Subgroups — C₇×#61369 #13238585

Order 1792.

1750 conjugacy classes of subgroups.

The subgroup lattice has 840 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×Q₈×#41	C₂	1	1	yes	maximal, characteristic
2	C₂×C₇×#557	C₂	1	1	yes	maximal, characteristic, complemented
3	C₇×#3390	C₂	1	4	yes	maximal, complemented
4	C₇×#3388	C₂	1	4	yes	maximal, complemented
5	C₇×#3387	C₂	1	2	yes	maximal, complemented
6	C₇×#3386	C₂	1	2	yes	maximal, complemented
7	C₇×#3383	C₂	1	2	yes	maximal, complemented
8	C₇×#3381	C₂	1	2	yes	maximal, complemented
9	C₇×#3166	C₂	1	2	yes	maximal, complemented
10	C₇×#3165	C₂	1	1	yes	maximal, characteristic, complemented
11	C₇×#3080	C₂	1	2	yes	maximal
12	C₇×#3079	C₂	1	1	yes	maximal, characteristic
13	C₇×#3078	C₂	1	1	yes	maximal, characteristic, complemented
14	C₇×#3078	C₂	1	2	yes	maximal, complemented
15	C₇×Q₈×M₁₆	C₂	1	1	yes	maximal, characteristic, complemented
16	C₄×C₇×#137	C₂	1	1	yes	maximal, characteristic
17	C₄×C₇×#137	C₂	1	2	yes	maximal
18	C₂×C₇×#137	C₂²	1	1	yes	characteristic
19	C₇×Q₈²	C₂²	1	1	yes	characteristic
20	C₇×#557	—	2	1	no	—
21	C₇×#557	—	2	2	no	—
22	C₇×#557	—	2	1	no	—
23	C₇×#557	C₂²	1	2	yes	—
24	C₇×#557	C₂²	1	2	yes	—
25	C₇×#557	C₂²	1	4	yes	—
26	C₇×#557	C₂²	1	1	yes	characteristic
27	C₇×#557	C₂²	1	2	yes	—
28	C₇×#554	—	2	1	no	—
29	C₇×#554	—	2	2	no	—
30	C₇×#554	C₂²	1	1	yes	characteristic
31	C₇×#554	C₂²	1	2	yes	—
32	C₇×D₄×Q₈	—	2	1	no	—
33	C₇×D₄×Q₈	C₂²	1	1	yes	characteristic
34	C₇×#533	—	2	2	no	—
35	C₇×#533	—	2	1	no	—
36	C₇×#533	C₂²	1	1	yes	characteristic
37	C₇×#533	C₂²	1	2	yes	—
38	C₂×C₇×C₄⋊Q₈	—	2	1	no	—
39	C₂×C₇×C₄⋊Q₈	C₂²	1	1	yes	characteristic
40	C₂×C₇×#125	—	2	2	no	—
41	C₂×C₇×#125	C₂²	1	2	yes	—
42	C₄×C₇×#41	C₂²	1	1	yes	characteristic
43	C₄×C₇×#41	C₂²	1	2	yes	—
44	C₂×C₄×C₇×Q₈	—	2	1	no	—
45	C₂×C₄×C₇×Q₈	—	2	1	no	—
46	C₂×C₄×C₇×Q₈	C₂²	1	2	yes	—
47	C₂×C₄×C₇×Q₈	C₂²	1	1	yes	characteristic
48	C₂×C₄×C₇×Q₈	C₂²	1	1	yes	characteristic
49	C₇×#501	C₂²	1	4	yes	—
50	C₇×#501	C₂²	1	4	yes	—
51	C₇×#501	C₂²	1	4	yes	—
52	C₇×#500	C₂²	1	2	yes	—
53	C₇×#499	C₂²	1	4	yes	—
54	C₇×#499	C₂²	1	4	yes	—
55	C₇×#498	C₂²	1	2	yes	—
56	C₇×#479	C₂²	1	4	yes	—
57	C₇×#479	C₂²	1	4	yes	—
58	C₇×#479	C₂²	1	4	yes	—
59	C₇×#479	C₂²	1	4	yes	—
60	C₇×#479	C₂²	1	4	yes	—
61	C₇×#478	C₂²	1	4	yes	—
62	C₇×#478	C₂²	1	4	yes	—
63	C₇×#477	C₂²	1	2	yes	—
64	C₇×#477	C₂²	1	4	yes	—
65	C₇×#477	C₂²	1	2	yes	—
66	C₇×#476	C₂²	1	2	yes	—
67	C₇×#475	C₂²	1	2	yes	—
68	C₇×#475	C₂²	1	4	yes	—
69	C₇×#475	C₂²	1	2	yes	—
70	C₇×#474	C₂²	1	2	yes	—
71	C₇×#446	C₂²	1	2	yes	—
72	C₇×#446	C₂²	1	4	yes	—
73	C₇×C₈×Q₈	C₂²	1	2	yes	—
74	C₇×#441	C₂²	1	4	yes	—
75	C₇×#441	C₂²	1	2	yes	—
76	C₇×#440	C₂²	1	4	yes	—
77	C₇×#440	C₂²	1	2	yes	—
78	C₄×C₇×Q₁₆	C₂²	1	2	yes	—
79	C₄×C₇×Q₁₆	C₂²	1	4	yes	—
80	C₄×C₇×SD₁₆	C₂²	1	2	yes	—
81	C₄×C₇×SD₁₆	C₂²	1	4	yes	—
82	C₇×#428	C₂²	1	2	yes	—
83	C₇×#428	C₂²	1	2	yes	—
84	C₇×#428	C₂²	1	1	yes	characteristic
85	C₇×#428	C₂²	1	2	yes	—
86	C₇×#428	C₂²	1	2	yes	—
87	C₇×#423	C₂²	1	1	yes	characteristic
88	C₇×#423	C₂²	1	2	yes	—
89	C₇×#419	C₂²	1	1	yes	characteristic
90	C₇×#419	C₂²	1	2	yes	—
91	C₇×#417	C₂²	1	2	yes	—
92	C₇×#417	C₂²	1	1	yes	characteristic
93	C₄×C₇×M₁₆	C₂²	1	1	yes	characteristic
94	C₄×C₇×M₁₆	C₂²	1	2	yes	—
95	#61369	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
96	C₂×C₇×#41	C₂³	1	1	yes	characteristic
97	C₂²×C₇×Q₈	—	2	1	no	—
98	C₂²×C₇×Q₈	—	2	1	no	—
99	C₂²×C₇×Q₈	D₄	1	1	yes	characteristic
100	C₂²×C₇×Q₈	C₂³	1	1	yes	characteristic
101	C₇×#137	Q₈	1	8	yes	complemented
102	C₂×C₇×Q₁₆	C₂³	1	2	yes	—
103	C₂×C₇×SD₁₆	C₂³	1	2	yes	—
104	C₂×C₇×M₁₆	C₂³	1	1	yes	characteristic
105	C₂×C₇×M₁₆	C₂³	1	2	yes	—
106	C₂×C₇×M₁₆	C₂³	1	1	yes	characteristic
107	C₇×C₄⋊Q₈	—	2	2	no	—
108	C₇×C₄⋊Q₈	—	2	2	no	—
109	C₇×C₄⋊Q₈	—	2	4	no	—
110	C₇×C₄⋊Q₈	—	2	1	no	—
111	C₇×C₄⋊Q₈	—	2	2	no	—
112	C₇×C₄⋊Q₈	—	2	1	no	—
113	C₇×C₄⋊Q₈	—	2	2	no	—
114	C₇×C₄⋊Q₈	—	2	1	no	—
115	C₇×C₄⋊Q₈	—	2	1	no	—
116	C₇×C₄⋊Q₈	C₂³	1	2	yes	—
117	C₇×C₄⋊Q₈	C₂³	1	1	yes	characteristic
118	C₇×C₄⋊Q₈	C₂³	1	2	yes	—
119	C₇×C₄⋊Q₈	C₂³	1	2	yes	—
120	C₇×C₄⋊Q₈	C₂³	1	1	yes	characteristic
121	C₇×C₄⋊Q₈	C₂³	1	2	yes	—
122	C₇×#125	—	2	4	no	—
123	C₇×#125	—	2	4	no	—
124	C₇×#125	—	2	4	no	—
125	C₇×#125	—	2	4	no	—
126	C₇×#125	—	2	2	no	—
127	C₇×#125	—	2	2	no	—
128	C₇×#125	—	2	2	no	—
129	C₇×#125	—	2	2	no	—
130	C₇×#125	—	2	2	no	—
131	C₇×#125	C₂³	1	4	yes	—
132	C₇×#125	C₂³	1	4	yes	—
133	C₇×#125	C₂³	1	2	yes	—
134	C₇×#125	C₂³	1	2	yes	—
135	C₇×#125	C₂³	1	2	yes	—
136	C₇×C₂²⋊Q₈	—	2	1	no	—
137	C₇×C₂²⋊Q₈	—	2	2	no	—
138	C₇×C₂²⋊Q₈	—	2	1	no	—
139	C₇×C₂²⋊Q₈	—	2	2	no	—
140	C₇×C₂²⋊Q₈	—	2	2	no	—
141	C₇×C₂²⋊Q₈	—	2	1	no	—
142	C₇×C₂²⋊Q₈	—	2	1	no	—
143	C₇×C₂²⋊Q₈	—	2	2	no	—
144	C₇×C₂²⋊Q₈	—	2	2	no	—
145	C₇×C₂²⋊Q₈	—	2	2	no	—
146	C₇×C₂²⋊Q₈	—	2	2	no	—
147	C₄×C₇×Q₈	—	2	1	no	—
148	C₄×C₇×Q₈	—	2	1	no	—
149	C₄×C₇×Q₈	—	2	2	no	—
150	C₄×C₇×Q₈	—	2	2	no	—
151	C₄×C₇×Q₈	—	2	4	no	—
152	C₄×C₇×Q₈	—	2	2	no	—
153	C₄×C₇×Q₈	—	2	2	no	—
154	C₄×C₇×Q₈	—	2	1	no	—
155	C₄×C₇×Q₈	—	2	2	no	—
156	C₄×C₇×Q₈	—	2	2	no	—
157	C₄×C₇×Q₈	—	2	1	no	—
158	C₄×C₇×Q₈	—	2	1	no	—
159	C₄×C₇×Q₈	—	2	2	no	—
160	C₄×C₇×Q₈	—	2	1	no	—
161	C₄×C₇×Q₈	D₄	1	1	yes	characteristic
162	C₄×C₇×Q₈	D₄	1	2	yes	—
163	C₄×C₇×Q₈	D₄	1	1	yes	characteristic
164	C₄×C₇×Q₈	C₂³	1	1	yes	characteristic
165	C₄×C₇×Q₈	C₂³	1	2	yes	—
166	C₄×C₇×Q₈	C₂³	1	4	yes	—
167	C₄×C₇×Q₈	C₂³	1	1	yes	characteristic
168	C₄×C₇×Q₈	C₂³	1	4	yes	—
169	C₄×C₇×Q₈	C₂³	1	2	yes	—
170	C₄×C₇×Q₈	C₂³	1	2	yes	—
171	C₄×C₇×Q₈	C₂³	1	2	yes	—
172	C₄×C₇×Q₈	C₂³	1	1	yes	characteristic
173	C₄×C₇×Q₈	C₂³	1	1	yes	characteristic
174	C₄×C₇×Q₈	C₂³	1	2	yes	—
175	C₄×C₇×D₄	—	2	1	no	—
176	C₄×C₇×D₄	—	2	2	no	—
177	C₄×C₇×D₄	—	2	2	no	—
178	C₄×C₇×D₄	—	2	1	no	—
179	C₄×C₇×D₄	C₂³	1	1	yes	characteristic
180	C₄×C₇×D₄	C₂³	1	1	yes	characteristic
181	C₄×C₇×D₄	C₂³	1	2	yes	—
182	C₄×C₇×D₄	C₂³	1	2	yes	—
183	C₇×#117	—	2	2	no	—
184	C₇×#117	—	2	1	no	—
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	1	no	—
189	C₂×C₇×C₄⋊C₄	—	2	2	no	—
190	C₂×C₇×C₄⋊C₄	—	2	1	no	—
191	C₂×C₇×C₄⋊C₄	—	2	2	no	—
192	C₂×C₇×C₄⋊C₄	—	2	1	no	—
193	C₂×C₇×C₄⋊C₄	—	2	2	no	—
194	C₂×C₇×C₄⋊C₄	D₄	1	1	yes	characteristic
195	C₂×C₇×C₄⋊C₄	D₄	1	2	yes	—
196	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
197	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
198	C₂×C₄²×C₇	—	2	2	no	—
199	C₂×C₄²×C₇	—	2	1	no	—
200	C₂×C₄²×C₇	—	2	2	no	—
201	C₂×C₄²×C₇	—	2	1	no	—
202	C₂×C₄²×C₇	C₂³	1	2	yes	—
203	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
204	C₇×#107	C₂³	1	4	yes	—
205	C₇×#107	C₂³	1	4	yes	—
206	C₇×#107	C₂³	1	4	yes	—
207	C₇×#107	C₂³	1	2	yes	—
208	C₇×#107	C₂³	1	4	yes	—
209	C₇×#106	C₂³	1	4	yes	—
210	C₇×#106	C₂³	1	4	yes	—
211	C₇×#106	C₂³	1	4	yes	—
212	C₇×#106	C₂³	1	4	yes	—
213	C₇×#106	C₂³	1	2	yes	—
214	C₇×C₄⋊C₈	C₂³	1	2	yes	—
215	C₇×C₄⋊C₈	C₂³	1	4	yes	—
216	C₇×C₄⋊C₈	C₂³	1	2	yes	—
217	C₇×C₄⋊C₈	C₂³	1	4	yes	—
218	C₇×#103	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×#102	C₂³	1	4	yes	—
225	C₇×#102	C₂³	1	2	yes	—
226	C₇×#97	C₂³	1	2	yes	—
227	C₇×#97	C₂³	1	4	yes	—
228	C₄×C₇×C₈	C₂³	1	2	yes	—
229	C₄×C₇×C₈	C₂³	1	4	yes	—
230	Q₈×#41	C₂×C₇	1	1	yes	characteristic
231	C₂×#557	C₂×C₇	1	1	yes	characteristic, complemented
232	#3390	C₂×C₇	1	4	yes	complemented
233	#3388	C₂×C₇	1	4	yes	complemented
234	#3387	C₂×C₇	1	2	yes	complemented
235	#3386	C₂×C₇	1	2	yes	complemented
236	#3383	C₂×C₇	1	2	yes	complemented
237	#3381	C₂×C₇	1	2	yes	complemented
238	#3166	C₂×C₇	1	2	yes	complemented
239	#3165	C₂×C₇	1	1	yes	characteristic, complemented
240	#3080	C₂×C₇	1	2	yes	—
241	#3079	C₂×C₇	1	1	yes	characteristic
242	#3078	C₂×C₇	1	1	yes	characteristic, complemented
243	#3078	C₂×C₇	1	2	yes	complemented
244	Q₈×M₁₆	C₂×C₇	1	1	yes	characteristic, complemented
245	C₄×#137	C₂×C₇	1	1	yes	characteristic
246	C₄×#137	C₂×C₇	1	2	yes	—
247	C₇×#41	—	2	2	no	—
248	C₇×#41	C₂×Q₈	1	4	yes	—
249	C₂×C₇×Q₈	—	2	1	no	—
250	C₂×C₇×Q₈	—	2	2	no	—
251	C₂×C₇×Q₈	—	2	1	no	—
252	C₂×C₇×Q₈	—	2	2	no	—
253	C₂×C₇×Q₈	—	2	2	no	—
254	C₂×C₇×Q₈	—	2	2	no	—
255	C₂×C₇×Q₈	—	2	1	no	—
256	C₂×C₇×Q₈	—	2	2	no	—
257	C₂×C₇×Q₈	—	4	2	no	—
258	C₂×C₇×Q₈	—	4	4	no	—
259	C₂×C₇×Q₈	—	4	4	no	—
260	C₂×C₇×Q₈	C₂×D₄	1	1	yes	characteristic
261	C₂×C₇×Q₈	C₂×D₄	1	1	yes	characteristic
262	C₂×C₇×Q₈	C₂×D₄	1	2	yes	—
263	C₂×C₇×Q₈	C₂×Q₈	1	4	yes	complemented
264	C₂×C₇×Q₈	C₂⁴	1	2	yes	—
265	C₂×C₇×Q₈	C₂⁴	1	1	yes	characteristic
266	C₂×C₇×D₄	—	2	1	no	—
267	C₂×C₇×D₄	C₂⁴	1	1	yes	characteristic
268	C₂²×C₄×C₇	—	2	1	no	—
269	C₂²×C₄×C₇	—	2	1	no	—
270	C₂²×C₄×C₇	—	2	1	no	—
271	C₂²×C₄×C₇	—	2	2	no	—
272	C₂²×C₄×C₇	—	2	2	no	—
273	C₂²×C₄×C₇	—	2	1	no	—
274	C₂²×C₄×C₇	—	2	2	no	—
275	C₂²×C₄×C₇	—	2	1	no	—
276	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
277	C₂²×C₄×C₇	C₂×D₄	1	2	yes	—
278	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
279	C₂²×C₄×C₇	C₂×D₄	1	2	yes	—
280	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
281	C₇×Q₁₆	C₂×Q₈	1	8	yes	complemented
282	C₇×SD₁₆	C₂×Q₈	1	8	yes	complemented
283	C₇×M₁₆	—	2	2	no	—
284	C₇×M₁₆	—	2	4	no	—
285	C₇×M₁₆	C₂×Q₈	1	4	yes	complemented
286	C₂×C₇×C₈	C₂⁴	1	2	yes	—
287	C₂×C₇×C₈	C₂⁴	1	4	yes	—
288	C₂×C₇×C₈	C₂⁴	1	2	yes	—
289	C₇×C₄⋊C₄	—	2	2	no	—
290	C₇×C₄⋊C₄	—	2	2	no	—
291	C₇×C₄⋊C₄	—	2	2	no	—
292	C₇×C₄⋊C₄	—	2	2	no	—
293	C₇×C₄⋊C₄	—	2	1	no	—
294	C₇×C₄⋊C₄	—	2	4	no	—
295	C₇×C₄⋊C₄	—	2	4	no	—
296	C₇×C₄⋊C₄	—	2	2	no	—
297	C₇×C₄⋊C₄	—	2	2	no	—
298	C₇×C₄⋊C₄	—	2	4	no	—
299	C₇×C₄⋊C₄	—	2	4	no	—
300	C₇×C₄⋊C₄	—	2	2	no	—
301	C₇×C₄⋊C₄	—	2	2	no	—
302	C₇×C₄⋊C₄	—	2	4	no	—
303	C₇×C₄⋊C₄	—	2	4	no	—
304	C₇×C₄⋊C₄	—	2	1	no	—
305	C₇×C₄⋊C₄	—	2	2	no	—
306	C₇×C₄⋊C₄	—	2	2	no	—
307	C₇×C₄⋊C₄	—	2	1	no	—
308	C₇×C₄⋊C₄	—	2	2	no	—
309	C₇×C₄⋊C₄	—	2	1	no	—
310	C₇×C₄⋊C₄	—	2	2	no	—
311	C₇×C₄⋊C₄	—	2	1	no	—
312	C₇×C₄⋊C₄	—	2	2	no	—
313	C₇×C₄⋊C₄	—	2	2	no	—
314	C₇×C₄⋊C₄	—	2	2	no	—
315	C₇×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
316	C₇×C₄⋊C₄	C₂×D₄	1	2	yes	—
317	C₇×C₄⋊C₄	C₂×D₄	1	2	yes	—
318	C₇×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
319	C₇×C₄⋊C₄	C₂×D₄	1	2	yes	—
320	C₇×C₄⋊C₄	C₂×D₄	1	2	yes	—
321	C₇×C₄⋊C₄	C₂×D₄	1	2	yes	—
322	C₇×C₄⋊C₄	C₂⁴	1	2	yes	—
323	C₇×C₄⋊C₄	C₂⁴	1	4	yes	—
324	C₇×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
325	C₇×C₄⋊C₄	C₂⁴	1	2	yes	—
326	C₇×C₄⋊C₄	C₂⁴	1	2	yes	—
327	C₇×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
328	C₇×C₂²⋊C₄	—	2	1	no	—
329	C₇×C₂²⋊C₄	—	2	2	no	—
330	C₇×C₂²⋊C₄	—	2	2	no	—
331	C₇×C₂²⋊C₄	—	2	1	no	—
332	C₇×C₂²⋊C₄	—	2	2	no	—
333	C₇×C₂²⋊C₄	—	2	1	no	—
334	C₄²×C₇	—	2	2	no	—
335	C₄²×C₇	—	2	1	no	—
336	C₄²×C₇	—	2	2	no	—
337	C₄²×C₇	—	2	1	no	—
338	C₄²×C₇	—	2	2	no	—
339	C₄²×C₇	—	2	1	no	—
340	C₄²×C₇	—	2	4	no	—
341	C₄²×C₇	—	2	4	no	—
342	C₄²×C₇	—	2	2	no	—
343	C₄²×C₇	—	2	2	no	—
344	C₄²×C₇	C₂×D₄	1	2	yes	—
345	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
346	C₄²×C₇	C₂×D₄	1	2	yes	—
347	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
348	C₄²×C₇	C₂⁴	1	2	yes	—
349	C₄²×C₇	C₂⁴	1	1	yes	characteristic
350	C₄²×C₇	C₂⁴	1	2	yes	—
351	C₄²×C₇	C₂⁴	1	1	yes	characteristic
352	C₂×#137	C₂²×C₇	1	1	yes	characteristic
353	Q₈²	C₂²×C₇	1	1	yes	characteristic
354	#557	—	2	1	no	—
355	#557	—	2	2	no	—
356	#557	—	2	1	no	—
357	#557	C₂²×C₇	1	2	yes	—
358	#557	C₂²×C₇	1	1	yes	characteristic
359	#557	C₂²×C₇	1	2	yes	—
360	#557	C₂²×C₇	1	4	yes	—
361	#557	C₂²×C₇	1	2	yes	—
362	#554	—	2	1	no	—
363	#554	—	2	2	no	—
364	#554	C₂²×C₇	1	1	yes	characteristic
365	#554	C₂²×C₇	1	2	yes	—
366	D₄×Q₈	—	2	1	no	—
367	D₄×Q₈	C₂²×C₇	1	1	yes	characteristic
368	#533	—	2	2	no	—
369	#533	—	2	1	no	—
370	#533	C₂²×C₇	1	1	yes	characteristic
371	#533	C₂²×C₇	1	2	yes	—
372	C₂×C₄⋊Q₈	—	2	1	no	—
373	C₂×C₄⋊Q₈	C₂²×C₇	1	1	yes	characteristic
374	C₂×#125	—	2	2	no	—
375	C₂×#125	C₂²×C₇	1	2	yes	—
376	C₄×#41	C₂²×C₇	1	1	yes	characteristic
377	C₄×#41	C₂²×C₇	1	2	yes	—
378	C₂×C₄×Q₈	—	2	1	no	—
379	C₂×C₄×Q₈	—	2	1	no	—
380	C₂×C₄×Q₈	C₂²×C₇	1	2	yes	—
381	C₂×C₄×Q₈	C₂²×C₇	1	1	yes	characteristic
382	C₂×C₄×Q₈	C₂²×C₇	1	1	yes	characteristic
383	#501	C₂²×C₇	1	4	yes	—
384	#501	C₂²×C₇	1	4	yes	—
385	#501	C₂²×C₇	1	4	yes	—
386	#500	C₂²×C₇	1	2	yes	—
387	#499	C₂²×C₇	1	4	yes	—
388	#499	C₂²×C₇	1	4	yes	—
389	#498	C₂²×C₇	1	2	yes	—
390	#479	C₂²×C₇	1	4	yes	—
391	#479	C₂²×C₇	1	4	yes	—
392	#479	C₂²×C₇	1	4	yes	—
393	#479	C₂²×C₇	1	4	yes	—
394	#479	C₂²×C₇	1	4	yes	—
395	#478	C₂²×C₇	1	4	yes	—
396	#478	C₂²×C₇	1	4	yes	—
397	#477	C₂²×C₇	1	2	yes	—
398	#477	C₂²×C₇	1	4	yes	—
399	#477	C₂²×C₇	1	2	yes	—
400	#476	C₂²×C₇	1	2	yes	—
401	#475	C₂²×C₇	1	2	yes	—
402	#475	C₂²×C₇	1	4	yes	—
403	#475	C₂²×C₇	1	2	yes	—
404	#474	C₂²×C₇	1	2	yes	—
405	#446	C₂²×C₇	1	2	yes	—
406	#446	C₂²×C₇	1	4	yes	—
407	C₈×Q₈	C₂²×C₇	1	2	yes	—
408	#441	C₂²×C₇	1	4	yes	—
409	#441	C₂²×C₇	1	2	yes	—
410	#440	C₂²×C₇	1	4	yes	—
411	#440	C₂²×C₇	1	2	yes	—
412	C₄×Q₁₆	C₂²×C₇	1	2	yes	—
413	C₄×Q₁₆	C₂²×C₇	1	4	yes	—
414	C₄×SD₁₆	C₂²×C₇	1	2	yes	—
415	C₄×SD₁₆	C₂²×C₇	1	4	yes	—
416	#428	C₂²×C₇	1	2	yes	—
417	#428	C₂²×C₇	1	2	yes	—
418	#428	C₂²×C₇	1	2	yes	—
419	#428	C₂²×C₇	1	2	yes	—
420	#428	C₂²×C₇	1	1	yes	characteristic
421	#423	C₂²×C₇	1	1	yes	characteristic
422	#423	C₂²×C₇	1	2	yes	—
423	#419	C₂²×C₇	1	2	yes	—
424	#419	C₂²×C₇	1	1	yes	characteristic
425	#417	C₂²×C₇	1	2	yes	—
426	#417	C₂²×C₇	1	1	yes	characteristic
427	C₄×M₁₆	C₂²×C₇	1	1	yes	characteristic
428	C₄×M₁₆	C₂²×C₇	1	2	yes	—
429	C₂³×C₇	—	2	1	no	—
430	C₂³×C₇	C₂²×D₄	1	1	yes	characteristic
431	C₇×Q₈	—	2	4	no	—
432	C₇×Q₈	—	2	2	no	—
433	C₇×Q₈	—	2	2	no	—
434	C₇×Q₈	—	2	2	no	—
435	C₇×Q₈	—	2	1	no	—
436	C₇×Q₈	—	4	2	no	—
437	C₇×Q₈	—	4	4	no	—
438	C₇×Q₈	—	4	4	no	—
439	C₇×Q₈	—	4	2	no	—
440	C₇×Q₈	—	4	4	no	—
441	C₇×Q₈	—	8	2	no	—
442	C₇×Q₈	—	8	1	no	—
443	C₇×Q₈	C₂²×Q₈	1	4	yes	—
444	C₇×Q₈	C₂²×Q₈	1	2	yes	—
445	C₇×D₄	—	2	4	no	—
446	C₇×D₄	—	2	1	no	—
447	C₇×D₄	C₂²×Q₈	1	2	yes	—
448	C₂×C₄×C₇	—	2	4	no	—
449	C₂×C₄×C₇	—	2	1	no	—
450	C₂×C₄×C₇	—	2	2	no	—
451	C₂×C₄×C₇	—	2	4	no	—
452	C₂×C₄×C₇	—	2	2	no	—
453	C₂×C₄×C₇	—	2	2	no	—
454	C₂×C₄×C₇	—	2	1	no	—
455	C₂×C₄×C₇	—	2	2	no	—
456	C₂×C₄×C₇	—	2	1	no	—
457	C₂×C₄×C₇	—	2	2	no	—
458	C₂×C₄×C₇	—	2	4	no	—
459	C₂×C₄×C₇	—	4	2	no	—
460	C₂×C₄×C₇	—	4	1	no	—
461	C₂×C₄×C₇	—	4	2	no	—
462	C₂×C₄×C₇	—	4	4	no	—
463	C₂×C₄×C₇	—	4	2	no	—
464	C₂×C₄×C₇	—	4	4	no	—
465	C₂×C₄×C₇	—	4	2	no	—
466	C₂×C₄×C₇	—	8	2	no	—
467	C₂×C₄×C₇	—	8	1	no	—
468	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
469	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
470	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
471	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
472	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
473	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
474	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
475	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
476	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
477	C₂×C₄×C₇	C₂²×Q₈	1	2	yes	—
478	C₂×C₄×C₇	2₋¹⁺⁴	1	2	yes	—
479	C₂×C₄×C₇	C₂⁵	1	1	yes	characteristic
480	C₇×C₈	—	2	2	no	—
481	C₇×C₈	—	2	4	no	—
482	C₇×C₈	C₂²×Q₈	1	4	yes	—
483	C₂×#41	C₂³×C₇	1	1	yes	characteristic
484	C₂²×Q₈	—	2	1	no	—
485	C₂²×Q₈	—	2	1	no	—
486	C₂²×Q₈	C₇×D₄	1	1	yes	characteristic
487	C₂²×Q₈	C₂³×C₇	1	1	yes	characteristic
488	#137	C₇×Q₈	1	8	yes	complemented
489	C₂×Q₁₆	C₂³×C₇	1	2	yes	—
490	C₂×SD₁₆	C₂³×C₇	1	2	yes	—
491	C₂×M₁₆	C₂³×C₇	1	1	yes	characteristic
492	C₂×M₁₆	C₂³×C₇	1	2	yes	—
493	C₂×M₁₆	C₂³×C₇	1	1	yes	characteristic
494	C₄⋊Q₈	—	2	2	no	—
495	C₄⋊Q₈	—	2	2	no	—
496	C₄⋊Q₈	—	2	4	no	—
497	C₄⋊Q₈	—	2	1	no	—
498	C₄⋊Q₈	—	2	2	no	—
499	C₄⋊Q₈	—	2	1	no	—
500	C₄⋊Q₈	—	2	2	no	—
501	C₄⋊Q₈	—	2	1	no	—
502	C₄⋊Q₈	—	2	1	no	—
503	C₄⋊Q₈	C₂³×C₇	1	2	yes	—
504	C₄⋊Q₈	C₂³×C₇	1	2	yes	—
505	C₄⋊Q₈	C₂³×C₇	1	1	yes	characteristic
506	C₄⋊Q₈	C₂³×C₇	1	2	yes	—
507	C₄⋊Q₈	C₂³×C₇	1	2	yes	—
508	C₄⋊Q₈	C₂³×C₇	1	1	yes	characteristic
509	#125	—	2	4	no	—
510	#125	—	2	4	no	—
511	#125	—	2	4	no	—
512	#125	—	2	4	no	—
513	#125	—	2	2	no	—
514	#125	—	2	2	no	—
515	#125	—	2	2	no	—
516	#125	—	2	2	no	—
517	#125	—	2	2	no	—
518	#125	C₂³×C₇	1	4	yes	—
519	#125	C₂³×C₇	1	4	yes	—
520	#125	C₂³×C₇	1	2	yes	—
521	#125	C₂³×C₇	1	2	yes	—
522	#125	C₂³×C₇	1	2	yes	—
523	C₂²⋊Q₈	—	2	1	no	—
524	C₂²⋊Q₈	—	2	2	no	—
525	C₂²⋊Q₈	—	2	1	no	—
526	C₂²⋊Q₈	—	2	2	no	—
527	C₂²⋊Q₈	—	2	2	no	—
528	C₂²⋊Q₈	—	2	1	no	—
529	C₂²⋊Q₈	—	2	1	no	—
530	C₂²⋊Q₈	—	2	2	no	—
531	C₂²⋊Q₈	—	2	2	no	—
532	C₂²⋊Q₈	—	2	2	no	—
533	C₂²⋊Q₈	—	2	2	no	—
534	C₄×Q₈	—	2	1	no	—
535	C₄×Q₈	—	2	1	no	—
536	C₄×Q₈	—	2	2	no	—
537	C₄×Q₈	—	2	2	no	—
538	C₄×Q₈	—	2	4	no	—
539	C₄×Q₈	—	2	2	no	—
540	C₄×Q₈	—	2	2	no	—
541	C₄×Q₈	—	2	1	no	—
542	C₄×Q₈	—	2	2	no	—
543	C₄×Q₈	—	2	2	no	—
544	C₄×Q₈	—	2	1	no	—
545	C₄×Q₈	—	2	1	no	—
546	C₄×Q₈	—	2	2	no	—
547	C₄×Q₈	—	2	1	no	—
548	C₄×Q₈	C₇×D₄	1	1	yes	characteristic
549	C₄×Q₈	C₇×D₄	1	2	yes	—
550	C₄×Q₈	C₇×D₄	1	1	yes	characteristic
551	C₄×Q₈	C₂³×C₇	1	2	yes	—
552	C₄×Q₈	C₂³×C₇	1	4	yes	—
553	C₄×Q₈	C₂³×C₇	1	4	yes	—
554	C₄×Q₈	C₂³×C₇	1	2	yes	—
555	C₄×Q₈	C₂³×C₇	1	2	yes	—
556	C₄×Q₈	C₂³×C₇	1	1	yes	characteristic
557	C₄×Q₈	C₂³×C₇	1	1	yes	characteristic
558	C₄×Q₈	C₂³×C₇	1	2	yes	—
559	C₄×Q₈	C₂³×C₇	1	1	yes	characteristic
560	C₄×Q₈	C₂³×C₇	1	1	yes	characteristic
561	C₄×Q₈	C₂³×C₇	1	2	yes	—
562	C₄×D₄	—	2	1	no	—
563	C₄×D₄	—	2	2	no	—
564	C₄×D₄	—	2	2	no	—
565	C₄×D₄	—	2	1	no	—
566	C₄×D₄	C₂³×C₇	1	1	yes	characteristic
567	C₄×D₄	C₂³×C₇	1	2	yes	—
568	C₄×D₄	C₂³×C₇	1	2	yes	—
569	C₄×D₄	C₂³×C₇	1	1	yes	characteristic
570	#117	—	2	2	no	—
571	#117	—	2	1	no	—
572	#117	C₂³×C₇	1	1	yes	characteristic
573	#117	C₂³×C₇	1	2	yes	—
574	C₂×C₄⋊C₄	—	2	2	no	—
575	C₂×C₄⋊C₄	—	2	1	no	—
576	C₂×C₄⋊C₄	—	2	2	no	—
577	C₂×C₄⋊C₄	—	2	1	no	—
578	C₂×C₄⋊C₄	—	2	2	no	—
579	C₂×C₄⋊C₄	—	2	1	no	—
580	C₂×C₄⋊C₄	—	2	2	no	—
581	C₂×C₄⋊C₄	C₇×D₄	1	1	yes	characteristic
582	C₂×C₄⋊C₄	C₇×D₄	1	2	yes	—
583	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
584	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
585	C₂×C₄²	—	2	2	no	—
586	C₂×C₄²	—	2	1	no	—
587	C₂×C₄²	—	2	2	no	—
588	C₂×C₄²	—	2	1	no	—
589	C₂×C₄²	C₂³×C₇	1	2	yes	—
590	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
591	#107	C₂³×C₇	1	2	yes	—
592	#107	C₂³×C₇	1	4	yes	—
593	#107	C₂³×C₇	1	4	yes	—
594	#107	C₂³×C₇	1	4	yes	—
595	#107	C₂³×C₇	1	4	yes	—
596	#106	C₂³×C₇	1	4	yes	—
597	#106	C₂³×C₇	1	2	yes	—
598	#106	C₂³×C₇	1	4	yes	—
599	#106	C₂³×C₇	1	4	yes	—
600	#106	C₂³×C₇	1	4	yes	—
601	C₄⋊C₈	C₂³×C₇	1	2	yes	—
602	C₄⋊C₈	C₂³×C₇	1	4	yes	—
603	C₄⋊C₈	C₂³×C₇	1	4	yes	—
604	C₄⋊C₈	C₂³×C₇	1	2	yes	—
605	#103	C₂³×C₇	1	4	yes	—
606	#103	C₂³×C₇	1	2	yes	—
607	#103	C₂³×C₇	1	4	yes	—
608	#103	C₂³×C₇	1	2	yes	—
609	#103	C₂³×C₇	1	2	yes	—
610	#103	C₂³×C₇	1	4	yes	—
611	#102	C₂³×C₇	1	4	yes	—
612	#102	C₂³×C₇	1	2	yes	—
613	#97	C₂³×C₇	1	2	yes	—
614	#97	C₂³×C₇	1	4	yes	—
615	C₄×C₈	C₂³×C₇	1	2	yes	—
616	C₄×C₈	C₂³×C₇	1	4	yes	—
617	C₂²×C₇	—	2	1	no	—
618	C₂²×C₇	—	2	1	no	—
619	C₂²×C₇	—	2	2	no	—
620	C₂²×C₇	—	4	1	no	—
621	C₂²×C₇	—	4	1	no	—
622	C₂²×C₇	D₄×Q₈	1	2	yes	—
623	C₂²×C₇	C₂³×D₄	1	1	yes	characteristic
624	C₄×C₇	—	2	2	no	—
625	C₄×C₇	—	2	1	no	—
626	C₄×C₇	—	2	2	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	—	2	2	no	—
632	C₄×C₇	—	2	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	—	4	1	no	—
638	C₄×C₇	—	4	4	no	—
639	C₄×C₇	D₄×Q₈	1	2	yes	—
640	C₄×C₇	#575	1	2	yes	—
641	C₄×C₇	C₂³×Q₈	1	1	yes	characteristic
642	C₄×C₇	C₂×2₋¹⁺⁴	1	1	yes	characteristic
643	#41	—	2	2	no	—
644	#41	C₂×C₇×Q₈	1	4	yes	—
645	C₂×Q₈	—	2	1	no	—
646	C₂×Q₈	—	2	2	no	—
647	C₂×Q₈	—	2	1	no	—
648	C₂×Q₈	—	2	2	no	—
649	C₂×Q₈	—	2	2	no	—
650	C₂×Q₈	—	2	2	no	—
651	C₂×Q₈	—	2	1	no	—
652	C₂×Q₈	—	2	2	no	—
653	C₂×Q₈	—	4	2	no	—
654	C₂×Q₈	—	4	4	no	—
655	C₂×Q₈	—	4	4	no	—
656	C₂×Q₈	C₂×C₇×D₄	1	1	yes	characteristic
657	C₂×Q₈	C₂×C₇×D₄	1	1	yes	characteristic
658	C₂×Q₈	C₂×C₇×D₄	1	2	yes	—
659	C₂×Q₈	C₂×C₇×Q₈	1	4	yes	complemented
660	C₂×Q₈	C₂⁴×C₇	1	2	yes	—
661	C₂×Q₈	C₂⁴×C₇	1	1	yes	characteristic
662	C₂×D₄	—	2	1	no	—
663	C₂×D₄	C₂⁴×C₇	1	1	yes	characteristic
664	C₂²×C₄	—	2	1	no	—
665	C₂²×C₄	—	2	1	no	—
666	C₂²×C₄	—	2	1	no	—
667	C₂²×C₄	—	2	2	no	—
668	C₂²×C₄	—	2	2	no	—
669	C₂²×C₄	—	2	1	no	—
670	C₂²×C₄	—	2	2	no	—
671	C₂²×C₄	—	2	1	no	—
672	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
673	C₂²×C₄	C₂×C₇×D₄	1	2	yes	—
674	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
675	C₂²×C₄	C₂×C₇×D₄	1	2	yes	—
676	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
677	Q₁₆	C₂×C₇×Q₈	1	8	yes	complemented
678	SD₁₆	C₂×C₇×Q₈	1	8	yes	complemented
679	M₁₆	—	2	2	no	—
680	M₁₆	—	2	4	no	—
681	M₁₆	C₂×C₇×Q₈	1	4	yes	complemented
682	C₂×C₈	C₂⁴×C₇	1	2	yes	—
683	C₂×C₈	C₂⁴×C₇	1	4	yes	—
684	C₂×C₈	C₂⁴×C₇	1	2	yes	—
685	C₄⋊C₄	—	2	2	no	—
686	C₄⋊C₄	—	2	2	no	—
687	C₄⋊C₄	—	2	2	no	—
688	C₄⋊C₄	—	2	2	no	—
689	C₄⋊C₄	—	2	1	no	—
690	C₄⋊C₄	—	2	4	no	—
691	C₄⋊C₄	—	2	4	no	—
692	C₄⋊C₄	—	2	2	no	—
693	C₄⋊C₄	—	2	2	no	—
694	C₄⋊C₄	—	2	4	no	—
695	C₄⋊C₄	—	2	4	no	—
696	C₄⋊C₄	—	2	2	no	—
697	C₄⋊C₄	—	2	2	no	—
698	C₄⋊C₄	—	2	4	no	—
699	C₄⋊C₄	—	2	4	no	—
700	C₄⋊C₄	—	2	1	no	—
701	C₄⋊C₄	—	2	2	no	—
702	C₄⋊C₄	—	2	2	no	—
703	C₄⋊C₄	—	2	1	no	—
704	C₄⋊C₄	—	2	2	no	—
705	C₄⋊C₄	—	2	1	no	—
706	C₄⋊C₄	—	2	2	no	—
707	C₄⋊C₄	—	2	1	no	—
708	C₄⋊C₄	—	2	2	no	—
709	C₄⋊C₄	—	2	2	no	—
710	C₄⋊C₄	—	2	2	no	—
711	C₄⋊C₄	C₂×C₇×D₄	1	1	yes	characteristic
712	C₄⋊C₄	C₂×C₇×D₄	1	2	yes	—
713	C₄⋊C₄	C₂×C₇×D₄	1	2	yes	—
714	C₄⋊C₄	C₂×C₇×D₄	1	1	yes	characteristic
715	C₄⋊C₄	C₂×C₇×D₄	1	2	yes	—
716	C₄⋊C₄	C₂×C₇×D₄	1	2	yes	—
717	C₄⋊C₄	C₂×C₇×D₄	1	2	yes	—
718	C₄⋊C₄	C₂⁴×C₇	1	2	yes	—
719	C₄⋊C₄	C₂⁴×C₇	1	4	yes	—
720	C₄⋊C₄	C₂⁴×C₇	1	2	yes	—
721	C₄⋊C₄	C₂⁴×C₇	1	1	yes	characteristic
722	C₄⋊C₄	C₂⁴×C₇	1	1	yes	characteristic
723	C₄⋊C₄	C₂⁴×C₇	1	2	yes	—
724	C₂²⋊C₄	—	2	1	no	—
725	C₂²⋊C₄	—	2	2	no	—
726	C₂²⋊C₄	—	2	2	no	—
727	C₂²⋊C₄	—	2	1	no	—
728	C₂²⋊C₄	—	2	2	no	—
729	C₂²⋊C₄	—	2	1	no	—
730	C₄²	—	2	2	no	—
731	C₄²	—	2	1	no	—
732	C₄²	—	2	2	no	—
733	C₄²	—	2	1	no	—
734	C₄²	—	2	2	no	—
735	C₄²	—	2	1	no	—
736	C₄²	—	2	4	no	—
737	C₄²	—	2	4	no	—
738	C₄²	—	2	2	no	—
739	C₄²	—	2	2	no	—
740	C₄²	C₂×C₇×D₄	1	2	yes	—
741	C₄²	C₂×C₇×D₄	1	1	yes	characteristic
742	C₄²	C₂×C₇×D₄	1	2	yes	—
743	C₄²	C₂×C₇×D₄	1	1	yes	characteristic
744	C₄²	C₂⁴×C₇	1	2	yes	—
745	C₄²	C₂⁴×C₇	1	1	yes	characteristic
746	C₄²	C₂⁴×C₇	1	2	yes	—
747	C₄²	C₂⁴×C₇	1	1	yes	characteristic
748	C₂×C₇	—	2	2	no	—
749	C₂×C₇	—	4	2	no	—
750	C₂×C₇	C₂×D₄×Q₈	1	1	yes	characteristic
751	C₂×C₇	C₂×#575	1	1	yes	characteristic
752	C₂×C₇	#3586	1	1	yes	characteristic
753	C₂³	—	2	1	no	—
754	C₂³	C₂²×C₇×D₄	1	1	yes	characteristic
755	Q₈	—	2	2	no	—
756	Q₈	—	2	1	no	—
757	Q₈	—	2	4	no	—
758	Q₈	—	2	2	no	—
759	Q₈	—	2	2	no	—
760	Q₈	—	4	2	no	—
761	Q₈	—	4	4	no	—
762	Q₈	—	4	4	no	—
763	Q₈	—	4	2	no	—
764	Q₈	—	4	4	no	—
765	Q₈	—	8	2	no	—
766	Q₈	—	8	1	no	—
767	Q₈	C₂²×C₇×Q₈	1	4	yes	—
768	Q₈	C₂²×C₇×Q₈	1	2	yes	—
769	D₄	—	2	4	no	—
770	D₄	—	2	1	no	—
771	D₄	C₂²×C₇×Q₈	1	2	yes	—
772	C₂×C₄	—	2	1	no	—
773	C₂×C₄	—	2	2	no	—
774	C₂×C₄	—	2	4	no	—
775	C₂×C₄	—	2	4	no	—
776	C₂×C₄	—	2	2	no	—
777	C₂×C₄	—	2	2	no	—
778	C₂×C₄	—	2	1	no	—
779	C₂×C₄	—	2	2	no	—
780	C₂×C₄	—	2	1	no	—
781	C₂×C₄	—	2	2	no	—
782	C₂×C₄	—	2	4	no	—
783	C₂×C₄	—	4	2	no	—
784	C₂×C₄	—	4	1	no	—
785	C₂×C₄	—	4	2	no	—
786	C₂×C₄	—	4	4	no	—
787	C₂×C₄	—	4	2	no	—
788	C₂×C₄	—	4	4	no	—
789	C₂×C₄	—	4	2	no	—
790	C₂×C₄	—	8	2	no	—
791	C₂×C₄	—	8	1	no	—
792	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
793	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
794	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
795	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
796	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
797	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
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×Q₈	1	2	yes	—
802	C₂×C₄	C₇×2₋¹⁺⁴	1	2	yes	—
803	C₂×C₄	C₂⁵×C₇	1	1	yes	characteristic
804	C₈	—	2	2	no	—
805	C₈	—	2	4	no	—
806	C₈	C₂²×C₇×Q₈	1	4	yes	—
807	C₇	#61369	1	1	yes	characteristic, direct product factor, Sylow
808	C₂²	—	2	1	no	—
809	C₂²	—	2	1	no	—
810	C₂²	—	2	2	no	—
811	C₂²	—	4	1	no	—
812	C₂²	—	4	1	no	—
813	C₂²	C₇×D₄×Q₈	1	2	yes	—
814	C₂²	C₂³×C₇×D₄	1	1	yes	characteristic
815	C₄	—	2	1	no	—
816	C₄	—	2	2	no	—
817	C₄	—	2	2	no	—
818	C₄	—	2	2	no	—
819	C₄	—	2	1	no	—
820	C₄	—	2	2	no	—
821	C₄	—	2	1	no	—
822	C₄	—	2	2	no	—
823	C₄	—	2	4	no	—
824	C₄	—	4	2	no	—
825	C₄	—	4	1	no	—
826	C₄	—	4	4	no	—
827	C₄	—	4	2	no	—
828	C₄	—	4	2	no	—
829	C₄	—	4	1	no	—
830	C₄	C₇×D₄×Q₈	1	2	yes	—
831	C₄	C₇×#575	1	2	yes	—
832	C₄	C₂³×C₇×Q₈	1	1	yes	characteristic
833	C₄	C₂×C₇×2₋¹⁺⁴	1	1	yes	characteristic
834	C₂	—	2	2	no	—
835	C₂	—	4	2	no	—
836	C₂	C₂×C₇×D₄×Q₈	1	1	yes	characteristic
837	C₂	C₂×C₇×#575	1	1	yes	characteristic
838	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	C₂×C₇×#41	C₂³
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₇ ◁ C₂×C₄×C₇×Q₈ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₇×#557	C₂	semidirect
3. C₇×#3390	C₂	semidirect
4. C₇×#3388	C₂	semidirect
5. C₇×#3387	C₂	semidirect
6. C₇×#3386	C₂	semidirect
7. C₇×#3383	C₂	semidirect
8. C₇×#3381	C₂	semidirect
9. C₇×#3166	C₂	semidirect
10. C₇×#3165	C₂	semidirect
13. C₇×#3078	C₂	semidirect
14. C₇×#3078	C₂	semidirect
15. C₇×Q₈×M₁₆	C₂	semidirect
95. #61369	C₇	direct (N × H)
101. C₇×#137	Q₈	semidirect
231. C₂×#557	C₂×C₇	semidirect
232. #3390	C₂×C₇	semidirect
233. #3388	C₂×C₇	semidirect
234. #3387	C₂×C₇	semidirect
235. #3386	C₂×C₇	semidirect
236. #3383	C₂×C₇	semidirect
237. #3381	C₂×C₇	semidirect
238. #3166	C₂×C₇	semidirect
239. #3165	C₂×C₇	semidirect
242. #3078	C₂×C₇	semidirect
243. #3078	C₂×C₇	semidirect
244. Q₈×M₁₆	C₂×C₇	semidirect
263. C₂×C₇×Q₈	C₂×Q₈	semidirect
281. C₇×Q₁₆	C₂×Q₈	semidirect
282. C₇×SD₁₆	C₂×Q₈	semidirect
285. C₇×M₁₆	C₂×Q₈	semidirect
488. #137	C₇×Q₈	semidirect
659. C₂×Q₈	C₂×C₇×Q₈	semidirect
677. Q₁₆	C₂×C₇×Q₈	semidirect
678. SD₁₆	C₂×C₇×Q₈	semidirect
681. M₁₆	C₂×C₇×Q₈	semidirect
807. C₇	#61369	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×Q₈×#41	2
C₂×C₇×#557	2
C₇×#3390	2
C₇×#3388	2
C₇×#3387	2
C₇×#3386	2
C₇×#3383	2
C₇×#3381	2
C₇×#3166	2
C₇×#3165	2
C₇×#3080	2
C₇×#3079	2
C₇×#3078	2
C₇×Q₈×M₁₆	2
C₄×C₇×#137	2
#61369	7

Subgroups — C7×#61369 #13238585

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×#61369 #13238585