Subgroups — C₂×C₇×#3540 #13239944

Order 1792.

7418 conjugacy classes of subgroups.

The subgroup lattice has 860 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×#3540	C₂	1	32	yes	maximal, direct product factor
2	C₂×C₇×H(3,𝔽₄)	C₂	1	2	yes	maximal, complemented
3	C₂×C₇×#560	C₂	1	2	yes	maximal, complemented
4	C₂×C₇×#559	C₂	1	2	yes	maximal, complemented
5	C₂×C₇×#556	C₂	1	2	yes	maximal, complemented
6	C₂×C₇×#555	C₂	1	2	yes	maximal, complemented
7	C₂×C₇×#551	C₂	1	2	yes	maximal, complemented
8	C₂×C₇×#548	C₂	1	2	yes	maximal, complemented
9	C₂×C₇×#546	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	4	yes	maximal, complemented
13	C₂×C₇×#536	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂×C₇×#535	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂×C₇×#525	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×C₇×#525	C₂	1	2	yes	maximal, complemented
17	C₂²×C₇×#41	C₂²	1	1	yes	characteristic
18	C₂²×C₇×#41	C₂²	1	2	yes	—
19	C₂³×C₇×Q₈	C₂²	1	1	yes	characteristic, complemented
20	C₂³×C₇×D₄	C₂²	1	1	yes	characteristic, complemented
21	C₂⁴×C₄×C₇	C₂²	1	1	yes	characteristic, complemented
22	C₇×H(3,𝔽₄)	C₂²	1	32	yes	complemented
23	C₇×#560	C₂²	1	32	yes	complemented
24	C₇×#559	C₂²	1	32	yes	complemented
25	C₇×#556	C₂²	1	32	yes	complemented
26	C₇×#555	C₂²	1	32	yes	complemented
27	C₇×#551	C₂²	1	32	yes	complemented
28	C₇×#548	C₂²	1	32	yes	complemented
29	C₇×#546	C₂²	1	32	yes	complemented
30	C₇×#542	C₂²	1	32	yes	complemented
31	C₇×#542	C₂²	1	64	yes	complemented
32	C₇×#538	C₂²	1	64	yes	complemented
33	C₇×#536	C₂²	1	16	yes	complemented
34	C₇×#535	C₂²	1	16	yes	complemented
35	C₂×C₇×C₄⋊Q₈	C₂²	1	2	yes	complemented
36	C₂×C₇×C₄⋊Q₈	C₂²	1	2	yes	complemented
37	C₂×C₇×#127	C₂²	1	2	yes	—
38	C₂×C₇×#126	C₂²	1	4	yes	complemented
39	C₂×C₇×#126	C₂²	1	4	yes	complemented
40	C₂×C₇×#126	C₂²	1	4	yes	complemented
41	C₂×C₇×#124	C₂²	1	2	yes	—
42	C₂×C₇×#124	C₂²	1	4	yes	—
43	C₂×C₇×#124	C₂²	1	2	yes	complemented
44	C₂×C₇×#124	C₂²	1	4	yes	complemented
45	C₂×C₇×#124	C₂²	1	2	yes	complemented
46	C₂×C₇×#124	C₂²	1	4	yes	complemented
47	C₂×C₇×#124	C₂²	1	4	yes	complemented
48	C₂×C₇×#124	C₂²	1	4	yes	complemented
49	C₇×#525	C₂²	1	16	yes	complemented
50	C₇×#525	C₂²	1	32	yes	complemented
51	C₂×C₇×#123	C₂²	1	1	yes	characteristic
52	C₂×C₇×#123	C₂²	1	4	yes	complemented
53	C₂×C₇×#123	C₂²	1	1	yes	characteristic, complemented
54	C₂×C₇×#123	C₂²	1	2	yes	complemented
55	C₂×C₇×#123	C₂²	1	2	yes	complemented
56	C₂×C₇×#123	C₂²	1	4	yes	complemented
57	C₂×C₇×#123	C₂²	1	4	yes	complemented
58	C₂×C₇×C₂²⋊Q₈	C₂²	1	2	yes	complemented
59	C₂×C₇×C₂²⋊Q₈	C₂²	1	2	yes	complemented
60	C₂×C₇×C₂²⋊Q₈	C₂²	1	2	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×C₂²⋊Q₈	C₂²	1	4	yes	complemented
64	C₂×C₇×#121	C₂²	1	2	yes	—
65	C₂×C₇×#121	C₂²	1	2	yes	—
66	C₂×C₇×#121	C₂²	1	2	yes	—
67	C₂×C₇×#121	C₂²	1	4	yes	—
68	C₂×C₇×#121	C₂²	1	2	yes	complemented
69	C₂×C₇×#121	C₂²	1	4	yes	complemented
70	C₂×C₇×#121	C₂²	1	4	yes	complemented
71	C₂×C₇×#120	C₂²	1	1	yes	characteristic
72	C₂×C₇×#120	C₂²	1	2	yes	—
73	C₂×C₇×#120	C₂²	1	4	yes	—
74	C₂×C₇×#120	C₂²	1	1	yes	characteristic, complemented
75	C₂×C₇×#120	C₂²	1	4	yes	complemented
76	C₂×C₇×#120	C₂²	1	2	yes	complemented
77	C₂×C₄×C₇×Q₈	C₂²	1	2	yes	complemented
78	C₂×C₄×C₇×Q₈	C₂²	1	4	yes	complemented
79	C₂×C₄×C₇×D₄	C₂²	1	2	yes	—
80	C₂×C₄×C₇×D₄	C₂²	1	4	yes	complemented
81	C₂×C₄×C₇×D₄	C₂²	1	2	yes	complemented
82	C₂×C₄×C₇×D₄	C₂²	1	4	yes	complemented
83	C₂×C₄×C₇×D₄	C₂²	1	4	yes	complemented
84	C₂×C₄×C₇×D₄	C₂²	1	2	yes	complemented
85	C₂×C₇×#117	C₂²	1	1	yes	characteristic, complemented
86	C₂×C₇×#117	C₂²	1	2	yes	complemented
87	C₂×C₇×#117	C₂²	1	1	yes	characteristic, complemented
88	C₂×C₇×#117	C₂²	1	1	yes	characteristic, complemented
89	C₂×C₇×#117	C₂²	1	4	yes	complemented
90	C₂²×C₇×C₂²⋊C₄	C₂²	1	4	yes	complemented
91	C₂×#3540	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
92	C₂⁵×C₇	C₂³	1	2	yes	—
93	C₂⁵×C₇	C₂³	1	1	yes	characteristic
94	C₂×C₇×#41	—	4	4	no	—
95	C₂×C₇×#41	—	4	8	no	—
96	C₂×C₇×#41	C₂³	1	8	yes	—
97	C₂×C₇×#41	C₂³	1	16	yes	—
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	1	yes	characteristic
102	C₂²×C₇×Q₈	C₂³	1	4	yes	—
103	C₂²×C₇×Q₈	C₂³	1	8	yes	complemented
104	C₂²×C₇×D₄	—	4	4	no	—
105	C₂²×C₇×D₄	C₂³	1	2	yes	—
106	C₂²×C₇×D₄	C₂³	1	2	yes	—
107	C₂²×C₇×D₄	C₂³	1	1	yes	characteristic
108	C₂²×C₇×D₄	C₂³	1	4	yes	—
109	C₂²×C₇×D₄	C₂³	1	1	yes	characteristic
110	C₂²×C₇×D₄	C₂³	1	1	yes	characteristic
111	C₂²×C₇×D₄	C₂³	1	2	yes	—
112	C₂²×C₇×D₄	C₂³	1	4	yes	—
113	C₂²×C₇×D₄	C₂³	1	4	yes	—
114	C₂²×C₇×D₄	C₂³	1	2	yes	—
115	C₂²×C₇×D₄	C₂³	1	4	yes	—
116	C₂²×C₇×D₄	C₂³	1	8	yes	complemented
117	C₂³×C₄×C₇	—	4	4	no	—
118	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
119	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
120	C₂³×C₄×C₇	C₂³	1	2	yes	—
121	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
122	C₂³×C₄×C₇	C₂³	1	2	yes	—
123	C₂³×C₄×C₇	C₂³	1	4	yes	—
124	C₂³×C₄×C₇	C₂³	1	4	yes	—
125	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
126	C₂³×C₄×C₇	C₂³	1	2	yes	—
127	C₂³×C₄×C₇	C₂³	1	8	yes	complemented
128	C₇×C₄⋊Q₈	C₂³	1	16	yes	complemented
129	C₇×C₄⋊Q₈	C₂³	1	16	yes	complemented
130	C₇×#127	C₂³	1	16	yes	—
131	C₇×#126	C₂³	1	32	yes	complemented
132	C₇×#126	C₂³	1	32	yes	complemented
133	C₇×#126	C₂³	1	32	yes	complemented
134	C₇×#124	C₂³	1	16	yes	—
135	C₇×#124	C₂³	1	32	yes	—
136	C₇×#124	C₂³	1	16	yes	complemented
137	C₇×#124	C₂³	1	32	yes	complemented
138	C₇×#124	C₂³	1	16	yes	complemented
139	C₇×#124	C₂³	1	32	yes	complemented
140	C₇×#124	C₂³	1	32	yes	complemented
141	C₇×#124	C₂³	1	32	yes	complemented
142	C₇×#123	C₂³	1	8	yes	—
143	C₇×#123	C₂³	1	32	yes	complemented
144	C₇×#123	C₂³	1	8	yes	complemented
145	C₇×#123	C₂³	1	16	yes	complemented
146	C₇×#123	C₂³	1	16	yes	complemented
147	C₇×#123	C₂³	1	32	yes	complemented
148	C₇×#123	C₂³	1	32	yes	complemented
149	C₇×C₂²⋊Q₈	C₂³	1	16	yes	complemented
150	C₇×C₂²⋊Q₈	C₂³	1	16	yes	complemented
151	C₇×C₂²⋊Q₈	C₂³	1	16	yes	complemented
152	C₇×C₂²⋊Q₈	C₂³	1	16	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	16	yes	—
156	C₇×#121	C₂³	1	16	yes	—
157	C₇×#121	C₂³	1	16	yes	—
158	C₇×#121	C₂³	1	32	yes	—
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×#120	C₂³	1	8	yes	—
163	C₇×#120	C₂³	1	16	yes	—
164	C₇×#120	C₂³	1	32	yes	—
165	C₇×#120	C₂³	1	8	yes	complemented
166	C₇×#120	C₂³	1	32	yes	complemented
167	C₇×#120	C₂³	1	16	yes	complemented
168	C₄×C₇×Q₈	C₂³	1	16	yes	complemented
169	C₄×C₇×Q₈	C₂³	1	32	yes	complemented
170	C₄×C₇×D₄	C₂³	1	16	yes	—
171	C₄×C₇×D₄	C₂³	1	32	yes	complemented
172	C₄×C₇×D₄	C₂³	1	16	yes	complemented
173	C₄×C₇×D₄	C₂³	1	32	yes	complemented
174	C₄×C₇×D₄	C₂³	1	32	yes	complemented
175	C₄×C₇×D₄	C₂³	1	16	yes	complemented
176	C₇×#117	C₂³	1	8	yes	complemented
177	C₇×#117	C₂³	1	16	yes	complemented
178	C₇×#117	C₂³	1	8	yes	complemented
179	C₇×#117	C₂³	1	8	yes	complemented
180	C₇×#117	C₂³	1	32	yes	complemented
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	4	yes	—
188	C₂×C₇×C₄⋊C₄	C₂³	1	4	yes	—
189	C₂×C₇×C₄⋊C₄	C₂³	1	4	yes	—
190	C₂×C₇×C₄⋊C₄	C₂³	1	4	yes	—
191	C₂×C₇×C₂²⋊C₄	C₂³	1	2	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	2	yes	—
196	C₂×C₇×C₂²⋊C₄	C₂³	1	4	yes	—
197	C₂×C₇×C₂²⋊C₄	C₂³	1	1	yes	characteristic
198	C₂×C₇×C₂²⋊C₄	C₂³	1	4	yes	—
199	C₂×C₇×C₂²⋊C₄	C₂³	1	1	yes	characteristic
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	2	yes	—
203	C₂×C₇×C₂²⋊C₄	C₂³	1	4	yes	—
204	C₂×C₇×C₂²⋊C₄	C₂³	1	2	yes	—
205	C₂×C₇×C₂²⋊C₄	C₂³	1	4	yes	—
206	C₂×C₇×C₂²⋊C₄	C₂³	1	4	yes	—
207	C₂×C₇×C₂²⋊C₄	C₂³	1	4	yes	—
208	C₂×C₇×C₂²⋊C₄	C₂³	1	4	yes	—
209	C₂×C₇×C₂²⋊C₄	C₂³	1	32	yes	complemented
210	C₂×C₄²×C₇	C₂³	1	2	yes	—
211	C₂×C₄²×C₇	C₂³	1	4	yes	—
212	C₂×C₄²×C₇	C₂³	1	2	yes	—
213	C₂×C₄²×C₇	C₂³	1	2	yes	—
214	C₂×C₄²×C₇	C₂³	1	4	yes	—
215	#3540	C₂×C₇	1	32	yes	direct product factor
216	C₂×H(3,𝔽₄)	C₂×C₇	1	2	yes	complemented
217	C₂×#560	C₂×C₇	1	2	yes	complemented
218	C₂×#559	C₂×C₇	1	2	yes	complemented
219	C₂×#556	C₂×C₇	1	2	yes	complemented
220	C₂×#555	C₂×C₇	1	2	yes	complemented
221	C₂×#551	C₂×C₇	1	2	yes	complemented
222	C₂×#548	C₂×C₇	1	2	yes	complemented
223	C₂×#546	C₂×C₇	1	2	yes	complemented
224	C₂×#542	C₂×C₇	1	2	yes	complemented
225	C₂×#542	C₂×C₇	1	4	yes	complemented
226	C₂×#538	C₂×C₇	1	4	yes	complemented
227	C₂×#536	C₂×C₇	1	1	yes	characteristic, complemented
228	C₂×#535	C₂×C₇	1	1	yes	characteristic, complemented
229	C₂×#525	C₂×C₇	1	1	yes	characteristic, complemented
230	C₂×#525	C₂×C₇	1	2	yes	complemented
231	C₂⁴×C₇	—	4	2	no	—
232	C₂⁴×C₇	—	4	4	no	—
233	C₂⁴×C₇	—	4	4	no	—
234	C₂⁴×C₇	—	4	8	no	—
235	C₂⁴×C₇	C₂⁴	1	1	yes	characteristic
236	C₂⁴×C₇	C₂⁴	1	1	yes	characteristic
237	C₂⁴×C₇	C₂⁴	1	2	yes	—
238	C₂⁴×C₇	C₂⁴	1	4	yes	—
239	C₂⁴×C₇	C₂⁴	1	1	yes	characteristic
240	C₂⁴×C₇	C₂⁴	1	8	yes	—
241	C₂⁴×C₇	C₂⁴	1	4	yes	—
242	C₇×#41	—	4	16	no	—
243	C₇×#41	—	4	32	no	—
244	C₂×C₇×Q₈	—	2	8	no	—
245	C₂×C₇×Q₈	—	4	4	no	—
246	C₂×C₇×Q₈	—	4	8	no	—
247	C₂×C₇×Q₈	—	4	2	no	—
248	C₂×C₇×Q₈	—	4	16	no	—
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×Q₈	C₂⁴	1	4	yes	—
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	4	no	—
257	C₂×C₇×D₄	—	4	8	no	—
258	C₂×C₇×D₄	—	4	8	no	—
259	C₂×C₇×D₄	—	4	8	no	—
260	C₂×C₇×D₄	—	4	4	no	—
261	C₂×C₇×D₄	—	4	2	no	—
262	C₂×C₇×D₄	—	4	2	no	—
263	C₂×C₇×D₄	—	4	2	no	—
264	C₂×C₇×D₄	—	4	8	no	—
265	C₂×C₇×D₄	C₂⁴	1	8	yes	—
266	C₂×C₇×D₄	C₂⁴	1	8	yes	—
267	C₂×C₇×D₄	C₂⁴	1	16	yes	—
268	C₂×C₇×D₄	C₂⁴	1	16	yes	—
269	C₂×C₇×D₄	C₂⁴	1	8	yes	—
270	C₂×C₇×D₄	C₂⁴	1	16	yes	—
271	C₂×C₇×D₄	C₂⁴	1	4	yes	—
272	C₂×C₇×D₄	C₂⁴	1	16	yes	—
273	C₂×C₇×D₄	C₂⁴	1	4	yes	—
274	C₂×C₇×D₄	C₂⁴	1	4	yes	—
275	C₂×C₇×D₄	C₂⁴	1	8	yes	—
276	C₂²×C₄×C₇	—	2	8	no	—
277	C₂²×C₄×C₇	—	2	4	no	—
278	C₂²×C₄×C₇	—	2	4	no	—
279	C₂²×C₄×C₇	—	2	4	no	—
280	C₂²×C₄×C₇	—	4	16	no	—
281	C₂²×C₄×C₇	—	4	2	no	—
282	C₂²×C₄×C₇	—	4	4	no	—
283	C₂²×C₄×C₇	—	4	8	no	—
284	C₂²×C₄×C₇	—	4	4	no	—
285	C₂²×C₄×C₇	—	4	8	no	—
286	C₂²×C₄×C₇	C₂⁴	1	4	yes	—
287	C₂²×C₄×C₇	C₂⁴	1	8	yes	—
288	C₂²×C₄×C₇	C₂⁴	1	4	yes	—
289	C₂²×C₄×C₇	C₂⁴	1	4	yes	—
290	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
291	C₂²×C₄×C₇	C₂⁴	1	4	yes	—
292	C₂²×C₄×C₇	C₂⁴	1	4	yes	—
293	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
294	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
295	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
296	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
297	C₂²×C₄×C₇	C₂⁴	1	4	yes	—
298	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
299	C₂²×C₄×C₇	C₂⁴	1	16	yes	—
300	C₂²×C₄×C₇	C₂⁴	1	16	yes	—
301	C₂²×C₄×C₇	C₂⁴	1	4	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	C₇×C₄⋊C₄	C₂⁴	1	8	yes	—
306	C₇×C₄⋊C₄	C₂⁴	1	8	yes	—
307	C₇×C₄⋊C₄	C₂⁴	1	8	yes	—
308	C₇×C₄⋊C₄	C₂⁴	1	8	yes	—
309	C₇×C₄⋊C₄	C₂⁴	1	16	yes	—
310	C₇×C₄⋊C₄	C₂⁴	1	8	yes	—
311	C₇×C₄⋊C₄	C₂⁴	1	16	yes	—
312	C₇×C₄⋊C₄	C₂⁴	1	16	yes	—
313	C₇×C₄⋊C₄	C₂⁴	1	16	yes	—
314	C₇×C₄⋊C₄	C₂⁴	1	16	yes	—
315	C₇×C₂²⋊C₄	C₂⁴	1	8	yes	—
316	C₇×C₂²⋊C₄	C₂⁴	1	16	yes	—
317	C₇×C₂²⋊C₄	C₂⁴	1	16	yes	—
318	C₇×C₂²⋊C₄	C₂⁴	1	16	yes	—
319	C₇×C₂²⋊C₄	C₂⁴	1	8	yes	—
320	C₇×C₂²⋊C₄	C₂⁴	1	16	yes	—
321	C₇×C₂²⋊C₄	C₂⁴	1	4	yes	—
322	C₇×C₂²⋊C₄	C₂⁴	1	16	yes	—
323	C₇×C₂²⋊C₄	C₂⁴	1	4	yes	—
324	C₇×C₂²⋊C₄	C₂⁴	1	8	yes	—
325	C₇×C₂²⋊C₄	C₂⁴	1	8	yes	—
326	C₇×C₂²⋊C₄	C₂⁴	1	8	yes	—
327	C₇×C₂²⋊C₄	C₂⁴	1	16	yes	—
328	C₇×C₂²⋊C₄	C₂⁴	1	8	yes	—
329	C₇×C₂²⋊C₄	C₂⁴	1	16	yes	—
330	C₇×C₂²⋊C₄	C₂⁴	1	16	yes	—
331	C₇×C₂²⋊C₄	C₂⁴	1	16	yes	—
332	C₇×C₂²⋊C₄	C₂⁴	1	16	yes	—
333	C₄²×C₇	C₂⁴	1	8	yes	—
334	C₄²×C₇	C₂⁴	1	16	yes	—
335	C₄²×C₇	C₂⁴	1	8	yes	—
336	C₄²×C₇	C₂⁴	1	8	yes	—
337	C₄²×C₇	C₂⁴	1	16	yes	—
338	C₂²×#41	C₂²×C₇	1	1	yes	characteristic
339	C₂²×#41	C₂²×C₇	1	2	yes	—
340	C₂³×Q₈	C₂²×C₇	1	1	yes	characteristic, complemented
341	C₂³×D₄	C₂²×C₇	1	1	yes	characteristic, complemented
342	C₂⁴×C₄	C₂²×C₇	1	1	yes	characteristic, complemented
343	H(3,𝔽₄)	C₂²×C₇	1	32	yes	complemented
344	#560	C₂²×C₇	1	32	yes	complemented
345	#559	C₂²×C₇	1	32	yes	complemented
346	#556	C₂²×C₇	1	32	yes	complemented
347	#555	C₂²×C₇	1	32	yes	complemented
348	#551	C₂²×C₇	1	32	yes	complemented
349	#548	C₂²×C₇	1	32	yes	complemented
350	#546	C₂²×C₇	1	32	yes	complemented
351	#542	C₂²×C₇	1	32	yes	complemented
352	#542	C₂²×C₇	1	64	yes	complemented
353	#538	C₂²×C₇	1	64	yes	complemented
354	#536	C₂²×C₇	1	16	yes	complemented
355	#535	C₂²×C₇	1	16	yes	complemented
356	C₂×C₄⋊Q₈	C₂²×C₇	1	2	yes	complemented
357	C₂×C₄⋊Q₈	C₂²×C₇	1	2	yes	complemented
358	C₂×#127	C₂²×C₇	1	2	yes	—
359	C₂×#126	C₂²×C₇	1	4	yes	complemented
360	C₂×#126	C₂²×C₇	1	4	yes	complemented
361	C₂×#126	C₂²×C₇	1	4	yes	complemented
362	C₂×#124	C₂²×C₇	1	2	yes	—
363	C₂×#124	C₂²×C₇	1	4	yes	—
364	C₂×#124	C₂²×C₇	1	2	yes	complemented
365	C₂×#124	C₂²×C₇	1	4	yes	complemented
366	C₂×#124	C₂²×C₇	1	2	yes	complemented
367	C₂×#124	C₂²×C₇	1	4	yes	complemented
368	C₂×#124	C₂²×C₇	1	4	yes	complemented
369	C₂×#124	C₂²×C₇	1	4	yes	complemented
370	#525	C₂²×C₇	1	16	yes	complemented
371	#525	C₂²×C₇	1	32	yes	complemented
372	C₂×#123	C₂²×C₇	1	1	yes	characteristic
373	C₂×#123	C₂²×C₇	1	4	yes	complemented
374	C₂×#123	C₂²×C₇	1	1	yes	characteristic, complemented
375	C₂×#123	C₂²×C₇	1	2	yes	complemented
376	C₂×#123	C₂²×C₇	1	2	yes	complemented
377	C₂×#123	C₂²×C₇	1	4	yes	complemented
378	C₂×#123	C₂²×C₇	1	4	yes	complemented
379	C₂×C₂²⋊Q₈	C₂²×C₇	1	2	yes	complemented
380	C₂×C₂²⋊Q₈	C₂²×C₇	1	2	yes	complemented
381	C₂×C₂²⋊Q₈	C₂²×C₇	1	2	yes	complemented
382	C₂×C₂²⋊Q₈	C₂²×C₇	1	2	yes	complemented
383	C₂×C₂²⋊Q₈	C₂²×C₇	1	4	yes	complemented
384	C₂×C₂²⋊Q₈	C₂²×C₇	1	4	yes	complemented
385	C₂×#121	C₂²×C₇	1	2	yes	—
386	C₂×#121	C₂²×C₇	1	2	yes	—
387	C₂×#121	C₂²×C₇	1	2	yes	—
388	C₂×#121	C₂²×C₇	1	4	yes	—
389	C₂×#121	C₂²×C₇	1	2	yes	complemented
390	C₂×#121	C₂²×C₇	1	4	yes	complemented
391	C₂×#121	C₂²×C₇	1	4	yes	complemented
392	C₂×#120	C₂²×C₇	1	1	yes	characteristic
393	C₂×#120	C₂²×C₇	1	2	yes	—
394	C₂×#120	C₂²×C₇	1	4	yes	—
395	C₂×#120	C₂²×C₇	1	1	yes	characteristic, complemented
396	C₂×#120	C₂²×C₇	1	4	yes	complemented
397	C₂×#120	C₂²×C₇	1	2	yes	complemented
398	C₂×C₄×Q₈	C₂²×C₇	1	2	yes	complemented
399	C₂×C₄×Q₈	C₂²×C₇	1	4	yes	complemented
400	C₂×C₄×D₄	C₂²×C₇	1	2	yes	—
401	C₂×C₄×D₄	C₂²×C₇	1	4	yes	complemented
402	C₂×C₄×D₄	C₂²×C₇	1	2	yes	complemented
403	C₂×C₄×D₄	C₂²×C₇	1	4	yes	complemented
404	C₂×C₄×D₄	C₂²×C₇	1	4	yes	complemented
405	C₂×C₄×D₄	C₂²×C₇	1	2	yes	complemented
406	C₂×#117	C₂²×C₇	1	1	yes	characteristic, complemented
407	C₂×#117	C₂²×C₇	1	2	yes	complemented
408	C₂×#117	C₂²×C₇	1	1	yes	characteristic, complemented
409	C₂×#117	C₂²×C₇	1	1	yes	characteristic, complemented
410	C₂×#117	C₂²×C₇	1	4	yes	complemented
411	C₂²×C₂²⋊C₄	C₂²×C₇	1	4	yes	complemented
412	C₂³×C₇	—	2	2	no	—
413	C₂³×C₇	—	2	4	no	—
414	C₂³×C₇	—	2	2	no	—
415	C₂³×C₇	—	2	2	no	—
416	C₂³×C₇	—	2	8	no	—
417	C₂³×C₇	—	2	8	no	—
418	C₂³×C₇	—	2	4	no	—
419	C₂³×C₇	—	2	4	no	—
420	C₂³×C₇	—	2	4	no	—
421	C₂³×C₇	—	2	4	no	—
422	C₂³×C₇	—	2	8	no	—
423	C₂³×C₇	—	2	4	no	—
424	C₂³×C₇	—	4	4	no	—
425	C₂³×C₇	—	4	8	no	—
426	C₂³×C₇	—	4	8	no	—
427	C₂³×C₇	—	4	16	no	—
428	C₂³×C₇	—	4	16	no	—
429	C₂³×C₇	—	8	16	no	—
430	C₂³×C₇	C₂⁵	1	2	yes	—
431	C₂³×C₇	C₂⁵	1	2	yes	—
432	C₂³×C₇	C₂⁵	1	4	yes	—
433	C₂³×C₇	C₂⁵	1	8	yes	—
434	C₂³×C₇	C₂⁵	1	2	yes	—
435	C₂³×C₇	C₂⁵	1	1	yes	characteristic
436	C₇×Q₈	—	2	16	no	—
437	C₇×Q₈	—	4	8	no	—
438	C₇×Q₈	—	4	16	no	—
439	C₇×Q₈	—	4	4	no	—
440	C₇×D₄	—	2	16	no	—
441	C₇×D₄	—	4	8	no	—
442	C₇×D₄	—	4	8	no	—
443	C₇×D₄	—	4	16	no	—
444	C₇×D₄	—	4	16	no	—
445	C₇×D₄	—	4	16	no	—
446	C₇×D₄	—	4	8	no	—
447	C₇×D₄	—	4	4	no	—
448	C₇×D₄	—	4	4	no	—
449	C₇×D₄	—	4	4	no	—
450	C₇×D₄	—	4	16	no	—
451	C₂×C₄×C₇	—	2	4	no	—
452	C₂×C₄×C₇	—	2	2	no	—
453	C₂×C₄×C₇	—	2	2	no	—
454	C₂×C₄×C₇	—	2	2	no	—
455	C₂×C₄×C₇	—	2	8	no	—
456	C₂×C₄×C₇	—	2	4	no	—
457	C₂×C₄×C₇	—	2	8	no	—
458	C₂×C₄×C₇	—	2	8	no	—
459	C₂×C₄×C₇	—	2	4	no	—
460	C₂×C₄×C₇	—	2	16	no	—
461	C₂×C₄×C₇	—	2	8	no	—
462	C₂×C₄×C₇	—	2	8	no	—
463	C₂×C₄×C₇	—	2	8	no	—
464	C₂×C₄×C₇	—	4	4	no	—
465	C₂×C₄×C₇	—	4	8	no	—
466	C₂×C₄×C₇	—	4	16	no	—
467	C₂×C₄×C₇	—	4	8	no	—
468	C₂×C₄×C₇	—	4	16	no	—
469	C₂×C₄×C₇	H(5,𝔽₂)	1	4	yes	—
470	C₂×C₄×C₇	C₂⁵	1	4	yes	—
471	C₂×C₄×C₇	C₂⁵	1	8	yes	—
472	C₂×C₄×C₇	C₂⁵	1	8	yes	—
473	C₂×C₄×C₇	C₂⁵	1	2	yes	—
474	C₂×C₄×C₇	C₂⁵	1	4	yes	—
475	C₂×C₄×C₇	C₂⁵	1	2	yes	—
476	C₂×C₄×C₇	C₂⁵	1	4	yes	—
477	C₂×C₄×C₇	C₂⁵	1	8	yes	—
478	C₂×C₄×C₇	C₂⁵	1	2	yes	—
479	C₂×C₄×C₇	C₂⁵	1	2	yes	—
480	C₂⁵	C₂³×C₇	1	2	yes	—
481	C₂⁵	C₂³×C₇	1	1	yes	characteristic
482	C₂×#41	—	4	4	no	—
483	C₂×#41	—	4	8	no	—
484	C₂×#41	C₂³×C₇	1	8	yes	—
485	C₂×#41	C₂³×C₇	1	16	yes	—
486	C₂²×Q₈	—	4	4	no	—
487	C₂²×Q₈	C₂³×C₇	1	2	yes	—
488	C₂²×Q₈	C₂³×C₇	1	4	yes	—
489	C₂²×Q₈	C₂³×C₇	1	2	yes	—
490	C₂²×Q₈	C₂³×C₇	1	1	yes	characteristic
491	C₂²×Q₈	C₂³×C₇	1	8	yes	complemented
492	C₂²×D₄	—	4	4	no	—
493	C₂²×D₄	C₂³×C₇	1	2	yes	—
494	C₂²×D₄	C₂³×C₇	1	2	yes	—
495	C₂²×D₄	C₂³×C₇	1	4	yes	—
496	C₂²×D₄	C₂³×C₇	1	4	yes	—
497	C₂²×D₄	C₂³×C₇	1	2	yes	—
498	C₂²×D₄	C₂³×C₇	1	4	yes	—
499	C₂²×D₄	C₂³×C₇	1	1	yes	characteristic
500	C₂²×D₄	C₂³×C₇	1	4	yes	—
501	C₂²×D₄	C₂³×C₇	1	1	yes	characteristic
502	C₂²×D₄	C₂³×C₇	1	1	yes	characteristic
503	C₂²×D₄	C₂³×C₇	1	2	yes	—
504	C₂²×D₄	C₂³×C₇	1	8	yes	complemented
505	C₂³×C₄	—	4	4	no	—
506	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
507	C₂³×C₄	C₂³×C₇	1	2	yes	—
508	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
509	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
510	C₂³×C₄	C₂³×C₇	1	4	yes	—
511	C₂³×C₄	C₂³×C₇	1	4	yes	—
512	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
513	C₂³×C₄	C₂³×C₇	1	2	yes	—
514	C₂³×C₄	C₂³×C₇	1	2	yes	—
515	C₂³×C₄	C₂³×C₇	1	8	yes	complemented
516	C₄⋊Q₈	C₂³×C₇	1	16	yes	complemented
517	C₄⋊Q₈	C₂³×C₇	1	16	yes	complemented
518	#127	C₂³×C₇	1	16	yes	—
519	#126	C₂³×C₇	1	32	yes	complemented
520	#126	C₂³×C₇	1	32	yes	complemented
521	#126	C₂³×C₇	1	32	yes	complemented
522	#124	C₂³×C₇	1	16	yes	—
523	#124	C₂³×C₇	1	32	yes	—
524	#124	C₂³×C₇	1	16	yes	complemented
525	#124	C₂³×C₇	1	32	yes	complemented
526	#124	C₂³×C₇	1	16	yes	complemented
527	#124	C₂³×C₇	1	32	yes	complemented
528	#124	C₂³×C₇	1	32	yes	complemented
529	#124	C₂³×C₇	1	32	yes	complemented
530	#123	C₂³×C₇	1	8	yes	—
531	#123	C₂³×C₇	1	32	yes	complemented
532	#123	C₂³×C₇	1	8	yes	complemented
533	#123	C₂³×C₇	1	16	yes	complemented
534	#123	C₂³×C₇	1	16	yes	complemented
535	#123	C₂³×C₇	1	32	yes	complemented
536	#123	C₂³×C₇	1	32	yes	complemented
537	C₂²⋊Q₈	C₂³×C₇	1	16	yes	complemented
538	C₂²⋊Q₈	C₂³×C₇	1	16	yes	complemented
539	C₂²⋊Q₈	C₂³×C₇	1	16	yes	complemented
540	C₂²⋊Q₈	C₂³×C₇	1	16	yes	complemented
541	C₂²⋊Q₈	C₂³×C₇	1	32	yes	complemented
542	C₂²⋊Q₈	C₂³×C₇	1	32	yes	complemented
543	#121	C₂³×C₇	1	16	yes	—
544	#121	C₂³×C₇	1	16	yes	—
545	#121	C₂³×C₇	1	16	yes	—
546	#121	C₂³×C₇	1	32	yes	—
547	#121	C₂³×C₇	1	16	yes	complemented
548	#121	C₂³×C₇	1	32	yes	complemented
549	#121	C₂³×C₇	1	32	yes	complemented
550	#120	C₂³×C₇	1	8	yes	—
551	#120	C₂³×C₇	1	16	yes	—
552	#120	C₂³×C₇	1	32	yes	—
553	#120	C₂³×C₇	1	8	yes	complemented
554	#120	C₂³×C₇	1	32	yes	complemented
555	#120	C₂³×C₇	1	16	yes	complemented
556	C₄×Q₈	C₂³×C₇	1	16	yes	complemented
557	C₄×Q₈	C₂³×C₇	1	32	yes	complemented
558	C₄×D₄	C₂³×C₇	1	16	yes	—
559	C₄×D₄	C₂³×C₇	1	32	yes	complemented
560	C₄×D₄	C₂³×C₇	1	16	yes	complemented
561	C₄×D₄	C₂³×C₇	1	32	yes	complemented
562	C₄×D₄	C₂³×C₇	1	32	yes	complemented
563	C₄×D₄	C₂³×C₇	1	16	yes	complemented
564	#117	C₂³×C₇	1	8	yes	complemented
565	#117	C₂³×C₇	1	16	yes	complemented
566	#117	C₂³×C₇	1	8	yes	complemented
567	#117	C₂³×C₇	1	8	yes	complemented
568	#117	C₂³×C₇	1	32	yes	complemented
569	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
570	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
571	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
572	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
573	C₂×C₄⋊C₄	C₂³×C₇	1	4	yes	—
574	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
575	C₂×C₄⋊C₄	C₂³×C₇	1	4	yes	—
576	C₂×C₄⋊C₄	C₂³×C₇	1	4	yes	—
577	C₂×C₄⋊C₄	C₂³×C₇	1	4	yes	—
578	C₂×C₄⋊C₄	C₂³×C₇	1	4	yes	—
579	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
580	C₂×C₂²⋊C₄	C₂³×C₇	1	4	yes	—
581	C₂×C₂²⋊C₄	C₂³×C₇	1	4	yes	—
582	C₂×C₂²⋊C₄	C₂³×C₇	1	4	yes	—
583	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
584	C₂×C₂²⋊C₄	C₂³×C₇	1	4	yes	—
585	C₂×C₂²⋊C₄	C₂³×C₇	1	1	yes	characteristic
586	C₂×C₂²⋊C₄	C₂³×C₇	1	4	yes	—
587	C₂×C₂²⋊C₄	C₂³×C₇	1	1	yes	characteristic
588	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
589	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
590	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
591	C₂×C₂²⋊C₄	C₂³×C₇	1	4	yes	—
592	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
593	C₂×C₂²⋊C₄	C₂³×C₇	1	4	yes	—
594	C₂×C₂²⋊C₄	C₂³×C₇	1	4	yes	—
595	C₂×C₂²⋊C₄	C₂³×C₇	1	4	yes	—
596	C₂×C₂²⋊C₄	C₂³×C₇	1	4	yes	—
597	C₂×C₂²⋊C₄	C₂³×C₇	1	32	yes	complemented
598	C₂×C₄²	C₂³×C₇	1	2	yes	—
599	C₂×C₄²	C₂³×C₇	1	4	yes	—
600	C₂×C₄²	C₂³×C₇	1	2	yes	—
601	C₂×C₄²	C₂³×C₇	1	2	yes	—
602	C₂×C₄²	C₂³×C₇	1	4	yes	—
603	C₂²×C₇	—	2	2	no	—
604	C₂²×C₇	—	2	4	no	—
605	C₂²×C₇	—	2	2	no	—
606	C₂²×C₇	—	2	2	no	—
607	C₂²×C₇	—	2	8	no	—
608	C₂²×C₇	—	2	8	no	—
609	C₂²×C₇	—	2	4	no	—
610	C₂²×C₇	—	2	4	no	—
611	C₂²×C₇	—	2	4	no	—
612	C₂²×C₇	—	2	4	no	—
613	C₂²×C₇	—	2	8	no	—
614	C₂²×C₇	—	2	4	no	—
615	C₂²×C₇	—	4	16	no	—
616	C₂²×C₇	—	4	4	no	—
617	C₂²×C₇	—	4	8	no	—
618	C₂²×C₇	—	4	4	no	—
619	C₂²×C₇	—	4	16	no	—
620	C₂²×C₇	—	4	4	no	—
621	C₂²×C₇	—	8	16	no	—
622	C₂²×C₇	C₂×H(5,𝔽₂)	1	2	yes	—
623	C₂²×C₇	#585	1	4	yes	—
624	C₂²×C₇	C₂⁶	1	1	yes	characteristic
625	C₄×C₇	—	2	4	no	—
626	C₄×C₇	—	2	2	no	—
627	C₄×C₇	—	2	2	no	—
628	C₄×C₇	—	2	2	no	—
629	C₄×C₇	—	2	8	no	—
630	C₄×C₇	—	2	4	no	—
631	C₄×C₇	—	2	8	no	—
632	C₄×C₇	—	2	8	no	—
633	C₄×C₇	—	2	4	no	—
634	C₄×C₇	C₂×H(5,𝔽₂)	1	4	yes	—
635	C₂⁴	—	4	2	no	—
636	C₂⁴	—	4	4	no	—
637	C₂⁴	—	4	4	no	—
638	C₂⁴	—	4	8	no	—
639	C₂⁴	C₂⁴×C₇	1	1	yes	characteristic
640	C₂⁴	C₂⁴×C₇	1	1	yes	characteristic
641	C₂⁴	C₂⁴×C₇	1	2	yes	—
642	C₂⁴	C₂⁴×C₇	1	4	yes	—
643	C₂⁴	C₂⁴×C₇	1	1	yes	characteristic
644	C₂⁴	C₂⁴×C₇	1	8	yes	—
645	C₂⁴	C₂⁴×C₇	1	4	yes	—
646	#41	—	4	16	no	—
647	#41	—	4	32	no	—
648	C₂×Q₈	—	2	8	no	—
649	C₂×Q₈	—	4	4	no	—
650	C₂×Q₈	—	4	2	no	—
651	C₂×Q₈	—	4	8	no	—
652	C₂×Q₈	—	4	16	no	—
653	C₂×Q₈	C₂⁴×C₇	1	8	yes	—
654	C₂×Q₈	C₂⁴×C₇	1	16	yes	—
655	C₂×Q₈	C₂⁴×C₇	1	8	yes	—
656	C₂×Q₈	C₂⁴×C₇	1	4	yes	—
657	C₂×D₄	—	2	8	no	—
658	C₂×D₄	—	4	16	no	—
659	C₂×D₄	—	4	4	no	—
660	C₂×D₄	—	4	2	no	—
661	C₂×D₄	—	4	2	no	—
662	C₂×D₄	—	4	2	no	—
663	C₂×D₄	—	4	8	no	—
664	C₂×D₄	—	4	4	no	—
665	C₂×D₄	—	4	8	no	—
666	C₂×D₄	—	4	8	no	—
667	C₂×D₄	—	4	8	no	—
668	C₂×D₄	—	4	4	no	—
669	C₂×D₄	C₂⁴×C₇	1	8	yes	—
670	C₂×D₄	C₂⁴×C₇	1	8	yes	—
671	C₂×D₄	C₂⁴×C₇	1	16	yes	—
672	C₂×D₄	C₂⁴×C₇	1	16	yes	—
673	C₂×D₄	C₂⁴×C₇	1	8	yes	—
674	C₂×D₄	C₂⁴×C₇	1	16	yes	—
675	C₂×D₄	C₂⁴×C₇	1	4	yes	—
676	C₂×D₄	C₂⁴×C₇	1	16	yes	—
677	C₂×D₄	C₂⁴×C₇	1	4	yes	—
678	C₂×D₄	C₂⁴×C₇	1	4	yes	—
679	C₂×D₄	C₂⁴×C₇	1	8	yes	—
680	C₂²×C₄	—	2	8	no	—
681	C₂²×C₄	—	2	4	no	—
682	C₂²×C₄	—	2	4	no	—
683	C₂²×C₄	—	2	4	no	—
684	C₂²×C₄	—	4	16	no	—
685	C₂²×C₄	—	4	2	no	—
686	C₂²×C₄	—	4	4	no	—
687	C₂²×C₄	—	4	4	no	—
688	C₂²×C₄	—	4	8	no	—
689	C₂²×C₄	—	4	8	no	—
690	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
691	C₂²×C₄	C₂⁴×C₇	1	4	yes	—
692	C₂²×C₄	C₂⁴×C₇	1	4	yes	—
693	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
694	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
695	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
696	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
697	C₂²×C₄	C₂⁴×C₇	1	4	yes	—
698	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
699	C₂²×C₄	C₂⁴×C₇	1	4	yes	—
700	C₂²×C₄	C₂⁴×C₇	1	8	yes	—
701	C₂²×C₄	C₂⁴×C₇	1	4	yes	—
702	C₂²×C₄	C₂⁴×C₇	1	4	yes	—
703	C₂²×C₄	C₂⁴×C₇	1	16	yes	—
704	C₂²×C₄	C₂⁴×C₇	1	16	yes	—
705	C₂²×C₄	C₂⁴×C₇	1	4	yes	—
706	C₂²×C₄	C₂⁴×C₇	1	8	yes	—
707	C₂²×C₄	C₂⁴×C₇	1	8	yes	—
708	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
709	C₄⋊C₄	C₂⁴×C₇	1	8	yes	—
710	C₄⋊C₄	C₂⁴×C₇	1	8	yes	—
711	C₄⋊C₄	C₂⁴×C₇	1	8	yes	—
712	C₄⋊C₄	C₂⁴×C₇	1	8	yes	—
713	C₄⋊C₄	C₂⁴×C₇	1	16	yes	—
714	C₄⋊C₄	C₂⁴×C₇	1	8	yes	—
715	C₄⋊C₄	C₂⁴×C₇	1	16	yes	—
716	C₄⋊C₄	C₂⁴×C₇	1	16	yes	—
717	C₄⋊C₄	C₂⁴×C₇	1	16	yes	—
718	C₄⋊C₄	C₂⁴×C₇	1	16	yes	—
719	C₂²⋊C₄	C₂⁴×C₇	1	8	yes	—
720	C₂²⋊C₄	C₂⁴×C₇	1	16	yes	—
721	C₂²⋊C₄	C₂⁴×C₇	1	16	yes	—
722	C₂²⋊C₄	C₂⁴×C₇	1	16	yes	—
723	C₂²⋊C₄	C₂⁴×C₇	1	8	yes	—
724	C₂²⋊C₄	C₂⁴×C₇	1	16	yes	—
725	C₂²⋊C₄	C₂⁴×C₇	1	4	yes	—
726	C₂²⋊C₄	C₂⁴×C₇	1	16	yes	—
727	C₂²⋊C₄	C₂⁴×C₇	1	4	yes	—
728	C₂²⋊C₄	C₂⁴×C₇	1	8	yes	—
729	C₂²⋊C₄	C₂⁴×C₇	1	8	yes	—
730	C₂²⋊C₄	C₂⁴×C₇	1	8	yes	—
731	C₂²⋊C₄	C₂⁴×C₇	1	16	yes	—
732	C₂²⋊C₄	C₂⁴×C₇	1	8	yes	—
733	C₂²⋊C₄	C₂⁴×C₇	1	16	yes	—
734	C₂²⋊C₄	C₂⁴×C₇	1	16	yes	—
735	C₂²⋊C₄	C₂⁴×C₇	1	16	yes	—
736	C₂²⋊C₄	C₂⁴×C₇	1	16	yes	—
737	C₄²	C₂⁴×C₇	1	8	yes	—
738	C₄²	C₂⁴×C₇	1	16	yes	—
739	C₄²	C₂⁴×C₇	1	8	yes	—
740	C₄²	C₂⁴×C₇	1	8	yes	—
741	C₄²	C₂⁴×C₇	1	16	yes	—
742	C₂×C₇	—	4	2	no	—
743	C₂×C₇	—	4	4	no	—
744	C₂×C₇	—	4	2	no	—
745	C₂×C₇	—	4	8	no	—
746	C₂×C₇	—	4	2	no	—
747	C₂×C₇	#3540	1	4	yes	direct product factor
748	C₂×C₇	C₂²×H(5,𝔽₂)	1	1	yes	characteristic
749	C₂×C₇	C₂×#585	1	2	yes	—
750	C₂³	—	2	2	no	—
751	C₂³	—	2	4	no	—
752	C₂³	—	2	2	no	—
753	C₂³	—	2	2	no	—
754	C₂³	—	2	8	no	—
755	C₂³	—	2	8	no	—
756	C₂³	—	2	4	no	—
757	C₂³	—	2	4	no	—
758	C₂³	—	2	4	no	—
759	C₂³	—	2	4	no	—
760	C₂³	—	2	8	no	—
761	C₂³	—	2	4	no	—
762	C₂³	—	4	4	no	—
763	C₂³	—	4	8	no	—
764	C₂³	—	4	8	no	—
765	C₂³	—	4	16	no	—
766	C₂³	—	4	16	no	—
767	C₂³	—	8	16	no	—
768	C₂³	C₂⁵×C₇	1	2	yes	—
769	C₂³	C₂⁵×C₇	1	2	yes	—
770	C₂³	C₂⁵×C₇	1	4	yes	—
771	C₂³	C₂⁵×C₇	1	8	yes	—
772	C₂³	C₂⁵×C₇	1	2	yes	—
773	C₂³	C₂⁵×C₇	1	1	yes	characteristic
774	Q₈	—	2	16	no	—
775	Q₈	—	4	8	no	—
776	Q₈	—	4	16	no	—
777	Q₈	—	4	4	no	—
778	D₄	—	2	16	no	—
779	D₄	—	4	8	no	—
780	D₄	—	4	8	no	—
781	D₄	—	4	16	no	—
782	D₄	—	4	16	no	—
783	D₄	—	4	16	no	—
784	D₄	—	4	8	no	—
785	D₄	—	4	4	no	—
786	D₄	—	4	4	no	—
787	D₄	—	4	4	no	—
788	D₄	—	4	16	no	—
789	C₂×C₄	—	2	4	no	—
790	C₂×C₄	—	2	2	no	—
791	C₂×C₄	—	2	2	no	—
792	C₂×C₄	—	2	2	no	—
793	C₂×C₄	—	2	8	no	—
794	C₂×C₄	—	2	4	no	—
795	C₂×C₄	—	2	8	no	—
796	C₂×C₄	—	2	8	no	—
797	C₂×C₄	—	2	4	no	—
798	C₂×C₄	—	2	16	no	—
799	C₂×C₄	—	2	8	no	—
800	C₂×C₄	—	2	8	no	—
801	C₂×C₄	—	2	8	no	—
802	C₂×C₄	—	4	4	no	—
803	C₂×C₄	—	4	8	no	—
804	C₂×C₄	—	4	16	no	—
805	C₂×C₄	—	4	8	no	—
806	C₂×C₄	—	4	16	no	—
807	C₂×C₄	C₇×H(5,𝔽₂)	1	4	yes	—
808	C₂×C₄	C₂⁵×C₇	1	4	yes	—
809	C₂×C₄	C₂⁵×C₇	1	8	yes	—
810	C₂×C₄	C₂⁵×C₇	1	8	yes	—
811	C₂×C₄	C₂⁵×C₇	1	2	yes	—
812	C₂×C₄	C₂⁵×C₇	1	4	yes	—
813	C₂×C₄	C₂⁵×C₇	1	2	yes	—
814	C₂×C₄	C₂⁵×C₇	1	4	yes	—
815	C₂×C₄	C₂⁵×C₇	1	8	yes	—
816	C₂×C₄	C₂⁵×C₇	1	2	yes	—
817	C₂×C₄	C₂⁵×C₇	1	2	yes	—
818	C₇	C₂×#3540	1	1	yes	characteristic, direct product factor, Sylow
819	C₂²	—	2	2	no	—
820	C₂²	—	2	4	no	—
821	C₂²	—	2	2	no	—
822	C₂²	—	2	2	no	—
823	C₂²	—	2	8	no	—
824	C₂²	—	2	8	no	—
825	C₂²	—	2	4	no	—
826	C₂²	—	2	4	no	—
827	C₂²	—	2	4	no	—
828	C₂²	—	2	4	no	—
829	C₂²	—	2	8	no	—
830	C₂²	—	2	4	no	—
831	C₂²	—	4	16	no	—
832	C₂²	—	4	8	no	—
833	C₂²	—	4	4	no	—
834	C₂²	—	4	4	no	—
835	C₂²	—	4	16	no	—
836	C₂²	—	4	4	no	—
837	C₂²	—	8	16	no	—
838	C₂²	C₂×C₇×H(5,𝔽₂)	1	2	yes	—
839	C₂²	C₇×#585	1	4	yes	—
840	C₂²	C₂⁶×C₇	1	1	yes	characteristic
841	C₄	—	2	4	no	—
842	C₄	—	2	2	no	—
843	C₄	—	2	2	no	—
844	C₄	—	2	2	no	—
845	C₄	—	2	8	no	—
846	C₄	—	2	4	no	—
847	C₄	—	2	8	no	—
848	C₄	—	2	8	no	—
849	C₄	—	2	4	no	—
850	C₄	C₂×C₇×H(5,𝔽₂)	1	4	yes	—
851	C₂	—	4	4	no	—
852	C₂	—	4	2	no	—
853	C₂	—	4	2	no	—
854	C₂	—	4	8	no	—
855	C₂	—	4	2	no	—
856	C₂	C₇×#3540	1	4	yes	direct product factor
857	C₂	C₂²×C₇×H(5,𝔽₂)	1	1	yes	characteristic
858	C₂	C₂×C₇×#585	1	2	yes	—

	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×#3540	C₂	direct (N × H)
2. C₂×C₇×H(3,𝔽₄)	C₂	semidirect
3. C₂×C₇×#560	C₂	semidirect
4. C₂×C₇×#559	C₂	semidirect
5. C₂×C₇×#556	C₂	semidirect
6. C₂×C₇×#555	C₂	semidirect
7. C₂×C₇×#551	C₂	semidirect
8. C₂×C₇×#548	C₂	semidirect
9. C₂×C₇×#546	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×#535	C₂	semidirect
15. C₂×C₇×#525	C₂	semidirect
16. C₂×C₇×#525	C₂	semidirect
19. C₂³×C₇×Q₈	C₂²	semidirect
20. C₂³×C₇×D₄	C₂²	semidirect
21. C₂⁴×C₄×C₇	C₂²	semidirect
22. C₇×H(3,𝔽₄)	C₂²	semidirect
23. C₇×#560	C₂²	semidirect
24. C₇×#559	C₂²	semidirect
25. C₇×#556	C₂²	semidirect
26. C₇×#555	C₂²	semidirect
27. C₇×#551	C₂²	semidirect
28. C₇×#548	C₂²	semidirect
29. C₇×#546	C₂²	semidirect
30. C₇×#542	C₂²	semidirect
31. C₇×#542	C₂²	semidirect
32. C₇×#538	C₂²	semidirect
33. C₇×#536	C₂²	semidirect
34. C₇×#535	C₂²	semidirect
35. C₂×C₇×C₄⋊Q₈	C₂²	semidirect
36. C₂×C₇×C₄⋊Q₈	C₂²	semidirect
38. C₂×C₇×#126	C₂²	semidirect
39. C₂×C₇×#126	C₂²	semidirect
40. C₂×C₇×#126	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. C₇×#525	C₂²	semidirect
50. C₇×#525	C₂²	semidirect
52. C₂×C₇×#123	C₂²	semidirect
53. C₂×C₇×#123	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×C₂²⋊Q₈	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
63. C₂×C₇×C₂²⋊Q₈	C₂²	semidirect
68. C₂×C₇×#121	C₂²	semidirect
69. C₂×C₇×#121	C₂²	semidirect
70. C₂×C₇×#121	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
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×C₇×#117	C₂²	semidirect
86. C₂×C₇×#117	C₂²	semidirect
87. C₂×C₇×#117	C₂²	semidirect
88. C₂×C₇×#117	C₂²	semidirect
89. C₂×C₇×#117	C₂²	semidirect
90. C₂²×C₇×C₂²⋊C₄	C₂²	semidirect
91. C₂×#3540	C₇	direct (N × H)
103. C₂²×C₇×Q₈	C₂³	semidirect
116. C₂²×C₇×D₄	C₂³	semidirect
127. C₂³×C₄×C₇	C₂³	semidirect
128. C₇×C₄⋊Q₈	C₂³	semidirect
129. C₇×C₄⋊Q₈	C₂³	semidirect
131. C₇×#126	C₂³	semidirect
132. C₇×#126	C₂³	semidirect
133. C₇×#126	C₂³	semidirect
136. C₇×#124	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
143. C₇×#123	C₂³	semidirect
144. C₇×#123	C₂³	semidirect
145. C₇×#123	C₂³	semidirect
146. C₇×#123	C₂³	semidirect
147. C₇×#123	C₂³	semidirect
148. C₇×#123	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
159. C₇×#121	C₂³	semidirect
160. C₇×#121	C₂³	semidirect
161. C₇×#121	C₂³	semidirect
165. C₇×#120	C₂³	semidirect
166. C₇×#120	C₂³	semidirect
167. C₇×#120	C₂³	semidirect
168. C₄×C₇×Q₈	C₂³	semidirect
169. C₄×C₇×Q₈	C₂³	semidirect
171. C₄×C₇×D₄	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. C₇×#117	C₂³	semidirect
177. C₇×#117	C₂³	semidirect
178. C₇×#117	C₂³	semidirect
179. C₇×#117	C₂³	semidirect
180. C₇×#117	C₂³	semidirect
209. C₂×C₇×C₂²⋊C₄	C₂³	semidirect
215. #3540	C₂×C₇	direct (N × H)
216. C₂×H(3,𝔽₄)	C₂×C₇	semidirect
217. C₂×#560	C₂×C₇	semidirect
218. C₂×#559	C₂×C₇	semidirect
219. C₂×#556	C₂×C₇	semidirect
220. C₂×#555	C₂×C₇	semidirect
221. C₂×#551	C₂×C₇	semidirect
222. C₂×#548	C₂×C₇	semidirect
223. C₂×#546	C₂×C₇	semidirect
224. C₂×#542	C₂×C₇	semidirect
225. C₂×#542	C₂×C₇	semidirect
226. C₂×#538	C₂×C₇	semidirect
227. C₂×#536	C₂×C₇	semidirect
228. C₂×#535	C₂×C₇	semidirect
229. C₂×#525	C₂×C₇	semidirect
230. C₂×#525	C₂×C₇	semidirect
340. C₂³×Q₈	C₂²×C₇	semidirect
341. C₂³×D₄	C₂²×C₇	semidirect
342. C₂⁴×C₄	C₂²×C₇	semidirect
343. H(3,𝔽₄)	C₂²×C₇	semidirect
344. #560	C₂²×C₇	semidirect
345. #559	C₂²×C₇	semidirect
346. #556	C₂²×C₇	semidirect
347. #555	C₂²×C₇	semidirect
348. #551	C₂²×C₇	semidirect
349. #548	C₂²×C₇	semidirect
350. #546	C₂²×C₇	semidirect
351. #542	C₂²×C₇	semidirect
352. #542	C₂²×C₇	semidirect
353. #538	C₂²×C₇	semidirect
354. #536	C₂²×C₇	semidirect
355. #535	C₂²×C₇	semidirect
356. C₂×C₄⋊Q₈	C₂²×C₇	semidirect
357. C₂×C₄⋊Q₈	C₂²×C₇	semidirect
359. C₂×#126	C₂²×C₇	semidirect
360. C₂×#126	C₂²×C₇	semidirect
361. C₂×#126	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
368. C₂×#124	C₂²×C₇	semidirect
369. C₂×#124	C₂²×C₇	semidirect
370. #525	C₂²×C₇	semidirect
371. #525	C₂²×C₇	semidirect
373. C₂×#123	C₂²×C₇	semidirect
374. C₂×#123	C₂²×C₇	semidirect
375. C₂×#123	C₂²×C₇	semidirect
376. C₂×#123	C₂²×C₇	semidirect
377. C₂×#123	C₂²×C₇	semidirect
378. C₂×#123	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
384. C₂×C₂²⋊Q₈	C₂²×C₇	semidirect
389. C₂×#121	C₂²×C₇	semidirect
390. C₂×#121	C₂²×C₇	semidirect
391. C₂×#121	C₂²×C₇	semidirect
395. C₂×#120	C₂²×C₇	semidirect
396. C₂×#120	C₂²×C₇	semidirect
397. C₂×#120	C₂²×C₇	semidirect
398. C₂×C₄×Q₈	C₂²×C₇	semidirect
399. C₂×C₄×Q₈	C₂²×C₇	semidirect
401. C₂×C₄×D₄	C₂²×C₇	semidirect
402. C₂×C₄×D₄	C₂²×C₇	semidirect
403. C₂×C₄×D₄	C₂²×C₇	semidirect
404. C₂×C₄×D₄	C₂²×C₇	semidirect
405. C₂×C₄×D₄	C₂²×C₇	semidirect
406. C₂×#117	C₂²×C₇	semidirect
407. C₂×#117	C₂²×C₇	semidirect
408. C₂×#117	C₂²×C₇	semidirect
409. C₂×#117	C₂²×C₇	semidirect
410. C₂×#117	C₂²×C₇	semidirect
411. C₂²×C₂²⋊C₄	C₂²×C₇	semidirect
491. C₂²×Q₈	C₂³×C₇	semidirect
504. C₂²×D₄	C₂³×C₇	semidirect
515. C₂³×C₄	C₂³×C₇	semidirect
516. C₄⋊Q₈	C₂³×C₇	semidirect
517. C₄⋊Q₈	C₂³×C₇	semidirect
519. #126	C₂³×C₇	semidirect
520. #126	C₂³×C₇	semidirect
521. #126	C₂³×C₇	semidirect
524. #124	C₂³×C₇	semidirect
525. #124	C₂³×C₇	semidirect
526. #124	C₂³×C₇	semidirect
527. #124	C₂³×C₇	semidirect
528. #124	C₂³×C₇	semidirect
529. #124	C₂³×C₇	semidirect
531. #123	C₂³×C₇	semidirect
532. #123	C₂³×C₇	semidirect
533. #123	C₂³×C₇	semidirect
534. #123	C₂³×C₇	semidirect
535. #123	C₂³×C₇	semidirect
536. #123	C₂³×C₇	semidirect
537. C₂²⋊Q₈	C₂³×C₇	semidirect
538. C₂²⋊Q₈	C₂³×C₇	semidirect
539. C₂²⋊Q₈	C₂³×C₇	semidirect
540. C₂²⋊Q₈	C₂³×C₇	semidirect
541. C₂²⋊Q₈	C₂³×C₇	semidirect
542. C₂²⋊Q₈	C₂³×C₇	semidirect
547. #121	C₂³×C₇	semidirect
548. #121	C₂³×C₇	semidirect
549. #121	C₂³×C₇	semidirect
553. #120	C₂³×C₇	semidirect
554. #120	C₂³×C₇	semidirect
555. #120	C₂³×C₇	semidirect
556. C₄×Q₈	C₂³×C₇	semidirect
557. C₄×Q₈	C₂³×C₇	semidirect
559. C₄×D₄	C₂³×C₇	semidirect
560. C₄×D₄	C₂³×C₇	semidirect
561. C₄×D₄	C₂³×C₇	semidirect
562. C₄×D₄	C₂³×C₇	semidirect
563. C₄×D₄	C₂³×C₇	semidirect
564. #117	C₂³×C₇	semidirect
565. #117	C₂³×C₇	semidirect
566. #117	C₂³×C₇	semidirect
567. #117	C₂³×C₇	semidirect
568. #117	C₂³×C₇	semidirect
597. C₂×C₂²⋊C₄	C₂³×C₇	semidirect
747. C₂×C₇	#3540	direct (N × H)
818. C₇	C₂×#3540	direct (N × H)
856. C₂	C₇×#3540	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×#3540	2
C₂×C₇×H(3,𝔽₄)	2
C₂×C₇×#560	2
C₂×C₇×#559	2
C₂×C₇×#556	2
C₂×C₇×#555	2
C₂×C₇×#551	2
C₂×C₇×#548	2
C₂×C₇×#546	2
C₂×C₇×#542	2
C₂×C₇×#538	2
C₂×C₇×#536	2
C₂×C₇×#535	2
C₂×C₇×#525	2
C₂×#3540	7

Subgroups — C2×C7×#3540 #13239944

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₇×#3540 #13239944