Subgroups — C₂×C₇×#3339 #13238446

Order 1792.

1994 conjugacy classes of subgroups.

The subgroup lattice has 524 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₇×#553	C₂	1	2	yes	maximal, complemented
2	C₇×#3339	C₂	1	16	yes	maximal, direct product factor
3	C₂×C₇×#499	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₇×#481	C₂	1	2	yes	maximal, complemented
5	C₂×C₇×#482	C₂	1	2	yes	maximal, complemented
6	C₂×C₇×#478	C₂	1	2	yes	maximal, complemented
7	C₂×C₇×#466	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₇×#466	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×C₄×C₇×D₈	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×C₇×C₈×D₄	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×C₇×#427	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×C₇×#107	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂²×C₇×D₈	C₂²	1	1	yes	characteristic
14	C₂³×C₇×C₈	C₂²	1	1	yes	characteristic
15	C₂³×C₇×C₈	C₂²	1	1	yes	characteristic
16	C₇×#553	—	2	8	no	—
17	C₇×#553	C₂²	1	16	yes	complemented
18	C₂×C₇×#126	—	2	2	no	—
19	C₂×C₇×#125	C₂²	1	2	yes	—
20	C₂×C₇×#123	—	2	2	no	—
21	C₂×C₇×#121	—	2	2	no	—
22	C₂×C₇×#121	C₂²	1	2	yes	—
23	C₂×C₇×#121	C₂²	1	2	yes	—
24	C₂×C₄×C₇×D₄	—	2	2	no	—
25	C₂×C₄×C₇×D₄	C₂²	1	2	yes	—
26	C₂×C₄×C₇×D₄	C₂²	1	1	yes	characteristic
27	C₂×C₇×#117	C₂²	1	2	yes	—
28	C₂²×C₇×C₄⋊C₄	C₂²	1	2	yes	—
29	C₇×#499	C₂²	1	8	yes	complemented
30	C₇×#482	C₂²	1	16	yes	complemented
31	C₇×#481	C₂²	1	16	yes	complemented
32	C₇×#478	C₂²	1	16	yes	complemented
33	C₇×#466	C₂²	1	8	yes	complemented
34	C₇×#466	C₂²	1	8	yes	complemented
35	C₄×C₇×D₈	C₂²	1	8	yes	complemented
36	C₇×C₈×D₄	C₂²	1	8	yes	complemented
37	C₇×#427	C₂²	1	8	yes	complemented
38	C₂×C₇×#107	C₂²	1	1	yes	characteristic
39	C₂×C₇×#107	C₂²	1	1	yes	characteristic
40	C₂×C₇×#107	C₂²	1	1	yes	characteristic
41	C₂×C₇×#107	C₂²	1	2	yes	—
42	C₂×C₇×#107	C₂²	1	8	yes	complemented
43	C₂×C₇×#106	C₂²	1	2	yes	—
44	C₂×C₇×#106	C₂²	1	2	yes	—
45	C₂×C₇×C₄⋊C₈	C₂²	1	1	yes	characteristic
46	C₂×C₇×#102	C₂²	1	2	yes	—
47	C₂×C₇×#102	C₂²	1	2	yes	—
48	C₂×C₇×#102	C₂²	1	2	yes	—
49	C₂×C₇×C₂²⋊C₈	C₂²	1	1	yes	characteristic
50	C₂×C₇×C₂²⋊C₈	C₂²	1	1	yes	characteristic
51	C₂×C₄×C₇×C₈	C₂²	1	1	yes	characteristic
52	C₂×#3339	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
53	C₂²×C₇×D₄	—	2	2	no	—
54	C₂²×C₇×D₄	—	2	2	no	—
55	C₂²×C₇×D₄	D₄	1	1	yes	characteristic
56	C₂²×C₇×D₄	C₂³	1	2	yes	—
57	C₂³×C₄×C₇	—	2	2	no	—
58	C₂³×C₄×C₇	—	2	2	no	—
59	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
60	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
61	C₂×C₇×D₈	—	2	4	no	—
62	C₂×C₇×D₈	C₂³	1	4	yes	—
63	C₂²×C₇×C₈	—	2	4	no	—
64	C₂²×C₇×C₈	—	2	4	no	—
65	C₂²×C₇×C₈	C₂³	1	4	yes	—
66	C₂²×C₇×C₈	C₂³	1	4	yes	—
67	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
68	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
69	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
70	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
71	C₇×#126	—	2	16	no	—
72	C₇×#125	—	2	4	no	—
73	C₇×#125	C₂³	1	8	yes	—
74	C₇×#123	—	2	16	no	—
75	C₇×#121	—	2	16	no	—
76	C₇×#121	—	2	4	no	—
77	C₇×#121	—	2	4	no	—
78	C₇×#121	C₂³	1	8	yes	—
79	C₇×#121	C₂³	1	8	yes	—
80	C₄×C₇×D₄	—	2	16	no	—
81	C₄×C₇×D₄	—	2	4	no	—
82	C₄×C₇×D₄	D₄	1	4	yes	—
83	C₄×C₇×D₄	C₂³	1	8	yes	—
84	C₄×C₇×D₄	C₂³	1	4	yes	—
85	C₇×#117	—	2	4	no	—
86	C₇×#117	C₂³	1	8	yes	—
87	C₂×C₇×C₄⋊C₄	—	2	2	no	—
88	C₂×C₇×C₄⋊C₄	—	2	4	no	—
89	C₂×C₇×C₄⋊C₄	—	2	2	no	—
90	C₂×C₇×C₄⋊C₄	—	2	2	no	—
91	C₂×C₇×C₄⋊C₄	D₄	1	1	yes	characteristic
92	C₂×C₇×C₄⋊C₄	C₂³	1	8	yes	—
93	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
94	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
95	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
96	C₂×C₇×C₂²⋊C₄	—	2	2	no	—
97	C₂×C₇×C₂²⋊C₄	—	2	2	no	—
98	C₂×C₇×C₂²⋊C₄	—	2	2	no	—
99	C₂×C₇×C₂²⋊C₄	—	2	2	no	—
100	C₂×C₇×C₂²⋊C₄	D₄	1	1	yes	characteristic
101	C₂×C₇×C₂²⋊C₄	D₄	1	1	yes	characteristic
102	C₂×C₄²×C₇	—	2	2	no	—
103	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
104	C₇×#107	C₂³	1	4	yes	—
105	C₇×#107	C₂³	1	4	yes	—
106	C₇×#107	C₂³	1	8	yes	—
107	C₇×#107	C₂³	1	4	yes	—
108	C₇×#106	C₂³	1	8	yes	—
109	C₇×#106	C₂³	1	8	yes	—
110	C₇×C₄⋊C₈	C₂³	1	4	yes	—
111	C₇×#102	C₂³	1	8	yes	—
112	C₇×#102	C₂³	1	8	yes	—
113	C₇×#102	C₂³	1	8	yes	—
114	C₇×C₂²⋊C₈	C₂³	1	4	yes	—
115	C₇×C₂²⋊C₈	C₂³	1	4	yes	—
116	C₄×C₇×C₈	C₂³	1	4	yes	—
117	C₂×#553	C₂×C₇	1	2	yes	complemented
118	#3339	C₂×C₇	1	16	yes	direct product factor
119	C₂×#499	C₂×C₇	1	1	yes	characteristic, complemented
120	C₂×#481	C₂×C₇	1	2	yes	complemented
121	C₂×#482	C₂×C₇	1	2	yes	complemented
122	C₂×#478	C₂×C₇	1	2	yes	complemented
123	C₂×#466	C₂×C₇	1	1	yes	characteristic, complemented
124	C₂×#466	C₂×C₇	1	1	yes	characteristic, complemented
125	C₂×C₄×D₈	C₂×C₇	1	1	yes	characteristic, complemented
126	C₂×C₈×D₄	C₂×C₇	1	1	yes	characteristic, complemented
127	C₂×#427	C₂×C₇	1	1	yes	characteristic, complemented
128	C₂²×#107	C₂×C₇	1	1	yes	characteristic, complemented
129	C₂⁴×C₇	—	2	2	no	—
130	C₂⁴×C₇	C₂×D₄	1	1	yes	characteristic
131	C₂⁴×C₇	C₂×D₄	1	1	yes	characteristic
132	C₂×C₇×D₄	—	2	4	no	—
133	C₂×C₇×D₄	—	2	8	no	—
134	C₂×C₇×D₄	—	2	8	no	—
135	C₂×C₇×D₄	—	2	2	no	—
136	C₂×C₇×D₄	—	2	4	no	—
137	C₂×C₇×D₄	—	2	4	no	—
138	C₂×C₇×D₄	—	4	8	no	—
139	C₂×C₇×D₄	—	8	4	no	—
140	C₂×C₇×D₄	C₂×D₄	1	4	yes	—
141	C₂×C₇×D₄	C₂⁴	1	4	yes	—
142	C₂²×C₄×C₇	—	2	2	no	—
143	C₂²×C₄×C₇	—	2	2	no	—
144	C₂²×C₄×C₇	—	2	2	no	—
145	C₂²×C₄×C₇	—	2	2	no	—
146	C₂²×C₄×C₇	—	2	2	no	—
147	C₂²×C₄×C₇	—	2	2	no	—
148	C₂²×C₄×C₇	—	2	2	no	—
149	C₂²×C₄×C₇	—	2	8	no	—
150	C₂²×C₄×C₇	—	2	8	no	—
151	C₂²×C₄×C₇	—	8	4	no	—
152	C₂²×C₄×C₇	—	8	4	no	—
153	C₂²×C₄×C₇	C₂×D₄	1	2	yes	—
154	C₂²×C₄×C₇	C₂×D₄	1	2	yes	—
155	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
156	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
157	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
158	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
159	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
160	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
161	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
162	C₇×D₈	—	2	8	no	—
163	C₂×C₇×C₈	—	2	2	no	—
164	C₂×C₇×C₈	—	2	2	no	—
165	C₂×C₇×C₈	—	2	2	no	—
166	C₂×C₇×C₈	—	2	8	no	—
167	C₂×C₇×C₈	—	2	8	no	—
168	C₂×C₇×C₈	#41	1	4	yes	—
169	C₂×C₇×C₈	C₂⁴	1	2	yes	—
170	C₂×C₇×C₈	C₂⁴	1	2	yes	—
171	C₂×C₇×C₈	C₂⁴	1	2	yes	—
172	C₂×C₇×C₈	C₂⁴	1	2	yes	—
173	C₇×C₄⋊C₄	—	2	2	no	—
174	C₇×C₄⋊C₄	—	2	2	no	—
175	C₇×C₄⋊C₄	—	2	8	no	—
176	C₇×C₄⋊C₄	—	2	8	no	—
177	C₇×C₄⋊C₄	—	2	8	no	—
178	C₇×C₄⋊C₄	—	2	2	no	—
179	C₇×C₄⋊C₄	C₂×D₄	1	4	yes	—
180	C₇×C₄⋊C₄	C₂⁴	1	4	yes	—
181	C₇×C₄⋊C₄	C₂⁴	1	4	yes	—
182	C₇×C₄⋊C₄	C₂⁴	1	4	yes	—
183	C₇×C₂²⋊C₄	—	2	8	no	—
184	C₇×C₂²⋊C₄	—	2	8	no	—
185	C₇×C₂²⋊C₄	—	2	8	no	—
186	C₇×C₂²⋊C₄	—	2	8	no	—
187	C₇×C₂²⋊C₄	C₂×D₄	1	4	yes	—
188	C₇×C₂²⋊C₄	C₂×D₄	1	4	yes	—
189	C₄²×C₇	—	2	8	no	—
190	C₄²×C₇	C₂×D₄	1	2	yes	—
191	C₄²×C₇	C₂⁴	1	2	yes	—
192	C₂²×D₈	C₂²×C₇	1	1	yes	characteristic
193	C₂³×C₈	C₂²×C₇	1	1	yes	characteristic
194	C₂³×C₈	C₂²×C₇	1	1	yes	characteristic
195	#553	—	2	8	no	—
196	#553	C₂²×C₇	1	16	yes	complemented
197	C₂×#126	—	2	2	no	—
198	C₂×#125	C₂²×C₇	1	2	yes	—
199	C₂×#123	—	2	2	no	—
200	C₂×#121	—	2	2	no	—
201	C₂×#121	C₂²×C₇	1	2	yes	—
202	C₂×#121	C₂²×C₇	1	2	yes	—
203	C₂×C₄×D₄	—	2	2	no	—
204	C₂×C₄×D₄	C₂²×C₇	1	2	yes	—
205	C₂×C₄×D₄	C₂²×C₇	1	1	yes	characteristic
206	C₂×#117	C₂²×C₇	1	2	yes	—
207	C₂²×C₄⋊C₄	C₂²×C₇	1	2	yes	—
208	#499	C₂²×C₇	1	8	yes	complemented
209	#482	C₂²×C₇	1	16	yes	complemented
210	#481	C₂²×C₇	1	16	yes	complemented
211	#478	C₂²×C₇	1	16	yes	complemented
212	#466	C₂²×C₇	1	8	yes	complemented
213	#466	C₂²×C₇	1	8	yes	complemented
214	C₄×D₈	C₂²×C₇	1	8	yes	complemented
215	C₈×D₄	C₂²×C₇	1	8	yes	complemented
216	#427	C₂²×C₇	1	8	yes	complemented
217	C₂×#107	C₂²×C₇	1	2	yes	—
218	C₂×#107	C₂²×C₇	1	1	yes	characteristic
219	C₂×#107	C₂²×C₇	1	1	yes	characteristic
220	C₂×#107	C₂²×C₇	1	1	yes	characteristic
221	C₂×#107	C₂²×C₇	1	8	yes	complemented
222	C₂×#106	C₂²×C₇	1	2	yes	—
223	C₂×#106	C₂²×C₇	1	2	yes	—
224	C₂×C₄⋊C₈	C₂²×C₇	1	1	yes	characteristic
225	C₂×#102	C₂²×C₇	1	2	yes	—
226	C₂×#102	C₂²×C₇	1	2	yes	—
227	C₂×#102	C₂²×C₇	1	2	yes	—
228	C₂×C₂²⋊C₈	C₂²×C₇	1	1	yes	characteristic
229	C₂×C₂²⋊C₈	C₂²×C₇	1	1	yes	characteristic
230	C₂×C₄×C₈	C₂²×C₇	1	1	yes	characteristic
231	C₂³×C₇	—	2	2	no	—
232	C₂³×C₇	—	2	2	no	—
233	C₂³×C₇	—	2	2	no	—
234	C₂³×C₇	—	2	2	no	—
235	C₂³×C₇	—	2	2	no	—
236	C₂³×C₇	—	2	4	no	—
237	C₂³×C₇	—	4	4	no	—
238	C₂³×C₇	—	4	4	no	—
239	C₂³×C₇	—	4	4	no	—
240	C₂³×C₇	#135	1	4	yes	—
241	C₂³×C₇	C₂²×D₄	1	2	yes	—
242	C₂³×C₇	C₂²×D₄	1	2	yes	—
243	C₂³×C₇	C₂²×D₄	1	1	yes	characteristic
244	C₇×D₄	—	2	8	no	—
245	C₇×D₄	—	2	4	no	—
246	C₇×D₄	—	2	4	no	—
247	C₇×D₄	—	4	16	no	—
248	C₇×D₄	—	4	4	no	—
249	C₇×D₄	—	8	8	no	—
250	C₂×C₄×C₇	—	2	2	no	—
251	C₂×C₄×C₇	—	2	2	no	—
252	C₂×C₄×C₇	—	2	2	no	—
253	C₂×C₄×C₇	—	2	2	no	—
254	C₂×C₄×C₇	—	2	4	no	—
255	C₂×C₄×C₇	—	2	4	no	—
256	C₂×C₄×C₇	—	2	2	no	—
257	C₂×C₄×C₇	—	2	2	no	—
258	C₂×C₄×C₇	—	2	2	no	—
259	C₂×C₄×C₇	—	2	2	no	—
260	C₂×C₄×C₇	—	2	4	no	—
261	C₂×C₄×C₇	—	2	4	no	—
262	C₂×C₄×C₇	—	2	4	no	—
263	C₂×C₄×C₇	—	4	4	no	—
264	C₂×C₄×C₇	—	4	4	no	—
265	C₂×C₄×C₇	—	4	4	no	—
266	C₂×C₄×C₇	—	8	8	no	—
267	C₂×C₄×C₇	—	8	8	no	—
268	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
269	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
270	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
271	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
272	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
273	C₂×C₄×C₇	C₂×#41	1	2	yes	—
274	C₂×C₄×C₇	2₋¹⁺⁴	1	2	yes	—
275	C₂×C₄×C₇	C₂⁵	1	1	yes	characteristic
276	C₇×C₈	—	2	2	no	—
277	C₇×C₈	—	2	2	no	—
278	C₇×C₈	—	2	2	no	—
279	C₇×C₈	C₂×#41	1	4	yes	—
280	C₂²×D₄	—	2	2	no	—
281	C₂²×D₄	—	2	2	no	—
282	C₂²×D₄	C₇×D₄	1	1	yes	characteristic
283	C₂²×D₄	C₂³×C₇	1	2	yes	—
284	C₂³×C₄	—	2	2	no	—
285	C₂³×C₄	—	2	2	no	—
286	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
287	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
288	C₂×D₈	—	2	4	no	—
289	C₂×D₈	C₂³×C₇	1	4	yes	—
290	C₂²×C₈	—	2	4	no	—
291	C₂²×C₈	—	2	4	no	—
292	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
293	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
294	C₂²×C₈	C₂³×C₇	1	4	yes	—
295	C₂²×C₈	C₂³×C₇	1	4	yes	—
296	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
297	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
298	#126	—	2	16	no	—
299	#125	—	2	4	no	—
300	#125	C₂³×C₇	1	8	yes	—
301	#123	—	2	16	no	—
302	#121	—	2	16	no	—
303	#121	—	2	4	no	—
304	#121	—	2	4	no	—
305	#121	C₂³×C₇	1	8	yes	—
306	#121	C₂³×C₇	1	8	yes	—
307	C₄×D₄	—	2	16	no	—
308	C₄×D₄	—	2	4	no	—
309	C₄×D₄	C₇×D₄	1	4	yes	—
310	C₄×D₄	C₂³×C₇	1	8	yes	—
311	C₄×D₄	C₂³×C₇	1	4	yes	—
312	#117	—	2	4	no	—
313	#117	C₂³×C₇	1	8	yes	—
314	C₂×C₄⋊C₄	—	2	2	no	—
315	C₂×C₄⋊C₄	—	2	4	no	—
316	C₂×C₄⋊C₄	—	2	2	no	—
317	C₂×C₄⋊C₄	—	2	2	no	—
318	C₂×C₄⋊C₄	C₇×D₄	1	1	yes	characteristic
319	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
320	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
321	C₂×C₄⋊C₄	C₂³×C₇	1	8	yes	—
322	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
323	C₂×C₂²⋊C₄	—	2	2	no	—
324	C₂×C₂²⋊C₄	—	2	2	no	—
325	C₂×C₂²⋊C₄	—	2	2	no	—
326	C₂×C₂²⋊C₄	—	2	2	no	—
327	C₂×C₂²⋊C₄	C₇×D₄	1	1	yes	characteristic
328	C₂×C₂²⋊C₄	C₇×D₄	1	1	yes	characteristic
329	C₂×C₄²	—	2	2	no	—
330	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
331	#107	C₂³×C₇	1	4	yes	—
332	#107	C₂³×C₇	1	4	yes	—
333	#107	C₂³×C₇	1	8	yes	—
334	#107	C₂³×C₇	1	4	yes	—
335	#106	C₂³×C₇	1	8	yes	—
336	#106	C₂³×C₇	1	8	yes	—
337	C₄⋊C₈	C₂³×C₇	1	4	yes	—
338	#102	C₂³×C₇	1	8	yes	—
339	#102	C₂³×C₇	1	8	yes	—
340	#102	C₂³×C₇	1	8	yes	—
341	C₂²⋊C₈	C₂³×C₇	1	4	yes	—
342	C₂²⋊C₈	C₂³×C₇	1	4	yes	—
343	C₄×C₈	C₂³×C₇	1	4	yes	—
344	C₂²×C₇	—	2	8	no	—
345	C₂²×C₇	—	2	2	no	—
346	C₂²×C₇	—	2	2	no	—
347	C₂²×C₇	—	2	2	no	—
348	C₂²×C₇	—	2	2	no	—
349	C₂²×C₇	—	2	2	no	—
350	C₂²×C₇	—	4	4	no	—
351	C₂²×C₇	—	4	4	no	—
352	C₂²×C₇	—	4	4	no	—
353	C₂²×C₇	—	4	4	no	—
354	C₂²×C₇	—	8	8	no	—
355	C₂²×C₇	#547	1	2	yes	—
356	C₂²×C₇	C₂×#135	1	4	yes	—
357	C₂²×C₇	C₂×#135	1	2	yes	—
358	C₂²×C₇	#576	1	2	yes	—
359	C₂²×C₇	C₂³×D₄	1	1	yes	characteristic
360	C₄×C₇	—	2	2	no	—
361	C₄×C₇	—	2	2	no	—
362	C₄×C₇	—	2	2	no	—
363	C₄×C₇	—	2	2	no	—
364	C₄×C₇	—	4	4	no	—
365	C₄×C₇	—	4	4	no	—
366	C₄×C₇	—	4	4	no	—
367	C₄×C₇	#547	1	2	yes	—
368	C₄×C₇	C₂²×#41	1	1	yes	characteristic
369	C₄×C₇	C₂×2₋¹⁺⁴	1	1	yes	characteristic
370	C₂⁴	—	2	2	no	—
371	C₂⁴	C₂×C₇×D₄	1	1	yes	characteristic
372	C₂⁴	C₂×C₇×D₄	1	1	yes	characteristic
373	C₂×D₄	—	2	4	no	—
374	C₂×D₄	—	2	8	no	—
375	C₂×D₄	—	2	8	no	—
376	C₂×D₄	—	2	2	no	—
377	C₂×D₄	—	2	4	no	—
378	C₂×D₄	—	2	4	no	—
379	C₂×D₄	—	4	8	no	—
380	C₂×D₄	—	8	4	no	—
381	C₂×D₄	C₂×C₇×D₄	1	4	yes	—
382	C₂×D₄	C₂⁴×C₇	1	4	yes	—
383	C₂²×C₄	—	2	2	no	—
384	C₂²×C₄	—	2	2	no	—
385	C₂²×C₄	—	2	2	no	—
386	C₂²×C₄	—	2	2	no	—
387	C₂²×C₄	—	2	2	no	—
388	C₂²×C₄	—	2	2	no	—
389	C₂²×C₄	—	2	2	no	—
390	C₂²×C₄	—	2	8	no	—
391	C₂²×C₄	—	2	8	no	—
392	C₂²×C₄	—	8	4	no	—
393	C₂²×C₄	—	8	4	no	—
394	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
395	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
396	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
397	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
398	C₂²×C₄	C₂×C₇×D₄	1	2	yes	—
399	C₂²×C₄	C₂×C₇×D₄	1	2	yes	—
400	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
401	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
402	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
403	D₈	—	2	8	no	—
404	C₂×C₈	—	2	2	no	—
405	C₂×C₈	—	2	2	no	—
406	C₂×C₈	—	2	2	no	—
407	C₂×C₈	—	2	8	no	—
408	C₂×C₈	—	2	8	no	—
409	C₂×C₈	C₇×#41	1	4	yes	—
410	C₂×C₈	C₂⁴×C₇	1	2	yes	—
411	C₂×C₈	C₂⁴×C₇	1	2	yes	—
412	C₂×C₈	C₂⁴×C₇	1	2	yes	—
413	C₂×C₈	C₂⁴×C₇	1	2	yes	—
414	C₄⋊C₄	—	2	2	no	—
415	C₄⋊C₄	—	2	2	no	—
416	C₄⋊C₄	—	2	8	no	—
417	C₄⋊C₄	—	2	8	no	—
418	C₄⋊C₄	—	2	8	no	—
419	C₄⋊C₄	—	2	2	no	—
420	C₄⋊C₄	C₂×C₇×D₄	1	4	yes	—
421	C₄⋊C₄	C₂⁴×C₇	1	4	yes	—
422	C₄⋊C₄	C₂⁴×C₇	1	4	yes	—
423	C₄⋊C₄	C₂⁴×C₇	1	4	yes	—
424	C₂²⋊C₄	—	2	8	no	—
425	C₂²⋊C₄	—	2	8	no	—
426	C₂²⋊C₄	—	2	8	no	—
427	C₂²⋊C₄	—	2	8	no	—
428	C₂²⋊C₄	C₂×C₇×D₄	1	4	yes	—
429	C₂²⋊C₄	C₂×C₇×D₄	1	4	yes	—
430	C₄²	—	2	8	no	—
431	C₄²	C₂×C₇×D₄	1	2	yes	—
432	C₄²	C₂⁴×C₇	1	2	yes	—
433	C₂×C₇	—	2	4	no	—
434	C₂×C₇	—	4	2	no	—
435	C₂×C₇	—	8	4	no	—
436	C₂×C₇	#3339	1	4	yes	direct product factor
437	C₂×C₇	C₂×#547	1	1	yes	characteristic
438	C₂×C₇	C₂²×#135	1	1	yes	characteristic
439	C₂×C₇	C₂×#576	1	1	yes	characteristic
440	C₂³	—	2	2	no	—
441	C₂³	—	2	2	no	—
442	C₂³	—	2	2	no	—
443	C₂³	—	2	2	no	—
444	C₂³	—	2	2	no	—
445	C₂³	—	2	4	no	—
446	C₂³	—	4	4	no	—
447	C₂³	—	4	4	no	—
448	C₂³	—	4	4	no	—
449	C₂³	C₇×#135	1	4	yes	—
450	C₂³	C₂²×C₇×D₄	1	2	yes	—
451	C₂³	C₂²×C₇×D₄	1	2	yes	—
452	C₂³	C₂²×C₇×D₄	1	1	yes	characteristic
453	D₄	—	2	8	no	—
454	D₄	—	2	4	no	—
455	D₄	—	2	4	no	—
456	D₄	—	4	16	no	—
457	D₄	—	4	4	no	—
458	D₄	—	8	8	no	—
459	C₂×C₄	—	2	2	no	—
460	C₂×C₄	—	2	2	no	—
461	C₂×C₄	—	2	2	no	—
462	C₂×C₄	—	2	2	no	—
463	C₂×C₄	—	2	2	no	—
464	C₂×C₄	—	2	2	no	—
465	C₂×C₄	—	2	2	no	—
466	C₂×C₄	—	2	2	no	—
467	C₂×C₄	—	2	4	no	—
468	C₂×C₄	—	2	4	no	—
469	C₂×C₄	—	2	4	no	—
470	C₂×C₄	—	2	4	no	—
471	C₂×C₄	—	2	4	no	—
472	C₂×C₄	—	4	4	no	—
473	C₂×C₄	—	4	4	no	—
474	C₂×C₄	—	4	4	no	—
475	C₂×C₄	—	8	8	no	—
476	C₂×C₄	—	8	8	no	—
477	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
478	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
479	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
480	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
481	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
482	C₂×C₄	C₂×C₇×#41	1	2	yes	—
483	C₂×C₄	C₇×2₋¹⁺⁴	1	2	yes	—
484	C₂×C₄	C₂⁵×C₇	1	1	yes	characteristic
485	C₈	—	2	2	no	—
486	C₈	—	2	2	no	—
487	C₈	—	2	2	no	—
488	C₈	C₂×C₇×#41	1	4	yes	—
489	C₇	C₂×#3339	1	1	yes	characteristic, direct product factor, Sylow
490	C₂²	—	2	2	no	—
491	C₂²	—	2	2	no	—
492	C₂²	—	2	8	no	—
493	C₂²	—	2	2	no	—
494	C₂²	—	2	2	no	—
495	C₂²	—	2	2	no	—
496	C₂²	—	4	4	no	—
497	C₂²	—	4	4	no	—
498	C₂²	—	4	4	no	—
499	C₂²	—	4	4	no	—
500	C₂²	—	8	8	no	—
501	C₂²	C₇×#547	1	2	yes	—
502	C₂²	C₂×C₇×#135	1	4	yes	—
503	C₂²	C₂×C₇×#135	1	2	yes	—
504	C₂²	C₇×#576	1	2	yes	—
505	C₂²	C₂³×C₇×D₄	1	1	yes	characteristic
506	C₄	—	2	2	no	—
507	C₄	—	2	2	no	—
508	C₄	—	2	2	no	—
509	C₄	—	2	2	no	—
510	C₄	—	4	4	no	—
511	C₄	—	4	4	no	—
512	C₄	—	4	4	no	—
513	C₄	C₇×#547	1	2	yes	—
514	C₄	C₂²×C₇×#41	1	1	yes	characteristic
515	C₄	C₂×C₇×2₋¹⁺⁴	1	1	yes	characteristic
516	C₂	—	2	4	no	—
517	C₂	—	4	2	no	—
518	C₂	—	8	4	no	—
519	C₂	C₇×#3339	1	4	yes	direct product factor
520	C₂	C₂×C₇×#547	1	1	yes	characteristic
521	C₂	C₂²×C₇×#135	1	1	yes	characteristic
522	C₂	C₂×C₇×#576	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₇	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₇
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₇ ◁ C₂×C₄×C₇×D₄ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₇×#553	C₂	semidirect
2. C₇×#3339	C₂	direct (N × H)
3. C₂×C₇×#499	C₂	semidirect
4. C₂×C₇×#481	C₂	semidirect
5. C₂×C₇×#482	C₂	semidirect
6. C₂×C₇×#478	C₂	semidirect
7. C₂×C₇×#466	C₂	semidirect
8. C₂×C₇×#466	C₂	semidirect
9. C₂×C₄×C₇×D₈	C₂	semidirect
10. C₂×C₇×C₈×D₄	C₂	semidirect
11. C₂×C₇×#427	C₂	semidirect
12. C₂²×C₇×#107	C₂	semidirect
17. C₇×#553	C₂²	semidirect
29. C₇×#499	C₂²	semidirect
30. C₇×#482	C₂²	semidirect
31. C₇×#481	C₂²	semidirect
32. C₇×#478	C₂²	semidirect
33. C₇×#466	C₂²	semidirect
34. C₇×#466	C₂²	semidirect
35. C₄×C₇×D₈	C₂²	semidirect
36. C₇×C₈×D₄	C₂²	semidirect
37. C₇×#427	C₂²	semidirect
42. C₂×C₇×#107	C₂²	semidirect
52. C₂×#3339	C₇	direct (N × H)
117. C₂×#553	C₂×C₇	semidirect
118. #3339	C₂×C₇	direct (N × H)
119. C₂×#499	C₂×C₇	semidirect
120. C₂×#481	C₂×C₇	semidirect
121. C₂×#482	C₂×C₇	semidirect
122. C₂×#478	C₂×C₇	semidirect
123. C₂×#466	C₂×C₇	semidirect
124. C₂×#466	C₂×C₇	semidirect
125. C₂×C₄×D₈	C₂×C₇	semidirect
126. C₂×C₈×D₄	C₂×C₇	semidirect
127. C₂×#427	C₂×C₇	semidirect
128. C₂²×#107	C₂×C₇	semidirect
196. #553	C₂²×C₇	semidirect
208. #499	C₂²×C₇	semidirect
209. #482	C₂²×C₇	semidirect
210. #481	C₂²×C₇	semidirect
211. #478	C₂²×C₇	semidirect
212. #466	C₂²×C₇	semidirect
213. #466	C₂²×C₇	semidirect
214. C₄×D₈	C₂²×C₇	semidirect
215. C₈×D₄	C₂²×C₇	semidirect
216. #427	C₂²×C₇	semidirect
221. C₂×#107	C₂²×C₇	semidirect
436. C₂×C₇	#3339	direct (N × H)
489. C₇	C₂×#3339	direct (N × H)
519. C₂	C₇×#3339	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×#553	2
C₇×#3339	2
C₂×C₇×#499	2
C₂×C₇×#481	2
C₂×C₇×#482	2
C₂×C₇×#478	2
C₂×C₇×#466	2
C₂×C₄×C₇×D₈	2
C₂×C₇×C₈×D₄	2
C₂×C₇×#427	2
C₂²×C₇×#107	2
C₂×#3339	7

Subgroups — C2×C7×#3339 #13238446

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₇×#3339 #13238446