Subgroups — C₇×#61206 #13238422

Order 1792.

2150 conjugacy classes of subgroups.

The subgroup lattice has 862 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×#3507	C₂	1	1	yes	maximal, characteristic, complemented
2	C₇×#3498	C₂	1	1	yes	maximal, characteristic
3	C₇×#3333	C₂	1	2	yes	maximal, complemented
4	C₇×#3324	C₂	1	2	yes	maximal, complemented
5	C₇×#3317	C₂	1	4	yes	maximal, complemented
6	C₇×#3310	C₂	1	4	yes	maximal, complemented
7	C₇×#3304	C₂	1	2	yes	maximal, complemented
8	C₇×#3295	C₂	1	2	yes	maximal, complemented
9	C₇×#3138	C₂	1	1	yes	maximal, characteristic, complemented
10	C₇×#3096	C₂	1	2	yes	maximal, complemented
11	C₇×#3076	C₂	1	1	yes	maximal, characteristic, complemented
12	C₇×#3057	C₂	1	2	yes	maximal, complemented
13	C₂×C₇×#460	C₂	1	1	yes	maximal, characteristic, complemented
14	C₇×#3009	C₂	1	2	yes	maximal, complemented
15	C₄×C₇×#137	C₂	1	1	yes	maximal, characteristic, complemented
16	C₇×#2935	C₂	1	1	yes	maximal, characteristic, complemented
17	C₇×#2897	C₂	1	2	yes	maximal, complemented
18	C₂×C₇×H(5,𝔽₂)	C₂²	1	2	yes	—
19	C₂×C₇×#137	C₂²	1	1	yes	characteristic
20	C₂²×C₇×SD₁₆	C₂²	1	2	yes	complemented
21	C₂×C₇×#131	C₂²	1	2	yes	complemented
22	C₇×#559	—	2	1	no	—
23	C₇×#557	—	2	1	no	—
24	C₇×#556	—	2	2	no	—
25	C₇×#556	C₂²	1	2	yes	complemented
26	C₇×#554	C₂²	1	2	yes	complemented
27	C₇×#552	C₂²	1	4	yes	complemented
28	C₇×#550	C₂²	1	2	yes	—
29	C₇×#550	C₂²	1	2	yes	—
30	C₇×D₄²	—	2	2	no	—
31	C₇×D₄²	—	2	2	no	—
32	C₇×D₄²	C₂²	1	2	yes	—
33	C₇×D₄²	C₂²	1	2	yes	—
34	C₇×#539	—	2	2	no	—
35	C₇×#536	C₂²	1	2	yes	complemented
36	C₇×#535	—	2	2	no	—
37	C₇×#535	C₂²	1	2	yes	—
38	C₇×#533	C₂²	1	1	yes	characteristic, complemented
39	C₇×#532	—	2	1	no	—
40	C₇×#532	C₂²	1	1	yes	characteristic
41	C₂×C₇×#127	—	2	1	no	—
42	C₂×C₇×#127	C₂²	1	1	yes	characteristic
43	C₇×#529	—	2	2	no	—
44	C₇×#520	C₂²	1	2	yes	complemented
45	C₄×C₇×#41	C₂²	1	1	yes	characteristic
46	C₂×C₄×C₇×Q₈	C₂²	1	1	yes	characteristic, complemented
47	C₇×#490	C₂²	1	4	yes	complemented
48	C₇×#486	C₂²	1	2	yes	complemented
49	C₇×#486	C₂²	1	2	yes	complemented
50	C₇×#482	C₂²	1	4	yes	complemented
51	C₇×#482	C₂²	1	4	yes	complemented
52	C₇×#481	C₂²	1	4	yes	complemented
53	C₇×#480	C₂²	1	4	yes	complemented
54	C₇×#479	C₂²	1	2	yes	complemented
55	C₇×#478	C₂²	1	2	yes	complemented
56	C₇×#477	C₂²	1	1	yes	characteristic, complemented
57	C₇×#476	C₂²	1	1	yes	characteristic, complemented
58	C₇×#475	C₂²	1	1	yes	characteristic, complemented
59	C₇×#474	C₂²	1	1	yes	characteristic, complemented
60	C₇×#468	C₂²	1	4	yes	complemented
61	C₇×#468	C₂²	1	4	yes	complemented
62	C₇×#465	C₂²	1	4	yes	complemented
63	C₇×#465	C₂²	1	4	yes	complemented
64	C₇×#460	C₂²	1	2	yes	complemented
65	C₇×#460	C₂²	1	4	yes	complemented
66	C₇×#460	C₂²	1	2	yes	complemented
67	C₇×#452	C₂²	1	4	yes	complemented
68	C₇×#452	C₂²	1	4	yes	complemented
69	C₇×#450	C₂²	1	4	yes	complemented
70	C₇×#450	C₂²	1	4	yes	complemented
71	C₇×#441	C₂²	1	2	yes	complemented
72	C₇×#440	C₂²	1	2	yes	complemented
73	C₄×C₇×Q₁₆	C₂²	1	2	yes	complemented
74	C₄×C₇×SD₁₆	C₂²	1	2	yes	complemented
75	C₇×#436	C₂²	1	2	yes	complemented
76	C₇×#435	C₂²	1	4	yes	complemented
77	C₇×C₈×D₄	C₂²	1	2	yes	complemented
78	C₇×#428	C₂²	1	1	yes	characteristic, complemented
79	C₇×#427	C₂²	1	2	yes	complemented
80	C₂×C₇×C₄⋊C₈	C₂²	1	1	yes	characteristic, complemented
81	C₇×#419	C₂²	1	1	yes	characteristic, complemented
82	C₇×#418	C₂²	1	2	yes	complemented
83	C₇×#418	C₂²	1	4	yes	complemented
84	C₇×#418	C₂²	1	2	yes	complemented
85	C₇×#417	C₂²	1	1	yes	characteristic
86	C₇×#417	C₂²	1	4	yes	complemented
87	C₇×#416	C₂²	1	2	yes	—
88	C₇×#416	C₂²	1	4	yes	complemented
89	C₂×C₇×#102	C₂²	1	2	yes	complemented
90	C₂×C₇×#102	C₂²	1	4	yes	complemented
91	C₇×#408	C₂²	1	2	yes	complemented
92	C₄×C₇×M₁₆	C₂²	1	1	yes	characteristic, complemented
93	#61206	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
94	C₇×H(5,𝔽₂)	—	2	8	no	—
95	C₇×H(5,𝔽₂)	—	4	4	no	—
96	C₂×C₇×#41	—	2	2	no	—
97	C₂×C₇×#41	C₂³	1	4	yes	—
98	C₂×C₇×#41	C₂³	1	1	yes	characteristic
99	C₂×C₇×#41	C₂³	1	2	yes	—
100	C₂²×C₇×Q₈	C₂³	1	1	yes	characteristic
101	C₂²×C₇×D₄	—	2	2	no	—
102	C₂²×C₇×D₄	—	2	4	no	—
103	C₂²×C₇×D₄	—	2	2	no	—
104	C₂²×C₇×D₄	—	2	2	no	—
105	C₂²×C₇×D₄	—	2	1	no	—
106	C₂²×C₇×D₄	—	2	1	no	—
107	C₂²×C₇×D₄	C₂³	1	2	yes	—
108	C₂²×C₇×D₄	C₂³	1	4	yes	—
109	C₇×#137	—	2	4	no	—
110	C₂×C₇×Q₁₆	C₂³	1	2	yes	—
111	C₂×C₇×SD₁₆	—	4	4	no	—
112	C₂×C₇×SD₁₆	C₂³	1	2	yes	—
113	C₂×C₇×SD₁₆	C₂³	1	4	yes	—
114	C₂×C₇×SD₁₆	C₂³	1	4	yes	—
115	C₇×#131	—	4	4	no	—
116	C₂×C₇×M₁₆	C₂³	1	1	yes	characteristic
117	C₂×C₇×M₁₆	C₂³	1	1	yes	characteristic
118	C₂×C₇×M₁₆	C₂³	1	4	yes	—
119	C₂²×C₇×C₈	C₂³	1	2	yes	—
120	C₂²×C₇×C₈	C₂³	1	4	yes	—
121	C₇×C₄⋊Q₈	—	2	2	no	—
122	C₇×C₄⋊Q₈	D₄	1	1	yes	characteristic
123	C₇×C₄⋊Q₈	C₂³	1	1	yes	characteristic
124	C₇×C₄⋊Q₈	C₂³	1	1	yes	characteristic
125	C₇×#127	—	2	2	no	—
126	C₇×#127	—	2	2	no	—
127	C₇×#127	—	2	2	no	—
128	C₇×#127	—	2	1	no	—
129	C₇×#127	—	2	1	no	—
130	C₇×#127	D₄	1	1	yes	characteristic
131	C₇×#127	C₂³	1	2	yes	—
132	C₇×#127	C₂³	1	2	yes	—
133	C₇×#126	—	2	4	no	—
134	C₇×#126	—	2	4	no	—
135	C₇×#125	—	2	2	no	—
136	C₇×#125	—	2	4	no	—
137	C₇×#125	C₂³	1	2	yes	—
138	C₇×#124	—	2	2	no	—
139	C₇×#124	—	2	2	no	—
140	C₇×#124	—	2	2	no	—
141	C₇×#124	D₄	1	2	yes	—
142	C₇×#123	—	2	4	no	—
143	C₇×#123	—	2	4	no	—
144	C₇×C₂²⋊Q₈	—	2	1	no	—
145	C₇×C₂²⋊Q₈	—	2	1	no	—
146	C₇×C₂²⋊Q₈	—	2	4	no	—
147	C₇×C₂²⋊Q₈	C₂³	1	4	yes	—
148	C₇×C₂²⋊Q₈	C₂³	1	4	yes	—
149	C₇×#121	—	2	2	no	—
150	C₇×#121	—	2	2	no	—
151	C₇×#121	—	2	4	no	—
152	C₇×#121	—	2	4	no	—
153	C₇×#121	D₄	1	2	yes	—
154	C₇×#121	D₄	1	2	yes	—
155	C₇×#121	C₂³	1	4	yes	—
156	C₇×#121	C₂³	1	4	yes	—
157	C₇×#120	—	2	4	no	—
158	C₇×#120	—	2	4	no	—
159	C₇×#120	—	2	4	no	—
160	C₄×C₇×Q₈	—	2	2	no	—
161	C₄×C₇×Q₈	—	2	2	no	—
162	C₄×C₇×Q₈	—	2	1	no	—
163	C₄×C₇×Q₈	—	2	1	no	—
164	C₄×C₇×Q₈	—	2	1	no	—
165	C₄×C₇×Q₈	—	2	1	no	—
166	C₄×C₇×Q₈	C₂³	1	1	yes	characteristic
167	C₄×C₇×Q₈	C₂³	1	1	yes	characteristic
168	C₄×C₇×Q₈	C₂³	1	2	yes	—
169	C₄×C₇×Q₈	C₂³	1	2	yes	—
170	C₄×C₇×D₄	—	2	4	no	—
171	C₄×C₇×D₄	—	2	2	no	—
172	C₄×C₇×D₄	—	2	2	no	—
173	C₄×C₇×D₄	—	2	1	no	—
174	C₄×C₇×D₄	—	2	1	no	—
175	C₄×C₇×D₄	—	2	2	no	—
176	C₄×C₇×D₄	—	2	2	no	—
177	C₄×C₇×D₄	C₂³	1	1	yes	characteristic
178	C₄×C₇×D₄	C₂³	1	1	yes	characteristic
179	C₄×C₇×D₄	C₂³	1	2	yes	—
180	C₄×C₇×D₄	C₂³	1	2	yes	—
181	C₇×#117	—	2	4	no	—
182	C₇×#117	—	2	1	no	—
183	C₇×#117	C₂³	1	4	yes	—
184	C₇×#117	C₂³	1	1	yes	characteristic
185	C₇×#117	C₂³	1	2	yes	—
186	C₂×C₇×C₄⋊C₄	—	2	1	no	—
187	C₂×C₇×C₄⋊C₄	C₂³	1	4	yes	—
188	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
189	C₂×C₄²×C₇	—	2	1	no	—
190	C₂×C₄²×C₇	—	2	1	no	—
191	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
192	C₇×#107	C₂³	1	2	yes	—
193	C₇×#107	C₂³	1	2	yes	—
194	C₇×#107	C₂³	1	2	yes	—
195	C₇×#106	C₂³	1	2	yes	—
196	C₇×#106	C₂³	1	2	yes	—
197	C₇×#106	C₂³	1	2	yes	—
198	C₇×C₄⋊C₈	C₂³	1	1	yes	characteristic
199	C₇×C₄⋊C₈	C₂³	1	1	yes	characteristic
200	C₇×C₄⋊C₈	C₂³	1	2	yes	—
201	C₇×#103	C₂³	1	2	yes	—
202	C₇×#103	C₂³	1	2	yes	—
203	C₇×#103	C₂³	1	2	yes	—
204	C₇×#103	C₂³	1	2	yes	—
205	C₇×#103	C₂³	1	2	yes	—
206	C₇×#102	C₂³	1	4	yes	—
207	C₇×#102	C₂³	1	4	yes	—
208	C₇×#102	C₂³	1	2	yes	—
209	C₇×#102	C₂³	1	2	yes	—
210	C₇×#102	C₂³	1	4	yes	—
211	C₇×#102	C₂³	1	4	yes	—
212	C₇×#102	C₂³	1	4	yes	—
213	C₇×#102	C₂³	1	4	yes	—
214	C₇×#102	C₂³	1	2	yes	—
215	C₇×C₂²⋊C₈	C₂³	1	4	yes	—
216	C₇×C₂²⋊C₈	C₂³	1	4	yes	—
217	C₇×#97	C₂³	1	2	yes	—
218	C₄×C₇×C₈	C₂³	1	2	yes	—
219	#3507	C₂×C₇	1	1	yes	characteristic, complemented
220	#3498	C₂×C₇	1	1	yes	characteristic
221	#3333	C₂×C₇	1	2	yes	complemented
222	#3324	C₂×C₇	1	2	yes	complemented
223	#3317	C₂×C₇	1	4	yes	complemented
224	#3310	C₂×C₇	1	4	yes	complemented
225	#3304	C₂×C₇	1	2	yes	complemented
226	#3295	C₂×C₇	1	2	yes	complemented
227	#3138	C₂×C₇	1	1	yes	characteristic, complemented
228	#3096	C₂×C₇	1	2	yes	complemented
229	#3076	C₂×C₇	1	1	yes	characteristic, complemented
230	#3057	C₂×C₇	1	2	yes	complemented
231	C₂×#460	C₂×C₇	1	1	yes	characteristic, complemented
232	#3009	C₂×C₇	1	2	yes	complemented
233	C₄×#137	C₂×C₇	1	1	yes	characteristic, complemented
234	#2935	C₂×C₇	1	1	yes	characteristic, complemented
235	#2897	C₂×C₇	1	2	yes	complemented
236	C₂⁴×C₇	—	2	4	no	—
237	C₂⁴×C₇	—	2	2	no	—
238	C₇×#41	—	2	4	no	—
239	C₇×#41	—	2	4	no	—
240	C₇×#41	—	2	2	no	—
241	C₇×#41	—	2	8	no	—
242	C₇×#41	—	4	4	no	—
243	C₇×#41	—	4	8	no	—
244	C₇×#41	#41	1	4	yes	—
245	C₂×C₇×Q₈	—	2	1	no	—
246	C₂×C₇×Q₈	—	2	1	no	—
247	C₂×C₇×Q₈	—	2	1	no	—
248	C₂×C₇×Q₈	—	2	2	no	—
249	C₂×C₇×Q₈	—	2	2	no	—
250	C₂×C₇×Q₈	C₂×D₄	1	2	yes	—
251	C₂×C₇×Q₈	C₂⁴	1	2	yes	—
252	C₂×C₇×Q₈	C₂⁴	1	1	yes	characteristic
253	C₂×C₇×D₄	—	2	1	no	—
254	C₂×C₇×D₄	—	2	8	no	—
255	C₂×C₇×D₄	—	2	4	no	—
256	C₂×C₇×D₄	—	2	4	no	—
257	C₂×C₇×D₄	—	2	4	no	—
258	C₂×C₇×D₄	—	2	2	no	—
259	C₂×C₇×D₄	—	2	2	no	—
260	C₂×C₇×D₄	—	2	4	no	—
261	C₂×C₇×D₄	—	2	2	no	—
262	C₂×C₇×D₄	—	2	2	no	—
263	C₂×C₇×D₄	—	2	2	no	—
264	C₂×C₇×D₄	—	2	4	no	—
265	C₂×C₇×D₄	—	2	4	no	—
266	C₂×C₇×D₄	—	4	4	no	—
267	C₂×C₇×D₄	—	4	8	no	—
268	C₂×C₇×D₄	—	4	16	no	—
269	C₂×C₇×D₄	—	8	2	no	—
270	C₂×C₇×D₄	—	8	4	no	—
271	C₂×C₇×D₄	—	8	2	no	—
272	C₂×C₇×D₄	—	8	4	no	—
273	C₂×C₇×D₄	C₂×D₄	1	2	yes	—
274	C₂×C₇×D₄	C₂×D₄	1	4	yes	—
275	C₂×C₇×D₄	C₂×D₄	1	2	yes	—
276	C₂×C₇×D₄	C₂×D₄	1	2	yes	—
277	C₂×C₇×D₄	C₂⁴	1	4	yes	—
278	C₂×C₇×D₄	C₂⁴	1	1	yes	characteristic
279	C₂²×C₄×C₇	—	2	1	no	—
280	C₂²×C₄×C₇	—	2	1	no	—
281	C₂²×C₄×C₇	—	2	1	no	—
282	C₂²×C₄×C₇	—	2	4	no	—
283	C₂²×C₄×C₇	—	2	1	no	—
284	C₂²×C₄×C₇	—	2	1	no	—
285	C₂²×C₄×C₇	—	2	4	no	—
286	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
287	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
288	C₂²×C₄×C₇	C₂⁴	1	4	yes	—
289	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
290	C₇×Q₁₆	—	2	4	no	—
291	C₇×SD₁₆	—	2	4	no	—
292	C₇×SD₁₆	—	4	4	no	—
293	C₇×SD₁₆	—	4	4	no	—
294	C₇×M₁₆	—	2	2	no	—
295	C₇×M₁₆	—	2	2	no	—
296	C₇×M₁₆	—	4	4	no	—
297	C₂×C₇×C₈	—	2	4	no	—
298	C₂×C₇×C₈	—	4	4	no	—
299	C₂×C₇×C₈	C₂⁴	1	2	yes	—
300	C₂×C₇×C₈	C₂⁴	1	2	yes	—
301	C₂×C₇×C₈	C₂⁴	1	2	yes	—
302	C₂×C₇×C₈	C₂⁴	1	2	yes	—
303	C₇×C₄⋊C₄	—	2	2	no	—
304	C₇×C₄⋊C₄	—	2	2	no	—
305	C₇×C₄⋊C₄	—	2	1	no	—
306	C₇×C₄⋊C₄	—	2	4	no	—
307	C₇×C₄⋊C₄	—	2	2	no	—
308	C₇×C₄⋊C₄	—	2	1	no	—
309	C₇×C₄⋊C₄	—	2	1	no	—
310	C₇×C₄⋊C₄	—	2	4	no	—
311	C₇×C₄⋊C₄	—	2	1	no	—
312	C₇×C₄⋊C₄	—	2	2	no	—
313	C₇×C₄⋊C₄	—	2	1	no	—
314	C₇×C₄⋊C₄	—	2	4	no	—
315	C₇×C₄⋊C₄	C₂×D₄	1	2	yes	—
316	C₇×C₄⋊C₄	C₂×D₄	1	2	yes	—
317	C₇×C₄⋊C₄	C₂⁴	1	2	yes	—
318	C₇×C₄⋊C₄	C₂⁴	1	2	yes	—
319	C₇×C₄⋊C₄	C₂⁴	1	2	yes	—
320	C₇×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
321	C₇×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
322	C₇×C₂²⋊C₄	—	2	4	no	—
323	C₇×C₂²⋊C₄	—	2	1	no	—
324	C₇×C₂²⋊C₄	—	2	2	no	—
325	C₇×C₂²⋊C₄	—	2	4	no	—
326	C₇×C₂²⋊C₄	—	2	4	no	—
327	C₇×C₂²⋊C₄	—	2	1	no	—
328	C₇×C₂²⋊C₄	—	2	1	no	—
329	C₇×C₂²⋊C₄	—	2	4	no	—
330	C₇×C₂²⋊C₄	—	2	4	no	—
331	C₇×C₂²⋊C₄	C₂×D₄	1	4	yes	—
332	C₇×C₂²⋊C₄	C₂×D₄	1	4	yes	—
333	C₄²×C₇	—	2	2	no	—
334	C₄²×C₇	—	2	1	no	—
335	C₄²×C₇	—	2	1	no	—
336	C₄²×C₇	—	2	1	no	—
337	C₄²×C₇	—	2	2	no	—
338	C₄²×C₇	—	2	4	no	—
339	C₄²×C₇	—	2	2	no	—
340	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
341	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
342	C₄²×C₇	C₂⁴	1	1	yes	characteristic
343	C₄²×C₇	C₂⁴	1	1	yes	characteristic
344	C₂×H(5,𝔽₂)	C₂²×C₇	1	2	yes	—
345	C₂×#137	C₂²×C₇	1	1	yes	characteristic
346	C₂²×SD₁₆	C₂²×C₇	1	2	yes	complemented
347	C₂×#131	C₂²×C₇	1	2	yes	complemented
348	#559	—	2	1	no	—
349	#557	—	2	1	no	—
350	#556	—	2	2	no	—
351	#556	C₂²×C₇	1	2	yes	complemented
352	#554	C₂²×C₇	1	2	yes	complemented
353	#552	C₂²×C₇	1	4	yes	complemented
354	#550	C₂²×C₇	1	2	yes	—
355	#550	C₂²×C₇	1	2	yes	—
356	D₄²	—	2	2	no	—
357	D₄²	—	2	2	no	—
358	D₄²	C₂²×C₇	1	2	yes	—
359	D₄²	C₂²×C₇	1	2	yes	—
360	#539	—	2	2	no	—
361	#536	C₂²×C₇	1	2	yes	complemented
362	#535	—	2	2	no	—
363	#535	C₂²×C₇	1	2	yes	—
364	#533	C₂²×C₇	1	1	yes	characteristic, complemented
365	#532	—	2	1	no	—
366	#532	C₂²×C₇	1	1	yes	characteristic
367	C₂×#127	—	2	1	no	—
368	C₂×#127	C₂²×C₇	1	1	yes	characteristic
369	#529	—	2	2	no	—
370	#520	C₂²×C₇	1	2	yes	complemented
371	C₄×#41	C₂²×C₇	1	1	yes	characteristic
372	C₂×C₄×Q₈	C₂²×C₇	1	1	yes	characteristic, complemented
373	#490	C₂²×C₇	1	4	yes	complemented
374	#486	C₂²×C₇	1	2	yes	complemented
375	#486	C₂²×C₇	1	2	yes	complemented
376	#482	C₂²×C₇	1	4	yes	complemented
377	#482	C₂²×C₇	1	4	yes	complemented
378	#481	C₂²×C₇	1	4	yes	complemented
379	#480	C₂²×C₇	1	4	yes	complemented
380	#479	C₂²×C₇	1	2	yes	complemented
381	#478	C₂²×C₇	1	2	yes	complemented
382	#477	C₂²×C₇	1	1	yes	characteristic, complemented
383	#476	C₂²×C₇	1	1	yes	characteristic, complemented
384	#475	C₂²×C₇	1	1	yes	characteristic, complemented
385	#474	C₂²×C₇	1	1	yes	characteristic, complemented
386	#468	C₂²×C₇	1	4	yes	complemented
387	#468	C₂²×C₇	1	4	yes	complemented
388	#465	C₂²×C₇	1	4	yes	complemented
389	#465	C₂²×C₇	1	4	yes	complemented
390	#460	C₂²×C₇	1	2	yes	complemented
391	#460	C₂²×C₇	1	2	yes	complemented
392	#460	C₂²×C₇	1	4	yes	complemented
393	#452	C₂²×C₇	1	4	yes	complemented
394	#452	C₂²×C₇	1	4	yes	complemented
395	#450	C₂²×C₇	1	4	yes	complemented
396	#450	C₂²×C₇	1	4	yes	complemented
397	#441	C₂²×C₇	1	2	yes	complemented
398	#440	C₂²×C₇	1	2	yes	complemented
399	C₄×Q₁₆	C₂²×C₇	1	2	yes	complemented
400	C₄×SD₁₆	C₂²×C₇	1	2	yes	complemented
401	#436	C₂²×C₇	1	2	yes	complemented
402	#435	C₂²×C₇	1	4	yes	complemented
403	C₈×D₄	C₂²×C₇	1	2	yes	complemented
404	#428	C₂²×C₇	1	1	yes	characteristic, complemented
405	#427	C₂²×C₇	1	2	yes	complemented
406	C₂×C₄⋊C₈	C₂²×C₇	1	1	yes	characteristic, complemented
407	#419	C₂²×C₇	1	1	yes	characteristic, complemented
408	#418	C₂²×C₇	1	2	yes	complemented
409	#418	C₂²×C₇	1	2	yes	complemented
410	#418	C₂²×C₇	1	4	yes	complemented
411	#417	C₂²×C₇	1	1	yes	characteristic
412	#417	C₂²×C₇	1	4	yes	complemented
413	#416	C₂²×C₇	1	2	yes	—
414	#416	C₂²×C₇	1	4	yes	complemented
415	C₂×#102	C₂²×C₇	1	2	yes	complemented
416	C₂×#102	C₂²×C₇	1	4	yes	complemented
417	#408	C₂²×C₇	1	2	yes	complemented
418	C₄×M₁₆	C₂²×C₇	1	1	yes	characteristic, complemented
419	C₂³×C₇	—	2	1	no	—
420	C₂³×C₇	—	2	4	no	—
421	C₂³×C₇	—	4	8	no	—
422	C₂³×C₇	—	4	4	no	—
423	C₂³×C₇	—	8	2	no	—
424	C₂³×C₇	—	8	2	no	—
425	C₂³×C₇	—	8	4	no	—
426	C₂³×C₇	—	8	4	no	—
427	C₂³×C₇	C₂²×D₄	1	4	yes	—
428	C₂³×C₇	C₂²×D₄	1	1	yes	characteristic
429	C₇×Q₈	—	2	4	no	—
430	C₇×Q₈	—	2	1	no	—
431	C₇×Q₈	—	2	2	no	—
432	C₇×Q₈	—	2	2	no	—
433	C₇×Q₈	—	4	2	no	—
434	C₇×Q₈	—	4	2	no	—
435	C₇×Q₈	—	8	1	no	—
436	C₇×Q₈	C₂×#41	1	2	yes	—
437	C₇×D₄	—	2	4	no	—
438	C₇×D₄	—	2	8	no	—
439	C₇×D₄	—	2	4	no	—
440	C₇×D₄	—	2	4	no	—
441	C₇×D₄	—	2	4	no	—
442	C₇×D₄	—	2	1	no	—
443	C₇×D₄	—	2	4	no	—
444	C₇×D₄	—	4	2	no	—
445	C₇×D₄	—	4	8	no	—
446	C₇×D₄	—	4	8	no	—
447	C₇×D₄	—	4	4	no	—
448	C₇×D₄	—	4	4	no	—
449	C₇×D₄	—	4	4	no	—
450	C₇×D₄	—	8	2	no	—
451	C₇×D₄	—	8	2	no	—
452	C₇×D₄	—	8	4	no	—
453	C₇×D₄	—	8	4	no	—
454	C₇×D₄	C₂×#41	1	2	yes	—
455	C₂×C₄×C₇	—	2	1	no	—
456	C₂×C₄×C₇	—	2	4	no	—
457	C₂×C₄×C₇	—	2	2	no	—
458	C₂×C₄×C₇	—	2	4	no	—
459	C₂×C₄×C₇	—	2	4	no	—
460	C₂×C₄×C₇	—	2	2	no	—
461	C₂×C₄×C₇	—	2	2	no	—
462	C₂×C₄×C₇	—	2	1	no	—
463	C₂×C₄×C₇	—	2	1	no	—
464	C₂×C₄×C₇	—	2	2	no	—
465	C₂×C₄×C₇	—	2	2	no	—
466	C₂×C₄×C₇	—	4	1	no	—
467	C₂×C₄×C₇	—	4	8	no	—
468	C₂×C₄×C₇	—	4	2	no	—
469	C₂×C₄×C₇	—	4	2	no	—
470	C₂×C₄×C₇	—	4	2	no	—
471	C₂×C₄×C₇	—	8	1	no	—
472	C₂×C₄×C₇	—	8	4	no	—
473	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
474	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
475	C₂×C₄×C₇	C₂²×D₄	1	4	yes	—
476	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
477	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
478	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
479	C₂×C₄×C₇	C₂×#41	1	2	yes	—
480	C₂×C₄×C₇	H(5,𝔽₂)	1	2	yes	—
481	C₂×C₄×C₇	C₂⁵	1	1	yes	characteristic
482	C₇×C₈	—	2	2	no	—
483	C₇×C₈	—	2	2	no	—
484	C₇×C₈	—	2	2	no	—
485	C₇×C₈	—	2	2	no	—
486	H(5,𝔽₂)	—	2	8	no	—
487	H(5,𝔽₂)	—	4	4	no	—
488	C₂×#41	—	2	2	no	—
489	C₂×#41	C₂³×C₇	1	4	yes	—
490	C₂×#41	C₂³×C₇	1	1	yes	characteristic
491	C₂×#41	C₂³×C₇	1	2	yes	—
492	C₂²×Q₈	C₂³×C₇	1	1	yes	characteristic
493	C₂²×D₄	—	2	2	no	—
494	C₂²×D₄	—	2	4	no	—
495	C₂²×D₄	—	2	2	no	—
496	C₂²×D₄	—	2	2	no	—
497	C₂²×D₄	—	2	1	no	—
498	C₂²×D₄	—	2	1	no	—
499	C₂²×D₄	C₂³×C₇	1	2	yes	—
500	C₂²×D₄	C₂³×C₇	1	4	yes	—
501	#137	—	2	4	no	—
502	C₂×Q₁₆	C₂³×C₇	1	2	yes	—
503	C₂×SD₁₆	—	4	4	no	—
504	C₂×SD₁₆	C₂³×C₇	1	2	yes	—
505	C₂×SD₁₆	C₂³×C₇	1	4	yes	—
506	C₂×SD₁₆	C₂³×C₇	1	4	yes	—
507	#131	—	4	4	no	—
508	C₂×M₁₆	C₂³×C₇	1	1	yes	characteristic
509	C₂×M₁₆	C₂³×C₇	1	1	yes	characteristic
510	C₂×M₁₆	C₂³×C₇	1	4	yes	—
511	C₂²×C₈	C₂³×C₇	1	2	yes	—
512	C₂²×C₈	C₂³×C₇	1	4	yes	—
513	C₄⋊Q₈	—	2	2	no	—
514	C₄⋊Q₈	C₇×D₄	1	1	yes	characteristic
515	C₄⋊Q₈	C₂³×C₇	1	1	yes	characteristic
516	C₄⋊Q₈	C₂³×C₇	1	1	yes	characteristic
517	#127	—	2	2	no	—
518	#127	—	2	2	no	—
519	#127	—	2	2	no	—
520	#127	—	2	1	no	—
521	#127	—	2	1	no	—
522	#127	C₇×D₄	1	1	yes	characteristic
523	#127	C₂³×C₇	1	2	yes	—
524	#127	C₂³×C₇	1	2	yes	—
525	#126	—	2	4	no	—
526	#126	—	2	4	no	—
527	#125	—	2	2	no	—
528	#125	—	2	4	no	—
529	#125	C₂³×C₇	1	2	yes	—
530	#124	—	2	2	no	—
531	#124	—	2	2	no	—
532	#124	—	2	2	no	—
533	#124	C₇×D₄	1	2	yes	—
534	#123	—	2	4	no	—
535	#123	—	2	4	no	—
536	C₂²⋊Q₈	—	2	1	no	—
537	C₂²⋊Q₈	—	2	1	no	—
538	C₂²⋊Q₈	—	2	4	no	—
539	C₂²⋊Q₈	C₂³×C₇	1	4	yes	—
540	C₂²⋊Q₈	C₂³×C₇	1	4	yes	—
541	#121	—	2	2	no	—
542	#121	—	2	2	no	—
543	#121	—	2	4	no	—
544	#121	—	2	4	no	—
545	#121	C₇×D₄	1	2	yes	—
546	#121	C₇×D₄	1	2	yes	—
547	#121	C₂³×C₇	1	4	yes	—
548	#121	C₂³×C₇	1	4	yes	—
549	#120	—	2	4	no	—
550	#120	—	2	4	no	—
551	#120	—	2	4	no	—
552	C₄×Q₈	—	2	2	no	—
553	C₄×Q₈	—	2	2	no	—
554	C₄×Q₈	—	2	1	no	—
555	C₄×Q₈	—	2	1	no	—
556	C₄×Q₈	—	2	1	no	—
557	C₄×Q₈	—	2	1	no	—
558	C₄×Q₈	C₂³×C₇	1	2	yes	—
559	C₄×Q₈	C₂³×C₇	1	2	yes	—
560	C₄×Q₈	C₂³×C₇	1	1	yes	characteristic
561	C₄×Q₈	C₂³×C₇	1	1	yes	characteristic
562	C₄×D₄	—	2	4	no	—
563	C₄×D₄	—	2	2	no	—
564	C₄×D₄	—	2	2	no	—
565	C₄×D₄	—	2	1	no	—
566	C₄×D₄	—	2	1	no	—
567	C₄×D₄	—	2	2	no	—
568	C₄×D₄	—	2	2	no	—
569	C₄×D₄	C₂³×C₇	1	1	yes	characteristic
570	C₄×D₄	C₂³×C₇	1	1	yes	characteristic
571	C₄×D₄	C₂³×C₇	1	2	yes	—
572	C₄×D₄	C₂³×C₇	1	2	yes	—
573	#117	—	2	4	no	—
574	#117	—	2	1	no	—
575	#117	C₂³×C₇	1	1	yes	characteristic
576	#117	C₂³×C₇	1	2	yes	—
577	#117	C₂³×C₇	1	4	yes	—
578	C₂×C₄⋊C₄	—	2	1	no	—
579	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
580	C₂×C₄⋊C₄	C₂³×C₇	1	4	yes	—
581	C₂×C₄²	—	2	1	no	—
582	C₂×C₄²	—	2	1	no	—
583	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
584	#107	C₂³×C₇	1	2	yes	—
585	#107	C₂³×C₇	1	2	yes	—
586	#107	C₂³×C₇	1	2	yes	—
587	#106	C₂³×C₇	1	2	yes	—
588	#106	C₂³×C₇	1	2	yes	—
589	#106	C₂³×C₇	1	2	yes	—
590	C₄⋊C₈	C₂³×C₇	1	1	yes	characteristic
591	C₄⋊C₈	C₂³×C₇	1	2	yes	—
592	C₄⋊C₈	C₂³×C₇	1	1	yes	characteristic
593	#103	C₂³×C₇	1	2	yes	—
594	#103	C₂³×C₇	1	2	yes	—
595	#103	C₂³×C₇	1	2	yes	—
596	#103	C₂³×C₇	1	2	yes	—
597	#103	C₂³×C₇	1	2	yes	—
598	#102	C₂³×C₇	1	2	yes	—
599	#102	C₂³×C₇	1	4	yes	—
600	#102	C₂³×C₇	1	2	yes	—
601	#102	C₂³×C₇	1	4	yes	—
602	#102	C₂³×C₇	1	4	yes	—
603	#102	C₂³×C₇	1	2	yes	—
604	#102	C₂³×C₇	1	4	yes	—
605	#102	C₂³×C₇	1	4	yes	—
606	#102	C₂³×C₇	1	4	yes	—
607	C₂²⋊C₈	C₂³×C₇	1	4	yes	—
608	C₂²⋊C₈	C₂³×C₇	1	4	yes	—
609	#97	C₂³×C₇	1	2	yes	—
610	C₄×C₈	C₂³×C₇	1	2	yes	—
611	C₂²×C₇	—	2	1	no	—
612	C₂²×C₇	—	2	1	no	—
613	C₂²×C₇	—	2	4	no	—
614	C₂²×C₇	—	2	4	no	—
615	C₂²×C₇	—	2	2	no	—
616	C₂²×C₇	—	2	4	no	—
617	C₂²×C₇	—	4	1	no	—
618	C₂²×C₇	—	4	1	no	—
619	C₂²×C₇	—	4	4	no	—
620	C₂²×C₇	—	4	4	no	—
621	C₂²×C₇	—	4	4	no	—
622	C₂²×C₇	—	16	4	no	—
623	C₂²×C₇	—	16	8	no	—
624	C₂²×C₇	#546	1	2	yes	—
625	C₂²×C₇	C₂³×D₄	1	1	yes	characteristic
626	C₄×C₇	—	2	1	no	—
627	C₄×C₇	—	2	1	no	—
628	C₄×C₇	—	2	2	no	—
629	C₄×C₇	—	2	4	no	—
630	C₄×C₇	—	2	1	no	—
631	C₄×C₇	—	4	1	no	—
632	C₄×C₇	—	4	2	no	—
633	C₄×C₇	—	4	2	no	—
634	C₄×C₇	—	4	2	no	—
635	C₄×C₇	—	4	1	no	—
636	C₄×C₇	—	4	2	no	—
637	C₄×C₇	#546	1	2	yes	—
638	C₄×C₇	#577	1	2	yes	—
639	C₄×C₇	C₂²×#41	1	1	yes	characteristic
640	C₄×C₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
641	C₂⁴	—	2	4	no	—
642	C₂⁴	—	2	2	no	—
643	#41	—	2	4	no	—
644	#41	—	2	4	no	—
645	#41	—	2	2	no	—
646	#41	—	2	8	no	—
647	#41	—	4	4	no	—
648	#41	—	4	8	no	—
649	#41	C₇×#41	1	4	yes	—
650	C₂×Q₈	—	2	1	no	—
651	C₂×Q₈	—	2	1	no	—
652	C₂×Q₈	—	2	1	no	—
653	C₂×Q₈	—	2	2	no	—
654	C₂×Q₈	—	2	2	no	—
655	C₂×Q₈	C₂×C₇×D₄	1	2	yes	—
656	C₂×Q₈	C₂⁴×C₇	1	2	yes	—
657	C₂×Q₈	C₂⁴×C₇	1	1	yes	characteristic
658	C₂×D₄	—	2	1	no	—
659	C₂×D₄	—	2	8	no	—
660	C₂×D₄	—	2	4	no	—
661	C₂×D₄	—	2	4	no	—
662	C₂×D₄	—	2	4	no	—
663	C₂×D₄	—	2	2	no	—
664	C₂×D₄	—	2	2	no	—
665	C₂×D₄	—	2	4	no	—
666	C₂×D₄	—	2	2	no	—
667	C₂×D₄	—	2	2	no	—
668	C₂×D₄	—	2	2	no	—
669	C₂×D₄	—	2	4	no	—
670	C₂×D₄	—	2	4	no	—
671	C₂×D₄	—	4	4	no	—
672	C₂×D₄	—	4	8	no	—
673	C₂×D₄	—	4	16	no	—
674	C₂×D₄	—	8	2	no	—
675	C₂×D₄	—	8	4	no	—
676	C₂×D₄	—	8	2	no	—
677	C₂×D₄	—	8	4	no	—
678	C₂×D₄	C₂×C₇×D₄	1	2	yes	—
679	C₂×D₄	C₂×C₇×D₄	1	4	yes	—
680	C₂×D₄	C₂×C₇×D₄	1	2	yes	—
681	C₂×D₄	C₂×C₇×D₄	1	2	yes	—
682	C₂×D₄	C₂⁴×C₇	1	4	yes	—
683	C₂×D₄	C₂⁴×C₇	1	1	yes	characteristic
684	C₂²×C₄	—	2	1	no	—
685	C₂²×C₄	—	2	1	no	—
686	C₂²×C₄	—	2	1	no	—
687	C₂²×C₄	—	2	4	no	—
688	C₂²×C₄	—	2	1	no	—
689	C₂²×C₄	—	2	1	no	—
690	C₂²×C₄	—	2	4	no	—
691	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
692	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
693	C₂²×C₄	C₂⁴×C₇	1	4	yes	—
694	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
695	Q₁₆	—	2	4	no	—
696	SD₁₆	—	2	4	no	—
697	SD₁₆	—	4	4	no	—
698	SD₁₆	—	4	4	no	—
699	M₁₆	—	2	2	no	—
700	M₁₆	—	2	2	no	—
701	M₁₆	—	4	4	no	—
702	C₂×C₈	—	2	4	no	—
703	C₂×C₈	—	4	4	no	—
704	C₂×C₈	C₂⁴×C₇	1	2	yes	—
705	C₂×C₈	C₂⁴×C₇	1	2	yes	—
706	C₂×C₈	C₂⁴×C₇	1	2	yes	—
707	C₂×C₈	C₂⁴×C₇	1	2	yes	—
708	C₄⋊C₄	—	2	2	no	—
709	C₄⋊C₄	—	2	2	no	—
710	C₄⋊C₄	—	2	1	no	—
711	C₄⋊C₄	—	2	4	no	—
712	C₄⋊C₄	—	2	2	no	—
713	C₄⋊C₄	—	2	1	no	—
714	C₄⋊C₄	—	2	1	no	—
715	C₄⋊C₄	—	2	4	no	—
716	C₄⋊C₄	—	2	1	no	—
717	C₄⋊C₄	—	2	2	no	—
718	C₄⋊C₄	—	2	1	no	—
719	C₄⋊C₄	—	2	4	no	—
720	C₄⋊C₄	C₂×C₇×D₄	1	2	yes	—
721	C₄⋊C₄	C₂×C₇×D₄	1	2	yes	—
722	C₄⋊C₄	C₂⁴×C₇	1	2	yes	—
723	C₄⋊C₄	C₂⁴×C₇	1	2	yes	—
724	C₄⋊C₄	C₂⁴×C₇	1	2	yes	—
725	C₄⋊C₄	C₂⁴×C₇	1	1	yes	characteristic
726	C₄⋊C₄	C₂⁴×C₇	1	1	yes	characteristic
727	C₂²⋊C₄	—	2	4	no	—
728	C₂²⋊C₄	—	2	1	no	—
729	C₂²⋊C₄	—	2	2	no	—
730	C₂²⋊C₄	—	2	4	no	—
731	C₂²⋊C₄	—	2	4	no	—
732	C₂²⋊C₄	—	2	1	no	—
733	C₂²⋊C₄	—	2	1	no	—
734	C₂²⋊C₄	—	2	4	no	—
735	C₂²⋊C₄	—	2	4	no	—
736	C₂²⋊C₄	C₂×C₇×D₄	1	4	yes	—
737	C₂²⋊C₄	C₂×C₇×D₄	1	4	yes	—
738	C₄²	—	2	2	no	—
739	C₄²	—	2	1	no	—
740	C₄²	—	2	1	no	—
741	C₄²	—	2	1	no	—
742	C₄²	—	2	2	no	—
743	C₄²	—	2	4	no	—
744	C₄²	—	2	2	no	—
745	C₄²	C₂×C₇×D₄	1	1	yes	characteristic
746	C₄²	C₂×C₇×D₄	1	1	yes	characteristic
747	C₄²	C₂⁴×C₇	1	1	yes	characteristic
748	C₄²	C₂⁴×C₇	1	1	yes	characteristic
749	C₂×C₇	—	2	2	no	—
750	C₂×C₇	—	4	4	no	—
751	C₂×C₇	—	4	2	no	—
752	C₂×C₇	—	8	4	no	—
753	C₂×C₇	C₂×#546	1	1	yes	characteristic
754	C₂×C₇	C₂×#577	1	1	yes	characteristic
755	C₂×C₇	#3585	1	1	yes	characteristic
756	C₂³	—	2	1	no	—
757	C₂³	—	2	4	no	—
758	C₂³	—	4	8	no	—
759	C₂³	—	4	4	no	—
760	C₂³	—	8	2	no	—
761	C₂³	—	8	2	no	—
762	C₂³	—	8	4	no	—
763	C₂³	—	8	4	no	—
764	C₂³	C₂²×C₇×D₄	1	4	yes	—
765	C₂³	C₂²×C₇×D₄	1	1	yes	characteristic
766	Q₈	—	2	1	no	—
767	Q₈	—	2	4	no	—
768	Q₈	—	2	2	no	—
769	Q₈	—	2	2	no	—
770	Q₈	—	4	2	no	—
771	Q₈	—	4	2	no	—
772	Q₈	—	8	1	no	—
773	Q₈	C₂×C₇×#41	1	2	yes	—
774	D₄	—	2	4	no	—
775	D₄	—	2	8	no	—
776	D₄	—	2	4	no	—
777	D₄	—	2	1	no	—
778	D₄	—	2	4	no	—
779	D₄	—	2	4	no	—
780	D₄	—	2	4	no	—
781	D₄	—	4	2	no	—
782	D₄	—	4	8	no	—
783	D₄	—	4	8	no	—
784	D₄	—	4	4	no	—
785	D₄	—	4	4	no	—
786	D₄	—	4	4	no	—
787	D₄	—	8	2	no	—
788	D₄	—	8	2	no	—
789	D₄	—	8	4	no	—
790	D₄	—	8	4	no	—
791	D₄	C₂×C₇×#41	1	2	yes	—
792	C₂×C₄	—	2	1	no	—
793	C₂×C₄	—	2	4	no	—
794	C₂×C₄	—	2	4	no	—
795	C₂×C₄	—	2	4	no	—
796	C₂×C₄	—	2	2	no	—
797	C₂×C₄	—	2	2	no	—
798	C₂×C₄	—	2	2	no	—
799	C₂×C₄	—	2	1	no	—
800	C₂×C₄	—	2	1	no	—
801	C₂×C₄	—	2	2	no	—
802	C₂×C₄	—	2	2	no	—
803	C₂×C₄	—	4	1	no	—
804	C₂×C₄	—	4	8	no	—
805	C₂×C₄	—	4	2	no	—
806	C₂×C₄	—	4	2	no	—
807	C₂×C₄	—	4	2	no	—
808	C₂×C₄	—	8	1	no	—
809	C₂×C₄	—	8	4	no	—
810	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
811	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
812	C₂×C₄	C₂²×C₇×D₄	1	4	yes	—
813	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
814	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
815	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
816	C₂×C₄	C₂×C₇×#41	1	2	yes	—
817	C₂×C₄	C₇×H(5,𝔽₂)	1	2	yes	—
818	C₂×C₄	C₂⁵×C₇	1	1	yes	characteristic
819	C₈	—	2	2	no	—
820	C₈	—	2	2	no	—
821	C₈	—	2	2	no	—
822	C₈	—	2	2	no	—
823	C₇	#61206	1	1	yes	characteristic, direct product factor, Sylow
824	C₂²	—	2	1	no	—
825	C₂²	—	2	1	no	—
826	C₂²	—	2	4	no	—
827	C₂²	—	2	4	no	—
828	C₂²	—	2	4	no	—
829	C₂²	—	2	2	no	—
830	C₂²	—	4	1	no	—
831	C₂²	—	4	1	no	—
832	C₂²	—	4	4	no	—
833	C₂²	—	4	4	no	—
834	C₂²	—	4	4	no	—
835	C₂²	—	16	4	no	—
836	C₂²	—	16	8	no	—
837	C₂²	C₇×#546	1	2	yes	—
838	C₂²	C₂³×C₇×D₄	1	1	yes	characteristic
839	C₄	—	2	1	no	—
840	C₄	—	2	1	no	—
841	C₄	—	2	1	no	—
842	C₄	—	2	2	no	—
843	C₄	—	2	4	no	—
844	C₄	—	4	1	no	—
845	C₄	—	4	2	no	—
846	C₄	—	4	1	no	—
847	C₄	—	4	2	no	—
848	C₄	—	4	2	no	—
849	C₄	—	4	2	no	—
850	C₄	C₇×#546	1	2	yes	—
851	C₄	C₇×#577	1	2	yes	—
852	C₄	C₂²×C₇×#41	1	1	yes	characteristic
853	C₄	C₂×C₇×H(5,𝔽₂)	1	1	yes	characteristic
854	C₂	—	2	2	no	—
855	C₂	—	4	4	no	—
856	C₂	—	4	2	no	—
857	C₂	—	8	4	no	—
858	C₂	C₂×C₇×#546	1	1	yes	characteristic
859	C₂	C₂×C₇×#577	1	1	yes	characteristic
860	C₂	C₇×#3585	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₇	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₇
prime radical	C₇×#3498	C₂
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×#3507	C₂	semidirect
3. C₇×#3333	C₂	semidirect
4. C₇×#3324	C₂	semidirect
5. C₇×#3317	C₂	semidirect
6. C₇×#3310	C₂	semidirect
7. C₇×#3304	C₂	semidirect
8. C₇×#3295	C₂	semidirect
9. C₇×#3138	C₂	semidirect
10. C₇×#3096	C₂	semidirect
11. C₇×#3076	C₂	semidirect
12. C₇×#3057	C₂	semidirect
13. C₂×C₇×#460	C₂	semidirect
14. C₇×#3009	C₂	semidirect
15. C₄×C₇×#137	C₂	semidirect
16. C₇×#2935	C₂	semidirect
17. C₇×#2897	C₂	semidirect
20. C₂²×C₇×SD₁₆	C₂²	semidirect
21. C₂×C₇×#131	C₂²	semidirect
25. C₇×#556	C₂²	semidirect
26. C₇×#554	C₂²	semidirect
27. C₇×#552	C₂²	semidirect
35. C₇×#536	C₂²	semidirect
38. C₇×#533	C₂²	semidirect
44. C₇×#520	C₂²	semidirect
46. C₂×C₄×C₇×Q₈	C₂²	semidirect
47. C₇×#490	C₂²	semidirect
48. C₇×#486	C₂²	semidirect
49. C₇×#486	C₂²	semidirect
50. C₇×#482	C₂²	semidirect
51. C₇×#482	C₂²	semidirect
52. C₇×#481	C₂²	semidirect
53. C₇×#480	C₂²	semidirect
54. C₇×#479	C₂²	semidirect
55. C₇×#478	C₂²	semidirect
56. C₇×#477	C₂²	semidirect
57. C₇×#476	C₂²	semidirect
58. C₇×#475	C₂²	semidirect
59. C₇×#474	C₂²	semidirect
60. C₇×#468	C₂²	semidirect
61. C₇×#468	C₂²	semidirect
62. C₇×#465	C₂²	semidirect
63. C₇×#465	C₂²	semidirect
64. C₇×#460	C₂²	semidirect
65. C₇×#460	C₂²	semidirect
66. C₇×#460	C₂²	semidirect
67. C₇×#452	C₂²	semidirect
68. C₇×#452	C₂²	semidirect
69. C₇×#450	C₂²	semidirect
70. C₇×#450	C₂²	semidirect
71. C₇×#441	C₂²	semidirect
72. C₇×#440	C₂²	semidirect
73. C₄×C₇×Q₁₆	C₂²	semidirect
74. C₄×C₇×SD₁₆	C₂²	semidirect
75. C₇×#436	C₂²	semidirect
76. C₇×#435	C₂²	semidirect
77. C₇×C₈×D₄	C₂²	semidirect
78. C₇×#428	C₂²	semidirect
79. C₇×#427	C₂²	semidirect
80. C₂×C₇×C₄⋊C₈	C₂²	semidirect
81. C₇×#419	C₂²	semidirect
82. C₇×#418	C₂²	semidirect
83. C₇×#418	C₂²	semidirect
84. C₇×#418	C₂²	semidirect
86. C₇×#417	C₂²	semidirect
88. C₇×#416	C₂²	semidirect
89. C₂×C₇×#102	C₂²	semidirect
90. C₂×C₇×#102	C₂²	semidirect
91. C₇×#408	C₂²	semidirect
92. C₄×C₇×M₁₆	C₂²	semidirect
93. #61206	C₇	direct (N × H)
219. #3507	C₂×C₇	semidirect
221. #3333	C₂×C₇	semidirect
222. #3324	C₂×C₇	semidirect
223. #3317	C₂×C₇	semidirect
224. #3310	C₂×C₇	semidirect
225. #3304	C₂×C₇	semidirect
226. #3295	C₂×C₇	semidirect
227. #3138	C₂×C₇	semidirect
228. #3096	C₂×C₇	semidirect
229. #3076	C₂×C₇	semidirect
230. #3057	C₂×C₇	semidirect
231. C₂×#460	C₂×C₇	semidirect
232. #3009	C₂×C₇	semidirect
233. C₄×#137	C₂×C₇	semidirect
234. #2935	C₂×C₇	semidirect
235. #2897	C₂×C₇	semidirect
346. C₂²×SD₁₆	C₂²×C₇	semidirect
347. C₂×#131	C₂²×C₇	semidirect
351. #556	C₂²×C₇	semidirect
352. #554	C₂²×C₇	semidirect
353. #552	C₂²×C₇	semidirect
361. #536	C₂²×C₇	semidirect
364. #533	C₂²×C₇	semidirect
370. #520	C₂²×C₇	semidirect
372. C₂×C₄×Q₈	C₂²×C₇	semidirect
373. #490	C₂²×C₇	semidirect
374. #486	C₂²×C₇	semidirect
375. #486	C₂²×C₇	semidirect
376. #482	C₂²×C₇	semidirect
377. #482	C₂²×C₇	semidirect
378. #481	C₂²×C₇	semidirect
379. #480	C₂²×C₇	semidirect
380. #479	C₂²×C₇	semidirect
381. #478	C₂²×C₇	semidirect
382. #477	C₂²×C₇	semidirect
383. #476	C₂²×C₇	semidirect
384. #475	C₂²×C₇	semidirect
385. #474	C₂²×C₇	semidirect
386. #468	C₂²×C₇	semidirect
387. #468	C₂²×C₇	semidirect
388. #465	C₂²×C₇	semidirect
389. #465	C₂²×C₇	semidirect
390. #460	C₂²×C₇	semidirect
391. #460	C₂²×C₇	semidirect
392. #460	C₂²×C₇	semidirect
393. #452	C₂²×C₇	semidirect
394. #452	C₂²×C₇	semidirect
395. #450	C₂²×C₇	semidirect
396. #450	C₂²×C₇	semidirect
397. #441	C₂²×C₇	semidirect
398. #440	C₂²×C₇	semidirect
399. C₄×Q₁₆	C₂²×C₇	semidirect
400. C₄×SD₁₆	C₂²×C₇	semidirect
401. #436	C₂²×C₇	semidirect
402. #435	C₂²×C₇	semidirect
403. C₈×D₄	C₂²×C₇	semidirect
404. #428	C₂²×C₇	semidirect
405. #427	C₂²×C₇	semidirect
406. C₂×C₄⋊C₈	C₂²×C₇	semidirect
407. #419	C₂²×C₇	semidirect
408. #418	C₂²×C₇	semidirect
409. #418	C₂²×C₇	semidirect
410. #418	C₂²×C₇	semidirect
412. #417	C₂²×C₇	semidirect
414. #416	C₂²×C₇	semidirect
415. C₂×#102	C₂²×C₇	semidirect
416. C₂×#102	C₂²×C₇	semidirect
417. #408	C₂²×C₇	semidirect
418. C₄×M₁₆	C₂²×C₇	semidirect
823. C₇	#61206	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×#3507	2
C₇×#3498	2
C₇×#3333	2
C₇×#3324	2
C₇×#3317	2
C₇×#3310	2
C₇×#3304	2
C₇×#3295	2
C₇×#3138	2
C₇×#3096	2
C₇×#3076	2
C₇×#3057	2
C₂×C₇×#460	2
C₇×#3009	2
C₄×C₇×#137	2
C₇×#2935	2
C₇×#2897	2
#61206	7

Subgroups — C7×#61206 #13238422

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×#61206 #13238422