Subgroups — C₇×#61254 #13238470

Order 1792.

1872 conjugacy classes of subgroups.

The subgroup lattice has 886 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×#3475	C₂	1	1	yes	maximal, characteristic
2	C₂×C₇×#554	C₂	1	1	yes	maximal, characteristic, complemented
3	C₇×#3357	C₂	1	2	yes	maximal, complemented
4	C₇×#3356	C₂	1	2	yes	maximal, complemented
5	C₇×#3346	C₂	1	4	yes	maximal, complemented
6	C₇×#3344	C₂	1	4	yes	maximal, complemented
7	C₇×#3338	C₂	1	2	yes	maximal, complemented
8	C₇×#3335	C₂	1	2	yes	maximal, complemented
9	C₇×#3165	C₂	1	1	yes	maximal, characteristic, complemented
10	C₇×#3095	C₂	1	2	yes	maximal, complemented
11	C₇×#3092	C₂	1	2	yes	maximal, complemented
12	C₇×#3079	C₂	1	1	yes	maximal, characteristic, complemented
13	C₇×#3078	C₂	1	1	yes	maximal, characteristic, complemented
14	C₇×#3056	C₂	1	2	yes	maximal, complemented
15	C₄×C₇×#137	C₂	1	1	yes	maximal, characteristic, complemented
16	C₇×D₄×M₁₆	C₂	1	1	yes	maximal, characteristic, complemented
17	C₂×C₇×#428	C₂	1	2	yes	maximal, complemented
18	C₂×C₇×#137	C₂²	1	1	yes	characteristic
19	C₂²×C₇×M₁₆	C₂²	1	2	yes	—
20	C₇×#556	C₂²	1	1	yes	characteristic
21	C₇×#555	C₂²	1	1	yes	characteristic
22	C₇×#554	—	2	1	no	—
23	C₇×#554	—	2	2	no	—
24	C₇×#554	—	2	1	no	—
25	C₇×#554	C₂²	1	2	yes	—
26	C₇×#554	C₂²	1	4	yes	—
27	C₇×#554	C₂²	1	2	yes	—
28	C₇×#554	C₂²	1	1	yes	characteristic
29	C₇×#553	C₂²	1	2	yes	—
30	C₇×#552	—	2	1	no	—
31	C₇×#552	C₂²	1	2	yes	—
32	C₇×#551	—	2	2	no	—
33	C₇×#547	C₂²	1	1	yes	characteristic
34	C₇×#546	—	2	1	no	—
35	C₇×#533	C₂²	1	1	yes	characteristic
36	C₂×C₇×C₄⋊Q₈	C₂²	1	1	yes	characteristic
37	C₇×#529	—	2	2	no	—
38	C₇×#529	—	2	1	no	—
39	C₂×C₇×#125	—	2	1	no	—
40	C₇×#525	C₂²	1	2	yes	—
41	C₂×C₇×C₂²⋊Q₈	—	2	2	no	—
42	C₂×C₇×C₂²⋊Q₈	C₂²	1	2	yes	—
43	C₄×C₇×#41	—	2	1	no	—
44	C₄×C₇×#41	C₂²	1	1	yes	characteristic
45	C₂×C₄×C₇×Q₈	C₂²	1	1	yes	characteristic
46	C₂×C₄×C₇×D₄	—	2	1	no	—
47	C₂×C₄×C₇×D₄	C₂²	1	1	yes	characteristic
48	C₂×C₇×#117	C₂²	1	2	yes	—
49	C₂²×C₇×C₄⋊C₄	C₂²	1	2	yes	—
50	C₇×#501	C₂²	1	4	yes	complemented
51	C₇×#500	C₂²	1	2	yes	complemented
52	C₇×#498	C₂²	1	2	yes	complemented
53	C₇×#485	C₂²	1	4	yes	complemented
54	C₇×#485	C₂²	1	4	yes	complemented
55	C₇×#484	C₂²	1	4	yes	complemented
56	C₇×#484	C₂²	1	4	yes	complemented
57	C₇×#483	C₂²	1	4	yes	complemented
58	C₇×#483	C₂²	1	4	yes	complemented
59	C₇×#481	C₂²	1	4	yes	complemented
60	C₇×#480	C₂²	1	4	yes	complemented
61	C₇×#479	C₂²	1	4	yes	complemented
62	C₇×#477	C₂²	1	2	yes	complemented
63	C₇×#477	C₂²	1	2	yes	complemented
64	C₇×#476	C₂²	1	2	yes	complemented
65	C₇×#475	C₂²	1	2	yes	complemented
66	C₇×#475	C₂²	1	2	yes	complemented
67	C₇×#474	C₂²	1	2	yes	complemented
68	C₇×#470	C₂²	1	4	yes	complemented
69	C₇×#468	C₂²	1	4	yes	complemented
70	C₇×#467	C₂²	1	4	yes	complemented
71	C₇×#465	C₂²	1	4	yes	complemented
72	C₇×#441	C₂²	1	2	yes	complemented
73	C₇×#440	C₂²	1	2	yes	complemented
74	C₄×C₇×Q₁₆	C₂²	1	2	yes	complemented
75	C₄×C₇×SD₁₆	C₂²	1	2	yes	complemented
76	C₇×#436	C₂²	1	2	yes	—
77	C₇×#435	C₂²	1	4	yes	—
78	C₇×C₈×D₄	C₂²	1	2	yes	—
79	C₇×#428	C₂²	1	2	yes	—
80	C₇×#428	C₂²	1	2	yes	—
81	C₇×#428	C₂²	1	1	yes	characteristic
82	C₇×#428	C₂²	1	2	yes	—
83	C₇×#428	C₂²	1	2	yes	—
84	C₇×#428	C₂²	1	4	yes	complemented
85	C₇×#428	C₂²	1	4	yes	complemented
86	C₂×C₇×#107	C₂²	1	4	yes	complemented
87	C₂×C₇×#106	C₂²	1	4	yes	complemented
88	C₇×#423	C₂²	1	1	yes	characteristic
89	C₇×#419	C₂²	1	1	yes	characteristic
90	C₇×#419	C₂²	1	2	yes	—
91	C₇×#417	C₂²	1	1	yes	characteristic
92	C₇×#417	C₂²	1	2	yes	—
93	C₇×#407	C₂²	1	2	yes	—
94	C₄×C₇×M₁₆	C₂²	1	1	yes	characteristic
95	#61254	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
96	C₂×C₇×#41	—	2	1	no	—
97	C₂×C₇×#41	C₂³	1	1	yes	characteristic
98	C₂²×C₇×Q₈	—	2	1	no	—
99	C₂²×C₇×Q₈	C₂³	1	1	yes	characteristic
100	C₂²×C₇×D₄	D₄	1	1	yes	characteristic
101	C₂³×C₄×C₇	—	2	2	no	—
102	C₂³×C₄×C₇	C₂³	1	2	yes	—
103	C₇×#137	—	2	4	no	—
104	C₂×C₇×Q₁₆	C₂³	1	2	yes	—
105	C₂×C₇×SD₁₆	C₂³	1	2	yes	—
106	C₂×C₇×M₁₆	—	2	8	no	—
107	C₂×C₇×M₁₆	C₂³	1	4	yes	—
108	C₂×C₇×M₁₆	C₂³	1	1	yes	characteristic
109	C₂×C₇×M₁₆	C₂³	1	2	yes	—
110	C₂×C₇×M₁₆	C₂³	1	1	yes	characteristic
111	C₂²×C₇×C₈	C₂³	1	4	yes	—
112	C₇×C₄⋊Q₈	—	2	1	no	—
113	C₇×C₄⋊Q₈	—	2	1	no	—
114	C₇×C₄⋊Q₈	C₂³	1	2	yes	—
115	C₇×C₄⋊Q₈	C₂³	1	1	yes	characteristic
116	C₇×C₄⋊Q₈	C₂³	1	2	yes	—
117	C₇×C₄⋊Q₈	C₂³	1	1	yes	characteristic
118	C₇×#126	—	2	2	no	—
119	C₇×#126	—	2	2	no	—
120	C₇×#126	—	2	2	no	—
121	C₇×#125	—	2	2	no	—
122	C₇×#125	—	2	2	no	—
123	C₇×#125	—	2	4	no	—
124	C₇×#125	—	2	2	no	—
125	C₇×#125	—	2	1	no	—
126	C₇×#125	C₂³	1	2	yes	—
127	C₇×#124	—	2	1	no	—
128	C₇×#124	—	2	2	no	—
129	C₇×#123	—	2	2	no	—
130	C₇×#123	—	2	2	no	—
131	C₇×#123	—	2	2	no	—
132	C₇×#123	—	2	2	no	—
133	C₇×C₂²⋊Q₈	—	2	2	no	—
134	C₇×C₂²⋊Q₈	—	2	2	no	—
135	C₇×C₂²⋊Q₈	—	2	1	no	—
136	C₇×C₂²⋊Q₈	—	2	1	no	—
137	C₇×C₂²⋊Q₈	—	2	1	no	—
138	C₇×C₂²⋊Q₈	—	2	4	no	—
139	C₇×C₂²⋊Q₈	—	2	4	no	—
140	C₇×C₂²⋊Q₈	—	2	4	no	—
141	C₇×C₂²⋊Q₈	—	2	4	no	—
142	C₇×C₂²⋊Q₈	—	2	2	no	—
143	C₇×C₂²⋊Q₈	C₂³	1	2	yes	—
144	C₇×C₂²⋊Q₈	C₂³	1	4	yes	—
145	C₇×C₂²⋊Q₈	C₂³	1	4	yes	—
146	C₇×C₂²⋊Q₈	C₂³	1	2	yes	—
147	C₇×#121	—	2	2	no	—
148	C₇×#121	—	2	1	no	—
149	C₇×#121	C₂³	1	2	yes	—
150	C₇×#121	C₂³	1	2	yes	—
151	C₇×#120	—	2	2	no	—
152	C₄×C₇×Q₈	—	2	1	no	—
153	C₄×C₇×Q₈	—	2	1	no	—
154	C₄×C₇×Q₈	—	2	1	no	—
155	C₄×C₇×Q₈	—	2	1	no	—
156	C₄×C₇×Q₈	—	2	1	no	—
157	C₄×C₇×Q₈	C₂³	1	1	yes	characteristic
158	C₄×C₇×Q₈	C₂³	1	2	yes	—
159	C₄×C₇×Q₈	C₂³	1	1	yes	characteristic
160	C₄×C₇×Q₈	C₂³	1	2	yes	—
161	C₄×C₇×D₄	—	2	4	no	—
162	C₄×C₇×D₄	—	2	2	no	—
163	C₄×C₇×D₄	—	2	2	no	—
164	C₄×C₇×D₄	—	2	1	no	—
165	C₄×C₇×D₄	—	2	2	no	—
166	C₄×C₇×D₄	—	2	1	no	—
167	C₄×C₇×D₄	—	2	1	no	—
168	C₄×C₇×D₄	—	2	2	no	—
169	C₄×C₇×D₄	—	2	2	no	—
170	C₄×C₇×D₄	D₄	1	1	yes	characteristic
171	C₄×C₇×D₄	D₄	1	1	yes	characteristic
172	C₄×C₇×D₄	D₄	1	2	yes	—
173	C₄×C₇×D₄	C₂³	1	1	yes	characteristic
174	C₄×C₇×D₄	C₂³	1	1	yes	characteristic
175	C₄×C₇×D₄	C₂³	1	1	yes	characteristic
176	C₄×C₇×D₄	C₂³	1	2	yes	—
177	C₄×C₇×D₄	C₂³	1	1	yes	characteristic
178	C₇×#117	—	2	2	no	—
179	C₇×#117	—	2	2	no	—
180	C₇×#117	—	2	1	no	—
181	C₇×#117	—	2	2	no	—
182	C₇×#117	—	2	1	no	—
183	C₇×#117	C₂³	1	2	yes	—
184	C₇×#117	C₂³	1	2	yes	—
185	C₇×#117	C₂³	1	1	yes	characteristic
186	C₇×#117	C₂³	1	2	yes	—
187	C₂×C₇×C₄⋊C₄	—	2	2	no	—
188	C₂×C₇×C₄⋊C₄	—	2	2	no	—
189	C₂×C₇×C₄⋊C₄	—	2	2	no	—
190	C₂×C₇×C₄⋊C₄	—	2	1	no	—
191	C₂×C₇×C₄⋊C₄	—	2	1	no	—
192	C₂×C₇×C₄⋊C₄	—	2	2	no	—
193	C₂×C₇×C₄⋊C₄	D₄	1	1	yes	characteristic
194	C₂×C₇×C₄⋊C₄	C₂³	1	4	yes	—
195	C₂×C₇×C₄⋊C₄	C₂³	1	4	yes	—
196	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
197	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
198	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
199	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
200	C₂×C₇×C₂²⋊C₄	—	2	2	no	—
201	C₂×C₇×C₂²⋊C₄	—	2	2	no	—
202	C₂×C₇×C₂²⋊C₄	D₄	1	2	yes	—
203	C₂×C₄²×C₇	—	2	2	no	—
204	C₂×C₄²×C₇	—	2	1	no	—
205	C₂×C₄²×C₇	—	2	1	no	—
206	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
207	C₇×#107	C₂³	1	4	yes	—
208	C₇×#107	C₂³	1	4	yes	—
209	C₇×#107	C₂³	1	4	yes	—
210	C₇×#107	C₂³	1	4	yes	—
211	C₇×#107	C₂³	1	2	yes	—
212	C₇×#106	C₂³	1	4	yes	—
213	C₇×#106	C₂³	1	4	yes	—
214	C₇×#106	C₂³	1	4	yes	—
215	C₇×#106	C₂³	1	4	yes	—
216	C₇×#106	C₂³	1	2	yes	—
217	C₇×C₄⋊C₈	C₂³	1	2	yes	—
218	C₇×C₄⋊C₈	C₂³	1	2	yes	—
219	C₇×#103	C₂³	1	4	yes	—
220	C₇×#103	C₂³	1	4	yes	—
221	C₇×#103	C₂³	1	4	yes	—
222	C₇×#103	C₂³	1	2	yes	—
223	C₇×#103	C₂³	1	2	yes	—
224	C₇×#103	C₂³	1	2	yes	—
225	C₇×#102	C₂³	1	4	yes	—
226	C₇×#102	C₂³	1	2	yes	—
227	C₇×C₂²⋊C₈	C₂³	1	4	yes	—
228	C₇×C₂²⋊C₈	C₂³	1	4	yes	—
229	C₇×#97	C₂³	1	2	yes	—
230	C₄×C₇×C₈	C₂³	1	2	yes	—
231	#3475	C₂×C₇	1	1	yes	characteristic
232	C₂×#554	C₂×C₇	1	1	yes	characteristic, complemented
233	#3357	C₂×C₇	1	2	yes	complemented
234	#3356	C₂×C₇	1	2	yes	complemented
235	#3346	C₂×C₇	1	4	yes	complemented
236	#3344	C₂×C₇	1	4	yes	complemented
237	#3338	C₂×C₇	1	2	yes	complemented
238	#3335	C₂×C₇	1	2	yes	complemented
239	#3165	C₂×C₇	1	1	yes	characteristic, complemented
240	#3095	C₂×C₇	1	2	yes	complemented
241	#3092	C₂×C₇	1	2	yes	complemented
242	#3079	C₂×C₇	1	1	yes	characteristic, complemented
243	#3078	C₂×C₇	1	1	yes	characteristic, complemented
244	#3056	C₂×C₇	1	2	yes	complemented
245	C₄×#137	C₂×C₇	1	1	yes	characteristic, complemented
246	D₄×M₁₆	C₂×C₇	1	1	yes	characteristic, complemented
247	C₂×#428	C₂×C₇	1	2	yes	complemented
248	C₂⁴×C₇	C₂×D₄	1	2	yes	—
249	C₇×#41	—	2	2	no	—
250	C₇×#41	—	2	2	no	—
251	C₇×#41	—	4	4	no	—
252	C₂×C₇×Q₈	—	2	1	no	—
253	C₂×C₇×Q₈	—	2	1	no	—
254	C₂×C₇×Q₈	—	2	1	no	—
255	C₂×C₇×Q₈	—	2	2	no	—
256	C₂×C₇×Q₈	—	2	2	no	—
257	C₂×C₇×Q₈	—	2	2	no	—
258	C₂×C₇×Q₈	—	2	2	no	—
259	C₂×C₇×Q₈	—	8	2	no	—
260	C₂×C₇×Q₈	C₂⁴	1	2	yes	—
261	C₂×C₇×Q₈	C₂⁴	1	1	yes	characteristic
262	C₂×C₇×D₄	—	2	4	no	—
263	C₂×C₇×D₄	—	2	1	no	—
264	C₂×C₇×D₄	—	2	2	no	—
265	C₂×C₇×D₄	—	2	2	no	—
266	C₂×C₇×D₄	C₂×D₄	1	2	yes	—
267	C₂×C₇×D₄	C₂×D₄	1	1	yes	characteristic
268	C₂×C₇×D₄	C₂×D₄	1	1	yes	characteristic
269	C₂×C₇×D₄	C₂⁴	1	1	yes	characteristic
270	C₂²×C₄×C₇	—	2	4	no	—
271	C₂²×C₄×C₇	—	2	4	no	—
272	C₂²×C₄×C₇	—	2	1	no	—
273	C₂²×C₄×C₇	—	2	2	no	—
274	C₂²×C₄×C₇	—	2	1	no	—
275	C₂²×C₄×C₇	—	2	2	no	—
276	C₂²×C₄×C₇	—	2	2	no	—
277	C₂²×C₄×C₇	—	2	4	no	—
278	C₂²×C₄×C₇	—	2	4	no	—
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	—	8	4	no	—
283	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
284	C₂²×C₄×C₇	C₂×D₄	1	2	yes	—
285	C₂²×C₄×C₇	C₂×D₄	1	2	yes	—
286	C₂²×C₄×C₇	C₂×D₄	1	2	yes	—
287	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
288	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
289	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
290	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
291	C₇×Q₁₆	—	2	4	no	—
292	C₇×SD₁₆	—	2	4	no	—
293	C₇×M₁₆	—	2	4	no	—
294	C₇×M₁₆	—	2	2	no	—
295	C₇×M₁₆	—	2	8	no	—
296	C₇×M₁₆	#41	1	4	yes	complemented
297	C₂×C₇×C₈	—	2	8	no	—
298	C₂×C₇×C₈	C₂⁴	1	2	yes	—
299	C₂×C₇×C₈	C₂⁴	1	4	yes	—
300	C₂×C₇×C₈	C₂⁴	1	2	yes	—
301	C₇×C₄⋊C₄	—	2	1	no	—
302	C₇×C₄⋊C₄	—	2	4	no	—
303	C₇×C₄⋊C₄	—	2	4	no	—
304	C₇×C₄⋊C₄	—	2	2	no	—
305	C₇×C₄⋊C₄	—	2	2	no	—
306	C₇×C₄⋊C₄	—	2	2	no	—
307	C₇×C₄⋊C₄	—	2	2	no	—
308	C₇×C₄⋊C₄	—	2	2	no	—
309	C₇×C₄⋊C₄	—	2	4	no	—
310	C₇×C₄⋊C₄	—	2	4	no	—
311	C₇×C₄⋊C₄	—	2	2	no	—
312	C₇×C₄⋊C₄	—	2	2	no	—
313	C₇×C₄⋊C₄	—	2	1	no	—
314	C₇×C₄⋊C₄	—	2	2	no	—
315	C₇×C₄⋊C₄	—	2	2	no	—
316	C₇×C₄⋊C₄	—	2	1	no	—
317	C₇×C₄⋊C₄	—	2	1	no	—
318	C₇×C₄⋊C₄	—	2	2	no	—
319	C₇×C₄⋊C₄	—	2	2	no	—
320	C₇×C₄⋊C₄	—	2	1	no	—
321	C₇×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
322	C₇×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
323	C₇×C₄⋊C₄	C₂×D₄	1	2	yes	—
324	C₇×C₄⋊C₄	C₂⁴	1	2	yes	—
325	C₇×C₄⋊C₄	C₂⁴	1	4	yes	—
326	C₇×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
327	C₇×C₄⋊C₄	C₂⁴	1	2	yes	—
328	C₇×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
329	C₇×C₄⋊C₄	C₂⁴	1	2	yes	—
330	C₇×C₂²⋊C₄	—	2	1	no	—
331	C₇×C₂²⋊C₄	—	2	2	no	—
332	C₇×C₂²⋊C₄	—	2	2	no	—
333	C₇×C₂²⋊C₄	—	2	2	no	—
334	C₇×C₂²⋊C₄	—	2	4	no	—
335	C₇×C₂²⋊C₄	—	2	4	no	—
336	C₇×C₂²⋊C₄	—	2	2	no	—
337	C₇×C₂²⋊C₄	—	2	2	no	—
338	C₇×C₂²⋊C₄	—	2	2	no	—
339	C₇×C₂²⋊C₄	—	2	1	no	—
340	C₇×C₂²⋊C₄	—	2	1	no	—
341	C₇×C₂²⋊C₄	—	2	2	no	—
342	C₇×C₂²⋊C₄	C₂×D₄	1	2	yes	—
343	C₇×C₂²⋊C₄	C₂×D₄	1	2	yes	—
344	C₇×C₂²⋊C₄	C₂×D₄	1	2	yes	—
345	C₇×C₂²⋊C₄	C₂×D₄	1	2	yes	—
346	C₄²×C₇	—	2	1	no	—
347	C₄²×C₇	—	2	2	no	—
348	C₄²×C₇	—	2	1	no	—
349	C₄²×C₇	—	2	2	no	—
350	C₄²×C₇	—	2	2	no	—
351	C₄²×C₇	—	2	1	no	—
352	C₄²×C₇	—	2	2	no	—
353	C₄²×C₇	—	2	2	no	—
354	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
355	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
356	C₄²×C₇	C₂⁴	1	1	yes	characteristic
357	C₄²×C₇	C₂⁴	1	1	yes	characteristic
358	C₂×#137	C₂²×C₇	1	1	yes	characteristic
359	C₂²×M₁₆	C₂²×C₇	1	2	yes	—
360	#556	C₂²×C₇	1	1	yes	characteristic
361	#555	C₂²×C₇	1	1	yes	characteristic
362	#554	—	2	1	no	—
363	#554	—	2	2	no	—
364	#554	—	2	1	no	—
365	#554	C₂²×C₇	1	2	yes	—
366	#554	C₂²×C₇	1	1	yes	characteristic
367	#554	C₂²×C₇	1	4	yes	—
368	#554	C₂²×C₇	1	2	yes	—
369	#553	C₂²×C₇	1	2	yes	—
370	#552	—	2	1	no	—
371	#552	C₂²×C₇	1	2	yes	—
372	#551	—	2	2	no	—
373	#547	C₂²×C₇	1	1	yes	characteristic
374	#546	—	2	1	no	—
375	#533	C₂²×C₇	1	1	yes	characteristic
376	C₂×C₄⋊Q₈	C₂²×C₇	1	1	yes	characteristic
377	#529	—	2	2	no	—
378	#529	—	2	1	no	—
379	C₂×#125	—	2	1	no	—
380	#525	C₂²×C₇	1	2	yes	—
381	C₂×C₂²⋊Q₈	—	2	2	no	—
382	C₂×C₂²⋊Q₈	C₂²×C₇	1	2	yes	—
383	C₄×#41	—	2	1	no	—
384	C₄×#41	C₂²×C₇	1	1	yes	characteristic
385	C₂×C₄×Q₈	C₂²×C₇	1	1	yes	characteristic
386	C₂×C₄×D₄	—	2	1	no	—
387	C₂×C₄×D₄	C₂²×C₇	1	1	yes	characteristic
388	C₂×#117	C₂²×C₇	1	2	yes	—
389	C₂²×C₄⋊C₄	C₂²×C₇	1	2	yes	—
390	#501	C₂²×C₇	1	4	yes	complemented
391	#500	C₂²×C₇	1	2	yes	complemented
392	#498	C₂²×C₇	1	2	yes	complemented
393	#485	C₂²×C₇	1	4	yes	complemented
394	#485	C₂²×C₇	1	4	yes	complemented
395	#484	C₂²×C₇	1	4	yes	complemented
396	#484	C₂²×C₇	1	4	yes	complemented
397	#483	C₂²×C₇	1	4	yes	complemented
398	#483	C₂²×C₇	1	4	yes	complemented
399	#481	C₂²×C₇	1	4	yes	complemented
400	#480	C₂²×C₇	1	4	yes	complemented
401	#479	C₂²×C₇	1	4	yes	complemented
402	#477	C₂²×C₇	1	2	yes	complemented
403	#477	C₂²×C₇	1	2	yes	complemented
404	#476	C₂²×C₇	1	2	yes	complemented
405	#475	C₂²×C₇	1	2	yes	complemented
406	#475	C₂²×C₇	1	2	yes	complemented
407	#474	C₂²×C₇	1	2	yes	complemented
408	#470	C₂²×C₇	1	4	yes	complemented
409	#468	C₂²×C₇	1	4	yes	complemented
410	#467	C₂²×C₇	1	4	yes	complemented
411	#465	C₂²×C₇	1	4	yes	complemented
412	#441	C₂²×C₇	1	2	yes	complemented
413	#440	C₂²×C₇	1	2	yes	complemented
414	C₄×Q₁₆	C₂²×C₇	1	2	yes	complemented
415	C₄×SD₁₆	C₂²×C₇	1	2	yes	complemented
416	#436	C₂²×C₇	1	2	yes	—
417	#435	C₂²×C₇	1	4	yes	—
418	C₈×D₄	C₂²×C₇	1	2	yes	—
419	#428	C₂²×C₇	1	2	yes	—
420	#428	C₂²×C₇	1	2	yes	—
421	#428	C₂²×C₇	1	2	yes	—
422	#428	C₂²×C₇	1	2	yes	—
423	#428	C₂²×C₇	1	1	yes	characteristic
424	#428	C₂²×C₇	1	4	yes	complemented
425	#428	C₂²×C₇	1	4	yes	complemented
426	C₂×#107	C₂²×C₇	1	4	yes	complemented
427	C₂×#106	C₂²×C₇	1	4	yes	complemented
428	#423	C₂²×C₇	1	1	yes	characteristic
429	#419	C₂²×C₇	1	2	yes	—
430	#419	C₂²×C₇	1	1	yes	characteristic
431	#417	C₂²×C₇	1	2	yes	—
432	#417	C₂²×C₇	1	1	yes	characteristic
433	#407	C₂²×C₇	1	2	yes	—
434	C₄×M₁₆	C₂²×C₇	1	1	yes	characteristic
435	C₂³×C₇	—	2	4	no	—
436	C₂³×C₇	—	2	4	no	—
437	C₂³×C₇	—	2	1	no	—
438	C₂³×C₇	—	4	2	no	—
439	C₂³×C₇	C₂²×D₄	1	2	yes	—
440	C₂³×C₇	C₂²×D₄	1	1	yes	characteristic
441	C₂³×C₇	C₂²×D₄	1	2	yes	—
442	C₇×Q₈	—	2	2	no	—
443	C₇×Q₈	—	2	1	no	—
444	C₇×Q₈	—	2	2	no	—
445	C₇×Q₈	—	2	1	no	—
446	C₇×Q₈	—	4	2	no	—
447	C₇×Q₈	—	4	2	no	—
448	C₇×Q₈	—	8	1	no	—
449	C₇×Q₈	—	8	2	no	—
450	C₇×Q₈	—	8	2	no	—
451	C₇×D₄	—	2	4	no	—
452	C₇×D₄	—	2	2	no	—
453	C₇×D₄	—	2	1	no	—
454	C₇×D₄	—	2	1	no	—
455	C₇×D₄	—	4	2	no	—
456	C₇×D₄	—	4	4	no	—
457	C₇×D₄	—	8	2	no	—
458	C₇×D₄	#137	1	4	yes	complemented
459	C₂×C₄×C₇	—	2	4	no	—
460	C₂×C₄×C₇	—	2	4	no	—
461	C₂×C₄×C₇	—	2	4	no	—
462	C₂×C₄×C₇	—	2	2	no	—
463	C₂×C₄×C₇	—	2	2	no	—
464	C₂×C₄×C₇	—	2	2	no	—
465	C₂×C₄×C₇	—	2	2	no	—
466	C₂×C₄×C₇	—	2	2	no	—
467	C₂×C₄×C₇	—	2	1	no	—
468	C₂×C₄×C₇	—	2	1	no	—
469	C₂×C₄×C₇	—	2	1	no	—
470	C₂×C₄×C₇	—	2	2	no	—
471	C₂×C₄×C₇	—	2	2	no	—
472	C₂×C₄×C₇	—	2	2	no	—
473	C₂×C₄×C₇	—	2	2	no	—
474	C₂×C₄×C₇	—	2	4	no	—
475	C₂×C₄×C₇	—	4	1	no	—
476	C₂×C₄×C₇	—	4	2	no	—
477	C₂×C₄×C₇	—	4	4	no	—
478	C₂×C₄×C₇	—	4	2	no	—
479	C₂×C₄×C₇	—	4	4	no	—
480	C₂×C₄×C₇	—	4	2	no	—
481	C₂×C₄×C₇	—	4	2	no	—
482	C₂×C₄×C₇	—	8	1	no	—
483	C₂×C₄×C₇	—	8	2	no	—
484	C₂×C₄×C₇	—	8	4	no	—
485	C₂×C₄×C₇	—	8	4	no	—
486	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
487	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
488	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
489	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
490	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
491	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
492	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
493	C₂×C₄×C₇	C₂×#41	1	2	yes	—
494	C₂×C₄×C₇	2₋¹⁺⁴	1	2	yes	—
495	C₂×C₄×C₇	C₂⁵	1	1	yes	characteristic
496	C₇×C₈	—	2	4	no	—
497	C₇×C₈	—	2	2	no	—
498	C₇×C₈	C₂×#41	1	4	yes	—
499	C₂×#41	—	2	1	no	—
500	C₂×#41	C₂³×C₇	1	1	yes	characteristic
501	C₂²×Q₈	—	2	1	no	—
502	C₂²×Q₈	C₂³×C₇	1	1	yes	characteristic
503	C₂²×D₄	C₇×D₄	1	1	yes	characteristic
504	C₂³×C₄	—	2	2	no	—
505	C₂³×C₄	C₂³×C₇	1	2	yes	—
506	#137	—	2	4	no	—
507	C₂×Q₁₆	C₂³×C₇	1	2	yes	—
508	C₂×SD₁₆	C₂³×C₇	1	2	yes	—
509	C₂×M₁₆	—	2	8	no	—
510	C₂×M₁₆	C₂³×C₇	1	2	yes	—
511	C₂×M₁₆	C₂³×C₇	1	4	yes	—
512	C₂×M₁₆	C₂³×C₇	1	1	yes	characteristic
513	C₂×M₁₆	C₂³×C₇	1	1	yes	characteristic
514	C₂²×C₈	C₂³×C₇	1	4	yes	—
515	C₄⋊Q₈	—	2	1	no	—
516	C₄⋊Q₈	—	2	1	no	—
517	C₄⋊Q₈	C₂³×C₇	1	2	yes	—
518	C₄⋊Q₈	C₂³×C₇	1	2	yes	—
519	C₄⋊Q₈	C₂³×C₇	1	1	yes	characteristic
520	C₄⋊Q₈	C₂³×C₇	1	1	yes	characteristic
521	#126	—	2	2	no	—
522	#126	—	2	2	no	—
523	#126	—	2	2	no	—
524	#125	—	2	2	no	—
525	#125	—	2	2	no	—
526	#125	—	2	4	no	—
527	#125	—	2	2	no	—
528	#125	—	2	1	no	—
529	#125	C₂³×C₇	1	2	yes	—
530	#124	—	2	1	no	—
531	#124	—	2	2	no	—
532	#123	—	2	2	no	—
533	#123	—	2	2	no	—
534	#123	—	2	2	no	—
535	#123	—	2	2	no	—
536	C₂²⋊Q₈	—	2	2	no	—
537	C₂²⋊Q₈	—	2	2	no	—
538	C₂²⋊Q₈	—	2	1	no	—
539	C₂²⋊Q₈	—	2	1	no	—
540	C₂²⋊Q₈	—	2	1	no	—
541	C₂²⋊Q₈	—	2	4	no	—
542	C₂²⋊Q₈	—	2	4	no	—
543	C₂²⋊Q₈	—	2	4	no	—
544	C₂²⋊Q₈	—	2	4	no	—
545	C₂²⋊Q₈	—	2	2	no	—
546	C₂²⋊Q₈	C₂³×C₇	1	4	yes	—
547	C₂²⋊Q₈	C₂³×C₇	1	4	yes	—
548	C₂²⋊Q₈	C₂³×C₇	1	2	yes	—
549	C₂²⋊Q₈	C₂³×C₇	1	2	yes	—
550	#121	—	2	2	no	—
551	#121	—	2	1	no	—
552	#121	C₂³×C₇	1	2	yes	—
553	#121	C₂³×C₇	1	2	yes	—
554	#120	—	2	2	no	—
555	C₄×Q₈	—	2	1	no	—
556	C₄×Q₈	—	2	1	no	—
557	C₄×Q₈	—	2	1	no	—
558	C₄×Q₈	—	2	1	no	—
559	C₄×Q₈	—	2	1	no	—
560	C₄×Q₈	C₂³×C₇	1	2	yes	—
561	C₄×Q₈	C₂³×C₇	1	2	yes	—
562	C₄×Q₈	C₂³×C₇	1	1	yes	characteristic
563	C₄×Q₈	C₂³×C₇	1	1	yes	characteristic
564	C₄×D₄	—	2	4	no	—
565	C₄×D₄	—	2	2	no	—
566	C₄×D₄	—	2	2	no	—
567	C₄×D₄	—	2	1	no	—
568	C₄×D₄	—	2	2	no	—
569	C₄×D₄	—	2	1	no	—
570	C₄×D₄	—	2	1	no	—
571	C₄×D₄	—	2	2	no	—
572	C₄×D₄	—	2	2	no	—
573	C₄×D₄	C₇×D₄	1	1	yes	characteristic
574	C₄×D₄	C₇×D₄	1	1	yes	characteristic
575	C₄×D₄	C₇×D₄	1	2	yes	—
576	C₄×D₄	C₂³×C₇	1	1	yes	characteristic
577	C₄×D₄	C₂³×C₇	1	1	yes	characteristic
578	C₄×D₄	C₂³×C₇	1	1	yes	characteristic
579	C₄×D₄	C₂³×C₇	1	2	yes	—
580	C₄×D₄	C₂³×C₇	1	1	yes	characteristic
581	#117	—	2	2	no	—
582	#117	—	2	2	no	—
583	#117	—	2	1	no	—
584	#117	—	2	2	no	—
585	#117	—	2	1	no	—
586	#117	C₂³×C₇	1	1	yes	characteristic
587	#117	C₂³×C₇	1	2	yes	—
588	#117	C₂³×C₇	1	2	yes	—
589	#117	C₂³×C₇	1	2	yes	—
590	C₂×C₄⋊C₄	—	2	2	no	—
591	C₂×C₄⋊C₄	—	2	2	no	—
592	C₂×C₄⋊C₄	—	2	2	no	—
593	C₂×C₄⋊C₄	—	2	1	no	—
594	C₂×C₄⋊C₄	—	2	1	no	—
595	C₂×C₄⋊C₄	—	2	2	no	—
596	C₂×C₄⋊C₄	C₇×D₄	1	1	yes	characteristic
597	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
598	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
599	C₂×C₄⋊C₄	C₂³×C₇	1	4	yes	—
600	C₂×C₄⋊C₄	C₂³×C₇	1	4	yes	—
601	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
602	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
603	C₂×C₂²⋊C₄	—	2	2	no	—
604	C₂×C₂²⋊C₄	—	2	2	no	—
605	C₂×C₂²⋊C₄	C₇×D₄	1	2	yes	—
606	C₂×C₄²	—	2	2	no	—
607	C₂×C₄²	—	2	1	no	—
608	C₂×C₄²	—	2	1	no	—
609	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
610	#107	C₂³×C₇	1	2	yes	—
611	#107	C₂³×C₇	1	4	yes	—
612	#107	C₂³×C₇	1	4	yes	—
613	#107	C₂³×C₇	1	4	yes	—
614	#107	C₂³×C₇	1	4	yes	—
615	#106	C₂³×C₇	1	2	yes	—
616	#106	C₂³×C₇	1	4	yes	—
617	#106	C₂³×C₇	1	4	yes	—
618	#106	C₂³×C₇	1	4	yes	—
619	#106	C₂³×C₇	1	4	yes	—
620	C₄⋊C₈	C₂³×C₇	1	2	yes	—
621	C₄⋊C₈	C₂³×C₇	1	2	yes	—
622	#103	C₂³×C₇	1	2	yes	—
623	#103	C₂³×C₇	1	4	yes	—
624	#103	C₂³×C₇	1	2	yes	—
625	#103	C₂³×C₇	1	2	yes	—
626	#103	C₂³×C₇	1	4	yes	—
627	#103	C₂³×C₇	1	4	yes	—
628	#102	C₂³×C₇	1	2	yes	—
629	#102	C₂³×C₇	1	4	yes	—
630	C₂²⋊C₈	C₂³×C₇	1	4	yes	—
631	C₂²⋊C₈	C₂³×C₇	1	4	yes	—
632	#97	C₂³×C₇	1	2	yes	—
633	C₄×C₈	C₂³×C₇	1	2	yes	—
634	C₂²×C₇	—	2	1	no	—
635	C₂²×C₇	—	2	2	no	—
636	C₂²×C₇	—	2	2	no	—
637	C₂²×C₇	—	2	1	no	—
638	C₂²×C₇	—	2	2	no	—
639	C₂²×C₇	—	2	2	no	—
640	C₂²×C₇	—	2	2	no	—
641	C₂²×C₇	—	4	8	no	—
642	C₂²×C₇	—	4	1	no	—
643	C₂²×C₇	—	4	1	no	—
644	C₂²×C₇	—	4	1	no	—
645	C₂²×C₇	#547	1	2	yes	—
646	C₂²×C₇	C₂×#137	1	4	yes	—
647	C₂²×C₇	C₂³×D₄	1	1	yes	characteristic
648	C₄×C₇	—	2	1	no	—
649	C₄×C₇	—	2	1	no	—
650	C₄×C₇	—	2	2	no	—
651	C₄×C₇	—	2	2	no	—
652	C₄×C₇	—	2	1	no	—
653	C₄×C₇	—	4	2	no	—
654	C₄×C₇	—	4	4	no	—
655	C₄×C₇	—	4	1	no	—
656	C₄×C₇	—	4	2	no	—
657	C₄×C₇	—	4	1	no	—
658	C₄×C₇	—	4	2	no	—
659	C₄×C₇	—	4	1	no	—
660	C₄×C₇	—	4	2	no	—
661	C₄×C₇	#547	1	2	yes	—
662	C₄×C₇	C₂×#137	1	2	yes	—
663	C₄×C₇	C₂²×#41	1	1	yes	characteristic
664	C₄×C₇	C₂×2₋¹⁺⁴	1	1	yes	characteristic
665	C₂⁴	C₂×C₇×D₄	1	2	yes	—
666	#41	—	2	2	no	—
667	#41	—	2	2	no	—
668	#41	—	4	4	no	—
669	C₂×Q₈	—	2	1	no	—
670	C₂×Q₈	—	2	1	no	—
671	C₂×Q₈	—	2	1	no	—
672	C₂×Q₈	—	2	2	no	—
673	C₂×Q₈	—	2	2	no	—
674	C₂×Q₈	—	2	2	no	—
675	C₂×Q₈	—	2	2	no	—
676	C₂×Q₈	—	8	2	no	—
677	C₂×Q₈	C₂⁴×C₇	1	2	yes	—
678	C₂×Q₈	C₂⁴×C₇	1	1	yes	characteristic
679	C₂×D₄	—	2	4	no	—
680	C₂×D₄	—	2	1	no	—
681	C₂×D₄	—	2	2	no	—
682	C₂×D₄	—	2	2	no	—
683	C₂×D₄	C₂×C₇×D₄	1	2	yes	—
684	C₂×D₄	C₂×C₇×D₄	1	1	yes	characteristic
685	C₂×D₄	C₂×C₇×D₄	1	1	yes	characteristic
686	C₂×D₄	C₂⁴×C₇	1	1	yes	characteristic
687	C₂²×C₄	—	2	4	no	—
688	C₂²×C₄	—	2	4	no	—
689	C₂²×C₄	—	2	1	no	—
690	C₂²×C₄	—	2	2	no	—
691	C₂²×C₄	—	2	1	no	—
692	C₂²×C₄	—	2	2	no	—
693	C₂²×C₄	—	2	2	no	—
694	C₂²×C₄	—	2	4	no	—
695	C₂²×C₄	—	2	4	no	—
696	C₂²×C₄	—	2	1	no	—
697	C₂²×C₄	—	2	1	no	—
698	C₂²×C₄	—	2	1	no	—
699	C₂²×C₄	—	8	4	no	—
700	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
701	C₂²×C₄	C₂×C₇×D₄	1	2	yes	—
702	C₂²×C₄	C₂×C₇×D₄	1	2	yes	—
703	C₂²×C₄	C₂×C₇×D₄	1	2	yes	—
704	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
705	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
706	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
707	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
708	Q₁₆	—	2	4	no	—
709	SD₁₆	—	2	4	no	—
710	M₁₆	—	2	4	no	—
711	M₁₆	—	2	2	no	—
712	M₁₆	—	2	8	no	—
713	M₁₆	C₇×#41	1	4	yes	complemented
714	C₂×C₈	—	2	8	no	—
715	C₂×C₈	C₂⁴×C₇	1	2	yes	—
716	C₂×C₈	C₂⁴×C₇	1	4	yes	—
717	C₂×C₈	C₂⁴×C₇	1	2	yes	—
718	C₄⋊C₄	—	2	1	no	—
719	C₄⋊C₄	—	2	4	no	—
720	C₄⋊C₄	—	2	4	no	—
721	C₄⋊C₄	—	2	2	no	—
722	C₄⋊C₄	—	2	2	no	—
723	C₄⋊C₄	—	2	2	no	—
724	C₄⋊C₄	—	2	2	no	—
725	C₄⋊C₄	—	2	2	no	—
726	C₄⋊C₄	—	2	4	no	—
727	C₄⋊C₄	—	2	4	no	—
728	C₄⋊C₄	—	2	2	no	—
729	C₄⋊C₄	—	2	2	no	—
730	C₄⋊C₄	—	2	1	no	—
731	C₄⋊C₄	—	2	2	no	—
732	C₄⋊C₄	—	2	2	no	—
733	C₄⋊C₄	—	2	1	no	—
734	C₄⋊C₄	—	2	1	no	—
735	C₄⋊C₄	—	2	2	no	—
736	C₄⋊C₄	—	2	2	no	—
737	C₄⋊C₄	—	2	1	no	—
738	C₄⋊C₄	C₂×C₇×D₄	1	1	yes	characteristic
739	C₄⋊C₄	C₂×C₇×D₄	1	1	yes	characteristic
740	C₄⋊C₄	C₂×C₇×D₄	1	2	yes	—
741	C₄⋊C₄	C₂⁴×C₇	1	2	yes	—
742	C₄⋊C₄	C₂⁴×C₇	1	4	yes	—
743	C₄⋊C₄	C₂⁴×C₇	1	1	yes	characteristic
744	C₄⋊C₄	C₂⁴×C₇	1	2	yes	—
745	C₄⋊C₄	C₂⁴×C₇	1	1	yes	characteristic
746	C₄⋊C₄	C₂⁴×C₇	1	2	yes	—
747	C₂²⋊C₄	—	2	1	no	—
748	C₂²⋊C₄	—	2	2	no	—
749	C₂²⋊C₄	—	2	2	no	—
750	C₂²⋊C₄	—	2	2	no	—
751	C₂²⋊C₄	—	2	4	no	—
752	C₂²⋊C₄	—	2	4	no	—
753	C₂²⋊C₄	—	2	2	no	—
754	C₂²⋊C₄	—	2	2	no	—
755	C₂²⋊C₄	—	2	2	no	—
756	C₂²⋊C₄	—	2	1	no	—
757	C₂²⋊C₄	—	2	1	no	—
758	C₂²⋊C₄	—	2	2	no	—
759	C₂²⋊C₄	C₂×C₇×D₄	1	2	yes	—
760	C₂²⋊C₄	C₂×C₇×D₄	1	2	yes	—
761	C₂²⋊C₄	C₂×C₇×D₄	1	2	yes	—
762	C₂²⋊C₄	C₂×C₇×D₄	1	2	yes	—
763	C₄²	—	2	1	no	—
764	C₄²	—	2	2	no	—
765	C₄²	—	2	1	no	—
766	C₄²	—	2	2	no	—
767	C₄²	—	2	2	no	—
768	C₄²	—	2	1	no	—
769	C₄²	—	2	2	no	—
770	C₄²	—	2	2	no	—
771	C₄²	C₂×C₇×D₄	1	1	yes	characteristic
772	C₄²	C₂×C₇×D₄	1	1	yes	characteristic
773	C₄²	C₂⁴×C₇	1	1	yes	characteristic
774	C₄²	C₂⁴×C₇	1	1	yes	characteristic
775	C₂×C₇	—	2	2	no	—
776	C₂×C₇	—	2	4	no	—
777	C₂×C₇	—	4	2	no	—
778	C₂×C₇	—	8	1	no	—
779	C₂×C₇	C₂×#547	1	1	yes	characteristic
780	C₂×C₇	C₂²×#137	1	1	yes	characteristic
781	C₂×C₇	#3585	1	1	yes	characteristic
782	C₂³	—	2	4	no	—
783	C₂³	—	2	4	no	—
784	C₂³	—	2	1	no	—
785	C₂³	—	4	2	no	—
786	C₂³	C₂²×C₇×D₄	1	2	yes	—
787	C₂³	C₂²×C₇×D₄	1	1	yes	characteristic
788	C₂³	C₂²×C₇×D₄	1	2	yes	—
789	Q₈	—	2	2	no	—
790	Q₈	—	2	1	no	—
791	Q₈	—	2	2	no	—
792	Q₈	—	2	1	no	—
793	Q₈	—	4	2	no	—
794	Q₈	—	4	2	no	—
795	Q₈	—	8	1	no	—
796	Q₈	—	8	2	no	—
797	Q₈	—	8	2	no	—
798	D₄	—	2	4	no	—
799	D₄	—	2	1	no	—
800	D₄	—	2	1	no	—
801	D₄	—	2	2	no	—
802	D₄	—	4	2	no	—
803	D₄	—	4	4	no	—
804	D₄	—	8	2	no	—
805	D₄	C₇×#137	1	4	yes	complemented
806	C₂×C₄	—	2	4	no	—
807	C₂×C₄	—	2	2	no	—
808	C₂×C₄	—	2	2	no	—
809	C₂×C₄	—	2	2	no	—
810	C₂×C₄	—	2	2	no	—
811	C₂×C₄	—	2	4	no	—
812	C₂×C₄	—	2	4	no	—
813	C₂×C₄	—	2	2	no	—
814	C₂×C₄	—	2	1	no	—
815	C₂×C₄	—	2	1	no	—
816	C₂×C₄	—	2	1	no	—
817	C₂×C₄	—	2	2	no	—
818	C₂×C₄	—	2	2	no	—
819	C₂×C₄	—	2	2	no	—
820	C₂×C₄	—	2	2	no	—
821	C₂×C₄	—	2	4	no	—
822	C₂×C₄	—	4	1	no	—
823	C₂×C₄	—	4	2	no	—
824	C₂×C₄	—	4	4	no	—
825	C₂×C₄	—	4	2	no	—
826	C₂×C₄	—	4	4	no	—
827	C₂×C₄	—	4	2	no	—
828	C₂×C₄	—	4	2	no	—
829	C₂×C₄	—	8	1	no	—
830	C₂×C₄	—	8	2	no	—
831	C₂×C₄	—	8	4	no	—
832	C₂×C₄	—	8	4	no	—
833	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
834	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
835	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
836	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
837	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
838	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
839	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
840	C₂×C₄	C₂×C₇×#41	1	2	yes	—
841	C₂×C₄	C₇×2₋¹⁺⁴	1	2	yes	—
842	C₂×C₄	C₂⁵×C₇	1	1	yes	characteristic
843	C₈	—	2	4	no	—
844	C₈	—	2	2	no	—
845	C₈	C₂×C₇×#41	1	4	yes	—
846	C₇	#61254	1	1	yes	characteristic, direct product factor, Sylow
847	C₂²	—	2	1	no	—
848	C₂²	—	2	1	no	—
849	C₂²	—	2	2	no	—
850	C₂²	—	2	2	no	—
851	C₂²	—	2	2	no	—
852	C₂²	—	2	2	no	—
853	C₂²	—	2	2	no	—
854	C₂²	—	4	8	no	—
855	C₂²	—	4	1	no	—
856	C₂²	—	4	1	no	—
857	C₂²	—	4	1	no	—
858	C₂²	C₇×#547	1	2	yes	—
859	C₂²	C₂×C₇×#137	1	4	yes	—
860	C₂²	C₂³×C₇×D₄	1	1	yes	characteristic
861	C₄	—	2	1	no	—
862	C₄	—	2	1	no	—
863	C₄	—	2	1	no	—
864	C₄	—	2	2	no	—
865	C₄	—	2	2	no	—
866	C₄	—	4	1	no	—
867	C₄	—	4	2	no	—
868	C₄	—	4	2	no	—
869	C₄	—	4	4	no	—
870	C₄	—	4	1	no	—
871	C₄	—	4	2	no	—
872	C₄	—	4	1	no	—
873	C₄	—	4	2	no	—
874	C₄	C₇×#547	1	2	yes	—
875	C₄	C₂×C₇×#137	1	2	yes	—
876	C₄	C₂²×C₇×#41	1	1	yes	characteristic
877	C₄	C₂×C₇×2₋¹⁺⁴	1	1	yes	characteristic
878	C₂	—	2	2	no	—
879	C₂	—	2	4	no	—
880	C₂	—	4	2	no	—
881	C₂	—	8	1	no	—
882	C₂	C₂×C₇×#547	1	1	yes	characteristic
883	C₂	C₂²×C₇×#137	1	1	yes	characteristic
884	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×#3475	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₇ ◁ C₂×C₄×C₇×D₄ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₇×#554	C₂	semidirect
3. C₇×#3357	C₂	semidirect
4. C₇×#3356	C₂	semidirect
5. C₇×#3346	C₂	semidirect
6. C₇×#3344	C₂	semidirect
7. C₇×#3338	C₂	semidirect
8. C₇×#3335	C₂	semidirect
9. C₇×#3165	C₂	semidirect
10. C₇×#3095	C₂	semidirect
11. C₇×#3092	C₂	semidirect
12. C₇×#3079	C₂	semidirect
13. C₇×#3078	C₂	semidirect
14. C₇×#3056	C₂	semidirect
15. C₄×C₇×#137	C₂	semidirect
16. C₇×D₄×M₁₆	C₂	semidirect
17. C₂×C₇×#428	C₂	semidirect
50. C₇×#501	C₂²	semidirect
51. C₇×#500	C₂²	semidirect
52. C₇×#498	C₂²	semidirect
53. C₇×#485	C₂²	semidirect
54. C₇×#485	C₂²	semidirect
55. C₇×#484	C₂²	semidirect
56. C₇×#484	C₂²	semidirect
57. C₇×#483	C₂²	semidirect
58. C₇×#483	C₂²	semidirect
59. C₇×#481	C₂²	semidirect
60. C₇×#480	C₂²	semidirect
61. C₇×#479	C₂²	semidirect
62. C₇×#477	C₂²	semidirect
63. C₇×#477	C₂²	semidirect
64. C₇×#476	C₂²	semidirect
65. C₇×#475	C₂²	semidirect
66. C₇×#475	C₂²	semidirect
67. C₇×#474	C₂²	semidirect
68. C₇×#470	C₂²	semidirect
69. C₇×#468	C₂²	semidirect
70. C₇×#467	C₂²	semidirect
71. C₇×#465	C₂²	semidirect
72. C₇×#441	C₂²	semidirect
73. C₇×#440	C₂²	semidirect
74. C₄×C₇×Q₁₆	C₂²	semidirect
75. C₄×C₇×SD₁₆	C₂²	semidirect
84. C₇×#428	C₂²	semidirect
85. C₇×#428	C₂²	semidirect
86. C₂×C₇×#107	C₂²	semidirect
87. C₂×C₇×#106	C₂²	semidirect
95. #61254	C₇	direct (N × H)
232. C₂×#554	C₂×C₇	semidirect
233. #3357	C₂×C₇	semidirect
234. #3356	C₂×C₇	semidirect
235. #3346	C₂×C₇	semidirect
236. #3344	C₂×C₇	semidirect
237. #3338	C₂×C₇	semidirect
238. #3335	C₂×C₇	semidirect
239. #3165	C₂×C₇	semidirect
240. #3095	C₂×C₇	semidirect
241. #3092	C₂×C₇	semidirect
242. #3079	C₂×C₇	semidirect
243. #3078	C₂×C₇	semidirect
244. #3056	C₂×C₇	semidirect
245. C₄×#137	C₂×C₇	semidirect
246. D₄×M₁₆	C₂×C₇	semidirect
247. C₂×#428	C₂×C₇	semidirect
296. C₇×M₁₆	#41	semidirect
390. #501	C₂²×C₇	semidirect
391. #500	C₂²×C₇	semidirect
392. #498	C₂²×C₇	semidirect
393. #485	C₂²×C₇	semidirect
394. #485	C₂²×C₇	semidirect
395. #484	C₂²×C₇	semidirect
396. #484	C₂²×C₇	semidirect
397. #483	C₂²×C₇	semidirect
398. #483	C₂²×C₇	semidirect
399. #481	C₂²×C₇	semidirect
400. #480	C₂²×C₇	semidirect
401. #479	C₂²×C₇	semidirect
402. #477	C₂²×C₇	semidirect
403. #477	C₂²×C₇	semidirect
404. #476	C₂²×C₇	semidirect
405. #475	C₂²×C₇	semidirect
406. #475	C₂²×C₇	semidirect
407. #474	C₂²×C₇	semidirect
408. #470	C₂²×C₇	semidirect
409. #468	C₂²×C₇	semidirect
410. #467	C₂²×C₇	semidirect
411. #465	C₂²×C₇	semidirect
412. #441	C₂²×C₇	semidirect
413. #440	C₂²×C₇	semidirect
414. C₄×Q₁₆	C₂²×C₇	semidirect
415. C₄×SD₁₆	C₂²×C₇	semidirect
424. #428	C₂²×C₇	semidirect
425. #428	C₂²×C₇	semidirect
426. C₂×#107	C₂²×C₇	semidirect
427. C₂×#106	C₂²×C₇	semidirect
458. C₇×D₄	#137	semidirect
713. M₁₆	C₇×#41	semidirect
805. D₄	C₇×#137	semidirect
846. C₇	#61254	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₇×#3475	2
C₂×C₇×#554	2
C₇×#3357	2
C₇×#3356	2
C₇×#3346	2
C₇×#3344	2
C₇×#3338	2
C₇×#3335	2
C₇×#3165	2
C₇×#3095	2
C₇×#3092	2
C₇×#3079	2
C₇×#3078	2
C₇×#3056	2
C₄×C₇×#137	2
C₇×D₄×M₁₆	2
C₂×C₇×#428	2
#61254	7

Subgroups — C7×#61254 #13238470

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×#61254 #13238470