154	#1962	C₂×C₇	1	1	yes	characteristic, complemented
155	#1806	C₂×C₇	1	1	yes	characteristic, complemented
156	#1806	C₂×C₇	1	2	yes	complemented
157	#1759	C₂×C₇	1	2	yes	complemented
158	C₄×#104	C₂×C₇	1	1	yes	characteristic, complemented
159	C₇×#41	—	2	1	no	—
160	C₇×#41	—	2	2	no	—
161	C₇×#41	—	2	1	no	—
162	C₇×#41	—	2	2	no	—
163	C₇×#41	—	2	1	no	—
164	C₇×#41	—	2	2	no	—
165	C₇×#41	—	2	1	no	—
166	C₇×#41	—	2	2	no	—
167	C₇×#41	—	4	4	no	—
168	C₂×C₇×Q₈	—	4	2	no	—
169	C₂×C₇×Q₈	C₂²⋊C₄	1	1	yes	characteristic
170	C₂×C₇×Q₈	C₂²⋊C₄	1	1	yes	characteristic
171	C₂×C₇×Q₈	C₂²⋊C₄	1	2	yes	—
172	C₂×C₇×Q₈	C₂²×C₄	1	1	yes	characteristic
173	C₂×C₇×Q₈	C₂²×C₄	1	2	yes	—
174	C₂×C₇×D₄	—	2	1	no	—
175	C₂×C₇×D₄	—	2	2	no	—
176	C₂×C₇×D₄	—	2	2	no	—
177	C₂×C₇×D₄	—	2	1	no	—
178	C₂×C₇×D₄	—	2	2	no	—
179	C₂×C₇×D₄	—	2	1	no	—
180	C₂×C₇×D₄	C₂²×C₄	1	1	yes	characteristic
181	C₂×C₇×D₄	C₂²×C₄	1	2	yes	—
182	C₂²×C₄×C₇	—	2	1	no	—
183	C₂²×C₄×C₇	—	2	1	no	—
184	C₂²×C₄×C₇	—	2	2	no	—
185	C₂²×C₄×C₇	—	2	1	no	—
186	C₂²×C₄×C₇	—	2	1	no	—
187	C₂²×C₄×C₇	—	2	2	no	—
188	C₂²×C₄×C₇	—	2	1	no	—
189	C₂²×C₄×C₇	—	2	2	no	—
190	C₂²×C₄×C₇	—	2	2	no	—
191	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
192	C₂²×C₄×C₇	C₂×D₄	1	2	yes	—
193	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
194	C₂²×C₄×C₇	C₂×D₄	1	2	yes	—
195	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
196	C₇×M₁₆	—	2	1	no	—
197	C₇×M₁₆	—	2	1	no	—
198	C₇×M₁₆	—	2	2	no	—
199	C₇×M₁₆	—	2	1	no	—
200	C₇×M₁₆	—	2	2	no	—
201	C₇×M₁₆	#41	1	2	yes	complemented
202	C₂×C₇×C₈	—	2	1	no	—
203	C₂×C₇×C₈	—	2	1	no	—
204	C₂×C₇×C₈	—	2	2	no	—
205	C₇×C₄⋊C₄	—	2	2	no	—
206	C₇×C₄⋊C₄	—	2	1	no	—
207	C₇×C₄⋊C₄	—	2	1	no	—
208	C₇×C₄⋊C₄	—	2	2	no	—
209	C₇×C₄⋊C₄	—	2	2	no	—
210	C₇×C₄⋊C₄	—	2	1	no	—
211	C₇×C₄⋊C₄	—	2	2	no	—
212	C₇×C₄⋊C₄	—	2	1	no	—
213	C₇×C₄⋊C₄	—	4	2	no	—
214	C₇×C₄⋊C₄	—	4	4	no	—
215	C₇×C₄⋊C₄	C₂²⋊C₄	1	2	yes	—
216	C₇×C₄⋊C₄	C₂²⋊C₄	1	1	yes	characteristic
217	C₇×C₄⋊C₄	C₂²⋊C₄	1	2	yes	—
218	C₇×C₄⋊C₄	C₂²⋊C₄	1	1	yes	characteristic
219	C₇×C₄⋊C₄	C₂²⋊C₄	1	2	yes	—
220	C₇×C₄⋊C₄	C₂²⋊C₄	1	2	yes	—
221	C₇×C₄⋊C₄	C₂²⋊C₄	1	2	yes	—
222	C₇×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
223	C₇×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
224	C₇×C₂²⋊C₄	—	2	1	no	—
225	C₇×C₂²⋊C₄	—	2	2	no	—
226	C₇×C₂²⋊C₄	—	2	2	no	—
227	C₇×C₂²⋊C₄	—	2	2	no	—
228	C₇×C₂²⋊C₄	—	2	2	no	—
229	C₇×C₂²⋊C₄	—	2	1	no	—
230	C₇×C₂²⋊C₄	—	2	1	no	—
231	C₇×C₂²⋊C₄	—	2	2	no	—
232	C₇×C₂²⋊C₄	—	2	2	no	—
233	C₇×C₂²⋊C₄	—	2	2	no	—
234	C₇×C₂²⋊C₄	—	2	2	no	—
235	C₄²×C₇	—	2	1	no	—
236	C₄²×C₇	—	2	2	no	—
237	C₄²×C₇	—	2	2	no	—
238	C₄²×C₇	—	2	1	no	—
239	C₄²×C₇	—	2	1	no	—
240	C₄²×C₇	—	2	1	no	—
241	C₄²×C₇	—	2	1	no	—
242	C₄²×C₇	—	2	2	no	—
243	C₄²×C₇	—	2	1	no	—
244	C₄²×C₇	—	2	2	no	—
245	C₄²×C₇	—	4	2	no	—
246	C₄²×C₇	—	4	2	no	—
247	C₄²×C₇	C₂²×C₄	1	1	yes	characteristic
248	C₄²×C₇	C₂²×C₄	1	2	yes	—
249	C₄²×C₇	C₂²×C₄	1	2	yes	—
250	C₄²×C₇	C₂²×C₄	1	1	yes	characteristic
251	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
252	C₄²×C₇	C₂×D₄	1	2	yes	—
253	C₄²×C₇	C₂×D₄	1	2	yes	—
254	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
255	C₄²×C₇	#41	1	2	yes	complemented
256	#559	C₄×C₇	1	2	yes	complemented
257	#559	C₄×C₇	1	1	yes	characteristic, complemented
258	#557	C₄×C₇	1	1	yes	characteristic, complemented
259	#556	C₄×C₇	1	1	yes	characteristic, complemented
260	#556	C₄×C₇	1	2	yes	complemented
261	#553	—	2	2	no	—
262	#553	—	2	1	no	—
263	#550	C₄×C₇	1	1	yes	characteristic, complemented
264	#548	—	2	1	no	—
265	#532	C₂²×C₇	1	1	yes	characteristic
266	#532	C₂²×C₇	1	2	yes	—
267	#529	—	2	1	no	—
268	#529	—	2	2	no	—
269	C₄×#41	—	2	1	no	—
270	C₄×#41	C₂²×C₇	1	1	yes	characteristic
271	C₄×#41	C₂²×C₇	1	2	yes	—
272	C₂×C₄×Q₈	C₂²×C₇	1	1	yes	characteristic
273	#446	—	2	1	no	—
274	#446	—	2	2	no	—
275	C₈×Q₈	—	2	1	no	—
276	#423	C₂²×C₇	1	1	yes	characteristic
277	#423	C₂²×C₇	1	2	yes	—
278	C₂×#104	C₂²×C₇	1	2	yes	—
279	C₂×#104	C₂²×C₇	1	1	yes	characteristic
280	C₂×#104	C₂²×C₇	1	1	yes	characteristic
281	C₂×#104	C₂²×C₇	1	2	yes	—
282	C₂×#104	C₂²×C₇	1	2	yes	—
283	C₂×#104	C₂²×C₇	1	2	yes	—
284	C₂×#104	C₂²×C₇	1	2	yes	—
285	C₄×M₁₆	C₂²×C₇	1	1	yes	characteristic
286	C₄×M₁₆	C₂²×C₇	1	2	yes	—
287	#391	—	2	1	no	—
288	#389	—	2	1	no	—
289	#387	—	2	2	no	—
290	C₄×C₄⋊C₄	C₂²×C₇	1	1	yes	characteristic
291	C₄×C₄⋊C₄	C₂²×C₇	1	2	yes	—
292	#376	C₂²×C₇	1	2	yes	—
293	C₄³	C₂²×C₇	1	1	yes	characteristic
294	#339	C₂²×C₇	1	1	yes	characteristic
295	#339	C₂²×C₇	1	2	yes	—
296	#339	C₂²×C₇	1	1	yes	characteristic
297	C₂³×C₇	—	2	2	no	—
298	C₂³×C₇	—	2	1	no	—
299	C₂³×C₇	C₂²×D₄	1	1	yes	characteristic
300	C₇×Q₈	—	2	2	no	—
301	C₇×Q₈	—	2	2	no	—
302	C₇×Q₈	—	2	1	no	—
303	C₇×Q₈	—	2	2	no	—
304	C₇×Q₈	—	2	1	no	—
305	C₇×Q₈	—	2	2	no	—
306	C₇×Q₈	—	4	2	no	—
307	C₇×D₄	—	2	1	no	—
308	C₇×D₄	—	2	2	no	—
309	C₇×D₄	—	2	1	no	—
310	C₇×D₄	—	2	2	no	—
311	C₇×D₄	—	4	4	no	—
312	C₇×D₄	—	4	1	no	—
313	C₇×D₄	—	4	2	no	—
314	C₇×D₄	—	4	1	no	—
315	C₇×D₄	—	4	2	no	—
316	C₇×D₄	—	4	2	no	—
317	C₇×D₄	—	8	1	no	—
318	C₇×D₄	—	8	2	no	—
319	C₂×C₄×C₇	—	2	2	no	—
320	C₂×C₄×C₇	—	2	2	no	—
321	C₂×C₄×C₇	—	2	1	no	—
322	C₂×C₄×C₇	—	2	1	no	—
323	C₂×C₄×C₇	—	2	2	no	—
324	C₂×C₄×C₇	—	2	1	no	—
325	C₂×C₄×C₇	—	2	2	no	—
326	C₂×C₄×C₇	—	4	1	no	—
327	C₂×C₄×C₇	—	4	2	no	—
328	C₂×C₄×C₇	—	4	2	no	—
329	C₂×C₄×C₇	—	4	4	no	—
330	C₂×C₄×C₇	—	4	1	no	—
331	C₂×C₄×C₇	—	4	1	no	—
332	C₂×C₄×C₇	—	4	1	no	—
333	C₂×C₄×C₇	—	4	1	no	—
334	C₂×C₄×C₇	—	4	1	no	—
335	C₂×C₄×C₇	—	4	2	no	—
336	C₂×C₄×C₇	—	4	1	no	—
337	C₂×C₄×C₇	—	4	2	no	—
338	C₂×C₄×C₇	—	4	2	no	—
339	C₂×C₄×C₇	—	4	2	no	—
340	C₂×C₄×C₇	—	4	2	no	—
341	C₂×C₄×C₇	—	4	2	no	—
342	C₂×C₄×C₇	—	8	1	no	—
343	C₂×C₄×C₇	—	8	2	no	—
344	C₂×C₄×C₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
345	C₂×C₄×C₇	C₂×C₂²⋊C₄	1	2	yes	—
346	C₂×C₄×C₇	C₂×C₂²⋊C₄	1	2	yes	—
347	C₂×C₄×C₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
348	C₂×C₄×C₇	C₂×C₂²⋊C₄	1	2	yes	—
349	C₂×C₄×C₇	C₂×C₂²⋊C₄	1	2	yes	—
350	C₂×C₄×C₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
351	C₂×C₄×C₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
352	C₂×C₄×C₇	C₂³×C₄	1	1	yes	characteristic
353	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
354	C₂×C₄×C₇	C₂×#41	1	1	yes	characteristic
355	C₂×C₄×C₇	C₂×#41	1	1	yes	characteristic
356	C₂×C₄×C₇	H(5,𝔽₂)	1	1	yes	characteristic
357	C₂×C₄×C₇	2₋¹⁺⁴	1	1	yes	characteristic
358	C₇×C₈	—	2	2	no	—
359	C₇×C₈	—	4	1	no	—
360	C₇×C₈	—	4	2	no	—
361	C₂×#41	—	2	1	no	—
362	C₂×#41	C₂³×C₇	1	1	yes	characteristic
363	C₂×#41	C₂³×C₇	1	2	yes	—
364	C₂²×Q₈	C₇×D₄	1	1	yes	characteristic
365	C₂×M₁₆	C₂³×C₇	1	1	yes	characteristic
366	C₂×M₁₆	C₂³×C₇	1	2	yes	—
367	C₂×M₁₆	C₂³×C₇	1	1	yes	characteristic
368	C₄⋊Q₈	C₂×C₄×C₇	1	1	yes	characteristic
369	C₄⋊Q₈	C₂×C₄×C₇	1	2	yes	—
370	#127	C₂×C₄×C₇	1	1	yes	characteristic
371	#127	C₂×C₄×C₇	1	2	yes	—
372	#126	—	2	2	no	—
373	#126	—	2	2	no	—
374	#126	—	2	2	no	—
375	#125	—	2	2	no	—
376	#125	—	2	1	no	—
377	#124	—	2	1	no	—
378	#124	—	2	2	no	—
379	#124	C₂×C₄×C₇	1	2	yes	—
380	#124	C₂×C₄×C₇	1	2	yes	—
381	#124	C₂×C₄×C₇	1	2	yes	—
382	#123	—	2	2	no	—
383	#123	—	2	2	no	—
384	#123	—	2	2	no	—
385	C₂²⋊Q₈	—	2	1	no	—
386	C₂²⋊Q₈	—	2	2	no	—
387	#121	—	2	1	no	—
388	#121	—	2	2	no	—
389	#121	—	2	1	no	—
390	#121	—	2	2	no	—
391	#121	—	2	2	no	—
392	#121	—	2	1	no	—
393	C₄×Q₈	—	2	1	no	—
394	C₄×Q₈	C₂×C₄×C₇	1	1	yes	characteristic
395	C₄×Q₈	C₂×C₄×C₇	1	2	yes	—
396	C₄×Q₈	C₂×C₄×C₇	1	1	yes	characteristic
397	C₄×Q₈	C₂×C₄×C₇	1	2	yes	—
398	C₄×Q₈	C₂×C₄×C₇	1	1	yes	characteristic
399	C₄×Q₈	C₂×C₄×C₇	1	1	yes	characteristic
400	C₄×Q₈	C₂×C₄×C₇	1	2	yes	—
401	C₄×Q₈	C₇×D₄	1	1	yes	characteristic
402	C₄×Q₈	C₇×D₄	1	1	yes	characteristic
403	C₄×Q₈	C₇×D₄	1	2	yes	—
404	C₄×D₄	—	2	1	no	—
405	C₄×D₄	—	2	2	no	—
406	C₄×D₄	—	2	1	no	—
407	C₄×D₄	—	2	2	no	—
408	C₄×D₄	—	2	2	no	—
409	C₄×D₄	—	2	1	no	—
410	C₄×D₄	—	2	1	no	—
411	C₄×D₄	—	2	2	no	—
412	C₄×D₄	—	2	2	no	—
413	C₄×D₄	—	2	1	no	—
414	C₄×D₄	C₂×C₄×C₇	1	1	yes	characteristic
415	C₄×D₄	C₂×C₄×C₇	1	2	yes	—
416	C₄×D₄	C₂×C₄×C₇	1	1	yes	characteristic
417	C₄×D₄	C₂×C₄×C₇	1	2	yes	—
418	#117	—	2	2	no	—
419	#117	—	2	1	no	—
420	#117	—	2	2	no	—
421	#117	—	2	1	no	—
422	#117	C₂³×C₇	1	1	yes	characteristic
423	C₂×C₄⋊C₄	—	2	2	no	—
424	C₂×C₄⋊C₄	—	2	1	no	—
425	C₂×C₄⋊C₄	C₇×D₄	1	2	yes	—
426	C₂×C₄⋊C₄	C₇×D₄	1	1	yes	characteristic
427	C₂×C₄²	—	2	1	no	—
428	C₂×C₄²	—	2	2	no	—
429	C₂×C₄²	—	2	1	no	—
430	C₂×C₄²	—	2	1	no	—
431	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
432	C₂×C₄²	C₂³×C₇	1	2	yes	—
433	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
434	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
435	C₂×C₄²	C₂³×C₇	1	2	yes	—
436	C₄⋊C₈	—	2	1	no	—
437	C₄⋊C₈	—	2	2	no	—
438	C₄⋊C₈	—	2	2	no	—
439	C₄⋊C₈	—	2	1	no	—
440	#104	—	2	2	no	—
441	#104	—	2	4	no	—
442	#104	—	2	4	no	—
443	#104	—	2	2	no	—
444	#104	—	4	2	no	—
445	#104	—	4	2	no	—
446	#104	—	4	2	no	—
447	#97	—	2	2	no	—
448	#97	—	2	1	no	—
449	C₄×C₈	—	2	1	no	—
450	C₄×C₈	—	2	2	no	—
451	#95	—	2	2	no	—
452	#95	—	2	2	no	—
453	#95	—	2	1	no	—
454	#95	—	2	2	no	—
455	C₂²×C₇	—	2	1	no	—
456	C₂²×C₇	—	2	1	no	—
457	C₂²×C₇	—	4	2	no	—
458	C₂²×C₇	—	4	1	no	—
459	C₂²×C₇	—	4	2	no	—
460	C₂²×C₇	—	4	1	no	—
461	C₂²×C₇	—	4	2	no	—
462	C₂²×C₇	—	4	1	no	—
463	C₂²×C₇	C₂²×C₂²⋊C₄	1	1	yes	characteristic
464	C₂²×C₇	#548	1	1	yes	characteristic
465	C₂²×C₇	#550	1	1	yes	characteristic
466	C₄×C₇	—	2	1	no	—
467	C₄×C₇	—	2	2	no	—
468	C₄×C₇	—	2	2	no	—
469	C₄×C₇	—	2	1	no	—
470	C₄×C₇	—	2	2	no	—
471	C₄×C₇	—	2	1	no	—
472	C₄×C₇	—	2	2	no	—
473	C₄×C₇	—	4	2	no	—
474	C₄×C₇	—	4	2	no	—
475	C₄×C₇	—	4	2	no	—
476	C₄×C₇	—	4	1	no	—
477	C₄×C₇	—	4	1	no	—
478	C₄×C₇	—	4	1	no	—
479	C₄×C₇	—	8	2	no	—
480	C₄×C₇	#421	1	2	yes	—
481	C₄×C₇	C₄×#41	1	1	yes	characteristic
482	C₄×C₇	#520	1	1	yes	characteristic
483	C₄×C₇	#548	1	1	yes	characteristic
484	C₄×C₇	#550	1	1	yes	characteristic
485	#41	—	2	1	no	—
486	#41	—	2	2	no	—
487	#41	—	2	2	no	—
488	#41	—	2	1	no	—
489	#41	—	2	2	no	—
490	#41	—	2	1	no	—
491	#41	—	2	1	no	—
492	#41	—	2	2	no	—
493	#41	—	4	4	no	—
494	C₂×Q₈	—	4	2	no	—
495	C₂×Q₈	C₇×C₂²⋊C₄	1	1	yes	characteristic
496	C₂×Q₈	C₇×C₂²⋊C₄	1	1	yes	characteristic
497	C₂×Q₈	C₇×C₂²⋊C₄	1	2	yes	—
498	C₂×Q₈	C₂²×C₄×C₇	1	1	yes	characteristic
499	C₂×Q₈	C₂²×C₄×C₇	1	2	yes	—
500	C₂×D₄	—	2	1	no	—
501	C₂×D₄	—	2	2	no	—
502	C₂×D₄	—	2	2	no	—
503	C₂×D₄	—	2	1	no	—
504	C₂×D₄	—	2	2	no	—
505	C₂×D₄	—	2	1	no	—
506	C₂×D₄	C₂²×C₄×C₇	1	1	yes	characteristic
507	C₂×D₄	C₂²×C₄×C₇	1	2	yes	—
508	C₂²×C₄	—	2	1	no	—
509	C₂²×C₄	—	2	1	no	—
510	C₂²×C₄	—	2	2	no	—
511	C₂²×C₄	—	2	1	no	—
512	C₂²×C₄	—	2	1	no	—
513	C₂²×C₄	—	2	2	no	—
514	C₂²×C₄	—	2	1	no	—
515	C₂²×C₄	—	2	2	no	—
516	C₂²×C₄	—	2	2	no	—
517	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
518	C₂²×C₄	C₂×C₇×D₄	1	2	yes	—
519	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
520	C₂²×C₄	C₂×C₇×D₄	1	2	yes	—
521	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
522	M₁₆	—	2	1	no	—
523	M₁₆	—	2	2	no	—
524	M₁₆	—	2	1	no	—
525	M₁₆	—	2	2	no	—
526	M₁₆	—	2	1	no	—
527	M₁₆	C₇×#41	1	2	yes	complemented
528	C₂×C₈	—	2	1	no	—
529	C₂×C₈	—	2	1	no	—
530	C₂×C₈	—	2	2	no	—
531	C₄⋊C₄	—	2	2	no	—
532	C₄⋊C₄	—	2	1	no	—
533	C₄⋊C₄	—	2	1	no	—
534	C₄⋊C₄	—	2	2	no	—
535	C₄⋊C₄	—	2	2	no	—
536	C₄⋊C₄	—	2	1	no	—
537	C₄⋊C₄	—	2	2	no	—
538	C₄⋊C₄	—	2	1	no	—
539	C₄⋊C₄	—	4	2	no	—
540	C₄⋊C₄	—	4	4	no	—
541	C₄⋊C₄	C₇×C₂²⋊C₄	1	2	yes	—
542	C₄⋊C₄	C₇×C₂²⋊C₄	1	1	yes	characteristic
543	C₄⋊C₄	C₇×C₂²⋊C₄	1	2	yes	—
544	C₄⋊C₄	C₇×C₂²⋊C₄	1	1	yes	characteristic
545	C₄⋊C₄	C₇×C₂²⋊C₄	1	2	yes	—
546	C₄⋊C₄	C₇×C₂²⋊C₄	1	2	yes	—
547	C₄⋊C₄	C₇×C₂²⋊C₄	1	2	yes	—
548	C₄⋊C₄	C₂²×C₄×C₇	1	1	yes	characteristic
549	C₄⋊C₄	C₂²×C₄×C₇	1	1	yes	characteristic
550	C₂²⋊C₄	—	2	1	no	—
551	C₂²⋊C₄	—	2	2	no	—
552	C₂²⋊C₄	—	2	2	no	—
553	C₂²⋊C₄	—	2	2	no	—
554	C₂²⋊C₄	—	2	2	no	—
555	C₂²⋊C₄	—	2	1	no	—
556	C₂²⋊C₄	—	2	1	no	—
557	C₂²⋊C₄	—	2	2	no	—
558	C₂²⋊C₄	—	2	2	no	—
559	C₂²⋊C₄	—	2	2	no	—
560	C₂²⋊C₄	—	2	2	no	—
561	C₄²	—	2	1	no	—
562	C₄²	—	2	2	no	—
563	C₄²	—	2	2	no	—
564	C₄²	—	2	1	no	—
565	C₄²	—	2	1	no	—
566	C₄²	—	2	1	no	—
567	C₄²	—	2	1	no	—
568	C₄²	—	2	2	no	—
569	C₄²	—	2	1	no	—
570	C₄²	—	2	2	no	—
571	C₄²	—	4	2	no	—
572	C₄²	—	4	2	no	—
573	C₄²	C₂²×C₄×C₇	1	1	yes	characteristic
574	C₄²	C₂²×C₄×C₇	1	2	yes	—
575	C₄²	C₂²×C₄×C₇	1	2	yes	—
576	C₄²	C₂²×C₄×C₇	1	1	yes	characteristic
577	C₄²	C₂×C₇×D₄	1	1	yes	characteristic
578	C₄²	C₂×C₇×D₄	1	2	yes	—
579	C₄²	C₂×C₇×D₄	1	2	yes	—
580	C₄²	C₂×C₇×D₄	1	1	yes	characteristic
581	C₄²	C₇×#41	1	2	yes	complemented
582	C₂×C₇	—	2	1	no	—
583	C₂×C₇	—	2	1	no	—
584	C₂×C₇	—	8	2	no	—
585	C₂×C₇	—	8	1	no	—
586	C₂×C₇	#2341	1	1	yes	characteristic
587	C₂×C₇	C₂×#421	1	1	yes	characteristic
588	C₂×C₇	#2901	1	1	yes	characteristic
589	C₂³	—	2	2	no	—
590	C₂³	—	2	1	no	—
591	C₂³	C₂²×C₇×D₄	1	1	yes	characteristic
592	Q₈	—	2	2	no	—
593	Q₈	—	2	2	no	—
594	Q₈	—	2	1	no	—
595	Q₈	—	2	2	no	—
596	Q₈	—	2	1	no	—
597	Q₈	—	2	2	no	—
598	Q₈	—	4	2	no	—
599	D₄	—	2	1	no	—
600	D₄	—	2	2	no	—
601	D₄	—	2	1	no	—
602	D₄	—	2	2	no	—
603	D₄	—	4	4	no	—
604	D₄	—	4	1	no	—
605	D₄	—	4	2	no	—
606	D₄	—	4	1	no	—
607	D₄	—	4	2	no	—
608	D₄	—	4	2	no	—
609	D₄	—	8	1	no	—
610	D₄	—	8	2	no	—
611	C₂×C₄	—	2	2	no	—
612	C₂×C₄	—	2	2	no	—
613	C₂×C₄	—	2	1	no	—
614	C₂×C₄	—	2	1	no	—
615	C₂×C₄	—	2	2	no	—
616	C₂×C₄	—	2	1	no	—
617	C₂×C₄	—	2	2	no	—
618	C₂×C₄	—	4	1	no	—
619	C₂×C₄	—	4	2	no	—
620	C₂×C₄	—	4	2	no	—
621	C₂×C₄	—	4	4	no	—
622	C₂×C₄	—	4	1	no	—
623	C₂×C₄	—	4	1	no	—
624	C₂×C₄	—	4	1	no	—
625	C₂×C₄	—	4	1	no	—
626	C₂×C₄	—	4	1	no	—
627	C₂×C₄	—	4	2	no	—
628	C₂×C₄	—	4	1	no	—
629	C₂×C₄	—	4	2	no	—
630	C₂×C₄	—	4	2	no	—
631	C₂×C₄	—	4	2	no	—
632	C₂×C₄	—	4	2	no	—
633	C₂×C₄	—	4	2	no	—
634	C₂×C₄	—	8	1	no	—
635	C₂×C₄	—	8	2	no	—
636	C₂×C₄	C₂×C₇×C₂²⋊C₄	1	1	yes	characteristic
637	C₂×C₄	C₂×C₇×C₂²⋊C₄	1	2	yes	—
638	C₂×C₄	C₂×C₇×C₂²⋊C₄	1	2	yes	—
639	C₂×C₄	C₂×C₇×C₂²⋊C₄	1	1	yes	characteristic
640	C₂×C₄	C₂×C₇×C₂²⋊C₄	1	2	yes	—
641	C₂×C₄	C₂×C₇×C₂²⋊C₄	1	2	yes	—
642	C₂×C₄	C₂×C₇×C₂²⋊C₄	1	1	yes	characteristic
643	C₂×C₄	C₂×C₇×C₂²⋊C₄	1	1	yes	characteristic
644	C₂×C₄	C₂³×C₄×C₇	1	1	yes	characteristic
645	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
646	C₂×C₄	C₂×C₇×#41	1	1	yes	characteristic
647	C₂×C₄	C₂×C₇×#41	1	1	yes	characteristic
648	C₂×C₄	C₇×H(5,𝔽₂)	1	1	yes	characteristic
649	C₂×C₄	C₇×2₋¹⁺⁴	1	1	yes	characteristic
650	C₈	—	2	2	no	—
651	C₈	—	4	1	no	—
652	C₈	—	4	2	no	—
653	C₇	#22551	1	1	yes	characteristic, direct product factor, Sylow
654	C₂²	—	2	1	no	—
655	C₂²	—	2	1	no	—
656	C₂²	—	4	2	no	—
657	C₂²	—	4	1	no	—
658	C₂²	—	4	2	no	—
659	C₂²	—	4	1	no	—
660	C₂²	—	4	2	no	—
661	C₂²	—	4	1	no	—
662	C₂²	C₂²×C₇×C₂²⋊C₄	1	1	yes	characteristic
663	C₂²	C₇×#548	1	1	yes	characteristic
664	C₂²	C₇×#550	1	1	yes	characteristic
665	C₄	—	2	1	no	—
666	C₄	—	2	2	no	—
667	C₄	—	2	2	no	—
668	C₄	—	2	1	no	—
669	C₄	—	2	2	no	—
670	C₄	—	2	1	no	—
671	C₄	—	2	2	no	—
672	C₄	—	4	2	no	—
673	C₄	—	4	2	no	—
674	C₄	—	4	1	no	—
675	C₄	—	4	1	no	—
676	C₄	—	4	2	no	—
677	C₄	—	4	1	no	—
678	C₄	—	8	2	no	—
679	C₄	C₇×#421	1	2	yes	—
680	C₄	C₄×C₇×#41	1	1	yes	characteristic
681	C₄	C₇×#520	1	1	yes	characteristic
682	C₄	C₇×#548	1	1	yes	characteristic
683	C₄	C₇×#550	1	1	yes	characteristic
684	C₂	—	2	1	no	—
685	C₂	—	2	1	no	—
686	C₂	—	8	2	no	—
687	C₂	—	8	1	no	—
688	C₂	C₇×#2341	1	1	yes	characteristic
689	C₂	C₂×C₇×#421	1	1	yes	characteristic
690	C₂	C₇×#2901	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×#3480	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₇ ◁ C₂×C₄×C₇×Q₈ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₇×Q₈×M₁₆	C₂	semidirect
3. C₇×#2295	C₂	semidirect
4. C₇×#1980	C₂	semidirect
5. C₇×#1980	C₂	semidirect
6. C₇×#1963	C₂	semidirect
7. C₇×#1962	C₂	semidirect
8. C₇×#1806	C₂	semidirect
9. C₇×#1806	C₂	semidirect
10. C₇×#1759	C₂	semidirect
11. C₄×C₇×#104	C₂	semidirect
12. C₇×#559	C₄	semidirect
13. C₇×#559	C₄	semidirect
14. C₇×#557	C₄	semidirect
15. C₇×#556	C₄	semidirect
16. C₇×#556	C₄	semidirect
19. C₇×#550	C₄	semidirect
53. #22551	C₇	direct (N × H)
149. Q₈×M₁₆	C₂×C₇	semidirect
150. #2295	C₂×C₇	semidirect
151. #1980	C₂×C₇	semidirect
152. #1980	C₂×C₇	semidirect
153. #1963	C₂×C₇	semidirect
154. #1962	C₂×C₇	semidirect
155. #1806	C₂×C₇	semidirect
156. #1806	C₂×C₇	semidirect
157. #1759	C₂×C₇	semidirect
158. C₄×#104	C₂×C₇	semidirect
201. C₇×M₁₆	#41	semidirect
255. C₄²×C₇	#41	semidirect
256. #559	C₄×C₇	semidirect
257. #559	C₄×C₇	semidirect
258. #557	C₄×C₇	semidirect
259. #556	C₄×C₇	semidirect
260. #556	C₄×C₇	semidirect
263. #550	C₄×C₇	semidirect
527. M₁₆	C₇×#41	semidirect
581. C₄²	C₇×#41	semidirect
653. C₇	#22551	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×#3480	2
C₇×Q₈×M₁₆	2
C₇×#2295	2
C₇×#1980	2
C₇×#1963	2
C₇×#1962	2
C₇×#1806	2
C₇×#1759	2
C₄×C₇×#104	2
#22551	7

Subgroups — C7×#22551 #13199767

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×#22551 #13199767