Subgroups — C₇×#60241 #13237457

Order 1792.

2130 conjugacy classes of subgroups.

The subgroup lattice has 858 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×D₄×#41	C₂	1	1	yes	maximal, characteristic
2	C₇×#2981	C₂	1	2	yes	maximal, complemented
3	C₇×#2979	C₂	1	2	yes	maximal, complemented
4	C₇×#2978	C₂	1	4	yes	maximal, complemented
5	C₇×#2976	C₂	1	4	yes	maximal, complemented
6	C₇×#2975	C₂	1	2	yes	maximal, complemented
7	C₇×#2974	C₂	1	2	yes	maximal, complemented
8	C₇×#2935	C₂	1	1	yes	maximal, characteristic, complemented
9	C₇×D₄×M₁₆	C₂	1	1	yes	maximal, characteristic, complemented
10	C₇×#2933	C₂	1	2	yes	maximal, complemented
11	C₇×#2931	C₂	1	1	yes	maximal, characteristic, complemented
12	C₇×#2930	C₂	1	2	yes	maximal, complemented
13	C₂×C₇×#436	C₂	1	1	yes	maximal, characteristic, complemented
14	C₇×#2925	C₂	1	1	yes	maximal, characteristic, complemented
15	C₇×#2922	C₂	1	1	yes	maximal, characteristic, complemented
16	C₇×#2880	C₂	1	2	yes	maximal, complemented
17	C₇×#2879	C₂	1	2	yes	maximal, complemented
18	C₂²×C₇×#41	C₂²	1	2	yes	—
19	C₂×C₇×#131	C₂²	1	2	yes	complemented
20	C₂×C₇×#131	C₂²	1	2	yes	complemented
21	C₂²×C₇×M₁₆	C₂²	1	2	yes	complemented
22	C₂²×C₇×M₁₆	C₂²	1	2	yes	complemented
23	C₇×#550	C₄	1	1	yes	characteristic
24	C₇×D₄×Q₈	C₄	1	1	yes	characteristic
25	C₇×#548	C₄	1	2	yes	—
26	C₇×#547	C₄	1	2	yes	—
27	C₇×#547	C₄	1	1	yes	characteristic
28	C₇×#546	C₄	1	4	yes	—
29	C₇×#546	C₄	1	2	yes	—
30	C₇×D₄²	C₄	1	1	yes	characteristic
31	C₇×D₄²	C₄	1	2	yes	—
32	C₇×#532	C₂²	1	1	yes	characteristic
33	C₇×#532	C₂²	1	2	yes	—
34	C₇×#525	C₂²	1	2	yes	—
35	C₇×#525	C₂²	1	4	yes	—
36	C₄×C₇×#41	C₂²	1	1	yes	characteristic
37	C₂×C₄×C₇×D₄	C₂²	1	1	yes	characteristic
38	C₂×C₄×C₇×D₄	C₂²	1	2	yes	—
39	C₇×#436	C₂²	1	1	yes	characteristic
40	C₇×#436	C₂²	1	1	yes	characteristic
41	C₇×#436	C₂²	1	2	yes	—
42	C₇×#436	C₂²	1	2	yes	complemented
43	C₇×#436	C₂²	1	2	yes	complemented
44	C₇×#436	C₂²	1	1	yes	characteristic, complemented
45	C₇×#436	C₂²	1	1	yes	characteristic, complemented
46	C₇×#436	C₂²	1	4	yes	complemented
47	C₇×#436	C₂²	1	4	yes	complemented
48	C₇×#436	C₂²	1	2	yes	complemented
49	C₇×#436	C₂²	1	2	yes	complemented
50	C₇×#436	C₂²	1	4	yes	complemented
51	C₇×#436	C₂²	1	2	yes	complemented
52	C₇×#435	C₂²	1	4	yes	complemented
53	C₇×#435	C₂²	1	4	yes	complemented
54	C₇×#435	C₂²	1	4	yes	complemented
55	C₇×#435	C₂²	1	4	yes	complemented
56	C₇×#435	C₂²	1	4	yes	complemented
57	C₇×#435	C₂²	1	4	yes	complemented
58	C₇×C₈×D₄	C₂²	1	2	yes	complemented
59	C₇×C₈×D₄	C₂²	1	2	yes	complemented
60	C₇×C₈×D₄	C₂²	1	4	yes	complemented
61	C₇×C₈×D₄	C₂²	1	2	yes	complemented
62	C₇×C₈×D₄	C₂²	1	2	yes	complemented
63	C₇×#433	C₂²	1	2	yes	complemented
64	C₇×#433	C₂²	1	2	yes	complemented
65	C₇×#433	C₂²	1	4	yes	complemented
66	C₇×#432	C₂²	1	2	yes	complemented
67	C₇×#431	C₂²	1	2	yes	complemented
68	C₇×#431	C₂²	1	2	yes	complemented
69	C₇×#431	C₂²	1	2	yes	complemented
70	C₇×#424	C₂²	1	1	yes	characteristic, complemented
71	C₇×#424	C₂²	1	1	yes	characteristic, complemented
72	C₇×#423	C₂²	1	1	yes	characteristic, complemented
73	C₂×C₇×C₄⋊C₈	C₂²	1	1	yes	characteristic, complemented
74	C₇×#408	C₂²	1	1	yes	characteristic
75	C₇×#408	C₂²	1	1	yes	characteristic
76	C₇×#408	C₂²	1	2	yes	—
77	C₇×#408	C₂²	1	2	yes	complemented
78	C₇×#408	C₂²	1	2	yes	complemented
79	C₇×#408	C₂²	1	4	yes	complemented
80	C₇×#408	C₂²	1	4	yes	complemented
81	C₇×#408	C₂²	1	4	yes	complemented
82	C₇×#408	C₂²	1	4	yes	complemented
83	C₇×#407	C₂²	1	2	yes	complemented
84	C₇×#407	C₂²	1	4	yes	complemented
85	C₇×#407	C₂²	1	4	yes	complemented
86	C₇×#407	C₂²	1	4	yes	complemented
87	C₂×C₇×C₂²⋊C₈	C₂²	1	2	yes	complemented
88	C₂×C₇×C₂²⋊C₈	C₂²	1	4	yes	complemented
89	C₇×#405	C₂²	1	2	yes	complemented
90	C₄×C₇×M₁₆	C₂²	1	1	yes	characteristic, complemented
91	C₂×C₄×C₇×C₈	C₂²	1	1	yes	characteristic, complemented
92	#60241	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
93	C₂×C₇×#41	—	4	4	no	—
94	C₂×C₇×#41	—	4	4	no	—
95	C₂×C₇×#41	C₂×C₄	1	4	yes	—
96	C₂×C₇×#41	C₂×C₄	1	2	yes	—
97	C₂×C₇×#41	C₂×C₄	1	2	yes	—
98	C₂×C₇×#41	C₂³	1	1	yes	characteristic
99	C₂×C₇×#41	C₂³	1	2	yes	—
100	C₂×C₇×#41	C₂³	1	4	yes	—
101	C₂²×C₇×Q₈	C₂×C₄	1	2	yes	—
102	C₂²×C₇×D₄	C₂×C₄	1	2	yes	—
103	C₂²×C₇×D₄	C₂×C₄	1	4	yes	—
104	C₂²×C₇×D₄	C₂×C₄	1	1	yes	characteristic
105	C₂²×C₇×D₄	C₂×C₄	1	2	yes	—
106	C₂³×C₄×C₇	C₂³	1	2	yes	—
107	C₂³×C₄×C₇	C₂³	1	4	yes	—
108	C₇×#131	—	4	4	no	—
109	C₇×#131	—	4	4	no	—
110	C₂×C₇×M₁₆	—	4	4	no	—
111	C₂×C₇×M₁₆	—	4	4	no	—
112	C₂×C₇×M₁₆	C₂³	1	1	yes	characteristic
113	C₂×C₇×M₁₆	C₂³	1	1	yes	characteristic
114	C₂×C₇×M₁₆	C₂³	1	2	yes	—
115	C₂×C₇×M₁₆	C₂³	1	2	yes	—
116	C₂×C₇×M₁₆	C₂³	1	4	yes	—
117	C₂×C₇×M₁₆	C₂³	1	2	yes	—
118	C₂×C₇×M₁₆	C₂³	1	4	yes	—
119	C₂×C₇×M₁₆	C₂³	1	4	yes	—
120	C₂×C₇×M₁₆	C₂³	1	2	yes	—
121	C₂×C₇×M₁₆	C₂³	1	2	yes	—
122	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
123	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
124	C₂²×C₇×C₈	C₂³	1	2	yes	—
125	C₂²×C₇×C₈	C₂³	1	4	yes	—
126	C₂²×C₇×C₈	C₂³	1	4	yes	—
127	C₂²×C₇×C₈	C₂³	1	4	yes	—
128	C₇×C₄⋊Q₈	C₂×C₄	1	1	yes	characteristic
129	C₇×C₄⋊Q₈	C₂×C₄	1	2	yes	—
130	C₇×#127	C₂×C₄	1	1	yes	characteristic
131	C₇×#127	C₂×C₄	1	2	yes	—
132	C₇×#124	C₂×C₄	1	2	yes	—
133	C₇×#124	C₂×C₄	1	4	yes	—
134	C₇×#123	C₂×C₄	1	4	yes	—
135	C₇×#123	C₂×C₄	1	4	yes	—
136	C₇×#123	C₂×C₄	1	4	yes	—
137	C₇×C₂²⋊Q₈	C₂×C₄	1	2	yes	—
138	C₇×C₂²⋊Q₈	C₂×C₄	1	4	yes	—
139	C₇×C₂²⋊Q₈	C₂×C₄	1	2	yes	—
140	C₇×C₂²⋊Q₈	C₂×C₄	1	4	yes	—
141	C₇×#121	C₂×C₄	1	2	yes	—
142	C₇×#121	C₂×C₄	1	4	yes	—
143	C₇×#121	C₂×C₄	1	2	yes	—
144	C₇×#121	C₂×C₄	1	4	yes	—
145	C₇×#121	C₂×C₄	1	2	yes	—
146	C₇×#121	C₂×C₄	1	2	yes	—
147	C₇×#121	C₂×C₄	1	2	yes	—
148	C₇×#121	C₂×C₄	1	2	yes	—
149	C₇×#121	C₂×C₄	1	4	yes	—
150	C₇×#120	C₂×C₄	1	4	yes	—
151	C₇×#120	C₂×C₄	1	4	yes	—
152	C₇×#120	C₂×C₄	1	4	yes	—
153	C₄×C₇×Q₈	C₂×C₄	1	1	yes	characteristic
154	C₄×C₇×Q₈	C₂×C₄	1	1	yes	characteristic
155	C₄×C₇×D₄	C₂×C₄	1	1	yes	characteristic
156	C₄×C₇×D₄	C₂×C₄	1	2	yes	—
157	C₄×C₇×D₄	C₂×C₄	1	2	yes	—
158	C₄×C₇×D₄	C₂×C₄	1	4	yes	—
159	C₄×C₇×D₄	C₂×C₄	1	1	yes	characteristic
160	C₄×C₇×D₄	C₂×C₄	1	2	yes	—
161	C₄×C₇×D₄	C₂×C₄	1	2	yes	—
162	C₄×C₇×D₄	C₂×C₄	1	1	yes	characteristic
163	C₄×C₇×D₄	C₂×C₄	1	2	yes	—
164	C₄×C₇×D₄	C₂×C₄	1	1	yes	characteristic
165	C₄×C₇×D₄	C₂³	1	1	yes	characteristic
166	C₄×C₇×D₄	C₂³	1	2	yes	—
167	C₄×C₇×D₄	C₂³	1	4	yes	—
168	C₄×C₇×D₄	C₂³	1	1	yes	characteristic
169	C₄×C₇×D₄	C₂³	1	2	yes	—
170	C₄×C₇×D₄	C₂³	1	4	yes	—
171	C₄×C₇×D₄	C₂³	1	2	yes	—
172	C₇×#117	C₂³	1	1	yes	characteristic
173	C₇×#117	C₂³	1	2	yes	—
174	C₂×C₇×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
175	C₂×C₇×C₄⋊C₄	C₂×C₄	1	2	yes	—
176	C₂×C₇×C₂²⋊C₄	C₂×C₄	1	2	yes	—
177	C₂×C₇×C₂²⋊C₄	C₂×C₄	1	4	yes	—
178	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
179	C₂×C₄²×C₇	C₂³	1	2	yes	—
180	C₇×C₄⋊C₈	C₂³	1	1	yes	characteristic
181	C₇×C₄⋊C₈	C₂³	1	1	yes	characteristic
182	C₇×C₄⋊C₈	C₂³	1	2	yes	—
183	C₇×C₄⋊C₈	C₂³	1	2	yes	—
184	C₇×C₄⋊C₈	C₂³	1	2	yes	—
185	C₇×C₄⋊C₈	C₂³	1	2	yes	—
186	C₇×C₄⋊C₈	C₂³	1	2	yes	—
187	C₇×C₄⋊C₈	C₂³	1	2	yes	—
188	C₇×C₄⋊C₈	C₂³	1	2	yes	—
189	C₇×C₂²⋊C₈	C₂³	1	2	yes	—
190	C₇×C₂²⋊C₈	C₂³	1	2	yes	—
191	C₇×C₂²⋊C₈	C₂³	1	4	yes	—
192	C₇×C₂²⋊C₈	C₂³	1	2	yes	—
193	C₇×C₂²⋊C₈	C₂³	1	4	yes	—
194	C₇×C₂²⋊C₈	C₂³	1	2	yes	—
195	C₇×C₂²⋊C₈	C₂³	1	2	yes	—
196	C₇×C₂²⋊C₈	C₂³	1	2	yes	—
197	C₇×C₂²⋊C₈	C₂³	1	2	yes	—
198	C₇×C₂²⋊C₈	C₂³	1	4	yes	—
199	C₇×C₂²⋊C₈	C₂³	1	2	yes	—
200	C₇×C₂²⋊C₈	C₂³	1	4	yes	—
201	C₇×C₂²⋊C₈	C₂³	1	4	yes	—
202	C₇×C₂²⋊C₈	C₂³	1	4	yes	—
203	C₇×C₂²⋊C₈	C₂³	1	4	yes	—
204	C₇×C₂²⋊C₈	C₂³	1	4	yes	—
205	C₇×#97	C₂³	1	2	yes	—
206	C₇×#97	C₂³	1	4	yes	—
207	C₄×C₇×C₈	C₂³	1	1	yes	characteristic
208	C₄×C₇×C₈	C₂³	1	1	yes	characteristic
209	C₄×C₇×C₈	C₂³	1	1	yes	characteristic
210	C₄×C₇×C₈	C₂³	1	1	yes	characteristic
211	C₄×C₇×C₈	C₂³	1	2	yes	—
212	C₄×C₇×C₈	C₂³	1	4	yes	—
213	D₄×#41	C₂×C₇	1	1	yes	characteristic
214	#2981	C₂×C₇	1	2	yes	complemented
215	#2979	C₂×C₇	1	2	yes	complemented
216	#2978	C₂×C₇	1	4	yes	complemented
217	#2976	C₂×C₇	1	4	yes	complemented
218	#2975	C₂×C₇	1	2	yes	complemented
219	#2974	C₂×C₇	1	2	yes	complemented
220	#2935	C₂×C₇	1	1	yes	characteristic, complemented
221	D₄×M₁₆	C₂×C₇	1	1	yes	characteristic, complemented
222	#2933	C₂×C₇	1	2	yes	complemented
223	#2931	C₂×C₇	1	1	yes	characteristic, complemented
224	#2930	C₂×C₇	1	2	yes	complemented
225	C₂×#436	C₂×C₇	1	1	yes	characteristic, complemented
226	#2925	C₂×C₇	1	1	yes	characteristic, complemented
227	#2922	C₂×C₇	1	1	yes	characteristic, complemented
228	#2880	C₂×C₇	1	2	yes	complemented
229	#2879	C₂×C₇	1	2	yes	complemented
230	C₂⁴×C₇	C₂²×C₄	1	2	yes	—
231	C₂⁴×C₇	C₂²×C₄	1	4	yes	—
232	C₇×#41	—	2	4	no	—
233	C₇×#41	—	2	4	no	—
234	C₇×#41	—	2	2	no	—
235	C₇×#41	—	2	2	no	—
236	C₇×#41	—	4	4	no	—
237	C₇×#41	—	4	4	no	—
238	C₇×#41	—	4	8	no	—
239	C₇×#41	—	4	4	no	—
240	C₇×#41	—	4	4	no	—
241	C₂×C₇×Q₈	—	4	4	no	—
242	C₂×C₇×Q₈	C₂²×C₄	1	1	yes	characteristic
243	C₂×C₇×Q₈	C₂²×C₄	1	2	yes	—
244	C₂×C₇×Q₈	C₂²×C₄	1	4	yes	—
245	C₂×C₇×D₄	—	4	2	no	—
246	C₂×C₇×D₄	—	4	4	no	—
247	C₂×C₇×D₄	—	4	4	no	—
248	C₂×C₇×D₄	—	4	8	no	—
249	C₂×C₇×D₄	C₂²×C₄	1	1	yes	characteristic
250	C₂×C₇×D₄	C₂²×C₄	1	2	yes	—
251	C₂×C₇×D₄	C₂²×C₄	1	1	yes	characteristic
252	C₂×C₇×D₄	C₂²×C₄	1	1	yes	characteristic
253	C₂×C₇×D₄	C₂²×C₄	1	2	yes	—
254	C₂×C₇×D₄	C₂²×C₄	1	4	yes	—
255	C₂×C₇×D₄	C₂²×C₄	1	2	yes	—
256	C₂×C₇×D₄	C₂²×C₄	1	2	yes	—
257	C₂×C₇×D₄	C₂²×C₄	1	4	yes	—
258	C₂×C₇×D₄	C₂²×C₄	1	4	yes	—
259	C₂×C₇×D₄	C₂²×C₄	1	2	yes	—
260	C₂×C₇×D₄	C₂²×C₄	1	4	yes	—
261	C₂×C₇×D₄	C₂²×C₄	1	4	yes	—
262	C₂×C₇×D₄	C₂²×C₄	1	4	yes	—
263	C₂²×C₄×C₇	—	2	4	no	—
264	C₂²×C₄×C₇	—	2	4	no	—
265	C₂²×C₄×C₇	—	4	4	no	—
266	C₂²×C₄×C₇	—	4	4	no	—
267	C₂²×C₄×C₇	C₂²×C₄	1	2	yes	—
268	C₂²×C₄×C₇	C₂²×C₄	1	1	yes	characteristic
269	C₂²×C₄×C₇	C₂²×C₄	1	2	yes	—
270	C₂²×C₄×C₇	C₂²×C₄	1	2	yes	—
271	C₂²×C₄×C₇	C₂²×C₄	1	2	yes	—
272	C₂²×C₄×C₇	C₂²×C₄	1	2	yes	—
273	C₂²×C₄×C₇	C₂²×C₄	1	1	yes	characteristic
274	C₂²×C₄×C₇	C₂²×C₄	1	4	yes	—
275	C₂²×C₄×C₇	C₂²×C₄	1	4	yes	—
276	C₂²×C₄×C₇	C₂²×C₄	1	4	yes	—
277	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
278	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
279	C₂²×C₄×C₇	C₂⁴	1	4	yes	—
280	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
281	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
282	C₇×M₁₆	—	2	2	no	—
283	C₇×M₁₆	—	2	4	no	—
284	C₇×M₁₆	—	2	2	no	—
285	C₇×M₁₆	—	4	2	no	—
286	C₇×M₁₆	—	4	2	no	—
287	C₇×M₁₆	—	4	2	no	—
288	C₇×M₁₆	—	4	2	no	—
289	C₇×M₁₆	—	4	4	no	—
290	C₇×M₁₆	—	4	4	no	—
291	C₇×M₁₆	—	4	4	no	—
292	C₂×C₇×C₈	—	2	2	no	—
293	C₂×C₇×C₈	—	2	4	no	—
294	C₂×C₇×C₈	—	2	2	no	—
295	C₂×C₇×C₈	—	4	4	no	—
296	C₂×C₇×C₈	—	4	4	no	—
297	C₂×C₇×C₈	—	4	4	no	—
298	C₂×C₇×C₈	C₂⁴	1	1	yes	characteristic
299	C₂×C₇×C₈	C₂⁴	1	1	yes	characteristic
300	C₂×C₇×C₈	C₂⁴	1	1	yes	characteristic
301	C₂×C₇×C₈	C₂⁴	1	1	yes	characteristic
302	C₂×C₇×C₈	C₂⁴	1	2	yes	—
303	C₂×C₇×C₈	C₂⁴	1	2	yes	—
304	C₂×C₇×C₈	C₂⁴	1	2	yes	—
305	C₂×C₇×C₈	C₂⁴	1	4	yes	—
306	C₂×C₇×C₈	C₂⁴	1	2	yes	—
307	C₇×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
308	C₇×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
309	C₇×C₄⋊C₄	C₂²×C₄	1	2	yes	—
310	C₇×C₄⋊C₄	C₂²×C₄	1	2	yes	—
311	C₇×C₄⋊C₄	C₂²×C₄	1	4	yes	—
312	C₇×C₄⋊C₄	C₂²×C₄	1	2	yes	—
313	C₇×C₄⋊C₄	C₂²×C₄	1	2	yes	—
314	C₇×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
315	C₇×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
316	C₇×C₄⋊C₄	C₂²×C₄	1	4	yes	—
317	C₇×C₄⋊C₄	C₂²×C₄	1	2	yes	—
318	C₇×C₂²⋊C₄	C₂²×C₄	1	2	yes	—
319	C₇×C₂²⋊C₄	C₂²×C₄	1	2	yes	—
320	C₇×C₂²⋊C₄	C₂²×C₄	1	4	yes	—
321	C₇×C₂²⋊C₄	C₂²×C₄	1	2	yes	—
322	C₇×C₂²⋊C₄	C₂²×C₄	1	4	yes	—
323	C₇×C₂²⋊C₄	C₂²×C₄	1	2	yes	—
324	C₇×C₂²⋊C₄	C₂²×C₄	1	4	yes	—
325	C₇×C₂²⋊C₄	C₂²×C₄	1	2	yes	—
326	C₇×C₂²⋊C₄	C₂²×C₄	1	2	yes	—
327	C₇×C₂²⋊C₄	C₂²×C₄	1	2	yes	—
328	C₇×C₂²⋊C₄	C₂²×C₄	1	4	yes	—
329	C₇×C₂²⋊C₄	C₂²×C₄	1	4	yes	—
330	C₇×C₂²⋊C₄	C₂²×C₄	1	4	yes	—
331	C₄²×C₇	C₂²×C₄	1	2	yes	—
332	C₄²×C₇	C₂²×C₄	1	1	yes	characteristic
333	C₄²×C₇	C₂²×C₄	1	2	yes	—
334	C₄²×C₇	C₂²×C₄	1	1	yes	characteristic
335	C₄²×C₇	C₂⁴	1	1	yes	characteristic
336	C₄²×C₇	C₂⁴	1	1	yes	characteristic
337	C₄²×C₇	C₂⁴	1	2	yes	—
338	C₂²×#41	C₂²×C₇	1	2	yes	—
339	C₂×#131	C₂²×C₇	1	2	yes	complemented
340	C₂×#131	C₂²×C₇	1	2	yes	complemented
341	C₂²×M₁₆	C₂²×C₇	1	2	yes	complemented
342	C₂²×M₁₆	C₂²×C₇	1	2	yes	complemented
343	#550	C₄×C₇	1	1	yes	characteristic
344	D₄×Q₈	C₄×C₇	1	1	yes	characteristic
345	#548	C₄×C₇	1	2	yes	—
346	#547	C₄×C₇	1	2	yes	—
347	#547	C₄×C₇	1	1	yes	characteristic
348	#546	C₄×C₇	1	4	yes	—
349	#546	C₄×C₇	1	2	yes	—
350	D₄²	C₄×C₇	1	1	yes	characteristic
351	D₄²	C₄×C₇	1	2	yes	—
352	#532	C₂²×C₇	1	1	yes	characteristic
353	#532	C₂²×C₇	1	2	yes	—
354	#525	C₂²×C₇	1	2	yes	—
355	#525	C₂²×C₇	1	4	yes	—
356	C₄×#41	C₂²×C₇	1	1	yes	characteristic
357	C₂×C₄×D₄	C₂²×C₇	1	1	yes	characteristic
358	C₂×C₄×D₄	C₂²×C₇	1	2	yes	—
359	#436	C₂²×C₇	1	1	yes	characteristic
360	#436	C₂²×C₇	1	1	yes	characteristic
361	#436	C₂²×C₇	1	2	yes	—
362	#436	C₂²×C₇	1	2	yes	complemented
363	#436	C₂²×C₇	1	2	yes	complemented
364	#436	C₂²×C₇	1	1	yes	characteristic, complemented
365	#436	C₂²×C₇	1	1	yes	characteristic, complemented
366	#436	C₂²×C₇	1	4	yes	complemented
367	#436	C₂²×C₇	1	4	yes	complemented
368	#436	C₂²×C₇	1	2	yes	complemented
369	#436	C₂²×C₇	1	2	yes	complemented
370	#436	C₂²×C₇	1	4	yes	complemented
371	#436	C₂²×C₇	1	2	yes	complemented
372	#435	C₂²×C₇	1	4	yes	complemented
373	#435	C₂²×C₇	1	4	yes	complemented
374	#435	C₂²×C₇	1	4	yes	complemented
375	#435	C₂²×C₇	1	4	yes	complemented
376	#435	C₂²×C₇	1	4	yes	complemented
377	#435	C₂²×C₇	1	4	yes	complemented
378	C₈×D₄	C₂²×C₇	1	2	yes	complemented
379	C₈×D₄	C₂²×C₇	1	2	yes	complemented
380	C₈×D₄	C₂²×C₇	1	4	yes	complemented
381	C₈×D₄	C₂²×C₇	1	2	yes	complemented
382	C₈×D₄	C₂²×C₇	1	2	yes	complemented
383	#433	C₂²×C₇	1	2	yes	complemented
384	#433	C₂²×C₇	1	2	yes	complemented
385	#433	C₂²×C₇	1	4	yes	complemented
386	#432	C₂²×C₇	1	2	yes	complemented
387	#431	C₂²×C₇	1	2	yes	complemented
388	#431	C₂²×C₇	1	2	yes	complemented
389	#431	C₂²×C₇	1	2	yes	complemented
390	#424	C₂²×C₇	1	1	yes	characteristic, complemented
391	#424	C₂²×C₇	1	1	yes	characteristic, complemented
392	#423	C₂²×C₇	1	1	yes	characteristic, complemented
393	C₂×C₄⋊C₈	C₂²×C₇	1	1	yes	characteristic, complemented
394	#408	C₂²×C₇	1	1	yes	characteristic
395	#408	C₂²×C₇	1	2	yes	—
396	#408	C₂²×C₇	1	1	yes	characteristic
397	#408	C₂²×C₇	1	2	yes	complemented
398	#408	C₂²×C₇	1	2	yes	complemented
399	#408	C₂²×C₇	1	4	yes	complemented
400	#408	C₂²×C₇	1	4	yes	complemented
401	#408	C₂²×C₇	1	4	yes	complemented
402	#408	C₂²×C₇	1	4	yes	complemented
403	#407	C₂²×C₇	1	4	yes	complemented
404	#407	C₂²×C₇	1	4	yes	complemented
405	#407	C₂²×C₇	1	2	yes	complemented
406	#407	C₂²×C₇	1	4	yes	complemented
407	C₂×C₂²⋊C₈	C₂²×C₇	1	2	yes	complemented
408	C₂×C₂²⋊C₈	C₂²×C₇	1	4	yes	complemented
409	#405	C₂²×C₇	1	2	yes	complemented
410	C₄×M₁₆	C₂²×C₇	1	1	yes	characteristic, complemented
411	C₂×C₄×C₈	C₂²×C₇	1	1	yes	characteristic, complemented
412	C₂³×C₇	—	2	4	no	—
413	C₂³×C₇	—	4	4	no	—
414	C₂³×C₇	—	4	2	no	—
415	C₂³×C₇	—	4	4	no	—
416	C₂³×C₇	—	4	2	no	—
417	C₂³×C₇	—	4	4	no	—
418	C₂³×C₇	C₂³×C₄	1	2	yes	—
419	C₂³×C₇	C₂³×C₄	1	2	yes	—
420	C₂³×C₇	C₂³×C₄	1	4	yes	—
421	C₂³×C₇	C₂³×C₄	1	2	yes	—
422	C₂³×C₇	C₂³×C₄	1	1	yes	characteristic
423	C₇×Q₈	—	2	2	no	—
424	C₇×Q₈	—	2	4	no	—
425	C₇×Q₈	—	4	4	no	—
426	C₇×D₄	—	2	4	no	—
427	C₇×D₄	—	2	8	no	—
428	C₇×D₄	—	2	2	no	—
429	C₇×D₄	—	2	4	no	—
430	C₇×D₄	—	2	2	no	—
431	C₇×D₄	—	2	2	no	—
432	C₇×D₄	—	2	4	no	—
433	C₇×D₄	—	4	2	no	—
434	C₇×D₄	—	4	4	no	—
435	C₇×D₄	—	4	4	no	—
436	C₇×D₄	—	4	4	no	—
437	C₇×D₄	—	4	4	no	—
438	C₇×D₄	—	4	2	no	—
439	C₇×D₄	—	4	4	no	—
440	C₂×C₄×C₇	—	2	4	no	—
441	C₂×C₄×C₇	—	2	4	no	—
442	C₂×C₄×C₇	—	2	4	no	—
443	C₂×C₄×C₇	—	2	2	no	—
444	C₂×C₄×C₇	—	2	4	no	—
445	C₂×C₄×C₇	—	2	2	no	—
446	C₂×C₄×C₇	—	2	4	no	—
447	C₂×C₄×C₇	—	2	4	no	—
448	C₂×C₄×C₇	—	2	2	no	—
449	C₂×C₄×C₇	—	2	2	no	—
450	C₂×C₄×C₇	—	2	2	no	—
451	C₂×C₄×C₇	—	2	2	no	—
452	C₂×C₄×C₇	—	2	2	no	—
453	C₂×C₄×C₇	—	4	4	no	—
454	C₂×C₄×C₇	—	4	4	no	—
455	C₂×C₄×C₇	—	4	4	no	—
456	C₂×C₄×C₇	—	4	1	no	—
457	C₂×C₄×C₇	—	4	2	no	—
458	C₂×C₄×C₇	C₂³×C₄	1	1	yes	characteristic
459	C₂×C₄×C₇	C₂³×C₄	1	2	yes	—
460	C₂×C₄×C₇	C₂³×C₄	1	2	yes	—
461	C₂×C₄×C₇	C₂³×C₄	1	1	yes	characteristic
462	C₂×C₄×C₇	C₂³×C₄	1	2	yes	—
463	C₂×C₄×C₇	C₂³×C₄	1	1	yes	characteristic
464	C₂×C₄×C₇	C₂³×C₄	1	2	yes	—
465	C₂×C₄×C₇	C₂³×C₄	1	2	yes	—
466	C₂×C₄×C₇	C₂³×C₄	1	4	yes	—
467	C₂×C₄×C₇	C₂³×C₄	1	1	yes	characteristic
468	C₂×C₄×C₇	C₂³×C₄	1	1	yes	characteristic
469	C₂×C₄×C₇	H(5,𝔽₂)	1	2	yes	—
470	C₂×C₄×C₇	H(5,𝔽₂)	1	2	yes	—
471	C₂×C₄×C₇	C₂⁵	1	1	yes	characteristic
472	C₇×C₈	—	2	1	no	—
473	C₇×C₈	—	2	2	no	—
474	C₇×C₈	—	2	1	no	—
475	C₇×C₈	—	2	1	no	—
476	C₇×C₈	—	2	2	no	—
477	C₇×C₈	—	2	1	no	—
478	C₇×C₈	—	2	2	no	—
479	C₇×C₈	—	2	4	no	—
480	C₇×C₈	—	2	2	no	—
481	C₂×#41	—	4	4	no	—
482	C₂×#41	—	4	4	no	—
483	C₂×#41	C₂×C₄×C₇	1	4	yes	—
484	C₂×#41	C₂×C₄×C₇	1	2	yes	—
485	C₂×#41	C₂×C₄×C₇	1	2	yes	—
486	C₂×#41	C₂³×C₇	1	1	yes	characteristic
487	C₂×#41	C₂³×C₇	1	2	yes	—
488	C₂×#41	C₂³×C₇	1	4	yes	—
489	C₂²×Q₈	C₂×C₄×C₇	1	2	yes	—
490	C₂²×D₄	C₂×C₄×C₇	1	1	yes	characteristic
491	C₂²×D₄	C₂×C₄×C₇	1	2	yes	—
492	C₂²×D₄	C₂×C₄×C₇	1	2	yes	—
493	C₂²×D₄	C₂×C₄×C₇	1	4	yes	—
494	C₂³×C₄	C₂³×C₇	1	2	yes	—
495	C₂³×C₄	C₂³×C₇	1	4	yes	—
496	#131	—	4	4	no	—
497	#131	—	4	4	no	—
498	C₂×M₁₆	—	4	4	no	—
499	C₂×M₁₆	—	4	4	no	—
500	C₂×M₁₆	C₂³×C₇	1	1	yes	characteristic
501	C₂×M₁₆	C₂³×C₇	1	2	yes	—
502	C₂×M₁₆	C₂³×C₇	1	1	yes	characteristic
503	C₂×M₁₆	C₂³×C₇	1	2	yes	—
504	C₂×M₁₆	C₂³×C₇	1	4	yes	—
505	C₂×M₁₆	C₂³×C₇	1	2	yes	—
506	C₂×M₁₆	C₂³×C₇	1	2	yes	—
507	C₂×M₁₆	C₂³×C₇	1	2	yes	—
508	C₂×M₁₆	C₂³×C₇	1	4	yes	—
509	C₂×M₁₆	C₂³×C₇	1	4	yes	—
510	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
511	C₂²×C₈	C₂³×C₇	1	2	yes	—
512	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
513	C₂²×C₈	C₂³×C₇	1	4	yes	—
514	C₂²×C₈	C₂³×C₇	1	4	yes	—
515	C₂²×C₈	C₂³×C₇	1	4	yes	—
516	C₄⋊Q₈	C₂×C₄×C₇	1	1	yes	characteristic
517	C₄⋊Q₈	C₂×C₄×C₇	1	2	yes	—
518	#127	C₂×C₄×C₇	1	1	yes	characteristic
519	#127	C₂×C₄×C₇	1	2	yes	—
520	#124	C₂×C₄×C₇	1	2	yes	—
521	#124	C₂×C₄×C₇	1	4	yes	—
522	#123	C₂×C₄×C₇	1	4	yes	—
523	#123	C₂×C₄×C₇	1	4	yes	—
524	#123	C₂×C₄×C₇	1	4	yes	—
525	C₂²⋊Q₈	C₂×C₄×C₇	1	2	yes	—
526	C₂²⋊Q₈	C₂×C₄×C₇	1	4	yes	—
527	C₂²⋊Q₈	C₂×C₄×C₇	1	2	yes	—
528	C₂²⋊Q₈	C₂×C₄×C₇	1	4	yes	—
529	#121	C₂×C₄×C₇	1	2	yes	—
530	#121	C₂×C₄×C₇	1	4	yes	—
531	#121	C₂×C₄×C₇	1	2	yes	—
532	#121	C₂×C₄×C₇	1	4	yes	—
533	#121	C₂×C₄×C₇	1	2	yes	—
534	#121	C₂×C₄×C₇	1	2	yes	—
535	#121	C₂×C₄×C₇	1	2	yes	—
536	#121	C₂×C₄×C₇	1	2	yes	—
537	#121	C₂×C₄×C₇	1	4	yes	—
538	#120	C₂×C₄×C₇	1	4	yes	—
539	#120	C₂×C₄×C₇	1	4	yes	—
540	#120	C₂×C₄×C₇	1	4	yes	—
541	C₄×Q₈	C₂×C₄×C₇	1	1	yes	characteristic
542	C₄×Q₈	C₂×C₄×C₇	1	1	yes	characteristic
543	C₄×D₄	C₂×C₄×C₇	1	1	yes	characteristic
544	C₄×D₄	C₂×C₄×C₇	1	2	yes	—
545	C₄×D₄	C₂×C₄×C₇	1	2	yes	—
546	C₄×D₄	C₂×C₄×C₇	1	4	yes	—
547	C₄×D₄	C₂×C₄×C₇	1	1	yes	characteristic
548	C₄×D₄	C₂×C₄×C₇	1	2	yes	—
549	C₄×D₄	C₂×C₄×C₇	1	2	yes	—
550	C₄×D₄	C₂×C₄×C₇	1	1	yes	characteristic
551	C₄×D₄	C₂×C₄×C₇	1	2	yes	—
552	C₄×D₄	C₂×C₄×C₇	1	1	yes	characteristic
553	C₄×D₄	C₂³×C₇	1	1	yes	characteristic
554	C₄×D₄	C₂³×C₇	1	2	yes	—
555	C₄×D₄	C₂³×C₇	1	4	yes	—
556	C₄×D₄	C₂³×C₇	1	1	yes	characteristic
557	C₄×D₄	C₂³×C₇	1	2	yes	—
558	C₄×D₄	C₂³×C₇	1	4	yes	—
559	C₄×D₄	C₂³×C₇	1	2	yes	—
560	#117	C₂³×C₇	1	1	yes	characteristic
561	#117	C₂³×C₇	1	2	yes	—
562	C₂×C₄⋊C₄	C₂×C₄×C₇	1	1	yes	characteristic
563	C₂×C₄⋊C₄	C₂×C₄×C₇	1	2	yes	—
564	C₂×C₂²⋊C₄	C₂×C₄×C₇	1	2	yes	—
565	C₂×C₂²⋊C₄	C₂×C₄×C₇	1	4	yes	—
566	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
567	C₂×C₄²	C₂³×C₇	1	2	yes	—
568	C₄⋊C₈	C₂³×C₇	1	1	yes	characteristic
569	C₄⋊C₈	C₂³×C₇	1	1	yes	characteristic
570	C₄⋊C₈	C₂³×C₇	1	2	yes	—
571	C₄⋊C₈	C₂³×C₇	1	2	yes	—
572	C₄⋊C₈	C₂³×C₇	1	2	yes	—
573	C₄⋊C₈	C₂³×C₇	1	2	yes	—
574	C₄⋊C₈	C₂³×C₇	1	2	yes	—
575	C₄⋊C₈	C₂³×C₇	1	2	yes	—
576	C₄⋊C₈	C₂³×C₇	1	2	yes	—
577	C₂²⋊C₈	C₂³×C₇	1	2	yes	—
578	C₂²⋊C₈	C₂³×C₇	1	2	yes	—
579	C₂²⋊C₈	C₂³×C₇	1	4	yes	—
580	C₂²⋊C₈	C₂³×C₇	1	2	yes	—
581	C₂²⋊C₈	C₂³×C₇	1	4	yes	—
582	C₂²⋊C₈	C₂³×C₇	1	2	yes	—
583	C₂²⋊C₈	C₂³×C₇	1	2	yes	—
584	C₂²⋊C₈	C₂³×C₇	1	2	yes	—
585	C₂²⋊C₈	C₂³×C₇	1	2	yes	—
586	C₂²⋊C₈	C₂³×C₇	1	4	yes	—
587	C₂²⋊C₈	C₂³×C₇	1	2	yes	—
588	C₂²⋊C₈	C₂³×C₇	1	4	yes	—
589	C₂²⋊C₈	C₂³×C₇	1	4	yes	—
590	C₂²⋊C₈	C₂³×C₇	1	4	yes	—
591	C₂²⋊C₈	C₂³×C₇	1	4	yes	—
592	C₂²⋊C₈	C₂³×C₇	1	4	yes	—
593	#97	C₂³×C₇	1	2	yes	—
594	#97	C₂³×C₇	1	4	yes	—
595	C₄×C₈	C₂³×C₇	1	1	yes	characteristic
596	C₄×C₈	C₂³×C₇	1	1	yes	characteristic
597	C₄×C₈	C₂³×C₇	1	1	yes	characteristic
598	C₄×C₈	C₂³×C₇	1	1	yes	characteristic
599	C₄×C₈	C₂³×C₇	1	2	yes	—
600	C₄×C₈	C₂³×C₇	1	4	yes	—
601	C₂²×C₇	—	2	1	no	—
602	C₂²×C₇	—	2	1	no	—
603	C₂²×C₇	—	2	2	no	—
604	C₂²×C₇	—	2	2	no	—
605	C₂²×C₇	—	2	2	no	—
606	C₂²×C₇	—	2	4	no	—
607	C₂²×C₇	—	2	2	no	—
608	C₂²×C₇	—	2	2	no	—
609	C₂²×C₇	—	2	2	no	—
610	C₂²×C₇	—	2	4	no	—
611	C₂²×C₇	—	2	2	no	—
612	C₂²×C₇	—	2	2	no	—
613	C₂²×C₇	—	2	4	no	—
614	C₂²×C₇	—	2	2	no	—
615	C₂²×C₇	—	8	4	no	—
616	C₂²×C₇	—	8	8	no	—
617	C₂²×C₇	#518	1	2	yes	—
618	C₂²×C₇	C₂⁴×C₄	1	1	yes	characteristic
619	C₄×C₇	—	2	2	no	—
620	C₄×C₇	—	2	2	no	—
621	C₄×C₇	—	2	2	no	—
622	C₄×C₇	—	2	4	no	—
623	C₄×C₇	—	2	1	no	—
624	C₄×C₇	—	2	2	no	—
625	C₄×C₇	—	2	1	no	—
626	C₄×C₇	—	2	1	no	—
627	C₄×C₇	—	2	2	no	—
628	C₄×C₇	#518	1	2	yes	—
629	C₄×C₇	#568	1	2	yes	—
630	C₄×C₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
631	C₄×C₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
632	C₂⁴	C₂²×C₄×C₇	1	2	yes	—
633	C₂⁴	C₂²×C₄×C₇	1	4	yes	—
634	#41	—	2	4	no	—
635	#41	—	2	4	no	—
636	#41	—	2	2	no	—
637	#41	—	2	2	no	—
638	#41	—	4	4	no	—
639	#41	—	4	4	no	—
640	#41	—	4	8	no	—
641	#41	—	4	4	no	—
642	#41	—	4	4	no	—
643	C₂×Q₈	—	4	4	no	—
644	C₂×Q₈	C₂²×C₄×C₇	1	1	yes	characteristic
645	C₂×Q₈	C₂²×C₄×C₇	1	2	yes	—
646	C₂×Q₈	C₂²×C₄×C₇	1	4	yes	—
647	C₂×D₄	—	4	4	no	—
648	C₂×D₄	—	4	2	no	—
649	C₂×D₄	—	4	4	no	—
650	C₂×D₄	—	4	8	no	—
651	C₂×D₄	C₂²×C₄×C₇	1	1	yes	characteristic
652	C₂×D₄	C₂²×C₄×C₇	1	2	yes	—
653	C₂×D₄	C₂²×C₄×C₇	1	1	yes	characteristic
654	C₂×D₄	C₂²×C₄×C₇	1	1	yes	characteristic
655	C₂×D₄	C₂²×C₄×C₇	1	2	yes	—
656	C₂×D₄	C₂²×C₄×C₇	1	4	yes	—
657	C₂×D₄	C₂²×C₄×C₇	1	2	yes	—
658	C₂×D₄	C₂²×C₄×C₇	1	2	yes	—
659	C₂×D₄	C₂²×C₄×C₇	1	4	yes	—
660	C₂×D₄	C₂²×C₄×C₇	1	4	yes	—
661	C₂×D₄	C₂²×C₄×C₇	1	2	yes	—
662	C₂×D₄	C₂²×C₄×C₇	1	4	yes	—
663	C₂×D₄	C₂²×C₄×C₇	1	4	yes	—
664	C₂×D₄	C₂²×C₄×C₇	1	4	yes	—
665	C₂²×C₄	—	2	4	no	—
666	C₂²×C₄	—	2	4	no	—
667	C₂²×C₄	—	4	4	no	—
668	C₂²×C₄	—	4	4	no	—
669	C₂²×C₄	C₂²×C₄×C₇	1	2	yes	—
670	C₂²×C₄	C₂²×C₄×C₇	1	1	yes	characteristic
671	C₂²×C₄	C₂²×C₄×C₇	1	2	yes	—
672	C₂²×C₄	C₂²×C₄×C₇	1	2	yes	—
673	C₂²×C₄	C₂²×C₄×C₇	1	2	yes	—
674	C₂²×C₄	C₂²×C₄×C₇	1	2	yes	—
675	C₂²×C₄	C₂²×C₄×C₇	1	1	yes	characteristic
676	C₂²×C₄	C₂²×C₄×C₇	1	4	yes	—
677	C₂²×C₄	C₂²×C₄×C₇	1	4	yes	—
678	C₂²×C₄	C₂²×C₄×C₇	1	4	yes	—
679	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
680	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
681	C₂²×C₄	C₂⁴×C₇	1	4	yes	—
682	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
683	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
684	M₁₆	—	2	2	no	—
685	M₁₆	—	2	4	no	—
686	M₁₆	—	2	2	no	—
687	M₁₆	—	4	2	no	—
688	M₁₆	—	4	2	no	—
689	M₁₆	—	4	2	no	—
690	M₁₆	—	4	2	no	—
691	M₁₆	—	4	4	no	—
692	M₁₆	—	4	4	no	—
693	M₁₆	—	4	4	no	—
694	C₂×C₈	—	2	2	no	—
695	C₂×C₈	—	2	4	no	—
696	C₂×C₈	—	2	2	no	—
697	C₂×C₈	—	4	4	no	—
698	C₂×C₈	—	4	4	no	—
699	C₂×C₈	—	4	4	no	—
700	C₂×C₈	C₂⁴×C₇	1	1	yes	characteristic
701	C₂×C₈	C₂⁴×C₇	1	1	yes	characteristic
702	C₂×C₈	C₂⁴×C₇	1	1	yes	characteristic
703	C₂×C₈	C₂⁴×C₇	1	1	yes	characteristic
704	C₂×C₈	C₂⁴×C₇	1	2	yes	—
705	C₂×C₈	C₂⁴×C₇	1	2	yes	—
706	C₂×C₈	C₂⁴×C₇	1	2	yes	—
707	C₂×C₈	C₂⁴×C₇	1	4	yes	—
708	C₂×C₈	C₂⁴×C₇	1	2	yes	—
709	C₄⋊C₄	C₂²×C₄×C₇	1	1	yes	characteristic
710	C₄⋊C₄	C₂²×C₄×C₇	1	1	yes	characteristic
711	C₄⋊C₄	C₂²×C₄×C₇	1	2	yes	—
712	C₄⋊C₄	C₂²×C₄×C₇	1	2	yes	—
713	C₄⋊C₄	C₂²×C₄×C₇	1	4	yes	—
714	C₄⋊C₄	C₂²×C₄×C₇	1	2	yes	—
715	C₄⋊C₄	C₂²×C₄×C₇	1	2	yes	—
716	C₄⋊C₄	C₂²×C₄×C₇	1	1	yes	characteristic
717	C₄⋊C₄	C₂²×C₄×C₇	1	1	yes	characteristic
718	C₄⋊C₄	C₂²×C₄×C₇	1	4	yes	—
719	C₄⋊C₄	C₂²×C₄×C₇	1	2	yes	—
720	C₂²⋊C₄	C₂²×C₄×C₇	1	2	yes	—
721	C₂²⋊C₄	C₂²×C₄×C₇	1	2	yes	—
722	C₂²⋊C₄	C₂²×C₄×C₇	1	4	yes	—
723	C₂²⋊C₄	C₂²×C₄×C₇	1	2	yes	—
724	C₂²⋊C₄	C₂²×C₄×C₇	1	4	yes	—
725	C₂²⋊C₄	C₂²×C₄×C₇	1	2	yes	—
726	C₂²⋊C₄	C₂²×C₄×C₇	1	4	yes	—
727	C₂²⋊C₄	C₂²×C₄×C₇	1	2	yes	—
728	C₂²⋊C₄	C₂²×C₄×C₇	1	2	yes	—
729	C₂²⋊C₄	C₂²×C₄×C₇	1	2	yes	—
730	C₂²⋊C₄	C₂²×C₄×C₇	1	4	yes	—
731	C₂²⋊C₄	C₂²×C₄×C₇	1	4	yes	—
732	C₂²⋊C₄	C₂²×C₄×C₇	1	4	yes	—
733	C₄²	C₂²×C₄×C₇	1	2	yes	—
734	C₄²	C₂²×C₄×C₇	1	1	yes	characteristic
735	C₄²	C₂²×C₄×C₇	1	2	yes	—
736	C₄²	C₂²×C₄×C₇	1	1	yes	characteristic
737	C₄²	C₂⁴×C₇	1	1	yes	characteristic
738	C₄²	C₂⁴×C₇	1	1	yes	characteristic
739	C₄²	C₂⁴×C₇	1	2	yes	—
740	C₂×C₇	—	2	2	no	—
741	C₂×C₇	—	4	2	no	—
742	C₂×C₇	—	4	4	no	—
743	C₂×C₇	—	4	2	no	—
744	C₂×C₇	—	4	2	no	—
745	C₂×C₇	C₂×#518	1	1	yes	characteristic
746	C₂×C₇	C₂×#568	1	1	yes	characteristic
747	C₂×C₇	#3573	1	1	yes	characteristic
748	C₂³	—	2	4	no	—
749	C₂³	—	4	4	no	—
750	C₂³	—	4	2	no	—
751	C₂³	—	4	4	no	—
752	C₂³	—	4	2	no	—
753	C₂³	—	4	4	no	—
754	C₂³	C₂³×C₄×C₇	1	2	yes	—
755	C₂³	C₂³×C₄×C₇	1	2	yes	—
756	C₂³	C₂³×C₄×C₇	1	4	yes	—
757	C₂³	C₂³×C₄×C₇	1	2	yes	—
758	C₂³	C₂³×C₄×C₇	1	1	yes	characteristic
759	Q₈	—	2	2	no	—
760	Q₈	—	2	4	no	—
761	Q₈	—	4	4	no	—
762	D₄	—	2	4	no	—
763	D₄	—	2	8	no	—
764	D₄	—	2	2	no	—
765	D₄	—	2	4	no	—
766	D₄	—	2	2	no	—
767	D₄	—	2	2	no	—
768	D₄	—	2	4	no	—
769	D₄	—	4	2	no	—
770	D₄	—	4	4	no	—
771	D₄	—	4	4	no	—
772	D₄	—	4	4	no	—
773	D₄	—	4	4	no	—
774	D₄	—	4	2	no	—
775	D₄	—	4	4	no	—
776	C₂×C₄	—	2	4	no	—
777	C₂×C₄	—	2	2	no	—
778	C₂×C₄	—	2	4	no	—
779	C₂×C₄	—	2	4	no	—
780	C₂×C₄	—	2	2	no	—
781	C₂×C₄	—	2	2	no	—
782	C₂×C₄	—	2	2	no	—
783	C₂×C₄	—	2	2	no	—
784	C₂×C₄	—	2	2	no	—
785	C₂×C₄	—	2	4	no	—
786	C₂×C₄	—	2	4	no	—
787	C₂×C₄	—	2	2	no	—
788	C₂×C₄	—	2	4	no	—
789	C₂×C₄	—	4	4	no	—
790	C₂×C₄	—	4	4	no	—
791	C₂×C₄	—	4	4	no	—
792	C₂×C₄	—	4	1	no	—
793	C₂×C₄	—	4	2	no	—
794	C₂×C₄	C₂³×C₄×C₇	1	1	yes	characteristic
795	C₂×C₄	C₂³×C₄×C₇	1	2	yes	—
796	C₂×C₄	C₂³×C₄×C₇	1	2	yes	—
797	C₂×C₄	C₂³×C₄×C₇	1	1	yes	characteristic
798	C₂×C₄	C₂³×C₄×C₇	1	2	yes	—
799	C₂×C₄	C₂³×C₄×C₇	1	1	yes	characteristic
800	C₂×C₄	C₂³×C₄×C₇	1	2	yes	—
801	C₂×C₄	C₂³×C₄×C₇	1	2	yes	—
802	C₂×C₄	C₂³×C₄×C₇	1	4	yes	—
803	C₂×C₄	C₂³×C₄×C₇	1	1	yes	characteristic
804	C₂×C₄	C₂³×C₄×C₇	1	1	yes	characteristic
805	C₂×C₄	C₇×H(5,𝔽₂)	1	2	yes	—
806	C₂×C₄	C₇×H(5,𝔽₂)	1	2	yes	—
807	C₂×C₄	C₂⁵×C₇	1	1	yes	characteristic
808	C₈	—	2	1	no	—
809	C₈	—	2	2	no	—
810	C₈	—	2	1	no	—
811	C₈	—	2	1	no	—
812	C₈	—	2	2	no	—
813	C₈	—	2	1	no	—
814	C₈	—	2	2	no	—
815	C₈	—	2	4	no	—
816	C₈	—	2	2	no	—
817	C₇	#60241	1	1	yes	characteristic, direct product factor, Sylow
818	C₂²	—	2	1	no	—
819	C₂²	—	2	1	no	—
820	C₂²	—	2	2	no	—
821	C₂²	—	2	2	no	—
822	C₂²	—	2	2	no	—
823	C₂²	—	2	4	no	—
824	C₂²	—	2	2	no	—
825	C₂²	—	2	2	no	—
826	C₂²	—	2	4	no	—
827	C₂²	—	2	2	no	—
828	C₂²	—	2	2	no	—
829	C₂²	—	2	2	no	—
830	C₂²	—	2	2	no	—
831	C₂²	—	2	4	no	—
832	C₂²	—	8	4	no	—
833	C₂²	—	8	8	no	—
834	C₂²	C₇×#518	1	2	yes	—
835	C₂²	C₂⁴×C₄×C₇	1	1	yes	characteristic
836	C₄	—	2	1	no	—
837	C₄	—	2	2	no	—
838	C₄	—	2	1	no	—
839	C₄	—	2	1	no	—
840	C₄	—	2	2	no	—
841	C₄	—	2	2	no	—
842	C₄	—	2	2	no	—
843	C₄	—	2	2	no	—
844	C₄	—	2	4	no	—
845	C₄	C₇×#518	1	2	yes	—
846	C₄	C₇×#568	1	2	yes	—
847	C₄	C₂×C₇×H(5,𝔽₂)	1	1	yes	characteristic
848	C₄	C₂×C₇×H(5,𝔽₂)	1	1	yes	characteristic
849	C₂	—	2	2	no	—
850	C₂	—	4	2	no	—
851	C₂	—	4	2	no	—
852	C₂	—	4	2	no	—
853	C₂	—	4	4	no	—
854	C₂	C₂×C₇×#518	1	1	yes	characteristic
855	C₂	C₂×C₇×#568	1	1	yes	characteristic
856	C₂	C₇×#3573	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₇	C₂⁵
commutator	C₂²	C₂⁴×C₄×C₇
Frattini, cosocle	C₂×C₄	C₂⁵×C₇
socle	C₂²×C₇	C₂⁴×C₄
prime radical	C₇×D₄×#41	C₂
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₇ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₇×#2981	C₂	semidirect
3. C₇×#2979	C₂	semidirect
4. C₇×#2978	C₂	semidirect
5. C₇×#2976	C₂	semidirect
6. C₇×#2975	C₂	semidirect
7. C₇×#2974	C₂	semidirect
8. C₇×#2935	C₂	semidirect
9. C₇×D₄×M₁₆	C₂	semidirect
10. C₇×#2933	C₂	semidirect
11. C₇×#2931	C₂	semidirect
12. C₇×#2930	C₂	semidirect
13. C₂×C₇×#436	C₂	semidirect
14. C₇×#2925	C₂	semidirect
15. C₇×#2922	C₂	semidirect
16. C₇×#2880	C₂	semidirect
17. C₇×#2879	C₂	semidirect
19. C₂×C₇×#131	C₂²	semidirect
20. C₂×C₇×#131	C₂²	semidirect
21. C₂²×C₇×M₁₆	C₂²	semidirect
22. C₂²×C₇×M₁₆	C₂²	semidirect
42. C₇×#436	C₂²	semidirect
43. C₇×#436	C₂²	semidirect
44. C₇×#436	C₂²	semidirect
45. C₇×#436	C₂²	semidirect
46. C₇×#436	C₂²	semidirect
47. C₇×#436	C₂²	semidirect
48. C₇×#436	C₂²	semidirect
49. C₇×#436	C₂²	semidirect
50. C₇×#436	C₂²	semidirect
51. C₇×#436	C₂²	semidirect
52. C₇×#435	C₂²	semidirect
53. C₇×#435	C₂²	semidirect
54. C₇×#435	C₂²	semidirect
55. C₇×#435	C₂²	semidirect
56. C₇×#435	C₂²	semidirect
57. C₇×#435	C₂²	semidirect
58. C₇×C₈×D₄	C₂²	semidirect
59. C₇×C₈×D₄	C₂²	semidirect
60. C₇×C₈×D₄	C₂²	semidirect
61. C₇×C₈×D₄	C₂²	semidirect
62. C₇×C₈×D₄	C₂²	semidirect
63. C₇×#433	C₂²	semidirect
64. C₇×#433	C₂²	semidirect
65. C₇×#433	C₂²	semidirect
66. C₇×#432	C₂²	semidirect
67. C₇×#431	C₂²	semidirect
68. C₇×#431	C₂²	semidirect
69. C₇×#431	C₂²	semidirect
70. C₇×#424	C₂²	semidirect
71. C₇×#424	C₂²	semidirect
72. C₇×#423	C₂²	semidirect
73. C₂×C₇×C₄⋊C₈	C₂²	semidirect
77. C₇×#408	C₂²	semidirect
78. C₇×#408	C₂²	semidirect
79. C₇×#408	C₂²	semidirect
80. C₇×#408	C₂²	semidirect
81. C₇×#408	C₂²	semidirect
82. C₇×#408	C₂²	semidirect
83. C₇×#407	C₂²	semidirect
84. C₇×#407	C₂²	semidirect
85. C₇×#407	C₂²	semidirect
86. C₇×#407	C₂²	semidirect
87. C₂×C₇×C₂²⋊C₈	C₂²	semidirect
88. C₂×C₇×C₂²⋊C₈	C₂²	semidirect
89. C₇×#405	C₂²	semidirect
90. C₄×C₇×M₁₆	C₂²	semidirect
91. C₂×C₄×C₇×C₈	C₂²	semidirect
92. #60241	C₇	direct (N × H)
214. #2981	C₂×C₇	semidirect
215. #2979	C₂×C₇	semidirect
216. #2978	C₂×C₇	semidirect
217. #2976	C₂×C₇	semidirect
218. #2975	C₂×C₇	semidirect
219. #2974	C₂×C₇	semidirect
220. #2935	C₂×C₇	semidirect
221. D₄×M₁₆	C₂×C₇	semidirect
222. #2933	C₂×C₇	semidirect
223. #2931	C₂×C₇	semidirect
224. #2930	C₂×C₇	semidirect
225. C₂×#436	C₂×C₇	semidirect
226. #2925	C₂×C₇	semidirect
227. #2922	C₂×C₇	semidirect
228. #2880	C₂×C₇	semidirect
229. #2879	C₂×C₇	semidirect
339. C₂×#131	C₂²×C₇	semidirect
340. C₂×#131	C₂²×C₇	semidirect
341. C₂²×M₁₆	C₂²×C₇	semidirect
342. C₂²×M₁₆	C₂²×C₇	semidirect
362. #436	C₂²×C₇	semidirect
363. #436	C₂²×C₇	semidirect
364. #436	C₂²×C₇	semidirect
365. #436	C₂²×C₇	semidirect
366. #436	C₂²×C₇	semidirect
367. #436	C₂²×C₇	semidirect
368. #436	C₂²×C₇	semidirect
369. #436	C₂²×C₇	semidirect
370. #436	C₂²×C₇	semidirect
371. #436	C₂²×C₇	semidirect
372. #435	C₂²×C₇	semidirect
373. #435	C₂²×C₇	semidirect
374. #435	C₂²×C₇	semidirect
375. #435	C₂²×C₇	semidirect
376. #435	C₂²×C₇	semidirect
377. #435	C₂²×C₇	semidirect
378. C₈×D₄	C₂²×C₇	semidirect
379. C₈×D₄	C₂²×C₇	semidirect
380. C₈×D₄	C₂²×C₇	semidirect
381. C₈×D₄	C₂²×C₇	semidirect
382. C₈×D₄	C₂²×C₇	semidirect
383. #433	C₂²×C₇	semidirect
384. #433	C₂²×C₇	semidirect
385. #433	C₂²×C₇	semidirect
386. #432	C₂²×C₇	semidirect
387. #431	C₂²×C₇	semidirect
388. #431	C₂²×C₇	semidirect
389. #431	C₂²×C₇	semidirect
390. #424	C₂²×C₇	semidirect
391. #424	C₂²×C₇	semidirect
392. #423	C₂²×C₇	semidirect
393. C₂×C₄⋊C₈	C₂²×C₇	semidirect
397. #408	C₂²×C₇	semidirect
398. #408	C₂²×C₇	semidirect
399. #408	C₂²×C₇	semidirect
400. #408	C₂²×C₇	semidirect
401. #408	C₂²×C₇	semidirect
402. #408	C₂²×C₇	semidirect
403. #407	C₂²×C₇	semidirect
404. #407	C₂²×C₇	semidirect
405. #407	C₂²×C₇	semidirect
406. #407	C₂²×C₇	semidirect
407. C₂×C₂²⋊C₈	C₂²×C₇	semidirect
408. C₂×C₂²⋊C₈	C₂²×C₇	semidirect
409. #405	C₂²×C₇	semidirect
410. C₄×M₁₆	C₂²×C₇	semidirect
411. C₂×C₄×C₈	C₂²×C₇	semidirect
817. C₇	#60241	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×D₄×#41	2
C₇×#2981	2
C₇×#2979	2
C₇×#2978	2
C₇×#2976	2
C₇×#2975	2
C₇×#2974	2
C₇×#2935	2
C₇×D₄×M₁₆	2
C₇×#2933	2
C₇×#2931	2
C₇×#2930	2
C₂×C₇×#436	2
C₇×#2925	2
C₇×#2922	2
C₇×#2880	2
C₇×#2879	2
#60241	7

Subgroups — C7×#60241 #13237457

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×#60241 #13237457