Subgroups — C₂×C₇×#3561 #13239947

Order 1792.

7258 conjugacy classes of subgroups.

The subgroup lattice has 824 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×#3561	C₂	1	32	yes	maximal, direct product factor
2	C₂×C₇×#563	C₂	1	2	yes	maximal, complemented
3	C₂×C₇×#562	C₂	1	2	yes	maximal, complemented
4	C₂×C₇×#556	C₂	1	2	yes	maximal, complemented
5	C₂×C₇×#551	C₂	1	4	yes	maximal, complemented
6	C₂×C₇×D₄×Q₈	C₂	1	2	yes	maximal, complemented
7	C₂×C₇×#548	C₂	1	2	yes	maximal, complemented
8	C₂×C₇×#546	C₂	1	2	yes	maximal, complemented
9	C₂×C₇×#543	C₂	1	2	yes	maximal, complemented
10	C₂×C₇×#542	C₂	1	2	yes	maximal, complemented
11	C₂×C₇×#542	C₂	1	4	yes	maximal, complemented
12	C₂×C₇×#538	C₂	1	2	yes	maximal, complemented
13	C₂×C₇×#536	C₂	1	2	yes	maximal, complemented
14	C₂×C₇×#533	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	—
18	C₂³×C₇×Q₈	C₂²	1	1	yes	characteristic
19	C₂³×C₇×Q₈	C₂²	1	2	yes	complemented
20	C₂³×C₇×D₄	C₂²	1	1	yes	characteristic
21	C₇×#563	C₂²	1	32	yes	complemented
22	C₇×#562	C₂²	1	32	yes	complemented
23	C₇×#556	C₂²	1	32	yes	complemented
24	C₇×#551	C₂²	1	64	yes	complemented
25	C₇×D₄×Q₈	C₂²	1	32	yes	complemented
26	C₇×#548	C₂²	1	32	yes	complemented
27	C₇×#546	C₂²	1	32	yes	complemented
28	C₇×#543	C₂²	1	32	yes	complemented
29	C₇×#542	C₂²	1	32	yes	complemented
30	C₇×#542	C₂²	1	64	yes	complemented
31	C₇×#538	C₂²	1	32	yes	complemented
32	C₇×#536	C₂²	1	32	yes	complemented
33	C₇×#533	C₂²	1	16	yes	complemented
34	C₂×C₇×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
35	C₂×C₇×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
36	C₂×C₇×C₄⋊Q₈	C₂²	1	2	yes	complemented
37	C₂×C₇×C₄⋊Q₈	C₂²	1	4	yes	complemented
38	C₇×#529	C₂²	1	16	yes	complemented
39	C₂×C₇×#126	C₂²	1	2	yes	complemented
40	C₂×C₇×#126	C₂²	1	4	yes	complemented
41	C₂×C₇×#126	C₂²	1	4	yes	complemented
42	C₂×C₇×#126	C₂²	1	4	yes	complemented
43	C₂×C₇×#125	C₂²	1	1	yes	characteristic, complemented
44	C₂×C₇×#125	C₂²	1	2	yes	complemented
45	C₂×C₇×#124	C₂²	1	2	yes	—
46	C₂×C₇×#124	C₂²	1	2	yes	—
47	C₂×C₇×#124	C₂²	1	2	yes	—
48	C₂×C₇×#124	C₂²	1	2	yes	—
49	C₂×C₇×#124	C₂²	1	2	yes	—
50	C₂×C₇×#124	C₂²	1	16	yes	complemented
51	C₂×C₇×#124	C₂²	1	1	yes	characteristic, complemented
52	C₂×C₇×#124	C₂²	1	4	yes	complemented
53	C₂×C₇×#124	C₂²	1	4	yes	complemented
54	C₂×C₇×#123	C₂²	1	2	yes	—
55	C₂×C₇×#123	C₂²	1	4	yes	—
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
60	C₂×C₇×C₂²⋊Q₈	C₂²	1	2	yes	—
61	C₂×C₇×C₂²⋊Q₈	C₂²	1	2	yes	—
62	C₂×C₇×C₂²⋊Q₈	C₂²	1	4	yes	—
63	C₂×C₇×C₂²⋊Q₈	C₂²	1	4	yes	complemented
64	C₂×C₇×C₂²⋊Q₈	C₂²	1	4	yes	complemented
65	C₂×C₇×C₂²⋊Q₈	C₂²	1	4	yes	complemented
66	C₂×C₇×C₂²⋊Q₈	C₂²	1	2	yes	complemented
67	C₂×C₇×C₂²⋊Q₈	C₂²	1	4	yes	complemented
68	C₂×C₇×C₂²⋊Q₈	C₂²	1	4	yes	complemented
69	C₂×C₇×C₂²⋊Q₈	C₂²	1	4	yes	complemented
70	C₂×C₇×#121	C₂²	1	1	yes	characteristic
71	C₂×C₇×#121	C₂²	1	2	yes	—
72	C₂×C₇×#121	C₂²	1	4	yes	—
73	C₂×C₇×#121	C₂²	1	4	yes	complemented
74	C₂×C₇×#120	C₂²	1	4	yes	—
75	C₂×C₄×C₇×Q₈	C₂²	1	1	yes	characteristic, complemented
76	C₂×C₄×C₇×Q₈	C₂²	1	2	yes	complemented
77	C₂×C₄×C₇×Q₈	C₂²	1	2	yes	complemented
78	C₂×C₄×C₇×Q₈	C₂²	1	2	yes	complemented
79	C₂×C₄×C₇×D₄	C₂²	1	2	yes	—
80	C₂×C₄×C₇×D₄	C₂²	1	4	yes	—
81	C₂×C₄×C₇×D₄	C₂²	1	2	yes	—
82	C₂×C₄×C₇×D₄	C₂²	1	1	yes	characteristic, complemented
83	C₂×C₄×C₇×D₄	C₂²	1	4	yes	complemented
84	C₂×C₇×#117	C₂²	1	2	yes	—
85	C₂×C₇×#117	C₂²	1	2	yes	complemented
86	C₂×C₇×#117	C₂²	1	4	yes	complemented
87	C₂²×C₇×C₂²⋊C₄	C₂²	1	2	yes	—
88	C₂²×C₇×C₂²⋊C₄	C₂²	1	2	yes	—
89	C₂²×C₇×C₂²⋊C₄	C₂²	1	4	yes	—
90	C₂²×C₄²×C₇	C₂²	1	1	yes	characteristic
91	C₂×#3561	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
92	C₂⁵×C₇	C₂³	1	2	yes	—
93	C₂×C₇×#41	—	4	8	no	—
94	C₂×C₇×#41	C₂³	1	16	yes	—
95	C₂²×C₇×Q₈	—	4	4	no	—
96	C₂²×C₇×Q₈	—	4	8	no	—
97	C₂²×C₇×Q₈	C₂³	1	2	yes	—
98	C₂²×C₇×Q₈	C₂³	1	2	yes	—
99	C₂²×C₇×Q₈	C₂³	1	2	yes	—
100	C₂²×C₇×Q₈	C₂³	1	8	yes	—
101	C₂²×C₇×Q₈	C₂³	1	4	yes	—
102	C₂²×C₇×Q₈	C₂³	1	1	yes	characteristic
103	C₂²×C₇×Q₈	C₂³	1	2	yes	—
104	C₂²×C₇×Q₈	C₂³	1	16	yes	complemented
105	C₂²×C₇×D₄	—	4	4	no	—
106	C₂²×C₇×D₄	C₂³	1	2	yes	—
107	C₂²×C₇×D₄	C₂³	1	2	yes	—
108	C₂²×C₇×D₄	C₂³	1	2	yes	—
109	C₂²×C₇×D₄	C₂³	1	8	yes	—
110	C₂²×C₇×D₄	C₂³	1	4	yes	—
111	C₂²×C₇×D₄	C₂³	1	4	yes	—
112	C₂²×C₇×D₄	C₂³	1	1	yes	characteristic
113	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
114	C₂³×C₄×C₇	C₂³	1	2	yes	—
115	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
116	C₂³×C₄×C₇	C₂³	1	2	yes	—
117	C₂³×C₄×C₇	C₂³	1	4	yes	—
118	C₂³×C₄×C₇	C₂³	1	4	yes	—
119	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
120	C₂³×C₄×C₇	C₂³	1	4	yes	—
121	C₇×C₄⋊Q₈	C₂³	1	8	yes	complemented
122	C₇×C₄⋊Q₈	C₂³	1	8	yes	complemented
123	C₇×C₄⋊Q₈	C₂³	1	16	yes	complemented
124	C₇×C₄⋊Q₈	C₂³	1	32	yes	complemented
125	C₇×#126	C₂³	1	16	yes	complemented
126	C₇×#126	C₂³	1	32	yes	complemented
127	C₇×#126	C₂³	1	32	yes	complemented
128	C₇×#126	C₂³	1	32	yes	complemented
129	C₇×#125	C₂³	1	8	yes	complemented
130	C₇×#125	C₂³	1	16	yes	complemented
131	C₇×#124	C₂³	1	16	yes	—
132	C₇×#124	C₂³	1	16	yes	—
133	C₇×#124	C₂³	1	16	yes	—
134	C₇×#124	C₂³	1	16	yes	—
135	C₇×#124	C₂³	1	16	yes	—
136	C₇×#124	C₂³	1	8	yes	complemented
137	C₇×#124	C₂³	1	32	yes	complemented
138	C₇×#124	C₂³	1	32	yes	complemented
139	C₇×#123	C₂³	1	16	yes	—
140	C₇×#123	C₂³	1	32	yes	—
141	C₇×#123	C₂³	1	32	yes	complemented
142	C₇×#123	C₂³	1	32	yes	complemented
143	C₇×#123	C₂³	1	32	yes	complemented
144	C₇×C₂²⋊Q₈	C₂³	1	8	yes	—
145	C₇×C₂²⋊Q₈	C₂³	1	16	yes	—
146	C₇×C₂²⋊Q₈	C₂³	1	16	yes	—
147	C₇×C₂²⋊Q₈	C₂³	1	32	yes	—
148	C₇×C₂²⋊Q₈	C₂³	1	32	yes	complemented
149	C₇×C₂²⋊Q₈	C₂³	1	32	yes	complemented
150	C₇×C₂²⋊Q₈	C₂³	1	32	yes	complemented
151	C₇×C₂²⋊Q₈	C₂³	1	16	yes	complemented
152	C₇×C₂²⋊Q₈	C₂³	1	32	yes	complemented
153	C₇×C₂²⋊Q₈	C₂³	1	32	yes	complemented
154	C₇×C₂²⋊Q₈	C₂³	1	32	yes	complemented
155	C₇×#121	C₂³	1	8	yes	—
156	C₇×#121	C₂³	1	16	yes	—
157	C₇×#121	C₂³	1	32	yes	—
158	C₇×#121	C₂³	1	32	yes	complemented
159	C₇×#120	C₂³	1	32	yes	—
160	C₄×C₇×Q₈	C₂³	1	8	yes	complemented
161	C₄×C₇×Q₈	C₂³	1	16	yes	complemented
162	C₄×C₇×Q₈	C₂³	1	16	yes	complemented
163	C₄×C₇×Q₈	C₂³	1	16	yes	complemented
164	C₄×C₇×D₄	C₂³	1	16	yes	—
165	C₄×C₇×D₄	C₂³	1	32	yes	—
166	C₄×C₇×D₄	C₂³	1	16	yes	—
167	C₄×C₇×D₄	C₂³	1	8	yes	complemented
168	C₄×C₇×D₄	C₂³	1	32	yes	complemented
169	C₇×#117	C₂³	1	16	yes	—
170	C₇×#117	C₂³	1	16	yes	complemented
171	C₇×#117	C₂³	1	32	yes	complemented
172	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
173	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
174	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
175	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
176	C₂×C₇×C₄⋊C₄	C₂³	1	4	yes	—
177	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
178	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
179	C₂×C₇×C₄⋊C₄	C₂³	1	4	yes	—
180	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
181	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
182	C₂×C₇×C₄⋊C₄	C₂³	1	4	yes	—
183	C₂×C₇×C₄⋊C₄	C₂³	1	4	yes	—
184	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
185	C₂×C₇×C₄⋊C₄	C₂³	1	4	yes	—
186	C₂×C₇×C₄⋊C₄	C₂³	1	4	yes	—
187	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
188	C₂×C₇×C₂²⋊C₄	C₂³	1	2	yes	—
189	C₂×C₇×C₂²⋊C₄	C₂³	1	4	yes	—
190	C₂×C₇×C₂²⋊C₄	C₂³	1	4	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	16	yes	—
197	C₂×C₇×C₂²⋊C₄	C₂³	1	16	yes	—
198	C₂×C₇×C₂²⋊C₄	C₂³	1	32	yes	—
199	C₂×C₇×C₂²⋊C₄	C₂³	1	4	yes	—
200	C₂×C₇×C₂²⋊C₄	C₂³	1	2	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	2	yes	—
204	C₂×C₇×C₂²⋊C₄	C₂³	1	4	yes	—
205	C₂×C₇×C₂²⋊C₄	C₂³	1	2	yes	—
206	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
207	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
208	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
209	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
210	C₂×C₄²×C₇	C₂³	1	8	yes	—
211	C₂×C₄²×C₇	C₂³	1	4	yes	—
212	C₂×C₄²×C₇	C₂³	1	2	yes	—
213	C₂×C₄²×C₇	C₂³	1	4	yes	—
214	#3561	C₂×C₇	1	32	yes	direct product factor
215	C₂×#563	C₂×C₇	1	2	yes	complemented
216	C₂×#562	C₂×C₇	1	2	yes	complemented
217	C₂×#556	C₂×C₇	1	2	yes	complemented
218	C₂×#551	C₂×C₇	1	4	yes	complemented
219	C₂×D₄×Q₈	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×#543	C₂×C₇	1	2	yes	complemented
223	C₂×#542	C₂×C₇	1	2	yes	complemented
224	C₂×#542	C₂×C₇	1	4	yes	complemented
225	C₂×#538	C₂×C₇	1	2	yes	complemented
226	C₂×#536	C₂×C₇	1	2	yes	complemented
227	C₂×#533	C₂×C₇	1	1	yes	characteristic, complemented
228	C₂×#529	C₂×C₇	1	1	yes	characteristic, complemented
229	C₂²×#124	C₂×C₇	1	1	yes	characteristic, complemented
230	C₂⁴×C₇	—	2	8	no	—
231	C₂⁴×C₇	—	4	4	no	—
232	C₂⁴×C₇	—	4	4	no	—
233	C₂⁴×C₇	C₂⁴	1	4	yes	—
234	C₂⁴×C₇	C₂⁴	1	2	yes	—
235	C₂⁴×C₇	C₂⁴	1	1	yes	characteristic
236	C₂⁴×C₇	C₂⁴	1	8	yes	—
237	C₇×#41	—	4	32	no	—
238	C₂×C₇×Q₈	—	2	8	no	—
239	C₂×C₇×Q₈	—	2	8	no	—
240	C₂×C₇×Q₈	—	4	8	no	—
241	C₂×C₇×Q₈	—	4	4	no	—
242	C₂×C₇×Q₈	—	4	2	no	—
243	C₂×C₇×Q₈	—	4	4	no	—
244	C₂×C₇×Q₈	—	4	16	no	—
245	C₂×C₇×Q₈	—	4	32	no	—
246	C₂×C₇×Q₈	C₂⁴	1	8	yes	—
247	C₂×C₇×Q₈	C₂⁴	1	8	yes	—
248	C₂×C₇×Q₈	C₂⁴	1	4	yes	—
249	C₂×C₇×Q₈	C₂⁴	1	8	yes	—
250	C₂×C₇×Q₈	C₂⁴	1	16	yes	—
251	C₂×C₇×Q₈	C₂⁴	1	8	yes	—
252	C₂×C₇×D₄	—	2	8	no	—
253	C₂×C₇×D₄	—	2	8	no	—
254	C₂×C₇×D₄	—	4	16	no	—
255	C₂×C₇×D₄	—	4	4	no	—
256	C₂×C₇×D₄	—	4	8	no	—
257	C₂×C₇×D₄	—	4	2	no	—
258	C₂×C₇×D₄	—	4	8	no	—
259	C₂×C₇×D₄	C₂⁴	1	8	yes	—
260	C₂×C₇×D₄	C₂⁴	1	8	yes	—
261	C₂×C₇×D₄	C₂⁴	1	16	yes	—
262	C₂×C₇×D₄	C₂⁴	1	4	yes	—
263	C₂×C₇×D₄	C₂⁴	1	16	yes	—
264	C₂×C₇×D₄	C₂⁴	1	8	yes	—
265	C₂²×C₄×C₇	—	2	4	no	—
266	C₂²×C₄×C₇	—	2	4	no	—
267	C₂²×C₄×C₇	—	2	8	no	—
268	C₂²×C₄×C₇	—	4	8	no	—
269	C₂²×C₄×C₇	—	4	2	no	—
270	C₂²×C₄×C₇	—	4	8	no	—
271	C₂²×C₄×C₇	—	4	4	no	—
272	C₂²×C₄×C₇	—	4	8	no	—
273	C₂²×C₄×C₇	C₂⁴	1	4	yes	—
274	C₂²×C₄×C₇	C₂⁴	1	4	yes	—
275	C₂²×C₄×C₇	C₂⁴	1	8	yes	—
276	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
277	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
278	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
279	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
280	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
281	C₂²×C₄×C₇	C₂⁴	1	4	yes	—
282	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
283	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
284	C₂²×C₄×C₇	C₂⁴	1	4	yes	—
285	C₂²×C₄×C₇	C₂⁴	1	4	yes	—
286	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
287	C₂²×C₄×C₇	C₂⁴	1	4	yes	—
288	C₂²×C₄×C₇	C₂⁴	1	8	yes	—
289	C₂²×C₄×C₇	C₂⁴	1	16	yes	—
290	C₂²×C₄×C₇	C₂⁴	1	16	yes	—
291	C₂²×C₄×C₇	C₂⁴	1	16	yes	—
292	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
293	C₇×C₄⋊C₄	C₂⁴	1	8	yes	—
294	C₇×C₄⋊C₄	C₂⁴	1	8	yes	—
295	C₇×C₄⋊C₄	C₂⁴	1	8	yes	—
296	C₇×C₄⋊C₄	C₂⁴	1	8	yes	—
297	C₇×C₄⋊C₄	C₂⁴	1	16	yes	—
298	C₇×C₄⋊C₄	C₂⁴	1	8	yes	—
299	C₇×C₄⋊C₄	C₂⁴	1	8	yes	—
300	C₇×C₄⋊C₄	C₂⁴	1	16	yes	—
301	C₇×C₄⋊C₄	C₂⁴	1	8	yes	—
302	C₇×C₄⋊C₄	C₂⁴	1	4	yes	—
303	C₇×C₄⋊C₄	C₂⁴	1	16	yes	—
304	C₇×C₄⋊C₄	C₂⁴	1	16	yes	—
305	C₇×C₄⋊C₄	C₂⁴	1	4	yes	—
306	C₇×C₄⋊C₄	C₂⁴	1	16	yes	—
307	C₇×C₄⋊C₄	C₂⁴	1	16	yes	—
308	C₇×C₄⋊C₄	C₂⁴	1	8	yes	—
309	C₇×C₂²⋊C₄	C₂⁴	1	8	yes	—
310	C₇×C₂²⋊C₄	C₂⁴	1	16	yes	—
311	C₇×C₂²⋊C₄	C₂⁴	1	16	yes	—
312	C₇×C₂²⋊C₄	C₂⁴	1	16	yes	—
313	C₇×C₂²⋊C₄	C₂⁴	1	16	yes	—
314	C₇×C₂²⋊C₄	C₂⁴	1	16	yes	—
315	C₇×C₂²⋊C₄	C₂⁴	1	16	yes	—
316	C₇×C₂²⋊C₄	C₂⁴	1	16	yes	—
317	C₇×C₂²⋊C₄	C₂⁴	1	16	yes	—
318	C₇×C₂²⋊C₄	C₂⁴	1	8	yes	—
319	C₇×C₂²⋊C₄	C₂⁴	1	8	yes	—
320	C₇×C₂²⋊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	8	yes	—
324	C₄²×C₇	C₂⁴	1	4	yes	—
325	C₄²×C₇	C₂⁴	1	4	yes	—
326	C₄²×C₇	C₂⁴	1	4	yes	—
327	C₄²×C₇	C₂⁴	1	4	yes	—
328	C₄²×C₇	C₂⁴	1	16	yes	—
329	C₄²×C₇	C₂⁴	1	8	yes	—
330	C₄²×C₇	C₂⁴	1	16	yes	—
331	C₂²×#41	C₂²×C₇	1	2	yes	—
332	C₂³×Q₈	C₂²×C₇	1	1	yes	characteristic
333	C₂³×Q₈	C₂²×C₇	1	2	yes	complemented
334	C₂³×D₄	C₂²×C₇	1	1	yes	characteristic
335	#563	C₂²×C₇	1	32	yes	complemented
336	#562	C₂²×C₇	1	32	yes	complemented
337	#556	C₂²×C₇	1	32	yes	complemented
338	#551	C₂²×C₇	1	64	yes	complemented
339	D₄×Q₈	C₂²×C₇	1	32	yes	complemented
340	#548	C₂²×C₇	1	32	yes	complemented
341	#546	C₂²×C₇	1	32	yes	complemented
342	#543	C₂²×C₇	1	32	yes	complemented
343	#542	C₂²×C₇	1	32	yes	complemented
344	#542	C₂²×C₇	1	64	yes	complemented
345	#538	C₂²×C₇	1	32	yes	complemented
346	#536	C₂²×C₇	1	32	yes	complemented
347	#533	C₂²×C₇	1	16	yes	complemented
348	C₂×C₄⋊Q₈	C₂²×C₇	1	1	yes	characteristic, complemented
349	C₂×C₄⋊Q₈	C₂²×C₇	1	1	yes	characteristic, complemented
350	C₂×C₄⋊Q₈	C₂²×C₇	1	2	yes	complemented
351	C₂×C₄⋊Q₈	C₂²×C₇	1	4	yes	complemented
352	#529	C₂²×C₇	1	16	yes	complemented
353	C₂×#126	C₂²×C₇	1	2	yes	complemented
354	C₂×#126	C₂²×C₇	1	4	yes	complemented
355	C₂×#126	C₂²×C₇	1	4	yes	complemented
356	C₂×#126	C₂²×C₇	1	4	yes	complemented
357	C₂×#125	C₂²×C₇	1	1	yes	characteristic, complemented
358	C₂×#125	C₂²×C₇	1	2	yes	complemented
359	C₂×#124	C₂²×C₇	1	2	yes	—
360	C₂×#124	C₂²×C₇	1	2	yes	—
361	C₂×#124	C₂²×C₇	1	2	yes	—
362	C₂×#124	C₂²×C₇	1	2	yes	—
363	C₂×#124	C₂²×C₇	1	2	yes	—
364	C₂×#124	C₂²×C₇	1	16	yes	complemented
365	C₂×#124	C₂²×C₇	1	1	yes	characteristic, complemented
366	C₂×#124	C₂²×C₇	1	4	yes	complemented
367	C₂×#124	C₂²×C₇	1	4	yes	complemented
368	C₂×#123	C₂²×C₇	1	2	yes	—
369	C₂×#123	C₂²×C₇	1	4	yes	—
370	C₂×#123	C₂²×C₇	1	4	yes	complemented
371	C₂×#123	C₂²×C₇	1	4	yes	complemented
372	C₂×#123	C₂²×C₇	1	4	yes	complemented
373	C₂×C₂²⋊Q₈	C₂²×C₇	1	1	yes	characteristic
374	C₂×C₂²⋊Q₈	C₂²×C₇	1	2	yes	—
375	C₂×C₂²⋊Q₈	C₂²×C₇	1	2	yes	—
376	C₂×C₂²⋊Q₈	C₂²×C₇	1	4	yes	—
377	C₂×C₂²⋊Q₈	C₂²×C₇	1	4	yes	complemented
378	C₂×C₂²⋊Q₈	C₂²×C₇	1	4	yes	complemented
379	C₂×C₂²⋊Q₈	C₂²×C₇	1	4	yes	complemented
380	C₂×C₂²⋊Q₈	C₂²×C₇	1	2	yes	complemented
381	C₂×C₂²⋊Q₈	C₂²×C₇	1	4	yes	complemented
382	C₂×C₂²⋊Q₈	C₂²×C₇	1	4	yes	complemented
383	C₂×C₂²⋊Q₈	C₂²×C₇	1	4	yes	complemented
384	C₂×#121	C₂²×C₇	1	1	yes	characteristic
385	C₂×#121	C₂²×C₇	1	2	yes	—
386	C₂×#121	C₂²×C₇	1	4	yes	—
387	C₂×#121	C₂²×C₇	1	4	yes	complemented
388	C₂×#120	C₂²×C₇	1	4	yes	—
389	C₂×C₄×Q₈	C₂²×C₇	1	1	yes	characteristic, complemented
390	C₂×C₄×Q₈	C₂²×C₇	1	2	yes	complemented
391	C₂×C₄×Q₈	C₂²×C₇	1	2	yes	complemented
392	C₂×C₄×Q₈	C₂²×C₇	1	2	yes	complemented
393	C₂×C₄×D₄	C₂²×C₇	1	2	yes	—
394	C₂×C₄×D₄	C₂²×C₇	1	4	yes	—
395	C₂×C₄×D₄	C₂²×C₇	1	2	yes	—
396	C₂×C₄×D₄	C₂²×C₇	1	1	yes	characteristic, complemented
397	C₂×C₄×D₄	C₂²×C₇	1	4	yes	complemented
398	C₂×#117	C₂²×C₇	1	2	yes	—
399	C₂×#117	C₂²×C₇	1	2	yes	complemented
400	C₂×#117	C₂²×C₇	1	4	yes	complemented
401	C₂²×C₂²⋊C₄	C₂²×C₇	1	2	yes	—
402	C₂²×C₂²⋊C₄	C₂²×C₇	1	2	yes	—
403	C₂²×C₂²⋊C₄	C₂²×C₇	1	4	yes	—
404	C₂²×C₄²	C₂²×C₇	1	1	yes	characteristic
405	C₂³×C₇	—	2	2	no	—
406	C₂³×C₇	—	2	2	no	—
407	C₂³×C₇	—	2	4	no	—
408	C₂³×C₇	—	2	8	no	—
409	C₂³×C₇	—	2	4	no	—
410	C₂³×C₇	—	2	8	no	—
411	C₂³×C₇	—	2	8	no	—
412	C₂³×C₇	—	2	4	no	—
413	C₂³×C₇	—	2	16	no	—
414	C₂³×C₇	—	4	8	no	—
415	C₂³×C₇	—	4	8	no	—
416	C₂³×C₇	—	8	16	no	—
417	C₂³×C₇	2₋¹⁺⁴	1	4	yes	—
418	C₂³×C₇	C₂⁵	1	8	yes	—
419	C₂³×C₇	C₂⁵	1	4	yes	—
420	C₂³×C₇	C₂⁵	1	2	yes	—
421	C₂³×C₇	C₂⁵	1	1	yes	characteristic
422	C₇×Q₈	—	2	16	no	—
423	C₇×Q₈	—	2	16	no	—
424	C₇×Q₈	—	4	16	no	—
425	C₇×Q₈	—	4	8	no	—
426	C₇×Q₈	—	4	4	no	—
427	C₇×Q₈	—	4	8	no	—
428	C₇×D₄	—	2	16	no	—
429	C₇×D₄	—	2	16	no	—
430	C₇×D₄	—	4	8	no	—
431	C₇×D₄	—	4	16	no	—
432	C₇×D₄	—	4	4	no	—
433	C₇×D₄	—	4	16	no	—
434	C₂×C₄×C₇	—	2	4	no	—
435	C₂×C₄×C₇	—	2	2	no	—
436	C₂×C₄×C₇	—	2	8	no	—
437	C₂×C₄×C₇	—	2	8	no	—
438	C₂×C₄×C₇	—	2	8	no	—
439	C₂×C₄×C₇	—	2	2	no	—
440	C₂×C₄×C₇	—	2	2	no	—
441	C₂×C₄×C₇	—	2	4	no	—
442	C₂×C₄×C₇	—	2	4	no	—
443	C₂×C₄×C₇	—	2	8	no	—
444	C₂×C₄×C₇	—	2	2	no	—
445	C₂×C₄×C₇	—	2	2	no	—
446	C₂×C₄×C₇	—	2	8	no	—
447	C₂×C₄×C₇	—	2	16	no	—
448	C₂×C₄×C₇	—	4	16	no	—
449	C₂×C₄×C₇	—	4	4	no	—
450	C₂×C₄×C₇	—	4	16	no	—
451	C₂×C₄×C₇	—	4	8	no	—
452	C₂×C₄×C₇	—	4	16	no	—
453	C₂×C₄×C₇	H(5,𝔽₂)	1	4	yes	—
454	C₂×C₄×C₇	C₂⁵	1	2	yes	—
455	C₂×C₄×C₇	C₂⁵	1	4	yes	—
456	C₂×C₄×C₇	C₂⁵	1	2	yes	—
457	C₂×C₄×C₇	C₂⁵	1	2	yes	—
458	C₂×C₄×C₇	C₂⁵	1	2	yes	—
459	C₂×C₄×C₇	C₂⁵	1	8	yes	—
460	C₂×C₄×C₇	C₂⁵	1	2	yes	—
461	C₂×C₄×C₇	C₂⁵	1	4	yes	—
462	C₂×C₄×C₇	C₂⁵	1	8	yes	—
463	C₂×C₄×C₇	C₂⁵	1	8	yes	—
464	C₂×C₄×C₇	C₂⁵	1	4	yes	—
465	C₂×C₄×C₇	C₂⁵	1	2	yes	—
466	C₂⁵	C₂³×C₇	1	2	yes	—
467	C₂×#41	—	4	8	no	—
468	C₂×#41	C₂³×C₇	1	16	yes	—
469	C₂²×Q₈	—	4	4	no	—
470	C₂²×Q₈	—	4	8	no	—
471	C₂²×Q₈	C₂³×C₇	1	2	yes	—
472	C₂²×Q₈	C₂³×C₇	1	2	yes	—
473	C₂²×Q₈	C₂³×C₇	1	1	yes	characteristic
474	C₂²×Q₈	C₂³×C₇	1	2	yes	—
475	C₂²×Q₈	C₂³×C₇	1	4	yes	—
476	C₂²×Q₈	C₂³×C₇	1	2	yes	—
477	C₂²×Q₈	C₂³×C₇	1	8	yes	—
478	C₂²×Q₈	C₂³×C₇	1	16	yes	complemented
479	C₂²×D₄	—	4	4	no	—
480	C₂²×D₄	C₂³×C₇	1	2	yes	—
481	C₂²×D₄	C₂³×C₇	1	2	yes	—
482	C₂²×D₄	C₂³×C₇	1	4	yes	—
483	C₂²×D₄	C₂³×C₇	1	1	yes	characteristic
484	C₂²×D₄	C₂³×C₇	1	4	yes	—
485	C₂²×D₄	C₂³×C₇	1	2	yes	—
486	C₂²×D₄	C₂³×C₇	1	8	yes	—
487	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
488	C₂³×C₄	C₂³×C₇	1	2	yes	—
489	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
490	C₂³×C₄	C₂³×C₇	1	2	yes	—
491	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
492	C₂³×C₄	C₂³×C₇	1	4	yes	—
493	C₂³×C₄	C₂³×C₇	1	4	yes	—
494	C₂³×C₄	C₂³×C₇	1	4	yes	—
495	C₄⋊Q₈	C₂³×C₇	1	8	yes	complemented
496	C₄⋊Q₈	C₂³×C₇	1	8	yes	complemented
497	C₄⋊Q₈	C₂³×C₇	1	16	yes	complemented
498	C₄⋊Q₈	C₂³×C₇	1	32	yes	complemented
499	#126	C₂³×C₇	1	16	yes	complemented
500	#126	C₂³×C₇	1	32	yes	complemented
501	#126	C₂³×C₇	1	32	yes	complemented
502	#126	C₂³×C₇	1	32	yes	complemented
503	#125	C₂³×C₇	1	8	yes	complemented
504	#125	C₂³×C₇	1	16	yes	complemented
505	#124	C₂³×C₇	1	16	yes	—
506	#124	C₂³×C₇	1	16	yes	—
507	#124	C₂³×C₇	1	16	yes	—
508	#124	C₂³×C₇	1	16	yes	—
509	#124	C₂³×C₇	1	16	yes	—
510	#124	C₂³×C₇	1	8	yes	complemented
511	#124	C₂³×C₇	1	32	yes	complemented
512	#124	C₂³×C₇	1	32	yes	complemented
513	#123	C₂³×C₇	1	16	yes	—
514	#123	C₂³×C₇	1	32	yes	—
515	#123	C₂³×C₇	1	32	yes	complemented
516	#123	C₂³×C₇	1	32	yes	complemented
517	#123	C₂³×C₇	1	32	yes	complemented
518	C₂²⋊Q₈	C₂³×C₇	1	8	yes	—
519	C₂²⋊Q₈	C₂³×C₇	1	16	yes	—
520	C₂²⋊Q₈	C₂³×C₇	1	16	yes	—
521	C₂²⋊Q₈	C₂³×C₇	1	32	yes	—
522	C₂²⋊Q₈	C₂³×C₇	1	32	yes	complemented
523	C₂²⋊Q₈	C₂³×C₇	1	32	yes	complemented
524	C₂²⋊Q₈	C₂³×C₇	1	32	yes	complemented
525	C₂²⋊Q₈	C₂³×C₇	1	16	yes	complemented
526	C₂²⋊Q₈	C₂³×C₇	1	32	yes	complemented
527	C₂²⋊Q₈	C₂³×C₇	1	32	yes	complemented
528	C₂²⋊Q₈	C₂³×C₇	1	32	yes	complemented
529	#121	C₂³×C₇	1	8	yes	—
530	#121	C₂³×C₇	1	16	yes	—
531	#121	C₂³×C₇	1	32	yes	—
532	#121	C₂³×C₇	1	32	yes	complemented
533	#120	C₂³×C₇	1	32	yes	—
534	C₄×Q₈	C₂³×C₇	1	8	yes	complemented
535	C₄×Q₈	C₂³×C₇	1	16	yes	complemented
536	C₄×Q₈	C₂³×C₇	1	16	yes	complemented
537	C₄×Q₈	C₂³×C₇	1	16	yes	complemented
538	C₄×D₄	C₂³×C₇	1	16	yes	—
539	C₄×D₄	C₂³×C₇	1	32	yes	—
540	C₄×D₄	C₂³×C₇	1	16	yes	—
541	C₄×D₄	C₂³×C₇	1	8	yes	complemented
542	C₄×D₄	C₂³×C₇	1	32	yes	complemented
543	#117	C₂³×C₇	1	16	yes	—
544	#117	C₂³×C₇	1	16	yes	complemented
545	#117	C₂³×C₇	1	32	yes	complemented
546	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
547	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
548	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
549	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
550	C₂×C₄⋊C₄	C₂³×C₇	1	4	yes	—
551	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
552	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
553	C₂×C₄⋊C₄	C₂³×C₇	1	4	yes	—
554	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
555	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
556	C₂×C₄⋊C₄	C₂³×C₇	1	4	yes	—
557	C₂×C₄⋊C₄	C₂³×C₇	1	4	yes	—
558	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
559	C₂×C₄⋊C₄	C₂³×C₇	1	4	yes	—
560	C₂×C₄⋊C₄	C₂³×C₇	1	4	yes	—
561	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
562	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
563	C₂×C₂²⋊C₄	C₂³×C₇	1	4	yes	—
564	C₂×C₂²⋊C₄	C₂³×C₇	1	4	yes	—
565	C₂×C₂²⋊C₄	C₂³×C₇	1	4	yes	—
566	C₂×C₂²⋊C₄	C₂³×C₇	1	4	yes	—
567	C₂×C₂²⋊C₄	C₂³×C₇	1	4	yes	—
568	C₂×C₂²⋊C₄	C₂³×C₇	1	4	yes	—
569	C₂×C₂²⋊C₄	C₂³×C₇	1	4	yes	—
570	C₂×C₂²⋊C₄	C₂³×C₇	1	16	yes	—
571	C₂×C₂²⋊C₄	C₂³×C₇	1	16	yes	—
572	C₂×C₂²⋊C₄	C₂³×C₇	1	32	yes	—
573	C₂×C₂²⋊C₄	C₂³×C₇	1	4	yes	—
574	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
575	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
576	C₂×C₂²⋊C₄	C₂³×C₇	1	4	yes	—
577	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
578	C₂×C₂²⋊C₄	C₂³×C₇	1	4	yes	—
579	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
580	C₂×C₄²	C₂³×C₇	1	4	yes	—
581	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
582	C₂×C₄²	C₂³×C₇	1	2	yes	—
583	C₂×C₄²	C₂³×C₇	1	4	yes	—
584	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
585	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
586	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
587	C₂×C₄²	C₂³×C₇	1	8	yes	—
588	C₂²×C₇	—	2	2	no	—
589	C₂²×C₇	—	2	2	no	—
590	C₂²×C₇	—	2	8	no	—
591	C₂²×C₇	—	2	4	no	—
592	C₂²×C₇	—	2	8	no	—
593	C₂²×C₇	—	2	4	no	—
594	C₂²×C₇	—	2	8	no	—
595	C₂²×C₇	—	2	8	no	—
596	C₂²×C₇	—	2	4	no	—
597	C₂²×C₇	—	4	8	no	—
598	C₂²×C₇	—	4	16	no	—
599	C₂²×C₇	—	8	16	no	—
600	C₂²×C₇	C₂×H(5,𝔽₂)	1	2	yes	—
601	C₂²×C₇	C₂×2₋¹⁺⁴	1	4	yes	—
602	C₂²×C₇	C₂×2₋¹⁺⁴	1	2	yes	—
603	C₂²×C₇	#585	1	2	yes	—
604	C₂²×C₇	C₂⁶	1	1	yes	characteristic
605	C₄×C₇	—	2	4	no	—
606	C₄×C₇	—	2	2	no	—
607	C₄×C₇	—	2	8	no	—
608	C₄×C₇	—	2	8	no	—
609	C₄×C₇	—	2	2	no	—
610	C₄×C₇	—	2	2	no	—
611	C₄×C₇	—	2	4	no	—
612	C₄×C₇	—	2	4	no	—
613	C₄×C₇	—	2	8	no	—
614	C₄×C₇	—	2	2	no	—
615	C₄×C₇	—	2	2	no	—
616	C₄×C₇	C₂×H(5,𝔽₂)	1	4	yes	—
617	C₂⁴	—	2	8	no	—
618	C₂⁴	—	4	4	no	—
619	C₂⁴	—	4	4	no	—
620	C₂⁴	C₂⁴×C₇	1	4	yes	—
621	C₂⁴	C₂⁴×C₇	1	2	yes	—
622	C₂⁴	C₂⁴×C₇	1	1	yes	characteristic
623	C₂⁴	C₂⁴×C₇	1	8	yes	—
624	#41	—	4	32	no	—
625	C₂×Q₈	—	2	8	no	—
626	C₂×Q₈	—	2	8	no	—
627	C₂×Q₈	—	4	8	no	—
628	C₂×Q₈	—	4	4	no	—
629	C₂×Q₈	—	4	2	no	—
630	C₂×Q₈	—	4	4	no	—
631	C₂×Q₈	—	4	16	no	—
632	C₂×Q₈	—	4	32	no	—
633	C₂×Q₈	C₂⁴×C₇	1	8	yes	—
634	C₂×Q₈	C₂⁴×C₇	1	8	yes	—
635	C₂×Q₈	C₂⁴×C₇	1	4	yes	—
636	C₂×Q₈	C₂⁴×C₇	1	8	yes	—
637	C₂×Q₈	C₂⁴×C₇	1	16	yes	—
638	C₂×Q₈	C₂⁴×C₇	1	8	yes	—
639	C₂×D₄	—	2	8	no	—
640	C₂×D₄	—	2	8	no	—
641	C₂×D₄	—	4	16	no	—
642	C₂×D₄	—	4	4	no	—
643	C₂×D₄	—	4	8	no	—
644	C₂×D₄	—	4	8	no	—
645	C₂×D₄	—	4	2	no	—
646	C₂×D₄	C₂⁴×C₇	1	8	yes	—
647	C₂×D₄	C₂⁴×C₇	1	8	yes	—
648	C₂×D₄	C₂⁴×C₇	1	16	yes	—
649	C₂×D₄	C₂⁴×C₇	1	4	yes	—
650	C₂×D₄	C₂⁴×C₇	1	16	yes	—
651	C₂×D₄	C₂⁴×C₇	1	8	yes	—
652	C₂²×C₄	—	2	4	no	—
653	C₂²×C₄	—	2	4	no	—
654	C₂²×C₄	—	2	8	no	—
655	C₂²×C₄	—	4	8	no	—
656	C₂²×C₄	—	4	4	no	—
657	C₂²×C₄	—	4	8	no	—
658	C₂²×C₄	—	4	2	no	—
659	C₂²×C₄	—	4	8	no	—
660	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
661	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
662	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
663	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
664	C₂²×C₄	C₂⁴×C₇	1	4	yes	—
665	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
666	C₂²×C₄	C₂⁴×C₇	1	4	yes	—
667	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
668	C₂²×C₄	C₂⁴×C₇	1	4	yes	—
669	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
670	C₂²×C₄	C₂⁴×C₇	1	4	yes	—
671	C₂²×C₄	C₂⁴×C₇	1	4	yes	—
672	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
673	C₂²×C₄	C₂⁴×C₇	1	8	yes	—
674	C₂²×C₄	C₂⁴×C₇	1	4	yes	—
675	C₂²×C₄	C₂⁴×C₇	1	8	yes	—
676	C₂²×C₄	C₂⁴×C₇	1	16	yes	—
677	C₂²×C₄	C₂⁴×C₇	1	16	yes	—
678	C₂²×C₄	C₂⁴×C₇	1	16	yes	—
679	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
680	C₄⋊C₄	C₂⁴×C₇	1	8	yes	—
681	C₄⋊C₄	C₂⁴×C₇	1	8	yes	—
682	C₄⋊C₄	C₂⁴×C₇	1	8	yes	—
683	C₄⋊C₄	C₂⁴×C₇	1	8	yes	—
684	C₄⋊C₄	C₂⁴×C₇	1	16	yes	—
685	C₄⋊C₄	C₂⁴×C₇	1	8	yes	—
686	C₄⋊C₄	C₂⁴×C₇	1	8	yes	—
687	C₄⋊C₄	C₂⁴×C₇	1	16	yes	—
688	C₄⋊C₄	C₂⁴×C₇	1	8	yes	—
689	C₄⋊C₄	C₂⁴×C₇	1	4	yes	—
690	C₄⋊C₄	C₂⁴×C₇	1	16	yes	—
691	C₄⋊C₄	C₂⁴×C₇	1	16	yes	—
692	C₄⋊C₄	C₂⁴×C₇	1	4	yes	—
693	C₄⋊C₄	C₂⁴×C₇	1	16	yes	—
694	C₄⋊C₄	C₂⁴×C₇	1	16	yes	—
695	C₄⋊C₄	C₂⁴×C₇	1	8	yes	—
696	C₂²⋊C₄	C₂⁴×C₇	1	8	yes	—
697	C₂²⋊C₄	C₂⁴×C₇	1	16	yes	—
698	C₂²⋊C₄	C₂⁴×C₇	1	16	yes	—
699	C₂²⋊C₄	C₂⁴×C₇	1	16	yes	—
700	C₂²⋊C₄	C₂⁴×C₇	1	16	yes	—
701	C₂²⋊C₄	C₂⁴×C₇	1	16	yes	—
702	C₂²⋊C₄	C₂⁴×C₇	1	16	yes	—
703	C₂²⋊C₄	C₂⁴×C₇	1	16	yes	—
704	C₂²⋊C₄	C₂⁴×C₇	1	16	yes	—
705	C₂²⋊C₄	C₂⁴×C₇	1	8	yes	—
706	C₂²⋊C₄	C₂⁴×C₇	1	8	yes	—
707	C₂²⋊C₄	C₂⁴×C₇	1	16	yes	—
708	C₂²⋊C₄	C₂⁴×C₇	1	8	yes	—
709	C₂²⋊C₄	C₂⁴×C₇	1	16	yes	—
710	C₂²⋊C₄	C₂⁴×C₇	1	8	yes	—
711	C₄²	C₂⁴×C₇	1	4	yes	—
712	C₄²	C₂⁴×C₇	1	4	yes	—
713	C₄²	C₂⁴×C₇	1	4	yes	—
714	C₄²	C₂⁴×C₇	1	4	yes	—
715	C₄²	C₂⁴×C₇	1	16	yes	—
716	C₄²	C₂⁴×C₇	1	8	yes	—
717	C₄²	C₂⁴×C₇	1	16	yes	—
718	C₂×C₇	—	2	4	no	—
719	C₂×C₇	—	4	4	no	—
720	C₂×C₇	—	4	8	no	—
721	C₂×C₇	#3561	1	4	yes	direct product factor
722	C₂×C₇	C₂²×H(5,𝔽₂)	1	1	yes	characteristic
723	C₂×C₇	C₂²×2₋¹⁺⁴	1	1	yes	characteristic
724	C₂×C₇	C₂×#585	1	1	yes	characteristic
725	C₂³	—	2	2	no	—
726	C₂³	—	2	2	no	—
727	C₂³	—	2	4	no	—
728	C₂³	—	2	8	no	—
729	C₂³	—	2	4	no	—
730	C₂³	—	2	8	no	—
731	C₂³	—	2	8	no	—
732	C₂³	—	2	4	no	—
733	C₂³	—	2	16	no	—
734	C₂³	—	4	8	no	—
735	C₂³	—	4	8	no	—
736	C₂³	—	8	16	no	—
737	C₂³	C₇×2₋¹⁺⁴	1	4	yes	—
738	C₂³	C₂⁵×C₇	1	8	yes	—
739	C₂³	C₂⁵×C₇	1	4	yes	—
740	C₂³	C₂⁵×C₇	1	2	yes	—
741	C₂³	C₂⁵×C₇	1	1	yes	characteristic
742	Q₈	—	2	16	no	—
743	Q₈	—	2	16	no	—
744	Q₈	—	4	16	no	—
745	Q₈	—	4	8	no	—
746	Q₈	—	4	4	no	—
747	Q₈	—	4	8	no	—
748	D₄	—	2	16	no	—
749	D₄	—	2	16	no	—
750	D₄	—	4	8	no	—
751	D₄	—	4	16	no	—
752	D₄	—	4	4	no	—
753	D₄	—	4	16	no	—
754	C₂×C₄	—	2	4	no	—
755	C₂×C₄	—	2	2	no	—
756	C₂×C₄	—	2	8	no	—
757	C₂×C₄	—	2	8	no	—
758	C₂×C₄	—	2	8	no	—
759	C₂×C₄	—	2	2	no	—
760	C₂×C₄	—	2	2	no	—
761	C₂×C₄	—	2	4	no	—
762	C₂×C₄	—	2	4	no	—
763	C₂×C₄	—	2	8	no	—
764	C₂×C₄	—	2	2	no	—
765	C₂×C₄	—	2	2	no	—
766	C₂×C₄	—	2	8	no	—
767	C₂×C₄	—	2	16	no	—
768	C₂×C₄	—	4	16	no	—
769	C₂×C₄	—	4	4	no	—
770	C₂×C₄	—	4	16	no	—
771	C₂×C₄	—	4	8	no	—
772	C₂×C₄	—	4	16	no	—
773	C₂×C₄	C₇×H(5,𝔽₂)	1	4	yes	—
774	C₂×C₄	C₂⁵×C₇	1	2	yes	—
775	C₂×C₄	C₂⁵×C₇	1	4	yes	—
776	C₂×C₄	C₂⁵×C₇	1	2	yes	—
777	C₂×C₄	C₂⁵×C₇	1	2	yes	—
778	C₂×C₄	C₂⁵×C₇	1	2	yes	—
779	C₂×C₄	C₂⁵×C₇	1	8	yes	—
780	C₂×C₄	C₂⁵×C₇	1	2	yes	—
781	C₂×C₄	C₂⁵×C₇	1	4	yes	—
782	C₂×C₄	C₂⁵×C₇	1	8	yes	—
783	C₂×C₄	C₂⁵×C₇	1	8	yes	—
784	C₂×C₄	C₂⁵×C₇	1	4	yes	—
785	C₂×C₄	C₂⁵×C₇	1	2	yes	—
786	C₇	C₂×#3561	1	1	yes	characteristic, direct product factor, Sylow
787	C₂²	—	2	8	no	—
788	C₂²	—	2	2	no	—
789	C₂²	—	2	2	no	—
790	C₂²	—	2	4	no	—
791	C₂²	—	2	8	no	—
792	C₂²	—	2	4	no	—
793	C₂²	—	2	8	no	—
794	C₂²	—	2	8	no	—
795	C₂²	—	2	4	no	—
796	C₂²	—	4	16	no	—
797	C₂²	—	4	8	no	—
798	C₂²	—	8	16	no	—
799	C₂²	C₂×C₇×H(5,𝔽₂)	1	2	yes	—
800	C₂²	C₂×C₇×2₋¹⁺⁴	1	4	yes	—
801	C₂²	C₂×C₇×2₋¹⁺⁴	1	2	yes	—
802	C₂²	C₇×#585	1	2	yes	—
803	C₂²	C₂⁶×C₇	1	1	yes	characteristic
804	C₄	—	2	4	no	—
805	C₄	—	2	2	no	—
806	C₄	—	2	8	no	—
807	C₄	—	2	8	no	—
808	C₄	—	2	2	no	—
809	C₄	—	2	2	no	—
810	C₄	—	2	4	no	—
811	C₄	—	2	4	no	—
812	C₄	—	2	8	no	—
813	C₄	—	2	2	no	—
814	C₄	—	2	2	no	—
815	C₄	C₂×C₇×H(5,𝔽₂)	1	4	yes	—
816	C₂	—	2	4	no	—
817	C₂	—	4	8	no	—
818	C₂	—	4	4	no	—
819	C₂	C₇×#3561	1	4	yes	direct product factor
820	C₂	C₂²×C₇×H(5,𝔽₂)	1	1	yes	characteristic
821	C₂	C₂²×C₇×2₋¹⁺⁴	1	1	yes	characteristic
822	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×#3561	C₂	direct (N × H)
2. C₂×C₇×#563	C₂	semidirect
3. C₂×C₇×#562	C₂	semidirect
4. C₂×C₇×#556	C₂	semidirect
5. C₂×C₇×#551	C₂	semidirect
6. C₂×C₇×D₄×Q₈	C₂	semidirect
7. C₂×C₇×#548	C₂	semidirect
8. C₂×C₇×#546	C₂	semidirect
9. C₂×C₇×#543	C₂	semidirect
10. C₂×C₇×#542	C₂	semidirect
11. C₂×C₇×#542	C₂	semidirect
12. C₂×C₇×#538	C₂	semidirect
13. C₂×C₇×#536	C₂	semidirect
14. C₂×C₇×#533	C₂	semidirect
15. C₂×C₇×#529	C₂	semidirect
16. C₂²×C₇×#124	C₂	semidirect
19. C₂³×C₇×Q₈	C₂²	semidirect
21. C₇×#563	C₂²	semidirect
22. C₇×#562	C₂²	semidirect
23. C₇×#556	C₂²	semidirect
24. C₇×#551	C₂²	semidirect
25. C₇×D₄×Q₈	C₂²	semidirect
26. C₇×#548	C₂²	semidirect
27. C₇×#546	C₂²	semidirect
28. C₇×#543	C₂²	semidirect
29. C₇×#542	C₂²	semidirect
30. C₇×#542	C₂²	semidirect
31. C₇×#538	C₂²	semidirect
32. C₇×#536	C₂²	semidirect
33. C₇×#533	C₂²	semidirect
34. C₂×C₇×C₄⋊Q₈	C₂²	semidirect
35. C₂×C₇×C₄⋊Q₈	C₂²	semidirect
36. C₂×C₇×C₄⋊Q₈	C₂²	semidirect
37. C₂×C₇×C₄⋊Q₈	C₂²	semidirect
38. C₇×#529	C₂²	semidirect
39. C₂×C₇×#126	C₂²	semidirect
40. C₂×C₇×#126	C₂²	semidirect
41. C₂×C₇×#126	C₂²	semidirect
42. C₂×C₇×#126	C₂²	semidirect
43. C₂×C₇×#125	C₂²	semidirect
44. C₂×C₇×#125	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
56. C₂×C₇×#123	C₂²	semidirect
57. C₂×C₇×#123	C₂²	semidirect
58. C₂×C₇×#123	C₂²	semidirect
63. C₂×C₇×C₂²⋊Q₈	C₂²	semidirect
64. C₂×C₇×C₂²⋊Q₈	C₂²	semidirect
65. C₂×C₇×C₂²⋊Q₈	C₂²	semidirect
66. C₂×C₇×C₂²⋊Q₈	C₂²	semidirect
67. C₂×C₇×C₂²⋊Q₈	C₂²	semidirect
68. C₂×C₇×C₂²⋊Q₈	C₂²	semidirect
69. C₂×C₇×C₂²⋊Q₈	C₂²	semidirect
73. C₂×C₇×#121	C₂²	semidirect
75. C₂×C₄×C₇×Q₈	C₂²	semidirect
76. C₂×C₄×C₇×Q₈	C₂²	semidirect
77. C₂×C₄×C₇×Q₈	C₂²	semidirect
78. C₂×C₄×C₇×Q₈	C₂²	semidirect
82. C₂×C₄×C₇×D₄	C₂²	semidirect
83. C₂×C₄×C₇×D₄	C₂²	semidirect
85. C₂×C₇×#117	C₂²	semidirect
86. C₂×C₇×#117	C₂²	semidirect
91. C₂×#3561	C₇	direct (N × H)
104. C₂²×C₇×Q₈	C₂³	semidirect
121. C₇×C₄⋊Q₈	C₂³	semidirect
122. C₇×C₄⋊Q₈	C₂³	semidirect
123. C₇×C₄⋊Q₈	C₂³	semidirect
124. C₇×C₄⋊Q₈	C₂³	semidirect
125. C₇×#126	C₂³	semidirect
126. C₇×#126	C₂³	semidirect
127. C₇×#126	C₂³	semidirect
128. C₇×#126	C₂³	semidirect
129. C₇×#125	C₂³	semidirect
130. C₇×#125	C₂³	semidirect
136. C₇×#124	C₂³	semidirect
137. C₇×#124	C₂³	semidirect
138. C₇×#124	C₂³	semidirect
141. C₇×#123	C₂³	semidirect
142. C₇×#123	C₂³	semidirect
143. C₇×#123	C₂³	semidirect
148. C₇×C₂²⋊Q₈	C₂³	semidirect
149. C₇×C₂²⋊Q₈	C₂³	semidirect
150. C₇×C₂²⋊Q₈	C₂³	semidirect
151. C₇×C₂²⋊Q₈	C₂³	semidirect
152. C₇×C₂²⋊Q₈	C₂³	semidirect
153. C₇×C₂²⋊Q₈	C₂³	semidirect
154. C₇×C₂²⋊Q₈	C₂³	semidirect
158. C₇×#121	C₂³	semidirect
160. C₄×C₇×Q₈	C₂³	semidirect
161. C₄×C₇×Q₈	C₂³	semidirect
162. C₄×C₇×Q₈	C₂³	semidirect
163. C₄×C₇×Q₈	C₂³	semidirect
167. C₄×C₇×D₄	C₂³	semidirect
168. C₄×C₇×D₄	C₂³	semidirect
170. C₇×#117	C₂³	semidirect
171. C₇×#117	C₂³	semidirect
214. #3561	C₂×C₇	direct (N × H)
215. C₂×#563	C₂×C₇	semidirect
216. C₂×#562	C₂×C₇	semidirect
217. C₂×#556	C₂×C₇	semidirect
218. C₂×#551	C₂×C₇	semidirect
219. C₂×D₄×Q₈	C₂×C₇	semidirect
220. C₂×#548	C₂×C₇	semidirect
221. C₂×#546	C₂×C₇	semidirect
222. C₂×#543	C₂×C₇	semidirect
223. C₂×#542	C₂×C₇	semidirect
224. C₂×#542	C₂×C₇	semidirect
225. C₂×#538	C₂×C₇	semidirect
226. C₂×#536	C₂×C₇	semidirect
227. C₂×#533	C₂×C₇	semidirect
228. C₂×#529	C₂×C₇	semidirect
229. C₂²×#124	C₂×C₇	semidirect
333. C₂³×Q₈	C₂²×C₇	semidirect
335. #563	C₂²×C₇	semidirect
336. #562	C₂²×C₇	semidirect
337. #556	C₂²×C₇	semidirect
338. #551	C₂²×C₇	semidirect
339. D₄×Q₈	C₂²×C₇	semidirect
340. #548	C₂²×C₇	semidirect
341. #546	C₂²×C₇	semidirect
342. #543	C₂²×C₇	semidirect
343. #542	C₂²×C₇	semidirect
344. #542	C₂²×C₇	semidirect
345. #538	C₂²×C₇	semidirect
346. #536	C₂²×C₇	semidirect
347. #533	C₂²×C₇	semidirect
348. C₂×C₄⋊Q₈	C₂²×C₇	semidirect
349. C₂×C₄⋊Q₈	C₂²×C₇	semidirect
350. C₂×C₄⋊Q₈	C₂²×C₇	semidirect
351. C₂×C₄⋊Q₈	C₂²×C₇	semidirect
352. #529	C₂²×C₇	semidirect
353. C₂×#126	C₂²×C₇	semidirect
354. C₂×#126	C₂²×C₇	semidirect
355. C₂×#126	C₂²×C₇	semidirect
356. C₂×#126	C₂²×C₇	semidirect
357. C₂×#125	C₂²×C₇	semidirect
358. C₂×#125	C₂²×C₇	semidirect
364. C₂×#124	C₂²×C₇	semidirect
365. C₂×#124	C₂²×C₇	semidirect
366. C₂×#124	C₂²×C₇	semidirect
367. C₂×#124	C₂²×C₇	semidirect
370. C₂×#123	C₂²×C₇	semidirect
371. C₂×#123	C₂²×C₇	semidirect
372. C₂×#123	C₂²×C₇	semidirect
377. C₂×C₂²⋊Q₈	C₂²×C₇	semidirect
378. C₂×C₂²⋊Q₈	C₂²×C₇	semidirect
379. C₂×C₂²⋊Q₈	C₂²×C₇	semidirect
380. C₂×C₂²⋊Q₈	C₂²×C₇	semidirect
381. C₂×C₂²⋊Q₈	C₂²×C₇	semidirect
382. C₂×C₂²⋊Q₈	C₂²×C₇	semidirect
383. C₂×C₂²⋊Q₈	C₂²×C₇	semidirect
387. C₂×#121	C₂²×C₇	semidirect
389. C₂×C₄×Q₈	C₂²×C₇	semidirect
390. C₂×C₄×Q₈	C₂²×C₇	semidirect
391. C₂×C₄×Q₈	C₂²×C₇	semidirect
392. C₂×C₄×Q₈	C₂²×C₇	semidirect
396. C₂×C₄×D₄	C₂²×C₇	semidirect
397. C₂×C₄×D₄	C₂²×C₇	semidirect
399. C₂×#117	C₂²×C₇	semidirect
400. C₂×#117	C₂²×C₇	semidirect
478. C₂²×Q₈	C₂³×C₇	semidirect
495. C₄⋊Q₈	C₂³×C₇	semidirect
496. C₄⋊Q₈	C₂³×C₇	semidirect
497. C₄⋊Q₈	C₂³×C₇	semidirect
498. C₄⋊Q₈	C₂³×C₇	semidirect
499. #126	C₂³×C₇	semidirect
500. #126	C₂³×C₇	semidirect
501. #126	C₂³×C₇	semidirect
502. #126	C₂³×C₇	semidirect
503. #125	C₂³×C₇	semidirect
504. #125	C₂³×C₇	semidirect
510. #124	C₂³×C₇	semidirect
511. #124	C₂³×C₇	semidirect
512. #124	C₂³×C₇	semidirect
515. #123	C₂³×C₇	semidirect
516. #123	C₂³×C₇	semidirect
517. #123	C₂³×C₇	semidirect
522. C₂²⋊Q₈	C₂³×C₇	semidirect
523. C₂²⋊Q₈	C₂³×C₇	semidirect
524. C₂²⋊Q₈	C₂³×C₇	semidirect
525. C₂²⋊Q₈	C₂³×C₇	semidirect
526. C₂²⋊Q₈	C₂³×C₇	semidirect
527. C₂²⋊Q₈	C₂³×C₇	semidirect
528. C₂²⋊Q₈	C₂³×C₇	semidirect
532. #121	C₂³×C₇	semidirect
534. C₄×Q₈	C₂³×C₇	semidirect
535. C₄×Q₈	C₂³×C₇	semidirect
536. C₄×Q₈	C₂³×C₇	semidirect
537. C₄×Q₈	C₂³×C₇	semidirect
541. C₄×D₄	C₂³×C₇	semidirect
542. C₄×D₄	C₂³×C₇	semidirect
544. #117	C₂³×C₇	semidirect
545. #117	C₂³×C₇	semidirect
721. C₂×C₇	#3561	direct (N × H)
786. C₇	C₂×#3561	direct (N × H)
819. C₂	C₇×#3561	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×#3561	2
C₂×C₇×#563	2
C₂×C₇×#562	2
C₂×C₇×#556	2
C₂×C₇×#551	2
C₂×C₇×D₄×Q₈	2
C₂×C₇×#548	2
C₂×C₇×#546	2
C₂×C₇×#543	2
C₂×C₇×#542	2
C₂×C₇×#538	2
C₂×C₇×#536	2
C₂×C₇×#533	2
C₂×C₇×#529	2
C₂²×C₇×#124	2
C₂×#3561	7

Subgroups — C2×C7×#3561 #13239947

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₇×#3561 #13239947