Subgroups — C₂×C₇×#3546 #13239963

Order 1792.

8046 conjugacy classes of subgroups.

The subgroup lattice has 964 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×#3546	C₂	1	32	yes	maximal, direct product factor
2	C₂×C₇×#560	C₂	1	4	yes	maximal, complemented
3	C₂×C₇×#556	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₇×#553	C₂	1	2	yes	maximal, complemented
5	C₂×C₇×#550	C₂	1	2	yes	maximal, complemented
6	C₂×C₇×#550	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₇×#547	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₇×#546	C₂	1	2	yes	maximal, complemented
9	C₂×C₇×#546	C₂	1	2	yes	maximal, complemented
10	C₂×C₇×D₄²	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×C₇×#542	C₂	1	2	yes	maximal, complemented
12	C₂×C₇×#538	C₂	1	4	yes	maximal, complemented
13	C₂×C₇×#537	C₂	1	2	yes	maximal, complemented
14	C₂×C₇×#535	C₂	1	2	yes	maximal, complemented
15	C₂×C₇×#535	C₂	1	2	yes	maximal, complemented
16	C₂×C₇×#532	C₂	1	1	yes	maximal, characteristic, complemented
17	C₂×C₇×#532	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂×C₇×#529	C₂	1	1	yes	maximal, characteristic, complemented
19	C₂²×C₇×#41	C₂²	1	2	yes	complemented
20	C₂²×C₇×#41	C₂²	1	2	yes	complemented
21	C₂²×C₇×#41	C₂²	1	2	yes	complemented
22	C₂²×C₇×#41	C₂²	1	2	yes	complemented
23	C₂³×C₇×D₄	C₂²	1	2	yes	—
24	C₂³×C₇×D₄	C₂²	1	2	yes	—
25	C₇×#560	C₂²	1	64	yes	complemented
26	C₇×#556	C₂²	1	16	yes	complemented
27	C₇×#553	C₂²	1	32	yes	complemented
28	C₇×#550	C₂²	1	32	yes	complemented
29	C₇×#550	C₂²	1	16	yes	complemented
30	C₇×#547	C₂²	1	16	yes	complemented
31	C₇×#546	C₂²	1	32	yes	complemented
32	C₇×#546	C₂²	1	32	yes	complemented
33	C₇×D₄²	C₂²	1	16	yes	complemented
34	C₇×#542	C₂²	1	32	yes	complemented
35	C₇×#538	C₂²	1	64	yes	complemented
36	C₇×#537	C₂²	1	32	yes	complemented
37	C₇×#535	C₂²	1	32	yes	complemented
38	C₇×#535	C₂²	1	32	yes	complemented
39	C₇×#532	C₂²	1	16	yes	complemented
40	C₇×#532	C₂²	1	16	yes	complemented
41	C₂×C₇×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
42	C₂×C₇×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
43	C₂×C₇×#127	C₂²	1	1	yes	characteristic
44	C₂×C₇×#127	C₂²	1	1	yes	characteristic
45	C₂×C₇×#127	C₂²	1	2	yes	complemented
46	C₂×C₇×#127	C₂²	1	4	yes	complemented
47	C₇×#529	C₂²	1	16	yes	complemented
48	C₂×C₇×#126	C₂²	1	2	yes	complemented
49	C₂×C₇×#126	C₂²	1	4	yes	complemented
50	C₂×C₇×#126	C₂²	1	4	yes	complemented
51	C₂×C₇×#125	C₂²	1	1	yes	characteristic, complemented
52	C₂×C₇×#124	C₂²	1	1	yes	characteristic
53	C₂×C₇×#124	C₂²	1	2	yes	—
54	C₂×C₇×#124	C₂²	1	2	yes	complemented
55	C₂×C₇×#124	C₂²	1	2	yes	complemented
56	C₂×C₇×#124	C₂²	1	4	yes	complemented
57	C₂×C₇×#123	C₂²	1	2	yes	complemented
58	C₂×C₇×#123	C₂²	1	4	yes	complemented
59	C₂×C₇×#123	C₂²	1	4	yes	complemented
60	C₂×C₇×#123	C₂²	1	4	yes	complemented
61	C₂×C₇×C₂²⋊Q₈	C₂²	1	1	yes	characteristic, complemented
62	C₂×C₇×C₂²⋊Q₈	C₂²	1	4	yes	complemented
63	C₂×C₇×C₂²⋊Q₈	C₂²	1	2	yes	complemented
64	C₂×C₇×C₂²⋊Q₈	C₂²	1	2	yes	complemented
65	C₂×C₇×#121	C₂²	1	1	yes	characteristic
66	C₂×C₇×#121	C₂²	1	1	yes	characteristic
67	C₂×C₇×#121	C₂²	1	2	yes	—
68	C₂×C₇×#121	C₂²	1	2	yes	—
69	C₂×C₇×#121	C₂²	1	2	yes	—
70	C₂×C₇×#121	C₂²	1	2	yes	complemented
71	C₂×C₇×#121	C₂²	1	1	yes	characteristic, complemented
72	C₂×C₇×#121	C₂²	1	2	yes	complemented
73	C₂×C₇×#121	C₂²	1	2	yes	complemented
74	C₂×C₇×#121	C₂²	1	4	yes	complemented
75	C₂×C₇×#121	C₂²	1	2	yes	complemented
76	C₂×C₇×#121	C₂²	1	4	yes	complemented
77	C₂×C₇×#121	C₂²	1	4	yes	complemented
78	C₂×C₇×#121	C₂²	1	4	yes	complemented
79	C₂×C₇×#121	C₂²	1	4	yes	complemented
80	C₂×C₇×#121	C₂²	1	4	yes	complemented
81	C₂×C₇×#120	C₂²	1	4	yes	—
82	C₂×C₇×#120	C₂²	1	4	yes	complemented
83	C₂×C₇×#120	C₂²	1	4	yes	complemented
84	C₂×C₇×#120	C₂²	1	4	yes	complemented
85	C₂×C₄×C₇×Q₈	C₂²	1	1	yes	characteristic, complemented
86	C₂×C₄×C₇×Q₈	C₂²	1	2	yes	complemented
87	C₂×C₄×C₇×D₄	C₂²	1	1	yes	characteristic
88	C₂×C₄×C₇×D₄	C₂²	1	1	yes	characteristic
89	C₂×C₄×C₇×D₄	C₂²	1	2	yes	complemented
90	C₂×C₄×C₇×D₄	C₂²	1	2	yes	complemented
91	C₂×C₄×C₇×D₄	C₂²	1	2	yes	complemented
92	C₂×C₄×C₇×D₄	C₂²	1	2	yes	complemented
93	C₂×C₄×C₇×D₄	C₂²	1	1	yes	characteristic, complemented
94	C₂×C₄×C₇×D₄	C₂²	1	4	yes	complemented
95	C₂×C₄×C₇×D₄	C₂²	1	2	yes	complemented
96	C₂×C₇×#117	C₂²	1	2	yes	complemented
97	C₂×C₇×#117	C₂²	1	2	yes	complemented
98	C₂²×C₇×C₄⋊C₄	C₂²	1	2	yes	complemented
99	C₂²×C₇×C₂²⋊C₄	C₂²	1	4	yes	complemented
100	C₂²×C₄²×C₇	C₂²	1	1	yes	characteristic, complemented
101	C₂×#3546	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
102	C₂⁵×C₇	C₂³	1	4	yes	—
103	C₂×C₇×#41	—	4	8	no	—
104	C₂×C₇×#41	—	4	8	no	—
105	C₂×C₇×#41	—	4	8	no	—
106	C₂×C₇×#41	—	4	8	no	—
107	C₂×C₇×#41	C₂³	1	16	yes	complemented
108	C₂×C₇×#41	C₂³	1	16	yes	complemented
109	C₂×C₇×#41	C₂³	1	16	yes	complemented
110	C₂×C₇×#41	C₂³	1	16	yes	complemented
111	C₂²×C₇×Q₈	C₂³	1	1	yes	characteristic
112	C₂²×C₇×Q₈	C₂³	1	2	yes	—
113	C₂²×C₇×Q₈	C₂³	1	2	yes	—
114	C₂²×C₇×D₄	—	4	8	no	—
115	C₂²×C₇×D₄	—	4	8	no	—
116	C₂²×C₇×D₄	C₂³	1	1	yes	characteristic
117	C₂²×C₇×D₄	C₂³	1	1	yes	characteristic
118	C₂²×C₇×D₄	C₂³	1	2	yes	—
119	C₂²×C₇×D₄	C₂³	1	2	yes	—
120	C₂²×C₇×D₄	C₂³	1	1	yes	characteristic
121	C₂²×C₇×D₄	C₂³	1	4	yes	—
122	C₂²×C₇×D₄	C₂³	1	4	yes	—
123	C₂²×C₇×D₄	C₂³	1	16	yes	—
124	C₂²×C₇×D₄	C₂³	1	16	yes	—
125	C₂²×C₇×D₄	C₂³	1	2	yes	—
126	C₂²×C₇×D₄	C₂³	1	4	yes	—
127	C₂²×C₇×D₄	C₂³	1	2	yes	—
128	C₂²×C₇×D₄	C₂³	1	4	yes	—
129	C₂²×C₇×D₄	C₂³	1	4	yes	—
130	C₂²×C₇×D₄	C₂³	1	2	yes	—
131	C₂²×C₇×D₄	C₂³	1	2	yes	—
132	C₂²×C₇×D₄	C₂³	1	2	yes	—
133	C₂²×C₇×D₄	C₂³	1	2	yes	—
134	C₂²×C₇×D₄	C₂³	1	4	yes	—
135	C₂³×C₄×C₇	C₂³	1	2	yes	—
136	C₂³×C₄×C₇	C₂³	1	2	yes	—
137	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
138	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
139	C₂³×C₄×C₇	C₂³	1	2	yes	—
140	C₂³×C₄×C₇	C₂³	1	4	yes	—
141	C₂³×C₄×C₇	C₂³	1	4	yes	—
142	C₂³×C₄×C₇	C₂³	1	4	yes	—
143	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
144	C₇×C₄⋊Q₈	C₂³	1	8	yes	complemented
145	C₇×C₄⋊Q₈	C₂³	1	8	yes	complemented
146	C₇×#127	C₂³	1	8	yes	—
147	C₇×#127	C₂³	1	8	yes	—
148	C₇×#127	C₂³	1	16	yes	complemented
149	C₇×#127	C₂³	1	32	yes	complemented
150	C₇×#126	C₂³	1	16	yes	complemented
151	C₇×#126	C₂³	1	32	yes	complemented
152	C₇×#126	C₂³	1	32	yes	complemented
153	C₇×#125	C₂³	1	8	yes	complemented
154	C₇×#124	C₂³	1	8	yes	—
155	C₇×#124	C₂³	1	16	yes	—
156	C₇×#124	C₂³	1	16	yes	complemented
157	C₇×#124	C₂³	1	16	yes	complemented
158	C₇×#124	C₂³	1	32	yes	complemented
159	C₇×#123	C₂³	1	16	yes	complemented
160	C₇×#123	C₂³	1	32	yes	complemented
161	C₇×#123	C₂³	1	32	yes	complemented
162	C₇×#123	C₂³	1	32	yes	complemented
163	C₇×C₂²⋊Q₈	C₂³	1	8	yes	complemented
164	C₇×C₂²⋊Q₈	C₂³	1	32	yes	complemented
165	C₇×C₂²⋊Q₈	C₂³	1	16	yes	complemented
166	C₇×C₂²⋊Q₈	C₂³	1	16	yes	complemented
167	C₇×#121	C₂³	1	8	yes	—
168	C₇×#121	C₂³	1	8	yes	—
169	C₇×#121	C₂³	1	16	yes	—
170	C₇×#121	C₂³	1	16	yes	—
171	C₇×#121	C₂³	1	16	yes	—
172	C₇×#121	C₂³	1	16	yes	complemented
173	C₇×#121	C₂³	1	8	yes	complemented
174	C₇×#121	C₂³	1	16	yes	complemented
175	C₇×#121	C₂³	1	16	yes	complemented
176	C₇×#121	C₂³	1	32	yes	complemented
177	C₇×#121	C₂³	1	16	yes	complemented
178	C₇×#121	C₂³	1	32	yes	complemented
179	C₇×#121	C₂³	1	32	yes	complemented
180	C₇×#121	C₂³	1	32	yes	complemented
181	C₇×#121	C₂³	1	32	yes	complemented
182	C₇×#121	C₂³	1	32	yes	complemented
183	C₇×#120	C₂³	1	32	yes	—
184	C₇×#120	C₂³	1	32	yes	complemented
185	C₇×#120	C₂³	1	32	yes	complemented
186	C₇×#120	C₂³	1	32	yes	complemented
187	C₄×C₇×Q₈	C₂³	1	8	yes	complemented
188	C₄×C₇×Q₈	C₂³	1	16	yes	complemented
189	C₄×C₇×D₄	C₂³	1	8	yes	—
190	C₄×C₇×D₄	C₂³	1	8	yes	—
191	C₄×C₇×D₄	C₂³	1	16	yes	complemented
192	C₄×C₇×D₄	C₂³	1	16	yes	complemented
193	C₄×C₇×D₄	C₂³	1	16	yes	complemented
194	C₄×C₇×D₄	C₂³	1	16	yes	complemented
195	C₄×C₇×D₄	C₂³	1	8	yes	complemented
196	C₄×C₇×D₄	C₂³	1	32	yes	complemented
197	C₄×C₇×D₄	C₂³	1	16	yes	complemented
198	C₇×#117	C₂³	1	16	yes	complemented
199	C₇×#117	C₂³	1	16	yes	complemented
200	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
201	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
202	C₂×C₇×C₄⋊C₄	C₂³	1	4	yes	—
203	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
204	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
205	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
206	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
207	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
208	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
209	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
210	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
211	C₂×C₇×C₄⋊C₄	C₂³	1	4	yes	—
212	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
213	C₂×C₇×C₄⋊C₄	C₂³	1	16	yes	complemented
214	C₂×C₇×C₂²⋊C₄	C₂³	1	2	yes	—
215	C₂×C₇×C₂²⋊C₄	C₂³	1	2	yes	—
216	C₂×C₇×C₂²⋊C₄	C₂³	1	4	yes	—
217	C₂×C₇×C₂²⋊C₄	C₂³	1	4	yes	—
218	C₂×C₇×C₂²⋊C₄	C₂³	1	2	yes	—
219	C₂×C₇×C₂²⋊C₄	C₂³	1	4	yes	—
220	C₂×C₇×C₂²⋊C₄	C₂³	1	2	yes	—
221	C₂×C₇×C₂²⋊C₄	C₂³	1	2	yes	—
222	C₂×C₇×C₂²⋊C₄	C₂³	1	2	yes	—
223	C₂×C₇×C₂²⋊C₄	C₂³	1	2	yes	—
224	C₂×C₇×C₂²⋊C₄	C₂³	1	4	yes	—
225	C₂×C₇×C₂²⋊C₄	C₂³	1	4	yes	—
226	C₂×C₇×C₂²⋊C₄	C₂³	1	4	yes	—
227	C₂×C₇×C₂²⋊C₄	C₂³	1	4	yes	—
228	C₂×C₇×C₂²⋊C₄	C₂³	1	2	yes	—
229	C₂×C₇×C₂²⋊C₄	C₂³	1	2	yes	—
230	C₂×C₇×C₂²⋊C₄	C₂³	1	32	yes	complemented
231	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
232	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
233	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
234	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
235	C₂×C₄²×C₇	C₂³	1	2	yes	—
236	C₂×C₄²×C₇	C₂³	1	4	yes	—
237	C₂×C₄²×C₇	C₂³	1	8	yes	complemented
238	#3546	C₂×C₇	1	32	yes	direct product factor
239	C₂×#560	C₂×C₇	1	4	yes	complemented
240	C₂×#556	C₂×C₇	1	1	yes	characteristic, complemented
241	C₂×#553	C₂×C₇	1	2	yes	complemented
242	C₂×#550	C₂×C₇	1	2	yes	complemented
243	C₂×#550	C₂×C₇	1	1	yes	characteristic, complemented
244	C₂×#547	C₂×C₇	1	1	yes	characteristic, complemented
245	C₂×#546	C₂×C₇	1	2	yes	complemented
246	C₂×#546	C₂×C₇	1	2	yes	complemented
247	C₂×D₄²	C₂×C₇	1	1	yes	characteristic, complemented
248	C₂×#542	C₂×C₇	1	2	yes	complemented
249	C₂×#538	C₂×C₇	1	4	yes	complemented
250	C₂×#537	C₂×C₇	1	2	yes	complemented
251	C₂×#535	C₂×C₇	1	2	yes	complemented
252	C₂×#535	C₂×C₇	1	2	yes	complemented
253	C₂×#532	C₂×C₇	1	1	yes	characteristic, complemented
254	C₂×#532	C₂×C₇	1	1	yes	characteristic, complemented
255	C₂×#529	C₂×C₇	1	1	yes	characteristic, complemented
256	C₂⁴×C₇	—	4	8	no	—
257	C₂⁴×C₇	—	4	8	no	—
258	C₂⁴×C₇	—	4	8	no	—
259	C₂⁴×C₇	C₂⁴	1	2	yes	—
260	C₂⁴×C₇	C₂⁴	1	2	yes	—
261	C₂⁴×C₇	C₂⁴	1	4	yes	—
262	C₂⁴×C₇	C₂⁴	1	1	yes	characteristic
263	C₂⁴×C₇	C₂⁴	1	2	yes	—
264	C₂⁴×C₇	C₂⁴	1	16	yes	—
265	C₇×#41	—	4	32	no	—
266	C₇×#41	—	4	32	no	—
267	C₇×#41	—	4	32	no	—
268	C₇×#41	—	4	32	no	—
269	C₂×C₇×Q₈	—	2	4	no	—
270	C₂×C₇×Q₈	—	2	8	no	—
271	C₂×C₇×Q₈	—	4	4	no	—
272	C₂×C₇×Q₈	C₂⁴	1	4	yes	—
273	C₂×C₇×Q₈	C₂⁴	1	8	yes	—
274	C₂×C₇×Q₈	C₂⁴	1	8	yes	—
275	C₂×C₇×D₄	—	2	4	no	—
276	C₂×C₇×D₄	—	2	4	no	—
277	C₂×C₇×D₄	—	2	8	no	—
278	C₂×C₇×D₄	—	2	8	no	—
279	C₂×C₇×D₄	—	2	4	no	—
280	C₂×C₇×D₄	—	4	32	no	—
281	C₂×C₇×D₄	—	4	32	no	—
282	C₂×C₇×D₄	—	4	8	no	—
283	C₂×C₇×D₄	—	4	8	no	—
284	C₂×C₇×D₄	—	4	4	no	—
285	C₂×C₇×D₄	—	4	4	no	—
286	C₂×C₇×D₄	—	4	4	no	—
287	C₂×C₇×D₄	—	4	8	no	—
288	C₂×C₇×D₄	—	4	4	no	—
289	C₂×C₇×D₄	—	4	4	no	—
290	C₂×C₇×D₄	—	4	4	no	—
291	C₂×C₇×D₄	—	4	8	no	—
292	C₂×C₇×D₄	—	4	8	no	—
293	C₂×C₇×D₄	—	4	8	no	—
294	C₂×C₇×D₄	C₂⁴	1	4	yes	—
295	C₂×C₇×D₄	C₂⁴	1	4	yes	—
296	C₂×C₇×D₄	C₂⁴	1	8	yes	—
297	C₂×C₇×D₄	C₂⁴	1	8	yes	—
298	C₂×C₇×D₄	C₂⁴	1	4	yes	—
299	C₂×C₇×D₄	C₂⁴	1	8	yes	—
300	C₂×C₇×D₄	C₂⁴	1	8	yes	—
301	C₂×C₇×D₄	C₂⁴	1	8	yes	—
302	C₂×C₇×D₄	C₂⁴	1	16	yes	—
303	C₂×C₇×D₄	C₂⁴	1	16	yes	—
304	C₂×C₇×D₄	C₂⁴	1	16	yes	—
305	C₂×C₇×D₄	C₂⁴	1	8	yes	—
306	C₂×C₇×D₄	C₂⁴	1	16	yes	—
307	C₂×C₇×D₄	C₂⁴	1	8	yes	—
308	C₂×C₇×D₄	C₂⁴	1	16	yes	—
309	C₂×C₇×D₄	C₂⁴	1	16	yes	—
310	C₂×C₇×D₄	C₂⁴	1	8	yes	—
311	C₂²×C₄×C₇	—	2	8	no	—
312	C₂²×C₄×C₇	—	2	8	no	—
313	C₂²×C₄×C₇	—	2	4	no	—
314	C₂²×C₄×C₇	—	2	8	no	—
315	C₂²×C₄×C₇	—	2	4	no	—
316	C₂²×C₄×C₇	—	4	2	no	—
317	C₂²×C₄×C₇	—	4	8	no	—
318	C₂²×C₄×C₇	—	4	8	no	—
319	C₂²×C₄×C₇	—	4	8	no	—
320	C₂²×C₄×C₇	C₂⁴	1	4	yes	—
321	C₂²×C₄×C₇	C₂⁴	1	4	yes	—
322	C₂²×C₄×C₇	C₂⁴	1	8	yes	—
323	C₂²×C₄×C₇	C₂⁴	1	8	yes	—
324	C₂²×C₄×C₇	C₂⁴	1	8	yes	—
325	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
326	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
327	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
328	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
329	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
330	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
331	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
332	C₂²×C₄×C₇	C₂⁴	1	4	yes	—
333	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
334	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
335	C₂²×C₄×C₇	C₂⁴	1	4	yes	—
336	C₂²×C₄×C₇	C₂⁴	1	16	yes	—
337	C₂²×C₄×C₇	C₂⁴	1	16	yes	—
338	C₂²×C₄×C₇	C₂⁴	1	16	yes	—
339	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
340	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
341	C₇×C₄⋊C₄	C₂⁴	1	4	yes	—
342	C₇×C₄⋊C₄	C₂⁴	1	8	yes	—
343	C₇×C₄⋊C₄	C₂⁴	1	16	yes	—
344	C₇×C₄⋊C₄	C₂⁴	1	4	yes	—
345	C₇×C₄⋊C₄	C₂⁴	1	8	yes	—
346	C₇×C₄⋊C₄	C₂⁴	1	8	yes	—
347	C₇×C₄⋊C₄	C₂⁴	1	4	yes	—
348	C₇×C₄⋊C₄	C₂⁴	1	4	yes	—
349	C₇×C₄⋊C₄	C₂⁴	1	8	yes	—
350	C₇×C₄⋊C₄	C₂⁴	1	8	yes	—
351	C₇×C₄⋊C₄	C₂⁴	1	8	yes	—
352	C₇×C₄⋊C₄	C₂⁴	1	16	yes	—
353	C₇×C₄⋊C₄	C₂⁴	1	8	yes	—
354	C₇×C₂²⋊C₄	C₂⁴	1	8	yes	—
355	C₇×C₂²⋊C₄	C₂⁴	1	8	yes	—
356	C₇×C₂²⋊C₄	C₂⁴	1	16	yes	—
357	C₇×C₂²⋊C₄	C₂⁴	1	16	yes	—
358	C₇×C₂²⋊C₄	C₂⁴	1	8	yes	—
359	C₇×C₂²⋊C₄	C₂⁴	1	16	yes	—
360	C₇×C₂²⋊C₄	C₂⁴	1	8	yes	—
361	C₇×C₂²⋊C₄	C₂⁴	1	8	yes	—
362	C₇×C₂²⋊C₄	C₂⁴	1	8	yes	—
363	C₇×C₂²⋊C₄	C₂⁴	1	8	yes	—
364	C₇×C₂²⋊C₄	C₂⁴	1	16	yes	—
365	C₇×C₂²⋊C₄	C₂⁴	1	16	yes	—
366	C₇×C₂²⋊C₄	C₂⁴	1	16	yes	—
367	C₇×C₂²⋊C₄	C₂⁴	1	16	yes	—
368	C₇×C₂²⋊C₄	C₂⁴	1	8	yes	—
369	C₇×C₂²⋊C₄	C₂⁴	1	8	yes	—
370	C₄²×C₇	C₂⁴	1	4	yes	—
371	C₄²×C₇	C₂⁴	1	4	yes	—
372	C₄²×C₇	C₂⁴	1	4	yes	—
373	C₄²×C₇	C₂⁴	1	4	yes	—
374	C₄²×C₇	C₂⁴	1	8	yes	—
375	C₄²×C₇	C₂⁴	1	16	yes	—
376	C₂²×#41	C₂²×C₇	1	2	yes	complemented
377	C₂²×#41	C₂²×C₇	1	2	yes	complemented
378	C₂²×#41	C₂²×C₇	1	2	yes	complemented
379	C₂²×#41	C₂²×C₇	1	2	yes	complemented
380	C₂³×D₄	C₂²×C₇	1	2	yes	—
381	C₂³×D₄	C₂²×C₇	1	2	yes	—
382	#560	C₂²×C₇	1	64	yes	complemented
383	#556	C₂²×C₇	1	16	yes	complemented
384	#553	C₂²×C₇	1	32	yes	complemented
385	#550	C₂²×C₇	1	32	yes	complemented
386	#550	C₂²×C₇	1	16	yes	complemented
387	#547	C₂²×C₇	1	16	yes	complemented
388	#546	C₂²×C₇	1	32	yes	complemented
389	#546	C₂²×C₇	1	32	yes	complemented
390	D₄²	C₂²×C₇	1	16	yes	complemented
391	#542	C₂²×C₇	1	32	yes	complemented
392	#538	C₂²×C₇	1	64	yes	complemented
393	#537	C₂²×C₇	1	32	yes	complemented
394	#535	C₂²×C₇	1	32	yes	complemented
395	#535	C₂²×C₇	1	32	yes	complemented
396	#532	C₂²×C₇	1	16	yes	complemented
397	#532	C₂²×C₇	1	16	yes	complemented
398	C₂×C₄⋊Q₈	C₂²×C₇	1	1	yes	characteristic, complemented
399	C₂×C₄⋊Q₈	C₂²×C₇	1	1	yes	characteristic, complemented
400	C₂×#127	C₂²×C₇	1	1	yes	characteristic
401	C₂×#127	C₂²×C₇	1	1	yes	characteristic
402	C₂×#127	C₂²×C₇	1	2	yes	complemented
403	C₂×#127	C₂²×C₇	1	4	yes	complemented
404	#529	C₂²×C₇	1	16	yes	complemented
405	C₂×#126	C₂²×C₇	1	2	yes	complemented
406	C₂×#126	C₂²×C₇	1	4	yes	complemented
407	C₂×#126	C₂²×C₇	1	4	yes	complemented
408	C₂×#125	C₂²×C₇	1	1	yes	characteristic, complemented
409	C₂×#124	C₂²×C₇	1	1	yes	characteristic
410	C₂×#124	C₂²×C₇	1	2	yes	—
411	C₂×#124	C₂²×C₇	1	2	yes	complemented
412	C₂×#124	C₂²×C₇	1	2	yes	complemented
413	C₂×#124	C₂²×C₇	1	4	yes	complemented
414	C₂×#123	C₂²×C₇	1	2	yes	complemented
415	C₂×#123	C₂²×C₇	1	4	yes	complemented
416	C₂×#123	C₂²×C₇	1	4	yes	complemented
417	C₂×#123	C₂²×C₇	1	4	yes	complemented
418	C₂×C₂²⋊Q₈	C₂²×C₇	1	1	yes	characteristic, complemented
419	C₂×C₂²⋊Q₈	C₂²×C₇	1	4	yes	complemented
420	C₂×C₂²⋊Q₈	C₂²×C₇	1	2	yes	complemented
421	C₂×C₂²⋊Q₈	C₂²×C₇	1	2	yes	complemented
422	C₂×#121	C₂²×C₇	1	1	yes	characteristic
423	C₂×#121	C₂²×C₇	1	1	yes	characteristic
424	C₂×#121	C₂²×C₇	1	2	yes	—
425	C₂×#121	C₂²×C₇	1	2	yes	—
426	C₂×#121	C₂²×C₇	1	2	yes	—
427	C₂×#121	C₂²×C₇	1	2	yes	complemented
428	C₂×#121	C₂²×C₇	1	1	yes	characteristic, complemented
429	C₂×#121	C₂²×C₇	1	2	yes	complemented
430	C₂×#121	C₂²×C₇	1	2	yes	complemented
431	C₂×#121	C₂²×C₇	1	4	yes	complemented
432	C₂×#121	C₂²×C₇	1	2	yes	complemented
433	C₂×#121	C₂²×C₇	1	4	yes	complemented
434	C₂×#121	C₂²×C₇	1	4	yes	complemented
435	C₂×#121	C₂²×C₇	1	4	yes	complemented
436	C₂×#121	C₂²×C₇	1	4	yes	complemented
437	C₂×#121	C₂²×C₇	1	4	yes	complemented
438	C₂×#120	C₂²×C₇	1	4	yes	—
439	C₂×#120	C₂²×C₇	1	4	yes	complemented
440	C₂×#120	C₂²×C₇	1	4	yes	complemented
441	C₂×#120	C₂²×C₇	1	4	yes	complemented
442	C₂×C₄×Q₈	C₂²×C₇	1	1	yes	characteristic, complemented
443	C₂×C₄×Q₈	C₂²×C₇	1	2	yes	complemented
444	C₂×C₄×D₄	C₂²×C₇	1	1	yes	characteristic
445	C₂×C₄×D₄	C₂²×C₇	1	1	yes	characteristic
446	C₂×C₄×D₄	C₂²×C₇	1	2	yes	complemented
447	C₂×C₄×D₄	C₂²×C₇	1	2	yes	complemented
448	C₂×C₄×D₄	C₂²×C₇	1	2	yes	complemented
449	C₂×C₄×D₄	C₂²×C₇	1	2	yes	complemented
450	C₂×C₄×D₄	C₂²×C₇	1	1	yes	characteristic, complemented
451	C₂×C₄×D₄	C₂²×C₇	1	4	yes	complemented
452	C₂×C₄×D₄	C₂²×C₇	1	2	yes	complemented
453	C₂×#117	C₂²×C₇	1	2	yes	complemented
454	C₂×#117	C₂²×C₇	1	2	yes	complemented
455	C₂²×C₄⋊C₄	C₂²×C₇	1	2	yes	complemented
456	C₂²×C₂²⋊C₄	C₂²×C₇	1	4	yes	complemented
457	C₂²×C₄²	C₂²×C₇	1	1	yes	characteristic, complemented
458	C₂³×C₇	—	2	2	no	—
459	C₂³×C₇	—	2	2	no	—
460	C₂³×C₇	—	2	4	no	—
461	C₂³×C₇	—	2	4	no	—
462	C₂³×C₇	—	2	4	no	—
463	C₂³×C₇	—	2	4	no	—
464	C₂³×C₇	—	2	8	no	—
465	C₂³×C₇	—	2	8	no	—
466	C₂³×C₇	—	2	4	no	—
467	C₂³×C₇	—	2	4	no	—
468	C₂³×C₇	—	2	2	no	—
469	C₂³×C₇	—	2	4	no	—
470	C₂³×C₇	—	2	8	no	—
471	C₂³×C₇	—	2	4	no	—
472	C₂³×C₇	—	2	4	no	—
473	C₂³×C₇	—	4	16	no	—
474	C₂³×C₇	—	4	16	no	—
475	C₂³×C₇	—	4	16	no	—
476	C₂³×C₇	—	8	32	no	—
477	C₂³×C₇	C₂⁵	1	4	yes	—
478	C₂³×C₇	C₂⁵	1	4	yes	—
479	C₂³×C₇	C₂⁵	1	8	yes	—
480	C₂³×C₇	C₂⁵	1	2	yes	—
481	C₂³×C₇	C₂⁵	1	4	yes	—
482	C₂³×C₇	C₂⁵	1	1	yes	characteristic
483	C₇×Q₈	—	2	8	no	—
484	C₇×Q₈	—	2	16	no	—
485	C₇×Q₈	—	4	8	no	—
486	C₇×D₄	—	2	8	no	—
487	C₇×D₄	—	2	8	no	—
488	C₇×D₄	—	2	16	no	—
489	C₇×D₄	—	2	16	no	—
490	C₇×D₄	—	2	8	no	—
491	C₇×D₄	—	4	16	no	—
492	C₇×D₄	—	4	16	no	—
493	C₇×D₄	—	4	8	no	—
494	C₇×D₄	—	4	8	no	—
495	C₇×D₄	—	4	8	no	—
496	C₇×D₄	—	4	16	no	—
497	C₇×D₄	—	4	8	no	—
498	C₇×D₄	—	4	8	no	—
499	C₇×D₄	—	4	8	no	—
500	C₇×D₄	—	4	16	no	—
501	C₇×D₄	—	4	16	no	—
502	C₇×D₄	—	4	16	no	—
503	C₂×C₄×C₇	—	2	2	no	—
504	C₂×C₄×C₇	—	2	4	no	—
505	C₂×C₄×C₇	—	2	4	no	—
506	C₂×C₄×C₇	—	2	4	no	—
507	C₂×C₄×C₇	—	2	2	no	—
508	C₂×C₄×C₇	—	2	8	no	—
509	C₂×C₄×C₇	—	2	4	no	—
510	C₂×C₄×C₇	—	2	2	no	—
511	C₂×C₄×C₇	—	2	2	no	—
512	C₂×C₄×C₇	—	2	4	no	—
513	C₂×C₄×C₇	—	2	16	no	—
514	C₂×C₄×C₇	—	2	16	no	—
515	C₂×C₄×C₇	—	2	8	no	—
516	C₂×C₄×C₇	—	2	16	no	—
517	C₂×C₄×C₇	—	2	8	no	—
518	C₂×C₄×C₇	—	4	4	no	—
519	C₂×C₄×C₇	—	4	16	no	—
520	C₂×C₄×C₇	—	4	16	no	—
521	C₂×C₄×C₇	—	4	16	no	—
522	C₂×C₄×C₇	H(5,𝔽₂)	1	4	yes	—
523	C₂×C₄×C₇	H(5,𝔽₂)	1	4	yes	—
524	C₂×C₄×C₇	C₂⁵	1	4	yes	—
525	C₂×C₄×C₇	C₂⁵	1	2	yes	—
526	C₂×C₄×C₇	C₂⁵	1	2	yes	—
527	C₂×C₄×C₇	C₂⁵	1	2	yes	—
528	C₂×C₄×C₇	C₂⁵	1	2	yes	—
529	C₂×C₄×C₇	C₂⁵	1	4	yes	—
530	C₂×C₄×C₇	C₂⁵	1	4	yes	—
531	C₂×C₄×C₇	C₂⁵	1	8	yes	—
532	C₂×C₄×C₇	C₂⁵	1	4	yes	—
533	C₂×C₄×C₇	C₂⁵	1	4	yes	—
534	C₂×C₄×C₇	C₂⁵	1	2	yes	—
535	C₂×C₄×C₇	C₂⁵	1	2	yes	—
536	C₂⁵	C₂³×C₇	1	4	yes	—
537	C₂×#41	—	4	8	no	—
538	C₂×#41	—	4	8	no	—
539	C₂×#41	—	4	8	no	—
540	C₂×#41	—	4	8	no	—
541	C₂×#41	C₂³×C₇	1	16	yes	complemented
542	C₂×#41	C₂³×C₇	1	16	yes	complemented
543	C₂×#41	C₂³×C₇	1	16	yes	complemented
544	C₂×#41	C₂³×C₇	1	16	yes	complemented
545	C₂²×Q₈	C₂³×C₇	1	1	yes	characteristic
546	C₂²×Q₈	C₂³×C₇	1	2	yes	—
547	C₂²×Q₈	C₂³×C₇	1	2	yes	—
548	C₂²×D₄	—	4	8	no	—
549	C₂²×D₄	—	4	8	no	—
550	C₂²×D₄	C₂³×C₇	1	1	yes	characteristic
551	C₂²×D₄	C₂³×C₇	1	1	yes	characteristic
552	C₂²×D₄	C₂³×C₇	1	2	yes	—
553	C₂²×D₄	C₂³×C₇	1	2	yes	—
554	C₂²×D₄	C₂³×C₇	1	1	yes	characteristic
555	C₂²×D₄	C₂³×C₇	1	2	yes	—
556	C₂²×D₄	C₂³×C₇	1	2	yes	—
557	C₂²×D₄	C₂³×C₇	1	2	yes	—
558	C₂²×D₄	C₂³×C₇	1	4	yes	—
559	C₂²×D₄	C₂³×C₇	1	4	yes	—
560	C₂²×D₄	C₂³×C₇	1	4	yes	—
561	C₂²×D₄	C₂³×C₇	1	2	yes	—
562	C₂²×D₄	C₂³×C₇	1	4	yes	—
563	C₂²×D₄	C₂³×C₇	1	2	yes	—
564	C₂²×D₄	C₂³×C₇	1	4	yes	—
565	C₂²×D₄	C₂³×C₇	1	4	yes	—
566	C₂²×D₄	C₂³×C₇	1	2	yes	—
567	C₂²×D₄	C₂³×C₇	1	16	yes	—
568	C₂²×D₄	C₂³×C₇	1	16	yes	—
569	C₂³×C₄	C₂³×C₇	1	2	yes	—
570	C₂³×C₄	C₂³×C₇	1	2	yes	—
571	C₂³×C₄	C₂³×C₇	1	2	yes	—
572	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
573	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
574	C₂³×C₄	C₂³×C₇	1	4	yes	—
575	C₂³×C₄	C₂³×C₇	1	4	yes	—
576	C₂³×C₄	C₂³×C₇	1	4	yes	—
577	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
578	C₄⋊Q₈	C₂³×C₇	1	8	yes	complemented
579	C₄⋊Q₈	C₂³×C₇	1	8	yes	complemented
580	#127	C₂³×C₇	1	8	yes	—
581	#127	C₂³×C₇	1	8	yes	—
582	#127	C₂³×C₇	1	16	yes	complemented
583	#127	C₂³×C₇	1	32	yes	complemented
584	#126	C₂³×C₇	1	16	yes	complemented
585	#126	C₂³×C₇	1	32	yes	complemented
586	#126	C₂³×C₇	1	32	yes	complemented
587	#125	C₂³×C₇	1	8	yes	complemented
588	#124	C₂³×C₇	1	8	yes	—
589	#124	C₂³×C₇	1	16	yes	—
590	#124	C₂³×C₇	1	16	yes	complemented
591	#124	C₂³×C₇	1	16	yes	complemented
592	#124	C₂³×C₇	1	32	yes	complemented
593	#123	C₂³×C₇	1	16	yes	complemented
594	#123	C₂³×C₇	1	32	yes	complemented
595	#123	C₂³×C₇	1	32	yes	complemented
596	#123	C₂³×C₇	1	32	yes	complemented
597	C₂²⋊Q₈	C₂³×C₇	1	8	yes	complemented
598	C₂²⋊Q₈	C₂³×C₇	1	32	yes	complemented
599	C₂²⋊Q₈	C₂³×C₇	1	16	yes	complemented
600	C₂²⋊Q₈	C₂³×C₇	1	16	yes	complemented
601	#121	C₂³×C₇	1	8	yes	—
602	#121	C₂³×C₇	1	8	yes	—
603	#121	C₂³×C₇	1	16	yes	—
604	#121	C₂³×C₇	1	16	yes	—
605	#121	C₂³×C₇	1	16	yes	—
606	#121	C₂³×C₇	1	16	yes	complemented
607	#121	C₂³×C₇	1	8	yes	complemented
608	#121	C₂³×C₇	1	16	yes	complemented
609	#121	C₂³×C₇	1	16	yes	complemented
610	#121	C₂³×C₇	1	32	yes	complemented
611	#121	C₂³×C₇	1	16	yes	complemented
612	#121	C₂³×C₇	1	32	yes	complemented
613	#121	C₂³×C₇	1	32	yes	complemented
614	#121	C₂³×C₇	1	32	yes	complemented
615	#121	C₂³×C₇	1	32	yes	complemented
616	#121	C₂³×C₇	1	32	yes	complemented
617	#120	C₂³×C₇	1	32	yes	—
618	#120	C₂³×C₇	1	32	yes	complemented
619	#120	C₂³×C₇	1	32	yes	complemented
620	#120	C₂³×C₇	1	32	yes	complemented
621	C₄×Q₈	C₂³×C₇	1	8	yes	complemented
622	C₄×Q₈	C₂³×C₇	1	16	yes	complemented
623	C₄×D₄	C₂³×C₇	1	8	yes	—
624	C₄×D₄	C₂³×C₇	1	8	yes	—
625	C₄×D₄	C₂³×C₇	1	16	yes	complemented
626	C₄×D₄	C₂³×C₇	1	16	yes	complemented
627	C₄×D₄	C₂³×C₇	1	16	yes	complemented
628	C₄×D₄	C₂³×C₇	1	16	yes	complemented
629	C₄×D₄	C₂³×C₇	1	8	yes	complemented
630	C₄×D₄	C₂³×C₇	1	32	yes	complemented
631	C₄×D₄	C₂³×C₇	1	16	yes	complemented
632	#117	C₂³×C₇	1	16	yes	complemented
633	#117	C₂³×C₇	1	16	yes	complemented
634	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
635	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
636	C₂×C₄⋊C₄	C₂³×C₇	1	4	yes	—
637	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
638	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
639	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
640	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
641	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
642	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
643	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
644	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
645	C₂×C₄⋊C₄	C₂³×C₇	1	4	yes	—
646	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
647	C₂×C₄⋊C₄	C₂³×C₇	1	16	yes	complemented
648	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
649	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
650	C₂×C₂²⋊C₄	C₂³×C₇	1	4	yes	—
651	C₂×C₂²⋊C₄	C₂³×C₇	1	4	yes	—
652	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
653	C₂×C₂²⋊C₄	C₂³×C₇	1	4	yes	—
654	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
655	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
656	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
657	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
658	C₂×C₂²⋊C₄	C₂³×C₇	1	4	yes	—
659	C₂×C₂²⋊C₄	C₂³×C₇	1	4	yes	—
660	C₂×C₂²⋊C₄	C₂³×C₇	1	4	yes	—
661	C₂×C₂²⋊C₄	C₂³×C₇	1	4	yes	—
662	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
663	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
664	C₂×C₂²⋊C₄	C₂³×C₇	1	32	yes	complemented
665	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
666	C₂×C₄²	C₂³×C₇	1	2	yes	—
667	C₂×C₄²	C₂³×C₇	1	4	yes	—
668	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
669	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
670	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
671	C₂×C₄²	C₂³×C₇	1	8	yes	complemented
672	C₂²×C₇	—	2	2	no	—
673	C₂²×C₇	—	2	2	no	—
674	C₂²×C₇	—	2	4	no	—
675	C₂²×C₇	—	2	4	no	—
676	C₂²×C₇	—	2	4	no	—
677	C₂²×C₇	—	2	4	no	—
678	C₂²×C₇	—	2	8	no	—
679	C₂²×C₇	—	2	8	no	—
680	C₂²×C₇	—	2	4	no	—
681	C₂²×C₇	—	2	4	no	—
682	C₂²×C₇	—	2	2	no	—
683	C₂²×C₇	—	2	4	no	—
684	C₂²×C₇	—	2	8	no	—
685	C₂²×C₇	—	2	4	no	—
686	C₂²×C₇	—	2	4	no	—
687	C₂²×C₇	—	4	4	no	—
688	C₂²×C₇	—	4	8	no	—
689	C₂²×C₇	—	4	16	no	—
690	C₂²×C₇	—	4	8	no	—
691	C₂²×C₇	—	4	8	no	—
692	C₂²×C₇	—	8	32	no	—
693	C₂²×C₇	C₂×H(5,𝔽₂)	1	2	yes	—
694	C₂²×C₇	C₂×H(5,𝔽₂)	1	2	yes	—
695	C₂²×C₇	#585	1	2	yes	—
696	C₂²×C₇	C₂⁶	1	1	yes	characteristic
697	C₄×C₇	—	2	2	no	—
698	C₄×C₇	—	2	4	no	—
699	C₄×C₇	—	2	4	no	—
700	C₄×C₇	—	2	4	no	—
701	C₄×C₇	—	2	2	no	—
702	C₄×C₇	—	2	8	no	—
703	C₄×C₇	—	2	4	no	—
704	C₄×C₇	—	2	2	no	—
705	C₄×C₇	—	2	2	no	—
706	C₄×C₇	—	2	4	no	—
707	C₄×C₇	C₂×H(5,𝔽₂)	1	4	yes	—
708	C₄×C₇	C₂×H(5,𝔽₂)	1	4	yes	—
709	C₂⁴	—	4	8	no	—
710	C₂⁴	—	4	8	no	—
711	C₂⁴	—	4	8	no	—
712	C₂⁴	C₂⁴×C₇	1	2	yes	—
713	C₂⁴	C₂⁴×C₇	1	2	yes	—
714	C₂⁴	C₂⁴×C₇	1	4	yes	—
715	C₂⁴	C₂⁴×C₇	1	1	yes	characteristic
716	C₂⁴	C₂⁴×C₇	1	2	yes	—
717	C₂⁴	C₂⁴×C₇	1	16	yes	—
718	#41	—	4	32	no	—
719	#41	—	4	32	no	—
720	#41	—	4	32	no	—
721	#41	—	4	32	no	—
722	C₂×Q₈	—	2	4	no	—
723	C₂×Q₈	—	2	8	no	—
724	C₂×Q₈	—	4	4	no	—
725	C₂×Q₈	C₂⁴×C₇	1	4	yes	—
726	C₂×Q₈	C₂⁴×C₇	1	8	yes	—
727	C₂×Q₈	C₂⁴×C₇	1	8	yes	—
728	C₂×D₄	—	2	4	no	—
729	C₂×D₄	—	2	4	no	—
730	C₂×D₄	—	2	8	no	—
731	C₂×D₄	—	2	8	no	—
732	C₂×D₄	—	2	4	no	—
733	C₂×D₄	—	4	32	no	—
734	C₂×D₄	—	4	32	no	—
735	C₂×D₄	—	4	8	no	—
736	C₂×D₄	—	4	8	no	—
737	C₂×D₄	—	4	4	no	—
738	C₂×D₄	—	4	4	no	—
739	C₂×D₄	—	4	4	no	—
740	C₂×D₄	—	4	8	no	—
741	C₂×D₄	—	4	8	no	—
742	C₂×D₄	—	4	8	no	—
743	C₂×D₄	—	4	4	no	—
744	C₂×D₄	—	4	4	no	—
745	C₂×D₄	—	4	4	no	—
746	C₂×D₄	—	4	8	no	—
747	C₂×D₄	C₂⁴×C₇	1	4	yes	—
748	C₂×D₄	C₂⁴×C₇	1	4	yes	—
749	C₂×D₄	C₂⁴×C₇	1	8	yes	—
750	C₂×D₄	C₂⁴×C₇	1	8	yes	—
751	C₂×D₄	C₂⁴×C₇	1	4	yes	—
752	C₂×D₄	C₂⁴×C₇	1	8	yes	—
753	C₂×D₄	C₂⁴×C₇	1	8	yes	—
754	C₂×D₄	C₂⁴×C₇	1	8	yes	—
755	C₂×D₄	C₂⁴×C₇	1	16	yes	—
756	C₂×D₄	C₂⁴×C₇	1	16	yes	—
757	C₂×D₄	C₂⁴×C₇	1	16	yes	—
758	C₂×D₄	C₂⁴×C₇	1	8	yes	—
759	C₂×D₄	C₂⁴×C₇	1	16	yes	—
760	C₂×D₄	C₂⁴×C₇	1	8	yes	—
761	C₂×D₄	C₂⁴×C₇	1	16	yes	—
762	C₂×D₄	C₂⁴×C₇	1	16	yes	—
763	C₂×D₄	C₂⁴×C₇	1	8	yes	—
764	C₂²×C₄	—	2	8	no	—
765	C₂²×C₄	—	2	8	no	—
766	C₂²×C₄	—	2	4	no	—
767	C₂²×C₄	—	2	8	no	—
768	C₂²×C₄	—	2	4	no	—
769	C₂²×C₄	—	4	2	no	—
770	C₂²×C₄	—	4	8	no	—
771	C₂²×C₄	—	4	8	no	—
772	C₂²×C₄	—	4	8	no	—
773	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
774	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
775	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
776	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
777	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
778	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
779	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
780	C₂²×C₄	C₂⁴×C₇	1	4	yes	—
781	C₂²×C₄	C₂⁴×C₇	1	4	yes	—
782	C₂²×C₄	C₂⁴×C₇	1	4	yes	—
783	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
784	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
785	C₂²×C₄	C₂⁴×C₇	1	8	yes	—
786	C₂²×C₄	C₂⁴×C₇	1	8	yes	—
787	C₂²×C₄	C₂⁴×C₇	1	8	yes	—
788	C₂²×C₄	C₂⁴×C₇	1	4	yes	—
789	C₂²×C₄	C₂⁴×C₇	1	16	yes	—
790	C₂²×C₄	C₂⁴×C₇	1	16	yes	—
791	C₂²×C₄	C₂⁴×C₇	1	16	yes	—
792	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
793	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
794	C₄⋊C₄	C₂⁴×C₇	1	4	yes	—
795	C₄⋊C₄	C₂⁴×C₇	1	8	yes	—
796	C₄⋊C₄	C₂⁴×C₇	1	16	yes	—
797	C₄⋊C₄	C₂⁴×C₇	1	4	yes	—
798	C₄⋊C₄	C₂⁴×C₇	1	8	yes	—
799	C₄⋊C₄	C₂⁴×C₇	1	8	yes	—
800	C₄⋊C₄	C₂⁴×C₇	1	4	yes	—
801	C₄⋊C₄	C₂⁴×C₇	1	4	yes	—
802	C₄⋊C₄	C₂⁴×C₇	1	8	yes	—
803	C₄⋊C₄	C₂⁴×C₇	1	8	yes	—
804	C₄⋊C₄	C₂⁴×C₇	1	8	yes	—
805	C₄⋊C₄	C₂⁴×C₇	1	16	yes	—
806	C₄⋊C₄	C₂⁴×C₇	1	8	yes	—
807	C₂²⋊C₄	C₂⁴×C₇	1	8	yes	—
808	C₂²⋊C₄	C₂⁴×C₇	1	8	yes	—
809	C₂²⋊C₄	C₂⁴×C₇	1	16	yes	—
810	C₂²⋊C₄	C₂⁴×C₇	1	16	yes	—
811	C₂²⋊C₄	C₂⁴×C₇	1	8	yes	—
812	C₂²⋊C₄	C₂⁴×C₇	1	16	yes	—
813	C₂²⋊C₄	C₂⁴×C₇	1	8	yes	—
814	C₂²⋊C₄	C₂⁴×C₇	1	8	yes	—
815	C₂²⋊C₄	C₂⁴×C₇	1	8	yes	—
816	C₂²⋊C₄	C₂⁴×C₇	1	8	yes	—
817	C₂²⋊C₄	C₂⁴×C₇	1	16	yes	—
818	C₂²⋊C₄	C₂⁴×C₇	1	16	yes	—
819	C₂²⋊C₄	C₂⁴×C₇	1	16	yes	—
820	C₂²⋊C₄	C₂⁴×C₇	1	16	yes	—
821	C₂²⋊C₄	C₂⁴×C₇	1	8	yes	—
822	C₂²⋊C₄	C₂⁴×C₇	1	8	yes	—
823	C₄²	C₂⁴×C₇	1	4	yes	—
824	C₄²	C₂⁴×C₇	1	4	yes	—
825	C₄²	C₂⁴×C₇	1	4	yes	—
826	C₄²	C₂⁴×C₇	1	4	yes	—
827	C₄²	C₂⁴×C₇	1	8	yes	—
828	C₄²	C₂⁴×C₇	1	16	yes	—
829	C₂×C₇	—	4	2	no	—
830	C₂×C₇	—	4	4	no	—
831	C₂×C₇	—	4	8	no	—
832	C₂×C₇	—	4	4	no	—
833	C₂×C₇	—	4	4	no	—
834	C₂×C₇	#3546	1	4	yes	direct product factor
835	C₂×C₇	C₂²×H(5,𝔽₂)	1	1	yes	characteristic
836	C₂×C₇	C₂²×H(5,𝔽₂)	1	1	yes	characteristic
837	C₂×C₇	C₂×#585	1	1	yes	characteristic
838	C₂³	—	2	2	no	—
839	C₂³	—	2	2	no	—
840	C₂³	—	2	4	no	—
841	C₂³	—	2	4	no	—
842	C₂³	—	2	4	no	—
843	C₂³	—	2	4	no	—
844	C₂³	—	2	8	no	—
845	C₂³	—	2	8	no	—
846	C₂³	—	2	4	no	—
847	C₂³	—	2	4	no	—
848	C₂³	—	2	2	no	—
849	C₂³	—	2	4	no	—
850	C₂³	—	2	8	no	—
851	C₂³	—	2	4	no	—
852	C₂³	—	2	4	no	—
853	C₂³	—	4	16	no	—
854	C₂³	—	4	16	no	—
855	C₂³	—	4	16	no	—
856	C₂³	—	8	32	no	—
857	C₂³	C₂⁵×C₇	1	4	yes	—
858	C₂³	C₂⁵×C₇	1	4	yes	—
859	C₂³	C₂⁵×C₇	1	8	yes	—
860	C₂³	C₂⁵×C₇	1	2	yes	—
861	C₂³	C₂⁵×C₇	1	4	yes	—
862	C₂³	C₂⁵×C₇	1	1	yes	characteristic
863	Q₈	—	2	8	no	—
864	Q₈	—	2	16	no	—
865	Q₈	—	4	8	no	—
866	D₄	—	2	8	no	—
867	D₄	—	2	8	no	—
868	D₄	—	2	16	no	—
869	D₄	—	2	16	no	—
870	D₄	—	2	8	no	—
871	D₄	—	4	16	no	—
872	D₄	—	4	16	no	—
873	D₄	—	4	8	no	—
874	D₄	—	4	8	no	—
875	D₄	—	4	8	no	—
876	D₄	—	4	16	no	—
877	D₄	—	4	8	no	—
878	D₄	—	4	8	no	—
879	D₄	—	4	8	no	—
880	D₄	—	4	16	no	—
881	D₄	—	4	16	no	—
882	D₄	—	4	16	no	—
883	C₂×C₄	—	2	2	no	—
884	C₂×C₄	—	2	4	no	—
885	C₂×C₄	—	2	4	no	—
886	C₂×C₄	—	2	4	no	—
887	C₂×C₄	—	2	2	no	—
888	C₂×C₄	—	2	8	no	—
889	C₂×C₄	—	2	4	no	—
890	C₂×C₄	—	2	2	no	—
891	C₂×C₄	—	2	2	no	—
892	C₂×C₄	—	2	4	no	—
893	C₂×C₄	—	2	16	no	—
894	C₂×C₄	—	2	16	no	—
895	C₂×C₄	—	2	8	no	—
896	C₂×C₄	—	2	16	no	—
897	C₂×C₄	—	2	8	no	—
898	C₂×C₄	—	4	4	no	—
899	C₂×C₄	—	4	16	no	—
900	C₂×C₄	—	4	16	no	—
901	C₂×C₄	—	4	16	no	—
902	C₂×C₄	C₇×H(5,𝔽₂)	1	4	yes	—
903	C₂×C₄	C₇×H(5,𝔽₂)	1	4	yes	—
904	C₂×C₄	C₂⁵×C₇	1	4	yes	—
905	C₂×C₄	C₂⁵×C₇	1	2	yes	—
906	C₂×C₄	C₂⁵×C₇	1	2	yes	—
907	C₂×C₄	C₂⁵×C₇	1	2	yes	—
908	C₂×C₄	C₂⁵×C₇	1	2	yes	—
909	C₂×C₄	C₂⁵×C₇	1	4	yes	—
910	C₂×C₄	C₂⁵×C₇	1	4	yes	—
911	C₂×C₄	C₂⁵×C₇	1	8	yes	—
912	C₂×C₄	C₂⁵×C₇	1	4	yes	—
913	C₂×C₄	C₂⁵×C₇	1	4	yes	—
914	C₂×C₄	C₂⁵×C₇	1	2	yes	—
915	C₂×C₄	C₂⁵×C₇	1	2	yes	—
916	C₇	C₂×#3546	1	1	yes	characteristic, direct product factor, Sylow
917	C₂²	—	2	2	no	—
918	C₂²	—	2	2	no	—
919	C₂²	—	2	4	no	—
920	C₂²	—	2	4	no	—
921	C₂²	—	2	4	no	—
922	C₂²	—	2	4	no	—
923	C₂²	—	2	8	no	—
924	C₂²	—	2	8	no	—
925	C₂²	—	2	4	no	—
926	C₂²	—	2	4	no	—
927	C₂²	—	2	2	no	—
928	C₂²	—	2	4	no	—
929	C₂²	—	2	8	no	—
930	C₂²	—	2	4	no	—
931	C₂²	—	2	4	no	—
932	C₂²	—	4	8	no	—
933	C₂²	—	4	8	no	—
934	C₂²	—	4	16	no	—
935	C₂²	—	4	4	no	—
936	C₂²	—	4	8	no	—
937	C₂²	—	8	32	no	—
938	C₂²	C₂×C₇×H(5,𝔽₂)	1	2	yes	—
939	C₂²	C₂×C₇×H(5,𝔽₂)	1	2	yes	—
940	C₂²	C₇×#585	1	2	yes	—
941	C₂²	C₂⁶×C₇	1	1	yes	characteristic
942	C₄	—	2	2	no	—
943	C₄	—	2	4	no	—
944	C₄	—	2	4	no	—
945	C₄	—	2	4	no	—
946	C₄	—	2	2	no	—
947	C₄	—	2	8	no	—
948	C₄	—	2	4	no	—
949	C₄	—	2	2	no	—
950	C₄	—	2	2	no	—
951	C₄	—	2	4	no	—
952	C₄	C₂×C₇×H(5,𝔽₂)	1	4	yes	—
953	C₄	C₂×C₇×H(5,𝔽₂)	1	4	yes	—
954	C₂	—	4	4	no	—
955	C₂	—	4	4	no	—
956	C₂	—	4	8	no	—
957	C₂	—	4	2	no	—
958	C₂	—	4	4	no	—
959	C₂	C₇×#3546	1	4	yes	direct product factor
960	C₂	C₂²×C₇×H(5,𝔽₂)	1	1	yes	characteristic
961	C₂	C₂²×C₇×H(5,𝔽₂)	1	1	yes	characteristic
962	C₂	C₂×C₇×#585	1	1	yes	characteristic

	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×#3546	C₂	direct (N × H)
2. C₂×C₇×#560	C₂	semidirect
3. C₂×C₇×#556	C₂	semidirect
4. C₂×C₇×#553	C₂	semidirect
5. C₂×C₇×#550	C₂	semidirect
6. C₂×C₇×#550	C₂	semidirect
7. C₂×C₇×#547	C₂	semidirect
8. C₂×C₇×#546	C₂	semidirect
9. C₂×C₇×#546	C₂	semidirect
10. C₂×C₇×D₄²	C₂	semidirect
11. C₂×C₇×#542	C₂	semidirect
12. C₂×C₇×#538	C₂	semidirect
13. C₂×C₇×#537	C₂	semidirect
14. C₂×C₇×#535	C₂	semidirect
15. C₂×C₇×#535	C₂	semidirect
16. C₂×C₇×#532	C₂	semidirect
17. C₂×C₇×#532	C₂	semidirect
18. C₂×C₇×#529	C₂	semidirect
19. C₂²×C₇×#41	C₂²	semidirect
20. C₂²×C₇×#41	C₂²	semidirect
21. C₂²×C₇×#41	C₂²	semidirect
22. C₂²×C₇×#41	C₂²	semidirect
25. C₇×#560	C₂²	semidirect
26. C₇×#556	C₂²	semidirect
27. C₇×#553	C₂²	semidirect
28. C₇×#550	C₂²	semidirect
29. C₇×#550	C₂²	semidirect
30. C₇×#547	C₂²	semidirect
31. C₇×#546	C₂²	semidirect
32. C₇×#546	C₂²	semidirect
33. C₇×D₄²	C₂²	semidirect
34. C₇×#542	C₂²	semidirect
35. C₇×#538	C₂²	semidirect
36. C₇×#537	C₂²	semidirect
37. C₇×#535	C₂²	semidirect
38. C₇×#535	C₂²	semidirect
39. C₇×#532	C₂²	semidirect
40. C₇×#532	C₂²	semidirect
41. C₂×C₇×C₄⋊Q₈	C₂²	semidirect
42. C₂×C₇×C₄⋊Q₈	C₂²	semidirect
45. C₂×C₇×#127	C₂²	semidirect
46. C₂×C₇×#127	C₂²	semidirect
47. C₇×#529	C₂²	semidirect
48. C₂×C₇×#126	C₂²	semidirect
49. C₂×C₇×#126	C₂²	semidirect
50. C₂×C₇×#126	C₂²	semidirect
51. C₂×C₇×#125	C₂²	semidirect
54. C₂×C₇×#124	C₂²	semidirect
55. C₂×C₇×#124	C₂²	semidirect
56. C₂×C₇×#124	C₂²	semidirect
57. C₂×C₇×#123	C₂²	semidirect
58. C₂×C₇×#123	C₂²	semidirect
59. C₂×C₇×#123	C₂²	semidirect
60. C₂×C₇×#123	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
70. C₂×C₇×#121	C₂²	semidirect
71. C₂×C₇×#121	C₂²	semidirect
72. C₂×C₇×#121	C₂²	semidirect
73. C₂×C₇×#121	C₂²	semidirect
74. C₂×C₇×#121	C₂²	semidirect
75. C₂×C₇×#121	C₂²	semidirect
76. C₂×C₇×#121	C₂²	semidirect
77. C₂×C₇×#121	C₂²	semidirect
78. C₂×C₇×#121	C₂²	semidirect
79. C₂×C₇×#121	C₂²	semidirect
80. C₂×C₇×#121	C₂²	semidirect
82. C₂×C₇×#120	C₂²	semidirect
83. C₂×C₇×#120	C₂²	semidirect
84. C₂×C₇×#120	C₂²	semidirect
85. C₂×C₄×C₇×Q₈	C₂²	semidirect
86. C₂×C₄×C₇×Q₈	C₂²	semidirect
89. C₂×C₄×C₇×D₄	C₂²	semidirect
90. C₂×C₄×C₇×D₄	C₂²	semidirect
91. C₂×C₄×C₇×D₄	C₂²	semidirect
92. C₂×C₄×C₇×D₄	C₂²	semidirect
93. C₂×C₄×C₇×D₄	C₂²	semidirect
94. C₂×C₄×C₇×D₄	C₂²	semidirect
95. C₂×C₄×C₇×D₄	C₂²	semidirect
96. C₂×C₇×#117	C₂²	semidirect
97. C₂×C₇×#117	C₂²	semidirect
98. C₂²×C₇×C₄⋊C₄	C₂²	semidirect
99. C₂²×C₇×C₂²⋊C₄	C₂²	semidirect
100. C₂²×C₄²×C₇	C₂²	semidirect
101. C₂×#3546	C₇	direct (N × H)
107. C₂×C₇×#41	C₂³	semidirect
108. C₂×C₇×#41	C₂³	semidirect
109. C₂×C₇×#41	C₂³	semidirect
110. C₂×C₇×#41	C₂³	semidirect
144. C₇×C₄⋊Q₈	C₂³	semidirect
145. C₇×C₄⋊Q₈	C₂³	semidirect
148. C₇×#127	C₂³	semidirect
149. C₇×#127	C₂³	semidirect
150. C₇×#126	C₂³	semidirect
151. C₇×#126	C₂³	semidirect
152. C₇×#126	C₂³	semidirect
153. C₇×#125	C₂³	semidirect
156. C₇×#124	C₂³	semidirect
157. C₇×#124	C₂³	semidirect
158. C₇×#124	C₂³	semidirect
159. C₇×#123	C₂³	semidirect
160. C₇×#123	C₂³	semidirect
161. C₇×#123	C₂³	semidirect
162. C₇×#123	C₂³	semidirect
163. C₇×C₂²⋊Q₈	C₂³	semidirect
164. C₇×C₂²⋊Q₈	C₂³	semidirect
165. C₇×C₂²⋊Q₈	C₂³	semidirect
166. C₇×C₂²⋊Q₈	C₂³	semidirect
172. C₇×#121	C₂³	semidirect
173. C₇×#121	C₂³	semidirect
174. C₇×#121	C₂³	semidirect
175. C₇×#121	C₂³	semidirect
176. C₇×#121	C₂³	semidirect
177. C₇×#121	C₂³	semidirect
178. C₇×#121	C₂³	semidirect
179. C₇×#121	C₂³	semidirect
180. C₇×#121	C₂³	semidirect
181. C₇×#121	C₂³	semidirect
182. C₇×#121	C₂³	semidirect
184. C₇×#120	C₂³	semidirect
185. C₇×#120	C₂³	semidirect
186. C₇×#120	C₂³	semidirect
187. C₄×C₇×Q₈	C₂³	semidirect
188. C₄×C₇×Q₈	C₂³	semidirect
191. C₄×C₇×D₄	C₂³	semidirect
192. C₄×C₇×D₄	C₂³	semidirect
193. C₄×C₇×D₄	C₂³	semidirect
194. C₄×C₇×D₄	C₂³	semidirect
195. C₄×C₇×D₄	C₂³	semidirect
196. C₄×C₇×D₄	C₂³	semidirect
197. C₄×C₇×D₄	C₂³	semidirect
198. C₇×#117	C₂³	semidirect
199. C₇×#117	C₂³	semidirect
213. C₂×C₇×C₄⋊C₄	C₂³	semidirect
230. C₂×C₇×C₂²⋊C₄	C₂³	semidirect
237. C₂×C₄²×C₇	C₂³	semidirect
238. #3546	C₂×C₇	direct (N × H)
239. C₂×#560	C₂×C₇	semidirect
240. C₂×#556	C₂×C₇	semidirect
241. C₂×#553	C₂×C₇	semidirect
242. C₂×#550	C₂×C₇	semidirect
243. C₂×#550	C₂×C₇	semidirect
244. C₂×#547	C₂×C₇	semidirect
245. C₂×#546	C₂×C₇	semidirect
246. C₂×#546	C₂×C₇	semidirect
247. C₂×D₄²	C₂×C₇	semidirect
248. C₂×#542	C₂×C₇	semidirect
249. C₂×#538	C₂×C₇	semidirect
250. C₂×#537	C₂×C₇	semidirect
251. C₂×#535	C₂×C₇	semidirect
252. C₂×#535	C₂×C₇	semidirect
253. C₂×#532	C₂×C₇	semidirect
254. C₂×#532	C₂×C₇	semidirect
255. C₂×#529	C₂×C₇	semidirect
376. C₂²×#41	C₂²×C₇	semidirect
377. C₂²×#41	C₂²×C₇	semidirect
378. C₂²×#41	C₂²×C₇	semidirect
379. C₂²×#41	C₂²×C₇	semidirect
382. #560	C₂²×C₇	semidirect
383. #556	C₂²×C₇	semidirect
384. #553	C₂²×C₇	semidirect
385. #550	C₂²×C₇	semidirect
386. #550	C₂²×C₇	semidirect
387. #547	C₂²×C₇	semidirect
388. #546	C₂²×C₇	semidirect
389. #546	C₂²×C₇	semidirect
390. D₄²	C₂²×C₇	semidirect
391. #542	C₂²×C₇	semidirect
392. #538	C₂²×C₇	semidirect
393. #537	C₂²×C₇	semidirect
394. #535	C₂²×C₇	semidirect
395. #535	C₂²×C₇	semidirect
396. #532	C₂²×C₇	semidirect
397. #532	C₂²×C₇	semidirect
398. C₂×C₄⋊Q₈	C₂²×C₇	semidirect
399. C₂×C₄⋊Q₈	C₂²×C₇	semidirect
402. C₂×#127	C₂²×C₇	semidirect
403. C₂×#127	C₂²×C₇	semidirect
404. #529	C₂²×C₇	semidirect
405. C₂×#126	C₂²×C₇	semidirect
406. C₂×#126	C₂²×C₇	semidirect
407. C₂×#126	C₂²×C₇	semidirect
408. C₂×#125	C₂²×C₇	semidirect
411. C₂×#124	C₂²×C₇	semidirect
412. C₂×#124	C₂²×C₇	semidirect
413. C₂×#124	C₂²×C₇	semidirect
414. C₂×#123	C₂²×C₇	semidirect
415. C₂×#123	C₂²×C₇	semidirect
416. C₂×#123	C₂²×C₇	semidirect
417. C₂×#123	C₂²×C₇	semidirect
418. C₂×C₂²⋊Q₈	C₂²×C₇	semidirect
419. C₂×C₂²⋊Q₈	C₂²×C₇	semidirect
420. C₂×C₂²⋊Q₈	C₂²×C₇	semidirect
421. C₂×C₂²⋊Q₈	C₂²×C₇	semidirect
427. C₂×#121	C₂²×C₇	semidirect
428. C₂×#121	C₂²×C₇	semidirect
429. C₂×#121	C₂²×C₇	semidirect
430. C₂×#121	C₂²×C₇	semidirect
431. C₂×#121	C₂²×C₇	semidirect
432. C₂×#121	C₂²×C₇	semidirect
433. C₂×#121	C₂²×C₇	semidirect
434. C₂×#121	C₂²×C₇	semidirect
435. C₂×#121	C₂²×C₇	semidirect
436. C₂×#121	C₂²×C₇	semidirect
437. C₂×#121	C₂²×C₇	semidirect
439. C₂×#120	C₂²×C₇	semidirect
440. C₂×#120	C₂²×C₇	semidirect
441. C₂×#120	C₂²×C₇	semidirect
442. C₂×C₄×Q₈	C₂²×C₇	semidirect
443. C₂×C₄×Q₈	C₂²×C₇	semidirect
446. C₂×C₄×D₄	C₂²×C₇	semidirect
447. C₂×C₄×D₄	C₂²×C₇	semidirect
448. C₂×C₄×D₄	C₂²×C₇	semidirect
449. C₂×C₄×D₄	C₂²×C₇	semidirect
450. C₂×C₄×D₄	C₂²×C₇	semidirect
451. C₂×C₄×D₄	C₂²×C₇	semidirect
452. C₂×C₄×D₄	C₂²×C₇	semidirect
453. C₂×#117	C₂²×C₇	semidirect
454. C₂×#117	C₂²×C₇	semidirect
455. C₂²×C₄⋊C₄	C₂²×C₇	semidirect
456. C₂²×C₂²⋊C₄	C₂²×C₇	semidirect
457. C₂²×C₄²	C₂²×C₇	semidirect
541. C₂×#41	C₂³×C₇	semidirect
542. C₂×#41	C₂³×C₇	semidirect
543. C₂×#41	C₂³×C₇	semidirect
544. C₂×#41	C₂³×C₇	semidirect
578. C₄⋊Q₈	C₂³×C₇	semidirect
579. C₄⋊Q₈	C₂³×C₇	semidirect
582. #127	C₂³×C₇	semidirect
583. #127	C₂³×C₇	semidirect
584. #126	C₂³×C₇	semidirect
585. #126	C₂³×C₇	semidirect
586. #126	C₂³×C₇	semidirect
587. #125	C₂³×C₇	semidirect
590. #124	C₂³×C₇	semidirect
591. #124	C₂³×C₇	semidirect
592. #124	C₂³×C₇	semidirect
593. #123	C₂³×C₇	semidirect
594. #123	C₂³×C₇	semidirect
595. #123	C₂³×C₇	semidirect
596. #123	C₂³×C₇	semidirect
597. C₂²⋊Q₈	C₂³×C₇	semidirect
598. C₂²⋊Q₈	C₂³×C₇	semidirect
599. C₂²⋊Q₈	C₂³×C₇	semidirect
600. C₂²⋊Q₈	C₂³×C₇	semidirect
606. #121	C₂³×C₇	semidirect
607. #121	C₂³×C₇	semidirect
608. #121	C₂³×C₇	semidirect
609. #121	C₂³×C₇	semidirect
610. #121	C₂³×C₇	semidirect
611. #121	C₂³×C₇	semidirect
612. #121	C₂³×C₇	semidirect
613. #121	C₂³×C₇	semidirect
614. #121	C₂³×C₇	semidirect
615. #121	C₂³×C₇	semidirect
616. #121	C₂³×C₇	semidirect
618. #120	C₂³×C₇	semidirect
619. #120	C₂³×C₇	semidirect
620. #120	C₂³×C₇	semidirect
621. C₄×Q₈	C₂³×C₇	semidirect
622. C₄×Q₈	C₂³×C₇	semidirect
625. C₄×D₄	C₂³×C₇	semidirect
626. C₄×D₄	C₂³×C₇	semidirect
627. C₄×D₄	C₂³×C₇	semidirect
628. C₄×D₄	C₂³×C₇	semidirect
629. C₄×D₄	C₂³×C₇	semidirect
630. C₄×D₄	C₂³×C₇	semidirect
631. C₄×D₄	C₂³×C₇	semidirect
632. #117	C₂³×C₇	semidirect
633. #117	C₂³×C₇	semidirect
647. C₂×C₄⋊C₄	C₂³×C₇	semidirect
664. C₂×C₂²⋊C₄	C₂³×C₇	semidirect
671. C₂×C₄²	C₂³×C₇	semidirect
834. C₂×C₇	#3546	direct (N × H)
916. C₇	C₂×#3546	direct (N × H)
959. C₂	C₇×#3546	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×#3546	2
C₂×C₇×#560	2
C₂×C₇×#556	2
C₂×C₇×#553	2
C₂×C₇×#550	2
C₂×C₇×#547	2
C₂×C₇×#546	2
C₂×C₇×D₄²	2
C₂×C₇×#542	2
C₂×C₇×#538	2
C₂×C₇×#537	2
C₂×C₇×#535	2
C₂×C₇×#532	2
C₂×C₇×#529	2
C₂×#3546	7

Subgroups — C2×C7×#3546 #13239963

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₇×#3546 #13239963