Subgroups — C₂×C₇×#3495 #13240019

Order 1792.

7206 conjugacy classes of subgroups.

The subgroup lattice has 904 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×#3495	C₂	1	32	yes	maximal, direct product factor
2	C₂×C₇×#556	C₂	1	2	yes	maximal, complemented
3	C₂×C₇×#554	C₂	1	2	yes	maximal, complemented
4	C₂×C₇×#552	C₂	1	2	yes	maximal, complemented
5	C₂×C₇×#552	C₂	1	4	yes	maximal, complemented
6	C₂×C₇×#552	C₂	1	2	yes	maximal, complemented
7	C₂×C₇×#551	C₂	1	4	yes	maximal, complemented
8	C₂×C₇×#544	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×C₇×#542	C₂	1	2	yes	maximal, complemented
10	C₂×C₇×#541	C₂	1	2	yes	maximal, complemented
11	C₂×C₇×#536	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₇×#533	C₂	1	2	yes	maximal, complemented
13	C₂×C₇×#529	C₂	1	2	yes	maximal, complemented
14	C₂×C₇×#525	C₂	1	1	yes	maximal, characteristic
15	C₂²×C₇×C₂²⋊Q₈	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×C₇×#520	C₂	1	1	yes	maximal, characteristic, complemented
17	C₂×C₇×#519	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂²×C₇×#117	C₂	1	1	yes	maximal, characteristic, complemented
19	C₂²×C₇×#41	C₂²	1	1	yes	characteristic
20	C₂³×C₇×Q₈	C₂²	1	1	yes	characteristic
21	C₂⁴×C₄×C₇	C₂²	1	1	yes	characteristic
22	C₇×#556	C₂²	1	32	yes	complemented
23	C₇×#554	C₂²	1	32	yes	complemented
24	C₇×#552	C₂²	1	32	yes	complemented
25	C₇×#552	C₂²	1	64	yes	complemented
26	C₇×#552	C₂²	1	32	yes	complemented
27	C₇×#551	C₂²	1	64	yes	complemented
28	C₇×#544	C₂²	1	16	yes	complemented
29	C₇×#542	C₂²	1	32	yes	complemented
30	C₇×#541	C₂²	1	32	yes	complemented
31	C₇×#536	C₂²	1	16	yes	complemented
32	C₇×#533	C₂²	1	32	yes	complemented
33	C₂×C₇×C₄⋊Q₈	C₂²	1	2	yes	complemented
34	C₂×C₇×C₄⋊Q₈	C₂²	1	2	yes	complemented
35	C₂×C₇×C₄⋊Q₈	C₂²	1	2	yes	complemented
36	C₇×#529	C₂²	1	32	yes	complemented
37	C₂×C₇×#126	C₂²	1	4	yes	—
38	C₂×C₇×#126	C₂²	1	4	yes	—
39	C₂×C₇×#126	C₂²	1	4	yes	complemented
40	C₂×C₇×#126	C₂²	1	4	yes	complemented
41	C₂×C₇×#125	C₂²	1	2	yes	complemented
42	C₂×C₇×#125	C₂²	1	4	yes	complemented
43	C₂×C₇×#125	C₂²	1	4	yes	complemented
44	C₂×C₇×#125	C₂²	1	4	yes	complemented
45	C₂×C₇×#125	C₂²	1	2	yes	complemented
46	C₂×C₇×#124	C₂²	1	4	yes	—
47	C₂×C₇×#124	C₂²	1	2	yes	complemented
48	C₇×#525	C₂²	1	16	yes	—
49	C₂×C₇×#123	C₂²	1	2	yes	—
50	C₂×C₇×#123	C₂²	1	4	yes	—
51	C₂×C₇×#123	C₂²	1	4	yes	—
52	C₂×C₇×#123	C₂²	1	4	yes	—
53	C₂×C₇×C₂²⋊Q₈	C₂²	1	2	yes	—
54	C₂×C₇×C₂²⋊Q₈	C₂²	1	2	yes	—
55	C₂×C₇×C₂²⋊Q₈	C₂²	1	2	yes	—
56	C₂×C₇×C₂²⋊Q₈	C₂²	1	2	yes	—
57	C₂×C₇×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
58	C₂×C₇×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
59	C₂×C₇×C₂²⋊Q₈	C₂²	1	4	yes	—
60	C₂×C₇×C₂²⋊Q₈	C₂²	1	4	yes	—
61	C₂×C₇×C₂²⋊Q₈	C₂²	1	16	yes	complemented
62	C₂×C₇×C₂²⋊Q₈	C₂²	1	2	yes	complemented
63	C₂×C₇×C₂²⋊Q₈	C₂²	1	2	yes	complemented
64	C₂×C₇×C₂²⋊Q₈	C₂²	1	4	yes	complemented
65	C₂×C₇×#121	C₂²	1	1	yes	characteristic
66	C₂×C₇×#121	C₂²	1	1	yes	characteristic
67	C₂×C₇×#120	C₂²	1	2	yes	—
68	C₇×#520	C₂²	1	16	yes	complemented
69	C₇×#519	C₂²	1	16	yes	complemented
70	C₂×C₄×C₇×Q₈	C₂²	1	2	yes	complemented
71	C₂×C₄×C₇×Q₈	C₂²	1	2	yes	complemented
72	C₂×C₄×C₇×Q₈	C₂²	1	2	yes	complemented
73	C₂×C₄×C₇×Q₈	C₂²	1	2	yes	complemented
74	C₂×C₄×C₇×Q₈	C₂²	1	2	yes	complemented
75	C₂×C₄×C₇×Q₈	C₂²	1	4	yes	complemented
76	C₂×C₄×C₇×D₄	C₂²	1	4	yes	—
77	C₂×C₄×C₇×D₄	C₂²	1	2	yes	—
78	C₂×C₄×C₇×D₄	C₂²	1	2	yes	—
79	C₂×C₄×C₇×D₄	C₂²	1	4	yes	—
80	C₂×C₄×C₇×D₄	C₂²	1	2	yes	complemented
81	C₂×C₇×#117	C₂²	1	1	yes	characteristic
82	C₂×C₇×#117	C₂²	1	1	yes	characteristic
83	C₂×C₇×#117	C₂²	1	2	yes	—
84	C₂×C₇×#117	C₂²	1	1	yes	characteristic
85	C₂×C₇×#117	C₂²	1	2	yes	—
86	C₂×C₇×#117	C₂²	1	1	yes	characteristic
87	C₂×C₇×#117	C₂²	1	1	yes	characteristic
88	C₂×C₇×#117	C₂²	1	4	yes	—
89	C₂×C₇×#117	C₂²	1	4	yes	—
90	C₂×C₇×#117	C₂²	1	16	yes	complemented
91	C₂×C₇×#117	C₂²	1	2	yes	complemented
92	C₂×C₇×#117	C₂²	1	4	yes	complemented
93	C₂²×C₇×C₄⋊C₄	C₂²	1	1	yes	characteristic
94	C₂²×C₇×C₄⋊C₄	C₂²	1	1	yes	characteristic
95	C₂²×C₇×C₄⋊C₄	C₂²	1	1	yes	characteristic
96	C₂²×C₇×C₄⋊C₄	C₂²	1	2	yes	—
97	C₂²×C₇×C₄⋊C₄	C₂²	1	2	yes	complemented
98	C₂²×C₇×C₂²⋊C₄	C₂²	1	2	yes	—
99	C₂²×C₇×C₂²⋊C₄	C₂²	1	2	yes	—
100	C₂²×C₄²×C₇	C₂²	1	2	yes	—
101	C₂×#3495	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
102	C₂⁵×C₇	C₂³	1	1	yes	characteristic
103	C₂×C₇×#41	—	2	8	no	—
104	C₂×C₇×#41	C₂³	1	8	yes	—
105	C₂²×C₇×Q₈	—	2	8	no	—
106	C₂²×C₇×Q₈	C₂³	1	2	yes	—
107	C₂²×C₇×Q₈	C₂³	1	2	yes	—
108	C₂²×C₇×Q₈	C₂³	1	8	yes	—
109	C₂²×C₇×Q₈	C₂³	1	1	yes	characteristic
110	C₂²×C₇×Q₈	C₂³	1	4	yes	—
111	C₂²×C₇×D₄	C₂³	1	2	yes	—
112	C₂²×C₇×D₄	C₂³	1	1	yes	characteristic
113	C₂²×C₇×D₄	C₂³	1	2	yes	—
114	C₂²×C₇×D₄	C₂³	1	2	yes	—
115	C₂³×C₄×C₇	—	2	8	no	—
116	C₂³×C₄×C₇	C₂³	1	2	yes	—
117	C₂³×C₄×C₇	C₂³	1	2	yes	—
118	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
119	C₂³×C₄×C₇	C₂³	1	2	yes	—
120	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
121	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
122	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
123	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
124	C₂³×C₄×C₇	C₂³	1	8	yes	—
125	C₂³×C₄×C₇	C₂³	1	2	yes	—
126	C₂³×C₄×C₇	C₂³	1	2	yes	—
127	C₂³×C₄×C₇	C₂³	1	4	yes	—
128	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
129	C₇×C₄⋊Q₈	C₂³	1	16	yes	complemented
130	C₇×C₄⋊Q₈	C₂³	1	16	yes	complemented
131	C₇×C₄⋊Q₈	C₂³	1	16	yes	complemented
132	C₇×#126	C₂³	1	32	yes	—
133	C₇×#126	C₂³	1	32	yes	—
134	C₇×#126	C₂³	1	32	yes	complemented
135	C₇×#126	C₂³	1	32	yes	complemented
136	C₇×#125	C₂³	1	16	yes	complemented
137	C₇×#125	C₂³	1	32	yes	complemented
138	C₇×#125	C₂³	1	32	yes	complemented
139	C₇×#125	C₂³	1	32	yes	complemented
140	C₇×#125	C₂³	1	16	yes	complemented
141	C₇×#124	C₂³	1	32	yes	—
142	C₇×#124	C₂³	1	16	yes	complemented
143	C₇×#123	C₂³	1	16	yes	—
144	C₇×#123	C₂³	1	32	yes	—
145	C₇×#123	C₂³	1	32	yes	—
146	C₇×#123	C₂³	1	32	yes	—
147	C₇×C₂²⋊Q₈	C₂³	1	16	yes	—
148	C₇×C₂²⋊Q₈	C₂³	1	16	yes	—
149	C₇×C₂²⋊Q₈	C₂³	1	16	yes	—
150	C₇×C₂²⋊Q₈	C₂³	1	16	yes	—
151	C₇×C₂²⋊Q₈	C₂³	1	8	yes	—
152	C₇×C₂²⋊Q₈	C₂³	1	8	yes	—
153	C₇×C₂²⋊Q₈	C₂³	1	32	yes	—
154	C₇×C₂²⋊Q₈	C₂³	1	32	yes	—
155	C₇×C₂²⋊Q₈	C₂³	1	16	yes	complemented
156	C₇×C₂²⋊Q₈	C₂³	1	16	yes	complemented
157	C₇×C₂²⋊Q₈	C₂³	1	32	yes	complemented
158	C₇×#121	C₂³	1	8	yes	—
159	C₇×#121	C₂³	1	8	yes	—
160	C₇×#120	C₂³	1	16	yes	—
161	C₄×C₇×Q₈	C₂³	1	16	yes	complemented
162	C₄×C₇×Q₈	C₂³	1	16	yes	complemented
163	C₄×C₇×Q₈	C₂³	1	16	yes	complemented
164	C₄×C₇×Q₈	C₂³	1	16	yes	complemented
165	C₄×C₇×Q₈	C₂³	1	16	yes	complemented
166	C₄×C₇×Q₈	C₂³	1	32	yes	complemented
167	C₄×C₇×D₄	C₂³	1	32	yes	—
168	C₄×C₇×D₄	C₂³	1	16	yes	—
169	C₄×C₇×D₄	C₂³	1	16	yes	—
170	C₄×C₇×D₄	C₂³	1	32	yes	—
171	C₄×C₇×D₄	C₂³	1	16	yes	complemented
172	C₇×#117	C₂³	1	8	yes	—
173	C₇×#117	C₂³	1	8	yes	—
174	C₇×#117	C₂³	1	16	yes	—
175	C₇×#117	C₂³	1	8	yes	—
176	C₇×#117	C₂³	1	16	yes	—
177	C₇×#117	C₂³	1	8	yes	—
178	C₇×#117	C₂³	1	8	yes	—
179	C₇×#117	C₂³	1	32	yes	—
180	C₇×#117	C₂³	1	32	yes	—
181	C₇×#117	C₂³	1	16	yes	complemented
182	C₇×#117	C₂³	1	32	yes	complemented
183	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
184	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
185	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
186	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
187	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
188	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
189	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
190	C₂×C₇×C₄⋊C₄	C₂³	1	8	yes	—
191	C₂×C₇×C₄⋊C₄	C₂³	1	8	yes	—
192	C₂×C₇×C₄⋊C₄	C₂³	1	4	yes	—
193	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
194	C₂×C₇×C₄⋊C₄	C₂³	1	8	yes	—
195	C₂×C₇×C₄⋊C₄	C₂³	1	4	yes	—
196	C₂×C₇×C₄⋊C₄	C₂³	1	16	yes	—
197	C₂×C₇×C₄⋊C₄	C₂³	1	4	yes	—
198	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
199	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
200	C₂×C₇×C₄⋊C₄	C₂³	1	4	yes	—
201	C₂×C₇×C₄⋊C₄	C₂³	1	4	yes	—
202	C₂×C₇×C₄⋊C₄	C₂³	1	4	yes	—
203	C₂×C₇×C₄⋊C₄	C₂³	1	4	yes	—
204	C₂×C₇×C₄⋊C₄	C₂³	1	4	yes	—
205	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
206	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
207	C₂×C₇×C₄⋊C₄	C₂³	1	4	yes	—
208	C₂×C₇×C₄⋊C₄	C₂³	1	4	yes	—
209	C₂×C₇×C₄⋊C₄	C₂³	1	16	yes	complemented
210	C₂×C₇×C₂²⋊C₄	C₂³	1	2	yes	—
211	C₂×C₇×C₂²⋊C₄	C₂³	1	2	yes	—
212	C₂×C₇×C₂²⋊C₄	C₂³	1	2	yes	—
213	C₂×C₇×C₂²⋊C₄	C₂³	1	2	yes	—
214	C₂×C₇×C₂²⋊C₄	C₂³	1	4	yes	—
215	C₂×C₇×C₂²⋊C₄	C₂³	1	16	yes	—
216	C₂×C₇×C₂²⋊C₄	C₂³	1	4	yes	—
217	C₂×C₇×C₂²⋊C₄	C₂³	1	16	yes	—
218	C₂×C₇×C₂²⋊C₄	C₂³	1	2	yes	—
219	C₂×C₇×C₂²⋊C₄	C₂³	1	2	yes	—
220	C₂×C₇×C₂²⋊C₄	C₂³	1	2	yes	—
221	C₂×C₇×C₂²⋊C₄	C₂³	1	4	yes	—
222	C₂×C₇×C₂²⋊C₄	C₂³	1	4	yes	—
223	C₂×C₇×C₂²⋊C₄	C₂³	1	2	yes	—
224	C₂×C₇×C₂²⋊C₄	C₂³	1	2	yes	—
225	C₂×C₇×C₂²⋊C₄	C₂³	1	4	yes	—
226	C₂×C₄²×C₇	C₂³	1	2	yes	—
227	C₂×C₄²×C₇	C₂³	1	2	yes	—
228	C₂×C₄²×C₇	C₂³	1	2	yes	—
229	C₂×C₄²×C₇	C₂³	1	2	yes	—
230	C₂×C₄²×C₇	C₂³	1	16	yes	—
231	C₂×C₄²×C₇	C₂³	1	4	yes	—
232	C₂×C₄²×C₇	C₂³	1	4	yes	—
233	C₂×C₄²×C₇	C₂³	1	4	yes	—
234	C₂×C₄²×C₇	C₂³	1	2	yes	—
235	#3495	C₂×C₇	1	32	yes	direct product factor
236	C₂×#556	C₂×C₇	1	2	yes	complemented
237	C₂×#554	C₂×C₇	1	2	yes	complemented
238	C₂×#552	C₂×C₇	1	2	yes	complemented
239	C₂×#552	C₂×C₇	1	4	yes	complemented
240	C₂×#552	C₂×C₇	1	2	yes	complemented
241	C₂×#551	C₂×C₇	1	4	yes	complemented
242	C₂×#544	C₂×C₇	1	1	yes	characteristic, complemented
243	C₂×#542	C₂×C₇	1	2	yes	complemented
244	C₂×#541	C₂×C₇	1	2	yes	complemented
245	C₂×#536	C₂×C₇	1	1	yes	characteristic, complemented
246	C₂×#533	C₂×C₇	1	2	yes	complemented
247	C₂×#529	C₂×C₇	1	2	yes	complemented
248	C₂×#525	C₂×C₇	1	1	yes	characteristic
249	C₂²×C₂²⋊Q₈	C₂×C₇	1	1	yes	characteristic, complemented
250	C₂×#520	C₂×C₇	1	1	yes	characteristic, complemented
251	C₂×#519	C₂×C₇	1	1	yes	characteristic, complemented
252	C₂²×#117	C₂×C₇	1	1	yes	characteristic, complemented
253	C₂⁴×C₇	—	2	4	no	—
254	C₂⁴×C₇	—	2	4	no	—
255	C₂⁴×C₇	—	4	2	no	—
256	C₂⁴×C₇	C₂⁴	1	1	yes	characteristic
257	C₂⁴×C₇	C₂⁴	1	2	yes	—
258	C₂⁴×C₇	C₂⁴	1	4	yes	—
259	C₂⁴×C₇	C₂⁴	1	1	yes	characteristic
260	C₂⁴×C₇	C₂⁴	1	1	yes	characteristic
261	C₇×#41	—	2	32	no	—
262	C₂×C₇×Q₈	—	2	8	no	—
263	C₂×C₇×Q₈	—	2	8	no	—
264	C₂×C₇×Q₈	—	2	32	no	—
265	C₂×C₇×Q₈	—	2	4	no	—
266	C₂×C₇×Q₈	—	4	8	no	—
267	C₂×C₇×Q₈	C₂⁴	1	8	yes	—
268	C₂×C₇×Q₈	C₂⁴	1	8	yes	—
269	C₂×C₇×Q₈	C₂⁴	1	4	yes	—
270	C₂×C₇×Q₈	C₂⁴	1	16	yes	—
271	C₂×C₇×D₄	—	2	8	no	—
272	C₂×C₇×D₄	—	2	8	no	—
273	C₂×C₇×D₄	—	2	4	no	—
274	C₂×C₇×D₄	—	4	4	no	—
275	C₂×C₇×D₄	C₂⁴	1	8	yes	—
276	C₂×C₇×D₄	C₂⁴	1	8	yes	—
277	C₂×C₇×D₄	C₂⁴	1	4	yes	—
278	C₂×C₇×D₄	C₂⁴	1	8	yes	—
279	C₂²×C₄×C₇	—	2	4	no	—
280	C₂²×C₄×C₇	—	2	8	no	—
281	C₂²×C₄×C₇	—	2	8	no	—
282	C₂²×C₄×C₇	—	2	4	no	—
283	C₂²×C₄×C₇	—	2	4	no	—
284	C₂²×C₄×C₇	—	2	4	no	—
285	C₂²×C₄×C₇	—	2	4	no	—
286	C₂²×C₄×C₇	—	2	32	no	—
287	C₂²×C₄×C₇	—	2	8	no	—
288	C₂²×C₄×C₇	—	4	8	no	—
289	C₂²×C₄×C₇	—	4	4	no	—
290	C₂²×C₄×C₇	—	4	4	no	—
291	C₂²×C₄×C₇	#41	1	8	yes	—
292	C₂²×C₄×C₇	C₂⁴	1	4	yes	—
293	C₂²×C₄×C₇	C₂⁴	1	8	yes	—
294	C₂²×C₄×C₇	C₂⁴	1	8	yes	—
295	C₂²×C₄×C₇	C₂⁴	1	4	yes	—
296	C₂²×C₄×C₇	C₂⁴	1	4	yes	—
297	C₂²×C₄×C₇	C₂⁴	1	8	yes	—
298	C₂²×C₄×C₇	C₂⁴	1	4	yes	—
299	C₂²×C₄×C₇	C₂⁴	1	4	yes	—
300	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
301	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
302	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
303	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
304	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
305	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
306	C₂²×C₄×C₇	C₂⁴	1	4	yes	—
307	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
308	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
309	C₂²×C₄×C₇	C₂⁴	1	4	yes	—
310	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
311	C₂²×C₄×C₇	C₂⁴	1	8	yes	—
312	C₂²×C₄×C₇	C₂⁴	1	8	yes	—
313	C₂²×C₄×C₇	C₂⁴	1	16	yes	—
314	C₂²×C₄×C₇	C₂⁴	1	4	yes	—
315	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
316	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
317	C₇×C₄⋊C₄	C₂⁴	1	4	yes	—
318	C₇×C₄⋊C₄	C₂⁴	1	8	yes	—
319	C₇×C₄⋊C₄	C₂⁴	1	4	yes	—
320	C₇×C₄⋊C₄	C₂⁴	1	8	yes	—
321	C₇×C₄⋊C₄	C₂⁴	1	4	yes	—
322	C₇×C₄⋊C₄	C₂⁴	1	4	yes	—
323	C₇×C₄⋊C₄	C₂⁴	1	8	yes	—
324	C₇×C₄⋊C₄	C₂⁴	1	16	yes	—
325	C₇×C₄⋊C₄	C₂⁴	1	8	yes	—
326	C₇×C₄⋊C₄	C₂⁴	1	16	yes	—
327	C₇×C₄⋊C₄	C₂⁴	1	16	yes	—
328	C₇×C₄⋊C₄	C₂⁴	1	4	yes	—
329	C₇×C₄⋊C₄	C₂⁴	1	4	yes	—
330	C₇×C₄⋊C₄	C₂⁴	1	16	yes	—
331	C₇×C₄⋊C₄	C₂⁴	1	16	yes	—
332	C₇×C₄⋊C₄	C₂⁴	1	16	yes	—
333	C₇×C₄⋊C₄	C₂⁴	1	16	yes	—
334	C₇×C₄⋊C₄	C₂⁴	1	16	yes	—
335	C₇×C₄⋊C₄	C₂⁴	1	8	yes	—
336	C₇×C₄⋊C₄	C₂⁴	1	8	yes	—
337	C₇×C₄⋊C₄	C₂⁴	1	16	yes	—
338	C₇×C₄⋊C₄	C₂⁴	1	16	yes	—
339	C₇×C₂²⋊C₄	C₂⁴	1	8	yes	—
340	C₇×C₂²⋊C₄	C₂⁴	1	8	yes	—
341	C₇×C₂²⋊C₄	C₂⁴	1	8	yes	—
342	C₇×C₂²⋊C₄	C₂⁴	1	8	yes	—
343	C₇×C₂²⋊C₄	C₂⁴	1	16	yes	—
344	C₇×C₂²⋊C₄	C₂⁴	1	16	yes	—
345	C₇×C₂²⋊C₄	C₂⁴	1	8	yes	—
346	C₇×C₂²⋊C₄	C₂⁴	1	8	yes	—
347	C₇×C₂²⋊C₄	C₂⁴	1	8	yes	—
348	C₇×C₂²⋊C₄	C₂⁴	1	16	yes	—
349	C₇×C₂²⋊C₄	C₂⁴	1	16	yes	—
350	C₇×C₂²⋊C₄	C₂⁴	1	8	yes	—
351	C₇×C₂²⋊C₄	C₂⁴	1	8	yes	—
352	C₇×C₂²⋊C₄	C₂⁴	1	16	yes	—
353	C₄²×C₇	C₂⁴	1	8	yes	—
354	C₄²×C₇	C₂⁴	1	8	yes	—
355	C₄²×C₇	C₂⁴	1	8	yes	—
356	C₄²×C₇	C₂⁴	1	8	yes	—
357	C₄²×C₇	C₂⁴	1	16	yes	—
358	C₄²×C₇	C₂⁴	1	16	yes	—
359	C₄²×C₇	C₂⁴	1	16	yes	—
360	C₄²×C₇	C₂⁴	1	8	yes	—
361	C₂²×#41	C₂²×C₇	1	1	yes	characteristic
362	C₂³×Q₈	C₂²×C₇	1	1	yes	characteristic
363	C₂⁴×C₄	C₂²×C₇	1	1	yes	characteristic
364	#556	C₂²×C₇	1	32	yes	complemented
365	#554	C₂²×C₇	1	32	yes	complemented
366	#552	C₂²×C₇	1	32	yes	complemented
367	#552	C₂²×C₇	1	64	yes	complemented
368	#552	C₂²×C₇	1	32	yes	complemented
369	#551	C₂²×C₇	1	64	yes	complemented
370	#544	C₂²×C₇	1	16	yes	complemented
371	#542	C₂²×C₇	1	32	yes	complemented
372	#541	C₂²×C₇	1	32	yes	complemented
373	#536	C₂²×C₇	1	16	yes	complemented
374	#533	C₂²×C₇	1	32	yes	complemented
375	C₂×C₄⋊Q₈	C₂²×C₇	1	2	yes	complemented
376	C₂×C₄⋊Q₈	C₂²×C₇	1	2	yes	complemented
377	C₂×C₄⋊Q₈	C₂²×C₇	1	2	yes	complemented
378	#529	C₂²×C₇	1	32	yes	complemented
379	C₂×#126	C₂²×C₇	1	4	yes	—
380	C₂×#126	C₂²×C₇	1	4	yes	—
381	C₂×#126	C₂²×C₇	1	4	yes	complemented
382	C₂×#126	C₂²×C₇	1	4	yes	complemented
383	C₂×#125	C₂²×C₇	1	2	yes	complemented
384	C₂×#125	C₂²×C₇	1	4	yes	complemented
385	C₂×#125	C₂²×C₇	1	4	yes	complemented
386	C₂×#125	C₂²×C₇	1	4	yes	complemented
387	C₂×#125	C₂²×C₇	1	2	yes	complemented
388	C₂×#124	C₂²×C₇	1	4	yes	—
389	C₂×#124	C₂²×C₇	1	2	yes	complemented
390	#525	C₂²×C₇	1	16	yes	—
391	C₂×#123	C₂²×C₇	1	2	yes	—
392	C₂×#123	C₂²×C₇	1	4	yes	—
393	C₂×#123	C₂²×C₇	1	4	yes	—
394	C₂×#123	C₂²×C₇	1	4	yes	—
395	C₂×C₂²⋊Q₈	C₂²×C₇	1	2	yes	—
396	C₂×C₂²⋊Q₈	C₂²×C₇	1	2	yes	—
397	C₂×C₂²⋊Q₈	C₂²×C₇	1	2	yes	—
398	C₂×C₂²⋊Q₈	C₂²×C₇	1	2	yes	—
399	C₂×C₂²⋊Q₈	C₂²×C₇	1	1	yes	characteristic
400	C₂×C₂²⋊Q₈	C₂²×C₇	1	1	yes	characteristic
401	C₂×C₂²⋊Q₈	C₂²×C₇	1	4	yes	—
402	C₂×C₂²⋊Q₈	C₂²×C₇	1	4	yes	—
403	C₂×C₂²⋊Q₈	C₂²×C₇	1	16	yes	complemented
404	C₂×C₂²⋊Q₈	C₂²×C₇	1	2	yes	complemented
405	C₂×C₂²⋊Q₈	C₂²×C₇	1	2	yes	complemented
406	C₂×C₂²⋊Q₈	C₂²×C₇	1	4	yes	complemented
407	C₂×#121	C₂²×C₇	1	1	yes	characteristic
408	C₂×#121	C₂²×C₇	1	1	yes	characteristic
409	C₂×#120	C₂²×C₇	1	2	yes	—
410	#520	C₂²×C₇	1	16	yes	complemented
411	#519	C₂²×C₇	1	16	yes	complemented
412	C₂×C₄×Q₈	C₂²×C₇	1	2	yes	complemented
413	C₂×C₄×Q₈	C₂²×C₇	1	2	yes	complemented
414	C₂×C₄×Q₈	C₂²×C₇	1	2	yes	complemented
415	C₂×C₄×Q₈	C₂²×C₇	1	2	yes	complemented
416	C₂×C₄×Q₈	C₂²×C₇	1	2	yes	complemented
417	C₂×C₄×Q₈	C₂²×C₇	1	4	yes	complemented
418	C₂×C₄×D₄	C₂²×C₇	1	4	yes	—
419	C₂×C₄×D₄	C₂²×C₇	1	2	yes	—
420	C₂×C₄×D₄	C₂²×C₇	1	2	yes	—
421	C₂×C₄×D₄	C₂²×C₇	1	4	yes	—
422	C₂×C₄×D₄	C₂²×C₇	1	2	yes	complemented
423	C₂×#117	C₂²×C₇	1	1	yes	characteristic
424	C₂×#117	C₂²×C₇	1	1	yes	characteristic
425	C₂×#117	C₂²×C₇	1	2	yes	—
426	C₂×#117	C₂²×C₇	1	1	yes	characteristic
427	C₂×#117	C₂²×C₇	1	2	yes	—
428	C₂×#117	C₂²×C₇	1	1	yes	characteristic
429	C₂×#117	C₂²×C₇	1	1	yes	characteristic
430	C₂×#117	C₂²×C₇	1	4	yes	—
431	C₂×#117	C₂²×C₇	1	4	yes	—
432	C₂×#117	C₂²×C₇	1	16	yes	complemented
433	C₂×#117	C₂²×C₇	1	2	yes	complemented
434	C₂×#117	C₂²×C₇	1	4	yes	complemented
435	C₂²×C₄⋊C₄	C₂²×C₇	1	1	yes	characteristic
436	C₂²×C₄⋊C₄	C₂²×C₇	1	1	yes	characteristic
437	C₂²×C₄⋊C₄	C₂²×C₇	1	1	yes	characteristic
438	C₂²×C₄⋊C₄	C₂²×C₇	1	2	yes	—
439	C₂²×C₄⋊C₄	C₂²×C₇	1	2	yes	complemented
440	C₂²×C₂²⋊C₄	C₂²×C₇	1	2	yes	—
441	C₂²×C₂²⋊C₄	C₂²×C₇	1	2	yes	—
442	C₂²×C₄²	C₂²×C₇	1	2	yes	—
443	C₂³×C₇	—	2	2	no	—
444	C₂³×C₇	—	2	2	no	—
445	C₂³×C₇	—	2	2	no	—
446	C₂³×C₇	—	2	2	no	—
447	C₂³×C₇	—	2	8	no	—
448	C₂³×C₇	—	2	2	no	—
449	C₂³×C₇	—	2	4	no	—
450	C₂³×C₇	—	2	4	no	—
451	C₂³×C₇	—	2	8	no	—
452	C₂³×C₇	—	2	2	no	—
453	C₂³×C₇	—	2	4	no	—
454	C₂³×C₇	—	2	2	no	—
455	C₂³×C₇	—	4	4	no	—
456	C₂³×C₇	—	4	16	no	—
457	C₂³×C₇	C₂×#41	1	4	yes	—
458	C₂³×C₇	2₋¹⁺⁴	1	4	yes	—
459	C₂³×C₇	C₂⁵	1	2	yes	—
460	C₂³×C₇	C₂⁵	1	4	yes	—
461	C₂³×C₇	C₂⁵	1	2	yes	—
462	C₂³×C₇	C₂⁵	1	2	yes	—
463	C₂³×C₇	C₂⁵	1	1	yes	characteristic
464	C₇×Q₈	—	2	16	no	—
465	C₇×Q₈	—	2	16	no	—
466	C₇×Q₈	—	2	8	no	—
467	C₇×Q₈	—	4	16	no	—
468	C₇×D₄	—	2	16	no	—
469	C₇×D₄	—	2	16	no	—
470	C₇×D₄	—	2	8	no	—
471	C₇×D₄	—	4	8	no	—
472	C₂×C₄×C₇	—	2	8	no	—
473	C₂×C₄×C₇	—	2	2	no	—
474	C₂×C₄×C₇	—	2	2	no	—
475	C₂×C₄×C₇	—	2	4	no	—
476	C₂×C₄×C₇	—	2	16	no	—
477	C₂×C₄×C₇	—	2	8	no	—
478	C₂×C₄×C₇	—	2	16	no	—
479	C₂×C₄×C₇	—	2	4	no	—
480	C₂×C₄×C₇	—	2	4	no	—
481	C₂×C₄×C₇	—	2	4	no	—
482	C₂×C₄×C₇	—	2	4	no	—
483	C₂×C₄×C₇	—	2	8	no	—
484	C₂×C₄×C₇	—	2	4	no	—
485	C₂×C₄×C₇	—	2	4	no	—
486	C₂×C₄×C₇	—	2	8	no	—
487	C₂×C₄×C₇	—	2	8	no	—
488	C₂×C₄×C₇	—	2	8	no	—
489	C₂×C₄×C₇	—	2	8	no	—
490	C₂×C₄×C₇	—	2	16	no	—
491	C₂×C₄×C₇	—	4	16	no	—
492	C₂×C₄×C₇	—	4	8	no	—
493	C₂×C₄×C₇	—	4	8	no	—
494	C₂×C₄×C₇	C₂×#41	1	4	yes	—
495	C₂×C₄×C₇	C₂×#41	1	4	yes	—
496	C₂×C₄×C₇	C₂×#41	1	16	yes	—
497	C₂×C₄×C₇	C₂⁵	1	4	yes	—
498	C₂×C₄×C₇	C₂⁵	1	2	yes	—
499	C₂×C₄×C₇	C₂⁵	1	4	yes	—
500	C₂×C₄×C₇	C₂⁵	1	4	yes	—
501	C₂×C₄×C₇	C₂⁵	1	4	yes	—
502	C₂×C₄×C₇	C₂⁵	1	4	yes	—
503	C₂×C₄×C₇	C₂⁵	1	8	yes	—
504	C₂×C₄×C₇	C₂⁵	1	4	yes	—
505	C₂×C₄×C₇	C₂⁵	1	4	yes	—
506	C₂×C₄×C₇	C₂⁵	1	8	yes	—
507	C₂×C₄×C₇	C₂⁵	1	2	yes	—
508	C₂×C₄×C₇	C₂⁵	1	2	yes	—
509	C₂×C₄×C₇	C₂⁵	1	2	yes	—
510	C₂⁵	C₂³×C₇	1	1	yes	characteristic
511	C₂×#41	—	2	8	no	—
512	C₂×#41	C₂³×C₇	1	8	yes	—
513	C₂²×Q₈	—	2	8	no	—
514	C₂²×Q₈	C₂³×C₇	1	2	yes	—
515	C₂²×Q₈	C₂³×C₇	1	2	yes	—
516	C₂²×Q₈	C₂³×C₇	1	1	yes	characteristic
517	C₂²×Q₈	C₂³×C₇	1	8	yes	—
518	C₂²×Q₈	C₂³×C₇	1	4	yes	—
519	C₂²×D₄	C₂³×C₇	1	2	yes	—
520	C₂²×D₄	C₂³×C₇	1	2	yes	—
521	C₂²×D₄	C₂³×C₇	1	1	yes	characteristic
522	C₂²×D₄	C₂³×C₇	1	2	yes	—
523	C₂³×C₄	—	2	8	no	—
524	C₂³×C₄	C₂³×C₇	1	2	yes	—
525	C₂³×C₄	C₂³×C₇	1	2	yes	—
526	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
527	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
528	C₂³×C₄	C₂³×C₇	1	2	yes	—
529	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
530	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
531	C₂³×C₄	C₂³×C₇	1	8	yes	—
532	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
533	C₂³×C₄	C₂³×C₇	1	2	yes	—
534	C₂³×C₄	C₂³×C₇	1	2	yes	—
535	C₂³×C₄	C₂³×C₇	1	4	yes	—
536	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
537	C₄⋊Q₈	C₂³×C₇	1	16	yes	complemented
538	C₄⋊Q₈	C₂³×C₇	1	16	yes	complemented
539	C₄⋊Q₈	C₂³×C₇	1	16	yes	complemented
540	#126	C₂³×C₇	1	32	yes	—
541	#126	C₂³×C₇	1	32	yes	—
542	#126	C₂³×C₇	1	32	yes	complemented
543	#126	C₂³×C₇	1	32	yes	complemented
544	#125	C₂³×C₇	1	16	yes	complemented
545	#125	C₂³×C₇	1	32	yes	complemented
546	#125	C₂³×C₇	1	32	yes	complemented
547	#125	C₂³×C₇	1	32	yes	complemented
548	#125	C₂³×C₇	1	16	yes	complemented
549	#124	C₂³×C₇	1	32	yes	—
550	#124	C₂³×C₇	1	16	yes	complemented
551	#123	C₂³×C₇	1	16	yes	—
552	#123	C₂³×C₇	1	32	yes	—
553	#123	C₂³×C₇	1	32	yes	—
554	#123	C₂³×C₇	1	32	yes	—
555	C₂²⋊Q₈	C₂³×C₇	1	16	yes	—
556	C₂²⋊Q₈	C₂³×C₇	1	16	yes	—
557	C₂²⋊Q₈	C₂³×C₇	1	16	yes	—
558	C₂²⋊Q₈	C₂³×C₇	1	16	yes	—
559	C₂²⋊Q₈	C₂³×C₇	1	8	yes	—
560	C₂²⋊Q₈	C₂³×C₇	1	8	yes	—
561	C₂²⋊Q₈	C₂³×C₇	1	32	yes	—
562	C₂²⋊Q₈	C₂³×C₇	1	32	yes	—
563	C₂²⋊Q₈	C₂³×C₇	1	16	yes	complemented
564	C₂²⋊Q₈	C₂³×C₇	1	16	yes	complemented
565	C₂²⋊Q₈	C₂³×C₇	1	32	yes	complemented
566	#121	C₂³×C₇	1	8	yes	—
567	#121	C₂³×C₇	1	8	yes	—
568	#120	C₂³×C₇	1	16	yes	—
569	C₄×Q₈	C₂³×C₇	1	16	yes	complemented
570	C₄×Q₈	C₂³×C₇	1	16	yes	complemented
571	C₄×Q₈	C₂³×C₇	1	16	yes	complemented
572	C₄×Q₈	C₂³×C₇	1	16	yes	complemented
573	C₄×Q₈	C₂³×C₇	1	16	yes	complemented
574	C₄×Q₈	C₂³×C₇	1	32	yes	complemented
575	C₄×D₄	C₂³×C₇	1	32	yes	—
576	C₄×D₄	C₂³×C₇	1	16	yes	—
577	C₄×D₄	C₂³×C₇	1	16	yes	—
578	C₄×D₄	C₂³×C₇	1	32	yes	—
579	C₄×D₄	C₂³×C₇	1	16	yes	complemented
580	#117	C₂³×C₇	1	8	yes	—
581	#117	C₂³×C₇	1	8	yes	—
582	#117	C₂³×C₇	1	16	yes	—
583	#117	C₂³×C₇	1	8	yes	—
584	#117	C₂³×C₇	1	16	yes	—
585	#117	C₂³×C₇	1	8	yes	—
586	#117	C₂³×C₇	1	8	yes	—
587	#117	C₂³×C₇	1	32	yes	—
588	#117	C₂³×C₇	1	32	yes	—
589	#117	C₂³×C₇	1	16	yes	complemented
590	#117	C₂³×C₇	1	32	yes	complemented
591	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
592	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
593	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
594	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
595	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
596	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
597	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
598	C₂×C₄⋊C₄	C₂³×C₇	1	8	yes	—
599	C₂×C₄⋊C₄	C₂³×C₇	1	8	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	8	yes	—
603	C₂×C₄⋊C₄	C₂³×C₇	1	4	yes	—
604	C₂×C₄⋊C₄	C₂³×C₇	1	16	yes	—
605	C₂×C₄⋊C₄	C₂³×C₇	1	4	yes	—
606	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
607	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
608	C₂×C₄⋊C₄	C₂³×C₇	1	4	yes	—
609	C₂×C₄⋊C₄	C₂³×C₇	1	4	yes	—
610	C₂×C₄⋊C₄	C₂³×C₇	1	4	yes	—
611	C₂×C₄⋊C₄	C₂³×C₇	1	4	yes	—
612	C₂×C₄⋊C₄	C₂³×C₇	1	4	yes	—
613	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
614	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
615	C₂×C₄⋊C₄	C₂³×C₇	1	4	yes	—
616	C₂×C₄⋊C₄	C₂³×C₇	1	4	yes	—
617	C₂×C₄⋊C₄	C₂³×C₇	1	16	yes	complemented
618	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
619	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
620	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
621	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
622	C₂×C₂²⋊C₄	C₂³×C₇	1	4	yes	—
623	C₂×C₂²⋊C₄	C₂³×C₇	1	16	yes	—
624	C₂×C₂²⋊C₄	C₂³×C₇	1	4	yes	—
625	C₂×C₂²⋊C₄	C₂³×C₇	1	16	yes	—
626	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
627	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
628	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
629	C₂×C₂²⋊C₄	C₂³×C₇	1	4	yes	—
630	C₂×C₂²⋊C₄	C₂³×C₇	1	4	yes	—
631	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
632	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
633	C₂×C₂²⋊C₄	C₂³×C₇	1	4	yes	—
634	C₂×C₄²	C₂³×C₇	1	2	yes	—
635	C₂×C₄²	C₂³×C₇	1	2	yes	—
636	C₂×C₄²	C₂³×C₇	1	4	yes	—
637	C₂×C₄²	C₂³×C₇	1	2	yes	—
638	C₂×C₄²	C₂³×C₇	1	2	yes	—
639	C₂×C₄²	C₂³×C₇	1	4	yes	—
640	C₂×C₄²	C₂³×C₇	1	4	yes	—
641	C₂×C₄²	C₂³×C₇	1	2	yes	—
642	C₂×C₄²	C₂³×C₇	1	16	yes	—
643	C₂²×C₇	—	2	2	no	—
644	C₂²×C₇	—	2	2	no	—
645	C₂²×C₇	—	2	2	no	—
646	C₂²×C₇	—	2	2	no	—
647	C₂²×C₇	—	2	8	no	—
648	C₂²×C₇	—	2	8	no	—
649	C₂²×C₇	—	2	2	no	—
650	C₂²×C₇	—	2	4	no	—
651	C₂²×C₇	—	2	4	no	—
652	C₂²×C₇	—	2	2	no	—
653	C₂²×C₇	—	2	4	no	—
654	C₂²×C₇	—	2	2	no	—
655	C₂²×C₇	—	4	16	no	—
656	C₂²×C₇	—	4	8	no	—
657	C₂²×C₇	—	4	4	no	—
658	C₂²×C₇	C₂²×#41	1	4	yes	—
659	C₂²×C₇	C₂²×#41	1	2	yes	—
660	C₂²×C₇	C₂×2₋¹⁺⁴	1	4	yes	—
661	C₂²×C₇	C₂×2₋¹⁺⁴	1	2	yes	—
662	C₂²×C₇	#585	1	2	yes	—
663	C₂²×C₇	C₂⁶	1	1	yes	characteristic
664	C₄×C₇	—	2	2	no	—
665	C₄×C₇	—	2	2	no	—
666	C₄×C₇	—	2	4	no	—
667	C₄×C₇	—	2	8	no	—
668	C₄×C₇	—	2	4	no	—
669	C₄×C₇	—	2	4	no	—
670	C₄×C₇	—	2	4	no	—
671	C₄×C₇	—	2	4	no	—
672	C₄×C₇	—	2	8	no	—
673	C₄×C₇	—	2	4	no	—
674	C₄×C₇	—	2	4	no	—
675	C₄×C₇	C₂²×#41	1	4	yes	—
676	C₄×C₇	C₂²×#41	1	4	yes	—
677	C₂⁴	—	2	4	no	—
678	C₂⁴	—	2	4	no	—
679	C₂⁴	—	4	2	no	—
680	C₂⁴	C₂⁴×C₇	1	1	yes	characteristic
681	C₂⁴	C₂⁴×C₇	1	2	yes	—
682	C₂⁴	C₂⁴×C₇	1	4	yes	—
683	C₂⁴	C₂⁴×C₇	1	1	yes	characteristic
684	C₂⁴	C₂⁴×C₇	1	1	yes	characteristic
685	#41	—	2	32	no	—
686	C₂×Q₈	—	2	8	no	—
687	C₂×Q₈	—	2	8	no	—
688	C₂×Q₈	—	2	32	no	—
689	C₂×Q₈	—	2	4	no	—
690	C₂×Q₈	—	4	8	no	—
691	C₂×Q₈	C₂⁴×C₇	1	8	yes	—
692	C₂×Q₈	C₂⁴×C₇	1	8	yes	—
693	C₂×Q₈	C₂⁴×C₇	1	4	yes	—
694	C₂×Q₈	C₂⁴×C₇	1	16	yes	—
695	C₂×D₄	—	2	8	no	—
696	C₂×D₄	—	2	8	no	—
697	C₂×D₄	—	2	4	no	—
698	C₂×D₄	—	4	4	no	—
699	C₂×D₄	C₂⁴×C₇	1	8	yes	—
700	C₂×D₄	C₂⁴×C₇	1	8	yes	—
701	C₂×D₄	C₂⁴×C₇	1	4	yes	—
702	C₂×D₄	C₂⁴×C₇	1	8	yes	—
703	C₂²×C₄	—	2	4	no	—
704	C₂²×C₄	—	2	8	no	—
705	C₂²×C₄	—	2	8	no	—
706	C₂²×C₄	—	2	4	no	—
707	C₂²×C₄	—	2	4	no	—
708	C₂²×C₄	—	2	4	no	—
709	C₂²×C₄	—	2	4	no	—
710	C₂²×C₄	—	2	32	no	—
711	C₂²×C₄	—	2	8	no	—
712	C₂²×C₄	—	4	8	no	—
713	C₂²×C₄	—	4	4	no	—
714	C₂²×C₄	—	4	4	no	—
715	C₂²×C₄	C₇×#41	1	8	yes	—
716	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
717	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
718	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
719	C₂²×C₄	C₂⁴×C₇	1	4	yes	—
720	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
721	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
722	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
723	C₂²×C₄	C₂⁴×C₇	1	4	yes	—
724	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
725	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
726	C₂²×C₄	C₂⁴×C₇	1	8	yes	—
727	C₂²×C₄	C₂⁴×C₇	1	4	yes	—
728	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
729	C₂²×C₄	C₂⁴×C₇	1	8	yes	—
730	C₂²×C₄	C₂⁴×C₇	1	4	yes	—
731	C₂²×C₄	C₂⁴×C₇	1	4	yes	—
732	C₂²×C₄	C₂⁴×C₇	1	8	yes	—
733	C₂²×C₄	C₂⁴×C₇	1	4	yes	—
734	C₂²×C₄	C₂⁴×C₇	1	4	yes	—
735	C₂²×C₄	C₂⁴×C₇	1	8	yes	—
736	C₂²×C₄	C₂⁴×C₇	1	8	yes	—
737	C₂²×C₄	C₂⁴×C₇	1	16	yes	—
738	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
739	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
740	C₂²×C₄	C₂⁴×C₇	1	4	yes	—
741	C₄⋊C₄	C₂⁴×C₇	1	4	yes	—
742	C₄⋊C₄	C₂⁴×C₇	1	8	yes	—
743	C₄⋊C₄	C₂⁴×C₇	1	4	yes	—
744	C₄⋊C₄	C₂⁴×C₇	1	8	yes	—
745	C₄⋊C₄	C₂⁴×C₇	1	4	yes	—
746	C₄⋊C₄	C₂⁴×C₇	1	4	yes	—
747	C₄⋊C₄	C₂⁴×C₇	1	8	yes	—
748	C₄⋊C₄	C₂⁴×C₇	1	16	yes	—
749	C₄⋊C₄	C₂⁴×C₇	1	8	yes	—
750	C₄⋊C₄	C₂⁴×C₇	1	16	yes	—
751	C₄⋊C₄	C₂⁴×C₇	1	16	yes	—
752	C₄⋊C₄	C₂⁴×C₇	1	4	yes	—
753	C₄⋊C₄	C₂⁴×C₇	1	4	yes	—
754	C₄⋊C₄	C₂⁴×C₇	1	16	yes	—
755	C₄⋊C₄	C₂⁴×C₇	1	16	yes	—
756	C₄⋊C₄	C₂⁴×C₇	1	16	yes	—
757	C₄⋊C₄	C₂⁴×C₇	1	16	yes	—
758	C₄⋊C₄	C₂⁴×C₇	1	16	yes	—
759	C₄⋊C₄	C₂⁴×C₇	1	8	yes	—
760	C₄⋊C₄	C₂⁴×C₇	1	8	yes	—
761	C₄⋊C₄	C₂⁴×C₇	1	16	yes	—
762	C₄⋊C₄	C₂⁴×C₇	1	16	yes	—
763	C₂²⋊C₄	C₂⁴×C₇	1	8	yes	—
764	C₂²⋊C₄	C₂⁴×C₇	1	8	yes	—
765	C₂²⋊C₄	C₂⁴×C₇	1	8	yes	—
766	C₂²⋊C₄	C₂⁴×C₇	1	8	yes	—
767	C₂²⋊C₄	C₂⁴×C₇	1	16	yes	—
768	C₂²⋊C₄	C₂⁴×C₇	1	16	yes	—
769	C₂²⋊C₄	C₂⁴×C₇	1	8	yes	—
770	C₂²⋊C₄	C₂⁴×C₇	1	8	yes	—
771	C₂²⋊C₄	C₂⁴×C₇	1	8	yes	—
772	C₂²⋊C₄	C₂⁴×C₇	1	16	yes	—
773	C₂²⋊C₄	C₂⁴×C₇	1	16	yes	—
774	C₂²⋊C₄	C₂⁴×C₇	1	8	yes	—
775	C₂²⋊C₄	C₂⁴×C₇	1	8	yes	—
776	C₂²⋊C₄	C₂⁴×C₇	1	16	yes	—
777	C₄²	C₂⁴×C₇	1	8	yes	—
778	C₄²	C₂⁴×C₇	1	8	yes	—
779	C₄²	C₂⁴×C₇	1	8	yes	—
780	C₄²	C₂⁴×C₇	1	8	yes	—
781	C₄²	C₂⁴×C₇	1	16	yes	—
782	C₄²	C₂⁴×C₇	1	16	yes	—
783	C₄²	C₂⁴×C₇	1	16	yes	—
784	C₄²	C₂⁴×C₇	1	8	yes	—
785	C₂×C₇	—	2	4	no	—
786	C₂×C₇	—	2	4	no	—
787	C₂×C₇	—	4	4	no	—
788	C₂×C₇	—	4	2	no	—
789	C₂×C₇	#3495	1	4	yes	direct product factor
790	C₂×C₇	C₂³×#41	1	1	yes	characteristic
791	C₂×C₇	C₂²×2₋¹⁺⁴	1	1	yes	characteristic
792	C₂×C₇	C₂×#585	1	1	yes	characteristic
793	C₂³	—	2	2	no	—
794	C₂³	—	2	2	no	—
795	C₂³	—	2	2	no	—
796	C₂³	—	2	2	no	—
797	C₂³	—	2	8	no	—
798	C₂³	—	2	2	no	—
799	C₂³	—	2	4	no	—
800	C₂³	—	2	4	no	—
801	C₂³	—	2	8	no	—
802	C₂³	—	2	2	no	—
803	C₂³	—	2	4	no	—
804	C₂³	—	2	2	no	—
805	C₂³	—	4	4	no	—
806	C₂³	—	4	16	no	—
807	C₂³	C₂×C₇×#41	1	4	yes	—
808	C₂³	C₇×2₋¹⁺⁴	1	4	yes	—
809	C₂³	C₂⁵×C₇	1	2	yes	—
810	C₂³	C₂⁵×C₇	1	4	yes	—
811	C₂³	C₂⁵×C₇	1	2	yes	—
812	C₂³	C₂⁵×C₇	1	2	yes	—
813	C₂³	C₂⁵×C₇	1	1	yes	characteristic
814	Q₈	—	2	16	no	—
815	Q₈	—	2	16	no	—
816	Q₈	—	2	8	no	—
817	Q₈	—	4	16	no	—
818	D₄	—	2	16	no	—
819	D₄	—	2	16	no	—
820	D₄	—	2	8	no	—
821	D₄	—	4	8	no	—
822	C₂×C₄	—	2	8	no	—
823	C₂×C₄	—	2	2	no	—
824	C₂×C₄	—	2	2	no	—
825	C₂×C₄	—	2	4	no	—
826	C₂×C₄	—	2	16	no	—
827	C₂×C₄	—	2	8	no	—
828	C₂×C₄	—	2	16	no	—
829	C₂×C₄	—	2	4	no	—
830	C₂×C₄	—	2	4	no	—
831	C₂×C₄	—	2	4	no	—
832	C₂×C₄	—	2	4	no	—
833	C₂×C₄	—	2	8	no	—
834	C₂×C₄	—	2	4	no	—
835	C₂×C₄	—	2	4	no	—
836	C₂×C₄	—	2	8	no	—
837	C₂×C₄	—	2	8	no	—
838	C₂×C₄	—	2	8	no	—
839	C₂×C₄	—	2	8	no	—
840	C₂×C₄	—	2	16	no	—
841	C₂×C₄	—	4	16	no	—
842	C₂×C₄	—	4	8	no	—
843	C₂×C₄	—	4	8	no	—
844	C₂×C₄	C₂×C₇×#41	1	4	yes	—
845	C₂×C₄	C₂×C₇×#41	1	4	yes	—
846	C₂×C₄	C₂×C₇×#41	1	16	yes	—
847	C₂×C₄	C₂⁵×C₇	1	4	yes	—
848	C₂×C₄	C₂⁵×C₇	1	2	yes	—
849	C₂×C₄	C₂⁵×C₇	1	4	yes	—
850	C₂×C₄	C₂⁵×C₇	1	4	yes	—
851	C₂×C₄	C₂⁵×C₇	1	4	yes	—
852	C₂×C₄	C₂⁵×C₇	1	4	yes	—
853	C₂×C₄	C₂⁵×C₇	1	8	yes	—
854	C₂×C₄	C₂⁵×C₇	1	4	yes	—
855	C₂×C₄	C₂⁵×C₇	1	4	yes	—
856	C₂×C₄	C₂⁵×C₇	1	8	yes	—
857	C₂×C₄	C₂⁵×C₇	1	2	yes	—
858	C₂×C₄	C₂⁵×C₇	1	2	yes	—
859	C₂×C₄	C₂⁵×C₇	1	2	yes	—
860	C₇	C₂×#3495	1	1	yes	characteristic, direct product factor, Sylow
861	C₂²	—	2	2	no	—
862	C₂²	—	2	2	no	—
863	C₂²	—	2	2	no	—
864	C₂²	—	2	2	no	—
865	C₂²	—	2	8	no	—
866	C₂²	—	2	8	no	—
867	C₂²	—	2	2	no	—
868	C₂²	—	2	4	no	—
869	C₂²	—	2	4	no	—
870	C₂²	—	2	2	no	—
871	C₂²	—	2	4	no	—
872	C₂²	—	2	2	no	—
873	C₂²	—	4	16	no	—
874	C₂²	—	4	4	no	—
875	C₂²	—	4	8	no	—
876	C₂²	C₂²×C₇×#41	1	4	yes	—
877	C₂²	C₂²×C₇×#41	1	2	yes	—
878	C₂²	C₂×C₇×2₋¹⁺⁴	1	4	yes	—
879	C₂²	C₂×C₇×2₋¹⁺⁴	1	2	yes	—
880	C₂²	C₇×#585	1	2	yes	—
881	C₂²	C₂⁶×C₇	1	1	yes	characteristic
882	C₄	—	2	2	no	—
883	C₄	—	2	2	no	—
884	C₄	—	2	4	no	—
885	C₄	—	2	8	no	—
886	C₄	—	2	4	no	—
887	C₄	—	2	4	no	—
888	C₄	—	2	4	no	—
889	C₄	—	2	4	no	—
890	C₄	—	2	8	no	—
891	C₄	—	2	4	no	—
892	C₄	—	2	4	no	—
893	C₄	C₂²×C₇×#41	1	4	yes	—
894	C₄	C₂²×C₇×#41	1	4	yes	—
895	C₂	—	2	4	no	—
896	C₂	—	2	4	no	—
897	C₂	—	4	2	no	—
898	C₂	—	4	4	no	—
899	C₂	C₇×#3495	1	4	yes	direct product factor
900	C₂	C₂³×C₇×#41	1	1	yes	characteristic
901	C₂	C₂²×C₇×2₋¹⁺⁴	1	1	yes	characteristic
902	C₂	C₂×C₇×#585	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₇	C₂⁵
commutator, Frattini, cosocle	C₂²	C₂⁶×C₇
prime radical	C₂×C₇×#525	C₂
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₇ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₇×#3495	C₂	direct (N × H)
2. C₂×C₇×#556	C₂	semidirect
3. C₂×C₇×#554	C₂	semidirect
4. C₂×C₇×#552	C₂	semidirect
5. C₂×C₇×#552	C₂	semidirect
6. C₂×C₇×#552	C₂	semidirect
7. C₂×C₇×#551	C₂	semidirect
8. C₂×C₇×#544	C₂	semidirect
9. C₂×C₇×#542	C₂	semidirect
10. C₂×C₇×#541	C₂	semidirect
11. C₂×C₇×#536	C₂	semidirect
12. C₂×C₇×#533	C₂	semidirect
13. C₂×C₇×#529	C₂	semidirect
15. C₂²×C₇×C₂²⋊Q₈	C₂	semidirect
16. C₂×C₇×#520	C₂	semidirect
17. C₂×C₇×#519	C₂	semidirect
18. C₂²×C₇×#117	C₂	semidirect
22. C₇×#556	C₂²	semidirect
23. C₇×#554	C₂²	semidirect
24. C₇×#552	C₂²	semidirect
25. C₇×#552	C₂²	semidirect
26. C₇×#552	C₂²	semidirect
27. C₇×#551	C₂²	semidirect
28. C₇×#544	C₂²	semidirect
29. C₇×#542	C₂²	semidirect
30. C₇×#541	C₂²	semidirect
31. C₇×#536	C₂²	semidirect
32. C₇×#533	C₂²	semidirect
33. C₂×C₇×C₄⋊Q₈	C₂²	semidirect
34. C₂×C₇×C₄⋊Q₈	C₂²	semidirect
35. C₂×C₇×C₄⋊Q₈	C₂²	semidirect
36. C₇×#529	C₂²	semidirect
39. C₂×C₇×#126	C₂²	semidirect
40. C₂×C₇×#126	C₂²	semidirect
41. C₂×C₇×#125	C₂²	semidirect
42. C₂×C₇×#125	C₂²	semidirect
43. C₂×C₇×#125	C₂²	semidirect
44. C₂×C₇×#125	C₂²	semidirect
45. C₂×C₇×#125	C₂²	semidirect
47. C₂×C₇×#124	C₂²	semidirect
61. C₂×C₇×C₂²⋊Q₈	C₂²	semidirect
62. C₂×C₇×C₂²⋊Q₈	C₂²	semidirect
63. C₂×C₇×C₂²⋊Q₈	C₂²	semidirect
64. C₂×C₇×C₂²⋊Q₈	C₂²	semidirect
68. C₇×#520	C₂²	semidirect
69. C₇×#519	C₂²	semidirect
70. C₂×C₄×C₇×Q₈	C₂²	semidirect
71. C₂×C₄×C₇×Q₈	C₂²	semidirect
72. C₂×C₄×C₇×Q₈	C₂²	semidirect
73. C₂×C₄×C₇×Q₈	C₂²	semidirect
74. C₂×C₄×C₇×Q₈	C₂²	semidirect
75. C₂×C₄×C₇×Q₈	C₂²	semidirect
80. C₂×C₄×C₇×D₄	C₂²	semidirect
90. C₂×C₇×#117	C₂²	semidirect
91. C₂×C₇×#117	C₂²	semidirect
92. C₂×C₇×#117	C₂²	semidirect
97. C₂²×C₇×C₄⋊C₄	C₂²	semidirect
101. C₂×#3495	C₇	direct (N × H)
129. C₇×C₄⋊Q₈	C₂³	semidirect
130. C₇×C₄⋊Q₈	C₂³	semidirect
131. C₇×C₄⋊Q₈	C₂³	semidirect
134. C₇×#126	C₂³	semidirect
135. C₇×#126	C₂³	semidirect
136. C₇×#125	C₂³	semidirect
137. C₇×#125	C₂³	semidirect
138. C₇×#125	C₂³	semidirect
139. C₇×#125	C₂³	semidirect
140. C₇×#125	C₂³	semidirect
142. C₇×#124	C₂³	semidirect
155. C₇×C₂²⋊Q₈	C₂³	semidirect
156. C₇×C₂²⋊Q₈	C₂³	semidirect
157. C₇×C₂²⋊Q₈	C₂³	semidirect
161. C₄×C₇×Q₈	C₂³	semidirect
162. C₄×C₇×Q₈	C₂³	semidirect
163. C₄×C₇×Q₈	C₂³	semidirect
164. C₄×C₇×Q₈	C₂³	semidirect
165. C₄×C₇×Q₈	C₂³	semidirect
166. C₄×C₇×Q₈	C₂³	semidirect
171. C₄×C₇×D₄	C₂³	semidirect
181. C₇×#117	C₂³	semidirect
182. C₇×#117	C₂³	semidirect
209. C₂×C₇×C₄⋊C₄	C₂³	semidirect
235. #3495	C₂×C₇	direct (N × H)
236. C₂×#556	C₂×C₇	semidirect
237. C₂×#554	C₂×C₇	semidirect
238. C₂×#552	C₂×C₇	semidirect
239. C₂×#552	C₂×C₇	semidirect
240. C₂×#552	C₂×C₇	semidirect
241. C₂×#551	C₂×C₇	semidirect
242. C₂×#544	C₂×C₇	semidirect
243. C₂×#542	C₂×C₇	semidirect
244. C₂×#541	C₂×C₇	semidirect
245. C₂×#536	C₂×C₇	semidirect
246. C₂×#533	C₂×C₇	semidirect
247. C₂×#529	C₂×C₇	semidirect
249. C₂²×C₂²⋊Q₈	C₂×C₇	semidirect
250. C₂×#520	C₂×C₇	semidirect
251. C₂×#519	C₂×C₇	semidirect
252. C₂²×#117	C₂×C₇	semidirect
364. #556	C₂²×C₇	semidirect
365. #554	C₂²×C₇	semidirect
366. #552	C₂²×C₇	semidirect
367. #552	C₂²×C₇	semidirect
368. #552	C₂²×C₇	semidirect
369. #551	C₂²×C₇	semidirect
370. #544	C₂²×C₇	semidirect
371. #542	C₂²×C₇	semidirect
372. #541	C₂²×C₇	semidirect
373. #536	C₂²×C₇	semidirect
374. #533	C₂²×C₇	semidirect
375. C₂×C₄⋊Q₈	C₂²×C₇	semidirect
376. C₂×C₄⋊Q₈	C₂²×C₇	semidirect
377. C₂×C₄⋊Q₈	C₂²×C₇	semidirect
378. #529	C₂²×C₇	semidirect
381. C₂×#126	C₂²×C₇	semidirect
382. C₂×#126	C₂²×C₇	semidirect
383. C₂×#125	C₂²×C₇	semidirect
384. C₂×#125	C₂²×C₇	semidirect
385. C₂×#125	C₂²×C₇	semidirect
386. C₂×#125	C₂²×C₇	semidirect
387. C₂×#125	C₂²×C₇	semidirect
389. C₂×#124	C₂²×C₇	semidirect
403. C₂×C₂²⋊Q₈	C₂²×C₇	semidirect
404. C₂×C₂²⋊Q₈	C₂²×C₇	semidirect
405. C₂×C₂²⋊Q₈	C₂²×C₇	semidirect
406. C₂×C₂²⋊Q₈	C₂²×C₇	semidirect
410. #520	C₂²×C₇	semidirect
411. #519	C₂²×C₇	semidirect
412. C₂×C₄×Q₈	C₂²×C₇	semidirect
413. C₂×C₄×Q₈	C₂²×C₇	semidirect
414. C₂×C₄×Q₈	C₂²×C₇	semidirect
415. C₂×C₄×Q₈	C₂²×C₇	semidirect
416. C₂×C₄×Q₈	C₂²×C₇	semidirect
417. C₂×C₄×Q₈	C₂²×C₇	semidirect
422. C₂×C₄×D₄	C₂²×C₇	semidirect
432. C₂×#117	C₂²×C₇	semidirect
433. C₂×#117	C₂²×C₇	semidirect
434. C₂×#117	C₂²×C₇	semidirect
439. C₂²×C₄⋊C₄	C₂²×C₇	semidirect
537. C₄⋊Q₈	C₂³×C₇	semidirect
538. C₄⋊Q₈	C₂³×C₇	semidirect
539. C₄⋊Q₈	C₂³×C₇	semidirect
542. #126	C₂³×C₇	semidirect
543. #126	C₂³×C₇	semidirect
544. #125	C₂³×C₇	semidirect
545. #125	C₂³×C₇	semidirect
546. #125	C₂³×C₇	semidirect
547. #125	C₂³×C₇	semidirect
548. #125	C₂³×C₇	semidirect
550. #124	C₂³×C₇	semidirect
563. C₂²⋊Q₈	C₂³×C₇	semidirect
564. C₂²⋊Q₈	C₂³×C₇	semidirect
565. C₂²⋊Q₈	C₂³×C₇	semidirect
569. C₄×Q₈	C₂³×C₇	semidirect
570. C₄×Q₈	C₂³×C₇	semidirect
571. C₄×Q₈	C₂³×C₇	semidirect
572. C₄×Q₈	C₂³×C₇	semidirect
573. C₄×Q₈	C₂³×C₇	semidirect
574. C₄×Q₈	C₂³×C₇	semidirect
579. C₄×D₄	C₂³×C₇	semidirect
589. #117	C₂³×C₇	semidirect
590. #117	C₂³×C₇	semidirect
617. C₂×C₄⋊C₄	C₂³×C₇	semidirect
789. C₂×C₇	#3495	direct (N × H)
860. C₇	C₂×#3495	direct (N × H)
899. C₂	C₇×#3495	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×#3495	2
C₂×C₇×#556	2
C₂×C₇×#554	2
C₂×C₇×#552	2
C₂×C₇×#551	2
C₂×C₇×#544	2
C₂×C₇×#542	2
C₂×C₇×#541	2
C₂×C₇×#536	2
C₂×C₇×#533	2
C₂×C₇×#529	2
C₂×C₇×#525	2
C₂²×C₇×C₂²⋊Q₈	2
C₂×C₇×#520	2
C₂×C₇×#519	2
C₂²×C₇×#117	2
C₂×#3495	7

Subgroups — C2×C7×#3495 #13240019

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₇×#3495 #13240019