Subgroups — C₇×#60322 #13237538

Order 1792.

1858 conjugacy classes of subgroups.

The subgroup lattice has 1038 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×#3459	C₂	1	1	yes	maximal, characteristic
2	C₇×#2995	C₂	1	2	yes	maximal, complemented
3	C₇×#2993	C₂	1	2	yes	maximal, complemented
4	C₇×#2992	C₂	1	1	yes	maximal, characteristic, complemented
5	C₇×#2992	C₂	1	1	yes	maximal, characteristic, complemented
6	C₇×#2978	C₂	1	2	yes	maximal, complemented
7	C₇×#2977	C₂	1	2	yes	maximal, complemented
8	C₇×#2976	C₂	1	2	yes	maximal, complemented
9	C₇×#2974	C₂	1	2	yes	maximal, complemented
10	C₇×#2973	C₂	1	1	yes	maximal, characteristic, complemented
11	C₇×#2969	C₂	1	2	yes	maximal, complemented
12	C₇×#2967	C₂	1	2	yes	maximal, complemented
13	C₇×#2966	C₂	1	1	yes	maximal, characteristic, complemented
14	C₇×#2966	C₂	1	1	yes	maximal, characteristic, complemented
15	C₇×D₄×M₁₆	C₂	1	2	yes	maximal, complemented
16	C₇×#2933	C₂	1	2	yes	maximal, complemented
17	C₇×#2933	C₂	1	2	yes	maximal, complemented
18	C₇×#2930	C₂	1	2	yes	maximal, complemented
19	C₂×C₇×#436	C₂	1	1	yes	maximal, characteristic, complemented
20	C₂×C₇×#131	C₂²	1	2	yes	complemented
21	C₂²×C₇×M₁₆	C₂²	1	1	yes	characteristic
22	C₂²×C₇×M₁₆	C₂²	1	1	yes	characteristic, complemented
23	C₂²×C₇×M₁₆	C₂²	1	2	yes	complemented
24	C₇×#543	C₄	1	1	yes	characteristic
25	C₇×#539	C₄	1	2	yes	—
26	C₇×#539	C₄	1	2	yes	—
27	C₇×#539	C₄	1	2	yes	—
28	C₇×#538	C₄	1	1	yes	characteristic
29	C₇×#538	C₄	1	1	yes	characteristic
30	C₇×#538	C₄	1	2	yes	—
31	C₇×#538	C₄	1	2	yes	—
32	C₇×#534	C₄	1	1	yes	characteristic
33	C₇×#534	C₄	1	2	yes	—
34	C₇×#529	C₂²	1	1	yes	characteristic
35	C₇×#529	C₂²	1	1	yes	characteristic
36	C₇×#529	C₂²	1	2	yes	—
37	C₇×#529	C₂²	1	2	yes	—
38	C₇×#525	C₂²	1	2	yes	—
39	C₇×#525	C₂²	1	2	yes	—
40	C₇×#525	C₂²	1	2	yes	—
41	C₂×C₄×C₇×D₄	C₂²	1	1	yes	characteristic
42	C₂×C₄×C₇×D₄	C₂²	1	2	yes	—
43	C₇×#446	C₂²	1	1	yes	characteristic, complemented
44	C₇×#446	C₂²	1	1	yes	characteristic, complemented
45	C₇×#446	C₂²	1	2	yes	complemented
46	C₇×#446	C₂²	1	2	yes	complemented
47	C₇×C₈×Q₈	C₂²	1	1	yes	characteristic, complemented
48	C₇×C₈×Q₈	C₂²	1	1	yes	characteristic, complemented
49	C₇×#436	C₂²	1	2	yes	complemented
50	C₇×#436	C₂²	1	2	yes	complemented
51	C₇×#436	C₂²	1	2	yes	complemented
52	C₇×#436	C₂²	1	2	yes	complemented
53	C₇×#436	C₂²	1	1	yes	characteristic, complemented
54	C₇×#436	C₂²	1	2	yes	complemented
55	C₇×#436	C₂²	1	2	yes	complemented
56	C₇×#436	C₂²	1	2	yes	complemented
57	C₇×#436	C₂²	1	2	yes	complemented
58	C₇×#436	C₂²	1	2	yes	complemented
59	C₇×#436	C₂²	1	1	yes	characteristic, complemented
60	C₇×#436	C₂²	1	2	yes	complemented
61	C₇×#435	C₂²	1	2	yes	complemented
62	C₇×#435	C₂²	1	2	yes	complemented
63	C₇×#435	C₂²	1	2	yes	complemented
64	C₇×#435	C₂²	1	2	yes	complemented
65	C₇×#435	C₂²	1	2	yes	complemented
66	C₇×#435	C₂²	1	2	yes	complemented
67	C₇×#435	C₂²	1	2	yes	complemented
68	C₇×#435	C₂²	1	2	yes	complemented
69	C₇×#435	C₂²	1	2	yes	complemented
70	C₇×#435	C₂²	1	2	yes	complemented
71	C₇×#435	C₂²	1	2	yes	complemented
72	C₇×#435	C₂²	1	2	yes	complemented
73	C₇×#435	C₂²	1	2	yes	complemented
74	C₇×#435	C₂²	1	2	yes	complemented
75	C₇×#435	C₂²	1	2	yes	complemented
76	C₇×#435	C₂²	1	2	yes	complemented
77	C₇×#435	C₂²	1	2	yes	complemented
78	C₇×#435	C₂²	1	2	yes	complemented
79	C₇×C₈×D₄	C₂²	1	1	yes	characteristic, complemented
80	C₇×C₈×D₄	C₂²	1	2	yes	complemented
81	C₇×C₈×D₄	C₂²	1	2	yes	complemented
82	C₇×C₈×D₄	C₂²	1	2	yes	complemented
83	C₇×C₈×D₄	C₂²	1	2	yes	complemented
84	C₇×C₈×D₄	C₂²	1	2	yes	complemented
85	C₇×C₈×D₄	C₂²	1	1	yes	characteristic, complemented
86	C₇×C₈×D₄	C₂²	1	2	yes	complemented
87	C₇×#433	C₂²	1	2	yes	complemented
88	C₇×#433	C₂²	1	2	yes	complemented
89	C₇×#433	C₂²	1	2	yes	complemented
90	C₇×#433	C₂²	1	2	yes	complemented
91	C₇×#433	C₂²	1	2	yes	complemented
92	C₇×#433	C₂²	1	2	yes	complemented
93	C₇×#432	C₂²	1	1	yes	characteristic, complemented
94	C₇×#432	C₂²	1	1	yes	characteristic, complemented
95	C₇×#432	C₂²	1	2	yes	complemented
96	C₇×#431	C₂²	1	2	yes	complemented
97	C₇×#424	C₂²	1	2	yes	complemented
98	C₇×#424	C₂²	1	2	yes	complemented
99	C₇×#424	C₂²	1	2	yes	complemented
100	C₇×#423	C₂²	1	2	yes	complemented
101	C₂×C₇×C₄⋊C₈	C₂²	1	1	yes	characteristic, complemented
102	C₇×#408	C₂²	1	2	yes	complemented
103	C₇×#408	C₂²	1	2	yes	complemented
104	C₇×#408	C₂²	1	2	yes	complemented
105	C₇×#407	C₂²	1	2	yes	—
106	C₇×#407	C₂²	1	2	yes	complemented
107	C₇×#407	C₂²	1	2	yes	complemented
108	C₂×C₇×C₂²⋊C₈	C₂²	1	1	yes	characteristic
109	C₂×C₇×C₂²⋊C₈	C₂²	1	1	yes	characteristic, complemented
110	C₂×C₇×C₂²⋊C₈	C₂²	1	2	yes	complemented
111	C₂×C₇×C₂²⋊C₈	C₂²	1	2	yes	complemented
112	C₇×#405	C₂²	1	2	yes	complemented
113	C₇×#405	C₂²	1	2	yes	complemented
114	C₇×#405	C₂²	1	2	yes	complemented
115	C₄×C₇×M₁₆	C₂²	1	2	yes	complemented
116	C₂×C₄×C₇×C₈	C₂²	1	1	yes	characteristic, complemented
117	#60322	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
118	C₂×C₇×#41	C₂³	1	2	yes	—
119	C₂²×C₇×D₄	C₂×C₄	1	1	yes	characteristic
120	C₂²×C₇×D₄	C₂×C₄	1	2	yes	—
121	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
122	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
123	C₂³×C₄×C₇	C₂³	1	2	yes	—
124	C₇×#131	—	4	4	no	—
125	C₂×C₇×M₁₆	—	4	2	no	—
126	C₂×C₇×M₁₆	—	4	2	no	—
127	C₂×C₇×M₁₆	—	4	4	no	—
128	C₂×C₇×M₁₆	C₂³	1	2	yes	—
129	C₂×C₇×M₁₆	C₂³	1	2	yes	—
130	C₂×C₇×M₁₆	C₂³	1	2	yes	—
131	C₂×C₇×M₁₆	C₂³	1	2	yes	—
132	C₂×C₇×M₁₆	C₂³	1	2	yes	—
133	C₂×C₇×M₁₆	C₂³	1	2	yes	—
134	C₂×C₇×M₁₆	C₂³	1	2	yes	—
135	C₂×C₇×M₁₆	C₂³	1	2	yes	—
136	C₂×C₇×M₁₆	C₂³	1	2	yes	—
137	C₂×C₇×M₁₆	C₂³	1	2	yes	—
138	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
139	C₂²×C₇×C₈	C₂³	1	2	yes	—
140	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
141	C₂²×C₇×C₈	C₂³	1	2	yes	—
142	C₂²×C₇×C₈	C₂³	1	2	yes	—
143	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
144	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
145	C₂²×C₇×C₈	C₂³	1	2	yes	—
146	C₂²×C₇×C₈	C₂³	1	2	yes	—
147	C₂²×C₇×C₈	C₂³	1	2	yes	—
148	C₇×#126	C₂×C₄	1	2	yes	—
149	C₇×#126	C₂×C₄	1	2	yes	—
150	C₇×#126	C₂×C₄	1	2	yes	—
151	C₇×#126	C₂×C₄	1	2	yes	—
152	C₇×#126	C₂×C₄	1	2	yes	—
153	C₇×#126	C₂×C₄	1	2	yes	—
154	C₇×#125	C₂×C₄	1	1	yes	characteristic
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×#123	C₂×C₄	1	2	yes	—
163	C₇×#123	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	2	yes	—
175	C₇×C₂²⋊Q₈	C₂×C₄	1	2	yes	—
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	1	yes	characteristic
181	C₇×C₂²⋊Q₈	C₂×C₄	1	1	yes	characteristic
182	C₇×C₂²⋊Q₈	C₂×C₄	1	2	yes	—
183	C₇×C₂²⋊Q₈	C₂×C₄	1	2	yes	—
184	C₇×#121	C₂×C₄	1	2	yes	—
185	C₇×#121	C₂×C₄	1	2	yes	—
186	C₇×#121	C₂×C₄	1	2	yes	—
187	C₇×#121	C₂×C₄	1	2	yes	—
188	C₇×#121	C₂×C₄	1	2	yes	—
189	C₇×#121	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×#120	C₂×C₄	1	2	yes	—
195	C₇×#120	C₂×C₄	1	2	yes	—
196	C₇×#120	C₂×C₄	1	2	yes	—
197	C₇×#120	C₂×C₄	1	2	yes	—
198	C₇×#120	C₂×C₄	1	2	yes	—
199	C₇×#120	C₂×C₄	1	2	yes	—
200	C₄×C₇×Q₈	C₂³	1	1	yes	characteristic
201	C₄×C₇×Q₈	C₂³	1	1	yes	characteristic
202	C₄×C₇×D₄	C₂×C₄	1	2	yes	—
203	C₄×C₇×D₄	C₂×C₄	1	2	yes	—
204	C₄×C₇×D₄	C₂×C₄	1	2	yes	—
205	C₄×C₇×D₄	C₂×C₄	1	2	yes	—
206	C₄×C₇×D₄	C₂×C₄	1	2	yes	—
207	C₄×C₇×D₄	C₂×C₄	1	2	yes	—
208	C₄×C₇×D₄	C₂³	1	2	yes	—
209	C₄×C₇×D₄	C₂³	1	2	yes	—
210	C₄×C₇×D₄	C₂³	1	2	yes	—
211	C₄×C₇×D₄	C₂³	1	2	yes	—
212	C₄×C₇×D₄	C₂³	1	2	yes	—
213	C₄×C₇×D₄	C₂³	1	2	yes	—
214	C₄×C₇×D₄	C₂³	1	1	yes	characteristic
215	C₄×C₇×D₄	C₂³	1	2	yes	—
216	C₄×C₇×D₄	C₂³	1	2	yes	—
217	C₄×C₇×D₄	C₂³	1	1	yes	characteristic
218	C₇×#117	C₂³	1	2	yes	—
219	C₇×#117	C₂³	1	2	yes	—
220	C₇×#117	C₂³	1	2	yes	—
221	C₂×C₇×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
222	C₂×C₇×C₄⋊C₄	C₂×C₄	1	2	yes	—
223	C₂×C₇×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
224	C₂×C₇×C₂²⋊C₄	C₂×C₄	1	2	yes	—
225	C₂×C₇×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
226	C₂×C₇×C₂²⋊C₄	C₂×C₄	1	2	yes	—
227	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
228	C₂×C₄²×C₇	C₂³	1	2	yes	—
229	C₇×C₄⋊C₈	C₂³	1	2	yes	—
230	C₇×C₄⋊C₈	C₂³	1	2	yes	—
231	C₇×C₄⋊C₈	C₂³	1	2	yes	—
232	C₇×C₄⋊C₈	C₂³	1	2	yes	—
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×C₄⋊C₈	C₂³	1	2	yes	—
240	C₇×C₄⋊C₈	C₂³	1	1	yes	characteristic
241	C₇×C₄⋊C₈	C₂³	1	2	yes	—
242	C₇×C₄⋊C₈	C₂³	1	1	yes	characteristic
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×C₂²⋊C₈	C₂³	1	2	yes	—
250	C₇×C₂²⋊C₈	C₂³	1	2	yes	—
251	C₇×C₂²⋊C₈	C₂³	1	2	yes	—
252	C₇×C₂²⋊C₈	C₂³	1	2	yes	—
253	C₇×C₂²⋊C₈	C₂³	1	2	yes	—
254	C₇×C₂²⋊C₈	C₂³	1	2	yes	—
255	C₇×C₂²⋊C₈	C₂³	1	2	yes	—
256	C₇×C₂²⋊C₈	C₂³	1	2	yes	—
257	C₇×C₂²⋊C₈	C₂³	1	2	yes	—
258	C₇×C₂²⋊C₈	C₂³	1	2	yes	—
259	C₇×C₂²⋊C₈	C₂³	1	2	yes	—
260	C₇×C₂²⋊C₈	C₂³	1	2	yes	—
261	C₇×#97	C₂³	1	2	yes	—
262	C₇×#97	C₂³	1	2	yes	—
263	C₇×#97	C₂³	1	2	yes	—
264	C₇×#97	C₂³	1	2	yes	—
265	C₇×#97	C₂³	1	2	yes	—
266	C₇×#97	C₂³	1	2	yes	—
267	C₄×C₇×C₈	C₂³	1	1	yes	characteristic
268	C₄×C₇×C₈	C₂³	1	1	yes	characteristic
269	C₄×C₇×C₈	C₂³	1	1	yes	characteristic
270	C₄×C₇×C₈	C₂³	1	1	yes	characteristic
271	C₄×C₇×C₈	C₂³	1	2	yes	—
272	C₄×C₇×C₈	C₂³	1	2	yes	—
273	C₄×C₇×C₈	C₂³	1	2	yes	—
274	C₄×C₇×C₈	C₂³	1	2	yes	—
275	#3459	C₂×C₇	1	1	yes	characteristic
276	#2995	C₂×C₇	1	2	yes	complemented
277	#2993	C₂×C₇	1	2	yes	complemented
278	#2992	C₂×C₇	1	1	yes	characteristic, complemented
279	#2992	C₂×C₇	1	1	yes	characteristic, complemented
280	#2978	C₂×C₇	1	2	yes	complemented
281	#2977	C₂×C₇	1	2	yes	complemented
282	#2976	C₂×C₇	1	2	yes	complemented
283	#2974	C₂×C₇	1	2	yes	complemented
284	#2973	C₂×C₇	1	1	yes	characteristic, complemented
285	#2969	C₂×C₇	1	2	yes	complemented
286	#2967	C₂×C₇	1	2	yes	complemented
287	#2966	C₂×C₇	1	1	yes	characteristic, complemented
288	#2966	C₂×C₇	1	1	yes	characteristic, complemented
289	D₄×M₁₆	C₂×C₇	1	2	yes	complemented
290	#2933	C₂×C₇	1	2	yes	complemented
291	#2933	C₂×C₇	1	2	yes	complemented
292	#2930	C₂×C₇	1	2	yes	complemented
293	C₂×#436	C₂×C₇	1	1	yes	characteristic, complemented
294	C₂⁴×C₇	C₂²×C₄	1	1	yes	characteristic
295	C₂⁴×C₇	C₂²×C₄	1	1	yes	characteristic
296	C₂⁴×C₇	C₂²×C₄	1	2	yes	—
297	C₇×#41	—	4	2	no	—
298	C₇×#41	—	4	2	no	—
299	C₂×C₇×Q₈	C₂²×C₄	1	1	yes	characteristic
300	C₂×C₇×Q₈	C₂²×C₄	1	1	yes	characteristic
301	C₂×C₇×Q₈	C₂²×C₄	1	2	yes	—
302	C₂×C₇×D₄	—	4	2	no	—
303	C₂×C₇×D₄	—	4	4	no	—
304	C₂×C₇×D₄	C₂²×C₄	1	2	yes	—
305	C₂×C₇×D₄	C₂²×C₄	1	2	yes	—
306	C₂×C₇×D₄	C₂²×C₄	1	2	yes	—
307	C₂×C₇×D₄	C₂²×C₄	1	2	yes	—
308	C₂×C₇×D₄	C₂²×C₄	1	2	yes	—
309	C₂×C₇×D₄	C₂²×C₄	1	2	yes	—
310	C₂×C₇×D₄	C₂²×C₄	1	1	yes	characteristic
311	C₂×C₇×D₄	C₂²×C₄	1	1	yes	characteristic
312	C₂×C₇×D₄	C₂²×C₄	1	2	yes	—
313	C₂×C₇×D₄	C₂²×C₄	1	2	yes	—
314	C₂×C₇×D₄	C₂²×C₄	1	2	yes	—
315	C₂×C₇×D₄	C₂²×C₄	1	2	yes	—
316	C₂×C₇×D₄	C₂²×C₄	1	2	yes	—
317	C₂²×C₄×C₇	—	4	1	no	—
318	C₂²×C₄×C₇	—	4	1	no	—
319	C₂²×C₄×C₇	—	4	2	no	—
320	C₂²×C₄×C₇	—	4	1	no	—
321	C₂²×C₄×C₇	—	4	1	no	—
322	C₂²×C₄×C₇	—	4	2	no	—
323	C₂²×C₄×C₇	C₂²×C₄	1	1	yes	characteristic
324	C₂²×C₄×C₇	C₂²×C₄	1	2	yes	—
325	C₂²×C₄×C₇	C₂²×C₄	1	1	yes	characteristic
326	C₂²×C₄×C₇	C₂²×C₄	1	2	yes	—
327	C₂²×C₄×C₇	C₂²×C₄	1	2	yes	—
328	C₂²×C₄×C₇	C₂²×C₄	1	1	yes	characteristic
329	C₂²×C₄×C₇	C₂²×C₄	1	2	yes	—
330	C₂²×C₄×C₇	C₂²×C₄	1	1	yes	characteristic
331	C₂²×C₄×C₇	C₂²×C₄	1	2	yes	—
332	C₂²×C₄×C₇	C₂²×C₄	1	2	yes	—
333	C₂²×C₄×C₇	C₂²×C₄	1	2	yes	—
334	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
335	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
336	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
337	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
338	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
339	C₇×M₁₆	—	2	4	no	—
340	C₇×M₁₆	—	2	4	no	—
341	C₇×M₁₆	—	2	4	no	—
342	C₇×M₁₆	—	4	2	no	—
343	C₇×M₁₆	—	4	2	no	—
344	C₇×M₁₆	—	4	2	no	—
345	C₇×M₁₆	—	4	2	no	—
346	C₇×M₁₆	—	4	2	no	—
347	C₇×M₁₆	—	4	2	no	—
348	C₇×M₁₆	—	4	2	no	—
349	C₂×C₇×C₈	—	2	2	no	—
350	C₂×C₇×C₈	—	2	4	no	—
351	C₂×C₇×C₈	—	4	2	no	—
352	C₂×C₇×C₈	—	4	1	no	—
353	C₂×C₇×C₈	—	4	2	no	—
354	C₂×C₇×C₈	—	4	1	no	—
355	C₂×C₇×C₈	—	4	1	no	—
356	C₂×C₇×C₈	—	4	2	no	—
357	C₂×C₇×C₈	—	4	2	no	—
358	C₂×C₇×C₈	—	4	2	no	—
359	C₂×C₇×C₈	C₂⁴	1	1	yes	characteristic
360	C₂×C₇×C₈	C₂⁴	1	1	yes	characteristic
361	C₂×C₇×C₈	C₂⁴	1	2	yes	—
362	C₂×C₇×C₈	C₂⁴	1	1	yes	characteristic
363	C₂×C₇×C₈	C₂⁴	1	2	yes	—
364	C₂×C₇×C₈	C₂⁴	1	2	yes	—
365	C₂×C₇×C₈	C₂⁴	1	2	yes	—
366	C₂×C₇×C₈	C₂⁴	1	2	yes	—
367	C₂×C₇×C₈	C₂⁴	1	2	yes	—
368	C₂×C₇×C₈	C₂⁴	1	1	yes	characteristic
369	C₇×C₄⋊C₄	C₂²×C₄	1	2	yes	—
370	C₇×C₄⋊C₄	C₂²×C₄	1	2	yes	—
371	C₇×C₄⋊C₄	C₂²×C₄	1	2	yes	—
372	C₇×C₄⋊C₄	C₂²×C₄	1	2	yes	—
373	C₇×C₄⋊C₄	C₂²×C₄	1	2	yes	—
374	C₇×C₄⋊C₄	C₂²×C₄	1	2	yes	—
375	C₇×C₄⋊C₄	C₂²×C₄	1	2	yes	—
376	C₇×C₄⋊C₄	C₂²×C₄	1	2	yes	—
377	C₇×C₄⋊C₄	C₂²×C₄	1	2	yes	—
378	C₇×C₄⋊C₄	C₂²×C₄	1	2	yes	—
379	C₇×C₄⋊C₄	C₂²×C₄	1	2	yes	—
380	C₇×C₄⋊C₄	C₂²×C₄	1	2	yes	—
381	C₇×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
382	C₇×C₄⋊C₄	C₂²×C₄	1	2	yes	—
383	C₇×C₄⋊C₄	C₂²×C₄	1	2	yes	—
384	C₇×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
385	C₇×C₄⋊C₄	C₂²×C₄	1	2	yes	—
386	C₇×C₄⋊C₄	C₂²×C₄	1	2	yes	—
387	C₇×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
388	C₇×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
389	C₇×C₂²⋊C₄	C₂²×C₄	1	2	yes	—
390	C₇×C₂²⋊C₄	C₂²×C₄	1	2	yes	—
391	C₇×C₂²⋊C₄	C₂²×C₄	1	2	yes	—
392	C₇×C₂²⋊C₄	C₂²×C₄	1	2	yes	—
393	C₇×C₂²⋊C₄	C₂²×C₄	1	2	yes	—
394	C₇×C₂²⋊C₄	C₂²×C₄	1	2	yes	—
395	C₇×C₂²⋊C₄	C₂²×C₄	1	2	yes	—
396	C₇×C₂²⋊C₄	C₂²×C₄	1	2	yes	—
397	C₇×C₂²⋊C₄	C₂²×C₄	1	2	yes	—
398	C₇×C₂²⋊C₄	C₂²×C₄	1	2	yes	—
399	C₇×C₂²⋊C₄	C₂²×C₄	1	2	yes	—
400	C₇×C₂²⋊C₄	C₂²×C₄	1	2	yes	—
401	C₇×C₂²⋊C₄	C₂²×C₄	1	2	yes	—
402	C₇×C₂²⋊C₄	C₂²×C₄	1	2	yes	—
403	C₇×C₂²⋊C₄	C₂²×C₄	1	2	yes	—
404	C₇×C₂²⋊C₄	C₂²×C₄	1	2	yes	—
405	C₇×C₂²⋊C₄	C₂²×C₄	1	2	yes	—
406	C₇×C₂²⋊C₄	C₂²×C₄	1	2	yes	—
407	C₇×C₂²⋊C₄	C₂²×C₄	1	2	yes	—
408	C₇×C₂²⋊C₄	C₂²×C₄	1	2	yes	—
409	C₇×C₂²⋊C₄	C₂²×C₄	1	2	yes	—
410	C₇×C₂²⋊C₄	C₂²×C₄	1	2	yes	—
411	C₇×C₂²⋊C₄	C₂²×C₄	1	2	yes	—
412	C₇×C₂²⋊C₄	C₂²×C₄	1	2	yes	—
413	C₄²×C₇	C₂²×C₄	1	1	yes	characteristic
414	C₄²×C₇	C₂²×C₄	1	1	yes	characteristic
415	C₄²×C₇	C₂²×C₄	1	2	yes	—
416	C₄²×C₇	C₂²×C₄	1	2	yes	—
417	C₄²×C₇	C₂⁴	1	1	yes	characteristic
418	C₄²×C₇	C₂⁴	1	1	yes	characteristic
419	C₄²×C₇	C₂⁴	1	2	yes	—
420	C₄²×C₇	C₂⁴	1	2	yes	—
421	C₂×#131	C₂²×C₇	1	2	yes	complemented
422	C₂²×M₁₆	C₂²×C₇	1	1	yes	characteristic
423	C₂²×M₁₆	C₂²×C₇	1	1	yes	characteristic, complemented
424	C₂²×M₁₆	C₂²×C₇	1	2	yes	complemented
425	#543	C₄×C₇	1	1	yes	characteristic
426	#539	C₄×C₇	1	2	yes	—
427	#539	C₄×C₇	1	2	yes	—
428	#539	C₄×C₇	1	2	yes	—
429	#538	C₄×C₇	1	1	yes	characteristic
430	#538	C₄×C₇	1	1	yes	characteristic
431	#538	C₄×C₇	1	2	yes	—
432	#538	C₄×C₇	1	2	yes	—
433	#534	C₄×C₇	1	1	yes	characteristic
434	#534	C₄×C₇	1	2	yes	—
435	#529	C₂²×C₇	1	1	yes	characteristic
436	#529	C₂²×C₇	1	1	yes	characteristic
437	#529	C₂²×C₇	1	2	yes	—
438	#529	C₂²×C₇	1	2	yes	—
439	#525	C₂²×C₇	1	2	yes	—
440	#525	C₂²×C₇	1	2	yes	—
441	#525	C₂²×C₇	1	2	yes	—
442	C₂×C₄×D₄	C₂²×C₇	1	1	yes	characteristic
443	C₂×C₄×D₄	C₂²×C₇	1	2	yes	—
444	#446	C₂²×C₇	1	1	yes	characteristic, complemented
445	#446	C₂²×C₇	1	1	yes	characteristic, complemented
446	#446	C₂²×C₇	1	2	yes	complemented
447	#446	C₂²×C₇	1	2	yes	complemented
448	C₈×Q₈	C₂²×C₇	1	1	yes	characteristic, complemented
449	C₈×Q₈	C₂²×C₇	1	1	yes	characteristic, complemented
450	#436	C₂²×C₇	1	2	yes	complemented
451	#436	C₂²×C₇	1	2	yes	complemented
452	#436	C₂²×C₇	1	2	yes	complemented
453	#436	C₂²×C₇	1	2	yes	complemented
454	#436	C₂²×C₇	1	1	yes	characteristic, complemented
455	#436	C₂²×C₇	1	2	yes	complemented
456	#436	C₂²×C₇	1	2	yes	complemented
457	#436	C₂²×C₇	1	2	yes	complemented
458	#436	C₂²×C₇	1	2	yes	complemented
459	#436	C₂²×C₇	1	2	yes	complemented
460	#436	C₂²×C₇	1	1	yes	characteristic, complemented
461	#436	C₂²×C₇	1	2	yes	complemented
462	#435	C₂²×C₇	1	2	yes	complemented
463	#435	C₂²×C₇	1	2	yes	complemented
464	#435	C₂²×C₇	1	2	yes	complemented
465	#435	C₂²×C₇	1	2	yes	complemented
466	#435	C₂²×C₇	1	2	yes	complemented
467	#435	C₂²×C₇	1	2	yes	complemented
468	#435	C₂²×C₇	1	2	yes	complemented
469	#435	C₂²×C₇	1	2	yes	complemented
470	#435	C₂²×C₇	1	2	yes	complemented
471	#435	C₂²×C₇	1	2	yes	complemented
472	#435	C₂²×C₇	1	2	yes	complemented
473	#435	C₂²×C₇	1	2	yes	complemented
474	#435	C₂²×C₇	1	2	yes	complemented
475	#435	C₂²×C₇	1	2	yes	complemented
476	#435	C₂²×C₇	1	2	yes	complemented
477	#435	C₂²×C₇	1	2	yes	complemented
478	#435	C₂²×C₇	1	2	yes	complemented
479	#435	C₂²×C₇	1	2	yes	complemented
480	C₈×D₄	C₂²×C₇	1	1	yes	characteristic, complemented
481	C₈×D₄	C₂²×C₇	1	2	yes	complemented
482	C₈×D₄	C₂²×C₇	1	2	yes	complemented
483	C₈×D₄	C₂²×C₇	1	2	yes	complemented
484	C₈×D₄	C₂²×C₇	1	2	yes	complemented
485	C₈×D₄	C₂²×C₇	1	2	yes	complemented
486	C₈×D₄	C₂²×C₇	1	1	yes	characteristic, complemented
487	C₈×D₄	C₂²×C₇	1	2	yes	complemented
488	#433	C₂²×C₇	1	2	yes	complemented
489	#433	C₂²×C₇	1	2	yes	complemented
490	#433	C₂²×C₇	1	2	yes	complemented
491	#433	C₂²×C₇	1	2	yes	complemented
492	#433	C₂²×C₇	1	2	yes	complemented
493	#433	C₂²×C₇	1	2	yes	complemented
494	#432	C₂²×C₇	1	1	yes	characteristic, complemented
495	#432	C₂²×C₇	1	1	yes	characteristic, complemented
496	#432	C₂²×C₇	1	2	yes	complemented
497	#431	C₂²×C₇	1	2	yes	complemented
498	#424	C₂²×C₇	1	2	yes	complemented
499	#424	C₂²×C₇	1	2	yes	complemented
500	#424	C₂²×C₇	1	2	yes	complemented
501	#423	C₂²×C₇	1	2	yes	complemented
502	C₂×C₄⋊C₈	C₂²×C₇	1	1	yes	characteristic, complemented
503	#408	C₂²×C₇	1	2	yes	complemented
504	#408	C₂²×C₇	1	2	yes	complemented
505	#408	C₂²×C₇	1	2	yes	complemented
506	#407	C₂²×C₇	1	2	yes	—
507	#407	C₂²×C₇	1	2	yes	complemented
508	#407	C₂²×C₇	1	2	yes	complemented
509	C₂×C₂²⋊C₈	C₂²×C₇	1	1	yes	characteristic
510	C₂×C₂²⋊C₈	C₂²×C₇	1	1	yes	characteristic, complemented
511	C₂×C₂²⋊C₈	C₂²×C₇	1	2	yes	complemented
512	C₂×C₂²⋊C₈	C₂²×C₇	1	2	yes	complemented
513	#405	C₂²×C₇	1	2	yes	complemented
514	#405	C₂²×C₇	1	2	yes	complemented
515	#405	C₂²×C₇	1	2	yes	complemented
516	C₄×M₁₆	C₂²×C₇	1	2	yes	complemented
517	C₂×C₄×C₈	C₂²×C₇	1	1	yes	characteristic, complemented
518	C₂³×C₇	—	2	2	no	—
519	C₂³×C₇	—	2	2	no	—
520	C₂³×C₇	—	4	1	no	—
521	C₂³×C₇	—	4	1	no	—
522	C₂³×C₇	—	4	2	no	—
523	C₂³×C₇	—	4	2	no	—
524	C₂³×C₇	—	4	1	no	—
525	C₂³×C₇	—	4	1	no	—
526	C₂³×C₇	—	4	2	no	—
527	C₂³×C₇	C₂³×C₄	1	2	yes	—
528	C₂³×C₇	C₂³×C₄	1	2	yes	—
529	C₂³×C₇	C₂³×C₄	1	2	yes	—
530	C₂³×C₇	C₂³×C₄	1	2	yes	—
531	C₂³×C₇	C₂³×C₄	1	1	yes	characteristic
532	C₇×Q₈	—	4	1	no	—
533	C₇×Q₈	—	4	1	no	—
534	C₇×Q₈	—	4	2	no	—
535	C₇×D₄	—	2	4	no	—
536	C₇×D₄	—	2	4	no	—
537	C₇×D₄	—	4	2	no	—
538	C₇×D₄	—	4	2	no	—
539	C₇×D₄	—	4	2	no	—
540	C₇×D₄	—	4	2	no	—
541	C₇×D₄	—	4	1	no	—
542	C₇×D₄	—	4	1	no	—
543	C₇×D₄	—	4	2	no	—
544	C₇×D₄	—	4	2	no	—
545	C₇×D₄	—	4	2	no	—
546	C₇×D₄	—	4	2	no	—
547	C₇×D₄	—	4	2	no	—
548	C₂×C₄×C₇	—	2	2	no	—
549	C₂×C₄×C₇	—	2	1	no	—
550	C₂×C₄×C₇	—	2	2	no	—
551	C₂×C₄×C₇	—	2	2	no	—
552	C₂×C₄×C₇	—	2	2	no	—
553	C₂×C₄×C₇	—	2	2	no	—
554	C₂×C₄×C₇	—	2	1	no	—
555	C₂×C₄×C₇	—	2	2	no	—
556	C₂×C₄×C₇	—	2	2	no	—
557	C₂×C₄×C₇	—	2	2	no	—
558	C₂×C₄×C₇	—	2	2	no	—
559	C₂×C₄×C₇	—	4	1	no	—
560	C₂×C₄×C₇	—	4	2	no	—
561	C₂×C₄×C₇	—	4	2	no	—
562	C₂×C₄×C₇	—	4	2	no	—
563	C₂×C₄×C₇	—	4	2	no	—
564	C₂×C₄×C₇	—	4	1	no	—
565	C₂×C₄×C₇	—	4	2	no	—
566	C₂×C₄×C₇	—	4	1	no	—
567	C₂×C₄×C₇	—	4	2	no	—
568	C₂×C₄×C₇	—	4	2	no	—
569	C₂×C₄×C₇	C₂³×C₄	1	1	yes	characteristic
570	C₂×C₄×C₇	C₂³×C₄	1	2	yes	—
571	C₂×C₄×C₇	C₂³×C₄	1	1	yes	characteristic
572	C₂×C₄×C₇	C₂³×C₄	1	1	yes	characteristic
573	C₂×C₄×C₇	C₂³×C₄	1	2	yes	—
574	C₂×C₄×C₇	C₂³×C₄	1	2	yes	—
575	C₂×C₄×C₇	C₂³×C₄	1	1	yes	characteristic
576	C₂×C₄×C₇	C₂³×C₄	1	1	yes	characteristic
577	C₂×C₄×C₇	C₂³×C₄	1	2	yes	—
578	C₂×C₄×C₇	C₂³×C₄	1	2	yes	—
579	C₂×C₄×C₇	C₂³×C₄	1	2	yes	—
580	C₂×C₄×C₇	C₂³×C₄	1	2	yes	—
581	C₂×C₄×C₇	C₂³×C₄	1	2	yes	—
582	C₂×C₄×C₇	C₂⁵	1	1	yes	characteristic
583	C₇×C₈	—	2	2	no	—
584	C₇×C₈	—	2	1	no	—
585	C₇×C₈	—	2	2	no	—
586	C₇×C₈	—	2	2	no	—
587	C₇×C₈	—	2	2	no	—
588	C₇×C₈	—	2	1	no	—
589	C₇×C₈	—	2	2	no	—
590	C₇×C₈	—	2	1	no	—
591	C₇×C₈	—	2	2	no	—
592	C₇×C₈	H(5,𝔽₂)	1	2	yes	—
593	C₂×#41	C₂³×C₇	1	2	yes	—
594	C₂²×D₄	C₂×C₄×C₇	1	1	yes	characteristic
595	C₂²×D₄	C₂×C₄×C₇	1	2	yes	—
596	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
597	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
598	C₂³×C₄	C₂³×C₇	1	2	yes	—
599	#131	—	4	4	no	—
600	C₂×M₁₆	—	4	2	no	—
601	C₂×M₁₆	—	4	2	no	—
602	C₂×M₁₆	—	4	4	no	—
603	C₂×M₁₆	C₂³×C₇	1	2	yes	—
604	C₂×M₁₆	C₂³×C₇	1	2	yes	—
605	C₂×M₁₆	C₂³×C₇	1	2	yes	—
606	C₂×M₁₆	C₂³×C₇	1	2	yes	—
607	C₂×M₁₆	C₂³×C₇	1	2	yes	—
608	C₂×M₁₆	C₂³×C₇	1	2	yes	—
609	C₂×M₁₆	C₂³×C₇	1	2	yes	—
610	C₂×M₁₆	C₂³×C₇	1	2	yes	—
611	C₂×M₁₆	C₂³×C₇	1	2	yes	—
612	C₂×M₁₆	C₂³×C₇	1	2	yes	—
613	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
614	C₂²×C₈	C₂³×C₇	1	2	yes	—
615	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
616	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
617	C₂²×C₈	C₂³×C₇	1	2	yes	—
618	C₂²×C₈	C₂³×C₇	1	2	yes	—
619	C₂²×C₈	C₂³×C₇	1	2	yes	—
620	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
621	C₂²×C₈	C₂³×C₇	1	2	yes	—
622	C₂²×C₈	C₂³×C₇	1	2	yes	—
623	#126	C₂×C₄×C₇	1	2	yes	—
624	#126	C₂×C₄×C₇	1	2	yes	—
625	#126	C₂×C₄×C₇	1	2	yes	—
626	#126	C₂×C₄×C₇	1	2	yes	—
627	#126	C₂×C₄×C₇	1	2	yes	—
628	#126	C₂×C₄×C₇	1	2	yes	—
629	#125	C₂×C₄×C₇	1	1	yes	characteristic
630	#125	C₂×C₄×C₇	1	1	yes	characteristic
631	#125	C₂×C₄×C₇	1	2	yes	—
632	#125	C₂×C₄×C₇	1	2	yes	—
633	#124	C₂×C₄×C₇	1	1	yes	characteristic
634	#124	C₂×C₄×C₇	1	1	yes	characteristic
635	#124	C₂×C₄×C₇	1	2	yes	—
636	#124	C₂×C₄×C₇	1	2	yes	—
637	#123	C₂×C₄×C₇	1	2	yes	—
638	#123	C₂×C₄×C₇	1	2	yes	—
639	#123	C₂×C₄×C₇	1	2	yes	—
640	#123	C₂×C₄×C₇	1	2	yes	—
641	#123	C₂×C₄×C₇	1	2	yes	—
642	#123	C₂×C₄×C₇	1	2	yes	—
643	#123	C₂×C₄×C₇	1	2	yes	—
644	#123	C₂×C₄×C₇	1	2	yes	—
645	#123	C₂×C₄×C₇	1	2	yes	—
646	#123	C₂×C₄×C₇	1	2	yes	—
647	#123	C₂×C₄×C₇	1	2	yes	—
648	#123	C₂×C₄×C₇	1	2	yes	—
649	C₂²⋊Q₈	C₂×C₄×C₇	1	2	yes	—
650	C₂²⋊Q₈	C₂×C₄×C₇	1	2	yes	—
651	C₂²⋊Q₈	C₂×C₄×C₇	1	2	yes	—
652	C₂²⋊Q₈	C₂×C₄×C₇	1	2	yes	—
653	C₂²⋊Q₈	C₂×C₄×C₇	1	2	yes	—
654	C₂²⋊Q₈	C₂×C₄×C₇	1	2	yes	—
655	C₂²⋊Q₈	C₂×C₄×C₇	1	1	yes	characteristic
656	C₂²⋊Q₈	C₂×C₄×C₇	1	1	yes	characteristic
657	C₂²⋊Q₈	C₂×C₄×C₇	1	2	yes	—
658	C₂²⋊Q₈	C₂×C₄×C₇	1	2	yes	—
659	#121	C₂×C₄×C₇	1	2	yes	—
660	#121	C₂×C₄×C₇	1	2	yes	—
661	#121	C₂×C₄×C₇	1	2	yes	—
662	#121	C₂×C₄×C₇	1	2	yes	—
663	#121	C₂×C₄×C₇	1	2	yes	—
664	#121	C₂×C₄×C₇	1	2	yes	—
665	#121	C₂×C₄×C₇	1	1	yes	characteristic
666	#121	C₂×C₄×C₇	1	1	yes	characteristic
667	#121	C₂×C₄×C₇	1	2	yes	—
668	#121	C₂×C₄×C₇	1	2	yes	—
669	#120	C₂×C₄×C₇	1	2	yes	—
670	#120	C₂×C₄×C₇	1	2	yes	—
671	#120	C₂×C₄×C₇	1	2	yes	—
672	#120	C₂×C₄×C₇	1	2	yes	—
673	#120	C₂×C₄×C₇	1	2	yes	—
674	#120	C₂×C₄×C₇	1	2	yes	—
675	C₄×Q₈	C₂³×C₇	1	1	yes	characteristic
676	C₄×Q₈	C₂³×C₇	1	1	yes	characteristic
677	C₄×D₄	C₂×C₄×C₇	1	2	yes	—
678	C₄×D₄	C₂×C₄×C₇	1	2	yes	—
679	C₄×D₄	C₂×C₄×C₇	1	2	yes	—
680	C₄×D₄	C₂×C₄×C₇	1	2	yes	—
681	C₄×D₄	C₂×C₄×C₇	1	2	yes	—
682	C₄×D₄	C₂×C₄×C₇	1	2	yes	—
683	C₄×D₄	C₂³×C₇	1	2	yes	—
684	C₄×D₄	C₂³×C₇	1	2	yes	—
685	C₄×D₄	C₂³×C₇	1	2	yes	—
686	C₄×D₄	C₂³×C₇	1	2	yes	—
687	C₄×D₄	C₂³×C₇	1	2	yes	—
688	C₄×D₄	C₂³×C₇	1	2	yes	—
689	C₄×D₄	C₂³×C₇	1	1	yes	characteristic
690	C₄×D₄	C₂³×C₇	1	2	yes	—
691	C₄×D₄	C₂³×C₇	1	2	yes	—
692	C₄×D₄	C₂³×C₇	1	1	yes	characteristic
693	#117	C₂³×C₇	1	2	yes	—
694	#117	C₂³×C₇	1	2	yes	—
695	#117	C₂³×C₇	1	2	yes	—
696	C₂×C₄⋊C₄	C₂×C₄×C₇	1	1	yes	characteristic
697	C₂×C₄⋊C₄	C₂×C₄×C₇	1	2	yes	—
698	C₂×C₂²⋊C₄	C₂×C₄×C₇	1	1	yes	characteristic
699	C₂×C₂²⋊C₄	C₂×C₄×C₇	1	2	yes	—
700	C₂×C₂²⋊C₄	C₂×C₄×C₇	1	1	yes	characteristic
701	C₂×C₂²⋊C₄	C₂×C₄×C₇	1	2	yes	—
702	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
703	C₂×C₄²	C₂³×C₇	1	2	yes	—
704	C₄⋊C₈	C₂³×C₇	1	2	yes	—
705	C₄⋊C₈	C₂³×C₇	1	2	yes	—
706	C₄⋊C₈	C₂³×C₇	1	2	yes	—
707	C₄⋊C₈	C₂³×C₇	1	2	yes	—
708	C₄⋊C₈	C₂³×C₇	1	2	yes	—
709	C₄⋊C₈	C₂³×C₇	1	2	yes	—
710	C₄⋊C₈	C₂³×C₇	1	2	yes	—
711	C₄⋊C₈	C₂³×C₇	1	1	yes	characteristic
712	C₄⋊C₈	C₂³×C₇	1	2	yes	—
713	C₄⋊C₈	C₂³×C₇	1	1	yes	characteristic
714	C₄⋊C₈	C₂³×C₇	1	2	yes	—
715	C₄⋊C₈	C₂³×C₇	1	1	yes	characteristic
716	C₄⋊C₈	C₂³×C₇	1	2	yes	—
717	C₄⋊C₈	C₂³×C₇	1	1	yes	characteristic
718	C₂²⋊C₈	C₂³×C₇	1	2	yes	—
719	C₂²⋊C₈	C₂³×C₇	1	2	yes	—
720	C₂²⋊C₈	C₂³×C₇	1	2	yes	—
721	C₂²⋊C₈	C₂³×C₇	1	2	yes	—
722	C₂²⋊C₈	C₂³×C₇	1	2	yes	—
723	C₂²⋊C₈	C₂³×C₇	1	2	yes	—
724	C₂²⋊C₈	C₂³×C₇	1	2	yes	—
725	C₂²⋊C₈	C₂³×C₇	1	2	yes	—
726	C₂²⋊C₈	C₂³×C₇	1	2	yes	—
727	C₂²⋊C₈	C₂³×C₇	1	2	yes	—
728	C₂²⋊C₈	C₂³×C₇	1	2	yes	—
729	C₂²⋊C₈	C₂³×C₇	1	2	yes	—
730	C₂²⋊C₈	C₂³×C₇	1	2	yes	—
731	C₂²⋊C₈	C₂³×C₇	1	2	yes	—
732	C₂²⋊C₈	C₂³×C₇	1	2	yes	—
733	C₂²⋊C₈	C₂³×C₇	1	2	yes	—
734	C₂²⋊C₈	C₂³×C₇	1	2	yes	—
735	C₂²⋊C₈	C₂³×C₇	1	2	yes	—
736	#97	C₂³×C₇	1	2	yes	—
737	#97	C₂³×C₇	1	2	yes	—
738	#97	C₂³×C₇	1	2	yes	—
739	#97	C₂³×C₇	1	2	yes	—
740	#97	C₂³×C₇	1	2	yes	—
741	#97	C₂³×C₇	1	2	yes	—
742	C₄×C₈	C₂³×C₇	1	1	yes	characteristic
743	C₄×C₈	C₂³×C₇	1	1	yes	characteristic
744	C₄×C₈	C₂³×C₇	1	1	yes	characteristic
745	C₄×C₈	C₂³×C₇	1	1	yes	characteristic
746	C₄×C₈	C₂³×C₇	1	2	yes	—
747	C₄×C₈	C₂³×C₇	1	2	yes	—
748	C₄×C₈	C₂³×C₇	1	2	yes	—
749	C₄×C₈	C₂³×C₇	1	2	yes	—
750	C₂²×C₇	—	2	1	no	—
751	C₂²×C₇	—	2	1	no	—
752	C₂²×C₇	—	2	2	no	—
753	C₂²×C₇	—	2	2	no	—
754	C₂²×C₇	—	2	2	no	—
755	C₂²×C₇	—	2	2	no	—
756	C₂²×C₇	—	2	2	no	—
757	C₂²×C₇	—	2	2	no	—
758	C₂²×C₇	—	2	2	no	—
759	C₂²×C₇	—	2	2	no	—
760	C₂²×C₇	—	2	2	no	—
761	C₂²×C₇	—	2	2	no	—
762	C₂²×C₇	—	2	2	no	—
763	C₂²×C₇	—	2	2	no	—
764	C₂²×C₇	—	8	2	no	—
765	C₂²×C₇	—	8	2	no	—
766	C₂²×C₇	—	8	4	no	—
767	C₂²×C₇	#568	1	2	yes	—
768	C₂²×C₇	C₂⁴×C₄	1	1	yes	characteristic
769	C₄×C₇	—	2	1	no	—
770	C₄×C₇	—	2	2	no	—
771	C₄×C₇	—	2	2	no	—
772	C₄×C₇	—	2	2	no	—
773	C₄×C₇	—	2	2	no	—
774	C₄×C₇	—	2	1	no	—
775	C₄×C₇	—	2	1	no	—
776	C₄×C₇	—	2	2	no	—
777	C₄×C₇	—	2	2	no	—
778	C₄×C₇	—	2	1	no	—
779	C₄×C₇	—	2	1	no	—
780	C₄×C₇	—	2	2	no	—
781	C₄×C₇	—	2	2	no	—
782	C₄×C₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
783	C₄×C₇	#585	1	1	yes	characteristic
784	C₂⁴	C₂²×C₄×C₇	1	1	yes	characteristic
785	C₂⁴	C₂²×C₄×C₇	1	1	yes	characteristic
786	C₂⁴	C₂²×C₄×C₇	1	2	yes	—
787	#41	—	4	2	no	—
788	#41	—	4	2	no	—
789	C₂×Q₈	C₂²×C₄×C₇	1	1	yes	characteristic
790	C₂×Q₈	C₂²×C₄×C₇	1	1	yes	characteristic
791	C₂×Q₈	C₂²×C₄×C₇	1	2	yes	—
792	C₂×D₄	—	4	2	no	—
793	C₂×D₄	—	4	4	no	—
794	C₂×D₄	C₂²×C₄×C₇	1	2	yes	—
795	C₂×D₄	C₂²×C₄×C₇	1	2	yes	—
796	C₂×D₄	C₂²×C₄×C₇	1	2	yes	—
797	C₂×D₄	C₂²×C₄×C₇	1	2	yes	—
798	C₂×D₄	C₂²×C₄×C₇	1	2	yes	—
799	C₂×D₄	C₂²×C₄×C₇	1	2	yes	—
800	C₂×D₄	C₂²×C₄×C₇	1	1	yes	characteristic
801	C₂×D₄	C₂²×C₄×C₇	1	1	yes	characteristic
802	C₂×D₄	C₂²×C₄×C₇	1	2	yes	—
803	C₂×D₄	C₂²×C₄×C₇	1	2	yes	—
804	C₂×D₄	C₂²×C₄×C₇	1	2	yes	—
805	C₂×D₄	C₂²×C₄×C₇	1	2	yes	—
806	C₂×D₄	C₂²×C₄×C₇	1	2	yes	—
807	C₂²×C₄	—	4	1	no	—
808	C₂²×C₄	—	4	1	no	—
809	C₂²×C₄	—	4	2	no	—
810	C₂²×C₄	—	4	1	no	—
811	C₂²×C₄	—	4	1	no	—
812	C₂²×C₄	—	4	2	no	—
813	C₂²×C₄	C₂²×C₄×C₇	1	1	yes	characteristic
814	C₂²×C₄	C₂²×C₄×C₇	1	2	yes	—
815	C₂²×C₄	C₂²×C₄×C₇	1	1	yes	characteristic
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	1	yes	characteristic
819	C₂²×C₄	C₂²×C₄×C₇	1	2	yes	—
820	C₂²×C₄	C₂²×C₄×C₇	1	1	yes	characteristic
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	C₂⁴×C₇	1	1	yes	characteristic
825	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
826	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
827	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
828	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
829	M₁₆	—	2	4	no	—
830	M₁₆	—	2	4	no	—
831	M₁₆	—	2	4	no	—
832	M₁₆	—	4	2	no	—
833	M₁₆	—	4	2	no	—
834	M₁₆	—	4	2	no	—
835	M₁₆	—	4	2	no	—
836	M₁₆	—	4	2	no	—
837	M₁₆	—	4	2	no	—
838	M₁₆	—	4	2	no	—
839	C₂×C₈	—	2	2	no	—
840	C₂×C₈	—	2	4	no	—
841	C₂×C₈	—	4	2	no	—
842	C₂×C₈	—	4	1	no	—
843	C₂×C₈	—	4	2	no	—
844	C₂×C₈	—	4	1	no	—
845	C₂×C₈	—	4	1	no	—
846	C₂×C₈	—	4	2	no	—
847	C₂×C₈	—	4	2	no	—
848	C₂×C₈	—	4	2	no	—
849	C₂×C₈	C₂⁴×C₇	1	1	yes	characteristic
850	C₂×C₈	C₂⁴×C₇	1	1	yes	characteristic
851	C₂×C₈	C₂⁴×C₇	1	2	yes	—
852	C₂×C₈	C₂⁴×C₇	1	1	yes	characteristic
853	C₂×C₈	C₂⁴×C₇	1	2	yes	—
854	C₂×C₈	C₂⁴×C₇	1	2	yes	—
855	C₂×C₈	C₂⁴×C₇	1	2	yes	—
856	C₂×C₈	C₂⁴×C₇	1	2	yes	—
857	C₂×C₈	C₂⁴×C₇	1	2	yes	—
858	C₂×C₈	C₂⁴×C₇	1	1	yes	characteristic
859	C₄⋊C₄	C₂²×C₄×C₇	1	2	yes	—
860	C₄⋊C₄	C₂²×C₄×C₇	1	2	yes	—
861	C₄⋊C₄	C₂²×C₄×C₇	1	2	yes	—
862	C₄⋊C₄	C₂²×C₄×C₇	1	2	yes	—
863	C₄⋊C₄	C₂²×C₄×C₇	1	2	yes	—
864	C₄⋊C₄	C₂²×C₄×C₇	1	2	yes	—
865	C₄⋊C₄	C₂²×C₄×C₇	1	2	yes	—
866	C₄⋊C₄	C₂²×C₄×C₇	1	2	yes	—
867	C₄⋊C₄	C₂²×C₄×C₇	1	2	yes	—
868	C₄⋊C₄	C₂²×C₄×C₇	1	2	yes	—
869	C₄⋊C₄	C₂²×C₄×C₇	1	2	yes	—
870	C₄⋊C₄	C₂²×C₄×C₇	1	2	yes	—
871	C₄⋊C₄	C₂²×C₄×C₇	1	1	yes	characteristic
872	C₄⋊C₄	C₂²×C₄×C₇	1	2	yes	—
873	C₄⋊C₄	C₂²×C₄×C₇	1	2	yes	—
874	C₄⋊C₄	C₂²×C₄×C₇	1	1	yes	characteristic
875	C₄⋊C₄	C₂²×C₄×C₇	1	2	yes	—
876	C₄⋊C₄	C₂²×C₄×C₇	1	2	yes	—
877	C₄⋊C₄	C₂²×C₄×C₇	1	1	yes	characteristic
878	C₄⋊C₄	C₂²×C₄×C₇	1	1	yes	characteristic
879	C₂²⋊C₄	C₂²×C₄×C₇	1	2	yes	—
880	C₂²⋊C₄	C₂²×C₄×C₇	1	2	yes	—
881	C₂²⋊C₄	C₂²×C₄×C₇	1	2	yes	—
882	C₂²⋊C₄	C₂²×C₄×C₇	1	2	yes	—
883	C₂²⋊C₄	C₂²×C₄×C₇	1	2	yes	—
884	C₂²⋊C₄	C₂²×C₄×C₇	1	2	yes	—
885	C₂²⋊C₄	C₂²×C₄×C₇	1	2	yes	—
886	C₂²⋊C₄	C₂²×C₄×C₇	1	2	yes	—
887	C₂²⋊C₄	C₂²×C₄×C₇	1	2	yes	—
888	C₂²⋊C₄	C₂²×C₄×C₇	1	2	yes	—
889	C₂²⋊C₄	C₂²×C₄×C₇	1	2	yes	—
890	C₂²⋊C₄	C₂²×C₄×C₇	1	2	yes	—
891	C₂²⋊C₄	C₂²×C₄×C₇	1	2	yes	—
892	C₂²⋊C₄	C₂²×C₄×C₇	1	2	yes	—
893	C₂²⋊C₄	C₂²×C₄×C₇	1	2	yes	—
894	C₂²⋊C₄	C₂²×C₄×C₇	1	2	yes	—
895	C₂²⋊C₄	C₂²×C₄×C₇	1	2	yes	—
896	C₂²⋊C₄	C₂²×C₄×C₇	1	2	yes	—
897	C₂²⋊C₄	C₂²×C₄×C₇	1	2	yes	—
898	C₂²⋊C₄	C₂²×C₄×C₇	1	2	yes	—
899	C₂²⋊C₄	C₂²×C₄×C₇	1	2	yes	—
900	C₂²⋊C₄	C₂²×C₄×C₇	1	2	yes	—
901	C₂²⋊C₄	C₂²×C₄×C₇	1	2	yes	—
902	C₂²⋊C₄	C₂²×C₄×C₇	1	2	yes	—
903	C₄²	C₂²×C₄×C₇	1	1	yes	characteristic
904	C₄²	C₂²×C₄×C₇	1	1	yes	characteristic
905	C₄²	C₂²×C₄×C₇	1	2	yes	—
906	C₄²	C₂²×C₄×C₇	1	2	yes	—
907	C₄²	C₂⁴×C₇	1	1	yes	characteristic
908	C₄²	C₂⁴×C₇	1	1	yes	characteristic
909	C₄²	C₂⁴×C₇	1	2	yes	—
910	C₄²	C₂⁴×C₇	1	2	yes	—
911	C₂×C₇	—	2	2	no	—
912	C₂×C₇	—	4	2	no	—
913	C₂×C₇	—	4	2	no	—
914	C₂×C₇	—	4	2	no	—
915	C₂×C₇	—	4	2	no	—
916	C₂×C₇	C₄×H(5,𝔽₂)	1	1	yes	characteristic
917	C₂×C₇	C₂×#568	1	1	yes	characteristic
918	C₂×C₇	#3573	1	1	yes	characteristic
919	C₂³	—	2	2	no	—
920	C₂³	—	2	2	no	—
921	C₂³	—	4	1	no	—
922	C₂³	—	4	1	no	—
923	C₂³	—	4	2	no	—
924	C₂³	—	4	2	no	—
925	C₂³	—	4	1	no	—
926	C₂³	—	4	1	no	—
927	C₂³	—	4	2	no	—
928	C₂³	C₂³×C₄×C₇	1	2	yes	—
929	C₂³	C₂³×C₄×C₇	1	2	yes	—
930	C₂³	C₂³×C₄×C₇	1	2	yes	—
931	C₂³	C₂³×C₄×C₇	1	2	yes	—
932	C₂³	C₂³×C₄×C₇	1	1	yes	characteristic
933	Q₈	—	4	1	no	—
934	Q₈	—	4	1	no	—
935	Q₈	—	4	2	no	—
936	D₄	—	2	4	no	—
937	D₄	—	2	4	no	—
938	D₄	—	4	2	no	—
939	D₄	—	4	2	no	—
940	D₄	—	4	2	no	—
941	D₄	—	4	2	no	—
942	D₄	—	4	1	no	—
943	D₄	—	4	1	no	—
944	D₄	—	4	2	no	—
945	D₄	—	4	2	no	—
946	D₄	—	4	2	no	—
947	D₄	—	4	2	no	—
948	D₄	—	4	2	no	—
949	C₂×C₄	—	2	2	no	—
950	C₂×C₄	—	2	1	no	—
951	C₂×C₄	—	2	2	no	—
952	C₂×C₄	—	2	2	no	—
953	C₂×C₄	—	2	2	no	—
954	C₂×C₄	—	2	2	no	—
955	C₂×C₄	—	2	1	no	—
956	C₂×C₄	—	2	2	no	—
957	C₂×C₄	—	2	2	no	—
958	C₂×C₄	—	2	2	no	—
959	C₂×C₄	—	2	2	no	—
960	C₂×C₄	—	4	1	no	—
961	C₂×C₄	—	4	2	no	—
962	C₂×C₄	—	4	2	no	—
963	C₂×C₄	—	4	2	no	—
964	C₂×C₄	—	4	2	no	—
965	C₂×C₄	—	4	1	no	—
966	C₂×C₄	—	4	2	no	—
967	C₂×C₄	—	4	1	no	—
968	C₂×C₄	—	4	2	no	—
969	C₂×C₄	—	4	2	no	—
970	C₂×C₄	C₂³×C₄×C₇	1	1	yes	characteristic
971	C₂×C₄	C₂³×C₄×C₇	1	2	yes	—
972	C₂×C₄	C₂³×C₄×C₇	1	1	yes	characteristic
973	C₂×C₄	C₂³×C₄×C₇	1	1	yes	characteristic
974	C₂×C₄	C₂³×C₄×C₇	1	2	yes	—
975	C₂×C₄	C₂³×C₄×C₇	1	2	yes	—
976	C₂×C₄	C₂³×C₄×C₇	1	1	yes	characteristic
977	C₂×C₄	C₂³×C₄×C₇	1	1	yes	characteristic
978	C₂×C₄	C₂³×C₄×C₇	1	2	yes	—
979	C₂×C₄	C₂³×C₄×C₇	1	2	yes	—
980	C₂×C₄	C₂³×C₄×C₇	1	2	yes	—
981	C₂×C₄	C₂³×C₄×C₇	1	2	yes	—
982	C₂×C₄	C₂³×C₄×C₇	1	2	yes	—
983	C₂×C₄	C₂⁵×C₇	1	1	yes	characteristic
984	C₈	—	2	2	no	—
985	C₈	—	2	1	no	—
986	C₈	—	2	2	no	—
987	C₈	—	2	2	no	—
988	C₈	—	2	2	no	—
989	C₈	—	2	1	no	—
990	C₈	—	2	2	no	—
991	C₈	—	2	1	no	—
992	C₈	—	2	2	no	—
993	C₈	C₇×H(5,𝔽₂)	1	2	yes	—
994	C₇	#60322	1	1	yes	characteristic, direct product factor, Sylow
995	C₂²	—	2	1	no	—
996	C₂²	—	2	1	no	—
997	C₂²	—	2	2	no	—
998	C₂²	—	2	2	no	—
999	C₂²	—	2	2	no	—
1000	C₂²	—	2	2	no	—
1001	C₂²	—	2	2	no	—
1002	C₂²	—	2	2	no	—
1003	C₂²	—	2	2	no	—
1004	C₂²	—	2	2	no	—
1005	C₂²	—	2	2	no	—
1006	C₂²	—	2	2	no	—
1007	C₂²	—	2	2	no	—
1008	C₂²	—	2	2	no	—
1009	C₂²	—	8	2	no	—
1010	C₂²	—	8	2	no	—
1011	C₂²	—	8	4	no	—
1012	C₂²	C₇×#568	1	2	yes	—
1013	C₂²	C₂⁴×C₄×C₇	1	1	yes	characteristic
1014	C₄	—	2	1	no	—
1015	C₄	—	2	1	no	—
1016	C₄	—	2	2	no	—
1017	C₄	—	2	2	no	—
1018	C₄	—	2	1	no	—
1019	C₄	—	2	1	no	—
1020	C₄	—	2	2	no	—
1021	C₄	—	2	2	no	—
1022	C₄	—	2	1	no	—
1023	C₄	—	2	2	no	—
1024	C₄	—	2	2	no	—
1025	C₄	—	2	2	no	—
1026	C₄	—	2	2	no	—
1027	C₄	C₂×C₇×H(5,𝔽₂)	1	1	yes	characteristic
1028	C₄	C₇×#585	1	1	yes	characteristic
1029	C₂	—	2	2	no	—
1030	C₂	—	4	2	no	—
1031	C₂	—	4	2	no	—
1032	C₂	—	4	2	no	—
1033	C₂	—	4	2	no	—
1034	C₂	C₄×C₇×H(5,𝔽₂)	1	1	yes	characteristic
1035	C₂	C₂×C₇×#568	1	1	yes	characteristic
1036	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×#3459	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×#2993	C₂	semidirect
4. C₇×#2992	C₂	semidirect
5. C₇×#2992	C₂	semidirect
6. C₇×#2978	C₂	semidirect
7. C₇×#2977	C₂	semidirect
8. C₇×#2976	C₂	semidirect
9. C₇×#2974	C₂	semidirect
10. C₇×#2973	C₂	semidirect
11. C₇×#2969	C₂	semidirect
12. C₇×#2967	C₂	semidirect
13. C₇×#2966	C₂	semidirect
14. C₇×#2966	C₂	semidirect
15. C₇×D₄×M₁₆	C₂	semidirect
16. C₇×#2933	C₂	semidirect
17. C₇×#2933	C₂	semidirect
18. C₇×#2930	C₂	semidirect
19. C₂×C₇×#436	C₂	semidirect
20. C₂×C₇×#131	C₂²	semidirect
22. C₂²×C₇×M₁₆	C₂²	semidirect
23. C₂²×C₇×M₁₆	C₂²	semidirect
43. C₇×#446	C₂²	semidirect
44. C₇×#446	C₂²	semidirect
45. C₇×#446	C₂²	semidirect
46. C₇×#446	C₂²	semidirect
47. C₇×C₈×Q₈	C₂²	semidirect
48. C₇×C₈×Q₈	C₂²	semidirect
49. C₇×#436	C₂²	semidirect
50. C₇×#436	C₂²	semidirect
51. C₇×#436	C₂²	semidirect
52. C₇×#436	C₂²	semidirect
53. C₇×#436	C₂²	semidirect
54. C₇×#436	C₂²	semidirect
55. C₇×#436	C₂²	semidirect
56. C₇×#436	C₂²	semidirect
57. C₇×#436	C₂²	semidirect
58. C₇×#436	C₂²	semidirect
59. C₇×#436	C₂²	semidirect
60. C₇×#436	C₂²	semidirect
61. C₇×#435	C₂²	semidirect
62. C₇×#435	C₂²	semidirect
63. C₇×#435	C₂²	semidirect
64. C₇×#435	C₂²	semidirect
65. C₇×#435	C₂²	semidirect
66. C₇×#435	C₂²	semidirect
67. C₇×#435	C₂²	semidirect
68. C₇×#435	C₂²	semidirect
69. C₇×#435	C₂²	semidirect
70. C₇×#435	C₂²	semidirect
71. C₇×#435	C₂²	semidirect
72. C₇×#435	C₂²	semidirect
73. C₇×#435	C₂²	semidirect
74. C₇×#435	C₂²	semidirect
75. C₇×#435	C₂²	semidirect
76. C₇×#435	C₂²	semidirect
77. C₇×#435	C₂²	semidirect
78. C₇×#435	C₂²	semidirect
79. C₇×C₈×D₄	C₂²	semidirect
80. C₇×C₈×D₄	C₂²	semidirect
81. C₇×C₈×D₄	C₂²	semidirect
82. C₇×C₈×D₄	C₂²	semidirect
83. C₇×C₈×D₄	C₂²	semidirect
84. C₇×C₈×D₄	C₂²	semidirect
85. C₇×C₈×D₄	C₂²	semidirect
86. C₇×C₈×D₄	C₂²	semidirect
87. C₇×#433	C₂²	semidirect
88. C₇×#433	C₂²	semidirect
89. C₇×#433	C₂²	semidirect
90. C₇×#433	C₂²	semidirect
91. C₇×#433	C₂²	semidirect
92. C₇×#433	C₂²	semidirect
93. C₇×#432	C₂²	semidirect
94. C₇×#432	C₂²	semidirect
95. C₇×#432	C₂²	semidirect
96. C₇×#431	C₂²	semidirect
97. C₇×#424	C₂²	semidirect
98. C₇×#424	C₂²	semidirect
99. C₇×#424	C₂²	semidirect
100. C₇×#423	C₂²	semidirect
101. C₂×C₇×C₄⋊C₈	C₂²	semidirect
102. C₇×#408	C₂²	semidirect
103. C₇×#408	C₂²	semidirect
104. C₇×#408	C₂²	semidirect
106. C₇×#407	C₂²	semidirect
107. C₇×#407	C₂²	semidirect
109. C₂×C₇×C₂²⋊C₈	C₂²	semidirect
110. C₂×C₇×C₂²⋊C₈	C₂²	semidirect
111. C₂×C₇×C₂²⋊C₈	C₂²	semidirect
112. C₇×#405	C₂²	semidirect
113. C₇×#405	C₂²	semidirect
114. C₇×#405	C₂²	semidirect
115. C₄×C₇×M₁₆	C₂²	semidirect
116. C₂×C₄×C₇×C₈	C₂²	semidirect
117. #60322	C₇	direct (N × H)
276. #2995	C₂×C₇	semidirect
277. #2993	C₂×C₇	semidirect
278. #2992	C₂×C₇	semidirect
279. #2992	C₂×C₇	semidirect
280. #2978	C₂×C₇	semidirect
281. #2977	C₂×C₇	semidirect
282. #2976	C₂×C₇	semidirect
283. #2974	C₂×C₇	semidirect
284. #2973	C₂×C₇	semidirect
285. #2969	C₂×C₇	semidirect
286. #2967	C₂×C₇	semidirect
287. #2966	C₂×C₇	semidirect
288. #2966	C₂×C₇	semidirect
289. D₄×M₁₆	C₂×C₇	semidirect
290. #2933	C₂×C₇	semidirect
291. #2933	C₂×C₇	semidirect
292. #2930	C₂×C₇	semidirect
293. C₂×#436	C₂×C₇	semidirect
421. C₂×#131	C₂²×C₇	semidirect
423. C₂²×M₁₆	C₂²×C₇	semidirect
424. C₂²×M₁₆	C₂²×C₇	semidirect
444. #446	C₂²×C₇	semidirect
445. #446	C₂²×C₇	semidirect
446. #446	C₂²×C₇	semidirect
447. #446	C₂²×C₇	semidirect
448. C₈×Q₈	C₂²×C₇	semidirect
449. C₈×Q₈	C₂²×C₇	semidirect
450. #436	C₂²×C₇	semidirect
451. #436	C₂²×C₇	semidirect
452. #436	C₂²×C₇	semidirect
453. #436	C₂²×C₇	semidirect
454. #436	C₂²×C₇	semidirect
455. #436	C₂²×C₇	semidirect
456. #436	C₂²×C₇	semidirect
457. #436	C₂²×C₇	semidirect
458. #436	C₂²×C₇	semidirect
459. #436	C₂²×C₇	semidirect
460. #436	C₂²×C₇	semidirect
461. #436	C₂²×C₇	semidirect
462. #435	C₂²×C₇	semidirect
463. #435	C₂²×C₇	semidirect
464. #435	C₂²×C₇	semidirect
465. #435	C₂²×C₇	semidirect
466. #435	C₂²×C₇	semidirect
467. #435	C₂²×C₇	semidirect
468. #435	C₂²×C₇	semidirect
469. #435	C₂²×C₇	semidirect
470. #435	C₂²×C₇	semidirect
471. #435	C₂²×C₇	semidirect
472. #435	C₂²×C₇	semidirect
473. #435	C₂²×C₇	semidirect
474. #435	C₂²×C₇	semidirect
475. #435	C₂²×C₇	semidirect
476. #435	C₂²×C₇	semidirect
477. #435	C₂²×C₇	semidirect
478. #435	C₂²×C₇	semidirect
479. #435	C₂²×C₇	semidirect
480. C₈×D₄	C₂²×C₇	semidirect
481. C₈×D₄	C₂²×C₇	semidirect
482. C₈×D₄	C₂²×C₇	semidirect
483. C₈×D₄	C₂²×C₇	semidirect
484. C₈×D₄	C₂²×C₇	semidirect
485. C₈×D₄	C₂²×C₇	semidirect
486. C₈×D₄	C₂²×C₇	semidirect
487. C₈×D₄	C₂²×C₇	semidirect
488. #433	C₂²×C₇	semidirect
489. #433	C₂²×C₇	semidirect
490. #433	C₂²×C₇	semidirect
491. #433	C₂²×C₇	semidirect
492. #433	C₂²×C₇	semidirect
493. #433	C₂²×C₇	semidirect
494. #432	C₂²×C₇	semidirect
495. #432	C₂²×C₇	semidirect
496. #432	C₂²×C₇	semidirect
497. #431	C₂²×C₇	semidirect
498. #424	C₂²×C₇	semidirect
499. #424	C₂²×C₇	semidirect
500. #424	C₂²×C₇	semidirect
501. #423	C₂²×C₇	semidirect
502. C₂×C₄⋊C₈	C₂²×C₇	semidirect
503. #408	C₂²×C₇	semidirect
504. #408	C₂²×C₇	semidirect
505. #408	C₂²×C₇	semidirect
507. #407	C₂²×C₇	semidirect
508. #407	C₂²×C₇	semidirect
510. C₂×C₂²⋊C₈	C₂²×C₇	semidirect
511. C₂×C₂²⋊C₈	C₂²×C₇	semidirect
512. C₂×C₂²⋊C₈	C₂²×C₇	semidirect
513. #405	C₂²×C₇	semidirect
514. #405	C₂²×C₇	semidirect
515. #405	C₂²×C₇	semidirect
516. C₄×M₁₆	C₂²×C₇	semidirect
517. C₂×C₄×C₈	C₂²×C₇	semidirect
994. C₇	#60322	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×#3459	2
C₇×#2995	2
C₇×#2993	2
C₇×#2992	2
C₇×#2978	2
C₇×#2977	2
C₇×#2976	2
C₇×#2974	2
C₇×#2973	2
C₇×#2969	2
C₇×#2967	2
C₇×#2966	2
C₇×D₄×M₁₆	2
C₇×#2933	2
C₇×#2930	2
C₂×C₇×#436	2
#60322	7

Subgroups — C7×#60322 #13237538

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×#60322 #13237538