Subgroups — C₇×#21515 #13198731

Order 1792.

1044 conjugacy classes of subgroups.

The subgroup lattice has 702 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₇×#460	C₂	1	1	yes	maximal, characteristic
2	C₂×C₇×#440	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₄×C₇×SD₁₆	C₂	1	1	yes	maximal, characteristic, complemented
4	C₇×#2328	C₂	1	1	yes	maximal, characteristic
5	C₇×#2276	C₂	1	1	yes	maximal, characteristic, complemented
6	C₇×#1982	C₂	1	1	yes	maximal, characteristic
7	C₇×#1949	C₂	1	1	yes	maximal, characteristic, complemented
8	C₇×#1926	C₂	1	1	yes	maximal, characteristic, complemented
9	C₇×#1925	C₂	1	1	yes	maximal, characteristic, complemented
10	C₇×#1880	C₂	1	1	yes	maximal, characteristic, complemented
11	C₇×#1880	C₂	1	1	yes	maximal, characteristic, complemented
12	C₇×#1805	C₂	1	1	yes	maximal, characteristic, complemented
13	C₇×#1768	C₂	1	1	yes	maximal, characteristic, complemented
14	C₇×#1762	C₂	1	1	yes	maximal, characteristic, complemented
15	C₄×C₇×#102	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×C₇×SD₁₆	C₂²	1	1	yes	characteristic
17	C₂²×C₇×SD₁₆	C₂²	1	1	yes	characteristic
18	C₂×C₇×#127	C₂²	1	1	yes	characteristic
19	C₂×C₄×C₇×Q₈	C₂²	1	1	yes	characteristic
20	C₂×C₄×C₇×Q₈	C₂²	1	1	yes	characteristic
21	C₂×C₄×C₇×Q₈	C₂²	1	1	yes	characteristic
22	C₂×C₄×C₇×D₄	C₂²	1	1	yes	characteristic
23	C₂×C₄×C₇×D₄	C₂²	1	1	yes	characteristic
24	C₇×#460	C₄	1	8	yes	complemented
25	C₇×#440	—	2	4	no	—
26	C₄×C₇×SD₁₆	—	2	4	no	—
27	C₂×C₇×#107	C₂²	1	1	yes	characteristic
28	C₂×C₇×#106	C₂²	1	1	yes	characteristic
29	C₂×C₇×C₄⋊C₈	C₂²	1	1	yes	characteristic
30	C₂×C₇×C₄⋊C₈	C₂²	1	1	yes	characteristic
31	C₂×C₇×#103	C₂²	1	1	yes	characteristic
32	C₂×C₇×#103	C₂²	1	1	yes	characteristic
33	C₂×C₇×#102	C₂²	1	1	yes	characteristic
34	C₂×C₇×#102	C₂²	1	1	yes	characteristic
35	C₂×C₇×#102	C₂²	1	1	yes	characteristic
36	C₂×C₇×#102	C₂²	1	1	yes	characteristic
37	C₂×C₇×#102	C₂²	1	1	yes	characteristic
38	C₂×C₇×#102	C₂²	1	1	yes	characteristic
39	C₂×C₇×#97	C₂²	1	1	yes	characteristic
40	C₂×C₄×C₇×C₈	C₂²	1	1	yes	characteristic
41	C₇×#390	C₂²	1	1	yes	characteristic
42	C₇×#390	C₂²	1	1	yes	characteristic
43	C₇×#386	—	2	1	no	—
44	C₇×#386	—	2	1	no	—
45	C₇×#386	—	2	1	no	—
46	C₇×#386	—	2	1	no	—
47	C₇×#382	C₂²	1	1	yes	characteristic
48	C₄×C₇×C₄⋊C₄	—	2	1	no	—
49	C₄×C₇×C₄⋊C₄	—	2	1	no	—
50	C₄×C₇×C₄⋊C₄	—	2	1	no	—
51	C₄×C₇×C₄⋊C₄	C₂²	1	1	yes	characteristic
52	C₄×C₇×C₄⋊C₄	C₂²	1	1	yes	characteristic
53	C₄×C₇×C₄⋊C₄	C₂²	1	1	yes	characteristic
54	C₇×#376	—	2	1	no	—
55	C₇×#376	C₂²	1	1	yes	characteristic
56	C₇×#340	C₂²	1	1	yes	characteristic
57	C₇×#340	C₂²	1	1	yes	characteristic
58	C₇×#340	C₂²	1	1	yes	characteristic
59	C₇×#340	C₂²	1	1	yes	characteristic
60	C₇×#336	C₂²	1	1	yes	characteristic
61	C₇×#336	C₂²	1	1	yes	characteristic
62	#21515	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
63	C₂²×C₇×Q₈	C₂³	1	1	yes	characteristic
64	C₂²×C₇×D₄	—	2	1	no	—
65	C₂²×C₇×D₄	—	2	1	no	—
66	C₂²×C₇×D₄	C₂³	1	1	yes	characteristic
67	C₂²×C₇×D₄	C₂³	1	1	yes	characteristic
68	C₂³×C₄×C₇	—	2	1	no	—
69	C₂³×C₄×C₇	—	2	1	no	—
70	C₂×C₇×SD₁₆	—	2	2	no	—
71	C₂×C₇×SD₁₆	—	2	2	no	—
72	C₂×C₇×SD₁₆	—	2	2	no	—
73	C₂×C₇×SD₁₆	—	2	2	no	—
74	C₂×C₇×SD₁₆	C₂×C₄	1	4	yes	complemented
75	C₂×C₇×SD₁₆	C₂×C₄	1	4	yes	complemented
76	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
77	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
78	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
79	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
80	C₇×#127	—	2	2	no	—
81	C₇×#127	C₂×C₄	1	4	yes	—
82	C₄×C₇×Q₈	—	2	2	no	—
83	C₄×C₇×Q₈	—	2	2	no	—
84	C₄×C₇×Q₈	—	2	2	no	—
85	C₄×C₇×Q₈	—	2	2	no	—
86	C₄×C₇×Q₈	C₂×C₄	1	4	yes	complemented
87	C₄×C₇×Q₈	D₄	1	4	yes	complemented
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	2	no	—
92	C₂×C₇×C₄⋊C₄	—	2	1	no	—
93	C₂×C₇×C₄⋊C₄	—	2	1	no	—
94	C₂×C₇×C₄⋊C₄	—	2	1	no	—
95	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
96	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
97	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
98	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
99	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
100	C₂×C₇×C₂²⋊C₄	—	2	1	no	—
101	C₂×C₇×C₂²⋊C₄	—	2	1	no	—
102	C₂×C₇×C₂²⋊C₄	—	2	1	no	—
103	C₂×C₇×C₂²⋊C₄	—	2	1	no	—
104	C₂×C₇×C₂²⋊C₄	—	2	1	no	—
105	C₂×C₇×C₂²⋊C₄	—	2	1	no	—
106	C₂×C₄²×C₇	—	2	1	no	—
107	C₂×C₄²×C₇	—	2	1	no	—
108	C₂×C₄²×C₇	—	2	1	no	—
109	C₂×C₄²×C₇	—	2	1	no	—
110	C₂×C₄²×C₇	—	2	1	no	—
111	C₂×C₄²×C₇	—	2	1	no	—
112	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
113	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
114	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
115	C₇×#107	—	2	2	no	—
116	C₇×#106	—	2	2	no	—
117	C₇×C₄⋊C₈	—	2	2	no	—
118	C₇×C₄⋊C₈	C₂×C₄	1	4	yes	complemented
119	C₇×#103	—	2	2	no	—
120	C₇×#103	—	2	2	no	—
121	C₇×#102	—	2	2	no	—
122	C₇×#102	—	2	2	no	—
123	C₇×#102	—	2	2	no	—
124	C₇×#102	—	2	2	no	—
125	C₇×#102	C₂×C₄	1	4	yes	complemented
126	C₇×#102	C₂×C₄	1	4	yes	complemented
127	C₇×#97	—	2	2	no	—
128	C₄×C₇×C₈	—	2	2	no	—
129	C₇×#95	—	2	1	no	—
130	C₇×#95	—	2	1	no	—
131	C₇×#95	—	2	1	no	—
132	C₇×#95	—	2	1	no	—
133	C₇×#95	—	2	1	no	—
134	C₇×#95	D₄	1	1	yes	characteristic
135	C₇×#95	D₄	1	1	yes	characteristic
136	C₇×#95	D₄	1	1	yes	characteristic
137	C₇×#95	D₄	1	1	yes	characteristic
138	C₂×#460	C₂×C₇	1	1	yes	characteristic
139	C₂×#440	C₂×C₇	1	1	yes	characteristic, complemented
140	C₂×C₄×SD₁₆	C₂×C₇	1	1	yes	characteristic, complemented
141	#2328	C₂×C₇	1	1	yes	characteristic
142	#2276	C₂×C₇	1	1	yes	characteristic, complemented
143	#1982	C₂×C₇	1	1	yes	characteristic
144	#1949	C₂×C₇	1	1	yes	characteristic, complemented
145	#1926	C₂×C₇	1	1	yes	characteristic, complemented
146	#1925	C₂×C₇	1	1	yes	characteristic, complemented
147	#1880	C₂×C₇	1	1	yes	characteristic, complemented
148	#1880	C₂×C₇	1	1	yes	characteristic, complemented
149	#1805	C₂×C₇	1	1	yes	characteristic, complemented
150	#1768	C₂×C₇	1	1	yes	characteristic, complemented
151	#1762	C₂×C₇	1	1	yes	characteristic, complemented
152	C₄×#102	C₂×C₇	1	1	yes	characteristic, complemented
153	C₂⁴×C₇	—	2	1	no	—
154	C₂⁴×C₇	—	2	1	no	—
155	C₂×C₇×Q₈	—	2	1	no	—
156	C₂×C₇×Q₈	—	2	1	no	—
157	C₂×C₇×Q₈	—	2	1	no	—
158	C₂×C₇×Q₈	C₂²×C₄	1	2	yes	—
159	C₂×C₇×Q₈	C₂×D₄	1	2	yes	—
160	C₂×C₇×Q₈	#41	1	2	yes	—
161	C₂×C₇×D₄	—	2	4	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	—	2	1	no	—
168	C₂×C₇×D₄	—	2	1	no	—
169	C₂×C₇×D₄	—	2	1	no	—
170	C₂×C₇×D₄	—	2	1	no	—
171	C₂×C₇×D₄	—	2	1	no	—
172	C₂×C₇×D₄	—	2	1	no	—
173	C₂×C₇×D₄	—	8	1	no	—
174	C₂×C₇×D₄	—	8	1	no	—
175	C₂×C₇×D₄	—	8	1	no	—
176	C₂×C₇×D₄	—	8	1	no	—
177	C₂×C₇×D₄	C₂²×C₄	1	2	yes	—
178	C₂×C₇×D₄	C₂²×C₄	1	2	yes	—
179	C₂²×C₄×C₇	—	2	1	no	—
180	C₂²×C₄×C₇	—	2	1	no	—
181	C₂²×C₄×C₇	—	2	1	no	—
182	C₂²×C₄×C₇	—	2	1	no	—
183	C₂²×C₄×C₇	—	2	1	no	—
184	C₂²×C₄×C₇	—	2	1	no	—
185	C₂²×C₄×C₇	—	4	2	no	—
186	C₂²×C₄×C₇	—	4	2	no	—
187	C₂²×C₄×C₇	—	8	1	no	—
188	C₂²×C₄×C₇	—	8	1	no	—
189	C₂²×C₄×C₇	—	8	1	no	—
190	C₂²×C₄×C₇	—	8	1	no	—
191	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
192	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
193	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
194	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
195	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
196	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
197	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
198	C₇×SD₁₆	—	2	8	no	—
199	C₇×SD₁₆	—	2	8	no	—
200	C₂×C₇×C₈	—	2	1	no	—
201	C₂×C₇×C₈	—	2	1	no	—
202	C₂×C₇×C₈	—	2	1	no	—
203	C₂×C₇×C₈	—	2	1	no	—
204	C₂×C₇×C₈	—	2	1	no	—
205	C₂×C₇×C₈	—	2	1	no	—
206	C₂×C₇×C₈	—	2	1	no	—
207	C₂×C₇×C₈	—	2	1	no	—
208	C₂×C₇×C₈	—	2	1	no	—
209	C₂×C₇×C₈	—	2	1	no	—
210	C₂×C₇×C₈	C₂²×C₄	1	2	yes	—
211	C₂×C₇×C₈	C₂²×C₄	1	2	yes	—
212	C₇×C₄⋊C₄	—	2	4	no	—
213	C₇×C₄⋊C₄	—	2	4	no	—
214	C₇×C₄⋊C₄	—	2	4	no	—
215	C₇×C₄⋊C₄	—	2	1	no	—
216	C₇×C₄⋊C₄	—	2	1	no	—
217	C₇×C₄⋊C₄	—	2	1	no	—
218	C₇×C₄⋊C₄	—	2	1	no	—
219	C₇×C₄⋊C₄	—	2	1	no	—
220	C₇×C₄⋊C₄	—	2	1	no	—
221	C₇×C₄⋊C₄	—	2	1	no	—
222	C₇×C₄⋊C₄	C₂²×C₄	1	2	yes	—
223	C₇×C₄⋊C₄	C₂×D₄	1	2	yes	—
224	C₇×C₄⋊C₄	#41	1	2	yes	—
225	C₇×C₂²⋊C₄	—	4	2	no	—
226	C₇×C₂²⋊C₄	—	4	2	no	—
227	C₇×C₂²⋊C₄	—	8	1	no	—
228	C₇×C₂²⋊C₄	—	8	1	no	—
229	C₇×C₂²⋊C₄	—	8	1	no	—
230	C₇×C₂²⋊C₄	—	8	1	no	—
231	C₄²×C₇	—	2	4	no	—
232	C₄²×C₇	—	2	4	no	—
233	C₄²×C₇	—	2	4	no	—
234	C₄²×C₇	—	2	1	no	—
235	C₄²×C₇	—	2	1	no	—
236	C₄²×C₇	—	8	1	no	—
237	C₄²×C₇	—	8	1	no	—
238	C₄²×C₇	—	8	1	no	—
239	C₄²×C₇	C₂²×C₄	1	2	yes	—
240	C₄²×C₇	C₂×D₄	1	2	yes	—
241	C₄²×C₇	#41	1	2	yes	—
242	C₄²×C₇	#41	1	2	yes	—
243	C₂²×SD₁₆	C₂²×C₇	1	1	yes	characteristic
244	C₂²×SD₁₆	C₂²×C₇	1	1	yes	characteristic
245	C₂×#127	C₂²×C₇	1	1	yes	characteristic
246	C₂×C₄×Q₈	C₂²×C₇	1	1	yes	characteristic
247	C₂×C₄×Q₈	C₂²×C₇	1	1	yes	characteristic
248	C₂×C₄×Q₈	C₂²×C₇	1	1	yes	characteristic
249	C₂×C₄×D₄	C₂²×C₇	1	1	yes	characteristic
250	C₂×C₄×D₄	C₂²×C₇	1	1	yes	characteristic
251	#460	C₄×C₇	1	8	yes	complemented
252	#440	—	2	4	no	—
253	C₄×SD₁₆	—	2	4	no	—
254	C₂×#107	C₂²×C₇	1	1	yes	characteristic
255	C₂×#106	C₂²×C₇	1	1	yes	characteristic
256	C₂×C₄⋊C₈	C₂²×C₇	1	1	yes	characteristic
257	C₂×C₄⋊C₈	C₂²×C₇	1	1	yes	characteristic
258	C₂×#103	C₂²×C₇	1	1	yes	characteristic
259	C₂×#103	C₂²×C₇	1	1	yes	characteristic
260	C₂×#102	C₂²×C₇	1	1	yes	characteristic
261	C₂×#102	C₂²×C₇	1	1	yes	characteristic
262	C₂×#102	C₂²×C₇	1	1	yes	characteristic
263	C₂×#102	C₂²×C₇	1	1	yes	characteristic
264	C₂×#102	C₂²×C₇	1	1	yes	characteristic
265	C₂×#102	C₂²×C₇	1	1	yes	characteristic
266	C₂×#97	C₂²×C₇	1	1	yes	characteristic
267	C₂×C₄×C₈	C₂²×C₇	1	1	yes	characteristic
268	#390	C₂²×C₇	1	1	yes	characteristic
269	#390	C₂²×C₇	1	1	yes	characteristic
270	#386	—	2	1	no	—
271	#386	—	2	1	no	—
272	#386	—	2	1	no	—
273	#386	—	2	1	no	—
274	#382	C₂²×C₇	1	1	yes	characteristic
275	C₄×C₄⋊C₄	—	2	1	no	—
276	C₄×C₄⋊C₄	—	2	1	no	—
277	C₄×C₄⋊C₄	—	2	1	no	—
278	C₄×C₄⋊C₄	C₂²×C₇	1	1	yes	characteristic
279	C₄×C₄⋊C₄	C₂²×C₇	1	1	yes	characteristic
280	C₄×C₄⋊C₄	C₂²×C₇	1	1	yes	characteristic
281	#376	—	2	1	no	—
282	#376	C₂²×C₇	1	1	yes	characteristic
283	#340	C₂²×C₇	1	1	yes	characteristic
284	#340	C₂²×C₇	1	1	yes	characteristic
285	#340	C₂²×C₇	1	1	yes	characteristic
286	#340	C₂²×C₇	1	1	yes	characteristic
287	#336	C₂²×C₇	1	1	yes	characteristic
288	#336	C₂²×C₇	1	1	yes	characteristic
289	C₂³×C₇	—	2	2	no	—
290	C₂³×C₇	—	2	2	no	—
291	C₂³×C₇	—	4	1	no	—
292	C₂³×C₇	—	4	1	no	—
293	C₂³×C₇	—	4	1	no	—
294	C₂³×C₇	—	4	1	no	—
295	C₂³×C₇	—	4	1	no	—
296	C₂³×C₇	—	4	1	no	—
297	C₂³×C₇	—	4	1	no	—
298	C₂³×C₇	—	4	1	no	—
299	C₂³×C₇	—	4	1	no	—
300	C₂³×C₇	—	4	1	no	—
301	C₂³×C₇	—	4	1	no	—
302	C₂³×C₇	—	4	1	no	—
303	C₂³×C₇	C₂²×D₄	1	1	yes	characteristic
304	C₇×Q₈	—	2	2	no	—
305	C₇×Q₈	—	2	2	no	—
306	C₇×Q₈	—	2	2	no	—
307	C₇×Q₈	C₄×D₄	1	4	yes	—
308	C₇×D₄	—	2	2	no	—
309	C₇×D₄	—	2	2	no	—
310	C₇×D₄	—	2	2	no	—
311	C₇×D₄	—	2	2	no	—
312	C₇×D₄	—	4	1	no	—
313	C₇×D₄	—	4	1	no	—
314	C₇×D₄	—	4	1	no	—
315	C₇×D₄	—	4	1	no	—
316	C₇×D₄	—	8	4	no	—
317	C₇×D₄	—	8	4	no	—
318	C₂×C₄×C₇	—	2	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	1	no	—
324	C₂×C₄×C₇	—	2	1	no	—
325	C₂×C₄×C₇	—	2	1	no	—
326	C₂×C₄×C₇	—	2	1	no	—
327	C₂×C₄×C₇	—	2	1	no	—
328	C₂×C₄×C₇	—	2	1	no	—
329	C₂×C₄×C₇	—	2	2	no	—
330	C₂×C₄×C₇	—	2	2	no	—
331	C₂×C₄×C₇	—	2	1	no	—
332	C₂×C₄×C₇	—	2	1	no	—
333	C₂×C₄×C₇	—	2	2	no	—
334	C₂×C₄×C₇	—	2	1	no	—
335	C₂×C₄×C₇	—	2	1	no	—
336	C₂×C₄×C₇	—	2	1	no	—
337	C₂×C₄×C₇	—	2	1	no	—
338	C₂×C₄×C₇	—	4	1	no	—
339	C₂×C₄×C₇	—	4	1	no	—
340	C₂×C₄×C₇	—	4	1	no	—
341	C₂×C₄×C₇	—	4	1	no	—
342	C₂×C₄×C₇	—	4	1	no	—
343	C₂×C₄×C₇	—	4	1	no	—
344	C₂×C₄×C₇	—	4	1	no	—
345	C₂×C₄×C₇	—	4	1	no	—
346	C₂×C₄×C₇	—	4	1	no	—
347	C₂×C₄×C₇	—	4	1	no	—
348	C₂×C₄×C₇	—	4	1	no	—
349	C₂×C₄×C₇	—	4	1	no	—
350	C₂×C₄×C₇	—	8	4	no	—
351	C₂×C₄×C₇	—	8	4	no	—
352	C₂×C₄×C₇	C₄×D₄	1	2	yes	—
353	C₂×C₄×C₇	C₄×D₄	1	2	yes	—
354	C₂×C₄×C₇	#121	1	2	yes	—
355	C₂×C₄×C₇	#121	1	2	yes	—
356	C₂×C₄×C₇	C₂³×C₄	1	1	yes	characteristic
357	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
358	C₂×C₄×C₇	C₂×#41	1	1	yes	characteristic
359	C₂×C₄×C₇	C₂×#41	1	1	yes	characteristic
360	C₂×C₄×C₇	C₂×#41	1	1	yes	characteristic
361	C₂×C₄×C₇	C₂×#41	1	1	yes	characteristic
362	C₇×C₈	—	2	2	no	—
363	C₇×C₈	—	2	2	no	—
364	C₇×C₈	—	4	1	no	—
365	C₇×C₈	—	4	1	no	—
366	C₂²×Q₈	C₂³×C₇	1	1	yes	characteristic
367	C₂²×D₄	—	2	1	no	—
368	C₂²×D₄	—	2	1	no	—
369	C₂²×D₄	C₂³×C₇	1	1	yes	characteristic
370	C₂²×D₄	C₂³×C₇	1	1	yes	characteristic
371	C₂³×C₄	—	2	1	no	—
372	C₂³×C₄	—	2	1	no	—
373	C₂×SD₁₆	—	2	2	no	—
374	C₂×SD₁₆	—	2	2	no	—
375	C₂×SD₁₆	—	2	2	no	—
376	C₂×SD₁₆	—	2	2	no	—
377	C₂×SD₁₆	C₂×C₄×C₇	1	4	yes	complemented
378	C₂×SD₁₆	C₂×C₄×C₇	1	4	yes	complemented
379	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
380	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
381	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
382	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
383	#127	—	2	2	no	—
384	#127	C₂×C₄×C₇	1	4	yes	—
385	C₄×Q₈	—	2	2	no	—
386	C₄×Q₈	—	2	2	no	—
387	C₄×Q₈	—	2	2	no	—
388	C₄×Q₈	—	2	2	no	—
389	C₄×Q₈	C₂×C₄×C₇	1	4	yes	complemented
390	C₄×Q₈	C₇×D₄	1	4	yes	complemented
391	C₄×D₄	—	2	2	no	—
392	C₄×D₄	—	2	2	no	—
393	C₄×D₄	—	2	2	no	—
394	C₄×D₄	—	2	2	no	—
395	C₂×C₄⋊C₄	—	2	1	no	—
396	C₂×C₄⋊C₄	—	2	1	no	—
397	C₂×C₄⋊C₄	—	2	1	no	—
398	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
399	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
400	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
401	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
402	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
403	C₂×C₂²⋊C₄	—	2	1	no	—
404	C₂×C₂²⋊C₄	—	2	1	no	—
405	C₂×C₂²⋊C₄	—	2	1	no	—
406	C₂×C₂²⋊C₄	—	2	1	no	—
407	C₂×C₂²⋊C₄	—	2	1	no	—
408	C₂×C₂²⋊C₄	—	2	1	no	—
409	C₂×C₄²	—	2	1	no	—
410	C₂×C₄²	—	2	1	no	—
411	C₂×C₄²	—	2	1	no	—
412	C₂×C₄²	—	2	1	no	—
413	C₂×C₄²	—	2	1	no	—
414	C₂×C₄²	—	2	1	no	—
415	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
416	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
417	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
418	#107	—	2	2	no	—
419	#106	—	2	2	no	—
420	C₄⋊C₈	—	2	2	no	—
421	C₄⋊C₈	C₂×C₄×C₇	1	4	yes	complemented
422	#103	—	2	2	no	—
423	#103	—	2	2	no	—
424	#102	—	2	2	no	—
425	#102	—	2	2	no	—
426	#102	—	2	2	no	—
427	#102	—	2	2	no	—
428	#102	C₂×C₄×C₇	1	4	yes	complemented
429	#102	C₂×C₄×C₇	1	4	yes	complemented
430	#97	—	2	2	no	—
431	C₄×C₈	—	2	2	no	—
432	#95	—	2	1	no	—
433	#95	—	2	1	no	—
434	#95	—	2	1	no	—
435	#95	—	2	1	no	—
436	#95	—	2	1	no	—
437	#95	C₇×D₄	1	1	yes	characteristic
438	#95	C₇×D₄	1	1	yes	characteristic
439	#95	C₇×D₄	1	1	yes	characteristic
440	#95	C₇×D₄	1	1	yes	characteristic
441	C₂²×C₇	—	4	2	no	—
442	C₂²×C₇	—	4	2	no	—
443	C₂²×C₇	—	4	2	no	—
444	C₂²×C₇	—	4	2	no	—
445	C₂²×C₇	—	4	2	no	—
446	C₂²×C₇	—	4	2	no	—
447	C₂²×C₇	—	8	1	no	—
448	C₂²×C₇	—	8	1	no	—
449	C₂²×C₇	—	8	1	no	—
450	C₂²×C₇	—	8	1	no	—
451	C₂²×C₇	—	8	1	no	—
452	C₂²×C₇	—	8	1	no	—
453	C₂²×C₇	—	8	1	no	—
454	C₂²×C₇	—	8	1	no	—
455	C₂²×C₇	C₂×C₄×D₄	1	1	yes	characteristic
456	C₂²×C₇	C₂×#121	1	1	yes	characteristic
457	C₂²×C₇	#525	1	1	yes	characteristic
458	C₂²×C₇	#576	1	1	yes	characteristic
459	C₂²×C₇	#577	1	1	yes	characteristic
460	C₂²×C₇	#577	1	1	yes	characteristic
461	C₂²×C₇	#577	1	1	yes	characteristic
462	C₄×C₇	—	2	2	no	—
463	C₄×C₇	—	2	2	no	—
464	C₄×C₇	—	2	2	no	—
465	C₄×C₇	—	2	2	no	—
466	C₄×C₇	—	2	4	no	—
467	C₄×C₇	—	4	1	no	—
468	C₄×C₇	—	4	2	no	—
469	C₄×C₇	—	4	1	no	—
470	C₄×C₇	—	4	2	no	—
471	C₄×C₇	—	4	2	no	—
472	C₄×C₇	—	8	1	no	—
473	C₄×C₇	—	8	1	no	—
474	C₄×C₇	C₂×C₄×D₄	1	1	yes	characteristic
475	C₄×C₇	C₄×#41	1	1	yes	characteristic
476	C₄×C₇	#529	1	1	yes	characteristic
477	C₄×C₇	#532	1	1	yes	characteristic
478	C₂⁴	—	2	1	no	—
479	C₂⁴	—	2	1	no	—
480	C₂×Q₈	—	2	1	no	—
481	C₂×Q₈	—	2	1	no	—
482	C₂×Q₈	—	2	1	no	—
483	C₂×Q₈	C₂²×C₄×C₇	1	2	yes	—
484	C₂×Q₈	C₂×C₇×D₄	1	2	yes	—
485	C₂×Q₈	C₇×#41	1	2	yes	—
486	C₂×D₄	—	2	4	no	—
487	C₂×D₄	—	2	4	no	—
488	C₂×D₄	—	2	1	no	—
489	C₂×D₄	—	2	1	no	—
490	C₂×D₄	—	2	1	no	—
491	C₂×D₄	—	2	1	no	—
492	C₂×D₄	—	2	1	no	—
493	C₂×D₄	—	2	1	no	—
494	C₂×D₄	—	2	1	no	—
495	C₂×D₄	—	2	1	no	—
496	C₂×D₄	—	2	1	no	—
497	C₂×D₄	—	2	1	no	—
498	C₂×D₄	—	8	1	no	—
499	C₂×D₄	—	8	1	no	—
500	C₂×D₄	—	8	1	no	—
501	C₂×D₄	—	8	1	no	—
502	C₂×D₄	C₂²×C₄×C₇	1	2	yes	—
503	C₂×D₄	C₂²×C₄×C₇	1	2	yes	—
504	C₂²×C₄	—	2	1	no	—
505	C₂²×C₄	—	2	1	no	—
506	C₂²×C₄	—	2	1	no	—
507	C₂²×C₄	—	2	1	no	—
508	C₂²×C₄	—	2	1	no	—
509	C₂²×C₄	—	2	1	no	—
510	C₂²×C₄	—	4	2	no	—
511	C₂²×C₄	—	4	2	no	—
512	C₂²×C₄	—	8	1	no	—
513	C₂²×C₄	—	8	1	no	—
514	C₂²×C₄	—	8	1	no	—
515	C₂²×C₄	—	8	1	no	—
516	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
517	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
518	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
519	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
520	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
521	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
522	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
523	SD₁₆	—	2	8	no	—
524	SD₁₆	—	2	8	no	—
525	C₂×C₈	—	2	1	no	—
526	C₂×C₈	—	2	1	no	—
527	C₂×C₈	—	2	1	no	—
528	C₂×C₈	—	2	1	no	—
529	C₂×C₈	—	2	1	no	—
530	C₂×C₈	—	2	1	no	—
531	C₂×C₈	—	2	1	no	—
532	C₂×C₈	—	2	1	no	—
533	C₂×C₈	—	2	1	no	—
534	C₂×C₈	—	2	1	no	—
535	C₂×C₈	C₂²×C₄×C₇	1	2	yes	—
536	C₂×C₈	C₂²×C₄×C₇	1	2	yes	—
537	C₄⋊C₄	—	2	4	no	—
538	C₄⋊C₄	—	2	4	no	—
539	C₄⋊C₄	—	2	4	no	—
540	C₄⋊C₄	—	2	1	no	—
541	C₄⋊C₄	—	2	1	no	—
542	C₄⋊C₄	—	2	1	no	—
543	C₄⋊C₄	—	2	1	no	—
544	C₄⋊C₄	—	2	1	no	—
545	C₄⋊C₄	—	2	1	no	—
546	C₄⋊C₄	—	2	1	no	—
547	C₄⋊C₄	C₂²×C₄×C₇	1	2	yes	—
548	C₄⋊C₄	C₂×C₇×D₄	1	2	yes	—
549	C₄⋊C₄	C₇×#41	1	2	yes	—
550	C₂²⋊C₄	—	4	2	no	—
551	C₂²⋊C₄	—	4	2	no	—
552	C₂²⋊C₄	—	8	1	no	—
553	C₂²⋊C₄	—	8	1	no	—
554	C₂²⋊C₄	—	8	1	no	—
555	C₂²⋊C₄	—	8	1	no	—
556	C₄²	—	2	4	no	—
557	C₄²	—	2	4	no	—
558	C₄²	—	2	4	no	—
559	C₄²	—	2	1	no	—
560	C₄²	—	2	1	no	—
561	C₄²	—	8	1	no	—
562	C₄²	—	8	1	no	—
563	C₄²	—	8	1	no	—
564	C₄²	C₂²×C₄×C₇	1	2	yes	—
565	C₄²	C₂×C₇×D₄	1	2	yes	—
566	C₄²	C₇×#41	1	2	yes	—
567	C₄²	C₇×#41	1	2	yes	—
568	C₂×C₇	—	8	2	no	—
569	C₂×C₇	—	8	2	no	—
570	C₂×C₇	C₄×#121	1	1	yes	characteristic
571	C₂×C₇	#2946	1	1	yes	characteristic
572	C₂×C₇	#2949	1	1	yes	characteristic
573	C₂×C₇	#3043	1	1	yes	characteristic
574	C₂×C₇	#3045	1	1	yes	characteristic
575	C₂×C₇	#3119	1	1	yes	characteristic
576	C₂×C₇	#3126	1	1	yes	characteristic
577	C₂³	—	2	2	no	—
578	C₂³	—	2	2	no	—
579	C₂³	—	4	1	no	—
580	C₂³	—	4	1	no	—
581	C₂³	—	4	1	no	—
582	C₂³	—	4	1	no	—
583	C₂³	—	4	1	no	—
584	C₂³	—	4	1	no	—
585	C₂³	—	4	1	no	—
586	C₂³	—	4	1	no	—
587	C₂³	—	4	1	no	—
588	C₂³	—	4	1	no	—
589	C₂³	—	4	1	no	—
590	C₂³	—	4	1	no	—
591	C₂³	C₂²×C₇×D₄	1	1	yes	characteristic
592	Q₈	—	2	2	no	—
593	Q₈	—	2	2	no	—
594	Q₈	—	2	2	no	—
595	Q₈	C₄×C₇×D₄	1	4	yes	—
596	D₄	—	2	2	no	—
597	D₄	—	2	2	no	—
598	D₄	—	2	2	no	—
599	D₄	—	2	2	no	—
600	D₄	—	4	1	no	—
601	D₄	—	4	1	no	—
602	D₄	—	4	1	no	—
603	D₄	—	4	1	no	—
604	D₄	—	8	4	no	—
605	D₄	—	8	4	no	—
606	C₂×C₄	—	2	2	no	—
607	C₂×C₄	—	2	2	no	—
608	C₂×C₄	—	2	2	no	—
609	C₂×C₄	—	2	1	no	—
610	C₂×C₄	—	2	1	no	—
611	C₂×C₄	—	2	1	no	—
612	C₂×C₄	—	2	1	no	—
613	C₂×C₄	—	2	1	no	—
614	C₂×C₄	—	2	1	no	—
615	C₂×C₄	—	2	1	no	—
616	C₂×C₄	—	2	1	no	—
617	C₂×C₄	—	2	2	no	—
618	C₂×C₄	—	2	2	no	—
619	C₂×C₄	—	2	1	no	—
620	C₂×C₄	—	2	1	no	—
621	C₂×C₄	—	2	2	no	—
622	C₂×C₄	—	2	1	no	—
623	C₂×C₄	—	2	1	no	—
624	C₂×C₄	—	2	1	no	—
625	C₂×C₄	—	2	1	no	—
626	C₂×C₄	—	4	1	no	—
627	C₂×C₄	—	4	1	no	—
628	C₂×C₄	—	4	1	no	—
629	C₂×C₄	—	4	1	no	—
630	C₂×C₄	—	4	1	no	—
631	C₂×C₄	—	4	1	no	—
632	C₂×C₄	—	4	1	no	—
633	C₂×C₄	—	4	1	no	—
634	C₂×C₄	—	4	1	no	—
635	C₂×C₄	—	4	1	no	—
636	C₂×C₄	—	4	1	no	—
637	C₂×C₄	—	4	1	no	—
638	C₂×C₄	—	8	4	no	—
639	C₂×C₄	—	8	4	no	—
640	C₂×C₄	C₄×C₇×D₄	1	2	yes	—
641	C₂×C₄	C₄×C₇×D₄	1	2	yes	—
642	C₂×C₄	C₇×#121	1	2	yes	—
643	C₂×C₄	C₇×#121	1	2	yes	—
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	C₂×C₇×#41	1	1	yes	characteristic
649	C₂×C₄	C₂×C₇×#41	1	1	yes	characteristic
650	C₈	—	2	2	no	—
651	C₈	—	2	2	no	—
652	C₈	—	4	1	no	—
653	C₈	—	4	1	no	—
654	C₇	#21515	1	1	yes	characteristic, direct product factor, Sylow
655	C₂²	—	4	2	no	—
656	C₂²	—	4	2	no	—
657	C₂²	—	4	2	no	—
658	C₂²	—	4	2	no	—
659	C₂²	—	4	2	no	—
660	C₂²	—	4	2	no	—
661	C₂²	—	8	1	no	—
662	C₂²	—	8	1	no	—
663	C₂²	—	8	1	no	—
664	C₂²	—	8	1	no	—
665	C₂²	—	8	1	no	—
666	C₂²	—	8	1	no	—
667	C₂²	—	8	1	no	—
668	C₂²	—	8	1	no	—
669	C₂²	C₂×C₄×C₇×D₄	1	1	yes	characteristic
670	C₂²	C₂×C₇×#121	1	1	yes	characteristic
671	C₂²	C₇×#525	1	1	yes	characteristic
672	C₂²	C₇×#576	1	1	yes	characteristic
673	C₂²	C₇×#577	1	1	yes	characteristic
674	C₂²	C₇×#577	1	1	yes	characteristic
675	C₂²	C₇×#577	1	1	yes	characteristic
676	C₄	—	2	2	no	—
677	C₄	—	2	2	no	—
678	C₄	—	2	2	no	—
679	C₄	—	2	2	no	—
680	C₄	—	2	4	no	—
681	C₄	—	4	2	no	—
682	C₄	—	4	2	no	—
683	C₄	—	4	1	no	—
684	C₄	—	4	2	no	—
685	C₄	—	4	1	no	—
686	C₄	—	8	1	no	—
687	C₄	—	8	1	no	—
688	C₄	C₂×C₄×C₇×D₄	1	1	yes	characteristic
689	C₄	C₄×C₇×#41	1	1	yes	characteristic
690	C₄	C₇×#529	1	1	yes	characteristic
691	C₄	C₇×#532	1	1	yes	characteristic
692	C₂	—	8	2	no	—
693	C₂	—	8	2	no	—
694	C₂	C₄×C₇×#121	1	1	yes	characteristic
695	C₂	C₇×#2946	1	1	yes	characteristic
696	C₂	C₇×#2949	1	1	yes	characteristic
697	C₂	C₇×#3043	1	1	yes	characteristic
698	C₂	C₇×#3045	1	1	yes	characteristic
699	C₂	C₇×#3119	1	1	yes	characteristic
700	C₂	C₇×#3126	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₇	C₂²×D₄
commutator	C₂×C₄	C₂³×C₄×C₇
Frattini, cosocle	C₂²×C₄	C₂⁴×C₇
prime radical	C₂×C₇×#127	C₂²
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₇ ◁ C₇×#376 ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₇×#440	C₂	semidirect
3. C₂×C₄×C₇×SD₁₆	C₂	semidirect
5. C₇×#2276	C₂	semidirect
7. C₇×#1949	C₂	semidirect
8. C₇×#1926	C₂	semidirect
9. C₇×#1925	C₂	semidirect
10. C₇×#1880	C₂	semidirect
11. C₇×#1880	C₂	semidirect
12. C₇×#1805	C₂	semidirect
13. C₇×#1768	C₂	semidirect
14. C₇×#1762	C₂	semidirect
15. C₄×C₇×#102	C₂	semidirect
24. C₇×#460	C₄	semidirect
62. #21515	C₇	direct (N × H)
74. C₂×C₇×SD₁₆	C₂×C₄	semidirect
75. C₂×C₇×SD₁₆	C₂×C₄	semidirect
86. C₄×C₇×Q₈	C₂×C₄	semidirect
87. C₄×C₇×Q₈	D₄	semidirect
118. C₇×C₄⋊C₈	C₂×C₄	semidirect
125. C₇×#102	C₂×C₄	semidirect
126. C₇×#102	C₂×C₄	semidirect
139. C₂×#440	C₂×C₇	semidirect
140. C₂×C₄×SD₁₆	C₂×C₇	semidirect
142. #2276	C₂×C₇	semidirect
144. #1949	C₂×C₇	semidirect
145. #1926	C₂×C₇	semidirect
146. #1925	C₂×C₇	semidirect
147. #1880	C₂×C₇	semidirect
148. #1880	C₂×C₇	semidirect
149. #1805	C₂×C₇	semidirect
150. #1768	C₂×C₇	semidirect
151. #1762	C₂×C₇	semidirect
152. C₄×#102	C₂×C₇	semidirect
251. #460	C₄×C₇	semidirect
377. C₂×SD₁₆	C₂×C₄×C₇	semidirect
378. C₂×SD₁₆	C₂×C₄×C₇	semidirect
389. C₄×Q₈	C₂×C₄×C₇	semidirect
390. C₄×Q₈	C₇×D₄	semidirect
421. C₄⋊C₈	C₂×C₄×C₇	semidirect
428. #102	C₂×C₄×C₇	semidirect
429. #102	C₂×C₄×C₇	semidirect
654. C₇	#21515	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×#460	2
C₂×C₇×#440	2
C₂×C₄×C₇×SD₁₆	2
C₇×#2328	2
C₇×#2276	2
C₇×#1982	2
C₇×#1949	2
C₇×#1926	2
C₇×#1925	2
C₇×#1880	2
C₇×#1805	2
C₇×#1768	2
C₇×#1762	2
C₄×C₇×#102	2
#21515	7

Subgroups — C7×#21515 #13198731

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×#21515 #13198731