Subgroups — C₇×#34398 #13211614

Order 1792.

2538 conjugacy classes of subgroups.

The subgroup lattice has 500 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₇×#532	C₂	1	1	yes	maximal, characteristic
2	C₇×#2379	C₂	1	4	yes	maximal, complemented
3	C₇×#2361	C₂	1	4	yes	maximal, complemented
4	C₇×#2357	C₂	1	2	yes	maximal, complemented
5	C₇×#2349	C₂	1	2	yes	maximal, complemented
6	C₇×#2339	C₂	1	4	yes	maximal, complemented
7	C₇×#2331	C₂	1	2	yes	maximal, complemented
8	C₇×#2328	C₂	1	2	yes	maximal, complemented
9	C₇×#2325	C₂	1	4	yes	maximal, complemented
10	C₇×#2318	C₂	1	4	yes	maximal, complemented
11	C₇×#2283	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₇×#382	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂²×C₇×#41	C₂²	1	2	yes	—
14	C₇×#532	C₄	1	16	yes	complemented
15	C₂×C₇×C₄⋊Q₈	C₂²	1	1	yes	characteristic
16	C₂×C₇×#127	C₂²	1	1	yes	characteristic
17	C₂×C₇×#124	C₂²	1	2	yes	—
18	C₂×C₇×#121	C₂²	1	2	yes	—
19	C₂×C₇×#121	C₂²	1	2	yes	—
20	C₂×C₄×C₇×D₄	C₂²	1	8	yes	—
21	C₂×C₄×C₇×D₄	C₂²	1	4	yes	—
22	C₂×C₄×C₇×D₄	C₂²	1	2	yes	—
23	C₂×C₄×C₇×D₄	C₂²	1	2	yes	—
24	C₂²×C₇×C₄⋊C₄	C₂²	1	2	yes	—
25	C₂²×C₄²×C₇	C₂²	1	1	yes	characteristic
26	C₇×#391	C₂²	1	8	yes	—
27	C₇×#390	C₂²	1	4	yes	—
28	C₇×#389	C₂²	1	4	yes	—
29	C₇×#388	C₂²	1	8	yes	—
30	C₇×#388	C₂²	1	8	yes	—
31	C₇×#387	C₂²	1	8	yes	—
32	C₇×#386	C₂²	1	8	yes	—
33	C₇×#386	C₂²	1	8	yes	—
34	C₇×#386	C₂²	1	8	yes	—
35	C₇×#385	C₂²	1	8	yes	—
36	C₇×#385	C₂²	1	8	yes	—
37	C₇×#383	C₂²	1	2	yes	—
38	C₇×#382	C₂²	1	2	yes	—
39	C₇×#382	C₂²	1	2	yes	—
40	C₇×#382	C₂²	1	2	yes	—
41	C₇×#382	C₂²	1	2	yes	—
42	C₇×#382	C₂²	1	2	yes	—
43	C₇×#381	C₂²	1	2	yes	—
44	C₇×#381	C₂²	1	4	yes	—
45	C₇×#380	C₂²	1	2	yes	—
46	C₇×#380	C₂²	1	4	yes	—
47	C₄×C₇×C₄⋊C₄	C₂²	1	1	yes	characteristic
48	C₄×C₇×C₄⋊C₄	C₂²	1	1	yes	characteristic
49	C₄×C₇×C₄⋊C₄	C₂²	1	4	yes	—
50	C₄×C₇×C₂²⋊C₄	C₂²	1	2	yes	—
51	C₄×C₇×C₂²⋊C₄	C₂²	1	4	yes	—
52	C₇×#376	C₂²	1	2	yes	—
53	C₂×C₇×#95	C₂²	1	2	yes	—
54	C₂×C₇×#95	C₂²	1	2	yes	—
55	C₂×C₇×#95	C₂²	1	4	yes	—
56	#34398	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
57	C₂×C₇×#41	—	4	8	no	—
58	C₂×C₇×#41	C₂×C₄	1	16	yes	complemented
59	C₂²×C₇×Q₈	C₂³	1	2	yes	—
60	C₂²×C₇×D₄	C₂³	1	4	yes	—
61	C₂²×C₇×D₄	C₂³	1	2	yes	—
62	C₂²×C₇×D₄	C₂³	1	2	yes	—
63	C₂²×C₇×D₄	C₂³	1	2	yes	—
64	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
65	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
66	C₂³×C₄×C₇	C₂³	1	4	yes	—
67	C₂³×C₄×C₇	C₂³	1	8	yes	—
68	C₂³×C₄×C₇	C₂³	1	4	yes	—
69	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
70	C₇×C₄⋊Q₈	C₂×C₄	1	8	yes	complemented
71	C₇×#127	C₂×C₄	1	8	yes	complemented
72	C₇×#124	C₂×C₄	1	16	yes	complemented
73	C₇×#121	C₂×C₄	1	16	yes	complemented
74	C₇×#121	C₂×C₄	1	16	yes	complemented
75	C₄×C₇×D₄	—	4	8	no	—
76	C₄×C₇×D₄	—	4	16	no	—
77	C₄×C₇×D₄	C₂×C₄	1	16	yes	complemented
78	C₄×C₇×D₄	C₂×C₄	1	16	yes	complemented
79	C₂×C₇×C₄⋊C₄	—	4	4	no	—
80	C₂×C₇×C₄⋊C₄	C₂³	1	4	yes	—
81	C₂×C₇×C₄⋊C₄	C₂³	1	4	yes	—
82	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
83	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
84	C₂×C₇×C₄⋊C₄	C₂³	1	8	yes	—
85	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
86	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
87	C₂×C₇×C₂²⋊C₄	C₂³	1	4	yes	—
88	C₂×C₇×C₂²⋊C₄	C₂³	1	8	yes	—
89	C₂×C₇×C₂²⋊C₄	C₂³	1	8	yes	—
90	C₂×C₇×C₂²⋊C₄	C₂³	1	8	yes	—
91	C₂×C₇×C₂²⋊C₄	C₂³	1	4	yes	—
92	C₂×C₇×C₂²⋊C₄	C₂³	1	4	yes	—
93	C₂×C₄²×C₇	C₂×C₄	1	8	yes	complemented
94	C₂×C₄²×C₇	C₂³	1	2	yes	—
95	C₂×C₄²×C₇	C₂³	1	2	yes	—
96	C₂×C₄²×C₇	C₂³	1	8	yes	—
97	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
98	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
99	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
100	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
101	C₇×#95	C₂³	1	4	yes	—
102	C₇×#95	C₂³	1	2	yes	—
103	C₇×#95	C₂³	1	4	yes	—
104	C₇×#95	C₂³	1	4	yes	—
105	C₇×#95	C₂³	1	4	yes	—
106	C₇×#95	C₂³	1	8	yes	—
107	C₇×#95	C₂³	1	4	yes	—
108	C₇×#95	C₂³	1	4	yes	—
109	C₇×#95	C₂³	1	2	yes	—
110	C₇×#95	C₂³	1	4	yes	—
111	C₇×#95	C₂³	1	8	yes	—
112	C₂×#532	C₂×C₇	1	1	yes	characteristic
113	#2379	C₂×C₇	1	4	yes	complemented
114	#2361	C₂×C₇	1	4	yes	complemented
115	#2357	C₂×C₇	1	2	yes	complemented
116	#2349	C₂×C₇	1	2	yes	complemented
117	#2339	C₂×C₇	1	4	yes	complemented
118	#2331	C₂×C₇	1	2	yes	complemented
119	#2328	C₂×C₇	1	2	yes	complemented
120	#2325	C₂×C₇	1	4	yes	complemented
121	#2318	C₂×C₇	1	4	yes	complemented
122	#2283	C₂×C₇	1	1	yes	characteristic, complemented
123	C₂×#382	C₂×C₇	1	1	yes	characteristic, complemented
124	C₂⁴×C₇	C₂⁴	1	4	yes	—
125	C₂⁴×C₇	C₂⁴	1	1	yes	characteristic
126	C₇×#41	—	4	32	no	—
127	C₂×C₇×Q₈	—	4	4	no	—
128	C₂×C₇×Q₈	C₂²×C₄	1	8	yes	—
129	C₂×C₇×D₄	—	2	16	no	—
130	C₂×C₇×D₄	—	2	4	no	—
131	C₂×C₇×D₄	—	2	4	no	—
132	C₂×C₇×D₄	—	4	4	no	—
133	C₂×C₇×D₄	—	4	4	no	—
134	C₂×C₇×D₄	C₂²×C₄	1	8	yes	—
135	C₂×C₇×D₄	C₂²×C₄	1	16	yes	—
136	C₂×C₇×D₄	C₂²×C₄	1	8	yes	—
137	C₂×C₇×D₄	C₂²×C₄	1	8	yes	—
138	C₂²×C₄×C₇	—	2	4	no	—
139	C₂²×C₄×C₇	—	2	2	no	—
140	C₂²×C₄×C₇	—	2	2	no	—
141	C₂²×C₄×C₇	—	2	8	no	—
142	C₂²×C₄×C₇	—	4	2	no	—
143	C₂²×C₄×C₇	—	4	8	no	—
144	C₂²×C₄×C₇	—	4	4	no	—
145	C₂²×C₄×C₇	—	4	8	no	—
146	C₂²×C₄×C₇	—	4	8	no	—
147	C₂²×C₄×C₇	—	4	4	no	—
148	C₂²×C₄×C₇	—	4	8	no	—
149	C₂²×C₄×C₇	C₂²×C₄	1	4	yes	—
150	C₂²×C₄×C₇	C₂²×C₄	1	4	yes	—
151	C₂²×C₄×C₇	C₂²×C₄	1	4	yes	—
152	C₂²×C₄×C₇	C₂²×C₄	1	16	yes	—
153	C₂²×C₄×C₇	C₂⁴	1	4	yes	—
154	C₂²×C₄×C₇	C₂⁴	1	4	yes	—
155	C₂²×C₄×C₇	C₂⁴	1	8	yes	—
156	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
157	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
158	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
159	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
160	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
161	C₂²×C₄×C₇	C₂⁴	1	4	yes	—
162	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
163	C₇×C₄⋊C₄	—	2	8	no	—
164	C₇×C₄⋊C₄	—	4	4	no	—
165	C₇×C₄⋊C₄	—	4	2	no	—
166	C₇×C₄⋊C₄	—	4	2	no	—
167	C₇×C₄⋊C₄	—	4	8	no	—
168	C₇×C₄⋊C₄	C₂²×C₄	1	8	yes	—
169	C₇×C₄⋊C₄	C₂²×C₄	1	8	yes	—
170	C₇×C₂²⋊C₄	—	2	8	no	—
171	C₇×C₂²⋊C₄	—	4	8	no	—
172	C₇×C₂²⋊C₄	—	4	8	no	—
173	C₇×C₂²⋊C₄	—	4	8	no	—
174	C₇×C₂²⋊C₄	C₂²×C₄	1	16	yes	—
175	C₇×C₂²⋊C₄	C₂²×C₄	1	16	yes	—
176	C₄²×C₇	—	2	4	no	—
177	C₄²×C₇	—	2	4	no	—
178	C₄²×C₇	—	4	8	no	—
179	C₄²×C₇	C₂²×C₄	1	4	yes	—
180	C₄²×C₇	C₂²×C₄	1	4	yes	—
181	C₄²×C₇	C₂²×C₄	1	4	yes	—
182	C₄²×C₇	C₂²×C₄	1	4	yes	—
183	C₂²×#41	C₂²×C₇	1	2	yes	—
184	#532	C₄×C₇	1	16	yes	complemented
185	C₂×C₄⋊Q₈	C₂²×C₇	1	1	yes	characteristic
186	C₂×#127	C₂²×C₇	1	1	yes	characteristic
187	C₂×#124	C₂²×C₇	1	2	yes	—
188	C₂×#121	C₂²×C₇	1	2	yes	—
189	C₂×#121	C₂²×C₇	1	2	yes	—
190	C₂×C₄×D₄	C₂²×C₇	1	8	yes	—
191	C₂×C₄×D₄	C₂²×C₇	1	4	yes	—
192	C₂×C₄×D₄	C₂²×C₇	1	2	yes	—
193	C₂×C₄×D₄	C₂²×C₇	1	2	yes	—
194	C₂²×C₄⋊C₄	C₂²×C₇	1	2	yes	—
195	C₂²×C₄²	C₂²×C₇	1	1	yes	characteristic
196	#391	C₂²×C₇	1	8	yes	—
197	#390	C₂²×C₇	1	4	yes	—
198	#389	C₂²×C₇	1	4	yes	—
199	#388	C₂²×C₇	1	8	yes	—
200	#388	C₂²×C₇	1	8	yes	—
201	#387	C₂²×C₇	1	8	yes	—
202	#386	C₂²×C₇	1	8	yes	—
203	#386	C₂²×C₇	1	8	yes	—
204	#386	C₂²×C₇	1	8	yes	—
205	#385	C₂²×C₇	1	8	yes	—
206	#385	C₂²×C₇	1	8	yes	—
207	#383	C₂²×C₇	1	2	yes	—
208	#382	C₂²×C₇	1	2	yes	—
209	#382	C₂²×C₇	1	2	yes	—
210	#382	C₂²×C₇	1	2	yes	—
211	#382	C₂²×C₇	1	2	yes	—
212	#382	C₂²×C₇	1	2	yes	—
213	#381	C₂²×C₇	1	4	yes	—
214	#381	C₂²×C₇	1	2	yes	—
215	#380	C₂²×C₇	1	4	yes	—
216	#380	C₂²×C₇	1	2	yes	—
217	C₄×C₄⋊C₄	C₂²×C₇	1	4	yes	—
218	C₄×C₄⋊C₄	C₂²×C₇	1	1	yes	characteristic
219	C₄×C₄⋊C₄	C₂²×C₇	1	1	yes	characteristic
220	C₄×C₂²⋊C₄	C₂²×C₇	1	4	yes	—
221	C₄×C₂²⋊C₄	C₂²×C₇	1	2	yes	—
222	#376	C₂²×C₇	1	2	yes	—
223	C₂×#95	C₂²×C₇	1	4	yes	—
224	C₂×#95	C₂²×C₇	1	2	yes	—
225	C₂×#95	C₂²×C₇	1	2	yes	—
226	C₂³×C₇	—	2	1	no	—
227	C₂³×C₇	—	2	1	no	—
228	C₂³×C₇	—	2	2	no	—
229	C₂³×C₇	—	2	4	no	—
230	C₂³×C₇	—	2	8	no	—
231	C₂³×C₇	—	2	4	no	—
232	C₂³×C₇	—	2	8	no	—
233	C₂³×C₇	C₂³×C₄	1	8	yes	—
234	C₂³×C₇	C₂³×C₄	1	2	yes	—
235	C₂³×C₇	H(5,𝔽₂)	1	4	yes	—
236	C₂³×C₇	C₂⁵	1	1	yes	characteristic
237	C₇×Q₈	—	4	8	no	—
238	C₇×D₄	—	2	32	no	—
239	C₇×D₄	—	2	16	no	—
240	C₇×D₄	—	4	8	no	—
241	C₇×D₄	—	4	8	no	—
242	C₂×C₄×C₇	—	2	8	no	—
243	C₂×C₄×C₇	—	2	8	no	—
244	C₂×C₄×C₇	—	2	1	no	—
245	C₂×C₄×C₇	—	2	2	no	—
246	C₂×C₄×C₇	—	2	2	no	—
247	C₂×C₄×C₇	—	2	1	no	—
248	C₂×C₄×C₇	—	2	2	no	—
249	C₂×C₄×C₇	—	2	2	no	—
250	C₂×C₄×C₇	—	2	8	no	—
251	C₂×C₄×C₇	—	2	4	no	—
252	C₂×C₄×C₇	—	2	4	no	—
253	C₂×C₄×C₇	—	2	8	no	—
254	C₂×C₄×C₇	—	2	4	no	—
255	C₂×C₄×C₇	—	2	8	no	—
256	C₂×C₄×C₇	—	2	4	no	—
257	C₂×C₄×C₇	—	2	4	no	—
258	C₂×C₄×C₇	—	2	8	no	—
259	C₂×C₄×C₇	—	2	4	no	—
260	C₂×C₄×C₇	—	4	4	no	—
261	C₂×C₄×C₇	—	4	16	no	—
262	C₂×C₄×C₇	—	8	8	no	—
263	C₂×C₄×C₇	—	8	16	no	—
264	C₂×C₄×C₇	C₂³×C₄	1	2	yes	—
265	C₂×C₄×C₇	C₂³×C₄	1	2	yes	—
266	C₂×C₄×C₇	C₂³×C₄	1	2	yes	—
267	C₂×C₄×C₇	C₂³×C₄	1	2	yes	—
268	C₂×C₄×C₇	C₂³×C₄	1	2	yes	—
269	C₂×C₄×C₇	C₂³×C₄	1	8	yes	—
270	C₂×C₄×C₇	C₂³×C₄	1	2	yes	—
271	C₂×C₄×C₇	H(5,𝔽₂)	1	2	yes	—
272	C₂×C₄×C₇	2₋¹⁺⁴	1	2	yes	—
273	C₂×#41	—	4	8	no	—
274	C₂×#41	C₂×C₄×C₇	1	16	yes	complemented
275	C₂²×Q₈	C₂³×C₇	1	2	yes	—
276	C₂²×D₄	C₂³×C₇	1	2	yes	—
277	C₂²×D₄	C₂³×C₇	1	4	yes	—
278	C₂²×D₄	C₂³×C₇	1	2	yes	—
279	C₂²×D₄	C₂³×C₇	1	2	yes	—
280	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
281	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
282	C₂³×C₄	C₂³×C₇	1	4	yes	—
283	C₂³×C₄	C₂³×C₇	1	8	yes	—
284	C₂³×C₄	C₂³×C₇	1	4	yes	—
285	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
286	C₄⋊Q₈	C₂×C₄×C₇	1	8	yes	complemented
287	#127	C₂×C₄×C₇	1	8	yes	complemented
288	#124	C₂×C₄×C₇	1	16	yes	complemented
289	#121	C₂×C₄×C₇	1	16	yes	complemented
290	#121	C₂×C₄×C₇	1	16	yes	complemented
291	C₄×D₄	—	4	8	no	—
292	C₄×D₄	—	4	16	no	—
293	C₄×D₄	C₂×C₄×C₇	1	16	yes	complemented
294	C₄×D₄	C₂×C₄×C₇	1	16	yes	complemented
295	C₂×C₄⋊C₄	—	4	4	no	—
296	C₂×C₄⋊C₄	C₂³×C₇	1	4	yes	—
297	C₂×C₄⋊C₄	C₂³×C₇	1	4	yes	—
298	C₂×C₄⋊C₄	C₂³×C₇	1	8	yes	—
299	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
300	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
301	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
302	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
303	C₂×C₂²⋊C₄	C₂³×C₇	1	4	yes	—
304	C₂×C₂²⋊C₄	C₂³×C₇	1	8	yes	—
305	C₂×C₂²⋊C₄	C₂³×C₇	1	8	yes	—
306	C₂×C₂²⋊C₄	C₂³×C₇	1	8	yes	—
307	C₂×C₂²⋊C₄	C₂³×C₇	1	4	yes	—
308	C₂×C₂²⋊C₄	C₂³×C₇	1	4	yes	—
309	C₂×C₄²	C₂×C₄×C₇	1	8	yes	complemented
310	C₂×C₄²	C₂³×C₇	1	2	yes	—
311	C₂×C₄²	C₂³×C₇	1	2	yes	—
312	C₂×C₄²	C₂³×C₇	1	8	yes	—
313	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
314	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
315	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
316	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
317	#95	C₂³×C₇	1	4	yes	—
318	#95	C₂³×C₇	1	2	yes	—
319	#95	C₂³×C₇	1	4	yes	—
320	#95	C₂³×C₇	1	4	yes	—
321	#95	C₂³×C₇	1	4	yes	—
322	#95	C₂³×C₇	1	8	yes	—
323	#95	C₂³×C₇	1	4	yes	—
324	#95	C₂³×C₇	1	4	yes	—
325	#95	C₂³×C₇	1	2	yes	—
326	#95	C₂³×C₇	1	4	yes	—
327	#95	C₂³×C₇	1	8	yes	—
328	C₂²×C₇	—	2	2	no	—
329	C₂²×C₇	—	2	2	no	—
330	C₂²×C₇	—	2	4	no	—
331	C₂²×C₇	—	2	4	no	—
332	C₂²×C₇	—	2	8	no	—
333	C₂²×C₇	—	2	8	no	—
334	C₂²×C₇	—	2	8	no	—
335	C₂²×C₇	—	4	8	no	—
336	C₂²×C₇	—	4	8	no	—
337	C₂²×C₇	#518	1	4	yes	—
338	C₂²×C₇	C₂⁴×C₄	1	1	yes	characteristic
339	C₂²×C₇	C₂×H(5,𝔽₂)	1	2	yes	—
340	C₂²×C₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
341	C₂²×C₇	C₂×2₋¹⁺⁴	1	1	yes	characteristic
342	C₂²×C₇	#585	1	2	yes	—
343	C₄×C₇	—	2	2	no	—
344	C₄×C₇	—	2	2	no	—
345	C₄×C₇	—	2	8	no	—
346	C₄×C₇	—	2	2	no	—
347	C₄×C₇	—	2	2	no	—
348	C₄×C₇	—	2	2	no	—
349	C₄×C₇	—	4	4	no	—
350	C₄×C₇	—	4	8	no	—
351	C₄×C₇	—	4	4	no	—
352	C₄×C₇	#520	1	4	yes	—
353	C₂⁴	C₂⁴×C₇	1	4	yes	—
354	C₂⁴	C₂⁴×C₇	1	1	yes	characteristic
355	#41	—	4	32	no	—
356	C₂×Q₈	—	4	4	no	—
357	C₂×Q₈	C₂²×C₄×C₇	1	8	yes	—
358	C₂×D₄	—	2	16	no	—
359	C₂×D₄	—	2	4	no	—
360	C₂×D₄	—	2	4	no	—
361	C₂×D₄	—	4	4	no	—
362	C₂×D₄	—	4	4	no	—
363	C₂×D₄	C₂²×C₄×C₇	1	8	yes	—
364	C₂×D₄	C₂²×C₄×C₇	1	16	yes	—
365	C₂×D₄	C₂²×C₄×C₇	1	8	yes	—
366	C₂×D₄	C₂²×C₄×C₇	1	8	yes	—
367	C₂²×C₄	—	2	4	no	—
368	C₂²×C₄	—	2	2	no	—
369	C₂²×C₄	—	2	2	no	—
370	C₂²×C₄	—	2	8	no	—
371	C₂²×C₄	—	4	2	no	—
372	C₂²×C₄	—	4	8	no	—
373	C₂²×C₄	—	4	4	no	—
374	C₂²×C₄	—	4	8	no	—
375	C₂²×C₄	—	4	8	no	—
376	C₂²×C₄	—	4	4	no	—
377	C₂²×C₄	—	4	8	no	—
378	C₂²×C₄	C₂²×C₄×C₇	1	4	yes	—
379	C₂²×C₄	C₂²×C₄×C₇	1	4	yes	—
380	C₂²×C₄	C₂²×C₄×C₇	1	4	yes	—
381	C₂²×C₄	C₂²×C₄×C₇	1	16	yes	—
382	C₂²×C₄	C₂⁴×C₇	1	4	yes	—
383	C₂²×C₄	C₂⁴×C₇	1	4	yes	—
384	C₂²×C₄	C₂⁴×C₇	1	8	yes	—
385	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
386	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
387	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
388	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
389	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
390	C₂²×C₄	C₂⁴×C₇	1	4	yes	—
391	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
392	C₄⋊C₄	—	2	8	no	—
393	C₄⋊C₄	—	4	4	no	—
394	C₄⋊C₄	—	4	8	no	—
395	C₄⋊C₄	—	4	2	no	—
396	C₄⋊C₄	—	4	2	no	—
397	C₄⋊C₄	C₂²×C₄×C₇	1	8	yes	—
398	C₄⋊C₄	C₂²×C₄×C₇	1	8	yes	—
399	C₂²⋊C₄	—	2	8	no	—
400	C₂²⋊C₄	—	4	8	no	—
401	C₂²⋊C₄	—	4	8	no	—
402	C₂²⋊C₄	—	4	8	no	—
403	C₂²⋊C₄	C₂²×C₄×C₇	1	16	yes	—
404	C₂²⋊C₄	C₂²×C₄×C₇	1	16	yes	—
405	C₄²	—	2	4	no	—
406	C₄²	—	2	4	no	—
407	C₄²	—	4	8	no	—
408	C₄²	C₂²×C₄×C₇	1	4	yes	—
409	C₄²	C₂²×C₄×C₇	1	4	yes	—
410	C₄²	C₂²×C₄×C₇	1	4	yes	—
411	C₄²	C₂²×C₄×C₇	1	4	yes	—
412	C₂×C₇	—	2	4	no	—
413	C₂×C₇	—	4	8	no	—
414	C₂×C₇	C₂×#518	1	1	yes	characteristic
415	C₂×C₇	C₂×#520	1	1	yes	characteristic
416	C₂×C₇	#3428	1	1	yes	characteristic
417	C₂×C₇	#3558	1	2	yes	—
418	C₂×C₇	#3559	1	2	yes	—
419	C₂³	—	2	1	no	—
420	C₂³	—	2	1	no	—
421	C₂³	—	2	2	no	—
422	C₂³	—	2	4	no	—
423	C₂³	—	2	8	no	—
424	C₂³	—	2	4	no	—
425	C₂³	—	2	8	no	—
426	C₂³	C₂³×C₄×C₇	1	8	yes	—
427	C₂³	C₂³×C₄×C₇	1	2	yes	—
428	C₂³	C₇×H(5,𝔽₂)	1	4	yes	—
429	C₂³	C₂⁵×C₇	1	1	yes	characteristic
430	Q₈	—	4	8	no	—
431	D₄	—	2	32	no	—
432	D₄	—	2	16	no	—
433	D₄	—	4	8	no	—
434	D₄	—	4	8	no	—
435	C₂×C₄	—	2	8	no	—
436	C₂×C₄	—	2	1	no	—
437	C₂×C₄	—	2	2	no	—
438	C₂×C₄	—	2	2	no	—
439	C₂×C₄	—	2	1	no	—
440	C₂×C₄	—	2	2	no	—
441	C₂×C₄	—	2	2	no	—
442	C₂×C₄	—	2	8	no	—
443	C₂×C₄	—	2	8	no	—
444	C₂×C₄	—	2	4	no	—
445	C₂×C₄	—	2	4	no	—
446	C₂×C₄	—	2	8	no	—
447	C₂×C₄	—	2	4	no	—
448	C₂×C₄	—	2	8	no	—
449	C₂×C₄	—	2	4	no	—
450	C₂×C₄	—	2	4	no	—
451	C₂×C₄	—	2	8	no	—
452	C₂×C₄	—	2	4	no	—
453	C₂×C₄	—	4	4	no	—
454	C₂×C₄	—	4	16	no	—
455	C₂×C₄	—	8	8	no	—
456	C₂×C₄	—	8	16	no	—
457	C₂×C₄	C₂³×C₄×C₇	1	2	yes	—
458	C₂×C₄	C₂³×C₄×C₇	1	2	yes	—
459	C₂×C₄	C₂³×C₄×C₇	1	2	yes	—
460	C₂×C₄	C₂³×C₄×C₇	1	2	yes	—
461	C₂×C₄	C₂³×C₄×C₇	1	2	yes	—
462	C₂×C₄	C₂³×C₄×C₇	1	8	yes	—
463	C₂×C₄	C₂³×C₄×C₇	1	2	yes	—
464	C₂×C₄	C₇×H(5,𝔽₂)	1	2	yes	—
465	C₂×C₄	C₇×2₋¹⁺⁴	1	2	yes	—
466	C₇	#34398	1	1	yes	characteristic, direct product factor, Sylow
467	C₂²	—	2	2	no	—
468	C₂²	—	2	2	no	—
469	C₂²	—	2	4	no	—
470	C₂²	—	2	4	no	—
471	C₂²	—	2	8	no	—
472	C₂²	—	2	8	no	—
473	C₂²	—	2	8	no	—
474	C₂²	—	4	8	no	—
475	C₂²	—	4	8	no	—
476	C₂²	C₇×#518	1	4	yes	—
477	C₂²	C₂⁴×C₄×C₇	1	1	yes	characteristic
478	C₂²	C₂×C₇×H(5,𝔽₂)	1	2	yes	—
479	C₂²	C₂×C₇×H(5,𝔽₂)	1	1	yes	characteristic
480	C₂²	C₂×C₇×2₋¹⁺⁴	1	1	yes	characteristic
481	C₂²	C₇×#585	1	2	yes	—
482	C₄	—	2	2	no	—
483	C₄	—	2	2	no	—
484	C₄	—	2	8	no	—
485	C₄	—	2	2	no	—
486	C₄	—	2	2	no	—
487	C₄	—	2	2	no	—
488	C₄	—	4	4	no	—
489	C₄	—	4	8	no	—
490	C₄	—	4	4	no	—
491	C₄	C₇×#520	1	4	yes	—
492	C₂	—	2	4	no	—
493	C₂	—	4	8	no	—
494	C₂	C₂×C₇×#518	1	1	yes	characteristic
495	C₂	C₂×C₇×#520	1	1	yes	characteristic
496	C₂	C₇×#3428	1	1	yes	characteristic
497	C₂	C₇×#3558	1	2	yes	—
498	C₂	C₇×#3559	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₇	C₂⁵
commutator	C₂²	C₂⁴×C₄×C₇
Frattini, cosocle	C₂³	C₂⁵×C₇
prime radical	C₂×C₇×#532	C₂
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₇ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₇×#2379	C₂	semidirect
3. C₇×#2361	C₂	semidirect
4. C₇×#2357	C₂	semidirect
5. C₇×#2349	C₂	semidirect
6. C₇×#2339	C₂	semidirect
7. C₇×#2331	C₂	semidirect
8. C₇×#2328	C₂	semidirect
9. C₇×#2325	C₂	semidirect
10. C₇×#2318	C₂	semidirect
11. C₇×#2283	C₂	semidirect
12. C₂×C₇×#382	C₂	semidirect
14. C₇×#532	C₄	semidirect
56. #34398	C₇	direct (N × H)
58. C₂×C₇×#41	C₂×C₄	semidirect
70. C₇×C₄⋊Q₈	C₂×C₄	semidirect
71. C₇×#127	C₂×C₄	semidirect
72. C₇×#124	C₂×C₄	semidirect
73. C₇×#121	C₂×C₄	semidirect
74. C₇×#121	C₂×C₄	semidirect
77. C₄×C₇×D₄	C₂×C₄	semidirect
78. C₄×C₇×D₄	C₂×C₄	semidirect
93. C₂×C₄²×C₇	C₂×C₄	semidirect
113. #2379	C₂×C₇	semidirect
114. #2361	C₂×C₇	semidirect
115. #2357	C₂×C₇	semidirect
116. #2349	C₂×C₇	semidirect
117. #2339	C₂×C₇	semidirect
118. #2331	C₂×C₇	semidirect
119. #2328	C₂×C₇	semidirect
120. #2325	C₂×C₇	semidirect
121. #2318	C₂×C₇	semidirect
122. #2283	C₂×C₇	semidirect
123. C₂×#382	C₂×C₇	semidirect
184. #532	C₄×C₇	semidirect
274. C₂×#41	C₂×C₄×C₇	semidirect
286. C₄⋊Q₈	C₂×C₄×C₇	semidirect
287. #127	C₂×C₄×C₇	semidirect
288. #124	C₂×C₄×C₇	semidirect
289. #121	C₂×C₄×C₇	semidirect
290. #121	C₂×C₄×C₇	semidirect
293. C₄×D₄	C₂×C₄×C₇	semidirect
294. C₄×D₄	C₂×C₄×C₇	semidirect
309. C₂×C₄²	C₂×C₄×C₇	semidirect
466. C₇	#34398	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₇×#532	2
C₇×#2379	2
C₇×#2361	2
C₇×#2357	2
C₇×#2349	2
C₇×#2339	2
C₇×#2331	2
C₇×#2328	2
C₇×#2325	2
C₇×#2318	2
C₇×#2283	2
C₂×C₇×#382	2
#34398	7

Subgroups — C7×#34398 #13211614

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×#34398 #13211614