Subgroups — C₂×C₇×#3547 #13239966

Order 1792.

7182 conjugacy classes of subgroups.

The subgroup lattice has 904 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×#3547	C₂	1	32	yes	maximal, direct product factor
2	C₂×C₇×#562	C₂	1	4	yes	maximal, complemented
3	C₂×C₇×#555	C₂	1	2	yes	maximal, complemented
4	C₂×C₇×#555	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₇×#554	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×C₇×#553	C₂	1	2	yes	maximal, complemented
7	C₂×C₇×#552	C₂	1	2	yes	maximal, complemented
8	C₂×C₇×D₄×Q₈	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×C₇×#548	C₂	1	2	yes	maximal, complemented
10	C₂×C₇×#547	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×C₇×#544	C₂	1	2	yes	maximal, complemented
12	C₂×C₇×#542	C₂	1	4	yes	maximal, complemented
13	C₂×C₇×#540	C₂	1	2	yes	maximal, complemented
14	C₂×C₇×#537	C₂	1	2	yes	maximal, complemented
15	C₂×C₇×#536	C₂	1	2	yes	maximal, complemented
16	C₂×C₇×#533	C₂	1	1	yes	maximal, characteristic, complemented
17	C₂×C₇×#532	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂×C₇×#529	C₂	1	1	yes	maximal, characteristic, complemented
19	C₂²×C₇×#41	C₂²	1	2	yes	—
20	C₂²×C₇×#41	C₂²	1	2	yes	—
21	C₂³×C₇×Q₈	C₂²	1	2	yes	—
22	C₇×#562	C₂²	1	64	yes	complemented
23	C₇×#555	C₂²	1	32	yes	complemented
24	C₇×#555	C₂²	1	16	yes	complemented
25	C₇×#554	C₂²	1	16	yes	complemented
26	C₇×#553	C₂²	1	32	yes	complemented
27	C₇×#552	C₂²	1	32	yes	complemented
28	C₇×D₄×Q₈	C₂²	1	16	yes	complemented
29	C₇×#548	C₂²	1	32	yes	complemented
30	C₇×#547	C₂²	1	16	yes	complemented
31	C₇×#544	C₂²	1	32	yes	complemented
32	C₇×#542	C₂²	1	64	yes	complemented
33	C₇×#540	C₂²	1	32	yes	complemented
34	C₇×#537	C₂²	1	32	yes	complemented
35	C₇×#536	C₂²	1	32	yes	complemented
36	C₇×#533	C₂²	1	16	yes	complemented
37	C₇×#532	C₂²	1	16	yes	complemented
38	C₂×C₇×C₄⋊Q₈	C₂²	1	1	yes	characteristic
39	C₂×C₇×C₄⋊Q₈	C₂²	1	1	yes	characteristic
40	C₂×C₇×C₄⋊Q₈	C₂²	1	1	yes	characteristic
41	C₂×C₇×C₄⋊Q₈	C₂²	1	4	yes	—
42	C₂×C₇×C₄⋊Q₈	C₂²	1	2	yes	—
43	C₂×C₇×#127	C₂²	1	1	yes	characteristic
44	C₇×#529	C₂²	1	16	yes	complemented
45	C₂×C₇×#126	C₂²	1	2	yes	—
46	C₂×C₇×#126	C₂²	1	4	yes	—
47	C₂×C₇×#125	C₂²	1	1	yes	characteristic
48	C₂×C₇×#125	C₂²	1	2	yes	—
49	C₂×C₇×#125	C₂²	1	4	yes	—
50	C₂×C₇×#125	C₂²	1	2	yes	—
51	C₂×C₇×#124	C₂²	1	1	yes	characteristic
52	C₂×C₇×#124	C₂²	1	2	yes	—
53	C₂×C₇×#124	C₂²	1	4	yes	—
54	C₂×C₇×#124	C₂²	1	4	yes	—
55	C₂×C₇×#124	C₂²	1	4	yes	—
56	C₂×C₇×#123	C₂²	1	2	yes	—
57	C₂×C₇×#123	C₂²	1	4	yes	—
58	C₂×C₇×#123	C₂²	1	4	yes	—
59	C₂×C₇×#123	C₂²	1	4	yes	—
60	C₂×C₇×#123	C₂²	1	4	yes	—
61	C₂×C₇×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
62	C₂×C₇×C₂²⋊Q₈	C₂²	1	2	yes	—
63	C₂×C₇×C₂²⋊Q₈	C₂²	1	2	yes	—
64	C₂×C₇×C₂²⋊Q₈	C₂²	1	2	yes	—
65	C₂×C₇×C₂²⋊Q₈	C₂²	1	2	yes	—
66	C₂×C₇×C₂²⋊Q₈	C₂²	1	4	yes	—
67	C₂×C₇×C₂²⋊Q₈	C₂²	1	2	yes	—
68	C₂×C₇×C₂²⋊Q₈	C₂²	1	4	yes	—
69	C₂×C₇×C₂²⋊Q₈	C₂²	1	4	yes	—
70	C₂×C₇×C₂²⋊Q₈	C₂²	1	4	yes	—
71	C₂×C₇×#121	C₂²	1	1	yes	characteristic
72	C₂×C₇×#121	C₂²	1	1	yes	characteristic
73	C₂×C₇×#121	C₂²	1	1	yes	characteristic
74	C₂×C₇×#121	C₂²	1	2	yes	—
75	C₂×C₇×#121	C₂²	1	4	yes	—
76	C₂×C₇×#121	C₂²	1	2	yes	—
77	C₂×C₇×#121	C₂²	1	4	yes	—
78	C₂×C₇×#121	C₂²	1	4	yes	—
79	C₂×C₇×#121	C₂²	1	2	yes	—
80	C₂×C₇×#121	C₂²	1	4	yes	—
81	C₂×C₇×#121	C₂²	1	2	yes	—
82	C₂×C₄×C₇×Q₈	C₂²	1	1	yes	characteristic
83	C₂×C₄×C₇×Q₈	C₂²	1	2	yes	—
84	C₂×C₄×C₇×Q₈	C₂²	1	2	yes	—
85	C₂×C₄×C₇×D₄	C₂²	1	1	yes	characteristic
86	C₂×C₄×C₇×D₄	C₂²	1	2	yes	—
87	C₂×C₄×C₇×D₄	C₂²	1	1	yes	characteristic
88	C₂×C₄×C₇×D₄	C₂²	1	2	yes	—
89	C₂×C₄×C₇×D₄	C₂²	1	1	yes	characteristic
90	C₂×C₄×C₇×D₄	C₂²	1	2	yes	—
91	C₂×C₄×C₇×D₄	C₂²	1	2	yes	—
92	C₂×C₄×C₇×D₄	C₂²	1	4	yes	—
93	C₂×C₇×#117	C₂²	1	2	yes	—
94	C₂×C₇×#117	C₂²	1	2	yes	—
95	C₂×C₇×#117	C₂²	1	2	yes	—
96	C₂×C₇×#117	C₂²	1	4	yes	—
97	C₂×C₇×#117	C₂²	1	2	yes	—
98	C₂²×C₇×C₄⋊C₄	C₂²	1	2	yes	—
99	C₂²×C₇×C₄⋊C₄	C₂²	1	2	yes	—
100	C₂²×C₄²×C₇	C₂²	1	1	yes	characteristic
101	C₂×#3547	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
102	C₂×C₇×#41	—	4	8	no	—
103	C₂×C₇×#41	—	4	8	no	—
104	C₂×C₇×#41	C₂³	1	16	yes	—
105	C₂×C₇×#41	C₂³	1	16	yes	—
106	C₂²×C₇×Q₈	—	4	8	no	—
107	C₂²×C₇×Q₈	C₂³	1	1	yes	characteristic
108	C₂²×C₇×Q₈	C₂³	1	2	yes	—
109	C₂²×C₇×Q₈	C₂³	1	4	yes	—
110	C₂²×C₇×Q₈	C₂³	1	16	yes	—
111	C₂²×C₇×Q₈	C₂³	1	2	yes	—
112	C₂²×C₇×Q₈	C₂³	1	2	yes	—
113	C₂²×C₇×D₄	C₂³	1	1	yes	characteristic
114	C₂²×C₇×D₄	C₂³	1	1	yes	characteristic
115	C₂²×C₇×D₄	C₂³	1	1	yes	characteristic
116	C₂²×C₇×D₄	C₂³	1	2	yes	—
117	C₂²×C₇×D₄	C₂³	1	4	yes	—
118	C₂²×C₇×D₄	C₂³	1	2	yes	—
119	C₂²×C₇×D₄	C₂³	1	2	yes	—
120	C₂²×C₇×D₄	C₂³	1	2	yes	—
121	C₂²×C₇×D₄	C₂³	1	4	yes	—
122	C₂²×C₇×D₄	C₂³	1	2	yes	—
123	C₂³×C₄×C₇	C₂³	1	2	yes	—
124	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
125	C₂³×C₄×C₇	C₂³	1	2	yes	—
126	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
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	C₂³×C₄×C₇	C₂³	1	4	yes	—
132	C₇×C₄⋊Q₈	C₂³	1	8	yes	—
133	C₇×C₄⋊Q₈	C₂³	1	8	yes	—
134	C₇×C₄⋊Q₈	C₂³	1	8	yes	—
135	C₇×C₄⋊Q₈	C₂³	1	32	yes	—
136	C₇×C₄⋊Q₈	C₂³	1	16	yes	—
137	C₇×#127	C₂³	1	8	yes	—
138	C₇×#126	C₂³	1	16	yes	—
139	C₇×#126	C₂³	1	32	yes	—
140	C₇×#125	C₂³	1	8	yes	—
141	C₇×#125	C₂³	1	16	yes	—
142	C₇×#125	C₂³	1	32	yes	—
143	C₇×#125	C₂³	1	16	yes	—
144	C₇×#124	C₂³	1	8	yes	—
145	C₇×#124	C₂³	1	16	yes	—
146	C₇×#124	C₂³	1	32	yes	—
147	C₇×#124	C₂³	1	32	yes	—
148	C₇×#124	C₂³	1	32	yes	—
149	C₇×#123	C₂³	1	16	yes	—
150	C₇×#123	C₂³	1	32	yes	—
151	C₇×#123	C₂³	1	32	yes	—
152	C₇×#123	C₂³	1	32	yes	—
153	C₇×#123	C₂³	1	32	yes	—
154	C₇×C₂²⋊Q₈	C₂³	1	8	yes	—
155	C₇×C₂²⋊Q₈	C₂³	1	16	yes	—
156	C₇×C₂²⋊Q₈	C₂³	1	16	yes	—
157	C₇×C₂²⋊Q₈	C₂³	1	16	yes	—
158	C₇×C₂²⋊Q₈	C₂³	1	16	yes	—
159	C₇×C₂²⋊Q₈	C₂³	1	32	yes	—
160	C₇×C₂²⋊Q₈	C₂³	1	16	yes	—
161	C₇×C₂²⋊Q₈	C₂³	1	32	yes	—
162	C₇×C₂²⋊Q₈	C₂³	1	32	yes	—
163	C₇×C₂²⋊Q₈	C₂³	1	32	yes	—
164	C₇×#121	C₂³	1	8	yes	—
165	C₇×#121	C₂³	1	8	yes	—
166	C₇×#121	C₂³	1	8	yes	—
167	C₇×#121	C₂³	1	16	yes	—
168	C₇×#121	C₂³	1	32	yes	—
169	C₇×#121	C₂³	1	16	yes	—
170	C₇×#121	C₂³	1	32	yes	—
171	C₇×#121	C₂³	1	32	yes	—
172	C₇×#121	C₂³	1	16	yes	—
173	C₇×#121	C₂³	1	32	yes	—
174	C₇×#121	C₂³	1	16	yes	—
175	C₄×C₇×Q₈	C₂³	1	8	yes	—
176	C₄×C₇×Q₈	C₂³	1	16	yes	—
177	C₄×C₇×Q₈	C₂³	1	16	yes	—
178	C₄×C₇×D₄	C₂³	1	8	yes	—
179	C₄×C₇×D₄	C₂³	1	16	yes	—
180	C₄×C₇×D₄	C₂³	1	8	yes	—
181	C₄×C₇×D₄	C₂³	1	16	yes	—
182	C₄×C₇×D₄	C₂³	1	8	yes	—
183	C₄×C₇×D₄	C₂³	1	16	yes	—
184	C₄×C₇×D₄	C₂³	1	16	yes	—
185	C₄×C₇×D₄	C₂³	1	32	yes	—
186	C₇×#117	C₂³	1	16	yes	—
187	C₇×#117	C₂³	1	16	yes	—
188	C₇×#117	C₂³	1	16	yes	—
189	C₇×#117	C₂³	1	32	yes	—
190	C₇×#117	C₂³	1	16	yes	—
191	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
192	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
193	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
194	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
195	C₂×C₇×C₄⋊C₄	C₂³	1	4	yes	—
196	C₂×C₇×C₄⋊C₄	C₂³	1	4	yes	—
197	C₂×C₇×C₄⋊C₄	C₂³	1	16	yes	—
198	C₂×C₇×C₄⋊C₄	C₂³	1	16	yes	—
199	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
200	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
201	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
202	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
203	C₂×C₇×C₄⋊C₄	C₂³	1	4	yes	—
204	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
205	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
206	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
207	C₂×C₇×C₄⋊C₄	C₂³	1	4	yes	—
208	C₂×C₇×C₄⋊C₄	C₂³	1	4	yes	—
209	C₂×C₇×C₄⋊C₄	C₂³	1	4	yes	—
210	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
211	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
212	C₂×C₇×C₂²⋊C₄	C₂³	1	2	yes	—
213	C₂×C₇×C₂²⋊C₄	C₂³	1	2	yes	—
214	C₂×C₇×C₂²⋊C₄	C₂³	1	4	yes	—
215	C₂×C₇×C₂²⋊C₄	C₂³	1	2	yes	—
216	C₂×C₇×C₂²⋊C₄	C₂³	1	4	yes	—
217	C₂×C₇×C₂²⋊C₄	C₂³	1	4	yes	—
218	C₂×C₇×C₂²⋊C₄	C₂³	1	4	yes	—
219	C₂×C₇×C₂²⋊C₄	C₂³	1	2	yes	—
220	C₂×C₇×C₂²⋊C₄	C₂³	1	2	yes	—
221	C₂×C₇×C₂²⋊C₄	C₂³	1	4	yes	—
222	C₂×C₇×C₂²⋊C₄	C₂³	1	2	yes	—
223	C₂×C₇×C₂²⋊C₄	C₂³	1	4	yes	—
224	C₂×C₇×C₂²⋊C₄	C₂³	1	2	yes	—
225	C₂×C₇×C₂²⋊C₄	C₂³	1	2	yes	—
226	C₂×C₇×C₂²⋊C₄	C₂³	1	2	yes	—
227	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
228	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
229	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
230	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
231	C₂×C₄²×C₇	C₂³	1	8	yes	—
232	C₂×C₄²×C₇	C₂³	1	4	yes	—
233	C₂×C₄²×C₇	C₂³	1	4	yes	—
234	C₂×C₄²×C₇	C₂³	1	2	yes	—
235	#3547	C₂×C₇	1	32	yes	direct product factor
236	C₂×#562	C₂×C₇	1	4	yes	complemented
237	C₂×#555	C₂×C₇	1	2	yes	complemented
238	C₂×#555	C₂×C₇	1	1	yes	characteristic, complemented
239	C₂×#554	C₂×C₇	1	1	yes	characteristic, complemented
240	C₂×#553	C₂×C₇	1	2	yes	complemented
241	C₂×#552	C₂×C₇	1	2	yes	complemented
242	C₂×D₄×Q₈	C₂×C₇	1	1	yes	characteristic, complemented
243	C₂×#548	C₂×C₇	1	2	yes	complemented
244	C₂×#547	C₂×C₇	1	1	yes	characteristic, complemented
245	C₂×#544	C₂×C₇	1	2	yes	complemented
246	C₂×#542	C₂×C₇	1	4	yes	complemented
247	C₂×#540	C₂×C₇	1	2	yes	complemented
248	C₂×#537	C₂×C₇	1	2	yes	complemented
249	C₂×#536	C₂×C₇	1	2	yes	complemented
250	C₂×#533	C₂×C₇	1	1	yes	characteristic, complemented
251	C₂×#532	C₂×C₇	1	1	yes	characteristic, complemented
252	C₂×#529	C₂×C₇	1	1	yes	characteristic, complemented
253	C₂⁴×C₇	C₂⁴	1	2	yes	—
254	C₂⁴×C₇	C₂⁴	1	1	yes	characteristic
255	C₂⁴×C₇	C₂⁴	1	2	yes	—
256	C₂⁴×C₇	C₂⁴	1	2	yes	—
257	C₇×#41	—	4	32	no	—
258	C₇×#41	—	4	32	no	—
259	C₂×C₇×Q₈	—	2	4	no	—
260	C₂×C₇×Q₈	—	2	8	no	—
261	C₂×C₇×Q₈	—	4	8	no	—
262	C₂×C₇×Q₈	—	4	4	no	—
263	C₂×C₇×Q₈	—	4	4	no	—
264	C₂×C₇×Q₈	—	4	32	no	—
265	C₂×C₇×Q₈	C₂⁴	1	4	yes	—
266	C₂×C₇×Q₈	C₂⁴	1	8	yes	—
267	C₂×C₇×Q₈	C₂⁴	1	8	yes	—
268	C₂×C₇×Q₈	C₂⁴	1	16	yes	—
269	C₂×C₇×Q₈	C₂⁴	1	8	yes	—
270	C₂×C₇×D₄	—	2	4	no	—
271	C₂×C₇×D₄	—	2	4	no	—
272	C₂×C₇×D₄	—	2	4	no	—
273	C₂×C₇×D₄	—	4	4	no	—
274	C₂×C₇×D₄	—	4	4	no	—
275	C₂×C₇×D₄	—	4	8	no	—
276	C₂×C₇×D₄	—	4	4	no	—
277	C₂×C₇×D₄	—	4	4	no	—
278	C₂×C₇×D₄	—	4	4	no	—
279	C₂×C₇×D₄	—	4	8	no	—
280	C₂×C₇×D₄	C₂⁴	1	4	yes	—
281	C₂×C₇×D₄	C₂⁴	1	4	yes	—
282	C₂×C₇×D₄	C₂⁴	1	4	yes	—
283	C₂×C₇×D₄	C₂⁴	1	8	yes	—
284	C₂×C₇×D₄	C₂⁴	1	16	yes	—
285	C₂×C₇×D₄	C₂⁴	1	8	yes	—
286	C₂×C₇×D₄	C₂⁴	1	8	yes	—
287	C₂×C₇×D₄	C₂⁴	1	16	yes	—
288	C₂×C₇×D₄	C₂⁴	1	8	yes	—
289	C₂×C₇×D₄	C₂⁴	1	8	yes	—
290	C₂²×C₄×C₇	—	2	8	no	—
291	C₂²×C₄×C₇	—	2	8	no	—
292	C₂²×C₄×C₇	—	2	4	no	—
293	C₂²×C₄×C₇	—	2	4	no	—
294	C₂²×C₄×C₇	—	2	8	no	—
295	C₂²×C₄×C₇	—	4	8	no	—
296	C₂²×C₄×C₇	—	4	2	no	—
297	C₂²×C₄×C₇	—	4	8	no	—
298	C₂²×C₄×C₇	—	4	8	no	—
299	C₂²×C₄×C₇	C₂⁴	1	4	yes	—
300	C₂²×C₄×C₇	C₂⁴	1	4	yes	—
301	C₂²×C₄×C₇	C₂⁴	1	8	yes	—
302	C₂²×C₄×C₇	C₂⁴	1	8	yes	—
303	C₂²×C₄×C₇	C₂⁴	1	8	yes	—
304	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
305	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
306	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
307	C₂²×C₄×C₇	C₂⁴	1	4	yes	—
308	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
309	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
310	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
311	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
312	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
313	C₂²×C₄×C₇	C₂⁴	1	4	yes	—
314	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
315	C₂²×C₄×C₇	C₂⁴	1	4	yes	—
316	C₂²×C₄×C₇	C₂⁴	1	16	yes	—
317	C₂²×C₄×C₇	C₂⁴	1	16	yes	—
318	C₂²×C₄×C₇	C₂⁴	1	16	yes	—
319	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
320	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
321	C₇×C₄⋊C₄	C₂⁴	1	4	yes	—
322	C₇×C₄⋊C₄	C₂⁴	1	4	yes	—
323	C₇×C₄⋊C₄	C₂⁴	1	8	yes	—
324	C₇×C₄⋊C₄	C₂⁴	1	8	yes	—
325	C₇×C₄⋊C₄	C₂⁴	1	16	yes	—
326	C₇×C₄⋊C₄	C₂⁴	1	16	yes	—
327	C₇×C₄⋊C₄	C₂⁴	1	8	yes	—
328	C₇×C₄⋊C₄	C₂⁴	1	4	yes	—
329	C₇×C₄⋊C₄	C₂⁴	1	4	yes	—
330	C₇×C₄⋊C₄	C₂⁴	1	8	yes	—
331	C₇×C₄⋊C₄	C₂⁴	1	16	yes	—
332	C₇×C₄⋊C₄	C₂⁴	1	8	yes	—
333	C₇×C₄⋊C₄	C₂⁴	1	8	yes	—
334	C₇×C₄⋊C₄	C₂⁴	1	8	yes	—
335	C₇×C₄⋊C₄	C₂⁴	1	16	yes	—
336	C₇×C₄⋊C₄	C₂⁴	1	16	yes	—
337	C₇×C₄⋊C₄	C₂⁴	1	16	yes	—
338	C₇×C₄⋊C₄	C₂⁴	1	8	yes	—
339	C₇×C₄⋊C₄	C₂⁴	1	8	yes	—
340	C₇×C₂²⋊C₄	C₂⁴	1	8	yes	—
341	C₇×C₂²⋊C₄	C₂⁴	1	8	yes	—
342	C₇×C₂²⋊C₄	C₂⁴	1	16	yes	—
343	C₇×C₂²⋊C₄	C₂⁴	1	8	yes	—
344	C₇×C₂²⋊C₄	C₂⁴	1	16	yes	—
345	C₇×C₂²⋊C₄	C₂⁴	1	16	yes	—
346	C₇×C₂²⋊C₄	C₂⁴	1	16	yes	—
347	C₇×C₂²⋊C₄	C₂⁴	1	8	yes	—
348	C₇×C₂²⋊C₄	C₂⁴	1	8	yes	—
349	C₇×C₂²⋊C₄	C₂⁴	1	16	yes	—
350	C₇×C₂²⋊C₄	C₂⁴	1	8	yes	—
351	C₇×C₂²⋊C₄	C₂⁴	1	16	yes	—
352	C₇×C₂²⋊C₄	C₂⁴	1	8	yes	—
353	C₇×C₂²⋊C₄	C₂⁴	1	8	yes	—
354	C₇×C₂²⋊C₄	C₂⁴	1	8	yes	—
355	C₄²×C₇	C₂⁴	1	4	yes	—
356	C₄²×C₇	C₂⁴	1	4	yes	—
357	C₄²×C₇	C₂⁴	1	4	yes	—
358	C₄²×C₇	C₂⁴	1	4	yes	—
359	C₄²×C₇	C₂⁴	1	16	yes	—
360	C₄²×C₇	C₂⁴	1	16	yes	—
361	C₄²×C₇	C₂⁴	1	8	yes	—
362	C₂²×#41	C₂²×C₇	1	2	yes	—
363	C₂²×#41	C₂²×C₇	1	2	yes	—
364	C₂³×Q₈	C₂²×C₇	1	2	yes	—
365	#562	C₂²×C₇	1	64	yes	complemented
366	#555	C₂²×C₇	1	32	yes	complemented
367	#555	C₂²×C₇	1	16	yes	complemented
368	#554	C₂²×C₇	1	16	yes	complemented
369	#553	C₂²×C₇	1	32	yes	complemented
370	#552	C₂²×C₇	1	32	yes	complemented
371	D₄×Q₈	C₂²×C₇	1	16	yes	complemented
372	#548	C₂²×C₇	1	32	yes	complemented
373	#547	C₂²×C₇	1	16	yes	complemented
374	#544	C₂²×C₇	1	32	yes	complemented
375	#542	C₂²×C₇	1	64	yes	complemented
376	#540	C₂²×C₇	1	32	yes	complemented
377	#537	C₂²×C₇	1	32	yes	complemented
378	#536	C₂²×C₇	1	32	yes	complemented
379	#533	C₂²×C₇	1	16	yes	complemented
380	#532	C₂²×C₇	1	16	yes	complemented
381	C₂×C₄⋊Q₈	C₂²×C₇	1	1	yes	characteristic
382	C₂×C₄⋊Q₈	C₂²×C₇	1	1	yes	characteristic
383	C₂×C₄⋊Q₈	C₂²×C₇	1	1	yes	characteristic
384	C₂×C₄⋊Q₈	C₂²×C₇	1	4	yes	—
385	C₂×C₄⋊Q₈	C₂²×C₇	1	2	yes	—
386	C₂×#127	C₂²×C₇	1	1	yes	characteristic
387	#529	C₂²×C₇	1	16	yes	complemented
388	C₂×#126	C₂²×C₇	1	2	yes	—
389	C₂×#126	C₂²×C₇	1	4	yes	—
390	C₂×#125	C₂²×C₇	1	1	yes	characteristic
391	C₂×#125	C₂²×C₇	1	2	yes	—
392	C₂×#125	C₂²×C₇	1	4	yes	—
393	C₂×#125	C₂²×C₇	1	2	yes	—
394	C₂×#124	C₂²×C₇	1	1	yes	characteristic
395	C₂×#124	C₂²×C₇	1	2	yes	—
396	C₂×#124	C₂²×C₇	1	4	yes	—
397	C₂×#124	C₂²×C₇	1	4	yes	—
398	C₂×#124	C₂²×C₇	1	4	yes	—
399	C₂×#123	C₂²×C₇	1	2	yes	—
400	C₂×#123	C₂²×C₇	1	4	yes	—
401	C₂×#123	C₂²×C₇	1	4	yes	—
402	C₂×#123	C₂²×C₇	1	4	yes	—
403	C₂×#123	C₂²×C₇	1	4	yes	—
404	C₂×C₂²⋊Q₈	C₂²×C₇	1	1	yes	characteristic
405	C₂×C₂²⋊Q₈	C₂²×C₇	1	2	yes	—
406	C₂×C₂²⋊Q₈	C₂²×C₇	1	2	yes	—
407	C₂×C₂²⋊Q₈	C₂²×C₇	1	2	yes	—
408	C₂×C₂²⋊Q₈	C₂²×C₇	1	2	yes	—
409	C₂×C₂²⋊Q₈	C₂²×C₇	1	4	yes	—
410	C₂×C₂²⋊Q₈	C₂²×C₇	1	2	yes	—
411	C₂×C₂²⋊Q₈	C₂²×C₇	1	4	yes	—
412	C₂×C₂²⋊Q₈	C₂²×C₇	1	4	yes	—
413	C₂×C₂²⋊Q₈	C₂²×C₇	1	4	yes	—
414	C₂×#121	C₂²×C₇	1	1	yes	characteristic
415	C₂×#121	C₂²×C₇	1	1	yes	characteristic
416	C₂×#121	C₂²×C₇	1	1	yes	characteristic
417	C₂×#121	C₂²×C₇	1	2	yes	—
418	C₂×#121	C₂²×C₇	1	4	yes	—
419	C₂×#121	C₂²×C₇	1	2	yes	—
420	C₂×#121	C₂²×C₇	1	4	yes	—
421	C₂×#121	C₂²×C₇	1	4	yes	—
422	C₂×#121	C₂²×C₇	1	2	yes	—
423	C₂×#121	C₂²×C₇	1	4	yes	—
424	C₂×#121	C₂²×C₇	1	2	yes	—
425	C₂×C₄×Q₈	C₂²×C₇	1	1	yes	characteristic
426	C₂×C₄×Q₈	C₂²×C₇	1	2	yes	—
427	C₂×C₄×Q₈	C₂²×C₇	1	2	yes	—
428	C₂×C₄×D₄	C₂²×C₇	1	1	yes	characteristic
429	C₂×C₄×D₄	C₂²×C₇	1	2	yes	—
430	C₂×C₄×D₄	C₂²×C₇	1	1	yes	characteristic
431	C₂×C₄×D₄	C₂²×C₇	1	2	yes	—
432	C₂×C₄×D₄	C₂²×C₇	1	1	yes	characteristic
433	C₂×C₄×D₄	C₂²×C₇	1	2	yes	—
434	C₂×C₄×D₄	C₂²×C₇	1	2	yes	—
435	C₂×C₄×D₄	C₂²×C₇	1	4	yes	—
436	C₂×#117	C₂²×C₇	1	2	yes	—
437	C₂×#117	C₂²×C₇	1	2	yes	—
438	C₂×#117	C₂²×C₇	1	2	yes	—
439	C₂×#117	C₂²×C₇	1	4	yes	—
440	C₂×#117	C₂²×C₇	1	2	yes	—
441	C₂²×C₄⋊C₄	C₂²×C₇	1	2	yes	—
442	C₂²×C₄⋊C₄	C₂²×C₇	1	2	yes	—
443	C₂²×C₄²	C₂²×C₇	1	1	yes	characteristic
444	C₂³×C₇	—	2	4	no	—
445	C₂³×C₇	—	2	2	no	—
446	C₂³×C₇	—	2	4	no	—
447	C₂³×C₇	—	2	4	no	—
448	C₂³×C₇	—	2	2	no	—
449	C₂³×C₇	—	2	4	no	—
450	C₂³×C₇	—	2	4	no	—
451	C₂³×C₇	—	2	4	no	—
452	C₂³×C₇	—	2	4	no	—
453	C₂³×C₇	—	2	2	no	—
454	C₂³×C₇	—	2	4	no	—
455	C₂³×C₇	—	2	4	no	—
456	C₂³×C₇	C₂⁵	1	4	yes	—
457	C₂³×C₇	C₂⁵	1	2	yes	—
458	C₂³×C₇	C₂⁵	1	4	yes	—
459	C₂³×C₇	C₂⁵	1	4	yes	—
460	C₂³×C₇	C₂⁵	1	1	yes	characteristic
461	C₇×Q₈	—	2	8	no	—
462	C₇×Q₈	—	2	16	no	—
463	C₇×Q₈	—	4	16	no	—
464	C₇×Q₈	—	4	8	no	—
465	C₇×Q₈	—	4	8	no	—
466	C₇×D₄	—	2	8	no	—
467	C₇×D₄	—	2	8	no	—
468	C₇×D₄	—	2	8	no	—
469	C₇×D₄	—	4	8	no	—
470	C₇×D₄	—	4	8	no	—
471	C₇×D₄	—	4	16	no	—
472	C₇×D₄	—	4	8	no	—
473	C₇×D₄	—	4	8	no	—
474	C₇×D₄	—	4	8	no	—
475	C₇×D₄	—	4	16	no	—
476	C₂×C₄×C₇	—	2	4	no	—
477	C₂×C₄×C₇	—	2	2	no	—
478	C₂×C₄×C₇	—	2	4	no	—
479	C₂×C₄×C₇	—	2	8	no	—
480	C₂×C₄×C₇	—	2	4	no	—
481	C₂×C₄×C₇	—	2	2	no	—
482	C₂×C₄×C₇	—	2	4	no	—
483	C₂×C₄×C₇	—	2	4	no	—
484	C₂×C₄×C₇	—	2	2	no	—
485	C₂×C₄×C₇	—	2	8	no	—
486	C₂×C₄×C₇	—	2	2	no	—
487	C₂×C₄×C₇	—	2	16	no	—
488	C₂×C₄×C₇	—	2	16	no	—
489	C₂×C₄×C₇	—	2	8	no	—
490	C₂×C₄×C₇	—	2	8	no	—
491	C₂×C₄×C₇	—	2	16	no	—
492	C₂×C₄×C₇	—	4	16	no	—
493	C₂×C₄×C₇	—	4	4	no	—
494	C₂×C₄×C₇	—	4	16	no	—
495	C₂×C₄×C₇	—	4	16	no	—
496	C₂×C₄×C₇	H(5,𝔽₂)	1	4	yes	—
497	C₂×C₄×C₇	2₋¹⁺⁴	1	4	yes	—
498	C₂×C₄×C₇	C₂⁵	1	2	yes	—
499	C₂×C₄×C₇	C₂⁵	1	4	yes	—
500	C₂×C₄×C₇	C₂⁵	1	2	yes	—
501	C₂×C₄×C₇	C₂⁵	1	8	yes	—
502	C₂×C₄×C₇	C₂⁵	1	4	yes	—
503	C₂×C₄×C₇	C₂⁵	1	2	yes	—
504	C₂×C₄×C₇	C₂⁵	1	2	yes	—
505	C₂×C₄×C₇	C₂⁵	1	4	yes	—
506	C₂×C₄×C₇	C₂⁵	1	4	yes	—
507	C₂×C₄×C₇	C₂⁵	1	8	yes	—
508	C₂×C₄×C₇	C₂⁵	1	4	yes	—
509	C₂×C₄×C₇	C₂⁵	1	2	yes	—
510	C₂×C₄×C₇	C₂⁵	1	2	yes	—
511	C₂×#41	—	4	8	no	—
512	C₂×#41	—	4	8	no	—
513	C₂×#41	C₂³×C₇	1	16	yes	—
514	C₂×#41	C₂³×C₇	1	16	yes	—
515	C₂²×Q₈	—	4	8	no	—
516	C₂²×Q₈	C₂³×C₇	1	1	yes	characteristic
517	C₂²×Q₈	C₂³×C₇	1	2	yes	—
518	C₂²×Q₈	C₂³×C₇	1	2	yes	—
519	C₂²×Q₈	C₂³×C₇	1	4	yes	—
520	C₂²×Q₈	C₂³×C₇	1	2	yes	—
521	C₂²×Q₈	C₂³×C₇	1	16	yes	—
522	C₂²×D₄	C₂³×C₇	1	1	yes	characteristic
523	C₂²×D₄	C₂³×C₇	1	1	yes	characteristic
524	C₂²×D₄	C₂³×C₇	1	1	yes	characteristic
525	C₂²×D₄	C₂³×C₇	1	2	yes	—
526	C₂²×D₄	C₂³×C₇	1	4	yes	—
527	C₂²×D₄	C₂³×C₇	1	2	yes	—
528	C₂²×D₄	C₂³×C₇	1	2	yes	—
529	C₂²×D₄	C₂³×C₇	1	4	yes	—
530	C₂²×D₄	C₂³×C₇	1	2	yes	—
531	C₂²×D₄	C₂³×C₇	1	2	yes	—
532	C₂³×C₄	C₂³×C₇	1	2	yes	—
533	C₂³×C₄	C₂³×C₇	1	2	yes	—
534	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
535	C₂³×C₄	C₂³×C₇	1	2	yes	—
536	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
537	C₂³×C₄	C₂³×C₇	1	4	yes	—
538	C₂³×C₄	C₂³×C₇	1	4	yes	—
539	C₂³×C₄	C₂³×C₇	1	4	yes	—
540	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
541	C₄⋊Q₈	C₂³×C₇	1	8	yes	—
542	C₄⋊Q₈	C₂³×C₇	1	8	yes	—
543	C₄⋊Q₈	C₂³×C₇	1	8	yes	—
544	C₄⋊Q₈	C₂³×C₇	1	32	yes	—
545	C₄⋊Q₈	C₂³×C₇	1	16	yes	—
546	#127	C₂³×C₇	1	8	yes	—
547	#126	C₂³×C₇	1	16	yes	—
548	#126	C₂³×C₇	1	32	yes	—
549	#125	C₂³×C₇	1	8	yes	—
550	#125	C₂³×C₇	1	16	yes	—
551	#125	C₂³×C₇	1	32	yes	—
552	#125	C₂³×C₇	1	16	yes	—
553	#124	C₂³×C₇	1	8	yes	—
554	#124	C₂³×C₇	1	16	yes	—
555	#124	C₂³×C₇	1	32	yes	—
556	#124	C₂³×C₇	1	32	yes	—
557	#124	C₂³×C₇	1	32	yes	—
558	#123	C₂³×C₇	1	16	yes	—
559	#123	C₂³×C₇	1	32	yes	—
560	#123	C₂³×C₇	1	32	yes	—
561	#123	C₂³×C₇	1	32	yes	—
562	#123	C₂³×C₇	1	32	yes	—
563	C₂²⋊Q₈	C₂³×C₇	1	8	yes	—
564	C₂²⋊Q₈	C₂³×C₇	1	16	yes	—
565	C₂²⋊Q₈	C₂³×C₇	1	16	yes	—
566	C₂²⋊Q₈	C₂³×C₇	1	16	yes	—
567	C₂²⋊Q₈	C₂³×C₇	1	16	yes	—
568	C₂²⋊Q₈	C₂³×C₇	1	32	yes	—
569	C₂²⋊Q₈	C₂³×C₇	1	16	yes	—
570	C₂²⋊Q₈	C₂³×C₇	1	32	yes	—
571	C₂²⋊Q₈	C₂³×C₇	1	32	yes	—
572	C₂²⋊Q₈	C₂³×C₇	1	32	yes	—
573	#121	C₂³×C₇	1	8	yes	—
574	#121	C₂³×C₇	1	8	yes	—
575	#121	C₂³×C₇	1	8	yes	—
576	#121	C₂³×C₇	1	16	yes	—
577	#121	C₂³×C₇	1	32	yes	—
578	#121	C₂³×C₇	1	16	yes	—
579	#121	C₂³×C₇	1	32	yes	—
580	#121	C₂³×C₇	1	32	yes	—
581	#121	C₂³×C₇	1	16	yes	—
582	#121	C₂³×C₇	1	32	yes	—
583	#121	C₂³×C₇	1	16	yes	—
584	C₄×Q₈	C₂³×C₇	1	8	yes	—
585	C₄×Q₈	C₂³×C₇	1	16	yes	—
586	C₄×Q₈	C₂³×C₇	1	16	yes	—
587	C₄×D₄	C₂³×C₇	1	8	yes	—
588	C₄×D₄	C₂³×C₇	1	16	yes	—
589	C₄×D₄	C₂³×C₇	1	8	yes	—
590	C₄×D₄	C₂³×C₇	1	16	yes	—
591	C₄×D₄	C₂³×C₇	1	8	yes	—
592	C₄×D₄	C₂³×C₇	1	16	yes	—
593	C₄×D₄	C₂³×C₇	1	16	yes	—
594	C₄×D₄	C₂³×C₇	1	32	yes	—
595	#117	C₂³×C₇	1	16	yes	—
596	#117	C₂³×C₇	1	16	yes	—
597	#117	C₂³×C₇	1	16	yes	—
598	#117	C₂³×C₇	1	32	yes	—
599	#117	C₂³×C₇	1	16	yes	—
600	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
601	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
602	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
603	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
604	C₂×C₄⋊C₄	C₂³×C₇	1	4	yes	—
605	C₂×C₄⋊C₄	C₂³×C₇	1	4	yes	—
606	C₂×C₄⋊C₄	C₂³×C₇	1	16	yes	—
607	C₂×C₄⋊C₄	C₂³×C₇	1	16	yes	—
608	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
609	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
610	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
611	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
612	C₂×C₄⋊C₄	C₂³×C₇	1	4	yes	—
613	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
614	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
615	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
616	C₂×C₄⋊C₄	C₂³×C₇	1	4	yes	—
617	C₂×C₄⋊C₄	C₂³×C₇	1	4	yes	—
618	C₂×C₄⋊C₄	C₂³×C₇	1	4	yes	—
619	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
620	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
621	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
622	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
623	C₂×C₂²⋊C₄	C₂³×C₇	1	4	yes	—
624	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
625	C₂×C₂²⋊C₄	C₂³×C₇	1	4	yes	—
626	C₂×C₂²⋊C₄	C₂³×C₇	1	4	yes	—
627	C₂×C₂²⋊C₄	C₂³×C₇	1	4	yes	—
628	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
629	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
630	C₂×C₂²⋊C₄	C₂³×C₇	1	4	yes	—
631	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
632	C₂×C₂²⋊C₄	C₂³×C₇	1	4	yes	—
633	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
634	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
635	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
636	C₂×C₄²	C₂³×C₇	1	4	yes	—
637	C₂×C₄²	C₂³×C₇	1	4	yes	—
638	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
639	C₂×C₄²	C₂³×C₇	1	2	yes	—
640	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
641	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
642	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
643	C₂×C₄²	C₂³×C₇	1	8	yes	—
644	C₂²×C₇	—	2	4	no	—
645	C₂²×C₇	—	2	2	no	—
646	C₂²×C₇	—	2	4	no	—
647	C₂²×C₇	—	2	4	no	—
648	C₂²×C₇	—	2	2	no	—
649	C₂²×C₇	—	2	4	no	—
650	C₂²×C₇	—	2	4	no	—
651	C₂²×C₇	—	2	4	no	—
652	C₂²×C₇	—	2	4	no	—
653	C₂²×C₇	—	2	2	no	—
654	C₂²×C₇	—	2	4	no	—
655	C₂²×C₇	—	2	4	no	—
656	C₂²×C₇	—	4	8	no	—
657	C₂²×C₇	—	4	4	no	—
658	C₂²×C₇	—	4	8	no	—
659	C₂²×C₇	—	4	8	no	—
660	C₂²×C₇	C₂×H(5,𝔽₂)	1	2	yes	—
661	C₂²×C₇	C₂×2₋¹⁺⁴	1	2	yes	—
662	C₂²×C₇	#585	1	2	yes	—
663	C₂²×C₇	C₂⁶	1	1	yes	characteristic
664	C₄×C₇	—	2	4	no	—
665	C₄×C₇	—	2	2	no	—
666	C₄×C₇	—	2	4	no	—
667	C₄×C₇	—	2	8	no	—
668	C₄×C₇	—	2	4	no	—
669	C₄×C₇	—	2	2	no	—
670	C₄×C₇	—	2	4	no	—
671	C₄×C₇	—	2	4	no	—
672	C₄×C₇	—	2	2	no	—
673	C₄×C₇	—	2	8	no	—
674	C₄×C₇	—	2	2	no	—
675	C₄×C₇	C₂×H(5,𝔽₂)	1	4	yes	—
676	C₄×C₇	C₂×2₋¹⁺⁴	1	4	yes	—
677	C₂⁴	C₂⁴×C₇	1	2	yes	—
678	C₂⁴	C₂⁴×C₇	1	1	yes	characteristic
679	C₂⁴	C₂⁴×C₇	1	2	yes	—
680	C₂⁴	C₂⁴×C₇	1	2	yes	—
681	#41	—	4	32	no	—
682	#41	—	4	32	no	—
683	C₂×Q₈	—	2	4	no	—
684	C₂×Q₈	—	2	8	no	—
685	C₂×Q₈	—	4	8	no	—
686	C₂×Q₈	—	4	4	no	—
687	C₂×Q₈	—	4	4	no	—
688	C₂×Q₈	—	4	32	no	—
689	C₂×Q₈	C₂⁴×C₇	1	4	yes	—
690	C₂×Q₈	C₂⁴×C₇	1	8	yes	—
691	C₂×Q₈	C₂⁴×C₇	1	8	yes	—
692	C₂×Q₈	C₂⁴×C₇	1	16	yes	—
693	C₂×Q₈	C₂⁴×C₇	1	8	yes	—
694	C₂×D₄	—	2	4	no	—
695	C₂×D₄	—	2	4	no	—
696	C₂×D₄	—	2	4	no	—
697	C₂×D₄	—	4	4	no	—
698	C₂×D₄	—	4	4	no	—
699	C₂×D₄	—	4	4	no	—
700	C₂×D₄	—	4	8	no	—
701	C₂×D₄	—	4	4	no	—
702	C₂×D₄	—	4	4	no	—
703	C₂×D₄	—	4	8	no	—
704	C₂×D₄	C₂⁴×C₇	1	4	yes	—
705	C₂×D₄	C₂⁴×C₇	1	4	yes	—
706	C₂×D₄	C₂⁴×C₇	1	4	yes	—
707	C₂×D₄	C₂⁴×C₇	1	8	yes	—
708	C₂×D₄	C₂⁴×C₇	1	16	yes	—
709	C₂×D₄	C₂⁴×C₇	1	8	yes	—
710	C₂×D₄	C₂⁴×C₇	1	8	yes	—
711	C₂×D₄	C₂⁴×C₇	1	16	yes	—
712	C₂×D₄	C₂⁴×C₇	1	8	yes	—
713	C₂×D₄	C₂⁴×C₇	1	8	yes	—
714	C₂²×C₄	—	2	8	no	—
715	C₂²×C₄	—	2	8	no	—
716	C₂²×C₄	—	2	4	no	—
717	C₂²×C₄	—	2	8	no	—
718	C₂²×C₄	—	2	4	no	—
719	C₂²×C₄	—	4	8	no	—
720	C₂²×C₄	—	4	8	no	—
721	C₂²×C₄	—	4	2	no	—
722	C₂²×C₄	—	4	8	no	—
723	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
724	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
725	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
726	C₂²×C₄	C₂⁴×C₇	1	4	yes	—
727	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
728	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
729	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
730	C₂²×C₄	C₂⁴×C₇	1	4	yes	—
731	C₂²×C₄	C₂⁴×C₇	1	4	yes	—
732	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
733	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
734	C₂²×C₄	C₂⁴×C₇	1	4	yes	—
735	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
736	C₂²×C₄	C₂⁴×C₇	1	8	yes	—
737	C₂²×C₄	C₂⁴×C₇	1	8	yes	—
738	C₂²×C₄	C₂⁴×C₇	1	8	yes	—
739	C₂²×C₄	C₂⁴×C₇	1	4	yes	—
740	C₂²×C₄	C₂⁴×C₇	1	16	yes	—
741	C₂²×C₄	C₂⁴×C₇	1	16	yes	—
742	C₂²×C₄	C₂⁴×C₇	1	16	yes	—
743	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
744	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
745	C₄⋊C₄	C₂⁴×C₇	1	4	yes	—
746	C₄⋊C₄	C₂⁴×C₇	1	4	yes	—
747	C₄⋊C₄	C₂⁴×C₇	1	8	yes	—
748	C₄⋊C₄	C₂⁴×C₇	1	8	yes	—
749	C₄⋊C₄	C₂⁴×C₇	1	16	yes	—
750	C₄⋊C₄	C₂⁴×C₇	1	16	yes	—
751	C₄⋊C₄	C₂⁴×C₇	1	8	yes	—
752	C₄⋊C₄	C₂⁴×C₇	1	4	yes	—
753	C₄⋊C₄	C₂⁴×C₇	1	4	yes	—
754	C₄⋊C₄	C₂⁴×C₇	1	8	yes	—
755	C₄⋊C₄	C₂⁴×C₇	1	16	yes	—
756	C₄⋊C₄	C₂⁴×C₇	1	8	yes	—
757	C₄⋊C₄	C₂⁴×C₇	1	8	yes	—
758	C₄⋊C₄	C₂⁴×C₇	1	8	yes	—
759	C₄⋊C₄	C₂⁴×C₇	1	16	yes	—
760	C₄⋊C₄	C₂⁴×C₇	1	16	yes	—
761	C₄⋊C₄	C₂⁴×C₇	1	16	yes	—
762	C₄⋊C₄	C₂⁴×C₇	1	8	yes	—
763	C₄⋊C₄	C₂⁴×C₇	1	8	yes	—
764	C₂²⋊C₄	C₂⁴×C₇	1	8	yes	—
765	C₂²⋊C₄	C₂⁴×C₇	1	8	yes	—
766	C₂²⋊C₄	C₂⁴×C₇	1	16	yes	—
767	C₂²⋊C₄	C₂⁴×C₇	1	8	yes	—
768	C₂²⋊C₄	C₂⁴×C₇	1	16	yes	—
769	C₂²⋊C₄	C₂⁴×C₇	1	16	yes	—
770	C₂²⋊C₄	C₂⁴×C₇	1	16	yes	—
771	C₂²⋊C₄	C₂⁴×C₇	1	8	yes	—
772	C₂²⋊C₄	C₂⁴×C₇	1	8	yes	—
773	C₂²⋊C₄	C₂⁴×C₇	1	16	yes	—
774	C₂²⋊C₄	C₂⁴×C₇	1	8	yes	—
775	C₂²⋊C₄	C₂⁴×C₇	1	16	yes	—
776	C₂²⋊C₄	C₂⁴×C₇	1	8	yes	—
777	C₂²⋊C₄	C₂⁴×C₇	1	8	yes	—
778	C₂²⋊C₄	C₂⁴×C₇	1	8	yes	—
779	C₄²	C₂⁴×C₇	1	4	yes	—
780	C₄²	C₂⁴×C₇	1	4	yes	—
781	C₄²	C₂⁴×C₇	1	4	yes	—
782	C₄²	C₂⁴×C₇	1	4	yes	—
783	C₄²	C₂⁴×C₇	1	16	yes	—
784	C₄²	C₂⁴×C₇	1	16	yes	—
785	C₄²	C₂⁴×C₇	1	8	yes	—
786	C₂×C₇	—	4	4	no	—
787	C₂×C₇	—	4	2	no	—
788	C₂×C₇	—	4	4	no	—
789	C₂×C₇	—	4	4	no	—
790	C₂×C₇	#3547	1	4	yes	direct product factor
791	C₂×C₇	C₂²×H(5,𝔽₂)	1	1	yes	characteristic
792	C₂×C₇	C₂²×2₋¹⁺⁴	1	1	yes	characteristic
793	C₂×C₇	C₂×#585	1	1	yes	characteristic
794	C₂³	—	2	4	no	—
795	C₂³	—	2	2	no	—
796	C₂³	—	2	4	no	—
797	C₂³	—	2	4	no	—
798	C₂³	—	2	2	no	—
799	C₂³	—	2	4	no	—
800	C₂³	—	2	4	no	—
801	C₂³	—	2	4	no	—
802	C₂³	—	2	4	no	—
803	C₂³	—	2	2	no	—
804	C₂³	—	2	4	no	—
805	C₂³	—	2	4	no	—
806	C₂³	C₂⁵×C₇	1	4	yes	—
807	C₂³	C₂⁵×C₇	1	2	yes	—
808	C₂³	C₂⁵×C₇	1	4	yes	—
809	C₂³	C₂⁵×C₇	1	4	yes	—
810	C₂³	C₂⁵×C₇	1	1	yes	characteristic
811	Q₈	—	2	8	no	—
812	Q₈	—	2	16	no	—
813	Q₈	—	4	16	no	—
814	Q₈	—	4	8	no	—
815	Q₈	—	4	8	no	—
816	D₄	—	2	8	no	—
817	D₄	—	2	8	no	—
818	D₄	—	2	8	no	—
819	D₄	—	4	8	no	—
820	D₄	—	4	8	no	—
821	D₄	—	4	16	no	—
822	D₄	—	4	8	no	—
823	D₄	—	4	8	no	—
824	D₄	—	4	8	no	—
825	D₄	—	4	16	no	—
826	C₂×C₄	—	2	4	no	—
827	C₂×C₄	—	2	2	no	—
828	C₂×C₄	—	2	4	no	—
829	C₂×C₄	—	2	8	no	—
830	C₂×C₄	—	2	4	no	—
831	C₂×C₄	—	2	2	no	—
832	C₂×C₄	—	2	4	no	—
833	C₂×C₄	—	2	4	no	—
834	C₂×C₄	—	2	2	no	—
835	C₂×C₄	—	2	8	no	—
836	C₂×C₄	—	2	2	no	—
837	C₂×C₄	—	2	16	no	—
838	C₂×C₄	—	2	16	no	—
839	C₂×C₄	—	2	8	no	—
840	C₂×C₄	—	2	8	no	—
841	C₂×C₄	—	2	16	no	—
842	C₂×C₄	—	4	16	no	—
843	C₂×C₄	—	4	4	no	—
844	C₂×C₄	—	4	16	no	—
845	C₂×C₄	—	4	16	no	—
846	C₂×C₄	C₇×H(5,𝔽₂)	1	4	yes	—
847	C₂×C₄	C₇×2₋¹⁺⁴	1	4	yes	—
848	C₂×C₄	C₂⁵×C₇	1	2	yes	—
849	C₂×C₄	C₂⁵×C₇	1	4	yes	—
850	C₂×C₄	C₂⁵×C₇	1	2	yes	—
851	C₂×C₄	C₂⁵×C₇	1	8	yes	—
852	C₂×C₄	C₂⁵×C₇	1	4	yes	—
853	C₂×C₄	C₂⁵×C₇	1	2	yes	—
854	C₂×C₄	C₂⁵×C₇	1	2	yes	—
855	C₂×C₄	C₂⁵×C₇	1	4	yes	—
856	C₂×C₄	C₂⁵×C₇	1	4	yes	—
857	C₂×C₄	C₂⁵×C₇	1	8	yes	—
858	C₂×C₄	C₂⁵×C₇	1	4	yes	—
859	C₂×C₄	C₂⁵×C₇	1	2	yes	—
860	C₂×C₄	C₂⁵×C₇	1	2	yes	—
861	C₇	C₂×#3547	1	1	yes	characteristic, direct product factor, Sylow
862	C₂²	—	2	4	no	—
863	C₂²	—	2	2	no	—
864	C₂²	—	2	4	no	—
865	C₂²	—	2	4	no	—
866	C₂²	—	2	2	no	—
867	C₂²	—	2	4	no	—
868	C₂²	—	2	4	no	—
869	C₂²	—	2	4	no	—
870	C₂²	—	2	4	no	—
871	C₂²	—	2	2	no	—
872	C₂²	—	2	4	no	—
873	C₂²	—	2	4	no	—
874	C₂²	—	4	8	no	—
875	C₂²	—	4	4	no	—
876	C₂²	—	4	8	no	—
877	C₂²	—	4	8	no	—
878	C₂²	C₂×C₇×H(5,𝔽₂)	1	2	yes	—
879	C₂²	C₂×C₇×2₋¹⁺⁴	1	2	yes	—
880	C₂²	C₇×#585	1	2	yes	—
881	C₂²	C₂⁶×C₇	1	1	yes	characteristic
882	C₄	—	2	4	no	—
883	C₄	—	2	2	no	—
884	C₄	—	2	4	no	—
885	C₄	—	2	8	no	—
886	C₄	—	2	4	no	—
887	C₄	—	2	2	no	—
888	C₄	—	2	4	no	—
889	C₄	—	2	4	no	—
890	C₄	—	2	2	no	—
891	C₄	—	2	8	no	—
892	C₄	—	2	2	no	—
893	C₄	C₂×C₇×H(5,𝔽₂)	1	4	yes	—
894	C₄	C₂×C₇×2₋¹⁺⁴	1	4	yes	—
895	C₂	—	4	4	no	—
896	C₂	—	4	2	no	—
897	C₂	—	4	4	no	—
898	C₂	—	4	4	no	—
899	C₂	C₇×#3547	1	4	yes	direct product factor
900	C₂	C₂²×C₇×H(5,𝔽₂)	1	1	yes	characteristic
901	C₂	C₂²×C₇×2₋¹⁺⁴	1	1	yes	characteristic
902	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×#3547	C₂	direct (N × H)
2. C₂×C₇×#562	C₂	semidirect
3. C₂×C₇×#555	C₂	semidirect
4. C₂×C₇×#555	C₂	semidirect
5. C₂×C₇×#554	C₂	semidirect
6. C₂×C₇×#553	C₂	semidirect
7. C₂×C₇×#552	C₂	semidirect
8. C₂×C₇×D₄×Q₈	C₂	semidirect
9. C₂×C₇×#548	C₂	semidirect
10. C₂×C₇×#547	C₂	semidirect
11. C₂×C₇×#544	C₂	semidirect
12. C₂×C₇×#542	C₂	semidirect
13. C₂×C₇×#540	C₂	semidirect
14. C₂×C₇×#537	C₂	semidirect
15. C₂×C₇×#536	C₂	semidirect
16. C₂×C₇×#533	C₂	semidirect
17. C₂×C₇×#532	C₂	semidirect
18. C₂×C₇×#529	C₂	semidirect
22. C₇×#562	C₂²	semidirect
23. C₇×#555	C₂²	semidirect
24. C₇×#555	C₂²	semidirect
25. C₇×#554	C₂²	semidirect
26. C₇×#553	C₂²	semidirect
27. C₇×#552	C₂²	semidirect
28. C₇×D₄×Q₈	C₂²	semidirect
29. C₇×#548	C₂²	semidirect
30. C₇×#547	C₂²	semidirect
31. C₇×#544	C₂²	semidirect
32. C₇×#542	C₂²	semidirect
33. C₇×#540	C₂²	semidirect
34. C₇×#537	C₂²	semidirect
35. C₇×#536	C₂²	semidirect
36. C₇×#533	C₂²	semidirect
37. C₇×#532	C₂²	semidirect
44. C₇×#529	C₂²	semidirect
101. C₂×#3547	C₇	direct (N × H)
235. #3547	C₂×C₇	direct (N × H)
236. C₂×#562	C₂×C₇	semidirect
237. C₂×#555	C₂×C₇	semidirect
238. C₂×#555	C₂×C₇	semidirect
239. C₂×#554	C₂×C₇	semidirect
240. C₂×#553	C₂×C₇	semidirect
241. C₂×#552	C₂×C₇	semidirect
242. C₂×D₄×Q₈	C₂×C₇	semidirect
243. C₂×#548	C₂×C₇	semidirect
244. C₂×#547	C₂×C₇	semidirect
245. C₂×#544	C₂×C₇	semidirect
246. C₂×#542	C₂×C₇	semidirect
247. C₂×#540	C₂×C₇	semidirect
248. C₂×#537	C₂×C₇	semidirect
249. C₂×#536	C₂×C₇	semidirect
250. C₂×#533	C₂×C₇	semidirect
251. C₂×#532	C₂×C₇	semidirect
252. C₂×#529	C₂×C₇	semidirect
365. #562	C₂²×C₇	semidirect
366. #555	C₂²×C₇	semidirect
367. #555	C₂²×C₇	semidirect
368. #554	C₂²×C₇	semidirect
369. #553	C₂²×C₇	semidirect
370. #552	C₂²×C₇	semidirect
371. D₄×Q₈	C₂²×C₇	semidirect
372. #548	C₂²×C₇	semidirect
373. #547	C₂²×C₇	semidirect
374. #544	C₂²×C₇	semidirect
375. #542	C₂²×C₇	semidirect
376. #540	C₂²×C₇	semidirect
377. #537	C₂²×C₇	semidirect
378. #536	C₂²×C₇	semidirect
379. #533	C₂²×C₇	semidirect
380. #532	C₂²×C₇	semidirect
387. #529	C₂²×C₇	semidirect
790. C₂×C₇	#3547	direct (N × H)
861. C₇	C₂×#3547	direct (N × H)
899. C₂	C₇×#3547	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×#3547	2
C₂×C₇×#562	2
C₂×C₇×#555	2
C₂×C₇×#554	2
C₂×C₇×#553	2
C₂×C₇×#552	2
C₂×C₇×D₄×Q₈	2
C₂×C₇×#548	2
C₂×C₇×#547	2
C₂×C₇×#544	2
C₂×C₇×#542	2
C₂×C₇×#540	2
C₂×C₇×#537	2
C₂×C₇×#536	2
C₂×C₇×#533	2
C₂×C₇×#532	2
C₂×C₇×#529	2
C₂×#3547	7

Subgroups — C2×C7×#3547 #13239966

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₇×#3547 #13239966