Subgroups — C₇×#61222 #13238438

Order 1792.

2088 conjugacy classes of subgroups.

The subgroup lattice has 1236 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×#3511	C₂	1	1	yes	maximal, characteristic, complemented
2	C₇×#3500	C₂	1	1	yes	maximal, characteristic, complemented
3	C₇×#3321	C₂	1	2	yes	maximal, complemented
4	C₇×#3319	C₂	1	2	yes	maximal, complemented
5	C₇×#3316	C₂	1	2	yes	maximal, complemented
6	C₇×#3314	C₂	1	2	yes	maximal, complemented
7	C₇×#3313	C₂	1	2	yes	maximal, complemented
8	C₇×#3311	C₂	1	2	yes	maximal, complemented
9	C₇×#3308	C₂	1	2	yes	maximal, complemented
10	C₇×#3306	C₂	1	2	yes	maximal, complemented
11	C₂×C₇×#489	C₂	1	1	yes	maximal, characteristic, complemented
12	C₇×#3097	C₂	1	1	yes	maximal, characteristic, complemented
13	C₇×#3096	C₂	1	1	yes	maximal, characteristic, complemented
14	C₇×#3079	C₂	1	1	yes	maximal, characteristic, complemented
15	C₇×#3063	C₂	1	1	yes	maximal, characteristic, complemented
16	C₇×#3062	C₂	1	1	yes	maximal, characteristic, complemented
17	C₇×#3040	C₂	1	1	yes	maximal, characteristic, complemented
18	C₇×#3013	C₂	1	1	yes	maximal, characteristic, complemented
19	C₇×#3012	C₂	1	1	yes	maximal, characteristic, complemented
20	C₇×#2943	C₂	1	1	yes	maximal, characteristic, complemented
21	C₇×#2932	C₂	1	1	yes	maximal, characteristic, complemented
22	C₇×#2898	C₂	1	1	yes	maximal, characteristic, complemented
23	C₇×#2897	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×C₇×2₋¹⁺⁴	C₂²	1	1	yes	characteristic
25	C₂×C₇×H(5,𝔽₂)	C₂²	1	1	yes	characteristic
26	C₂×C₇×#137	C₂²	1	1	yes	characteristic, complemented
27	C₂×C₇×AGL(1,ℤ/8)	C₂²	1	1	yes	characteristic
28	C₂×C₇×#135	C₂²	1	1	yes	characteristic
29	C₂×C₇×#131	C₂²	1	1	yes	characteristic
30	C₂×C₇×#131	C₂²	1	1	yes	characteristic, complemented
31	C₇×#556	C₂²	1	2	yes	complemented
32	C₇×#555	C₂²	1	2	yes	complemented
33	C₇×#554	C₂²	1	2	yes	complemented
34	C₇×#553	—	2	2	no	—
35	C₇×#548	—	2	2	no	—
36	C₇×#548	C₂²	1	2	yes	—
37	C₇×#548	C₂²	1	2	yes	—
38	C₇×#547	C₂²	1	2	yes	complemented
39	C₇×#546	—	2	2	no	—
40	C₇×#546	—	2	2	no	—
41	C₇×#546	C₂²	1	2	yes	—
42	C₇×#546	C₂²	1	2	yes	—
43	C₇×#542	—	2	1	no	—
44	C₇×#542	—	2	1	no	—
45	C₇×#537	C₂²	1	1	yes	characteristic
46	C₇×#537	C₂²	1	1	yes	characteristic, complemented
47	C₇×#536	—	2	1	no	—
48	C₇×#536	C₂²	1	1	yes	characteristic
49	C₇×#535	—	2	1	no	—
50	C₇×#535	C₂²	1	1	yes	characteristic
51	C₇×#533	—	2	1	no	—
52	C₇×#532	—	2	1	no	—
53	C₇×#532	—	2	1	no	—
54	C₇×#532	C₂²	1	1	yes	characteristic
55	C₂×C₇×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
56	C₂×C₇×#124	—	2	1	no	—
57	C₂×C₇×#124	C₂²	1	1	yes	characteristic
58	C₇×#520	C₂²	1	1	yes	characteristic
59	C₇×#520	C₂²	1	1	yes	characteristic, complemented
60	C₄×C₇×#41	C₂²	1	1	yes	characteristic
61	C₄×C₇×#41	C₂²	1	1	yes	characteristic, complemented
62	C₇×#489	C₂²	1	2	yes	complemented
63	C₇×#489	C₂²	1	2	yes	complemented
64	C₇×#489	C₂²	1	2	yes	complemented
65	C₇×#489	C₂²	1	2	yes	complemented
66	C₇×#485	C₂²	1	2	yes	complemented
67	C₇×#485	C₂²	1	2	yes	complemented
68	C₇×#484	C₂²	1	2	yes	complemented
69	C₇×#483	C₂²	1	2	yes	complemented
70	C₇×#482	C₂²	1	2	yes	complemented
71	C₇×#482	C₂²	1	2	yes	complemented
72	C₇×#481	C₂²	1	2	yes	complemented
73	C₇×#480	C₂²	1	2	yes	complemented
74	C₇×#477	C₂²	1	2	yes	complemented
75	C₇×#476	C₂²	1	2	yes	complemented
76	C₇×#475	C₂²	1	2	yes	complemented
77	C₇×#474	C₂²	1	2	yes	complemented
78	C₇×#470	C₂²	1	2	yes	complemented
79	C₇×#469	C₂²	1	2	yes	complemented
80	C₇×#468	C₂²	1	2	yes	complemented
81	C₇×#468	C₂²	1	2	yes	complemented
82	C₇×#467	C₂²	1	2	yes	complemented
83	C₇×#466	C₂²	1	2	yes	complemented
84	C₇×#465	C₂²	1	2	yes	complemented
85	C₇×#465	C₂²	1	2	yes	complemented
86	C₇×#464	C₂²	1	2	yes	complemented
87	C₇×#464	C₂²	1	2	yes	complemented
88	C₇×#463	C₂²	1	2	yes	complemented
89	C₇×#463	C₂²	1	2	yes	complemented
90	C₇×#452	C₂²	1	2	yes	—
91	C₇×#452	C₂²	1	2	yes	complemented
92	C₇×#451	C₂²	1	2	yes	complemented
93	C₇×#450	C₂²	1	2	yes	—
94	C₇×#449	C₂²	1	2	yes	—
95	C₇×#449	C₂²	1	2	yes	complemented
96	C₇×#448	C₂²	1	2	yes	complemented
97	C₇×#447	C₂²	1	2	yes	—
98	C₇×#442	C₂²	1	1	yes	characteristic, complemented
99	C₇×#442	C₂²	1	1	yes	characteristic, complemented
100	C₇×#441	C₂²	1	1	yes	characteristic, complemented
101	C₇×#441	C₂²	1	1	yes	characteristic, complemented
102	C₇×#440	C₂²	1	1	yes	characteristic, complemented
103	C₇×#440	C₂²	1	1	yes	characteristic, complemented
104	C₇×#440	C₂²	1	1	yes	characteristic, complemented
105	C₇×#440	C₂²	1	1	yes	characteristic, complemented
106	C₇×#435	C₂²	1	2	yes	complemented
107	C₇×#435	C₂²	1	2	yes	complemented
108	C₇×#435	C₂²	1	2	yes	complemented
109	C₇×#435	C₂²	1	2	yes	complemented
110	C₇×#428	C₂²	1	1	yes	characteristic, complemented
111	C₇×#428	C₂²	1	1	yes	characteristic, complemented
112	C₇×#427	C₂²	1	1	yes	characteristic, complemented
113	C₇×#423	C₂²	1	1	yes	characteristic, complemented
114	C₇×#419	C₂²	1	1	yes	characteristic, complemented
115	C₇×#419	C₂²	1	2	yes	complemented
116	C₇×#418	C₂²	1	1	yes	characteristic
117	C₇×#418	C₂²	1	2	yes	—
118	C₇×#417	C₂²	1	1	yes	characteristic
119	C₇×#417	C₂²	1	1	yes	characteristic
120	C₇×#417	C₂²	1	2	yes	—
121	C₇×#417	C₂²	1	2	yes	complemented
122	C₇×#416	C₂²	1	1	yes	characteristic
123	C₇×#416	C₂²	1	2	yes	—
124	C₇×#416	C₂²	1	1	yes	characteristic, complemented
125	C₇×#416	C₂²	1	2	yes	complemented
126	C₂×C₇×#103	C₂²	1	1	yes	characteristic, complemented
127	C₂×C₇×#103	C₂²	1	2	yes	complemented
128	C₂×C₇×#103	C₂²	1	1	yes	characteristic, complemented
129	C₂×C₇×#102	C₂²	1	1	yes	characteristic
130	C₂×C₇×#102	C₂²	1	2	yes	—
131	C₂×C₇×#102	C₂²	1	1	yes	characteristic
132	C₇×#408	C₂²	1	1	yes	characteristic
133	C₇×#408	C₂²	1	1	yes	characteristic, complemented
134	C₂×C₇×#97	C₂²	1	1	yes	characteristic, complemented
135	#61222	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
136	C₇×2₋¹⁺⁴	—	2	4	no	—
137	C₇×2₋¹⁺⁴	—	4	2	no	—
138	C₇×H(5,𝔽₂)	—	2	4	no	—
139	C₇×H(5,𝔽₂)	—	4	2	no	—
140	C₂×C₇×#41	—	2	1	no	—
141	C₂×C₇×#41	—	2	1	no	—
142	C₂×C₇×#41	—	2	2	no	—
143	C₂×C₇×#41	—	2	2	no	—
144	C₂×C₇×#41	C₂³	1	1	yes	characteristic
145	C₂×C₇×#41	C₂³	1	2	yes	—
146	C₂×C₇×#41	C₂³	1	2	yes	—
147	C₂×C₇×#41	C₂³	1	1	yes	characteristic
148	C₂×C₇×#41	C₂³	1	1	yes	characteristic
149	C₂×C₇×#41	C₂³	1	1	yes	characteristic
150	C₂²×C₇×Q₈	—	2	1	no	—
151	C₂²×C₇×Q₈	—	2	1	no	—
152	C₂²×C₇×Q₈	C₂³	1	1	yes	characteristic
153	C₂²×C₇×Q₈	C₂³	1	2	yes	—
154	C₂²×C₇×D₄	—	2	1	no	—
155	C₂²×C₇×D₄	—	2	2	no	—
156	C₂²×C₇×D₄	C₂³	1	1	yes	characteristic
157	C₂²×C₇×D₄	C₂³	1	2	yes	—
158	C₇×#137	—	4	2	no	—
159	C₇×AGL(1,ℤ/8)	—	4	2	no	—
160	C₇×#135	—	2	4	no	—
161	C₂×C₇×Q₁₆	C₂³	1	1	yes	characteristic
162	C₂×C₇×Q₁₆	C₂³	1	2	yes	—
163	C₂×C₇×SD₁₆	C₂³	1	1	yes	characteristic
164	C₂×C₇×SD₁₆	C₂³	1	1	yes	characteristic
165	C₂×C₇×SD₁₆	C₂³	1	2	yes	—
166	C₂×C₇×SD₁₆	C₂³	1	2	yes	—
167	C₂×C₇×D₈	C₂³	1	1	yes	characteristic
168	C₂×C₇×D₈	C₂³	1	2	yes	—
169	C₇×#131	—	4	2	no	—
170	C₇×#131	—	4	2	no	—
171	C₂×C₇×M₁₆	C₂³	1	1	yes	characteristic
172	C₂×C₇×M₁₆	C₂³	1	1	yes	characteristic
173	C₂×C₇×M₁₆	C₂³	1	2	yes	—
174	C₂×C₇×M₁₆	C₂³	1	2	yes	—
175	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
176	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
177	C₂²×C₇×C₈	C₂³	1	2	yes	—
178	C₂²×C₇×C₈	C₂³	1	2	yes	—
179	C₇×C₄⋊Q₈	—	2	1	no	—
180	C₇×C₄⋊Q₈	—	2	1	no	—
181	C₇×C₄⋊Q₈	—	2	1	no	—
182	C₇×C₄⋊Q₈	D₄	1	1	yes	characteristic
183	C₇×C₄⋊Q₈	C₂³	1	2	yes	—
184	C₇×C₄⋊Q₈	C₂³	1	2	yes	—
185	C₇×#127	—	2	1	no	—
186	C₇×#127	D₄	1	1	yes	characteristic
187	C₇×#126	—	2	2	no	—
188	C₇×#126	—	2	2	no	—
189	C₇×#125	—	2	2	no	—
190	C₇×#124	—	2	1	no	—
191	C₇×#124	—	2	1	no	—
192	C₇×#124	—	2	2	no	—
193	C₇×#124	—	2	2	no	—
194	C₇×#124	—	2	2	no	—
195	C₇×#124	—	2	2	no	—
196	C₇×#124	—	2	2	no	—
197	C₇×#124	—	2	1	no	—
198	C₇×#124	—	2	1	no	—
199	C₇×#124	D₄	1	1	yes	characteristic
200	C₇×#124	D₄	1	1	yes	characteristic
201	C₇×#124	C₂³	1	2	yes	—
202	C₇×#124	C₂³	1	2	yes	—
203	C₇×#123	—	2	2	no	—
204	C₇×#123	—	2	2	no	—
205	C₇×#123	—	2	2	no	—
206	C₇×#123	—	2	2	no	—
207	C₇×#123	—	2	2	no	—
208	C₇×C₂²⋊Q₈	—	2	1	no	—
209	C₇×C₂²⋊Q₈	—	2	1	no	—
210	C₇×C₂²⋊Q₈	—	2	2	no	—
211	C₇×C₂²⋊Q₈	—	2	2	no	—
212	C₇×C₂²⋊Q₈	—	2	2	no	—
213	C₇×C₂²⋊Q₈	—	2	2	no	—
214	C₇×C₂²⋊Q₈	—	2	2	no	—
215	C₇×C₂²⋊Q₈	C₂³	1	2	yes	—
216	C₇×C₂²⋊Q₈	C₂³	1	2	yes	—
217	C₇×C₂²⋊Q₈	C₂³	1	2	yes	—
218	C₇×C₂²⋊Q₈	C₂³	1	2	yes	—
219	C₇×#121	—	2	1	no	—
220	C₇×#121	—	2	1	no	—
221	C₇×#121	—	2	2	no	—
222	C₇×#121	—	2	2	no	—
223	C₇×#121	—	2	2	no	—
224	C₇×#121	—	2	2	no	—
225	C₇×#121	—	2	2	no	—
226	C₇×#121	—	2	2	no	—
227	C₇×#121	—	2	2	no	—
228	C₇×#121	D₄	1	2	yes	—
229	C₇×#121	D₄	1	2	yes	—
230	C₇×#121	C₂³	1	2	yes	—
231	C₇×#121	C₂³	1	2	yes	—
232	C₇×#121	C₂³	1	2	yes	—
233	C₇×#121	C₂³	1	2	yes	—
234	C₇×#120	—	2	2	no	—
235	C₇×#120	—	2	2	no	—
236	C₇×#120	—	2	2	no	—
237	C₄×C₇×Q₈	—	2	1	no	—
238	C₄×C₇×Q₈	—	2	1	no	—
239	C₄×C₇×Q₈	—	2	2	no	—
240	C₄×C₇×Q₈	C₂³	1	1	yes	characteristic
241	C₄×C₇×Q₈	C₂³	1	1	yes	characteristic
242	C₄×C₇×Q₈	C₂³	1	1	yes	characteristic
243	C₄×C₇×Q₈	C₂³	1	1	yes	characteristic
244	C₄×C₇×D₄	—	2	1	no	—
245	C₄×C₇×D₄	—	2	2	no	—
246	C₄×C₇×D₄	—	2	1	no	—
247	C₄×C₇×D₄	—	2	2	no	—
248	C₄×C₇×D₄	—	2	2	no	—
249	C₄×C₇×D₄	—	2	1	no	—
250	C₄×C₇×D₄	—	2	1	no	—
251	C₄×C₇×D₄	—	2	1	no	—
252	C₄×C₇×D₄	—	2	1	no	—
253	C₄×C₇×D₄	—	2	2	no	—
254	C₄×C₇×D₄	—	2	2	no	—
255	C₄×C₇×D₄	C₂³	1	1	yes	characteristic
256	C₄×C₇×D₄	C₂³	1	1	yes	characteristic
257	C₄×C₇×D₄	C₂³	1	1	yes	characteristic
258	C₄×C₇×D₄	C₂³	1	1	yes	characteristic
259	C₄×C₇×D₄	C₂³	1	2	yes	—
260	C₄×C₇×D₄	C₂³	1	2	yes	—
261	C₇×#117	—	2	2	no	—
262	C₇×#117	—	2	1	no	—
263	C₇×#117	—	2	1	no	—
264	C₇×#117	C₂³	1	2	yes	—
265	C₇×#117	C₂³	1	2	yes	—
266	C₇×#117	C₂³	1	1	yes	characteristic
267	C₇×#117	C₂³	1	1	yes	characteristic
268	C₂×C₇×C₄⋊C₄	—	2	1	no	—
269	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
270	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
271	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
272	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
273	C₂×C₇×C₂²⋊C₄	—	2	1	no	—
274	C₂×C₇×C₂²⋊C₄	—	2	1	no	—
275	C₂×C₇×C₂²⋊C₄	—	2	2	no	—
276	C₂×C₇×C₂²⋊C₄	—	2	2	no	—
277	C₂×C₄²×C₇	—	2	1	no	—
278	C₂×C₄²×C₇	—	2	1	no	—
279	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
280	C₇×#107	C₂³	1	2	yes	—
281	C₇×#107	C₂³	1	2	yes	—
282	C₇×#107	C₂³	1	1	yes	characteristic
283	C₇×#107	C₂³	1	1	yes	characteristic
284	C₇×#106	C₂³	1	2	yes	—
285	C₇×#106	C₂³	1	2	yes	—
286	C₇×#106	C₂³	1	1	yes	characteristic
287	C₇×#106	C₂³	1	1	yes	characteristic
288	C₇×C₄⋊C₈	C₂³	1	2	yes	—
289	C₇×C₄⋊C₈	C₂³	1	2	yes	—
290	C₇×#103	C₂³	1	1	yes	characteristic
291	C₇×#103	C₂³	1	2	yes	—
292	C₇×#103	C₂³	1	2	yes	—
293	C₇×#103	C₂³	1	1	yes	characteristic
294	C₇×#103	C₂³	1	2	yes	—
295	C₇×#103	C₂³	1	2	yes	—
296	C₇×#103	C₂³	1	2	yes	—
297	C₇×#103	C₂³	1	2	yes	—
298	C₇×#103	C₂³	1	2	yes	—
299	C₇×#103	C₂³	1	2	yes	—
300	C₇×#103	C₂³	1	1	yes	characteristic
301	C₇×#103	C₂³	1	1	yes	characteristic
302	C₇×#102	C₂³	1	1	yes	characteristic
303	C₇×#102	C₂³	1	2	yes	—
304	C₇×#102	C₂³	1	2	yes	—
305	C₇×#102	C₂³	1	1	yes	characteristic
306	C₇×#102	C₂³	1	2	yes	—
307	C₇×#102	C₂³	1	2	yes	—
308	C₇×#102	C₂³	1	2	yes	—
309	C₇×#102	C₂³	1	2	yes	—
310	C₇×#102	C₂³	1	2	yes	—
311	C₇×#102	C₂³	1	2	yes	—
312	C₇×#102	C₂³	1	1	yes	characteristic
313	C₇×#102	C₂³	1	1	yes	characteristic
314	C₇×C₂²⋊C₈	C₂³	1	2	yes	—
315	C₇×C₂²⋊C₈	C₂³	1	2	yes	—
316	C₇×C₂²⋊C₈	C₂³	1	2	yes	—
317	C₇×C₂²⋊C₈	C₂³	1	2	yes	—
318	C₇×#97	C₂³	1	1	yes	characteristic
319	C₇×#97	C₂³	1	1	yes	characteristic
320	C₇×#97	C₂³	1	1	yes	characteristic
321	C₇×#97	C₂³	1	1	yes	characteristic
322	#3511	C₂×C₇	1	1	yes	characteristic, complemented
323	#3500	C₂×C₇	1	1	yes	characteristic, complemented
324	#3321	C₂×C₇	1	2	yes	complemented
325	#3319	C₂×C₇	1	2	yes	complemented
326	#3316	C₂×C₇	1	2	yes	complemented
327	#3314	C₂×C₇	1	2	yes	complemented
328	#3313	C₂×C₇	1	2	yes	complemented
329	#3311	C₂×C₇	1	2	yes	complemented
330	#3308	C₂×C₇	1	2	yes	complemented
331	#3306	C₂×C₇	1	2	yes	complemented
332	C₂×#489	C₂×C₇	1	1	yes	characteristic, complemented
333	#3097	C₂×C₇	1	1	yes	characteristic, complemented
334	#3096	C₂×C₇	1	1	yes	characteristic, complemented
335	#3079	C₂×C₇	1	1	yes	characteristic, complemented
336	#3063	C₂×C₇	1	1	yes	characteristic, complemented
337	#3062	C₂×C₇	1	1	yes	characteristic, complemented
338	#3040	C₂×C₇	1	1	yes	characteristic, complemented
339	#3013	C₂×C₇	1	1	yes	characteristic, complemented
340	#3012	C₂×C₇	1	1	yes	characteristic, complemented
341	#2943	C₂×C₇	1	1	yes	characteristic, complemented
342	#2932	C₂×C₇	1	1	yes	characteristic, complemented
343	#2898	C₂×C₇	1	1	yes	characteristic, complemented
344	#2897	C₂×C₇	1	1	yes	characteristic, complemented
345	C₂⁴×C₇	—	2	2	no	—
346	C₂⁴×C₇	—	2	1	no	—
347	C₇×#41	—	2	2	no	—
348	C₇×#41	—	2	2	no	—
349	C₇×#41	—	2	2	no	—
350	C₇×#41	—	2	2	no	—
351	C₇×#41	—	2	2	no	—
352	C₇×#41	—	2	4	no	—
353	C₇×#41	—	2	4	no	—
354	C₇×#41	—	2	2	no	—
355	C₇×#41	—	2	2	no	—
356	C₇×#41	—	4	2	no	—
357	C₇×#41	—	4	2	no	—
358	C₇×#41	—	4	4	no	—
359	C₇×#41	—	4	4	no	—
360	C₇×#41	—	4	8	no	—
361	C₇×#41	—	8	4	no	—
362	C₇×#41	#41	1	4	yes	complemented
363	C₂×C₇×Q₈	—	2	2	no	—
364	C₂×C₇×Q₈	—	2	2	no	—
365	C₂×C₇×Q₈	—	2	1	no	—
366	C₂×C₇×Q₈	—	2	2	no	—
367	C₂×C₇×Q₈	—	2	4	no	—
368	C₂×C₇×Q₈	—	2	2	no	—
369	C₂×C₇×Q₈	—	2	2	no	—
370	C₂×C₇×Q₈	—	4	2	no	—
371	C₂×C₇×Q₈	—	4	4	no	—
372	C₂×C₇×Q₈	—	8	2	no	—
373	C₂×C₇×Q₈	C₂×D₄	1	1	yes	characteristic
374	C₂×C₇×Q₈	C₂×D₄	1	1	yes	characteristic
375	C₂×C₇×Q₈	C₂⁴	1	2	yes	—
376	C₂×C₇×Q₈	C₂⁴	1	1	yes	characteristic
377	C₂×C₇×Q₈	C₂⁴	1	1	yes	characteristic
378	C₂×C₇×D₄	—	2	1	no	—
379	C₂×C₇×D₄	—	2	4	no	—
380	C₂×C₇×D₄	—	2	1	no	—
381	C₂×C₇×D₄	—	2	2	no	—
382	C₂×C₇×D₄	—	2	2	no	—
383	C₂×C₇×D₄	—	2	2	no	—
384	C₂×C₇×D₄	—	2	2	no	—
385	C₂×C₇×D₄	—	2	2	no	—
386	C₂×C₇×D₄	—	2	2	no	—
387	C₂×C₇×D₄	—	2	2	no	—
388	C₂×C₇×D₄	—	2	1	no	—
389	C₂×C₇×D₄	—	2	2	no	—
390	C₂×C₇×D₄	—	2	2	no	—
391	C₂×C₇×D₄	—	4	2	no	—
392	C₂×C₇×D₄	—	4	4	no	—
393	C₂×C₇×D₄	—	4	8	no	—
394	C₂×C₇×D₄	C₂×D₄	1	2	yes	—
395	C₂×C₇×D₄	C₂×D₄	1	2	yes	—
396	C₂×C₇×D₄	C₂×D₄	1	1	yes	characteristic
397	C₂×C₇×D₄	C₂×D₄	1	1	yes	characteristic
398	C₂×C₇×D₄	C₂×D₄	1	2	yes	—
399	C₂×C₇×D₄	C₂×D₄	1	2	yes	—
400	C₂×C₇×D₄	C₂⁴	1	2	yes	—
401	C₂×C₇×D₄	C₂⁴	1	1	yes	characteristic
402	C₂×C₇×D₄	C₂⁴	1	1	yes	characteristic
403	C₂²×C₄×C₇	—	2	1	no	—
404	C₂²×C₄×C₇	—	2	1	no	—
405	C₂²×C₄×C₇	—	2	2	no	—
406	C₂²×C₄×C₇	—	2	1	no	—
407	C₂²×C₄×C₇	—	2	1	no	—
408	C₂²×C₄×C₇	—	2	2	no	—
409	C₂²×C₄×C₇	—	2	2	no	—
410	C₂²×C₄×C₇	—	2	1	no	—
411	C₂²×C₄×C₇	—	2	1	no	—
412	C₂²×C₄×C₇	—	2	1	no	—
413	C₂²×C₄×C₇	—	2	2	no	—
414	C₂²×C₄×C₇	—	2	2	no	—
415	C₂²×C₄×C₇	—	2	1	no	—
416	C₂²×C₄×C₇	—	2	1	no	—
417	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
418	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
419	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
420	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
421	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
422	C₇×Q₁₆	—	2	2	no	—
423	C₇×Q₁₆	—	4	2	no	—
424	C₇×SD₁₆	—	2	2	no	—
425	C₇×SD₁₆	—	2	2	no	—
426	C₇×SD₁₆	—	4	2	no	—
427	C₇×SD₁₆	—	4	2	no	—
428	C₇×D₈	—	2	2	no	—
429	C₇×D₈	—	4	2	no	—
430	C₇×M₁₆	—	2	2	no	—
431	C₇×M₁₆	—	2	2	no	—
432	C₇×M₁₆	—	4	2	no	—
433	C₇×M₁₆	—	4	2	no	—
434	C₂×C₇×C₈	—	2	2	no	—
435	C₂×C₇×C₈	—	2	2	no	—
436	C₂×C₇×C₈	—	4	2	no	—
437	C₂×C₇×C₈	—	4	2	no	—
438	C₂×C₇×C₈	C₂⁴	1	1	yes	characteristic
439	C₂×C₇×C₈	C₂⁴	1	1	yes	characteristic
440	C₂×C₇×C₈	C₂⁴	1	1	yes	characteristic
441	C₂×C₇×C₈	C₂⁴	1	1	yes	characteristic
442	C₂×C₇×C₈	C₂⁴	1	2	yes	—
443	C₂×C₇×C₈	C₂⁴	1	2	yes	—
444	C₇×C₄⋊C₄	—	2	2	no	—
445	C₇×C₄⋊C₄	—	2	2	no	—
446	C₇×C₄⋊C₄	—	2	1	no	—
447	C₇×C₄⋊C₄	—	2	1	no	—
448	C₇×C₄⋊C₄	—	2	2	no	—
449	C₇×C₄⋊C₄	—	2	2	no	—
450	C₇×C₄⋊C₄	—	2	1	no	—
451	C₇×C₄⋊C₄	—	2	1	no	—
452	C₇×C₄⋊C₄	—	2	1	no	—
453	C₇×C₄⋊C₄	—	2	1	no	—
454	C₇×C₄⋊C₄	—	2	2	no	—
455	C₇×C₄⋊C₄	—	2	2	no	—
456	C₇×C₄⋊C₄	—	2	2	no	—
457	C₇×C₄⋊C₄	—	2	2	no	—
458	C₇×C₄⋊C₄	C₂×D₄	1	2	yes	—
459	C₇×C₄⋊C₄	C₂×D₄	1	2	yes	—
460	C₇×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
461	C₇×C₄⋊C₄	C₂⁴	1	2	yes	—
462	C₇×C₄⋊C₄	C₂⁴	1	2	yes	—
463	C₇×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
464	C₇×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
465	C₇×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
466	C₇×C₂²⋊C₄	—	2	2	no	—
467	C₇×C₂²⋊C₄	—	2	2	no	—
468	C₇×C₂²⋊C₄	—	2	1	no	—
469	C₇×C₂²⋊C₄	—	2	1	no	—
470	C₇×C₂²⋊C₄	—	2	2	no	—
471	C₇×C₂²⋊C₄	—	2	2	no	—
472	C₇×C₂²⋊C₄	—	2	2	no	—
473	C₇×C₂²⋊C₄	—	2	2	no	—
474	C₇×C₂²⋊C₄	—	2	2	no	—
475	C₇×C₂²⋊C₄	—	2	2	no	—
476	C₇×C₂²⋊C₄	—	2	2	no	—
477	C₇×C₂²⋊C₄	—	2	2	no	—
478	C₇×C₂²⋊C₄	—	2	2	no	—
479	C₇×C₂²⋊C₄	—	2	2	no	—
480	C₇×C₂²⋊C₄	—	2	1	no	—
481	C₇×C₂²⋊C₄	—	2	1	no	—
482	C₇×C₂²⋊C₄	—	2	1	no	—
483	C₇×C₂²⋊C₄	—	2	1	no	—
484	C₇×C₂²⋊C₄	—	2	2	no	—
485	C₇×C₂²⋊C₄	—	2	2	no	—
486	C₇×C₂²⋊C₄	C₂×D₄	1	2	yes	—
487	C₇×C₂²⋊C₄	C₂×D₄	1	2	yes	—
488	C₇×C₂²⋊C₄	C₂×D₄	1	2	yes	—
489	C₇×C₂²⋊C₄	C₂×D₄	1	2	yes	—
490	C₄²×C₇	—	2	1	no	—
491	C₄²×C₇	—	2	1	no	—
492	C₄²×C₇	—	2	1	no	—
493	C₄²×C₇	—	2	1	no	—
494	C₄²×C₇	—	2	1	no	—
495	C₄²×C₇	—	2	1	no	—
496	C₄²×C₇	—	2	2	no	—
497	C₄²×C₇	—	2	2	no	—
498	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
499	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
500	C₄²×C₇	C₂⁴	1	1	yes	characteristic
501	C₄²×C₇	C₂⁴	1	1	yes	characteristic
502	C₂×2₋¹⁺⁴	C₂²×C₇	1	1	yes	characteristic
503	C₂×H(5,𝔽₂)	C₂²×C₇	1	1	yes	characteristic
504	C₂×#137	C₂²×C₇	1	1	yes	characteristic, complemented
505	C₂×AGL(1,ℤ/8)	C₂²×C₇	1	1	yes	characteristic
506	C₂×#135	C₂²×C₇	1	1	yes	characteristic
507	C₂×#131	C₂²×C₇	1	1	yes	characteristic
508	C₂×#131	C₂²×C₇	1	1	yes	characteristic, complemented
509	#556	C₂²×C₇	1	2	yes	complemented
510	#555	C₂²×C₇	1	2	yes	complemented
511	#554	C₂²×C₇	1	2	yes	complemented
512	#553	—	2	2	no	—
513	#548	—	2	2	no	—
514	#548	C₂²×C₇	1	2	yes	—
515	#548	C₂²×C₇	1	2	yes	—
516	#547	C₂²×C₇	1	2	yes	complemented
517	#546	—	2	2	no	—
518	#546	—	2	2	no	—
519	#546	C₂²×C₇	1	2	yes	—
520	#546	C₂²×C₇	1	2	yes	—
521	#542	—	2	1	no	—
522	#542	—	2	1	no	—
523	#537	C₂²×C₇	1	1	yes	characteristic
524	#537	C₂²×C₇	1	1	yes	characteristic, complemented
525	#536	—	2	1	no	—
526	#536	C₂²×C₇	1	1	yes	characteristic
527	#535	—	2	1	no	—
528	#535	C₂²×C₇	1	1	yes	characteristic
529	#533	—	2	1	no	—
530	#532	—	2	1	no	—
531	#532	—	2	1	no	—
532	#532	C₂²×C₇	1	1	yes	characteristic
533	C₂×C₄⋊Q₈	C₂²×C₇	1	1	yes	characteristic, complemented
534	C₂×#124	—	2	1	no	—
535	C₂×#124	C₂²×C₇	1	1	yes	characteristic
536	#520	C₂²×C₇	1	1	yes	characteristic
537	#520	C₂²×C₇	1	1	yes	characteristic, complemented
538	C₄×#41	C₂²×C₇	1	1	yes	characteristic
539	C₄×#41	C₂²×C₇	1	1	yes	characteristic, complemented
540	#489	C₂²×C₇	1	2	yes	complemented
541	#489	C₂²×C₇	1	2	yes	complemented
542	#489	C₂²×C₇	1	2	yes	complemented
543	#489	C₂²×C₇	1	2	yes	complemented
544	#485	C₂²×C₇	1	2	yes	complemented
545	#485	C₂²×C₇	1	2	yes	complemented
546	#484	C₂²×C₇	1	2	yes	complemented
547	#483	C₂²×C₇	1	2	yes	complemented
548	#482	C₂²×C₇	1	2	yes	complemented
549	#482	C₂²×C₇	1	2	yes	complemented
550	#481	C₂²×C₇	1	2	yes	complemented
551	#480	C₂²×C₇	1	2	yes	complemented
552	#477	C₂²×C₇	1	2	yes	complemented
553	#476	C₂²×C₇	1	2	yes	complemented
554	#475	C₂²×C₇	1	2	yes	complemented
555	#474	C₂²×C₇	1	2	yes	complemented
556	#470	C₂²×C₇	1	2	yes	complemented
557	#469	C₂²×C₇	1	2	yes	complemented
558	#468	C₂²×C₇	1	2	yes	complemented
559	#468	C₂²×C₇	1	2	yes	complemented
560	#467	C₂²×C₇	1	2	yes	complemented
561	#466	C₂²×C₇	1	2	yes	complemented
562	#465	C₂²×C₇	1	2	yes	complemented
563	#465	C₂²×C₇	1	2	yes	complemented
564	#464	C₂²×C₇	1	2	yes	complemented
565	#464	C₂²×C₇	1	2	yes	complemented
566	#463	C₂²×C₇	1	2	yes	complemented
567	#463	C₂²×C₇	1	2	yes	complemented
568	#452	C₂²×C₇	1	2	yes	—
569	#452	C₂²×C₇	1	2	yes	complemented
570	#451	C₂²×C₇	1	2	yes	complemented
571	#450	C₂²×C₇	1	2	yes	—
572	#449	C₂²×C₇	1	2	yes	—
573	#449	C₂²×C₇	1	2	yes	complemented
574	#448	C₂²×C₇	1	2	yes	complemented
575	#447	C₂²×C₇	1	2	yes	—
576	#442	C₂²×C₇	1	1	yes	characteristic, complemented
577	#442	C₂²×C₇	1	1	yes	characteristic, complemented
578	#441	C₂²×C₇	1	1	yes	characteristic, complemented
579	#441	C₂²×C₇	1	1	yes	characteristic, complemented
580	#440	C₂²×C₇	1	1	yes	characteristic, complemented
581	#440	C₂²×C₇	1	1	yes	characteristic, complemented
582	#440	C₂²×C₇	1	1	yes	characteristic, complemented
583	#440	C₂²×C₇	1	1	yes	characteristic, complemented
584	#435	C₂²×C₇	1	2	yes	complemented
585	#435	C₂²×C₇	1	2	yes	complemented
586	#435	C₂²×C₇	1	2	yes	complemented
587	#435	C₂²×C₇	1	2	yes	complemented
588	#428	C₂²×C₇	1	1	yes	characteristic, complemented
589	#428	C₂²×C₇	1	1	yes	characteristic, complemented
590	#427	C₂²×C₇	1	1	yes	characteristic, complemented
591	#423	C₂²×C₇	1	1	yes	characteristic, complemented
592	#419	C₂²×C₇	1	1	yes	characteristic, complemented
593	#419	C₂²×C₇	1	2	yes	complemented
594	#418	C₂²×C₇	1	1	yes	characteristic
595	#418	C₂²×C₇	1	2	yes	—
596	#417	C₂²×C₇	1	1	yes	characteristic
597	#417	C₂²×C₇	1	1	yes	characteristic
598	#417	C₂²×C₇	1	2	yes	—
599	#417	C₂²×C₇	1	2	yes	complemented
600	#416	C₂²×C₇	1	1	yes	characteristic
601	#416	C₂²×C₇	1	2	yes	—
602	#416	C₂²×C₇	1	2	yes	complemented
603	#416	C₂²×C₇	1	1	yes	characteristic, complemented
604	C₂×#103	C₂²×C₇	1	1	yes	characteristic, complemented
605	C₂×#103	C₂²×C₇	1	1	yes	characteristic, complemented
606	C₂×#103	C₂²×C₇	1	2	yes	complemented
607	C₂×#102	C₂²×C₇	1	1	yes	characteristic
608	C₂×#102	C₂²×C₇	1	1	yes	characteristic
609	C₂×#102	C₂²×C₇	1	2	yes	—
610	#408	C₂²×C₇	1	1	yes	characteristic
611	#408	C₂²×C₇	1	1	yes	characteristic, complemented
612	C₂×#97	C₂²×C₇	1	1	yes	characteristic, complemented
613	C₂³×C₇	—	2	1	no	—
614	C₂³×C₇	—	2	1	no	—
615	C₂³×C₇	—	2	2	no	—
616	C₂³×C₇	—	4	4	no	—
617	C₂³×C₇	—	4	2	no	—
618	C₂³×C₇	—	8	1	no	—
619	C₂³×C₇	—	8	1	no	—
620	C₂³×C₇	—	8	2	no	—
621	C₂³×C₇	—	8	2	no	—
622	C₂³×C₇	C₂²×D₄	1	2	yes	—
623	C₂³×C₇	C₂²×D₄	1	2	yes	—
624	C₂³×C₇	C₂²×D₄	1	1	yes	characteristic
625	C₇×Q₈	—	2	2	no	—
626	C₇×Q₈	—	2	2	no	—
627	C₇×Q₈	—	2	1	no	—
628	C₇×Q₈	—	2	1	no	—
629	C₇×Q₈	—	2	2	no	—
630	C₇×Q₈	—	2	1	no	—
631	C₇×Q₈	—	2	2	no	—
632	C₇×Q₈	—	4	4	no	—
633	C₇×Q₈	—	4	4	no	—
634	C₇×Q₈	—	4	2	no	—
635	C₇×Q₈	—	8	2	no	—
636	C₇×Q₈	C₂×#41	1	2	yes	—
637	C₇×D₄	—	2	4	no	—
638	C₇×D₄	—	2	4	no	—
639	C₇×D₄	—	2	4	no	—
640	C₇×D₄	—	2	2	no	—
641	C₇×D₄	—	2	2	no	—
642	C₇×D₄	—	2	1	no	—
643	C₇×D₄	—	2	2	no	—
644	C₇×D₄	—	2	1	no	—
645	C₇×D₄	—	2	1	no	—
646	C₇×D₄	—	2	2	no	—
647	C₇×D₄	—	4	2	no	—
648	C₇×D₄	—	4	2	no	—
649	C₇×D₄	—	4	4	no	—
650	C₇×D₄	—	4	4	no	—
651	C₇×D₄	—	4	4	no	—
652	C₇×D₄	—	4	2	no	—
653	C₇×D₄	—	4	2	no	—
654	C₇×D₄	—	8	2	no	—
655	C₇×D₄	—	8	2	no	—
656	C₇×D₄	—	8	2	no	—
657	C₇×D₄	—	8	2	no	—
658	C₇×D₄	C₂×#41	1	2	yes	—
659	C₂×C₄×C₇	—	2	1	no	—
660	C₂×C₄×C₇	—	2	4	no	—
661	C₂×C₄×C₇	—	2	2	no	—
662	C₂×C₄×C₇	—	2	2	no	—
663	C₂×C₄×C₇	—	2	2	no	—
664	C₂×C₄×C₇	—	2	2	no	—
665	C₂×C₄×C₇	—	2	1	no	—
666	C₂×C₄×C₇	—	2	1	no	—
667	C₂×C₄×C₇	—	2	1	no	—
668	C₂×C₄×C₇	—	2	1	no	—
669	C₂×C₄×C₇	—	2	1	no	—
670	C₂×C₄×C₇	—	2	2	no	—
671	C₂×C₄×C₇	—	2	2	no	—
672	C₂×C₄×C₇	—	2	2	no	—
673	C₂×C₄×C₇	—	4	1	no	—
674	C₂×C₄×C₇	—	4	1	no	—
675	C₂×C₄×C₇	—	4	4	no	—
676	C₂×C₄×C₇	—	4	4	no	—
677	C₂×C₄×C₇	—	4	4	no	—
678	C₂×C₄×C₇	—	4	2	no	—
679	C₂×C₄×C₇	—	4	2	no	—
680	C₂×C₄×C₇	—	4	2	no	—
681	C₂×C₄×C₇	—	4	2	no	—
682	C₂×C₄×C₇	—	8	1	no	—
683	C₂×C₄×C₇	—	8	1	no	—
684	C₂×C₄×C₇	—	8	1	no	—
685	C₂×C₄×C₇	—	8	1	no	—
686	C₂×C₄×C₇	—	8	2	no	—
687	C₂×C₄×C₇	—	8	2	no	—
688	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
689	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
690	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
691	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
692	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
693	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
694	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
695	C₂×C₄×C₇	C₂×#41	1	2	yes	—
696	C₂×C₄×C₇	H(5,𝔽₂)	1	2	yes	—
697	C₂×C₄×C₇	C₂⁵	1	1	yes	characteristic
698	C₇×C₈	—	2	1	no	—
699	C₇×C₈	—	2	1	no	—
700	C₇×C₈	—	2	1	no	—
701	C₇×C₈	—	2	1	no	—
702	C₇×C₈	—	2	2	no	—
703	C₇×C₈	—	2	2	no	—
704	2₋¹⁺⁴	—	2	4	no	—
705	2₋¹⁺⁴	—	4	2	no	—
706	H(5,𝔽₂)	—	2	4	no	—
707	H(5,𝔽₂)	—	4	2	no	—
708	C₂×#41	—	2	1	no	—
709	C₂×#41	—	2	1	no	—
710	C₂×#41	—	2	2	no	—
711	C₂×#41	—	2	2	no	—
712	C₂×#41	C₂³×C₇	1	1	yes	characteristic
713	C₂×#41	C₂³×C₇	1	2	yes	—
714	C₂×#41	C₂³×C₇	1	2	yes	—
715	C₂×#41	C₂³×C₇	1	1	yes	characteristic
716	C₂×#41	C₂³×C₇	1	1	yes	characteristic
717	C₂×#41	C₂³×C₇	1	1	yes	characteristic
718	C₂²×Q₈	—	2	1	no	—
719	C₂²×Q₈	—	2	1	no	—
720	C₂²×Q₈	C₂³×C₇	1	1	yes	characteristic
721	C₂²×Q₈	C₂³×C₇	1	2	yes	—
722	C₂²×D₄	—	2	1	no	—
723	C₂²×D₄	—	2	2	no	—
724	C₂²×D₄	C₂³×C₇	1	1	yes	characteristic
725	C₂²×D₄	C₂³×C₇	1	2	yes	—
726	#137	—	4	2	no	—
727	AGL(1,ℤ/8)	—	4	2	no	—
728	#135	—	2	4	no	—
729	C₂×Q₁₆	C₂³×C₇	1	1	yes	characteristic
730	C₂×Q₁₆	C₂³×C₇	1	2	yes	—
731	C₂×SD₁₆	C₂³×C₇	1	1	yes	characteristic
732	C₂×SD₁₆	C₂³×C₇	1	1	yes	characteristic
733	C₂×SD₁₆	C₂³×C₇	1	2	yes	—
734	C₂×SD₁₆	C₂³×C₇	1	2	yes	—
735	C₂×D₈	C₂³×C₇	1	1	yes	characteristic
736	C₂×D₈	C₂³×C₇	1	2	yes	—
737	#131	—	4	2	no	—
738	#131	—	4	2	no	—
739	C₂×M₁₆	C₂³×C₇	1	1	yes	characteristic
740	C₂×M₁₆	C₂³×C₇	1	1	yes	characteristic
741	C₂×M₁₆	C₂³×C₇	1	2	yes	—
742	C₂×M₁₆	C₂³×C₇	1	2	yes	—
743	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
744	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
745	C₂²×C₈	C₂³×C₇	1	2	yes	—
746	C₂²×C₈	C₂³×C₇	1	2	yes	—
747	C₄⋊Q₈	—	2	1	no	—
748	C₄⋊Q₈	—	2	1	no	—
749	C₄⋊Q₈	—	2	1	no	—
750	C₄⋊Q₈	C₇×D₄	1	1	yes	characteristic
751	C₄⋊Q₈	C₂³×C₇	1	2	yes	—
752	C₄⋊Q₈	C₂³×C₇	1	2	yes	—
753	#127	—	2	1	no	—
754	#127	C₇×D₄	1	1	yes	characteristic
755	#126	—	2	2	no	—
756	#126	—	2	2	no	—
757	#125	—	2	2	no	—
758	#124	—	2	1	no	—
759	#124	—	2	1	no	—
760	#124	—	2	2	no	—
761	#124	—	2	2	no	—
762	#124	—	2	2	no	—
763	#124	—	2	2	no	—
764	#124	—	2	2	no	—
765	#124	—	2	1	no	—
766	#124	—	2	1	no	—
767	#124	C₇×D₄	1	1	yes	characteristic
768	#124	C₇×D₄	1	1	yes	characteristic
769	#124	C₂³×C₇	1	2	yes	—
770	#124	C₂³×C₇	1	2	yes	—
771	#123	—	2	2	no	—
772	#123	—	2	2	no	—
773	#123	—	2	2	no	—
774	#123	—	2	2	no	—
775	#123	—	2	2	no	—
776	C₂²⋊Q₈	—	2	1	no	—
777	C₂²⋊Q₈	—	2	1	no	—
778	C₂²⋊Q₈	—	2	2	no	—
779	C₂²⋊Q₈	—	2	2	no	—
780	C₂²⋊Q₈	—	2	2	no	—
781	C₂²⋊Q₈	—	2	2	no	—
782	C₂²⋊Q₈	—	2	2	no	—
783	C₂²⋊Q₈	C₂³×C₇	1	2	yes	—
784	C₂²⋊Q₈	C₂³×C₇	1	2	yes	—
785	C₂²⋊Q₈	C₂³×C₇	1	2	yes	—
786	C₂²⋊Q₈	C₂³×C₇	1	2	yes	—
787	#121	—	2	1	no	—
788	#121	—	2	1	no	—
789	#121	—	2	2	no	—
790	#121	—	2	2	no	—
791	#121	—	2	2	no	—
792	#121	—	2	2	no	—
793	#121	—	2	2	no	—
794	#121	—	2	2	no	—
795	#121	—	2	2	no	—
796	#121	C₇×D₄	1	2	yes	—
797	#121	C₇×D₄	1	2	yes	—
798	#121	C₂³×C₇	1	2	yes	—
799	#121	C₂³×C₇	1	2	yes	—
800	#121	C₂³×C₇	1	2	yes	—
801	#121	C₂³×C₇	1	2	yes	—
802	#120	—	2	2	no	—
803	#120	—	2	2	no	—
804	#120	—	2	2	no	—
805	C₄×Q₈	—	2	1	no	—
806	C₄×Q₈	—	2	1	no	—
807	C₄×Q₈	—	2	2	no	—
808	C₄×Q₈	C₂³×C₇	1	1	yes	characteristic
809	C₄×Q₈	C₂³×C₇	1	1	yes	characteristic
810	C₄×Q₈	C₂³×C₇	1	1	yes	characteristic
811	C₄×Q₈	C₂³×C₇	1	1	yes	characteristic
812	C₄×D₄	—	2	1	no	—
813	C₄×D₄	—	2	2	no	—
814	C₄×D₄	—	2	1	no	—
815	C₄×D₄	—	2	2	no	—
816	C₄×D₄	—	2	2	no	—
817	C₄×D₄	—	2	1	no	—
818	C₄×D₄	—	2	1	no	—
819	C₄×D₄	—	2	1	no	—
820	C₄×D₄	—	2	1	no	—
821	C₄×D₄	—	2	2	no	—
822	C₄×D₄	—	2	2	no	—
823	C₄×D₄	C₂³×C₇	1	1	yes	characteristic
824	C₄×D₄	C₂³×C₇	1	1	yes	characteristic
825	C₄×D₄	C₂³×C₇	1	1	yes	characteristic
826	C₄×D₄	C₂³×C₇	1	1	yes	characteristic
827	C₄×D₄	C₂³×C₇	1	2	yes	—
828	C₄×D₄	C₂³×C₇	1	2	yes	—
829	#117	—	2	2	no	—
830	#117	—	2	1	no	—
831	#117	—	2	1	no	—
832	#117	C₂³×C₇	1	1	yes	characteristic
833	#117	C₂³×C₇	1	1	yes	characteristic
834	#117	C₂³×C₇	1	2	yes	—
835	#117	C₂³×C₇	1	2	yes	—
836	C₂×C₄⋊C₄	—	2	1	no	—
837	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
838	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
839	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
840	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
841	C₂×C₂²⋊C₄	—	2	1	no	—
842	C₂×C₂²⋊C₄	—	2	1	no	—
843	C₂×C₂²⋊C₄	—	2	2	no	—
844	C₂×C₂²⋊C₄	—	2	2	no	—
845	C₂×C₄²	—	2	1	no	—
846	C₂×C₄²	—	2	1	no	—
847	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
848	#107	C₂³×C₇	1	1	yes	characteristic
849	#107	C₂³×C₇	1	1	yes	characteristic
850	#107	C₂³×C₇	1	2	yes	—
851	#107	C₂³×C₇	1	2	yes	—
852	#106	C₂³×C₇	1	1	yes	characteristic
853	#106	C₂³×C₇	1	1	yes	characteristic
854	#106	C₂³×C₇	1	2	yes	—
855	#106	C₂³×C₇	1	2	yes	—
856	C₄⋊C₈	C₂³×C₇	1	2	yes	—
857	C₄⋊C₈	C₂³×C₇	1	2	yes	—
858	#103	C₂³×C₇	1	1	yes	characteristic
859	#103	C₂³×C₇	1	2	yes	—
860	#103	C₂³×C₇	1	2	yes	—
861	#103	C₂³×C₇	1	2	yes	—
862	#103	C₂³×C₇	1	2	yes	—
863	#103	C₂³×C₇	1	2	yes	—
864	#103	C₂³×C₇	1	2	yes	—
865	#103	C₂³×C₇	1	1	yes	characteristic
866	#103	C₂³×C₇	1	2	yes	—
867	#103	C₂³×C₇	1	2	yes	—
868	#103	C₂³×C₇	1	1	yes	characteristic
869	#103	C₂³×C₇	1	1	yes	characteristic
870	#102	C₂³×C₇	1	1	yes	characteristic
871	#102	C₂³×C₇	1	2	yes	—
872	#102	C₂³×C₇	1	2	yes	—
873	#102	C₂³×C₇	1	2	yes	—
874	#102	C₂³×C₇	1	2	yes	—
875	#102	C₂³×C₇	1	2	yes	—
876	#102	C₂³×C₇	1	2	yes	—
877	#102	C₂³×C₇	1	1	yes	characteristic
878	#102	C₂³×C₇	1	2	yes	—
879	#102	C₂³×C₇	1	2	yes	—
880	#102	C₂³×C₇	1	1	yes	characteristic
881	#102	C₂³×C₇	1	1	yes	characteristic
882	C₂²⋊C₈	C₂³×C₇	1	2	yes	—
883	C₂²⋊C₈	C₂³×C₇	1	2	yes	—
884	C₂²⋊C₈	C₂³×C₇	1	2	yes	—
885	C₂²⋊C₈	C₂³×C₇	1	2	yes	—
886	#97	C₂³×C₇	1	1	yes	characteristic
887	#97	C₂³×C₇	1	1	yes	characteristic
888	#97	C₂³×C₇	1	1	yes	characteristic
889	#97	C₂³×C₇	1	1	yes	characteristic
890	C₂²×C₇	—	2	1	no	—
891	C₂²×C₇	—	2	1	no	—
892	C₂²×C₇	—	2	2	no	—
893	C₂²×C₇	—	2	2	no	—
894	C₂²×C₇	—	2	2	no	—
895	C₂²×C₇	—	2	2	no	—
896	C₂²×C₇	—	2	2	no	—
897	C₂²×C₇	—	2	2	no	—
898	C₂²×C₇	—	2	2	no	—
899	C₂²×C₇	—	4	1	no	—
900	C₂²×C₇	—	4	1	no	—
901	C₂²×C₇	—	4	1	no	—
902	C₂²×C₇	—	4	2	no	—
903	C₂²×C₇	—	4	1	no	—
904	C₂²×C₇	—	4	2	no	—
905	C₂²×C₇	—	4	2	no	—
906	C₂²×C₇	—	4	1	no	—
907	C₂²×C₇	—	16	2	no	—
908	C₂²×C₇	—	16	4	no	—
909	C₂²×C₇	#546	1	2	yes	—
910	C₂²×C₇	C₂³×D₄	1	1	yes	characteristic
911	C₄×C₇	—	2	1	no	—
912	C₄×C₇	—	2	1	no	—
913	C₄×C₇	—	2	1	no	—
914	C₄×C₇	—	2	1	no	—
915	C₄×C₇	—	2	2	no	—
916	C₄×C₇	—	2	2	no	—
917	C₄×C₇	—	2	2	no	—
918	C₄×C₇	—	4	1	no	—
919	C₄×C₇	—	4	2	no	—
920	C₄×C₇	—	4	2	no	—
921	C₄×C₇	—	4	1	no	—
922	C₄×C₇	—	4	1	no	—
923	C₄×C₇	—	4	1	no	—
924	C₄×C₇	—	4	2	no	—
925	C₄×C₇	—	4	1	no	—
926	C₄×C₇	#546	1	2	yes	—
927	C₄×C₇	C₂²×#41	1	1	yes	characteristic
928	C₄×C₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
929	C₂⁴	—	2	2	no	—
930	C₂⁴	—	2	1	no	—
931	#41	—	2	2	no	—
932	#41	—	2	2	no	—
933	#41	—	2	2	no	—
934	#41	—	2	2	no	—
935	#41	—	2	2	no	—
936	#41	—	2	4	no	—
937	#41	—	2	4	no	—
938	#41	—	2	2	no	—
939	#41	—	2	2	no	—
940	#41	—	4	2	no	—
941	#41	—	4	2	no	—
942	#41	—	4	4	no	—
943	#41	—	4	4	no	—
944	#41	—	4	8	no	—
945	#41	—	8	4	no	—
946	#41	C₇×#41	1	4	yes	complemented
947	C₂×Q₈	—	2	2	no	—
948	C₂×Q₈	—	2	2	no	—
949	C₂×Q₈	—	2	1	no	—
950	C₂×Q₈	—	2	2	no	—
951	C₂×Q₈	—	2	4	no	—
952	C₂×Q₈	—	2	2	no	—
953	C₂×Q₈	—	2	2	no	—
954	C₂×Q₈	—	4	2	no	—
955	C₂×Q₈	—	4	4	no	—
956	C₂×Q₈	—	8	2	no	—
957	C₂×Q₈	C₂×C₇×D₄	1	1	yes	characteristic
958	C₂×Q₈	C₂×C₇×D₄	1	1	yes	characteristic
959	C₂×Q₈	C₂⁴×C₇	1	2	yes	—
960	C₂×Q₈	C₂⁴×C₇	1	1	yes	characteristic
961	C₂×Q₈	C₂⁴×C₇	1	1	yes	characteristic
962	C₂×D₄	—	2	1	no	—
963	C₂×D₄	—	2	4	no	—
964	C₂×D₄	—	2	1	no	—
965	C₂×D₄	—	2	2	no	—
966	C₂×D₄	—	2	2	no	—
967	C₂×D₄	—	2	2	no	—
968	C₂×D₄	—	2	2	no	—
969	C₂×D₄	—	2	2	no	—
970	C₂×D₄	—	2	2	no	—
971	C₂×D₄	—	2	2	no	—
972	C₂×D₄	—	2	1	no	—
973	C₂×D₄	—	2	2	no	—
974	C₂×D₄	—	2	2	no	—
975	C₂×D₄	—	4	2	no	—
976	C₂×D₄	—	4	4	no	—
977	C₂×D₄	—	4	8	no	—
978	C₂×D₄	C₂×C₇×D₄	1	2	yes	—
979	C₂×D₄	C₂×C₇×D₄	1	2	yes	—
980	C₂×D₄	C₂×C₇×D₄	1	1	yes	characteristic
981	C₂×D₄	C₂×C₇×D₄	1	1	yes	characteristic
982	C₂×D₄	C₂×C₇×D₄	1	2	yes	—
983	C₂×D₄	C₂×C₇×D₄	1	2	yes	—
984	C₂×D₄	C₂⁴×C₇	1	2	yes	—
985	C₂×D₄	C₂⁴×C₇	1	1	yes	characteristic
986	C₂×D₄	C₂⁴×C₇	1	1	yes	characteristic
987	C₂²×C₄	—	2	1	no	—
988	C₂²×C₄	—	2	1	no	—
989	C₂²×C₄	—	2	2	no	—
990	C₂²×C₄	—	2	1	no	—
991	C₂²×C₄	—	2	1	no	—
992	C₂²×C₄	—	2	2	no	—
993	C₂²×C₄	—	2	2	no	—
994	C₂²×C₄	—	2	1	no	—
995	C₂²×C₄	—	2	1	no	—
996	C₂²×C₄	—	2	1	no	—
997	C₂²×C₄	—	2	2	no	—
998	C₂²×C₄	—	2	2	no	—
999	C₂²×C₄	—	2	1	no	—
1000	C₂²×C₄	—	2	1	no	—
1001	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
1002	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
1003	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
1004	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
1005	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
1006	Q₁₆	—	2	2	no	—
1007	Q₁₆	—	4	2	no	—
1008	SD₁₆	—	2	2	no	—
1009	SD₁₆	—	2	2	no	—
1010	SD₁₆	—	4	2	no	—
1011	SD₁₆	—	4	2	no	—
1012	D₈	—	2	2	no	—
1013	D₈	—	4	2	no	—
1014	M₁₆	—	2	2	no	—
1015	M₁₆	—	2	2	no	—
1016	M₁₆	—	4	2	no	—
1017	M₁₆	—	4	2	no	—
1018	C₂×C₈	—	2	2	no	—
1019	C₂×C₈	—	2	2	no	—
1020	C₂×C₈	—	4	2	no	—
1021	C₂×C₈	—	4	2	no	—
1022	C₂×C₈	C₂⁴×C₇	1	1	yes	characteristic
1023	C₂×C₈	C₂⁴×C₇	1	1	yes	characteristic
1024	C₂×C₈	C₂⁴×C₇	1	1	yes	characteristic
1025	C₂×C₈	C₂⁴×C₇	1	1	yes	characteristic
1026	C₂×C₈	C₂⁴×C₇	1	2	yes	—
1027	C₂×C₈	C₂⁴×C₇	1	2	yes	—
1028	C₄⋊C₄	—	2	2	no	—
1029	C₄⋊C₄	—	2	2	no	—
1030	C₄⋊C₄	—	2	1	no	—
1031	C₄⋊C₄	—	2	1	no	—
1032	C₄⋊C₄	—	2	2	no	—
1033	C₄⋊C₄	—	2	2	no	—
1034	C₄⋊C₄	—	2	1	no	—
1035	C₄⋊C₄	—	2	1	no	—
1036	C₄⋊C₄	—	2	1	no	—
1037	C₄⋊C₄	—	2	1	no	—
1038	C₄⋊C₄	—	2	2	no	—
1039	C₄⋊C₄	—	2	2	no	—
1040	C₄⋊C₄	—	2	2	no	—
1041	C₄⋊C₄	—	2	2	no	—
1042	C₄⋊C₄	C₂×C₇×D₄	1	2	yes	—
1043	C₄⋊C₄	C₂×C₇×D₄	1	2	yes	—
1044	C₄⋊C₄	C₂⁴×C₇	1	1	yes	characteristic
1045	C₄⋊C₄	C₂⁴×C₇	1	2	yes	—
1046	C₄⋊C₄	C₂⁴×C₇	1	2	yes	—
1047	C₄⋊C₄	C₂⁴×C₇	1	1	yes	characteristic
1048	C₄⋊C₄	C₂⁴×C₇	1	1	yes	characteristic
1049	C₄⋊C₄	C₂⁴×C₇	1	1	yes	characteristic
1050	C₂²⋊C₄	—	2	2	no	—
1051	C₂²⋊C₄	—	2	2	no	—
1052	C₂²⋊C₄	—	2	1	no	—
1053	C₂²⋊C₄	—	2	1	no	—
1054	C₂²⋊C₄	—	2	2	no	—
1055	C₂²⋊C₄	—	2	2	no	—
1056	C₂²⋊C₄	—	2	2	no	—
1057	C₂²⋊C₄	—	2	2	no	—
1058	C₂²⋊C₄	—	2	2	no	—
1059	C₂²⋊C₄	—	2	2	no	—
1060	C₂²⋊C₄	—	2	2	no	—
1061	C₂²⋊C₄	—	2	2	no	—
1062	C₂²⋊C₄	—	2	2	no	—
1063	C₂²⋊C₄	—	2	2	no	—
1064	C₂²⋊C₄	—	2	1	no	—
1065	C₂²⋊C₄	—	2	1	no	—
1066	C₂²⋊C₄	—	2	1	no	—
1067	C₂²⋊C₄	—	2	1	no	—
1068	C₂²⋊C₄	—	2	2	no	—
1069	C₂²⋊C₄	—	2	2	no	—
1070	C₂²⋊C₄	C₂×C₇×D₄	1	2	yes	—
1071	C₂²⋊C₄	C₂×C₇×D₄	1	2	yes	—
1072	C₂²⋊C₄	C₂×C₇×D₄	1	2	yes	—
1073	C₂²⋊C₄	C₂×C₇×D₄	1	2	yes	—
1074	C₄²	—	2	1	no	—
1075	C₄²	—	2	1	no	—
1076	C₄²	—	2	1	no	—
1077	C₄²	—	2	1	no	—
1078	C₄²	—	2	1	no	—
1079	C₄²	—	2	1	no	—
1080	C₄²	—	2	2	no	—
1081	C₄²	—	2	2	no	—
1082	C₄²	C₂×C₇×D₄	1	1	yes	characteristic
1083	C₄²	C₂×C₇×D₄	1	1	yes	characteristic
1084	C₄²	C₂⁴×C₇	1	1	yes	characteristic
1085	C₄²	C₂⁴×C₇	1	1	yes	characteristic
1086	C₂×C₇	—	2	2	no	—
1087	C₂×C₇	—	4	2	no	—
1088	C₂×C₇	—	4	2	no	—
1089	C₂×C₇	—	4	2	no	—
1090	C₂×C₇	—	8	1	no	—
1091	C₂×C₇	—	8	2	no	—
1092	C₂×C₇	C₂×#546	1	1	yes	characteristic
1093	C₂×C₇	#3585	1	1	yes	characteristic
1094	C₂×C₇	#3586	1	1	yes	characteristic
1095	C₂³	—	2	1	no	—
1096	C₂³	—	2	1	no	—
1097	C₂³	—	2	2	no	—
1098	C₂³	—	4	4	no	—
1099	C₂³	—	4	2	no	—
1100	C₂³	—	8	1	no	—
1101	C₂³	—	8	1	no	—
1102	C₂³	—	8	2	no	—
1103	C₂³	—	8	2	no	—
1104	C₂³	C₂²×C₇×D₄	1	2	yes	—
1105	C₂³	C₂²×C₇×D₄	1	2	yes	—
1106	C₂³	C₂²×C₇×D₄	1	1	yes	characteristic
1107	Q₈	—	2	1	no	—
1108	Q₈	—	2	2	no	—
1109	Q₈	—	2	2	no	—
1110	Q₈	—	2	1	no	—
1111	Q₈	—	2	2	no	—
1112	Q₈	—	2	1	no	—
1113	Q₈	—	2	2	no	—
1114	Q₈	—	4	4	no	—
1115	Q₈	—	4	4	no	—
1116	Q₈	—	4	2	no	—
1117	Q₈	—	8	2	no	—
1118	Q₈	C₂×C₇×#41	1	2	yes	—
1119	D₄	—	2	4	no	—
1120	D₄	—	2	4	no	—
1121	D₄	—	2	4	no	—
1122	D₄	—	2	1	no	—
1123	D₄	—	2	2	no	—
1124	D₄	—	2	1	no	—
1125	D₄	—	2	1	no	—
1126	D₄	—	2	2	no	—
1127	D₄	—	2	2	no	—
1128	D₄	—	2	2	no	—
1129	D₄	—	4	2	no	—
1130	D₄	—	4	2	no	—
1131	D₄	—	4	4	no	—
1132	D₄	—	4	4	no	—
1133	D₄	—	4	4	no	—
1134	D₄	—	4	2	no	—
1135	D₄	—	4	2	no	—
1136	D₄	—	8	2	no	—
1137	D₄	—	8	2	no	—
1138	D₄	—	8	2	no	—
1139	D₄	—	8	2	no	—
1140	D₄	C₂×C₇×#41	1	2	yes	—
1141	C₂×C₄	—	2	1	no	—
1142	C₂×C₄	—	2	2	no	—
1143	C₂×C₄	—	2	2	no	—
1144	C₂×C₄	—	2	2	no	—
1145	C₂×C₄	—	2	2	no	—
1146	C₂×C₄	—	2	4	no	—
1147	C₂×C₄	—	2	1	no	—
1148	C₂×C₄	—	2	1	no	—
1149	C₂×C₄	—	2	1	no	—
1150	C₂×C₄	—	2	1	no	—
1151	C₂×C₄	—	2	1	no	—
1152	C₂×C₄	—	2	2	no	—
1153	C₂×C₄	—	2	2	no	—
1154	C₂×C₄	—	2	2	no	—
1155	C₂×C₄	—	4	1	no	—
1156	C₂×C₄	—	4	1	no	—
1157	C₂×C₄	—	4	4	no	—
1158	C₂×C₄	—	4	4	no	—
1159	C₂×C₄	—	4	4	no	—
1160	C₂×C₄	—	4	2	no	—
1161	C₂×C₄	—	4	2	no	—
1162	C₂×C₄	—	4	2	no	—
1163	C₂×C₄	—	4	2	no	—
1164	C₂×C₄	—	8	1	no	—
1165	C₂×C₄	—	8	1	no	—
1166	C₂×C₄	—	8	1	no	—
1167	C₂×C₄	—	8	1	no	—
1168	C₂×C₄	—	8	2	no	—
1169	C₂×C₄	—	8	2	no	—
1170	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
1171	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
1172	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
1173	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
1174	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
1175	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
1176	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
1177	C₂×C₄	C₂×C₇×#41	1	2	yes	—
1178	C₂×C₄	C₇×H(5,𝔽₂)	1	2	yes	—
1179	C₂×C₄	C₂⁵×C₇	1	1	yes	characteristic
1180	C₈	—	2	1	no	—
1181	C₈	—	2	1	no	—
1182	C₈	—	2	1	no	—
1183	C₈	—	2	1	no	—
1184	C₈	—	2	2	no	—
1185	C₈	—	2	2	no	—
1186	C₇	#61222	1	1	yes	characteristic, direct product factor, Sylow
1187	C₂²	—	2	1	no	—
1188	C₂²	—	2	1	no	—
1189	C₂²	—	2	2	no	—
1190	C₂²	—	2	2	no	—
1191	C₂²	—	2	2	no	—
1192	C₂²	—	2	2	no	—
1193	C₂²	—	2	2	no	—
1194	C₂²	—	2	2	no	—
1195	C₂²	—	2	2	no	—
1196	C₂²	—	4	1	no	—
1197	C₂²	—	4	1	no	—
1198	C₂²	—	4	1	no	—
1199	C₂²	—	4	2	no	—
1200	C₂²	—	4	1	no	—
1201	C₂²	—	4	2	no	—
1202	C₂²	—	4	2	no	—
1203	C₂²	—	4	1	no	—
1204	C₂²	—	16	2	no	—
1205	C₂²	—	16	4	no	—
1206	C₂²	C₇×#546	1	2	yes	—
1207	C₂²	C₂³×C₇×D₄	1	1	yes	characteristic
1208	C₄	—	2	1	no	—
1209	C₄	—	2	1	no	—
1210	C₄	—	2	1	no	—
1211	C₄	—	2	1	no	—
1212	C₄	—	2	2	no	—
1213	C₄	—	2	2	no	—
1214	C₄	—	2	2	no	—
1215	C₄	—	4	1	no	—
1216	C₄	—	4	2	no	—
1217	C₄	—	4	2	no	—
1218	C₄	—	4	1	no	—
1219	C₄	—	4	1	no	—
1220	C₄	—	4	1	no	—
1221	C₄	—	4	2	no	—
1222	C₄	—	4	1	no	—
1223	C₄	C₇×#546	1	2	yes	—
1224	C₄	C₂²×C₇×#41	1	1	yes	characteristic
1225	C₄	C₂×C₇×H(5,𝔽₂)	1	1	yes	characteristic
1226	C₂	—	2	2	no	—
1227	C₂	—	4	2	no	—
1228	C₂	—	4	2	no	—
1229	C₂	—	4	2	no	—
1230	C₂	—	8	2	no	—
1231	C₂	—	8	1	no	—
1232	C₂	C₂×C₇×#546	1	1	yes	characteristic
1233	C₂	C₇×#3585	1	1	yes	characteristic
1234	C₂	C₇×#3586	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₇	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₇
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₇ ◁ C₇×#532 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₇×#3511	C₂	semidirect
2. C₇×#3500	C₂	semidirect
3. C₇×#3321	C₂	semidirect
4. C₇×#3319	C₂	semidirect
5. C₇×#3316	C₂	semidirect
6. C₇×#3314	C₂	semidirect
7. C₇×#3313	C₂	semidirect
8. C₇×#3311	C₂	semidirect
9. C₇×#3308	C₂	semidirect
10. C₇×#3306	C₂	semidirect
11. C₂×C₇×#489	C₂	semidirect
12. C₇×#3097	C₂	semidirect
13. C₇×#3096	C₂	semidirect
14. C₇×#3079	C₂	semidirect
15. C₇×#3063	C₂	semidirect
16. C₇×#3062	C₂	semidirect
17. C₇×#3040	C₂	semidirect
18. C₇×#3013	C₂	semidirect
19. C₇×#3012	C₂	semidirect
20. C₇×#2943	C₂	semidirect
21. C₇×#2932	C₂	semidirect
22. C₇×#2898	C₂	semidirect
23. C₇×#2897	C₂	semidirect
26. C₂×C₇×#137	C₂²	semidirect
30. C₂×C₇×#131	C₂²	semidirect
31. C₇×#556	C₂²	semidirect
32. C₇×#555	C₂²	semidirect
33. C₇×#554	C₂²	semidirect
38. C₇×#547	C₂²	semidirect
46. C₇×#537	C₂²	semidirect
55. C₂×C₇×C₄⋊Q₈	C₂²	semidirect
59. C₇×#520	C₂²	semidirect
61. C₄×C₇×#41	C₂²	semidirect
62. C₇×#489	C₂²	semidirect
63. C₇×#489	C₂²	semidirect
64. C₇×#489	C₂²	semidirect
65. C₇×#489	C₂²	semidirect
66. C₇×#485	C₂²	semidirect
67. C₇×#485	C₂²	semidirect
68. C₇×#484	C₂²	semidirect
69. C₇×#483	C₂²	semidirect
70. C₇×#482	C₂²	semidirect
71. C₇×#482	C₂²	semidirect
72. C₇×#481	C₂²	semidirect
73. C₇×#480	C₂²	semidirect
74. C₇×#477	C₂²	semidirect
75. C₇×#476	C₂²	semidirect
76. C₇×#475	C₂²	semidirect
77. C₇×#474	C₂²	semidirect
78. C₇×#470	C₂²	semidirect
79. C₇×#469	C₂²	semidirect
80. C₇×#468	C₂²	semidirect
81. C₇×#468	C₂²	semidirect
82. C₇×#467	C₂²	semidirect
83. C₇×#466	C₂²	semidirect
84. C₇×#465	C₂²	semidirect
85. C₇×#465	C₂²	semidirect
86. C₇×#464	C₂²	semidirect
87. C₇×#464	C₂²	semidirect
88. C₇×#463	C₂²	semidirect
89. C₇×#463	C₂²	semidirect
91. C₇×#452	C₂²	semidirect
92. C₇×#451	C₂²	semidirect
95. C₇×#449	C₂²	semidirect
96. C₇×#448	C₂²	semidirect
98. C₇×#442	C₂²	semidirect
99. C₇×#442	C₂²	semidirect
100. C₇×#441	C₂²	semidirect
101. C₇×#441	C₂²	semidirect
102. C₇×#440	C₂²	semidirect
103. C₇×#440	C₂²	semidirect
104. C₇×#440	C₂²	semidirect
105. C₇×#440	C₂²	semidirect
106. C₇×#435	C₂²	semidirect
107. C₇×#435	C₂²	semidirect
108. C₇×#435	C₂²	semidirect
109. C₇×#435	C₂²	semidirect
110. C₇×#428	C₂²	semidirect
111. C₇×#428	C₂²	semidirect
112. C₇×#427	C₂²	semidirect
113. C₇×#423	C₂²	semidirect
114. C₇×#419	C₂²	semidirect
115. C₇×#419	C₂²	semidirect
121. C₇×#417	C₂²	semidirect
124. C₇×#416	C₂²	semidirect
125. C₇×#416	C₂²	semidirect
126. C₂×C₇×#103	C₂²	semidirect
127. C₂×C₇×#103	C₂²	semidirect
128. C₂×C₇×#103	C₂²	semidirect
133. C₇×#408	C₂²	semidirect
134. C₂×C₇×#97	C₂²	semidirect
135. #61222	C₇	direct (N × H)
322. #3511	C₂×C₇	semidirect
323. #3500	C₂×C₇	semidirect
324. #3321	C₂×C₇	semidirect
325. #3319	C₂×C₇	semidirect
326. #3316	C₂×C₇	semidirect
327. #3314	C₂×C₇	semidirect
328. #3313	C₂×C₇	semidirect
329. #3311	C₂×C₇	semidirect
330. #3308	C₂×C₇	semidirect
331. #3306	C₂×C₇	semidirect
332. C₂×#489	C₂×C₇	semidirect
333. #3097	C₂×C₇	semidirect
334. #3096	C₂×C₇	semidirect
335. #3079	C₂×C₇	semidirect
336. #3063	C₂×C₇	semidirect
337. #3062	C₂×C₇	semidirect
338. #3040	C₂×C₇	semidirect
339. #3013	C₂×C₇	semidirect
340. #3012	C₂×C₇	semidirect
341. #2943	C₂×C₇	semidirect
342. #2932	C₂×C₇	semidirect
343. #2898	C₂×C₇	semidirect
344. #2897	C₂×C₇	semidirect
362. C₇×#41	#41	semidirect
504. C₂×#137	C₂²×C₇	semidirect
508. C₂×#131	C₂²×C₇	semidirect
509. #556	C₂²×C₇	semidirect
510. #555	C₂²×C₇	semidirect
511. #554	C₂²×C₇	semidirect
516. #547	C₂²×C₇	semidirect
524. #537	C₂²×C₇	semidirect
533. C₂×C₄⋊Q₈	C₂²×C₇	semidirect
537. #520	C₂²×C₇	semidirect
539. C₄×#41	C₂²×C₇	semidirect
540. #489	C₂²×C₇	semidirect
541. #489	C₂²×C₇	semidirect
542. #489	C₂²×C₇	semidirect
543. #489	C₂²×C₇	semidirect
544. #485	C₂²×C₇	semidirect
545. #485	C₂²×C₇	semidirect
546. #484	C₂²×C₇	semidirect
547. #483	C₂²×C₇	semidirect
548. #482	C₂²×C₇	semidirect
549. #482	C₂²×C₇	semidirect
550. #481	C₂²×C₇	semidirect
551. #480	C₂²×C₇	semidirect
552. #477	C₂²×C₇	semidirect
553. #476	C₂²×C₇	semidirect
554. #475	C₂²×C₇	semidirect
555. #474	C₂²×C₇	semidirect
556. #470	C₂²×C₇	semidirect
557. #469	C₂²×C₇	semidirect
558. #468	C₂²×C₇	semidirect
559. #468	C₂²×C₇	semidirect
560. #467	C₂²×C₇	semidirect
561. #466	C₂²×C₇	semidirect
562. #465	C₂²×C₇	semidirect
563. #465	C₂²×C₇	semidirect
564. #464	C₂²×C₇	semidirect
565. #464	C₂²×C₇	semidirect
566. #463	C₂²×C₇	semidirect
567. #463	C₂²×C₇	semidirect
569. #452	C₂²×C₇	semidirect
570. #451	C₂²×C₇	semidirect
573. #449	C₂²×C₇	semidirect
574. #448	C₂²×C₇	semidirect
576. #442	C₂²×C₇	semidirect
577. #442	C₂²×C₇	semidirect
578. #441	C₂²×C₇	semidirect
579. #441	C₂²×C₇	semidirect
580. #440	C₂²×C₇	semidirect
581. #440	C₂²×C₇	semidirect
582. #440	C₂²×C₇	semidirect
583. #440	C₂²×C₇	semidirect
584. #435	C₂²×C₇	semidirect
585. #435	C₂²×C₇	semidirect
586. #435	C₂²×C₇	semidirect
587. #435	C₂²×C₇	semidirect
588. #428	C₂²×C₇	semidirect
589. #428	C₂²×C₇	semidirect
590. #427	C₂²×C₇	semidirect
591. #423	C₂²×C₇	semidirect
592. #419	C₂²×C₇	semidirect
593. #419	C₂²×C₇	semidirect
599. #417	C₂²×C₇	semidirect
602. #416	C₂²×C₇	semidirect
603. #416	C₂²×C₇	semidirect
604. C₂×#103	C₂²×C₇	semidirect
605. C₂×#103	C₂²×C₇	semidirect
606. C₂×#103	C₂²×C₇	semidirect
611. #408	C₂²×C₇	semidirect
612. C₂×#97	C₂²×C₇	semidirect
946. #41	C₇×#41	semidirect
1186. C₇	#61222	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×#3511	2
C₇×#3500	2
C₇×#3321	2
C₇×#3319	2
C₇×#3316	2
C₇×#3314	2
C₇×#3313	2
C₇×#3311	2
C₇×#3308	2
C₇×#3306	2
C₂×C₇×#489	2
C₇×#3097	2
C₇×#3096	2
C₇×#3079	2
C₇×#3063	2
C₇×#3062	2
C₇×#3040	2
C₇×#3013	2
C₇×#3012	2
C₇×#2943	2
C₇×#2932	2
C₇×#2898	2
C₇×#2897	2
#61222	7

Subgroups — C7×#61222 #13238438

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×#61222 #13238438