Subgroups — C₂×C₇×#3551 #13239955

Order 1792.

7354 conjugacy classes of subgroups.

The subgroup lattice has 856 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×#3551	C₂	1	32	yes	maximal, direct product factor
2	C₂×C₇×#563	C₂	1	2	yes	maximal, complemented
3	C₂×C₇×#560	C₂	1	2	yes	maximal, complemented
4	C₂×C₇×#555	C₂	1	2	yes	maximal, complemented
5	C₂×C₇×#553	C₂	1	2	yes	maximal, complemented
6	C₂×C₇×#552	C₂	1	2	yes	maximal, complemented
7	C₂×C₇×#551	C₂	1	2	yes	maximal, complemented
8	C₂×C₇×#548	C₂	1	2	yes	maximal, complemented
9	C₂×C₇×#546	C₂	1	2	yes	maximal, complemented
10	C₂×C₇×#540	C₂	1	4	yes	maximal, complemented
11	C₂×C₇×#538	C₂	1	4	yes	maximal, complemented
12	C₂×C₇×#537	C₂	1	2	yes	maximal, complemented
13	C₂×C₇×#536	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂×C₇×#535	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂×C₇×#532	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×C₇×#529	C₂	1	2	yes	maximal, complemented
17	C₂²×C₇×#41	C₂²	1	1	yes	characteristic
18	C₂²×C₇×#41	C₂²	1	2	yes	—
19	C₂²×C₇×#41	C₂²	1	1	yes	characteristic, complemented
20	C₂³×C₇×Q₈	C₂²	1	1	yes	characteristic, complemented
21	C₂³×C₇×D₄	C₂²	1	1	yes	characteristic
22	C₇×#563	C₂²	1	32	yes	complemented
23	C₇×#560	C₂²	1	32	yes	complemented
24	C₇×#555	C₂²	1	32	yes	complemented
25	C₇×#553	C₂²	1	32	yes	complemented
26	C₇×#552	C₂²	1	32	yes	complemented
27	C₇×#551	C₂²	1	32	yes	complemented
28	C₇×#548	C₂²	1	32	yes	complemented
29	C₇×#546	C₂²	1	32	yes	complemented
30	C₇×#540	C₂²	1	64	yes	complemented
31	C₇×#538	C₂²	1	64	yes	complemented
32	C₇×#537	C₂²	1	32	yes	complemented
33	C₇×#536	C₂²	1	16	yes	complemented
34	C₇×#535	C₂²	1	16	yes	complemented
35	C₇×#532	C₂²	1	16	yes	complemented
36	C₂×C₇×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
37	C₂×C₇×C₄⋊Q₈	C₂²	1	2	yes	complemented
38	C₂×C₇×#127	C₂²	1	1	yes	characteristic
39	C₂×C₇×#127	C₂²	1	2	yes	—
40	C₇×#529	C₂²	1	32	yes	complemented
41	C₂×C₇×#126	C₂²	1	4	yes	—
42	C₂×C₇×#126	C₂²	1	4	yes	complemented
43	C₂×C₇×#126	C₂²	1	4	yes	complemented
44	C₂×C₇×#125	C₂²	1	2	yes	complemented
45	C₂×C₇×#125	C₂²	1	4	yes	complemented
46	C₂×C₇×#124	C₂²	1	2	yes	—
47	C₂×C₇×#124	C₂²	1	1	yes	characteristic
48	C₂×C₇×#124	C₂²	1	2	yes	—
49	C₂×C₇×#124	C₂²	1	2	yes	—
50	C₂×C₇×#124	C₂²	1	1	yes	characteristic, complemented
51	C₂×C₇×#124	C₂²	1	4	yes	complemented
52	C₂×C₇×#123	C₂²	1	2	yes	—
53	C₂×C₇×#123	C₂²	1	4	yes	—
54	C₂×C₇×#123	C₂²	1	4	yes	—
55	C₂×C₇×#123	C₂²	1	4	yes	complemented
56	C₂×C₇×#123	C₂²	1	2	yes	complemented
57	C₂×C₇×#123	C₂²	1	4	yes	complemented
58	C₂×C₇×C₂²⋊Q₈	C₂²	1	2	yes	—
59	C₂×C₇×C₂²⋊Q₈	C₂²	1	2	yes	complemented
60	C₂×C₇×C₂²⋊Q₈	C₂²	1	2	yes	complemented
61	C₂×C₇×C₂²⋊Q₈	C₂²	1	4	yes	complemented
62	C₂×C₇×C₂²⋊Q₈	C₂²	1	4	yes	complemented
63	C₂×C₇×#121	C₂²	1	2	yes	—
64	C₂×C₇×#121	C₂²	1	2	yes	—
65	C₂×C₇×#121	C₂²	1	2	yes	—
66	C₂×C₇×#121	C₂²	1	2	yes	—
67	C₂×C₇×#121	C₂²	1	4	yes	—
68	C₂×C₇×#121	C₂²	1	2	yes	complemented
69	C₂×C₇×#121	C₂²	1	4	yes	complemented
70	C₂×C₇×#121	C₂²	1	4	yes	complemented
71	C₂×C₇×#121	C₂²	1	4	yes	complemented
72	C₂×C₇×#121	C₂²	1	4	yes	complemented
73	C₂×C₇×#121	C₂²	1	4	yes	complemented
74	C₂×C₇×#120	C₂²	1	2	yes	—
75	C₂×C₇×#120	C₂²	1	2	yes	—
76	C₂×C₇×#120	C₂²	1	4	yes	—
77	C₂×C₄×C₇×Q₈	C₂²	1	2	yes	complemented
78	C₂×C₄×C₇×D₄	C₂²	1	2	yes	—
79	C₂×C₄×C₇×D₄	C₂²	1	2	yes	—
80	C₂×C₄×C₇×D₄	C₂²	1	4	yes	complemented
81	C₂×C₄×C₇×D₄	C₂²	1	2	yes	complemented
82	C₂×C₄×C₇×D₄	C₂²	1	4	yes	complemented
83	C₂×C₄×C₇×D₄	C₂²	1	4	yes	complemented
84	C₂×C₇×#117	C₂²	1	1	yes	characteristic
85	C₂×C₇×#117	C₂²	1	4	yes	complemented
86	C₂×C₇×#117	C₂²	1	1	yes	characteristic, complemented
87	C₂×C₇×#117	C₂²	1	4	yes	complemented
88	C₂²×C₇×C₄⋊C₄	C₂²	1	2	yes	complemented
89	C₂²×C₇×C₂²⋊C₄	C₂²	1	4	yes	—
90	C₂²×C₄²×C₇	C₂²	1	1	yes	characteristic, complemented
91	C₂×#3551	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
92	C₂⁵×C₇	C₂³	1	2	yes	—
93	C₂×C₇×#41	—	4	4	no	—
94	C₂×C₇×#41	—	4	4	no	—
95	C₂×C₇×#41	—	4	8	no	—
96	C₂×C₇×#41	C₂³	1	8	yes	—
97	C₂×C₇×#41	C₂³	1	16	yes	—
98	C₂×C₇×#41	C₂³	1	8	yes	complemented
99	C₂²×C₇×Q₈	—	4	4	no	—
100	C₂²×C₇×Q₈	C₂³	1	2	yes	—
101	C₂²×C₇×Q₈	C₂³	1	2	yes	—
102	C₂²×C₇×Q₈	C₂³	1	1	yes	characteristic
103	C₂²×C₇×Q₈	C₂³	1	1	yes	characteristic
104	C₂²×C₇×Q₈	C₂³	1	8	yes	complemented
105	C₂²×C₇×D₄	—	4	4	no	—
106	C₂²×C₇×D₄	C₂³	1	2	yes	—
107	C₂²×C₇×D₄	C₂³	1	2	yes	—
108	C₂²×C₇×D₄	C₂³	1	8	yes	—
109	C₂²×C₇×D₄	C₂³	1	1	yes	characteristic
110	C₂²×C₇×D₄	C₂³	1	1	yes	characteristic
111	C₂²×C₇×D₄	C₂³	1	4	yes	—
112	C₂²×C₇×D₄	C₂³	1	1	yes	characteristic
113	C₂²×C₇×D₄	C₂³	1	2	yes	—
114	C₂²×C₇×D₄	C₂³	1	1	yes	characteristic
115	C₂²×C₇×D₄	C₂³	1	2	yes	—
116	C₂²×C₇×D₄	C₂³	1	4	yes	—
117	C₂²×C₇×D₄	C₂³	1	4	yes	—
118	C₂²×C₇×D₄	C₂³	1	4	yes	—
119	C₂²×C₇×D₄	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	2	yes	—
124	C₂³×C₄×C₇	C₂³	1	2	yes	—
125	C₂³×C₄×C₇	C₂³	1	4	yes	—
126	C₂³×C₄×C₇	C₂³	1	2	yes	—
127	C₂³×C₄×C₇	C₂³	1	4	yes	—
128	C₂³×C₄×C₇	C₂³	1	4	yes	—
129	C₇×C₄⋊Q₈	C₂³	1	8	yes	complemented
130	C₇×C₄⋊Q₈	C₂³	1	16	yes	complemented
131	C₇×#127	C₂³	1	8	yes	—
132	C₇×#127	C₂³	1	16	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×#124	C₂³	1	16	yes	—
139	C₇×#124	C₂³	1	8	yes	—
140	C₇×#124	C₂³	1	16	yes	—
141	C₇×#124	C₂³	1	16	yes	—
142	C₇×#124	C₂³	1	8	yes	complemented
143	C₇×#124	C₂³	1	32	yes	complemented
144	C₇×#123	C₂³	1	16	yes	—
145	C₇×#123	C₂³	1	32	yes	—
146	C₇×#123	C₂³	1	32	yes	—
147	C₇×#123	C₂³	1	32	yes	complemented
148	C₇×#123	C₂³	1	16	yes	complemented
149	C₇×#123	C₂³	1	32	yes	complemented
150	C₇×C₂²⋊Q₈	C₂³	1	16	yes	—
151	C₇×C₂²⋊Q₈	C₂³	1	16	yes	complemented
152	C₇×C₂²⋊Q₈	C₂³	1	16	yes	complemented
153	C₇×C₂²⋊Q₈	C₂³	1	32	yes	complemented
154	C₇×C₂²⋊Q₈	C₂³	1	32	yes	complemented
155	C₇×#121	C₂³	1	16	yes	—
156	C₇×#121	C₂³	1	16	yes	—
157	C₇×#121	C₂³	1	16	yes	—
158	C₇×#121	C₂³	1	16	yes	—
159	C₇×#121	C₂³	1	32	yes	—
160	C₇×#121	C₂³	1	16	yes	complemented
161	C₇×#121	C₂³	1	32	yes	complemented
162	C₇×#121	C₂³	1	32	yes	complemented
163	C₇×#121	C₂³	1	32	yes	complemented
164	C₇×#121	C₂³	1	32	yes	complemented
165	C₇×#121	C₂³	1	32	yes	complemented
166	C₇×#120	C₂³	1	16	yes	—
167	C₇×#120	C₂³	1	16	yes	—
168	C₇×#120	C₂³	1	32	yes	—
169	C₄×C₇×Q₈	C₂³	1	16	yes	complemented
170	C₄×C₇×D₄	C₂³	1	16	yes	—
171	C₄×C₇×D₄	C₂³	1	16	yes	—
172	C₄×C₇×D₄	C₂³	1	32	yes	complemented
173	C₄×C₇×D₄	C₂³	1	16	yes	complemented
174	C₄×C₇×D₄	C₂³	1	32	yes	complemented
175	C₄×C₇×D₄	C₂³	1	32	yes	complemented
176	C₇×#117	C₂³	1	8	yes	—
177	C₇×#117	C₂³	1	32	yes	complemented
178	C₇×#117	C₂³	1	8	yes	complemented
179	C₇×#117	C₂³	1	32	yes	complemented
180	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
181	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
182	C₂×C₇×C₄⋊C₄	C₂³	1	4	yes	—
183	C₂×C₇×C₄⋊C₄	C₂³	1	4	yes	—
184	C₂×C₇×C₄⋊C₄	C₂³	1	4	yes	—
185	C₂×C₇×C₄⋊C₄	C₂³	1	4	yes	—
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	4	yes	—
190	C₂×C₇×C₄⋊C₄	C₂³	1	4	yes	—
191	C₂×C₇×C₄⋊C₄	C₂³	1	16	yes	complemented
192	C₂×C₇×C₂²⋊C₄	C₂³	1	2	yes	—
193	C₂×C₇×C₂²⋊C₄	C₂³	1	4	yes	—
194	C₂×C₇×C₂²⋊C₄	C₂³	1	4	yes	—
195	C₂×C₇×C₂²⋊C₄	C₂³	1	4	yes	—
196	C₂×C₇×C₂²⋊C₄	C₂³	1	32	yes	—
197	C₂×C₇×C₂²⋊C₄	C₂³	1	2	yes	—
198	C₂×C₇×C₂²⋊C₄	C₂³	1	2	yes	—
199	C₂×C₇×C₂²⋊C₄	C₂³	1	4	yes	—
200	C₂×C₇×C₂²⋊C₄	C₂³	1	4	yes	—
201	C₂×C₇×C₂²⋊C₄	C₂³	1	2	yes	—
202	C₂×C₇×C₂²⋊C₄	C₂³	1	4	yes	—
203	C₂×C₇×C₂²⋊C₄	C₂³	1	2	yes	—
204	C₂×C₇×C₂²⋊C₄	C₂³	1	2	yes	—
205	C₂×C₇×C₂²⋊C₄	C₂³	1	4	yes	—
206	C₂×C₇×C₂²⋊C₄	C₂³	1	4	yes	—
207	C₂×C₇×C₂²⋊C₄	C₂³	1	4	yes	—
208	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
209	C₂×C₄²×C₇	C₂³	1	2	yes	—
210	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
211	C₂×C₄²×C₇	C₂³	1	2	yes	—
212	C₂×C₄²×C₇	C₂³	1	4	yes	—
213	C₂×C₄²×C₇	C₂³	1	2	yes	—
214	C₂×C₄²×C₇	C₂³	1	8	yes	complemented
215	#3551	C₂×C₇	1	32	yes	direct product factor
216	C₂×#563	C₂×C₇	1	2	yes	complemented
217	C₂×#560	C₂×C₇	1	2	yes	complemented
218	C₂×#555	C₂×C₇	1	2	yes	complemented
219	C₂×#553	C₂×C₇	1	2	yes	complemented
220	C₂×#552	C₂×C₇	1	2	yes	complemented
221	C₂×#551	C₂×C₇	1	2	yes	complemented
222	C₂×#548	C₂×C₇	1	2	yes	complemented
223	C₂×#546	C₂×C₇	1	2	yes	complemented
224	C₂×#540	C₂×C₇	1	4	yes	complemented
225	C₂×#538	C₂×C₇	1	4	yes	complemented
226	C₂×#537	C₂×C₇	1	2	yes	complemented
227	C₂×#536	C₂×C₇	1	1	yes	characteristic, complemented
228	C₂×#535	C₂×C₇	1	1	yes	characteristic, complemented
229	C₂×#532	C₂×C₇	1	1	yes	characteristic, complemented
230	C₂×#529	C₂×C₇	1	2	yes	complemented
231	C₂⁴×C₇	—	4	4	no	—
232	C₂⁴×C₇	—	4	8	no	—
233	C₂⁴×C₇	C₂⁴	1	1	yes	characteristic
234	C₂⁴×C₇	C₂⁴	1	4	yes	—
235	C₂⁴×C₇	C₂⁴	1	1	yes	characteristic
236	C₂⁴×C₇	C₂⁴	1	2	yes	—
237	C₂⁴×C₇	C₂⁴	1	1	yes	characteristic
238	C₂⁴×C₇	C₂⁴	1	8	yes	—
239	C₇×#41	—	4	16	no	—
240	C₇×#41	—	4	16	no	—
241	C₇×#41	—	4	32	no	—
242	C₂×C₇×Q₈	—	2	8	no	—
243	C₂×C₇×Q₈	—	4	4	no	—
244	C₂×C₇×Q₈	—	4	2	no	—
245	C₂×C₇×Q₈	—	4	2	no	—
246	C₂×C₇×Q₈	—	4	16	no	—
247	C₂×C₇×Q₈	C₂⁴	1	8	yes	—
248	C₂×C₇×Q₈	C₂⁴	1	4	yes	—
249	C₂×C₇×Q₈	C₂⁴	1	8	yes	—
250	C₂×C₇×Q₈	C₂⁴	1	4	yes	—
251	C₂×C₇×D₄	—	2	8	no	—
252	C₂×C₇×D₄	—	4	16	no	—
253	C₂×C₇×D₄	—	4	4	no	—
254	C₂×C₇×D₄	—	4	8	no	—
255	C₂×C₇×D₄	—	4	4	no	—
256	C₂×C₇×D₄	—	4	8	no	—
257	C₂×C₇×D₄	—	4	8	no	—
258	C₂×C₇×D₄	—	4	4	no	—
259	C₂×C₇×D₄	—	4	4	no	—
260	C₂×C₇×D₄	—	4	2	no	—
261	C₂×C₇×D₄	—	4	2	no	—
262	C₂×C₇×D₄	—	4	2	no	—
263	C₂×C₇×D₄	—	4	2	no	—
264	C₂×C₇×D₄	—	4	8	no	—
265	C₂×C₇×D₄	C₂⁴	1	8	yes	—
266	C₂×C₇×D₄	C₂⁴	1	8	yes	—
267	C₂×C₇×D₄	C₂⁴	1	16	yes	—
268	C₂×C₇×D₄	C₂⁴	1	16	yes	—
269	C₂×C₇×D₄	C₂⁴	1	16	yes	—
270	C₂×C₇×D₄	C₂⁴	1	8	yes	—
271	C₂×C₇×D₄	C₂⁴	1	4	yes	—
272	C₂×C₇×D₄	C₂⁴	1	4	yes	—
273	C₂×C₇×D₄	C₂⁴	1	16	yes	—
274	C₂×C₇×D₄	C₂⁴	1	8	yes	—
275	C₂×C₇×D₄	C₂⁴	1	8	yes	—
276	C₂×C₇×D₄	C₂⁴	1	4	yes	—
277	C₂×C₇×D₄	C₂⁴	1	4	yes	—
278	C₂²×C₄×C₇	—	2	4	no	—
279	C₂²×C₄×C₇	—	2	4	no	—
280	C₂²×C₄×C₇	—	2	8	no	—
281	C₂²×C₄×C₇	—	2	4	no	—
282	C₂²×C₄×C₇	—	4	8	no	—
283	C₂²×C₄×C₇	—	4	4	no	—
284	C₂²×C₄×C₇	—	4	8	no	—
285	C₂²×C₄×C₇	—	4	4	no	—
286	C₂²×C₄×C₇	—	4	8	no	—
287	C₂²×C₄×C₇	C₂⁴	1	4	yes	—
288	C₂²×C₄×C₇	C₂⁴	1	8	yes	—
289	C₂²×C₄×C₇	C₂⁴	1	4	yes	—
290	C₂²×C₄×C₇	C₂⁴	1	4	yes	—
291	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
292	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
293	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
294	C₂²×C₄×C₇	C₂⁴	1	4	yes	—
295	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
296	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
297	C₂²×C₄×C₇	C₂⁴	1	4	yes	—
298	C₂²×C₄×C₇	C₂⁴	1	4	yes	—
299	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
300	C₂²×C₄×C₇	C₂⁴	1	8	yes	—
301	C₂²×C₄×C₇	C₂⁴	1	16	yes	—
302	C₂²×C₄×C₇	C₂⁴	1	16	yes	—
303	C₂²×C₄×C₇	C₂⁴	1	16	yes	—
304	C₂²×C₄×C₇	C₂⁴	1	8	yes	—
305	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
306	C₇×C₄⋊C₄	C₂⁴	1	8	yes	—
307	C₇×C₄⋊C₄	C₂⁴	1	8	yes	—
308	C₇×C₄⋊C₄	C₂⁴	1	16	yes	—
309	C₇×C₄⋊C₄	C₂⁴	1	16	yes	—
310	C₇×C₄⋊C₄	C₂⁴	1	16	yes	—
311	C₇×C₄⋊C₄	C₂⁴	1	16	yes	—
312	C₇×C₄⋊C₄	C₂⁴	1	8	yes	—
313	C₇×C₄⋊C₄	C₂⁴	1	8	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×C₂²⋊C₄	C₂⁴	1	8	yes	—
318	C₇×C₂²⋊C₄	C₂⁴	1	16	yes	—
319	C₇×C₂²⋊C₄	C₂⁴	1	16	yes	—
320	C₇×C₂²⋊C₄	C₂⁴	1	16	yes	—
321	C₇×C₂²⋊C₄	C₂⁴	1	8	yes	—
322	C₇×C₂²⋊C₄	C₂⁴	1	8	yes	—
323	C₇×C₂²⋊C₄	C₂⁴	1	16	yes	—
324	C₇×C₂²⋊C₄	C₂⁴	1	16	yes	—
325	C₇×C₂²⋊C₄	C₂⁴	1	8	yes	—
326	C₇×C₂²⋊C₄	C₂⁴	1	16	yes	—
327	C₇×C₂²⋊C₄	C₂⁴	1	8	yes	—
328	C₇×C₂²⋊C₄	C₂⁴	1	8	yes	—
329	C₇×C₂²⋊C₄	C₂⁴	1	16	yes	—
330	C₇×C₂²⋊C₄	C₂⁴	1	16	yes	—
331	C₇×C₂²⋊C₄	C₂⁴	1	16	yes	—
332	C₄²×C₇	C₂⁴	1	4	yes	—
333	C₄²×C₇	C₂⁴	1	8	yes	—
334	C₄²×C₇	C₂⁴	1	4	yes	—
335	C₄²×C₇	C₂⁴	1	8	yes	—
336	C₄²×C₇	C₂⁴	1	16	yes	—
337	C₄²×C₇	C₂⁴	1	8	yes	—
338	C₂²×#41	C₂²×C₇	1	1	yes	characteristic
339	C₂²×#41	C₂²×C₇	1	2	yes	—
340	C₂²×#41	C₂²×C₇	1	1	yes	characteristic, complemented
341	C₂³×Q₈	C₂²×C₇	1	1	yes	characteristic, complemented
342	C₂³×D₄	C₂²×C₇	1	1	yes	characteristic
343	#563	C₂²×C₇	1	32	yes	complemented
344	#560	C₂²×C₇	1	32	yes	complemented
345	#555	C₂²×C₇	1	32	yes	complemented
346	#553	C₂²×C₇	1	32	yes	complemented
347	#552	C₂²×C₇	1	32	yes	complemented
348	#551	C₂²×C₇	1	32	yes	complemented
349	#548	C₂²×C₇	1	32	yes	complemented
350	#546	C₂²×C₇	1	32	yes	complemented
351	#540	C₂²×C₇	1	64	yes	complemented
352	#538	C₂²×C₇	1	64	yes	complemented
353	#537	C₂²×C₇	1	32	yes	complemented
354	#536	C₂²×C₇	1	16	yes	complemented
355	#535	C₂²×C₇	1	16	yes	complemented
356	#532	C₂²×C₇	1	16	yes	complemented
357	C₂×C₄⋊Q₈	C₂²×C₇	1	1	yes	characteristic, complemented
358	C₂×C₄⋊Q₈	C₂²×C₇	1	2	yes	complemented
359	C₂×#127	C₂²×C₇	1	1	yes	characteristic
360	C₂×#127	C₂²×C₇	1	2	yes	—
361	#529	C₂²×C₇	1	32	yes	complemented
362	C₂×#126	C₂²×C₇	1	4	yes	—
363	C₂×#126	C₂²×C₇	1	4	yes	complemented
364	C₂×#126	C₂²×C₇	1	4	yes	complemented
365	C₂×#125	C₂²×C₇	1	2	yes	complemented
366	C₂×#125	C₂²×C₇	1	4	yes	complemented
367	C₂×#124	C₂²×C₇	1	2	yes	—
368	C₂×#124	C₂²×C₇	1	1	yes	characteristic
369	C₂×#124	C₂²×C₇	1	2	yes	—
370	C₂×#124	C₂²×C₇	1	2	yes	—
371	C₂×#124	C₂²×C₇	1	1	yes	characteristic, complemented
372	C₂×#124	C₂²×C₇	1	4	yes	complemented
373	C₂×#123	C₂²×C₇	1	2	yes	—
374	C₂×#123	C₂²×C₇	1	4	yes	—
375	C₂×#123	C₂²×C₇	1	4	yes	—
376	C₂×#123	C₂²×C₇	1	4	yes	complemented
377	C₂×#123	C₂²×C₇	1	2	yes	complemented
378	C₂×#123	C₂²×C₇	1	4	yes	complemented
379	C₂×C₂²⋊Q₈	C₂²×C₇	1	2	yes	—
380	C₂×C₂²⋊Q₈	C₂²×C₇	1	2	yes	complemented
381	C₂×C₂²⋊Q₈	C₂²×C₇	1	2	yes	complemented
382	C₂×C₂²⋊Q₈	C₂²×C₇	1	4	yes	complemented
383	C₂×C₂²⋊Q₈	C₂²×C₇	1	4	yes	complemented
384	C₂×#121	C₂²×C₇	1	2	yes	—
385	C₂×#121	C₂²×C₇	1	2	yes	—
386	C₂×#121	C₂²×C₇	1	2	yes	—
387	C₂×#121	C₂²×C₇	1	2	yes	—
388	C₂×#121	C₂²×C₇	1	4	yes	—
389	C₂×#121	C₂²×C₇	1	2	yes	complemented
390	C₂×#121	C₂²×C₇	1	4	yes	complemented
391	C₂×#121	C₂²×C₇	1	4	yes	complemented
392	C₂×#121	C₂²×C₇	1	4	yes	complemented
393	C₂×#121	C₂²×C₇	1	4	yes	complemented
394	C₂×#121	C₂²×C₇	1	4	yes	complemented
395	C₂×#120	C₂²×C₇	1	2	yes	—
396	C₂×#120	C₂²×C₇	1	2	yes	—
397	C₂×#120	C₂²×C₇	1	4	yes	—
398	C₂×C₄×Q₈	C₂²×C₇	1	2	yes	complemented
399	C₂×C₄×D₄	C₂²×C₇	1	2	yes	—
400	C₂×C₄×D₄	C₂²×C₇	1	2	yes	—
401	C₂×C₄×D₄	C₂²×C₇	1	4	yes	complemented
402	C₂×C₄×D₄	C₂²×C₇	1	2	yes	complemented
403	C₂×C₄×D₄	C₂²×C₇	1	4	yes	complemented
404	C₂×C₄×D₄	C₂²×C₇	1	4	yes	complemented
405	C₂×#117	C₂²×C₇	1	1	yes	characteristic
406	C₂×#117	C₂²×C₇	1	4	yes	complemented
407	C₂×#117	C₂²×C₇	1	1	yes	characteristic, complemented
408	C₂×#117	C₂²×C₇	1	4	yes	complemented
409	C₂²×C₄⋊C₄	C₂²×C₇	1	2	yes	complemented
410	C₂²×C₂²⋊C₄	C₂²×C₇	1	4	yes	—
411	C₂²×C₄²	C₂²×C₇	1	1	yes	characteristic, complemented
412	C₂³×C₇	—	2	2	no	—
413	C₂³×C₇	—	2	4	no	—
414	C₂³×C₇	—	2	2	no	—
415	C₂³×C₇	—	2	2	no	—
416	C₂³×C₇	—	2	8	no	—
417	C₂³×C₇	—	2	4	no	—
418	C₂³×C₇	—	2	4	no	—
419	C₂³×C₇	—	2	8	no	—
420	C₂³×C₇	—	2	4	no	—
421	C₂³×C₇	—	2	4	no	—
422	C₂³×C₇	—	2	8	no	—
423	C₂³×C₇	—	2	4	no	—
424	C₂³×C₇	—	4	8	no	—
425	C₂³×C₇	—	4	16	no	—
426	C₂³×C₇	—	8	16	no	—
427	C₂³×C₇	C₂⁵	1	2	yes	—
428	C₂³×C₇	C₂⁵	1	8	yes	—
429	C₂³×C₇	C₂⁵	1	2	yes	—
430	C₂³×C₇	C₂⁵	1	4	yes	—
431	C₂³×C₇	C₂⁵	1	2	yes	—
432	C₂³×C₇	C₂⁵	1	1	yes	characteristic
433	C₇×Q₈	—	2	16	no	—
434	C₇×Q₈	—	4	8	no	—
435	C₇×Q₈	—	4	4	no	—
436	C₇×Q₈	—	4	4	no	—
437	C₇×D₄	—	2	16	no	—
438	C₇×D₄	—	4	8	no	—
439	C₇×D₄	—	4	16	no	—
440	C₇×D₄	—	4	8	no	—
441	C₇×D₄	—	4	16	no	—
442	C₇×D₄	—	4	16	no	—
443	C₇×D₄	—	4	8	no	—
444	C₇×D₄	—	4	8	no	—
445	C₇×D₄	—	4	4	no	—
446	C₇×D₄	—	4	4	no	—
447	C₇×D₄	—	4	4	no	—
448	C₇×D₄	—	4	4	no	—
449	C₇×D₄	—	4	16	no	—
450	C₂×C₄×C₇	—	2	4	no	—
451	C₂×C₄×C₇	—	2	2	no	—
452	C₂×C₄×C₇	—	2	2	no	—
453	C₂×C₄×C₇	—	2	2	no	—
454	C₂×C₄×C₇	—	2	8	no	—
455	C₂×C₄×C₇	—	2	4	no	—
456	C₂×C₄×C₇	—	2	8	no	—
457	C₂×C₄×C₇	—	2	4	no	—
458	C₂×C₄×C₇	—	2	8	no	—
459	C₂×C₄×C₇	—	2	8	no	—
460	C₂×C₄×C₇	—	2	8	no	—
461	C₂×C₄×C₇	—	2	16	no	—
462	C₂×C₄×C₇	—	2	8	no	—
463	C₂×C₄×C₇	—	4	16	no	—
464	C₂×C₄×C₇	—	4	8	no	—
465	C₂×C₄×C₇	—	4	16	no	—
466	C₂×C₄×C₇	—	4	8	no	—
467	C₂×C₄×C₇	—	4	16	no	—
468	C₂×C₄×C₇	H(5,𝔽₂)	1	4	yes	—
469	C₂×C₄×C₇	C₂⁵	1	4	yes	—
470	C₂×C₄×C₇	C₂⁵	1	2	yes	—
471	C₂×C₄×C₇	C₂⁵	1	4	yes	—
472	C₂×C₄×C₇	C₂⁵	1	8	yes	—
473	C₂×C₄×C₇	C₂⁵	1	2	yes	—
474	C₂×C₄×C₇	C₂⁵	1	2	yes	—
475	C₂×C₄×C₇	C₂⁵	1	8	yes	—
476	C₂×C₄×C₇	C₂⁵	1	8	yes	—
477	C₂×C₄×C₇	C₂⁵	1	4	yes	—
478	C₂×C₄×C₇	C₂⁵	1	2	yes	—
479	C₂⁵	C₂³×C₇	1	2	yes	—
480	C₂×#41	—	4	4	no	—
481	C₂×#41	—	4	4	no	—
482	C₂×#41	—	4	8	no	—
483	C₂×#41	C₂³×C₇	1	8	yes	—
484	C₂×#41	C₂³×C₇	1	16	yes	—
485	C₂×#41	C₂³×C₇	1	8	yes	complemented
486	C₂²×Q₈	—	4	4	no	—
487	C₂²×Q₈	C₂³×C₇	1	2	yes	—
488	C₂²×Q₈	C₂³×C₇	1	1	yes	characteristic
489	C₂²×Q₈	C₂³×C₇	1	2	yes	—
490	C₂²×Q₈	C₂³×C₇	1	1	yes	characteristic
491	C₂²×Q₈	C₂³×C₇	1	8	yes	complemented
492	C₂²×D₄	—	4	4	no	—
493	C₂²×D₄	C₂³×C₇	1	2	yes	—
494	C₂²×D₄	C₂³×C₇	1	2	yes	—
495	C₂²×D₄	C₂³×C₇	1	4	yes	—
496	C₂²×D₄	C₂³×C₇	1	4	yes	—
497	C₂²×D₄	C₂³×C₇	1	4	yes	—
498	C₂²×D₄	C₂³×C₇	1	2	yes	—
499	C₂²×D₄	C₂³×C₇	1	1	yes	characteristic
500	C₂²×D₄	C₂³×C₇	1	1	yes	characteristic
501	C₂²×D₄	C₂³×C₇	1	4	yes	—
502	C₂²×D₄	C₂³×C₇	1	2	yes	—
503	C₂²×D₄	C₂³×C₇	1	2	yes	—
504	C₂²×D₄	C₂³×C₇	1	1	yes	characteristic
505	C₂²×D₄	C₂³×C₇	1	1	yes	characteristic
506	C₂²×D₄	C₂³×C₇	1	8	yes	—
507	C₂³×C₄	C₂³×C₇	1	2	yes	—
508	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
509	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
510	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
511	C₂³×C₄	C₂³×C₇	1	4	yes	—
512	C₂³×C₄	C₂³×C₇	1	4	yes	—
513	C₂³×C₄	C₂³×C₇	1	4	yes	—
514	C₂³×C₄	C₂³×C₇	1	2	yes	—
515	C₂³×C₄	C₂³×C₇	1	2	yes	—
516	C₄⋊Q₈	C₂³×C₇	1	8	yes	complemented
517	C₄⋊Q₈	C₂³×C₇	1	16	yes	complemented
518	#127	C₂³×C₇	1	8	yes	—
519	#127	C₂³×C₇	1	16	yes	—
520	#126	C₂³×C₇	1	32	yes	—
521	#126	C₂³×C₇	1	32	yes	complemented
522	#126	C₂³×C₇	1	32	yes	complemented
523	#125	C₂³×C₇	1	16	yes	complemented
524	#125	C₂³×C₇	1	32	yes	complemented
525	#124	C₂³×C₇	1	16	yes	—
526	#124	C₂³×C₇	1	8	yes	—
527	#124	C₂³×C₇	1	16	yes	—
528	#124	C₂³×C₇	1	16	yes	—
529	#124	C₂³×C₇	1	8	yes	complemented
530	#124	C₂³×C₇	1	32	yes	complemented
531	#123	C₂³×C₇	1	16	yes	—
532	#123	C₂³×C₇	1	32	yes	—
533	#123	C₂³×C₇	1	32	yes	—
534	#123	C₂³×C₇	1	32	yes	complemented
535	#123	C₂³×C₇	1	16	yes	complemented
536	#123	C₂³×C₇	1	32	yes	complemented
537	C₂²⋊Q₈	C₂³×C₇	1	16	yes	—
538	C₂²⋊Q₈	C₂³×C₇	1	16	yes	complemented
539	C₂²⋊Q₈	C₂³×C₇	1	16	yes	complemented
540	C₂²⋊Q₈	C₂³×C₇	1	32	yes	complemented
541	C₂²⋊Q₈	C₂³×C₇	1	32	yes	complemented
542	#121	C₂³×C₇	1	16	yes	—
543	#121	C₂³×C₇	1	16	yes	—
544	#121	C₂³×C₇	1	16	yes	—
545	#121	C₂³×C₇	1	16	yes	—
546	#121	C₂³×C₇	1	32	yes	—
547	#121	C₂³×C₇	1	16	yes	complemented
548	#121	C₂³×C₇	1	32	yes	complemented
549	#121	C₂³×C₇	1	32	yes	complemented
550	#121	C₂³×C₇	1	32	yes	complemented
551	#121	C₂³×C₇	1	32	yes	complemented
552	#121	C₂³×C₇	1	32	yes	complemented
553	#120	C₂³×C₇	1	16	yes	—
554	#120	C₂³×C₇	1	16	yes	—
555	#120	C₂³×C₇	1	32	yes	—
556	C₄×Q₈	C₂³×C₇	1	16	yes	complemented
557	C₄×D₄	C₂³×C₇	1	16	yes	—
558	C₄×D₄	C₂³×C₇	1	16	yes	—
559	C₄×D₄	C₂³×C₇	1	32	yes	complemented
560	C₄×D₄	C₂³×C₇	1	16	yes	complemented
561	C₄×D₄	C₂³×C₇	1	32	yes	complemented
562	C₄×D₄	C₂³×C₇	1	32	yes	complemented
563	#117	C₂³×C₇	1	8	yes	—
564	#117	C₂³×C₇	1	32	yes	complemented
565	#117	C₂³×C₇	1	8	yes	complemented
566	#117	C₂³×C₇	1	32	yes	complemented
567	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
568	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
569	C₂×C₄⋊C₄	C₂³×C₇	1	4	yes	—
570	C₂×C₄⋊C₄	C₂³×C₇	1	4	yes	—
571	C₂×C₄⋊C₄	C₂³×C₇	1	4	yes	—
572	C₂×C₄⋊C₄	C₂³×C₇	1	4	yes	—
573	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
574	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
575	C₂×C₄⋊C₄	C₂³×C₇	1	4	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	16	yes	complemented
579	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
580	C₂×C₂²⋊C₄	C₂³×C₇	1	4	yes	—
581	C₂×C₂²⋊C₄	C₂³×C₇	1	4	yes	—
582	C₂×C₂²⋊C₄	C₂³×C₇	1	4	yes	—
583	C₂×C₂²⋊C₄	C₂³×C₇	1	32	yes	—
584	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
585	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
586	C₂×C₂²⋊C₄	C₂³×C₇	1	4	yes	—
587	C₂×C₂²⋊C₄	C₂³×C₇	1	4	yes	—
588	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
589	C₂×C₂²⋊C₄	C₂³×C₇	1	4	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	4	yes	—
594	C₂×C₂²⋊C₄	C₂³×C₇	1	4	yes	—
595	C₂×C₄²	C₂³×C₇	1	2	yes	—
596	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
597	C₂×C₄²	C₂³×C₇	1	4	yes	—
598	C₂×C₄²	C₂³×C₇	1	2	yes	—
599	C₂×C₄²	C₂³×C₇	1	2	yes	—
600	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
601	C₂×C₄²	C₂³×C₇	1	8	yes	complemented
602	C₂²×C₇	—	2	2	no	—
603	C₂²×C₇	—	2	4	no	—
604	C₂²×C₇	—	2	2	no	—
605	C₂²×C₇	—	2	2	no	—
606	C₂²×C₇	—	2	8	no	—
607	C₂²×C₇	—	2	4	no	—
608	C₂²×C₇	—	2	4	no	—
609	C₂²×C₇	—	2	8	no	—
610	C₂²×C₇	—	2	4	no	—
611	C₂²×C₇	—	2	4	no	—
612	C₂²×C₇	—	2	8	no	—
613	C₂²×C₇	—	2	4	no	—
614	C₂²×C₇	—	4	4	no	—
615	C₂²×C₇	—	4	8	no	—
616	C₂²×C₇	—	4	4	no	—
617	C₂²×C₇	—	4	16	no	—
618	C₂²×C₇	—	4	4	no	—
619	C₂²×C₇	—	8	16	no	—
620	C₂²×C₇	C₂×H(5,𝔽₂)	1	2	yes	—
621	C₂²×C₇	#585	1	4	yes	—
622	C₂²×C₇	C₂⁶	1	1	yes	characteristic
623	C₄×C₇	—	2	4	no	—
624	C₄×C₇	—	2	2	no	—
625	C₄×C₇	—	2	2	no	—
626	C₄×C₇	—	2	2	no	—
627	C₄×C₇	—	2	8	no	—
628	C₄×C₇	—	2	4	no	—
629	C₄×C₇	—	2	8	no	—
630	C₄×C₇	—	2	4	no	—
631	C₄×C₇	—	2	8	no	—
632	C₄×C₇	C₂×H(5,𝔽₂)	1	4	yes	—
633	C₂⁴	—	4	4	no	—
634	C₂⁴	—	4	8	no	—
635	C₂⁴	C₂⁴×C₇	1	1	yes	characteristic
636	C₂⁴	C₂⁴×C₇	1	4	yes	—
637	C₂⁴	C₂⁴×C₇	1	1	yes	characteristic
638	C₂⁴	C₂⁴×C₇	1	2	yes	—
639	C₂⁴	C₂⁴×C₇	1	1	yes	characteristic
640	C₂⁴	C₂⁴×C₇	1	8	yes	—
641	#41	—	4	16	no	—
642	#41	—	4	16	no	—
643	#41	—	4	32	no	—
644	C₂×Q₈	—	2	8	no	—
645	C₂×Q₈	—	4	4	no	—
646	C₂×Q₈	—	4	2	no	—
647	C₂×Q₈	—	4	2	no	—
648	C₂×Q₈	—	4	16	no	—
649	C₂×Q₈	C₂⁴×C₇	1	8	yes	—
650	C₂×Q₈	C₂⁴×C₇	1	4	yes	—
651	C₂×Q₈	C₂⁴×C₇	1	8	yes	—
652	C₂×Q₈	C₂⁴×C₇	1	4	yes	—
653	C₂×D₄	—	2	8	no	—
654	C₂×D₄	—	4	16	no	—
655	C₂×D₄	—	4	4	no	—
656	C₂×D₄	—	4	4	no	—
657	C₂×D₄	—	4	2	no	—
658	C₂×D₄	—	4	2	no	—
659	C₂×D₄	—	4	2	no	—
660	C₂×D₄	—	4	2	no	—
661	C₂×D₄	—	4	8	no	—
662	C₂×D₄	—	4	8	no	—
663	C₂×D₄	—	4	4	no	—
664	C₂×D₄	—	4	8	no	—
665	C₂×D₄	—	4	8	no	—
666	C₂×D₄	—	4	4	no	—
667	C₂×D₄	C₂⁴×C₇	1	8	yes	—
668	C₂×D₄	C₂⁴×C₇	1	8	yes	—
669	C₂×D₄	C₂⁴×C₇	1	16	yes	—
670	C₂×D₄	C₂⁴×C₇	1	16	yes	—
671	C₂×D₄	C₂⁴×C₇	1	16	yes	—
672	C₂×D₄	C₂⁴×C₇	1	8	yes	—
673	C₂×D₄	C₂⁴×C₇	1	4	yes	—
674	C₂×D₄	C₂⁴×C₇	1	4	yes	—
675	C₂×D₄	C₂⁴×C₇	1	16	yes	—
676	C₂×D₄	C₂⁴×C₇	1	8	yes	—
677	C₂×D₄	C₂⁴×C₇	1	8	yes	—
678	C₂×D₄	C₂⁴×C₇	1	4	yes	—
679	C₂×D₄	C₂⁴×C₇	1	4	yes	—
680	C₂²×C₄	—	2	4	no	—
681	C₂²×C₄	—	2	4	no	—
682	C₂²×C₄	—	2	8	no	—
683	C₂²×C₄	—	2	4	no	—
684	C₂²×C₄	—	4	4	no	—
685	C₂²×C₄	—	4	8	no	—
686	C₂²×C₄	—	4	4	no	—
687	C₂²×C₄	—	4	8	no	—
688	C₂²×C₄	—	4	8	no	—
689	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
690	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
691	C₂²×C₄	C₂⁴×C₇	1	4	yes	—
692	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
693	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
694	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
695	C₂²×C₄	C₂⁴×C₇	1	4	yes	—
696	C₂²×C₄	C₂⁴×C₇	1	4	yes	—
697	C₂²×C₄	C₂⁴×C₇	1	4	yes	—
698	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
699	C₂²×C₄	C₂⁴×C₇	1	8	yes	—
700	C₂²×C₄	C₂⁴×C₇	1	4	yes	—
701	C₂²×C₄	C₂⁴×C₇	1	4	yes	—
702	C₂²×C₄	C₂⁴×C₇	1	8	yes	—
703	C₂²×C₄	C₂⁴×C₇	1	16	yes	—
704	C₂²×C₄	C₂⁴×C₇	1	16	yes	—
705	C₂²×C₄	C₂⁴×C₇	1	16	yes	—
706	C₂²×C₄	C₂⁴×C₇	1	8	yes	—
707	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
708	C₄⋊C₄	C₂⁴×C₇	1	8	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	C₄⋊C₄	C₂⁴×C₇	1	16	yes	—
713	C₄⋊C₄	C₂⁴×C₇	1	16	yes	—
714	C₄⋊C₄	C₂⁴×C₇	1	8	yes	—
715	C₄⋊C₄	C₂⁴×C₇	1	8	yes	—
716	C₄⋊C₄	C₂⁴×C₇	1	16	yes	—
717	C₄⋊C₄	C₂⁴×C₇	1	16	yes	—
718	C₄⋊C₄	C₂⁴×C₇	1	16	yes	—
719	C₂²⋊C₄	C₂⁴×C₇	1	8	yes	—
720	C₂²⋊C₄	C₂⁴×C₇	1	16	yes	—
721	C₂²⋊C₄	C₂⁴×C₇	1	16	yes	—
722	C₂²⋊C₄	C₂⁴×C₇	1	16	yes	—
723	C₂²⋊C₄	C₂⁴×C₇	1	8	yes	—
724	C₂²⋊C₄	C₂⁴×C₇	1	8	yes	—
725	C₂²⋊C₄	C₂⁴×C₇	1	16	yes	—
726	C₂²⋊C₄	C₂⁴×C₇	1	16	yes	—
727	C₂²⋊C₄	C₂⁴×C₇	1	8	yes	—
728	C₂²⋊C₄	C₂⁴×C₇	1	16	yes	—
729	C₂²⋊C₄	C₂⁴×C₇	1	8	yes	—
730	C₂²⋊C₄	C₂⁴×C₇	1	8	yes	—
731	C₂²⋊C₄	C₂⁴×C₇	1	16	yes	—
732	C₂²⋊C₄	C₂⁴×C₇	1	16	yes	—
733	C₂²⋊C₄	C₂⁴×C₇	1	16	yes	—
734	C₄²	C₂⁴×C₇	1	4	yes	—
735	C₄²	C₂⁴×C₇	1	8	yes	—
736	C₄²	C₂⁴×C₇	1	4	yes	—
737	C₄²	C₂⁴×C₇	1	8	yes	—
738	C₄²	C₂⁴×C₇	1	16	yes	—
739	C₄²	C₂⁴×C₇	1	8	yes	—
740	C₂×C₇	—	4	2	no	—
741	C₂×C₇	—	4	4	no	—
742	C₂×C₇	—	4	2	no	—
743	C₂×C₇	—	4	8	no	—
744	C₂×C₇	—	4	2	no	—
745	C₂×C₇	#3551	1	4	yes	direct product factor
746	C₂×C₇	C₂²×H(5,𝔽₂)	1	1	yes	characteristic
747	C₂×C₇	C₂×#585	1	2	yes	—
748	C₂³	—	2	2	no	—
749	C₂³	—	2	4	no	—
750	C₂³	—	2	2	no	—
751	C₂³	—	2	2	no	—
752	C₂³	—	2	8	no	—
753	C₂³	—	2	4	no	—
754	C₂³	—	2	4	no	—
755	C₂³	—	2	8	no	—
756	C₂³	—	2	4	no	—
757	C₂³	—	2	4	no	—
758	C₂³	—	2	8	no	—
759	C₂³	—	2	4	no	—
760	C₂³	—	4	8	no	—
761	C₂³	—	4	16	no	—
762	C₂³	—	8	16	no	—
763	C₂³	C₂⁵×C₇	1	2	yes	—
764	C₂³	C₂⁵×C₇	1	8	yes	—
765	C₂³	C₂⁵×C₇	1	2	yes	—
766	C₂³	C₂⁵×C₇	1	4	yes	—
767	C₂³	C₂⁵×C₇	1	2	yes	—
768	C₂³	C₂⁵×C₇	1	1	yes	characteristic
769	Q₈	—	2	16	no	—
770	Q₈	—	4	8	no	—
771	Q₈	—	4	4	no	—
772	Q₈	—	4	4	no	—
773	D₄	—	2	16	no	—
774	D₄	—	4	8	no	—
775	D₄	—	4	16	no	—
776	D₄	—	4	8	no	—
777	D₄	—	4	16	no	—
778	D₄	—	4	16	no	—
779	D₄	—	4	8	no	—
780	D₄	—	4	8	no	—
781	D₄	—	4	4	no	—
782	D₄	—	4	4	no	—
783	D₄	—	4	4	no	—
784	D₄	—	4	4	no	—
785	D₄	—	4	16	no	—
786	C₂×C₄	—	2	4	no	—
787	C₂×C₄	—	2	2	no	—
788	C₂×C₄	—	2	2	no	—
789	C₂×C₄	—	2	2	no	—
790	C₂×C₄	—	2	8	no	—
791	C₂×C₄	—	2	4	no	—
792	C₂×C₄	—	2	8	no	—
793	C₂×C₄	—	2	4	no	—
794	C₂×C₄	—	2	8	no	—
795	C₂×C₄	—	2	8	no	—
796	C₂×C₄	—	2	8	no	—
797	C₂×C₄	—	2	16	no	—
798	C₂×C₄	—	2	8	no	—
799	C₂×C₄	—	4	16	no	—
800	C₂×C₄	—	4	8	no	—
801	C₂×C₄	—	4	16	no	—
802	C₂×C₄	—	4	8	no	—
803	C₂×C₄	—	4	16	no	—
804	C₂×C₄	C₇×H(5,𝔽₂)	1	4	yes	—
805	C₂×C₄	C₂⁵×C₇	1	4	yes	—
806	C₂×C₄	C₂⁵×C₇	1	2	yes	—
807	C₂×C₄	C₂⁵×C₇	1	4	yes	—
808	C₂×C₄	C₂⁵×C₇	1	8	yes	—
809	C₂×C₄	C₂⁵×C₇	1	2	yes	—
810	C₂×C₄	C₂⁵×C₇	1	2	yes	—
811	C₂×C₄	C₂⁵×C₇	1	8	yes	—
812	C₂×C₄	C₂⁵×C₇	1	8	yes	—
813	C₂×C₄	C₂⁵×C₇	1	4	yes	—
814	C₂×C₄	C₂⁵×C₇	1	2	yes	—
815	C₇	C₂×#3551	1	1	yes	characteristic, direct product factor, Sylow
816	C₂²	—	2	2	no	—
817	C₂²	—	2	4	no	—
818	C₂²	—	2	2	no	—
819	C₂²	—	2	2	no	—
820	C₂²	—	2	8	no	—
821	C₂²	—	2	4	no	—
822	C₂²	—	2	4	no	—
823	C₂²	—	2	8	no	—
824	C₂²	—	2	4	no	—
825	C₂²	—	2	4	no	—
826	C₂²	—	2	8	no	—
827	C₂²	—	2	4	no	—
828	C₂²	—	4	4	no	—
829	C₂²	—	4	16	no	—
830	C₂²	—	4	4	no	—
831	C₂²	—	4	8	no	—
832	C₂²	—	4	4	no	—
833	C₂²	—	8	16	no	—
834	C₂²	C₂×C₇×H(5,𝔽₂)	1	2	yes	—
835	C₂²	C₇×#585	1	4	yes	—
836	C₂²	C₂⁶×C₇	1	1	yes	characteristic
837	C₄	—	2	4	no	—
838	C₄	—	2	2	no	—
839	C₄	—	2	2	no	—
840	C₄	—	2	2	no	—
841	C₄	—	2	8	no	—
842	C₄	—	2	4	no	—
843	C₄	—	2	8	no	—
844	C₄	—	2	4	no	—
845	C₄	—	2	8	no	—
846	C₄	C₂×C₇×H(5,𝔽₂)	1	4	yes	—
847	C₂	—	4	2	no	—
848	C₂	—	4	8	no	—
849	C₂	—	4	2	no	—
850	C₂	—	4	4	no	—
851	C₂	—	4	2	no	—
852	C₂	C₇×#3551	1	4	yes	direct product factor
853	C₂	C₂²×C₇×H(5,𝔽₂)	1	1	yes	characteristic
854	C₂	C₂×C₇×#585	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₇	C₂⁵
commutator, Frattini, cosocle	C₂²	C₂⁶×C₇
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×#3551	C₂	direct (N × H)
2. C₂×C₇×#563	C₂	semidirect
3. C₂×C₇×#560	C₂	semidirect
4. C₂×C₇×#555	C₂	semidirect
5. C₂×C₇×#553	C₂	semidirect
6. C₂×C₇×#552	C₂	semidirect
7. C₂×C₇×#551	C₂	semidirect
8. C₂×C₇×#548	C₂	semidirect
9. C₂×C₇×#546	C₂	semidirect
10. C₂×C₇×#540	C₂	semidirect
11. C₂×C₇×#538	C₂	semidirect
12. C₂×C₇×#537	C₂	semidirect
13. C₂×C₇×#536	C₂	semidirect
14. C₂×C₇×#535	C₂	semidirect
15. C₂×C₇×#532	C₂	semidirect
16. C₂×C₇×#529	C₂	semidirect
19. C₂²×C₇×#41	C₂²	semidirect
20. C₂³×C₇×Q₈	C₂²	semidirect
22. C₇×#563	C₂²	semidirect
23. C₇×#560	C₂²	semidirect
24. C₇×#555	C₂²	semidirect
25. C₇×#553	C₂²	semidirect
26. C₇×#552	C₂²	semidirect
27. C₇×#551	C₂²	semidirect
28. C₇×#548	C₂²	semidirect
29. C₇×#546	C₂²	semidirect
30. C₇×#540	C₂²	semidirect
31. C₇×#538	C₂²	semidirect
32. C₇×#537	C₂²	semidirect
33. C₇×#536	C₂²	semidirect
34. C₇×#535	C₂²	semidirect
35. C₇×#532	C₂²	semidirect
36. C₂×C₇×C₄⋊Q₈	C₂²	semidirect
37. C₂×C₇×C₄⋊Q₈	C₂²	semidirect
40. C₇×#529	C₂²	semidirect
42. C₂×C₇×#126	C₂²	semidirect
43. C₂×C₇×#126	C₂²	semidirect
44. C₂×C₇×#125	C₂²	semidirect
45. C₂×C₇×#125	C₂²	semidirect
50. C₂×C₇×#124	C₂²	semidirect
51. C₂×C₇×#124	C₂²	semidirect
55. C₂×C₇×#123	C₂²	semidirect
56. C₂×C₇×#123	C₂²	semidirect
57. C₂×C₇×#123	C₂²	semidirect
59. C₂×C₇×C₂²⋊Q₈	C₂²	semidirect
60. C₂×C₇×C₂²⋊Q₈	C₂²	semidirect
61. C₂×C₇×C₂²⋊Q₈	C₂²	semidirect
62. C₂×C₇×C₂²⋊Q₈	C₂²	semidirect
68. C₂×C₇×#121	C₂²	semidirect
69. C₂×C₇×#121	C₂²	semidirect
70. C₂×C₇×#121	C₂²	semidirect
71. C₂×C₇×#121	C₂²	semidirect
72. C₂×C₇×#121	C₂²	semidirect
73. C₂×C₇×#121	C₂²	semidirect
77. C₂×C₄×C₇×Q₈	C₂²	semidirect
80. C₂×C₄×C₇×D₄	C₂²	semidirect
81. C₂×C₄×C₇×D₄	C₂²	semidirect
82. C₂×C₄×C₇×D₄	C₂²	semidirect
83. C₂×C₄×C₇×D₄	C₂²	semidirect
85. C₂×C₇×#117	C₂²	semidirect
86. C₂×C₇×#117	C₂²	semidirect
87. C₂×C₇×#117	C₂²	semidirect
88. C₂²×C₇×C₄⋊C₄	C₂²	semidirect
90. C₂²×C₄²×C₇	C₂²	semidirect
91. C₂×#3551	C₇	direct (N × H)
98. C₂×C₇×#41	C₂³	semidirect
104. C₂²×C₇×Q₈	C₂³	semidirect
129. C₇×C₄⋊Q₈	C₂³	semidirect
130. 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
142. C₇×#124	C₂³	semidirect
143. C₇×#124	C₂³	semidirect
147. C₇×#123	C₂³	semidirect
148. C₇×#123	C₂³	semidirect
149. C₇×#123	C₂³	semidirect
151. C₇×C₂²⋊Q₈	C₂³	semidirect
152. C₇×C₂²⋊Q₈	C₂³	semidirect
153. C₇×C₂²⋊Q₈	C₂³	semidirect
154. C₇×C₂²⋊Q₈	C₂³	semidirect
160. C₇×#121	C₂³	semidirect
161. C₇×#121	C₂³	semidirect
162. C₇×#121	C₂³	semidirect
163. C₇×#121	C₂³	semidirect
164. C₇×#121	C₂³	semidirect
165. C₇×#121	C₂³	semidirect
169. C₄×C₇×Q₈	C₂³	semidirect
172. C₄×C₇×D₄	C₂³	semidirect
173. C₄×C₇×D₄	C₂³	semidirect
174. C₄×C₇×D₄	C₂³	semidirect
175. C₄×C₇×D₄	C₂³	semidirect
177. C₇×#117	C₂³	semidirect
178. C₇×#117	C₂³	semidirect
179. C₇×#117	C₂³	semidirect
191. C₂×C₇×C₄⋊C₄	C₂³	semidirect
214. C₂×C₄²×C₇	C₂³	semidirect
215. #3551	C₂×C₇	direct (N × H)
216. C₂×#563	C₂×C₇	semidirect
217. C₂×#560	C₂×C₇	semidirect
218. C₂×#555	C₂×C₇	semidirect
219. C₂×#553	C₂×C₇	semidirect
220. C₂×#552	C₂×C₇	semidirect
221. C₂×#551	C₂×C₇	semidirect
222. C₂×#548	C₂×C₇	semidirect
223. C₂×#546	C₂×C₇	semidirect
224. C₂×#540	C₂×C₇	semidirect
225. C₂×#538	C₂×C₇	semidirect
226. C₂×#537	C₂×C₇	semidirect
227. C₂×#536	C₂×C₇	semidirect
228. C₂×#535	C₂×C₇	semidirect
229. C₂×#532	C₂×C₇	semidirect
230. C₂×#529	C₂×C₇	semidirect
340. C₂²×#41	C₂²×C₇	semidirect
341. C₂³×Q₈	C₂²×C₇	semidirect
343. #563	C₂²×C₇	semidirect
344. #560	C₂²×C₇	semidirect
345. #555	C₂²×C₇	semidirect
346. #553	C₂²×C₇	semidirect
347. #552	C₂²×C₇	semidirect
348. #551	C₂²×C₇	semidirect
349. #548	C₂²×C₇	semidirect
350. #546	C₂²×C₇	semidirect
351. #540	C₂²×C₇	semidirect
352. #538	C₂²×C₇	semidirect
353. #537	C₂²×C₇	semidirect
354. #536	C₂²×C₇	semidirect
355. #535	C₂²×C₇	semidirect
356. #532	C₂²×C₇	semidirect
357. C₂×C₄⋊Q₈	C₂²×C₇	semidirect
358. C₂×C₄⋊Q₈	C₂²×C₇	semidirect
361. #529	C₂²×C₇	semidirect
363. C₂×#126	C₂²×C₇	semidirect
364. C₂×#126	C₂²×C₇	semidirect
365. C₂×#125	C₂²×C₇	semidirect
366. C₂×#125	C₂²×C₇	semidirect
371. C₂×#124	C₂²×C₇	semidirect
372. C₂×#124	C₂²×C₇	semidirect
376. C₂×#123	C₂²×C₇	semidirect
377. C₂×#123	C₂²×C₇	semidirect
378. C₂×#123	C₂²×C₇	semidirect
380. C₂×C₂²⋊Q₈	C₂²×C₇	semidirect
381. C₂×C₂²⋊Q₈	C₂²×C₇	semidirect
382. C₂×C₂²⋊Q₈	C₂²×C₇	semidirect
383. C₂×C₂²⋊Q₈	C₂²×C₇	semidirect
389. C₂×#121	C₂²×C₇	semidirect
390. C₂×#121	C₂²×C₇	semidirect
391. C₂×#121	C₂²×C₇	semidirect
392. C₂×#121	C₂²×C₇	semidirect
393. C₂×#121	C₂²×C₇	semidirect
394. C₂×#121	C₂²×C₇	semidirect
398. C₂×C₄×Q₈	C₂²×C₇	semidirect
401. C₂×C₄×D₄	C₂²×C₇	semidirect
402. C₂×C₄×D₄	C₂²×C₇	semidirect
403. C₂×C₄×D₄	C₂²×C₇	semidirect
404. C₂×C₄×D₄	C₂²×C₇	semidirect
406. C₂×#117	C₂²×C₇	semidirect
407. C₂×#117	C₂²×C₇	semidirect
408. C₂×#117	C₂²×C₇	semidirect
409. C₂²×C₄⋊C₄	C₂²×C₇	semidirect
411. C₂²×C₄²	C₂²×C₇	semidirect
485. C₂×#41	C₂³×C₇	semidirect
491. C₂²×Q₈	C₂³×C₇	semidirect
516. C₄⋊Q₈	C₂³×C₇	semidirect
517. C₄⋊Q₈	C₂³×C₇	semidirect
521. #126	C₂³×C₇	semidirect
522. #126	C₂³×C₇	semidirect
523. #125	C₂³×C₇	semidirect
524. #125	C₂³×C₇	semidirect
529. #124	C₂³×C₇	semidirect
530. #124	C₂³×C₇	semidirect
534. #123	C₂³×C₇	semidirect
535. #123	C₂³×C₇	semidirect
536. #123	C₂³×C₇	semidirect
538. C₂²⋊Q₈	C₂³×C₇	semidirect
539. C₂²⋊Q₈	C₂³×C₇	semidirect
540. C₂²⋊Q₈	C₂³×C₇	semidirect
541. C₂²⋊Q₈	C₂³×C₇	semidirect
547. #121	C₂³×C₇	semidirect
548. #121	C₂³×C₇	semidirect
549. #121	C₂³×C₇	semidirect
550. #121	C₂³×C₇	semidirect
551. #121	C₂³×C₇	semidirect
552. #121	C₂³×C₇	semidirect
556. C₄×Q₈	C₂³×C₇	semidirect
559. C₄×D₄	C₂³×C₇	semidirect
560. C₄×D₄	C₂³×C₇	semidirect
561. C₄×D₄	C₂³×C₇	semidirect
562. C₄×D₄	C₂³×C₇	semidirect
564. #117	C₂³×C₇	semidirect
565. #117	C₂³×C₇	semidirect
566. #117	C₂³×C₇	semidirect
578. C₂×C₄⋊C₄	C₂³×C₇	semidirect
601. C₂×C₄²	C₂³×C₇	semidirect
745. C₂×C₇	#3551	direct (N × H)
815. C₇	C₂×#3551	direct (N × H)
852. C₂	C₇×#3551	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×#3551	2
C₂×C₇×#563	2
C₂×C₇×#560	2
C₂×C₇×#555	2
C₂×C₇×#553	2
C₂×C₇×#552	2
C₂×C₇×#551	2
C₂×C₇×#548	2
C₂×C₇×#546	2
C₂×C₇×#540	2
C₂×C₇×#538	2
C₂×C₇×#537	2
C₂×C₇×#536	2
C₂×C₇×#535	2
C₂×C₇×#532	2
C₂×C₇×#529	2
C₂×#3551	7

Subgroups — C2×C7×#3551 #13239955

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₇×#3551 #13239955