Subgroups — C₇×#60346 #13237562

Order 1792.

1628 conjugacy classes of subgroups.

The subgroup lattice has 932 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×#3531	C₂	1	1	yes	maximal, characteristic
2	C₇×#2995	C₂	1	1	yes	maximal, characteristic, complemented
3	C₇×#2995	C₂	1	1	yes	maximal, characteristic, complemented
4	C₇×#2994	C₂	1	2	yes	maximal, complemented
5	C₇×#2993	C₂	1	2	yes	maximal, complemented
6	C₇×#2993	C₂	1	2	yes	maximal, complemented
7	C₇×#2992	C₂	1	2	yes	maximal, complemented
8	C₇×#2987	C₂	1	1	yes	maximal, characteristic, complemented
9	C₇×#2986	C₂	1	2	yes	maximal, complemented
10	C₇×#2985	C₂	1	2	yes	maximal, complemented
11	C₇×#2969	C₂	1	2	yes	maximal, complemented
12	C₇×#2968	C₂	1	2	yes	maximal, complemented
13	C₇×#2968	C₂	1	2	yes	maximal, complemented
14	C₇×#2967	C₂	1	2	yes	maximal, complemented
15	C₇×#2966	C₂	1	1	yes	maximal, characteristic, complemented
16	C₇×#2966	C₂	1	1	yes	maximal, characteristic, complemented
17	C₇×#2962	C₂	1	2	yes	maximal, complemented
18	C₇×#2961	C₂	1	2	yes	maximal, complemented
19	C₇×#2960	C₂	1	1	yes	maximal, characteristic, complemented
20	C₇×#564	C₄	1	1	yes	characteristic
21	C₇×#563	C₄	1	2	yes	—
22	C₇×#563	C₄	1	2	yes	—
23	C₇×#563	C₄	1	2	yes	—
24	C₇×#563	C₄	1	1	yes	characteristic
25	C₇×#563	C₄	1	2	yes	—
26	C₇×#563	C₄	1	1	yes	characteristic
27	C₇×#562	C₄	1	2	yes	—
28	C₇×#562	C₄	1	2	yes	—
29	C₇×#562	C₄	1	1	yes	characteristic
30	C₇×#533	C₂²	1	1	yes	characteristic
31	C₇×#533	C₂²	1	2	yes	—
32	C₇×#533	C₂²	1	2	yes	—
33	C₇×#529	C₂²	1	1	yes	characteristic
34	C₇×#529	C₂²	1	1	yes	characteristic
35	C₇×#529	C₂²	1	2	yes	—
36	C₇×#529	C₂²	1	2	yes	—
37	C₇×#529	C₂²	1	2	yes	—
38	C₇×#529	C₂²	1	2	yes	—
39	C₇×#446	C₂²	1	2	yes	—
40	C₇×#446	C₂²	1	2	yes	—
41	C₇×#446	C₂²	1	1	yes	characteristic
42	C₇×#446	C₂²	1	2	yes	—
43	C₇×#446	C₂²	1	2	yes	—
44	C₇×#446	C₂²	1	2	yes	—
45	C₇×#446	C₂²	1	2	yes	—
46	C₇×#446	C₂²	1	2	yes	—
47	C₇×#446	C₂²	1	2	yes	—
48	C₇×#446	C₂²	1	2	yes	—
49	C₇×#446	C₂²	1	2	yes	—
50	C₇×#446	C₂²	1	2	yes	—
51	C₇×#446	C₂²	1	1	yes	characteristic
52	C₇×#446	C₂²	1	2	yes	—
53	C₇×#446	C₂²	1	2	yes	—
54	C₇×#446	C₂²	1	2	yes	—
55	C₇×C₈×Q₈	C₂²	1	2	yes	—
56	C₇×C₈×Q₈	C₂²	1	2	yes	—
57	C₇×C₈×Q₈	C₂²	1	1	yes	characteristic
58	C₇×C₈×Q₈	C₂²	1	2	yes	—
59	C₇×C₈×Q₈	C₂²	1	1	yes	characteristic
60	C₇×C₈×Q₈	C₂²	1	2	yes	—
61	C₇×#436	C₂²	1	1	yes	characteristic
62	C₇×#436	C₂²	1	1	yes	characteristic
63	C₇×#436	C₂²	1	2	yes	—
64	C₇×#436	C₂²	1	2	yes	—
65	C₇×#436	C₂²	1	2	yes	—
66	C₇×#436	C₂²	1	2	yes	—
67	C₇×#435	C₂²	1	2	yes	—
68	C₇×#435	C₂²	1	2	yes	—
69	C₇×#435	C₂²	1	2	yes	—
70	C₇×#435	C₂²	1	2	yes	—
71	C₇×#435	C₂²	1	2	yes	—
72	C₇×#435	C₂²	1	2	yes	—
73	C₇×#435	C₂²	1	2	yes	—
74	C₇×#435	C₂²	1	2	yes	—
75	C₇×#435	C₂²	1	2	yes	—
76	C₇×#435	C₂²	1	2	yes	—
77	C₇×C₈×D₄	C₂²	1	1	yes	characteristic
78	C₇×C₈×D₄	C₂²	1	2	yes	—
79	C₇×C₈×D₄	C₂²	1	2	yes	—
80	C₇×C₈×D₄	C₂²	1	1	yes	characteristic
81	C₇×C₈×D₄	C₂²	1	2	yes	—
82	C₇×C₈×D₄	C₂²	1	2	yes	—
83	C₇×#433	C₂²	1	2	yes	—
84	C₇×#433	C₂²	1	2	yes	—
85	C₇×#433	C₂²	1	2	yes	—
86	C₇×#433	C₂²	1	2	yes	—
87	C₇×#433	C₂²	1	2	yes	—
88	C₇×#433	C₂²	1	2	yes	—
89	C₇×#433	C₂²	1	2	yes	—
90	C₇×#433	C₂²	1	2	yes	—
91	C₇×#433	C₂²	1	2	yes	—
92	C₇×#433	C₂²	1	2	yes	—
93	C₇×#432	C₂²	1	1	yes	characteristic
94	C₇×#432	C₂²	1	1	yes	characteristic
95	C₇×#432	C₂²	1	2	yes	—
96	C₇×#431	C₂²	1	2	yes	—
97	C₇×#431	C₂²	1	2	yes	—
98	C₇×#431	C₂²	1	2	yes	—
99	C₇×#424	C₂²	1	1	yes	characteristic
100	C₇×#424	C₂²	1	1	yes	characteristic
101	C₇×#424	C₂²	1	2	yes	—
102	C₇×#424	C₂²	1	2	yes	—
103	C₇×#424	C₂²	1	2	yes	—
104	C₇×#424	C₂²	1	2	yes	—
105	C₇×#423	C₂²	1	1	yes	characteristic
106	C₇×#423	C₂²	1	2	yes	—
107	C₂×C₇×C₄⋊C₈	C₂²	1	2	yes	—
108	C₇×#405	C₂²	1	1	yes	characteristic
109	C₇×#405	C₂²	1	1	yes	characteristic
110	C₇×#405	C₂²	1	2	yes	—
111	C₇×#405	C₂²	1	2	yes	—
112	C₇×#405	C₂²	1	2	yes	—
113	C₇×#405	C₂²	1	2	yes	—
114	C₄×C₇×M₁₆	C₂²	1	2	yes	—
115	C₂×C₇×#97	C₂²	1	2	yes	—
116	C₂×C₄×C₇×C₈	C₂²	1	1	yes	characteristic
117	#60346	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
118	C₂×C₇×M₁₆	C₂³	1	2	yes	—
119	C₂×C₇×M₁₆	C₂³	1	2	yes	—
120	C₂×C₇×M₁₆	C₂³	1	1	yes	characteristic
121	C₂×C₇×M₁₆	C₂³	1	2	yes	—
122	C₂×C₇×M₁₆	C₂³	1	2	yes	—
123	C₂×C₇×M₁₆	C₂³	1	1	yes	characteristic
124	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
125	C₂²×C₇×C₈	C₂³	1	2	yes	—
126	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
127	C₂²×C₇×C₈	C₂³	1	2	yes	—
128	C₂²×C₇×C₈	C₂³	1	2	yes	—
129	C₂²×C₇×C₈	C₂³	1	2	yes	—
130	C₇×C₄⋊Q₈	C₂×C₄	1	1	yes	characteristic
131	C₇×C₄⋊Q₈	C₂×C₄	1	1	yes	characteristic
132	C₇×C₄⋊Q₈	C₂×C₄	1	2	yes	—
133	C₇×C₄⋊Q₈	C₂×C₄	1	2	yes	—
134	C₇×C₄⋊Q₈	C₂×C₄	1	2	yes	—
135	C₇×C₄⋊Q₈	C₂×C₄	1	2	yes	—
136	C₇×#126	C₂×C₄	1	2	yes	—
137	C₇×#126	C₂×C₄	1	2	yes	—
138	C₇×#126	C₂×C₄	1	2	yes	—
139	C₇×#126	C₂×C₄	1	2	yes	—
140	C₇×#126	C₂×C₄	1	2	yes	—
141	C₇×#126	C₂×C₄	1	2	yes	—
142	C₇×#126	C₂×C₄	1	2	yes	—
143	C₇×#126	C₂×C₄	1	2	yes	—
144	C₇×#126	C₂×C₄	1	2	yes	—
145	C₇×#126	C₂×C₄	1	2	yes	—
146	C₇×#125	C₂×C₄	1	1	yes	characteristic
147	C₇×#125	C₂×C₄	1	1	yes	characteristic
148	C₇×#125	C₂×C₄	1	2	yes	—
149	C₇×#125	C₂×C₄	1	2	yes	—
150	C₇×#125	C₂×C₄	1	2	yes	—
151	C₇×#125	C₂×C₄	1	2	yes	—
152	C₇×#125	C₂×C₄	1	1	yes	characteristic
153	C₇×#125	C₂×C₄	1	2	yes	—
154	C₇×#125	C₂×C₄	1	2	yes	—
155	C₇×#125	C₂×C₄	1	1	yes	characteristic
156	C₇×#125	C₂×C₄	1	2	yes	—
157	C₇×#125	C₂×C₄	1	2	yes	—
158	C₇×#124	C₂×C₄	1	1	yes	characteristic
159	C₇×#124	C₂×C₄	1	1	yes	characteristic
160	C₇×#124	C₂×C₄	1	2	yes	—
161	C₇×#124	C₂×C₄	1	2	yes	—
162	C₇×#124	C₂×C₄	1	2	yes	—
163	C₇×#124	C₂×C₄	1	2	yes	—
164	C₇×#123	C₂×C₄	1	2	yes	—
165	C₇×#123	C₂×C₄	1	2	yes	—
166	C₇×#123	C₂×C₄	1	2	yes	—
167	C₇×#123	C₂×C₄	1	2	yes	—
168	C₇×#123	C₂×C₄	1	2	yes	—
169	C₇×#123	C₂×C₄	1	2	yes	—
170	C₇×#123	C₂×C₄	1	2	yes	—
171	C₇×#123	C₂×C₄	1	2	yes	—
172	C₇×#123	C₂×C₄	1	2	yes	—
173	C₇×#123	C₂×C₄	1	2	yes	—
174	C₇×C₂²⋊Q₈	C₂×C₄	1	1	yes	characteristic
175	C₇×C₂²⋊Q₈	C₂×C₄	1	1	yes	characteristic
176	C₇×C₂²⋊Q₈	C₂×C₄	1	2	yes	—
177	C₇×C₂²⋊Q₈	C₂×C₄	1	2	yes	—
178	C₇×C₂²⋊Q₈	C₂×C₄	1	2	yes	—
179	C₇×C₂²⋊Q₈	C₂×C₄	1	2	yes	—
180	C₇×C₂²⋊Q₈	C₂×C₄	1	2	yes	—
181	C₇×C₂²⋊Q₈	C₂×C₄	1	2	yes	—
182	C₇×C₂²⋊Q₈	C₂×C₄	1	2	yes	—
183	C₇×C₂²⋊Q₈	C₂×C₄	1	2	yes	—
184	C₇×C₂²⋊Q₈	C₂×C₄	1	2	yes	—
185	C₇×C₂²⋊Q₈	C₂×C₄	1	2	yes	—
186	C₇×C₂²⋊Q₈	C₂×C₄	1	2	yes	—
187	C₇×C₂²⋊Q₈	C₂×C₄	1	2	yes	—
188	C₇×C₂²⋊Q₈	C₂×C₄	1	2	yes	—
189	C₇×C₂²⋊Q₈	C₂×C₄	1	2	yes	—
190	C₇×#121	C₂×C₄	1	1	yes	characteristic
191	C₇×#121	C₂×C₄	1	1	yes	characteristic
192	C₇×#121	C₂×C₄	1	2	yes	—
193	C₇×#121	C₂×C₄	1	2	yes	—
194	C₇×#121	C₂×C₄	1	2	yes	—
195	C₇×#121	C₂×C₄	1	2	yes	—
196	C₄×C₇×Q₈	C₂³	1	1	yes	characteristic
197	C₄×C₇×Q₈	C₂³	1	1	yes	characteristic
198	C₄×C₇×Q₈	C₂³	1	2	yes	—
199	C₄×C₇×Q₈	C₂³	1	2	yes	—
200	C₄×C₇×Q₈	C₂³	1	2	yes	—
201	C₄×C₇×Q₈	C₂³	1	2	yes	—
202	C₄×C₇×D₄	C₂³	1	1	yes	characteristic
203	C₄×C₇×D₄	C₂³	1	1	yes	characteristic
204	C₄×C₇×D₄	C₂³	1	2	yes	—
205	C₄×C₇×D₄	C₂³	1	2	yes	—
206	C₄×C₇×D₄	C₂³	1	2	yes	—
207	C₄×C₇×D₄	C₂³	1	2	yes	—
208	C₇×#117	C₂³	1	2	yes	—
209	C₇×#117	C₂³	1	2	yes	—
210	C₇×#117	C₂³	1	2	yes	—
211	C₇×#117	C₂³	1	1	yes	characteristic
212	C₇×#117	C₂³	1	2	yes	—
213	C₇×#117	C₂³	1	1	yes	characteristic
214	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
215	C₂×C₄²×C₇	C₂³	1	2	yes	—
216	C₂×C₄²×C₇	C₂³	1	2	yes	—
217	C₇×C₄⋊C₈	C₂³	1	2	yes	—
218	C₇×C₄⋊C₈	C₂³	1	2	yes	—
219	C₇×C₄⋊C₈	C₂³	1	2	yes	—
220	C₇×C₄⋊C₈	C₂³	1	2	yes	—
221	C₇×C₄⋊C₈	C₂³	1	2	yes	—
222	C₇×C₄⋊C₈	C₂³	1	2	yes	—
223	C₇×C₄⋊C₈	C₂³	1	2	yes	—
224	C₇×C₄⋊C₈	C₂³	1	2	yes	—
225	C₇×C₄⋊C₈	C₂³	1	2	yes	—
226	C₇×C₄⋊C₈	C₂³	1	2	yes	—
227	C₇×C₄⋊C₈	C₂³	1	2	yes	—
228	C₇×C₄⋊C₈	C₂³	1	2	yes	—
229	C₇×C₄⋊C₈	C₂³	1	2	yes	—
230	C₇×C₄⋊C₈	C₂³	1	1	yes	characteristic
231	C₇×C₄⋊C₈	C₂³	1	2	yes	—
232	C₇×C₄⋊C₈	C₂³	1	1	yes	characteristic
233	C₇×C₄⋊C₈	C₂³	1	2	yes	—
234	C₇×C₄⋊C₈	C₂³	1	2	yes	—
235	C₇×C₄⋊C₈	C₂³	1	2	yes	—
236	C₇×C₄⋊C₈	C₂³	1	1	yes	characteristic
237	C₇×C₄⋊C₈	C₂³	1	2	yes	—
238	C₇×C₄⋊C₈	C₂³	1	1	yes	characteristic
239	C₇×C₂²⋊C₈	C₂³	1	2	yes	—
240	C₇×C₂²⋊C₈	C₂³	1	2	yes	—
241	C₇×C₂²⋊C₈	C₂³	1	2	yes	—
242	C₇×C₂²⋊C₈	C₂³	1	2	yes	—
243	C₇×C₂²⋊C₈	C₂³	1	2	yes	—
244	C₇×C₂²⋊C₈	C₂³	1	2	yes	—
245	C₇×C₂²⋊C₈	C₂³	1	2	yes	—
246	C₇×C₂²⋊C₈	C₂³	1	2	yes	—
247	C₇×C₂²⋊C₈	C₂³	1	2	yes	—
248	C₇×C₂²⋊C₈	C₂³	1	2	yes	—
249	C₇×#97	C₂³	1	2	yes	—
250	C₇×#97	C₂³	1	2	yes	—
251	C₇×#97	C₂³	1	2	yes	—
252	C₇×#97	C₂³	1	2	yes	—
253	C₇×#97	C₂³	1	2	yes	—
254	C₇×#97	C₂³	1	2	yes	—
255	C₇×#97	C₂³	1	2	yes	—
256	C₇×#97	C₂³	1	2	yes	—
257	C₇×#97	C₂³	1	2	yes	—
258	C₇×#97	C₂³	1	2	yes	—
259	C₄×C₇×C₈	C₂³	1	1	yes	characteristic
260	C₄×C₇×C₈	C₂³	1	1	yes	characteristic
261	C₄×C₇×C₈	C₂³	1	1	yes	characteristic
262	C₄×C₇×C₈	C₂³	1	1	yes	characteristic
263	C₄×C₇×C₈	C₂³	1	2	yes	—
264	C₄×C₇×C₈	C₂³	1	2	yes	—
265	C₄×C₇×C₈	C₂³	1	2	yes	—
266	C₄×C₇×C₈	C₂³	1	2	yes	—
267	C₄×C₇×C₈	C₂³	1	2	yes	—
268	C₄×C₇×C₈	C₂³	1	2	yes	—
269	C₄×C₇×C₈	C₂³	1	2	yes	—
270	C₄×C₇×C₈	C₂³	1	2	yes	—
271	#3531	C₂×C₇	1	1	yes	characteristic
272	#2995	C₂×C₇	1	1	yes	characteristic, complemented
273	#2995	C₂×C₇	1	1	yes	characteristic, complemented
274	#2994	C₂×C₇	1	2	yes	complemented
275	#2993	C₂×C₇	1	2	yes	complemented
276	#2993	C₂×C₇	1	2	yes	complemented
277	#2992	C₂×C₇	1	2	yes	complemented
278	#2987	C₂×C₇	1	1	yes	characteristic, complemented
279	#2986	C₂×C₇	1	2	yes	complemented
280	#2985	C₂×C₇	1	2	yes	complemented
281	#2969	C₂×C₇	1	2	yes	complemented
282	#2968	C₂×C₇	1	2	yes	complemented
283	#2968	C₂×C₇	1	2	yes	complemented
284	#2967	C₂×C₇	1	2	yes	complemented
285	#2966	C₂×C₇	1	1	yes	characteristic, complemented
286	#2966	C₂×C₇	1	1	yes	characteristic, complemented
287	#2962	C₂×C₇	1	2	yes	complemented
288	#2961	C₂×C₇	1	2	yes	complemented
289	#2960	C₂×C₇	1	1	yes	characteristic, complemented
290	C₂×C₇×Q₈	C₂²×C₄	1	1	yes	characteristic
291	C₂×C₇×Q₈	C₂²×C₄	1	1	yes	characteristic
292	C₂×C₇×Q₈	C₂²×C₄	1	2	yes	—
293	C₂×C₇×Q₈	C₂²×C₄	1	2	yes	—
294	C₂×C₇×Q₈	C₂²×C₄	1	2	yes	—
295	C₂×C₇×Q₈	C₂²×C₄	1	2	yes	—
296	C₂×C₇×D₄	C₂²×C₄	1	1	yes	characteristic
297	C₂×C₇×D₄	C₂²×C₄	1	1	yes	characteristic
298	C₂×C₇×D₄	C₂²×C₄	1	2	yes	—
299	C₂×C₇×D₄	C₂²×C₄	1	2	yes	—
300	C₂×C₇×D₄	C₂²×C₄	1	2	yes	—
301	C₂×C₇×D₄	C₂²×C₄	1	2	yes	—
302	C₂²×C₄×C₇	C₂²×C₄	1	1	yes	characteristic
303	C₂²×C₄×C₇	C₂²×C₄	1	1	yes	characteristic
304	C₂²×C₄×C₇	C₂²×C₄	1	2	yes	—
305	C₂²×C₄×C₇	C₂²×C₄	1	2	yes	—
306	C₂²×C₄×C₇	C₂²×C₄	1	2	yes	—
307	C₂²×C₄×C₇	C₂²×C₄	1	2	yes	—
308	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
309	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
310	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
311	C₇×M₁₆	—	2	4	no	—
312	C₇×M₁₆	—	4	1	no	—
313	C₇×M₁₆	—	4	2	no	—
314	C₇×M₁₆	—	4	2	no	—
315	C₇×M₁₆	—	4	2	no	—
316	C₇×M₁₆	—	4	1	no	—
317	C₂×C₇×C₈	—	2	2	no	—
318	C₂×C₇×C₈	—	2	4	no	—
319	C₂×C₇×C₈	—	4	2	no	—
320	C₂×C₇×C₈	—	4	1	no	—
321	C₂×C₇×C₈	—	4	2	no	—
322	C₂×C₇×C₈	—	4	2	no	—
323	C₂×C₇×C₈	C₂⁴	1	1	yes	characteristic
324	C₂×C₇×C₈	C₂⁴	1	1	yes	characteristic
325	C₂×C₇×C₈	C₂⁴	1	2	yes	—
326	C₂×C₇×C₈	C₂⁴	1	2	yes	—
327	C₂×C₇×C₈	C₂⁴	1	2	yes	—
328	C₂×C₇×C₈	C₂⁴	1	1	yes	characteristic
329	C₂×C₇×C₈	C₂⁴	1	2	yes	—
330	C₂×C₇×C₈	C₂⁴	1	2	yes	—
331	C₂×C₇×C₈	C₂⁴	1	2	yes	—
332	C₂×C₇×C₈	C₂⁴	1	1	yes	characteristic
333	C₇×C₄⋊C₄	C₂²×C₄	1	2	yes	—
334	C₇×C₄⋊C₄	C₂²×C₄	1	2	yes	—
335	C₇×C₄⋊C₄	C₂²×C₄	1	2	yes	—
336	C₇×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
337	C₇×C₄⋊C₄	C₂²×C₄	1	2	yes	—
338	C₇×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
339	C₇×C₄⋊C₄	C₂²×C₄	1	2	yes	—
340	C₇×C₄⋊C₄	C₂²×C₄	1	2	yes	—
341	C₇×C₄⋊C₄	C₂²×C₄	1	2	yes	—
342	C₇×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
343	C₇×C₄⋊C₄	C₂²×C₄	1	2	yes	—
344	C₇×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
345	C₇×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
346	C₇×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
347	C₇×C₄⋊C₄	C₂²×C₄	1	2	yes	—
348	C₇×C₄⋊C₄	C₂²×C₄	1	2	yes	—
349	C₇×C₄⋊C₄	C₂²×C₄	1	2	yes	—
350	C₇×C₄⋊C₄	C₂²×C₄	1	2	yes	—
351	C₇×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
352	C₇×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
353	C₇×C₄⋊C₄	C₂²×C₄	1	2	yes	—
354	C₇×C₄⋊C₄	C₂²×C₄	1	2	yes	—
355	C₇×C₄⋊C₄	C₂²×C₄	1	2	yes	—
356	C₇×C₄⋊C₄	C₂²×C₄	1	2	yes	—
357	C₇×C₄⋊C₄	C₂²×C₄	1	2	yes	—
358	C₇×C₄⋊C₄	C₂²×C₄	1	2	yes	—
359	C₇×C₄⋊C₄	C₂²×C₄	1	2	yes	—
360	C₇×C₄⋊C₄	C₂²×C₄	1	2	yes	—
361	C₇×C₄⋊C₄	C₂²×C₄	1	2	yes	—
362	C₇×C₄⋊C₄	C₂²×C₄	1	2	yes	—
363	C₇×C₄⋊C₄	C₂²×C₄	1	2	yes	—
364	C₇×C₄⋊C₄	C₂²×C₄	1	2	yes	—
365	C₇×C₄⋊C₄	C₂²×C₄	1	2	yes	—
366	C₇×C₄⋊C₄	C₂²×C₄	1	2	yes	—
367	C₇×C₂²⋊C₄	C₂²×C₄	1	2	yes	—
368	C₇×C₂²⋊C₄	C₂²×C₄	1	2	yes	—
369	C₇×C₂²⋊C₄	C₂²×C₄	1	2	yes	—
370	C₇×C₂²⋊C₄	C₂²×C₄	1	2	yes	—
371	C₇×C₂²⋊C₄	C₂²×C₄	1	2	yes	—
372	C₇×C₂²⋊C₄	C₂²×C₄	1	2	yes	—
373	C₇×C₂²⋊C₄	C₂²×C₄	1	2	yes	—
374	C₇×C₂²⋊C₄	C₂²×C₄	1	2	yes	—
375	C₇×C₂²⋊C₄	C₂²×C₄	1	2	yes	—
376	C₇×C₂²⋊C₄	C₂²×C₄	1	2	yes	—
377	C₇×C₂²⋊C₄	C₂²×C₄	1	2	yes	—
378	C₇×C₂²⋊C₄	C₂²×C₄	1	2	yes	—
379	C₇×C₂²⋊C₄	C₂²×C₄	1	2	yes	—
380	C₇×C₂²⋊C₄	C₂²×C₄	1	2	yes	—
381	C₇×C₂²⋊C₄	C₂²×C₄	1	2	yes	—
382	C₇×C₂²⋊C₄	C₂²×C₄	1	2	yes	—
383	C₇×C₂²⋊C₄	C₂²×C₄	1	2	yes	—
384	C₇×C₂²⋊C₄	C₂²×C₄	1	2	yes	—
385	C₇×C₂²⋊C₄	C₂²×C₄	1	2	yes	—
386	C₇×C₂²⋊C₄	C₂²×C₄	1	2	yes	—
387	C₄²×C₇	C₂²×C₄	1	1	yes	characteristic
388	C₄²×C₇	C₂²×C₄	1	2	yes	—
389	C₄²×C₇	C₂²×C₄	1	2	yes	—
390	C₄²×C₇	C₂²×C₄	1	1	yes	characteristic
391	C₄²×C₇	C₂²×C₄	1	2	yes	—
392	C₄²×C₇	C₂²×C₄	1	2	yes	—
393	C₄²×C₇	C₂⁴	1	1	yes	characteristic
394	C₄²×C₇	C₂⁴	1	1	yes	characteristic
395	C₄²×C₇	C₂⁴	1	2	yes	—
396	C₄²×C₇	C₂⁴	1	2	yes	—
397	C₄²×C₇	C₂⁴	1	2	yes	—
398	C₄²×C₇	C₂⁴	1	2	yes	—
399	#564	C₄×C₇	1	1	yes	characteristic
400	#563	C₄×C₇	1	2	yes	—
401	#563	C₄×C₇	1	2	yes	—
402	#563	C₄×C₇	1	2	yes	—
403	#563	C₄×C₇	1	1	yes	characteristic
404	#563	C₄×C₇	1	2	yes	—
405	#563	C₄×C₇	1	1	yes	characteristic
406	#562	C₄×C₇	1	2	yes	—
407	#562	C₄×C₇	1	2	yes	—
408	#562	C₄×C₇	1	1	yes	characteristic
409	#533	C₂²×C₇	1	1	yes	characteristic
410	#533	C₂²×C₇	1	2	yes	—
411	#533	C₂²×C₇	1	2	yes	—
412	#529	C₂²×C₇	1	1	yes	characteristic
413	#529	C₂²×C₇	1	1	yes	characteristic
414	#529	C₂²×C₇	1	2	yes	—
415	#529	C₂²×C₇	1	2	yes	—
416	#529	C₂²×C₇	1	2	yes	—
417	#529	C₂²×C₇	1	2	yes	—
418	#446	C₂²×C₇	1	2	yes	—
419	#446	C₂²×C₇	1	2	yes	—
420	#446	C₂²×C₇	1	1	yes	characteristic
421	#446	C₂²×C₇	1	2	yes	—
422	#446	C₂²×C₇	1	2	yes	—
423	#446	C₂²×C₇	1	2	yes	—
424	#446	C₂²×C₇	1	2	yes	—
425	#446	C₂²×C₇	1	2	yes	—
426	#446	C₂²×C₇	1	2	yes	—
427	#446	C₂²×C₇	1	2	yes	—
428	#446	C₂²×C₇	1	2	yes	—
429	#446	C₂²×C₇	1	2	yes	—
430	#446	C₂²×C₇	1	1	yes	characteristic
431	#446	C₂²×C₇	1	2	yes	—
432	#446	C₂²×C₇	1	2	yes	—
433	#446	C₂²×C₇	1	2	yes	—
434	C₈×Q₈	C₂²×C₇	1	2	yes	—
435	C₈×Q₈	C₂²×C₇	1	2	yes	—
436	C₈×Q₈	C₂²×C₇	1	1	yes	characteristic
437	C₈×Q₈	C₂²×C₇	1	2	yes	—
438	C₈×Q₈	C₂²×C₇	1	1	yes	characteristic
439	C₈×Q₈	C₂²×C₇	1	2	yes	—
440	#436	C₂²×C₇	1	1	yes	characteristic
441	#436	C₂²×C₇	1	1	yes	characteristic
442	#436	C₂²×C₇	1	2	yes	—
443	#436	C₂²×C₇	1	2	yes	—
444	#436	C₂²×C₇	1	2	yes	—
445	#436	C₂²×C₇	1	2	yes	—
446	#435	C₂²×C₇	1	2	yes	—
447	#435	C₂²×C₇	1	2	yes	—
448	#435	C₂²×C₇	1	2	yes	—
449	#435	C₂²×C₇	1	2	yes	—
450	#435	C₂²×C₇	1	2	yes	—
451	#435	C₂²×C₇	1	2	yes	—
452	#435	C₂²×C₇	1	2	yes	—
453	#435	C₂²×C₇	1	2	yes	—
454	#435	C₂²×C₇	1	2	yes	—
455	#435	C₂²×C₇	1	2	yes	—
456	C₈×D₄	C₂²×C₇	1	1	yes	characteristic
457	C₈×D₄	C₂²×C₇	1	2	yes	—
458	C₈×D₄	C₂²×C₇	1	2	yes	—
459	C₈×D₄	C₂²×C₇	1	1	yes	characteristic
460	C₈×D₄	C₂²×C₇	1	2	yes	—
461	C₈×D₄	C₂²×C₇	1	2	yes	—
462	#433	C₂²×C₇	1	2	yes	—
463	#433	C₂²×C₇	1	2	yes	—
464	#433	C₂²×C₇	1	2	yes	—
465	#433	C₂²×C₇	1	2	yes	—
466	#433	C₂²×C₇	1	2	yes	—
467	#433	C₂²×C₇	1	2	yes	—
468	#433	C₂²×C₇	1	2	yes	—
469	#433	C₂²×C₇	1	2	yes	—
470	#433	C₂²×C₇	1	2	yes	—
471	#433	C₂²×C₇	1	2	yes	—
472	#432	C₂²×C₇	1	1	yes	characteristic
473	#432	C₂²×C₇	1	1	yes	characteristic
474	#432	C₂²×C₇	1	2	yes	—
475	#431	C₂²×C₇	1	2	yes	—
476	#431	C₂²×C₇	1	2	yes	—
477	#431	C₂²×C₇	1	2	yes	—
478	#424	C₂²×C₇	1	1	yes	characteristic
479	#424	C₂²×C₇	1	1	yes	characteristic
480	#424	C₂²×C₇	1	2	yes	—
481	#424	C₂²×C₇	1	2	yes	—
482	#424	C₂²×C₇	1	2	yes	—
483	#424	C₂²×C₇	1	2	yes	—
484	#423	C₂²×C₇	1	1	yes	characteristic
485	#423	C₂²×C₇	1	2	yes	—
486	C₂×C₄⋊C₈	C₂²×C₇	1	2	yes	—
487	#405	C₂²×C₇	1	1	yes	characteristic
488	#405	C₂²×C₇	1	1	yes	characteristic
489	#405	C₂²×C₇	1	2	yes	—
490	#405	C₂²×C₇	1	2	yes	—
491	#405	C₂²×C₇	1	2	yes	—
492	#405	C₂²×C₇	1	2	yes	—
493	C₄×M₁₆	C₂²×C₇	1	2	yes	—
494	C₂×#97	C₂²×C₇	1	2	yes	—
495	C₂×C₄×C₈	C₂²×C₇	1	1	yes	characteristic
496	C₂³×C₇	C₂³×C₄	1	1	yes	characteristic
497	C₂³×C₇	C₂³×C₄	1	2	yes	—
498	C₂³×C₇	C₂³×C₄	1	2	yes	—
499	C₇×Q₈	—	4	1	no	—
500	C₇×Q₈	—	4	1	no	—
501	C₇×Q₈	—	4	2	no	—
502	C₇×Q₈	—	4	2	no	—
503	C₇×Q₈	—	4	2	no	—
504	C₇×Q₈	—	4	2	no	—
505	C₇×D₄	—	4	1	no	—
506	C₇×D₄	—	4	1	no	—
507	C₇×D₄	—	4	2	no	—
508	C₇×D₄	—	4	2	no	—
509	C₇×D₄	—	4	2	no	—
510	C₇×D₄	—	4	2	no	—
511	C₂×C₄×C₇	—	2	1	no	—
512	C₂×C₄×C₇	—	2	2	no	—
513	C₂×C₄×C₇	—	2	2	no	—
514	C₂×C₄×C₇	—	2	2	no	—
515	C₂×C₄×C₇	—	2	1	no	—
516	C₂×C₄×C₇	—	2	2	no	—
517	C₂×C₄×C₇	—	4	1	no	—
518	C₂×C₄×C₇	—	4	1	no	—
519	C₂×C₄×C₇	—	4	2	no	—
520	C₂×C₄×C₇	—	4	2	no	—
521	C₂×C₄×C₇	—	4	2	no	—
522	C₂×C₄×C₇	—	4	2	no	—
523	C₂×C₄×C₇	C₂³×C₄	1	1	yes	characteristic
524	C₂×C₄×C₇	C₂³×C₄	1	2	yes	—
525	C₂×C₄×C₇	C₂³×C₄	1	2	yes	—
526	C₂×C₄×C₇	C₂³×C₄	1	1	yes	characteristic
527	C₂×C₄×C₇	C₂³×C₄	1	1	yes	characteristic
528	C₂×C₄×C₇	C₂³×C₄	1	2	yes	—
529	C₂×C₄×C₇	C₂³×C₄	1	2	yes	—
530	C₂×C₄×C₇	C₂³×C₄	1	2	yes	—
531	C₂×C₄×C₇	C₂³×C₄	1	2	yes	—
532	C₂×C₄×C₇	C₂³×C₄	1	1	yes	characteristic
533	C₂×C₄×C₇	C₂³×C₄	1	1	yes	characteristic
534	C₂×C₄×C₇	C₂³×C₄	1	2	yes	—
535	C₂×C₄×C₇	C₂³×C₄	1	2	yes	—
536	C₂×C₄×C₇	C₂³×C₄	1	2	yes	—
537	C₂×C₄×C₇	C₂³×C₄	1	2	yes	—
538	C₂×C₄×C₇	C₂⁵	1	1	yes	characteristic
539	C₇×C₈	—	2	1	no	—
540	C₇×C₈	—	2	2	no	—
541	C₇×C₈	—	2	2	no	—
542	C₇×C₈	—	2	1	no	—
543	C₇×C₈	—	2	2	no	—
544	C₇×C₈	—	2	2	no	—
545	C₇×C₈	—	2	1	no	—
546	C₇×C₈	—	2	2	no	—
547	C₇×C₈	—	2	2	no	—
548	C₇×C₈	2₋¹⁺⁴	1	2	yes	—
549	C₂×M₁₆	C₂³×C₇	1	2	yes	—
550	C₂×M₁₆	C₂³×C₇	1	2	yes	—
551	C₂×M₁₆	C₂³×C₇	1	1	yes	characteristic
552	C₂×M₁₆	C₂³×C₇	1	2	yes	—
553	C₂×M₁₆	C₂³×C₇	1	2	yes	—
554	C₂×M₁₆	C₂³×C₇	1	1	yes	characteristic
555	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
556	C₂²×C₈	C₂³×C₇	1	2	yes	—
557	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
558	C₂²×C₈	C₂³×C₇	1	2	yes	—
559	C₂²×C₈	C₂³×C₇	1	2	yes	—
560	C₂²×C₈	C₂³×C₇	1	2	yes	—
561	C₄⋊Q₈	C₂×C₄×C₇	1	1	yes	characteristic
562	C₄⋊Q₈	C₂×C₄×C₇	1	1	yes	characteristic
563	C₄⋊Q₈	C₂×C₄×C₇	1	2	yes	—
564	C₄⋊Q₈	C₂×C₄×C₇	1	2	yes	—
565	C₄⋊Q₈	C₂×C₄×C₇	1	2	yes	—
566	C₄⋊Q₈	C₂×C₄×C₇	1	2	yes	—
567	#126	C₂×C₄×C₇	1	2	yes	—
568	#126	C₂×C₄×C₇	1	2	yes	—
569	#126	C₂×C₄×C₇	1	2	yes	—
570	#126	C₂×C₄×C₇	1	2	yes	—
571	#126	C₂×C₄×C₇	1	2	yes	—
572	#126	C₂×C₄×C₇	1	2	yes	—
573	#126	C₂×C₄×C₇	1	2	yes	—
574	#126	C₂×C₄×C₇	1	2	yes	—
575	#126	C₂×C₄×C₇	1	2	yes	—
576	#126	C₂×C₄×C₇	1	2	yes	—
577	#125	C₂×C₄×C₇	1	1	yes	characteristic
578	#125	C₂×C₄×C₇	1	1	yes	characteristic
579	#125	C₂×C₄×C₇	1	2	yes	—
580	#125	C₂×C₄×C₇	1	2	yes	—
581	#125	C₂×C₄×C₇	1	2	yes	—
582	#125	C₂×C₄×C₇	1	2	yes	—
583	#125	C₂×C₄×C₇	1	1	yes	characteristic
584	#125	C₂×C₄×C₇	1	2	yes	—
585	#125	C₂×C₄×C₇	1	2	yes	—
586	#125	C₂×C₄×C₇	1	1	yes	characteristic
587	#125	C₂×C₄×C₇	1	2	yes	—
588	#125	C₂×C₄×C₇	1	2	yes	—
589	#124	C₂×C₄×C₇	1	1	yes	characteristic
590	#124	C₂×C₄×C₇	1	1	yes	characteristic
591	#124	C₂×C₄×C₇	1	2	yes	—
592	#124	C₂×C₄×C₇	1	2	yes	—
593	#124	C₂×C₄×C₇	1	2	yes	—
594	#124	C₂×C₄×C₇	1	2	yes	—
595	#123	C₂×C₄×C₇	1	2	yes	—
596	#123	C₂×C₄×C₇	1	2	yes	—
597	#123	C₂×C₄×C₇	1	2	yes	—
598	#123	C₂×C₄×C₇	1	2	yes	—
599	#123	C₂×C₄×C₇	1	2	yes	—
600	#123	C₂×C₄×C₇	1	2	yes	—
601	#123	C₂×C₄×C₇	1	2	yes	—
602	#123	C₂×C₄×C₇	1	2	yes	—
603	#123	C₂×C₄×C₇	1	2	yes	—
604	#123	C₂×C₄×C₇	1	2	yes	—
605	C₂²⋊Q₈	C₂×C₄×C₇	1	1	yes	characteristic
606	C₂²⋊Q₈	C₂×C₄×C₇	1	1	yes	characteristic
607	C₂²⋊Q₈	C₂×C₄×C₇	1	2	yes	—
608	C₂²⋊Q₈	C₂×C₄×C₇	1	2	yes	—
609	C₂²⋊Q₈	C₂×C₄×C₇	1	2	yes	—
610	C₂²⋊Q₈	C₂×C₄×C₇	1	2	yes	—
611	C₂²⋊Q₈	C₂×C₄×C₇	1	2	yes	—
612	C₂²⋊Q₈	C₂×C₄×C₇	1	2	yes	—
613	C₂²⋊Q₈	C₂×C₄×C₇	1	2	yes	—
614	C₂²⋊Q₈	C₂×C₄×C₇	1	2	yes	—
615	C₂²⋊Q₈	C₂×C₄×C₇	1	2	yes	—
616	C₂²⋊Q₈	C₂×C₄×C₇	1	2	yes	—
617	C₂²⋊Q₈	C₂×C₄×C₇	1	2	yes	—
618	C₂²⋊Q₈	C₂×C₄×C₇	1	2	yes	—
619	C₂²⋊Q₈	C₂×C₄×C₇	1	2	yes	—
620	C₂²⋊Q₈	C₂×C₄×C₇	1	2	yes	—
621	#121	C₂×C₄×C₇	1	1	yes	characteristic
622	#121	C₂×C₄×C₇	1	1	yes	characteristic
623	#121	C₂×C₄×C₇	1	2	yes	—
624	#121	C₂×C₄×C₇	1	2	yes	—
625	#121	C₂×C₄×C₇	1	2	yes	—
626	#121	C₂×C₄×C₇	1	2	yes	—
627	C₄×Q₈	C₂³×C₇	1	1	yes	characteristic
628	C₄×Q₈	C₂³×C₇	1	1	yes	characteristic
629	C₄×Q₈	C₂³×C₇	1	2	yes	—
630	C₄×Q₈	C₂³×C₇	1	2	yes	—
631	C₄×Q₈	C₂³×C₇	1	2	yes	—
632	C₄×Q₈	C₂³×C₇	1	2	yes	—
633	C₄×D₄	C₂³×C₇	1	1	yes	characteristic
634	C₄×D₄	C₂³×C₇	1	1	yes	characteristic
635	C₄×D₄	C₂³×C₇	1	2	yes	—
636	C₄×D₄	C₂³×C₇	1	2	yes	—
637	C₄×D₄	C₂³×C₇	1	2	yes	—
638	C₄×D₄	C₂³×C₇	1	2	yes	—
639	#117	C₂³×C₇	1	2	yes	—
640	#117	C₂³×C₇	1	2	yes	—
641	#117	C₂³×C₇	1	2	yes	—
642	#117	C₂³×C₇	1	1	yes	characteristic
643	#117	C₂³×C₇	1	2	yes	—
644	#117	C₂³×C₇	1	1	yes	characteristic
645	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
646	C₂×C₄²	C₂³×C₇	1	2	yes	—
647	C₂×C₄²	C₂³×C₇	1	2	yes	—
648	C₄⋊C₈	C₂³×C₇	1	2	yes	—
649	C₄⋊C₈	C₂³×C₇	1	2	yes	—
650	C₄⋊C₈	C₂³×C₇	1	2	yes	—
651	C₄⋊C₈	C₂³×C₇	1	2	yes	—
652	C₄⋊C₈	C₂³×C₇	1	2	yes	—
653	C₄⋊C₈	C₂³×C₇	1	2	yes	—
654	C₄⋊C₈	C₂³×C₇	1	2	yes	—
655	C₄⋊C₈	C₂³×C₇	1	2	yes	—
656	C₄⋊C₈	C₂³×C₇	1	2	yes	—
657	C₄⋊C₈	C₂³×C₇	1	2	yes	—
658	C₄⋊C₈	C₂³×C₇	1	2	yes	—
659	C₄⋊C₈	C₂³×C₇	1	2	yes	—
660	C₄⋊C₈	C₂³×C₇	1	2	yes	—
661	C₄⋊C₈	C₂³×C₇	1	1	yes	characteristic
662	C₄⋊C₈	C₂³×C₇	1	2	yes	—
663	C₄⋊C₈	C₂³×C₇	1	1	yes	characteristic
664	C₄⋊C₈	C₂³×C₇	1	2	yes	—
665	C₄⋊C₈	C₂³×C₇	1	2	yes	—
666	C₄⋊C₈	C₂³×C₇	1	2	yes	—
667	C₄⋊C₈	C₂³×C₇	1	1	yes	characteristic
668	C₄⋊C₈	C₂³×C₇	1	2	yes	—
669	C₄⋊C₈	C₂³×C₇	1	1	yes	characteristic
670	C₂²⋊C₈	C₂³×C₇	1	2	yes	—
671	C₂²⋊C₈	C₂³×C₇	1	2	yes	—
672	C₂²⋊C₈	C₂³×C₇	1	2	yes	—
673	C₂²⋊C₈	C₂³×C₇	1	2	yes	—
674	C₂²⋊C₈	C₂³×C₇	1	2	yes	—
675	C₂²⋊C₈	C₂³×C₇	1	2	yes	—
676	C₂²⋊C₈	C₂³×C₇	1	2	yes	—
677	C₂²⋊C₈	C₂³×C₇	1	2	yes	—
678	C₂²⋊C₈	C₂³×C₇	1	2	yes	—
679	C₂²⋊C₈	C₂³×C₇	1	2	yes	—
680	#97	C₂³×C₇	1	2	yes	—
681	#97	C₂³×C₇	1	2	yes	—
682	#97	C₂³×C₇	1	2	yes	—
683	#97	C₂³×C₇	1	2	yes	—
684	#97	C₂³×C₇	1	2	yes	—
685	#97	C₂³×C₇	1	2	yes	—
686	#97	C₂³×C₇	1	2	yes	—
687	#97	C₂³×C₇	1	2	yes	—
688	#97	C₂³×C₇	1	2	yes	—
689	#97	C₂³×C₇	1	2	yes	—
690	C₄×C₈	C₂³×C₇	1	1	yes	characteristic
691	C₄×C₈	C₂³×C₇	1	1	yes	characteristic
692	C₄×C₈	C₂³×C₇	1	1	yes	characteristic
693	C₄×C₈	C₂³×C₇	1	1	yes	characteristic
694	C₄×C₈	C₂³×C₇	1	2	yes	—
695	C₄×C₈	C₂³×C₇	1	2	yes	—
696	C₄×C₈	C₂³×C₇	1	2	yes	—
697	C₄×C₈	C₂³×C₇	1	2	yes	—
698	C₄×C₈	C₂³×C₇	1	2	yes	—
699	C₄×C₈	C₂³×C₇	1	2	yes	—
700	C₄×C₈	C₂³×C₇	1	2	yes	—
701	C₄×C₈	C₂³×C₇	1	2	yes	—
702	C₂²×C₇	—	2	1	no	—
703	C₂²×C₇	—	2	2	no	—
704	C₂²×C₇	—	2	2	no	—
705	C₂²×C₇	—	2	1	no	—
706	C₂²×C₇	—	2	1	no	—
707	C₂²×C₇	—	2	2	no	—
708	C₂²×C₇	—	2	2	no	—
709	C₂²×C₇	—	2	2	no	—
710	C₂²×C₇	—	2	2	no	—
711	C₂²×C₇	C₂⁴×C₄	1	1	yes	characteristic
712	C₄×C₇	—	2	1	no	—
713	C₄×C₇	—	2	2	no	—
714	C₄×C₇	—	2	2	no	—
715	C₄×C₇	—	2	1	no	—
716	C₄×C₇	—	2	1	no	—
717	C₄×C₇	—	2	2	no	—
718	C₄×C₇	—	2	2	no	—
719	C₄×C₇	—	2	2	no	—
720	C₄×C₇	—	2	2	no	—
721	C₄×C₇	—	2	1	no	—
722	C₄×C₇	—	2	1	no	—
723	C₄×C₇	—	2	2	no	—
724	C₄×C₇	—	2	2	no	—
725	C₄×C₇	—	2	2	no	—
726	C₄×C₇	—	2	2	no	—
727	C₄×C₇	C₂×2₋¹⁺⁴	1	1	yes	characteristic
728	C₄×C₇	#585	1	1	yes	characteristic
729	C₂×Q₈	C₂²×C₄×C₇	1	1	yes	characteristic
730	C₂×Q₈	C₂²×C₄×C₇	1	1	yes	characteristic
731	C₂×Q₈	C₂²×C₄×C₇	1	2	yes	—
732	C₂×Q₈	C₂²×C₄×C₇	1	2	yes	—
733	C₂×Q₈	C₂²×C₄×C₇	1	2	yes	—
734	C₂×Q₈	C₂²×C₄×C₇	1	2	yes	—
735	C₂×D₄	C₂²×C₄×C₇	1	1	yes	characteristic
736	C₂×D₄	C₂²×C₄×C₇	1	1	yes	characteristic
737	C₂×D₄	C₂²×C₄×C₇	1	2	yes	—
738	C₂×D₄	C₂²×C₄×C₇	1	2	yes	—
739	C₂×D₄	C₂²×C₄×C₇	1	2	yes	—
740	C₂×D₄	C₂²×C₄×C₇	1	2	yes	—
741	C₂²×C₄	C₂²×C₄×C₇	1	1	yes	characteristic
742	C₂²×C₄	C₂²×C₄×C₇	1	1	yes	characteristic
743	C₂²×C₄	C₂²×C₄×C₇	1	2	yes	—
744	C₂²×C₄	C₂²×C₄×C₇	1	2	yes	—
745	C₂²×C₄	C₂²×C₄×C₇	1	2	yes	—
746	C₂²×C₄	C₂²×C₄×C₇	1	2	yes	—
747	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
748	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
749	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
750	M₁₆	—	2	4	no	—
751	M₁₆	—	4	1	no	—
752	M₁₆	—	4	2	no	—
753	M₁₆	—	4	2	no	—
754	M₁₆	—	4	2	no	—
755	M₁₆	—	4	1	no	—
756	C₂×C₈	—	2	2	no	—
757	C₂×C₈	—	2	4	no	—
758	C₂×C₈	—	4	2	no	—
759	C₂×C₈	—	4	1	no	—
760	C₂×C₈	—	4	2	no	—
761	C₂×C₈	—	4	2	no	—
762	C₂×C₈	C₂⁴×C₇	1	1	yes	characteristic
763	C₂×C₈	C₂⁴×C₇	1	1	yes	characteristic
764	C₂×C₈	C₂⁴×C₇	1	2	yes	—
765	C₂×C₈	C₂⁴×C₇	1	2	yes	—
766	C₂×C₈	C₂⁴×C₇	1	2	yes	—
767	C₂×C₈	C₂⁴×C₇	1	1	yes	characteristic
768	C₂×C₈	C₂⁴×C₇	1	2	yes	—
769	C₂×C₈	C₂⁴×C₇	1	2	yes	—
770	C₂×C₈	C₂⁴×C₇	1	2	yes	—
771	C₂×C₈	C₂⁴×C₇	1	1	yes	characteristic
772	C₄⋊C₄	C₂²×C₄×C₇	1	2	yes	—
773	C₄⋊C₄	C₂²×C₄×C₇	1	2	yes	—
774	C₄⋊C₄	C₂²×C₄×C₇	1	2	yes	—
775	C₄⋊C₄	C₂²×C₄×C₇	1	1	yes	characteristic
776	C₄⋊C₄	C₂²×C₄×C₇	1	2	yes	—
777	C₄⋊C₄	C₂²×C₄×C₇	1	1	yes	characteristic
778	C₄⋊C₄	C₂²×C₄×C₇	1	2	yes	—
779	C₄⋊C₄	C₂²×C₄×C₇	1	2	yes	—
780	C₄⋊C₄	C₂²×C₄×C₇	1	2	yes	—
781	C₄⋊C₄	C₂²×C₄×C₇	1	1	yes	characteristic
782	C₄⋊C₄	C₂²×C₄×C₇	1	2	yes	—
783	C₄⋊C₄	C₂²×C₄×C₇	1	1	yes	characteristic
784	C₄⋊C₄	C₂²×C₄×C₇	1	1	yes	characteristic
785	C₄⋊C₄	C₂²×C₄×C₇	1	1	yes	characteristic
786	C₄⋊C₄	C₂²×C₄×C₇	1	2	yes	—
787	C₄⋊C₄	C₂²×C₄×C₇	1	2	yes	—
788	C₄⋊C₄	C₂²×C₄×C₇	1	2	yes	—
789	C₄⋊C₄	C₂²×C₄×C₇	1	2	yes	—
790	C₄⋊C₄	C₂²×C₄×C₇	1	1	yes	characteristic
791	C₄⋊C₄	C₂²×C₄×C₇	1	1	yes	characteristic
792	C₄⋊C₄	C₂²×C₄×C₇	1	2	yes	—
793	C₄⋊C₄	C₂²×C₄×C₇	1	2	yes	—
794	C₄⋊C₄	C₂²×C₄×C₇	1	2	yes	—
795	C₄⋊C₄	C₂²×C₄×C₇	1	2	yes	—
796	C₄⋊C₄	C₂²×C₄×C₇	1	2	yes	—
797	C₄⋊C₄	C₂²×C₄×C₇	1	2	yes	—
798	C₄⋊C₄	C₂²×C₄×C₇	1	2	yes	—
799	C₄⋊C₄	C₂²×C₄×C₇	1	2	yes	—
800	C₄⋊C₄	C₂²×C₄×C₇	1	2	yes	—
801	C₄⋊C₄	C₂²×C₄×C₇	1	2	yes	—
802	C₄⋊C₄	C₂²×C₄×C₇	1	2	yes	—
803	C₄⋊C₄	C₂²×C₄×C₇	1	2	yes	—
804	C₄⋊C₄	C₂²×C₄×C₇	1	2	yes	—
805	C₄⋊C₄	C₂²×C₄×C₇	1	2	yes	—
806	C₂²⋊C₄	C₂²×C₄×C₇	1	2	yes	—
807	C₂²⋊C₄	C₂²×C₄×C₇	1	2	yes	—
808	C₂²⋊C₄	C₂²×C₄×C₇	1	2	yes	—
809	C₂²⋊C₄	C₂²×C₄×C₇	1	2	yes	—
810	C₂²⋊C₄	C₂²×C₄×C₇	1	2	yes	—
811	C₂²⋊C₄	C₂²×C₄×C₇	1	2	yes	—
812	C₂²⋊C₄	C₂²×C₄×C₇	1	2	yes	—
813	C₂²⋊C₄	C₂²×C₄×C₇	1	2	yes	—
814	C₂²⋊C₄	C₂²×C₄×C₇	1	2	yes	—
815	C₂²⋊C₄	C₂²×C₄×C₇	1	2	yes	—
816	C₂²⋊C₄	C₂²×C₄×C₇	1	2	yes	—
817	C₂²⋊C₄	C₂²×C₄×C₇	1	2	yes	—
818	C₂²⋊C₄	C₂²×C₄×C₇	1	2	yes	—
819	C₂²⋊C₄	C₂²×C₄×C₇	1	2	yes	—
820	C₂²⋊C₄	C₂²×C₄×C₇	1	2	yes	—
821	C₂²⋊C₄	C₂²×C₄×C₇	1	2	yes	—
822	C₂²⋊C₄	C₂²×C₄×C₇	1	2	yes	—
823	C₂²⋊C₄	C₂²×C₄×C₇	1	2	yes	—
824	C₂²⋊C₄	C₂²×C₄×C₇	1	2	yes	—
825	C₂²⋊C₄	C₂²×C₄×C₇	1	2	yes	—
826	C₄²	C₂²×C₄×C₇	1	1	yes	characteristic
827	C₄²	C₂²×C₄×C₇	1	2	yes	—
828	C₄²	C₂²×C₄×C₇	1	2	yes	—
829	C₄²	C₂²×C₄×C₇	1	1	yes	characteristic
830	C₄²	C₂²×C₄×C₇	1	2	yes	—
831	C₄²	C₂²×C₄×C₇	1	2	yes	—
832	C₄²	C₂⁴×C₇	1	1	yes	characteristic
833	C₄²	C₂⁴×C₇	1	1	yes	characteristic
834	C₄²	C₂⁴×C₇	1	2	yes	—
835	C₄²	C₂⁴×C₇	1	2	yes	—
836	C₄²	C₂⁴×C₇	1	2	yes	—
837	C₄²	C₂⁴×C₇	1	2	yes	—
838	C₂×C₇	—	4	1	no	—
839	C₂×C₇	—	4	2	no	—
840	C₂×C₇	—	4	2	no	—
841	C₂×C₇	C₄×2₋¹⁺⁴	1	1	yes	characteristic
842	C₂×C₇	#3573	1	1	yes	characteristic
843	C₂×C₇	#3573	1	1	yes	characteristic
844	C₂³	C₂³×C₄×C₇	1	1	yes	characteristic
845	C₂³	C₂³×C₄×C₇	1	2	yes	—
846	C₂³	C₂³×C₄×C₇	1	2	yes	—
847	Q₈	—	4	1	no	—
848	Q₈	—	4	1	no	—
849	Q₈	—	4	2	no	—
850	Q₈	—	4	2	no	—
851	Q₈	—	4	2	no	—
852	Q₈	—	4	2	no	—
853	D₄	—	4	1	no	—
854	D₄	—	4	1	no	—
855	D₄	—	4	2	no	—
856	D₄	—	4	2	no	—
857	D₄	—	4	2	no	—
858	D₄	—	4	2	no	—
859	C₂×C₄	—	2	1	no	—
860	C₂×C₄	—	2	2	no	—
861	C₂×C₄	—	2	2	no	—
862	C₂×C₄	—	2	2	no	—
863	C₂×C₄	—	2	1	no	—
864	C₂×C₄	—	2	2	no	—
865	C₂×C₄	—	4	1	no	—
866	C₂×C₄	—	4	1	no	—
867	C₂×C₄	—	4	2	no	—
868	C₂×C₄	—	4	2	no	—
869	C₂×C₄	—	4	2	no	—
870	C₂×C₄	—	4	2	no	—
871	C₂×C₄	C₂³×C₄×C₇	1	1	yes	characteristic
872	C₂×C₄	C₂³×C₄×C₇	1	2	yes	—
873	C₂×C₄	C₂³×C₄×C₇	1	2	yes	—
874	C₂×C₄	C₂³×C₄×C₇	1	1	yes	characteristic
875	C₂×C₄	C₂³×C₄×C₇	1	1	yes	characteristic
876	C₂×C₄	C₂³×C₄×C₇	1	2	yes	—
877	C₂×C₄	C₂³×C₄×C₇	1	2	yes	—
878	C₂×C₄	C₂³×C₄×C₇	1	2	yes	—
879	C₂×C₄	C₂³×C₄×C₇	1	2	yes	—
880	C₂×C₄	C₂³×C₄×C₇	1	1	yes	characteristic
881	C₂×C₄	C₂³×C₄×C₇	1	1	yes	characteristic
882	C₂×C₄	C₂³×C₄×C₇	1	2	yes	—
883	C₂×C₄	C₂³×C₄×C₇	1	2	yes	—
884	C₂×C₄	C₂³×C₄×C₇	1	2	yes	—
885	C₂×C₄	C₂³×C₄×C₇	1	2	yes	—
886	C₂×C₄	C₂⁵×C₇	1	1	yes	characteristic
887	C₈	—	2	1	no	—
888	C₈	—	2	2	no	—
889	C₈	—	2	2	no	—
890	C₈	—	2	1	no	—
891	C₈	—	2	2	no	—
892	C₈	—	2	2	no	—
893	C₈	—	2	1	no	—
894	C₈	—	2	2	no	—
895	C₈	—	2	2	no	—
896	C₈	C₇×2₋¹⁺⁴	1	2	yes	—
897	C₇	#60346	1	1	yes	characteristic, direct product factor, Sylow
898	C₂²	—	2	1	no	—
899	C₂²	—	2	1	no	—
900	C₂²	—	2	2	no	—
901	C₂²	—	2	2	no	—
902	C₂²	—	2	2	no	—
903	C₂²	—	2	2	no	—
904	C₂²	—	2	1	no	—
905	C₂²	—	2	2	no	—
906	C₂²	—	2	2	no	—
907	C₂²	C₂⁴×C₄×C₇	1	1	yes	characteristic
908	C₄	—	2	1	no	—
909	C₄	—	2	1	no	—
910	C₄	—	2	2	no	—
911	C₄	—	2	2	no	—
912	C₄	—	2	2	no	—
913	C₄	—	2	2	no	—
914	C₄	—	2	1	no	—
915	C₄	—	2	1	no	—
916	C₄	—	2	2	no	—
917	C₄	—	2	2	no	—
918	C₄	—	2	2	no	—
919	C₄	—	2	2	no	—
920	C₄	—	2	1	no	—
921	C₄	—	2	2	no	—
922	C₄	—	2	2	no	—
923	C₄	C₂×C₇×2₋¹⁺⁴	1	1	yes	characteristic
924	C₄	C₇×#585	1	1	yes	characteristic
925	C₂	—	4	1	no	—
926	C₂	—	4	2	no	—
927	C₂	—	4	2	no	—
928	C₂	C₄×C₇×2₋¹⁺⁴	1	1	yes	characteristic
929	C₂	C₇×#3573	1	1	yes	characteristic
930	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×#3531	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×#2995	C₂	semidirect
3. C₇×#2995	C₂	semidirect
4. C₇×#2994	C₂	semidirect
5. C₇×#2993	C₂	semidirect
6. C₇×#2993	C₂	semidirect
7. C₇×#2992	C₂	semidirect
8. C₇×#2987	C₂	semidirect
9. C₇×#2986	C₂	semidirect
10. C₇×#2985	C₂	semidirect
11. C₇×#2969	C₂	semidirect
12. C₇×#2968	C₂	semidirect
13. C₇×#2968	C₂	semidirect
14. C₇×#2967	C₂	semidirect
15. C₇×#2966	C₂	semidirect
16. C₇×#2966	C₂	semidirect
17. C₇×#2962	C₂	semidirect
18. C₇×#2961	C₂	semidirect
19. C₇×#2960	C₂	semidirect
117. #60346	C₇	direct (N × H)
272. #2995	C₂×C₇	semidirect
273. #2995	C₂×C₇	semidirect
274. #2994	C₂×C₇	semidirect
275. #2993	C₂×C₇	semidirect
276. #2993	C₂×C₇	semidirect
277. #2992	C₂×C₇	semidirect
278. #2987	C₂×C₇	semidirect
279. #2986	C₂×C₇	semidirect
280. #2985	C₂×C₇	semidirect
281. #2969	C₂×C₇	semidirect
282. #2968	C₂×C₇	semidirect
283. #2968	C₂×C₇	semidirect
284. #2967	C₂×C₇	semidirect
285. #2966	C₂×C₇	semidirect
286. #2966	C₂×C₇	semidirect
287. #2962	C₂×C₇	semidirect
288. #2961	C₂×C₇	semidirect
289. #2960	C₂×C₇	semidirect
897. C₇	#60346	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×#3531	2
C₇×#2995	2
C₇×#2994	2
C₇×#2993	2
C₇×#2992	2
C₇×#2987	2
C₇×#2986	2
C₇×#2985	2
C₇×#2969	2
C₇×#2968	2
C₇×#2967	2
C₇×#2966	2
C₇×#2962	2
C₇×#2961	2
C₇×#2960	2
#60346	7

Subgroups — C7×#60346 #13237562

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×#60346 #13237562