Subgroups — C₇×#60217 #13237433

Order 1792.

1914 conjugacy classes of subgroups.

The subgroup lattice has 796 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×#3475	C₂	1	1	yes	maximal, characteristic
2	C₇×#2971	C₂	1	2	yes	maximal, complemented
3	C₇×#2969	C₂	1	2	yes	maximal, complemented
4	C₇×#2969	C₂	1	4	yes	maximal, complemented
5	C₇×#2967	C₂	1	4	yes	maximal, complemented
6	C₇×#2966	C₂	1	2	yes	maximal, complemented
7	C₇×#2965	C₂	1	2	yes	maximal, complemented
8	C₇×#2962	C₂	1	1	yes	maximal, characteristic, complemented
9	C₇×#2960	C₂	1	1	yes	maximal, characteristic, complemented
10	C₇×D₄×M₁₆	C₂	1	1	yes	maximal, characteristic, complemented
11	C₇×#2933	C₂	1	2	yes	maximal, 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×#2924	C₂	1	2	yes	maximal, complemented
16	C₄×C₇×#131	C₂	1	1	yes	maximal, characteristic, complemented
17	C₇×#2873	C₂	1	2	yes	maximal, complemented
18	C₂×C₇×#131	C₂²	1	1	yes	characteristic
19	C₂×C₇×#131	C₂²	1	1	yes	characteristic
20	C₂²×C₇×M₁₆	C₂²	1	2	yes	—
21	C₂²×C₇×M₁₆	C₂²	1	2	yes	—
22	C₇×#556	C₄	1	1	yes	characteristic
23	C₇×#555	C₄	1	1	yes	characteristic
24	C₇×#554	C₄	1	1	yes	characteristic
25	C₇×#553	C₄	1	2	yes	—
26	C₇×#552	C₄	1	2	yes	—
27	C₇×#552	C₄	1	2	yes	—
28	C₇×#551	C₄	1	4	yes	—
29	C₇×#547	C₄	1	1	yes	characteristic
30	C₇×#546	C₄	1	2	yes	—
31	C₇×#533	C₂²	1	1	yes	characteristic
32	C₇×#529	C₂²	1	2	yes	—
33	C₇×#529	C₂²	1	4	yes	—
34	C₇×#525	C₂²	1	2	yes	—
35	C₄×C₇×#41	C₂²	1	2	yes	—
36	C₄×C₇×#41	C₂²	1	1	yes	characteristic
37	C₂×C₄×C₇×D₄	C₂²	1	1	yes	characteristic
38	C₂×C₇×#117	C₂²	1	2	yes	—
39	C₇×#446	C₂²	1	2	yes	complemented
40	C₇×#446	C₂²	1	2	yes	complemented
41	C₇×#446	C₂²	1	2	yes	complemented
42	C₇×#446	C₂²	1	4	yes	complemented
43	C₇×C₈×Q₈	C₂²	1	2	yes	complemented
44	C₇×C₈×Q₈	C₂²	1	2	yes	complemented
45	C₇×C₈×Q₈	C₂²	1	2	yes	complemented
46	C₇×#436	C₂²	1	1	yes	characteristic
47	C₇×#436	C₂²	1	1	yes	characteristic
48	C₇×#436	C₂²	1	2	yes	—
49	C₇×#436	C₂²	1	1	yes	characteristic
50	C₇×#436	C₂²	1	2	yes	—
51	C₇×#436	C₂²	1	1	yes	characteristic
52	C₇×#436	C₂²	1	2	yes	—
53	C₇×#436	C₂²	1	4	yes	complemented
54	C₇×#436	C₂²	1	4	yes	complemented
55	C₇×#436	C₂²	1	4	yes	complemented
56	C₇×#435	C₂²	1	4	yes	—
57	C₇×#435	C₂²	1	4	yes	complemented
58	C₇×#435	C₂²	1	4	yes	complemented
59	C₇×#435	C₂²	1	4	yes	complemented
60	C₇×#435	C₂²	1	4	yes	complemented
61	C₇×C₈×D₄	C₂²	1	2	yes	—
62	C₇×C₈×D₄	C₂²	1	4	yes	complemented
63	C₇×#433	C₂²	1	4	yes	complemented
64	C₇×#433	C₂²	1	4	yes	complemented
65	C₇×#433	C₂²	1	4	yes	complemented
66	C₇×#432	C₂²	1	4	yes	complemented
67	C₇×#432	C₂²	1	2	yes	complemented
68	C₇×#431	C₂²	1	4	yes	complemented
69	C₇×#431	C₂²	1	2	yes	complemented
70	C₇×#424	C₂²	1	2	yes	—
71	C₇×#424	C₂²	1	2	yes	—
72	C₇×#423	C₂²	1	1	yes	characteristic
73	C₂×C₇×C₄⋊C₈	C₂²	1	1	yes	characteristic
74	C₇×#408	C₂²	1	2	yes	—
75	C₇×#407	C₂²	1	2	yes	—
76	C₂×C₇×C₂²⋊C₈	C₂²	1	2	yes	—
77	C₇×#405	C₂²	1	1	yes	characteristic
78	C₇×#405	C₂²	1	2	yes	—
79	C₇×#405	C₂²	1	2	yes	—
80	C₇×#405	C₂²	1	2	yes	—
81	C₇×#405	C₂²	1	1	yes	characteristic
82	C₇×#405	C₂²	1	4	yes	complemented
83	C₇×#405	C₂²	1	2	yes	complemented
84	C₇×#405	C₂²	1	4	yes	complemented
85	C₇×#405	C₂²	1	2	yes	complemented
86	C₄×C₇×M₁₆	C₂²	1	1	yes	characteristic
87	C₄×C₇×M₁₆	C₂²	1	4	yes	complemented
88	C₄×C₇×M₁₆	C₂²	1	4	yes	complemented
89	C₄×C₇×M₁₆	C₂²	1	2	yes	complemented
90	C₂×C₄×C₇×C₈	C₂²	1	1	yes	characteristic
91	C₂×C₄×C₇×C₈	C₂²	1	2	yes	complemented
92	#60217	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
93	C₂×C₇×#41	C₂×C₄	1	2	yes	—
94	C₂×C₇×#41	C₂³	1	1	yes	characteristic
95	C₂²×C₇×D₄	C₂×C₄	1	1	yes	characteristic
96	C₂³×C₄×C₇	C₂³	1	2	yes	—
97	C₇×#131	—	2	4	no	—
98	C₇×#131	—	2	4	no	—
99	C₂×C₇×M₁₆	—	2	8	no	—
100	C₂×C₇×M₁₆	—	2	8	no	—
101	C₂×C₇×M₁₆	C₂³	1	1	yes	characteristic
102	C₂×C₇×M₁₆	C₂³	1	4	yes	—
103	C₂×C₇×M₁₆	C₂³	1	2	yes	—
104	C₂×C₇×M₁₆	C₂³	1	2	yes	—
105	C₂×C₇×M₁₆	C₂³	1	2	yes	—
106	C₂×C₇×M₁₆	C₂³	1	2	yes	—
107	C₂×C₇×M₁₆	C₂³	1	2	yes	—
108	C₂×C₇×M₁₆	C₂³	1	2	yes	—
109	C₂×C₇×M₁₆	C₂³	1	2	yes	—
110	C₂×C₇×M₁₆	C₂³	1	1	yes	characteristic
111	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
112	C₂²×C₇×C₈	C₂³	1	2	yes	—
113	C₂²×C₇×C₈	C₂³	1	2	yes	—
114	C₂²×C₇×C₈	C₂³	1	2	yes	—
115	C₂²×C₇×C₈	C₂³	1	4	yes	—
116	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
117	C₇×C₄⋊Q₈	C₂×C₄	1	1	yes	characteristic
118	C₇×C₄⋊Q₈	C₂×C₄	1	1	yes	characteristic
119	C₇×#126	C₂×C₄	1	4	yes	—
120	C₇×#126	C₂×C₄	1	4	yes	—
121	C₇×#126	C₂×C₄	1	4	yes	—
122	C₇×#125	C₂×C₄	1	4	yes	—
123	C₇×#125	C₂×C₄	1	2	yes	—
124	C₇×#125	C₂×C₄	1	2	yes	—
125	C₇×#124	C₂×C₄	1	2	yes	—
126	C₇×#124	C₂×C₄	1	4	yes	—
127	C₇×#123	C₂×C₄	1	4	yes	—
128	C₇×#123	C₂×C₄	1	4	yes	—
129	C₇×#123	C₂×C₄	1	4	yes	—
130	C₇×#123	C₂×C₄	1	4	yes	—
131	C₇×C₂²⋊Q₈	C₂×C₄	1	2	yes	—
132	C₇×C₂²⋊Q₈	C₂×C₄	1	2	yes	—
133	C₇×C₂²⋊Q₈	C₂×C₄	1	2	yes	—
134	C₇×C₂²⋊Q₈	C₂×C₄	1	4	yes	—
135	C₇×C₂²⋊Q₈	C₂×C₄	1	2	yes	—
136	C₇×C₂²⋊Q₈	C₂×C₄	1	2	yes	—
137	C₇×#121	C₂×C₄	1	2	yes	—
138	C₇×#121	C₂×C₄	1	2	yes	—
139	C₇×#121	C₂×C₄	1	4	yes	—
140	C₇×#121	C₂×C₄	1	2	yes	—
141	C₇×#120	C₂×C₄	1	4	yes	—
142	C₄×C₇×Q₈	C₂×C₄	1	1	yes	characteristic
143	C₄×C₇×Q₈	C₂×C₄	1	2	yes	—
144	C₄×C₇×Q₈	C₂×C₄	1	1	yes	characteristic
145	C₄×C₇×Q₈	C₂³	1	2	yes	—
146	C₄×C₇×Q₈	C₂³	1	2	yes	—
147	C₄×C₇×D₄	C₂×C₄	1	1	yes	characteristic
148	C₄×C₇×D₄	C₂×C₄	1	2	yes	—
149	C₄×C₇×D₄	C₂×C₄	1	1	yes	characteristic
150	C₄×C₇×D₄	C₂×C₄	1	2	yes	—
151	C₄×C₇×D₄	C₂×C₄	1	2	yes	—
152	C₄×C₇×D₄	C₂×C₄	1	1	yes	characteristic
153	C₄×C₇×D₄	C₂×C₄	1	2	yes	—
154	C₄×C₇×D₄	C₂×C₄	1	4	yes	—
155	C₄×C₇×D₄	C₂×C₄	1	1	yes	characteristic
156	C₄×C₇×D₄	C₂³	1	1	yes	characteristic
157	C₄×C₇×D₄	C₂³	1	1	yes	characteristic
158	C₄×C₇×D₄	C₂³	1	2	yes	—
159	C₄×C₇×D₄	C₂³	1	4	yes	—
160	C₄×C₇×D₄	C₂³	1	4	yes	—
161	C₇×#117	C₂×C₄	1	4	yes	—
162	C₇×#117	C₂×C₄	1	2	yes	—
163	C₇×#117	C₂×C₄	1	2	yes	—
164	C₇×#117	C₂×C₄	1	4	yes	—
165	C₇×#117	C₂×C₄	1	2	yes	—
166	C₇×#117	C₂³	1	1	yes	characteristic
167	C₇×#117	C₂³	1	2	yes	—
168	C₇×#117	C₂³	1	4	yes	—
169	C₇×#117	C₂³	1	2	yes	—
170	C₂×C₇×C₄⋊C₄	C₂×C₄	1	2	yes	—
171	C₂×C₇×C₄⋊C₄	C₂×C₄	1	2	yes	—
172	C₂×C₇×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
173	C₂×C₇×C₂²⋊C₄	C₂×C₄	1	4	yes	—
174	C₂×C₇×C₂²⋊C₄	C₂×C₄	1	2	yes	—
175	C₂×C₄²×C₇	C₂³	1	4	yes	—
176	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
177	C₂×C₄²×C₇	C₂³	1	2	yes	—
178	C₇×C₄⋊C₈	C₂³	1	1	yes	characteristic
179	C₇×C₄⋊C₈	C₂³	1	1	yes	characteristic
180	C₇×C₄⋊C₈	C₂³	1	2	yes	—
181	C₇×C₄⋊C₈	C₂³	1	2	yes	—
182	C₇×C₄⋊C₈	C₂³	1	2	yes	—
183	C₇×C₄⋊C₈	C₂³	1	4	yes	—
184	C₇×C₄⋊C₈	C₂³	1	4	yes	—
185	C₇×C₄⋊C₈	C₂³	1	4	yes	—
186	C₇×C₄⋊C₈	C₂³	1	4	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	2	yes	—
191	C₇×C₂²⋊C₈	C₂³	1	4	yes	—
192	C₇×C₂²⋊C₈	C₂³	1	4	yes	—
193	C₇×C₂²⋊C₈	C₂³	1	4	yes	—
194	C₇×C₂²⋊C₈	C₂³	1	4	yes	—
195	C₇×#97	C₂³	1	2	yes	—
196	C₇×#97	C₂³	1	2	yes	—
197	C₇×#97	C₂³	1	4	yes	—
198	C₇×#97	C₂³	1	2	yes	—
199	C₇×#97	C₂³	1	4	yes	—
200	C₇×#97	C₂³	1	4	yes	—
201	C₄×C₇×C₈	C₂³	1	1	yes	characteristic
202	C₄×C₇×C₈	C₂³	1	1	yes	characteristic
203	C₄×C₇×C₈	C₂³	1	1	yes	characteristic
204	C₄×C₇×C₈	C₂³	1	1	yes	characteristic
205	C₄×C₇×C₈	C₂³	1	2	yes	—
206	C₄×C₇×C₈	C₂³	1	2	yes	—
207	C₄×C₇×C₈	C₂³	1	2	yes	—
208	C₄×C₇×C₈	C₂³	1	4	yes	—
209	C₄×C₇×C₈	C₂³	1	4	yes	—
210	C₄×C₇×C₈	C₂³	1	4	yes	—
211	#3475	C₂×C₇	1	1	yes	characteristic
212	#2971	C₂×C₇	1	2	yes	complemented
213	#2969	C₂×C₇	1	2	yes	complemented
214	#2969	C₂×C₇	1	4	yes	complemented
215	#2967	C₂×C₇	1	4	yes	complemented
216	#2966	C₂×C₇	1	2	yes	complemented
217	#2965	C₂×C₇	1	2	yes	complemented
218	#2962	C₂×C₇	1	1	yes	characteristic, complemented
219	#2960	C₂×C₇	1	1	yes	characteristic, complemented
220	D₄×M₁₆	C₂×C₇	1	1	yes	characteristic, complemented
221	#2933	C₂×C₇	1	2	yes	complemented
222	#2930	C₂×C₇	1	2	yes	complemented
223	C₂×#436	C₂×C₇	1	1	yes	characteristic, complemented
224	#2925	C₂×C₇	1	1	yes	characteristic, complemented
225	#2924	C₂×C₇	1	2	yes	complemented
226	C₄×#131	C₂×C₇	1	1	yes	characteristic, complemented
227	#2873	C₂×C₇	1	2	yes	complemented
228	C₂⁴×C₇	C₂²×C₄	1	2	yes	—
229	C₇×#41	—	2	2	no	—
230	C₇×#41	—	2	2	no	—
231	C₇×#41	—	4	4	no	—
232	C₂×C₇×Q₈	C₂²×C₄	1	1	yes	characteristic
233	C₂×C₇×Q₈	C₂²×C₄	1	2	yes	—
234	C₂×C₇×Q₈	C₂²×C₄	1	2	yes	—
235	C₂×C₇×D₄	—	4	2	no	—
236	C₂×C₇×D₄	C₂²×C₄	1	1	yes	characteristic
237	C₂×C₇×D₄	C₂²×C₄	1	2	yes	—
238	C₂×C₇×D₄	C₂²×C₄	1	1	yes	characteristic
239	C₂×C₇×D₄	C₂²×C₄	1	1	yes	characteristic
240	C₂×C₇×D₄	C₂²×C₄	1	4	yes	—
241	C₂×C₇×D₄	C₂²×C₄	1	2	yes	—
242	C₂×C₇×D₄	C₂²×C₄	1	4	yes	—
243	C₂²×C₄×C₇	—	2	4	no	—
244	C₂²×C₄×C₇	—	2	4	no	—
245	C₂²×C₄×C₇	C₂²×C₄	1	1	yes	characteristic
246	C₂²×C₄×C₇	C₂²×C₄	1	2	yes	—
247	C₂²×C₄×C₇	C₂²×C₄	1	2	yes	—
248	C₂²×C₄×C₇	C₂²×C₄	1	2	yes	—
249	C₂²×C₄×C₇	C₂²×C₄	1	2	yes	—
250	C₂²×C₄×C₇	C₂²×C₄	1	1	yes	characteristic
251	C₂²×C₄×C₇	C₂²×C₄	1	4	yes	—
252	C₂²×C₄×C₇	C₂²×C₄	1	4	yes	—
253	C₂²×C₄×C₇	C₂²×C₄	1	2	yes	—
254	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
255	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
256	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
257	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
258	C₇×M₁₆	—	2	4	no	—
259	C₇×M₁₆	—	2	2	no	—
260	C₇×M₁₆	—	2	8	no	—
261	C₇×M₁₆	—	2	4	no	—
262	C₇×M₁₆	—	2	4	no	—
263	C₇×M₁₆	—	2	4	no	—
264	C₇×M₁₆	—	2	4	no	—
265	C₇×M₁₆	—	2	4	no	—
266	C₇×M₁₆	—	2	4	no	—
267	C₇×M₁₆	#41	1	4	yes	complemented
268	C₂×C₇×C₈	—	2	4	no	—
269	C₂×C₇×C₈	—	2	2	no	—
270	C₂×C₇×C₈	—	2	8	no	—
271	C₂×C₇×C₈	—	2	4	no	—
272	C₂×C₇×C₈	—	2	4	no	—
273	C₂×C₇×C₈	#41	1	4	yes	complemented
274	C₂×C₇×C₈	C₂⁴	1	1	yes	characteristic
275	C₂×C₇×C₈	C₂⁴	1	1	yes	characteristic
276	C₂×C₇×C₈	C₂⁴	1	2	yes	—
277	C₂×C₇×C₈	C₂⁴	1	2	yes	—
278	C₂×C₇×C₈	C₂⁴	1	4	yes	—
279	C₂×C₇×C₈	C₂⁴	1	2	yes	—
280	C₂×C₇×C₈	C₂⁴	1	1	yes	characteristic
281	C₂×C₇×C₈	C₂⁴	1	2	yes	—
282	C₂×C₇×C₈	C₂⁴	1	1	yes	characteristic
283	C₇×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
284	C₇×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
285	C₇×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
286	C₇×C₄⋊C₄	C₂²×C₄	1	2	yes	—
287	C₇×C₄⋊C₄	C₂²×C₄	1	2	yes	—
288	C₇×C₄⋊C₄	C₂²×C₄	1	4	yes	—
289	C₇×C₄⋊C₄	C₂²×C₄	1	4	yes	—
290	C₇×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
291	C₇×C₄⋊C₄	C₂²×C₄	1	2	yes	—
292	C₇×C₄⋊C₄	C₂²×C₄	1	2	yes	—
293	C₇×C₄⋊C₄	C₂²×C₄	1	4	yes	—
294	C₇×C₄⋊C₄	C₂²×C₄	1	4	yes	—
295	C₇×C₄⋊C₄	C₂²×C₄	1	2	yes	—
296	C₇×C₄⋊C₄	C₂²×C₄	1	2	yes	—
297	C₇×C₄⋊C₄	C₂²×C₄	1	4	yes	—
298	C₇×C₄⋊C₄	C₂²×C₄	1	4	yes	—
299	C₇×C₄⋊C₄	C₂²×C₄	1	2	yes	—
300	C₇×C₂²⋊C₄	C₂²×C₄	1	2	yes	—
301	C₇×C₂²⋊C₄	C₂²×C₄	1	2	yes	—
302	C₇×C₂²⋊C₄	C₂²×C₄	1	4	yes	—
303	C₇×C₂²⋊C₄	C₂²×C₄	1	4	yes	—
304	C₇×C₂²⋊C₄	C₂²×C₄	1	4	yes	—
305	C₇×C₂²⋊C₄	C₂²×C₄	1	2	yes	—
306	C₇×C₂²⋊C₄	C₂²×C₄	1	2	yes	—
307	C₇×C₂²⋊C₄	C₂²×C₄	1	2	yes	—
308	C₇×C₂²⋊C₄	C₂²×C₄	1	4	yes	—
309	C₇×C₂²⋊C₄	C₂²×C₄	1	4	yes	—
310	C₇×C₂²⋊C₄	C₂²×C₄	1	2	yes	—
311	C₇×C₂²⋊C₄	C₂²×C₄	1	2	yes	—
312	C₇×C₂²⋊C₄	C₂²×C₄	1	4	yes	—
313	C₇×C₂²⋊C₄	C₂²×C₄	1	4	yes	—
314	C₄²×C₇	C₂²×C₄	1	4	yes	—
315	C₄²×C₇	C₂²×C₄	1	4	yes	—
316	C₄²×C₇	C₂²×C₄	1	2	yes	—
317	C₄²×C₇	C₂²×C₄	1	1	yes	characteristic
318	C₄²×C₇	C₂²×C₄	1	1	yes	characteristic
319	C₄²×C₇	C₂²×C₄	1	2	yes	—
320	C₄²×C₇	C₂⁴	1	2	yes	—
321	C₄²×C₇	C₂⁴	1	1	yes	characteristic
322	C₄²×C₇	C₂⁴	1	1	yes	characteristic
323	C₄²×C₇	C₂⁴	1	4	yes	—
324	C₂×#131	C₂²×C₇	1	1	yes	characteristic
325	C₂×#131	C₂²×C₇	1	1	yes	characteristic
326	C₂²×M₁₆	C₂²×C₇	1	2	yes	—
327	C₂²×M₁₆	C₂²×C₇	1	2	yes	—
328	#556	C₄×C₇	1	1	yes	characteristic
329	#555	C₄×C₇	1	1	yes	characteristic
330	#554	C₄×C₇	1	1	yes	characteristic
331	#553	C₄×C₇	1	2	yes	—
332	#552	C₄×C₇	1	2	yes	—
333	#552	C₄×C₇	1	2	yes	—
334	#551	C₄×C₇	1	4	yes	—
335	#547	C₄×C₇	1	1	yes	characteristic
336	#546	C₄×C₇	1	2	yes	—
337	#533	C₂²×C₇	1	1	yes	characteristic
338	#529	C₂²×C₇	1	2	yes	—
339	#529	C₂²×C₇	1	4	yes	—
340	#525	C₂²×C₇	1	2	yes	—
341	C₄×#41	C₂²×C₇	1	2	yes	—
342	C₄×#41	C₂²×C₇	1	1	yes	characteristic
343	C₂×C₄×D₄	C₂²×C₇	1	1	yes	characteristic
344	C₂×#117	C₂²×C₇	1	2	yes	—
345	#446	C₂²×C₇	1	2	yes	complemented
346	#446	C₂²×C₇	1	2	yes	complemented
347	#446	C₂²×C₇	1	2	yes	complemented
348	#446	C₂²×C₇	1	4	yes	complemented
349	C₈×Q₈	C₂²×C₇	1	2	yes	complemented
350	C₈×Q₈	C₂²×C₇	1	2	yes	complemented
351	C₈×Q₈	C₂²×C₇	1	2	yes	complemented
352	#436	C₂²×C₇	1	1	yes	characteristic
353	#436	C₂²×C₇	1	1	yes	characteristic
354	#436	C₂²×C₇	1	2	yes	—
355	#436	C₂²×C₇	1	1	yes	characteristic
356	#436	C₂²×C₇	1	2	yes	—
357	#436	C₂²×C₇	1	1	yes	characteristic
358	#436	C₂²×C₇	1	2	yes	—
359	#436	C₂²×C₇	1	4	yes	complemented
360	#436	C₂²×C₇	1	4	yes	complemented
361	#436	C₂²×C₇	1	4	yes	complemented
362	#435	C₂²×C₇	1	4	yes	—
363	#435	C₂²×C₇	1	4	yes	complemented
364	#435	C₂²×C₇	1	4	yes	complemented
365	#435	C₂²×C₇	1	4	yes	complemented
366	#435	C₂²×C₇	1	4	yes	complemented
367	C₈×D₄	C₂²×C₇	1	2	yes	—
368	C₈×D₄	C₂²×C₇	1	4	yes	complemented
369	#433	C₂²×C₇	1	4	yes	complemented
370	#433	C₂²×C₇	1	4	yes	complemented
371	#433	C₂²×C₇	1	4	yes	complemented
372	#432	C₂²×C₇	1	4	yes	complemented
373	#432	C₂²×C₇	1	2	yes	complemented
374	#431	C₂²×C₇	1	4	yes	complemented
375	#431	C₂²×C₇	1	2	yes	complemented
376	#424	C₂²×C₇	1	2	yes	—
377	#424	C₂²×C₇	1	2	yes	—
378	#423	C₂²×C₇	1	1	yes	characteristic
379	C₂×C₄⋊C₈	C₂²×C₇	1	1	yes	characteristic
380	#408	C₂²×C₇	1	2	yes	—
381	#407	C₂²×C₇	1	2	yes	—
382	C₂×C₂²⋊C₈	C₂²×C₇	1	2	yes	—
383	#405	C₂²×C₇	1	1	yes	characteristic
384	#405	C₂²×C₇	1	2	yes	—
385	#405	C₂²×C₇	1	2	yes	—
386	#405	C₂²×C₇	1	2	yes	—
387	#405	C₂²×C₇	1	1	yes	characteristic
388	#405	C₂²×C₇	1	4	yes	complemented
389	#405	C₂²×C₇	1	4	yes	complemented
390	#405	C₂²×C₇	1	2	yes	complemented
391	#405	C₂²×C₇	1	2	yes	complemented
392	C₄×M₁₆	C₂²×C₇	1	1	yes	characteristic
393	C₄×M₁₆	C₂²×C₇	1	4	yes	complemented
394	C₄×M₁₆	C₂²×C₇	1	4	yes	complemented
395	C₄×M₁₆	C₂²×C₇	1	2	yes	complemented
396	C₂×C₄×C₈	C₂²×C₇	1	1	yes	characteristic
397	C₂×C₄×C₈	C₂²×C₇	1	2	yes	complemented
398	C₂³×C₇	—	2	4	no	—
399	C₂³×C₇	—	4	2	no	—
400	C₂³×C₇	—	4	2	no	—
401	C₂³×C₇	C₂³×C₄	1	2	yes	—
402	C₂³×C₇	C₂³×C₄	1	2	yes	—
403	C₂³×C₇	C₂³×C₄	1	2	yes	—
404	C₂³×C₇	C₂³×C₄	1	1	yes	characteristic
405	C₇×Q₈	—	2	2	no	—
406	C₇×Q₈	—	2	4	no	—
407	C₇×Q₈	—	4	2	no	—
408	C₇×D₄	—	2	4	no	—
409	C₇×D₄	—	2	2	no	—
410	C₇×D₄	—	2	2	no	—
411	C₇×D₄	—	2	2	no	—
412	C₇×D₄	—	4	2	no	—
413	C₇×D₄	—	4	4	no	—
414	C₇×D₄	—	4	4	no	—
415	C₂×C₄×C₇	—	2	4	no	—
416	C₂×C₄×C₇	—	2	4	no	—
417	C₂×C₄×C₇	—	2	4	no	—
418	C₂×C₄×C₇	—	2	2	no	—
419	C₂×C₄×C₇	—	2	4	no	—
420	C₂×C₄×C₇	—	2	2	no	—
421	C₂×C₄×C₇	—	2	2	no	—
422	C₂×C₄×C₇	—	2	2	no	—
423	C₂×C₄×C₇	—	2	2	no	—
424	C₂×C₄×C₇	—	2	2	no	—
425	C₂×C₄×C₇	—	2	2	no	—
426	C₂×C₄×C₇	—	4	2	no	—
427	C₂×C₄×C₇	—	4	4	no	—
428	C₂×C₄×C₇	—	4	1	no	—
429	C₂×C₄×C₇	—	4	4	no	—
430	C₂×C₄×C₇	C₂³×C₄	1	2	yes	—
431	C₂×C₄×C₇	C₂³×C₄	1	2	yes	—
432	C₂×C₄×C₇	C₂³×C₄	1	1	yes	characteristic
433	C₂×C₄×C₇	C₂³×C₄	1	2	yes	—
434	C₂×C₄×C₇	C₂³×C₄	1	2	yes	—
435	C₂×C₄×C₇	C₂³×C₄	1	1	yes	characteristic
436	C₂×C₄×C₇	C₂³×C₄	1	4	yes	—
437	C₂×C₄×C₇	C₂³×C₄	1	4	yes	—
438	C₂×C₄×C₇	C₂³×C₄	1	1	yes	characteristic
439	C₂×C₄×C₇	C₂³×C₄	1	2	yes	—
440	C₂×C₄×C₇	C₂³×C₄	1	1	yes	characteristic
441	C₂×C₄×C₇	C₂³×C₄	1	1	yes	characteristic
442	C₂×C₄×C₇	C₂×#41	1	2	yes	—
443	C₂×C₄×C₇	C₂×#41	1	2	yes	—
444	C₂×C₄×C₇	C₂⁵	1	1	yes	characteristic
445	C₇×C₈	—	2	1	no	—
446	C₇×C₈	—	2	2	no	—
447	C₇×C₈	—	2	2	no	—
448	C₇×C₈	—	2	1	no	—
449	C₇×C₈	—	2	4	no	—
450	C₇×C₈	—	2	2	no	—
451	C₇×C₈	C₂×#41	1	4	yes	—
452	C₇×C₈	C₂×#41	1	2	yes	—
453	C₇×C₈	C₂×#41	1	2	yes	—
454	C₂×#41	C₂×C₄×C₇	1	2	yes	—
455	C₂×#41	C₂³×C₇	1	1	yes	characteristic
456	C₂²×D₄	C₂×C₄×C₇	1	1	yes	characteristic
457	C₂³×C₄	C₂³×C₇	1	2	yes	—
458	#131	—	2	4	no	—
459	#131	—	2	4	no	—
460	C₂×M₁₆	—	2	8	no	—
461	C₂×M₁₆	—	2	8	no	—
462	C₂×M₁₆	C₂³×C₇	1	4	yes	—
463	C₂×M₁₆	C₂³×C₇	1	2	yes	—
464	C₂×M₁₆	C₂³×C₇	1	2	yes	—
465	C₂×M₁₆	C₂³×C₇	1	2	yes	—
466	C₂×M₁₆	C₂³×C₇	1	2	yes	—
467	C₂×M₁₆	C₂³×C₇	1	2	yes	—
468	C₂×M₁₆	C₂³×C₇	1	1	yes	characteristic
469	C₂×M₁₆	C₂³×C₇	1	2	yes	—
470	C₂×M₁₆	C₂³×C₇	1	2	yes	—
471	C₂×M₁₆	C₂³×C₇	1	1	yes	characteristic
472	C₂²×C₈	C₂³×C₇	1	2	yes	—
473	C₂²×C₈	C₂³×C₇	1	4	yes	—
474	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
475	C₂²×C₈	C₂³×C₇	1	2	yes	—
476	C₂²×C₈	C₂³×C₇	1	2	yes	—
477	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
478	C₄⋊Q₈	C₂×C₄×C₇	1	1	yes	characteristic
479	C₄⋊Q₈	C₂×C₄×C₇	1	1	yes	characteristic
480	#126	C₂×C₄×C₇	1	4	yes	—
481	#126	C₂×C₄×C₇	1	4	yes	—
482	#126	C₂×C₄×C₇	1	4	yes	—
483	#125	C₂×C₄×C₇	1	4	yes	—
484	#125	C₂×C₄×C₇	1	2	yes	—
485	#125	C₂×C₄×C₇	1	2	yes	—
486	#124	C₂×C₄×C₇	1	2	yes	—
487	#124	C₂×C₄×C₇	1	4	yes	—
488	#123	C₂×C₄×C₇	1	4	yes	—
489	#123	C₂×C₄×C₇	1	4	yes	—
490	#123	C₂×C₄×C₇	1	4	yes	—
491	#123	C₂×C₄×C₇	1	4	yes	—
492	C₂²⋊Q₈	C₂×C₄×C₇	1	2	yes	—
493	C₂²⋊Q₈	C₂×C₄×C₇	1	2	yes	—
494	C₂²⋊Q₈	C₂×C₄×C₇	1	2	yes	—
495	C₂²⋊Q₈	C₂×C₄×C₇	1	4	yes	—
496	C₂²⋊Q₈	C₂×C₄×C₇	1	2	yes	—
497	C₂²⋊Q₈	C₂×C₄×C₇	1	2	yes	—
498	#121	C₂×C₄×C₇	1	2	yes	—
499	#121	C₂×C₄×C₇	1	2	yes	—
500	#121	C₂×C₄×C₇	1	4	yes	—
501	#121	C₂×C₄×C₇	1	2	yes	—
502	#120	C₂×C₄×C₇	1	4	yes	—
503	C₄×Q₈	C₂×C₄×C₇	1	1	yes	characteristic
504	C₄×Q₈	C₂×C₄×C₇	1	2	yes	—
505	C₄×Q₈	C₂×C₄×C₇	1	1	yes	characteristic
506	C₄×Q₈	C₂³×C₇	1	2	yes	—
507	C₄×Q₈	C₂³×C₇	1	2	yes	—
508	C₄×D₄	C₂×C₄×C₇	1	1	yes	characteristic
509	C₄×D₄	C₂×C₄×C₇	1	2	yes	—
510	C₄×D₄	C₂×C₄×C₇	1	1	yes	characteristic
511	C₄×D₄	C₂×C₄×C₇	1	2	yes	—
512	C₄×D₄	C₂×C₄×C₇	1	2	yes	—
513	C₄×D₄	C₂×C₄×C₇	1	1	yes	characteristic
514	C₄×D₄	C₂×C₄×C₇	1	2	yes	—
515	C₄×D₄	C₂×C₄×C₇	1	4	yes	—
516	C₄×D₄	C₂×C₄×C₇	1	1	yes	characteristic
517	C₄×D₄	C₂³×C₇	1	1	yes	characteristic
518	C₄×D₄	C₂³×C₇	1	1	yes	characteristic
519	C₄×D₄	C₂³×C₇	1	2	yes	—
520	C₄×D₄	C₂³×C₇	1	4	yes	—
521	C₄×D₄	C₂³×C₇	1	4	yes	—
522	#117	C₂×C₄×C₇	1	4	yes	—
523	#117	C₂×C₄×C₇	1	2	yes	—
524	#117	C₂×C₄×C₇	1	2	yes	—
525	#117	C₂×C₄×C₇	1	4	yes	—
526	#117	C₂×C₄×C₇	1	2	yes	—
527	#117	C₂³×C₇	1	1	yes	characteristic
528	#117	C₂³×C₇	1	2	yes	—
529	#117	C₂³×C₇	1	4	yes	—
530	#117	C₂³×C₇	1	2	yes	—
531	C₂×C₄⋊C₄	C₂×C₄×C₇	1	2	yes	—
532	C₂×C₄⋊C₄	C₂×C₄×C₇	1	2	yes	—
533	C₂×C₄⋊C₄	C₂×C₄×C₇	1	1	yes	characteristic
534	C₂×C₂²⋊C₄	C₂×C₄×C₇	1	4	yes	—
535	C₂×C₂²⋊C₄	C₂×C₄×C₇	1	2	yes	—
536	C₂×C₄²	C₂³×C₇	1	4	yes	—
537	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
538	C₂×C₄²	C₂³×C₇	1	2	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	2	yes	—
543	C₄⋊C₈	C₂³×C₇	1	2	yes	—
544	C₄⋊C₈	C₂³×C₇	1	4	yes	—
545	C₄⋊C₈	C₂³×C₇	1	4	yes	—
546	C₄⋊C₈	C₂³×C₇	1	4	yes	—
547	C₄⋊C₈	C₂³×C₇	1	4	yes	—
548	C₂²⋊C₈	C₂³×C₇	1	2	yes	—
549	C₂²⋊C₈	C₂³×C₇	1	2	yes	—
550	C₂²⋊C₈	C₂³×C₇	1	2	yes	—
551	C₂²⋊C₈	C₂³×C₇	1	2	yes	—
552	C₂²⋊C₈	C₂³×C₇	1	4	yes	—
553	C₂²⋊C₈	C₂³×C₇	1	4	yes	—
554	C₂²⋊C₈	C₂³×C₇	1	4	yes	—
555	C₂²⋊C₈	C₂³×C₇	1	4	yes	—
556	#97	C₂³×C₇	1	2	yes	—
557	#97	C₂³×C₇	1	2	yes	—
558	#97	C₂³×C₇	1	4	yes	—
559	#97	C₂³×C₇	1	2	yes	—
560	#97	C₂³×C₇	1	4	yes	—
561	#97	C₂³×C₇	1	4	yes	—
562	C₄×C₈	C₂³×C₇	1	1	yes	characteristic
563	C₄×C₈	C₂³×C₇	1	1	yes	characteristic
564	C₄×C₈	C₂³×C₇	1	1	yes	characteristic
565	C₄×C₈	C₂³×C₇	1	1	yes	characteristic
566	C₄×C₈	C₂³×C₇	1	2	yes	—
567	C₄×C₈	C₂³×C₇	1	2	yes	—
568	C₄×C₈	C₂³×C₇	1	2	yes	—
569	C₄×C₈	C₂³×C₇	1	4	yes	—
570	C₄×C₈	C₂³×C₇	1	4	yes	—
571	C₄×C₈	C₂³×C₇	1	4	yes	—
572	C₂²×C₇	—	2	1	no	—
573	C₂²×C₇	—	2	1	no	—
574	C₂²×C₇	—	2	2	no	—
575	C₂²×C₇	—	2	2	no	—
576	C₂²×C₇	—	2	2	no	—
577	C₂²×C₇	—	2	2	no	—
578	C₂²×C₇	—	2	2	no	—
579	C₂²×C₇	—	2	2	no	—
580	C₂²×C₇	—	2	2	no	—
581	C₂²×C₇	—	2	2	no	—
582	C₂²×C₇	—	2	2	no	—
583	C₂²×C₇	—	8	4	no	—
584	C₂²×C₇	C₄×#41	1	2	yes	—
585	C₂²×C₇	C₂⁴×C₄	1	1	yes	characteristic
586	C₄×C₇	—	2	2	no	—
587	C₄×C₇	—	2	2	no	—
588	C₄×C₇	—	2	2	no	—
589	C₄×C₇	—	2	2	no	—
590	C₄×C₇	—	2	1	no	—
591	C₄×C₇	—	2	4	no	—
592	C₄×C₇	—	2	1	no	—
593	C₄×C₇	—	2	2	no	—
594	C₄×C₇	—	2	4	no	—
595	C₄×C₇	—	2	1	no	—
596	C₄×C₇	C₄×#41	1	2	yes	—
597	C₄×C₇	#568	1	2	yes	—
598	C₄×C₇	C₂²×#41	1	1	yes	characteristic
599	C₄×C₇	C₂²×#41	1	1	yes	characteristic
600	C₂⁴	C₂²×C₄×C₇	1	2	yes	—
601	#41	—	2	2	no	—
602	#41	—	2	2	no	—
603	#41	—	4	4	no	—
604	C₂×Q₈	C₂²×C₄×C₇	1	1	yes	characteristic
605	C₂×Q₈	C₂²×C₄×C₇	1	2	yes	—
606	C₂×Q₈	C₂²×C₄×C₇	1	2	yes	—
607	C₂×D₄	—	4	2	no	—
608	C₂×D₄	C₂²×C₄×C₇	1	1	yes	characteristic
609	C₂×D₄	C₂²×C₄×C₇	1	2	yes	—
610	C₂×D₄	C₂²×C₄×C₇	1	1	yes	characteristic
611	C₂×D₄	C₂²×C₄×C₇	1	1	yes	characteristic
612	C₂×D₄	C₂²×C₄×C₇	1	4	yes	—
613	C₂×D₄	C₂²×C₄×C₇	1	2	yes	—
614	C₂×D₄	C₂²×C₄×C₇	1	4	yes	—
615	C₂²×C₄	—	2	4	no	—
616	C₂²×C₄	—	2	4	no	—
617	C₂²×C₄	C₂²×C₄×C₇	1	1	yes	characteristic
618	C₂²×C₄	C₂²×C₄×C₇	1	2	yes	—
619	C₂²×C₄	C₂²×C₄×C₇	1	2	yes	—
620	C₂²×C₄	C₂²×C₄×C₇	1	2	yes	—
621	C₂²×C₄	C₂²×C₄×C₇	1	2	yes	—
622	C₂²×C₄	C₂²×C₄×C₇	1	1	yes	characteristic
623	C₂²×C₄	C₂²×C₄×C₇	1	4	yes	—
624	C₂²×C₄	C₂²×C₄×C₇	1	4	yes	—
625	C₂²×C₄	C₂²×C₄×C₇	1	2	yes	—
626	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
627	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
628	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
629	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
630	M₁₆	—	2	4	no	—
631	M₁₆	—	2	2	no	—
632	M₁₆	—	2	8	no	—
633	M₁₆	—	2	4	no	—
634	M₁₆	—	2	4	no	—
635	M₁₆	—	2	4	no	—
636	M₁₆	—	2	4	no	—
637	M₁₆	—	2	4	no	—
638	M₁₆	—	2	4	no	—
639	M₁₆	C₇×#41	1	4	yes	complemented
640	C₂×C₈	—	2	4	no	—
641	C₂×C₈	—	2	2	no	—
642	C₂×C₈	—	2	8	no	—
643	C₂×C₈	—	2	4	no	—
644	C₂×C₈	—	2	4	no	—
645	C₂×C₈	C₇×#41	1	4	yes	complemented
646	C₂×C₈	C₂⁴×C₇	1	1	yes	characteristic
647	C₂×C₈	C₂⁴×C₇	1	1	yes	characteristic
648	C₂×C₈	C₂⁴×C₇	1	2	yes	—
649	C₂×C₈	C₂⁴×C₇	1	2	yes	—
650	C₂×C₈	C₂⁴×C₇	1	4	yes	—
651	C₂×C₈	C₂⁴×C₇	1	2	yes	—
652	C₂×C₈	C₂⁴×C₇	1	1	yes	characteristic
653	C₂×C₈	C₂⁴×C₇	1	2	yes	—
654	C₂×C₈	C₂⁴×C₇	1	1	yes	characteristic
655	C₄⋊C₄	C₂²×C₄×C₇	1	1	yes	characteristic
656	C₄⋊C₄	C₂²×C₄×C₇	1	1	yes	characteristic
657	C₄⋊C₄	C₂²×C₄×C₇	1	1	yes	characteristic
658	C₄⋊C₄	C₂²×C₄×C₇	1	2	yes	—
659	C₄⋊C₄	C₂²×C₄×C₇	1	2	yes	—
660	C₄⋊C₄	C₂²×C₄×C₇	1	4	yes	—
661	C₄⋊C₄	C₂²×C₄×C₇	1	4	yes	—
662	C₄⋊C₄	C₂²×C₄×C₇	1	1	yes	characteristic
663	C₄⋊C₄	C₂²×C₄×C₇	1	2	yes	—
664	C₄⋊C₄	C₂²×C₄×C₇	1	2	yes	—
665	C₄⋊C₄	C₂²×C₄×C₇	1	4	yes	—
666	C₄⋊C₄	C₂²×C₄×C₇	1	4	yes	—
667	C₄⋊C₄	C₂²×C₄×C₇	1	2	yes	—
668	C₄⋊C₄	C₂²×C₄×C₇	1	2	yes	—
669	C₄⋊C₄	C₂²×C₄×C₇	1	4	yes	—
670	C₄⋊C₄	C₂²×C₄×C₇	1	4	yes	—
671	C₄⋊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	4	yes	—
675	C₂²⋊C₄	C₂²×C₄×C₇	1	4	yes	—
676	C₂²⋊C₄	C₂²×C₄×C₇	1	4	yes	—
677	C₂²⋊C₄	C₂²×C₄×C₇	1	2	yes	—
678	C₂²⋊C₄	C₂²×C₄×C₇	1	2	yes	—
679	C₂²⋊C₄	C₂²×C₄×C₇	1	2	yes	—
680	C₂²⋊C₄	C₂²×C₄×C₇	1	4	yes	—
681	C₂²⋊C₄	C₂²×C₄×C₇	1	4	yes	—
682	C₂²⋊C₄	C₂²×C₄×C₇	1	2	yes	—
683	C₂²⋊C₄	C₂²×C₄×C₇	1	2	yes	—
684	C₂²⋊C₄	C₂²×C₄×C₇	1	4	yes	—
685	C₂²⋊C₄	C₂²×C₄×C₇	1	4	yes	—
686	C₄²	C₂²×C₄×C₇	1	4	yes	—
687	C₄²	C₂²×C₄×C₇	1	4	yes	—
688	C₄²	C₂²×C₄×C₇	1	2	yes	—
689	C₄²	C₂²×C₄×C₇	1	1	yes	characteristic
690	C₄²	C₂²×C₄×C₇	1	1	yes	characteristic
691	C₄²	C₂²×C₄×C₇	1	2	yes	—
692	C₄²	C₂⁴×C₇	1	2	yes	—
693	C₄²	C₂⁴×C₇	1	1	yes	characteristic
694	C₄²	C₂⁴×C₇	1	1	yes	characteristic
695	C₄²	C₂⁴×C₇	1	4	yes	—
696	C₂×C₇	—	2	2	no	—
697	C₂×C₇	—	4	2	no	—
698	C₂×C₇	—	4	2	no	—
699	C₂×C₇	—	4	2	no	—
700	C₂×C₇	C₂×C₄×#41	1	1	yes	characteristic
701	C₂×C₇	C₂×#568	1	1	yes	characteristic
702	C₂×C₇	#3573	1	1	yes	characteristic
703	C₂³	—	2	4	no	—
704	C₂³	—	4	2	no	—
705	C₂³	—	4	2	no	—
706	C₂³	C₂³×C₄×C₇	1	2	yes	—
707	C₂³	C₂³×C₄×C₇	1	2	yes	—
708	C₂³	C₂³×C₄×C₇	1	2	yes	—
709	C₂³	C₂³×C₄×C₇	1	1	yes	characteristic
710	Q₈	—	2	2	no	—
711	Q₈	—	2	4	no	—
712	Q₈	—	4	2	no	—
713	D₄	—	2	4	no	—
714	D₄	—	2	2	no	—
715	D₄	—	2	2	no	—
716	D₄	—	2	2	no	—
717	D₄	—	4	2	no	—
718	D₄	—	4	4	no	—
719	D₄	—	4	4	no	—
720	C₂×C₄	—	2	4	no	—
721	C₂×C₄	—	2	2	no	—
722	C₂×C₄	—	2	2	no	—
723	C₂×C₄	—	2	2	no	—
724	C₂×C₄	—	2	2	no	—
725	C₂×C₄	—	2	2	no	—
726	C₂×C₄	—	2	2	no	—
727	C₂×C₄	—	2	4	no	—
728	C₂×C₄	—	2	4	no	—
729	C₂×C₄	—	2	2	no	—
730	C₂×C₄	—	2	4	no	—
731	C₂×C₄	—	4	2	no	—
732	C₂×C₄	—	4	4	no	—
733	C₂×C₄	—	4	1	no	—
734	C₂×C₄	—	4	4	no	—
735	C₂×C₄	C₂³×C₄×C₇	1	2	yes	—
736	C₂×C₄	C₂³×C₄×C₇	1	2	yes	—
737	C₂×C₄	C₂³×C₄×C₇	1	1	yes	characteristic
738	C₂×C₄	C₂³×C₄×C₇	1	2	yes	—
739	C₂×C₄	C₂³×C₄×C₇	1	2	yes	—
740	C₂×C₄	C₂³×C₄×C₇	1	1	yes	characteristic
741	C₂×C₄	C₂³×C₄×C₇	1	4	yes	—
742	C₂×C₄	C₂³×C₄×C₇	1	4	yes	—
743	C₂×C₄	C₂³×C₄×C₇	1	1	yes	characteristic
744	C₂×C₄	C₂³×C₄×C₇	1	2	yes	—
745	C₂×C₄	C₂³×C₄×C₇	1	1	yes	characteristic
746	C₂×C₄	C₂³×C₄×C₇	1	1	yes	characteristic
747	C₂×C₄	C₂×C₇×#41	1	2	yes	—
748	C₂×C₄	C₂×C₇×#41	1	2	yes	—
749	C₂×C₄	C₂⁵×C₇	1	1	yes	characteristic
750	C₈	—	2	1	no	—
751	C₈	—	2	2	no	—
752	C₈	—	2	2	no	—
753	C₈	—	2	1	no	—
754	C₈	—	2	4	no	—
755	C₈	—	2	2	no	—
756	C₈	C₂×C₇×#41	1	4	yes	—
757	C₈	C₂×C₇×#41	1	2	yes	—
758	C₈	C₂×C₇×#41	1	2	yes	—
759	C₇	#60217	1	1	yes	characteristic, direct product factor, Sylow
760	C₂²	—	2	1	no	—
761	C₂²	—	2	1	no	—
762	C₂²	—	2	2	no	—
763	C₂²	—	2	2	no	—
764	C₂²	—	2	2	no	—
765	C₂²	—	2	2	no	—
766	C₂²	—	2	2	no	—
767	C₂²	—	2	2	no	—
768	C₂²	—	2	2	no	—
769	C₂²	—	2	2	no	—
770	C₂²	—	2	2	no	—
771	C₂²	—	8	4	no	—
772	C₂²	C₄×C₇×#41	1	2	yes	—
773	C₂²	C₂⁴×C₄×C₇	1	1	yes	characteristic
774	C₄	—	2	2	no	—
775	C₄	—	2	1	no	—
776	C₄	—	2	4	no	—
777	C₄	—	2	1	no	—
778	C₄	—	2	2	no	—
779	C₄	—	2	4	no	—
780	C₄	—	2	1	no	—
781	C₄	—	2	2	no	—
782	C₄	—	2	2	no	—
783	C₄	—	2	2	no	—
784	C₄	C₄×C₇×#41	1	2	yes	—
785	C₄	C₇×#568	1	2	yes	—
786	C₄	C₂²×C₇×#41	1	1	yes	characteristic
787	C₄	C₂²×C₇×#41	1	1	yes	characteristic
788	C₂	—	2	2	no	—
789	C₂	—	4	2	no	—
790	C₂	—	4	2	no	—
791	C₂	—	4	2	no	—
792	C₂	C₂×C₄×C₇×#41	1	1	yes	characteristic
793	C₂	C₂×C₇×#568	1	1	yes	characteristic
794	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×#3475	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×#2971	C₂	semidirect
3. C₇×#2969	C₂	semidirect
4. C₇×#2969	C₂	semidirect
5. C₇×#2967	C₂	semidirect
6. C₇×#2966	C₂	semidirect
7. C₇×#2965	C₂	semidirect
8. C₇×#2962	C₂	semidirect
9. C₇×#2960	C₂	semidirect
10. C₇×D₄×M₁₆	C₂	semidirect
11. C₇×#2933	C₂	semidirect
12. C₇×#2930	C₂	semidirect
13. C₂×C₇×#436	C₂	semidirect
14. C₇×#2925	C₂	semidirect
15. C₇×#2924	C₂	semidirect
16. C₄×C₇×#131	C₂	semidirect
17. C₇×#2873	C₂	semidirect
39. C₇×#446	C₂²	semidirect
40. C₇×#446	C₂²	semidirect
41. C₇×#446	C₂²	semidirect
42. C₇×#446	C₂²	semidirect
43. C₇×C₈×Q₈	C₂²	semidirect
44. C₇×C₈×Q₈	C₂²	semidirect
45. C₇×C₈×Q₈	C₂²	semidirect
53. C₇×#436	C₂²	semidirect
54. C₇×#436	C₂²	semidirect
55. C₇×#436	C₂²	semidirect
57. C₇×#435	C₂²	semidirect
58. C₇×#435	C₂²	semidirect
59. C₇×#435	C₂²	semidirect
60. C₇×#435	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×#432	C₂²	semidirect
68. C₇×#431	C₂²	semidirect
69. C₇×#431	C₂²	semidirect
82. C₇×#405	C₂²	semidirect
83. C₇×#405	C₂²	semidirect
84. C₇×#405	C₂²	semidirect
85. C₇×#405	C₂²	semidirect
87. C₄×C₇×M₁₆	C₂²	semidirect
88. C₄×C₇×M₁₆	C₂²	semidirect
89. C₄×C₇×M₁₆	C₂²	semidirect
91. C₂×C₄×C₇×C₈	C₂²	semidirect
92. #60217	C₇	direct (N × H)
212. #2971	C₂×C₇	semidirect
213. #2969	C₂×C₇	semidirect
214. #2969	C₂×C₇	semidirect
215. #2967	C₂×C₇	semidirect
216. #2966	C₂×C₇	semidirect
217. #2965	C₂×C₇	semidirect
218. #2962	C₂×C₇	semidirect
219. #2960	C₂×C₇	semidirect
220. D₄×M₁₆	C₂×C₇	semidirect
221. #2933	C₂×C₇	semidirect
222. #2930	C₂×C₇	semidirect
223. C₂×#436	C₂×C₇	semidirect
224. #2925	C₂×C₇	semidirect
225. #2924	C₂×C₇	semidirect
226. C₄×#131	C₂×C₇	semidirect
227. #2873	C₂×C₇	semidirect
267. C₇×M₁₆	#41	semidirect
273. C₂×C₇×C₈	#41	semidirect
345. #446	C₂²×C₇	semidirect
346. #446	C₂²×C₇	semidirect
347. #446	C₂²×C₇	semidirect
348. #446	C₂²×C₇	semidirect
349. C₈×Q₈	C₂²×C₇	semidirect
350. C₈×Q₈	C₂²×C₇	semidirect
351. C₈×Q₈	C₂²×C₇	semidirect
359. #436	C₂²×C₇	semidirect
360. #436	C₂²×C₇	semidirect
361. #436	C₂²×C₇	semidirect
363. #435	C₂²×C₇	semidirect
364. #435	C₂²×C₇	semidirect
365. #435	C₂²×C₇	semidirect
366. #435	C₂²×C₇	semidirect
368. C₈×D₄	C₂²×C₇	semidirect
369. #433	C₂²×C₇	semidirect
370. #433	C₂²×C₇	semidirect
371. #433	C₂²×C₇	semidirect
372. #432	C₂²×C₇	semidirect
373. #432	C₂²×C₇	semidirect
374. #431	C₂²×C₇	semidirect
375. #431	C₂²×C₇	semidirect
388. #405	C₂²×C₇	semidirect
389. #405	C₂²×C₇	semidirect
390. #405	C₂²×C₇	semidirect
391. #405	C₂²×C₇	semidirect
393. C₄×M₁₆	C₂²×C₇	semidirect
394. C₄×M₁₆	C₂²×C₇	semidirect
395. C₄×M₁₆	C₂²×C₇	semidirect
397. C₂×C₄×C₈	C₂²×C₇	semidirect
639. M₁₆	C₇×#41	semidirect
645. C₂×C₈	C₇×#41	semidirect
759. C₇	#60217	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×#3475	2
C₇×#2971	2
C₇×#2969	2
C₇×#2967	2
C₇×#2966	2
C₇×#2965	2
C₇×#2962	2
C₇×#2960	2
C₇×D₄×M₁₆	2
C₇×#2933	2
C₇×#2930	2
C₂×C₇×#436	2
C₇×#2925	2
C₇×#2924	2
C₄×C₇×#131	2
C₇×#2873	2
#60217	7

Subgroups — C7×#60217 #13237433

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×#60217 #13237433