Subgroups — C₇×#62044 #13239260

Order 1792.

1830 conjugacy classes of subgroups.

The subgroup lattice has 1164 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×#3546	C₂	1	1	yes	maximal, characteristic
2	C₇×#3523	C₂	1	1	yes	maximal, characteristic, complemented
3	C₇×#3398	C₂	1	1	yes	maximal, characteristic, complemented
4	C₇×#3392	C₂	1	1	yes	maximal, characteristic, complemented
5	C₇×#3368	C₂	1	1	yes	maximal, characteristic, complemented
6	C₇×#3364	C₂	1	1	yes	maximal, characteristic, complemented
7	C₇×#3324	C₂	1	1	yes	maximal, characteristic, complemented
8	C₇×#3323	C₂	1	2	yes	maximal, complemented
9	C₇×#3317	C₂	1	2	yes	maximal, complemented
10	C₇×#3302	C₂	1	1	yes	maximal, characteristic, complemented
11	C₇×D₄×SD₁₆	C₂	1	1	yes	maximal, characteristic, complemented
12	C₇×#3278	C₂	1	2	yes	maximal, complemented
13	C₇×#3276	C₂	1	1	yes	maximal, characteristic, complemented
14	C₇×#3266	C₂	1	2	yes	maximal, complemented
15	C₇×#3258	C₂	1	2	yes	maximal, complemented
16	C₇×#3254	C₂	1	1	yes	maximal, characteristic, complemented
17	C₇×#3222	C₂	1	2	yes	maximal, complemented
18	C₇×#3210	C₂	1	1	yes	maximal, characteristic, complemented
19	C₇×#3121	C₂	1	2	yes	maximal, complemented
20	C₇×#3103	C₂	1	1	yes	maximal, characteristic, complemented
21	C₇×#3043	C₂	1	2	yes	maximal, complemented
22	C₇×#3037	C₂	1	1	yes	maximal, characteristic, complemented
23	C₇×#2993	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×C₇×#137	C₂²	1	2	yes	complemented
25	C₂×C₇×#137	C₂²	1	2	yes	complemented
26	C₂²×C₇×SD₁₆	C₂²	1	2	yes	—
27	C₇×#560	—	2	2	no	—
28	C₇×#557	—	2	1	no	—
29	C₇×#557	C₂²	1	1	yes	characteristic, complemented
30	C₇×#557	C₂²	1	1	yes	characteristic, complemented
31	C₇×#556	—	2	1	no	—
32	C₇×#556	C₂²	1	1	yes	characteristic
33	C₇×#556	C₂²	1	1	yes	characteristic
34	C₇×#553	—	2	1	no	—
35	C₇×#552	—	2	2	no	—
36	C₇×#552	C₂²	1	2	yes	complemented
37	C₇×#550	C₂²	1	2	yes	—
38	C₇×#550	C₂²	1	1	yes	characteristic
39	C₇×D₄×Q₈	C₂²	1	1	yes	characteristic
40	C₇×D₄×Q₈	C₂²	1	2	yes	complemented
41	C₇×#547	C₂²	1	1	yes	characteristic
42	C₇×#546	—	2	1	no	—
43	C₇×#546	C₂²	1	2	yes	—
44	C₇×D₄²	C₂²	1	1	yes	characteristic
45	C₇×#542	C₂²	1	2	yes	—
46	C₇×#541	—	2	2	no	—
47	C₇×#541	C₂²	1	2	yes	complemented
48	C₇×#538	—	2	2	no	—
49	C₇×#537	—	2	1	no	—
50	C₇×#535	—	2	1	no	—
51	C₇×#535	C₂²	1	2	yes	—
52	C₇×#533	—	2	1	no	—
53	C₇×#533	C₂²	1	1	yes	characteristic, complemented
54	C₇×#532	C₂²	1	1	yes	characteristic
55	C₇×#532	C₂²	1	1	yes	characteristic
56	C₇×#529	—	2	1	no	—
57	C₇×#529	C₂²	1	1	yes	characteristic
58	C₇×#519	C₂²	1	2	yes	complemented
59	C₂×C₄×C₇×Q₈	C₂²	1	1	yes	characteristic, complemented
60	C₇×#497	C₂²	1	2	yes	—
61	C₇×#494	C₂²	1	1	yes	characteristic, complemented
62	C₇×#492	C₂²	1	1	yes	characteristic
63	C₇×#492	C₂²	1	2	yes	complemented
64	C₇×#490	C₂²	1	2	yes	complemented
65	C₇×#488	C₂²	1	2	yes	—
66	C₇×#487	C₂²	1	1	yes	characteristic, complemented
67	C₇×#486	C₂²	1	1	yes	characteristic
68	C₇×#485	C₂²	1	2	yes	complemented
69	C₇×#482	C₂²	1	2	yes	—
70	C₇×#481	C₂²	1	1	yes	characteristic
71	C₇×#481	C₂²	1	1	yes	characteristic, complemented
72	C₇×#479	C₂²	1	2	yes	complemented
73	C₇×#478	C₂²	1	2	yes	complemented
74	C₇×#477	C₂²	1	2	yes	complemented
75	C₇×#475	C₂²	1	1	yes	characteristic, complemented
76	C₇×#475	C₂²	1	1	yes	characteristic, complemented
77	C₇×#474	C₂²	1	1	yes	characteristic
78	C₇×#474	C₂²	1	1	yes	characteristic, complemented
79	C₇×#470	C₂²	1	2	yes	complemented
80	C₇×#468	C₂²	1	2	yes	—
81	C₇×#468	C₂²	1	2	yes	—
82	C₇×#468	C₂²	1	2	yes	complemented
83	C₇×#467	C₂²	1	2	yes	complemented
84	C₇×#465	C₂²	1	2	yes	—
85	C₇×#464	C₂²	1	2	yes	—
86	C₇×#464	C₂²	1	2	yes	—
87	C₇×#464	C₂²	1	2	yes	complemented
88	C₇×#464	C₂²	1	2	yes	complemented
89	C₇×#464	C₂²	1	2	yes	complemented
90	C₇×#464	C₂²	1	2	yes	complemented
91	C₇×#462	C₂²	1	2	yes	complemented
92	C₇×#462	C₂²	1	1	yes	characteristic, complemented
93	C₇×#462	C₂²	1	1	yes	characteristic, complemented
94	C₇×#461	C₂²	1	1	yes	characteristic
95	C₇×#461	C₂²	1	1	yes	characteristic, complemented
96	C₇×#461	C₂²	1	2	yes	complemented
97	C₇×#460	C₂²	1	1	yes	characteristic
98	C₇×#460	C₂²	1	2	yes	—
99	C₇×#460	C₂²	1	1	yes	characteristic
100	C₇×#460	C₂²	1	1	yes	characteristic
101	C₇×#460	C₂²	1	1	yes	characteristic
102	C₇×#460	C₂²	1	2	yes	complemented
103	C₇×#460	C₂²	1	2	yes	complemented
104	C₇×#452	C₂²	1	2	yes	complemented
105	C₇×#452	C₂²	1	2	yes	complemented
106	C₇×#452	C₂²	1	2	yes	complemented
107	C₇×#452	C₂²	1	2	yes	complemented
108	C₇×#451	C₂²	1	2	yes	complemented
109	C₇×#450	C₂²	1	2	yes	—
110	C₇×#450	C₂²	1	2	yes	—
111	C₇×#448	C₂²	1	1	yes	characteristic
112	C₇×#448	C₂²	1	2	yes	—
113	C₇×#448	C₂²	1	1	yes	characteristic, complemented
114	C₇×#446	C₂²	1	1	yes	characteristic, complemented
115	C₇×C₈×Q₈	C₂²	1	1	yes	characteristic, complemented
116	C₇×#441	C₂²	1	2	yes	complemented
117	C₇×#440	C₂²	1	2	yes	complemented
118	C₄×C₇×Q₁₆	C₂²	1	2	yes	complemented
119	C₄×C₇×SD₁₆	C₂²	1	1	yes	characteristic
120	C₄×C₇×SD₁₆	C₂²	1	1	yes	characteristic
121	C₄×C₇×SD₁₆	C₂²	1	1	yes	characteristic, complemented
122	C₄×C₇×SD₁₆	C₂²	1	1	yes	characteristic, complemented
123	C₄×C₇×SD₁₆	C₂²	1	2	yes	complemented
124	C₇×#436	C₂²	1	1	yes	characteristic
125	C₇×#436	C₂²	1	2	yes	complemented
126	C₇×#435	C₂²	1	2	yes	complemented
127	C₇×C₈×D₄	C₂²	1	1	yes	characteristic
128	C₇×#433	C₂²	1	2	yes	complemented
129	C₇×#431	C₂²	1	1	yes	characteristic, complemented
130	C₇×#424	C₂²	1	2	yes	complemented
131	C₇×#423	C₂²	1	1	yes	characteristic, complemented
132	C₇×#418	C₂²	1	2	yes	—
133	C₇×#417	C₂²	1	2	yes	complemented
134	C₇×#416	C₂²	1	2	yes	complemented
135	#62044	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
136	C₂×C₇×#41	—	2	1	no	—
137	C₂×C₇×#41	—	2	1	no	—
138	C₂×C₇×#41	C₂³	1	2	yes	—
139	C₂×C₇×#41	C₂³	1	2	yes	—
140	C₂²×C₇×Q₈	C₂³	1	1	yes	characteristic
141	C₂²×C₇×Q₈	C₂³	1	2	yes	—
142	C₂²×C₇×D₄	—	2	1	no	—
143	C₂²×C₇×D₄	C₂³	1	2	yes	—
144	C₇×#137	—	4	4	no	—
145	C₇×#137	—	4	4	no	—
146	C₂×C₇×Q₁₆	C₂³	1	2	yes	—
147	C₂×C₇×Q₁₆	C₂³	1	2	yes	—
148	C₂×C₇×Q₁₆	C₂³	1	2	yes	—
149	C₂×C₇×Q₁₆	C₂³	1	2	yes	—
150	C₂×C₇×SD₁₆	—	4	4	no	—
151	C₂×C₇×SD₁₆	C₂³	1	1	yes	characteristic
152	C₂×C₇×SD₁₆	C₂³	1	2	yes	—
153	C₂×C₇×SD₁₆	C₂³	1	1	yes	characteristic
154	C₂×C₇×SD₁₆	C₂³	1	2	yes	—
155	C₂×C₇×SD₁₆	C₂³	1	2	yes	—
156	C₂×C₇×SD₁₆	C₂³	1	2	yes	—
157	C₂×C₇×SD₁₆	C₂³	1	2	yes	—
158	C₂×C₇×SD₁₆	C₂³	1	2	yes	—
159	C₂×C₇×SD₁₆	C₂³	1	1	yes	characteristic
160	C₂×C₇×SD₁₆	C₂³	1	1	yes	characteristic
161	C₂×C₇×M₁₆	C₂³	1	2	yes	—
162	C₂×C₇×M₁₆	C₂³	1	2	yes	—
163	C₂²×C₇×C₈	C₂³	1	2	yes	—
164	C₇×C₄⋊Q₈	—	2	1	no	—
165	C₇×C₄⋊Q₈	—	2	1	no	—
166	C₇×C₄⋊Q₈	—	2	2	no	—
167	C₇×C₄⋊Q₈	C₂³	1	1	yes	characteristic
168	C₇×C₄⋊Q₈	C₂³	1	1	yes	characteristic
169	C₇×C₄⋊Q₈	C₂³	1	2	yes	—
170	C₇×C₄⋊Q₈	C₂³	1	1	yes	characteristic
171	C₇×C₄⋊Q₈	C₂³	1	1	yes	characteristic
172	C₇×#127	—	2	2	no	—
173	C₇×#127	C₂³	1	1	yes	characteristic
174	C₇×#127	C₂³	1	2	yes	—
175	C₇×#127	C₂³	1	1	yes	characteristic
176	C₇×#126	—	2	2	no	—
177	C₇×#126	—	2	2	no	—
178	C₇×#126	—	2	2	no	—
179	C₇×#126	—	2	2	no	—
180	C₇×#126	—	2	2	no	—
181	C₇×#126	—	2	2	no	—
182	C₇×#126	D₄	1	2	yes	—
183	C₇×#125	—	2	1	no	—
184	C₇×#125	—	2	2	no	—
185	C₇×#125	—	2	2	no	—
186	C₇×#125	—	2	2	no	—
187	C₇×#125	—	2	2	no	—
188	C₇×#125	—	2	2	no	—
189	C₇×#125	—	2	1	no	—
190	C₇×#125	D₄	1	1	yes	characteristic
191	C₇×#125	C₂³	1	2	yes	—
192	C₇×#124	—	2	1	no	—
193	C₇×#124	—	2	2	no	—
194	C₇×#124	—	2	1	no	—
195	C₇×#124	D₄	1	1	yes	characteristic
196	C₇×#124	C₂³	1	2	yes	—
197	C₇×#124	C₂³	1	2	yes	—
198	C₇×#123	—	2	2	no	—
199	C₇×#123	—	2	2	no	—
200	C₇×#123	—	2	2	no	—
201	C₇×#123	—	2	2	no	—
202	C₇×#123	D₄	1	2	yes	—
203	C₇×C₂²⋊Q₈	—	2	1	no	—
204	C₇×C₂²⋊Q₈	—	2	1	no	—
205	C₇×C₂²⋊Q₈	—	2	2	no	—
206	C₇×C₂²⋊Q₈	—	2	2	no	—
207	C₇×C₂²⋊Q₈	—	2	2	no	—
208	C₇×C₂²⋊Q₈	—	2	2	no	—
209	C₇×C₂²⋊Q₈	D₄	1	1	yes	characteristic
210	C₇×C₂²⋊Q₈	C₂³	1	2	yes	—
211	C₇×C₂²⋊Q₈	C₂³	1	2	yes	—
212	C₇×C₂²⋊Q₈	C₂³	1	2	yes	—
213	C₇×C₂²⋊Q₈	C₂³	1	2	yes	—
214	C₇×#121	—	2	1	no	—
215	C₇×#121	—	2	1	no	—
216	C₇×#121	—	2	1	no	—
217	C₇×#121	—	2	1	no	—
218	C₇×#121	—	2	1	no	—
219	C₇×#121	—	2	2	no	—
220	C₇×#121	—	2	2	no	—
221	C₇×#121	—	2	1	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	D₄	1	1	yes	characteristic
227	C₇×#121	C₂³	1	1	yes	characteristic
228	C₇×#121	C₂³	1	2	yes	—
229	C₇×#121	C₂³	1	1	yes	characteristic
230	C₇×#120	—	2	2	no	—
231	C₇×#120	—	2	2	no	—
232	C₇×#120	—	2	2	no	—
233	C₇×#120	—	2	2	no	—
234	C₄×C₇×Q₈	—	2	1	no	—
235	C₄×C₇×Q₈	—	2	2	no	—
236	C₄×C₇×Q₈	—	2	2	no	—
237	C₄×C₇×Q₈	—	2	1	no	—
238	C₄×C₇×Q₈	—	2	1	no	—
239	C₄×C₇×Q₈	—	2	1	no	—
240	C₄×C₇×Q₈	—	2	1	no	—
241	C₄×C₇×Q₈	—	2	1	no	—
242	C₄×C₇×Q₈	C₂³	1	1	yes	characteristic
243	C₄×C₇×Q₈	C₂³	1	1	yes	characteristic
244	C₄×C₇×Q₈	C₂³	1	2	yes	—
245	C₄×C₇×Q₈	C₂³	1	2	yes	—
246	C₄×C₇×Q₈	C₂³	1	1	yes	characteristic
247	C₄×C₇×Q₈	C₂³	1	1	yes	characteristic
248	C₄×C₇×Q₈	C₂³	1	2	yes	—
249	C₄×C₇×Q₈	C₂³	1	2	yes	—
250	C₄×C₇×Q₈	C₂³	1	1	yes	characteristic
251	C₄×C₇×D₄	—	2	1	no	—
252	C₄×C₇×D₄	—	2	2	no	—
253	C₄×C₇×D₄	—	2	2	no	—
254	C₄×C₇×D₄	—	2	1	no	—
255	C₄×C₇×D₄	—	2	1	no	—
256	C₄×C₇×D₄	—	2	1	no	—
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	1	yes	characteristic
261	C₄×C₇×D₄	C₂³	1	2	yes	—
262	C₇×#117	—	2	1	no	—
263	C₇×#117	—	2	1	no	—
264	C₇×#117	—	2	2	no	—
265	C₇×#117	—	2	2	no	—
266	C₇×#117	—	2	2	no	—
267	C₇×#117	C₂³	1	2	yes	—
268	C₇×#117	C₂³	1	2	yes	—
269	C₂×C₇×C₄⋊C₄	—	2	1	no	—
270	C₂×C₇×C₄⋊C₄	—	2	1	no	—
271	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
272	C₂×C₇×C₂²⋊C₄	—	2	2	no	—
273	C₂×C₄²×C₇	—	2	1	no	—
274	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
275	C₇×#107	C₂³	1	2	yes	—
276	C₇×#107	C₂³	1	2	yes	—
277	C₇×#106	C₂³	1	1	yes	characteristic
278	C₇×#106	C₂³	1	1	yes	characteristic
279	C₇×#106	C₂³	1	1	yes	characteristic
280	C₇×#106	C₂³	1	1	yes	characteristic
281	C₇×C₄⋊C₈	C₂³	1	1	yes	characteristic
282	C₇×C₄⋊C₈	C₂³	1	1	yes	characteristic
283	C₇×C₄⋊C₈	C₂³	1	1	yes	characteristic
284	C₇×C₄⋊C₈	C₂³	1	1	yes	characteristic
285	C₇×C₄⋊C₈	C₂³	1	2	yes	—
286	C₇×C₄⋊C₈	C₂³	1	2	yes	—
287	C₇×C₄⋊C₈	C₂³	1	2	yes	—
288	C₇×#103	C₂³	1	1	yes	characteristic
289	C₇×#103	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	2	yes	—
294	C₇×#103	C₂³	1	1	yes	characteristic
295	C₇×#103	C₂³	1	1	yes	characteristic
296	C₇×#103	C₂³	1	2	yes	—
297	C₇×#103	C₂³	1	2	yes	—
298	C₇×#102	C₂³	1	2	yes	—
299	C₇×#102	C₂³	1	2	yes	—
300	C₇×#102	C₂³	1	2	yes	—
301	C₇×#102	C₂³	1	2	yes	—
302	C₇×#102	C₂³	1	1	yes	characteristic
303	C₇×#102	C₂³	1	1	yes	characteristic
304	C₇×#102	C₂³	1	1	yes	characteristic
305	C₇×#102	C₂³	1	1	yes	characteristic
306	C₇×#102	C₂³	1	2	yes	—
307	C₇×#102	C₂³	1	2	yes	—
308	C₇×C₂²⋊C₈	C₂³	1	1	yes	characteristic
309	C₇×C₂²⋊C₈	C₂³	1	1	yes	characteristic
310	C₇×C₂²⋊C₈	C₂³	1	2	yes	—
311	C₇×C₂²⋊C₈	C₂³	1	2	yes	—
312	C₇×#97	C₂³	1	2	yes	—
313	C₄×C₇×C₈	C₂³	1	1	yes	characteristic
314	C₄×C₇×C₈	C₂³	1	1	yes	characteristic
315	C₄×C₇×C₈	C₂³	1	2	yes	—
316	#3546	C₂×C₇	1	1	yes	characteristic
317	#3523	C₂×C₇	1	1	yes	characteristic, complemented
318	#3398	C₂×C₇	1	1	yes	characteristic, complemented
319	#3392	C₂×C₇	1	1	yes	characteristic, complemented
320	#3368	C₂×C₇	1	1	yes	characteristic, complemented
321	#3364	C₂×C₇	1	1	yes	characteristic, complemented
322	#3324	C₂×C₇	1	1	yes	characteristic, complemented
323	#3323	C₂×C₇	1	2	yes	complemented
324	#3317	C₂×C₇	1	2	yes	complemented
325	#3302	C₂×C₇	1	1	yes	characteristic, complemented
326	D₄×SD₁₆	C₂×C₇	1	1	yes	characteristic, complemented
327	#3278	C₂×C₇	1	2	yes	complemented
328	#3276	C₂×C₇	1	1	yes	characteristic, complemented
329	#3266	C₂×C₇	1	2	yes	complemented
330	#3258	C₂×C₇	1	2	yes	complemented
331	#3254	C₂×C₇	1	1	yes	characteristic, complemented
332	#3222	C₂×C₇	1	2	yes	complemented
333	#3210	C₂×C₇	1	1	yes	characteristic, complemented
334	#3121	C₂×C₇	1	2	yes	complemented
335	#3103	C₂×C₇	1	1	yes	characteristic, complemented
336	#3043	C₂×C₇	1	2	yes	complemented
337	#3037	C₂×C₇	1	1	yes	characteristic, complemented
338	#2993	C₂×C₇	1	1	yes	characteristic, complemented
339	C₂⁴×C₇	—	2	2	no	—
340	C₇×#41	—	4	2	no	—
341	C₇×#41	—	4	2	no	—
342	C₇×#41	—	4	2	no	—
343	C₇×#41	—	4	2	no	—
344	C₇×#41	—	8	2	no	—
345	C₇×#41	—	8	2	no	—
346	C₂×C₇×Q₈	—	2	1	no	—
347	C₂×C₇×Q₈	—	2	2	no	—
348	C₂×C₇×Q₈	—	2	1	no	—
349	C₂×C₇×Q₈	—	2	1	no	—
350	C₂×C₇×Q₈	—	2	4	no	—
351	C₂×C₇×Q₈	—	2	2	no	—
352	C₂×C₇×Q₈	—	4	2	no	—
353	C₂×C₇×Q₈	—	4	1	no	—
354	C₂×C₇×Q₈	C₂×D₄	1	1	yes	characteristic
355	C₂×C₇×Q₈	C₂⁴	1	2	yes	—
356	C₂×C₇×Q₈	C₂⁴	1	2	yes	—
357	C₂×C₇×Q₈	C₂⁴	1	1	yes	characteristic
358	C₂×C₇×Q₈	C₂⁴	1	1	yes	characteristic
359	C₂×C₇×D₄	—	2	1	no	—
360	C₂×C₇×D₄	—	2	2	no	—
361	C₂×C₇×D₄	—	2	2	no	—
362	C₂×C₇×D₄	—	2	2	no	—
363	C₂×C₇×D₄	—	2	1	no	—
364	C₂×C₇×D₄	—	2	1	no	—
365	C₂×C₇×D₄	—	2	1	no	—
366	C₂×C₇×D₄	—	2	1	no	—
367	C₂×C₇×D₄	—	2	2	no	—
368	C₂×C₇×D₄	—	2	1	no	—
369	C₂×C₇×D₄	—	2	2	no	—
370	C₂×C₇×D₄	—	2	2	no	—
371	C₂×C₇×D₄	—	4	2	no	—
372	C₂×C₇×D₄	—	4	2	no	—
373	C₂×C₇×D₄	—	8	2	no	—
374	C₂×C₇×D₄	C₂×D₄	1	1	yes	characteristic
375	C₂×C₇×D₄	C₂×D₄	1	2	yes	—
376	C₂×C₇×D₄	C₂⁴	1	1	yes	characteristic
377	C₂×C₇×D₄	C₂⁴	1	2	yes	—
378	C₂×C₇×D₄	C₂⁴	1	1	yes	characteristic
379	C₂²×C₄×C₇	—	2	1	no	—
380	C₂²×C₄×C₇	—	2	1	no	—
381	C₂²×C₄×C₇	—	2	2	no	—
382	C₂²×C₄×C₇	—	2	1	no	—
383	C₂²×C₄×C₇	—	2	1	no	—
384	C₂²×C₄×C₇	—	2	2	no	—
385	C₂²×C₄×C₇	—	2	2	no	—
386	C₂²×C₄×C₇	—	2	2	no	—
387	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
388	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
389	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
390	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
391	C₇×Q₁₆	—	2	4	no	—
392	C₇×Q₁₆	—	4	2	no	—
393	C₇×Q₁₆	—	4	2	no	—
394	C₇×Q₁₆	—	4	2	no	—
395	C₇×SD₁₆	—	2	2	no	—
396	C₇×SD₁₆	—	2	4	no	—
397	C₇×SD₁₆	—	2	2	no	—
398	C₇×SD₁₆	—	4	2	no	—
399	C₇×SD₁₆	—	4	2	no	—
400	C₇×SD₁₆	—	4	2	no	—
401	C₇×SD₁₆	—	4	1	no	—
402	C₇×SD₁₆	—	4	1	no	—
403	C₇×SD₁₆	—	4	2	no	—
404	C₇×SD₁₆	—	4	2	no	—
405	C₇×M₁₆	—	4	2	no	—
406	C₇×M₁₆	—	4	2	no	—
407	C₂×C₇×C₈	—	4	2	no	—
408	C₂×C₇×C₈	C₂⁴	1	1	yes	characteristic
409	C₂×C₇×C₈	C₂⁴	1	1	yes	characteristic
410	C₂×C₇×C₈	C₂⁴	1	1	yes	characteristic
411	C₂×C₇×C₈	C₂⁴	1	2	yes	—
412	C₂×C₇×C₈	C₂⁴	1	1	yes	characteristic
413	C₂×C₇×C₈	C₂⁴	1	2	yes	—
414	C₇×C₄⋊C₄	—	2	1	no	—
415	C₇×C₄⋊C₄	—	2	1	no	—
416	C₇×C₄⋊C₄	—	2	1	no	—
417	C₇×C₄⋊C₄	—	2	1	no	—
418	C₇×C₄⋊C₄	—	2	1	no	—
419	C₇×C₄⋊C₄	—	2	2	no	—
420	C₇×C₄⋊C₄	—	2	1	no	—
421	C₇×C₄⋊C₄	—	2	2	no	—
422	C₇×C₄⋊C₄	—	2	2	no	—
423	C₇×C₄⋊C₄	—	2	2	no	—
424	C₇×C₄⋊C₄	—	2	1	no	—
425	C₇×C₄⋊C₄	—	2	2	no	—
426	C₇×C₄⋊C₄	—	2	1	no	—
427	C₇×C₄⋊C₄	—	2	2	no	—
428	C₇×C₄⋊C₄	—	2	1	no	—
429	C₇×C₄⋊C₄	—	2	1	no	—
430	C₇×C₄⋊C₄	—	2	1	no	—
431	C₇×C₄⋊C₄	—	2	2	no	—
432	C₇×C₄⋊C₄	—	2	2	no	—
433	C₇×C₄⋊C₄	—	2	2	no	—
434	C₇×C₄⋊C₄	—	2	2	no	—
435	C₇×C₄⋊C₄	—	2	2	no	—
436	C₇×C₄⋊C₄	—	2	2	no	—
437	C₇×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
438	C₇×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
439	C₇×C₄⋊C₄	C₂×D₄	1	2	yes	—
440	C₇×C₄⋊C₄	C₂×D₄	1	2	yes	—
441	C₇×C₄⋊C₄	C₂×D₄	1	2	yes	—
442	C₇×C₄⋊C₄	C₂×D₄	1	2	yes	—
443	C₇×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
444	C₇×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
445	C₇×C₄⋊C₄	C₂⁴	1	2	yes	—
446	C₇×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
447	C₇×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
448	C₇×C₂²⋊C₄	—	2	2	no	—
449	C₇×C₂²⋊C₄	—	2	2	no	—
450	C₇×C₂²⋊C₄	—	2	2	no	—
451	C₇×C₂²⋊C₄	—	2	2	no	—
452	C₇×C₂²⋊C₄	—	2	2	no	—
453	C₇×C₂²⋊C₄	—	2	1	no	—
454	C₇×C₂²⋊C₄	—	2	2	no	—
455	C₇×C₂²⋊C₄	—	2	2	no	—
456	C₇×C₂²⋊C₄	—	2	1	no	—
457	C₇×C₂²⋊C₄	—	2	2	no	—
458	C₇×C₂²⋊C₄	—	2	2	no	—
459	C₇×C₂²⋊C₄	—	2	2	no	—
460	C₇×C₂²⋊C₄	—	2	1	no	—
461	C₇×C₂²⋊C₄	—	2	2	no	—
462	C₇×C₂²⋊C₄	—	2	1	no	—
463	C₇×C₂²⋊C₄	C₂×D₄	1	2	yes	—
464	C₇×C₂²⋊C₄	C₂×D₄	1	2	yes	—
465	C₇×C₂²⋊C₄	C₂×D₄	1	2	yes	—
466	C₇×C₂²⋊C₄	C₂×D₄	1	2	yes	—
467	C₇×C₂²⋊C₄	C₂×D₄	1	2	yes	—
468	C₄²×C₇	—	2	1	no	—
469	C₄²×C₇	—	2	1	no	—
470	C₄²×C₇	—	2	1	no	—
471	C₄²×C₇	—	2	1	no	—
472	C₄²×C₇	—	2	2	no	—
473	C₄²×C₇	—	2	2	no	—
474	C₄²×C₇	—	2	2	no	—
475	C₄²×C₇	—	2	2	no	—
476	C₄²×C₇	—	2	2	no	—
477	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
478	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
479	C₄²×C₇	C₂⁴	1	1	yes	characteristic
480	C₄²×C₇	C₂⁴	1	2	yes	—
481	C₄²×C₇	C₂⁴	1	1	yes	characteristic
482	C₂×#137	C₂²×C₇	1	2	yes	complemented
483	C₂×#137	C₂²×C₇	1	2	yes	complemented
484	C₂²×SD₁₆	C₂²×C₇	1	2	yes	—
485	#560	—	2	2	no	—
486	#557	—	2	1	no	—
487	#557	C₂²×C₇	1	1	yes	characteristic, complemented
488	#557	C₂²×C₇	1	1	yes	characteristic, complemented
489	#556	—	2	1	no	—
490	#556	C₂²×C₇	1	1	yes	characteristic
491	#556	C₂²×C₇	1	1	yes	characteristic
492	#553	—	2	1	no	—
493	#552	—	2	2	no	—
494	#552	C₂²×C₇	1	2	yes	complemented
495	#550	C₂²×C₇	1	2	yes	—
496	#550	C₂²×C₇	1	1	yes	characteristic
497	D₄×Q₈	C₂²×C₇	1	1	yes	characteristic
498	D₄×Q₈	C₂²×C₇	1	2	yes	complemented
499	#547	C₂²×C₇	1	1	yes	characteristic
500	#546	—	2	1	no	—
501	#546	C₂²×C₇	1	2	yes	—
502	D₄²	C₂²×C₇	1	1	yes	characteristic
503	#542	C₂²×C₇	1	2	yes	—
504	#541	—	2	2	no	—
505	#541	C₂²×C₇	1	2	yes	complemented
506	#538	—	2	2	no	—
507	#537	—	2	1	no	—
508	#535	—	2	1	no	—
509	#535	C₂²×C₇	1	2	yes	—
510	#533	—	2	1	no	—
511	#533	C₂²×C₇	1	1	yes	characteristic, complemented
512	#532	C₂²×C₇	1	1	yes	characteristic
513	#532	C₂²×C₇	1	1	yes	characteristic
514	#529	—	2	1	no	—
515	#529	C₂²×C₇	1	1	yes	characteristic
516	#519	C₂²×C₇	1	2	yes	complemented
517	C₂×C₄×Q₈	C₂²×C₇	1	1	yes	characteristic, complemented
518	#497	C₂²×C₇	1	2	yes	—
519	#494	C₂²×C₇	1	1	yes	characteristic, complemented
520	#492	C₂²×C₇	1	1	yes	characteristic
521	#492	C₂²×C₇	1	2	yes	complemented
522	#490	C₂²×C₇	1	2	yes	complemented
523	#488	C₂²×C₇	1	2	yes	—
524	#487	C₂²×C₇	1	1	yes	characteristic, complemented
525	#486	C₂²×C₇	1	1	yes	characteristic
526	#485	C₂²×C₇	1	2	yes	complemented
527	#482	C₂²×C₇	1	2	yes	—
528	#481	C₂²×C₇	1	1	yes	characteristic
529	#481	C₂²×C₇	1	1	yes	characteristic, complemented
530	#479	C₂²×C₇	1	2	yes	complemented
531	#478	C₂²×C₇	1	2	yes	complemented
532	#477	C₂²×C₇	1	2	yes	complemented
533	#475	C₂²×C₇	1	1	yes	characteristic, complemented
534	#475	C₂²×C₇	1	1	yes	characteristic, complemented
535	#474	C₂²×C₇	1	1	yes	characteristic
536	#474	C₂²×C₇	1	1	yes	characteristic, complemented
537	#470	C₂²×C₇	1	2	yes	complemented
538	#468	C₂²×C₇	1	2	yes	—
539	#468	C₂²×C₇	1	2	yes	—
540	#468	C₂²×C₇	1	2	yes	complemented
541	#467	C₂²×C₇	1	2	yes	complemented
542	#465	C₂²×C₇	1	2	yes	—
543	#464	C₂²×C₇	1	2	yes	—
544	#464	C₂²×C₇	1	2	yes	—
545	#464	C₂²×C₇	1	2	yes	complemented
546	#464	C₂²×C₇	1	2	yes	complemented
547	#464	C₂²×C₇	1	2	yes	complemented
548	#464	C₂²×C₇	1	2	yes	complemented
549	#462	C₂²×C₇	1	1	yes	characteristic, complemented
550	#462	C₂²×C₇	1	2	yes	complemented
551	#462	C₂²×C₇	1	1	yes	characteristic, complemented
552	#461	C₂²×C₇	1	1	yes	characteristic
553	#461	C₂²×C₇	1	1	yes	characteristic, complemented
554	#461	C₂²×C₇	1	2	yes	complemented
555	#460	C₂²×C₇	1	1	yes	characteristic
556	#460	C₂²×C₇	1	1	yes	characteristic
557	#460	C₂²×C₇	1	1	yes	characteristic
558	#460	C₂²×C₇	1	1	yes	characteristic
559	#460	C₂²×C₇	1	2	yes	—
560	#460	C₂²×C₇	1	2	yes	complemented
561	#460	C₂²×C₇	1	2	yes	complemented
562	#452	C₂²×C₇	1	2	yes	complemented
563	#452	C₂²×C₇	1	2	yes	complemented
564	#452	C₂²×C₇	1	2	yes	complemented
565	#452	C₂²×C₇	1	2	yes	complemented
566	#451	C₂²×C₇	1	2	yes	complemented
567	#450	C₂²×C₇	1	2	yes	—
568	#450	C₂²×C₇	1	2	yes	—
569	#448	C₂²×C₇	1	1	yes	characteristic
570	#448	C₂²×C₇	1	2	yes	—
571	#448	C₂²×C₇	1	1	yes	characteristic, complemented
572	#446	C₂²×C₇	1	1	yes	characteristic, complemented
573	C₈×Q₈	C₂²×C₇	1	1	yes	characteristic, complemented
574	#441	C₂²×C₇	1	2	yes	complemented
575	#440	C₂²×C₇	1	2	yes	complemented
576	C₄×Q₁₆	C₂²×C₇	1	2	yes	complemented
577	C₄×SD₁₆	C₂²×C₇	1	1	yes	characteristic
578	C₄×SD₁₆	C₂²×C₇	1	1	yes	characteristic
579	C₄×SD₁₆	C₂²×C₇	1	1	yes	characteristic, complemented
580	C₄×SD₁₆	C₂²×C₇	1	1	yes	characteristic, complemented
581	C₄×SD₁₆	C₂²×C₇	1	2	yes	complemented
582	#436	C₂²×C₇	1	1	yes	characteristic
583	#436	C₂²×C₇	1	2	yes	complemented
584	#435	C₂²×C₇	1	2	yes	complemented
585	C₈×D₄	C₂²×C₇	1	1	yes	characteristic
586	#433	C₂²×C₇	1	2	yes	complemented
587	#431	C₂²×C₇	1	1	yes	characteristic, complemented
588	#424	C₂²×C₇	1	2	yes	complemented
589	#423	C₂²×C₇	1	1	yes	characteristic, complemented
590	#418	C₂²×C₇	1	2	yes	—
591	#417	C₂²×C₇	1	2	yes	complemented
592	#416	C₂²×C₇	1	2	yes	complemented
593	C₂³×C₇	—	2	1	no	—
594	C₂³×C₇	—	2	2	no	—
595	C₂³×C₇	—	2	1	no	—
596	C₂³×C₇	—	8	2	no	—
597	C₂³×C₇	—	8	2	no	—
598	C₂³×C₇	—	8	2	no	—
599	C₂³×C₇	C₂²×D₄	1	2	yes	—
600	C₂³×C₇	C₂²×D₄	1	1	yes	characteristic
601	C₇×Q₈	—	2	2	no	—
602	C₇×Q₈	—	2	1	no	—
603	C₇×Q₈	—	2	2	no	—
604	C₇×Q₈	—	2	1	no	—
605	C₇×Q₈	—	2	2	no	—
606	C₇×Q₈	—	2	1	no	—
607	C₇×Q₈	—	2	2	no	—
608	C₇×Q₈	—	2	2	no	—
609	C₇×Q₈	—	4	2	no	—
610	C₇×Q₈	—	4	4	no	—
611	C₇×Q₈	—	4	2	no	—
612	C₇×Q₈	—	8	1	no	—
613	C₇×Q₈	H(5,𝔽₂)	1	2	yes	—
614	C₇×D₄	—	2	2	no	—
615	C₇×D₄	—	2	1	no	—
616	C₇×D₄	—	2	2	no	—
617	C₇×D₄	—	2	1	no	—
618	C₇×D₄	—	2	1	no	—
619	C₇×D₄	—	2	2	no	—
620	C₇×D₄	—	2	1	no	—
621	C₇×D₄	—	4	2	no	—
622	C₇×D₄	—	4	2	no	—
623	C₇×D₄	—	8	1	no	—
624	C₇×D₄	—	8	1	no	—
625	C₇×D₄	—	8	2	no	—
626	C₇×D₄	—	8	2	no	—
627	C₇×D₄	—	8	1	no	—
628	C₇×D₄	—	8	2	no	—
629	C₇×D₄	—	8	2	no	—
630	C₇×D₄	—	8	2	no	—
631	C₇×D₄	—	8	2	no	—
632	C₇×D₄	—	8	1	no	—
633	C₇×D₄	—	8	1	no	—
634	C₂×C₄×C₇	—	2	1	no	—
635	C₂×C₄×C₇	—	2	2	no	—
636	C₂×C₄×C₇	—	2	2	no	—
637	C₂×C₄×C₇	—	2	1	no	—
638	C₂×C₄×C₇	—	2	2	no	—
639	C₂×C₄×C₇	—	2	1	no	—
640	C₂×C₄×C₇	—	2	1	no	—
641	C₂×C₄×C₇	—	2	2	no	—
642	C₂×C₄×C₇	—	2	1	no	—
643	C₂×C₄×C₇	—	2	1	no	—
644	C₂×C₄×C₇	—	2	1	no	—
645	C₂×C₄×C₇	—	2	2	no	—
646	C₂×C₄×C₇	—	2	2	no	—
647	C₂×C₄×C₇	—	2	1	no	—
648	C₂×C₄×C₇	—	4	1	no	—
649	C₂×C₄×C₇	—	4	2	no	—
650	C₂×C₄×C₇	—	4	4	no	—
651	C₂×C₄×C₇	—	4	2	no	—
652	C₂×C₄×C₇	—	4	2	no	—
653	C₂×C₄×C₇	—	4	2	no	—
654	C₂×C₄×C₇	—	8	2	no	—
655	C₂×C₄×C₇	—	8	2	no	—
656	C₂×C₄×C₇	—	8	2	no	—
657	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
658	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
659	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
660	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
661	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
662	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
663	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
664	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
665	C₂×C₄×C₇	C₂⁵	1	1	yes	characteristic
666	C₇×C₈	—	2	1	no	—
667	C₇×C₈	—	2	2	no	—
668	C₇×C₈	—	2	1	no	—
669	C₇×C₈	—	2	2	no	—
670	C₇×C₈	—	2	1	no	—
671	C₇×C₈	—	2	1	no	—
672	C₂×#41	—	2	1	no	—
673	C₂×#41	—	2	1	no	—
674	C₂×#41	C₂³×C₇	1	2	yes	—
675	C₂×#41	C₂³×C₇	1	2	yes	—
676	C₂²×Q₈	C₂³×C₇	1	1	yes	characteristic
677	C₂²×Q₈	C₂³×C₇	1	2	yes	—
678	C₂²×D₄	—	2	1	no	—
679	C₂²×D₄	C₂³×C₇	1	2	yes	—
680	#137	—	4	4	no	—
681	#137	—	4	4	no	—
682	C₂×Q₁₆	C₂³×C₇	1	2	yes	—
683	C₂×Q₁₆	C₂³×C₇	1	2	yes	—
684	C₂×Q₁₆	C₂³×C₇	1	2	yes	—
685	C₂×Q₁₆	C₂³×C₇	1	2	yes	—
686	C₂×SD₁₆	—	4	4	no	—
687	C₂×SD₁₆	C₂³×C₇	1	1	yes	characteristic
688	C₂×SD₁₆	C₂³×C₇	1	2	yes	—
689	C₂×SD₁₆	C₂³×C₇	1	1	yes	characteristic
690	C₂×SD₁₆	C₂³×C₇	1	2	yes	—
691	C₂×SD₁₆	C₂³×C₇	1	2	yes	—
692	C₂×SD₁₆	C₂³×C₇	1	2	yes	—
693	C₂×SD₁₆	C₂³×C₇	1	2	yes	—
694	C₂×SD₁₆	C₂³×C₇	1	1	yes	characteristic
695	C₂×SD₁₆	C₂³×C₇	1	2	yes	—
696	C₂×SD₁₆	C₂³×C₇	1	1	yes	characteristic
697	C₂×M₁₆	C₂³×C₇	1	2	yes	—
698	C₂×M₁₆	C₂³×C₇	1	2	yes	—
699	C₂²×C₈	C₂³×C₇	1	2	yes	—
700	C₄⋊Q₈	—	2	1	no	—
701	C₄⋊Q₈	—	2	1	no	—
702	C₄⋊Q₈	—	2	2	no	—
703	C₄⋊Q₈	C₂³×C₇	1	1	yes	characteristic
704	C₄⋊Q₈	C₂³×C₇	1	1	yes	characteristic
705	C₄⋊Q₈	C₂³×C₇	1	2	yes	—
706	C₄⋊Q₈	C₂³×C₇	1	1	yes	characteristic
707	C₄⋊Q₈	C₂³×C₇	1	1	yes	characteristic
708	#127	—	2	2	no	—
709	#127	C₂³×C₇	1	1	yes	characteristic
710	#127	C₂³×C₇	1	1	yes	characteristic
711	#127	C₂³×C₇	1	2	yes	—
712	#126	—	2	2	no	—
713	#126	—	2	2	no	—
714	#126	—	2	2	no	—
715	#126	—	2	2	no	—
716	#126	—	2	2	no	—
717	#126	—	2	2	no	—
718	#126	C₇×D₄	1	2	yes	—
719	#125	—	2	1	no	—
720	#125	—	2	2	no	—
721	#125	—	2	2	no	—
722	#125	—	2	2	no	—
723	#125	—	2	2	no	—
724	#125	—	2	2	no	—
725	#125	—	2	1	no	—
726	#125	C₇×D₄	1	1	yes	characteristic
727	#125	C₂³×C₇	1	2	yes	—
728	#124	—	2	1	no	—
729	#124	—	2	2	no	—
730	#124	—	2	1	no	—
731	#124	C₇×D₄	1	1	yes	characteristic
732	#124	C₂³×C₇	1	2	yes	—
733	#124	C₂³×C₇	1	2	yes	—
734	#123	—	2	2	no	—
735	#123	—	2	2	no	—
736	#123	—	2	2	no	—
737	#123	—	2	2	no	—
738	#123	C₇×D₄	1	2	yes	—
739	C₂²⋊Q₈	—	2	1	no	—
740	C₂²⋊Q₈	—	2	1	no	—
741	C₂²⋊Q₈	—	2	2	no	—
742	C₂²⋊Q₈	—	2	2	no	—
743	C₂²⋊Q₈	—	2	2	no	—
744	C₂²⋊Q₈	—	2	2	no	—
745	C₂²⋊Q₈	C₇×D₄	1	1	yes	characteristic
746	C₂²⋊Q₈	C₂³×C₇	1	2	yes	—
747	C₂²⋊Q₈	C₂³×C₇	1	2	yes	—
748	C₂²⋊Q₈	C₂³×C₇	1	2	yes	—
749	C₂²⋊Q₈	C₂³×C₇	1	2	yes	—
750	#121	—	2	1	no	—
751	#121	—	2	1	no	—
752	#121	—	2	1	no	—
753	#121	—	2	1	no	—
754	#121	—	2	1	no	—
755	#121	—	2	2	no	—
756	#121	—	2	2	no	—
757	#121	—	2	1	no	—
758	#121	—	2	2	no	—
759	#121	—	2	2	no	—
760	#121	—	2	2	no	—
761	#121	—	2	2	no	—
762	#121	C₇×D₄	1	1	yes	characteristic
763	#121	C₂³×C₇	1	1	yes	characteristic
764	#121	C₂³×C₇	1	1	yes	characteristic
765	#121	C₂³×C₇	1	2	yes	—
766	#120	—	2	2	no	—
767	#120	—	2	2	no	—
768	#120	—	2	2	no	—
769	#120	—	2	2	no	—
770	C₄×Q₈	—	2	1	no	—
771	C₄×Q₈	—	2	2	no	—
772	C₄×Q₈	—	2	2	no	—
773	C₄×Q₈	—	2	1	no	—
774	C₄×Q₈	—	2	1	no	—
775	C₄×Q₈	—	2	1	no	—
776	C₄×Q₈	—	2	1	no	—
777	C₄×Q₈	—	2	1	no	—
778	C₄×Q₈	C₂³×C₇	1	1	yes	characteristic
779	C₄×Q₈	C₂³×C₇	1	1	yes	characteristic
780	C₄×Q₈	C₂³×C₇	1	1	yes	characteristic
781	C₄×Q₈	C₂³×C₇	1	1	yes	characteristic
782	C₄×Q₈	C₂³×C₇	1	2	yes	—
783	C₄×Q₈	C₂³×C₇	1	2	yes	—
784	C₄×Q₈	C₂³×C₇	1	2	yes	—
785	C₄×Q₈	C₂³×C₇	1	2	yes	—
786	C₄×Q₈	C₂³×C₇	1	1	yes	characteristic
787	C₄×D₄	—	2	1	no	—
788	C₄×D₄	—	2	2	no	—
789	C₄×D₄	—	2	2	no	—
790	C₄×D₄	—	2	1	no	—
791	C₄×D₄	—	2	1	no	—
792	C₄×D₄	—	2	1	no	—
793	C₄×D₄	C₂³×C₇	1	1	yes	characteristic
794	C₄×D₄	C₂³×C₇	1	1	yes	characteristic
795	C₄×D₄	C₂³×C₇	1	2	yes	—
796	C₄×D₄	C₂³×C₇	1	1	yes	characteristic
797	C₄×D₄	C₂³×C₇	1	2	yes	—
798	#117	—	2	1	no	—
799	#117	—	2	1	no	—
800	#117	—	2	2	no	—
801	#117	—	2	2	no	—
802	#117	—	2	2	no	—
803	#117	C₂³×C₇	1	2	yes	—
804	#117	C₂³×C₇	1	2	yes	—
805	C₂×C₄⋊C₄	—	2	1	no	—
806	C₂×C₄⋊C₄	—	2	1	no	—
807	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
808	C₂×C₂²⋊C₄	—	2	2	no	—
809	C₂×C₄²	—	2	1	no	—
810	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
811	#107	C₂³×C₇	1	2	yes	—
812	#107	C₂³×C₇	1	2	yes	—
813	#106	C₂³×C₇	1	1	yes	characteristic
814	#106	C₂³×C₇	1	1	yes	characteristic
815	#106	C₂³×C₇	1	1	yes	characteristic
816	#106	C₂³×C₇	1	1	yes	characteristic
817	C₄⋊C₈	C₂³×C₇	1	2	yes	—
818	C₄⋊C₈	C₂³×C₇	1	1	yes	characteristic
819	C₄⋊C₈	C₂³×C₇	1	1	yes	characteristic
820	C₄⋊C₈	C₂³×C₇	1	1	yes	characteristic
821	C₄⋊C₈	C₂³×C₇	1	2	yes	—
822	C₄⋊C₈	C₂³×C₇	1	2	yes	—
823	C₄⋊C₈	C₂³×C₇	1	1	yes	characteristic
824	#103	C₂³×C₇	1	2	yes	—
825	#103	C₂³×C₇	1	2	yes	—
826	#103	C₂³×C₇	1	2	yes	—
827	#103	C₂³×C₇	1	1	yes	characteristic
828	#103	C₂³×C₇	1	1	yes	characteristic
829	#103	C₂³×C₇	1	1	yes	characteristic
830	#103	C₂³×C₇	1	1	yes	characteristic
831	#103	C₂³×C₇	1	2	yes	—
832	#103	C₂³×C₇	1	2	yes	—
833	#103	C₂³×C₇	1	2	yes	—
834	#102	C₂³×C₇	1	1	yes	characteristic
835	#102	C₂³×C₇	1	2	yes	—
836	#102	C₂³×C₇	1	2	yes	—
837	#102	C₂³×C₇	1	2	yes	—
838	#102	C₂³×C₇	1	1	yes	characteristic
839	#102	C₂³×C₇	1	2	yes	—
840	#102	C₂³×C₇	1	2	yes	—
841	#102	C₂³×C₇	1	1	yes	characteristic
842	#102	C₂³×C₇	1	1	yes	characteristic
843	#102	C₂³×C₇	1	2	yes	—
844	C₂²⋊C₈	C₂³×C₇	1	1	yes	characteristic
845	C₂²⋊C₈	C₂³×C₇	1	1	yes	characteristic
846	C₂²⋊C₈	C₂³×C₇	1	2	yes	—
847	C₂²⋊C₈	C₂³×C₇	1	2	yes	—
848	#97	C₂³×C₇	1	2	yes	—
849	C₄×C₈	C₂³×C₇	1	1	yes	characteristic
850	C₄×C₈	C₂³×C₇	1	1	yes	characteristic
851	C₄×C₈	C₂³×C₇	1	2	yes	—
852	C₂²×C₇	—	2	1	no	—
853	C₂²×C₇	—	2	2	no	—
854	C₂²×C₇	—	2	1	no	—
855	C₂²×C₇	—	2	2	no	—
856	C₂²×C₇	—	2	1	no	—
857	C₂²×C₇	—	2	2	no	—
858	C₂²×C₇	—	4	1	no	—
859	C₂²×C₇	—	4	2	no	—
860	C₂²×C₇	—	4	1	no	—
861	C₂²×C₇	—	4	1	no	—
862	C₂²×C₇	—	4	2	no	—
863	C₂²×C₇	—	4	1	no	—
864	C₂²×C₇	—	4	1	no	—
865	C₂²×C₇	—	4	1	no	—
866	C₂²×C₇	—	4	2	no	—
867	C₂²×C₇	—	16	4	no	—
868	C₂²×C₇	C₂³×D₄	1	1	yes	characteristic
869	C₄×C₇	—	2	1	no	—
870	C₄×C₇	—	2	1	no	—
871	C₄×C₇	—	2	2	no	—
872	C₄×C₇	—	2	1	no	—
873	C₄×C₇	—	2	2	no	—
874	C₄×C₇	—	2	2	no	—
875	C₄×C₇	—	2	1	no	—
876	C₄×C₇	—	2	2	no	—
877	C₄×C₇	—	4	1	no	—
878	C₄×C₇	—	4	1	no	—
879	C₄×C₇	—	4	2	no	—
880	C₄×C₇	—	4	1	no	—
881	C₄×C₇	—	4	2	no	—
882	C₄×C₇	—	4	1	no	—
883	C₄×C₇	—	4	1	no	—
884	C₄×C₇	—	4	2	no	—
885	C₄×C₇	#577	1	2	yes	—
886	C₄×C₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
887	C₄×C₇	#585	1	1	yes	characteristic
888	C₂⁴	—	2	2	no	—
889	#41	—	4	2	no	—
890	#41	—	4	2	no	—
891	#41	—	4	2	no	—
892	#41	—	4	2	no	—
893	#41	—	8	2	no	—
894	#41	—	8	2	no	—
895	C₂×Q₈	—	2	1	no	—
896	C₂×Q₈	—	2	2	no	—
897	C₂×Q₈	—	2	1	no	—
898	C₂×Q₈	—	2	1	no	—
899	C₂×Q₈	—	2	4	no	—
900	C₂×Q₈	—	2	2	no	—
901	C₂×Q₈	—	4	2	no	—
902	C₂×Q₈	—	4	1	no	—
903	C₂×Q₈	C₂×C₇×D₄	1	1	yes	characteristic
904	C₂×Q₈	C₂⁴×C₇	1	2	yes	—
905	C₂×Q₈	C₂⁴×C₇	1	2	yes	—
906	C₂×Q₈	C₂⁴×C₇	1	1	yes	characteristic
907	C₂×Q₈	C₂⁴×C₇	1	1	yes	characteristic
908	C₂×D₄	—	2	1	no	—
909	C₂×D₄	—	2	2	no	—
910	C₂×D₄	—	2	2	no	—
911	C₂×D₄	—	2	2	no	—
912	C₂×D₄	—	2	1	no	—
913	C₂×D₄	—	2	1	no	—
914	C₂×D₄	—	2	1	no	—
915	C₂×D₄	—	2	1	no	—
916	C₂×D₄	—	2	2	no	—
917	C₂×D₄	—	2	1	no	—
918	C₂×D₄	—	2	2	no	—
919	C₂×D₄	—	2	2	no	—
920	C₂×D₄	—	4	2	no	—
921	C₂×D₄	—	4	2	no	—
922	C₂×D₄	—	8	2	no	—
923	C₂×D₄	C₂×C₇×D₄	1	1	yes	characteristic
924	C₂×D₄	C₂×C₇×D₄	1	2	yes	—
925	C₂×D₄	C₂⁴×C₇	1	1	yes	characteristic
926	C₂×D₄	C₂⁴×C₇	1	2	yes	—
927	C₂×D₄	C₂⁴×C₇	1	1	yes	characteristic
928	C₂²×C₄	—	2	1	no	—
929	C₂²×C₄	—	2	1	no	—
930	C₂²×C₄	—	2	2	no	—
931	C₂²×C₄	—	2	1	no	—
932	C₂²×C₄	—	2	1	no	—
933	C₂²×C₄	—	2	2	no	—
934	C₂²×C₄	—	2	2	no	—
935	C₂²×C₄	—	2	2	no	—
936	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
937	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
938	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
939	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
940	Q₁₆	—	2	4	no	—
941	Q₁₆	—	4	2	no	—
942	Q₁₆	—	4	2	no	—
943	Q₁₆	—	4	2	no	—
944	SD₁₆	—	2	2	no	—
945	SD₁₆	—	2	4	no	—
946	SD₁₆	—	2	2	no	—
947	SD₁₆	—	4	2	no	—
948	SD₁₆	—	4	2	no	—
949	SD₁₆	—	4	2	no	—
950	SD₁₆	—	4	1	no	—
951	SD₁₆	—	4	1	no	—
952	SD₁₆	—	4	2	no	—
953	SD₁₆	—	4	2	no	—
954	M₁₆	—	4	2	no	—
955	M₁₆	—	4	2	no	—
956	C₂×C₈	—	4	2	no	—
957	C₂×C₈	C₂⁴×C₇	1	1	yes	characteristic
958	C₂×C₈	C₂⁴×C₇	1	1	yes	characteristic
959	C₂×C₈	C₂⁴×C₇	1	1	yes	characteristic
960	C₂×C₈	C₂⁴×C₇	1	2	yes	—
961	C₂×C₈	C₂⁴×C₇	1	1	yes	characteristic
962	C₂×C₈	C₂⁴×C₇	1	2	yes	—
963	C₄⋊C₄	—	2	1	no	—
964	C₄⋊C₄	—	2	1	no	—
965	C₄⋊C₄	—	2	1	no	—
966	C₄⋊C₄	—	2	1	no	—
967	C₄⋊C₄	—	2	1	no	—
968	C₄⋊C₄	—	2	2	no	—
969	C₄⋊C₄	—	2	1	no	—
970	C₄⋊C₄	—	2	2	no	—
971	C₄⋊C₄	—	2	2	no	—
972	C₄⋊C₄	—	2	2	no	—
973	C₄⋊C₄	—	2	1	no	—
974	C₄⋊C₄	—	2	2	no	—
975	C₄⋊C₄	—	2	1	no	—
976	C₄⋊C₄	—	2	2	no	—
977	C₄⋊C₄	—	2	1	no	—
978	C₄⋊C₄	—	2	1	no	—
979	C₄⋊C₄	—	2	1	no	—
980	C₄⋊C₄	—	2	2	no	—
981	C₄⋊C₄	—	2	2	no	—
982	C₄⋊C₄	—	2	2	no	—
983	C₄⋊C₄	—	2	2	no	—
984	C₄⋊C₄	—	2	2	no	—
985	C₄⋊C₄	—	2	2	no	—
986	C₄⋊C₄	C₂×C₇×D₄	1	1	yes	characteristic
987	C₄⋊C₄	C₂×C₇×D₄	1	1	yes	characteristic
988	C₄⋊C₄	C₂×C₇×D₄	1	2	yes	—
989	C₄⋊C₄	C₂×C₇×D₄	1	2	yes	—
990	C₄⋊C₄	C₂×C₇×D₄	1	2	yes	—
991	C₄⋊C₄	C₂×C₇×D₄	1	2	yes	—
992	C₄⋊C₄	C₂⁴×C₇	1	1	yes	characteristic
993	C₄⋊C₄	C₂⁴×C₇	1	1	yes	characteristic
994	C₄⋊C₄	C₂⁴×C₇	1	2	yes	—
995	C₄⋊C₄	C₂⁴×C₇	1	1	yes	characteristic
996	C₄⋊C₄	C₂⁴×C₇	1	1	yes	characteristic
997	C₂²⋊C₄	—	2	2	no	—
998	C₂²⋊C₄	—	2	2	no	—
999	C₂²⋊C₄	—	2	2	no	—
1000	C₂²⋊C₄	—	2	2	no	—
1001	C₂²⋊C₄	—	2	2	no	—
1002	C₂²⋊C₄	—	2	1	no	—
1003	C₂²⋊C₄	—	2	2	no	—
1004	C₂²⋊C₄	—	2	2	no	—
1005	C₂²⋊C₄	—	2	1	no	—
1006	C₂²⋊C₄	—	2	2	no	—
1007	C₂²⋊C₄	—	2	2	no	—
1008	C₂²⋊C₄	—	2	2	no	—
1009	C₂²⋊C₄	—	2	1	no	—
1010	C₂²⋊C₄	—	2	2	no	—
1011	C₂²⋊C₄	—	2	1	no	—
1012	C₂²⋊C₄	C₂×C₇×D₄	1	2	yes	—
1013	C₂²⋊C₄	C₂×C₇×D₄	1	2	yes	—
1014	C₂²⋊C₄	C₂×C₇×D₄	1	2	yes	—
1015	C₂²⋊C₄	C₂×C₇×D₄	1	2	yes	—
1016	C₂²⋊C₄	C₂×C₇×D₄	1	2	yes	—
1017	C₄²	—	2	1	no	—
1018	C₄²	—	2	1	no	—
1019	C₄²	—	2	1	no	—
1020	C₄²	—	2	1	no	—
1021	C₄²	—	2	2	no	—
1022	C₄²	—	2	2	no	—
1023	C₄²	—	2	2	no	—
1024	C₄²	—	2	2	no	—
1025	C₄²	—	2	2	no	—
1026	C₄²	C₂×C₇×D₄	1	1	yes	characteristic
1027	C₄²	C₂×C₇×D₄	1	1	yes	characteristic
1028	C₄²	C₂⁴×C₇	1	1	yes	characteristic
1029	C₄²	C₂⁴×C₇	1	2	yes	—
1030	C₄²	C₂⁴×C₇	1	1	yes	characteristic
1031	C₂×C₇	—	4	1	no	—
1032	C₂×C₇	—	4	2	no	—
1033	C₂×C₇	—	8	1	no	—
1034	C₂×C₇	—	8	2	no	—
1035	C₂×C₇	—	8	1	no	—
1036	C₂×C₇	#3488	1	1	yes	characteristic
1037	C₂×C₇	C₂×#577	1	1	yes	characteristic
1038	C₂×C₇	#3586	1	1	yes	characteristic
1039	C₂³	—	2	1	no	—
1040	C₂³	—	2	2	no	—
1041	C₂³	—	2	1	no	—
1042	C₂³	—	8	2	no	—
1043	C₂³	—	8	2	no	—
1044	C₂³	—	8	2	no	—
1045	C₂³	C₂²×C₇×D₄	1	2	yes	—
1046	C₂³	C₂²×C₇×D₄	1	1	yes	characteristic
1047	Q₈	—	2	1	no	—
1048	Q₈	—	2	2	no	—
1049	Q₈	—	2	2	no	—
1050	Q₈	—	2	1	no	—
1051	Q₈	—	2	2	no	—
1052	Q₈	—	2	1	no	—
1053	Q₈	—	2	2	no	—
1054	Q₈	—	2	2	no	—
1055	Q₈	—	4	2	no	—
1056	Q₈	—	4	4	no	—
1057	Q₈	—	4	2	no	—
1058	Q₈	—	8	1	no	—
1059	Q₈	C₇×H(5,𝔽₂)	1	2	yes	—
1060	D₄	—	2	1	no	—
1061	D₄	—	2	2	no	—
1062	D₄	—	2	1	no	—
1063	D₄	—	2	1	no	—
1064	D₄	—	2	2	no	—
1065	D₄	—	2	1	no	—
1066	D₄	—	2	2	no	—
1067	D₄	—	4	2	no	—
1068	D₄	—	4	2	no	—
1069	D₄	—	8	1	no	—
1070	D₄	—	8	1	no	—
1071	D₄	—	8	2	no	—
1072	D₄	—	8	2	no	—
1073	D₄	—	8	1	no	—
1074	D₄	—	8	2	no	—
1075	D₄	—	8	2	no	—
1076	D₄	—	8	2	no	—
1077	D₄	—	8	2	no	—
1078	D₄	—	8	1	no	—
1079	D₄	—	8	1	no	—
1080	C₂×C₄	—	2	1	no	—
1081	C₂×C₄	—	2	2	no	—
1082	C₂×C₄	—	2	1	no	—
1083	C₂×C₄	—	2	2	no	—
1084	C₂×C₄	—	2	1	no	—
1085	C₂×C₄	—	2	2	no	—
1086	C₂×C₄	—	2	1	no	—
1087	C₂×C₄	—	2	2	no	—
1088	C₂×C₄	—	2	1	no	—
1089	C₂×C₄	—	2	1	no	—
1090	C₂×C₄	—	2	1	no	—
1091	C₂×C₄	—	2	2	no	—
1092	C₂×C₄	—	2	2	no	—
1093	C₂×C₄	—	2	1	no	—
1094	C₂×C₄	—	4	1	no	—
1095	C₂×C₄	—	4	2	no	—
1096	C₂×C₄	—	4	4	no	—
1097	C₂×C₄	—	4	2	no	—
1098	C₂×C₄	—	4	2	no	—
1099	C₂×C₄	—	4	2	no	—
1100	C₂×C₄	—	8	2	no	—
1101	C₂×C₄	—	8	2	no	—
1102	C₂×C₄	—	8	2	no	—
1103	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
1104	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
1105	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
1106	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
1107	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
1108	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
1109	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
1110	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
1111	C₂×C₄	C₂⁵×C₇	1	1	yes	characteristic
1112	C₈	—	2	1	no	—
1113	C₈	—	2	2	no	—
1114	C₈	—	2	1	no	—
1115	C₈	—	2	2	no	—
1116	C₈	—	2	1	no	—
1117	C₈	—	2	1	no	—
1118	C₇	#62044	1	1	yes	characteristic, direct product factor, Sylow
1119	C₂²	—	2	1	no	—
1120	C₂²	—	2	2	no	—
1121	C₂²	—	2	1	no	—
1122	C₂²	—	2	2	no	—
1123	C₂²	—	2	1	no	—
1124	C₂²	—	2	2	no	—
1125	C₂²	—	4	1	no	—
1126	C₂²	—	4	1	no	—
1127	C₂²	—	4	2	no	—
1128	C₂²	—	4	1	no	—
1129	C₂²	—	4	2	no	—
1130	C₂²	—	4	1	no	—
1131	C₂²	—	4	1	no	—
1132	C₂²	—	4	2	no	—
1133	C₂²	—	4	1	no	—
1134	C₂²	—	16	4	no	—
1135	C₂²	C₂³×C₇×D₄	1	1	yes	characteristic
1136	C₄	—	2	1	no	—
1137	C₄	—	2	2	no	—
1138	C₄	—	2	1	no	—
1139	C₄	—	2	1	no	—
1140	C₄	—	2	2	no	—
1141	C₄	—	2	1	no	—
1142	C₄	—	2	2	no	—
1143	C₄	—	2	2	no	—
1144	C₄	—	4	1	no	—
1145	C₄	—	4	1	no	—
1146	C₄	—	4	2	no	—
1147	C₄	—	4	1	no	—
1148	C₄	—	4	1	no	—
1149	C₄	—	4	2	no	—
1150	C₄	—	4	1	no	—
1151	C₄	—	4	2	no	—
1152	C₄	C₇×#577	1	2	yes	—
1153	C₄	C₂×C₇×H(5,𝔽₂)	1	1	yes	characteristic
1154	C₄	C₇×#585	1	1	yes	characteristic
1155	C₂	—	4	2	no	—
1156	C₂	—	4	1	no	—
1157	C₂	—	8	1	no	—
1158	C₂	—	8	2	no	—
1159	C₂	—	8	1	no	—
1160	C₂	C₇×#3488	1	1	yes	characteristic
1161	C₂	C₂×C₇×#577	1	1	yes	characteristic
1162	C₂	C₇×#3586	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₇	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₇
prime radical	C₇×#3546	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₇ ◁ C₇×#529 ◁ G

Complements

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

N	H ≅ G/N	type
2. C₇×#3523	C₂	semidirect
3. C₇×#3398	C₂	semidirect
4. C₇×#3392	C₂	semidirect
5. C₇×#3368	C₂	semidirect
6. C₇×#3364	C₂	semidirect
7. C₇×#3324	C₂	semidirect
8. C₇×#3323	C₂	semidirect
9. C₇×#3317	C₂	semidirect
10. C₇×#3302	C₂	semidirect
11. C₇×D₄×SD₁₆	C₂	semidirect
12. C₇×#3278	C₂	semidirect
13. C₇×#3276	C₂	semidirect
14. C₇×#3266	C₂	semidirect
15. C₇×#3258	C₂	semidirect
16. C₇×#3254	C₂	semidirect
17. C₇×#3222	C₂	semidirect
18. C₇×#3210	C₂	semidirect
19. C₇×#3121	C₂	semidirect
20. C₇×#3103	C₂	semidirect
21. C₇×#3043	C₂	semidirect
22. C₇×#3037	C₂	semidirect
23. C₇×#2993	C₂	semidirect
24. C₂×C₇×#137	C₂²	semidirect
25. C₂×C₇×#137	C₂²	semidirect
29. C₇×#557	C₂²	semidirect
30. C₇×#557	C₂²	semidirect
36. C₇×#552	C₂²	semidirect
40. C₇×D₄×Q₈	C₂²	semidirect
47. C₇×#541	C₂²	semidirect
53. C₇×#533	C₂²	semidirect
58. C₇×#519	C₂²	semidirect
59. C₂×C₄×C₇×Q₈	C₂²	semidirect
61. C₇×#494	C₂²	semidirect
63. C₇×#492	C₂²	semidirect
64. C₇×#490	C₂²	semidirect
66. C₇×#487	C₂²	semidirect
68. C₇×#485	C₂²	semidirect
71. C₇×#481	C₂²	semidirect
72. C₇×#479	C₂²	semidirect
73. C₇×#478	C₂²	semidirect
74. C₇×#477	C₂²	semidirect
75. C₇×#475	C₂²	semidirect
76. C₇×#475	C₂²	semidirect
78. C₇×#474	C₂²	semidirect
79. C₇×#470	C₂²	semidirect
82. C₇×#468	C₂²	semidirect
83. C₇×#467	C₂²	semidirect
87. C₇×#464	C₂²	semidirect
88. C₇×#464	C₂²	semidirect
89. C₇×#464	C₂²	semidirect
90. C₇×#464	C₂²	semidirect
91. C₇×#462	C₂²	semidirect
92. C₇×#462	C₂²	semidirect
93. C₇×#462	C₂²	semidirect
95. C₇×#461	C₂²	semidirect
96. C₇×#461	C₂²	semidirect
102. C₇×#460	C₂²	semidirect
103. C₇×#460	C₂²	semidirect
104. C₇×#452	C₂²	semidirect
105. C₇×#452	C₂²	semidirect
106. C₇×#452	C₂²	semidirect
107. C₇×#452	C₂²	semidirect
108. C₇×#451	C₂²	semidirect
113. C₇×#448	C₂²	semidirect
114. C₇×#446	C₂²	semidirect
115. C₇×C₈×Q₈	C₂²	semidirect
116. C₇×#441	C₂²	semidirect
117. C₇×#440	C₂²	semidirect
118. C₄×C₇×Q₁₆	C₂²	semidirect
121. C₄×C₇×SD₁₆	C₂²	semidirect
122. C₄×C₇×SD₁₆	C₂²	semidirect
123. C₄×C₇×SD₁₆	C₂²	semidirect
125. C₇×#436	C₂²	semidirect
126. C₇×#435	C₂²	semidirect
128. C₇×#433	C₂²	semidirect
129. C₇×#431	C₂²	semidirect
130. C₇×#424	C₂²	semidirect
131. C₇×#423	C₂²	semidirect
133. C₇×#417	C₂²	semidirect
134. C₇×#416	C₂²	semidirect
135. #62044	C₇	direct (N × H)
317. #3523	C₂×C₇	semidirect
318. #3398	C₂×C₇	semidirect
319. #3392	C₂×C₇	semidirect
320. #3368	C₂×C₇	semidirect
321. #3364	C₂×C₇	semidirect
322. #3324	C₂×C₇	semidirect
323. #3323	C₂×C₇	semidirect
324. #3317	C₂×C₇	semidirect
325. #3302	C₂×C₇	semidirect
326. D₄×SD₁₆	C₂×C₇	semidirect
327. #3278	C₂×C₇	semidirect
328. #3276	C₂×C₇	semidirect
329. #3266	C₂×C₇	semidirect
330. #3258	C₂×C₇	semidirect
331. #3254	C₂×C₇	semidirect
332. #3222	C₂×C₇	semidirect
333. #3210	C₂×C₇	semidirect
334. #3121	C₂×C₇	semidirect
335. #3103	C₂×C₇	semidirect
336. #3043	C₂×C₇	semidirect
337. #3037	C₂×C₇	semidirect
338. #2993	C₂×C₇	semidirect
482. C₂×#137	C₂²×C₇	semidirect
483. C₂×#137	C₂²×C₇	semidirect
487. #557	C₂²×C₇	semidirect
488. #557	C₂²×C₇	semidirect
494. #552	C₂²×C₇	semidirect
498. D₄×Q₈	C₂²×C₇	semidirect
505. #541	C₂²×C₇	semidirect
511. #533	C₂²×C₇	semidirect
516. #519	C₂²×C₇	semidirect
517. C₂×C₄×Q₈	C₂²×C₇	semidirect
519. #494	C₂²×C₇	semidirect
521. #492	C₂²×C₇	semidirect
522. #490	C₂²×C₇	semidirect
524. #487	C₂²×C₇	semidirect
526. #485	C₂²×C₇	semidirect
529. #481	C₂²×C₇	semidirect
530. #479	C₂²×C₇	semidirect
531. #478	C₂²×C₇	semidirect
532. #477	C₂²×C₇	semidirect
533. #475	C₂²×C₇	semidirect
534. #475	C₂²×C₇	semidirect
536. #474	C₂²×C₇	semidirect
537. #470	C₂²×C₇	semidirect
540. #468	C₂²×C₇	semidirect
541. #467	C₂²×C₇	semidirect
545. #464	C₂²×C₇	semidirect
546. #464	C₂²×C₇	semidirect
547. #464	C₂²×C₇	semidirect
548. #464	C₂²×C₇	semidirect
549. #462	C₂²×C₇	semidirect
550. #462	C₂²×C₇	semidirect
551. #462	C₂²×C₇	semidirect
553. #461	C₂²×C₇	semidirect
554. #461	C₂²×C₇	semidirect
560. #460	C₂²×C₇	semidirect
561. #460	C₂²×C₇	semidirect
562. #452	C₂²×C₇	semidirect
563. #452	C₂²×C₇	semidirect
564. #452	C₂²×C₇	semidirect
565. #452	C₂²×C₇	semidirect
566. #451	C₂²×C₇	semidirect
571. #448	C₂²×C₇	semidirect
572. #446	C₂²×C₇	semidirect
573. C₈×Q₈	C₂²×C₇	semidirect
574. #441	C₂²×C₇	semidirect
575. #440	C₂²×C₇	semidirect
576. C₄×Q₁₆	C₂²×C₇	semidirect
579. C₄×SD₁₆	C₂²×C₇	semidirect
580. C₄×SD₁₆	C₂²×C₇	semidirect
581. C₄×SD₁₆	C₂²×C₇	semidirect
583. #436	C₂²×C₇	semidirect
584. #435	C₂²×C₇	semidirect
586. #433	C₂²×C₇	semidirect
587. #431	C₂²×C₇	semidirect
588. #424	C₂²×C₇	semidirect
589. #423	C₂²×C₇	semidirect
591. #417	C₂²×C₇	semidirect
592. #416	C₂²×C₇	semidirect
1118. C₇	#62044	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×#3546	2
C₇×#3523	2
C₇×#3398	2
C₇×#3392	2
C₇×#3368	2
C₇×#3364	2
C₇×#3324	2
C₇×#3323	2
C₇×#3317	2
C₇×#3302	2
C₇×D₄×SD₁₆	2
C₇×#3278	2
C₇×#3276	2
C₇×#3266	2
C₇×#3258	2
C₇×#3254	2
C₇×#3222	2
C₇×#3210	2
C₇×#3121	2
C₇×#3103	2
C₇×#3043	2
C₇×#3037	2
C₇×#2993	2
#62044	7

Subgroups — C7×#62044 #13239260

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×#62044 #13239260