Subgroups — C₇×#60918 #13238134

Order 1792.

1888 conjugacy classes of subgroups.

The subgroup lattice has 852 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×#3444	C₂	1	1	yes	maximal, characteristic
2	C₂×C₇×#533	C₂	1	1	yes	maximal, characteristic, complemented
3	C₇×#3255	C₂	1	2	yes	maximal, complemented
4	C₇×#3254	C₂	1	2	yes	maximal, complemented
5	C₇×#3252	C₂	1	4	yes	maximal, complemented
6	C₇×#3249	C₂	1	2	yes	maximal, complemented
7	C₇×#3248	C₂	1	4	yes	maximal, complemented
8	C₇×#3246	C₂	1	2	yes	maximal, complemented
9	C₇×#3079	C₂	1	2	yes	maximal, complemented
10	C₇×#3078	C₂	1	2	yes	maximal, complemented
11	C₇×#3056	C₂	1	4	yes	maximal, complemented
12	C₇×#3039	C₂	1	2	yes	maximal, complemented
13	C₇×#3037	C₂	1	2	yes	maximal, complemented
14	C₂×C₇×#423	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂×C₇×#137	C₂²	1	4	yes	—
16	C₂²×C₇×M₁₆	C₂²	1	2	yes	—
17	C₇×#533	—	2	1	no	—
18	C₇×#533	—	2	1	no	—
19	C₇×#533	—	2	1	no	—
20	C₇×#533	—	2	1	no	—
21	C₇×#533	C₂²	1	2	yes	—
22	C₇×#533	C₂²	1	2	yes	—
23	C₇×#533	C₂²	1	1	yes	characteristic
24	C₇×#533	C₂²	1	2	yes	—
25	C₇×#533	C₂²	1	2	yes	—
26	C₇×#533	C₂²	1	1	yes	characteristic
27	C₇×#533	C₂²	1	1	yes	characteristic
28	C₇×#532	C₂²	1	1	yes	characteristic
29	C₇×#532	C₂²	1	1	yes	characteristic
30	C₇×#532	C₂²	1	1	yes	characteristic
31	C₂×C₇×C₄⋊Q₈	C₂²	1	1	yes	characteristic
32	C₂×C₇×C₄⋊Q₈	C₂²	1	1	yes	characteristic
33	C₇×#529	—	2	1	no	—
34	C₇×#529	—	2	1	no	—
35	C₇×#529	—	2	1	no	—
36	C₇×#529	—	2	1	no	—
37	C₇×#529	C₂²	1	2	yes	—
38	C₇×#529	C₂²	1	2	yes	—
39	C₂×C₇×#125	—	2	1	no	—
40	C₇×#525	—	2	1	no	—
41	C₇×#525	—	2	1	no	—
42	C₇×#525	C₂²	1	2	yes	—
43	C₂×C₇×C₂²⋊Q₈	—	2	1	no	—
44	C₂×C₇×C₂²⋊Q₈	C₂²	1	2	yes	—
45	C₄×C₇×#41	—	2	1	no	—
46	C₄×C₇×#41	—	2	1	no	—
47	C₄×C₇×#41	C₂²	1	2	yes	—
48	C₂×C₄×C₇×Q₈	—	2	1	no	—
49	C₂×C₄×C₇×Q₈	C₂²	1	2	yes	—
50	C₂×C₇×#117	—	2	1	no	—
51	C₂²×C₄²×C₇	C₂²	1	1	yes	characteristic
52	C₇×#479	C₂²	1	8	yes	complemented
53	C₇×#477	C₂²	1	4	yes	complemented
54	C₇×#477	C₂²	1	4	yes	complemented
55	C₇×#476	C₂²	1	4	yes	complemented
56	C₇×#475	C₂²	1	4	yes	complemented
57	C₇×#475	C₂²	1	4	yes	complemented
58	C₇×#474	C₂²	1	4	yes	complemented
59	C₇×#470	C₂²	1	8	yes	—
60	C₇×#468	C₂²	1	8	yes	—
61	C₇×#467	C₂²	1	8	yes	—
62	C₇×#465	C₂²	1	8	yes	—
63	C₇×#464	C₂²	1	8	yes	complemented
64	C₇×#462	C₂²	1	4	yes	complemented
65	C₇×#462	C₂²	1	4	yes	complemented
66	C₇×#462	C₂²	1	4	yes	complemented
67	C₇×#461	C₂²	1	4	yes	complemented
68	C₇×#461	C₂²	1	4	yes	complemented
69	C₇×#460	C₂²	1	4	yes	complemented
70	C₇×#428	C₂²	1	4	yes	—
71	C₇×#423	C₂²	1	2	yes	—
72	C₇×#423	C₂²	1	2	yes	—
73	C₇×#423	C₂²	1	2	yes	—
74	C₇×#423	C₂²	1	2	yes	—
75	C₂×C₇×C₄⋊C₈	C₂²	1	2	yes	—
76	C₂×C₇×C₄⋊C₈	C₂²	1	2	yes	—
77	C₇×#419	C₂²	1	4	yes	—
78	C₇×#417	C₂²	1	4	yes	—
79	#60918	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
80	C₂×C₇×#41	—	2	1	no	—
81	C₂×C₇×#41	—	2	1	no	—
82	C₂×C₇×#41	C₂³	1	2	yes	—
83	C₂²×C₇×Q₈	—	2	1	no	—
84	C₂²×C₇×Q₈	C₂³	1	2	yes	—
85	C₂³×C₄×C₇	D₄	1	1	yes	characteristic
86	C₂³×C₄×C₇	D₄	1	1	yes	characteristic
87	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
88	C₇×#137	—	4	8	no	—
89	C₂×C₇×Q₁₆	C₂³	1	8	yes	—
90	C₂×C₇×SD₁₆	C₂³	1	8	yes	—
91	C₂×C₇×M₁₆	—	4	4	no	—
92	C₂×C₇×M₁₆	C₂³	1	4	yes	—
93	C₂×C₇×M₁₆	C₂³	1	4	yes	—
94	C₂²×C₇×C₈	C₂³	1	4	yes	—
95	C₇×C₄⋊Q₈	—	2	1	no	—
96	C₇×C₄⋊Q₈	—	2	1	no	—
97	C₇×C₄⋊Q₈	—	2	1	no	—
98	C₇×C₄⋊Q₈	—	2	1	no	—
99	C₇×C₄⋊Q₈	C₂³	1	2	yes	—
100	C₇×C₄⋊Q₈	C₂³	1	2	yes	—
101	C₇×C₄⋊Q₈	C₂³	1	1	yes	characteristic
102	C₇×C₄⋊Q₈	C₂³	1	2	yes	—
103	C₇×C₄⋊Q₈	C₂³	1	1	yes	characteristic
104	C₇×C₄⋊Q₈	C₂³	1	2	yes	—
105	C₇×C₄⋊Q₈	C₂³	1	1	yes	characteristic
106	C₇×#127	C₂³	1	1	yes	characteristic
107	C₇×#126	—	2	2	no	—
108	C₇×#126	—	2	2	no	—
109	C₇×#125	—	2	2	no	—
110	C₇×#125	—	2	2	no	—
111	C₇×#125	—	2	2	no	—
112	C₇×#125	—	2	2	no	—
113	C₇×#125	—	2	1	no	—
114	C₇×#125	—	2	1	no	—
115	C₇×#125	C₂³	1	2	yes	—
116	C₇×#124	—	2	1	no	—
117	C₇×#124	—	2	1	no	—
118	C₇×#124	C₂³	1	2	yes	—
119	C₇×#123	—	2	2	no	—
120	C₇×#123	—	2	2	no	—
121	C₇×#123	—	2	2	no	—
122	C₇×C₂²⋊Q₈	—	2	2	no	—
123	C₇×C₂²⋊Q₈	—	2	2	no	—
124	C₇×C₂²⋊Q₈	—	2	2	no	—
125	C₇×C₂²⋊Q₈	—	2	2	no	—
126	C₇×C₂²⋊Q₈	—	2	2	no	—
127	C₇×C₂²⋊Q₈	—	2	2	no	—
128	C₇×C₂²⋊Q₈	—	2	1	no	—
129	C₇×C₂²⋊Q₈	—	2	1	no	—
130	C₇×C₂²⋊Q₈	—	2	1	no	—
131	C₇×C₂²⋊Q₈	—	2	1	no	—
132	C₇×C₂²⋊Q₈	C₂³	1	2	yes	—
133	C₇×C₂²⋊Q₈	C₂³	1	4	yes	—
134	C₇×C₂²⋊Q₈	C₂³	1	4	yes	—
135	C₇×C₂²⋊Q₈	C₂³	1	2	yes	—
136	C₇×#121	—	2	1	no	—
137	C₇×#121	—	2	1	no	—
138	C₇×#121	—	2	1	no	—
139	C₇×#121	—	2	1	no	—
140	C₇×#121	C₂³	1	2	yes	—
141	C₇×#121	C₂³	1	2	yes	—
142	C₇×#120	—	2	2	no	—
143	C₄×C₇×Q₈	—	2	2	no	—
144	C₄×C₇×Q₈	—	2	2	no	—
145	C₄×C₇×Q₈	—	2	2	no	—
146	C₄×C₇×Q₈	—	2	2	no	—
147	C₄×C₇×Q₈	—	2	2	no	—
148	C₄×C₇×Q₈	—	2	2	no	—
149	C₄×C₇×Q₈	—	2	1	no	—
150	C₄×C₇×Q₈	—	2	1	no	—
151	C₄×C₇×Q₈	—	2	1	no	—
152	C₄×C₇×Q₈	—	2	1	no	—
153	C₄×C₇×Q₈	C₂³	1	2	yes	—
154	C₄×C₇×Q₈	C₂³	1	4	yes	—
155	C₄×C₇×Q₈	C₂³	1	2	yes	—
156	C₄×C₇×Q₈	C₂³	1	4	yes	—
157	C₄×C₇×D₄	—	2	2	no	—
158	C₄×C₇×D₄	—	2	2	no	—
159	C₄×C₇×D₄	—	2	2	no	—
160	C₄×C₇×D₄	—	2	2	no	—
161	C₄×C₇×D₄	—	2	2	no	—
162	C₄×C₇×D₄	—	2	2	no	—
163	C₄×C₇×D₄	—	2	1	no	—
164	C₄×C₇×D₄	—	2	1	no	—
165	C₄×C₇×D₄	—	2	1	no	—
166	C₄×C₇×D₄	—	2	1	no	—
167	C₄×C₇×D₄	C₂³	1	2	yes	—
168	C₄×C₇×D₄	C₂³	1	2	yes	—
169	C₇×#117	—	2	2	no	—
170	C₇×#117	—	2	2	no	—
171	C₇×#117	—	2	2	no	—
172	C₇×#117	—	2	2	no	—
173	C₇×#117	—	2	1	no	—
174	C₇×#117	—	2	1	no	—
175	C₇×#117	—	2	2	no	—
176	C₇×#117	—	2	2	no	—
177	C₇×#117	—	2	2	no	—
178	C₇×#117	C₂³	1	2	yes	—
179	C₂×C₇×C₄⋊C₄	—	2	1	no	—
180	C₂×C₇×C₄⋊C₄	—	2	1	no	—
181	C₂×C₇×C₄⋊C₄	—	2	1	no	—
182	C₂×C₇×C₄⋊C₄	—	2	2	no	—
183	C₂×C₇×C₄⋊C₄	—	2	2	no	—
184	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
185	C₂×C₇×C₂²⋊C₄	—	2	2	no	—
186	C₂×C₄²×C₇	—	2	2	no	—
187	C₂×C₄²×C₇	—	2	2	no	—
188	C₂×C₄²×C₇	D₄	1	1	yes	characteristic
189	C₂×C₄²×C₇	D₄	1	1	yes	characteristic
190	C₂×C₄²×C₇	D₄	1	1	yes	characteristic
191	C₂×C₄²×C₇	D₄	1	1	yes	characteristic
192	C₂×C₄²×C₇	D₄	1	1	yes	characteristic
193	C₂×C₄²×C₇	D₄	1	1	yes	characteristic
194	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
195	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
196	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
197	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
198	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
199	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
200	C₇×#107	C₂³	1	8	yes	—
201	C₇×#106	C₂³	1	8	yes	—
202	C₇×C₄⋊C₈	C₂³	1	4	yes	—
203	C₇×C₄⋊C₈	C₂³	1	4	yes	—
204	C₇×C₄⋊C₈	C₂³	1	4	yes	—
205	C₇×C₄⋊C₈	C₂³	1	4	yes	—
206	C₇×#103	C₂³	1	8	yes	—
207	C₇×#103	C₂³	1	8	yes	—
208	C₇×#103	C₂³	1	8	yes	—
209	C₇×#102	C₂³	1	8	yes	—
210	#3444	C₂×C₇	1	1	yes	characteristic
211	C₂×#533	C₂×C₇	1	1	yes	characteristic, complemented
212	#3255	C₂×C₇	1	2	yes	complemented
213	#3254	C₂×C₇	1	2	yes	complemented
214	#3252	C₂×C₇	1	4	yes	complemented
215	#3249	C₂×C₇	1	2	yes	complemented
216	#3248	C₂×C₇	1	4	yes	complemented
217	#3246	C₂×C₇	1	2	yes	complemented
218	#3079	C₂×C₇	1	2	yes	complemented
219	#3078	C₂×C₇	1	2	yes	complemented
220	#3056	C₂×C₇	1	4	yes	complemented
221	#3039	C₂×C₇	1	2	yes	complemented
222	#3037	C₂×C₇	1	2	yes	complemented
223	C₂×#423	C₂×C₇	1	1	yes	characteristic, complemented
224	C₂⁴×C₇	C₂×D₄	1	1	yes	characteristic
225	C₇×#41	—	2	4	no	—
226	C₇×#41	—	2	4	no	—
227	C₇×#41	—	4	4	no	—
228	C₇×#41	—	4	4	no	—
229	C₂×C₇×Q₈	—	2	1	no	—
230	C₂×C₇×Q₈	—	2	1	no	—
231	C₂×C₇×Q₈	—	2	2	no	—
232	C₂×C₇×Q₈	—	2	2	no	—
233	C₂×C₇×Q₈	—	2	2	no	—
234	C₂×C₇×Q₈	—	2	4	no	—
235	C₂×C₇×Q₈	—	2	4	no	—
236	C₂×C₇×Q₈	—	4	4	no	—
237	C₂×C₇×Q₈	C₂⁴	1	2	yes	—
238	C₂×C₇×Q₈	C₂⁴	1	4	yes	—
239	C₂×C₇×D₄	—	2	2	no	—
240	C₂×C₇×D₄	—	2	2	no	—
241	C₂×C₇×D₄	—	2	2	no	—
242	C₂×C₇×D₄	—	2	1	no	—
243	C₂×C₇×D₄	—	2	1	no	—
244	C₂×C₇×D₄	C₂⁴	1	2	yes	—
245	C₂²×C₄×C₇	—	2	4	no	—
246	C₂²×C₄×C₇	—	2	2	no	—
247	C₂²×C₄×C₇	—	2	2	no	—
248	C₂²×C₄×C₇	—	2	2	no	—
249	C₂²×C₄×C₇	—	2	2	no	—
250	C₂²×C₄×C₇	—	2	2	no	—
251	C₂²×C₄×C₇	—	2	2	no	—
252	C₂²×C₄×C₇	—	2	2	no	—
253	C₂²×C₄×C₇	—	4	2	no	—
254	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
255	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
256	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
257	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
258	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
259	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
260	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
261	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
262	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
263	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
264	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
265	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
266	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
267	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
268	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
269	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
270	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
271	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
272	C₇×Q₁₆	—	4	8	no	—
273	C₇×SD₁₆	—	4	8	no	—
274	C₇×M₁₆	—	2	8	no	—
275	C₇×M₁₆	—	4	4	no	—
276	C₂×C₇×C₈	—	4	4	no	—
277	C₂×C₇×C₈	C₂⁴	1	8	yes	—
278	C₇×C₄⋊C₄	—	2	2	no	—
279	C₇×C₄⋊C₄	—	2	2	no	—
280	C₇×C₄⋊C₄	—	2	2	no	—
281	C₇×C₄⋊C₄	—	2	2	no	—
282	C₇×C₄⋊C₄	—	2	2	no	—
283	C₇×C₄⋊C₄	—	2	2	no	—
284	C₇×C₄⋊C₄	—	2	4	no	—
285	C₇×C₄⋊C₄	—	2	4	no	—
286	C₇×C₄⋊C₄	—	2	4	no	—
287	C₇×C₄⋊C₄	—	2	4	no	—
288	C₇×C₄⋊C₄	—	2	2	no	—
289	C₇×C₄⋊C₄	—	2	1	no	—
290	C₇×C₄⋊C₄	—	2	1	no	—
291	C₇×C₄⋊C₄	—	2	1	no	—
292	C₇×C₄⋊C₄	—	2	1	no	—
293	C₇×C₄⋊C₄	—	2	2	no	—
294	C₇×C₄⋊C₄	—	2	2	no	—
295	C₇×C₄⋊C₄	—	2	2	no	—
296	C₇×C₄⋊C₄	—	2	2	no	—
297	C₇×C₄⋊C₄	—	2	2	no	—
298	C₇×C₄⋊C₄	—	2	2	no	—
299	C₇×C₄⋊C₄	C₂⁴	1	4	yes	—
300	C₇×C₄⋊C₄	C₂⁴	1	2	yes	—
301	C₇×C₄⋊C₄	C₂⁴	1	2	yes	—
302	C₇×C₂²⋊C₄	—	2	4	no	—
303	C₇×C₂²⋊C₄	—	2	4	no	—
304	C₇×C₂²⋊C₄	—	2	2	no	—
305	C₇×C₂²⋊C₄	—	2	2	no	—
306	C₇×C₂²⋊C₄	—	2	2	no	—
307	C₇×C₂²⋊C₄	—	2	2	no	—
308	C₇×C₂²⋊C₄	—	2	2	no	—
309	C₇×C₂²⋊C₄	—	2	2	no	—
310	C₇×C₂²⋊C₄	—	2	2	no	—
311	C₇×C₂²⋊C₄	—	2	2	no	—
312	C₇×C₂²⋊C₄	—	2	2	no	—
313	C₄²×C₇	—	2	2	no	—
314	C₄²×C₇	—	2	2	no	—
315	C₄²×C₇	—	2	4	no	—
316	C₄²×C₇	—	2	4	no	—
317	C₄²×C₇	—	2	2	no	—
318	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
319	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
320	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
321	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
322	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
323	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
324	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
325	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
326	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
327	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
328	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
329	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
330	C₄²×C₇	C₂⁴	1	1	yes	characteristic
331	C₄²×C₇	C₂⁴	1	1	yes	characteristic
332	C₄²×C₇	C₂⁴	1	1	yes	characteristic
333	C₄²×C₇	C₂⁴	1	1	yes	characteristic
334	C₂×#137	C₂²×C₇	1	4	yes	—
335	C₂²×M₁₆	C₂²×C₇	1	2	yes	—
336	#533	—	2	1	no	—
337	#533	—	2	1	no	—
338	#533	—	2	1	no	—
339	#533	—	2	1	no	—
340	#533	C₂²×C₇	1	2	yes	—
341	#533	C₂²×C₇	1	2	yes	—
342	#533	C₂²×C₇	1	2	yes	—
343	#533	C₂²×C₇	1	2	yes	—
344	#533	C₂²×C₇	1	1	yes	characteristic
345	#533	C₂²×C₇	1	1	yes	characteristic
346	#533	C₂²×C₇	1	1	yes	characteristic
347	#532	C₂²×C₇	1	1	yes	characteristic
348	#532	C₂²×C₇	1	1	yes	characteristic
349	#532	C₂²×C₇	1	1	yes	characteristic
350	C₂×C₄⋊Q₈	C₂²×C₇	1	1	yes	characteristic
351	C₂×C₄⋊Q₈	C₂²×C₇	1	1	yes	characteristic
352	#529	—	2	1	no	—
353	#529	—	2	1	no	—
354	#529	—	2	1	no	—
355	#529	—	2	1	no	—
356	#529	C₂²×C₇	1	2	yes	—
357	#529	C₂²×C₇	1	2	yes	—
358	C₂×#125	—	2	1	no	—
359	#525	—	2	1	no	—
360	#525	—	2	1	no	—
361	#525	C₂²×C₇	1	2	yes	—
362	C₂×C₂²⋊Q₈	—	2	1	no	—
363	C₂×C₂²⋊Q₈	C₂²×C₇	1	2	yes	—
364	C₄×#41	—	2	1	no	—
365	C₄×#41	—	2	1	no	—
366	C₄×#41	C₂²×C₇	1	2	yes	—
367	C₂×C₄×Q₈	—	2	1	no	—
368	C₂×C₄×Q₈	C₂²×C₇	1	2	yes	—
369	C₂×#117	—	2	1	no	—
370	C₂²×C₄²	C₂²×C₇	1	1	yes	characteristic
371	#479	C₂²×C₇	1	8	yes	complemented
372	#477	C₂²×C₇	1	4	yes	complemented
373	#477	C₂²×C₇	1	4	yes	complemented
374	#476	C₂²×C₇	1	4	yes	complemented
375	#475	C₂²×C₇	1	4	yes	complemented
376	#475	C₂²×C₇	1	4	yes	complemented
377	#474	C₂²×C₇	1	4	yes	complemented
378	#470	C₂²×C₇	1	8	yes	—
379	#468	C₂²×C₇	1	8	yes	—
380	#467	C₂²×C₇	1	8	yes	—
381	#465	C₂²×C₇	1	8	yes	—
382	#464	C₂²×C₇	1	8	yes	complemented
383	#462	C₂²×C₇	1	4	yes	complemented
384	#462	C₂²×C₇	1	4	yes	complemented
385	#462	C₂²×C₇	1	4	yes	complemented
386	#461	C₂²×C₇	1	4	yes	complemented
387	#461	C₂²×C₇	1	4	yes	complemented
388	#460	C₂²×C₇	1	4	yes	complemented
389	#428	C₂²×C₇	1	4	yes	—
390	#423	C₂²×C₇	1	2	yes	—
391	#423	C₂²×C₇	1	2	yes	—
392	#423	C₂²×C₇	1	2	yes	—
393	#423	C₂²×C₇	1	2	yes	—
394	C₂×C₄⋊C₈	C₂²×C₇	1	2	yes	—
395	C₂×C₄⋊C₈	C₂²×C₇	1	2	yes	—
396	#419	C₂²×C₇	1	4	yes	—
397	#417	C₂²×C₇	1	4	yes	—
398	C₂³×C₇	—	2	2	no	—
399	C₂³×C₇	—	2	2	no	—
400	C₂³×C₇	—	2	2	no	—
401	C₂³×C₇	—	4	1	no	—
402	C₂³×C₇	C₂²×D₄	1	1	yes	characteristic
403	C₂³×C₇	C₂²×D₄	1	1	yes	characteristic
404	C₂³×C₇	C₂²×D₄	1	1	yes	characteristic
405	C₇×Q₈	—	2	4	no	—
406	C₇×Q₈	—	2	2	no	—
407	C₇×Q₈	—	2	4	no	—
408	C₇×Q₈	—	2	2	no	—
409	C₇×Q₈	—	4	4	no	—
410	C₇×Q₈	—	4	2	no	—
411	C₇×Q₈	—	4	4	no	—
412	C₇×Q₈	—	4	2	no	—
413	C₇×Q₈	—	4	4	no	—
414	C₇×D₄	—	2	2	no	—
415	C₇×D₄	—	2	2	no	—
416	C₇×D₄	—	4	2	no	—
417	C₇×D₄	—	4	4	no	—
418	C₇×D₄	—	4	4	no	—
419	C₇×D₄	—	4	4	no	—
420	C₇×D₄	—	4	2	no	—
421	C₂×C₄×C₇	—	2	2	no	—
422	C₂×C₄×C₇	—	2	2	no	—
423	C₂×C₄×C₇	—	2	2	no	—
424	C₂×C₄×C₇	—	2	2	no	—
425	C₂×C₄×C₇	—	2	2	no	—
426	C₂×C₄×C₇	—	2	2	no	—
427	C₂×C₄×C₇	—	2	2	no	—
428	C₂×C₄×C₇	—	2	2	no	—
429	C₂×C₄×C₇	—	2	2	no	—
430	C₂×C₄×C₇	—	2	2	no	—
431	C₂×C₄×C₇	—	2	2	no	—
432	C₂×C₄×C₇	—	2	1	no	—
433	C₂×C₄×C₇	—	2	1	no	—
434	C₂×C₄×C₇	—	2	1	no	—
435	C₂×C₄×C₇	—	2	1	no	—
436	C₂×C₄×C₇	—	2	2	no	—
437	C₂×C₄×C₇	—	2	2	no	—
438	C₂×C₄×C₇	—	2	2	no	—
439	C₂×C₄×C₇	—	2	4	no	—
440	C₂×C₄×C₇	—	2	4	no	—
441	C₂×C₄×C₇	—	4	1	no	—
442	C₂×C₄×C₇	—	4	1	no	—
443	C₂×C₄×C₇	—	4	1	no	—
444	C₂×C₄×C₇	—	4	4	no	—
445	C₂×C₄×C₇	—	4	4	no	—
446	C₂×C₄×C₇	—	4	4	no	—
447	C₂×C₄×C₇	—	4	4	no	—
448	C₂×C₄×C₇	—	4	4	no	—
449	C₂×C₄×C₇	#137	1	4	yes	complemented
450	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
451	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
452	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
453	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
454	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
455	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
456	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
457	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
458	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
459	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
460	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
461	C₂×C₄×C₇	H(5,𝔽₂)	1	2	yes	—
462	C₂×C₄×C₇	2₋¹⁺⁴	1	2	yes	—
463	C₂×C₄×C₇	C₂⁵	1	1	yes	characteristic
464	C₇×C₈	—	2	8	no	—
465	C₂×#41	—	2	1	no	—
466	C₂×#41	—	2	1	no	—
467	C₂×#41	C₂³×C₇	1	2	yes	—
468	C₂²×Q₈	—	2	1	no	—
469	C₂²×Q₈	C₂³×C₇	1	2	yes	—
470	C₂³×C₄	C₇×D₄	1	1	yes	characteristic
471	C₂³×C₄	C₇×D₄	1	1	yes	characteristic
472	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
473	#137	—	4	8	no	—
474	C₂×Q₁₆	C₂³×C₇	1	8	yes	—
475	C₂×SD₁₆	C₂³×C₇	1	8	yes	—
476	C₂×M₁₆	—	4	4	no	—
477	C₂×M₁₆	C₂³×C₇	1	4	yes	—
478	C₂×M₁₆	C₂³×C₇	1	4	yes	—
479	C₂²×C₈	C₂³×C₇	1	4	yes	—
480	C₄⋊Q₈	—	2	1	no	—
481	C₄⋊Q₈	—	2	1	no	—
482	C₄⋊Q₈	—	2	1	no	—
483	C₄⋊Q₈	—	2	1	no	—
484	C₄⋊Q₈	C₂³×C₇	1	2	yes	—
485	C₄⋊Q₈	C₂³×C₇	1	2	yes	—
486	C₄⋊Q₈	C₂³×C₇	1	1	yes	characteristic
487	C₄⋊Q₈	C₂³×C₇	1	2	yes	—
488	C₄⋊Q₈	C₂³×C₇	1	2	yes	—
489	C₄⋊Q₈	C₂³×C₇	1	1	yes	characteristic
490	C₄⋊Q₈	C₂³×C₇	1	1	yes	characteristic
491	#127	C₂³×C₇	1	1	yes	characteristic
492	#126	—	2	2	no	—
493	#126	—	2	2	no	—
494	#125	—	2	2	no	—
495	#125	—	2	2	no	—
496	#125	—	2	2	no	—
497	#125	—	2	2	no	—
498	#125	—	2	1	no	—
499	#125	—	2	1	no	—
500	#125	C₂³×C₇	1	2	yes	—
501	#124	—	2	1	no	—
502	#124	—	2	1	no	—
503	#124	C₂³×C₇	1	2	yes	—
504	#123	—	2	2	no	—
505	#123	—	2	2	no	—
506	#123	—	2	2	no	—
507	C₂²⋊Q₈	—	2	2	no	—
508	C₂²⋊Q₈	—	2	2	no	—
509	C₂²⋊Q₈	—	2	2	no	—
510	C₂²⋊Q₈	—	2	2	no	—
511	C₂²⋊Q₈	—	2	2	no	—
512	C₂²⋊Q₈	—	2	2	no	—
513	C₂²⋊Q₈	—	2	1	no	—
514	C₂²⋊Q₈	—	2	1	no	—
515	C₂²⋊Q₈	—	2	1	no	—
516	C₂²⋊Q₈	—	2	1	no	—
517	C₂²⋊Q₈	C₂³×C₇	1	4	yes	—
518	C₂²⋊Q₈	C₂³×C₇	1	4	yes	—
519	C₂²⋊Q₈	C₂³×C₇	1	2	yes	—
520	C₂²⋊Q₈	C₂³×C₇	1	2	yes	—
521	#121	—	2	1	no	—
522	#121	—	2	1	no	—
523	#121	—	2	1	no	—
524	#121	—	2	1	no	—
525	#121	C₂³×C₇	1	2	yes	—
526	#121	C₂³×C₇	1	2	yes	—
527	#120	—	2	2	no	—
528	C₄×Q₈	—	2	2	no	—
529	C₄×Q₈	—	2	2	no	—
530	C₄×Q₈	—	2	2	no	—
531	C₄×Q₈	—	2	2	no	—
532	C₄×Q₈	—	2	2	no	—
533	C₄×Q₈	—	2	2	no	—
534	C₄×Q₈	—	2	1	no	—
535	C₄×Q₈	—	2	1	no	—
536	C₄×Q₈	—	2	1	no	—
537	C₄×Q₈	—	2	1	no	—
538	C₄×Q₈	C₂³×C₇	1	4	yes	—
539	C₄×Q₈	C₂³×C₇	1	4	yes	—
540	C₄×Q₈	C₂³×C₇	1	2	yes	—
541	C₄×Q₈	C₂³×C₇	1	2	yes	—
542	C₄×D₄	—	2	2	no	—
543	C₄×D₄	—	2	2	no	—
544	C₄×D₄	—	2	2	no	—
545	C₄×D₄	—	2	2	no	—
546	C₄×D₄	—	2	2	no	—
547	C₄×D₄	—	2	2	no	—
548	C₄×D₄	—	2	1	no	—
549	C₄×D₄	—	2	1	no	—
550	C₄×D₄	—	2	1	no	—
551	C₄×D₄	—	2	1	no	—
552	C₄×D₄	C₂³×C₇	1	2	yes	—
553	C₄×D₄	C₂³×C₇	1	2	yes	—
554	#117	—	2	2	no	—
555	#117	—	2	2	no	—
556	#117	—	2	2	no	—
557	#117	—	2	2	no	—
558	#117	—	2	1	no	—
559	#117	—	2	1	no	—
560	#117	—	2	2	no	—
561	#117	—	2	2	no	—
562	#117	—	2	2	no	—
563	#117	C₂³×C₇	1	2	yes	—
564	C₂×C₄⋊C₄	—	2	1	no	—
565	C₂×C₄⋊C₄	—	2	1	no	—
566	C₂×C₄⋊C₄	—	2	1	no	—
567	C₂×C₄⋊C₄	—	2	2	no	—
568	C₂×C₄⋊C₄	—	2	2	no	—
569	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
570	C₂×C₂²⋊C₄	—	2	2	no	—
571	C₂×C₄²	—	2	2	no	—
572	C₂×C₄²	—	2	2	no	—
573	C₂×C₄²	C₇×D₄	1	1	yes	characteristic
574	C₂×C₄²	C₇×D₄	1	1	yes	characteristic
575	C₂×C₄²	C₇×D₄	1	1	yes	characteristic
576	C₂×C₄²	C₇×D₄	1	1	yes	characteristic
577	C₂×C₄²	C₇×D₄	1	1	yes	characteristic
578	C₂×C₄²	C₇×D₄	1	1	yes	characteristic
579	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
580	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
581	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
582	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
583	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
584	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
585	#107	C₂³×C₇	1	8	yes	—
586	#106	C₂³×C₇	1	8	yes	—
587	C₄⋊C₈	C₂³×C₇	1	4	yes	—
588	C₄⋊C₈	C₂³×C₇	1	4	yes	—
589	C₄⋊C₈	C₂³×C₇	1	4	yes	—
590	C₄⋊C₈	C₂³×C₇	1	4	yes	—
591	#103	C₂³×C₇	1	8	yes	—
592	#103	C₂³×C₇	1	8	yes	—
593	#103	C₂³×C₇	1	8	yes	—
594	#102	C₂³×C₇	1	8	yes	—
595	C₂²×C₇	—	2	1	no	—
596	C₂²×C₇	—	2	1	no	—
597	C₂²×C₇	—	2	1	no	—
598	C₂²×C₇	—	2	1	no	—
599	C₂²×C₇	—	2	1	no	—
600	C₂²×C₇	—	2	1	no	—
601	C₂²×C₇	—	2	1	no	—
602	C₂²×C₇	—	4	4	no	—
603	C₂²×C₇	—	4	2	no	—
604	C₂²×C₇	—	4	2	no	—
605	C₂²×C₇	—	4	2	no	—
606	C₂²×C₇	#537	1	2	yes	—
607	C₂²×C₇	C₂×#137	1	2	yes	—
608	C₂²×C₇	C₂³×D₄	1	1	yes	characteristic
609	C₄×C₇	—	2	1	no	—
610	C₄×C₇	—	2	1	no	—
611	C₄×C₇	—	2	1	no	—
612	C₄×C₇	—	2	1	no	—
613	C₄×C₇	—	2	1	no	—
614	C₄×C₇	—	2	1	no	—
615	C₄×C₇	—	2	1	no	—
616	C₄×C₇	—	4	2	no	—
617	C₄×C₇	—	4	4	no	—
618	C₄×C₇	—	4	2	no	—
619	C₄×C₇	—	4	2	no	—
620	C₄×C₇	—	4	4	no	—
621	C₄×C₇	#537	1	2	yes	—
622	C₄×C₇	C₂×#137	1	2	yes	—
623	C₄×C₇	C₂×#137	1	2	yes	—
624	C₄×C₇	#575	1	2	yes	—
625	C₄×C₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
626	C₄×C₇	C₂×2₋¹⁺⁴	1	1	yes	characteristic
627	C₂⁴	C₂×C₇×D₄	1	1	yes	characteristic
628	#41	—	2	4	no	—
629	#41	—	2	4	no	—
630	#41	—	4	4	no	—
631	#41	—	4	4	no	—
632	C₂×Q₈	—	2	1	no	—
633	C₂×Q₈	—	2	1	no	—
634	C₂×Q₈	—	2	2	no	—
635	C₂×Q₈	—	2	2	no	—
636	C₂×Q₈	—	2	2	no	—
637	C₂×Q₈	—	2	4	no	—
638	C₂×Q₈	—	2	4	no	—
639	C₂×Q₈	—	4	4	no	—
640	C₂×Q₈	C₂⁴×C₇	1	2	yes	—
641	C₂×Q₈	C₂⁴×C₇	1	4	yes	—
642	C₂×D₄	—	2	2	no	—
643	C₂×D₄	—	2	2	no	—
644	C₂×D₄	—	2	2	no	—
645	C₂×D₄	—	2	1	no	—
646	C₂×D₄	—	2	1	no	—
647	C₂×D₄	C₂⁴×C₇	1	2	yes	—
648	C₂²×C₄	—	2	4	no	—
649	C₂²×C₄	—	2	2	no	—
650	C₂²×C₄	—	2	2	no	—
651	C₂²×C₄	—	2	2	no	—
652	C₂²×C₄	—	2	2	no	—
653	C₂²×C₄	—	2	2	no	—
654	C₂²×C₄	—	2	2	no	—
655	C₂²×C₄	—	2	2	no	—
656	C₂²×C₄	—	4	2	no	—
657	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
658	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
659	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
660	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
661	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
662	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
663	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
664	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
665	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
666	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
667	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
668	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
669	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
670	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
671	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
672	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
673	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
674	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
675	Q₁₆	—	4	8	no	—
676	SD₁₆	—	4	8	no	—
677	M₁₆	—	2	8	no	—
678	M₁₆	—	4	4	no	—
679	C₂×C₈	—	4	4	no	—
680	C₂×C₈	C₂⁴×C₇	1	8	yes	—
681	C₄⋊C₄	—	2	2	no	—
682	C₄⋊C₄	—	2	2	no	—
683	C₄⋊C₄	—	2	2	no	—
684	C₄⋊C₄	—	2	2	no	—
685	C₄⋊C₄	—	2	2	no	—
686	C₄⋊C₄	—	2	2	no	—
687	C₄⋊C₄	—	2	4	no	—
688	C₄⋊C₄	—	2	4	no	—
689	C₄⋊C₄	—	2	4	no	—
690	C₄⋊C₄	—	2	4	no	—
691	C₄⋊C₄	—	2	2	no	—
692	C₄⋊C₄	—	2	1	no	—
693	C₄⋊C₄	—	2	1	no	—
694	C₄⋊C₄	—	2	1	no	—
695	C₄⋊C₄	—	2	1	no	—
696	C₄⋊C₄	—	2	2	no	—
697	C₄⋊C₄	—	2	2	no	—
698	C₄⋊C₄	—	2	2	no	—
699	C₄⋊C₄	—	2	2	no	—
700	C₄⋊C₄	—	2	2	no	—
701	C₄⋊C₄	—	2	2	no	—
702	C₄⋊C₄	C₂⁴×C₇	1	4	yes	—
703	C₄⋊C₄	C₂⁴×C₇	1	2	yes	—
704	C₄⋊C₄	C₂⁴×C₇	1	2	yes	—
705	C₂²⋊C₄	—	2	4	no	—
706	C₂²⋊C₄	—	2	4	no	—
707	C₂²⋊C₄	—	2	2	no	—
708	C₂²⋊C₄	—	2	2	no	—
709	C₂²⋊C₄	—	2	2	no	—
710	C₂²⋊C₄	—	2	2	no	—
711	C₂²⋊C₄	—	2	2	no	—
712	C₂²⋊C₄	—	2	2	no	—
713	C₂²⋊C₄	—	2	2	no	—
714	C₂²⋊C₄	—	2	2	no	—
715	C₂²⋊C₄	—	2	2	no	—
716	C₄²	—	2	2	no	—
717	C₄²	—	2	2	no	—
718	C₄²	—	2	4	no	—
719	C₄²	—	2	4	no	—
720	C₄²	—	2	2	no	—
721	C₄²	C₂×C₇×D₄	1	1	yes	characteristic
722	C₄²	C₂×C₇×D₄	1	1	yes	characteristic
723	C₄²	C₂×C₇×D₄	1	1	yes	characteristic
724	C₄²	C₂×C₇×D₄	1	1	yes	characteristic
725	C₄²	C₂×C₇×D₄	1	1	yes	characteristic
726	C₄²	C₂×C₇×D₄	1	1	yes	characteristic
727	C₄²	C₂×C₇×D₄	1	1	yes	characteristic
728	C₄²	C₂×C₇×D₄	1	1	yes	characteristic
729	C₄²	C₂×C₇×D₄	1	1	yes	characteristic
730	C₄²	C₂×C₇×D₄	1	1	yes	characteristic
731	C₄²	C₂×C₇×D₄	1	1	yes	characteristic
732	C₄²	C₂×C₇×D₄	1	1	yes	characteristic
733	C₄²	C₂⁴×C₇	1	1	yes	characteristic
734	C₄²	C₂⁴×C₇	1	1	yes	characteristic
735	C₄²	C₂⁴×C₇	1	1	yes	characteristic
736	C₄²	C₂⁴×C₇	1	1	yes	characteristic
737	C₂×C₇	—	2	2	no	—
738	C₂×C₇	—	2	2	no	—
739	C₂×C₇	—	4	1	no	—
740	C₂×C₇	—	8	2	no	—
741	C₂×C₇	C₂×#537	1	1	yes	characteristic
742	C₂×C₇	C₂²×#137	1	1	yes	characteristic
743	C₂×C₇	C₂×#575	1	1	yes	characteristic
744	C₂³	—	2	2	no	—
745	C₂³	—	2	2	no	—
746	C₂³	—	2	2	no	—
747	C₂³	—	4	1	no	—
748	C₂³	C₂²×C₇×D₄	1	1	yes	characteristic
749	C₂³	C₂²×C₇×D₄	1	1	yes	characteristic
750	C₂³	C₂²×C₇×D₄	1	1	yes	characteristic
751	Q₈	—	2	4	no	—
752	Q₈	—	2	2	no	—
753	Q₈	—	2	4	no	—
754	Q₈	—	2	2	no	—
755	Q₈	—	4	4	no	—
756	Q₈	—	4	2	no	—
757	Q₈	—	4	4	no	—
758	Q₈	—	4	2	no	—
759	Q₈	—	4	4	no	—
760	D₄	—	2	2	no	—
761	D₄	—	2	2	no	—
762	D₄	—	4	2	no	—
763	D₄	—	4	4	no	—
764	D₄	—	4	4	no	—
765	D₄	—	4	4	no	—
766	D₄	—	4	2	no	—
767	C₂×C₄	—	2	2	no	—
768	C₂×C₄	—	2	2	no	—
769	C₂×C₄	—	2	1	no	—
770	C₂×C₄	—	2	1	no	—
771	C₂×C₄	—	2	1	no	—
772	C₂×C₄	—	2	1	no	—
773	C₂×C₄	—	2	2	no	—
774	C₂×C₄	—	2	2	no	—
775	C₂×C₄	—	2	2	no	—
776	C₂×C₄	—	2	2	no	—
777	C₂×C₄	—	2	2	no	—
778	C₂×C₄	—	2	2	no	—
779	C₂×C₄	—	2	2	no	—
780	C₂×C₄	—	2	2	no	—
781	C₂×C₄	—	2	2	no	—
782	C₂×C₄	—	2	2	no	—
783	C₂×C₄	—	2	2	no	—
784	C₂×C₄	—	2	2	no	—
785	C₂×C₄	—	2	4	no	—
786	C₂×C₄	—	2	4	no	—
787	C₂×C₄	—	4	1	no	—
788	C₂×C₄	—	4	1	no	—
789	C₂×C₄	—	4	1	no	—
790	C₂×C₄	—	4	4	no	—
791	C₂×C₄	—	4	4	no	—
792	C₂×C₄	—	4	4	no	—
793	C₂×C₄	—	4	4	no	—
794	C₂×C₄	—	4	4	no	—
795	C₂×C₄	C₇×#137	1	4	yes	complemented
796	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
797	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
798	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
799	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
800	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
801	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
802	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
803	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
804	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
805	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
806	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
807	C₂×C₄	C₇×H(5,𝔽₂)	1	2	yes	—
808	C₂×C₄	C₇×2₋¹⁺⁴	1	2	yes	—
809	C₂×C₄	C₂⁵×C₇	1	1	yes	characteristic
810	C₈	—	2	8	no	—
811	C₇	#60918	1	1	yes	characteristic, direct product factor, Sylow
812	C₂²	—	2	1	no	—
813	C₂²	—	2	1	no	—
814	C₂²	—	2	1	no	—
815	C₂²	—	2	1	no	—
816	C₂²	—	2	1	no	—
817	C₂²	—	2	1	no	—
818	C₂²	—	2	1	no	—
819	C₂²	—	4	4	no	—
820	C₂²	—	4	2	no	—
821	C₂²	—	4	2	no	—
822	C₂²	—	4	2	no	—
823	C₂²	C₇×#537	1	2	yes	—
824	C₂²	C₂×C₇×#137	1	2	yes	—
825	C₂²	C₂³×C₇×D₄	1	1	yes	characteristic
826	C₄	—	2	1	no	—
827	C₄	—	2	1	no	—
828	C₄	—	2	1	no	—
829	C₄	—	2	1	no	—
830	C₄	—	2	1	no	—
831	C₄	—	2	1	no	—
832	C₄	—	2	1	no	—
833	C₄	—	4	2	no	—
834	C₄	—	4	2	no	—
835	C₄	—	4	4	no	—
836	C₄	—	4	2	no	—
837	C₄	—	4	4	no	—
838	C₄	C₇×#537	1	2	yes	—
839	C₄	C₂×C₇×#137	1	2	yes	—
840	C₄	C₂×C₇×#137	1	2	yes	—
841	C₄	C₇×#575	1	2	yes	—
842	C₄	C₂×C₇×H(5,𝔽₂)	1	1	yes	characteristic
843	C₄	C₂×C₇×2₋¹⁺⁴	1	1	yes	characteristic
844	C₂	—	2	2	no	—
845	C₂	—	2	2	no	—
846	C₂	—	4	1	no	—
847	C₂	—	8	2	no	—
848	C₂	C₂×C₇×#537	1	1	yes	characteristic
849	C₂	C₂²×C₇×#137	1	1	yes	characteristic
850	C₂	C₂×C₇×#575	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₇	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₇
prime radical	C₇×#3444	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₇ ◁ C₂²×C₄²×C₇ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₇×#533	C₂	semidirect
3. C₇×#3255	C₂	semidirect
4. C₇×#3254	C₂	semidirect
5. C₇×#3252	C₂	semidirect
6. C₇×#3249	C₂	semidirect
7. C₇×#3248	C₂	semidirect
8. C₇×#3246	C₂	semidirect
9. C₇×#3079	C₂	semidirect
10. C₇×#3078	C₂	semidirect
11. C₇×#3056	C₂	semidirect
12. C₇×#3039	C₂	semidirect
13. C₇×#3037	C₂	semidirect
14. C₂×C₇×#423	C₂	semidirect
52. C₇×#479	C₂²	semidirect
53. C₇×#477	C₂²	semidirect
54. C₇×#477	C₂²	semidirect
55. C₇×#476	C₂²	semidirect
56. C₇×#475	C₂²	semidirect
57. C₇×#475	C₂²	semidirect
58. C₇×#474	C₂²	semidirect
63. C₇×#464	C₂²	semidirect
64. C₇×#462	C₂²	semidirect
65. C₇×#462	C₂²	semidirect
66. C₇×#462	C₂²	semidirect
67. C₇×#461	C₂²	semidirect
68. C₇×#461	C₂²	semidirect
69. C₇×#460	C₂²	semidirect
79. #60918	C₇	direct (N × H)
211. C₂×#533	C₂×C₇	semidirect
212. #3255	C₂×C₇	semidirect
213. #3254	C₂×C₇	semidirect
214. #3252	C₂×C₇	semidirect
215. #3249	C₂×C₇	semidirect
216. #3248	C₂×C₇	semidirect
217. #3246	C₂×C₇	semidirect
218. #3079	C₂×C₇	semidirect
219. #3078	C₂×C₇	semidirect
220. #3056	C₂×C₇	semidirect
221. #3039	C₂×C₇	semidirect
222. #3037	C₂×C₇	semidirect
223. C₂×#423	C₂×C₇	semidirect
371. #479	C₂²×C₇	semidirect
372. #477	C₂²×C₇	semidirect
373. #477	C₂²×C₇	semidirect
374. #476	C₂²×C₇	semidirect
375. #475	C₂²×C₇	semidirect
376. #475	C₂²×C₇	semidirect
377. #474	C₂²×C₇	semidirect
382. #464	C₂²×C₇	semidirect
383. #462	C₂²×C₇	semidirect
384. #462	C₂²×C₇	semidirect
385. #462	C₂²×C₇	semidirect
386. #461	C₂²×C₇	semidirect
387. #461	C₂²×C₇	semidirect
388. #460	C₂²×C₇	semidirect
449. C₂×C₄×C₇	#137	semidirect
795. C₂×C₄	C₇×#137	semidirect
811. C₇	#60918	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×#3444	2
C₂×C₇×#533	2
C₇×#3255	2
C₇×#3254	2
C₇×#3252	2
C₇×#3249	2
C₇×#3248	2
C₇×#3246	2
C₇×#3079	2
C₇×#3078	2
C₇×#3056	2
C₇×#3039	2
C₇×#3037	2
C₂×C₇×#423	2
#60918	7

Subgroups — C7×#60918 #13238134

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×#60918 #13238134