Subgroups — C₂×C₇×#2438 #13211947

Order 1792.

3006 conjugacy classes of subgroups.

The subgroup lattice has 752 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₇×C₂²⋊Q₈	C₂	1	1	yes	maximal, characteristic
2	C₂²×C₇×#117	C₂	1	1	yes	maximal, characteristic
3	C₇×#2438	C₂	1	16	yes	maximal, direct product factor
4	C₂×C₇×#400	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₇×#398	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×C₇×#398	C₂	1	1	yes	maximal, characteristic, complemented
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×#387	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×C₇×#387	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₇×#385	C₂	1	1	yes	maximal, characteristic
13	C₂×C₇×#385	C₂	1	1	yes	maximal, characteristic
14	C₂×C₇×#381	C₂	1	1	yes	maximal, characteristic
15	C₂×C₇×#380	C₂	1	1	yes	maximal, characteristic
16	C₂²×C₇×#95	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	C₂⁴×C₄×C₇	C₂²	1	1	yes	characteristic
20	C₂⁴×C₄×C₇	C₂²	1	1	yes	characteristic
21	C₂×C₇×C₂²⋊Q₈	—	2	8	no	—
22	C₂×C₇×C₂²⋊Q₈	C₂²	1	8	yes	—
23	C₂×C₇×#117	—	2	8	no	—
24	C₂×C₇×#117	C₂²	1	8	yes	—
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×C₄²×C₇	C₂²	1	1	yes	characteristic
41	C₂²×C₄²×C₇	C₂²	1	1	yes	characteristic
42	C₇×#400	C₂²	1	8	yes	complemented
43	C₇×#398	C₂²	1	8	yes	complemented
44	C₇×#398	C₂²	1	8	yes	complemented
45	C₇×#395	C₂²	1	8	yes	complemented
46	C₇×#391	C₂²	1	8	yes	complemented
47	C₇×#389	C₂²	1	8	yes	complemented
48	C₇×#387	C₂²	1	8	yes	complemented
49	C₇×#387	C₂²	1	8	yes	complemented
50	C₇×#385	C₂²	1	8	yes	—
51	C₇×#385	C₂²	1	8	yes	—
52	C₇×#381	C₂²	1	8	yes	—
53	C₇×#380	C₂²	1	8	yes	—
54	C₂×C₇×#95	C₂²	1	1	yes	characteristic
55	C₂×C₇×#95	C₂²	1	1	yes	characteristic
56	C₂×C₇×#95	C₂²	1	1	yes	characteristic
57	C₂×C₇×#95	C₂²	1	1	yes	characteristic
58	C₂×C₇×#95	C₂²	1	1	yes	characteristic
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	8	yes	—
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×#2438	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	—	2	4	no	—
78	C₂³×C₄×C₇	—	2	4	no	—
79	C₂³×C₄×C₇	—	2	4	no	—
80	C₂³×C₄×C₇	—	2	4	no	—
81	C₂³×C₄×C₇	—	4	2	no	—
82	C₂³×C₄×C₇	—	4	2	no	—
83	C₂³×C₄×C₇	Q₈	1	8	yes	complemented
84	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
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	4	yes	—
93	C₂³×C₄×C₇	C₂³	1	4	yes	—
94	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
95	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
96	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
97	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
98	C₂³×C₄×C₇	C₂³	1	4	yes	—
99	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
100	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
101	C₇×C₂²⋊Q₈	—	2	32	no	—
102	C₇×#117	—	2	32	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	—	2	4	no	—
107	C₂×C₇×C₄⋊C₄	—	2	4	no	—
108	C₂×C₇×C₄⋊C₄	—	2	4	no	—
109	C₂×C₇×C₄⋊C₄	—	2	4	no	—
110	C₂×C₇×C₄⋊C₄	—	2	4	no	—
111	C₂×C₇×C₄⋊C₄	—	4	2	no	—
112	C₂×C₇×C₄⋊C₄	—	4	2	no	—
113	C₂×C₇×C₄⋊C₄	—	4	2	no	—
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×C₄⋊C₄	C₂³	1	4	yes	—
122	C₂×C₇×C₄⋊C₄	C₂³	1	4	yes	—
123	C₂×C₇×C₄⋊C₄	C₂³	1	4	yes	—
124	C₂×C₇×C₄⋊C₄	C₂³	1	4	yes	—
125	C₂×C₇×C₂²⋊C₄	—	2	4	no	—
126	C₂×C₇×C₂²⋊C₄	—	2	4	no	—
127	C₂×C₇×C₂²⋊C₄	—	2	4	no	—
128	C₂×C₇×C₂²⋊C₄	D₄	1	8	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	C₂³	1	4	yes	—
136	C₂×C₄²×C₇	C₂³	1	4	yes	—
137	C₇×#95	C₂³	1	4	yes	—
138	C₇×#95	C₂³	1	4	yes	—
139	C₇×#95	C₂³	1	4	yes	—
140	C₇×#95	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×C₂²⋊Q₈	C₂×C₇	1	1	yes	characteristic
152	C₂²×#117	C₂×C₇	1	1	yes	characteristic
153	#2438	C₂×C₇	1	16	yes	direct product factor
154	C₂×#400	C₂×C₇	1	1	yes	characteristic, complemented
155	C₂×#398	C₂×C₇	1	1	yes	characteristic, complemented
156	C₂×#398	C₂×C₇	1	1	yes	characteristic, complemented
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×#387	C₂×C₇	1	1	yes	characteristic, complemented
161	C₂×#387	C₂×C₇	1	1	yes	characteristic, complemented
162	C₂×#385	C₂×C₇	1	1	yes	characteristic
163	C₂×#385	C₂×C₇	1	1	yes	characteristic
164	C₂×#381	C₂×C₇	1	1	yes	characteristic
165	C₂×#380	C₂×C₇	1	1	yes	characteristic
166	C₂²×#95	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	C₂×D₄	1	4	yes	—
172	C₂⁴×C₇	C₂×Q₈	1	4	yes	—
173	C₂⁴×C₇	#41	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	32	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	8	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	8	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	8	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	8	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	2	no	—
215	C₂²×C₄×C₇	—	2	2	no	—
216	C₂²×C₄×C₇	—	2	2	no	—
217	C₂²×C₄×C₇	—	2	2	no	—
218	C₂²×C₄×C₇	—	2	2	no	—
219	C₂²×C₄×C₇	—	2	2	no	—
220	C₂²×C₄×C₇	—	2	2	no	—
221	C₂²×C₄×C₇	—	2	8	no	—
222	C₂²×C₄×C₇	—	2	8	no	—
223	C₂²×C₄×C₇	—	4	4	no	—
224	C₂²×C₄×C₇	—	4	4	no	—
225	C₂²×C₄×C₇	—	4	16	no	—
226	C₂²×C₄×C₇	—	4	16	no	—
227	C₂²×C₄×C₇	C₂×D₄	1	4	yes	—
228	C₂²×C₄×C₇	C₂×D₄	1	4	yes	—
229	C₂²×C₄×C₇	C₂×Q₈	1	4	yes	—
230	C₂²×C₄×C₇	C₂×Q₈	1	4	yes	—
231	C₂²×C₄×C₇	C₂×Q₈	1	16	yes	complemented
232	C₂²×C₄×C₇	#41	1	4	yes	—
233	C₂²×C₄×C₇	#41	1	4	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	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
241	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
242	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
243	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
244	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
245	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
246	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
247	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
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	—	2	8	no	—
252	C₇×C₄⋊C₄	—	2	8	no	—
253	C₇×C₄⋊C₄	—	2	8	no	—
254	C₇×C₄⋊C₄	—	2	8	no	—
255	C₇×C₄⋊C₄	—	2	8	no	—
256	C₇×C₄⋊C₄	—	4	4	no	—
257	C₇×C₄⋊C₄	—	4	4	no	—
258	C₇×C₄⋊C₄	—	4	4	no	—
259	C₇×C₂²⋊C₄	—	2	8	no	—
260	C₇×C₂²⋊C₄	—	2	8	no	—
261	C₇×C₂²⋊C₄	—	2	8	no	—
262	C₇×C₂²⋊C₄	C₂×D₄	1	16	yes	—
263	C₄²×C₇	—	2	8	no	—
264	C₄²×C₇	—	2	8	no	—
265	C₂³×Q₈	C₂²×C₇	1	1	yes	characteristic
266	C₂⁴×C₄	C₂²×C₇	1	1	yes	characteristic
267	C₂⁴×C₄	C₂²×C₇	1	1	yes	characteristic
268	C₂⁴×C₄	C₂²×C₇	1	1	yes	characteristic
269	C₂×C₂²⋊Q₈	—	2	8	no	—
270	C₂×C₂²⋊Q₈	C₂²×C₇	1	8	yes	—
271	C₂×#117	—	2	8	no	—
272	C₂×#117	C₂²×C₇	1	8	yes	—
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×C₄⋊C₄	C₂²×C₇	1	1	yes	characteristic
283	C₂²×C₄⋊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	#400	C₂²×C₇	1	8	yes	complemented
291	#398	C₂²×C₇	1	8	yes	complemented
292	#398	C₂²×C₇	1	8	yes	complemented
293	#395	C₂²×C₇	1	8	yes	complemented
294	#391	C₂²×C₇	1	8	yes	complemented
295	#389	C₂²×C₇	1	8	yes	complemented
296	#387	C₂²×C₇	1	8	yes	complemented
297	#387	C₂²×C₇	1	8	yes	complemented
298	#385	C₂²×C₇	1	8	yes	—
299	#385	C₂²×C₇	1	8	yes	—
300	#381	C₂²×C₇	1	8	yes	—
301	#380	C₂²×C₇	1	8	yes	—
302	C₂×#95	C₂²×C₇	1	1	yes	characteristic
303	C₂×#95	C₂²×C₇	1	1	yes	characteristic
304	C₂×#95	C₂²×C₇	1	1	yes	characteristic
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	8	yes	—
313	C₂×#95	C₂²×C₇	1	1	yes	characteristic
314	C₂×#95	C₂²×C₇	1	1	yes	characteristic
315	C₂×#95	C₂²×C₇	1	1	yes	characteristic
316	C₂×#95	C₂²×C₇	1	1	yes	characteristic
317	C₂³×C₇	—	2	8	no	—
318	C₂³×C₇	—	2	8	no	—
319	C₂³×C₇	—	2	8	no	—
320	C₂³×C₇	—	2	8	no	—
321	C₂³×C₇	—	2	8	no	—
322	C₂³×C₇	—	2	8	no	—
323	C₂³×C₇	—	2	2	no	—
324	C₂³×C₇	—	2	2	no	—
325	C₂³×C₇	—	2	2	no	—
326	C₂³×C₇	—	2	2	no	—
327	C₂³×C₇	C₂²⋊Q₈	1	16	yes	—
328	C₂³×C₇	C₂²×D₄	1	4	yes	—
329	C₂³×C₇	C₂²×D₄	1	2	yes	—
330	C₂³×C₇	C₂²×Q₈	1	4	yes	—
331	C₂³×C₇	C₂²×Q₈	1	2	yes	—
332	C₂³×C₇	C₂×#41	1	4	yes	—
333	C₂³×C₇	C₂×#41	1	2	yes	—
334	C₂³×C₇	C₂×#41	1	2	yes	—
335	C₂³×C₇	C₂×#41	1	2	yes	—
336	C₂³×C₇	H(5,𝔽₂)	1	2	yes	—
337	C₂³×C₇	2₋¹⁺⁴	1	2	yes	—
338	C₂³×C₇	C₂⁵	1	1	yes	characteristic
339	C₇×Q₈	—	4	16	no	—
340	C₂×C₄×C₇	—	2	8	no	—
341	C₂×C₄×C₇	—	2	8	no	—
342	C₂×C₄×C₇	—	2	32	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	8	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	—	2	2	no	—
381	C₂×C₄×C₇	—	2	2	no	—
382	C₂×C₄×C₇	—	2	2	no	—
383	C₂×C₄×C₇	—	4	16	no	—
384	C₂×C₄×C₇	—	4	16	no	—
385	C₂×C₄×C₇	—	4	4	no	—
386	C₂×C₄×C₇	—	4	4	no	—
387	C₂×C₄×C₇	—	4	4	no	—
388	C₂×C₄×C₇	—	4	4	no	—
389	C₂×C₄×C₇	—	4	4	no	—
390	C₂×C₄×C₇	—	4	4	no	—
391	C₂×C₄×C₇	—	4	4	no	—
392	C₂×C₄×C₇	—	4	4	no	—
393	C₂×C₄×C₇	C₂²×D₄	1	4	yes	—
394	C₂×C₄×C₇	C₂²×D₄	1	4	yes	—
395	C₂×C₄×C₇	C₂²×Q₈	1	4	yes	—
396	C₂×C₄×C₇	C₂²×Q₈	1	4	yes	—
397	C₂×C₄×C₇	C₂×#41	1	4	yes	—
398	C₂×C₄×C₇	C₂×#41	1	4	yes	—
399	C₂⁵	C₂³×C₇	1	1	yes	characteristic
400	C₂²×Q₈	—	2	4	no	—
401	C₂²×Q₈	—	2	4	no	—
402	C₂²×Q₈	—	4	2	no	—
403	C₂²×Q₈	C₂³×C₇	1	4	yes	—
404	C₂³×C₄	—	2	4	no	—
405	C₂³×C₄	—	2	4	no	—
406	C₂³×C₄	—	2	4	no	—
407	C₂³×C₄	—	2	4	no	—
408	C₂³×C₄	—	2	4	no	—
409	C₂³×C₄	—	2	4	no	—
410	C₂³×C₄	—	4	2	no	—
411	C₂³×C₄	—	4	2	no	—
412	C₂³×C₄	C₇×Q₈	1	8	yes	complemented
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	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
419	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
420	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
421	C₂³×C₄	C₂³×C₇	1	4	yes	—
422	C₂³×C₄	C₂³×C₇	1	4	yes	—
423	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
424	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
425	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
426	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
427	C₂³×C₄	C₂³×C₇	1	4	yes	—
428	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
429	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
430	C₂²⋊Q₈	—	2	32	no	—
431	#117	—	2	32	no	—
432	C₂×C₄⋊C₄	—	2	4	no	—
433	C₂×C₄⋊C₄	—	2	4	no	—
434	C₂×C₄⋊C₄	—	2	4	no	—
435	C₂×C₄⋊C₄	—	2	4	no	—
436	C₂×C₄⋊C₄	—	2	4	no	—
437	C₂×C₄⋊C₄	—	2	4	no	—
438	C₂×C₄⋊C₄	—	2	4	no	—
439	C₂×C₄⋊C₄	—	2	4	no	—
440	C₂×C₄⋊C₄	—	4	2	no	—
441	C₂×C₄⋊C₄	—	4	2	no	—
442	C₂×C₄⋊C₄	—	4	2	no	—
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×C₄⋊C₄	C₂³×C₇	1	4	yes	—
447	C₂×C₄⋊C₄	C₂³×C₇	1	4	yes	—
448	C₂×C₄⋊C₄	C₂³×C₇	1	4	yes	—
449	C₂×C₄⋊C₄	C₂³×C₇	1	4	yes	—
450	C₂×C₄⋊C₄	C₂³×C₇	1	4	yes	—
451	C₂×C₄⋊C₄	C₂³×C₇	1	4	yes	—
452	C₂×C₄⋊C₄	C₂³×C₇	1	4	yes	—
453	C₂×C₄⋊C₄	C₂³×C₇	1	4	yes	—
454	C₂×C₂²⋊C₄	—	2	4	no	—
455	C₂×C₂²⋊C₄	—	2	4	no	—
456	C₂×C₂²⋊C₄	—	2	4	no	—
457	C₂×C₂²⋊C₄	C₇×D₄	1	8	yes	—
458	C₂×C₂²⋊C₄	C₂³×C₇	1	4	yes	—
459	C₂×C₂²⋊C₄	C₂³×C₇	1	4	yes	—
460	C₂×C₂²⋊C₄	C₂³×C₇	1	4	yes	—
461	C₂×C₂²⋊C₄	C₂³×C₇	1	4	yes	—
462	C₂×C₄²	—	2	4	no	—
463	C₂×C₄²	—	2	4	no	—
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	#95	C₂³×C₇	1	4	yes	—
477	#95	C₂³×C₇	1	4	yes	—
478	#95	C₂³×C₇	1	4	yes	—
479	#95	C₂³×C₇	1	4	yes	—
480	C₂²×C₇	—	2	4	no	—
481	C₂²×C₇	—	2	4	no	—
482	C₂²×C₇	—	2	32	no	—
483	C₂²×C₇	—	2	4	no	—
484	C₂²×C₇	—	2	4	no	—
485	C₂²×C₇	—	2	4	no	—
486	C₂²×C₇	—	2	4	no	—
487	C₂²×C₇	C₂×C₂²⋊Q₈	1	8	yes	—
488	C₂²×C₇	C₂×C₂²⋊Q₈	1	4	yes	—
489	C₂²×C₇	#533	1	4	yes	—
490	C₂²×C₇	#544	1	4	yes	—
491	C₂²×C₇	#546	1	4	yes	—
492	C₂²×C₇	#547	1	4	yes	—
493	C₂²×C₇	#551	1	4	yes	—
494	C₂²×C₇	#552	1	4	yes	—
495	C₂²×C₇	C₂³×D₄	1	1	yes	characteristic
496	C₂²×C₇	C₂³×Q₈	1	1	yes	characteristic
497	C₂²×C₇	C₂²×#41	1	1	yes	characteristic
498	C₂²×C₇	C₂²×#41	1	1	yes	characteristic
499	C₂²×C₇	C₂²×#41	1	1	yes	characteristic
500	C₂²×C₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
501	C₂²×C₇	C₂×2₋¹⁺⁴	1	1	yes	characteristic
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	—	2	4	no	—
507	C₄×C₇	—	2	4	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	C₄×C₇	—	4	2	no	—
513	C₄×C₇	—	4	2	no	—
514	C₄×C₇	—	4	2	no	—
515	C₄×C₇	—	4	2	no	—
516	C₂⁴	—	2	2	no	—
517	C₂⁴	—	2	2	no	—
518	C₂⁴	—	2	2	no	—
519	C₂⁴	—	2	2	no	—
520	C₂⁴	C₂×C₇×D₄	1	4	yes	—
521	C₂⁴	C₂×C₇×Q₈	1	4	yes	—
522	C₂⁴	C₇×#41	1	4	yes	—
523	C₂⁴	C₂⁴×C₇	1	2	yes	—
524	C₂⁴	C₂⁴×C₇	1	1	yes	characteristic
525	C₂×Q₈	—	2	8	no	—
526	C₂×Q₈	—	2	8	no	—
527	C₂×Q₈	—	4	4	no	—
528	C₂×Q₈	—	4	16	no	—
529	C₂²×C₄	—	2	32	no	—
530	C₂²×C₄	—	2	2	no	—
531	C₂²×C₄	—	2	2	no	—
532	C₂²×C₄	—	2	2	no	—
533	C₂²×C₄	—	2	8	no	—
534	C₂²×C₄	—	2	2	no	—
535	C₂²×C₄	—	2	2	no	—
536	C₂²×C₄	—	2	2	no	—
537	C₂²×C₄	—	2	8	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	8	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	8	no	—
558	C₂²×C₄	—	2	2	no	—
559	C₂²×C₄	—	2	2	no	—
560	C₂²×C₄	—	2	2	no	—
561	C₂²×C₄	—	2	2	no	—
562	C₂²×C₄	—	2	2	no	—
563	C₂²×C₄	—	2	2	no	—
564	C₂²×C₄	—	2	2	no	—
565	C₂²×C₄	—	2	2	no	—
566	C₂²×C₄	—	2	2	no	—
567	C₂²×C₄	—	2	2	no	—
568	C₂²×C₄	—	2	2	no	—
569	C₂²×C₄	—	2	2	no	—
570	C₂²×C₄	—	2	8	no	—
571	C₂²×C₄	—	2	8	no	—
572	C₂²×C₄	—	4	4	no	—
573	C₂²×C₄	—	4	4	no	—
574	C₂²×C₄	—	4	16	no	—
575	C₂²×C₄	—	4	16	no	—
576	C₂²×C₄	C₂×C₇×D₄	1	4	yes	—
577	C₂²×C₄	C₂×C₇×D₄	1	4	yes	—
578	C₂²×C₄	C₂×C₇×Q₈	1	4	yes	—
579	C₂²×C₄	C₂×C₇×Q₈	1	4	yes	—
580	C₂²×C₄	C₂×C₇×Q₈	1	16	yes	complemented
581	C₂²×C₄	C₇×#41	1	4	yes	—
582	C₂²×C₄	C₇×#41	1	4	yes	—
583	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
584	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
585	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
586	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
587	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
588	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
589	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
590	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
591	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
592	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
593	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
594	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
595	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
596	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
597	C₄⋊C₄	—	2	8	no	—
598	C₄⋊C₄	—	2	8	no	—
599	C₄⋊C₄	—	2	8	no	—
600	C₄⋊C₄	—	2	8	no	—
601	C₄⋊C₄	—	2	8	no	—
602	C₄⋊C₄	—	2	8	no	—
603	C₄⋊C₄	—	2	8	no	—
604	C₄⋊C₄	—	2	8	no	—
605	C₄⋊C₄	—	4	4	no	—
606	C₄⋊C₄	—	4	4	no	—
607	C₄⋊C₄	—	4	4	no	—
608	C₂²⋊C₄	—	2	8	no	—
609	C₂²⋊C₄	—	2	8	no	—
610	C₂²⋊C₄	—	2	8	no	—
611	C₂²⋊C₄	C₂×C₇×D₄	1	16	yes	—
612	C₄²	—	2	8	no	—
613	C₄²	—	2	8	no	—
614	C₂×C₇	—	2	8	no	—
615	C₂×C₇	#2438	1	8	yes	direct product factor
616	C₂×C₇	C₂²×C₂²⋊Q₈	1	1	yes	characteristic
617	C₂×C₇	C₂×#533	1	1	yes	characteristic
618	C₂×C₇	C₂×#544	1	1	yes	characteristic
619	C₂×C₇	C₂×#546	1	1	yes	characteristic
620	C₂×C₇	C₂×#547	1	1	yes	characteristic
621	C₂×C₇	C₂×#551	1	1	yes	characteristic
622	C₂×C₇	C₂×#552	1	1	yes	characteristic
623	C₂³	—	2	2	no	—
624	C₂³	—	2	2	no	—
625	C₂³	—	2	2	no	—
626	C₂³	—	2	2	no	—
627	C₂³	—	2	8	no	—
628	C₂³	—	2	8	no	—
629	C₂³	—	2	8	no	—
630	C₂³	—	2	8	no	—
631	C₂³	—	2	8	no	—
632	C₂³	—	2	8	no	—
633	C₂³	C₇×C₂²⋊Q₈	1	16	yes	—
634	C₂³	C₂²×C₇×D₄	1	4	yes	—
635	C₂³	C₂²×C₇×D₄	1	2	yes	—
636	C₂³	C₂²×C₇×Q₈	1	4	yes	—
637	C₂³	C₂²×C₇×Q₈	1	2	yes	—
638	C₂³	C₂×C₇×#41	1	4	yes	—
639	C₂³	C₂×C₇×#41	1	2	yes	—
640	C₂³	C₂×C₇×#41	1	2	yes	—
641	C₂³	C₂×C₇×#41	1	2	yes	—
642	C₂³	C₇×H(5,𝔽₂)	1	2	yes	—
643	C₂³	C₇×2₋¹⁺⁴	1	2	yes	—
644	C₂³	C₂⁵×C₇	1	1	yes	characteristic
645	Q₈	—	4	16	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	2	no	—
657	C₂×C₄	—	2	2	no	—
658	C₂×C₄	—	2	8	no	—
659	C₂×C₄	—	2	8	no	—
660	C₂×C₄	—	2	32	no	—
661	C₂×C₄	—	2	8	no	—
662	C₂×C₄	—	2	8	no	—
663	C₂×C₄	—	2	8	no	—
664	C₂×C₄	—	2	8	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	—	2	2	no	—
683	C₂×C₄	—	2	2	no	—
684	C₂×C₄	—	2	2	no	—
685	C₂×C₄	—	2	2	no	—
686	C₂×C₄	—	2	2	no	—
687	C₂×C₄	—	2	2	no	—
688	C₂×C₄	—	2	2	no	—
689	C₂×C₄	—	4	16	no	—
690	C₂×C₄	—	4	16	no	—
691	C₂×C₄	—	4	4	no	—
692	C₂×C₄	—	4	4	no	—
693	C₂×C₄	—	4	4	no	—
694	C₂×C₄	—	4	4	no	—
695	C₂×C₄	—	4	4	no	—
696	C₂×C₄	—	4	4	no	—
697	C₂×C₄	—	4	4	no	—
698	C₂×C₄	—	4	4	no	—
699	C₂×C₄	C₂²×C₇×D₄	1	4	yes	—
700	C₂×C₄	C₂²×C₇×D₄	1	4	yes	—
701	C₂×C₄	C₂²×C₇×Q₈	1	4	yes	—
702	C₂×C₄	C₂²×C₇×Q₈	1	4	yes	—
703	C₂×C₄	C₂×C₇×#41	1	4	yes	—
704	C₂×C₄	C₂×C₇×#41	1	4	yes	—
705	C₇	C₂×#2438	1	1	yes	characteristic, direct product factor, Sylow
706	C₂²	—	2	32	no	—
707	C₂²	—	2	4	no	—
708	C₂²	—	2	4	no	—
709	C₂²	—	2	4	no	—
710	C₂²	—	2	4	no	—
711	C₂²	—	2	4	no	—
712	C₂²	—	2	4	no	—
713	C₂²	C₂×C₇×C₂²⋊Q₈	1	8	yes	—
714	C₂²	C₂×C₇×C₂²⋊Q₈	1	4	yes	—
715	C₂²	C₇×#533	1	4	yes	—
716	C₂²	C₇×#544	1	4	yes	—
717	C₂²	C₇×#546	1	4	yes	—
718	C₂²	C₇×#547	1	4	yes	—
719	C₂²	C₇×#551	1	4	yes	—
720	C₂²	C₇×#552	1	4	yes	—
721	C₂²	C₂³×C₇×D₄	1	1	yes	characteristic
722	C₂²	C₂³×C₇×Q₈	1	1	yes	characteristic
723	C₂²	C₂²×C₇×#41	1	1	yes	characteristic
724	C₂²	C₂²×C₇×#41	1	1	yes	characteristic
725	C₂²	C₂²×C₇×#41	1	1	yes	characteristic
726	C₂²	C₂×C₇×H(5,𝔽₂)	1	1	yes	characteristic
727	C₂²	C₂×C₇×2₋¹⁺⁴	1	1	yes	characteristic
728	C₄	—	2	4	no	—
729	C₄	—	2	4	no	—
730	C₄	—	2	4	no	—
731	C₄	—	2	4	no	—
732	C₄	—	2	4	no	—
733	C₄	—	2	4	no	—
734	C₄	—	4	2	no	—
735	C₄	—	4	2	no	—
736	C₄	—	4	2	no	—
737	C₄	—	4	2	no	—
738	C₄	—	4	2	no	—
739	C₄	—	4	2	no	—
740	C₄	—	4	2	no	—
741	C₄	—	4	2	no	—
742	C₂	—	2	8	no	—
743	C₂	C₇×#2438	1	8	yes	direct product factor
744	C₂	C₂²×C₇×C₂²⋊Q₈	1	1	yes	characteristic
745	C₂	C₂×C₇×#533	1	1	yes	characteristic
746	C₂	C₂×C₇×#544	1	1	yes	characteristic
747	C₂	C₂×C₇×#546	1	1	yes	characteristic
748	C₂	C₂×C₇×#547	1	1	yes	characteristic
749	C₂	C₂×C₇×#551	1	1	yes	characteristic
750	C₂	C₂×C₇×#552	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
3. C₇×#2438	C₂	direct (N × H)
4. C₂×C₇×#400	C₂	semidirect
5. C₂×C₇×#398	C₂	semidirect
6. 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×#387	C₂	semidirect
11. C₂×C₇×#387	C₂	semidirect
42. C₇×#400	C₂²	semidirect
43. C₇×#398	C₂²	semidirect
44. C₇×#398	C₂²	semidirect
45. C₇×#395	C₂²	semidirect
46. C₇×#391	C₂²	semidirect
47. C₇×#389	C₂²	semidirect
48. C₇×#387	C₂²	semidirect
49. C₇×#387	C₂²	semidirect
69. C₂×#2438	C₇	direct (N × H)
83. C₂³×C₄×C₇	Q₈	semidirect
153. #2438	C₂×C₇	direct (N × H)
154. C₂×#400	C₂×C₇	semidirect
155. C₂×#398	C₂×C₇	semidirect
156. 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×#387	C₂×C₇	semidirect
161. C₂×#387	C₂×C₇	semidirect
231. C₂²×C₄×C₇	C₂×Q₈	semidirect
290. #400	C₂²×C₇	semidirect
291. #398	C₂²×C₇	semidirect
292. #398	C₂²×C₇	semidirect
293. #395	C₂²×C₇	semidirect
294. #391	C₂²×C₇	semidirect
295. #389	C₂²×C₇	semidirect
296. #387	C₂²×C₇	semidirect
297. #387	C₂²×C₇	semidirect
412. C₂³×C₄	C₇×Q₈	semidirect
580. C₂²×C₄	C₂×C₇×Q₈	semidirect
615. C₂×C₇	#2438	direct (N × H)
705. C₇	C₂×#2438	direct (N × H)
743. C₂	C₇×#2438	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×C₂²⋊Q₈	2
C₂²×C₇×#117	2
C₇×#2438	2
C₂×C₇×#400	2
C₂×C₇×#398	2
C₂×C₇×#395	2
C₂×C₇×#391	2
C₂×C₇×#389	2
C₂×C₇×#387	2
C₂×C₇×#385	2
C₂×C₇×#381	2
C₂×C₇×#380	2
C₂²×C₇×#95	2
C₂×#2438	7

Subgroups — C2×C7×#2438 #13211947

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₇×#2438 #13211947