Subgroups — C₂×C₇×#2482 #13212020

Order 1792.

4166 conjugacy classes of subgroups.

The subgroup lattice has 436 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₇×#117	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂³×C₇×C₂²⋊C₄	C₂	1	1	yes	maximal, characteristic
3	C₇×#2482	C₂	1	16	yes	maximal, direct product factor
4	C₂×C₇×#399	C₂	1	2	yes	maximal, complemented
5	C₂×C₇×#397	C₂	1	2	yes	maximal, complemented
6	C₂×C₇×#388	C₂	1	4	yes	maximal, complemented
7	C₂×C₇×#385	C₂	1	2	yes	maximal, complemented
8	C₂×C₇×#381	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×C₇×#379	C₂	1	2	yes	maximal
10	C₂⁶×C₇	C₂²	1	1	yes	characteristic
11	C₂⁴×C₄×C₇	C₂²	1	1	yes	characteristic
12	C₂⁴×C₄×C₇	C₂²	1	1	yes	characteristic
13	C₂×C₇×#117	—	2	8	no	—
14	C₂×C₇×#117	C₂²	1	8	yes	complemented
15	C₂²×C₇×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
16	C₂²×C₇×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
17	C₂²×C₇×C₄⋊C₄	C₂²	1	4	yes	complemented
18	C₂²×C₇×C₂²⋊C₄	—	2	8	no	—
19	C₂²×C₇×C₂²⋊C₄	C₂²	1	2	yes	—
20	C₂²×C₇×C₂²⋊C₄	C₂²	1	4	yes	—
21	C₂²×C₇×C₂²⋊C₄	C₂²	1	8	yes	—
22	C₂²×C₇×C₂²⋊C₄	C₂²	1	2	yes	—
23	C₂²×C₇×C₂²⋊C₄	C₂²	1	2	yes	—
24	C₂²×C₇×C₂²⋊C₄	C₂²	1	2	yes	—
25	C₂²×C₇×C₂²⋊C₄	C₂²	1	4	yes	—
26	C₂²×C₄²×C₇	C₂²	1	2	yes	complemented
27	C₇×#399	C₂²	1	16	yes	complemented
28	C₇×#397	C₂²	1	16	yes	complemented
29	C₇×#388	C₂²	1	32	yes	complemented
30	C₇×#385	C₂²	1	16	yes	complemented
31	C₇×#381	C₂²	1	8	yes	complemented
32	C₇×#379	C₂²	1	16	yes	—
33	C₂×C₇×#95	C₂²	1	2	yes	complemented
34	C₂×C₇×#95	C₂²	1	4	yes	complemented
35	C₂×C₇×#95	C₂²	1	2	yes	complemented
36	C₂×#2482	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
37	C₂⁵×C₇	—	2	4	no	—
38	C₂⁵×C₇	—	2	8	no	—
39	C₂⁵×C₇	—	2	8	no	—
40	C₂⁵×C₇	—	4	4	no	—
41	C₂⁵×C₇	C₂³	1	2	yes	—
42	C₂⁵×C₇	C₂³	1	4	yes	—
43	C₂⁵×C₇	C₂³	1	1	yes	characteristic
44	C₂³×C₄×C₇	—	2	8	no	—
45	C₂³×C₄×C₇	—	2	4	no	—
46	C₂³×C₄×C₇	—	4	4	no	—
47	C₂³×C₄×C₇	D₄	1	8	yes	—
48	C₂³×C₄×C₇	C₂³	1	2	yes	—
49	C₂³×C₄×C₇	C₂³	1	2	yes	—
50	C₂³×C₄×C₇	C₂³	1	4	yes	—
51	C₂³×C₄×C₇	C₂³	1	2	yes	—
52	C₂³×C₄×C₇	C₂³	1	4	yes	—
53	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
54	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
55	C₂³×C₄×C₇	C₂³	1	4	yes	—
56	C₇×#117	—	2	32	no	—
57	C₂×C₇×C₄⋊C₄	—	2	4	no	—
58	C₂×C₇×C₄⋊C₄	—	2	4	no	—
59	C₂×C₇×C₄⋊C₄	—	4	8	no	—
60	C₂×C₇×C₄⋊C₄	C₂³	1	4	yes	complemented
61	C₂×C₇×C₄⋊C₄	C₂³	1	4	yes	complemented
62	C₂×C₇×C₄⋊C₄	C₂³	1	16	yes	complemented
63	C₂×C₇×C₂²⋊C₄	—	2	8	no	—
64	C₂×C₇×C₂²⋊C₄	—	2	16	no	—
65	C₂×C₇×C₂²⋊C₄	—	2	8	no	—
66	C₂×C₇×C₂²⋊C₄	—	2	8	no	—
67	C₂×C₇×C₂²⋊C₄	—	2	8	no	—
68	C₂×C₇×C₂²⋊C₄	—	2	32	no	—
69	C₂×C₇×C₂²⋊C₄	—	4	8	no	—
70	C₂×C₇×C₂²⋊C₄	C₂³	1	8	yes	—
71	C₂×C₇×C₂²⋊C₄	C₂³	1	8	yes	—
72	C₂×C₇×C₂²⋊C₄	C₂³	1	8	yes	—
73	C₂×C₇×C₂²⋊C₄	C₂³	1	8	yes	—
74	C₂×C₇×C₂²⋊C₄	C₂³	1	16	yes	—
75	C₂×C₇×C₂²⋊C₄	C₂³	1	16	yes	—
76	C₂×C₄²×C₇	—	2	8	no	—
77	C₂×C₄²×C₇	C₂³	1	8	yes	complemented
78	C₇×#95	C₂³	1	8	yes	complemented
79	C₇×#95	C₂³	1	8	yes	complemented
80	C₇×#95	C₂³	1	16	yes	complemented
81	C₂²×#117	C₂×C₇	1	1	yes	characteristic, complemented
82	C₂³×C₂²⋊C₄	C₂×C₇	1	1	yes	characteristic
83	#2482	C₂×C₇	1	16	yes	direct product factor
84	C₂×#399	C₂×C₇	1	2	yes	complemented
85	C₂×#397	C₂×C₇	1	2	yes	complemented
86	C₂×#388	C₂×C₇	1	4	yes	complemented
87	C₂×#385	C₂×C₇	1	2	yes	complemented
88	C₂×#381	C₂×C₇	1	1	yes	characteristic, complemented
89	C₂×#379	C₂×C₇	1	2	yes	—
90	C₂⁴×C₇	—	2	4	no	—
91	C₂⁴×C₇	—	2	4	no	—
92	C₂⁴×C₇	—	2	32	no	—
93	C₂⁴×C₇	—	2	8	no	—
94	C₂⁴×C₇	—	2	4	no	—
95	C₂⁴×C₇	—	2	16	no	—
96	C₂⁴×C₇	—	2	4	no	—
97	C₂⁴×C₇	—	2	8	no	—
98	C₂⁴×C₇	—	2	8	no	—
99	C₂⁴×C₇	—	2	16	no	—
100	C₂⁴×C₇	—	4	8	no	—
101	C₂⁴×C₇	—	4	64	no	—
102	C₂⁴×C₇	—	4	16	no	—
103	C₂⁴×C₇	—	4	16	no	—
104	C₂⁴×C₇	C₂×D₄	1	4	yes	—
105	C₂⁴×C₇	#41	1	8	yes	—
106	C₂⁴×C₇	#41	1	8	yes	—
107	C₂⁴×C₇	C₂⁴	1	4	yes	—
108	C₂⁴×C₇	C₂⁴	1	2	yes	—
109	C₂⁴×C₇	C₂⁴	1	1	yes	characteristic
110	C₂²×C₄×C₇	—	2	32	no	—
111	C₂²×C₄×C₇	—	2	16	no	—
112	C₂²×C₄×C₇	—	2	4	no	—
113	C₂²×C₄×C₇	—	2	4	no	—
114	C₂²×C₄×C₇	—	2	4	no	—
115	C₂²×C₄×C₇	—	2	4	no	—
116	C₂²×C₄×C₇	—	2	8	no	—
117	C₂²×C₄×C₇	—	2	4	no	—
118	C₂²×C₄×C₇	—	2	8	no	—
119	C₂²×C₄×C₇	—	2	8	no	—
120	C₂²×C₄×C₇	—	2	8	no	—
121	C₂²×C₄×C₇	—	2	8	no	—
122	C₂²×C₄×C₇	—	2	8	no	—
123	C₂²×C₄×C₇	—	2	8	no	—
124	C₂²×C₄×C₇	—	4	8	no	—
125	C₂²×C₄×C₇	—	4	16	no	—
126	C₂²×C₄×C₇	C₂×D₄	1	4	yes	—
127	C₂²×C₄×C₇	C₂×D₄	1	4	yes	—
128	C₂²×C₄×C₇	C₂×D₄	1	16	yes	—
129	C₂²×C₄×C₇	C₂⁴	1	8	yes	—
130	C₂²×C₄×C₇	C₂⁴	1	4	yes	—
131	C₂²×C₄×C₇	C₂⁴	1	4	yes	—
132	C₂²×C₄×C₇	C₂⁴	1	4	yes	—
133	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
134	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
135	C₇×C₄⋊C₄	—	2	8	no	—
136	C₇×C₄⋊C₄	—	2	8	no	—
137	C₇×C₄⋊C₄	—	4	16	no	—
138	C₇×C₂²⋊C₄	—	2	16	no	—
139	C₇×C₂²⋊C₄	—	2	32	no	—
140	C₇×C₂²⋊C₄	—	2	16	no	—
141	C₇×C₂²⋊C₄	—	2	16	no	—
142	C₇×C₂²⋊C₄	—	2	16	no	—
143	C₇×C₂²⋊C₄	—	4	16	no	—
144	C₄²×C₇	—	2	16	no	—
145	C₂⁶	C₂²×C₇	1	1	yes	characteristic
146	C₂⁴×C₄	C₂²×C₇	1	1	yes	characteristic
147	C₂⁴×C₄	C₂²×C₇	1	1	yes	characteristic
148	C₂×#117	—	2	8	no	—
149	C₂×#117	C₂²×C₇	1	8	yes	complemented
150	C₂²×C₄⋊C₄	C₂²×C₇	1	1	yes	characteristic, complemented
151	C₂²×C₄⋊C₄	C₂²×C₇	1	1	yes	characteristic, complemented
152	C₂²×C₄⋊C₄	C₂²×C₇	1	4	yes	complemented
153	C₂²×C₂²⋊C₄	—	2	8	no	—
154	C₂²×C₂²⋊C₄	C₂²×C₇	1	2	yes	—
155	C₂²×C₂²⋊C₄	C₂²×C₇	1	4	yes	—
156	C₂²×C₂²⋊C₄	C₂²×C₇	1	8	yes	—
157	C₂²×C₂²⋊C₄	C₂²×C₇	1	2	yes	—
158	C₂²×C₂²⋊C₄	C₂²×C₇	1	2	yes	—
159	C₂²×C₂²⋊C₄	C₂²×C₇	1	2	yes	—
160	C₂²×C₂²⋊C₄	C₂²×C₇	1	4	yes	—
161	C₂²×C₄²	C₂²×C₇	1	2	yes	complemented
162	#399	C₂²×C₇	1	16	yes	complemented
163	#397	C₂²×C₇	1	16	yes	complemented
164	#388	C₂²×C₇	1	32	yes	complemented
165	#385	C₂²×C₇	1	16	yes	complemented
166	#381	C₂²×C₇	1	8	yes	complemented
167	#379	C₂²×C₇	1	16	yes	—
168	C₂×#95	C₂²×C₇	1	2	yes	complemented
169	C₂×#95	C₂²×C₇	1	4	yes	complemented
170	C₂×#95	C₂²×C₇	1	2	yes	complemented
171	C₂³×C₇	—	2	8	no	—
172	C₂³×C₇	—	2	8	no	—
173	C₂³×C₇	—	2	32	no	—
174	C₂³×C₇	—	2	4	no	—
175	C₂³×C₇	—	2	4	no	—
176	C₂³×C₇	—	2	32	no	—
177	C₂³×C₇	—	2	16	no	—
178	C₂³×C₇	—	2	32	no	—
179	C₂³×C₇	—	2	4	no	—
180	C₂³×C₇	—	2	4	no	—
181	C₂³×C₇	—	2	8	no	—
182	C₂³×C₇	—	2	8	no	—
183	C₂³×C₇	—	4	64	no	—
184	C₂³×C₇	—	4	16	no	—
185	C₂³×C₇	—	4	128	no	—
186	C₂³×C₇	—	4	16	no	—
187	C₂³×C₇	—	4	8	no	—
188	C₂³×C₇	—	4	8	no	—
189	C₂³×C₇	—	4	16	no	—
190	C₂³×C₇	#123	1	16	yes	—
191	C₂³×C₇	C₂²×D₄	1	4	yes	—
192	C₂³×C₇	C₂²×D₄	1	2	yes	—
193	C₂³×C₇	C₂×#41	1	8	yes	—
194	C₂³×C₇	C₂×#41	1	8	yes	—
195	C₂³×C₇	C₂×#41	1	4	yes	—
196	C₂³×C₇	C₂×#41	1	4	yes	—
197	C₂³×C₇	H(5,𝔽₂)	1	4	yes	—
198	C₂³×C₇	C₂⁵	1	1	yes	characteristic
199	C₂×C₄×C₇	—	2	32	no	—
200	C₂×C₄×C₇	—	2	8	no	—
201	C₂×C₄×C₇	—	2	8	no	—
202	C₂×C₄×C₇	—	2	4	no	—
203	C₂×C₄×C₇	—	2	4	no	—
204	C₂×C₄×C₇	—	2	4	no	—
205	C₂×C₄×C₇	—	2	4	no	—
206	C₂×C₄×C₇	—	2	4	no	—
207	C₂×C₄×C₇	—	2	8	no	—
208	C₂×C₄×C₇	—	2	8	no	—
209	C₂×C₄×C₇	—	2	8	no	—
210	C₂×C₄×C₇	—	2	8	no	—
211	C₂×C₄×C₇	—	2	8	no	—
212	C₂×C₄×C₇	—	2	8	no	—
213	C₂×C₄×C₇	—	4	16	no	—
214	C₂×C₄×C₇	—	4	8	no	—
215	C₂×C₄×C₇	—	4	8	no	—
216	C₂×C₄×C₇	—	4	8	no	—
217	C₂×C₄×C₇	—	4	16	no	—
218	C₂×C₄×C₇	C₂²×D₄	1	4	yes	—
219	C₂×C₄×C₇	C₂²×D₄	1	4	yes	—
220	C₂⁵	—	2	4	no	—
221	C₂⁵	—	2	8	no	—
222	C₂⁵	—	2	8	no	—
223	C₂⁵	—	4	4	no	—
224	C₂⁵	C₂³×C₇	1	2	yes	—
225	C₂⁵	C₂³×C₇	1	4	yes	—
226	C₂⁵	C₂³×C₇	1	1	yes	characteristic
227	C₂³×C₄	—	2	8	no	—
228	C₂³×C₄	—	2	4	no	—
229	C₂³×C₄	—	4	4	no	—
230	C₂³×C₄	C₇×D₄	1	8	yes	—
231	C₂³×C₄	C₂³×C₇	1	2	yes	—
232	C₂³×C₄	C₂³×C₇	1	4	yes	—
233	C₂³×C₄	C₂³×C₇	1	2	yes	—
234	C₂³×C₄	C₂³×C₇	1	2	yes	—
235	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
236	C₂³×C₄	C₂³×C₇	1	4	yes	—
237	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
238	C₂³×C₄	C₂³×C₇	1	4	yes	—
239	#117	—	2	32	no	—
240	C₂×C₄⋊C₄	—	2	4	no	—
241	C₂×C₄⋊C₄	—	2	4	no	—
242	C₂×C₄⋊C₄	—	4	8	no	—
243	C₂×C₄⋊C₄	C₂³×C₇	1	4	yes	complemented
244	C₂×C₄⋊C₄	C₂³×C₇	1	4	yes	complemented
245	C₂×C₄⋊C₄	C₂³×C₇	1	16	yes	complemented
246	C₂×C₂²⋊C₄	—	2	8	no	—
247	C₂×C₂²⋊C₄	—	2	16	no	—
248	C₂×C₂²⋊C₄	—	2	8	no	—
249	C₂×C₂²⋊C₄	—	2	8	no	—
250	C₂×C₂²⋊C₄	—	2	8	no	—
251	C₂×C₂²⋊C₄	—	2	32	no	—
252	C₂×C₂²⋊C₄	—	4	8	no	—
253	C₂×C₂²⋊C₄	C₂³×C₇	1	8	yes	—
254	C₂×C₂²⋊C₄	C₂³×C₇	1	8	yes	—
255	C₂×C₂²⋊C₄	C₂³×C₇	1	8	yes	—
256	C₂×C₂²⋊C₄	C₂³×C₇	1	8	yes	—
257	C₂×C₂²⋊C₄	C₂³×C₇	1	16	yes	—
258	C₂×C₂²⋊C₄	C₂³×C₇	1	16	yes	—
259	C₂×C₄²	—	2	8	no	—
260	C₂×C₄²	C₂³×C₇	1	8	yes	complemented
261	#95	C₂³×C₇	1	8	yes	complemented
262	#95	C₂³×C₇	1	8	yes	complemented
263	#95	C₂³×C₇	1	16	yes	complemented
264	C₂²×C₇	—	2	4	no	—
265	C₂²×C₇	—	2	4	no	—
266	C₂²×C₇	—	2	16	no	—
267	C₂²×C₇	—	2	32	no	—
268	C₂²×C₇	—	2	8	no	—
269	C₂²×C₇	—	2	16	no	—
270	C₂²×C₇	—	4	64	no	—
271	C₂²×C₇	—	4	4	no	—
272	C₂²×C₇	—	4	4	no	—
273	C₂²×C₇	—	4	8	no	—
274	C₂²×C₇	—	4	32	no	—
275	C₂²×C₇	C₂×#123	1	8	yes	—
276	C₂²×C₇	C₂×#123	1	4	yes	—
277	C₂²×C₇	#525	1	4	yes	—
278	C₂²×C₇	#535	1	4	yes	—
279	C₂²×C₇	#551	1	16	yes	—
280	C₂²×C₇	C₂³×D₄	1	1	yes	characteristic
281	C₂²×C₇	C₂²×#41	1	2	yes	—
282	C₂²×C₇	C₂²×#41	1	2	yes	—
283	C₂²×C₇	C₂×H(5,𝔽₂)	1	2	yes	—
284	C₄×C₇	—	2	4	no	—
285	C₄×C₇	—	2	4	no	—
286	C₄×C₇	—	4	4	no	—
287	C₄×C₇	—	4	4	no	—
288	C₄×C₇	—	4	4	no	—
289	C₄×C₇	—	4	8	no	—
290	C₂⁴	—	2	4	no	—
291	C₂⁴	—	2	4	no	—
292	C₂⁴	—	2	32	no	—
293	C₂⁴	—	2	8	no	—
294	C₂⁴	—	2	4	no	—
295	C₂⁴	—	2	16	no	—
296	C₂⁴	—	2	4	no	—
297	C₂⁴	—	2	8	no	—
298	C₂⁴	—	2	8	no	—
299	C₂⁴	—	2	16	no	—
300	C₂⁴	—	4	8	no	—
301	C₂⁴	—	4	64	no	—
302	C₂⁴	—	4	16	no	—
303	C₂⁴	—	4	16	no	—
304	C₂⁴	C₂×C₇×D₄	1	4	yes	—
305	C₂⁴	C₇×#41	1	8	yes	—
306	C₂⁴	C₇×#41	1	8	yes	—
307	C₂⁴	C₂⁴×C₇	1	4	yes	—
308	C₂⁴	C₂⁴×C₇	1	2	yes	—
309	C₂⁴	C₂⁴×C₇	1	1	yes	characteristic
310	C₂²×C₄	—	2	32	no	—
311	C₂²×C₄	—	2	16	no	—
312	C₂²×C₄	—	2	4	no	—
313	C₂²×C₄	—	2	4	no	—
314	C₂²×C₄	—	2	4	no	—
315	C₂²×C₄	—	2	4	no	—
316	C₂²×C₄	—	2	8	no	—
317	C₂²×C₄	—	2	4	no	—
318	C₂²×C₄	—	2	8	no	—
319	C₂²×C₄	—	2	8	no	—
320	C₂²×C₄	—	2	8	no	—
321	C₂²×C₄	—	2	8	no	—
322	C₂²×C₄	—	2	8	no	—
323	C₂²×C₄	—	2	8	no	—
324	C₂²×C₄	—	4	8	no	—
325	C₂²×C₄	—	4	16	no	—
326	C₂²×C₄	C₂×C₇×D₄	1	4	yes	—
327	C₂²×C₄	C₂×C₇×D₄	1	4	yes	—
328	C₂²×C₄	C₂×C₇×D₄	1	16	yes	—
329	C₂²×C₄	C₂⁴×C₇	1	8	yes	—
330	C₂²×C₄	C₂⁴×C₇	1	4	yes	—
331	C₂²×C₄	C₂⁴×C₇	1	4	yes	—
332	C₂²×C₄	C₂⁴×C₇	1	4	yes	—
333	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
334	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
335	C₄⋊C₄	—	2	8	no	—
336	C₄⋊C₄	—	2	8	no	—
337	C₄⋊C₄	—	4	16	no	—
338	C₂²⋊C₄	—	2	16	no	—
339	C₂²⋊C₄	—	2	32	no	—
340	C₂²⋊C₄	—	2	16	no	—
341	C₂²⋊C₄	—	2	16	no	—
342	C₂²⋊C₄	—	2	16	no	—
343	C₂²⋊C₄	—	4	16	no	—
344	C₄²	—	2	16	no	—
345	C₂×C₇	—	2	8	no	—
346	C₂×C₇	—	4	8	no	—
347	C₂×C₇	#2482	1	8	yes	direct product factor
348	C₂×C₇	C₂²×#123	1	1	yes	characteristic
349	C₂×C₇	C₂×#525	1	1	yes	characteristic
350	C₂×C₇	C₂×#535	1	1	yes	characteristic
351	C₂×C₇	C₂×#551	1	4	yes	—
352	C₂³	—	2	4	no	—
353	C₂³	—	2	4	no	—
354	C₂³	—	2	8	no	—
355	C₂³	—	2	8	no	—
356	C₂³	—	2	32	no	—
357	C₂³	—	2	32	no	—
358	C₂³	—	2	4	no	—
359	C₂³	—	2	4	no	—
360	C₂³	—	2	8	no	—
361	C₂³	—	2	8	no	—
362	C₂³	—	2	16	no	—
363	C₂³	—	2	32	no	—
364	C₂³	—	4	64	no	—
365	C₂³	—	4	128	no	—
366	C₂³	—	4	16	no	—
367	C₂³	—	4	16	no	—
368	C₂³	—	4	8	no	—
369	C₂³	—	4	8	no	—
370	C₂³	—	4	16	no	—
371	C₂³	C₇×#123	1	16	yes	—
372	C₂³	C₂²×C₇×D₄	1	4	yes	—
373	C₂³	C₂²×C₇×D₄	1	2	yes	—
374	C₂³	C₂×C₇×#41	1	8	yes	—
375	C₂³	C₂×C₇×#41	1	8	yes	—
376	C₂³	C₂×C₇×#41	1	4	yes	—
377	C₂³	C₂×C₇×#41	1	4	yes	—
378	C₂³	C₇×H(5,𝔽₂)	1	4	yes	—
379	C₂³	C₂⁵×C₇	1	1	yes	characteristic
380	C₂×C₄	—	2	4	no	—
381	C₂×C₄	—	2	4	no	—
382	C₂×C₄	—	2	32	no	—
383	C₂×C₄	—	2	8	no	—
384	C₂×C₄	—	2	8	no	—
385	C₂×C₄	—	2	4	no	—
386	C₂×C₄	—	2	4	no	—
387	C₂×C₄	—	2	4	no	—
388	C₂×C₄	—	2	8	no	—
389	C₂×C₄	—	2	8	no	—
390	C₂×C₄	—	2	8	no	—
391	C₂×C₄	—	2	8	no	—
392	C₂×C₄	—	2	8	no	—
393	C₂×C₄	—	2	8	no	—
394	C₂×C₄	—	4	16	no	—
395	C₂×C₄	—	4	8	no	—
396	C₂×C₄	—	4	8	no	—
397	C₂×C₄	—	4	8	no	—
398	C₂×C₄	—	4	16	no	—
399	C₂×C₄	C₂²×C₇×D₄	1	4	yes	—
400	C₂×C₄	C₂²×C₇×D₄	1	4	yes	—
401	C₇	C₂×#2482	1	1	yes	characteristic, direct product factor, Sylow
402	C₂²	—	2	32	no	—
403	C₂²	—	2	4	no	—
404	C₂²	—	2	4	no	—
405	C₂²	—	2	16	no	—
406	C₂²	—	2	8	no	—
407	C₂²	—	2	16	no	—
408	C₂²	—	4	64	no	—
409	C₂²	—	4	32	no	—
410	C₂²	—	4	4	no	—
411	C₂²	—	4	4	no	—
412	C₂²	—	4	8	no	—
413	C₂²	C₂×C₇×#123	1	8	yes	—
414	C₂²	C₂×C₇×#123	1	4	yes	—
415	C₂²	C₇×#525	1	4	yes	—
416	C₂²	C₇×#535	1	4	yes	—
417	C₂²	C₇×#551	1	16	yes	—
418	C₂²	C₂³×C₇×D₄	1	1	yes	characteristic
419	C₂²	C₂²×C₇×#41	1	2	yes	—
420	C₂²	C₂²×C₇×#41	1	2	yes	—
421	C₂²	C₂×C₇×H(5,𝔽₂)	1	2	yes	—
422	C₄	—	2	4	no	—
423	C₄	—	2	4	no	—
424	C₄	—	4	4	no	—
425	C₄	—	4	4	no	—
426	C₄	—	4	4	no	—
427	C₄	—	4	8	no	—
428	C₂	—	2	8	no	—
429	C₂	—	4	8	no	—
430	C₂	C₇×#2482	1	8	yes	direct product factor
431	C₂	C₂²×C₇×#123	1	1	yes	characteristic
432	C₂	C₂×C₇×#525	1	1	yes	characteristic
433	C₂	C₂×C₇×#535	1	1	yes	characteristic
434	C₂	C₂×C₇×#551	1	4	yes	—

	subgroup	G/H
center, socle	C₂⁴×C₇	C₂⁴
commutator, Frattini, cosocle	C₂³	C₂⁵×C₇
prime radical	C₂⁶×C₇	C₂²
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂⁴×C₇ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂²×C₇×#117	C₂	semidirect
3. C₇×#2482	C₂	direct (N × H)
4. C₂×C₇×#399	C₂	semidirect
5. C₂×C₇×#397	C₂	semidirect
6. C₂×C₇×#388	C₂	semidirect
7. C₂×C₇×#385	C₂	semidirect
8. C₂×C₇×#381	C₂	semidirect
14. C₂×C₇×#117	C₂²	semidirect
15. C₂²×C₇×C₄⋊C₄	C₂²	semidirect
16. C₂²×C₇×C₄⋊C₄	C₂²	semidirect
17. C₂²×C₇×C₄⋊C₄	C₂²	semidirect
26. C₂²×C₄²×C₇	C₂²	semidirect
27. C₇×#399	C₂²	semidirect
28. C₇×#397	C₂²	semidirect
29. C₇×#388	C₂²	semidirect
30. C₇×#385	C₂²	semidirect
31. C₇×#381	C₂²	semidirect
33. C₂×C₇×#95	C₂²	semidirect
34. C₂×C₇×#95	C₂²	semidirect
35. C₂×C₇×#95	C₂²	semidirect
36. C₂×#2482	C₇	direct (N × H)
60. C₂×C₇×C₄⋊C₄	C₂³	semidirect
61. C₂×C₇×C₄⋊C₄	C₂³	semidirect
62. C₂×C₇×C₄⋊C₄	C₂³	semidirect
77. C₂×C₄²×C₇	C₂³	semidirect
78. C₇×#95	C₂³	semidirect
79. C₇×#95	C₂³	semidirect
80. C₇×#95	C₂³	semidirect
81. C₂²×#117	C₂×C₇	semidirect
83. #2482	C₂×C₇	direct (N × H)
84. C₂×#399	C₂×C₇	semidirect
85. C₂×#397	C₂×C₇	semidirect
86. C₂×#388	C₂×C₇	semidirect
87. C₂×#385	C₂×C₇	semidirect
88. C₂×#381	C₂×C₇	semidirect
149. C₂×#117	C₂²×C₇	semidirect
150. C₂²×C₄⋊C₄	C₂²×C₇	semidirect
151. C₂²×C₄⋊C₄	C₂²×C₇	semidirect
152. C₂²×C₄⋊C₄	C₂²×C₇	semidirect
161. C₂²×C₄²	C₂²×C₇	semidirect
162. #399	C₂²×C₇	semidirect
163. #397	C₂²×C₇	semidirect
164. #388	C₂²×C₇	semidirect
165. #385	C₂²×C₇	semidirect
166. #381	C₂²×C₇	semidirect
168. C₂×#95	C₂²×C₇	semidirect
169. C₂×#95	C₂²×C₇	semidirect
170. C₂×#95	C₂²×C₇	semidirect
243. C₂×C₄⋊C₄	C₂³×C₇	semidirect
244. C₂×C₄⋊C₄	C₂³×C₇	semidirect
245. C₂×C₄⋊C₄	C₂³×C₇	semidirect
260. C₂×C₄²	C₂³×C₇	semidirect
261. #95	C₂³×C₇	semidirect
262. #95	C₂³×C₇	semidirect
263. #95	C₂³×C₇	semidirect
347. C₂×C₇	#2482	direct (N × H)
401. C₇	C₂×#2482	direct (N × H)
430. C₂	C₇×#2482	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×C₇×#117	2
C₂³×C₇×C₂²⋊C₄	2
C₇×#2482	2
C₂×C₇×#399	2
C₂×C₇×#397	2
C₂×C₇×#388	2
C₂×C₇×#385	2
C₂×C₇×#381	2
C₂×C₇×#379	2
C₂×#2482	7

Subgroups — C2×C7×#2482 #13212020

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₇×#2482 #13212020