Subgroups — C₂×C₇×#3555 #13239967

Order 1792.

6446 conjugacy classes of subgroups.

The subgroup lattice has 828 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×#3555	C₂	1	32	yes	maximal, direct product factor
2	C₂×C₇×#563	C₂	1	4	yes	maximal, complemented
3	C₂×C₇×Q₈²	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₇×#557	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₇×#557	C₂	1	2	yes	maximal, complemented
6	C₂×C₇×#556	C₂	1	2	yes	maximal, complemented
7	C₂×C₇×#556	C₂	1	2	yes	maximal, complemented
8	C₂×C₇×#556	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×C₇×#554	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×C₇×#552	C₂	1	2	yes	maximal, complemented
11	C₂×C₇×#544	C₂	1	2	yes	maximal, complemented
12	C₂×C₇×#542	C₂	1	2	yes	maximal
13	C₂×C₇×#541	C₂	1	2	yes	maximal, complemented
14	C₂×C₇×#541	C₂	1	2	yes	maximal, complemented
15	C₂×C₇×#541	C₂	1	4	yes	maximal, complemented
16	C₂×C₇×#533	C₂	1	1	yes	maximal, characteristic, complemented
17	C₂×C₇×#533	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂×C₇×#529	C₂	1	1	yes	maximal, characteristic
19	C₇×#563	C₂²	1	64	yes	complemented
20	C₇×Q₈²	C₂²	1	16	yes	complemented
21	C₇×#557	C₂²	1	16	yes	complemented
22	C₇×#557	C₂²	1	32	yes	complemented
23	C₇×#556	C₂²	1	32	yes	complemented
24	C₇×#556	C₂²	1	32	yes	complemented
25	C₇×#556	C₂²	1	16	yes	complemented
26	C₇×#554	C₂²	1	16	yes	complemented
27	C₇×#552	C₂²	1	32	yes	complemented
28	C₇×#544	C₂²	1	32	yes	complemented
29	C₇×#542	C₂²	1	32	yes	—
30	C₇×#541	C₂²	1	32	yes	complemented
31	C₇×#541	C₂²	1	32	yes	complemented
32	C₇×#541	C₂²	1	64	yes	complemented
33	C₇×#533	C₂²	1	16	yes	complemented
34	C₇×#533	C₂²	1	16	yes	complemented
35	C₂×C₇×C₄⋊Q₈	C₂²	1	1	yes	characteristic
36	C₂×C₇×C₄⋊Q₈	C₂²	1	1	yes	characteristic
37	C₂×C₇×C₄⋊Q₈	C₂²	1	1	yes	characteristic
38	C₂×C₇×C₄⋊Q₈	C₂²	1	1	yes	characteristic
39	C₂×C₇×C₄⋊Q₈	C₂²	1	2	yes	—
40	C₂×C₇×C₄⋊Q₈	C₂²	1	4	yes	—
41	C₂×C₇×C₄⋊Q₈	C₂²	1	2	yes	—
42	C₂×C₇×C₄⋊Q₈	C₂²	1	2	yes	—
43	C₂×C₇×C₄⋊Q₈	C₂²	1	4	yes	—
44	C₇×#529	C₂²	1	16	yes	—
45	C₂×C₇×#126	C₂²	1	2	yes	—
46	C₂×C₇×#126	C₂²	1	4	yes	—
47	C₂×C₇×#126	C₂²	1	4	yes	—
48	C₂×C₇×#126	C₂²	1	4	yes	—
49	C₂×C₇×#126	C₂²	1	4	yes	—
50	C₂×C₇×#126	C₂²	1	4	yes	—
51	C₂×C₇×#126	C₂²	1	4	yes	—
52	C₂×C₇×#125	C₂²	1	1	yes	characteristic
53	C₂×C₇×#125	C₂²	1	2	yes	—
54	C₂×C₇×#125	C₂²	1	2	yes	—
55	C₂×C₇×#125	C₂²	1	4	yes	—
56	C₂×C₇×#125	C₂²	1	4	yes	—
57	C₂×C₇×#125	C₂²	1	4	yes	—
58	C₂×C₇×#125	C₂²	1	2	yes	—
59	C₂×C₇×#125	C₂²	1	4	yes	—
60	C₂×C₇×#125	C₂²	1	4	yes	—
61	C₂×C₇×#125	C₂²	1	2	yes	—
62	C₂×C₇×#124	C₂²	1	1	yes	characteristic
63	C₂×C₇×#124	C₂²	1	2	yes	—
64	C₂×C₇×#124	C₂²	1	4	yes	—
65	C₂×C₇×#123	C₂²	1	2	yes	—
66	C₂×C₇×#123	C₂²	1	4	yes	—
67	C₂×C₇×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
68	C₂×C₇×C₂²⋊Q₈	C₂²	1	2	yes	—
69	C₂×C₇×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
70	C₂×C₇×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
71	C₂×C₇×C₂²⋊Q₈	C₂²	1	2	yes	—
72	C₂×C₇×C₂²⋊Q₈	C₂²	1	2	yes	—
73	C₂×C₇×C₂²⋊Q₈	C₂²	1	4	yes	—
74	C₂×C₇×C₂²⋊Q₈	C₂²	1	2	yes	—
75	C₂×C₇×C₂²⋊Q₈	C₂²	1	2	yes	—
76	C₂×C₇×C₂²⋊Q₈	C₂²	1	4	yes	—
77	C₂×C₇×C₂²⋊Q₈	C₂²	1	4	yes	—
78	C₂×C₇×#121	C₂²	1	1	yes	characteristic
79	C₂×C₄×C₇×Q₈	C₂²	1	1	yes	characteristic
80	C₂×C₄×C₇×Q₈	C₂²	1	2	yes	—
81	C₂×C₄×C₇×Q₈	C₂²	1	1	yes	characteristic
82	C₂×C₄×C₇×Q₈	C₂²	1	2	yes	—
83	C₂×C₄×C₇×Q₈	C₂²	1	2	yes	—
84	C₂×C₄×C₇×Q₈	C₂²	1	1	yes	characteristic
85	C₂×C₄×C₇×Q₈	C₂²	1	2	yes	—
86	C₂×C₄×C₇×Q₈	C₂²	1	4	yes	—
87	C₂×C₄×C₇×Q₈	C₂²	1	2	yes	—
88	C₂×C₄×C₇×Q₈	C₂²	1	2	yes	—
89	C₂×C₄×C₇×Q₈	C₂²	1	2	yes	—
90	C₂×C₄×C₇×Q₈	C₂²	1	2	yes	—
91	C₂×C₄×C₇×D₄	C₂²	1	2	yes	—
92	C₂×C₄×C₇×D₄	C₂²	1	1	yes	characteristic
93	C₂×C₄×C₇×D₄	C₂²	1	2	yes	—
94	C₂×C₇×#117	C₂²	1	2	yes	—
95	C₂×C₇×#117	C₂²	1	2	yes	—
96	C₂×C₇×#117	C₂²	1	2	yes	—
97	C₂×C₇×#117	C₂²	1	4	yes	—
98	C₂×C₇×#117	C₂²	1	2	yes	—
99	C₂²×C₇×C₄⋊C₄	C₂²	1	2	yes	—
100	C₂²×C₄²×C₇	C₂²	1	1	yes	characteristic
101	C₂×#3555	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
102	C₂²×C₇×Q₈	C₂³	1	1	yes	characteristic
103	C₂²×C₇×Q₈	C₂³	1	1	yes	characteristic
104	C₂²×C₇×Q₈	C₂³	1	1	yes	characteristic
105	C₂²×C₇×Q₈	C₂³	1	2	yes	—
106	C₂²×C₇×Q₈	C₂³	1	2	yes	—
107	C₂²×C₇×Q₈	C₂³	1	2	yes	—
108	C₂²×C₇×Q₈	C₂³	1	4	yes	—
109	C₂²×C₇×D₄	C₂³	1	1	yes	characteristic
110	C₂²×C₇×D₄	C₂³	1	2	yes	—
111	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
112	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
113	C₂³×C₄×C₇	C₂³	1	2	yes	—
114	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
115	C₂³×C₄×C₇	C₂³	1	4	yes	—
116	C₇×C₄⋊Q₈	C₂³	1	8	yes	—
117	C₇×C₄⋊Q₈	C₂³	1	8	yes	—
118	C₇×C₄⋊Q₈	C₂³	1	8	yes	—
119	C₇×C₄⋊Q₈	C₂³	1	8	yes	—
120	C₇×C₄⋊Q₈	C₂³	1	16	yes	—
121	C₇×C₄⋊Q₈	C₂³	1	32	yes	—
122	C₇×C₄⋊Q₈	C₂³	1	16	yes	—
123	C₇×C₄⋊Q₈	C₂³	1	16	yes	—
124	C₇×C₄⋊Q₈	C₂³	1	32	yes	—
125	C₇×#126	C₂³	1	16	yes	—
126	C₇×#126	C₂³	1	32	yes	—
127	C₇×#126	C₂³	1	32	yes	—
128	C₇×#126	C₂³	1	32	yes	—
129	C₇×#126	C₂³	1	32	yes	—
130	C₇×#126	C₂³	1	32	yes	—
131	C₇×#126	C₂³	1	32	yes	—
132	C₇×#125	C₂³	1	8	yes	—
133	C₇×#125	C₂³	1	16	yes	—
134	C₇×#125	C₂³	1	16	yes	—
135	C₇×#125	C₂³	1	32	yes	—
136	C₇×#125	C₂³	1	32	yes	—
137	C₇×#125	C₂³	1	32	yes	—
138	C₇×#125	C₂³	1	16	yes	—
139	C₇×#125	C₂³	1	32	yes	—
140	C₇×#125	C₂³	1	32	yes	—
141	C₇×#125	C₂³	1	16	yes	—
142	C₇×#124	C₂³	1	8	yes	—
143	C₇×#124	C₂³	1	16	yes	—
144	C₇×#124	C₂³	1	32	yes	—
145	C₇×#123	C₂³	1	16	yes	—
146	C₇×#123	C₂³	1	32	yes	—
147	C₇×C₂²⋊Q₈	C₂³	1	8	yes	—
148	C₇×C₂²⋊Q₈	C₂³	1	16	yes	—
149	C₇×C₂²⋊Q₈	C₂³	1	8	yes	—
150	C₇×C₂²⋊Q₈	C₂³	1	8	yes	—
151	C₇×C₂²⋊Q₈	C₂³	1	16	yes	—
152	C₇×C₂²⋊Q₈	C₂³	1	16	yes	—
153	C₇×C₂²⋊Q₈	C₂³	1	32	yes	—
154	C₇×C₂²⋊Q₈	C₂³	1	16	yes	—
155	C₇×C₂²⋊Q₈	C₂³	1	16	yes	—
156	C₇×C₂²⋊Q₈	C₂³	1	32	yes	—
157	C₇×C₂²⋊Q₈	C₂³	1	32	yes	—
158	C₇×#121	C₂³	1	8	yes	—
159	C₄×C₇×Q₈	C₂³	1	8	yes	—
160	C₄×C₇×Q₈	C₂³	1	16	yes	—
161	C₄×C₇×Q₈	C₂³	1	8	yes	—
162	C₄×C₇×Q₈	C₂³	1	16	yes	—
163	C₄×C₇×Q₈	C₂³	1	16	yes	—
164	C₄×C₇×Q₈	C₂³	1	8	yes	—
165	C₄×C₇×Q₈	C₂³	1	16	yes	—
166	C₄×C₇×Q₈	C₂³	1	32	yes	—
167	C₄×C₇×Q₈	C₂³	1	16	yes	—
168	C₄×C₇×Q₈	C₂³	1	16	yes	—
169	C₄×C₇×Q₈	C₂³	1	16	yes	—
170	C₄×C₇×Q₈	C₂³	1	16	yes	—
171	C₄×C₇×D₄	C₂³	1	16	yes	—
172	C₄×C₇×D₄	C₂³	1	8	yes	—
173	C₄×C₇×D₄	C₂³	1	16	yes	—
174	C₇×#117	C₂³	1	16	yes	—
175	C₇×#117	C₂³	1	16	yes	—
176	C₇×#117	C₂³	1	16	yes	—
177	C₇×#117	C₂³	1	32	yes	—
178	C₇×#117	C₂³	1	16	yes	—
179	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
180	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
181	C₂×C₇×C₄⋊C₄	C₂³	1	4	yes	—
182	C₂×C₇×C₄⋊C₄	C₂³	1	16	yes	—
183	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
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	2	yes	—
188	C₂×C₇×C₄⋊C₄	C₂³	1	4	yes	—
189	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
190	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
191	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
192	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
193	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
194	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
195	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
196	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
197	C₂×C₇×C₄⋊C₄	C₂³	1	4	yes	—
198	C₂×C₇×C₄⋊C₄	C₂³	1	4	yes	—
199	C₂×C₇×C₄⋊C₄	C₂³	1	4	yes	—
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	2	yes	—
203	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
204	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
205	C₂×C₇×C₄⋊C₄	C₂³	1	4	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×C₂²⋊C₄	C₂³	1	2	yes	—
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	4	yes	—
214	C₂×C₇×C₂²⋊C₄	C₂³	1	2	yes	—
215	C₂×C₇×C₂²⋊C₄	C₂³	1	4	yes	—
216	C₂×C₇×C₂²⋊C₄	C₂³	1	4	yes	—
217	C₂×C₇×C₂²⋊C₄	C₂³	1	2	yes	—
218	C₂×C₇×C₂²⋊C₄	C₂³	1	4	yes	—
219	C₂×C₇×C₂²⋊C₄	C₂³	1	2	yes	—
220	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
221	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
222	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
223	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
224	C₂×C₄²×C₇	C₂³	1	8	yes	—
225	C₂×C₄²×C₇	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	4	yes	—
230	C₂×C₄²×C₇	C₂³	1	4	yes	—
231	C₂×C₄²×C₇	C₂³	1	4	yes	—
232	#3555	C₂×C₇	1	32	yes	direct product factor
233	C₂×#563	C₂×C₇	1	4	yes	complemented
234	C₂×Q₈²	C₂×C₇	1	1	yes	characteristic, complemented
235	C₂×#557	C₂×C₇	1	1	yes	characteristic, complemented
236	C₂×#557	C₂×C₇	1	2	yes	complemented
237	C₂×#556	C₂×C₇	1	2	yes	complemented
238	C₂×#556	C₂×C₇	1	2	yes	complemented
239	C₂×#556	C₂×C₇	1	1	yes	characteristic, complemented
240	C₂×#554	C₂×C₇	1	1	yes	characteristic, complemented
241	C₂×#552	C₂×C₇	1	2	yes	complemented
242	C₂×#544	C₂×C₇	1	2	yes	complemented
243	C₂×#542	C₂×C₇	1	2	yes	—
244	C₂×#541	C₂×C₇	1	2	yes	complemented
245	C₂×#541	C₂×C₇	1	2	yes	complemented
246	C₂×#541	C₂×C₇	1	4	yes	complemented
247	C₂×#533	C₂×C₇	1	1	yes	characteristic, complemented
248	C₂×#533	C₂×C₇	1	1	yes	characteristic, complemented
249	C₂×#529	C₂×C₇	1	1	yes	characteristic
250	C₂⁴×C₇	C₂⁴	1	1	yes	characteristic
251	C₂⁴×C₇	C₂⁴	1	2	yes	—
252	C₂×C₇×Q₈	—	2	4	no	—
253	C₂×C₇×Q₈	—	2	4	no	—
254	C₂×C₇×Q₈	—	2	4	no	—
255	C₂×C₇×Q₈	—	2	8	no	—
256	C₂×C₇×Q₈	—	4	4	no	—
257	C₂×C₇×Q₈	—	4	4	no	—
258	C₂×C₇×Q₈	—	4	8	no	—
259	C₂×C₇×Q₈	C₂⁴	1	4	yes	—
260	C₂×C₇×Q₈	C₂⁴	1	4	yes	—
261	C₂×C₇×Q₈	C₂⁴	1	4	yes	—
262	C₂×C₇×Q₈	C₂⁴	1	8	yes	—
263	C₂×C₇×Q₈	C₂⁴	1	8	yes	—
264	C₂×C₇×Q₈	C₂⁴	1	8	yes	—
265	C₂×C₇×Q₈	C₂⁴	1	16	yes	—
266	C₂×C₇×D₄	—	2	4	no	—
267	C₂×C₇×D₄	—	4	4	no	—
268	C₂×C₇×D₄	C₂⁴	1	4	yes	—
269	C₂×C₇×D₄	C₂⁴	1	8	yes	—
270	C₂²×C₄×C₇	—	2	4	no	—
271	C₂²×C₄×C₇	—	2	8	no	—
272	C₂²×C₄×C₇	—	2	4	no	—
273	C₂²×C₄×C₇	—	4	8	no	—
274	C₂²×C₄×C₇	—	4	2	no	—
275	C₂²×C₄×C₇	C₂⁴	1	4	yes	—
276	C₂²×C₄×C₇	C₂⁴	1	4	yes	—
277	C₂²×C₄×C₇	C₂⁴	1	8	yes	—
278	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
279	C₂²×C₄×C₇	C₂⁴	1	4	yes	—
280	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
281	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
282	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
283	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
284	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
285	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
286	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
287	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
288	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
289	C₂²×C₄×C₇	C₂⁴	1	4	yes	—
290	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
291	C₂²×C₄×C₇	C₂⁴	1	4	yes	—
292	C₂²×C₄×C₇	C₂⁴	1	16	yes	—
293	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
294	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
295	C₇×C₄⋊C₄	C₂⁴	1	4	yes	—
296	C₇×C₄⋊C₄	C₂⁴	1	8	yes	—
297	C₇×C₄⋊C₄	C₂⁴	1	16	yes	—
298	C₇×C₄⋊C₄	C₂⁴	1	8	yes	—
299	C₇×C₄⋊C₄	C₂⁴	1	8	yes	—
300	C₇×C₄⋊C₄	C₂⁴	1	4	yes	—
301	C₇×C₄⋊C₄	C₂⁴	1	8	yes	—
302	C₇×C₄⋊C₄	C₂⁴	1	8	yes	—
303	C₇×C₄⋊C₄	C₂⁴	1	16	yes	—
304	C₇×C₄⋊C₄	C₂⁴	1	8	yes	—
305	C₇×C₄⋊C₄	C₂⁴	1	8	yes	—
306	C₇×C₄⋊C₄	C₂⁴	1	4	yes	—
307	C₇×C₄⋊C₄	C₂⁴	1	8	yes	—
308	C₇×C₄⋊C₄	C₂⁴	1	8	yes	—
309	C₇×C₄⋊C₄	C₂⁴	1	4	yes	—
310	C₇×C₄⋊C₄	C₂⁴	1	8	yes	—
311	C₇×C₄⋊C₄	C₂⁴	1	8	yes	—
312	C₇×C₄⋊C₄	C₂⁴	1	16	yes	—
313	C₇×C₄⋊C₄	C₂⁴	1	16	yes	—
314	C₇×C₄⋊C₄	C₂⁴	1	16	yes	—
315	C₇×C₄⋊C₄	C₂⁴	1	16	yes	—
316	C₇×C₄⋊C₄	C₂⁴	1	16	yes	—
317	C₇×C₄⋊C₄	C₂⁴	1	8	yes	—
318	C₇×C₄⋊C₄	C₂⁴	1	8	yes	—
319	C₇×C₄⋊C₄	C₂⁴	1	8	yes	—
320	C₇×C₄⋊C₄	C₂⁴	1	16	yes	—
321	C₇×C₄⋊C₄	C₂⁴	1	8	yes	—
322	C₇×C₄⋊C₄	C₂⁴	1	16	yes	—
323	C₇×C₄⋊C₄	C₂⁴	1	16	yes	—
324	C₇×C₂²⋊C₄	C₂⁴	1	8	yes	—
325	C₇×C₂²⋊C₄	C₂⁴	1	8	yes	—
326	C₇×C₂²⋊C₄	C₂⁴	1	8	yes	—
327	C₇×C₂²⋊C₄	C₂⁴	1	8	yes	—
328	C₇×C₂²⋊C₄	C₂⁴	1	16	yes	—
329	C₇×C₂²⋊C₄	C₂⁴	1	8	yes	—
330	C₇×C₂²⋊C₄	C₂⁴	1	16	yes	—
331	C₇×C₂²⋊C₄	C₂⁴	1	16	yes	—
332	C₇×C₂²⋊C₄	C₂⁴	1	8	yes	—
333	C₇×C₂²⋊C₄	C₂⁴	1	16	yes	—
334	C₇×C₂²⋊C₄	C₂⁴	1	8	yes	—
335	C₄²×C₇	C₂⁴	1	4	yes	—
336	C₄²×C₇	C₂⁴	1	4	yes	—
337	C₄²×C₇	C₂⁴	1	4	yes	—
338	C₄²×C₇	C₂⁴	1	4	yes	—
339	C₄²×C₇	C₂⁴	1	16	yes	—
340	C₄²×C₇	C₂⁴	1	8	yes	—
341	C₄²×C₇	C₂⁴	1	8	yes	—
342	C₄²×C₇	C₂⁴	1	8	yes	—
343	C₄²×C₇	C₂⁴	1	16	yes	—
344	C₄²×C₇	C₂⁴	1	16	yes	—
345	C₄²×C₇	C₂⁴	1	16	yes	—
346	#563	C₂²×C₇	1	64	yes	complemented
347	Q₈²	C₂²×C₇	1	16	yes	complemented
348	#557	C₂²×C₇	1	16	yes	complemented
349	#557	C₂²×C₇	1	32	yes	complemented
350	#556	C₂²×C₇	1	32	yes	complemented
351	#556	C₂²×C₇	1	32	yes	complemented
352	#556	C₂²×C₇	1	16	yes	complemented
353	#554	C₂²×C₇	1	16	yes	complemented
354	#552	C₂²×C₇	1	32	yes	complemented
355	#544	C₂²×C₇	1	32	yes	complemented
356	#542	C₂²×C₇	1	32	yes	—
357	#541	C₂²×C₇	1	32	yes	complemented
358	#541	C₂²×C₇	1	32	yes	complemented
359	#541	C₂²×C₇	1	64	yes	complemented
360	#533	C₂²×C₇	1	16	yes	complemented
361	#533	C₂²×C₇	1	16	yes	complemented
362	C₂×C₄⋊Q₈	C₂²×C₇	1	1	yes	characteristic
363	C₂×C₄⋊Q₈	C₂²×C₇	1	1	yes	characteristic
364	C₂×C₄⋊Q₈	C₂²×C₇	1	1	yes	characteristic
365	C₂×C₄⋊Q₈	C₂²×C₇	1	1	yes	characteristic
366	C₂×C₄⋊Q₈	C₂²×C₇	1	2	yes	—
367	C₂×C₄⋊Q₈	C₂²×C₇	1	4	yes	—
368	C₂×C₄⋊Q₈	C₂²×C₇	1	2	yes	—
369	C₂×C₄⋊Q₈	C₂²×C₇	1	2	yes	—
370	C₂×C₄⋊Q₈	C₂²×C₇	1	4	yes	—
371	#529	C₂²×C₇	1	16	yes	—
372	C₂×#126	C₂²×C₇	1	2	yes	—
373	C₂×#126	C₂²×C₇	1	4	yes	—
374	C₂×#126	C₂²×C₇	1	4	yes	—
375	C₂×#126	C₂²×C₇	1	4	yes	—
376	C₂×#126	C₂²×C₇	1	4	yes	—
377	C₂×#126	C₂²×C₇	1	4	yes	—
378	C₂×#126	C₂²×C₇	1	4	yes	—
379	C₂×#125	C₂²×C₇	1	1	yes	characteristic
380	C₂×#125	C₂²×C₇	1	2	yes	—
381	C₂×#125	C₂²×C₇	1	2	yes	—
382	C₂×#125	C₂²×C₇	1	4	yes	—
383	C₂×#125	C₂²×C₇	1	4	yes	—
384	C₂×#125	C₂²×C₇	1	4	yes	—
385	C₂×#125	C₂²×C₇	1	2	yes	—
386	C₂×#125	C₂²×C₇	1	4	yes	—
387	C₂×#125	C₂²×C₇	1	4	yes	—
388	C₂×#125	C₂²×C₇	1	2	yes	—
389	C₂×#124	C₂²×C₇	1	1	yes	characteristic
390	C₂×#124	C₂²×C₇	1	2	yes	—
391	C₂×#124	C₂²×C₇	1	4	yes	—
392	C₂×#123	C₂²×C₇	1	2	yes	—
393	C₂×#123	C₂²×C₇	1	4	yes	—
394	C₂×C₂²⋊Q₈	C₂²×C₇	1	1	yes	characteristic
395	C₂×C₂²⋊Q₈	C₂²×C₇	1	2	yes	—
396	C₂×C₂²⋊Q₈	C₂²×C₇	1	1	yes	characteristic
397	C₂×C₂²⋊Q₈	C₂²×C₇	1	1	yes	characteristic
398	C₂×C₂²⋊Q₈	C₂²×C₇	1	2	yes	—
399	C₂×C₂²⋊Q₈	C₂²×C₇	1	2	yes	—
400	C₂×C₂²⋊Q₈	C₂²×C₇	1	4	yes	—
401	C₂×C₂²⋊Q₈	C₂²×C₇	1	2	yes	—
402	C₂×C₂²⋊Q₈	C₂²×C₇	1	2	yes	—
403	C₂×C₂²⋊Q₈	C₂²×C₇	1	4	yes	—
404	C₂×C₂²⋊Q₈	C₂²×C₇	1	4	yes	—
405	C₂×#121	C₂²×C₇	1	1	yes	characteristic
406	C₂×C₄×Q₈	C₂²×C₇	1	1	yes	characteristic
407	C₂×C₄×Q₈	C₂²×C₇	1	2	yes	—
408	C₂×C₄×Q₈	C₂²×C₇	1	1	yes	characteristic
409	C₂×C₄×Q₈	C₂²×C₇	1	2	yes	—
410	C₂×C₄×Q₈	C₂²×C₇	1	2	yes	—
411	C₂×C₄×Q₈	C₂²×C₇	1	1	yes	characteristic
412	C₂×C₄×Q₈	C₂²×C₇	1	2	yes	—
413	C₂×C₄×Q₈	C₂²×C₇	1	4	yes	—
414	C₂×C₄×Q₈	C₂²×C₇	1	2	yes	—
415	C₂×C₄×Q₈	C₂²×C₇	1	2	yes	—
416	C₂×C₄×Q₈	C₂²×C₇	1	2	yes	—
417	C₂×C₄×Q₈	C₂²×C₇	1	2	yes	—
418	C₂×C₄×D₄	C₂²×C₇	1	2	yes	—
419	C₂×C₄×D₄	C₂²×C₇	1	1	yes	characteristic
420	C₂×C₄×D₄	C₂²×C₇	1	2	yes	—
421	C₂×#117	C₂²×C₇	1	2	yes	—
422	C₂×#117	C₂²×C₇	1	2	yes	—
423	C₂×#117	C₂²×C₇	1	2	yes	—
424	C₂×#117	C₂²×C₇	1	4	yes	—
425	C₂×#117	C₂²×C₇	1	2	yes	—
426	C₂²×C₄⋊C₄	C₂²×C₇	1	2	yes	—
427	C₂²×C₄²	C₂²×C₇	1	1	yes	characteristic
428	C₂³×C₇	—	2	2	no	—
429	C₂³×C₇	—	2	2	no	—
430	C₂³×C₇	—	2	4	no	—
431	C₂³×C₇	—	2	4	no	—
432	C₂³×C₇	—	2	4	no	—
433	C₂³×C₇	—	2	2	no	—
434	C₂³×C₇	C₂⁵	1	2	yes	—
435	C₂³×C₇	C₂⁵	1	4	yes	—
436	C₂³×C₇	C₂⁵	1	1	yes	characteristic
437	C₇×Q₈	—	2	8	no	—
438	C₇×Q₈	—	2	8	no	—
439	C₇×Q₈	—	2	8	no	—
440	C₇×Q₈	—	2	16	no	—
441	C₇×Q₈	—	4	8	no	—
442	C₇×Q₈	—	4	8	no	—
443	C₇×Q₈	—	4	16	no	—
444	C₇×D₄	—	2	8	no	—
445	C₇×D₄	—	4	8	no	—
446	C₂×C₄×C₇	—	2	2	no	—
447	C₂×C₄×C₇	—	2	4	no	—
448	C₂×C₄×C₇	—	2	2	no	—
449	C₂×C₄×C₇	—	2	4	no	—
450	C₂×C₄×C₇	—	2	4	no	—
451	C₂×C₄×C₇	—	2	8	no	—
452	C₂×C₄×C₇	—	2	4	no	—
453	C₂×C₄×C₇	—	2	4	no	—
454	C₂×C₄×C₇	—	2	8	no	—
455	C₂×C₄×C₇	—	2	2	no	—
456	C₂×C₄×C₇	—	2	2	no	—
457	C₂×C₄×C₇	—	2	4	no	—
458	C₂×C₄×C₇	—	2	4	no	—
459	C₂×C₄×C₇	—	2	8	no	—
460	C₂×C₄×C₇	—	2	16	no	—
461	C₂×C₄×C₇	—	2	8	no	—
462	C₂×C₄×C₇	—	4	16	no	—
463	C₂×C₄×C₇	—	4	4	no	—
464	C₂×C₄×C₇	2₋¹⁺⁴	1	4	yes	—
465	C₂×C₄×C₇	2₋¹⁺⁴	1	4	yes	—
466	C₂×C₄×C₇	C₂⁵	1	2	yes	—
467	C₂×C₄×C₇	C₂⁵	1	8	yes	—
468	C₂×C₄×C₇	C₂⁵	1	4	yes	—
469	C₂×C₄×C₇	C₂⁵	1	4	yes	—
470	C₂×C₄×C₇	C₂⁵	1	4	yes	—
471	C₂×C₄×C₇	C₂⁵	1	4	yes	—
472	C₂×C₄×C₇	C₂⁵	1	4	yes	—
473	C₂×C₄×C₇	C₂⁵	1	2	yes	—
474	C₂×C₄×C₇	C₂⁵	1	4	yes	—
475	C₂×C₄×C₇	C₂⁵	1	2	yes	—
476	C₂×C₄×C₇	C₂⁵	1	2	yes	—
477	C₂×C₄×C₇	C₂⁵	1	8	yes	—
478	C₂×C₄×C₇	C₂⁵	1	4	yes	—
479	C₂×C₄×C₇	C₂⁵	1	2	yes	—
480	C₂×C₄×C₇	C₂⁵	1	2	yes	—
481	C₂²×Q₈	C₂³×C₇	1	1	yes	characteristic
482	C₂²×Q₈	C₂³×C₇	1	1	yes	characteristic
483	C₂²×Q₈	C₂³×C₇	1	1	yes	characteristic
484	C₂²×Q₈	C₂³×C₇	1	2	yes	—
485	C₂²×Q₈	C₂³×C₇	1	2	yes	—
486	C₂²×Q₈	C₂³×C₇	1	2	yes	—
487	C₂²×Q₈	C₂³×C₇	1	4	yes	—
488	C₂²×D₄	C₂³×C₇	1	1	yes	characteristic
489	C₂²×D₄	C₂³×C₇	1	2	yes	—
490	C₂³×C₄	C₂³×C₇	1	2	yes	—
491	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
492	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
493	C₂³×C₄	C₂³×C₇	1	4	yes	—
494	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
495	C₄⋊Q₈	C₂³×C₇	1	8	yes	—
496	C₄⋊Q₈	C₂³×C₇	1	8	yes	—
497	C₄⋊Q₈	C₂³×C₇	1	8	yes	—
498	C₄⋊Q₈	C₂³×C₇	1	8	yes	—
499	C₄⋊Q₈	C₂³×C₇	1	16	yes	—
500	C₄⋊Q₈	C₂³×C₇	1	32	yes	—
501	C₄⋊Q₈	C₂³×C₇	1	16	yes	—
502	C₄⋊Q₈	C₂³×C₇	1	16	yes	—
503	C₄⋊Q₈	C₂³×C₇	1	32	yes	—
504	#126	C₂³×C₇	1	16	yes	—
505	#126	C₂³×C₇	1	32	yes	—
506	#126	C₂³×C₇	1	32	yes	—
507	#126	C₂³×C₇	1	32	yes	—
508	#126	C₂³×C₇	1	32	yes	—
509	#126	C₂³×C₇	1	32	yes	—
510	#126	C₂³×C₇	1	32	yes	—
511	#125	C₂³×C₇	1	8	yes	—
512	#125	C₂³×C₇	1	16	yes	—
513	#125	C₂³×C₇	1	16	yes	—
514	#125	C₂³×C₇	1	32	yes	—
515	#125	C₂³×C₇	1	32	yes	—
516	#125	C₂³×C₇	1	32	yes	—
517	#125	C₂³×C₇	1	16	yes	—
518	#125	C₂³×C₇	1	32	yes	—
519	#125	C₂³×C₇	1	32	yes	—
520	#125	C₂³×C₇	1	16	yes	—
521	#124	C₂³×C₇	1	8	yes	—
522	#124	C₂³×C₇	1	16	yes	—
523	#124	C₂³×C₇	1	32	yes	—
524	#123	C₂³×C₇	1	16	yes	—
525	#123	C₂³×C₇	1	32	yes	—
526	C₂²⋊Q₈	C₂³×C₇	1	8	yes	—
527	C₂²⋊Q₈	C₂³×C₇	1	16	yes	—
528	C₂²⋊Q₈	C₂³×C₇	1	8	yes	—
529	C₂²⋊Q₈	C₂³×C₇	1	8	yes	—
530	C₂²⋊Q₈	C₂³×C₇	1	16	yes	—
531	C₂²⋊Q₈	C₂³×C₇	1	16	yes	—
532	C₂²⋊Q₈	C₂³×C₇	1	32	yes	—
533	C₂²⋊Q₈	C₂³×C₇	1	16	yes	—
534	C₂²⋊Q₈	C₂³×C₇	1	16	yes	—
535	C₂²⋊Q₈	C₂³×C₇	1	32	yes	—
536	C₂²⋊Q₈	C₂³×C₇	1	32	yes	—
537	#121	C₂³×C₇	1	8	yes	—
538	C₄×Q₈	C₂³×C₇	1	8	yes	—
539	C₄×Q₈	C₂³×C₇	1	16	yes	—
540	C₄×Q₈	C₂³×C₇	1	8	yes	—
541	C₄×Q₈	C₂³×C₇	1	16	yes	—
542	C₄×Q₈	C₂³×C₇	1	16	yes	—
543	C₄×Q₈	C₂³×C₇	1	8	yes	—
544	C₄×Q₈	C₂³×C₇	1	16	yes	—
545	C₄×Q₈	C₂³×C₇	1	32	yes	—
546	C₄×Q₈	C₂³×C₇	1	16	yes	—
547	C₄×Q₈	C₂³×C₇	1	16	yes	—
548	C₄×Q₈	C₂³×C₇	1	16	yes	—
549	C₄×Q₈	C₂³×C₇	1	16	yes	—
550	C₄×D₄	C₂³×C₇	1	16	yes	—
551	C₄×D₄	C₂³×C₇	1	8	yes	—
552	C₄×D₄	C₂³×C₇	1	16	yes	—
553	#117	C₂³×C₇	1	16	yes	—
554	#117	C₂³×C₇	1	16	yes	—
555	#117	C₂³×C₇	1	16	yes	—
556	#117	C₂³×C₇	1	32	yes	—
557	#117	C₂³×C₇	1	16	yes	—
558	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
559	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
560	C₂×C₄⋊C₄	C₂³×C₇	1	4	yes	—
561	C₂×C₄⋊C₄	C₂³×C₇	1	16	yes	—
562	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
563	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
564	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
565	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
566	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
567	C₂×C₄⋊C₄	C₂³×C₇	1	4	yes	—
568	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
569	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
570	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
571	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
572	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
573	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
574	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
575	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
576	C₂×C₄⋊C₄	C₂³×C₇	1	4	yes	—
577	C₂×C₄⋊C₄	C₂³×C₇	1	4	yes	—
578	C₂×C₄⋊C₄	C₂³×C₇	1	4	yes	—
579	C₂×C₄⋊C₄	C₂³×C₇	1	4	yes	—
580	C₂×C₄⋊C₄	C₂³×C₇	1	4	yes	—
581	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
582	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
583	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
584	C₂×C₄⋊C₄	C₂³×C₇	1	4	yes	—
585	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
586	C₂×C₄⋊C₄	C₂³×C₇	1	4	yes	—
587	C₂×C₄⋊C₄	C₂³×C₇	1	4	yes	—
588	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
589	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
590	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
591	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
592	C₂×C₂²⋊C₄	C₂³×C₇	1	4	yes	—
593	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
594	C₂×C₂²⋊C₄	C₂³×C₇	1	4	yes	—
595	C₂×C₂²⋊C₄	C₂³×C₇	1	4	yes	—
596	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
597	C₂×C₂²⋊C₄	C₂³×C₇	1	4	yes	—
598	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
599	C₂×C₄²	C₂³×C₇	1	4	yes	—
600	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
601	C₂×C₄²	C₂³×C₇	1	2	yes	—
602	C₂×C₄²	C₂³×C₇	1	2	yes	—
603	C₂×C₄²	C₂³×C₇	1	2	yes	—
604	C₂×C₄²	C₂³×C₇	1	4	yes	—
605	C₂×C₄²	C₂³×C₇	1	4	yes	—
606	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
607	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
608	C₂×C₄²	C₂³×C₇	1	4	yes	—
609	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
610	C₂×C₄²	C₂³×C₇	1	8	yes	—
611	C₂²×C₇	—	2	2	no	—
612	C₂²×C₇	—	2	2	no	—
613	C₂²×C₇	—	2	4	no	—
614	C₂²×C₇	—	2	4	no	—
615	C₂²×C₇	—	2	4	no	—
616	C₂²×C₇	—	2	2	no	—
617	C₂²×C₇	—	4	4	no	—
618	C₂²×C₇	—	4	8	no	—
619	C₂²×C₇	C₂×2₋¹⁺⁴	1	2	yes	—
620	C₂²×C₇	C₂×2₋¹⁺⁴	1	2	yes	—
621	C₂²×C₇	#585	1	2	yes	—
622	C₂²×C₇	C₂⁶	1	1	yes	characteristic
623	C₄×C₇	—	2	2	no	—
624	C₄×C₇	—	2	4	no	—
625	C₄×C₇	—	2	2	no	—
626	C₄×C₇	—	2	4	no	—
627	C₄×C₇	—	2	4	no	—
628	C₄×C₇	—	2	8	no	—
629	C₄×C₇	—	2	4	no	—
630	C₄×C₇	—	2	4	no	—
631	C₄×C₇	—	2	8	no	—
632	C₄×C₇	—	2	2	no	—
633	C₄×C₇	—	2	2	no	—
634	C₄×C₇	—	2	4	no	—
635	C₄×C₇	—	2	4	no	—
636	C₄×C₇	C₂×2₋¹⁺⁴	1	4	yes	—
637	C₄×C₇	C₂×2₋¹⁺⁴	1	4	yes	—
638	C₂⁴	C₂⁴×C₇	1	1	yes	characteristic
639	C₂⁴	C₂⁴×C₇	1	2	yes	—
640	C₂×Q₈	—	2	4	no	—
641	C₂×Q₈	—	2	4	no	—
642	C₂×Q₈	—	2	4	no	—
643	C₂×Q₈	—	2	8	no	—
644	C₂×Q₈	—	4	4	no	—
645	C₂×Q₈	—	4	4	no	—
646	C₂×Q₈	—	4	8	no	—
647	C₂×Q₈	C₂⁴×C₇	1	4	yes	—
648	C₂×Q₈	C₂⁴×C₇	1	4	yes	—
649	C₂×Q₈	C₂⁴×C₇	1	4	yes	—
650	C₂×Q₈	C₂⁴×C₇	1	8	yes	—
651	C₂×Q₈	C₂⁴×C₇	1	8	yes	—
652	C₂×Q₈	C₂⁴×C₇	1	8	yes	—
653	C₂×Q₈	C₂⁴×C₇	1	16	yes	—
654	C₂×D₄	—	2	4	no	—
655	C₂×D₄	—	4	4	no	—
656	C₂×D₄	C₂⁴×C₇	1	4	yes	—
657	C₂×D₄	C₂⁴×C₇	1	8	yes	—
658	C₂²×C₄	—	2	8	no	—
659	C₂²×C₄	—	2	4	no	—
660	C₂²×C₄	—	2	4	no	—
661	C₂²×C₄	—	4	8	no	—
662	C₂²×C₄	—	4	2	no	—
663	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
664	C₂²×C₄	C₂⁴×C₇	1	4	yes	—
665	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
666	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
667	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
668	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
669	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
670	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
671	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
672	C₂²×C₄	C₂⁴×C₇	1	4	yes	—
673	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
674	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
675	C₂²×C₄	C₂⁴×C₇	1	4	yes	—
676	C₂²×C₄	C₂⁴×C₇	1	4	yes	—
677	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
678	C₂²×C₄	C₂⁴×C₇	1	8	yes	—
679	C₂²×C₄	C₂⁴×C₇	1	4	yes	—
680	C₂²×C₄	C₂⁴×C₇	1	16	yes	—
681	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
682	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
683	C₄⋊C₄	C₂⁴×C₇	1	4	yes	—
684	C₄⋊C₄	C₂⁴×C₇	1	8	yes	—
685	C₄⋊C₄	C₂⁴×C₇	1	16	yes	—
686	C₄⋊C₄	C₂⁴×C₇	1	8	yes	—
687	C₄⋊C₄	C₂⁴×C₇	1	8	yes	—
688	C₄⋊C₄	C₂⁴×C₇	1	4	yes	—
689	C₄⋊C₄	C₂⁴×C₇	1	8	yes	—
690	C₄⋊C₄	C₂⁴×C₇	1	8	yes	—
691	C₄⋊C₄	C₂⁴×C₇	1	16	yes	—
692	C₄⋊C₄	C₂⁴×C₇	1	8	yes	—
693	C₄⋊C₄	C₂⁴×C₇	1	8	yes	—
694	C₄⋊C₄	C₂⁴×C₇	1	4	yes	—
695	C₄⋊C₄	C₂⁴×C₇	1	8	yes	—
696	C₄⋊C₄	C₂⁴×C₇	1	8	yes	—
697	C₄⋊C₄	C₂⁴×C₇	1	4	yes	—
698	C₄⋊C₄	C₂⁴×C₇	1	8	yes	—
699	C₄⋊C₄	C₂⁴×C₇	1	8	yes	—
700	C₄⋊C₄	C₂⁴×C₇	1	16	yes	—
701	C₄⋊C₄	C₂⁴×C₇	1	16	yes	—
702	C₄⋊C₄	C₂⁴×C₇	1	16	yes	—
703	C₄⋊C₄	C₂⁴×C₇	1	16	yes	—
704	C₄⋊C₄	C₂⁴×C₇	1	16	yes	—
705	C₄⋊C₄	C₂⁴×C₇	1	8	yes	—
706	C₄⋊C₄	C₂⁴×C₇	1	8	yes	—
707	C₄⋊C₄	C₂⁴×C₇	1	8	yes	—
708	C₄⋊C₄	C₂⁴×C₇	1	16	yes	—
709	C₄⋊C₄	C₂⁴×C₇	1	8	yes	—
710	C₄⋊C₄	C₂⁴×C₇	1	16	yes	—
711	C₄⋊C₄	C₂⁴×C₇	1	16	yes	—
712	C₂²⋊C₄	C₂⁴×C₇	1	8	yes	—
713	C₂²⋊C₄	C₂⁴×C₇	1	8	yes	—
714	C₂²⋊C₄	C₂⁴×C₇	1	8	yes	—
715	C₂²⋊C₄	C₂⁴×C₇	1	8	yes	—
716	C₂²⋊C₄	C₂⁴×C₇	1	16	yes	—
717	C₂²⋊C₄	C₂⁴×C₇	1	8	yes	—
718	C₂²⋊C₄	C₂⁴×C₇	1	16	yes	—
719	C₂²⋊C₄	C₂⁴×C₇	1	16	yes	—
720	C₂²⋊C₄	C₂⁴×C₇	1	8	yes	—
721	C₂²⋊C₄	C₂⁴×C₇	1	16	yes	—
722	C₂²⋊C₄	C₂⁴×C₇	1	8	yes	—
723	C₄²	C₂⁴×C₇	1	4	yes	—
724	C₄²	C₂⁴×C₇	1	4	yes	—
725	C₄²	C₂⁴×C₇	1	4	yes	—
726	C₄²	C₂⁴×C₇	1	4	yes	—
727	C₄²	C₂⁴×C₇	1	16	yes	—
728	C₄²	C₂⁴×C₇	1	8	yes	—
729	C₄²	C₂⁴×C₇	1	8	yes	—
730	C₄²	C₂⁴×C₇	1	8	yes	—
731	C₄²	C₂⁴×C₇	1	16	yes	—
732	C₄²	C₂⁴×C₇	1	16	yes	—
733	C₄²	C₂⁴×C₇	1	16	yes	—
734	C₂×C₇	—	4	2	no	—
735	C₂×C₇	—	4	4	no	—
736	C₂×C₇	#3555	1	4	yes	direct product factor
737	C₂×C₇	C₂²×2₋¹⁺⁴	1	1	yes	characteristic
738	C₂×C₇	C₂²×2₋¹⁺⁴	1	1	yes	characteristic
739	C₂×C₇	C₂×#585	1	1	yes	characteristic
740	C₂³	—	2	2	no	—
741	C₂³	—	2	2	no	—
742	C₂³	—	2	4	no	—
743	C₂³	—	2	4	no	—
744	C₂³	—	2	4	no	—
745	C₂³	—	2	2	no	—
746	C₂³	C₂⁵×C₇	1	2	yes	—
747	C₂³	C₂⁵×C₇	1	4	yes	—
748	C₂³	C₂⁵×C₇	1	1	yes	characteristic
749	Q₈	—	2	8	no	—
750	Q₈	—	2	8	no	—
751	Q₈	—	2	8	no	—
752	Q₈	—	2	16	no	—
753	Q₈	—	4	8	no	—
754	Q₈	—	4	8	no	—
755	Q₈	—	4	16	no	—
756	D₄	—	2	8	no	—
757	D₄	—	4	8	no	—
758	C₂×C₄	—	2	2	no	—
759	C₂×C₄	—	2	4	no	—
760	C₂×C₄	—	2	2	no	—
761	C₂×C₄	—	2	4	no	—
762	C₂×C₄	—	2	4	no	—
763	C₂×C₄	—	2	8	no	—
764	C₂×C₄	—	2	4	no	—
765	C₂×C₄	—	2	4	no	—
766	C₂×C₄	—	2	8	no	—
767	C₂×C₄	—	2	2	no	—
768	C₂×C₄	—	2	2	no	—
769	C₂×C₄	—	2	4	no	—
770	C₂×C₄	—	2	4	no	—
771	C₂×C₄	—	2	8	no	—
772	C₂×C₄	—	2	16	no	—
773	C₂×C₄	—	2	8	no	—
774	C₂×C₄	—	4	16	no	—
775	C₂×C₄	—	4	4	no	—
776	C₂×C₄	C₇×2₋¹⁺⁴	1	4	yes	—
777	C₂×C₄	C₇×2₋¹⁺⁴	1	4	yes	—
778	C₂×C₄	C₂⁵×C₇	1	2	yes	—
779	C₂×C₄	C₂⁵×C₇	1	8	yes	—
780	C₂×C₄	C₂⁵×C₇	1	4	yes	—
781	C₂×C₄	C₂⁵×C₇	1	4	yes	—
782	C₂×C₄	C₂⁵×C₇	1	4	yes	—
783	C₂×C₄	C₂⁵×C₇	1	4	yes	—
784	C₂×C₄	C₂⁵×C₇	1	4	yes	—
785	C₂×C₄	C₂⁵×C₇	1	2	yes	—
786	C₂×C₄	C₂⁵×C₇	1	4	yes	—
787	C₂×C₄	C₂⁵×C₇	1	2	yes	—
788	C₂×C₄	C₂⁵×C₇	1	2	yes	—
789	C₂×C₄	C₂⁵×C₇	1	8	yes	—
790	C₂×C₄	C₂⁵×C₇	1	4	yes	—
791	C₂×C₄	C₂⁵×C₇	1	2	yes	—
792	C₂×C₄	C₂⁵×C₇	1	2	yes	—
793	C₇	C₂×#3555	1	1	yes	characteristic, direct product factor, Sylow
794	C₂²	—	2	2	no	—
795	C₂²	—	2	2	no	—
796	C₂²	—	2	4	no	—
797	C₂²	—	2	4	no	—
798	C₂²	—	2	4	no	—
799	C₂²	—	2	2	no	—
800	C₂²	—	4	4	no	—
801	C₂²	—	4	8	no	—
802	C₂²	C₂×C₇×2₋¹⁺⁴	1	2	yes	—
803	C₂²	C₂×C₇×2₋¹⁺⁴	1	2	yes	—
804	C₂²	C₇×#585	1	2	yes	—
805	C₂²	C₂⁶×C₇	1	1	yes	characteristic
806	C₄	—	2	2	no	—
807	C₄	—	2	4	no	—
808	C₄	—	2	2	no	—
809	C₄	—	2	4	no	—
810	C₄	—	2	4	no	—
811	C₄	—	2	8	no	—
812	C₄	—	2	4	no	—
813	C₄	—	2	4	no	—
814	C₄	—	2	8	no	—
815	C₄	—	2	2	no	—
816	C₄	—	2	2	no	—
817	C₄	—	2	4	no	—
818	C₄	—	2	4	no	—
819	C₄	C₂×C₇×2₋¹⁺⁴	1	4	yes	—
820	C₄	C₂×C₇×2₋¹⁺⁴	1	4	yes	—
821	C₂	—	4	2	no	—
822	C₂	—	4	4	no	—
823	C₂	C₇×#3555	1	4	yes	direct product factor
824	C₂	C₂²×C₇×2₋¹⁺⁴	1	1	yes	characteristic
825	C₂	C₂²×C₇×2₋¹⁺⁴	1	1	yes	characteristic
826	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×#121	C₂²
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×#3555	C₂	direct (N × H)
2. C₂×C₇×#563	C₂	semidirect
3. C₂×C₇×Q₈²	C₂	semidirect
4. C₂×C₇×#557	C₂	semidirect
5. C₂×C₇×#557	C₂	semidirect
6. C₂×C₇×#556	C₂	semidirect
7. C₂×C₇×#556	C₂	semidirect
8. C₂×C₇×#556	C₂	semidirect
9. C₂×C₇×#554	C₂	semidirect
10. C₂×C₇×#552	C₂	semidirect
11. C₂×C₇×#544	C₂	semidirect
13. C₂×C₇×#541	C₂	semidirect
14. C₂×C₇×#541	C₂	semidirect
15. C₂×C₇×#541	C₂	semidirect
16. C₂×C₇×#533	C₂	semidirect
17. C₂×C₇×#533	C₂	semidirect
19. C₇×#563	C₂²	semidirect
20. C₇×Q₈²	C₂²	semidirect
21. C₇×#557	C₂²	semidirect
22. C₇×#557	C₂²	semidirect
23. C₇×#556	C₂²	semidirect
24. C₇×#556	C₂²	semidirect
25. C₇×#556	C₂²	semidirect
26. C₇×#554	C₂²	semidirect
27. C₇×#552	C₂²	semidirect
28. C₇×#544	C₂²	semidirect
30. C₇×#541	C₂²	semidirect
31. C₇×#541	C₂²	semidirect
32. C₇×#541	C₂²	semidirect
33. C₇×#533	C₂²	semidirect
34. C₇×#533	C₂²	semidirect
101. C₂×#3555	C₇	direct (N × H)
232. #3555	C₂×C₇	direct (N × H)
233. C₂×#563	C₂×C₇	semidirect
234. C₂×Q₈²	C₂×C₇	semidirect
235. C₂×#557	C₂×C₇	semidirect
236. C₂×#557	C₂×C₇	semidirect
237. C₂×#556	C₂×C₇	semidirect
238. C₂×#556	C₂×C₇	semidirect
239. C₂×#556	C₂×C₇	semidirect
240. C₂×#554	C₂×C₇	semidirect
241. C₂×#552	C₂×C₇	semidirect
242. C₂×#544	C₂×C₇	semidirect
244. C₂×#541	C₂×C₇	semidirect
245. C₂×#541	C₂×C₇	semidirect
246. C₂×#541	C₂×C₇	semidirect
247. C₂×#533	C₂×C₇	semidirect
248. C₂×#533	C₂×C₇	semidirect
346. #563	C₂²×C₇	semidirect
347. Q₈²	C₂²×C₇	semidirect
348. #557	C₂²×C₇	semidirect
349. #557	C₂²×C₇	semidirect
350. #556	C₂²×C₇	semidirect
351. #556	C₂²×C₇	semidirect
352. #556	C₂²×C₇	semidirect
353. #554	C₂²×C₇	semidirect
354. #552	C₂²×C₇	semidirect
355. #544	C₂²×C₇	semidirect
357. #541	C₂²×C₇	semidirect
358. #541	C₂²×C₇	semidirect
359. #541	C₂²×C₇	semidirect
360. #533	C₂²×C₇	semidirect
361. #533	C₂²×C₇	semidirect
736. C₂×C₇	#3555	direct (N × H)
793. C₇	C₂×#3555	direct (N × H)
823. C₂	C₇×#3555	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×#3555	2
C₂×C₇×#563	2
C₂×C₇×Q₈²	2
C₂×C₇×#557	2
C₂×C₇×#556	2
C₂×C₇×#554	2
C₂×C₇×#552	2
C₂×C₇×#544	2
C₂×C₇×#542	2
C₂×C₇×#541	2
C₂×C₇×#533	2
C₂×C₇×#529	2
C₂×#3555	7

Subgroups — C2×C7×#3555 #13239967

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₇×#3555 #13239967