Subgroups — C₂×C₇×#2556 #13212040

Order 1792.

2726 conjugacy classes of subgroups.

The subgroup lattice has 744 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₇×#125	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×C₇×C₂²⋊Q₈	C₂	1	1	yes	maximal, characteristic
3	C₇×#2556	C₂	1	16	yes	maximal, direct product factor
4	C₂×C₇×#399	C₂	1	1	yes	maximal, characteristic
5	C₂×C₇×#398	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×C₇×#396	C₂	1	1	yes	maximal, characteristic
7	C₂×C₇×#395	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₇×#391	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×C₇×#389	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×C₇×#389	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×C₇×#388	C₂	1	1	yes	maximal, characteristic
12	C₂×C₇×#388	C₂	1	1	yes	maximal, characteristic
13	C₂×C₇×#387	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂×C₇×#385	C₂	1	1	yes	maximal, characteristic
15	C₂×C₄×C₇×C₄⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×C₄×C₇×C₂²⋊C₄	C₂	1	1	yes	maximal, characteristic
17	C₂³×C₇×Q₈	C₂²	1	1	yes	characteristic
18	C₂⁴×C₄×C₇	C₂²	1	1	yes	characteristic
19	C₂×C₇×#125	—	2	8	no	—
20	C₂×C₇×#125	C₂²	1	8	yes	complemented
21	C₂×C₇×C₂²⋊Q₈	—	2	8	no	—
22	C₂×C₇×C₂²⋊Q₈	C₂²	1	8	yes	—
23	C₂²×C₇×C₄⋊C₄	C₂²	1	1	yes	characteristic
24	C₂²×C₇×C₄⋊C₄	C₂²	1	1	yes	characteristic
25	C₂²×C₇×C₄⋊C₄	C₂²	1	1	yes	characteristic
26	C₂²×C₇×C₄⋊C₄	C₂²	1	1	yes	characteristic
27	C₂²×C₇×C₄⋊C₄	C₂²	1	1	yes	characteristic
28	C₂²×C₇×C₄⋊C₄	C₂²	1	1	yes	characteristic
29	C₂²×C₇×C₄⋊C₄	C₂²	1	1	yes	characteristic
30	C₂²×C₇×C₄⋊C₄	C₂²	1	1	yes	characteristic
31	C₂²×C₇×C₄⋊C₄	C₂²	1	1	yes	characteristic
32	C₂²×C₇×C₄⋊C₄	C₂²	1	1	yes	characteristic
33	C₂²×C₇×C₄⋊C₄	C₂²	1	1	yes	characteristic
34	C₂²×C₇×C₄⋊C₄	C₂²	1	1	yes	characteristic
35	C₂²×C₇×C₄⋊C₄	C₂²	1	1	yes	characteristic
36	C₂²×C₇×C₂²⋊C₄	C₂²	1	1	yes	characteristic
37	C₂²×C₇×C₂²⋊C₄	C₂²	1	1	yes	characteristic
38	C₂²×C₇×C₂²⋊C₄	C₂²	1	1	yes	characteristic
39	C₂²×C₇×C₂²⋊C₄	C₂²	1	1	yes	characteristic
40	C₂²×C₇×C₂²⋊C₄	C₂²	1	1	yes	characteristic
41	C₂²×C₇×C₂²⋊C₄	C₂²	1	1	yes	characteristic
42	C₂²×C₄²×C₇	C₂²	1	1	yes	characteristic
43	C₂²×C₄²×C₇	C₂²	1	1	yes	characteristic
44	C₂²×C₄²×C₇	C₂²	1	1	yes	characteristic
45	C₂²×C₄²×C₇	C₂²	1	1	yes	characteristic
46	C₇×#399	C₂²	1	8	yes	—
47	C₇×#398	C₂²	1	8	yes	complemented
48	C₇×#396	C₂²	1	8	yes	—
49	C₇×#395	C₂²	1	8	yes	complemented
50	C₇×#391	C₂²	1	8	yes	complemented
51	C₇×#389	C₂²	1	8	yes	complemented
52	C₇×#389	C₂²	1	8	yes	complemented
53	C₇×#388	C₂²	1	8	yes	—
54	C₇×#388	C₂²	1	8	yes	—
55	C₇×#387	C₂²	1	8	yes	complemented
56	C₇×#385	C₂²	1	8	yes	—
57	C₄×C₇×C₄⋊C₄	C₂²	1	8	yes	complemented
58	C₄×C₇×C₂²⋊C₄	C₂²	1	8	yes	—
59	C₂×C₇×#95	C₂²	1	1	yes	characteristic
60	C₂×C₇×#95	C₂²	1	1	yes	characteristic
61	C₂×C₇×#95	C₂²	1	1	yes	characteristic
62	C₂×C₇×#95	C₂²	1	1	yes	characteristic
63	C₂×C₇×#95	C₂²	1	1	yes	characteristic
64	C₂×C₇×#95	C₂²	1	1	yes	characteristic
65	C₂×C₇×#95	C₂²	1	1	yes	characteristic
66	C₂×C₇×#95	C₂²	1	1	yes	characteristic
67	C₂×C₇×#95	C₂²	1	1	yes	characteristic
68	C₂×C₇×#95	C₂²	1	1	yes	characteristic
69	C₂×#2556	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
70	C₂⁵×C₇	C₂³	1	1	yes	characteristic
71	C₂²×C₇×Q₈	—	2	4	no	—
72	C₂²×C₇×Q₈	—	2	4	no	—
73	C₂²×C₇×Q₈	—	4	2	no	—
74	C₂²×C₇×Q₈	C₂³	1	4	yes	—
75	C₂³×C₄×C₇	—	2	4	no	—
76	C₂³×C₄×C₇	—	2	4	no	—
77	C₂³×C₄×C₇	—	4	2	no	—
78	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
79	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
80	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
81	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
82	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
83	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
84	C₂³×C₄×C₇	C₂³	1	4	yes	—
85	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
86	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
87	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
88	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
89	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
90	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
91	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
92	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
93	C₇×#125	—	2	32	no	—
94	C₇×C₂²⋊Q₈	—	2	32	no	—
95	C₂×C₇×C₄⋊C₄	—	2	4	no	—
96	C₂×C₇×C₄⋊C₄	—	2	4	no	—
97	C₂×C₇×C₄⋊C₄	—	2	4	no	—
98	C₂×C₇×C₄⋊C₄	—	2	4	no	—
99	C₂×C₇×C₄⋊C₄	—	2	4	no	—
100	C₂×C₇×C₄⋊C₄	—	2	4	no	—
101	C₂×C₇×C₄⋊C₄	—	2	4	no	—
102	C₂×C₇×C₄⋊C₄	—	2	4	no	—
103	C₂×C₇×C₄⋊C₄	—	2	4	no	—
104	C₂×C₇×C₄⋊C₄	—	2	4	no	—
105	C₂×C₇×C₄⋊C₄	—	2	4	no	—
106	C₂×C₇×C₄⋊C₄	—	4	2	no	—
107	C₂×C₇×C₄⋊C₄	D₄	1	8	yes	—
108	C₂×C₇×C₄⋊C₄	C₂³	1	4	yes	—
109	C₂×C₇×C₄⋊C₄	C₂³	1	4	yes	—
110	C₂×C₇×C₄⋊C₄	C₂³	1	4	yes	—
111	C₂×C₇×C₄⋊C₄	C₂³	1	4	yes	—
112	C₂×C₇×C₄⋊C₄	C₂³	1	4	yes	—
113	C₂×C₇×C₄⋊C₄	C₂³	1	4	yes	—
114	C₂×C₇×C₄⋊C₄	C₂³	1	4	yes	—
115	C₂×C₇×C₄⋊C₄	C₂³	1	4	yes	—
116	C₂×C₇×C₄⋊C₄	C₂³	1	4	yes	—
117	C₂×C₇×C₄⋊C₄	C₂³	1	4	yes	—
118	C₂×C₇×C₄⋊C₄	C₂³	1	4	yes	—
119	C₂×C₇×C₄⋊C₄	C₂³	1	4	yes	—
120	C₂×C₇×C₄⋊C₄	C₂³	1	4	yes	—
121	C₂×C₇×C₂²⋊C₄	—	2	4	no	—
122	C₂×C₇×C₂²⋊C₄	—	2	4	no	—
123	C₂×C₇×C₂²⋊C₄	—	2	4	no	—
124	C₂×C₇×C₂²⋊C₄	—	2	4	no	—
125	C₂×C₇×C₂²⋊C₄	—	4	2	no	—
126	C₂×C₇×C₂²⋊C₄	Q₈	1	8	yes	complemented
127	C₂×C₇×C₂²⋊C₄	C₂³	1	4	yes	—
128	C₂×C₇×C₂²⋊C₄	C₂³	1	4	yes	—
129	C₂×C₇×C₂²⋊C₄	C₂³	1	4	yes	—
130	C₂×C₇×C₂²⋊C₄	C₂³	1	4	yes	—
131	C₂×C₇×C₂²⋊C₄	C₂³	1	4	yes	—
132	C₂×C₇×C₂²⋊C₄	C₂³	1	4	yes	—
133	C₂×C₄²×C₇	—	2	4	no	—
134	C₂×C₄²×C₇	—	2	4	no	—
135	C₂×C₄²×C₇	—	4	2	no	—
136	C₂×C₄²×C₇	—	4	2	no	—
137	C₂×C₄²×C₇	C₂³	1	4	yes	—
138	C₂×C₄²×C₇	C₂³	1	4	yes	—
139	C₂×C₄²×C₇	C₂³	1	4	yes	—
140	C₂×C₄²×C₇	C₂³	1	4	yes	—
141	C₇×#95	C₂³	1	4	yes	—
142	C₇×#95	C₂³	1	4	yes	—
143	C₇×#95	C₂³	1	4	yes	—
144	C₇×#95	C₂³	1	4	yes	—
145	C₇×#95	C₂³	1	4	yes	—
146	C₇×#95	C₂³	1	4	yes	—
147	C₇×#95	C₂³	1	4	yes	—
148	C₇×#95	C₂³	1	4	yes	—
149	C₇×#95	C₂³	1	4	yes	—
150	C₇×#95	C₂³	1	4	yes	—
151	C₂²×#125	C₂×C₇	1	1	yes	characteristic, complemented
152	C₂²×C₂²⋊Q₈	C₂×C₇	1	1	yes	characteristic
153	#2556	C₂×C₇	1	16	yes	direct product factor
154	C₂×#399	C₂×C₇	1	1	yes	characteristic
155	C₂×#398	C₂×C₇	1	1	yes	characteristic, complemented
156	C₂×#396	C₂×C₇	1	1	yes	characteristic
157	C₂×#395	C₂×C₇	1	1	yes	characteristic, complemented
158	C₂×#391	C₂×C₇	1	1	yes	characteristic, complemented
159	C₂×#389	C₂×C₇	1	1	yes	characteristic, complemented
160	C₂×#389	C₂×C₇	1	1	yes	characteristic, complemented
161	C₂×#388	C₂×C₇	1	1	yes	characteristic
162	C₂×#388	C₂×C₇	1	1	yes	characteristic
163	C₂×#387	C₂×C₇	1	1	yes	characteristic, complemented
164	C₂×#385	C₂×C₇	1	1	yes	characteristic
165	C₂×C₄×C₄⋊C₄	C₂×C₇	1	1	yes	characteristic, complemented
166	C₂×C₄×C₂²⋊C₄	C₂×C₇	1	1	yes	characteristic
167	C₂⁴×C₇	—	2	2	no	—
168	C₂⁴×C₇	—	2	2	no	—
169	C₂⁴×C₇	—	2	2	no	—
170	C₂⁴×C₇	—	2	2	no	—
171	C₂⁴×C₇	—	2	2	no	—
172	C₂⁴×C₇	—	2	2	no	—
173	C₂⁴×C₇	C₂×Q₈	1	4	yes	—
174	C₂⁴×C₇	C₂⁴	1	2	yes	—
175	C₂⁴×C₇	C₂⁴	1	1	yes	characteristic
176	C₂×C₇×Q₈	—	2	8	no	—
177	C₂×C₇×Q₈	—	2	8	no	—
178	C₂×C₇×Q₈	—	4	4	no	—
179	C₂×C₇×Q₈	—	4	16	no	—
180	C₂²×C₄×C₇	—	2	2	no	—
181	C₂²×C₄×C₇	—	2	2	no	—
182	C₂²×C₄×C₇	—	2	2	no	—
183	C₂²×C₄×C₇	—	2	2	no	—
184	C₂²×C₄×C₇	—	2	2	no	—
185	C₂²×C₄×C₇	—	2	2	no	—
186	C₂²×C₄×C₇	—	2	2	no	—
187	C₂²×C₄×C₇	—	2	2	no	—
188	C₂²×C₄×C₇	—	2	2	no	—
189	C₂²×C₄×C₇	—	2	2	no	—
190	C₂²×C₄×C₇	—	2	2	no	—
191	C₂²×C₄×C₇	—	2	2	no	—
192	C₂²×C₄×C₇	—	2	2	no	—
193	C₂²×C₄×C₇	—	2	2	no	—
194	C₂²×C₄×C₇	—	2	2	no	—
195	C₂²×C₄×C₇	—	2	2	no	—
196	C₂²×C₄×C₇	—	2	2	no	—
197	C₂²×C₄×C₇	—	2	2	no	—
198	C₂²×C₄×C₇	—	2	2	no	—
199	C₂²×C₄×C₇	—	2	2	no	—
200	C₂²×C₄×C₇	—	2	2	no	—
201	C₂²×C₄×C₇	—	2	2	no	—
202	C₂²×C₄×C₇	—	2	2	no	—
203	C₂²×C₄×C₇	—	2	2	no	—
204	C₂²×C₄×C₇	—	2	2	no	—
205	C₂²×C₄×C₇	—	2	2	no	—
206	C₂²×C₄×C₇	—	2	2	no	—
207	C₂²×C₄×C₇	—	2	2	no	—
208	C₂²×C₄×C₇	—	2	2	no	—
209	C₂²×C₄×C₇	—	2	2	no	—
210	C₂²×C₄×C₇	—	2	2	no	—
211	C₂²×C₄×C₇	—	2	2	no	—
212	C₂²×C₄×C₇	—	2	2	no	—
213	C₂²×C₄×C₇	—	2	2	no	—
214	C₂²×C₄×C₇	—	2	8	no	—
215	C₂²×C₄×C₇	—	2	8	no	—
216	C₂²×C₄×C₇	—	4	4	no	—
217	C₂²×C₄×C₇	—	4	16	no	—
218	C₂²×C₄×C₇	C₂×D₄	1	4	yes	—
219	C₂²×C₄×C₇	C₂×D₄	1	4	yes	—
220	C₂²×C₄×C₇	C₂×D₄	1	4	yes	—
221	C₂²×C₄×C₇	C₂×Q₈	1	4	yes	—
222	C₂²×C₄×C₇	C₂×Q₈	1	4	yes	—
223	C₂²×C₄×C₇	#41	1	4	yes	—
224	C₂²×C₄×C₇	#41	1	4	yes	—
225	C₂²×C₄×C₇	#41	1	4	yes	—
226	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
227	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
228	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
229	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
230	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
231	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
232	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
233	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
234	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
235	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
236	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
237	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
238	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
239	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
240	C₇×C₄⋊C₄	—	2	8	no	—
241	C₇×C₄⋊C₄	—	2	8	no	—
242	C₇×C₄⋊C₄	—	2	8	no	—
243	C₇×C₄⋊C₄	—	2	8	no	—
244	C₇×C₄⋊C₄	—	2	8	no	—
245	C₇×C₄⋊C₄	—	2	8	no	—
246	C₇×C₄⋊C₄	—	2	8	no	—
247	C₇×C₄⋊C₄	—	2	8	no	—
248	C₇×C₄⋊C₄	—	2	8	no	—
249	C₇×C₄⋊C₄	—	2	8	no	—
250	C₇×C₄⋊C₄	—	2	8	no	—
251	C₇×C₄⋊C₄	—	4	4	no	—
252	C₇×C₄⋊C₄	C₂×D₄	1	16	yes	—
253	C₇×C₂²⋊C₄	—	2	8	no	—
254	C₇×C₂²⋊C₄	—	2	8	no	—
255	C₇×C₂²⋊C₄	—	2	8	no	—
256	C₇×C₂²⋊C₄	—	2	8	no	—
257	C₇×C₂²⋊C₄	—	4	4	no	—
258	C₇×C₂²⋊C₄	C₂×Q₈	1	16	yes	complemented
259	C₄²×C₇	—	2	8	no	—
260	C₄²×C₇	—	2	8	no	—
261	C₄²×C₇	—	4	4	no	—
262	C₄²×C₇	—	4	4	no	—
263	C₂³×Q₈	C₂²×C₇	1	1	yes	characteristic
264	C₂⁴×C₄	C₂²×C₇	1	1	yes	characteristic
265	C₂×#125	—	2	8	no	—
266	C₂×#125	C₂²×C₇	1	8	yes	complemented
267	C₂×C₂²⋊Q₈	—	2	8	no	—
268	C₂×C₂²⋊Q₈	C₂²×C₇	1	8	yes	—
269	C₂²×C₄⋊C₄	C₂²×C₇	1	1	yes	characteristic
270	C₂²×C₄⋊C₄	C₂²×C₇	1	1	yes	characteristic
271	C₂²×C₄⋊C₄	C₂²×C₇	1	1	yes	characteristic
272	C₂²×C₄⋊C₄	C₂²×C₇	1	1	yes	characteristic
273	C₂²×C₄⋊C₄	C₂²×C₇	1	1	yes	characteristic
274	C₂²×C₄⋊C₄	C₂²×C₇	1	1	yes	characteristic
275	C₂²×C₄⋊C₄	C₂²×C₇	1	1	yes	characteristic
276	C₂²×C₄⋊C₄	C₂²×C₇	1	1	yes	characteristic
277	C₂²×C₄⋊C₄	C₂²×C₇	1	1	yes	characteristic
278	C₂²×C₄⋊C₄	C₂²×C₇	1	1	yes	characteristic
279	C₂²×C₄⋊C₄	C₂²×C₇	1	1	yes	characteristic
280	C₂²×C₄⋊C₄	C₂²×C₇	1	1	yes	characteristic
281	C₂²×C₄⋊C₄	C₂²×C₇	1	1	yes	characteristic
282	C₂²×C₂²⋊C₄	C₂²×C₇	1	1	yes	characteristic
283	C₂²×C₂²⋊C₄	C₂²×C₇	1	1	yes	characteristic
284	C₂²×C₂²⋊C₄	C₂²×C₇	1	1	yes	characteristic
285	C₂²×C₂²⋊C₄	C₂²×C₇	1	1	yes	characteristic
286	C₂²×C₂²⋊C₄	C₂²×C₇	1	1	yes	characteristic
287	C₂²×C₂²⋊C₄	C₂²×C₇	1	1	yes	characteristic
288	C₂²×C₄²	C₂²×C₇	1	1	yes	characteristic
289	C₂²×C₄²	C₂²×C₇	1	1	yes	characteristic
290	C₂²×C₄²	C₂²×C₇	1	1	yes	characteristic
291	C₂²×C₄²	C₂²×C₇	1	1	yes	characteristic
292	#399	C₂²×C₇	1	8	yes	—
293	#398	C₂²×C₇	1	8	yes	complemented
294	#396	C₂²×C₇	1	8	yes	—
295	#395	C₂²×C₇	1	8	yes	complemented
296	#391	C₂²×C₇	1	8	yes	complemented
297	#389	C₂²×C₇	1	8	yes	complemented
298	#389	C₂²×C₇	1	8	yes	complemented
299	#388	C₂²×C₇	1	8	yes	—
300	#388	C₂²×C₇	1	8	yes	—
301	#387	C₂²×C₇	1	8	yes	complemented
302	#385	C₂²×C₇	1	8	yes	—
303	C₄×C₄⋊C₄	C₂²×C₇	1	8	yes	complemented
304	C₄×C₂²⋊C₄	C₂²×C₇	1	8	yes	—
305	C₂×#95	C₂²×C₇	1	1	yes	characteristic
306	C₂×#95	C₂²×C₇	1	1	yes	characteristic
307	C₂×#95	C₂²×C₇	1	1	yes	characteristic
308	C₂×#95	C₂²×C₇	1	1	yes	characteristic
309	C₂×#95	C₂²×C₇	1	1	yes	characteristic
310	C₂×#95	C₂²×C₇	1	1	yes	characteristic
311	C₂×#95	C₂²×C₇	1	1	yes	characteristic
312	C₂×#95	C₂²×C₇	1	1	yes	characteristic
313	C₂×#95	C₂²×C₇	1	1	yes	characteristic
314	C₂×#95	C₂²×C₇	1	1	yes	characteristic
315	C₂³×C₇	—	2	8	no	—
316	C₂³×C₇	—	2	8	no	—
317	C₂³×C₇	—	2	8	no	—
318	C₂³×C₇	—	2	2	no	—
319	C₂³×C₇	—	2	2	no	—
320	C₂³×C₇	—	2	2	no	—
321	C₂³×C₇	—	2	2	no	—
322	C₂³×C₇	—	2	2	no	—
323	C₂³×C₇	—	2	2	no	—
324	C₂³×C₇	—	4	4	no	—
325	C₂³×C₇	—	4	4	no	—
326	C₂³×C₇	—	4	4	no	—
327	C₂³×C₇	—	4	4	no	—
328	C₂³×C₇	C₂²×D₄	1	2	yes	—
329	C₂³×C₇	C₂²×Q₈	1	4	yes	—
330	C₂³×C₇	C₂²×Q₈	1	2	yes	—
331	C₂³×C₇	C₂×#41	1	2	yes	—
332	C₂³×C₇	C₂×#41	1	2	yes	—
333	C₂³×C₇	C₂×#41	1	2	yes	—
334	C₂³×C₇	H(5,𝔽₂)	1	2	yes	—
335	C₂³×C₇	2₋¹⁺⁴	1	2	yes	—
336	C₂³×C₇	C₂⁵	1	1	yes	characteristic
337	C₇×Q₈	—	4	16	no	—
338	C₂×C₄×C₇	—	2	8	no	—
339	C₂×C₄×C₇	—	2	8	no	—
340	C₂×C₄×C₇	—	2	8	no	—
341	C₂×C₄×C₇	—	2	8	no	—
342	C₂×C₄×C₇	—	2	8	no	—
343	C₂×C₄×C₇	—	2	8	no	—
344	C₂×C₄×C₇	—	2	8	no	—
345	C₂×C₄×C₇	—	2	8	no	—
346	C₂×C₄×C₇	—	2	2	no	—
347	C₂×C₄×C₇	—	2	2	no	—
348	C₂×C₄×C₇	—	2	2	no	—
349	C₂×C₄×C₇	—	2	2	no	—
350	C₂×C₄×C₇	—	2	2	no	—
351	C₂×C₄×C₇	—	2	2	no	—
352	C₂×C₄×C₇	—	2	2	no	—
353	C₂×C₄×C₇	—	2	2	no	—
354	C₂×C₄×C₇	—	2	2	no	—
355	C₂×C₄×C₇	—	2	2	no	—
356	C₂×C₄×C₇	—	2	2	no	—
357	C₂×C₄×C₇	—	2	2	no	—
358	C₂×C₄×C₇	—	2	2	no	—
359	C₂×C₄×C₇	—	2	2	no	—
360	C₂×C₄×C₇	—	2	2	no	—
361	C₂×C₄×C₇	—	2	2	no	—
362	C₂×C₄×C₇	—	2	2	no	—
363	C₂×C₄×C₇	—	2	2	no	—
364	C₂×C₄×C₇	—	2	2	no	—
365	C₂×C₄×C₇	—	2	2	no	—
366	C₂×C₄×C₇	—	2	2	no	—
367	C₂×C₄×C₇	—	2	2	no	—
368	C₂×C₄×C₇	—	2	2	no	—
369	C₂×C₄×C₇	—	2	2	no	—
370	C₂×C₄×C₇	—	2	2	no	—
371	C₂×C₄×C₇	—	2	2	no	—
372	C₂×C₄×C₇	—	2	2	no	—
373	C₂×C₄×C₇	—	2	2	no	—
374	C₂×C₄×C₇	—	2	2	no	—
375	C₂×C₄×C₇	—	2	2	no	—
376	C₂×C₄×C₇	—	2	2	no	—
377	C₂×C₄×C₇	—	2	2	no	—
378	C₂×C₄×C₇	—	2	2	no	—
379	C₂×C₄×C₇	—	2	2	no	—
380	C₂×C₄×C₇	—	4	16	no	—
381	C₂×C₄×C₇	—	4	4	no	—
382	C₂×C₄×C₇	—	4	4	no	—
383	C₂×C₄×C₇	—	4	4	no	—
384	C₂×C₄×C₇	—	4	4	no	—
385	C₂×C₄×C₇	—	4	4	no	—
386	C₂×C₄×C₇	—	4	4	no	—
387	C₂×C₄×C₇	C₂²×D₄	1	4	yes	—
388	C₂×C₄×C₇	C₂²×D₄	1	4	yes	—
389	C₂×C₄×C₇	C₂²×D₄	1	4	yes	—
390	C₂×C₄×C₇	C₂²×Q₈	1	4	yes	—
391	C₂×C₄×C₇	C₂²×Q₈	1	4	yes	—
392	C₂×C₄×C₇	C₂×#41	1	4	yes	—
393	C₂×C₄×C₇	C₂×#41	1	4	yes	—
394	C₂×C₄×C₇	C₂×#41	1	4	yes	—
395	C₂⁵	C₂³×C₇	1	1	yes	characteristic
396	C₂²×Q₈	—	2	4	no	—
397	C₂²×Q₈	—	2	4	no	—
398	C₂²×Q₈	—	4	2	no	—
399	C₂²×Q₈	C₂³×C₇	1	4	yes	—
400	C₂³×C₄	—	2	4	no	—
401	C₂³×C₄	—	2	4	no	—
402	C₂³×C₄	—	4	2	no	—
403	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
404	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
405	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
406	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
407	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
408	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
409	C₂³×C₄	C₂³×C₇	1	4	yes	—
410	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
411	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
412	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
413	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
414	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
415	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
416	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
417	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
418	#125	—	2	32	no	—
419	C₂²⋊Q₈	—	2	32	no	—
420	C₂×C₄⋊C₄	—	2	4	no	—
421	C₂×C₄⋊C₄	—	2	4	no	—
422	C₂×C₄⋊C₄	—	2	4	no	—
423	C₂×C₄⋊C₄	—	2	4	no	—
424	C₂×C₄⋊C₄	—	2	4	no	—
425	C₂×C₄⋊C₄	—	2	4	no	—
426	C₂×C₄⋊C₄	—	2	4	no	—
427	C₂×C₄⋊C₄	—	2	4	no	—
428	C₂×C₄⋊C₄	—	2	4	no	—
429	C₂×C₄⋊C₄	—	2	4	no	—
430	C₂×C₄⋊C₄	—	2	4	no	—
431	C₂×C₄⋊C₄	—	4	2	no	—
432	C₂×C₄⋊C₄	C₇×D₄	1	8	yes	—
433	C₂×C₄⋊C₄	C₂³×C₇	1	4	yes	—
434	C₂×C₄⋊C₄	C₂³×C₇	1	4	yes	—
435	C₂×C₄⋊C₄	C₂³×C₇	1	4	yes	—
436	C₂×C₄⋊C₄	C₂³×C₇	1	4	yes	—
437	C₂×C₄⋊C₄	C₂³×C₇	1	4	yes	—
438	C₂×C₄⋊C₄	C₂³×C₇	1	4	yes	—
439	C₂×C₄⋊C₄	C₂³×C₇	1	4	yes	—
440	C₂×C₄⋊C₄	C₂³×C₇	1	4	yes	—
441	C₂×C₄⋊C₄	C₂³×C₇	1	4	yes	—
442	C₂×C₄⋊C₄	C₂³×C₇	1	4	yes	—
443	C₂×C₄⋊C₄	C₂³×C₇	1	4	yes	—
444	C₂×C₄⋊C₄	C₂³×C₇	1	4	yes	—
445	C₂×C₄⋊C₄	C₂³×C₇	1	4	yes	—
446	C₂×C₂²⋊C₄	—	2	4	no	—
447	C₂×C₂²⋊C₄	—	2	4	no	—
448	C₂×C₂²⋊C₄	—	2	4	no	—
449	C₂×C₂²⋊C₄	—	2	4	no	—
450	C₂×C₂²⋊C₄	—	4	2	no	—
451	C₂×C₂²⋊C₄	C₇×Q₈	1	8	yes	complemented
452	C₂×C₂²⋊C₄	C₂³×C₇	1	4	yes	—
453	C₂×C₂²⋊C₄	C₂³×C₇	1	4	yes	—
454	C₂×C₂²⋊C₄	C₂³×C₇	1	4	yes	—
455	C₂×C₂²⋊C₄	C₂³×C₇	1	4	yes	—
456	C₂×C₂²⋊C₄	C₂³×C₇	1	4	yes	—
457	C₂×C₂²⋊C₄	C₂³×C₇	1	4	yes	—
458	C₂×C₄²	—	2	4	no	—
459	C₂×C₄²	—	2	4	no	—
460	C₂×C₄²	—	4	2	no	—
461	C₂×C₄²	—	4	2	no	—
462	C₂×C₄²	C₂³×C₇	1	4	yes	—
463	C₂×C₄²	C₂³×C₇	1	4	yes	—
464	C₂×C₄²	C₂³×C₇	1	4	yes	—
465	C₂×C₄²	C₂³×C₇	1	4	yes	—
466	#95	C₂³×C₇	1	4	yes	—
467	#95	C₂³×C₇	1	4	yes	—
468	#95	C₂³×C₇	1	4	yes	—
469	#95	C₂³×C₇	1	4	yes	—
470	#95	C₂³×C₇	1	4	yes	—
471	#95	C₂³×C₇	1	4	yes	—
472	#95	C₂³×C₇	1	4	yes	—
473	#95	C₂³×C₇	1	4	yes	—
474	#95	C₂³×C₇	1	4	yes	—
475	#95	C₂³×C₇	1	4	yes	—
476	C₂²×C₇	—	2	4	no	—
477	C₂²×C₇	—	2	4	no	—
478	C₂²×C₇	—	2	4	no	—
479	C₂²×C₇	—	4	2	no	—
480	C₂²×C₇	—	4	2	no	—
481	C₂²×C₇	—	4	2	no	—
482	C₂²×C₇	—	4	2	no	—
483	C₂²×C₇	—	4	16	no	—
484	C₂²×C₇	#532	1	4	yes	—
485	C₂²×C₇	#533	1	4	yes	—
486	C₂²×C₇	#539	1	4	yes	—
487	C₂²×C₇	#546	1	4	yes	—
488	C₂²×C₇	D₄×Q₈	1	4	yes	—
489	C₂²×C₇	#552	1	4	yes	—
490	C₂²×C₇	#554	1	4	yes	—
491	C₂²×C₇	C₂³×D₄	1	1	yes	characteristic
492	C₂²×C₇	C₂³×Q₈	1	1	yes	characteristic
493	C₂²×C₇	C₂²×#41	1	1	yes	characteristic
494	C₂²×C₇	C₂²×#41	1	1	yes	characteristic
495	C₂²×C₇	C₂²×#41	1	1	yes	characteristic
496	C₂²×C₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
497	C₂²×C₇	C₂×2₋¹⁺⁴	1	1	yes	characteristic
498	C₄×C₇	—	2	4	no	—
499	C₄×C₇	—	2	4	no	—
500	C₄×C₇	—	2	4	no	—
501	C₄×C₇	—	2	4	no	—
502	C₄×C₇	—	2	4	no	—
503	C₄×C₇	—	2	4	no	—
504	C₄×C₇	—	2	4	no	—
505	C₄×C₇	—	2	4	no	—
506	C₄×C₇	—	4	2	no	—
507	C₄×C₇	—	4	2	no	—
508	C₄×C₇	—	4	2	no	—
509	C₄×C₇	—	4	2	no	—
510	C₄×C₇	—	4	2	no	—
511	C₄×C₇	—	4	2	no	—
512	C₂⁴	—	2	2	no	—
513	C₂⁴	—	2	2	no	—
514	C₂⁴	—	2	2	no	—
515	C₂⁴	—	2	2	no	—
516	C₂⁴	—	2	2	no	—
517	C₂⁴	—	2	2	no	—
518	C₂⁴	C₂×C₇×Q₈	1	4	yes	—
519	C₂⁴	C₂⁴×C₇	1	2	yes	—
520	C₂⁴	C₂⁴×C₇	1	1	yes	characteristic
521	C₂×Q₈	—	2	8	no	—
522	C₂×Q₈	—	2	8	no	—
523	C₂×Q₈	—	4	4	no	—
524	C₂×Q₈	—	4	16	no	—
525	C₂²×C₄	—	2	2	no	—
526	C₂²×C₄	—	2	2	no	—
527	C₂²×C₄	—	2	2	no	—
528	C₂²×C₄	—	2	2	no	—
529	C₂²×C₄	—	2	2	no	—
530	C₂²×C₄	—	2	2	no	—
531	C₂²×C₄	—	2	2	no	—
532	C₂²×C₄	—	2	2	no	—
533	C₂²×C₄	—	2	2	no	—
534	C₂²×C₄	—	2	2	no	—
535	C₂²×C₄	—	2	2	no	—
536	C₂²×C₄	—	2	2	no	—
537	C₂²×C₄	—	2	2	no	—
538	C₂²×C₄	—	2	2	no	—
539	C₂²×C₄	—	2	2	no	—
540	C₂²×C₄	—	2	2	no	—
541	C₂²×C₄	—	2	2	no	—
542	C₂²×C₄	—	2	2	no	—
543	C₂²×C₄	—	2	2	no	—
544	C₂²×C₄	—	2	2	no	—
545	C₂²×C₄	—	2	2	no	—
546	C₂²×C₄	—	2	2	no	—
547	C₂²×C₄	—	2	2	no	—
548	C₂²×C₄	—	2	2	no	—
549	C₂²×C₄	—	2	2	no	—
550	C₂²×C₄	—	2	2	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	2	no	—
556	C₂²×C₄	—	2	2	no	—
557	C₂²×C₄	—	2	2	no	—
558	C₂²×C₄	—	2	2	no	—
559	C₂²×C₄	—	2	8	no	—
560	C₂²×C₄	—	2	8	no	—
561	C₂²×C₄	—	4	4	no	—
562	C₂²×C₄	—	4	16	no	—
563	C₂²×C₄	C₂×C₇×D₄	1	4	yes	—
564	C₂²×C₄	C₂×C₇×D₄	1	4	yes	—
565	C₂²×C₄	C₂×C₇×D₄	1	4	yes	—
566	C₂²×C₄	C₂×C₇×Q₈	1	4	yes	—
567	C₂²×C₄	C₂×C₇×Q₈	1	4	yes	—
568	C₂²×C₄	C₇×#41	1	4	yes	—
569	C₂²×C₄	C₇×#41	1	4	yes	—
570	C₂²×C₄	C₇×#41	1	4	yes	—
571	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
572	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
573	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
574	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
575	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
576	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
577	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
578	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
579	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
580	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
581	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
582	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
583	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
584	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
585	C₄⋊C₄	—	2	8	no	—
586	C₄⋊C₄	—	2	8	no	—
587	C₄⋊C₄	—	2	8	no	—
588	C₄⋊C₄	—	2	8	no	—
589	C₄⋊C₄	—	2	8	no	—
590	C₄⋊C₄	—	2	8	no	—
591	C₄⋊C₄	—	2	8	no	—
592	C₄⋊C₄	—	2	8	no	—
593	C₄⋊C₄	—	2	8	no	—
594	C₄⋊C₄	—	2	8	no	—
595	C₄⋊C₄	—	2	8	no	—
596	C₄⋊C₄	—	4	4	no	—
597	C₄⋊C₄	C₂×C₇×D₄	1	16	yes	—
598	C₂²⋊C₄	—	2	8	no	—
599	C₂²⋊C₄	—	2	8	no	—
600	C₂²⋊C₄	—	2	8	no	—
601	C₂²⋊C₄	—	2	8	no	—
602	C₂²⋊C₄	—	4	4	no	—
603	C₂²⋊C₄	C₂×C₇×Q₈	1	16	yes	complemented
604	C₄²	—	2	8	no	—
605	C₄²	—	2	8	no	—
606	C₄²	—	4	4	no	—
607	C₄²	—	4	4	no	—
608	C₂×C₇	—	4	4	no	—
609	C₂×C₇	#2556	1	8	yes	direct product factor
610	C₂×C₇	C₂×#532	1	1	yes	characteristic
611	C₂×C₇	C₂×#533	1	1	yes	characteristic
612	C₂×C₇	C₂×#539	1	1	yes	characteristic
613	C₂×C₇	C₂×#546	1	1	yes	characteristic
614	C₂×C₇	C₂×D₄×Q₈	1	1	yes	characteristic
615	C₂×C₇	C₂×#552	1	1	yes	characteristic
616	C₂×C₇	C₂×#554	1	1	yes	characteristic
617	C₂³	—	2	2	no	—
618	C₂³	—	2	2	no	—
619	C₂³	—	2	2	no	—
620	C₂³	—	2	2	no	—
621	C₂³	—	2	2	no	—
622	C₂³	—	2	2	no	—
623	C₂³	—	2	8	no	—
624	C₂³	—	2	8	no	—
625	C₂³	—	2	8	no	—
626	C₂³	—	4	4	no	—
627	C₂³	—	4	4	no	—
628	C₂³	—	4	4	no	—
629	C₂³	—	4	4	no	—
630	C₂³	C₂²×C₇×D₄	1	2	yes	—
631	C₂³	C₂²×C₇×Q₈	1	4	yes	—
632	C₂³	C₂²×C₇×Q₈	1	2	yes	—
633	C₂³	C₂×C₇×#41	1	2	yes	—
634	C₂³	C₂×C₇×#41	1	2	yes	—
635	C₂³	C₂×C₇×#41	1	2	yes	—
636	C₂³	C₇×H(5,𝔽₂)	1	2	yes	—
637	C₂³	C₇×2₋¹⁺⁴	1	2	yes	—
638	C₂³	C₂⁵×C₇	1	1	yes	characteristic
639	Q₈	—	4	16	no	—
640	C₂×C₄	—	2	2	no	—
641	C₂×C₄	—	2	2	no	—
642	C₂×C₄	—	2	2	no	—
643	C₂×C₄	—	2	2	no	—
644	C₂×C₄	—	2	2	no	—
645	C₂×C₄	—	2	2	no	—
646	C₂×C₄	—	2	2	no	—
647	C₂×C₄	—	2	2	no	—
648	C₂×C₄	—	2	2	no	—
649	C₂×C₄	—	2	2	no	—
650	C₂×C₄	—	2	2	no	—
651	C₂×C₄	—	2	2	no	—
652	C₂×C₄	—	2	2	no	—
653	C₂×C₄	—	2	2	no	—
654	C₂×C₄	—	2	2	no	—
655	C₂×C₄	—	2	2	no	—
656	C₂×C₄	—	2	8	no	—
657	C₂×C₄	—	2	8	no	—
658	C₂×C₄	—	2	8	no	—
659	C₂×C₄	—	2	8	no	—
660	C₂×C₄	—	2	8	no	—
661	C₂×C₄	—	2	8	no	—
662	C₂×C₄	—	2	8	no	—
663	C₂×C₄	—	2	8	no	—
664	C₂×C₄	—	2	2	no	—
665	C₂×C₄	—	2	2	no	—
666	C₂×C₄	—	2	2	no	—
667	C₂×C₄	—	2	2	no	—
668	C₂×C₄	—	2	2	no	—
669	C₂×C₄	—	2	2	no	—
670	C₂×C₄	—	2	2	no	—
671	C₂×C₄	—	2	2	no	—
672	C₂×C₄	—	2	2	no	—
673	C₂×C₄	—	2	2	no	—
674	C₂×C₄	—	2	2	no	—
675	C₂×C₄	—	2	2	no	—
676	C₂×C₄	—	2	2	no	—
677	C₂×C₄	—	2	2	no	—
678	C₂×C₄	—	2	2	no	—
679	C₂×C₄	—	2	2	no	—
680	C₂×C₄	—	2	2	no	—
681	C₂×C₄	—	2	2	no	—
682	C₂×C₄	—	4	16	no	—
683	C₂×C₄	—	4	4	no	—
684	C₂×C₄	—	4	4	no	—
685	C₂×C₄	—	4	4	no	—
686	C₂×C₄	—	4	4	no	—
687	C₂×C₄	—	4	4	no	—
688	C₂×C₄	—	4	4	no	—
689	C₂×C₄	C₂²×C₇×D₄	1	4	yes	—
690	C₂×C₄	C₂²×C₇×D₄	1	4	yes	—
691	C₂×C₄	C₂²×C₇×D₄	1	4	yes	—
692	C₂×C₄	C₂²×C₇×Q₈	1	4	yes	—
693	C₂×C₄	C₂²×C₇×Q₈	1	4	yes	—
694	C₂×C₄	C₂×C₇×#41	1	4	yes	—
695	C₂×C₄	C₂×C₇×#41	1	4	yes	—
696	C₂×C₄	C₂×C₇×#41	1	4	yes	—
697	C₇	C₂×#2556	1	1	yes	characteristic, direct product factor, Sylow
698	C₂²	—	2	4	no	—
699	C₂²	—	2	4	no	—
700	C₂²	—	2	4	no	—
701	C₂²	—	4	2	no	—
702	C₂²	—	4	2	no	—
703	C₂²	—	4	2	no	—
704	C₂²	—	4	2	no	—
705	C₂²	—	4	16	no	—
706	C₂²	C₇×#532	1	4	yes	—
707	C₂²	C₇×#533	1	4	yes	—
708	C₂²	C₇×#539	1	4	yes	—
709	C₂²	C₇×#546	1	4	yes	—
710	C₂²	C₇×D₄×Q₈	1	4	yes	—
711	C₂²	C₇×#552	1	4	yes	—
712	C₂²	C₇×#554	1	4	yes	—
713	C₂²	C₂³×C₇×D₄	1	1	yes	characteristic
714	C₂²	C₂³×C₇×Q₈	1	1	yes	characteristic
715	C₂²	C₂²×C₇×#41	1	1	yes	characteristic
716	C₂²	C₂²×C₇×#41	1	1	yes	characteristic
717	C₂²	C₂²×C₇×#41	1	1	yes	characteristic
718	C₂²	C₂×C₇×H(5,𝔽₂)	1	1	yes	characteristic
719	C₂²	C₂×C₇×2₋¹⁺⁴	1	1	yes	characteristic
720	C₄	—	2	4	no	—
721	C₄	—	2	4	no	—
722	C₄	—	2	4	no	—
723	C₄	—	2	4	no	—
724	C₄	—	2	4	no	—
725	C₄	—	2	4	no	—
726	C₄	—	2	4	no	—
727	C₄	—	2	4	no	—
728	C₄	—	4	2	no	—
729	C₄	—	4	2	no	—
730	C₄	—	4	2	no	—
731	C₄	—	4	2	no	—
732	C₄	—	4	2	no	—
733	C₄	—	4	2	no	—
734	C₂	—	4	4	no	—
735	C₂	C₇×#2556	1	8	yes	direct product factor
736	C₂	C₂×C₇×#532	1	1	yes	characteristic
737	C₂	C₂×C₇×#533	1	1	yes	characteristic
738	C₂	C₂×C₇×#539	1	1	yes	characteristic
739	C₂	C₂×C₇×#546	1	1	yes	characteristic
740	C₂	C₂×C₇×D₄×Q₈	1	1	yes	characteristic
741	C₂	C₂×C₇×#552	1	1	yes	characteristic
742	C₂	C₂×C₇×#554	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂⁴×C₇	C₂⁴
commutator, Frattini, cosocle	C₂³	C₂⁵×C₇
prime radical	C₂⁵×C₇	C₂³
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×#125	C₂	semidirect
3. C₇×#2556	C₂	direct (N × H)
5. C₂×C₇×#398	C₂	semidirect
7. C₂×C₇×#395	C₂	semidirect
8. C₂×C₇×#391	C₂	semidirect
9. C₂×C₇×#389	C₂	semidirect
10. C₂×C₇×#389	C₂	semidirect
13. C₂×C₇×#387	C₂	semidirect
15. C₂×C₄×C₇×C₄⋊C₄	C₂	semidirect
20. C₂×C₇×#125	C₂²	semidirect
47. C₇×#398	C₂²	semidirect
49. C₇×#395	C₂²	semidirect
50. C₇×#391	C₂²	semidirect
51. C₇×#389	C₂²	semidirect
52. C₇×#389	C₂²	semidirect
55. C₇×#387	C₂²	semidirect
57. C₄×C₇×C₄⋊C₄	C₂²	semidirect
69. C₂×#2556	C₇	direct (N × H)
126. C₂×C₇×C₂²⋊C₄	Q₈	semidirect
151. C₂²×#125	C₂×C₇	semidirect
153. #2556	C₂×C₇	direct (N × H)
155. C₂×#398	C₂×C₇	semidirect
157. C₂×#395	C₂×C₇	semidirect
158. C₂×#391	C₂×C₇	semidirect
159. C₂×#389	C₂×C₇	semidirect
160. C₂×#389	C₂×C₇	semidirect
163. C₂×#387	C₂×C₇	semidirect
165. C₂×C₄×C₄⋊C₄	C₂×C₇	semidirect
258. C₇×C₂²⋊C₄	C₂×Q₈	semidirect
266. C₂×#125	C₂²×C₇	semidirect
293. #398	C₂²×C₇	semidirect
295. #395	C₂²×C₇	semidirect
296. #391	C₂²×C₇	semidirect
297. #389	C₂²×C₇	semidirect
298. #389	C₂²×C₇	semidirect
301. #387	C₂²×C₇	semidirect
303. C₄×C₄⋊C₄	C₂²×C₇	semidirect
451. C₂×C₂²⋊C₄	C₇×Q₈	semidirect
603. C₂²⋊C₄	C₂×C₇×Q₈	semidirect
609. C₂×C₇	#2556	direct (N × H)
697. C₇	C₂×#2556	direct (N × H)
735. C₂	C₇×#2556	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×#125	2
C₂²×C₇×C₂²⋊Q₈	2
C₇×#2556	2
C₂×C₇×#399	2
C₂×C₇×#398	2
C₂×C₇×#396	2
C₂×C₇×#395	2
C₂×C₇×#391	2
C₂×C₇×#389	2
C₂×C₇×#388	2
C₂×C₇×#387	2
C₂×C₇×#385	2
C₂×C₄×C₇×C₄⋊C₄	2
C₂×C₄×C₇×C₂²⋊C₄	2
C₂×#2556	7

Subgroups — C2×C7×#2556 #13212040

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₇×#2556 #13212040