Subgroups — C₂×C₇×#3558 #13239946

Order 1792.

8122 conjugacy classes of subgroups.

The subgroup lattice has 880 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×#3558	C₂	1	32	yes	maximal, direct product factor
2	C₂×C₇×#562	C₂	1	2	yes	maximal, complemented
3	C₂×C₇×H(3,𝔽₄)	C₂	1	2	yes	maximal, complemented
4	C₂×C₇×#559	C₂	1	2	yes	maximal, complemented
5	C₂×C₇×#548	C₂	1	2	yes	maximal, complemented
6	C₂×C₇×#546	C₂	1	2	yes	maximal, complemented
7	C₂×C₇×#546	C₂	1	4	yes	maximal, complemented
8	C₂×C₇×D₄²	C₂	1	2	yes	maximal, complemented
9	C₂×C₇×#542	C₂	1	2	yes	maximal, complemented
10	C₂×C₇×#538	C₂	1	2	yes	maximal, complemented
11	C₂×C₇×#538	C₂	1	4	yes	maximal, complemented
12	C₂×C₇×#535	C₂	1	2	yes	maximal, complemented
13	C₂×C₇×#534	C₂	1	2	yes	maximal, complemented
14	C₂×C₇×#532	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂×C₇×#529	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×C₇×#124	C₂	1	1	yes	maximal, characteristic, complemented
17	C₂²×C₇×#41	C₂²	1	2	yes	complemented
18	C₂²×C₇×#41	C₂²	1	2	yes	complemented
19	C₂³×C₇×Q₈	C₂²	1	1	yes	characteristic, complemented
20	C₂³×C₇×D₄	C₂²	1	1	yes	characteristic
21	C₂³×C₇×D₄	C₂²	1	4	yes	complemented
22	C₂³×C₇×D₄	C₂²	1	2	yes	complemented
23	C₇×#562	C₂²	1	32	yes	complemented
24	C₇×H(3,𝔽₄)	C₂²	1	32	yes	complemented
25	C₇×#559	C₂²	1	32	yes	complemented
26	C₇×#548	C₂²	1	32	yes	complemented
27	C₇×#546	C₂²	1	32	yes	complemented
28	C₇×#546	C₂²	1	64	yes	complemented
29	C₇×D₄²	C₂²	1	32	yes	complemented
30	C₇×#542	C₂²	1	32	yes	complemented
31	C₇×#538	C₂²	1	32	yes	complemented
32	C₇×#538	C₂²	1	64	yes	complemented
33	C₇×#535	C₂²	1	32	yes	complemented
34	C₇×#534	C₂²	1	32	yes	complemented
35	C₇×#532	C₂²	1	16	yes	complemented
36	C₂×C₇×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
37	C₂×C₇×#127	C₂²	1	2	yes	—
38	C₂×C₇×#127	C₂²	1	1	yes	characteristic, complemented
39	C₇×#529	C₂²	1	16	yes	complemented
40	C₂×C₇×#126	C₂²	1	2	yes	complemented
41	C₂×C₇×#126	C₂²	1	4	yes	complemented
42	C₂×C₇×#125	C₂²	1	1	yes	characteristic, complemented
43	C₂×C₇×#124	C₂²	1	2	yes	complemented
44	C₂×C₇×#124	C₂²	1	2	yes	complemented
45	C₂×C₇×#124	C₂²	1	2	yes	complemented
46	C₂×C₇×#124	C₂²	1	2	yes	complemented
47	C₂×C₇×#124	C₂²	1	1	yes	characteristic, complemented
48	C₂×C₇×#124	C₂²	1	2	yes	complemented
49	C₂×C₇×#124	C₂²	1	2	yes	complemented
50	C₂×C₇×#124	C₂²	1	4	yes	complemented
51	C₂×C₇×#124	C₂²	1	4	yes	complemented
52	C₂×C₇×#124	C₂²	1	4	yes	complemented
53	C₂×C₇×#124	C₂²	1	16	yes	complemented
54	C₂×C₇×#123	C₂²	1	2	yes	complemented
55	C₂×C₇×#123	C₂²	1	4	yes	complemented
56	C₂×C₇×#123	C₂²	1	4	yes	complemented
57	C₂×C₇×#123	C₂²	1	4	yes	complemented
58	C₂×C₇×#123	C₂²	1	4	yes	complemented
59	C₂×C₇×C₂²⋊Q₈	C₂²	1	1	yes	characteristic, complemented
60	C₂×C₇×C₂²⋊Q₈	C₂²	1	4	yes	complemented
61	C₂×C₇×C₂²⋊Q₈	C₂²	1	2	yes	complemented
62	C₂×C₇×C₂²⋊Q₈	C₂²	1	4	yes	complemented
63	C₂×C₇×#121	C₂²	1	1	yes	characteristic
64	C₂×C₇×#121	C₂²	1	2	yes	—
65	C₂×C₇×#121	C₂²	1	2	yes	complemented
66	C₂×C₇×#121	C₂²	1	2	yes	complemented
67	C₂×C₇×#121	C₂²	1	4	yes	complemented
68	C₂×C₇×#121	C₂²	1	4	yes	complemented
69	C₂×C₇×#121	C₂²	1	4	yes	complemented
70	C₂×C₇×#121	C₂²	1	4	yes	complemented
71	C₂×C₇×#121	C₂²	1	4	yes	complemented
72	C₂×C₇×#120	C₂²	1	4	yes	complemented
73	C₂×C₇×#120	C₂²	1	4	yes	complemented
74	C₂×C₇×#120	C₂²	1	4	yes	complemented
75	C₂×C₇×#120	C₂²	1	4	yes	complemented
76	C₂×C₇×#120	C₂²	1	4	yes	complemented
77	C₂×C₄×C₇×Q₈	C₂²	1	1	yes	characteristic, complemented
78	C₂×C₄×C₇×Q₈	C₂²	1	2	yes	complemented
79	C₂×C₄×C₇×D₄	C₂²	1	2	yes	complemented
80	C₂×C₄×C₇×D₄	C₂²	1	1	yes	characteristic, complemented
81	C₂×C₄×C₇×D₄	C₂²	1	2	yes	complemented
82	C₂×C₄×C₇×D₄	C₂²	1	2	yes	complemented
83	C₂×C₄×C₇×D₄	C₂²	1	4	yes	complemented
84	C₂×C₄×C₇×D₄	C₂²	1	4	yes	complemented
85	C₂×C₄×C₇×D₄	C₂²	1	2	yes	complemented
86	C₂×C₇×#117	C₂²	1	2	yes	complemented
87	C₂²×C₇×C₂²⋊C₄	C₂²	1	2	yes	complemented
88	C₂²×C₇×C₂²⋊C₄	C₂²	1	2	yes	complemented
89	C₂²×C₇×C₂²⋊C₄	C₂²	1	4	yes	complemented
90	C₂²×C₄²×C₇	C₂²	1	1	yes	characteristic, complemented
91	C₂×#3558	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
92	C₂⁵×C₇	C₂³	1	2	yes	—
93	C₂⁵×C₇	C₂³	1	4	yes	—
94	C₂×C₇×#41	—	4	8	no	—
95	C₂×C₇×#41	—	4	8	no	—
96	C₂×C₇×#41	C₂³	1	16	yes	complemented
97	C₂×C₇×#41	C₂³	1	16	yes	complemented
98	C₂²×C₇×Q₈	—	4	4	no	—
99	C₂²×C₇×Q₈	C₂³	1	2	yes	—
100	C₂²×C₇×Q₈	C₂³	1	2	yes	—
101	C₂²×C₇×Q₈	C₂³	1	2	yes	—
102	C₂²×C₇×Q₈	C₂³	1	1	yes	characteristic
103	C₂²×C₇×Q₈	C₂³	1	8	yes	complemented
104	C₂²×C₇×D₄	—	4	4	no	—
105	C₂²×C₇×D₄	—	4	8	no	—
106	C₂²×C₇×D₄	—	4	16	no	—
107	C₂²×C₇×D₄	C₂³	1	2	yes	—
108	C₂²×C₇×D₄	C₂³	1	2	yes	—
109	C₂²×C₇×D₄	C₂³	1	4	yes	—
110	C₂²×C₇×D₄	C₂³	1	2	yes	—
111	C₂²×C₇×D₄	C₂³	1	2	yes	—
112	C₂²×C₇×D₄	C₂³	1	8	yes	—
113	C₂²×C₇×D₄	C₂³	1	4	yes	—
114	C₂²×C₇×D₄	C₂³	1	4	yes	—
115	C₂²×C₇×D₄	C₂³	1	4	yes	—
116	C₂²×C₇×D₄	C₂³	1	4	yes	—
117	C₂²×C₇×D₄	C₂³	1	2	yes	—
118	C₂²×C₇×D₄	C₂³	1	1	yes	characteristic
119	C₂²×C₇×D₄	C₂³	1	4	yes	—
120	C₂²×C₇×D₄	C₂³	1	2	yes	—
121	C₂²×C₇×D₄	C₂³	1	32	yes	complemented
122	C₂²×C₇×D₄	C₂³	1	16	yes	complemented
123	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
124	C₂³×C₄×C₇	C₂³	1	2	yes	—
125	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
126	C₂³×C₄×C₇	C₂³	1	4	yes	—
127	C₂³×C₄×C₇	C₂³	1	2	yes	—
128	C₂³×C₄×C₇	C₂³	1	4	yes	—
129	C₂³×C₄×C₇	C₂³	1	4	yes	—
130	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
131	C₇×C₄⋊Q₈	C₂³	1	8	yes	complemented
132	C₇×#127	C₂³	1	16	yes	—
133	C₇×#127	C₂³	1	8	yes	complemented
134	C₇×#126	C₂³	1	16	yes	complemented
135	C₇×#126	C₂³	1	32	yes	complemented
136	C₇×#125	C₂³	1	8	yes	complemented
137	C₇×#124	C₂³	1	16	yes	complemented
138	C₇×#124	C₂³	1	16	yes	complemented
139	C₇×#124	C₂³	1	16	yes	complemented
140	C₇×#124	C₂³	1	16	yes	complemented
141	C₇×#124	C₂³	1	8	yes	complemented
142	C₇×#124	C₂³	1	16	yes	complemented
143	C₇×#124	C₂³	1	16	yes	complemented
144	C₇×#124	C₂³	1	32	yes	complemented
145	C₇×#124	C₂³	1	32	yes	complemented
146	C₇×#124	C₂³	1	32	yes	complemented
147	C₇×#123	C₂³	1	16	yes	complemented
148	C₇×#123	C₂³	1	32	yes	complemented
149	C₇×#123	C₂³	1	32	yes	complemented
150	C₇×#123	C₂³	1	32	yes	complemented
151	C₇×#123	C₂³	1	32	yes	complemented
152	C₇×C₂²⋊Q₈	C₂³	1	8	yes	complemented
153	C₇×C₂²⋊Q₈	C₂³	1	32	yes	complemented
154	C₇×C₂²⋊Q₈	C₂³	1	16	yes	complemented
155	C₇×C₂²⋊Q₈	C₂³	1	32	yes	complemented
156	C₇×#121	C₂³	1	8	yes	—
157	C₇×#121	C₂³	1	16	yes	—
158	C₇×#121	C₂³	1	16	yes	complemented
159	C₇×#121	C₂³	1	16	yes	complemented
160	C₇×#121	C₂³	1	32	yes	complemented
161	C₇×#121	C₂³	1	32	yes	complemented
162	C₇×#121	C₂³	1	32	yes	complemented
163	C₇×#121	C₂³	1	32	yes	complemented
164	C₇×#121	C₂³	1	32	yes	complemented
165	C₇×#120	C₂³	1	32	yes	complemented
166	C₇×#120	C₂³	1	32	yes	complemented
167	C₇×#120	C₂³	1	32	yes	complemented
168	C₇×#120	C₂³	1	32	yes	complemented
169	C₇×#120	C₂³	1	32	yes	complemented
170	C₄×C₇×Q₈	C₂³	1	8	yes	complemented
171	C₄×C₇×Q₈	C₂³	1	16	yes	complemented
172	C₄×C₇×D₄	C₂³	1	16	yes	complemented
173	C₄×C₇×D₄	C₂³	1	8	yes	complemented
174	C₄×C₇×D₄	C₂³	1	16	yes	complemented
175	C₄×C₇×D₄	C₂³	1	16	yes	complemented
176	C₄×C₇×D₄	C₂³	1	32	yes	complemented
177	C₄×C₇×D₄	C₂³	1	32	yes	complemented
178	C₄×C₇×D₄	C₂³	1	16	yes	complemented
179	C₇×#117	C₂³	1	16	yes	complemented
180	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
181	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
182	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
183	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
184	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
185	C₂×C₇×C₄⋊C₄	C₂³	1	4	yes	—
186	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
187	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
188	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
189	C₂×C₇×C₄⋊C₄	C₂³	1	4	yes	—
190	C₂×C₇×C₂²⋊C₄	C₂³	1	2	yes	—
191	C₂×C₇×C₂²⋊C₄	C₂³	1	4	yes	—
192	C₂×C₇×C₂²⋊C₄	C₂³	1	4	yes	—
193	C₂×C₇×C₂²⋊C₄	C₂³	1	4	yes	—
194	C₂×C₇×C₂²⋊C₄	C₂³	1	4	yes	—
195	C₂×C₇×C₂²⋊C₄	C₂³	1	4	yes	—
196	C₂×C₇×C₂²⋊C₄	C₂³	1	4	yes	—
197	C₂×C₇×C₂²⋊C₄	C₂³	1	2	yes	—
198	C₂×C₇×C₂²⋊C₄	C₂³	1	2	yes	—
199	C₂×C₇×C₂²⋊C₄	C₂³	1	2	yes	—
200	C₂×C₇×C₂²⋊C₄	C₂³	1	4	yes	—
201	C₂×C₇×C₂²⋊C₄	C₂³	1	2	yes	—
202	C₂×C₇×C₂²⋊C₄	C₂³	1	4	yes	—
203	C₂×C₇×C₂²⋊C₄	C₂³	1	4	yes	—
204	C₂×C₇×C₂²⋊C₄	C₂³	1	4	yes	—
205	C₂×C₇×C₂²⋊C₄	C₂³	1	4	yes	—
206	C₂×C₇×C₂²⋊C₄	C₂³	1	16	yes	complemented
207	C₂×C₇×C₂²⋊C₄	C₂³	1	16	yes	complemented
208	C₂×C₇×C₂²⋊C₄	C₂³	1	32	yes	complemented
209	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
210	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
211	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
212	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
213	C₂×C₄²×C₇	C₂³	1	2	yes	—
214	C₂×C₄²×C₇	C₂³	1	4	yes	—
215	C₂×C₄²×C₇	C₂³	1	8	yes	complemented
216	#3558	C₂×C₇	1	32	yes	direct product factor
217	C₂×#562	C₂×C₇	1	2	yes	complemented
218	C₂×H(3,𝔽₄)	C₂×C₇	1	2	yes	complemented
219	C₂×#559	C₂×C₇	1	2	yes	complemented
220	C₂×#548	C₂×C₇	1	2	yes	complemented
221	C₂×#546	C₂×C₇	1	2	yes	complemented
222	C₂×#546	C₂×C₇	1	4	yes	complemented
223	C₂×D₄²	C₂×C₇	1	2	yes	complemented
224	C₂×#542	C₂×C₇	1	2	yes	complemented
225	C₂×#538	C₂×C₇	1	2	yes	complemented
226	C₂×#538	C₂×C₇	1	4	yes	complemented
227	C₂×#535	C₂×C₇	1	2	yes	complemented
228	C₂×#534	C₂×C₇	1	2	yes	complemented
229	C₂×#532	C₂×C₇	1	1	yes	characteristic, complemented
230	C₂×#529	C₂×C₇	1	1	yes	characteristic, complemented
231	C₂²×#124	C₂×C₇	1	1	yes	characteristic, complemented
232	C₂⁴×C₇	—	2	8	no	—
233	C₂⁴×C₇	—	4	4	no	—
234	C₂⁴×C₇	—	4	8	no	—
235	C₂⁴×C₇	—	4	8	no	—
236	C₂⁴×C₇	—	4	4	no	—
237	C₂⁴×C₇	—	4	8	no	—
238	C₂⁴×C₇	C₂⁴	1	2	yes	—
239	C₂⁴×C₇	C₂⁴	1	4	yes	—
240	C₂⁴×C₇	C₂⁴	1	4	yes	—
241	C₂⁴×C₇	C₂⁴	1	1	yes	characteristic
242	C₂⁴×C₇	C₂⁴	1	8	yes	—
243	C₂⁴×C₇	C₂⁴	1	16	yes	—
244	C₇×#41	—	4	32	no	—
245	C₇×#41	—	4	32	no	—
246	C₂×C₇×Q₈	—	2	8	no	—
247	C₂×C₇×Q₈	—	4	4	no	—
248	C₂×C₇×Q₈	—	4	2	no	—
249	C₂×C₇×Q₈	—	4	4	no	—
250	C₂×C₇×Q₈	—	4	16	no	—
251	C₂×C₇×Q₈	C₂⁴	1	8	yes	—
252	C₂×C₇×Q₈	C₂⁴	1	4	yes	—
253	C₂×C₇×Q₈	C₂⁴	1	8	yes	—
254	C₂×C₇×Q₈	C₂⁴	1	8	yes	—
255	C₂×C₇×D₄	—	2	8	no	—
256	C₂×C₇×D₄	—	2	16	no	—
257	C₂×C₇×D₄	—	2	8	no	—
258	C₂×C₇×D₄	—	2	8	no	—
259	C₂×C₇×D₄	—	4	16	no	—
260	C₂×C₇×D₄	—	4	32	no	—
261	C₂×C₇×D₄	—	4	8	no	—
262	C₂×C₇×D₄	—	4	4	no	—
263	C₂×C₇×D₄	—	4	8	no	—
264	C₂×C₇×D₄	—	4	8	no	—
265	C₂×C₇×D₄	—	4	4	no	—
266	C₂×C₇×D₄	—	4	2	no	—
267	C₂×C₇×D₄	—	4	8	no	—
268	C₂×C₇×D₄	—	4	4	no	—
269	C₂×C₇×D₄	—	4	8	no	—
270	C₂×C₇×D₄	—	4	64	no	—
271	C₂×C₇×D₄	C₂⁴	1	16	yes	—
272	C₂×C₇×D₄	C₂⁴	1	8	yes	—
273	C₂×C₇×D₄	C₂⁴	1	8	yes	—
274	C₂×C₇×D₄	C₂⁴	1	8	yes	—
275	C₂×C₇×D₄	C₂⁴	1	4	yes	—
276	C₂×C₇×D₄	C₂⁴	1	16	yes	—
277	C₂×C₇×D₄	C₂⁴	1	8	yes	—
278	C₂×C₇×D₄	C₂⁴	1	16	yes	—
279	C₂×C₇×D₄	C₂⁴	1	16	yes	—
280	C₂×C₇×D₄	C₂⁴	1	8	yes	—
281	C₂×C₇×D₄	C₂⁴	1	8	yes	—
282	C₂×C₇×D₄	C₂⁴	1	16	yes	—
283	C₂×C₇×D₄	C₂⁴	1	16	yes	—
284	C₂²×C₄×C₇	—	2	4	no	—
285	C₂²×C₄×C₇	—	2	4	no	—
286	C₂²×C₄×C₇	—	2	8	no	—
287	C₂²×C₄×C₇	—	4	2	no	—
288	C₂²×C₄×C₇	—	4	8	no	—
289	C₂²×C₄×C₇	—	4	4	no	—
290	C₂²×C₄×C₇	—	4	8	no	—
291	C₂²×C₄×C₇	—	4	8	no	—
292	C₂²×C₄×C₇	C₂⁴	1	4	yes	—
293	C₂²×C₄×C₇	C₂⁴	1	4	yes	—
294	C₂²×C₄×C₇	C₂⁴	1	8	yes	—
295	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
296	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
297	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
298	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
299	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
300	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
301	C₂²×C₄×C₇	C₂⁴	1	4	yes	—
302	C₂²×C₄×C₇	C₂⁴	1	4	yes	—
303	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
304	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
305	C₂²×C₄×C₇	C₂⁴	1	4	yes	—
306	C₂²×C₄×C₇	C₂⁴	1	8	yes	—
307	C₂²×C₄×C₇	C₂⁴	1	16	yes	—
308	C₂²×C₄×C₇	C₂⁴	1	16	yes	—
309	C₂²×C₄×C₇	C₂⁴	1	16	yes	—
310	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
311	C₇×C₄⋊C₄	C₂⁴	1	8	yes	—
312	C₇×C₄⋊C₄	C₂⁴	1	8	yes	—
313	C₇×C₄⋊C₄	C₂⁴	1	8	yes	—
314	C₇×C₄⋊C₄	C₂⁴	1	8	yes	—
315	C₇×C₄⋊C₄	C₂⁴	1	8	yes	—
316	C₇×C₄⋊C₄	C₂⁴	1	16	yes	—
317	C₇×C₄⋊C₄	C₂⁴	1	8	yes	—
318	C₇×C₄⋊C₄	C₂⁴	1	4	yes	—
319	C₇×C₄⋊C₄	C₂⁴	1	4	yes	—
320	C₇×C₄⋊C₄	C₂⁴	1	16	yes	—
321	C₇×C₂²⋊C₄	C₂⁴	1	8	yes	—
322	C₇×C₂²⋊C₄	C₂⁴	1	16	yes	—
323	C₇×C₂²⋊C₄	C₂⁴	1	16	yes	—
324	C₇×C₂²⋊C₄	C₂⁴	1	16	yes	—
325	C₇×C₂²⋊C₄	C₂⁴	1	16	yes	—
326	C₇×C₂²⋊C₄	C₂⁴	1	16	yes	—
327	C₇×C₂²⋊C₄	C₂⁴	1	16	yes	—
328	C₇×C₂²⋊C₄	C₂⁴	1	8	yes	—
329	C₇×C₂²⋊C₄	C₂⁴	1	8	yes	—
330	C₇×C₂²⋊C₄	C₂⁴	1	8	yes	—
331	C₇×C₂²⋊C₄	C₂⁴	1	16	yes	—
332	C₇×C₂²⋊C₄	C₂⁴	1	8	yes	—
333	C₇×C₂²⋊C₄	C₂⁴	1	16	yes	—
334	C₇×C₂²⋊C₄	C₂⁴	1	16	yes	—
335	C₇×C₂²⋊C₄	C₂⁴	1	16	yes	—
336	C₇×C₂²⋊C₄	C₂⁴	1	16	yes	—
337	C₄²×C₇	C₂⁴	1	4	yes	—
338	C₄²×C₇	C₂⁴	1	4	yes	—
339	C₄²×C₇	C₂⁴	1	4	yes	—
340	C₄²×C₇	C₂⁴	1	4	yes	—
341	C₄²×C₇	C₂⁴	1	8	yes	—
342	C₄²×C₇	C₂⁴	1	16	yes	—
343	C₂²×#41	C₂²×C₇	1	2	yes	complemented
344	C₂²×#41	C₂²×C₇	1	2	yes	complemented
345	C₂³×Q₈	C₂²×C₇	1	1	yes	characteristic, complemented
346	C₂³×D₄	C₂²×C₇	1	1	yes	characteristic
347	C₂³×D₄	C₂²×C₇	1	4	yes	complemented
348	C₂³×D₄	C₂²×C₇	1	2	yes	complemented
349	#562	C₂²×C₇	1	32	yes	complemented
350	H(3,𝔽₄)	C₂²×C₇	1	32	yes	complemented
351	#559	C₂²×C₇	1	32	yes	complemented
352	#548	C₂²×C₇	1	32	yes	complemented
353	#546	C₂²×C₇	1	32	yes	complemented
354	#546	C₂²×C₇	1	64	yes	complemented
355	D₄²	C₂²×C₇	1	32	yes	complemented
356	#542	C₂²×C₇	1	32	yes	complemented
357	#538	C₂²×C₇	1	32	yes	complemented
358	#538	C₂²×C₇	1	64	yes	complemented
359	#535	C₂²×C₇	1	32	yes	complemented
360	#534	C₂²×C₇	1	32	yes	complemented
361	#532	C₂²×C₇	1	16	yes	complemented
362	C₂×C₄⋊Q₈	C₂²×C₇	1	1	yes	characteristic, complemented
363	C₂×#127	C₂²×C₇	1	2	yes	—
364	C₂×#127	C₂²×C₇	1	1	yes	characteristic, complemented
365	#529	C₂²×C₇	1	16	yes	complemented
366	C₂×#126	C₂²×C₇	1	2	yes	complemented
367	C₂×#126	C₂²×C₇	1	4	yes	complemented
368	C₂×#125	C₂²×C₇	1	1	yes	characteristic, complemented
369	C₂×#124	C₂²×C₇	1	2	yes	complemented
370	C₂×#124	C₂²×C₇	1	2	yes	complemented
371	C₂×#124	C₂²×C₇	1	2	yes	complemented
372	C₂×#124	C₂²×C₇	1	2	yes	complemented
373	C₂×#124	C₂²×C₇	1	1	yes	characteristic, complemented
374	C₂×#124	C₂²×C₇	1	2	yes	complemented
375	C₂×#124	C₂²×C₇	1	2	yes	complemented
376	C₂×#124	C₂²×C₇	1	4	yes	complemented
377	C₂×#124	C₂²×C₇	1	4	yes	complemented
378	C₂×#124	C₂²×C₇	1	4	yes	complemented
379	C₂×#124	C₂²×C₇	1	16	yes	complemented
380	C₂×#123	C₂²×C₇	1	2	yes	complemented
381	C₂×#123	C₂²×C₇	1	4	yes	complemented
382	C₂×#123	C₂²×C₇	1	4	yes	complemented
383	C₂×#123	C₂²×C₇	1	4	yes	complemented
384	C₂×#123	C₂²×C₇	1	4	yes	complemented
385	C₂×C₂²⋊Q₈	C₂²×C₇	1	1	yes	characteristic, complemented
386	C₂×C₂²⋊Q₈	C₂²×C₇	1	4	yes	complemented
387	C₂×C₂²⋊Q₈	C₂²×C₇	1	2	yes	complemented
388	C₂×C₂²⋊Q₈	C₂²×C₇	1	4	yes	complemented
389	C₂×#121	C₂²×C₇	1	1	yes	characteristic
390	C₂×#121	C₂²×C₇	1	2	yes	—
391	C₂×#121	C₂²×C₇	1	2	yes	complemented
392	C₂×#121	C₂²×C₇	1	2	yes	complemented
393	C₂×#121	C₂²×C₇	1	4	yes	complemented
394	C₂×#121	C₂²×C₇	1	4	yes	complemented
395	C₂×#121	C₂²×C₇	1	4	yes	complemented
396	C₂×#121	C₂²×C₇	1	4	yes	complemented
397	C₂×#121	C₂²×C₇	1	4	yes	complemented
398	C₂×#120	C₂²×C₇	1	4	yes	complemented
399	C₂×#120	C₂²×C₇	1	4	yes	complemented
400	C₂×#120	C₂²×C₇	1	4	yes	complemented
401	C₂×#120	C₂²×C₇	1	4	yes	complemented
402	C₂×#120	C₂²×C₇	1	4	yes	complemented
403	C₂×C₄×Q₈	C₂²×C₇	1	1	yes	characteristic, complemented
404	C₂×C₄×Q₈	C₂²×C₇	1	2	yes	complemented
405	C₂×C₄×D₄	C₂²×C₇	1	2	yes	complemented
406	C₂×C₄×D₄	C₂²×C₇	1	1	yes	characteristic, complemented
407	C₂×C₄×D₄	C₂²×C₇	1	2	yes	complemented
408	C₂×C₄×D₄	C₂²×C₇	1	2	yes	complemented
409	C₂×C₄×D₄	C₂²×C₇	1	4	yes	complemented
410	C₂×C₄×D₄	C₂²×C₇	1	4	yes	complemented
411	C₂×C₄×D₄	C₂²×C₇	1	2	yes	complemented
412	C₂×#117	C₂²×C₇	1	2	yes	complemented
413	C₂²×C₂²⋊C₄	C₂²×C₇	1	2	yes	complemented
414	C₂²×C₂²⋊C₄	C₂²×C₇	1	2	yes	complemented
415	C₂²×C₂²⋊C₄	C₂²×C₇	1	4	yes	complemented
416	C₂²×C₄²	C₂²×C₇	1	1	yes	characteristic, complemented
417	C₂³×C₇	—	2	2	no	—
418	C₂³×C₇	—	2	2	no	—
419	C₂³×C₇	—	2	4	no	—
420	C₂³×C₇	—	2	8	no	—
421	C₂³×C₇	—	2	8	no	—
422	C₂³×C₇	—	2	8	no	—
423	C₂³×C₇	—	2	4	no	—
424	C₂³×C₇	—	2	8	no	—
425	C₂³×C₇	—	2	8	no	—
426	C₂³×C₇	—	2	4	no	—
427	C₂³×C₇	—	2	8	no	—
428	C₂³×C₇	—	2	16	no	—
429	C₂³×C₇	—	4	8	no	—
430	C₂³×C₇	—	4	16	no	—
431	C₂³×C₇	—	4	16	no	—
432	C₂³×C₇	—	4	8	no	—
433	C₂³×C₇	—	4	16	no	—
434	C₂³×C₇	—	8	16	no	—
435	C₂³×C₇	—	8	32	no	—
436	C₂³×C₇	H(5,𝔽₂)	1	4	yes	—
437	C₂³×C₇	C₂⁵	1	4	yes	—
438	C₂³×C₇	C₂⁵	1	8	yes	—
439	C₂³×C₇	C₂⁵	1	8	yes	—
440	C₂³×C₇	C₂⁵	1	2	yes	—
441	C₂³×C₇	C₂⁵	1	1	yes	characteristic
442	C₇×Q₈	—	2	16	no	—
443	C₇×Q₈	—	4	8	no	—
444	C₇×Q₈	—	4	4	no	—
445	C₇×Q₈	—	4	8	no	—
446	C₇×D₄	—	2	16	no	—
447	C₇×D₄	—	2	32	no	—
448	C₇×D₄	—	2	16	no	—
449	C₇×D₄	—	2	16	no	—
450	C₇×D₄	—	4	16	no	—
451	C₇×D₄	—	4	8	no	—
452	C₇×D₄	—	4	16	no	—
453	C₇×D₄	—	4	16	no	—
454	C₇×D₄	—	4	8	no	—
455	C₇×D₄	—	4	4	no	—
456	C₇×D₄	—	4	16	no	—
457	C₇×D₄	—	4	8	no	—
458	C₇×D₄	—	4	16	no	—
459	C₂×C₄×C₇	—	2	2	no	—
460	C₂×C₄×C₇	—	2	4	no	—
461	C₂×C₄×C₇	—	2	2	no	—
462	C₂×C₄×C₇	—	2	2	no	—
463	C₂×C₄×C₇	—	2	8	no	—
464	C₂×C₄×C₇	—	2	4	no	—
465	C₂×C₄×C₇	—	2	8	no	—
466	C₂×C₄×C₇	—	2	8	no	—
467	C₂×C₄×C₇	—	2	2	no	—
468	C₂×C₄×C₇	—	2	2	no	—
469	C₂×C₄×C₇	—	2	4	no	—
470	C₂×C₄×C₇	—	2	8	no	—
471	C₂×C₄×C₇	—	2	16	no	—
472	C₂×C₄×C₇	—	4	4	no	—
473	C₂×C₄×C₇	—	4	16	no	—
474	C₂×C₄×C₇	—	4	8	no	—
475	C₂×C₄×C₇	—	4	16	no	—
476	C₂×C₄×C₇	—	4	16	no	—
477	C₂×C₄×C₇	H(5,𝔽₂)	1	4	yes	—
478	C₂×C₄×C₇	C₂⁵	1	4	yes	—
479	C₂×C₄×C₇	C₂⁵	1	2	yes	—
480	C₂×C₄×C₇	C₂⁵	1	2	yes	—
481	C₂×C₄×C₇	C₂⁵	1	2	yes	—
482	C₂×C₄×C₇	C₂⁵	1	2	yes	—
483	C₂×C₄×C₇	C₂⁵	1	2	yes	—
484	C₂×C₄×C₇	C₂⁵	1	8	yes	—
485	C₂×C₄×C₇	C₂⁵	1	8	yes	—
486	C₂×C₄×C₇	C₂⁵	1	4	yes	—
487	C₂×C₄×C₇	C₂⁵	1	4	yes	—
488	C₂×C₄×C₇	C₂⁵	1	2	yes	—
489	C₂⁵	C₂³×C₇	1	2	yes	—
490	C₂⁵	C₂³×C₇	1	4	yes	—
491	C₂×#41	—	4	8	no	—
492	C₂×#41	—	4	8	no	—
493	C₂×#41	C₂³×C₇	1	16	yes	complemented
494	C₂×#41	C₂³×C₇	1	16	yes	complemented
495	C₂²×Q₈	—	4	4	no	—
496	C₂²×Q₈	C₂³×C₇	1	2	yes	—
497	C₂²×Q₈	C₂³×C₇	1	1	yes	characteristic
498	C₂²×Q₈	C₂³×C₇	1	2	yes	—
499	C₂²×Q₈	C₂³×C₇	1	2	yes	—
500	C₂²×Q₈	C₂³×C₇	1	8	yes	complemented
501	C₂²×D₄	—	4	4	no	—
502	C₂²×D₄	—	4	8	no	—
503	C₂²×D₄	—	4	16	no	—
504	C₂²×D₄	C₂³×C₇	1	4	yes	—
505	C₂²×D₄	C₂³×C₇	1	2	yes	—
506	C₂²×D₄	C₂³×C₇	1	2	yes	—
507	C₂²×D₄	C₂³×C₇	1	2	yes	—
508	C₂²×D₄	C₂³×C₇	1	1	yes	characteristic
509	C₂²×D₄	C₂³×C₇	1	4	yes	—
510	C₂²×D₄	C₂³×C₇	1	2	yes	—
511	C₂²×D₄	C₂³×C₇	1	4	yes	—
512	C₂²×D₄	C₂³×C₇	1	4	yes	—
513	C₂²×D₄	C₂³×C₇	1	2	yes	—
514	C₂²×D₄	C₂³×C₇	1	2	yes	—
515	C₂²×D₄	C₂³×C₇	1	4	yes	—
516	C₂²×D₄	C₂³×C₇	1	4	yes	—
517	C₂²×D₄	C₂³×C₇	1	8	yes	—
518	C₂²×D₄	C₂³×C₇	1	32	yes	complemented
519	C₂²×D₄	C₂³×C₇	1	16	yes	complemented
520	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
521	C₂³×C₄	C₂³×C₇	1	2	yes	—
522	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
523	C₂³×C₄	C₂³×C₇	1	2	yes	—
524	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
525	C₂³×C₄	C₂³×C₇	1	4	yes	—
526	C₂³×C₄	C₂³×C₇	1	4	yes	—
527	C₂³×C₄	C₂³×C₇	1	4	yes	—
528	C₄⋊Q₈	C₂³×C₇	1	8	yes	complemented
529	#127	C₂³×C₇	1	16	yes	—
530	#127	C₂³×C₇	1	8	yes	complemented
531	#126	C₂³×C₇	1	16	yes	complemented
532	#126	C₂³×C₇	1	32	yes	complemented
533	#125	C₂³×C₇	1	8	yes	complemented
534	#124	C₂³×C₇	1	16	yes	complemented
535	#124	C₂³×C₇	1	16	yes	complemented
536	#124	C₂³×C₇	1	16	yes	complemented
537	#124	C₂³×C₇	1	16	yes	complemented
538	#124	C₂³×C₇	1	8	yes	complemented
539	#124	C₂³×C₇	1	16	yes	complemented
540	#124	C₂³×C₇	1	16	yes	complemented
541	#124	C₂³×C₇	1	32	yes	complemented
542	#124	C₂³×C₇	1	32	yes	complemented
543	#124	C₂³×C₇	1	32	yes	complemented
544	#123	C₂³×C₇	1	16	yes	complemented
545	#123	C₂³×C₇	1	32	yes	complemented
546	#123	C₂³×C₇	1	32	yes	complemented
547	#123	C₂³×C₇	1	32	yes	complemented
548	#123	C₂³×C₇	1	32	yes	complemented
549	C₂²⋊Q₈	C₂³×C₇	1	8	yes	complemented
550	C₂²⋊Q₈	C₂³×C₇	1	32	yes	complemented
551	C₂²⋊Q₈	C₂³×C₇	1	16	yes	complemented
552	C₂²⋊Q₈	C₂³×C₇	1	32	yes	complemented
553	#121	C₂³×C₇	1	8	yes	—
554	#121	C₂³×C₇	1	16	yes	—
555	#121	C₂³×C₇	1	16	yes	complemented
556	#121	C₂³×C₇	1	16	yes	complemented
557	#121	C₂³×C₇	1	32	yes	complemented
558	#121	C₂³×C₇	1	32	yes	complemented
559	#121	C₂³×C₇	1	32	yes	complemented
560	#121	C₂³×C₇	1	32	yes	complemented
561	#121	C₂³×C₇	1	32	yes	complemented
562	#120	C₂³×C₇	1	32	yes	complemented
563	#120	C₂³×C₇	1	32	yes	complemented
564	#120	C₂³×C₇	1	32	yes	complemented
565	#120	C₂³×C₇	1	32	yes	complemented
566	#120	C₂³×C₇	1	32	yes	complemented
567	C₄×Q₈	C₂³×C₇	1	8	yes	complemented
568	C₄×Q₈	C₂³×C₇	1	16	yes	complemented
569	C₄×D₄	C₂³×C₇	1	16	yes	complemented
570	C₄×D₄	C₂³×C₇	1	8	yes	complemented
571	C₄×D₄	C₂³×C₇	1	16	yes	complemented
572	C₄×D₄	C₂³×C₇	1	16	yes	complemented
573	C₄×D₄	C₂³×C₇	1	32	yes	complemented
574	C₄×D₄	C₂³×C₇	1	32	yes	complemented
575	C₄×D₄	C₂³×C₇	1	16	yes	complemented
576	#117	C₂³×C₇	1	16	yes	complemented
577	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
578	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
579	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
580	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
581	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
582	C₂×C₄⋊C₄	C₂³×C₇	1	4	yes	—
583	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
584	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
585	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
586	C₂×C₄⋊C₄	C₂³×C₇	1	4	yes	—
587	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
588	C₂×C₂²⋊C₄	C₂³×C₇	1	4	yes	—
589	C₂×C₂²⋊C₄	C₂³×C₇	1	4	yes	—
590	C₂×C₂²⋊C₄	C₂³×C₇	1	4	yes	—
591	C₂×C₂²⋊C₄	C₂³×C₇	1	4	yes	—
592	C₂×C₂²⋊C₄	C₂³×C₇	1	4	yes	—
593	C₂×C₂²⋊C₄	C₂³×C₇	1	4	yes	—
594	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
595	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
596	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
597	C₂×C₂²⋊C₄	C₂³×C₇	1	4	yes	—
598	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
599	C₂×C₂²⋊C₄	C₂³×C₇	1	4	yes	—
600	C₂×C₂²⋊C₄	C₂³×C₇	1	4	yes	—
601	C₂×C₂²⋊C₄	C₂³×C₇	1	4	yes	—
602	C₂×C₂²⋊C₄	C₂³×C₇	1	4	yes	—
603	C₂×C₂²⋊C₄	C₂³×C₇	1	16	yes	complemented
604	C₂×C₂²⋊C₄	C₂³×C₇	1	16	yes	complemented
605	C₂×C₂²⋊C₄	C₂³×C₇	1	32	yes	complemented
606	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
607	C₂×C₄²	C₂³×C₇	1	2	yes	—
608	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
609	C₂×C₄²	C₂³×C₇	1	4	yes	—
610	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
611	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
612	C₂×C₄²	C₂³×C₇	1	8	yes	complemented
613	C₂²×C₇	—	2	2	no	—
614	C₂²×C₇	—	2	2	no	—
615	C₂²×C₇	—	2	8	no	—
616	C₂²×C₇	—	2	4	no	—
617	C₂²×C₇	—	2	8	no	—
618	C₂²×C₇	—	2	8	no	—
619	C₂²×C₇	—	2	8	no	—
620	C₂²×C₇	—	2	4	no	—
621	C₂²×C₇	—	2	8	no	—
622	C₂²×C₇	—	2	8	no	—
623	C₂²×C₇	—	2	4	no	—
624	C₂²×C₇	—	2	8	no	—
625	C₂²×C₇	—	4	16	no	—
626	C₂²×C₇	—	4	8	no	—
627	C₂²×C₇	—	4	16	no	—
628	C₂²×C₇	—	8	16	no	—
629	C₂²×C₇	—	8	32	no	—
630	C₂²×C₇	C₂×H(5,𝔽₂)	1	4	yes	—
631	C₂²×C₇	C₂×H(5,𝔽₂)	1	2	yes	—
632	C₂²×C₇	C₂×H(5,𝔽₂)	1	2	yes	—
633	C₂²×C₇	#585	1	2	yes	—
634	C₂²×C₇	C₂⁶	1	1	yes	characteristic
635	C₄×C₇	—	2	2	no	—
636	C₄×C₇	—	2	4	no	—
637	C₄×C₇	—	2	2	no	—
638	C₄×C₇	—	2	2	no	—
639	C₄×C₇	—	2	4	no	—
640	C₄×C₇	—	2	8	no	—
641	C₄×C₇	—	2	8	no	—
642	C₄×C₇	—	2	2	no	—
643	C₄×C₇	—	2	2	no	—
644	C₄×C₇	—	2	4	no	—
645	C₄×C₇	C₂×H(5,𝔽₂)	1	4	yes	—
646	C₂⁴	—	2	8	no	—
647	C₂⁴	—	4	4	no	—
648	C₂⁴	—	4	8	no	—
649	C₂⁴	—	4	8	no	—
650	C₂⁴	—	4	4	no	—
651	C₂⁴	—	4	8	no	—
652	C₂⁴	C₂⁴×C₇	1	2	yes	—
653	C₂⁴	C₂⁴×C₇	1	4	yes	—
654	C₂⁴	C₂⁴×C₇	1	4	yes	—
655	C₂⁴	C₂⁴×C₇	1	1	yes	characteristic
656	C₂⁴	C₂⁴×C₇	1	8	yes	—
657	C₂⁴	C₂⁴×C₇	1	16	yes	—
658	#41	—	4	32	no	—
659	#41	—	4	32	no	—
660	C₂×Q₈	—	2	8	no	—
661	C₂×Q₈	—	4	4	no	—
662	C₂×Q₈	—	4	4	no	—
663	C₂×Q₈	—	4	2	no	—
664	C₂×Q₈	—	4	16	no	—
665	C₂×Q₈	C₂⁴×C₇	1	8	yes	—
666	C₂×Q₈	C₂⁴×C₇	1	4	yes	—
667	C₂×Q₈	C₂⁴×C₇	1	8	yes	—
668	C₂×Q₈	C₂⁴×C₇	1	8	yes	—
669	C₂×D₄	—	2	8	no	—
670	C₂×D₄	—	2	16	no	—
671	C₂×D₄	—	2	8	no	—
672	C₂×D₄	—	2	8	no	—
673	C₂×D₄	—	4	16	no	—
674	C₂×D₄	—	4	32	no	—
675	C₂×D₄	—	4	8	no	—
676	C₂×D₄	—	4	4	no	—
677	C₂×D₄	—	4	8	no	—
678	C₂×D₄	—	4	8	no	—
679	C₂×D₄	—	4	4	no	—
680	C₂×D₄	—	4	8	no	—
681	C₂×D₄	—	4	4	no	—
682	C₂×D₄	—	4	2	no	—
683	C₂×D₄	—	4	8	no	—
684	C₂×D₄	—	4	64	no	—
685	C₂×D₄	C₂⁴×C₇	1	16	yes	—
686	C₂×D₄	C₂⁴×C₇	1	8	yes	—
687	C₂×D₄	C₂⁴×C₇	1	8	yes	—
688	C₂×D₄	C₂⁴×C₇	1	8	yes	—
689	C₂×D₄	C₂⁴×C₇	1	4	yes	—
690	C₂×D₄	C₂⁴×C₇	1	16	yes	—
691	C₂×D₄	C₂⁴×C₇	1	8	yes	—
692	C₂×D₄	C₂⁴×C₇	1	16	yes	—
693	C₂×D₄	C₂⁴×C₇	1	16	yes	—
694	C₂×D₄	C₂⁴×C₇	1	8	yes	—
695	C₂×D₄	C₂⁴×C₇	1	8	yes	—
696	C₂×D₄	C₂⁴×C₇	1	16	yes	—
697	C₂×D₄	C₂⁴×C₇	1	16	yes	—
698	C₂²×C₄	—	2	4	no	—
699	C₂²×C₄	—	2	4	no	—
700	C₂²×C₄	—	2	8	no	—
701	C₂²×C₄	—	4	8	no	—
702	C₂²×C₄	—	4	4	no	—
703	C₂²×C₄	—	4	2	no	—
704	C₂²×C₄	—	4	8	no	—
705	C₂²×C₄	—	4	8	no	—
706	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
707	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
708	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
709	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
710	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
711	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
712	C₂²×C₄	C₂⁴×C₇	1	4	yes	—
713	C₂²×C₄	C₂⁴×C₇	1	4	yes	—
714	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
715	C₂²×C₄	C₂⁴×C₇	1	4	yes	—
716	C₂²×C₄	C₂⁴×C₇	1	4	yes	—
717	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
718	C₂²×C₄	C₂⁴×C₇	1	8	yes	—
719	C₂²×C₄	C₂⁴×C₇	1	4	yes	—
720	C₂²×C₄	C₂⁴×C₇	1	8	yes	—
721	C₂²×C₄	C₂⁴×C₇	1	16	yes	—
722	C₂²×C₄	C₂⁴×C₇	1	16	yes	—
723	C₂²×C₄	C₂⁴×C₇	1	16	yes	—
724	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
725	C₄⋊C₄	C₂⁴×C₇	1	8	yes	—
726	C₄⋊C₄	C₂⁴×C₇	1	8	yes	—
727	C₄⋊C₄	C₂⁴×C₇	1	8	yes	—
728	C₄⋊C₄	C₂⁴×C₇	1	8	yes	—
729	C₄⋊C₄	C₂⁴×C₇	1	8	yes	—
730	C₄⋊C₄	C₂⁴×C₇	1	16	yes	—
731	C₄⋊C₄	C₂⁴×C₇	1	8	yes	—
732	C₄⋊C₄	C₂⁴×C₇	1	4	yes	—
733	C₄⋊C₄	C₂⁴×C₇	1	4	yes	—
734	C₄⋊C₄	C₂⁴×C₇	1	16	yes	—
735	C₂²⋊C₄	C₂⁴×C₇	1	8	yes	—
736	C₂²⋊C₄	C₂⁴×C₇	1	16	yes	—
737	C₂²⋊C₄	C₂⁴×C₇	1	16	yes	—
738	C₂²⋊C₄	C₂⁴×C₇	1	16	yes	—
739	C₂²⋊C₄	C₂⁴×C₇	1	16	yes	—
740	C₂²⋊C₄	C₂⁴×C₇	1	16	yes	—
741	C₂²⋊C₄	C₂⁴×C₇	1	16	yes	—
742	C₂²⋊C₄	C₂⁴×C₇	1	8	yes	—
743	C₂²⋊C₄	C₂⁴×C₇	1	8	yes	—
744	C₂²⋊C₄	C₂⁴×C₇	1	8	yes	—
745	C₂²⋊C₄	C₂⁴×C₇	1	16	yes	—
746	C₂²⋊C₄	C₂⁴×C₇	1	8	yes	—
747	C₂²⋊C₄	C₂⁴×C₇	1	16	yes	—
748	C₂²⋊C₄	C₂⁴×C₇	1	16	yes	—
749	C₂²⋊C₄	C₂⁴×C₇	1	16	yes	—
750	C₂²⋊C₄	C₂⁴×C₇	1	16	yes	—
751	C₄²	C₂⁴×C₇	1	4	yes	—
752	C₄²	C₂⁴×C₇	1	4	yes	—
753	C₄²	C₂⁴×C₇	1	4	yes	—
754	C₄²	C₂⁴×C₇	1	4	yes	—
755	C₄²	C₂⁴×C₇	1	8	yes	—
756	C₄²	C₂⁴×C₇	1	16	yes	—
757	C₂×C₇	—	2	4	no	—
758	C₂×C₇	—	4	8	no	—
759	C₂×C₇	—	4	4	no	—
760	C₂×C₇	—	4	8	no	—
761	C₂×C₇	#3558	1	4	yes	direct product factor
762	C₂×C₇	C₂²×H(5,𝔽₂)	1	1	yes	characteristic
763	C₂×C₇	C₂²×H(5,𝔽₂)	1	1	yes	characteristic
764	C₂×C₇	C₂×#585	1	1	yes	characteristic
765	C₂³	—	2	2	no	—
766	C₂³	—	2	2	no	—
767	C₂³	—	2	4	no	—
768	C₂³	—	2	8	no	—
769	C₂³	—	2	8	no	—
770	C₂³	—	2	8	no	—
771	C₂³	—	2	4	no	—
772	C₂³	—	2	8	no	—
773	C₂³	—	2	8	no	—
774	C₂³	—	2	4	no	—
775	C₂³	—	2	8	no	—
776	C₂³	—	2	16	no	—
777	C₂³	—	4	8	no	—
778	C₂³	—	4	16	no	—
779	C₂³	—	4	16	no	—
780	C₂³	—	4	8	no	—
781	C₂³	—	4	16	no	—
782	C₂³	—	8	16	no	—
783	C₂³	—	8	32	no	—
784	C₂³	C₇×H(5,𝔽₂)	1	4	yes	—
785	C₂³	C₂⁵×C₇	1	4	yes	—
786	C₂³	C₂⁵×C₇	1	8	yes	—
787	C₂³	C₂⁵×C₇	1	8	yes	—
788	C₂³	C₂⁵×C₇	1	2	yes	—
789	C₂³	C₂⁵×C₇	1	1	yes	characteristic
790	Q₈	—	2	16	no	—
791	Q₈	—	4	8	no	—
792	Q₈	—	4	4	no	—
793	Q₈	—	4	8	no	—
794	D₄	—	2	16	no	—
795	D₄	—	2	32	no	—
796	D₄	—	2	16	no	—
797	D₄	—	2	16	no	—
798	D₄	—	4	16	no	—
799	D₄	—	4	8	no	—
800	D₄	—	4	16	no	—
801	D₄	—	4	16	no	—
802	D₄	—	4	8	no	—
803	D₄	—	4	4	no	—
804	D₄	—	4	16	no	—
805	D₄	—	4	8	no	—
806	D₄	—	4	16	no	—
807	C₂×C₄	—	2	2	no	—
808	C₂×C₄	—	2	4	no	—
809	C₂×C₄	—	2	2	no	—
810	C₂×C₄	—	2	2	no	—
811	C₂×C₄	—	2	8	no	—
812	C₂×C₄	—	2	4	no	—
813	C₂×C₄	—	2	8	no	—
814	C₂×C₄	—	2	8	no	—
815	C₂×C₄	—	2	2	no	—
816	C₂×C₄	—	2	2	no	—
817	C₂×C₄	—	2	4	no	—
818	C₂×C₄	—	2	8	no	—
819	C₂×C₄	—	2	16	no	—
820	C₂×C₄	—	4	4	no	—
821	C₂×C₄	—	4	16	no	—
822	C₂×C₄	—	4	8	no	—
823	C₂×C₄	—	4	16	no	—
824	C₂×C₄	—	4	16	no	—
825	C₂×C₄	C₇×H(5,𝔽₂)	1	4	yes	—
826	C₂×C₄	C₂⁵×C₇	1	4	yes	—
827	C₂×C₄	C₂⁵×C₇	1	2	yes	—
828	C₂×C₄	C₂⁵×C₇	1	2	yes	—
829	C₂×C₄	C₂⁵×C₇	1	2	yes	—
830	C₂×C₄	C₂⁵×C₇	1	2	yes	—
831	C₂×C₄	C₂⁵×C₇	1	2	yes	—
832	C₂×C₄	C₂⁵×C₇	1	8	yes	—
833	C₂×C₄	C₂⁵×C₇	1	8	yes	—
834	C₂×C₄	C₂⁵×C₇	1	4	yes	—
835	C₂×C₄	C₂⁵×C₇	1	4	yes	—
836	C₂×C₄	C₂⁵×C₇	1	2	yes	—
837	C₇	C₂×#3558	1	1	yes	characteristic, direct product factor, Sylow
838	C₂²	—	2	2	no	—
839	C₂²	—	2	2	no	—
840	C₂²	—	2	8	no	—
841	C₂²	—	2	4	no	—
842	C₂²	—	2	8	no	—
843	C₂²	—	2	8	no	—
844	C₂²	—	2	8	no	—
845	C₂²	—	2	4	no	—
846	C₂²	—	2	8	no	—
847	C₂²	—	2	8	no	—
848	C₂²	—	2	4	no	—
849	C₂²	—	2	8	no	—
850	C₂²	—	4	8	no	—
851	C₂²	—	4	16	no	—
852	C₂²	—	4	16	no	—
853	C₂²	—	8	16	no	—
854	C₂²	—	8	32	no	—
855	C₂²	C₂×C₇×H(5,𝔽₂)	1	4	yes	—
856	C₂²	C₂×C₇×H(5,𝔽₂)	1	2	yes	—
857	C₂²	C₂×C₇×H(5,𝔽₂)	1	2	yes	—
858	C₂²	C₇×#585	1	2	yes	—
859	C₂²	C₂⁶×C₇	1	1	yes	characteristic
860	C₄	—	2	2	no	—
861	C₄	—	2	4	no	—
862	C₄	—	2	2	no	—
863	C₄	—	2	2	no	—
864	C₄	—	2	4	no	—
865	C₄	—	2	8	no	—
866	C₄	—	2	8	no	—
867	C₄	—	2	2	no	—
868	C₄	—	2	2	no	—
869	C₄	—	2	4	no	—
870	C₄	C₂×C₇×H(5,𝔽₂)	1	4	yes	—
871	C₂	—	2	4	no	—
872	C₂	—	4	4	no	—
873	C₂	—	4	8	no	—
874	C₂	—	4	8	no	—
875	C₂	C₇×#3558	1	4	yes	direct product factor
876	C₂	C₂²×C₇×H(5,𝔽₂)	1	1	yes	characteristic
877	C₂	C₂²×C₇×H(5,𝔽₂)	1	1	yes	characteristic
878	C₂	C₂×C₇×#585	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
1. C₇×#3558	C₂	direct (N × H)
2. C₂×C₇×#562	C₂	semidirect
3. C₂×C₇×H(3,𝔽₄)	C₂	semidirect
4. C₂×C₇×#559	C₂	semidirect
5. C₂×C₇×#548	C₂	semidirect
6. C₂×C₇×#546	C₂	semidirect
7. C₂×C₇×#546	C₂	semidirect
8. C₂×C₇×D₄²	C₂	semidirect
9. C₂×C₇×#542	C₂	semidirect
10. C₂×C₇×#538	C₂	semidirect
11. C₂×C₇×#538	C₂	semidirect
12. C₂×C₇×#535	C₂	semidirect
13. C₂×C₇×#534	C₂	semidirect
14. C₂×C₇×#532	C₂	semidirect
15. C₂×C₇×#529	C₂	semidirect
16. C₂²×C₇×#124	C₂	semidirect
17. C₂²×C₇×#41	C₂²	semidirect
18. C₂²×C₇×#41	C₂²	semidirect
19. C₂³×C₇×Q₈	C₂²	semidirect
21. C₂³×C₇×D₄	C₂²	semidirect
22. C₂³×C₇×D₄	C₂²	semidirect
23. C₇×#562	C₂²	semidirect
24. C₇×H(3,𝔽₄)	C₂²	semidirect
25. C₇×#559	C₂²	semidirect
26. C₇×#548	C₂²	semidirect
27. C₇×#546	C₂²	semidirect
28. C₇×#546	C₂²	semidirect
29. C₇×D₄²	C₂²	semidirect
30. C₇×#542	C₂²	semidirect
31. C₇×#538	C₂²	semidirect
32. C₇×#538	C₂²	semidirect
33. C₇×#535	C₂²	semidirect
34. C₇×#534	C₂²	semidirect
35. C₇×#532	C₂²	semidirect
36. C₂×C₇×C₄⋊Q₈	C₂²	semidirect
38. C₂×C₇×#127	C₂²	semidirect
39. C₇×#529	C₂²	semidirect
40. C₂×C₇×#126	C₂²	semidirect
41. C₂×C₇×#126	C₂²	semidirect
42. C₂×C₇×#125	C₂²	semidirect
43. C₂×C₇×#124	C₂²	semidirect
44. C₂×C₇×#124	C₂²	semidirect
45. C₂×C₇×#124	C₂²	semidirect
46. C₂×C₇×#124	C₂²	semidirect
47. C₂×C₇×#124	C₂²	semidirect
48. C₂×C₇×#124	C₂²	semidirect
49. C₂×C₇×#124	C₂²	semidirect
50. C₂×C₇×#124	C₂²	semidirect
51. C₂×C₇×#124	C₂²	semidirect
52. C₂×C₇×#124	C₂²	semidirect
53. C₂×C₇×#124	C₂²	semidirect
54. C₂×C₇×#123	C₂²	semidirect
55. C₂×C₇×#123	C₂²	semidirect
56. C₂×C₇×#123	C₂²	semidirect
57. C₂×C₇×#123	C₂²	semidirect
58. C₂×C₇×#123	C₂²	semidirect
59. C₂×C₇×C₂²⋊Q₈	C₂²	semidirect
60. C₂×C₇×C₂²⋊Q₈	C₂²	semidirect
61. C₂×C₇×C₂²⋊Q₈	C₂²	semidirect
62. C₂×C₇×C₂²⋊Q₈	C₂²	semidirect
65. C₂×C₇×#121	C₂²	semidirect
66. C₂×C₇×#121	C₂²	semidirect
67. C₂×C₇×#121	C₂²	semidirect
68. C₂×C₇×#121	C₂²	semidirect
69. C₂×C₇×#121	C₂²	semidirect
70. C₂×C₇×#121	C₂²	semidirect
71. C₂×C₇×#121	C₂²	semidirect
72. C₂×C₇×#120	C₂²	semidirect
73. C₂×C₇×#120	C₂²	semidirect
74. C₂×C₇×#120	C₂²	semidirect
75. C₂×C₇×#120	C₂²	semidirect
76. C₂×C₇×#120	C₂²	semidirect
77. C₂×C₄×C₇×Q₈	C₂²	semidirect
78. C₂×C₄×C₇×Q₈	C₂²	semidirect
79. C₂×C₄×C₇×D₄	C₂²	semidirect
80. C₂×C₄×C₇×D₄	C₂²	semidirect
81. C₂×C₄×C₇×D₄	C₂²	semidirect
82. C₂×C₄×C₇×D₄	C₂²	semidirect
83. C₂×C₄×C₇×D₄	C₂²	semidirect
84. C₂×C₄×C₇×D₄	C₂²	semidirect
85. C₂×C₄×C₇×D₄	C₂²	semidirect
86. C₂×C₇×#117	C₂²	semidirect
87. C₂²×C₇×C₂²⋊C₄	C₂²	semidirect
88. C₂²×C₇×C₂²⋊C₄	C₂²	semidirect
89. C₂²×C₇×C₂²⋊C₄	C₂²	semidirect
90. C₂²×C₄²×C₇	C₂²	semidirect
91. C₂×#3558	C₇	direct (N × H)
96. C₂×C₇×#41	C₂³	semidirect
97. C₂×C₇×#41	C₂³	semidirect
103. C₂²×C₇×Q₈	C₂³	semidirect
121. C₂²×C₇×D₄	C₂³	semidirect
122. C₂²×C₇×D₄	C₂³	semidirect
131. C₇×C₄⋊Q₈	C₂³	semidirect
133. C₇×#127	C₂³	semidirect
134. C₇×#126	C₂³	semidirect
135. C₇×#126	C₂³	semidirect
136. C₇×#125	C₂³	semidirect
137. C₇×#124	C₂³	semidirect
138. C₇×#124	C₂³	semidirect
139. C₇×#124	C₂³	semidirect
140. C₇×#124	C₂³	semidirect
141. C₇×#124	C₂³	semidirect
142. C₇×#124	C₂³	semidirect
143. C₇×#124	C₂³	semidirect
144. C₇×#124	C₂³	semidirect
145. C₇×#124	C₂³	semidirect
146. C₇×#124	C₂³	semidirect
147. C₇×#123	C₂³	semidirect
148. C₇×#123	C₂³	semidirect
149. C₇×#123	C₂³	semidirect
150. C₇×#123	C₂³	semidirect
151. C₇×#123	C₂³	semidirect
152. C₇×C₂²⋊Q₈	C₂³	semidirect
153. C₇×C₂²⋊Q₈	C₂³	semidirect
154. C₇×C₂²⋊Q₈	C₂³	semidirect
155. C₇×C₂²⋊Q₈	C₂³	semidirect
158. C₇×#121	C₂³	semidirect
159. C₇×#121	C₂³	semidirect
160. C₇×#121	C₂³	semidirect
161. C₇×#121	C₂³	semidirect
162. C₇×#121	C₂³	semidirect
163. C₇×#121	C₂³	semidirect
164. C₇×#121	C₂³	semidirect
165. C₇×#120	C₂³	semidirect
166. C₇×#120	C₂³	semidirect
167. C₇×#120	C₂³	semidirect
168. C₇×#120	C₂³	semidirect
169. C₇×#120	C₂³	semidirect
170. C₄×C₇×Q₈	C₂³	semidirect
171. C₄×C₇×Q₈	C₂³	semidirect
172. C₄×C₇×D₄	C₂³	semidirect
173. C₄×C₇×D₄	C₂³	semidirect
174. C₄×C₇×D₄	C₂³	semidirect
175. C₄×C₇×D₄	C₂³	semidirect
176. C₄×C₇×D₄	C₂³	semidirect
177. C₄×C₇×D₄	C₂³	semidirect
178. C₄×C₇×D₄	C₂³	semidirect
179. C₇×#117	C₂³	semidirect
206. C₂×C₇×C₂²⋊C₄	C₂³	semidirect
207. C₂×C₇×C₂²⋊C₄	C₂³	semidirect
208. C₂×C₇×C₂²⋊C₄	C₂³	semidirect
215. C₂×C₄²×C₇	C₂³	semidirect
216. #3558	C₂×C₇	direct (N × H)
217. C₂×#562	C₂×C₇	semidirect
218. C₂×H(3,𝔽₄)	C₂×C₇	semidirect
219. C₂×#559	C₂×C₇	semidirect
220. C₂×#548	C₂×C₇	semidirect
221. C₂×#546	C₂×C₇	semidirect
222. C₂×#546	C₂×C₇	semidirect
223. C₂×D₄²	C₂×C₇	semidirect
224. C₂×#542	C₂×C₇	semidirect
225. C₂×#538	C₂×C₇	semidirect
226. C₂×#538	C₂×C₇	semidirect
227. C₂×#535	C₂×C₇	semidirect
228. C₂×#534	C₂×C₇	semidirect
229. C₂×#532	C₂×C₇	semidirect
230. C₂×#529	C₂×C₇	semidirect
231. C₂²×#124	C₂×C₇	semidirect
343. C₂²×#41	C₂²×C₇	semidirect
344. C₂²×#41	C₂²×C₇	semidirect
345. C₂³×Q₈	C₂²×C₇	semidirect
347. C₂³×D₄	C₂²×C₇	semidirect
348. C₂³×D₄	C₂²×C₇	semidirect
349. #562	C₂²×C₇	semidirect
350. H(3,𝔽₄)	C₂²×C₇	semidirect
351. #559	C₂²×C₇	semidirect
352. #548	C₂²×C₇	semidirect
353. #546	C₂²×C₇	semidirect
354. #546	C₂²×C₇	semidirect
355. D₄²	C₂²×C₇	semidirect
356. #542	C₂²×C₇	semidirect
357. #538	C₂²×C₇	semidirect
358. #538	C₂²×C₇	semidirect
359. #535	C₂²×C₇	semidirect
360. #534	C₂²×C₇	semidirect
361. #532	C₂²×C₇	semidirect
362. C₂×C₄⋊Q₈	C₂²×C₇	semidirect
364. C₂×#127	C₂²×C₇	semidirect
365. #529	C₂²×C₇	semidirect
366. C₂×#126	C₂²×C₇	semidirect
367. C₂×#126	C₂²×C₇	semidirect
368. C₂×#125	C₂²×C₇	semidirect
369. C₂×#124	C₂²×C₇	semidirect
370. C₂×#124	C₂²×C₇	semidirect
371. C₂×#124	C₂²×C₇	semidirect
372. C₂×#124	C₂²×C₇	semidirect
373. C₂×#124	C₂²×C₇	semidirect
374. C₂×#124	C₂²×C₇	semidirect
375. C₂×#124	C₂²×C₇	semidirect
376. C₂×#124	C₂²×C₇	semidirect
377. C₂×#124	C₂²×C₇	semidirect
378. C₂×#124	C₂²×C₇	semidirect
379. C₂×#124	C₂²×C₇	semidirect
380. C₂×#123	C₂²×C₇	semidirect
381. C₂×#123	C₂²×C₇	semidirect
382. C₂×#123	C₂²×C₇	semidirect
383. C₂×#123	C₂²×C₇	semidirect
384. C₂×#123	C₂²×C₇	semidirect
385. C₂×C₂²⋊Q₈	C₂²×C₇	semidirect
386. C₂×C₂²⋊Q₈	C₂²×C₇	semidirect
387. C₂×C₂²⋊Q₈	C₂²×C₇	semidirect
388. C₂×C₂²⋊Q₈	C₂²×C₇	semidirect
391. C₂×#121	C₂²×C₇	semidirect
392. C₂×#121	C₂²×C₇	semidirect
393. C₂×#121	C₂²×C₇	semidirect
394. C₂×#121	C₂²×C₇	semidirect
395. C₂×#121	C₂²×C₇	semidirect
396. C₂×#121	C₂²×C₇	semidirect
397. C₂×#121	C₂²×C₇	semidirect
398. C₂×#120	C₂²×C₇	semidirect
399. C₂×#120	C₂²×C₇	semidirect
400. C₂×#120	C₂²×C₇	semidirect
401. C₂×#120	C₂²×C₇	semidirect
402. C₂×#120	C₂²×C₇	semidirect
403. C₂×C₄×Q₈	C₂²×C₇	semidirect
404. C₂×C₄×Q₈	C₂²×C₇	semidirect
405. C₂×C₄×D₄	C₂²×C₇	semidirect
406. C₂×C₄×D₄	C₂²×C₇	semidirect
407. C₂×C₄×D₄	C₂²×C₇	semidirect
408. C₂×C₄×D₄	C₂²×C₇	semidirect
409. C₂×C₄×D₄	C₂²×C₇	semidirect
410. C₂×C₄×D₄	C₂²×C₇	semidirect
411. C₂×C₄×D₄	C₂²×C₇	semidirect
412. C₂×#117	C₂²×C₇	semidirect
413. C₂²×C₂²⋊C₄	C₂²×C₇	semidirect
414. C₂²×C₂²⋊C₄	C₂²×C₇	semidirect
415. C₂²×C₂²⋊C₄	C₂²×C₇	semidirect
416. C₂²×C₄²	C₂²×C₇	semidirect
493. C₂×#41	C₂³×C₇	semidirect
494. C₂×#41	C₂³×C₇	semidirect
500. C₂²×Q₈	C₂³×C₇	semidirect
518. C₂²×D₄	C₂³×C₇	semidirect
519. C₂²×D₄	C₂³×C₇	semidirect
528. C₄⋊Q₈	C₂³×C₇	semidirect
530. #127	C₂³×C₇	semidirect
531. #126	C₂³×C₇	semidirect
532. #126	C₂³×C₇	semidirect
533. #125	C₂³×C₇	semidirect
534. #124	C₂³×C₇	semidirect
535. #124	C₂³×C₇	semidirect
536. #124	C₂³×C₇	semidirect
537. #124	C₂³×C₇	semidirect
538. #124	C₂³×C₇	semidirect
539. #124	C₂³×C₇	semidirect
540. #124	C₂³×C₇	semidirect
541. #124	C₂³×C₇	semidirect
542. #124	C₂³×C₇	semidirect
543. #124	C₂³×C₇	semidirect
544. #123	C₂³×C₇	semidirect
545. #123	C₂³×C₇	semidirect
546. #123	C₂³×C₇	semidirect
547. #123	C₂³×C₇	semidirect
548. #123	C₂³×C₇	semidirect
549. C₂²⋊Q₈	C₂³×C₇	semidirect
550. C₂²⋊Q₈	C₂³×C₇	semidirect
551. C₂²⋊Q₈	C₂³×C₇	semidirect
552. C₂²⋊Q₈	C₂³×C₇	semidirect
555. #121	C₂³×C₇	semidirect
556. #121	C₂³×C₇	semidirect
557. #121	C₂³×C₇	semidirect
558. #121	C₂³×C₇	semidirect
559. #121	C₂³×C₇	semidirect
560. #121	C₂³×C₇	semidirect
561. #121	C₂³×C₇	semidirect
562. #120	C₂³×C₇	semidirect
563. #120	C₂³×C₇	semidirect
564. #120	C₂³×C₇	semidirect
565. #120	C₂³×C₇	semidirect
566. #120	C₂³×C₇	semidirect
567. C₄×Q₈	C₂³×C₇	semidirect
568. C₄×Q₈	C₂³×C₇	semidirect
569. C₄×D₄	C₂³×C₇	semidirect
570. C₄×D₄	C₂³×C₇	semidirect
571. C₄×D₄	C₂³×C₇	semidirect
572. C₄×D₄	C₂³×C₇	semidirect
573. C₄×D₄	C₂³×C₇	semidirect
574. C₄×D₄	C₂³×C₇	semidirect
575. C₄×D₄	C₂³×C₇	semidirect
576. #117	C₂³×C₇	semidirect
603. C₂×C₂²⋊C₄	C₂³×C₇	semidirect
604. C₂×C₂²⋊C₄	C₂³×C₇	semidirect
605. C₂×C₂²⋊C₄	C₂³×C₇	semidirect
612. C₂×C₄²	C₂³×C₇	semidirect
761. C₂×C₇	#3558	direct (N × H)
837. C₇	C₂×#3558	direct (N × H)
875. C₂	C₇×#3558	direct (N × H)

Maximal subgroups

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

subgroup	index
C₇×#3558	2
C₂×C₇×#562	2
C₂×C₇×H(3,𝔽₄)	2
C₂×C₇×#559	2
C₂×C₇×#548	2
C₂×C₇×#546	2
C₂×C₇×D₄²	2
C₂×C₇×#542	2
C₂×C₇×#538	2
C₂×C₇×#535	2
C₂×C₇×#534	2
C₂×C₇×#532	2
C₂×C₇×#529	2
C₂²×C₇×#124	2
C₂×#3558	7

Subgroups — C2×C7×#3558 #13239946

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₇×#3558 #13239946