Subgroups — C₇×#60341 #13237557

Order 1792.

1748 conjugacy classes of subgroups.

The subgroup lattice has 750 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×#3482	C₂	1	1	yes	maximal, characteristic
2	C₇×#2994	C₂	1	2	yes	maximal, complemented
3	C₇×#2992	C₂	1	4	yes	maximal, complemented
4	C₇×#2990	C₂	1	1	yes	maximal, characteristic, complemented
5	C₇×#2990	C₂	1	1	yes	maximal, characteristic, complemented
6	C₇×#2988	C₂	1	2	yes	maximal, complemented
7	C₇×#2986	C₂	1	1	yes	maximal, characteristic, complemented
8	C₇×#2985	C₂	1	2	yes	maximal, complemented
9	C₇×#2984	C₂	1	2	yes	maximal, complemented
10	C₇×#2970	C₂	1	2	yes	maximal, complemented
11	C₇×#2968	C₂	1	4	yes	maximal, complemented
12	C₇×#2966	C₂	1	2	yes	maximal, complemented
13	C₇×#2965	C₂	1	1	yes	maximal, characteristic, complemented
14	C₇×C₈×#41	C₂	1	1	yes	maximal, characteristic, complemented
15	C₇×#2962	C₂	1	2	yes	maximal, complemented
16	C₇×#2960	C₂	1	1	yes	maximal, characteristic, complemented
17	C₂×C₇×#446	C₂	1	2	yes	maximal, complemented
18	C₇×#557	C₄	1	1	yes	characteristic
19	C₇×#556	C₄	1	2	yes	—
20	C₇×#556	C₄	1	1	yes	characteristic
21	C₇×#552	C₄	1	2	yes	—
22	C₇×#552	C₄	1	4	yes	—
23	C₇×D₄×Q₈	C₄	1	1	yes	characteristic
24	C₇×#548	C₄	1	2	yes	—
25	C₇×#547	C₄	1	1	yes	characteristic
26	C₇×#547	C₄	1	2	yes	—
27	C₇×#533	C₂²	1	1	yes	characteristic
28	C₇×#533	C₂²	1	2	yes	—
29	C₇×#529	C₂²	1	2	yes	—
30	C₇×#529	C₂²	1	4	yes	—
31	C₄×C₇×#41	C₂²	1	1	yes	characteristic
32	C₄×C₇×#41	C₂²	1	1	yes	characteristic
33	C₄×C₇×#41	C₂²	1	2	yes	—
34	C₂×C₄×C₇×Q₈	C₂²	1	2	yes	—
35	C₇×#446	C₂²	1	1	yes	characteristic
36	C₇×#446	C₂²	1	2	yes	—
37	C₇×#446	C₂²	1	4	yes	—
38	C₇×#446	C₂²	1	2	yes	—
39	C₇×#446	C₂²	1	4	yes	—
40	C₇×#446	C₂²	1	2	yes	—
41	C₇×#446	C₂²	1	2	yes	—
42	C₇×#446	C₂²	1	4	yes	—
43	C₇×#446	C₂²	1	2	yes	—
44	C₇×#446	C₂²	1	1	yes	characteristic
45	C₇×#446	C₂²	1	4	yes	—
46	C₇×#446	C₂²	1	2	yes	—
47	C₇×C₈×Q₈	C₂²	1	2	yes	—
48	C₇×C₈×Q₈	C₂²	1	2	yes	—
49	C₇×C₈×Q₈	C₂²	1	1	yes	characteristic
50	C₇×C₈×Q₈	C₂²	1	2	yes	—
51	C₇×C₈×Q₈	C₂²	1	1	yes	characteristic
52	C₇×C₈×Q₈	C₂²	1	2	yes	—
53	C₇×#436	C₂²	1	1	yes	characteristic
54	C₇×#436	C₂²	1	1	yes	characteristic
55	C₇×#435	C₂²	1	2	yes	—
56	C₇×#435	C₂²	1	2	yes	—
57	C₇×#435	C₂²	1	4	yes	—
58	C₇×#435	C₂²	1	4	yes	—
59	C₇×#435	C₂²	1	4	yes	—
60	C₇×#435	C₂²	1	4	yes	—
61	C₇×C₈×D₄	C₂²	1	2	yes	—
62	C₇×C₈×D₄	C₂²	1	1	yes	characteristic
63	C₇×C₈×D₄	C₂²	1	1	yes	characteristic
64	C₇×C₈×D₄	C₂²	1	2	yes	—
65	C₇×C₈×D₄	C₂²	1	4	yes	—
66	C₇×C₈×D₄	C₂²	1	2	yes	—
67	C₇×C₈×D₄	C₂²	1	4	yes	—
68	C₇×C₈×D₄	C₂²	1	2	yes	—
69	C₇×#433	C₂²	1	4	yes	—
70	C₇×#433	C₂²	1	4	yes	—
71	C₇×#433	C₂²	1	4	yes	—
72	C₇×#432	C₂²	1	2	yes	—
73	C₇×#432	C₂²	1	4	yes	—
74	C₇×#432	C₂²	1	2	yes	—
75	C₇×#431	C₂²	1	2	yes	—
76	C₇×#431	C₂²	1	1	yes	characteristic
77	C₇×#431	C₂²	1	2	yes	—
78	C₇×#431	C₂²	1	1	yes	characteristic
79	C₇×#431	C₂²	1	4	yes	—
80	C₇×#424	C₂²	1	2	yes	—
81	C₇×#424	C₂²	1	4	yes	—
82	C₇×#423	C₂²	1	1	yes	characteristic
83	C₂×C₇×C₄⋊C₈	C₂²	1	4	yes	—
84	C₂×C₇×C₄⋊C₈	C₂²	1	2	yes	—
85	C₂×C₇×C₄⋊C₈	C₂²	1	2	yes	—
86	C₇×#405	C₂²	1	2	yes	—
87	C₇×#405	C₂²	1	4	yes	—
88	C₄×C₇×M₁₆	C₂²	1	2	yes	—
89	C₂×C₇×#97	C₂²	1	4	yes	—
90	C₂×C₄×C₇×C₈	C₂²	1	2	yes	—
91	C₂×C₄×C₇×C₈	C₂²	1	1	yes	characteristic
92	#60341	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
93	C₂×C₇×#41	C₂×C₄	1	1	yes	characteristic
94	C₂×C₇×#41	C₂×C₄	1	2	yes	—
95	C₂×C₇×#41	C₂×C₄	1	1	yes	characteristic
96	C₂²×C₇×Q₈	C₂×C₄	1	2	yes	—
97	C₂×C₇×M₁₆	C₂³	1	2	yes	—
98	C₂×C₇×M₁₆	C₂³	1	2	yes	—
99	C₂×C₇×M₁₆	C₂³	1	2	yes	—
100	C₂²×C₇×C₈	C₂³	1	2	yes	—
101	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
102	C₂²×C₇×C₈	C₂³	1	2	yes	—
103	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
104	C₂²×C₇×C₈	C₂³	1	4	yes	—
105	C₂²×C₇×C₈	C₂³	1	4	yes	—
106	C₇×C₄⋊Q₈	C₂×C₄	1	1	yes	characteristic
107	C₇×C₄⋊Q₈	C₂×C₄	1	2	yes	—
108	C₇×C₄⋊Q₈	C₂×C₄	1	1	yes	characteristic
109	C₇×C₄⋊Q₈	C₂×C₄	1	2	yes	—
110	C₇×#126	C₂×C₄	1	4	yes	—
111	C₇×#126	C₂×C₄	1	4	yes	—
112	C₇×#126	C₂×C₄	1	4	yes	—
113	C₇×#125	C₂×C₄	1	2	yes	—
114	C₇×#125	C₂×C₄	1	4	yes	—
115	C₇×#125	C₂×C₄	1	2	yes	—
116	C₇×#125	C₂×C₄	1	4	yes	—
117	C₇×#124	C₂×C₄	1	2	yes	—
118	C₇×#124	C₂×C₄	1	4	yes	—
119	C₇×#123	C₂×C₄	1	4	yes	—
120	C₇×#123	C₂×C₄	1	4	yes	—
121	C₇×#123	C₂×C₄	1	4	yes	—
122	C₇×C₂²⋊Q₈	C₂×C₄	1	2	yes	—
123	C₇×C₂²⋊Q₈	C₂×C₄	1	4	yes	—
124	C₇×C₂²⋊Q₈	C₂×C₄	1	2	yes	—
125	C₇×C₂²⋊Q₈	C₂×C₄	1	2	yes	—
126	C₇×C₂²⋊Q₈	C₂×C₄	1	2	yes	—
127	C₇×C₂²⋊Q₈	C₂×C₄	1	2	yes	—
128	C₇×C₂²⋊Q₈	C₂×C₄	1	4	yes	—
129	C₇×#121	C₂×C₄	1	2	yes	—
130	C₇×#121	C₂×C₄	1	4	yes	—
131	C₄×C₇×Q₈	C₂×C₄	1	2	yes	—
132	C₄×C₇×Q₈	C₂×C₄	1	2	yes	—
133	C₄×C₇×Q₈	C₂×C₄	1	4	yes	—
134	C₄×C₇×Q₈	C₂×C₄	1	1	yes	characteristic
135	C₄×C₇×Q₈	C₂×C₄	1	1	yes	characteristic
136	C₄×C₇×Q₈	C₂×C₄	1	2	yes	—
137	C₄×C₇×Q₈	C₂³	1	1	yes	characteristic
138	C₄×C₇×Q₈	C₂³	1	2	yes	—
139	C₄×C₇×Q₈	C₂³	1	4	yes	—
140	C₄×C₇×Q₈	C₂³	1	1	yes	characteristic
141	C₄×C₇×Q₈	C₂³	1	2	yes	—
142	C₄×C₇×D₄	C₂×C₄	1	1	yes	characteristic
143	C₄×C₇×D₄	C₂×C₄	1	2	yes	—
144	C₄×C₇×D₄	C₂×C₄	1	1	yes	characteristic
145	C₄×C₇×D₄	C₂×C₄	1	2	yes	—
146	C₄×C₇×D₄	C₂×C₄	1	2	yes	—
147	C₄×C₇×D₄	C₂×C₄	1	4	yes	—
148	C₄×C₇×D₄	C₂³	1	1	yes	characteristic
149	C₄×C₇×D₄	C₂³	1	2	yes	—
150	C₄×C₇×D₄	C₂³	1	4	yes	—
151	C₄×C₇×D₄	C₂³	1	1	yes	characteristic
152	C₄×C₇×D₄	C₂³	1	2	yes	—
153	C₇×#117	C₂×C₄	1	1	yes	characteristic
154	C₇×#117	C₂×C₄	1	2	yes	—
155	C₇×#117	C₂×C₄	1	2	yes	—
156	C₇×#117	C₂×C₄	1	4	yes	—
157	C₇×#117	C₂×C₄	1	1	yes	characteristic
158	C₇×#117	C₂×C₄	1	2	yes	—
159	C₇×#117	C₂³	1	4	yes	—
160	C₇×#117	C₂³	1	2	yes	—
161	C₂×C₇×C₄⋊C₄	C₂×C₄	1	2	yes	—
162	C₂×C₇×C₄⋊C₄	C₂×C₄	1	4	yes	—
163	C₂×C₄²×C₇	C₂³	1	2	yes	—
164	C₂×C₄²×C₇	C₂³	1	4	yes	—
165	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
166	C₂×C₄²×C₇	C₂³	1	2	yes	—
167	C₇×C₄⋊C₈	C₂³	1	1	yes	characteristic
168	C₇×C₄⋊C₈	C₂³	1	2	yes	—
169	C₇×C₄⋊C₈	C₂³	1	4	yes	—
170	C₇×C₄⋊C₈	C₂³	1	1	yes	characteristic
171	C₇×C₄⋊C₈	C₂³	1	2	yes	—
172	C₇×C₄⋊C₈	C₂³	1	2	yes	—
173	C₇×C₄⋊C₈	C₂³	1	4	yes	—
174	C₇×C₄⋊C₈	C₂³	1	4	yes	—
175	C₇×C₄⋊C₈	C₂³	1	4	yes	—
176	C₇×C₄⋊C₈	C₂³	1	2	yes	—
177	C₇×C₄⋊C₈	C₂³	1	4	yes	—
178	C₇×C₄⋊C₈	C₂³	1	2	yes	—
179	C₇×C₄⋊C₈	C₂³	1	1	yes	characteristic
180	C₇×C₄⋊C₈	C₂³	1	1	yes	characteristic
181	C₇×C₄⋊C₈	C₂³	1	2	yes	—
182	C₇×C₄⋊C₈	C₂³	1	4	yes	—
183	C₇×C₂²⋊C₈	C₂³	1	2	yes	—
184	C₇×C₂²⋊C₈	C₂³	1	4	yes	—
185	C₇×C₂²⋊C₈	C₂³	1	2	yes	—
186	C₇×C₂²⋊C₈	C₂³	1	2	yes	—
187	C₇×C₂²⋊C₈	C₂³	1	2	yes	—
188	C₇×C₂²⋊C₈	C₂³	1	2	yes	—
189	C₇×C₂²⋊C₈	C₂³	1	2	yes	—
190	C₇×C₂²⋊C₈	C₂³	1	4	yes	—
191	C₇×#97	C₂³	1	2	yes	—
192	C₇×#97	C₂³	1	4	yes	—
193	C₇×#97	C₂³	1	4	yes	—
194	C₇×#97	C₂³	1	4	yes	—
195	C₇×#97	C₂³	1	2	yes	—
196	C₇×#97	C₂³	1	4	yes	—
197	C₄×C₇×C₈	C₂³	1	1	yes	characteristic
198	C₄×C₇×C₈	C₂³	1	1	yes	characteristic
199	C₄×C₇×C₈	C₂³	1	2	yes	—
200	C₄×C₇×C₈	C₂³	1	1	yes	characteristic
201	C₄×C₇×C₈	C₂³	1	2	yes	—
202	C₄×C₇×C₈	C₂³	1	1	yes	characteristic
203	C₄×C₇×C₈	C₂³	1	2	yes	—
204	C₄×C₇×C₈	C₂³	1	2	yes	—
205	C₄×C₇×C₈	C₂³	1	4	yes	—
206	C₄×C₇×C₈	C₂³	1	4	yes	—
207	#3482	C₂×C₇	1	1	yes	characteristic
208	#2994	C₂×C₇	1	2	yes	complemented
209	#2992	C₂×C₇	1	4	yes	complemented
210	#2990	C₂×C₇	1	1	yes	characteristic, complemented
211	#2990	C₂×C₇	1	1	yes	characteristic, complemented
212	#2988	C₂×C₇	1	2	yes	complemented
213	#2986	C₂×C₇	1	1	yes	characteristic, complemented
214	#2985	C₂×C₇	1	2	yes	complemented
215	#2984	C₂×C₇	1	2	yes	complemented
216	#2970	C₂×C₇	1	2	yes	complemented
217	#2968	C₂×C₇	1	4	yes	complemented
218	#2966	C₂×C₇	1	2	yes	complemented
219	#2965	C₂×C₇	1	1	yes	characteristic, complemented
220	C₈×#41	C₂×C₇	1	1	yes	characteristic, complemented
221	#2962	C₂×C₇	1	2	yes	complemented
222	#2960	C₂×C₇	1	1	yes	characteristic, complemented
223	C₂×#446	C₂×C₇	1	2	yes	complemented
224	C₇×#41	—	2	4	no	—
225	C₇×#41	—	2	8	no	—
226	C₇×#41	—	4	2	no	—
227	C₂×C₇×Q₈	—	4	4	no	—
228	C₂×C₇×Q₈	C₂²×C₄	1	1	yes	characteristic
229	C₂×C₇×Q₈	C₂²×C₄	1	2	yes	—
230	C₂×C₇×Q₈	C₂²×C₄	1	1	yes	characteristic
231	C₂×C₇×Q₈	C₂²×C₄	1	2	yes	—
232	C₂×C₇×Q₈	C₂²×C₄	1	4	yes	—
233	C₂×C₇×D₄	C₂²×C₄	1	2	yes	—
234	C₂×C₇×D₄	C₂²×C₄	1	4	yes	—
235	C₂×C₇×D₄	C₂²×C₄	1	1	yes	characteristic
236	C₂×C₇×D₄	C₂²×C₄	1	2	yes	—
237	C₂×C₇×D₄	C₂²×C₄	1	1	yes	characteristic
238	C₂²×C₄×C₇	C₂²×C₄	1	2	yes	—
239	C₂²×C₄×C₇	C₂²×C₄	1	4	yes	—
240	C₂²×C₄×C₇	C₂²×C₄	1	2	yes	—
241	C₂²×C₄×C₇	C₂²×C₄	1	1	yes	characteristic
242	C₂²×C₄×C₇	C₂²×C₄	1	2	yes	—
243	C₂²×C₄×C₇	C₂²×C₄	1	1	yes	characteristic
244	C₂²×C₄×C₇	C₂²×C₄	1	4	yes	—
245	C₂²×C₄×C₇	C₂²×C₄	1	2	yes	—
246	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
247	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
248	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
249	C₇×M₁₆	—	2	4	no	—
250	C₇×M₁₆	—	4	2	no	—
251	C₇×M₁₆	—	4	2	no	—
252	C₂×C₇×C₈	—	2	4	no	—
253	C₂×C₇×C₈	—	2	2	no	—
254	C₂×C₇×C₈	—	4	2	no	—
255	C₂×C₇×C₈	—	4	4	no	—
256	C₂×C₇×C₈	—	4	1	no	—
257	C₂×C₇×C₈	—	4	4	no	—
258	C₂×C₇×C₈	C₂⁴	1	1	yes	characteristic
259	C₂×C₇×C₈	C₂⁴	1	1	yes	characteristic
260	C₂×C₇×C₈	C₂⁴	1	2	yes	—
261	C₂×C₇×C₈	C₂⁴	1	2	yes	—
262	C₂×C₇×C₈	C₂⁴	1	2	yes	—
263	C₂×C₇×C₈	C₂⁴	1	1	yes	characteristic
264	C₂×C₇×C₈	C₂⁴	1	2	yes	—
265	C₂×C₇×C₈	C₂⁴	1	4	yes	—
266	C₂×C₇×C₈	C₂⁴	1	1	yes	characteristic
267	C₇×C₄⋊C₄	C₂²×C₄	1	2	yes	—
268	C₇×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
269	C₇×C₄⋊C₄	C₂²×C₄	1	4	yes	—
270	C₇×C₄⋊C₄	C₂²×C₄	1	2	yes	—
271	C₇×C₄⋊C₄	C₂²×C₄	1	4	yes	—
272	C₇×C₄⋊C₄	C₂²×C₄	1	4	yes	—
273	C₇×C₄⋊C₄	C₂²×C₄	1	4	yes	—
274	C₇×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
275	C₇×C₄⋊C₄	C₂²×C₄	1	2	yes	—
276	C₇×C₄⋊C₄	C₂²×C₄	1	4	yes	—
277	C₇×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
278	C₇×C₄⋊C₄	C₂²×C₄	1	2	yes	—
279	C₇×C₄⋊C₄	C₂²×C₄	1	2	yes	—
280	C₇×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
281	C₇×C₄⋊C₄	C₂²×C₄	1	2	yes	—
282	C₇×C₄⋊C₄	C₂²×C₄	1	4	yes	—
283	C₇×C₄⋊C₄	C₂²×C₄	1	4	yes	—
284	C₇×C₄⋊C₄	C₂²×C₄	1	2	yes	—
285	C₇×C₄⋊C₄	C₂²×C₄	1	4	yes	—
286	C₇×C₄⋊C₄	C₂²×C₄	1	2	yes	—
287	C₇×C₂²⋊C₄	C₂²×C₄	1	2	yes	—
288	C₇×C₂²⋊C₄	C₂²×C₄	1	2	yes	—
289	C₇×C₂²⋊C₄	C₂²×C₄	1	4	yes	—
290	C₇×C₂²⋊C₄	C₂²×C₄	1	2	yes	—
291	C₇×C₂²⋊C₄	C₂²×C₄	1	2	yes	—
292	C₇×C₂²⋊C₄	C₂²×C₄	1	2	yes	—
293	C₇×C₂²⋊C₄	C₂²×C₄	1	2	yes	—
294	C₇×C₂²⋊C₄	C₂²×C₄	1	4	yes	—
295	C₇×C₂²⋊C₄	C₂²×C₄	1	4	yes	—
296	C₇×C₂²⋊C₄	C₂²×C₄	1	4	yes	—
297	C₇×C₂²⋊C₄	C₂²×C₄	1	4	yes	—
298	C₄²×C₇	C₂²×C₄	1	1	yes	characteristic
299	C₄²×C₇	C₂²×C₄	1	2	yes	—
300	C₄²×C₇	C₂²×C₄	1	2	yes	—
301	C₄²×C₇	C₂²×C₄	1	4	yes	—
302	C₄²×C₇	C₂²×C₄	1	2	yes	—
303	C₄²×C₇	C₂²×C₄	1	1	yes	characteristic
304	C₄²×C₇	C₂²×C₄	1	4	yes	—
305	C₄²×C₇	C₂²×C₄	1	2	yes	—
306	C₄²×C₇	C₂⁴	1	1	yes	characteristic
307	C₄²×C₇	C₂⁴	1	1	yes	characteristic
308	C₄²×C₇	C₂⁴	1	2	yes	—
309	C₄²×C₇	C₂⁴	1	4	yes	—
310	C₄²×C₇	C₂⁴	1	2	yes	—
311	#557	C₄×C₇	1	1	yes	characteristic
312	#556	C₄×C₇	1	2	yes	—
313	#556	C₄×C₇	1	1	yes	characteristic
314	#552	C₄×C₇	1	2	yes	—
315	#552	C₄×C₇	1	4	yes	—
316	D₄×Q₈	C₄×C₇	1	1	yes	characteristic
317	#548	C₄×C₇	1	2	yes	—
318	#547	C₄×C₇	1	1	yes	characteristic
319	#547	C₄×C₇	1	2	yes	—
320	#533	C₂²×C₇	1	1	yes	characteristic
321	#533	C₂²×C₇	1	2	yes	—
322	#529	C₂²×C₇	1	2	yes	—
323	#529	C₂²×C₇	1	4	yes	—
324	C₄×#41	C₂²×C₇	1	1	yes	characteristic
325	C₄×#41	C₂²×C₇	1	1	yes	characteristic
326	C₄×#41	C₂²×C₇	1	2	yes	—
327	C₂×C₄×Q₈	C₂²×C₇	1	2	yes	—
328	#446	C₂²×C₇	1	1	yes	characteristic
329	#446	C₂²×C₇	1	2	yes	—
330	#446	C₂²×C₇	1	4	yes	—
331	#446	C₂²×C₇	1	2	yes	—
332	#446	C₂²×C₇	1	4	yes	—
333	#446	C₂²×C₇	1	2	yes	—
334	#446	C₂²×C₇	1	2	yes	—
335	#446	C₂²×C₇	1	4	yes	—
336	#446	C₂²×C₇	1	2	yes	—
337	#446	C₂²×C₇	1	1	yes	characteristic
338	#446	C₂²×C₇	1	4	yes	—
339	#446	C₂²×C₇	1	2	yes	—
340	C₈×Q₈	C₂²×C₇	1	2	yes	—
341	C₈×Q₈	C₂²×C₇	1	2	yes	—
342	C₈×Q₈	C₂²×C₇	1	1	yes	characteristic
343	C₈×Q₈	C₂²×C₇	1	2	yes	—
344	C₈×Q₈	C₂²×C₇	1	1	yes	characteristic
345	C₈×Q₈	C₂²×C₇	1	2	yes	—
346	#436	C₂²×C₇	1	1	yes	characteristic
347	#436	C₂²×C₇	1	1	yes	characteristic
348	#435	C₂²×C₇	1	2	yes	—
349	#435	C₂²×C₇	1	2	yes	—
350	#435	C₂²×C₇	1	4	yes	—
351	#435	C₂²×C₇	1	4	yes	—
352	#435	C₂²×C₇	1	4	yes	—
353	#435	C₂²×C₇	1	4	yes	—
354	C₈×D₄	C₂²×C₇	1	2	yes	—
355	C₈×D₄	C₂²×C₇	1	1	yes	characteristic
356	C₈×D₄	C₂²×C₇	1	1	yes	characteristic
357	C₈×D₄	C₂²×C₇	1	2	yes	—
358	C₈×D₄	C₂²×C₇	1	4	yes	—
359	C₈×D₄	C₂²×C₇	1	2	yes	—
360	C₈×D₄	C₂²×C₇	1	4	yes	—
361	C₈×D₄	C₂²×C₇	1	2	yes	—
362	#433	C₂²×C₇	1	4	yes	—
363	#433	C₂²×C₇	1	4	yes	—
364	#433	C₂²×C₇	1	4	yes	—
365	#432	C₂²×C₇	1	2	yes	—
366	#432	C₂²×C₇	1	4	yes	—
367	#432	C₂²×C₇	1	2	yes	—
368	#431	C₂²×C₇	1	2	yes	—
369	#431	C₂²×C₇	1	1	yes	characteristic
370	#431	C₂²×C₇	1	2	yes	—
371	#431	C₂²×C₇	1	1	yes	characteristic
372	#431	C₂²×C₇	1	4	yes	—
373	#424	C₂²×C₇	1	2	yes	—
374	#424	C₂²×C₇	1	4	yes	—
375	#423	C₂²×C₇	1	1	yes	characteristic
376	C₂×C₄⋊C₈	C₂²×C₇	1	4	yes	—
377	C₂×C₄⋊C₈	C₂²×C₇	1	2	yes	—
378	C₂×C₄⋊C₈	C₂²×C₇	1	2	yes	—
379	#405	C₂²×C₇	1	2	yes	—
380	#405	C₂²×C₇	1	4	yes	—
381	C₄×M₁₆	C₂²×C₇	1	2	yes	—
382	C₂×#97	C₂²×C₇	1	4	yes	—
383	C₂×C₄×C₈	C₂²×C₇	1	2	yes	—
384	C₂×C₄×C₈	C₂²×C₇	1	1	yes	characteristic
385	C₂³×C₇	C₂³×C₄	1	1	yes	characteristic
386	C₂³×C₇	C₂³×C₄	1	2	yes	—
387	C₂³×C₇	C₂³×C₄	1	2	yes	—
388	C₇×Q₈	—	2	2	no	—
389	C₇×Q₈	—	2	4	no	—
390	C₇×Q₈	—	2	2	no	—
391	C₇×Q₈	—	2	4	no	—
392	C₇×Q₈	—	4	4	no	—
393	C₇×D₄	—	2	4	no	—
394	C₇×D₄	—	2	8	no	—
395	C₇×D₄	—	2	2	no	—
396	C₇×D₄	—	4	2	no	—
397	C₇×D₄	#131	1	4	yes	—
398	C₂×C₄×C₇	—	2	4	no	—
399	C₂×C₄×C₇	—	2	8	no	—
400	C₂×C₄×C₇	—	2	2	no	—
401	C₂×C₄×C₇	—	2	4	no	—
402	C₂×C₄×C₇	—	2	4	no	—
403	C₂×C₄×C₇	—	2	2	no	—
404	C₂×C₄×C₇	—	2	2	no	—
405	C₂×C₄×C₇	—	2	1	no	—
406	C₂×C₄×C₇	—	2	2	no	—
407	C₂×C₄×C₇	—	2	2	no	—
408	C₂×C₄×C₇	—	2	2	no	—
409	C₂×C₄×C₇	—	2	1	no	—
410	C₂×C₄×C₇	—	4	4	no	—
411	C₂×C₄×C₇	—	4	2	no	—
412	C₂×C₄×C₇	C₂³×C₄	1	2	yes	—
413	C₂×C₄×C₇	C₂³×C₄	1	1	yes	characteristic
414	C₂×C₄×C₇	C₂³×C₄	1	2	yes	—
415	C₂×C₄×C₇	C₂³×C₄	1	1	yes	characteristic
416	C₂×C₄×C₇	C₂³×C₄	1	2	yes	—
417	C₂×C₄×C₇	C₂³×C₄	1	1	yes	characteristic
418	C₂×C₄×C₇	C₂³×C₄	1	2	yes	—
419	C₂×C₄×C₇	C₂³×C₄	1	2	yes	—
420	C₂×C₄×C₇	C₂³×C₄	1	4	yes	—
421	C₂×C₄×C₇	C₂³×C₄	1	4	yes	—
422	C₂×C₄×C₇	C₂³×C₄	1	2	yes	—
423	C₂×C₄×C₇	C₂³×C₄	1	1	yes	characteristic
424	C₂×C₄×C₇	C₂³×C₄	1	1	yes	characteristic
425	C₂×C₄×C₇	C₂⁵	1	1	yes	characteristic
426	C₇×C₈	—	2	1	no	—
427	C₇×C₈	—	2	2	no	—
428	C₇×C₈	—	2	2	no	—
429	C₇×C₈	—	2	1	no	—
430	C₇×C₈	—	2	2	no	—
431	C₇×C₈	—	2	4	no	—
432	C₇×C₈	—	2	2	no	—
433	C₇×C₈	—	2	1	no	—
434	C₇×C₈	2₋¹⁺⁴	1	2	yes	—
435	C₂×#41	C₂×C₄×C₇	1	1	yes	characteristic
436	C₂×#41	C₂×C₄×C₇	1	2	yes	—
437	C₂×#41	C₂×C₄×C₇	1	1	yes	characteristic
438	C₂²×Q₈	C₂×C₄×C₇	1	2	yes	—
439	C₂×M₁₆	C₂³×C₇	1	2	yes	—
440	C₂×M₁₆	C₂³×C₇	1	2	yes	—
441	C₂×M₁₆	C₂³×C₇	1	2	yes	—
442	C₂²×C₈	C₂³×C₇	1	2	yes	—
443	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
444	C₂²×C₈	C₂³×C₇	1	2	yes	—
445	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
446	C₂²×C₈	C₂³×C₇	1	4	yes	—
447	C₂²×C₈	C₂³×C₇	1	4	yes	—
448	C₄⋊Q₈	C₂×C₄×C₇	1	1	yes	characteristic
449	C₄⋊Q₈	C₂×C₄×C₇	1	2	yes	—
450	C₄⋊Q₈	C₂×C₄×C₇	1	1	yes	characteristic
451	C₄⋊Q₈	C₂×C₄×C₇	1	2	yes	—
452	#126	C₂×C₄×C₇	1	4	yes	—
453	#126	C₂×C₄×C₇	1	4	yes	—
454	#126	C₂×C₄×C₇	1	4	yes	—
455	#125	C₂×C₄×C₇	1	2	yes	—
456	#125	C₂×C₄×C₇	1	4	yes	—
457	#125	C₂×C₄×C₇	1	2	yes	—
458	#125	C₂×C₄×C₇	1	4	yes	—
459	#124	C₂×C₄×C₇	1	2	yes	—
460	#124	C₂×C₄×C₇	1	4	yes	—
461	#123	C₂×C₄×C₇	1	4	yes	—
462	#123	C₂×C₄×C₇	1	4	yes	—
463	#123	C₂×C₄×C₇	1	4	yes	—
464	C₂²⋊Q₈	C₂×C₄×C₇	1	2	yes	—
465	C₂²⋊Q₈	C₂×C₄×C₇	1	4	yes	—
466	C₂²⋊Q₈	C₂×C₄×C₇	1	2	yes	—
467	C₂²⋊Q₈	C₂×C₄×C₇	1	2	yes	—
468	C₂²⋊Q₈	C₂×C₄×C₇	1	2	yes	—
469	C₂²⋊Q₈	C₂×C₄×C₇	1	2	yes	—
470	C₂²⋊Q₈	C₂×C₄×C₇	1	4	yes	—
471	#121	C₂×C₄×C₇	1	2	yes	—
472	#121	C₂×C₄×C₇	1	4	yes	—
473	C₄×Q₈	C₂×C₄×C₇	1	2	yes	—
474	C₄×Q₈	C₂×C₄×C₇	1	2	yes	—
475	C₄×Q₈	C₂×C₄×C₇	1	4	yes	—
476	C₄×Q₈	C₂×C₄×C₇	1	1	yes	characteristic
477	C₄×Q₈	C₂×C₄×C₇	1	1	yes	characteristic
478	C₄×Q₈	C₂×C₄×C₇	1	2	yes	—
479	C₄×Q₈	C₂³×C₇	1	1	yes	characteristic
480	C₄×Q₈	C₂³×C₇	1	2	yes	—
481	C₄×Q₈	C₂³×C₇	1	4	yes	—
482	C₄×Q₈	C₂³×C₇	1	1	yes	characteristic
483	C₄×Q₈	C₂³×C₇	1	2	yes	—
484	C₄×D₄	C₂×C₄×C₇	1	1	yes	characteristic
485	C₄×D₄	C₂×C₄×C₇	1	2	yes	—
486	C₄×D₄	C₂×C₄×C₇	1	1	yes	characteristic
487	C₄×D₄	C₂×C₄×C₇	1	2	yes	—
488	C₄×D₄	C₂×C₄×C₇	1	2	yes	—
489	C₄×D₄	C₂×C₄×C₇	1	4	yes	—
490	C₄×D₄	C₂³×C₇	1	1	yes	characteristic
491	C₄×D₄	C₂³×C₇	1	2	yes	—
492	C₄×D₄	C₂³×C₇	1	4	yes	—
493	C₄×D₄	C₂³×C₇	1	1	yes	characteristic
494	C₄×D₄	C₂³×C₇	1	2	yes	—
495	#117	C₂×C₄×C₇	1	1	yes	characteristic
496	#117	C₂×C₄×C₇	1	2	yes	—
497	#117	C₂×C₄×C₇	1	2	yes	—
498	#117	C₂×C₄×C₇	1	4	yes	—
499	#117	C₂×C₄×C₇	1	1	yes	characteristic
500	#117	C₂×C₄×C₇	1	2	yes	—
501	#117	C₂³×C₇	1	4	yes	—
502	#117	C₂³×C₇	1	2	yes	—
503	C₂×C₄⋊C₄	C₂×C₄×C₇	1	2	yes	—
504	C₂×C₄⋊C₄	C₂×C₄×C₇	1	4	yes	—
505	C₂×C₄²	C₂³×C₇	1	2	yes	—
506	C₂×C₄²	C₂³×C₇	1	4	yes	—
507	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
508	C₂×C₄²	C₂³×C₇	1	2	yes	—
509	C₄⋊C₈	C₂³×C₇	1	1	yes	characteristic
510	C₄⋊C₈	C₂³×C₇	1	2	yes	—
511	C₄⋊C₈	C₂³×C₇	1	4	yes	—
512	C₄⋊C₈	C₂³×C₇	1	1	yes	characteristic
513	C₄⋊C₈	C₂³×C₇	1	2	yes	—
514	C₄⋊C₈	C₂³×C₇	1	2	yes	—
515	C₄⋊C₈	C₂³×C₇	1	4	yes	—
516	C₄⋊C₈	C₂³×C₇	1	4	yes	—
517	C₄⋊C₈	C₂³×C₇	1	4	yes	—
518	C₄⋊C₈	C₂³×C₇	1	2	yes	—
519	C₄⋊C₈	C₂³×C₇	1	4	yes	—
520	C₄⋊C₈	C₂³×C₇	1	2	yes	—
521	C₄⋊C₈	C₂³×C₇	1	1	yes	characteristic
522	C₄⋊C₈	C₂³×C₇	1	1	yes	characteristic
523	C₄⋊C₈	C₂³×C₇	1	2	yes	—
524	C₄⋊C₈	C₂³×C₇	1	4	yes	—
525	C₂²⋊C₈	C₂³×C₇	1	2	yes	—
526	C₂²⋊C₈	C₂³×C₇	1	4	yes	—
527	C₂²⋊C₈	C₂³×C₇	1	2	yes	—
528	C₂²⋊C₈	C₂³×C₇	1	2	yes	—
529	C₂²⋊C₈	C₂³×C₇	1	2	yes	—
530	C₂²⋊C₈	C₂³×C₇	1	2	yes	—
531	C₂²⋊C₈	C₂³×C₇	1	2	yes	—
532	C₂²⋊C₈	C₂³×C₇	1	4	yes	—
533	#97	C₂³×C₇	1	2	yes	—
534	#97	C₂³×C₇	1	4	yes	—
535	#97	C₂³×C₇	1	4	yes	—
536	#97	C₂³×C₇	1	4	yes	—
537	#97	C₂³×C₇	1	2	yes	—
538	#97	C₂³×C₇	1	4	yes	—
539	C₄×C₈	C₂³×C₇	1	1	yes	characteristic
540	C₄×C₈	C₂³×C₇	1	1	yes	characteristic
541	C₄×C₈	C₂³×C₇	1	2	yes	—
542	C₄×C₈	C₂³×C₇	1	1	yes	characteristic
543	C₄×C₈	C₂³×C₇	1	2	yes	—
544	C₄×C₈	C₂³×C₇	1	1	yes	characteristic
545	C₄×C₈	C₂³×C₇	1	2	yes	—
546	C₄×C₈	C₂³×C₇	1	2	yes	—
547	C₄×C₈	C₂³×C₇	1	4	yes	—
548	C₄×C₈	C₂³×C₇	1	4	yes	—
549	C₂²×C₇	—	2	2	no	—
550	C₂²×C₇	—	2	2	no	—
551	C₂²×C₇	—	2	1	no	—
552	C₂²×C₇	—	2	2	no	—
553	C₂²×C₇	—	2	1	no	—
554	C₂²×C₇	—	2	2	no	—
555	C₂²×C₇	—	2	1	no	—
556	C₂²×C₇	—	2	2	no	—
557	C₂²×C₇	C₂×#131	1	4	yes	—
558	C₂²×C₇	C₂⁴×C₄	1	1	yes	characteristic
559	C₄×C₇	—	2	2	no	—
560	C₄×C₇	—	2	1	no	—
561	C₄×C₇	—	2	2	no	—
562	C₄×C₇	—	2	1	no	—
563	C₄×C₇	—	2	2	no	—
564	C₄×C₇	—	2	2	no	—
565	C₄×C₇	—	2	4	no	—
566	C₄×C₇	—	2	1	no	—
567	C₄×C₇	—	2	2	no	—
568	C₄×C₇	—	2	2	no	—
569	C₄×C₇	—	2	4	no	—
570	C₄×C₇	C₂×#131	1	2	yes	—
571	C₄×C₇	#568	1	2	yes	—
572	C₄×C₇	C₂×2₋¹⁺⁴	1	1	yes	characteristic
573	C₄×C₇	#585	1	1	yes	characteristic
574	#41	—	2	4	no	—
575	#41	—	2	8	no	—
576	#41	—	4	2	no	—
577	C₂×Q₈	—	4	4	no	—
578	C₂×Q₈	C₂²×C₄×C₇	1	1	yes	characteristic
579	C₂×Q₈	C₂²×C₄×C₇	1	2	yes	—
580	C₂×Q₈	C₂²×C₄×C₇	1	1	yes	characteristic
581	C₂×Q₈	C₂²×C₄×C₇	1	2	yes	—
582	C₂×Q₈	C₂²×C₄×C₇	1	4	yes	—
583	C₂×D₄	C₂²×C₄×C₇	1	2	yes	—
584	C₂×D₄	C₂²×C₄×C₇	1	4	yes	—
585	C₂×D₄	C₂²×C₄×C₇	1	1	yes	characteristic
586	C₂×D₄	C₂²×C₄×C₇	1	2	yes	—
587	C₂×D₄	C₂²×C₄×C₇	1	1	yes	characteristic
588	C₂²×C₄	C₂²×C₄×C₇	1	2	yes	—
589	C₂²×C₄	C₂²×C₄×C₇	1	4	yes	—
590	C₂²×C₄	C₂²×C₄×C₇	1	2	yes	—
591	C₂²×C₄	C₂²×C₄×C₇	1	1	yes	characteristic
592	C₂²×C₄	C₂²×C₄×C₇	1	2	yes	—
593	C₂²×C₄	C₂²×C₄×C₇	1	1	yes	characteristic
594	C₂²×C₄	C₂²×C₄×C₇	1	4	yes	—
595	C₂²×C₄	C₂²×C₄×C₇	1	2	yes	—
596	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
597	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
598	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
599	M₁₆	—	2	4	no	—
600	M₁₆	—	4	2	no	—
601	M₁₆	—	4	2	no	—
602	C₂×C₈	—	2	4	no	—
603	C₂×C₈	—	2	2	no	—
604	C₂×C₈	—	4	2	no	—
605	C₂×C₈	—	4	4	no	—
606	C₂×C₈	—	4	1	no	—
607	C₂×C₈	—	4	4	no	—
608	C₂×C₈	C₂⁴×C₇	1	1	yes	characteristic
609	C₂×C₈	C₂⁴×C₇	1	1	yes	characteristic
610	C₂×C₈	C₂⁴×C₇	1	2	yes	—
611	C₂×C₈	C₂⁴×C₇	1	2	yes	—
612	C₂×C₈	C₂⁴×C₇	1	2	yes	—
613	C₂×C₈	C₂⁴×C₇	1	1	yes	characteristic
614	C₂×C₈	C₂⁴×C₇	1	2	yes	—
615	C₂×C₈	C₂⁴×C₇	1	4	yes	—
616	C₂×C₈	C₂⁴×C₇	1	1	yes	characteristic
617	C₄⋊C₄	C₂²×C₄×C₇	1	2	yes	—
618	C₄⋊C₄	C₂²×C₄×C₇	1	1	yes	characteristic
619	C₄⋊C₄	C₂²×C₄×C₇	1	4	yes	—
620	C₄⋊C₄	C₂²×C₄×C₇	1	2	yes	—
621	C₄⋊C₄	C₂²×C₄×C₇	1	4	yes	—
622	C₄⋊C₄	C₂²×C₄×C₇	1	4	yes	—
623	C₄⋊C₄	C₂²×C₄×C₇	1	4	yes	—
624	C₄⋊C₄	C₂²×C₄×C₇	1	1	yes	characteristic
625	C₄⋊C₄	C₂²×C₄×C₇	1	2	yes	—
626	C₄⋊C₄	C₂²×C₄×C₇	1	4	yes	—
627	C₄⋊C₄	C₂²×C₄×C₇	1	1	yes	characteristic
628	C₄⋊C₄	C₂²×C₄×C₇	1	2	yes	—
629	C₄⋊C₄	C₂²×C₄×C₇	1	2	yes	—
630	C₄⋊C₄	C₂²×C₄×C₇	1	1	yes	characteristic
631	C₄⋊C₄	C₂²×C₄×C₇	1	2	yes	—
632	C₄⋊C₄	C₂²×C₄×C₇	1	4	yes	—
633	C₄⋊C₄	C₂²×C₄×C₇	1	4	yes	—
634	C₄⋊C₄	C₂²×C₄×C₇	1	2	yes	—
635	C₄⋊C₄	C₂²×C₄×C₇	1	4	yes	—
636	C₄⋊C₄	C₂²×C₄×C₇	1	2	yes	—
637	C₂²⋊C₄	C₂²×C₄×C₇	1	2	yes	—
638	C₂²⋊C₄	C₂²×C₄×C₇	1	2	yes	—
639	C₂²⋊C₄	C₂²×C₄×C₇	1	4	yes	—
640	C₂²⋊C₄	C₂²×C₄×C₇	1	2	yes	—
641	C₂²⋊C₄	C₂²×C₄×C₇	1	2	yes	—
642	C₂²⋊C₄	C₂²×C₄×C₇	1	2	yes	—
643	C₂²⋊C₄	C₂²×C₄×C₇	1	2	yes	—
644	C₂²⋊C₄	C₂²×C₄×C₇	1	4	yes	—
645	C₂²⋊C₄	C₂²×C₄×C₇	1	4	yes	—
646	C₂²⋊C₄	C₂²×C₄×C₇	1	4	yes	—
647	C₂²⋊C₄	C₂²×C₄×C₇	1	4	yes	—
648	C₄²	C₂²×C₄×C₇	1	1	yes	characteristic
649	C₄²	C₂²×C₄×C₇	1	2	yes	—
650	C₄²	C₂²×C₄×C₇	1	2	yes	—
651	C₄²	C₂²×C₄×C₇	1	4	yes	—
652	C₄²	C₂²×C₄×C₇	1	2	yes	—
653	C₄²	C₂²×C₄×C₇	1	1	yes	characteristic
654	C₄²	C₂²×C₄×C₇	1	4	yes	—
655	C₄²	C₂²×C₄×C₇	1	2	yes	—
656	C₄²	C₂⁴×C₇	1	1	yes	characteristic
657	C₄²	C₂⁴×C₇	1	1	yes	characteristic
658	C₄²	C₂⁴×C₇	1	2	yes	—
659	C₄²	C₂⁴×C₇	1	4	yes	—
660	C₄²	C₂⁴×C₇	1	2	yes	—
661	C₂×C₇	—	2	4	no	—
662	C₂×C₇	—	4	1	no	—
663	C₂×C₇	—	4	2	no	—
664	C₂×C₇	C₄×2₋¹⁺⁴	1	1	yes	characteristic
665	C₂×C₇	C₂²×#131	1	1	yes	characteristic
666	C₂×C₇	C₂×#568	1	1	yes	characteristic
667	C₂³	C₂³×C₄×C₇	1	1	yes	characteristic
668	C₂³	C₂³×C₄×C₇	1	2	yes	—
669	C₂³	C₂³×C₄×C₇	1	2	yes	—
670	Q₈	—	2	2	no	—
671	Q₈	—	2	4	no	—
672	Q₈	—	2	2	no	—
673	Q₈	—	2	4	no	—
674	Q₈	—	4	4	no	—
675	D₄	—	2	4	no	—
676	D₄	—	2	8	no	—
677	D₄	—	2	2	no	—
678	D₄	—	4	2	no	—
679	D₄	C₇×#131	1	4	yes	—
680	C₂×C₄	—	2	4	no	—
681	C₂×C₄	—	2	8	no	—
682	C₂×C₄	—	2	2	no	—
683	C₂×C₄	—	2	1	no	—
684	C₂×C₄	—	2	2	no	—
685	C₂×C₄	—	2	2	no	—
686	C₂×C₄	—	2	2	no	—
687	C₂×C₄	—	2	1	no	—
688	C₂×C₄	—	2	2	no	—
689	C₂×C₄	—	2	4	no	—
690	C₂×C₄	—	2	4	no	—
691	C₂×C₄	—	2	2	no	—
692	C₂×C₄	—	4	4	no	—
693	C₂×C₄	—	4	2	no	—
694	C₂×C₄	C₂³×C₄×C₇	1	2	yes	—
695	C₂×C₄	C₂³×C₄×C₇	1	1	yes	characteristic
696	C₂×C₄	C₂³×C₄×C₇	1	2	yes	—
697	C₂×C₄	C₂³×C₄×C₇	1	1	yes	characteristic
698	C₂×C₄	C₂³×C₄×C₇	1	2	yes	—
699	C₂×C₄	C₂³×C₄×C₇	1	1	yes	characteristic
700	C₂×C₄	C₂³×C₄×C₇	1	2	yes	—
701	C₂×C₄	C₂³×C₄×C₇	1	2	yes	—
702	C₂×C₄	C₂³×C₄×C₇	1	4	yes	—
703	C₂×C₄	C₂³×C₄×C₇	1	4	yes	—
704	C₂×C₄	C₂³×C₄×C₇	1	2	yes	—
705	C₂×C₄	C₂³×C₄×C₇	1	1	yes	characteristic
706	C₂×C₄	C₂³×C₄×C₇	1	1	yes	characteristic
707	C₂×C₄	C₂⁵×C₇	1	1	yes	characteristic
708	C₈	—	2	1	no	—
709	C₈	—	2	2	no	—
710	C₈	—	2	2	no	—
711	C₈	—	2	1	no	—
712	C₈	—	2	2	no	—
713	C₈	—	2	4	no	—
714	C₈	—	2	2	no	—
715	C₈	—	2	1	no	—
716	C₈	C₇×2₋¹⁺⁴	1	2	yes	—
717	C₇	#60341	1	1	yes	characteristic, direct product factor, Sylow
718	C₂²	—	2	2	no	—
719	C₂²	—	2	2	no	—
720	C₂²	—	2	1	no	—
721	C₂²	—	2	2	no	—
722	C₂²	—	2	1	no	—
723	C₂²	—	2	2	no	—
724	C₂²	—	2	1	no	—
725	C₂²	—	2	2	no	—
726	C₂²	C₂×C₇×#131	1	4	yes	—
727	C₂²	C₂⁴×C₄×C₇	1	1	yes	characteristic
728	C₄	—	2	1	no	—
729	C₄	—	2	2	no	—
730	C₄	—	2	2	no	—
731	C₄	—	2	4	no	—
732	C₄	—	2	1	no	—
733	C₄	—	2	2	no	—
734	C₄	—	2	2	no	—
735	C₄	—	2	4	no	—
736	C₄	—	2	2	no	—
737	C₄	—	2	1	no	—
738	C₄	—	2	2	no	—
739	C₄	C₂×C₇×#131	1	2	yes	—
740	C₄	C₇×#568	1	2	yes	—
741	C₄	C₂×C₇×2₋¹⁺⁴	1	1	yes	characteristic
742	C₄	C₇×#585	1	1	yes	characteristic
743	C₂	—	2	4	no	—
744	C₂	—	4	1	no	—
745	C₂	—	4	2	no	—
746	C₂	C₄×C₇×2₋¹⁺⁴	1	1	yes	characteristic
747	C₂	C₂²×C₇×#131	1	1	yes	characteristic
748	C₂	C₂×C₇×#568	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×#3482	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×#2994	C₂	semidirect
3. C₇×#2992	C₂	semidirect
4. C₇×#2990	C₂	semidirect
5. C₇×#2990	C₂	semidirect
6. C₇×#2988	C₂	semidirect
7. C₇×#2986	C₂	semidirect
8. C₇×#2985	C₂	semidirect
9. C₇×#2984	C₂	semidirect
10. C₇×#2970	C₂	semidirect
11. C₇×#2968	C₂	semidirect
12. C₇×#2966	C₂	semidirect
13. C₇×#2965	C₂	semidirect
14. C₇×C₈×#41	C₂	semidirect
15. C₇×#2962	C₂	semidirect
16. C₇×#2960	C₂	semidirect
17. C₂×C₇×#446	C₂	semidirect
92. #60341	C₇	direct (N × H)
208. #2994	C₂×C₇	semidirect
209. #2992	C₂×C₇	semidirect
210. #2990	C₂×C₇	semidirect
211. #2990	C₂×C₇	semidirect
212. #2988	C₂×C₇	semidirect
213. #2986	C₂×C₇	semidirect
214. #2985	C₂×C₇	semidirect
215. #2984	C₂×C₇	semidirect
216. #2970	C₂×C₇	semidirect
217. #2968	C₂×C₇	semidirect
218. #2966	C₂×C₇	semidirect
219. #2965	C₂×C₇	semidirect
220. C₈×#41	C₂×C₇	semidirect
221. #2962	C₂×C₇	semidirect
222. #2960	C₂×C₇	semidirect
223. C₂×#446	C₂×C₇	semidirect
717. C₇	#60341	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×#3482	2
C₇×#2994	2
C₇×#2992	2
C₇×#2990	2
C₇×#2988	2
C₇×#2986	2
C₇×#2985	2
C₇×#2984	2
C₇×#2970	2
C₇×#2968	2
C₇×#2966	2
C₇×#2965	2
C₇×C₈×#41	2
C₇×#2962	2
C₇×#2960	2
C₂×C₇×#446	2
#60341	7

Subgroups — C7×#60341 #13237557

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×#60341 #13237557